LMFDB - Embedded newform 1110.2.l.b.697.7

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			697.7
Character	$\chi$	$=$	1110.697
Dual form			1110.2.l.b.43.7

$q$-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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

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

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	0.810945	−	0.585122i	$-0.198953\pi$
$7$	0.597471	+	0.597471i	0.225823	+	0.225823i	−0.585122	+	0.810945i	$0.698953\pi$
$8$		−	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	$-0.612170\pi$
$11$		−	6.22563i		−	1.87710i	0.345144	−	0.938550i	$-0.387830\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$			0.986429i			0.273586i	0.990600	+	0.136793i	$0.0436796\pi$
$13$			0.986429i			0.273586i	−0.990600	+	0.136793i	$0.956320\pi$
$14$	−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	0.897834	−	0.440334i	$-0.145140\pi$
$19$	1.99420	+	1.99420i	0.457500	+	0.457500i	−0.440334	+	0.897834i	$0.645140\pi$
$20$	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	$0.0640868\pi$
$23$			1.91811i			0.399954i	−0.979801	+	0.199977i	$0.935913\pi$
$24$	−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	−0.934932	−	0.354826i	$-0.884540\pi$
$29$	−3.12397	+	3.12397i	−0.580107	+	0.580107i	0.354826	+	0.934932i	$0.384540\pi$
$30$	−1.79455	−	1.33401i	−0.327639	−	0.243555i
$31$	−0.922513	−	0.922513i	−0.165688	−	0.165688i	0.619393	−	0.785081i	$-0.287379\pi$
$31$	−0.922513	−	0.922513i	−0.165688	−	0.165688i	−0.785081	+	0.619393i	$0.787379\pi$
$32$			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	$0.0387053\pi$
$41$			1.55336i			0.242594i	−0.992616	+	0.121297i	$0.961295\pi$
$42$	0.844952			0.130379
$43$			6.23715i			0.951157i	0.879673	+	0.475578i	$0.157761\pi$
$43$			6.23715i			0.951157i	−0.879673	+	0.475578i	$0.842239\pi$
$44$			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	0.536903	−	0.843644i	$-0.319594\pi$
$47$	−2.10291	−	2.10291i	−0.306741	−	0.306741i	−0.843644	+	0.536903i	$0.819594\pi$
$48$	−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	0.278223	−	0.960516i	$-0.410255\pi$
$53$	9.01816	−	9.01816i	1.23874	−	1.23874i	0.960516	−	0.278223i	$-0.0897454\pi$
$54$	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	0.245381	−	0.969427i	$-0.421087\pi$
$59$	−5.56150	−	5.56150i	−0.724046	−	0.724046i	−0.969427	+	0.245381i	$0.921087\pi$
$60$	1.33401	−	1.79455i	0.172220	−	0.231676i
$61$	−1.20352	−	1.20352i	−0.154096	−	0.154096i	0.625849	−	0.779944i	$-0.284753\pi$
$61$	−1.20352	−	1.20352i	−0.154096	−	0.154096i	−0.779944	+	0.625849i	$0.784753\pi$
$62$	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	−0.216896	+	0.976195i	$0.569593\pi$
$67$	−9.76587	+	9.76587i	−1.19309	+	1.19309i	−0.976195	+	0.216896i	$0.930407\pi$
$68$	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	−0.999952	−	0.00984027i	$-0.996868\pi$
$73$	−8.62767	−	8.62767i	−1.00979	−	1.00979i	−0.00984027	−	0.999952i	$-0.503132\pi$
$74$	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	0.403954	−	0.914779i	$-0.367635\pi$
$79$	−4.54031	−	4.54031i	−0.510825	−	0.510825i	−0.914779	+	0.403954i	$0.867635\pi$
$80$	−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	−0.983277	−	0.182116i	$-0.941705\pi$
$83$	−7.29893	+	7.29893i	−0.801161	+	0.801161i	0.182116	+	0.983277i	$0.441705\pi$
$84$			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	−0.473045	−	0.881038i	$-0.656845\pi$
$89$	3.84900	−	3.84900i	0.407994	−	0.407994i	0.881038	+	0.473045i	$0.156845\pi$
$90$	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	$-0.837199\pi$
$101$		−	9.83775i		−	0.978893i	0.872033	−	0.489447i	$-0.162801\pi$
$102$	−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	0.688836	−	0.724917i	$-0.258122\pi$
$107$	−0.373231	−	0.373231i	−0.0360816	−	0.0360816i	−0.724917	+	0.688836i	$0.758122\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	7.16221	+	7.16221i	0.686015	+	0.686015i	0.961349	−	0.275333i	$-0.0887882\pi$
$109$	7.16221	+	7.16221i	0.686015	+	0.686015i	−0.275333	+	0.961349i	$0.588788\pi$
$110$	−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	0.927507	−	0.373806i	$-0.121947\pi$
$127$	6.23989	+	6.23989i	0.553701	+	0.553701i	−0.373806	+	0.927507i	$0.621947\pi$
$128$		−	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	0.981156	+	0.193215i	$0.0618915\pi$
$131$	13.4413	+	13.4413i	1.17437	+	1.17437i	0.193215	+	0.981156i	$0.438109\pi$
$132$	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	0.595434	−	0.803404i	$-0.296980\pi$
$137$	−2.43423	−	2.43423i	−0.207970	−	0.207970i	−0.803404	+	0.595434i	$0.796980\pi$
$138$	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	$-0.649587\pi$
$149$		−	21.7666i		−	1.78319i	0.452834	−	0.891595i	$-0.350413\pi$
$150$	−2.36672	+	4.40439i	−0.193242	+	0.359617i
$151$		−	15.4134i		−	1.25432i	−0.778888	−	0.627162i	$-0.784216\pi$
$151$		−	15.4134i		−	1.25432i	0.778888	−	0.627162i	$-0.215784\pi$
$152$	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	0.603463	−	0.797391i	$-0.293787\pi$
$157$	−2.42992	−	2.42992i	−0.193928	−	0.193928i	−0.797391	+	0.603463i	$0.793787\pi$
$158$	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	0.931441	−	0.363891i	$-0.118552\pi$
$173$	7.46496	+	7.46496i	0.567550	+	0.567550i	−0.363891	+	0.931441i	$0.618552\pi$
$174$			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	−0.479915	−	0.877315i	$-0.659333\pi$
$179$	5.31685	−	5.31685i	0.397400	−	0.397400i	0.877315	+	0.479915i	$0.159333\pi$
$180$	−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	−0.831910	−	0.554910i	$-0.812753\pi$
$191$	−3.82822	+	3.82822i	−0.277000	+	0.277000i	0.554910	+	0.831910i	$0.312753\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$			5.48394i			0.394743i	0.980329	+	0.197371i	$0.0632405\pi$
$193$			5.48394i			0.394743i	−0.980329	+	0.197371i	$0.936760\pi$
$194$			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	0.815141	−	0.579262i	$-0.196659\pi$
$197$	3.31072	+	3.31072i	0.235879	+	0.235879i	−0.579262	+	0.815141i	$0.696659\pi$
$198$			6.22563i			0.442437i
$199$	6.97405	−	6.97405i	0.494377	−	0.494377i	−0.415305	−	0.909682i	$-0.636325\pi$
$199$	6.97405	−	6.97405i	0.494377	−	0.494377i	0.909682	+	0.415305i	$0.136325\pi$
$200$	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	−0.434010	+	0.900908i	$0.642902\pi$
$223$	−19.9346	+	19.9346i	−1.33492	+	1.33492i	−0.900908	+	0.434010i	$0.857098\pi$
$224$	−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	$0.171660\pi$
$229$			15.5420i			1.02704i	−0.858076	+	0.513522i	$0.828340\pi$
$230$	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	0.903523	−	0.428539i	$-0.140971\pi$
$233$	7.25032	+	7.25032i	0.474985	+	0.474985i	−0.428539	+	0.903523i	$0.640971\pi$
$234$		−	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	0.157709	−	0.987486i	$-0.449589\pi$
$239$	−12.8280	−	12.8280i	−0.829777	−	0.829777i	−0.987486	+	0.157709i	$0.949589\pi$
$240$	−1.33401	+	1.79455i	−0.0861098	+	0.115838i
$241$	9.19108	−	9.19108i	0.592050	−	0.592050i	−0.346135	−	0.938185i	$-0.612506\pi$
$241$	9.19108	−	9.19108i	0.592050	−	0.592050i	0.938185	+	0.346135i	$0.112506\pi$
$242$		−	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	0.596634	−	0.802514i	$-0.296504\pi$
$251$	−3.26175	−	3.26175i	−0.205880	−	0.205880i	−0.802514	+	0.596634i	$0.796504\pi$
$252$	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	0.902415	−	0.430868i	$-0.141792\pi$
$263$	7.64722	+	7.64722i	0.471548	+	0.471548i	−0.430868	+	0.902415i	$0.641792\pi$
$264$	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	$-0.764373\pi$
$269$		−	22.1242i		−	1.34893i	0.738305	−	0.674467i	$-0.235627\pi$
$270$	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	$0.102138\pi$
$277$			10.4985i			0.630796i	−0.948959	+	0.315398i	$0.897862\pi$
$278$		−	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	−0.160863	−	0.986977i	$-0.551428\pi$
$281$	13.8482	−	13.8482i	0.826114	−	0.826114i	0.986977	+	0.160863i	$0.0514276\pi$
$282$	−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	−0.612373	−	0.790569i	$-0.709785\pi$
$293$	3.05021	−	3.05021i	0.178195	−	0.178195i	0.790569	+	0.612373i	$0.209785\pi$
$294$	−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	0.430819	−	0.902438i	$-0.358225\pi$
$307$	23.3606	−	23.3606i	1.33326	−	1.33326i	0.902438	−	0.430819i	$-0.141775\pi$
$308$	−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	−0.998592	−	0.0530421i	$-0.983108\pi$
$311$	−18.5458	−	18.5458i	−1.05163	−	1.05163i	−0.0530421	−	0.998592i	$-0.516892\pi$
$312$	−0.697511	−	0.697511i	−0.0394888	−	0.0394888i
$313$		−	33.3726i		−	1.88633i	−0.332320	−	0.943167i	$-0.607831\pi$
$313$		−	33.3726i		−	1.88633i	0.332320	−	0.943167i	$-0.392169\pi$
$314$	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	0.0532273	−	0.998582i	$-0.483049\pi$
$317$	18.7269	−	18.7269i	1.05181	−	1.05181i	0.998582	−	0.0532273i	$-0.0169508\pi$
$318$		−	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	0.152304	−	0.988334i	$-0.451331\pi$
$331$	20.7521	−	20.7521i	1.14064	−	1.14064i	0.988334	−	0.152304i	$-0.0486692\pi$
$332$	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	−0.983262	−	0.182196i	$-0.941680\pi$
$337$	−14.7056	+	14.7056i	−0.801067	+	0.801067i	0.182196	+	0.983262i	$0.441680\pi$
$338$			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	$0.152891\pi$
$347$			17.2146i			0.924127i	−0.886847	+	0.462063i	$0.847109\pi$
$348$	−4.41796			−0.236827
$349$			28.4058i			1.52053i	0.649616	+	0.760263i	$0.274930\pi$
$349$			28.4058i			1.52053i	−0.649616	+	0.760263i	$0.725070\pi$
$350$	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	$-0.947065\pi$
$359$		−	6.27293i		−	0.331072i	0.986204	−	0.165536i	$-0.0529355\pi$
$360$	−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	0.701120	−	0.713043i	$-0.252684\pi$
$367$	−0.228414	−	0.228414i	−0.0119231	−	0.0119231i	−0.713043	+	0.701120i	$0.752684\pi$
$368$			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	0.249472	−	0.968382i	$-0.419743\pi$
$373$	−13.8845	−	13.8845i	−0.718910	−	0.718910i	−0.968382	+	0.249472i	$0.919743\pi$
$374$	−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	$-0.997978\pi$
$379$		−	0.247309i		−	0.0127034i	0.999980	−	0.00635171i	$-0.00202183\pi$
$380$	−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	$0.0653481\pi$
$383$			7.97917i			0.407716i	−0.979000	+	0.203858i	$0.934652\pi$
$384$	−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	0.699202	−	0.714924i	$-0.253539\pi$
$389$	−0.310092	−	0.310092i	−0.0157223	−	0.0157223i	−0.714924	+	0.699202i	$0.753539\pi$
$390$	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	−0.0618525	−	0.998085i	$-0.519701\pi$
$397$	18.6543	−	18.6543i	0.936233	−	0.936233i	0.998085	+	0.0618525i	$0.0197008\pi$
$398$	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	−0.996768	−	0.0803350i	$-0.974401\pi$
$401$	−21.5690	−	21.5690i	−1.07710	−	1.07710i	−0.0803350	−	0.996768i	$-0.525599\pi$
$402$			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	0.0968567	−	0.995298i	$-0.469121\pi$
$409$	22.0875	−	22.0875i	1.09216	−	1.09216i	0.995298	−	0.0968567i	$-0.0308789\pi$
$410$	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	$0.103708\pi$
$419$			13.1035i			0.640150i	−0.947392	+	0.320075i	$0.896292\pi$
$420$	1.86922	−	0.275164i	0.0912088	−	0.0134266i
$421$	6.69042	+	6.69042i	0.326071	+	0.326071i	0.851090	−	0.525019i	$-0.175942\pi$
$421$	6.69042	+	6.69042i	0.326071	+	0.326071i	−0.525019	+	0.851090i	$0.675942\pi$
$422$		−	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	0.869428	−	0.494059i	$-0.164488\pi$
$431$	7.79285	+	7.79285i	0.375369	+	0.375369i	−0.494059	+	0.869428i	$0.664488\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−1.28687	+	1.28687i	−0.0618431	+	0.0618431i	−0.737352	−	0.675509i	$-0.763924\pi$
$433$	−1.28687	+	1.28687i	−0.0618431	+	0.0618431i	0.675509	+	0.737352i	$0.263924\pi$
$434$	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	−0.560171	−	0.828377i	$-0.689265\pi$
$439$	5.61954	−	5.61954i	0.268206	−	0.268206i	0.828377	+	0.560171i	$0.189265\pi$
$440$	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	0.958872	−	0.283838i	$-0.0916079\pi$
$443$	14.2078	+	14.2078i	0.675034	+	0.675034i	−0.283838	+	0.958872i	$0.591608\pi$
$444$	−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	0.555431	−	0.831563i	$-0.312553\pi$
$449$	−5.85112	−	5.85112i	−0.276132	−	0.276132i	−0.831563	+	0.555431i	$0.812553\pi$
$450$	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	−0.710914	−	0.703279i	$-0.751718\pi$
$461$	−0.163914	+	0.163914i	−0.00763424	+	0.00763424i	0.703279	+	0.710914i	$0.251718\pi$
$462$		−	5.26036i		−	0.244734i
$463$		−	24.0434i		−	1.11739i	−0.829373	−	0.558695i	$-0.811302\pi$
$463$		−	24.0434i		−	1.11739i	0.829373	−	0.558695i	$-0.188698\pi$
$464$	−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	0.990899	−	0.134609i	$-0.0429779\pi$
$479$	18.7408	+	18.7408i	0.856290	+	0.856290i	−0.134609	+	0.990899i	$0.542978\pi$
$480$	−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	−0.860970	−	0.508656i	$-0.830143\pi$
$499$	−7.87010	+	7.87010i	−0.352314	+	0.352314i	0.508656	+	0.860970i	$0.330143\pi$
$500$	−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	$-0.804788\pi$
$503$		−	25.8165i		−	1.15110i	0.817766	−	0.575551i	$-0.195212\pi$
$504$	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	$-0.582664\pi$
$521$		−	44.1201i		−	1.93294i	0.256786	−	0.966468i	$-0.417336\pi$
$522$	3.12397	−	3.12397i	0.136732	−	0.136732i
$523$		−	30.8971i		−	1.35104i	−0.737343	−	0.675519i	$-0.763920\pi$
$523$		−	30.8971i		−	1.35104i	0.737343	−	0.675519i	$-0.236080\pi$
$524$	−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	−0.195661	+	0.980672i	$0.562685\pi$
$541$	−27.3608	+	27.3608i	−1.17633	+	1.17633i	−0.980672	+	0.195661i	$0.937315\pi$
$542$			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	$0.151724\pi$
$547$			21.4614i			0.917621i	−0.888534	+	0.458811i	$0.848276\pi$
$548$	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	$-0.997789\pi$
$557$		−	0.327825i		−	0.0138904i	0.999976	−	0.00694520i	$-0.00221074\pi$
$558$	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	$-0.808375\pi$
$563$		−	26.8738i		−	1.13260i	0.824200	−	0.566299i	$-0.191625\pi$
$564$		−	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	−0.903079	−	0.429475i	$-0.858699\pi$
$569$	−11.2972	+	11.2972i	−0.473604	+	0.473604i	0.429475	+	0.903079i	$0.358699\pi$
$570$	−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	$-0.856389\pi$
$587$		−	21.1277i		−	0.872034i	0.899938	−	0.436017i	$-0.143611\pi$
$588$	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	−0.673484	−	0.739201i	$-0.735203\pi$
$593$	1.60032	−	1.60032i	0.0657171	−	0.0657171i	0.739201	+	0.673484i	$0.235203\pi$
$594$	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	$0.215213\pi$
$599$			30.6306i			1.25153i	−0.780011	+	0.625765i	$0.784787\pi$
$600$	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	$-0.953718\pi$
$607$		−	7.13929i		−	0.289775i	0.989448	−	0.144887i	$-0.0462820\pi$
$608$	−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	0.786897	−	0.617084i	$-0.211686\pi$
$613$	4.20436	+	4.20436i	0.169812	+	0.169812i	−0.617084	+	0.786897i	$0.711686\pi$
$614$	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	−0.169703	−	0.985495i	$-0.554281\pi$
$617$	20.2638	−	20.2638i	0.815792	−	0.815792i	0.985495	+	0.169703i	$0.0542810\pi$
$618$	−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	0.934522	−	0.355906i	$-0.115828\pi$
$631$	14.5347	+	14.5347i	0.578616	+	0.578616i	−0.355906	+	0.934522i	$0.615828\pi$
$632$	−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	$0.107051\pi$
$647$			16.7883i			0.660015i	−0.943978	+	0.330007i	$0.892949\pi$
$648$			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	−0.900931	−	0.433963i	$-0.857115\pi$
$661$	−34.3200	−	34.3200i	−1.33489	−	1.33489i	−0.433963	−	0.900931i	$-0.642885\pi$
$662$	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	−0.0410514	−	0.999157i	$-0.513071\pi$
$673$	24.8554	−	24.8554i	0.958106	−	0.958106i	0.999157	+	0.0410514i	$0.0130707\pi$
$674$	−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	−0.315725	+	0.948851i	$0.602248\pi$
$677$	−32.9033	+	32.9033i	−1.26458	+	1.26458i	−0.948851	+	0.315725i	$0.897752\pi$
$678$	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	$-0.828351\pi$
$683$		−	26.8396i		−	1.02699i	0.858093	−	0.513494i	$-0.171649\pi$
$684$	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	$0.0324652\pi$
$691$			5.35284i			0.203631i	−0.994803	+	0.101816i	$0.967535\pi$
$692$	−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	−0.151541	−	0.988451i	$-0.548423\pi$
$701$	22.1584	−	22.1584i	0.836910	−	0.836910i	0.988451	+	0.151541i	$0.0484235\pi$
$702$	−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	0.960551	−	0.278103i	$-0.0897055\pi$
$709$	18.1716	+	18.1716i	0.682449	+	0.682449i	−0.278103	+	0.960551i	$0.589706\pi$
$710$	−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	$-0.986823\pi$
$719$		−	2.21940i		−	0.0827695i	0.999143	−	0.0413848i	$-0.0131769\pi$
$720$	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	$-0.821965\pi$
$727$		−	28.6133i		−	1.06121i	0.847619	−	0.530605i	$-0.178035\pi$
$728$	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	0.267484	−	0.963562i	$-0.413808\pi$
$733$	−18.8456	−	18.8456i	−0.696079	−	0.696079i	−0.963562	+	0.267484i	$0.913808\pi$
$734$	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	0.959354	−	0.282205i	$-0.0910660\pi$
$743$	18.4577	+	18.4577i	0.677149	+	0.677149i	−0.282205	+	0.959354i	$0.591066\pi$
$744$	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	$0.196362\pi$
$751$			31.7070i			1.15700i	−0.815681	+	0.578502i	$0.803638\pi$
$752$	−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	$-0.993763\pi$
$761$		−	1.08101i		−	0.0391865i	0.999808	−	0.0195933i	$-0.00623713\pi$
$762$	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	−0.836407	−	0.548109i	$-0.815348\pi$
$769$	−7.99476	+	7.99476i	−0.288298	+	0.288298i	0.548109	+	0.836407i	$0.315348\pi$
$770$	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	−0.584564	−	0.811347i	$-0.698735\pi$
$773$	6.30521	−	6.30521i	0.226783	−	0.226783i	0.811347	+	0.584564i	$0.198735\pi$
$774$		−	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	0.597320	−	0.802003i	$-0.296232\pi$
$787$	−5.74208	−	5.74208i	−0.204683	−	0.204683i	−0.802003	+	0.597320i	$0.796232\pi$
$788$	−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	$-0.953120\pi$
$797$		−	8.28561i		−	0.293491i	0.989174	−	0.146746i	$-0.0468799\pi$
$798$	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	−0.548315	+	0.836272i	$0.684730\pi$
$809$	−39.3817	+	39.3817i	−1.38459	+	1.38459i	−0.836272	+	0.548315i	$0.815270\pi$
$810$	−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	−0.0101470	+	0.999949i	$0.503230\pi$
$823$	−28.9776	+	28.9776i	−1.01010	+	1.01010i	−0.999949	+	0.0101470i	$0.996770\pi$
$824$			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	−0.500244	−	0.865884i	$-0.666756\pi$
$829$	10.5276	−	10.5276i	0.365640	−	0.365640i	0.865884	+	0.500244i	$0.166756\pi$
$830$	−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	0.854420	−	0.519583i	$-0.173913\pi$
$859$	9.81362	+	9.81362i	0.334837	+	0.334837i	−0.519583	+	0.854420i	$0.673913\pi$
$860$	−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	−0.123331	+	0.992366i	$0.539358\pi$
$863$	−32.7757	+	32.7757i	−1.11570	+	1.11570i	−0.992366	+	0.123331i	$0.960642\pi$
$864$	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	0.831358	−	0.555738i	$-0.187564\pi$
$877$	8.16227	+	8.16227i	0.275620	+	0.275620i	−0.555738	+	0.831358i	$0.687564\pi$
$878$	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	$-0.969517\pi$
$881$		−	5.67632i		−	0.191240i	0.995418	−	0.0956201i	$-0.0304834\pi$
$882$			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	−0.125399	+	0.992106i	$0.540021\pi$
$887$	−33.2822	+	33.2822i	−1.11751	+	1.11751i	−0.992106	+	0.125399i	$0.959979\pi$
$888$	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	−0.990492	−	0.137573i	$-0.956070\pi$
$911$	−25.7434	+	25.7434i	−0.852918	+	0.852918i	0.137573	+	0.990492i	$0.456070\pi$
$912$		−	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	−0.733935	−	0.679219i	$-0.762318\pi$
$919$	−1.65871	+	1.65871i	−0.0547159	+	0.0547159i	0.679219	+	0.733935i	$0.262318\pi$
$920$	−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	0.575900	−	0.817520i	$-0.304652\pi$
$937$	−7.39610	−	7.39610i	−0.241620	−	0.241620i	−0.817520	+	0.575900i	$0.804652\pi$
$938$		−	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	0.514463	−	0.857512i	$-0.327991\pi$
$953$	−10.5902	−	10.5902i	−0.343049	−	0.343049i	−0.857512	+	0.514463i	$0.827991\pi$
$954$	−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	$-0.972243\pi$
$977$		−	5.44447i		−	0.174184i	0.996200	−	0.0870920i	$-0.0277574\pi$
$978$	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	0.636673	−	0.771134i	$-0.280310\pi$
$983$	−4.21575	−	4.21575i	−0.134462	−	0.134462i	−0.771134	+	0.636673i	$0.780310\pi$
$984$	−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	0.999146	+	0.0413260i	$0.0131582\pi$
$991$	32.7542	+	32.7542i	1.04047	+	1.04047i	0.0413260	+	0.999146i	$0.486842\pi$
$992$	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.697.7	yes	40
5.3	odd	4		1110.2.o.b.253.14	yes	40
37.6	odd	4		1110.2.o.b.487.14	yes	40
185.43	even	4	inner	1110.2.l.b.43.7	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.7	✓	40	185.43	even	4	inner
1110.2.l.b.697.7	yes	40	1.1	even	1	trivial
1110.2.o.b.253.14	yes	40	5.3	odd	4
1110.2.o.b.487.14	yes	40	37.6	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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