LMFDB - Embedded newform 585.2.bt.b.571.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			571.8
Character	$\chi$	$=$	585.571
Dual form			585.2.bt.b.376.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.85413 + 1.07048i) q^{2} +(-1.70628 - 0.297682i) q^{3} +(1.29187 - 2.23759i) q^{4} +(0.866025 + 0.500000i) q^{5} +(3.48233 - 1.27460i) q^{6} +(-4.18669 + 2.41719i) q^{7} +1.24978i q^{8} +(2.82277 + 1.01586i) q^{9} +O(q^{10})$	\(q+(-1.85413 + 1.07048i) q^{2} +(-1.70628 - 0.297682i) q^{3} +(1.29187 - 2.23759i) q^{4} +(0.866025 + 0.500000i) q^{5} +(3.48233 - 1.27460i) q^{6} +(-4.18669 + 2.41719i) q^{7} +1.24978i q^{8} +(2.82277 + 1.01586i) q^{9} -2.14097 q^{10} +(-0.777530 + 0.448907i) q^{11} +(-2.87039 + 3.43338i) q^{12} +(3.48463 + 0.925930i) q^{13} +(5.17513 - 8.96358i) q^{14} +(-1.32884 - 1.11094i) q^{15} +(1.24587 + 2.15792i) q^{16} -5.40665 q^{17} +(-6.32125 + 1.13820i) q^{18} +6.78820i q^{19} +(2.23759 - 1.29187i) q^{20} +(7.86322 - 2.87809i) q^{21} +(0.961096 - 1.66467i) q^{22} +(0.544448 - 0.943012i) q^{23} +(0.372038 - 2.13248i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-7.45216 + 2.01345i) q^{26} +(-4.51403 - 2.57362i) q^{27} +12.4908i q^{28} +(-1.28370 - 2.22344i) q^{29} +(3.65309 + 0.637329i) q^{30} +(-4.42594 - 2.55532i) q^{31} +(-6.78472 - 3.91716i) q^{32} +(1.46031 - 0.534504i) q^{33} +(10.0246 - 5.78773i) q^{34} -4.83438 q^{35} +(5.91974 - 5.00384i) q^{36} -2.86635i q^{37} +(-7.26667 - 12.5862i) q^{38} +(-5.67012 - 2.61721i) q^{39} +(-0.624892 + 1.08234i) q^{40} +(-3.50683 - 2.02467i) q^{41} +(-11.4985 + 13.7538i) q^{42} +(2.08636 + 3.61369i) q^{43} +2.31972i q^{44} +(1.93666 + 2.29114i) q^{45} +2.33129i q^{46} +(6.64992 - 3.83933i) q^{47} +(-1.48343 - 4.05288i) q^{48} +(8.18560 - 14.1779i) q^{49} +(-1.85413 - 1.07048i) q^{50} +(9.22525 + 1.60946i) q^{51} +(6.57355 - 6.60099i) q^{52} +6.85899 q^{53} +(11.1246 - 0.0603536i) q^{54} -0.897814 q^{55} +(-3.02096 - 5.23246i) q^{56} +(2.02073 - 11.5826i) q^{57} +(4.76031 + 2.74837i) q^{58} +(-13.0778 - 7.55048i) q^{59} +(-4.20252 + 1.53820i) q^{60} +(-3.04265 - 5.27002i) q^{61} +10.9417 q^{62} +(-14.2736 + 2.57008i) q^{63} +11.7895 q^{64} +(2.55481 + 2.54419i) q^{65} +(-2.13544 + 2.55428i) q^{66} +(5.26815 + 3.04157i) q^{67} +(-6.98471 + 12.0979i) q^{68} +(-1.20970 + 1.44697i) q^{69} +(8.96358 - 5.17513i) q^{70} -13.3088i q^{71} +(-1.26960 + 3.52785i) q^{72} -11.8477i q^{73} +(3.06838 + 5.31459i) q^{74} +(-0.595339 - 1.62652i) q^{75} +(15.1892 + 8.76950i) q^{76} +(2.17019 - 3.75887i) q^{77} +(13.3148 - 1.21712i) q^{78} +(-1.01631 - 1.76030i) q^{79} +2.49175i q^{80} +(6.93607 + 5.73507i) q^{81} +8.66951 q^{82} +(-1.21390 + 0.700846i) q^{83} +(3.71829 - 21.3128i) q^{84} +(-4.68230 - 2.70333i) q^{85} +(-7.73679 - 4.46684i) q^{86} +(1.52848 + 4.17594i) q^{87} +(-0.561037 - 0.971744i) q^{88} -3.44366i q^{89} +(-6.04346 - 2.17492i) q^{90} +(-16.8272 + 4.54643i) q^{91} +(-1.40672 - 2.43650i) q^{92} +(6.79122 + 5.67761i) q^{93} +(-8.21989 + 14.2373i) q^{94} +(-3.39410 + 5.87876i) q^{95} +(10.4105 + 8.70345i) q^{96} +(-15.9996 + 9.23740i) q^{97} +35.0502i q^{98} +(-2.65081 + 0.477302i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

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 $

$2$	−1.85413	+	1.07048i	−1.31107	+	0.756947i	−0.982273	−	0.187454i	$-0.939976\pi$
$2$	−1.85413	+	1.07048i	−1.31107	+	0.756947i	−0.328797	+	0.944401i	$0.606643\pi$
$3$	−1.70628	−	0.297682i	−0.985120	−	0.171867i
$3$	−1.70628	−	0.297682i	−0.985120	−	0.171867i
$4$	1.29187	−	2.23759i	0.645937	−	1.11880i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	3.48233	−	1.27460i	1.42166	−	0.520354i
$7$	−4.18669	+	2.41719i	−1.58242	+	0.913612i	−0.587917	+	0.808921i	$0.700052\pi$
$7$	−4.18669	+	2.41719i	−1.58242	+	0.913612i	−0.994505	+	0.104690i	$0.966615\pi$
$8$			1.24978i			0.441865i
$9$	2.82277	+	1.01586i	0.940923	+	0.338619i
$10$	−2.14097			−0.677034
$11$	−0.777530	+	0.448907i	−0.234434	+	0.135351i	−0.612616	−	0.790381i	$-0.709883\pi$
$11$	−0.777530	+	0.448907i	−0.234434	+	0.135351i	0.378182	+	0.925731i	$0.376549\pi$
$12$	−2.87039	+	3.43338i	−0.828609	+	0.991132i
$13$	3.48463	+	0.925930i	0.966463	+	0.256807i
$13$	3.48463	+	0.925930i	0.966463	+	0.256807i
$14$	5.17513	−	8.96358i	1.38311	−	2.39562i
$15$	−1.32884	−	1.11094i	−0.343105	−	0.286843i
$16$	1.24587	+	2.15792i	0.311468	+	0.539479i
$17$	−5.40665			−1.31131			−0.655653	−	0.755063i	$-0.727606\pi$
$17$	−5.40665			−1.31131			−0.655653	+	0.755063i	$0.727606\pi$
$18$	−6.32125	+	1.13820i	−1.48993	+	0.268275i
$19$			6.78820i			1.55732i	0.627446	+	0.778660i	$0.284100\pi$
$19$			6.78820i			1.55732i	−0.627446	+	0.778660i	$0.715900\pi$
$20$	2.23759	−	1.29187i	0.500340	−	0.288872i
$21$	7.86322	−	2.87809i	1.71590	−	0.628051i
$22$	0.961096	−	1.66467i	0.204906	−	0.354908i
$23$	0.544448	−	0.943012i	0.113525	−	0.196632i	−0.803664	−	0.595083i	$-0.797119\pi$
$23$	0.544448	−	0.943012i	0.113525	−	0.196632i	0.917189	+	0.398452i	$0.130452\pi$
$24$	0.372038	−	2.13248i	0.0759420	−	0.435290i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−7.45216	+	2.01345i	−1.46149	+	0.394869i
$27$	−4.51403	−	2.57362i	−0.868725	−	0.495294i
$28$			12.4908i			2.36054i
$29$	−1.28370	−	2.22344i	−0.238378	−	0.412882i	0.721871	−	0.692027i	$-0.243282\pi$
$29$	−1.28370	−	2.22344i	−0.238378	−	0.412882i	−0.960249	+	0.279145i	$0.909949\pi$
$30$	3.65309	+	0.637329i	0.666960	+	0.116360i
$31$	−4.42594	−	2.55532i	−0.794923	−	0.458949i	0.0467698	−	0.998906i	$-0.485107\pi$
$31$	−4.42594	−	2.55532i	−0.794923	−	0.458949i	−0.841693	+	0.539957i	$0.818441\pi$
$32$	−6.78472	−	3.91716i	−1.19938	−	0.692462i
$33$	1.46031	−	0.534504i	0.254208	−	0.0930451i
$34$	10.0246	−	5.78773i	1.71921	−	0.992588i
$35$	−4.83438			−0.817159
$36$	5.91974	−	5.00384i	0.986623	−	0.833974i
$37$		−	2.86635i		−	0.471224i	−0.971847	−	0.235612i	$-0.924290\pi$
$37$		−	2.86635i		−	0.471224i	0.971847	−	0.235612i	$-0.0757095\pi$
$38$	−7.26667	−	12.5862i	−1.17881	−	2.04176i
$39$	−5.67012	−	2.61721i	−0.907945	−	0.419089i
$40$	−0.624892	+	1.08234i	−0.0988041	+	0.171134i
$41$	−3.50683	−	2.02467i	−0.547675	−	0.316200i	0.200509	−	0.979692i	$-0.435741\pi$
$41$	−3.50683	−	2.02467i	−0.547675	−	0.316200i	−0.748184	+	0.663492i	$0.769074\pi$
$42$	−11.4985	+	13.7538i	−1.77426	+	2.12226i
$43$	2.08636	+	3.61369i	0.318167	+	0.551082i	0.980106	−	0.198476i	$-0.0635993\pi$
$43$	2.08636	+	3.61369i	0.318167	+	0.551082i	−0.661938	+	0.749558i	$0.730266\pi$
$44$			2.31972i			0.349712i
$45$	1.93666	+	2.29114i	0.288701	+	0.341544i
$46$			2.33129i			0.343731i
$47$	6.64992	−	3.83933i	0.969991	−	0.560024i	0.0707572	−	0.997494i	$-0.477458\pi$
$47$	6.64992	−	3.83933i	0.969991	−	0.560024i	0.899233	+	0.437469i	$0.144125\pi$
$48$	−1.48343	−	4.05288i	−0.214115	−	0.584983i
$49$	8.18560	−	14.1779i	1.16937	−	2.02541i
$50$	−1.85413	−	1.07048i	−0.262214	−	0.151389i
$51$	9.22525	+	1.60946i	1.29179	+	0.225370i
$52$	6.57355	−	6.60099i	0.911588	−	0.915393i
$53$	6.85899			0.942155			0.471077	−	0.882092i	$-0.343865\pi$
$53$	6.85899			0.942155			0.471077	+	0.882092i	$0.343865\pi$
$54$	11.1246	−	0.0603536i	1.51387	−	0.00821308i
$55$	−0.897814			−0.121061
$56$	−3.02096	−	5.23246i	−0.403693	−	0.699217i
$57$	2.02073	−	11.5826i	0.267652	−	1.53415i
$58$	4.76031	+	2.74837i	0.625059	+	0.360878i
$59$	−13.0778	−	7.55048i	−1.70259	−	0.982989i	−0.943125	−	0.332438i	$-0.892129\pi$
$59$	−13.0778	−	7.55048i	−1.70259	−	0.982989i	−0.759462	−	0.650552i	$-0.774538\pi$
$60$	−4.20252	+	1.53820i	−0.542543	+	0.198581i
$61$	−3.04265	−	5.27002i	−0.389571	−	0.674757i	0.602821	−	0.797877i	$-0.294043\pi$
$61$	−3.04265	−	5.27002i	−0.389571	−	0.674757i	−0.992392	+	0.123120i	$0.960710\pi$
$62$	10.9417			1.38960
$63$	−14.2736	+	2.57008i	−1.79830	+	0.323800i
$64$	11.7895			1.47369
$65$	2.55481	+	2.54419i	0.316886	+	0.315568i
$66$	−2.13544	+	2.55428i	−0.262854	+	0.314411i
$67$	5.26815	+	3.04157i	0.643607	+	0.371587i	0.786003	−	0.618223i	$-0.212147\pi$
$67$	5.26815	+	3.04157i	0.643607	+	0.371587i	−0.142395	+	0.989810i	$0.545480\pi$
$68$	−6.98471	+	12.0979i	−0.847020	+	1.46708i
$69$	−1.20970	+	1.44697i	−0.145631	+	0.174195i
$70$	8.96358	−	5.17513i	1.07135	−	0.618546i
$71$		−	13.3088i		−	1.57946i	−0.613456	−	0.789729i	$-0.710221\pi$
$71$		−	13.3088i		−	1.57946i	0.613456	−	0.789729i	$-0.289779\pi$
$72$	−1.26960	+	3.52785i	−0.149624	+	0.415761i
$73$		−	11.8477i		−	1.38666i	−0.720618	−	0.693332i	$-0.756142\pi$
$73$		−	11.8477i		−	1.38666i	0.720618	−	0.693332i	$-0.243858\pi$
$74$	3.06838	+	5.31459i	0.356692	+	0.617808i
$75$	−0.595339	−	1.62652i	−0.0687438	−	0.187815i
$76$	15.1892	+	8.76950i	1.74232	+	1.00593i
$77$	2.17019	−	3.75887i	0.247316	−	0.428363i
$78$	13.3148	−	1.21712i	1.50761	−	0.137812i
$79$	−1.01631	−	1.76030i	−0.114344	−	0.198049i	0.803174	−	0.595745i	$-0.203143\pi$
$79$	−1.01631	−	1.76030i	−0.114344	−	0.198049i	−0.917517	+	0.397696i	$0.869810\pi$
$80$			2.49175i			0.278586i
$81$	6.93607	+	5.73507i	0.770674	+	0.637230i
$82$	8.66951			0.957387
$83$	−1.21390	+	0.700846i	−0.133243	+	0.0769279i	−0.565140	−	0.824995i	$-0.691178\pi$
$83$	−1.21390	+	0.700846i	−0.133243	+	0.0769279i	0.431897	+	0.901923i	$0.357844\pi$
$84$	3.71829	−	21.3128i	0.405699	−	2.32542i
$85$	−4.68230	−	2.70333i	−0.507866	−	0.293217i
$86$	−7.73679	−	4.46684i	−0.834279	−	0.481671i
$87$	1.52848	+	4.17594i	0.163870	+	0.447708i
$88$	−0.561037	−	0.971744i	−0.0598067	−	0.103588i
$89$		−	3.44366i		−	0.365028i	−0.983203	−	0.182514i	$-0.941577\pi$
$89$		−	3.44366i		−	0.365028i	0.983203	−	0.182514i	$-0.0584234\pi$
$90$	−6.04346	−	2.17492i	−0.637037	−	0.229257i
$91$	−16.8272	+	4.54643i	−1.76397	+	0.476595i
$92$	−1.40672	−	2.43650i	−0.146660	−	0.254023i
$93$	6.79122	+	5.67761i	0.704216	+	0.588741i
$94$	−8.21989	+	14.2373i	−0.847817	+	1.46846i
$95$	−3.39410	+	5.87876i	−0.348227	+	0.603148i
$96$	10.4105	+	8.70345i	1.06252	+	0.888292i
$97$	−15.9996	+	9.23740i	−1.62452	+	0.937916i	−0.638828	+	0.769350i	$0.720580\pi$
$97$	−15.9996	+	9.23740i	−1.62452	+	0.937916i	−0.985690	+	0.168566i	$0.946086\pi$
$98$			35.0502i			3.54061i
$99$	−2.65081	+	0.477302i	−0.266417	+	0.0479706i
$100$	2.58375			0.258375
$101$	2.91486	+	5.04868i	0.290039	+	0.502363i	0.973819	−	0.227326i	$-0.0729983\pi$
$101$	2.91486	+	5.04868i	0.290039	+	0.502363i	−0.683779	+	0.729689i	$0.739665\pi$
$102$	−18.8277	+	6.89132i	−1.86422	+	0.682343i
$103$	−0.990415	+	1.71545i	−0.0975885	+	0.169028i	−0.910686	−	0.413099i	$-0.864446\pi$
$103$	−0.990415	+	1.71545i	−0.0975885	+	0.169028i	0.813098	+	0.582128i	$0.197780\pi$
$104$	−1.15721	+	4.35503i	−0.113474	+	0.427046i
$105$	8.24879	+	1.43911i	0.805000	+	0.140443i
$106$	−12.7175	+	7.34244i	−1.23523	+	0.713161i
$107$	−12.4750			−1.20600			−0.603001	−	0.797740i	$-0.706028\pi$
$107$	−12.4750			−1.20600			−0.603001	+	0.797740i	$0.706028\pi$
$108$	−11.5903	+	6.77575i	−1.11527	+	0.651997i
$109$		−	2.37143i		−	0.227141i	−0.993530	−	0.113571i	$-0.963771\pi$
$109$		−	2.37143i		−	0.227141i	0.993530	−	0.113571i	$-0.0362288\pi$
$110$	1.66467	−	0.961096i	0.158720	−	0.0916369i
$111$	−0.853261	+	4.89078i	−0.0809879	+	0.464213i
$112$	−10.4322	−	6.02302i	−0.985748	−	0.569122i
$113$	2.67560	−	4.63428i	0.251700	−	0.435957i	−0.712294	−	0.701881i	$-0.752344\pi$
$113$	2.67560	−	4.63428i	0.251700	−	0.435957i	0.963994	+	0.265924i	$0.0856772\pi$
$114$	8.65225	+	23.6388i	0.810358	+	2.21397i
$115$	0.943012	−	0.544448i	0.0879363	−	0.0507701i
$116$	−6.63352			−0.615907
$117$	8.89570	+	6.15358i	0.822408	+	0.568898i
$118$	32.3307			2.97628
$119$	22.6360	−	13.0689i	2.07504	−	1.19802i
$120$	1.38843	−	1.66076i	0.126746	−	0.151606i
$121$	−5.09696	+	8.82820i	−0.463360	+	0.802564i
$122$	11.2830	+	6.51422i	1.02151	+	0.589769i
$123$	5.38092	+	4.49857i	0.485181	+	0.405623i
$124$	−11.4355	+	6.60230i	−1.02694	+	0.592904i
$125$			1.00000i			0.0894427i
$126$	23.7139	−	20.0449i	2.11260	−	1.78575i
$127$	−8.84295			−0.784685			−0.392342	−	0.919819i	$-0.628335\pi$
$127$	−8.84295			−0.784685			−0.392342	+	0.919819i	$0.628335\pi$
$128$	−8.28993	+	4.78620i	−0.732734	+	0.423044i
$129$	−2.48418	−	6.78703i	−0.218720	−	0.597564i
$130$	−7.46049	−	1.98239i	−0.654328	−	0.173867i
$131$	−2.06627	+	3.57888i	−0.180531	+	0.312688i	−0.942061	−	0.335441i	$-0.891115\pi$
$131$	−2.06627	+	3.57888i	−0.180531	+	0.312688i	0.761531	+	0.648129i	$0.224448\pi$
$132$	0.690541	−	3.95810i	0.0601039	−	0.344508i
$133$	−16.4084	−	28.4201i	−1.42279	−	2.46434i
$134$	−13.0238			−1.12509
$135$	−2.62245	−	4.48584i	−0.225705	−	0.386080i
$136$		−	6.75714i		−	0.579420i
$137$	2.10209	−	1.21364i	0.179594	−	0.103689i	−0.407508	−	0.913202i	$-0.633602\pi$
$137$	2.10209	−	1.21364i	0.179594	−	0.103689i	0.587102	+	0.809513i	$0.300269\pi$
$138$	0.693985	−	3.97784i	0.0590759	−	0.338616i
$139$	−3.49052	+	6.04575i	−0.296062	+	0.512794i	−0.975231	−	0.221187i	$-0.929007\pi$
$139$	−3.49052	+	6.04575i	−0.296062	+	0.512794i	0.679170	+	0.733981i	$0.262340\pi$
$140$	−6.24540	+	10.8174i	−0.527833	+	0.914234i
$141$	−12.4895	+	4.57141i	−1.05181	+	0.384982i
$142$	14.2468	+	24.6762i	1.19557	+	2.07078i
$143$	−3.12506	+	0.844338i	−0.261331	+	0.0706071i
$144$	1.32468	+	7.35693i	0.110390	+	0.613077i
$145$		−	2.56740i		−	0.213211i
$146$	12.6827	+	21.9671i	1.04963	+	1.81801i
$147$	−18.1874	+	21.7547i	−1.50007	+	1.79430i
$148$	−6.41371	−	3.70296i	−0.527204	−	0.304381i
$149$	−1.48831	−	0.859277i	−0.121927	−	0.0703947i	0.437796	−	0.899074i	$-0.355759\pi$
$149$	−1.48831	−	0.859277i	−0.121927	−	0.0703947i	−0.559723	+	0.828680i	$0.689093\pi$
$150$	2.84500	+	2.37849i	0.232294	+	0.194203i
$151$	−7.65117	+	4.41740i	−0.622643	+	0.359483i	−0.777897	−	0.628391i	$-0.783714\pi$
$151$	−7.65117	+	4.41740i	−0.622643	+	0.359483i	0.155254	+	0.987875i	$0.450380\pi$
$152$	−8.48378			−0.688126
$153$	−15.2617	−	5.49239i	−1.23384	−	0.444033i
$154$			9.29260i			0.748819i
$155$	−2.55532	−	4.42594i	−0.205248	−	0.355500i
$156$	−13.1813	+	9.30630i	−1.05535	+	0.745100i
$157$	7.46860	−	12.9360i	0.596060	−	1.03241i	−0.397337	−	0.917673i	$-0.630066\pi$
$157$	7.46860	−	12.9360i	0.596060	−	1.03241i	0.993396	−	0.114733i	$-0.0366011\pi$
$158$	3.76874	+	2.17588i	0.299825	+	0.173104i
$159$	−11.7033	−	2.04180i	−0.928136	−	0.161925i
$160$	−3.91716	−	6.78472i	−0.309679	−	0.536379i
$161$			5.26414i			0.414872i
$162$	−18.9997	−	3.20863i	−1.49276	−	0.252094i
$163$		−	14.8005i		−	1.15927i	−0.814877	−	0.579634i	$-0.803196\pi$
$163$		−	14.8005i		−	1.15927i	0.814877	−	0.579634i	$-0.196804\pi$
$164$	−9.06076	+	5.23123i	−0.707527	+	0.408491i
$165$	1.53192	+	0.267263i	0.119260	+	0.0208064i
$166$	1.50049	−	2.59892i	0.116461	−	0.201716i
$167$	9.92278	+	5.72892i	0.767848	+	0.443317i	0.832106	−	0.554616i	$-0.187135\pi$
$167$	9.92278	+	5.72892i	0.767848	+	0.443317i	−0.0642587	+	0.997933i	$0.520468\pi$
$168$	3.59699	+	9.82732i	0.277514	+	0.758194i
$169$	11.2853	+	6.45305i	0.868101	+	0.496388i
$170$	11.5755			0.887798
$171$	−6.89585	+	19.1615i	−0.527339	+	1.46532i
$172$	10.7813			0.822064
$173$	−0.532863	−	0.922946i	−0.0405128	−	0.0701703i	0.845058	−	0.534675i	$-0.179566\pi$
$173$	−0.532863	−	0.922946i	−0.0405128	−	0.0701703i	−0.885571	+	0.464504i	$0.846233\pi$
$174$	−7.30427	−	6.10654i	−0.553735	−	0.462935i
$175$	−4.18669	−	2.41719i	−0.316484	−	0.182722i
$176$	−1.93741	−	1.11856i	−0.146038	−	0.0843148i
$177$	20.0668	+	16.7763i	1.50831	+	1.26098i
$178$	3.68639	+	6.38501i	0.276306	+	0.478577i
$179$	−14.1315			−1.05623			−0.528117	−	0.849171i	$-0.677102\pi$
$179$	−14.1315			−1.05623			−0.528117	+	0.849171i	$0.677102\pi$
$180$	7.62856	−	1.37359i	0.568600	−	0.102381i
$181$	−7.24067			−0.538195			−0.269098	−	0.963113i	$-0.586725\pi$
$181$	−7.24067			−0.538195			−0.269098	+	0.963113i	$0.586725\pi$
$182$	26.3331	−	26.4430i	1.95194	−	1.96008i
$183$	3.62281	+	9.89787i	0.267806	+	0.731671i
$184$	1.17856	+	0.680443i	0.0868847	+	0.0501629i
$185$	1.43317	−	2.48233i	0.105369	−	0.182504i
$186$	−18.6696	−	3.25716i	−1.36892	−	0.238826i
$187$	4.20383	−	2.42708i	0.307415	−	0.177486i
$188$		−	19.8397i		−	1.44696i
$189$	25.1198	−	0.136280i	1.82720	−	0.00991294i
$190$		−	14.5333i		−	1.05436i
$191$	7.58943	+	13.1453i	0.549152	+	0.951159i	0.998333	+	0.0577183i	$0.0183825\pi$
$191$	7.58943	+	13.1453i	0.549152	+	0.951159i	−0.449181	+	0.893441i	$0.648284\pi$
$192$	−20.1162	−	3.50954i	−1.45176	−	0.253279i
$193$	−0.912999	−	0.527120i	−0.0657191	−	0.0379429i	0.466780	−	0.884373i	$-0.345414\pi$
$193$	−0.912999	−	0.527120i	−0.0657191	−	0.0379429i	−0.532500	+	0.846430i	$0.678747\pi$
$194$	19.7770	−	34.2547i	1.41990	−	2.45935i
$195$	−3.60186	−	5.10163i	−0.257935	−	0.365335i
$196$	−21.1495	−	36.6321i	−1.51068	−	2.61658i
$197$			26.7149i			1.90336i	0.307090	+	0.951681i	$0.400645\pi$
$197$			26.7149i			1.90336i	−0.307090	+	0.951681i	$0.599355\pi$
$198$	4.40402	−	3.72264i	0.312980	−	0.264556i
$199$	22.6640			1.60661			0.803305	−	0.595567i	$-0.203073\pi$
$199$	22.6640			1.60661			0.803305	+	0.595567i	$0.203073\pi$
$200$	−1.08234	+	0.624892i	−0.0765333	+	0.0441865i
$201$	−8.08351	−	6.75800i	−0.570167	−	0.476673i
$202$	−10.8091	−	6.24062i	−0.760524	−	0.439089i
$203$	10.7489	+	6.20590i	0.754427	+	0.435569i
$204$	15.5192	−	18.5631i	1.08656	−	1.29968i
$205$	−2.02467	−	3.50683i	−0.141409	−	0.244928i
$206$		−	4.24089i		−	0.295477i
$207$	2.49482	−	2.10882i	0.173402	−	0.146573i
$208$	2.34333	+	8.67313i	0.162481	+	0.601373i
$209$	−3.04727	−	5.27803i	−0.210784	−	0.365089i
$210$	−16.8349	+	6.16190i	−1.16172	+	0.425212i
$211$	13.5355	−	23.4442i	0.931822	−	1.61396i	0.151617	−	0.988439i	$-0.451552\pi$
$211$	13.5355	−	23.4442i	0.931822	−	1.61396i	0.780205	−	0.625524i	$-0.215115\pi$
$212$	8.86095	−	15.3476i	0.608572	−	1.05408i
$213$	−3.96178	+	22.7084i	−0.271457	+	1.55596i
$214$	23.1303	−	13.3543i	1.58115	−	0.912879i
$215$			4.17273i			0.284578i
$216$	3.21647	−	5.64156i	0.218853	−	0.383859i
$217$	24.7068			1.67720
$218$	2.53857	+	4.39694i	0.171934	+	0.297798i
$219$	−3.52684	+	20.2154i	−0.238322	+	1.36603i
$220$	−1.15986	+	2.00894i	−0.0781979	+	0.135443i
$221$	−18.8402	−	5.00618i	−1.26733	−	0.336752i
$222$	−3.65345	−	9.98157i	−0.245203	−	0.669919i
$223$	−6.74105	+	3.89195i	−0.451414	+	0.260624i	−0.708427	−	0.705784i	$-0.750595\pi$
$223$	−6.74105	+	3.89195i	−0.451414	+	0.260624i	0.257013	+	0.966408i	$0.417262\pi$
$224$	37.8741			2.53057
$225$	0.531627	+	2.95252i	0.0354418	+	0.196835i
$226$			11.4568i			0.762093i
$227$	20.8614	−	12.0443i	1.38462	−	0.799410i	0.391917	−	0.920001i	$-0.371812\pi$
$227$	20.8614	−	12.0443i	1.38462	−	0.799410i	0.992702	+	0.120591i	$0.0384788\pi$
$228$	−23.3065	−	19.4848i	−1.54351	−	1.29041i
$229$	2.42948	+	1.40266i	0.160545	+	0.0926906i	0.578120	−	0.815952i	$-0.303787\pi$
$229$	2.42948	+	1.40266i	0.160545	+	0.0926906i	−0.417575	+	0.908642i	$0.637120\pi$
$230$	−1.16565	+	2.01896i	−0.0768605	+	0.133126i
$231$	−4.82189	+	5.76766i	−0.317257	+	0.379484i
$232$	2.77882	−	1.60435i	0.182438	−	0.105331i
$233$	−8.14156			−0.533371			−0.266686	−	0.963784i	$-0.585929\pi$
$233$	−8.14156			−0.533371			−0.266686	+	0.963784i	$0.585929\pi$
$234$	−23.0811	−	1.88684i	−1.50886	−	0.123347i
$235$	7.67867			0.500901
$236$	−33.7898	+	19.5085i	−2.19953	+	1.26990i
$237$	1.21009	+	3.30609i	0.0786041	+	0.214754i
$238$	−27.9801	+	48.4629i	−1.81368	+	3.14139i
$239$	−15.8962	−	9.17768i	−1.02824	−	0.593655i	−0.111760	−	0.993735i	$-0.535649\pi$
$239$	−15.8962	−	9.17768i	−1.02824	−	0.593655i	−0.916480	+	0.400081i	$0.868982\pi$
$240$	0.741749	−	4.25161i	0.0478797	−	0.274440i
$241$	2.21794	−	1.28053i	0.142870	−	0.0824863i	−0.426861	−	0.904317i	$-0.640381\pi$
$241$	2.21794	−	1.28053i	0.142870	−	0.0824863i	0.569731	+	0.821831i	$0.307047\pi$
$242$		−	21.8249i		−	1.40296i
$243$	−10.1276	−	11.8504i	−0.649688	−	0.760201i
$244$	−15.7229			−1.00655
$245$	14.1779	−	8.18560i	0.905792	−	0.522959i
$246$	−14.7926	−	2.58076i	−0.943141	−	0.164543i
$247$	−6.28540	+	23.6544i	−0.399930	+	1.50509i
$248$	3.19360	−	5.53147i	0.202794	−	0.351249i
$249$	2.27988	−	0.834482i	0.144482	−	0.0528831i
$250$	−1.07048	−	1.85413i	−0.0677034	−	0.117266i
$251$	7.25941			0.458210			0.229105	−	0.973402i	$-0.426420\pi$
$251$	7.25941			0.458210			0.229105	+	0.973402i	$0.426420\pi$
$252$	−12.6889	+	35.2587i	−0.799325	+	2.22109i
$253$			0.977627i			0.0614629i
$254$	16.3960	−	9.46624i	1.02878	−	0.593965i
$255$	7.18457	+	6.00646i	0.449915	+	0.376139i
$256$	−1.54244	+	2.67159i	−0.0964025	+	0.166974i
$257$	−4.69146	+	8.12585i	−0.292645	+	0.506876i	−0.974434	−	0.224672i	$-0.927869\pi$
$257$	−4.69146	+	8.12585i	−0.292645	+	0.506876i	0.681789	+	0.731549i	$0.261202\pi$
$258$	11.8714	+	9.92477i	0.739082	+	0.617889i
$259$	6.92850	+	12.0005i	0.430516	+	0.745676i
$260$	8.99336	−	2.42985i	0.557745	−	0.150693i
$261$	−1.36490	−	7.58031i	−0.0844852	−	0.469210i
$262$		−	8.84762i		−	0.546608i
$263$	−6.05462	−	10.4869i	−0.373344	−	0.646650i	0.616734	−	0.787172i	$-0.288455\pi$
$263$	−6.05462	−	10.4869i	−0.373344	−	0.646650i	−0.990078	+	0.140521i	$0.955122\pi$
$264$	0.668014	+	1.82508i	0.0411134	+	0.112326i
$265$	5.94006	+	3.42950i	0.364895	+	0.210672i
$266$	60.8466	+	35.1298i	3.73074	+	2.15395i
$267$	−1.02512	+	5.87585i	−0.0627362	+	0.359596i
$268$	13.6116	−	7.85865i	0.831459	−	0.480043i
$269$	−23.8192			−1.45228			−0.726141	−	0.687546i	$-0.758688\pi$
$269$	−23.8192			−1.45228			−0.726141	+	0.687546i	$0.758688\pi$
$270$	9.66439	+	5.51005i	0.588156	+	0.335331i
$271$		−	17.6076i		−	1.06958i	−0.844984	−	0.534792i	$-0.820390\pi$
$271$		−	17.6076i		−	1.06958i	0.844984	−	0.534792i	$-0.179610\pi$
$272$	−6.73600	−	11.6671i	−0.408430	−	0.707421i
$273$	30.0653	−	2.74830i	1.81964	−	0.166335i
$274$	−2.59837	+	4.50052i	−0.156974	+	0.271886i
$275$	−0.777530	−	0.448907i	−0.0468868	−	0.0270701i
$276$	1.67495	+	4.57611i	0.100820	+	0.275449i
$277$	9.47362	+	16.4088i	0.569215	+	0.985909i	0.996644	+	0.0818601i	$0.0260861\pi$
$277$	9.47362	+	16.4088i	0.569215	+	0.985909i	−0.427429	+	0.904049i	$0.640581\pi$
$278$		−	14.9462i		−	0.896412i
$279$	−9.89758	−	11.7092i	−0.592553	−	0.701012i
$280$		−	6.04193i		−	0.361074i
$281$	−2.04247	+	1.17922i	−0.121843	+	0.0703463i	−0.559683	−	0.828707i	$-0.689077\pi$
$281$	−2.04247	+	1.17922i	−0.121843	+	0.0703463i	0.437840	+	0.899053i	$0.355744\pi$
$282$	18.2636	−	21.8458i	1.08758	−	1.30090i
$283$	−7.90234	+	13.6873i	−0.469745	+	0.813623i	−0.999402	−	0.0345895i	$-0.988988\pi$
$283$	−7.90234	+	13.6873i	−0.469745	+	0.813623i	0.529656	+	0.848212i	$0.322321\pi$
$284$	−29.7795	−	17.1932i	−1.76709	−	1.02023i
$285$	7.54128	−	9.02043i	0.446707	−	0.534324i
$286$	4.89043	−	4.91084i	0.289177	−	0.290384i
$287$	19.5760			1.15554
$288$	−15.1724	−	17.9495i	−0.894044	−	1.05769i
$289$	12.2319			0.719521
$290$	2.74837	+	4.76031i	0.161390	+	0.279535i
$291$	30.0497	−	10.9988i	1.76154	−	0.644759i
$292$	−26.5102	−	15.3057i	−1.55139	−	0.895697i
$293$	−0.725271	−	0.418735i	−0.0423708	−	0.0244628i	0.478665	−	0.877998i	$-0.341121\pi$
$293$	−0.725271	−	0.418735i	−0.0423708	−	0.0244628i	−0.521036	+	0.853535i	$0.674454\pi$
$294$	10.4338	−	59.8055i	0.608514	−	3.48793i
$295$	−7.55048	−	13.0778i	−0.439606	−	0.761420i
$296$	3.58231			0.208218
$297$	4.66511	−	0.0253092i	0.270697	−	0.00146859i
$298$	3.67937			0.213140
$299$	2.77036	−	2.78193i	0.160214	−	0.160883i
$300$	−4.40859	−	0.769136i	−0.254530	−	0.0444061i
$301$	−17.4699	−	10.0863i	−1.00695	−	0.581363i
$302$	9.45752	−	16.3809i	0.544219	−	0.942615i
$303$	−3.47066	−	9.48216i	−0.199384	−	0.544736i
$304$	−14.6484	+	8.45724i	−0.840142	+	0.485056i
$305$		−	6.08530i		−	0.348443i
$306$	34.1768	−	6.15383i	1.95376	−	0.351791i
$307$		−	18.6008i		−	1.06160i	−0.847496	−	0.530802i	$-0.821891\pi$
$307$		−	18.6008i		−	1.06160i	0.847496	−	0.530802i	$-0.178109\pi$
$308$	−5.60721	−	9.71198i	−0.319501	−	0.553391i
$309$	2.20058	−	2.63220i	0.125187	−	0.149741i
$310$	9.47581	+	5.47086i	0.538190	+	0.310724i
$311$	−15.8716	+	27.4904i	−0.899995	+	1.55884i	−0.0724959	+	0.997369i	$0.523096\pi$
$311$	−15.8716	+	27.4904i	−0.899995	+	1.55884i	−0.827499	+	0.561468i	$0.810237\pi$
$312$	3.27094	−	7.08642i	0.185181	−	0.401189i
$313$	−12.2467	−	21.2119i	−0.692224	−	1.19897i	−0.971108	−	0.238642i	$-0.923298\pi$
$313$	−12.2467	−	21.2119i	−0.692224	−	1.19897i	0.278884	−	0.960325i	$-0.410035\pi$
$314$			31.9801i			1.80474i
$315$	−13.6463	−	4.91104i	−0.768884	−	0.276706i
$316$	−5.25177			−0.295435
$317$	−26.0050	+	15.0140i	−1.46059	+	0.843271i	−0.999038	−	0.0438433i	$-0.986040\pi$
$317$	−26.0050	+	15.0140i	−1.46059	+	0.843271i	−0.461550	+	0.887114i	$0.652706\pi$
$318$	23.8853	−	8.74248i	1.33942	−	0.490254i
$319$	1.99623	+	1.15253i	0.111768	+	0.0645291i
$320$	10.2100	+	5.89477i	0.570758	+	0.329528i
$321$	21.2858	+	3.71358i	1.18806	+	0.207272i
$322$	−5.63518	−	9.76041i	−0.314036	−	0.543927i
$323$		−	36.7014i		−	2.04212i
$324$	21.7932	−	8.11109i	1.21074	−	0.450616i
$325$	0.940437	+	3.48074i	0.0521660	+	0.193077i
$326$	15.8437	+	27.4422i	0.877504	+	1.51988i
$327$	−0.705932	+	4.04631i	−0.0390381	+	0.223762i
$328$	2.53040	−	4.38278i	0.139718	−	0.241999i
$329$	−18.5608	+	32.1482i	−1.02329	+	1.77239i
$330$	−3.12649	+	1.14436i	−0.172107	+	0.0629947i
$331$	27.7998	−	16.0502i	1.52802	−	0.882201i	0.528573	−	0.848888i	$-0.322727\pi$
$331$	27.7998	−	16.0502i	1.52802	−	0.882201i	0.999445	−	0.0333132i	$-0.0106059\pi$
$332$			3.62162i			0.198762i
$333$	2.91180	−	8.09104i	0.159566	−	0.443386i
$334$	−24.5309			−1.34227
$335$	3.04157	+	5.26815i	0.166179	+	0.287830i
$336$	16.0073	+	13.3824i	0.873267	+	0.730071i
$337$	8.85846	−	15.3433i	0.482551	−	0.835803i	−0.517248	−	0.855836i	$-0.673044\pi$
$337$	8.85846	−	15.3433i	0.482551	−	0.835803i	0.999799	+	0.0200322i	$0.00637688\pi$
$338$	−27.8324	+	0.115935i	−1.51388	+	0.00630605i
$339$	−5.94487	+	7.11089i	−0.322881	+	0.386211i
$340$	−12.0979	+	6.98471i	−0.656099	+	0.378799i
$341$	4.58840			0.248476
$342$	−7.72630	−	42.9099i	−0.417791	−	2.32030i
$343$			45.3040i			2.44618i
$344$	−4.51633	+	2.60750i	−0.243504	+	0.140587i
$345$	−1.77111	+	0.648262i	−0.0953536	+	0.0349013i
$346$	1.97600	+	1.14084i	0.106230	+	0.0613321i
$347$	12.5697	−	21.7714i	0.674777	−	1.16875i	−0.301757	−	0.953385i	$-0.597573\pi$
$347$	12.5697	−	21.7714i	0.674777	−	1.16875i	0.976534	−	0.215363i	$-0.0690935\pi$
$348$	11.3186	+	1.97468i	0.606743	+	0.105854i
$349$	−19.0001	+	10.9697i	−1.01705	+	0.587195i	−0.913248	−	0.407403i	$-0.866434\pi$
$349$	−19.0001	+	10.9697i	−1.01705	+	0.587195i	−0.103803	+	0.994598i	$0.533101\pi$
$350$	10.3503			0.553244
$351$	−13.3467	−	13.1478i	−0.712396	−	0.701778i
$352$	7.03376			0.374901
$353$	6.53543	−	3.77323i	0.347846	−	0.200829i	−0.315890	−	0.948796i	$-0.602303\pi$
$353$	6.53543	−	3.77323i	0.347846	−	0.200829i	0.663736	+	0.747967i	$0.268970\pi$
$354$	−55.1652	−	9.62428i	−2.93200	−	0.511525i
$355$	6.65438	−	11.5257i	0.353178	−	0.611722i
$356$	−7.70551	−	4.44878i	−0.408391	−	0.235785i
$357$	−42.5137	+	15.5608i	−2.25006	+	0.823567i
$358$	26.2016	−	15.1275i	1.38480	−	0.799513i
$359$			23.0882i			1.21855i	0.792959	+	0.609275i	$0.208539\pi$
$359$			23.0882i			1.21855i	−0.792959	+	0.609275i	$0.791461\pi$
$360$	−2.86343	+	2.42041i	−0.150916	+	0.127567i
$361$	−27.0797			−1.42525
$362$	13.4252	−	7.75103i	0.705612	−	0.407385i
$363$	11.3248	−	13.5461i	0.594400	−	0.710985i
$364$	−11.5656	+	43.5259i	−0.606203	+	2.28137i
$365$	5.92383	−	10.2604i	0.310067	−	0.537053i
$366$	−17.3127	−	14.4738i	−0.904949	−	0.756558i
$367$	−6.44302	−	11.1596i	−0.336323	−	0.582528i	0.647415	−	0.762137i	$-0.275850\pi$
$367$	−6.44302	−	11.1596i	−0.336323	−	0.582528i	−0.983738	+	0.179609i	$0.942517\pi$
$368$	2.71325			0.141438
$369$	−7.84220	−	9.27762i	−0.408249	−	0.482974i
$370$			6.13676i			0.319035i
$371$	−28.7165	+	16.5795i	−1.49089	+	0.860764i
$372$	21.4776	−	7.86121i	1.11356	−	0.407585i
$373$	2.98747	−	5.17445i	0.154685	−	0.267923i	−0.778259	−	0.627943i	$-0.783897\pi$
$373$	2.98747	−	5.17445i	0.154685	−	0.267923i	0.932944	+	0.360021i	$0.117230\pi$
$374$	−5.19631	+	9.00027i	−0.268695	+	0.465393i
$375$	0.297682	−	1.70628i	0.0153722	−	0.0881118i
$376$	4.79834	+	8.31096i	0.247455	+	0.428605i
$377$	−2.41448	−	8.93648i	−0.124352	−	0.460252i
$378$	−46.4296	+	27.1430i	−2.38808	+	1.39609i
$379$			9.57609i			0.491891i	0.969284	+	0.245945i	$0.0790984\pi$
$379$			9.57609i			0.491891i	−0.969284	+	0.245945i	$0.920902\pi$
$380$	8.76950	+	15.1892i	0.449866	+	0.779190i
$381$	15.0885	+	2.63239i	0.773009	+	0.134861i
$382$	−28.1436	−	16.2487i	−1.43995	−	0.831358i
$383$	−0.246903	−	0.142550i	−0.0126162	−	0.00728395i	0.493679	−	0.869644i	$-0.335652\pi$
$383$	−0.246903	−	0.142550i	−0.0126162	−	0.00728395i	−0.506295	+	0.862360i	$0.668985\pi$
$384$	15.5697	−	5.69881i	0.794538	−	0.290816i
$385$	3.75887	−	2.17019i	0.191570	−	0.110603i
$386$	2.25710			0.114883
$387$	2.21833	+	12.3201i	0.112764	+	0.626264i
$388$			47.7342i			2.42334i
$389$	−13.8173	−	23.9323i	−0.700566	−	1.21342i	−0.968268	−	0.249914i	$-0.919598\pi$
$389$	−13.8173	−	23.9323i	−0.700566	−	1.21342i	0.267702	−	0.963502i	$-0.413736\pi$
$390$	12.1395	+	5.60336i	0.614710	+	0.283737i
$391$	−2.94364	+	5.09854i	−0.148866	+	0.257844i
$392$	17.7193	+	10.2302i	0.894959	+	0.516705i
$393$	4.59099	−	5.49147i	0.231585	−	0.277008i
$394$	−28.5979	−	49.5331i	−1.44074	−	2.49544i
$395$		−	2.03262i		−	0.102272i
$396$	−2.35651	+	6.54805i	−0.118419	+	0.329052i
$397$			5.54421i			0.278256i	0.990274	+	0.139128i	$0.0444300\pi$
$397$			5.54421i			0.278256i	−0.990274	+	0.139128i	$0.955570\pi$
$398$	−42.0221	+	24.2615i	−2.10638	+	1.21612i
$399$	19.5371	+	53.3771i	0.978077	+	2.67220i
$400$	−1.24587	+	2.15792i	−0.0622937	+	0.107896i
$401$	7.33434	+	4.23448i	0.366259	+	0.211460i	0.671823	−	0.740712i	$-0.265512\pi$
$401$	7.33434	+	4.23448i	0.366259	+	0.211460i	−0.305564	+	0.952172i	$0.598845\pi$
$402$	22.2222	+	3.87696i	1.10834	+	0.193365i
$403$	−13.0567	−	13.0025i	−0.650402	−	0.647699i
$404$	15.0625			0.749388
$405$	3.13928	+	8.43475i	0.155992	+	0.419126i
$406$	−26.5733			−1.31881
$407$	1.28672	+	2.22867i	0.0637805	+	0.110471i
$408$	−2.01148	+	11.5296i	−0.0995832	+	0.570798i
$409$	6.55796	+	3.78624i	0.324270	+	0.187218i	0.653294	−	0.757104i	$-0.273386\pi$
$409$	6.55796	+	3.78624i	0.324270	+	0.187218i	−0.329024	+	0.944322i	$0.606720\pi$
$410$	7.50802	+	4.33475i	0.370794	+	0.214078i
$411$	−3.94804	+	1.44506i	−0.194742	+	0.0712795i
$412$	2.55898	+	4.43228i	0.126072	+	0.218363i
$413$	73.0038			3.59228
$414$	−2.36826	+	6.58071i	−0.116394	+	0.323424i
$415$	−1.40169			−0.0688064
$416$	−20.0152	−	19.9320i	−0.981327	−	0.977248i
$417$	7.75550	−	9.27667i	0.379789	−	0.454280i
$418$	11.3001	+	6.52412i	0.552706	+	0.319105i
$419$	5.41851	−	9.38513i	0.264711	−	0.458493i	−0.702777	−	0.711411i	$-0.748057\pi$
$419$	5.41851	−	9.38513i	0.264711	−	0.458493i	0.967488	+	0.252917i	$0.0813900\pi$
$420$	13.8765	−	16.5983i	0.677105	−	0.809913i
$421$	20.3325	−	11.7390i	0.990943	−	0.572121i	0.0853872	−	0.996348i	$-0.472787\pi$
$421$	20.3325	−	11.7390i	0.990943	−	0.572121i	0.905556	+	0.424226i	$0.139454\pi$
$422$			57.9581i			2.82136i
$423$	22.6714	−	4.08218i	1.10232	−	0.198483i
$424$			8.57225i			0.416305i
$425$	−2.70333	−	4.68230i	−0.131131	−	0.227125i
$426$	−16.9634	−	46.3455i	−0.821877	−	2.24545i
$427$	25.4773	+	14.7093i	1.23293	+	0.711834i
$428$	−16.1161	+	27.9139i	−0.779001	+	1.34927i
$429$	5.58357	−	0.510399i	0.269577	−	0.0246423i
$430$	−4.46684	−	7.73679i	−0.215410	−	0.373101i
$431$			23.0970i			1.11254i	0.831001	+	0.556271i	$0.187768\pi$
$431$			23.0970i			1.11254i	−0.831001	+	0.556271i	$0.812232\pi$
$432$	−0.0702419	−	12.9473i	−0.00337952	−	0.622927i
$433$	−27.7448			−1.33333			−0.666666	−	0.745357i	$-0.732279\pi$
$433$	−27.7448			−1.33333			−0.666666	+	0.745357i	$0.732279\pi$
$434$	−45.8096	+	26.4482i	−2.19893	+	1.26955i
$435$	−0.764271	+	4.38071i	−0.0366440	+	0.210039i
$436$	−5.30628	−	3.06358i	−0.254125	−	0.146719i
$437$	6.40136	+	3.69583i	0.306219	+	0.176795i
$438$	−15.1010	−	41.2575i	−0.721556	−	1.97136i
$439$	−4.58446	−	7.94051i	−0.218804	−	0.378980i	0.735639	−	0.677374i	$-0.236882\pi$
$439$	−4.58446	−	7.94051i	−0.218804	−	0.378980i	−0.954443	+	0.298394i	$0.903549\pi$
$440$		−	1.12207i		−	0.0534928i
$441$	37.5088	−	31.7055i	1.78613	−	1.50979i
$442$	40.2912	−	10.8860i	1.91646	−	0.517794i
$443$	12.8822	+	22.3126i	0.612051	+	1.06010i	0.990894	+	0.134643i	$0.0429886\pi$
$443$	12.8822	+	22.3126i	0.612051	+	1.06010i	−0.378843	+	0.925461i	$0.623678\pi$
$444$	9.84127	+	8.22752i	0.467046	+	0.390461i
$445$	1.72183	−	2.98230i	0.0816227	−	0.141375i
$446$	8.33254	−	14.4324i	0.394557	−	0.683393i
$447$	2.28368	+	1.90921i	0.108014	+	0.0903025i
$448$	−49.3592	+	28.4975i	−2.33200	+	1.34638i
$449$			13.1355i			0.619904i	0.950752	+	0.309952i	$0.100313\pi$
$449$			13.1355i			0.619904i	−0.950752	+	0.309952i	$0.899687\pi$
$450$	−4.14633	−	4.90527i	−0.195460	−	0.231237i
$451$	3.63556			0.171192
$452$	−6.91308	−	11.9738i	−0.325164	−	0.563201i
$453$	14.3700	−	5.25970i	0.675162	−	0.247122i
$454$	−25.7865	+	44.6636i	−1.21022	+	2.09617i
$455$	−16.8460	−	4.47629i	−0.789754	−	0.209852i
$456$	14.4757	+	2.52547i	0.677887	+	0.118266i
$457$	4.13673	−	2.38834i	0.193508	−	0.111722i	−0.400116	−	0.916465i	$-0.631030\pi$
$457$	4.13673	−	2.38834i	0.193508	−	0.111722i	0.593624	+	0.804743i	$0.297697\pi$
$458$	−6.00611			−0.280647
$459$	24.4058	+	13.9147i	1.13916	+	0.649482i
$460$		−	2.81343i		−	0.131177i
$461$	4.55466	−	2.62963i	0.212132	−	0.122474i	−0.390170	−	0.920743i	$-0.627584\pi$
$461$	4.55466	−	2.62963i	0.212132	−	0.122474i	0.602302	+	0.798269i	$0.294250\pi$
$462$	2.76624	−	15.8558i	0.128697	−	0.737677i
$463$	−21.7963	−	12.5841i	−1.01296	−	0.584834i	−0.100904	−	0.994896i	$-0.532174\pi$
$463$	−21.7963	−	12.5841i	−1.01296	−	0.584834i	−0.912057	+	0.410062i	$0.865507\pi$
$464$	3.19866	−	5.54024i	0.148494	−	0.257199i
$465$	3.04256	+	8.31256i	0.141095	+	0.385486i
$466$	15.0955	−	8.71541i	0.699287	−	0.403734i
$467$	−27.3504			−1.26563			−0.632813	−	0.774305i	$-0.718100\pi$
$467$	−27.3504			−1.26563			−0.632813	+	0.774305i	$0.718100\pi$
$468$	25.2613	−	11.9553i	1.16770	−	0.552634i
$469$	−29.4082			−1.35794
$470$	−14.2373	+	8.21989i	−0.656716	+	0.379155i
$471$	−16.5943	+	19.8491i	−0.764627	+	0.914600i
$472$	9.43647	−	16.3444i	0.434349	−	0.752314i
$473$	−3.24442	−	1.87317i	−0.149179	−	0.0861283i
$474$	−5.78280	−	4.83455i	−0.265613	−	0.222058i
$475$	−5.87876	+	3.39410i	−0.269736	+	0.155732i
$476$		−	67.5334i		−	3.09539i
$477$	19.3614	+	6.96776i	0.886496	+	0.319032i
$478$	39.2982			1.79746
$479$	−10.8097	+	6.24101i	−0.493910	+	0.285159i	−0.726195	−	0.687489i	$-0.758713\pi$
$479$	−10.8097	+	6.24101i	−0.493910	+	0.285159i	0.232285	+	0.972648i	$0.425380\pi$
$480$	4.66407	+	12.7427i	0.212885	+	0.581621i
$481$	2.65404	−	9.98816i	0.121014	−	0.455421i
$482$	−2.74158	+	4.74855i	−0.124875	+	0.216291i
$483$	1.56704	−	8.98208i	0.0713028	−	0.408699i
$484$	13.1693	+	22.8098i	0.598603	+	1.03681i
$485$	−18.4748			−0.838898
$486$	31.4636	+	11.1307i	1.42722	+	0.504898i
$487$		−	7.18173i		−	0.325435i	−0.986673	−	0.162718i	$-0.947974\pi$
$487$		−	7.18173i		−	0.325435i	0.986673	−	0.162718i	$-0.0520260\pi$
$488$	6.58639	−	3.80265i	0.298152	−	0.172138i
$489$	−4.40586	+	25.2538i	−0.199240	+	1.14202i
$490$	−17.5251	+	30.3544i	−0.791704	+	1.37127i
$491$	0.474406	−	0.821696i	0.0214097	−	0.0370826i	−0.855122	−	0.518427i	$-0.826518\pi$
$491$	0.474406	−	0.821696i	0.0214097	−	0.0370826i	0.876532	+	0.481344i	$0.159851\pi$
$492$	17.0174	−	6.22871i	0.767205	−	0.280812i
$493$	6.94053	+	12.0213i	0.312586	+	0.541414i
$494$	−13.6677	−	50.5868i	−0.614938	−	2.27601i
$495$	−2.53432	−	0.912052i	−0.113909	−	0.0409937i
$496$		−	12.7344i		−	0.571792i
$497$	32.1698	+	55.7197i	1.44301	+	2.49937i
$498$	−3.33391	+	3.98782i	−0.149396	+	0.178698i
$499$	19.1929	+	11.0810i	0.859192	+	0.496055i	0.863741	−	0.503935i	$-0.168115\pi$
$499$	19.1929	+	11.0810i	0.859192	+	0.496055i	−0.00454988	+	0.999990i	$0.501448\pi$
$500$	2.23759	+	1.29187i	0.100068	+	0.0577743i
$501$	−15.2256	−	12.7290i	−0.680231	−	0.568688i
$502$	−13.4599	+	7.77108i	−0.600745	+	0.346840i
$503$	−34.8531			−1.55402			−0.777012	−	0.629485i	$-0.783266\pi$
$503$	−34.8531			−1.55402			−0.777012	+	0.629485i	$0.783266\pi$
$504$	−3.21205	−	17.8389i	−0.143076	−	0.794608i
$505$			5.82972i			0.259419i
$506$	−1.04653	−	1.81265i	−0.0465241	−	0.0805822i
$507$	−17.3349	−	14.3701i	−0.769871	−	0.638200i
$508$	−11.4240	+	19.7869i	−0.506857	+	0.877902i
$509$	−13.5976	−	7.85060i	−0.602704	−	0.347972i	0.167400	−	0.985889i	$-0.446463\pi$
$509$	−13.5976	−	7.85060i	−0.602704	−	0.347972i	−0.770105	+	0.637917i	$0.779796\pi$
$510$	−19.7510	−	3.44581i	−0.874588	−	0.152583i
$511$	28.6380	+	49.6025i	1.26687	+	2.19429i
$512$		−	25.7494i		−	1.13797i
$513$	17.4703	−	30.6421i	0.771332	−	1.35288i
$514$		−	20.0885i		−	0.886067i
$515$	−1.71545	+	0.990415i	−0.0755917	+	0.0436429i
$516$	−18.3958	−	3.20939i	−0.809832	−	0.141286i
$517$	−3.44701	+	5.97039i	−0.151599	+	0.262578i
$518$	−25.6927	−	14.8337i	−1.12887	−	0.651755i
$519$	0.634468	+	1.73343i	0.0278501	+	0.0760890i
$520$	−3.17969	+	3.19296i	−0.139439	+	0.140021i
$521$	19.6835			0.862348			0.431174	−	0.902269i	$-0.358100\pi$
$521$	19.6835			0.862348			0.431174	+	0.902269i	$0.358100\pi$
$522$	10.6453	+	12.5938i	0.465933	+	0.551216i
$523$	−10.2353			−0.447559			−0.223780	−	0.974640i	$-0.571840\pi$
$523$	−10.2353			−0.447559			−0.223780	+	0.974640i	$0.571840\pi$
$524$	5.33871	+	9.24692i	0.233223	+	0.403953i
$525$	6.42411	+	5.37070i	0.280371	+	0.234397i
$526$	22.4521	+	12.9627i	0.978960	+	0.565203i
$527$	23.9295	+	13.8157i	1.04239	+	0.601822i
$528$	2.97278	+	2.48531i	0.129374	+	0.108159i
$529$	10.9072	+	18.8917i	0.474224	+	0.821380i
$530$	−14.6849			−0.637871
$531$	−29.2455	−	34.5985i	−1.26915	−	1.50145i
$532$	−84.7901			−3.67612
$533$	−10.3453	−	10.3023i	−0.448105	−	0.446242i
$534$	−4.38930	−	11.9920i	−0.189944	−	0.518944i
$535$	−10.8037	−	6.23749i	−0.467083	−	0.269670i
$536$	−3.80130	+	6.58405i	−0.164191	+	0.284388i
$537$	24.1122	+	4.20669i	1.04052	+	0.181532i
$538$	44.1640	−	25.4981i	1.90404	−	1.09930i
$539$			14.6983i			0.633101i
$540$	−13.4253	+	0.0728354i	−0.577735	+	0.00313434i
$541$			28.3807i			1.22018i	0.792331	+	0.610092i	$0.208867\pi$
$541$			28.3807i			1.22018i	−0.792331	+	0.610092i	$0.791133\pi$
$542$	18.8486	+	32.6468i	0.809619	+	1.40230i
$543$	12.3546	+	2.15542i	0.530187	+	0.0924980i
$544$	36.6826	+	21.1787i	1.57275	+	0.908030i
$545$	1.18571	−	2.05372i	0.0507904	−	0.0879715i
$546$	−52.8031	+	37.2802i	−2.25976	+	1.59544i
$547$	−3.92999	−	6.80694i	−0.168034	−	0.291044i	0.769694	−	0.638412i	$-0.220409\pi$
$547$	−3.92999	−	6.80694i	−0.168034	−	0.291044i	−0.937729	+	0.347369i	$0.887075\pi$
$548$		−	6.27150i		−	0.267905i
$549$	−3.23511	−	17.9670i	−0.138071	−	0.766811i
$550$	1.92219			0.0819626
$551$	15.0931	−	8.71403i	0.642990	−	0.371230i
$552$	−1.80840	−	1.51186i	−0.0769705	−	0.0643491i
$553$	8.50994	+	4.91322i	0.361880	+	0.208931i
$554$	−35.1307	−	20.2827i	−1.49256	−	0.861731i
$555$	−3.18434	+	3.80891i	−0.135168	+	0.161679i
$556$	9.01861	+	15.6207i	0.382474	+	0.662465i
$557$		−	15.1275i		−	0.640973i	−0.947253	−	0.320486i	$-0.896154\pi$
$557$		−	15.1275i		−	0.640973i	0.947253	−	0.320486i	$-0.103846\pi$
$558$	30.8860	+	11.1152i	1.30751	+	0.470545i
$559$	3.92418	+	14.5242i	0.165975	+	0.614308i
$560$	−6.02302	−	10.4322i	−0.254519	−	0.440840i
$561$	−7.89541	+	2.88987i	−0.333344	+	0.122011i
$562$	2.52467	−	4.37286i	0.106497	−	0.184458i
$563$	8.73118	−	15.1229i	0.367975	−	0.637352i	−0.621273	−	0.783594i	$-0.713384\pi$
$563$	8.73118	−	15.1229i	0.367975	−	0.637352i	0.989249	+	0.146242i	$0.0467177\pi$
$564$	−5.90594	+	33.8521i	−0.248685	+	1.42543i
$565$	4.63428	−	2.67560i	0.194966	−	0.112564i
$566$		−	33.8373i		−	1.42229i
$567$	−42.9019	−	7.24519i	−1.80171	−	0.304269i
$568$	16.6331			0.697908
$569$	9.91390	+	17.1714i	0.415612	+	0.719862i	0.995493	−	0.0948400i	$-0.0302340\pi$
$569$	9.91390	+	17.1714i	0.415612	+	0.719862i	−0.579880	+	0.814702i	$0.696901\pi$
$570$	−4.32632	+	24.7979i	−0.181209	+	1.03867i
$571$	1.09585	−	1.89806i	0.0458597	−	0.0794314i	−0.842184	−	0.539190i	$-0.818731\pi$
$571$	1.09585	−	1.89806i	0.0458597	−	0.0794314i	0.888044	+	0.459758i	$0.152064\pi$
$572$	−2.14790	+	8.08338i	−0.0898083	+	0.337983i
$573$	−9.03656	−	24.6887i	−0.377508	−	1.03139i
$574$	−36.2966	+	20.9558i	−1.51499	+	0.874680i
$575$	1.08890			0.0454101
$576$	33.2792	+	11.9765i	1.38663	+	0.499020i
$577$			22.8348i			0.950626i	0.879817	+	0.475313i	$0.157665\pi$
$577$			22.8348i			0.950626i	−0.879817	+	0.475313i	$0.842335\pi$
$578$	−22.6795	+	13.0940i	−0.943343	+	0.544639i
$579$	1.40092	+	1.17120i	0.0582201	+	0.0486733i
$580$	−5.74480	−	3.31676i	−0.238540	−	0.137721i
$581$	3.38816	−	5.86846i	0.140564	−	0.243465i
$582$	−43.9421	+	52.5609i	−1.82146	+	2.17872i
$583$	−5.33307	+	3.07905i	−0.220873	+	0.127521i
$584$	14.8070			0.612718
$585$	4.62711	+	9.77700i	0.191308	+	0.404229i
$586$	1.79300			0.0740681
$587$	10.1203	−	5.84296i	0.417710	−	0.241165i	−0.276387	−	0.961046i	$-0.589137\pi$
$587$	10.1203	−	5.84296i	0.417710	−	0.241165i	0.694097	+	0.719882i	$0.255804\pi$
$588$	25.1823	+	68.8003i	1.03850	+	2.83728i
$589$	17.3460	−	30.0442i	0.714731	−	1.23795i
$590$	27.9992	+	16.1653i	1.15271	+	0.665517i
$591$	7.95257	−	45.5831i	0.327125	−	1.87504i
$592$	6.18533	−	3.57110i	0.254216	−	0.146771i
$593$			28.5839i			1.17380i	0.809659	+	0.586900i	$0.199652\pi$
$593$			28.5839i			1.17380i	−0.809659	+	0.586900i	$0.800348\pi$
$594$	−8.62264	+	5.04086i	−0.353791	+	0.206829i
$595$	26.1378			1.07154
$596$	−3.84542	+	2.22015i	−0.157514	+	0.0909410i
$597$	−38.6711	−	6.74668i	−1.58270	−	0.276123i
$598$	−2.15861	+	8.12370i	−0.0882723	+	0.332203i
$599$	−6.17571	+	10.6966i	−0.252333	+	0.437053i	−0.964168	−	0.265294i	$-0.914531\pi$
$599$	−6.17571	+	10.6966i	−0.252333	+	0.437053i	0.711835	+	0.702347i	$0.247864\pi$
$600$	2.03280	−	0.744044i	0.0829887	−	0.0303755i
$601$	−0.772027	−	1.33719i	−0.0314916	−	0.0545451i	0.849850	−	0.527025i	$-0.176692\pi$
$601$	−0.772027	−	1.33719i	−0.0314916	−	0.0545451i	−0.881342	+	0.472479i	$0.843359\pi$
$602$	43.1888			1.76024
$603$	11.7810	+	13.9373i	0.479759	+	0.567573i
$604$			22.8269i			0.928814i
$605$	−8.82820	+	5.09696i	−0.358917	+	0.207221i
$606$	16.5856	+	13.8659i	0.673742	+	0.563264i
$607$	−17.5724	+	30.4364i	−0.713243	+	1.23537i	0.250390	+	0.968145i	$0.419441\pi$
$607$	−17.5724	+	30.4364i	−0.713243	+	1.23537i	−0.963633	+	0.267229i	$0.913892\pi$
$608$	26.5905	−	46.0560i	1.07839	−	1.86782i
$609$	−16.4933	−	13.7888i	−0.668342	−	0.558749i
$610$	6.51422	+	11.2830i	0.263753	+	0.456833i
$611$	26.7275	−	7.22130i	1.08128	−	0.292143i
$612$	−32.0059	+	27.0540i	−1.29376	+	1.09359i
$613$			22.9393i			0.926508i	0.886226	+	0.463254i	$0.153318\pi$
$613$			22.9393i			0.926508i	−0.886226	+	0.463254i	$0.846682\pi$
$614$	19.9119	+	34.4884i	0.803578	+	1.39184i
$615$	2.41073	+	6.58634i	0.0972099	+	0.265587i
$616$	4.69778	+	2.71226i	0.189279	+	0.109280i
$617$	−23.2993	−	13.4518i	−0.937993	−	0.541551i	−0.0486624	−	0.998815i	$-0.515496\pi$
$617$	−23.2993	−	13.4518i	−0.937993	−	0.541551i	−0.889331	+	0.457265i	$0.848829\pi$
$618$	−1.26244	+	7.23614i	−0.0507828	+	0.291080i
$619$	−18.9976	+	10.9683i	−0.763579	+	0.440853i	−0.830579	−	0.556900i	$-0.811991\pi$
$619$	−18.9976	+	10.9683i	−0.763579	+	0.440853i	0.0670002	+	0.997753i	$0.478657\pi$
$620$	−13.2046			−0.530309
$621$	−4.88462	+	2.85558i	−0.196013	+	0.114590i
$622$		−	67.9611i		−	2.72499i
$623$	8.32399	+	14.4176i	0.333493	+	0.577628i
$624$	−1.41653	−	15.4963i	−0.0567068	−	0.620350i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	45.4140	+	26.2198i	1.81511	+	1.04795i
$627$	3.62832	+	9.91291i	0.144901	+	0.395883i
$628$	−19.2970	−	33.4234i	−0.770033	−	1.33374i
$629$			15.4973i			0.617919i
$630$	30.5593	−	5.50247i	1.21751	−	0.219224i
$631$		−	9.27074i		−	0.369062i	−0.982827	−	0.184531i	$-0.940923\pi$
$631$		−	9.27074i		−	0.369062i	0.982827	−	0.184531i	$-0.0590767\pi$
$632$	2.19999	−	1.27017i	0.0875109	−	0.0505245i
$633$	−30.0742	+	35.9730i	−1.19534	+	1.42980i
$634$	32.1445	−	55.6760i	1.27662	−	2.21117i
$635$	−7.65822	−	4.42147i	−0.303907	−	0.175461i
$636$	−19.6880	+	23.5495i	−0.780678	+	0.933800i
$637$	41.6515	−	41.8254i	1.65029	−	1.65718i
$638$	−4.93504			−0.195380
$639$	13.5198	−	37.5676i	0.534835	−	1.48615i
$640$	−9.57239			−0.378382
$641$	−8.48981	−	14.7048i	−0.335327	−	0.580804i	0.648220	−	0.761453i	$-0.275514\pi$
$641$	−8.48981	−	14.7048i	−0.335327	−	0.580804i	−0.983548	+	0.180649i	$0.942180\pi$
$642$	−43.4420	+	15.9006i	−1.71452	+	0.627548i
$643$	−35.3969	−	20.4364i	−1.39592	−	0.805932i	−0.401954	−	0.915660i	$-0.631669\pi$
$643$	−35.3969	−	20.4364i	−1.39592	−	0.805932i	−0.993962	+	0.109727i	$0.965002\pi$
$644$	11.7790	+	6.80060i	0.464157	+	0.267981i
$645$	1.24215	−	7.11983i	0.0489095	−	0.280343i
$646$	39.2883	+	68.0494i	1.54578	+	2.67737i
$647$	−12.1958			−0.479465			−0.239733	−	0.970839i	$-0.577060\pi$
$647$	−12.1958			−0.479465			−0.239733	+	0.970839i	$0.577060\pi$
$648$	−7.16759	+	8.66858i	−0.281570	+	0.340534i
$649$	13.5579			0.532193
$650$	−5.46978	−	5.44704i	−0.214542	−	0.213650i
$651$	−42.1566	−	7.35477i	−1.65225	−	0.288256i
$652$	−33.1175	−	19.1204i	−1.29698	−	0.748813i
$653$	5.85446	−	10.1402i	0.229103	−	0.396818i	−0.728440	−	0.685110i	$-0.759754\pi$
$653$	5.85446	−	10.1402i	0.229103	−	0.396818i	0.957542	+	0.288292i	$0.0930875\pi$
$654$	−3.02262	−	8.25809i	−0.118194	−	0.322917i
$655$	−3.57888	+	2.06627i	−0.139838	+	0.0807357i
$656$		−	10.0899i		−	0.393945i
$657$	12.0355	−	33.4432i	0.469551	−	1.30474i
$658$		−	79.4761i		−	3.09830i
$659$	−22.7579	−	39.4179i	−0.886523	−	1.53550i	−0.843958	−	0.536409i	$-0.819781\pi$
$659$	−22.7579	−	39.4179i	−0.886523	−	1.53550i	−0.0425646	−	0.999094i	$-0.513553\pi$
$660$	2.57707	−	3.08254i	0.100312	−	0.119988i
$661$	−2.17429	−	1.25532i	−0.0845699	−	0.0488265i	0.457119	−	0.889406i	$-0.348881\pi$
$661$	−2.17429	−	1.25532i	−0.0845699	−	0.0488265i	−0.541689	+	0.840579i	$0.682215\pi$
$662$	−34.3631	+	59.5186i	−1.33556	+	2.31326i
$663$	30.6563	+	14.1503i	1.19059	+	0.549553i
$664$	−0.875906	−	1.51711i	−0.0339918	−	0.0588754i
$665$		−	32.8167i		−	1.27258i
$666$	3.26246	+	18.1189i	0.126418	+	0.702093i
$667$	−2.79564			−0.108248
$668$	25.6379	−	14.8021i	0.991962	−	0.572709i
$669$	12.6607	−	4.63405i	0.489490	−	0.179163i
$670$	−11.2789	−	6.51190i	−0.435744	−	0.251577i
$671$	4.73150	+	2.73173i	0.182658	+	0.105457i
$672$	−64.6237	−	11.2744i	−2.49291	−	0.434921i
$673$	16.7111	+	28.9445i	0.644166	+	1.11573i	0.984493	+	0.175422i	$0.0561289\pi$
$673$	16.7111	+	28.9445i	0.644166	+	1.11573i	−0.340327	+	0.940307i	$0.610538\pi$
$674$			37.9314i			1.46106i
$675$	−0.0281898	−	5.19608i	−0.00108503	−	0.199997i
$676$	29.0185	−	16.9154i	1.11609	−	0.650591i
$677$	11.9015	+	20.6140i	0.457412	+	0.792262i	0.998823	−	0.0484965i	$-0.0154430\pi$
$677$	11.9015	+	20.6140i	0.457412	+	0.792262i	−0.541411	+	0.840758i	$0.682110\pi$
$678$	3.41048	−	19.5484i	0.130979	−	0.750753i
$679$	44.6571	−	77.3484i	1.71378	−	2.96836i
$680$	3.37857	−	5.85186i	0.129562	−	0.224408i
$681$	−39.1807	+	14.3409i	−1.50141	+	0.549545i
$682$	−8.50751	+	4.91182i	−0.325770	+	0.188083i
$683$		−	23.5247i		−	0.900149i	−0.892991	−	0.450075i	$-0.851397\pi$
$683$		−	23.5247i		−	0.900149i	0.892991	−	0.450075i	$-0.148603\pi$
$684$	33.9671	+	40.1844i	1.29876	+	1.53649i
$685$	2.42729			0.0927419
$686$	−48.4972	−	83.9996i	−1.85163	−	3.20712i
$687$	−3.72783	−	3.11655i	−0.142225	−	0.118904i
$688$	−5.19869	+	9.00439i	−0.198198	+	0.343289i
$689$	23.9011	+	6.35094i	0.910558	+	0.241952i
$690$	2.58993	−	3.09791i	0.0985968	−	0.117936i
$691$	−26.7105	+	15.4213i	−1.01612	+	0.586655i	−0.912976	−	0.408012i	$-0.866222\pi$
$691$	−26.7105	+	15.4213i	−1.01612	+	0.586655i	−0.103139	+	0.994667i	$0.532889\pi$
$692$	−2.75357			−0.104675
$693$	9.94442	−	8.40584i	0.377757	−	0.319311i
$694$			53.8227i			2.04308i
$695$	−6.04575	+	3.49052i	−0.229328	+	0.132403i
$696$	−5.21902	+	1.91026i	−0.197826	+	0.0724083i
$697$	18.9602	+	10.9467i	0.718169	+	0.414635i
$698$	23.4858	−	40.6786i	0.888951	−	1.53971i
$699$	13.8918	+	2.42360i	0.525435	+	0.0916689i
$700$	−10.8174	+	6.24540i	−0.408858	+	0.236054i
$701$	−35.3702			−1.33592			−0.667958	−	0.744199i	$-0.732831\pi$
$701$	−35.3702			−1.33592			−0.667958	+	0.744199i	$0.732831\pi$
$702$	38.8211	+	10.0903i	1.46521	+	0.380835i
$703$	19.4573			0.733847
$704$	−9.16672	+	5.29241i	−0.345484	+	0.199465i
$705$	−13.1019	−	2.28580i	−0.493448	−	0.0860883i
$706$	−8.07838	+	13.9922i	−0.304034	+	0.526602i
$707$	−24.4072	−	14.0915i	−0.917929	−	0.529967i
$708$	63.4621	−	23.2284i	2.38505	−	0.872976i
$709$	33.4410	−	19.3071i	1.25590	−	0.725095i	0.283626	−	0.958935i	$-0.408462\pi$
$709$	33.4410	−	19.3071i	1.25590	−	0.725095i	0.972275	+	0.233840i	$0.0751292\pi$
$710$			28.4936i			1.06935i
$711$	−1.08059	−	6.00134i	−0.0405254	−	0.225068i
$712$	4.30383			0.161293
$713$	−4.81940	+	2.78248i	−0.180488	+	0.104205i
$714$	62.1684	−	74.3621i	2.32659	−	2.78293i
$715$	−3.12855	−	0.831313i	−0.117001	−	0.0310893i
$716$	−18.2561	+	31.6204i	−0.682261	+	1.18171i
$717$	24.3913	+	20.3917i	0.910910	+	0.761542i
$718$	−24.7156	−	42.8087i	−0.922378	−	1.59760i
$719$	2.67155			0.0996320			0.0498160	−	0.998758i	$-0.484137\pi$
$719$	2.67155			0.0996320			0.0498160	+	0.998758i	$0.484137\pi$
$720$	−2.53126	+	7.03363i	−0.0943345	+	0.262128i
$721$		−	9.57608i		−	0.356632i
$722$	50.2094	−	28.9884i	1.86860	−	1.07884i
$723$	−4.16562	+	1.52470i	−0.154921	+	0.0567042i
$724$	−9.35403	+	16.2017i	−0.347640	+	0.602130i
$725$	1.28370	−	2.22344i	0.0476755	−	0.0825764i
$726$	−6.49688	+	37.2393i	−0.241122	+	1.38208i
$727$	23.1562	+	40.1077i	0.858815	+	1.48751i	0.873060	+	0.487613i	$0.162132\pi$
$727$	23.1562	+	40.1077i	0.858815	+	1.48751i	−0.0142447	+	0.999899i	$0.504534\pi$
$728$	−5.68205	−	21.0304i	−0.210591	−	0.779438i
$729$	13.7529	+	23.2348i	0.509367	+	0.860549i
$730$			25.3655i			0.938818i
$731$	−11.2802	−	19.5379i	−0.417214	−	0.722637i
$732$	26.8276	+	4.68042i	0.991576	+	0.172993i
$733$	−18.9203	−	10.9236i	−0.698838	−	0.403474i	0.108077	−	0.994143i	$-0.465531\pi$
$733$	−18.9203	−	10.9236i	−0.698838	−	0.403474i	−0.806914	+	0.590668i	$0.798864\pi$
$734$	23.8924	+	13.7943i	0.881886	+	0.509157i
$735$	−26.6281	+	9.74641i	−0.982193	+	0.359502i
$736$	−7.38786	+	4.26538i	−0.272320	+	0.157224i
$737$	−5.46153			−0.201178
$738$	24.4720	+	8.80699i	0.900828	+	0.324190i
$739$		−	49.1079i		−	1.80646i	−0.429154	−	0.903231i	$-0.641188\pi$
$739$		−	49.1079i		−	1.80646i	0.429154	−	0.903231i	$-0.358812\pi$
$740$	−3.70296	−	6.41371i	−0.136123	−	0.235773i
$741$	17.7661	−	38.4899i	0.652655	−	1.41396i
$742$	35.4961	−	61.4811i	1.30310	−	2.25704i
$743$	2.30517	+	1.33089i	0.0845686	+	0.0488257i	0.541688	−	0.840580i	$-0.317785\pi$
$743$	2.30517	+	1.33089i	0.0845686	+	0.0488257i	−0.457119	+	0.889405i	$0.651119\pi$
$744$	−7.09579	+	8.48755i	−0.260144	+	0.311169i
$745$	−0.859277	−	1.48831i	−0.0314815	−	0.0545275i
$746$			12.7921i			0.468354i
$747$	−4.13853	+	0.745177i	−0.151421	+	0.0272646i
$748$		−	12.5419i		−	0.458579i
$749$	52.2289	−	30.1544i	1.90840	−	1.10182i
$750$	1.27460	+	3.48233i	0.0465419	+	0.127157i
$751$	7.21091	−	12.4897i	0.263130	−	0.455754i	−0.703942	−	0.710257i	$-0.748579\pi$
$751$	7.21091	−	12.4897i	0.263130	−	0.455754i	0.967072	+	0.254503i	$0.0819120\pi$
$752$	16.5699	+	9.56664i	0.604243	+	0.348860i
$753$	−12.3866	−	2.16100i	−0.451392	−	0.0787511i
$754$	14.0431	+	13.9848i	0.511421	+	0.509295i
$755$	−8.83481			−0.321532
$756$	32.1467	−	56.3839i	1.16916	−	2.05066i
$757$	−24.9195			−0.905715			−0.452858	−	0.891583i	$-0.649595\pi$
$757$	−24.9195			−0.905715			−0.452858	+	0.891583i	$0.649595\pi$
$758$	−10.2511	−	17.7554i	−0.372335	−	0.644903i
$759$	0.291022	−	1.66810i	0.0105634	−	0.0605483i
$760$	−7.34717	−	4.24189i	−0.266510	−	0.153870i
$761$	−9.79868	−	5.65727i	−0.355202	−	0.205076i	0.311772	−	0.950157i	$-0.399077\pi$
$761$	−9.79868	−	5.65727i	−0.355202	−	0.205076i	−0.666974	+	0.745081i	$0.732411\pi$
$762$	−30.7941	+	11.2712i	−1.11555	+	0.408314i
$763$	5.73218	+	9.92843i	0.207519	+	0.359433i
$764$	39.2183			1.41887
$765$	−10.4709	−	12.3874i	−0.378575	−	0.447868i
$766$	0.610389			0.0220543
$767$	−38.5802	−	38.4198i	−1.39305	−	1.38726i
$768$	3.42712	−	4.09931i	0.123665	−	0.147921i
$769$	21.5515	+	12.4428i	0.777167	+	0.448698i	0.835425	−	0.549604i	$-0.185221\pi$
$769$	21.5515	+	12.4428i	0.777167	+	0.448698i	−0.0582583	+	0.998302i	$0.518555\pi$
$770$	−4.64630	+	8.04763i	−0.167441	+	0.290016i
$771$	10.4239	−	12.4684i	0.375406	−	0.449038i
$772$	−2.35896	+	1.36195i	−0.0849008	+	0.0490175i
$773$		−	23.0894i		−	0.830467i	−0.909715	−	0.415234i	$-0.863700\pi$
$773$		−	23.0894i		−	0.830467i	0.909715	−	0.415234i	$-0.136300\pi$
$774$	−17.3015	−	20.4683i	−0.621890	−	0.735719i
$775$		−	5.11064i		−	0.183580i
$776$	−11.5448	−	19.9961i	−0.414432	−	0.717818i
$777$	−8.24961	−	22.5387i	−0.295953	−	0.808572i
$778$	51.2383	+	29.5825i	1.83698	+	1.06058i
$779$	13.7439	−	23.8051i	0.492425	−	0.852906i
$780$	−16.0685	+	1.46884i	−0.575345	+	0.0525928i
$781$	5.97439	+	10.3480i	0.213781	+	0.370279i
$782$		−	12.6045i		−	0.450736i
$783$	0.0723747	+	13.3404i	0.00258646	+	0.476748i
$784$	40.7929			1.45689
$785$	12.9360	−	7.46860i	0.461706	−	0.266566i
$786$	−2.63378	+	15.0965i	−0.0939439	+	0.538475i
$787$	6.83515	+	3.94628i	0.243647	+	0.140670i	0.616852	−	0.787079i	$-0.288408\pi$
$787$	6.83515	+	3.94628i	0.243647	+	0.140670i	−0.373205	+	0.927749i	$0.621741\pi$
$788$	59.7771	+	34.5123i	2.12947	+	1.22945i
$789$	7.20910	+	19.6959i	0.256651	+	0.701194i
$790$	2.17588	+	3.76874i	0.0774145	+	0.134086i
$791$			25.8698i			0.919823i
$792$	−0.596524	−	3.31294i	−0.0211966	−	0.117720i
$793$	−5.72284	−	21.1814i	−0.203224	−	0.752172i
$794$	−5.93499	−	10.2797i	−0.210625	−	0.364813i
$795$	−9.11450	−	7.61992i	−0.323258	−	0.270251i
$796$	29.2791	−	50.7128i	1.03777	−	1.79747i
$797$	−11.4557	+	19.8418i	−0.405780	+	0.702832i	−0.994412	−	0.105569i	$-0.966334\pi$
$797$	−11.4557	+	19.8418i	−0.405780	+	0.702832i	0.588632	+	0.808401i	$0.299667\pi$
$798$	−93.3637	−	78.0542i	−3.30504	−	2.76309i
$799$	−35.9538	+	20.7579i	−1.27195	+	0.734363i
$800$		−	7.83432i		−	0.276985i
$801$	3.49827	−	9.72067i	0.123605	−	0.343463i
$802$	−18.1318			−0.640255
$803$	5.31850	+	9.21191i	0.187686	+	0.325081i
$804$	−25.5645	+	9.35711i	−0.901591	+	0.330000i
$805$	−2.63207	+	4.55888i	−0.0927682	+	0.160679i
$806$	38.1279	+	10.1313i	1.34300	+	0.356859i
$807$	40.6422	+	7.09056i	1.43067	+	0.249599i
$808$	−6.30976	+	3.64294i	−0.221977	+	0.128158i
$809$	−14.2599			−0.501350			−0.250675	−	0.968071i	$-0.580653\pi$
$809$	−14.2599			−0.501350			−0.250675	+	0.968071i	$0.580653\pi$
$810$	−14.8499	−	12.2786i	−0.521772	−	0.431426i
$811$		−	32.5368i		−	1.14252i	−0.820769	−	0.571261i	$-0.806455\pi$
$811$		−	32.5368i		−	1.14252i	0.820769	−	0.571261i	$-0.193545\pi$
$812$	27.7725	−	16.0345i	0.974625	−	0.562700i
$813$	−5.24147	+	30.0434i	−0.183826	+	1.05367i
$814$	−4.77151	−	2.75483i	−0.167241	−	0.0965569i
$815$	7.40027	−	12.8176i	0.259220	−	0.448982i
$816$	8.02040	+	21.9125i	0.280770	+	0.767091i
$817$	−24.5304	+	14.1627i	−0.858211	+	0.495489i
$818$	−16.2124			−0.566855
$819$	−52.1179	−	4.26055i	−1.82115	−	0.148876i
$820$	−10.4625			−0.365365
$821$	−47.9894	+	27.7067i	−1.67484	+	0.966971i	−0.709977	+	0.704225i	$0.751295\pi$
$821$	−47.9894	+	27.7067i	−1.67484	+	0.966971i	−0.964865	+	0.262746i	$0.915372\pi$
$822$	5.77327	−	6.90564i	0.201366	−	0.240862i
$823$	−11.3764	+	19.7045i	−0.396556	+	0.686856i	−0.993298	−	0.115577i	$-0.963128\pi$
$823$	−11.3764	+	19.7045i	−0.396556	+	0.686856i	0.596742	+	0.802433i	$0.296462\pi$
$824$	−2.14394	−	1.23780i	−0.0746877	−	0.0431209i
$825$	1.19305	+	0.997417i	0.0415367	+	0.0347256i
$826$	−135.359	+	78.1494i	−4.70973	+	2.71917i
$827$			35.0903i			1.22021i	0.792321	+	0.610105i	$0.208873\pi$
$827$			35.0903i			1.22021i	−0.792321	+	0.610105i	$0.791127\pi$
$828$	−1.49570	−	8.30672i	−0.0519790	−	0.288678i
$829$	−33.7146			−1.17096			−0.585478	−	0.810688i	$-0.699093\pi$
$829$	−33.7146			−1.17096			−0.585478	+	0.810688i	$0.699093\pi$
$830$	2.59892	−	1.50049i	0.0902100	−	0.0520828i
$831$	−11.2800	−	30.8181i	−0.391300	−	1.06907i
$832$	41.0822	+	10.9163i	1.42427	+	0.378454i
$833$	−44.2567	+	76.6549i	−1.53340	+	2.65593i
$834$	−4.44921	+	25.5023i	−0.154064	+	0.883073i
$835$	5.72892	+	9.92278i	0.198257	+	0.343392i
$836$	−15.7468			−0.544613
$837$	13.4024	+	22.9255i	0.463255	+	0.792421i
$838$			23.2017i			0.801490i
$839$	−30.0271	+	17.3362i	−1.03665	+	0.598510i	−0.918883	−	0.394531i	$-0.870907\pi$
$839$	−30.0271	+	17.3362i	−1.03665	+	0.598510i	−0.117768	+	0.993041i	$0.537574\pi$
$840$	−1.79857	+	10.3092i	−0.0620567	+	0.355701i
$841$	11.2042	−	19.4063i	0.386352	−	0.669182i
$842$	−25.1327	+	43.5312i	−0.866131	+	1.50018i
$843$	3.83605	−	1.40407i	0.132121	−	0.0483587i
$844$	−34.9723	−	60.5738i	−1.20380	−	2.08504i
$845$	6.54684	+	11.2312i	0.225218	+	0.386364i
$846$	−37.6659	+	31.8383i	−1.29498	+	1.09462i
$847$		−	49.2813i		−	1.69333i
$848$	8.54543	+	14.8011i	0.293451	+	0.508273i
$849$	17.5580	−	21.0019i	0.602591	−	0.720783i
$850$	10.0246	+	5.78773i	0.343843	+	0.198518i
$851$	−2.70300	−	1.56058i	−0.0926576	−	0.0534959i
$852$	45.6941	+	38.2013i	1.56545	+	1.30875i
$853$	27.0238	−	15.6022i	0.925276	−	0.534208i	0.0399615	−	0.999201i	$-0.487276\pi$
$853$	27.0238	−	15.6022i	0.925276	−	0.534208i	0.885314	+	0.464993i	$0.153943\pi$
$854$	−62.9844			−2.15528
$855$	−15.5527	+	13.1465i	−0.531893	+	0.449599i
$856$		−	15.5910i		−	0.532890i
$857$	−10.0301	−	17.3727i	−0.342622	−	0.593439i	0.642297	−	0.766456i	$-0.277982\pi$
$857$	−10.0301	−	17.3727i	−0.342622	−	0.593439i	−0.984919	+	0.173017i	$0.944648\pi$
$858$	−9.80631	+	6.92347i	−0.334782	+	0.236363i
$859$	−22.7832	+	39.4617i	−0.777353	+	1.34641i	0.156109	+	0.987740i	$0.450105\pi$
$859$	−22.7832	+	39.4617i	−0.777353	+	1.34641i	−0.933462	+	0.358675i	$0.883229\pi$
$860$	9.33685	+	5.39063i	0.318384	+	0.183819i
$861$	−33.4022	−	5.82744i	−1.13834	−	0.198599i
$862$	−24.7250	−	42.8249i	−0.842135	−	1.45862i
$863$			38.9293i			1.32517i	0.748987	+	0.662585i	$0.230541\pi$
$863$			38.9293i			1.32517i	−0.748987	+	0.662585i	$0.769459\pi$
$864$	20.5451	+	35.1435i	0.698959	+	1.19561i
$865$		−	1.06573i		−	0.0362358i
$866$	51.4426	−	29.7004i	1.74809	−	1.00926i
$867$	−20.8710	−	3.64121i	−0.708815	−	0.123662i
$868$	31.9180	−	55.2836i	1.08337	−	1.87645i
$869$	1.58042	+	0.912456i	0.0536121	+	0.0309529i
$870$	−3.27242	−	8.94055i	−0.110945	−	0.303113i
$871$	15.5413	+	15.4767i	0.526596	+	0.524408i
$872$	2.96377			0.100366
$873$	−54.5472	+	9.82170i	−1.84614	+	0.332414i
$874$	−15.8253			−0.535299
$875$	−2.41719	−	4.18669i	−0.0817159	−	0.141536i
$876$	40.6776	+	34.0074i	1.37437	+	1.14900i
$877$	−16.3151	−	9.41955i	−0.550923	−	0.318076i	0.198571	−	0.980086i	$-0.436370\pi$
$877$	−16.3151	−	9.41955i	−0.550923	−	0.318076i	−0.749494	+	0.662011i	$0.769703\pi$
$878$	17.0004	+	9.81517i	0.573735	+	0.331246i
$879$	1.11286	+	0.930379i	0.0375360	+	0.0313809i
$880$	−1.11856	−	1.93741i	−0.0377067	−	0.0653100i
$881$	14.6211			0.492598			0.246299	−	0.969194i	$-0.420785\pi$
$881$	14.6211			0.492598			0.246299	+	0.969194i	$0.420785\pi$
$882$	−35.6061	+	98.9388i	−1.19892	+	3.33144i
$883$	33.2697			1.11961			0.559807	−	0.828623i	$-0.310875\pi$
$883$	33.2697			1.11961			0.559807	+	0.828623i	$0.310875\pi$
$884$	−35.5409	+	35.6893i	−1.19537	+	1.20036i
$885$	8.99019	+	24.5620i	0.302202	+	0.825644i
$886$	−47.7706	−	27.5804i	−1.60488	−	0.926580i
$887$	0.453731	−	0.785886i	0.0152348	−	0.0263875i	−0.858307	−	0.513136i	$-0.828484\pi$
$887$	0.453731	−	0.785886i	0.0152348	−	0.0263875i	0.873542	+	0.486748i	$0.161817\pi$
$888$	−6.11242	−	1.06639i	−0.205119	−	0.0357857i
$889$	37.0227	−	21.3751i	1.24170	−	0.716897i
$890$			7.37278i			0.247136i
$891$	−7.96751	−	1.34554i	−0.266922	−	0.0450772i
$892$			20.1116i			0.673387i
$893$	26.0622	+	45.1410i	0.872137	+	1.51059i
$894$	−6.27803	−	1.09528i	−0.209969	−	0.0366317i
$895$	−12.2382	−	7.06573i	−0.409078	−	0.236181i
$896$	23.1383	−	40.0767i	0.772996	−	1.33887i
$897$	−5.55514	+	3.92206i	−0.185481	+	0.130954i
$898$	−14.0614	−	24.3550i	−0.469234	−	0.812737i
$899$			13.1211i			0.437612i
$900$	7.29332	+	2.62472i	0.243111	+	0.0874906i
$901$	−37.0842			−1.23545
$902$	−6.74080	+	3.89180i	−0.224444	+	0.129583i
$903$	26.8060	+	22.4105i	0.892049	+	0.745774i
$904$	5.79185	+	3.34393i	0.192634	+	0.111217i
$905$	−6.27061	−	3.62034i	−0.208442	−	0.120344i
$906$	−21.0135	+	25.1351i	−0.698126	+	0.835056i
$907$	−15.7587	−	27.2948i	−0.523257	−	0.906308i	−0.999634	−	0.0270669i	$-0.991383\pi$
$907$	−15.7587	−	27.2948i	−0.523257	−	0.906308i	0.476376	−	0.879242i	$-0.341950\pi$
$908$		−	62.2390i		−	2.06547i
$909$	3.09923	+	17.2124i	0.102795	+	0.570898i
$910$	36.0266	−	9.73376i	1.19427	−	0.322671i
$911$	−21.3769	−	37.0258i	−0.708247	−	1.22672i	−0.965507	−	0.260377i	$-0.916153\pi$
$911$	−21.3769	−	37.0258i	−0.708247	−	1.22672i	0.257260	−	0.966342i	$-0.417180\pi$
$912$	27.5118	−	10.0698i	0.911005	−	0.333446i
$913$	0.629230	−	1.08986i	0.0208245	−	0.0360690i
$914$	−5.11337	+	8.85661i	−0.169135	+	0.292951i
$915$	−1.81149	+	10.3832i	−0.0598859	+	0.343258i
$916$	6.27717	−	3.62413i	0.207403	−	0.119744i
$917$		−	19.9782i		−	0.659739i
$918$	−60.1470	+	0.326311i	−1.98515	+	0.0107699i
$919$	−49.7451			−1.64094			−0.820469	−	0.571691i	$-0.806288\pi$
$919$	−49.7451			−1.64094			−0.820469	+	0.571691i	$0.806288\pi$
$920$	0.680443	+	1.17856i	0.0224335	+	0.0388560i
$921$	−5.53713	+	31.7381i	−0.182455	+	1.04581i
$922$	−5.62996	+	9.75138i	−0.185413	+	0.321145i
$923$	12.3230	−	46.3761i	0.405616	−	1.52649i
$924$	6.67638	+	18.2405i	0.219637	+	0.600069i
$925$	2.48233	−	1.43317i	0.0816185	−	0.0471224i
$926$	53.8844			1.77075
$927$	−4.53837	+	3.83620i	−0.149059	+	0.125997i
$928$			20.1139i			0.660270i
$929$	−29.1090	+	16.8061i	−0.955037	+	0.551391i	−0.894642	−	0.446784i	$-0.852569\pi$
$929$	−29.1090	+	16.8061i	−0.955037	+	0.551391i	−0.0603948	+	0.998175i	$0.519236\pi$
$930$	−14.5398	−	12.1556i	−0.476778	−	0.398597i
$931$	96.2424	+	55.5655i	3.15422	+	1.82109i
$932$	−10.5179	+	18.2175i	−0.344524	+	0.596733i
$933$	35.2647	−	42.1815i	1.15452	−	1.38096i
$934$	50.7113	−	29.2782i	1.65932	−	0.958011i
$935$	4.85417			0.158748
$936$	−7.69064	+	11.1177i	−0.251376	+	0.363393i
$937$	−25.4455			−0.831269			−0.415635	−	0.909532i	$-0.636440\pi$
$937$	−25.4455			−0.831269			−0.415635	+	0.909532i	$0.636440\pi$
$938$	54.5267	−	31.4810i	1.78036	−	1.02789i
$939$	14.5818	+	39.8390i	0.475861	+	1.30010i
$940$	9.91987	−	17.1817i	0.323550	−	0.560406i
$941$	11.1114	+	6.41516i	0.362221	+	0.209128i	0.670055	−	0.742312i	$-0.266271\pi$
$941$	11.1114	+	6.41516i	0.362221	+	0.209128i	−0.307834	+	0.951440i	$0.599604\pi$
$942$	9.51991	−	54.5669i	0.310175	−	1.77789i
$943$	−3.81858	+	2.20466i	−0.124350	+	0.0717935i
$944$		−	37.6278i		−	1.22468i
$945$	21.8225	+	12.4419i	0.709887	+	0.404734i
$946$	8.02078			0.260778
$947$	−22.4869	+	12.9828i	−0.730725	+	0.421885i	−0.818688	−	0.574239i	$-0.805298\pi$
$947$	−22.4869	+	12.9828i	−0.730725	+	0.421885i	0.0879621	+	0.996124i	$0.471965\pi$
$948$	8.96097	+	1.56336i	0.291039	+	0.0507755i
$949$	10.9701	−	41.2847i	0.356105	−	1.34016i
$950$	7.26667	−	12.5862i	0.235762	−	0.408351i
$951$	48.8412	−	17.8768i	1.58379	−	0.579696i
$952$	16.3333	+	28.2901i	0.529365	+	0.916887i
$953$	−13.5125			−0.437713			−0.218857	−	0.975757i	$-0.570233\pi$
$953$	−13.5125			−0.437713			−0.218857	+	0.975757i	$0.570233\pi$
$954$	−43.3574	+	7.80688i	−1.40375	+	0.252757i
$955$			15.1789i			0.491176i
$956$	−41.0718	+	23.7128i	−1.32836	+	0.766927i
$957$	−3.06304	−	2.56077i	−0.0990141	−	0.0827781i
$958$	13.3618	−	23.1433i	0.431700	−	0.747727i
$959$	−5.86721	+	10.1623i	−0.189462	+	0.328158i
$960$	−15.6664	−	13.0975i	−0.505631	−	0.422719i
$961$	−2.44068	−	4.22739i	−0.0787317	−	0.136367i
$962$	5.77123	+	21.3605i	0.186072	+	0.688690i
$963$	−35.2140	−	12.6728i	−1.13476	−	0.408375i
$964$		−	6.61714i		−	0.213124i
$965$	−0.527120	−	0.912999i	−0.0169686	−	0.0293905i
$966$	6.70968	+	18.3315i	0.215880	+	0.589805i
$967$	−29.9119	−	17.2697i	−0.961903	−	0.555355i	−0.0651449	−	0.997876i	$-0.520751\pi$
$967$	−29.9119	−	17.2697i	−0.961903	−	0.555355i	−0.896758	+	0.442521i	$0.854084\pi$
$968$	−11.0333	−	6.37010i	−0.354625	−	0.204743i
$969$	−10.9254	+	62.6229i	−0.350973	+	2.01174i
$970$	34.2547	−	19.7770i	1.09985	−	0.635001i
$971$	−8.17157			−0.262238			−0.131119	−	0.991367i	$-0.541857\pi$
$971$	−8.17157			−0.262238			−0.131119	+	0.991367i	$0.541857\pi$
$972$	−39.5999	+	7.35232i	−1.27017	+	0.235826i
$973$		−	33.7489i		−	1.08194i
$974$	7.68793	+	13.3159i	0.246337	+	0.426669i
$975$	−0.568491	−	6.21907i	−0.0182063	−	0.199170i
$976$	7.58151	−	13.1316i	0.242678	−	0.420331i
$977$	17.5741	+	10.1464i	0.562244	+	0.324612i	0.754046	−	0.656822i	$-0.228100\pi$
$977$	17.5741	+	10.1464i	0.562244	+	0.324612i	−0.191802	+	0.981434i	$0.561433\pi$
$978$	−18.8648	−	51.5404i	−0.603229	−	1.64808i
$979$	1.54589	+	2.67755i	0.0494067	+	0.0855749i
$980$		−	42.2991i		−	1.35119i
$981$	2.40903	−	6.69399i	0.0769145	−	0.213723i
$982$			2.03138i			0.0648239i
$983$	27.6249	−	15.9493i	0.881099	−	0.508703i	0.0100782	−	0.999949i	$-0.496792\pi$
$983$	27.6249	−	15.9493i	0.881099	−	0.508703i	0.871021	+	0.491247i	$0.163459\pi$
$984$	−5.62224	+	6.72499i	−0.179230	+	0.214385i
$985$	−13.3575	+	23.1358i	−0.425604	+	0.737169i
$986$	−25.7373	−	14.8595i	−0.819644	−	0.473221i
$987$	41.2398	−	49.3286i	1.31268	−	1.57015i
$988$	44.8089	+	44.6226i	1.42556	+	1.41963i
$989$	4.54367			0.144480
$990$	5.67531	−	1.02189i	0.180373	−	0.0324777i
$991$	52.2461			1.65965			0.829826	−	0.558023i	$-0.188440\pi$
$991$	52.2461			1.65965			0.829826	+	0.558023i	$0.188440\pi$
$992$	20.0192	+	34.6742i	0.635610	+	1.10091i
$993$	−52.2121	+	19.1107i	−1.65690	+	0.606459i
$994$	−119.294	−	68.8745i	−3.78378	−	2.18457i
$995$	19.6276	+	11.3320i	0.622238	+	0.359249i
$996$	1.07809	−	6.17949i	0.0341607	−	0.195805i
$997$	−26.1801	−	45.3452i	−0.829131	−	1.43610i	−0.898721	−	0.438521i	$-0.855502\pi$
$997$	−26.1801	−	45.3452i	−0.829131	−	1.43610i	0.0695901	−	0.997576i	$-0.477831\pi$
$998$	−47.4482			−1.50195
$999$	−7.37690	+	12.9388i	−0.233395	+	0.409365i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.571.8	yes	108
9.7	even	3	inner	585.2.bt.b.376.47	yes	108
13.12	even	2	inner	585.2.bt.b.571.47	yes	108
117.25	even	6	inner	585.2.bt.b.376.8	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.8	✓	108	117.25	even	6	inner
585.2.bt.b.376.47	yes	108	9.7	even	3	inner
585.2.bt.b.571.8	yes	108	1.1	even	1	trivial
585.2.bt.b.571.47	yes	108	13.12	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.85413 + 1.07048i) q^{2} +(-1.70628 - 0.297682i) q^{3} +(1.29187 - 2.23759i) q^{4} +(0.866025 + 0.500000i) q^{5} +(3.48233 - 1.27460i) q^{6} +(-4.18669 + 2.41719i) q^{7} +1.24978i q^{8} +(2.82277 + 1.01586i) q^{9} +O(q^{10})\)	\(q+(-1.85413 + 1.07048i) q^{2} +(-1.70628 - 0.297682i) q^{3} +(1.29187 - 2.23759i) q^{4} +(0.866025 + 0.500000i) q^{5} +(3.48233 - 1.27460i) q^{6} +(-4.18669 + 2.41719i) q^{7} +1.24978i q^{8} +(2.82277 + 1.01586i) q^{9} -2.14097 q^{10} +(-0.777530 + 0.448907i) q^{11} +(-2.87039 + 3.43338i) q^{12} +(3.48463 + 0.925930i) q^{13} +(5.17513 - 8.96358i) q^{14} +(-1.32884 - 1.11094i) q^{15} +(1.24587 + 2.15792i) q^{16} -5.40665 q^{17} +(-6.32125 + 1.13820i) q^{18} +6.78820i q^{19} +(2.23759 - 1.29187i) q^{20} +(7.86322 - 2.87809i) q^{21} +(0.961096 - 1.66467i) q^{22} +(0.544448 - 0.943012i) q^{23} +(0.372038 - 2.13248i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-7.45216 + 2.01345i) q^{26} +(-4.51403 - 2.57362i) q^{27} +12.4908i q^{28} +(-1.28370 - 2.22344i) q^{29} +(3.65309 + 0.637329i) q^{30} +(-4.42594 - 2.55532i) q^{31} +(-6.78472 - 3.91716i) q^{32} +(1.46031 - 0.534504i) q^{33} +(10.0246 - 5.78773i) q^{34} -4.83438 q^{35} +(5.91974 - 5.00384i) q^{36} -2.86635i q^{37} +(-7.26667 - 12.5862i) q^{38} +(-5.67012 - 2.61721i) q^{39} +(-0.624892 + 1.08234i) q^{40} +(-3.50683 - 2.02467i) q^{41} +(-11.4985 + 13.7538i) q^{42} +(2.08636 + 3.61369i) q^{43} +2.31972i q^{44} +(1.93666 + 2.29114i) q^{45} +2.33129i q^{46} +(6.64992 - 3.83933i) q^{47} +(-1.48343 - 4.05288i) q^{48} +(8.18560 - 14.1779i) q^{49} +(-1.85413 - 1.07048i) q^{50} +(9.22525 + 1.60946i) q^{51} +(6.57355 - 6.60099i) q^{52} +6.85899 q^{53} +(11.1246 - 0.0603536i) q^{54} -0.897814 q^{55} +(-3.02096 - 5.23246i) q^{56} +(2.02073 - 11.5826i) q^{57} +(4.76031 + 2.74837i) q^{58} +(-13.0778 - 7.55048i) q^{59} +(-4.20252 + 1.53820i) q^{60} +(-3.04265 - 5.27002i) q^{61} +10.9417 q^{62} +(-14.2736 + 2.57008i) q^{63} +11.7895 q^{64} +(2.55481 + 2.54419i) q^{65} +(-2.13544 + 2.55428i) q^{66} +(5.26815 + 3.04157i) q^{67} +(-6.98471 + 12.0979i) q^{68} +(-1.20970 + 1.44697i) q^{69} +(8.96358 - 5.17513i) q^{70} -13.3088i q^{71} +(-1.26960 + 3.52785i) q^{72} -11.8477i q^{73} +(3.06838 + 5.31459i) q^{74} +(-0.595339 - 1.62652i) q^{75} +(15.1892 + 8.76950i) q^{76} +(2.17019 - 3.75887i) q^{77} +(13.3148 - 1.21712i) q^{78} +(-1.01631 - 1.76030i) q^{79} +2.49175i q^{80} +(6.93607 + 5.73507i) q^{81} +8.66951 q^{82} +(-1.21390 + 0.700846i) q^{83} +(3.71829 - 21.3128i) q^{84} +(-4.68230 - 2.70333i) q^{85} +(-7.73679 - 4.46684i) q^{86} +(1.52848 + 4.17594i) q^{87} +(-0.561037 - 0.971744i) q^{88} -3.44366i q^{89} +(-6.04346 - 2.17492i) q^{90} +(-16.8272 + 4.54643i) q^{91} +(-1.40672 - 2.43650i) q^{92} +(6.79122 + 5.67761i) q^{93} +(-8.21989 + 14.2373i) q^{94} +(-3.39410 + 5.87876i) q^{95} +(10.4105 + 8.70345i) q^{96} +(-15.9996 + 9.23740i) q^{97} +35.0502i q^{98} +(-2.65081 + 0.477302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

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