LMFDB - Embedded newform 357.2.p.a.16.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(16,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("357.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.p (of order $6$, degree $2$, 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			16.15
Character	$\chi$	$=$	357.16
Dual form			357.2.p.a.67.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.262370 - 0.454438i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.862324 + 1.49359i) q^{4} +(3.41917 + 1.97406i) q^{5} +0.524739i q^{6} +(-2.63978 + 0.177717i) q^{7} +1.95447 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.262370 - 0.454438i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.862324 + 1.49359i) q^{4} +(3.41917 + 1.97406i) q^{5} +0.524739i q^{6} +(-2.63978 + 0.177717i) q^{7} +1.95447 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.79417 - 1.03587i) q^{10} +(-2.72471 + 1.57311i) q^{11} +(-1.49359 - 0.862324i) q^{12} +0.881206 q^{13} +(-0.611836 + 1.24624i) q^{14} -3.94812 q^{15} +(-1.21186 + 2.09899i) q^{16} +(-4.11556 - 0.249302i) q^{17} +(-0.262370 - 0.454438i) q^{18} +(1.76691 - 3.06038i) q^{19} +6.80911i q^{20} +(2.19725 - 1.47380i) q^{21} +1.65095i q^{22} +(2.87027 + 1.65715i) q^{23} +(-1.69262 + 0.977235i) q^{24} +(5.29381 + 9.16915i) q^{25} +(0.231202 - 0.400453i) q^{26} +1.00000i q^{27} +(-2.54178 - 3.78949i) q^{28} -8.73480i q^{29} +(-1.03587 + 1.79417i) q^{30} +(3.05508 - 1.76385i) q^{31} +(2.59038 + 4.48667i) q^{32} +(1.57311 - 2.72471i) q^{33} +(-1.19309 + 1.80486i) q^{34} +(-9.37666 - 4.60343i) q^{35} +1.72465 q^{36} +(10.3688 + 5.98645i) q^{37} +(-0.927167 - 1.60590i) q^{38} +(-0.763146 + 0.440603i) q^{39} +(6.68266 + 3.85824i) q^{40} -6.52657i q^{41} +(-0.0932550 - 1.38519i) q^{42} +3.56197 q^{43} +(-4.69916 - 2.71306i) q^{44} +(3.41917 - 1.97406i) q^{45} +(1.50614 - 0.869572i) q^{46} +(-4.34796 + 7.53089i) q^{47} -2.42371i q^{48} +(6.93683 - 0.938266i) q^{49} +5.55574 q^{50} +(3.68883 - 1.84188i) q^{51} +(0.759885 + 1.31616i) q^{52} +(2.38577 + 4.13228i) q^{53} +(0.454438 + 0.262370i) q^{54} -12.4216 q^{55} +(-5.15936 + 0.347342i) q^{56} +3.53382i q^{57} +(-3.96942 - 2.29175i) q^{58} +(-6.39036 - 11.0684i) q^{59} +(-3.40456 - 5.89687i) q^{60} +(-6.80373 - 3.92813i) q^{61} -1.85112i q^{62} +(-1.16598 + 2.37497i) q^{63} -2.12888 q^{64} +(3.01299 + 1.73955i) q^{65} +(-0.825473 - 1.42976i) q^{66} +(-1.65233 - 2.86192i) q^{67} +(-3.17659 - 6.36194i) q^{68} -3.31430 q^{69} +(-4.55212 + 3.05331i) q^{70} -4.10813i q^{71} +(0.977235 - 1.69262i) q^{72} +(9.52688 - 5.50035i) q^{73} +(5.44094 - 3.14133i) q^{74} +(-9.16915 - 5.29381i) q^{75} +6.09460 q^{76} +(6.91305 - 4.63689i) q^{77} +0.462403i q^{78} +(-3.03542 - 1.75250i) q^{79} +(-8.28708 + 4.78455i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.96592 - 1.71237i) q^{82} -10.1912 q^{83} +(4.09599 + 2.01091i) q^{84} +(-13.5797 - 8.97677i) q^{85} +(0.934553 - 1.61869i) q^{86} +(4.36740 + 7.56456i) q^{87} +(-5.32536 + 3.07460i) q^{88} +(0.556702 - 0.964235i) q^{89} -2.07173i q^{90} +(-2.32619 + 0.156605i) q^{91} +5.71601i q^{92} +(-1.76385 + 3.05508i) q^{93} +(2.28155 + 3.95175i) q^{94} +(12.0827 - 6.97597i) q^{95} +(-4.48667 - 2.59038i) q^{96} -4.98168i q^{97} +(1.39363 - 3.39853i) q^{98} +3.14622i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{4} + 24 q^{9}+O(q^{10}) $ 48 * q - 24 * q^4 + 24 * q^9	$ 48 q - 24 q^{4} + 24 q^{9} + 16 q^{13} - 40 q^{16} + 8 q^{17} + 16 q^{19} + 36 q^{25} - 52 q^{26} + 24 q^{30} + 20 q^{32} - 8 q^{33} - 32 q^{34} - 36 q^{35} - 48 q^{36} + 40 q^{38} + 4 q^{42} + 40 q^{43} - 80 q^{50} - 12 q^{52} - 60 q^{53} - 24 q^{59} + 112 q^{64} + 4 q^{66} - 4 q^{67} + 88 q^{68} + 64 q^{69} - 24 q^{70} - 184 q^{76} - 72 q^{77} - 24 q^{81} - 88 q^{83} - 20 q^{84} + 16 q^{85} + 60 q^{86} + 36 q^{87} + 12 q^{89} - 24 q^{93} - 32 q^{94} + 48 q^{98}+O(q^{100}) $ 48 * q - 24 * q^4 + 24 * q^9 + 16 * q^13 - 40 * q^16 + 8 * q^17 + 16 * q^19 + 36 * q^25 - 52 * q^26 + 24 * q^30 + 20 * q^32 - 8 * q^33 - 32 * q^34 - 36 * q^35 - 48 * q^36 + 40 * q^38 + 4 * q^42 + 40 * q^43 - 80 * q^50 - 12 * q^52 - 60 * q^53 - 24 * q^59 + 112 * q^64 + 4 * q^66 - 4 * q^67 + 88 * q^68 + 64 * q^69 - 24 * q^70 - 184 * q^76 - 72 * q^77 - 24 * q^81 - 88 * q^83 - 20 * q^84 + 16 * q^85 + 60 * q^86 + 36 * q^87 + 12 * q^89 - 24 * q^93 - 32 * q^94 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

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 $

$2$	0.262370	−	0.454438i	0.185523	−	0.321336i	−0.758229	−	0.651988i	$-0.773935\pi$
$2$	0.262370	−	0.454438i	0.185523	−	0.321336i	0.943753	+	0.330652i	$0.107269\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.862324	+	1.49359i	0.431162	+	0.746795i
$5$	3.41917	+	1.97406i	1.52910	+	0.882826i	0.999400	+	0.0346402i	$0.0110285\pi$
$5$	3.41917	+	1.97406i	1.52910	+	0.882826i	0.529699	+	0.848186i	$0.322305\pi$
$6$			0.524739i			0.214224i
$7$	−2.63978	+	0.177717i	−0.997741	+	0.0671707i
$7$	−2.63978	+	0.177717i	−0.997741	+	0.0671707i
$8$	1.95447			0.691009
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.79417	−	1.03587i	0.567367	−	0.327570i
$11$	−2.72471	+	1.57311i	−0.821530	+	0.474311i	−0.850944	−	0.525257i	$-0.823969\pi$
$11$	−2.72471	+	1.57311i	−0.821530	+	0.474311i	0.0294136	+	0.999567i	$0.490636\pi$
$12$	−1.49359	−	0.862324i	−0.431162	−	0.248932i
$13$	0.881206			0.244402			0.122201	−	0.992505i	$-0.461005\pi$
$13$	0.881206			0.244402			0.122201	+	0.992505i	$0.461005\pi$
$14$	−0.611836	+	1.24624i	−0.163520	+	0.333072i
$15$	−3.94812			−1.01940
$16$	−1.21186	+	2.09899i	−0.302964	+	0.524749i
$17$	−4.11556	−	0.249302i	−0.998170	−	0.0604647i
$17$	−4.11556	−	0.249302i	−0.998170	−	0.0604647i
$18$	−0.262370	−	0.454438i	−0.0618411	−	0.107112i
$19$	1.76691	−	3.06038i	0.405357	−	0.702099i	−0.589006	−	0.808129i	$-0.700481\pi$
$19$	1.76691	−	3.06038i	0.405357	−	0.702099i	0.994363	+	0.106030i	$0.0338138\pi$
$20$			6.80911i			1.52256i
$21$	2.19725	−	1.47380i	0.479480	−	0.321608i
$22$			1.65095i			0.351983i
$23$	2.87027	+	1.65715i	0.598492	+	0.345540i	0.768448	−	0.639912i	$-0.221029\pi$
$23$	2.87027	+	1.65715i	0.598492	+	0.345540i	−0.169956	+	0.985452i	$0.554362\pi$
$24$	−1.69262	+	0.977235i	−0.345505	+	0.199477i
$25$	5.29381	+	9.16915i	1.05876	+	1.83383i
$26$	0.231202	−	0.400453i	0.0453424	−	0.0785353i
$27$			1.00000i			0.192450i
$28$	−2.54178	−	3.78949i	−0.480351	−	0.716147i
$29$		−	8.73480i		−	1.62201i	−0.585038	−	0.811006i	$-0.698920\pi$
$29$		−	8.73480i		−	1.62201i	0.585038	−	0.811006i	$-0.301080\pi$
$30$	−1.03587	+	1.79417i	−0.189122	+	0.327570i
$31$	3.05508	−	1.76385i	0.548708	−	0.316797i	−0.199893	−	0.979818i	$-0.564059\pi$
$31$	3.05508	−	1.76385i	0.548708	−	0.316797i	0.748601	+	0.663021i	$0.230726\pi$
$32$	2.59038	+	4.48667i	0.457918	+	0.793138i
$33$	1.57311	−	2.72471i	0.273843	−	0.474311i
$34$	−1.19309	+	1.80486i	−0.204613	+	0.309530i
$35$	−9.37666	−	4.60343i	−1.58495	−	0.778121i
$36$	1.72465			0.287441
$37$	10.3688	+	5.98645i	1.70463	+	0.984167i	0.940935	+	0.338586i	$0.109949\pi$
$37$	10.3688	+	5.98645i	1.70463	+	0.984167i	0.763692	+	0.645581i	$0.223385\pi$
$38$	−0.927167	−	1.60590i	−0.150406	−	0.260512i
$39$	−0.763146	+	0.440603i	−0.122201	+	0.0705529i
$40$	6.68266	+	3.85824i	1.05662	+	0.610041i
$41$		−	6.52657i		−	1.01928i	−0.860388	−	0.509640i	$-0.829779\pi$
$41$		−	6.52657i		−	1.01928i	0.860388	−	0.509640i	$-0.170221\pi$
$42$	−0.0932550	−	1.38519i	−0.0143896	−	0.213740i
$43$	3.56197			0.543195			0.271598	−	0.962411i	$-0.412448\pi$
$43$	3.56197			0.543195			0.271598	+	0.962411i	$0.412448\pi$
$44$	−4.69916	−	2.71306i	−0.708426	−	0.409010i
$45$	3.41917	−	1.97406i	0.509700	−	0.294275i
$46$	1.50614	−	0.869572i	0.222069	−	0.128211i
$47$	−4.34796	+	7.53089i	−0.634215	+	1.09849i	0.352466	+	0.935825i	$0.385343\pi$
$47$	−4.34796	+	7.53089i	−0.634215	+	1.09849i	−0.986681	+	0.162668i	$0.947990\pi$
$48$		−	2.42371i		−	0.349832i
$49$	6.93683	−	0.938266i	0.990976	−	0.134038i
$50$	5.55574			0.785701
$51$	3.68883	−	1.84188i	0.516540	−	0.257915i
$52$	0.759885	+	1.31616i	0.105377	+	0.182518i
$53$	2.38577	+	4.13228i	0.327711	+	0.567612i	0.982057	−	0.188583i	$-0.0603894\pi$
$53$	2.38577	+	4.13228i	0.327711	+	0.567612i	−0.654346	+	0.756195i	$0.727056\pi$
$54$	0.454438	+	0.262370i	0.0618411	+	0.0357040i
$55$	−12.4216			−1.67493
$56$	−5.15936	+	0.347342i	−0.689449	+	0.0464156i
$57$			3.53382i			0.468066i
$58$	−3.96942	−	2.29175i	−0.521211	−	0.300921i
$59$	−6.39036	−	11.0684i	−0.831953	−	1.44099i	−0.896487	−	0.443070i	$-0.853889\pi$
$59$	−6.39036	−	11.0684i	−0.831953	−	1.44099i	0.0645336	−	0.997916i	$-0.479444\pi$
$60$	−3.40456	−	5.89687i	−0.439526	−	0.761282i
$61$	−6.80373	−	3.92813i	−0.871128	−	0.502946i	−0.00340495	−	0.999994i	$-0.501084\pi$
$61$	−6.80373	−	3.92813i	−0.871128	−	0.502946i	−0.867723	+	0.497048i	$0.834417\pi$
$62$		−	1.85112i		−	0.235093i
$63$	−1.16598	+	2.37497i	−0.146900	+	0.299218i
$64$	−2.12888			−0.266109
$65$	3.01299	+	1.73955i	0.373716	+	0.215765i
$66$	−0.825473	−	1.42976i	−0.101609	−	0.175991i
$67$	−1.65233	−	2.86192i	−0.201865	−	0.349640i	0.747265	−	0.664527i	$-0.231367\pi$
$67$	−1.65233	−	2.86192i	−0.201865	−	0.349640i	−0.949129	+	0.314887i	$0.898033\pi$
$68$	−3.17659	−	6.36194i	−0.385219	−	0.771498i
$69$	−3.31430			−0.398995
$70$	−4.55212	+	3.05331i	−0.544083	+	0.364940i
$71$		−	4.10813i		−	0.487545i	−0.969832	−	0.243772i	$-0.921615\pi$
$71$		−	4.10813i		−	0.487545i	0.969832	−	0.243772i	$-0.0783850\pi$
$72$	0.977235	−	1.69262i	0.115168	−	0.199477i
$73$	9.52688	−	5.50035i	1.11504	−	0.643767i	0.174908	−	0.984585i	$-0.444037\pi$
$73$	9.52688	−	5.50035i	1.11504	−	0.643767i	0.940129	+	0.340818i	$0.110704\pi$
$74$	5.44094	−	3.14133i	0.632496	−	0.365172i
$75$	−9.16915	−	5.29381i	−1.05876	−	0.611277i
$76$	6.09460			0.699099
$77$	6.91305	−	4.63689i	0.787815	−	0.528422i
$78$			0.462403i			0.0523569i
$79$	−3.03542	−	1.75250i	−0.341512	−	0.197172i	0.319429	−	0.947610i	$-0.396509\pi$
$79$	−3.03542	−	1.75250i	−0.341512	−	0.197172i	−0.660940	+	0.750439i	$0.729842\pi$
$80$	−8.28708	+	4.78455i	−0.926523	+	0.534929i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.96592	−	1.71237i	−0.327531	−	0.189100i
$83$	−10.1912			−1.11863			−0.559314	−	0.828956i	$-0.688935\pi$
$83$	−10.1912			−1.11863			−0.559314	+	0.828956i	$0.688935\pi$
$84$	4.09599	+	2.01091i	0.446909	+	0.219408i
$85$	−13.5797	−	8.97677i	−1.47292	−	0.973667i
$86$	0.934553	−	1.61869i	0.100775	−	0.174548i
$87$	4.36740	+	7.56456i	0.468234	+	0.811006i
$88$	−5.32536	+	3.07460i	−0.567685	+	0.327753i
$89$	0.556702	−	0.964235i	0.0590103	−	0.102209i	−0.835011	−	0.550233i	$-0.814539\pi$
$89$	0.556702	−	0.964235i	0.0590103	−	0.102209i	0.894021	+	0.448024i	$0.147872\pi$
$90$		−	2.07173i		−	0.218380i
$91$	−2.32619	+	0.156605i	−0.243850	+	0.0164167i
$92$			5.71601i			0.595935i
$93$	−1.76385	+	3.05508i	−0.182903	+	0.316797i
$94$	2.28155	+	3.95175i	0.235323	+	0.407592i
$95$	12.0827	−	6.97597i	1.23966	−	0.715719i
$96$	−4.48667	−	2.59038i	−0.457918	−	0.264379i
$97$		−	4.98168i		−	0.505813i	−0.967491	−	0.252907i	$-0.918613\pi$
$97$		−	4.98168i		−	0.505813i	0.967491	−	0.252907i	$-0.0813866\pi$
$98$	1.39363	−	3.39853i	0.140778	−	0.343303i
$99$			3.14622i			0.316207i
$100$	−9.12997	+	15.8136i	−0.912997	+	1.58136i
$101$	5.22082	+	9.04272i	0.519491	+	0.899784i	0.999743	+	0.0226541i	$0.00721164\pi$
$101$	5.22082	+	9.04272i	0.519491	+	0.899784i	−0.480253	+	0.877130i	$0.659455\pi$
$102$	0.130819	−	2.15960i	0.0129530	−	0.213832i
$103$	1.96640	−	3.40591i	0.193756	−	0.335595i	−0.752736	−	0.658322i	$-0.771266\pi$
$103$	1.96640	−	3.40591i	0.193756	−	0.335595i	0.946492	+	0.322728i	$0.104600\pi$
$104$	1.72229			0.168884
$105$	10.4221	−	0.701647i	1.01710	−	0.0684737i
$106$	2.50382			0.243192
$107$	−1.66112	−	0.959050i	−0.160587	−	0.0927148i	0.417553	−	0.908653i	$-0.362888\pi$
$107$	−1.66112	−	0.959050i	−0.160587	−	0.0927148i	−0.578140	+	0.815938i	$0.696221\pi$
$108$	−1.49359	+	0.862324i	−0.143721	+	0.0829772i
$109$	8.20123	−	4.73498i	0.785535	−	0.453529i	−0.0528532	−	0.998602i	$-0.516832\pi$
$109$	8.20123	−	4.73498i	0.785535	−	0.453529i	0.838388	+	0.545073i	$0.183498\pi$
$110$	−3.25906	+	5.64486i	−0.310740	+	0.538217i
$111$	−11.9729			−1.13642
$112$	2.82600	−	5.75624i	0.267032	−	0.543914i
$113$			6.18373i			0.581717i	0.956766	+	0.290858i	$0.0939409\pi$
$113$			6.18373i			0.581717i	−0.956766	+	0.290858i	$0.906059\pi$
$114$	1.60590	+	0.927167i	0.150406	+	0.0868372i
$115$	6.54262	+	11.3322i	0.610103	+	1.05673i
$116$	13.0462	−	7.53223i	1.21131	−	0.699350i
$117$	0.440603	−	0.763146i	0.0407337	−	0.0705529i
$118$	−6.70654			−0.617387
$119$	10.9085	−	0.0733026i	0.999977	−	0.00671964i
$120$	−7.71647			−0.704414
$121$	−0.550645	+	0.953746i	−0.0500587	+	0.0867042i
$122$	−3.57018	+	2.06125i	−0.323229	+	0.186616i
$123$	3.26329	+	5.65218i	0.294241	+	0.509640i
$124$	5.26894	+	3.04202i	0.473164	+	0.273182i
$125$			22.0606i			1.97316i
$126$	0.773358	+	1.15299i	0.0688962	+	0.102716i
$127$	19.4346			1.72454			0.862272	−	0.506446i	$-0.169041\pi$
$127$	19.4346			1.72454			0.862272	+	0.506446i	$0.169041\pi$
$128$	−5.73931	+	9.94077i	−0.507288	+	0.878648i
$129$	−3.08476	+	1.78098i	−0.271598	+	0.156807i
$130$	1.58103	−	0.912811i	0.138666	−	0.0800588i
$131$	−4.97882	−	2.87452i	−0.435001	−	0.251148i	0.266474	−	0.963842i	$-0.414141\pi$
$131$	−4.97882	−	2.87452i	−0.435001	−	0.251148i	−0.701475	+	0.712694i	$0.747475\pi$
$132$	5.42613			0.472284
$133$	−4.12037	+	8.39273i	−0.357281	+	0.727742i
$134$	−1.73409			−0.149802
$135$	−1.97406	+	3.41917i	−0.169900	+	0.294275i
$136$	−8.04374	−	0.487254i	−0.689745	−	0.0417817i
$137$	−5.68727	−	9.85064i	−0.485896	−	0.841597i	0.513973	−	0.857807i	$-0.328173\pi$
$137$	−5.68727	−	9.85064i	−0.485896	−	0.841597i	−0.999869	+	0.0162100i	$0.994840\pi$
$138$	−0.869572	+	1.50614i	−0.0740229	+	0.128211i
$139$		−	1.61965i		−	0.137377i	−0.997638	−	0.0686886i	$-0.978119\pi$
$139$		−	1.61965i		−	0.137377i	0.997638	−	0.0686886i	$-0.0218815\pi$
$140$	−1.21009	−	17.9745i	−0.102272	−	1.51913i
$141$		−	8.69592i		−	0.732329i
$142$	−1.86689	−	1.07785i	−0.156666	−	0.0904509i
$143$	−2.40103	+	1.38623i	−0.200784	+	0.115923i
$144$	1.21186	+	2.09899i	0.100988	+	0.174916i
$145$	17.2430	−	29.8658i	1.43195	−	2.48022i
$146$		−	5.77250i		−	0.477735i
$147$	−5.53834	+	4.28098i	−0.456795	+	0.353089i
$148$			20.6491i			1.69734i
$149$	2.43008	−	4.20902i	0.199080	−	0.344816i	−0.749150	−	0.662400i	$-0.769538\pi$
$149$	2.43008	−	4.20902i	0.199080	−	0.344816i	0.948230	+	0.317583i	$0.102871\pi$
$150$	−4.81142	+	2.77787i	−0.392850	+	0.226812i
$151$	5.63671	+	9.76307i	0.458709	+	0.794507i	0.998893	−	0.0470396i	$-0.0149787\pi$
$151$	5.63671	+	9.76307i	0.458709	+	0.794507i	−0.540184	+	0.841547i	$0.681645\pi$
$152$	3.45337	−	5.98142i	0.280106	−	0.485157i
$153$	−2.27368	+	3.43953i	−0.183816	+	0.278070i
$154$	−0.293401	−	4.35813i	−0.0236429	−	0.351188i
$155$	13.9278			1.11871
$156$	−1.31616	−	0.759885i	−0.105377	−	0.0608395i
$157$	−11.6010	−	20.0936i	−0.925863	−	1.60364i	−0.790168	−	0.612890i	$-0.790007\pi$
$157$	−11.6010	−	20.0936i	−0.925863	−	1.60364i	−0.135695	−	0.990751i	$-0.543327\pi$
$158$	−1.59280	+	0.919606i	−0.126717	+	0.0731600i
$159$	−4.13228	−	2.38577i	−0.327711	−	0.189204i
$160$			20.4542i			1.61705i
$161$	−7.87137	−	3.86441i	−0.620351	−	0.304558i
$162$	−0.524739			−0.0412274
$163$	−2.53868	−	1.46571i	−0.198845	−	0.114803i	0.397272	−	0.917701i	$-0.369957\pi$
$163$	−2.53868	−	1.46571i	−0.198845	−	0.114803i	−0.596117	+	0.802898i	$0.703290\pi$
$164$	9.74802	−	5.62802i	0.761192	−	0.439475i
$165$	10.7575	−	6.21082i	0.837467	−	0.483512i
$166$	−2.67386	+	4.63126i	−0.207532	+	0.359455i
$167$		−	3.85772i		−	0.298519i	−0.988798	−	0.149260i	$-0.952311\pi$
$167$		−	3.85772i		−	0.298519i	0.988798	−	0.149260i	$-0.0476890\pi$
$168$	4.29447	−	2.88049i	0.331325	−	0.222234i
$169$	−12.2235			−0.940267
$170$	−7.64227	+	3.81588i	−0.586135	+	0.292665i
$171$	−1.76691	−	3.06038i	−0.135119	−	0.234033i
$172$	3.07157	+	5.32012i	0.234205	+	0.405655i
$173$	−14.7421	−	8.51133i	−1.12082	−	0.647104i	−0.179208	−	0.983811i	$-0.557354\pi$
$173$	−14.7421	−	8.51133i	−1.12082	−	0.647104i	−0.941610	+	0.336707i	$0.890687\pi$
$174$	4.58349			0.347474
$175$	−15.6040	−	23.2637i	−1.17955	−	1.75857i
$176$		−	7.62553i		−	0.574796i
$177$	11.0684	+	6.39036i	0.831953	+	0.480329i
$178$	−0.292123	−	0.505972i	−0.0218956	−	0.0379242i
$179$	−4.48115	−	7.76157i	−0.334937	−	0.580127i	0.648536	−	0.761184i	$-0.275382\pi$
$179$	−4.48115	−	7.76157i	−0.334937	−	0.580127i	−0.983473	+	0.181057i	$0.942048\pi$
$180$	5.89687	+	3.40456i	0.439526	+	0.253761i
$181$			17.4488i			1.29696i	0.761231	+	0.648481i	$0.224595\pi$
$181$			17.4488i			1.29696i	−0.761231	+	0.648481i	$0.775405\pi$
$182$	−0.539153	+	1.09819i	−0.0399647	+	0.0814036i
$183$	7.85627			0.580752
$184$	5.60985	+	3.23885i	0.413564	+	0.238771i
$185$	23.6352	+	40.9374i	1.73770	+	3.00978i
$186$	0.925561	+	1.60312i	0.0678655	+	0.117546i
$187$	11.6059	−	5.79496i	0.848706	−	0.423769i
$188$	−14.9974			−1.09380
$189$	−0.177717	−	2.63978i	−0.0129270	−	0.192015i
$190$		−	7.32113i		−	0.531131i
$191$	−1.05824	+	1.83293i	−0.0765719	+	0.132626i	−0.901769	−	0.432219i	$-0.857731\pi$
$191$	−1.05824	+	1.83293i	−0.0765719	+	0.132626i	0.825197	+	0.564845i	$0.191064\pi$
$192$	1.84366	−	1.06444i	0.133055	−	0.0768192i
$193$	−20.5920	+	11.8888i	−1.48225	+	0.855776i	−0.999797	−	0.0201469i	$-0.993587\pi$
$193$	−20.5920	+	11.8888i	−1.48225	+	0.855776i	−0.482451	+	0.875923i	$0.660253\pi$
$194$	−2.26386	−	1.30704i	−0.162536	−	0.0938402i
$195$	−3.47910			−0.249144
$196$	7.38318	+	9.55169i	0.527370	+	0.682264i
$197$			20.3392i			1.44911i	0.689219	+	0.724553i	$0.257954\pi$
$197$			20.3392i			1.44911i	−0.689219	+	0.724553i	$0.742046\pi$
$198$	1.42976	+	0.825473i	0.101609	+	0.0586638i
$199$	15.5463	−	8.97568i	1.10205	−	0.636269i	0.165291	−	0.986245i	$-0.447144\pi$
$199$	15.5463	−	8.97568i	1.10205	−	0.636269i	0.936759	+	0.349976i	$0.113810\pi$
$200$	10.3466	+	17.9208i	0.731615	+	1.26719i
$201$	2.86192	+	1.65233i	0.201865	+	0.116547i
$202$	5.47914			0.385511
$203$	1.55232	+	23.0579i	0.108952	+	1.61835i
$204$	5.93198	+	3.92130i	0.415322	+	0.274546i
$205$	12.8838	−	22.3155i	0.899846	−	1.55858i
$206$	−1.03185	−	1.78722i	−0.0718924	−	0.124521i
$207$	2.87027	−	1.65715i	0.199497	−	0.115180i
$208$	−1.06789	+	1.84965i	−0.0740451	+	0.128250i
$209$			11.1182i			0.769061i
$210$	2.41560	−	4.92030i	0.166692	−	0.339533i
$211$			1.86073i			0.128098i	0.997947	+	0.0640489i	$0.0204014\pi$
$211$			1.86073i			0.128098i	−0.997947	+	0.0640489i	$0.979599\pi$
$212$	−4.11462	+	7.12673i	−0.282593	+	0.489466i
$213$	2.05406	+	3.55774i	0.140742	+	0.243772i
$214$	−0.871656	+	0.503251i	−0.0595852	+	0.0344015i
$215$	12.1790	+	7.03154i	0.830599	+	0.479547i
$216$			1.95447i			0.132985i
$217$	−7.75126	+	5.19911i	−0.526189	+	0.352938i
$218$		−	4.96926i		−	0.336561i
$219$	−5.50035	+	9.52688i	−0.371679	+	0.643767i
$220$	−10.7115	−	18.5528i	−0.722169	−	1.25083i
$221$	−3.62666	−	0.219687i	−0.243955	−	0.0147777i
$222$	−3.14133	+	5.44094i	−0.210832	+	0.365172i
$223$	−6.89198			−0.461521			−0.230761	−	0.973011i	$-0.574121\pi$
$223$	−6.89198			−0.461521			−0.230761	+	0.973011i	$0.574121\pi$
$224$	−7.63537	−	11.3834i	−0.510160	−	0.760588i
$225$	10.5876			0.705842
$226$	2.81012	+	1.62242i	0.186926	+	0.107922i
$227$	−3.13873	+	1.81215i	−0.208325	+	0.120276i	−0.600533	−	0.799600i	$-0.705045\pi$
$227$	−3.13873	+	1.81215i	−0.208325	+	0.120276i	0.392208	+	0.919877i	$0.371711\pi$
$228$	−5.27808	+	3.04730i	−0.349549	+	0.201812i
$229$	−5.92085	+	10.2552i	−0.391261	+	0.677683i	−0.992616	−	0.121298i	$-0.961294\pi$
$229$	−5.92085	+	10.2552i	−0.391261	+	0.677683i	0.601355	+	0.798982i	$0.294628\pi$
$230$	6.86634			0.452753
$231$	−3.66843	+	7.47219i	−0.241365	+	0.491634i
$232$		−	17.0719i		−	1.12083i
$233$	−3.86669	−	2.23243i	−0.253315	−	0.146252i	0.367966	−	0.929839i	$-0.380054\pi$
$233$	−3.86669	−	2.23243i	−0.253315	−	0.146252i	−0.621281	+	0.783588i	$0.713388\pi$
$234$	−0.231202	−	0.400453i	−0.0151141	−	0.0261784i
$235$	−29.7328	+	17.1663i	−1.93956	+	1.11980i
$236$	11.0211	−	19.0891i	0.717414	−	1.24260i
$237$	3.50500			0.227674
$238$	2.82874	−	4.97645i	0.183360	−	0.322575i
$239$	0.597778			0.0386670			0.0193335	−	0.999813i	$-0.493846\pi$
$239$	0.597778			0.0386670			0.0193335	+	0.999813i	$0.493846\pi$
$240$	4.78455	−	8.28708i	0.308841	−	0.534929i
$241$	1.77806	−	1.02656i	0.114535	−	0.0661267i	−0.441638	−	0.897193i	$-0.645603\pi$
$241$	1.77806	−	1.02656i	0.114535	−	0.0661267i	0.556173	+	0.831067i	$0.312269\pi$
$242$	0.288945	+	0.500468i	0.0185741	+	0.0321713i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$		−	13.5493i		−	0.867405i
$245$	25.5704	+	10.4856i	1.63363	+	0.669902i
$246$	3.42475			0.218354
$247$	1.55701	−	2.69682i	0.0990703	−	0.171595i
$248$	5.97106	−	3.44739i	0.379162	−	0.218910i
$249$	8.82582	−	5.09559i	0.559314	−	0.322920i
$250$	10.0252	+	5.78803i	0.634047	+	0.366067i
$251$	5.98660			0.377871			0.188936	−	0.981989i	$-0.439496\pi$
$251$	5.98660			0.377871			0.188936	+	0.981989i	$0.439496\pi$
$252$	−4.55269	+	0.306499i	−0.286792	+	0.0193076i
$253$	−10.4275			−0.655573
$254$	5.09905	−	8.83182i	0.319943	−	0.554158i
$255$	16.2487	+	0.984275i	1.01753	+	0.0616377i
$256$	0.882765	+	1.52899i	0.0551728	+	0.0955621i
$257$	−4.21568	+	7.30178i	−0.262967	+	0.455472i	−0.967029	−	0.254666i	$-0.918034\pi$
$257$	−4.21568	+	7.30178i	−0.262967	+	0.455472i	0.704062	+	0.710139i	$0.251368\pi$
$258$			1.86911i			0.116365i
$259$	−28.4353	−	13.9602i	−1.76688	−	0.867443i
$260$			6.00023i			0.372118i
$261$	−7.56456	−	4.36740i	−0.468234	−	0.270335i
$262$	−2.61258	+	1.50837i	−0.161406	+	0.0931877i
$263$	3.08641	+	5.34582i	0.190316	+	0.329637i	0.945355	−	0.326043i	$-0.105715\pi$
$263$	3.08641	+	5.34582i	0.190316	+	0.329637i	−0.755039	+	0.655680i	$0.772382\pi$
$264$	3.07460	−	5.32536i	0.189228	−	0.327753i
$265$			18.8386i			1.15725i
$266$	2.73291	+	4.07445i	0.167565	+	0.249820i
$267$			1.11340i			0.0681392i
$268$	2.84969	−	4.93581i	0.174073	−	0.301503i
$269$	6.69495	−	3.86533i	0.408199	−	0.235674i	−0.281817	−	0.959468i	$-0.590937\pi$
$269$	6.69495	−	3.86533i	0.408199	−	0.235674i	0.690015	+	0.723795i	$0.257604\pi$
$270$	1.03587	+	1.79417i	0.0630408	+	0.109190i
$271$	−3.69428	+	6.39869i	−0.224412	+	0.388693i	−0.956143	−	0.292901i	$-0.905379\pi$
$271$	−3.69428	+	6.39869i	−0.224412	+	0.388693i	0.731731	+	0.681593i	$0.238713\pi$
$272$	5.51075	−	8.33642i	0.334138	−	0.505470i
$273$	1.93623	−	1.29872i	0.117186	−	0.0786019i
$274$	−5.96867			−0.360580
$275$	−28.8482	−	16.6555i	−1.73961	−	1.00437i
$276$	−2.85800	−	4.95021i	−0.172032	−	0.297967i
$277$	−19.8730	+	11.4737i	−1.19405	+	0.689388i	−0.959224	−	0.282649i	$-0.908787\pi$
$277$	−19.8730	+	11.4737i	−1.19405	+	0.689388i	−0.234831	+	0.972036i	$0.575454\pi$
$278$	−0.736031	−	0.424948i	−0.0441442	−	0.0254867i
$279$		−	3.52770i		−	0.211198i
$280$	−18.3264	−	8.99726i	−1.09521	−	0.537689i
$281$	−29.9362			−1.78584			−0.892922	−	0.450212i	$-0.851349\pi$
$281$	−29.9362			−1.78584			−0.892922	+	0.450212i	$0.851349\pi$
$282$	−3.95175	−	2.28155i	−0.235323	−	0.135864i
$283$	−25.3699	+	14.6473i	−1.50808	+	0.870693i	−0.508128	+	0.861282i	$0.669662\pi$
$283$	−25.3699	+	14.6473i	−1.50808	+	0.870693i	−0.999956	+	0.00941090i	$0.997004\pi$
$284$	6.13585	−	3.54254i	0.364096	−	0.210211i
$285$	−6.97597	+	12.0827i	−0.413221	+	0.715719i
$286$			1.45482i			0.0860255i
$287$	1.15988	+	17.2287i	0.0684657	+	1.01698i
$288$	5.18076			0.305279
$289$	16.8757	+	2.05204i	0.992688	+	0.120708i
$290$	−9.04808	−	15.6717i	−0.531322	−	0.920276i
$291$	2.49084	+	4.31427i	0.146016	+	0.252907i
$292$	16.4305	+	9.48617i	0.961524	+	0.555136i
$293$	1.29200			0.0754792			0.0377396	−	0.999288i	$-0.487984\pi$
$293$	1.29200			0.0754792			0.0377396	+	0.999288i	$0.487984\pi$
$294$	0.492345	+	3.64003i	0.0287141	+	0.212291i
$295$		−	50.4597i		−	2.93788i
$296$	20.2656	+	11.7003i	1.17791	+	0.680069i
$297$	−1.57311	−	2.72471i	−0.0912811	−	0.158104i
$298$	−1.27516	−	2.20864i	−0.0738679	−	0.127943i
$299$	2.52930	+	1.46029i	0.146273	+	0.0844508i
$300$		−	18.2599i		−	1.05424i
$301$	−9.40280	+	0.633022i	−0.541968	+	0.0364868i
$302$	5.91561			0.340405
$303$	−9.04272	−	5.22082i	−0.519491	−	0.299928i
$304$	4.28248	+	7.41747i	0.245617	+	0.425421i
$305$	−15.5087	−	26.8619i	−0.888027	−	1.53811i
$306$	0.966506	+	1.93568i	0.0552515	+	0.110655i
$307$	27.3475			1.56080			0.780402	−	0.625278i	$-0.215014\pi$
$307$	27.3475			1.56080			0.780402	+	0.625278i	$0.215014\pi$
$308$	12.8869	+	6.32676i	0.734299	+	0.360501i
$309$			3.93281i			0.223730i
$310$	3.65422	−	6.32930i	0.207546	−	0.359480i
$311$	1.52215	−	0.878811i	0.0863129	−	0.0498328i	−0.456222	−	0.889866i	$-0.650798\pi$
$311$	1.52215	−	0.878811i	0.0863129	−	0.0498328i	0.542535	+	0.840033i	$0.317464\pi$
$312$	−1.49155	+	0.861145i	−0.0844422	+	0.0487527i
$313$	5.77045	+	3.33157i	0.326165	+	0.188311i	0.654137	−	0.756376i	$-0.273032\pi$
$313$	5.77045	+	3.33157i	0.326165	+	0.188311i	−0.327972	+	0.944687i	$0.606365\pi$
$314$	−12.1750			−0.687076
$315$	−8.67502	+	5.81872i	−0.488782	+	0.327848i
$316$		−	6.04490i		−	0.340052i
$317$	7.67483	+	4.43106i	0.431061	+	0.248873i	0.699799	−	0.714340i	$-0.253273\pi$
$317$	7.67483	+	4.43106i	0.431061	+	0.248873i	−0.268737	+	0.963213i	$0.586606\pi$
$318$	−2.16837	+	1.25191i	−0.121596	+	0.0702036i
$319$	13.7408	+	23.7998i	0.769338	+	1.33253i
$320$	−7.27899	−	4.20252i	−0.406908	−	0.234928i
$321$	1.91810			0.107058
$322$	−3.82134	+	2.56314i	−0.212955	+	0.142838i
$323$	−8.03479	+	12.1547i	−0.447068	+	0.676305i
$324$	0.862324	−	1.49359i	0.0479069	−	0.0829772i
$325$	4.66494	+	8.07991i	0.258764	+	0.448193i
$326$	−1.33215	+	0.769116i	−0.0737808	+	0.0425974i
$327$	−4.73498	+	8.20123i	−0.261845	+	0.453529i
$328$		−	12.7560i		−	0.704331i
$329$	10.1393	−	20.6526i	0.558996	−	1.13861i
$330$		−	6.51813i		−	0.358811i
$331$	6.58321	−	11.4025i	0.361846	−	0.626736i	−0.626419	−	0.779487i	$-0.715480\pi$
$331$	6.58321	−	11.4025i	0.361846	−	0.626736i	0.988265	+	0.152751i	$0.0488132\pi$
$332$	−8.78811	−	15.2214i	−0.482310	−	0.835385i
$333$	10.3688	−	5.98645i	0.568209	−	0.328056i
$334$	−1.75309	−	1.01215i	−0.0959249	−	0.0553823i
$335$		−	13.0472i		−	0.712845i
$336$	0.430734	+	6.39805i	0.0234985	+	0.349042i
$337$		−	18.5405i		−	1.00997i	−0.863129	−	0.504983i	$-0.831499\pi$
$337$		−	18.5405i		−	1.00997i	0.863129	−	0.504983i	$-0.168501\pi$
$338$	−3.20707	+	5.55481i	−0.174442	+	0.302142i
$339$	−3.09187	−	5.35527i	−0.167927	−	0.290858i
$340$	1.69753	−	28.0233i	0.0920614	−	1.51978i
$341$	−5.54946	+	9.61195i	−0.300520	+	0.520516i
$342$	−1.85433			−0.100271
$343$	−18.1449	+	3.70960i	−0.979735	+	0.200300i
$344$	6.96176			0.375353
$345$	−11.3322	−	6.54262i	−0.610103	−	0.352243i
$346$	−7.73573	+	4.46623i	−0.415876	+	0.240106i
$347$	21.4320	−	12.3737i	1.15053	−	0.664257i	0.201512	−	0.979486i	$-0.435415\pi$
$347$	21.4320	−	12.3737i	1.15053	−	0.664257i	0.949016	+	0.315229i	$0.102081\pi$
$348$	−7.53223	+	13.0462i	−0.403770	+	0.699350i
$349$	−23.1652			−1.24001			−0.620003	−	0.784599i	$-0.712869\pi$
$349$	−23.1652			−1.24001			−0.620003	+	0.784599i	$0.712869\pi$
$350$	−14.6659	+	0.987350i	−0.783926	+	0.0527761i
$351$			0.881206i			0.0470353i
$352$	−14.1160	−	8.14990i	−0.752388	−	0.434391i
$353$	11.2072	+	19.4114i	0.596498	+	1.03316i	0.993334	+	0.115275i	$0.0367748\pi$
$353$	11.2072	+	19.4114i	0.596498	+	1.03316i	−0.396836	+	0.917890i	$0.629892\pi$
$354$	5.80803	−	3.35327i	0.308694	−	0.178224i
$355$	8.10968	−	14.0464i	0.430417	−	0.745504i
$356$	1.92023			0.101772
$357$	−9.41036	+	5.51771i	−0.498049	+	0.292028i
$358$	−4.70287			−0.248554
$359$	−14.0101	+	24.2662i	−0.739424	+	1.28072i	0.213331	+	0.976980i	$0.431569\pi$
$359$	−14.0101	+	24.2662i	−0.739424	+	1.28072i	−0.952755	+	0.303740i	$0.901764\pi$
$360$	6.68266	−	3.85824i	0.352207	−	0.203347i
$361$	3.25605	+	5.63965i	0.171371	+	0.296824i
$362$	7.92941	+	4.57805i	0.416760	+	0.240617i
$363$		−	1.10129i		−	0.0578028i
$364$	−2.23983	−	3.33932i	−0.117399	−	0.175028i
$365$	43.4320			2.27334
$366$	2.06125	−	3.57018i	0.107743	−	0.186616i
$367$	14.2493	−	8.22682i	0.743806	−	0.429436i	−0.0796457	−	0.996823i	$-0.525379\pi$
$367$	14.2493	−	8.22682i	0.743806	−	0.429436i	0.823451	+	0.567387i	$0.192046\pi$
$368$	−6.95670	+	4.01645i	−0.362643	+	0.209372i
$369$	−5.65218	−	3.26329i	−0.294241	−	0.169880i
$370$	24.8047			1.28953
$371$	−7.03228	−	10.4843i	−0.365098	−	0.544318i
$372$	−6.08404			−0.315443
$373$	−6.59906	+	11.4299i	−0.341686	+	0.591818i	−0.984746	−	0.173998i	$-0.944331\pi$
$373$	−6.59906	+	11.4299i	−0.341686	+	0.591818i	0.643060	+	0.765816i	$0.277665\pi$
$374$	0.411585	−	6.79457i	0.0212825	−	0.351339i
$375$	−11.0303	−	19.1050i	−0.569602	−	0.986580i
$376$	−8.49796	+	14.7189i	−0.438249	+	0.759069i
$377$		−	7.69716i		−	0.396424i
$378$	−1.24624	−	0.611836i	−0.0640997	−	0.0314694i
$379$			7.07128i			0.363227i	0.983370	+	0.181614i	$0.0581320\pi$
$379$			7.07128i			0.363227i	−0.983370	+	0.181614i	$0.941868\pi$
$380$	20.8385	+	12.0311i	1.06899	+	0.617182i
$381$	−16.8309	+	9.71731i	−0.862272	+	0.497833i
$382$	0.555302	+	0.961812i	0.0284117	+	0.0492106i
$383$	9.14863	−	15.8459i	0.467473	−	0.809687i	−0.531836	−	0.846847i	$-0.678498\pi$
$383$	9.14863	−	15.8459i	0.467473	−	0.809687i	0.999309	+	0.0371601i	$0.0118312\pi$
$384$		−	11.4786i		−	0.585766i
$385$	32.7904	−	2.20754i	1.67115	−	0.112507i
$386$			12.4771i			0.635066i
$387$	1.78098	−	3.08476i	0.0905326	−	0.156807i
$388$	7.44059	−	4.29583i	0.377739	−	0.218088i
$389$	−10.3759	−	17.9716i	−0.526079	−	0.911195i	−0.999538	−	0.0303794i	$-0.990328\pi$
$389$	−10.3759	−	17.9716i	−0.526079	−	0.911195i	0.473460	−	0.880815i	$-0.343005\pi$
$390$	−0.912811	+	1.58103i	−0.0462220	+	0.0800588i
$391$	−11.3996	−	7.53567i	−0.576504	−	0.381095i
$392$	13.5578	−	1.83381i	0.684774	−	0.0926215i
$393$	5.74904			0.290001
$394$	9.24288	+	5.33638i	0.465650	+	0.268843i
$395$	−6.91908	−	11.9842i	−0.348137	−	0.602991i
$396$	−4.69916	+	2.71306i	−0.236142	+	0.136337i
$397$	−7.04005	−	4.06457i	−0.353330	−	0.203995i	0.312821	−	0.949812i	$-0.398726\pi$
$397$	−7.04005	−	4.06457i	−0.353330	−	0.203995i	−0.666151	+	0.745817i	$0.732059\pi$
$398$		−	9.41978i		−	0.472171i
$399$	−0.628020	−	9.32850i	−0.0314403	−	0.467009i
$400$	−25.6613			−1.28307
$401$	−25.1535	−	14.5224i	−1.25611	−	0.725214i	−0.283792	−	0.958886i	$-0.591593\pi$
$401$	−25.1535	−	14.5224i	−1.25611	−	0.725214i	−0.972316	+	0.233672i	$0.924926\pi$
$402$	1.50176	−	0.867044i	0.0749012	−	0.0432442i
$403$	2.69215	−	1.55431i	0.134106	−	0.0774259i
$404$	−9.00407	+	15.5955i	−0.447969	+	0.775906i
$405$		−	3.94812i		−	0.196184i
$406$	10.8857	+	5.34426i	0.540246	+	0.265231i
$407$	−37.6694			−1.86720
$408$	7.20971	−	3.59990i	0.356934	−	0.178221i
$409$	−9.92796	−	17.1957i	−0.490906	−	0.850274i	0.509039	−	0.860743i	$-0.330001\pi$
$409$	−9.92796	−	17.1957i	−0.490906	−	0.850274i	−0.999945	+	0.0104691i	$0.996668\pi$
$410$	−6.76065	−	11.7098i	−0.333885	−	0.578306i
$411$	9.85064	+	5.68727i	0.485896	+	0.280532i
$412$	6.78271			0.334160
$413$	18.8362	+	28.0825i	0.926866	+	1.38185i
$414$		−	1.73914i		−	0.0854743i
$415$	−34.8454	−	20.1180i	−1.71049	−	0.987553i
$416$	2.28266	+	3.95367i	0.111916	+	0.193845i
$417$	0.809826	+	1.40266i	0.0396574	+	0.0686886i
$418$	5.05252	+	2.91707i	0.247127	+	0.142679i
$419$			9.95587i			0.486376i	0.969979	+	0.243188i	$0.0781932\pi$
$419$			9.95587i			0.486376i	−0.969979	+	0.243188i	$0.921807\pi$
$420$	10.0352	+	14.9614i	0.489670	+	0.730040i
$421$	19.7581			0.962950			0.481475	−	0.876460i	$-0.340101\pi$
$421$	19.7581			0.962950			0.481475	+	0.876460i	$0.340101\pi$
$422$	0.845584	+	0.488198i	0.0411624	+	0.0237651i
$423$	4.34796	+	7.53089i	0.211405	+	0.366164i
$424$	4.66292	+	8.07641i	0.226451	+	0.392225i
$425$	−19.5011	−	39.0560i	−0.945943	−	1.89449i
$426$	2.15569			0.104444
$427$	18.6584	+	9.16025i	0.902944	+	0.443296i
$428$		−	3.30805i		−	0.159901i
$429$	1.38623	−	2.40103i	0.0669280	−	0.115923i
$430$	6.39079	−	3.68972i	0.308191	−	0.177934i
$431$	−23.2412	+	13.4183i	−1.11949	+	0.646337i	−0.941270	−	0.337654i	$-0.890367\pi$
$431$	−23.2412	+	13.4183i	−1.11949	+	0.646337i	−0.178219	+	0.983991i	$0.557033\pi$
$432$	−2.09899	−	1.21186i	−0.100988	−	0.0583054i
$433$	−14.8038			−0.711424			−0.355712	−	0.934596i	$-0.615762\pi$
$433$	−14.8038			−0.711424			−0.355712	+	0.934596i	$0.615762\pi$
$434$	0.328976	+	4.88655i	0.0157913	+	0.234562i
$435$			34.4860i			1.65348i
$436$	14.1442	+	8.16618i	0.677386	+	0.391089i
$437$	10.1430	−	5.85607i	0.485206	−	0.280134i
$438$	2.88625	+	4.99913i	0.137910	+	0.238868i
$439$	15.7900	+	9.11635i	0.753615	+	0.435100i	0.826998	−	0.562204i	$-0.190046\pi$
$439$	15.7900	+	9.11635i	0.753615	+	0.435100i	−0.0733838	+	0.997304i	$0.523380\pi$
$440$	−24.2777			−1.15740
$441$	2.65585	−	6.47661i	0.126469	−	0.308410i
$442$	−1.05136	+	1.59045i	−0.0500080	+	0.0756500i
$443$	11.6806	−	20.2314i	0.554963	−	0.961224i	−0.442944	−	0.896549i	$-0.646066\pi$
$443$	11.6806	−	20.2314i	0.554963	−	0.961224i	0.997906	−	0.0646742i	$-0.0206008\pi$
$444$	−10.3245	−	17.8826i	−0.489981	−	0.848671i
$445$	3.80691	−	2.19792i	0.180465	−	0.104192i
$446$	−1.80825	+	3.13197i	−0.0856229	+	0.148303i
$447$			4.86016i			0.229878i
$448$	5.61975	−	0.378337i	0.265508	−	0.0178747i
$449$		−	20.7793i		−	0.980635i	−0.871544	−	0.490317i	$-0.836881\pi$
$449$		−	20.7793i		−	0.980635i	0.871544	−	0.490317i	$-0.163119\pi$
$450$	2.77787	−	4.81142i	0.130950	−	0.226812i
$451$	10.2670	+	17.7830i	0.483455	+	0.837369i
$452$	−9.23596	+	5.33239i	−0.434423	+	0.250814i
$453$	−9.76307	−	5.63671i	−0.458709	−	0.264836i
$454$			1.90181i			0.0892563i
$455$	−8.26277	−	4.05657i	−0.387365	−	0.190175i
$456$			6.90675i			0.323438i
$457$	9.08014	−	15.7273i	0.424751	−	0.735690i	−0.571646	−	0.820500i	$-0.693695\pi$
$457$	9.08014	−	15.7273i	0.424751	−	0.735690i	0.996397	+	0.0848098i	$0.0270283\pi$
$458$	3.10690	+	5.38131i	0.145176	+	0.251452i
$459$	0.249302	−	4.11556i	0.0116364	−	0.192098i
$460$	−11.2837	+	19.5440i	−0.526107	+	0.911243i
$461$	23.4048			1.09007			0.545035	−	0.838413i	$-0.316516\pi$
$461$	23.4048			1.09007			0.545035	+	0.838413i	$0.316516\pi$
$462$	2.43316	+	3.62755i	0.113201	+	0.168769i
$463$	11.3279			0.526450			0.263225	−	0.964734i	$-0.415214\pi$
$463$	11.3279			0.526450			0.263225	+	0.964734i	$0.415214\pi$
$464$	18.3343	+	10.5853i	0.851149	+	0.491411i
$465$	−12.0618	+	6.96389i	−0.559353	+	0.322942i
$466$	−2.02900	+	1.17145i	−0.0939918	+	0.0542662i
$467$	−19.9227	+	34.5071i	−0.921912	+	1.59680i	−0.125459	+	0.992099i	$0.540040\pi$
$467$	−19.9227	+	34.5071i	−0.921912	+	1.59680i	−0.796453	+	0.604700i	$0.793293\pi$
$468$	1.51977			0.0702514
$469$	4.87040	+	7.26119i	0.224894	+	0.335291i
$470$			18.0156i			0.830999i
$471$	20.0936	+	11.6010i	0.925863	+	0.534547i
$472$	−12.4898	−	21.6329i	−0.574888	−	0.995734i
$473$	−9.70533	+	5.60337i	−0.446251	+	0.257643i
$474$	0.919606	−	1.59280i	0.0422389	−	0.0731600i
$475$	37.4148			1.71671
$476$	9.51612	+	16.2296i	0.436171	+	0.743881i
$477$	4.77155			0.218474
$478$	0.156839	−	0.271653i	0.00717364	−	0.0124251i
$479$	−12.9347	+	7.46784i	−0.591000	+	0.341214i	−0.765493	−	0.643444i	$-0.777505\pi$
$479$	−12.9347	+	7.46784i	−0.591000	+	0.341214i	0.174493	+	0.984658i	$0.444171\pi$
$480$	−10.2271	−	17.7139i	−0.466802	−	0.808524i
$481$	9.13708	+	5.27530i	0.416615	+	0.240533i
$482$		−	1.07736i		−	0.0490722i
$483$	8.74901	−	0.589007i	0.398094	−	0.0268008i
$484$	−1.89934			−0.0863336
$485$	9.83414	−	17.0332i	0.446545	−	0.773439i
$486$	0.454438	−	0.262370i	0.0206137	−	0.0119013i
$487$	2.20905	−	1.27540i	0.100102	−	0.0577937i	−0.449113	−	0.893475i	$-0.648260\pi$
$487$	2.20905	−	1.27540i	0.100102	−	0.0577937i	0.549215	+	0.835681i	$0.314927\pi$
$488$	−13.2977	−	7.67742i	−0.601957	−	0.347540i
$489$	2.93142			0.132563
$490$	11.4740	−	8.86904i	0.518341	−	0.400662i
$491$	8.42710			0.380310			0.190155	−	0.981754i	$-0.439101\pi$
$491$	8.42710			0.380310			0.190155	+	0.981754i	$0.439101\pi$
$492$	−5.62802	+	9.74802i	−0.253731	+	0.439475i
$493$	−2.17761	+	35.9486i	−0.0980745	+	1.61904i
$494$	−0.817025	−	1.41513i	−0.0367597	−	0.0636697i
$495$	−6.21082	+	10.7575i	−0.279156	+	0.483512i
$496$			8.55012i			0.383912i
$497$	0.730083	+	10.8445i	0.0327487	+	0.486444i
$498$		−	5.34771i		−	0.239637i
$499$	30.6923	+	17.7202i	1.37397	+	0.793264i	0.991426	−	0.130671i	$-0.0417132\pi$
$499$	30.6923	+	17.7202i	1.37397	+	0.793264i	0.382548	+	0.923936i	$0.375047\pi$
$500$	−32.9495	+	19.0234i	−1.47355	+	0.850752i
$501$	1.92886	+	3.34088i	0.0861751	+	0.149260i
$502$	1.57070	−	2.72054i	0.0701039	−	0.121424i
$503$		−	22.9796i		−	1.02461i	−0.858803	−	0.512306i	$-0.828791\pi$
$503$		−	22.9796i		−	1.02461i	0.858803	−	0.512306i	$-0.171209\pi$
$504$	−2.27887	+	4.64181i	−0.101509	+	0.206763i
$505$			41.2248i			1.83448i
$506$	−2.73587	+	4.73866i	−0.121624	+	0.210659i
$507$	10.5858	−	6.11174i	0.470134	−	0.271432i
$508$	16.7589	+	29.0273i	0.743558	+	1.28788i
$509$	3.24495	−	5.62042i	0.143830	−	0.249121i	−0.785106	−	0.619362i	$-0.787391\pi$
$509$	3.24495	−	5.62042i	0.143830	−	0.249121i	0.928936	+	0.370241i	$0.120725\pi$
$510$	4.71046	−	7.12578i	0.208583	−	0.315535i
$511$	−24.1713	+	16.2128i	−1.06928	+	0.717211i
$512$	−22.0308			−0.973632
$513$	3.06038	+	1.76691i	0.135119	+	0.0780110i
$514$	2.21213	+	3.83153i	0.0975731	+	0.169001i
$515$	13.4469	−	7.76359i	0.592543	−	0.342105i
$516$	−5.32012	−	3.07157i	−0.234205	−	0.135218i
$517$		−	27.3593i		−	1.20326i
$518$	−13.8046	+	9.25935i	−0.606539	+	0.406832i
$519$	17.0227			0.747212
$520$	5.88880	+	3.39990i	0.258241	+	0.149095i
$521$	7.41911	−	4.28343i	0.325037	−	0.187660i	−0.328598	−	0.944470i	$-0.606576\pi$
$521$	7.41911	−	4.28343i	0.325037	−	0.187660i	0.653636	+	0.756809i	$0.273243\pi$
$522$	−3.96942	+	2.29175i	−0.173737	+	0.100307i
$523$	−14.2665	+	24.7103i	−0.623830	+	1.08051i	0.364935	+	0.931033i	$0.381091\pi$
$523$	−14.2665	+	24.7103i	−0.623830	+	1.08051i	−0.988766	+	0.149473i	$0.952242\pi$
$524$		−	9.91508i		−	0.433142i
$525$	25.1453	+	12.3450i	1.09743	+	0.538779i
$526$	3.23912			0.141232
$527$	−13.0131	+	6.49760i	−0.566859	+	0.283040i
$528$	3.81276	+	6.60390i	0.165929	+	0.287398i
$529$	−6.00770	−	10.4056i	−0.261204	−	0.452419i
$530$	8.56098	+	4.94268i	0.371865	+	0.214696i
$531$	−12.7807			−0.554636
$532$	−16.0884	+	1.08311i	−0.697520	+	0.0469589i
$533$		−	5.75125i		−	0.249114i
$534$	0.505972	+	0.292123i	0.0218956	+	0.0126414i
$535$	−3.78644	−	6.55831i	−0.163702	−	0.283540i
$536$	−3.22943	−	5.59354i	−0.139490	−	0.241604i
$537$	7.76157	+	4.48115i	0.334937	+	0.193376i
$538$		−	4.05659i		−	0.174892i
$539$	−17.4248	+	13.4689i	−0.750541	+	0.580147i
$540$	−6.80911			−0.293018
$541$	14.2027	+	8.19993i	0.610622	+	0.352543i	0.773209	−	0.634152i	$-0.218651\pi$
$541$	14.2027	+	8.19993i	0.610622	+	0.352543i	−0.162587	+	0.986694i	$0.551984\pi$
$542$	1.93854	+	3.35764i	0.0832672	+	0.144223i
$543$	−8.72442	−	15.1111i	−0.374401	−	0.648481i
$544$	−9.54232	−	19.1109i	−0.409124	−	0.819375i
$545$	37.3885			1.60155
$546$	−0.0821769	−	1.22064i	−0.00351684	−	0.0522386i
$547$			15.8926i			0.679519i	0.940512	+	0.339759i	$0.110346\pi$
$547$			15.8926i			0.679519i	−0.940512	+	0.339759i	$0.889654\pi$
$548$	9.80854	−	16.9889i	0.419000	−	0.725729i
$549$	−6.80373	+	3.92813i	−0.290376	+	0.167649i
$550$	−15.1378	+	8.73980i	−0.645477	+	0.372666i
$551$	−26.7318	−	15.4336i	−1.13881	−	0.657494i
$552$	−6.47770			−0.275709
$553$	8.32428	+	4.08677i	0.353984	+	0.173787i
$554$			12.0414i			0.511590i
$555$	−40.9374	−	23.6352i	−1.73770	−	1.00326i
$556$	2.41910	−	1.39667i	0.102593	−	0.0592318i
$557$	−9.45205	−	16.3714i	−0.400496	−	0.693680i	0.593290	−	0.804989i	$-0.297829\pi$
$557$	−9.45205	−	16.3714i	−0.400496	−	0.693680i	−0.993786	+	0.111309i	$0.964496\pi$
$558$	−1.60312	−	0.925561i	−0.0678655	−	0.0391821i
$559$	3.13883			0.132758
$560$	21.0257	−	14.1029i	0.888499	−	0.595956i
$561$	−7.15351	+	10.8215i	−0.302021	+	0.456885i
$562$	−7.85435	+	13.6041i	−0.331316	+	0.573856i
$563$	0.762601	+	1.32086i	0.0321398	+	0.0556678i	0.881648	−	0.471908i	$-0.156434\pi$
$563$	0.762601	+	1.32086i	0.0321398	+	0.0556678i	−0.849508	+	0.527576i	$0.823101\pi$
$564$	12.9881	−	7.49871i	0.546899	−	0.315752i
$565$	−12.2071	+	21.1432i	−0.513555	+	0.889503i
$566$			15.3720i			0.646135i
$567$	1.47380	+	2.19725i	0.0618936	+	0.0922760i
$568$		−	8.02921i		−	0.336898i
$569$	18.0752	−	31.3072i	0.757753	−	1.31247i	−0.186241	−	0.982504i	$-0.559631\pi$
$569$	18.0752	−	31.3072i	0.757753	−	1.31247i	0.943994	−	0.329962i	$-0.107036\pi$
$570$	3.66057	+	6.34029i	0.153324	+	0.265565i
$571$	−4.95620	+	2.86147i	−0.207411	+	0.119749i	−0.600107	−	0.799919i	$-0.704876\pi$
$571$	−4.95620	+	2.86147i	−0.207411	+	0.119749i	0.392697	+	0.919668i	$0.371542\pi$
$572$	−4.14093	−	2.39077i	−0.173141	−	0.0999630i
$573$		−	2.11649i		−	0.0884176i
$574$	8.13368	+	3.99319i	0.339493	+	0.166673i
$575$			35.0906i			1.46338i
$576$	−1.06444	+	1.84366i	−0.0443516	+	0.0768192i
$577$	7.35989	+	12.7477i	0.306396	+	0.530694i	0.977571	−	0.210605i	$-0.0675434\pi$
$577$	7.35989	+	12.7477i	0.306396	+	0.530694i	−0.671175	+	0.741299i	$0.734210\pi$
$578$	5.36019	−	7.13056i	0.222955	−	0.296592i
$579$	11.8888	−	20.5920i	0.494083	−	0.855776i
$580$	59.4763			2.46962
$581$	26.9024	−	1.81115i	1.11610	−	0.0751390i
$582$	2.61409			0.108357
$583$	−13.0011	−	7.50617i	−0.538449	−	0.310874i
$584$	18.6200	−	10.7503i	0.770501	−	0.444849i
$585$	3.01299	−	1.73955i	0.124572	−	0.0719216i
$586$	0.338980	−	0.587131i	0.0140031	−	0.0242542i
$587$	0.254477			0.0105034			0.00525170	−	0.999986i	$-0.498328\pi$
$587$	0.254477			0.0105034			0.00525170	+	0.999986i	$0.498328\pi$
$588$	−11.1699	−	4.58042i	−0.460638	−	0.188893i
$589$		−	12.4663i		−	0.513663i
$590$	−22.9308	−	13.2391i	−0.944046	−	0.545045i
$591$	−10.1696	−	17.6142i	−0.418321	−	0.724553i
$592$	−25.1311	+	14.5094i	−1.03288	+	0.596334i
$593$	5.80934	−	10.0621i	0.238561	−	0.413200i	−0.721741	−	0.692164i	$-0.756658\pi$
$593$	5.80934	−	10.0621i	0.238561	−	0.413200i	0.960302	+	0.278964i	$0.0899910\pi$
$594$	−1.65095			−0.0677391
$595$	37.4426	+	21.2833i	1.53500	+	0.872531i
$596$	8.38207			0.343343
$597$	−8.97568	+	15.5463i	−0.367350	+	0.636269i
$598$	1.32722	−	0.766272i	0.0542741	−	0.0313352i
$599$	−0.898032	−	1.55544i	−0.0366926	−	0.0635534i	0.847096	−	0.531440i	$-0.178349\pi$
$599$	−0.898032	−	1.55544i	−0.0366926	−	0.0635534i	−0.883789	+	0.467887i	$0.845016\pi$
$600$	−17.9208	−	10.3466i	−0.731615	−	0.422398i
$601$			21.7215i			0.886038i	0.896512	+	0.443019i	$0.146093\pi$
$601$			21.7215i			0.886038i	−0.896512	+	0.443019i	$0.853907\pi$
$602$	−2.17934	+	4.43907i	−0.0888233	+	0.180923i
$603$	−3.30467			−0.134576
$604$	−9.72135	+	16.8379i	−0.395556	+	0.685123i
$605$	−3.76550	+	2.17401i	−0.153089	+	0.0883862i
$606$	−4.74507	+	2.73957i	−0.192755	+	0.111287i
$607$	6.57697	+	3.79722i	0.266951	+	0.154124i	0.627501	−	0.778615i	$-0.284078\pi$
$607$	6.57697	+	3.79722i	0.266951	+	0.154124i	−0.360550	+	0.932740i	$0.617411\pi$
$608$	18.3079			0.742482
$609$	−12.8733	−	19.1926i	−0.521653	−	0.777723i
$610$	−16.2761			−0.658999
$611$	−3.83145	+	6.63626i	−0.155004	+	0.268474i
$612$	−7.09790	−	0.429959i	−0.286916	−	0.0173801i
$613$	−17.6575	−	30.5837i	−0.713180	−	1.23526i	−0.963657	−	0.267141i	$-0.913921\pi$
$613$	−17.6575	−	30.5837i	−0.713180	−	1.23526i	0.250478	−	0.968122i	$-0.419412\pi$
$614$	7.17515	−	12.4277i	0.289566	−	0.501542i
$615$			25.7677i			1.03905i
$616$	13.5113	−	9.06265i	0.544388	−	0.365145i
$617$			28.3849i			1.14273i	0.820695	+	0.571367i	$0.193587\pi$
$617$			28.3849i			1.14273i	−0.820695	+	0.571367i	$0.806413\pi$
$618$	1.78722	+	1.03185i	0.0718924	+	0.0415071i
$619$	37.9247	−	21.8959i	1.52432	−	0.880069i	0.524739	−	0.851263i	$-0.324163\pi$
$619$	37.9247	−	21.8959i	1.52432	−	0.880069i	0.999585	−	0.0288058i	$-0.00917043\pi$
$620$	12.0103	+	20.8024i	0.482344	+	0.835444i
$621$	−1.65715	+	2.87027i	−0.0664992	+	0.115180i
$622$		−	0.922293i		−	0.0369806i
$623$	−1.29821	+	2.64430i	−0.0520115	+	0.105942i
$624$		−	2.13579i		−	0.0854999i
$625$	−17.0799	+	29.5832i	−0.683194	+	1.18333i
$626$	3.02798	−	1.74820i	0.121022	−	0.0698723i
$627$	−5.55909	−	9.62863i	−0.222009	−	0.384530i
$628$	20.0077	−	34.6543i	0.798394	−	1.38286i
$629$	−41.1812	−	27.2226i	−1.64200	−	1.08544i
$630$	0.368182	+	5.46891i	0.0146687	+	0.217887i
$631$	−35.7358			−1.42262			−0.711309	−	0.702879i	$-0.751897\pi$
$631$	−35.7358			−1.42262			−0.711309	+	0.702879i	$0.751897\pi$
$632$	−5.93264	−	3.42521i	−0.235988	−	0.136248i
$633$	−0.930363	−	1.61144i	−0.0369786	−	0.0640489i
$634$	4.02728	−	2.32515i	0.159944	−	0.0923436i
$635$	66.4503	+	38.3651i	2.63700	+	1.52247i
$636$		−	8.22924i		−	0.326311i
$637$	6.11278	−	0.826805i	0.242197	−	0.0327592i
$638$	14.4207			0.570920
$639$	−3.55774	−	2.05406i	−0.140742	−	0.0812575i
$640$	−39.2473	+	22.6595i	−1.55139	+	0.895694i
$641$	−33.1558	+	19.1425i	−1.30958	+	0.756084i	−0.982025	−	0.188750i	$-0.939556\pi$
$641$	−33.1558	+	19.1425i	−1.30958	+	0.756084i	−0.327550	+	0.944834i	$0.606223\pi$
$642$	0.503251	−	0.871656i	0.0198617	−	0.0344015i
$643$			28.8295i			1.13692i	0.822709	+	0.568462i	$0.192461\pi$
$643$			28.8295i			1.13692i	−0.822709	+	0.568462i	$0.807539\pi$
$644$	−1.01583	−	15.0890i	−0.0400293	−	0.594589i
$645$	−14.0631			−0.553733
$646$	3.41546	+	6.84033i	0.134379	+	0.269129i
$647$	−16.8078	−	29.1119i	−0.660782	−	1.14451i	−0.980410	−	0.196965i	$-0.936891\pi$
$647$	−16.8078	−	29.1119i	−0.660782	−	1.14451i	0.319628	−	0.947543i	$-0.396442\pi$
$648$	−0.977235	−	1.69262i	−0.0383894	−	0.0664924i
$649$	34.8237	+	20.1055i	1.36695	+	0.789209i
$650$	4.89575			0.192027
$651$	4.11323	−	8.37819i	0.161210	−	0.328367i
$652$		−	5.05567i		−	0.197995i
$653$	4.62911	+	2.67262i	0.181151	+	0.104588i	0.587833	−	0.808982i	$-0.299981\pi$
$653$	4.62911	+	2.67262i	0.181151	+	0.104588i	−0.406682	+	0.913570i	$0.633314\pi$
$654$	2.48463	+	4.30351i	0.0971567	+	0.168280i
$655$	−11.3489	−	19.6570i	−0.443440	−	0.768061i
$656$	13.6992	+	7.90926i	0.534865	+	0.308805i
$657$		−	11.0007i		−	0.429178i
$658$	−6.72506	−	10.0263i	−0.262170	−	0.390865i
$659$	18.7631			0.730905			0.365453	−	0.930830i	$-0.380914\pi$
$659$	18.7631			0.730905			0.365453	+	0.930830i	$0.380914\pi$
$660$	18.5528	+	10.7115i	0.722169	+	0.416944i
$661$	−1.34834	−	2.33540i	−0.0524444	−	0.0908364i	0.838611	−	0.544730i	$-0.183368\pi$
$661$	−1.34834	−	2.33540i	−0.0524444	−	0.0908364i	−0.891056	+	0.453894i	$0.850035\pi$
$662$	−3.45447	−	5.98332i	−0.134262	−	0.232548i
$663$	3.25062	−	1.62307i	0.126244	−	0.0630350i
$664$	−19.9184			−0.772982
$665$	−30.6560	+	20.5623i	−1.18879	+	0.797372i
$666$		−	6.28266i		−	0.243448i
$667$	14.4749	−	25.0712i	0.560470	−	0.970762i
$668$	5.76185	−	3.32661i	0.222933	−	0.128710i
$669$	5.96863	−	3.44599i	0.230761	−	0.133230i
$670$	−5.92914	−	3.42319i	−0.229063	−	0.132249i
$671$	24.7176			0.954210
$672$	12.3041	+	6.04066i	0.474643	+	0.233024i
$673$		−	25.0509i		−	0.965642i	−0.875719	−	0.482821i	$-0.839612\pi$
$673$		−	25.0509i		−	0.965642i	0.875719	−	0.482821i	$-0.160388\pi$
$674$	−8.42551	−	4.86447i	−0.324539	−	0.187372i
$675$	−9.16915	+	5.29381i	−0.352921	+	0.203759i
$676$	−10.5406	−	18.2569i	−0.405408	−	0.702187i
$677$	26.6177	+	15.3677i	1.02300	+	0.590630i	0.914972	−	0.403518i	$-0.132213\pi$
$677$	26.6177	+	15.3677i	1.02300	+	0.590630i	0.108029	+	0.994148i	$0.465546\pi$
$678$	−3.24485			−0.124618
$679$	0.885330	+	13.1505i	0.0339758	+	0.504671i
$680$	−26.5410	−	17.5448i	−1.01780	−	0.672813i
$681$	1.81215	−	3.13873i	0.0694416	−	0.120276i
$682$	2.91202	+	5.04377i	0.111507	+	0.193136i
$683$	−32.4078	+	18.7107i	−1.24005	+	0.715944i	−0.969104	−	0.246651i	$-0.920670\pi$
$683$	−32.4078	+	18.7107i	−1.24005	+	0.715944i	−0.270946	+	0.962594i	$0.587337\pi$
$684$	3.04730	−	5.27808i	0.116516	−	0.201812i
$685$		−	44.9080i		−	1.71585i
$686$	−3.07490	+	9.21903i	−0.117400	+	0.351984i
$687$		−	11.8417i		−	0.451789i
$688$	−4.31659	+	7.47656i	−0.164569	+	0.285041i
$689$	2.10236	+	3.64139i	0.0800934	+	0.138726i
$690$	−5.94643	+	3.43317i	−0.226377	+	0.130699i
$691$	−43.7189	−	25.2411i	−1.66315	−	0.960218i	−0.971199	−	0.238268i	$-0.923420\pi$
$691$	−43.7189	−	25.2411i	−1.66315	−	0.960218i	−0.691946	−	0.721949i	$-0.743246\pi$
$692$		−	29.3581i		−	1.11603i
$693$	−0.559137	−	8.30532i	−0.0212398	−	0.315493i
$694$		−	12.9860i		−	0.492941i
$695$	3.19729	−	5.53787i	0.121280	−	0.210063i
$696$	8.53595	+	14.7847i	0.323554	+	0.560413i
$697$	−1.62709	+	26.8605i	−0.0616304	+	1.01741i
$698$	−6.07785	+	10.5271i	−0.230050	+	0.398458i
$699$	4.46487			0.168877
$700$	21.2907	−	43.3668i	0.804714	−	1.63911i
$701$	−13.7310			−0.518613			−0.259306	−	0.965795i	$-0.583494\pi$
$701$	−13.7310			−0.518613			−0.259306	+	0.965795i	$0.583494\pi$
$702$	0.400453	+	0.231202i	0.0151141	+	0.00872614i
$703$	36.6416	−	21.1551i	1.38197	−	0.797878i
$704$	5.80056	−	3.34896i	0.218617	−	0.126219i
$705$	17.1663	−	29.7328i	0.646519	−	1.11980i
$706$	11.7617			0.442657
$707$	−15.3888	−	22.9429i	−0.578757	−	0.862858i
$708$			22.0422i			0.828398i
$709$	1.47125	+	0.849427i	0.0552540	+	0.0319009i	0.527373	−	0.849634i	$-0.323177\pi$
$709$	1.47125	+	0.849427i	0.0552540	+	0.0319009i	−0.472119	+	0.881535i	$0.656511\pi$
$710$	−4.25547	−	7.37069i	−0.159705	−	0.276617i
$711$	−3.03542	+	1.75250i	−0.113837	+	0.0657239i
$712$	1.08806	−	1.88457i	0.0407766	−	0.0706272i
$713$	11.6919			0.437864
$714$	0.0384647	+	5.72410i	0.00143951	+	0.214219i
$715$	−10.9460			−0.409358
$716$	7.72840	−	13.3860i	0.288824	−	0.500258i
$717$	−0.517691	+	0.298889i	−0.0193335	+	0.0111622i
$718$	7.35164	+	12.7334i	0.274361	+	0.475207i
$719$	21.0367	+	12.1455i	0.784535	+	0.452951i	0.838035	−	0.545616i	$-0.183704\pi$
$719$	21.0367	+	12.1455i	0.784535	+	0.452951i	−0.0535001	+	0.998568i	$0.517038\pi$
$720$			9.56909i			0.356619i
$721$	−4.58558	+	9.34031i	−0.170776	+	0.347851i
$722$	3.41716			0.127173
$723$	−1.02656	+	1.77806i	−0.0381783	+	0.0661267i
$724$	−26.0614	+	15.0466i	−0.968565	+	0.559201i
$725$	80.0907	−	46.2404i	2.97450	−	1.71733i
$726$	−0.500468	−	0.288945i	−0.0185741	−	0.0107238i
$727$	−21.9394			−0.813689			−0.406844	−	0.913497i	$-0.633371\pi$
$727$	−21.9394			−0.813689			−0.406844	+	0.913497i	$0.633371\pi$
$728$	−4.54646	+	0.306080i	−0.168503	+	0.0113441i
$729$	−1.00000			−0.0370370
$730$	11.3952	−	19.7371i	0.421757	−	0.730505i
$731$	−14.6595	−	0.888007i	−0.542201	−	0.0328441i
$732$	6.77465	+	11.7340i	0.250398	+	0.433702i
$733$	3.31674	−	5.74476i	0.122507	−	0.212188i	−0.798249	−	0.602328i	$-0.794240\pi$
$733$	3.31674	−	5.74476i	0.122507	−	0.212188i	0.920756	+	0.390140i	$0.127573\pi$
$734$		−	8.63387i		−	0.318682i
$735$	−27.3874	+	3.70438i	−1.01020	+	0.136638i
$736$			17.1706i			0.632916i
$737$	9.00425	+	5.19860i	0.331676	+	0.191493i
$738$	−2.96592	+	1.71237i	−0.109177	+	0.0630334i
$739$	11.1509	+	19.3140i	0.410194	+	0.710477i	0.994911	−	0.100761i	$-0.0321276\pi$
$739$	11.1509	+	19.3140i	0.410194	+	0.710477i	−0.584717	+	0.811238i	$0.698794\pi$
$740$	−40.7625	+	70.6026i	−1.49846	+	2.59540i
$741$			3.11402i			0.114397i
$742$	−6.60952	+	0.444971i	−0.242643	+	0.0163354i
$743$		−	31.1925i		−	1.14434i	−0.820134	−	0.572171i	$-0.806101\pi$
$743$		−	31.1925i		−	1.14434i	0.820134	−	0.572171i	$-0.193899\pi$
$744$	−3.44739	+	5.97106i	−0.126387	+	0.218910i
$745$	16.6177	−	9.59424i	0.608826	−	0.351506i
$746$	3.46279	+	5.99772i	0.126782	+	0.219592i
$747$	−5.09559	+	8.82582i	−0.186438	+	0.322920i
$748$	18.6633	+	12.3373i	0.682399	+	0.451096i
$749$	4.55543	+	2.23647i	0.166452	+	0.0817187i
$750$	−11.5761			−0.422698
$751$	8.02312	+	4.63215i	0.292768	+	0.169030i	0.639189	−	0.769049i	$-0.279270\pi$
$751$	8.02312	+	4.63215i	0.292768	+	0.169030i	−0.346422	+	0.938079i	$0.612603\pi$
$752$	−10.5382	−	18.2527i	−0.384289	−	0.665607i
$753$	−5.18455	+	2.99330i	−0.188936	+	0.109082i
$754$	−3.49788	−	2.01950i	−0.127385	−	0.0735458i
$755$			44.5088i			1.61984i
$756$	3.78949	−	2.54178i	0.137822	−	0.0924436i
$757$	−26.2641			−0.954584			−0.477292	−	0.878745i	$-0.658382\pi$
$757$	−26.2641			−0.954584			−0.477292	+	0.878745i	$0.658382\pi$
$758$	3.21345	+	1.85529i	0.116718	+	0.0673871i
$759$	9.03050	−	5.21376i	0.327786	−	0.189248i
$760$	23.6153	−	13.6343i	0.856618	−	0.494569i
$761$	−1.27087	+	2.20122i	−0.0460691	+	0.0797940i	−0.888140	−	0.459572i	$-0.848003\pi$
$761$	−1.27087	+	2.20122i	−0.0460691	+	0.0797940i	0.842071	+	0.539366i	$0.181336\pi$
$762$			10.1981i			0.369439i
$763$	−20.8079	+	13.9568i	−0.753297	+	0.505270i
$764$	−3.65020			−0.132060
$765$	−14.5639	+	7.27195i	−0.526560	+	0.262918i
$766$	−4.80064	−	8.31496i	−0.173454	−	0.300432i
$767$	−5.63122	−	9.75355i	−0.203331	−	0.352180i
$768$	−1.52899	−	0.882765i	−0.0551728	−	0.0318540i
$769$	20.9202			0.754403			0.377201	−	0.926131i	$-0.376886\pi$
$769$	20.9202			0.754403			0.377201	+	0.926131i	$0.376886\pi$
$770$	7.60001	−	15.4804i	0.273885	−	0.557874i
$771$		−	8.43136i		−	0.303648i
$772$	−35.5140	−	20.5040i	−1.27818	−	0.737957i
$773$	1.92270	+	3.33021i	0.0691546	+	0.119779i	0.898529	−	0.438913i	$-0.144636\pi$
$773$	1.92270	+	3.33021i	0.0691546	+	0.119779i	−0.829375	+	0.558693i	$0.811303\pi$
$774$	−0.934553	−	1.61869i	−0.0335918	−	0.0581827i
$775$	32.3460	+	18.6750i	1.16190	+	0.670825i
$776$		−	9.73655i		−	0.349522i
$777$	31.6058	−	2.12779i	1.13385	−	0.0763340i
$778$	−10.8893			−0.390399
$779$	−19.9738	−	11.5319i	−0.715635	−	0.413172i
$780$	−3.00011	−	5.19635i	−0.107421	−	0.186059i
$781$	6.46254	+	11.1934i	0.231248	+	0.400533i
$782$	−6.41541	+	3.20329i	−0.229415	+	0.114550i
$783$	8.73480			0.312156
$784$	−6.43702	+	15.6974i	−0.229894	+	0.560622i
$785$		−	91.6044i		−	3.26950i
$786$	1.50837	−	2.61258i	0.0538019	−	0.0931877i
$787$	4.32323	−	2.49602i	0.154107	−	0.0889735i	−0.420964	−	0.907077i	$-0.638308\pi$
$787$	4.32323	−	2.49602i	0.154107	−	0.0889735i	0.575070	+	0.818104i	$0.304975\pi$
$788$	−30.3784	+	17.5390i	−1.08218	+	0.624800i
$789$	−5.34582	−	3.08641i	−0.190316	−	0.109879i
$790$	−7.26143			−0.258350
$791$	−1.09895	−	16.3237i	−0.0390743	−	0.580403i
$792$			6.14919i			0.218502i
$793$	−5.99548	−	3.46149i	−0.212906	−	0.122921i
$794$	−3.69419	+	2.13284i	−0.131102	+	0.0756917i
$795$	−9.41931	−	16.3147i	−0.334068	−	0.578624i
$796$	26.8120	+	15.4799i	0.950324	+	0.548670i
$797$	9.44898			0.334700			0.167350	−	0.985898i	$-0.446479\pi$
$797$	9.44898			0.334700			0.167350	+	0.985898i	$0.446479\pi$
$798$	−4.40399	−	2.16212i	−0.155900	−	0.0765382i
$799$	19.7718	−	29.9099i	0.699475	−	1.05814i
$800$	−27.4260	+	47.5031i	−0.969654	+	1.67949i
$801$	−0.556702	−	0.964235i	−0.0196701	−	0.0340696i
$802$	−13.1991	+	7.62048i	−0.466075	+	0.269088i
$803$	−17.3053	+	29.9737i	−0.610691	+	1.05775i
$804$			5.69939i			0.201002i
$805$	−19.2850	−	28.7516i	−0.679706	−	1.01336i
$806$		−	1.63122i		−	0.0574573i
$807$	−3.86533	+	6.69495i	−0.136066	+	0.235674i
$808$	10.2039	+	17.6737i	0.358973	+	0.621759i
$809$	−11.0705	+	6.39154i	−0.389217	+	0.224714i	−0.681821	−	0.731519i	$-0.738812\pi$
$809$	−11.0705	+	6.39154i	−0.389217	+	0.224714i	0.292604	+	0.956234i	$0.405478\pi$
$810$	−1.79417	−	1.03587i	−0.0630408	−	0.0363966i
$811$		−	39.3249i		−	1.38088i	−0.723388	−	0.690442i	$-0.757416\pi$
$811$		−	39.3249i		−	1.38088i	0.723388	−	0.690442i	$-0.242584\pi$
$812$	−33.1005	+	22.2019i	−1.16160	+	0.779135i
$813$		−	7.38857i		−	0.259128i
$814$	−9.88331	+	17.1184i	−0.346410	+	0.600000i
$815$	−5.78680	−	10.0230i	−0.202703	−	0.351091i
$816$	−0.604237	+	9.97493i	−0.0211525	+	0.349192i
$817$	6.29368	−	10.9010i	0.220188	−	0.381377i
$818$	−10.4192			−0.364298
$819$	−1.02747	+	2.09284i	−0.0359027	+	0.0731297i
$820$	44.4402			1.55192
$821$	16.3585	+	9.44460i	0.570917	+	0.329619i	0.757515	−	0.652817i	$-0.226413\pi$
$821$	16.3585	+	9.44460i	0.570917	+	0.329619i	−0.186599	+	0.982436i	$0.559746\pi$
$822$	5.16902	−	2.98433i	0.180290	−	0.104091i
$823$	−4.20168	+	2.42584i	−0.146461	+	0.0845595i	−0.571440	−	0.820644i	$-0.693615\pi$
$823$	−4.20168	+	2.42584i	−0.146461	+	0.0845595i	0.424979	+	0.905203i	$0.360282\pi$
$824$	3.84328	−	6.65675i	0.133887	−	0.231899i
$825$	33.3110			1.15974
$826$	17.7038	−	1.19187i	0.615993	−	0.0414703i
$827$			33.5279i			1.16588i	0.812516	+	0.582939i	$0.198097\pi$
$827$			33.5279i			1.16588i	−0.812516	+	0.582939i	$0.801903\pi$
$828$	4.95021	+	2.85800i	0.172032	+	0.0993225i
$829$	−18.2842	−	31.6692i	−0.635036	−	1.09992i	−0.986507	−	0.163717i	$-0.947652\pi$
$829$	−18.2842	−	31.6692i	−0.635036	−	1.09992i	0.351471	−	0.936199i	$-0.385682\pi$
$830$	−18.2847	+	10.5567i	−0.634673	+	0.366428i
$831$	11.4737	−	19.8730i	0.398018	−	0.689388i
$832$	−1.87598			−0.0650378
$833$	−28.7829	+	2.13212i	−0.997268	+	0.0738736i
$834$	0.849895			0.0294295
$835$	7.61536	−	13.1902i	0.263540	−	0.456466i
$836$	−16.6060	+	9.58748i	−0.574331	+	0.331590i
$837$	1.76385	+	3.05508i	0.0609676	+	0.105599i
$838$	4.52432	+	2.61212i	0.156290	+	0.0902341i
$839$		−	3.39453i		−	0.117192i	−0.998282	−	0.0585961i	$-0.981338\pi$
$839$		−	3.39453i		−	0.117192i	0.998282	−	0.0585961i	$-0.0186624\pi$
$840$	20.3698	−	1.37135i	0.702824	−	0.0473160i
$841$	−47.2967			−1.63092
$842$	5.18392	−	8.97881i	0.178650	−	0.309430i
$843$	25.9255	−	14.9681i	0.892922	−	0.515529i
$844$	−2.77916	+	1.60455i	−0.0956627	+	0.0552309i
$845$	−41.7941	−	24.1299i	−1.43776	−	0.830092i
$846$	4.56309			0.156882
$847$	1.28408	−	2.61553i	0.0441216	−	0.0898708i
$848$	−11.5648			−0.397138
$849$	14.6473	−	25.3699i	0.502695	−	0.870693i
$850$	−22.8650	−	1.38506i	−0.784263	−	0.0475072i
$851$	19.8409	+	34.3655i	0.680138	+	1.17803i
$852$	−3.54254	+	6.13585i	−0.121365	+	0.210211i
$853$			55.1187i			1.88723i	0.331048	+	0.943614i	$0.392598\pi$
$853$			55.1187i			1.88723i	−0.331048	+	0.943614i	$0.607402\pi$
$854$	9.05816	−	6.07571i	0.309964	−	0.207906i
$855$		−	13.9519i		−	0.477146i
$856$	−3.24661	−	1.87443i	−0.110967	−	0.0640668i
$857$	−30.7761	+	17.7686i	−1.05129	+	0.606964i	−0.923011	−	0.384774i	$-0.874280\pi$
$857$	−30.7761	+	17.7686i	−1.05129	+	0.606964i	−0.128282	+	0.991738i	$0.540946\pi$
$858$	−0.727411	−	1.25991i	−0.0248334	−	0.0430127i
$859$	8.85048	−	15.3295i	0.301975	−	0.523035i	−0.674609	−	0.738176i	$-0.735688\pi$
$859$	8.85048	−	15.3295i	0.301975	−	0.523035i	0.976583	+	0.215140i	$0.0690209\pi$
$860$			24.2539i			0.827050i
$861$	−9.61883	−	14.3405i	−0.327809	−	0.488724i
$862$			14.0822i			0.479643i
$863$	21.1654	−	36.6596i	0.720479	−	1.24791i	−0.240329	−	0.970691i	$-0.577255\pi$
$863$	21.1654	−	36.6596i	0.720479	−	1.24791i	0.960808	−	0.277215i	$-0.0894113\pi$
$864$	−4.48667	+	2.59038i	−0.152639	+	0.0881264i
$865$	−33.6037	−	58.2034i	−1.14256	−	1.97897i
$866$	−3.88406	+	6.72739i	−0.131986	+	0.228606i
$867$	−15.6408	+	6.66073i	−0.531189	+	0.226210i
$868$	−14.4494	−	7.09388i	−0.490446	−	0.240782i
$869$	11.0275			0.374083
$870$	15.6717	+	9.04808i	0.531322	+	0.306759i
$871$	−1.45604	−	2.52194i	−0.0493362	−	0.0854528i
$872$	16.0290	−	9.25438i	0.542812	−	0.313393i
$873$	−4.31427	−	2.49084i	−0.146016	−	0.0843022i
$874$		−	6.14582i		−	0.207886i
$875$	−3.92054	−	58.2351i	−0.132539	−	1.96870i
$876$	−18.9723			−0.641016
$877$	−12.4124	−	7.16629i	−0.419136	−	0.241988i	0.275571	−	0.961281i	$-0.411133\pi$
$877$	−12.4124	−	7.16629i	−0.419136	−	0.241988i	−0.694708	+	0.719292i	$0.744466\pi$
$878$	8.28562	−	4.78371i	0.279626	−	0.161442i
$879$	−1.11890	+	0.645998i	−0.0377396	+	0.0217890i
$880$	15.0532	−	26.0730i	0.507445	−	0.878920i
$881$		−	23.7723i		−	0.800910i	−0.916317	−	0.400455i	$-0.868852\pi$
$881$		−	23.7723i		−	0.800910i	0.916317	−	0.400455i	$-0.131148\pi$
$882$	−2.24640	−	2.90619i	−0.0756401	−	0.0978563i
$883$	52.7233			1.77428			0.887141	−	0.461499i	$-0.152688\pi$
$883$	52.7233			1.77428			0.887141	+	0.461499i	$0.152688\pi$
$884$	−2.79923	−	5.60618i	−0.0941484	−	0.188556i
$885$	25.2299	+	43.6994i	0.848093	+	1.46894i
$886$	−6.12928	−	10.6162i	−0.205917	−	0.356659i
$887$	−14.7128	−	8.49445i	−0.494008	−	0.285216i	0.232228	−	0.972661i	$-0.425399\pi$
$887$	−14.7128	−	8.49445i	−0.494008	−	0.285216i	−0.726236	+	0.687446i	$0.758732\pi$
$888$	−23.4007			−0.785276
$889$	−51.3030	+	3.45386i	−1.72065	+	0.115839i
$890$		−	2.30667i		−	0.0773199i
$891$	2.72471	+	1.57311i	0.0912811	+	0.0527012i
$892$	−5.94312	−	10.2938i	−0.198990	−	0.344662i
$893$	15.3649	+	26.6128i	0.514167	+	0.890564i
$894$	2.20864	+	1.27516i	0.0738679	+	0.0426477i
$895$		−	35.3842i		−	1.18276i
$896$	13.3838	−	27.2614i	0.447123	−	0.910739i
$897$	−2.92058			−0.0975154
$898$	−9.44288	−	5.45185i	−0.315113	−	0.181931i
$899$	−15.4069	−	26.6855i	−0.513848	−	0.890011i
$900$	9.12997	+	15.8136i	0.304332	+	0.527119i
$901$	−8.78861	−	17.6014i	−0.292791	−	0.586389i
$902$	10.7750			0.358769
$903$	7.82655	−	5.24961i	0.260451	−	0.174696i
$904$			12.0859i			0.401972i
$905$	−34.4450	+	59.6605i	−1.14499	+	1.98318i
$906$	−5.12307	+	2.95780i	−0.170202	+	0.0982664i
$907$	−19.0038	+	10.9719i	−0.631012	+	0.364315i	−0.781144	−	0.624351i	$-0.785363\pi$
$907$	−19.0038	+	10.9719i	−0.631012	+	0.364315i	0.150132	+	0.988666i	$0.452030\pi$
$908$	−5.41321	−	3.12532i	−0.179644	−	0.103717i
$909$	10.4416			0.346327
$910$	−4.01136	+	2.69059i	−0.132975	+	0.0891923i
$911$		−	12.2367i		−	0.405421i	−0.979239	−	0.202711i	$-0.935025\pi$
$911$		−	12.2367i		−	0.405421i	0.979239	−	0.202711i	$-0.0649751\pi$
$912$	−7.41747	−	4.28248i	−0.245617	−	0.141807i
$913$	27.7680	−	16.0319i	0.918986	−	0.530577i
$914$	−4.76471	−	8.25271i	−0.157602	−	0.272976i
$915$	26.8619	+	15.5087i	0.888027	+	0.512703i
$916$	−20.4228			−0.674787
$917$	13.6538	+	6.70327i	0.450889	+	0.221362i
$918$	−1.80486	−	1.19309i	−0.0595691	−	0.0393779i
$919$	12.4392	−	21.5454i	0.410332	−	0.710717i	−0.584594	−	0.811326i	$-0.698746\pi$
$919$	12.4392	−	21.5454i	0.410332	−	0.710717i	0.994926	+	0.100610i	$0.0320793\pi$
$920$	12.7874	+	22.1484i	0.421587	+	0.730210i
$921$	−23.6836	+	13.6737i	−0.780402	+	0.450565i
$922$	6.14071	−	10.6360i	0.202233	−	0.350279i
$923$		−	3.62010i		−	0.119157i
$924$	−14.3238	+	0.964314i	−0.471217	+	0.0317236i
$925$			126.765i			4.16800i
$926$	2.97209	−	5.14780i	0.0976688	−	0.169167i
$927$	−1.96640	−	3.40591i	−0.0645852	−	0.111865i
$928$	39.1901	−	22.6264i	1.28648	−	0.742749i
$929$	11.5459	+	6.66604i	0.378809	+	0.218706i	0.677300	−	0.735707i	$-0.263150\pi$
$929$	11.5459	+	6.66604i	0.378809	+	0.218706i	−0.298491	+	0.954412i	$0.596483\pi$
$930$			7.30845i			0.239653i
$931$	9.38532	−	22.8872i	0.307591	−	0.750097i
$932$		−	7.70033i		−	0.252233i
$933$	−0.878811	+	1.52215i	−0.0287710	+	0.0498328i
$934$	10.4542	+	18.1072i	0.342073	+	0.592487i
$935$	51.1221	+	3.09675i	1.67187	+	0.101274i
$936$	0.861145	−	1.49155i	0.0281474	−	0.0487527i
$937$	−1.81301			−0.0592285			−0.0296142	−	0.999561i	$-0.509428\pi$
$937$	−1.81301			−0.0592285			−0.0296142	+	0.999561i	$0.509428\pi$
$938$	4.57760	−	0.308177i	0.149464	−	0.0100623i
$939$	−6.66314			−0.217443
$940$	−51.2787	−	29.6058i	−1.67253	−	0.965634i
$941$	−15.7681	+	9.10373i	−0.514026	+	0.296773i	−0.734487	−	0.678623i	$-0.762577\pi$
$941$	−15.7681	+	9.10373i	−0.514026	+	0.296773i	0.220461	+	0.975396i	$0.429244\pi$
$942$	10.5439	−	6.08751i	0.343538	−	0.198342i
$943$	10.8155	−	18.7330i	0.352202	−	0.610031i
$944$	30.9767			1.00821
$945$	4.60343	−	9.37666i	0.149750	−	0.305023i
$946$			5.88062i			0.191195i
$947$	45.3198	+	26.1654i	1.47270	+	0.850262i	0.999528	−	0.0307102i	$-0.00977688\pi$
$947$	45.3198	+	26.1654i	1.47270	+	0.850262i	0.473168	+	0.880972i	$0.343110\pi$
$948$	3.02245	+	5.23504i	0.0981646	+	0.170026i
$949$	8.39514	−	4.84694i	0.272518	−	0.157338i
$950$	9.81650	−	17.0027i	0.318489	−	0.551640i
$951$	−8.86213			−0.287374
$952$	21.3203	−	0.143268i	0.690994	−	0.00464333i
$953$	14.5346			0.470823			0.235411	−	0.971896i	$-0.424356\pi$
$953$	14.5346			0.470823			0.235411	+	0.971896i	$0.424356\pi$
$954$	1.25191	−	2.16837i	0.0405320	−	0.0702036i
$955$	−7.23663	+	4.17807i	−0.234172	+	0.135199i
$956$	0.515478	+	0.892835i	0.0166718	+	0.0288763i
$957$	−23.7998	−	13.7408i	−0.769338	−	0.444177i
$958$			7.83733i			0.253213i
$959$	16.7637	+	24.9927i	0.541329	+	0.807058i
$960$	8.40505			0.271272
$961$	−9.27767	+	16.0694i	−0.299280	+	0.518367i
$962$	4.79459	−	2.76816i	0.154584	−	0.0892489i
$963$	−1.66112	+	0.959050i	−0.0535289	+	0.0309049i
$964$	3.06653	+	1.77046i	0.0987662	+	0.0570227i
$965$	−93.8769			−3.02201
$966$	2.02781	−	4.13042i	0.0652437	−	0.132894i
$967$	33.4397			1.07535			0.537673	−	0.843153i	$-0.319303\pi$
$967$	33.4397			1.07535			0.537673	+	0.843153i	$0.319303\pi$
$968$	−1.07622	+	1.86407i	−0.0345910	+	0.0599134i
$969$	0.880990	−	14.5437i	0.0283015	−	0.467210i
$970$	−5.16036	−	8.93800i	−0.165689	−	0.286982i
$971$	−9.35752	+	16.2077i	−0.300297	+	0.520130i	−0.976203	−	0.216858i	$-0.930419\pi$
$971$	−9.35752	+	16.2077i	−0.300297	+	0.520130i	0.675906	+	0.736988i	$0.263753\pi$
$972$			1.72465i			0.0553181i
$973$	0.287840	+	4.27552i	0.00922771	+	0.137067i
$974$		−	1.33850i		−	0.0428883i
$975$	−8.07991	−	4.66494i	−0.258764	−	0.149398i
$976$	16.4903	−	9.52066i	0.527840	−	0.304749i
$977$	5.92714	+	10.2661i	0.189626	+	0.328442i	0.945126	−	0.326707i	$-0.105939\pi$
$977$	5.92714	+	10.2661i	0.189626	+	0.328442i	−0.755499	+	0.655149i	$0.772606\pi$
$978$	0.769116	−	1.33215i	0.0245936	−	0.0425974i
$979$			3.50301i			0.111957i
$980$	6.38876	+	47.2337i	0.204081	+	1.50883i
$981$		−	9.46996i		−	0.302353i
$982$	2.21102	−	3.82959i	0.0705564	−	0.122207i
$983$	−14.8167	+	8.55441i	−0.472578	+	0.272843i	−0.717318	−	0.696745i	$-0.754631\pi$
$983$	−14.8167	+	8.55441i	−0.472578	+	0.272843i	0.244740	+	0.969589i	$0.421297\pi$
$984$	6.37799	+	11.0470i	0.203323	+	0.352166i
$985$	−40.1507	+	69.5431i	−1.27931	+	2.21583i
$986$	15.7651	+	10.4214i	0.502062	+	0.331885i
$987$	1.54541	+	22.9553i	0.0491910	+	0.730675i
$988$	5.37060			0.170861
$989$	10.2238	+	5.90272i	0.325098	+	0.187696i
$990$	3.25906	+	5.64486i	0.103580	+	0.179406i
$991$	18.6242	−	10.7527i	0.591616	−	0.341570i	−0.174120	−	0.984724i	$-0.555708\pi$
$991$	18.6242	−	10.7527i	0.591616	−	0.341570i	0.765736	+	0.643155i	$0.222375\pi$
$992$	15.8276	+	9.13808i	0.502527	+	0.290134i
$993$			13.1664i			0.417824i
$994$	5.11971	+	2.51350i	0.162387	+	0.0797233i
$995$	70.8740			2.24686
$996$	15.2214	+	8.78811i	0.482310	+	0.278462i
$997$	−14.2408	+	8.22193i	−0.451011	+	0.260391i	−0.708257	−	0.705955i	$-0.750518\pi$
$997$	−14.2408	+	8.22193i	−0.451011	+	0.260391i	0.257246	+	0.966346i	$0.417185\pi$
$998$	16.1054	−	9.29848i	0.509809	−	0.294338i
$999$	−5.98645	+	10.3688i	−0.189403	+	0.328056i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.p.a.16.15	✓	48
7.4	even	3	inner	357.2.p.a.67.16	yes	48
17.16	even	2	inner	357.2.p.a.16.16	yes	48
119.67	even	6	inner	357.2.p.a.67.15	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.p.a.16.15	✓	48	1.1	even	1	trivial
357.2.p.a.16.16	yes	48	17.16	even	2	inner
357.2.p.a.67.15	yes	48	119.67	even	6	inner
357.2.p.a.67.16	yes	48	7.4	even	3	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.262370 - 0.454438i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.862324 + 1.49359i) q^{4} +(3.41917 + 1.97406i) q^{5} +0.524739i q^{6} +(-2.63978 + 0.177717i) q^{7} +1.95447 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.262370 - 0.454438i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.862324 + 1.49359i) q^{4} +(3.41917 + 1.97406i) q^{5} +0.524739i q^{6} +(-2.63978 + 0.177717i) q^{7} +1.95447 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.79417 - 1.03587i) q^{10} +(-2.72471 + 1.57311i) q^{11} +(-1.49359 - 0.862324i) q^{12} +0.881206 q^{13} +(-0.611836 + 1.24624i) q^{14} -3.94812 q^{15} +(-1.21186 + 2.09899i) q^{16} +(-4.11556 - 0.249302i) q^{17} +(-0.262370 - 0.454438i) q^{18} +(1.76691 - 3.06038i) q^{19} +6.80911i q^{20} +(2.19725 - 1.47380i) q^{21} +1.65095i q^{22} +(2.87027 + 1.65715i) q^{23} +(-1.69262 + 0.977235i) q^{24} +(5.29381 + 9.16915i) q^{25} +(0.231202 - 0.400453i) q^{26} +1.00000i q^{27} +(-2.54178 - 3.78949i) q^{28} -8.73480i q^{29} +(-1.03587 + 1.79417i) q^{30} +(3.05508 - 1.76385i) q^{31} +(2.59038 + 4.48667i) q^{32} +(1.57311 - 2.72471i) q^{33} +(-1.19309 + 1.80486i) q^{34} +(-9.37666 - 4.60343i) q^{35} +1.72465 q^{36} +(10.3688 + 5.98645i) q^{37} +(-0.927167 - 1.60590i) q^{38} +(-0.763146 + 0.440603i) q^{39} +(6.68266 + 3.85824i) q^{40} -6.52657i q^{41} +(-0.0932550 - 1.38519i) q^{42} +3.56197 q^{43} +(-4.69916 - 2.71306i) q^{44} +(3.41917 - 1.97406i) q^{45} +(1.50614 - 0.869572i) q^{46} +(-4.34796 + 7.53089i) q^{47} -2.42371i q^{48} +(6.93683 - 0.938266i) q^{49} +5.55574 q^{50} +(3.68883 - 1.84188i) q^{51} +(0.759885 + 1.31616i) q^{52} +(2.38577 + 4.13228i) q^{53} +(0.454438 + 0.262370i) q^{54} -12.4216 q^{55} +(-5.15936 + 0.347342i) q^{56} +3.53382i q^{57} +(-3.96942 - 2.29175i) q^{58} +(-6.39036 - 11.0684i) q^{59} +(-3.40456 - 5.89687i) q^{60} +(-6.80373 - 3.92813i) q^{61} -1.85112i q^{62} +(-1.16598 + 2.37497i) q^{63} -2.12888 q^{64} +(3.01299 + 1.73955i) q^{65} +(-0.825473 - 1.42976i) q^{66} +(-1.65233 - 2.86192i) q^{67} +(-3.17659 - 6.36194i) q^{68} -3.31430 q^{69} +(-4.55212 + 3.05331i) q^{70} -4.10813i q^{71} +(0.977235 - 1.69262i) q^{72} +(9.52688 - 5.50035i) q^{73} +(5.44094 - 3.14133i) q^{74} +(-9.16915 - 5.29381i) q^{75} +6.09460 q^{76} +(6.91305 - 4.63689i) q^{77} +0.462403i q^{78} +(-3.03542 - 1.75250i) q^{79} +(-8.28708 + 4.78455i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.96592 - 1.71237i) q^{82} -10.1912 q^{83} +(4.09599 + 2.01091i) q^{84} +(-13.5797 - 8.97677i) q^{85} +(0.934553 - 1.61869i) q^{86} +(4.36740 + 7.56456i) q^{87} +(-5.32536 + 3.07460i) q^{88} +(0.556702 - 0.964235i) q^{89} -2.07173i q^{90} +(-2.32619 + 0.156605i) q^{91} +5.71601i q^{92} +(-1.76385 + 3.05508i) q^{93} +(2.28155 + 3.95175i) q^{94} +(12.0827 - 6.97597i) q^{95} +(-4.48667 - 2.59038i) q^{96} -4.98168i q^{97} +(1.39363 - 3.39853i) q^{98} +3.14622i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{4} + 24 q^{9}+O(q^{10}) \) 48 * q - 24 * q^4 + 24 * q^9	\( 48 q - 24 q^{4} + 24 q^{9} + 16 q^{13} - 40 q^{16} + 8 q^{17} + 16 q^{19} + 36 q^{25} - 52 q^{26} + 24 q^{30} + 20 q^{32} - 8 q^{33} - 32 q^{34} - 36 q^{35} - 48 q^{36} + 40 q^{38} + 4 q^{42} + 40 q^{43} - 80 q^{50} - 12 q^{52} - 60 q^{53} - 24 q^{59} + 112 q^{64} + 4 q^{66} - 4 q^{67} + 88 q^{68} + 64 q^{69} - 24 q^{70} - 184 q^{76} - 72 q^{77} - 24 q^{81} - 88 q^{83} - 20 q^{84} + 16 q^{85} + 60 q^{86} + 36 q^{87} + 12 q^{89} - 24 q^{93} - 32 q^{94} + 48 q^{98}+O(q^{100}) \) 48 * q - 24 * q^4 + 24 * q^9 + 16 * q^13 - 40 * q^16 + 8 * q^17 + 16 * q^19 + 36 * q^25 - 52 * q^26 + 24 * q^30 + 20 * q^32 - 8 * q^33 - 32 * q^34 - 36 * q^35 - 48 * q^36 + 40 * q^38 + 4 * q^42 + 40 * q^43 - 80 * q^50 - 12 * q^52 - 60 * q^53 - 24 * q^59 + 112 * q^64 + 4 * q^66 - 4 * q^67 + 88 * q^68 + 64 * q^69 - 24 * q^70 - 184 * q^76 - 72 * q^77 - 24 * q^81 - 88 * q^83 - 20 * q^84 + 16 * q^85 + 60 * q^86 + 36 * q^87 + 12 * q^89 - 24 * q^93 - 32 * q^94 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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