LMFDB - Embedded newform 342.2.f.g.49.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(7,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("342.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 4 x^{16} - 6 x^{15} + x^{14} - 21 x^{13} - 12 x^{12} + 9 x^{10} + 135 x^{9} + 27 x^{8} + \cdots + 19683 $ x^18 + 4x^16 - 6x^15 + x^14 - 21x^13 - 12x^12 + 9x^10 + 135x^9 + 27x^8 - 324x^6 - 1701x^5 + 243x^4 - 4374x^3 + 8748x^2 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.7
Root			$-0.614525 + 1.61937i$ of defining polynomial
Character	$\chi$	$=$	342.49
Dual form			342.2.f.g.7.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(1.09515 + 1.34188i) q^{3} +1.00000 q^{4} +(0.789777 + 1.36793i) q^{5} +(-1.09515 - 1.34188i) q^{6} +(2.31561 + 4.01075i) q^{7} -1.00000 q^{8} +(-0.601280 + 2.93913i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(1.09515 + 1.34188i) q^{3} +1.00000 q^{4} +(0.789777 + 1.36793i) q^{5} +(-1.09515 - 1.34188i) q^{6} +(2.31561 + 4.01075i) q^{7} -1.00000 q^{8} +(-0.601280 + 2.93913i) q^{9} +(-0.789777 - 1.36793i) q^{10} +(-1.83826 - 3.18396i) q^{11} +(1.09515 + 1.34188i) q^{12} -5.57353 q^{13} +(-2.31561 - 4.01075i) q^{14} +(-0.970675 + 2.55788i) q^{15} +1.00000 q^{16} +(3.65387 - 6.32868i) q^{17} +(0.601280 - 2.93913i) q^{18} +(3.55454 + 2.52294i) q^{19} +(0.789777 + 1.36793i) q^{20} +(-2.84600 + 7.49965i) q^{21} +(1.83826 + 3.18396i) q^{22} -2.10449 q^{23} +(-1.09515 - 1.34188i) q^{24} +(1.25250 - 2.16940i) q^{25} +5.57353 q^{26} +(-4.60245 + 2.41195i) q^{27} +(2.31561 + 4.01075i) q^{28} +(-2.66226 + 4.61117i) q^{29} +(0.970675 - 2.55788i) q^{30} +(0.587415 - 1.01743i) q^{31} -1.00000 q^{32} +(2.25931 - 5.95364i) q^{33} +(-3.65387 + 6.32868i) q^{34} +(-3.65763 + 6.33520i) q^{35} +(-0.601280 + 2.93913i) q^{36} +1.16827 q^{37} +(-3.55454 - 2.52294i) q^{38} +(-6.10386 - 7.47900i) q^{39} +(-0.789777 - 1.36793i) q^{40} +(2.24640 + 3.89087i) q^{41} +(2.84600 - 7.49965i) q^{42} +8.49469 q^{43} +(-1.83826 - 3.18396i) q^{44} +(-4.49541 + 1.49874i) q^{45} +2.10449 q^{46} +(2.87781 - 4.98452i) q^{47} +(1.09515 + 1.34188i) q^{48} +(-7.22408 + 12.5125i) q^{49} +(-1.25250 + 2.16940i) q^{50} +(12.4939 - 2.02783i) q^{51} -5.57353 q^{52} +(1.69773 + 2.94055i) q^{53} +(4.60245 - 2.41195i) q^{54} +(2.90363 - 5.02923i) q^{55} +(-2.31561 - 4.01075i) q^{56} +(0.507293 + 7.53277i) q^{57} +(2.66226 - 4.61117i) q^{58} +(0.992410 + 1.71891i) q^{59} +(-0.970675 + 2.55788i) q^{60} +(-1.59300 + 2.75915i) q^{61} +(-0.587415 + 1.01743i) q^{62} +(-13.1804 + 4.39428i) q^{63} +1.00000 q^{64} +(-4.40184 - 7.62422i) q^{65} +(-2.25931 + 5.95364i) q^{66} +12.5843 q^{67} +(3.65387 - 6.32868i) q^{68} +(-2.30473 - 2.82396i) q^{69} +(3.65763 - 6.33520i) q^{70} +(4.03312 - 6.98558i) q^{71} +(0.601280 - 2.93913i) q^{72} +(7.45107 - 12.9056i) q^{73} -1.16827 q^{74} +(4.28276 - 0.695117i) q^{75} +(3.55454 + 2.52294i) q^{76} +(8.51338 - 14.7456i) q^{77} +(6.10386 + 7.47900i) q^{78} -5.98637 q^{79} +(0.789777 + 1.36793i) q^{80} +(-8.27693 - 3.53447i) q^{81} +(-2.24640 - 3.89087i) q^{82} +(-5.85781 - 10.1460i) q^{83} +(-2.84600 + 7.49965i) q^{84} +11.5430 q^{85} -8.49469 q^{86} +(-9.10322 + 1.47751i) q^{87} +(1.83826 + 3.18396i) q^{88} +(3.00802 + 5.21004i) q^{89} +(4.49541 - 1.49874i) q^{90} +(-12.9061 - 22.3540i) q^{91} -2.10449 q^{92} +(2.00858 - 0.326004i) q^{93} +(-2.87781 + 4.98452i) q^{94} +(-0.643914 + 6.85494i) q^{95} +(-1.09515 - 1.34188i) q^{96} -11.9403 q^{97} +(7.22408 - 12.5125i) q^{98} +(10.4634 - 3.48843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 18 q^{2} + 18 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9}+O(q^{10}) $ 18 * q - 18 * q^2 + 18 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9	$ 18 q - 18 q^{2} + 18 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9} + q^{11} - 2 q^{13} - 5 q^{14} + 18 q^{16} - 5 q^{17} - 4 q^{18} + 9 q^{19} - 4 q^{21} - q^{22} + 4 q^{23} - 9 q^{25} + 2 q^{26} - 18 q^{27} + 5 q^{28} - 9 q^{29} + 4 q^{31} - 18 q^{32} + 16 q^{33} + 5 q^{34} + 6 q^{35} + 4 q^{36} + 20 q^{37} - 9 q^{38} + 4 q^{39} + q^{41} + 4 q^{42} - 14 q^{43} + q^{44} + 30 q^{45} - 4 q^{46} + 19 q^{47} + 6 q^{49} + 9 q^{50} + 16 q^{51} - 2 q^{52} - 10 q^{53} + 18 q^{54} + 6 q^{55} - 5 q^{56} - 36 q^{57} + 9 q^{58} - 5 q^{59} + 18 q^{61} - 4 q^{62} - 15 q^{63} + 18 q^{64} - 45 q^{65} - 16 q^{66} - 44 q^{67} - 5 q^{68} - 26 q^{69} - 6 q^{70} + 11 q^{71} - 4 q^{72} + 44 q^{73} - 20 q^{74} + 9 q^{76} - 2 q^{77} - 4 q^{78} - 4 q^{79} - 32 q^{81} - q^{82} - 7 q^{83} - 4 q^{84} + 14 q^{86} + 3 q^{87} - q^{88} + q^{89} - 30 q^{90} - 25 q^{91} + 4 q^{92} + 10 q^{93} - 19 q^{94} - 24 q^{95} - 6 q^{98} + 8 q^{99}+O(q^{100}) $ 18 * q - 18 * q^2 + 18 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9 + q^11 - 2 * q^13 - 5 * q^14 + 18 * q^16 - 5 * q^17 - 4 * q^18 + 9 * q^19 - 4 * q^21 - q^22 + 4 * q^23 - 9 * q^25 + 2 * q^26 - 18 * q^27 + 5 * q^28 - 9 * q^29 + 4 * q^31 - 18 * q^32 + 16 * q^33 + 5 * q^34 + 6 * q^35 + 4 * q^36 + 20 * q^37 - 9 * q^38 + 4 * q^39 + q^41 + 4 * q^42 - 14 * q^43 + q^44 + 30 * q^45 - 4 * q^46 + 19 * q^47 + 6 * q^49 + 9 * q^50 + 16 * q^51 - 2 * q^52 - 10 * q^53 + 18 * q^54 + 6 * q^55 - 5 * q^56 - 36 * q^57 + 9 * q^58 - 5 * q^59 + 18 * q^61 - 4 * q^62 - 15 * q^63 + 18 * q^64 - 45 * q^65 - 16 * q^66 - 44 * q^67 - 5 * q^68 - 26 * q^69 - 6 * q^70 + 11 * q^71 - 4 * q^72 + 44 * q^73 - 20 * q^74 + 9 * q^76 - 2 * q^77 - 4 * q^78 - 4 * q^79 - 32 * q^81 - q^82 - 7 * q^83 - 4 * q^84 + 14 * q^86 + 3 * q^87 - q^88 + q^89 - 30 * q^90 - 25 * q^91 + 4 * q^92 + 10 * q^93 - 19 * q^94 - 24 * q^95 - 6 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	1.09515	+	1.34188i	0.632287	+	0.774734i
$3$	1.09515	+	1.34188i	0.632287	+	0.774734i
$4$	1.00000			0.500000
$5$	0.789777	+	1.36793i	0.353199	+	0.611759i	0.986808	−	0.161895i	$-0.0517605\pi$
$5$	0.789777	+	1.36793i	0.353199	+	0.611759i	−0.633609	+	0.773653i	$0.718427\pi$
$6$	−1.09515	−	1.34188i	−0.447094	−	0.547820i
$7$	2.31561	+	4.01075i	0.875218	+	1.51592i	0.856531	+	0.516096i	$0.172615\pi$
$7$	2.31561	+	4.01075i	0.875218	+	1.51592i	0.0186867	+	0.999825i	$0.494051\pi$
$8$	−1.00000			−0.353553
$9$	−0.601280	+	2.93913i	−0.200427	+	0.979709i
$10$	−0.789777	−	1.36793i	−0.249749	−	0.432579i
$11$	−1.83826	−	3.18396i	−0.554256	−	0.960000i	−0.997961	−	0.0638268i	$-0.979669\pi$
$11$	−1.83826	−	3.18396i	−0.554256	−	0.960000i	0.443705	−	0.896173i	$-0.353664\pi$
$12$	1.09515	+	1.34188i	0.316143	+	0.387367i
$13$	−5.57353			−1.54582			−0.772909	−	0.634517i	$-0.781199\pi$
$13$	−5.57353			−1.54582			−0.772909	+	0.634517i	$0.781199\pi$
$14$	−2.31561	−	4.01075i	−0.618872	−	1.07192i
$15$	−0.970675	+	2.55788i	−0.250627	+	0.660442i
$16$	1.00000			0.250000
$17$	3.65387	−	6.32868i	0.886193	−	1.53493i	0.0418529	−	0.999124i	$-0.486674\pi$
$17$	3.65387	−	6.32868i	0.886193	−	1.53493i	0.844340	−	0.535808i	$-0.179993\pi$
$18$	0.601280	−	2.93913i	0.141723	−	0.692759i
$19$	3.55454	+	2.52294i	0.815468	+	0.578802i
$19$	3.55454	+	2.52294i	0.815468	+	0.578802i
$20$	0.789777	+	1.36793i	0.176599	+	0.305879i
$21$	−2.84600	+	7.49965i	−0.621048	+	1.63656i
$22$	1.83826	+	3.18396i	0.391918	+	0.678822i
$23$	−2.10449			−0.438815			−0.219408	−	0.975633i	$-0.570412\pi$
$23$	−2.10449			−0.438815			−0.219408	+	0.975633i	$0.570412\pi$
$24$	−1.09515	−	1.34188i	−0.223547	−	0.273910i
$25$	1.25250	−	2.16940i	0.250501	−	0.433880i
$26$	5.57353			1.09306
$27$	−4.60245	+	2.41195i	−0.885741	+	0.464180i
$28$	2.31561	+	4.01075i	0.437609	+	0.757961i
$29$	−2.66226	+	4.61117i	−0.494369	+	0.856273i	−0.999979	−	0.00648954i	$-0.997934\pi$
$29$	−2.66226	+	4.61117i	−0.494369	+	0.856273i	0.505610	+	0.862762i	$0.331268\pi$
$30$	0.970675	−	2.55788i	0.177220	−	0.467003i
$31$	0.587415	−	1.01743i	0.105503	−	0.182736i	−0.808441	−	0.588578i	$-0.799688\pi$
$31$	0.587415	−	1.01743i	0.105503	−	0.182736i	0.913944	+	0.405841i	$0.133021\pi$
$32$	−1.00000			−0.176777
$33$	2.25931	−	5.95364i	0.393296	−	1.03640i
$34$	−3.65387	+	6.32868i	−0.626633	+	1.08536i
$35$	−3.65763	+	6.33520i	−0.618252	+	1.07084i
$36$	−0.601280	+	2.93913i	−0.100213	+	0.489854i
$37$	1.16827			0.192062			0.0960312	−	0.995378i	$-0.469385\pi$
$37$	1.16827			0.192062			0.0960312	+	0.995378i	$0.469385\pi$
$38$	−3.55454	−	2.52294i	−0.576623	−	0.409275i
$39$	−6.10386	−	7.47900i	−0.977401	−	1.19760i
$40$	−0.789777	−	1.36793i	−0.124875	−	0.216289i
$41$	2.24640	+	3.89087i	0.350828	+	0.607652i	0.986395	−	0.164394i	$-0.0525668\pi$
$41$	2.24640	+	3.89087i	0.350828	+	0.607652i	−0.635567	+	0.772046i	$0.719233\pi$
$42$	2.84600	−	7.49965i	0.439147	−	1.15722i
$43$	8.49469			1.29543			0.647714	−	0.761884i	$-0.275725\pi$
$43$	8.49469			1.29543			0.647714	+	0.761884i	$0.275725\pi$
$44$	−1.83826	−	3.18396i	−0.277128	−	0.480000i
$45$	−4.49541	+	1.49874i	−0.670136	+	0.223419i
$46$	2.10449			0.310289
$47$	2.87781	−	4.98452i	0.419772	−	0.727066i	−0.576144	−	0.817348i	$-0.695443\pi$
$47$	2.87781	−	4.98452i	0.419772	−	0.727066i	0.995916	+	0.0902817i	$0.0287767\pi$
$48$	1.09515	+	1.34188i	0.158072	+	0.193684i
$49$	−7.22408	+	12.5125i	−1.03201	+	1.78750i
$50$	−1.25250	+	2.16940i	−0.177131	+	0.306800i
$51$	12.4939	−	2.02783i	1.74949	−	0.283953i
$52$	−5.57353			−0.772909
$53$	1.69773	+	2.94055i	0.233201	+	0.403916i	0.958748	−	0.284256i	$-0.0917467\pi$
$53$	1.69773	+	2.94055i	0.233201	+	0.403916i	−0.725547	+	0.688172i	$0.758413\pi$
$54$	4.60245	−	2.41195i	0.626314	−	0.328225i
$55$	2.90363	−	5.02923i	0.391525	−	0.678142i
$56$	−2.31561	−	4.01075i	−0.309436	−	0.535959i
$57$	0.507293	+	7.53277i	0.0671925	+	0.997740i
$58$	2.66226	−	4.61117i	0.349572	−	0.605476i
$59$	0.992410	+	1.71891i	0.129201	+	0.223782i	0.923367	−	0.383918i	$-0.125425\pi$
$59$	0.992410	+	1.71891i	0.129201	+	0.223782i	−0.794166	+	0.607700i	$0.792092\pi$
$60$	−0.970675	+	2.55788i	−0.125314	+	0.330221i
$61$	−1.59300	+	2.75915i	−0.203962	+	0.353273i	−0.949802	−	0.312853i	$-0.898715\pi$
$61$	−1.59300	+	2.75915i	−0.203962	+	0.353273i	0.745839	+	0.666126i	$0.232049\pi$
$62$	−0.587415	+	1.01743i	−0.0746018	+	0.129214i
$63$	−13.1804	+	4.39428i	−1.66058	+	0.553627i
$64$	1.00000			0.125000
$65$	−4.40184	−	7.62422i	−0.545981	−	0.945668i
$66$	−2.25931	+	5.95364i	−0.278102	+	0.732843i
$67$	12.5843			1.53741			0.768706	−	0.639602i	$-0.220901\pi$
$67$	12.5843			1.53741			0.768706	+	0.639602i	$0.220901\pi$
$68$	3.65387	−	6.32868i	0.443097	−	0.767466i
$69$	−2.30473	−	2.82396i	−0.277457	−	0.339965i
$70$	3.65763	−	6.33520i	0.437170	−	0.757201i
$71$	4.03312	−	6.98558i	0.478644	−	0.829035i	−0.521056	−	0.853522i	$-0.674462\pi$
$71$	4.03312	−	6.98558i	0.478644	−	0.829035i	0.999700	+	0.0244869i	$0.00779519\pi$
$72$	0.601280	−	2.93913i	0.0708615	−	0.346379i
$73$	7.45107	−	12.9056i	0.872082	−	1.51049i	0.0122430	−	0.999925i	$-0.496103\pi$
$73$	7.45107	−	12.9056i	0.872082	−	1.51049i	0.859839	−	0.510565i	$-0.170564\pi$
$74$	−1.16827			−0.135809
$75$	4.28276	−	0.695117i	0.494531	−	0.0802652i
$76$	3.55454	+	2.52294i	0.407734	+	0.289401i
$77$	8.51338	−	14.7456i	0.970189	−	1.68042i
$78$	6.10386	+	7.47900i	0.691127	+	0.846830i
$79$	−5.98637			−0.673519			−0.336760	−	0.941591i	$-0.609331\pi$
$79$	−5.98637			−0.673519			−0.336760	+	0.941591i	$0.609331\pi$
$80$	0.789777	+	1.36793i	0.0882997	+	0.152940i
$81$	−8.27693	−	3.53447i	−0.919658	−	0.392719i
$82$	−2.24640	−	3.89087i	−0.248073	−	0.429675i
$83$	−5.85781	−	10.1460i	−0.642978	−	1.11367i	−0.984765	−	0.173893i	$-0.944365\pi$
$83$	−5.85781	−	10.1460i	−0.642978	−	1.11367i	0.341787	−	0.939778i	$-0.388968\pi$
$84$	−2.84600	+	7.49965i	−0.310524	+	0.818279i
$85$	11.5430			1.25201
$86$	−8.49469			−0.916006
$87$	−9.10322	+	1.47751i	−0.975967	+	0.158405i
$88$	1.83826	+	3.18396i	0.195959	+	0.339411i
$89$	3.00802	+	5.21004i	0.318849	+	0.552263i	0.980248	−	0.197771i	$-0.0633703\pi$
$89$	3.00802	+	5.21004i	0.318849	+	0.552263i	−0.661399	+	0.750034i	$0.730037\pi$
$90$	4.49541	−	1.49874i	0.473857	−	0.157981i
$91$	−12.9061	−	22.3540i	−1.35293	−	2.34334i
$92$	−2.10449			−0.219408
$93$	2.00858	−	0.326004i	0.208280	−	0.0338051i
$94$	−2.87781	+	4.98452i	−0.296824	+	0.514114i
$95$	−0.643914	+	6.85494i	−0.0660642	+	0.703302i
$96$	−1.09515	−	1.34188i	−0.111774	−	0.136955i
$97$	−11.9403			−1.21236			−0.606179	−	0.795328i	$-0.707299\pi$
$97$	−11.9403			−1.21236			−0.606179	+	0.795328i	$0.707299\pi$
$98$	7.22408	−	12.5125i	0.729742	−	1.26395i
$99$	10.4634	−	3.48843i	1.05161	−	0.350600i
$100$	1.25250	−	2.16940i	0.125250	−	0.216940i
$101$	−5.44662	+	9.43383i	−0.541959	+	0.938701i	0.456832	+	0.889553i	$0.348984\pi$
$101$	−5.44662	+	9.43383i	−0.541959	+	0.938701i	−0.998792	+	0.0491479i	$0.984349\pi$
$102$	−12.4939	+	2.02783i	−1.23708	+	0.200785i
$103$	6.09893	−	10.5637i	0.600945	−	1.04087i	−0.391733	−	0.920079i	$-0.628124\pi$
$103$	6.09893	−	10.5637i	0.600945	−	1.04087i	0.992678	−	0.120789i	$-0.0385423\pi$
$104$	5.57353			0.546529
$105$	−12.5067	+	2.02992i	−1.22053	+	0.198099i
$106$	−1.69773	−	2.94055i	−0.164898	−	0.285612i
$107$	−6.89925			−0.666976			−0.333488	−	0.942754i	$-0.608226\pi$
$107$	−6.89925			−0.666976			−0.333488	+	0.942754i	$0.608226\pi$
$108$	−4.60245	+	2.41195i	−0.442871	+	0.232090i
$109$	−2.02428	+	3.50615i	−0.193890	+	0.335828i	−0.946536	−	0.322598i	$-0.895444\pi$
$109$	−2.02428	+	3.50615i	−0.193890	+	0.335828i	0.752646	+	0.658426i	$0.228777\pi$
$110$	−2.90363	+	5.02923i	−0.276850	+	0.479519i
$111$	1.27943	+	1.56768i	0.121439	+	0.148797i
$112$	2.31561	+	4.01075i	0.218804	+	0.378980i
$113$	−0.671292	+	1.16271i	−0.0631498	+	0.109379i	−0.895872	−	0.444313i	$-0.853448\pi$
$113$	−0.671292	+	1.16271i	−0.0631498	+	0.109379i	0.832722	+	0.553691i	$0.186781\pi$
$114$	−0.507293	−	7.53277i	−0.0475123	−	0.705509i
$115$	−1.66207	−	2.87880i	−0.154989	−	0.268449i
$116$	−2.66226	+	4.61117i	−0.247185	+	0.428136i
$117$	3.35125	−	16.3813i	0.309823	−	1.51445i
$118$	−0.992410	−	1.71891i	−0.0913588	−	0.158238i
$119$	33.8437			3.10245
$120$	0.970675	−	2.55788i	0.0886101	−	0.233502i
$121$	−1.25840	+	2.17961i	−0.114400	+	0.198146i
$122$	1.59300	−	2.75915i	0.144223	−	0.249802i
$123$	−2.76093	+	7.27549i	−0.248945	+	0.656009i
$124$	0.587415	−	1.01743i	0.0527514	−	0.0913681i
$125$	11.8546			1.06030
$126$	13.1804	−	4.39428i	1.17421	−	0.391474i
$127$	−3.95754	−	6.85466i	−0.351175	−	0.608253i	0.635281	−	0.772281i	$-0.280884\pi$
$127$	−3.95754	−	6.85466i	−0.351175	−	0.608253i	−0.986456	+	0.164029i	$0.947551\pi$
$128$	−1.00000			−0.0883883
$129$	9.30298	+	11.3988i	0.819082	+	1.00361i
$130$	4.40184	+	7.62422i	0.386067	+	0.668688i
$131$	0.696502	+	1.20638i	0.0608537	+	0.105402i	0.894847	−	0.446373i	$-0.147284\pi$
$131$	0.696502	+	1.20638i	0.0608537	+	0.105402i	−0.833994	+	0.551774i	$0.813951\pi$
$132$	2.25931	−	5.95364i	0.196648	−	0.518198i
$133$	−1.88794	+	20.0985i	−0.163705	+	1.74276i
$134$	−12.5843			−1.08711
$135$	−6.93429	−	4.39094i	−0.596809	−	0.377912i
$136$	−3.65387	+	6.32868i	−0.313317	+	0.542680i
$137$	−1.20442	+	2.08612i	−0.102901	+	0.178229i	−0.912879	−	0.408231i	$-0.866146\pi$
$137$	−1.20442	+	2.08612i	−0.102901	+	0.178229i	0.809978	+	0.586460i	$0.199479\pi$
$138$	2.30473	+	2.82396i	0.196192	+	0.240392i
$139$	−8.47018			−0.718431			−0.359216	−	0.933255i	$-0.616956\pi$
$139$	−8.47018			−0.718431			−0.359216	+	0.933255i	$0.616956\pi$
$140$	−3.65763	+	6.33520i	−0.309126	+	0.535422i
$141$	9.84026	−	1.59713i	0.828699	−	0.134503i
$142$	−4.03312	+	6.98558i	−0.338452	+	0.586217i
$143$	10.2456	+	17.7459i	0.856779	+	1.48399i
$144$	−0.601280	+	2.93913i	−0.0501066	+	0.244927i
$145$	−8.41037			−0.698443
$146$	−7.45107	+	12.9056i	−0.616655	+	1.06808i
$147$	−24.7017	+	4.00923i	−2.03736	+	0.330676i
$148$	1.16827			0.0960312
$149$	4.81128	+	8.33338i	0.394155	+	0.682697i	0.992993	−	0.118173i	$-0.0377039\pi$
$149$	4.81128	+	8.33338i	0.394155	+	0.682697i	−0.598838	+	0.800870i	$0.704371\pi$
$150$	−4.28276	+	0.695117i	−0.349686	+	0.0567561i
$151$	−11.4046	−	19.7534i	−0.928094	−	1.60751i	−0.786507	−	0.617581i	$-0.788113\pi$
$151$	−11.4046	−	19.7534i	−0.928094	−	1.60751i	−0.141587	−	0.989926i	$-0.545220\pi$
$152$	−3.55454	−	2.52294i	−0.288312	−	0.204637i
$153$	16.4038	+	14.5445i	1.32617	+	1.17585i
$154$	−8.51338	+	14.7456i	−0.686027	+	1.18823i
$155$	1.85571			0.149054
$156$	−6.10386	−	7.47900i	−0.488700	−	0.598799i
$157$	2.18674	+	3.78754i	0.174521	+	0.302279i	0.939995	−	0.341187i	$-0.110829\pi$
$157$	2.18674	+	3.78754i	0.174521	+	0.302279i	−0.765475	+	0.643466i	$0.777496\pi$
$158$	5.98637			0.476250
$159$	−2.08659	+	5.49850i	−0.165478	+	0.436060i
$160$	−0.789777	−	1.36793i	−0.0624373	−	0.108145i
$161$	−4.87316	−	8.44056i	−0.384059	−	0.665210i
$162$	8.27693	+	3.53447i	0.650297	+	0.277694i
$163$	6.36953			0.498900			0.249450	−	0.968388i	$-0.419750\pi$
$163$	6.36953			0.498900			0.249450	+	0.968388i	$0.419750\pi$
$164$	2.24640	+	3.89087i	0.175414	+	0.303826i
$165$	9.92854	−	1.61146i	0.772936	−	0.125452i
$166$	5.85781	+	10.1460i	0.454654	+	0.787484i
$167$	−6.17140			−0.477557			−0.238779	−	0.971074i	$-0.576747\pi$
$167$	−6.17140			−0.477557			−0.238779	+	0.971074i	$0.576747\pi$
$168$	2.84600	−	7.49965i	0.219573	−	0.578611i
$169$	18.0642			1.38955
$170$	−11.5430			−0.885305
$171$	−9.55251	+	8.93026i	−0.730498	+	0.682914i
$172$	8.49469			0.647714
$173$	−7.51338			−0.571232			−0.285616	−	0.958344i	$-0.592198\pi$
$173$	−7.51338			−0.571232			−0.285616	+	0.958344i	$0.592198\pi$
$174$	9.10322	−	1.47751i	0.690113	−	0.112009i
$175$	11.6012			0.876971
$176$	−1.83826	−	3.18396i	−0.138564	−	0.240000i
$177$	−1.21972	+	3.21416i	−0.0916799	+	0.241591i
$178$	−3.00802	−	5.21004i	−0.225460	−	0.390509i
$179$	21.7463			1.62540			0.812698	−	0.582685i	$-0.197998\pi$
$179$	21.7463			1.62540			0.812698	+	0.582685i	$0.197998\pi$
$180$	−4.49541	+	1.49874i	−0.335068	+	0.111710i
$181$	2.33180	+	4.03880i	0.173322	+	0.300202i	0.939579	−	0.342332i	$-0.111217\pi$
$181$	2.33180	+	4.03880i	0.173322	+	0.300202i	−0.766258	+	0.642534i	$0.777883\pi$
$182$	12.9061	+	22.3540i	0.956664	+	1.65699i
$183$	−5.44702	+	0.884083i	−0.402655	+	0.0653533i
$184$	2.10449			0.155145
$185$	0.922673	+	1.59812i	0.0678363	+	0.117496i
$186$	−2.00858	+	0.326004i	−0.147276	+	0.0239038i
$187$	−26.8670			−1.96471
$188$	2.87781	−	4.98452i	0.209886	−	0.363533i
$189$	−20.3312	−	12.8741i	−1.47888	−	0.936456i
$190$	0.643914	−	6.85494i	0.0467145	−	0.497310i
$191$	2.83934	+	4.91788i	0.205447	+	0.355845i	0.950275	−	0.311411i	$-0.100802\pi$
$191$	2.83934	+	4.91788i	0.205447	+	0.355845i	−0.744828	+	0.667257i	$0.767468\pi$
$192$	1.09515	+	1.34188i	0.0790359	+	0.0968418i
$193$	−4.93611	−	8.54959i	−0.355309	−	0.615413i	0.631862	−	0.775081i	$-0.282291\pi$
$193$	−4.93611	−	8.54959i	−0.355309	−	0.615413i	−0.987171	+	0.159668i	$0.948958\pi$
$194$	11.9403			0.857267
$195$	5.41008	−	14.2564i	0.387424	−	1.02092i
$196$	−7.22408	+	12.5125i	−0.516006	+	0.893748i
$197$	−25.0810			−1.78695			−0.893474	−	0.449114i	$-0.851740\pi$
$197$	−25.0810			−1.78695			−0.893474	+	0.449114i	$0.851740\pi$
$198$	−10.4634	+	3.48843i	−0.743599	+	0.247912i
$199$	4.46649	+	7.73619i	0.316621	+	0.548404i	0.979781	−	0.200074i	$-0.0641183\pi$
$199$	4.46649	+	7.73619i	0.316621	+	0.548404i	−0.663160	+	0.748478i	$0.730785\pi$
$200$	−1.25250	+	2.16940i	−0.0885655	+	0.153400i
$201$	13.7817	+	16.8866i	0.972086	+	1.19109i
$202$	5.44662	−	9.43383i	0.383223	−	0.663762i
$203$	−24.6590			−1.73072
$204$	12.4939	−	2.02783i	0.874746	−	0.141976i
$205$	−3.54830	+	6.14584i	−0.247824	+	0.429244i
$206$	−6.09893	+	10.5637i	−0.424932	+	0.736004i
$207$	1.26538	−	6.18535i	0.0879503	−	0.429911i
$208$	−5.57353			−0.386455
$209$	1.49875	−	15.9553i	0.103671	−	1.10365i
$210$	12.5067	−	2.02992i	0.863046	−	0.140077i
$211$	−3.16229	−	5.47724i	−0.217701	−	0.377069i	0.736404	−	0.676542i	$-0.236522\pi$
$211$	−3.16229	−	5.47724i	−0.217701	−	0.377069i	−0.954105	+	0.299473i	$0.903189\pi$
$212$	1.69773	+	2.94055i	0.116601	+	0.201958i
$213$	13.7907	−	2.23831i	0.944922	−	0.153366i
$214$	6.89925			0.471623
$215$	6.70891	+	11.6202i	0.457544	+	0.792489i
$216$	4.60245	−	2.41195i	0.313157	−	0.164112i
$217$	5.44089			0.369352
$218$	2.02428	−	3.50615i	0.137101	−	0.237466i
$219$	25.4779	−	4.13521i	1.72163	−	0.279431i
$220$	2.90363	−	5.02923i	0.195763	−	0.339071i
$221$	−20.3649	+	35.2731i	−1.36989	+	2.37272i
$222$	−1.27943	−	1.56768i	−0.0858700	−	0.105216i
$223$	1.75762			0.117699			0.0588496	−	0.998267i	$-0.481257\pi$
$223$	1.75762			0.117699			0.0588496	+	0.998267i	$0.481257\pi$
$224$	−2.31561	−	4.01075i	−0.154718	−	0.267980i
$225$	5.62304	+	4.98569i	0.374869	+	0.332379i
$226$	0.671292	−	1.16271i	0.0446537	−	0.0773424i
$227$	−6.41556	−	11.1121i	−0.425816	−	0.737535i	0.570680	−	0.821172i	$-0.306680\pi$
$227$	−6.41556	−	11.1121i	−0.425816	−	0.737535i	−0.996496	+	0.0836376i	$0.973346\pi$
$228$	0.507293	+	7.53277i	0.0335963	+	0.498870i
$229$	−0.207385	+	0.359201i	−0.0137044	+	0.0237367i	−0.872796	−	0.488085i	$-0.837696\pi$
$229$	−0.207385	+	0.359201i	−0.0137044	+	0.0237367i	0.859092	+	0.511821i	$0.171029\pi$
$230$	1.66207	+	2.87880i	0.109594	+	0.189822i
$231$	29.1103	−	4.72477i	1.91531	−	0.310867i
$232$	2.66226	−	4.61117i	0.174786	−	0.302738i
$233$	−6.42184	+	11.1229i	−0.420709	+	0.728689i	−0.996009	−	0.0892537i	$-0.971552\pi$
$233$	−6.42184	+	11.1229i	−0.420709	+	0.728689i	0.575300	+	0.817942i	$0.304885\pi$
$234$	−3.35125	+	16.3813i	−0.219078	+	1.07088i
$235$	9.09132			0.593052
$236$	0.992410	+	1.71891i	0.0646004	+	0.111891i
$237$	−6.55599	−	8.03299i	−0.425857	−	0.521798i
$238$	−33.8437			−2.19376
$239$	6.27082	−	10.8614i	0.405626	−	0.702564i	−0.588768	−	0.808302i	$-0.700387\pi$
$239$	6.27082	−	10.8614i	0.405626	−	0.702564i	0.994394	+	0.105738i	$0.0337204\pi$
$240$	−0.970675	+	2.55788i	−0.0626568	+	0.165111i
$241$	2.02478	−	3.50702i	0.130427	−	0.225907i	−0.793414	−	0.608682i	$-0.791698\pi$
$241$	2.02478	−	3.50702i	0.130427	−	0.225907i	0.923841	+	0.382775i	$0.125032\pi$
$242$	1.25840	−	2.17961i	0.0808928	−	0.140110i
$243$	−4.32166	−	14.9774i	−0.277235	−	0.960802i
$244$	−1.59300	+	2.75915i	−0.101981	+	0.176637i
$245$	−22.8216			−1.45802
$246$	2.76093	−	7.27549i	0.176031	−	0.463868i
$247$	−19.8113	−	14.0617i	−1.26057	−	0.894722i
$248$	−0.587415	+	1.01743i	−0.0373009	+	0.0646070i
$249$	7.19954	−	18.9719i	0.456252	−	1.20230i
$250$	−11.8546			−0.749749
$251$	−9.59620	−	16.6211i	−0.605707	−	1.04912i	−0.991939	−	0.126714i	$-0.959557\pi$
$251$	−9.59620	−	16.6211i	−0.605707	−	1.04912i	0.386232	−	0.922402i	$-0.373776\pi$
$252$	−13.1804	+	4.39428i	−0.830289	+	0.276814i
$253$	3.86859	+	6.70059i	0.243216	+	0.421263i
$254$	3.95754	+	6.85466i	0.248318	+	0.430100i
$255$	12.6413	+	15.4893i	0.791629	+	0.969975i
$256$	1.00000			0.0625000
$257$	−1.56919			−0.0978832			−0.0489416	−	0.998802i	$-0.515585\pi$
$257$	−1.56919			−0.0978832			−0.0489416	+	0.998802i	$0.515585\pi$
$258$	−9.30298	−	11.3988i	−0.579178	−	0.709661i
$259$	2.70526	+	4.68564i	0.168096	+	0.291152i
$260$	−4.40184	−	7.62422i	−0.272991	−	0.472834i
$261$	−11.9520	−	10.5973i	−0.739813	−	0.655958i
$262$	−0.696502	−	1.20638i	−0.0430301	−	0.0745302i
$263$	27.8248			1.71575			0.857876	−	0.513857i	$-0.171784\pi$
$263$	27.8248			1.71575			0.857876	+	0.513857i	$0.171784\pi$
$264$	−2.25931	+	5.95364i	−0.139051	+	0.366421i
$265$	−2.68165	+	4.64476i	−0.164733	+	0.285325i
$266$	1.88794	−	20.0985i	0.115757	−	1.23232i
$267$	−3.69700	+	9.74219i	−0.226253	+	0.596212i
$268$	12.5843			0.768706
$269$	0.0554458	−	0.0960349i	0.00338059	−	0.00585535i	−0.864330	−	0.502925i	$-0.832257\pi$
$269$	0.0554458	−	0.0960349i	0.00338059	−	0.00585535i	0.867711	+	0.497069i	$0.165591\pi$
$270$	6.93429	+	4.39094i	0.422007	+	0.267224i
$271$	−4.79718	+	8.30896i	−0.291408	+	0.504733i	−0.974143	−	0.225933i	$-0.927457\pi$
$271$	−4.79718	+	8.30896i	−0.291408	+	0.504733i	0.682735	+	0.730666i	$0.260790\pi$
$272$	3.65387	−	6.32868i	0.221548	−	0.383733i
$273$	15.8622	−	41.7995i	0.960027	−	2.52982i
$274$	1.20442	−	2.08612i	0.0727617	−	0.126027i
$275$	−9.20972			−0.555367
$276$	−2.30473	−	2.82396i	−0.138729	−	0.169983i
$277$	−7.63856	−	13.2304i	−0.458956	−	0.794936i	0.539950	−	0.841697i	$-0.318443\pi$
$277$	−7.63856	−	13.2304i	−0.458956	−	0.794936i	−0.998906	+	0.0467615i	$0.985110\pi$
$278$	8.47018			0.508007
$279$	2.63716	+	2.33825i	0.157883	+	0.139987i
$280$	3.65763	−	6.33520i	0.218585	−	0.378600i
$281$	−2.22648	+	3.85638i	−0.132821	+	0.230052i	−0.924763	−	0.380544i	$-0.875737\pi$
$281$	−2.22648	+	3.85638i	−0.132821	+	0.230052i	0.791942	+	0.610596i	$0.209070\pi$
$282$	−9.84026	+	1.59713i	−0.585979	+	0.0951078i
$283$	−2.89090	−	5.00718i	−0.171846	−	0.297646i	0.767219	−	0.641385i	$-0.221640\pi$
$283$	−2.89090	−	5.00718i	−0.171846	−	0.297646i	−0.939065	+	0.343739i	$0.888307\pi$
$284$	4.03312	−	6.98558i	0.239322	−	0.414518i
$285$	−9.90369	+	6.64315i	−0.586644	+	0.393506i
$286$	−10.2456	−	17.7459i	−0.605834	−	1.04934i
$287$	−10.4035	+	18.0195i	−0.614102	+	1.06366i
$288$	0.601280	−	2.93913i	0.0354307	−	0.173190i
$289$	−18.2015	−	31.5259i	−1.07068	−	1.85447i
$290$	8.41037			0.493874
$291$	−13.0765	−	16.0225i	−0.766559	−	0.939256i
$292$	7.45107	−	12.9056i	0.436041	−	0.755245i
$293$	−9.50767	+	16.4678i	−0.555444	+	0.962057i	0.442425	+	0.896806i	$0.354118\pi$
$293$	−9.50767	+	16.4678i	−0.555444	+	0.962057i	−0.997869	+	0.0652515i	$0.979215\pi$
$294$	24.7017	−	4.00923i	1.44063	−	0.233823i
$295$	−1.56757	+	2.71510i	−0.0912672	+	0.158079i
$296$	−1.16827			−0.0679043
$297$	16.1400	+	10.2202i	0.936540	+	0.593037i
$298$	−4.81128	−	8.33338i	−0.278710	−	0.482740i
$299$	11.7294			0.678329
$300$	4.28276	−	0.695117i	0.247265	−	0.0401326i
$301$	19.6704	+	34.0701i	1.13378	+	1.96377i
$302$	11.4046	+	19.7534i	0.656262	+	1.13668i
$303$	−18.6239	+	3.02277i	−1.06992	+	0.173654i
$304$	3.55454	+	2.52294i	0.203867	+	0.144700i
$305$	−5.03245			−0.288157
$306$	−16.4038	−	14.5445i	−0.937743	−	0.831453i
$307$	−12.2704	+	21.2529i	−0.700306	+	1.21297i	0.268053	+	0.963404i	$0.413620\pi$
$307$	−12.2704	+	21.2529i	−0.700306	+	1.21297i	−0.968359	+	0.249561i	$0.919714\pi$
$308$	8.51338	−	14.7456i	0.485095	−	0.840209i
$309$	20.8544	−	3.38479i	1.18637	−	0.192554i
$310$	−1.85571			−0.105397
$311$	1.73597	−	3.00679i	0.0984379	−	0.170500i	−0.812600	−	0.582821i	$-0.801949\pi$
$311$	1.73597	−	3.00679i	0.0984379	−	0.170500i	0.911038	+	0.412322i	$0.135282\pi$
$312$	6.10386	+	7.47900i	0.345563	+	0.423415i
$313$	−2.06042	+	3.56876i	−0.116462	+	0.201718i	−0.918363	−	0.395739i	$-0.870489\pi$
$313$	−2.06042	+	3.56876i	−0.116462	+	0.201718i	0.801901	+	0.597457i	$0.203822\pi$
$314$	−2.18674	−	3.78754i	−0.123405	−	0.213743i
$315$	−16.4207	−	14.5595i	−0.925201	−	0.820332i
$316$	−5.98637			−0.336760
$317$	10.8195	−	18.7399i	0.607683	−	1.05254i	−0.383938	−	0.923359i	$-0.625432\pi$
$317$	10.8195	−	18.7399i	0.607683	−	1.05254i	0.991621	−	0.129179i	$-0.0412342\pi$
$318$	2.08659	−	5.49850i	0.117010	−	0.308341i
$319$	19.5757			1.09603
$320$	0.789777	+	1.36793i	0.0441499	+	0.0764698i
$321$	−7.55574	−	9.25797i	−0.421720	−	0.516729i
$322$	4.87316	+	8.44056i	0.271571	+	0.470374i
$323$	28.9547	−	13.2771i	1.61108	−	0.738758i
$324$	−8.27693	−	3.53447i	−0.459829	−	0.196360i
$325$	−6.98087	+	12.0912i	−0.387229	+	0.670700i
$326$	−6.36953			−0.352775
$327$	−6.92172	+	1.12344i	−0.382772	+	0.0621261i
$328$	−2.24640	−	3.89087i	−0.124036	−	0.214837i
$329$	26.6555			1.46957
$330$	−9.92854	+	1.61146i	−0.546548	+	0.0887080i
$331$	−8.48039	−	14.6885i	−0.466125	−	0.807352i	0.533127	−	0.846035i	$-0.321017\pi$
$331$	−8.48039	−	14.6885i	−0.466125	−	0.807352i	−0.999252	+	0.0386837i	$0.987684\pi$
$332$	−5.85781	−	10.1460i	−0.321489	−	0.556835i
$333$	−0.702457	+	3.43369i	−0.0384944	+	0.188165i
$334$	6.17140			0.337684
$335$	9.93876	+	17.2144i	0.543012	+	0.940525i
$336$	−2.84600	+	7.49965i	−0.155262	+	0.409140i
$337$	11.6163	+	20.1200i	0.632779	+	1.09601i	0.986981	+	0.160836i	$0.0514192\pi$
$337$	11.6163	+	20.1200i	0.632779	+	1.09601i	−0.354202	+	0.935169i	$0.615248\pi$
$338$	−18.0642			−0.982563
$339$	−2.29539	+	0.372555i	−0.124668	+	0.0202344i
$340$	11.5430			0.626005
$341$	−4.31928			−0.233902
$342$	9.55251	−	8.93026i	0.516540	−	0.482893i
$343$	−34.4940			−1.86250
$344$	−8.49469			−0.458003
$345$	2.04277	−	5.38302i	0.109979	−	0.289812i
$346$	7.51338			0.403922
$347$	−8.20150	−	14.2054i	−0.440280	−	0.762587i	0.557430	−	0.830224i	$-0.311787\pi$
$347$	−8.20150	−	14.2054i	−0.440280	−	0.762587i	−0.997710	+	0.0676371i	$0.978454\pi$
$348$	−9.10322	+	1.47751i	−0.487984	+	0.0792026i
$349$	1.92719	+	3.33798i	0.103160	+	0.178678i	0.912985	−	0.407993i	$-0.133771\pi$
$349$	1.92719	+	3.33798i	0.103160	+	0.178678i	−0.809825	+	0.586671i	$0.800438\pi$
$350$	−11.6012			−0.620112
$351$	25.6519	−	13.4431i	1.36919	−	0.717537i
$352$	1.83826	+	3.18396i	0.0979796	+	0.169706i
$353$	−4.42315	−	7.66112i	−0.235421	−	0.407760i	0.723974	−	0.689827i	$-0.242313\pi$
$353$	−4.42315	−	7.66112i	−0.235421	−	0.407760i	−0.959395	+	0.282067i	$0.908980\pi$
$354$	1.21972	−	3.21416i	0.0648275	−	0.170831i
$355$	12.7411			0.676226
$356$	3.00802	+	5.21004i	0.159425	+	0.276131i
$357$	37.0640	+	45.4142i	1.96164	+	2.40357i
$358$	−21.7463			−1.14933
$359$	−11.0150	+	19.0785i	−0.581349	+	1.00693i	0.413971	+	0.910290i	$0.364142\pi$
$359$	−11.0150	+	19.0785i	−0.581349	+	1.00693i	−0.995320	+	0.0966358i	$0.969192\pi$
$360$	4.49541	−	1.49874i	0.236929	−	0.0789907i
$361$	6.26957	+	17.9358i	0.329977	+	0.943989i
$362$	−2.33180	−	4.03880i	−0.122557	−	0.212275i
$363$	−4.30291	+	0.698387i	−0.225844	+	0.0366558i
$364$	−12.9061	−	22.3540i	−0.676464	−	1.17167i
$365$	23.5387			1.23207
$366$	5.44702	−	0.884083i	0.284720	−	0.0462118i
$367$	−6.18264	+	10.7087i	−0.322731	+	0.558987i	−0.981051	−	0.193752i	$-0.937934\pi$
$367$	−6.18264	+	10.7087i	−0.322731	+	0.558987i	0.658319	+	0.752739i	$0.271268\pi$
$368$	−2.10449			−0.109704
$369$	−12.7865	+	4.26294i	−0.665637	+	0.221920i
$370$	−0.922673	−	1.59812i	−0.0479675	−	0.0830821i
$371$	−7.86255	+	13.6183i	−0.408203	+	0.707029i
$372$	2.00858	−	0.326004i	0.104140	−	0.0169025i
$373$	3.36121	−	5.82178i	0.174037	−	0.301440i	−0.765791	−	0.643090i	$-0.777652\pi$
$373$	3.36121	−	5.82178i	0.174037	−	0.301440i	0.939827	+	0.341649i	$0.110986\pi$
$374$	26.8670			1.38926
$375$	12.9826	+	15.9074i	0.670417	+	0.821454i
$376$	−2.87781	+	4.98452i	−0.148412	+	0.257057i
$377$	14.8382	−	25.7005i	0.764205	−	1.32364i
$378$	20.3312	+	12.8741i	1.04572	+	0.662174i
$379$	26.1451			1.34298			0.671491	−	0.741013i	$-0.265654\pi$
$379$	26.1451			1.34298			0.671491	+	0.741013i	$0.265654\pi$
$380$	−0.643914	+	6.85494i	−0.0330321	+	0.351651i
$381$	4.86402	−	12.8174i	0.249191	−	0.656658i
$382$	−2.83934	−	4.91788i	−0.145273	−	0.251621i
$383$	−6.86972	−	11.8987i	−0.351026	−	0.607995i	0.635403	−	0.772180i	$-0.280834\pi$
$383$	−6.86972	−	11.8987i	−0.351026	−	0.607995i	−0.986430	+	0.164185i	$0.947501\pi$
$384$	−1.09515	−	1.34188i	−0.0558868	−	0.0684775i
$385$	26.8947			1.37068
$386$	4.93611	+	8.54959i	0.251241	+	0.435163i
$387$	−5.10768	+	24.9670i	−0.259638	+	1.26914i
$388$	−11.9403			−0.606179
$389$	−15.2002	+	26.3276i	−0.770683	+	1.33486i	0.166507	+	0.986040i	$0.446751\pi$
$389$	−15.2002	+	26.3276i	−0.770683	+	1.33486i	−0.937189	+	0.348821i	$0.886582\pi$
$390$	−5.41008	+	14.2564i	−0.273950	+	0.721902i
$391$	−7.68951	+	13.3186i	−0.388875	+	0.673552i
$392$	7.22408	−	12.5125i	0.364871	−	0.631975i
$393$	−0.856036	+	2.25579i	−0.0431813	+	0.113790i
$394$	25.0810			1.26356
$395$	−4.72790	−	8.18896i	−0.237886	−	0.412031i
$396$	10.4634	−	3.48843i	0.525804	−	0.175300i
$397$	9.16006	−	15.8657i	0.459730	−	0.796277i	−0.539216	−	0.842168i	$-0.681279\pi$
$397$	9.16006	−	15.8657i	0.459730	−	0.796277i	0.998946	+	0.0458910i	$0.0146127\pi$
$398$	−4.46649	−	7.73619i	−0.223885	−	0.387780i
$399$	−29.0374	+	19.4776i	−1.45369	+	0.975098i
$400$	1.25250	−	2.16940i	0.0626252	−	0.108470i
$401$	−17.3023	−	29.9685i	−0.864035	−	1.49655i	−0.868002	−	0.496561i	$-0.834596\pi$
$401$	−17.3023	−	29.9685i	−0.864035	−	1.49655i	0.00396662	−	0.999992i	$-0.498737\pi$
$402$	−13.7817	−	16.8866i	−0.687368	−	0.842225i
$403$	−3.27397	+	5.67069i	−0.163088	+	0.282477i
$404$	−5.44662	+	9.43383i	−0.270980	+	0.469350i
$405$	−1.70200	−	14.1137i	−0.0845730	−	0.701317i
$406$	24.6590			1.22381
$407$	−2.14758	−	3.71972i	−0.106452	−	0.184380i
$408$	−12.4939	+	2.02783i	−0.618539	+	0.100392i
$409$	−5.01138			−0.247797			−0.123898	−	0.992295i	$-0.539540\pi$
$409$	−5.01138			−0.247797			−0.123898	+	0.992295i	$0.539540\pi$
$410$	3.54830	−	6.14584i	0.175238	−	0.303521i
$411$	−4.11834	+	0.668431i	−0.203143	+	0.0329713i
$412$	6.09893	−	10.5637i	0.300473	−	0.520434i
$413$	−4.59607	+	7.96062i	−0.226158	+	0.391717i
$414$	−1.26538	+	6.18535i	−0.0621902	+	0.303993i
$415$	9.25272	−	16.0262i	0.454198	−	0.786695i
$416$	5.57353			0.273265
$417$	−9.27614	−	11.3660i	−0.454255	−	0.556593i
$418$	−1.49875	+	15.9553i	−0.0733065	+	0.780401i
$419$	−14.5553	+	25.2106i	−0.711074	+	1.23162i	0.253380	+	0.967367i	$0.418458\pi$
$419$	−14.5553	+	25.2106i	−0.711074	+	1.23162i	−0.964454	+	0.264250i	$0.914876\pi$
$420$	−12.5067	+	2.02992i	−0.610266	+	0.0990497i
$421$	−3.43970			−0.167641			−0.0838204	−	0.996481i	$-0.526712\pi$
$421$	−3.43970			−0.167641			−0.0838204	+	0.996481i	$0.526712\pi$
$422$	3.16229	+	5.47724i	0.153938	+	0.266628i
$423$	12.9198	+	11.4553i	0.628180	+	0.556978i
$424$	−1.69773	−	2.94055i	−0.0824490	−	0.142806i
$425$	−9.15297	−	15.8534i	−0.443984	−	0.769004i
$426$	−13.7907	+	2.23831i	−0.668161	+	0.108446i
$427$	−14.7550			−0.714045
$428$	−6.89925			−0.333488
$429$	−12.5923	+	33.1828i	−0.607964	+	1.60208i
$430$	−6.70891	−	11.6202i	−0.323532	−	0.560374i
$431$	−4.96062	−	8.59205i	−0.238945	−	0.413865i	0.721467	−	0.692449i	$-0.243468\pi$
$431$	−4.96062	−	8.59205i	−0.238945	−	0.413865i	−0.960412	+	0.278584i	$0.910135\pi$
$432$	−4.60245	+	2.41195i	−0.221435	+	0.116045i
$433$	0.263521	+	0.456432i	0.0126640	+	0.0219347i	0.872288	−	0.488993i	$-0.162635\pi$
$433$	0.263521	+	0.456432i	0.0126640	+	0.0219347i	−0.859624	+	0.510927i	$0.829302\pi$
$434$	−5.44089			−0.261171
$435$	−9.21064	−	11.2857i	−0.441616	−	0.541108i
$436$	−2.02428	+	3.50615i	−0.0969452	+	0.167914i
$437$	−7.48049	−	5.30948i	−0.357840	−	0.253987i
$438$	−25.4779	+	4.13521i	−1.21738	+	0.197588i
$439$	−16.3504			−0.780361			−0.390180	−	0.920738i	$-0.627587\pi$
$439$	−16.3504			−0.780361			−0.390180	+	0.920738i	$0.627587\pi$
$440$	−2.90363	+	5.02923i	−0.138425	+	0.239759i
$441$	−32.4320	−	28.7560i	−1.54438	−	1.36933i
$442$	20.3649	−	35.2731i	0.968661	−	1.67777i
$443$	−2.89318	+	5.01113i	−0.137459	+	0.238086i	−0.926534	−	0.376211i	$-0.877227\pi$
$443$	−2.89318	+	5.01113i	−0.137459	+	0.238086i	0.789075	+	0.614297i	$0.210560\pi$
$444$	1.27943	+	1.56768i	0.0607193	+	0.0743987i
$445$	−4.75133	+	8.22954i	−0.225234	+	0.390117i
$446$	−1.75762			−0.0832258
$447$	−5.91330	+	15.5825i	−0.279690	+	0.737026i
$448$	2.31561	+	4.01075i	0.109402	+	0.189490i
$449$	−10.4180			−0.491658			−0.245829	−	0.969313i	$-0.579060\pi$
$449$	−10.4180			−0.491658			−0.245829	+	0.969313i	$0.579060\pi$
$450$	−5.62304	−	4.98569i	−0.265073	−	0.235028i
$451$	8.25892	−	14.3049i	0.388897	−	0.673590i
$452$	−0.671292	+	1.16271i	−0.0315749	+	0.0546894i
$453$	14.0168	−	36.9366i	0.658569	−	1.73543i
$454$	6.41556	+	11.1121i	0.301097	+	0.521516i
$455$	20.3859	−	35.3094i	0.955705	−	1.65533i
$456$	−0.507293	−	7.53277i	−0.0237562	−	0.352754i
$457$	−10.3149	−	17.8659i	−0.482510	−	0.835733i	0.517288	−	0.855811i	$-0.326942\pi$
$457$	−10.3149	−	17.8659i	−0.482510	−	0.835733i	−0.999798	+	0.0200789i	$0.993608\pi$
$458$	0.207385	−	0.359201i	0.00969047	−	0.0167844i
$459$	−1.55227	+	37.9404i	−0.0724536	+	1.77090i
$460$	−1.66207	−	2.87880i	−0.0774946	−	0.134225i
$461$	−15.3064			−0.712890			−0.356445	−	0.934316i	$-0.616011\pi$
$461$	−15.3064			−0.712890			−0.356445	+	0.934316i	$0.616011\pi$
$462$	−29.1103	+	4.72477i	−1.35433	+	0.219816i
$463$	4.73547	−	8.20208i	0.220076	−	0.381183i	−0.734755	−	0.678333i	$-0.762703\pi$
$463$	4.73547	−	8.20208i	0.220076	−	0.381183i	0.954831	+	0.297150i	$0.0960361\pi$
$464$	−2.66226	+	4.61117i	−0.123592	+	0.214068i
$465$	2.03228	+	2.49013i	0.0942449	+	0.115477i
$466$	6.42184	−	11.1229i	0.297486	−	0.515261i
$467$	−15.0904			−0.698299			−0.349149	−	0.937067i	$-0.613529\pi$
$467$	−15.0904			−0.698299			−0.349149	+	0.937067i	$0.613529\pi$
$468$	3.35125	−	16.3813i	0.154912	−	0.757226i
$469$	29.1402	+	50.4723i	1.34557	+	2.33060i
$470$	−9.09132			−0.419351
$471$	−2.68761	+	7.08227i	−0.123839	+	0.326334i
$472$	−0.992410	−	1.71891i	−0.0456794	−	0.0791190i
$473$	−15.6154	−	27.0467i	−0.717999	−	1.24361i
$474$	6.55599	+	8.03299i	0.301127	+	0.368967i
$475$	9.92535	−	4.55124i	0.455406	−	0.208825i
$476$	33.8437			1.55122
$477$	−9.66347	+	3.22175i	−0.442460	+	0.147514i
$478$	−6.27082	+	10.8614i	−0.286821	+	0.496788i
$479$	−13.8928	+	24.0631i	−0.634779	+	1.09947i	0.351783	+	0.936082i	$0.385576\pi$
$479$	−13.8928	+	24.0631i	−0.634779	+	1.09947i	−0.986562	+	0.163388i	$0.947758\pi$
$480$	0.970675	−	2.55788i	0.0443051	−	0.116751i
$481$	−6.51139			−0.296894
$482$	−2.02478	+	3.50702i	−0.0922261	+	0.159740i
$483$	5.98936	−	15.7829i	0.272525	−	0.718147i
$484$	−1.25840	+	2.17961i	−0.0571998	+	0.0990730i
$485$	−9.43021	−	16.3336i	−0.428204	−	0.741671i
$486$	4.32166	+	14.9774i	0.196035	+	0.679390i
$487$	26.0008			1.17821			0.589105	−	0.808057i	$-0.299480\pi$
$487$	26.0008			1.17821			0.589105	+	0.808057i	$0.299480\pi$
$488$	1.59300	−	2.75915i	0.0721116	−	0.124901i
$489$	6.97561	+	8.54713i	0.315448	+	0.386515i
$490$	22.8216			1.03098
$491$	16.4765	+	28.5381i	0.743572	+	1.28790i	0.950859	+	0.309624i	$0.100203\pi$
$491$	16.4765	+	28.5381i	0.743572	+	1.28790i	−0.207287	+	0.978280i	$0.566463\pi$
$492$	−2.76093	+	7.27549i	−0.124472	+	0.328004i
$493$	19.4551	+	33.6972i	0.876213	+	1.51765i
$494$	19.8113	+	14.0617i	0.891355	+	0.632664i
$495$	13.0357	+	11.5581i	0.585909	+	0.519498i
$496$	0.587415	−	1.01743i	0.0263757	−	0.0456841i
$497$	37.3565			1.67567
$498$	−7.19954	+	18.9719i	−0.322619	+	0.850152i
$499$	−2.04254	−	3.53779i	−0.0914368	−	0.158373i	0.816679	−	0.577092i	$-0.195813\pi$
$499$	−2.04254	−	3.53779i	−0.0914368	−	0.158373i	−0.908116	+	0.418719i	$0.862479\pi$
$500$	11.8546			0.530152
$501$	−6.75863	−	8.28127i	−0.301953	−	0.369980i
$502$	9.59620	+	16.6211i	0.428300	+	0.741837i
$503$	4.15278	+	7.19283i	0.185163	+	0.320712i	0.943632	−	0.330998i	$-0.107385\pi$
$503$	4.15278	+	7.19283i	0.185163	+	0.320712i	−0.758468	+	0.651710i	$0.774052\pi$
$504$	13.1804	−	4.39428i	0.587103	−	0.195737i
$505$	−17.2065			−0.765678
$506$	−3.86859	−	6.70059i	−0.171980	−	0.297878i
$507$	19.7831	+	24.2400i	0.878597	+	1.07654i
$508$	−3.95754	−	6.85466i	−0.175587	−	0.304126i
$509$	−14.7633			−0.654373			−0.327186	−	0.944960i	$-0.606101\pi$
$509$	−14.7633			−0.654373			−0.327186	+	0.944960i	$0.606101\pi$
$510$	−12.6413	−	15.4893i	−0.559767	−	0.685876i
$511$	69.0150			3.05305
$512$	−1.00000			−0.0441942
$513$	−22.4448	−	3.03831i	−0.990962	−	0.134144i
$514$	1.56919			0.0692139
$515$	19.2672			0.849013
$516$	9.30298	+	11.3988i	0.409541	+	0.501806i
$517$	−21.1607			−0.930645
$518$	−2.70526	−	4.68564i	−0.118862	−	0.205875i
$519$	−8.22830	−	10.0821i	−0.361182	−	0.442553i
$520$	4.40184	+	7.62422i	0.193034	+	0.334344i
$521$	31.7044			1.38899			0.694497	−	0.719495i	$-0.255627\pi$
$521$	31.7044			1.38899			0.694497	+	0.719495i	$0.255627\pi$
$522$	11.9520	+	10.5973i	0.523127	+	0.463832i
$523$	14.4395	+	25.0100i	0.631396	+	1.09361i	0.987267	+	0.159075i	$0.0508511\pi$
$523$	14.4395	+	25.0100i	0.631396	+	1.09361i	−0.355870	+	0.934535i	$0.615816\pi$
$524$	0.696502	+	1.20638i	0.0304268	+	0.0527008i
$525$	12.7051	+	15.5675i	0.554497	+	0.679420i
$526$	−27.8248			−1.21322
$527$	−4.29267	−	7.43513i	−0.186992	−	0.323879i
$528$	2.25931	−	5.95364i	0.0983240	−	0.259099i
$529$	−18.5711			−0.807441
$530$	2.68165	−	4.64476i	0.116484	−	0.201756i
$531$	−5.64880	+	1.88328i	−0.245137	+	0.0817273i
$532$	−1.88794	+	20.0985i	−0.0818527	+	0.871382i
$533$	−12.5203	−	21.6859i	−0.542316	−	0.939320i
$534$	3.69700	−	9.74219i	0.159985	−	0.421586i
$535$	−5.44887	−	9.43772i	−0.235575	−	0.408028i
$536$	−12.5843			−0.543557
$537$	23.8156	+	29.1809i	1.02772	+	1.25925i
$538$	−0.0554458	+	0.0960349i	−0.00239044	+	0.00414036i
$539$	53.1189			2.28799
$540$	−6.93429	−	4.39094i	−0.298404	−	0.188956i
$541$	−14.3701	−	24.8898i	−0.617820	−	1.07010i	−0.989883	−	0.141888i	$-0.954683\pi$
$541$	−14.3701	−	24.8898i	−0.617820	−	1.07010i	0.372063	−	0.928208i	$-0.378651\pi$
$542$	4.79718	−	8.30896i	0.206056	−	0.356900i
$543$	−2.86590	+	7.55211i	−0.122988	+	0.324092i
$544$	−3.65387	+	6.32868i	−0.156658	+	0.271340i
$545$	−6.39490			−0.273928
$546$	−15.8622	+	41.7995i	−0.678841	+	1.78885i
$547$	−3.12120	+	5.40608i	−0.133453	+	0.231147i	−0.925005	−	0.379954i	$-0.875940\pi$
$547$	−3.12120	+	5.40608i	−0.133453	+	0.231147i	0.791552	+	0.611101i	$0.209273\pi$
$548$	−1.20442	+	2.08612i	−0.0514503	+	0.0891145i
$549$	−7.15166	−	6.34104i	−0.305225	−	0.270629i
$550$	9.20972			0.392704
$551$	−21.0968	+	9.67389i	−0.898755	+	0.412122i
$552$	2.30473	+	2.82396i	0.0980960	+	0.120196i
$553$	−13.8621	−	24.0098i	−0.589476	−	1.02100i
$554$	7.63856	+	13.2304i	0.324531	+	0.562104i
$555$	−1.13401	+	2.98830i	−0.0481361	+	0.126846i
$556$	−8.47018			−0.359216
$557$	6.56478	+	11.3705i	0.278159	+	0.481785i	0.970927	−	0.239375i	$-0.0769426\pi$
$557$	6.56478	+	11.3705i	0.278159	+	0.481785i	−0.692769	+	0.721160i	$0.743609\pi$
$558$	−2.63716	−	2.33825i	−0.111640	−	0.0989859i
$559$	−47.3454			−2.00250
$560$	−3.65763	+	6.33520i	−0.154563	+	0.267711i
$561$	−29.4235	−	36.0523i	−1.24226	−	1.52213i
$562$	2.22648	−	3.85638i	0.0939185	−	0.162672i
$563$	−6.22302	+	10.7786i	−0.262269	+	0.454264i	−0.966845	−	0.255366i	$-0.917804\pi$
$563$	−6.22302	+	10.7786i	−0.262269	+	0.454264i	0.704575	+	0.709629i	$0.251137\pi$
$564$	9.84026	−	1.59713i	0.414350	−	0.0672514i
$565$	−2.12068			−0.0892178
$566$	2.89090	+	5.00718i	0.121514	+	0.210468i
$567$	−4.99022	−	41.3811i	−0.209570	−	1.73784i
$568$	−4.03312	+	6.98558i	−0.169226	+	0.293108i
$569$	−17.5284	−	30.3601i	−0.734830	−	1.27276i	−0.954798	−	0.297255i	$-0.903929\pi$
$569$	−17.5284	−	30.3601i	−0.734830	−	1.27276i	0.219968	−	0.975507i	$-0.429405\pi$
$570$	9.90369	−	6.64315i	0.414820	−	0.278251i
$571$	−3.38933	+	5.87049i	−0.141839	+	0.245672i	−0.928189	−	0.372109i	$-0.878635\pi$
$571$	−3.38933	+	5.87049i	−0.141839	+	0.245672i	0.786350	+	0.617781i	$0.211968\pi$
$572$	10.2456	+	17.7459i	0.428390	+	0.741993i
$573$	−3.48969	+	9.19588i	−0.145784	+	0.384163i
$574$	10.4035	−	18.0195i	0.434235	−	0.752118i
$575$	−2.63588	+	4.56547i	−0.109924	+	0.190393i
$576$	−0.601280	+	2.93913i	−0.0250533	+	0.122464i
$577$	−40.8352			−1.69999			−0.849997	−	0.526788i	$-0.823396\pi$
$577$	−40.8352			−1.69999			−0.849997	+	0.526788i	$0.823396\pi$
$578$	18.2015	+	31.5259i	0.757082	+	1.31131i
$579$	6.06672	−	15.9868i	0.252124	−	0.664388i
$580$	−8.41037			−0.349222
$581$	27.1288	−	46.9884i	1.12549	−	1.94941i
$582$	13.0765	+	16.0225i	0.542039	+	0.664154i
$583$	6.24173	−	10.8110i	0.258506	−	0.447746i
$584$	−7.45107	+	12.9056i	−0.308328	+	0.534039i
$585$	25.0553	−	8.35329i	1.03591	−	0.345366i
$586$	9.50767	−	16.4678i	0.392758	−	0.680277i
$587$	12.2021			0.503633			0.251817	−	0.967775i	$-0.418972\pi$
$587$	12.2021			0.503633			0.251817	+	0.967775i	$0.418972\pi$
$588$	−24.7017	+	4.00923i	−1.01868	+	0.165338i
$589$	4.65491	−	2.13450i	0.191802	−	0.0879504i
$590$	1.56757	−	2.71510i	0.0645357	−	0.111779i
$591$	−27.4676	−	33.6557i	−1.12986	−	1.38441i
$592$	1.16827			0.0480156
$593$	5.17093	+	8.95632i	0.212345	+	0.367792i	0.952448	−	0.304702i	$-0.0985567\pi$
$593$	5.17093	+	8.95632i	0.212345	+	0.367792i	−0.740103	+	0.672493i	$0.765223\pi$
$594$	−16.1400	−	10.2202i	−0.662234	−	0.419340i
$595$	26.7290	+	46.2959i	1.09578	+	1.89795i
$596$	4.81128	+	8.33338i	0.197078	+	0.341348i
$597$	−5.48954	+	14.4658i	−0.224672	+	0.592046i
$598$	−11.7294			−0.479651
$599$	13.1418			0.536960			0.268480	−	0.963285i	$-0.413479\pi$
$599$	13.1418			0.536960			0.268480	+	0.963285i	$0.413479\pi$
$600$	−4.28276	+	0.695117i	−0.174843	+	0.0283780i
$601$	−4.17421	−	7.22994i	−0.170269	−	0.294915i	0.768245	−	0.640156i	$-0.221130\pi$
$601$	−4.17421	−	7.22994i	−0.170269	−	0.294915i	−0.938514	+	0.345241i	$0.887797\pi$
$602$	−19.6704	−	34.0701i	−0.801704	−	1.38859i
$603$	−7.56666	+	36.9867i	−0.308138	+	1.50622i
$604$	−11.4046	−	19.7534i	−0.464047	−	0.803753i
$605$	−3.97541			−0.161623
$606$	18.6239	−	3.02277i	0.756546	−	0.122792i
$607$	2.44638	−	4.23725i	0.0992953	−	0.171985i	−0.812098	−	0.583521i	$-0.801674\pi$
$607$	2.44638	−	4.23725i	0.0992953	−	0.171985i	0.911393	+	0.411537i	$0.135008\pi$
$608$	−3.55454	−	2.52294i	−0.144156	−	0.102319i
$609$	−27.0054	−	33.0894i	−1.09431	−	1.34085i
$610$	5.03245			0.203758
$611$	−16.0396	+	27.7813i	−0.648891	+	1.12391i
$612$	16.4038	+	14.5445i	0.663085	+	0.587926i
$613$	−5.76017	+	9.97691i	−0.232651	+	0.402964i	−0.958587	−	0.284798i	$-0.908073\pi$
$613$	−5.76017	+	9.97691i	−0.232651	+	0.402964i	0.725936	+	0.687762i	$0.241407\pi$
$614$	12.2704	−	21.2529i	0.495191	−	0.857696i
$615$	−12.1329	+	1.96924i	−0.489246	+	0.0794075i
$616$	−8.51338	+	14.7456i	−0.343014	+	0.594117i
$617$	−20.8853			−0.840812			−0.420406	−	0.907336i	$-0.638112\pi$
$617$	−20.8853			−0.840812			−0.420406	+	0.907336i	$0.638112\pi$
$618$	−20.8544	+	3.38479i	−0.838887	+	0.136156i
$619$	22.7753	+	39.4479i	0.915415	+	1.58555i	0.806292	+	0.591518i	$0.201471\pi$
$619$	22.7753	+	39.4479i	0.915415	+	1.58555i	0.109124	+	0.994028i	$0.465196\pi$
$620$	1.85571			0.0745270
$621$	9.68578	−	5.07591i	0.388677	−	0.203689i
$622$	−1.73597	+	3.00679i	−0.0696061	+	0.120561i
$623$	−13.9308	+	24.1288i	−0.558125	+	0.966701i
$624$	−6.10386	−	7.47900i	−0.244350	−	0.299400i
$625$	3.09994	+	5.36925i	0.123998	+	0.214770i
$626$	2.06042	−	3.56876i	0.0823511	−	0.142636i
$627$	23.0515	−	15.4624i	0.920588	−	0.617508i
$628$	2.18674	+	3.78754i	0.0872603	+	0.151139i
$629$	4.26870	−	7.39361i	0.170204	−	0.294803i
$630$	16.4207	+	14.5595i	0.654216	+	0.580063i
$631$	19.0978	+	33.0784i	0.760272	+	1.31683i	0.942710	+	0.333612i	$0.108268\pi$
$631$	19.0978	+	33.0784i	0.760272	+	1.31683i	−0.182439	+	0.983217i	$0.558399\pi$
$632$	5.98637			0.238125
$633$	3.88661	−	10.2418i	0.154479	−	0.407076i
$634$	−10.8195	+	18.7399i	−0.429697	+	0.744257i
$635$	6.25115	−	10.8273i	0.248069	−	0.429669i
$636$	−2.08659	+	5.49850i	−0.0827388	+	0.218030i
$637$	40.2636	−	69.7386i	1.59530	−	2.76314i
$638$	−19.5757			−0.775010
$639$	18.1065	+	16.0541i	0.716280	+	0.635092i
$640$	−0.789777	−	1.36793i	−0.0312187	−	0.0540723i
$641$	−35.5713			−1.40498			−0.702491	−	0.711693i	$-0.747929\pi$
$641$	−35.5713			−1.40498			−0.702491	+	0.711693i	$0.747929\pi$
$642$	7.55574	+	9.25797i	0.298201	+	0.365383i
$643$	−4.34236	−	7.52118i	−0.171246	−	0.296607i	0.767610	−	0.640917i	$-0.221446\pi$
$643$	−4.34236	−	7.52118i	−0.171246	−	0.296607i	−0.938856	+	0.344311i	$0.888113\pi$
$644$	−4.87316	−	8.44056i	−0.192029	−	0.332605i
$645$	−8.24558	+	21.7284i	−0.324669	+	0.855555i
$646$	−28.9547	+	13.2771i	−1.13921	+	0.522381i
$647$	8.66501			0.340657			0.170328	−	0.985387i	$-0.445517\pi$
$647$	8.66501			0.340657			0.170328	+	0.985387i	$0.445517\pi$
$648$	8.27693	+	3.53447i	0.325148	+	0.138847i
$649$	3.64862	−	6.31959i	0.143221	−	0.248066i
$650$	6.98087	−	12.0912i	0.273812	−	0.474257i
$651$	5.95861	+	7.30102i	0.233536	+	0.286149i
$652$	6.36953			0.249450
$653$	22.1970	−	38.4463i	0.868635	−	1.50452i	0.00524262	−	0.999986i	$-0.498331\pi$
$653$	22.1970	−	38.4463i	0.868635	−	1.50452i	0.863392	−	0.504533i	$-0.168335\pi$
$654$	6.92172	−	1.12344i	0.270661	−	0.0439298i
$655$	−1.10016	+	1.90554i	−0.0429869	+	0.0744555i
$656$	2.24640	+	3.89087i	0.0877070	+	0.151913i
$657$	33.4511	+	29.6595i	1.30505	+	1.15713i
$658$	−26.6555			−1.03914
$659$	4.52096	−	7.83054i	0.176112	−	0.305035i	−0.764434	−	0.644702i	$-0.776981\pi$
$659$	4.52096	−	7.83054i	0.176112	−	0.305035i	0.940545	+	0.339668i	$0.110315\pi$
$660$	9.92854	−	1.61146i	0.386468	−	0.0627260i
$661$	7.38050			0.287068			0.143534	−	0.989645i	$-0.454153\pi$
$661$	7.38050			0.287068			0.143534	+	0.989645i	$0.454153\pi$
$662$	8.48039	+	14.6885i	0.329600	+	0.570884i
$663$	−69.6349	+	11.3022i	−2.70440	+	0.438939i
$664$	5.85781	+	10.1460i	0.227327	+	0.393742i
$665$	−28.9845	+	13.2908i	−1.12397	+	0.515394i
$666$	0.702457	−	3.43369i	0.0272197	−	0.133053i
$667$	5.60269	−	9.70414i	0.216937	−	0.375746i
$668$	−6.17140			−0.238779
$669$	1.92487	+	2.35852i	0.0744196	+	0.0911855i
$670$	−9.93876	−	17.2144i	−0.383968	−	0.665052i
$671$	11.7134			0.452189
$672$	2.84600	−	7.49965i	0.109787	−	0.289305i
$673$	10.3428	+	17.9142i	0.398685	+	0.690544i	0.993564	−	0.113272i	$-0.0361332\pi$
$673$	10.3428	+	17.9142i	0.398685	+	0.690544i	−0.594879	+	0.803816i	$0.702800\pi$
$674$	−11.6163	−	20.1200i	−0.447442	−	0.774993i
$675$	−0.532100	+	13.0055i	−0.0204805	+	0.500583i
$676$	18.0642			0.694777
$677$	13.9362	+	24.1381i	0.535610	+	0.927704i	0.999134	+	0.0416191i	$0.0132516\pi$
$677$	13.9362	+	24.1381i	0.535610	+	0.927704i	−0.463524	+	0.886085i	$0.653415\pi$
$678$	2.29539	−	0.372555i	0.0881538	−	0.0143079i
$679$	−27.6492	−	47.8898i	−1.06108	−	1.83784i
$680$	−11.5430			−0.442652
$681$	7.88505	−	20.7783i	0.302156	−	0.796228i
$682$	4.31928			0.165394
$683$	−22.0360			−0.843183			−0.421591	−	0.906786i	$-0.638528\pi$
$683$	−22.0360			−0.843183			−0.421591	+	0.906786i	$0.638528\pi$
$684$	−9.55251	+	8.93026i	−0.365249	+	0.341457i
$685$	−3.80489			−0.145378
$686$	34.4940			1.31699
$687$	−0.709123	+	0.115095i	−0.0270547	+	0.00439114i
$688$	8.49469			0.323857
$689$	−9.46234	−	16.3893i	−0.360486	−	0.624381i
$690$	−2.04277	+	5.38302i	−0.0777670	+	0.204928i
$691$	11.6097	+	20.1087i	0.441656	+	0.764970i	0.997813	−	0.0661073i	$-0.0210580\pi$
$691$	11.6097	+	20.1087i	0.441656	+	0.764970i	−0.556157	+	0.831077i	$0.687725\pi$
$692$	−7.51338			−0.285616
$693$	38.2203	+	33.8881i	1.45187	+	1.28730i
$694$	8.20150	+	14.2054i	0.311325	+	0.539230i
$695$	−6.68955	−	11.5866i	−0.253749	−	0.439506i
$696$	9.10322	−	1.47751i	0.345057	−	0.0560047i
$697$	32.8321			1.24361
$698$	−1.92719	−	3.33798i	−0.0729451	−	0.126345i
$699$	−21.9585	+	3.56400i	−0.830549	+	0.134803i
$700$	11.6012			0.438486
$701$	−0.439487	+	0.761215i	−0.0165992	+	0.0287507i	−0.874206	−	0.485556i	$-0.838617\pi$
$701$	−0.439487	+	0.761215i	−0.0165992	+	0.0287507i	0.857606	+	0.514306i	$0.171951\pi$
$702$	−25.6519	+	13.4431i	−0.968167	+	0.507376i
$703$	4.15267	+	2.94747i	0.156621	+	0.111166i
$704$	−1.83826	−	3.18396i	−0.0692820	−	0.120000i
$705$	9.95638	+	12.1994i	0.374979	+	0.459458i
$706$	4.42315	+	7.66112i	0.166468	+	0.288330i
$707$	−50.4490			−1.89733
$708$	−1.21972	+	3.21416i	−0.0458400	+	0.120796i
$709$	5.55657	−	9.62427i	0.208682	−	0.361447i	−0.742618	−	0.669715i	$-0.766416\pi$
$709$	5.55657	−	9.62427i	0.208682	−	0.361447i	0.951299	+	0.308268i	$0.0997495\pi$
$710$	−12.7411			−0.478164
$711$	3.59948	−	17.5947i	0.134991	−	0.659853i
$712$	−3.00802	−	5.21004i	−0.112730	−	0.195254i
$713$	−1.23621	+	2.14117i	−0.0462963	+	0.0801875i
$714$	−37.0640	−	45.4142i	−1.38709	−	1.69958i
$715$	−16.1835	+	28.0306i	−0.605227	+	1.04828i
$716$	21.7463			0.812698
$717$	21.4422	−	3.48019i	0.800772	−	0.129970i
$718$	11.0150	−	19.0785i	0.411076	−	0.712004i
$719$	−2.95842	+	5.12414i	−0.110331	+	0.191098i	−0.915904	−	0.401398i	$-0.868524\pi$
$719$	−2.95842	+	5.12414i	−0.110331	+	0.191098i	0.805573	+	0.592497i	$0.201858\pi$
$720$	−4.49541	+	1.49874i	−0.167534	+	0.0558549i
$721$	56.4909			2.10383
$722$	−6.26957	−	17.9358i	−0.233329	−	0.667501i
$723$	6.92344	−	1.12371i	0.257485	−	0.0417914i
$724$	2.33180	+	4.03880i	0.0866608	+	0.150101i
$725$	6.66899	+	11.5510i	0.247680	+	0.428994i
$726$	4.30291	−	0.698387i	0.159696	−	0.0259196i
$727$	40.0576			1.48566			0.742828	−	0.669483i	$-0.233484\pi$
$727$	40.0576			1.48566			0.742828	+	0.669483i	$0.233484\pi$
$728$	12.9061	+	22.3540i	0.478332	+	0.828495i
$729$	15.3650	−	22.2017i	0.569074	−	0.822286i
$730$	−23.5387			−0.871208
$731$	31.0385	−	53.7602i	1.14800	−	1.98839i
$732$	−5.44702	+	0.884083i	−0.201328	+	0.0326767i
$733$	17.5793	−	30.4482i	0.649306	−	1.12463i	−0.333983	−	0.942579i	$-0.608393\pi$
$733$	17.5793	−	30.4482i	0.649306	−	1.12463i	0.983289	−	0.182052i	$-0.0582738\pi$
$734$	6.18264	−	10.7087i	0.228205	−	0.395264i
$735$	−24.9932	−	30.6239i	−0.921888	−	1.12958i
$736$	2.10449			0.0775723
$737$	−23.1331	−	40.0678i	−0.852120	−	1.47592i
$738$	12.7865	−	4.26294i	0.470677	−	0.156921i
$739$	6.34630	−	10.9921i	0.233453	−	0.404352i	−0.725369	−	0.688360i	$-0.758331\pi$
$739$	6.34630	−	10.9921i	0.233453	−	0.404352i	0.958822	+	0.284008i	$0.0916643\pi$
$740$	0.922673	+	1.59812i	0.0339181	+	0.0587479i
$741$	−2.82741	−	41.9841i	−0.103867	−	1.54232i
$742$	7.86255	−	13.6183i	0.288643	−	0.499945i
$743$	2.89496	+	5.01421i	0.106206	+	0.183954i	0.914230	−	0.405195i	$-0.132796\pi$
$743$	2.89496	+	5.01421i	0.106206	+	0.183954i	−0.808025	+	0.589149i	$0.799463\pi$
$744$	−2.00858	+	0.326004i	−0.0736381	+	0.0119519i
$745$	−7.59967	+	13.1630i	−0.278430	+	0.482256i
$746$	−3.36121	+	5.82178i	−0.123062	+	0.213150i
$747$	33.3426	−	11.1162i	1.21994	−	0.406722i
$748$	−26.8670			−0.982356
$749$	−15.9760	−	27.6712i	−0.583749	−	1.01108i
$750$	−12.9826	−	15.9074i	−0.474056	−	0.580856i
$751$	−3.27598			−0.119542			−0.0597712	−	0.998212i	$-0.519037\pi$
$751$	−3.27598			−0.119542			−0.0597712	+	0.998212i	$0.519037\pi$
$752$	2.87781	−	4.98452i	0.104943	−	0.181767i
$753$	11.7942	−	31.0796i	0.429805	−	1.13260i
$754$	−14.8382	+	25.7005i	−0.540375	+	0.935956i
$755$	18.0142	−	31.2015i	0.655604	−	1.13554i
$756$	−20.3312	−	12.8741i	−0.739438	−	0.468228i
$757$	−25.2937	+	43.8099i	−0.919314	+	1.59230i	−0.118854	+	0.992912i	$0.537922\pi$
$757$	−25.2937	+	43.8099i	−0.919314	+	1.59230i	−0.800460	+	0.599386i	$0.795411\pi$
$758$	−26.1451			−0.949631
$759$	−4.75469	+	12.5294i	−0.172584	+	0.454787i
$760$	0.643914	−	6.85494i	0.0233572	−	0.248655i
$761$	−17.8934	+	30.9923i	−0.648636	+	1.12347i	0.334813	+	0.942285i	$0.391327\pi$
$761$	−17.8934	+	30.9923i	−0.648636	+	1.12347i	−0.983449	+	0.181186i	$0.942006\pi$
$762$	−4.86402	+	12.8174i	−0.176205	+	0.464327i
$763$	−18.7497			−0.678785
$764$	2.83934	+	4.91788i	0.102724	+	0.177923i
$765$	−6.94055	+	33.9262i	−0.250936	+	1.22661i
$766$	6.86972	+	11.8987i	0.248213	+	0.429917i
$767$	−5.53123	−	9.58037i	−0.199721	−	0.345927i
$768$	1.09515	+	1.34188i	0.0395179	+	0.0484209i
$769$	−37.3638			−1.34737			−0.673687	−	0.739016i	$-0.735291\pi$
$769$	−37.3638			−1.34737			−0.673687	+	0.739016i	$0.735291\pi$
$770$	−26.8947			−0.969217
$771$	−1.71850	−	2.10566i	−0.0618903	−	0.0758335i
$772$	−4.93611	−	8.54959i	−0.177654	−	0.307706i
$773$	−9.33015	−	16.1603i	−0.335582	−	0.581245i	0.648014	−	0.761628i	$-0.275600\pi$
$773$	−9.33015	−	16.1603i	−0.335582	−	0.581245i	−0.983596	+	0.180383i	$0.942266\pi$
$774$	5.10768	−	24.9670i	0.183592	−	0.897419i
$775$	−1.47148	−	2.54868i	−0.0528571	−	0.0915512i
$776$	11.9403			0.428634
$777$	−3.32489	+	8.76162i	−0.119280	+	0.314321i
$778$	15.2002	−	26.3276i	0.544955	−	0.943889i
$779$	−1.83151	+	19.4978i	−0.0656208	+	0.698581i
$780$	5.41008	−	14.2564i	0.193712	−	0.510462i
$781$	−29.6557			−1.06117
$782$	7.68951	−	13.3186i	0.274976	−	0.476273i
$783$	1.13100	−	27.6439i	0.0404188	−	0.987912i
$784$	−7.22408	+	12.5125i	−0.258003	+	0.446874i
$785$	−3.45407	+	5.98262i	−0.123281	+	0.213529i
$786$	0.856036	−	2.25579i	0.0305338	−	0.0804614i
$787$	15.7775	−	27.3274i	0.562406	−	0.974116i	−0.434880	−	0.900489i	$-0.643209\pi$
$787$	15.7775	−	27.3274i	0.562406	−	0.974116i	0.997286	−	0.0736276i	$-0.0234576\pi$
$788$	−25.0810			−0.893474
$789$	30.4724	+	37.3375i	1.08485	+	1.32925i
$790$	4.72790	+	8.18896i	0.168211	+	0.291350i
$791$	−6.21780			−0.221079
$792$	−10.4634	+	3.48843i	−0.371799	+	0.123956i
$793$	8.87861	−	15.3782i	0.315289	−	0.546096i
$794$	−9.16006	+	15.8657i	−0.325079	+	0.563053i
$795$	−9.16953	+	1.48827i	−0.325210	+	0.0527834i
$796$	4.46649	+	7.73619i	0.158311	+	0.274202i
$797$	−16.9685	+	29.3903i	−0.601055	+	1.04106i	0.391606	+	0.920133i	$0.371920\pi$
$797$	−16.9685	+	29.3903i	−0.601055	+	1.04106i	−0.992662	+	0.120926i	$0.961414\pi$
$798$	29.0374	−	19.4776i	1.02791	−	0.689499i
$799$	−21.0303	−	36.4255i	−0.743998	−	1.28864i
$800$	−1.25250	+	2.16940i	−0.0442827	+	0.0766999i
$801$	−17.1216	+	5.70825i	−0.604963	+	0.201691i
$802$	17.3023	+	29.9685i	0.610965	+	1.05822i
$803$	−54.7880			−1.93343
$804$	13.7817	+	16.8866i	0.486043	+	0.595543i
$805$	7.69742	−	13.3323i	0.271298	−	0.469903i
$806$	3.27397	−	5.67069i	0.115321	−	0.199741i
$807$	0.189589	−	0.0307714i	0.00667384	−	0.00108320i
$808$	5.44662	−	9.43383i	0.191611	−	0.331881i
$809$	41.0728			1.44404			0.722021	−	0.691871i	$-0.243213\pi$
$809$	41.0728			1.44404			0.722021	+	0.691871i	$0.243213\pi$
$810$	1.70200	+	14.1137i	0.0598022	+	0.495906i
$811$	−21.7934	−	37.7472i	−0.765269	−	1.32549i	−0.940104	−	0.340887i	$-0.889273\pi$
$811$	−21.7934	−	37.7472i	−0.765269	−	1.32549i	0.174835	−	0.984598i	$-0.444061\pi$
$812$	−24.6590			−0.865361
$813$	−16.4033	+	2.66235i	−0.575288	+	0.0933725i
$814$	2.14758	+	3.71972i	0.0752728	+	0.130376i
$815$	5.03050	+	8.71309i	0.176211	+	0.305206i
$816$	12.4939	−	2.02783i	0.437373	−	0.0709882i
$817$	30.1947	+	21.4316i	1.05638	+	0.749795i
$818$	5.01138			0.175219
$819$	73.4615	−	24.4916i	2.56695	−	0.855807i
$820$	−3.54830	+	6.14584i	−0.123912	+	0.214622i
$821$	11.1308	−	19.2791i	0.388467	−	0.672845i	−0.603776	−	0.797154i	$-0.706338\pi$
$821$	11.1308	−	19.2791i	0.388467	−	0.672845i	0.992244	+	0.124309i	$0.0396713\pi$
$822$	4.11834	−	0.668431i	0.143644	−	0.0233142i
$823$	−1.41545			−0.0493395			−0.0246697	−	0.999696i	$-0.507853\pi$
$823$	−1.41545			−0.0493395			−0.0246697	+	0.999696i	$0.507853\pi$
$824$	−6.09893	+	10.5637i	−0.212466	+	0.368002i
$825$	−10.0860	−	12.3583i	−0.351151	−	0.430262i
$826$	4.59607	−	7.96062i	0.159918	−	0.276985i
$827$	−27.8318	−	48.2061i	−0.967807	−	1.67629i	−0.701876	−	0.712300i	$-0.747654\pi$
$827$	−27.8318	−	48.2061i	−0.967807	−	1.67629i	−0.265932	−	0.963992i	$-0.585680\pi$
$828$	1.26538	−	6.18535i	0.0439751	−	0.214956i
$829$	−35.2830			−1.22543			−0.612714	−	0.790305i	$-0.709922\pi$
$829$	−35.2830			−1.22543			−0.612714	+	0.790305i	$0.709922\pi$
$830$	−9.25272	+	16.0262i	−0.321167	+	0.556277i
$831$	9.38817	−	24.7393i	0.325672	−	0.858197i
$832$	−5.57353			−0.193227
$833$	52.7917	+	91.4378i	1.82912	+	3.16813i
$834$	9.27614	+	11.3660i	0.321206	+	0.393571i
$835$	−4.87403	−	8.44206i	−0.168673	−	0.292150i
$836$	1.49875	−	15.9553i	0.0518355	−	0.551827i
$837$	−0.249551	+	6.09949i	−0.00862573	+	0.210829i
$838$	14.5553	−	25.2106i	0.502805	−	0.870885i
$839$	30.8920			1.06651			0.533255	−	0.845955i	$-0.320969\pi$
$839$	30.8920			1.06651			0.533255	+	0.845955i	$0.320969\pi$
$840$	12.5067	−	2.02992i	0.431523	−	0.0700387i
$841$	0.324738	+	0.562463i	0.0111979	+	0.0193953i
$842$	3.43970			0.118540
$843$	−7.61314	+	1.23566i	−0.262210	+	0.0425583i
$844$	−3.16229	−	5.47724i	−0.108850	−	0.188534i
$845$	14.2667	+	24.7106i	0.490789	+	0.850072i
$846$	−12.9198	−	11.4553i	−0.444190	−	0.393843i
$847$	−11.6558			−0.400498
$848$	1.69773	+	2.94055i	0.0583003	+	0.100979i
$849$	3.55306	−	9.36287i	0.121941	−	0.321333i
$850$	9.15297	+	15.8534i	0.313944	+	0.543768i
$851$	−2.45861			−0.0842800
$852$	13.7907	−	2.23831i	0.472461	−	0.0766832i
$853$	−34.9926			−1.19812			−0.599062	−	0.800702i	$-0.704460\pi$
$853$	−34.9926			−1.19812			−0.599062	+	0.800702i	$0.704460\pi$
$854$	14.7550			0.504906
$855$	−19.7604	−	6.01428i	−0.675790	−	0.205684i
$856$	6.89925			0.235812
$857$	12.5598			0.429036			0.214518	−	0.976720i	$-0.431182\pi$
$857$	12.5598			0.429036			0.214518	+	0.976720i	$0.431182\pi$
$858$	12.5923	−	33.1828i	0.429895	−	1.13284i
$859$	10.8363			0.369728			0.184864	−	0.982764i	$-0.440815\pi$
$859$	10.8363			0.369728			0.184864	+	0.982764i	$0.440815\pi$
$860$	6.70891	+	11.6202i	0.228772	+	0.396244i
$861$	−35.5734	+	5.77377i	−1.21234	+	0.196770i
$862$	4.96062	+	8.59205i	0.168959	+	0.292646i
$863$	53.4590			1.81977			0.909883	−	0.414866i	$-0.136171\pi$
$863$	53.4590			1.81977			0.909883	+	0.414866i	$0.136171\pi$
$864$	4.60245	−	2.41195i	0.156578	−	0.0820561i
$865$	−5.93390	−	10.2778i	−0.201759	−	0.349456i
$866$	−0.263521	−	0.456432i	−0.00895482	−	0.0155102i
$867$	22.3705	−	58.9499i	0.759744	−	2.00204i
$868$	5.44089			0.184676
$869$	11.0045	+	19.0604i	0.373302	+	0.646578i
$870$	9.21064	+	11.2857i	0.312270	+	0.382621i
$871$	−70.1387			−2.37656
$872$	2.02428	−	3.50615i	0.0685506	−	0.118733i
$873$	7.17949	−	35.0942i	0.242989	−	1.18776i
$874$	7.48049	+	5.30948i	0.253031	+	0.179596i
$875$	27.4505	+	47.5457i	0.927997	+	1.60734i
$876$	25.4779	−	4.13521i	0.860817	−	0.139716i
$877$	−1.09297	−	1.89307i	−0.0369068	−	0.0639245i	0.846982	−	0.531622i	$-0.178417\pi$
$877$	−1.09297	−	1.89307i	−0.0369068	−	0.0639245i	−0.883889	+	0.467697i	$0.845084\pi$
$878$	16.3504			0.551798
$879$	−32.5101	+	5.27658i	−1.09654	+	0.177975i
$880$	2.90363	−	5.02923i	0.0978813	−	0.169535i
$881$	29.8678			1.00627			0.503135	−	0.864208i	$-0.332180\pi$
$881$	29.8678			1.00627			0.503135	+	0.864208i	$0.332180\pi$
$882$	32.4320	+	28.7560i	1.09204	+	0.968264i
$883$	3.18840	+	5.52247i	0.107298	+	0.185846i	0.914675	−	0.404191i	$-0.132447\pi$
$883$	3.18840	+	5.52247i	0.107298	+	0.185846i	−0.807377	+	0.590036i	$0.799113\pi$
$884$	−20.3649	+	35.2731i	−0.684947	+	1.18636i
$885$	−5.36007	+	0.869970i	−0.180177	+	0.0292437i
$886$	2.89318	−	5.01113i	0.0971982	−	0.168352i
$887$	−25.0159			−0.839951			−0.419976	−	0.907535i	$-0.637961\pi$
$887$	−25.0159			−0.839951			−0.419976	+	0.907535i	$0.637961\pi$
$888$	−1.27943	−	1.56768i	−0.0429350	−	0.0526078i
$889$	18.3282	−	31.7454i	0.614709	−	1.06471i
$890$	4.75133	−	8.22954i	0.159265	−	0.275855i
$891$	3.96152	+	32.8507i	0.132716	+	1.10054i
$892$	1.75762			0.0588496
$893$	22.8049	−	10.4571i	0.763138	−	0.349935i
$894$	5.91330	−	15.5825i	0.197770	−	0.521156i
$895$	17.1747	+	29.7475i	0.574088	+	0.994350i
$896$	−2.31561	−	4.01075i	−0.0773590	−	0.133990i
$897$	12.8455	+	15.7394i	0.428899	+	0.525525i
$898$	10.4180			0.347654
$899$	3.12770	+	5.41734i	0.104315	+	0.180678i
$900$	5.62304	+	4.98569i	0.187435	+	0.166190i
$901$	24.8131			0.826644
$902$	−8.25892	+	14.3049i	−0.274992	+	0.476300i
$903$	−24.1759	+	63.7072i	−0.804522	+	2.12004i
$904$	0.671292	−	1.16271i	0.0223268	−	0.0386712i
$905$	−3.68321	+	6.37951i	−0.122434	+	0.212062i
$906$	−14.0168	+	36.9366i	−0.465678	+	1.22714i
$907$	−12.1314			−0.402818			−0.201409	−	0.979507i	$-0.564552\pi$
$907$	−12.1314			−0.402818			−0.201409	+	0.979507i	$0.564552\pi$
$908$	−6.41556	−	11.1121i	−0.212908	−	0.368767i
$909$	−24.4523	−	21.6807i	−0.811030	−	0.719103i
$910$	−20.3859	+	35.3094i	−0.675785	+	1.17049i
$911$	−5.82232	−	10.0846i	−0.192902	−	0.334116i	0.753309	−	0.657667i	$-0.228457\pi$
$911$	−5.82232	−	10.0846i	−0.192902	−	0.334116i	−0.946211	+	0.323551i	$0.895123\pi$
$912$	0.507293	+	7.53277i	0.0167981	+	0.249435i
$913$	−21.5363	+	37.3020i	−0.712749	+	1.23452i
$914$	10.3149	+	17.8659i	0.341186	+	0.590952i
$915$	−5.51130	−	6.75294i	−0.182198	−	0.223245i
$916$	−0.207385	+	0.359201i	−0.00685220	+	0.0118683i
$917$	−3.22565	+	5.58699i	−0.106520	+	0.184499i
$918$	1.55227	−	37.9404i	0.0512325	−	1.25222i
$919$	−49.1168			−1.62021			−0.810107	−	0.586282i	$-0.800591\pi$
$919$	−49.1168			−1.62021			−0.810107	+	0.586282i	$0.800591\pi$
$920$	1.66207	+	2.87880i	0.0547969	+	0.0949111i
$921$	−41.9567	+	6.80982i	−1.38252	+	0.224391i
$922$	15.3064			0.504089
$923$	−22.4787	+	38.9343i	−0.739896	+	1.28154i
$924$	29.1103	−	4.72477i	0.957657	−	0.155433i
$925$	1.46326	−	2.53445i	0.0481118	−	0.0833321i
$926$	−4.73547	+	8.20208i	−0.155617	+	0.269537i
$927$	27.3807	+	24.2772i	0.899302	+	0.797369i
$928$	2.66226	−	4.61117i	0.0873930	−	0.151369i
$929$	38.6025			1.26651			0.633253	−	0.773945i	$-0.281719\pi$
$929$	38.6025			1.26651			0.633253	+	0.773945i	$0.281719\pi$
$930$	−2.03228	−	2.49013i	−0.0666412	−	0.0816547i
$931$	−57.2465	+	26.2502i	−1.87618	+	0.860317i
$932$	−6.42184	+	11.1229i	−0.210354	+	0.364344i
$933$	5.93591	−	0.963432i	0.194333	−	0.0315414i
$934$	15.0904			0.493772
$935$	−21.2190	−	36.7523i	−0.693934	−	1.20193i
$936$	−3.35125	+	16.3813i	−0.109539	+	0.535439i
$937$	14.3272	+	24.8154i	0.468049	+	0.810685i	0.999333	−	0.0365089i	$-0.0116237\pi$
$937$	14.3272	+	24.8154i	0.468049	+	0.810685i	−0.531284	+	0.847194i	$0.678290\pi$
$938$	−29.1402	−	50.4723i	−0.951462	−	1.64798i
$939$	−7.04532	+	1.14350i	−0.229915	+	0.0373166i
$940$	9.09132			0.296526
$941$	60.2102			1.96280			0.981398	−	0.191986i	$-0.0614927\pi$
$941$	60.2102			1.96280			0.981398	+	0.191986i	$0.0614927\pi$
$942$	2.68761	−	7.08227i	0.0875671	−	0.230753i
$943$	−4.72751	−	8.18828i	−0.153949	−	0.266647i
$944$	0.992410	+	1.71891i	0.0323002	+	0.0559456i
$945$	1.55386	−	37.9794i	0.0505472	−	1.23547i
$946$	15.6154	+	27.0467i	0.507702	+	0.879365i
$947$	−22.6629			−0.736446			−0.368223	−	0.929738i	$-0.620034\pi$
$947$	−22.6629			−0.736446			−0.368223	+	0.929738i	$0.620034\pi$
$948$	−6.55599	−	8.03299i	−0.212929	−	0.260899i
$949$	−41.5287	+	71.9299i	−1.34808	+	2.33494i
$950$	−9.92535	+	4.55124i	−0.322021	+	0.147662i
$951$	36.9957	−	6.00462i	1.19967	−	0.194713i
$952$	−33.8437			−1.09688
$953$	0.368894	−	0.638943i	0.0119496	−	0.0206974i	−0.859989	−	0.510313i	$-0.829530\pi$
$953$	0.368894	−	0.638943i	0.0119496	−	0.0206974i	0.871938	+	0.489616i	$0.162863\pi$
$954$	9.66347	−	3.22175i	0.312866	−	0.104308i
$955$	−4.48489	+	7.76806i	−0.145128	+	0.251368i
$956$	6.27082	−	10.8614i	0.202813	−	0.351282i
$957$	21.4384	+	26.2682i	0.693005	+	0.849131i
$958$	13.8928	−	24.0631i	0.448857	−	0.777443i
$959$	−11.1559			−0.360242
$960$	−0.970675	+	2.55788i	−0.0313284	+	0.0825553i
$961$	14.8099	+	25.6515i	0.477738	+	0.827467i
$962$	6.51139			0.209935
$963$	4.14838	−	20.2778i	0.133680	−	0.653442i
$964$	2.02478	−	3.50702i	0.0652137	−	0.112953i
$965$	7.79685	−	13.5045i	0.250989	−	0.434726i
$966$	−5.98936	+	15.7829i	−0.192704	+	0.507807i
$967$	−21.5492	−	37.3243i	−0.692975	−	1.20027i	−0.970859	−	0.239653i	$-0.922966\pi$
$967$	−21.5492	−	37.3243i	−0.692975	−	1.20027i	0.277884	−	0.960615i	$-0.410367\pi$
$968$	1.25840	−	2.17961i	0.0404464	−	0.0700552i
$969$	49.5261	+	24.3133i	1.59101	+	0.781054i
$970$	9.43021	+	16.3336i	0.302786	+	0.524441i
$971$	−15.9702	+	27.6611i	−0.512507	+	0.887687i	0.487388	+	0.873185i	$0.337950\pi$
$971$	−15.9702	+	27.6611i	−0.512507	+	0.887687i	−0.999895	+	0.0145021i	$0.995384\pi$
$972$	−4.32166	−	14.9774i	−0.138617	−	0.480401i
$973$	−19.6136	−	33.9718i	−0.628783	−	1.08908i
$974$	−26.0008			−0.833120
$975$	−23.8701	+	3.87425i	−0.764454	+	0.124075i
$976$	−1.59300	+	2.75915i	−0.0509906	+	0.0883183i
$977$	−2.30771	+	3.99708i	−0.0738303	+	0.127878i	−0.900577	−	0.434697i	$-0.856856\pi$
$977$	−2.30771	+	3.99708i	−0.0738303	+	0.127878i	0.826747	+	0.562574i	$0.190189\pi$
$978$	−6.97561	−	8.54713i	−0.223055	−	0.273307i
$979$	11.0590	−	19.1548i	0.353448	−	0.612190i
$980$	−22.8216			−0.729011
$981$	−9.08786	−	8.05778i	−0.290153	−	0.257265i
$982$	−16.4765	−	28.5381i	−0.525785	−	0.910686i
$983$	25.4542			0.811863			0.405932	−	0.913903i	$-0.366947\pi$
$983$	25.4542			0.811863			0.405932	+	0.913903i	$0.366947\pi$
$984$	2.76093	−	7.27549i	0.0880153	−	0.231934i
$985$	−19.8084	−	34.3092i	−0.631148	−	1.09318i
$986$	−19.4551	−	33.6972i	−0.619576	−	1.07314i
$987$	29.1919	+	35.7685i	0.929188	+	1.13852i
$988$	−19.8113	−	14.0617i	−0.630283	−	0.447361i
$989$	−17.8769			−0.568454
$990$	−13.0357	−	11.5581i	−0.414301	−	0.367341i
$991$	2.51258	−	4.35191i	0.0798147	−	0.138243i	−0.823355	−	0.567526i	$-0.807900\pi$
$991$	2.51258	−	4.35191i	0.0798147	−	0.138243i	0.903170	+	0.429283i	$0.141234\pi$
$992$	−0.587415	+	1.01743i	−0.0186504	+	0.0323035i
$993$	10.4228	−	27.4658i	0.330758	−	0.871601i
$994$	−37.3565			−1.18488
$995$	−7.05506	+	12.2197i	−0.223661	+	0.387392i
$996$	7.19954	−	18.9719i	0.228126	−	0.601148i
$997$	25.6735	−	44.4677i	0.813086	−	1.40831i	−0.0976075	−	0.995225i	$-0.531119\pi$
$997$	25.6735	−	44.4677i	0.813086	−	1.40831i	0.910694	−	0.413082i	$-0.135548\pi$
$998$	2.04254	+	3.53779i	0.0646556	+	0.111987i
$999$	−5.37690	+	2.81781i	−0.170118	+	0.0891515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.f.g.49.7	yes	18
3.2	odd	2		1026.2.f.g.847.3		18
9.2	odd	6		1026.2.h.g.505.7		18
9.7	even	3		342.2.h.g.277.1	yes	18
19.7	even	3		342.2.h.g.121.1	yes	18
57.26	odd	6		1026.2.h.g.577.7		18
171.7	even	3	inner	342.2.f.g.7.7	✓	18
171.83	odd	6		1026.2.f.g.235.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.f.g.7.7	✓	18	171.7	even	3	inner
342.2.f.g.49.7	yes	18	1.1	even	1	trivial
342.2.h.g.121.1	yes	18	19.7	even	3
342.2.h.g.277.1	yes	18	9.7	even	3
1026.2.f.g.235.3		18	171.83	odd	6
1026.2.f.g.847.3		18	3.2	odd	2
1026.2.h.g.505.7		18	9.2	odd	6
1026.2.h.g.577.7		18	57.26	odd	6

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.09515 + 1.34188i) q^{3} +1.00000 q^{4} +(0.789777 + 1.36793i) q^{5} +(-1.09515 - 1.34188i) q^{6} +(2.31561 + 4.01075i) q^{7} -1.00000 q^{8} +(-0.601280 + 2.93913i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(1.09515 + 1.34188i) q^{3} +1.00000 q^{4} +(0.789777 + 1.36793i) q^{5} +(-1.09515 - 1.34188i) q^{6} +(2.31561 + 4.01075i) q^{7} -1.00000 q^{8} +(-0.601280 + 2.93913i) q^{9} +(-0.789777 - 1.36793i) q^{10} +(-1.83826 - 3.18396i) q^{11} +(1.09515 + 1.34188i) q^{12} -5.57353 q^{13} +(-2.31561 - 4.01075i) q^{14} +(-0.970675 + 2.55788i) q^{15} +1.00000 q^{16} +(3.65387 - 6.32868i) q^{17} +(0.601280 - 2.93913i) q^{18} +(3.55454 + 2.52294i) q^{19} +(0.789777 + 1.36793i) q^{20} +(-2.84600 + 7.49965i) q^{21} +(1.83826 + 3.18396i) q^{22} -2.10449 q^{23} +(-1.09515 - 1.34188i) q^{24} +(1.25250 - 2.16940i) q^{25} +5.57353 q^{26} +(-4.60245 + 2.41195i) q^{27} +(2.31561 + 4.01075i) q^{28} +(-2.66226 + 4.61117i) q^{29} +(0.970675 - 2.55788i) q^{30} +(0.587415 - 1.01743i) q^{31} -1.00000 q^{32} +(2.25931 - 5.95364i) q^{33} +(-3.65387 + 6.32868i) q^{34} +(-3.65763 + 6.33520i) q^{35} +(-0.601280 + 2.93913i) q^{36} +1.16827 q^{37} +(-3.55454 - 2.52294i) q^{38} +(-6.10386 - 7.47900i) q^{39} +(-0.789777 - 1.36793i) q^{40} +(2.24640 + 3.89087i) q^{41} +(2.84600 - 7.49965i) q^{42} +8.49469 q^{43} +(-1.83826 - 3.18396i) q^{44} +(-4.49541 + 1.49874i) q^{45} +2.10449 q^{46} +(2.87781 - 4.98452i) q^{47} +(1.09515 + 1.34188i) q^{48} +(-7.22408 + 12.5125i) q^{49} +(-1.25250 + 2.16940i) q^{50} +(12.4939 - 2.02783i) q^{51} -5.57353 q^{52} +(1.69773 + 2.94055i) q^{53} +(4.60245 - 2.41195i) q^{54} +(2.90363 - 5.02923i) q^{55} +(-2.31561 - 4.01075i) q^{56} +(0.507293 + 7.53277i) q^{57} +(2.66226 - 4.61117i) q^{58} +(0.992410 + 1.71891i) q^{59} +(-0.970675 + 2.55788i) q^{60} +(-1.59300 + 2.75915i) q^{61} +(-0.587415 + 1.01743i) q^{62} +(-13.1804 + 4.39428i) q^{63} +1.00000 q^{64} +(-4.40184 - 7.62422i) q^{65} +(-2.25931 + 5.95364i) q^{66} +12.5843 q^{67} +(3.65387 - 6.32868i) q^{68} +(-2.30473 - 2.82396i) q^{69} +(3.65763 - 6.33520i) q^{70} +(4.03312 - 6.98558i) q^{71} +(0.601280 - 2.93913i) q^{72} +(7.45107 - 12.9056i) q^{73} -1.16827 q^{74} +(4.28276 - 0.695117i) q^{75} +(3.55454 + 2.52294i) q^{76} +(8.51338 - 14.7456i) q^{77} +(6.10386 + 7.47900i) q^{78} -5.98637 q^{79} +(0.789777 + 1.36793i) q^{80} +(-8.27693 - 3.53447i) q^{81} +(-2.24640 - 3.89087i) q^{82} +(-5.85781 - 10.1460i) q^{83} +(-2.84600 + 7.49965i) q^{84} +11.5430 q^{85} -8.49469 q^{86} +(-9.10322 + 1.47751i) q^{87} +(1.83826 + 3.18396i) q^{88} +(3.00802 + 5.21004i) q^{89} +(4.49541 - 1.49874i) q^{90} +(-12.9061 - 22.3540i) q^{91} -2.10449 q^{92} +(2.00858 - 0.326004i) q^{93} +(-2.87781 + 4.98452i) q^{94} +(-0.643914 + 6.85494i) q^{95} +(-1.09515 - 1.34188i) q^{96} -11.9403 q^{97} +(7.22408 - 12.5125i) q^{98} +(10.4634 - 3.48843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 18 q^{2} + 18 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9}+O(q^{10}) \) 18 * q - 18 * q^2 + 18 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9	\( 18 q - 18 q^{2} + 18 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9} + q^{11} - 2 q^{13} - 5 q^{14} + 18 q^{16} - 5 q^{17} - 4 q^{18} + 9 q^{19} - 4 q^{21} - q^{22} + 4 q^{23} - 9 q^{25} + 2 q^{26} - 18 q^{27} + 5 q^{28} - 9 q^{29} + 4 q^{31} - 18 q^{32} + 16 q^{33} + 5 q^{34} + 6 q^{35} + 4 q^{36} + 20 q^{37} - 9 q^{38} + 4 q^{39} + q^{41} + 4 q^{42} - 14 q^{43} + q^{44} + 30 q^{45} - 4 q^{46} + 19 q^{47} + 6 q^{49} + 9 q^{50} + 16 q^{51} - 2 q^{52} - 10 q^{53} + 18 q^{54} + 6 q^{55} - 5 q^{56} - 36 q^{57} + 9 q^{58} - 5 q^{59} + 18 q^{61} - 4 q^{62} - 15 q^{63} + 18 q^{64} - 45 q^{65} - 16 q^{66} - 44 q^{67} - 5 q^{68} - 26 q^{69} - 6 q^{70} + 11 q^{71} - 4 q^{72} + 44 q^{73} - 20 q^{74} + 9 q^{76} - 2 q^{77} - 4 q^{78} - 4 q^{79} - 32 q^{81} - q^{82} - 7 q^{83} - 4 q^{84} + 14 q^{86} + 3 q^{87} - q^{88} + q^{89} - 30 q^{90} - 25 q^{91} + 4 q^{92} + 10 q^{93} - 19 q^{94} - 24 q^{95} - 6 q^{98} + 8 q^{99}+O(q^{100}) \) 18 * q - 18 * q^2 + 18 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9 + q^11 - 2 * q^13 - 5 * q^14 + 18 * q^16 - 5 * q^17 - 4 * q^18 + 9 * q^19 - 4 * q^21 - q^22 + 4 * q^23 - 9 * q^25 + 2 * q^26 - 18 * q^27 + 5 * q^28 - 9 * q^29 + 4 * q^31 - 18 * q^32 + 16 * q^33 + 5 * q^34 + 6 * q^35 + 4 * q^36 + 20 * q^37 - 9 * q^38 + 4 * q^39 + q^41 + 4 * q^42 - 14 * q^43 + q^44 + 30 * q^45 - 4 * q^46 + 19 * q^47 + 6 * q^49 + 9 * q^50 + 16 * q^51 - 2 * q^52 - 10 * q^53 + 18 * q^54 + 6 * q^55 - 5 * q^56 - 36 * q^57 + 9 * q^58 - 5 * q^59 + 18 * q^61 - 4 * q^62 - 15 * q^63 + 18 * q^64 - 45 * q^65 - 16 * q^66 - 44 * q^67 - 5 * q^68 - 26 * q^69 - 6 * q^70 + 11 * q^71 - 4 * q^72 + 44 * q^73 - 20 * q^74 + 9 * q^76 - 2 * q^77 - 4 * q^78 - 4 * q^79 - 32 * q^81 - q^82 - 7 * q^83 - 4 * q^84 + 14 * q^86 + 3 * q^87 - q^88 + q^89 - 30 * q^90 - 25 * q^91 + 4 * q^92 + 10 * q^93 - 19 * q^94 - 24 * q^95 - 6 * q^98 + 8 * q^99

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