LMFDB - Embedded newform 1110.2.l.b.43.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(43,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.l (of order $4$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.7
Character	$\chi$	$=$	1110.43
Dual form			1110.2.l.b.697.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-0.325656 + 2.21223i) q^{5} +(0.707107 + 0.707107i) q^{6} +(0.597471 - 0.597471i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-0.325656 + 2.21223i) q^{5} +(0.707107 + 0.707107i) q^{6} +(0.597471 - 0.597471i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(2.21223 + 0.325656i) q^{10} +6.22563i q^{11} +(0.707107 - 0.707107i) q^{12} -0.986429i q^{13} +(-0.597471 - 0.597471i) q^{14} +(-1.33401 - 1.79455i) q^{15} +1.00000 q^{16} -5.73489 q^{17} -1.00000 q^{18} +(1.99420 - 1.99420i) q^{19} +(0.325656 - 2.21223i) q^{20} +0.844952i q^{21} +6.22563 q^{22} -1.91811i q^{23} +(-0.707107 - 0.707107i) q^{24} +(-4.78790 - 1.44085i) q^{25} -0.986429 q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.597471 + 0.597471i) q^{28} +(-3.12397 - 3.12397i) q^{29} +(-1.79455 + 1.33401i) q^{30} +(-0.922513 + 0.922513i) q^{31} -1.00000i q^{32} +(-4.40219 - 4.40219i) q^{33} +5.73489i q^{34} +(1.12717 + 1.51631i) q^{35} +1.00000i q^{36} +(-6.02093 + 0.865086i) q^{37} +(-1.99420 - 1.99420i) q^{38} +(0.697511 + 0.697511i) q^{39} +(-2.21223 - 0.325656i) q^{40} -1.55336i q^{41} +0.844952 q^{42} -6.23715i q^{43} -6.22563i q^{44} +(2.21223 + 0.325656i) q^{45} -1.91811 q^{46} +(-2.10291 + 2.10291i) q^{47} +(-0.707107 + 0.707107i) q^{48} +6.28606i q^{49} +(-1.44085 + 4.78790i) q^{50} +(4.05518 - 4.05518i) q^{51} +0.986429i q^{52} +(9.01816 + 9.01816i) q^{53} +(0.707107 - 0.707107i) q^{54} +(-13.7725 - 2.02742i) q^{55} +(0.597471 + 0.597471i) q^{56} +2.82022i q^{57} +(-3.12397 + 3.12397i) q^{58} +(-5.56150 + 5.56150i) q^{59} +(1.33401 + 1.79455i) q^{60} +(-1.20352 + 1.20352i) q^{61} +(0.922513 + 0.922513i) q^{62} +(-0.597471 - 0.597471i) q^{63} -1.00000 q^{64} +(2.18221 + 0.321237i) q^{65} +(-4.40219 + 4.40219i) q^{66} +(-9.76587 - 9.76587i) q^{67} +5.73489 q^{68} +(1.35631 + 1.35631i) q^{69} +(1.51631 - 1.12717i) q^{70} -14.9453 q^{71} +1.00000 q^{72} +(-8.62767 + 8.62767i) q^{73} +(0.865086 + 6.02093i) q^{74} +(4.40439 - 2.36672i) q^{75} +(-1.99420 + 1.99420i) q^{76} +(3.71964 + 3.71964i) q^{77} +(0.697511 - 0.697511i) q^{78} +(-4.54031 + 4.54031i) q^{79} +(-0.325656 + 2.21223i) q^{80} -1.00000 q^{81} -1.55336 q^{82} +(-7.29893 - 7.29893i) q^{83} -0.844952i q^{84} +(1.86760 - 12.6869i) q^{85} -6.23715 q^{86} +4.41796 q^{87} -6.22563 q^{88} +(3.84900 + 3.84900i) q^{89} +(0.325656 - 2.21223i) q^{90} +(-0.589363 - 0.589363i) q^{91} +1.91811i q^{92} -1.30463i q^{93} +(2.10291 + 2.10291i) q^{94} +(3.76219 + 5.06103i) q^{95} +(0.707107 + 0.707107i) q^{96} +12.5351 q^{97} +6.28606 q^{98} +6.22563 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{4} - 4 q^{7}+O(q^{10}) $ 40 * q - 40 * q^4 - 4 * q^7	$ 40 q - 40 q^{4} - 4 q^{7} + 4 q^{14} + 40 q^{16} + 24 q^{17} - 40 q^{18} + 4 q^{19} + 8 q^{22} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 28 q^{31} - 4 q^{33} + 20 q^{35} + 20 q^{37} - 4 q^{38} + 4 q^{39} + 16 q^{42} - 16 q^{47} + 16 q^{51} + 20 q^{53} + 16 q^{55} - 4 q^{56} - 4 q^{59} - 8 q^{61} - 28 q^{62} + 4 q^{63} - 40 q^{64} - 4 q^{65} - 4 q^{66} + 16 q^{67} - 24 q^{68} - 8 q^{69} + 12 q^{70} + 40 q^{71} + 40 q^{72} + 8 q^{73} - 8 q^{74} + 16 q^{75} - 4 q^{76} - 24 q^{77} + 4 q^{78} - 12 q^{79} - 40 q^{81} - 24 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{88} + 12 q^{89} - 24 q^{91} + 16 q^{94} - 28 q^{95} + 40 q^{97} - 56 q^{98} + 8 q^{99}+O(q^{100}) $ 40 * q - 40 * q^4 - 4 * q^7 + 4 * q^14 + 40 * q^16 + 24 * q^17 - 40 * q^18 + 4 * q^19 + 8 * q^22 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 28 * q^31 - 4 * q^33 + 20 * q^35 + 20 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^42 - 16 * q^47 + 16 * q^51 + 20 * q^53 + 16 * q^55 - 4 * q^56 - 4 * q^59 - 8 * q^61 - 28 * q^62 + 4 * q^63 - 40 * q^64 - 4 * q^65 - 4 * q^66 + 16 * q^67 - 24 * q^68 - 8 * q^69 + 12 * q^70 + 40 * q^71 + 40 * q^72 + 8 * q^73 - 8 * q^74 + 16 * q^75 - 4 * q^76 - 24 * q^77 + 4 * q^78 - 12 * q^79 - 40 * q^81 - 24 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^88 + 12 * q^89 - 24 * q^91 + 16 * q^94 - 28 * q^95 + 40 * q^97 - 56 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−1.00000			−0.500000
$5$	−0.325656	+	2.21223i	−0.145638	+	0.989338i
$5$	−0.325656	+	2.21223i	−0.145638	+	0.989338i
$6$	0.707107	+	0.707107i	0.288675	+	0.288675i
$7$	0.597471	−	0.597471i	0.225823	−	0.225823i	−0.585122	−	0.810945i	$-0.698953\pi$
$7$	0.597471	−	0.597471i	0.225823	−	0.225823i	0.810945	+	0.585122i	$0.198953\pi$
$8$			1.00000i			0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	2.21223	+	0.325656i	0.699568	+	0.102981i
$11$			6.22563i			1.87710i	0.345144	+	0.938550i	$0.387830\pi$
$11$			6.22563i			1.87710i	−0.345144	+	0.938550i	$0.612170\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$		−	0.986429i		−	0.273586i	−0.990600	−	0.136793i	$-0.956320\pi$
$13$		−	0.986429i		−	0.273586i	0.990600	−	0.136793i	$-0.0436796\pi$
$14$	−0.597471	−	0.597471i	−0.159681	−	0.159681i
$15$	−1.33401	−	1.79455i	−0.344439	−	0.463352i
$16$	1.00000			0.250000
$17$	−5.73489			−1.39092			−0.695458	−	0.718567i	$-0.744798\pi$
$17$	−5.73489			−1.39092			−0.695458	+	0.718567i	$0.744798\pi$
$18$	−1.00000			−0.235702
$19$	1.99420	−	1.99420i	0.457500	−	0.457500i	−0.440334	−	0.897834i	$-0.645140\pi$
$19$	1.99420	−	1.99420i	0.457500	−	0.457500i	0.897834	+	0.440334i	$0.145140\pi$
$20$	0.325656	−	2.21223i	0.0728189	−	0.494669i
$21$			0.844952i			0.184384i
$22$	6.22563			1.32731
$23$		−	1.91811i		−	0.399954i	−0.979801	−	0.199977i	$-0.935913\pi$
$23$		−	1.91811i		−	0.399954i	0.979801	−	0.199977i	$-0.0640868\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$	−4.78790	−	1.44085i	−0.957579	−	0.288170i
$26$	−0.986429			−0.193455
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−0.597471	+	0.597471i	−0.112911	+	0.112911i
$29$	−3.12397	−	3.12397i	−0.580107	−	0.580107i	0.354826	−	0.934932i	$-0.384540\pi$
$29$	−3.12397	−	3.12397i	−0.580107	−	0.580107i	−0.934932	+	0.354826i	$0.884540\pi$
$30$	−1.79455	+	1.33401i	−0.327639	+	0.243555i
$31$	−0.922513	+	0.922513i	−0.165688	+	0.165688i	−0.785081	−	0.619393i	$-0.787379\pi$
$31$	−0.922513	+	0.922513i	−0.165688	+	0.165688i	0.619393	+	0.785081i	$0.287379\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−4.40219	−	4.40219i	−0.766323	−	0.766323i
$34$			5.73489i			0.983526i
$35$	1.12717	+	1.51631i	0.190527	+	0.256303i
$36$			1.00000i			0.166667i
$37$	−6.02093	+	0.865086i	−0.989835	+	0.142219i
$37$	−6.02093	+	0.865086i	−0.989835	+	0.142219i
$38$	−1.99420	−	1.99420i	−0.323501	−	0.323501i
$39$	0.697511	+	0.697511i	0.111691	+	0.111691i
$40$	−2.21223	−	0.325656i	−0.349784	−	0.0514907i
$41$		−	1.55336i		−	0.242594i	−0.992616	−	0.121297i	$-0.961295\pi$
$41$		−	1.55336i		−	0.242594i	0.992616	−	0.121297i	$-0.0387053\pi$
$42$	0.844952			0.130379
$43$		−	6.23715i		−	0.951157i	−0.879673	−	0.475578i	$-0.842239\pi$
$43$		−	6.23715i		−	0.951157i	0.879673	−	0.475578i	$-0.157761\pi$
$44$		−	6.22563i		−	0.938550i
$45$	2.21223	+	0.325656i	0.329779	+	0.0485459i
$46$	−1.91811			−0.282810
$47$	−2.10291	+	2.10291i	−0.306741	+	0.306741i	−0.843644	−	0.536903i	$-0.819594\pi$
$47$	−2.10291	+	2.10291i	−0.306741	+	0.306741i	0.536903	+	0.843644i	$0.319594\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$			6.28606i			0.898008i
$50$	−1.44085	+	4.78790i	−0.203767	+	0.677111i
$51$	4.05518	−	4.05518i	0.567839	−	0.567839i
$52$			0.986429i			0.136793i
$53$	9.01816	+	9.01816i	1.23874	+	1.23874i	0.960516	+	0.278223i	$0.0897454\pi$
$53$	9.01816	+	9.01816i	1.23874	+	1.23874i	0.278223	+	0.960516i	$0.410255\pi$
$54$	0.707107	−	0.707107i	0.0962250	−	0.0962250i
$55$	−13.7725	−	2.02742i	−1.85709	−	0.273377i
$56$	0.597471	+	0.597471i	0.0798404	+	0.0798404i
$57$			2.82022i			0.373547i
$58$	−3.12397	+	3.12397i	−0.410197	+	0.410197i
$59$	−5.56150	+	5.56150i	−0.724046	+	0.724046i	−0.969427	−	0.245381i	$-0.921087\pi$
$59$	−5.56150	+	5.56150i	−0.724046	+	0.724046i	0.245381	+	0.969427i	$0.421087\pi$
$60$	1.33401	+	1.79455i	0.172220	+	0.231676i
$61$	−1.20352	+	1.20352i	−0.154096	+	0.154096i	−0.779944	−	0.625849i	$-0.784753\pi$
$61$	−1.20352	+	1.20352i	−0.154096	+	0.154096i	0.625849	+	0.779944i	$0.284753\pi$
$62$	0.922513	+	0.922513i	0.117159	+	0.117159i
$63$	−0.597471	−	0.597471i	−0.0752743	−	0.0752743i
$64$	−1.00000			−0.125000
$65$	2.18221	+	0.321237i	0.270669	+	0.0398445i
$66$	−4.40219	+	4.40219i	−0.541872	+	0.541872i
$67$	−9.76587	−	9.76587i	−1.19309	−	1.19309i	−0.976195	−	0.216896i	$-0.930407\pi$
$67$	−9.76587	−	9.76587i	−1.19309	−	1.19309i	−0.216896	−	0.976195i	$-0.569593\pi$
$68$	5.73489			0.695458
$69$	1.35631	+	1.35631i	0.163281	+	0.163281i
$70$	1.51631	−	1.12717i	0.181234	−	0.134723i
$71$	−14.9453			−1.77368			−0.886842	−	0.462073i	$-0.847106\pi$
$71$	−14.9453			−1.77368			−0.886842	+	0.462073i	$0.847106\pi$
$72$	1.00000			0.117851
$73$	−8.62767	+	8.62767i	−1.00979	+	1.00979i	−0.00984027	+	0.999952i	$0.503132\pi$
$73$	−8.62767	+	8.62767i	−1.00979	+	1.00979i	−0.999952	+	0.00984027i	$0.996868\pi$
$74$	0.865086	+	6.02093i	0.100564	+	0.699919i
$75$	4.40439	−	2.36672i	0.508575	−	0.273285i
$76$	−1.99420	+	1.99420i	−0.228750	+	0.228750i
$77$	3.71964	+	3.71964i	0.423892	+	0.423892i
$78$	0.697511	−	0.697511i	0.0789776	−	0.0789776i
$79$	−4.54031	+	4.54031i	−0.510825	+	0.510825i	−0.914779	−	0.403954i	$-0.867635\pi$
$79$	−4.54031	+	4.54031i	−0.510825	+	0.510825i	0.403954	+	0.914779i	$0.367635\pi$
$80$	−0.325656	+	2.21223i	−0.0364095	+	0.247334i
$81$	−1.00000			−0.111111
$82$	−1.55336			−0.171540
$83$	−7.29893	−	7.29893i	−0.801161	−	0.801161i	0.182116	−	0.983277i	$-0.441705\pi$
$83$	−7.29893	−	7.29893i	−0.801161	−	0.801161i	−0.983277	+	0.182116i	$0.941705\pi$
$84$		−	0.844952i		−	0.0921918i
$85$	1.86760	−	12.6869i	0.202570	−	1.37609i
$86$	−6.23715			−0.672569
$87$	4.41796			0.473655
$88$	−6.22563			−0.663655
$89$	3.84900	+	3.84900i	0.407994	+	0.407994i	0.881038	−	0.473045i	$-0.156845\pi$
$89$	3.84900	+	3.84900i	0.407994	+	0.407994i	−0.473045	+	0.881038i	$0.656845\pi$
$90$	0.325656	−	2.21223i	0.0343272	−	0.233189i
$91$	−0.589363	−	0.589363i	−0.0617820	−	0.0617820i
$92$			1.91811i			0.199977i
$93$		−	1.30463i		−	0.135284i
$94$	2.10291	+	2.10291i	0.216899	+	0.216899i
$95$	3.76219	+	5.06103i	0.385993	+	0.519251i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	12.5351			1.27275			0.636374	−	0.771380i	$-0.280433\pi$
$97$	12.5351			1.27275			0.636374	+	0.771380i	$0.280433\pi$
$98$	6.28606			0.634988
$99$	6.22563			0.625700
$100$	4.78790	+	1.44085i	0.478790	+	0.144085i
$101$			9.83775i			0.978893i	0.872033	+	0.489447i	$0.162801\pi$
$101$			9.83775i			0.978893i	−0.872033	+	0.489447i	$0.837199\pi$
$102$	−4.05518	−	4.05518i	−0.401523	−	0.401523i
$103$	−11.7463			−1.15740			−0.578700	−	0.815540i	$-0.696440\pi$
$103$	−11.7463			−1.15740			−0.578700	+	0.815540i	$0.696440\pi$
$104$	0.986429			0.0967274
$105$	−1.86922	−	0.275164i	−0.182418	−	0.0268532i
$106$	9.01816	−	9.01816i	0.875921	−	0.875921i
$107$	−0.373231	+	0.373231i	−0.0360816	+	0.0360816i	−0.724917	−	0.688836i	$-0.758122\pi$
$107$	−0.373231	+	0.373231i	−0.0360816	+	0.0360816i	0.688836	+	0.724917i	$0.258122\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	7.16221	−	7.16221i	0.686015	−	0.686015i	−0.275333	−	0.961349i	$-0.588788\pi$
$109$	7.16221	−	7.16221i	0.686015	−	0.686015i	0.961349	+	0.275333i	$0.0887882\pi$
$110$	−2.02742	+	13.7725i	−0.193306	+	1.31316i
$111$	3.64573	−	4.86915i	0.346038	−	0.462159i
$112$	0.597471	−	0.597471i	0.0564557	−	0.0564557i
$113$	8.61878			0.810787			0.405393	−	0.914142i	$-0.367135\pi$
$113$	8.61878			0.810787			0.405393	+	0.914142i	$0.367135\pi$
$114$	2.82022			0.264138
$115$	4.24330	+	0.624645i	0.395690	+	0.0582485i
$116$	3.12397	+	3.12397i	0.290053	+	0.290053i
$117$	−0.986429			−0.0911954
$118$	5.56150	+	5.56150i	0.511978	+	0.511978i
$119$	−3.42643	+	3.42643i	−0.314101	+	0.314101i
$120$	1.79455	−	1.33401i	0.163820	−	0.121778i
$121$	−27.7585			−2.52350
$122$	1.20352	+	1.20352i	0.108962	+	0.108962i
$123$	1.09839	+	1.09839i	0.0990384	+	0.0990384i
$124$	0.922513	−	0.922513i	0.0828441	−	0.0828441i
$125$	4.74670	−	10.1227i	0.424557	−	0.905401i
$126$	−0.597471	+	0.597471i	−0.0532269	+	0.0532269i
$127$	6.23989	−	6.23989i	0.553701	−	0.553701i	−0.373806	−	0.927507i	$-0.621947\pi$
$127$	6.23989	−	6.23989i	0.553701	−	0.553701i	0.927507	+	0.373806i	$0.121947\pi$
$128$			1.00000i			0.0883883i
$129$	4.41033	+	4.41033i	0.388308	+	0.388308i
$130$	0.321237	−	2.18221i	0.0281743	−	0.191392i
$131$	13.4413	−	13.4413i	1.17437	−	1.17437i	0.193215	−	0.981156i	$-0.438109\pi$
$131$	13.4413	−	13.4413i	1.17437	−	1.17437i	0.981156	−	0.193215i	$-0.0618915\pi$
$132$	4.40219	+	4.40219i	0.383161	+	0.383161i
$133$		−	2.38295i		−	0.206628i
$134$	−9.76587	+	9.76587i	−0.843642	+	0.843642i
$135$	−1.79455	+	1.33401i	−0.154451	+	0.114813i
$136$		−	5.73489i		−	0.491763i
$137$	−2.43423	+	2.43423i	−0.207970	+	0.207970i	−0.803404	−	0.595434i	$-0.796980\pi$
$137$	−2.43423	+	2.43423i	−0.207970	+	0.207970i	0.595434	+	0.803404i	$0.296980\pi$
$138$	1.35631	−	1.35631i	0.115457	−	0.115457i
$139$	−0.295024			−0.0250236			−0.0125118	−	0.999922i	$-0.503983\pi$
$139$	−0.295024			−0.0250236			−0.0125118	+	0.999922i	$0.503983\pi$
$140$	−1.12717	−	1.51631i	−0.0952634	−	0.128152i
$141$		−	2.97397i		−	0.250453i
$142$			14.9453i			1.25418i
$143$	6.14115			0.513549
$144$		−	1.00000i		−	0.0833333i
$145$	7.92827	−	5.89359i	0.658407	−	0.489436i
$146$	8.62767	+	8.62767i	0.714031	+	0.714031i
$147$	−4.44491	−	4.44491i	−0.366610	−	0.366610i
$148$	6.02093	−	0.865086i	0.494918	−	0.0711096i
$149$			21.7666i			1.78319i	0.452834	+	0.891595i	$0.350413\pi$
$149$			21.7666i			1.78319i	−0.452834	+	0.891595i	$0.649587\pi$
$150$	−2.36672	−	4.40439i	−0.193242	−	0.359617i
$151$			15.4134i			1.25432i	0.778888	+	0.627162i	$0.215784\pi$
$151$			15.4134i			1.25432i	−0.778888	+	0.627162i	$0.784216\pi$
$152$	1.99420	+	1.99420i	0.161751	+	0.161751i
$153$			5.73489i			0.463639i
$154$	3.71964	−	3.71964i	0.299737	−	0.299737i
$155$	−1.74039	−	2.34123i	−0.139791	−	0.188052i
$156$	−0.697511	−	0.697511i	−0.0558456	−	0.0558456i
$157$	−2.42992	+	2.42992i	−0.193928	+	0.193928i	−0.797391	−	0.603463i	$-0.793787\pi$
$157$	−2.42992	+	2.42992i	−0.193928	+	0.193928i	0.603463	+	0.797391i	$0.293787\pi$
$158$	4.54031	+	4.54031i	0.361208	+	0.361208i
$159$	−12.7536			−1.01143
$160$	2.21223	+	0.325656i	0.174892	+	0.0257454i
$161$	−1.14602	−	1.14602i	−0.0903188	−	0.0903188i
$162$			1.00000i			0.0785674i
$163$	23.0110			1.80236			0.901180	−	0.433445i	$-0.142702\pi$
$163$	23.0110			1.80236			0.901180	+	0.433445i	$0.142702\pi$
$164$			1.55336i			0.121297i
$165$	11.1722	−	8.30504i	0.869758	−	0.646546i
$166$	−7.29893	+	7.29893i	−0.566507	+	0.566507i
$167$	0.763298			0.0590657			0.0295329	−	0.999564i	$-0.490598\pi$
$167$	0.763298			0.0590657			0.0295329	+	0.999564i	$0.490598\pi$
$168$	−0.844952			−0.0651894
$169$	12.0270			0.925151
$170$	−12.6869	−	1.86760i	−0.973040	−	0.143239i
$171$	−1.99420	−	1.99420i	−0.152500	−	0.152500i
$172$			6.23715i			0.475578i
$173$	7.46496	−	7.46496i	0.567550	−	0.567550i	−0.363891	−	0.931441i	$-0.618552\pi$
$173$	7.46496	−	7.46496i	0.567550	−	0.567550i	0.931441	+	0.363891i	$0.118552\pi$
$174$		−	4.41796i		−	0.334925i
$175$	−3.72150	+	1.99976i	−0.281319	+	0.151168i
$176$			6.22563i			0.469275i
$177$		−	7.86515i		−	0.591181i
$178$	3.84900	−	3.84900i	0.288495	−	0.288495i
$179$	5.31685	+	5.31685i	0.397400	+	0.397400i	0.877315	−	0.479915i	$-0.159333\pi$
$179$	5.31685	+	5.31685i	0.397400	+	0.397400i	−0.479915	+	0.877315i	$0.659333\pi$
$180$	−2.21223	−	0.325656i	−0.164890	−	0.0242730i
$181$	−12.3877			−0.920770			−0.460385	−	0.887719i	$-0.652289\pi$
$181$	−12.3877			−0.920770			−0.460385	+	0.887719i	$0.652289\pi$
$182$	−0.589363	+	0.589363i	−0.0436865	+	0.0436865i
$183$		−	1.70204i		−	0.125819i
$184$	1.91811			0.141405
$185$	0.0469870	−	13.6014i	0.00345455	−	0.999994i
$186$	−1.30463			−0.0956601
$187$		−	35.7033i		−	2.61089i
$188$	2.10291	−	2.10291i	0.153371	−	0.153371i
$189$	0.844952			0.0614612
$190$	5.06103	−	3.76219i	0.367166	−	0.272938i
$191$	−3.82822	−	3.82822i	−0.277000	−	0.277000i	0.554910	−	0.831910i	$-0.312753\pi$
$191$	−3.82822	−	3.82822i	−0.277000	−	0.277000i	−0.831910	+	0.554910i	$0.812753\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$		−	5.48394i		−	0.394743i	−0.980329	−	0.197371i	$-0.936760\pi$
$193$		−	5.48394i		−	0.394743i	0.980329	−	0.197371i	$-0.0632405\pi$
$194$		−	12.5351i		−	0.899969i
$195$	−1.77020	+	1.31590i	−0.126767	+	0.0942338i
$196$		−	6.28606i		−	0.449004i
$197$	3.31072	−	3.31072i	0.235879	−	0.235879i	−0.579262	−	0.815141i	$-0.696659\pi$
$197$	3.31072	−	3.31072i	0.235879	−	0.235879i	0.815141	+	0.579262i	$0.196659\pi$
$198$		−	6.22563i		−	0.442437i
$199$	6.97405	+	6.97405i	0.494377	+	0.494377i	0.909682	−	0.415305i	$-0.136325\pi$
$199$	6.97405	+	6.97405i	0.494377	+	0.494377i	−0.415305	+	0.909682i	$0.636325\pi$
$200$	1.44085	−	4.78790i	0.101884	−	0.338555i
$201$	13.8110			0.974154
$202$	9.83775			0.692182
$203$	−3.73296			−0.262003
$204$	−4.05518	+	4.05518i	−0.283919	+	0.283919i
$205$	3.43638	+	0.505860i	0.240007	+	0.0353308i
$206$			11.7463i			0.818406i
$207$	−1.91811			−0.133318
$208$		−	0.986429i		−	0.0683966i
$209$	12.4151	+	12.4151i	0.858773	+	0.858773i
$210$	−0.275164	+	1.86922i	−0.0189881	+	0.128989i
$211$	−4.37831			−0.301415			−0.150708	−	0.988578i	$-0.548155\pi$
$211$	−4.37831			−0.301415			−0.150708	+	0.988578i	$0.548155\pi$
$212$	−9.01816	−	9.01816i	−0.619370	−	0.619370i
$213$	10.5679	−	10.5679i	0.724103	−	0.724103i
$214$	0.373231	+	0.373231i	0.0255136	+	0.0255136i
$215$	13.7980	+	2.03117i	0.941015	+	0.138524i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$			1.10235i			0.0748323i
$218$	−7.16221	−	7.16221i	−0.485086	−	0.485086i
$219$		−	12.2014i		−	0.824492i
$220$	13.7725	+	2.02742i	0.928543	+	0.136688i
$221$			5.65707i			0.380535i
$222$	−4.86915	−	3.64573i	−0.326796	−	0.244686i
$223$	−19.9346	−	19.9346i	−1.33492	−	1.33492i	−0.900908	−	0.434010i	$-0.857098\pi$
$223$	−19.9346	−	19.9346i	−1.33492	−	1.33492i	−0.434010	−	0.900908i	$-0.642902\pi$
$224$	−0.597471	−	0.597471i	−0.0399202	−	0.0399202i
$225$	−1.44085	+	4.78790i	−0.0960567	+	0.319193i
$226$		−	8.61878i		−	0.573313i
$227$	−14.0813			−0.934611			−0.467306	−	0.884096i	$-0.654775\pi$
$227$	−14.0813			−0.934611			−0.467306	+	0.884096i	$0.654775\pi$
$228$		−	2.82022i		−	0.186774i
$229$		−	15.5420i		−	1.02704i	−0.858076	−	0.513522i	$-0.828340\pi$
$229$		−	15.5420i		−	1.02704i	0.858076	−	0.513522i	$-0.171660\pi$
$230$	0.624645	−	4.24330i	0.0411879	−	0.279795i
$231$	−5.26036			−0.346106
$232$	3.12397	−	3.12397i	0.205099	−	0.205099i
$233$	7.25032	−	7.25032i	0.474985	−	0.474985i	−0.428539	−	0.903523i	$-0.640971\pi$
$233$	7.25032	−	7.25032i	0.474985	−	0.474985i	0.903523	+	0.428539i	$0.140971\pi$
$234$			0.986429i			0.0644849i
$235$	−3.96729	−	5.33694i	−0.258798	−	0.348144i
$236$	5.56150	−	5.56150i	0.362023	−	0.362023i
$237$		−	6.42097i		−	0.417087i
$238$	3.42643	+	3.42643i	0.222103	+	0.222103i
$239$	−12.8280	+	12.8280i	−0.829777	+	0.829777i	−0.987486	−	0.157709i	$-0.949589\pi$
$239$	−12.8280	+	12.8280i	−0.829777	+	0.829777i	0.157709	+	0.987486i	$0.449589\pi$
$240$	−1.33401	−	1.79455i	−0.0861098	−	0.115838i
$241$	9.19108	+	9.19108i	0.592050	+	0.592050i	0.938185	−	0.346135i	$-0.112506\pi$
$241$	9.19108	+	9.19108i	0.592050	+	0.592050i	−0.346135	+	0.938185i	$0.612506\pi$
$242$			27.7585i			1.78438i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	1.20352	−	1.20352i	0.0770478	−	0.0770478i
$245$	−13.9062	−	2.04709i	−0.888434	−	0.130784i
$246$	1.09839	−	1.09839i	0.0700307	−	0.0700307i
$247$	−1.96713	−	1.96713i	−0.125166	−	0.125166i
$248$	−0.922513	−	0.922513i	−0.0585796	−	0.0585796i
$249$	10.3222			0.654146
$250$	−10.1227	−	4.74670i	−0.640215	−	0.300207i
$251$	−3.26175	+	3.26175i	−0.205880	+	0.205880i	−0.802514	−	0.596634i	$-0.796504\pi$
$251$	−3.26175	+	3.26175i	−0.205880	+	0.205880i	0.596634	+	0.802514i	$0.296504\pi$
$252$	0.597471	+	0.597471i	0.0376371	+	0.0376371i
$253$	11.9415			0.750754
$254$	−6.23989	−	6.23989i	−0.391526	−	0.391526i
$255$	7.65039	+	10.2916i	0.479086	+	0.644484i
$256$	1.00000			0.0625000
$257$	−12.9116			−0.805400			−0.402700	−	0.915332i	$-0.631928\pi$
$257$	−12.9116			−0.805400			−0.402700	+	0.915332i	$0.631928\pi$
$258$	4.41033	−	4.41033i	0.274575	−	0.274575i
$259$	−3.08047	+	4.11420i	−0.191411	+	0.255644i
$260$	−2.18221	−	0.321237i	−0.135335	−	0.0199223i
$261$	−3.12397	+	3.12397i	−0.193369	+	0.193369i
$262$	−13.4413	−	13.4413i	−0.830406	−	0.830406i
$263$	7.64722	−	7.64722i	0.471548	−	0.471548i	−0.430868	−	0.902415i	$-0.641792\pi$
$263$	7.64722	−	7.64722i	0.471548	−	0.471548i	0.902415	+	0.430868i	$0.141792\pi$
$264$	4.40219	−	4.40219i	0.270936	−	0.270936i
$265$	−22.8870	+	17.0134i	−1.40594	+	1.04512i
$266$	−2.38295			−0.146108
$267$	−5.44331			−0.333125
$268$	9.76587	+	9.76587i	0.596545	+	0.596545i
$269$			22.1242i			1.34893i	0.738305	+	0.674467i	$0.235627\pi$
$269$			22.1242i			1.34893i	−0.738305	+	0.674467i	$0.764373\pi$
$270$	1.33401	+	1.79455i	0.0811851	+	0.109213i
$271$	1.96662			0.119464			0.0597319	−	0.998214i	$-0.480975\pi$
$271$	1.96662			0.119464			0.0597319	+	0.998214i	$0.480975\pi$
$272$	−5.73489			−0.347729
$273$	0.833485			0.0504448
$274$	2.43423	+	2.43423i	0.147057	+	0.147057i
$275$	8.97021	−	29.8077i	0.540924	−	1.79747i
$276$	−1.35631	−	1.35631i	−0.0816403	−	0.0816403i
$277$		−	10.4985i		−	0.630796i	−0.948959	−	0.315398i	$-0.897862\pi$
$277$		−	10.4985i		−	0.630796i	0.948959	−	0.315398i	$-0.102138\pi$
$278$			0.295024i			0.0176944i
$279$	0.922513	+	0.922513i	0.0552294	+	0.0552294i
$280$	−1.51631	+	1.12717i	−0.0906169	+	0.0673614i
$281$	13.8482	+	13.8482i	0.826114	+	0.826114i	0.986977	−	0.160863i	$-0.0514276\pi$
$281$	13.8482	+	13.8482i	0.826114	+	0.826114i	−0.160863	+	0.986977i	$0.551428\pi$
$282$	−2.97397			−0.177097
$283$	−16.7535			−0.995893			−0.497947	−	0.867208i	$-0.665912\pi$
$283$	−16.7535			−0.995893			−0.497947	+	0.867208i	$0.665912\pi$
$284$	14.9453			0.886842
$285$	−6.23896	−	0.918421i	−0.369564	−	0.0544026i
$286$		−	6.14115i		−	0.363134i
$287$	−0.928086	−	0.928086i	−0.0547832	−	0.0547832i
$288$	−1.00000			−0.0589256
$289$	15.8890			0.934647
$290$	−5.89359	−	7.92827i	−0.346083	−	0.465564i
$291$	−8.86367	+	8.86367i	−0.519597	+	0.519597i
$292$	8.62767	−	8.62767i	0.504896	−	0.504896i
$293$	3.05021	+	3.05021i	0.178195	+	0.178195i	0.790569	−	0.612373i	$-0.209785\pi$
$293$	3.05021	+	3.05021i	0.178195	+	0.178195i	−0.612373	+	0.790569i	$0.709785\pi$
$294$	−4.44491	+	4.44491i	−0.259233	+	0.259233i
$295$	−10.4922	−	14.1144i	−0.610878	−	0.821774i
$296$	−0.865086	−	6.02093i	−0.0502821	−	0.349960i
$297$	−4.40219	+	4.40219i	−0.255441	+	0.255441i
$298$	21.7666			1.26091
$299$	−1.89208			−0.109422
$300$	−4.40439	+	2.36672i	−0.254288	+	0.136643i
$301$	−3.72652	−	3.72652i	−0.214793	−	0.214793i
$302$	15.4134			0.886942
$303$	−6.95634	−	6.95634i	−0.399631	−	0.399631i
$304$	1.99420	−	1.99420i	0.114375	−	0.114375i
$305$	−2.27054	−	3.05441i	−0.130010	−	0.174895i
$306$	5.73489			0.327842
$307$	23.3606	+	23.3606i	1.33326	+	1.33326i	0.902438	+	0.430819i	$0.141775\pi$
$307$	23.3606	+	23.3606i	1.33326	+	1.33326i	0.430819	+	0.902438i	$0.358225\pi$
$308$	−3.71964	−	3.71964i	−0.211946	−	0.211946i
$309$	8.30591	−	8.30591i	0.472507	−	0.472507i
$310$	−2.34123	+	1.74039i	−0.132973	+	0.0988473i
$311$	−18.5458	+	18.5458i	−1.05163	+	1.05163i	−0.0530421	+	0.998592i	$0.516892\pi$
$311$	−18.5458	+	18.5458i	−1.05163	+	1.05163i	−0.998592	+	0.0530421i	$0.983108\pi$
$312$	−0.697511	+	0.697511i	−0.0394888	+	0.0394888i
$313$			33.3726i			1.88633i	0.332320	+	0.943167i	$0.392169\pi$
$313$			33.3726i			1.88633i	−0.332320	+	0.943167i	$0.607831\pi$
$314$	2.42992	+	2.42992i	0.137128	+	0.137128i
$315$	1.51631	−	1.12717i	0.0854345	−	0.0635089i
$316$	4.54031	−	4.54031i	0.255412	−	0.255412i
$317$	18.7269	+	18.7269i	1.05181	+	1.05181i	0.998582	+	0.0532273i	$0.0169508\pi$
$317$	18.7269	+	18.7269i	1.05181	+	1.05181i	0.0532273	+	0.998582i	$0.483049\pi$
$318$			12.7536i			0.715187i
$319$	19.4487	−	19.4487i	1.08892	−	1.08892i
$320$	0.325656	−	2.21223i	0.0182047	−	0.123667i
$321$		−	0.527829i		−	0.0294605i
$322$	−1.14602	+	1.14602i	−0.0638650	+	0.0638650i
$323$	−11.4365	+	11.4365i	−0.636344	+	0.636344i
$324$	1.00000			0.0555556
$325$	−1.42130	+	4.72292i	−0.0788394	+	0.261981i
$326$		−	23.0110i		−	1.27446i
$327$			10.1289i			0.560129i
$328$	1.55336			0.0857698
$329$			2.51286i			0.138538i
$330$	−8.30504	−	11.1722i	−0.457177	−	0.615011i
$331$	20.7521	+	20.7521i	1.14064	+	1.14064i	0.988334	+	0.152304i	$0.0486692\pi$
$331$	20.7521	+	20.7521i	1.14064	+	1.14064i	0.152304	+	0.988334i	$0.451331\pi$
$332$	7.29893	+	7.29893i	0.400581	+	0.400581i
$333$	0.865086	+	6.02093i	0.0474064	+	0.329945i
$334$		−	0.763298i		−	0.0417658i
$335$	24.7846	−	18.4240i	1.35413	−	1.00661i
$336$			0.844952i			0.0460959i
$337$	−14.7056	−	14.7056i	−0.801067	−	0.801067i	0.182196	−	0.983262i	$-0.441680\pi$
$337$	−14.7056	−	14.7056i	−0.801067	−	0.801067i	−0.983262	+	0.182196i	$0.941680\pi$
$338$		−	12.0270i		−	0.654180i
$339$	−6.09440	+	6.09440i	−0.331002	+	0.331002i
$340$	−1.86760	+	12.6869i	−0.101285	+	0.688043i
$341$	−5.74323	−	5.74323i	−0.311013	−	0.311013i
$342$	−1.99420	+	1.99420i	−0.107834	+	0.107834i
$343$	7.93803	+	7.93803i	0.428614	+	0.428614i
$344$	6.23715			0.336285
$345$	−3.44216	+	2.55878i	−0.185320	+	0.137760i
$346$	−7.46496	−	7.46496i	−0.401319	−	0.401319i
$347$		−	17.2146i		−	0.924127i	−0.886847	−	0.462063i	$-0.847109\pi$
$347$		−	17.2146i		−	0.924127i	0.886847	−	0.462063i	$-0.152891\pi$
$348$	−4.41796			−0.236827
$349$		−	28.4058i		−	1.52053i	−0.649616	−	0.760263i	$-0.725070\pi$
$349$		−	28.4058i		−	1.52053i	0.649616	−	0.760263i	$-0.274930\pi$
$350$	1.99976	+	3.72150i	0.106892	+	0.198922i
$351$	0.697511	−	0.697511i	0.0372304	−	0.0372304i
$352$	6.22563			0.331827
$353$	−12.3989			−0.659929			−0.329965	−	0.943993i	$-0.607037\pi$
$353$	−12.3989			−0.659929			−0.329965	+	0.943993i	$0.607037\pi$
$354$	−7.86515			−0.418028
$355$	4.86703	−	33.0624i	0.258315	−	1.75477i
$356$	−3.84900	−	3.84900i	−0.203997	−	0.203997i
$357$		−	4.84571i		−	0.256462i
$358$	5.31685	−	5.31685i	0.281004	−	0.281004i
$359$			6.27293i			0.331072i	0.986204	+	0.165536i	$0.0529355\pi$
$359$			6.27293i			0.331072i	−0.986204	+	0.165536i	$0.947065\pi$
$360$	−0.325656	+	2.21223i	−0.0171636	+	0.116595i
$361$			11.0464i			0.581388i
$362$			12.3877i			0.651082i
$363$	19.6282	−	19.6282i	1.03022	−	1.03022i
$364$	0.589363	+	0.589363i	0.0308910	+	0.0308910i
$365$	−16.2767	−	21.8960i	−0.851962	−	1.14609i
$366$	−1.70204			−0.0889671
$367$	−0.228414	+	0.228414i	−0.0119231	+	0.0119231i	−0.713043	−	0.701120i	$-0.752684\pi$
$367$	−0.228414	+	0.228414i	−0.0119231	+	0.0119231i	0.701120	+	0.713043i	$0.252684\pi$
$368$		−	1.91811i		−	0.0999886i
$369$	−1.55336			−0.0808645
$370$	−13.6014	−	0.0469870i	−0.707103	−	0.00244274i
$371$	10.7762			0.559471
$372$			1.30463i			0.0676419i
$373$	−13.8845	+	13.8845i	−0.718910	+	0.718910i	−0.968382	−	0.249472i	$-0.919743\pi$
$373$	−13.8845	+	13.8845i	−0.718910	+	0.718910i	0.249472	+	0.968382i	$0.419743\pi$
$374$	−35.7033			−1.84618
$375$	3.80140	+	10.5142i	0.196304	+	0.542953i
$376$	−2.10291	−	2.10291i	−0.108449	−	0.108449i
$377$	−3.08158	+	3.08158i	−0.158709	+	0.158709i
$378$		−	0.844952i		−	0.0434596i
$379$			0.247309i			0.0127034i	0.999980	+	0.00635171i	$0.00202183\pi$
$379$			0.247309i			0.0127034i	−0.999980	+	0.00635171i	$0.997978\pi$
$380$	−3.76219	−	5.06103i	−0.192996	−	0.259626i
$381$			8.82454i			0.452095i
$382$	−3.82822	+	3.82822i	−0.195869	+	0.195869i
$383$		−	7.97917i		−	0.407716i	−0.979000	−	0.203858i	$-0.934652\pi$
$383$		−	7.97917i		−	0.407716i	0.979000	−	0.203858i	$-0.0653481\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	−9.44000	+	7.01736i	−0.481107	+	0.357638i
$386$	−5.48394			−0.279125
$387$	−6.23715			−0.317052
$388$	−12.5351			−0.636374
$389$	−0.310092	+	0.310092i	−0.0157223	+	0.0157223i	−0.714924	−	0.699202i	$-0.753539\pi$
$389$	−0.310092	+	0.310092i	−0.0157223	+	0.0157223i	0.699202	+	0.714924i	$0.253539\pi$
$390$	1.31590	+	1.77020i	0.0666334	+	0.0896376i
$391$			11.0002i			0.556303i
$392$	−6.28606			−0.317494
$393$			19.0089i			0.958870i
$394$	−3.31072	−	3.31072i	−0.166791	−	0.166791i
$395$	−8.56561	−	11.5228i	−0.430983	−	0.579774i
$396$	−6.22563			−0.312850
$397$	18.6543	+	18.6543i	0.936233	+	0.936233i	0.998085	−	0.0618525i	$-0.0197008\pi$
$397$	18.6543	+	18.6543i	0.936233	+	0.936233i	−0.0618525	+	0.998085i	$0.519701\pi$
$398$	6.97405	−	6.97405i	0.349578	−	0.349578i
$399$	1.68500	+	1.68500i	0.0843554	+	0.0843554i
$400$	−4.78790	−	1.44085i	−0.239395	−	0.0720425i
$401$	−21.5690	+	21.5690i	−1.07710	+	1.07710i	−0.0803350	+	0.996768i	$0.525599\pi$
$401$	−21.5690	+	21.5690i	−1.07710	+	1.07710i	−0.996768	+	0.0803350i	$0.974401\pi$
$402$		−	13.8110i		−	0.688831i
$403$	0.909994	+	0.909994i	0.0453300	+	0.0453300i
$404$		−	9.83775i		−	0.489447i
$405$	0.325656	−	2.21223i	0.0161820	−	0.109926i
$406$			3.73296i			0.185264i
$407$	−5.38571	−	37.4841i	−0.266960	−	1.85802i
$408$	4.05518	+	4.05518i	0.200761	+	0.200761i
$409$	22.0875	+	22.0875i	1.09216	+	1.09216i	0.995298	+	0.0968567i	$0.0308789\pi$
$409$	22.0875	+	22.0875i	1.09216	+	1.09216i	0.0968567	+	0.995298i	$0.469121\pi$
$410$	0.505860	−	3.43638i	0.0249826	−	0.169711i
$411$		−	3.44252i		−	0.169807i
$412$	11.7463			0.578700
$413$			6.64567i			0.327012i
$414$			1.91811i			0.0942701i
$415$	18.5238	−	13.7699i	0.909299	−	0.675940i
$416$	−0.986429			−0.0483637
$417$	0.208614	−	0.208614i	0.0102159	−	0.0102159i
$418$	12.4151	−	12.4151i	0.607244	−	0.607244i
$419$		−	13.1035i		−	0.640150i	−0.947392	−	0.320075i	$-0.896292\pi$
$419$		−	13.1035i		−	0.640150i	0.947392	−	0.320075i	$-0.103708\pi$
$420$	1.86922	+	0.275164i	0.0912088	+	0.0134266i
$421$	6.69042	−	6.69042i	0.326071	−	0.326071i	−0.525019	−	0.851090i	$-0.675942\pi$
$421$	6.69042	−	6.69042i	0.326071	−	0.326071i	0.851090	+	0.525019i	$0.175942\pi$
$422$			4.37831i			0.213133i
$423$	2.10291	+	2.10291i	0.102247	+	0.102247i
$424$	−9.01816	+	9.01816i	−0.437961	+	0.437961i
$425$	27.4581	+	8.26312i	1.33191	+	0.400820i
$426$	−10.5679	−	10.5679i	−0.512018	−	0.512018i
$427$			1.43814i			0.0695966i
$428$	0.373231	−	0.373231i	0.0180408	−	0.0180408i
$429$	−4.34245	+	4.34245i	−0.209655	+	0.209655i
$430$	2.03117	−	13.7980i	0.0979515	−	0.665398i
$431$	7.79285	−	7.79285i	0.375369	−	0.375369i	−0.494059	−	0.869428i	$-0.664488\pi$
$431$	7.79285	−	7.79285i	0.375369	−	0.375369i	0.869428	+	0.494059i	$0.164488\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	−1.28687	−	1.28687i	−0.0618431	−	0.0618431i	0.675509	−	0.737352i	$-0.263924\pi$
$433$	−1.28687	−	1.28687i	−0.0618431	−	0.0618431i	−0.737352	+	0.675509i	$0.763924\pi$
$434$	1.10235			0.0529145
$435$	−1.43874	+	9.77353i	−0.0689821	+	0.468605i
$436$	−7.16221	+	7.16221i	−0.343008	+	0.343008i
$437$	−3.82509	−	3.82509i	−0.182979	−	0.182979i
$438$	−12.2014			−0.583004
$439$	5.61954	+	5.61954i	0.268206	+	0.268206i	0.828377	−	0.560171i	$-0.189265\pi$
$439$	5.61954	+	5.61954i	0.268206	+	0.268206i	−0.560171	+	0.828377i	$0.689265\pi$
$440$	2.02742	−	13.7725i	0.0966532	−	0.656579i
$441$	6.28606			0.299336
$442$	5.65707			0.269079
$443$	14.2078	−	14.2078i	0.675034	−	0.675034i	−0.283838	−	0.958872i	$-0.591608\pi$
$443$	14.2078	−	14.2078i	0.675034	−	0.675034i	0.958872	+	0.283838i	$0.0916079\pi$
$444$	−3.64573	+	4.86915i	−0.173019	+	0.231080i
$445$	−9.76832	+	7.26142i	−0.463063	+	0.344224i
$446$	−19.9346	+	19.9346i	−0.943930	+	0.943930i
$447$	−15.3913	−	15.3913i	−0.727984	−	0.727984i
$448$	−0.597471	+	0.597471i	−0.0282279	+	0.0282279i
$449$	−5.85112	+	5.85112i	−0.276132	+	0.276132i	−0.831563	−	0.555431i	$-0.812553\pi$
$449$	−5.85112	+	5.85112i	−0.276132	+	0.276132i	0.555431	+	0.831563i	$0.312553\pi$
$450$	4.78790	+	1.44085i	0.225704	+	0.0679223i
$451$	9.67063			0.455372
$452$	−8.61878			−0.405393
$453$	−10.8989	−	10.8989i	−0.512076	−	0.512076i
$454$			14.0813i			0.660870i
$455$	1.49573	−	1.11188i	0.0701211	−	0.0521255i
$456$	−2.82022			−0.132069
$457$	−0.0348084			−0.00162827			−0.000814134	−	1.00000i	$-0.500259\pi$
$457$	−0.0348084			−0.00162827			−0.000814134		1.00000i	$0.500259\pi$
$458$	−15.5420			−0.726230
$459$	−4.05518	−	4.05518i	−0.189280	−	0.189280i
$460$	−4.24330	−	0.624645i	−0.197845	−	0.0291242i
$461$	−0.163914	−	0.163914i	−0.00763424	−	0.00763424i	0.703279	−	0.710914i	$-0.251718\pi$
$461$	−0.163914	−	0.163914i	−0.00763424	−	0.00763424i	−0.710914	+	0.703279i	$0.751718\pi$
$462$			5.26036i			0.244734i
$463$			24.0434i			1.11739i	0.829373	+	0.558695i	$0.188698\pi$
$463$			24.0434i			1.11739i	−0.829373	+	0.558695i	$0.811302\pi$
$464$	−3.12397	−	3.12397i	−0.145027	−	0.145027i
$465$	2.88614	+	0.424861i	0.133841	+	0.0197024i
$466$	−7.25032	−	7.25032i	−0.335865	−	0.335865i
$467$	−1.37090			−0.0634376			−0.0317188	−	0.999497i	$-0.510098\pi$
$467$	−1.37090			−0.0634376			−0.0317188	+	0.999497i	$0.510098\pi$
$468$	0.986429			0.0455977
$469$	−11.6696			−0.538854
$470$	−5.33694	+	3.96729i	−0.246175	+	0.182998i
$471$		−	3.43642i		−	0.158342i
$472$	−5.56150	−	5.56150i	−0.255989	−	0.255989i
$473$	38.8302			1.78542
$474$	−6.42097			−0.294925
$475$	−12.4213	+	6.67466i	−0.569930	+	0.306255i
$476$	3.42643	−	3.42643i	0.157050	−	0.157050i
$477$	9.01816	−	9.01816i	0.412913	−	0.412913i
$478$	12.8280	+	12.8280i	0.586741	+	0.586741i
$479$	18.7408	−	18.7408i	0.856290	−	0.856290i	−0.134609	−	0.990899i	$-0.542978\pi$
$479$	18.7408	−	18.7408i	0.856290	−	0.856290i	0.990899	+	0.134609i	$0.0429779\pi$
$480$	−1.79455	+	1.33401i	−0.0819098	+	0.0608888i
$481$	0.853346	+	5.93922i	0.0389092	+	0.270805i
$482$	9.19108	−	9.19108i	0.418642	−	0.418642i
$483$	1.62071			0.0737450
$484$	27.7585			1.26175
$485$	−4.08214	+	27.7305i	−0.185360	+	1.25918i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	23.7276			1.07520			0.537599	−	0.843201i	$-0.319331\pi$
$487$	23.7276			1.07520			0.537599	+	0.843201i	$0.319331\pi$
$488$	−1.20352	−	1.20352i	−0.0544810	−	0.0544810i
$489$	−16.2712	+	16.2712i	−0.735810	+	0.735810i
$490$	−2.04709	+	13.9062i	−0.0924782	+	0.628217i
$491$	−2.30518			−0.104031			−0.0520156	−	0.998646i	$-0.516565\pi$
$491$	−2.30518			−0.104031			−0.0520156	+	0.998646i	$0.516565\pi$
$492$	−1.09839	−	1.09839i	−0.0495192	−	0.0495192i
$493$	17.9156	+	17.9156i	0.806879	+	0.806879i
$494$	−1.96713	+	1.96713i	−0.0885055	+	0.0885055i
$495$	−2.02742	+	13.7725i	−0.0911255	+	0.619029i
$496$	−0.922513	+	0.922513i	−0.0414220	+	0.0414220i
$497$	−8.92940	+	8.92940i	−0.400538	+	0.400538i
$498$		−	10.3222i		−	0.462551i
$499$	−7.87010	−	7.87010i	−0.352314	−	0.352314i	0.508656	−	0.860970i	$-0.330143\pi$
$499$	−7.87010	−	7.87010i	−0.352314	−	0.352314i	−0.860970	+	0.508656i	$0.830143\pi$
$500$	−4.74670	+	10.1227i	−0.212279	+	0.452701i
$501$	−0.539733	+	0.539733i	−0.0241135	+	0.0241135i
$502$	3.26175	+	3.26175i	0.145579	+	0.145579i
$503$			25.8165i			1.15110i	0.817766	+	0.575551i	$0.195212\pi$
$503$			25.8165i			1.15110i	−0.817766	+	0.575551i	$0.804788\pi$
$504$	0.597471	−	0.597471i	0.0266135	−	0.0266135i
$505$	−21.7633	−	3.20372i	−0.968456	−	0.142564i
$506$		−	11.9415i		−	0.530863i
$507$	−8.50434	+	8.50434i	−0.377691	+	0.377691i
$508$	−6.23989	+	6.23989i	−0.276850	+	0.276850i
$509$	3.51184			0.155660			0.0778299	−	0.996967i	$-0.475201\pi$
$509$	3.51184			0.155660			0.0778299	+	0.996967i	$0.475201\pi$
$510$	10.2916	−	7.65039i	0.455719	−	0.338765i
$511$			10.3096i			0.456068i
$512$		−	1.00000i		−	0.0441942i
$513$	2.82022			0.124516
$514$			12.9116i			0.569504i
$515$	3.82527	−	25.9856i	0.168561	−	1.14506i
$516$	−4.41033	−	4.41033i	−0.194154	−	0.194154i
$517$	−13.0920	−	13.0920i	−0.575784	−	0.575784i
$518$	4.11420	+	3.08047i	0.180767	+	0.135348i
$519$			10.5570i			0.463403i
$520$	−0.321237	+	2.18221i	−0.0140872	+	0.0956960i
$521$			44.1201i			1.93294i	0.256786	+	0.966468i	$0.417336\pi$
$521$			44.1201i			1.93294i	−0.256786	+	0.966468i	$0.582664\pi$
$522$	3.12397	+	3.12397i	0.136732	+	0.136732i
$523$			30.8971i			1.35104i	0.737343	+	0.675519i	$0.236080\pi$
$523$			30.8971i			1.35104i	−0.737343	+	0.675519i	$0.763920\pi$
$524$	−13.4413	+	13.4413i	−0.587186	+	0.587186i
$525$	1.21745	−	4.04554i	0.0531338	−	0.176562i
$526$	−7.64722	−	7.64722i	−0.333434	−	0.333434i
$527$	5.29051	−	5.29051i	0.230458	−	0.230458i
$528$	−4.40219	−	4.40219i	−0.191581	−	0.191581i
$529$	19.3208			0.840037
$530$	17.0134	+	22.8870i	0.739015	+	0.994149i
$531$	5.56150	+	5.56150i	0.241349	+	0.241349i
$532$			2.38295i			0.103314i
$533$	−1.53228			−0.0663703
$534$			5.44331i			0.235555i
$535$	−0.704127	−	0.947217i	−0.0304421	−	0.0409518i
$536$	9.76587	−	9.76587i	0.421821	−	0.421821i
$537$	−7.51916			−0.324476
$538$	22.1242			0.953841
$539$	−39.1347			−1.68565
$540$	1.79455	−	1.33401i	0.0772253	−	0.0574065i
$541$	−27.3608	−	27.3608i	−1.17633	−	1.17633i	−0.980672	−	0.195661i	$-0.937315\pi$
$541$	−27.3608	−	27.3608i	−1.17633	−	1.17633i	−0.195661	−	0.980672i	$-0.562685\pi$
$542$		−	1.96662i		−	0.0844736i
$543$	8.75942	−	8.75942i	0.375903	−	0.375903i
$544$			5.73489i			0.245881i
$545$	13.5120	+	18.1769i	0.578791	+	0.778611i
$546$		−	0.833485i		−	0.0356699i
$547$		−	21.4614i		−	0.917621i	−0.888534	−	0.458811i	$-0.848276\pi$
$547$		−	21.4614i		−	0.917621i	0.888534	−	0.458811i	$-0.151724\pi$
$548$	2.43423	−	2.43423i	0.103985	−	0.103985i
$549$	1.20352	+	1.20352i	0.0513652	+	0.0513652i
$550$	−29.8077	−	8.97021i	−1.27100	−	0.382491i
$551$	−12.4596			−0.530797
$552$	−1.35631	+	1.35631i	−0.0577284	+	0.0577284i
$553$			5.42541i			0.230712i
$554$	−10.4985			−0.446040
$555$	9.58441	+	9.65086i	0.406836	+	0.409656i
$556$	0.295024			0.0125118
$557$			0.327825i			0.0138904i	0.999976	+	0.00694520i	$0.00221074\pi$
$557$			0.327825i			0.0138904i	−0.999976	+	0.00694520i	$0.997789\pi$
$558$	0.922513	−	0.922513i	0.0390531	−	0.0390531i
$559$	−6.15251			−0.260223
$560$	1.12717	+	1.51631i	0.0476317	+	0.0640759i
$561$	25.2461	+	25.2461i	1.06589	+	1.06589i
$562$	13.8482	−	13.8482i	0.584151	−	0.584151i
$563$			26.8738i			1.13260i	0.824200	+	0.566299i	$0.191625\pi$
$563$			26.8738i			1.13260i	−0.824200	+	0.566299i	$0.808375\pi$
$564$			2.97397i			0.125227i
$565$	−2.80676	+	19.0667i	−0.118081	+	0.802142i
$566$			16.7535i			0.704203i
$567$	−0.597471	+	0.597471i	−0.0250914	+	0.0250914i
$568$		−	14.9453i		−	0.627092i
$569$	−11.2972	−	11.2972i	−0.473604	−	0.473604i	0.429475	−	0.903079i	$-0.358699\pi$
$569$	−11.2972	−	11.2972i	−0.473604	−	0.473604i	−0.903079	+	0.429475i	$0.858699\pi$
$570$	−0.918421	+	6.23896i	−0.0384684	+	0.261321i
$571$	−22.8094			−0.954544			−0.477272	−	0.878756i	$-0.658374\pi$
$571$	−22.8094			−0.954544			−0.477272	+	0.878756i	$0.658374\pi$
$572$	−6.14115			−0.256774
$573$	5.41392			0.226170
$574$	−0.928086	+	0.928086i	−0.0387375	+	0.0387375i
$575$	−2.76371	+	9.18373i	−0.115255	+	0.382988i
$576$			1.00000i			0.0416667i
$577$	−28.9467			−1.20507			−0.602534	−	0.798093i	$-0.705842\pi$
$577$	−28.9467			−1.20507			−0.602534	+	0.798093i	$0.705842\pi$
$578$		−	15.8890i		−	0.660895i
$579$	3.87773	+	3.87773i	0.161153	+	0.161153i
$580$	−7.92827	+	5.89359i	−0.329203	+	0.244718i
$581$	−8.72179			−0.361841
$582$	8.86367	+	8.86367i	0.367411	+	0.367411i
$583$	−56.1438	+	56.1438i	−2.32524	+	2.32524i
$584$	−8.62767	−	8.62767i	−0.357015	−	0.357015i
$585$	0.321237	−	2.18221i	0.0132815	−	0.0902231i
$586$	3.05021	−	3.05021i	0.126003	−	0.126003i
$587$			21.1277i			0.872034i	0.899938	+	0.436017i	$0.143611\pi$
$587$			21.1277i			0.872034i	−0.899938	+	0.436017i	$0.856389\pi$
$588$	4.44491	+	4.44491i	0.183305	+	0.183305i
$589$			3.67934i			0.151605i
$590$	−14.1144	+	10.4922i	−0.581082	+	0.431956i
$591$			4.68206i			0.192594i
$592$	−6.02093	+	0.865086i	−0.247459	+	0.0355548i
$593$	1.60032	+	1.60032i	0.0657171	+	0.0657171i	0.739201	−	0.673484i	$-0.235203\pi$
$593$	1.60032	+	1.60032i	0.0657171	+	0.0657171i	−0.673484	+	0.739201i	$0.735203\pi$
$594$	4.40219	+	4.40219i	0.180624	+	0.180624i
$595$	−6.46421	−	8.69588i	−0.265007	−	0.356496i
$596$		−	21.7666i		−	0.891595i
$597$	−9.86280			−0.403658
$598$			1.89208i			0.0773730i
$599$		−	30.6306i		−	1.25153i	−0.780011	−	0.625765i	$-0.784787\pi$
$599$		−	30.6306i		−	1.25153i	0.780011	−	0.625765i	$-0.215213\pi$
$600$	2.36672	+	4.40439i	0.0966209	+	0.179808i
$601$	11.2697			0.459700			0.229850	−	0.973226i	$-0.426176\pi$
$601$	11.2697			0.459700			0.229850	+	0.973226i	$0.426176\pi$
$602$	−3.72652	+	3.72652i	−0.151881	+	0.151881i
$603$	−9.76587	+	9.76587i	−0.397697	+	0.397697i
$604$		−	15.4134i		−	0.627162i
$605$	9.03973	−	61.4081i	0.367517	−	2.49660i
$606$	−6.95634	+	6.95634i	−0.282582	+	0.282582i
$607$			7.13929i			0.289775i	0.989448	+	0.144887i	$0.0462820\pi$
$607$			7.13929i			0.289775i	−0.989448	+	0.144887i	$0.953718\pi$
$608$	−1.99420	−	1.99420i	−0.0808753	−	0.0808753i
$609$	2.63960	−	2.63960i	0.106962	−	0.106962i
$610$	−3.05441	+	2.27054i	−0.123669	+	0.0919313i
$611$	2.07437	+	2.07437i	0.0839202	+	0.0839202i
$612$		−	5.73489i		−	0.231819i
$613$	4.20436	−	4.20436i	0.169812	−	0.169812i	−0.617084	−	0.786897i	$-0.711686\pi$
$613$	4.20436	−	4.20436i	0.169812	−	0.169812i	0.786897	+	0.617084i	$0.211686\pi$
$614$	23.3606	−	23.3606i	0.942755	−	0.942755i
$615$	−2.78758	+	2.07219i	−0.112406	+	0.0835587i
$616$	−3.71964	+	3.71964i	−0.149868	+	0.149868i
$617$	20.2638	+	20.2638i	0.815792	+	0.815792i	0.985495	−	0.169703i	$-0.0542810\pi$
$617$	20.2638	+	20.2638i	0.815792	+	0.815792i	−0.169703	+	0.985495i	$0.554281\pi$
$618$	−8.30591	−	8.30591i	−0.334113	−	0.334113i
$619$	−15.2874			−0.614452			−0.307226	−	0.951637i	$-0.599401\pi$
$619$	−15.2874			−0.614452			−0.307226	+	0.951637i	$0.599401\pi$
$620$	1.74039	+	2.34123i	0.0698956	+	0.0940260i
$621$	1.35631	−	1.35631i	0.0544269	−	0.0544269i
$622$	18.5458	+	18.5458i	0.743618	+	0.743618i
$623$	4.59934			0.184268
$624$	0.697511	+	0.697511i	0.0279228	+	0.0279228i
$625$	20.8479	+	13.7973i	0.833916	+	0.551891i
$626$	33.3726			1.33384
$627$	−17.5576			−0.701185
$628$	2.42992	−	2.42992i	0.0969642	−	0.0969642i
$629$	34.5294	−	4.96117i	1.37678	−	0.197815i
$630$	−1.12717	−	1.51631i	−0.0449076	−	0.0604113i
$631$	14.5347	−	14.5347i	0.578616	−	0.578616i	−0.355906	−	0.934522i	$-0.615828\pi$
$631$	14.5347	−	14.5347i	0.578616	−	0.578616i	0.934522	+	0.355906i	$0.115828\pi$
$632$	−4.54031	−	4.54031i	−0.180604	−	0.180604i
$633$	3.09593	−	3.09593i	0.123052	−	0.123052i
$634$	18.7269	−	18.7269i	0.743742	−	0.743742i
$635$	11.7720	+	15.8361i	0.467157	+	0.628437i
$636$	12.7536			0.505713
$637$	6.20075			0.245683
$638$	−19.4487	−	19.4487i	−0.769981	−	0.769981i
$639$			14.9453i			0.591228i
$640$	−2.21223	−	0.325656i	−0.0874459	−	0.0128727i
$641$	−10.5777			−0.417793			−0.208897	−	0.977938i	$-0.566987\pi$
$641$	−10.5777			−0.417793			−0.208897	+	0.977938i	$0.566987\pi$
$642$	−0.527829			−0.0208317
$643$	−30.1992			−1.19094			−0.595470	−	0.803378i	$-0.703034\pi$
$643$	−30.1992			−1.19094			−0.595470	+	0.803378i	$0.703034\pi$
$644$	1.14602	+	1.14602i	0.0451594	+	0.0451594i
$645$	−11.1929	+	8.32040i	−0.440720	+	0.327616i
$646$	11.4365	+	11.4365i	0.449963	+	0.449963i
$647$		−	16.7883i		−	0.660015i	−0.943978	−	0.330007i	$-0.892949\pi$
$647$		−	16.7883i		−	0.660015i	0.943978	−	0.330007i	$-0.107051\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−34.6239	−	34.6239i	−1.35911	−	1.35911i
$650$	4.72292	+	1.42130i	0.185248	+	0.0557479i
$651$	−0.779479	−	0.779479i	−0.0305502	−	0.0305502i
$652$	−23.0110			−0.901180
$653$	−2.45128			−0.0959259			−0.0479629	−	0.998849i	$-0.515273\pi$
$653$	−2.45128			−0.0959259			−0.0479629	+	0.998849i	$0.515273\pi$
$654$	10.1289			0.396071
$655$	25.3580	+	34.1124i	0.990817	+	1.33288i
$656$		−	1.55336i		−	0.0606484i
$657$	8.62767	+	8.62767i	0.336597	+	0.336597i
$658$	2.51286			0.0979614
$659$	−9.82402			−0.382690			−0.191345	−	0.981523i	$-0.561285\pi$
$659$	−9.82402			−0.382690			−0.191345	+	0.981523i	$0.561285\pi$
$660$	−11.1722	+	8.30504i	−0.434879	+	0.323273i
$661$	−34.3200	+	34.3200i	−1.33489	+	1.33489i	−0.433963	+	0.900931i	$0.642885\pi$
$661$	−34.3200	+	34.3200i	−1.33489	+	1.33489i	−0.900931	+	0.433963i	$0.857115\pi$
$662$	20.7521	−	20.7521i	0.806553	−	0.806553i
$663$	−4.00015	−	4.00015i	−0.155353	−	0.155353i
$664$	7.29893	−	7.29893i	0.283253	−	0.283253i
$665$	5.27162	+	0.776021i	0.204425	+	0.0300928i
$666$	6.02093	−	0.865086i	0.233306	−	0.0335214i
$667$	−5.99213	+	5.99213i	−0.232016	+	0.232016i
$668$	−0.763298			−0.0295329
$669$	28.1917			1.08996
$670$	−18.4240	−	24.7846i	−0.711781	−	0.957514i
$671$	−7.49271	−	7.49271i	−0.289253	−	0.289253i
$672$	0.844952			0.0325947
$673$	24.8554	+	24.8554i	0.958106	+	0.958106i	0.999157	−	0.0410514i	$-0.0130707\pi$
$673$	24.8554	+	24.8554i	0.958106	+	0.958106i	−0.0410514	+	0.999157i	$0.513071\pi$
$674$	−14.7056	+	14.7056i	−0.566440	+	0.566440i
$675$	−2.36672	−	4.40439i	−0.0910951	−	0.169525i
$676$	−12.0270			−0.462575
$677$	−32.9033	−	32.9033i	−1.26458	−	1.26458i	−0.948851	−	0.315725i	$-0.897752\pi$
$677$	−32.9033	−	32.9033i	−1.26458	−	1.26458i	−0.315725	−	0.948851i	$-0.602248\pi$
$678$	6.09440	+	6.09440i	0.234054	+	0.234054i
$679$	7.48937	−	7.48937i	0.287416	−	0.287416i
$680$	12.6869	+	1.86760i	0.486520	+	0.0716193i
$681$	9.95701	−	9.95701i	0.381553	−	0.381553i
$682$	−5.74323	+	5.74323i	−0.219919	+	0.219919i
$683$			26.8396i			1.02699i	0.858093	+	0.513494i	$0.171649\pi$
$683$			26.8396i			1.02699i	−0.858093	+	0.513494i	$0.828351\pi$
$684$	1.99420	+	1.99420i	0.0762500	+	0.0762500i
$685$	−4.59235	−	6.17779i	−0.175465	−	0.236041i
$686$	7.93803	−	7.93803i	0.303076	−	0.303076i
$687$	10.9899	+	10.9899i	0.419289	+	0.419289i
$688$		−	6.23715i		−	0.237789i
$689$	8.89578	−	8.89578i	0.338902	−	0.338902i
$690$	2.55878	+	3.44216i	0.0974110	+	0.131041i
$691$		−	5.35284i		−	0.203631i	−0.994803	−	0.101816i	$-0.967535\pi$
$691$		−	5.35284i		−	0.203631i	0.994803	−	0.101816i	$-0.0324652\pi$
$692$	−7.46496	+	7.46496i	−0.283775	+	0.283775i
$693$	3.71964	−	3.71964i	0.141297	−	0.141297i
$694$	−17.2146			−0.653456
$695$	0.0960764	−	0.652660i	0.00364439	−	0.0247568i
$696$			4.41796i			0.167462i
$697$			8.90833i			0.337427i
$698$	−28.4058			−1.07517
$699$			10.2535i			0.387823i
$700$	3.72150	−	1.99976i	0.140659	−	0.0755839i
$701$	22.1584	+	22.1584i	0.836910	+	0.836910i	0.988451	−	0.151541i	$-0.0484235\pi$
$701$	22.1584	+	22.1584i	0.836910	+	0.836910i	−0.151541	+	0.988451i	$0.548423\pi$
$702$	−0.697511	−	0.697511i	−0.0263259	−	0.0263259i
$703$	−10.2818	+	13.7321i	−0.387784	+	0.517915i
$704$		−	6.22563i		−	0.234637i
$705$	6.57909	+	0.968490i	0.247783	+	0.0364755i
$706$			12.3989i			0.466641i
$707$	5.87777	+	5.87777i	0.221056	+	0.221056i
$708$			7.86515i			0.295590i
$709$	18.1716	−	18.1716i	0.682449	−	0.682449i	−0.278103	−	0.960551i	$-0.589706\pi$
$709$	18.1716	−	18.1716i	0.682449	−	0.682449i	0.960551	+	0.278103i	$0.0897055\pi$
$710$	−33.0624	−	4.86703i	−1.24081	−	0.182657i
$711$	4.54031	+	4.54031i	0.170275	+	0.170275i
$712$	−3.84900	+	3.84900i	−0.144247	+	0.144247i
$713$	1.76948	+	1.76948i	0.0662677	+	0.0662677i
$714$	−4.84571			−0.181346
$715$	−1.99990	+	13.5856i	−0.0747921	+	0.508073i
$716$	−5.31685	−	5.31685i	−0.198700	−	0.198700i
$717$		−	18.1416i		−	0.677510i
$718$	6.27293			0.234104
$719$			2.21940i			0.0827695i	0.999143	+	0.0413848i	$0.0131769\pi$
$719$			2.21940i			0.0827695i	−0.999143	+	0.0413848i	$0.986823\pi$
$720$	2.21223	+	0.325656i	0.0824448	+	0.0121365i
$721$	−7.01810	+	7.01810i	−0.261368	+	0.261368i
$722$	11.0464			0.411103
$723$	−12.9982			−0.483406
$724$	12.3877			0.460385
$725$	10.4561	+	19.4584i	0.388329	+	0.722667i
$726$	−19.6282	−	19.6282i	−0.728472	−	0.728472i
$727$			28.6133i			1.06121i	0.847619	+	0.530605i	$0.178035\pi$
$727$			28.6133i			1.06121i	−0.847619	+	0.530605i	$0.821965\pi$
$728$	0.589363	−	0.589363i	0.0218432	−	0.0218432i
$729$			1.00000i			0.0370370i
$730$	−21.8960	+	16.2767i	−0.810408	+	0.602428i
$731$			35.7694i			1.32298i
$732$			1.70204i			0.0629093i
$733$	−18.8456	+	18.8456i	−0.696079	+	0.696079i	−0.963562	−	0.267484i	$-0.913808\pi$
$733$	−18.8456	+	18.8456i	−0.696079	+	0.696079i	0.267484	+	0.963562i	$0.413808\pi$
$734$	0.228414	+	0.228414i	0.00843090	+	0.00843090i
$735$	11.2807	−	8.38564i	0.416094	−	0.309309i
$736$	−1.91811			−0.0707026
$737$	60.7987	−	60.7987i	2.23955	−	2.23955i
$738$			1.55336i			0.0571798i
$739$	22.5110			0.828079			0.414040	−	0.910259i	$-0.364117\pi$
$739$	22.5110			0.828079			0.414040	+	0.910259i	$0.364117\pi$
$740$	−0.0469870	+	13.6014i	−0.00172728	+	0.499997i
$741$	2.78195			0.102197
$742$		−	10.7762i		−	0.395606i
$743$	18.4577	−	18.4577i	0.677149	−	0.677149i	−0.282205	−	0.959354i	$-0.591066\pi$
$743$	18.4577	−	18.4577i	0.677149	−	0.677149i	0.959354	+	0.282205i	$0.0910660\pi$
$744$	1.30463			0.0478301
$745$	−48.1527	−	7.08843i	−1.76418	−	0.259700i
$746$	13.8845	+	13.8845i	0.508346	+	0.508346i
$747$	−7.29893	+	7.29893i	−0.267054	+	0.267054i
$748$			35.7033i			1.30544i
$749$			0.445990i			0.0162961i
$750$	10.5142	−	3.80140i	0.383926	−	0.138808i
$751$		−	31.7070i		−	1.15700i	−0.815681	−	0.578502i	$-0.803638\pi$
$751$		−	31.7070i		−	1.15700i	0.815681	−	0.578502i	$-0.196362\pi$
$752$	−2.10291	+	2.10291i	−0.0766853	+	0.0766853i
$753$		−	4.61281i		−	0.168100i
$754$	3.08158	+	3.08158i	0.112224	+	0.112224i
$755$	−34.0979	−	5.01947i	−1.24095	−	0.182677i
$756$	−0.844952			−0.0307306
$757$	−16.4593			−0.598224			−0.299112	−	0.954218i	$-0.596690\pi$
$757$	−16.4593			−0.598224			−0.299112	+	0.954218i	$0.596690\pi$
$758$	0.247309			0.00898268
$759$	−8.44389	+	8.44389i	−0.306494	+	0.306494i
$760$	−5.06103	+	3.76219i	−0.183583	+	0.136469i
$761$			1.08101i			0.0391865i	0.999808	+	0.0195933i	$0.00623713\pi$
$761$			1.08101i			0.0391865i	−0.999808	+	0.0195933i	$0.993763\pi$
$762$	8.82454			0.319679
$763$		−	8.55843i		−	0.309836i
$764$	3.82822	+	3.82822i	0.138500	+	0.138500i
$765$	−12.6869	−	1.86760i	−0.458695	−	0.0675233i
$766$	−7.97917			−0.288299
$767$	5.48603	+	5.48603i	0.198089	+	0.198089i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	−7.99476	−	7.99476i	−0.288298	−	0.288298i	0.548109	−	0.836407i	$-0.315348\pi$
$769$	−7.99476	−	7.99476i	−0.288298	−	0.288298i	−0.836407	+	0.548109i	$0.815348\pi$
$770$	7.01736	+	9.44000i	0.252888	+	0.340194i
$771$	9.12984	−	9.12984i	0.328803	−	0.328803i
$772$			5.48394i			0.197371i
$773$	6.30521	+	6.30521i	0.226783	+	0.226783i	0.811347	−	0.584564i	$-0.198735\pi$
$773$	6.30521	+	6.30521i	0.226783	+	0.226783i	−0.584564	+	0.811347i	$0.698735\pi$
$774$			6.23715i			0.224190i
$775$	5.74610	−	3.08769i	0.206406	−	0.110913i
$776$			12.5351i			0.449985i
$777$	−0.730956	−	5.08740i	−0.0262229	−	0.182509i
$778$	0.310092	+	0.310092i	0.0111173	+	0.0111173i
$779$	−3.09770	−	3.09770i	−0.110987	−	0.110987i
$780$	1.77020	−	1.31590i	0.0633834	−	0.0471169i
$781$		−	93.0441i		−	3.32938i
$782$	11.0002			0.393365
$783$		−	4.41796i		−	0.157885i
$784$			6.28606i			0.224502i
$785$	−4.58421	−	6.16684i	−0.163617	−	0.220104i
$786$	19.0089			0.678024
$787$	−5.74208	+	5.74208i	−0.204683	+	0.204683i	−0.802003	−	0.597320i	$-0.796232\pi$
$787$	−5.74208	+	5.74208i	−0.204683	+	0.204683i	0.597320	+	0.802003i	$0.296232\pi$
$788$	−3.31072	+	3.31072i	−0.117939	+	0.117939i
$789$			10.8148i			0.385017i
$790$	−11.5228	+	8.56561i	−0.409962	+	0.304751i
$791$	5.14947	−	5.14947i	0.183094	−	0.183094i
$792$			6.22563i			0.221218i
$793$	1.18719	+	1.18719i	0.0421584	+	0.0421584i
$794$	18.6543	−	18.6543i	0.662017	−	0.662017i
$795$	4.15329	−	28.2139i	0.147302	−	1.00064i
$796$	−6.97405	−	6.97405i	−0.247189	−	0.247189i
$797$			8.28561i			0.293491i	0.989174	+	0.146746i	$0.0468799\pi$
$797$			8.28561i			0.293491i	−0.989174	+	0.146746i	$0.953120\pi$
$798$	1.68500	−	1.68500i	0.0596483	−	0.0596483i
$799$	12.0600	−	12.0600i	0.426651	−	0.426651i
$800$	−1.44085	+	4.78790i	−0.0509418	+	0.169278i
$801$	3.84900	−	3.84900i	0.135998	−	0.135998i
$802$	21.5690	+	21.5690i	0.761627	+	0.761627i
$803$	−53.7127	−	53.7127i	−1.89548	−	1.89548i
$804$	−13.8110			−0.487077
$805$	2.90846	−	2.16204i	0.102510	−	0.0762020i
$806$	0.909994	−	0.909994i	0.0320532	−	0.0320532i
$807$	−15.6442	−	15.6442i	−0.550700	−	0.550700i
$808$	−9.83775			−0.346091
$809$	−39.3817	−	39.3817i	−1.38459	−	1.38459i	−0.836272	−	0.548315i	$-0.815270\pi$
$809$	−39.3817	−	39.3817i	−1.38459	−	1.38459i	−0.548315	−	0.836272i	$-0.684730\pi$
$810$	−2.21223	−	0.325656i	−0.0777297	−	0.0114424i
$811$	55.7968			1.95929			0.979645	−	0.200737i	$-0.0643337\pi$
$811$	55.7968			1.95929			0.979645	+	0.200737i	$0.0643337\pi$
$812$	3.73296			0.131001
$813$	−1.39061	+	1.39061i	−0.0487709	+	0.0487709i
$814$	−37.4841	+	5.38571i	−1.31382	+	0.188769i
$815$	−7.49367	+	50.9055i	−0.262492	+	1.78314i
$816$	4.05518	−	4.05518i	0.141960	−	0.141960i
$817$	−12.4381	−	12.4381i	−0.435154	−	0.435154i
$818$	22.0875	−	22.0875i	0.772270	−	0.772270i
$819$	−0.589363	+	0.589363i	−0.0205940	+	0.0205940i
$820$	−3.43638	−	0.505860i	−0.120004	−	0.0176654i
$821$	9.02391			0.314937			0.157468	−	0.987524i	$-0.449667\pi$
$821$	9.02391			0.314937			0.157468	+	0.987524i	$0.449667\pi$
$822$	−3.44252			−0.120072
$823$	−28.9776	−	28.9776i	−1.01010	−	1.01010i	−0.999949	−	0.0101470i	$-0.996770\pi$
$823$	−28.9776	−	28.9776i	−1.01010	−	1.01010i	−0.0101470	−	0.999949i	$-0.503230\pi$
$824$		−	11.7463i		−	0.409203i
$825$	14.7343	+	27.4201i	0.512983	+	0.954646i
$826$	6.64567			0.231232
$827$	−16.3920			−0.570004			−0.285002	−	0.958527i	$-0.591994\pi$
$827$	−16.3920			−0.570004			−0.285002	+	0.958527i	$0.591994\pi$
$828$	1.91811			0.0666590
$829$	10.5276	+	10.5276i	0.365640	+	0.365640i	0.865884	−	0.500244i	$-0.166756\pi$
$829$	10.5276	+	10.5276i	0.365640	+	0.365640i	−0.500244	+	0.865884i	$0.666756\pi$
$830$	−13.7699	−	18.5238i	−0.477962	−	0.642971i
$831$	7.42359	+	7.42359i	0.257521	+	0.257521i
$832$			0.986429i			0.0341983i
$833$		−	36.0499i		−	1.24905i
$834$	−0.208614	−	0.208614i	−0.00722370	−	0.00722370i
$835$	−0.248573	+	1.68859i	−0.00860221	+	0.0584360i
$836$	−12.4151	−	12.4151i	−0.429386	−	0.429386i
$837$	−1.30463			−0.0450946
$838$	−13.1035			−0.452654
$839$	−29.0325			−1.00231			−0.501156	−	0.865357i	$-0.667092\pi$
$839$	−29.0325			−1.00231			−0.501156	+	0.865357i	$0.667092\pi$
$840$	0.275164	−	1.86922i	0.00949405	−	0.0644944i
$841$		−	9.48163i		−	0.326953i
$842$	−6.69042	−	6.69042i	−0.230567	−	0.230567i
$843$	−19.5843			−0.674519
$844$	4.37831			0.150708
$845$	−3.91665	+	26.6064i	−0.134737	+	0.915287i
$846$	2.10291	−	2.10291i	0.0722996	−	0.0722996i
$847$	−16.5849	+	16.5849i	−0.569864	+	0.569864i
$848$	9.01816	+	9.01816i	0.309685	+	0.309685i
$849$	11.8465	−	11.8465i	0.406572	−	0.406572i
$850$	8.26312	−	27.4581i	0.283423	−	0.941804i
$851$	1.65933	+	11.5488i	0.0568812	+	0.395889i
$852$	−10.5679	+	10.5679i	−0.362052	+	0.362052i
$853$	15.1435			0.518505			0.259252	−	0.965810i	$-0.416524\pi$
$853$	15.1435			0.518505			0.259252	+	0.965810i	$0.416524\pi$
$854$	1.43814			0.0492122
$855$	5.06103	−	3.76219i	0.173084	−	0.128664i
$856$	−0.373231	−	0.373231i	−0.0127568	−	0.0127568i
$857$	31.3980			1.07253			0.536267	−	0.844048i	$-0.319834\pi$
$857$	31.3980			1.07253			0.536267	+	0.844048i	$0.319834\pi$
$858$	4.34245	+	4.34245i	0.148249	+	0.148249i
$859$	9.81362	−	9.81362i	0.334837	−	0.334837i	−0.519583	−	0.854420i	$-0.673913\pi$
$859$	9.81362	−	9.81362i	0.334837	−	0.334837i	0.854420	+	0.519583i	$0.173913\pi$
$860$	−13.7980	−	2.03117i	−0.470508	−	0.0692622i
$861$	1.31251			0.0447303
$862$	−7.79285	−	7.79285i	−0.265426	−	0.265426i
$863$	−32.7757	−	32.7757i	−1.11570	−	1.11570i	−0.992366	−	0.123331i	$-0.960642\pi$
$863$	−32.7757	−	32.7757i	−1.11570	−	1.11570i	−0.123331	−	0.992366i	$-0.539358\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$	14.0832	+	18.9452i	0.478842	+	0.644156i
$866$	−1.28687	+	1.28687i	−0.0437297	+	0.0437297i
$867$	−11.2352	+	11.2352i	−0.381568	+	0.381568i
$868$		−	1.10235i		−	0.0374162i
$869$	−28.2663	−	28.2663i	−0.958868	−	0.958868i
$870$	9.77353	+	1.43874i	0.331354	+	0.0487777i
$871$	−9.63334	+	9.63334i	−0.326413	+	0.326413i
$872$	7.16221	+	7.16221i	0.242543	+	0.242543i
$873$		−	12.5351i		−	0.424250i
$874$	−3.82509	+	3.82509i	−0.129386	+	0.129386i
$875$	−3.21200	−	8.88403i	−0.108585	−	0.300335i
$876$			12.2014i			0.412246i
$877$	8.16227	−	8.16227i	0.275620	−	0.275620i	−0.555738	−	0.831358i	$-0.687564\pi$
$877$	8.16227	−	8.16227i	0.275620	−	0.275620i	0.831358	+	0.555738i	$0.187564\pi$
$878$	5.61954	−	5.61954i	0.189650	−	0.189650i
$879$	−4.31365			−0.145496
$880$	−13.7725	−	2.02742i	−0.464271	−	0.0683442i
$881$			5.67632i			0.191240i	0.995418	+	0.0956201i	$0.0304834\pi$
$881$			5.67632i			0.191240i	−0.995418	+	0.0956201i	$0.969517\pi$
$882$		−	6.28606i		−	0.211663i
$883$	24.7648			0.833401			0.416701	−	0.909044i	$-0.363186\pi$
$883$	24.7648			0.833401			0.416701	+	0.909044i	$0.363186\pi$
$884$		−	5.65707i		−	0.190268i
$885$	17.3995	+	2.56133i	0.584878	+	0.0860983i
$886$	−14.2078	−	14.2078i	−0.477321	−	0.477321i
$887$	−33.2822	−	33.2822i	−1.11751	−	1.11751i	−0.992106	−	0.125399i	$-0.959979\pi$
$887$	−33.2822	−	33.2822i	−1.11751	−	1.11751i	−0.125399	−	0.992106i	$-0.540021\pi$
$888$	4.86915	+	3.64573i	0.163398	+	0.122343i
$889$		−	7.45631i		−	0.250077i
$890$	7.26142	+	9.76832i	0.243403	+	0.327435i
$891$		−	6.22563i		−	0.208567i
$892$	19.9346	+	19.9346i	0.667459	+	0.667459i
$893$			8.38724i			0.280668i
$894$	−15.3913	+	15.3913i	−0.514762	+	0.514762i
$895$	−13.4935	+	10.0306i	−0.451039	+	0.335286i
$896$	0.597471	+	0.597471i	0.0199601	+	0.0199601i
$897$	1.33790	−	1.33790i	0.0446713	−	0.0446713i
$898$	5.85112	+	5.85112i	0.195255	+	0.195255i
$899$	5.76380			0.192234
$900$	1.44085	−	4.78790i	0.0480283	−	0.159597i
$901$	−51.7182	−	51.7182i	−1.72298	−	1.72298i
$902$		−	9.67063i		−	0.321997i
$903$	5.27009			0.175378
$904$			8.61878i			0.286656i
$905$	4.03413	−	27.4044i	0.134099	−	0.910952i
$906$	−10.8989	+	10.8989i	−0.362092	+	0.362092i
$907$	43.0003			1.42780			0.713901	−	0.700247i	$-0.246927\pi$
$907$	43.0003			1.42780			0.713901	+	0.700247i	$0.246927\pi$
$908$	14.0813			0.467306
$909$	9.83775			0.326298
$910$	−1.11188	−	1.49573i	−0.0368583	−	0.0495831i
$911$	−25.7434	−	25.7434i	−0.852918	−	0.852918i	0.137573	−	0.990492i	$-0.456070\pi$
$911$	−25.7434	−	25.7434i	−0.852918	−	0.852918i	−0.990492	+	0.137573i	$0.956070\pi$
$912$			2.82022i			0.0933868i
$913$	45.4404	−	45.4404i	1.50386	−	1.50386i
$914$			0.0348084i			0.00115136i
$915$	3.76530	+	0.554280i	0.124477	+	0.0183239i
$916$			15.5420i			0.513522i
$917$		−	16.0616i		−	0.530400i
$918$	−4.05518	+	4.05518i	−0.133841	+	0.133841i
$919$	−1.65871	−	1.65871i	−0.0547159	−	0.0547159i	0.679219	−	0.733935i	$-0.262318\pi$
$919$	−1.65871	−	1.65871i	−0.0547159	−	0.0547159i	−0.733935	+	0.679219i	$0.762318\pi$
$920$	−0.624645	+	4.24330i	−0.0205939	+	0.139898i
$921$	−33.0368			−1.08860
$922$	−0.163914	+	0.163914i	−0.00539822	+	0.00539822i
$923$			14.7425i			0.485255i
$924$	5.26036			0.173053
$925$	30.0741	+	4.53332i	0.988829	+	0.149055i
$926$	24.0434			0.790114
$927$			11.7463i			0.385800i
$928$	−3.12397	+	3.12397i	−0.102549	+	0.102549i
$929$	12.4196			0.407473			0.203737	−	0.979026i	$-0.434691\pi$
$929$	12.4196			0.407473			0.203737	+	0.979026i	$0.434691\pi$
$930$	0.424861	−	2.88614i	0.0139317	−	0.0946402i
$931$	12.5356	+	12.5356i	0.410839	+	0.410839i
$932$	−7.25032	+	7.25032i	−0.237492	+	0.237492i
$933$		−	26.2277i		−	0.858656i
$934$			1.37090i			0.0448572i
$935$	78.9839	+	11.6270i	2.58305	+	0.380244i
$936$		−	0.986429i		−	0.0322425i
$937$	−7.39610	+	7.39610i	−0.241620	+	0.241620i	−0.817520	−	0.575900i	$-0.804652\pi$
$937$	−7.39610	+	7.39610i	−0.241620	+	0.241620i	0.575900	+	0.817520i	$0.304652\pi$
$938$			11.6696i			0.381027i
$939$	−23.5980	−	23.5980i	−0.770092	−	0.770092i
$940$	3.96729	+	5.33694i	0.129399	+	0.174072i
$941$	12.8513			0.418940			0.209470	−	0.977815i	$-0.432826\pi$
$941$	12.8513			0.418940			0.209470	+	0.977815i	$0.432826\pi$
$942$	−3.43642			−0.111965
$943$	−2.97951			−0.0970263
$944$	−5.56150	+	5.56150i	−0.181011	+	0.181011i
$945$	−0.275164	+	1.86922i	−0.00895107	+	0.0608059i
$946$		−	38.8302i		−	1.26248i
$947$	−10.5534			−0.342939			−0.171469	−	0.985189i	$-0.554851\pi$
$947$	−10.5534			−0.342939			−0.171469	+	0.985189i	$0.554851\pi$
$948$			6.42097i			0.208543i
$949$	8.51058	+	8.51058i	0.276265	+	0.276265i
$950$	6.67466	+	12.4213i	0.216555	+	0.403001i
$951$	−26.4839			−0.858799
$952$	−3.42643	−	3.42643i	−0.111051	−	0.111051i
$953$	−10.5902	+	10.5902i	−0.343049	+	0.343049i	−0.857512	−	0.514463i	$-0.827991\pi$
$953$	−10.5902	+	10.5902i	−0.343049	+	0.343049i	0.514463	+	0.857512i	$0.327991\pi$
$954$	−9.01816	−	9.01816i	−0.291974	−	0.291974i
$955$	9.71557	−	7.22220i	0.314388	−	0.233705i
$956$	12.8280	−	12.8280i	0.414888	−	0.414888i
$957$			27.5046i			0.889097i
$958$	−18.7408	−	18.7408i	−0.605488	−	0.605488i
$959$			2.90877i			0.0939289i
$960$	1.33401	+	1.79455i	0.0430549	+	0.0579190i
$961$			29.2979i			0.945095i
$962$	5.93922	−	0.853346i	0.191488	−	0.0275130i
$963$	0.373231	+	0.373231i	0.0120272	+	0.0120272i
$964$	−9.19108	−	9.19108i	−0.296025	−	0.296025i
$965$	12.1317	+	1.78588i	0.390534	+	0.0574895i
$966$		−	1.62071i		−	0.0521456i
$967$	13.3489			0.429271			0.214635	−	0.976694i	$-0.431144\pi$
$967$	13.3489			0.429271			0.214635	+	0.976694i	$0.431144\pi$
$968$		−	27.7585i		−	0.892192i
$969$		−	16.1736i		−	0.519572i
$970$	27.7305	+	4.08214i	0.890374	+	0.131070i
$971$	−51.0652			−1.63876			−0.819380	−	0.573250i	$-0.805682\pi$
$971$	−51.0652			−1.63876			−0.819380	+	0.573250i	$0.805682\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	−0.176268	+	0.176268i	−0.00565090	+	0.00565090i
$974$		−	23.7276i		−	0.760280i
$975$	−2.33460	−	4.34462i	−0.0747671	−	0.139139i
$976$	−1.20352	+	1.20352i	−0.0385239	+	0.0385239i
$977$			5.44447i			0.174184i	0.996200	+	0.0870920i	$0.0277574\pi$
$977$			5.44447i			0.174184i	−0.996200	+	0.0870920i	$0.972243\pi$
$978$	16.2712	+	16.2712i	0.520296	+	0.520296i
$979$	−23.9625	+	23.9625i	−0.765844	+	0.765844i
$980$	13.9062	+	2.04709i	0.444217	+	0.0653920i
$981$	−7.16221	−	7.16221i	−0.228672	−	0.228672i
$982$			2.30518i			0.0735611i
$983$	−4.21575	+	4.21575i	−0.134462	+	0.134462i	−0.771134	−	0.636673i	$-0.780310\pi$
$983$	−4.21575	+	4.21575i	−0.134462	+	0.134462i	0.636673	+	0.771134i	$0.280310\pi$
$984$	−1.09839	+	1.09839i	−0.0350154	+	0.0350154i
$985$	6.24590	+	8.40221i	0.199011	+	0.267717i
$986$	17.9156	−	17.9156i	0.570550	−	0.570550i
$987$	−1.77686	−	1.77686i	−0.0565580	−	0.0565580i
$988$	1.96713	+	1.96713i	0.0625828	+	0.0625828i
$989$	−11.9636			−0.380419
$990$	13.7725	+	2.02742i	0.437719	+	0.0644355i
$991$	32.7542	−	32.7542i	1.04047	−	1.04047i	0.0413260	−	0.999146i	$-0.486842\pi$
$991$	32.7542	−	32.7542i	1.04047	−	1.04047i	0.999146	−	0.0413260i	$-0.0131582\pi$
$992$	0.922513	+	0.922513i	0.0292898	+	0.0292898i
$993$	−29.3479			−0.931327
$994$	8.92940	+	8.92940i	0.283223	+	0.283223i
$995$	−17.6993	+	13.1570i	−0.561106	+	0.417106i
$996$	−10.3222			−0.327073
$997$	6.16248			0.195168			0.0975838	−	0.995227i	$-0.468889\pi$
$997$	6.16248			0.195168			0.0975838	+	0.995227i	$0.468889\pi$
$998$	−7.87010	+	7.87010i	−0.249124	+	0.249124i
$999$	−4.86915	−	3.64573i	−0.154053	−	0.115346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.b.43.7	✓	40
5.2	odd	4		1110.2.o.b.487.14	yes	40
37.31	odd	4		1110.2.o.b.253.14	yes	40
185.142	even	4	inner	1110.2.l.b.697.7	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.7	✓	40	1.1	even	1	trivial
1110.2.l.b.697.7	yes	40	185.142	even	4	inner
1110.2.o.b.253.14	yes	40	37.31	odd	4
1110.2.o.b.487.14	yes	40	5.2	odd	4

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-0.325656 + 2.21223i) q^{5} +(0.707107 + 0.707107i) q^{6} +(0.597471 - 0.597471i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-0.325656 + 2.21223i) q^{5} +(0.707107 + 0.707107i) q^{6} +(0.597471 - 0.597471i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(2.21223 + 0.325656i) q^{10} +6.22563i q^{11} +(0.707107 - 0.707107i) q^{12} -0.986429i q^{13} +(-0.597471 - 0.597471i) q^{14} +(-1.33401 - 1.79455i) q^{15} +1.00000 q^{16} -5.73489 q^{17} -1.00000 q^{18} +(1.99420 - 1.99420i) q^{19} +(0.325656 - 2.21223i) q^{20} +0.844952i q^{21} +6.22563 q^{22} -1.91811i q^{23} +(-0.707107 - 0.707107i) q^{24} +(-4.78790 - 1.44085i) q^{25} -0.986429 q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.597471 + 0.597471i) q^{28} +(-3.12397 - 3.12397i) q^{29} +(-1.79455 + 1.33401i) q^{30} +(-0.922513 + 0.922513i) q^{31} -1.00000i q^{32} +(-4.40219 - 4.40219i) q^{33} +5.73489i q^{34} +(1.12717 + 1.51631i) q^{35} +1.00000i q^{36} +(-6.02093 + 0.865086i) q^{37} +(-1.99420 - 1.99420i) q^{38} +(0.697511 + 0.697511i) q^{39} +(-2.21223 - 0.325656i) q^{40} -1.55336i q^{41} +0.844952 q^{42} -6.23715i q^{43} -6.22563i q^{44} +(2.21223 + 0.325656i) q^{45} -1.91811 q^{46} +(-2.10291 + 2.10291i) q^{47} +(-0.707107 + 0.707107i) q^{48} +6.28606i q^{49} +(-1.44085 + 4.78790i) q^{50} +(4.05518 - 4.05518i) q^{51} +0.986429i q^{52} +(9.01816 + 9.01816i) q^{53} +(0.707107 - 0.707107i) q^{54} +(-13.7725 - 2.02742i) q^{55} +(0.597471 + 0.597471i) q^{56} +2.82022i q^{57} +(-3.12397 + 3.12397i) q^{58} +(-5.56150 + 5.56150i) q^{59} +(1.33401 + 1.79455i) q^{60} +(-1.20352 + 1.20352i) q^{61} +(0.922513 + 0.922513i) q^{62} +(-0.597471 - 0.597471i) q^{63} -1.00000 q^{64} +(2.18221 + 0.321237i) q^{65} +(-4.40219 + 4.40219i) q^{66} +(-9.76587 - 9.76587i) q^{67} +5.73489 q^{68} +(1.35631 + 1.35631i) q^{69} +(1.51631 - 1.12717i) q^{70} -14.9453 q^{71} +1.00000 q^{72} +(-8.62767 + 8.62767i) q^{73} +(0.865086 + 6.02093i) q^{74} +(4.40439 - 2.36672i) q^{75} +(-1.99420 + 1.99420i) q^{76} +(3.71964 + 3.71964i) q^{77} +(0.697511 - 0.697511i) q^{78} +(-4.54031 + 4.54031i) q^{79} +(-0.325656 + 2.21223i) q^{80} -1.00000 q^{81} -1.55336 q^{82} +(-7.29893 - 7.29893i) q^{83} -0.844952i q^{84} +(1.86760 - 12.6869i) q^{85} -6.23715 q^{86} +4.41796 q^{87} -6.22563 q^{88} +(3.84900 + 3.84900i) q^{89} +(0.325656 - 2.21223i) q^{90} +(-0.589363 - 0.589363i) q^{91} +1.91811i q^{92} -1.30463i q^{93} +(2.10291 + 2.10291i) q^{94} +(3.76219 + 5.06103i) q^{95} +(0.707107 + 0.707107i) q^{96} +12.5351 q^{97} +6.28606 q^{98} +6.22563 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{4} - 4 q^{7}+O(q^{10}) \) 40 * q - 40 * q^4 - 4 * q^7	\( 40 q - 40 q^{4} - 4 q^{7} + 4 q^{14} + 40 q^{16} + 24 q^{17} - 40 q^{18} + 4 q^{19} + 8 q^{22} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 28 q^{31} - 4 q^{33} + 20 q^{35} + 20 q^{37} - 4 q^{38} + 4 q^{39} + 16 q^{42} - 16 q^{47} + 16 q^{51} + 20 q^{53} + 16 q^{55} - 4 q^{56} - 4 q^{59} - 8 q^{61} - 28 q^{62} + 4 q^{63} - 40 q^{64} - 4 q^{65} - 4 q^{66} + 16 q^{67} - 24 q^{68} - 8 q^{69} + 12 q^{70} + 40 q^{71} + 40 q^{72} + 8 q^{73} - 8 q^{74} + 16 q^{75} - 4 q^{76} - 24 q^{77} + 4 q^{78} - 12 q^{79} - 40 q^{81} - 24 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{88} + 12 q^{89} - 24 q^{91} + 16 q^{94} - 28 q^{95} + 40 q^{97} - 56 q^{98} + 8 q^{99}+O(q^{100}) \) 40 * q - 40 * q^4 - 4 * q^7 + 4 * q^14 + 40 * q^16 + 24 * q^17 - 40 * q^18 + 4 * q^19 + 8 * q^22 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 28 * q^31 - 4 * q^33 + 20 * q^35 + 20 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^42 - 16 * q^47 + 16 * q^51 + 20 * q^53 + 16 * q^55 - 4 * q^56 - 4 * q^59 - 8 * q^61 - 28 * q^62 + 4 * q^63 - 40 * q^64 - 4 * q^65 - 4 * q^66 + 16 * q^67 - 24 * q^68 - 8 * q^69 + 12 * q^70 + 40 * q^71 + 40 * q^72 + 8 * q^73 - 8 * q^74 + 16 * q^75 - 4 * q^76 - 24 * q^77 + 4 * q^78 - 12 * q^79 - 40 * q^81 - 24 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^88 + 12 * q^89 - 24 * q^91 + 16 * q^94 - 28 * q^95 + 40 * q^97 - 56 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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