LMFDB - Embedded newform 418.2.f.f.267.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(115,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("418.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.f (of order $5$, degree $4$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 24 x^{14} - 62 x^{13} + 148 x^{12} - 232 x^{11} + 432 x^{10} - 356 x^{9} + 424 x^{8} + \cdots + 16 $ x^16 - 6x^15 + 24x^14 - 62x^13 + 148x^12 - 232x^11 + 432x^10 - 356x^9 + 424x^8 - 320x^7 + 712x^6 - 936x^5 + 968x^4 - 336x^3 + 208x^2 - 80*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			267.2
Root			$0.253418 - 0.184119i$ of defining polynomial
Character	$\chi$	$=$	418.267
Dual form			418.2.f.f.191.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.670482 - 2.06353i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.44869 - 1.05254i) q^{5} +(1.75534 + 1.27533i) q^{6} +(1.45655 - 4.48281i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.38156 + 1.00376i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.670482 - 2.06353i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.44869 - 1.05254i) q^{5} +(1.75534 + 1.27533i) q^{6} +(1.45655 - 4.48281i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.38156 + 1.00376i) q^{9} +1.79068 q^{10} +(3.03398 - 1.33977i) q^{11} -2.16972 q^{12} +(-5.54899 + 4.03158i) q^{13} +(1.45655 + 4.48281i) q^{14} +(-1.20062 + 3.69513i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.0745226 + 0.0541438i) q^{17} +(0.527710 - 1.62412i) q^{18} +(-0.309017 - 0.951057i) q^{19} +(-1.44869 + 1.05254i) q^{20} -10.2270 q^{21} +(-1.66704 + 2.86722i) q^{22} +4.91452 q^{23} +(1.75534 - 1.27533i) q^{24} +(-0.554210 - 1.70568i) q^{25} +(2.11952 - 6.52323i) q^{26} +(-2.26842 - 1.64811i) q^{27} +(-3.81331 - 2.77053i) q^{28} +(-0.990376 + 3.04806i) q^{29} +(-1.20062 - 3.69513i) q^{30} +(-5.76130 + 4.18583i) q^{31} +1.00000 q^{32} +(-4.79888 - 5.36242i) q^{33} -0.0921150 q^{34} +(-6.82842 + 4.96114i) q^{35} +(0.527710 + 1.62412i) q^{36} +(1.82728 - 5.62380i) q^{37} +(0.809017 + 0.587785i) q^{38} +(12.0398 + 8.74741i) q^{39} +(0.553351 - 1.70304i) q^{40} +(1.11382 + 3.42797i) q^{41} +(8.27383 - 6.01129i) q^{42} -7.91031 q^{43} +(-0.336644 - 3.29950i) q^{44} +3.05796 q^{45} +(-3.97593 + 2.88868i) q^{46} +(0.859197 + 2.64434i) q^{47} +(-0.670482 + 2.06353i) q^{48} +(-12.3109 - 8.94442i) q^{49} +(1.45094 + 1.05417i) q^{50} +(0.0617614 - 0.190082i) q^{51} +(2.11952 + 6.52323i) q^{52} +(5.88873 - 4.27841i) q^{53} +2.80392 q^{54} +(-5.80545 - 1.25246i) q^{55} +4.71351 q^{56} +(-1.75534 + 1.27533i) q^{57} +(-0.990376 - 3.04806i) q^{58} +(2.52234 - 7.76295i) q^{59} +(3.14326 + 2.28371i) q^{60} +(9.80794 + 7.12588i) q^{61} +(2.20062 - 6.77281i) q^{62} +(2.48736 + 7.65532i) q^{63} +(-0.809017 + 0.587785i) q^{64} +12.2822 q^{65} +(7.03432 + 1.51758i) q^{66} -10.7693 q^{67} +(0.0745226 - 0.0541438i) q^{68} +(-3.29509 - 10.1413i) q^{69} +(2.60822 - 8.02729i) q^{70} +(8.70896 + 6.32743i) q^{71} +(-1.38156 - 1.00376i) q^{72} +(1.81416 - 5.58341i) q^{73} +(1.82728 + 5.62380i) q^{74} +(-3.14814 + 2.28726i) q^{75} -1.00000 q^{76} +(-1.58678 - 15.5522i) q^{77} -14.8820 q^{78} +(11.3353 - 8.23559i) q^{79} +(0.553351 + 1.70304i) q^{80} +(-3.46311 + 10.6584i) q^{81} +(-2.91601 - 2.11860i) q^{82} +(1.62384 + 1.17979i) q^{83} +(-3.16032 + 9.72647i) q^{84} +(-0.0509719 - 0.156875i) q^{85} +(6.39958 - 4.64956i) q^{86} +6.95380 q^{87} +(2.21175 + 2.47147i) q^{88} -9.13077 q^{89} +(-2.47394 + 1.79742i) q^{90} +(9.99040 + 30.7473i) q^{91} +(1.51867 - 4.67398i) q^{92} +(12.5004 + 9.08209i) q^{93} +(-2.24941 - 1.63429i) q^{94} +(-0.553351 + 1.70304i) q^{95} +(-0.670482 - 2.06353i) q^{96} +(9.89309 - 7.18775i) q^{97} +15.2172 q^{98} +(-2.84682 + 4.89637i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{7} - 4 q^{8} - 20 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^7 - 4 * q^8 - 20 * q^9	$ 16 q - 4 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{7} - 4 q^{8} - 20 q^{9} + 4 q^{10} + 2 q^{11} - 14 q^{13} + 6 q^{14} - 10 q^{15} - 4 q^{16} + 8 q^{17} + 4 q^{19} + 4 q^{20} + 28 q^{21} + 2 q^{22} + 24 q^{23} - 4 q^{26} - 18 q^{27} - 14 q^{28} - 22 q^{29} - 10 q^{30} - 24 q^{31} + 16 q^{32} + 2 q^{33} + 8 q^{34} - 20 q^{35} + 6 q^{37} + 4 q^{38} + 72 q^{39} - 6 q^{40} - 14 q^{41} - 22 q^{42} + 56 q^{43} + 12 q^{44} - 56 q^{45} + 4 q^{46} - 38 q^{47} - 36 q^{49} + 56 q^{51} - 4 q^{52} + 22 q^{53} - 48 q^{54} - 6 q^{55} + 16 q^{56} - 22 q^{58} - 28 q^{59} + 12 q^{61} + 26 q^{62} - 20 q^{63} - 4 q^{64} - 32 q^{65} + 12 q^{66} - 44 q^{67} + 8 q^{68} + 64 q^{69} - 20 q^{70} + 16 q^{71} - 20 q^{72} + 12 q^{73} + 6 q^{74} + 32 q^{75} - 16 q^{76} - 12 q^{77} - 8 q^{78} + 48 q^{79} - 6 q^{80} - 64 q^{81} + 6 q^{82} + 14 q^{83} + 8 q^{84} + 6 q^{85} - 14 q^{86} + 84 q^{87} - 8 q^{88} - 56 q^{89} + 34 q^{90} + 26 q^{91} - 16 q^{92} - 46 q^{93} + 32 q^{94} + 6 q^{95} - 24 q^{97} + 64 q^{98} - 56 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^7 - 4 * q^8 - 20 * q^9 + 4 * q^10 + 2 * q^11 - 14 * q^13 + 6 * q^14 - 10 * q^15 - 4 * q^16 + 8 * q^17 + 4 * q^19 + 4 * q^20 + 28 * q^21 + 2 * q^22 + 24 * q^23 - 4 * q^26 - 18 * q^27 - 14 * q^28 - 22 * q^29 - 10 * q^30 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 8 * q^34 - 20 * q^35 + 6 * q^37 + 4 * q^38 + 72 * q^39 - 6 * q^40 - 14 * q^41 - 22 * q^42 + 56 * q^43 + 12 * q^44 - 56 * q^45 + 4 * q^46 - 38 * q^47 - 36 * q^49 + 56 * q^51 - 4 * q^52 + 22 * q^53 - 48 * q^54 - 6 * q^55 + 16 * q^56 - 22 * q^58 - 28 * q^59 + 12 * q^61 + 26 * q^62 - 20 * q^63 - 4 * q^64 - 32 * q^65 + 12 * q^66 - 44 * q^67 + 8 * q^68 + 64 * q^69 - 20 * q^70 + 16 * q^71 - 20 * q^72 + 12 * q^73 + 6 * q^74 + 32 * q^75 - 16 * q^76 - 12 * q^77 - 8 * q^78 + 48 * q^79 - 6 * q^80 - 64 * q^81 + 6 * q^82 + 14 * q^83 + 8 * q^84 + 6 * q^85 - 14 * q^86 + 84 * q^87 - 8 * q^88 - 56 * q^89 + 34 * q^90 + 26 * q^91 - 16 * q^92 - 46 * q^93 + 32 * q^94 + 6 * q^95 - 24 * q^97 + 64 * q^98 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	−0.670482	−	2.06353i	−0.387103	−	1.19138i	−0.934943	−	0.354797i	$-0.884550\pi$
$3$	−0.670482	−	2.06353i	−0.387103	−	1.19138i	0.547840	−	0.836583i	$-0.315450\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−1.44869	−	1.05254i	−0.647875	−	0.470708i	0.214672	−	0.976686i	$-0.431132\pi$
$5$	−1.44869	−	1.05254i	−0.647875	−	0.470708i	−0.862547	+	0.505978i	$0.831132\pi$
$6$	1.75534	+	1.27533i	0.716616	+	0.520652i
$7$	1.45655	−	4.48281i	0.550526	−	1.69434i	−0.156950	−	0.987606i	$-0.550166\pi$
$7$	1.45655	−	4.48281i	0.550526	−	1.69434i	0.707476	−	0.706737i	$-0.249834\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−1.38156	+	1.00376i	−0.460521	+	0.334588i
$10$	1.79068			0.566263
$11$	3.03398	−	1.33977i	0.914779	−	0.403955i
$11$	3.03398	−	1.33977i	0.914779	−	0.403955i
$12$	−2.16972			−0.626346
$13$	−5.54899	+	4.03158i	−1.53901	+	1.11816i	−0.588062	+	0.808816i	$0.700109\pi$
$13$	−5.54899	+	4.03158i	−1.53901	+	1.11816i	−0.950951	+	0.309342i	$0.899891\pi$
$14$	1.45655	+	4.48281i	0.389280	+	1.19808i
$15$	−1.20062	+	3.69513i	−0.309999	+	0.954077i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.0745226	+	0.0541438i	0.0180744	+	0.0131318i	0.596786	−	0.802401i	$-0.296444\pi$
$17$	0.0745226	+	0.0541438i	0.0180744	+	0.0131318i	−0.578711	+	0.815532i	$0.696444\pi$
$18$	0.527710	−	1.62412i	0.124382	−	0.382810i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	−1.44869	+	1.05254i	−0.323937	+	0.235354i
$21$	−10.2270			−2.23172
$22$	−1.66704	+	2.86722i	−0.355415	+	0.611294i
$23$	4.91452			1.02475			0.512374	−	0.858763i	$-0.328766\pi$
$23$	4.91452			1.02475			0.512374	+	0.858763i	$0.328766\pi$
$24$	1.75534	−	1.27533i	0.358308	−	0.260326i
$25$	−0.554210	−	1.70568i	−0.110842	−	0.341136i
$26$	2.11952	−	6.52323i	0.415673	−	1.27931i
$27$	−2.26842	−	1.64811i	−0.436558	−	0.317178i
$28$	−3.81331	−	2.77053i	−0.720647	−	0.523581i
$29$	−0.990376	+	3.04806i	−0.183908	+	0.566011i	−0.999928	−	0.0120130i	$-0.996176\pi$
$29$	−0.990376	+	3.04806i	−0.183908	+	0.566011i	0.816020	+	0.578024i	$0.196176\pi$
$30$	−1.20062	−	3.69513i	−0.219202	−	0.674635i
$31$	−5.76130	+	4.18583i	−1.03476	+	0.751797i	−0.969256	−	0.246056i	$-0.920865\pi$
$31$	−5.76130	+	4.18583i	−1.03476	+	0.751797i	−0.0655036	+	0.997852i	$0.520865\pi$
$32$	1.00000			0.176777
$33$	−4.79888	−	5.36242i	−0.835378	−	0.933477i
$34$	−0.0921150			−0.0157976
$35$	−6.82842	+	4.96114i	−1.15421	+	0.838585i
$36$	0.527710	+	1.62412i	0.0879516	+	0.270687i
$37$	1.82728	−	5.62380i	0.300403	−	0.924547i	−0.680949	−	0.732331i	$-0.738433\pi$
$37$	1.82728	−	5.62380i	0.300403	−	0.924547i	0.981353	−	0.192216i	$-0.0615674\pi$
$38$	0.809017	+	0.587785i	0.131240	+	0.0953514i
$39$	12.0398	+	8.74741i	1.92791	+	1.40071i
$40$	0.553351	−	1.70304i	0.0874925	−	0.269274i
$41$	1.11382	+	3.42797i	0.173949	+	0.535360i	0.999584	−	0.0288450i	$-0.00918292\pi$
$41$	1.11382	+	3.42797i	0.173949	+	0.535360i	−0.825635	+	0.564205i	$0.809183\pi$
$42$	8.27383	−	6.01129i	1.27668	−	0.927562i
$43$	−7.91031			−1.20631			−0.603156	−	0.797624i	$-0.706090\pi$
$43$	−7.91031			−1.20631			−0.603156	+	0.797624i	$0.706090\pi$
$44$	−0.336644	−	3.29950i	−0.0507510	−	0.497418i
$45$	3.05796			0.455853
$46$	−3.97593	+	2.88868i	−0.586218	+	0.425913i
$47$	0.859197	+	2.64434i	0.125327	+	0.385716i	0.993960	−	0.109739i	$-0.0350014\pi$
$47$	0.859197	+	2.64434i	0.125327	+	0.385716i	−0.868634	+	0.495455i	$0.835001\pi$
$48$	−0.670482	+	2.06353i	−0.0967757	+	0.297845i
$49$	−12.3109	−	8.94442i	−1.75871	−	1.27777i
$50$	1.45094	+	1.05417i	0.205194	+	0.149082i
$51$	0.0617614	−	0.190082i	0.00864833	−	0.0266168i
$52$	2.11952	+	6.52323i	0.293925	+	0.904609i
$53$	5.88873	−	4.27841i	0.808879	−	0.587685i	−0.104626	−	0.994512i	$-0.533365\pi$
$53$	5.88873	−	4.27841i	0.808879	−	0.587685i	0.913505	+	0.406826i	$0.133365\pi$
$54$	2.80392			0.381566
$55$	−5.80545	−	1.25246i	−0.782807	−	0.168882i
$56$	4.71351			0.629869
$57$	−1.75534	+	1.27533i	−0.232501	+	0.168922i
$58$	−0.990376	−	3.04806i	−0.130043	−	0.400230i
$59$	2.52234	−	7.76295i	0.328380	−	1.01065i	−0.641512	−	0.767113i	$-0.721692\pi$
$59$	2.52234	−	7.76295i	0.328380	−	1.01065i	0.969892	−	0.243537i	$-0.0783076\pi$
$60$	3.14326	+	2.28371i	0.405793	+	0.294826i
$61$	9.80794	+	7.12588i	1.25578	+	0.912376i	0.998542	−	0.0539729i	$-0.0171885\pi$
$61$	9.80794	+	7.12588i	1.25578	+	0.912376i	0.257235	+	0.966349i	$0.417188\pi$
$62$	2.20062	−	6.77281i	0.279479	−	0.860148i
$63$	2.48736	+	7.65532i	0.313378	+	0.964480i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	12.2822			1.52341
$66$	7.03432	+	1.51758i	0.865865	+	0.186801i
$67$	−10.7693			−1.31568			−0.657841	−	0.753157i	$-0.728530\pi$
$67$	−10.7693			−1.31568			−0.657841	+	0.753157i	$0.728530\pi$
$68$	0.0745226	−	0.0541438i	0.00903719	−	0.00656590i
$69$	−3.29509	−	10.1413i	−0.396683	−	1.22086i
$70$	2.60822	−	8.02729i	0.311742	−	0.959444i
$71$	8.70896	+	6.32743i	1.03356	+	0.750928i	0.969019	−	0.246987i	$-0.0794405\pi$
$71$	8.70896	+	6.32743i	1.03356	+	0.750928i	0.0645448	+	0.997915i	$0.479440\pi$
$72$	−1.38156	−	1.00376i	−0.162819	−	0.118295i
$73$	1.81416	−	5.58341i	0.212331	−	0.653488i	−0.787001	−	0.616952i	$-0.788367\pi$
$73$	1.81416	−	5.58341i	0.212331	−	0.653488i	0.999332	−	0.0365368i	$-0.0116326\pi$
$74$	1.82728	+	5.62380i	0.212417	+	0.653753i
$75$	−3.14814	+	2.28726i	−0.363516	+	0.264110i
$76$	−1.00000			−0.114708
$77$	−1.58678	−	15.5522i	−0.180830	−	1.77234i
$78$	−14.8820			−1.68505
$79$	11.3353	−	8.23559i	1.27532	−	0.926576i	0.275921	−	0.961180i	$-0.411017\pi$
$79$	11.3353	−	8.23559i	1.27532	−	0.926576i	0.999401	+	0.0346046i	$0.0110172\pi$
$80$	0.553351	+	1.70304i	0.0618665	+	0.190406i
$81$	−3.46311	+	10.6584i	−0.384790	+	1.18426i
$82$	−2.91601	−	2.11860i	−0.322019	−	0.233961i
$83$	1.62384	+	1.17979i	0.178239	+	0.129498i	0.673328	−	0.739344i	$-0.264864\pi$
$83$	1.62384	+	1.17979i	0.178239	+	0.129498i	−0.495088	+	0.868843i	$0.664864\pi$
$84$	−3.16032	+	9.72647i	−0.344819	+	1.06124i
$85$	−0.0509719	−	0.156875i	−0.00552868	−	0.0170155i
$86$	6.39958	−	4.64956i	0.690084	−	0.501375i
$87$	6.95380			0.745526
$88$	2.21175	+	2.47147i	0.235773	+	0.263460i
$89$	−9.13077			−0.967860			−0.483930	−	0.875107i	$-0.660791\pi$
$89$	−9.13077			−0.967860			−0.483930	+	0.875107i	$0.660791\pi$
$90$	−2.47394	+	1.79742i	−0.260776	+	0.189465i
$91$	9.99040	+	30.7473i	1.04728	+	3.22319i
$92$	1.51867	−	4.67398i	0.158332	−	0.487296i
$93$	12.5004	+	9.08209i	1.29623	+	0.941769i
$94$	−2.24941	−	1.63429i	−0.232009	−	0.168564i
$95$	−0.553351	+	1.70304i	−0.0567726	+	0.174728i
$96$	−0.670482	−	2.06353i	−0.0684308	−	0.210608i
$97$	9.89309	−	7.18775i	1.00449	−	0.729805i	0.0414445	−	0.999141i	$-0.486804\pi$
$97$	9.89309	−	7.18775i	1.00449	−	0.729805i	0.963046	+	0.269335i	$0.0868040\pi$
$98$	15.2172			1.53716
$99$	−2.84682	+	4.89637i	−0.286116	+	0.492104i
$100$	−1.79346			−0.179346
$101$	−6.69584	+	4.86481i	−0.666261	+	0.484067i	−0.868771	−	0.495213i	$-0.835090\pi$
$101$	−6.69584	+	4.86481i	−0.666261	+	0.484067i	0.202511	+	0.979280i	$0.435090\pi$
$102$	0.0617614	+	0.190082i	0.00611529	+	0.0188209i
$103$	1.68167	−	5.17564i	0.165700	−	0.509971i	−0.833388	−	0.552689i	$-0.813602\pi$
$103$	1.68167	−	5.17564i	0.165700	−	0.509971i	0.999087	+	0.0427182i	$0.0136018\pi$
$104$	−5.54899	−	4.03158i	−0.544123	−	0.395329i
$105$	14.8158	+	10.7643i	1.44587	+	1.05049i
$106$	−2.24929	+	6.92262i	−0.218471	+	0.672384i
$107$	−0.630804	−	1.94141i	−0.0609821	−	0.187684i	0.915924	−	0.401351i	$-0.131459\pi$
$107$	−0.630804	−	1.94141i	−0.0609821	−	0.187684i	−0.976907	+	0.213667i	$0.931459\pi$
$108$	−2.26842	+	1.64811i	−0.218279	+	0.158589i
$109$	3.04609			0.291762			0.145881	−	0.989302i	$-0.453398\pi$
$109$	3.04609			0.291762			0.145881	+	0.989302i	$0.453398\pi$
$110$	5.43289	−	2.39910i	0.518006	−	0.228745i
$111$	−12.8300			−1.21777
$112$	−3.81331	+	2.77053i	−0.360324	+	0.261791i
$113$	−2.60916	−	8.03017i	−0.245449	−	0.755415i	−0.995562	−	0.0941054i	$-0.970001\pi$
$113$	−2.60916	−	8.03017i	−0.245449	−	0.755415i	0.750113	−	0.661310i	$-0.229999\pi$
$114$	0.670482	−	2.06353i	0.0627964	−	0.193267i
$115$	−7.11962	−	5.17271i	−0.663908	−	0.482357i
$116$	2.59284	+	1.88381i	0.240739	+	0.174907i
$117$	3.61952	−	11.1397i	0.334625	−	1.02987i
$118$	2.52234	+	7.76295i	0.232200	+	0.714638i
$119$	0.351263	−	0.255207i	0.0322002	−	0.0233948i
$120$	−3.88529			−0.354676
$121$	7.41004	−	8.12965i	0.673640	−	0.739059i
$122$	−12.1233			−1.09759
$123$	6.32694	−	4.59679i	0.570481	−	0.414478i
$124$	2.20062	+	6.77281i	0.197621	+	0.608216i
$125$	−3.75917	+	11.5695i	−0.336230	+	1.03481i
$126$	−6.51200	−	4.73125i	−0.580135	−	0.421493i
$127$	−1.86222	−	1.35298i	−0.165245	−	0.120058i	0.502089	−	0.864816i	$-0.332565\pi$
$127$	−1.86222	−	1.35298i	−0.165245	−	0.120058i	−0.667335	+	0.744758i	$0.732565\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	5.30372	+	16.3232i	0.466966	+	1.43717i
$130$	−9.93647	+	7.21927i	−0.871486	+	0.633172i
$131$	10.0556			0.878559			0.439279	−	0.898350i	$-0.355234\pi$
$131$	10.0556			0.878559			0.439279	+	0.898350i	$0.355234\pi$
$132$	−6.58290	+	2.90693i	−0.572968	+	0.253016i
$133$	−4.71351			−0.408713
$134$	8.71257	−	6.33005i	0.752651	−	0.546833i
$135$	1.55155	+	4.77519i	0.133537	+	0.410983i
$136$	−0.0284651	+	0.0876066i	−0.00244086	+	0.00751220i
$137$	−5.56726	−	4.04485i	−0.475643	−	0.345575i	0.323994	−	0.946059i	$-0.394974\pi$
$137$	−5.56726	−	4.04485i	−0.475643	−	0.345575i	−0.799636	+	0.600485i	$0.794974\pi$
$138$	8.62667	+	6.26764i	0.734351	+	0.533537i
$139$	1.50444	−	4.63021i	0.127605	−	0.392729i	−0.866761	−	0.498723i	$-0.833802\pi$
$139$	1.50444	−	4.63021i	0.127605	−	0.392729i	0.994367	+	0.105994i	$0.0338025\pi$
$140$	2.60822	+	8.02729i	0.220435	+	0.678430i
$141$	4.88060	−	3.54596i	0.411020	−	0.298624i
$142$	−10.7649			−0.903368
$143$	−11.4341	+	19.6661i	−0.956170	+	1.64456i
$144$	1.70770			0.142309
$145$	4.64295	−	3.37330i	0.385576	−	0.280137i
$146$	1.81416	+	5.58341i	0.150141	+	0.462086i
$147$	−10.2028	+	31.4011i	−0.841515	+	2.58992i
$148$	−4.78389	−	3.47570i	−0.393233	−	0.285701i
$149$	1.81184	+	1.31638i	0.148432	+	0.107842i	0.659523	−	0.751685i	$-0.270758\pi$
$149$	1.81184	+	1.31638i	0.148432	+	0.107842i	−0.511091	+	0.859527i	$0.670758\pi$
$150$	1.20248	−	3.70086i	0.0981823	−	0.302174i
$151$	1.74357	+	5.36614i	0.141889	+	0.436690i	0.996598	−	0.0824177i	$-0.0262642\pi$
$151$	1.74357	+	5.36614i	0.141889	+	0.436690i	−0.854709	+	0.519108i	$0.826264\pi$
$152$	0.809017	−	0.587785i	0.0656199	−	0.0476757i
$153$	−0.157305			−0.0127174
$154$	10.4251	+	11.6493i	0.840077	+	0.938728i
$155$	12.7521			1.02427
$156$	12.0398	−	8.74741i	0.963954	−	0.700353i
$157$	−3.08996	−	9.50992i	−0.246606	−	0.758975i	−0.995368	−	0.0961361i	$-0.969352\pi$
$157$	−3.08996	−	9.50992i	−0.246606	−	0.758975i	0.748762	−	0.662838i	$-0.230648\pi$
$158$	−4.32970	+	13.3255i	−0.344453	+	1.06012i
$159$	−12.7769	−	9.28298i	−1.01328	−	0.736188i
$160$	−1.44869	−	1.05254i	−0.114529	−	0.0832103i
$161$	7.15826	−	22.0309i	0.564150	−	1.73627i
$162$	−3.46311	−	10.6584i	−0.272088	−	0.837400i
$163$	0.331429	−	0.240797i	0.0259595	−	0.0188607i	−0.574730	−	0.818343i	$-0.694893\pi$
$163$	0.331429	−	0.240797i	0.0259595	−	0.0188607i	0.600689	+	0.799483i	$0.294893\pi$
$164$	3.60439			0.281455
$165$	1.30796	+	12.8195i	0.101824	+	0.997995i
$166$	−2.00717			−0.155787
$167$	12.9617	−	9.41720i	1.00300	−	0.728725i	0.0402735	−	0.999189i	$-0.487177\pi$
$167$	12.9617	−	9.41720i	1.00300	−	0.728725i	0.962730	+	0.270464i	$0.0871771\pi$
$168$	−3.16032	−	9.72647i	−0.243824	−	0.750413i
$169$	10.5204	−	32.3786i	0.809265	−	2.49066i
$170$	0.133446	+	0.0969543i	0.0102349	+	0.00743606i
$171$	1.38156	+	1.00376i	0.105651	+	0.0767597i
$172$	−2.44442	+	7.52315i	−0.186385	+	0.573635i
$173$	−5.90590	−	18.1765i	−0.449017	−	1.38193i	−0.878018	−	0.478629i	$-0.841134\pi$
$173$	−5.90590	−	18.1765i	−0.449017	−	1.38193i	0.429000	−	0.903304i	$-0.358866\pi$
$174$	−5.62574	+	4.08734i	−0.426487	+	0.309861i
$175$	−8.45349			−0.639024
$176$	−3.24204	−	0.699432i	−0.244378	−	0.0527217i
$177$	−17.7103			−1.33119
$178$	7.38695	−	5.36693i	0.553675	−	0.402268i
$179$	−4.05533	−	12.4810i	−0.303110	−	0.932876i	−0.980376	−	0.197138i	$-0.936835\pi$
$179$	−4.05533	−	12.4810i	−0.303110	−	0.932876i	0.677266	−	0.735738i	$-0.263165\pi$
$180$	0.944960	−	2.90829i	0.0704332	−	0.216771i
$181$	−10.7333	−	7.79816i	−0.797796	−	0.579633i	0.112470	−	0.993655i	$-0.464124\pi$
$181$	−10.7333	−	7.79816i	−0.797796	−	0.579633i	−0.910267	+	0.414022i	$0.864124\pi$
$182$	−26.1552	−	19.0029i	−1.93875	−	1.40859i
$183$	8.12844	−	25.0168i	0.600871	−	1.84929i
$184$	1.51867	+	4.67398i	0.111958	+	0.344571i
$185$	−8.56642	+	6.22387i	−0.629816	+	0.457588i
$186$	−15.4514			−1.13295
$187$	0.298640	+	0.0644282i	0.0218387	+	0.00471146i
$188$	2.78042			0.202783
$189$	−10.6922	+	7.76836i	−0.777745	+	0.565065i
$190$	−0.553351	−	1.70304i	−0.0401443	−	0.123551i
$191$	6.72988	−	20.7124i	0.486957	−	1.49870i	−0.342169	−	0.939638i	$-0.611162\pi$
$191$	6.72988	−	20.7124i	0.486957	−	1.49870i	0.829126	−	0.559061i	$-0.188838\pi$
$192$	1.75534	+	1.27533i	0.126681	+	0.0920392i
$193$	−1.22832	−	0.892423i	−0.0884161	−	0.0642380i	0.542699	−	0.839927i	$-0.317402\pi$
$193$	−1.22832	−	0.892423i	−0.0884161	−	0.0642380i	−0.631115	+	0.775689i	$0.717402\pi$
$194$	−3.77882	+	11.6300i	−0.271304	+	0.834987i
$195$	−8.23496	−	25.3446i	−0.589718	−	1.81496i
$196$	−12.3109	+	8.94442i	−0.879353	+	0.638887i
$197$	−12.8759			−0.917370			−0.458685	−	0.888599i	$-0.651679\pi$
$197$	−12.8759			−0.917370			−0.458685	+	0.888599i	$0.651679\pi$
$198$	−0.574889	−	5.63456i	−0.0408556	−	0.400431i
$199$	10.2537			0.726864			0.363432	−	0.931621i	$-0.381605\pi$
$199$	10.2537			0.726864			0.363432	+	0.931621i	$0.381605\pi$
$200$	1.45094	−	1.05417i	0.102597	−	0.0745410i
$201$	7.22064	+	22.2228i	0.509304	+	1.56748i
$202$	2.55758	−	7.87143i	0.179951	−	0.553832i
$203$	12.2214	+	8.87934i	0.857771	+	0.623207i
$204$	−0.161693	−	0.117477i	−0.0113208	−	0.00822505i
$205$	1.99449	−	6.13841i	0.139301	−	0.428725i
$206$	1.68167	+	5.17564i	0.117167	+	0.360604i
$207$	−6.78971	+	4.93301i	−0.471918	+	0.342868i
$208$	6.85893			0.475581
$209$	−2.21175	−	2.47147i	−0.152990	−	0.170955i
$210$	−18.3133			−1.26374
$211$	−13.7872	+	10.0170i	−0.949149	+	0.689597i	−0.950605	−	0.310402i	$-0.899536\pi$
$211$	−13.7872	+	10.0170i	−0.949149	+	0.689597i	0.00145659	+	0.999999i	$0.499536\pi$
$212$	−2.24929	−	6.92262i	−0.154482	−	0.475447i
$213$	7.21765	−	22.2136i	0.494545	−	1.52205i
$214$	1.65147	+	1.19986i	0.112892	+	0.0820207i
$215$	11.4596	+	8.32589i	0.781538	+	0.567821i
$216$	0.866460	−	2.66669i	0.0589552	−	0.181445i
$217$	10.3726	+	31.9237i	0.704140	+	2.16712i
$218$	−2.46434	+	1.79045i	−0.166906	+	0.121264i
$219$	−12.7379			−0.860747
$220$	−2.98514	+	5.13428i	−0.201258	+	0.346153i
$221$	−0.631810			−0.0425001
$222$	10.3797	−	7.54131i	0.696641	−	0.506139i
$223$	−1.83609	−	5.65091i	−0.122954	−	0.378413i	0.870569	−	0.492046i	$-0.163751\pi$
$223$	−1.83609	−	5.65091i	−0.122954	−	0.378413i	−0.993523	+	0.113634i	$0.963751\pi$
$224$	1.45655	−	4.48281i	0.0973201	−	0.299520i
$225$	2.47778	+	1.80021i	0.165185	+	0.120014i
$226$	6.83087	+	4.96292i	0.454383	+	0.330128i
$227$	4.89684	−	15.0709i	0.325015	−	1.00029i	−0.646419	−	0.762982i	$-0.723734\pi$
$227$	4.89684	−	15.0709i	0.325015	−	1.00029i	0.971434	−	0.237310i	$-0.0762657\pi$
$228$	0.670482	+	2.06353i	0.0444037	+	0.136661i
$229$	−7.37474	+	5.35806i	−0.487337	+	0.354071i	−0.804159	−	0.594414i	$-0.797384\pi$
$229$	−7.37474	+	5.35806i	−0.487337	+	0.354071i	0.316823	+	0.948485i	$0.397384\pi$
$230$	8.80033			0.580277
$231$	−31.0285	+	13.7018i	−2.04153	+	0.901514i
$232$	−3.20492			−0.210414
$233$	5.29820	−	3.84937i	0.347096	−	0.252180i	−0.400553	−	0.916273i	$-0.631182\pi$
$233$	5.29820	−	3.84937i	0.347096	−	0.252180i	0.747650	+	0.664093i	$0.231182\pi$
$234$	3.61952	+	11.1397i	0.236616	+	0.728228i
$235$	1.53855	−	4.73517i	0.100364	−	0.308888i
$236$	−6.60356	−	4.79777i	−0.429855	−	0.312308i
$237$	−24.5945	−	17.8690i	−1.59758	−	1.16071i
$238$	−0.134170	+	0.412934i	−0.00869698	+	0.0267665i
$239$	5.47862	+	16.8615i	0.354382	+	1.09068i	0.956367	+	0.292169i	$0.0943769\pi$
$239$	5.47862	+	16.8615i	0.354382	+	1.09068i	−0.601984	+	0.798508i	$0.705623\pi$
$240$	3.14326	−	2.28371i	0.202897	−	0.147413i
$241$	8.44210			0.543804			0.271902	−	0.962325i	$-0.412347\pi$
$241$	8.44210			0.543804			0.271902	+	0.962325i	$0.412347\pi$
$242$	−1.21636	+	10.9325i	−0.0781907	+	0.702770i
$243$	15.9040			1.02024
$244$	9.80794	−	7.12588i	0.627889	−	0.456188i
$245$	8.42043	+	25.9154i	0.537961	+	1.65567i
$246$	−2.41667	+	7.43776i	−0.154082	+	0.474214i
$247$	5.54899	+	4.03158i	0.353074	+	0.256523i
$248$	−5.76130	−	4.18583i	−0.365843	−	0.265800i
$249$	1.34577	−	4.14186i	0.0852849	−	0.262480i
$250$	−3.75917	−	11.5695i	−0.237751	−	0.731721i
$251$	−16.8956	+	12.2754i	−1.06644	+	0.774813i	−0.975269	−	0.221022i	$-0.929061\pi$
$251$	−16.8956	+	12.2754i	−1.06644	+	0.774813i	−0.0911704	+	0.995835i	$0.529061\pi$
$252$	8.04928			0.507057
$253$	14.9105	−	6.58431i	0.937417	−	0.413952i
$254$	2.30183			0.144430
$255$	−0.289542	+	0.210364i	−0.0181318	+	0.0131735i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−7.99254	+	24.5985i	−0.498561	+	1.53441i	0.312771	+	0.949828i	$0.398743\pi$
$257$	−7.99254	+	24.5985i	−0.498561	+	1.53441i	−0.811333	+	0.584585i	$0.801257\pi$
$258$	−13.8853	−	10.0883i	−0.864462	−	0.628068i
$259$	−22.5489	−	16.3827i	−1.40112	−	1.01797i
$260$	3.79539	−	11.6810i	0.235380	−	0.724426i
$261$	−1.69127	−	5.20519i	−0.104687	−	0.322193i
$262$	−8.13512	+	5.91051i	−0.502590	+	0.365153i
$263$	31.2182			1.92500			0.962498	−	0.271287i	$-0.0874494\pi$
$263$	31.2182			1.92500			0.962498	+	0.271287i	$0.0874494\pi$
$264$	3.61703	−	6.22108i	0.222613	−	0.382881i
$265$	−13.0341			−0.800681
$266$	3.81331	−	2.77053i	0.233809	−	0.169872i
$267$	6.12201	+	18.8416i	0.374661	+	1.15309i
$268$	−3.32790	+	10.2422i	−0.203284	+	0.625644i
$269$	17.3897	+	12.6343i	1.06027	+	0.770329i	0.974138	−	0.225955i	$-0.0725503\pi$
$269$	17.3897	+	12.6343i	1.06027	+	0.770329i	0.0861290	+	0.996284i	$0.472550\pi$
$270$	−4.06202	−	2.95123i	−0.247207	−	0.179606i
$271$	−1.09670	+	3.37529i	−0.0666197	+	0.205034i	−0.978825	−	0.204699i	$-0.934378\pi$
$271$	−1.09670	+	3.37529i	−0.0666197	+	0.205034i	0.912205	+	0.409734i	$0.134378\pi$
$272$	−0.0284651	−	0.0876066i	−0.00172595	−	0.00531193i
$273$	56.7496	−	41.2310i	3.43464	−	2.49541i
$274$	6.88151			0.415727
$275$	−3.96668	−	4.43249i	−0.239200	−	0.267289i
$276$	−10.6631			−0.641846
$277$	−13.1491	+	9.55341i	−0.790056	+	0.574009i	−0.907980	−	0.419014i	$-0.862376\pi$
$277$	−13.1491	+	9.55341i	−0.790056	+	0.574009i	0.117924	+	0.993023i	$0.462376\pi$
$278$	1.50444	+	4.63021i	0.0902306	+	0.277701i
$279$	3.75801	−	11.5660i	0.224986	−	0.692436i
$280$	−6.82842	−	4.96114i	−0.408076	−	0.296485i
$281$	3.62933	+	2.63686i	0.216508	+	0.157302i	0.690753	−	0.723091i	$-0.257279\pi$
$281$	3.62933	+	2.63686i	0.216508	+	0.157302i	−0.474246	+	0.880393i	$0.657279\pi$
$282$	−1.86422	+	5.73748i	−0.111013	+	0.341662i
$283$	5.44840	+	16.7684i	0.323874	+	0.996780i	0.971947	+	0.235202i	$0.0755752\pi$
$283$	5.44840	+	16.7684i	0.323874	+	0.996780i	−0.648073	+	0.761578i	$0.724425\pi$
$284$	8.70896	−	6.32743i	0.516782	−	0.375464i
$285$	3.88529			0.230144
$286$	−2.30902	−	22.6310i	−0.136535	−	1.33820i
$287$	16.9893			1.00285
$288$	−1.38156	+	1.00376i	−0.0814093	+	0.0591473i
$289$	−5.25067	−	16.1599i	−0.308863	−	0.950582i
$290$	−1.77345	+	5.45811i	−0.104140	+	0.320511i
$291$	−21.4653	−	15.5954i	−1.25832	−	0.914221i
$292$	−4.74953	−	3.45074i	−0.277945	−	0.201939i
$293$	−4.74046	+	14.5896i	−0.276941	+	0.852335i	0.711759	+	0.702424i	$0.247899\pi$
$293$	−4.74046	+	14.5896i	−0.276941	+	0.852335i	−0.988699	+	0.149911i	$0.952101\pi$
$294$	−10.2028	−	31.4011i	−0.595041	−	1.83135i
$295$	−11.8249	+	8.59127i	−0.688471	+	0.500203i
$296$	5.91321			0.343698
$297$	−9.09042	−	1.96116i	−0.527480	−	0.113798i
$298$	−2.23956			−0.129734
$299$	−27.2706	+	19.8132i	−1.57710	+	1.14583i
$300$	1.20248	+	3.70086i	0.0694254	+	0.213669i
$301$	−11.5218	+	35.4604i	−0.664105	+	2.04391i
$302$	−4.56471	−	3.31646i	−0.262670	−	0.190841i
$303$	14.5281	+	10.5553i	0.834619	+	0.606386i
$304$	−0.309017	+	0.951057i	−0.0177233	+	0.0545468i
$305$	−6.70843	−	20.6464i	−0.384123	−	1.18221i
$306$	0.127263	−	0.0924617i	0.00727512	−	0.00528568i
$307$	−19.5442			−1.11545			−0.557724	−	0.830027i	$-0.688325\pi$
$307$	−19.5442			−1.11545			−0.557724	+	0.830027i	$0.688325\pi$
$308$	−15.2814	−	3.29678i	−0.870736	−	0.187851i
$309$	−11.8076			−0.671712
$310$	−10.3166	+	7.49548i	−0.585946	+	0.425715i
$311$	−2.66109	−	8.18998i	−0.150896	−	0.464411i	0.846826	−	0.531870i	$-0.178511\pi$
$311$	−2.66109	−	8.18998i	−0.150896	−	0.464411i	−0.997722	+	0.0674594i	$0.978511\pi$
$312$	−4.59879	+	14.1536i	−0.260355	+	0.801290i
$313$	2.33955	+	1.69978i	0.132239	+	0.0960775i	0.651939	−	0.758272i	$-0.273956\pi$
$313$	2.33955	+	1.69978i	0.132239	+	0.0960775i	−0.519699	+	0.854349i	$0.673956\pi$
$314$	8.08962	+	5.87746i	0.456524	+	0.331684i
$315$	4.45408	−	13.7082i	0.250959	−	0.772372i
$316$	−4.32970	−	13.3255i	−0.243565	−	0.749616i
$317$	20.7713	−	15.0912i	1.16663	−	0.847606i	0.176028	−	0.984385i	$-0.443675\pi$
$317$	20.7713	−	15.0912i	1.16663	−	0.847606i	0.990602	+	0.136779i	$0.0436750\pi$
$318$	15.7931			0.885635
$319$	1.07892	+	10.5746i	0.0604079	+	0.592066i
$320$	1.79068			0.100102
$321$	−3.58323	+	2.60337i	−0.199996	+	0.145306i
$322$	7.15826	+	22.0309i	0.398914	+	1.22773i
$323$	0.0284651	−	0.0876066i	0.00158384	−	0.00487456i
$324$	9.06654	+	6.58723i	0.503697	+	0.365957i
$325$	9.95189	+	7.23047i	0.552032	+	0.401074i
$326$	−0.126595	+	0.389618i	−0.00701143	+	0.0215790i
$327$	−2.04235	−	6.28570i	−0.112942	−	0.347600i
$328$	−2.91601	+	2.11860i	−0.161010	+	0.116980i
$329$	13.1055			0.722532
$330$	−8.59326	−	9.60238i	−0.473044	−	0.528594i
$331$	0.669770			0.0368139			0.0184069	−	0.999831i	$-0.494141\pi$
$331$	0.669770			0.0368139			0.0184069	+	0.999831i	$0.494141\pi$
$332$	1.62384	−	1.17979i	0.0891196	−	0.0647492i
$333$	3.12046	+	9.60379i	0.171000	+	0.526284i
$334$	−4.95091	+	15.2373i	−0.270902	+	0.833751i
$335$	15.6014	+	11.3351i	0.852397	+	0.619303i
$336$	8.27383	+	6.01129i	0.451374	+	0.327943i
$337$	8.90772	−	27.4152i	0.485235	−	1.49340i	−0.346406	−	0.938085i	$-0.612598\pi$
$337$	8.90772	−	27.4152i	0.485235	−	1.49340i	0.831641	−	0.555314i	$-0.187402\pi$
$338$	10.5204	+	32.3786i	0.572237	+	1.76116i
$339$	−14.8211	+	10.7682i	−0.804972	+	0.584847i
$340$	−0.164949			−0.00894559
$341$	−11.8716	+	20.4185i	−0.642884	+	1.10572i
$342$	−1.70770			−0.0923421
$343$	−31.3345	+	22.7659i	−1.69191	+	1.22924i
$344$	−2.44442	−	7.52315i	−0.131794	−	0.405621i
$345$	−5.90046	+	18.1598i	−0.317670	+	0.977688i
$346$	15.4618	+	11.2337i	0.831234	+	0.603927i
$347$	17.0753	+	12.4059i	0.916648	+	0.665984i	0.942688	−	0.333677i	$-0.108289\pi$
$347$	17.0753	+	12.4059i	0.916648	+	0.665984i	−0.0260390	+	0.999661i	$0.508289\pi$
$348$	2.14884	−	6.61346i	0.115190	−	0.354519i
$349$	−2.11889	−	6.52127i	−0.113422	−	0.349076i	0.878193	−	0.478307i	$-0.158749\pi$
$349$	−2.11889	−	6.52127i	−0.113422	−	0.349076i	−0.991615	+	0.129231i	$0.958749\pi$
$350$	6.83902	−	4.96884i	0.365561	−	0.265595i
$351$	19.2319			1.02652
$352$	3.03398	−	1.33977i	0.161712	−	0.0714099i
$353$	18.5941			0.989666			0.494833	−	0.868988i	$-0.335229\pi$
$353$	18.5941			0.989666			0.494833	+	0.868988i	$0.335229\pi$
$354$	14.3279	−	10.4098i	0.761520	−	0.553276i
$355$	−5.95675	−	18.3330i	−0.316152	−	0.973014i
$356$	−2.82156	+	8.68388i	−0.149543	+	0.460245i
$357$	−0.762144	−	0.553730i	−0.0403369	−	0.0293065i
$358$	10.6170	+	7.71370i	0.561126	+	0.407682i
$359$	−9.36941	+	28.8361i	−0.494498	+	1.52191i	0.323239	+	0.946317i	$0.395228\pi$
$359$	−9.36941	+	28.8361i	−0.494498	+	1.52191i	−0.817737	+	0.575592i	$0.804772\pi$
$360$	0.944960	+	2.90829i	0.0498038	+	0.153280i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	13.2670			0.697300
$363$	−21.7441	−	9.84007i	−1.14127	−	0.516470i
$364$	32.3296			1.69453
$365$	−8.50490	+	6.17917i	−0.445167	+	0.323432i
$366$	8.12844	+	25.0168i	0.424880	+	1.30765i
$367$	4.41597	−	13.5910i	0.230512	−	0.709443i	−0.767173	−	0.641440i	$-0.778337\pi$
$367$	4.41597	−	13.5910i	0.230512	−	0.709443i	0.997685	−	0.0680028i	$-0.0216627\pi$
$368$	−3.97593	−	2.88868i	−0.207260	−	0.150583i
$369$	−4.97968	−	3.61795i	−0.259232	−	0.188343i
$370$	3.27208	−	10.0704i	0.170107	−	0.523537i
$371$	−10.6021	−	32.6298i	−0.550432	−	1.69406i
$372$	12.5004	−	9.08209i	0.648117	−	0.470884i
$373$	23.0852			1.19530			0.597652	−	0.801755i	$-0.296100\pi$
$373$	23.0852			1.19530			0.597652	+	0.801755i	$0.296100\pi$
$374$	−0.279475	+	0.123413i	−0.0144513	+	0.00638152i
$375$	26.3945			1.36301
$376$	−2.24941	+	1.63429i	−0.116004	+	0.0842821i
$377$	−6.79292	−	20.9064i	−0.349853	−	1.07674i
$378$	4.08407	−	12.5695i	0.210062	−	0.646504i
$379$	14.7083	+	10.6862i	0.755516	+	0.548915i	0.897532	−	0.440950i	$-0.145358\pi$
$379$	14.7083	+	10.6862i	0.755516	+	0.548915i	−0.142016	+	0.989864i	$0.545358\pi$
$380$	1.44869	+	1.05254i	0.0743163	+	0.0539940i
$381$	−1.54334	+	4.74990i	−0.0790674	+	0.243345i
$382$	6.72988	+	20.7124i	0.344331	+	1.05974i
$383$	−22.8700	+	16.6160i	−1.16860	+	0.849039i	−0.990841	−	0.135034i	$-0.956886\pi$
$383$	−22.8700	+	16.6160i	−1.16860	+	0.849039i	−0.177761	+	0.984074i	$0.556886\pi$
$384$	−2.16972			−0.110723
$385$	−14.0705	+	24.2005i	−0.717099	+	1.23337i
$386$	1.51828			0.0772785
$387$	10.9286	−	7.94008i	0.555531	−	0.403617i
$388$	−3.77882	−	11.6300i	−0.191841	−	0.590425i
$389$	−9.06759	+	27.9072i	−0.459745	+	1.41495i	0.405728	+	0.913994i	$0.367018\pi$
$389$	−9.06759	+	27.9072i	−0.459745	+	1.41495i	−0.865473	+	0.500956i	$0.832982\pi$
$390$	21.5594	+	15.6638i	1.09170	+	0.793169i
$391$	0.366242	+	0.266091i	0.0185217	+	0.0134568i
$392$	4.70236	−	14.4724i	0.237505	−	0.730965i
$393$	−6.74207	−	20.7500i	−0.340093	−	1.04670i
$394$	10.4168	−	7.56826i	0.524792	−	0.381284i
$395$	−25.0896			−1.26240
$396$	3.77701	+	4.22055i	0.189802	+	0.212090i
$397$	2.08500			0.104643			0.0523216	−	0.998630i	$-0.483338\pi$
$397$	2.08500			0.104643			0.0523216	+	0.998630i	$0.483338\pi$
$398$	−8.29540	+	6.02696i	−0.415811	+	0.302104i
$399$	3.16032	+	9.72647i	0.158214	+	0.486932i
$400$	−0.554210	+	1.70568i	−0.0277105	+	0.0852841i
$401$	−9.33009	−	6.77871i	−0.465923	−	0.338513i	0.329927	−	0.944006i	$-0.392976\pi$
$401$	−9.33009	−	6.77871i	−0.465923	−	0.338513i	−0.795850	+	0.605494i	$0.792976\pi$
$402$	−18.9039	−	13.7345i	−0.942839	−	0.685013i
$403$	15.0939	−	46.4542i	0.751880	−	2.31405i
$404$	2.55758	+	7.87143i	0.127244	+	0.391618i
$405$	16.2353	−	11.7956i	0.806738	−	0.586129i
$406$	−15.1064			−0.749720
$407$	−1.99065	−	19.5106i	−0.0986728	−	0.967105i
$408$	0.199864			0.00989475
$409$	0.592468	−	0.430453i	0.0292957	−	0.0212845i	−0.573041	−	0.819527i	$-0.694236\pi$
$409$	0.592468	−	0.430453i	0.0292957	−	0.0212845i	0.602337	+	0.798242i	$0.294236\pi$
$410$	1.99449	+	6.13841i	0.0985008	+	0.303154i
$411$	−4.61393	+	14.2002i	−0.227588	+	0.700444i
$412$	−4.40266	−	3.19872i	−0.216904	−	0.157590i
$413$	−31.1259	−	22.6143i	−1.53161	−	1.11278i
$414$	2.59344	−	7.98178i	0.127461	−	0.392283i
$415$	−1.11067	−	3.41829i	−0.0545207	−	0.167797i
$416$	−5.54899	+	4.03158i	−0.272062	+	0.197664i
$417$	−10.5633			−0.517286
$418$	3.24204	+	0.699432i	0.158573	+	0.0342104i
$419$	13.2156			0.645623			0.322812	−	0.946463i	$-0.395372\pi$
$419$	13.2156			0.645623			0.322812	+	0.946463i	$0.395372\pi$
$420$	14.8158	−	10.7643i	0.722936	−	0.525244i
$421$	3.21870	+	9.90614i	0.156870	+	0.482796i	0.998346	−	0.0574993i	$-0.0183127\pi$
$421$	3.21870	+	9.90614i	0.156870	+	0.482796i	−0.841476	+	0.540295i	$0.818313\pi$
$422$	5.26624	−	16.2078i	0.256356	−	0.788984i
$423$	−3.84133	−	2.79089i	−0.186772	−	0.135698i
$424$	5.88873	+	4.27841i	0.285982	+	0.207778i
$425$	0.0510510	−	0.157119i	0.00247634	−	0.00762139i
$426$	7.21765	+	22.2136i	0.349696	+	1.07625i
$427$	46.2298	−	33.5879i	2.23722	−	1.62543i
$428$	−2.04132			−0.0986711
$429$	48.2479	+	10.4089i	2.32943	+	0.502548i
$430$	−14.1648			−0.683089
$431$	9.13954	−	6.64027i	0.440236	−	0.319850i	−0.345492	−	0.938422i	$-0.612288\pi$
$431$	9.13954	−	6.64027i	0.440236	−	0.319850i	0.785729	+	0.618571i	$0.212288\pi$
$432$	0.866460	+	2.66669i	0.0416876	+	0.128301i
$433$	−6.86876	+	21.1399i	−0.330091	+	1.01592i	0.638998	+	0.769208i	$0.279349\pi$
$433$	−6.86876	+	21.1399i	−0.330091	+	1.01592i	−0.969090	+	0.246709i	$0.920651\pi$
$434$	−27.1559	−	19.7299i	−1.30353	−	0.947067i
$435$	−10.0739	−	7.31913i	−0.483007	−	0.350925i
$436$	0.941293	−	2.89700i	0.0450798	−	0.138741i
$437$	−1.51867	−	4.67398i	−0.0726478	−	0.223587i
$438$	10.3052	−	7.48715i	0.492400	−	0.357750i
$439$	25.2534			1.20528			0.602641	−	0.798013i	$-0.294115\pi$
$439$	25.2534			1.20528			0.602641	+	0.798013i	$0.294115\pi$
$440$	−0.602823	−	5.90835i	−0.0287384	−	0.281669i
$441$	25.9864			1.23745
$442$	0.511145	−	0.371369i	0.0243127	−	0.0176642i
$443$	−1.28871	−	3.96626i	−0.0612287	−	0.188442i	0.915763	−	0.401718i	$-0.131587\pi$
$443$	−1.28871	−	3.96626i	−0.0612287	−	0.188442i	−0.976992	+	0.213276i	$0.931587\pi$
$444$	−3.96470	+	12.2021i	−0.188156	+	0.579086i
$445$	13.2277	+	9.61046i	0.627052	+	0.455580i
$446$	4.80695	+	3.49245i	0.227616	+	0.165372i
$447$	1.50158	−	4.62140i	0.0710225	−	0.218585i
$448$	1.45655	+	4.48281i	0.0688157	+	0.211793i
$449$	6.93686	−	5.03992i	0.327371	−	0.237849i	−0.411944	−	0.911209i	$-0.635150\pi$
$449$	6.93686	−	5.03992i	0.327371	−	0.237849i	0.739314	+	0.673361i	$0.235150\pi$
$450$	−3.06270			−0.144377
$451$	7.97198	+	8.90814i	0.375386	+	0.419468i
$452$	−8.44342			−0.397145
$453$	9.90417	−	7.19580i	0.465339	−	0.338088i
$454$	4.89684	+	15.0709i	0.229820	+	0.707314i
$455$	17.8896	−	55.0586i	0.838678	−	2.58119i
$456$	−1.75534	−	1.27533i	−0.0822015	−	0.0597229i
$457$	9.72307	+	7.06423i	0.454826	+	0.330451i	0.791498	−	0.611171i	$-0.209301\pi$
$457$	9.72307	+	7.06423i	0.454826	+	0.330451i	−0.336672	+	0.941622i	$0.609301\pi$
$458$	2.81690	−	8.66953i	0.131625	−	0.405100i
$459$	−0.0798140	−	0.245642i	−0.00372540	−	0.0114656i
$460$	−7.11962	+	5.17271i	−0.331954	+	0.241179i
$461$	3.00764			0.140080			0.0700398	−	0.997544i	$-0.477687\pi$
$461$	3.00764			0.140080			0.0700398	+	0.997544i	$0.477687\pi$
$462$	17.0489	−	29.3231i	0.793186	−	1.36424i
$463$	20.2752			0.942270			0.471135	−	0.882061i	$-0.343844\pi$
$463$	20.2752			0.942270			0.471135	+	0.882061i	$0.343844\pi$
$464$	2.59284	−	1.88381i	0.120369	−	0.0874535i
$465$	−8.55003	−	26.3143i	−0.396498	−	1.22030i
$466$	−2.02373	+	6.22840i	−0.0937475	+	0.288525i
$467$	17.3353	+	12.5948i	0.802181	+	0.582819i	0.911553	−	0.411182i	$-0.134884\pi$
$467$	17.3353	+	12.5948i	0.802181	+	0.582819i	−0.109372	+	0.994001i	$0.534884\pi$
$468$	−9.47604	−	6.88474i	−0.438030	−	0.318247i
$469$	−15.6861	+	48.2769i	−0.724317	+	2.22922i
$470$	1.53855	+	4.73517i	0.0709680	+	0.218417i
$471$	−17.5523	+	12.7525i	−0.808765	+	0.587602i
$472$	8.16245			0.375707
$473$	−23.9997	+	10.5980i	−1.10351	+	0.487296i
$474$	30.4005			1.39634
$475$	−1.45094	+	1.05417i	−0.0665737	+	0.0483686i
$476$	−0.134170	−	0.412934i	−0.00614969	−	0.0189268i
$477$	−3.84113	+	11.8218i	−0.175873	+	0.541282i
$478$	−14.3432	−	10.4210i	−0.656043	−	0.476643i
$479$	−21.8499	−	15.8749i	−0.998349	−	0.725343i	−0.0366153	−	0.999329i	$-0.511658\pi$
$479$	−21.8499	−	15.8749i	−0.998349	−	0.725343i	−0.961734	+	0.273987i	$0.911658\pi$
$480$	−1.20062	+	3.69513i	−0.0548005	+	0.168659i
$481$	12.5332	+	38.5732i	0.571465	+	1.75879i
$482$	−6.82981	+	4.96214i	−0.311089	+	0.226020i
$483$	−50.2608			−2.28695
$484$	−5.44193	−	9.55957i	−0.247360	−	0.434526i
$485$	−21.8974			−0.994310
$486$	−12.8666	+	9.34815i	−0.583642	+	0.424041i
$487$	−0.741546	−	2.28224i	−0.0336027	−	0.103418i	0.932848	−	0.360269i	$-0.117315\pi$
$487$	−0.741546	−	2.28224i	−0.0336027	−	0.103418i	−0.966451	+	0.256851i	$0.917315\pi$
$488$	−3.74630	+	11.5299i	−0.169587	+	0.521935i
$489$	−0.719110	−	0.522464i	−0.0325193	−	0.0236266i
$490$	−22.0450	−	16.0166i	−0.995890	−	0.723556i
$491$	−4.09373	+	12.5992i	−0.184747	+	0.568594i	−0.999944	−	0.0105906i	$-0.996629\pi$
$491$	−4.09373	+	12.5992i	−0.184747	+	0.568594i	0.815197	+	0.579184i	$0.196629\pi$
$492$	−2.41667	−	7.43776i	−0.108952	−	0.335320i
$493$	−0.238839	+	0.173527i	−0.0107568	+	0.00781526i
$494$	−6.85893			−0.308598
$495$	9.27777	−	4.09695i	0.417005	−	0.184144i
$496$	7.12135			0.319758
$497$	41.0498	−	29.8244i	1.84133	−	1.33781i
$498$	1.34577	+	4.14186i	0.0603055	+	0.185601i
$499$	9.12099	−	28.0715i	0.408312	−	1.25665i	−0.509787	−	0.860301i	$-0.670276\pi$
$499$	9.12099	−	28.0715i	0.408312	−	1.25665i	0.918098	−	0.396353i	$-0.129724\pi$
$500$	9.84163	+	7.15036i	0.440131	+	0.319774i
$501$	−28.1232	−	20.4327i	−1.25645	−	0.912867i
$502$	6.45354	−	19.8619i	0.288035	−	0.886482i
$503$	9.26332	+	28.5096i	0.413031	+	1.27118i	0.914000	+	0.405713i	$0.132977\pi$
$503$	9.26332	+	28.5096i	0.413031	+	1.27118i	−0.500970	+	0.865465i	$0.667023\pi$
$504$	−6.51200	+	4.73125i	−0.290068	+	0.210747i
$505$	14.8206			0.659508
$506$	−8.19271	+	14.0910i	−0.364211	+	0.626422i
$507$	−73.8680			−3.28059
$508$	−1.86222	+	1.35298i	−0.0826226	+	0.0600289i
$509$	−8.33496	−	25.6524i	−0.369441	−	1.13702i	−0.947153	−	0.320781i	$-0.896055\pi$
$509$	−8.33496	−	25.6524i	−0.369441	−	1.13702i	0.577713	−	0.816240i	$-0.303945\pi$
$510$	0.110595	−	0.340376i	0.00489723	−	0.0150721i
$511$	−22.3869	−	16.2651i	−0.990340	−	0.719524i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−0.866460	+	2.66669i	−0.0382552	+	0.117737i
$514$	−7.99254	−	24.5985i	−0.352536	−	1.08499i
$515$	−7.88376	+	5.72789i	−0.347400	+	0.252401i
$516$	17.1632			0.755568
$517$	6.14958	+	6.87174i	0.270458	+	0.302219i
$518$	27.8720			1.22462
$519$	−33.5479	+	24.3740i	−1.47259	+	1.06990i
$520$	3.79539	+	11.6810i	0.166439	+	0.512247i
$521$	−10.4935	+	32.2955i	−0.459727	+	1.41489i	0.405769	+	0.913976i	$0.367004\pi$
$521$	−10.4935	+	32.2955i	−0.459727	+	1.41489i	−0.865495	+	0.500917i	$0.832996\pi$
$522$	4.42780	+	3.21699i	0.193800	+	0.140804i
$523$	30.0497	+	21.8324i	1.31398	+	0.954665i	0.999986	+	0.00524074i	$0.00166819\pi$
$523$	30.0497	+	21.8324i	1.31398	+	0.954665i	0.313997	+	0.949424i	$0.398332\pi$
$524$	3.10734	−	9.56341i	0.135745	−	0.417780i
$525$	5.66791	+	17.4440i	0.247368	+	0.761320i
$526$	−25.2561	+	18.3496i	−1.10122	+	0.800080i
$527$	−0.655983			−0.0285751
$528$	0.730425	+	7.15900i	0.0317877	+	0.311555i
$529$	1.15247			0.0501074
$530$	10.5448	−	7.66127i	0.458038	−	0.332784i
$531$	4.30740	+	13.2568i	0.186925	+	0.575297i
$532$	−1.45655	+	4.48281i	−0.0631496	+	0.194355i
$533$	−20.0007	−	14.5314i	−0.866326	−	0.629423i
$534$	−16.0276	−	11.6448i	−0.693584	−	0.503918i
$535$	−1.12957	+	3.47645i	−0.0488355	+	0.150300i
$536$	−3.32790	−	10.2422i	−0.143744	−	0.442397i
$537$	−23.0360	+	16.7366i	−0.994075	+	0.722238i
$538$	−21.4948			−0.926707
$539$	−49.3346	−	10.6434i	−2.12499	−	0.458442i
$540$	5.02094			0.216067
$541$	−5.89865	+	4.28562i	−0.253603	+	0.184253i	−0.707322	−	0.706891i	$-0.750097\pi$
$541$	−5.89865	+	4.28562i	−0.253603	+	0.184253i	0.453719	+	0.891145i	$0.350097\pi$
$542$	−1.09670	−	3.37529i	−0.0471072	−	0.144981i
$543$	−8.89530	+	27.3769i	−0.381734	+	1.17486i
$544$	0.0745226	+	0.0541438i	0.00319513	+	0.00232140i
$545$	−4.41284	−	3.20612i	−0.189025	−	0.137335i
$546$	−21.6764	+	66.7131i	−0.927665	+	2.85506i
$547$	7.17891	+	22.0944i	0.306948	+	0.944689i	0.978943	+	0.204134i	$0.0654377\pi$
$547$	7.17891	+	22.0944i	0.306948	+	0.944689i	−0.671995	+	0.740556i	$0.734562\pi$
$548$	−5.56726	+	4.04485i	−0.237821	+	0.172787i
$549$	−20.7030			−0.883582
$550$	5.81446	+	1.25440i	0.247929	+	0.0534880i
$551$	3.20492			0.136534
$552$	8.62667	−	6.26764i	0.367175	−	0.266769i
$553$	−20.4081	−	62.8096i	−0.867840	−	2.67094i
$554$	5.02253	−	15.4577i	0.213387	−	0.656737i
$555$	18.5868	+	13.5041i	0.788964	+	0.573216i
$556$	−3.93869	−	2.86162i	−0.167038	−	0.121360i
$557$	−5.07224	+	15.6107i	−0.214917	+	0.661448i	0.784242	+	0.620455i	$0.213052\pi$
$557$	−5.07224	+	15.6107i	−0.214917	+	0.661448i	−0.999159	+	0.0409929i	$0.986948\pi$
$558$	3.75801	+	11.5660i	0.159089	+	0.489626i
$559$	43.8942	−	31.8910i	1.85653	−	1.34885i
$560$	8.44039			0.356672
$561$	−0.0672831	−	0.659451i	−0.00284070	−	0.0278420i
$562$	−4.48610			−0.189235
$563$	14.7951	−	10.7493i	0.623540	−	0.453028i	−0.230616	−	0.973045i	$-0.574074\pi$
$563$	14.7951	−	10.7493i	0.623540	−	0.453028i	0.854156	+	0.520016i	$0.174074\pi$
$564$	−1.86422	−	5.73748i	−0.0784979	−	0.241592i
$565$	−4.67218	+	14.3795i	−0.196560	+	0.604949i
$566$	−14.2641	−	10.3635i	−0.599564	−	0.435609i
$567$	42.7352	+	31.0489i	1.79471	+	1.30393i
$568$	−3.32653	+	10.2380i	−0.139578	+	0.429577i
$569$	−6.69050	−	20.5912i	−0.280480	−	0.863229i	−0.987717	−	0.156253i	$-0.950059\pi$
$569$	−6.69050	−	20.5912i	−0.280480	−	0.863229i	0.707237	−	0.706977i	$-0.249941\pi$
$570$	−3.14326	+	2.28371i	−0.131657	+	0.0956542i
$571$	19.4212			0.812751			0.406375	−	0.913706i	$-0.366793\pi$
$571$	19.4212			0.812751			0.406375	+	0.913706i	$0.366793\pi$
$572$	15.1702	+	16.9517i	0.634298	+	0.708784i
$573$	−47.2530			−1.97402
$574$	−13.7446	+	9.98606i	−0.573690	+	0.416810i
$575$	−2.72367	−	8.38260i	−0.113585	−	0.349579i
$576$	0.527710	−	1.62412i	0.0219879	−	0.0676718i
$577$	−29.7216	−	21.5940i	−1.23733	−	0.898971i	−0.239910	−	0.970795i	$-0.577118\pi$
$577$	−29.7216	−	21.5940i	−1.23733	−	0.898971i	−0.997417	+	0.0718241i	$0.977118\pi$
$578$	13.7464	+	9.98736i	0.571776	+	0.415419i
$579$	−1.01798	+	3.13302i	−0.0423058	+	0.130204i
$580$	−1.77345	−	5.45811i	−0.0736384	−	0.226636i
$581$	7.65397	−	5.56093i	0.317540	−	0.230706i
$582$	26.5325			1.09981
$583$	12.1342	−	20.8701i	0.502547	−	0.864353i
$584$	5.87074			0.242933
$585$	−16.9686	+	12.3284i	−0.701564	+	0.509716i
$586$	−4.74046	−	14.5896i	−0.195827	−	0.602692i
$587$	−0.442067	+	1.36054i	−0.0182461	+	0.0561556i	−0.959765	−	0.280805i	$-0.909399\pi$
$587$	−0.442067	+	1.36054i	−0.0182461	+	0.0561556i	0.941519	+	0.336960i	$0.109399\pi$
$588$	26.7113	+	19.4069i	1.10156	+	0.800328i
$589$	5.76130	+	4.18583i	0.237390	+	0.172474i
$590$	4.51670	−	13.9010i	0.185950	−	0.572294i
$591$	8.63305	+	26.5698i	0.355116	+	1.09294i
$592$	−4.78389	+	3.47570i	−0.196617	+	0.142850i
$593$	−43.4676			−1.78500			−0.892499	−	0.451049i	$-0.851050\pi$
$593$	−43.4676			−1.78500			−0.892499	+	0.451049i	$0.851050\pi$
$594$	8.50704	−	3.75661i	0.349048	−	0.154135i
$595$	−0.777486			−0.0318738
$596$	1.81184	−	1.31638i	0.0742160	−	0.0539211i
$597$	−6.87490	−	21.1588i	−0.281371	−	0.865971i
$598$	10.4164	−	32.0585i	0.425960	−	1.31097i
$599$	36.3042	+	26.3765i	1.48335	+	1.07772i	0.976458	+	0.215706i	$0.0692054\pi$
$599$	36.3042	+	26.3765i	1.48335	+	1.07772i	0.506891	+	0.862010i	$0.330795\pi$
$600$	−3.14814	−	2.28726i	−0.128522	−	0.0933769i
$601$	1.09693	−	3.37599i	0.0447445	−	0.137709i	−0.926189	−	0.377061i	$-0.876935\pi$
$601$	1.09693	−	3.37599i	0.0447445	−	0.137709i	0.970933	+	0.239351i	$0.0769348\pi$
$602$	−11.5218	−	35.4604i	−0.469593	−	1.44526i
$603$	14.8785	−	10.8099i	0.605899	−	0.440211i
$604$	5.64230			0.229582
$605$	−19.2916	+	3.97802i	−0.784316	+	0.161730i
$606$	−17.9577			−0.729484
$607$	−24.3441	+	17.6870i	−0.988095	+	0.717893i	−0.959503	−	0.281698i	$-0.909102\pi$
$607$	−24.3441	+	17.6870i	−0.988095	+	0.717893i	−0.0285923	+	0.999591i	$0.509102\pi$
$608$	−0.309017	−	0.951057i	−0.0125323	−	0.0385704i
$609$	10.1286	−	31.1726i	0.410431	−	1.26318i
$610$	17.5629	+	12.7602i	0.711101	+	0.516645i
$611$	−15.4285	−	11.2095i	−0.624171	−	0.453487i
$612$	−0.0486100	+	0.149606i	−0.00196494	+	0.00604747i
$613$	12.1716	+	37.4604i	0.491608	+	1.51301i	0.822177	+	0.569231i	$0.192759\pi$
$613$	12.1716	+	37.4604i	0.491608	+	1.51301i	−0.330570	+	0.943782i	$0.607241\pi$
$614$	15.8116	−	11.4878i	0.638104	−	0.463610i
$615$	−14.0041			−0.564698
$616$	14.3007	−	6.31501i	0.576191	−	0.254439i
$617$	−2.17245			−0.0874597			−0.0437299	−	0.999043i	$-0.513924\pi$
$617$	−2.17245			−0.0874597			−0.0437299	+	0.999043i	$0.513924\pi$
$618$	9.55256	−	6.94034i	0.384260	−	0.279182i
$619$	−10.4598	−	32.1920i	−0.420416	−	1.29391i	−0.907316	−	0.420450i	$-0.861872\pi$
$619$	−10.4598	−	32.1920i	−0.420416	−	1.29391i	0.486900	−	0.873458i	$-0.338128\pi$
$620$	3.94061	−	12.1279i	0.158259	−	0.487070i
$621$	−11.1482	−	8.09964i	−0.447362	−	0.325027i
$622$	6.96681	+	5.06168i	0.279344	+	0.202955i
$623$	−13.2995	+	40.9315i	−0.532831	+	1.63989i
$624$	−4.59879	−	14.1536i	−0.184099	−	0.566598i
$625$	10.3685	−	7.53317i	0.414741	−	0.301327i
$626$	−2.89185			−0.115581
$627$	−3.61703	+	6.22108i	−0.144450	+	0.248446i
$628$	−9.99933			−0.399017
$629$	0.440668	−	0.320164i	0.0175706	−	0.0127658i
$630$	4.45408	+	13.7082i	0.177455	+	0.546149i
$631$	−2.56932	+	7.90755i	−0.102283	+	0.314795i	−0.989083	−	0.147358i	$-0.952923\pi$
$631$	−2.56932	+	7.90755i	−0.102283	+	0.314795i	0.886800	+	0.462153i	$0.152923\pi$
$632$	11.3353	+	8.23559i	0.450894	+	0.327594i
$633$	29.9144	+	21.7341i	1.18899	+	0.863852i
$634$	−7.93391	+	24.4181i	−0.315096	+	0.969766i
$635$	1.27372	+	3.92011i	0.0505460	+	0.155565i
$636$	−12.7769	+	9.28298i	−0.506638	+	0.368094i
$637$	104.373			4.13542
$638$	−7.08848	−	7.92088i	−0.280635	−	0.313591i
$639$	−18.3832			−0.727229
$640$	−1.44869	+	1.05254i	−0.0572646	+	0.0416051i
$641$	6.31700	+	19.4417i	0.249506	+	0.767902i	0.994863	+	0.101235i	$0.0322794\pi$
$641$	6.31700	+	19.4417i	0.249506	+	0.767902i	−0.745356	+	0.666666i	$0.767721\pi$
$642$	1.36867	−	4.21233i	0.0540171	−	0.166248i
$643$	−17.2527	−	12.5348i	−0.680381	−	0.494325i	0.193103	−	0.981178i	$-0.438145\pi$
$643$	−17.2527	−	12.5348i	−0.680381	−	0.494325i	−0.873484	+	0.486853i	$0.838145\pi$
$644$	−18.7406	−	13.6158i	−0.738482	−	0.536538i
$645$	9.49727	−	29.2296i	0.373955	−	1.15091i
$646$	0.0284651	+	0.0876066i	0.00111994	+	0.00344683i
$647$	5.86761	−	4.26307i	0.230679	−	0.167598i	−0.466441	−	0.884552i	$-0.654464\pi$
$647$	5.86761	−	4.26307i	0.230679	−	0.167598i	0.697121	+	0.716954i	$0.254464\pi$
$648$	−11.2069			−0.440247
$649$	−2.74784	−	26.9320i	−0.107862	−	1.05717i
$650$	−12.3012			−0.482493
$651$	58.9209	−	42.8085i	2.30929	−	1.67780i
$652$	−0.126595	−	0.389618i	−0.00495783	−	0.0152586i
$653$	6.68692	−	20.5802i	0.261680	−	0.805367i	−0.730760	−	0.682634i	$-0.760834\pi$
$653$	6.68692	−	20.5802i	0.261680	−	0.805367i	0.992440	−	0.122733i	$-0.0391657\pi$
$654$	5.34693	+	3.88477i	0.209082	+	0.151907i
$655$	−14.5674	−	10.5838i	−0.569196	−	0.413545i
$656$	1.11382	−	3.42797i	0.0434872	−	0.133840i
$657$	3.09805	+	9.53481i	0.120866	+	0.371988i
$658$	−10.6026	+	7.70324i	−0.413332	+	0.300304i
$659$	−13.1333			−0.511602			−0.255801	−	0.966729i	$-0.582339\pi$
$659$	−13.1333			−0.511602			−0.255801	+	0.966729i	$0.582339\pi$
$660$	12.5962	+	2.71749i	0.490308	+	0.105778i
$661$	9.99561			0.388784			0.194392	−	0.980924i	$-0.437727\pi$
$661$	9.99561			0.388784			0.194392	+	0.980924i	$0.437727\pi$
$662$	−0.541855	+	0.393681i	−0.0210598	+	0.0153008i
$663$	0.423617	+	1.30376i	0.0164519	+	0.0506338i
$664$	−0.620251	+	1.90894i	−0.0240704	+	0.0740810i
$665$	6.82842	+	4.96114i	0.264795	+	0.192385i
$666$	−8.16947	−	5.93547i	−0.316560	−	0.229995i
$667$	−4.86722	+	14.9798i	−0.188459	+	0.580018i
$668$	−4.95091	−	15.2373i	−0.191557	−	0.589551i
$669$	−10.4298	+	7.57766i	−0.403238	+	0.292969i
$670$	−19.2844			−0.745022
$671$	39.3041	+	8.47941i	1.51732	+	0.327344i
$672$	−10.2270			−0.394516
$673$	−31.4666	+	22.8618i	−1.21295	+	0.881258i	−0.995495	−	0.0948130i	$-0.969775\pi$
$673$	−31.4666	+	22.8618i	−1.21295	+	0.881258i	−0.217452	+	0.976071i	$0.569775\pi$
$674$	8.90772	+	27.4152i	0.343113	+	1.05599i
$675$	−1.55396	+	4.78260i	−0.0598120	+	0.184082i
$676$	−27.5429	−	20.0111i	−1.05934	−	0.769657i
$677$	−7.18134	−	5.21755i	−0.276001	−	0.200527i	0.441170	−	0.897423i	$-0.354564\pi$
$677$	−7.18134	−	5.21755i	−0.276001	−	0.200527i	−0.717171	+	0.696897i	$0.754564\pi$
$678$	5.66116	−	17.4233i	0.217416	−	0.669136i
$679$	−17.8115	−	54.8182i	−0.683543	−	2.10373i
$680$	0.133446	−	0.0969543i	0.00511743	−	0.00371803i
$681$	−34.3826			−1.31754
$682$	−2.39736	−	23.4969i	−0.0917998	−	0.899742i
$683$	15.0170			0.574610			0.287305	−	0.957839i	$-0.407241\pi$
$683$	15.0170			0.574610			0.287305	+	0.957839i	$0.407241\pi$
$684$	1.38156	−	1.00376i	0.0528254	−	0.0383799i
$685$	3.80789	+	11.7195i	0.145492	+	0.447778i
$686$	11.9687	−	36.8360i	0.456968	−	1.40640i
$687$	16.0012	+	11.6255i	0.610482	+	0.443541i
$688$	6.39958	+	4.64956i	0.243982	+	0.177263i
$689$	−15.4277	+	47.4817i	−0.587750	+	1.80891i
$690$	−5.90046	−	18.1598i	−0.224627	−	0.691330i
$691$	11.5883	−	8.41941i	0.440841	−	0.320289i	−0.345128	−	0.938556i	$-0.612165\pi$
$691$	11.5883	−	8.41941i	0.440841	−	0.320289i	0.785969	+	0.618266i	$0.212165\pi$
$692$	−19.1119			−0.726525
$693$	17.8030	+	19.8936i	0.676279	+	0.755695i
$694$	−21.1062			−0.801180
$695$	−7.05293	+	5.12426i	−0.267533	+	0.194374i
$696$	2.14884	+	6.61346i	0.0814517	+	0.250682i
$697$	−0.102599	+	0.315768i	−0.00388622	+	0.0119606i
$698$	5.54733	+	4.03037i	0.209969	+	0.152552i
$699$	−11.4956	−	8.35206i	−0.434805	−	0.315904i
$700$	−2.61227	+	8.03975i	−0.0987346	+	0.303874i
$701$	6.27325	+	19.3071i	0.236937	+	0.729218i	0.996858	+	0.0792031i	$0.0252376\pi$
$701$	6.27325	+	19.3071i	0.236937	+	0.729218i	−0.759921	+	0.650015i	$0.774762\pi$
$702$	−15.5589	+	11.3042i	−0.587235	+	0.426651i
$703$	−5.91321			−0.223021
$704$	−1.66704	+	2.86722i	−0.0628291	+	0.108063i
$705$	−10.8027			−0.406854
$706$	−15.0430	+	10.9294i	−0.566150	+	0.411332i
$707$	12.0552	+	37.1020i	0.453382	+	1.39537i
$708$	−5.47277	+	16.8435i	−0.205679	+	0.633016i
$709$	−4.24482	−	3.08404i	−0.159417	−	0.115824i	0.505217	−	0.862993i	$-0.331413\pi$
$709$	−4.24482	−	3.08404i	−0.159417	−	0.115824i	−0.664634	+	0.747169i	$0.731413\pi$
$710$	15.5950	+	11.3304i	0.585269	+	0.425223i
$711$	−7.39386	+	22.7559i	−0.277291	+	0.853415i
$712$	−2.82156	−	8.68388i	−0.105743	−	0.325442i
$713$	−28.3140	+	20.5713i	−1.06037	+	0.770402i
$714$	0.942061			0.0352558
$715$	37.2638	−	16.4552i	1.39359	−	0.615391i
$716$	−13.1233			−0.490442
$717$	31.1208	−	22.6106i	1.16223	−	0.844408i
$718$	−9.36941	−	28.8361i	−0.349663	−	1.07615i
$719$	5.23852	−	16.1225i	0.195364	−	0.601268i	−0.804608	−	0.593806i	$-0.797625\pi$
$719$	5.23852	−	16.1225i	0.195364	−	0.601268i	0.999972	−	0.00746203i	$-0.00237526\pi$
$720$	−2.47394	−	1.79742i	−0.0921982	−	0.0669859i
$721$	−20.7520	−	15.0772i	−0.772844	−	0.561504i
$722$	0.309017	−	0.951057i	0.0115004	−	0.0353947i
$723$	−5.66028	−	17.4205i	−0.210508	−	0.647877i
$724$	−10.7333	+	7.79816i	−0.398898	+	0.289816i
$725$	5.74790			0.213472
$726$	23.3752	−	4.82007i	0.867534	−	0.178890i
$727$	−27.7361			−1.02867			−0.514337	−	0.857588i	$-0.671962\pi$
$727$	−27.7361			−1.02867			−0.514337	+	0.857588i	$0.671962\pi$
$728$	−26.1552	+	19.0029i	−0.969376	+	0.704293i
$729$	−0.274029	−	0.843374i	−0.0101492	−	0.0312361i
$730$	3.24858	−	9.99810i	0.120235	−	0.370046i
$731$	−0.589497	−	0.428294i	−0.0218033	−	0.0158410i
$732$	−21.2805	−	15.4612i	−0.786551	−	0.571463i
$733$	−9.33566	+	28.7322i	−0.344821	+	1.06125i	0.616859	+	0.787074i	$0.288405\pi$
$733$	−9.33566	+	28.7322i	−0.344821	+	1.06125i	−0.961680	+	0.274175i	$0.911595\pi$
$734$	4.41597	+	13.5910i	0.162997	+	0.501652i
$735$	47.8315	−	34.7516i	1.76429	−	1.28183i
$736$	4.91452			0.181151
$737$	−32.6739	+	14.4284i	−1.20356	+	0.531477i
$738$	6.15523			0.226577
$739$	19.6921	−	14.3071i	0.724384	−	0.526296i	−0.163398	−	0.986560i	$-0.552245\pi$
$739$	19.6921	−	14.3071i	0.724384	−	0.526296i	0.887782	+	0.460264i	$0.152245\pi$
$740$	3.27208	+	10.0704i	0.120284	+	0.370196i
$741$	4.59879	−	14.1536i	0.168941	−	0.519946i
$742$	27.7566	+	20.1663i	1.01898	+	0.740329i
$743$	−31.0815	−	22.5821i	−1.14027	−	0.828455i	−0.153114	−	0.988209i	$-0.548930\pi$
$743$	−31.0815	−	22.5821i	−1.14027	−	0.828455i	−0.987157	+	0.159753i	$0.948930\pi$
$744$	−4.77474	+	14.6951i	−0.175050	+	0.538750i
$745$	−1.23926	−	3.81406i	−0.0454031	−	0.139736i
$746$	−18.6763	+	13.5691i	−0.683788	+	0.496801i
$747$	−3.42766			−0.125412
$748$	0.153560	−	0.264114i	0.00561470	−	0.00965697i
$749$	−9.62180			−0.351573
$750$	−21.3536	+	15.5143i	−0.779724	+	0.566503i
$751$	−4.96528	−	15.2816i	−0.181186	−	0.557632i	0.818676	−	0.574255i	$-0.194708\pi$
$751$	−4.96528	−	15.2816i	−0.181186	−	0.557632i	−0.999862	+	0.0166233i	$0.994708\pi$
$752$	0.859197	−	2.64434i	0.0313317	−	0.0964291i
$753$	36.6587	+	26.6341i	1.33592	+	0.970602i
$754$	17.7841	+	12.9209i	0.647658	+	0.470551i
$755$	3.12217	−	9.60905i	0.113627	−	0.349709i
$756$	4.08407	+	12.5695i	0.148536	+	0.457147i
$757$	20.5061	−	14.8985i	0.745306	−	0.541496i	−0.149062	−	0.988828i	$-0.547626\pi$
$757$	20.5061	−	14.8985i	0.745306	−	0.541496i	0.894368	+	0.447331i	$0.147626\pi$
$758$	−18.1805			−0.660345
$759$	−23.5842	−	26.3537i	−0.856051	−	0.956578i
$760$	−1.79068			−0.0649548
$761$	26.3968	−	19.1784i	0.956885	−	0.695218i	0.00445971	−	0.999990i	$-0.498580\pi$
$761$	26.3968	−	19.1784i	0.956885	−	0.695218i	0.952425	+	0.304772i	$0.0985804\pi$
$762$	−1.54334	−	4.74990i	−0.0559091	−	0.172071i
$763$	4.43679	−	13.6550i	0.160623	−	0.494346i
$764$	−17.6191	−	12.8010i	−0.637435	−	0.463124i
$765$	0.227887	+	0.165569i	0.00823926	+	0.00598617i
$766$	8.73556	−	26.8853i	0.315629	−	0.971405i
$767$	17.3005	+	53.2455i	0.624685	+	1.92258i
$768$	1.75534	−	1.27533i	0.0633405	−	0.0460196i
$769$	−2.15033			−0.0775430			−0.0387715	−	0.999248i	$-0.512344\pi$
$769$	−2.15033			−0.0775430			−0.0387715	+	0.999248i	$0.512344\pi$
$770$	−2.84141	−	27.8490i	−0.102397	−	1.00361i
$771$	56.1186			2.02106
$772$	−1.22832	+	0.892423i	−0.0442080	+	0.0321190i
$773$	−4.62976	−	14.2489i	−0.166521	−	0.512499i	0.832624	−	0.553838i	$-0.186837\pi$
$773$	−4.62976	−	14.2489i	−0.166521	−	0.512499i	−0.999145	+	0.0413396i	$0.986837\pi$
$774$	−4.17435	+	12.8473i	−0.150044	+	0.461788i
$775$	10.3327	+	7.50711i	0.371160	+	0.269663i
$776$	9.89309	+	7.18775i	0.355141	+	0.258025i
$777$	−18.6876	+	57.5147i	−0.670415	+	2.06333i
$778$	−9.06759	−	27.9072i	−0.325089	−	1.00052i
$779$	2.91601	−	2.11860i	0.104477	−	0.0759069i
$780$	−26.6489			−0.954183
$781$	34.9001	+	7.52930i	1.24882	+	0.269419i
$782$	−0.452701			−0.0161885
$783$	7.27012	−	5.28205i	0.259813	−	0.188765i
$784$	4.70236	+	14.4724i	0.167941	+	0.516870i
$785$	−5.53314	+	17.0292i	−0.197486	+	0.607800i
$786$	17.6510	+	12.8242i	0.629590	+	0.457424i
$787$	21.6713	+	15.7451i	0.772499	+	0.561254i	0.902719	−	0.430232i	$-0.141568\pi$
$787$	21.6713	+	15.7451i	0.772499	+	0.561254i	−0.130219	+	0.991485i	$0.541568\pi$
$788$	−3.97887	+	12.2457i	−0.141741	+	0.436235i
$789$	−20.9312	−	64.4197i	−0.745172	−	2.29340i
$790$	20.2979	−	14.7473i	0.722168	−	0.524686i
$791$	−39.7981			−1.41506
$792$	−5.53644	−	1.19442i	−0.196729	−	0.0424420i
$793$	−83.1527			−2.95284
$794$	−1.68680	+	1.22553i	−0.0598623	+	0.0434925i
$795$	8.73915	+	26.8963i	0.309946	+	0.953915i
$796$	3.16856	−	9.75182i	0.112307	−	0.345644i
$797$	10.6588	+	7.74404i	0.377552	+	0.274308i	0.760336	−	0.649530i	$-0.225034\pi$
$797$	10.6588	+	7.74404i	0.377552	+	0.274308i	−0.382783	+	0.923838i	$0.625034\pi$
$798$	−8.27383	−	6.01129i	−0.292890	−	0.212797i
$799$	−0.0791450	+	0.243583i	−0.00279995	+	0.00861735i
$800$	−0.554210	−	1.70568i	−0.0195943	−	0.0603050i
$801$	12.6147	−	9.16513i	0.445719	−	0.323834i
$802$	11.5326			0.407231
$803$	−1.97635	−	19.3705i	−0.0697439	−	0.683570i
$804$	23.3665			0.824072
$805$	−33.5584	+	24.3816i	−1.18278	+	0.859338i
$806$	15.0939	+	46.4542i	0.531659	+	1.63628i
$807$	14.4119	−	44.3552i	0.507322	−	1.56138i
$808$	−6.69584	−	4.86481i	−0.235559	−	0.171143i
$809$	−7.59168	−	5.51568i	−0.266909	−	0.193921i	0.446278	−	0.894894i	$-0.352749\pi$
$809$	−7.59168	−	5.51568i	−0.266909	−	0.193921i	−0.713187	+	0.700973i	$0.752749\pi$
$810$	−6.20133	+	19.0857i	−0.217892	+	0.670604i
$811$	−15.1076	−	46.4963i	−0.530499	−	1.63271i	−0.753179	−	0.657815i	$-0.771481\pi$
$811$	−15.1076	−	46.4963i	−0.530499	−	1.63271i	0.222681	−	0.974891i	$-0.428519\pi$
$812$	12.2214	−	8.87934i	0.428886	−	0.311604i
$813$	7.70033			0.270062
$814$	13.0785	+	14.6143i	0.458402	+	0.512232i
$815$	−0.733587			−0.0256964
$816$	−0.161693	+	0.117477i	−0.00566040	+	0.00411252i
$817$	2.44442	+	7.52315i	0.0855194	+	0.263202i
$818$	−0.226303	+	0.696488i	−0.00791249	+	0.0243521i
$819$	−44.6654	−	32.4513i	−1.56073	−	1.13394i
$820$	−5.22164	−	3.79375i	−0.182348	−	0.132483i
$821$	8.26517	−	25.4376i	0.288456	−	0.887777i	−0.696885	−	0.717183i	$-0.745431\pi$
$821$	8.26517	−	25.4376i	0.288456	−	0.887777i	0.985341	−	0.170594i	$-0.0545688\pi$
$822$	−4.61393	−	14.2002i	−0.160929	−	0.495289i
$823$	28.9371	−	21.0241i	1.00868	−	0.732852i	0.0447519	−	0.998998i	$-0.485750\pi$
$823$	28.9371	−	21.0241i	1.00868	−	0.732852i	0.963933	+	0.266146i	$0.0857503\pi$
$824$	5.44199			0.189581
$825$	−6.48699	+	11.1573i	−0.225848	+	0.388446i
$826$	38.4738			1.33867
$827$	−0.0316430	+	0.0229900i	−0.00110033	+	0.000799439i	−0.588335	−	0.808617i	$-0.700216\pi$
$827$	−0.0316430	+	0.0229900i	−0.00110033	+	0.000799439i	0.587235	+	0.809417i	$0.300216\pi$
$828$	2.59344	+	7.98178i	0.0901282	+	0.277386i
$829$	5.97065	−	18.3758i	0.207369	−	0.638217i	−0.792239	−	0.610211i	$-0.791084\pi$
$829$	5.97065	−	18.3758i	0.207369	−	0.638217i	0.999608	−	0.0280053i	$-0.00891554\pi$
$830$	2.90777	+	2.11262i	0.100930	+	0.0733302i
$831$	28.5300	+	20.7283i	0.989696	+	0.719056i
$832$	2.11952	−	6.52323i	0.0734813	−	0.226152i
$833$	−0.433158	−	1.33312i	−0.0150080	−	0.0461900i
$834$	8.54587	−	6.20894i	0.295919	−	0.214998i
$835$	−28.6894			−0.992837
$836$	−3.03398	+	1.33977i	−0.104932	+	0.0463368i
$837$	19.9677			0.690186
$838$	−10.6916	+	7.76792i	−0.369336	+	0.268338i
$839$	−8.05711	−	24.7972i	−0.278162	−	0.856096i	−0.988365	−	0.152099i	$-0.951397\pi$
$839$	−8.05711	−	24.7972i	−0.278162	−	0.856096i	0.710203	−	0.703997i	$-0.248603\pi$
$840$	−5.65913	+	17.4170i	−0.195258	+	0.600944i
$841$	15.1516	+	11.0083i	0.522471	+	0.379597i
$842$	−8.42666	−	6.12233i	−0.290402	−	0.210989i
$843$	3.00785	−	9.25720i	0.103596	−	0.318835i
$844$	5.26624	+	16.2078i	0.181271	+	0.557896i
$845$	−49.3205	+	35.8335i	−1.69668	+	1.23271i
$846$	4.74814			0.163244
$847$	−25.6506	−	45.0591i	−0.881364	−	1.54825i
$848$	−7.27887			−0.249957
$849$	30.9491	−	22.4859i	1.06217	−	0.771713i
$850$	0.0510510	+	0.157119i	0.00175104	+	0.00538913i
$851$	8.98021	−	27.6382i	0.307838	−	0.947427i
$852$	−18.8960	−	13.7288i	−0.647368	−	0.470340i
$853$	4.32562	+	3.14275i	0.148106	+	0.107606i	0.659371	−	0.751818i	$-0.270823\pi$
$853$	4.32562	+	3.14275i	0.148106	+	0.107606i	−0.511264	+	0.859423i	$0.670823\pi$
$854$	−17.6582	+	54.3464i	−0.604251	+	1.85969i
$855$	−0.944960	−	2.90829i	−0.0323170	−	0.0994614i
$856$	1.65147	−	1.19986i	0.0564459	−	0.0410104i
$857$	34.3568			1.17361			0.586803	−	0.809730i	$-0.300386\pi$
$857$	34.3568			1.17361			0.586803	+	0.809730i	$0.300386\pi$
$858$	−45.1516	+	19.9384i	−1.54145	+	0.680686i
$859$	18.8263			0.642346			0.321173	−	0.947021i	$-0.395923\pi$
$859$	18.8263			0.642346			0.321173	+	0.947021i	$0.395923\pi$
$860$	11.4596	−	8.32589i	0.390769	−	0.283910i
$861$	−11.3910	−	35.0579i	−0.388205	−	1.19477i
$862$	−3.49100	+	10.7442i	−0.118904	+	0.365948i
$863$	22.8506	+	16.6019i	0.777842	+	0.565135i	0.904331	−	0.426833i	$-0.140371\pi$
$863$	22.8506	+	16.6019i	0.777842	+	0.565135i	−0.126489	+	0.991968i	$0.540371\pi$
$864$	−2.26842	−	1.64811i	−0.0771733	−	0.0560697i
$865$	−10.5756	+	32.5483i	−0.359581	+	1.10668i
$866$	−6.86876	−	21.1399i	−0.233410	−	0.718362i
$867$	−29.8260	+	21.6698i	−1.01294	+	0.735946i
$868$	33.5666			1.13932
$869$	23.3573	−	40.1733i	0.792342	−	1.36278i
$870$	12.4520			0.422164
$871$	59.7589	−	43.4173i	2.02485	−	1.47114i
$872$	0.941293	+	2.89700i	0.0318762	+	0.0981049i
$873$	−6.45312	+	19.8606i	−0.218405	+	0.672181i
$874$	3.97593	+	2.88868i	0.134488	+	0.0977111i
$875$	46.3886	+	33.7033i	1.56822	+	1.13938i
$876$	−3.93623	+	12.1145i	−0.132993	+	0.409310i
$877$	−3.36165	−	10.3461i	−0.113515	−	0.349363i	0.878120	−	0.478441i	$-0.158798\pi$
$877$	−3.36165	−	10.3461i	−0.113515	−	0.349363i	−0.991634	+	0.129079i	$0.958798\pi$
$878$	−20.4305	+	14.8436i	−0.689495	+	0.500947i
$879$	33.2845			1.12266
$880$	3.96053	+	4.42562i	0.133510	+	0.149188i
$881$	29.2426			0.985208			0.492604	−	0.870254i	$-0.336045\pi$
$881$	29.2426			0.985208			0.492604	+	0.870254i	$0.336045\pi$
$882$	−21.0234	+	15.2744i	−0.707896	+	0.514317i
$883$	−0.392996	−	1.20952i	−0.0132254	−	0.0407035i	0.944226	−	0.329298i	$-0.106812\pi$
$883$	−0.392996	−	1.20952i	−0.0132254	−	0.0407035i	−0.957451	+	0.288595i	$0.906812\pi$
$884$	−0.195240	+	0.600887i	−0.00656663	+	0.0202100i
$885$	25.6567	+	18.6407i	0.862441	+	0.626600i
$886$	3.37390	+	2.45128i	0.113348	+	0.0823524i
$887$	4.75848	−	14.6451i	0.159774	−	0.491735i	−0.838839	−	0.544380i	$-0.816765\pi$
$887$	4.75848	−	14.6451i	0.159774	−	0.491735i	0.998613	+	0.0526449i	$0.0167651\pi$
$888$	−3.96470	−	12.2021i	−0.133047	−	0.409475i
$889$	−8.77759	+	6.37729i	−0.294391	+	0.213887i
$890$	−16.3503			−0.548063
$891$	3.77272	+	36.9770i	0.126391	+	1.23878i
$892$	−5.94172			−0.198943
$893$	2.24941	−	1.63429i	0.0752736	−	0.0546894i
$894$	1.50158	+	4.62140i	0.0502205	+	0.154563i
$895$	−7.26181	+	22.3496i	−0.242736	+	0.747063i
$896$	−3.81331	−	2.77053i	−0.127394	−	0.0925569i
$897$	59.1697	+	42.9893i	1.97562	+	1.43537i
$898$	−2.64964	+	8.15476i	−0.0884198	+	0.272128i
$899$	−7.05282	−	21.7063i	−0.235225	−	0.723947i
$900$	2.47778	−	1.80021i	0.0825926	−	0.0600070i
$901$	0.670493			0.0223374
$902$	−11.6855	−	2.52102i	−0.389086	−	0.0839409i
$903$	80.8989			2.69215
$904$	6.83087	−	4.96292i	0.227191	−	0.165064i
$905$	7.34132	+	22.5943i	0.244034	+	0.751059i
$906$	−3.78306	+	11.6431i	−0.125684	+	0.386814i
$907$	12.6745	+	9.20857i	0.420850	+	0.305766i	0.777980	−	0.628289i	$-0.216245\pi$
$907$	12.6745	+	9.20857i	0.420850	+	0.305766i	−0.357130	+	0.934055i	$0.616245\pi$
$908$	−12.8201	−	9.31434i	−0.425450	−	0.309107i
$909$	4.36760	−	13.4421i	0.144864	−	0.445846i
$910$	17.8896	+	55.0586i	0.593035	+	1.82517i
$911$	−23.4606	+	17.0451i	−0.777285	+	0.564730i	−0.904163	−	0.427188i	$-0.859504\pi$
$911$	−23.4606	+	17.0451i	−0.777285	+	0.564730i	0.126878	+	0.991918i	$0.459504\pi$
$912$	2.16972			0.0718468
$913$	6.50733	+	1.40388i	0.215361	+	0.0464617i
$914$	−12.0184			−0.397533
$915$	−38.1066	+	27.6861i	−1.25977	+	0.915274i
$916$	2.81690	+	8.66953i	0.0930730	+	0.286449i
$917$	14.6465	−	45.0772i	0.483669	−	1.48858i
$918$	0.208956	+	0.151815i	0.00689657	+	0.00501065i
$919$	−2.11791	−	1.53875i	−0.0698634	−	0.0507587i	0.552305	−	0.833642i	$-0.313748\pi$
$919$	−2.11791	−	1.53875i	−0.0698634	−	0.0507587i	−0.622169	+	0.782883i	$0.713748\pi$
$920$	2.71945	−	8.36961i	0.0896577	−	0.275938i
$921$	13.1040	+	40.3301i	0.431793	+	1.32892i
$922$	−2.43323	+	1.76785i	−0.0801342	+	0.0582209i
$923$	−73.8355			−2.43032
$924$	3.44287	+	33.7440i	0.113262	+	1.11010i
$925$	−10.6051			−0.348694
$926$	−16.4030	+	11.9175i	−0.539036	+	0.391633i
$927$	2.87179	+	8.83846i	0.0943220	+	0.290293i
$928$	−0.990376	+	3.04806i	−0.0325107	+	0.100058i
$929$	38.3315	+	27.8494i	1.25761	+	0.913710i	0.998638	−	0.0521736i	$-0.0166149\pi$
$929$	38.3315	+	27.8494i	1.25761	+	0.913710i	0.258976	+	0.965884i	$0.416615\pi$
$930$	22.3843	+	16.2631i	0.734009	+	0.533289i
$931$	−4.70236	+	14.4724i	−0.154114	+	0.474313i
$932$	−2.02373	−	6.22840i	−0.0662895	−	0.204018i
$933$	−15.1161	+	10.9825i	−0.494878	+	0.359550i
$934$	−21.4276			−0.701132
$935$	−0.364824	−	0.407666i	−0.0119310	−	0.0133321i
$936$	11.7130			0.382852
$937$	−3.86671	+	2.80933i	−0.126320	+	0.0917767i	−0.649151	−	0.760659i	$-0.724876\pi$
$937$	−3.86671	+	2.80933i	−0.126320	+	0.0917767i	0.522831	+	0.852436i	$0.324876\pi$
$938$	−15.6861	−	48.2769i	−0.512169	−	1.57630i
$939$	1.93893	−	5.96741i	0.0632746	−	0.194739i
$940$	−4.02797	−	2.92649i	−0.131378	−	0.0954517i
$941$	−21.8342	−	15.8634i	−0.711773	−	0.517133i	0.171972	−	0.985102i	$-0.444986\pi$
$941$	−21.8342	−	15.8634i	−0.711773	−	0.517133i	−0.883745	+	0.467968i	$0.844986\pi$
$942$	6.70437	−	20.6339i	0.218440	−	0.672289i
$943$	5.47387	+	16.8468i	0.178254	+	0.548608i
$944$	−6.60356	+	4.79777i	−0.214928	+	0.156154i
$945$	23.6662			0.769862
$946$	13.1868	−	22.6806i	0.428741	−	0.737411i
$947$	−7.94684			−0.258238			−0.129119	−	0.991629i	$-0.541215\pi$
$947$	−7.94684			−0.258238			−0.129119	+	0.991629i	$0.541215\pi$
$948$	−24.5945	+	17.8690i	−0.798792	+	0.580357i
$949$	12.4432	+	38.2962i	0.403923	+	1.24315i
$950$	0.554210	−	1.70568i	0.0179809	−	0.0553396i
$951$	−45.0679	−	32.7437i	−1.46143	−	1.06179i
$952$	0.351263	+	0.255207i	0.0113845	+	0.00827132i
$953$	−8.22934	+	25.3273i	−0.266574	+	0.820432i	0.724752	+	0.689010i	$0.241954\pi$
$953$	−8.22934	+	25.3273i	−0.266574	+	0.820432i	−0.991327	+	0.131422i	$0.958046\pi$
$954$	−3.84113	−	11.8218i	−0.124361	−	0.382744i
$955$	−31.5501	+	22.9225i	−1.02094	+	0.741755i
$956$	17.7292			0.573403
$957$	21.0977	−	9.31648i	0.681991	−	0.301159i
$958$	27.0080			0.872589
$959$	−26.2413	+	19.0654i	−0.847376	+	0.615655i
$960$	−1.20062	−	3.69513i	−0.0387498	−	0.119260i
$961$	6.09186	−	18.7488i	0.196512	−	0.604801i
$962$	−32.8123	−	23.8396i	−1.05791	−	0.768618i
$963$	2.82022	+	2.04901i	0.0908802	+	0.0660283i
$964$	2.60875	−	8.02892i	0.0840223	−	0.258594i
$965$	0.840142	+	2.58569i	0.0270451	+	0.0832364i
$966$	40.6619	−	29.5426i	1.30827	−	0.950517i
$967$	−37.0849			−1.19257			−0.596284	−	0.802773i	$-0.703357\pi$
$967$	−37.0849			−1.19257			−0.596284	+	0.802773i	$0.703357\pi$
$968$	10.0216	+	4.53517i	0.322106	+	0.145766i
$969$	−0.199864			−0.00642056
$970$	17.7154	−	12.8710i	0.568806	−	0.413262i
$971$	1.65904	+	5.10601i	0.0532413	+	0.163860i	0.974142	−	0.225938i	$-0.0725448\pi$
$971$	1.65904	+	5.10601i	0.0532413	+	0.163860i	−0.920900	+	0.389798i	$0.872545\pi$
$972$	4.91461	−	15.1256i	0.157636	−	0.485155i
$973$	−18.5650	−	13.4883i	−0.595168	−	0.432415i
$974$	1.94139	+	1.41050i	0.0622063	+	0.0451955i
$975$	8.24774	−	25.3839i	0.264139	−	0.812936i
$976$	−3.74630	−	11.5299i	−0.119916	−	0.369064i
$977$	6.98946	−	5.07814i	0.223613	−	0.162464i	−0.470339	−	0.882486i	$-0.655868\pi$
$977$	6.98946	−	5.07814i	0.223613	−	0.162464i	0.693951	+	0.720022i	$0.255868\pi$
$978$	0.888869			0.0284229
$979$	−27.7025	+	12.2331i	−0.885377	+	0.390972i
$980$	27.2491			0.870440
$981$	−4.20836	+	3.05755i	−0.134363	+	0.0976202i
$982$	−4.09373	−	12.5992i	−0.130636	−	0.402056i
$983$	−10.1154	+	31.1319i	−0.322630	+	0.992952i	0.649870	+	0.760046i	$0.274824\pi$
$983$	−10.1154	+	31.1319i	−0.322630	+	0.992952i	−0.972499	+	0.232906i	$0.925176\pi$
$984$	6.32694	+	4.59679i	0.201695	+	0.146540i
$985$	18.6532	+	13.5523i	0.594341	+	0.431814i
$986$	0.0912285	−	0.280772i	0.00290531	−	0.00894161i
$987$	−8.78702	−	27.0437i	−0.279694	−	0.860810i
$988$	5.54899	−	4.03158i	0.176537	−	0.128262i
$989$	−38.8753			−1.23616
$990$	−5.09775	+	8.76784i	−0.162017	+	0.278660i
$991$	33.6052			1.06750			0.533752	−	0.845641i	$-0.320782\pi$
$991$	33.6052			1.06750			0.533752	+	0.845641i	$0.320782\pi$
$992$	−5.76130	+	4.18583i	−0.182921	+	0.132900i
$993$	−0.449069	−	1.38209i	−0.0142508	−	0.0438593i
$994$	−15.6796	+	48.2569i	−0.497327	+	1.53062i
$995$	−14.8544	−	10.7924i	−0.470917	−	0.342141i
$996$	−3.52328	−	2.55981i	−0.111639	−	0.0811108i
$997$	−2.91409	+	8.96865i	−0.0922902	+	0.284040i	−0.986538	−	0.163532i	$-0.947711\pi$
$997$	−2.91409	+	8.96865i	−0.0922902	+	0.284040i	0.894248	+	0.447572i	$0.147711\pi$
$998$	9.12099	+	28.0715i	0.288720	+	0.888588i
$999$	−13.4137	+	9.74559i	−0.424389	+	0.308337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.f.267.2	yes	16
11.2	odd	10		4598.2.a.bx.1.3		8
11.4	even	5	inner	418.2.f.f.191.2	✓	16
11.9	even	5		4598.2.a.ca.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.f.191.2	✓	16	11.4	even	5	inner
418.2.f.f.267.2	yes	16	1.1	even	1	trivial
4598.2.a.bx.1.3		8	11.2	odd	10
4598.2.a.ca.1.3		8	11.9	even	5

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.670482 - 2.06353i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.44869 - 1.05254i) q^{5} +(1.75534 + 1.27533i) q^{6} +(1.45655 - 4.48281i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.38156 + 1.00376i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.670482 - 2.06353i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.44869 - 1.05254i) q^{5} +(1.75534 + 1.27533i) q^{6} +(1.45655 - 4.48281i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.38156 + 1.00376i) q^{9} +1.79068 q^{10} +(3.03398 - 1.33977i) q^{11} -2.16972 q^{12} +(-5.54899 + 4.03158i) q^{13} +(1.45655 + 4.48281i) q^{14} +(-1.20062 + 3.69513i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.0745226 + 0.0541438i) q^{17} +(0.527710 - 1.62412i) q^{18} +(-0.309017 - 0.951057i) q^{19} +(-1.44869 + 1.05254i) q^{20} -10.2270 q^{21} +(-1.66704 + 2.86722i) q^{22} +4.91452 q^{23} +(1.75534 - 1.27533i) q^{24} +(-0.554210 - 1.70568i) q^{25} +(2.11952 - 6.52323i) q^{26} +(-2.26842 - 1.64811i) q^{27} +(-3.81331 - 2.77053i) q^{28} +(-0.990376 + 3.04806i) q^{29} +(-1.20062 - 3.69513i) q^{30} +(-5.76130 + 4.18583i) q^{31} +1.00000 q^{32} +(-4.79888 - 5.36242i) q^{33} -0.0921150 q^{34} +(-6.82842 + 4.96114i) q^{35} +(0.527710 + 1.62412i) q^{36} +(1.82728 - 5.62380i) q^{37} +(0.809017 + 0.587785i) q^{38} +(12.0398 + 8.74741i) q^{39} +(0.553351 - 1.70304i) q^{40} +(1.11382 + 3.42797i) q^{41} +(8.27383 - 6.01129i) q^{42} -7.91031 q^{43} +(-0.336644 - 3.29950i) q^{44} +3.05796 q^{45} +(-3.97593 + 2.88868i) q^{46} +(0.859197 + 2.64434i) q^{47} +(-0.670482 + 2.06353i) q^{48} +(-12.3109 - 8.94442i) q^{49} +(1.45094 + 1.05417i) q^{50} +(0.0617614 - 0.190082i) q^{51} +(2.11952 + 6.52323i) q^{52} +(5.88873 - 4.27841i) q^{53} +2.80392 q^{54} +(-5.80545 - 1.25246i) q^{55} +4.71351 q^{56} +(-1.75534 + 1.27533i) q^{57} +(-0.990376 - 3.04806i) q^{58} +(2.52234 - 7.76295i) q^{59} +(3.14326 + 2.28371i) q^{60} +(9.80794 + 7.12588i) q^{61} +(2.20062 - 6.77281i) q^{62} +(2.48736 + 7.65532i) q^{63} +(-0.809017 + 0.587785i) q^{64} +12.2822 q^{65} +(7.03432 + 1.51758i) q^{66} -10.7693 q^{67} +(0.0745226 - 0.0541438i) q^{68} +(-3.29509 - 10.1413i) q^{69} +(2.60822 - 8.02729i) q^{70} +(8.70896 + 6.32743i) q^{71} +(-1.38156 - 1.00376i) q^{72} +(1.81416 - 5.58341i) q^{73} +(1.82728 + 5.62380i) q^{74} +(-3.14814 + 2.28726i) q^{75} -1.00000 q^{76} +(-1.58678 - 15.5522i) q^{77} -14.8820 q^{78} +(11.3353 - 8.23559i) q^{79} +(0.553351 + 1.70304i) q^{80} +(-3.46311 + 10.6584i) q^{81} +(-2.91601 - 2.11860i) q^{82} +(1.62384 + 1.17979i) q^{83} +(-3.16032 + 9.72647i) q^{84} +(-0.0509719 - 0.156875i) q^{85} +(6.39958 - 4.64956i) q^{86} +6.95380 q^{87} +(2.21175 + 2.47147i) q^{88} -9.13077 q^{89} +(-2.47394 + 1.79742i) q^{90} +(9.99040 + 30.7473i) q^{91} +(1.51867 - 4.67398i) q^{92} +(12.5004 + 9.08209i) q^{93} +(-2.24941 - 1.63429i) q^{94} +(-0.553351 + 1.70304i) q^{95} +(-0.670482 - 2.06353i) q^{96} +(9.89309 - 7.18775i) q^{97} +15.2172 q^{98} +(-2.84682 + 4.89637i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{7} - 4 q^{8} - 20 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^7 - 4 * q^8 - 20 * q^9	\( 16 q - 4 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{7} - 4 q^{8} - 20 q^{9} + 4 q^{10} + 2 q^{11} - 14 q^{13} + 6 q^{14} - 10 q^{15} - 4 q^{16} + 8 q^{17} + 4 q^{19} + 4 q^{20} + 28 q^{21} + 2 q^{22} + 24 q^{23} - 4 q^{26} - 18 q^{27} - 14 q^{28} - 22 q^{29} - 10 q^{30} - 24 q^{31} + 16 q^{32} + 2 q^{33} + 8 q^{34} - 20 q^{35} + 6 q^{37} + 4 q^{38} + 72 q^{39} - 6 q^{40} - 14 q^{41} - 22 q^{42} + 56 q^{43} + 12 q^{44} - 56 q^{45} + 4 q^{46} - 38 q^{47} - 36 q^{49} + 56 q^{51} - 4 q^{52} + 22 q^{53} - 48 q^{54} - 6 q^{55} + 16 q^{56} - 22 q^{58} - 28 q^{59} + 12 q^{61} + 26 q^{62} - 20 q^{63} - 4 q^{64} - 32 q^{65} + 12 q^{66} - 44 q^{67} + 8 q^{68} + 64 q^{69} - 20 q^{70} + 16 q^{71} - 20 q^{72} + 12 q^{73} + 6 q^{74} + 32 q^{75} - 16 q^{76} - 12 q^{77} - 8 q^{78} + 48 q^{79} - 6 q^{80} - 64 q^{81} + 6 q^{82} + 14 q^{83} + 8 q^{84} + 6 q^{85} - 14 q^{86} + 84 q^{87} - 8 q^{88} - 56 q^{89} + 34 q^{90} + 26 q^{91} - 16 q^{92} - 46 q^{93} + 32 q^{94} + 6 q^{95} - 24 q^{97} + 64 q^{98} - 56 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^7 - 4 * q^8 - 20 * q^9 + 4 * q^10 + 2 * q^11 - 14 * q^13 + 6 * q^14 - 10 * q^15 - 4 * q^16 + 8 * q^17 + 4 * q^19 + 4 * q^20 + 28 * q^21 + 2 * q^22 + 24 * q^23 - 4 * q^26 - 18 * q^27 - 14 * q^28 - 22 * q^29 - 10 * q^30 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 8 * q^34 - 20 * q^35 + 6 * q^37 + 4 * q^38 + 72 * q^39 - 6 * q^40 - 14 * q^41 - 22 * q^42 + 56 * q^43 + 12 * q^44 - 56 * q^45 + 4 * q^46 - 38 * q^47 - 36 * q^49 + 56 * q^51 - 4 * q^52 + 22 * q^53 - 48 * q^54 - 6 * q^55 + 16 * q^56 - 22 * q^58 - 28 * q^59 + 12 * q^61 + 26 * q^62 - 20 * q^63 - 4 * q^64 - 32 * q^65 + 12 * q^66 - 44 * q^67 + 8 * q^68 + 64 * q^69 - 20 * q^70 + 16 * q^71 - 20 * q^72 + 12 * q^73 + 6 * q^74 + 32 * q^75 - 16 * q^76 - 12 * q^77 - 8 * q^78 + 48 * q^79 - 6 * q^80 - 64 * q^81 + 6 * q^82 + 14 * q^83 + 8 * q^84 + 6 * q^85 - 14 * q^86 + 84 * q^87 - 8 * q^88 - 56 * q^89 + 34 * q^90 + 26 * q^91 - 16 * q^92 - 46 * q^93 + 32 * q^94 + 6 * q^95 - 24 * q^97 + 64 * q^98 - 56 * q^99

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