LMFDB - Embedded newform 605.2.g.n.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(81,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("605.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			251.2
Root			$1.43801 - 1.04478i$ of defining polynomial
Character	$\chi$	$=$	605.251
Dual form			605.2.g.n.511.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.579725 - 1.78421i) q^{2} +(1.43801 - 1.04478i) q^{3} +(-1.22929 - 0.893133i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-1.03045 - 3.17141i) q^{6} +(3.44479 + 2.50279i) q^{7} +(0.729292 - 0.529862i) q^{8} +(0.0492728 - 0.151646i) q^{9} +O(q^{10})$	\(q+(0.579725 - 1.78421i) q^{2} +(1.43801 - 1.04478i) q^{3} +(-1.22929 - 0.893133i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-1.03045 - 3.17141i) q^{6} +(3.44479 + 2.50279i) q^{7} +(0.729292 - 0.529862i) q^{8} +(0.0492728 - 0.151646i) q^{9} +1.87603 q^{10} -2.70087 q^{12} +(-0.420275 + 1.29347i) q^{13} +(6.46253 - 4.69530i) q^{14} +(1.43801 + 1.04478i) q^{15} +(-1.46169 - 4.49862i) q^{16} +(-0.648486 - 1.99584i) q^{17} +(-0.242004 - 0.175826i) q^{18} +(0.489036 - 0.355305i) q^{19} +(0.469548 - 1.44512i) q^{20} +7.56852 q^{21} -4.39768 q^{23} +(0.495144 - 1.52390i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(2.06418 + 1.49972i) q^{26} +(1.56024 + 4.80192i) q^{27} +(-1.99933 - 6.15331i) q^{28} +(-5.36507 - 3.89795i) q^{29} +(2.69776 - 1.96004i) q^{30} +(-0.678271 + 2.08750i) q^{31} -7.07096 q^{32} -3.93693 q^{34} +(-1.31579 + 4.04959i) q^{35} +(-0.196011 + 0.142410i) q^{36} +(-4.99124 - 3.62634i) q^{37} +(-0.350433 - 1.07852i) q^{38} +(0.747032 + 2.29913i) q^{39} +(0.729292 + 0.529862i) q^{40} +(5.99124 - 4.35289i) q^{41} +(4.38766 - 13.5038i) q^{42} -12.6671 q^{43} +0.159450 q^{45} +(-2.54945 + 7.84639i) q^{46} +(2.48729 - 1.80712i) q^{47} +(-6.80200 - 4.94194i) q^{48} +(3.43952 + 10.5858i) q^{49} +(0.579725 + 1.78421i) q^{50} +(-3.01774 - 2.19252i) q^{51} +(1.67188 - 1.21469i) q^{52} +(-2.05605 + 6.32787i) q^{53} +9.47214 q^{54} +3.83839 q^{56} +(0.332025 - 1.02187i) q^{57} +(-10.0650 + 7.31267i) q^{58} +(-9.73827 - 7.07527i) q^{59} +(-0.834614 - 2.56868i) q^{60} +(1.75800 + 5.41056i) q^{61} +(3.33133 + 2.42036i) q^{62} +(0.549273 - 0.399070i) q^{63} +(-1.17583 + 3.61884i) q^{64} -1.36004 q^{65} +9.86416 q^{67} +(-0.985367 + 3.03265i) q^{68} +(-6.32393 + 4.59460i) q^{69} +(6.46253 + 4.69530i) q^{70} +(-1.61887 - 4.98238i) q^{71} +(-0.0444172 - 0.136702i) q^{72} +(-0.584753 - 0.424848i) q^{73} +(-9.36371 + 6.80313i) q^{74} +(-0.549273 + 1.69049i) q^{75} -0.918503 q^{76} +4.53520 q^{78} +(-1.75230 + 5.39303i) q^{79} +(3.82676 - 2.78030i) q^{80} +(7.64758 + 5.55629i) q^{81} +(-4.29320 - 13.2131i) q^{82} +(0.294384 + 0.906022i) q^{83} +(-9.30392 - 6.75969i) q^{84} +(1.69776 - 1.23349i) q^{85} +(-7.34342 + 22.6007i) q^{86} -11.7875 q^{87} +1.24095 q^{89} +(0.0924373 - 0.284493i) q^{90} +(-4.68505 + 3.40389i) q^{91} +(5.40603 + 3.92771i) q^{92} +(1.20562 + 3.71050i) q^{93} +(-1.78234 - 5.48548i) q^{94} +(0.489036 + 0.355305i) q^{95} +(-10.1681 + 7.38759i) q^{96} +(3.56701 - 10.9781i) q^{97} +20.8812 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 5 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 + q^3 - 6 * q^4 - 2 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 5 * q^9	$ 8 q + 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 5 q^{9} - 6 q^{10} - 28 q^{12} - 4 q^{13} + 16 q^{14} + q^{15} - 20 q^{16} - q^{17} - 14 q^{18} + q^{19} - q^{20} + 12 q^{21} - 18 q^{23} - 25 q^{24} - 2 q^{25} - 14 q^{26} + 10 q^{27} - 4 q^{28} - 19 q^{29} + 12 q^{30} + 6 q^{31} - 12 q^{32} - 20 q^{34} + 8 q^{35} + 21 q^{36} + 4 q^{37} - 6 q^{38} - 9 q^{39} + 2 q^{40} + 4 q^{41} + 29 q^{42} - 42 q^{43} + 41 q^{46} + 4 q^{47} - 19 q^{48} - 15 q^{49} + 4 q^{50} - 13 q^{51} + 26 q^{52} + 3 q^{53} + 40 q^{54} + 30 q^{56} + 5 q^{57} - 6 q^{58} - 19 q^{59} + 22 q^{60} + 2 q^{61} + 38 q^{62} - q^{63} + 6 q^{64} - 14 q^{65} - 2 q^{67} - 35 q^{68} - 21 q^{69} + 16 q^{70} + 40 q^{71} + 34 q^{72} + 23 q^{73} - 48 q^{74} + q^{75} - 16 q^{76} + 12 q^{78} - 17 q^{79} + 15 q^{80} + 2 q^{82} + 25 q^{83} + 4 q^{84} + 4 q^{85} - 31 q^{86} - 30 q^{87} + 16 q^{90} - 12 q^{91} + 81 q^{92} - 13 q^{93} - 33 q^{94} + q^{95} - 23 q^{96} + 12 q^{97} + 84 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 + q^3 - 6 * q^4 - 2 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 5 * q^9 - 6 * q^10 - 28 * q^12 - 4 * q^13 + 16 * q^14 + q^15 - 20 * q^16 - q^17 - 14 * q^18 + q^19 - q^20 + 12 * q^21 - 18 * q^23 - 25 * q^24 - 2 * q^25 - 14 * q^26 + 10 * q^27 - 4 * q^28 - 19 * q^29 + 12 * q^30 + 6 * q^31 - 12 * q^32 - 20 * q^34 + 8 * q^35 + 21 * q^36 + 4 * q^37 - 6 * q^38 - 9 * q^39 + 2 * q^40 + 4 * q^41 + 29 * q^42 - 42 * q^43 + 41 * q^46 + 4 * q^47 - 19 * q^48 - 15 * q^49 + 4 * q^50 - 13 * q^51 + 26 * q^52 + 3 * q^53 + 40 * q^54 + 30 * q^56 + 5 * q^57 - 6 * q^58 - 19 * q^59 + 22 * q^60 + 2 * q^61 + 38 * q^62 - q^63 + 6 * q^64 - 14 * q^65 - 2 * q^67 - 35 * q^68 - 21 * q^69 + 16 * q^70 + 40 * q^71 + 34 * q^72 + 23 * q^73 - 48 * q^74 + q^75 - 16 * q^76 + 12 * q^78 - 17 * q^79 + 15 * q^80 + 2 * q^82 + 25 * q^83 + 4 * q^84 + 4 * q^85 - 31 * q^86 - 30 * q^87 + 16 * q^90 - 12 * q^91 + 81 * q^92 - 13 * q^93 - 33 * q^94 + q^95 - 23 * q^96 + 12 * q^97 + 84 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.579725	−	1.78421i	0.409928	−	1.26163i	−0.506782	−	0.862074i	$-0.669165\pi$
$2$	0.579725	−	1.78421i	0.409928	−	1.26163i	0.916710	−	0.399553i	$-0.130835\pi$
$3$	1.43801	−	1.04478i	0.830238	−	0.603203i	−0.0893884	−	0.995997i	$-0.528491\pi$
$3$	1.43801	−	1.04478i	0.830238	−	0.603203i	0.919627	+	0.392793i	$0.128491\pi$
$4$	−1.22929	−	0.893133i	−0.614646	−	0.446566i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$6$	−1.03045	−	3.17141i	−0.420680	−	1.29472i
$7$	3.44479	+	2.50279i	1.30201	+	0.945965i	0.999973	−	0.00733202i	$-0.00233387\pi$
$7$	3.44479	+	2.50279i	1.30201	+	0.945965i	0.302036	+	0.953297i	$0.402334\pi$
$8$	0.729292	−	0.529862i	0.257844	−	0.187334i
$9$	0.0492728	−	0.151646i	0.0164243	−	0.0505487i
$10$	1.87603			0.593253
$11$		0			0
$11$		0			0
$12$	−2.70087			−0.779673
$13$	−0.420275	+	1.29347i	−0.116563	+	0.358745i	−0.992270	−	0.124099i	$-0.960396\pi$
$13$	−0.420275	+	1.29347i	−0.116563	+	0.358745i	0.875707	+	0.482844i	$0.160396\pi$
$14$	6.46253	−	4.69530i	1.72718	−	1.25487i
$15$	1.43801	+	1.04478i	0.371294	+	0.269761i
$16$	−1.46169	−	4.49862i	−0.365423	−	1.12466i
$17$	−0.648486	−	1.99584i	−0.157281	−	0.484061i	0.841104	−	0.540874i	$-0.181906\pi$
$17$	−0.648486	−	1.99584i	−0.157281	−	0.484061i	−0.998385	+	0.0568124i	$0.981906\pi$
$18$	−0.242004	−	0.175826i	−0.0570409	−	0.0414426i
$19$	0.489036	−	0.355305i	0.112193	−	0.0815127i	−0.530274	−	0.847826i	$-0.677911\pi$
$19$	0.489036	−	0.355305i	0.112193	−	0.0815127i	0.642467	+	0.766313i	$0.277911\pi$
$20$	0.469548	−	1.44512i	0.104994	−	0.323138i
$21$	7.56852			1.65159
$22$		0			0
$23$	−4.39768			−0.916979			−0.458490	−	0.888700i	$-0.651609\pi$
$23$	−4.39768			−0.916979			−0.458490	+	0.888700i	$0.651609\pi$
$24$	0.495144	−	1.52390i	0.101071	−	0.311064i
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	2.06418	+	1.49972i	0.404820	+	0.294119i
$27$	1.56024	+	4.80192i	0.300268	+	0.924129i
$28$	−1.99933	−	6.15331i	−0.377838	−	1.16287i
$29$	−5.36507	−	3.89795i	−0.996268	−	0.723831i	−0.0349830	−	0.999388i	$-0.511138\pi$
$29$	−5.36507	−	3.89795i	−0.996268	−	0.723831i	−0.961285	+	0.275557i	$0.911138\pi$
$30$	2.69776	−	1.96004i	0.492541	−	0.357852i
$31$	−0.678271	+	2.08750i	−0.121821	+	0.374927i	−0.993309	−	0.115491i	$-0.963156\pi$
$31$	−0.678271	+	2.08750i	−0.121821	+	0.374927i	0.871487	+	0.490418i	$0.163156\pi$
$32$	−7.07096			−1.24998
$33$		0			0
$34$	−3.93693			−0.675179
$35$	−1.31579	+	4.04959i	−0.222410	+	0.684506i
$36$	−0.196011	+	0.142410i	−0.0326685	+	0.0237350i
$37$	−4.99124	−	3.62634i	−0.820554	−	0.596167i	0.0963171	−	0.995351i	$-0.469294\pi$
$37$	−4.99124	−	3.62634i	−0.820554	−	0.596167i	−0.916871	+	0.399183i	$0.869294\pi$
$38$	−0.350433	−	1.07852i	−0.0568478	−	0.174959i
$39$	0.747032	+	2.29913i	0.119621	+	0.368155i
$40$	0.729292	+	0.529862i	0.115311	+	0.0837785i
$41$	5.99124	−	4.35289i	0.935674	−	0.679807i	−0.0117016	−	0.999932i	$-0.503725\pi$
$41$	5.99124	−	4.35289i	0.935674	−	0.679807i	0.947375	+	0.320125i	$0.103725\pi$
$42$	4.38766	−	13.5038i	0.677031	−	2.08369i
$43$	−12.6671			−1.93171			−0.965855	−	0.259084i	$-0.916579\pi$
$43$	−12.6671			−1.93171			−0.965855	+	0.259084i	$0.916579\pi$
$44$		0			0
$45$	0.159450			0.0237694
$46$	−2.54945	+	7.84639i	−0.375895	+	1.15689i
$47$	2.48729	−	1.80712i	0.362808	−	0.263596i	−0.391414	−	0.920215i	$-0.628014\pi$
$47$	2.48729	−	1.80712i	0.362808	−	0.263596i	0.754222	+	0.656619i	$0.228014\pi$
$48$	−6.80200	−	4.94194i	−0.981784	−	0.713308i
$49$	3.43952	+	10.5858i	0.491360	+	1.51225i
$50$	0.579725	+	1.78421i	0.0819855	+	0.252325i
$51$	−3.01774	−	2.19252i	−0.422568	−	0.307014i
$52$	1.67188	−	1.21469i	0.231849	−	0.168448i
$53$	−2.05605	+	6.32787i	−0.282420	+	0.869200i	0.704740	+	0.709466i	$0.251064\pi$
$53$	−2.05605	+	6.32787i	−0.282420	+	0.869200i	−0.987160	+	0.159734i	$0.948936\pi$
$54$	9.47214			1.28899
$55$		0			0
$56$	3.83839			0.512926
$57$	0.332025	−	1.02187i	0.0439778	−	0.135350i
$58$	−10.0650	+	7.31267i	−1.32160	+	0.960200i
$59$	−9.73827	−	7.07527i	−1.26781	−	0.921121i	−0.268701	−	0.963224i	$-0.586594\pi$
$59$	−9.73827	−	7.07527i	−1.26781	−	0.921121i	−0.999113	+	0.0421025i	$0.986594\pi$
$60$	−0.834614	−	2.56868i	−0.107748	−	0.331615i
$61$	1.75800	+	5.41056i	0.225088	+	0.692751i	0.998283	+	0.0585814i	$0.0186577\pi$
$61$	1.75800	+	5.41056i	0.225088	+	0.692751i	−0.773194	+	0.634169i	$0.781342\pi$
$62$	3.33133	+	2.42036i	0.423080	+	0.307385i
$63$	0.549273	−	0.399070i	0.0692019	−	0.0502781i
$64$	−1.17583	+	3.61884i	−0.146979	+	0.452355i
$65$	−1.36004			−0.168692
$66$		0			0
$67$	9.86416			1.20510			0.602549	−	0.798082i	$-0.294152\pi$
$67$	9.86416			1.20510			0.602549	+	0.798082i	$0.294152\pi$
$68$	−0.985367	+	3.03265i	−0.119493	+	0.367763i
$69$	−6.32393	+	4.59460i	−0.761312	+	0.553125i
$70$	6.46253	+	4.69530i	0.772420	+	0.561196i
$71$	−1.61887	−	4.98238i	−0.192125	−	0.591300i	−0.999998	−	0.00194349i	$-0.999381\pi$
$71$	−1.61887	−	4.98238i	−0.192125	−	0.591300i	0.807873	−	0.589356i	$-0.200619\pi$
$72$	−0.0444172	−	0.136702i	−0.00523462	−	0.0161105i
$73$	−0.584753	−	0.424848i	−0.0684402	−	0.0497247i	0.553039	−	0.833155i	$-0.313468\pi$
$73$	−0.584753	−	0.424848i	−0.0684402	−	0.0497247i	−0.621479	+	0.783431i	$0.713468\pi$
$74$	−9.36371	+	6.80313i	−1.08851	+	0.790848i
$75$	−0.549273	+	1.69049i	−0.0634246	+	0.195201i
$76$	−0.918503			−0.105360
$77$		0			0
$78$	4.53520			0.513510
$79$	−1.75230	+	5.39303i	−0.197149	+	0.606763i	0.802796	+	0.596254i	$0.203345\pi$
$79$	−1.75230	+	5.39303i	−0.197149	+	0.606763i	−0.999945	+	0.0105085i	$0.996655\pi$
$80$	3.82676	−	2.78030i	0.427844	−	0.310847i
$81$	7.64758	+	5.55629i	0.849731	+	0.617366i
$82$	−4.29320	−	13.2131i	−0.474104	−	1.45914i
$83$	0.294384	+	0.906022i	0.0323129	+	0.0994488i	0.965912	−	0.258870i	$-0.0833501\pi$
$83$	0.294384	+	0.906022i	0.0323129	+	0.0994488i	−0.933599	+	0.358319i	$0.883350\pi$
$84$	−9.30392	−	6.75969i	−1.01514	−	0.737543i
$85$	1.69776	−	1.23349i	0.184148	−	0.133791i
$86$	−7.34342	+	22.6007i	−0.791861	+	2.43710i
$87$	−11.7875			−1.26376
$88$		0			0
$89$	1.24095			0.131540			0.0657701	−	0.997835i	$-0.479050\pi$
$89$	1.24095			0.131540			0.0657701	+	0.997835i	$0.479050\pi$
$90$	0.0924373	−	0.284493i	0.00974375	−	0.0299882i
$91$	−4.68505	+	3.40389i	−0.491126	+	0.356824i
$92$	5.40603	+	3.92771i	0.563618	+	0.409492i
$93$	1.20562	+	3.71050i	0.125017	+	0.384761i
$94$	−1.78234	−	5.48548i	−0.183834	−	0.565784i
$95$	0.489036	+	0.355305i	0.0501740	+	0.0364536i
$96$	−10.1681	+	7.38759i	−1.03778	+	0.753993i
$97$	3.56701	−	10.9781i	0.362175	−	1.11466i	−0.589556	−	0.807728i	$-0.700697\pi$
$97$	3.56701	−	10.9781i	0.362175	−	1.11466i	0.951731	−	0.306933i	$-0.0993028\pi$
$98$	20.8812			2.10932
$99$		0			0
$100$	1.51949			0.151949
$101$	−0.867333	+	2.66938i	−0.0863029	+	0.265613i	−0.984890	−	0.173183i	$-0.944595\pi$
$101$	−0.867333	+	2.66938i	−0.0863029	+	0.265613i	0.898587	+	0.438796i	$0.144595\pi$
$102$	−5.66137	+	4.11323i	−0.560559	+	0.407270i
$103$	0.328505	+	0.238673i	0.0323686	+	0.0235172i	0.603852	−	0.797097i	$-0.293632\pi$
$103$	0.328505	+	0.238673i	0.0323686	+	0.0235172i	−0.571483	+	0.820614i	$0.693632\pi$
$104$	0.378859	+	1.16601i	0.0371501	+	0.114336i
$105$	2.33880	+	7.19809i	0.228244	+	0.702462i
$106$	10.0983	+	7.33685i	0.980834	+	0.712618i
$107$	12.4577	−	9.05103i	1.20433	−	0.874996i	0.209625	−	0.977782i	$-0.432776\pi$
$107$	12.4577	−	9.05103i	1.20433	−	0.874996i	0.994704	+	0.102786i	$0.0327755\pi$
$108$	2.37076	−	7.29645i	0.228127	−	0.702102i
$109$	3.07312			0.294352			0.147176	−	0.989110i	$-0.452982\pi$
$109$	3.07312			0.294352			0.147176	+	0.989110i	$0.452982\pi$
$110$		0			0
$111$	−10.9662			−1.04087
$112$	6.22387	−	19.1551i	0.588101	−	1.80999i
$113$	9.11322	−	6.62114i	0.857299	−	0.622864i	−0.0698496	−	0.997558i	$-0.522252\pi$
$113$	9.11322	−	6.62114i	0.857299	−	0.622864i	0.927149	+	0.374693i	$0.122252\pi$
$114$	−1.63075	−	1.18481i	−0.152733	−	0.110967i
$115$	−1.35896	−	4.18244i	−0.126723	−	0.390015i
$116$	3.11385	+	9.58343i	0.289113	+	0.889799i
$117$	0.175442	+	0.127466i	0.0162196	+	0.0117843i
$118$	−18.2693	+	13.2734i	−1.68182	+	1.22192i
$119$	2.76125	−	8.49826i	0.253124	−	0.779034i
$120$	1.60232			0.146271
$121$		0			0
$122$	10.6727			0.966263
$123$	4.06768	−	12.5190i	0.366770	−	1.12880i
$124$	2.69821	−	1.96036i	0.242306	−	0.176046i
$125$	−0.809017	−	0.587785i	−0.0723607	−	0.0525731i
$126$	−0.393598	−	1.21137i	−0.0350645	−	0.107917i
$127$	−0.0349610	−	0.107599i	−0.00310229	−	0.00954786i	0.949493	−	0.313787i	$-0.101598\pi$
$127$	−0.0349610	−	0.107599i	−0.00310229	−	0.00954786i	−0.952596	+	0.304239i	$0.901598\pi$
$128$	−5.66595	−	4.11655i	−0.500804	−	0.363855i
$129$	−18.2154	+	13.2343i	−1.60378	+	1.16521i
$130$	−0.788448	+	2.42659i	−0.0691515	+	0.212826i
$131$	−0.474297			−0.0414395			−0.0207198	−	0.999785i	$-0.506596\pi$
$131$	−0.474297			−0.0414395			−0.0207198	+	0.999785i	$0.506596\pi$
$132$		0			0
$133$	2.57388			0.223184
$134$	5.71850	−	17.5997i	0.494003	−	1.52039i
$135$	−4.08475	+	2.96775i	−0.351560	+	0.255423i
$136$	−1.53045	−	1.11194i	−0.131235	−	0.0953480i
$137$	−0.268441	−	0.826176i	−0.0229344	−	0.0705850i	0.938934	−	0.344097i	$-0.111815\pi$
$137$	−0.268441	−	0.826176i	−0.0229344	−	0.0705850i	−0.961869	+	0.273512i	$0.911815\pi$
$138$	4.53160	+	13.9468i	0.385755	+	1.18723i
$139$	15.6863	+	11.3968i	1.33050	+	0.966663i	0.999737	+	0.0229488i	$0.00730546\pi$
$139$	15.6863	+	11.3968i	1.33050	+	0.966663i	0.330761	+	0.943714i	$0.392695\pi$
$140$	5.23432	−	3.80296i	0.442381	−	0.321408i
$141$	1.68872	−	5.19733i	0.142216	−	0.437694i
$142$	−9.82812			−0.824758
$143$		0			0
$144$	−0.754221			−0.0628517
$145$	2.04927	−	6.30701i	0.170183	−	0.523769i
$146$	−1.09701	+	0.797027i	−0.0907895	+	0.0659625i
$147$	16.0059	+	11.6289i	1.32014	+	0.959139i
$148$	2.89688	+	8.91567i	0.238122	+	0.732864i
$149$	0.343806	+	1.05813i	0.0281657	+	0.0866850i	0.964151	−	0.265353i	$-0.0854886\pi$
$149$	0.343806	+	1.05813i	0.0281657	+	0.0866850i	−0.935986	+	0.352038i	$0.885489\pi$
$150$	2.69776	+	1.96004i	0.220271	+	0.160036i
$151$	4.60707	−	3.34723i	0.374918	−	0.272394i	−0.384329	−	0.923196i	$-0.625567\pi$
$151$	4.60707	−	3.34723i	0.374918	−	0.272394i	0.759247	+	0.650802i	$0.225567\pi$
$152$	0.168387	−	0.518243i	0.0136580	−	0.0420350i
$153$	−0.334614			−0.0270519
$154$		0			0
$155$	−2.19493			−0.176301
$156$	1.13511	−	3.49350i	0.0908812	−	0.279704i
$157$	−0.842298	+	0.611965i	−0.0672227	+	0.0488401i	−0.620889	−	0.783898i	$-0.713228\pi$
$157$	−0.842298	+	0.611965i	−0.0672227	+	0.0488401i	0.553666	+	0.832739i	$0.313228\pi$
$158$	8.60644	+	6.25295i	0.684692	+	0.497458i
$159$	3.65459	+	11.2477i	0.289828	+	0.892000i
$160$	−2.18505	−	6.72488i	−0.172743	−	0.531649i
$161$	−15.1491	−	11.0065i	−1.19392	−	0.867430i
$162$	14.3471	−	10.4238i	1.12721	−	0.818969i
$163$	−3.98988	+	12.2796i	−0.312511	+	0.961811i	0.664256	+	0.747506i	$0.268749\pi$
$163$	−3.98988	+	12.2796i	−0.312511	+	0.961811i	−0.976767	+	0.214305i	$0.931251\pi$
$164$	−11.2527			−0.878687
$165$		0			0
$166$	1.78720			0.138713
$167$	−1.30591	+	4.01918i	−0.101054	+	0.311013i	−0.988784	−	0.149352i	$-0.952281\pi$
$167$	−1.30591	+	4.01918i	−0.101054	+	0.311013i	0.887730	+	0.460365i	$0.152281\pi$
$168$	5.51966	−	4.01027i	0.425851	−	0.309399i
$169$	9.02078	+	6.55398i	0.693906	+	0.504152i
$170$	−1.21658	−	3.74425i	−0.0933074	−	0.287171i
$171$	−0.0297845	−	0.0916674i	−0.00227768	−	0.00700998i
$172$	15.5715	+	11.3134i	1.18732	+	0.862637i
$173$	1.08870	−	0.790987i	0.0827724	−	0.0601376i	−0.545629	−	0.838027i	$-0.683709\pi$
$173$	1.08870	−	0.790987i	0.0827724	−	0.0601376i	0.628402	+	0.777889i	$0.283709\pi$
$174$	−6.83353	+	21.0315i	−0.518049	+	1.59439i
$175$	−4.25800			−0.321874
$176$		0			0
$177$	−21.3959			−1.60821
$178$	0.719408	−	2.21411i	0.0539219	−	0.165955i
$179$	−10.0551	+	7.30549i	−0.751557	+	0.546038i	−0.896309	−	0.443430i	$-0.853761\pi$
$179$	−10.0551	+	7.30549i	−0.751557	+	0.546038i	0.144752	+	0.989468i	$0.453761\pi$
$180$	−0.196011	−	0.142410i	−0.0146098	−	0.0106146i
$181$	5.34883	+	16.4620i	0.397576	+	1.22361i	0.926937	+	0.375216i	$0.122431\pi$
$181$	5.34883	+	16.4620i	0.397576	+	1.22361i	−0.529362	+	0.848396i	$0.677569\pi$
$182$	3.35721	+	10.3324i	0.248853	+	0.765891i
$183$	8.18086	+	5.94374i	0.604747	+	0.439374i
$184$	−3.20719	+	2.33016i	−0.236437	+	0.171782i
$185$	1.90648	−	5.86755i	0.140167	−	0.431391i
$186$	7.31925			0.536673
$187$		0			0
$188$	−4.67160			−0.340712
$189$	−6.64348	+	20.4465i	−0.483242	+	1.48727i
$190$	0.917446	−	0.666564i	0.0665585	−	0.0483576i
$191$	15.8974	+	11.5502i	1.15030	+	0.835741i	0.988521	−	0.151087i	$-0.0482772\pi$
$191$	15.8974	+	11.5502i	1.15030	+	0.835741i	0.161778	+	0.986827i	$0.448277\pi$
$192$	2.09002	+	6.43242i	0.150834	+	0.464220i
$193$	−3.14011	−	9.66427i	−0.226030	−	0.695649i	−0.998185	−	0.0602153i	$-0.980821\pi$
$193$	−3.14011	−	9.66427i	−0.226030	−	0.695649i	0.772155	−	0.635434i	$-0.219179\pi$
$194$	−17.5194	−	12.7286i	−1.25782	−	0.913860i
$195$	−1.95576	+	1.42094i	−0.140055	+	0.101756i
$196$	5.22631	−	16.0849i	0.373308	−	1.14892i
$197$	8.45375			0.602305			0.301152	−	0.953576i	$-0.402629\pi$
$197$	8.45375			0.602305			0.301152	+	0.953576i	$0.402629\pi$
$198$		0			0
$199$	−6.51033			−0.461505			−0.230753	−	0.973012i	$-0.574119\pi$
$199$	−6.51033			−0.461505			−0.230753	+	0.973012i	$0.574119\pi$
$200$	−0.278565	+	0.857334i	−0.0196975	+	0.0606227i
$201$	14.1848	−	10.3059i	1.00052	−	0.726920i
$202$	4.25992	+	3.09501i	0.299727	+	0.217764i
$203$	−8.72580	−	26.8552i	−0.612431	−	1.88487i
$204$	1.75147	+	5.39049i	0.122628	+	0.377409i
$205$	5.99124	+	4.35289i	0.418446	+	0.304019i
$206$	0.616286	−	0.447758i	0.0429387	−	0.0311968i
$207$	−0.216686	+	0.666891i	−0.0150607	+	0.0463522i
$208$	6.43316			0.446059
$209$		0			0
$210$	14.1988			0.979808
$211$	−1.24040	+	3.81757i	−0.0853930	+	0.262813i	−0.984631	−	0.174647i	$-0.944122\pi$
$211$	−1.24040	+	3.81757i	−0.0853930	+	0.262813i	0.899238	+	0.437459i	$0.144122\pi$
$212$	8.17911	−	5.94247i	0.561744	−	0.408131i
$213$	−7.53345	−	5.47337i	−0.516184	−	0.375029i
$214$	−8.92692	−	27.4742i	−0.610231	−	1.87810i
$215$	−3.91434	−	12.0471i	−0.266956	−	0.821605i
$216$	3.68222	+	2.67529i	0.250543	+	0.182030i
$217$	−7.56108	+	5.49344i	−0.513279	+	0.372919i
$218$	1.78157	−	5.48310i	0.120663	−	0.371362i
$219$	−1.28476			−0.0868158
$220$		0			0
$221$	2.85410			0.191988
$222$	−6.35738	+	19.5660i	−0.426680	+	1.31318i
$223$	−12.3836	+	8.99725i	−0.829270	+	0.602500i	−0.919353	−	0.393434i	$-0.871287\pi$
$223$	−12.3836	+	8.99725i	−0.829270	+	0.602500i	0.0900825	+	0.995934i	$0.471287\pi$
$224$	−24.3580	−	17.6971i	−1.62749	−	1.18244i
$225$	0.0492728	+	0.151646i	0.00328486	+	0.0101097i
$226$	−6.53035	−	20.0983i	−0.434392	−	1.33692i
$227$	9.30522	+	6.76064i	0.617609	+	0.448719i	0.852086	−	0.523403i	$-0.175338\pi$
$227$	9.30522	+	6.76064i	0.617609	+	0.448719i	−0.234477	+	0.972122i	$0.575338\pi$
$228$	−1.32082	+	0.959633i	−0.0874735	+	0.0635532i
$229$	−8.50636	+	26.1799i	−0.562116	+	1.73002i	0.114251	+	0.993452i	$0.463553\pi$
$229$	−8.50636	+	26.1799i	−0.562116	+	1.73002i	−0.676368	+	0.736564i	$0.736447\pi$
$230$	−8.25018			−0.544001
$231$		0			0
$232$	−5.97807			−0.392480
$233$	−2.84366	+	8.75188i	−0.186294	+	0.573355i	−0.999968	−	0.00796680i	$-0.997464\pi$
$233$	−2.84366	+	8.75188i	−0.186294	+	0.573355i	0.813674	+	0.581321i	$0.197464\pi$
$234$	0.329135	−	0.239130i	0.0215162	−	0.0156324i
$235$	2.48729	+	1.80712i	0.162253	+	0.117884i
$236$	5.65202	+	17.3951i	0.367915	+	1.13233i
$237$	3.11469	+	9.58602i	0.202321	+	0.622679i
$238$	−13.5619	−	9.85331i	−0.879089	−	0.638695i
$239$	10.2389	−	7.43899i	0.662299	−	0.481189i	−0.205139	−	0.978733i	$-0.565765\pi$
$239$	10.2389	−	7.43899i	0.662299	−	0.481189i	0.867439	+	0.497544i	$0.165765\pi$
$240$	2.59813	−	7.99623i	0.167709	−	0.516154i
$241$	−7.33167			−0.472275			−0.236137	−	0.971720i	$-0.575882\pi$
$241$	−7.33167			−0.472275			−0.236137	+	0.971720i	$0.575882\pi$
$242$		0			0
$243$	1.65533			0.106190
$244$	2.67125	−	8.22128i	0.171010	−	0.526313i
$245$	−9.00479	+	6.54236i	−0.575295	+	0.417976i
$246$	−19.9785	−	14.5152i	−1.27378	−	0.925455i
$247$	0.254048	+	0.781881i	0.0161647	+	0.0497499i
$248$	0.611430	+	1.88179i	0.0388259	+	0.119494i
$249$	1.36992	+	0.995306i	0.0868153	+	0.0630750i
$250$	−1.51774	+	1.10270i	−0.0959903	+	0.0697410i
$251$	9.65921	−	29.7280i	0.609684	−	1.87641i	0.149034	−	0.988832i	$-0.452383\pi$
$251$	9.65921	−	29.7280i	0.609684	−	1.87641i	0.460649	−	0.887582i	$-0.347617\pi$
$252$	−1.03164			−0.0649872
$253$		0			0
$254$	−0.212247			−0.0133176
$255$	1.15267	−	3.54757i	0.0721833	−	0.222157i
$256$	−16.7862	+	12.1959i	−1.04914	+	0.762244i
$257$	6.73125	+	4.89054i	0.419884	+	0.305063i	0.777591	−	0.628770i	$-0.216441\pi$
$257$	6.73125	+	4.89054i	0.419884	+	0.305063i	−0.357707	+	0.933834i	$0.616441\pi$
$258$	13.0528	+	40.1724i	0.812632	+	2.50103i
$259$	−8.11779	−	24.9840i	−0.504415	−	1.55243i
$260$	1.67188	+	1.21469i	0.103686	+	0.0753322i
$261$	−0.855461	+	0.621529i	−0.0529517	+	0.0384717i
$262$	−0.274962	+	0.846245i	−0.0169872	+	0.0522812i
$263$	2.87171			0.177077			0.0885386	−	0.996073i	$-0.471780\pi$
$263$	2.87171			0.177077			0.0885386	+	0.996073i	$0.471780\pi$
$264$		0			0
$265$	−6.65351			−0.408722
$266$	1.49214	−	4.59235i	0.0914892	−	0.281575i
$267$	1.78450	−	1.29652i	0.109210	−	0.0793455i
$268$	−12.1259	−	8.81000i	−0.740709	−	0.538157i
$269$	−0.0383089	−	0.117903i	−0.00233573	−	0.00718864i	0.949882	−	0.312609i	$-0.101203\pi$
$269$	−0.0383089	−	0.117903i	−0.00233573	−	0.00718864i	−0.952218	+	0.305420i	$0.901203\pi$
$270$	2.92705	+	9.00854i	0.178135	+	0.548242i
$271$	−13.7799	−	10.0117i	−0.837067	−	0.608165i	0.0844831	−	0.996425i	$-0.473076\pi$
$271$	−13.7799	−	10.0117i	−0.837067	−	0.608165i	−0.921550	+	0.388260i	$0.873076\pi$
$272$	−8.03062	+	5.83459i	−0.486928	+	0.353774i
$273$	−3.18086	+	9.78968i	−0.192514	+	0.592498i
$274$	−1.62969			−0.0984534
$275$		0			0
$276$	11.8775			0.714944
$277$	−7.02738	+	21.6281i	−0.422235	+	1.29950i	0.483383	+	0.875409i	$0.339408\pi$
$277$	−7.02738	+	21.6281i	−0.422235	+	1.29950i	−0.905618	+	0.424095i	$0.860592\pi$
$278$	29.4280	−	21.3807i	1.76498	−	1.28233i
$279$	0.283142	+	0.205714i	0.0169512	+	0.0123158i
$280$	1.18613	+	3.65052i	0.0708847	+	0.218161i
$281$	4.00175	+	12.3161i	0.238724	+	0.734718i	0.996606	+	0.0823252i	$0.0262346\pi$
$281$	4.00175	+	12.3161i	0.238724	+	0.734718i	−0.757881	+	0.652393i	$0.773765\pi$
$282$	−8.29414	−	6.02605i	−0.493909	−	0.358846i
$283$	12.7969	−	9.29750i	0.760697	−	0.552679i	−0.138427	−	0.990373i	$-0.544205\pi$
$283$	12.7969	−	9.29750i	0.760697	−	0.552679i	0.899124	+	0.437694i	$0.144205\pi$
$284$	−2.45986	+	7.57067i	−0.145966	+	0.449237i
$285$	1.07446			0.0636453
$286$		0			0
$287$	31.5329			1.86133
$288$	−0.348406	+	1.07228i	−0.0205300	+	0.0631850i
$289$	10.1905	−	7.40381i	0.599439	−	0.435518i
$290$	−10.0650	−	7.31267i	−0.591039	−	0.429415i
$291$	−6.34031	−	19.5135i	−0.371676	−	1.14390i
$292$	0.339387	+	1.04452i	0.0198611	+	0.0611262i
$293$	−20.1693	−	14.6538i	−1.17830	−	0.856086i	−0.186322	−	0.982489i	$-0.559657\pi$
$293$	−20.1693	−	14.6538i	−1.17830	−	0.856086i	−0.991979	+	0.126403i	$0.959657\pi$
$294$	30.0275	−	21.8162i	1.75124	−	1.27235i
$295$	3.71969	−	11.4480i	0.216569	−	0.666529i
$296$	−5.56153			−0.323257
$297$		0			0
$298$	2.08723			0.120910
$299$	1.84823	−	5.68828i	0.106886	−	0.328962i
$300$	2.18505	−	1.58753i	0.126154	−	0.0916561i
$301$	−43.6354	−	31.7030i	−2.51510	−	1.82733i
$302$	−3.30133	−	10.1605i	−0.189970	−	0.584669i
$303$	1.54167	+	4.74478i	0.0885667	+	0.272580i
$304$	−2.31320	−	1.68064i	−0.132671	−	0.0963914i
$305$	−4.60249	+	3.34391i	−0.263538	+	0.191472i
$306$	−0.193984	+	0.597021i	−0.0110893	+	0.0341294i
$307$	4.95566			0.282835			0.141417	−	0.989950i	$-0.454834\pi$
$307$	4.95566			0.282835			0.141417	+	0.989950i	$0.454834\pi$
$308$		0			0
$309$	0.721756			0.0410593
$310$	−1.27246	+	3.91622i	−0.0722707	+	0.222426i
$311$	7.76233	−	5.63966i	0.440161	−	0.319796i	−0.345538	−	0.938405i	$-0.612303\pi$
$311$	7.76233	−	5.63966i	0.440161	−	0.319796i	0.785699	+	0.618609i	$0.212303\pi$
$312$	1.76302	+	1.28091i	0.0998116	+	0.0725174i
$313$	−8.33908	−	25.6651i	−0.471353	−	1.45067i	−0.850814	−	0.525467i	$-0.823891\pi$
$313$	−8.33908	−	25.6651i	−0.471353	−	1.45067i	0.379461	−	0.925208i	$-0.376109\pi$
$314$	0.603574	+	1.85761i	0.0340616	+	0.104831i
$315$	0.549273	+	0.399070i	0.0309480	+	0.0224851i
$316$	6.97078	−	5.06457i	0.392137	−	0.284904i
$317$	−4.39444	+	13.5247i	−0.246816	+	0.759622i	0.748516	+	0.663116i	$0.230767\pi$
$317$	−4.39444	+	13.5247i	−0.246816	+	0.759622i	−0.995332	+	0.0965057i	$0.969233\pi$
$318$	22.1869			1.24418
$319$		0			0
$320$	−3.80507			−0.212710
$321$	8.45800	−	26.0310i	0.472079	−	1.45291i
$322$	−28.4201	+	20.6484i	−1.58379	+	1.15069i
$323$	−1.02626	−	0.745625i	−0.0571029	−	0.0414877i
$324$	−4.43860	−	13.6606i	−0.246589	−	0.758923i
$325$	−0.420275	−	1.29347i	−0.0233127	−	0.0717490i
$326$	19.5963	+	14.2376i	1.08534	+	0.788545i
$327$	4.41919	−	3.21073i	0.244382	−	0.177554i
$328$	2.06293	−	6.34905i	0.113906	−	0.350568i
$329$	13.0910			0.721732
$330$		0			0
$331$	−8.55985			−0.470492			−0.235246	−	0.971936i	$-0.575590\pi$
$331$	−8.55985			−0.470492			−0.235246	+	0.971936i	$0.575590\pi$
$332$	0.447314	−	1.37669i	0.0245495	−	0.0755556i
$333$	−0.795854	+	0.578222i	−0.0436125	+	0.0316863i
$334$	6.41399	+	4.66004i	0.350958	+	0.254986i
$335$	3.04819	+	9.38137i	0.166541	+	0.512559i
$336$	−11.0628	−	34.0479i	−0.603527	−	1.85747i
$337$	−12.6887	−	9.21889i	−0.691198	−	0.502185i	0.185855	−	0.982577i	$-0.440494\pi$
$337$	−12.6887	−	9.21889i	−0.691198	−	0.502185i	−0.877054	+	0.480392i	$0.840494\pi$
$338$	16.9233	−	12.2955i	0.920504	−	0.668785i
$339$	6.18731	−	19.0426i	0.336049	−	1.03425i
$340$	−3.18872			−0.172932
$341$		0			0
$342$	−0.180821			−0.00977766
$343$	−5.43492	+	16.7270i	−0.293458	+	0.903172i
$344$	−9.23799	+	6.71179i	−0.498079	+	0.361876i
$345$	−6.32393	−	4.59460i	−0.340469	−	0.247365i
$346$	−0.780141	−	2.40103i	−0.0419406	−	0.129080i
$347$	−2.30375	−	7.09021i	−0.123672	−	0.380622i	0.869985	−	0.493078i	$-0.164128\pi$
$347$	−2.30375	−	7.09021i	−0.123672	−	0.380622i	−0.993657	+	0.112456i	$0.964128\pi$
$348$	14.4903	+	10.5278i	0.776763	+	0.564351i
$349$	−24.6534	+	17.9118i	−1.31967	+	0.958795i	−0.319732	+	0.947508i	$0.603593\pi$
$349$	−24.6534	+	17.9118i	−1.31967	+	0.958795i	−0.999936	+	0.0112876i	$0.996407\pi$
$350$	−2.46847	+	7.59716i	−0.131945	+	0.406085i
$351$	−6.86688			−0.366527
$352$		0			0
$353$	−17.5379			−0.933449			−0.466725	−	0.884403i	$-0.654566\pi$
$353$	−17.5379			−0.933449			−0.466725	+	0.884403i	$0.654566\pi$
$354$	−12.4037	+	38.1747i	−0.659250	+	2.02896i
$355$	4.23827	−	3.07928i	0.224944	−	0.163431i
$356$	−1.52549	−	1.10833i	−0.0808506	−	0.0587414i
$357$	−4.90808	−	15.1055i	−0.259763	−	0.799469i
$358$	7.20531	+	22.1757i	0.380812	+	1.17202i
$359$	−2.43055	−	1.76590i	−0.128279	−	0.0932004i	0.521795	−	0.853071i	$-0.325262\pi$
$359$	−2.43055	−	1.76590i	−0.128279	−	0.0932004i	−0.650075	+	0.759870i	$0.725262\pi$
$360$	0.116286	−	0.0844866i	0.00612880	−	0.00445283i
$361$	−5.75841	+	17.7226i	−0.303074	+	0.932766i
$362$	32.4726			1.70672
$363$		0			0
$364$	8.79941			0.461215
$365$	0.223356	−	0.687418i	0.0116910	−	0.0359811i
$366$	15.3475	−	11.1506i	0.802229	−	0.582853i
$367$	−5.00231	−	3.63439i	−0.261118	−	0.189714i	0.449522	−	0.893269i	$-0.351594\pi$
$367$	−5.00231	−	3.63439i	−0.261118	−	0.189714i	−0.710640	+	0.703556i	$0.751594\pi$
$368$	6.42805	+	19.7835i	0.335085	+	1.03129i
$369$	−0.364894	−	1.12303i	−0.0189956	−	0.0584625i
$370$	−9.36371	−	6.80313i	−0.486796	−	0.353678i
$371$	−22.9200	+	16.6523i	−1.18995	+	0.864546i
$372$	1.83192	−	5.63807i	0.0949806	−	0.292320i
$373$	−20.8707			−1.08064			−0.540321	−	0.841459i	$-0.681697\pi$
$373$	−20.8707			−1.08064			−0.540321	+	0.841459i	$0.681697\pi$
$374$		0			0
$375$	−1.77748			−0.0917889
$376$	0.856435	−	2.63584i	0.0441673	−	0.135933i
$377$	7.29669	−	5.30136i	0.375799	−	0.273034i
$378$	32.6295	+	23.7067i	1.67828	+	1.21934i
$379$	−0.761492	−	2.34363i	−0.0391152	−	0.120384i	0.929592	−	0.368590i	$-0.120159\pi$
$379$	−0.761492	−	2.34363i	−0.0391152	−	0.120384i	−0.968707	+	0.248205i	$0.920159\pi$
$380$	−0.283833	−	0.873548i	−0.0145603	−	0.0448121i
$381$	−0.162692	−	0.118202i	−0.00833494	−	0.00605569i
$382$	29.8241	−	21.6685i	1.52593	−	1.10865i
$383$	5.31621	−	16.3616i	0.271645	−	0.836039i	−0.718442	−	0.695587i	$-0.755144\pi$
$383$	5.31621	−	16.3616i	0.271645	−	0.836039i	0.990088	−	0.140452i	$-0.0448555\pi$
$384$	−12.4486			−0.635265
$385$		0			0
$386$	−19.0635			−0.970306
$387$	−0.624142	+	1.92091i	−0.0317269	+	0.0976455i
$388$	−14.1898	+	10.3095i	−0.720380	+	0.523386i
$389$	14.6066	+	10.6123i	0.740585	+	0.538066i	0.892894	−	0.450267i	$-0.148671\pi$
$389$	14.6066	+	10.6123i	0.740585	+	0.538066i	−0.152310	+	0.988333i	$0.548671\pi$
$390$	1.40145	+	4.31323i	0.0709654	+	0.218409i
$391$	2.85183	+	8.77704i	0.144223	+	0.443874i
$392$	8.11740	+	5.89764i	0.409991	+	0.297876i
$393$	−0.682046	+	0.495535i	−0.0344047	+	0.0249965i
$394$	4.90085	−	15.0833i	0.246901	−	0.759884i
$395$	−5.67056			−0.285317
$396$		0			0
$397$	−16.7432			−0.840317			−0.420159	−	0.907451i	$-0.638026\pi$
$397$	−16.7432			−0.840317			−0.420159	+	0.907451i	$0.638026\pi$
$398$	−3.77420	+	11.6158i	−0.189184	+	0.582248i
$399$	3.70128	−	2.68914i	0.185296	−	0.134625i
$400$	3.82676	+	2.78030i	0.191338	+	0.139015i
$401$	8.94279	+	27.5231i	0.446582	+	1.37444i	0.880740	+	0.473600i	$0.157046\pi$
$401$	8.94279	+	27.5231i	0.446582	+	1.37444i	−0.434159	+	0.900836i	$0.642954\pi$
$402$	−10.1645	−	31.2832i	−0.506961	−	1.56027i
$403$	−2.41507	−	1.75465i	−0.120303	−	0.0874053i
$404$	3.45031	−	2.50680i	0.171660	−	0.124718i
$405$	−2.92111	+	8.99027i	−0.145151	+	0.446730i
$406$	−52.9740			−2.62905
$407$		0			0
$408$	−3.36254			−0.166471
$409$	9.23134	−	28.4112i	0.456461	−	1.40484i	−0.412951	−	0.910753i	$-0.635502\pi$
$409$	9.23134	−	28.4112i	0.456461	−	1.40484i	0.869412	−	0.494088i	$-0.164498\pi$
$410$	11.2397	−	8.16615i	0.555091	−	0.403297i
$411$	−1.24919	−	0.907592i	−0.0616181	−	0.0447682i
$412$	−0.190662	−	0.586798i	−0.00939325	−	0.0289094i
$413$	−15.8384	−	48.7456i	−0.779357	−	2.39862i
$414$	1.06426	+	0.773227i	0.0523053	+	0.0380021i
$415$	−0.770708	+	0.559952i	−0.0378326	+	0.0274870i
$416$	2.97175	−	9.14610i	0.145702	−	0.448424i
$417$	34.4643			1.68772
$418$		0			0
$419$	−8.29831			−0.405399			−0.202699	−	0.979241i	$-0.564971\pi$
$419$	−8.29831			−0.405399			−0.202699	+	0.979241i	$0.564971\pi$
$420$	3.55378	−	10.9374i	0.173407	−	0.533691i
$421$	18.4999	−	13.4410i	0.901632	−	0.655074i	−0.0372530	−	0.999306i	$-0.511861\pi$
$421$	18.4999	−	13.4410i	0.901632	−	0.655074i	0.938885	+	0.344232i	$0.111861\pi$
$422$	6.09226	+	4.42629i	0.296567	+	0.215468i
$423$	−0.151487	−	0.466230i	−0.00736556	−	0.0226689i
$424$	1.85343	+	5.70428i	0.0900107	+	0.277025i
$425$	1.69776	+	1.23349i	0.0823534	+	0.0598333i
$426$	−14.1330	+	10.2682i	−0.684745	+	0.497497i
$427$	−7.48554	+	23.0381i	−0.362251	+	1.11489i
$428$	−23.3979			−1.13098
$429$		0			0
$430$	−23.7638			−1.14599
$431$	6.29212	−	19.3651i	0.303081	−	0.932786i	−0.677306	−	0.735702i	$-0.736853\pi$
$431$	6.29212	−	19.3651i	0.303081	−	0.932786i	0.980386	−	0.197085i	$-0.0631474\pi$
$432$	19.3214	−	14.0378i	0.929602	−	0.675396i
$433$	−17.3040	−	12.5721i	−0.831575	−	0.604175i	0.0884293	−	0.996082i	$-0.471815\pi$
$433$	−17.3040	−	12.5721i	−0.831575	−	0.604175i	−0.920005	+	0.391908i	$0.871815\pi$
$434$	5.41811	+	16.6752i	0.260078	+	0.800437i
$435$	−3.64255	−	11.2106i	−0.174647	−	0.537508i
$436$	−3.77776	−	2.74471i	−0.180922	−	0.131448i
$437$	−2.15062	+	1.56252i	−0.102878	+	0.0747454i
$438$	−0.744805	+	2.29227i	−0.0355882	+	0.109529i
$439$	35.2311			1.68149			0.840744	−	0.541432i	$-0.182118\pi$
$439$	35.2311			1.68149			0.840744	+	0.541432i	$0.182118\pi$
$440$		0			0
$441$	1.77477			0.0845127
$442$	1.65459	−	5.09232i	0.0787010	−	0.242217i
$443$	−18.8196	+	13.6732i	−0.894147	+	0.649636i	−0.936956	−	0.349448i	$-0.886369\pi$
$443$	−18.8196	+	13.6732i	−0.894147	+	0.649636i	0.0428092	+	0.999083i	$0.486369\pi$
$444$	13.4807	+	9.79427i	0.639764	+	0.464816i
$445$	0.383474	+	1.18021i	0.0181784	+	0.0559474i
$446$	8.87387	+	27.3110i	0.420190	+	1.29321i
$447$	1.59990	+	1.16240i	0.0756729	+	0.0549796i
$448$	−13.1077	+	9.52328i	−0.619279	+	0.449933i
$449$	7.67963	−	23.6355i	0.362424	−	1.11543i	−0.589154	−	0.808021i	$-0.700539\pi$
$449$	7.67963	−	23.6355i	0.362424	−	1.11543i	0.951578	−	0.307406i	$-0.0994610\pi$
$450$	0.299133			0.0141013
$451$		0			0
$452$	−17.1164			−0.805086
$453$	3.12792	−	9.62674i	0.146962	−	0.452304i
$454$	17.4569	−	12.6832i	0.819291	−	0.595250i
$455$	−4.68505	−	3.40389i	−0.219638	−	0.159577i
$456$	−0.299306	−	0.921168i	−0.0140163	−	0.0431377i
$457$	−1.82577	−	5.61914i	−0.0854058	−	0.262852i	0.899229	−	0.437478i	$-0.144128\pi$
$457$	−1.82577	−	5.61914i	−0.0854058	−	0.262852i	−0.984635	+	0.174626i	$0.944128\pi$
$458$	41.7791	+	30.3543i	1.95221	+	1.41836i
$459$	8.57204	−	6.22795i	0.400109	−	0.290696i
$460$	−2.06492	+	6.35517i	−0.0962774	+	0.296311i
$461$	17.3587			0.808475			0.404238	−	0.914654i	$-0.367537\pi$
$461$	17.3587			0.808475			0.404238	+	0.914654i	$0.367537\pi$
$462$		0			0
$463$	34.6937			1.61235			0.806176	−	0.591675i	$-0.201533\pi$
$463$	34.6937			1.61235			0.806176	+	0.591675i	$0.201533\pi$
$464$	−9.69333	+	29.8330i	−0.450002	+	1.38496i
$465$	−3.15634	+	2.29322i	−0.146372	+	0.106345i
$466$	13.9667	+	10.1474i	0.646993	+	0.470068i
$467$	2.83245	+	8.71739i	0.131070	+	0.403393i	0.994958	−	0.100291i	$-0.0319775\pi$
$467$	2.83245	+	8.71739i	0.131070	+	0.403393i	−0.863888	+	0.503684i	$0.831978\pi$
$468$	−0.101825	−	0.313386i	−0.00470688	−	0.0144863i
$469$	33.9800	+	24.6879i	1.56905	+	1.13998i
$470$	4.66623	−	3.39021i	0.215237	−	0.156379i
$471$	−0.571869	+	1.76003i	−0.0263503	+	0.0810979i
$472$	−10.8510			−0.499455
$473$		0			0
$474$	18.9091			0.868525
$475$	−0.186795	+	0.574896i	−0.00857075	+	0.0263781i
$476$	−10.9845	+	7.98068i	−0.503472	+	0.365794i
$477$	0.858290	+	0.623584i	0.0392984	+	0.0285520i
$478$	−7.33699	−	22.5809i	−0.335586	−	1.03283i
$479$	12.6178	+	38.8335i	0.576521	+	1.77435i	0.630941	+	0.775831i	$0.282669\pi$
$479$	12.6178	+	38.8335i	0.576521	+	1.77435i	−0.0544196	+	0.998518i	$0.517331\pi$
$480$	−10.1681	−	7.38759i	−0.464110	−	0.337196i
$481$	6.78827	−	4.93197i	0.309518	−	0.224878i
$482$	−4.25036	+	13.0813i	−0.193598	+	0.595835i
$483$	−33.2839			−1.51447
$484$		0			0
$485$	11.5431			0.524145
$486$	0.959637	−	2.95346i	0.0435300	−	0.133972i
$487$	21.1637	−	15.3763i	0.959020	−	0.696769i	0.00609678	−	0.999981i	$-0.498059\pi$
$487$	21.1637	−	15.3763i	0.959020	−	0.696769i	0.952923	+	0.303213i	$0.0980593\pi$
$488$	4.14894	+	3.01438i	0.187814	+	0.136455i
$489$	7.09194	+	21.8268i	0.320709	+	0.987040i
$490$	6.45265	+	19.8592i	0.291501	+	0.897148i
$491$	18.6084	+	13.5198i	0.839784	+	0.610138i	0.922310	−	0.386450i	$-0.126299\pi$
$491$	18.6084	+	13.5198i	0.839784	+	0.610138i	−0.0825266	+	0.996589i	$0.526299\pi$
$492$	−16.1815	+	11.7566i	−0.729520	+	0.530027i
$493$	−4.30049	+	13.2356i	−0.193684	+	0.596099i
$494$	1.54232			0.0693922
$495$		0			0
$496$	10.3823			0.466180
$497$	6.89316	−	21.2150i	0.309200	−	0.951621i
$498$	2.57001	−	1.86722i	0.115165	−	0.0836723i
$499$	21.2076	+	15.4082i	0.949381	+	0.689766i	0.950660	−	0.310233i	$-0.100407\pi$
$499$	21.2076	+	15.4082i	0.949381	+	0.689766i	−0.00127906	+	0.999999i	$0.500407\pi$
$500$	0.469548	+	1.44512i	0.0209988	+	0.0646277i
$501$	2.32123	+	7.14402i	0.103705	+	0.319171i
$502$	−47.4413	−	34.4681i	−2.11741	−	1.53839i
$503$	1.36287	−	0.990181i	0.0607672	−	0.0441500i	−0.556987	−	0.830521i	$-0.688043\pi$
$503$	1.36287	−	0.990181i	0.0607672	−	0.0441500i	0.617754	+	0.786371i	$0.288043\pi$
$504$	0.189128	−	0.582077i	0.00842445	−	0.0259278i
$505$	−2.80675			−0.124899
$506$		0			0
$507$	19.8195			0.880214
$508$	−0.0531229	+	0.163495i	−0.00235695	+	0.00725393i
$509$	−14.4396	+	10.4910i	−0.640023	+	0.465004i	−0.859858	−	0.510533i	$-0.829448\pi$
$509$	−14.4396	+	10.4910i	−0.640023	+	0.465004i	0.219835	+	0.975537i	$0.429448\pi$
$510$	−5.66137	−	4.11323i	−0.250690	−	0.182137i
$511$	−0.951048	−	2.92702i	−0.0420719	−	0.129484i
$512$	7.70026	+	23.6990i	0.340307	+	1.04736i
$513$	2.46916	+	1.79395i	0.109016	+	0.0792048i
$514$	12.6280	−	9.17480i	0.556998	−	0.404683i
$515$	−0.125478	+	0.386181i	−0.00552922	+	0.0170172i
$516$	34.2121			1.50610
$517$		0			0
$518$	−49.2828			−2.16536
$519$	0.739161	−	2.27490i	0.0324456	−	0.0998572i
$520$	−0.991865	+	0.720632i	−0.0434961	+	0.0316018i
$521$	7.72077	+	5.60947i	0.338253	+	0.245755i	0.743924	−	0.668264i	$-0.232962\pi$
$521$	7.72077	+	5.60947i	0.338253	+	0.245755i	−0.405671	+	0.914019i	$0.632962\pi$
$522$	0.613006	+	1.88664i	0.0268305	+	0.0825759i
$523$	6.71971	+	20.6811i	0.293832	+	0.904323i	0.983611	+	0.180303i	$0.0577078\pi$
$523$	6.71971	+	20.6811i	0.293832	+	0.904323i	−0.689779	+	0.724020i	$0.742292\pi$
$524$	0.583049	+	0.423610i	0.0254706	+	0.0185055i
$525$	−6.12306	+	4.44866i	−0.267232	+	0.194156i
$526$	1.66480	−	5.12373i	0.0725888	−	0.223405i
$527$	4.60616			0.200648
$528$		0			0
$529$	−3.66042			−0.159149
$530$	−3.85721	+	11.8713i	−0.167546	+	0.515655i
$531$	−1.55277	+	1.12815i	−0.0673844	+	0.0489577i
$532$	−3.16405	−	2.29882i	−0.137179	−	0.0996664i
$533$	3.11238	+	9.57891i	0.134812	+	0.414909i
$534$	−1.27874	−	3.93555i	−0.0553364	−	0.170308i
$535$	12.4577	+	9.05103i	0.538592	+	0.391310i
$536$	7.19385	−	5.22664i	0.310727	−	0.225756i
$537$	−6.82682	+	21.0108i	−0.294599	+	0.906683i
$538$	−0.232572			−0.0100269
$539$		0			0
$540$	7.67195			0.330148
$541$	−4.16789	+	12.8275i	−0.179192	+	0.551495i	−0.999800	−	0.0199957i	$-0.993635\pi$
$541$	−4.16789	+	12.8275i	−0.179192	+	0.551495i	0.820608	+	0.571491i	$0.193635\pi$
$542$	−25.8514	+	18.7822i	−1.11041	+	0.806763i
$543$	24.8909	+	18.0843i	1.06817	+	0.776071i
$544$	4.58542	+	14.1125i	0.196598	+	0.605067i
$545$	0.949647	+	2.92271i	0.0406784	+	0.125195i
$546$	15.6228	+	11.3506i	0.668595	+	0.485763i
$547$	−19.7575	+	14.3547i	−0.844771	+	0.613762i	−0.923699	−	0.383118i	$-0.874850\pi$
$547$	−19.7575	+	14.3547i	−0.844771	+	0.613762i	0.0789281	+	0.996880i	$0.474850\pi$
$548$	−0.407893	+	1.25536i	−0.0174243	+	0.0536265i
$549$	0.907112			0.0387146
$550$		0			0
$551$	−4.00867			−0.170775
$552$	−2.17749	+	6.70161i	−0.0926800	+	0.285240i
$553$	−19.5339	+	14.1922i	−0.830666	+	0.603514i
$554$	34.5151	+	25.0767i	1.46640	+	1.06541i
$555$	−3.38874	−	10.4295i	−0.143844	−	0.442707i
$556$	−9.10424	−	28.0200i	−0.386106	−	1.18831i
$557$	−20.8678	−	15.1613i	−0.884197	−	0.642407i	0.0501614	−	0.998741i	$-0.484026\pi$
$557$	−20.8678	−	15.1613i	−0.884197	−	0.642407i	−0.934359	+	0.356334i	$0.884026\pi$
$558$	0.531182	−	0.385926i	0.0224867	−	0.0163376i
$559$	5.32365	−	16.3845i	0.225166	−	0.692991i
$560$	20.1409			0.851108
$561$		0			0
$562$	24.2945			1.02480
$563$	12.4751	−	38.3944i	0.525763	−	1.61813i	−0.237040	−	0.971500i	$-0.576177\pi$
$563$	12.4751	−	38.3944i	0.525763	−	1.61813i	0.762803	−	0.646631i	$-0.223823\pi$
$564$	−6.71783	+	4.88079i	−0.282872	+	0.205518i
$565$	9.11322	+	6.62114i	0.383396	+	0.278553i
$566$	−9.17000	−	28.2224i	−0.385444	−	1.18627i
$567$	12.4381	+	38.2805i	0.522351	+	1.60763i
$568$	−3.82060	−	2.77583i	−0.160309	−	0.116471i
$569$	−8.53848	+	6.20357i	−0.357952	+	0.260067i	−0.752197	−	0.658938i	$-0.771006\pi$
$569$	−8.53848	+	6.20357i	−0.357952	+	0.260067i	0.394246	+	0.919005i	$0.371006\pi$
$570$	0.622890	−	1.91706i	0.0260900	−	0.0802967i
$571$	9.77700			0.409155			0.204577	−	0.978850i	$-0.434418\pi$
$571$	9.77700			0.409155			0.204577	+	0.978850i	$0.434418\pi$
$572$		0			0
$573$	34.9281			1.45914
$574$	18.2804	−	56.2613i	0.763010	−	2.34830i
$575$	3.55780	−	2.58489i	0.148370	−	0.107797i
$576$	0.490846	+	0.356621i	0.0204519	+	0.0148592i
$577$	−5.03574	−	15.4984i	−0.209640	−	0.645207i	−0.999491	−	0.0319073i	$-0.989842\pi$
$577$	−5.03574	−	15.4984i	−0.209640	−	0.645207i	0.789850	−	0.613300i	$-0.210158\pi$
$578$	−7.30228	−	22.4741i	−0.303735	−	0.934800i
$579$	−14.6125	−	10.6166i	−0.607277	−	0.441212i
$580$	−8.15215	+	5.92289i	−0.338500	+	0.245935i
$581$	−1.25349	+	3.85784i	−0.0520034	+	0.160050i
$582$	−38.4918			−1.59554
$583$		0			0
$584$	−0.651566			−0.0269620
$585$	−0.0670129	+	0.206245i	−0.00277064	+	0.00852717i
$586$	−37.8381	+	27.4910i	−1.56308	+	1.13564i
$587$	−27.2499	−	19.7982i	−1.12472	−	0.817159i	−0.139805	−	0.990179i	$-0.544648\pi$
$587$	−27.2499	−	19.7982i	−1.12472	−	0.817159i	−0.984918	+	0.173020i	$0.944648\pi$
$588$	−9.28969	−	28.5907i	−0.383100	−	1.17906i
$589$	0.410002	+	1.26186i	0.0168939	+	0.0519939i
$590$	−18.2693	−	13.2734i	−0.752134	−	0.546458i
$591$	12.1566	−	8.83230i	0.500057	−	0.363312i
$592$	−9.01791	+	27.7543i	−0.370634	+	1.14069i
$593$	21.3355			0.876143			0.438071	−	0.898940i	$-0.355662\pi$
$593$	21.3355			0.876143			0.438071	+	0.898940i	$0.355662\pi$
$594$		0			0
$595$	8.93560			0.366324
$596$	0.522409	−	1.60781i	0.0213987	−	0.0658584i
$597$	−9.36196	+	6.80186i	−0.383159	+	0.278382i
$598$	−9.07762	−	6.59528i	−0.371211	−	0.269701i
$599$	−5.07083	−	15.6064i	−0.207189	−	0.637661i	−0.999616	−	0.0276951i	$-0.991183\pi$
$599$	−5.07083	−	15.6064i	−0.207189	−	0.637661i	0.792428	−	0.609966i	$-0.208817\pi$
$600$	0.495144	+	1.52390i	0.0202142	+	0.0622129i
$601$	−11.1607	−	8.10874i	−0.455255	−	0.330762i	0.336412	−	0.941715i	$-0.390787\pi$
$601$	−11.1607	−	8.10874i	−0.455255	−	0.330762i	−0.791667	+	0.610953i	$0.790787\pi$
$602$	−81.8613	+	59.4757i	−3.33642	+	2.42405i
$603$	0.486035	−	1.49586i	0.0197929	−	0.0609162i
$604$	−8.65296			−0.352084
$605$		0			0
$606$	9.35943			0.380201
$607$	1.74394	−	5.36729i	0.0707843	−	0.217852i	−0.909406	−	0.415909i	$-0.863463\pi$
$607$	1.74394	−	5.36729i	0.0707843	−	0.217852i	0.980190	+	0.198058i	$0.0634633\pi$
$608$	−3.45795	+	2.51235i	−0.140239	+	0.101889i
$609$	−40.6056	−	29.5017i	−1.64542	−	1.19547i
$610$	3.29805	+	10.1504i	0.133534	+	0.410976i
$611$	1.29212	+	3.97673i	0.0522735	+	0.160881i
$612$	0.411338	+	0.298854i	0.0166273	+	0.0120805i
$613$	−2.69487	+	1.95794i	−0.108845	+	0.0790803i	−0.640876	−	0.767644i	$-0.721429\pi$
$613$	−2.69487	+	1.95794i	−0.108845	+	0.0790803i	0.532031	+	0.846725i	$0.321429\pi$
$614$	2.87292	−	8.84195i	0.115942	−	0.356832i
$615$	13.1633			0.530795
$616$		0			0
$617$	−9.45854			−0.380786			−0.190393	−	0.981708i	$-0.560976\pi$
$617$	−9.45854			−0.380786			−0.190393	+	0.981708i	$0.560976\pi$
$618$	0.418420	−	1.28776i	0.0168313	−	0.0518015i
$619$	22.0109	−	15.9919i	0.884694	−	0.642768i	−0.0497950	−	0.998759i	$-0.515857\pi$
$619$	22.0109	−	15.9919i	0.884694	−	0.642768i	0.934489	+	0.355992i	$0.115857\pi$
$620$	2.69821	+	1.96036i	0.108363	+	0.0787301i
$621$	−6.86142	−	21.1173i	−0.275339	−	0.847407i
$622$	−5.56233	−	17.1191i	−0.223029	−	0.686413i
$623$	4.27480	+	3.10583i	0.171266	+	0.124432i
$624$	9.25098	−	6.72123i	0.370336	−	0.269065i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	−50.6262			−2.02343
$627$		0			0
$628$	1.58200			0.0631285
$629$	−4.00084	+	12.3133i	−0.159524	+	0.490964i
$630$	1.03045	−	0.748667i	0.0410542	−	0.0298276i
$631$	24.5364	+	17.8268i	0.976780	+	0.709672i	0.956987	−	0.290132i	$-0.0936992\pi$
$631$	24.5364	+	17.8268i	0.976780	+	0.709672i	0.0197932	+	0.999804i	$0.493699\pi$
$632$	1.57962	+	4.86157i	0.0628339	+	0.193383i
$633$	2.20480	+	6.78567i	0.0876329	+	0.269706i
$634$	21.5833	+	15.6812i	0.857183	+	0.622780i
$635$	0.0915291	−	0.0664998i	0.00363222	−	0.00263896i
$636$	5.55311	−	17.0907i	0.220195	−	0.677691i
$637$	−15.1379			−0.599787
$638$		0			0
$639$	−0.835326			−0.0330450
$640$	2.16420	−	6.66072i	0.0855475	−	0.263288i
$641$	−32.2242	+	23.4122i	−1.27278	+	0.924727i	−0.999310	−	0.0371536i	$-0.988171\pi$
$641$	−32.2242	+	23.4122i	−1.27278	+	0.924727i	−0.273468	+	0.961881i	$0.588171\pi$
$642$	−41.5415	−	30.1817i	−1.63951	−	1.19118i
$643$	−8.45213	−	26.0130i	−0.333319	−	1.02585i	−0.967544	−	0.252703i	$-0.918681\pi$
$643$	−8.45213	−	26.0130i	−0.333319	−	1.02585i	0.634225	−	0.773149i	$-0.281319\pi$
$644$	8.79242	+	27.0603i	0.346470	+	1.06632i
$645$	−18.2154	−	13.2343i	−0.717232	−	0.521099i
$646$	−1.92530	+	1.39881i	−0.0757500	+	0.0550356i
$647$	6.88299	−	21.1837i	0.270598	−	0.832816i	−0.719752	−	0.694231i	$-0.755745\pi$
$647$	6.88299	−	21.1837i	0.270598	−	0.832816i	0.990351	−	0.138585i	$-0.0442554\pi$
$648$	8.52138			0.334751
$649$		0			0
$650$	−2.55147			−0.100077
$651$	−5.13351	+	15.7993i	−0.201198	+	0.619224i
$652$	15.8720	−	11.5317i	0.621596	−	0.451616i
$653$	−23.7780	−	17.2758i	−0.930507	−	0.676053i	0.0156100	−	0.999878i	$-0.495031\pi$
$653$	−23.7780	−	17.2758i	−0.930507	−	0.676053i	−0.946117	+	0.323825i	$0.895031\pi$
$654$	−3.16670	−	9.74612i	−0.123828	−	0.381103i
$655$	−0.146566	−	0.451083i	−0.00572680	−	0.0176253i
$656$	−28.3393	−	20.5897i	−1.10647	−	0.803894i
$657$	−0.0932390	+	0.0677421i	−0.00363760	+	0.00264287i
$658$	7.58920	−	23.3571i	0.295858	−	0.910556i
$659$	−22.8429			−0.889832			−0.444916	−	0.895572i	$-0.646766\pi$
$659$	−22.8429			−0.889832			−0.444916	+	0.895572i	$0.646766\pi$
$660$		0			0
$661$	32.0302			1.24583			0.622916	−	0.782289i	$-0.285948\pi$
$661$	32.0302			1.24583			0.622916	+	0.782289i	$0.285948\pi$
$662$	−4.96236	+	15.2726i	−0.192868	+	0.593585i
$663$	4.10424	−	2.98191i	0.159396	−	0.115808i
$664$	0.694758	+	0.504771i	0.0269618	+	0.0195889i
$665$	0.795373	+	2.44791i	0.0308432	+	0.0949257i
$666$	0.570293	+	1.75518i	0.0220984	+	0.0680119i
$667$	23.5938	+	17.1419i	0.913557	+	0.663738i
$668$	5.19500	−	3.77439i	0.201001	−	0.146036i
$669$	−8.40773	+	25.8763i	−0.325062	+	1.00044i
$670$	18.5055			0.714928
$671$		0			0
$672$	−53.5167			−2.06445
$673$	−4.19458	+	12.9096i	−0.161689	+	0.497629i	−0.998777	−	0.0494401i	$-0.984256\pi$
$673$	−4.19458	+	12.9096i	−0.161689	+	0.497629i	0.837088	+	0.547069i	$0.184256\pi$
$674$	−23.8044	+	17.2949i	−0.916912	+	0.666175i
$675$	−4.08475	−	2.96775i	−0.157222	−	0.114229i
$676$	−5.23560	−	16.1135i	−0.201369	−	0.619750i
$677$	−0.489060	−	1.50517i	−0.0187961	−	0.0578484i	0.941219	−	0.337798i	$-0.109682\pi$
$677$	−0.489060	−	1.50517i	−0.0187961	−	0.0578484i	−0.960015	+	0.279950i	$0.909682\pi$
$678$	−30.3891	−	22.0789i	−1.16708	−	0.847937i
$679$	39.7636	−	28.8899i	1.52599	−	1.10869i
$680$	0.584581	−	1.79915i	0.0224176	−	0.0689944i
$681$	20.4444			0.783432
$682$		0			0
$683$	33.8348			1.29465			0.647325	−	0.762214i	$-0.275887\pi$
$683$	33.8348			1.29465			0.647325	+	0.762214i	$0.275887\pi$
$684$	−0.0452573	+	0.139287i	−0.00173045	+	0.00532579i
$685$	0.702787	−	0.510605i	0.0268521	−	0.0195092i
$686$	26.6937	+	19.3941i	1.01917	+	0.740470i
$687$	15.1199	+	46.5344i	0.576861	+	1.77540i
$688$	18.5153	+	56.9844i	0.705891	+	2.17251i
$689$	−7.32082	−	5.31889i	−0.278901	−	0.202633i
$690$	−11.8639	+	8.61961i	−0.451650	+	0.328143i
$691$	−10.4277	+	32.0931i	−0.396687	+	1.22088i	0.530953	+	0.847401i	$0.321834\pi$
$691$	−10.4277	+	32.0931i	−0.396687	+	1.22088i	−0.927640	+	0.373476i	$0.878166\pi$
$692$	−2.04479			−0.0777311
$693$		0			0
$694$	−13.9860			−0.530900
$695$	−5.99165	+	18.4404i	−0.227276	+	0.699484i
$696$	−8.59656	+	6.24576i	−0.325852	+	0.236745i
$697$	−12.5729	−	9.13473i	−0.476232	−	0.346003i
$698$	17.6662	+	54.3708i	0.668674	+	2.05797i
$699$	5.05456	+	15.5563i	0.191181	+	0.588394i
$700$	5.23432	+	3.80296i	0.197839	+	0.143738i
$701$	1.52692	−	1.10937i	0.0576709	−	0.0419003i	−0.558576	−	0.829453i	$-0.688652\pi$
$701$	1.52692	−	1.10937i	0.0576709	−	0.0419003i	0.616247	+	0.787553i	$0.288652\pi$
$702$	−3.98090	+	12.2520i	−0.150249	+	0.462420i
$703$	−3.72935			−0.140655
$704$		0			0
$705$	5.46480			0.205816
$706$	−10.1672	+	31.2913i	−0.382647	+	1.17767i
$707$	−9.66867	+	7.02470i	−0.363628	+	0.264191i
$708$	26.3018	+	19.1093i	0.988481	+	0.718173i
$709$	−2.17492	−	6.69372i	−0.0816809	−	0.251388i	0.901873	−	0.432000i	$-0.142192\pi$
$709$	−2.17492	−	6.69372i	−0.0816809	−	0.251388i	−0.983554	+	0.180612i	$0.942192\pi$
$710$	−3.03706	−	9.34710i	−0.113979	−	0.350790i
$711$	0.731491	+	0.531459i	0.0274331	+	0.0199313i
$712$	0.905013	−	0.657530i	0.0339168	−	0.0246420i
$713$	2.98282	−	9.18017i	0.111707	−	0.343800i
$714$	−29.7968			−1.11512
$715$		0			0
$716$	18.8855			0.705783
$717$	6.95158	−	21.3948i	0.259612	−	0.799002i
$718$	−4.55978	+	3.31287i	−0.170169	+	0.123635i
$719$	−6.49518	−	4.71903i	−0.242229	−	0.175990i	0.460047	−	0.887895i	$-0.347833\pi$
$719$	−6.49518	−	4.71903i	−0.242229	−	0.175990i	−0.702276	+	0.711905i	$0.747833\pi$
$720$	−0.233067	−	0.717307i	−0.00868590	−	0.0267324i
$721$	0.534284	+	1.64436i	0.0198978	+	0.0612391i
$722$	28.2825	+	20.5484i	1.05257	+	0.764733i
$723$	−10.5431	+	7.65998i	−0.392101	+	0.284878i
$724$	8.12749	−	25.0138i	0.302056	−	0.929632i
$725$	6.63159			0.246291
$726$		0			0
$727$	−29.8123			−1.10568			−0.552838	−	0.833289i	$-0.686455\pi$
$727$	−29.8123			−1.10568			−0.552838	+	0.833289i	$0.686455\pi$
$728$	−1.61318	+	4.96485i	−0.0597884	+	0.184010i
$729$	−20.5623	+	14.9394i	−0.761568	+	0.553312i
$730$	−1.09701	−	0.797027i	−0.0406023	−	0.0294993i
$731$	8.21442	+	25.2814i	0.303821	+	0.935066i
$732$	−4.74811	−	14.6132i	−0.175495	−	0.540119i
$733$	33.1039	+	24.0514i	1.22272	+	0.888358i	0.996323	−	0.0856768i	$-0.0273052\pi$
$733$	33.1039	+	24.0514i	1.22272	+	0.888358i	0.226397	+	0.974035i	$0.427305\pi$
$734$	−9.38448	+	6.81823i	−0.346388	+	0.251665i
$735$	−6.11370	+	18.8160i	−0.225507	+	0.694040i
$736$	31.0958			1.14621
$737$		0			0
$738$	−2.21526			−0.0815447
$739$	1.34879	−	4.15115i	0.0496161	−	0.152703i	−0.923179	−	0.384371i	$-0.874418\pi$
$739$	1.34879	−	4.15115i	0.0496161	−	0.152703i	0.972795	+	0.231668i	$0.0744184\pi$
$740$	−7.58412	+	5.51019i	−0.278798	+	0.202559i
$741$	1.18222	+	0.858932i	0.0434299	+	0.0315536i
$742$	16.4240	+	50.5478i	0.602943	+	1.85567i
$743$	−6.08934	−	18.7411i	−0.223396	−	0.687543i	−0.998450	−	0.0556484i	$-0.982277\pi$
$743$	−6.08934	−	18.7411i	−0.223396	−	0.687543i	0.775054	−	0.631895i	$-0.217723\pi$
$744$	2.84530	+	2.06723i	0.104314	+	0.0757884i
$745$	−0.900095	+	0.653957i	−0.0329769	+	0.0239591i
$746$	−12.0993	+	37.2377i	−0.442985	+	1.36337i
$747$	0.151900			0.00555773
$748$		0			0
$749$	65.5669			2.39576
$750$	−1.03045	+	3.17141i	−0.0376268	+	0.115803i
$751$	31.5147	−	22.8968i	1.14999	−	0.835514i	0.161508	−	0.986871i	$-0.448364\pi$
$751$	31.5147	−	22.8968i	1.14999	−	0.835514i	0.988479	+	0.151357i	$0.0483643\pi$
$752$	−11.7652	−	8.54792i	−0.429033	−	0.311710i
$753$	−17.1691	−	52.8410i	−0.625677	−	1.92563i
$754$	−5.22866	−	16.0922i	−0.190417	−	0.586042i
$755$	4.60707	+	3.34723i	0.167668	+	0.121818i
$756$	26.4283	−	19.2012i	0.961186	−	0.698343i
$757$	16.4297	−	50.5653i	0.597146	−	1.83783i	0.0534073	−	0.998573i	$-0.482992\pi$
$757$	16.4297	−	50.5653i	0.597146	−	1.83783i	0.543739	−	0.839254i	$-0.317008\pi$
$758$	−4.62299			−0.167915
$759$		0			0
$760$	0.544913			0.0197661
$761$	−15.8459	+	48.7685i	−0.574412	+	1.76786i	0.0637615	+	0.997965i	$0.479690\pi$
$761$	−15.8459	+	48.7685i	−0.574412	+	1.76786i	−0.638173	+	0.769893i	$0.720310\pi$
$762$	−0.305214	+	0.221751i	−0.0110567	+	0.00803320i
$763$	10.5863	+	7.69137i	0.383248	+	0.278446i
$764$	−9.22676	−	28.3970i	−0.333812	−	1.02737i
$765$	−0.103401	−	0.318237i	−0.00373848	−	0.0115059i
$766$	−26.1106	−	18.9705i	−0.943414	−	0.685431i
$767$	13.2444	−	9.62263i	0.478228	−	0.347453i
$768$	−11.3968	+	35.0758i	−0.411247	+	1.26569i
$769$	−45.0332			−1.62394			−0.811970	−	0.583699i	$-0.801605\pi$
$769$	−45.0332			−1.62394			−0.811970	+	0.583699i	$0.801605\pi$
$770$		0			0
$771$	14.7892			0.532619
$772$	−4.77136	+	14.6847i	−0.171725	+	0.528515i
$773$	40.4052	−	29.3561i	1.45328	−	1.05587i	0.468223	−	0.883610i	$-0.344894\pi$
$773$	40.4052	−	29.3561i	1.45328	−	1.05587i	0.985052	−	0.172256i	$-0.0551055\pi$
$774$	3.06548	+	2.22720i	0.110186	+	0.0800551i
$775$	−0.678271	−	2.08750i	−0.0243642	−	0.0749853i
$776$	−3.21550	−	9.89629i	−0.115430	−	0.355256i
$777$	−37.7763	−	27.4461i	−1.35522	−	0.984622i
$778$	27.4024	−	19.9090i	0.982425	−	0.713774i
$779$	1.38333	−	4.25744i	0.0495628	−	0.152539i
$780$	3.67328			0.131525
$781$		0			0
$782$	17.3134			0.619125
$783$	10.3468	−	31.8443i	0.369766	−	1.13802i
$784$	42.5938	−	30.9462i	1.52121	−	1.10522i
$785$	−0.842298	−	0.611965i	−0.0300629	−	0.0218420i
$786$	0.488740	+	1.50419i	0.0174328	+	0.0536526i
$787$	−3.02381	−	9.30633i	−0.107787	−	0.331735i	0.882587	−	0.470149i	$-0.155800\pi$
$787$	−3.02381	−	9.30633i	−0.107787	−	0.331735i	−0.990375	+	0.138414i	$0.955800\pi$
$788$	−10.3921	−	7.55032i	−0.370204	−	0.268969i
$789$	4.12956	−	3.00030i	0.147016	−	0.106814i
$790$	−3.28737	+	10.1175i	−0.116959	+	0.359964i
$791$	47.9644			1.70542
$792$		0			0
$793$	−7.73725			−0.274758
$794$	−9.70646	+	29.8734i	−0.344469	+	1.06017i
$795$	−9.56785	+	6.95145i	−0.339337	+	0.246543i
$796$	8.00310	+	5.81459i	0.283662	+	0.206093i
$797$	11.1755	+	34.3946i	0.395856	+	1.21832i	0.928293	+	0.371851i	$0.121277\pi$
$797$	11.1755	+	34.3946i	0.395856	+	1.21832i	−0.532436	+	0.846470i	$0.678723\pi$
$798$	−2.65226	−	8.16282i	−0.0938890	−	0.288961i
$799$	−5.21969	−	3.79232i	−0.184659	−	0.134163i
$800$	5.72053	−	4.15621i	0.202251	−	0.146944i
$801$	0.0611450	−	0.188185i	0.00216045	−	0.00664919i
$802$	54.2913			1.91709
$803$		0			0
$804$	−26.6418			−0.939583
$805$	5.78644	−	17.8088i	0.203945	−	0.627678i
$806$	−4.53074	+	3.29178i	−0.159589	+	0.115948i
$807$	−0.178271	−	0.129521i	−0.00627543	−	0.00455937i
$808$	0.781861	+	2.40632i	0.0275058	+	0.0846541i
$809$	−5.04801	−	15.5362i	−0.177478	−	0.546222i	0.822260	−	0.569113i	$-0.192713\pi$
$809$	−5.04801	−	15.5362i	−0.177478	−	0.546222i	−0.999738	+	0.0228902i	$0.992713\pi$
$810$	14.3471	+	10.4238i	0.504105	+	0.366254i
$811$	41.8228	−	30.3861i	1.46860	−	1.06700i	0.487581	−	0.873078i	$-0.337879\pi$
$811$	41.8228	−	30.3861i	1.46860	−	1.06700i	0.981017	−	0.193921i	$-0.0621205\pi$
$812$	−13.2587	+	40.8062i	−0.465291	+	1.43202i
$813$	−30.2756			−1.06181
$814$		0			0
$815$	−12.9115			−0.452270
$816$	−5.45230	+	16.7805i	−0.190869	+	0.587433i
$817$	−6.19465	+	4.50068i	−0.216723	+	0.157459i
$818$	−45.3398	−	32.9413i	−1.58527	−	1.15177i
$819$	0.285341	+	0.878189i	0.00997062	+	0.0306864i
$820$	−3.47727	−	10.7019i	−0.121432	−	0.373728i
$821$	31.2858	+	22.7304i	1.09188	+	0.793298i	0.979716	−	0.200392i	$-0.0642215\pi$
$821$	31.2858	+	22.7304i	1.09188	+	0.793298i	0.112165	+	0.993690i	$0.464222\pi$
$822$	−2.34352	+	1.70267i	−0.0817398	+	0.0593874i
$823$	−1.63920	+	5.04495i	−0.0571390	+	0.175856i	−0.975553	−	0.219766i	$-0.929471\pi$
$823$	−1.63920	+	5.04495i	−0.0571390	+	0.175856i	0.918414	+	0.395621i	$0.129471\pi$
$824$	0.366040			0.0127516
$825$		0			0
$826$	−96.1544			−3.34564
$827$	3.66624	−	11.2835i	0.127487	−	0.392366i	−0.866859	−	0.498554i	$-0.833865\pi$
$827$	3.66624	−	11.2835i	0.127487	−	0.392366i	0.994346	+	0.106188i	$0.0338645\pi$
$828$	0.861993	−	0.626275i	0.0299563	−	0.0217645i
$829$	39.9215	+	29.0046i	1.38653	+	1.00737i	0.996236	+	0.0866829i	$0.0276267\pi$
$829$	39.9215	+	29.0046i	1.38653	+	1.00737i	0.390294	+	0.920690i	$0.372373\pi$
$830$	0.552274	+	1.69972i	0.0191697	+	0.0589983i
$831$	12.4911	+	38.4435i	0.433310	+	1.33359i
$832$	−4.18669	−	3.04181i	−0.145148	−	0.105456i
$833$	18.8970	−	13.7294i	0.654741	−	0.475697i
$834$	19.9798	−	61.4916i	0.691845	−	2.12928i
$835$	−4.22601			−0.146247
$836$		0			0
$837$	−11.0823			−0.383059
$838$	−4.81074	+	14.8059i	−0.166184	+	0.511462i
$839$	17.3195	−	12.5834i	0.597936	−	0.434426i	−0.247210	−	0.968962i	$-0.579514\pi$
$839$	17.3195	−	12.5834i	0.597936	−	0.434426i	0.845145	+	0.534536i	$0.179514\pi$
$840$	5.51966	+	4.01027i	0.190446	+	0.138367i
$841$	4.62844	+	14.2449i	0.159601	+	0.491202i
$842$	−13.2567	−	40.7999i	−0.456855	−	1.40606i
$843$	18.6222	+	13.5298i	0.641382	+	0.465992i
$844$	4.93442	−	3.58506i	0.169850	−	0.123403i
$845$	−3.44563	+	10.6046i	−0.118533	+	0.364808i
$846$	−0.919673			−0.0316190
$847$		0			0
$848$	31.4720			1.08075
$849$	8.68831	−	26.7399i	0.298182	−	0.917710i
$850$	3.18505	−	2.31407i	0.109246	−	0.0793720i
$851$	21.9499	+	15.9475i	0.752431	+	0.546673i
$852$	4.37236	+	13.4567i	0.149795	+	0.461021i
$853$	−9.60459	−	29.5599i	−0.328855	−	1.01211i	−0.969670	−	0.244416i	$-0.921404\pi$
$853$	−9.60459	−	29.5599i	−0.328855	−	1.01211i	0.640816	−	0.767695i	$-0.278596\pi$
$854$	36.7653	+	26.7116i	1.25808	+	0.914051i
$855$	0.0779769	−	0.0566535i	0.00266675	−	0.00193751i
$856$	4.28949	−	13.2017i	0.146612	−	0.451224i
$857$	−33.2665			−1.13636			−0.568181	−	0.822904i	$-0.692353\pi$
$857$	−33.2665			−1.13636			−0.568181	+	0.822904i	$0.692353\pi$
$858$		0			0
$859$	−18.9045			−0.645012			−0.322506	−	0.946567i	$-0.604525\pi$
$859$	−18.9045			−0.645012			−0.322506	+	0.946567i	$0.604525\pi$
$860$	−5.94779	+	18.3054i	−0.202818	+	0.624210i
$861$	45.3448	−	32.9449i	1.54535	−	1.12276i
$862$	−30.9038	−	22.4529i	−1.05259	−	0.764750i
$863$	4.27446	+	13.1554i	0.145504	+	0.447816i	0.997075	−	0.0764229i	$-0.0243499\pi$
$863$	4.27446	+	13.1554i	0.145504	+	0.447816i	−0.851571	+	0.524239i	$0.824350\pi$
$864$	−11.0324	−	33.9542i	−0.375329	−	1.15514i
$865$	1.08870	+	0.790987i	0.0370169	+	0.0268944i
$866$	−32.4627	+	23.5856i	−1.10313	+	0.801470i
$867$	6.91870	−	21.2936i	0.234971	−	0.723167i
$868$	14.2011			0.482018
$869$		0			0
$870$	−22.1138			−0.749727
$871$	−4.14566	+	12.7590i	−0.140470	+	0.432323i
$872$	2.24120	−	1.62833i	0.0758967	−	0.0551422i
$873$	−1.48904	−	1.08185i	−0.0503962	−	0.0366150i
$874$	1.54109	+	4.74300i	0.0521283	+	0.160434i
$875$	−1.31579	−	4.04959i	−0.0444819	−	0.136901i
$876$	1.57934	+	1.14746i	0.0533610	+	0.0387690i
$877$	−39.1081	+	28.4137i	−1.32059	+	0.959462i	−0.320662	+	0.947194i	$0.603905\pi$
$877$	−39.1081	+	28.4137i	−1.32059	+	0.959462i	−0.999925	+	0.0122684i	$0.996095\pi$
$878$	20.4244	−	62.8597i	0.689289	−	2.12141i
$879$	−44.3137			−1.49466
$880$		0			0
$881$	−33.4457			−1.12682			−0.563408	−	0.826179i	$-0.690510\pi$
$881$	−33.4457			−1.12682			−0.563408	+	0.826179i	$0.690510\pi$
$882$	1.02888	−	3.16656i	0.0346441	−	0.106623i
$883$	−14.7772	+	10.7363i	−0.497294	+	0.361305i	−0.807982	−	0.589207i	$-0.799440\pi$
$883$	−14.7772	+	10.7363i	−0.497294	+	0.361305i	0.310689	+	0.950512i	$0.399440\pi$
$884$	−3.50852	−	2.54909i	−0.118004	−	0.0857352i
$885$	−6.61169	−	20.3487i	−0.222249	−	0.684013i
$886$	13.4858	+	41.5049i	0.453063	+	1.39438i
$887$	−12.6911	−	9.22065i	−0.426126	−	0.309599i	0.353972	−	0.935256i	$-0.384831\pi$
$887$	−12.6911	−	9.22065i	−0.426126	−	0.309599i	−0.780098	+	0.625657i	$0.784831\pi$
$888$	−7.99756	+	5.81057i	−0.268381	+	0.194990i
$889$	0.148864	−	0.458156i	0.00499273	−	0.0153661i
$890$	2.32805			0.0780366
$891$		0			0
$892$	23.2589			0.778764
$893$	0.574294	−	1.76749i	0.0192180	−	0.0591469i
$894$	3.00147	−	2.18070i	0.100384	−	0.0729334i
$895$	−10.0551	−	7.30549i	−0.336106	−	0.244196i
$896$	−9.21515	−	28.3613i	−0.307857	−	0.947485i
$897$	−3.28521	−	10.1108i	−0.109690	−	0.337591i
$898$	−37.7186	−	27.4042i	−1.25869	−	0.914488i
$899$	11.7759	−	8.55573i	0.392750	−	0.285349i
$900$	0.0748695	−	0.230425i	0.00249565	−	0.00768082i
$901$	13.9627			0.465165
$902$		0			0
$903$	−95.8710			−3.19039
$904$	3.13791	−	9.65749i	0.104365	−	0.321203i
$905$	−14.0034	+	10.1741i	−0.465490	+	0.338198i
$906$	−15.3628	−	11.1617i	−0.510395	−	0.370824i
$907$	−8.00205	−	24.6278i	−0.265704	−	0.817752i	−0.991530	−	0.129874i	$-0.958543\pi$
$907$	−8.00205	−	24.6278i	−0.265704	−	0.817752i	0.725827	−	0.687878i	$-0.241457\pi$
$908$	−5.40068	−	16.6216i	−0.179228	−	0.551607i
$909$	0.362065	+	0.263056i	0.0120089	+	0.00872500i
$910$	−8.78929	+	6.38579i	−0.291362	+	0.211687i
$911$	4.77511	−	14.6963i	0.158206	−	0.486909i	−0.840265	−	0.542176i	$-0.817601\pi$
$911$	4.77511	−	14.6963i	0.158206	−	0.486909i	0.998472	+	0.0552662i	$0.0176007\pi$
$912$	−5.08232			−0.168293
$913$		0			0
$914$	−11.0842			−0.366632
$915$	−3.12481	+	9.61718i	−0.103303	+	0.317934i
$916$	33.8389	−	24.5854i	1.11807	−	0.812325i
$917$	−1.63385	−	1.18706i	−0.0539546	−	0.0392003i
$918$	−6.14255	−	18.9048i	−0.202734	−	0.623952i
$919$	−14.7442	−	45.3781i	−0.486368	−	1.49689i	−0.829990	−	0.557778i	$-0.811654\pi$
$919$	−14.7442	−	45.3781i	−0.486368	−	1.49689i	0.343623	−	0.939108i	$-0.388346\pi$
$920$	−3.20719	−	2.33016i	−0.105738	−	0.0768231i
$921$	7.12632	−	5.17757i	0.234820	−	0.170607i
$922$	10.0633	−	30.9716i	0.331416	−	1.01999i
$923$	7.12495			0.234521
$924$		0			0
$925$	6.16951			0.202852
$926$	20.1128	−	61.9008i	0.660948	−	2.03419i
$927$	0.0523803	−	0.0380565i	0.00172039	−	0.00124994i
$928$	37.9362	+	27.5622i	1.24532	+	0.904775i
$929$	−11.6664	−	35.9056i	−0.382763	−	1.17802i	−0.938090	−	0.346391i	$-0.887407\pi$
$929$	−11.6664	−	35.9056i	−0.382763	−	1.17802i	0.555327	−	0.831632i	$-0.312593\pi$
$930$	2.26177	+	6.96102i	0.0741664	+	0.228261i
$931$	5.44323	+	3.95474i	0.178395	+	0.129611i
$932$	11.3123	−	8.21885i	0.370546	−	0.269217i
$933$	5.27015	−	16.2198i	0.172537	−	0.531014i
$934$	17.1957			0.562661
$935$		0			0
$936$	0.195488			0.00638972
$937$	15.3391	−	47.2088i	0.501105	−	1.54224i	−0.306116	−	0.951994i	$-0.599030\pi$
$937$	15.3391	−	47.2088i	0.501105	−	1.54224i	0.807221	−	0.590249i	$-0.200970\pi$
$938$	63.7474	−	46.3152i	2.08143	−	1.51225i
$939$	−38.8060	−	28.1942i	−1.26639	−	0.920084i
$940$	−1.44360	−	4.44296i	−0.0470852	−	0.144913i
$941$	−10.2961	−	31.6881i	−0.335643	−	1.03300i	−0.966405	−	0.257025i	$-0.917258\pi$
$941$	−10.2961	−	31.6881i	−0.335643	−	1.03300i	0.630762	−	0.775976i	$-0.282742\pi$
$942$	2.80874	+	2.04067i	0.0915136	+	0.0664885i
$943$	−26.3475	+	19.1426i	−0.857994	+	0.623369i
$944$	−17.5946	+	54.1506i	−0.572656	+	1.76245i
$945$	−21.4988			−0.699355
$946$		0			0
$947$	−22.6463			−0.735907			−0.367954	−	0.929844i	$-0.619941\pi$
$947$	−22.6463			−0.735907			−0.367954	+	0.929844i	$0.619941\pi$
$948$	4.73273	−	14.5658i	0.153712	−	0.473077i
$949$	0.795286	−	0.577809i	0.0258161	−	0.0187565i
$950$	0.917446	+	0.666564i	0.0297659	+	0.0216262i
$951$	7.81104	+	24.0399i	0.253290	+	0.779548i
$952$	−2.48914	−	7.66079i	−0.0806736	−	0.248288i
$953$	39.2679	+	28.5298i	1.27201	+	0.924171i	0.999281	−	0.0379197i	$-0.0120731\pi$
$953$	39.2679	+	28.5298i	1.27201	+	0.924171i	0.272731	+	0.962090i	$0.412073\pi$
$954$	1.61018	−	1.16986i	0.0521314	−	0.0378757i
$955$	−6.07228	+	18.6886i	−0.196494	+	0.604748i
$956$	−19.2306			−0.621962
$957$		0			0
$958$	76.6020			2.47490
$959$	1.14302	−	3.51785i	0.0369100	−	0.113597i
$960$	−5.47175	+	3.97546i	−0.176600	+	0.128307i
$961$	21.1819	+	15.3896i	0.683287	+	0.496437i
$962$	−4.86434	−	14.9709i	−0.156832	−	0.482681i
$963$	−0.758730	−	2.33513i	−0.0244497	−	0.0752485i
$964$	9.01277	+	6.54816i	0.290282	+	0.210902i
$965$	8.22092	−	5.97285i	0.264641	−	0.192273i
$966$	−19.2955	+	59.3855i	−0.620823	+	1.91070i
$967$	47.2983			1.52101			0.760505	−	0.649332i	$-0.224952\pi$
$967$	47.2983			1.52101			0.760505	+	0.649332i	$0.224952\pi$
$968$		0			0
$969$	−2.25480			−0.0724345
$970$	6.69182	−	20.5953i	0.214861	−	0.661276i
$971$	−15.5993	+	11.3335i	−0.500604	+	0.363710i	−0.809248	−	0.587468i	$-0.800125\pi$
$971$	−15.5993	+	11.3335i	−0.500604	+	0.363710i	0.308644	+	0.951178i	$0.400125\pi$
$972$	−2.03488	−	1.47843i	−0.0652689	−	0.0474207i
$973$	25.5124	+	78.5191i	0.817890	+	2.51721i
$974$	−15.1655	−	46.6746i	−0.485934	−	1.49555i
$975$	−1.95576	−	1.42094i	−0.0626343	−	0.0455065i
$976$	21.7704	−	15.8171i	0.696854	−	0.506294i
$977$	9.85058	−	30.3170i	0.315148	−	0.969926i	−0.660545	−	0.750786i	$-0.729675\pi$
$977$	9.85058	−	30.3170i	0.315148	−	0.969926i	0.975693	−	0.219140i	$-0.0703251\pi$
$978$	43.0549			1.37674
$979$		0			0
$980$	16.9127			0.540257
$981$	0.151421	−	0.466027i	0.00483451	−	0.0148791i
$982$	34.9098	−	25.3635i	1.11402	−	0.809381i
$983$	−1.29592	−	0.941538i	−0.0413333	−	0.0300304i	0.566927	−	0.823768i	$-0.308132\pi$
$983$	−1.29592	−	0.941538i	−0.0413333	−	0.0300304i	−0.608260	+	0.793738i	$0.708132\pi$
$984$	−3.66683	−	11.2853i	−0.116894	−	0.359763i
$985$	2.61235	+	8.04000i	0.0832365	+	0.256176i
$986$	21.1219	+	15.3460i	0.672659	+	0.488715i
$987$	18.8251	−	13.6772i	0.599209	−	0.435351i
$988$	0.386024	−	1.18806i	0.0122811	−	0.0377972i
$989$	55.7057			1.77134
$990$		0			0
$991$	48.3005			1.53432			0.767158	−	0.641458i	$-0.221670\pi$
$991$	48.3005			1.53432			0.767158	+	0.641458i	$0.221670\pi$
$992$	4.79603	−	14.7607i	0.152274	−	0.468651i
$993$	−12.3092	+	8.94315i	−0.390620	+	0.283802i
$994$	−33.8558	−	24.5977i	−1.07384	−	0.780191i
$995$	−2.01180	−	6.19170i	−0.0637785	−	0.196290i
$996$	−0.795093	−	2.44704i	−0.0251935	−	0.0775376i
$997$	−18.5004	−	13.4413i	−0.585913	−	0.425691i	0.254938	−	0.966957i	$-0.417945\pi$
$997$	−18.5004	−	13.4413i	−0.585913	−	0.425691i	−0.840851	+	0.541267i	$0.817945\pi$
$998$	39.7860	−	28.9063i	1.25941	−	0.915011i
$999$	9.62589	−	29.6254i	0.304550	−	0.937308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.n.251.2		8
11.2	odd	10		605.2.g.j.366.2		8
11.3	even	5		605.2.g.g.81.1		8
11.4	even	5		605.2.a.i.1.4		4
11.5	even	5	inner	605.2.g.n.511.2		8
11.6	odd	10		55.2.g.a.16.1	✓	8
11.7	odd	10		605.2.a.l.1.1		4
11.8	odd	10		605.2.g.j.81.2		8
11.9	even	5		605.2.g.g.366.1		8
11.10	odd	2		55.2.g.a.31.1	yes	8
33.17	even	10		495.2.n.f.181.2		8
33.26	odd	10		5445.2.a.bu.1.1		4
33.29	even	10		5445.2.a.bg.1.4		4
33.32	even	2		495.2.n.f.361.2		8
44.7	even	10		9680.2.a.cs.1.3		4
44.15	odd	10		9680.2.a.cv.1.3		4
44.39	even	10		880.2.bo.e.401.1		8
44.43	even	2		880.2.bo.e.801.1		8
55.4	even	10		3025.2.a.be.1.1		4
55.17	even	20		275.2.z.b.49.3		16
55.28	even	20		275.2.z.b.49.2		16
55.29	odd	10		3025.2.a.v.1.4		4
55.32	even	4		275.2.z.b.174.2		16
55.39	odd	10		275.2.h.b.126.2		8
55.43	even	4		275.2.z.b.174.3		16
55.54	odd	2		275.2.h.b.251.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.16.1	✓	8	11.6	odd	10
55.2.g.a.31.1	yes	8	11.10	odd	2
275.2.h.b.126.2		8	55.39	odd	10
275.2.h.b.251.2		8	55.54	odd	2
275.2.z.b.49.2		16	55.28	even	20
275.2.z.b.49.3		16	55.17	even	20
275.2.z.b.174.2		16	55.32	even	4
275.2.z.b.174.3		16	55.43	even	4
495.2.n.f.181.2		8	33.17	even	10
495.2.n.f.361.2		8	33.32	even	2
605.2.a.i.1.4		4	11.4	even	5
605.2.a.l.1.1		4	11.7	odd	10
605.2.g.g.81.1		8	11.3	even	5
605.2.g.g.366.1		8	11.9	even	5
605.2.g.j.81.2		8	11.8	odd	10
605.2.g.j.366.2		8	11.2	odd	10
605.2.g.n.251.2		8	1.1	even	1	trivial
605.2.g.n.511.2		8	11.5	even	5	inner
880.2.bo.e.401.1		8	44.39	even	10
880.2.bo.e.801.1		8	44.43	even	2
3025.2.a.v.1.4		4	55.29	odd	10
3025.2.a.be.1.1		4	55.4	even	10
5445.2.a.bg.1.4		4	33.29	even	10
5445.2.a.bu.1.1		4	33.26	odd	10
9680.2.a.cs.1.3		4	44.7	even	10
9680.2.a.cv.1.3		4	44.15	odd	10

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.579725 - 1.78421i) q^{2} +(1.43801 - 1.04478i) q^{3} +(-1.22929 - 0.893133i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-1.03045 - 3.17141i) q^{6} +(3.44479 + 2.50279i) q^{7} +(0.729292 - 0.529862i) q^{8} +(0.0492728 - 0.151646i) q^{9} +O(q^{10})\)	\(q+(0.579725 - 1.78421i) q^{2} +(1.43801 - 1.04478i) q^{3} +(-1.22929 - 0.893133i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-1.03045 - 3.17141i) q^{6} +(3.44479 + 2.50279i) q^{7} +(0.729292 - 0.529862i) q^{8} +(0.0492728 - 0.151646i) q^{9} +1.87603 q^{10} -2.70087 q^{12} +(-0.420275 + 1.29347i) q^{13} +(6.46253 - 4.69530i) q^{14} +(1.43801 + 1.04478i) q^{15} +(-1.46169 - 4.49862i) q^{16} +(-0.648486 - 1.99584i) q^{17} +(-0.242004 - 0.175826i) q^{18} +(0.489036 - 0.355305i) q^{19} +(0.469548 - 1.44512i) q^{20} +7.56852 q^{21} -4.39768 q^{23} +(0.495144 - 1.52390i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(2.06418 + 1.49972i) q^{26} +(1.56024 + 4.80192i) q^{27} +(-1.99933 - 6.15331i) q^{28} +(-5.36507 - 3.89795i) q^{29} +(2.69776 - 1.96004i) q^{30} +(-0.678271 + 2.08750i) q^{31} -7.07096 q^{32} -3.93693 q^{34} +(-1.31579 + 4.04959i) q^{35} +(-0.196011 + 0.142410i) q^{36} +(-4.99124 - 3.62634i) q^{37} +(-0.350433 - 1.07852i) q^{38} +(0.747032 + 2.29913i) q^{39} +(0.729292 + 0.529862i) q^{40} +(5.99124 - 4.35289i) q^{41} +(4.38766 - 13.5038i) q^{42} -12.6671 q^{43} +0.159450 q^{45} +(-2.54945 + 7.84639i) q^{46} +(2.48729 - 1.80712i) q^{47} +(-6.80200 - 4.94194i) q^{48} +(3.43952 + 10.5858i) q^{49} +(0.579725 + 1.78421i) q^{50} +(-3.01774 - 2.19252i) q^{51} +(1.67188 - 1.21469i) q^{52} +(-2.05605 + 6.32787i) q^{53} +9.47214 q^{54} +3.83839 q^{56} +(0.332025 - 1.02187i) q^{57} +(-10.0650 + 7.31267i) q^{58} +(-9.73827 - 7.07527i) q^{59} +(-0.834614 - 2.56868i) q^{60} +(1.75800 + 5.41056i) q^{61} +(3.33133 + 2.42036i) q^{62} +(0.549273 - 0.399070i) q^{63} +(-1.17583 + 3.61884i) q^{64} -1.36004 q^{65} +9.86416 q^{67} +(-0.985367 + 3.03265i) q^{68} +(-6.32393 + 4.59460i) q^{69} +(6.46253 + 4.69530i) q^{70} +(-1.61887 - 4.98238i) q^{71} +(-0.0444172 - 0.136702i) q^{72} +(-0.584753 - 0.424848i) q^{73} +(-9.36371 + 6.80313i) q^{74} +(-0.549273 + 1.69049i) q^{75} -0.918503 q^{76} +4.53520 q^{78} +(-1.75230 + 5.39303i) q^{79} +(3.82676 - 2.78030i) q^{80} +(7.64758 + 5.55629i) q^{81} +(-4.29320 - 13.2131i) q^{82} +(0.294384 + 0.906022i) q^{83} +(-9.30392 - 6.75969i) q^{84} +(1.69776 - 1.23349i) q^{85} +(-7.34342 + 22.6007i) q^{86} -11.7875 q^{87} +1.24095 q^{89} +(0.0924373 - 0.284493i) q^{90} +(-4.68505 + 3.40389i) q^{91} +(5.40603 + 3.92771i) q^{92} +(1.20562 + 3.71050i) q^{93} +(-1.78234 - 5.48548i) q^{94} +(0.489036 + 0.355305i) q^{95} +(-10.1681 + 7.38759i) q^{96} +(3.56701 - 10.9781i) q^{97} +20.8812 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 5 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 + q^3 - 6 * q^4 - 2 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 5 * q^9	\( 8 q + 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 5 q^{9} - 6 q^{10} - 28 q^{12} - 4 q^{13} + 16 q^{14} + q^{15} - 20 q^{16} - q^{17} - 14 q^{18} + q^{19} - q^{20} + 12 q^{21} - 18 q^{23} - 25 q^{24} - 2 q^{25} - 14 q^{26} + 10 q^{27} - 4 q^{28} - 19 q^{29} + 12 q^{30} + 6 q^{31} - 12 q^{32} - 20 q^{34} + 8 q^{35} + 21 q^{36} + 4 q^{37} - 6 q^{38} - 9 q^{39} + 2 q^{40} + 4 q^{41} + 29 q^{42} - 42 q^{43} + 41 q^{46} + 4 q^{47} - 19 q^{48} - 15 q^{49} + 4 q^{50} - 13 q^{51} + 26 q^{52} + 3 q^{53} + 40 q^{54} + 30 q^{56} + 5 q^{57} - 6 q^{58} - 19 q^{59} + 22 q^{60} + 2 q^{61} + 38 q^{62} - q^{63} + 6 q^{64} - 14 q^{65} - 2 q^{67} - 35 q^{68} - 21 q^{69} + 16 q^{70} + 40 q^{71} + 34 q^{72} + 23 q^{73} - 48 q^{74} + q^{75} - 16 q^{76} + 12 q^{78} - 17 q^{79} + 15 q^{80} + 2 q^{82} + 25 q^{83} + 4 q^{84} + 4 q^{85} - 31 q^{86} - 30 q^{87} + 16 q^{90} - 12 q^{91} + 81 q^{92} - 13 q^{93} - 33 q^{94} + q^{95} - 23 q^{96} + 12 q^{97} + 84 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 + q^3 - 6 * q^4 - 2 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 5 * q^9 - 6 * q^10 - 28 * q^12 - 4 * q^13 + 16 * q^14 + q^15 - 20 * q^16 - q^17 - 14 * q^18 + q^19 - q^20 + 12 * q^21 - 18 * q^23 - 25 * q^24 - 2 * q^25 - 14 * q^26 + 10 * q^27 - 4 * q^28 - 19 * q^29 + 12 * q^30 + 6 * q^31 - 12 * q^32 - 20 * q^34 + 8 * q^35 + 21 * q^36 + 4 * q^37 - 6 * q^38 - 9 * q^39 + 2 * q^40 + 4 * q^41 + 29 * q^42 - 42 * q^43 + 41 * q^46 + 4 * q^47 - 19 * q^48 - 15 * q^49 + 4 * q^50 - 13 * q^51 + 26 * q^52 + 3 * q^53 + 40 * q^54 + 30 * q^56 + 5 * q^57 - 6 * q^58 - 19 * q^59 + 22 * q^60 + 2 * q^61 + 38 * q^62 - q^63 + 6 * q^64 - 14 * q^65 - 2 * q^67 - 35 * q^68 - 21 * q^69 + 16 * q^70 + 40 * q^71 + 34 * q^72 + 23 * q^73 - 48 * q^74 + q^75 - 16 * q^76 + 12 * q^78 - 17 * q^79 + 15 * q^80 + 2 * q^82 + 25 * q^83 + 4 * q^84 + 4 * q^85 - 31 * q^86 - 30 * q^87 + 16 * q^90 - 12 * q^91 + 81 * q^92 - 13 * q^93 - 33 * q^94 + q^95 - 23 * q^96 + 12 * q^97 + 84 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more