LMFDB - Embedded newform 605.2.g.p.366.3

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:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 6 x^{10} - 12 x^{9} + 43 x^{8} + 72 x^{7} + 155 x^{6} + 162 x^{5} + 541 x^{4} + \cdots + 1 $ x^12 - x^11 + 6x^10 - 12x^9 + 43x^8 + 72x^7 + 155x^6 + 162x^5 + 541x^4 + 114x^3 + 24x^2 + 5x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			366.3
Root			$-0.885704 - 2.72592i$ of defining polynomial
Character	$\chi$	$=$	605.366
Dual form			605.2.g.p.81.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.90030 - 1.38065i) q^{2} +(0.885704 + 2.72592i) q^{3} +(1.08691 - 3.34515i) q^{4} +(0.809017 + 0.587785i) q^{5} +(5.44662 + 3.95720i) q^{6} +(1.04556 - 3.21790i) q^{7} +(-1.10133 - 3.38955i) q^{8} +(-4.21910 + 3.06535i) q^{9} +O(q^{10})$	\(q+(1.90030 - 1.38065i) q^{2} +(0.885704 + 2.72592i) q^{3} +(1.08691 - 3.34515i) q^{4} +(0.809017 + 0.587785i) q^{5} +(5.44662 + 3.95720i) q^{6} +(1.04556 - 3.21790i) q^{7} +(-1.10133 - 3.38955i) q^{8} +(-4.21910 + 3.06535i) q^{9} +2.34889 q^{10} +10.0813 q^{12} +(1.19953 - 0.871507i) q^{13} +(-2.45591 - 7.55851i) q^{14} +(-0.885704 + 2.72592i) q^{15} +(-1.08151 - 0.785763i) q^{16} +(-3.01957 - 2.19385i) q^{17} +(-3.78537 + 11.6502i) q^{18} +(0.993518 + 3.05773i) q^{19} +(2.84556 - 2.06742i) q^{20} +9.69779 q^{21} -2.51730 q^{23} +(8.26418 - 6.00428i) q^{24} +(0.309017 + 0.951057i) q^{25} +(1.07621 - 3.31224i) q^{26} +(-5.13636 - 3.73179i) q^{27} +(-9.62795 - 6.99512i) q^{28} +(-1.45170 + 4.46786i) q^{29} +(2.08042 + 6.40289i) q^{30} +(-7.45517 + 5.41650i) q^{31} +3.98793 q^{32} -8.76700 q^{34} +(2.73731 - 1.98877i) q^{35} +(5.66832 + 17.4453i) q^{36} +(-0.833662 + 2.56575i) q^{37} +(6.10963 + 4.43890i) q^{38} +(3.43808 + 2.49791i) q^{39} +(1.10133 - 3.38955i) q^{40} +(-1.40662 - 4.32913i) q^{41} +(18.4287 - 13.3892i) q^{42} -5.38350 q^{43} -5.21509 q^{45} +(-4.78362 + 3.47550i) q^{46} +(-3.25376 - 10.0140i) q^{47} +(1.18403 - 3.64406i) q^{48} +(-3.59858 - 2.61452i) q^{49} +(1.90030 + 1.38065i) q^{50} +(3.30580 - 10.1742i) q^{51} +(-1.61155 - 4.95985i) q^{52} +(2.03654 - 1.47963i) q^{53} -14.9129 q^{54} -12.0588 q^{56} +(-7.45517 + 5.41650i) q^{57} +(3.40988 + 10.4945i) q^{58} +(3.68128 - 11.3298i) q^{59} +(8.15594 + 5.92563i) q^{60} +(-11.0673 - 8.04083i) q^{61} +(-6.68876 + 20.5859i) q^{62} +(5.45269 + 16.7817i) q^{63} +(9.74126 - 7.07744i) q^{64} +1.48270 q^{65} +7.83159 q^{67} +(-10.6208 + 7.71643i) q^{68} +(-2.22959 - 6.86196i) q^{69} +(2.45591 - 7.55851i) q^{70} +(-2.03654 - 1.47963i) q^{71} +(15.0368 + 10.9249i) q^{72} +(0.916356 - 2.82026i) q^{73} +(1.95818 + 6.02667i) q^{74} +(-2.31880 + 1.68471i) q^{75} +11.3085 q^{76} +9.98210 q^{78} +(5.47462 - 3.97755i) q^{79} +(-0.413100 - 1.27139i) q^{80} +(0.788584 - 2.42701i) q^{81} +(-8.64998 - 6.28458i) q^{82} +(6.10963 + 4.43890i) q^{83} +(10.5406 - 32.4406i) q^{84} +(-1.15337 - 3.54972i) q^{85} +(-10.2302 + 7.43271i) q^{86} -13.4648 q^{87} +10.8016 q^{89} +(-9.91022 + 7.20019i) q^{90} +(-1.55025 - 4.77117i) q^{91} +(-2.73607 + 8.42077i) q^{92} +(-21.3680 - 15.5247i) q^{93} +(-20.0089 - 14.5373i) q^{94} +(-0.993518 + 3.05773i) q^{95} +(3.53212 + 10.8708i) q^{96} +(-8.91270 + 6.47546i) q^{97} -10.4481 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} - q^{3} - 9 q^{4} + 3 q^{5} + 5 q^{6} - q^{7} - 9 q^{8} - 2 q^{9}+O(q^{10}) $ 12 * q + q^2 - q^3 - 9 * q^4 + 3 * q^5 + 5 * q^6 - q^7 - 9 * q^8 - 2 * q^9	$ 12 q + q^{2} - q^{3} - 9 q^{4} + 3 q^{5} + 5 q^{6} - q^{7} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 36 q^{12} + 6 q^{13} - 5 q^{14} + q^{15} - 13 q^{16} + 4 q^{17} + 20 q^{18} + 4 q^{19} + 9 q^{20} + 68 q^{21} - 24 q^{23} + 17 q^{24} - 3 q^{25} - 12 q^{26} - 13 q^{27} - 25 q^{28} + 2 q^{29} - 5 q^{30} - 14 q^{31} + 108 q^{32} - 32 q^{34} + q^{35} - 2 q^{36} - 4 q^{37} + 18 q^{38} - 4 q^{39} + 9 q^{40} + 9 q^{41} + 35 q^{42} - 28 q^{43} - 8 q^{45} + 8 q^{46} + 15 q^{47} - 7 q^{48} - 18 q^{49} + q^{50} - 20 q^{51} + 2 q^{52} + 6 q^{53} - 76 q^{54} - 12 q^{56} - 14 q^{57} - 30 q^{58} - 10 q^{59} + 9 q^{60} + 3 q^{61} + 24 q^{62} - 12 q^{63} - 29 q^{64} + 24 q^{65} + 76 q^{67} + 8 q^{69} + 5 q^{70} - 6 q^{71} + 48 q^{72} - 12 q^{73} - 28 q^{74} - q^{75} - 64 q^{76} - 8 q^{78} + 2 q^{79} + 13 q^{80} - 3 q^{81} + 27 q^{82} + 18 q^{83} - 31 q^{84} - 4 q^{85} + 3 q^{86} - 40 q^{87} + 44 q^{89} - 20 q^{90} - 20 q^{91} + 34 q^{92} - 20 q^{93} - 59 q^{94} - 4 q^{95} - 7 q^{96} + 2 q^{97} - 144 q^{98}+O(q^{100}) $ 12 * q + q^2 - q^3 - 9 * q^4 + 3 * q^5 + 5 * q^6 - q^7 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 36 * q^12 + 6 * q^13 - 5 * q^14 + q^15 - 13 * q^16 + 4 * q^17 + 20 * q^18 + 4 * q^19 + 9 * q^20 + 68 * q^21 - 24 * q^23 + 17 * q^24 - 3 * q^25 - 12 * q^26 - 13 * q^27 - 25 * q^28 + 2 * q^29 - 5 * q^30 - 14 * q^31 + 108 * q^32 - 32 * q^34 + q^35 - 2 * q^36 - 4 * q^37 + 18 * q^38 - 4 * q^39 + 9 * q^40 + 9 * q^41 + 35 * q^42 - 28 * q^43 - 8 * q^45 + 8 * q^46 + 15 * q^47 - 7 * q^48 - 18 * q^49 + q^50 - 20 * q^51 + 2 * q^52 + 6 * q^53 - 76 * q^54 - 12 * q^56 - 14 * q^57 - 30 * q^58 - 10 * q^59 + 9 * q^60 + 3 * q^61 + 24 * q^62 - 12 * q^63 - 29 * q^64 + 24 * q^65 + 76 * q^67 + 8 * q^69 + 5 * q^70 - 6 * q^71 + 48 * q^72 - 12 * q^73 - 28 * q^74 - q^75 - 64 * q^76 - 8 * q^78 + 2 * q^79 + 13 * q^80 - 3 * q^81 + 27 * q^82 + 18 * q^83 - 31 * q^84 - 4 * q^85 + 3 * q^86 - 40 * q^87 + 44 * q^89 - 20 * q^90 - 20 * q^91 + 34 * q^92 - 20 * q^93 - 59 * q^94 - 4 * q^95 - 7 * q^96 + 2 * q^97 - 144 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	1.90030	−	1.38065i	1.34371	−	0.976264i	0.344413	−	0.938818i	$-0.388078\pi$
$2$	1.90030	−	1.38065i	1.34371	−	0.976264i	0.999299	−	0.0374455i	$-0.0119221\pi$
$3$	0.885704	+	2.72592i	0.511361	+	1.57381i	0.789806	+	0.613356i	$0.210181\pi$
$3$	0.885704	+	2.72592i	0.511361	+	1.57381i	−0.278445	+	0.960452i	$0.589819\pi$
$4$	1.08691	−	3.34515i	0.543453	−	1.67258i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$	5.44662	+	3.95720i	2.22357	+	1.61552i
$7$	1.04556	−	3.21790i	0.395184	−	1.21625i	−0.533633	−	0.845716i	$-0.679174\pi$
$7$	1.04556	−	3.21790i	0.395184	−	1.21625i	0.928818	−	0.370537i	$-0.120826\pi$
$8$	−1.10133	−	3.38955i	−0.389380	−	1.19839i
$9$	−4.21910	+	3.06535i	−1.40637	+	1.02178i
$10$	2.34889			0.742786
$11$		0			0
$11$		0			0
$12$	10.0813			2.91022
$13$	1.19953	−	0.871507i	0.332689	−	0.241713i	−0.408882	−	0.912587i	$-0.634081\pi$
$13$	1.19953	−	0.871507i	0.332689	−	0.241713i	0.741571	+	0.670875i	$0.234081\pi$
$14$	−2.45591	−	7.55851i	−0.656369	−	2.02010i
$15$	−0.885704	+	2.72592i	−0.228688	+	0.703829i
$16$	−1.08151	−	0.785763i	−0.270377	−	0.196441i
$17$	−3.01957	−	2.19385i	−0.732354	−	0.532086i	0.157953	−	0.987447i	$-0.449510\pi$
$17$	−3.01957	−	2.19385i	−0.732354	−	0.532086i	−0.890307	+	0.455360i	$0.849510\pi$
$18$	−3.78537	+	11.6502i	−0.892219	+	2.74597i
$19$	0.993518	+	3.05773i	0.227929	+	0.701492i	0.997981	+	0.0635118i	$0.0202300\pi$
$19$	0.993518	+	3.05773i	0.227929	+	0.701492i	−0.770052	+	0.637981i	$0.779770\pi$
$20$	2.84556	−	2.06742i	0.636286	−	0.462289i
$21$	9.69779			2.11623
$22$		0			0
$23$	−2.51730			−0.524894			−0.262447	−	0.964946i	$-0.584530\pi$
$23$	−2.51730			−0.524894			−0.262447	+	0.964946i	$0.584530\pi$
$24$	8.26418	−	6.00428i	1.68692	−	1.22562i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	1.07621	−	3.31224i	0.211063	−	0.649584i
$27$	−5.13636	−	3.73179i	−0.988494	−	0.718183i
$28$	−9.62795	−	6.99512i	−1.81951	−	1.32195i
$29$	−1.45170	+	4.46786i	−0.269573	+	0.829661i	0.721031	+	0.692903i	$0.243668\pi$
$29$	−1.45170	+	4.46786i	−0.269573	+	0.829661i	−0.990604	+	0.136759i	$0.956332\pi$
$30$	2.08042	+	6.40289i	0.379832	+	1.16900i
$31$	−7.45517	+	5.41650i	−1.33899	+	0.972831i	−0.339507	+	0.940604i	$0.610260\pi$
$31$	−7.45517	+	5.41650i	−1.33899	+	0.972831i	−0.999481	+	0.0322277i	$0.989740\pi$
$32$	3.98793			0.704972
$33$		0			0
$34$	−8.76700			−1.50353
$35$	2.73731	−	1.98877i	0.462690	−	0.336164i
$36$	5.66832	+	17.4453i	0.944720	+	2.90755i
$37$	−0.833662	+	2.56575i	−0.137053	+	0.421807i	−0.995904	−	0.0904198i	$-0.971179\pi$
$37$	−0.833662	+	2.56575i	−0.137053	+	0.421807i	0.858850	+	0.512226i	$0.171179\pi$
$38$	6.10963	+	4.43890i	0.991112	+	0.720085i
$39$	3.43808	+	2.49791i	0.550533	+	0.399986i
$40$	1.10133	−	3.38955i	0.174136	−	0.535935i
$41$	−1.40662	−	4.32913i	−0.219677	−	0.676096i	−0.998788	−	0.0492106i	$-0.984329\pi$
$41$	−1.40662	−	4.32913i	−0.219677	−	0.676096i	0.779112	−	0.626885i	$-0.215671\pi$
$42$	18.4287	−	13.3892i	2.84360	−	2.06600i
$43$	−5.38350			−0.820976			−0.410488	−	0.911866i	$-0.634642\pi$
$43$	−5.38350			−0.820976			−0.410488	+	0.911866i	$0.634642\pi$
$44$		0			0
$45$	−5.21509			−0.777420
$46$	−4.78362	+	3.47550i	−0.705306	+	0.512435i
$47$	−3.25376	−	10.0140i	−0.474609	−	1.46070i	−0.846484	−	0.532414i	$-0.821285\pi$
$47$	−3.25376	−	10.0140i	−0.474609	−	1.46070i	0.371875	−	0.928283i	$-0.378715\pi$
$48$	1.18403	−	3.64406i	0.170900	−	0.525975i
$49$	−3.59858	−	2.61452i	−0.514083	−	0.373503i
$50$	1.90030	+	1.38065i	0.268742	+	0.195253i
$51$	3.30580	−	10.1742i	0.462904	−	1.42467i
$52$	−1.61155	−	4.95985i	−0.223482	−	0.687807i
$53$	2.03654	−	1.47963i	0.279741	−	0.203243i	−0.439064	−	0.898456i	$-0.644690\pi$
$53$	2.03654	−	1.47963i	0.279741	−	0.203243i	0.718804	+	0.695213i	$0.244690\pi$
$54$	−14.9129			−2.02939
$55$		0			0
$56$	−12.0588			−1.61142
$57$	−7.45517	+	5.41650i	−0.987461	+	0.717432i
$58$	3.40988	+	10.4945i	0.447739	+	1.37800i
$59$	3.68128	−	11.3298i	0.479262	−	1.47502i	−0.360860	−	0.932620i	$-0.617517\pi$
$59$	3.68128	−	11.3298i	0.479262	−	1.47502i	0.840122	−	0.542397i	$-0.182483\pi$
$60$	8.15594	+	5.92563i	1.05293	+	0.764996i
$61$	−11.0673	−	8.04083i	−1.41702	−	1.02952i	−0.992255	−	0.124219i	$-0.960358\pi$
$61$	−11.0673	−	8.04083i	−1.41702	−	1.02952i	−0.424763	−	0.905305i	$-0.639642\pi$
$62$	−6.68876	+	20.5859i	−0.849473	+	2.61441i
$63$	5.45269	+	16.7817i	0.686974	+	2.11429i
$64$	9.74126	−	7.07744i	1.21766	−	0.884680i
$65$	1.48270			0.183906
$66$		0			0
$67$	7.83159			0.956781			0.478391	−	0.878147i	$-0.341220\pi$
$67$	7.83159			0.956781			0.478391	+	0.878147i	$0.341220\pi$
$68$	−10.6208	+	7.71643i	−1.28796	+	0.935754i
$69$	−2.22959	−	6.86196i	−0.268411	−	0.826083i
$70$	2.45591	−	7.55851i	0.293537	−	0.903415i
$71$	−2.03654	−	1.47963i	−0.241693	−	0.175600i	0.460344	−	0.887741i	$-0.347726\pi$
$71$	−2.03654	−	1.47963i	−0.241693	−	0.175600i	−0.702037	+	0.712140i	$0.747726\pi$
$72$	15.0368	+	10.9249i	1.77211	+	1.28751i
$73$	0.916356	−	2.82026i	0.107251	−	0.330086i	−0.883001	−	0.469371i	$-0.844481\pi$
$73$	0.916356	−	2.82026i	0.107251	−	0.330086i	0.990252	+	0.139285i	$0.0444806\pi$
$74$	1.95818	+	6.02667i	0.227634	+	0.700587i
$75$	−2.31880	+	1.68471i	−0.267752	+	0.194533i
$76$	11.3085			1.29717
$77$		0			0
$78$	9.98210			1.13025
$79$	5.47462	−	3.97755i	0.615943	−	0.447509i	−0.235559	−	0.971860i	$-0.575692\pi$
$79$	5.47462	−	3.97755i	0.615943	−	0.447509i	0.851502	+	0.524351i	$0.175692\pi$
$80$	−0.413100	−	1.27139i	−0.0461860	−	0.142146i
$81$	0.788584	−	2.42701i	0.0876205	−	0.269668i
$82$	−8.64998	−	6.28458i	−0.955230	−	0.694015i
$83$	6.10963	+	4.43890i	0.670618	+	0.487233i	0.870232	−	0.492642i	$-0.163969\pi$
$83$	6.10963	+	4.43890i	0.670618	+	0.487233i	−0.199614	+	0.979875i	$0.563969\pi$
$84$	10.5406	−	32.4406i	1.15007	−	3.53956i
$85$	−1.15337	−	3.54972i	−0.125101	−	0.385021i
$86$	−10.2302	+	7.43271i	−1.10316	+	0.801489i
$87$	−13.4648			−1.44358
$88$		0			0
$89$	10.8016			1.14497			0.572484	−	0.819916i	$-0.305980\pi$
$89$	10.8016			1.14497			0.572484	+	0.819916i	$0.305980\pi$
$90$	−9.91022	+	7.20019i	−1.04463	+	0.758967i
$91$	−1.55025	−	4.77117i	−0.162510	−	0.500155i
$92$	−2.73607	+	8.42077i	−0.285256	+	0.877926i
$93$	−21.3680	−	15.5247i	−2.21576	−	1.60984i
$94$	−20.0089	−	14.5373i	−2.06376	−	1.49941i
$95$	−0.993518	+	3.05773i	−0.101933	+	0.313717i
$96$	3.53212	+	10.8708i	0.360496	+	1.10949i
$97$	−8.91270	+	6.47546i	−0.904948	+	0.657483i	−0.939732	−	0.341912i	$-0.888926\pi$
$97$	−8.91270	+	6.47546i	−0.904948	+	0.657483i	0.0347843	+	0.999395i	$0.488926\pi$
$98$	−10.4481			−1.05542
$99$		0			0
$100$	3.51730			0.351730
$101$	−10.3007	+	7.48391i	−1.02496	+	0.744677i	−0.967294	−	0.253659i	$-0.918366\pi$
$101$	−10.3007	+	7.48391i	−1.02496	+	0.744677i	−0.0576666	+	0.998336i	$0.518366\pi$
$102$	−7.76497	−	23.8981i	−0.768847	−	2.36627i
$103$	−5.66832	+	17.4453i	−0.558516	+	1.71894i	0.127956	+	0.991780i	$0.459158\pi$
$103$	−5.66832	+	17.4453i	−0.558516	+	1.71894i	−0.686472	+	0.727156i	$0.740842\pi$
$104$	−4.27510	−	3.10604i	−0.419208	−	0.304572i
$105$	7.84568	+	5.70022i	0.765660	+	0.556284i
$106$	1.82718	−	5.62348i	0.177471	−	0.546201i
$107$	−2.20447	−	6.78465i	−0.213114	−	0.655897i	−0.999282	−	0.0378844i	$-0.987938\pi$
$107$	−2.20447	−	6.78465i	−0.213114	−	0.655897i	0.786168	−	0.618012i	$-0.212062\pi$
$108$	−18.0662	+	13.1258i	−1.73842	+	1.26303i
$109$	−4.14588			−0.397103			−0.198551	−	0.980090i	$-0.563624\pi$
$109$	−4.14588			−0.397103			−0.198551	+	0.980090i	$0.563624\pi$
$110$		0			0
$111$	−7.73240			−0.733927
$112$	−3.65929	+	2.65863i	−0.345770	+	0.251217i
$113$	0.452646	+	1.39310i	0.0425813	+	0.131052i	0.970087	−	0.242757i	$-0.0780517\pi$
$113$	0.452646	+	1.39310i	0.0425813	+	0.131052i	−0.927506	+	0.373809i	$0.878052\pi$
$114$	−6.68876	+	20.5859i	−0.626460	+	1.92804i
$115$	−2.03654	−	1.47963i	−0.189908	−	0.137977i
$116$	13.3678	+	9.71230i	1.24117	+	0.901764i
$117$	−2.38944	+	7.35395i	−0.220904	+	0.679873i
$118$	−8.64694	−	26.6126i	−0.796016	−	2.44988i
$119$	−10.2167	+	7.42289i	−0.936566	+	0.680455i
$120$	10.2151			0.932506
$121$		0			0
$122$	−32.1326			−2.90915
$123$	10.5550	−	7.66865i	0.951711	−	0.691459i
$124$	10.0159	+	30.8259i	0.899459	+	2.76825i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	33.5312	+	24.3619i	2.98720	+	2.17033i
$127$	9.13897	+	6.63985i	0.810952	+	0.589191i	0.914107	−	0.405474i	$-0.132894\pi$
$127$	9.13897	+	6.63985i	0.810952	+	0.589191i	−0.103154	+	0.994665i	$0.532894\pi$
$128$	6.27516	−	19.3130i	0.554651	−	1.70704i
$129$	−4.76819	−	14.6750i	−0.419816	−	1.29206i
$130$	2.81756	−	2.04708i	0.247116	−	0.179541i
$131$	14.6799			1.28259			0.641294	−	0.767295i	$-0.278398\pi$
$131$	14.6799			1.28259			0.641294	+	0.767295i	$0.278398\pi$
$132$		0			0
$133$	10.8783			0.943266
$134$	14.8823	−	10.8126i	1.28564	−	0.934071i
$135$	−1.96192	−	6.03816i	−0.168855	−	0.519682i
$136$	−4.11061	+	12.6512i	−0.352482	+	1.08483i
$137$	12.6573	+	9.19606i	1.08139	+	0.785673i	0.977924	−	0.208961i	$-0.0670081\pi$
$137$	12.6573	+	9.19606i	1.08139	+	0.785673i	0.103462	+	0.994633i	$0.467008\pi$
$138$	−13.7108	−	9.96148i	−1.16714	−	0.847978i
$139$	−2.36252	+	7.27109i	−0.200386	+	0.616726i	0.799485	+	0.600686i	$0.205106\pi$
$139$	−2.36252	+	7.27109i	−0.200386	+	0.616726i	−0.999871	+	0.0160398i	$0.994894\pi$
$140$	−3.67755	−	11.3183i	−0.310810	−	0.956574i
$141$	24.4156	−	17.7389i	2.05616	−	1.49389i
$142$	−5.91288			−0.496198
$143$		0			0
$144$	6.97164			0.580970
$145$	−3.80059	+	2.76129i	−0.315622	+	0.229313i
$146$	−2.15242	−	6.62448i	−0.178136	−	0.548246i
$147$	3.93969	−	12.1251i	0.324940	−	1.00006i
$148$	7.67672	+	5.57746i	0.631022	+	0.458464i
$149$	5.24461	+	3.81043i	0.429655	+	0.312163i	0.781511	−	0.623891i	$-0.214449\pi$
$149$	5.24461	+	3.81043i	0.429655	+	0.312163i	−0.351856	+	0.936054i	$0.614449\pi$
$150$	−2.08042	+	6.40289i	−0.169866	+	0.522794i
$151$	−3.36157	−	10.3459i	−0.273561	−	0.841934i	−0.989597	−	0.143870i	$-0.954045\pi$
$151$	−3.36157	−	10.3459i	−0.273561	−	0.841934i	0.716036	−	0.698064i	$-0.245955\pi$
$152$	9.27016	−	6.73516i	0.751909	−	0.546294i
$153$	19.4648			1.57364
$154$		0			0
$155$	−9.21509			−0.740174
$156$	12.0928	−	8.78591i	0.968197	−	0.703436i
$157$	3.22310	+	9.91970i	0.257232	+	0.791678i	0.993382	+	0.114859i	$0.0366418\pi$
$157$	3.22310	+	9.91970i	0.257232	+	0.791678i	−0.736150	+	0.676818i	$0.763358\pi$
$158$	4.91182	−	15.1170i	0.390763	−	1.20265i
$159$	5.83713	+	4.24092i	0.462915	+	0.336327i
$160$	3.22630	+	2.34404i	0.255061	+	0.185313i
$161$	−2.63199	+	8.10044i	−0.207430	+	0.638404i
$162$	−1.85230	−	5.70080i	−0.145531	−	0.447897i
$163$	8.28747	−	6.02120i	0.649124	−	0.471617i	−0.213848	−	0.976867i	$-0.568600\pi$
$163$	8.28747	−	6.02120i	0.649124	−	0.471617i	0.862973	+	0.505250i	$0.168600\pi$
$164$	−16.0105			−1.25021
$165$		0			0
$166$	17.7386			1.37679
$167$	−0.846784	+	0.615225i	−0.0655261	+	0.0476075i	−0.620066	−	0.784550i	$-0.712894\pi$
$167$	−0.846784	+	0.615225i	−0.0655261	+	0.0476075i	0.554540	+	0.832157i	$0.312894\pi$
$168$	−10.6805	−	32.8712i	−0.824018	−	2.53607i
$169$	−3.33788	+	10.2729i	−0.256760	+	0.790226i
$170$	−7.09266	−	5.15312i	−0.543982	−	0.395226i
$171$	−13.5648	−	9.85540i	−1.03733	−	0.753661i
$172$	−5.85136	+	18.0086i	−0.446162	+	1.37315i
$173$	−3.68128	−	11.3298i	−0.279883	−	0.861390i	−0.987886	−	0.155181i	$-0.950404\pi$
$173$	−3.68128	−	11.3298i	−0.279883	−	0.861390i	0.708003	−	0.706209i	$-0.249596\pi$
$174$	−25.5871	+	18.5901i	−1.93975	+	1.40931i
$175$	3.38350			0.255769
$176$		0			0
$177$	34.1447			2.56647
$178$	20.5263	−	14.9132i	1.53851	−	1.11779i
$179$	−1.04929	−	3.22939i	−0.0784277	−	0.241376i	0.904154	−	0.427207i	$-0.140502\pi$
$179$	−1.04929	−	3.22939i	−0.0784277	−	0.241376i	−0.982582	+	0.185831i	$0.940502\pi$
$180$	−5.66832	+	17.4453i	−0.422492	+	1.30030i
$181$	4.60961	+	3.34908i	0.342629	+	0.248935i	0.745770	−	0.666203i	$-0.232082\pi$
$181$	4.60961	+	3.34908i	0.342629	+	0.248935i	−0.403141	+	0.915138i	$0.632082\pi$
$182$	−9.53322	−	6.92629i	−0.706649	−	0.513411i
$183$	12.1163	−	37.2902i	0.895665	−	2.75657i
$184$	2.77239	+	8.53253i	0.204383	+	0.629027i
$185$	−2.18256	+	1.58572i	−0.160465	+	0.116584i
$186$	−62.0397			−4.54897
$187$		0			0
$188$	−37.0350			−2.70106
$189$	−17.3789	+	12.6265i	−1.26413	+	0.918443i
$190$	2.33367	+	7.18230i	0.169302	+	0.521058i
$191$	−2.78632	+	8.57540i	−0.201611	+	0.620494i	0.798225	+	0.602360i	$0.205773\pi$
$191$	−2.78632	+	8.57540i	−0.201611	+	0.620494i	−0.999836	+	0.0181343i	$0.994227\pi$
$192$	27.9204	+	20.2853i	2.01498	+	1.46397i
$193$	21.2220	+	15.4187i	1.52759	+	1.10986i	0.957559	+	0.288237i	$0.0930691\pi$
$193$	21.2220	+	15.4187i	1.52759	+	1.10986i	0.570032	+	0.821623i	$0.306931\pi$
$194$	−7.99646	+	24.6106i	−0.574112	+	1.76694i
$195$	1.31323	+	4.04171i	0.0940423	+	0.289433i
$196$	−12.6573	+	9.19606i	−0.904093	+	0.656862i
$197$	16.6978			1.18967			0.594834	−	0.803849i	$-0.297218\pi$
$197$	16.6978			1.18967			0.594834	+	0.803849i	$0.297218\pi$
$198$		0			0
$199$	−16.7912			−1.19029			−0.595147	−	0.803617i	$-0.702906\pi$
$199$	−16.7912			−1.19029			−0.595147	+	0.803617i	$0.702906\pi$
$200$	2.88333	−	2.09486i	0.203882	−	0.148129i
$201$	6.93647	+	21.3483i	0.489261	+	1.50579i
$202$	−9.24179	+	28.4433i	−0.650250	+	2.00126i
$203$	12.8593	+	9.34283i	0.902546	+	0.655738i
$204$	−30.4412	−	22.1168i	−2.13131	−	1.54849i
$205$	1.40662	−	4.32913i	0.0982425	−	0.302359i
$206$	13.3143	+	40.9771i	0.927650	+	2.85501i
$207$	10.6208	−	7.71643i	0.738193	−	0.536329i
$208$	−1.98210			−0.137434
$209$		0			0
$210$	22.7791			1.57191
$211$	6.18516	−	4.49378i	0.425804	−	0.309365i	−0.354165	−	0.935183i	$-0.615235\pi$
$211$	6.18516	−	4.49378i	0.425804	−	0.309365i	0.779969	+	0.625818i	$0.215235\pi$
$212$	−2.73607	−	8.42077i	−0.187914	−	0.578341i
$213$	2.22959	−	6.86196i	0.152769	−	0.470174i
$214$	−13.5563	−	9.84925i	−0.926692	−	0.673281i
$215$	−4.35534	−	3.16434i	−0.297032	−	0.215806i
$216$	−6.99224	+	21.5199i	−0.475762	+	1.46424i
$217$	9.63493	+	29.6533i	0.654062	+	2.01299i
$218$	−7.87839	+	5.72398i	−0.533592	+	0.387677i
$219$	8.49940			0.574336
$220$		0			0
$221$	−5.53401			−0.372258
$222$	−14.6938	+	10.6757i	−0.986186	+	0.716506i
$223$	−1.17103	−	3.60406i	−0.0784181	−	0.241346i	0.904161	−	0.427192i	$-0.140497\pi$
$223$	−1.17103	−	3.60406i	−0.0784181	−	0.241346i	−0.982579	+	0.185846i	$0.940497\pi$
$224$	4.16961	−	12.8328i	0.278594	−	0.857424i
$225$	−4.21910	−	3.06535i	−0.281273	−	0.204357i
$226$	2.78354	+	2.02236i	0.185158	+	0.134525i
$227$	6.04007	−	18.5894i	0.400894	−	1.23382i	−0.523382	−	0.852098i	$-0.675330\pi$
$227$	6.04007	−	18.5894i	0.400894	−	1.23382i	0.924276	−	0.381726i	$-0.124670\pi$
$228$	10.0159	+	30.8259i	0.663322	+	2.04150i
$229$	−4.17662	+	3.03449i	−0.275999	+	0.200525i	−0.717170	−	0.696898i	$-0.754563\pi$
$229$	−4.17662	+	3.03449i	−0.275999	+	0.200525i	0.441172	+	0.897423i	$0.354563\pi$
$230$	−5.91288			−0.389884
$231$		0			0
$232$	16.7429			1.09922
$233$	5.05611	−	3.67348i	0.331237	−	0.240658i	−0.409718	−	0.912212i	$-0.634373\pi$
$233$	5.05611	−	3.67348i	0.331237	−	0.240658i	0.740955	+	0.671554i	$0.234373\pi$
$234$	5.61255	+	17.2736i	0.366904	+	1.12921i
$235$	3.25376	−	10.0140i	0.212252	−	0.653244i
$236$	−33.8988	−	24.6289i	−2.20662	−	1.60321i
$237$	15.6914	+	11.4004i	1.01926	+	0.740538i
$238$	−9.16643	+	28.2114i	−0.594171	+	1.82867i
$239$	−1.42478	−	4.38501i	−0.0921610	−	0.283643i	0.894342	−	0.447383i	$-0.147644\pi$
$239$	−1.42478	−	4.38501i	−0.0921610	−	0.283643i	−0.986503	+	0.163741i	$0.947644\pi$
$240$	3.09982	−	2.25215i	0.200093	−	0.145376i
$241$	−7.87827			−0.507484			−0.253742	−	0.967272i	$-0.581661\pi$
$241$	−7.87827			−0.507484			−0.253742	+	0.967272i	$0.581661\pi$
$242$		0			0
$243$	−11.7324			−0.752634
$244$	−38.9269	+	28.2821i	−2.49204	+	1.81057i
$245$	−1.37453	−	4.23038i	−0.0878158	−	0.270269i
$246$	9.46991	−	29.1454i	0.603780	−	1.85824i
$247$	3.85659	+	2.80198i	0.245389	+	0.178285i
$248$	26.5701	+	19.3043i	1.68720	+	1.22583i
$249$	−6.68876	+	20.5859i	−0.423883	+	1.30458i
$250$	0.725848	+	2.23393i	0.0459067	+	0.141286i
$251$	−8.62067	+	6.26328i	−0.544132	+	0.395335i	−0.825617	−	0.564231i	$-0.809173\pi$
$251$	−8.62067	+	6.26328i	−0.544132	+	0.395335i	0.281485	+	0.959566i	$0.409173\pi$
$252$	62.0638			3.90965
$253$		0			0
$254$	26.5340			1.66489
$255$	8.65469	−	6.28800i	0.541978	−	0.393770i
$256$	−7.29803	−	22.4610i	−0.456127	−	1.40381i
$257$	0.868046	−	2.67157i	0.0541472	−	0.166648i	−0.920326	−	0.391153i	$-0.872076\pi$
$257$	0.868046	−	2.67157i	0.0541472	−	0.166648i	0.974473	+	0.224505i	$0.0720764\pi$
$258$	−29.3219	−	21.3036i	−1.82550	−	1.32631i
$259$	7.38469	+	5.36529i	0.458862	+	0.333383i
$260$	1.61155	−	4.95985i	0.0999442	−	0.307597i
$261$	−7.57073	−	23.3003i	−0.468617	−	1.44225i
$262$	27.8961	−	20.2677i	1.72343	−	1.25214i
$263$	−27.6453			−1.70468			−0.852340	−	0.522987i	$-0.824817\pi$
$263$	−27.6453			−1.70468			−0.852340	+	0.522987i	$0.824817\pi$
$264$		0			0
$265$	2.51730			0.154637
$266$	20.6719	−	15.0190i	1.26748	−	0.920876i
$267$	9.56703	+	29.4443i	0.585493	+	1.80196i
$268$	8.51221	−	26.1979i	0.519966	−	1.60029i
$269$	11.7923	+	8.56759i	0.718988	+	0.522375i	0.886061	−	0.463569i	$-0.153431\pi$
$269$	11.7923	+	8.56759i	0.718988	+	0.522375i	−0.167073	+	0.985945i	$0.553431\pi$
$270$	−12.0648	−	8.76557i	−0.734239	−	0.533456i
$271$	0.668274	−	2.05674i	0.0405948	−	0.124938i	−0.928705	−	0.370819i	$-0.879077\pi$
$271$	0.668274	−	2.05674i	0.0405948	−	0.124938i	0.969300	+	0.245881i	$0.0790772\pi$
$272$	1.54185	+	4.74534i	0.0934886	+	0.287728i
$273$	11.6328	−	8.45169i	0.704046	−	0.511519i
$274$	36.7491			2.22009
$275$		0			0
$276$	−25.3777			−1.52756
$277$	−12.3797	+	8.99441i	−0.743827	+	0.540422i	−0.893907	−	0.448252i	$-0.852047\pi$
$277$	−12.3797	+	8.99441i	−0.743827	+	0.540422i	0.150080	+	0.988674i	$0.452047\pi$
$278$	5.54931	+	17.0790i	0.332826	+	1.02433i
$279$	14.8506	−	45.7055i	0.889082	−	2.73631i
$280$	−9.75574	−	7.08796i	−0.583017	−	0.423587i
$281$	1.73003	+	1.25694i	0.103205	+	0.0749827i	0.638191	−	0.769878i	$-0.279683\pi$
$281$	1.73003	+	1.25694i	0.103205	+	0.0749827i	−0.534986	+	0.844861i	$0.679683\pi$
$282$	21.9056	−	67.4184i	1.30446	−	4.01471i
$283$	−1.33835	−	4.11902i	−0.0795566	−	0.244850i	0.903366	−	0.428871i	$-0.141089\pi$
$283$	−1.33835	−	4.11902i	−0.0795566	−	0.244850i	−0.982922	+	0.184021i	$0.941089\pi$
$284$	−7.16314	+	5.20432i	−0.425054	+	0.308820i
$285$	−9.21509			−0.545855
$286$		0			0
$287$	−15.4014			−0.909116
$288$	−16.8255	+	12.2244i	−0.991449	+	0.720330i
$289$	−0.948440	−	2.91900i	−0.0557906	−	0.171706i
$290$	−3.40988	+	10.4945i	−0.200235	+	0.616260i
$291$	−25.5456	−	18.5599i	−1.49751	−	1.08800i
$292$	−8.43820	−	6.13071i	−0.493808	−	0.358773i
$293$	4.17384	−	12.8458i	0.243839	−	0.750458i	−0.751987	−	0.659178i	$-0.770904\pi$
$293$	4.17384	−	12.8458i	0.243839	−	0.750458i	0.995825	−	0.0912798i	$-0.0290958\pi$
$294$	−9.25391	−	28.4806i	−0.539699	−	1.66102i
$295$	9.63772	−	7.00222i	0.561130	−	0.407685i
$296$	9.61488			0.558854
$297$		0			0
$298$	15.2272			0.882086
$299$	−3.01957	+	2.19385i	−0.174626	+	0.126873i
$300$	3.11529	+	9.58788i	0.179861	+	0.553556i
$301$	−5.62877	+	17.3236i	−0.324437	+	0.998515i
$302$	−20.6719	−	15.0190i	−1.18954	−	0.864248i
$303$	−29.5239	−	21.4504i	−1.69610	−	1.23229i
$304$	1.32815	−	4.08764i	0.0761749	−	0.234442i
$305$	−4.22732	−	13.0103i	−0.242055	−	0.744970i
$306$	36.9889	−	26.8740i	2.11451	−	1.53628i
$307$	2.37887			0.135769			0.0678847	−	0.997693i	$-0.478375\pi$
$307$	2.37887			0.135769			0.0678847	+	0.997693i	$0.478375\pi$
$308$		0			0
$309$	−52.5749			−2.99088
$310$	−17.5114	+	12.7228i	−0.994581	+	0.722605i
$311$	−6.84308	−	21.0608i	−0.388036	−	1.19425i	−0.934254	−	0.356608i	$-0.883933\pi$
$311$	−6.84308	−	21.0608i	−0.388036	−	1.19425i	0.546219	−	0.837643i	$-0.316067\pi$
$312$	4.68033	−	14.4046i	0.264972	−	0.815499i
$313$	22.0735	+	16.0373i	1.24767	+	0.906483i	0.998084	−	0.0618710i	$-0.0197068\pi$
$313$	22.0735	+	16.0373i	1.24767	+	0.906483i	0.249582	+	0.968354i	$0.419707\pi$
$314$	19.8204	+	14.4004i	1.11853	+	0.812661i
$315$	−5.45269	+	16.7817i	−0.307224	+	0.945539i
$316$	−7.35510	−	22.6367i	−0.413757	−	1.27341i
$317$	12.4553	−	9.04929i	0.699558	−	0.508259i	−0.180230	−	0.983625i	$-0.557684\pi$
$317$	12.4553	−	9.04929i	0.699558	−	0.508259i	0.879788	+	0.475366i	$0.157684\pi$
$318$	16.9475			0.950368
$319$		0			0
$320$	12.0409			0.673104
$321$	16.5419	−	12.0184i	0.923278	−	0.670801i
$322$	6.18227	+	19.0271i	0.344524	+	1.06034i
$323$	3.70820	−	11.4127i	0.206330	−	0.635018i
$324$	−7.26162	−	5.27587i	−0.403423	−	0.293104i
$325$	1.19953	+	0.871507i	0.0665377	+	0.0483425i
$326$	7.43550	−	22.8841i	0.411814	−	1.26743i
$327$	−3.67202	−	11.3013i	−0.203063	−	0.624964i
$328$	−13.1246	+	9.53561i	−0.724687	+	0.526516i
$329$	−35.6262			−1.96413
$330$		0			0
$331$	25.9129			1.42430			0.712150	−	0.702027i	$-0.247721\pi$
$331$	25.9129			1.42430			0.712150	+	0.702027i	$0.247721\pi$
$332$	21.4894	−	15.6130i	1.17938	−	0.856873i
$333$	−4.34763	−	13.3806i	−0.238248	−	0.733253i
$334$	−0.759733	+	2.33822i	−0.0415707	+	0.127942i
$335$	6.33589	+	4.60329i	0.346167	+	0.251505i
$336$	−10.4883	−	7.62016i	−0.572181	−	0.415714i
$337$	−4.32071	+	13.2978i	−0.235364	+	0.724375i	0.761709	+	0.647919i	$0.224361\pi$
$337$	−4.32071	+	13.2978i	−0.235364	+	0.724375i	−0.997073	+	0.0764562i	$0.975639\pi$
$338$	7.84033	+	24.1301i	0.426458	+	1.31250i
$339$	−3.39657	+	2.46775i	−0.184476	+	0.134030i
$340$	−13.1280			−0.711964
$341$		0			0
$342$	−39.3839			−2.12964
$343$	6.98538	−	5.07517i	0.377175	−	0.274034i
$344$	5.92903	+	18.2477i	0.319672	+	0.983848i
$345$	2.22959	−	6.86196i	0.120037	−	0.369436i
$346$	−22.6380	−	16.4475i	−1.21703	−	0.884221i
$347$	−25.1173	−	18.2488i	−1.34837	−	0.979646i	−0.999091	−	0.0426260i	$-0.986428\pi$
$347$	−25.1173	−	18.2488i	−1.34837	−	0.979646i	−0.349276	−	0.937020i	$-0.613572\pi$
$348$	−14.6350	+	45.0418i	−0.784517	+	2.41449i
$349$	−1.13198	−	3.48389i	−0.0605938	−	0.186488i	0.916178	−	0.400772i	$-0.131258\pi$
$349$	−1.13198	−	3.48389i	−0.0605938	−	0.186488i	−0.976771	+	0.214284i	$0.931258\pi$
$350$	6.42965	−	4.67142i	0.343679	−	0.249698i
$351$	−9.41348			−0.502454
$352$		0			0
$353$	24.5749			1.30799			0.653994	−	0.756500i	$-0.273092\pi$
$353$	24.5749			1.30799			0.653994	+	0.756500i	$0.273092\pi$
$354$	64.8850	−	47.1417i	3.44860	−	2.50555i
$355$	−0.777890	−	2.39410i	−0.0412861	−	0.127066i
$356$	11.7403	−	36.1331i	0.622237	−	1.91505i
$357$	−29.2832	−	21.2755i	−1.54983	−	1.12602i
$358$	−6.45260	−	4.68809i	−0.341030	−	0.247773i
$359$	2.03535	−	6.26415i	0.107421	−	0.330609i	−0.882870	−	0.469618i	$-0.844392\pi$
$359$	2.03535	−	6.26415i	0.107421	−	0.330609i	0.990291	+	0.139009i	$0.0443916\pi$
$360$	5.74355	+	17.6768i	0.302712	+	0.931651i
$361$	7.00866	−	5.09209i	0.368877	−	0.268005i
$362$	13.3835			0.703421
$363$		0			0
$364$	−17.6453			−0.924864
$365$	2.39905	−	1.74301i	0.125572	−	0.0912335i
$366$	−28.4600	−	87.5908i	−1.48763	−	4.57844i
$367$	2.52418	−	7.76862i	0.131761	−	0.405519i	−0.863311	−	0.504672i	$-0.831613\pi$
$367$	2.52418	−	7.76862i	0.131761	−	0.405519i	0.995072	+	0.0991534i	$0.0316134\pi$
$368$	2.72249	+	1.97800i	0.141920	+	0.103111i
$369$	19.2050	+	13.9532i	0.999771	+	0.726376i
$370$	−1.95818	+	6.02667i	−0.101801	+	0.313312i
$371$	−2.63199	−	8.10044i	−0.136646	−	0.420554i
$372$	−75.1577	+	54.6053i	−3.89675	+	2.83115i
$373$	27.0409			1.40012			0.700061	−	0.714083i	$-0.253156\pi$
$373$	27.0409			1.40012			0.700061	+	0.714083i	$0.253156\pi$
$374$		0			0
$375$	−2.86620			−0.148010
$376$	−30.3596	+	22.0576i	−1.56568	+	1.13753i
$377$	2.15242	+	6.62448i	0.110856	+	0.341178i
$378$	−15.5923	+	47.9882i	−0.801982	+	2.46825i
$379$	−26.4241	−	19.1982i	−1.35731	−	0.986147i	−0.998611	−	0.0526956i	$-0.983219\pi$
$379$	−26.4241	−	19.1982i	−1.35731	−	0.986147i	−0.358704	−	0.933451i	$-0.616781\pi$
$380$	9.14873	+	6.64694i	0.469320	+	0.340981i
$381$	−10.0053	+	30.7930i	−0.512585	+	1.57757i
$382$	6.54476	+	20.1427i	0.334859	+	1.03059i
$383$	2.14104	−	1.55556i	0.109402	−	0.0794854i	−0.531739	−	0.846908i	$-0.678461\pi$
$383$	2.14104	−	1.55556i	0.109402	−	0.0794854i	0.641141	+	0.767423i	$0.278461\pi$
$384$	58.2034			2.97018
$385$		0			0
$386$	61.6157			3.13616
$387$	22.7135	−	16.5023i	1.15459	−	0.838861i
$388$	11.9741	+	36.8526i	0.607894	+	1.87091i
$389$	−8.97735	+	27.6294i	−0.455170	+	1.40087i	0.415766	+	0.909472i	$0.363513\pi$
$389$	−8.97735	+	27.6294i	−0.455170	+	1.40087i	−0.870936	+	0.491397i	$0.836487\pi$
$390$	8.07569	+	5.86733i	0.408928	+	0.297104i
$391$	7.60118	+	5.52258i	0.384408	+	0.279289i
$392$	−4.89882	+	15.0770i	−0.247428	+	0.761505i
$393$	13.0020	+	40.0161i	0.655866	+	2.01855i
$394$	31.7307	−	23.0537i	1.59857	−	1.16143i
$395$	6.76700			0.340485
$396$		0			0
$397$	−9.35977			−0.469753			−0.234877	−	0.972025i	$-0.575469\pi$
$397$	−9.35977			−0.469753			−0.234877	+	0.972025i	$0.575469\pi$
$398$	−31.9082	+	23.1826i	−1.59941	+	1.16204i
$399$	9.63493	+	29.6533i	0.482350	+	1.48452i
$400$	0.413100	−	1.27139i	0.0206550	−	0.0635696i
$401$	−3.98909	−	2.89824i	−0.199206	−	0.144731i	0.483711	−	0.875228i	$-0.339289\pi$
$401$	−3.98909	−	2.89824i	−0.199206	−	0.144731i	−0.682916	+	0.730497i	$0.739289\pi$
$402$	42.6557	+	30.9912i	2.12747	+	1.54570i
$403$	−4.22215	+	12.9945i	−0.210321	+	0.647300i
$404$	13.8389	+	42.5918i	0.688512	+	2.11902i
$405$	2.06454	−	1.49998i	0.102588	−	0.0745344i
$406$	37.3356			1.85294
$407$		0			0
$408$	−38.1268			−1.88756
$409$	−30.9922	+	22.5171i	−1.53247	+	1.11340i	−0.577617	+	0.816308i	$0.696017\pi$
$409$	−30.9922	+	22.5171i	−1.53247	+	1.11340i	−0.954848	+	0.297093i	$0.903983\pi$
$410$	−3.30400	−	10.1687i	−0.163173	−	0.502194i
$411$	−13.8571	+	42.6477i	−0.683520	+	2.10366i
$412$	52.1963	+	37.9228i	2.57153	+	1.86832i
$413$	−32.6093	−	23.6920i	−1.60460	−	1.16581i
$414$	9.52892	−	29.3270i	0.468321	−	1.44134i
$415$	2.33367	+	7.18230i	0.114555	+	0.352565i
$416$	4.78362	−	3.47550i	0.234536	−	0.170401i
$417$	−21.9129			−1.07308
$418$		0			0
$419$	37.3777			1.82602			0.913009	−	0.407938i	$-0.133752\pi$
$419$	37.3777			1.82602			0.913009	+	0.407938i	$0.133752\pi$
$420$	27.5956	−	20.0494i	1.34653	−	0.978310i
$421$	9.08889	+	27.9727i	0.442966	+	1.36331i	0.884699	+	0.466162i	$0.154364\pi$
$421$	9.08889	+	27.9727i	0.442966	+	1.36331i	−0.441734	+	0.897146i	$0.645636\pi$
$422$	5.54931	−	17.0790i	0.270136	−	0.831394i
$423$	44.4245	+	32.2763i	2.15999	+	1.56933i
$424$	−7.25821	−	5.27340i	−0.352490	−	0.256099i
$425$	1.15337	−	3.54972i	0.0559469	−	0.172187i
$426$	−5.23706	−	16.1180i	−0.253736	−	0.780921i
$427$	−37.4461	+	27.2062i	−1.81214	+	1.31660i
$428$	−25.0917			−1.21286
$429$		0			0
$430$	−12.6453			−0.609809
$431$	1.43051	−	1.03932i	0.0689050	−	0.0500624i	−0.552800	−	0.833314i	$-0.686440\pi$
$431$	1.43051	−	1.03932i	0.0689050	−	0.0500624i	0.621705	+	0.783252i	$0.286440\pi$
$432$	2.62273	+	8.07193i	0.126186	+	0.388361i
$433$	3.10603	−	9.55937i	0.149266	−	0.459394i	−0.848269	−	0.529566i	$-0.822355\pi$
$433$	3.10603	−	9.55937i	0.149266	−	0.459394i	0.997535	+	0.0701721i	$0.0223548\pi$
$434$	59.2499	+	43.0475i	2.84408	+	2.06635i
$435$	−10.8932	−	7.91441i	−0.522291	−	0.379467i
$436$	−4.50618	+	13.8686i	−0.215807	+	0.664185i
$437$	−2.50099	−	7.69725i	−0.119638	−	0.368209i
$438$	16.1514	−	11.7347i	0.771742	−	0.560704i
$439$	−39.1972			−1.87078			−0.935390	−	0.353618i	$-0.884951\pi$
$439$	−39.1972			−1.87078			−0.935390	+	0.353618i	$0.884951\pi$
$440$		0			0
$441$	23.1972			1.10463
$442$	−10.5163	+	7.64050i	−0.500207	+	0.363422i
$443$	−4.32997	−	13.3263i	−0.205723	−	0.633150i	−0.999683	−	0.0251803i	$-0.991984\pi$
$443$	−4.32997	−	13.3263i	−0.205723	−	0.633150i	0.793960	−	0.607970i	$-0.208016\pi$
$444$	−8.40439	+	25.8661i	−0.398855	+	1.22755i
$445$	8.73869	+	6.34903i	0.414254	+	0.300973i
$446$	−7.20124	−	5.23201i	−0.340989	−	0.247743i
$447$	−5.74175	+	17.6713i	−0.271575	+	0.835823i
$448$	−12.5894	−	38.7463i	−0.594795	−	1.83059i
$449$	−2.08408	+	1.51417i	−0.0983537	+	0.0714581i	−0.635875	−	0.771792i	$-0.719361\pi$
$449$	−2.08408	+	1.51417i	−0.0983537	+	0.0714581i	0.537521	+	0.843250i	$0.319361\pi$
$450$	−12.2497			−0.577456
$451$		0			0
$452$	5.15212			0.242335
$453$	25.2246	−	18.3267i	1.18515	−	0.861065i
$454$	−14.1875	−	43.6646i	−0.665852	−	2.04928i
$455$	1.55025	−	4.77117i	0.0726767	−	0.223676i
$456$	26.5701	+	19.3043i	1.24426	+	0.904008i
$457$	12.2337	+	8.88833i	0.572270	+	0.415778i	0.835929	−	0.548837i	$-0.184929\pi$
$457$	12.2337	+	8.88833i	0.572270	+	0.415778i	−0.263659	+	0.964616i	$0.584929\pi$
$458$	−3.74725	+	11.5329i	−0.175098	+	0.538895i
$459$	7.32265	+	22.5368i	0.341792	+	1.05193i
$460$	−7.16314	+	5.20432i	−0.333983	+	0.242653i
$461$	−9.83622			−0.458118			−0.229059	−	0.973412i	$-0.573565\pi$
$461$	−9.83622			−0.458118			−0.229059	+	0.973412i	$0.573565\pi$
$462$		0			0
$463$	21.2093			0.985678			0.492839	−	0.870120i	$-0.335959\pi$
$463$	21.2093			0.985678			0.492839	+	0.870120i	$0.335959\pi$
$464$	5.08070	−	3.69135i	0.235866	−	0.171367i
$465$	−8.16184	−	25.1196i	−0.378496	−	1.16489i
$466$	4.53633	−	13.9614i	0.210142	−	0.646749i
$467$	7.73743	+	5.62157i	0.358045	+	0.260135i	0.752236	−	0.658893i	$-0.228975\pi$
$467$	7.73743	+	5.62157i	0.358045	+	0.260135i	−0.394191	+	0.919029i	$0.628975\pi$
$468$	22.0030	+	15.9861i	1.01709	+	0.738958i
$469$	8.18840	−	25.2013i	0.378105	−	1.16369i
$470$	−7.64273	−	23.5219i	−0.352533	−	1.08498i
$471$	−24.1855	+	17.5718i	−1.11441	+	0.809667i
$472$	−42.4573			−1.95426
$473$		0			0
$474$	45.5582			2.09256
$475$	−2.60106	+	1.88978i	−0.119345	+	0.0867092i
$476$	13.7261	+	42.2445i	0.629134	+	1.93627i
$477$	−4.05677	+	12.4854i	−0.185747	+	0.571669i
$478$	−8.76163	−	6.36570i	−0.400748	−	0.291160i
$479$	−13.9128	−	10.1083i	−0.635693	−	0.461858i	0.222675	−	0.974893i	$-0.428521\pi$
$479$	−13.9128	−	10.1083i	−0.635693	−	0.461858i	−0.858368	+	0.513035i	$0.828521\pi$
$480$	−3.53212	+	10.8708i	−0.161219	+	0.496180i
$481$	1.23607	+	3.80423i	0.0563598	+	0.173458i
$482$	−14.9710	+	10.8771i	−0.681912	+	0.495438i
$483$	−24.4123			−1.11080
$484$		0			0
$485$	−11.0167			−0.500243
$486$	−22.2950	+	16.1983i	−1.01132	+	0.734769i
$487$	4.80581	+	14.7907i	0.217772	+	0.670233i	0.998945	+	0.0459186i	$0.0146215\pi$
$487$	4.80581	+	14.7907i	0.217772	+	0.670233i	−0.781173	+	0.624314i	$0.785379\pi$
$488$	−15.0661	+	46.3687i	−0.682010	+	2.09901i
$489$	23.7535	+	17.2579i	1.07417	+	0.780431i
$490$	−8.45268	−	6.14123i	−0.381853	−	0.277433i
$491$	2.79931	−	8.61539i	0.126331	−	0.388807i	−0.867810	−	0.496896i	$-0.834473\pi$
$491$	2.79931	−	8.61539i	0.126331	−	0.388807i	0.994141	+	0.108089i	$0.0344731\pi$
$492$	−14.1805	−	43.6432i	−0.639308	−	1.96759i
$493$	14.1853	−	10.3062i	0.638874	−	0.464169i
$494$	11.1972			0.503785
$495$		0			0
$496$	12.3189			0.553136
$497$	−6.89064	+	5.00635i	−0.309088	+	0.224565i
$498$	15.7112	+	48.3541i	0.704035	+	2.16680i
$499$	7.59212	−	23.3661i	0.339870	−	1.04601i	−0.624403	−	0.781102i	$-0.714658\pi$
$499$	7.59212	−	23.3661i	0.339870	−	1.04601i	0.964273	−	0.264910i	$-0.0853423\pi$
$500$	2.84556	+	2.06742i	0.127257	+	0.0924578i
$501$	−2.42705	−	1.76336i	−0.108433	−	0.0787809i
$502$	−7.73445	+	23.8042i	−0.345205	+	1.06243i
$503$	3.50184	+	10.7776i	0.156139	+	0.480547i	0.998275	−	0.0587190i	$-0.0187016\pi$
$503$	3.50184	+	10.7776i	0.156139	+	0.480547i	−0.842135	+	0.539266i	$0.818702\pi$
$504$	50.8771	−	36.9644i	2.26625	−	1.64652i
$505$	−12.7324			−0.566584
$506$		0			0
$507$	−30.9596			−1.37496
$508$	32.1445	−	23.3544i	1.42618	−	1.03618i
$509$	−8.18553	−	25.1925i	−0.362817	−	1.11664i	−0.951337	−	0.308154i	$-0.900289\pi$
$509$	−8.18553	−	25.1925i	−0.362817	−	1.11664i	0.588519	−	0.808483i	$-0.299711\pi$
$510$	7.76497	−	23.8981i	0.343839	−	1.05823i
$511$	−8.11720	−	5.89749i	−0.359084	−	0.260890i
$512$	−12.0220	−	8.73446i	−0.531300	−	0.386012i
$513$	6.30774	−	19.4132i	0.278494	−	0.857115i
$514$	−2.03895	−	6.27524i	−0.0899342	−	0.276789i
$515$	−14.8399	+	10.7818i	−0.653922	+	0.475102i
$516$	−54.2727			−2.38922
$517$		0			0
$518$	21.4406			0.942048
$519$	27.6236	−	20.0697i	1.21254	−	0.880964i
$520$	−1.63294	−	5.02568i	−0.0716092	−	0.220390i
$521$	8.24970	−	25.3900i	0.361426	−	1.11235i	−0.590763	−	0.806845i	$-0.701173\pi$
$521$	8.24970	−	25.3900i	0.361426	−	1.11235i	0.952189	−	0.305510i	$-0.0988268\pi$
$522$	−46.5561	−	33.8250i	−2.03771	−	1.48048i
$523$	−3.92707	−	2.85318i	−0.171719	−	0.124761i	0.498606	−	0.866829i	$-0.333845\pi$
$523$	−3.92707	−	2.85318i	−0.171719	−	0.124761i	−0.670325	+	0.742068i	$0.733845\pi$
$524$	15.9557	−	49.1065i	0.697027	−	2.14523i
$525$	2.99678	+	9.22314i	0.130790	+	0.402531i
$526$	−52.5342	+	38.1683i	−2.29060	+	1.66422i
$527$	34.3944			1.49824
$528$		0			0
$529$	−16.6632			−0.724486
$530$	4.78362	−	3.47550i	0.207787	−	0.150966i
$531$	19.1982	+	59.0861i	0.833132	+	2.56412i
$532$	11.8237	−	36.3895i	0.512621	−	1.57769i
$533$	−5.46014	−	3.96702i	−0.236505	−	0.171831i
$534$	58.8323	+	42.7442i	2.54592	+	1.84972i
$535$	2.20447	−	6.78465i	0.0953074	−	0.293326i
$536$	−8.62518	−	26.5456i	−0.372551	−	1.14659i
$537$	7.87367	−	5.72056i	0.339774	−	0.246860i
$538$	34.2376			1.47609
$539$		0			0
$540$	−22.3310			−0.960973
$541$	16.0384	−	11.6526i	0.689545	−	0.500984i	−0.186965	−	0.982366i	$-0.559865\pi$
$541$	16.0384	−	11.6526i	0.689545	−	0.500984i	0.876511	+	0.481383i	$0.159865\pi$
$542$	−1.56971	−	4.83106i	−0.0674246	−	0.207512i
$543$	−5.04655	+	15.5317i	−0.216568	+	0.666529i
$544$	−12.0418	−	8.74890i	−0.516289	−	0.375106i
$545$	−3.35408	−	2.43688i	−0.143673	−	0.104385i
$546$	10.4369	−	32.1214i	0.446657	−	1.37467i
$547$	−4.52887	−	13.9384i	−0.193641	−	0.595964i	−0.999990	−	0.00452464i	$-0.998560\pi$
$547$	−4.52887	−	13.9384i	−0.193641	−	0.595964i	0.806349	−	0.591440i	$-0.201440\pi$
$548$	44.5196	−	32.3454i	1.90178	−	1.38172i
$549$	71.3419			3.04480
$550$		0			0
$551$	−15.1038			−0.643445
$552$	−20.8035	+	15.1146i	−0.885454	+	0.643320i
$553$	−7.07531	−	21.7756i	−0.300873	−	0.925991i
$554$	−11.1071	+	34.1841i	−0.471895	+	1.45234i
$555$	−6.25564	−	4.54499i	−0.265537	−	0.192924i
$556$	21.7551	+	15.8060i	0.922621	+	0.670324i
$557$	−1.80386	+	5.55171i	−0.0764321	+	0.235234i	−0.981972	−	0.189028i	$-0.939466\pi$
$557$	−1.80386	+	5.55171i	−0.0764321	+	0.235234i	0.905540	+	0.424262i	$0.139466\pi$
$558$	−34.8825	−	107.357i	−1.47669	−	4.54480i
$559$	−6.45765	+	4.69176i	−0.273130	+	0.198440i
$560$	−4.52313			−0.191137
$561$		0			0
$562$	5.02295			0.211880
$563$	−31.7965	+	23.1015i	−1.34006	+	0.973612i	−0.340621	+	0.940201i	$0.610637\pi$
$563$	−31.7965	+	23.1015i	−1.34006	+	0.973612i	−0.999442	+	0.0334116i	$0.989363\pi$
$564$	−32.8021	−	100.954i	−1.38122	−	4.25095i
$565$	−0.452646	+	1.39310i	−0.0190430	+	0.0586082i
$566$	−8.23016	−	5.97956i	−0.345940	−	0.251340i
$567$	−6.98538	−	5.07517i	−0.293358	−	0.213137i
$568$	−2.77239	+	8.53253i	−0.116327	+	0.358017i
$569$	2.50615	+	7.71314i	0.105063	+	0.323351i	0.989745	−	0.142843i	$-0.0456245\pi$
$569$	2.50615	+	7.71314i	0.105063	+	0.323351i	−0.884682	+	0.466195i	$0.845625\pi$
$570$	−17.5114	+	12.7228i	−0.733472	+	0.532898i
$571$	−35.6274			−1.49096			−0.745480	−	0.666528i	$-0.767780\pi$
$571$	−35.6274			−1.49096			−0.745480	+	0.666528i	$0.767780\pi$
$572$		0			0
$573$	−25.8437			−1.07963
$574$	−29.2672	+	21.2639i	−1.22159	+	0.887537i
$575$	−0.777890	−	2.39410i	−0.0324402	−	0.0998408i
$576$	−19.4045	+	59.7208i	−0.808519	+	2.48837i
$577$	25.7696	+	18.7227i	1.07280	+	0.779435i	0.976414	−	0.215909i	$-0.0692713\pi$
$577$	25.7696	+	18.7227i	1.07280	+	0.779435i	0.0963872	+	0.995344i	$0.469271\pi$
$578$	−5.83242	−	4.23750i	−0.242597	−	0.176257i
$579$	−23.2336	+	71.5057i	−0.965556	+	2.97168i
$580$	5.10606	+	15.7148i	0.212018	+	0.652523i
$581$	20.6719	−	15.0190i	0.857616	−	0.623095i
$582$	−74.1688			−3.07440
$583$		0			0
$584$	−10.5686			−0.437332
$585$	−6.25564	+	4.54499i	−0.258639	+	0.187912i
$586$	−9.80392	−	30.1734i	−0.404996	−	1.24645i
$587$	−13.7149	+	42.2101i	−0.566074	+	1.74220i	0.0986650	+	0.995121i	$0.468543\pi$
$587$	−13.7149	+	42.2101i	−0.566074	+	1.74220i	−0.664739	+	0.747076i	$0.731457\pi$
$588$	−36.2783	−	26.3577i	−1.49609	−	1.08697i
$589$	−23.9690	−	17.4145i	−0.987627	−	0.717553i
$590$	8.64694	−	26.6126i	0.355989	−	1.09562i
$591$	14.7893	+	45.5168i	0.608350	+	1.87231i
$592$	2.91768	−	2.11982i	0.119916	−	0.0871241i
$593$	41.9463			1.72253			0.861264	−	0.508158i	$-0.169673\pi$
$593$	41.9463			1.72253			0.861264	+	0.508158i	$0.169673\pi$
$594$		0			0
$595$	−12.6286			−0.517721
$596$	18.4469	−	13.4025i	0.755614	−	0.548986i
$597$	−14.8720	−	45.7713i	−0.608670	−	1.87329i
$598$	−2.70915	+	8.33792i	−0.110786	+	0.340963i
$599$	−13.4383	−	9.76351i	−0.549075	−	0.398926i	0.278370	−	0.960474i	$-0.410206\pi$
$599$	−13.4383	−	9.76351i	−0.549075	−	0.398926i	−0.827444	+	0.561548i	$0.810206\pi$
$600$	8.26418	+	6.00428i	0.337384	+	0.245124i
$601$	4.07816	−	12.5513i	0.166351	−	0.511977i	−0.832782	−	0.553601i	$-0.813253\pi$
$601$	4.07816	−	12.5513i	0.166351	−	0.511977i	0.999133	+	0.0416241i	$0.0132532\pi$
$602$	13.2214	+	40.6913i	0.538864	+	1.65845i
$603$	−33.0422	+	24.0066i	−1.34558	+	0.977624i
$604$	−38.2622			−1.55687
$605$		0			0
$606$	−85.7195			−3.48212
$607$	−7.31420	+	5.31408i	−0.296874	+	0.215692i	−0.726244	−	0.687437i	$-0.758736\pi$
$607$	−7.31420	+	5.31408i	−0.296874	+	0.215692i	0.429370	+	0.903129i	$0.358736\pi$
$608$	3.96208	+	12.1940i	0.160683	+	0.494533i
$609$	−14.0782	+	43.3284i	−0.570479	+	1.75575i
$610$	−25.9958	−	18.8871i	−1.05254	−	0.764715i
$611$	−12.6303	−	9.17643i	−0.510966	−	0.371238i
$612$	21.1564	−	65.1127i	0.855197	−	2.63203i
$613$	2.36805	+	7.28812i	0.0956448	+	0.294364i	0.987421	−	0.158112i	$-0.0505407\pi$
$613$	2.36805	+	7.28812i	0.0956448	+	0.294364i	−0.891776	+	0.452476i	$0.850541\pi$
$614$	4.52056	−	3.28438i	0.182435	−	0.132547i
$615$	13.0467			0.526093
$616$		0			0
$617$	−2.67989			−0.107888			−0.0539441	−	0.998544i	$-0.517179\pi$
$617$	−2.67989			−0.107888			−0.0539441	+	0.998544i	$0.517179\pi$
$618$	−99.9078	+	72.5872i	−4.01888	+	2.91989i
$619$	2.52598	+	7.77416i	0.101528	+	0.312470i	0.988900	−	0.148584i	$-0.0474715\pi$
$619$	2.52598	+	7.77416i	0.101528	+	0.312470i	−0.887372	+	0.461054i	$0.847471\pi$
$620$	−10.0159	+	30.8259i	−0.402250	+	1.23800i
$621$	12.9298	+	9.39404i	0.518855	+	0.376970i
$622$	−42.0814	−	30.5739i	−1.68731	−	1.22590i
$623$	11.2937	−	34.7585i	0.452474	−	1.39257i
$624$	−1.75555	−	5.40303i	−0.0702783	−	0.216294i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	64.0880			2.56147
$627$		0			0
$628$	36.6861			1.46394
$629$	8.14617	−	5.91854i	0.324809	−	0.235988i
$630$	12.8078	+	39.4183i	0.510275	+	1.57046i
$631$	1.72117	−	5.29721i	0.0685186	−	0.210879i	−0.910934	−	0.412551i	$-0.864638\pi$
$631$	1.72117	−	5.29721i	0.0685186	−	0.210879i	0.979453	+	0.201673i	$0.0646377\pi$
$632$	−19.5115	−	14.1759i	−0.776125	−	0.563888i
$633$	17.7279	+	12.8801i	0.704620	+	0.511937i
$634$	11.1749	−	34.3927i	0.443810	−	1.36591i
$635$	3.49077	+	10.7435i	0.138527	+	0.426343i
$636$	20.5310	−	14.9166i	0.814106	−	0.591483i
$637$	−6.59516			−0.261310
$638$		0			0
$639$	13.1280			0.519335
$640$	16.4286	−	11.9361i	0.649397	−	0.471814i
$641$	−4.10701	−	12.6401i	−0.162217	−	0.499253i	0.836603	−	0.547809i	$-0.184538\pi$
$641$	−4.10701	−	12.6401i	−0.162217	−	0.499253i	−0.998820	+	0.0485563i	$0.984538\pi$
$642$	14.8413	−	45.6769i	0.585741	−	1.80273i
$643$	−14.4116	−	10.4706i	−0.568337	−	0.412921i	0.266164	−	0.963928i	$-0.414244\pi$
$643$	−14.4116	−	10.4706i	−0.568337	−	0.412921i	−0.834501	+	0.551007i	$0.814244\pi$
$644$	24.2365	+	17.6088i	0.955051	+	0.693886i
$645$	4.76819	−	14.6750i	0.187747	−	0.577827i
$646$	−8.71018	−	26.8072i	−0.342697	−	1.05471i
$647$	20.9397	−	15.2136i	0.823225	−	0.598108i	−0.0944095	−	0.995533i	$-0.530096\pi$
$647$	20.9397	−	15.2136i	0.823225	−	0.598108i	0.917634	+	0.397426i	$0.130096\pi$
$648$	−9.09498			−0.357285
$649$		0			0
$650$	3.48270			0.136603
$651$	−72.2986	+	52.5280i	−2.83361	+	2.05874i
$652$	−11.1341	−	34.2673i	−0.436046	−	1.34201i
$653$	4.12093	−	12.6829i	0.161265	−	0.496321i	−0.837477	−	0.546473i	$-0.815970\pi$
$653$	4.12093	−	12.6829i	0.161265	−	0.496321i	0.998742	+	0.0501511i	$0.0159703\pi$
$654$	−22.5810	−	16.4061i	−0.882988	−	0.641528i
$655$	11.8763	+	8.62862i	0.464045	+	0.337148i
$656$	−1.88039	+	5.78726i	−0.0734171	+	0.225955i
$657$	4.77888	+	14.7079i	0.186442	+	0.573810i
$658$	−67.7003	+	49.1871i	−2.63923	+	1.91751i
$659$	24.4877			0.953907			0.476954	−	0.878929i	$-0.341741\pi$
$659$	24.4877			0.953907			0.476954	+	0.878929i	$0.341741\pi$
$660$		0			0
$661$	−23.2738			−0.905248			−0.452624	−	0.891702i	$-0.649512\pi$
$661$	−23.2738			−0.905248			−0.452624	+	0.891702i	$0.649512\pi$
$662$	49.2421	−	35.7765i	1.91385	−	1.39049i
$663$	−4.90149	−	15.0852i	−0.190358	−	0.585862i
$664$	8.31717	−	25.5976i	0.322769	−	0.993380i
$665$	8.80071	+	6.39409i	0.341277	+	0.247952i
$666$	−26.7357	−	19.4246i	−1.03599	−	0.752688i
$667$	3.65436	−	11.2470i	0.141497	−	0.435484i
$668$	1.13765	+	3.50132i	0.0440169	+	0.135470i
$669$	8.78719	−	6.38427i	0.339733	−	0.246830i
$670$	18.3956			0.710683
$671$		0			0
$672$	38.6741			1.49188
$673$	9.17770	−	6.66799i	0.353774	−	0.257032i	−0.396676	−	0.917959i	$-0.629836\pi$
$673$	9.17770	−	6.66799i	0.353774	−	0.257032i	0.750451	+	0.660926i	$0.229836\pi$
$674$	10.1489	+	31.2350i	0.390920	+	1.20313i
$675$	1.96192	−	6.03816i	0.0755142	−	0.232409i
$676$	30.7366	+	22.3315i	1.18218	+	0.858902i
$677$	−17.3094	−	12.5760i	−0.665254	−	0.483335i	0.203179	−	0.979142i	$-0.434873\pi$
$677$	−17.3094	−	12.5760i	−0.665254	−	0.483335i	−0.868433	+	0.495806i	$0.834873\pi$
$678$	−3.04739	+	9.37891i	−0.117034	+	0.360195i
$679$	11.5186	+	35.4507i	0.442044	+	1.36047i
$680$	−10.7617	+	7.81884i	−0.412693	+	0.299839i
$681$	56.0230			2.14680
$682$		0			0
$683$	−5.11590			−0.195754			−0.0978772	−	0.995198i	$-0.531205\pi$
$683$	−5.11590			−0.195754			−0.0978772	+	0.995198i	$0.531205\pi$
$684$	−47.7115	+	34.6644i	−1.82429	+	1.32543i
$685$	4.83466	+	14.8795i	0.184723	+	0.568518i
$686$	6.26726	−	19.2887i	0.239285	−	0.736444i
$687$	−11.9710	−	8.69745i	−0.456723	−	0.331828i
$688$	5.82231	+	4.23016i	0.221974	+	0.161273i
$689$	1.15337	−	3.54972i	0.0439400	−	0.135234i
$690$	−5.23706	−	16.1180i	−0.199372	−	0.613603i
$691$	18.5359	−	13.4671i	0.705140	−	0.512315i	−0.176462	−	0.984307i	$-0.556465\pi$
$691$	18.5359	−	13.4671i	0.705140	−	0.512315i	0.881602	+	0.471993i	$0.156465\pi$
$692$	−41.9012			−1.59285
$693$		0			0
$694$	−72.9254			−2.76821
$695$	−6.18516	+	4.49378i	−0.234616	+	0.170459i
$696$	14.8292	+	45.6396i	0.562100	+	1.72997i
$697$	−5.25006	+	16.1580i	−0.198860	+	0.612028i
$698$	−6.96112	−	5.05755i	−0.263482	−	0.191431i
$699$	14.4918	+	10.5289i	0.548131	+	0.398241i
$700$	3.67755	−	11.3183i	0.138998	−	0.427793i
$701$	11.7177	+	36.0632i	0.442570	+	1.36209i	0.885127	+	0.465349i	$0.154071\pi$
$701$	11.7177	+	36.0632i	0.442570	+	1.36209i	−0.442557	+	0.896740i	$0.645929\pi$
$702$	−17.8884	+	12.9967i	−0.675154	+	0.490528i
$703$	−8.67364			−0.327133
$704$		0			0
$705$	30.1793			1.13662
$706$	46.6995	−	33.9292i	1.75756	−	1.27694i
$707$	13.3125	+	40.9716i	0.500667	+	1.54090i
$708$	37.1121	−	114.219i	1.39476	−	4.29262i
$709$	4.26907	+	3.10166i	0.160328	+	0.116485i	0.665057	−	0.746793i	$-0.268407\pi$
$709$	4.26907	+	3.10166i	0.160328	+	0.116485i	−0.504728	+	0.863278i	$0.668407\pi$
$710$	−4.78362	−	3.47550i	−0.179526	−	0.130433i
$711$	−10.9054	+	33.5633i	−0.408984	+	1.25872i
$712$	−11.8962	−	36.6126i	−0.445828	−	1.37212i
$713$	18.7669	−	13.6350i	0.702827	−	0.510633i
$714$	−85.0206			−3.18181
$715$		0			0
$716$	−11.9433			−0.446341
$717$	10.6912	−	7.76764i	0.399271	−	0.290088i
$718$	−4.78081	−	14.7138i	−0.178418	−	0.549115i
$719$	9.55224	−	29.3988i	0.356238	−	1.09639i	−0.599050	−	0.800712i	$-0.704455\pi$
$719$	9.55224	−	29.3988i	0.356238	−	1.09639i	0.955288	−	0.295677i	$-0.0955452\pi$
$720$	5.64017	+	4.09783i	0.210197	+	0.152717i
$721$	50.2107	+	36.4802i	1.86994	+	1.35859i
$722$	6.28815	−	19.3529i	0.234021	−	0.720242i
$723$	−6.97782	−	21.4755i	−0.259508	−	0.798683i
$724$	16.2134	−	11.7797i	0.602566	−	0.437790i
$725$	−4.69779			−0.174471
$726$		0			0
$727$	8.24387			0.305748			0.152874	−	0.988246i	$-0.451147\pi$
$727$	8.24387			0.305748			0.152874	+	0.988246i	$0.451147\pi$
$728$	−14.4648	+	10.5093i	−0.536101	+	0.389500i
$729$	−12.7572	−	39.2626i	−0.472488	−	1.45417i
$730$	2.15242	−	6.62448i	0.0796648	−	0.245183i
$731$	16.2559	+	11.8106i	0.601245	+	0.436830i
$732$	−111.572	−	81.0620i	−4.12383	−	2.99614i
$733$	−13.4064	+	41.2606i	−0.495176	+	1.52399i	0.321507	+	0.946907i	$0.395810\pi$
$733$	−13.4064	+	41.2606i	−0.495176	+	1.52399i	−0.816683	+	0.577087i	$0.804190\pi$
$734$	−5.92903	−	18.2477i	−0.218844	−	0.673534i
$735$	10.3142	−	7.49373i	0.380446	−	0.276411i
$736$	−10.0388			−0.370036
$737$		0			0
$738$	55.7596			2.05254
$739$	0.243525	−	0.176931i	0.00895822	−	0.00650853i	−0.583297	−	0.812259i	$-0.698238\pi$
$739$	0.243525	−	0.176931i	0.00895822	−	0.00650853i	0.592255	+	0.805750i	$0.298238\pi$
$740$	2.93224	+	9.02452i	0.107791	+	0.331748i
$741$	−4.22215	+	12.9945i	−0.155105	+	0.477363i
$742$	−16.1854	−	11.7594i	−0.594184	−	0.431700i
$743$	25.4873	+	18.5176i	0.935038	+	0.679345i	0.947221	−	0.320581i	$-0.103878\pi$
$743$	25.4873	+	18.5176i	0.935038	+	0.679345i	−0.0121830	+	0.999926i	$0.503878\pi$
$744$	−29.0887	+	89.5258i	−1.06644	+	3.28218i
$745$	2.00326	+	6.16541i	0.0733939	+	0.225883i
$746$	51.3856	−	37.3338i	1.88136	−	1.36689i
$747$	−39.3839			−1.44098
$748$		0			0
$749$	−24.1372			−0.881955
$750$	−5.44662	+	3.95720i	−0.198883	+	0.144497i
$751$	10.2873	+	31.6612i	0.375391	+	1.15533i	0.943215	+	0.332184i	$0.107785\pi$
$751$	10.2873	+	31.6612i	0.375391	+	1.15533i	−0.567824	+	0.823150i	$0.692215\pi$
$752$	−4.34969	+	13.3870i	−0.158617	+	0.488172i
$753$	−24.7086	−	17.9518i	−0.900430	−	0.654201i
$754$	13.2363	+	9.61674i	0.482038	+	0.350221i
$755$	3.36157	−	10.3459i	0.122340	−	0.376524i
$756$	23.3484	+	71.8589i	0.849173	+	2.61348i
$757$	−12.5453	+	9.11469i	−0.455967	+	0.331279i	−0.791947	−	0.610590i	$-0.790932\pi$
$757$	−12.5453	+	9.11469i	−0.455967	+	0.331279i	0.335980	+	0.941869i	$0.390932\pi$
$758$	−76.7195			−2.78658
$759$		0			0
$760$	11.4585			0.415645
$761$	−42.3879	+	30.7966i	−1.53656	+	1.11638i	−0.584116	+	0.811670i	$0.698559\pi$
$761$	−42.3879	+	30.7966i	−1.53656	+	1.11638i	−0.952446	+	0.304707i	$0.901441\pi$
$762$	23.5013	+	72.3295i	0.851361	+	2.62022i
$763$	−4.33476	+	13.3410i	−0.156929	+	0.482977i
$764$	25.6576	+	18.6413i	0.928258	+	0.674419i
$765$	15.7473	+	11.4411i	0.569347	+	0.413655i
$766$	1.92094	−	5.91204i	0.0694064	−	0.213611i
$767$	−5.45822	−	16.7987i	−0.197085	−	0.606565i
$768$	54.7630	−	39.7876i	1.97609	−	1.43571i
$769$	−44.2652			−1.59624			−0.798122	−	0.602496i	$-0.794173\pi$
$769$	−44.2652			−1.59624			−0.798122	+	0.602496i	$0.794173\pi$
$770$		0			0
$771$	8.05131			0.289961
$772$	74.6441	−	54.2321i	2.68650	−	1.95186i
$773$	−10.9138	−	33.5891i	−0.392541	−	1.20812i	−0.930860	−	0.365376i	$-0.880940\pi$
$773$	−10.9138	−	33.5891i	−0.392541	−	1.20812i	0.538319	−	0.842741i	$-0.319060\pi$
$774$	20.3785	−	62.7187i	0.732491	−	2.25438i
$775$	−7.45517	−	5.41650i	−0.267797	−	0.194566i
$776$	31.7648	+	23.0784i	1.14029	+	0.828468i
$777$	−8.08468	+	24.8821i	−0.290036	+	0.892640i
$778$	21.0868	+	64.8986i	0.756000	+	2.32673i
$779$	11.8398	−	8.60213i	0.424205	−	0.308203i
$780$	14.9475			0.535206
$781$		0			0
$782$	22.0692			0.789194
$783$	24.1295	−	17.5311i	0.862320	−	0.626512i
$784$	1.83751	+	5.65526i	0.0656252	+	0.201974i
$785$	−3.22310	+	9.91970i	−0.115038	+	0.354049i
$786$	79.9558	+	58.0913i	2.85193	+	2.07205i
$787$	−29.6844	−	21.5670i	−1.05814	−	0.768780i	−0.0843928	−	0.996433i	$-0.526895\pi$
$787$	−29.6844	−	21.5670i	−1.05814	−	0.768780i	−0.973742	+	0.227652i	$0.926895\pi$
$788$	18.1489	−	55.8567i	0.646529	−	1.98981i
$789$	−24.4855	−	75.3587i	−0.871708	−	2.68284i
$790$	12.8593	−	9.34283i	0.457514	−	0.332403i
$791$	4.95613			0.176220
$792$		0			0
$793$	−20.2831			−0.720274
$794$	−17.7863	+	12.9225i	−0.631213	+	0.458603i
$795$	2.22959	+	6.86196i	0.0790753	+	0.243369i
$796$	−18.2504	+	56.1690i	−0.646869	+	1.99086i
$797$	2.30903	+	1.67761i	0.0817902	+	0.0594241i	0.627929	−	0.778271i	$-0.283903\pi$
$797$	2.30903	+	1.67761i	0.0817902	+	0.0594241i	−0.546139	+	0.837695i	$0.683903\pi$
$798$	59.2499	+	43.0475i	2.09742	+	1.52387i
$799$	−12.1443	+	37.3763i	−0.429635	+	1.32228i
$800$	1.23234	+	3.79274i	0.0435697	+	0.134094i
$801$	−45.5731	+	33.1108i	−1.61025	+	1.16991i
$802$	−11.5819			−0.408971
$803$		0			0
$804$	78.9525			2.78444
$805$	−6.89064	+	5.00635i	−0.242863	+	0.176451i
$806$	9.91740	+	30.5226i	0.349325	+	1.07511i
$807$	−12.9101	+	39.7331i	−0.454456	+	1.39867i
$808$	36.7116	+	26.6726i	1.29151	+	0.938338i
$809$	−21.1100	−	15.3373i	−0.742187	−	0.539231i	0.151208	−	0.988502i	$-0.451684\pi$
$809$	−21.1100	−	15.3373i	−0.742187	−	0.539231i	−0.893395	+	0.449271i	$0.851684\pi$
$810$	1.85230	−	5.70080i	0.0650832	−	0.200306i
$811$	−6.07072	−	18.6838i	−0.213172	−	0.656076i	−0.999278	−	0.0379846i	$-0.987906\pi$
$811$	−6.07072	−	18.6838i	−0.213172	−	0.656076i	0.786106	−	0.618091i	$-0.212094\pi$
$812$	45.2301	−	32.8616i	1.58727	−	1.15322i
$813$	6.19839			0.217387
$814$		0			0
$815$	10.2439			0.358827
$816$	−11.5698	+	8.40593i	−0.405023	+	0.294266i
$817$	−5.34861	−	16.4613i	−0.187124	−	0.575909i
$818$	−27.8061	+	85.5785i	−0.972218	+	2.99218i
$819$	21.1660	+	15.3780i	0.739599	+	0.537350i
$820$	−12.9527	−	9.41071i	−0.452329	−	0.328636i
$821$	−16.0416	+	49.3709i	−0.559855	+	1.72306i	0.122908	+	0.992418i	$0.460778\pi$
$821$	−16.0416	+	49.3709i	−0.559855	+	1.72306i	−0.682763	+	0.730640i	$0.739222\pi$
$822$	32.5488	+	100.175i	1.13527	+	3.49400i
$823$	−12.8836	+	9.36045i	−0.449093	+	0.326285i	−0.789237	−	0.614088i	$-0.789524\pi$
$823$	−12.8836	+	9.36045i	−0.449093	+	0.326285i	0.340145	+	0.940373i	$0.389524\pi$
$824$	65.3744			2.27743
$825$		0			0
$826$	−94.6775			−3.29425
$827$	−7.90542	+	5.74362i	−0.274898	+	0.199725i	−0.716689	−	0.697393i	$-0.754343\pi$
$827$	−7.90542	+	5.74362i	−0.274898	+	0.199725i	0.441791	+	0.897118i	$0.354343\pi$
$828$	−14.2689	−	43.9151i	−0.495878	−	1.52616i
$829$	0.314549	−	0.968083i	0.0109247	−	0.0336229i	−0.945446	−	0.325780i	$-0.894373\pi$
$829$	0.314549	−	0.968083i	0.0109247	−	0.0336229i	0.956370	+	0.292157i	$0.0943731\pi$
$830$	14.3509	+	10.4265i	0.498126	+	0.361910i
$831$	−35.4828	−	25.7798i	−1.23089	−	0.894290i
$832$	5.51686	−	16.9791i	0.191263	−	0.588646i
$833$	5.13031	+	15.7895i	0.177755	+	0.547073i
$834$	−41.6409	+	30.2539i	−1.44191	+	1.04761i
$835$	−1.04668			−0.0362219
$836$		0			0
$837$	58.5056			2.02225
$838$	71.0286	−	51.6053i	2.45364	−	1.78268i
$839$	4.26133	+	13.1150i	0.147117	+	0.452781i	0.997277	−	0.0737438i	$-0.0234947\pi$
$839$	4.26133	+	13.1150i	0.147117	+	0.452781i	−0.850160	+	0.526525i	$0.823495\pi$
$840$	10.6805	−	32.8712i	0.368512	−	1.13416i
$841$	5.60712	+	4.07381i	0.193349	+	0.140476i
$842$	55.8920	+	40.6079i	1.92617	+	1.39944i
$843$	−1.89402	+	5.82919i	−0.0652334	+	0.200768i
$844$	−8.30970	−	25.5746i	−0.286032	−	0.880315i
$845$	−8.73869	+	6.34903i	−0.300620	+	0.218413i
$846$	128.982			4.43448
$847$		0			0
$848$	−3.36518			−0.115561
$849$	10.0427	−	7.29646i	0.344665	−	0.250414i
$850$	−2.70915	−	8.33792i	−0.0929232	−	0.285988i
$851$	2.09858	−	6.45877i	0.0719385	−	0.221404i
$852$	−20.5310	−	14.9166i	−0.703379	−	0.511035i
$853$	22.1075	+	16.0620i	0.756946	+	0.549953i	0.897972	−	0.440052i	$-0.145040\pi$
$853$	22.1075	+	16.0620i	0.756946	+	0.549953i	−0.141026	+	0.990006i	$0.545040\pi$
$854$	−33.5966	+	103.400i	−1.14965	+	3.53826i
$855$	−5.18129	−	15.9464i	−0.177196	−	0.545354i
$856$	−20.5691	+	14.9443i	−0.703036	+	0.510786i
$857$	−22.2318			−0.759424			−0.379712	−	0.925105i	$-0.623977\pi$
$857$	−22.2318			−0.759424			−0.379712	+	0.925105i	$0.623977\pi$
$858$		0			0
$859$	28.5173			0.972998			0.486499	−	0.873681i	$-0.338274\pi$
$859$	28.5173			0.972998			0.486499	+	0.873681i	$0.338274\pi$
$860$	−15.3191	+	11.1300i	−0.522376	+	0.379528i
$861$	−13.6411	−	41.9829i	−0.464887	−	1.43077i
$862$	1.28345	−	3.95004i	0.0437144	−	0.134539i
$863$	−42.2787	−	30.7173i	−1.43918	−	1.04563i	−0.988212	−	0.153091i	$-0.951077\pi$
$863$	−42.2787	−	30.7173i	−1.43918	−	1.04563i	−0.450972	−	0.892538i	$-0.648923\pi$
$864$	−20.4834	−	14.8821i	−0.696861	−	0.506299i
$865$	3.68128	−	11.3298i	0.125167	−	0.385226i
$866$	−7.29573	−	22.4539i	−0.247919	−	0.763016i
$867$	7.11691	−	5.17074i	0.241703	−	0.175607i
$868$	109.667			3.72234
$869$		0			0
$870$	−31.6274			−1.07227
$871$	9.39420	−	6.82528i	0.318310	−	0.231266i
$872$	4.56599	+	14.0527i	0.154624	+	0.475883i
$873$	17.7540	−	54.6412i	0.600882	−	1.84932i
$874$	−15.3798	−	11.1741i	−0.520229	−	0.377968i
$875$	2.73731	+	1.98877i	0.0925380	+	0.0672328i
$876$	9.23806	−	28.4318i	0.312125	−	0.960622i
$877$	6.49166	+	19.9793i	0.219208	+	0.674652i	0.998828	+	0.0483995i	$0.0154121\pi$
$877$	6.49166	+	19.9793i	0.219208	+	0.674652i	−0.779620	+	0.626252i	$0.784588\pi$
$878$	−74.4862	+	54.1174i	−2.51379	+	1.82637i
$879$	38.7133			1.30577
$880$		0			0
$881$	46.0743			1.55228			0.776141	−	0.630560i	$-0.217175\pi$
$881$	46.0743			1.55228			0.776141	+	0.630560i	$0.217175\pi$
$882$	44.0815	−	32.0271i	1.48430	−	1.07841i
$883$	0.192309	+	0.591867i	0.00647172	+	0.0199179i	0.954240	−	0.299041i	$-0.0966668\pi$
$883$	0.192309	+	0.591867i	0.00647172	+	0.0199179i	−0.947769	+	0.318959i	$0.896667\pi$
$884$	−6.01495	+	18.5121i	−0.202305	+	0.622630i
$885$	27.6236	+	20.0697i	0.928558	+	0.674637i
$886$	−26.6271	−	19.3457i	−0.894554	−	0.649932i
$887$	−3.52516	+	10.8493i	−0.118363	+	0.364285i	−0.992634	−	0.121155i	$-0.961340\pi$
$887$	−3.52516	+	10.8493i	−0.118363	+	0.364285i	0.874270	+	0.485439i	$0.161340\pi$
$888$	8.51594	+	26.2094i	0.285776	+	0.879529i
$889$	30.9217	−	22.4659i	1.03708	−	0.753483i
$890$	25.3718			0.850466
$891$		0			0
$892$	−13.3290			−0.446287
$893$	27.3876	−	19.8983i	0.916491	−	0.665870i
$894$	13.4868	+	41.5080i	0.451065	+	1.38823i
$895$	1.04929	−	3.22939i	0.0350739	−	0.107946i
$896$	−55.5861	−	40.3857i	−1.85700	−	1.34919i
$897$	−8.65469	−	6.28800i	−0.288972	−	0.209950i
$898$	−1.86983	+	5.75474i	−0.0623970	+	0.192038i
$899$	−13.3775	−	41.1718i	−0.446165	−	1.37316i
$900$	−14.8399	+	10.7818i	−0.494662	+	0.359393i
$901$	−9.39558			−0.313012
$902$		0			0
$903$	−52.2081			−1.73738
$904$	4.22348	−	3.06853i	0.140471	−	0.102058i
$905$	1.76071	+	5.41892i	0.0585281	+	0.180131i
$906$	22.6314	−	69.6524i	0.751879	−	2.31405i
$907$	−31.4849	−	22.8751i	−1.04544	−	0.759557i	−0.0740999	−	0.997251i	$-0.523608\pi$
$907$	−31.4849	−	22.8751i	−1.04544	−	0.759557i	−0.971340	+	0.237694i	$0.923608\pi$
$908$	−55.6195	−	40.4100i	−1.84580	−	1.34105i
$909$	20.5189	−	63.1507i	0.680570	−	2.09458i
$910$	−3.64137	−	11.2070i	−0.120710	−	0.371508i
$911$	−30.8182	+	22.3907i	−1.02105	+	0.741838i	−0.966498	−	0.256673i	$-0.917374\pi$
$911$	−30.8182	+	22.3907i	−1.02105	+	0.741838i	−0.0545536	+	0.998511i	$0.517374\pi$
$912$	12.3189			0.407920
$913$		0			0
$914$	35.5193			1.17488
$915$	31.7210	−	23.0466i	1.04866	−	0.761898i
$916$	5.61124	+	17.2696i	0.185401	+	0.570605i
$917$	15.3487	−	47.2384i	0.506859	−	1.55995i
$918$	45.0305	+	32.7166i	1.48623	+	1.07981i
$919$	−15.5919	−	11.3282i	−0.514329	−	0.373682i	0.300134	−	0.953897i	$-0.402969\pi$
$919$	−15.5919	−	11.3282i	−0.514329	−	0.373682i	−0.814463	+	0.580215i	$0.802969\pi$
$920$	−2.77239	+	8.53253i	−0.0914029	+	0.281309i
$921$	2.10698	+	6.48461i	0.0694272	+	0.213675i
$922$	−18.6917	+	13.5803i	−0.615579	+	0.447244i
$923$	−3.73240			−0.122853
$924$		0			0
$925$	−2.69779			−0.0887027
$926$	40.3039	−	29.2825i	1.32447	−	0.962282i
$927$	−29.5608	−	90.9788i	−0.970904	−	2.98814i
$928$	−5.78926	+	17.8175i	−0.190042	+	0.584888i
$929$	−25.2195	−	18.3231i	−0.827426	−	0.601160i	0.0914042	−	0.995814i	$-0.470864\pi$
$929$	−25.2195	−	18.3231i	−0.827426	−	0.601160i	−0.918830	+	0.394654i	$0.870864\pi$
$930$	−50.1911	−	36.4660i	−1.64583	−	1.19577i
$931$	4.41926	−	13.6011i	0.144835	−	0.445757i
$932$	−6.79284	−	20.9062i	−0.222507	−	0.684806i
$933$	51.3491	−	37.3073i	1.68110	−	1.22139i
$934$	22.4648			0.735070
$935$		0			0
$936$	27.5582			0.900767
$937$	−20.9299	+	15.2065i	−0.683751	+	0.496774i	−0.874600	−	0.484845i	$-0.838876\pi$
$937$	−20.9299	+	15.2065i	−0.683751	+	0.496774i	0.190849	+	0.981619i	$0.438876\pi$
$938$	−19.2337	−	59.1952i	−0.628002	−	1.93279i
$939$	−24.1658	+	74.3747i	−0.788622	+	2.42713i
$940$	−29.9620	−	21.7686i	−0.977252	−	0.710015i
$941$	−23.8365	−	17.3183i	−0.777049	−	0.564559i	0.127043	−	0.991897i	$-0.459451\pi$
$941$	−23.8365	−	17.3183i	−0.777049	−	0.564559i	−0.904092	+	0.427338i	$0.859451\pi$
$942$	−21.6992	+	66.7833i	−0.706999	+	2.17592i
$943$	3.54089	+	10.8977i	0.115307	+	0.354879i
$944$	−12.8839	+	9.36070i	−0.419335	+	0.304665i
$945$	−21.4815			−0.698793
$946$		0			0
$947$	−14.3881			−0.467551			−0.233776	−	0.972291i	$-0.575108\pi$
$947$	−14.3881			−0.467551			−0.233776	+	0.972291i	$0.575108\pi$
$948$	55.1913	−	40.0988i	1.79253	−	1.30235i
$949$	−1.35868	−	4.18158i	−0.0441046	−	0.135740i
$950$	−2.33367	+	7.18230i	−0.0757142	+	0.233024i
$951$	35.6993	+	25.9371i	1.15763	+	0.841067i
$952$	36.4123	+	26.4551i	1.18013	+	0.857414i
$953$	−9.86355	+	30.3569i	−0.319512	+	0.983356i	0.654346	+	0.756196i	$0.272944\pi$
$953$	−9.86355	+	30.3569i	−0.319512	+	0.983356i	−0.973857	+	0.227161i	$0.927056\pi$
$954$	9.52892	+	29.3270i	0.308510	+	0.949496i
$955$	−7.29467	+	5.29989i	−0.236050	+	0.171500i
$956$	−16.2171			−0.524499
$957$		0			0
$958$	−40.3944			−1.30508
$959$	42.8260	−	31.1149i	1.38292	−	1.00475i
$960$	10.6646	+	32.8224i	0.344200	+	1.05934i
$961$	16.6616	−	51.2790i	0.537470	−	1.65416i
$962$	7.60118	+	5.52258i	0.245072	+	0.178055i
$963$	30.0982	+	21.8676i	0.969901	+	0.704675i
$964$	−8.56295	+	26.3540i	−0.275794	+	0.848807i
$965$	8.10607	+	24.9479i	0.260944	+	0.803102i
$966$	−46.3905	+	33.7047i	−1.49259	+	1.08443i
$967$	46.8425			1.50635			0.753176	−	0.657819i	$-0.228521\pi$
$967$	46.8425			1.50635			0.753176	+	0.657819i	$0.228521\pi$
$968$		0			0
$969$	34.3944			1.10491
$970$	−20.9350	+	15.2102i	−0.672182	+	0.488369i
$971$	−2.05867	−	6.33592i	−0.0660657	−	0.203329i	0.912574	−	0.408911i	$-0.134091\pi$
$971$	−2.05867	−	6.33592i	−0.0660657	−	0.203329i	−0.978640	+	0.205582i	$0.934091\pi$
$972$	−12.7520	+	39.2467i	−0.409021	+	1.25884i
$973$	20.9275	+	15.2047i	0.670905	+	0.487441i
$974$	29.5532	+	21.4717i	0.946946	+	0.687997i
$975$	−1.31323	+	4.04171i	−0.0420570	+	0.129438i
$976$	5.65116	+	17.3925i	0.180889	+	0.556720i
$977$	19.5750	−	14.2220i	0.626259	−	0.455004i	−0.228843	−	0.973463i	$-0.573494\pi$
$977$	19.5750	−	14.2220i	0.626259	−	0.455004i	0.855102	+	0.518460i	$0.173494\pi$
$978$	68.9658			2.20528
$979$		0			0
$980$	−15.6453			−0.499770
$981$	17.4919	−	12.7086i	0.558472	−	0.405754i
$982$	−6.57528	−	20.2366i	−0.209826	−	0.645777i
$983$	−8.58191	+	26.4124i	−0.273720	+	0.842425i	0.715835	+	0.698270i	$0.246046\pi$
$983$	−8.58191	+	26.4124i	−0.273720	+	0.842425i	−0.989555	+	0.144155i	$0.953954\pi$
$984$	−37.6178	−	27.3310i	−1.19921	−	0.871279i
$985$	13.5088	+	9.81471i	0.430426	+	0.312723i
$986$	12.7270	−	39.1698i	0.405311	−	1.24742i
$987$	−31.5542	−	97.1140i	−1.00438	−	3.09117i
$988$	13.5648	−	9.85540i	0.431554	−	0.313542i
$989$	13.5519			0.430926
$990$		0			0
$991$	45.4227			1.44290			0.721450	−	0.692466i	$-0.243476\pi$
$991$	45.4227			1.44290			0.721450	+	0.692466i	$0.243476\pi$
$992$	−29.7306	+	21.6006i	−0.943949	+	0.685819i
$993$	22.9511	+	70.6364i	0.728332	+	2.24158i
$994$	−6.18227	+	19.0271i	−0.196090	+	0.603502i
$995$	−13.5843	−	9.86959i	−0.430652	−	0.312887i
$996$	61.5929	+	44.7499i	1.95165	+	1.41795i
$997$	15.6823	−	48.2653i	0.496665	−	1.52858i	−0.317682	−	0.948197i	$-0.602904\pi$
$997$	15.6823	−	48.2653i	0.496665	−	1.52858i	0.814347	−	0.580379i	$-0.197096\pi$
$998$	−17.8331	−	54.8846i	−0.564497	−	1.73734i
$999$	13.8568	−	10.0676i	0.438410	−	0.318524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.p.366.3		12
11.2	odd	10		605.2.a.h.1.3	yes	3
11.3	even	5	inner	605.2.g.p.511.1		12
11.4	even	5	inner	605.2.g.p.81.3		12
11.5	even	5	inner	605.2.g.p.251.1		12
11.6	odd	10		605.2.g.o.251.3		12
11.7	odd	10		605.2.g.o.81.1		12
11.8	odd	10		605.2.g.o.511.3		12
11.9	even	5		605.2.a.g.1.1	✓	3
11.10	odd	2		605.2.g.o.366.1		12
33.2	even	10		5445.2.a.bb.1.1		3
33.20	odd	10		5445.2.a.bd.1.3		3
44.31	odd	10		9680.2.a.bz.1.1		3
44.35	even	10		9680.2.a.cb.1.1		3
55.9	even	10		3025.2.a.u.1.3		3
55.24	odd	10		3025.2.a.p.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.g.1.1	✓	3	11.9	even	5
605.2.a.h.1.3	yes	3	11.2	odd	10
605.2.g.o.81.1		12	11.7	odd	10
605.2.g.o.251.3		12	11.6	odd	10
605.2.g.o.366.1		12	11.10	odd	2
605.2.g.o.511.3		12	11.8	odd	10
605.2.g.p.81.3		12	11.4	even	5	inner
605.2.g.p.251.1		12	11.5	even	5	inner
605.2.g.p.366.3		12	1.1	even	1	trivial
605.2.g.p.511.1		12	11.3	even	5	inner
3025.2.a.p.1.1		3	55.24	odd	10
3025.2.a.u.1.3		3	55.9	even	10
5445.2.a.bb.1.1		3	33.2	even	10
5445.2.a.bd.1.3		3	33.20	odd	10
9680.2.a.bz.1.1		3	44.31	odd	10
9680.2.a.cb.1.1		3	44.35	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)

\(f(q)\)	\(=\)	\(q+(1.90030 - 1.38065i) q^{2} +(0.885704 + 2.72592i) q^{3} +(1.08691 - 3.34515i) q^{4} +(0.809017 + 0.587785i) q^{5} +(5.44662 + 3.95720i) q^{6} +(1.04556 - 3.21790i) q^{7} +(-1.10133 - 3.38955i) q^{8} +(-4.21910 + 3.06535i) q^{9} +O(q^{10})\)	\(q+(1.90030 - 1.38065i) q^{2} +(0.885704 + 2.72592i) q^{3} +(1.08691 - 3.34515i) q^{4} +(0.809017 + 0.587785i) q^{5} +(5.44662 + 3.95720i) q^{6} +(1.04556 - 3.21790i) q^{7} +(-1.10133 - 3.38955i) q^{8} +(-4.21910 + 3.06535i) q^{9} +2.34889 q^{10} +10.0813 q^{12} +(1.19953 - 0.871507i) q^{13} +(-2.45591 - 7.55851i) q^{14} +(-0.885704 + 2.72592i) q^{15} +(-1.08151 - 0.785763i) q^{16} +(-3.01957 - 2.19385i) q^{17} +(-3.78537 + 11.6502i) q^{18} +(0.993518 + 3.05773i) q^{19} +(2.84556 - 2.06742i) q^{20} +9.69779 q^{21} -2.51730 q^{23} +(8.26418 - 6.00428i) q^{24} +(0.309017 + 0.951057i) q^{25} +(1.07621 - 3.31224i) q^{26} +(-5.13636 - 3.73179i) q^{27} +(-9.62795 - 6.99512i) q^{28} +(-1.45170 + 4.46786i) q^{29} +(2.08042 + 6.40289i) q^{30} +(-7.45517 + 5.41650i) q^{31} +3.98793 q^{32} -8.76700 q^{34} +(2.73731 - 1.98877i) q^{35} +(5.66832 + 17.4453i) q^{36} +(-0.833662 + 2.56575i) q^{37} +(6.10963 + 4.43890i) q^{38} +(3.43808 + 2.49791i) q^{39} +(1.10133 - 3.38955i) q^{40} +(-1.40662 - 4.32913i) q^{41} +(18.4287 - 13.3892i) q^{42} -5.38350 q^{43} -5.21509 q^{45} +(-4.78362 + 3.47550i) q^{46} +(-3.25376 - 10.0140i) q^{47} +(1.18403 - 3.64406i) q^{48} +(-3.59858 - 2.61452i) q^{49} +(1.90030 + 1.38065i) q^{50} +(3.30580 - 10.1742i) q^{51} +(-1.61155 - 4.95985i) q^{52} +(2.03654 - 1.47963i) q^{53} -14.9129 q^{54} -12.0588 q^{56} +(-7.45517 + 5.41650i) q^{57} +(3.40988 + 10.4945i) q^{58} +(3.68128 - 11.3298i) q^{59} +(8.15594 + 5.92563i) q^{60} +(-11.0673 - 8.04083i) q^{61} +(-6.68876 + 20.5859i) q^{62} +(5.45269 + 16.7817i) q^{63} +(9.74126 - 7.07744i) q^{64} +1.48270 q^{65} +7.83159 q^{67} +(-10.6208 + 7.71643i) q^{68} +(-2.22959 - 6.86196i) q^{69} +(2.45591 - 7.55851i) q^{70} +(-2.03654 - 1.47963i) q^{71} +(15.0368 + 10.9249i) q^{72} +(0.916356 - 2.82026i) q^{73} +(1.95818 + 6.02667i) q^{74} +(-2.31880 + 1.68471i) q^{75} +11.3085 q^{76} +9.98210 q^{78} +(5.47462 - 3.97755i) q^{79} +(-0.413100 - 1.27139i) q^{80} +(0.788584 - 2.42701i) q^{81} +(-8.64998 - 6.28458i) q^{82} +(6.10963 + 4.43890i) q^{83} +(10.5406 - 32.4406i) q^{84} +(-1.15337 - 3.54972i) q^{85} +(-10.2302 + 7.43271i) q^{86} -13.4648 q^{87} +10.8016 q^{89} +(-9.91022 + 7.20019i) q^{90} +(-1.55025 - 4.77117i) q^{91} +(-2.73607 + 8.42077i) q^{92} +(-21.3680 - 15.5247i) q^{93} +(-20.0089 - 14.5373i) q^{94} +(-0.993518 + 3.05773i) q^{95} +(3.53212 + 10.8708i) q^{96} +(-8.91270 + 6.47546i) q^{97} -10.4481 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} - q^{3} - 9 q^{4} + 3 q^{5} + 5 q^{6} - q^{7} - 9 q^{8} - 2 q^{9}+O(q^{10}) \) 12 * q + q^2 - q^3 - 9 * q^4 + 3 * q^5 + 5 * q^6 - q^7 - 9 * q^8 - 2 * q^9	\( 12 q + q^{2} - q^{3} - 9 q^{4} + 3 q^{5} + 5 q^{6} - q^{7} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 36 q^{12} + 6 q^{13} - 5 q^{14} + q^{15} - 13 q^{16} + 4 q^{17} + 20 q^{18} + 4 q^{19} + 9 q^{20} + 68 q^{21} - 24 q^{23} + 17 q^{24} - 3 q^{25} - 12 q^{26} - 13 q^{27} - 25 q^{28} + 2 q^{29} - 5 q^{30} - 14 q^{31} + 108 q^{32} - 32 q^{34} + q^{35} - 2 q^{36} - 4 q^{37} + 18 q^{38} - 4 q^{39} + 9 q^{40} + 9 q^{41} + 35 q^{42} - 28 q^{43} - 8 q^{45} + 8 q^{46} + 15 q^{47} - 7 q^{48} - 18 q^{49} + q^{50} - 20 q^{51} + 2 q^{52} + 6 q^{53} - 76 q^{54} - 12 q^{56} - 14 q^{57} - 30 q^{58} - 10 q^{59} + 9 q^{60} + 3 q^{61} + 24 q^{62} - 12 q^{63} - 29 q^{64} + 24 q^{65} + 76 q^{67} + 8 q^{69} + 5 q^{70} - 6 q^{71} + 48 q^{72} - 12 q^{73} - 28 q^{74} - q^{75} - 64 q^{76} - 8 q^{78} + 2 q^{79} + 13 q^{80} - 3 q^{81} + 27 q^{82} + 18 q^{83} - 31 q^{84} - 4 q^{85} + 3 q^{86} - 40 q^{87} + 44 q^{89} - 20 q^{90} - 20 q^{91} + 34 q^{92} - 20 q^{93} - 59 q^{94} - 4 q^{95} - 7 q^{96} + 2 q^{97} - 144 q^{98}+O(q^{100}) \) 12 * q + q^2 - q^3 - 9 * q^4 + 3 * q^5 + 5 * q^6 - q^7 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 36 * q^12 + 6 * q^13 - 5 * q^14 + q^15 - 13 * q^16 + 4 * q^17 + 20 * q^18 + 4 * q^19 + 9 * q^20 + 68 * q^21 - 24 * q^23 + 17 * q^24 - 3 * q^25 - 12 * q^26 - 13 * q^27 - 25 * q^28 + 2 * q^29 - 5 * q^30 - 14 * q^31 + 108 * q^32 - 32 * q^34 + q^35 - 2 * q^36 - 4 * q^37 + 18 * q^38 - 4 * q^39 + 9 * q^40 + 9 * q^41 + 35 * q^42 - 28 * q^43 - 8 * q^45 + 8 * q^46 + 15 * q^47 - 7 * q^48 - 18 * q^49 + q^50 - 20 * q^51 + 2 * q^52 + 6 * q^53 - 76 * q^54 - 12 * q^56 - 14 * q^57 - 30 * q^58 - 10 * q^59 + 9 * q^60 + 3 * q^61 + 24 * q^62 - 12 * q^63 - 29 * q^64 + 24 * q^65 + 76 * q^67 + 8 * q^69 + 5 * q^70 - 6 * q^71 + 48 * q^72 - 12 * q^73 - 28 * q^74 - q^75 - 64 * q^76 - 8 * q^78 + 2 * q^79 + 13 * q^80 - 3 * q^81 + 27 * q^82 + 18 * q^83 - 31 * q^84 - 4 * q^85 + 3 * q^86 - 40 * q^87 + 44 * q^89 - 20 * q^90 - 20 * q^91 + 34 * q^92 - 20 * q^93 - 59 * q^94 - 4 * q^95 - 7 * q^96 + 2 * q^97 - 144 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more