LMFDB - Embedded newform 605.2.g.p.251.1

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			251.1
Root			$2.31880 - 1.68471i$ of defining polynomial
Character	$\chi$	$=$	605.251
Dual form			605.2.g.p.511.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.725848 + 2.23393i) q^{2} +(-2.31880 + 1.68471i) q^{3} +(-2.84556 - 2.06742i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-2.08042 - 6.40289i) q^{6} +(-2.73731 - 1.98877i) q^{7} +(2.88333 - 2.09486i) q^{8} +(1.61155 - 4.95985i) q^{9} +O(q^{10})$	\(q+(-0.725848 + 2.23393i) q^{2} +(-2.31880 + 1.68471i) q^{3} +(-2.84556 - 2.06742i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-2.08042 - 6.40289i) q^{6} +(-2.73731 - 1.98877i) q^{7} +(2.88333 - 2.09486i) q^{8} +(1.61155 - 4.95985i) q^{9} +2.34889 q^{10} +10.0813 q^{12} +(-0.458178 + 1.41013i) q^{13} +(6.42965 - 4.67142i) q^{14} +(2.31880 + 1.68471i) q^{15} +(0.413100 + 1.27139i) q^{16} +(1.15337 + 3.54972i) q^{17} +(9.91022 + 7.20019i) q^{18} +(-2.60106 + 1.88978i) q^{19} +(-1.08691 + 3.34515i) q^{20} +9.69779 q^{21} -2.51730 q^{23} +(-3.15664 + 9.71513i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-2.81756 - 2.04708i) q^{26} +(1.96192 + 6.03816i) q^{27} +(3.67755 + 11.3183i) q^{28} +(3.80059 + 2.76129i) q^{29} +(-5.44662 + 3.95720i) q^{30} +(2.84762 - 8.76407i) q^{31} +3.98793 q^{32} -8.76700 q^{34} +(-1.04556 + 3.21790i) q^{35} +(-14.8399 + 10.7818i) q^{36} +(2.18256 + 1.58572i) q^{37} +(-2.33367 - 7.18230i) q^{38} +(-1.31323 - 4.04171i) q^{39} +(-2.88333 - 2.09486i) q^{40} +(3.68257 - 2.67555i) q^{41} +(-7.03912 + 21.6642i) q^{42} -5.38350 q^{43} -5.21509 q^{45} +(1.82718 - 5.62348i) q^{46} +(8.51845 - 6.18901i) q^{47} +(-3.09982 - 2.25215i) q^{48} +(1.37453 + 4.23038i) q^{49} +(-0.725848 - 2.23393i) q^{50} +(-8.65469 - 6.28800i) q^{51} +(4.21910 - 3.06535i) q^{52} +(-0.777890 + 2.39410i) q^{53} -14.9129 q^{54} -12.0588 q^{56} +(2.84762 - 8.76407i) q^{57} +(-8.92719 + 6.48598i) q^{58} +(-9.63772 - 7.00222i) q^{59} +(-3.11529 - 9.58788i) q^{60} +(4.22732 + 13.0103i) q^{61} +(17.5114 + 12.7228i) q^{62} +(-14.2753 + 10.3716i) q^{63} +(-3.72083 + 11.4515i) q^{64} +1.48270 q^{65} +7.83159 q^{67} +(4.05677 - 12.4854i) q^{68} +(5.83713 - 4.24092i) q^{69} +(-6.42965 - 4.67142i) q^{70} +(0.777890 + 2.39410i) q^{71} +(-5.74355 - 17.6768i) q^{72} +(-2.39905 - 1.74301i) q^{73} +(-5.12659 + 3.72469i) q^{74} +(0.885704 - 2.72592i) q^{75} +11.3085 q^{76} +9.98210 q^{78} +(-2.09112 + 6.43580i) q^{79} +(1.08151 - 0.785763i) q^{80} +(-2.06454 - 1.49998i) q^{81} +(3.30400 + 10.1687i) q^{82} +(-2.33367 - 7.18230i) q^{83} +(-27.5956 - 20.0494i) q^{84} +(3.01957 - 2.19385i) q^{85} +(3.90761 - 12.0264i) q^{86} -13.4648 q^{87} +10.8016 q^{89} +(3.78537 - 11.6502i) q^{90} +(4.05860 - 2.94875i) q^{91} +(7.16314 + 5.20432i) q^{92} +(8.16184 + 25.1196i) q^{93} +(7.64273 + 23.5219i) q^{94} +(2.60106 + 1.88978i) q^{95} +(-9.24721 + 6.71849i) q^{96} +(3.40435 - 10.4775i) 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 $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.725848	+	2.23393i	−0.513252	+	1.57963i	0.273187	+	0.961961i	$0.411922\pi$
$2$	−0.725848	+	2.23393i	−0.513252	+	1.57963i	−0.786440	+	0.617667i	$0.788078\pi$
$3$	−2.31880	+	1.68471i	−1.33876	+	0.972667i	−0.339273	+	0.940688i	$0.610181\pi$
$3$	−2.31880	+	1.68471i	−1.33876	+	0.972667i	−0.999489	+	0.0319793i	$0.989819\pi$
$4$	−2.84556	−	2.06742i	−1.42278	−	1.03371i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$	−2.08042	−	6.40289i	−0.849330	−	2.61397i
$7$	−2.73731	−	1.98877i	−1.03461	−	0.751685i	−0.0653808	−	0.997860i	$-0.520826\pi$
$7$	−2.73731	−	1.98877i	−1.03461	−	0.751685i	−0.969225	+	0.246175i	$0.920826\pi$
$8$	2.88333	−	2.09486i	1.01941	−	0.740644i
$9$	1.61155	−	4.95985i	0.537184	−	1.65328i
$10$	2.34889			0.742786
$11$		0			0
$11$		0			0
$12$	10.0813			2.91022
$13$	−0.458178	+	1.41013i	−0.127076	+	0.391099i	−0.994274	−	0.106865i	$-0.965919\pi$
$13$	−0.458178	+	1.41013i	−0.127076	+	0.391099i	0.867198	+	0.497964i	$0.165919\pi$
$14$	6.42965	−	4.67142i	1.71840	−	1.24849i
$15$	2.31880	+	1.68471i	0.598712	+	0.434990i
$16$	0.413100	+	1.27139i	0.103275	+	0.317848i
$17$	1.15337	+	3.54972i	0.279734	+	0.860934i	0.987928	+	0.154915i	$0.0495104\pi$
$17$	1.15337	+	3.54972i	0.279734	+	0.860934i	−0.708194	+	0.706018i	$0.750490\pi$
$18$	9.91022	+	7.20019i	2.33586	+	1.69710i
$19$	−2.60106	+	1.88978i	−0.596725	+	0.433546i	−0.844715	−	0.535216i	$-0.820230\pi$
$19$	−2.60106	+	1.88978i	−0.596725	+	0.433546i	0.247990	+	0.968763i	$0.420230\pi$
$20$	−1.08691	+	3.34515i	−0.243040	+	0.747999i
$21$	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	$0.584530\pi$
$24$	−3.15664	+	9.71513i	−0.644346	+	1.98309i
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	−2.81756	−	2.04708i	−0.552569	−	0.401465i
$27$	1.96192	+	6.03816i	0.377571	+	1.16204i
$28$	3.67755	+	11.3183i	0.694992	+	2.13897i
$29$	3.80059	+	2.76129i	0.705752	+	0.512759i	0.881800	−	0.471623i	$-0.156332\pi$
$29$	3.80059	+	2.76129i	0.705752	+	0.512759i	−0.176048	+	0.984381i	$0.556332\pi$
$30$	−5.44662	+	3.95720i	−0.994413	+	0.722483i
$31$	2.84762	−	8.76407i	0.511448	−	1.57407i	−0.278206	−	0.960521i	$-0.589740\pi$
$31$	2.84762	−	8.76407i	0.511448	−	1.57407i	0.789654	−	0.613553i	$-0.210260\pi$
$32$	3.98793			0.704972
$33$		0			0
$34$	−8.76700			−1.50353
$35$	−1.04556	+	3.21790i	−0.176732	+	0.543925i
$36$	−14.8399	+	10.7818i	−2.47331	+	1.79696i
$37$	2.18256	+	1.58572i	0.358810	+	0.260691i	0.752556	−	0.658529i	$-0.228821\pi$
$37$	2.18256	+	1.58572i	0.358810	+	0.260691i	−0.393746	+	0.919219i	$0.628821\pi$
$38$	−2.33367	−	7.18230i	−0.378571	−	1.16512i
$39$	−1.31323	−	4.04171i	−0.210285	−	0.647191i
$40$	−2.88333	−	2.09486i	−0.455894	−	0.331226i
$41$	3.68257	−	2.67555i	0.575121	−	0.417850i	−0.261841	−	0.965111i	$-0.584329\pi$
$41$	3.68257	−	2.67555i	0.575121	−	0.417850i	0.836962	+	0.547261i	$0.184329\pi$
$42$	−7.03912	+	21.6642i	−1.08616	+	3.34286i
$43$	−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
$46$	1.82718	−	5.62348i	0.269403	−	0.829137i
$47$	8.51845	−	6.18901i	1.24254	−	0.902760i	0.244778	−	0.969579i	$-0.421285\pi$
$47$	8.51845	−	6.18901i	1.24254	−	0.902760i	0.997765	+	0.0668188i	$0.0212849\pi$
$48$	−3.09982	−	2.25215i	−0.447421	−	0.325070i
$49$	1.37453	+	4.23038i	0.196362	+	0.604340i
$50$	−0.725848	−	2.23393i	−0.102650	−	0.315926i
$51$	−8.65469	−	6.28800i	−1.21190	−	0.880496i
$52$	4.21910	−	3.06535i	0.585084	−	0.425088i
$53$	−0.777890	+	2.39410i	−0.106851	+	0.328855i	−0.990161	−	0.139936i	$-0.955310\pi$
$53$	−0.777890	+	2.39410i	−0.106851	+	0.328855i	0.883309	+	0.468791i	$0.155310\pi$
$54$	−14.9129			−2.02939
$55$		0			0
$56$	−12.0588			−1.61142
$57$	2.84762	−	8.76407i	0.377177	−	1.16083i
$58$	−8.92719	+	6.48598i	−1.17220	+	0.851651i
$59$	−9.63772	−	7.00222i	−1.25472	−	0.911611i	−0.256238	−	0.966614i	$-0.582483\pi$
$59$	−9.63772	−	7.00222i	−1.25472	−	0.911611i	−0.998486	+	0.0550028i	$0.982483\pi$
$60$	−3.11529	−	9.58788i	−0.402182	−	1.23779i
$61$	4.22732	+	13.0103i	0.541252	+	1.66580i	0.729737	+	0.683728i	$0.239642\pi$
$61$	4.22732	+	13.0103i	0.541252	+	1.66580i	−0.188485	+	0.982076i	$0.560358\pi$
$62$	17.5114	+	12.7228i	2.22395	+	1.61579i
$63$	−14.2753	+	10.3716i	−1.79852	+	1.30670i
$64$	−3.72083	+	11.4515i	−0.465104	+	1.43144i
$65$	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	$0.341220\pi$
$68$	4.05677	−	12.4854i	0.491955	−	1.51408i
$69$	5.83713	−	4.24092i	0.702708	−	0.510547i
$70$	−6.42965	−	4.67142i	−0.768491	−	0.558341i
$71$	0.777890	+	2.39410i	0.0923185	+	0.284127i	0.986546	−	0.163486i	$-0.0522740\pi$
$71$	0.777890	+	2.39410i	0.0923185	+	0.284127i	−0.894227	+	0.447614i	$0.852274\pi$
$72$	−5.74355	−	17.6768i	−0.676884	−	2.08323i
$73$	−2.39905	−	1.74301i	−0.280788	−	0.204004i	0.438473	−	0.898744i	$-0.355519\pi$
$73$	−2.39905	−	1.74301i	−0.280788	−	0.204004i	−0.719261	+	0.694740i	$0.755519\pi$
$74$	−5.12659	+	3.72469i	−0.595955	+	0.432986i
$75$	0.885704	−	2.72592i	0.102272	−	0.314762i
$76$	11.3085			1.29717
$77$		0			0
$78$	9.98210			1.13025
$79$	−2.09112	+	6.43580i	−0.235269	+	0.724085i	0.761816	+	0.647793i	$0.224308\pi$
$79$	−2.09112	+	6.43580i	−0.235269	+	0.724085i	−0.997086	+	0.0762913i	$0.975692\pi$
$80$	1.08151	−	0.785763i	0.120916	−	0.0878510i
$81$	−2.06454	−	1.49998i	−0.229393	−	0.166664i
$82$	3.30400	+	10.1687i	0.364865	+	1.12294i
$83$	−2.33367	−	7.18230i	−0.256153	−	0.788359i	−0.993600	−	0.112954i	$-0.963969\pi$
$83$	−2.33367	−	7.18230i	−0.256153	−	0.788359i	0.737447	−	0.675405i	$-0.236031\pi$
$84$	−27.5956	−	20.0494i	−3.01093	−	2.18757i
$85$	3.01957	−	2.19385i	0.327519	−	0.237956i
$86$	3.90761	−	12.0264i	0.421368	−	1.29684i
$87$	−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	$0.305980\pi$
$90$	3.78537	−	11.6502i	0.399013	−	1.22803i
$91$	4.05860	−	2.94875i	0.425457	−	0.309113i
$92$	7.16314	+	5.20432i	0.746809	+	0.542588i
$93$	8.16184	+	25.1196i	0.846344	+	2.60478i
$94$	7.64273	+	23.5219i	0.788287	+	2.42610i
$95$	2.60106	+	1.88978i	0.266864	+	0.193888i
$96$	−9.24721	+	6.71849i	−0.943790	+	0.685703i
$97$	3.40435	−	10.4775i	0.345659	−	1.06383i	−0.615571	−	0.788082i	$-0.711074\pi$
$97$	3.40435	−	10.4775i	0.345659	−	1.06383i	0.961230	−	0.275748i	$-0.0889256\pi$
$98$	−10.4481			−1.05542
$99$		0			0
$100$	3.51730			0.351730
$101$	3.93453	−	12.1092i	0.391500	−	1.20491i	−0.540154	−	0.841566i	$-0.681634\pi$
$101$	3.93453	−	12.1092i	0.391500	−	1.20491i	0.931654	−	0.363347i	$-0.118366\pi$
$102$	20.3290	−	14.7699i	2.01287	−	1.46243i
$103$	14.8399	+	10.7818i	1.46221	+	1.06236i	0.982779	+	0.184783i	$0.0591583\pi$
$103$	14.8399	+	10.7818i	1.46221	+	1.06236i	0.479435	+	0.877578i	$0.340842\pi$
$104$	1.63294	+	5.02568i	0.160123	+	0.492808i
$105$	−2.99678	−	9.22314i	−0.292456	−	0.900087i
$106$	−4.78362	−	3.47550i	−0.464626	−	0.337571i
$107$	5.77137	−	4.19314i	0.557939	−	0.405366i	−0.272765	−	0.962081i	$-0.587938\pi$
$107$	5.77137	−	4.19314i	0.557939	−	0.405366i	0.830704	+	0.556714i	$0.187938\pi$
$108$	6.90066	−	21.2380i	0.664016	−	2.04363i
$109$	−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
$112$	1.39772	−	4.30175i	0.132073	−	0.406478i
$113$	−1.18504	+	0.860984i	−0.111479	+	0.0809945i	−0.642128	−	0.766597i	$-0.721948\pi$
$113$	−1.18504	+	0.860984i	−0.111479	+	0.0809945i	0.530649	+	0.847592i	$0.321948\pi$
$114$	17.5114	+	12.7228i	1.64009	+	1.19160i
$115$	0.777890	+	2.39410i	0.0725386	+	0.223251i
$116$	−5.10606	−	15.7148i	−0.474086	−	1.45909i
$117$	6.25564	+	4.54499i	0.578334	+	0.420184i
$118$	22.6380	−	16.4475i	2.08400	−	1.51411i
$119$	3.90244	−	12.0105i	0.357736	−	1.10100i
$120$	10.2151			0.932506
$121$		0			0
$122$	−32.1326			−2.90915
$123$	−4.03165	+	12.4081i	−0.363521	+	1.11880i
$124$	−26.2221	+	19.0515i	−2.35481	+	1.71087i
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$	−12.8078	−	39.4183i	−1.14101	−	3.51166i
$127$	−3.49077	−	10.7435i	−0.309756	−	0.953331i	−0.977859	−	0.209263i	$-0.932894\pi$
$127$	−3.49077	−	10.7435i	−0.309756	−	0.953331i	0.668103	−	0.744069i	$-0.267106\pi$
$128$	−16.4286	−	11.9361i	−1.45210	−	1.05501i
$129$	12.4833	−	9.06964i	1.09909	−	0.798537i
$130$	−1.07621	+	3.31224i	−0.0943901	+	0.290503i
$131$	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
$134$	−5.68455	+	17.4952i	−0.491070	+	1.51136i
$135$	5.13636	−	3.73179i	0.442068	−	0.321181i
$136$	10.7617	+	7.81884i	0.922809	+	0.670460i
$137$	−4.83466	−	14.8795i	−0.413053	−	1.27125i	−0.913981	−	0.405757i	$-0.867008\pi$
$137$	−4.83466	−	14.8795i	−0.413053	−	1.27125i	0.500929	−	0.865489i	$-0.332992\pi$
$138$	5.23706	+	16.1180i	0.445808	+	1.37206i
$139$	6.18516	+	4.49378i	0.524618	+	0.381158i	0.818341	−	0.574733i	$-0.194894\pi$
$139$	6.18516	+	4.49378i	0.524618	+	0.381158i	−0.293722	+	0.955891i	$0.594894\pi$
$140$	9.62795	−	6.99512i	0.813711	−	0.591195i
$141$	−9.32591	+	28.7022i	−0.785384	+	2.41716i
$142$	−5.91288			−0.496198
$143$		0			0
$144$	6.97164			0.580970
$145$	1.45170	−	4.46786i	0.120557	−	0.371036i
$146$	5.63512	−	4.09415i	0.466366	−	0.338835i
$147$	−10.3142	−	7.49373i	−0.850704	−	0.618073i
$148$	−2.93224	−	9.02452i	−0.241029	−	0.741811i
$149$	−2.00326	−	6.16541i	−0.164114	−	0.505090i	0.834856	−	0.550468i	$-0.185551\pi$
$149$	−2.00326	−	6.16541i	−0.164114	−	0.505090i	−0.998970	+	0.0453781i	$0.985551\pi$
$150$	5.44662	+	3.95720i	0.444715	+	0.323104i
$151$	8.80071	−	6.39409i	0.716191	−	0.520344i	−0.168974	−	0.985621i	$-0.554045\pi$
$151$	8.80071	−	6.39409i	0.716191	−	0.520344i	0.885165	+	0.465277i	$0.154045\pi$
$152$	−3.54089	+	10.8977i	−0.287204	+	0.883922i
$153$	19.4648			1.57364
$154$		0			0
$155$	−9.21509			−0.740174
$156$	−4.61903	+	14.2159i	−0.369818	+	1.13818i
$157$	−8.43820	+	6.13071i	−0.673441	+	0.489284i	−0.871175	−	0.490972i	$-0.836642\pi$
$157$	−8.43820	+	6.13071i	−0.673441	+	0.489284i	0.197734	+	0.980256i	$0.436642\pi$
$158$	−12.8593	−	9.34283i	−1.02303	−	0.743276i
$159$	−2.22959	−	6.86196i	−0.176818	−	0.544189i
$160$	−1.23234	−	3.79274i	−0.0974248	−	0.299843i
$161$	6.89064	+	5.00635i	0.543059	+	0.394555i
$162$	4.84939	−	3.52329i	0.381004	−	0.276815i
$163$	−3.16553	+	9.74250i	−0.247943	+	0.763092i	0.747195	+	0.664605i	$0.231400\pi$
$163$	−3.16553	+	9.74250i	−0.247943	+	0.763092i	−0.995138	+	0.0984866i	$0.968600\pi$
$164$	−16.0105			−1.25021
$165$		0			0
$166$	17.7386			1.37679
$167$	0.323443	−	0.995454i	0.0250287	−	0.0770306i	−0.937762	−	0.347279i	$-0.887106\pi$
$167$	0.323443	−	0.995454i	0.0250287	−	0.0770306i	0.962791	+	0.270248i	$0.0871058\pi$
$168$	27.9619	−	20.3155i	2.15731	−	1.56737i
$169$	8.73869	+	6.34903i	0.672207	+	0.488387i
$170$	2.70915	+	8.33792i	0.207783	+	0.639489i
$171$	5.18129	+	15.9464i	0.396223	+	1.21945i
$172$	15.3191	+	11.1300i	1.16807	+	0.848651i
$173$	9.63772	−	7.00222i	0.732743	−	0.532369i	−0.157687	−	0.987489i	$-0.550404\pi$
$173$	9.63772	−	7.00222i	0.732743	−	0.532369i	0.890430	+	0.455120i	$0.150404\pi$
$174$	9.77340	−	30.0794i	0.740919	−	2.28031i
$175$	3.38350			0.255769
$176$		0			0
$177$	34.1447			2.56647
$178$	−7.84033	+	24.1301i	−0.587658	+	1.80862i
$179$	2.74708	−	1.99587i	0.205326	−	0.149178i	−0.480370	−	0.877066i	$-0.659498\pi$
$179$	2.74708	−	1.99587i	0.205326	−	0.149178i	0.685697	+	0.727887i	$0.259498\pi$
$180$	14.8399	+	10.7818i	1.10610	+	0.803627i
$181$	−1.76071	−	5.41892i	−0.130873	−	0.402785i	0.864052	−	0.503402i	$-0.167918\pi$
$181$	−1.76071	−	5.41892i	−0.130873	−	0.402785i	−0.994925	+	0.100617i	$0.967918\pi$
$182$	3.64137	+	11.2070i	0.269916	+	0.830716i
$183$	−31.7210	−	23.0466i	−2.34488	−	1.70366i
$184$	−7.25821	+	5.27340i	−0.535082	+	0.388760i
$185$	0.833662	−	2.56575i	0.0612921	−	0.188638i
$186$	−62.0397			−4.54897
$187$		0			0
$188$	−37.0350			−2.70106
$189$	6.63815	−	20.4301i	0.482854	−	1.48607i
$190$	−6.10963	+	4.43890i	−0.443239	+	0.322032i
$191$	7.29467	+	5.29989i	0.527824	+	0.383486i	0.819543	−	0.573018i	$-0.194227\pi$
$191$	7.29467	+	5.29989i	0.527824	+	0.383486i	−0.291719	+	0.956504i	$0.594227\pi$
$192$	−10.6646	−	32.8224i	−0.769654	−	2.36875i
$193$	−8.10607	−	24.9479i	−0.583488	−	1.79579i	−0.605260	−	0.796028i	$-0.706931\pi$
$193$	−8.10607	−	24.9479i	−0.583488	−	1.79579i	0.0217723	−	0.999763i	$-0.493069\pi$
$194$	20.9350	+	15.2102i	1.50304	+	1.09203i
$195$	−3.43808	+	2.49791i	−0.246206	+	0.178879i
$196$	4.83466	−	14.8795i	0.345333	−	1.06282i
$197$	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	$0.702906\pi$
$200$	−1.10133	+	3.38955i	−0.0778760	+	0.239678i
$201$	−18.1599	+	13.1940i	−1.28090	+	0.930630i
$202$	24.1953	+	17.5789i	1.70238	+	1.23685i
$203$	−4.91182	−	15.1170i	−0.344742	−	1.06101i
$204$	11.6275	+	35.7858i	0.814088	+	2.50550i
$205$	−3.68257	−	2.67555i	−0.257202	−	0.186868i
$206$	−34.8572	+	25.3253i	−2.42862	+	1.76450i
$207$	−4.05677	+	12.4854i	−0.281965	+	0.867798i
$208$	−1.98210			−0.137434
$209$		0			0
$210$	22.7791			1.57191
$211$	−2.36252	+	7.27109i	−0.162643	+	0.500563i	−0.998855	−	0.0478434i	$-0.984765\pi$
$211$	−2.36252	+	7.27109i	−0.162643	+	0.500563i	0.836212	+	0.548406i	$0.184765\pi$
$212$	7.16314	−	5.20432i	0.491966	−	0.357434i
$213$	−5.83713	−	4.24092i	−0.399954	−	0.290583i
$214$	5.17806	+	15.9364i	0.353965	+	1.08939i
$215$	1.66359	+	5.12001i	0.113456	+	0.349182i
$216$	18.3059	+	13.3000i	1.24556	+	0.904953i
$217$	−25.2246	+	18.3267i	−1.71236	+	1.24410i
$218$	3.00928	−	9.26160i	0.203814	−	0.627275i
$219$	8.49940			0.574336
$220$		0			0
$221$	−5.53401			−0.372258
$222$	5.61255	−	17.2736i	0.376689	−	1.15933i
$223$	3.06580	−	2.22743i	0.205301	−	0.149160i	−0.480384	−	0.877058i	$-0.659503\pi$
$223$	3.06580	−	2.22743i	0.205301	−	0.149160i	0.685685	+	0.727898i	$0.259503\pi$
$224$	−10.9162	−	7.93108i	−0.729369	−	0.529917i
$225$	1.61155	+	4.95985i	0.107437	+	0.330657i
$226$	−1.06322	−	3.27225i	−0.0707242	−	0.217667i
$227$	−15.8131	−	11.4889i	−1.04955	−	0.762545i	−0.0774258	−	0.996998i	$-0.524670\pi$
$227$	−15.8131	−	11.4889i	−1.04955	−	0.762545i	−0.972127	+	0.234453i	$0.924670\pi$
$228$	−26.2221	+	19.0515i	−1.73660	+	1.26171i
$229$	1.59533	−	4.90991i	0.105422	−	0.324456i	−0.884407	−	0.466716i	$-0.845437\pi$
$229$	1.59533	−	4.90991i	0.105422	−	0.324456i	0.989829	+	0.142260i	$0.0454370\pi$
$230$	−5.91288			−0.389884
$231$		0			0
$232$	16.7429			1.09922
$233$	−1.93126	+	5.94382i	−0.126521	+	0.389392i	−0.994175	−	0.107776i	$-0.965627\pi$
$233$	−1.93126	+	5.94382i	−0.126521	+	0.389392i	0.867654	+	0.497169i	$0.165627\pi$
$234$	−14.6938	+	10.6757i	−0.960566	+	0.697892i
$235$	−8.51845	−	6.18901i	−0.555682	−	0.403727i
$236$	12.9482	+	39.8504i	0.842855	+	2.59404i
$237$	−5.99356	−	18.4463i	−0.389324	−	1.19822i
$238$	23.9980	+	17.4356i	1.55556	+	1.13018i
$239$	3.73011	−	2.71008i	0.241281	−	0.175301i	−0.460573	−	0.887622i	$-0.652356\pi$
$239$	3.73011	−	2.71008i	0.241281	−	0.175301i	0.701854	+	0.712321i	$0.252356\pi$
$240$	−1.18403	+	3.64406i	−0.0764286	+	0.235223i
$241$	−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
$244$	14.8688	−	45.7613i	0.951875	−	2.92957i
$245$	3.59858	−	2.61452i	0.229905	−	0.167036i
$246$	−24.7926	−	18.0128i	−1.58072	−	1.14846i
$247$	−1.47309	−	4.53369i	−0.0937302	−	0.288472i
$248$	−10.1489	−	31.2350i	−0.644455	−	1.98343i
$249$	17.5114	+	12.7228i	1.10974	+	0.806273i
$250$	−1.90030	+	1.38065i	−0.120185	+	0.0873197i
$251$	3.29280	−	10.1342i	0.207840	−	0.639666i	−0.791745	−	0.610852i	$-0.790827\pi$
$251$	3.29280	−	10.1342i	0.207840	−	0.639666i	0.999585	−	0.0288136i	$-0.00917293\pi$
$252$	62.0638			3.90965
$253$		0			0
$254$	26.5340			1.66489
$255$	−3.30580	+	10.1742i	−0.207017	+	0.637133i
$256$	19.1065	−	13.8817i	1.19416	−	0.867605i
$257$	−2.27257	−	1.65112i	−0.141759	−	0.102994i	0.514645	−	0.857403i	$-0.327924\pi$
$257$	−2.27257	−	1.65112i	−0.141759	−	0.102994i	−0.656405	+	0.754409i	$0.727924\pi$
$258$	11.2000	+	34.4700i	0.697280	+	2.14601i
$259$	−2.82070	−	8.68122i	−0.175270	−	0.539425i
$260$	−4.21910	−	3.06535i	−0.261657	−	0.190105i
$261$	19.8204	−	14.4004i	1.22685	−	0.891362i
$262$	−10.6554	+	32.7939i	−0.658291	+	2.02601i
$263$	−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
$266$	−7.89598	+	24.3013i	−0.484133	+	1.49001i
$267$	−25.0468	+	18.1976i	−1.53284	+	1.11367i
$268$	−22.2852	−	16.1912i	−1.36129	−	0.989034i
$269$	−4.50425	−	13.8627i	−0.274629	−	0.845221i	−0.989317	−	0.145778i	$-0.953431\pi$
$269$	−4.50425	−	13.8627i	−0.274629	−	0.845221i	0.714688	−	0.699443i	$-0.246569\pi$
$270$	4.60833	+	14.1830i	0.280454	+	0.863149i
$271$	−1.74957	−	1.27113i	−0.106279	−	0.0772159i	0.533377	−	0.845878i	$-0.320923\pi$
$271$	−1.74957	−	1.27113i	−0.106279	−	0.0772159i	−0.639655	+	0.768662i	$0.720923\pi$
$272$	−4.03662	+	2.93278i	−0.244756	+	0.177826i
$273$	−4.44332	+	13.6751i	−0.268922	+	0.827656i
$274$	36.7491			2.22009
$275$		0			0
$276$	−25.3777			−1.52756
$277$	4.72864	−	14.5533i	0.284117	−	0.874421i	−0.702545	−	0.711639i	$-0.747953\pi$
$277$	4.72864	−	14.5533i	0.284117	−	0.874421i	0.986662	−	0.162782i	$-0.0520468\pi$
$278$	−14.5283	+	10.5554i	−0.871349	+	0.633072i
$279$	−38.8794	−	28.2475i	−2.32765	−	1.69114i
$280$	3.72636	+	11.4686i	0.222693	+	0.685378i
$281$	−0.660812	−	2.03377i	−0.0394207	−	0.121325i	0.929410	−	0.369050i	$-0.120317\pi$
$281$	−0.660812	−	2.03377i	−0.0394207	−	0.121325i	−0.968830	+	0.247725i	$0.920317\pi$
$282$	−57.3496	−	41.6669i	−3.41512	−	2.48123i
$283$	3.50385	−	2.54569i	0.208282	−	0.151326i	−0.478754	−	0.877949i	$-0.658911\pi$
$283$	3.50385	−	2.54569i	0.208282	−	0.151326i	0.687036	+	0.726623i	$0.258911\pi$
$284$	2.73607	−	8.42077i	0.162356	−	0.499681i
$285$	−9.21509			−0.545855
$286$		0			0
$287$	−15.4014			−0.909116
$288$	6.42675	−	19.7795i	0.378700	−	1.16552i
$289$	2.48305	−	1.80404i	0.146062	−	0.106120i
$290$	8.92719	+	6.48598i	0.524222	+	0.380870i
$291$	9.75754	+	30.0306i	0.571997	+	1.76043i
$292$	3.22310	+	9.91970i	0.188618	+	0.580506i
$293$	−10.9273	−	7.93912i	−0.638378	−	0.463809i	0.220915	−	0.975293i	$-0.429096\pi$
$293$	−10.9273	−	7.93912i	−0.638378	−	0.463809i	−0.859292	+	0.511485i	$0.829096\pi$
$294$	24.2271	−	17.6020i	1.41295	−	1.02657i
$295$	−3.68128	+	11.3298i	−0.214333	+	0.659648i
$296$	9.61488			0.558854
$297$		0			0
$298$	15.2272			0.882086
$299$	1.15337	−	3.54972i	0.0667013	−	0.205286i
$300$	−8.15594	+	5.92563i	−0.470883	+	0.342117i
$301$	14.7363	+	10.7066i	0.849387	+	0.617116i
$302$	7.89598	+	24.3013i	0.454362	+	1.39838i
$303$	11.2771	+	34.7075i	0.647854	+	1.99389i
$304$	−3.47715	−	2.52630i	−0.199428	−	0.144893i
$305$	11.0673	−	8.04083i	0.633709	−	0.460417i
$306$	−14.1285	+	43.4830i	−0.807672	+	2.48576i
$307$	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
$310$	6.68876	−	20.5859i	0.379896	−	1.16920i
$311$	17.9154	−	13.0163i	1.01589	−	0.738088i	0.0504540	−	0.998726i	$-0.483933\pi$
$311$	17.9154	−	13.0163i	1.01589	−	0.738088i	0.965436	+	0.260639i	$0.0839332\pi$
$312$	−12.2533	−	8.90252i	−0.693705	−	0.504006i
$313$	−8.43132	−	25.9489i	−0.476566	−	1.46672i	−0.843834	−	0.536604i	$-0.819707\pi$
$313$	−8.43132	−	25.9489i	−0.476566	−	1.46672i	0.367268	−	0.930115i	$-0.380293\pi$
$314$	−7.57073	−	23.3003i	−0.427241	−	1.31491i
$315$	14.2753	+	10.3716i	0.804324	+	0.584375i
$316$	19.2559	−	13.9902i	1.08323	−	0.787012i
$317$	−4.75749	+	14.6421i	−0.267208	+	0.822380i	0.723969	+	0.689832i	$0.242316\pi$
$317$	−4.75749	+	14.6421i	−0.267208	+	0.822380i	−0.991177	+	0.132548i	$0.957684\pi$
$318$	16.9475			0.950368
$319$		0			0
$320$	12.0409			0.673104
$321$	−6.31844	+	19.4461i	−0.352661	+	1.08538i
$322$	−16.1854	+	11.7594i	−0.901977	+	0.655324i
$323$	−9.70820	−	7.05342i	−0.540179	−	0.392463i
$324$	2.77369	+	8.53654i	0.154094	+	0.474252i
$325$	−0.458178	−	1.41013i	−0.0254152	−	0.0782198i
$326$	−19.4664	−	14.1432i	−1.07814	−	0.783317i
$327$	9.61347	−	6.98460i	0.531626	−	0.386249i
$328$	5.01317	−	15.4289i	0.276806	−	0.851921i
$329$	−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	$0.247721\pi$
$332$	−8.20822	+	25.2623i	−0.450485	+	1.38645i
$333$	11.3822	−	8.26968i	0.623743	−	0.453176i
$334$	1.98901	+	1.44510i	0.108834	+	0.0790722i
$335$	−2.42009	−	7.44828i	−0.132224	−	0.406943i
$336$	4.00616	+	12.3297i	0.218554	+	0.672639i
$337$	11.3118	+	8.21847i	0.616191	+	0.447689i	0.851589	−	0.524210i	$-0.175639\pi$
$337$	11.3118	+	8.21847i	0.616191	+	0.447689i	−0.235398	+	0.971899i	$0.575639\pi$
$338$	−20.5263	+	14.9132i	−1.11648	+	0.811171i
$339$	1.29737	−	3.99290i	0.0704636	−	0.216865i
$340$	−13.1280			−0.711964
$341$		0			0
$342$	−39.3839			−2.12964
$343$	−2.66818	+	8.21180i	−0.144068	+	0.443396i
$344$	−15.5224	+	11.2777i	−0.836911	+	0.608052i
$345$	−5.83713	−	4.24092i	−0.314261	−	0.228324i
$346$	8.64694	+	26.6126i	0.464863	+	1.43070i
$347$	9.59395	+	29.5271i	0.515030	+	1.58510i	0.783227	+	0.621736i	$0.213572\pi$
$347$	9.59395	+	29.5271i	0.515030	+	1.58510i	−0.268196	+	0.963364i	$0.586428\pi$
$348$	38.3149	+	27.8374i	2.05389	+	1.49224i
$349$	2.96358	−	2.15316i	0.158637	−	0.115256i	−0.505635	−	0.862747i	$-0.668742\pi$
$349$	2.96358	−	2.15316i	0.158637	−	0.115256i	0.664272	+	0.747491i	$0.268742\pi$
$350$	−2.45591	+	7.55851i	−0.131274	+	0.404019i
$351$	−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	$0.273092\pi$
$354$	−24.7839	+	76.2769i	−1.31725	+	4.05407i
$355$	2.03654	−	1.47963i	0.108088	−	0.0785308i
$356$	−30.7366	−	22.3315i	−1.62904	−	1.18357i
$357$	11.1852	+	34.4244i	0.591982	+	1.82193i
$358$	2.46467	+	7.58548i	0.130262	+	0.400905i
$359$	−5.32861	−	3.87146i	−0.281233	−	0.204328i	0.438222	−	0.898867i	$-0.355608\pi$
$359$	−5.32861	−	3.87146i	−0.281233	−	0.204328i	−0.719455	+	0.694539i	$0.755608\pi$
$360$	−15.0368	+	10.9249i	−0.792510	+	0.575792i
$361$	−2.67707	+	8.23917i	−0.140898	+	0.433641i
$362$	13.3835			0.703421
$363$		0			0
$364$	−17.6453			−0.924864
$365$	−0.916356	+	2.82026i	−0.0479643	+	0.147619i
$366$	74.5092	−	54.1341i	3.89466	−	2.82963i
$367$	−6.60838	−	4.80127i	−0.344955	−	0.250624i	0.401795	−	0.915730i	$-0.368387\pi$
$367$	−6.60838	−	4.80127i	−0.344955	−	0.250624i	−0.746749	+	0.665105i	$0.768387\pi$
$368$	−1.03990	−	3.20048i	−0.0542084	−	0.166836i
$369$	−7.33564	−	22.5768i	−0.381878	−	1.17530i
$370$	5.12659	+	3.72469i	0.266519	+	0.193637i
$371$	6.89064	−	5.00635i	0.357744	−	0.259917i
$372$	28.7077	−	88.3532i	1.48842	−	4.58090i
$373$	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
$376$	11.5963	−	35.6899i	0.598036	−	1.84057i
$377$	−5.63512	+	4.09415i	−0.290223	+	0.210860i
$378$	40.8212	+	29.6583i	2.09962	+	1.52546i
$379$	10.0931	+	31.0634i	0.518448	+	1.59562i	0.776919	+	0.629600i	$0.216781\pi$
$379$	10.0931	+	31.0634i	0.518448	+	1.59562i	−0.258471	+	0.966019i	$0.583219\pi$
$380$	−3.49451	−	10.7550i	−0.179264	−	0.551719i
$381$	26.1941	+	19.0311i	1.34196	+	0.974994i
$382$	−17.1344	+	12.4489i	−0.876672	+	0.636940i
$383$	−0.817806	+	2.51695i	−0.0417879	+	0.128610i	−0.969774	−	0.244005i	$-0.921539\pi$
$383$	−0.817806	+	2.51695i	−0.0417879	+	0.128610i	0.927986	+	0.372615i	$0.121539\pi$
$384$	58.2034			2.97018
$385$		0			0
$386$	61.6157			3.13616
$387$	−8.67580	+	26.7014i	−0.441015	+	1.35731i
$388$	−31.3487	+	22.7762i	−1.59149	+	1.15628i
$389$	23.5030	+	17.0759i	1.19165	+	0.865784i	0.993438	−	0.114375i	$-0.0364865\pi$
$389$	23.5030	+	17.0759i	1.19165	+	0.865784i	0.198212	+	0.980159i	$0.436487\pi$
$390$	−3.08464	−	9.49354i	−0.156197	−	0.480724i
$391$	−2.90339	−	8.93572i	−0.146831	−	0.451899i
$392$	12.8253	+	9.31812i	0.647775	+	0.470636i
$393$	−34.0398	+	24.7313i	−1.71708	+	1.24753i
$394$	−12.1201	+	37.3017i	−0.610600	+	1.87923i
$395$	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	$0.575469\pi$
$398$	12.1878	−	37.5103i	0.610921	−	1.88022i
$399$	−25.2246	+	18.3267i	−1.26281	+	0.917484i
$400$	−1.08151	−	0.785763i	−0.0540755	−	0.0392881i
$401$	1.52370	+	4.68945i	0.0760897	+	0.234180i	0.981866	−	0.189576i	$-0.0607113\pi$
$401$	1.52370	+	4.68945i	0.0760897	+	0.234180i	−0.905776	+	0.423756i	$0.860711\pi$
$402$	−16.2930	−	50.1448i	−0.812623	−	2.50100i
$403$	11.0537	+	8.03102i	0.550626	+	0.400053i
$404$	−36.2308	+	26.3232i	−1.80255	+	1.30963i
$405$	−0.788584	+	2.42701i	−0.0391851	+	0.120599i
$406$	37.3356			1.85294
$407$		0			0
$408$	−38.1268			−1.88756
$409$	11.8380	−	36.4335i	0.585350	−	1.80152i	−0.0125120	−	0.999922i	$-0.503983\pi$
$409$	11.8380	−	36.4335i	0.585350	−	1.80152i	0.597862	−	0.801599i	$-0.296017\pi$
$410$	8.64998	−	6.28458i	0.427192	−	0.310373i
$411$	36.2783	+	26.3577i	1.78948	+	1.30013i
$412$	−19.9372	−	61.3604i	−0.982235	−	3.02301i
$413$	12.4556	+	38.3345i	0.612901	+	1.88632i
$414$	−24.9470	−	18.1251i	−1.22608	−	0.890799i
$415$	−6.10963	+	4.43890i	−0.299910	+	0.217897i
$416$	−1.82718	+	5.62348i	−0.0895849	+	0.275714i
$417$	−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	$0.133752\pi$
$420$	−10.5406	+	32.4406i	−0.514328	+	1.58294i
$421$	−23.7950	+	17.2881i	−1.15970	+	0.842571i	−0.989740	−	0.142880i	$-0.954364\pi$
$421$	−23.7950	+	17.2881i	−1.15970	+	0.842571i	−0.169959	+	0.985451i	$0.554364\pi$
$422$	−14.5283	−	10.5554i	−0.707226	−	0.513830i
$423$	−16.9686	−	52.2241i	−0.825044	−	2.53922i
$424$	2.77239	+	8.53253i	0.134639	+	0.414377i
$425$	−3.01957	−	2.19385i	−0.146471	−	0.106417i
$426$	13.7108	−	9.96148i	0.664291	−	0.482635i
$427$	14.3031	−	44.0205i	0.692177	−	2.13030i
$428$	−25.0917			−1.21286
$429$		0			0
$430$	−12.6453			−0.609809
$431$	−0.546405	+	1.68166i	−0.0263194	+	0.0810027i	−0.963353	−	0.268235i	$-0.913560\pi$
$431$	−0.546405	+	1.68166i	−0.0263194	+	0.0810027i	0.937034	+	0.349238i	$0.113560\pi$
$432$	−6.86639	+	4.98873i	−0.330359	+	0.240020i
$433$	−8.13168	−	5.90801i	−0.390784	−	0.283921i	0.374993	−	0.927028i	$-0.377645\pi$
$433$	−8.13168	−	5.90801i	−0.390784	−	0.283921i	−0.765777	+	0.643107i	$0.777645\pi$
$434$	−22.6314	−	69.6524i	−1.08634	−	3.34342i
$435$	4.16085	+	12.8058i	0.199497	+	0.613990i
$436$	11.7973	+	8.57127i	0.564990	+	0.410489i
$437$	6.54767	−	4.75716i	0.313218	−	0.227566i
$438$	−6.16928	+	18.9871i	−0.294779	+	0.907238i
$439$	−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
$442$	4.01685	−	12.3626i	0.191062	−	0.588029i
$443$	11.3360	−	8.23609i	0.538590	−	0.391308i	−0.284971	−	0.958536i	$-0.591984\pi$
$443$	11.3360	−	8.23609i	0.538590	−	0.391308i	0.823561	+	0.567228i	$0.191984\pi$
$444$	22.0030	+	15.9861i	1.04422	+	0.758667i
$445$	−3.33788	−	10.2729i	−0.158231	−	0.486984i
$446$	2.75063	+	8.46557i	0.130246	+	0.400856i
$447$	15.0321	+	10.9215i	0.710994	+	0.516567i
$448$	32.9596	−	23.9465i	1.55719	−	1.13137i
$449$	0.796047	−	2.44998i	0.0375678	−	0.115622i	−0.930514	−	0.366256i	$-0.880639\pi$
$449$	0.796047	−	2.44998i	0.0375678	−	0.115622i	0.968082	+	0.250635i	$0.0806393\pi$
$450$	−12.2497			−0.577456
$451$		0			0
$452$	5.15212			0.242335
$453$	−9.63493	+	29.6533i	−0.452688	+	1.39323i
$454$	37.1433	−	26.9862i	1.74322	−	1.26653i
$455$	−4.05860	−	2.94875i	−0.190270	−	0.138239i
$456$	−10.1489	−	31.2350i	−0.475265	−	1.46271i
$457$	−4.67287	−	14.3816i	−0.218588	−	0.672744i	−0.998879	−	0.0473280i	$-0.984929\pi$
$457$	−4.67287	−	14.3816i	−0.218588	−	0.672744i	0.780292	−	0.625416i	$-0.215071\pi$
$458$	9.81043	+	7.12769i	0.458411	+	0.333055i
$459$	−19.1709	+	13.9285i	−0.894823	+	0.650127i
$460$	2.73607	−	8.42077i	0.127570	−	0.392621i
$461$	−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	$0.335959\pi$
$464$	−1.94066	+	5.97273i	−0.0900927	+	0.277277i
$465$	21.3680	−	15.5247i	0.990917	−	0.719943i
$466$	−11.8763	−	8.62862i	−0.550158	−	0.399713i
$467$	−2.95543	−	9.09589i	−0.136761	−	0.420908i	0.859099	−	0.511810i	$-0.171025\pi$
$467$	−2.95543	−	9.09589i	−0.136761	−	0.420908i	−0.995860	+	0.0909024i	$0.971025\pi$
$468$	−8.40439	−	25.8661i	−0.388493	−	1.19566i
$469$	−21.4375	−	15.5753i	−0.989892	−	0.719198i
$470$	20.0089	−	14.5373i	0.922943	−	0.670557i
$471$	9.23806	−	28.4318i	0.425667	−	1.31007i
$472$	−42.4573			−1.95426
$473$		0			0
$474$	45.5582			2.09256
$475$	0.993518	−	3.05773i	0.0455857	−	0.140298i
$476$	−35.9353	+	26.1086i	−1.64709	+	1.19668i
$477$	10.6208	+	7.71643i	0.486291	+	0.353311i
$478$	3.34665	+	10.2999i	0.153072	+	0.471107i
$479$	5.31422	+	16.3555i	0.242813	+	0.747302i	0.995988	+	0.0894820i	$0.0285212\pi$
$479$	5.31422	+	16.3555i	0.242813	+	0.747302i	−0.753175	+	0.657820i	$0.771479\pi$
$480$	9.24721	+	6.71849i	0.422076	+	0.306656i
$481$	−3.23607	+	2.35114i	−0.147552	+	0.107203i
$482$	5.71843	−	17.5995i	0.260467	−	0.801636i
$483$	−24.4123			−1.11080
$484$		0			0
$485$	−11.0167			−0.500243
$486$	8.51594	−	26.2094i	0.386291	−	1.18888i
$487$	−12.5818	+	9.14118i	−0.570134	+	0.414227i	−0.835154	−	0.550016i	$-0.814621\pi$
$487$	−12.5818	+	9.14118i	−0.570134	+	0.414227i	0.265020	+	0.964243i	$0.414621\pi$
$488$	39.4436	+	28.6574i	1.78553	+	1.29726i
$489$	−9.07304	−	27.9239i	−0.410297	−	1.26276i
$490$	3.22864	+	9.93672i	0.145855	+	0.448895i
$491$	−7.32869	−	5.32460i	−0.330739	−	0.240296i	0.410005	−	0.912083i	$-0.365527\pi$
$491$	−7.32869	−	5.32460i	−0.330739	−	0.240296i	−0.740744	+	0.671787i	$0.765527\pi$
$492$	37.1251	−	26.9730i	1.67373	−	1.21604i
$493$	−5.41831	+	16.6758i	−0.244028	+	0.751042i
$494$	11.1972			0.503785
$495$		0			0
$496$	12.3189			0.553136
$497$	2.63199	−	8.10044i	0.118061	−	0.363354i
$498$	−41.1324	+	29.8845i	−1.84319	+	1.33915i
$499$	−19.8764	−	14.4411i	−0.889791	−	0.646471i	0.0460324	−	0.998940i	$-0.485342\pi$
$499$	−19.8764	−	14.4411i	−0.889791	−	0.646471i	−0.935824	+	0.352469i	$0.885342\pi$
$500$	−1.08691	−	3.34515i	−0.0486079	−	0.149600i
$501$	0.927051	+	2.85317i	0.0414176	+	0.127470i
$502$	20.2490	+	14.7118i	0.903759	+	0.656619i
$503$	−9.16793	+	6.66089i	−0.408778	+	0.296995i	−0.773107	−	0.634276i	$-0.781298\pi$
$503$	−9.16793	+	6.66089i	−0.408778	+	0.296995i	0.364329	+	0.931270i	$0.381298\pi$
$504$	−19.4333	+	59.8096i	−0.865629	+	2.66413i
$505$	−12.7324			−0.566584
$506$		0			0
$507$	−30.9596			−1.37496
$508$	−12.2781	+	37.7882i	−0.544753	+	1.67658i
$509$	21.4300	−	15.5698i	0.949868	−	0.690120i	−0.000907460	−	1.00000i	$-0.500289\pi$
$509$	21.4300	−	15.5698i	0.949868	−	0.690120i	0.950776	+	0.309880i	$0.100289\pi$
$510$	−20.3290	−	14.7699i	−0.900181	−	0.654020i
$511$	3.10049	+	9.54234i	0.137158	+	0.422128i
$512$	4.59198	+	14.1327i	0.202939	+	0.624581i
$513$	−16.5139	−	11.9980i	−0.729106	−	0.529726i
$514$	5.33804	−	3.87831i	0.235451	−	0.171065i
$515$	5.66832	−	17.4453i	0.249776	−	0.768731i
$516$	−54.2727			−2.38922
$517$		0			0
$518$	21.4406			0.942048
$519$	−10.5513	+	32.4735i	−0.463150	+	1.42543i
$520$	4.27510	−	3.10604i	0.187475	−	0.136209i
$521$	−21.5980	−	15.6919i	−0.946225	−	0.687473i	0.00368574	−	0.999993i	$-0.498827\pi$
$521$	−21.5980	−	15.6919i	−0.946225	−	0.687473i	−0.949911	+	0.312520i	$0.898827\pi$
$522$	17.7828	+	54.7300i	0.778334	+	2.39547i
$523$	1.50001	+	4.61655i	0.0655907	+	0.201867i	0.978481	−	0.206338i	$-0.0661547\pi$
$523$	1.50001	+	4.61655i	0.0655907	+	0.201867i	−0.912890	+	0.408206i	$0.866155\pi$
$524$	−41.7725	−	30.3495i	−1.82484	−	1.32582i
$525$	−7.84568	+	5.70022i	−0.342413	+	0.248778i
$526$	20.0663	−	61.7576i	0.874931	−	2.69276i
$527$	34.3944			1.49824
$528$		0			0
$529$	−16.6632			−0.724486
$530$	−1.82718	+	5.62348i	−0.0793677	+	0.244269i
$531$	−50.2616	+	36.5172i	−2.18117	+	1.58471i
$532$	−30.9548	−	22.4900i	−1.34206	−	0.975063i
$533$	2.08559	+	6.41878i	0.0903368	+	0.278028i
$534$	−22.4719	−	69.1615i	−0.972456	−	2.99291i
$535$	−5.77137	−	4.19314i	−0.249518	−	0.181285i
$536$	22.5810	−	16.4061i	0.975352	−	0.708635i
$537$	−3.00748	+	9.25606i	−0.129782	+	0.399428i
$538$	34.2376			1.47609
$539$		0			0
$540$	−22.3310			−0.960973
$541$	−6.12613	+	18.8543i	−0.263383	+	0.810609i	0.728679	+	0.684856i	$0.240135\pi$
$541$	−6.12613	+	18.8543i	−0.263383	+	0.810609i	−0.992062	+	0.125753i	$0.959865\pi$
$542$	4.10954	−	2.98576i	0.176520	−	0.128249i
$543$	13.2120	+	9.59912i	0.566983	+	0.411937i
$544$	4.59957	+	14.1560i	0.197205	+	0.606934i
$545$	1.28115	+	3.94296i	0.0548783	+	0.168898i
$546$	−27.3241	−	19.8521i	−1.16936	−	0.849592i
$547$	11.8567	−	8.61443i	0.506958	−	0.368326i	−0.304711	−	0.952445i	$-0.598560\pi$
$547$	11.8567	−	8.61443i	0.506958	−	0.368326i	0.811668	+	0.584119i	$0.198560\pi$
$548$	−17.0050	+	52.3359i	−0.726416	+	2.23568i
$549$	71.3419			3.04480
$550$		0			0
$551$	−15.1038			−0.643445
$552$	7.94622	−	24.4559i	0.338213	−	1.04091i
$553$	18.5234	−	13.4580i	0.787695	−	0.572294i
$554$	29.0787	+	21.1269i	1.23544	+	0.897597i
$555$	2.38944	+	7.35395i	0.101426	+	0.312158i
$556$	−8.30970	−	25.5746i	−0.352410	−	1.08461i
$557$	4.72257	+	3.43115i	0.200102	+	0.145382i	0.683324	−	0.730115i	$-0.260534\pi$
$557$	4.72257	+	3.43115i	0.200102	+	0.145382i	−0.483222	+	0.875498i	$0.660534\pi$
$558$	91.3236	−	66.3504i	3.86603	−	2.80884i
$559$	2.46660	−	7.59143i	0.104326	−	0.321083i
$560$	−4.52313			−0.191137
$561$		0			0
$562$	5.02295			0.211880
$563$	12.1452	−	37.3790i	0.511858	−	1.57534i	−0.277068	−	0.960850i	$-0.589363\pi$
$563$	12.1452	−	37.3790i	0.511858	−	1.57534i	0.788926	−	0.614488i	$-0.210637\pi$
$564$	85.8769	−	62.3932i	3.61607	−	2.62723i
$565$	1.18504	+	0.860984i	0.0498551	+	0.0362219i
$566$	3.14364	+	9.67514i	0.132137	+	0.406676i
$567$	2.66818	+	8.21180i	0.112053	+	0.344863i
$568$	7.25821	+	5.27340i	0.304548	+	0.221267i
$569$	−6.56118	+	4.76698i	−0.275059	+	0.199842i	−0.716759	−	0.697320i	$-0.754375\pi$
$569$	−6.56118	+	4.76698i	−0.275059	+	0.199842i	0.441700	+	0.897163i	$0.354375\pi$
$570$	6.68876	−	20.5859i	0.280161	−	0.862248i
$571$	−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
$574$	11.1791	−	34.4057i	0.466606	−	1.43607i
$575$	2.03654	−	1.47963i	0.0849297	−	0.0617050i
$576$	50.8015	+	36.9095i	2.11673	+	1.53790i
$577$	−9.84310	−	30.2939i	−0.409773	−	1.26115i	−0.916843	−	0.399248i	$-0.869271\pi$
$577$	−9.84310	−	30.2939i	−0.409773	−	1.26115i	0.507070	−	0.861905i	$-0.330729\pi$
$578$	2.22779	+	6.85642i	0.0926636	+	0.285189i
$579$	60.8264	+	44.1929i	2.52786	+	1.83660i
$580$	−13.3678	+	9.71230i	−0.555069	+	0.403281i
$581$	−7.89598	+	24.3013i	−0.327580	+	1.00819i
$582$	−74.1688			−3.07440
$583$		0			0
$584$	−10.5686			−0.437332
$585$	2.38944	−	7.35395i	0.0987913	−	0.304048i
$586$	25.6670	−	18.6482i	1.06029	−	0.770349i
$587$	35.9060	+	26.0873i	1.48200	+	1.07674i	0.976905	+	0.213673i	$0.0685428\pi$
$587$	35.9060	+	26.0873i	1.48200	+	1.07674i	0.505096	+	0.863063i	$0.331457\pi$
$588$	13.8571	+	42.6477i	0.571457	+	1.75876i
$589$	9.15536	+	28.1773i	0.377240	+	1.16103i
$590$	−22.6380	−	16.4475i	−0.931991	−	0.677131i
$591$	−38.7189	+	28.1309i	−1.59268	+	1.15715i
$592$	−1.11446	+	3.42994i	−0.0458039	+	0.140970i
$593$	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
$596$	−7.04609	+	21.6856i	−0.288619	+	0.888278i
$597$	38.9354	−	28.2882i	1.59352	−	1.15776i
$598$	7.09266	+	5.15312i	0.290040	+	0.210727i
$599$	5.13298	+	15.7977i	0.209728	+	0.645476i	0.999486	+	0.0320576i	$0.0102060\pi$
$599$	5.13298	+	15.7977i	0.209728	+	0.645476i	−0.789758	+	0.613418i	$0.789794\pi$
$600$	−3.15664	−	9.71513i	−0.128869	−	0.396619i
$601$	−10.6768	−	7.75711i	−0.435514	−	0.316419i	0.348336	−	0.937370i	$-0.386747\pi$
$601$	−10.6768	−	7.75711i	−0.435514	−	0.316419i	−0.783850	+	0.620950i	$0.786747\pi$
$602$	−34.6141	+	25.1486i	−1.41076	+	1.02498i
$603$	12.6210	−	38.8435i	0.513968	−	1.58183i
$604$	−38.2622			−1.55687
$605$		0			0
$606$	−85.7195			−3.48212
$607$	2.79378	−	8.59836i	0.113396	−	0.348997i	−0.878213	−	0.478269i	$-0.841264\pi$
$607$	2.79378	−	8.59836i	0.113396	−	0.348997i	0.991609	+	0.129273i	$0.0412642\pi$
$608$	−10.3729	+	7.53632i	−0.420675	+	0.305638i
$609$	36.8573	+	26.7784i	1.49353	+	1.08512i
$610$	9.92952	+	30.5599i	0.402035	+	1.23734i
$611$	4.82433	+	14.8478i	0.195172	+	0.600676i
$612$	−55.3882	−	40.2419i	−2.23894	−	1.62668i
$613$	−6.19964	+	4.50430i	−0.250401	+	0.181927i	−0.705905	−	0.708307i	$-0.749459\pi$
$613$	−6.19964	+	4.50430i	−0.250401	+	0.181927i	0.455503	+	0.890234i	$0.349459\pi$
$614$	−1.72670	+	5.31424i	−0.0696839	+	0.214465i
$615$	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	$0.517179\pi$
$618$	38.1614	−	117.449i	1.53508	−	4.72448i
$619$	−6.61310	+	4.80470i	−0.265803	+	0.193117i	−0.712701	−	0.701468i	$-0.752529\pi$
$619$	−6.61310	+	4.80470i	−0.265803	+	0.193117i	0.446899	+	0.894585i	$0.352529\pi$
$620$	26.2221	+	19.0515i	1.05310	+	0.765125i
$621$	−4.93874	−	15.1999i	−0.198185	−	0.609950i
$622$	16.0737	+	49.4697i	0.644496	+	1.98355i
$623$	−29.5674	−	21.4820i	−1.18459	−	0.860656i
$624$	4.59609	−	3.33926i	0.183991	−	0.133677i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	64.0880			2.56147
$627$		0			0
$628$	36.6861			1.46394
$629$	−3.11156	+	9.57639i	−0.124066	+	0.381836i
$630$	−33.5312	+	24.3619i	−1.33592	+	0.970600i
$631$	−4.50608	−	3.27386i	−0.179384	−	0.130330i	0.494470	−	0.869195i	$-0.335362\pi$
$631$	−4.50608	−	3.27386i	−0.179384	−	0.130330i	−0.673854	+	0.738865i	$0.735362\pi$
$632$	7.45272	+	22.9371i	0.296453	+	0.912390i
$633$	−6.77145	−	20.8404i	−0.269141	−	0.828331i
$634$	−29.2561	−	21.2558i	−1.16191	−	0.844177i
$635$	−9.13897	+	6.63985i	−0.362669	+	0.263494i
$636$	−7.84213	+	24.1356i	−0.310961	+	0.957039i
$637$	−6.59516			−0.261310
$638$		0			0
$639$	13.1280			0.519335
$640$	−6.27516	+	19.3130i	−0.248047	+	0.763412i
$641$	10.7523	−	7.81199i	0.424690	−	0.308555i	−0.354832	−	0.934930i	$-0.615462\pi$
$641$	10.7523	−	7.81199i	0.424690	−	0.308555i	0.779522	+	0.626375i	$0.215462\pi$
$642$	−38.8551	−	28.2299i	−1.53349	−	1.11415i
$643$	5.50473	+	16.9418i	0.217085	+	0.668120i	0.998999	+	0.0447334i	$0.0142438\pi$
$643$	5.50473	+	16.9418i	0.217085	+	0.668120i	−0.781914	+	0.623387i	$0.785756\pi$
$644$	−9.25752	−	28.4917i	−0.364797	−	1.12273i
$645$	−12.4833	−	9.06964i	−0.491529	−	0.357117i
$646$	22.8035	−	16.5677i	0.897193	−	0.651849i
$647$	−7.99826	+	24.6161i	−0.314444	+	0.967759i	0.661539	+	0.749911i	$0.269904\pi$
$647$	−7.99826	+	24.6161i	−0.314444	+	0.967759i	−0.975983	+	0.217848i	$0.930096\pi$
$648$	−9.09498			−0.357285
$649$		0			0
$650$	3.48270			0.136603
$651$	27.6156	−	84.9921i	1.08234	−	3.33110i
$652$	29.1495	−	21.1784i	1.14158	−	0.829409i
$653$	−10.7887	−	7.83848i	−0.422196	−	0.306744i	0.356325	−	0.934362i	$-0.384030\pi$
$653$	−10.7887	−	7.83848i	−0.422196	−	0.306744i	−0.778521	+	0.627619i	$0.784030\pi$
$654$	8.62518	+	26.5456i	0.337271	+	1.03801i
$655$	−4.53633	−	13.9614i	−0.177249	−	0.545517i
$656$	4.92294	+	3.57672i	0.192208	+	0.139648i
$657$	−12.5113	+	9.08998i	−0.488112	+	0.354634i
$658$	25.8592	−	79.5864i	1.00810	−	3.10260i
$659$	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	$0.649512\pi$
$662$	−18.8088	+	57.8876i	−0.731026	+	2.24987i
$663$	12.8323	−	9.32320i	0.498364	−	0.362083i
$664$	−21.7746	−	15.8202i	−0.845019	−	0.613942i
$665$	−3.36157	−	10.3459i	−0.130356	−	0.401195i
$666$	10.2121	+	31.4297i	0.395711	+	1.21787i
$667$	−9.56724	−	6.95101i	−0.370445	−	0.269144i
$668$	−2.97840	+	2.16393i	−0.115238	+	0.0837250i
$669$	−3.35641	+	10.3300i	−0.129766	+	0.399380i
$670$	18.3956			0.710683
$671$		0			0
$672$	38.6741			1.49188
$673$	−3.50557	+	10.7890i	−0.135130	+	0.415887i	−0.995610	−	0.0935968i	$-0.970164\pi$
$673$	−3.50557	+	10.7890i	−0.135130	+	0.415887i	0.860480	+	0.509484i	$0.170164\pi$
$674$	−26.5701	+	19.3043i	−1.02344	+	0.743575i
$675$	−5.13636	−	3.73179i	−0.197699	−	0.143637i
$676$	−11.7403	−	36.1331i	−0.451552	−	1.38973i
$677$	6.61160	+	20.3484i	0.254104	+	0.782053i	0.994005	+	0.109336i	$0.0348726\pi$
$677$	6.61160	+	20.3484i	0.254104	+	0.782053i	−0.739901	+	0.672716i	$0.765127\pi$
$678$	7.97818	+	5.79648i	0.306400	+	0.222613i
$679$	−30.1561	+	21.9097i	−1.15729	+	0.840818i
$680$	4.11061	−	12.6512i	0.157635	−	0.485150i
$681$	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	$0.531205\pi$
$684$	18.2242	−	56.0882i	0.696819	−	2.14459i
$685$	−12.6573	+	9.19606i	−0.483610	+	0.351364i
$686$	−16.4079	−	11.9210i	−0.626457	−	0.455148i
$687$	4.57252	+	14.0728i	0.174452	+	0.536910i
$688$	−2.22392	−	6.84454i	−0.0847863	−	0.260946i
$689$	−3.01957	−	2.19385i	−0.115037	−	0.0835789i
$690$	13.7108	−	9.96148i	0.521961	−	0.379227i
$691$	−7.08010	+	21.7903i	−0.269340	+	0.828942i	0.721322	+	0.692600i	$0.243535\pi$
$691$	−7.08010	+	21.7903i	−0.269340	+	0.828942i	−0.990662	+	0.136343i	$0.956465\pi$
$692$	−41.9012			−1.59285
$693$		0			0
$694$	−72.9254			−2.76821
$695$	2.36252	−	7.27109i	0.0896155	−	0.275808i
$696$	−38.8234	+	28.2068i	−1.47160	+	1.06918i
$697$	13.7448	+	9.98620i	0.520622	+	0.378254i
$698$	2.65891	+	8.18329i	0.100641	+	0.309742i
$699$	−5.53538	−	17.0362i	−0.209367	−	0.644367i
$700$	−9.62795	−	6.99512i	−0.363902	−	0.264391i
$701$	−30.6772	+	22.2883i	−1.15866	+	0.841818i	−0.989608	−	0.143789i	$-0.954071\pi$
$701$	−30.6772	+	22.2883i	−1.15866	+	0.841818i	−0.169054	+	0.985607i	$0.554071\pi$
$702$	6.83276	−	21.0291i	0.257886	−	0.793691i
$703$	−8.67364			−0.327133
$704$		0			0
$705$	30.1793			1.13662
$706$	−17.8376	+	54.8986i	−0.671328	+	2.06613i
$707$	−34.8525	+	25.3218i	−1.31076	+	0.952326i
$708$	−97.1607	−	70.5914i	−3.65152	−	2.65299i
$709$	−1.63064	−	5.01860i	−0.0612400	−	0.188477i	0.915756	−	0.401735i	$-0.131593\pi$
$709$	−1.63064	−	5.01860i	−0.0612400	−	0.188477i	−0.976996	+	0.213258i	$0.931593\pi$
$710$	1.82718	+	5.62348i	0.0685729	+	0.211046i
$711$	28.5507	+	20.7433i	1.07073	+	0.777933i
$712$	31.1446	−	22.6279i	1.16719	−	0.848015i
$713$	−7.16833	+	22.0618i	−0.268456	+	0.826222i
$714$	−85.0206			−3.18181
$715$		0			0
$716$	−11.9433			−0.446341
$717$	−4.08369	+	12.5683i	−0.152508	+	0.469372i
$718$	12.5163	−	9.09365i	0.467105	−	0.339372i
$719$	−25.0081	−	18.1694i	−0.932644	−	0.677605i	0.0139948	−	0.999902i	$-0.495545\pi$
$719$	−25.0081	−	18.1694i	−0.932644	−	0.677605i	−0.946639	+	0.322297i	$0.895545\pi$
$720$	−2.15435	−	6.63042i	−0.0802881	−	0.247101i
$721$	−19.1788	−	59.0262i	−0.714255	−	2.19825i
$722$	−16.4626	−	11.9608i	−0.612675	−	0.445134i
$723$	18.2682	−	13.2726i	0.679400	−	0.493613i
$724$	−6.19296	+	19.0600i	−0.230160	+	0.708359i
$725$	−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	$0.451147\pi$
$728$	5.52506	−	17.0044i	0.204772	−	0.630225i
$729$	33.3987	−	24.2656i	1.23699	−	0.898726i
$730$	−5.63512	−	4.09415i	−0.208565	−	0.151531i
$731$	−6.20919	−	19.1099i	−0.229655	−	0.706806i
$732$	42.6168	+	131.161i	1.57516	+	4.84785i
$733$	35.0983	+	25.5004i	1.29639	+	0.941880i	0.999913	−	0.0131614i	$-0.00418953\pi$
$733$	35.0983	+	25.5004i	1.29639	+	0.941880i	0.296473	+	0.955041i	$0.404190\pi$
$734$	15.5224	−	11.2777i	0.572942	−	0.416267i
$735$	−3.93969	+	12.1251i	−0.145318	+	0.447242i
$736$	−10.0388			−0.370036
$737$		0			0
$738$	55.7596			2.05254
$739$	−0.0930184	+	0.286281i	−0.00342174	+	0.0105310i	−0.952753	−	0.303747i	$-0.901762\pi$
$739$	−0.0930184	+	0.286281i	−0.00342174	+	0.0105310i	0.949331	+	0.314278i	$0.101762\pi$
$740$	−7.67672	+	5.57746i	−0.282202	+	0.205032i
$741$	11.0537	+	8.03102i	0.406069	+	0.295027i
$742$	6.18227	+	19.0271i	0.226958	+	0.698506i
$743$	−9.73528	−	29.9621i	−0.357153	−	1.09920i	−0.954751	−	0.297407i	$-0.903878\pi$
$743$	−9.73528	−	29.9621i	−0.357153	−	1.09920i	0.597598	−	0.801796i	$-0.296122\pi$
$744$	76.1552	+	55.3300i	2.79199	+	2.02850i
$745$	−5.24461	+	3.81043i	−0.192148	+	0.139603i
$746$	−19.6276	+	60.4074i	−0.718616	+	2.21167i
$747$	−39.3839			−1.44098
$748$		0			0
$749$	−24.1372			−0.881955
$750$	2.08042	−	6.40289i	0.0759664	−	0.233800i
$751$	−26.9326	+	19.5677i	−0.982785	+	0.714035i	−0.958329	−	0.285665i	$-0.907785\pi$
$751$	−26.9326	+	19.5677i	−0.982785	+	0.714035i	−0.0244560	+	0.999701i	$0.507785\pi$
$752$	11.3876	+	8.27359i	0.415264	+	0.301707i
$753$	9.43783	+	29.0466i	0.343934	+	1.05852i
$754$	−5.05582	−	15.5602i	−0.184122	−	0.566669i
$755$	−8.80071	−	6.39409i	−0.320291	−	0.232705i
$756$	−61.1269	+	44.4113i	−2.22316	+	1.61522i
$757$	4.79188	−	14.7479i	0.174164	−	0.536021i	−0.825430	−	0.564504i	$-0.809068\pi$
$757$	4.79188	−	14.7479i	0.174164	−	0.536021i	0.999594	+	0.0284827i	$0.00906756\pi$
$758$	−76.7195			−2.78658
$759$		0			0
$760$	11.4585			0.415645
$761$	16.1908	−	49.8300i	0.586914	−	1.80634i	−0.00452850	−	0.999990i	$-0.501441\pi$
$761$	16.1908	−	49.8300i	0.586914	−	1.80634i	0.591443	−	0.806347i	$-0.298559\pi$
$762$	−61.5271	+	44.7021i	−2.22889	+	1.61939i
$763$	11.3486	+	8.24521i	0.410845	+	0.298496i
$764$	−9.80032	−	30.1623i	−0.354563	−	1.09123i
$765$	−6.01495	−	18.5121i	−0.217471	−	0.669307i
$766$	−5.02908	−	3.65384i	−0.181708	−	0.132019i
$767$	14.2898	−	10.3822i	0.515975	−	0.374878i
$768$	−20.9176	+	64.3777i	−0.754799	+	2.32303i
$769$	−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
$772$	−28.5115	+	87.7494i	−1.02615	+	3.15817i
$773$	28.5726	−	20.7592i	1.02769	−	0.746658i	0.0598420	−	0.998208i	$-0.480940\pi$
$773$	28.5726	−	20.7592i	1.02769	−	0.746658i	0.967844	+	0.251550i	$0.0809403\pi$
$774$	−53.3517	−	38.7623i	−1.91769	−	1.39328i
$775$	2.84762	+	8.76407i	0.102290	+	0.314815i
$776$	−12.1331	−	37.3417i	−0.435551	−	1.34049i
$777$	21.1660	+	15.3780i	0.759325	+	0.551682i
$778$	−55.2061	+	40.1096i	−1.97923	+	1.43800i
$779$	−4.52241	+	13.9185i	−0.162032	+	0.498683i
$780$	14.9475			0.535206
$781$		0			0
$782$	22.0692			0.789194
$783$	−9.21667	+	28.3660i	−0.329377	+	1.01372i
$784$	−4.81065	+	3.49514i	−0.171809	+	0.124827i
$785$	8.43820	+	6.13071i	0.301172	+	0.218814i
$786$	−30.5404	−	93.9937i	−1.08934	−	3.35264i
$787$	11.3384	+	34.8961i	0.404172	+	1.24391i	0.921585	+	0.388177i	$0.126895\pi$
$787$	11.3384	+	34.8961i	0.404172	+	1.24391i	−0.517413	+	0.855736i	$0.673105\pi$
$788$	−47.5145	−	34.5213i	−1.69264	−	1.22977i
$789$	64.1040	−	46.5742i	2.28216	−	1.65809i
$790$	−4.91182	+	15.1170i	−0.174755	+	0.537840i
$791$	4.95613			0.176220
$792$		0			0
$793$	−20.2831			−0.720274
$794$	6.79377	−	20.9091i	0.241102	−	0.742036i
$795$	−5.83713	+	4.24092i	−0.207022	+	0.150410i
$796$	47.7802	+	34.7144i	1.69352	+	1.23042i
$797$	−0.881973	−	2.71443i	−0.0312411	−	0.0961501i	0.934220	−	0.356697i	$-0.116097\pi$
$797$	−0.881973	−	2.71443i	−0.0312411	−	0.0961501i	−0.965461	+	0.260547i	$0.916097\pi$
$798$	−22.6314	−	69.6524i	−0.801144	−	2.46567i
$799$	31.7942	+	23.0999i	1.12480	+	0.817214i
$800$	−3.22630	+	2.34404i	−0.114067	+	0.0828745i
$801$	17.4074	−	53.5744i	0.615059	−	1.89296i
$802$	−11.5819			−0.408971
$803$		0			0
$804$	78.9525			2.78444
$805$	2.63199	−	8.10044i	0.0927655	−	0.285503i
$806$	−25.9641	+	18.8640i	−0.914546	+	0.664456i
$807$	33.7990	+	24.5564i	1.18978	+	0.864427i
$808$	−14.0226	−	43.1571i	−0.493313	−	1.51826i
$809$	8.06329	+	24.8163i	0.283490	+	0.872493i	0.986847	+	0.161656i	$0.0516836\pi$
$809$	8.06329	+	24.8163i	0.283490	+	0.872493i	−0.703357	+	0.710837i	$0.748316\pi$
$810$	−4.84939	−	3.52329i	−0.170390	−	0.123796i
$811$	15.8934	−	11.5472i	0.558091	−	0.405477i	−0.272668	−	0.962108i	$-0.587906\pi$
$811$	15.8934	−	11.5472i	0.558091	−	0.405477i	0.830760	+	0.556631i	$0.187906\pi$
$812$	−17.2764	+	53.1712i	−0.606281	+	1.86594i
$813$	6.19839			0.217387
$814$		0			0
$815$	10.2439			0.358827
$816$	4.41926	−	13.6011i	0.154705	−	0.476133i
$817$	14.0028	−	10.1737i	0.489897	−	0.355931i
$818$	72.7974	+	52.8904i	2.54530	+	1.84927i
$819$	−8.08468	−	24.8821i	−0.282502	−	0.869451i
$820$	4.94750	+	15.2269i	0.172774	+	0.531745i
$821$	41.9974	+	30.5129i	1.46572	+	1.06491i	0.981826	+	0.189782i	$0.0607781\pi$
$821$	41.9974	+	30.5129i	1.46572	+	1.06491i	0.483894	+	0.875126i	$0.339222\pi$
$822$	−85.2139	+	61.9115i	−2.97218	+	2.15941i
$823$	4.92108	−	15.1455i	0.171538	−	0.527940i	−0.827920	−	0.560846i	$-0.810476\pi$
$823$	4.92108	−	15.1455i	0.171538	−	0.527940i	0.999458	+	0.0329056i	$0.0104761\pi$
$824$	65.3744			2.27743
$825$		0			0
$826$	−94.6775			−3.29425
$827$	3.01960	−	9.29338i	0.105002	−	0.323162i	−0.884729	−	0.466106i	$-0.845657\pi$
$827$	3.01960	−	9.29338i	0.105002	−	0.323162i	0.989731	+	0.142943i	$0.0456567\pi$
$828$	37.3564	−	27.1410i	1.29823	−	0.943216i
$829$	−0.823501	−	0.598308i	−0.0286014	−	0.0207801i	0.573393	−	0.819281i	$-0.305627\pi$
$829$	−0.823501	−	0.598308i	−0.0286014	−	0.0207801i	−0.601994	+	0.798501i	$0.705627\pi$
$830$	−5.48154	−	16.8705i	−0.190267	−	0.585582i
$831$	13.5532	+	41.7126i	0.470156	+	1.44699i
$832$	−14.4433	−	10.4937i	−0.500732	−	0.363803i
$833$	−13.4313	+	9.75843i	−0.465368	+	0.338109i
$834$	15.9054	−	48.9519i	0.550760	−	1.69506i
$835$	−1.04668			−0.0362219
$836$		0			0
$837$	58.5056			2.02225
$838$	−27.1305	+	83.4992i	−0.937208	+	2.88443i
$839$	−11.1563	+	8.10553i	−0.385159	+	0.279834i	−0.763469	−	0.645845i	$-0.776505\pi$
$839$	−11.1563	+	8.10553i	−0.385159	+	0.279834i	0.378310	+	0.925679i	$0.376505\pi$
$840$	−27.9619	−	20.3155i	−0.964777	−	0.700951i
$841$	−2.14173	−	6.59157i	−0.0738528	−	0.227295i
$842$	−21.3489	−	65.7050i	−0.735730	−	2.26434i
$843$	4.95860	+	3.60264i	0.170783	+	0.124081i
$844$	21.7551	−	15.8060i	0.748841	−	0.544065i
$845$	3.33788	−	10.2729i	0.114827	−	0.353400i
$846$	128.982			4.43448
$847$		0			0
$848$	−3.36518			−0.115561
$849$	−3.83598	+	11.8059i	−0.131650	+	0.405178i
$850$	7.09266	−	5.15312i	0.243276	−	0.176750i
$851$	−5.49416	−	3.99174i	−0.188337	−	0.136835i
$852$	7.84213	+	24.1356i	0.268667	+	0.826872i
$853$	−8.44431	−	25.9889i	−0.289128	−	0.889843i	−0.985131	−	0.171805i	$-0.945040\pi$
$853$	−8.44431	−	25.9889i	−0.289128	−	0.889843i	0.696003	−	0.718039i	$-0.254960\pi$
$854$	87.9569	+	63.9044i	3.00982	+	2.18677i
$855$	13.5648	−	9.85540i	0.463906	−	0.337048i
$856$	7.85669	−	24.1804i	0.268536	−	0.826469i
$857$	−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	$0.338274\pi$
$860$	5.85136	−	18.0086i	0.199530	−	0.614090i
$861$	35.7128	−	25.9469i	1.21709	−	0.884268i
$862$	−3.36011	−	2.44126i	−0.114446	−	0.0831497i
$863$	16.1490	+	49.7016i	0.549720	+	1.69186i	0.709496	+	0.704710i	$0.248923\pi$
$863$	16.1490	+	49.7016i	0.549720	+	1.69186i	−0.159776	+	0.987153i	$0.551077\pi$
$864$	7.82398	+	24.0797i	0.266177	+	0.819209i
$865$	−9.63772	−	7.00222i	−0.327692	−	0.238082i
$866$	19.1005	−	13.8773i	0.649060	−	0.471570i
$867$	−2.71842	+	8.36643i	−0.0923223	+	0.284139i
$868$	109.667			3.72234
$869$		0			0
$870$	−31.6274			−1.07227
$871$	−3.58826	+	11.0435i	−0.121584	+	0.374196i
$872$	−11.9539	+	8.68503i	−0.404811	+	0.294112i
$873$	−46.4806	−	33.7701i	−1.57313	−	1.14294i
$874$	5.87455	+	18.0800i	0.198710	+	0.611566i
$875$	−1.04556	−	3.21790i	−0.0353464	−	0.108785i
$876$	−24.1855	−	17.5718i	−0.817154	−	0.593697i
$877$	−16.9954	+	12.3479i	−0.573893	+	0.416958i	−0.836517	−	0.547940i	$-0.815412\pi$
$877$	−16.9954	+	12.3479i	−0.573893	+	0.416958i	0.262624	+	0.964898i	$0.415412\pi$
$878$	28.4512	−	87.5638i	0.960182	−	2.95514i
$879$	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	$0.217175\pi$
$882$	−16.8376	+	51.8209i	−0.566953	+	1.74490i
$883$	−0.503472	+	0.365794i	−0.0169432	+	0.0123100i	−0.596225	−	0.802818i	$-0.703333\pi$
$883$	−0.503472	+	0.365794i	−0.0169432	+	0.0123100i	0.579281	+	0.815128i	$0.303333\pi$
$884$	15.7473	+	11.4411i	0.529641	+	0.384806i
$885$	−10.5513	−	32.4735i	−0.354678	−	1.09159i
$886$	10.1706	+	31.3020i	0.341689	+	1.05161i
$887$	9.22898	+	6.70525i	0.309879	+	0.225140i	0.731845	−	0.681472i	$-0.238660\pi$
$887$	9.22898	+	6.70525i	0.309879	+	0.225140i	−0.421966	+	0.906612i	$0.638660\pi$
$888$	−22.2950	+	16.1983i	−0.748172	+	0.543579i
$889$	−11.8110	+	36.3507i	−0.396130	+	1.21916i
$890$	25.3718			0.850466
$891$		0			0
$892$	−13.3290			−0.446287
$893$	−10.4611	+	32.1960i	−0.350068	+	1.07740i
$894$	−35.3088	+	25.6533i	−1.18090	+	0.857976i
$895$	−2.74708	−	1.99587i	−0.0918247	−	0.0667146i
$896$	21.2320	+	65.3454i	0.709312	+	2.18304i
$897$	3.30580	+	10.1742i	0.110377	+	0.339707i
$898$	4.89528	+	3.55663i	0.163358	+	0.118686i
$899$	35.0228	−	25.4455i	1.16808	−	0.848657i
$900$	5.66832	−	17.4453i	0.188944	−	0.581510i
$901$	−9.39558			−0.313012
$902$		0			0
$903$	−52.2081			−1.73738
$904$	−1.61322	+	4.96499i	−0.0536550	+	0.165133i
$905$	−4.60961	+	3.34908i	−0.153229	+	0.111327i
$906$	−59.2499	−	43.0475i	−1.96844	−	1.43016i
$907$	12.0262	+	37.0128i	0.399323	+	1.22899i	0.925544	+	0.378641i	$0.123608\pi$
$907$	12.0262	+	37.0128i	0.399323	+	1.22899i	−0.526221	+	0.850348i	$0.676392\pi$
$908$	21.2448	+	65.3847i	0.705032	+	2.16987i
$909$	−53.7192	−	39.0293i	−1.78175	−	1.29452i
$910$	9.53322	−	6.92629i	0.316023	−	0.229604i
$911$	11.7715	−	36.2289i	0.390007	−	1.20032i	−0.542775	−	0.839878i	$-0.682626\pi$
$911$	11.7715	−	36.2289i	0.390007	−	1.20032i	0.932782	−	0.360440i	$-0.117374\pi$
$912$	12.3189			0.407920
$913$		0			0
$914$	35.5193			1.17488
$915$	−12.1163	+	37.2902i	−0.400553	+	1.23278i
$916$	−14.6904	+	10.6732i	−0.485385	+	0.352653i
$917$	−40.1834	−	29.1950i	−1.32697	−	0.964102i
$918$	−17.2001	−	52.9366i	−0.567689	−	1.74717i
$919$	5.95558	+	18.3294i	0.196456	+	0.604630i	0.999957	+	0.00932595i	$0.00296859\pi$
$919$	5.95558	+	18.3294i	0.196456	+	0.604630i	−0.803500	+	0.595305i	$0.797031\pi$
$920$	7.25821	+	5.27340i	0.239296	+	0.173859i
$921$	−5.51614	+	4.00771i	−0.181763	+	0.132058i
$922$	7.13960	−	21.9734i	0.235130	−	0.723657i
$923$	−3.73240			−0.122853
$924$		0			0
$925$	−2.69779			−0.0887027
$926$	−15.3947	+	47.3800i	−0.505901	+	1.55700i
$927$	77.3912	−	56.2280i	2.54186	−	1.84677i
$928$	15.1565	+	11.0118i	0.497536	+	0.361481i
$929$	9.63300	+	29.6473i	0.316048	+	0.972697i	0.975321	+	0.220793i	$0.0708645\pi$
$929$	9.63300	+	29.6473i	0.316048	+	0.972697i	−0.659272	+	0.751904i	$0.729136\pi$
$930$	19.1713	+	59.0032i	0.628652	+	1.93479i
$931$	−11.5698	−	8.40593i	−0.379184	−	0.275493i
$932$	17.7839	−	12.9208i	0.582531	−	0.423233i
$933$	−19.6136	+	60.3645i	−0.642121	+	1.97625i
$934$	22.4648			0.735070
$935$		0			0
$936$	27.5582			0.900767
$937$	7.99453	−	24.6046i	0.261170	−	0.803798i	−0.731381	−	0.681969i	$-0.761124\pi$
$937$	7.99453	−	24.6046i	0.261170	−	0.803798i	0.992551	−	0.121829i	$-0.0388760\pi$
$938$	50.3544	−	36.5846i	1.64413	−	1.19453i
$939$	63.2669	+	45.9661i	2.06464	+	1.50005i
$940$	11.4445	+	35.2224i	0.373277	+	1.14883i
$941$	9.10475	+	28.0215i	0.296806	+	0.913476i	0.982609	+	0.185688i	$0.0594515\pi$
$941$	9.10475	+	28.0215i	0.296806	+	0.913476i	−0.685802	+	0.727788i	$0.740549\pi$
$942$	56.8093	+	41.2744i	1.85095	+	1.34479i
$943$	−9.27016	+	6.73516i	−0.301878	+	0.219327i
$944$	4.92121	−	15.1459i	0.160172	−	0.492958i
$945$	−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	$0.575108\pi$
$948$	−21.0812	+	64.8812i	−0.684685	+	2.10724i
$949$	3.55707	−	2.58436i	0.115467	−	0.0838919i
$950$	6.10963	+	4.43890i	0.198222	+	0.144017i
$951$	−13.6359	−	41.9671i	−0.442175	−	1.36088i
$952$	−13.9083	−	42.8052i	−0.450769	−	1.38732i
$953$	25.8231	+	18.7616i	0.836493	+	0.607748i	0.921389	−	0.388642i	$-0.127056\pi$
$953$	25.8231	+	18.7616i	0.836493	+	0.607748i	−0.0848960	+	0.996390i	$0.527056\pi$
$954$	−24.9470	+	18.1251i	−0.807690	+	0.586821i
$955$	2.78632	−	8.57540i	0.0901630	−	0.277493i
$956$	−16.2171			−0.524499
$957$		0			0
$958$	−40.3944			−1.30508
$959$	−16.3581	+	50.3450i	−0.528230	+	1.62572i
$960$	−27.9204	+	20.2853i	−0.901126	+	0.654706i
$961$	−43.6205	−	31.6922i	−1.40711	−	1.02233i
$962$	−2.90339	−	8.93572i	−0.0936091	−	0.288099i
$963$	−11.4965	−	35.3826i	−0.370469	−	1.14019i
$964$	22.4181	+	16.2877i	0.722038	+	0.524591i
$965$	−21.2220	+	15.4187i	−0.683159	+	0.496344i
$966$	17.7196	−	54.5354i	0.570119	−	1.75465i
$967$	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
$970$	7.99646	−	24.6106i	0.256751	−	0.790197i
$971$	5.38966	−	3.91582i	0.172962	−	0.125664i	−0.497936	−	0.867214i	$-0.665909\pi$
$971$	5.38966	−	3.91582i	0.172962	−	0.125664i	0.670898	+	0.741549i	$0.265909\pi$
$972$	33.3852	+	24.2558i	1.07083	+	0.778005i
$973$	−7.99359	−	24.6018i	−0.256263	−	0.788696i
$974$	−11.2883	−	34.7419i	−0.361701	−	1.11320i
$975$	3.43808	+	2.49791i	0.110107	+	0.0799972i
$976$	−14.7949	+	10.7491i	−0.473574	+	0.344072i
$977$	−7.47697	+	23.0118i	−0.239210	+	0.736211i	0.757326	+	0.653038i	$0.226506\pi$
$977$	−7.47697	+	23.0118i	−0.239210	+	0.736211i	−0.996535	+	0.0831737i	$0.973494\pi$
$978$	68.9658			2.20528
$979$		0			0
$980$	−15.6453			−0.499770
$981$	−6.68130	+	20.5629i	−0.213317	+	0.656523i
$982$	17.2143	−	12.5069i	0.549331	−	0.399112i
$983$	22.4677	+	16.3238i	0.716609	+	0.520647i	0.885299	−	0.465022i	$-0.153954\pi$
$983$	22.4677	+	16.3238i	0.716609	+	0.520647i	−0.168690	+	0.985669i	$0.553954\pi$
$984$	14.3687	+	44.2224i	0.458059	+	1.40976i
$985$	−5.15990	−	15.8805i	−0.164408	−	0.505996i
$986$	−33.3198	−	24.2082i	−1.06112	−	0.770948i
$987$	82.6101	−	60.0197i	2.62951	−	1.91045i
$988$	−5.18129	+	15.9464i	−0.164839	+	0.507322i
$989$	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	$0.243476\pi$
$992$	11.3561	−	34.9505i	0.360556	−	1.10968i
$993$	−60.0869	+	43.6557i	−1.90680	+	1.38537i
$994$	16.1854	+	11.7594i	0.513369	+	0.372985i
$995$	5.18875	+	15.9693i	0.164494	+	0.506262i
$996$	−23.5264	−	72.4068i	−0.745462	−	2.29430i
$997$	−41.0569	−	29.8296i	−1.30028	−	0.944712i	−0.300326	−	0.953837i	$-0.597096\pi$
$997$	−41.0569	−	29.8296i	−1.30028	−	0.944712i	−0.999958	+	0.00912447i	$0.997096\pi$
$998$	46.6876	−	33.9205i	1.47787	−	1.07374i
$999$	−5.29283	+	16.2897i	−0.167458	+	0.515382i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.p.251.1		12
11.2	odd	10		605.2.g.o.366.1		12
11.3	even	5	inner	605.2.g.p.81.3		12
11.4	even	5		605.2.a.g.1.1	✓	3
11.5	even	5	inner	605.2.g.p.511.1		12
11.6	odd	10		605.2.g.o.511.3		12
11.7	odd	10		605.2.a.h.1.3	yes	3
11.8	odd	10		605.2.g.o.81.1		12
11.9	even	5	inner	605.2.g.p.366.3		12
11.10	odd	2		605.2.g.o.251.3		12
33.26	odd	10		5445.2.a.bd.1.3		3
33.29	even	10		5445.2.a.bb.1.1		3
44.7	even	10		9680.2.a.cb.1.1		3
44.15	odd	10		9680.2.a.bz.1.1		3
55.4	even	10		3025.2.a.u.1.3		3
55.29	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	11.4	even	5
605.2.a.h.1.3	yes	3	11.7	odd	10
605.2.g.o.81.1		12	11.8	odd	10
605.2.g.o.251.3		12	11.10	odd	2
605.2.g.o.366.1		12	11.2	odd	10
605.2.g.o.511.3		12	11.6	odd	10
605.2.g.p.81.3		12	11.3	even	5	inner
605.2.g.p.251.1		12	1.1	even	1	trivial
605.2.g.p.366.3		12	11.9	even	5	inner
605.2.g.p.511.1		12	11.5	even	5	inner
3025.2.a.p.1.1		3	55.29	odd	10
3025.2.a.u.1.3		3	55.4	even	10
5445.2.a.bb.1.1		3	33.29	even	10
5445.2.a.bd.1.3		3	33.26	odd	10
9680.2.a.bz.1.1		3	44.15	odd	10
9680.2.a.cb.1.1		3	44.7	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)

\(f(q)\)	\(=\)	\(q+(-0.725848 + 2.23393i) q^{2} +(-2.31880 + 1.68471i) q^{3} +(-2.84556 - 2.06742i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-2.08042 - 6.40289i) q^{6} +(-2.73731 - 1.98877i) q^{7} +(2.88333 - 2.09486i) q^{8} +(1.61155 - 4.95985i) q^{9} +O(q^{10})\)	\(q+(-0.725848 + 2.23393i) q^{2} +(-2.31880 + 1.68471i) q^{3} +(-2.84556 - 2.06742i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-2.08042 - 6.40289i) q^{6} +(-2.73731 - 1.98877i) q^{7} +(2.88333 - 2.09486i) q^{8} +(1.61155 - 4.95985i) q^{9} +2.34889 q^{10} +10.0813 q^{12} +(-0.458178 + 1.41013i) q^{13} +(6.42965 - 4.67142i) q^{14} +(2.31880 + 1.68471i) q^{15} +(0.413100 + 1.27139i) q^{16} +(1.15337 + 3.54972i) q^{17} +(9.91022 + 7.20019i) q^{18} +(-2.60106 + 1.88978i) q^{19} +(-1.08691 + 3.34515i) q^{20} +9.69779 q^{21} -2.51730 q^{23} +(-3.15664 + 9.71513i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-2.81756 - 2.04708i) q^{26} +(1.96192 + 6.03816i) q^{27} +(3.67755 + 11.3183i) q^{28} +(3.80059 + 2.76129i) q^{29} +(-5.44662 + 3.95720i) q^{30} +(2.84762 - 8.76407i) q^{31} +3.98793 q^{32} -8.76700 q^{34} +(-1.04556 + 3.21790i) q^{35} +(-14.8399 + 10.7818i) q^{36} +(2.18256 + 1.58572i) q^{37} +(-2.33367 - 7.18230i) q^{38} +(-1.31323 - 4.04171i) q^{39} +(-2.88333 - 2.09486i) q^{40} +(3.68257 - 2.67555i) q^{41} +(-7.03912 + 21.6642i) q^{42} -5.38350 q^{43} -5.21509 q^{45} +(1.82718 - 5.62348i) q^{46} +(8.51845 - 6.18901i) q^{47} +(-3.09982 - 2.25215i) q^{48} +(1.37453 + 4.23038i) q^{49} +(-0.725848 - 2.23393i) q^{50} +(-8.65469 - 6.28800i) q^{51} +(4.21910 - 3.06535i) q^{52} +(-0.777890 + 2.39410i) q^{53} -14.9129 q^{54} -12.0588 q^{56} +(2.84762 - 8.76407i) q^{57} +(-8.92719 + 6.48598i) q^{58} +(-9.63772 - 7.00222i) q^{59} +(-3.11529 - 9.58788i) q^{60} +(4.22732 + 13.0103i) q^{61} +(17.5114 + 12.7228i) q^{62} +(-14.2753 + 10.3716i) q^{63} +(-3.72083 + 11.4515i) q^{64} +1.48270 q^{65} +7.83159 q^{67} +(4.05677 - 12.4854i) q^{68} +(5.83713 - 4.24092i) q^{69} +(-6.42965 - 4.67142i) q^{70} +(0.777890 + 2.39410i) q^{71} +(-5.74355 - 17.6768i) q^{72} +(-2.39905 - 1.74301i) q^{73} +(-5.12659 + 3.72469i) q^{74} +(0.885704 - 2.72592i) q^{75} +11.3085 q^{76} +9.98210 q^{78} +(-2.09112 + 6.43580i) q^{79} +(1.08151 - 0.785763i) q^{80} +(-2.06454 - 1.49998i) q^{81} +(3.30400 + 10.1687i) q^{82} +(-2.33367 - 7.18230i) q^{83} +(-27.5956 - 20.0494i) q^{84} +(3.01957 - 2.19385i) q^{85} +(3.90761 - 12.0264i) q^{86} -13.4648 q^{87} +10.8016 q^{89} +(3.78537 - 11.6502i) q^{90} +(4.05860 - 2.94875i) q^{91} +(7.16314 + 5.20432i) q^{92} +(8.16184 + 25.1196i) q^{93} +(7.64273 + 23.5219i) q^{94} +(2.60106 + 1.88978i) q^{95} +(-9.24721 + 6.71849i) q^{96} +(3.40435 - 10.4775i) 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

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