LMFDB - Embedded newform 560.2.bd.a.141.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(141,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))

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

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

chi := DirichletCharacter("560.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bd (of order $4$, degree $2$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			141.4
Character	$\chi$	$=$	560.141
Dual form			560.2.bd.a.421.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37680 + 0.323129i) q^{2} +(-1.67958 - 1.67958i) q^{3} +(1.79118 - 0.889770i) q^{4} +(0.707107 - 0.707107i) q^{5} +(2.85517 + 1.76973i) q^{6} -1.00000i q^{7} +(-2.17859 + 1.80382i) q^{8} +2.64195i q^{9} +O(q^{10})$	\(q+(-1.37680 + 0.323129i) q^{2} +(-1.67958 - 1.67958i) q^{3} +(1.79118 - 0.889770i) q^{4} +(0.707107 - 0.707107i) q^{5} +(2.85517 + 1.76973i) q^{6} -1.00000i q^{7} +(-2.17859 + 1.80382i) q^{8} +2.64195i q^{9} +(-0.745060 + 1.20203i) q^{10} +(-4.03337 + 4.03337i) q^{11} +(-4.50285 - 1.51398i) q^{12} +(-4.75317 - 4.75317i) q^{13} +(0.323129 + 1.37680i) q^{14} -2.37528 q^{15} +(2.41662 - 3.18747i) q^{16} +4.01138 q^{17} +(-0.853692 - 3.63745i) q^{18} +(1.17869 + 1.17869i) q^{19} +(0.637389 - 1.89571i) q^{20} +(-1.67958 + 1.67958i) q^{21} +(4.24986 - 6.85646i) q^{22} -0.610935i q^{23} +(6.68875 + 0.629448i) q^{24} -1.00000i q^{25} +(8.08006 + 5.00829i) q^{26} +(-0.601365 + 0.601365i) q^{27} +(-0.889770 - 1.79118i) q^{28} +(2.42606 + 2.42606i) q^{29} +(3.27029 - 0.767522i) q^{30} -8.63834 q^{31} +(-2.29724 + 5.16940i) q^{32} +13.5487 q^{33} +(-5.52289 + 1.29619i) q^{34} +(-0.707107 - 0.707107i) q^{35} +(2.35073 + 4.73220i) q^{36} +(-1.14755 + 1.14755i) q^{37} +(-2.00369 - 1.24196i) q^{38} +15.9666i q^{39} +(-0.264999 + 2.81599i) q^{40} -1.24783i q^{41} +(1.76973 - 2.85517i) q^{42} +(-8.70723 + 8.70723i) q^{43} +(-3.63570 + 10.8132i) q^{44} +(1.86814 + 1.86814i) q^{45} +(0.197411 + 0.841137i) q^{46} +7.92976 q^{47} +(-9.41249 + 1.29470i) q^{48} -1.00000 q^{49} +(0.323129 + 1.37680i) q^{50} +(-6.73743 - 6.73743i) q^{51} +(-12.7430 - 4.28453i) q^{52} +(-5.64673 + 5.64673i) q^{53} +(0.633643 - 1.02228i) q^{54} +5.70405i q^{55} +(1.80382 + 2.17859i) q^{56} -3.95940i q^{57} +(-4.12414 - 2.55628i) q^{58} +(-1.23973 + 1.23973i) q^{59} +(-4.25454 + 2.11345i) q^{60} +(5.71963 + 5.71963i) q^{61} +(11.8933 - 2.79130i) q^{62} +2.64195 q^{63} +(1.49247 - 7.85955i) q^{64} -6.72199 q^{65} +(-18.6539 + 4.37798i) q^{66} +(2.38301 + 2.38301i) q^{67} +(7.18509 - 3.56921i) q^{68} +(-1.02611 + 1.02611i) q^{69} +(1.20203 + 0.745060i) q^{70} -1.57667i q^{71} +(-4.76561 - 5.75572i) q^{72} +1.85964i q^{73} +(1.20914 - 1.95075i) q^{74} +(-1.67958 + 1.67958i) q^{75} +(3.16001 + 1.06248i) q^{76} +(4.03337 + 4.03337i) q^{77} +(-5.15928 - 21.9829i) q^{78} +3.14874 q^{79} +(-0.545075 - 3.96269i) q^{80} +9.94594 q^{81} +(0.403211 + 1.71802i) q^{82} +(-6.01779 - 6.01779i) q^{83} +(-1.51398 + 4.50285i) q^{84} +(2.83648 - 2.83648i) q^{85} +(9.17458 - 14.8017i) q^{86} -8.14951i q^{87} +(1.51157 - 16.0625i) q^{88} +18.0907i q^{89} +(-3.17572 - 1.96842i) q^{90} +(-4.75317 + 4.75317i) q^{91} +(-0.543592 - 1.09429i) q^{92} +(14.5087 + 14.5087i) q^{93} +(-10.9177 + 2.56234i) q^{94} +1.66692 q^{95} +(12.5408 - 4.82400i) q^{96} -10.6607 q^{97} +(1.37680 - 0.323129i) q^{98} +(-10.6560 - 10.6560i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 12 q^{4} + 12 q^{6}+O(q^{10}) $ 44 * q + 12 * q^4 + 12 * q^6	$ 44 q + 12 q^{4} + 12 q^{6} - 4 q^{10} + 12 q^{11} - 16 q^{12} + 4 q^{14} + 8 q^{15} - 8 q^{16} - 20 q^{18} + 8 q^{19} - 36 q^{22} + 12 q^{24} + 44 q^{26} - 24 q^{27} - 4 q^{28} + 12 q^{29} - 40 q^{32} - 16 q^{34} + 4 q^{36} + 28 q^{37} - 16 q^{38} + 4 q^{42} - 44 q^{43} - 32 q^{44} - 16 q^{46} - 32 q^{48} - 44 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 12 q^{53} - 80 q^{54} + 8 q^{56} + 4 q^{58} + 24 q^{59} - 16 q^{61} + 28 q^{63} + 72 q^{64} - 40 q^{65} - 20 q^{66} - 28 q^{67} + 56 q^{68} + 40 q^{69} + 12 q^{72} + 24 q^{74} - 12 q^{77} + 84 q^{78} - 16 q^{79} + 20 q^{81} + 48 q^{82} + 16 q^{85} - 64 q^{86} + 28 q^{88} - 36 q^{90} - 16 q^{92} + 88 q^{93} + 96 q^{94} - 32 q^{95} + 48 q^{96} + 28 q^{99}+O(q^{100}) $ 44 * q + 12 * q^4 + 12 * q^6 - 4 * q^10 + 12 * q^11 - 16 * q^12 + 4 * q^14 + 8 * q^15 - 8 * q^16 - 20 * q^18 + 8 * q^19 - 36 * q^22 + 12 * q^24 + 44 * q^26 - 24 * q^27 - 4 * q^28 + 12 * q^29 - 40 * q^32 - 16 * q^34 + 4 * q^36 + 28 * q^37 - 16 * q^38 + 4 * q^42 - 44 * q^43 - 32 * q^44 - 16 * q^46 - 32 * q^48 - 44 * q^49 + 4 * q^50 - 8 * q^51 + 16 * q^52 - 12 * q^53 - 80 * q^54 + 8 * q^56 + 4 * q^58 + 24 * q^59 - 16 * q^61 + 28 * q^63 + 72 * q^64 - 40 * q^65 - 20 * q^66 - 28 * q^67 + 56 * q^68 + 40 * q^69 + 12 * q^72 + 24 * q^74 - 12 * q^77 + 84 * q^78 - 16 * q^79 + 20 * q^81 + 48 * q^82 + 16 * q^85 - 64 * q^86 + 28 * q^88 - 36 * q^90 - 16 * q^92 + 88 * q^93 + 96 * q^94 - 32 * q^95 + 48 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.37680	+	0.323129i	−0.973547	+	0.228487i
$2$	−1.37680	+	0.323129i	−0.973547	+	0.228487i
$3$	−1.67958	−	1.67958i	−0.969704	−	0.969704i	0.0298505	−	0.999554i	$-0.490497\pi$
$3$	−1.67958	−	1.67958i	−0.969704	−	0.969704i	−0.999554	+	0.0298505i	$0.990497\pi$
$4$	1.79118	−	0.889770i	0.895588	−	0.444885i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	2.85517	+	1.76973i	1.16562	+	0.722488i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−2.17859	+	1.80382i	−0.770246	+	0.637747i
$9$			2.64195i			0.880651i
$10$	−0.745060	+	1.20203i	−0.235609	+	0.380116i
$11$	−4.03337	+	4.03337i	−1.21611	+	1.21611i	−0.247122	+	0.968984i	$0.579485\pi$
$11$	−4.03337	+	4.03337i	−1.21611	+	1.21611i	−0.968984	+	0.247122i	$0.920515\pi$
$12$	−4.50285	−	1.51398i	−1.29986	−	0.437048i
$13$	−4.75317	−	4.75317i	−1.31829	−	1.31829i	−0.915128	−	0.403163i	$-0.867911\pi$
$13$	−4.75317	−	4.75317i	−1.31829	−	1.31829i	−0.403163	−	0.915128i	$-0.632089\pi$
$14$	0.323129	+	1.37680i	0.0863599	+	0.367966i
$15$	−2.37528			−0.613295
$16$	2.41662	−	3.18747i	0.604154	−	0.796867i
$17$	4.01138			0.972903			0.486452	−	0.873707i	$-0.338291\pi$
$17$	4.01138			0.972903			0.486452	+	0.873707i	$0.338291\pi$
$18$	−0.853692	−	3.63745i	−0.201217	−	0.857356i
$19$	1.17869	+	1.17869i	0.270410	+	0.270410i	0.829265	−	0.558855i	$-0.188759\pi$
$19$	1.17869	+	1.17869i	0.270410	+	0.270410i	−0.558855	+	0.829265i	$0.688759\pi$
$20$	0.637389	−	1.89571i	0.142525	−	0.423895i
$21$	−1.67958	+	1.67958i	−0.366514	+	0.366514i
$22$	4.24986	−	6.85646i	0.906073	−	1.46180i
$23$		−	0.610935i		−	0.127389i	−0.997969	−	0.0636944i	$-0.979712\pi$
$23$		−	0.610935i		−	0.127389i	0.997969	−	0.0636944i	$-0.0202883\pi$
$24$	6.68875	+	0.629448i	1.36534	+	0.128485i
$25$		−	1.00000i		−	0.200000i
$26$	8.08006	+	5.00829i	1.58463	+	0.982206i
$27$	−0.601365	+	0.601365i	−0.115733	+	0.115733i
$28$	−0.889770	−	1.79118i	−0.168151	−	0.338500i
$29$	2.42606	+	2.42606i	0.450508	+	0.450508i	0.895523	−	0.445015i	$-0.146802\pi$
$29$	2.42606	+	2.42606i	0.450508	+	0.450508i	−0.445015	+	0.895523i	$0.646802\pi$
$30$	3.27029	−	0.767522i	0.597071	−	0.140130i
$31$	−8.63834			−1.55149			−0.775746	−	0.631046i	$-0.782626\pi$
$31$	−8.63834			−1.55149			−0.775746	+	0.631046i	$0.782626\pi$
$32$	−2.29724	+	5.16940i	−0.406099	+	0.913829i
$33$	13.5487			2.35853
$34$	−5.52289	+	1.29619i	−0.947167	+	0.222296i
$35$	−0.707107	−	0.707107i	−0.119523	−	0.119523i
$36$	2.35073	+	4.73220i	0.391789	+	0.788700i
$37$	−1.14755	+	1.14755i	−0.188655	+	0.188655i	−0.795115	−	0.606459i	$-0.792589\pi$
$37$	−1.14755	+	1.14755i	−0.188655	+	0.188655i	0.606459	+	0.795115i	$0.292589\pi$
$38$	−2.00369	−	1.24196i	−0.325042	−	0.201472i
$39$			15.9666i			2.55670i
$40$	−0.264999	+	2.81599i	−0.0419001	+	0.445246i
$41$		−	1.24783i		−	0.194879i	−0.995241	−	0.0974394i	$-0.968935\pi$
$41$		−	1.24783i		−	0.194879i	0.995241	−	0.0974394i	$-0.0310652\pi$
$42$	1.76973	−	2.85517i	0.273075	−	0.440562i
$43$	−8.70723	+	8.70723i	−1.32784	+	1.32784i	−0.420588	+	0.907252i	$0.638176\pi$
$43$	−8.70723	+	8.70723i	−1.32784	+	1.32784i	−0.907252	+	0.420588i	$0.861824\pi$
$44$	−3.63570	+	10.8132i	−0.548102	+	1.63016i
$45$	1.86814	+	1.86814i	0.278486	+	0.278486i
$46$	0.197411	+	0.841137i	0.0291066	+	0.124019i
$47$	7.92976			1.15667			0.578337	−	0.815798i	$-0.303702\pi$
$47$	7.92976			1.15667			0.578337	+	0.815798i	$0.303702\pi$
$48$	−9.41249	+	1.29470i	−1.35858	+	0.186875i
$49$	−1.00000			−0.142857
$50$	0.323129	+	1.37680i	0.0456974	+	0.194709i
$51$	−6.73743	−	6.73743i	−0.943428	−	0.943428i
$52$	−12.7430	−	4.28453i	−1.76713	−	0.594157i
$53$	−5.64673	+	5.64673i	−0.775638	+	0.775638i	−0.979086	−	0.203447i	$-0.934785\pi$
$53$	−5.64673	+	5.64673i	−0.775638	+	0.775638i	0.203447	+	0.979086i	$0.434785\pi$
$54$	0.633643	−	1.02228i	0.0862279	−	0.139115i
$55$			5.70405i			0.769133i
$56$	1.80382	+	2.17859i	0.241046	+	0.291126i
$57$		−	3.95940i		−	0.524436i
$58$	−4.12414	−	2.55628i	−0.541526	−	0.335656i
$59$	−1.23973	+	1.23973i	−0.161399	+	0.161399i	−0.783186	−	0.621787i	$-0.786407\pi$
$59$	−1.23973	+	1.23973i	−0.161399	+	0.161399i	0.621787	+	0.783186i	$0.286407\pi$
$60$	−4.25454	+	2.11345i	−0.549259	+	0.272846i
$61$	5.71963	+	5.71963i	0.732324	+	0.732324i	0.971080	−	0.238756i	$-0.0767396\pi$
$61$	5.71963	+	5.71963i	0.732324	+	0.732324i	−0.238756	+	0.971080i	$0.576740\pi$
$62$	11.8933	−	2.79130i	1.51045	−	0.354495i
$63$	2.64195			0.332855
$64$	1.49247	−	7.85955i	0.186559	−	0.982444i
$65$	−6.72199			−0.833761
$66$	−18.6539	+	4.37798i	−2.29614	+	0.538892i
$67$	2.38301	+	2.38301i	0.291132	+	0.291132i	0.837527	−	0.546396i	$-0.184000\pi$
$67$	2.38301	+	2.38301i	0.291132	+	0.291132i	−0.546396	+	0.837527i	$0.684000\pi$
$68$	7.18509	−	3.56921i	0.871320	−	0.432830i
$69$	−1.02611	+	1.02611i	−0.123529	+	0.123529i
$70$	1.20203	+	0.745060i	0.143671	+	0.0890517i
$71$		−	1.57667i		−	0.187116i	−0.995614	−	0.0935580i	$-0.970176\pi$
$71$		−	1.57667i		−	0.187116i	0.995614	−	0.0935580i	$-0.0298240\pi$
$72$	−4.76561	−	5.75572i	−0.561632	−	0.678318i
$73$			1.85964i			0.217655i	0.994061	+	0.108827i	$0.0347096\pi$
$73$			1.85964i			0.217655i	−0.994061	+	0.108827i	$0.965290\pi$
$74$	1.20914	−	1.95075i	0.140560	−	0.226770i
$75$	−1.67958	+	1.67958i	−0.193941	+	0.193941i
$76$	3.16001	+	1.06248i	0.362478	+	0.121875i
$77$	4.03337	+	4.03337i	0.459645	+	0.459645i
$78$	−5.15928	−	21.9829i	−0.584173	−	2.48907i
$79$	3.14874			0.354261			0.177130	−	0.984187i	$-0.443319\pi$
$79$	3.14874			0.354261			0.177130	+	0.984187i	$0.443319\pi$
$80$	−0.545075	−	3.96269i	−0.0609412	−	0.443042i
$81$	9.94594			1.10510
$82$	0.403211	+	1.71802i	0.0445272	+	0.189724i
$83$	−6.01779	−	6.01779i	−0.660538	−	0.660538i	0.294969	−	0.955507i	$-0.404691\pi$
$83$	−6.01779	−	6.01779i	−0.660538	−	0.660538i	−0.955507	+	0.294969i	$0.904691\pi$
$84$	−1.51398	+	4.50285i	−0.165189	+	0.491302i
$85$	2.83648	−	2.83648i	0.307659	−	0.307659i
$86$	9.17458	−	14.8017i	0.989320	−	1.59611i
$87$		−	8.14951i		−	0.873719i
$88$	1.51157	−	16.0625i	0.161134	−	1.71227i
$89$			18.0907i			1.91761i	0.284060	+	0.958806i	$0.408318\pi$
$89$			18.0907i			1.91761i	−0.284060	+	0.958806i	$0.591682\pi$
$90$	−3.17572	−	1.96842i	−0.334750	−	0.207489i
$91$	−4.75317	+	4.75317i	−0.498267	+	0.498267i
$92$	−0.543592	−	1.09429i	−0.0566734	−	0.114088i
$93$	14.5087	+	14.5087i	1.50449	+	1.50449i
$94$	−10.9177	+	2.56234i	−1.12608	+	0.264285i
$95$	1.66692			0.171022
$96$	12.5408	−	4.82400i	1.27994	−	0.492348i
$97$	−10.6607			−1.08243			−0.541213	−	0.840886i	$-0.682035\pi$
$97$	−10.6607			−1.08243			−0.541213	+	0.840886i	$0.682035\pi$
$98$	1.37680	−	0.323129i	0.139078	−	0.0326410i
$99$	−10.6560	−	10.6560i	−1.07097	−	1.07097i
$100$	−0.889770	−	1.79118i	−0.0889770	−	0.179118i
$101$	3.13938	−	3.13938i	0.312380	−	0.312380i	−0.533451	−	0.845831i	$-0.679105\pi$
$101$	3.13938	−	3.13938i	0.312380	−	0.312380i	0.845831	+	0.533451i	$0.179105\pi$
$102$	11.4532	+	7.09905i	1.13403	+	0.702911i
$103$			3.04008i			0.299548i	0.988720	+	0.149774i	$0.0478546\pi$
$103$			3.04008i			0.299548i	−0.988720	+	0.149774i	$0.952145\pi$
$104$	18.9290	+	1.78132i	1.85614	+	0.174673i
$105$			2.37528i			0.231804i
$106$	5.94982	−	9.59907i	0.577897	−	0.932344i
$107$	0.349930	−	0.349930i	0.0338290	−	0.0338290i	−0.689990	−	0.723819i	$-0.742385\pi$
$107$	0.349930	−	0.349930i	0.0338290	−	0.0338290i	0.723819	+	0.689990i	$0.242385\pi$
$108$	−0.542074	+	1.61223i	−0.0521611	+	0.155137i
$109$	−9.66324	−	9.66324i	−0.925571	−	0.925571i	0.0718452	−	0.997416i	$-0.477111\pi$
$109$	−9.66324	−	9.66324i	−0.925571	−	0.925571i	−0.997416	+	0.0718452i	$0.977111\pi$
$110$	−1.84314	−	7.85335i	−0.175737	−	0.748788i
$111$	3.85478			0.365880
$112$	−3.18747	−	2.41662i	−0.301188	−	0.228349i
$113$	−15.6991			−1.47685			−0.738425	−	0.674335i	$-0.764430\pi$
$113$	−15.6991			−1.47685			−0.738425	+	0.674335i	$0.764430\pi$
$114$	1.27940	+	5.45132i	0.119827	+	0.510563i
$115$	−0.431996	−	0.431996i	−0.0402839	−	0.0402839i
$116$	6.50414	+	2.18686i	0.603894	+	0.203045i
$117$	12.5576	−	12.5576i	1.16095	−	1.16095i
$118$	1.30627	−	2.10746i	0.120252	−	0.194008i
$119$		−	4.01138i		−	0.367723i
$120$	5.17475	−	4.28458i	0.472388	−	0.391127i
$121$		−	21.5361i		−	1.95783i
$122$	−9.72299	−	6.02663i	−0.880278	−	0.545625i
$123$	−2.09583	+	2.09583i	−0.188975	+	0.188975i
$124$	−15.4728	+	7.68614i	−1.38950	+	0.690236i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−3.63745	+	0.853692i	−0.324050	+	0.0760529i
$127$	−9.68222			−0.859158			−0.429579	−	0.903029i	$-0.641338\pi$
$127$	−9.68222			−0.859158			−0.429579	+	0.903029i	$0.641338\pi$
$128$	0.484813	+	11.3033i	0.0428518	+	0.999081i
$129$	29.2489			2.57522
$130$	9.25486	−	2.17207i	0.811705	−	0.190503i
$131$	−10.3532	−	10.3532i	−0.904562	−	0.904562i	0.0912644	−	0.995827i	$-0.470909\pi$
$131$	−10.3532	−	10.3532i	−0.904562	−	0.904562i	−0.995827	+	0.0912644i	$0.970909\pi$
$132$	24.2681	−	12.0552i	2.11227	−	1.04927i
$133$	1.17869	−	1.17869i	0.102205	−	0.102205i
$134$	−4.05096	−	2.51092i	−0.349950	−	0.216911i
$135$			0.850459i			0.0731958i
$136$	−8.73914	+	7.23581i	−0.749375	+	0.620466i
$137$		−	7.80415i		−	0.666754i	−0.942794	−	0.333377i	$-0.891812\pi$
$137$		−	7.80415i		−	0.666754i	0.942794	−	0.333377i	$-0.108188\pi$
$138$	1.08119	−	1.74432i	0.0920368	−	0.148486i
$139$	12.8660	−	12.8660i	1.09128	−	1.09128i	0.0958852	−	0.995392i	$-0.469432\pi$
$139$	12.8660	−	12.8660i	1.09128	−	1.09128i	0.995392	−	0.0958852i	$-0.0305682\pi$
$140$	−1.89571	−	0.637389i	−0.160217	−	0.0538692i
$141$	−13.3186	−	13.3186i	−1.12163	−	1.12163i
$142$	0.509467	+	2.17076i	0.0427535	+	0.182166i
$143$	38.3426			3.20637
$144$	8.42115	+	6.38459i	0.701762	+	0.532049i
$145$	3.43097			0.284926
$146$	−0.600905	−	2.56037i	−0.0497313	−	0.211897i
$147$	1.67958	+	1.67958i	0.138529	+	0.138529i
$148$	−1.03440	+	3.07651i	−0.0850275	+	0.252888i
$149$	−7.43213	+	7.43213i	−0.608864	+	0.608864i	−0.942649	−	0.333785i	$-0.891674\pi$
$149$	−7.43213	+	7.43213i	−0.608864	+	0.608864i	0.333785	+	0.942649i	$0.391674\pi$
$150$	1.76973	−	2.85517i	0.144498	−	0.233123i
$151$		−	17.0059i		−	1.38392i	−0.721936	−	0.691960i	$-0.756747\pi$
$151$		−	17.0059i		−	1.38392i	0.721936	−	0.691960i	$-0.243253\pi$
$152$	−4.69402	−	0.441733i	−0.380736	−	0.0358293i
$153$			10.5979i			0.856789i
$154$	−6.85646	−	4.24986i	−0.552509	−	0.342463i
$155$	−6.10823	+	6.10823i	−0.490625	+	0.490625i
$156$	14.2066	+	28.5990i	1.13744	+	2.28975i
$157$	−10.2852	−	10.2852i	−0.820847	−	0.820847i	0.165383	−	0.986229i	$-0.447114\pi$
$157$	−10.2852	−	10.2852i	−0.820847	−	0.820847i	−0.986229	+	0.165383i	$0.947114\pi$
$158$	−4.33519	+	1.01745i	−0.344890	+	0.0809439i
$159$	18.9682			1.50428
$160$	2.03092	+	5.27971i	0.160558	+	0.417398i
$161$	−0.610935			−0.0481484
$162$	−13.6936	+	3.21382i	−1.07587	+	0.252502i
$163$	−1.57991	−	1.57991i	−0.123748	−	0.123748i	0.642521	−	0.766268i	$-0.277889\pi$
$163$	−1.57991	−	1.57991i	−0.123748	−	0.123748i	−0.766268	+	0.642521i	$0.777889\pi$
$164$	−1.11029	−	2.23509i	−0.0866987	−	0.174531i
$165$	9.58038	−	9.58038i	0.745832	−	0.745832i
$166$	10.2298	+	6.34079i	0.793989	+	0.492141i
$167$			19.4076i			1.50180i	0.660414	+	0.750902i	$0.270381\pi$
$167$			19.4076i			1.50180i	−0.660414	+	0.750902i	$0.729619\pi$
$168$	0.629448	−	6.68875i	0.0485629	−	0.516049i
$169$			32.1852i			2.47578i
$170$	−2.98872	+	4.82182i	−0.229225	+	0.369817i
$171$	−3.11405	+	3.11405i	−0.238137	+	0.238137i
$172$	−7.84874	+	23.3436i	−0.598460	+	1.77993i
$173$	−2.53665	−	2.53665i	−0.192858	−	0.192858i	0.604072	−	0.796930i	$-0.293544\pi$
$173$	−2.53665	−	2.53665i	−0.192858	−	0.192858i	−0.796930	+	0.604072i	$0.793544\pi$
$174$	2.63334	+	11.2203i	0.199633	+	0.850607i
$175$	−1.00000			−0.0755929
$176$	3.10913	+	22.6034i	0.234360	+	1.70379i
$177$	4.16445			0.313019
$178$	−5.84564	−	24.9074i	−0.438149	−	1.86689i
$179$	−0.426744	−	0.426744i	−0.0318964	−	0.0318964i	0.690979	−	0.722875i	$-0.257180\pi$
$179$	−0.426744	−	0.426744i	−0.0318964	−	0.0318964i	−0.722875	+	0.690979i	$0.757180\pi$
$180$	5.00839	+	1.68395i	0.373303	+	0.125515i
$181$	4.85919	−	4.85919i	0.361181	−	0.361181i	−0.503067	−	0.864248i	$-0.667795\pi$
$181$	4.85919	−	4.85919i	0.361181	−	0.361181i	0.864248	+	0.503067i	$0.167795\pi$
$182$	5.00829	−	8.08006i	0.371239	−	0.598934i
$183$		−	19.2131i		−	1.42027i
$184$	1.10202	+	1.33097i	0.0812417	+	0.0981207i
$185$			1.62288i			0.119316i
$186$	−24.6639	−	15.2875i	−1.80844	−	1.12093i
$187$	−16.1794	+	16.1794i	−1.18315	+	1.18315i
$188$	14.2036	−	7.05567i	1.03590	−	0.514587i
$189$	0.601365	+	0.601365i	0.0437429	+	0.0437429i
$190$	−2.29502	+	0.538631i	−0.166498	+	0.0390764i
$191$	−11.4717			−0.830062			−0.415031	−	0.909807i	$-0.636229\pi$
$191$	−11.4717			−0.830062			−0.415031	+	0.909807i	$0.636229\pi$
$192$	−15.7074	+	10.6940i	−1.13359	+	0.771773i
$193$	13.4250			0.966355			0.483177	−	0.875522i	$-0.339483\pi$
$193$	13.4250			0.966355			0.483177	+	0.875522i	$0.339483\pi$
$194$	14.6776	−	3.44477i	1.05379	−	0.247320i
$195$	11.2901	+	11.2901i	0.808501	+	0.808501i
$196$	−1.79118	+	0.889770i	−0.127941	+	0.0635550i
$197$	10.2883	−	10.2883i	0.733015	−	0.733015i	−0.238201	−	0.971216i	$-0.576558\pi$
$197$	10.2883	−	10.2883i	0.733015	−	0.733015i	0.971216	+	0.238201i	$0.0765578\pi$
$198$	18.1144	+	11.2279i	1.28734	+	0.797934i
$199$		−	25.7491i		−	1.82530i	−0.408737	−	0.912652i	$-0.634031\pi$
$199$		−	25.7491i		−	1.82530i	0.408737	−	0.912652i	$-0.365969\pi$
$200$	1.80382	+	2.17859i	0.127549	+	0.154049i
$201$		−	8.00491i		−	0.564623i
$202$	−3.30788	+	5.33674i	−0.232742	+	0.375491i
$203$	2.42606	−	2.42606i	0.170276	−	0.170276i
$204$	−18.0627	−	6.07315i	−1.26464	−	0.425205i
$205$	−0.882352	−	0.882352i	−0.0616261	−	0.0616261i
$206$	−0.982337	−	4.18559i	−0.0684427	−	0.291624i
$207$	1.61406			0.112185
$208$	−26.6372	+	3.66399i	−1.84695	+	0.254052i
$209$	−9.50819			−0.657695
$210$	−0.767522	−	3.27029i	−0.0529640	−	0.225672i
$211$	−12.1272	−	12.1272i	−0.834868	−	0.834868i	0.153310	−	0.988178i	$-0.451007\pi$
$211$	−12.1272	−	12.1272i	−0.834868	−	0.834868i	−0.988178	+	0.153310i	$0.951007\pi$
$212$	−5.08999	+	15.1386i	−0.349582	+	1.03972i
$213$	−2.64813	+	2.64813i	−0.181447	+	0.181447i
$214$	−0.368712	+	0.594857i	−0.0252046	+	0.0406636i
$215$			12.3139i			0.839799i
$216$	0.225371	−	2.39488i	0.0153346	−	0.162951i
$217$			8.63834i			0.586409i
$218$	16.4269	+	10.1819i	1.11257	+	0.689606i
$219$	3.12342	−	3.12342i	0.211061	−	0.211061i
$220$	5.07529	+	10.2169i	0.342176	+	0.688826i
$221$	−19.0668	−	19.0668i	−1.28257	−	1.28257i
$222$	−5.30728	+	1.24559i	−0.356201	+	0.0835987i
$223$	1.64904			0.110428			0.0552140	−	0.998475i	$-0.482416\pi$
$223$	1.64904			0.110428			0.0552140	+	0.998475i	$0.482416\pi$
$224$	5.16940	+	2.29724i	0.345395	+	0.153491i
$225$	2.64195			0.176130
$226$	21.6146	−	5.07285i	1.43778	−	0.337441i
$227$	0.582397	+	0.582397i	0.0386551	+	0.0386551i	0.726170	−	0.687515i	$-0.241298\pi$
$227$	0.582397	+	0.582397i	0.0386551	+	0.0386551i	−0.687515	+	0.726170i	$0.741298\pi$
$228$	−3.52296	−	7.09198i	−0.233314	−	0.469678i
$229$	5.72794	−	5.72794i	0.378513	−	0.378513i	−0.492053	−	0.870565i	$-0.663753\pi$
$229$	5.72794	−	5.72794i	0.378513	−	0.378513i	0.870565	+	0.492053i	$0.163753\pi$
$230$	0.734364	+	0.455183i	0.0484226	+	0.0300139i
$231$		−	13.5487i		−	0.891439i
$232$	−9.66156	−	0.909205i	−0.634312	−	0.0596922i
$233$		−	1.17346i		−	0.0768760i	−0.999261	−	0.0384380i	$-0.987762\pi$
$233$		−	1.17346i		−	0.0768760i	0.999261	−	0.0384380i	$-0.0122382\pi$
$234$	−13.2317	+	21.3472i	−0.864981	+	1.39551i
$235$	5.60719	−	5.60719i	0.365773	−	0.365773i
$236$	−1.11750	+	3.32366i	−0.0727431	+	0.216352i
$237$	−5.28855	−	5.28855i	−0.343528	−	0.343528i
$238$	1.29619	+	5.52289i	0.0840198	+	0.357996i
$239$	−28.4618			−1.84104			−0.920520	−	0.390697i	$-0.872234\pi$
$239$	−28.4618			−1.84104			−0.920520	+	0.390697i	$0.872234\pi$
$240$	−5.74014	+	7.57113i	−0.370525	+	0.488714i
$241$	−18.9114			−1.21819			−0.609096	−	0.793097i	$-0.708467\pi$
$241$	−18.9114			−1.21819			−0.609096	+	0.793097i	$0.708467\pi$
$242$	6.95895	+	29.6510i	0.447338	+	1.90604i
$243$	−14.9009	−	14.9009i	−0.955891	−	0.955891i
$244$	15.3340	+	5.15570i	0.981660	+	0.330060i
$245$	−0.707107	+	0.707107i	−0.0451754	+	0.0451754i
$246$	2.20832	−	3.56277i	0.140798	−	0.227154i
$247$		−	11.2050i		−	0.712959i
$248$	18.8194	−	15.5820i	1.19503	−	0.989458i
$249$			20.2147i			1.28105i
$250$	1.20203	+	0.745060i	0.0760233	+	0.0471217i
$251$	−9.17726	+	9.17726i	−0.579263	+	0.579263i	−0.934700	−	0.355437i	$-0.884332\pi$
$251$	−9.17726	+	9.17726i	−0.579263	+	0.579263i	0.355437	+	0.934700i	$0.384332\pi$
$252$	4.73220	−	2.35073i	0.298101	−	0.148082i
$253$	2.46413	+	2.46413i	0.154918	+	0.154918i
$254$	13.3305	−	3.12861i	0.836430	−	0.196306i
$255$	−9.52816			−0.596676
$256$	−4.31992	−	15.4058i	−0.269995	−	0.962862i
$257$	−17.4767			−1.09017			−0.545084	−	0.838381i	$-0.683502\pi$
$257$	−17.4767			−1.09017			−0.545084	+	0.838381i	$0.683502\pi$
$258$	−40.2700	+	9.45117i	−2.50710	+	0.588404i
$259$	1.14755	+	1.14755i	0.0713051	+	0.0713051i
$260$	−12.0403	+	5.98103i	−0.746706	+	0.370928i
$261$	−6.40954	+	6.40954i	−0.396741	+	0.396741i
$262$	17.5997	+	10.9089i	1.08731	+	0.673953i
$263$			14.7508i			0.909575i	0.890600	+	0.454787i	$0.150285\pi$
$263$			14.7508i			0.909575i	−0.890600	+	0.454787i	$0.849715\pi$
$264$	−29.5170	+	24.4394i	−1.81665	+	1.50414i
$265$			7.98569i			0.490557i
$266$	−1.24196	+	2.00369i	−0.0761492	+	0.122854i
$267$	30.3848	−	30.3848i	1.85952	−	1.85952i
$268$	6.38873	+	2.14806i	0.390254	+	0.131214i
$269$	−7.14150	−	7.14150i	−0.435425	−	0.435425i	0.455044	−	0.890469i	$-0.349624\pi$
$269$	−7.14150	−	7.14150i	−0.435425	−	0.435425i	−0.890469	+	0.455044i	$0.849624\pi$
$270$	−0.274808	−	1.17091i	−0.0167243	−	0.0712596i
$271$	24.2531			1.47327			0.736634	−	0.676292i	$-0.236414\pi$
$271$	24.2531			1.47327			0.736634	+	0.676292i	$0.236414\pi$
$272$	9.69398	−	12.7862i	0.587784	−	0.775275i
$273$	15.9666			0.966343
$274$	2.52175	+	10.7448i	0.152344	+	0.649116i
$275$	4.03337	+	4.03337i	0.243221	+	0.243221i
$276$	−0.924942	+	2.75095i	−0.0556750	+	0.165588i
$277$	−13.6965	+	13.6965i	−0.822945	+	0.822945i	−0.986529	−	0.163585i	$-0.947694\pi$
$277$	−13.6965	+	13.6965i	−0.822945	+	0.822945i	0.163585	+	0.986529i	$0.447694\pi$
$278$	−13.5565	+	21.8713i	−0.813068	+	1.31175i
$279$		−	22.8221i		−	1.36632i
$280$	2.81599	+	0.264999i	0.168287	+	0.0158367i
$281$			16.1993i			0.966367i	0.875519	+	0.483184i	$0.160520\pi$
$281$			16.1993i			0.966367i	−0.875519	+	0.483184i	$0.839480\pi$
$282$	22.6408	+	14.0335i	1.34824	+	0.835683i
$283$	10.7931	−	10.7931i	0.641584	−	0.641584i	−0.309361	−	0.950945i	$-0.600115\pi$
$283$	10.7931	−	10.7931i	0.641584	−	0.641584i	0.950945	+	0.309361i	$0.100115\pi$
$284$	−1.40287	−	2.82409i	−0.0832451	−	0.167579i
$285$	−2.79972	−	2.79972i	−0.165841	−	0.165841i
$286$	−52.7902	+	12.3896i	−3.12155	+	0.732612i
$287$	−1.24783			−0.0736573
$288$	−13.6573	−	6.06921i	−0.804765	−	0.357632i
$289$	−0.908803			−0.0534590
$290$	−4.72377	+	1.10865i	−0.277389	+	0.0651019i
$291$	17.9054	+	17.9054i	1.04963	+	1.04963i
$292$	1.65466	+	3.33095i	0.0968315	+	0.194929i
$293$	4.38233	−	4.38233i	0.256019	−	0.256019i	−0.567414	−	0.823433i	$-0.692056\pi$
$293$	4.38233	−	4.38233i	0.256019	−	0.256019i	0.823433	+	0.567414i	$0.192056\pi$
$294$	−2.85517	−	1.76973i	−0.166517	−	0.103213i
$295$			1.75325i			0.102078i
$296$	0.430061	−	4.57000i	0.0249968	−	0.265626i
$297$		−	4.85106i		−	0.281487i
$298$	7.83104	−	12.6341i	0.453640	−	0.731875i
$299$	−2.90388	+	2.90388i	−0.167935	+	0.167935i
$300$	−1.51398	+	4.50285i	−0.0874096	+	0.259972i
$301$	8.70723	+	8.70723i	0.501876	+	0.501876i
$302$	5.49510	+	23.4138i	0.316207	+	1.34731i
$303$	−10.5457			−0.605832
$304$	6.60549	−	0.908596i	0.378851	−	0.0521116i
$305$	8.08878			0.463162
$306$	−3.42449	−	14.5912i	−0.195765	−	0.834124i
$307$	−8.17429	−	8.17429i	−0.466531	−	0.466531i	0.434258	−	0.900789i	$-0.357011\pi$
$307$	−8.17429	−	8.17429i	−0.466531	−	0.466531i	−0.900789	+	0.434258i	$0.857011\pi$
$308$	10.8132	+	3.63570i	0.616142	+	0.207163i
$309$	5.10604	−	5.10604i	0.290473	−	0.290473i
$310$	6.43608	−	10.3836i	0.365545	−	0.589747i
$311$			18.4682i			1.04724i	0.851953	+	0.523618i	$0.175418\pi$
$311$			18.4682i			1.04724i	−0.851953	+	0.523618i	$0.824582\pi$
$312$	−28.8009	−	34.7846i	−1.63053	−	1.96929i
$313$			8.02087i			0.453366i	0.973969	+	0.226683i	$0.0727882\pi$
$313$			8.02087i			0.453366i	−0.973969	+	0.226683i	$0.927212\pi$
$314$	17.4841	+	10.8372i	0.986685	+	0.611580i
$315$	1.86814	−	1.86814i	0.105258	−	0.105258i
$316$	5.63994	−	2.80165i	0.317272	−	0.157605i
$317$	9.62720	+	9.62720i	0.540717	+	0.540717i	0.923739	−	0.383022i	$-0.125117\pi$
$317$	9.62720	+	9.62720i	0.540717	+	0.540717i	−0.383022	+	0.923739i	$0.625117\pi$
$318$	−26.1155	+	6.12919i	−1.46449	+	0.343708i
$319$	−19.5704			−1.09573
$320$	−4.50221	−	6.61288i	−0.251681	−	0.369671i
$321$	−1.17547			−0.0656082
$322$	0.841137	−	0.197411i	0.0468748	−	0.0110013i
$323$	4.72818	+	4.72818i	0.263083	+	0.263083i
$324$	17.8149	−	8.84960i	0.989718	−	0.491645i
$325$	−4.75317	+	4.75317i	−0.263658	+	0.263658i
$326$	2.68574	+	1.66471i	0.148749	+	0.0921997i
$327$			32.4603i			1.79506i
$328$	2.25087	+	2.71851i	0.124283	+	0.150105i
$329$		−	7.92976i		−	0.437182i
$330$	−10.0946	+	16.2860i	−0.555690	+	0.896515i
$331$	−14.5030	+	14.5030i	−0.797159	+	0.797159i	−0.982647	−	0.185488i	$-0.940614\pi$
$331$	−14.5030	+	14.5030i	−0.797159	+	0.797159i	0.185488	+	0.982647i	$0.440614\pi$
$332$	−16.1334	−	5.42446i	−0.885434	−	0.297706i
$333$	−3.03177	−	3.03177i	−0.166140	−	0.166140i
$334$	−6.27116	−	26.7204i	−0.343142	−	1.46208i
$335$	3.37009			0.184128
$336$	1.29470	+	9.41249i	0.0706319	+	0.513494i
$337$	−6.26474			−0.341262			−0.170631	−	0.985335i	$-0.554581\pi$
$337$	−6.26474			−0.341262			−0.170631	+	0.985335i	$0.554581\pi$
$338$	−10.4000	−	44.3127i	−0.565684	−	2.41029i
$339$	26.3679	+	26.3679i	1.43211	+	1.43211i
$340$	2.55681	−	7.60444i	0.138663	−	0.412409i
$341$	34.8416	−	34.8416i	1.88678	−	1.88678i
$342$	3.28119	−	5.29367i	0.177427	−	0.286249i
$343$			1.00000i			0.0539949i
$344$	3.26317	−	34.6757i	0.175938	−	1.86959i
$345$			1.45114i			0.0781268i
$346$	4.31213	+	2.67280i	0.231822	+	0.143691i
$347$	−1.52476	+	1.52476i	−0.0818535	+	0.0818535i	−0.746848	−	0.664995i	$-0.768434\pi$
$347$	−1.52476	+	1.52476i	−0.0818535	+	0.0818535i	0.664995	+	0.746848i	$0.268434\pi$
$348$	−7.25119	−	14.5972i	−0.388705	−	0.782492i
$349$	0.611349	+	0.611349i	0.0327248	+	0.0327248i	0.723280	−	0.690555i	$-0.242634\pi$
$349$	0.611349	+	0.611349i	0.0327248	+	0.0327248i	−0.690555	+	0.723280i	$0.742634\pi$
$350$	1.37680	−	0.323129i	0.0735932	−	0.0172720i
$351$	5.71678			0.305139
$352$	−11.5845	−	30.1157i	−0.617454	−	1.60517i
$353$	−24.7889			−1.31938			−0.659690	−	0.751538i	$-0.729312\pi$
$353$	−24.7889			−1.31938			−0.659690	+	0.751538i	$0.729312\pi$
$354$	−5.73363	+	1.34566i	−0.304739	+	0.0715208i
$355$	−1.11487	−	1.11487i	−0.0591713	−	0.0591713i
$356$	16.0966	+	32.4037i	0.853118	+	1.71739i
$357$	−6.73743	+	6.73743i	−0.356582	+	0.356582i
$358$	0.725436	+	0.449649i	0.0383405	+	0.0237647i
$359$		−	17.3351i		−	0.914911i	−0.889233	−	0.457455i	$-0.848761\pi$
$359$		−	17.3351i		−	0.914911i	0.889233	−	0.457455i	$-0.151239\pi$
$360$	−7.43971	−	0.700116i	−0.392107	−	0.0368994i
$361$		−	16.2214i		−	0.853757i
$362$	−5.12001	+	8.26030i	−0.269102	+	0.434152i
$363$	−36.1716	+	36.1716i	−1.89852	+	1.89852i
$364$	−4.28453	+	12.7430i	−0.224570	+	0.667914i
$365$	1.31497	+	1.31497i	0.0688285	+	0.0688285i
$366$	6.20832	+	26.4527i	0.324514	+	1.38270i
$367$	6.87342			0.358790			0.179395	−	0.983777i	$-0.442586\pi$
$367$	6.87342			0.358790			0.179395	+	0.983777i	$0.442586\pi$
$368$	−1.94734	−	1.47640i	−0.101512	−	0.0769625i
$369$	3.29672			0.171620
$370$	−0.524398	−	2.23438i	−0.0272622	−	0.116160i
$371$	5.64673	+	5.64673i	0.293164	+	0.293164i
$372$	38.8972	+	13.0783i	2.01672	+	0.678076i
$373$	20.1924	−	20.1924i	1.04552	−	1.04552i	0.0466080	−	0.998913i	$-0.485159\pi$
$373$	20.1924	−	20.1924i	1.04552	−	1.04552i	0.998913	−	0.0466080i	$-0.0148412\pi$
$374$	17.0478	−	27.5039i	0.881521	−	1.42219i
$375$			2.37528i			0.122659i
$376$	−17.2757	+	14.3039i	−0.890924	+	0.737665i
$377$		−	23.0629i		−	1.18780i
$378$	−1.02228	−	0.633643i	−0.0525804	−	0.0325911i
$379$	−3.43766	+	3.43766i	−0.176581	+	0.176581i	−0.789864	−	0.613283i	$-0.789849\pi$
$379$	−3.43766	+	3.43766i	−0.176581	+	0.176581i	0.613283	+	0.789864i	$0.289849\pi$
$380$	2.98575	−	1.48318i	0.153166	−	0.0760854i
$381$	16.2620	+	16.2620i	0.833129	+	0.833129i
$382$	15.7943	−	3.70684i	0.808105	−	0.189658i
$383$	17.7783			0.908431			0.454216	−	0.890892i	$-0.349920\pi$
$383$	17.7783			0.908431			0.454216	+	0.890892i	$0.349920\pi$
$384$	18.1705	−	19.7991i	0.927260	−	1.01037i
$385$	5.70405			0.290705
$386$	−18.4836	+	4.33802i	−0.940792	+	0.220799i
$387$	−23.0041	−	23.0041i	−1.16936	−	1.16936i
$388$	−19.0951	+	9.48554i	−0.969407	+	0.481555i
$389$	17.7695	−	17.7695i	0.900951	−	0.900951i	−0.0945674	−	0.995518i	$-0.530147\pi$
$389$	17.7695	−	17.7695i	0.900951	−	0.900951i	0.995518	+	0.0945674i	$0.0301468\pi$
$390$	−19.1924	−	11.8961i	−0.971845	−	0.602382i
$391$		−	2.45069i		−	0.123937i
$392$	2.17859	−	1.80382i	0.110035	−	0.0911067i
$393$			34.7779i			1.75432i
$394$	−10.8406	+	17.4895i	−0.546140	+	0.881108i
$395$	2.22649	−	2.22649i	0.112027	−	0.112027i
$396$	−28.5681	−	9.60535i	−1.43560	−	0.482687i
$397$	12.7634	+	12.7634i	0.640575	+	0.640575i	0.950697	−	0.310122i	$-0.100370\pi$
$397$	12.7634	+	12.7634i	0.640575	+	0.640575i	−0.310122	+	0.950697i	$0.600370\pi$
$398$	8.32028	+	35.4514i	0.417058	+	1.77702i
$399$	−3.95940			−0.198218
$400$	−3.18747	−	2.41662i	−0.159373	−	0.120831i
$401$	20.5555			1.02649			0.513245	−	0.858242i	$-0.328443\pi$
$401$	20.5555			1.02649			0.513245	+	0.858242i	$0.328443\pi$
$402$	2.58662	+	11.0212i	0.129009	+	0.549687i
$403$	41.0595	+	41.0595i	2.04532	+	2.04532i
$404$	2.82985	−	8.41651i	0.140790	−	0.418737i
$405$	7.03284	−	7.03284i	0.349465	−	0.349465i
$406$	−2.55628	+	4.12414i	−0.126866	+	0.204678i
$407$		−	9.25696i		−	0.458850i
$408$	26.8312	+	2.52496i	1.32834	+	0.125004i
$409$			20.7319i			1.02513i	0.858649	+	0.512564i	$0.171304\pi$
$409$			20.7319i			1.02513i	−0.858649	+	0.512564i	$0.828696\pi$
$410$	1.49994	+	0.929711i	0.0740767	+	0.0459152i
$411$	−13.1077	+	13.1077i	−0.646554	+	0.646554i
$412$	2.70497	+	5.44531i	0.133264	+	0.268271i
$413$	1.23973	+	1.23973i	0.0610033	+	0.0610033i
$414$	−2.22225	+	0.521550i	−0.109217	+	0.0256328i
$415$	−8.51044			−0.417761
$416$	35.4902	−	13.6518i	1.74005	−	0.669336i
$417$	−43.2188			−2.11643
$418$	13.0909	−	3.07237i	0.640297	−	0.150275i
$419$	3.85590	+	3.85590i	0.188373	+	0.188373i	0.794992	−	0.606620i	$-0.207475\pi$
$419$	3.85590	+	3.85590i	0.188373	+	0.188373i	−0.606620	+	0.794992i	$0.707475\pi$
$420$	2.11345	+	4.25454i	0.103126	+	0.207600i
$421$	−0.480906	+	0.480906i	−0.0234379	+	0.0234379i	−0.718729	−	0.695291i	$-0.755276\pi$
$421$	−0.480906	+	0.480906i	−0.0234379	+	0.0234379i	0.695291	+	0.718729i	$0.255276\pi$
$422$	20.6154	+	12.7781i	1.00354	+	0.622027i
$423$			20.9501i			1.01863i
$424$	2.11620	−	22.4876i	0.102772	−	1.09209i
$425$		−	4.01138i		−	0.194581i
$426$	2.79027	−	4.50165i	0.135189	−	0.218105i
$427$	5.71963	−	5.71963i	0.276792	−	0.276792i
$428$	0.315428	−	0.938142i	0.0152468	−	0.0453468i
$429$	−64.3992	−	64.3992i	−3.10923	−	3.10923i
$430$	−3.97897	−	16.9538i	−0.191883	−	0.817584i
$431$	15.8219			0.762114			0.381057	−	0.924551i	$-0.375560\pi$
$431$	15.8219			0.762114			0.381057	+	0.924551i	$0.375560\pi$
$432$	0.463564	+	3.37010i	0.0223032	+	0.162144i
$433$	−10.7353			−0.515906			−0.257953	−	0.966157i	$-0.583048\pi$
$433$	−10.7353			−0.515906			−0.257953	+	0.966157i	$0.583048\pi$
$434$	−2.79130	−	11.8933i	−0.133987	−	0.570896i
$435$	−5.76257	−	5.76257i	−0.276294	−	0.276294i
$436$	−25.9066	−	8.71049i	−1.24070	−	0.417157i
$437$	0.720104	−	0.720104i	0.0344472	−	0.0344472i
$438$	−3.29106	+	5.30960i	−0.157253	+	0.253702i
$439$		−	32.3977i		−	1.54626i	−0.634250	−	0.773128i	$-0.718691\pi$
$439$		−	32.3977i		−	1.54626i	0.634250	−	0.773128i	$-0.281309\pi$
$440$	−10.2891	−	12.4268i	−0.490512	−	0.592422i
$441$		−	2.64195i		−	0.125807i
$442$	32.4122	+	20.0902i	1.54169	+	0.955592i
$443$	−19.5555	+	19.5555i	−0.929110	+	0.929110i	−0.997648	−	0.0685383i	$-0.978166\pi$
$443$	−19.5555	+	19.5555i	−0.929110	+	0.929110i	0.0685383	+	0.997648i	$0.478166\pi$
$444$	6.90459	−	3.42987i	0.327678	−	0.162775i
$445$	12.7921	+	12.7921i	0.606402	+	0.606402i
$446$	−2.27040	+	0.532853i	−0.107507	+	0.0252313i
$447$	24.9657			1.18083
$448$	−7.85955	−	1.49247i	−0.371329	−	0.0705125i
$449$	−41.8148			−1.97336			−0.986680	−	0.162673i	$-0.947989\pi$
$449$	−41.8148			−1.97336			−0.986680	+	0.162673i	$0.947989\pi$
$450$	−3.63745	+	0.853692i	−0.171471	+	0.0402434i
$451$	5.03297	+	5.03297i	0.236993	+	0.236993i
$452$	−28.1199	+	13.9686i	−1.32265	+	0.657029i
$453$	−28.5627	+	28.5627i	−1.34199	+	1.34199i
$454$	−0.990036	−	0.613657i	−0.0464647	−	0.0288003i
$455$			6.72199i			0.315132i
$456$	7.14205	+	8.62590i	0.334457	+	0.403945i
$457$			18.4598i			0.863515i	0.901990	+	0.431757i	$0.142106\pi$
$457$			18.4598i			0.863515i	−0.901990	+	0.431757i	$0.857894\pi$
$458$	−6.03538	+	9.73710i	−0.282015	+	0.454985i
$459$	−2.41231	+	2.41231i	−0.112597	+	0.112597i
$460$	−1.15816	−	0.389404i	−0.0539994	−	0.0181560i
$461$	6.90312	+	6.90312i	0.321510	+	0.321510i	0.849346	−	0.527836i	$-0.176996\pi$
$461$	6.90312	+	6.90312i	0.321510	+	0.321510i	−0.527836	+	0.849346i	$0.676996\pi$
$462$	4.37798	+	18.6539i	0.203682	+	0.867858i
$463$	23.8189			1.10696			0.553480	−	0.832862i	$-0.313300\pi$
$463$	23.8189			1.10696			0.553480	+	0.832862i	$0.313300\pi$
$464$	13.5959	−	1.87013i	0.631172	−	0.0868188i
$465$	20.5185			0.951521
$466$	0.379179	+	1.61562i	0.0175651	+	0.0748424i
$467$	9.73816	+	9.73816i	0.450628	+	0.450628i	0.895563	−	0.444935i	$-0.146773\pi$
$467$	9.73816	+	9.73816i	0.450628	+	0.450628i	−0.444935	+	0.895563i	$0.646773\pi$
$468$	11.3195	−	33.6664i	0.523245	−	1.55623i
$469$	2.38301	−	2.38301i	0.110037	−	0.110037i
$470$	−5.90815	+	9.53184i	−0.272523	+	0.439671i
$471$			34.5495i			1.59196i
$472$	0.464609	−	4.93712i	0.0213854	−	0.227249i
$473$		−	70.2389i		−	3.22959i
$474$	8.99018	+	5.57241i	0.412932	+	0.255949i
$475$	1.17869	−	1.17869i	0.0540820	−	0.0540820i
$476$	−3.56921	−	7.18509i	−0.163594	−	0.329328i
$477$	−14.9184	−	14.9184i	−0.683067	−	0.683067i
$478$	39.1863	−	9.19683i	1.79234	−	0.420653i
$479$	−26.2926			−1.20134			−0.600670	−	0.799497i	$-0.705100\pi$
$479$	−26.2926			−1.20134			−0.600670	+	0.799497i	$0.705100\pi$
$480$	5.45659	−	12.2788i	0.249058	−	0.560446i
$481$	10.9090			0.497406
$482$	26.0373	−	6.11083i	1.18597	−	0.278341i
$483$	1.02611	+	1.02611i	0.0466897	+	0.0466897i
$484$	−19.1622	−	38.5750i	−0.871010	−	1.75341i
$485$	−7.53822	+	7.53822i	−0.342293	+	0.342293i
$486$	25.3305	+	15.7007i	1.14901	+	0.712197i
$487$			9.31040i			0.421895i	0.977497	+	0.210947i	$0.0676549\pi$
$487$			9.31040i			0.421895i	−0.977497	+	0.210947i	$0.932345\pi$
$488$	−22.7779	−	2.14352i	−1.03111	−	0.0970327i
$489$			5.30715i			0.239998i
$490$	0.745060	−	1.20203i	0.0336584	−	0.0543024i
$491$	17.8430	−	17.8430i	0.805245	−	0.805245i	−0.178665	−	0.983910i	$-0.557178\pi$
$491$	17.8430	−	17.8430i	0.805245	−	0.805245i	0.983910	+	0.178665i	$0.0571778\pi$
$492$	−1.88919	+	5.61881i	−0.0851714	+	0.253316i
$493$	9.73186	+	9.73186i	0.438301	+	0.438301i
$494$	3.62067	+	15.4271i	0.162902	+	0.694099i
$495$	−15.0698			−0.677338
$496$	−20.8756	+	27.5344i	−0.937340	+	1.23633i
$497$	−1.57667			−0.0707232
$498$	−6.53195	−	27.8316i	−0.292704	−	1.24717i
$499$	24.3976	+	24.3976i	1.09219	+	1.09219i	0.995295	+	0.0968934i	$0.0308906\pi$
$499$	24.3976	+	24.3976i	1.09219	+	1.09219i	0.0968934	+	0.995295i	$0.469109\pi$
$500$	−1.89571	−	0.637389i	−0.0847789	−	0.0285049i
$501$	32.5965	−	32.5965i	1.45631	−	1.45631i
$502$	9.66984	−	15.6007i	0.431586	−	0.696294i
$503$		−	41.9958i		−	1.87250i	−0.351336	−	0.936249i	$-0.614273\pi$
$503$		−	41.9958i		−	1.87250i	0.351336	−	0.936249i	$-0.385727\pi$
$504$	−5.75572	+	4.76561i	−0.256380	+	0.212277i
$505$		−	4.43975i		−	0.197566i
$506$	−4.18885	−	2.59639i	−0.186217	−	0.115423i
$507$	54.0575	−	54.0575i	2.40078	−	2.40078i
$508$	−17.3425	+	8.61495i	−0.769451	+	0.382227i
$509$	−7.57957	−	7.57957i	−0.335959	−	0.335959i	0.518885	−	0.854844i	$-0.326347\pi$
$509$	−7.57957	−	7.57957i	−0.335959	−	0.335959i	−0.854844	+	0.518885i	$0.826347\pi$
$510$	13.1184	−	3.07882i	0.580893	−	0.136333i
$511$	1.85964			0.0822658
$512$	10.9257	+	19.8148i	0.482854	+	0.875701i
$513$	−1.41765			−0.0625907
$514$	24.0620	−	5.64724i	1.06133	−	0.249089i
$515$	2.14966	+	2.14966i	0.0947253	+	0.0947253i
$516$	52.3899	−	26.0248i	2.30634	−	1.14568i
$517$	−31.9837	+	31.9837i	−1.40664	+	1.40664i
$518$	−1.95075	−	1.20914i	−0.0857111	−	0.0531266i
$519$			8.52099i			0.374030i
$520$	14.6444	−	12.1253i	0.642201	−	0.531728i
$521$			11.7275i			0.513793i	0.966439	+	0.256897i	$0.0827000\pi$
$521$			11.7275i			0.513793i	−0.966439	+	0.256897i	$0.917300\pi$
$522$	6.75357	−	10.8958i	0.295596	−	0.476896i
$523$	18.3603	−	18.3603i	0.802839	−	0.802839i	−0.180699	−	0.983538i	$-0.557836\pi$
$523$	18.3603	−	18.3603i	0.802839	−	0.802839i	0.983538	+	0.180699i	$0.0578361\pi$
$524$	−27.7563	−	9.33241i	−1.21254	−	0.407688i
$525$	1.67958	+	1.67958i	0.0733027	+	0.0733027i
$526$	−4.76642	−	20.3090i	−0.207826	−	0.885514i
$527$	−34.6517			−1.50945
$528$	32.7420	−	43.1861i	1.42491	−	1.87943i
$529$	22.6268			0.983772
$530$	−2.58041	−	10.9947i	−0.112086	−	0.477580i
$531$	−3.27532	−	3.27532i	−0.142137	−	0.142137i
$532$	1.06248	−	3.16001i	0.0460642	−	0.137004i
$533$	−5.93116	+	5.93116i	−0.256907	+	0.256907i
$534$	−32.0156	+	51.6520i	−1.38545	+	2.23520i
$535$		−	0.494875i		−	0.0213953i
$536$	−9.49013	−	0.893072i	−0.409911	−	0.0385749i
$537$			1.43350i			0.0618600i
$538$	12.1401	+	7.52482i	0.523396	+	0.324418i
$539$	4.03337	−	4.03337i	0.173730	−	0.173730i
$540$	0.756713	+	1.52332i	0.0325637	+	0.0655533i
$541$	−8.83042	−	8.83042i	−0.379649	−	0.379649i	0.491326	−	0.870976i	$-0.336512\pi$
$541$	−8.83042	−	8.83042i	−0.379649	−	0.379649i	−0.870976	+	0.491326i	$0.836512\pi$
$542$	−33.3917	+	7.83687i	−1.43430	+	0.336622i
$543$	−16.3228			−0.700477
$544$	−9.21512	+	20.7364i	−0.395095	+	0.889067i
$545$	−13.6659			−0.585382
$546$	−21.9829	+	5.15928i	−0.940781	+	0.220797i
$547$	−13.7417	−	13.7417i	−0.587552	−	0.587552i	0.349416	−	0.936968i	$-0.386380\pi$
$547$	−13.7417	−	13.7417i	−0.587552	−	0.587552i	−0.936968	+	0.349416i	$0.886380\pi$
$548$	−6.94390	−	13.9786i	−0.296629	−	0.597136i
$549$	−15.1110	+	15.1110i	−0.644922	+	0.644922i
$550$	−6.85646	−	4.24986i	−0.292360	−	0.181215i
$551$			5.71915i			0.243644i
$552$	0.384552	−	4.08639i	0.0163676	−	0.173928i
$553$		−	3.14874i		−	0.133898i
$554$	14.4317	−	23.2832i	0.613143	−	0.989207i
$555$	2.72574	−	2.72574i	0.115701	−	0.115701i
$556$	11.5974	−	34.4930i	0.491841	−	1.46283i
$557$	−2.00922	−	2.00922i	−0.0851335	−	0.0851335i	0.663258	−	0.748391i	$-0.269173\pi$
$557$	−2.00922	−	2.00922i	−0.0851335	−	0.0851335i	−0.748391	+	0.663258i	$0.769173\pi$
$558$	7.37448	+	31.4215i	0.312187	+	1.33018i
$559$	82.7738			3.50096
$560$	−3.96269	+	0.545075i	−0.167454	+	0.0230336i
$561$	54.3490			2.29462
$562$	−5.23445	−	22.3032i	−0.220802	−	0.940804i
$563$	−12.4610	−	12.4610i	−0.525167	−	0.525167i	0.393961	−	0.919127i	$-0.371105\pi$
$563$	−12.4610	−	12.4610i	−0.525167	−	0.525167i	−0.919127	+	0.393961i	$0.871105\pi$
$564$	−35.7065	−	12.0055i	−1.50352	−	0.505522i
$565$	−11.1010	+	11.1010i	−0.467021	+	0.467021i
$566$	−11.3724	+	18.3476i	−0.478019	+	0.771206i
$567$		−	9.94594i		−	0.417690i
$568$	2.84402	+	3.43490i	0.119333	+	0.144125i
$569$		−	22.7065i		−	0.951905i	−0.879471	−	0.475952i	$-0.842104\pi$
$569$		−	22.7065i		−	0.951905i	0.879471	−	0.475952i	$-0.157896\pi$
$570$	4.75934	+	2.94999i	0.199347	+	0.123562i
$571$	−10.2731	+	10.2731i	−0.429915	+	0.429915i	−0.888599	−	0.458684i	$-0.848321\pi$
$571$	−10.2731	+	10.2731i	−0.429915	+	0.429915i	0.458684	+	0.888599i	$0.348321\pi$
$572$	68.6782	−	34.1161i	2.87158	−	1.42646i
$573$	19.2676	+	19.2676i	0.804915	+	0.804915i
$574$	1.71802	−	0.403211i	0.0717088	−	0.0168297i
$575$	−0.610935			−0.0254778
$576$	20.7646	+	3.94304i	0.865191	+	0.164293i
$577$	−18.1866			−0.757120			−0.378560	−	0.925577i	$-0.623581\pi$
$577$	−18.1866			−0.757120			−0.378560	+	0.925577i	$0.623581\pi$
$578$	1.25124	−	0.293661i	0.0520449	−	0.0122147i
$579$	−22.5484	−	22.5484i	−0.937078	−	0.937078i
$580$	6.14547	−	3.05277i	0.255177	−	0.126760i
$581$	−6.01779	+	6.01779i	−0.249660	+	0.249660i
$582$	−30.4380	−	18.8664i	−1.26169	−	0.782039i
$583$		−	45.5507i		−	1.88652i
$584$	−3.35446	−	4.05140i	−0.138809	−	0.167648i
$585$		−	17.7592i		−	0.734252i
$586$	−4.61755	+	7.44967i	−0.190749	+	0.307743i
$587$	14.3795	−	14.3795i	0.593504	−	0.593504i	−0.345072	−	0.938576i	$-0.612145\pi$
$587$	14.3795	−	14.3795i	0.593504	−	0.593504i	0.938576	+	0.345072i	$0.112145\pi$
$588$	4.50285	+	1.51398i	0.185695	+	0.0624354i
$589$	−10.1819	−	10.1819i	−0.419539	−	0.419539i
$590$	−0.566525	−	2.41388i	−0.0233235	−	0.0993777i
$591$	−34.5601			−1.42161
$592$	0.884589	+	6.43095i	0.0363564	+	0.264310i
$593$	−43.2423			−1.77575			−0.887875	−	0.460085i	$-0.847819\pi$
$593$	−43.2423			−1.77575			−0.887875	+	0.460085i	$0.847819\pi$
$594$	1.56752	+	6.67895i	0.0643160	+	0.274041i
$595$	−2.83648	−	2.83648i	−0.116284	−	0.116284i
$596$	−6.69936	+	19.9251i	−0.274416	+	0.816165i
$597$	−43.2476	+	43.2476i	−1.77000	+	1.77000i
$598$	3.05974	−	4.93639i	0.125122	−	0.201864i
$599$			12.2633i			0.501067i	0.968108	+	0.250533i	$0.0806060\pi$
$599$			12.2633i			0.501067i	−0.968108	+	0.250533i	$0.919394\pi$
$600$	0.629448	−	6.68875i	0.0256971	−	0.273067i
$601$		−	10.1758i		−	0.415078i	−0.978227	−	0.207539i	$-0.933455\pi$
$601$		−	10.1758i		−	0.415078i	0.978227	−	0.207539i	$-0.0665455\pi$
$602$	−14.8017	−	9.17458i	−0.603272	−	0.373928i
$603$	−6.29582	+	6.29582i	−0.256385	+	0.256385i
$604$	−15.1313	−	30.4605i	−0.615686	−	1.23942i
$605$	−15.2283	−	15.2283i	−0.619120	−	0.619120i
$606$	14.5193	−	3.40761i	0.589806	−	0.138425i
$607$	34.7601			1.41087			0.705434	−	0.708776i	$-0.250752\pi$
$607$	34.7601			1.41087			0.705434	+	0.708776i	$0.250752\pi$
$608$	−8.80086	+	3.38538i	−0.356922	+	0.137295i
$609$	−8.14951			−0.330235
$610$	−11.1367	+	2.61372i	−0.450910	+	0.105826i
$611$	−37.6915	−	37.6915i	−1.52483	−	1.52483i
$612$	9.42969	+	18.9827i	0.381173	+	0.767329i
$613$	−21.1023	+	21.1023i	−0.852314	+	0.852314i	−0.990418	−	0.138103i	$-0.955899\pi$
$613$	−21.1023	+	21.1023i	−0.852314	+	0.852314i	0.138103	+	0.990418i	$0.455899\pi$
$614$	13.8957	+	8.61303i	0.560786	+	0.347594i
$615$			2.96395i			0.119518i
$616$	−16.0625	−	1.51157i	−0.647177	−	0.0609028i
$617$			29.6621i			1.19415i	0.802185	+	0.597075i	$0.203671\pi$
$617$			29.6621i			1.19415i	−0.802185	+	0.597075i	$0.796329\pi$
$618$	−5.38011	+	8.67993i	−0.216420	+	0.349158i
$619$	−22.1895	+	22.1895i	−0.891872	+	0.891872i	−0.994699	−	0.102827i	$-0.967211\pi$
$619$	−22.1895	+	22.1895i	−0.891872	+	0.891872i	0.102827	+	0.994699i	$0.467211\pi$
$620$	−5.50599	+	16.3758i	−0.221126	+	0.657669i
$621$	0.367395	+	0.367395i	0.0147431	+	0.0147431i
$622$	−5.96762	−	25.4271i	−0.239280	−	1.01953i
$623$	18.0907			0.724790
$624$	50.8931	+	38.5852i	2.03735	+	1.54464i
$625$	−1.00000			−0.0400000
$626$	−2.59177	−	11.0432i	−0.103588	−	0.441373i
$627$	15.9697	+	15.9697i	0.637770	+	0.637770i
$628$	−27.5740	−	9.27111i	−1.10032	−	0.369958i
$629$	−4.60325	+	4.60325i	−0.183544	+	0.183544i
$630$	−1.96842	+	3.17572i	−0.0784235	+	0.126524i
$631$			24.2301i			0.964583i	0.876011	+	0.482292i	$0.160195\pi$
$631$			24.2301i			0.964583i	−0.876011	+	0.482292i	$0.839805\pi$
$632$	−6.85980	+	5.67976i	−0.272868	+	0.225929i
$633$			40.7370i			1.61915i
$634$	−16.3656	−	10.1439i	−0.649961	−	0.402867i
$635$	−6.84636	+	6.84636i	−0.271690	+	0.271690i
$636$	33.9754	−	16.8774i	1.34721	−	0.669232i
$637$	4.75317	+	4.75317i	0.188327	+	0.188327i
$638$	26.9446	−	6.32377i	1.06675	−	0.250360i
$639$	4.16548			0.164784
$640$	8.33547	+	7.64984i	0.329488	+	0.302386i
$641$	−29.6060			−1.16937			−0.584683	−	0.811262i	$-0.698781\pi$
$641$	−29.6060			−1.16937			−0.584683	+	0.811262i	$0.698781\pi$
$642$	1.61839	−	0.379827i	0.0638726	−	0.0149906i
$643$	−23.5440	−	23.5440i	−0.928485	−	0.928485i	0.0691234	−	0.997608i	$-0.477980\pi$
$643$	−23.5440	−	23.5440i	−0.928485	−	0.928485i	−0.997608	+	0.0691234i	$0.977980\pi$
$644$	−1.09429	+	0.543592i	−0.0431211	+	0.0214205i
$645$	20.6821	−	20.6821i	0.814357	−	0.814357i
$646$	−8.03759	−	4.98196i	−0.316235	−	0.196013i
$647$			0.629008i			0.0247288i	0.999924	+	0.0123644i	$0.00393582\pi$
$647$			0.629008i			0.0247288i	−0.999924	+	0.0123644i	$0.996064\pi$
$648$	−21.6681	+	17.9407i	−0.851203	+	0.704777i
$649$		−	10.0006i		−	0.392558i
$650$	5.00829	−	8.08006i	0.196441	−	0.316926i
$651$	14.5087	−	14.5087i	0.568643	−	0.568643i
$652$	−4.23565	−	1.42414i	−0.165881	−	0.0557735i
$653$	16.0838	+	16.0838i	0.629409	+	0.629409i	0.947919	−	0.318510i	$-0.103183\pi$
$653$	16.0838	+	16.0838i	0.629409	+	0.629409i	−0.318510	+	0.947919i	$0.603183\pi$
$654$	−10.4889	−	44.6915i	−0.410147	−	1.74757i
$655$	−14.6416			−0.572095
$656$	−3.97743	−	3.01554i	−0.155293	−	0.117737i
$657$	−4.91310			−0.191678
$658$	2.56234	+	10.9177i	0.0998903	+	0.425617i
$659$	32.6711	+	32.6711i	1.27268	+	1.27268i	0.944674	+	0.328011i	$0.106378\pi$
$659$	32.6711	+	32.6711i	1.27268	+	1.27268i	0.328011	+	0.944674i	$0.393622\pi$
$660$	8.63580	−	25.6845i	0.336148	−	0.999767i
$661$	−12.6881	+	12.6881i	−0.493512	+	0.493512i	−0.909411	−	0.415899i	$-0.863467\pi$
$661$	−12.6881	+	12.6881i	−0.493512	+	0.493512i	0.415899	+	0.909411i	$0.363467\pi$
$662$	15.2815	−	24.6542i	0.593932	−	0.958212i
$663$			64.0482i			2.48743i
$664$	23.9653	+	2.25526i	0.930033	+	0.0875211i
$665$		−	1.66692i		−	0.0646404i
$666$	5.15380	+	3.19449i	0.199706	+	0.123784i
$667$	1.48217	−	1.48217i	0.0573897	−	0.0573897i
$668$	17.2683	+	34.7624i	0.668130	+	1.34500i
$669$	−2.76969	−	2.76969i	−0.107082	−	0.107082i
$670$	−4.63995	+	1.08897i	−0.179257	+	0.0420708i
$671$	−46.1388			−1.78117
$672$	−4.82400	−	12.5408i	−0.186090	−	0.483772i
$673$	45.0856			1.73792			0.868961	−	0.494880i	$-0.164788\pi$
$673$	45.0856			1.73792			0.868961	+	0.494880i	$0.164788\pi$
$674$	8.62532	−	2.02432i	0.332235	−	0.0779739i
$675$	0.601365	+	0.601365i	0.0231466	+	0.0231466i
$676$	28.6374	+	57.6493i	1.10144	+	2.21728i
$677$	6.31413	−	6.31413i	0.242672	−	0.242672i	−0.575283	−	0.817955i	$-0.695108\pi$
$677$	6.31413	−	6.31413i	0.242672	−	0.242672i	0.817955	+	0.575283i	$0.195108\pi$
$678$	−44.8236	−	27.7832i	−1.72144	−	1.06701i
$679$			10.6607i			0.409118i
$680$	−1.06301	+	11.2960i	−0.0407647	+	0.433182i
$681$		−	1.95636i		−	0.0749679i
$682$	−36.7117	+	59.2284i	−1.40576	+	2.26797i
$683$	−1.23835	+	1.23835i	−0.0473841	+	0.0473841i	−0.730402	−	0.683018i	$-0.760667\pi$
$683$	−1.23835	+	1.23835i	−0.0473841	+	0.0473841i	0.683018	+	0.730402i	$0.260667\pi$
$684$	−2.80702	+	8.34859i	−0.107329	+	0.319216i
$685$	−5.51837	−	5.51837i	−0.210846	−	0.210846i
$686$	−0.323129	−	1.37680i	−0.0123371	−	0.0525666i
$687$	−19.2410			−0.734090
$688$	6.71198	+	48.7960i	0.255892	+	1.86033i
$689$	53.6797			2.04503
$690$	−0.468906	−	1.99794i	−0.0178509	−	0.0760601i
$691$	4.67186	+	4.67186i	0.177726	+	0.177726i	0.790364	−	0.612638i	$-0.209892\pi$
$691$	4.67186	+	4.67186i	0.177726	+	0.177726i	−0.612638	+	0.790364i	$0.709892\pi$
$692$	−6.80062	−	2.28655i	−0.258521	−	0.0869215i
$693$	−10.6560	+	10.6560i	−0.404787	+	0.404787i
$694$	1.60660	−	2.59199i	0.0609858	−	0.0983907i
$695$		−	18.1952i		−	0.690185i
$696$	14.7002	+	17.7544i	0.557211	+	0.672979i
$697$		−	5.00554i		−	0.189598i
$698$	−1.03925	−	0.644163i	−0.0393363	−	0.0243819i
$699$	−1.97092	+	1.97092i	−0.0745469	+	0.0745469i
$700$	−1.79118	+	0.889770i	−0.0677001	+	0.0336302i
$701$	13.3471	+	13.3471i	0.504113	+	0.504113i	0.912713	−	0.408600i	$-0.133983\pi$
$701$	13.3471	+	13.3471i	0.504113	+	0.504113i	−0.408600	+	0.912713i	$0.633983\pi$
$702$	−7.87088	+	1.84726i	−0.297067	+	0.0697202i
$703$	−2.70521			−0.102029
$704$	25.6808	+	37.7202i	0.967881	+	1.42163i
$705$	−18.8354			−0.709382
$706$	34.1294	−	8.01001i	1.28448	−	0.301461i
$707$	−3.13938	−	3.13938i	−0.118069	−	0.118069i
$708$	7.45926	−	3.70541i	0.280336	−	0.139258i
$709$	−28.0487	+	28.0487i	−1.05339	+	1.05339i	−0.0548997	+	0.998492i	$0.517484\pi$
$709$	−28.0487	+	28.0487i	−1.05339	+	1.05339i	−0.998492	+	0.0548997i	$0.982516\pi$
$710$	1.89521	+	1.17471i	0.0711258	+	0.0440861i
$711$			8.31883i			0.311980i
$712$	−32.6324	−	39.4122i	−1.22295	−	1.47703i
$713$			5.27746i			0.197643i
$714$	7.09905	−	11.4532i	0.265675	−	0.428624i
$715$	27.1123	−	27.1123i	1.01394	−	1.01394i
$716$	−1.14408	−	0.384669i	−0.0427562	−	0.0143758i
$717$	47.8037	+	47.8037i	1.78526	+	1.78526i
$718$	5.60147	+	23.8670i	0.209045	+	0.890708i
$719$	1.45224			0.0541594			0.0270797	−	0.999633i	$-0.491379\pi$
$719$	1.45224			0.0541594			0.0270797	+	0.999633i	$0.491379\pi$
$720$	10.4692	−	1.44006i	0.390166	−	0.0536680i
$721$	3.04008			0.113218
$722$	5.24160	+	22.3336i	0.195072	+	0.831172i
$723$	31.7632	+	31.7632i	1.18128	+	1.18128i
$724$	4.38010	−	13.0272i	0.162785	−	0.484153i
$725$	2.42606	−	2.42606i	0.0901017	−	0.0901017i
$726$	38.1131	−	61.4893i	1.41451	−	2.28208i
$727$		−	1.90322i		−	0.0705866i	−0.999377	−	0.0352933i	$-0.988763\pi$
$727$		−	1.90322i		−	0.0705866i	0.999377	−	0.0352933i	$-0.0112365\pi$
$728$	1.78132	−	18.9290i	0.0660203	−	0.701557i
$729$			20.2165i			0.748759i
$730$	−2.23536	−	1.38555i	−0.0827342	−	0.0512814i
$731$	−34.9280	+	34.9280i	−1.29186	+	1.29186i
$732$	−17.0953	−	34.4141i	−0.631859	−	1.27198i
$733$	−13.0224	−	13.0224i	−0.480993	−	0.480993i	0.424456	−	0.905449i	$-0.360465\pi$
$733$	−13.0224	−	13.0224i	−0.480993	−	0.480993i	−0.905449	+	0.424456i	$0.860465\pi$
$734$	−9.46335	+	2.22100i	−0.349299	+	0.0819787i
$735$	2.37528			0.0876135
$736$	3.15817	+	1.40347i	0.116412	+	0.0517324i
$737$	−19.2232			−0.708094
$738$	−4.53893	+	1.06527i	−0.167080	+	0.0392130i
$739$	0.749479	+	0.749479i	0.0275700	+	0.0275700i	0.720757	−	0.693187i	$-0.243794\pi$
$739$	0.749479	+	0.749479i	0.0275700	+	0.0275700i	−0.693187	+	0.720757i	$0.743794\pi$
$740$	1.44399	+	2.90686i	0.0530820	+	0.106858i
$741$	−18.8197	+	18.8197i	−0.691359	+	0.691359i
$742$	−9.59907	−	5.94982i	−0.352393	−	0.218425i
$743$			34.5259i			1.26663i	0.773893	+	0.633317i	$0.218307\pi$
$743$			34.5259i			1.26663i	−0.773893	+	0.633317i	$0.781693\pi$
$744$	−57.7797	−	5.43738i	−2.11831	−	0.199344i
$745$			10.5106i			0.385079i
$746$	−21.2762	+	34.3257i	−0.778976	+	1.25675i
$747$	15.8987	−	15.8987i	0.581704	−	0.581704i
$748$	−14.5842	+	43.3761i	−0.533250	+	1.58599i
$749$	−0.349930	−	0.349930i	−0.0127861	−	0.0127861i
$750$	−0.767522	−	3.27029i	−0.0280259	−	0.119414i
$751$	−1.69258			−0.0617631			−0.0308815	−	0.999523i	$-0.509831\pi$
$751$	−1.69258			−0.0617631			−0.0308815	+	0.999523i	$0.509831\pi$
$752$	19.1632	−	25.2759i	0.698810	−	0.921716i
$753$	30.8278			1.12343
$754$	7.45231	+	31.7531i	0.271397	+	1.15638i
$755$	−12.0250	−	12.0250i	−0.437634	−	0.437634i
$756$	1.61223	+	0.542074i	0.0586361	+	0.0197150i
$757$	17.2025	−	17.2025i	0.625235	−	0.625235i	−0.321630	−	0.946865i	$-0.604231\pi$
$757$	17.2025	−	17.2025i	0.625235	−	0.625235i	0.946865	+	0.321630i	$0.104231\pi$
$758$	3.62218	−	5.84380i	0.131563	−	0.212256i
$759$		−	8.27738i		−	0.300450i
$760$	−3.63153	+	3.00682i	−0.131729	+	0.109069i
$761$		−	15.5249i		−	0.562778i	−0.959594	−	0.281389i	$-0.909205\pi$
$761$		−	15.5249i		−	0.562778i	0.959594	−	0.281389i	$-0.0907951\pi$
$762$	−27.6443	−	17.1349i	−1.00145	−	0.620731i
$763$	−9.66324	+	9.66324i	−0.349833	+	0.349833i
$764$	−20.5478	+	10.2072i	−0.743394	+	0.369282i
$765$	7.49384	+	7.49384i	0.270940	+	0.270940i
$766$	−24.4773	+	5.74470i	−0.884401	+	0.207565i
$767$	11.7853			0.425543
$768$	−18.6196	+	33.1308i	−0.671875	+	1.19551i
$769$	−3.03643			−0.109496			−0.0547482	−	0.998500i	$-0.517436\pi$
$769$	−3.03643			−0.109496			−0.0547482	+	0.998500i	$0.517436\pi$
$770$	−7.85335	+	1.84314i	−0.283015	+	0.0664223i
$771$	29.3535	+	29.3535i	1.05714	+	1.05714i
$772$	24.0466	−	11.9452i	0.865455	−	0.429917i
$773$	−28.2372	+	28.2372i	−1.01562	+	1.01562i	−0.0157441	+	0.999876i	$0.505012\pi$
$773$	−28.2372	+	28.2372i	−1.01562	+	1.01562i	−0.999876	+	0.0157441i	$0.994988\pi$
$774$	39.1054	+	24.2388i	1.40561	+	0.871246i
$775$			8.63834i			0.310298i
$776$	23.2252	−	19.2299i	0.833734	−	0.690313i
$777$		−	3.85478i		−	0.138290i
$778$	−18.7233	+	30.2070i	−0.671263	+	1.08297i
$779$	1.47081	−	1.47081i	0.0526972	−	0.0526972i
$780$	30.2681	+	10.1770i	1.08377	+	0.364393i
$781$	6.35928	+	6.35928i	0.227553	+	0.227553i
$782$	0.791891	+	3.37412i	0.0283180	+	0.120658i
$783$	−2.91790			−0.104277
$784$	−2.41662	+	3.18747i	−0.0863078	+	0.113838i
$785$	−14.5454			−0.519149
$786$	−11.2378	−	47.8824i	−0.400838	−	1.70791i
$787$	−8.21518	−	8.21518i	−0.292839	−	0.292839i	0.545362	−	0.838201i	$-0.316392\pi$
$787$	−8.21518	−	8.21518i	−0.292839	−	0.292839i	−0.838201	+	0.545362i	$0.816392\pi$
$788$	9.27397	−	27.5825i	0.330371	−	0.982586i
$789$	24.7751	−	24.7751i	0.882018	−	0.882018i
$790$	−2.34600	+	3.78489i	−0.0834670	+	0.134660i
$791$			15.6991i			0.558197i
$792$	42.4364	+	3.99350i	1.50791	+	0.141903i
$793$		−	54.3727i		−	1.93083i
$794$	−21.6968	−	13.4484i	−0.769992	−	0.477267i
$795$	13.4126	−	13.4126i	0.475695	−	0.475695i
$796$	−22.9108	−	46.1211i	−0.812051	−	1.63472i
$797$	21.3358	+	21.3358i	0.755754	+	0.755754i	0.975547	−	0.219793i	$-0.0705381\pi$
$797$	21.3358	+	21.3358i	0.755754	+	0.755754i	−0.219793	+	0.975547i	$0.570538\pi$
$798$	5.45132	−	1.27940i	0.192975	−	0.0452902i
$799$	31.8093			1.12533
$800$	5.16940	+	2.29724i	0.182766	+	0.0812198i
$801$	−47.7949			−1.68875
$802$	−28.3008	+	6.64207i	−0.999337	+	0.234540i
$803$	−7.50063	−	7.50063i	−0.264692	−	0.264692i
$804$	−7.12253	−	14.3382i	−0.251192	−	0.505669i
$805$	−0.431996	+	0.431996i	−0.0152259	+	0.0152259i
$806$	−69.7983	−	43.2633i	−2.45854	−	1.52388i
$807$			23.9894i			0.844467i
$808$	−1.17653	+	12.5023i	−0.0413903	+	0.439829i
$809$		−	18.4079i		−	0.647186i	−0.946196	−	0.323593i	$-0.895109\pi$
$809$		−	18.4079i		−	0.647186i	0.946196	−	0.323593i	$-0.104891\pi$
$810$	−7.41033	+	11.9554i	−0.260372	+	0.420068i
$811$	30.9453	−	30.9453i	1.08664	−	1.08664i	0.0907642	−	0.995872i	$-0.471069\pi$
$811$	30.9453	−	30.9453i	1.08664	−	1.08664i	0.995872	−	0.0907642i	$-0.0289310\pi$
$812$	2.18686	−	6.50414i	0.0767439	−	0.228251i
$813$	−40.7349	−	40.7349i	−1.42863	−	1.42863i
$814$	2.99119	+	12.7450i	0.104841	+	0.446712i
$815$	−2.23433			−0.0782651
$816$	−37.7571	+	5.19356i	−1.32176	+	0.181811i
$817$	−20.5263			−0.718123
$818$	−6.69908	−	28.5438i	−0.234228	−	0.998010i
$819$	−12.5576	−	12.5576i	−0.438800	−	0.438800i
$820$	−2.36554	−	0.795356i	−0.0826081	−	0.0277750i
$821$	−26.7423	+	26.7423i	−0.933312	+	0.933312i	−0.997911	−	0.0645994i	$-0.979423\pi$
$821$	−26.7423	+	26.7423i	−0.933312	+	0.933312i	0.0645994	+	0.997911i	$0.479423\pi$
$822$	13.8112	−	22.2822i	0.481721	−	0.777179i
$823$		−	17.1926i		−	0.599297i	−0.954050	−	0.299649i	$-0.903131\pi$
$823$		−	17.1926i		−	0.599297i	0.954050	−	0.299649i	$-0.0968694\pi$
$824$	−5.48375	−	6.62307i	−0.191036	−	0.230725i
$825$		−	13.5487i		−	0.471705i
$826$	−2.10746	−	1.30627i	−0.0733280	−	0.0454511i
$827$	20.7087	−	20.7087i	0.720112	−	0.720112i	−0.248516	−	0.968628i	$-0.579943\pi$
$827$	20.7087	−	20.7087i	0.720112	−	0.720112i	0.968628	+	0.248516i	$0.0799429\pi$
$828$	2.89107	−	1.43614i	0.100472	−	0.0499095i
$829$	23.2314	+	23.2314i	0.806860	+	0.806860i	0.984157	−	0.177297i	$-0.0567354\pi$
$829$	23.2314	+	23.2314i	0.806860	+	0.806860i	−0.177297	+	0.984157i	$0.556735\pi$
$830$	11.7172	−	2.74997i	0.406710	−	0.0954529i
$831$	46.0087			1.59603
$832$	−44.4517	+	30.2638i	−1.54109	+	1.04921i
$833$	−4.01138			−0.138986
$834$	59.5038	−	13.9652i	2.06045	−	0.483577i
$835$	13.7232	+	13.7232i	0.474912	+	0.474912i
$836$	−17.0308	+	8.46011i	−0.589024	+	0.292599i
$837$	5.19480	−	5.19480i	0.179558	−	0.179558i
$838$	−6.55476	−	4.06286i	−0.226430	−	0.140349i
$839$		−	3.91663i		−	0.135217i	−0.997712	−	0.0676085i	$-0.978463\pi$
$839$		−	3.91663i		−	0.135217i	0.997712	−	0.0676085i	$-0.0215369\pi$
$840$	−4.28458	−	5.17475i	−0.147832	−	0.178546i
$841$		−	17.2285i		−	0.594085i
$842$	0.506718	−	0.817507i	0.0174627	−	0.0281732i
$843$	27.2079	−	27.2079i	0.937090	−	0.937090i
$844$	−32.5123	−	10.9315i	−1.11912	−	0.376277i
$845$	22.7584	+	22.7584i	0.782911	+	0.782911i
$846$	−6.76957	−	28.8441i	−0.232743	−	0.991681i
$847$	−21.5361			−0.739990
$848$	4.35280	+	31.6448i	0.149476	+	1.08669i
$849$	−36.2557			−1.24429
$850$	1.29619	+	5.52289i	0.0444591	+	0.189433i
$851$	0.701076	+	0.701076i	0.0240326	+	0.0240326i
$852$	−2.38704	+	7.09950i	−0.0817786	+	0.243225i
$853$	−19.3540	+	19.3540i	−0.662667	+	0.662667i	−0.956008	−	0.293341i	$-0.905233\pi$
$853$	−19.3540	+	19.3540i	−0.662667	+	0.662667i	0.293341	+	0.956008i	$0.405233\pi$
$854$	−6.02663	+	9.72299i	−0.206227	+	0.332714i
$855$			4.40393i			0.150611i
$856$	−0.131142	+	1.39356i	−0.00448233	+	0.0476309i
$857$		−	57.3516i		−	1.95909i	−0.201218	−	0.979546i	$-0.564490\pi$
$857$		−	57.3516i		−	1.95909i	0.201218	−	0.979546i	$-0.435510\pi$
$858$	109.474	+	67.8558i	3.73739	+	2.31656i
$859$	−14.9811	+	14.9811i	−0.511150	+	0.511150i	−0.914879	−	0.403729i	$-0.867714\pi$
$859$	−14.9811	+	14.9811i	−0.511150	+	0.511150i	0.403729	+	0.914879i	$0.367714\pi$
$860$	10.9565	+	22.0563i	0.373614	+	0.752114i
$861$	2.09583	+	2.09583i	0.0714258	+	0.0714258i
$862$	−21.7837	+	5.11252i	−0.741954	+	0.174133i
$863$	28.9117			0.984167			0.492083	−	0.870548i	$-0.336235\pi$
$863$	28.9117			0.984167			0.492083	+	0.870548i	$0.336235\pi$
$864$	−1.72721	−	4.49018i	−0.0587610	−	0.152759i
$865$	−3.58736			−0.121974
$866$	14.7804	−	3.46889i	0.502259	−	0.117878i
$867$	1.52640	+	1.52640i	0.0518394	+	0.0518394i
$868$	7.68614	+	15.4728i	0.260885	+	0.525180i
$869$	−12.7000	+	12.7000i	−0.430819	+	0.430819i
$870$	9.79599	+	6.07188i	0.332115	+	0.205856i
$871$		−	22.6537i		−	0.767592i
$872$	38.4829	+	3.62145i	1.30320	+	0.122638i
$873$		−	28.1650i		−	0.953240i
$874$	−0.758755	+	1.22413i	−0.0256653	+	0.0414067i
$875$	−0.707107	+	0.707107i	−0.0239046	+	0.0239046i
$876$	2.81546	−	8.37371i	0.0951256	−	0.282921i
$877$	17.3785	+	17.3785i	0.586829	+	0.586829i	0.936771	−	0.349942i	$-0.113799\pi$
$877$	17.3785	+	17.3785i	0.586829	+	0.586829i	−0.349942	+	0.936771i	$0.613799\pi$
$878$	10.4686	+	44.6052i	0.353299	+	1.50535i
$879$	−14.7209			−0.496525
$880$	18.1815	+	13.7845i	0.612897	+	0.464675i
$881$	10.8578			0.365807			0.182904	−	0.983131i	$-0.441450\pi$
$881$	10.8578			0.365807			0.182904	+	0.983131i	$0.441450\pi$
$882$	0.853692	+	3.63745i	0.0287453	+	0.122479i
$883$	16.5408	+	16.5408i	0.556644	+	0.556644i	0.928350	−	0.371707i	$-0.121227\pi$
$883$	16.5408	+	16.5408i	0.556644	+	0.556644i	−0.371707	+	0.928350i	$0.621227\pi$
$884$	−51.1170	−	17.1869i	−1.71925	−	0.578057i
$885$	2.94471	−	2.94471i	0.0989854	−	0.0989854i
$886$	20.6051	−	33.2430i	0.692243	−	1.11682i
$887$		−	31.7134i		−	1.06483i	−0.846483	−	0.532416i	$-0.821284\pi$
$887$		−	31.7134i		−	1.06483i	0.846483	−	0.532416i	$-0.178716\pi$
$888$	−8.39798	+	6.95334i	−0.281818	+	0.233339i
$889$			9.68222i			0.324731i
$890$	−21.7457	−	13.4787i	−0.728916	−	0.451806i
$891$	−40.1157	+	40.1157i	−1.34392	+	1.34392i
$892$	2.95372	−	1.46727i	0.0988979	−	0.0491278i
$893$	9.34674	+	9.34674i	0.312777	+	0.312777i
$894$	−34.3728	+	8.06713i	−1.14960	+	0.269805i
$895$	−0.603507			−0.0201730
$896$	11.3033	−	0.484813i	0.377617	−	0.0161965i
$897$	9.75456			0.325695
$898$	57.5707	−	13.5116i	1.92116	−	0.450887i
$899$	−20.9571	−	20.9571i	−0.698960	−	0.698960i
$900$	4.73220	−	2.35073i	0.157740	−	0.0783578i
$901$	−22.6512	+	22.6512i	−0.754621	+	0.754621i
$902$	−8.55572	−	5.30312i	−0.284874	−	0.176574i
$903$		−	29.2489i		−	0.973343i
$904$	34.2019	−	28.3184i	1.13754	−	0.941856i
$905$		−	6.87194i		−	0.228431i
$906$	30.0958	−	48.5547i	0.999865	−	1.61312i
$907$	−26.9647	+	26.9647i	−0.895347	+	0.895347i	−0.995020	−	0.0996733i	$-0.968220\pi$
$907$	−26.9647	+	26.9647i	−0.895347	+	0.895347i	0.0996733	+	0.995020i	$0.468220\pi$
$908$	1.56137	+	0.524976i	0.0518160	+	0.0174219i
$909$	8.29410	+	8.29410i	0.275098	+	0.275098i
$910$	−2.17207	−	9.25486i	−0.0720035	−	0.306796i
$911$	3.58613			0.118814			0.0594070	−	0.998234i	$-0.481079\pi$
$911$	3.58613			0.118814			0.0594070	+	0.998234i	$0.481079\pi$
$912$	−12.6205	−	9.56836i	−0.417906	−	0.316840i
$913$	48.5439			1.60657
$914$	−5.96491	−	25.4156i	−0.197302	−	0.840672i
$915$	−13.5857	−	13.5857i	−0.449130	−	0.449130i
$916$	5.16319	−	15.3563i	0.170597	−	0.507386i
$917$	−10.3532	+	10.3532i	−0.341892	+	0.341892i
$918$	2.54179	−	4.10076i	0.0838914	−	0.135345i
$919$			23.7442i			0.783249i	0.920125	+	0.391624i	$0.128087\pi$
$919$			23.7442i			0.783249i	−0.920125	+	0.391624i	$0.871913\pi$
$920$	1.72038	+	0.161897i	0.0567194	+	0.00533760i
$921$			27.4587i			0.904794i
$922$	−11.7348	−	7.27364i	−0.386466	−	0.239545i
$923$	−7.49416	+	7.49416i	−0.246673	+	0.246673i
$924$	−12.0552	−	24.2681i	−0.396588	−	0.798362i
$925$	1.14755	+	1.14755i	0.0377311	+	0.0377311i
$926$	−32.7940	+	7.69659i	−1.07768	+	0.252926i
$927$	−8.03174			−0.263797
$928$	−18.1145	+	6.96802i	−0.594639	+	0.228737i
$929$	5.63142			0.184761			0.0923805	−	0.995724i	$-0.470552\pi$
$929$	5.63142			0.184761			0.0923805	+	0.995724i	$0.470552\pi$
$930$	−28.2499	+	6.63011i	−0.926351	+	0.217410i
$931$	−1.17869	−	1.17869i	−0.0386300	−	0.0386300i
$932$	−1.04411	−	2.10187i	−0.0342010	−	0.0688492i
$933$	31.0188	−	31.0188i	1.01551	−	1.01551i
$934$	−16.5542	−	10.2609i	−0.541670	−	0.335745i
$935$			22.8811i			0.748292i
$936$	−4.70618	+	50.0096i	−0.153826	+	1.63462i
$937$			22.1711i			0.724299i	0.932120	+	0.362150i	$0.117957\pi$
$937$			22.1711i			0.724299i	−0.932120	+	0.362150i	$0.882043\pi$
$938$	−2.51092	+	4.05096i	−0.0819845	+	0.132269i
$939$	13.4717	−	13.4717i	0.439631	−	0.439631i
$940$	5.05435	−	15.0326i	0.164855	−	0.490308i
$941$	−23.5907	−	23.5907i	−0.769036	−	0.769036i	0.208900	−	0.977937i	$-0.433012\pi$
$941$	−23.5907	−	23.5907i	−0.769036	−	0.769036i	−0.977937	+	0.208900i	$0.933012\pi$
$942$	−11.1639	−	47.5679i	−0.363741	−	1.54984i
$943$	−0.762345			−0.0248254
$944$	0.955651	+	6.94757i	0.0311038	+	0.226124i
$945$	0.850459			0.0276654
$946$	22.6962	+	96.7052i	0.737918	+	3.14416i
$947$	17.6049	+	17.6049i	0.572084	+	0.572084i	0.932710	−	0.360627i	$-0.117437\pi$
$947$	17.6049	+	17.6049i	0.572084	+	0.572084i	−0.360627	+	0.932710i	$0.617437\pi$
$948$	−14.1783	−	4.76712i	−0.460490	−	0.154829i
$949$	8.83920	−	8.83920i	0.286933	−	0.286933i
$950$	−1.24196	+	2.00369i	−0.0402944	+	0.0650084i
$951$		−	32.3392i		−	1.04867i
$952$	7.23581	+	8.73914i	0.234514	+	0.283237i
$953$			27.9895i			0.906670i	0.891340	+	0.453335i	$0.149766\pi$
$953$			27.9895i			0.906670i	−0.891340	+	0.453335i	$0.850234\pi$
$954$	25.3603	+	15.7191i	0.821070	+	0.508926i
$955$	−8.11171	+	8.11171i	−0.262489	+	0.262489i
$956$	−50.9800	+	25.3244i	−1.64881	+	0.819051i
$957$	32.8700	+	32.8700i	1.06254	+	1.06254i
$958$	36.1998	−	8.49591i	1.16956	−	0.274490i
$959$	−7.80415			−0.252009
$960$	−3.54503	+	18.6686i	−0.114415	+	0.602528i
$961$	43.6209			1.40713
$962$	−15.0195	+	3.52500i	−0.484248	+	0.113651i
$963$	0.924498	+	0.924498i	0.0297915	+	0.0297915i
$964$	−33.8737	+	16.8268i	−1.09100	+	0.541955i
$965$	9.49293	−	9.49293i	0.305588	−	0.305588i
$966$	−1.74432	−	1.08119i	−0.0561226	−	0.0347867i
$967$		−	32.9438i		−	1.05940i	−0.848185	−	0.529700i	$-0.822304\pi$
$967$		−	32.9438i		−	1.05940i	0.848185	−	0.529700i	$-0.177696\pi$
$968$	38.8473	+	46.9183i	1.24860	+	1.50801i
$969$		−	15.8827i		−	0.510225i
$970$	7.94283	−	12.8145i	0.255029	−	0.411448i
$971$	3.25667	−	3.25667i	0.104512	−	0.104512i	−0.652917	−	0.757429i	$-0.726455\pi$
$971$	3.25667	−	3.25667i	0.104512	−	0.104512i	0.757429	+	0.652917i	$0.226455\pi$
$972$	−39.9484	−	13.4317i	−1.28135	−	0.430823i
$973$	−12.8660	−	12.8660i	−0.412464	−	0.412464i
$974$	−3.00846	−	12.8186i	−0.0963974	−	0.410734i
$975$	15.9666			0.511341
$976$	32.0533	−	4.40899i	1.02600	−	0.141128i
$977$	14.8275			0.474373			0.237187	−	0.971464i	$-0.423775\pi$
$977$	14.8275			0.474373			0.237187	+	0.971464i	$0.423775\pi$
$978$	−1.71490	−	7.30691i	−0.0548363	−	0.233649i
$979$	−72.9666	−	72.9666i	−2.33202	−	2.33202i
$980$	−0.637389	+	1.89571i	−0.0203607	+	0.0605564i
$981$	25.5298	−	25.5298i	0.815105	−	0.815105i
$982$	−18.8008	+	30.3320i	−0.599956	+	0.967932i
$983$			10.9665i			0.349778i	0.984588	+	0.174889i	$0.0559567\pi$
$983$			10.9665i			0.349778i	−0.984588	+	0.174889i	$0.944043\pi$
$984$	0.785446	−	8.34645i	0.0250391	−	0.266075i
$985$		−	14.5499i		−	0.463599i
$986$	−16.5435	−	10.2542i	−0.526853	−	0.326561i
$987$	−13.3186	+	13.3186i	−0.423937	+	0.423937i
$988$	−9.96990	−	20.0702i	−0.317185	−	0.638517i
$989$	5.31955	+	5.31955i	0.169152	+	0.169152i
$990$	20.7482	−	4.86950i	0.659421	−	0.154763i
$991$	−44.7006			−1.41996			−0.709981	−	0.704221i	$-0.751297\pi$
$991$	−44.7006			−1.41996			−0.709981	+	0.704221i	$0.751297\pi$
$992$	19.8444	−	44.6550i	0.630059	−	1.41780i
$993$	48.7179			1.54602
$994$	2.17076	−	0.509467i	0.0688523	−	0.0161593i
$995$	−18.2074	−	18.2074i	−0.577212	−	0.577212i
$996$	17.9864	+	36.2080i	0.569922	+	1.14730i
$997$	29.8446	−	29.8446i	0.945187	−	0.945187i	−0.0533873	−	0.998574i	$-0.517002\pi$
$997$	29.8446	−	29.8446i	0.945187	−	0.945187i	0.998574	+	0.0533873i	$0.0170018\pi$
$998$	−41.4743	−	25.7072i	−1.31285	−	0.813746i
$999$		−	1.38019i		−	0.0436673i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bd.a.141.4	✓	44
4.3	odd	2		2240.2.bd.a.1681.20		44
16.5	even	4	inner	560.2.bd.a.421.4	yes	44
16.11	odd	4		2240.2.bd.a.561.20		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.a.141.4	✓	44	1.1	even	1	trivial
560.2.bd.a.421.4	yes	44	16.5	even	4	inner
2240.2.bd.a.561.20		44	16.11	odd	4
2240.2.bd.a.1681.20		44	4.3	odd	2

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bd (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37680 + 0.323129i) q^{2} +(-1.67958 - 1.67958i) q^{3} +(1.79118 - 0.889770i) q^{4} +(0.707107 - 0.707107i) q^{5} +(2.85517 + 1.76973i) q^{6} -1.00000i q^{7} +(-2.17859 + 1.80382i) q^{8} +2.64195i q^{9} +O(q^{10})\)	\(q+(-1.37680 + 0.323129i) q^{2} +(-1.67958 - 1.67958i) q^{3} +(1.79118 - 0.889770i) q^{4} +(0.707107 - 0.707107i) q^{5} +(2.85517 + 1.76973i) q^{6} -1.00000i q^{7} +(-2.17859 + 1.80382i) q^{8} +2.64195i q^{9} +(-0.745060 + 1.20203i) q^{10} +(-4.03337 + 4.03337i) q^{11} +(-4.50285 - 1.51398i) q^{12} +(-4.75317 - 4.75317i) q^{13} +(0.323129 + 1.37680i) q^{14} -2.37528 q^{15} +(2.41662 - 3.18747i) q^{16} +4.01138 q^{17} +(-0.853692 - 3.63745i) q^{18} +(1.17869 + 1.17869i) q^{19} +(0.637389 - 1.89571i) q^{20} +(-1.67958 + 1.67958i) q^{21} +(4.24986 - 6.85646i) q^{22} -0.610935i q^{23} +(6.68875 + 0.629448i) q^{24} -1.00000i q^{25} +(8.08006 + 5.00829i) q^{26} +(-0.601365 + 0.601365i) q^{27} +(-0.889770 - 1.79118i) q^{28} +(2.42606 + 2.42606i) q^{29} +(3.27029 - 0.767522i) q^{30} -8.63834 q^{31} +(-2.29724 + 5.16940i) q^{32} +13.5487 q^{33} +(-5.52289 + 1.29619i) q^{34} +(-0.707107 - 0.707107i) q^{35} +(2.35073 + 4.73220i) q^{36} +(-1.14755 + 1.14755i) q^{37} +(-2.00369 - 1.24196i) q^{38} +15.9666i q^{39} +(-0.264999 + 2.81599i) q^{40} -1.24783i q^{41} +(1.76973 - 2.85517i) q^{42} +(-8.70723 + 8.70723i) q^{43} +(-3.63570 + 10.8132i) q^{44} +(1.86814 + 1.86814i) q^{45} +(0.197411 + 0.841137i) q^{46} +7.92976 q^{47} +(-9.41249 + 1.29470i) q^{48} -1.00000 q^{49} +(0.323129 + 1.37680i) q^{50} +(-6.73743 - 6.73743i) q^{51} +(-12.7430 - 4.28453i) q^{52} +(-5.64673 + 5.64673i) q^{53} +(0.633643 - 1.02228i) q^{54} +5.70405i q^{55} +(1.80382 + 2.17859i) q^{56} -3.95940i q^{57} +(-4.12414 - 2.55628i) q^{58} +(-1.23973 + 1.23973i) q^{59} +(-4.25454 + 2.11345i) q^{60} +(5.71963 + 5.71963i) q^{61} +(11.8933 - 2.79130i) q^{62} +2.64195 q^{63} +(1.49247 - 7.85955i) q^{64} -6.72199 q^{65} +(-18.6539 + 4.37798i) q^{66} +(2.38301 + 2.38301i) q^{67} +(7.18509 - 3.56921i) q^{68} +(-1.02611 + 1.02611i) q^{69} +(1.20203 + 0.745060i) q^{70} -1.57667i q^{71} +(-4.76561 - 5.75572i) q^{72} +1.85964i q^{73} +(1.20914 - 1.95075i) q^{74} +(-1.67958 + 1.67958i) q^{75} +(3.16001 + 1.06248i) q^{76} +(4.03337 + 4.03337i) q^{77} +(-5.15928 - 21.9829i) q^{78} +3.14874 q^{79} +(-0.545075 - 3.96269i) q^{80} +9.94594 q^{81} +(0.403211 + 1.71802i) q^{82} +(-6.01779 - 6.01779i) q^{83} +(-1.51398 + 4.50285i) q^{84} +(2.83648 - 2.83648i) q^{85} +(9.17458 - 14.8017i) q^{86} -8.14951i q^{87} +(1.51157 - 16.0625i) q^{88} +18.0907i q^{89} +(-3.17572 - 1.96842i) q^{90} +(-4.75317 + 4.75317i) q^{91} +(-0.543592 - 1.09429i) q^{92} +(14.5087 + 14.5087i) q^{93} +(-10.9177 + 2.56234i) q^{94} +1.66692 q^{95} +(12.5408 - 4.82400i) q^{96} -10.6607 q^{97} +(1.37680 - 0.323129i) q^{98} +(-10.6560 - 10.6560i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{4} + 12 q^{6}+O(q^{10}) \) 44 * q + 12 * q^4 + 12 * q^6	\( 44 q + 12 q^{4} + 12 q^{6} - 4 q^{10} + 12 q^{11} - 16 q^{12} + 4 q^{14} + 8 q^{15} - 8 q^{16} - 20 q^{18} + 8 q^{19} - 36 q^{22} + 12 q^{24} + 44 q^{26} - 24 q^{27} - 4 q^{28} + 12 q^{29} - 40 q^{32} - 16 q^{34} + 4 q^{36} + 28 q^{37} - 16 q^{38} + 4 q^{42} - 44 q^{43} - 32 q^{44} - 16 q^{46} - 32 q^{48} - 44 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 12 q^{53} - 80 q^{54} + 8 q^{56} + 4 q^{58} + 24 q^{59} - 16 q^{61} + 28 q^{63} + 72 q^{64} - 40 q^{65} - 20 q^{66} - 28 q^{67} + 56 q^{68} + 40 q^{69} + 12 q^{72} + 24 q^{74} - 12 q^{77} + 84 q^{78} - 16 q^{79} + 20 q^{81} + 48 q^{82} + 16 q^{85} - 64 q^{86} + 28 q^{88} - 36 q^{90} - 16 q^{92} + 88 q^{93} + 96 q^{94} - 32 q^{95} + 48 q^{96} + 28 q^{99}+O(q^{100}) \) 44 * q + 12 * q^4 + 12 * q^6 - 4 * q^10 + 12 * q^11 - 16 * q^12 + 4 * q^14 + 8 * q^15 - 8 * q^16 - 20 * q^18 + 8 * q^19 - 36 * q^22 + 12 * q^24 + 44 * q^26 - 24 * q^27 - 4 * q^28 + 12 * q^29 - 40 * q^32 - 16 * q^34 + 4 * q^36 + 28 * q^37 - 16 * q^38 + 4 * q^42 - 44 * q^43 - 32 * q^44 - 16 * q^46 - 32 * q^48 - 44 * q^49 + 4 * q^50 - 8 * q^51 + 16 * q^52 - 12 * q^53 - 80 * q^54 + 8 * q^56 + 4 * q^58 + 24 * q^59 - 16 * q^61 + 28 * q^63 + 72 * q^64 - 40 * q^65 - 20 * q^66 - 28 * q^67 + 56 * q^68 + 40 * q^69 + 12 * q^72 + 24 * q^74 - 12 * q^77 + 84 * q^78 - 16 * q^79 + 20 * q^81 + 48 * q^82 + 16 * q^85 - 64 * q^86 + 28 * q^88 - 36 * q^90 - 16 * q^92 + 88 * q^93 + 96 * q^94 - 32 * q^95 + 48 * q^96 + 28 * q^99

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