LMFDB - Embedded newform 605.2.g.j.81.2

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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.2
Root			$1.43801 - 1.04478i$ of defining polynomial
Character	$\chi$	$=$	605.81
Dual form			605.2.g.j.366.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.51774 + 1.10270i) q^{2} +(-0.549273 + 1.69049i) q^{3} +(0.469548 + 1.44512i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-2.69776 + 1.96004i) q^{6} +(1.31579 + 4.04959i) q^{7} +(0.278565 - 0.857334i) q^{8} +(-0.128998 - 0.0937225i) q^{9} +O(q^{10})$	\(q+(1.51774 + 1.10270i) q^{2} +(-0.549273 + 1.69049i) q^{3} +(0.469548 + 1.44512i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-2.69776 + 1.96004i) q^{6} +(1.31579 + 4.04959i) q^{7} +(0.278565 - 0.857334i) q^{8} +(-0.128998 - 0.0937225i) q^{9} -1.87603 q^{10} -2.70087 q^{12} +(-1.10029 - 0.799410i) q^{13} +(-2.46847 + 7.59716i) q^{14} +(-0.549273 - 1.69049i) q^{15} +(3.82676 - 2.78030i) q^{16} +(-1.69776 + 1.23349i) q^{17} +(-0.0924373 - 0.284493i) q^{18} +(0.186795 - 0.574896i) q^{19} +(-1.22929 - 0.893133i) q^{20} -7.56852 q^{21} -4.39768 q^{23} +(1.29630 + 0.941821i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-0.788448 - 2.42659i) q^{26} +(-4.08475 + 2.96775i) q^{27} +(-5.23432 + 3.80296i) q^{28} +(-2.04927 - 6.30701i) q^{29} +(1.03045 - 3.17141i) q^{30} +(1.77574 + 1.29015i) q^{31} +7.07096 q^{32} -3.93693 q^{34} +(-3.44479 - 2.50279i) q^{35} +(0.0748695 - 0.230425i) q^{36} +(1.90648 + 5.86755i) q^{37} +(0.917446 - 0.666564i) q^{38} +(1.95576 - 1.42094i) q^{39} +(0.278565 + 0.857334i) q^{40} +(2.28845 - 7.04312i) q^{41} +(-11.4870 - 8.34583i) q^{42} +12.6671 q^{43} +0.159450 q^{45} +(-6.67453 - 4.84933i) q^{46} +(-0.950059 + 2.92398i) q^{47} +(2.59813 + 7.99623i) q^{48} +(-9.00479 + 6.54236i) q^{49} +(1.51774 - 1.10270i) q^{50} +(-1.15267 - 3.54757i) q^{51} +(0.638603 - 1.96542i) q^{52} +(5.38281 + 3.91084i) q^{53} -9.47214 q^{54} +3.83839 q^{56} +(0.869254 + 0.631550i) q^{57} +(3.84450 - 11.8321i) q^{58} +(3.71969 + 11.4480i) q^{59} +(2.18505 - 1.58753i) q^{60} +(4.60249 - 3.34391i) q^{61} +(1.27246 + 3.91622i) q^{62} +(0.209804 - 0.645709i) q^{63} +(3.07837 + 2.23656i) q^{64} +1.36004 q^{65} +9.86416 q^{67} +(-2.57973 - 1.87428i) q^{68} +(2.41553 - 7.43422i) q^{69} +(-2.46847 - 7.59716i) q^{70} +(4.23827 - 3.07928i) q^{71} +(-0.116286 + 0.0844866i) q^{72} +(-0.223356 - 0.687418i) q^{73} +(-3.57662 + 11.0077i) q^{74} +(1.43801 + 1.04478i) q^{75} +0.918503 q^{76} +4.53520 q^{78} +(-4.58758 - 3.33307i) q^{79} +(-1.46169 + 4.49862i) q^{80} +(-2.92111 - 8.99027i) q^{81} +(11.2397 - 8.16615i) q^{82} +(0.770708 - 0.559952i) q^{83} +(-3.55378 - 10.9374i) q^{84} +(0.648486 - 1.99584i) q^{85} +(19.2253 + 13.9680i) q^{86} +11.7875 q^{87} +1.24095 q^{89} +(0.242004 + 0.175826i) q^{90} +(1.78953 - 5.50760i) q^{91} +(-2.06492 - 6.35517i) q^{92} +(-3.15634 + 2.29322i) q^{93} +(-4.66623 + 3.39021i) q^{94} +(0.186795 + 0.574896i) q^{95} +(-3.88389 + 11.9534i) q^{96} +(-9.33856 - 6.78486i) q^{97} -20.8812 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - 12 q^{6} - 8 q^{7} - 7 q^{8} + 5 q^{9}+O(q^{10}) $ 8 * q + q^2 + q^3 - q^4 - 2 * q^5 - 12 * q^6 - 8 * q^7 - 7 * q^8 + 5 * q^9	$ 8 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - 12 q^{6} - 8 q^{7} - 7 q^{8} + 5 q^{9} + 6 q^{10} - 28 q^{12} - 11 q^{13} - 14 q^{14} + q^{15} + 15 q^{16} - 4 q^{17} - 16 q^{18} - 11 q^{19} - 6 q^{20} - 12 q^{21} - 18 q^{23} - 10 q^{24} - 2 q^{25} + q^{26} - 5 q^{27} - 11 q^{28} - 11 q^{29} + 13 q^{30} - 9 q^{31} + 12 q^{32} - 20 q^{34} - 3 q^{35} - 29 q^{36} - q^{37} - 6 q^{38} - 6 q^{39} - 7 q^{40} + 11 q^{41} - 31 q^{42} + 42 q^{43} + 29 q^{46} - q^{47} + 21 q^{48} + q^{50} - 22 q^{51} - q^{52} + 8 q^{53} - 40 q^{54} + 30 q^{56} + 4 q^{58} + 26 q^{59} - 8 q^{60} - 2 q^{61} + 27 q^{62} - 4 q^{63} + 21 q^{64} + 14 q^{65} - 2 q^{67} - 20 q^{68} + 49 q^{69} - 14 q^{70} - 25 q^{71} + 21 q^{72} + 32 q^{73} - 12 q^{74} + q^{75} + 16 q^{76} + 12 q^{78} - 23 q^{79} - 20 q^{80} + 20 q^{81} + 42 q^{82} + 10 q^{83} + 51 q^{84} + q^{85} + 34 q^{86} + 30 q^{87} + 14 q^{90} + 8 q^{91} - 99 q^{92} - 8 q^{93} - 22 q^{94} - 11 q^{95} + 3 q^{96} - 18 q^{97} - 84 q^{98}+O(q^{100}) $ 8 * q + q^2 + q^3 - q^4 - 2 * q^5 - 12 * q^6 - 8 * q^7 - 7 * q^8 + 5 * q^9 + 6 * q^10 - 28 * q^12 - 11 * q^13 - 14 * q^14 + q^15 + 15 * q^16 - 4 * q^17 - 16 * q^18 - 11 * q^19 - 6 * q^20 - 12 * q^21 - 18 * q^23 - 10 * q^24 - 2 * q^25 + q^26 - 5 * q^27 - 11 * q^28 - 11 * q^29 + 13 * q^30 - 9 * q^31 + 12 * q^32 - 20 * q^34 - 3 * q^35 - 29 * q^36 - q^37 - 6 * q^38 - 6 * q^39 - 7 * q^40 + 11 * q^41 - 31 * q^42 + 42 * q^43 + 29 * q^46 - q^47 + 21 * q^48 + q^50 - 22 * q^51 - q^52 + 8 * q^53 - 40 * q^54 + 30 * q^56 + 4 * q^58 + 26 * q^59 - 8 * q^60 - 2 * q^61 + 27 * q^62 - 4 * q^63 + 21 * q^64 + 14 * q^65 - 2 * q^67 - 20 * q^68 + 49 * q^69 - 14 * q^70 - 25 * q^71 + 21 * q^72 + 32 * q^73 - 12 * q^74 + q^75 + 16 * q^76 + 12 * q^78 - 23 * q^79 - 20 * q^80 + 20 * q^81 + 42 * q^82 + 10 * q^83 + 51 * q^84 + q^85 + 34 * q^86 + 30 * q^87 + 14 * q^90 + 8 * q^91 - 99 * q^92 - 8 * q^93 - 22 * q^94 - 11 * q^95 + 3 * q^96 - 18 * q^97 - 84 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.51774	+	1.10270i	1.07320	+	0.779729i	0.976485	−	0.215583i	$-0.0691652\pi$
$2$	1.51774	+	1.10270i	1.07320	+	0.779729i	0.0967188	+	0.995312i	$0.469165\pi$
$3$	−0.549273	+	1.69049i	−0.317123	+	0.976004i	0.657749	+	0.753237i	$0.271509\pi$
$3$	−0.549273	+	1.69049i	−0.317123	+	0.976004i	−0.974872	+	0.222767i	$0.928491\pi$
$4$	0.469548	+	1.44512i	0.234774	+	0.722560i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$6$	−2.69776	+	1.96004i	−1.10136	+	0.800182i
$7$	1.31579	+	4.04959i	0.497323	+	1.53060i	0.813305	+	0.581838i	$0.197666\pi$
$7$	1.31579	+	4.04959i	0.497323	+	1.53060i	−0.315982	+	0.948765i	$0.602334\pi$
$8$	0.278565	−	0.857334i	0.0984875	−	0.303113i
$9$	−0.128998	−	0.0937225i	−0.0429993	−	0.0312408i
$10$	−1.87603			−0.593253
$11$		0			0
$11$		0			0
$12$	−2.70087			−0.779673
$13$	−1.10029	−	0.799410i	−0.305167	−	0.221717i	0.424653	−	0.905356i	$-0.360396\pi$
$13$	−1.10029	−	0.799410i	−0.305167	−	0.221717i	−0.729820	+	0.683640i	$0.760396\pi$
$14$	−2.46847	+	7.59716i	−0.659726	+	2.03043i
$15$	−0.549273	−	1.69049i	−0.141822	−	0.436482i
$16$	3.82676	−	2.78030i	0.956689	−	0.695075i
$17$	−1.69776	+	1.23349i	−0.411767	+	0.299166i	−0.774317	−	0.632798i	$-0.781906\pi$
$17$	−1.69776	+	1.23349i	−0.411767	+	0.299166i	0.362550	+	0.931964i	$0.381906\pi$
$18$	−0.0924373	−	0.284493i	−0.0217877	−	0.0670556i
$19$	0.186795	−	0.574896i	0.0428537	−	0.131890i	−0.927341	−	0.374218i	$-0.877911\pi$
$19$	0.186795	−	0.574896i	0.0428537	−	0.131890i	0.970194	+	0.242328i	$0.0779110\pi$
$20$	−1.22929	−	0.893133i	−0.274878	−	0.199711i
$21$	−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	$0.651609\pi$
$24$	1.29630	+	0.941821i	0.264607	+	0.192248i
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	−0.788448	−	2.42659i	−0.154627	−	0.475894i
$27$	−4.08475	+	2.96775i	−0.786111	+	0.571143i
$28$	−5.23432	+	3.80296i	−0.989193	+	0.718691i
$29$	−2.04927	−	6.30701i	−0.380540	−	1.17118i	−0.939664	−	0.342099i	$-0.888862\pi$
$29$	−2.04927	−	6.30701i	−0.380540	−	1.17118i	0.559124	−	0.829084i	$-0.311138\pi$
$30$	1.03045	−	3.17141i	0.188134	−	0.579017i
$31$	1.77574	+	1.29015i	0.318932	+	0.231717i	0.735719	−	0.677286i	$-0.236844\pi$
$31$	1.77574	+	1.29015i	0.318932	+	0.231717i	−0.416788	+	0.909004i	$0.636844\pi$
$32$	7.07096			1.24998
$33$		0			0
$34$	−3.93693			−0.675179
$35$	−3.44479	−	2.50279i	−0.582276	−	0.423048i
$36$	0.0748695	−	0.230425i	0.0124783	−	0.0384041i
$37$	1.90648	+	5.86755i	0.313424	+	0.964619i	0.976398	+	0.215977i	$0.0692937\pi$
$37$	1.90648	+	5.86755i	0.313424	+	0.964619i	−0.662975	+	0.748642i	$0.730706\pi$
$38$	0.917446	−	0.666564i	0.148829	−	0.108131i
$39$	1.95576	−	1.42094i	0.313171	−	0.227532i
$40$	0.278565	+	0.857334i	0.0440449	+	0.135556i
$41$	2.28845	−	7.04312i	0.357396	−	1.09995i	−0.597212	−	0.802084i	$-0.703725\pi$
$41$	2.28845	−	7.04312i	0.357396	−	1.09995i	0.954607	−	0.297867i	$-0.0962752\pi$
$42$	−11.4870	−	8.34583i	−1.77249	−	1.28779i
$43$	12.6671			1.93171			0.965855	−	0.259084i	$-0.0834207\pi$
$43$	12.6671			1.93171			0.965855	+	0.259084i	$0.0834207\pi$
$44$		0			0
$45$	0.159450			0.0237694
$46$	−6.67453	−	4.84933i	−0.984106	−	0.714995i
$47$	−0.950059	+	2.92398i	−0.138580	+	0.426507i	−0.996130	−	0.0878951i	$-0.971986\pi$
$47$	−0.950059	+	2.92398i	−0.138580	+	0.426507i	0.857549	+	0.514402i	$0.171986\pi$
$48$	2.59813	+	7.99623i	0.375008	+	1.15416i
$49$	−9.00479	+	6.54236i	−1.28640	+	0.934623i
$50$	1.51774	−	1.10270i	0.214641	−	0.155946i
$51$	−1.15267	−	3.54757i	−0.161407	−	0.496759i
$52$	0.638603	−	1.96542i	0.0885583	−	0.272554i
$53$	5.38281	+	3.91084i	0.739385	+	0.537195i	0.892519	−	0.451011i	$-0.148936\pi$
$53$	5.38281	+	3.91084i	0.739385	+	0.537195i	−0.153133	+	0.988206i	$0.548936\pi$
$54$	−9.47214			−1.28899
$55$		0			0
$56$	3.83839			0.512926
$57$	0.869254	+	0.631550i	0.115135	+	0.0836508i
$58$	3.84450	−	11.8321i	0.504807	−	1.55364i
$59$	3.71969	+	11.4480i	0.484262	+	1.49041i	0.833047	+	0.553202i	$0.186594\pi$
$59$	3.71969	+	11.4480i	0.484262	+	1.49041i	−0.348785	+	0.937203i	$0.613406\pi$
$60$	2.18505	−	1.58753i	0.282088	−	0.204949i
$61$	4.60249	−	3.34391i	0.589289	−	0.428143i	−0.252772	−	0.967526i	$-0.581342\pi$
$61$	4.60249	−	3.34391i	0.589289	−	0.428143i	0.842061	+	0.539382i	$0.181342\pi$
$62$	1.27246	+	3.91622i	0.161602	+	0.497360i
$63$	0.209804	−	0.645709i	0.0264328	−	0.0813517i
$64$	3.07837	+	2.23656i	0.384796	+	0.279570i
$65$	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	$0.294152\pi$
$68$	−2.57973	−	1.87428i	−0.312838	−	0.227290i
$69$	2.41553	−	7.43422i	0.290795	−	0.894975i
$70$	−2.46847	−	7.59716i	−0.295038	−	0.908034i
$71$	4.23827	−	3.07928i	0.502990	−	0.365443i	−0.307168	−	0.951655i	$-0.599381\pi$
$71$	4.23827	−	3.07928i	0.502990	−	0.365443i	0.810158	+	0.586212i	$0.199381\pi$
$72$	−0.116286	+	0.0844866i	−0.0137044	+	0.00995684i
$73$	−0.223356	−	0.687418i	−0.0261418	−	0.0804562i	0.937134	−	0.348969i	$-0.113468\pi$
$73$	−0.223356	−	0.687418i	−0.0261418	−	0.0804562i	−0.963276	+	0.268512i	$0.913468\pi$
$74$	−3.57662	+	11.0077i	−0.415773	+	1.27962i
$75$	1.43801	+	1.04478i	0.166048	+	0.120641i
$76$	0.918503			0.105360
$77$		0			0
$78$	4.53520			0.513510
$79$	−4.58758	−	3.33307i	−0.516143	−	0.375000i	0.299006	−	0.954251i	$-0.403345\pi$
$79$	−4.58758	−	3.33307i	−0.516143	−	0.375000i	−0.815149	+	0.579251i	$0.803345\pi$
$80$	−1.46169	+	4.49862i	−0.163422	+	0.502961i
$81$	−2.92111	−	8.99027i	−0.324568	−	0.998919i
$82$	11.2397	−	8.16615i	1.24122	−	0.901800i
$83$	0.770708	−	0.559952i	0.0845962	−	0.0614627i	−0.544683	−	0.838642i	$-0.683350\pi$
$83$	0.770708	−	0.559952i	0.0845962	−	0.0614627i	0.629279	+	0.777179i	$0.283350\pi$
$84$	−3.55378	−	10.9374i	−0.387749	−	1.19337i
$85$	0.648486	−	1.99584i	0.0703382	−	0.216479i
$86$	19.2253	+	13.9680i	2.07312	+	1.50621i
$87$	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	$0.479050\pi$
$90$	0.242004	+	0.175826i	0.0255095	+	0.0185337i
$91$	1.78953	−	5.50760i	0.187594	−	0.577354i
$92$	−2.06492	−	6.35517i	−0.215283	−	0.662572i
$93$	−3.15634	+	2.29322i	−0.327298	+	0.237796i
$94$	−4.66623	+	3.39021i	−0.481285	+	0.349674i
$95$	0.186795	+	0.574896i	0.0191648	+	0.0589831i
$96$	−3.88389	+	11.9534i	−0.396398	+	1.21999i
$97$	−9.33856	−	6.78486i	−0.948187	−	0.688898i	0.00219020	−	0.999998i	$-0.499303\pi$
$97$	−9.33856	−	6.78486i	−0.948187	−	0.688898i	−0.950377	+	0.311099i	$0.899303\pi$
$98$	−20.8812			−2.10932
$99$		0			0
$100$	1.51949			0.151949
$101$	−2.27071	−	1.64977i	−0.225944	−	0.164158i	0.469054	−	0.883169i	$-0.344595\pi$
$101$	−2.27071	−	1.64977i	−0.225944	−	0.164158i	−0.694998	+	0.719011i	$0.744595\pi$
$102$	2.16245	−	6.65534i	0.214115	−	0.658977i
$103$	−0.125478	−	0.386181i	−0.0123637	−	0.0380516i	0.944684	−	0.327981i	$-0.106368\pi$
$103$	−0.125478	−	0.386181i	−0.0123637	−	0.0380516i	−0.957048	+	0.289929i	$0.906368\pi$
$104$	−0.991865	+	0.720632i	−0.0972603	+	0.0706638i
$105$	6.12306	−	4.44866i	0.597550	−	0.434145i
$106$	3.85721	+	11.8713i	0.374645	+	1.15304i
$107$	4.75841	−	14.6449i	0.460013	−	1.41577i	−0.405135	−	0.914257i	$-0.632776\pi$
$107$	4.75841	−	14.6449i	0.460013	−	1.41577i	0.865148	−	0.501517i	$-0.167224\pi$
$108$	−6.20673	−	4.50946i	−0.597243	−	0.433923i
$109$	−3.07312			−0.294352			−0.147176	−	0.989110i	$-0.547018\pi$
$109$	−3.07312			−0.294352			−0.147176	+	0.989110i	$0.547018\pi$
$110$		0			0
$111$	−10.9662			−1.04087
$112$	16.2943	+	11.8385i	1.53967	+	1.11863i
$113$	−3.48094	+	10.7132i	−0.327459	+	1.00782i	0.642859	+	0.765984i	$0.277748\pi$
$113$	−3.48094	+	10.7132i	−0.327459	+	1.00782i	−0.970318	+	0.241831i	$0.922252\pi$
$114$	0.622890	+	1.91706i	0.0583390	+	0.179549i
$115$	3.55780	−	2.58489i	0.331766	−	0.241042i
$116$	8.15215	−	5.92289i	0.756909	−	0.549926i
$117$	0.0670129	+	0.206245i	0.00619535	+	0.0190673i
$118$	−6.97824	+	21.4768i	−0.642399	+	1.97710i
$119$	−7.22905	−	5.25221i	−0.662686	−	0.481470i
$120$	−1.60232			−0.146271
$121$		0			0
$122$	10.6727			0.966263
$123$	10.6493	+	7.73719i	0.960217	+	0.697639i
$124$	−1.03062	+	3.17194i	−0.0925528	+	0.284848i
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$	1.03045	−	0.748667i	0.0918000	−	0.0666966i
$127$	−0.0915291	+	0.0664998i	−0.00812190	+	0.00590090i	−0.591839	−	0.806056i	$-0.701598\pi$
$127$	−0.0915291	+	0.0664998i	−0.00812190	+	0.00590090i	0.583717	+	0.811957i	$0.301598\pi$
$128$	−2.16420	−	6.66072i	−0.191290	−	0.588730i
$129$	−6.95768	+	21.4135i	−0.612589	+	1.88536i
$130$	2.06418	+	1.49972i	0.181041	+	0.131534i
$131$	0.474297			0.0414395			0.0207198	−	0.999785i	$-0.493404\pi$
$131$	0.474297			0.0414395			0.0207198	+	0.999785i	$0.493404\pi$
$132$		0			0
$133$	2.57388			0.223184
$134$	14.9712	+	10.8772i	1.29332	+	0.939650i
$135$	1.56024	−	4.80192i	0.134284	−	0.413283i
$136$	0.584581	+	1.79915i	0.0501274	+	0.154276i
$137$	0.702787	−	0.510605i	0.0600431	−	0.0436239i	−0.557359	−	0.830272i	$-0.688185\pi$
$137$	0.702787	−	0.510605i	0.0600431	−	0.0436239i	0.617402	+	0.786648i	$0.288185\pi$
$138$	11.8639	−	8.61961i	1.00992	−	0.733750i
$139$	5.99165	+	18.4404i	0.508205	+	1.56409i	0.795315	+	0.606196i	$0.207305\pi$
$139$	5.99165	+	18.4404i	0.508205	+	1.56409i	−0.287110	+	0.957898i	$0.592695\pi$
$140$	1.99933	−	6.15331i	0.168974	−	0.520050i
$141$	−4.42111	−	3.21213i	−0.372325	−	0.270510i
$142$	9.82812			0.824758
$143$		0			0
$144$	−0.754221			−0.0628517
$145$	5.36507	+	3.89795i	0.445544	+	0.323707i
$146$	0.419022	−	1.28962i	0.0346785	−	0.106730i
$147$	−6.11370	−	18.8160i	−0.504249	−	1.55192i
$148$	−7.58412	+	5.51019i	−0.623411	+	0.452935i
$149$	0.900095	−	0.653957i	0.0737387	−	0.0535743i	−0.550305	−	0.834964i	$-0.685489\pi$
$149$	0.900095	−	0.653957i	0.0737387	−	0.0535743i	0.624044	+	0.781389i	$0.285489\pi$
$150$	1.03045	+	3.17141i	0.0841361	+	0.258944i
$151$	1.75974	−	5.41594i	0.143206	−	0.440743i	−0.853570	−	0.520978i	$-0.825567\pi$
$151$	1.75974	−	5.41594i	0.143206	−	0.440743i	0.996776	+	0.0802356i	$0.0255673\pi$
$152$	−0.440844	−	0.320292i	−0.0357571	−	0.0259791i
$153$	0.334614			0.0270519
$154$		0			0
$155$	−2.19493			−0.176301
$156$	2.97175	+	2.15910i	0.237930	+	0.172866i
$157$	0.321729	−	0.990181i	0.0256768	−	0.0790250i	−0.937397	−	0.348263i	$-0.886772\pi$
$157$	0.321729	−	0.990181i	0.0256768	−	0.0790250i	0.963074	+	0.269238i	$0.0867717\pi$
$158$	−3.28737	−	10.1175i	−0.261529	−	0.804903i
$159$	−9.56785	+	6.95145i	−0.758780	+	0.551286i
$160$	−5.72053	+	4.15621i	−0.452247	+	0.328577i
$161$	−5.78644	−	17.8088i	−0.456035	−	1.40353i
$162$	5.48010	−	16.8660i	0.430557	−	1.32512i
$163$	10.4456	+	7.58920i	0.818165	+	0.594432i	0.916186	−	0.400753i	$-0.131251\pi$
$163$	10.4456	+	7.58920i	0.818165	+	0.594432i	−0.0980213	+	0.995184i	$0.531251\pi$
$164$	11.2527			0.878687
$165$		0			0
$166$	1.78720			0.138713
$167$	−3.41892	−	2.48399i	−0.264564	−	0.192217i	0.447593	−	0.894237i	$-0.352281\pi$
$167$	−3.41892	−	2.48399i	−0.264564	−	0.192217i	−0.712157	+	0.702021i	$0.752281\pi$
$168$	−2.10832	+	6.48875i	−0.162661	+	0.500618i
$169$	−3.44563	−	10.6046i	−0.265049	−	0.815736i
$170$	3.18505	−	2.31407i	0.244282	−	0.177481i
$171$	−0.0779769	+	0.0566535i	−0.00596304	+	0.00433241i
$172$	5.94779	+	18.3054i	0.453515	+	1.39578i
$173$	0.415847	−	1.27984i	0.0316162	−	0.0973048i	−0.934003	−	0.357265i	$-0.883709\pi$
$173$	0.415847	−	1.27984i	0.0316162	−	0.0973048i	0.965619	+	0.259960i	$0.0837094\pi$
$174$	17.8904	+	12.9982i	1.35627	+	0.985387i
$175$	4.25800			0.321874
$176$		0			0
$177$	−21.3959			−1.60821
$178$	1.88344	+	1.36840i	0.141169	+	0.102566i
$179$	3.84072	−	11.8205i	0.287069	−	0.883508i	−0.698702	−	0.715413i	$-0.746239\pi$
$179$	3.84072	−	11.8205i	0.287069	−	0.883508i	0.985771	−	0.168095i	$-0.0537614\pi$
$180$	0.0748695	+	0.230425i	0.00558044	+	0.0171748i
$181$	−14.0034	+	10.1741i	−1.04087	+	0.756234i	−0.970455	−	0.241284i	$-0.922431\pi$
$181$	−14.0034	+	10.1741i	−1.04087	+	0.756234i	−0.0704121	+	0.997518i	$0.522431\pi$
$182$	8.78929	−	6.38579i	0.651505	−	0.473346i
$183$	3.12481	+	9.61718i	0.230993	+	0.710922i
$184$	−1.22504	+	3.77028i	−0.0903110	+	0.277949i
$185$	−4.99124	−	3.62634i	−0.366963	−	0.266614i
$186$	−7.31925			−0.536673
$187$		0			0
$188$	−4.67160			−0.340712
$189$	−17.3929	−	12.6367i	−1.26514	−	0.919181i
$190$	−0.350433	+	1.07852i	−0.0254231	+	0.0782443i
$191$	−6.07228	−	18.6886i	−0.439375	−	1.35226i	−0.888536	−	0.458806i	$-0.848277\pi$
$191$	−6.07228	−	18.6886i	−0.439375	−	1.35226i	0.449162	−	0.893451i	$-0.351723\pi$
$192$	−5.47175	+	3.97546i	−0.394889	+	0.286904i
$193$	−8.22092	+	5.97285i	−0.591754	+	0.429935i	−0.842943	−	0.538003i	$-0.819179\pi$
$193$	−8.22092	+	5.97285i	−0.591754	+	0.429935i	0.251188	+	0.967938i	$0.419179\pi$
$194$	−6.69182	−	20.5953i	−0.480445	−	1.47866i
$195$	−0.747032	+	2.29913i	−0.0534961	+	0.164644i
$196$	−13.6827	−	9.94104i	−0.977334	−	0.710074i
$197$	−8.45375			−0.602305			−0.301152	−	0.953576i	$-0.597371\pi$
$197$	−8.45375			−0.602305			−0.301152	+	0.953576i	$0.597371\pi$
$198$		0			0
$199$	−6.51033			−0.461505			−0.230753	−	0.973012i	$-0.574119\pi$
$199$	−6.51033			−0.461505			−0.230753	+	0.973012i	$0.574119\pi$
$200$	−0.729292	−	0.529862i	−0.0515687	−	0.0374669i
$201$	−5.41811	+	16.6752i	−0.382164	+	1.17618i
$202$	−1.62714	−	5.00783i	−0.114485	−	0.352350i
$203$	22.8444	−	16.5974i	1.60336	−	1.16491i
$204$	4.58542	−	3.33150i	0.321044	−	0.233252i
$205$	2.28845	+	7.04312i	0.159832	+	0.491913i
$206$	0.235400	−	0.724487i	0.0164011	−	0.0504774i
$207$	0.567292	+	0.412162i	0.0394295	+	0.0286472i
$208$	−6.43316			−0.446059
$209$		0			0
$210$	14.1988			0.979808
$211$	−3.24742	−	2.35939i	−0.223562	−	0.162427i	0.470367	−	0.882471i	$-0.344122\pi$
$211$	−3.24742	−	2.35939i	−0.223562	−	0.162427i	−0.693928	+	0.720044i	$0.744122\pi$
$212$	−3.12414	+	9.61512i	−0.214567	+	0.660369i
$213$	2.87752	+	8.85611i	0.197165	+	0.606810i
$214$	23.3710	−	16.9800i	1.59761	−	1.16073i
$215$	−10.2479	+	7.44551i	−0.698899	+	0.507780i
$216$	1.40648	+	4.32871i	0.0956990	+	0.294531i
$217$	−2.88807	+	8.88858i	−0.196055	+	0.603396i
$218$	−4.66420	−	3.38874i	−0.315899	−	0.229514i
$219$	1.28476			0.0868158
$220$		0			0
$221$	2.85410			0.191988
$222$	−16.6438	−	12.0925i	−1.11706	−	0.811593i
$223$	4.73013	−	14.5578i	0.316753	−	0.974866i	−0.658274	−	0.752779i	$-0.728713\pi$
$223$	4.73013	−	14.5578i	0.316753	−	0.974866i	0.975027	−	0.222087i	$-0.0712869\pi$
$224$	9.30392	+	28.6345i	0.621644	+	1.91322i
$225$	−0.128998	+	0.0937225i	−0.00859986	+	0.00624817i
$226$	−17.0967	+	12.4215i	−1.13725	+	0.826263i
$227$	3.55428	+	10.9389i	0.235906	+	0.726043i	0.997000	+	0.0774017i	$0.0246624\pi$
$227$	3.55428	+	10.9389i	0.235906	+	0.726043i	−0.761094	+	0.648641i	$0.775338\pi$
$228$	−0.504509	+	1.55272i	−0.0334119	+	0.102831i
$229$	22.2699	+	16.1801i	1.47164	+	1.06921i	0.980134	+	0.198334i	$0.0635531\pi$
$229$	22.2699	+	16.1801i	1.47164	+	1.06921i	0.491505	+	0.870875i	$0.336447\pi$
$230$	8.25018			0.544001
$231$		0			0
$232$	−5.97807			−0.392480
$233$	−7.44479	−	5.40896i	−0.487724	−	0.354353i	0.316584	−	0.948564i	$-0.397464\pi$
$233$	−7.44479	−	5.40896i	−0.487724	−	0.354353i	−0.804309	+	0.594212i	$0.797464\pi$
$234$	−0.125718	+	0.386921i	−0.00821846	+	0.0252938i
$235$	−0.950059	−	2.92398i	−0.0619750	−	0.190740i
$236$	−14.7972	+	10.7508i	−0.963215	+	0.699816i
$237$	8.15435	−	5.92449i	0.529682	−	0.384837i
$238$	−5.18019	−	15.9430i	−0.335782	−	1.03343i
$239$	3.91091	−	12.0365i	0.252976	−	0.778579i	−0.741246	−	0.671234i	$-0.765765\pi$
$239$	3.91091	−	12.0365i	0.252976	−	0.778579i	0.994222	−	0.107346i	$-0.0342352\pi$
$240$	−6.80200	−	4.94194i	−0.439067	−	0.319001i
$241$	7.33167			0.472275			0.236137	−	0.971720i	$-0.424118\pi$
$241$	7.33167			0.472275			0.236137	+	0.971720i	$0.424118\pi$
$242$		0			0
$243$	1.65533			0.106190
$244$	6.99343	+	5.08103i	0.447709	+	0.325279i
$245$	3.43952	−	10.5858i	0.219743	−	0.676300i
$246$	7.63109	+	23.4861i	0.486541	+	1.49742i
$247$	−0.665108	+	0.483229i	−0.0423198	+	0.0307471i
$248$	1.60074	−	1.16301i	0.101647	−	0.0738512i
$249$	0.523263	+	1.61044i	0.0331605	+	0.102057i
$250$	−0.579725	+	1.78421i	−0.0366650	+	0.112843i
$251$	−25.2881	−	18.3729i	−1.59617	−	1.15969i	−0.894381	−	0.447306i	$-0.852383\pi$
$251$	−25.2881	−	18.3729i	−1.59617	−	1.15969i	−0.701792	−	0.712382i	$-0.747617\pi$
$252$	1.03164			0.0649872
$253$		0			0
$254$	−0.212247			−0.0133176
$255$	3.01774	+	2.19252i	0.188978	+	0.137301i
$256$	6.41177	−	19.7334i	0.400735	−	1.23334i
$257$	−2.57111	−	7.91306i	−0.160381	−	0.493603i	0.838285	−	0.545232i	$-0.183559\pi$
$257$	−2.57111	−	7.91306i	−0.160381	−	0.493603i	−0.998666	+	0.0516293i	$0.983559\pi$
$258$	−34.1727	+	24.8279i	−2.12750	+	1.54572i
$259$	−21.2527	+	15.4410i	−1.32058	+	0.959455i
$260$	0.638603	+	1.96542i	0.0396045	+	0.121890i
$261$	−0.326757	+	1.00565i	−0.0202258	+	0.0622485i
$262$	0.719859	+	0.523008i	0.0444731	+	0.0323116i
$263$	−2.87171			−0.177077			−0.0885386	−	0.996073i	$-0.528220\pi$
$263$	−2.87171			−0.177077			−0.0885386	+	0.996073i	$0.528220\pi$
$264$		0			0
$265$	−6.65351			−0.408722
$266$	3.90648	+	2.83823i	0.239522	+	0.174023i
$267$	−0.681619	+	2.09781i	−0.0417144	+	0.128384i
$268$	4.63169	+	14.2549i	0.282926	+	0.870756i
$269$	0.100294	−	0.0728678i	0.00611503	−	0.00444283i	−0.584724	−	0.811233i	$-0.698797\pi$
$269$	0.100294	−	0.0728678i	0.00611503	−	0.00444283i	0.590839	+	0.806790i	$0.298797\pi$
$270$	7.66312	−	5.56758i	0.466363	−	0.338832i
$271$	−5.26344	−	16.1992i	−0.319731	−	0.984031i	−0.973763	−	0.227564i	$-0.926924\pi$
$271$	−5.26344	−	16.1992i	−0.319731	−	0.984031i	0.654032	−	0.756467i	$-0.273076\pi$
$272$	−3.06743	+	9.44057i	−0.185990	+	0.572418i
$273$	8.32760	+	6.05035i	0.504009	+	0.366184i
$274$	1.62969			0.0984534
$275$		0			0
$276$	11.8775			0.714944
$277$	−18.3979	−	13.3669i	−1.10542	−	0.803138i	−0.123487	−	0.992346i	$-0.539408\pi$
$277$	−18.3979	−	13.3669i	−1.10542	−	0.803138i	−0.981937	+	0.189208i	$0.939408\pi$
$278$	−11.2405	+	34.5947i	−0.674161	+	2.07485i
$279$	−0.108150	−	0.332853i	−0.00647480	−	0.0199274i
$280$	−3.10532	+	2.25615i	−0.185578	+	0.134831i
$281$	10.4767	−	7.61178i	0.624988	−	0.454081i	−0.229672	−	0.973268i	$-0.573765\pi$
$281$	10.4767	−	7.61178i	0.624988	−	0.454081i	0.854660	+	0.519187i	$0.173765\pi$
$282$	−3.16808	−	9.75035i	−0.188656	−	0.580625i
$283$	4.88798	−	15.0437i	0.290560	−	0.894253i	−0.694116	−	0.719863i	$-0.744205\pi$
$283$	4.88798	−	15.0437i	0.290560	−	0.894253i	0.984677	−	0.174390i	$-0.0557954\pi$
$284$	6.44000	+	4.67893i	0.382144	+	0.277644i
$285$	−1.07446			−0.0636453
$286$		0			0
$287$	31.5329			1.86133
$288$	−0.912140	−	0.662708i	−0.0537483	−	0.0390505i
$289$	−3.89241	+	11.9796i	−0.228965	+	0.704683i
$290$	3.84450	+	11.8321i	0.225757	+	0.694808i
$291$	16.5991	−	12.0600i	0.973059	−	0.706969i
$292$	0.888525	−	0.645551i	0.0519970	−	0.0377780i
$293$	−7.70397	−	23.7104i	−0.450071	−	1.38518i	−0.876826	−	0.480809i	$-0.840343\pi$
$293$	−7.70397	−	23.7104i	−0.450071	−	1.38518i	0.426755	−	0.904367i	$-0.359657\pi$
$294$	11.4695	−	35.2994i	0.668914	−	2.05870i
$295$	−9.73827	−	7.07527i	−0.566984	−	0.411938i
$296$	5.56153			0.323257
$297$		0			0
$298$	2.08723			0.120910
$299$	4.83874	+	3.51555i	0.279832	+	0.203310i
$300$	−0.834614	+	2.56868i	−0.0481864	+	0.148303i
$301$	16.6672	+	51.2965i	0.960684	+	2.95668i
$302$	8.64300	−	6.27951i	0.497349	−	0.361345i
$303$	4.03615	−	2.93243i	0.231871	−	0.168464i
$304$	−0.883566	−	2.71934i	−0.0506760	−	0.155965i
$305$	−1.75800	+	5.41056i	−0.100663	+	0.309807i
$306$	0.507857	+	0.368979i	0.0290322	+	0.0210931i
$307$	−4.95566			−0.282835			−0.141417	−	0.989950i	$-0.545166\pi$
$307$	−4.95566			−0.282835			−0.141417	+	0.989950i	$0.545166\pi$
$308$		0			0
$309$	0.721756			0.0410593
$310$	−3.33133	−	2.42036i	−0.189207	−	0.137467i
$311$	−2.96495	+	9.12517i	−0.168127	+	0.517441i	−0.999253	−	0.0386427i	$-0.987697\pi$
$311$	−2.96495	+	9.12517i	−0.168127	+	0.517441i	0.831126	+	0.556084i	$0.187697\pi$
$312$	−0.673415	−	2.07256i	−0.0381246	−	0.117336i
$313$	21.8320	−	15.8619i	1.23402	−	0.896566i	0.236833	−	0.971550i	$-0.423891\pi$
$313$	21.8320	−	15.8619i	1.23402	−	0.896566i	0.997185	+	0.0749844i	$0.0238907\pi$
$314$	1.58018	−	1.14807i	0.0891745	−	0.0647891i
$315$	0.209804	+	0.645709i	0.0118211	+	0.0363816i
$316$	2.66260	−	8.19464i	0.149783	−	0.460984i
$317$	11.5048	+	8.35872i	0.646173	+	0.469472i	0.861965	−	0.506967i	$-0.169233\pi$
$317$	11.5048	+	8.35872i	0.646173	+	0.469472i	−0.215792	+	0.976439i	$0.569233\pi$
$318$	−22.1869			−1.24418
$319$		0			0
$320$	−3.80507			−0.212710
$321$	22.1433	+	16.0881i	1.23592	+	0.897948i
$322$	10.8555	−	33.4099i	0.604955	−	1.86186i
$323$	0.391998	+	1.20645i	0.0218114	+	0.0671285i
$324$	11.6204	−	8.44272i	0.645578	−	0.469040i
$325$	−1.10029	+	0.799410i	−0.0610333	+	0.0443433i
$326$	7.48513	+	23.0369i	0.414563	+	1.27589i
$327$	1.68798	−	5.19507i	0.0933456	−	0.287288i
$328$	−5.40082	−	3.92393i	−0.298211	−	0.216663i
$329$	−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	$0.575590\pi$
$332$	1.17108	+	0.850841i	0.0642715	+	0.0466960i
$333$	0.303989	−	0.935582i	0.0166585	−	0.0512696i
$334$	−2.44993	−	7.54010i	−0.134054	−	0.412576i
$335$	−7.98027	+	5.79801i	−0.436009	+	0.316779i
$336$	−28.9629	+	21.0428i	−1.58006	+	1.14798i
$337$	−4.84666	−	14.9165i	−0.264014	−	0.812552i	−0.991919	−	0.126874i	$-0.959506\pi$
$337$	−4.84666	−	14.9165i	−0.264014	−	0.812552i	0.727905	−	0.685678i	$-0.240494\pi$
$338$	6.46411	−	19.8945i	0.351601	−	1.08212i
$339$	−16.1986	−	11.7690i	−0.879787	−	0.639203i
$340$	3.18872			0.172932
$341$		0			0
$342$	−0.180821			−0.00977766
$343$	−14.2288	−	10.3378i	−0.768284	−	0.558191i
$344$	3.52860	−	10.8599i	0.190249	−	0.585527i
$345$	2.41553	+	7.43422i	0.130048	+	0.400245i
$346$	2.04243	−	1.48392i	0.109802	−	0.0797758i
$347$	−6.03129	+	4.38199i	−0.323777	+	0.235238i	−0.737785	−	0.675035i	$-0.764128\pi$
$347$	−6.03129	+	4.38199i	−0.323777	+	0.235238i	0.414009	+	0.910273i	$0.364128\pi$
$348$	5.53481	+	17.0344i	0.296697	+	0.913140i
$349$	−9.41678	+	28.9819i	−0.504069	+	1.55136i	0.298262	+	0.954484i	$0.403593\pi$
$349$	−9.41678	+	28.9819i	−0.504069	+	1.55136i	−0.802331	+	0.596880i	$0.796407\pi$
$350$	6.46253	+	4.69530i	0.345437	+	0.250975i
$351$	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	$0.654566\pi$
$354$	−32.4734	−	23.5933i	−1.72594	−	1.25397i
$355$	−1.61887	+	4.98238i	−0.0859209	+	0.264437i
$356$	0.582684	+	1.79332i	0.0308822	+	0.0950456i
$357$	12.8495	−	9.33573i	0.680069	−	0.494099i
$358$	18.8637	−	13.7053i	0.996980	−	0.724348i
$359$	−0.928386	−	2.85728i	−0.0489984	−	0.150801i	0.923564	−	0.383445i	$-0.125262\pi$
$359$	−0.928386	−	2.85728i	−0.0489984	−	0.150801i	−0.972562	+	0.232644i	$0.925262\pi$
$360$	0.0444172	−	0.136702i	0.00234099	−	0.00720483i
$361$	15.0757	+	10.9531i	0.793458	+	0.576481i
$362$	−32.4726			−1.70672
$363$		0			0
$364$	8.79941			0.461215
$365$	0.584753	+	0.424848i	0.0306074	+	0.0222376i
$366$	−5.86224	+	18.0421i	−0.306424	+	0.943076i
$367$	1.91071	+	5.88057i	0.0997384	+	0.306963i	0.988460	−	0.151485i	$-0.0484055\pi$
$367$	1.91071	+	5.88057i	0.0997384	+	0.306963i	−0.888721	+	0.458448i	$0.848406\pi$
$368$	−16.8288	+	12.2269i	−0.877264	+	0.637370i
$369$	−0.955304	+	0.694069i	−0.0497311	+	0.0361318i
$370$	−3.57662	−	11.0077i	−0.185940	−	0.572263i
$371$	−8.75465	+	26.9440i	−0.454519	+	1.39886i
$372$	−4.79603	−	3.48452i	−0.248662	−	0.180664i
$373$	20.8707			1.08064			0.540321	−	0.841459i	$-0.318303\pi$
$373$	20.8707			1.08064			0.540321	+	0.841459i	$0.318303\pi$
$374$		0			0
$375$	−1.77748			−0.0917889
$376$	2.24218	+	1.62904i	0.115631	+	0.0840111i
$377$	−2.78709	+	8.57778i	−0.143542	+	0.441778i
$378$	−12.4634	−	38.3583i	−0.641047	−	1.97294i
$379$	1.99361	−	1.44844i	0.102405	−	0.0744016i	−0.535404	−	0.844596i	$-0.679841\pi$
$379$	1.99361	−	1.44844i	0.102405	−	0.0744016i	0.637809	+	0.770194i	$0.279841\pi$
$380$	−0.743085	+	0.539882i	−0.0381194	+	0.0276954i
$381$	−0.0621427	−	0.191255i	−0.00318367	−	0.00979831i
$382$	11.3918	−	35.0603i	0.582854	−	1.79384i
$383$	−13.9180	−	10.1120i	−0.711177	−	0.516700i	0.172376	−	0.985031i	$-0.444856\pi$
$383$	−13.9180	−	10.1120i	−0.711177	−	0.516700i	−0.883553	+	0.468331i	$0.844856\pi$
$384$	12.4486			0.635265
$385$		0			0
$386$	−19.0635			−0.970306
$387$	−1.63403	−	1.18719i	−0.0830622	−	0.0603482i
$388$	5.42003	−	16.6812i	0.275161	−	0.846857i
$389$	−5.57923	−	17.1711i	−0.282878	−	0.870609i	−0.987027	−	0.160557i	$-0.948671\pi$
$389$	−5.57923	−	17.1711i	−0.282878	−	0.870609i	0.704148	−	0.710053i	$-0.251329\pi$
$390$	−3.66906	+	2.66572i	−0.185790	+	0.134984i
$391$	7.46620	−	5.42451i	0.377582	−	0.274329i
$392$	3.10057	+	9.54258i	0.156603	+	0.481973i
$393$	−0.260518	+	0.801793i	−0.0131414	+	0.0404451i
$394$	−12.8306	−	9.32198i	−0.646396	−	0.469634i
$395$	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	$0.638026\pi$
$398$	−9.88100	−	7.17896i	−0.495290	−	0.359849i
$399$	−1.41376	+	4.35111i	−0.0707767	+	0.217828i
$400$	−1.46169	−	4.49862i	−0.0730846	−	0.224931i
$401$	−23.4125	+	17.0102i	−1.16917	+	0.849449i	−0.990909	−	0.134535i	$-0.957046\pi$
$401$	−23.4125	+	17.0102i	−1.16917	+	0.849449i	−0.178257	+	0.983984i	$0.557046\pi$
$402$	−26.6111	+	19.3341i	−1.32724	+	0.964298i
$403$	−0.922474	−	2.83908i	−0.0459517	−	0.141425i
$404$	1.31790	−	4.05609i	0.0655681	−	0.201798i
$405$	7.64758	+	5.55629i	0.380011	+	0.276094i
$406$	52.9740			2.62905
$407$		0			0
$408$	−3.36254			−0.166471
$409$	24.1680	+	17.5591i	1.19503	+	0.868239i	0.993787	−	0.111302i	$-0.0355021\pi$
$409$	24.1680	+	17.5591i	1.19503	+	0.868239i	0.201242	+	0.979541i	$0.435502\pi$
$410$	−4.29320	+	13.2131i	−0.212026	+	0.652549i
$411$	0.477149	+	1.46851i	0.0235360	+	0.0724365i
$412$	0.499160	−	0.362661i	0.0245918	−	0.0178670i
$413$	−41.4655	+	30.1265i	−2.04038	+	1.48243i
$414$	0.406510	+	1.25111i	0.0199789	+	0.0614886i
$415$	−0.294384	+	0.906022i	−0.0144508	+	0.0444749i
$416$	−7.78013	−	5.65260i	−0.381452	−	0.277141i
$417$	−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	$0.564971\pi$
$420$	9.30392	+	6.75969i	0.453985	+	0.329839i
$421$	−7.06635	+	21.7480i	−0.344393	+	1.05993i	0.617516	+	0.786559i	$0.288139\pi$
$421$	−7.06635	+	21.7480i	−0.344393	+	1.05993i	−0.961908	+	0.273373i	$0.911861\pi$
$422$	−2.32704	−	7.16188i	−0.113278	−	0.348635i
$423$	0.396599	−	0.288146i	0.0192833	−	0.0140101i
$424$	4.85235	−	3.52544i	0.235651	−	0.171211i
$425$	0.648486	+	1.99584i	0.0314562	+	0.0968122i
$426$	−5.39832	+	16.6143i	−0.261549	+	0.804966i
$427$	19.5974	+	14.2383i	0.948385	+	0.689042i
$428$	23.3979			1.13098
$429$		0			0
$430$	−23.7638			−1.14599
$431$	16.4730	+	11.9683i	0.793475	+	0.576494i	0.908993	−	0.416812i	$-0.136853\pi$
$431$	16.4730	+	11.9683i	0.793475	+	0.576494i	−0.115517	+	0.993305i	$0.536853\pi$
$432$	−7.38013	+	22.7137i	−0.355076	+	1.09281i
$433$	6.60952	+	20.3420i	0.317633	+	0.977575i	0.974657	+	0.223705i	$0.0718153\pi$
$433$	6.60952	+	20.3420i	0.317633	+	0.977575i	−0.657023	+	0.753870i	$0.728185\pi$
$434$	−14.1848	+	10.3059i	−0.680893	+	0.494697i
$435$	−9.53632	+	6.92854i	−0.457232	+	0.332198i
$436$	−1.44298	−	4.44103i	−0.0691061	−	0.212687i
$437$	−0.821465	+	2.52821i	−0.0392960	+	0.120941i
$438$	1.94993	+	1.41670i	0.0931710	+	0.0676927i
$439$	−35.2311			−1.68149			−0.840744	−	0.541432i	$-0.817882\pi$
$439$	−35.2311			−1.68149			−0.840744	+	0.541432i	$0.817882\pi$
$440$		0			0
$441$	1.77477			0.0845127
$442$	4.33178	+	3.14723i	0.206042	+	0.149698i
$443$	7.18845	−	22.1238i	0.341534	−	1.05113i	−0.621880	−	0.783113i	$-0.713631\pi$
$443$	7.18845	−	22.1238i	0.341534	−	1.05113i	0.963413	−	0.268020i	$-0.0863692\pi$
$444$	−5.14915	−	15.8475i	−0.244368	−	0.752087i
$445$	−1.00395	+	0.729411i	−0.0475917	+	0.0345774i
$446$	23.2321	−	16.8791i	1.10007	−	0.799249i
$447$	0.611109	+	1.88080i	0.0289045	+	0.0889588i
$448$	−5.00668	+	15.4090i	−0.236544	+	0.728006i
$449$	−20.1055	−	14.6075i	−0.948839	−	0.689372i	0.00169319	−	0.999999i	$-0.499461\pi$
$449$	−20.1055	−	14.6075i	−0.948839	−	0.689372i	−0.950532	+	0.310627i	$0.899461\pi$
$450$	−0.299133			−0.0141013
$451$		0			0
$452$	−17.1164			−0.805086
$453$	8.18899	+	5.94965i	0.384753	+	0.279539i
$454$	−6.66793	+	20.5218i	−0.312941	+	0.963135i
$455$	1.78953	+	5.50760i	0.0838944	+	0.258200i
$456$	0.783593	−	0.569313i	0.0366951	−	0.0266605i
$457$	−4.77992	+	3.47282i	−0.223595	+	0.162452i	−0.693944	−	0.720029i	$-0.744128\pi$
$457$	−4.77992	+	3.47282i	−0.223595	+	0.162452i	0.470348	+	0.882481i	$0.344128\pi$
$458$	15.9582	+	49.1143i	0.745677	+	2.29496i
$459$	3.27423	−	10.0770i	0.152828	−	0.470356i
$460$	5.40603	+	3.92771i	0.252058	+	0.183130i
$461$	−17.3587			−0.808475			−0.404238	−	0.914654i	$-0.632463\pi$
$461$	−17.3587			−0.808475			−0.404238	+	0.914654i	$0.632463\pi$
$462$		0			0
$463$	34.6937			1.61235			0.806176	−	0.591675i	$-0.201533\pi$
$463$	34.6937			1.61235			0.806176	+	0.591675i	$0.201533\pi$
$464$	−25.3775	−	18.4378i	−1.17812	−	0.855954i
$465$	1.20562	−	3.71050i	0.0559091	−	0.172070i
$466$	−5.33479	−	16.4188i	−0.247129	−	0.760585i
$467$	−7.41546	+	5.38765i	−0.343146	+	0.249310i	−0.745988	−	0.665959i	$-0.768022\pi$
$467$	−7.41546	+	5.38765i	−0.343146	+	0.249310i	0.402842	+	0.915270i	$0.368022\pi$
$468$	−0.266582	+	0.193683i	−0.0123228	+	0.00895302i
$469$	12.9792	+	39.9458i	0.599323	+	1.84453i
$470$	1.78234	−	5.48548i	0.0822132	−	0.253026i
$471$	1.49717	+	1.08776i	0.0689860	+	0.0501213i
$472$	10.8510			0.499455
$473$		0			0
$474$	18.9091			0.868525
$475$	−0.489036	−	0.355305i	−0.0224385	−	0.0163025i
$476$	4.19569	−	12.9130i	0.192309	−	0.591867i
$477$	−0.327838	−	1.00898i	−0.0150107	−	0.0461980i
$478$	19.2085	−	13.9558i	0.878575	−	0.638322i
$479$	33.0338	−	24.0004i	1.50935	−	1.09661i	0.542888	−	0.839805i	$-0.317331\pi$
$479$	33.0338	−	24.0004i	1.50935	−	1.09661i	0.966464	−	0.256803i	$-0.0826692\pi$
$480$	−3.88389	−	11.9534i	−0.177274	−	0.545594i
$481$	2.59289	−	7.98009i	0.118226	−	0.363861i
$482$	11.1276	+	8.08466i	0.506847	+	0.368246i
$483$	33.2839			1.51447
$484$		0			0
$485$	11.5431			0.524145
$486$	2.51236	+	1.82534i	0.113963	+	0.0827990i
$487$	−8.08382	+	24.8794i	−0.366313	+	1.12740i	0.582842	+	0.812586i	$0.301941\pi$
$487$	−8.08382	+	24.8794i	−0.366313	+	1.12740i	−0.949155	+	0.314810i	$0.898059\pi$
$488$	−1.58475	−	4.87737i	−0.0717384	−	0.220788i
$489$	−18.5669	+	13.4897i	−0.839626	+	0.610024i
$490$	16.8933	−	12.2737i	0.763159	−	0.554468i
$491$	7.10776	+	21.8754i	0.320769	+	0.987225i	0.973314	+	0.229475i	$0.0737011\pi$
$491$	7.10776	+	21.8754i	0.320769	+	0.987225i	−0.652546	+	0.757749i	$0.726299\pi$
$492$	−6.18079	+	19.0225i	−0.278652	+	0.857602i
$493$	11.2588	+	8.18002i	0.507072	+	0.368410i
$494$	−1.54232			−0.0693922
$495$		0			0
$496$	10.3823			0.466180
$497$	18.0465	+	13.1116i	0.809497	+	0.588134i
$498$	−0.981658	+	3.02123i	−0.0439891	+	0.135385i
$499$	−8.10057	−	24.9310i	−0.362631	−	1.11606i	−0.951451	−	0.307800i	$-0.900407\pi$
$499$	−8.10057	−	24.9310i	−0.362631	−	1.11606i	0.588820	−	0.808265i	$-0.299593\pi$
$500$	−1.22929	+	0.893133i	−0.0549756	+	0.0399421i
$501$	6.07707	−	4.41525i	0.271503	−	0.197259i
$502$	−18.1210	−	55.7706i	−0.808778	−	2.48916i
$503$	0.520569	−	1.60215i	0.0232110	−	0.0714362i	−0.938780	−	0.344517i	$-0.888043\pi$
$503$	0.520569	−	1.60215i	0.0232110	−	0.0714362i	0.961991	+	0.273081i	$0.0880427\pi$
$504$	−0.495144	−	0.359743i	−0.0220555	−	0.0160242i
$505$	2.80675			0.124899
$506$		0			0
$507$	19.8195			0.880214
$508$	−0.139077	−	0.101046i	−0.00617057	−	0.00448318i
$509$	5.51543	−	16.9747i	0.244467	−	0.752393i	−0.751256	−	0.660010i	$-0.770552\pi$
$509$	5.51543	−	16.9747i	0.244467	−	0.752393i	0.995724	−	0.0923822i	$-0.0294481\pi$
$510$	2.16245	+	6.65534i	0.0957549	+	0.294703i
$511$	2.48988	−	1.80900i	0.110146	−	0.0800255i
$512$	20.1596	−	14.6468i	0.890935	−	0.647302i
$513$	0.943135	+	2.90267i	0.0416404	+	0.128156i
$514$	4.82348	−	14.8451i	0.212754	−	0.654791i
$515$	0.328505	+	0.238673i	0.0144757	+	0.0105172i
$516$	−34.2121			−1.50610
$517$		0			0
$518$	−49.2828			−2.16536
$519$	1.93515	+	1.40597i	0.0849436	+	0.0617151i
$520$	0.378859	−	1.16601i	0.0166140	−	0.0511328i
$521$	−2.94907	−	9.07631i	−0.129201	−	0.397640i	0.865442	−	0.501009i	$-0.167038\pi$
$521$	−2.94907	−	9.07631i	−0.129201	−	0.397640i	−0.994643	+	0.103369i	$0.967038\pi$
$522$	−1.60487	+	1.16601i	−0.0702433	+	0.0510347i
$523$	17.5924	−	12.7816i	0.769263	−	0.558903i	−0.132474	−	0.991186i	$-0.542292\pi$
$523$	17.5924	−	12.7816i	0.769263	−	0.558903i	0.901738	+	0.432284i	$0.142292\pi$
$524$	0.222705	+	0.685416i	0.00972891	+	0.0299425i
$525$	−2.33880	+	7.19809i	−0.102074	+	0.314150i
$526$	−4.35851	−	3.16664i	−0.190040	−	0.138072i
$527$	−4.60616			−0.200648
$528$		0			0
$529$	−3.66042			−0.159149
$530$	−10.0983	−	7.33685i	−0.438642	−	0.318692i
$531$	0.593105	−	1.82539i	0.0257386	−	0.0792152i
$532$	1.20856	+	3.71956i	0.0523977	+	0.161264i
$533$	−8.14831	+	5.92009i	−0.352942	+	0.256428i
$534$	−3.34778	+	2.43230i	−0.144872	+	0.105256i
$535$	4.75841	+	14.6449i	0.205724	+	0.633153i
$536$	2.74781	−	8.45688i	0.118687	−	0.365281i
$537$	17.8729	+	12.9854i	0.771271	+	0.560361i
$538$	0.232572			0.0100269
$539$		0			0
$540$	7.67195			0.330148
$541$	−10.9117	−	7.92780i	−0.469130	−	0.340843i	0.327972	−	0.944687i	$-0.393635\pi$
$541$	−10.9117	−	7.92780i	−0.469130	−	0.340843i	−0.797102	+	0.603845i	$0.793635\pi$
$542$	9.87436	−	30.3902i	0.424140	−	1.30537i
$543$	−9.50747	−	29.2610i	−0.408004	−	1.25571i
$544$	−12.0048	+	8.72199i	−0.514701	+	0.373952i
$545$	2.48621	−	1.80634i	0.106497	−	0.0773749i
$546$	5.96739	+	18.3657i	0.255381	+	0.785981i
$547$	−7.54671	+	23.2264i	−0.322674	+	0.993088i	0.649806	+	0.760100i	$0.274850\pi$
$547$	−7.54671	+	23.2264i	−0.322674	+	0.993088i	−0.972480	+	0.232988i	$0.925150\pi$
$548$	1.06788	+	0.775858i	0.0456174	+	0.0331430i
$549$	−0.907112			−0.0387146
$550$		0			0
$551$	−4.00867			−0.170775
$552$	−5.70073	−	4.14182i	−0.242639	−	0.176288i
$553$	7.46129	−	22.9635i	0.317286	−	0.976507i
$554$	−13.1836	−	40.5749i	−0.560117	−	1.72386i
$555$	8.87184	−	6.44577i	0.376589	−	0.273608i
$556$	−23.8352	+	17.3173i	−1.01084	+	0.734417i
$557$	−7.97079	−	24.5316i	−0.337733	−	1.03944i	−0.965360	−	0.260922i	$-0.915974\pi$
$557$	−7.97079	−	24.5316i	−0.337733	−	1.03944i	0.627627	−	0.778514i	$-0.284026\pi$
$558$	0.202893	−	0.624442i	0.00858917	−	0.0264347i
$559$	−13.9375	−	10.1262i	−0.589493	−	0.428292i
$560$	−20.1409			−0.851108
$561$		0			0
$562$	24.2945			1.02480
$563$	32.6602	+	23.7290i	1.37646	+	1.00006i	0.997201	+	0.0747711i	$0.0238226\pi$
$563$	32.6602	+	23.7290i	1.37646	+	1.00006i	0.379264	+	0.925289i	$0.376177\pi$
$564$	2.56598	−	7.89729i	0.108047	−	0.332536i
$565$	−3.48094	−	10.7132i	−0.146444	−	0.450709i
$566$	24.0074	−	17.4424i	1.00911	−	0.733158i
$567$	32.5634	−	23.6587i	1.36753	−	0.993570i
$568$	−1.45934	−	4.49139i	−0.0612326	−	0.188455i
$569$	−3.26141	+	10.0376i	−0.136725	+	0.420798i	−0.995854	−	0.0909616i	$-0.971006\pi$
$569$	−3.26141	+	10.0376i	−0.136725	+	0.420798i	0.859129	+	0.511759i	$0.171006\pi$
$570$	−1.63075	−	1.18481i	−0.0683044	−	0.0496261i
$571$	−9.77700			−0.409155			−0.204577	−	0.978850i	$-0.565582\pi$
$571$	−9.77700			−0.409155			−0.204577	+	0.978850i	$0.565582\pi$
$572$		0			0
$573$	34.9281			1.45914
$574$	47.8588	+	34.7714i	1.99759	+	1.45133i
$575$	−1.35896	+	4.18244i	−0.0566724	+	0.174420i
$576$	−0.187487	−	0.577024i	−0.00781194	−	0.0240427i
$577$	13.1837	−	9.57854i	0.548846	−	0.398760i	−0.278514	−	0.960432i	$-0.589842\pi$
$577$	13.1837	−	9.57854i	0.548846	−	0.398760i	0.827360	+	0.561672i	$0.189842\pi$
$578$	−19.1176	+	13.8898i	−0.795188	+	0.577738i
$579$	−5.58150	−	17.1781i	−0.231959	−	0.713897i
$580$	−3.11385	+	9.58343i	−0.129295	+	0.397930i
$581$	3.28167	+	2.38427i	0.136147	+	0.0989164i
$582$	38.4918			1.59554
$583$		0			0
$584$	−0.651566			−0.0269620
$585$	−0.175442	−	0.127466i	−0.00725364	−	0.00527008i
$586$	14.4529	−	44.4814i	0.597043	−	1.83751i
$587$	10.4085	+	32.0342i	0.429606	+	1.32219i	0.898514	+	0.438945i	$0.144648\pi$
$587$	10.4085	+	32.0342i	0.429606	+	1.32219i	−0.468908	+	0.883247i	$0.655352\pi$
$588$	24.3207	−	17.6700i	1.00297	−	0.728700i
$589$	1.07340	−	0.779871i	0.0442287	−	0.0321340i
$590$	−6.97824	−	21.4768i	−0.287290	−	0.884187i
$591$	4.64342	−	14.2910i	0.191005	−	0.587852i
$592$	23.6092	+	17.1531i	0.970332	+	0.704988i
$593$	−21.3355			−0.876143			−0.438071	−	0.898940i	$-0.644338\pi$
$593$	−21.3355			−0.876143			−0.438071	+	0.898940i	$0.644338\pi$
$594$		0			0
$595$	8.93560			0.366324
$596$	1.36768	+	0.993681i	0.0560225	+	0.0407027i
$597$	3.57595	−	11.0056i	0.146354	−	0.450431i
$598$	3.46734	+	10.6714i	0.141790	+	0.436385i
$599$	13.2756	−	9.64529i	0.542427	−	0.394096i	−0.282559	−	0.959250i	$-0.591183\pi$
$599$	13.2756	−	9.64529i	0.542427	−	0.394096i	0.824985	+	0.565154i	$0.191183\pi$
$600$	1.29630	−	0.941821i	0.0529214	−	0.0384497i
$601$	−4.26301	−	13.1202i	−0.173892	−	0.535185i	0.825689	−	0.564125i	$-0.190787\pi$
$601$	−4.26301	−	13.1202i	−0.173892	−	0.535185i	−0.999581	+	0.0289409i	$0.990787\pi$
$602$	−31.2682	+	96.2337i	−1.27440	+	3.92219i
$603$	−1.27246	−	0.924494i	−0.0518184	−	0.0376483i
$604$	8.65296			0.352084
$605$		0			0
$606$	9.35943			0.380201
$607$	4.56569	+	3.31717i	0.185316	+	0.134640i	0.676575	−	0.736373i	$-0.263463\pi$
$607$	4.56569	+	3.31717i	0.185316	+	0.134640i	−0.491260	+	0.871013i	$0.663463\pi$
$608$	1.32082	−	4.06507i	0.0535664	−	0.164860i
$609$	15.5100	+	47.7348i	0.628495	+	1.93431i
$610$	−8.63441	+	6.27327i	−0.349597	+	0.253997i
$611$	3.38281	−	2.45775i	0.136854	−	0.0994300i
$612$	0.157117	+	0.483557i	0.00635108	+	0.0195466i
$613$	−1.02935	+	3.16801i	−0.0415750	+	0.127955i	−0.969690	−	0.244340i	$-0.921429\pi$
$613$	−1.02935	+	3.16801i	−0.0415750	+	0.127955i	0.928115	+	0.372294i	$0.121429\pi$
$614$	−7.52141	−	5.46462i	−0.303539	−	0.220534i
$615$	−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	$0.560976\pi$
$618$	1.09544	+	0.795882i	0.0440650	+	0.0320151i
$619$	−8.40743	+	25.8754i	−0.337923	+	1.04002i	0.627341	+	0.778745i	$0.284143\pi$
$619$	−8.40743	+	25.8754i	−0.337923	+	1.04002i	−0.965264	+	0.261276i	$0.915857\pi$
$620$	−1.03062	−	3.17194i	−0.0413909	−	0.127388i
$621$	17.9634	−	13.0512i	0.720848	−	0.523727i
$622$	−14.5624	+	10.5802i	−0.583898	+	0.424227i
$623$	1.63283	+	5.02533i	0.0654179	+	0.201336i
$624$	3.53356	−	10.8752i	0.141456	−	0.435356i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	50.6262			2.02343
$627$		0			0
$628$	1.58200			0.0631285
$629$	−10.4743	−	7.61005i	−0.417639	−	0.303433i
$630$	−0.393598	+	1.21137i	−0.0156813	+	0.0482621i
$631$	−9.37208	−	28.8443i	−0.373097	−	1.14827i	−0.944754	−	0.327781i	$-0.893699\pi$
$631$	−9.37208	−	28.8443i	−0.373097	−	1.14827i	0.571657	−	0.820493i	$-0.306301\pi$
$632$	−4.13550	+	3.00461i	−0.164501	+	0.119517i
$633$	5.77224	−	4.19378i	0.229426	−	0.166688i
$634$	8.24410	+	25.3727i	0.327415	+	1.00768i
$635$	0.0349610	−	0.107599i	0.00138739	−	0.00426993i
$636$	−14.5382	−	10.5627i	−0.576479	−	0.418836i
$637$	15.1379			0.599787
$638$		0			0
$639$	−0.835326			−0.0330450
$640$	5.66595	+	4.11655i	0.223966	+	0.162721i
$641$	12.3085	−	37.8818i	0.486158	−	1.49624i	−0.344139	−	0.938919i	$-0.611829\pi$
$641$	12.3085	−	37.8818i	0.486158	−	1.49624i	0.830297	−	0.557322i	$-0.188171\pi$
$642$	15.8675	+	48.8350i	0.626238	+	1.92736i
$643$	22.1280	−	16.0769i	0.872642	−	0.634011i	−0.0586529	−	0.998278i	$-0.518681\pi$
$643$	22.1280	−	16.0769i	0.872642	−	0.634011i	0.931294	+	0.364267i	$0.118681\pi$
$644$	23.0189	−	16.7242i	0.907070	−	0.659025i
$645$	−6.95768	−	21.4135i	−0.273958	−	0.843157i
$646$	−0.735400	+	2.26333i	−0.0289339	+	0.0890495i
$647$	−18.0199	−	13.0922i	−0.708436	−	0.514709i	0.174233	−	0.984704i	$-0.444255\pi$
$647$	−18.0199	−	13.0922i	−0.708436	−	0.514709i	−0.882669	+	0.469996i	$0.844255\pi$
$648$	−8.52138			−0.334751
$649$		0			0
$650$	−2.55147			−0.100077
$651$	−13.4397	−	9.76451i	−0.526743	−	0.382701i
$652$	−6.06257	+	18.6587i	−0.237429	+	0.730730i
$653$	9.08241	+	27.9528i	0.355422	+	1.09388i	0.955764	+	0.294133i	$0.0950310\pi$
$653$	9.08241	+	27.9528i	0.355422	+	1.09388i	−0.600342	+	0.799743i	$0.704969\pi$
$654$	8.29054	−	6.02343i	0.324186	−	0.235535i
$655$	−0.383714	+	0.278785i	−0.0149930	+	0.0108930i
$656$	−10.8247	−	33.3149i	−0.422632	−	1.30073i
$657$	−0.0356141	+	0.109609i	−0.00138944	+	0.00427626i
$658$	−19.8688	−	14.4355i	−0.774565	−	0.562755i
$659$	22.8429			0.889832			0.444916	−	0.895572i	$-0.353234\pi$
$659$	22.8429			0.889832			0.444916	+	0.895572i	$0.353234\pi$
$660$		0			0
$661$	32.0302			1.24583			0.622916	−	0.782289i	$-0.285948\pi$
$661$	32.0302			1.24583			0.622916	+	0.782289i	$0.285948\pi$
$662$	−12.9916	−	9.43897i	−0.504934	−	0.366856i
$663$	−1.56768	+	4.82483i	−0.0608837	+	0.187381i
$664$	−0.265374	−	0.816737i	−0.0102985	−	0.0316956i
$665$	−2.08231	+	1.51289i	−0.0807486	+	0.0586673i
$666$	1.49305	−	1.08476i	0.0578543	−	0.0420336i
$667$	9.01204	+	27.7362i	0.348948	+	1.07395i
$668$	1.98431	−	6.10709i	0.0767754	−	0.236290i
$669$	22.0117	+	15.9925i	0.851023	+	0.618304i
$670$	−18.5055			−0.714928
$671$		0			0
$672$	−53.5167			−2.06445
$673$	−10.9816	−	7.97857i	−0.423308	−	0.307551i	0.355659	−	0.934616i	$-0.384256\pi$
$673$	−10.9816	−	7.97857i	−0.423308	−	0.307551i	−0.778968	+	0.627064i	$0.784256\pi$
$674$	9.09248	−	27.9838i	0.350229	−	1.07789i
$675$	1.56024	+	4.80192i	0.0600535	+	0.184826i
$676$	13.7070	−	9.95870i	0.527191	−	0.383027i
$677$	−1.28037	+	0.930247i	−0.0492088	+	0.0357523i	−0.612118	−	0.790767i	$-0.709682\pi$
$677$	−1.28037	+	0.930247i	−0.0492088	+	0.0357523i	0.562909	+	0.826519i	$0.309682\pi$
$678$	−11.6076	−	35.7245i	−0.445787	−	1.37199i
$679$	15.1883	−	46.7449i	0.582874	−	1.79390i
$680$	−1.53045	−	1.11194i	−0.0586902	−	0.0426409i
$681$	−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	$0.275887\pi$
$684$	−0.118485	−	0.0860844i	−0.00453039	−	0.00329152i
$685$	−0.268441	+	0.826176i	−0.0102566	+	0.0315666i
$686$	−10.1961	−	31.3803i	−0.389288	−	1.19811i
$687$	−39.5845	+	28.7598i	−1.51024	+	1.09726i
$688$	48.4738	−	35.2183i	1.84805	−	1.34268i
$689$	−2.79630	−	8.60614i	−0.106531	−	0.327868i
$690$	−4.53160	+	13.9468i	−0.172515	+	0.530947i
$691$	27.3000	+	19.8346i	1.03854	+	0.754544i	0.970000	−	0.243105i	$-0.0781659\pi$
$691$	27.3000	+	19.8346i	1.03854	+	0.754544i	0.0685402	+	0.997648i	$0.478166\pi$
$692$	2.04479			0.0777311
$693$		0			0
$694$	−13.9860			−0.530900
$695$	−15.6863	−	11.3968i	−0.595017	−	0.432305i
$696$	3.28359	−	10.1059i	0.124464	−	0.383062i
$697$	4.80241	+	14.7803i	0.181904	+	0.559844i
$698$	−46.2506	+	33.6030i	−1.75061	+	1.27189i
$699$	13.2330	−	9.61434i	0.500518	−	0.363648i
$700$	1.99933	+	6.15331i	0.0755677	+	0.232573i
$701$	0.583231	−	1.79500i	0.0220283	−	0.0677962i	−0.939438	−	0.342719i	$-0.888652\pi$
$701$	0.583231	−	1.79500i	0.0220283	−	0.0677962i	0.961466	+	0.274923i	$0.0886522\pi$
$702$	10.4221	+	7.57212i	0.393358	+	0.285791i
$703$	3.72935			0.140655
$704$		0			0
$705$	5.46480			0.205816
$706$	−26.6180	−	19.3391i	−1.00178	−	0.727837i
$707$	3.69310	−	11.3662i	0.138893	−	0.427470i
$708$	−10.0464	−	30.9196i	−0.377566	−	1.16203i
$709$	5.69402	−	4.13695i	0.213843	−	0.155366i	−0.475707	−	0.879604i	$-0.657808\pi$
$709$	5.69402	−	4.13695i	0.213843	−	0.155366i	0.689551	+	0.724237i	$0.257808\pi$
$710$	−7.95112	+	5.77682i	−0.298400	+	0.216800i
$711$	0.279405	+	0.859919i	0.0104785	+	0.0322495i
$712$	0.345684	−	1.06391i	0.0129551	−	0.0398716i
$713$	−7.80912	−	5.67366i	−0.292454	−	0.212480i
$714$	29.7968			1.11512
$715$		0			0
$716$	18.8855			0.705783
$717$	18.1995	+	13.2227i	0.679672	+	0.493811i
$718$	1.74168	−	5.36034i	0.0649990	−	0.200046i
$719$	2.48094	+	7.63555i	0.0925234	+	0.284758i	0.986600	−	0.163156i	$-0.0521673\pi$
$719$	2.48094	+	7.63555i	0.0925234	+	0.284758i	−0.894077	+	0.447913i	$0.852167\pi$
$720$	0.610177	−	0.443320i	0.0227400	−	0.0165216i
$721$	1.39877	−	1.01627i	0.0520931	−	0.0378478i
$722$	10.8029	+	33.2481i	0.402044	+	1.23736i
$723$	−4.02709	+	12.3941i	−0.149769	+	0.460942i
$724$	−21.2780	−	15.4594i	−0.790792	−	0.574544i
$725$	−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	$0.686455\pi$
$728$	−4.22336	−	3.06845i	−0.156528	−	0.113724i
$729$	7.85412	−	24.1725i	0.290893	−	0.895277i
$730$	0.419022	+	1.28962i	0.0155087	+	0.0477309i
$731$	−21.5056	+	15.6248i	−0.795414	+	0.577902i
$732$	−12.4307	+	9.03145i	−0.459453	+	0.333812i
$733$	12.6446	+	38.9160i	0.467038	+	1.43739i	0.856402	+	0.516310i	$0.172695\pi$
$733$	12.6446	+	38.9160i	0.467038	+	1.43739i	−0.389364	+	0.921084i	$0.627305\pi$
$734$	−3.58455	+	11.0321i	−0.132308	+	0.407203i
$735$	16.0059	+	11.6289i	0.590385	+	0.428940i
$736$	−31.0958			−1.14621
$737$		0			0
$738$	−2.21526			−0.0815447
$739$	3.53118	+	2.56555i	0.129897	+	0.0943754i	0.650836	−	0.759218i	$-0.274418\pi$
$739$	3.53118	+	2.56555i	0.129897	+	0.0943754i	−0.520940	+	0.853593i	$0.674418\pi$
$740$	2.89688	−	8.91567i	0.106491	−	0.327747i
$741$	−0.451567	−	1.38978i	−0.0165887	−	0.0510549i
$742$	−42.9985	+	31.2403i	−1.57853	+	1.14687i
$743$	−15.9421	+	11.5826i	−0.584859	+	0.424925i	−0.840473	−	0.541854i	$-0.817723\pi$
$743$	−15.9421	+	11.5826i	−0.584859	+	0.424925i	0.255613	+	0.966779i	$0.417723\pi$
$744$	1.08681	+	3.34485i	0.0398443	+	0.122628i
$745$	−0.343806	+	1.05813i	−0.0125961	+	0.0387667i
$746$	31.6763	+	23.0141i	1.15975	+	0.842608i
$747$	−0.151900			−0.00555773
$748$		0			0
$749$	65.5669			2.39576
$750$	−2.69776	−	1.96004i	−0.0985082	−	0.0715704i
$751$	−12.0375	+	37.0477i	−0.439256	+	1.35189i	0.449406	+	0.893328i	$0.351636\pi$
$751$	−12.0375	+	37.0477i	−0.439256	+	1.35189i	−0.888662	+	0.458563i	$0.848364\pi$
$752$	4.49391	+	13.8308i	0.163876	+	0.504358i
$753$	44.9493	−	32.6576i	1.63804	−	1.19011i
$754$	−13.6888	+	9.94551i	−0.498517	+	0.362194i
$755$	1.75974	+	5.41594i	0.0640436	+	0.197106i
$756$	10.0947	−	31.0683i	0.367140	−	1.12994i
$757$	−43.0134	−	31.2511i	−1.56335	−	1.13584i	−0.933195	−	0.359369i	$-0.882992\pi$
$757$	−43.0134	−	31.2511i	−1.56335	−	1.13584i	−0.630154	−	0.776470i	$-0.717008\pi$
$758$	4.62299			0.167915
$759$		0			0
$760$	0.544913			0.0197661
$761$	−41.4850	−	30.1406i	−1.50383	−	1.09260i	−0.968825	−	0.247747i	$-0.920310\pi$
$761$	−41.4850	−	30.1406i	−1.50383	−	1.09260i	−0.535005	−	0.844849i	$-0.679690\pi$
$762$	0.116582	−	0.358801i	0.00422330	−	0.0129980i
$763$	−4.04359	−	12.4449i	−0.146388	−	0.450535i
$764$	24.1560	−	17.5503i	0.873932	−	0.634949i
$765$	−0.270708	+	0.196681i	−0.00978747	+	0.00711102i
$766$	−9.97336	−	30.6948i	−0.360352	−	1.10905i
$767$	5.05892	−	15.5697i	0.182667	−	0.562191i
$768$	29.8372	+	21.6780i	1.07666	+	0.782238i
$769$	45.0332			1.62394			0.811970	−	0.583699i	$-0.198395\pi$
$769$	45.0332			1.62394			0.811970	+	0.583699i	$0.198395\pi$
$770$		0			0
$771$	14.7892			0.532619
$772$	−12.4916	−	9.07567i	−0.449582	−	0.326640i
$773$	−15.4334	+	47.4992i	−0.555102	+	1.70843i	0.140573	+	0.990070i	$0.455106\pi$
$773$	−15.4334	+	47.4992i	−0.555102	+	1.70843i	−0.695675	+	0.718357i	$0.744894\pi$
$774$	−1.17091	−	3.60369i	−0.0420875	−	0.129532i
$775$	1.77574	−	1.29015i	0.0637863	−	0.0463435i
$776$	−8.41829	+	6.11624i	−0.302199	+	0.219560i
$777$	−14.4293	−	44.4087i	−0.517646	−	1.59315i
$778$	10.4668	−	32.2135i	0.375253	−	1.15491i
$779$	−3.62159	−	2.63124i	−0.129757	−	0.0942740i
$780$	−3.67328			−0.131525
$781$		0			0
$782$	17.3134			0.619125
$783$	27.0884	+	19.6809i	0.968060	+	0.703337i
$784$	−16.2694	+	50.0721i	−0.581050	+	1.78829i
$785$	0.321729	+	0.990181i	0.0114830	+	0.0353411i
$786$	−1.27954	+	0.929639i	−0.0456396	+	0.0331591i
$787$	−7.91644	+	5.75163i	−0.282191	+	0.205023i	−0.719872	−	0.694107i	$-0.755800\pi$
$787$	−7.91644	+	5.75163i	−0.282191	+	0.205023i	0.437682	+	0.899130i	$0.355800\pi$
$788$	−3.96944	−	12.2167i	−0.141405	−	0.435201i
$789$	1.57735	−	4.85459i	0.0561552	−	0.172828i
$790$	8.60644	+	6.25295i	0.306203	+	0.222470i
$791$	−47.9644			−1.70542
$792$		0			0
$793$	−7.73725			−0.274758
$794$	−25.4118	−	18.4628i	−0.901832	−	0.655219i
$795$	3.65459	−	11.2477i	0.129615	−	0.398914i
$796$	−3.05691	−	9.40821i	−0.108349	−	0.333465i
$797$	−29.2578	+	21.2571i	−1.03637	+	0.752964i	−0.969573	−	0.244803i	$-0.921277\pi$
$797$	−29.2578	+	21.2571i	−1.03637	+	0.752964i	−0.0667929	+	0.997767i	$0.521277\pi$
$798$	−6.94371	+	5.04490i	−0.245805	+	0.178588i
$799$	−1.99374	−	6.13611i	−0.0705336	−	0.217080i
$800$	2.18505	−	6.72488i	0.0772531	−	0.237761i
$801$	−0.160080	−	0.116305i	−0.00565614	−	0.00410942i
$802$	−54.2913			−1.91709
$803$		0			0
$804$	−26.6418			−0.939583
$805$	15.1491	+	11.0065i	0.533935	+	0.387927i
$806$	1.73059	−	5.32621i	0.0609574	−	0.187608i
$807$	0.0680934	+	0.209570i	0.00239700	+	0.00737721i
$808$	−2.04694	+	1.48719i	−0.0720111	+	0.0523191i
$809$	−13.2158	+	9.60188i	−0.464645	+	0.337584i	−0.795350	−	0.606150i	$-0.792713\pi$
$809$	−13.2158	+	9.60188i	−0.464645	+	0.337584i	0.330706	+	0.943734i	$0.392713\pi$
$810$	5.48010	+	16.8660i	0.192551	+	0.592611i
$811$	15.9749	−	49.1657i	0.560954	−	1.72644i	−0.118721	−	0.992928i	$-0.537879\pi$
$811$	15.9749	−	49.1657i	0.560954	−	1.72644i	0.679676	−	0.733513i	$-0.262121\pi$
$812$	34.7118	+	25.2196i	1.21815	+	0.885036i
$813$	30.2756			1.06181
$814$		0			0
$815$	−12.9115			−0.452270
$816$	−14.2743	−	10.3709i	−0.499701	−	0.363054i
$817$	2.36615	−	7.28225i	0.0827810	−	0.254774i
$818$	17.3183	+	53.3002i	0.605519	+	1.86360i
$819$	−0.747032	+	0.542750i	−0.0261034	+	0.0189652i
$820$	−9.10361	+	6.61416i	−0.317912	+	0.230977i
$821$	11.9501	+	36.7786i	0.417061	+	1.28358i	0.910394	+	0.413742i	$0.135778\pi$
$821$	11.9501	+	36.7786i	0.417061	+	1.28358i	−0.493333	+	0.869841i	$0.664222\pi$
$822$	−0.895146	+	2.75498i	−0.0312218	+	0.0960908i
$823$	4.29149	+	3.11795i	0.149592	+	0.108685i	0.660064	−	0.751210i	$-0.270529\pi$
$823$	4.29149	+	3.11795i	0.149592	+	0.108685i	−0.510472	+	0.859894i	$0.670529\pi$
$824$	−0.366040			−0.0127516
$825$		0			0
$826$	−96.1544			−3.34564
$827$	9.59833	+	6.97359i	0.333767	+	0.242496i	0.742027	−	0.670370i	$-0.233865\pi$
$827$	9.59833	+	6.97359i	0.333767	+	0.242496i	−0.408261	+	0.912865i	$0.633865\pi$
$828$	−0.329252	+	1.01333i	−0.0114423	+	0.0352158i
$829$	−15.2486	−	46.9305i	−0.529607	−	1.62996i	−0.755021	−	0.655701i	$-0.772373\pi$
$829$	−15.2486	−	46.9305i	−0.529607	−	1.62996i	0.225414	−	0.974263i	$-0.427627\pi$
$830$	−1.44587	+	1.05049i	−0.0501869	+	0.0364629i
$831$	32.7020	−	23.7594i	1.13442	−	0.824205i
$832$	−1.59918	−	4.92175i	−0.0554414	−	0.170631i
$833$	7.21800	−	22.2147i	0.250089	−	0.769694i
$834$	−52.3079	−	38.0039i	−1.81127	−	1.31597i
$835$	4.22601			0.146247
$836$		0			0
$837$	−11.0823			−0.383059
$838$	−12.5947	−	9.15057i	−0.435076	−	0.316101i
$839$	−6.61546	+	20.3603i	−0.228391	+	0.702915i	0.769539	+	0.638600i	$0.220486\pi$
$839$	−6.61546	+	20.3603i	−0.228391	+	0.702915i	−0.997930	+	0.0643151i	$0.979514\pi$
$840$	−2.10832	−	6.48875i	−0.0727440	−	0.223883i
$841$	−12.1174	+	8.80381i	−0.417842	+	0.303580i
$842$	−34.7064	+	25.2157i	−1.19606	+	0.868990i
$843$	7.11304	+	21.8917i	0.244986	+	0.753990i
$844$	1.88478	−	5.80076i	0.0648768	−	0.199670i
$845$	9.02078	+	6.55398i	0.310324	+	0.225464i
$846$	0.919673			0.0316190
$847$		0			0
$848$	31.4720			1.08075
$849$	22.7463	+	16.5262i	0.780651	+	0.567176i
$850$	−1.21658	+	3.74425i	−0.0417283	+	0.128427i
$851$	−8.38410	−	25.8036i	−0.287403	−	0.884536i
$852$	−11.4470	+	8.31673i	−0.392168	+	0.284926i
$853$	−25.1451	+	18.2690i	−0.860953	+	0.625519i	−0.928144	−	0.372221i	$-0.878596\pi$
$853$	−25.1451	+	18.2690i	−0.860953	+	0.625519i	0.0671911	+	0.997740i	$0.478596\pi$
$854$	14.0431	+	43.2202i	0.480545	+	1.47897i
$855$	0.0297845	−	0.0916674i	0.00101861	−	0.00313496i
$856$	−11.2300	−	8.15909i	−0.383834	−	0.278872i
$857$	33.2665			1.13636			0.568181	−	0.822904i	$-0.307647\pi$
$857$	33.2665			1.13636			0.568181	+	0.822904i	$0.307647\pi$
$858$		0			0
$859$	−18.9045			−0.645012			−0.322506	−	0.946567i	$-0.604525\pi$
$859$	−18.9045			−0.645012			−0.322506	+	0.946567i	$0.604525\pi$
$860$	−15.5715	−	11.3134i	−0.530984	−	0.385783i
$861$	−17.3202	+	53.3060i	−0.590270	+	1.81666i
$862$	11.8042	+	36.3296i	0.402053	+	1.23739i
$863$	−11.1907	+	8.13050i	−0.380935	+	0.276765i	−0.761731	−	0.647894i	$-0.775650\pi$
$863$	−11.1907	+	8.13050i	−0.380935	+	0.276765i	0.380796	+	0.924659i	$0.375650\pi$
$864$	−28.8831	+	20.9848i	−0.982624	+	0.713918i
$865$	0.415847	+	1.27984i	0.0141392	+	0.0435160i
$866$	−12.3997	+	38.1622i	−0.421358	+	1.29681i
$867$	−18.1134	−	13.1601i	−0.615163	−	0.446942i
$868$	−14.2011			−0.482018
$869$		0			0
$870$	−22.1138			−0.749727
$871$	−10.8535	−	7.88551i	−0.367756	−	0.267190i
$872$	−0.856063	+	2.63469i	−0.0289900	+	0.0892219i
$873$	0.568761	+	1.75047i	0.0192496	+	0.0592443i
$874$	−4.03463	+	2.93133i	−0.136474	+	0.0991538i
$875$	−3.44479	+	2.50279i	−0.116455	+	0.0846097i
$876$	0.603254	+	1.85663i	0.0203821	+	0.0627296i
$877$	−14.9380	+	45.9743i	−0.504419	+	1.55244i	0.297326	+	0.954776i	$0.403905\pi$
$877$	−14.9380	+	45.9743i	−0.504419	+	1.55244i	−0.801745	+	0.597666i	$0.796095\pi$
$878$	−53.4717	−	38.8494i	−1.80458	−	1.31110i
$879$	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	$0.690510\pi$
$882$	2.69363	+	1.95704i	0.0906994	+	0.0658969i
$883$	5.64440	−	17.3717i	0.189949	−	0.584604i	−0.810049	−	0.586362i	$-0.800560\pi$
$883$	5.64440	−	17.3717i	0.189949	−	0.584604i	0.999998	+	0.00175806i	$0.000559609\pi$
$884$	1.34014	+	4.12452i	0.0450737	+	0.138723i
$885$	17.3096	−	12.5762i	0.581856	−	0.422743i
$886$	35.3062	−	25.6514i	1.18613	−	0.861776i
$887$	−4.84758	−	14.9193i	−0.162766	−	0.500942i	0.836099	−	0.548579i	$-0.184831\pi$
$887$	−4.84758	−	14.9193i	−0.162766	−	0.500942i	−0.998865	+	0.0476370i	$0.984831\pi$
$888$	−3.05480	+	9.40170i	−0.102512	+	0.315500i
$889$	−0.389731	−	0.283156i	−0.0130711	−	0.00949675i
$890$	−2.32805			−0.0780366
$891$		0			0
$892$	23.2589			0.778764
$893$	1.50352	+	1.09237i	0.0503134	+	0.0365548i
$894$	−1.14646	+	3.52844i	−0.0383433	+	0.118009i
$895$	3.84072	+	11.8205i	0.128381	+	0.395117i
$896$	24.1256	−	17.5283i	0.805979	−	0.585578i
$897$	−8.60078	+	6.24883i	−0.287172	+	0.208643i
$898$	−14.4072	−	44.3409i	−0.480775	−	1.47967i
$899$	4.49801	−	13.8435i	0.150017	−	0.461705i
$900$	−0.196011	−	0.142410i	−0.00653370	−	0.00474701i
$901$	−13.9627			−0.465165
$902$		0			0
$903$	−95.8710			−3.19039
$904$	8.21515	+	5.96865i	0.273232	+	0.198515i
$905$	5.34883	−	16.4620i	0.177801	−	0.547216i
$906$	5.86807	+	18.0601i	0.194953	+	0.600005i
$907$	20.9496	−	15.2208i	0.695621	−	0.505399i	−0.182882	−	0.983135i	$-0.558543\pi$
$907$	20.9496	−	15.2208i	0.695621	−	0.505399i	0.878503	+	0.477736i	$0.158543\pi$
$908$	−14.1392	+	10.2727i	−0.469225	+	0.340912i
$909$	0.138297	+	0.425633i	0.00458701	+	0.0141174i
$910$	−3.35721	+	10.3324i	−0.111290	+	0.342517i
$911$	−12.5014	−	9.08280i	−0.414190	−	0.300927i	0.361106	−	0.932525i	$-0.382399\pi$
$911$	−12.5014	−	9.08280i	−0.414190	−	0.300927i	−0.775296	+	0.631598i	$0.782399\pi$
$912$	5.08232			0.168293
$913$		0			0
$914$	−11.0842			−0.366632
$915$	−8.18086	−	5.94374i	−0.270451	−	0.196494i
$916$	−12.9253	+	39.7800i	−0.427065	+	1.31437i
$917$	0.624077	+	1.92071i	0.0206088	+	0.0634274i
$918$	16.0814	−	11.6838i	0.530765	−	0.385624i
$919$	−38.6009	+	28.0452i	−1.27333	+	0.925126i	−0.999330	−	0.0366042i	$-0.988346\pi$
$919$	−38.6009	+	28.0452i	−1.27333	+	0.925126i	−0.273997	+	0.961730i	$0.588346\pi$
$920$	−1.22504	−	3.77028i	−0.0403883	−	0.124302i
$921$	2.72201	−	8.37749i	0.0896933	−	0.276048i
$922$	−26.3460	−	19.1415i	−0.867659	−	0.630391i
$923$	−7.12495			−0.234521
$924$		0			0
$925$	6.16951			0.202852
$926$	52.6560	+	38.2568i	1.73038	+	1.25720i
$927$	−0.0200075	+	0.0615767i	−0.000657132	+	0.00202244i
$928$	−14.4903	−	44.5966i	−0.475668	−	1.46396i
$929$	30.5431	−	22.1909i	1.00209	−	0.728058i	0.0395518	−	0.999218i	$-0.487407\pi$
$929$	30.5431	−	22.1909i	1.00209	−	0.728058i	0.962535	+	0.271159i	$0.0874070\pi$
$930$	5.92139	−	4.30214i	0.194170	−	0.141073i
$931$	2.07913	+	6.39890i	0.0681407	+	0.209715i
$932$	4.32090	−	13.2984i	0.141536	−	0.435603i
$933$	−13.7974	−	10.0244i	−0.451707	−	0.328185i
$934$	−17.1957			−0.562661
$935$		0			0
$936$	0.195488			0.00638972
$937$	40.1582	+	29.1766i	1.31191	+	0.953158i	0.999995	+	0.00304836i	$0.000970326\pi$
$937$	40.1582	+	29.1766i	1.31191	+	0.953158i	0.311915	+	0.950110i	$0.399030\pi$
$938$	−24.3494	+	74.9396i	−0.795034	+	2.44686i
$939$	14.8226	+	45.6192i	0.483717	+	1.48873i
$940$	3.77940	−	2.74590i	0.123271	−	0.0895613i
$941$	−26.9555	+	19.5843i	−0.878724	+	0.638430i	−0.932914	−	0.360101i	$-0.882742\pi$
$941$	−26.9555	+	19.5843i	−0.878724	+	0.638430i	0.0541898	+	0.998531i	$0.482742\pi$
$942$	1.07284	+	3.30187i	0.0349551	+	0.107581i
$943$	−10.0639	+	30.9734i	−0.327724	+	1.00863i
$944$	46.0633	+	33.4669i	1.49923	+	1.08926i
$945$	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	$0.619941\pi$
$948$	12.3904	+	9.00219i	0.402423	+	0.292377i
$949$	−0.303772	+	0.934915i	−0.00986087	+	0.0303486i
$950$	−0.350433	−	1.07852i	−0.0113696	−	0.0349919i
$951$	−20.4496	+	14.8575i	−0.663123	+	0.481787i
$952$	−6.51666	+	4.73463i	−0.211206	+	0.153450i
$953$	14.9990	+	46.1622i	0.485865	+	1.49534i	0.830724	+	0.556685i	$0.187927\pi$
$953$	14.9990	+	46.1622i	0.485865	+	1.49534i	−0.344858	+	0.938655i	$0.612073\pi$
$954$	0.615033	−	1.89288i	0.0199124	−	0.0612842i
$955$	15.8974	+	11.5502i	0.514429	+	0.373755i
$956$	19.2306			0.621962
$957$		0			0
$958$	76.6020			2.47490
$959$	2.99246	+	2.17415i	0.0966317	+	0.0702070i
$960$	2.09002	−	6.43242i	0.0674551	−	0.207606i
$961$	−8.09077	−	24.9008i	−0.260993	−	0.803253i
$962$	12.7350	−	9.25252i	0.410593	−	0.298313i
$963$	−1.98638	+	1.44319i	−0.0640102	+	0.0465061i
$964$	3.44257	+	10.5951i	0.110878	+	0.341247i
$965$	3.14011	−	9.66427i	0.101084	−	0.311104i
$966$	50.5163	+	36.7023i	1.62534	+	1.18088i
$967$	−47.2983			−1.52101			−0.760505	−	0.649332i	$-0.775048\pi$
$967$	−47.2983			−1.52101			−0.760505	+	0.649332i	$0.775048\pi$
$968$		0			0
$969$	−2.25480			−0.0724345
$970$	17.5194	+	12.7286i	0.562515	+	0.408691i
$971$	5.95839	−	18.3380i	0.191214	−	0.588495i	−0.808786	−	0.588103i	$-0.799875\pi$
$971$	5.95839	−	18.3380i	0.191214	−	0.588495i	1.00000		0.000392485i	$-0.000124932\pi$
$972$	0.777257	+	2.39215i	0.0249305	+	0.0767282i
$973$	−66.7924	+	48.5275i	−2.14126	+	1.55572i
$974$	−39.7038	+	28.8465i	−1.27219	+	0.924301i
$975$	−0.747032	−	2.29913i	−0.0239242	−	0.0736310i
$976$	8.31555	−	25.5926i	0.266174	−	0.819200i
$977$	−25.7892	−	18.7369i	−0.825068	−	0.599447i	0.0930915	−	0.995658i	$-0.470325\pi$
$977$	−25.7892	−	18.7369i	−0.825068	−	0.599447i	−0.918160	+	0.396210i	$0.870325\pi$
$978$	−43.0549			−1.37674
$979$		0			0
$980$	16.9127			0.540257
$981$	0.396426	+	0.288021i	0.0126569	+	0.00919579i
$982$	−13.3344	+	41.0390i	−0.425517	+	1.30961i
$983$	0.494996	+	1.52344i	0.0157879	+	0.0485902i	0.958640	−	0.284621i	$-0.0918678\pi$
$983$	0.494996	+	1.52344i	0.0157879	+	0.0485902i	−0.942852	+	0.333211i	$0.891868\pi$
$984$	9.59988	−	6.97472i	0.306033	−	0.222346i
$985$	6.83923	−	4.96899i	0.217916	−	0.158325i
$986$	8.06785	+	24.8303i	0.256933	+	0.790758i
$987$	7.19054	−	22.1302i	0.228878	−	0.704413i
$988$	−1.01062	−	0.734261i	−0.0321522	−	0.0233599i
$989$	−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	$0.221670\pi$
$992$	12.5562	+	9.12258i	0.398658	+	0.289642i
$993$	4.70169	−	14.4703i	0.149204	−	0.459202i
$994$	12.9318	+	39.7999i	0.410171	+	1.26238i
$995$	5.26697	−	3.82668i	0.166974	−	0.121314i
$996$	−2.08158	+	1.51236i	−0.0659574	+	0.0479208i
$997$	−7.06652	−	21.7485i	−0.223799	−	0.688782i	−0.998411	−	0.0563459i	$-0.982055\pi$
$997$	−7.06652	−	21.7485i	−0.223799	−	0.688782i	0.774612	−	0.632436i	$-0.217945\pi$
$998$	15.1969	−	46.7713i	0.481050	−	1.48052i
$999$	−25.2009	−	18.3095i	−0.797321	−	0.579288i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.16.1	✓	8	11.9	even	5
55.2.g.a.31.1	yes	8	11.4	even	5
275.2.h.b.126.2		8	55.9	even	10
275.2.h.b.251.2		8	55.4	even	10
275.2.z.b.49.2		16	55.53	odd	20
275.2.z.b.49.3		16	55.42	odd	20
275.2.z.b.174.2		16	55.37	odd	20
275.2.z.b.174.3		16	55.48	odd	20
495.2.n.f.181.2		8	33.20	odd	10
495.2.n.f.361.2		8	33.26	odd	10
605.2.a.i.1.4		4	11.6	odd	10
605.2.a.l.1.1		4	11.5	even	5
605.2.g.g.81.1		8	11.10	odd	2
605.2.g.g.366.1		8	11.8	odd	10
605.2.g.j.81.2		8	1.1	even	1	trivial
605.2.g.j.366.2		8	11.3	even	5	inner
605.2.g.n.251.2		8	11.7	odd	10
605.2.g.n.511.2		8	11.2	odd	10
880.2.bo.e.401.1		8	44.31	odd	10
880.2.bo.e.801.1		8	44.15	odd	10
3025.2.a.v.1.4		4	55.49	even	10
3025.2.a.be.1.1		4	55.39	odd	10
5445.2.a.bg.1.4		4	33.5	odd	10
5445.2.a.bu.1.1		4	33.17	even	10
9680.2.a.cs.1.3		4	44.27	odd	10
9680.2.a.cv.1.3		4	44.39	even	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)

\(f(q)\)	\(=\)	\(q+(1.51774 + 1.10270i) q^{2} +(-0.549273 + 1.69049i) q^{3} +(0.469548 + 1.44512i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-2.69776 + 1.96004i) q^{6} +(1.31579 + 4.04959i) q^{7} +(0.278565 - 0.857334i) q^{8} +(-0.128998 - 0.0937225i) q^{9} +O(q^{10})\)	\(q+(1.51774 + 1.10270i) q^{2} +(-0.549273 + 1.69049i) q^{3} +(0.469548 + 1.44512i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-2.69776 + 1.96004i) q^{6} +(1.31579 + 4.04959i) q^{7} +(0.278565 - 0.857334i) q^{8} +(-0.128998 - 0.0937225i) q^{9} -1.87603 q^{10} -2.70087 q^{12} +(-1.10029 - 0.799410i) q^{13} +(-2.46847 + 7.59716i) q^{14} +(-0.549273 - 1.69049i) q^{15} +(3.82676 - 2.78030i) q^{16} +(-1.69776 + 1.23349i) q^{17} +(-0.0924373 - 0.284493i) q^{18} +(0.186795 - 0.574896i) q^{19} +(-1.22929 - 0.893133i) q^{20} -7.56852 q^{21} -4.39768 q^{23} +(1.29630 + 0.941821i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-0.788448 - 2.42659i) q^{26} +(-4.08475 + 2.96775i) q^{27} +(-5.23432 + 3.80296i) q^{28} +(-2.04927 - 6.30701i) q^{29} +(1.03045 - 3.17141i) q^{30} +(1.77574 + 1.29015i) q^{31} +7.07096 q^{32} -3.93693 q^{34} +(-3.44479 - 2.50279i) q^{35} +(0.0748695 - 0.230425i) q^{36} +(1.90648 + 5.86755i) q^{37} +(0.917446 - 0.666564i) q^{38} +(1.95576 - 1.42094i) q^{39} +(0.278565 + 0.857334i) q^{40} +(2.28845 - 7.04312i) q^{41} +(-11.4870 - 8.34583i) q^{42} +12.6671 q^{43} +0.159450 q^{45} +(-6.67453 - 4.84933i) q^{46} +(-0.950059 + 2.92398i) q^{47} +(2.59813 + 7.99623i) q^{48} +(-9.00479 + 6.54236i) q^{49} +(1.51774 - 1.10270i) q^{50} +(-1.15267 - 3.54757i) q^{51} +(0.638603 - 1.96542i) q^{52} +(5.38281 + 3.91084i) q^{53} -9.47214 q^{54} +3.83839 q^{56} +(0.869254 + 0.631550i) q^{57} +(3.84450 - 11.8321i) q^{58} +(3.71969 + 11.4480i) q^{59} +(2.18505 - 1.58753i) q^{60} +(4.60249 - 3.34391i) q^{61} +(1.27246 + 3.91622i) q^{62} +(0.209804 - 0.645709i) q^{63} +(3.07837 + 2.23656i) q^{64} +1.36004 q^{65} +9.86416 q^{67} +(-2.57973 - 1.87428i) q^{68} +(2.41553 - 7.43422i) q^{69} +(-2.46847 - 7.59716i) q^{70} +(4.23827 - 3.07928i) q^{71} +(-0.116286 + 0.0844866i) q^{72} +(-0.223356 - 0.687418i) q^{73} +(-3.57662 + 11.0077i) q^{74} +(1.43801 + 1.04478i) q^{75} +0.918503 q^{76} +4.53520 q^{78} +(-4.58758 - 3.33307i) q^{79} +(-1.46169 + 4.49862i) q^{80} +(-2.92111 - 8.99027i) q^{81} +(11.2397 - 8.16615i) q^{82} +(0.770708 - 0.559952i) q^{83} +(-3.55378 - 10.9374i) q^{84} +(0.648486 - 1.99584i) q^{85} +(19.2253 + 13.9680i) q^{86} +11.7875 q^{87} +1.24095 q^{89} +(0.242004 + 0.175826i) q^{90} +(1.78953 - 5.50760i) q^{91} +(-2.06492 - 6.35517i) q^{92} +(-3.15634 + 2.29322i) q^{93} +(-4.66623 + 3.39021i) q^{94} +(0.186795 + 0.574896i) q^{95} +(-3.88389 + 11.9534i) q^{96} +(-9.33856 - 6.78486i) q^{97} -20.8812 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - 12 q^{6} - 8 q^{7} - 7 q^{8} + 5 q^{9}+O(q^{10}) \) 8 * q + q^2 + q^3 - q^4 - 2 * q^5 - 12 * q^6 - 8 * q^7 - 7 * q^8 + 5 * q^9	\( 8 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - 12 q^{6} - 8 q^{7} - 7 q^{8} + 5 q^{9} + 6 q^{10} - 28 q^{12} - 11 q^{13} - 14 q^{14} + q^{15} + 15 q^{16} - 4 q^{17} - 16 q^{18} - 11 q^{19} - 6 q^{20} - 12 q^{21} - 18 q^{23} - 10 q^{24} - 2 q^{25} + q^{26} - 5 q^{27} - 11 q^{28} - 11 q^{29} + 13 q^{30} - 9 q^{31} + 12 q^{32} - 20 q^{34} - 3 q^{35} - 29 q^{36} - q^{37} - 6 q^{38} - 6 q^{39} - 7 q^{40} + 11 q^{41} - 31 q^{42} + 42 q^{43} + 29 q^{46} - q^{47} + 21 q^{48} + q^{50} - 22 q^{51} - q^{52} + 8 q^{53} - 40 q^{54} + 30 q^{56} + 4 q^{58} + 26 q^{59} - 8 q^{60} - 2 q^{61} + 27 q^{62} - 4 q^{63} + 21 q^{64} + 14 q^{65} - 2 q^{67} - 20 q^{68} + 49 q^{69} - 14 q^{70} - 25 q^{71} + 21 q^{72} + 32 q^{73} - 12 q^{74} + q^{75} + 16 q^{76} + 12 q^{78} - 23 q^{79} - 20 q^{80} + 20 q^{81} + 42 q^{82} + 10 q^{83} + 51 q^{84} + q^{85} + 34 q^{86} + 30 q^{87} + 14 q^{90} + 8 q^{91} - 99 q^{92} - 8 q^{93} - 22 q^{94} - 11 q^{95} + 3 q^{96} - 18 q^{97} - 84 q^{98}+O(q^{100}) \) 8 * q + q^2 + q^3 - q^4 - 2 * q^5 - 12 * q^6 - 8 * q^7 - 7 * q^8 + 5 * q^9 + 6 * q^10 - 28 * q^12 - 11 * q^13 - 14 * q^14 + q^15 + 15 * q^16 - 4 * q^17 - 16 * q^18 - 11 * q^19 - 6 * q^20 - 12 * q^21 - 18 * q^23 - 10 * q^24 - 2 * q^25 + q^26 - 5 * q^27 - 11 * q^28 - 11 * q^29 + 13 * q^30 - 9 * q^31 + 12 * q^32 - 20 * q^34 - 3 * q^35 - 29 * q^36 - q^37 - 6 * q^38 - 6 * q^39 - 7 * q^40 + 11 * q^41 - 31 * q^42 + 42 * q^43 + 29 * q^46 - q^47 + 21 * q^48 + q^50 - 22 * q^51 - q^52 + 8 * q^53 - 40 * q^54 + 30 * q^56 + 4 * q^58 + 26 * q^59 - 8 * q^60 - 2 * q^61 + 27 * q^62 - 4 * q^63 + 21 * q^64 + 14 * q^65 - 2 * q^67 - 20 * q^68 + 49 * q^69 - 14 * q^70 - 25 * q^71 + 21 * q^72 + 32 * q^73 - 12 * q^74 + q^75 + 16 * q^76 + 12 * q^78 - 23 * q^79 - 20 * q^80 + 20 * q^81 + 42 * q^82 + 10 * q^83 + 51 * q^84 + q^85 + 34 * q^86 + 30 * q^87 + 14 * q^90 + 8 * q^91 - 99 * q^92 - 8 * q^93 - 22 * q^94 - 11 * q^95 + 3 * q^96 - 18 * q^97 - 84 * q^98

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