LMFDB - Embedded newform 690.2.i.f.323.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(47,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("690.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.i (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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.7
Character	$\chi$	$=$	690.323
Dual form			690.2.i.f.47.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(1.12660 + 1.31559i) q^{3} +1.00000i q^{4} +(-0.192443 - 2.22777i) q^{5} +(0.133641 - 1.72689i) q^{6} +(1.96010 - 1.96010i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.461565 + 2.96428i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.12660 + 1.31559i) q^{3} +1.00000i q^{4} +(-0.192443 - 2.22777i) q^{5} +(0.133641 - 1.72689i) q^{6} +(1.96010 - 1.96010i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.461565 + 2.96428i) q^{9} +(-1.43919 + 1.71135i) q^{10} -2.97195i q^{11} +(-1.31559 + 1.12660i) q^{12} +(-1.33263 - 1.33263i) q^{13} -2.77200 q^{14} +(2.71403 - 2.76297i) q^{15} -1.00000 q^{16} +(0.217329 + 0.217329i) q^{17} +(2.42244 - 1.76969i) q^{18} -6.42606i q^{19} +(2.22777 - 0.192443i) q^{20} +(4.78694 + 0.370453i) q^{21} +(-2.10149 + 2.10149i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(1.72689 + 0.133641i) q^{24} +(-4.92593 + 0.857436i) q^{25} +1.88462i q^{26} +(-4.41978 + 2.73231i) q^{27} +(1.96010 + 1.96010i) q^{28} -1.22002 q^{29} +(-3.87283 + 0.0346053i) q^{30} +6.33502 q^{31} +(0.707107 + 0.707107i) q^{32} +(3.90988 - 3.34819i) q^{33} -0.307349i q^{34} +(-4.74387 - 3.98945i) q^{35} +(-2.96428 - 0.461565i) q^{36} +(1.43305 - 1.43305i) q^{37} +(-4.54391 + 4.54391i) q^{38} +(0.251863 - 3.25453i) q^{39} +(-1.71135 - 1.43919i) q^{40} +3.04579i q^{41} +(-3.12292 - 3.64682i) q^{42} +(-1.80190 - 1.80190i) q^{43} +2.97195 q^{44} +(6.69256 + 0.457809i) q^{45} +1.00000 q^{46} +(0.199419 + 0.199419i) q^{47} +(-1.12660 - 1.31559i) q^{48} -0.683996i q^{49} +(4.08946 + 2.87686i) q^{50} +(-0.0410744 + 0.530758i) q^{51} +(1.33263 - 1.33263i) q^{52} +(9.17886 - 9.17886i) q^{53} +(5.05729 + 1.19322i) q^{54} +(-6.62083 + 0.571930i) q^{55} -2.77200i q^{56} +(8.45408 - 7.23957i) q^{57} +(0.862686 + 0.862686i) q^{58} +9.43000 q^{59} +(2.76297 + 2.71403i) q^{60} +5.57225 q^{61} +(-4.47954 - 4.47954i) q^{62} +(4.90558 + 6.71501i) q^{63} -1.00000i q^{64} +(-2.71234 + 3.22525i) q^{65} +(-5.13223 - 0.397175i) q^{66} +(9.41060 - 9.41060i) q^{67} +(-0.217329 + 0.217329i) q^{68} +(-1.72689 - 0.133641i) q^{69} +(0.533451 + 6.17539i) q^{70} +7.64983i q^{71} +(1.76969 + 2.42244i) q^{72} +(-4.05708 - 4.05708i) q^{73} -2.02664 q^{74} +(-6.67757 - 5.51453i) q^{75} +6.42606 q^{76} +(-5.82533 - 5.82533i) q^{77} +(-2.47940 + 2.12321i) q^{78} +14.4298i q^{79} +(0.192443 + 2.22777i) q^{80} +(-8.57391 - 2.73642i) q^{81} +(2.15370 - 2.15370i) q^{82} +(-12.1736 + 12.1736i) q^{83} +(-0.370453 + 4.78694i) q^{84} +(0.442336 - 0.525982i) q^{85} +2.54827i q^{86} +(-1.37447 - 1.60505i) q^{87} +(-2.10149 - 2.10149i) q^{88} -2.45643 q^{89} +(-4.40864 - 5.05608i) q^{90} -5.22418 q^{91} +(-0.707107 - 0.707107i) q^{92} +(7.13701 + 8.33431i) q^{93} -0.282021i q^{94} +(-14.3158 + 1.23665i) q^{95} +(-0.133641 + 1.72689i) q^{96} +(8.98748 - 8.98748i) q^{97} +(-0.483658 + 0.483658i) q^{98} +(8.80970 + 1.37175i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7}+O(q^{10}) $ 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7	$ 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7} - 4 q^{12} - 12 q^{15} - 32 q^{16} + 8 q^{18} - 40 q^{22} + 32 q^{25} + 4 q^{27} + 8 q^{28} - 20 q^{30} + 8 q^{31} + 8 q^{33} + 20 q^{36} - 16 q^{37} + 8 q^{40} - 8 q^{42} - 80 q^{43} - 4 q^{45} + 32 q^{46} - 4 q^{48} + 36 q^{51} + 12 q^{57} - 16 q^{58} - 4 q^{60} + 8 q^{61} + 44 q^{63} + 52 q^{66} + 64 q^{67} + 64 q^{70} - 8 q^{72} - 56 q^{73} - 68 q^{75} - 8 q^{76} + 60 q^{78} - 44 q^{81} - 48 q^{85} - 60 q^{87} - 40 q^{88} - 64 q^{90} + 40 q^{91} + 92 q^{93} - 12 q^{96} - 40 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7 - 4 * q^12 - 12 * q^15 - 32 * q^16 + 8 * q^18 - 40 * q^22 + 32 * q^25 + 4 * q^27 + 8 * q^28 - 20 * q^30 + 8 * q^31 + 8 * q^33 + 20 * q^36 - 16 * q^37 + 8 * q^40 - 8 * q^42 - 80 * q^43 - 4 * q^45 + 32 * q^46 - 4 * q^48 + 36 * q^51 + 12 * q^57 - 16 * q^58 - 4 * q^60 + 8 * q^61 + 44 * q^63 + 52 * q^66 + 64 * q^67 + 64 * q^70 - 8 * q^72 - 56 * q^73 - 68 * q^75 - 8 * q^76 + 60 * q^78 - 44 * q^81 - 48 * q^85 - 60 * q^87 - 40 * q^88 - 64 * q^90 + 40 * q^91 + 92 * q^93 - 12 * q^96 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	1.12660	+	1.31559i	0.650440	+	0.759557i
$3$	1.12660	+	1.31559i	0.650440	+	0.759557i
$4$			1.00000i			0.500000i
$5$	−0.192443	−	2.22777i	−0.0860629	−	0.996290i
$5$	−0.192443	−	2.22777i	−0.0860629	−	0.996290i
$6$	0.133641	−	1.72689i	0.0545587	−	0.704999i
$7$	1.96010	−	1.96010i	0.740849	−	0.740849i	−0.231893	−	0.972741i	$-0.574492\pi$
$7$	1.96010	−	1.96010i	0.740849	−	0.740849i	0.972741	+	0.231893i	$0.0744918\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.461565	+	2.96428i	−0.153855	+	0.988093i
$10$	−1.43919	+	1.71135i	−0.455113	+	0.541176i
$11$		−	2.97195i		−	0.896078i	−0.894014	−	0.448039i	$-0.852123\pi$
$11$		−	2.97195i		−	0.896078i	0.894014	−	0.448039i	$-0.147877\pi$
$12$	−1.31559	+	1.12660i	−0.379779	+	0.325220i
$13$	−1.33263	−	1.33263i	−0.369605	−	0.369605i	0.497728	−	0.867333i	$-0.334168\pi$
$13$	−1.33263	−	1.33263i	−0.369605	−	0.369605i	−0.867333	+	0.497728i	$0.834168\pi$
$14$	−2.77200			−0.740849
$15$	2.71403	−	2.76297i	0.700761	−	0.713397i
$16$	−1.00000			−0.250000
$17$	0.217329	+	0.217329i	0.0527100	+	0.0527100i	0.732970	−	0.680260i	$-0.238133\pi$
$17$	0.217329	+	0.217329i	0.0527100	+	0.0527100i	−0.680260	+	0.732970i	$0.738133\pi$
$18$	2.42244	−	1.76969i	0.570974	−	0.417119i
$19$		−	6.42606i		−	1.47424i	−0.675762	−	0.737120i	$-0.736185\pi$
$19$		−	6.42606i		−	1.47424i	0.675762	−	0.737120i	$-0.263815\pi$
$20$	2.22777	−	0.192443i	0.498145	−	0.0430315i
$21$	4.78694	+	0.370453i	1.04459	+	0.0808394i
$22$	−2.10149	+	2.10149i	−0.448039	+	0.448039i
$23$	−0.707107	+	0.707107i	−0.147442	+	0.147442i
$23$	−0.707107	+	0.707107i	−0.147442	+	0.147442i
$24$	1.72689	+	0.133641i	0.352499	+	0.0272793i
$25$	−4.92593	+	0.857436i	−0.985186	+	0.171487i
$26$			1.88462i			0.369605i
$27$	−4.41978	+	2.73231i	−0.850587	+	0.525834i
$28$	1.96010	+	1.96010i	0.370424	+	0.370424i
$29$	−1.22002			−0.226552			−0.113276	−	0.993564i	$-0.536134\pi$
$29$	−1.22002			−0.226552			−0.113276	+	0.993564i	$0.536134\pi$
$30$	−3.87283	+	0.0346053i	−0.707079	+	0.00631804i
$31$	6.33502			1.13780			0.568902	−	0.822405i	$-0.307368\pi$
$31$	6.33502			1.13780			0.568902	+	0.822405i	$0.307368\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	3.90988	−	3.34819i	0.680623	−	0.582845i
$34$		−	0.307349i		−	0.0527100i
$35$	−4.74387	−	3.98945i	−0.801860	−	0.674340i
$36$	−2.96428	−	0.461565i	−0.494047	−	0.0769276i
$37$	1.43305	−	1.43305i	0.235592	−	0.235592i	−0.579430	−	0.815022i	$-0.696725\pi$
$37$	1.43305	−	1.43305i	0.235592	−	0.235592i	0.815022	+	0.579430i	$0.196725\pi$
$38$	−4.54391	+	4.54391i	−0.737120	+	0.737120i
$39$	0.251863	−	3.25453i	0.0403303	−	0.521142i
$40$	−1.71135	−	1.43919i	−0.270588	−	0.227557i
$41$			3.04579i			0.475672i	0.971305	+	0.237836i	$0.0764380\pi$
$41$			3.04579i			0.475672i	−0.971305	+	0.237836i	$0.923562\pi$
$42$	−3.12292	−	3.64682i	−0.481878	−	0.562717i
$43$	−1.80190	−	1.80190i	−0.274786	−	0.274786i	0.556237	−	0.831024i	$-0.312245\pi$
$43$	−1.80190	−	1.80190i	−0.274786	−	0.274786i	−0.831024	+	0.556237i	$0.812245\pi$
$44$	2.97195			0.448039
$45$	6.69256	+	0.457809i	0.997669	+	0.0682461i
$46$	1.00000			0.147442
$47$	0.199419	+	0.199419i	0.0290883	+	0.0290883i	0.721501	−	0.692413i	$-0.243452\pi$
$47$	0.199419	+	0.199419i	0.0290883	+	0.0290883i	−0.692413	+	0.721501i	$0.743452\pi$
$48$	−1.12660	−	1.31559i	−0.162610	−	0.189889i
$49$		−	0.683996i		−	0.0977137i
$50$	4.08946	+	2.87686i	0.578337	+	0.406850i
$51$	−0.0410744	+	0.530758i	−0.00575157	+	0.0743210i
$52$	1.33263	−	1.33263i	0.184803	−	0.184803i
$53$	9.17886	−	9.17886i	1.26081	−	1.26081i	0.310114	−	0.950699i	$-0.399633\pi$
$53$	9.17886	−	9.17886i	1.26081	−	1.26081i	0.950699	−	0.310114i	$-0.100367\pi$
$54$	5.05729	+	1.19322i	0.688211	+	0.162377i
$55$	−6.62083	+	0.571930i	−0.892753	+	0.0771191i
$56$		−	2.77200i		−	0.370424i
$57$	8.45408	−	7.23957i	1.11977	−	0.958905i
$58$	0.862686	+	0.862686i	0.113276	+	0.113276i
$59$	9.43000			1.22768			0.613841	−	0.789430i	$-0.289624\pi$
$59$	9.43000			1.22768			0.613841	+	0.789430i	$0.289624\pi$
$60$	2.76297	+	2.71403i	0.356698	+	0.350380i
$61$	5.57225			0.713454			0.356727	−	0.934209i	$-0.383893\pi$
$61$	5.57225			0.713454			0.356727	+	0.934209i	$0.383893\pi$
$62$	−4.47954	−	4.47954i	−0.568902	−	0.568902i
$63$	4.90558	+	6.71501i	0.618044	+	0.846011i
$64$		−	1.00000i		−	0.125000i
$65$	−2.71234	+	3.22525i	−0.336425	+	0.400043i
$66$	−5.13223	−	0.397175i	−0.631734	−	0.0488888i
$67$	9.41060	−	9.41060i	1.14969	−	1.14969i	0.163074	−	0.986614i	$-0.447859\pi$
$67$	9.41060	−	9.41060i	1.14969	−	1.14969i	0.986614	−	0.163074i	$-0.0521410\pi$
$68$	−0.217329	+	0.217329i	−0.0263550	+	0.0263550i
$69$	−1.72689	−	0.133641i	−0.207893	−	0.0160885i
$70$	0.533451	+	6.17539i	0.0637596	+	0.738100i
$71$			7.64983i			0.907868i	0.891035	+	0.453934i	$0.149980\pi$
$71$			7.64983i			0.907868i	−0.891035	+	0.453934i	$0.850020\pi$
$72$	1.76969	+	2.42244i	0.208560	+	0.285487i
$73$	−4.05708	−	4.05708i	−0.474845	−	0.474845i	0.428633	−	0.903479i	$-0.358995\pi$
$73$	−4.05708	−	4.05708i	−0.474845	−	0.474845i	−0.903479	+	0.428633i	$0.858995\pi$
$74$	−2.02664			−0.235592
$75$	−6.67757	−	5.51453i	−0.771059	−	0.636763i
$76$	6.42606			0.737120
$77$	−5.82533	−	5.82533i	−0.663858	−	0.663858i
$78$	−2.47940	+	2.12321i	−0.280736	+	0.240406i
$79$			14.4298i			1.62348i	0.584018	+	0.811741i	$0.301480\pi$
$79$			14.4298i			1.62348i	−0.584018	+	0.811741i	$0.698520\pi$
$80$	0.192443	+	2.22777i	0.0215157	+	0.249072i
$81$	−8.57391	−	2.73642i	−0.952657	−	0.304047i
$82$	2.15370	−	2.15370i	0.237836	−	0.237836i
$83$	−12.1736	+	12.1736i	−1.33622	+	1.33622i	−0.436533	+	0.899688i	$0.643794\pi$
$83$	−12.1736	+	12.1736i	−1.33622	+	1.33622i	−0.899688	+	0.436533i	$0.856206\pi$
$84$	−0.370453	+	4.78694i	−0.0404197	+	0.522297i
$85$	0.442336	−	0.525982i	0.0479780	−	0.0570508i
$86$			2.54827i			0.274786i
$87$	−1.37447	−	1.60505i	−0.147359	−	0.172080i
$88$	−2.10149	−	2.10149i	−0.224019	−	0.224019i
$89$	−2.45643			−0.260381			−0.130191	−	0.991489i	$-0.541559\pi$
$89$	−2.45643			−0.260381			−0.130191	+	0.991489i	$0.541559\pi$
$90$	−4.40864	−	5.05608i	−0.464711	−	0.532957i
$91$	−5.22418			−0.547643
$92$	−0.707107	−	0.707107i	−0.0737210	−	0.0737210i
$93$	7.13701	+	8.33431i	0.740073	+	0.864227i
$94$		−	0.282021i		−	0.0290883i
$95$	−14.3158	+	1.23665i	−1.46877	+	0.126877i
$96$	−0.133641	+	1.72689i	−0.0136397	+	0.176250i
$97$	8.98748	−	8.98748i	0.912541	−	0.912541i	−0.0839309	−	0.996472i	$-0.526748\pi$
$97$	8.98748	−	8.98748i	0.912541	−	0.912541i	0.996472	+	0.0839309i	$0.0267475\pi$
$98$	−0.483658	+	0.483658i	−0.0488568	+	0.0488568i
$99$	8.80970	+	1.37175i	0.885409	+	0.137866i
$100$	−0.857436	−	4.92593i	−0.0857436	−	0.492593i
$101$			3.00976i			0.299482i	0.988725	+	0.149741i	$0.0478440\pi$
$101$			3.00976i			0.299482i	−0.988725	+	0.149741i	$0.952156\pi$
$102$	0.404346	−	0.346258i	0.0400363	−	0.0342847i
$103$	−1.81831	−	1.81831i	−0.179163	−	0.179163i	0.611828	−	0.790991i	$-0.290435\pi$
$103$	−1.81831	−	1.81831i	−0.179163	−	0.179163i	−0.790991	+	0.611828i	$0.790435\pi$
$104$	−1.88462			−0.184803
$105$	−0.0959261	−	10.7355i	−0.00936143	−	1.04768i
$106$	−12.9809			−1.26081
$107$	−10.1552	−	10.1552i	−0.981744	−	0.981744i	0.0180921	−	0.999836i	$-0.494241\pi$
$107$	−10.1552	−	10.1552i	−0.981744	−	0.981744i	−0.999836	+	0.0180921i	$0.994241\pi$
$108$	−2.73231	−	4.41978i	−0.262917	−	0.425294i
$109$			3.22282i			0.308690i	0.988017	+	0.154345i	$0.0493268\pi$
$109$			3.22282i			0.308690i	−0.988017	+	0.154345i	$0.950673\pi$
$110$	5.08605	+	4.27722i	0.484936	+	0.407817i
$111$	3.49978	+	0.270842i	0.332184	+	0.0257072i
$112$	−1.96010	+	1.96010i	−0.185212	+	0.185212i
$113$	−3.72990	+	3.72990i	−0.350880	+	0.350880i	−0.860437	−	0.509557i	$-0.829809\pi$
$113$	−3.72990	+	3.72990i	−0.350880	+	0.350880i	0.509557	+	0.860437i	$0.329809\pi$
$114$	−11.0971	−	0.858785i	−1.03934	−	0.0804326i
$115$	1.71135	+	1.43919i	0.159584	+	0.134206i
$116$		−	1.22002i		−	0.113276i
$117$	4.56539	−	3.33519i	0.422070	−	0.308339i
$118$	−6.66802	−	6.66802i	−0.613841	−	0.613841i
$119$	0.851973			0.0781003
$120$	−0.0346053	−	3.87283i	−0.00315902	−	0.353539i
$121$	2.16749			0.197044
$122$	−3.94018	−	3.94018i	−0.356727	−	0.356727i
$123$	−4.00701	+	3.43137i	−0.361300	+	0.309396i
$124$			6.33502i			0.568902i
$125$	2.85813	+	10.8088i	0.255639	+	0.966772i
$126$	1.27946	−	8.21699i	0.113983	−	0.732028i
$127$	−9.95020	+	9.95020i	−0.882938	+	0.882938i	−0.993832	−	0.110895i	$-0.964628\pi$
$127$	−9.95020	+	9.95020i	−0.882938	+	0.882938i	0.110895	+	0.993832i	$0.464628\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	0.340552	−	4.40057i	0.0299840	−	0.387448i
$130$	4.19851	−	0.362682i	0.368234	−	0.0318093i
$131$			4.14724i			0.362346i	0.983451	+	0.181173i	$0.0579894\pi$
$131$			4.14724i			0.362346i	−0.983451	+	0.181173i	$0.942011\pi$
$132$	3.34819	+	3.90988i	0.291423	+	0.340311i
$133$	−12.5957	−	12.5957i	−1.09219	−	1.09219i
$134$	−13.3086			−1.14969
$135$	6.93752	+	9.32045i	0.597087	+	0.802177i
$136$	0.307349			0.0263550
$137$	6.71805	+	6.71805i	0.573962	+	0.573962i	0.933233	−	0.359271i	$-0.116975\pi$
$137$	6.71805	+	6.71805i	0.573962	+	0.573962i	−0.359271	+	0.933233i	$0.616975\pi$
$138$	1.12660	+	1.31559i	0.0959022	+	0.111991i
$139$			21.3303i			1.80921i	0.426247	+	0.904607i	$0.359835\pi$
$139$			21.3303i			1.80921i	−0.426247	+	0.904607i	$0.640165\pi$
$140$	3.98945	−	4.74387i	0.337170	−	0.400930i
$141$	−0.0376896	+	0.487019i	−0.00317404	+	0.0410144i
$142$	5.40925	−	5.40925i	0.453934	−	0.453934i
$143$	−3.96052	+	3.96052i	−0.331195	+	0.331195i
$144$	0.461565	−	2.96428i	0.0384638	−	0.247023i
$145$	0.234784	+	2.71793i	0.0194978	+	0.225712i
$146$			5.73758i			0.474845i
$147$	0.899860	−	0.770587i	0.0742192	−	0.0635569i
$148$	1.43305	+	1.43305i	0.117796	+	0.117796i
$149$	2.04707			0.167703			0.0838514	−	0.996478i	$-0.473278\pi$
$149$	2.04707			0.167703			0.0838514	+	0.996478i	$0.473278\pi$
$150$	0.822390	+	8.62112i	0.0671479	+	0.703911i
$151$	−2.64015			−0.214852			−0.107426	−	0.994213i	$-0.534261\pi$
$151$	−2.64015			−0.214852			−0.107426	+	0.994213i	$0.534261\pi$
$152$	−4.54391	−	4.54391i	−0.368560	−	0.368560i
$153$	−0.744535	+	0.543912i	−0.0601921	+	0.0439727i
$154$			8.23826i			0.663858i
$155$	−1.21913	−	14.1130i	−0.0979227	−	1.13358i
$156$	3.25453	+	0.251863i	0.260571	+	0.0201652i
$157$	0.750993	−	0.750993i	0.0599358	−	0.0599358i	−0.676504	−	0.736439i	$-0.736506\pi$
$157$	0.750993	−	0.750993i	0.0599358	−	0.0599358i	0.736439	+	0.676504i	$0.236506\pi$
$158$	10.2034	−	10.2034i	0.811741	−	0.811741i
$159$	22.4165	+	1.73477i	1.77774	+	0.137577i
$160$	1.43919	−	1.71135i	0.113778	−	0.135294i
$161$			2.77200i			0.218464i
$162$	4.12773	+	7.99761i	0.324305	+	0.628352i
$163$	6.60415	+	6.60415i	0.517277	+	0.517277i	0.916747	−	0.399469i	$-0.130806\pi$
$163$	6.60415	+	6.60415i	0.517277	+	0.517277i	−0.399469	+	0.916747i	$0.630806\pi$
$164$	−3.04579			−0.237836
$165$	−8.21143	−	8.06598i	−0.639259	−	0.627936i
$166$	17.2160			1.33622
$167$	5.25056	+	5.25056i	0.406300	+	0.406300i	0.880446	−	0.474146i	$-0.157243\pi$
$167$	5.25056	+	5.25056i	0.406300	+	0.406300i	−0.474146	+	0.880446i	$0.657243\pi$
$168$	3.64682	−	3.12292i	0.281359	−	0.240939i
$169$		−	9.44819i		−	0.726784i
$170$	−0.684704	+	0.0591471i	−0.0525144	+	0.00453638i
$171$	19.0487	+	2.96605i	1.45669	+	0.226819i
$172$	1.80190	−	1.80190i	0.137393	−	0.137393i
$173$	−16.1787	+	16.1787i	−1.23004	+	1.23004i	−0.266093	+	0.963947i	$0.585733\pi$
$173$	−16.1787	+	16.1787i	−1.23004	+	1.23004i	−0.963947	+	0.266093i	$0.914267\pi$
$174$	−0.163045	+	2.10684i	−0.0123604	+	0.159719i
$175$	−7.97466	+	11.3360i	−0.602828	+	0.856920i
$176$			2.97195i			0.224019i
$177$	10.6238	+	12.4060i	0.798533	+	0.932495i
$178$	1.73696	+	1.73696i	0.130191	+	0.130191i
$179$	12.6087			0.942418			0.471209	−	0.882022i	$-0.343818\pi$
$179$	12.6087			0.942418			0.471209	+	0.882022i	$0.343818\pi$
$180$	−0.457809	+	6.69256i	−0.0341230	+	0.498834i
$181$	−1.75381			−0.130360			−0.0651799	−	0.997874i	$-0.520762\pi$
$181$	−1.75381			−0.130360			−0.0651799	+	0.997874i	$0.520762\pi$
$182$	3.69405	+	3.69405i	0.273822	+	0.273822i
$183$	6.27767	+	7.33081i	0.464059	+	0.541909i
$184$			1.00000i			0.0737210i
$185$	−3.46829	−	2.91673i	−0.254994	−	0.214442i
$186$	0.846618	−	10.9399i	0.0620771	−	0.802150i
$187$	0.645891	−	0.645891i	0.0472322	−	0.0472322i
$188$	−0.199419	+	0.199419i	−0.0145441	+	0.0145441i
$189$	−3.30761	+	14.0188i	−0.240593	+	1.01972i
$190$	10.9972	+	9.24836i	0.797824	+	0.670946i
$191$			26.9285i			1.94848i	0.225520	+	0.974238i	$0.427592\pi$
$191$			26.9285i			1.94848i	−0.225520	+	0.974238i	$0.572408\pi$
$192$	1.31559	−	1.12660i	0.0949447	−	0.0813050i
$193$	−10.9317	−	10.9317i	−0.786878	−	0.786878i	0.194103	−	0.980981i	$-0.437820\pi$
$193$	−10.9317	−	10.9317i	−0.786878	−	0.786878i	−0.980981	+	0.194103i	$0.937820\pi$
$194$	−12.7102			−0.912541
$195$	−7.29883	+	0.0652180i	−0.522680	+	0.00467036i
$196$	0.683996			0.0488568
$197$	−1.97929	−	1.97929i	−0.141019	−	0.141019i	0.633073	−	0.774092i	$-0.281793\pi$
$197$	−1.97929	−	1.97929i	−0.141019	−	0.141019i	−0.774092	+	0.633073i	$0.781793\pi$
$198$	−5.25943	−	7.19938i	−0.373771	−	0.511637i
$199$			15.8892i			1.12636i	0.826336	+	0.563178i	$0.190421\pi$
$199$			15.8892i			1.12636i	−0.826336	+	0.563178i	$0.809579\pi$
$200$	−2.87686	+	4.08946i	−0.203425	+	0.289168i
$201$	22.9825	+	1.77857i	1.62106	+	0.125451i
$202$	2.12822	−	2.12822i	0.149741	−	0.149741i
$203$	−2.39137	+	2.39137i	−0.167841	+	0.167841i
$204$	−0.530758	−	0.0410744i	−0.0371605	−	0.00287579i
$205$	6.78531	−	0.586139i	0.473907	−	0.0409377i
$206$			2.57147i			0.179163i
$207$	−1.76969	−	2.42244i	−0.123002	−	0.168371i
$208$	1.33263	+	1.33263i	0.0924013	+	0.0924013i
$209$	−19.0980			−1.32103
$210$	−7.52331	+	7.65897i	−0.519158	+	0.528519i
$211$	11.3907			0.784169			0.392085	−	0.919929i	$-0.371754\pi$
$211$	11.3907			0.784169			0.392085	+	0.919929i	$0.371754\pi$
$212$	9.17886	+	9.17886i	0.630407	+	0.630407i
$213$	−10.0641	+	8.61826i	−0.689578	+	0.590514i
$214$			14.3617i			0.981744i
$215$	−3.66745	+	4.36097i	−0.250118	+	0.297416i
$216$	−1.19322	+	5.05729i	−0.0811884	+	0.344105i
$217$	12.4173	−	12.4173i	0.842941	−	0.842941i
$218$	2.27888	−	2.27888i	0.154345	−	0.154345i
$219$	0.766775	−	9.90815i	0.0518138	−	0.669531i
$220$	−0.571930	−	6.62083i	−0.0385595	−	0.446377i
$221$		−	0.579238i		−	0.0389638i
$222$	−2.28320	−	2.66623i	−0.153239	−	0.178946i
$223$	−10.4680	−	10.4680i	−0.700989	−	0.700989i	0.263634	−	0.964623i	$-0.415079\pi$
$223$	−10.4680	−	10.4680i	−0.700989	−	0.700989i	−0.964623	+	0.263634i	$0.915079\pi$
$224$	2.77200			0.185212
$225$	−0.268041	−	14.9976i	−0.0178694	−	0.999840i
$226$	5.27488			0.350880
$227$	−16.1663	−	16.1663i	−1.07299	−	1.07299i	−0.997117	−	0.0758747i	$-0.975825\pi$
$227$	−16.1663	−	16.1663i	−1.07299	−	1.07299i	−0.0758747	−	0.997117i	$-0.524175\pi$
$228$	7.23957	+	8.45408i	0.479453	+	0.559885i
$229$			16.0298i			1.05928i	0.848224	+	0.529638i	$0.177672\pi$
$229$			16.0298i			1.05928i	−0.848224	+	0.529638i	$0.822328\pi$
$230$	−0.192443	−	2.22777i	−0.0126893	−	0.146895i
$231$	1.10097	−	14.2266i	0.0724384	−	0.936038i
$232$	−0.862686	+	0.862686i	−0.0566381	+	0.0566381i
$233$	−4.14654	+	4.14654i	−0.271649	+	0.271649i	−0.829764	−	0.558115i	$-0.811525\pi$
$233$	−4.14654	+	4.14654i	−0.271649	+	0.271649i	0.558115	+	0.829764i	$0.311525\pi$
$234$	−5.58655	−	0.869877i	−0.365204	−	0.0568657i
$235$	0.405884	−	0.482637i	0.0264769	−	0.0314838i
$236$			9.43000i			0.613841i
$237$	−18.9838	+	16.2566i	−1.23313	+	1.05598i
$238$	−0.602436	−	0.602436i	−0.0390501	−	0.0390501i
$239$	29.7656			1.92538			0.962690	−	0.270608i	$-0.0872246\pi$
$239$	29.7656			1.92538			0.962690	+	0.270608i	$0.0872246\pi$
$240$	−2.71403	+	2.76297i	−0.175190	+	0.178349i
$241$	−18.1553			−1.16949			−0.584743	−	0.811219i	$-0.698805\pi$
$241$	−18.1553			−1.16949			−0.584743	+	0.811219i	$0.698805\pi$
$242$	−1.53265	−	1.53265i	−0.0985222	−	0.0985222i
$243$	−6.05932	−	14.3626i	−0.388706	−	0.921362i
$244$			5.57225i			0.356727i
$245$	−1.52379	+	0.131630i	−0.0973512	+	0.00840953i
$246$	5.25973	+	0.407041i	0.335348	+	0.0259520i
$247$	−8.56357	+	8.56357i	−0.544887	+	0.544887i
$248$	4.47954	−	4.47954i	0.284451	−	0.284451i
$249$	−29.7301	−	2.30076i	−1.88407	−	0.145805i
$250$	5.62200	−	9.66401i	0.355567	−	0.611206i
$251$		−	19.1213i		−	1.20693i	−0.797390	−	0.603464i	$-0.793787\pi$
$251$		−	19.1213i		−	1.20693i	0.797390	−	0.603464i	$-0.206213\pi$
$252$	−6.71501	+	4.90558i	−0.423006	+	0.309022i
$253$	2.10149	+	2.10149i	0.132119	+	0.132119i
$254$	14.0717			0.882938
$255$	1.19031	−	0.0106359i	0.0745402	−	0.000666048i
$256$	1.00000			0.0625000
$257$	17.0084	+	17.0084i	1.06096	+	1.06096i	0.998017	+	0.0629387i	$0.0200473\pi$
$257$	17.0084	+	17.0084i	1.06096	+	1.06096i	0.0629387	+	0.998017i	$0.479953\pi$
$258$	−3.35248	+	2.87086i	−0.208716	+	0.178732i
$259$		−	5.61785i		−	0.349076i
$260$	−3.22525	−	2.71234i	−0.200022	−	0.168212i
$261$	0.563120	−	3.61649i	0.0348563	−	0.223855i
$262$	2.93254	−	2.93254i	0.181173	−	0.181173i
$263$	12.3574	−	12.3574i	0.761992	−	0.761992i	−0.214690	−	0.976682i	$-0.568874\pi$
$263$	12.3574	−	12.3574i	0.761992	−	0.761992i	0.976682	+	0.214690i	$0.0688741\pi$
$264$	0.397175	−	5.13223i	0.0244444	−	0.315867i
$265$	−22.2148	−	18.6820i	−1.36464	−	1.14763i
$266$			17.8131i			1.09219i
$267$	−2.76740	−	3.23166i	−0.169362	−	0.197774i
$268$	9.41060	+	9.41060i	0.574844	+	0.574844i
$269$	20.0999			1.22552			0.612758	−	0.790271i	$-0.290060\pi$
$269$	20.0999			1.22552			0.612758	+	0.790271i	$0.290060\pi$
$270$	1.68498	−	11.4961i	0.102545	−	0.699632i
$271$	−27.8676			−1.69284			−0.846419	−	0.532518i	$-0.821246\pi$
$271$	−27.8676			−1.69284			−0.846419	+	0.532518i	$0.821246\pi$
$272$	−0.217329	−	0.217329i	−0.0131775	−	0.0131775i
$273$	−5.88554	−	6.87289i	−0.356209	−	0.415966i
$274$		−	9.50076i		−	0.573962i
$275$	2.54826	+	14.6396i	0.153666	+	0.882804i
$276$	0.133641	−	1.72689i	0.00804423	−	0.103946i
$277$	7.04930	−	7.04930i	0.423551	−	0.423551i	−0.462873	−	0.886424i	$-0.653182\pi$
$277$	7.04930	−	7.04930i	0.423551	−	0.423551i	0.886424	+	0.462873i	$0.153182\pi$
$278$	15.0828	−	15.0828i	0.904607	−	0.904607i
$279$	−2.92403	+	18.7788i	−0.175057	+	1.12426i
$280$	−6.17539	+	0.533451i	−0.369050	+	0.0318798i
$281$		−	15.7886i		−	0.941867i	−0.882169	−	0.470934i	$-0.843917\pi$
$281$		−	15.7886i		−	0.941867i	0.882169	−	0.470934i	$-0.156083\pi$
$282$	0.371025	−	0.317724i	0.0220942	−	0.0189202i
$283$	13.2043	+	13.2043i	0.784912	+	0.784912i	0.980655	−	0.195743i	$-0.0627118\pi$
$283$	13.2043	+	13.2043i	0.784912	+	0.784912i	−0.195743	+	0.980655i	$0.562712\pi$
$284$	−7.64983			−0.453934
$285$	−17.7550	−	17.4406i	−1.05172	−	1.03309i
$286$	5.60102			0.331195
$287$	5.97005	+	5.97005i	0.352401	+	0.352401i
$288$	−2.42244	+	1.76969i	−0.142744	+	0.104280i
$289$		−	16.9055i		−	0.994443i
$290$	1.75585	−	2.08788i	0.103107	−	0.122605i
$291$	21.9491	+	1.69860i	1.28668	+	0.0995740i
$292$	4.05708	−	4.05708i	0.237423	−	0.237423i
$293$	6.93824	−	6.93824i	0.405336	−	0.405336i	−0.474772	−	0.880109i	$-0.657470\pi$
$293$	6.93824	−	6.93824i	0.405336	−	0.405336i	0.880109	+	0.474772i	$0.157470\pi$
$294$	−1.18118	−	0.0914098i	−0.0688880	−	0.00533113i
$295$	−1.81473	−	21.0079i	−0.105658	−	1.22313i
$296$		−	2.02664i		−	0.117796i
$297$	8.12031	+	13.1354i	0.471188	+	0.762192i
$298$	−1.44750	−	1.44750i	−0.0838514	−	0.0838514i
$299$	1.88462			0.108991
$300$	5.51453	−	6.67757i	0.318382	−	0.385530i
$301$	−7.06380			−0.407150
$302$	1.86687	+	1.86687i	0.107426	+	0.107426i
$303$	−3.95962	+	3.39078i	−0.227474	+	0.194795i
$304$			6.42606i			0.368560i
$305$	−1.07234	−	12.4137i	−0.0614019	−	0.710807i
$306$	0.911070	+	0.141862i	0.0520824	+	0.00810970i
$307$	−8.38939	+	8.38939i	−0.478808	+	0.478808i	−0.904750	−	0.425943i	$-0.859943\pi$
$307$	−8.38939	+	8.38939i	−0.478808	+	0.478808i	0.425943	+	0.904750i	$0.359943\pi$
$308$	5.82533	−	5.82533i	0.331929	−	0.331929i
$309$	0.343654	−	4.44065i	0.0195498	−	0.252620i
$310$	−9.11733	+	10.8414i	−0.517830	+	0.615753i
$311$		−	22.7094i		−	1.28773i	−0.765139	−	0.643865i	$-0.777330\pi$
$311$		−	22.7094i		−	1.28773i	0.765139	−	0.643865i	$-0.222670\pi$
$312$	−2.12321	−	2.47940i	−0.120203	−	0.140368i
$313$	−19.0911	−	19.0911i	−1.07909	−	1.07909i	−0.996591	−	0.0825035i	$-0.973708\pi$
$313$	−19.0911	−	19.0911i	−1.07909	−	1.07909i	−0.0825035	−	0.996591i	$-0.526292\pi$
$314$	−1.06206			−0.0599358
$315$	14.0155	−	12.2208i	0.789681	−	0.688561i
$316$	−14.4298			−0.811741
$317$	−0.0275450	−	0.0275450i	−0.00154708	−	0.00154708i	0.706333	−	0.707880i	$-0.250348\pi$
$317$	−0.0275450	−	0.0275450i	−0.00154708	−	0.00154708i	−0.707880	+	0.706333i	$0.750348\pi$
$318$	−14.6242	−	17.0775i	−0.820084	−	0.957660i
$319$			3.62585i			0.203009i
$320$	−2.22777	+	0.192443i	−0.124536	+	0.0107579i
$321$	1.91931	−	24.8010i	0.107125	−	1.38426i
$322$	1.96010	−	1.96010i	0.109232	−	0.109232i
$323$	1.39657	−	1.39657i	0.0777072	−	0.0777072i
$324$	2.73642	−	8.57391i	0.152023	−	0.476329i
$325$	7.70709	+	5.42180i	0.427513	+	0.300747i
$326$		−	9.33968i		−	0.517277i
$327$	−4.23992	+	3.63082i	−0.234468	+	0.200785i
$328$	2.15370	+	2.15370i	0.118918	+	0.118918i
$329$	0.781764			0.0431000
$330$	0.102845	+	11.5099i	0.00566146	+	0.633597i
$331$	1.05162			0.0578024			0.0289012	−	0.999582i	$-0.490799\pi$
$331$	1.05162			0.0578024			0.0289012	+	0.999582i	$0.490799\pi$
$332$	−12.1736	−	12.1736i	−0.668111	−	0.668111i
$333$	3.58652	+	4.90941i	0.196540	+	0.269034i
$334$		−	7.42541i		−	0.406300i
$335$	−22.7757	−	19.1537i	−1.24437	−	1.04648i
$336$	−4.78694	−	0.370453i	−0.261149	−	0.0202099i
$337$	−10.0242	+	10.0242i	−0.546054	+	0.546054i	−0.925297	−	0.379243i	$-0.876184\pi$
$337$	−10.0242	+	10.0242i	−0.546054	+	0.546054i	0.379243	+	0.925297i	$0.376184\pi$
$338$	−6.68088	+	6.68088i	−0.363392	+	0.363392i
$339$	−9.10912	−	0.704939i	−0.494740	−	0.0382871i
$340$	0.525982	+	0.442336i	0.0285254	+	0.0239890i
$341$		−	18.8274i		−	1.01956i
$342$	−11.3721	−	15.5667i	−0.614934	−	0.841753i
$343$	12.3800	+	12.3800i	0.668458	+	0.668458i
$344$	−2.54827			−0.137393
$345$	0.0346053	+	3.87283i	0.00186309	+	0.208506i
$346$	22.8801			1.23004
$347$	18.2887	+	18.2887i	0.981790	+	0.981790i	0.999837	−	0.0180467i	$-0.00574476\pi$
$347$	18.2887	+	18.2887i	0.981790	+	0.981790i	−0.0180467	+	0.999837i	$0.505745\pi$
$348$	1.60505	−	1.37447i	0.0860398	−	0.0736794i
$349$			28.7041i			1.53649i	0.640154	+	0.768247i	$0.278871\pi$
$349$			28.7041i			1.53649i	−0.640154	+	0.768247i	$0.721129\pi$
$350$	13.6547	−	2.37681i	0.729874	−	0.127046i
$351$	9.53110	+	2.24877i	0.508732	+	0.120031i
$352$	2.10149	−	2.10149i	0.112010	−	0.112010i
$353$	10.4582	−	10.4582i	0.556631	−	0.556631i	−0.371715	−	0.928347i	$-0.621230\pi$
$353$	10.4582	−	10.4582i	0.556631	−	0.556631i	0.928347	+	0.371715i	$0.121230\pi$
$354$	1.26023	−	16.2846i	0.0669807	−	0.865514i
$355$	17.0421	−	1.47215i	0.904499	−	0.0781337i
$356$		−	2.45643i		−	0.130191i
$357$	0.959829	+	1.12085i	0.0507995	+	0.0593216i
$358$	−8.91569	−	8.91569i	−0.471209	−	0.471209i
$359$	−10.4419			−0.551105			−0.275552	−	0.961286i	$-0.588861\pi$
$359$	−10.4419			−0.551105			−0.275552	+	0.961286i	$0.588861\pi$
$360$	5.05608	−	4.40864i	0.266479	−	0.232356i
$361$	−22.2943			−1.17338
$362$	1.24013	+	1.24013i	0.0651799	+	0.0651799i
$363$	2.44188	+	2.85153i	0.128166	+	0.149667i
$364$		−	5.22418i		−	0.273822i
$365$	−8.25749	+	9.81900i	−0.432217	+	0.513950i
$366$	0.744681	−	9.62265i	0.0389251	−	0.502984i
$367$	11.3139	−	11.3139i	0.590580	−	0.590580i	−0.347208	−	0.937788i	$-0.612870\pi$
$367$	11.3139	−	11.3139i	0.590580	−	0.590580i	0.937788	+	0.347208i	$0.112870\pi$
$368$	0.707107	−	0.707107i	0.0368605	−	0.0368605i
$369$	−9.02856	−	1.40583i	−0.470008	−	0.0731846i
$370$	0.390012	+	4.51489i	0.0202758	+	0.234718i
$371$		−	35.9830i		−	1.86814i
$372$	−8.33431	+	7.13701i	−0.432114	+	0.370037i
$373$	−20.2494	−	20.2494i	−1.04847	−	1.04847i	−0.998764	−	0.0497082i	$-0.984171\pi$
$373$	−20.2494	−	20.2494i	−1.04847	−	1.04847i	−0.0497082	−	0.998764i	$-0.515829\pi$
$374$	−0.913428			−0.0472322
$375$	−11.0001	+	15.9373i	−0.568041	+	0.823000i
$376$	0.282021			0.0145441
$377$	1.62584	+	1.62584i	0.0837349	+	0.0837349i
$378$	12.2516	−	7.57398i	0.630157	−	0.389563i
$379$			31.4641i			1.61620i	0.589042	+	0.808102i	$0.299505\pi$
$379$			31.4641i			1.61620i	−0.589042	+	0.808102i	$0.700495\pi$
$380$	−1.23665	−	14.3158i	−0.0634387	−	0.734385i
$381$	−24.3003	−	1.88056i	−1.24494	−	0.0963438i
$382$	19.0413	−	19.0413i	0.974238	−	0.974238i
$383$	−5.10098	+	5.10098i	−0.260648	+	0.260648i	−0.825317	−	0.564669i	$-0.809004\pi$
$383$	−5.10098	+	5.10098i	−0.260648	+	0.260648i	0.564669	+	0.825317i	$0.309004\pi$
$384$	−1.72689	−	0.133641i	−0.0881249	−	0.00681983i
$385$	−11.8565	+	14.0985i	−0.604261	+	0.718529i
$386$			15.4597i			0.786878i
$387$	6.17302	−	4.50963i	0.313792	−	0.229237i
$388$	8.98748	+	8.98748i	0.456270	+	0.456270i
$389$	18.3647			0.931129			0.465565	−	0.885014i	$-0.345851\pi$
$389$	18.3647			0.931129			0.465565	+	0.885014i	$0.345851\pi$
$390$	5.20717	+	5.11493i	0.263675	+	0.259005i
$391$	−0.307349			−0.0155433
$392$	−0.483658	−	0.483658i	−0.0244284	−	0.0244284i
$393$	−5.45608	+	4.67226i	−0.275223	+	0.235685i
$394$			2.79914i			0.141019i
$395$	32.1463	−	2.77691i	1.61746	−	0.139722i
$396$	−1.37175	+	8.80970i	−0.0689331	+	0.442704i
$397$	−6.90089	+	6.90089i	−0.346346	+	0.346346i	−0.858746	−	0.512401i	$-0.828756\pi$
$397$	−6.90089	+	6.90089i	−0.346346	+	0.346346i	0.512401	+	0.858746i	$0.328756\pi$
$398$	11.2354	−	11.2354i	0.563178	−	0.563178i
$399$	2.38055	−	30.7612i	0.119177	−	1.53998i
$400$	4.92593	−	0.857436i	0.246297	−	0.0428718i
$401$			18.3481i			0.916261i	0.888885	+	0.458131i	$0.151481\pi$
$401$			18.3481i			0.916261i	−0.888885	+	0.458131i	$0.848519\pi$
$402$	−14.9934	−	17.5087i	−0.747803	−	0.873254i
$403$	−8.44225	−	8.44225i	−0.420538	−	0.420538i
$404$	−3.00976			−0.149741
$405$	−4.44613	+	19.6273i	−0.220930	+	0.975290i
$406$	3.38190			0.167841
$407$	−4.25896	−	4.25896i	−0.211109	−	0.211109i
$408$	0.346258	+	0.404346i	0.0171423	+	0.0200181i
$409$		−	15.8713i		−	0.784783i	−0.919798	−	0.392392i	$-0.871648\pi$
$409$		−	15.8713i		−	0.784783i	0.919798	−	0.392392i	$-0.128352\pi$
$410$	−5.21240	−	4.38348i	−0.257422	−	0.216485i
$411$	−1.26969	+	16.4067i	−0.0626292	+	0.809285i
$412$	1.81831	−	1.81831i	0.0895816	−	0.0895816i
$413$	18.4838	−	18.4838i	0.909526	−	0.909526i
$414$	−0.461565	+	2.96428i	−0.0226847	+	0.145686i
$415$	29.4626	+	24.7772i	1.44626	+	1.21626i
$416$		−	1.88462i		−	0.0924013i
$417$	−28.0620	+	24.0306i	−1.37420	+	1.17679i
$418$	13.5043	+	13.5043i	0.660517	+	0.660517i
$419$	−19.9035			−0.972349			−0.486175	−	0.873862i	$-0.661608\pi$
$419$	−19.9035			−0.972349			−0.486175	+	0.873862i	$0.661608\pi$
$420$	10.7355	−	0.0959261i	0.523838	−	0.00468071i
$421$	−9.07200			−0.442142			−0.221071	−	0.975258i	$-0.570955\pi$
$421$	−9.07200			−0.442142			−0.221071	+	0.975258i	$0.570955\pi$
$422$	−8.05445	−	8.05445i	−0.392085	−	0.392085i
$423$	−0.683180	+	0.499089i	−0.0332173	+	0.0242666i
$424$		−	12.9809i		−	0.630407i
$425$	−1.25689	−	0.884201i	−0.0609682	−	0.0428901i
$426$	13.2104	+	1.02233i	0.640046	+	0.0495320i
$427$	10.9222	−	10.9222i	0.528561	−	0.528561i
$428$	10.1552	−	10.1552i	0.490872	−	0.490872i
$429$	−9.67232	−	0.748525i	−0.466984	−	0.0361391i
$430$	5.67695	−	0.490395i	0.273767	−	0.0236489i
$431$		−	6.60333i		−	0.318071i	−0.987273	−	0.159036i	$-0.949162\pi$
$431$		−	6.60333i		−	0.318071i	0.987273	−	0.159036i	$-0.0508384\pi$
$432$	4.41978	−	2.73231i	0.212647	−	0.131458i
$433$	−2.95935	−	2.95935i	−0.142217	−	0.142217i	0.632414	−	0.774631i	$-0.282064\pi$
$433$	−2.95935	−	2.95935i	−0.142217	−	0.142217i	−0.774631	+	0.632414i	$0.782064\pi$
$434$	−17.5607			−0.842941
$435$	−3.31118	+	3.37089i	−0.158759	+	0.161622i
$436$	−3.22282			−0.154345
$437$	4.54391	+	4.54391i	0.217365	+	0.217365i
$438$	−7.54831	+	6.46393i	−0.360672	+	0.308858i
$439$			11.2528i			0.537068i	0.963270	+	0.268534i	$0.0865392\pi$
$439$			11.2528i			0.537068i	−0.963270	+	0.268534i	$0.913461\pi$
$440$	−4.27722	+	5.08605i	−0.203909	+	0.242468i
$441$	2.02756	+	0.315709i	0.0965503	+	0.0150338i
$442$	−0.409583	+	0.409583i	−0.0194819	+	0.0194819i
$443$	16.2317	−	16.2317i	0.771194	−	0.771194i	−0.207122	−	0.978315i	$-0.566410\pi$
$443$	16.2317	−	16.2317i	0.771194	−	0.771194i	0.978315	+	0.207122i	$0.0664096\pi$
$444$	−0.270842	+	3.49978i	−0.0128536	+	0.166092i
$445$	0.472722	+	5.47236i	0.0224092	+	0.259415i
$446$			14.8040i			0.700989i
$447$	2.30622	+	2.69311i	0.109081	+	0.127380i
$448$	−1.96010	−	1.96010i	−0.0926061	−	0.0926061i
$449$	3.47861			0.164166			0.0820828	−	0.996626i	$-0.473843\pi$
$449$	3.47861			0.164166			0.0820828	+	0.996626i	$0.473843\pi$
$450$	−10.4154	+	10.7944i	−0.490985	+	0.508855i
$451$	9.05193			0.426239
$452$	−3.72990	−	3.72990i	−0.175440	−	0.175440i
$453$	−2.97438	−	3.47336i	−0.139749	−	0.163193i
$454$			22.8625i			1.07299i
$455$	1.00535	+	11.6383i	0.0471318	+	0.545611i
$456$	0.858785	−	11.0971i	0.0402163	−	0.519669i
$457$	24.5212	−	24.5212i	1.14705	−	1.14705i	0.159925	−	0.987129i	$-0.448875\pi$
$457$	24.5212	−	24.5212i	1.14705	−	1.14705i	0.987129	−	0.159925i	$-0.0511251\pi$
$458$	11.3347	−	11.3347i	0.529638	−	0.529638i
$459$	−1.55436	−	0.366736i	−0.0725511	−	0.0171178i
$460$	−1.43919	+	1.71135i	−0.0671028	+	0.0797921i
$461$		−	7.06441i		−	0.329022i	−0.986375	−	0.164511i	$-0.947395\pi$
$461$		−	7.06441i		−	0.329022i	0.986375	−	0.164511i	$-0.0526047\pi$
$462$	−10.8382	+	9.28119i	−0.504238	+	0.431800i
$463$	4.91698	+	4.91698i	0.228512	+	0.228512i	0.812071	−	0.583559i	$-0.198340\pi$
$463$	4.91698	+	4.91698i	0.228512	+	0.228512i	−0.583559	+	0.812071i	$0.698340\pi$
$464$	1.22002			0.0566381
$465$	17.1935	−	17.5035i	0.797328	−	0.811705i
$466$	5.86409			0.271649
$467$	−0.279235	−	0.279235i	−0.0129214	−	0.0129214i	0.700617	−	0.713538i	$-0.252908\pi$
$467$	−0.279235	−	0.279235i	−0.0129214	−	0.0129214i	−0.713538	+	0.700617i	$0.752908\pi$
$468$	3.33519	+	4.56539i	0.154169	+	0.211035i
$469$		−	36.8915i		−	1.70349i
$470$	−0.628279	+	0.0542729i	−0.0289804	+	0.00250342i
$471$	1.83407	+	0.141935i	0.0845093	+	0.00654003i
$472$	6.66802	−	6.66802i	0.306920	−	0.306920i
$473$	−5.35515	+	5.35515i	−0.246230	+	0.246230i
$474$	24.9187	+	1.92841i	1.14455	+	0.0885750i
$475$	5.50994	+	31.6544i	0.252813	+	1.45240i
$476$			0.851973i			0.0390501i
$477$	22.9721	+	31.4454i	1.05182	+	1.43978i
$478$	−21.0475	−	21.0475i	−0.962690	−	0.962690i
$479$	19.9714			0.912518			0.456259	−	0.889847i	$-0.349189\pi$
$479$	19.9714			0.912518			0.456259	+	0.889847i	$0.349189\pi$
$480$	3.87283	−	0.0346053i	0.176770	−	0.00157951i
$481$	−3.81946			−0.174152
$482$	12.8377	+	12.8377i	0.584743	+	0.584743i
$483$	−3.64682	+	3.12292i	−0.165936	+	0.142098i
$484$			2.16749i			0.0985222i
$485$	−21.7516	−	18.2925i	−0.987691	−	0.830619i
$486$	−5.87131	+	14.4405i	−0.266328	+	0.655034i
$487$	−1.40410	+	1.40410i	−0.0636258	+	0.0636258i	−0.738204	−	0.674578i	$-0.764326\pi$
$487$	−1.40410	+	1.40410i	−0.0636258	+	0.0636258i	0.674578	+	0.738204i	$0.264326\pi$
$488$	3.94018	−	3.94018i	0.178363	−	0.178363i
$489$	−1.24816	+	16.1286i	−0.0564439	+	0.729360i
$490$	1.17056	+	0.984403i	0.0528803	+	0.0444708i
$491$			6.45884i			0.291483i	0.989323	+	0.145742i	$0.0465568\pi$
$491$			6.45884i			0.291483i	−0.989323	+	0.145742i	$0.953443\pi$
$492$	−3.43137	−	4.00701i	−0.154698	−	0.180650i
$493$	−0.265146	−	0.265146i	−0.0119416	−	0.0119416i
$494$	12.1107			0.544887
$495$	1.36059	−	19.8900i	0.0611538	−	0.893989i
$496$	−6.33502			−0.284451
$497$	14.9944	+	14.9944i	0.672593	+	0.672593i
$498$	19.3955	+	22.6492i	0.869132	+	1.01494i
$499$		−	9.53761i		−	0.426962i	−0.976947	−	0.213481i	$-0.931520\pi$
$499$		−	9.53761i		−	0.426962i	0.976947	−	0.213481i	$-0.0684802\pi$
$500$	−10.8088	+	2.85813i	−0.483386	+	0.127819i
$501$	−0.992338	+	12.8228i	−0.0443344	+	0.572883i
$502$	−13.5208	+	13.5208i	−0.603464	+	0.603464i
$503$	−15.2096	+	15.2096i	−0.678161	+	0.678161i	−0.959584	−	0.281423i	$-0.909194\pi$
$503$	−15.2096	+	15.2096i	−0.678161	+	0.678161i	0.281423	+	0.959584i	$0.409194\pi$
$504$	8.21699	+	1.27946i	0.366014	+	0.0569917i
$505$	6.70506	−	0.579206i	0.298371	−	0.0257743i
$506$		−	2.97195i		−	0.132119i
$507$	12.4300	−	10.6443i	0.552034	−	0.472730i
$508$	−9.95020	−	9.95020i	−0.441469	−	0.441469i
$509$	27.1370			1.20282			0.601412	−	0.798939i	$-0.294605\pi$
$509$	27.1370			1.20282			0.601412	+	0.798939i	$0.294605\pi$
$510$	−0.849198	−	0.834157i	−0.0376031	−	0.0369371i
$511$	−15.9046			−0.703577
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	17.5580	+	28.4018i	0.775205	+	1.25397i
$514$		−	24.0535i		−	1.06096i
$515$	−3.70085	+	4.40069i	−0.163079	+	0.193918i
$516$	4.40057	+	0.340552i	0.193724	+	0.0149920i
$517$	0.592665	−	0.592665i	0.0260654	−	0.0260654i
$518$	−3.97242	+	3.97242i	−0.174538	+	0.174538i
$519$	−39.5113	−	3.05771i	−1.73435	−	0.134219i
$520$	0.362682	+	4.19851i	0.0159047	+	0.184117i
$521$		−	41.9658i		−	1.83855i	−0.393611	−	0.919277i	$-0.628774\pi$
$521$		−	41.9658i		−	1.83855i	0.393611	−	0.919277i	$-0.371226\pi$
$522$	−2.95543	+	2.15906i	−0.129356	+	0.0944994i
$523$	22.7710	+	22.7710i	0.995704	+	0.995704i	0.999991	−	0.00428643i	$-0.00136442\pi$
$523$	22.7710	+	22.7710i	0.995704	+	0.995704i	−0.00428643	+	0.999991i	$0.501364\pi$
$524$	−4.14724			−0.181173
$525$	−23.8978	+	2.27967i	−1.04298	+	0.0994928i
$526$	−17.4761			−0.761992
$527$	1.37678	+	1.37678i	0.0599736	+	0.0599736i
$528$	−3.90988	+	3.34819i	−0.170156	+	0.145711i
$529$		−	1.00000i		−	0.0434783i
$530$	2.49807	+	28.9184i	0.108509	+	1.25614i
$531$	−4.35256	+	27.9532i	−0.188885	+	1.21306i
$532$	12.5957	−	12.5957i	0.546094	−	0.546094i
$533$	4.05891	−	4.05891i	0.175811	−	0.175811i
$534$	−0.328279	+	4.24198i	−0.0142060	+	0.183568i
$535$	−20.6693	+	24.5779i	−0.893610	+	1.06259i
$536$		−	13.3086i		−	0.574844i
$537$	14.2049	+	16.5879i	0.612986	+	0.715820i
$538$	−14.2128	−	14.2128i	−0.612758	−	0.612758i
$539$	−2.03280			−0.0875591
$540$	−9.32045	+	6.93752i	−0.401088	+	0.298543i
$541$	8.43337			0.362579			0.181290	−	0.983430i	$-0.441973\pi$
$541$	8.43337			0.362579			0.181290	+	0.983430i	$0.441973\pi$
$542$	19.7054	+	19.7054i	0.846419	+	0.846419i
$543$	−1.97584	−	2.30730i	−0.0847912	−	0.0990157i
$544$			0.307349i			0.0131775i
$545$	7.17971	−	0.620208i	0.307545	−	0.0265668i
$546$	−0.698164	+	9.02157i	−0.0298787	+	0.386088i
$547$	−13.9532	+	13.9532i	−0.596597	+	0.596597i	−0.939405	−	0.342808i	$-0.888622\pi$
$547$	−13.9532	+	13.9532i	−0.596597	+	0.596597i	0.342808	+	0.939405i	$0.388622\pi$
$548$	−6.71805	+	6.71805i	−0.286981	+	0.286981i
$549$	−2.57196	+	16.5177i	−0.109769	+	0.704959i
$550$	8.54990	−	12.1537i	0.364569	−	0.518235i
$551$			7.83994i			0.333993i
$552$	−1.31559	+	1.12660i	−0.0559953	+	0.0479511i
$553$	28.2839	+	28.2839i	1.20275	+	1.20275i
$554$	−9.96921			−0.423551
$555$	−0.0701326	−	7.84883i	−0.00297696	−	0.333164i
$556$	−21.3303			−0.904607
$557$	−19.9924	−	19.9924i	−0.847106	−	0.847106i	0.142665	−	0.989771i	$-0.454433\pi$
$557$	−19.9924	−	19.9924i	−0.847106	−	0.847106i	−0.989771	+	0.142665i	$0.954433\pi$
$558$	15.3462	−	11.2110i	0.649657	−	0.474600i
$559$			4.80252i			0.203125i
$560$	4.74387	+	3.98945i	0.200465	+	0.168585i
$561$	1.57739	+	0.122071i	0.0665974	+	0.00515386i
$562$	−11.1642	+	11.1642i	−0.470934	+	0.470934i
$563$	−31.0332	+	31.0332i	−1.30789	+	1.30789i	−0.384957	+	0.922935i	$0.625784\pi$
$563$	−31.0332	+	31.0332i	−1.30789	+	1.30789i	−0.922935	+	0.384957i	$0.874216\pi$
$564$	−0.487019	−	0.0376896i	−0.0205072	−	0.00158702i
$565$	9.02716	+	7.59158i	0.379776	+	0.319380i
$566$		−	18.6737i		−	0.784912i
$567$	−22.1694	+	11.4421i	−0.931027	+	0.480522i
$568$	5.40925	+	5.40925i	0.226967	+	0.226967i
$569$	−30.3632			−1.27289			−0.636447	−	0.771321i	$-0.719596\pi$
$569$	−30.3632			−1.27289			−0.636447	+	0.771321i	$0.719596\pi$
$570$	0.222376	+	24.8870i	0.00931431	+	1.04240i
$571$	−13.6437			−0.570973			−0.285486	−	0.958383i	$-0.592155\pi$
$571$	−13.6437			−0.570973			−0.285486	+	0.958383i	$0.592155\pi$
$572$	−3.96052	−	3.96052i	−0.165598	−	0.165598i
$573$	−35.4269	+	30.3375i	−1.47998	+	1.26737i
$574$		−	8.44292i		−	0.352401i
$575$	2.87686	−	4.08946i	0.119973	−	0.170542i
$576$	2.96428	+	0.461565i	0.123512	+	0.0192319i
$577$	29.2454	−	29.2454i	1.21750	−	1.21750i	0.249001	−	0.968503i	$-0.419898\pi$
$577$	29.2454	−	29.2454i	1.21750	−	1.21750i	0.968503	−	0.249001i	$-0.0801021\pi$
$578$	−11.9540	+	11.9540i	−0.497222	+	0.497222i
$579$	2.06605	−	26.6972i	0.0858620	−	1.10950i
$580$	−2.71793	+	0.234784i	−0.112856	+	0.00974888i
$581$			47.7228i			1.97988i
$582$	−14.3193	−	16.7215i	−0.593553	−	0.693127i
$583$	−27.2791	−	27.2791i	−1.12979	−	1.12979i
$584$	−5.73758			−0.237423
$585$	−8.30862	−	9.52880i	−0.343519	−	0.393968i
$586$	−9.81215			−0.405336
$587$	−30.7364	−	30.7364i	−1.26863	−	1.26863i	−0.946798	−	0.321830i	$-0.895702\pi$
$587$	−30.7364	−	30.7364i	−1.26863	−	1.26863i	−0.321830	−	0.946798i	$-0.604298\pi$
$588$	0.770587	+	0.899860i	0.0317785	+	0.0371096i
$589$		−	40.7093i		−	1.67740i
$590$	−13.5716	+	16.1380i	−0.558734	+	0.664392i
$591$	0.374079	−	4.83380i	0.0153876	−	0.198836i
$592$	−1.43305	+	1.43305i	−0.0588980	+	0.0588980i
$593$	24.9741	−	24.9741i	1.02557	−	1.02557i	0.0259005	−	0.999665i	$-0.491755\pi$
$593$	24.9741	−	24.9741i	1.02557	−	1.02557i	0.999665	−	0.0259005i	$-0.00824531\pi$
$594$	3.54620	−	15.0300i	0.145502	−	0.616690i
$595$	−0.163956	−	1.89800i	−0.00672154	−	0.0778105i
$596$			2.04707i			0.0838514i
$597$	−20.9037	+	17.9007i	−0.855531	+	0.732627i
$598$	−1.33263	−	1.33263i	−0.0544953	−	0.0544953i
$599$	35.3695			1.44516			0.722579	−	0.691288i	$-0.242956\pi$
$599$	35.3695			1.44516			0.722579	+	0.691288i	$0.242956\pi$
$600$	−8.62112	+	0.822390i	−0.351956	+	0.0335739i
$601$	36.5041			1.48903			0.744517	−	0.667604i	$-0.232680\pi$
$601$	36.5041			1.48903			0.744517	+	0.667604i	$0.232680\pi$
$602$	4.99486	+	4.99486i	0.203575	+	0.203575i
$603$	23.5521	+	32.2393i	0.959114	+	1.31288i
$604$		−	2.64015i		−	0.107426i
$605$	−0.417117	−	4.82867i	−0.0169582	−	0.196313i
$606$	5.19752	+	0.402227i	0.211135	+	0.0163394i
$607$	22.0917	−	22.0917i	0.896673	−	0.896673i	−0.0984669	−	0.995140i	$-0.531394\pi$
$607$	22.0917	−	22.0917i	0.896673	−	0.896673i	0.995140	+	0.0984669i	$0.0313939\pi$
$608$	4.54391	−	4.54391i	0.184280	−	0.184280i
$609$	−5.84017	−	0.451961i	−0.236656	−	0.0183144i
$610$	−8.01956	+	9.53607i	−0.324702	+	0.386104i
$611$		−	0.531504i		−	0.0215024i
$612$	−0.543912	−	0.744535i	−0.0219863	−	0.0300960i
$613$	16.7926	+	16.7926i	0.678246	+	0.678246i	0.959603	−	0.281357i	$-0.0907845\pi$
$613$	16.7926	+	16.7926i	0.678246	+	0.678246i	−0.281357	+	0.959603i	$0.590784\pi$
$614$	11.8644			0.478808
$615$	8.41542	+	8.26636i	0.339343	+	0.333332i
$616$	−8.23826			−0.331929
$617$	26.9980	+	26.9980i	1.08690	+	1.08690i	0.995846	+	0.0910505i	$0.0290225\pi$
$617$	26.9980	+	26.9980i	1.08690	+	1.08690i	0.0910505	+	0.995846i	$0.470978\pi$
$618$	−3.38301	+	2.89701i	−0.136085	+	0.116535i
$619$		−	31.5835i		−	1.26945i	−0.772739	−	0.634724i	$-0.781114\pi$
$619$		−	31.5835i		−	1.26945i	0.772739	−	0.634724i	$-0.218886\pi$
$620$	14.1130	−	1.21913i	0.566791	−	0.0489614i
$621$	1.19322	−	5.05729i	0.0478823	−	0.202942i
$622$	−16.0579	+	16.0579i	−0.643865	+	0.643865i
$623$	−4.81485	+	4.81485i	−0.192903	+	0.192903i
$624$	−0.251863	+	3.25453i	−0.0100826	+	0.130286i
$625$	23.5296	−	8.44734i	0.941184	−	0.337894i
$626$			26.9989i			1.07909i
$627$	−21.5157	−	25.1251i	−0.859254	−	1.00340i
$628$	0.750993	+	0.750993i	0.0299679	+	0.0299679i
$629$	0.622887			0.0248361
$630$	−18.5518	−	1.26905i	−0.739121	−	0.0505600i
$631$	−27.4404			−1.09239			−0.546193	−	0.837659i	$-0.683924\pi$
$631$	−27.4404			−1.09239			−0.546193	+	0.837659i	$0.683924\pi$
$632$	10.2034	+	10.2034i	0.405870	+	0.405870i
$633$	12.8327	+	14.9855i	0.510055	+	0.595622i
$634$			0.0389545i			0.00154708i
$635$	24.0816	+	20.2519i	0.955650	+	0.803673i
$636$	−1.73477	+	22.4165i	−0.0687883	+	0.888872i
$637$	−0.911514	+	0.911514i	−0.0361155	+	0.0361155i
$638$	2.56386	−	2.56386i	0.101504	−	0.101504i
$639$	−22.6762	−	3.53090i	−0.897058	−	0.139680i
$640$	1.71135	+	1.43919i	0.0676470	+	0.0568892i
$641$			1.78898i			0.0706606i	0.999376	+	0.0353303i	$0.0112483\pi$
$641$			1.78898i			0.0706606i	−0.999376	+	0.0353303i	$0.988752\pi$
$642$	−18.8941	+	16.1798i	−0.745691	+	0.638566i
$643$	24.6839	+	24.6839i	0.973437	+	0.973437i	0.999656	−	0.0262188i	$-0.00834667\pi$
$643$	24.6839	+	24.6839i	0.973437	+	0.973437i	−0.0262188	+	0.999656i	$0.508347\pi$
$644$	−2.77200			−0.109232
$645$	−9.86899	+	0.0881836i	−0.388591	+	0.00347222i
$646$	−1.97505			−0.0777072
$647$	2.36727	+	2.36727i	0.0930671	+	0.0930671i	0.752108	−	0.659040i	$-0.229037\pi$
$647$	2.36727	+	2.36727i	0.0930671	+	0.0930671i	−0.659040	+	0.752108i	$0.729037\pi$
$648$	−7.99761	+	4.12773i	−0.314176	+	0.162153i
$649$		−	28.0255i		−	1.10010i
$650$	−1.61594	−	9.28353i	−0.0633826	−	0.364130i
$651$	30.3254	+	2.34683i	1.18854	+	0.0919794i
$652$	−6.60415	+	6.60415i	−0.258639	+	0.258639i
$653$	2.10868	−	2.10868i	0.0825189	−	0.0825189i	−0.664643	−	0.747161i	$-0.731416\pi$
$653$	2.10868	−	2.10868i	0.0825189	−	0.0825189i	0.747161	+	0.664643i	$0.231416\pi$
$654$	5.56545	+	0.430701i	0.217626	+	0.0168417i
$655$	9.23911	−	0.798106i	0.361002	−	0.0311846i
$656$		−	3.04579i		−	0.118918i
$657$	13.8989	−	10.1537i	0.542249	−	0.396134i
$658$	−0.552791	−	0.552791i	−0.0215500	−	0.0215500i
$659$	40.8784			1.59240			0.796199	−	0.605035i	$-0.206841\pi$
$659$	40.8784			1.59240			0.796199	+	0.605035i	$0.206841\pi$
$660$	8.06598	−	8.21143i	0.313968	−	0.319629i
$661$	17.8125			0.692828			0.346414	−	0.938082i	$-0.387399\pi$
$661$	17.8125			0.692828			0.346414	+	0.938082i	$0.387399\pi$
$662$	−0.743610	−	0.743610i	−0.0289012	−	0.0289012i
$663$	0.762041	−	0.652567i	0.0295952	−	0.0253436i
$664$			17.2160i			0.668111i
$665$	−25.6365	+	30.4844i	−0.994140	+	1.18213i
$666$	0.935427	−	6.00753i	0.0362471	−	0.232787i
$667$	0.862686	−	0.862686i	0.0334033	−	0.0334033i
$668$	−5.25056	+	5.25056i	−0.203150	+	0.203150i
$669$	1.97842	−	25.5648i	0.0764900	−	0.988392i
$670$	2.56114	+	29.6485i	0.0989455	+	1.14542i
$671$		−	16.5605i		−	0.639310i
$672$	3.12292	+	3.64682i	0.120469	+	0.140679i
$673$	13.7420	+	13.7420i	0.529714	+	0.529714i	0.920487	−	0.390773i	$-0.127792\pi$
$673$	13.7420	+	13.7420i	0.529714	+	0.529714i	−0.390773	+	0.920487i	$0.627792\pi$
$674$	14.1764			0.546054
$675$	19.4288	−	17.2489i	0.747813	−	0.663909i
$676$	9.44819			0.363392
$677$	1.91031	+	1.91031i	0.0734192	+	0.0734192i	0.742863	−	0.669444i	$-0.233467\pi$
$677$	1.91031	+	1.91031i	0.0734192	+	0.0734192i	−0.669444	+	0.742863i	$0.733467\pi$
$678$	5.94265	+	6.93959i	0.228226	+	0.266513i
$679$		−	35.2328i		−	1.35211i
$680$	−0.0591471	−	0.684704i	−0.00226819	−	0.0262572i
$681$	3.05537	−	39.4810i	0.117082	−	1.51292i
$682$	−13.3130	+	13.3130i	−0.509780	+	0.509780i
$683$	−33.5563	+	33.5563i	−1.28400	+	1.28400i	−0.345623	+	0.938374i	$0.612332\pi$
$683$	−33.5563	+	33.5563i	−1.28400	+	1.28400i	−0.938374	+	0.345623i	$0.887668\pi$
$684$	−2.96605	+	19.0487i	−0.113410	+	0.728344i
$685$	13.6735	−	16.2591i	0.522436	−	0.621229i
$686$		−	17.5080i		−	0.668458i
$687$	−21.0886	+	18.0590i	−0.804581	+	0.688996i
$688$	1.80190	+	1.80190i	0.0686966	+	0.0686966i
$689$	−24.4641			−0.932006
$690$	2.71403	−	2.76297i	0.103322	−	0.105185i
$691$	−27.4000			−1.04234			−0.521172	−	0.853451i	$-0.674505\pi$
$691$	−27.4000			−1.04234			−0.521172	+	0.853451i	$0.674505\pi$
$692$	−16.1787	−	16.1787i	−0.615020	−	0.615020i
$693$	19.9567	−	14.5791i	0.758092	−	0.553816i
$694$		−	25.8642i		−	0.981790i
$695$	47.5191	−	4.10486i	1.80250	−	0.155706i
$696$	−2.10684	−	0.163045i	−0.0798596	−	0.00618020i
$697$	−0.661937	+	0.661937i	−0.0250727	+	0.0250727i
$698$	20.2968	−	20.2968i	0.768247	−	0.768247i
$699$	−10.1266	−	0.783682i	−0.383024	−	0.0296416i
$700$	−11.3360	−	7.97466i	−0.428460	−	0.301414i
$701$			17.7628i			0.670893i	0.942059	+	0.335446i	$0.108887\pi$
$701$			17.7628i			0.670893i	−0.942059	+	0.335446i	$0.891113\pi$
$702$	−5.14938	−	8.32963i	−0.194351	−	0.314381i
$703$	−9.20888	−	9.20888i	−0.347319	−	0.347319i
$704$	−2.97195			−0.112010
$705$	1.09222	−	0.00975945i	0.0411354	−	0.000367562i
$706$	−14.7901			−0.556631
$707$	5.89944	+	5.89944i	0.221871	+	0.221871i
$708$	−12.4060	+	10.6238i	−0.466247	+	0.399267i
$709$		−	25.1030i		−	0.942763i	−0.881929	−	0.471382i	$-0.843755\pi$
$709$		−	25.1030i		−	0.942763i	0.881929	−	0.471382i	$-0.156245\pi$
$710$	−13.0915	−	11.0096i	−0.491316	−	0.413183i
$711$	−42.7740	−	6.66031i	−1.60415	−	0.249781i
$712$	−1.73696	+	1.73696i	−0.0650953	+	0.0650953i
$713$	−4.47954	+	4.47954i	−0.167760	+	0.167760i
$714$	0.113858	−	1.47126i	0.00426104	−	0.0550606i
$715$	9.58530	+	8.06095i	0.358470	+	0.301463i
$716$			12.6087i			0.471209i
$717$	33.5338	+	39.1594i	1.25234	+	1.46244i
$718$	7.38357	+	7.38357i	0.275552	+	0.275552i
$719$	7.11858			0.265478			0.132739	−	0.991151i	$-0.457623\pi$
$719$	7.11858			0.265478			0.132739	+	0.991151i	$0.457623\pi$
$720$	−6.69256	−	0.457809i	−0.249417	−	0.0170615i
$721$	−7.12813			−0.265466
$722$	15.7644	+	15.7644i	0.586692	+	0.586692i
$723$	−20.4537	−	23.8850i	−0.760681	−	0.888292i
$724$		−	1.75381i		−	0.0651799i
$725$	6.00975	−	1.04609i	0.223196	−	0.0388508i
$726$	0.289665	−	3.74301i	0.0107505	−	0.138916i
$727$	−21.0233	+	21.0233i	−0.779711	+	0.779711i	−0.979782	−	0.200070i	$-0.935883\pi$
$727$	−21.0233	+	21.0233i	−0.779711	+	0.779711i	0.200070	+	0.979782i	$0.435883\pi$
$728$	−3.69405	+	3.69405i	−0.136911	+	0.136911i
$729$	12.0689	−	24.1524i	0.446998	−	0.894535i
$730$	12.7820	−	1.10415i	0.473083	−	0.0408666i
$731$		−	0.783208i		−	0.0289680i
$732$	−7.33081	+	6.27767i	−0.270955	+	0.232030i
$733$	−8.70985	−	8.70985i	−0.321706	−	0.321706i	0.527715	−	0.849421i	$-0.323049\pi$
$733$	−8.70985	−	8.70985i	−0.321706	−	0.321706i	−0.849421	+	0.527715i	$0.823049\pi$
$734$	−16.0003			−0.590580
$735$	−1.88986	−	1.85639i	−0.0697086	−	0.0684739i
$736$	−1.00000			−0.0368605
$737$	−27.9679	−	27.9679i	−1.03021	−	1.03021i
$738$	5.39009	+	7.37823i	0.198412	+	0.271596i
$739$			13.3134i			0.489743i	0.969556	+	0.244871i	$0.0787458\pi$
$739$			13.3134i			0.489743i	−0.969556	+	0.244871i	$0.921254\pi$
$740$	2.91673	−	3.46829i	0.107221	−	0.127497i
$741$	−20.9138	−	1.61849i	−0.768289	−	0.0594566i
$742$	−25.4438	+	25.4438i	−0.934072	+	0.934072i
$743$	−31.8345	+	31.8345i	−1.16789	+	1.16789i	−0.185193	+	0.982702i	$0.559291\pi$
$743$	−31.8345	+	31.8345i	−1.16789	+	1.16789i	−0.982702	+	0.185193i	$0.940709\pi$
$744$	10.9399	+	0.846618i	0.401075	+	0.0310385i
$745$	−0.393944	−	4.56041i	−0.0144330	−	0.167081i
$746$			28.6369i			1.04847i
$747$	−30.4669	−	41.7047i	−1.11473	−	1.52590i
$748$	0.645891	+	0.645891i	0.0236161	+	0.0236161i
$749$	−39.8106			−1.45465
$750$	19.0476	−	3.49117i	0.695521	−	0.127479i
$751$	1.87068			0.0682622			0.0341311	−	0.999417i	$-0.489134\pi$
$751$	1.87068			0.0682622			0.0341311	+	0.999417i	$0.489134\pi$
$752$	−0.199419	−	0.199419i	−0.00727207	−	0.00727207i
$753$	25.1559	−	21.5420i	0.916732	−	0.785035i
$754$		−	2.29928i		−	0.0837349i
$755$	0.508077	+	5.88165i	0.0184908	+	0.214055i
$756$	−14.0188	−	3.30761i	−0.509860	−	0.120297i
$757$	−4.50446	+	4.50446i	−0.163717	+	0.163717i	−0.784211	−	0.620494i	$-0.786932\pi$
$757$	−4.50446	+	4.50446i	−0.163717	+	0.163717i	0.620494	+	0.784211i	$0.286932\pi$
$758$	22.2485	−	22.2485i	0.808102	−	0.808102i
$759$	−0.397175	+	5.13223i	−0.0144165	+	0.186288i
$760$	−9.24836	+	10.9972i	−0.335473	+	0.398912i
$761$			29.5482i			1.07112i	0.844497	+	0.535561i	$0.179900\pi$
$761$			29.5482i			1.07112i	−0.844497	+	0.535561i	$0.820100\pi$
$762$	15.8531	+	18.5126i	0.574298	+	0.670642i
$763$	6.31706	+	6.31706i	0.228693	+	0.228693i
$764$	−26.9285			−0.974238
$765$	1.35499	+	1.55398i	0.0489898	+	0.0561843i
$766$	7.21387			0.260648
$767$	−12.5667	−	12.5667i	−0.453757	−	0.453757i
$768$	1.12660	+	1.31559i	0.0406525	+	0.0474723i
$769$		−	14.7558i		−	0.532107i	−0.963958	−	0.266054i	$-0.914280\pi$
$769$		−	14.7558i		−	0.532107i	0.963958	−	0.266054i	$-0.0857199\pi$
$770$	18.3530	−	1.58539i	0.661395	−	0.0571336i
$771$	−3.21454	+	41.5378i	−0.115769	+	1.49595i
$772$	10.9317	−	10.9317i	0.393439	−	0.393439i
$773$	9.22983	−	9.22983i	0.331974	−	0.331974i	−0.521362	−	0.853336i	$-0.674576\pi$
$773$	9.22983	−	9.22983i	0.331974	−	0.331974i	0.853336	+	0.521362i	$0.174576\pi$
$774$	−7.55377	−	1.17619i	−0.271515	−	0.0422773i
$775$	−31.2059	+	5.43188i	−1.12095	+	0.195119i
$776$		−	12.7102i		−	0.456270i
$777$	7.39080	−	6.32905i	0.265144	−	0.227053i
$778$	−12.9858	−	12.9858i	−0.465565	−	0.465565i
$779$	19.5724			0.701254
$780$	−0.0652180	−	7.29883i	−0.00233518	−	0.261340i
$781$	22.7349			0.813520
$782$	0.217329	+	0.217329i	0.00777166	+	0.00777166i
$783$	5.39223	−	3.33348i	0.192703	−	0.119129i
$784$			0.683996i			0.0244284i
$785$	−1.81756	−	1.52852i	−0.0648716	−	0.0545551i
$786$	7.16182	+	0.554241i	0.255454	+	0.0197691i
$787$	21.4398	−	21.4398i	0.764246	−	0.764246i	−0.212841	−	0.977087i	$-0.568272\pi$
$787$	21.4398	−	21.4398i	0.764246	−	0.764246i	0.977087	+	0.212841i	$0.0682716\pi$
$788$	1.97929	−	1.97929i	0.0705093	−	0.0705093i
$789$	30.1792	+	2.33552i	1.07441	+	0.0831466i
$790$	−24.6945	−	20.7673i	−0.878590	−	0.738868i
$791$			14.6220i			0.519898i
$792$	7.19938	−	5.25943i	0.255819	−	0.186886i
$793$	−7.42575	−	7.42575i	−0.263696	−	0.263696i
$794$	9.75933			0.346346
$795$	−0.449207	−	50.2727i	−0.0159317	−	1.78299i
$796$	−15.8892			−0.563178
$797$	−18.1902	−	18.1902i	−0.644331	−	0.644331i	0.307286	−	0.951617i	$-0.400579\pi$
$797$	−18.1902	−	18.1902i	−0.644331	−	0.644331i	−0.951617	+	0.307286i	$0.900579\pi$
$798$	−23.4347	+	20.0681i	−0.829580	+	0.710404i
$799$			0.0866791i			0.00306649i
$800$	−4.08946	−	2.87686i	−0.144584	−	0.101712i
$801$	1.13380	−	7.28155i	0.0400610	−	0.257281i
$802$	12.9741	−	12.9741i	0.458131	−	0.458131i
$803$	−12.0575	+	12.0575i	−0.425498	+	0.425498i
$804$	−1.77857	+	22.9825i	−0.0627254	+	0.810529i
$805$	6.17539	−	0.533451i	0.217654	−	0.0188017i
$806$			11.9391i			0.420538i
$807$	22.6445	+	26.4433i	0.797124	+	0.930849i
$808$	2.12822	+	2.12822i	0.0748706	+	0.0748706i
$809$	−37.6524			−1.32379			−0.661893	−	0.749598i	$-0.730247\pi$
$809$	−37.6524			−1.32379			−0.661893	+	0.749598i	$0.730247\pi$
$810$	17.0225	−	10.7347i	0.598110	−	0.377180i
$811$	34.7632			1.22070			0.610350	−	0.792132i	$-0.291029\pi$
$811$	34.7632			1.22070			0.610350	+	0.792132i	$0.291029\pi$
$812$	−2.39137	−	2.39137i	−0.0839205	−	0.0839205i
$813$	−31.3955	−	36.6624i	−1.10109	−	1.28581i
$814$			6.02308i			0.211109i
$815$	13.4416	−	15.9835i	0.470839	−	0.559876i
$816$	0.0410744	−	0.530758i	0.00143789	−	0.0185802i
$817$	−11.5791	+	11.5791i	−0.405101	+	0.405101i
$818$	−11.2227	+	11.2227i	−0.392392	+	0.392392i
$819$	2.41130	−	15.4859i	0.0842577	−	0.541122i
$820$	0.586139	+	6.78531i	0.0204689	+	0.236953i
$821$		−	22.5188i		−	0.785913i	−0.919557	−	0.392957i	$-0.871452\pi$
$821$		−	22.5188i		−	0.785913i	0.919557	−	0.392957i	$-0.128548\pi$
$822$	12.4991	−	10.7035i	0.435957	−	0.373328i
$823$	20.6173	+	20.6173i	0.718674	+	0.718674i	0.968334	−	0.249660i	$-0.0803188\pi$
$823$	20.6173	+	20.6173i	0.718674	+	0.718674i	−0.249660	+	0.968334i	$0.580319\pi$
$824$	−2.57147			−0.0895816
$825$	−16.3889	+	19.8454i	−0.570590	+	0.690929i
$826$	−26.1400			−0.909526
$827$	7.61157	+	7.61157i	0.264680	+	0.264680i	0.826952	−	0.562272i	$-0.190073\pi$
$827$	7.61157	+	7.61157i	0.264680	+	0.264680i	−0.562272	+	0.826952i	$0.690073\pi$
$828$	2.42244	−	1.76969i	0.0841856	−	0.0615009i
$829$			42.8945i			1.48979i	0.667184	+	0.744893i	$0.267500\pi$
$829$			42.8945i			1.48979i	−0.667184	+	0.744893i	$0.732500\pi$
$830$	−3.31309	−	38.3533i	−0.114999	−	1.33126i
$831$	17.2157	+	1.33229i	0.597206	+	0.0462168i
$832$	−1.33263	+	1.33263i	−0.0462006	+	0.0462006i
$833$	0.148652	−	0.148652i	0.00515049	−	0.00515049i
$834$	36.8350	+	2.85060i	1.27549	+	0.0987083i
$835$	10.6866	−	12.7075i	0.369826	−	0.439760i
$836$		−	19.0980i		−	0.660517i
$837$	−27.9994	+	17.3093i	−0.967802	+	0.598296i
$838$	14.0739	+	14.0739i	0.486175	+	0.486175i
$839$	−41.0356			−1.41671			−0.708353	−	0.705858i	$-0.750562\pi$
$839$	−41.0356			−1.41671			−0.708353	+	0.705858i	$0.750562\pi$
$840$	−7.65897	−	7.52331i	−0.264259	−	0.259579i
$841$	−27.5115			−0.948674
$842$	6.41487	+	6.41487i	0.221071	+	0.221071i
$843$	20.7713	−	17.7873i	0.715402	−	0.612628i
$844$			11.3907i			0.392085i
$845$	−21.0484	+	1.81823i	−0.724087	+	0.0625492i
$846$	0.835990	+	0.130171i	0.0287419	+	0.00447538i
$847$	4.24850	−	4.24850i	0.145980	−	0.145980i
$848$	−9.17886	+	9.17886i	−0.315203	+	0.315203i
$849$	−2.49556	+	32.2473i	−0.0856475	+	1.10672i
$850$	0.263532	+	1.51398i	0.00903909	+	0.0519292i
$851$			2.02664i			0.0694723i
$852$	−8.61826	−	10.0641i	−0.295257	−	0.344789i
$853$	−7.35122	−	7.35122i	−0.251701	−	0.251701i	0.569967	−	0.821668i	$-0.306956\pi$
$853$	−7.35122	−	7.35122i	−0.251701	−	0.251701i	−0.821668	+	0.569967i	$0.806956\pi$
$854$	−15.4463			−0.528561
$855$	2.94191	−	43.0068i	0.100611	−	1.47080i
$856$	−14.3617			−0.490872
$857$	−6.84555	−	6.84555i	−0.233839	−	0.233839i	0.580454	−	0.814293i	$-0.302875\pi$
$857$	−6.84555	−	6.84555i	−0.233839	−	0.233839i	−0.814293	+	0.580454i	$0.802875\pi$
$858$	6.31008	+	7.36865i	0.215423	+	0.251562i
$859$		−	28.4706i		−	0.971403i	−0.874125	−	0.485702i	$-0.838564\pi$
$859$		−	28.4706i		−	0.971403i	0.874125	−	0.485702i	$-0.161436\pi$
$860$	−4.36097	−	3.66745i	−0.148708	−	0.125059i
$861$	−1.12832	+	14.5800i	−0.0384530	+	0.496884i
$862$	−4.66926	+	4.66926i	−0.159036	+	0.159036i
$863$	−25.7598	+	25.7598i	−0.876873	+	0.876873i	−0.993210	−	0.116337i	$-0.962885\pi$
$863$	−25.7598	+	25.7598i	−0.876873	+	0.876873i	0.116337	+	0.993210i	$0.462885\pi$
$864$	−5.05729	−	1.19322i	−0.172053	−	0.0405942i
$865$	39.1558	+	32.9289i	1.33134	+	1.11962i
$866$			4.18515i			0.142217i
$867$	22.2408	−	19.0457i	0.755337	−	0.646826i
$868$	12.4173	+	12.4173i	0.421470	+	0.421470i
$869$	42.8848			1.45477
$870$	4.72494	−	0.0422193i	0.160190	−	0.00143137i
$871$	−25.0817			−0.849861
$872$	2.27888	+	2.27888i	0.0771726	+	0.0771726i
$873$	22.4931	+	30.7897i	0.761276	+	1.04207i
$874$		−	6.42606i		−	0.217365i
$875$	26.7887	+	15.5842i	0.905622	+	0.526842i
$876$	9.90815	+	0.766775i	0.334765	+	0.0259069i
$877$	15.9225	−	15.9225i	0.537663	−	0.537663i	−0.385179	−	0.922842i	$-0.625860\pi$
$877$	15.9225	−	15.9225i	0.537663	−	0.537663i	0.922842	+	0.385179i	$0.125860\pi$
$878$	7.95695	−	7.95695i	0.268534	−	0.268534i
$879$	16.9445	+	1.31130i	0.571523	+	0.0442292i
$880$	6.62083	−	0.571930i	0.223188	−	0.0192798i
$881$			23.1667i			0.780505i	0.920708	+	0.390253i	$0.127612\pi$
$881$			23.1667i			0.780505i	−0.920708	+	0.390253i	$0.872388\pi$
$882$	−1.21046	−	1.65694i	−0.0407583	−	0.0557920i
$883$	−19.6995	−	19.6995i	−0.662940	−	0.662940i	0.293132	−	0.956072i	$-0.405302\pi$
$883$	−19.6995	−	19.6995i	−0.662940	−	0.662940i	−0.956072	+	0.293132i	$0.905302\pi$
$884$	0.579238			0.0194819
$885$	25.5933	−	26.0548i	0.860311	−	0.875824i
$886$	−22.9552			−0.771194
$887$	−5.93272	−	5.93272i	−0.199201	−	0.199201i	0.600456	−	0.799658i	$-0.294986\pi$
$887$	−5.93272	−	5.93272i	−0.199201	−	0.199201i	−0.799658	+	0.600456i	$0.794986\pi$
$888$	2.66623	−	2.28320i	0.0894729	−	0.0766193i
$889$			39.0068i			1.30825i
$890$	3.53528	−	4.20381i	0.118503	−	0.140912i
$891$	−8.13251	+	25.4813i	−0.272449	+	0.853655i
$892$	10.4680	−	10.4680i	0.350494	−	0.350494i
$893$	1.28148	−	1.28148i	0.0428831	−	0.0428831i
$894$	0.273573	−	3.53507i	0.00914964	−	0.118230i
$895$	−2.42645	−	28.0893i	−0.0811072	−	0.938921i
$896$			2.77200i			0.0926061i
$897$	2.12321	+	2.47940i	0.0708919	+	0.0827846i
$898$	−2.45975	−	2.45975i	−0.0820828	−	0.0820828i
$899$	−7.72887			−0.257772
$900$	14.9976	−	0.268041i	0.499920	−	0.00893470i
$901$	3.98966			0.132915
$902$	−6.40068	−	6.40068i	−0.213119	−	0.213119i
$903$	−7.95804	−	9.29307i	−0.264827	−	0.309254i
$904$			5.27488i			0.175440i
$905$	0.337508	+	3.90709i	0.0112191	+	0.129876i
$906$	−0.352832	+	4.55924i	−0.0117221	+	0.151471i
$907$	−28.2405	+	28.2405i	−0.937710	+	0.937710i	−0.998171	−	0.0604604i	$-0.980743\pi$
$907$	−28.2405	+	28.2405i	−0.937710	+	0.937710i	0.0604604	+	0.998171i	$0.480743\pi$
$908$	16.1663	−	16.1663i	0.536496	−	0.536496i
$909$	−8.92177	−	1.38920i	−0.295917	−	0.0460769i
$910$	7.51862	−	8.94040i	0.249240	−	0.296371i
$911$			0.663646i			0.0219876i	0.999940	+	0.0109938i	$0.00349950\pi$
$911$			0.663646i			0.0219876i	−0.999940	+	0.0109938i	$0.996501\pi$
$912$	−8.45408	+	7.23957i	−0.279943	+	0.239726i
$913$	36.1792	+	36.1792i	1.19736	+	1.19736i
$914$	−34.6782			−1.14705
$915$	15.1233	−	15.3960i	0.499960	−	0.508976i
$916$	−16.0298			−0.529638
$917$	8.12901	+	8.12901i	0.268444	+	0.268444i
$918$	0.839775	+	1.35842i	0.0277167	+	0.0448344i
$919$			12.5913i			0.415350i	0.978198	+	0.207675i	$0.0665897\pi$
$919$			12.5913i			0.415350i	−0.978198	+	0.207675i	$0.933410\pi$
$920$	2.22777	−	0.192443i	0.0734475	−	0.00634464i
$921$	−20.4885	−	1.58557i	−0.675117	−	0.0522462i
$922$	−4.99529	+	4.99529i	−0.164511	+	0.164511i
$923$	10.1944	−	10.1944i	0.335553	−	0.335553i
$924$	14.2266	+	1.10097i	0.468019	+	0.0362192i
$925$	−5.83036	+	8.28786i	−0.191701	+	0.272503i
$926$		−	6.95367i		−	0.228512i
$927$	6.22924	−	4.55070i	0.204595	−	0.149465i
$928$	−0.862686	−	0.862686i	−0.0283191	−	0.0283191i
$929$	5.22216			0.171334			0.0856668	−	0.996324i	$-0.472698\pi$
$929$	5.22216			0.171334			0.0856668	+	0.996324i	$0.472698\pi$
$930$	−24.5345	+	0.219226i	−0.804517	+	0.00718869i
$931$	−4.39540			−0.144053
$932$	−4.14654	−	4.14654i	−0.135824	−	0.135824i
$933$	29.8763	−	25.5843i	0.978105	−	0.837591i
$934$			0.394898i			0.0129214i
$935$	−1.56320	−	1.31460i	−0.0511219	−	0.0429921i
$936$	0.869877	−	5.58655i	0.0284328	−	0.182602i
$937$	−5.96477	+	5.96477i	−0.194861	+	0.194861i	−0.797793	−	0.602932i	$-0.793999\pi$
$937$	−5.96477	+	5.96477i	−0.194861	+	0.194861i	0.602932	+	0.797793i	$0.293999\pi$
$938$	−26.0862	+	26.0862i	−0.851745	+	0.851745i
$939$	3.60816	−	46.6241i	0.117748	−	1.52152i
$940$	0.482637	+	0.405884i	0.0157419	+	0.0132385i
$941$		−	9.07148i		−	0.295722i	−0.989008	−	0.147861i	$-0.952761\pi$
$941$		−	9.07148i		−	0.295722i	0.989008	−	0.147861i	$-0.0472388\pi$
$942$	−1.19652	−	1.39724i	−0.0389846	−	0.0455247i
$943$	−2.15370	−	2.15370i	−0.0701340	−	0.0701340i
$944$	−9.43000			−0.306920
$945$	31.8673	+	4.67078i	1.03664	+	0.151940i
$946$	7.57333			0.246230
$947$	−0.282615	−	0.282615i	−0.00918377	−	0.00918377i	0.702500	−	0.711684i	$-0.252067\pi$
$947$	−0.282615	−	0.282615i	−0.00918377	−	0.00918377i	−0.711684	+	0.702500i	$0.752067\pi$
$948$	−16.2566	−	18.9838i	−0.527989	−	0.616564i
$949$			10.8132i			0.351011i
$950$	18.4869	−	26.2791i	0.599794	−	0.852607i
$951$	0.00520591	−	0.0672700i	0.000168813	−	0.00218138i
$952$	0.602436	−	0.602436i	0.0195251	−	0.0195251i
$953$	−11.5078	+	11.5078i	−0.372773	+	0.372773i	−0.868486	−	0.495713i	$-0.834907\pi$
$953$	−11.5078	+	11.5078i	−0.372773	+	0.372773i	0.495713	+	0.868486i	$0.334907\pi$
$954$	5.99152	−	38.4789i	0.193983	−	1.24580i
$955$	59.9905	−	5.18219i	1.94125	−	0.167692i
$956$			29.7656i			0.962690i
$957$	−4.77014	+	4.08487i	−0.154197	+	0.132045i
$958$	−14.1219	−	14.1219i	−0.456259	−	0.456259i
$959$	26.3361			0.850438
$960$	−2.76297	−	2.71403i	−0.0891746	−	0.0875951i
$961$	9.13253			0.294598
$962$	2.70076	+	2.70076i	0.0870761	+	0.0870761i
$963$	34.7903	−	25.4157i	1.12110	−	0.819009i
$964$		−	18.1553i		−	0.584743i
$965$	−22.2495	+	26.4570i	−0.716238	+	0.851680i
$966$	4.78694	+	0.370453i	0.154017	+	0.0119191i
$967$	−40.1895	+	40.1895i	−1.29241	+	1.29241i	−0.359113	+	0.933294i	$0.616921\pi$
$967$	−40.1895	+	40.1895i	−1.29241	+	1.29241i	−0.933294	+	0.359113i	$0.883079\pi$
$968$	1.53265	−	1.53265i	0.0492611	−	0.0492611i
$969$	3.41068	+	0.263947i	0.109567	+	0.00847920i
$970$	2.44599	+	28.3155i	0.0785359	+	0.909155i
$971$			20.3254i			0.652272i	0.945323	+	0.326136i	$0.105747\pi$
$971$			20.3254i			0.652272i	−0.945323	+	0.326136i	$0.894253\pi$
$972$	14.3626	−	6.05932i	0.460681	−	0.194353i
$973$	41.8096	+	41.8096i	1.34035	+	1.34035i
$974$	1.98570			0.0636258
$975$	1.54990	+	16.2476i	0.0496364	+	0.520339i
$976$	−5.57225			−0.178363
$977$	31.6440	+	31.6440i	1.01238	+	1.01238i	0.999922	+	0.0124590i	$0.00396594\pi$
$977$	31.6440	+	31.6440i	1.01238	+	1.01238i	0.0124590	+	0.999922i	$0.496034\pi$
$978$	12.2872	−	10.5220i	0.392902	−	0.336458i
$979$			7.30040i			0.233322i
$980$	−0.131630	−	1.52379i	−0.00420476	−	0.0486756i
$981$	−9.55335	−	1.48754i	−0.305015	−	0.0474936i
$982$	4.56709	−	4.56709i	0.145742	−	0.145742i
$983$	14.9031	−	14.9031i	0.475336	−	0.475336i	−0.428301	−	0.903636i	$-0.640888\pi$
$983$	14.9031	−	14.9031i	0.475336	−	0.475336i	0.903636	+	0.428301i	$0.140888\pi$
$984$	−0.407041	+	5.25973i	−0.0129760	+	0.167674i
$985$	−4.02851	+	4.79031i	−0.128359	+	0.152632i
$986$			0.374973i			0.0119416i
$987$	0.880732	+	1.02848i	0.0280340	+	0.0327370i
$988$	−8.56357	−	8.56357i	−0.272443	−	0.272443i
$989$	2.54827			0.0810301
$990$	−15.0264	+	13.1023i	−0.477571	+	0.416417i
$991$	−30.3099			−0.962827			−0.481414	−	0.876494i	$-0.659876\pi$
$991$	−30.3099			−0.962827			−0.481414	+	0.876494i	$0.659876\pi$
$992$	4.47954	+	4.47954i	0.142225	+	0.142225i
$993$	1.18475	+	1.38351i	0.0375970	+	0.0439043i
$994$		−	21.2053i		−	0.672593i
$995$	35.3975	−	3.05776i	1.12218	−	0.0969374i
$996$	2.30076	−	29.7301i	0.0729024	−	0.942034i
$997$	19.3131	−	19.3131i	0.611651	−	0.611651i	−0.331725	−	0.943376i	$-0.607631\pi$
$997$	19.3131	−	19.3131i	0.611651	−	0.611651i	0.943376	+	0.331725i	$0.107631\pi$
$998$	−6.74411	+	6.74411i	−0.213481	+	0.213481i
$999$	−2.41823	+	10.2493i	−0.0765094	+	0.324274i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.f.323.7	yes	32
3.2	odd	2	inner	690.2.i.f.323.14	yes	32
5.2	odd	4	inner	690.2.i.f.47.14	yes	32
15.2	even	4	inner	690.2.i.f.47.7	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.f.47.7	✓	32	15.2	even	4	inner
690.2.i.f.47.14	yes	32	5.2	odd	4	inner
690.2.i.f.323.7	yes	32	1.1	even	1	trivial
690.2.i.f.323.14	yes	32	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.12660 + 1.31559i) q^{3} +1.00000i q^{4} +(-0.192443 - 2.22777i) q^{5} +(0.133641 - 1.72689i) q^{6} +(1.96010 - 1.96010i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.461565 + 2.96428i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.12660 + 1.31559i) q^{3} +1.00000i q^{4} +(-0.192443 - 2.22777i) q^{5} +(0.133641 - 1.72689i) q^{6} +(1.96010 - 1.96010i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.461565 + 2.96428i) q^{9} +(-1.43919 + 1.71135i) q^{10} -2.97195i q^{11} +(-1.31559 + 1.12660i) q^{12} +(-1.33263 - 1.33263i) q^{13} -2.77200 q^{14} +(2.71403 - 2.76297i) q^{15} -1.00000 q^{16} +(0.217329 + 0.217329i) q^{17} +(2.42244 - 1.76969i) q^{18} -6.42606i q^{19} +(2.22777 - 0.192443i) q^{20} +(4.78694 + 0.370453i) q^{21} +(-2.10149 + 2.10149i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(1.72689 + 0.133641i) q^{24} +(-4.92593 + 0.857436i) q^{25} +1.88462i q^{26} +(-4.41978 + 2.73231i) q^{27} +(1.96010 + 1.96010i) q^{28} -1.22002 q^{29} +(-3.87283 + 0.0346053i) q^{30} +6.33502 q^{31} +(0.707107 + 0.707107i) q^{32} +(3.90988 - 3.34819i) q^{33} -0.307349i q^{34} +(-4.74387 - 3.98945i) q^{35} +(-2.96428 - 0.461565i) q^{36} +(1.43305 - 1.43305i) q^{37} +(-4.54391 + 4.54391i) q^{38} +(0.251863 - 3.25453i) q^{39} +(-1.71135 - 1.43919i) q^{40} +3.04579i q^{41} +(-3.12292 - 3.64682i) q^{42} +(-1.80190 - 1.80190i) q^{43} +2.97195 q^{44} +(6.69256 + 0.457809i) q^{45} +1.00000 q^{46} +(0.199419 + 0.199419i) q^{47} +(-1.12660 - 1.31559i) q^{48} -0.683996i q^{49} +(4.08946 + 2.87686i) q^{50} +(-0.0410744 + 0.530758i) q^{51} +(1.33263 - 1.33263i) q^{52} +(9.17886 - 9.17886i) q^{53} +(5.05729 + 1.19322i) q^{54} +(-6.62083 + 0.571930i) q^{55} -2.77200i q^{56} +(8.45408 - 7.23957i) q^{57} +(0.862686 + 0.862686i) q^{58} +9.43000 q^{59} +(2.76297 + 2.71403i) q^{60} +5.57225 q^{61} +(-4.47954 - 4.47954i) q^{62} +(4.90558 + 6.71501i) q^{63} -1.00000i q^{64} +(-2.71234 + 3.22525i) q^{65} +(-5.13223 - 0.397175i) q^{66} +(9.41060 - 9.41060i) q^{67} +(-0.217329 + 0.217329i) q^{68} +(-1.72689 - 0.133641i) q^{69} +(0.533451 + 6.17539i) q^{70} +7.64983i q^{71} +(1.76969 + 2.42244i) q^{72} +(-4.05708 - 4.05708i) q^{73} -2.02664 q^{74} +(-6.67757 - 5.51453i) q^{75} +6.42606 q^{76} +(-5.82533 - 5.82533i) q^{77} +(-2.47940 + 2.12321i) q^{78} +14.4298i q^{79} +(0.192443 + 2.22777i) q^{80} +(-8.57391 - 2.73642i) q^{81} +(2.15370 - 2.15370i) q^{82} +(-12.1736 + 12.1736i) q^{83} +(-0.370453 + 4.78694i) q^{84} +(0.442336 - 0.525982i) q^{85} +2.54827i q^{86} +(-1.37447 - 1.60505i) q^{87} +(-2.10149 - 2.10149i) q^{88} -2.45643 q^{89} +(-4.40864 - 5.05608i) q^{90} -5.22418 q^{91} +(-0.707107 - 0.707107i) q^{92} +(7.13701 + 8.33431i) q^{93} -0.282021i q^{94} +(-14.3158 + 1.23665i) q^{95} +(-0.133641 + 1.72689i) q^{96} +(8.98748 - 8.98748i) q^{97} +(-0.483658 + 0.483658i) q^{98} +(8.80970 + 1.37175i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7}+O(q^{10}) \) 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7	\( 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7} - 4 q^{12} - 12 q^{15} - 32 q^{16} + 8 q^{18} - 40 q^{22} + 32 q^{25} + 4 q^{27} + 8 q^{28} - 20 q^{30} + 8 q^{31} + 8 q^{33} + 20 q^{36} - 16 q^{37} + 8 q^{40} - 8 q^{42} - 80 q^{43} - 4 q^{45} + 32 q^{46} - 4 q^{48} + 36 q^{51} + 12 q^{57} - 16 q^{58} - 4 q^{60} + 8 q^{61} + 44 q^{63} + 52 q^{66} + 64 q^{67} + 64 q^{70} - 8 q^{72} - 56 q^{73} - 68 q^{75} - 8 q^{76} + 60 q^{78} - 44 q^{81} - 48 q^{85} - 60 q^{87} - 40 q^{88} - 64 q^{90} + 40 q^{91} + 92 q^{93} - 12 q^{96} - 40 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7 - 4 * q^12 - 12 * q^15 - 32 * q^16 + 8 * q^18 - 40 * q^22 + 32 * q^25 + 4 * q^27 + 8 * q^28 - 20 * q^30 + 8 * q^31 + 8 * q^33 + 20 * q^36 - 16 * q^37 + 8 * q^40 - 8 * q^42 - 80 * q^43 - 4 * q^45 + 32 * q^46 - 4 * q^48 + 36 * q^51 + 12 * q^57 - 16 * q^58 - 4 * q^60 + 8 * q^61 + 44 * q^63 + 52 * q^66 + 64 * q^67 + 64 * q^70 - 8 * q^72 - 56 * q^73 - 68 * q^75 - 8 * q^76 + 60 * q^78 - 44 * q^81 - 48 * q^85 - 60 * q^87 - 40 * q^88 - 64 * q^90 + 40 * q^91 + 92 * q^93 - 12 * q^96 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more