LMFDB - Embedded newform 875.2.h.d.176.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(176,875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(875, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("875.176");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.h (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			176.6
Character	$\chi$	$=$	875.176
Dual form			875.2.h.d.701.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.875013 + 0.635734i) q^{2} +(0.987513 - 3.03925i) q^{3} +(-0.256544 + 0.789562i) q^{4} +(1.06807 + 3.28718i) q^{6} -1.00000 q^{7} +(-0.945922 - 2.91125i) q^{8} +(-5.83482 - 4.23925i) q^{9} +O(q^{10})$	\(q+(-0.875013 + 0.635734i) q^{2} +(0.987513 - 3.03925i) q^{3} +(-0.256544 + 0.789562i) q^{4} +(1.06807 + 3.28718i) q^{6} -1.00000 q^{7} +(-0.945922 - 2.91125i) q^{8} +(-5.83482 - 4.23925i) q^{9} +(-3.82981 + 2.78252i) q^{11} +(2.14634 + 1.55941i) q^{12} +(1.22285 + 0.888450i) q^{13} +(0.875013 - 0.635734i) q^{14} +(1.33519 + 0.970074i) q^{16} +(0.193520 + 0.595592i) q^{17} +7.80058 q^{18} +(0.975363 + 3.00186i) q^{19} +(-0.987513 + 3.03925i) q^{21} +(1.58219 - 4.86949i) q^{22} +(-4.97076 + 3.61147i) q^{23} -9.78213 q^{24} -1.63482 q^{26} +(-10.8901 + 7.91211i) q^{27} +(0.256544 - 0.789562i) q^{28} +(-1.68504 + 5.18603i) q^{29} +(-0.975100 - 3.00105i) q^{31} +4.33712 q^{32} +(4.67480 + 14.3875i) q^{33} +(-0.547970 - 0.398124i) q^{34} +(4.84404 - 3.51940i) q^{36} +(-0.676287 - 0.491351i) q^{37} +(-2.76184 - 2.00659i) q^{38} +(3.90780 - 2.83918i) q^{39} +(-3.59928 - 2.61503i) q^{41} +(-1.06807 - 3.28718i) q^{42} +4.43071 q^{43} +(-1.21446 - 3.73771i) q^{44} +(2.05355 - 6.32016i) q^{46} +(-3.25033 + 10.0035i) q^{47} +(4.26682 - 3.10003i) q^{48} +1.00000 q^{49} +2.00126 q^{51} +(-1.01520 + 0.737586i) q^{52} +(3.33360 - 10.2598i) q^{53} +(4.49897 - 13.8464i) q^{54} +(0.945922 + 2.91125i) q^{56} +10.0866 q^{57} +(-1.82250 - 5.60908i) q^{58} +(1.92813 + 1.40087i) q^{59} +(-4.88772 + 3.55114i) q^{61} +(2.76109 + 2.00605i) q^{62} +(5.83482 + 4.23925i) q^{63} +(-6.46542 + 4.69740i) q^{64} +(-13.2372 - 9.61736i) q^{66} +(-3.60747 - 11.1026i) q^{67} -0.519903 q^{68} +(6.06747 + 18.6738i) q^{69} +(-0.968731 + 2.98145i) q^{71} +(-6.82222 + 20.9966i) q^{72} +(-8.56745 + 6.22462i) q^{73} +0.904129 q^{74} -2.62038 q^{76} +(3.82981 - 2.78252i) q^{77} +(-1.61441 + 4.96864i) q^{78} +(-2.31523 + 7.12553i) q^{79} +(6.60669 + 20.3333i) q^{81} +4.81187 q^{82} +(2.58614 + 7.95931i) q^{83} +(-2.14634 - 1.55941i) q^{84} +(-3.87693 + 2.81675i) q^{86} +(14.0976 + 10.2425i) q^{87} +(11.7233 + 8.51749i) q^{88} +(-10.3651 + 7.53070i) q^{89} +(-1.22285 - 0.888450i) q^{91} +(-1.57626 - 4.85122i) q^{92} -10.0839 q^{93} +(-3.51547 - 10.8195i) q^{94} +(4.28296 - 13.1816i) q^{96} +(3.82534 - 11.7732i) q^{97} +(-0.875013 + 0.635734i) q^{98} +34.1421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{2} - 4 q^{3} - 12 q^{4} - 56 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) $ 56 * q - 4 * q^2 - 4 * q^3 - 12 * q^4 - 56 * q^7 - 12 * q^8 - 6 * q^9	$ 56 q - 4 q^{2} - 4 q^{3} - 12 q^{4} - 56 q^{7} - 12 q^{8} - 6 q^{9} + 8 q^{11} - 12 q^{12} - 8 q^{13} + 4 q^{14} - 32 q^{16} - 20 q^{17} + 48 q^{18} - 12 q^{19} + 4 q^{21} - 8 q^{22} - 16 q^{23} + 28 q^{24} + 12 q^{26} - 16 q^{27} + 12 q^{28} + 2 q^{29} + 12 q^{31} + 112 q^{32} - 14 q^{33} - 14 q^{36} - 16 q^{37} - 20 q^{38} + 4 q^{39} + 4 q^{41} + 32 q^{43} - 22 q^{44} - 4 q^{46} - 18 q^{47} - 48 q^{48} + 56 q^{49} - 44 q^{51} + 16 q^{52} - 20 q^{53} - 54 q^{54} + 12 q^{56} + 152 q^{57} + 32 q^{58} + 6 q^{59} - 4 q^{61} + 18 q^{62} + 6 q^{63} - 24 q^{64} - 74 q^{66} - 32 q^{67} + 124 q^{68} + 78 q^{69} - 8 q^{71} - 100 q^{72} - 48 q^{73} - 60 q^{74} + 52 q^{76} - 8 q^{77} + 124 q^{78} - 72 q^{81} + 44 q^{82} + 10 q^{83} + 12 q^{84} - 20 q^{86} + 26 q^{87} - 88 q^{88} - 38 q^{89} + 8 q^{91} - 96 q^{92} + 96 q^{93} - 88 q^{94} - 28 q^{96} - 90 q^{97} - 4 q^{98} - 60 q^{99}+O(q^{100}) $ 56 * q - 4 * q^2 - 4 * q^3 - 12 * q^4 - 56 * q^7 - 12 * q^8 - 6 * q^9 + 8 * q^11 - 12 * q^12 - 8 * q^13 + 4 * q^14 - 32 * q^16 - 20 * q^17 + 48 * q^18 - 12 * q^19 + 4 * q^21 - 8 * q^22 - 16 * q^23 + 28 * q^24 + 12 * q^26 - 16 * q^27 + 12 * q^28 + 2 * q^29 + 12 * q^31 + 112 * q^32 - 14 * q^33 - 14 * q^36 - 16 * q^37 - 20 * q^38 + 4 * q^39 + 4 * q^41 + 32 * q^43 - 22 * q^44 - 4 * q^46 - 18 * q^47 - 48 * q^48 + 56 * q^49 - 44 * q^51 + 16 * q^52 - 20 * q^53 - 54 * q^54 + 12 * q^56 + 152 * q^57 + 32 * q^58 + 6 * q^59 - 4 * q^61 + 18 * q^62 + 6 * q^63 - 24 * q^64 - 74 * q^66 - 32 * q^67 + 124 * q^68 + 78 * q^69 - 8 * q^71 - 100 * q^72 - 48 * q^73 - 60 * q^74 + 52 * q^76 - 8 * q^77 + 124 * q^78 - 72 * q^81 + 44 * q^82 + 10 * q^83 + 12 * q^84 - 20 * q^86 + 26 * q^87 - 88 * q^88 - 38 * q^89 + 8 * q^91 - 96 * q^92 + 96 * q^93 - 88 * q^94 - 28 * q^96 - 90 * q^97 - 4 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−0.875013	+	0.635734i	−0.618728	+	0.449532i	−0.852477	−	0.522765i	$-0.824901\pi$
$2$	−0.875013	+	0.635734i	−0.618728	+	0.449532i	0.233749	+	0.972297i	$0.424901\pi$
$3$	0.987513	−	3.03925i	0.570141	−	1.75471i	−0.0820177	−	0.996631i	$-0.526136\pi$
$3$	0.987513	−	3.03925i	0.570141	−	1.75471i	0.652159	−	0.758083i	$-0.273864\pi$
$4$	−0.256544	+	0.789562i	−0.128272	+	0.394781i
$5$		0			0
$5$		0			0
$6$	1.06807	+	3.28718i	0.436038	+	1.34199i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−0.945922	−	2.91125i	−0.334434	−	1.02928i
$9$	−5.83482	−	4.23925i	−1.94494	−	1.41308i
$10$		0			0
$11$	−3.82981	+	2.78252i	−1.15473	+	0.838962i	−0.989103	−	0.147226i	$-0.952966\pi$
$11$	−3.82981	+	2.78252i	−1.15473	+	0.838962i	−0.165629	+	0.986188i	$0.552966\pi$
$12$	2.14634	+	1.55941i	0.619594	+	0.450162i
$13$	1.22285	+	0.888450i	0.339157	+	0.246412i	0.744306	−	0.667839i	$-0.232780\pi$
$13$	1.22285	+	0.888450i	0.339157	+	0.246412i	−0.405149	+	0.914251i	$0.632780\pi$
$14$	0.875013	−	0.635734i	0.233857	−	0.169907i
$15$		0			0
$16$	1.33519	+	0.970074i	0.333798	+	0.242518i
$17$	0.193520	+	0.595592i	0.0469354	+	0.144452i	0.971778	−	0.235898i	$-0.0758033\pi$
$17$	0.193520	+	0.595592i	0.0469354	+	0.144452i	−0.924842	+	0.380351i	$0.875803\pi$
$18$	7.80058			1.83861
$19$	0.975363	+	3.00186i	0.223764	+	0.688674i	0.998415	+	0.0562849i	$0.0179255\pi$
$19$	0.975363	+	3.00186i	0.223764	+	0.688674i	−0.774651	+	0.632389i	$0.782074\pi$
$20$		0			0
$21$	−0.987513	+	3.03925i	−0.215493	+	0.663219i
$22$	1.58219	−	4.86949i	0.337324	−	1.03818i
$23$	−4.97076	+	3.61147i	−1.03647	+	0.753043i	−0.969594	−	0.244718i	$-0.921305\pi$
$23$	−4.97076	+	3.61147i	−1.03647	+	0.753043i	−0.0668806	+	0.997761i	$0.521305\pi$
$24$	−9.78213			−1.99677
$25$		0			0
$26$	−1.63482			−0.320615
$27$	−10.8901	+	7.91211i	−2.09580	+	1.52269i
$28$	0.256544	−	0.789562i	0.0484823	−	0.149213i
$29$	−1.68504	+	5.18603i	−0.312904	+	0.963021i	0.663704	+	0.747995i	$0.268983\pi$
$29$	−1.68504	+	5.18603i	−0.312904	+	0.963021i	−0.976608	+	0.215026i	$0.931017\pi$
$30$		0			0
$31$	−0.975100	−	3.00105i	−0.175133	−	0.539004i	0.824506	−	0.565853i	$-0.191453\pi$
$31$	−0.975100	−	3.00105i	−0.175133	−	0.539004i	−0.999640	+	0.0268483i	$0.991453\pi$
$32$	4.33712			0.766702
$33$	4.67480	+	14.3875i	0.813778	+	2.50455i
$34$	−0.547970	−	0.398124i	−0.0939762	−	0.0682777i
$35$		0			0
$36$	4.84404	−	3.51940i	0.807340	−	0.586567i
$37$	−0.676287	−	0.491351i	−0.111181	−	0.0807777i	0.530806	−	0.847494i	$-0.321889\pi$
$37$	−0.676287	−	0.491351i	−0.111181	−	0.0807777i	−0.641986	+	0.766716i	$0.721889\pi$
$38$	−2.76184	−	2.00659i	−0.448030	−	0.325513i
$39$	3.90780	−	2.83918i	0.625749	−	0.454633i
$40$		0			0
$41$	−3.59928	−	2.61503i	−0.562112	−	0.408399i	0.270119	−	0.962827i	$-0.412937\pi$
$41$	−3.59928	−	2.61503i	−0.562112	−	0.408399i	−0.832231	+	0.554428i	$0.812937\pi$
$42$	−1.06807	−	3.28718i	−0.164807	−	0.507223i
$43$	4.43071			0.675677			0.337838	−	0.941204i	$-0.390304\pi$
$43$	4.43071			0.675677			0.337838	+	0.941204i	$0.390304\pi$
$44$	−1.21446	−	3.73771i	−0.183086	−	0.563482i
$45$		0			0
$46$	2.05355	−	6.32016i	0.302779	−	0.931857i
$47$	−3.25033	+	10.0035i	−0.474109	+	1.45916i	0.373047	+	0.927812i	$0.378313\pi$
$47$	−3.25033	+	10.0035i	−0.474109	+	1.45916i	−0.847156	+	0.531344i	$0.821687\pi$
$48$	4.26682	−	3.10003i	0.615862	−	0.447450i
$49$	1.00000			0.142857
$50$		0			0
$51$	2.00126			0.280232
$52$	−1.01520	+	0.737586i	−0.140783	+	0.102285i
$53$	3.33360	−	10.2598i	0.457905	−	1.40929i	−0.409786	−	0.912182i	$-0.634397\pi$
$53$	3.33360	−	10.2598i	0.457905	−	1.40929i	0.867691	−	0.497104i	$-0.165603\pi$
$54$	4.49897	−	13.8464i	0.612232	−	1.88426i
$55$		0			0
$56$	0.945922	+	2.91125i	0.126404	+	0.389032i
$57$	10.0866			1.33600
$58$	−1.82250	−	5.60908i	−0.239306	−	0.736508i
$59$	1.92813	+	1.40087i	0.251021	+	0.182377i	0.706179	−	0.708033i	$-0.250417\pi$
$59$	1.92813	+	1.40087i	0.251021	+	0.182377i	−0.455158	+	0.890410i	$0.650417\pi$
$60$		0			0
$61$	−4.88772	+	3.55114i	−0.625809	+	0.454677i	−0.854946	−	0.518718i	$-0.826410\pi$
$61$	−4.88772	+	3.55114i	−0.625809	+	0.454677i	0.229137	+	0.973394i	$0.426410\pi$
$62$	2.76109	+	2.00605i	0.350659	+	0.254769i
$63$	5.83482	+	4.23925i	0.735119	+	0.534095i
$64$	−6.46542	+	4.69740i	−0.808177	+	0.587175i
$65$		0			0
$66$	−13.2372	−	9.61736i	−1.62938	−	1.18382i
$67$	−3.60747	−	11.1026i	−0.440722	−	1.35640i	−0.887107	−	0.461563i	$-0.847289\pi$
$67$	−3.60747	−	11.1026i	−0.440722	−	1.35640i	0.446385	−	0.894841i	$-0.352711\pi$
$68$	−0.519903			−0.0630475
$69$	6.06747	+	18.6738i	0.730438	+	2.24806i
$70$		0			0
$71$	−0.968731	+	2.98145i	−0.114967	+	0.353833i	−0.991940	−	0.126707i	$-0.959559\pi$
$71$	−0.968731	+	2.98145i	−0.114967	+	0.353833i	0.876973	+	0.480540i	$0.159559\pi$
$72$	−6.82222	+	20.9966i	−0.804006	+	2.47448i
$73$	−8.56745	+	6.22462i	−1.00274	+	0.728536i	−0.962675	−	0.270661i	$-0.912758\pi$
$73$	−8.56745	+	6.22462i	−1.00274	+	0.728536i	−0.0400692	+	0.999197i	$0.512758\pi$
$74$	0.904129			0.105103
$75$		0			0
$76$	−2.62038			−0.300578
$77$	3.82981	−	2.78252i	0.436448	−	0.317098i
$78$	−1.61441	+	4.96864i	−0.182796	+	0.562588i
$79$	−2.31523	+	7.12553i	−0.260483	+	0.801685i	0.732216	+	0.681072i	$0.238486\pi$
$79$	−2.31523	+	7.12553i	−0.260483	+	0.801685i	−0.992700	+	0.120613i	$0.961514\pi$
$80$		0			0
$81$	6.60669	+	20.3333i	0.734076	+	2.25925i
$82$	4.81187			0.531383
$83$	2.58614	+	7.95931i	0.283865	+	0.873648i	0.986736	+	0.162331i	$0.0519011\pi$
$83$	2.58614	+	7.95931i	0.283865	+	0.873648i	−0.702871	+	0.711317i	$0.748099\pi$
$84$	−2.14634	−	1.55941i	−0.234185	−	0.170145i
$85$		0			0
$86$	−3.87693	+	2.81675i	−0.418060	+	0.303738i
$87$	14.0976	+	10.2425i	1.51143	+	1.09812i
$88$	11.7233	+	8.51749i	1.24971	+	0.907968i
$89$	−10.3651	+	7.53070i	−1.09870	+	0.798253i	−0.980847	−	0.194778i	$-0.937601\pi$
$89$	−10.3651	+	7.53070i	−1.09870	+	0.798253i	−0.117853	+	0.993031i	$0.537601\pi$
$90$		0			0
$91$	−1.22285	−	0.888450i	−0.128189	−	0.0931348i
$92$	−1.57626	−	4.85122i	−0.164336	−	0.505775i
$93$	−10.0839			−1.04565
$94$	−3.51547	−	10.8195i	−0.362593	−	1.11595i
$95$		0			0
$96$	4.28296	−	13.1816i	0.437128	−	1.34534i
$97$	3.82534	−	11.7732i	0.388404	−	1.19539i	−0.545576	−	0.838061i	$-0.683689\pi$
$97$	3.82534	−	11.7732i	0.388404	−	1.19539i	0.933980	−	0.357324i	$-0.116311\pi$
$98$	−0.875013	+	0.635734i	−0.0883897	+	0.0642188i
$99$	34.1421			3.43141
$100$		0			0
$101$	−6.84519			−0.681122			−0.340561	−	0.940222i	$-0.610617\pi$
$101$	−6.84519			−0.681122			−0.340561	+	0.940222i	$0.610617\pi$
$102$	−1.75113	+	1.27227i	−0.173387	+	0.125973i
$103$	1.86175	−	5.72986i	0.183443	−	0.564580i	−0.816475	−	0.577381i	$-0.804075\pi$
$103$	1.86175	−	5.72986i	0.183443	−	0.564580i	0.999918	+	0.0128009i	$0.00407475\pi$
$104$	1.42978	−	4.40042i	0.140202	−	0.431496i
$105$		0			0
$106$	3.60554	+	11.0967i	0.350201	+	1.07781i
$107$	−6.71648			−0.649307			−0.324653	−	0.945833i	$-0.605248\pi$
$107$	−6.71648			−0.649307			−0.324653	+	0.945833i	$0.605248\pi$
$108$	−3.45331	−	10.6282i	−0.332295	−	1.02270i
$109$	9.78078	+	7.10616i	0.936829	+	0.680646i	0.947655	−	0.319295i	$-0.103446\pi$
$109$	9.78078	+	7.10616i	0.936829	+	0.680646i	−0.0108262	+	0.999941i	$0.503446\pi$
$110$		0			0
$111$	−2.16118	+	1.57019i	−0.205130	+	0.149036i
$112$	−1.33519	−	0.970074i	−0.126164	−	0.0916633i
$113$	−6.66695	−	4.84382i	−0.627174	−	0.455668i	0.228246	−	0.973603i	$-0.426701\pi$
$113$	−6.66695	−	4.84382i	−0.627174	−	0.455668i	−0.855420	+	0.517935i	$0.826701\pi$
$114$	−8.82590	+	6.41239i	−0.826621	+	0.600576i
$115$		0			0
$116$	−3.66240	−	2.66089i	−0.340045	−	0.247057i
$117$	−3.36873	−	10.3679i	−0.311440	−	0.958512i
$118$	−2.57771			−0.237298
$119$	−0.193520	−	0.595592i	−0.0177399	−	0.0545978i
$120$		0			0
$121$	3.52585	−	10.8515i	0.320532	−	0.986496i
$122$	2.01924	−	6.21458i	0.182813	−	0.562642i
$123$	−11.5021	+	8.35673i	−1.03711	+	0.753501i
$124$	2.61967			0.235253
$125$		0			0
$126$	−7.80058			−0.694931
$127$	−6.07828	+	4.41613i	−0.539360	+	0.391868i	−0.823847	−	0.566812i	$-0.808177\pi$
$127$	−6.07828	+	4.41613i	−0.539360	+	0.391868i	0.284487	+	0.958680i	$0.408177\pi$
$128$	−0.00946027	+	0.0291157i	−0.000836177	+	0.00257349i
$129$	4.37538	−	13.4660i	0.385231	−	1.18562i
$130$		0			0
$131$	0.890551	+	2.74083i	0.0778078	+	0.239468i	0.982393	−	0.186824i	$-0.0598196\pi$
$131$	0.890551	+	2.74083i	0.0778078	+	0.239468i	−0.904586	+	0.426292i	$0.859820\pi$
$132$	−12.5592			−1.09313
$133$	−0.975363	−	3.00186i	−0.0845747	−	0.260294i
$134$	10.2149	+	7.42157i	0.882434	+	0.641126i
$135$		0			0
$136$	1.55086	−	1.12677i	0.132985	−	0.0966196i
$137$	−12.5205	−	9.09664i	−1.06969	−	0.777179i	−0.0938373	−	0.995588i	$-0.529913\pi$
$137$	−12.5205	−	9.09664i	−1.06969	−	0.777179i	−0.975857	+	0.218409i	$0.929913\pi$
$138$	−17.1807	−	12.4825i	−1.46252	−	1.06258i
$139$	4.94263	−	3.59103i	0.419228	−	0.304587i	−0.358099	−	0.933684i	$-0.616575\pi$
$139$	4.94263	−	3.59103i	0.419228	−	0.304587i	0.777327	+	0.629097i	$0.216575\pi$
$140$		0			0
$141$	27.1933	+	19.7571i	2.29009	+	1.66385i
$142$	−1.04776	−	3.22466i	−0.0879257	−	0.270607i
$143$	−7.15540			−0.598365
$144$	−3.67823	−	11.3204i	−0.306519	−	0.943368i
$145$		0			0
$146$	3.53943	−	10.8932i	0.292925	−	0.901531i
$147$	0.987513	−	3.03925i	0.0814487	−	0.250673i
$148$	0.561450	−	0.407917i	0.0461509	−	0.0335306i
$149$	−23.5516			−1.92942			−0.964710	−	0.263316i	$-0.915184\pi$
$149$	−23.5516			−1.92942			−0.964710	+	0.263316i	$0.915184\pi$
$150$		0			0
$151$	5.35326			0.435642			0.217821	−	0.975989i	$-0.430105\pi$
$151$	5.35326			0.435642			0.217821	+	0.975989i	$0.430105\pi$
$152$	7.81655	−	5.67905i	0.634006	−	0.460632i
$153$	1.39571	−	4.29555i	0.112836	−	0.347275i
$154$	−1.58219	+	4.86949i	−0.127497	+	0.392394i
$155$		0			0
$156$	1.23919	+	3.81383i	0.0992144	+	0.305350i
$157$	−7.56734			−0.603940			−0.301970	−	0.953317i	$-0.597644\pi$
$157$	−7.56734			−0.603940			−0.301970	+	0.953317i	$0.597644\pi$
$158$	−2.50409	−	7.70680i	−0.199215	−	0.613120i
$159$	−27.8900	−	20.2633i	−2.21182	−	1.60698i
$160$		0			0
$161$	4.97076	−	3.61147i	0.391751	−	0.284624i
$162$	−18.7075	−	13.5918i	−1.46980	−	1.06787i
$163$	2.74872	+	1.99706i	0.215296	+	0.156422i	0.690207	−	0.723612i	$-0.257520\pi$
$163$	2.74872	+	1.99706i	0.215296	+	0.156422i	−0.474910	+	0.880034i	$0.657520\pi$
$164$	2.98810	−	2.17098i	0.233331	−	0.169525i
$165$		0			0
$166$	−7.32291	−	5.32040i	−0.568368	−	0.412943i
$167$	−3.67288	−	11.3040i	−0.284216	−	0.874728i	−0.986632	−	0.162961i	$-0.947895\pi$
$167$	−3.67288	−	11.3040i	−0.284216	−	0.874728i	0.702416	−	0.711767i	$-0.252105\pi$
$168$	9.78213			0.754708
$169$	−3.31121	−	10.1909i	−0.254709	−	0.783912i
$170$		0			0
$171$	7.03455	−	21.6501i	0.537946	−	1.65563i
$172$	−1.13667	+	3.49832i	−0.0866705	+	0.266744i
$173$	20.7007	−	15.0399i	1.57384	−	1.14346i	0.650490	−	0.759515i	$-0.274563\pi$
$173$	20.7007	−	15.0399i	1.57384	−	1.14346i	0.923354	−	0.383950i	$-0.125437\pi$
$174$	−18.8472			−1.42880
$175$		0			0
$176$	−7.81279			−0.588911
$177$	6.16163	−	4.47669i	0.463137	−	0.336489i
$178$	4.28209	−	13.1789i	0.320956	−	0.987802i
$179$	−2.87123	+	8.83672i	−0.214605	+	0.660488i	0.784576	+	0.620033i	$0.212881\pi$
$179$	−2.87123	+	8.83672i	−0.214605	+	0.660488i	−0.999181	+	0.0404549i	$0.987119\pi$
$180$		0			0
$181$	1.22697	+	3.77621i	0.0911996	+	0.280684i	0.986245	−	0.165292i	$-0.0528567\pi$
$181$	1.22697	+	3.77621i	0.0911996	+	0.280684i	−0.895045	+	0.445976i	$0.852857\pi$
$182$	1.63482			0.121181
$183$	5.96612	+	18.3618i	0.441028	+	1.35734i
$184$	15.2158	+	11.0550i	1.12173	+	0.814982i
$185$		0			0
$186$	8.82352	−	6.41066i	0.646972	−	0.470053i
$187$	−2.39839	−	1.74253i	−0.175388	−	0.127427i
$188$	−7.06451	−	5.13267i	−0.515232	−	0.374338i
$189$	10.8901	−	7.91211i	0.792137	−	0.575521i
$190$		0			0
$191$	7.92919	+	5.76089i	0.573736	+	0.416844i	0.836460	−	0.548027i	$-0.184621\pi$
$191$	7.92919	+	5.76089i	0.573736	+	0.416844i	−0.262724	+	0.964871i	$0.584621\pi$
$192$	7.89191	+	24.2888i	0.569549	+	1.75289i
$193$	−6.32794			−0.455495			−0.227748	−	0.973720i	$-0.573136\pi$
$193$	−6.32794			−0.455495			−0.227748	+	0.973720i	$0.573136\pi$
$194$	4.13739	+	12.7336i	0.297048	+	0.914218i
$195$		0			0
$196$	−0.256544	+	0.789562i	−0.0183246	+	0.0563973i
$197$	4.18643	−	12.8845i	0.298271	−	0.917983i	−0.683832	−	0.729639i	$-0.739688\pi$
$197$	4.18643	−	12.8845i	0.298271	−	0.917983i	0.982103	−	0.188344i	$-0.0603120\pi$
$198$	−29.8748	+	21.7053i	−2.12311	+	1.54253i
$199$	19.5717			1.38740			0.693702	−	0.720262i	$-0.255979\pi$
$199$	19.5717			1.38740			0.693702	+	0.720262i	$0.255979\pi$
$200$		0			0
$201$	−37.3062			−2.63137
$202$	5.98963	−	4.35172i	0.421429	−	0.306186i
$203$	1.68504	−	5.18603i	0.118267	−	0.363988i
$204$	−0.513411	+	1.58012i	−0.0359460	+	0.110630i
$205$		0			0
$206$	2.01362	+	6.19728i	0.140295	+	0.431785i
$207$	44.3134			3.08000
$208$	0.770873	+	2.37250i	0.0534504	+	0.164503i
$209$	−12.0882	−	8.78259i	−0.836158	−	0.607505i
$210$		0			0
$211$	5.75133	−	4.17859i	0.395938	−	0.287666i	−0.371946	−	0.928254i	$-0.621309\pi$
$211$	5.75133	−	4.17859i	0.395938	−	0.287666i	0.767884	+	0.640588i	$0.221309\pi$
$212$	7.24550	+	5.26416i	0.497623	+	0.361544i
$213$	8.10474	+	5.88844i	0.555327	+	0.403469i
$214$	5.87701	−	4.26990i	0.401744	−	0.291884i
$215$		0			0
$216$	33.3353	+	24.2195i	2.26818	+	1.64793i
$217$	0.975100	+	3.00105i	0.0661941	+	0.203725i
$218$	−13.0759			−0.885614
$219$	10.4577	+	32.1855i	0.706667	+	2.17490i
$220$		0			0
$221$	−0.292509	+	0.900250i	−0.0196763	+	0.0605574i
$222$	0.892839	−	2.74788i	0.0599234	−	0.184425i
$223$	−7.01680	+	5.09800i	−0.469880	+	0.341388i	−0.797394	−	0.603458i	$-0.793789\pi$
$223$	−7.01680	+	5.09800i	−0.469880	+	0.341388i	0.327515	+	0.944846i	$0.393789\pi$
$224$	−4.33712			−0.289786
$225$		0			0
$226$	8.91305			0.592887
$227$	5.39080	−	3.91664i	0.357800	−	0.259957i	−0.394334	−	0.918967i	$-0.629025\pi$
$227$	5.39080	−	3.91664i	0.357800	−	0.259957i	0.752134	+	0.659010i	$0.229025\pi$
$228$	−2.58766	+	7.96399i	−0.171372	+	0.527428i
$229$	4.04355	−	12.4448i	0.267205	−	0.822373i	−0.723972	−	0.689830i	$-0.757685\pi$
$229$	4.04355	−	12.4448i	0.267205	−	0.822373i	0.991177	−	0.132544i	$-0.0423145\pi$
$230$		0			0
$231$	−4.67480	−	14.3875i	−0.307579	−	0.946631i
$232$	16.6917			1.09587
$233$	−5.26526	−	16.2048i	−0.344939	−	1.06161i	−0.961617	−	0.274397i	$-0.911522\pi$
$233$	−5.26526	−	16.2048i	−0.344939	−	1.06161i	0.616678	−	0.787216i	$-0.288478\pi$
$234$	9.53891	+	6.93043i	0.623578	+	0.453056i
$235$		0			0
$236$	−1.60072	+	1.16299i	−0.104198	+	0.0757043i
$237$	19.3700	+	14.0731i	1.25822	+	0.914147i
$238$	0.547970	+	0.398124i	0.0355196	+	0.0258065i
$239$	−21.1591	+	15.3730i	−1.36867	+	0.994398i	−0.370831	+	0.928700i	$0.620927\pi$
$239$	−21.1591	+	15.3730i	−1.36867	+	0.994398i	−0.997840	+	0.0656974i	$0.979073\pi$
$240$		0			0
$241$	6.89901	+	5.01242i	0.444404	+	0.322879i	0.787382	−	0.616465i	$-0.211436\pi$
$241$	6.89901	+	5.01242i	0.444404	+	0.322879i	−0.342978	+	0.939343i	$0.611436\pi$
$242$	3.81348	+	11.7367i	0.245139	+	0.754462i
$243$	27.9395			1.79232
$244$	−1.54993	−	4.77018i	−0.0992239	−	0.305380i
$245$		0			0
$246$	4.75179	−	14.6245i	0.302963	−	0.932424i
$247$	−1.47428	+	4.53737i	−0.0938063	+	0.288706i
$248$	−7.81444	+	5.67752i	−0.496217	+	0.360523i
$249$	26.7442			1.69484
$250$		0			0
$251$	−6.38022			−0.402716			−0.201358	−	0.979518i	$-0.564535\pi$
$251$	−6.38022			−0.402716			−0.201358	+	0.979518i	$0.564535\pi$
$252$	−4.84404	+	3.51940i	−0.305146	+	0.221701i
$253$	8.98809	−	27.6625i	0.565076	−	1.73913i
$254$	2.51109	−	7.72834i	0.157560	−	0.484919i
$255$		0			0
$256$	−4.94937	−	15.2326i	−0.309336	−	0.952038i
$257$	−15.4987			−0.966781			−0.483390	−	0.875405i	$-0.660595\pi$
$257$	−15.4987			−0.966781			−0.483390	+	0.875405i	$0.660595\pi$
$258$	4.73231	+	14.5645i	0.294621	+	0.906749i
$259$	0.676287	+	0.491351i	0.0420224	+	0.0305311i
$260$		0			0
$261$	31.8168	−	23.1162i	1.96941	−	1.43086i
$262$	−2.52168	−	1.83211i	−0.155790	−	0.113188i
$263$	5.98245	+	4.34650i	0.368893	+	0.268017i	0.756752	−	0.653702i	$-0.226785\pi$
$263$	5.98245	+	4.34650i	0.368893	+	0.268017i	−0.387859	+	0.921719i	$0.626785\pi$
$264$	37.4637	−	27.2190i	2.30573	−	1.67521i
$265$		0			0
$266$	2.76184	+	2.00659i	0.169339	+	0.123032i
$267$	12.6520	+	38.9389i	0.774291	+	2.38302i
$268$	9.69170			0.592015
$269$	−4.53999	−	13.9727i	−0.276808	−	0.851928i	−0.988735	−	0.149674i	$-0.952177\pi$
$269$	−4.53999	−	13.9727i	−0.276808	−	0.851928i	0.711927	−	0.702253i	$-0.247823\pi$
$270$		0			0
$271$	−0.681130	+	2.09630i	−0.0413757	+	0.127341i	−0.969611	−	0.244653i	$-0.921326\pi$
$271$	−0.681130	+	2.09630i	−0.0413757	+	0.127341i	0.928235	+	0.371994i	$0.121326\pi$
$272$	−0.319382	+	0.982958i	−0.0193654	+	0.0596006i
$273$	−3.90780	+	2.83918i	−0.236511	+	0.171835i
$274$	16.7386			1.01122
$275$		0			0
$276$	−16.3007			−0.981185
$277$	6.73499	−	4.89326i	0.404666	−	0.294007i	−0.366773	−	0.930311i	$-0.619537\pi$
$277$	6.73499	−	4.89326i	0.404666	−	0.294007i	0.771439	+	0.636303i	$0.219537\pi$
$278$	−2.04192	+	6.28439i	−0.122466	+	0.376913i
$279$	−7.03266	+	21.6443i	−0.421034	+	1.29581i
$280$		0			0
$281$	−7.91576	−	24.3622i	−0.472215	−	1.45333i	−0.849678	−	0.527302i	$-0.823203\pi$
$281$	−7.91576	−	24.3622i	−0.472215	−	1.45333i	0.377463	−	0.926025i	$-0.376797\pi$
$282$	−36.3548			−2.16490
$283$	5.06847	+	15.5992i	0.301289	+	0.927274i	0.981036	+	0.193826i	$0.0620899\pi$
$283$	5.06847	+	15.5992i	0.301289	+	0.927274i	−0.679746	+	0.733447i	$0.737910\pi$
$284$	−2.10551	−	1.52975i	−0.124939	−	0.0907737i
$285$		0			0
$286$	6.26107	−	4.54893i	0.370225	−	0.268984i
$287$	3.59928	+	2.61503i	0.212458	+	0.154360i
$288$	−25.3063	−	18.3861i	−1.49119	−	1.08341i
$289$	13.4360	−	9.76183i	0.790353	−	0.574225i
$290$		0			0
$291$	−32.0041	−	23.2523i	−1.87611	−	1.36308i
$292$	−2.71679	−	8.36142i	−0.158988	−	0.489315i
$293$	−8.33846			−0.487138			−0.243569	−	0.969884i	$-0.578318\pi$
$293$	−8.33846			−0.487138			−0.243569	+	0.969884i	$0.578318\pi$
$294$	1.06807	+	3.28718i	0.0622911	+	0.191712i
$295$		0			0
$296$	−0.790731	+	2.43362i	−0.0459603	+	0.141451i
$297$	19.6914	−	60.6038i	1.14261	−	3.51659i
$298$	20.6079	−	14.9725i	1.19379	−	0.867336i
$299$	−9.28708			−0.537086
$300$		0			0
$301$	−4.43071			−0.255382
$302$	−4.68417	+	3.40325i	−0.269544	+	0.195835i
$303$	−6.75972	+	20.8043i	−0.388336	+	1.19517i
$304$	−1.60973	+	4.95423i	−0.0923242	+	0.284145i
$305$		0			0
$306$	1.50957	+	4.64597i	0.0862961	+	0.265592i
$307$	−25.6753			−1.46537			−0.732684	−	0.680569i	$-0.761732\pi$
$307$	−25.6753			−1.46537			−0.732684	+	0.680569i	$0.761732\pi$
$308$	1.21446	+	3.73771i	0.0692001	+	0.212976i
$309$	−15.5760	−	11.3166i	−0.886088	−	0.643780i
$310$		0			0
$311$	9.11025	−	6.61898i	0.516595	−	0.375328i	−0.298725	−	0.954339i	$-0.596561\pi$
$311$	9.11025	−	6.61898i	0.516595	−	0.375328i	0.815320	+	0.579011i	$0.196561\pi$
$312$	−11.9620	−	8.69094i	−0.677218	−	0.492027i
$313$	−1.59320	−	1.15753i	−0.0900531	−	0.0654274i	0.541848	−	0.840477i	$-0.317725\pi$
$313$	−1.59320	−	1.15753i	−0.0900531	−	0.0654274i	−0.631901	+	0.775049i	$0.717725\pi$
$314$	6.62152	−	4.81082i	0.373674	−	0.271490i
$315$		0			0
$316$	−5.03209	−	3.65603i	−0.283077	−	0.205668i
$317$	9.51016	+	29.2692i	0.534144	+	1.64392i	0.745492	+	0.666514i	$0.232214\pi$
$317$	9.51016	+	29.2692i	0.534144	+	1.64392i	−0.211349	+	0.977411i	$0.567786\pi$
$318$	37.2862			2.09091
$319$	−7.97684	−	24.5502i	−0.446617	−	1.37455i
$320$		0			0
$321$	−6.63261	+	20.4131i	−0.370196	+	1.13935i
$322$	−2.05355	+	6.32016i	−0.114440	+	0.352209i
$323$	−1.59913	+	1.16184i	−0.0889781	+	0.0646464i
$324$	−17.7493			−0.986072
$325$		0			0
$326$	−3.67477			−0.203527
$327$	31.2561	−	22.7089i	1.72846	−	1.25580i
$328$	−4.20836	+	12.9520i	−0.232368	+	0.715155i
$329$	3.25033	−	10.0035i	0.179196	−	0.551509i
$330$		0			0
$331$	8.21432	+	25.2811i	0.451500	+	1.38957i	0.875195	+	0.483770i	$0.160733\pi$
$331$	8.21432	+	25.2811i	0.451500	+	1.38957i	−0.423695	+	0.905805i	$0.639267\pi$
$332$	−6.94783			−0.381312
$333$	1.86306	+	5.73390i	0.102095	+	0.314216i
$334$	10.4001	+	7.55615i	0.569071	+	0.413454i
$335$		0			0
$336$	−4.26682	+	3.10003i	−0.232774	+	0.169120i
$337$	−6.04475	−	4.39177i	−0.329278	−	0.239235i	0.410846	−	0.911705i	$-0.365233\pi$
$337$	−6.04475	−	4.39177i	−0.329278	−	0.239235i	−0.740124	+	0.672470i	$0.765233\pi$
$338$	9.37603	+	6.81208i	0.509989	+	0.370529i
$339$	−21.3053	+	15.4792i	−1.15715	+	0.840715i
$340$		0			0
$341$	12.0849	+	8.78022i	0.654436	+	0.475476i
$342$	7.60840	+	23.4163i	0.411415	+	1.26621i
$343$	−1.00000			−0.0539949
$344$	−4.19111	−	12.8989i	−0.225969	−	0.695462i
$345$		0			0
$346$	−8.55197	+	26.3203i	−0.459757	+	1.41499i
$347$	−1.96331	+	6.04244i	−0.105396	+	0.324375i	−0.989823	−	0.142303i	$-0.954549\pi$
$347$	−1.96331	+	6.04244i	−0.105396	+	0.324375i	0.884427	+	0.466678i	$0.154549\pi$
$348$	−11.7038	+	8.50330i	−0.627389	+	0.455825i
$349$	−3.14477			−0.168336			−0.0841679	−	0.996452i	$-0.526823\pi$
$349$	−3.14477			−0.168336			−0.0841679	+	0.996452i	$0.526823\pi$
$350$		0			0
$351$	−20.3464			−1.08601
$352$	−16.6104	+	12.0681i	−0.885335	+	0.643233i
$353$	−2.50790	+	7.71854i	−0.133482	+	0.410816i	−0.995351	−	0.0963155i	$-0.969294\pi$
$353$	−2.50790	+	7.71854i	−0.133482	+	0.410816i	0.861869	+	0.507132i	$0.169294\pi$
$354$	−2.54553	+	7.83432i	−0.135293	+	0.416389i
$355$		0			0
$356$	−3.28684	−	10.1159i	−0.174202	−	0.536140i
$357$	−2.00126			−0.105918
$358$	−3.10545	−	9.55758i	−0.164128	−	0.505134i
$359$	10.0273	+	7.28529i	0.529223	+	0.384503i	0.820067	−	0.572268i	$-0.193936\pi$
$359$	10.0273	+	7.28529i	0.529223	+	0.384503i	−0.290844	+	0.956770i	$0.593936\pi$
$360$		0			0
$361$	7.31149	−	5.31211i	0.384815	−	0.279585i
$362$	−3.47428	−	2.52421i	−0.182604	−	0.132670i
$363$	−29.4985	−	21.4319i	−1.54827	−	1.12488i
$364$	1.01520	−	0.737586i	0.0532110	−	0.0386600i
$365$		0			0
$366$	−16.8937	−	12.2740i	−0.883046	−	0.641570i
$367$	−2.08442	−	6.41517i	−0.108806	−	0.334869i	0.881799	−	0.471625i	$-0.156332\pi$
$367$	−2.08442	−	6.41517i	−0.108806	−	0.334869i	−0.990605	+	0.136756i	$0.956332\pi$
$368$	−10.1403			−0.528600
$369$	9.91539	+	30.5164i	0.516175	+	1.58862i
$370$		0			0
$371$	−3.33360	+	10.2598i	−0.173072	+	0.532660i
$372$	2.58696	−	7.96184i	0.134128	−	0.412802i
$373$	17.6450	−	12.8198i	0.913621	−	0.663785i	−0.0283067	−	0.999599i	$-0.509012\pi$
$373$	17.6450	−	12.8198i	0.913621	−	0.663785i	0.941928	+	0.335814i	$0.109012\pi$
$374$	3.20641			0.165800
$375$		0			0
$376$	32.1972			1.66044
$377$	−6.66807	+	4.84464i	−0.343423	+	0.249512i
$378$	−4.49897	+	13.8464i	−0.231402	+	0.712182i
$379$	−4.39393	+	13.5231i	−0.225701	+	0.694637i	0.772519	+	0.634992i	$0.218997\pi$
$379$	−4.39393	+	13.5231i	−0.225701	+	0.694637i	−0.998220	+	0.0596445i	$0.981003\pi$
$380$		0			0
$381$	7.41935	+	22.8344i	0.380105	+	1.16984i
$382$	−10.6005			−0.542371
$383$	6.83844	+	21.0466i	0.349428	+	1.07543i	0.959170	+	0.282829i	$0.0912729\pi$
$383$	6.83844	+	21.0466i	0.349428	+	1.07543i	−0.609742	+	0.792600i	$0.708727\pi$
$384$	0.0791479	+	0.0575043i	0.00403900	+	0.00293450i
$385$		0			0
$386$	5.53703	−	4.02289i	0.281827	−	0.204760i
$387$	−25.8524	−	18.7829i	−1.31415	−	0.954787i
$388$	8.31429	+	6.04068i	0.422094	+	0.306669i
$389$	−14.2282	+	10.3374i	−0.721399	+	0.524127i	−0.886831	−	0.462094i	$-0.847098\pi$
$389$	−14.2282	+	10.3374i	−0.721399	+	0.524127i	0.165432	+	0.986221i	$0.447098\pi$
$390$		0			0
$391$	−3.11290	−	2.26166i	−0.157426	−	0.114377i
$392$	−0.945922	−	2.91125i	−0.0477763	−	0.147040i
$393$	9.20951			0.464559
$394$	4.52794	+	13.9356i	0.228114	+	0.702064i
$395$		0			0
$396$	−8.75896	+	26.9573i	−0.440154	+	1.35465i
$397$	−4.85473	+	14.9413i	−0.243652	+	0.749883i	0.752203	+	0.658931i	$0.228991\pi$
$397$	−4.85473	+	14.9413i	−0.243652	+	0.749883i	−0.995855	+	0.0909522i	$0.971009\pi$
$398$	−17.1255	+	12.4424i	−0.858425	+	0.623682i
$399$	−10.0866			−0.504961
$400$		0			0
$401$	0.840486			0.0419719			0.0209859	−	0.999780i	$-0.493319\pi$
$401$	0.840486			0.0419719			0.0209859	+	0.999780i	$0.493319\pi$
$402$	32.6434	−	23.7168i	1.62810	−	1.18289i
$403$	1.47388	−	4.53615i	0.0734194	−	0.225962i
$404$	1.75609	−	5.40470i	0.0873690	−	0.268894i
$405$		0			0
$406$	1.82250	+	5.60908i	0.0904492	+	0.278374i
$407$	3.95725			0.196154
$408$	−1.89304	−	5.82616i	−0.0937192	−	0.288438i
$409$	15.7099	+	11.4139i	0.776804	+	0.564381i	0.904018	−	0.427494i	$-0.140603\pi$
$409$	15.7099	+	11.4139i	0.776804	+	0.564381i	−0.127214	+	0.991875i	$0.540603\pi$
$410$		0			0
$411$	−40.0111	+	29.0698i	−1.97360	+	1.43391i
$412$	4.04646	+	2.93993i	0.199355	+	0.144840i
$413$	−1.92813	−	1.40087i	−0.0948769	−	0.0689321i
$414$	−38.7748	+	28.1715i	−1.90568	+	1.38456i
$415$		0			0
$416$	5.30363	+	3.85331i	0.260032	+	0.188924i
$417$	−6.03313	−	18.5681i	−0.295444	−	0.909283i
$418$	16.1607			0.790447
$419$	−9.64569	−	29.6864i	−0.471223	−	1.45027i	−0.850985	−	0.525191i	$-0.823994\pi$
$419$	−9.64569	−	29.6864i	−0.471223	−	1.45027i	0.379762	−	0.925084i	$-0.376006\pi$
$420$		0			0
$421$	−3.26385	+	10.0451i	−0.159070	+	0.489568i	−0.998551	−	0.0538223i	$-0.982860\pi$
$421$	−3.26385	+	10.0451i	−0.159070	+	0.489568i	0.839480	+	0.543390i	$0.182860\pi$
$422$	−2.37602	+	7.31264i	−0.115663	+	0.355974i
$423$	61.3723	−	44.5896i	2.98402	−	2.16802i
$424$	−33.0220			−1.60369
$425$		0			0
$426$	−10.8352			−0.524968
$427$	4.88772	−	3.55114i	0.236533	−	0.171852i
$428$	1.72307	−	5.30308i	0.0832879	−	0.256334i
$429$	−7.06606	+	21.7471i	−0.341152	+	1.04996i
$430$		0			0
$431$	−0.198095	−	0.609672i	−0.00954188	−	0.0293669i	0.946172	−	0.323664i	$-0.104915\pi$
$431$	−0.198095	−	0.609672i	−0.00954188	−	0.0293669i	−0.955714	+	0.294297i	$0.904915\pi$
$432$	−22.2157			−1.06885
$433$	−0.995751	−	3.06461i	−0.0478528	−	0.147276i	0.924275	−	0.381727i	$-0.124671\pi$
$433$	−0.995751	−	3.06461i	−0.0478528	−	0.147276i	−0.972128	+	0.234451i	$0.924671\pi$
$434$	−2.76109	−	2.00605i	−0.132537	−	0.0962936i
$435$		0			0
$436$	−8.11995	+	5.89949i	−0.388875	+	0.282534i
$437$	−15.6894	−	11.3990i	−0.750527	−	0.545289i
$438$	−29.6121	−	21.5144i	−1.41492	−	1.02800i
$439$	3.95294	−	2.87198i	0.188664	−	0.137072i	−0.489444	−	0.872035i	$-0.662800\pi$
$439$	3.95294	−	2.87198i	0.188664	−	0.137072i	0.678108	+	0.734963i	$0.262800\pi$
$440$		0			0
$441$	−5.83482	−	4.23925i	−0.277849	−	0.201869i
$442$	−0.316371	−	0.973689i	−0.0150482	−	0.0463136i
$443$	−30.6647			−1.45692			−0.728461	−	0.685087i	$-0.759764\pi$
$443$	−30.6647			−1.45692			−0.728461	+	0.685087i	$0.759764\pi$
$444$	−0.685324	−	2.10921i	−0.0325241	−	0.100099i
$445$		0			0
$446$	2.89882	−	8.92164i	0.137263	−	0.422452i
$447$	−23.2575	+	71.5792i	−1.10004	+	3.38558i
$448$	6.46542	−	4.69740i	0.305462	−	0.221931i
$449$	−16.0918			−0.759420			−0.379710	−	0.925105i	$-0.623976\pi$
$449$	−16.0918			−0.759420			−0.379710	+	0.925105i	$0.623976\pi$
$450$		0			0
$451$	21.0609			0.991720
$452$	5.53487	−	4.02131i	0.260338	−	0.189147i
$453$	5.28641	−	16.2699i	0.248377	−	0.764426i
$454$	−2.22707	+	6.85423i	−0.104522	+	0.321685i
$455$		0			0
$456$	−9.54114	−	29.3646i	−0.446805	−	1.37512i
$457$	−4.65892			−0.217935			−0.108968	−	0.994045i	$-0.534754\pi$
$457$	−4.65892			−0.217935			−0.108968	+	0.994045i	$0.534754\pi$
$458$	4.37340	+	13.4600i	0.204356	+	0.628942i
$459$	−6.81984	−	4.95490i	−0.318323	−	0.231275i
$460$		0			0
$461$	22.8070	−	16.5703i	1.06223	−	0.771754i	0.0877288	−	0.996144i	$-0.472039\pi$
$461$	22.8070	−	16.5703i	1.06223	−	0.771754i	0.974499	+	0.224391i	$0.0720391\pi$
$462$	13.2372	+	9.61736i	0.615849	+	0.447440i
$463$	16.2774	+	11.8262i	0.756473	+	0.549610i	0.897826	−	0.440349i	$-0.145145\pi$
$463$	16.2774	+	11.8262i	0.756473	+	0.549610i	−0.141354	+	0.989959i	$0.545145\pi$
$464$	−7.28068	+	5.28973i	−0.337997	+	0.245569i
$465$		0			0
$466$	14.9091	+	10.8321i	0.690652	+	0.501788i
$467$	3.54158	+	10.8999i	0.163885	+	0.504385i	0.998952	−	0.0457619i	$-0.0145715\pi$
$467$	3.54158	+	10.8999i	0.163885	+	0.504385i	−0.835068	+	0.550147i	$0.814572\pi$
$468$	9.05033			0.418351
$469$	3.60747	+	11.1026i	0.166577	+	0.512673i
$470$		0			0
$471$	−7.47285	+	22.9991i	−0.344331	+	1.05974i
$472$	2.25441	−	6.93837i	0.103768	−	0.319364i
$473$	−16.9688	+	12.3285i	−0.780226	+	0.566867i
$474$	−25.8957			−1.18943
$475$		0			0
$476$	0.519903			0.0238297
$477$	−62.9446	+	45.7319i	−2.88204	+	2.09392i
$478$	8.74137	−	26.9032i	0.399821	−	1.23052i
$479$	5.30740	−	16.3345i	0.242501	−	0.746343i	−0.753536	−	0.657407i	$-0.771653\pi$
$479$	5.30740	−	16.3345i	0.242501	−	0.746343i	0.996037	−	0.0889360i	$-0.0283466\pi$
$480$		0			0
$481$	−0.390454	−	1.20169i	−0.0178032	−	0.0547925i
$482$	−9.22329			−0.420109
$483$	−6.06747	−	18.6738i	−0.276080	−	0.849686i
$484$	7.66336	+	5.56776i	0.348335	+	0.253080i
$485$		0			0
$486$	−24.4475	+	17.7621i	−1.10896	+	0.805706i
$487$	5.74507	+	4.17404i	0.260334	+	0.189144i	0.710294	−	0.703905i	$-0.248562\pi$
$487$	5.74507	+	4.17404i	0.260334	+	0.189144i	−0.449960	+	0.893049i	$0.648562\pi$
$488$	14.9617	+	10.8703i	0.677282	+	0.492074i
$489$	8.78398	−	6.38193i	0.397225	−	0.288601i
$490$		0			0
$491$	−0.533590	−	0.387676i	−0.0240806	−	0.0174956i	0.575680	−	0.817675i	$-0.304737\pi$
$491$	−0.533590	−	0.387676i	−0.0240806	−	0.0174956i	−0.599760	+	0.800180i	$0.704737\pi$
$492$	−3.64737	−	11.2255i	−0.164436	−	0.506083i
$493$	−3.41485			−0.153797
$494$	−1.59455	−	4.90751i	−0.0717421	−	0.220799i
$495$		0			0
$496$	1.60929	−	4.95290i	0.0722594	−	0.222392i
$497$	0.968731	−	2.98145i	0.0434535	−	0.133736i
$498$	−23.4015	+	17.0022i	−1.04865	+	0.761887i
$499$	9.78180			0.437894			0.218947	−	0.975737i	$-0.429738\pi$
$499$	9.78180			0.437894			0.218947	+	0.975737i	$0.429738\pi$
$500$		0			0
$501$	−37.9827			−1.69694
$502$	5.58277	−	4.05612i	0.249171	−	0.181034i
$503$	4.43813	−	13.6592i	0.197886	−	0.609032i	−0.802044	−	0.597265i	$-0.796254\pi$
$503$	4.43813	−	13.6592i	0.197886	−	0.609032i	0.999931	−	0.0117673i	$-0.00374574\pi$
$504$	6.82222	−	20.9966i	0.303886	−	0.935264i
$505$		0			0
$506$	9.72130	+	29.9191i	0.432164	+	1.33007i
$507$	−34.2425			−1.52076
$508$	−1.92746	−	5.93211i	−0.0855172	−	0.263195i
$509$	18.9394	+	13.7603i	0.839476	+	0.609915i	0.922224	−	0.386656i	$-0.126370\pi$
$509$	18.9394	+	13.7603i	0.839476	+	0.609915i	−0.0827485	+	0.996570i	$0.526370\pi$
$510$		0			0
$511$	8.56745	−	6.22462i	0.379002	−	0.275361i
$512$	13.9651	+	10.1462i	0.617177	+	0.448405i
$513$	−34.3728	−	24.9733i	−1.51760	−	1.10260i
$514$	13.5615	−	9.85303i	0.598174	−	0.434599i
$515$		0			0
$516$	9.50979	+	6.90927i	0.418645	+	0.304164i
$517$	−15.3867	−	47.3555i	−0.676708	−	2.08269i
$518$	−0.904129			−0.0397251
$519$	−25.2679	−	77.7667i	−1.10914	−	3.41358i
$520$		0			0
$521$	−10.5241	+	32.3899i	−0.461070	+	1.41903i	0.402789	+	0.915293i	$0.368041\pi$
$521$	−10.5241	+	32.3899i	−0.461070	+	1.41903i	−0.863859	+	0.503734i	$0.831959\pi$
$522$	−13.1443	+	40.4540i	−0.575311	+	1.77062i
$523$	−30.0675	+	21.8453i	−1.31476	+	0.955230i	−0.314779	+	0.949165i	$0.601931\pi$
$523$	−30.0675	+	21.8453i	−1.31476	+	0.955230i	−0.999982	+	0.00606484i	$0.998069\pi$
$524$	−2.39252			−0.104518
$525$		0			0
$526$	−7.99794			−0.348727
$527$	1.59870	−	1.16152i	0.0696405	−	0.0505968i
$528$	−7.71523	+	23.7450i	−0.335762	+	1.03337i
$529$	4.55835	−	14.0292i	0.198189	−	0.609964i
$530$		0			0
$531$	−5.31166	−	16.3476i	−0.230506	−	0.709426i
$532$	2.62038			0.113608
$533$	−2.07804	−	6.39555i	−0.0900099	−	0.277022i
$534$	−35.8255	−	26.0287i	−1.55032	−	1.12637i
$535$		0			0
$536$	−28.9102	+	21.0045i	−1.24873	+	0.907255i
$537$	24.0217	+	17.4528i	1.03661	+	0.753142i
$538$	12.8554	+	9.34003i	0.554237	+	0.402677i
$539$	−3.82981	+	2.78252i	−0.164962	+	0.119852i
$540$		0			0
$541$	8.65467	+	6.28799i	0.372093	+	0.270342i	0.758078	−	0.652163i	$-0.226138\pi$
$541$	8.65467	+	6.28799i	0.372093	+	0.270342i	−0.385985	+	0.922505i	$0.626138\pi$
$542$	−0.736694	−	2.26731i	−0.0316437	−	0.0973893i
$543$	12.6885			0.544516
$544$	0.839318	+	2.58315i	0.0359854	+	0.110752i
$545$		0			0
$546$	1.61441	−	4.96864i	0.0690904	−	0.212638i
$547$	−4.60912	+	14.1854i	−0.197072	+	0.606524i	0.802875	+	0.596148i	$0.203303\pi$
$547$	−4.60912	+	14.1854i	−0.197072	+	0.606524i	−0.999946	+	0.0103761i	$0.996697\pi$
$548$	10.3944	−	7.55198i	0.444027	−	0.322605i
$549$	43.5732			1.85966
$550$		0			0
$551$	−17.2113			−0.733224
$552$	48.6246	−	35.3279i	2.06960	−	1.50365i
$553$	2.31523	−	7.12553i	0.0984534	−	0.303008i
$554$	−2.78239	+	8.56333i	−0.118213	+	0.363821i
$555$		0			0
$556$	1.56734	+	4.82377i	0.0664699	+	0.204573i
$557$	25.0829			1.06280			0.531399	−	0.847122i	$-0.321666\pi$
$557$	25.0829			1.06280			0.531399	+	0.847122i	$0.321666\pi$
$558$	−7.60635	−	23.4099i	−0.322002	−	0.991021i
$559$	5.41807	+	3.93646i	0.229160	+	0.166495i
$560$		0			0
$561$	−7.66445	+	5.56855i	−0.323593	+	0.235104i
$562$	22.4143	+	16.2849i	0.945489	+	0.686938i
$563$	26.9777	+	19.6004i	1.13697	+	0.826059i	0.986695	−	0.162585i	$-0.0519831\pi$
$563$	26.9777	+	19.6004i	1.13697	+	0.826059i	0.150278	+	0.988644i	$0.451983\pi$
$564$	−22.5758	+	16.4023i	−0.950611	+	0.690659i
$565$		0			0
$566$	−14.3519	−	10.4273i	−0.603255	−	0.438291i
$567$	−6.60669	−	20.3333i	−0.277455	−	0.853918i
$568$	9.59608			0.402643
$569$	0.330852	+	1.01826i	0.0138700	+	0.0426876i	0.957752	−	0.287595i	$-0.0928558\pi$
$569$	0.330852	+	1.01826i	0.0138700	+	0.0426876i	−0.943882	+	0.330283i	$0.892856\pi$
$570$		0			0
$571$	8.55331	−	26.3244i	0.357945	−	1.10164i	−0.596337	−	0.802734i	$-0.703378\pi$
$571$	8.55331	−	26.3244i	0.357945	−	1.10164i	0.954282	−	0.298907i	$-0.0966221\pi$
$572$	1.83568	−	5.64963i	0.0767535	−	0.236223i
$573$	25.3390	−	18.4099i	1.05855	−	0.769083i
$574$	−4.81187			−0.200844
$575$		0			0
$576$	57.6380			2.40158
$577$	−20.6390	+	14.9951i	−0.859213	+	0.624254i	−0.927671	−	0.373400i	$-0.878192\pi$
$577$	−20.6390	+	14.9951i	−0.859213	+	0.624254i	0.0684580	+	0.997654i	$0.478192\pi$
$578$	−5.55075	+	17.0835i	−0.230881	+	0.710578i
$579$	−6.24892	+	19.2322i	−0.259696	+	0.799263i
$580$		0			0
$581$	−2.58614	−	7.95931i	−0.107291	−	0.330208i
$582$	42.7863			1.77355
$583$	15.7809	+	48.5688i	0.653580	+	2.01151i
$584$	26.2256	+	19.0540i	1.08522	+	0.788459i
$585$		0			0
$586$	7.29626	−	5.30104i	0.301406	−	0.218984i
$587$	−10.0925	−	7.33260i	−0.416561	−	0.302649i	0.359692	−	0.933071i	$-0.382882\pi$
$587$	−10.0925	−	7.33260i	−0.416561	−	0.302649i	−0.776252	+	0.630422i	$0.782882\pi$
$588$	2.14634	+	1.55941i	0.0885135	+	0.0643088i
$589$	8.05765	−	5.85423i	0.332010	−	0.241219i
$590$		0			0
$591$	−35.0251	−	25.4472i	−1.44074	−	1.04676i
$592$	−0.426326	−	1.31210i	−0.0175219	−	0.0539268i
$593$	12.0433			0.494561			0.247280	−	0.968944i	$-0.420463\pi$
$593$	12.0433			0.494561			0.247280	+	0.968944i	$0.420463\pi$
$594$	21.2977	+	65.5476i	0.873855	+	2.68945i
$595$		0			0
$596$	6.04202	−	18.5954i	0.247491	−	0.761698i
$597$	19.3273	−	59.4835i	0.791016	−	2.43450i
$598$	8.12632	−	5.90411i	0.332310	−	0.241437i
$599$	2.89855			0.118431			0.0592157	−	0.998245i	$-0.481140\pi$
$599$	2.89855			0.118431			0.0592157	+	0.998245i	$0.481140\pi$
$600$		0			0
$601$	4.30169			0.175470			0.0877348	−	0.996144i	$-0.472037\pi$
$601$	4.30169			0.175470			0.0877348	+	0.996144i	$0.472037\pi$
$602$	3.87693	−	2.81675i	0.158012	−	0.114802i
$603$	−26.0179	+	80.0749i	−1.05953	+	3.26090i
$604$	−1.37335	+	4.22673i	−0.0558807	+	0.171983i
$605$		0			0
$606$	−7.31115	−	22.5014i	−0.296995	−	0.914057i
$607$	32.8653			1.33396			0.666980	−	0.745076i	$-0.267587\pi$
$607$	32.8653			1.33396			0.666980	+	0.745076i	$0.267587\pi$
$608$	4.23027	+	13.0194i	0.171560	+	0.528007i
$609$	−14.0976	−	10.2425i	−0.571265	−	0.415049i
$610$		0			0
$611$	−12.8622	+	9.34496i	−0.520350	+	0.378057i
$612$	3.03354	+	2.20400i	0.122624	+	0.0890914i
$613$	−1.10463	−	0.802562i	−0.0446157	−	0.0324152i	0.565254	−	0.824917i	$-0.308778\pi$
$613$	−1.10463	−	0.802562i	−0.0446157	−	0.0324152i	−0.609870	+	0.792502i	$0.708778\pi$
$614$	22.4662	−	16.3227i	0.906663	−	0.658729i
$615$		0			0
$616$	−11.7233	−	8.51749i	−0.472346	−	0.343180i
$617$	11.0515	+	34.0130i	0.444917	+	1.36931i	0.882575	+	0.470171i	$0.155808\pi$
$617$	11.0515	+	34.0130i	0.444917	+	1.36931i	−0.437659	+	0.899141i	$0.644192\pi$
$618$	20.8236			0.837647
$619$	−7.09355	−	21.8317i	−0.285114	−	0.877490i	−0.986364	−	0.164576i	$-0.947375\pi$
$619$	−7.09355	−	21.8317i	−0.285114	−	0.877490i	0.701251	−	0.712915i	$-0.252625\pi$
$620$		0			0
$621$	25.5577	−	78.6584i	1.02559	−	3.15645i
$622$	−3.76367	+	11.5834i	−0.150909	+	0.464452i
$623$	10.3651	−	7.53070i	0.415270	−	0.301711i
$624$	7.97188			0.319131
$625$		0			0
$626$	2.12995			0.0851300
$627$	−38.6298	+	28.0662i	−1.54272	+	1.12086i
$628$	1.94136	−	5.97488i	0.0774686	−	0.238424i
$629$	0.161770	−	0.497877i	0.00645020	−	0.0198517i
$630$		0			0
$631$	15.2414	+	46.9081i	0.606749	+	1.86738i	0.484291	+	0.874907i	$0.339078\pi$
$631$	15.2414	+	46.9081i	0.606749	+	1.86738i	0.122458	+	0.992474i	$0.460922\pi$
$632$	22.9342			0.912275
$633$	−7.02027	−	21.6062i	−0.279031	−	0.858768i
$634$	−26.9290	−	19.5650i	−1.06949	−	0.777027i
$635$		0			0
$636$	23.1541	−	16.8225i	0.918122	−	0.667054i
$637$	1.22285	+	0.888450i	0.0484509	+	0.0352017i
$638$	22.5872	+	16.4106i	0.894237	+	0.649701i
$639$	18.2915	−	13.2895i	0.723599	−	0.525726i
$640$		0			0
$641$	18.9868	+	13.7947i	0.749932	+	0.544857i	0.895806	−	0.444446i	$-0.146599\pi$
$641$	18.9868	+	13.7947i	0.749932	+	0.544857i	−0.145874	+	0.989303i	$0.546599\pi$
$642$	−7.17367	−	22.0783i	−0.283122	−	0.871360i
$643$	−29.2544			−1.15368			−0.576840	−	0.816857i	$-0.695714\pi$
$643$	−29.2544			−1.15368			−0.576840	+	0.816857i	$0.695714\pi$
$644$	1.57626	+	4.85122i	0.0621133	+	0.191165i
$645$		0			0
$646$	0.660642	−	2.03325i	0.0259926	−	0.0799970i
$647$	−1.65724	+	5.10046i	−0.0651529	+	0.200520i	−0.978334	−	0.207035i	$-0.933619\pi$
$647$	−1.65724	+	5.10046i	−0.0651529	+	0.200520i	0.913181	+	0.407555i	$0.133619\pi$
$648$	52.9459	−	38.4674i	2.07991	−	1.51114i
$649$	−11.2823			−0.442869
$650$		0			0
$651$	10.0839			0.395218
$652$	−2.28197	+	1.65795i	−0.0893690	+	0.0649304i
$653$	−6.53608	+	20.1160i	−0.255776	+	0.787199i	0.737899	+	0.674911i	$0.235818\pi$
$653$	−6.53608	+	20.1160i	−0.255776	+	0.787199i	−0.993676	+	0.112288i	$0.964182\pi$
$654$	−12.9127	+	39.7411i	−0.504925	+	1.55400i
$655$		0			0
$656$	−2.26895	−	6.98312i	−0.0885878	−	0.272645i
$657$	76.3773			2.97976
$658$	3.51547	+	10.8195i	0.137047	+	0.421788i
$659$	34.2703	+	24.8988i	1.33498	+	0.969920i	0.999613	+	0.0278334i	$0.00886079\pi$
$659$	34.2703	+	24.8988i	1.33498	+	0.969920i	0.335368	+	0.942087i	$0.391139\pi$
$660$		0			0
$661$	−32.6672	+	23.7341i	−1.27061	+	0.923150i	−0.999227	−	0.0393227i	$-0.987480\pi$
$661$	−32.6672	+	23.7341i	−1.27061	+	0.923150i	−0.271380	+	0.962472i	$0.587480\pi$
$662$	−23.2597	−	16.8992i	−0.904014	−	0.656804i
$663$	2.44723	+	1.77802i	0.0950426	+	0.0690525i
$664$	20.7253	−	15.0578i	0.804296	−	0.584355i
$665$		0			0
$666$	−5.27543	−	3.83283i	−0.204419	−	0.148519i
$667$	−10.3532	−	31.8640i	−0.400879	−	1.23378i
$668$	9.86745			0.381783
$669$	8.56494	+	26.3602i	0.331140	+	1.01914i
$670$		0			0
$671$	8.83794	−	27.2004i	0.341185	−	1.05006i
$672$	−4.28296	+	13.1816i	−0.165219	+	0.508491i
$673$	−28.1985	+	20.4874i	−1.08697	+	0.789732i	−0.978885	−	0.204410i	$-0.934472\pi$
$673$	−28.1985	+	20.4874i	−1.08697	+	0.789732i	−0.108087	+	0.994141i	$0.534472\pi$
$674$	8.08123			0.311277
$675$		0			0
$676$	8.89579			0.342146
$677$	−15.9478	+	11.5868i	−0.612925	+	0.445316i	−0.850443	−	0.526067i	$-0.823666\pi$
$677$	−15.9478	+	11.5868i	−0.612925	+	0.445316i	0.237518	+	0.971383i	$0.423666\pi$
$678$	8.80175	−	27.0890i	0.338029	−	1.04035i
$679$	−3.82534	+	11.7732i	−0.146803	+	0.451813i
$680$		0			0
$681$	−6.58019	−	20.2517i	−0.252153	−	0.776048i
$682$	−16.1564			−0.618659
$683$	6.72356	+	20.6930i	0.257270	+	0.791795i	0.993374	+	0.114927i	$0.0366633\pi$
$683$	6.72356	+	20.6930i	0.257270	+	0.791795i	−0.736104	+	0.676868i	$0.763337\pi$
$684$	15.2894	+	11.1084i	0.584607	+	0.424742i
$685$		0			0
$686$	0.875013	−	0.635734i	0.0334081	−	0.0242724i
$687$	−33.8297	−	24.5787i	−1.29068	−	0.937737i
$688$	5.91585	+	4.29811i	0.225539	+	0.163864i
$689$	13.1918	−	9.58437i	0.502566	−	0.365135i
$690$		0			0
$691$	27.8070	+	20.2030i	1.05783	+	0.768558i	0.973686	−	0.227896i	$-0.0731845\pi$
$691$	27.8070	+	20.2030i	1.05783	+	0.768558i	0.0841438	+	0.996454i	$0.473184\pi$
$692$	6.56431	+	20.2029i	0.249538	+	0.767998i
$693$	−34.1421			−1.29695
$694$	−2.12346	−	6.53535i	−0.0806056	−	0.248078i
$695$		0			0
$696$	16.4833	−	50.7304i	0.624798	−	1.92293i
$697$	0.860959	−	2.64976i	0.0326111	−	0.100367i
$698$	2.75172	−	1.99924i	0.104154	−	0.0756723i
$699$	−54.4500			−2.05949
$700$		0			0
$701$	23.4591			0.886039			0.443020	−	0.896512i	$-0.353907\pi$
$701$	23.4591			0.886039			0.443020	+	0.896512i	$0.353907\pi$
$702$	17.8034	−	12.9349i	0.671945	−	0.488197i
$703$	0.815342	−	2.50937i	0.0307512	−	0.0946425i
$704$	11.6907	−	35.9803i	0.440611	−	1.35606i
$705$		0			0
$706$	−2.71249	−	8.34818i	−0.102086	−	0.314188i
$707$	6.84519			0.257440
$708$	1.95389	+	6.01346i	0.0734317	+	0.226000i
$709$	−16.4621	−	11.9604i	−0.618248	−	0.449183i	0.234061	−	0.972222i	$-0.424798\pi$
$709$	−16.4621	−	11.9604i	−0.618248	−	0.449183i	−0.852309	+	0.523039i	$0.824798\pi$
$710$		0			0
$711$	43.7158	−	31.7614i	1.63947	−	1.19115i
$712$	31.7283	+	23.0520i	1.18907	+	0.863910i
$713$	15.6852	+	11.3960i	0.587415	+	0.426782i
$714$	1.75113	−	1.27227i	0.0655343	−	0.0476134i
$715$		0			0
$716$	−6.24054	−	4.53402i	−0.233220	−	0.169444i
$717$	25.8275	+	79.4890i	0.964548	+	2.96857i
$718$	−13.4056			−0.500291
$719$	5.61288	+	17.2747i	0.209325	+	0.644236i	0.999508	+	0.0313653i	$0.00998553\pi$
$719$	5.61288	+	17.2747i	0.209325	+	0.644236i	−0.790183	+	0.612871i	$0.790014\pi$
$720$		0			0
$721$	−1.86175	+	5.72986i	−0.0693350	+	0.213391i
$722$	−3.02056	+	9.29633i	−0.112414	+	0.345974i
$723$	22.0469	−	16.0180i	0.819932	−	0.595716i
$724$	−3.29632			−0.122507
$725$		0			0
$726$	39.4366			1.46363
$727$	−19.6931	+	14.3079i	−0.730377	+	0.530650i	−0.889683	−	0.456580i	$-0.849074\pi$
$727$	−19.6931	+	14.3079i	−0.730377	+	0.530650i	0.159306	+	0.987229i	$0.449074\pi$
$728$	−1.42978	+	4.40042i	−0.0529912	+	0.163090i
$729$	7.77060	−	23.9154i	0.287800	−	0.885757i
$730$		0			0
$731$	0.857429	+	2.63890i	0.0317132	+	0.0976031i
$732$	−16.0284			−0.592425
$733$	−11.6604	−	35.8871i	−0.430688	−	1.32552i	−0.897441	−	0.441134i	$-0.854576\pi$
$733$	−11.6604	−	35.8871i	−0.430688	−	1.32552i	0.466753	−	0.884388i	$-0.345424\pi$
$734$	5.90223	+	4.28822i	0.217855	+	0.158281i
$735$		0			0
$736$	−21.5588	+	15.6634i	−0.794667	+	0.577359i
$737$	44.7093	+	32.4832i	1.64689	+	1.19653i
$738$	−28.0764	−	20.3987i	−1.03351	−	0.750887i
$739$	33.0253	−	23.9943i	1.21486	−	0.882645i	0.219193	−	0.975681i	$-0.429657\pi$
$739$	33.0253	−	23.9943i	1.21486	−	0.882645i	0.995663	+	0.0930368i	$0.0296574\pi$
$740$		0			0
$741$	12.3344	+	8.96143i	0.453114	+	0.329206i
$742$	−3.60554	−	11.0967i	−0.132363	−	0.407373i
$743$	24.9128			0.913962			0.456981	−	0.889476i	$-0.348931\pi$
$743$	24.9128			0.913962			0.456981	+	0.889476i	$0.348931\pi$
$744$	9.53856	+	29.3567i	0.349701	+	1.07627i
$745$		0			0
$746$	−7.28958	+	22.4350i	−0.266890	+	0.821404i
$747$	18.6518	−	57.4045i	0.682435	−	2.10032i
$748$	1.99113	−	1.44664i	0.0728030	−	0.0528945i
$749$	6.71648			0.245415
$750$		0			0
$751$	12.0413			0.439393			0.219697	−	0.975568i	$-0.429493\pi$
$751$	12.0413			0.439393			0.219697	+	0.975568i	$0.429493\pi$
$752$	−14.0439	+	10.2035i	−0.512129	+	0.372083i
$753$	−6.30055	+	19.3911i	−0.229605	+	0.706651i
$754$	2.75475	−	8.47824i	0.100322	−	0.308759i
$755$		0			0
$756$	3.45331	+	10.6282i	0.125596	+	0.386544i
$757$	−0.867358			−0.0315247			−0.0157623	−	0.999876i	$-0.505018\pi$
$757$	−0.867358			−0.0315247			−0.0157623	+	0.999876i	$0.505018\pi$
$758$	−4.75237	−	14.6263i	−0.172614	−	0.531251i
$759$	−75.1975	−	54.6342i	−2.72949	−	1.98309i
$760$		0			0
$761$	−11.3657	+	8.25768i	−0.412007	+	0.299340i	−0.774414	−	0.632679i	$-0.781955\pi$
$761$	−11.3657	+	8.25768i	−0.412007	+	0.299340i	0.362407	+	0.932020i	$0.381955\pi$
$762$	−21.0086	−	15.2637i	−0.761063	−	0.552945i
$763$	−9.78078	−	7.10616i	−0.354088	−	0.257260i
$764$	−6.58277	+	4.78266i	−0.238156	+	0.173031i
$765$		0			0
$766$	−19.3637	−	14.0686i	−0.699640	−	0.508318i
$767$	1.11320	+	3.42609i	0.0401954	+	0.123709i
$768$	−51.1833			−1.84692
$769$	12.6101	+	38.8098i	0.454731	+	1.39952i	0.871450	+	0.490484i	$0.163180\pi$
$769$	12.6101	+	38.8098i	0.454731	+	1.39952i	−0.416719	+	0.909035i	$0.636820\pi$
$770$		0			0
$771$	−15.3051	+	47.1044i	−0.551201	+	1.69642i
$772$	1.62340	−	4.99630i	0.0584273	−	0.179821i
$773$	−17.8798	+	12.9905i	−0.643093	+	0.467234i	−0.860911	−	0.508755i	$-0.830106\pi$
$773$	−17.8798	+	12.9905i	−0.643093	+	0.467234i	0.217819	+	0.975989i	$0.430106\pi$
$774$	34.5621			1.24231
$775$		0			0
$776$	−37.8932			−1.36028
$777$	2.16118	−	1.57019i	0.0775320	−	0.0563303i
$778$	5.87803	−	18.0907i	0.210738	−	0.648583i
$779$	4.33934	−	13.3551i	0.155473	−	0.478497i
$780$		0			0
$781$	−4.58588	−	14.1139i	−0.164096	−	0.505035i
$782$	4.16164			0.148820
$783$	−22.6822	−	69.8085i	−0.810594	−	2.49475i
$784$	1.33519	+	0.970074i	0.0476854	+	0.0346455i
$785$		0			0
$786$	−8.05844	+	5.85480i	−0.287435	+	0.208834i
$787$	−25.8592	−	18.7878i	−0.921781	−	0.669713i	0.0221854	−	0.999754i	$-0.492938\pi$
$787$	−25.8592	−	18.7878i	−0.921781	−	0.669713i	−0.943967	+	0.330041i	$0.892938\pi$
$788$	9.09911	+	6.61089i	0.324142	+	0.235503i
$789$	19.1179	−	13.8899i	0.680614	−	0.494495i
$790$		0			0
$791$	6.66695	+	4.84382i	0.237049	+	0.172227i
$792$	−32.2958	−	99.3961i	−1.14758	−	3.53189i
$793$	−9.13194			−0.324285
$794$	−5.25075	−	16.1602i	−0.186342	−	0.573503i
$795$		0			0
$796$	−5.02102	+	15.4531i	−0.177965	+	0.547721i
$797$	6.44844	−	19.8463i	0.228416	−	0.702991i	−0.769511	−	0.638633i	$-0.779500\pi$
$797$	6.44844	−	19.8463i	0.228416	−	0.702991i	0.997927	−	0.0643577i	$-0.0204999\pi$
$798$	8.82590	−	6.41239i	0.312434	−	0.226996i
$799$	−6.58699			−0.233031
$800$		0			0
$801$	92.4032			3.26491
$802$	−0.735436	+	0.534325i	−0.0259691	+	0.0188677i
$803$	15.4916	−	47.6782i	0.546687	−	1.68253i
$804$	9.57068	−	29.4555i	0.337532	−	1.03882i
$805$		0			0
$806$	1.59412	+	4.90619i	0.0561504	+	0.172813i
$807$	−46.9497			−1.65271
$808$	6.47502	+	19.9281i	0.227790	+	0.701067i
$809$	20.6875	+	15.0303i	0.727333	+	0.528438i	0.888719	−	0.458453i	$-0.151596\pi$
$809$	20.6875	+	15.0303i	0.727333	+	0.528438i	−0.161386	+	0.986891i	$0.551596\pi$
$810$		0			0
$811$	−41.5595	+	30.1947i	−1.45935	+	1.06028i	−0.475819	+	0.879543i	$0.657848\pi$
$811$	−41.5595	+	30.1947i	−1.45935	+	1.06028i	−0.983531	+	0.180737i	$0.942152\pi$
$812$	3.66240	+	2.66089i	0.128525	+	0.0933789i
$813$	5.69857	+	4.14025i	0.199858	+	0.145205i
$814$	−3.46264	+	2.51576i	−0.121366	+	0.0881773i
$815$		0			0
$816$	2.67206	+	1.94137i	0.0935410	+	0.0679615i
$817$	4.32155	+	13.3004i	0.151192	+	0.465321i
$818$	−21.0026			−0.734338
$819$	3.36873	+	10.3679i	0.117713	+	0.362284i
$820$		0			0
$821$	11.5240	−	35.4673i	0.402191	−	1.23782i	−0.521028	−	0.853540i	$-0.674451\pi$
$821$	11.5240	−	35.4673i	0.402191	−	1.23782i	0.923218	−	0.384276i	$-0.125549\pi$
$822$	16.5296	−	50.8729i	0.576536	−	1.77439i
$823$	21.6872	−	15.7566i	0.755967	−	0.549242i	−0.141704	−	0.989909i	$-0.545258\pi$
$823$	21.6872	−	15.7566i	0.755967	−	0.549242i	0.897671	+	0.440667i	$0.145258\pi$
$824$	−18.4421			−0.642462
$825$		0			0
$826$	2.57771			0.0896901
$827$	−6.17908	+	4.48937i	−0.214868	+	0.156111i	−0.690013	−	0.723797i	$-0.742395\pi$
$827$	−6.17908	+	4.48937i	−0.214868	+	0.156111i	0.475146	+	0.879907i	$0.342395\pi$
$828$	−11.3684	+	34.9882i	−0.395077	+	1.21592i
$829$	−10.2779	+	31.6322i	−0.356967	+	1.09863i	0.597892	+	0.801576i	$0.296005\pi$
$829$	−10.2779	+	31.6322i	−0.356967	+	1.09863i	−0.954860	+	0.297056i	$0.903995\pi$
$830$		0			0
$831$	−8.22095	−	25.3015i	−0.285182	−	0.877699i
$832$	−12.0796			−0.418785
$833$	0.193520	+	0.595592i	0.00670506	+	0.0206360i
$834$	17.0834	+	12.4118i	0.591551	+	0.429787i
$835$		0			0
$836$	10.0356	−	7.29126i	0.347087	−	0.252174i
$837$	34.3636	+	24.9666i	1.18778	+	0.862971i
$838$	27.3128	+	19.8439i	0.943503	+	0.685495i
$839$	−17.0630	+	12.3970i	−0.589081	+	0.427992i	−0.841986	−	0.539499i	$-0.818614\pi$
$839$	−17.0630	+	12.3970i	−0.589081	+	0.427992i	0.252906	+	0.967491i	$0.418614\pi$
$840$		0			0
$841$	−0.594011	−	0.431574i	−0.0204831	−	0.0148819i
$842$	−3.53010	−	10.8645i	−0.121655	−	0.374416i
$843$	−81.8598			−2.81940
$844$	1.82378	+	5.61302i	0.0627772	+	0.193208i
$845$		0			0
$846$	−25.3544	+	78.0329i	−0.871703	+	2.68283i
$847$	−3.52585	+	10.8515i	−0.121150	+	0.372861i
$848$	14.4037	−	10.4649i	0.494626	−	0.359366i
$849$	52.4150			1.79888
$850$		0			0
$851$	5.13616			0.176065
$852$	−6.72851	+	4.88855i	−0.230515	+	0.167479i
$853$	−10.7286	+	33.0192i	−0.367340	+	1.13056i	0.581163	+	0.813787i	$0.302598\pi$
$853$	−10.7286	+	33.0192i	−0.367340	+	1.13056i	−0.948503	+	0.316768i	$0.897402\pi$
$854$	−2.01924	+	6.21458i	−0.0690970	+	0.212659i
$855$		0			0
$856$	6.35327	+	19.5533i	0.217150	+	0.668320i
$857$	43.3883			1.48212			0.741058	−	0.671441i	$-0.234324\pi$
$857$	43.3883			1.48212			0.741058	+	0.671441i	$0.234324\pi$
$858$	−7.64247	−	23.5211i	−0.260910	−	0.802997i
$859$	−42.1658	−	30.6353i	−1.43868	−	1.04526i	−0.988316	−	0.152417i	$-0.951294\pi$
$859$	−42.1658	−	30.6353i	−1.43868	−	1.04526i	−0.450363	−	0.892845i	$-0.648706\pi$
$860$		0			0
$861$	11.5021	−	8.35673i	0.391989	−	0.284797i
$862$	0.560925	+	0.407536i	0.0191052	+	0.0138807i
$863$	−26.6845	−	19.3874i	−0.908350	−	0.659955i	0.0322468	−	0.999480i	$-0.489734\pi$
$863$	−26.6845	−	19.3874i	−0.908350	−	0.659955i	−0.940597	+	0.339525i	$0.889734\pi$
$864$	−47.2316	+	34.3158i	−1.60685	+	1.16745i
$865$		0			0
$866$	2.81957	+	2.04854i	0.0958129	+	0.0696122i
$867$	−16.4004	−	50.4754i	−0.556988	−	1.71423i
$868$	−2.61967			−0.0889174
$869$	−10.9601	−	33.7316i	−0.371795	−	1.14427i
$870$		0			0
$871$	5.45276	−	16.7819i	0.184760	−	0.568632i
$872$	11.4359	−	35.1962i	0.387269	−	1.19189i
$873$	−72.2296	+	52.4779i	−2.44460	+	1.77611i
$874$	20.9752			0.709497
$875$		0			0
$876$	−28.0953			−0.949253
$877$	16.6617	−	12.1055i	0.562627	−	0.408772i	−0.269793	−	0.962918i	$-0.586955\pi$
$877$	16.6617	−	12.1055i	0.562627	−	0.408772i	0.832419	+	0.554146i	$0.186955\pi$
$878$	−1.63306	+	5.02604i	−0.0551131	+	0.169621i
$879$	−8.23434	+	25.3427i	−0.277737	+	0.854787i
$880$		0			0
$881$	−6.83622	−	21.0397i	−0.230318	−	0.708847i	−0.997708	−	0.0676657i	$-0.978445\pi$
$881$	−6.83622	−	21.0397i	−0.230318	−	0.708847i	0.767390	−	0.641181i	$-0.221555\pi$
$882$	7.80058			0.262659
$883$	−17.0894	−	52.5956i	−0.575102	−	1.76998i	−0.635830	−	0.771829i	$-0.719342\pi$
$883$	−17.0894	−	52.5956i	−0.575102	−	1.76998i	0.0607278	−	0.998154i	$-0.480658\pi$
$884$	−0.635762	−	0.461908i	−0.0213830	−	0.0155356i
$885$		0			0
$886$	26.8320	−	19.4946i	0.901438	−	0.654933i
$887$	−18.6966	−	13.5839i	−0.627770	−	0.456102i	0.227857	−	0.973695i	$-0.426828\pi$
$887$	−18.6966	−	13.5839i	−0.627770	−	0.456102i	−0.855627	+	0.517593i	$0.826828\pi$
$888$	6.61553	+	4.80646i	0.222003	+	0.161294i
$889$	6.07828	−	4.41613i	0.203859	−	0.148112i
$890$		0			0
$891$	−81.8802	−	59.4894i	−2.74309	−	1.99297i
$892$	−2.22507	−	6.84806i	−0.0745009	−	0.229290i
$893$	−33.1993			−1.11097
$894$	−25.1547	−	77.4183i	−0.841300	−	2.58925i
$895$		0			0
$896$	0.00946027	−	0.0291157i	0.000316045	−	0.000972687i
$897$	−9.17112	+	28.2258i	−0.306215	+	0.942432i
$898$	14.0806	−	10.2301i	0.469874	−	0.341384i
$899$	17.2066			0.573872
$900$		0			0
$901$	6.75575			0.225067
$902$	−18.4286	+	13.3891i	−0.613604	+	0.445810i
$903$	−4.37538	+	13.4660i	−0.145604	+	0.448122i
$904$	−7.79516	+	23.9910i	−0.259263	+	0.797930i
$905$		0			0
$906$	5.71765	+	17.5971i	0.189956	+	0.584625i
$907$	41.7280			1.38555			0.692777	−	0.721152i	$-0.256387\pi$
$907$	41.7280			1.38555			0.692777	+	0.721152i	$0.256387\pi$
$908$	1.70945	+	5.26116i	0.0567302	+	0.174598i
$909$	39.9405	+	29.0185i	1.32474	+	0.962482i
$910$		0			0
$911$	−0.539553	+	0.392008i	−0.0178762	+	0.0129878i	−0.596687	−	0.802474i	$-0.703517\pi$
$911$	−0.539553	+	0.392008i	−0.0178762	+	0.0129878i	0.578811	+	0.815462i	$0.303517\pi$
$912$	13.4675	+	9.78474i	0.445955	+	0.324005i
$913$	−32.0514	−	23.2867i	−1.06075	−	0.770677i
$914$	4.07662	−	2.96184i	0.134843	−	0.0979688i
$915$		0			0
$916$	8.78856	+	6.38527i	0.290382	+	0.210975i
$917$	−0.890551	−	2.74083i	−0.0294086	−	0.0905103i
$918$	9.11744			0.300920
$919$	−0.640781	−	1.97212i	−0.0211374	−	0.0650543i	0.939931	−	0.341363i	$-0.110889\pi$
$919$	−0.640781	−	1.97212i	−0.0211374	−	0.0650543i	−0.961069	+	0.276309i	$0.910889\pi$
$920$		0			0
$921$	−25.3547	+	78.0338i	−0.835466	+	2.57130i
$922$	−9.42214	+	28.9984i	−0.310302	+	0.955011i
$923$	−3.83347	+	2.78518i	−0.126180	+	0.0916754i
$924$	12.5592			0.413166
$925$		0			0
$926$	−21.7612			−0.715118
$927$	−35.1533	+	25.5403i	−1.15458	+	0.838855i
$928$	−7.30823	+	22.4924i	−0.239904	+	0.738350i
$929$	−14.8296	+	45.6410i	−0.486545	+	1.49743i	0.343186	+	0.939267i	$0.388494\pi$
$929$	−14.8296	+	45.6410i	−0.486545	+	1.49743i	−0.829731	+	0.558164i	$0.811506\pi$
$930$		0			0
$931$	0.975363	+	3.00186i	0.0319662	+	0.0983820i
$932$	14.1455			0.463350
$933$	−11.1203	−	34.2247i	−0.364061	−	1.12047i
$934$	−10.0283	−	7.28602i	−0.328137	−	0.238406i
$935$		0			0
$936$	−26.9970	+	19.6145i	−0.882424	+	0.641118i
$937$	−13.8744	−	10.0803i	−0.453256	−	0.329310i	0.337624	−	0.941281i	$-0.390377\pi$
$937$	−13.8744	−	10.0803i	−0.453256	−	0.329310i	−0.790880	+	0.611971i	$0.790377\pi$
$938$	−10.2149	−	7.42157i	−0.333529	−	0.242323i
$939$	−5.09133	+	3.69907i	−0.166149	+	0.120715i
$940$		0			0
$941$	−29.3666	−	21.3361i	−0.957324	−	0.695536i	−0.00479596	−	0.999988i	$-0.501527\pi$
$941$	−29.3666	−	21.3361i	−0.957324	−	0.695536i	−0.952528	+	0.304452i	$0.901527\pi$
$942$	−8.08245	−	24.8752i	−0.263340	−	0.810479i
$943$	27.3352			0.890157
$944$	1.21548	+	3.74085i	0.0395604	+	0.121754i
$945$		0			0
$946$	7.01023	−	21.5753i	0.227922	−	0.701473i
$947$	−6.80262	+	20.9363i	−0.221055	+	0.680338i	0.777613	+	0.628744i	$0.216430\pi$
$947$	−6.80262	+	20.9363i	−0.221055	+	0.680338i	−0.998668	+	0.0515949i	$0.983570\pi$
$948$	−16.0808	+	11.6834i	−0.522282	+	0.379460i
$949$	−16.0069			−0.519607
$950$		0			0
$951$	98.3480			3.18915
$952$	−1.55086	+	1.12677i	−0.0502638	+	0.0365188i
$953$	13.9495	−	42.9320i	0.451867	−	1.39071i	−0.422906	−	0.906173i	$-0.638990\pi$
$953$	13.9495	−	42.9320i	0.451867	−	1.39071i	0.874774	−	0.484532i	$-0.161010\pi$
$954$	26.0040	−	80.0321i	0.841910	−	2.59113i
$955$		0			0
$956$	−6.70969	−	20.6503i	−0.217007	−	0.667879i
$957$	−82.4914			−2.66657
$958$	5.74036	+	17.6670i	0.185463	+	0.570795i
$959$	12.5205	+	9.09664i	0.404307	+	0.293746i
$960$		0			0
$961$	17.0240	−	12.3687i	0.549163	−	0.398990i
$962$	1.10561	+	0.803273i	0.0356463	+	0.0258986i
$963$	39.1895	+	28.4728i	1.26286	+	0.917524i
$964$	−5.72752	+	4.16129i	−0.184471	+	0.134026i
$965$		0			0
$966$	17.1807	+	12.4825i	0.552779	+	0.401617i
$967$	−18.9759	−	58.4019i	−0.610225	−	1.87808i	−0.455819	−	0.890072i	$-0.650654\pi$
$967$	−18.9759	−	58.4019i	−0.610225	−	1.87808i	−0.154406	−	0.988008i	$-0.549346\pi$
$968$	−34.9265			−1.12258
$969$	1.95195	+	6.00750i	0.0627058	+	0.192989i
$970$		0			0
$971$	−13.9420	+	42.9091i	−0.447421	+	1.37702i	0.432386	+	0.901688i	$0.357672\pi$
$971$	−13.9420	+	42.9091i	−0.447421	+	1.37702i	−0.879807	+	0.475331i	$0.842328\pi$
$972$	−7.16773	+	22.0600i	−0.229905	+	0.707575i
$973$	−4.94263	+	3.59103i	−0.158453	+	0.115123i
$974$	−7.68059			−0.246102
$975$		0			0
$976$	−9.97091			−0.319161
$977$	6.55947	−	4.76573i	0.209856	−	0.152469i	−0.477892	−	0.878418i	$-0.658599\pi$
$977$	6.55947	−	4.76573i	0.209856	−	0.152469i	0.687749	+	0.725949i	$0.258599\pi$
$978$	−3.62888	+	11.1685i	−0.116039	+	0.357131i
$979$	18.7421	−	57.6824i	0.599001	−	1.84354i
$980$		0			0
$981$	−26.9444	−	82.9263i	−0.860268	−	2.64763i
$982$	0.713357			0.0227641
$983$	−6.49456	−	19.9882i	−0.207144	−	0.637525i	−0.999619	−	0.0276192i	$-0.991207\pi$
$983$	−6.49456	−	19.9882i	−0.207144	−	0.637525i	0.792474	−	0.609905i	$-0.208793\pi$
$984$	35.2086	+	25.5805i	1.12241	+	0.815478i
$985$		0			0
$986$	2.98803	−	2.17093i	0.0951584	−	0.0691366i
$987$	−27.1933	−	19.7571i	−0.865574	−	0.628876i
$988$	−3.20432	−	2.32807i	−0.101943	−	0.0740659i
$989$	−22.0240	+	16.0014i	−0.700322	+	0.508814i
$990$		0			0
$991$	−10.1275	−	7.35808i	−0.321712	−	0.233737i	0.415194	−	0.909733i	$-0.363714\pi$
$991$	−10.1275	−	7.35808i	−0.321712	−	0.233737i	−0.736905	+	0.675996i	$0.763714\pi$
$992$	−4.22913	−	13.0159i	−0.134275	−	0.413256i
$993$	84.9474			2.69572
$994$	1.04776	+	3.22466i	0.0332328	+	0.102280i
$995$		0			0
$996$	−6.86107	+	21.1162i	−0.217401	+	0.669093i
$997$	−10.8677	+	33.4473i	−0.344183	+	1.05929i	0.617837	+	0.786307i	$0.288009\pi$
$997$	−10.8677	+	33.4473i	−0.344183	+	1.05929i	−0.962020	+	0.272980i	$0.911991\pi$
$998$	−8.55920	+	6.21862i	−0.270937	+	0.196847i
$999$	11.2524			0.356012

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.h.d.176.6		56
5.2	odd	4		175.2.n.a.64.4	✓	56
5.3	odd	4		875.2.n.c.449.11		56
5.4	even	2		875.2.h.e.176.9		56
25.4	even	10		4375.2.a.o.1.11		28
25.9	even	10		875.2.h.e.701.9		56
25.12	odd	20		875.2.n.c.799.11		56
25.13	odd	20		175.2.n.a.134.4	yes	56
25.16	even	5	inner	875.2.h.d.701.6		56
25.21	even	5		4375.2.a.p.1.18		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.n.a.64.4	✓	56	5.2	odd	4
175.2.n.a.134.4	yes	56	25.13	odd	20
875.2.h.d.176.6		56	1.1	even	1	trivial
875.2.h.d.701.6		56	25.16	even	5	inner
875.2.h.e.176.9		56	5.4	even	2
875.2.h.e.701.9		56	25.9	even	10
875.2.n.c.449.11		56	5.3	odd	4
875.2.n.c.799.11		56	25.12	odd	20
4375.2.a.o.1.11		28	25.4	even	10
4375.2.a.p.1.18		28	25.21	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.h (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.875013 + 0.635734i) q^{2} +(0.987513 - 3.03925i) q^{3} +(-0.256544 + 0.789562i) q^{4} +(1.06807 + 3.28718i) q^{6} -1.00000 q^{7} +(-0.945922 - 2.91125i) q^{8} +(-5.83482 - 4.23925i) q^{9} +O(q^{10})\)	\(q+(-0.875013 + 0.635734i) q^{2} +(0.987513 - 3.03925i) q^{3} +(-0.256544 + 0.789562i) q^{4} +(1.06807 + 3.28718i) q^{6} -1.00000 q^{7} +(-0.945922 - 2.91125i) q^{8} +(-5.83482 - 4.23925i) q^{9} +(-3.82981 + 2.78252i) q^{11} +(2.14634 + 1.55941i) q^{12} +(1.22285 + 0.888450i) q^{13} +(0.875013 - 0.635734i) q^{14} +(1.33519 + 0.970074i) q^{16} +(0.193520 + 0.595592i) q^{17} +7.80058 q^{18} +(0.975363 + 3.00186i) q^{19} +(-0.987513 + 3.03925i) q^{21} +(1.58219 - 4.86949i) q^{22} +(-4.97076 + 3.61147i) q^{23} -9.78213 q^{24} -1.63482 q^{26} +(-10.8901 + 7.91211i) q^{27} +(0.256544 - 0.789562i) q^{28} +(-1.68504 + 5.18603i) q^{29} +(-0.975100 - 3.00105i) q^{31} +4.33712 q^{32} +(4.67480 + 14.3875i) q^{33} +(-0.547970 - 0.398124i) q^{34} +(4.84404 - 3.51940i) q^{36} +(-0.676287 - 0.491351i) q^{37} +(-2.76184 - 2.00659i) q^{38} +(3.90780 - 2.83918i) q^{39} +(-3.59928 - 2.61503i) q^{41} +(-1.06807 - 3.28718i) q^{42} +4.43071 q^{43} +(-1.21446 - 3.73771i) q^{44} +(2.05355 - 6.32016i) q^{46} +(-3.25033 + 10.0035i) q^{47} +(4.26682 - 3.10003i) q^{48} +1.00000 q^{49} +2.00126 q^{51} +(-1.01520 + 0.737586i) q^{52} +(3.33360 - 10.2598i) q^{53} +(4.49897 - 13.8464i) q^{54} +(0.945922 + 2.91125i) q^{56} +10.0866 q^{57} +(-1.82250 - 5.60908i) q^{58} +(1.92813 + 1.40087i) q^{59} +(-4.88772 + 3.55114i) q^{61} +(2.76109 + 2.00605i) q^{62} +(5.83482 + 4.23925i) q^{63} +(-6.46542 + 4.69740i) q^{64} +(-13.2372 - 9.61736i) q^{66} +(-3.60747 - 11.1026i) q^{67} -0.519903 q^{68} +(6.06747 + 18.6738i) q^{69} +(-0.968731 + 2.98145i) q^{71} +(-6.82222 + 20.9966i) q^{72} +(-8.56745 + 6.22462i) q^{73} +0.904129 q^{74} -2.62038 q^{76} +(3.82981 - 2.78252i) q^{77} +(-1.61441 + 4.96864i) q^{78} +(-2.31523 + 7.12553i) q^{79} +(6.60669 + 20.3333i) q^{81} +4.81187 q^{82} +(2.58614 + 7.95931i) q^{83} +(-2.14634 - 1.55941i) q^{84} +(-3.87693 + 2.81675i) q^{86} +(14.0976 + 10.2425i) q^{87} +(11.7233 + 8.51749i) q^{88} +(-10.3651 + 7.53070i) q^{89} +(-1.22285 - 0.888450i) q^{91} +(-1.57626 - 4.85122i) q^{92} -10.0839 q^{93} +(-3.51547 - 10.8195i) q^{94} +(4.28296 - 13.1816i) q^{96} +(3.82534 - 11.7732i) q^{97} +(-0.875013 + 0.635734i) q^{98} +34.1421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{2} - 4 q^{3} - 12 q^{4} - 56 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) \) 56 * q - 4 * q^2 - 4 * q^3 - 12 * q^4 - 56 * q^7 - 12 * q^8 - 6 * q^9	\( 56 q - 4 q^{2} - 4 q^{3} - 12 q^{4} - 56 q^{7} - 12 q^{8} - 6 q^{9} + 8 q^{11} - 12 q^{12} - 8 q^{13} + 4 q^{14} - 32 q^{16} - 20 q^{17} + 48 q^{18} - 12 q^{19} + 4 q^{21} - 8 q^{22} - 16 q^{23} + 28 q^{24} + 12 q^{26} - 16 q^{27} + 12 q^{28} + 2 q^{29} + 12 q^{31} + 112 q^{32} - 14 q^{33} - 14 q^{36} - 16 q^{37} - 20 q^{38} + 4 q^{39} + 4 q^{41} + 32 q^{43} - 22 q^{44} - 4 q^{46} - 18 q^{47} - 48 q^{48} + 56 q^{49} - 44 q^{51} + 16 q^{52} - 20 q^{53} - 54 q^{54} + 12 q^{56} + 152 q^{57} + 32 q^{58} + 6 q^{59} - 4 q^{61} + 18 q^{62} + 6 q^{63} - 24 q^{64} - 74 q^{66} - 32 q^{67} + 124 q^{68} + 78 q^{69} - 8 q^{71} - 100 q^{72} - 48 q^{73} - 60 q^{74} + 52 q^{76} - 8 q^{77} + 124 q^{78} - 72 q^{81} + 44 q^{82} + 10 q^{83} + 12 q^{84} - 20 q^{86} + 26 q^{87} - 88 q^{88} - 38 q^{89} + 8 q^{91} - 96 q^{92} + 96 q^{93} - 88 q^{94} - 28 q^{96} - 90 q^{97} - 4 q^{98} - 60 q^{99}+O(q^{100}) \) 56 * q - 4 * q^2 - 4 * q^3 - 12 * q^4 - 56 * q^7 - 12 * q^8 - 6 * q^9 + 8 * q^11 - 12 * q^12 - 8 * q^13 + 4 * q^14 - 32 * q^16 - 20 * q^17 + 48 * q^18 - 12 * q^19 + 4 * q^21 - 8 * q^22 - 16 * q^23 + 28 * q^24 + 12 * q^26 - 16 * q^27 + 12 * q^28 + 2 * q^29 + 12 * q^31 + 112 * q^32 - 14 * q^33 - 14 * q^36 - 16 * q^37 - 20 * q^38 + 4 * q^39 + 4 * q^41 + 32 * q^43 - 22 * q^44 - 4 * q^46 - 18 * q^47 - 48 * q^48 + 56 * q^49 - 44 * q^51 + 16 * q^52 - 20 * q^53 - 54 * q^54 + 12 * q^56 + 152 * q^57 + 32 * q^58 + 6 * q^59 - 4 * q^61 + 18 * q^62 + 6 * q^63 - 24 * q^64 - 74 * q^66 - 32 * q^67 + 124 * q^68 + 78 * q^69 - 8 * q^71 - 100 * q^72 - 48 * q^73 - 60 * q^74 + 52 * q^76 - 8 * q^77 + 124 * q^78 - 72 * q^81 + 44 * q^82 + 10 * q^83 + 12 * q^84 - 20 * q^86 + 26 * q^87 - 88 * q^88 - 38 * q^89 + 8 * q^91 - 96 * q^92 + 96 * q^93 - 88 * q^94 - 28 * q^96 - 90 * q^97 - 4 * q^98 - 60 * q^99

Introduction

L-functions

Modular forms

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