LMFDB - Embedded newform 825.2.n.p.751.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.n (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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			751.5
Character	$\chi$	$=$	825.751
Dual form			825.2.n.p.301.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.54314 - 1.12116i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.506258 - 1.55810i) q^{4} +(1.54314 + 1.12116i) q^{6} +(-1.37739 + 4.23918i) q^{7} +(0.213204 + 0.656175i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.54314 - 1.12116i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.506258 - 1.55810i) q^{4} +(1.54314 + 1.12116i) q^{6} +(-1.37739 + 4.23918i) q^{7} +(0.213204 + 0.656175i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-1.22140 - 3.08354i) q^{11} +1.63829 q^{12} +(-0.432021 + 0.313882i) q^{13} +(2.62728 + 8.08594i) q^{14} +(3.71548 + 2.69946i) q^{16} +(3.67635 + 2.67102i) q^{17} +(-0.589428 + 1.81407i) q^{18} +(0.594714 + 1.83034i) q^{19} -4.45734 q^{21} +(-5.34192 - 3.38895i) q^{22} +5.18745 q^{23} +(-0.558176 + 0.405538i) q^{24} +(-0.314759 + 0.968729i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(5.90776 + 4.29224i) q^{28} +(-1.46923 + 4.52183i) q^{29} +(-2.82936 + 2.05565i) q^{31} +7.38016 q^{32} +(2.55518 - 2.11448i) q^{33} +8.66777 q^{34} +(0.506258 + 1.55810i) q^{36} +(0.162896 - 0.501344i) q^{37} +(2.96983 + 2.15771i) q^{38} +(-0.432021 - 0.313882i) q^{39} +(1.45107 + 4.46595i) q^{41} +(-6.87831 + 4.99738i) q^{42} -3.02459 q^{43} +(-5.42281 + 0.341997i) q^{44} +(8.00498 - 5.81596i) q^{46} +(-3.70442 - 11.4010i) q^{47} +(-1.41919 + 4.36781i) q^{48} +(-10.4103 - 7.56354i) q^{49} +(-1.40424 + 4.32181i) q^{51} +(0.270346 + 0.832039i) q^{52} +(4.06485 - 2.95328i) q^{53} -1.90743 q^{54} -3.07531 q^{56} +(-1.55698 + 1.13121i) q^{57} +(2.80246 + 8.62507i) q^{58} +(4.21793 - 12.9815i) q^{59} +(-9.45864 - 6.87210i) q^{61} +(-2.06140 + 6.34433i) q^{62} +(-1.37739 - 4.23918i) q^{63} +(3.95767 - 2.87541i) q^{64} +(1.57234 - 6.12771i) q^{66} +11.5622 q^{67} +(6.02291 - 4.37590i) q^{68} +(1.60301 + 4.93356i) q^{69} +(-2.72305 - 1.97841i) q^{71} +(-0.558176 - 0.405538i) q^{72} +(0.200982 - 0.618559i) q^{73} +(-0.310714 - 0.956278i) q^{74} +3.15294 q^{76} +(14.7540 - 0.930481i) q^{77} -1.01858 q^{78} +(14.3357 - 10.4155i) q^{79} +(0.309017 - 0.951057i) q^{81} +(7.24625 + 5.26471i) q^{82} +(3.43620 + 2.49655i) q^{83} +(-2.25656 + 6.94499i) q^{84} +(-4.66738 + 3.39105i) q^{86} -4.75453 q^{87} +(1.76293 - 1.45887i) q^{88} -8.24094 q^{89} +(-0.735538 - 2.26375i) q^{91} +(2.62619 - 8.08259i) q^{92} +(-2.82936 - 2.05565i) q^{93} +(-18.4988 - 13.4402i) q^{94} +(2.28059 + 7.01895i) q^{96} +(0.920978 - 0.669130i) q^{97} -24.5445 q^{98} +(2.80059 + 1.77671i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} - 6 q^{3} - 6 q^{4} + 2 q^{6} + 4 q^{7} + 6 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 - 6 * q^3 - 6 * q^4 + 2 * q^6 + 4 * q^7 + 6 * q^8 - 6 * q^9	$ 24 q + 2 q^{2} - 6 q^{3} - 6 q^{4} + 2 q^{6} + 4 q^{7} + 6 q^{8} - 6 q^{9} + 24 q^{12} + 4 q^{13} + 2 q^{14} - 22 q^{16} + 4 q^{17} + 2 q^{18} + 8 q^{19} - 16 q^{21} - 4 q^{22} + 6 q^{24} - 38 q^{26} - 6 q^{27} + 30 q^{28} - 10 q^{31} - 56 q^{32} + 10 q^{33} + 12 q^{34} - 6 q^{36} + 10 q^{37} + 4 q^{38} + 4 q^{39} + 30 q^{41} - 8 q^{42} - 64 q^{43} + 24 q^{44} + 54 q^{46} - 8 q^{47} - 2 q^{48} + 14 q^{49} + 14 q^{51} + 14 q^{52} + 26 q^{53} - 8 q^{54} + 12 q^{56} + 8 q^{57} + 20 q^{58} - 30 q^{59} + 20 q^{61} - 50 q^{62} + 4 q^{63} - 32 q^{64} + 6 q^{66} + 20 q^{67} - 62 q^{68} - 10 q^{69} - 16 q^{71} + 6 q^{72} - 12 q^{73} + 16 q^{74} - 68 q^{76} - 2 q^{77} + 32 q^{78} + 26 q^{79} - 6 q^{81} + 56 q^{82} + 48 q^{83} - 52 q^{86} + 48 q^{88} - 20 q^{89} - 20 q^{91} + 46 q^{92} - 10 q^{93} - 36 q^{94} + 14 q^{96} - 14 q^{97} - 120 q^{98}+O(q^{100}) $ 24 * q + 2 * q^2 - 6 * q^3 - 6 * q^4 + 2 * q^6 + 4 * q^7 + 6 * q^8 - 6 * q^9 + 24 * q^12 + 4 * q^13 + 2 * q^14 - 22 * q^16 + 4 * q^17 + 2 * q^18 + 8 * q^19 - 16 * q^21 - 4 * q^22 + 6 * q^24 - 38 * q^26 - 6 * q^27 + 30 * q^28 - 10 * q^31 - 56 * q^32 + 10 * q^33 + 12 * q^34 - 6 * q^36 + 10 * q^37 + 4 * q^38 + 4 * q^39 + 30 * q^41 - 8 * q^42 - 64 * q^43 + 24 * q^44 + 54 * q^46 - 8 * q^47 - 2 * q^48 + 14 * q^49 + 14 * q^51 + 14 * q^52 + 26 * q^53 - 8 * q^54 + 12 * q^56 + 8 * q^57 + 20 * q^58 - 30 * q^59 + 20 * q^61 - 50 * q^62 + 4 * q^63 - 32 * q^64 + 6 * q^66 + 20 * q^67 - 62 * q^68 - 10 * q^69 - 16 * q^71 + 6 * q^72 - 12 * q^73 + 16 * q^74 - 68 * q^76 - 2 * q^77 + 32 * q^78 + 26 * q^79 - 6 * q^81 + 56 * q^82 + 48 * q^83 - 52 * q^86 + 48 * q^88 - 20 * q^89 - 20 * q^91 + 46 * q^92 - 10 * q^93 - 36 * q^94 + 14 * q^96 - 14 * q^97 - 120 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	1.54314	−	1.12116i	1.09117	−	0.792779i	0.111571	−	0.993756i	$-0.464412\pi$
$2$	1.54314	−	1.12116i	1.09117	−	0.792779i	0.979596	+	0.200977i	$0.0644118\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.506258	−	1.55810i	0.253129	−	0.779052i
$5$		0			0
$5$		0			0
$6$	1.54314	+	1.12116i	0.629985	+	0.457711i
$7$	−1.37739	+	4.23918i	−0.520606	+	1.60226i	0.252239	+	0.967665i	$0.418833\pi$
$7$	−1.37739	+	4.23918i	−0.520606	+	1.60226i	−0.772845	+	0.634595i	$0.781167\pi$
$8$	0.213204	+	0.656175i	0.0753790	+	0.231993i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	−1.22140	−	3.08354i	−0.368265	−	0.929721i
$11$	−1.22140	−	3.08354i	−0.368265	−	0.929721i
$12$	1.63829			0.472933
$13$	−0.432021	+	0.313882i	−0.119821	+	0.0870551i	−0.646082	−	0.763268i	$-0.723594\pi$
$13$	−0.432021	+	0.313882i	−0.119821	+	0.0870551i	0.526261	+	0.850323i	$0.323594\pi$
$14$	2.62728	+	8.08594i	0.702170	+	2.16106i
$15$		0			0
$16$	3.71548	+	2.69946i	0.928871	+	0.674864i
$17$	3.67635	+	2.67102i	0.891645	+	0.647818i	0.936306	−	0.351184i	$-0.114221\pi$
$17$	3.67635	+	2.67102i	0.891645	+	0.647818i	−0.0446611	+	0.999002i	$0.514221\pi$
$18$	−0.589428	+	1.81407i	−0.138930	+	0.427581i
$19$	0.594714	+	1.83034i	0.136437	+	0.419909i	0.995811	−	0.0914385i	$-0.0291465\pi$
$19$	0.594714	+	1.83034i	0.136437	+	0.419909i	−0.859374	+	0.511348i	$0.829147\pi$
$20$		0			0
$21$	−4.45734			−0.972671
$22$	−5.34192	−	3.38895i	−1.13890	−	0.722528i
$23$	5.18745			1.08166			0.540830	−	0.841132i	$-0.318110\pi$
$23$	5.18745			1.08166			0.540830	+	0.841132i	$0.318110\pi$
$24$	−0.558176	+	0.405538i	−0.113937	+	0.0827801i
$25$		0			0
$26$	−0.314759	+	0.968729i	−0.0617293	+	0.189983i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	5.90776	+	4.29224i	1.11646	+	0.811157i
$29$	−1.46923	+	4.52183i	−0.272829	+	0.839683i	0.716956	+	0.697118i	$0.245535\pi$
$29$	−1.46923	+	4.52183i	−0.272829	+	0.839683i	−0.989786	+	0.142564i	$0.954465\pi$
$30$		0			0
$31$	−2.82936	+	2.05565i	−0.508168	+	0.369206i	−0.812128	−	0.583479i	$-0.801691\pi$
$31$	−2.82936	+	2.05565i	−0.508168	+	0.369206i	0.303960	+	0.952685i	$0.401691\pi$
$32$	7.38016			1.30464
$33$	2.55518	−	2.11448i	0.444800	−	0.368084i
$34$	8.66777			1.48651
$35$		0			0
$36$	0.506258	+	1.55810i	0.0843764	+	0.259684i
$37$	0.162896	−	0.501344i	0.0267800	−	0.0824204i	−0.936773	−	0.349937i	$-0.886203\pi$
$37$	0.162896	−	0.501344i	0.0267800	−	0.0824204i	0.963553	+	0.267517i	$0.0862030\pi$
$38$	2.96983	+	2.15771i	0.481770	+	0.350027i
$39$	−0.432021	−	0.313882i	−0.0691787	−	0.0502613i
$40$		0			0
$41$	1.45107	+	4.46595i	0.226620	+	0.697464i	0.998123	+	0.0612387i	$0.0195051\pi$
$41$	1.45107	+	4.46595i	0.226620	+	0.697464i	−0.771503	+	0.636225i	$0.780495\pi$
$42$	−6.87831	+	4.99738i	−1.06135	+	0.771113i
$43$	−3.02459			−0.461246			−0.230623	−	0.973043i	$-0.574076\pi$
$43$	−3.02459			−0.461246			−0.230623	+	0.973043i	$0.574076\pi$
$44$	−5.42281	+	0.341997i	−0.817519	+	0.0515580i
$45$		0			0
$46$	8.00498	−	5.81596i	1.18027	−	0.857517i
$47$	−3.70442	−	11.4010i	−0.540346	−	1.66301i	−0.731807	−	0.681512i	$-0.761323\pi$
$47$	−3.70442	−	11.4010i	−0.540346	−	1.66301i	0.191461	−	0.981500i	$-0.438677\pi$
$48$	−1.41919	+	4.36781i	−0.204842	+	0.630439i
$49$	−10.4103	−	7.56354i	−1.48719	−	1.08051i
$50$		0			0
$51$	−1.40424	+	4.32181i	−0.196633	+	0.605174i
$52$	0.270346	+	0.832039i	0.0374902	+	0.115383i
$53$	4.06485	−	2.95328i	0.558350	−	0.405665i	−0.272505	−	0.962154i	$-0.587852\pi$
$53$	4.06485	−	2.95328i	0.558350	−	0.405665i	0.830855	+	0.556490i	$0.187852\pi$
$54$	−1.90743			−0.259568
$55$		0			0
$56$	−3.07531			−0.410955
$57$	−1.55698	+	1.13121i	−0.206227	+	0.149833i
$58$	2.80246	+	8.62507i	0.367980	+	1.13253i
$59$	4.21793	−	12.9815i	0.549128	−	1.69004i	−0.161839	−	0.986817i	$-0.551742\pi$
$59$	4.21793	−	12.9815i	0.549128	−	1.69004i	0.710967	−	0.703225i	$-0.248258\pi$
$60$		0			0
$61$	−9.45864	−	6.87210i	−1.21105	−	0.879883i	−0.215728	−	0.976453i	$-0.569213\pi$
$61$	−9.45864	−	6.87210i	−1.21105	−	0.879883i	−0.995326	+	0.0965707i	$0.969213\pi$
$62$	−2.06140	+	6.34433i	−0.261798	+	0.805730i
$63$	−1.37739	−	4.23918i	−0.173535	−	0.534087i
$64$	3.95767	−	2.87541i	0.494708	−	0.359427i
$65$		0			0
$66$	1.57234	−	6.12771i	0.193542	−	0.754270i
$67$	11.5622			1.41255			0.706276	−	0.707936i	$-0.250374\pi$
$67$	11.5622			1.41255			0.706276	+	0.707936i	$0.250374\pi$
$68$	6.02291	−	4.37590i	0.730385	−	0.530656i
$69$	1.60301	+	4.93356i	0.192980	+	0.593931i
$70$		0			0
$71$	−2.72305	−	1.97841i	−0.323166	−	0.234794i	0.414359	−	0.910113i	$-0.364006\pi$
$71$	−2.72305	−	1.97841i	−0.323166	−	0.234794i	−0.737525	+	0.675319i	$0.764006\pi$
$72$	−0.558176	−	0.405538i	−0.0657816	−	0.0477931i
$73$	0.200982	−	0.618559i	0.0235232	−	0.0723969i	−0.938606	−	0.344992i	$-0.887882\pi$
$73$	0.200982	−	0.618559i	0.0235232	−	0.0723969i	0.962129	+	0.272595i	$0.0878818\pi$
$74$	−0.310714	−	0.956278i	−0.0361197	−	0.111165i
$75$		0			0
$76$	3.15294			0.361667
$77$	14.7540	−	0.930481i	1.68137	−	0.106038i
$78$	−1.01858			−0.115332
$79$	14.3357	−	10.4155i	1.61289	−	1.17184i	0.759628	−	0.650358i	$-0.225381\pi$
$79$	14.3357	−	10.4155i	1.61289	−	1.17184i	0.853265	−	0.521477i	$-0.174619\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	7.24625	+	5.26471i	0.800215	+	0.581390i
$83$	3.43620	+	2.49655i	0.377172	+	0.274031i	0.760179	−	0.649714i	$-0.225111\pi$
$83$	3.43620	+	2.49655i	0.377172	+	0.274031i	−0.383007	+	0.923746i	$0.625111\pi$
$84$	−2.25656	+	6.94499i	−0.246211	+	0.757761i
$85$		0			0
$86$	−4.66738	+	3.39105i	−0.503297	+	0.365666i
$87$	−4.75453			−0.509739
$88$	1.76293	−	1.45887i	0.187929	−	0.155516i
$89$	−8.24094			−0.873538			−0.436769	−	0.899574i	$-0.643877\pi$
$89$	−8.24094			−0.873538			−0.436769	+	0.899574i	$0.643877\pi$
$90$		0			0
$91$	−0.735538	−	2.26375i	−0.0771054	−	0.237306i
$92$	2.62619	−	8.08259i	0.273799	−	0.842668i
$93$	−2.82936	−	2.05565i	−0.293391	−	0.213161i
$94$	−18.4988	−	13.4402i	−1.90801	−	1.38625i
$95$		0			0
$96$	2.28059	+	7.01895i	0.232762	+	0.716368i
$97$	0.920978	−	0.669130i	0.0935112	−	0.0679398i	−0.540047	−	0.841635i	$-0.681594\pi$
$97$	0.920978	−	0.669130i	0.0935112	−	0.0679398i	0.633558	+	0.773695i	$0.281594\pi$
$98$	−24.5445			−2.47937
$99$	2.80059	+	1.77671i	0.281470	+	0.178566i
$100$		0			0
$101$	0.828229	−	0.601744i	0.0824119	−	0.0598757i	−0.545816	−	0.837905i	$-0.683780\pi$
$101$	0.828229	−	0.601744i	0.0824119	−	0.0598757i	0.628228	+	0.778029i	$0.283780\pi$
$102$	2.67849	+	8.24354i	0.265210	+	0.816232i
$103$	−1.48041	+	4.55623i	−0.145869	+	0.448939i	−0.997122	−	0.0758171i	$-0.975843\pi$
$103$	−1.48041	+	4.55623i	−0.145869	+	0.448939i	0.851253	+	0.524756i	$0.175843\pi$
$104$	−0.298070	−	0.216560i	−0.0292282	−	0.0212355i
$105$		0			0
$106$	2.96154	−	9.11468i	0.287650	−	0.885296i
$107$	−0.227427	−	0.699950i	−0.0219862	−	0.0676667i	0.939461	−	0.342655i	$-0.111326\pi$
$107$	−0.227427	−	0.699950i	−0.0219862	−	0.0676667i	−0.961448	+	0.274988i	$0.911326\pi$
$108$	−1.32540	+	0.962961i	−0.127537	+	0.0926609i
$109$	−0.0433994			−0.00415691			−0.00207845	−	0.999998i	$-0.500662\pi$
$109$	−0.0433994			−0.00415691			−0.00207845	+	0.999998i	$0.500662\pi$
$110$		0			0
$111$	0.527144			0.0500343
$112$	−16.5612	+	12.0324i	−1.56488	+	1.13695i
$113$	3.46117	+	10.6524i	0.325600	+	1.00209i	0.971169	+	0.238391i	$0.0766200\pi$
$113$	3.46117	+	10.6524i	0.325600	+	1.00209i	−0.645570	+	0.763701i	$0.723380\pi$
$114$	−1.13437	+	3.49125i	−0.106244	+	0.326985i
$115$		0			0
$116$	6.30167	+	4.57843i	0.585095	+	0.425096i
$117$	0.165017	−	0.507871i	0.0152559	−	0.0469527i
$118$	−8.04541	−	24.7612i	−0.740640	−	2.27946i
$119$	−16.3867	+	11.9057i	−1.50217	+	1.09139i
$120$		0			0
$121$	−8.01638	+	7.53244i	−0.728762	+	0.684767i
$122$	−22.3007			−2.01901
$123$	−3.79896	+	2.76011i	−0.342541	+	0.248871i
$124$	1.77053	+	5.44913i	0.158998	+	0.489346i
$125$		0			0
$126$	−6.87831	−	4.99738i	−0.612768	−	0.445202i
$127$	−6.61362	−	4.80507i	−0.586863	−	0.426381i	0.254328	−	0.967118i	$-0.418146\pi$
$127$	−6.61362	−	4.80507i	−0.586863	−	0.426381i	−0.841192	+	0.540737i	$0.818146\pi$
$128$	−1.67774	+	5.16355i	−0.148292	+	0.456397i
$129$	−0.934651	−	2.87656i	−0.0822914	−	0.253267i
$130$		0			0
$131$	17.7054			1.54693			0.773465	−	0.633839i	$-0.218522\pi$
$131$	17.7054			1.54693			0.773465	+	0.633839i	$0.218522\pi$
$132$	−2.00100	−	5.05171i	−0.174165	−	0.439695i
$133$	−8.57830			−0.743833
$134$	17.8422	−	12.9631i	1.54133	−	1.11984i
$135$		0			0
$136$	−0.968845	+	2.98180i	−0.0830778	+	0.255687i
$137$	4.43814	+	3.22449i	0.379176	+	0.275487i	0.761006	−	0.648745i	$-0.224706\pi$
$137$	4.43814	+	3.22449i	0.379176	+	0.275487i	−0.381830	+	0.924233i	$0.624706\pi$
$138$	8.00498	+	5.81596i	0.681429	+	0.495087i
$139$	1.00725	−	3.09999i	0.0854337	−	0.262938i	−0.899209	−	0.437519i	$-0.855857\pi$
$139$	1.00725	−	3.09999i	0.0854337	−	0.262938i	0.984643	+	0.174581i	$0.0558572\pi$
$140$		0			0
$141$	9.69830	−	7.04623i	0.816745	−	0.593400i
$142$	−6.42016			−0.538768
$143$	1.49553	+	0.948778i	0.125063	+	0.0793408i
$144$	−4.59259			−0.382716
$145$		0			0
$146$	−0.383359	−	1.17986i	−0.0317270	−	0.0976457i
$147$	3.97639	−	12.2381i	0.327967	−	1.00938i
$148$	−0.698678	−	0.507619i	−0.0574310	−	0.0417260i
$149$	−2.27038	−	1.64953i	−0.185997	−	0.135135i	0.490890	−	0.871221i	$-0.336672\pi$
$149$	−2.27038	−	1.64953i	−0.185997	−	0.135135i	−0.676887	+	0.736087i	$0.736672\pi$
$150$		0			0
$151$	−4.37685	−	13.4706i	−0.356183	−	1.09622i	−0.955320	−	0.295573i	$-0.904489\pi$
$151$	−4.37685	−	13.4706i	−0.356183	−	1.09622i	0.599137	−	0.800647i	$-0.295511\pi$
$152$	−1.07423	+	0.780472i	−0.0871314	+	0.0633047i
$153$	−4.54422			−0.367378
$154$	21.7243	−	17.9774i	1.75060	−	1.44866i
$155$		0			0
$156$	−0.707774	+	0.514228i	−0.0566673	+	0.0411712i
$157$	−0.961303	−	2.95859i	−0.0767204	−	0.236121i	0.905340	−	0.424687i	$-0.139616\pi$
$157$	−0.961303	−	2.95859i	−0.0767204	−	0.236121i	−0.982060	+	0.188566i	$0.939616\pi$
$158$	10.4446	−	32.1452i	0.830929	−	2.55734i
$159$	4.06485	+	2.95328i	0.322363	+	0.234211i
$160$		0			0
$161$	−7.14516	+	21.9906i	−0.563118	+	1.73310i
$162$	−0.589428	−	1.81407i	−0.0463098	−	0.142527i
$163$	15.6743	−	11.3880i	1.22770	−	0.891978i	0.230987	−	0.972957i	$-0.425805\pi$
$163$	15.6743	−	11.3880i	1.22770	−	0.891978i	0.996716	+	0.0809786i	$0.0258045\pi$
$164$	7.69303			0.600724
$165$		0			0
$166$	8.10157			0.628804
$167$	3.35735	−	2.43926i	0.259800	−	0.188756i	−0.450259	−	0.892898i	$-0.648668\pi$
$167$	3.35735	−	2.43926i	0.259800	−	0.188756i	0.710059	+	0.704142i	$0.248668\pi$
$168$	−0.950323	−	2.92479i	−0.0733190	−	0.225653i
$169$	−3.92910	+	12.0925i	−0.302238	+	0.930194i
$170$		0			0
$171$	−1.55698	−	1.13121i	−0.119065	−	0.0865060i
$172$	−1.53123	+	4.71263i	−0.116755	+	0.359335i
$173$	3.29580	+	10.1434i	0.250575	+	0.771191i	0.994669	+	0.103116i	$0.0328813\pi$
$173$	3.29580	+	10.1434i	0.250575	+	0.771191i	−0.744094	+	0.668075i	$0.767119\pi$
$174$	−7.33692	+	5.33059i	−0.556211	+	0.404111i
$175$		0			0
$176$	3.78579	−	14.7539i	0.285365	−	1.11212i
$177$	13.6495			1.02596
$178$	−12.7169	+	9.23940i	−0.953175	+	0.692523i
$179$	6.99420	+	21.5259i	0.522771	+	1.60892i	0.768681	+	0.639632i	$0.220913\pi$
$179$	6.99420	+	21.5259i	0.522771	+	1.60892i	−0.245910	+	0.969293i	$0.579087\pi$
$180$		0			0
$181$	−11.7973	−	8.57121i	−0.876883	−	0.637093i	0.0555418	−	0.998456i	$-0.482311\pi$
$181$	−11.7973	−	8.57121i	−0.876883	−	0.637093i	−0.932425	+	0.361363i	$0.882311\pi$
$182$	−3.67307	−	2.66864i	−0.272266	−	0.197813i
$183$	3.61288	−	11.1193i	0.267072	−	0.821962i
$184$	1.10599	+	3.40388i	0.0815344	+	0.250937i
$185$		0			0
$186$	−6.67082			−0.489128
$187$	3.74591	−	14.5985i	0.273928	−	1.06755i
$188$	−19.6394			−1.43235
$189$	3.60606	−	2.61996i	0.262302	−	0.190574i
$190$		0			0
$191$	1.22505	−	3.77031i	0.0886414	−	0.272810i	−0.896903	−	0.442227i	$-0.854188\pi$
$191$	1.22505	−	3.77031i	0.0886414	−	0.272810i	0.985544	+	0.169417i	$0.0541885\pi$
$192$	3.95767	+	2.87541i	0.285620	+	0.207515i
$193$	−0.0243135	−	0.0176648i	−0.00175012	−	0.00127154i	0.586910	−	0.809652i	$-0.300344\pi$
$193$	−0.0243135	−	0.0176648i	−0.00175012	−	0.00127154i	−0.588660	+	0.808381i	$0.700344\pi$
$194$	0.671000	−	2.06513i	0.0481750	−	0.148267i
$195$		0			0
$196$	−17.0551	+	12.3912i	−1.21822	+	0.885089i
$197$	−5.50562			−0.392259			−0.196130	−	0.980578i	$-0.562837\pi$
$197$	−5.50562			−0.392259			−0.196130	+	0.980578i	$0.562837\pi$
$198$	6.31368	−	0.398181i	0.448694	−	0.0282975i
$199$	−3.12623			−0.221612			−0.110806	−	0.993842i	$-0.535343\pi$
$199$	−3.12623			−0.221612			−0.110806	+	0.993842i	$0.535343\pi$
$200$		0			0
$201$	3.57293	+	10.9963i	0.252015	+	0.775622i
$202$	0.603426	−	1.85715i	0.0424569	−	0.130669i
$203$	−17.1451	−	12.4567i	−1.20335	−	0.874287i
$204$	6.02291	+	4.37590i	0.421688	+	0.306374i
$205$		0			0
$206$	2.82378	+	8.69069i	0.196742	+	0.605509i
$207$	−4.19674	+	3.04911i	−0.291694	+	0.211928i
$208$	−2.45248			−0.170049
$209$	4.91754	−	4.06939i	0.340153	−	0.281486i
$210$		0			0
$211$	16.4962	−	11.9852i	1.13564	−	0.825094i	0.149138	−	0.988816i	$-0.452350\pi$
$211$	16.4962	−	11.9852i	1.13564	−	0.825094i	0.986506	+	0.163722i	$0.0523501\pi$
$212$	−2.54366	−	7.82857i	−0.174699	−	0.537669i
$213$	1.04011	−	3.20113i	0.0712673	−	0.219338i
$214$	−1.13571	−	0.825140i	−0.0776354	−	0.0564054i
$215$		0			0
$216$	0.213204	−	0.656175i	0.0145067	−	0.0446470i
$217$	−4.81713	−	14.8256i	−0.327008	−	1.00643i
$218$	−0.0669715	+	0.0486576i	−0.00453588	+	0.00329551i
$219$	0.650391			0.0439494
$220$		0			0
$221$	−2.42665			−0.163234
$222$	0.813459	−	0.591012i	0.0545958	−	0.0396661i
$223$	−3.18346	−	9.79767i	−0.213180	−	0.656101i	−0.999278	−	0.0379985i	$-0.987902\pi$
$223$	−3.18346	−	9.79767i	−0.213180	−	0.656101i	0.786098	−	0.618102i	$-0.212098\pi$
$224$	−10.1654	+	31.2858i	−0.679203	+	2.09037i
$225$		0			0
$226$	17.2841	+	12.5576i	1.14972	+	0.835321i
$227$	−1.93829	+	5.96545i	−0.128649	+	0.395941i	−0.994548	−	0.104278i	$-0.966747\pi$
$227$	−1.93829	+	5.96545i	−0.128649	+	0.395941i	0.865899	+	0.500218i	$0.166747\pi$
$228$	0.974312	+	2.99862i	0.0645254	+	0.198589i
$229$	−1.11734	+	0.811793i	−0.0738358	+	0.0536448i	−0.624091	−	0.781352i	$-0.714530\pi$
$229$	−1.11734	+	0.811793i	−0.0738358	+	0.0536448i	0.550255	+	0.834997i	$0.314530\pi$
$230$		0			0
$231$	5.44418	+	13.7444i	0.358201	+	0.904312i
$232$	−3.28036			−0.215366
$233$	−6.71844	+	4.88123i	−0.440139	+	0.319780i	−0.785690	−	0.618620i	$-0.787692\pi$
$233$	−6.71844	+	4.88123i	−0.440139	+	0.319780i	0.345551	+	0.938400i	$0.387692\pi$
$234$	−0.314759	−	0.968729i	−0.0205764	−	0.0633278i
$235$		0			0
$236$	−18.0911	−	13.1440i	−1.17763	−	0.855598i
$237$	14.3357	+	10.4155i	0.931204	+	0.676559i
$238$	−11.9389	+	36.7442i	−0.773886	+	2.38178i
$239$	3.18134	+	9.79117i	0.205784	+	0.633338i	0.999680	+	0.0252850i	$0.00804932\pi$
$239$	3.18134	+	9.79117i	0.205784	+	0.633338i	−0.793896	+	0.608053i	$0.791951\pi$
$240$		0			0
$241$	12.2340			0.788060			0.394030	−	0.919097i	$-0.371081\pi$
$241$	12.2340			0.788060			0.394030	+	0.919097i	$0.371081\pi$
$242$	−3.92535	+	20.6113i	−0.252331	+	1.32494i
$243$	1.00000			0.0641500
$244$	−15.4960	+	11.2585i	−0.992027	+	0.720750i
$245$		0			0
$246$	−2.76782	+	8.51848i	−0.176470	+	0.543118i
$247$	−0.831439	−	0.604076i	−0.0529032	−	0.0384364i
$248$	−1.95210	−	1.41828i	−0.123958	−	0.0900610i
$249$	−1.31251	+	4.03950i	−0.0831770	+	0.255993i
$250$		0			0
$251$	3.76725	−	2.73707i	0.237787	−	0.172762i	−0.462510	−	0.886614i	$-0.653051\pi$
$251$	3.76725	−	2.73707i	0.237787	−	0.172762i	0.700297	+	0.713852i	$0.253051\pi$
$252$	−7.30240			−0.460008
$253$	−6.33594	−	15.9957i	−0.398337	−	1.00564i
$254$	−15.5930			−0.978392
$255$		0			0
$256$	6.22355	+	19.1541i	0.388972	+	1.19713i
$257$	−5.66627	+	17.4390i	−0.353452	+	1.08781i	0.603449	+	0.797401i	$0.293793\pi$
$257$	−5.66627	+	17.4390i	−0.353452	+	1.08781i	−0.956901	+	0.290413i	$0.906207\pi$
$258$	−4.66738	−	3.39105i	−0.290578	−	0.211118i
$259$	1.90091	+	1.38110i	0.118117	+	0.0858171i
$260$		0			0
$261$	−1.46923	−	4.52183i	−0.0909432	−	0.279894i
$262$	27.3220	−	19.8506i	1.68796	−	1.22637i
$263$	9.80198			0.604416			0.302208	−	0.953242i	$-0.402276\pi$
$263$	9.80198			0.604416			0.302208	+	0.953242i	$0.402276\pi$
$264$	1.93225	+	1.22583i	0.118921	+	0.0754447i
$265$		0			0
$266$	−13.2375	+	9.61764i	−0.811646	+	0.589695i
$267$	−2.54659	−	7.83760i	−0.155849	−	0.479653i
$268$	5.85348	−	18.0152i	0.357558	−	1.10045i
$269$	−9.65232	−	7.01282i	−0.588512	−	0.427579i	0.253270	−	0.967396i	$-0.418494\pi$
$269$	−9.65232	−	7.01282i	−0.588512	−	0.427579i	−0.841783	+	0.539816i	$0.818494\pi$
$270$		0			0
$271$	−9.39561	+	28.9167i	−0.570743	+	1.75657i	0.0794962	+	0.996835i	$0.474669\pi$
$271$	−9.39561	+	28.9167i	−0.570743	+	1.75657i	−0.650239	+	0.759730i	$0.725331\pi$
$272$	6.44910	+	19.8483i	0.391034	+	1.20348i
$273$	1.92566	−	1.39908i	0.116547	−	0.0846760i
$274$	10.4638			0.632144
$275$		0			0
$276$	8.49854			0.511552
$277$	17.9152	−	13.0162i	1.07642	−	0.782065i	0.0993645	−	0.995051i	$-0.468319\pi$
$277$	17.9152	−	13.0162i	1.07642	−	0.782065i	0.977055	+	0.212986i	$0.0683190\pi$
$278$	−1.92126	−	5.91302i	−0.115229	−	0.354639i
$279$	1.08072	−	3.32611i	0.0647010	−	0.199129i
$280$		0			0
$281$	−13.7794	−	10.0113i	−0.822009	−	0.597225i	0.0952780	−	0.995451i	$-0.469626\pi$
$281$	−13.7794	−	10.0113i	−0.822009	−	0.597225i	−0.917287	+	0.398226i	$0.869626\pi$
$282$	7.06592	−	21.7467i	0.420770	−	1.29500i
$283$	2.44788	+	7.53379i	0.145511	+	0.447838i	0.997076	−	0.0764113i	$-0.0243462\pi$
$283$	2.44788	+	7.53379i	0.145511	+	0.447838i	−0.851565	+	0.524249i	$0.824346\pi$
$284$	−4.46113	+	3.24120i	−0.264719	+	0.192330i
$285$		0			0
$286$	3.37155	−	0.212632i	0.199364	−	0.0125732i
$287$	−20.9307			−1.23550
$288$	−5.97067	+	4.33795i	−0.351825	+	0.255616i
$289$	1.12788	+	3.47126i	0.0663459	+	0.204192i
$290$		0			0
$291$	0.920978	+	0.669130i	0.0539887	+	0.0392251i
$292$	−0.862030	−	0.626301i	−0.0504465	−	0.0366515i
$293$	−6.90330	+	21.2462i	−0.403295	+	1.24121i	0.519015	+	0.854765i	$0.326299\pi$
$293$	−6.90330	+	21.2462i	−0.403295	+	1.24121i	−0.922310	+	0.386450i	$0.873701\pi$
$294$	−7.58468	−	23.3432i	−0.442347	−	1.36141i
$295$		0			0
$296$	0.363699			0.0211396
$297$	−0.824326	+	3.21255i	−0.0478322	+	0.186411i
$298$	−5.35291			−0.310086
$299$	−2.24109	+	1.62825i	−0.129606	+	0.0941640i
$300$		0			0
$301$	4.16606	−	12.8218i	0.240127	−	0.739036i
$302$	−21.8568	−	15.8799i	−1.25772	−	0.913784i
$303$	0.828229	+	0.601744i	0.0475805	+	0.0345693i
$304$	−2.73128	+	8.40601i	−0.156649	+	0.482117i
$305$		0			0
$306$	−7.01237	+	5.09479i	−0.400871	+	0.291250i
$307$	9.33327			0.532678			0.266339	−	0.963879i	$-0.414186\pi$
$307$	9.33327			0.532678			0.266339	+	0.963879i	$0.414186\pi$
$308$	6.01955	−	23.4593i	0.342996	−	1.33672i
$309$	−4.79071			−0.272534
$310$		0			0
$311$	−3.47582	−	10.6975i	−0.197096	−	0.606598i	−0.999946	−	0.0104169i	$-0.996684\pi$
$311$	−3.47582	−	10.6975i	−0.197096	−	0.606598i	0.802850	−	0.596181i	$-0.203316\pi$
$312$	0.113853	−	0.350402i	0.00644563	−	0.0198376i
$313$	8.78916	+	6.38570i	0.496792	+	0.360941i	0.807790	−	0.589470i	$-0.200663\pi$
$313$	8.78916	+	6.38570i	0.496792	+	0.360941i	−0.310998	+	0.950411i	$0.600663\pi$
$314$	−4.80047	−	3.48775i	−0.270906	−	0.196825i
$315$		0			0
$316$	−8.97085	−	27.6094i	−0.504650	−	1.55315i
$317$	−10.2660	+	7.45871i	−0.576598	+	0.418923i	−0.837496	−	0.546443i	$-0.815981\pi$
$317$	−10.2660	+	7.45871i	−0.576598	+	0.418923i	0.260898	+	0.965366i	$0.415981\pi$
$318$	9.58374			0.537429
$319$	15.7377	−	0.992522i	0.881144	−	0.0555706i
$320$		0			0
$321$	0.595413	−	0.432593i	0.0332327	−	0.0241450i
$322$	13.6289	+	41.9454i	0.759509	+	2.33753i
$323$	−2.70251	+	8.31746i	−0.150372	+	0.462796i
$324$	−1.32540	−	0.962961i	−0.0736334	−	0.0534978i
$325$		0			0
$326$	11.4198	−	35.1467i	0.632487	−	1.94659i
$327$	−0.0134112	−	0.0412753i	−0.000741638	−	0.00228253i
$328$	−2.62107	+	1.90432i	−0.144724	+	0.105148i
$329$	53.4335			2.94588
$330$		0			0
$331$	−23.0627			−1.26764			−0.633821	−	0.773480i	$-0.718514\pi$
$331$	−23.0627			−1.26764			−0.633821	+	0.773480i	$0.718514\pi$
$332$	5.62948	−	4.09006i	0.308958	−	0.224471i
$333$	0.162896	+	0.501344i	0.00892667	+	0.0274735i
$334$	2.44608	−	7.52826i	0.133843	−	0.411928i
$335$		0			0
$336$	−16.5612	−	12.0324i	−0.903486	−	0.656421i
$337$	−10.0007	+	30.7791i	−0.544774	+	1.67664i	0.176753	+	0.984255i	$0.443441\pi$
$337$	−10.0007	+	30.7791i	−0.544774	+	1.67664i	−0.721527	+	0.692386i	$0.756559\pi$
$338$	7.49448	+	23.0656i	0.407646	+	1.25461i
$339$	−9.06146	+	6.58354i	−0.492151	+	0.357569i
$340$		0			0
$341$	9.79444	+	6.21367i	0.530399	+	0.336489i
$342$	−3.67091			−0.198500
$343$	21.1599	−	15.3735i	1.14253	−	0.830093i
$344$	−0.644856	−	1.98466i	−0.0347683	−	0.107006i
$345$		0			0
$346$	16.4583	+	11.9576i	0.884803	+	0.642847i
$347$	23.5297	+	17.0953i	1.26314	+	0.917725i	0.998907	−	0.0467340i	$-0.0148813\pi$
$347$	23.5297	+	17.0953i	1.26314	+	0.917725i	0.264233	+	0.964459i	$0.414881\pi$
$348$	−2.40702	+	7.40805i	−0.129030	+	0.397113i
$349$	−4.45099	−	13.6987i	−0.238256	−	0.733276i	−0.996673	−	0.0815064i	$-0.974027\pi$
$349$	−4.45099	−	13.6987i	−0.238256	−	0.733276i	0.758417	−	0.651770i	$-0.225973\pi$
$350$		0			0
$351$	0.534008			0.0285032
$352$	−9.01410	−	22.7570i	−0.480453	−	1.21295i
$353$	−28.9227			−1.53940			−0.769700	−	0.638406i	$-0.779594\pi$
$353$	−28.9227			−1.53940			−0.769700	+	0.638406i	$0.779594\pi$
$354$	21.0632	−	15.3033i	1.11949	−	0.813360i
$355$		0			0
$356$	−4.17205	+	12.8402i	−0.221118	+	0.680531i
$357$	−16.3867	−	11.9057i	−0.867277	−	0.630114i
$358$	34.9271	+	25.3760i	1.84595	+	1.34116i
$359$	7.26682	−	22.3650i	0.383528	−	1.18038i	−0.554014	−	0.832507i	$-0.686905\pi$
$359$	7.26682	−	22.3650i	0.383528	−	1.18038i	0.937542	−	0.347871i	$-0.113095\pi$
$360$		0			0
$361$	12.3749	−	8.99086i	0.651308	−	0.473203i
$362$	−27.8145			−1.46190
$363$	−9.64097	−	5.29638i	−0.506020	−	0.277988i
$364$	−3.89953			−0.204391
$365$		0			0
$366$	−6.89131	−	21.2093i	−0.360215	−	1.10863i
$367$	−7.81928	+	24.0653i	−0.408163	+	1.25620i	0.510062	+	0.860137i	$0.329622\pi$
$367$	−7.81928	+	24.0653i	−0.408163	+	1.25620i	−0.918225	+	0.396059i	$0.870378\pi$
$368$	19.2739	+	14.0033i	1.00472	+	0.729973i
$369$	−3.79896	−	2.76011i	−0.197766	−	0.143685i
$370$		0			0
$371$	6.92061	+	21.2994i	0.359300	+	1.10581i
$372$	−4.63530	+	3.36775i	−0.240329	+	0.174609i
$373$	16.2682			0.842334			0.421167	−	0.906983i	$-0.361621\pi$
$373$	16.2682			0.842334			0.421167	+	0.906983i	$0.361621\pi$
$374$	−10.5868	−	26.7274i	−0.547430	−	1.38204i
$375$		0			0
$376$	6.69128	−	4.86150i	0.345076	−	0.250713i
$377$	−0.784581	−	2.41469i	−0.0404080	−	0.124363i
$378$	2.62728	−	8.08594i	0.135133	−	0.415896i
$379$	−20.2467	−	14.7101i	−1.04000	−	0.755607i	−0.0697177	−	0.997567i	$-0.522210\pi$
$379$	−20.2467	−	14.7101i	−1.04000	−	0.755607i	−0.970286	+	0.241960i	$0.922210\pi$
$380$		0			0
$381$	2.52618	−	7.77477i	0.129420	−	0.398314i
$382$	−2.33669	−	7.19160i	−0.119556	−	0.367954i
$383$	10.5974	−	7.69944i	0.541500	−	0.393423i	−0.283142	−	0.959078i	$-0.591377\pi$
$383$	10.5974	−	7.69944i	0.541500	−	0.393423i	0.824642	+	0.565655i	$0.191377\pi$
$384$	−5.42927			−0.277061
$385$		0			0
$386$	−0.0573242			−0.00291772
$387$	2.44695	−	1.77781i	0.124385	−	0.0903713i
$388$	−0.576320	−	1.77373i	−0.0292582	−	0.0900476i
$389$	5.16480	−	15.8956i	0.261866	−	0.805940i	−0.730533	−	0.682877i	$-0.760728\pi$
$389$	5.16480	−	15.8956i	0.261866	−	0.805940i	0.992399	−	0.123063i	$-0.0392717\pi$
$390$		0			0
$391$	19.0709	+	13.8558i	0.964456	+	0.700718i
$392$	2.74348	−	8.44356i	0.138567	−	0.426464i
$393$	5.47128	+	16.8389i	0.275990	+	0.849408i
$394$	−8.49596	+	6.17267i	−0.428020	+	0.310975i
$395$		0			0
$396$	4.18612	−	3.46413i	0.210361	−	0.174079i
$397$	−4.22375			−0.211984			−0.105992	−	0.994367i	$-0.533802\pi$
$397$	−4.22375			−0.211984			−0.105992	+	0.994367i	$0.533802\pi$
$398$	−4.82421	+	3.50500i	−0.241816	+	0.175690i
$399$	−2.65084	−	8.15845i	−0.132708	−	0.408433i
$400$		0			0
$401$	16.9460	+	12.3120i	0.846241	+	0.614830i	0.924107	−	0.382134i	$-0.124811\pi$
$401$	16.9460	+	12.3120i	0.846241	+	0.614830i	−0.0778663	+	0.996964i	$0.524811\pi$
$402$	17.8422	+	12.9631i	0.889887	+	0.646541i
$403$	0.577112	−	1.77617i	0.0287480	−	0.0884773i
$404$	−0.518281	−	1.59510i	−0.0257854	−	0.0793594i
$405$		0			0
$406$	−40.4233			−2.00618
$407$	−1.74487	+	0.110043i	−0.0864901	+	0.00545462i
$408$	−3.13525			−0.155218
$409$	5.54999	−	4.03231i	0.274429	−	0.199385i	−0.442055	−	0.896988i	$-0.645750\pi$
$409$	5.54999	−	4.03231i	0.274429	−	0.199385i	0.716484	+	0.697603i	$0.245750\pi$
$410$		0			0
$411$	−1.69522	+	5.21734i	−0.0836189	+	0.257353i
$412$	6.34961	+	4.61326i	0.312823	+	0.227279i
$413$	49.2210	+	35.7612i	2.42201	+	1.75969i
$414$	−3.05763	+	9.41042i	−0.150274	+	0.462497i
$415$		0			0
$416$	−3.18838	+	2.31650i	−0.156323	+	0.113576i
$417$	3.25952			0.159620
$418$	3.02603	−	11.7930i	0.148008	−	0.576814i
$419$	−19.0865			−0.932435			−0.466217	−	0.884670i	$-0.654384\pi$
$419$	−19.0865			−0.932435			−0.466217	+	0.884670i	$0.654384\pi$
$420$		0			0
$421$	−3.78642	−	11.6534i	−0.184539	−	0.567952i	0.815401	−	0.578896i	$-0.196516\pi$
$421$	−3.78642	−	11.6534i	−0.184539	−	0.567952i	−0.999940	+	0.0109440i	$0.996516\pi$
$422$	12.0187	−	36.9897i	0.585060	−	1.80063i
$423$	9.69830	+	7.04623i	0.471548	+	0.342599i
$424$	2.80451	+	2.03760i	0.136199	+	0.0989545i
$425$		0			0
$426$	−1.98394	−	6.10594i	−0.0961222	−	0.295834i
$427$	42.1603	−	30.6313i	2.04028	−	1.48235i
$428$	−1.20573			−0.0582812
$429$	−0.440196	+	1.71553i	−0.0212529	+	0.0828264i
$430$		0			0
$431$	5.68128	−	4.12769i	0.273658	−	0.198824i	−0.442489	−	0.896774i	$-0.645904\pi$
$431$	5.68128	−	4.12769i	0.273658	−	0.198824i	0.716146	+	0.697950i	$0.245904\pi$
$432$	−1.41919	−	4.36781i	−0.0682807	−	0.210146i
$433$	8.49487	−	26.1445i	0.408238	−	1.25643i	−0.509924	−	0.860220i	$-0.670326\pi$
$433$	8.49487	−	26.1445i	0.408238	−	1.25643i	0.918161	−	0.396207i	$-0.129674\pi$
$434$	−24.0554	−	17.4773i	−1.15470	−	0.838935i
$435$		0			0
$436$	−0.0219713	+	0.0676207i	−0.00105223	+	0.00323845i
$437$	3.08505	+	9.49481i	0.147578	+	0.454198i
$438$	1.00365	−	0.729192i	0.0479561	−	0.0348421i
$439$	−17.6992			−0.844736			−0.422368	−	0.906425i	$-0.638801\pi$
$439$	−17.6992			−0.844736			−0.422368	+	0.906425i	$0.638801\pi$
$440$		0			0
$441$	12.8679			0.612755
$442$	−3.74466	+	2.72065i	−0.178115	+	0.129408i
$443$	−5.12660	−	15.7780i	−0.243572	−	0.749638i	−0.995868	−	0.0908124i	$-0.971054\pi$
$443$	−5.12660	−	15.7780i	−0.243572	−	0.749638i	0.752296	−	0.658825i	$-0.228946\pi$
$444$	0.266871	−	0.821345i	0.0126651	−	0.0389793i
$445$		0			0
$446$	−15.8973	−	11.5500i	−0.752758	−	0.546911i
$447$	0.867210	−	2.66900i	0.0410176	−	0.126239i
$448$	6.73813	+	20.7378i	0.318347	+	0.979771i
$449$	21.2665	−	15.4510i	1.00363	−	0.729179i	0.0407653	−	0.999169i	$-0.487020\pi$
$449$	21.2665	−	15.4510i	1.00363	−	0.729179i	0.962863	+	0.269990i	$0.0870204\pi$
$450$		0			0
$451$	11.9986	−	9.92913i	0.564991	−	0.467545i
$452$	18.3498			0.863100
$453$	11.4588	−	8.32527i	0.538379	−	0.391155i
$454$	3.69715	+	11.3787i	0.173516	+	0.534027i
$455$		0			0
$456$	−1.07423	−	0.780472i	−0.0503053	−	0.0365490i
$457$	−22.2087	−	16.1356i	−1.03888	−	0.754790i	−0.0688132	−	0.997630i	$-0.521921\pi$
$457$	−22.2087	−	16.1356i	−1.03888	−	0.754790i	−0.970067	+	0.242839i	$0.921921\pi$
$458$	−0.814062	+	2.50543i	−0.0380386	+	0.117071i
$459$	−1.40424	−	4.32181i	−0.0655443	−	0.201725i
$460$		0			0
$461$	16.7991			0.782410			0.391205	−	0.920304i	$-0.372058\pi$
$461$	16.7991			0.782410			0.391205	+	0.920304i	$0.372058\pi$
$462$	23.8108	+	15.1057i	1.10778	+	0.702782i
$463$	−32.2574			−1.49913			−0.749565	−	0.661930i	$-0.769737\pi$
$463$	−32.2574			−1.49913			−0.749565	+	0.661930i	$0.769737\pi$
$464$	−17.6654	+	12.8347i	−0.820095	+	0.595834i
$465$		0			0
$466$	−4.89487	+	15.0649i	−0.226751	+	0.697866i
$467$	−1.85767	−	1.34967i	−0.0859626	−	0.0624555i	0.543974	−	0.839102i	$-0.316919\pi$
$467$	−1.85767	−	1.34967i	−0.0859626	−	0.0624555i	−0.629936	+	0.776647i	$0.716919\pi$
$468$	−0.707774	−	0.514228i	−0.0327169	−	0.0237702i
$469$	−15.9258	+	49.0144i	−0.735383	+	2.26328i
$470$		0			0
$471$	2.51672	−	1.82851i	0.115965	−	0.0842532i
$472$	9.41739			0.433470
$473$	3.69423	+	9.32644i	0.169861	+	0.428830i
$474$	33.7995			1.55246
$475$		0			0
$476$	10.2543	+	31.5595i	0.470006	+	1.44653i
$477$	−1.55263	+	4.77851i	−0.0710902	+	0.218793i
$478$	15.8867	+	11.5424i	0.726642	+	0.527936i
$479$	−0.275970	−	0.200504i	−0.0126094	−	0.00916125i	0.581463	−	0.813573i	$-0.302481\pi$
$479$	−0.275970	−	0.200504i	−0.0126094	−	0.00916125i	−0.594072	+	0.804412i	$0.702481\pi$
$480$		0			0
$481$	0.0869880	+	0.267721i	0.00396631	+	0.0122070i
$482$	18.8788	−	13.7162i	0.859905	−	0.624758i
$483$	−23.1222			−1.05210
$484$	7.67796	+	16.3037i	0.348998	+	0.741078i
$485$		0			0
$486$	1.54314	−	1.12116i	0.0699984	−	0.0508568i
$487$	4.89955	+	15.0793i	0.222020	+	0.683306i	0.998580	+	0.0532640i	$0.0169625\pi$
$487$	4.89955	+	15.0793i	0.222020	+	0.683306i	−0.776561	+	0.630042i	$0.783038\pi$
$488$	2.49268	−	7.67168i	0.112838	−	0.347281i
$489$	15.6743	+	11.3880i	0.708815	+	0.514984i
$490$		0			0
$491$	9.27370	−	28.5415i	0.418516	−	1.28806i	−0.490552	−	0.871412i	$-0.663205\pi$
$491$	9.27370	−	28.5415i	0.418516	−	1.28806i	0.909068	−	0.416648i	$-0.136795\pi$
$492$	2.37728	+	7.31650i	0.107176	+	0.329853i
$493$	−17.4793	+	12.6995i	−0.787229	+	0.571955i
$494$	−1.96030			−0.0881978
$495$		0			0
$496$	−16.0616			−0.721186
$497$	12.1375	−	8.81844i	0.544443	−	0.395561i
$498$	2.50352	+	7.70505i	0.112186	+	0.345272i
$499$	1.12951	−	3.47626i	0.0505636	−	0.155619i	−0.922586	−	0.385790i	$-0.873929\pi$
$499$	1.12951	−	3.47626i	0.0505636	−	0.155619i	0.973150	+	0.230172i	$0.0739288\pi$
$500$		0			0
$501$	3.35735	+	2.43926i	0.149996	+	0.108978i
$502$	2.74472	−	8.44737i	0.122503	−	0.377025i
$503$	−9.63458	−	29.6522i	−0.429585	−	1.32213i	−0.898535	−	0.438901i	$-0.855368\pi$
$503$	−9.63458	−	29.6522i	−0.429585	−	1.32213i	0.468951	−	0.883224i	$-0.344632\pi$
$504$	2.48798	−	1.80762i	0.110823	−	0.0805178i
$505$		0			0
$506$	−27.7110	−	17.5800i	−1.23190	−	0.781529i
$507$	−12.7148			−0.564686
$508$	−10.8350	+	7.87209i	−0.480725	+	0.349267i
$509$	−4.55180	−	14.0090i	−0.201755	−	0.620938i	−0.999831	−	0.0183813i	$-0.994149\pi$
$509$	−4.55180	−	14.0090i	−0.201755	−	0.620938i	0.798076	−	0.602557i	$-0.205851\pi$
$510$		0			0
$511$	2.34535	+	1.70400i	0.103752	+	0.0753804i
$512$	22.2939	+	16.1975i	0.985261	+	0.715834i
$513$	0.594714	−	1.83034i	0.0262573	−	0.0808115i
$514$	10.8080	+	33.2636i	0.476721	+	1.46720i
$515$		0			0
$516$	−4.95515			−0.218138
$517$	−30.6309	+	25.3479i	−1.34715	+	1.11480i
$518$	4.48181			0.196919
$519$	−8.62852	+	6.26898i	−0.378750	+	0.275178i
$520$		0			0
$521$	−0.400394	+	1.23229i	−0.0175416	+	0.0539875i	−0.959444	−	0.281899i	$-0.909036\pi$
$521$	−0.400394	+	1.23229i	−0.0175416	+	0.0539875i	0.941903	+	0.335886i	$0.109036\pi$
$522$	−7.33692	−	5.33059i	−0.321128	−	0.233313i
$523$	−24.8762	−	18.0736i	−1.08776	−	0.790305i	−0.108742	−	0.994070i	$-0.534682\pi$
$523$	−24.8762	−	18.0736i	−1.08776	−	0.790305i	−0.979020	+	0.203765i	$0.934682\pi$
$524$	8.96352	−	27.5869i	0.391573	−	1.20514i
$525$		0			0
$526$	15.1259	−	10.9896i	0.659519	−	0.479168i
$527$	−15.8924			−0.692284
$528$	15.2017	−	0.958716i	0.661569	−	0.0417227i
$529$	3.90968			0.169986
$530$		0			0
$531$	4.21793	+	12.9815i	0.183043	+	0.563348i
$532$	−4.34284	+	13.3659i	−0.188286	+	0.579484i
$533$	−2.02867	−	1.47392i	−0.0878716	−	0.0638425i
$534$	−12.7169	−	9.23940i	−0.550316	−	0.399828i
$535$		0			0
$536$	2.46512	+	7.58685i	0.106477	+	0.327702i
$537$	−18.3111	+	13.3038i	−0.790181	+	0.574100i
$538$	−22.7574			−0.981141
$539$	−10.6073	+	41.3387i	−0.456889	+	1.78058i
$540$		0			0
$541$	−12.7461	+	9.26058i	−0.547998	+	0.398144i	−0.827047	−	0.562133i	$-0.809981\pi$
$541$	−12.7461	+	9.26058i	−0.547998	+	0.398144i	0.279049	+	0.960277i	$0.409981\pi$
$542$	17.9215	+	55.1566i	0.769793	+	2.36918i
$543$	4.50615	−	13.8685i	0.193377	−	0.595155i
$544$	27.1320	+	19.7126i	1.16328	+	0.845169i
$545$		0			0
$546$	1.40299	−	4.31795i	0.0600423	−	0.184791i
$547$	−4.74641	−	14.6079i	−0.202942	−	0.624591i	−0.999792	−	0.0204133i	$-0.993502\pi$
$547$	−4.74641	−	14.6079i	−0.202942	−	0.624591i	0.796850	−	0.604178i	$-0.206498\pi$
$548$	7.27094	−	5.28265i	0.310599	−	0.225663i
$549$	11.6915			0.498982
$550$		0			0
$551$	−9.15026			−0.389814
$552$	−2.89551	+	2.10371i	−0.123241	+	0.0895399i
$553$	24.4073	+	75.1179i	1.03790	+	3.19434i
$554$	13.0525	−	40.1716i	0.554549	−	1.70673i
$555$		0			0
$556$	−4.32018	−	3.13879i	−0.183216	−	0.133115i
$557$	11.0996	−	34.1609i	0.470303	−	1.44745i	−0.381885	−	0.924210i	$-0.624725\pi$
$557$	11.0996	−	34.1609i	0.470303	−	1.44745i	0.852188	−	0.523235i	$-0.175275\pi$
$558$	−2.06140	−	6.34433i	−0.0872659	−	0.268577i
$559$	1.30669	−	0.949365i	0.0552670	−	0.0401539i
$560$		0			0
$561$	15.0416	−	0.948618i	0.635056	−	0.0400507i
$562$	−32.4878			−1.37042
$563$	−25.0475	+	18.1981i	−1.05563	+	0.766958i	−0.973274	−	0.229645i	$-0.926244\pi$
$563$	−25.0475	+	18.1981i	−1.05563	+	0.766958i	−0.0823531	+	0.996603i	$0.526244\pi$
$564$	−6.06891	−	18.6782i	−0.255547	−	0.786493i
$565$		0			0
$566$	12.2240	+	8.88126i	0.513813	+	0.373307i
$567$	3.60606	+	2.61996i	0.151440	+	0.110028i
$568$	0.717618	−	2.20860i	0.0301106	−	0.0926708i
$569$	0.721169	+	2.21953i	0.0302330	+	0.0930475i	0.965034	−	0.262123i	$-0.0844227\pi$
$569$	0.721169	+	2.21953i	0.0302330	+	0.0930475i	−0.934801	+	0.355171i	$0.884423\pi$
$570$		0			0
$571$	−26.6093			−1.11357			−0.556783	−	0.830658i	$-0.687964\pi$
$571$	−26.6093			−1.11357			−0.556783	+	0.830658i	$0.687964\pi$
$572$	2.23542	−	1.84987i	0.0934677	−	0.0773470i
$573$	3.96434			0.165613
$574$	−32.2990	+	23.4666i	−1.34813	+	0.979477i
$575$		0			0
$576$	−1.51169	+	4.65252i	−0.0629872	+	0.193855i
$577$	2.99229	+	2.17403i	0.124571	+	0.0905059i	0.648326	−	0.761363i	$-0.275469\pi$
$577$	2.99229	+	2.17403i	0.124571	+	0.0905059i	−0.523755	+	0.851869i	$0.675469\pi$
$578$	5.63231	+	4.09212i	0.234273	+	0.170210i
$579$	0.00928692	−	0.0285822i	0.000385951	−	0.00118784i
$580$		0			0
$581$	−15.3163	+	11.1279i	−0.635427	+	0.461665i
$582$	2.17140			0.0900075
$583$	−14.0713	−	8.92696i	−0.582776	−	0.369717i
$584$	0.448733			0.0185687
$585$		0			0
$586$	13.1676	+	40.5256i	0.543947	+	1.67410i
$587$	9.69003	−	29.8228i	0.399950	−	1.23092i	−0.525088	−	0.851048i	$-0.675968\pi$
$587$	9.69003	−	29.8228i	0.399950	−	1.23092i	0.925039	−	0.379873i	$-0.124032\pi$
$588$	−17.0551	−	12.3912i	−0.703340	−	0.511006i
$589$	−5.44520	−	3.95617i	−0.224366	−	0.163011i
$590$		0			0
$591$	−1.70133	−	5.23616i	−0.0699834	−	0.215387i
$592$	1.95860	−	1.42300i	0.0804978	−	0.0584851i
$593$	32.0728			1.31707			0.658535	−	0.752550i	$-0.271176\pi$
$593$	32.0728			1.31707			0.658535	+	0.752550i	$0.271176\pi$
$594$	2.32973	+	5.88163i	0.0955899	+	0.241326i
$595$		0			0
$596$	−3.71954	+	2.70240i	−0.152358	+	0.110695i
$597$	−0.966057	−	2.97322i	−0.0395381	−	0.121686i
$598$	−1.63280	+	5.02524i	−0.0667701	+	0.205497i
$599$	16.4442	+	11.9474i	0.671892	+	0.488158i	0.870658	−	0.491889i	$-0.163693\pi$
$599$	16.4442	+	11.9474i	0.671892	+	0.488158i	−0.198766	+	0.980047i	$0.563693\pi$
$600$		0			0
$601$	−3.59254	+	11.0567i	−0.146543	+	0.451012i	−0.997206	−	0.0746984i	$-0.976201\pi$
$601$	−3.59254	+	11.0567i	−0.146543	+	0.451012i	0.850663	+	0.525711i	$0.176201\pi$
$602$	−7.94646	−	24.4567i	−0.323873	−	0.996780i
$603$	−9.35405	+	6.79611i	−0.380926	+	0.276759i
$604$	−23.2044			−0.944172
$605$		0			0
$606$	1.95273			0.0793241
$607$	−20.7734	+	15.0927i	−0.843164	+	0.612595i	−0.923253	−	0.384193i	$-0.874480\pi$
$607$	−20.7734	+	15.0927i	−0.843164	+	0.612595i	0.0800885	+	0.996788i	$0.474480\pi$
$608$	4.38908	+	13.5082i	0.178001	+	0.547830i
$609$	6.54886	−	20.1553i	0.265373	−	0.816735i
$610$		0			0
$611$	5.17897	+	3.76274i	0.209519	+	0.152224i
$612$	−2.30055	+	7.08036i	−0.0929941	+	0.286206i
$613$	−2.03469	−	6.26213i	−0.0821804	−	0.252925i	0.901521	−	0.432736i	$-0.142452\pi$
$613$	−2.03469	−	6.26213i	−0.0821804	−	0.252925i	−0.983701	+	0.179810i	$0.942452\pi$
$614$	14.4026	−	10.4641i	0.581240	−	0.422296i
$615$		0			0
$616$	3.75617	+	9.48282i	0.151341	+	0.382074i
$617$	25.4721			1.02547			0.512734	−	0.858548i	$-0.328633\pi$
$617$	25.4721			1.02547			0.512734	+	0.858548i	$0.328633\pi$
$618$	−7.39274	+	5.37114i	−0.297380	+	0.216059i
$619$	−0.334663	−	1.02999i	−0.0134513	−	0.0413987i	0.944106	−	0.329643i	$-0.106928\pi$
$619$	−0.334663	−	1.02999i	−0.0134513	−	0.0413987i	−0.957557	+	0.288244i	$0.906928\pi$
$620$		0			0
$621$	−4.19674	−	3.04911i	−0.168409	−	0.122357i
$622$	−17.3572	−	12.6108i	−0.695962	−	0.505646i
$623$	11.3510	−	34.9348i	0.454769	−	1.39963i
$624$	−0.757857	−	2.33244i	−0.0303386	−	0.0933725i
$625$		0			0
$626$	20.7223			0.828230
$627$	5.38983	+	3.41935i	0.215249	+	0.136556i
$628$	−5.09645			−0.203371
$629$	1.93797	−	1.40801i	0.0772717	−	0.0561412i
$630$		0			0
$631$	9.59703	−	29.5366i	0.382052	−	1.17583i	−0.556545	−	0.830817i	$-0.687873\pi$
$631$	9.59703	−	29.5366i	0.382052	−	1.17583i	0.938597	−	0.345017i	$-0.112127\pi$
$632$	9.89082	+	7.18610i	0.393436	+	0.285848i
$633$	16.4962	+	11.9852i	0.655665	+	0.476368i
$634$	−7.47956	+	23.0197i	−0.297051	+	0.914230i
$635$		0			0
$636$	6.65938	−	4.83832i	0.264062	−	0.191852i
$637$	6.87153			0.272260
$638$	23.1728	−	19.1761i	0.917420	−	0.759189i
$639$	3.36587			0.133152
$640$		0			0
$641$	−6.92776	−	21.3214i	−0.273630	−	0.842147i	−0.989579	−	0.143994i	$-0.954006\pi$
$641$	−6.92776	−	21.3214i	−0.273630	−	0.842147i	0.715949	−	0.698153i	$-0.245994\pi$
$642$	0.433802	−	1.33510i	0.0171208	−	0.0526924i
$643$	−11.1785	−	8.12166i	−0.440837	−	0.320287i	0.345130	−	0.938555i	$-0.387835\pi$
$643$	−11.1785	−	8.12166i	−0.440837	−	0.320287i	−0.785968	+	0.618268i	$0.787835\pi$
$644$	30.6463	+	22.2658i	1.20763	+	0.877396i
$645$		0			0
$646$	5.15484	+	15.8650i	0.202815	+	0.624199i
$647$	−20.1836	+	14.6642i	−0.793499	+	0.576511i	−0.909000	−	0.416797i	$-0.863153\pi$
$647$	−20.1836	+	14.6642i	−0.793499	+	0.576511i	0.115501	+	0.993307i	$0.463153\pi$
$648$	0.689943			0.0271035
$649$	−45.1806	+	2.84937i	−1.77349	+	0.111848i
$650$		0			0
$651$	12.6114	−	9.16273i	0.494280	−	0.359116i
$652$	−9.80848	−	30.1874i	−0.384130	−	1.18223i
$653$	−5.82866	+	17.9388i	−0.228093	+	0.701999i	0.769870	+	0.638201i	$0.220321\pi$
$653$	−5.82866	+	17.9388i	−0.228093	+	0.701999i	−0.997963	+	0.0637975i	$0.979679\pi$
$654$	−0.0669715	−	0.0486576i	−0.00261879	−	0.00190266i
$655$		0			0
$656$	−6.66419	+	20.5103i	−0.260193	+	0.800791i
$657$	0.200982	+	0.618559i	0.00784105	+	0.0241323i
$658$	82.4555	−	59.9075i	3.21445	−	2.33544i
$659$	−2.97553			−0.115910			−0.0579550	−	0.998319i	$-0.518458\pi$
$659$	−2.97553			−0.115910			−0.0579550	+	0.998319i	$0.518458\pi$
$660$		0			0
$661$	−39.0164			−1.51756			−0.758782	−	0.651345i	$-0.774205\pi$
$661$	−39.0164			−1.51756			−0.758782	+	0.651345i	$0.774205\pi$
$662$	−35.5891	+	25.8570i	−1.38321	+	1.00496i
$663$	−0.749875	−	2.30788i	−0.0291227	−	0.0896305i
$664$	−0.905558	+	2.78702i	−0.0351425	+	0.108157i
$665$		0			0
$666$	0.813459	+	0.591012i	0.0315209	+	0.0229013i
$667$	−7.62157	+	23.4568i	−0.295108	+	0.908250i
$668$	−2.10093	−	6.46600i	−0.0812875	−	0.250177i
$669$	8.33440	−	6.05529i	0.322226	−	0.234111i
$670$		0			0
$671$	−9.63762	+	37.5596i	−0.372056	+	1.44997i
$672$	−32.8958			−1.26898
$673$	−12.3199	+	8.95090i	−0.474896	+	0.345032i	−0.799346	−	0.600871i	$-0.794821\pi$
$673$	−12.3199	+	8.95090i	−0.474896	+	0.345032i	0.324450	+	0.945903i	$0.394821\pi$
$674$	19.0757	+	58.7089i	0.734767	+	2.26138i
$675$		0			0
$676$	16.8523	+	12.2439i	0.648164	+	0.470919i
$677$	0.670727	+	0.487311i	0.0257781	+	0.0187289i	0.600600	−	0.799550i	$-0.294929\pi$
$677$	0.670727	+	0.487311i	0.0257781	+	0.0187289i	−0.574822	+	0.818279i	$0.694929\pi$
$678$	−6.60194	+	20.3187i	−0.253546	+	0.780334i
$679$	1.56801	+	4.82585i	0.0601748	+	0.185199i
$680$		0			0
$681$	−6.27244			−0.240361
$682$	22.0807	−	1.39255i	0.845515	−	0.0533236i
$683$	−1.03468			−0.0395910			−0.0197955	−	0.999804i	$-0.506302\pi$
$683$	−1.03468			−0.0395910			−0.0197955	+	0.999804i	$0.506302\pi$
$684$	−2.55078	+	1.85325i	−0.0975315	+	0.0708608i
$685$		0			0
$686$	15.4165	−	47.4472i	0.588605	−	1.81154i
$687$	−1.11734	−	0.811793i	−0.0426291	−	0.0309718i
$688$	−11.2378	−	8.16476i	−0.428438	−	0.311279i
$689$	−0.829118	+	2.55176i	−0.0315869	+	0.0972144i
$690$		0			0
$691$	−15.5969	+	11.3318i	−0.593332	+	0.431081i	−0.843506	−	0.537120i	$-0.819512\pi$
$691$	−15.5969	+	11.3318i	−0.593332	+	0.431081i	0.250174	+	0.968201i	$0.419512\pi$
$692$	17.4730			0.664225
$693$	−11.3893	+	9.42496i	−0.432644	+	0.358025i
$694$	55.4762			2.10585
$695$		0			0
$696$	−1.01369	−	3.11980i	−0.0384237	−	0.118256i
$697$	−6.59400	+	20.2942i	−0.249765	+	0.768699i
$698$	−22.2270	−	16.1488i	−0.841303	−	0.611242i
$699$	−6.71844	−	4.88123i	−0.254115	−	0.184625i
$700$		0			0
$701$	1.01927	+	3.13700i	0.0384974	+	0.118483i	0.968458	−	0.249175i	$-0.0801596\pi$
$701$	1.01927	+	3.13700i	0.0384974	+	0.118483i	−0.929961	+	0.367658i	$0.880160\pi$
$702$	0.824050	−	0.598707i	0.0311018	−	0.0225967i
$703$	1.01451			0.0382629
$704$	−13.7003	−	8.69158i	−0.516350	−	0.327576i
$705$		0			0
$706$	−44.6318	+	32.4269i	−1.67974	+	1.22040i
$707$	1.41010	+	4.33985i	0.0530324	+	0.163217i
$708$	6.91018	−	21.2674i	0.259701	−	0.799276i
$709$	30.5479	+	22.1943i	1.14725	+	0.833526i	0.988113	−	0.153730i	$-0.0491287\pi$
$709$	30.5479	+	22.1943i	1.14725	+	0.833526i	0.159137	+	0.987256i	$0.449129\pi$
$710$		0			0
$711$	−5.47575	+	16.8526i	−0.205357	+	0.632023i
$712$	−1.75700	−	5.40750i	−0.0658464	−	0.202654i
$713$	−14.6772	+	10.6636i	−0.549665	+	0.399355i
$714$	−38.6352			−1.44589
$715$		0			0
$716$	37.0805			1.38576
$717$	−8.32887	+	6.05128i	−0.311047	+	0.225989i
$718$	−13.8610	−	42.6596i	−0.517286	−	1.59204i
$719$	−8.99176	+	27.6738i	−0.335336	+	1.03206i	0.631220	+	0.775604i	$0.282554\pi$
$719$	−8.99176	+	27.6738i	−0.335336	+	1.03206i	−0.966556	+	0.256455i	$0.917446\pi$
$720$		0			0
$721$	−17.2756	−	12.5514i	−0.643377	−	0.467440i
$722$	9.01599	−	27.7484i	0.335540	−	1.03269i
$723$	3.78051	+	11.6352i	0.140599	+	0.432718i
$724$	−19.3273	+	14.0421i	−0.718293	+	0.521870i
$725$		0			0
$726$	−20.8155	+	2.63600i	−0.772535	+	0.0978310i
$727$	−38.1331			−1.41428			−0.707140	−	0.707074i	$-0.750015\pi$
$727$	−38.1331			−1.41428			−0.707140	+	0.707074i	$0.750015\pi$
$728$	1.32860	−	0.965283i	0.0492411	−	0.0357758i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−11.1195	−	8.07876i	−0.411268	−	0.298804i
$732$	−15.4960	−	11.2585i	−0.572747	−	0.416125i
$733$	−12.3622	+	38.0468i	−0.456607	+	1.40529i	0.412632	+	0.910898i	$0.364610\pi$
$733$	−12.3622	+	38.0468i	−0.456607	+	1.40529i	−0.869238	+	0.494393i	$0.835390\pi$
$734$	14.9147	+	45.9028i	0.550512	+	1.69430i
$735$		0			0
$736$	38.2842			1.41118
$737$	−14.1221	−	35.6526i	−0.520194	−	1.31328i
$738$	−8.95686			−0.329707
$739$	33.5714	−	24.3910i	1.23494	−	0.897238i	0.237692	−	0.971341i	$-0.423609\pi$
$739$	33.5714	−	24.3910i	1.23494	−	0.897238i	0.997251	+	0.0741026i	$0.0236092\pi$
$740$		0			0
$741$	0.317582	−	0.977416i	0.0116667	−	0.0359063i
$742$	34.5596	+	25.1090i	1.26872	+	0.921780i
$743$	2.18030	+	1.58408i	0.0799876	+	0.0581144i	0.627060	−	0.778971i	$-0.284258\pi$
$743$	2.18030	+	1.58408i	0.0799876	+	0.0581144i	−0.547073	+	0.837085i	$0.684258\pi$
$744$	0.745635	−	2.29483i	0.0273363	−	0.0841325i
$745$		0			0
$746$	25.1041	−	18.2392i	0.919127	−	0.667785i
$747$	−4.24738			−0.155403
$748$	−20.8496	−	13.2271i	−0.762337	−	0.483632i
$749$	3.28047			0.119866
$750$		0			0
$751$	−14.1019	−	43.4012i	−0.514586	−	1.58373i	−0.784034	−	0.620718i	$-0.786841\pi$
$751$	−14.1019	−	43.4012i	−0.514586	−	1.58373i	0.269448	−	0.963015i	$-0.413159\pi$
$752$	17.0129	−	52.3603i	0.620396	−	1.90938i
$753$	3.76725	+	2.73707i	0.137286	+	0.0997443i
$754$	−3.91797	−	2.84657i	−0.142684	−	0.103666i
$755$		0			0
$756$	−2.25656	−	6.94499i	−0.0820705	−	0.252587i
$757$	7.27458	−	5.28529i	0.264399	−	0.192097i	−0.447685	−	0.894191i	$-0.647751\pi$
$757$	7.27458	−	5.28529i	0.264399	−	0.192097i	0.712084	+	0.702094i	$0.247751\pi$
$758$	−47.7359			−1.73385
$759$	13.2549	−	10.9688i	0.481122	−	0.398142i
$760$		0			0
$761$	12.1822	−	8.85092i	0.441606	−	0.320845i	−0.344667	−	0.938725i	$-0.612008\pi$
$761$	12.1822	−	8.85092i	0.441606	−	0.320845i	0.786273	+	0.617880i	$0.212008\pi$
$762$	−4.81850	−	14.8298i	−0.174556	−	0.537228i
$763$	0.0597780	−	0.183978i	0.00216411	−	0.00666045i
$764$	−5.25434	−	3.81750i	−0.190095	−	0.138112i
$765$		0			0
$766$	7.72096	−	23.7627i	0.278970	−	0.858580i
$767$	2.25241	+	6.93220i	0.0813297	+	0.250307i
$768$	−16.2935	+	11.8379i	−0.587940	+	0.427164i
$769$	−48.1314			−1.73566			−0.867831	−	0.496859i	$-0.834487\pi$
$769$	−48.1314			−1.73566			−0.867831	+	0.496859i	$0.834487\pi$
$770$		0			0
$771$	−18.3364			−0.660371
$772$	−0.0398324	+	0.0289400i	−0.00143360	+	0.00104157i
$773$	−8.82402	−	27.1575i	−0.317378	−	0.976789i	−0.974765	−	0.223235i	$-0.928338\pi$
$773$	−8.82402	−	27.1575i	−0.317378	−	0.976789i	0.657387	−	0.753553i	$-0.271662\pi$
$774$	1.78278	−	5.48683i	0.0640807	−	0.197220i
$775$		0			0
$776$	0.635422	+	0.461661i	0.0228103	+	0.0165727i
$777$	−0.726085	+	2.23466i	−0.0260481	+	0.0801679i
$778$	−9.85149	−	30.3198i	−0.353193	−	1.08702i
$779$	−7.31123	+	5.31192i	−0.261952	+	0.190319i
$780$		0			0
$781$	−2.77457	+	10.8130i	−0.0992821	+	0.386921i
$782$	44.9637			1.60790
$783$	3.84650	−	2.79464i	0.137463	−	0.0998724i
$784$	−18.2619	−	56.2044i	−0.652211	−	2.00730i
$785$		0			0
$786$	27.3220	+	19.8506i	0.974544	+	0.708047i
$787$	34.5547	+	25.1054i	1.23174	+	0.894912i	0.997019	−	0.0771507i	$-0.0245823\pi$
$787$	34.5547	+	25.1054i	1.23174	+	0.894912i	0.234721	+	0.972063i	$0.424582\pi$
$788$	−2.78727	+	8.57832i	−0.0992923	+	0.305590i
$789$	3.02898	+	9.32224i	0.107834	+	0.331880i
$790$		0			0
$791$	−49.9248			−1.77512
$792$	−0.568738	+	2.21648i	−0.0202092	+	0.0787591i
$793$	6.24336			0.221708
$794$	−6.51784	+	4.73549i	−0.231310	+	0.168056i
$795$		0			0
$796$	−1.58268	+	4.87098i	−0.0560966	+	0.172647i
$797$	−6.91606	−	5.02481i	−0.244979	−	0.177988i	0.458519	−	0.888684i	$-0.348380\pi$
$797$	−6.91606	−	5.02481i	−0.244979	−	0.177988i	−0.703499	+	0.710696i	$0.748380\pi$
$798$	−13.2375	−	9.61764i	−0.468604	−	0.340461i
$799$	16.8337	−	51.8088i	0.595533	−	1.83286i
$800$		0			0
$801$	6.66706	−	4.84390i	0.235569	−	0.171151i
$802$	39.9537			1.41081
$803$	−2.15283	+	0.135771i	−0.0759716	+	0.00479125i
$804$	18.9423			0.668042
$805$		0			0
$806$	−1.10080	−	3.38792i	−0.0387741	−	0.119334i
$807$	3.68686	−	11.3470i	0.129784	−	0.399433i
$808$	0.571431	+	0.415169i	0.0201029	+	0.0146056i
$809$	−10.3702	−	7.53436i	−0.364595	−	0.264894i	0.390371	−	0.920658i	$-0.372347\pi$
$809$	−10.3702	−	7.53436i	−0.364595	−	0.264894i	−0.754966	+	0.655764i	$0.772347\pi$
$810$		0			0
$811$	10.5227	+	32.3855i	0.369502	+	1.13721i	0.947114	+	0.320898i	$0.103985\pi$
$811$	10.5227	+	32.3855i	0.369502	+	1.13721i	−0.577612	+	0.816312i	$0.696015\pi$
$812$	−28.0887	+	20.4076i	−0.985719	+	0.716166i
$813$	−30.4048			−1.06634
$814$	−2.56921	+	2.12609i	−0.0900508	+	0.0745195i
$815$		0			0
$816$	−16.8840	+	12.2669i	−0.591057	+	0.429428i
$817$	−1.79877	−	5.53604i	−0.0629309	−	0.193681i
$818$	4.04358	−	12.4448i	0.141380	−	0.435124i
$819$	1.92566	+	1.39908i	0.0672882	+	0.0488877i
$820$		0			0
$821$	5.35752	−	16.4888i	0.186979	−	0.575462i	−0.812998	−	0.582266i	$-0.802166\pi$
$821$	5.35752	−	16.4888i	0.186979	−	0.575462i	0.999977	+	0.00680474i	$0.00216603\pi$
$822$	3.23351	+	9.95171i	0.112782	+	0.347106i
$823$	−19.0664	+	13.8525i	−0.664611	+	0.482868i	−0.868217	−	0.496185i	$-0.834734\pi$
$823$	−19.0664	+	13.8525i	−0.664611	+	0.482868i	0.203606	+	0.979053i	$0.434734\pi$
$824$	−3.30531			−0.115146
$825$		0			0
$826$	116.049			4.03786
$827$	12.4032	−	9.01142i	0.431300	−	0.313358i	−0.350869	−	0.936425i	$-0.614114\pi$
$827$	12.4032	−	9.01142i	0.431300	−	0.313358i	0.782169	+	0.623067i	$0.214114\pi$
$828$	2.62619	+	8.08259i	0.0912665	+	0.280889i
$829$	−6.93630	+	21.3477i	−0.240908	+	0.741437i	0.755375	+	0.655293i	$0.227455\pi$
$829$	−6.93630	+	21.3477i	−0.240908	+	0.741437i	−0.996283	+	0.0861445i	$0.972545\pi$
$830$		0			0
$831$	17.9152	+	13.0162i	0.621471	+	0.451525i
$832$	−0.807256	+	2.48448i	−0.0279866	+	0.0861338i
$833$	−18.0696	−	55.6124i	−0.626073	−	1.92686i
$834$	5.02991	−	3.65444i	0.174172	−	0.126543i
$835$		0			0
$836$	−3.85099	−	9.72220i	−0.133189	−	0.336249i
$837$	3.49728			0.120884
$838$	−29.4531	+	21.3990i	−1.01744	+	0.739215i
$839$	−14.3542	−	44.1776i	−0.495561	−	1.52518i	−0.816080	−	0.577939i	$-0.803857\pi$
$839$	−14.3542	−	44.1776i	−0.495561	−	1.52518i	0.320519	−	0.947242i	$-0.396143\pi$
$840$		0			0
$841$	5.17319	+	3.75854i	0.178386	+	0.129605i
$842$	−18.9083	−	13.7377i	−0.651623	−	0.473432i
$843$	5.26326	−	16.1986i	0.181276	−	0.557911i
$844$	−10.3228	−	31.7704i	−0.355326	−	1.09358i
$845$		0			0
$846$	22.8658			0.786143
$847$	−20.8897	−	44.3580i	−0.717778	−	1.52416i
$848$	23.0751			0.792403
$849$	−6.40863	+	4.65614i	−0.219944	+	0.159798i
$850$		0			0
$851$	0.845018	−	2.60070i	0.0289669	−	0.0891508i
$852$	−4.46113	−	3.24120i	−0.152836	−	0.111042i
$853$	28.8270	+	20.9440i	0.987016	+	0.717109i	0.959266	−	0.282506i	$-0.0911656\pi$
$853$	28.8270	+	20.9440i	0.987016	+	0.717109i	0.0277505	+	0.999615i	$0.491166\pi$
$854$	30.7169	−	94.5369i	1.05111	−	3.23499i
$855$		0			0
$856$	0.410801	−	0.298464i	0.0140409	−	0.0102013i
$857$	−12.7176			−0.434424			−0.217212	−	0.976124i	$-0.569696\pi$
$857$	−12.7176			−0.434424			−0.217212	+	0.976124i	$0.569696\pi$
$858$	1.24409	+	3.14083i	0.0424726	+	0.107226i
$859$	−12.9964			−0.443431			−0.221715	−	0.975111i	$-0.571166\pi$
$859$	−12.9964			−0.443431			−0.221715	+	0.975111i	$0.571166\pi$
$860$		0			0
$861$	−6.46793	−	19.9062i	−0.220426	−	0.678403i
$862$	4.13923	−	12.7392i	0.140983	−	0.433900i
$863$	−43.0267	−	31.2607i	−1.46465	−	1.06413i	−0.982122	−	0.188244i	$-0.939720\pi$
$863$	−43.0267	−	31.2607i	−1.46465	−	1.06413i	−0.482523	−	0.875883i	$-0.660280\pi$
$864$	−5.97067	−	4.33795i	−0.203126	−	0.147580i
$865$		0			0
$866$	−16.2034	−	49.8689i	−0.550613	−	1.69461i
$867$	−2.95283	+	2.14536i	−0.100283	+	0.0728601i
$868$	−25.5385			−0.866835
$869$	−49.6262	−	31.4832i	−1.68345	−	1.06799i
$870$		0			0
$871$	−4.99513	+	3.62918i	−0.169254	+	0.122970i
$872$	−0.00925293	−	0.0284776i	−0.000313344	−	0.000964373i
$873$	−0.351782	+	1.08267i	−0.0119060	+	0.0366430i
$874$	15.4059	+	11.1930i	0.521111	+	0.378609i
$875$		0			0
$876$	0.329266	−	1.01338i	0.0111249	−	0.0342388i
$877$	2.90686	+	8.94641i	0.0981578	+	0.302099i	0.988064	−	0.154045i	$-0.0492302\pi$
$877$	2.90686	+	8.94641i	0.0981578	+	0.302099i	−0.889906	+	0.456144i	$0.849230\pi$
$878$	−27.3124	+	19.8436i	−0.921747	+	0.669689i
$879$	−22.3396			−0.753494
$880$		0			0
$881$	−26.5160			−0.893345			−0.446673	−	0.894697i	$-0.647391\pi$
$881$	−26.5160			−0.893345			−0.446673	+	0.894697i	$0.647391\pi$
$882$	19.8569	−	14.4269i	0.668618	−	0.485780i
$883$	−3.55444	−	10.9394i	−0.119616	−	0.368141i	0.873266	−	0.487245i	$-0.161998\pi$
$883$	−3.55444	−	10.9394i	−0.119616	−	0.368141i	−0.992882	+	0.119103i	$0.961998\pi$
$884$	−1.22851	+	3.78096i	−0.0413192	+	0.127168i
$885$		0			0
$886$	−25.6008	−	18.6001i	−0.860075	−	0.624881i
$887$	−9.97420	+	30.6974i	−0.334901	+	1.03072i	0.631870	+	0.775074i	$0.282288\pi$
$887$	−9.97420	+	30.6974i	−0.334901	+	1.03072i	−0.966771	+	0.255645i	$0.917712\pi$
$888$	0.112389	+	0.345899i	0.00377154	+	0.0116076i
$889$	29.4791	−	21.4178i	0.988698	−	0.718331i
$890$		0			0
$891$	−3.31005	+	0.208753i	−0.110891	+	0.00699348i
$892$	−16.8774			−0.565098
$893$	18.6647	−	13.5607i	0.624591	−	0.453792i
$894$	−1.65414	−	5.09092i	−0.0553228	−	0.170266i
$895$		0			0
$896$	−19.5783	−	14.2245i	−0.654065	−	0.475206i
$897$	−2.24109	−	1.62825i	−0.0748278	−	0.0543656i
$898$	15.4942	−	47.6863i	0.517048	−	1.59131i
$899$	−5.13832	−	15.8141i	−0.171372	−	0.527430i
$900$		0			0
$901$	22.8321			0.760647
$902$	7.38337	−	28.7744i	0.245839	−	0.958082i
$903$	13.4816			0.448641
$904$	−6.25189	+	4.54226i	−0.207935	+	0.151073i
$905$		0			0
$906$	8.34854	−	25.6942i	0.277362	−	0.853631i
$907$	−18.6147	−	13.5243i	−0.618090	−	0.449068i	0.234164	−	0.972197i	$-0.424765\pi$
$907$	−18.6147	−	13.5243i	−0.618090	−	0.449068i	−0.852254	+	0.523129i	$0.824765\pi$
$908$	8.31350	+	6.04011i	0.275893	+	0.200448i
$909$	−0.316355	+	0.973642i	−0.0104928	+	0.0322937i
$910$		0			0
$911$	24.4145	−	17.7382i	0.808888	−	0.587692i	−0.104620	−	0.994512i	$-0.533363\pi$
$911$	24.4145	−	17.7382i	0.808888	−	0.587692i	0.913508	+	0.406820i	$0.133363\pi$
$912$	−8.83860			−0.292675
$913$	3.50122	−	13.6449i	0.115874	−	0.451581i
$914$	−52.3618			−1.73197
$915$		0			0
$916$	0.699196	+	2.15190i	0.0231021	+	0.0711009i
$917$	−24.3873	+	75.0565i	−0.805341	+	2.47858i
$918$	−7.01237	−	5.09479i	−0.231443	−	0.168153i
$919$	22.9351	+	16.6633i	0.756558	+	0.549672i	0.897853	−	0.440296i	$-0.145126\pi$
$919$	22.9351	+	16.6633i	0.756558	+	0.549672i	−0.141294	+	0.989968i	$0.545126\pi$
$920$		0			0
$921$	2.88414	+	8.87647i	0.0950356	+	0.292490i
$922$	25.9233	−	18.8344i	0.853740	−	0.620278i
$923$	1.79740			0.0591622
$924$	24.1713	−	1.52440i	0.795177	−	0.0501489i
$925$		0			0
$926$	−49.7778	+	36.1657i	−1.63580	+	1.18848i
$927$	−1.48041	−	4.55623i	−0.0486230	−	0.149646i
$928$	−10.8432	+	33.3718i	−0.355944	+	1.09548i
$929$	25.7821	+	18.7318i	0.845885	+	0.614571i	0.924008	−	0.382372i	$-0.124893\pi$
$929$	25.7821	+	18.7318i	0.845885	+	0.614571i	−0.0781235	+	0.996944i	$0.524893\pi$
$930$		0			0
$931$	7.65269	−	23.5526i	0.250807	−	0.771904i
$932$	4.20419	+	12.9392i	0.137713	+	0.423837i
$933$	9.09981	−	6.61140i	0.297914	−	0.216447i
$934$	−4.37985			−0.143313
$935$		0			0
$936$	0.368435			0.0120427
$937$	17.9834	−	13.0657i	0.587494	−	0.426839i	−0.253924	−	0.967224i	$-0.581721\pi$
$937$	17.9834	−	13.0657i	0.587494	−	0.426839i	0.841418	+	0.540385i	$0.181721\pi$
$938$	30.3772	+	93.4915i	0.991852	+	3.05261i
$939$	−3.35716	+	10.3323i	−0.109557	+	0.337181i
$940$		0			0
$941$	1.16490	+	0.846351i	0.0379747	+	0.0275903i	0.606611	−	0.794999i	$-0.292529\pi$
$941$	1.16490	+	0.846351i	0.0379747	+	0.0275903i	−0.568636	+	0.822589i	$0.692529\pi$
$942$	1.83362	−	5.64330i	0.0597425	−	0.183869i
$943$	7.52738	+	23.1669i	0.245125	+	0.754418i
$944$	50.7146	−	36.8463i	1.65062	−	1.19924i
$945$		0			0
$946$	16.1571	+	10.2502i	0.525314	+	0.333263i
$947$	22.8848			0.743655			0.371827	−	0.928302i	$-0.378731\pi$
$947$	22.8848			0.743655			0.371827	+	0.928302i	$0.378731\pi$
$948$	23.4860	−	17.0636i	0.762790	−	0.554199i
$949$	0.107326	+	0.330315i	0.00348395	+	0.0107225i
$950$		0			0
$951$	−10.2660	−	7.45871i	−0.332899	−	0.241865i
$952$	−11.3059	−	8.21422i	−0.366426	−	0.266224i
$953$	−4.32227	+	13.3026i	−0.140012	+	0.430913i	−0.996336	−	0.0855263i	$-0.972743\pi$
$953$	−4.32227	+	13.3026i	−0.140012	+	0.430913i	0.856324	+	0.516439i	$0.172743\pi$
$954$	2.96154	+	9.11468i	0.0958833	+	0.295099i
$955$		0			0
$956$	16.8662			0.545493
$957$	5.80717	+	14.6608i	0.187719	+	0.473915i
$958$	−0.650657			−0.0210218
$959$	−19.7823	+	14.3727i	−0.638803	+	0.464118i
$960$		0			0
$961$	−5.79995	+	17.8504i	−0.187095	+	0.575819i
$962$	0.434393	+	0.315605i	0.0140054	+	0.0101755i
$963$	0.595413	+	0.432593i	0.0191869	+	0.0139401i
$964$	6.19356	−	19.0618i	0.199481	−	0.613940i
$965$		0			0
$966$	−35.6809	+	25.9237i	−1.14801	+	0.834081i
$967$	−34.3901			−1.10591			−0.552955	−	0.833211i	$-0.686500\pi$
$967$	−34.3901			−1.10591			−0.552955	+	0.833211i	$0.686500\pi$
$968$	−6.65172	−	3.65420i	−0.213794	−	0.117450i
$969$	−8.74550			−0.280946
$970$		0			0
$971$	12.4857	+	38.4271i	0.400686	+	1.23318i	0.924444	+	0.381317i	$0.124529\pi$
$971$	12.4857	+	38.4271i	0.400686	+	1.23318i	−0.523758	+	0.851867i	$0.675471\pi$
$972$	0.506258	−	1.55810i	0.0162382	−	0.0499762i
$973$	11.7540	+	8.53982i	0.376817	+	0.273774i
$974$	24.4669	+	17.7763i	0.783971	+	0.569589i
$975$		0			0
$976$	−16.5925	−	51.0664i	−0.531112	−	1.63459i
$977$	−39.5384	+	28.7264i	−1.26495	+	0.919038i	−0.998989	−	0.0449470i	$-0.985688\pi$
$977$	−39.5384	+	28.7264i	−1.26495	+	0.919038i	−0.265958	+	0.963985i	$0.585688\pi$
$978$	36.9554			1.18170
$979$	10.0655	+	25.4112i	0.321693	+	0.812146i
$980$		0			0
$981$	0.0351108	−	0.0255095i	0.00112100	−	0.000814456i
$982$	−17.6889	−	54.4409i	−0.564476	−	1.73728i
$983$	3.09310	−	9.51959i	0.0986546	−	0.303628i	−0.889534	−	0.456868i	$-0.848971\pi$
$983$	3.09310	−	9.51959i	0.0986546	−	0.303628i	0.988189	+	0.153241i	$0.0489710\pi$
$984$	−2.62107	−	1.90432i	−0.0835566	−	0.0607074i
$985$		0			0
$986$	−12.7350	+	39.1942i	−0.405564	+	1.24820i
$987$	16.5119	+	50.8183i	0.525578	+	1.61756i
$988$	−1.36214	+	0.989650i	−0.0433353	+	0.0314850i
$989$	−15.6899			−0.498911
$990$		0			0
$991$	31.6029			1.00390			0.501949	−	0.864897i	$-0.332617\pi$
$991$	31.6029			1.00390			0.501949	+	0.864897i	$0.332617\pi$
$992$	−20.8811	+	15.1710i	−0.662976	+	0.481680i
$993$	−7.12678	−	21.9340i	−0.226161	−	0.696053i
$994$	8.84309	−	27.2162i	0.280486	−	0.863246i
$995$		0			0
$996$	5.62948	+	4.09006i	0.178377	+	0.129598i
$997$	−16.5018	+	50.7872i	−0.522616	+	1.60845i	0.246365	+	0.969177i	$0.420764\pi$
$997$	−16.5018	+	50.7872i	−0.522616	+	1.60845i	−0.768982	+	0.639271i	$0.779236\pi$
$998$	−2.15445	−	6.63072i	−0.0681980	−	0.209892i
$999$	−0.426469	+	0.309848i	−0.0134929	+	0.00980314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.p.751.5		24
5.2	odd	4		165.2.s.a.124.10	yes	48
5.3	odd	4		165.2.s.a.124.3	yes	48
5.4	even	2		825.2.n.o.751.2		24
11.2	odd	10		9075.2.a.ea.1.9		12
11.4	even	5	inner	825.2.n.p.301.5		24
11.9	even	5		9075.2.a.dy.1.4		12
15.2	even	4		495.2.ba.c.289.3		48
15.8	even	4		495.2.ba.c.289.10		48
55.2	even	20		1815.2.c.k.364.19		24
55.4	even	10		825.2.n.o.301.2		24
55.9	even	10		9075.2.a.dz.1.9		12
55.13	even	20		1815.2.c.k.364.6		24
55.24	odd	10		9075.2.a.dx.1.4		12
55.37	odd	20		165.2.s.a.4.3	✓	48
55.42	odd	20		1815.2.c.j.364.6		24
55.48	odd	20		165.2.s.a.4.10	yes	48
55.53	odd	20		1815.2.c.j.364.19		24
165.92	even	20		495.2.ba.c.334.10		48
165.158	even	20		495.2.ba.c.334.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.4.3	✓	48	55.37	odd	20
165.2.s.a.4.10	yes	48	55.48	odd	20
165.2.s.a.124.3	yes	48	5.3	odd	4
165.2.s.a.124.10	yes	48	5.2	odd	4
495.2.ba.c.289.3		48	15.2	even	4
495.2.ba.c.289.10		48	15.8	even	4
495.2.ba.c.334.3		48	165.158	even	20
495.2.ba.c.334.10		48	165.92	even	20
825.2.n.o.301.2		24	55.4	even	10
825.2.n.o.751.2		24	5.4	even	2
825.2.n.p.301.5		24	11.4	even	5	inner
825.2.n.p.751.5		24	1.1	even	1	trivial
1815.2.c.j.364.6		24	55.42	odd	20
1815.2.c.j.364.19		24	55.53	odd	20
1815.2.c.k.364.6		24	55.13	even	20
1815.2.c.k.364.19		24	55.2	even	20
9075.2.a.dx.1.4		12	55.24	odd	10
9075.2.a.dy.1.4		12	11.9	even	5
9075.2.a.dz.1.9		12	55.9	even	10
9075.2.a.ea.1.9		12	11.2	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.54314 - 1.12116i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.506258 - 1.55810i) q^{4} +(1.54314 + 1.12116i) q^{6} +(-1.37739 + 4.23918i) q^{7} +(0.213204 + 0.656175i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.54314 - 1.12116i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.506258 - 1.55810i) q^{4} +(1.54314 + 1.12116i) q^{6} +(-1.37739 + 4.23918i) q^{7} +(0.213204 + 0.656175i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-1.22140 - 3.08354i) q^{11} +1.63829 q^{12} +(-0.432021 + 0.313882i) q^{13} +(2.62728 + 8.08594i) q^{14} +(3.71548 + 2.69946i) q^{16} +(3.67635 + 2.67102i) q^{17} +(-0.589428 + 1.81407i) q^{18} +(0.594714 + 1.83034i) q^{19} -4.45734 q^{21} +(-5.34192 - 3.38895i) q^{22} +5.18745 q^{23} +(-0.558176 + 0.405538i) q^{24} +(-0.314759 + 0.968729i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(5.90776 + 4.29224i) q^{28} +(-1.46923 + 4.52183i) q^{29} +(-2.82936 + 2.05565i) q^{31} +7.38016 q^{32} +(2.55518 - 2.11448i) q^{33} +8.66777 q^{34} +(0.506258 + 1.55810i) q^{36} +(0.162896 - 0.501344i) q^{37} +(2.96983 + 2.15771i) q^{38} +(-0.432021 - 0.313882i) q^{39} +(1.45107 + 4.46595i) q^{41} +(-6.87831 + 4.99738i) q^{42} -3.02459 q^{43} +(-5.42281 + 0.341997i) q^{44} +(8.00498 - 5.81596i) q^{46} +(-3.70442 - 11.4010i) q^{47} +(-1.41919 + 4.36781i) q^{48} +(-10.4103 - 7.56354i) q^{49} +(-1.40424 + 4.32181i) q^{51} +(0.270346 + 0.832039i) q^{52} +(4.06485 - 2.95328i) q^{53} -1.90743 q^{54} -3.07531 q^{56} +(-1.55698 + 1.13121i) q^{57} +(2.80246 + 8.62507i) q^{58} +(4.21793 - 12.9815i) q^{59} +(-9.45864 - 6.87210i) q^{61} +(-2.06140 + 6.34433i) q^{62} +(-1.37739 - 4.23918i) q^{63} +(3.95767 - 2.87541i) q^{64} +(1.57234 - 6.12771i) q^{66} +11.5622 q^{67} +(6.02291 - 4.37590i) q^{68} +(1.60301 + 4.93356i) q^{69} +(-2.72305 - 1.97841i) q^{71} +(-0.558176 - 0.405538i) q^{72} +(0.200982 - 0.618559i) q^{73} +(-0.310714 - 0.956278i) q^{74} +3.15294 q^{76} +(14.7540 - 0.930481i) q^{77} -1.01858 q^{78} +(14.3357 - 10.4155i) q^{79} +(0.309017 - 0.951057i) q^{81} +(7.24625 + 5.26471i) q^{82} +(3.43620 + 2.49655i) q^{83} +(-2.25656 + 6.94499i) q^{84} +(-4.66738 + 3.39105i) q^{86} -4.75453 q^{87} +(1.76293 - 1.45887i) q^{88} -8.24094 q^{89} +(-0.735538 - 2.26375i) q^{91} +(2.62619 - 8.08259i) q^{92} +(-2.82936 - 2.05565i) q^{93} +(-18.4988 - 13.4402i) q^{94} +(2.28059 + 7.01895i) q^{96} +(0.920978 - 0.669130i) q^{97} -24.5445 q^{98} +(2.80059 + 1.77671i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} - 6 q^{3} - 6 q^{4} + 2 q^{6} + 4 q^{7} + 6 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 - 6 * q^3 - 6 * q^4 + 2 * q^6 + 4 * q^7 + 6 * q^8 - 6 * q^9	\( 24 q + 2 q^{2} - 6 q^{3} - 6 q^{4} + 2 q^{6} + 4 q^{7} + 6 q^{8} - 6 q^{9} + 24 q^{12} + 4 q^{13} + 2 q^{14} - 22 q^{16} + 4 q^{17} + 2 q^{18} + 8 q^{19} - 16 q^{21} - 4 q^{22} + 6 q^{24} - 38 q^{26} - 6 q^{27} + 30 q^{28} - 10 q^{31} - 56 q^{32} + 10 q^{33} + 12 q^{34} - 6 q^{36} + 10 q^{37} + 4 q^{38} + 4 q^{39} + 30 q^{41} - 8 q^{42} - 64 q^{43} + 24 q^{44} + 54 q^{46} - 8 q^{47} - 2 q^{48} + 14 q^{49} + 14 q^{51} + 14 q^{52} + 26 q^{53} - 8 q^{54} + 12 q^{56} + 8 q^{57} + 20 q^{58} - 30 q^{59} + 20 q^{61} - 50 q^{62} + 4 q^{63} - 32 q^{64} + 6 q^{66} + 20 q^{67} - 62 q^{68} - 10 q^{69} - 16 q^{71} + 6 q^{72} - 12 q^{73} + 16 q^{74} - 68 q^{76} - 2 q^{77} + 32 q^{78} + 26 q^{79} - 6 q^{81} + 56 q^{82} + 48 q^{83} - 52 q^{86} + 48 q^{88} - 20 q^{89} - 20 q^{91} + 46 q^{92} - 10 q^{93} - 36 q^{94} + 14 q^{96} - 14 q^{97} - 120 q^{98}+O(q^{100}) \) 24 * q + 2 * q^2 - 6 * q^3 - 6 * q^4 + 2 * q^6 + 4 * q^7 + 6 * q^8 - 6 * q^9 + 24 * q^12 + 4 * q^13 + 2 * q^14 - 22 * q^16 + 4 * q^17 + 2 * q^18 + 8 * q^19 - 16 * q^21 - 4 * q^22 + 6 * q^24 - 38 * q^26 - 6 * q^27 + 30 * q^28 - 10 * q^31 - 56 * q^32 + 10 * q^33 + 12 * q^34 - 6 * q^36 + 10 * q^37 + 4 * q^38 + 4 * q^39 + 30 * q^41 - 8 * q^42 - 64 * q^43 + 24 * q^44 + 54 * q^46 - 8 * q^47 - 2 * q^48 + 14 * q^49 + 14 * q^51 + 14 * q^52 + 26 * q^53 - 8 * q^54 + 12 * q^56 + 8 * q^57 + 20 * q^58 - 30 * q^59 + 20 * q^61 - 50 * q^62 + 4 * q^63 - 32 * q^64 + 6 * q^66 + 20 * q^67 - 62 * q^68 - 10 * q^69 - 16 * q^71 + 6 * q^72 - 12 * q^73 + 16 * q^74 - 68 * q^76 - 2 * q^77 + 32 * q^78 + 26 * q^79 - 6 * q^81 + 56 * q^82 + 48 * q^83 - 52 * q^86 + 48 * q^88 - 20 * q^89 - 20 * q^91 + 46 * q^92 - 10 * q^93 - 36 * q^94 + 14 * q^96 - 14 * q^97 - 120 * q^98

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