LMFDB - Embedded newform 250.3.f.c.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,3,Mod(7,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([17]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("250.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	250.f (of order $20$, degree $8$, 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:	$6.81200660901$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 30x^{14} + 351x^{12} + 2130x^{10} + 7341x^{8} + 14480x^{6} + 15196x^{4} + 6560x^{2} + 16 $ x^16 + 30x^14 + 351x^12 + 2130x^10 + 7341x^8 + 14480x^6 + 15196x^4 + 6560*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			107.1
Root			$1.84816i$ of defining polynomial
Character	$\chi$	$=$	250.107
Dual form			250.3.f.c.243.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642040 - 1.26007i) q^{2} +(-0.396386 + 2.50268i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(2.89907 + 2.10629i) q^{6} +(1.84619 + 1.84619i) q^{7} +(-2.79360 + 0.442463i) q^{8} +(2.45322 + 0.797099i) q^{9} +O(q^{10})$	\(q+(0.642040 - 1.26007i) q^{2} +(-0.396386 + 2.50268i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(2.89907 + 2.10629i) q^{6} +(1.84619 + 1.84619i) q^{7} +(-2.79360 + 0.442463i) q^{8} +(2.45322 + 0.797099i) q^{9} +(0.224918 + 0.692225i) q^{11} +(4.51540 - 2.30071i) q^{12} +(5.57900 + 10.9494i) q^{13} +(3.51167 - 1.14101i) q^{14} +(-1.23607 + 3.80423i) q^{16} +(3.31453 + 20.9271i) q^{17} +(2.57947 - 2.57947i) q^{18} +(4.52135 - 6.22310i) q^{19} +(-5.35223 + 3.88862i) q^{21} +(1.01666 + 0.161023i) q^{22} +(35.3452 + 18.0093i) q^{23} -7.16689i q^{24} +17.3790 q^{26} +(-13.3205 + 26.1430i) q^{27} +(0.816872 - 5.15753i) q^{28} +(-28.3088 - 38.9637i) q^{29} +(31.6215 + 22.9744i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-1.82157 + 0.288509i) q^{33} +(28.4978 + 9.25950i) q^{34} +(-1.59420 - 4.90644i) q^{36} +(16.0598 - 8.18285i) q^{37} +(-4.93868 - 9.69270i) q^{38} +(-29.6143 + 9.62228i) q^{39} +(-2.02980 + 6.24709i) q^{41} +(1.46361 + 9.24086i) q^{42} +(-15.0496 + 15.0496i) q^{43} +(0.855637 - 1.17768i) q^{44} +(45.3860 - 32.9749i) q^{46} +(-83.0166 - 13.1485i) q^{47} +(-9.03080 - 4.60142i) q^{48} -42.1832i q^{49} -53.6878 q^{51} +(11.1580 - 21.8988i) q^{52} +(10.2271 - 64.5712i) q^{53} +(24.3898 + 33.5696i) q^{54} +(-5.97440 - 4.34066i) q^{56} +(13.7822 + 13.7822i) q^{57} +(-67.2725 + 10.6549i) q^{58} +(74.4974 + 24.2057i) q^{59} +(-20.0819 - 61.8056i) q^{61} +(49.2517 - 25.0950i) q^{62} +(3.05752 + 6.00071i) q^{63} +(7.60845 - 2.47214i) q^{64} +(-0.805979 + 2.48055i) q^{66} +(-9.69353 - 61.2025i) q^{67} +(29.9644 - 29.9644i) q^{68} +(-59.0818 + 81.3191i) q^{69} +(-43.2855 + 31.4488i) q^{71} +(-7.20601 - 1.14132i) q^{72} +(-30.3151 - 15.4463i) q^{73} -25.4902i q^{74} -15.3843 q^{76} +(-0.862739 + 1.69322i) q^{77} +(-6.88879 + 43.4941i) q^{78} +(13.7883 + 18.9780i) q^{79} +(-41.3660 - 30.0541i) q^{81} +(6.56858 + 6.56858i) q^{82} +(51.1748 - 8.10529i) q^{83} +(12.5839 + 4.08874i) q^{84} +(9.30114 + 28.6260i) q^{86} +(108.735 - 55.4032i) q^{87} +(-0.934615 - 1.83428i) q^{88} +(-142.975 + 46.4555i) q^{89} +(-9.91480 + 30.5146i) q^{91} +(-12.4112 - 78.3609i) q^{92} +(-70.0319 + 70.0319i) q^{93} +(-69.8680 + 96.1651i) q^{94} +(-11.5963 + 8.42518i) q^{96} +(-63.0263 - 9.98239i) q^{97} +(-53.1539 - 27.0833i) q^{98} +1.87746i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 2 q^{3} + 4 q^{6} + 2 q^{7} - 8 q^{8} + 40 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 - 2 * q^3 + 4 * q^6 + 2 * q^7 - 8 * q^8 + 40 * q^9	$ 16 q + 4 q^{2} - 2 q^{3} + 4 q^{6} + 2 q^{7} - 8 q^{8} + 40 q^{9} + 32 q^{11} + 16 q^{12} + 8 q^{13} + 30 q^{14} + 16 q^{16} - 8 q^{17} + 16 q^{18} - 30 q^{19} - 68 q^{21} + 8 q^{22} - 42 q^{23} - 56 q^{26} + 40 q^{27} - 4 q^{28} - 100 q^{29} + 132 q^{31} + 64 q^{32} - 134 q^{33} - 100 q^{34} + 48 q^{36} + 82 q^{37} - 20 q^{38} + 320 q^{39} - 88 q^{41} + 128 q^{42} + 78 q^{43} - 40 q^{44} - 26 q^{46} - 168 q^{47} - 32 q^{48} - 168 q^{51} + 16 q^{52} + 518 q^{53} - 80 q^{54} + 48 q^{56} - 280 q^{57} - 80 q^{58} + 350 q^{59} + 372 q^{61} + 158 q^{62} - 142 q^{63} - 202 q^{66} - 158 q^{67} + 196 q^{68} + 30 q^{69} + 122 q^{71} - 68 q^{72} - 352 q^{73} + 40 q^{76} - 96 q^{77} - 158 q^{78} - 760 q^{79} - 144 q^{81} - 352 q^{82} - 32 q^{83} + 20 q^{84} + 264 q^{86} + 440 q^{87} + 244 q^{88} - 550 q^{89} - 798 q^{91} + 436 q^{92} - 54 q^{93} - 190 q^{94} - 16 q^{96} - 618 q^{97} - 336 q^{98}+O(q^{100}) $ 16 * q + 4 * q^2 - 2 * q^3 + 4 * q^6 + 2 * q^7 - 8 * q^8 + 40 * q^9 + 32 * q^11 + 16 * q^12 + 8 * q^13 + 30 * q^14 + 16 * q^16 - 8 * q^17 + 16 * q^18 - 30 * q^19 - 68 * q^21 + 8 * q^22 - 42 * q^23 - 56 * q^26 + 40 * q^27 - 4 * q^28 - 100 * q^29 + 132 * q^31 + 64 * q^32 - 134 * q^33 - 100 * q^34 + 48 * q^36 + 82 * q^37 - 20 * q^38 + 320 * q^39 - 88 * q^41 + 128 * q^42 + 78 * q^43 - 40 * q^44 - 26 * q^46 - 168 * q^47 - 32 * q^48 - 168 * q^51 + 16 * q^52 + 518 * q^53 - 80 * q^54 + 48 * q^56 - 280 * q^57 - 80 * q^58 + 350 * q^59 + 372 * q^61 + 158 * q^62 - 142 * q^63 - 202 * q^66 - 158 * q^67 + 196 * q^68 + 30 * q^69 + 122 * q^71 - 68 * q^72 - 352 * q^73 + 40 * q^76 - 96 * q^77 - 158 * q^78 - 760 * q^79 - 144 * q^81 - 352 * q^82 - 32 * q^83 + 20 * q^84 + 264 * q^86 + 440 * q^87 + 244 * q^88 - 550 * q^89 - 798 * q^91 + 436 * q^92 - 54 * q^93 - 190 * q^94 - 16 * q^96 - 618 * q^97 - 336 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{13}{20}\right)$

Coefficient data

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

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

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

$2$	0.642040	−	1.26007i	0.321020	−	0.630037i
$2$	0.642040	−	1.26007i	0.321020	−	0.630037i
$3$	−0.396386	+	2.50268i	−0.132129	+	0.834227i	0.829226	+	0.558913i	$0.188782\pi$
$3$	−0.396386	+	2.50268i	−0.132129	+	0.834227i	−0.961355	+	0.275313i	$0.911218\pi$
$4$	−1.17557	−	1.61803i	−0.293893	−	0.404508i
$5$		0			0
$5$		0			0
$6$	2.89907	+	2.10629i	0.483178	+	0.351049i
$7$	1.84619	+	1.84619i	0.263742	+	0.263742i	0.826572	−	0.562831i	$-0.190288\pi$
$7$	1.84619	+	1.84619i	0.263742	+	0.263742i	−0.562831	+	0.826572i	$0.690288\pi$
$8$	−2.79360	+	0.442463i	−0.349201	+	0.0553079i
$9$	2.45322	+	0.797099i	0.272580	+	0.0885666i
$10$		0			0
$11$	0.224918	+	0.692225i	0.0204470	+	0.0629295i	0.960759	−	0.277383i	$-0.0894671\pi$
$11$	0.224918	+	0.692225i	0.0204470	+	0.0629295i	−0.940312	+	0.340313i	$0.889467\pi$
$12$	4.51540	−	2.30071i	0.376283	−	0.191726i
$13$	5.57900	+	10.9494i	0.429154	+	0.842262i	0.999778	+	0.0210512i	$0.00670129\pi$
$13$	5.57900	+	10.9494i	0.429154	+	0.842262i	−0.570624	+	0.821211i	$0.693299\pi$
$14$	3.51167	−	1.14101i	0.250833	−	0.0815007i
$15$		0			0
$16$	−1.23607	+	3.80423i	−0.0772542	+	0.237764i
$17$	3.31453	+	20.9271i	0.194973	+	1.23101i	0.869939	+	0.493160i	$0.164158\pi$
$17$	3.31453	+	20.9271i	0.194973	+	1.23101i	−0.674966	+	0.737849i	$0.735842\pi$
$18$	2.57947	−	2.57947i	0.143304	−	0.143304i
$19$	4.52135	−	6.22310i	0.237966	−	0.327532i	−0.673286	−	0.739382i	$-0.735118\pi$
$19$	4.52135	−	6.22310i	0.237966	−	0.327532i	0.911251	+	0.411851i	$0.135118\pi$
$20$		0			0
$21$	−5.35223	+	3.88862i	−0.254868	+	0.185173i
$22$	1.01666	+	0.161023i	0.0462118	+	0.00731923i
$23$	35.3452	+	18.0093i	1.53675	+	0.783012i	0.998223	−	0.0595970i	$-0.0189816\pi$
$23$	35.3452	+	18.0093i	1.53675	+	0.783012i	0.538525	+	0.842609i	$0.318982\pi$
$24$		−	7.16689i		−	0.298620i
$25$		0			0
$26$	17.3790			0.668423
$27$	−13.3205	+	26.1430i	−0.493352	+	0.968258i
$28$	0.816872	−	5.15753i	0.0291740	−	0.184197i
$29$	−28.3088	−	38.9637i	−0.976165	−	1.34358i	−0.938870	−	0.344272i	$-0.888126\pi$
$29$	−28.3088	−	38.9637i	−0.976165	−	1.34358i	−0.0372955	−	0.999304i	$-0.511874\pi$
$30$		0			0
$31$	31.6215	+	22.9744i	1.02005	+	0.741110i	0.966293	−	0.257445i	$-0.0828805\pi$
$31$	31.6215	+	22.9744i	1.02005	+	0.741110i	0.0537567	+	0.998554i	$0.482880\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−1.82157	+	0.288509i	−0.0551992	+	0.00874269i
$34$	28.4978	+	9.25950i	0.838171	+	0.272338i
$35$		0			0
$36$	−1.59420	−	4.90644i	−0.0442833	−	0.136290i
$37$	16.0598	−	8.18285i	0.434047	−	0.221158i	−0.223294	−	0.974751i	$-0.571681\pi$
$37$	16.0598	−	8.18285i	0.434047	−	0.221158i	0.657341	+	0.753593i	$0.271681\pi$
$38$	−4.93868	−	9.69270i	−0.129965	−	0.255071i
$39$	−29.6143	+	9.62228i	−0.759342	+	0.246725i
$40$		0			0
$41$	−2.02980	+	6.24709i	−0.0495074	+	0.152368i	−0.972754	−	0.231840i	$-0.925525\pi$
$41$	−2.02980	+	6.24709i	−0.0495074	+	0.152368i	0.923247	+	0.384208i	$0.125525\pi$
$42$	1.46361	+	9.24086i	0.0348478	+	0.220020i
$43$	−15.0496	+	15.0496i	−0.349990	+	0.349990i	−0.860106	−	0.510116i	$-0.829603\pi$
$43$	−15.0496	+	15.0496i	−0.349990	+	0.349990i	0.510116	+	0.860106i	$0.329603\pi$
$44$	0.855637	−	1.17768i	0.0194463	−	0.0267655i
$45$		0			0
$46$	45.3860	−	32.9749i	0.986653	−	0.716845i
$47$	−83.0166	−	13.1485i	−1.76631	−	0.279756i	−0.813113	−	0.582106i	$-0.802229\pi$
$47$	−83.0166	−	13.1485i	−1.76631	−	0.279756i	−0.953197	+	0.302350i	$0.902229\pi$
$48$	−9.03080	−	4.60142i	−0.188142	−	0.0958630i
$49$		−	42.1832i		−	0.860881i
$50$		0			0
$51$	−53.6878			−1.05270
$52$	11.1580	−	21.8988i	0.214577	−	0.421131i
$53$	10.2271	−	64.5712i	0.192964	−	1.21832i	−0.680982	−	0.732300i	$-0.738447\pi$
$53$	10.2271	−	64.5712i	0.192964	−	1.21832i	0.873945	−	0.486024i	$-0.161553\pi$
$54$	24.3898	+	33.5696i	0.451663	+	0.621660i
$55$		0			0
$56$	−5.97440	−	4.34066i	−0.106686	−	0.0775117i
$57$	13.7822	+	13.7822i	0.241794	+	0.241794i
$58$	−67.2725	+	10.6549i	−1.15987	+	0.183706i
$59$	74.4974	+	24.2057i	1.26267	+	0.410266i	0.862445	−	0.506151i	$-0.168932\pi$
$59$	74.4974	+	24.2057i	1.26267	+	0.410266i	0.400224	+	0.916417i	$0.368932\pi$
$60$		0			0
$61$	−20.0819	−	61.8056i	−0.329211	−	1.01321i	−0.969504	−	0.245076i	$-0.921187\pi$
$61$	−20.0819	−	61.8056i	−0.329211	−	1.01321i	0.640293	−	0.768131i	$-0.278813\pi$
$62$	49.2517	−	25.0950i	0.794382	−	0.404758i
$63$	3.05752	+	6.00071i	0.0485320	+	0.0952494i
$64$	7.60845	−	2.47214i	0.118882	−	0.0386271i
$65$		0			0
$66$	−0.805979	+	2.48055i	−0.0122118	+	0.0375841i
$67$	−9.69353	−	61.2025i	−0.144679	−	0.913470i	−0.948080	−	0.318032i	$-0.896978\pi$
$67$	−9.69353	−	61.2025i	−0.144679	−	0.913470i	0.803401	−	0.595439i	$-0.203022\pi$
$68$	29.9644	−	29.9644i	0.440652	−	0.440652i
$69$	−59.0818	+	81.3191i	−0.856258	+	1.17854i
$70$		0			0
$71$	−43.2855	+	31.4488i	−0.609656	+	0.442941i	−0.849293	−	0.527922i	$-0.822971\pi$
$71$	−43.2855	+	31.4488i	−0.609656	+	0.442941i	0.239637	+	0.970862i	$0.422971\pi$
$72$	−7.20601	−	1.14132i	−0.100084	−	0.0158517i
$73$	−30.3151	−	15.4463i	−0.415276	−	0.211594i	0.233853	−	0.972272i	$-0.424866\pi$
$73$	−30.3151	−	15.4463i	−0.415276	−	0.211594i	−0.649129	+	0.760678i	$0.724866\pi$
$74$		−	25.4902i		−	0.344462i
$75$		0			0
$76$	−15.3843			−0.202426
$77$	−0.862739	+	1.69322i	−0.0112044	+	0.0219899i
$78$	−6.88879	+	43.4941i	−0.0883178	+	0.557617i
$79$	13.7883	+	18.9780i	0.174536	+	0.240228i	0.887319	−	0.461157i	$-0.152565\pi$
$79$	13.7883	+	18.9780i	0.174536	+	0.240228i	−0.712783	+	0.701385i	$0.752565\pi$
$80$		0			0
$81$	−41.3660	−	30.0541i	−0.510691	−	0.371039i
$82$	6.56858	+	6.56858i	0.0801046	+	0.0801046i
$83$	51.1748	−	8.10529i	0.616564	−	0.0976541i	0.159663	−	0.987172i	$-0.448959\pi$
$83$	51.1748	−	8.10529i	0.616564	−	0.0976541i	0.456901	+	0.889517i	$0.348959\pi$
$84$	12.5839	+	4.08874i	0.149808	+	0.0486755i
$85$		0			0
$86$	9.30114	+	28.6260i	0.108153	+	0.332860i
$87$	108.735	−	55.4032i	1.24983	−	0.636819i
$88$	−0.934615	−	1.83428i	−0.0106206	−	0.0208441i
$89$	−142.975	+	46.4555i	−1.60646	+	0.521972i	−0.968695	−	0.248255i	$-0.920143\pi$
$89$	−142.975	+	46.4555i	−1.60646	+	0.521972i	−0.637770	+	0.770227i	$0.720143\pi$
$90$		0			0
$91$	−9.91480	+	30.5146i	−0.108954	+	0.335326i
$92$	−12.4112	−	78.3609i	−0.134904	−	0.851749i
$93$	−70.0319	+	70.0319i	−0.753031	+	0.753031i
$94$	−69.8680	+	96.1651i	−0.743277	+	1.02303i
$95$		0			0
$96$	−11.5963	+	8.42518i	−0.120794	+	0.0877623i
$97$	−63.0263	−	9.98239i	−0.649756	−	0.102911i	−0.177148	−	0.984184i	$-0.556687\pi$
$97$	−63.0263	−	9.98239i	−0.649756	−	0.102911i	−0.472608	+	0.881273i	$0.656687\pi$
$98$	−53.1539	−	27.0833i	−0.542386	−	0.276360i
$99$			1.87746i			0.0189643i
$100$		0			0
$101$	−60.0228			−0.594285			−0.297142	−	0.954833i	$-0.596034\pi$
$101$	−60.0228			−0.594285			−0.297142	+	0.954833i	$0.596034\pi$
$102$	−34.4697	+	67.6506i	−0.337938	+	0.663241i
$103$	−5.85890	+	36.9917i	−0.0568825	+	0.359142i	0.942786	+	0.333398i	$0.108195\pi$
$103$	−5.85890	+	36.9917i	−0.0568825	+	0.359142i	−0.999669	+	0.0257438i	$0.991805\pi$
$104$	−20.4302	−	28.1198i	−0.196445	−	0.270383i
$105$		0			0
$106$	−74.7983	−	54.3441i	−0.705644	−	0.512681i
$107$	9.46731	+	9.46731i	0.0884795	+	0.0884795i	0.749961	−	0.661482i	$-0.230072\pi$
$107$	9.46731	+	9.46731i	0.0884795	+	0.0884795i	−0.661482	+	0.749961i	$0.730072\pi$
$108$	57.9594	−	9.17987i	0.536661	−	0.0849988i
$109$	159.887	+	51.9505i	1.46685	+	0.476610i	0.930156	−	0.367164i	$-0.119671\pi$
$109$	159.887	+	51.9505i	1.46685	+	0.476610i	0.536698	+	0.843774i	$0.319671\pi$
$110$		0			0
$111$	14.1132	+	43.4360i	0.127146	+	0.391315i
$112$	−9.30535	+	4.74131i	−0.0830835	+	0.0423331i
$113$	−54.9006	−	107.749i	−0.485846	−	0.953527i	−0.995644	−	0.0932331i	$-0.970280\pi$
$113$	−54.9006	−	107.749i	−0.485846	−	0.953527i	0.509798	−	0.860294i	$-0.329720\pi$
$114$	26.2154	−	8.51789i	0.229959	−	0.0747183i
$115$		0			0
$116$	−29.7656	+	91.6092i	−0.256600	+	0.789734i
$117$	4.95875	+	31.3083i	0.0423825	+	0.267593i
$118$	78.3313	−	78.3313i	0.663824	−	0.663824i
$119$	−32.5163	+	44.7548i	−0.273246	+	0.376091i
$120$		0			0
$121$	97.4625	−	70.8106i	0.805475	−	0.585212i
$122$	−90.7730	−	14.3770i	−0.744041	−	0.117844i
$123$	−14.8299	−	7.55620i	−0.120568	−	0.0614326i
$124$		−	78.1728i		−	0.630425i
$125$		0			0
$126$	9.52438			0.0755904
$127$	−10.6308	+	20.8642i	−0.0837074	+	0.164285i	−0.929066	−	0.369915i	$-0.879387\pi$
$127$	−10.6308	+	20.8642i	−0.0837074	+	0.164285i	0.845358	+	0.534200i	$0.179387\pi$
$128$	1.76985	−	11.1744i	0.0138270	−	0.0873001i
$129$	−31.6988	−	43.6297i	−0.245727	−	0.338215i
$130$		0			0
$131$	87.8890	+	63.8551i	0.670908	+	0.487443i	0.870329	−	0.492471i	$-0.163906\pi$
$131$	87.8890	+	63.8551i	0.670908	+	0.487443i	−0.199421	+	0.979914i	$0.563906\pi$
$132$	2.60820	+	2.60820i	0.0197591	+	0.0197591i
$133$	19.8363	−	3.14176i	0.149145	−	0.0236223i
$134$	−83.3433	−	27.0799i	−0.621965	−	0.202089i
$135$		0			0
$136$	−18.5190	−	56.9956i	−0.136169	−	0.419085i
$137$	−14.2785	+	7.27525i	−0.104223	+	0.0531040i	−0.505325	−	0.862929i	$-0.668627\pi$
$137$	−14.2785	+	7.27525i	−0.104223	+	0.0531040i	0.401102	+	0.916033i	$0.368627\pi$
$138$	64.5352	+	126.658i	0.467647	+	0.917808i
$139$	190.092	−	61.7647i	1.36757	−	0.444350i	0.469007	−	0.883195i	$-0.344612\pi$
$139$	190.092	−	61.7647i	1.36757	−	0.444350i	0.898563	+	0.438844i	$0.144612\pi$
$140$		0			0
$141$	65.8132	−	202.552i	0.466760	−	1.43654i
$142$	11.8368	+	74.7343i	0.0833574	+	0.526298i
$143$	−6.32464	+	6.32464i	−0.0442283	+	0.0442283i
$144$	−6.06469	+	8.34733i	−0.0421159	+	0.0579676i
$145$		0			0
$146$	−38.9270	+	28.2821i	−0.266623	+	0.193713i
$147$	105.571	+	16.7208i	0.718170	+	0.113747i
$148$	−32.1195	−	16.3657i	−0.217024	−	0.110579i
$149$		−	278.483i		−	1.86902i	−0.355942	−	0.934508i	$-0.615840\pi$
$149$		−	278.483i		−	1.86902i	0.355942	−	0.934508i	$-0.384160\pi$
$150$		0			0
$151$	216.796			1.43574			0.717869	−	0.696178i	$-0.245118\pi$
$151$	216.796			1.43574			0.717869	+	0.696178i	$0.245118\pi$
$152$	−9.87736	+	19.3854i	−0.0649826	+	0.127536i
$153$	−8.54973	+	53.9809i	−0.0558806	+	0.352816i
$154$	1.57967	+	2.17423i	0.0102576	+	0.0141184i
$155$		0			0
$156$	50.3829	+	36.6053i	0.322967	+	0.234649i
$157$	113.262	+	113.262i	0.721414	+	0.721414i	0.968893	−	0.247479i	$-0.0796022\pi$
$157$	113.262	+	113.262i	0.721414	+	0.721414i	−0.247479	+	0.968893i	$0.579602\pi$
$158$	32.7663	−	5.18968i	0.207382	−	0.0328461i
$159$	157.547	+	51.1902i	0.990863	+	0.321951i
$160$		0			0
$161$	32.0054	+	98.5026i	0.198792	+	0.611817i
$162$	−64.4290	+	32.8282i	−0.397710	+	0.202643i
$163$	−24.3460	−	47.7817i	−0.149362	−	0.293139i	0.804188	−	0.594376i	$-0.202601\pi$
$163$	−24.3460	−	47.7817i	−0.149362	−	0.293139i	−0.953550	+	0.301236i	$0.902601\pi$
$164$	12.4942	−	4.05960i	0.0761840	−	0.0247537i
$165$		0			0
$166$	22.6430	−	69.6879i	0.136404	−	0.419807i
$167$	−41.3623	−	261.151i	−0.247678	−	1.56378i	−0.727310	−	0.686309i	$-0.759230\pi$
$167$	−41.3623	−	261.151i	−0.247678	−	1.56378i	0.479632	−	0.877470i	$-0.340770\pi$
$168$	13.2314	−	13.2314i	0.0787586	−	0.0787586i
$169$	10.5714	−	14.5502i	0.0625525	−	0.0860961i
$170$		0			0
$171$	16.0523	−	11.6627i	0.0938730	−	0.0682027i
$172$	42.0425	+	6.65888i	0.244433	+	0.0387144i
$173$	36.7868	+	18.7438i	0.212641	+	0.108346i	0.557067	−	0.830467i	$-0.311927\pi$
$173$	36.7868	+	18.7438i	0.212641	+	0.108346i	−0.344426	+	0.938813i	$0.611927\pi$
$174$		−	172.585i		−	0.991868i
$175$		0			0
$176$	−2.91139			−0.0165420
$177$	−90.1088	+	176.849i	−0.509089	+	0.999144i
$178$	−33.2585	+	209.986i	−0.186845	+	1.17970i
$179$	−84.9216	−	116.885i	−0.474422	−	0.652986i	0.502999	−	0.864287i	$-0.332230\pi$
$179$	−84.9216	−	116.885i	−0.474422	−	0.652986i	−0.977421	+	0.211301i	$0.932230\pi$
$180$		0			0
$181$	−35.1000	−	25.5016i	−0.193923	−	0.140893i	0.486587	−	0.873632i	$-0.338242\pi$
$181$	−35.1000	−	25.5016i	−0.193923	−	0.140893i	−0.680510	+	0.732739i	$0.738242\pi$
$182$	32.0850	+	32.0850i	0.176291	+	0.176291i
$183$	162.640	−	25.7596i	0.888742	−	0.140763i
$184$	−106.709	−	34.6718i	−0.579940	−	0.188434i
$185$		0			0
$186$	43.2821	+	133.209i	0.232699	+	0.716175i
$187$	−13.7408	+	7.00128i	−0.0734802	+	0.0374400i
$188$	76.3171	+	149.781i	0.405942	+	0.796706i
$189$	−72.8572	+	23.6727i	−0.385488	+	0.125253i
$190$		0			0
$191$	−48.7314	+	149.980i	−0.255138	+	0.785235i	0.738664	+	0.674074i	$0.235457\pi$
$191$	−48.7314	+	149.980i	−0.255138	+	0.785235i	−0.993802	+	0.111161i	$0.964543\pi$
$192$	3.17109	+	20.0214i	0.0165161	+	0.104278i
$193$	−76.0787	+	76.0787i	−0.394190	+	0.394190i	−0.876178	−	0.481988i	$-0.839915\pi$
$193$	−76.0787	+	76.0787i	−0.394190	+	0.394190i	0.481988	+	0.876178i	$0.339915\pi$
$194$	−53.0440	+	73.0087i	−0.273422	+	0.376334i
$195$		0			0
$196$	−68.2538	+	49.5893i	−0.348234	+	0.253006i
$197$	37.6748	+	5.96711i	0.191243	+	0.0302899i	0.251321	−	0.967904i	$-0.419135\pi$
$197$	37.6748	+	5.96711i	0.191243	+	0.0302899i	−0.0600782	+	0.998194i	$0.519135\pi$
$198$	2.36574	+	1.20540i	0.0119482	+	0.00608790i
$199$			201.504i			1.01259i	0.862362	+	0.506293i	$0.168984\pi$
$199$			201.504i			1.01259i	−0.862362	+	0.506293i	$0.831016\pi$
$200$		0			0
$201$	157.013			0.781158
$202$	−38.5370	+	75.6331i	−0.190777	+	0.374421i
$203$	19.6710	−	124.198i	0.0969016	−	0.611813i
$204$	63.1138	+	86.8687i	0.309381	+	0.425827i
$205$		0			0
$206$	42.8506	+	31.1328i	0.208012	+	0.151130i
$207$	72.3544	+	72.3544i	0.349538	+	0.349538i
$208$	−48.5501	+	7.68958i	−0.233414	+	0.0369691i
$209$	5.32471	+	1.73010i	0.0254771	+	0.00827801i
$210$		0			0
$211$	6.78952	+	20.8960i	0.0321778	+	0.0990332i	0.965856	−	0.259081i	$-0.0834198\pi$
$211$	6.78952	+	20.8960i	0.0321778	+	0.0990332i	−0.933678	+	0.358114i	$0.883420\pi$
$212$	−116.501	+	59.3603i	−0.549533	+	0.280001i
$213$	−61.5485	−	120.796i	−0.288960	−	0.567116i
$214$	18.0079	−	5.85112i	0.0841490	−	0.0273417i
$215$		0			0
$216$	25.6449	−	78.9270i	0.118727	−	0.365403i
$217$	15.9643	+	100.795i	0.0735682	+	0.464491i
$218$	168.115	−	168.115i	0.771171	−	0.771171i
$219$	50.6737	−	69.7464i	0.231387	−	0.318477i
$220$		0			0
$221$	−210.648	+	153.045i	−0.953159	+	0.692510i
$222$	63.7938	+	10.1039i	0.287359	+	0.0455133i
$223$	373.349	+	190.231i	1.67421	+	0.853053i	0.992613	+	0.121328i	$0.0387152\pi$
$223$	373.349	+	190.231i	1.67421	+	0.853053i	0.681599	+	0.731726i	$0.261285\pi$
$224$			14.7695i			0.0659354i
$225$		0			0
$226$	−171.020			−0.756724
$227$	50.1388	−	98.4029i	0.220876	−	0.433493i	−0.753804	−	0.657100i	$-0.771783\pi$
$227$	50.1388	−	98.4029i	0.220876	−	0.433493i	0.974679	+	0.223607i	$0.0717831\pi$
$228$	6.09813	−	38.5021i	0.0267462	−	0.168869i
$229$	7.87652	+	10.8411i	0.0343953	+	0.0473410i	0.825868	−	0.563863i	$-0.190685\pi$
$229$	7.87652	+	10.8411i	0.0343953	+	0.0473410i	−0.791473	+	0.611204i	$0.790685\pi$
$230$		0			0
$231$	−3.89561	−	2.83033i	−0.0168641	−	0.0122525i
$232$	96.3236	+	96.3236i	0.415188	+	0.415188i
$233$	−300.082	+	47.5283i	−1.28790	+	0.203984i	−0.762567	−	0.646909i	$-0.776061\pi$
$233$	−300.082	+	47.5283i	−1.28790	+	0.203984i	−0.525338	+	0.850894i	$0.676061\pi$
$234$	42.6345	+	13.8528i	0.182199	+	0.0592000i
$235$		0			0
$236$	−48.4114	−	148.995i	−0.205133	−	0.631334i
$237$	−52.9614	+	26.9852i	−0.223466	+	0.113862i
$238$	35.5176	+	69.7072i	0.149234	+	0.292887i
$239$	−272.615	+	88.5779i	−1.14065	+	0.370619i	−0.817613	−	0.575768i	$-0.804703\pi$
$239$	−272.615	+	88.5779i	−1.14065	+	0.370619i	−0.323035	+	0.946387i	$0.604703\pi$
$240$		0			0
$241$	−18.3766	+	56.5573i	−0.0762514	+	0.234678i	−0.981916	−	0.189317i	$-0.939373\pi$
$241$	−18.3766	+	56.5573i	−0.0762514	+	0.234678i	0.905665	+	0.423995i	$0.139373\pi$
$242$	−26.6518	−	168.273i	−0.110132	−	0.695343i
$243$	−95.1119	+	95.1119i	−0.391407	+	0.391407i
$244$	−76.3959	+	105.150i	−0.313098	+	0.430943i
$245$		0			0
$246$	−19.0427	+	13.8354i	−0.0774095	+	0.0562413i
$247$	93.3639	+	14.7874i	0.377991	+	0.0598680i
$248$	−98.5034	−	50.1900i	−0.397191	−	0.202379i
$249$			131.287i			0.527257i
$250$		0			0
$251$	−130.804			−0.521132			−0.260566	−	0.965456i	$-0.583909\pi$
$251$	−130.804			−0.521132			−0.260566	+	0.965456i	$0.583909\pi$
$252$	6.11503	−	12.0014i	0.0242660	−	0.0476247i
$253$	−4.51672	+	28.5174i	−0.0178526	+	0.112717i
$254$	19.4650	+	26.7913i	0.0766339	+	0.105477i
$255$		0			0
$256$	−12.9443	−	9.40456i	−0.0505636	−	0.0367366i
$257$	−64.9358	−	64.9358i	−0.252668	−	0.252668i	0.569395	−	0.822064i	$-0.307177\pi$
$257$	−64.9358	−	64.9358i	−0.252668	−	0.252668i	−0.822064	+	0.569395i	$0.807177\pi$
$258$	−75.3285	+	11.9309i	−0.291971	+	0.0462437i
$259$	44.7565	+	14.5423i	0.172805	+	0.0561477i
$260$		0			0
$261$	−38.3897	−	118.151i	−0.147087	−	0.452688i
$262$	136.890	−	69.7491i	0.522482	−	0.266218i
$263$	−71.0644	−	139.472i	−0.270207	−	0.530311i	0.715535	−	0.698577i	$-0.246183\pi$
$263$	−71.0644	−	139.472i	−0.270207	−	0.530311i	−0.985742	+	0.168266i	$0.946183\pi$
$264$	4.96110	−	1.61196i	0.0187920	−	0.00610590i
$265$		0			0
$266$	8.77684	−	27.0123i	0.0329956	−	0.101550i
$267$	−59.5899	−	376.236i	−0.223183	−	1.40912i
$268$	−87.6323	+	87.6323i	−0.326986	+	0.326986i
$269$	194.659	−	267.925i	0.723640	−	0.996005i	−0.275755	−	0.961228i	$-0.588928\pi$
$269$	194.659	−	267.925i	0.723640	−	0.996005i	0.999395	−	0.0347774i	$-0.0110722\pi$
$270$		0			0
$271$	151.790	−	110.282i	0.560111	−	0.406945i	−0.271388	−	0.962470i	$-0.587483\pi$
$271$	151.790	−	110.282i	0.560111	−	0.406945i	0.831500	+	0.555525i	$0.187483\pi$
$272$	−83.7086	−	13.2581i	−0.307752	−	0.0487431i
$273$	−72.4383	−	36.9091i	−0.265342	−	0.135198i
$274$			22.6629i			0.0827114i
$275$		0			0
$276$	201.032			0.728377
$277$	127.429	−	250.094i	0.460033	−	0.902865i	−0.538164	−	0.842840i	$-0.680882\pi$
$277$	127.429	−	250.094i	0.460033	−	0.902865i	0.998197	−	0.0600250i	$-0.0191180\pi$
$278$	44.2186	−	279.186i	0.159060	−	1.00426i
$279$	59.2617	+	81.5668i	0.212408	+	0.292354i
$280$		0			0
$281$	−253.823	−	184.413i	−0.903284	−	0.656274i	0.0360233	−	0.999351i	$-0.488531\pi$
$281$	−253.823	−	184.413i	−0.903284	−	0.656274i	−0.939307	+	0.343077i	$0.888531\pi$
$282$	−212.976	−	212.976i	−0.755234	−	0.755234i
$283$	−93.3349	+	14.7828i	−0.329805	+	0.0522360i	−0.319141	−	0.947707i	$-0.603394\pi$
$283$	−93.3349	+	14.7828i	−0.329805	+	0.0522360i	−0.0106639	+	0.999943i	$0.503394\pi$
$284$	101.770	+	33.0672i	0.358347	+	0.116434i
$285$		0			0
$286$	3.90884	+	12.0302i	0.0136673	+	0.0420636i
$287$	−15.2807	+	7.78592i	−0.0532430	+	0.0271286i
$288$	6.62448	+	13.0013i	0.0230017	+	0.0451433i
$289$	−152.104	+	49.4215i	−0.526311	+	0.171009i
$290$		0			0
$291$	49.9655	−	153.778i	0.171703	−	0.528447i
$292$	10.6449	+	67.2092i	0.0364551	+	0.230168i
$293$	−100.122	+	100.122i	−0.341714	+	0.341714i	−0.857012	−	0.515297i	$-0.827682\pi$
$293$	−100.122	+	100.122i	−0.341714	+	0.341714i	0.515297	+	0.857012i	$0.327682\pi$
$294$	88.8502	−	122.292i	0.302211	−	0.415958i
$295$		0			0
$296$	−41.2440	+	29.9655i	−0.139338	+	0.101235i
$297$	−21.0928	−	3.34078i	−0.0710196	−	0.0112484i
$298$	−350.910	−	178.797i	−1.17755	−	0.599991i
$299$			487.483i			1.63038i
$300$		0			0
$301$	−55.5688			−0.184614
$302$	139.192	−	273.179i	0.460900	−	0.904568i
$303$	23.7922	−	150.218i	0.0785220	−	0.495768i
$304$	18.0854	+	24.8924i	0.0594914	+	0.0818829i
$305$		0			0
$306$	62.5306	+	45.4312i	0.204348	+	0.148468i
$307$	−268.414	−	268.414i	−0.874313	−	0.874313i	0.118626	−	0.992939i	$-0.462151\pi$
$307$	−268.414	−	268.414i	−0.874313	−	0.874313i	−0.992939	+	0.118626i	$0.962151\pi$
$308$	3.75390	−	0.594559i	0.0121880	−	0.00193039i
$309$	−90.2559	−	29.3259i	−0.292090	−	0.0949059i
$310$		0			0
$311$	−24.7131	−	76.0590i	−0.0794632	−	0.244563i	0.903431	−	0.428733i	$-0.141040\pi$
$311$	−24.7131	−	76.0590i	−0.0794632	−	0.244563i	−0.982894	+	0.184171i	$0.941040\pi$
$312$	78.4732	−	39.9841i	0.251517	−	0.128154i
$313$	−75.5464	−	148.268i	−0.241362	−	0.473700i	0.738269	−	0.674507i	$-0.235644\pi$
$313$	−75.5464	−	148.268i	−0.241362	−	0.473700i	−0.979631	+	0.200807i	$0.935644\pi$
$314$	215.437	−	69.9998i	0.686106	−	0.222929i
$315$		0			0
$316$	14.4979	−	44.6200i	0.0458795	−	0.141202i
$317$	75.4156	+	476.155i	0.237904	+	1.50207i	0.760417	+	0.649436i	$0.224995\pi$
$317$	75.4156	+	476.155i	0.237904	+	1.50207i	−0.522513	+	0.852632i	$0.675005\pi$
$318$	165.655	−	165.655i	0.520928	−	0.520928i
$319$	20.6045	−	28.3597i	0.0645909	−	0.0889018i
$320$		0			0
$321$	−27.4463	+	19.9409i	−0.0855026	+	0.0621213i
$322$	144.669	+	22.9134i	0.449284	+	0.0711595i
$323$	145.218	+	73.9922i	0.449591	+	0.229078i
$324$			102.262i			0.315624i
$325$		0			0
$326$	−75.8395			−0.232637
$327$	−193.392	+	379.554i	−0.591414	+	1.16072i
$328$	2.90636	−	18.3500i	0.00886084	−	0.0559452i
$329$	−128.990	−	177.539i	−0.392066	−	0.539633i
$330$		0			0
$331$	−219.259	−	159.301i	−0.662413	−	0.481271i	0.205064	−	0.978749i	$-0.434260\pi$
$331$	−219.259	−	159.301i	−0.662413	−	0.481271i	−0.867477	+	0.497477i	$0.834260\pi$
$332$	−73.2742	−	73.2742i	−0.220706	−	0.220706i
$333$	45.9206	−	7.27312i	0.137900	−	0.0218412i
$334$	−355.626	−	115.550i	−1.06475	−	0.345957i
$335$		0			0
$336$	−8.17748	−	25.1677i	−0.0243377	−	0.0749039i
$337$	−353.552	+	180.144i	−1.04912	+	0.534551i	−0.891533	−	0.452955i	$-0.850370\pi$
$337$	−353.552	+	180.144i	−1.04912	+	0.534551i	−0.157582	+	0.987506i	$0.550370\pi$
$338$	−11.5471	−	22.6625i	−0.0341631	−	0.0670489i
$339$	291.422	−	94.6888i	0.859652	−	0.279318i
$340$		0			0
$341$	−8.79121	+	27.0566i	−0.0257807	+	0.0793448i
$342$	−4.38962	−	27.7150i	−0.0128351	−	0.0810379i
$343$	168.342	−	168.342i	0.490792	−	0.490792i
$344$	35.3837	−	48.7014i	0.102859	−	0.141574i
$345$		0			0
$346$	47.2372	−	34.3198i	0.136524	−	0.0991903i
$347$	−118.028	−	18.6937i	−0.340137	−	0.0538724i	−0.0159706	−	0.999872i	$-0.505084\pi$
$347$	−118.028	−	18.6937i	−0.340137	−	0.0538724i	−0.324167	+	0.946000i	$0.605084\pi$
$348$	−217.470	−	110.806i	−0.624913	−	0.318409i
$349$			282.531i			0.809544i	0.914418	+	0.404772i	$0.132649\pi$
$349$			282.531i			0.809544i	−0.914418	+	0.404772i	$0.867351\pi$
$350$		0			0
$351$	−360.565			−1.02725
$352$	−1.86923	+	3.66857i	−0.00531031	+	0.0104221i
$353$	63.6566	−	401.912i	0.180330	−	1.13856i	−0.716958	−	0.697116i	$-0.754466\pi$
$353$	63.6566	−	401.912i	0.180330	−	1.13856i	0.897288	−	0.441445i	$-0.145534\pi$
$354$	164.989	+	227.087i	0.466070	+	0.641490i
$355$		0			0
$356$	243.244	+	176.727i	0.683270	+	0.496425i
$357$	−99.1180	−	99.1180i	−0.277641	−	0.277641i
$358$	−201.806	+	31.9630i	−0.563704	+	0.0892820i
$359$	−539.418	−	175.268i	−1.50256	−	0.488210i	−0.561795	−	0.827277i	$-0.689889\pi$
$359$	−539.418	−	175.268i	−1.50256	−	0.488210i	−0.940763	+	0.339066i	$0.889889\pi$
$360$		0			0
$361$	93.2707	+	287.058i	0.258368	+	0.795174i
$362$	−54.6695	+	27.8555i	−0.151021	+	0.0769489i
$363$	138.584	+	271.986i	0.381773	+	0.749272i
$364$	61.0293	−	19.8296i	0.167663	−	0.0544769i
$365$		0			0
$366$	71.9622	−	221.477i	0.196618	−	0.605128i
$367$	62.7832	+	396.398i	0.171071	+	1.08010i	0.912502	+	0.409073i	$0.134148\pi$
$367$	62.7832	+	396.398i	0.171071	+	1.08010i	−0.741430	+	0.671030i	$0.765852\pi$
$368$	−112.200	+	112.200i	−0.304893	+	0.304893i
$369$	−9.95910	+	13.7075i	−0.0269894	+	0.0371478i
$370$		0			0
$371$	138.092	−	100.330i	0.372216	−	0.270430i
$372$	195.641	+	30.9866i	0.525918	+	0.0832972i
$373$	367.546	+	187.274i	0.985379	+	0.502075i	0.870958	−	0.491357i	$-0.163499\pi$
$373$	367.546	+	187.274i	0.985379	+	0.502075i	0.114420	+	0.993432i	$0.463499\pi$
$374$			21.8095i			0.0583142i
$375$		0			0
$376$	237.733			0.632269
$377$	268.695	−	527.343i	0.712719	−	1.39879i
$378$	−16.9478	+	107.004i	−0.0448355	+	0.283080i
$379$	−68.8055	−	94.7026i	−0.181545	−	0.249875i	0.708539	−	0.705671i	$-0.249355\pi$
$379$	−68.8055	−	94.7026i	−0.181545	−	0.249875i	−0.890084	+	0.455796i	$0.849355\pi$
$380$		0			0
$381$	−48.0025	−	34.8759i	−0.125991	−	0.0915377i
$382$	157.698	+	157.698i	0.412822	+	0.412822i
$383$	90.4436	−	14.3249i	0.236145	−	0.0374017i	−0.0372401	−	0.999306i	$-0.511857\pi$
$383$	90.4436	−	14.3249i	0.236145	−	0.0374017i	0.273385	+	0.961905i	$0.411857\pi$
$384$	27.2645	+	8.85876i	0.0710012	+	0.0230697i
$385$		0			0
$386$	47.0192	+	144.710i	0.121811	+	0.374897i
$387$	−48.9159	+	24.9239i	−0.126398	+	0.0644028i
$388$	57.9401	+	113.714i	0.149330	+	0.293077i
$389$	−206.217	+	67.0040i	−0.530121	+	0.172247i	−0.561833	−	0.827250i	$-0.689904\pi$
$389$	−206.217	+	67.0040i	−0.530121	+	0.172247i	0.0317127	+	0.999497i	$0.489904\pi$
$390$		0			0
$391$	−259.730	+	799.367i	−0.664271	+	2.04442i
$392$	18.6645	+	117.843i	0.0476135	+	0.300620i
$393$	−194.647	+	194.647i	−0.495285	+	0.495285i
$394$	31.7077	−	43.6420i	0.0804765	−	0.110766i
$395$		0			0
$396$	3.03780	−	2.20709i	0.00767120	−	0.00557346i
$397$	−134.416	−	21.2893i	−0.338578	−	0.0536255i	−0.0151696	−	0.999885i	$-0.504829\pi$
$397$	−134.416	−	21.2893i	−0.338578	−	0.0536255i	−0.323409	+	0.946259i	$0.604829\pi$
$398$	253.910	+	129.374i	0.637966	+	0.325060i
$399$			50.8893i			0.127542i
$400$		0			0
$401$	−23.8319			−0.0594311			−0.0297156	−	0.999558i	$-0.509460\pi$
$401$	−23.8319			−0.0594311			−0.0297156	+	0.999558i	$0.509460\pi$
$402$	100.808	−	197.848i	0.250767	−	0.492158i
$403$	−75.1394	+	474.412i	−0.186450	+	1.17720i
$404$	70.5610	+	97.1189i	0.174656	+	0.240393i
$405$		0			0
$406$	−143.869	−	104.527i	−0.354357	−	0.257456i
$407$	9.27649	+	9.27649i	0.0227924	+	0.0227924i
$408$	149.982	−	23.7549i	0.367604	−	0.0582228i
$409$	−287.240	−	93.3299i	−0.702298	−	0.228190i	−0.0639666	−	0.997952i	$-0.520375\pi$
$409$	−287.240	−	93.3299i	−0.702298	−	0.228190i	−0.638332	+	0.769762i	$0.720375\pi$
$410$		0			0
$411$	−12.5478	−	38.6183i	−0.0305300	−	0.0939618i
$412$	66.7413	−	34.0064i	0.161993	−	0.0825398i
$413$	92.8482	+	182.225i	0.224814	+	0.441223i
$414$	137.626	−	44.7175i	0.332430	−	0.108013i
$415$		0			0
$416$	−21.4816	+	66.1137i	−0.0516385	+	0.158927i
$417$	79.2275	+	500.223i	0.189994	+	1.19957i
$418$	5.59874	−	5.59874i	0.0133941	−	0.0133941i
$419$	400.071	−	550.650i	0.954823	−	1.31420i	0.00547150	−	0.999985i	$-0.498258\pi$
$419$	400.071	−	550.650i	0.954823	−	1.31420i	0.949351	−	0.314216i	$-0.101742\pi$
$420$		0			0
$421$	218.505	−	158.753i	0.519014	−	0.377086i	−0.297218	−	0.954810i	$-0.596059\pi$
$421$	218.505	−	158.753i	0.519014	−	0.377086i	0.816232	+	0.577724i	$0.196059\pi$
$422$	30.6896	+	4.86076i	0.0727243	+	0.0115184i
$423$	−193.177	−	98.4287i	−0.456684	−	0.232692i
$424$			184.912i			0.436112i
$425$		0			0
$426$	−191.728			−0.450066
$427$	77.0300	−	151.180i	0.180398	−	0.354051i
$428$	4.18894	−	26.4479i	0.00978724	−	0.0617942i
$429$	−13.3216	−	18.3356i	−0.0310526	−	0.0427402i
$430$		0			0
$431$	668.833	+	485.936i	1.55182	+	1.12746i	0.942340	+	0.334656i	$0.108620\pi$
$431$	668.833	+	485.936i	1.55182	+	1.12746i	0.609476	+	0.792804i	$0.291380\pi$
$432$	−82.9887	−	82.9887i	−0.192104	−	0.192104i
$433$	719.567	−	113.968i	1.66182	−	0.263206i	0.746337	−	0.665568i	$-0.231811\pi$
$433$	719.567	−	113.968i	1.66182	−	0.263206i	0.915481	+	0.402362i	$0.131811\pi$
$434$	137.258	+	44.5979i	0.316263	+	0.102760i
$435$		0			0
$436$	−103.901	−	319.774i	−0.238305	−	0.733427i
$437$	271.881	−	138.531i	0.622154	−	0.317003i
$438$	−55.3510	−	108.633i	−0.126372	−	0.248020i
$439$	472.354	−	153.477i	1.07598	−	0.349606i	0.283164	−	0.959071i	$-0.408616\pi$
$439$	472.354	−	153.477i	1.07598	−	0.349606i	0.792813	+	0.609465i	$0.208616\pi$
$440$		0			0
$441$	33.6242	−	103.485i	0.0762453	−	0.234659i
$442$	57.6033	+	363.693i	0.130324	+	0.822835i
$443$	−367.664	+	367.664i	−0.829940	+	0.829940i	−0.987508	−	0.157568i	$-0.949635\pi$
$443$	−367.664	+	367.664i	−0.829940	+	0.829940i	0.157568	+	0.987508i	$0.449635\pi$
$444$	53.6898	−	73.8977i	0.120923	−	0.166436i
$445$		0			0
$446$	479.410	−	348.312i	1.07491	−	0.780968i
$447$	696.955	+	110.387i	1.55918	+	0.246950i
$448$	18.6107	+	9.48262i	0.0415417	+	0.0211666i
$449$		−	43.4706i		−	0.0968165i	−0.998828	−	0.0484082i	$-0.984585\pi$
$449$		−	43.4706i		−	0.0968165i	0.998828	−	0.0484082i	$-0.0154148\pi$
$450$		0			0
$451$	−4.78093			−0.0106007
$452$	−109.801	+	215.497i	−0.242923	+	0.476764i
$453$	−85.9350	+	542.572i	−0.189702	+	1.19773i
$454$	−91.8038	−	126.357i	−0.202211	−	0.278320i
$455$		0			0
$456$	−44.6002	−	32.4040i	−0.0978075	−	0.0710613i
$457$	−181.132	−	181.132i	−0.396349	−	0.396349i	0.480594	−	0.876943i	$-0.340421\pi$
$457$	−181.132	−	181.132i	−0.396349	−	0.396349i	−0.876943	+	0.480594i	$0.840421\pi$
$458$	18.7176	−	2.96458i	0.0408682	−	0.00647288i
$459$	−591.249	−	192.108i	−1.28812	−	0.418537i
$460$		0			0
$461$	−64.2056	−	197.605i	−0.139275	−	0.428643i	0.856956	−	0.515390i	$-0.172353\pi$
$461$	−64.2056	−	197.605i	−0.139275	−	0.428643i	−0.996230	+	0.0867467i	$0.972353\pi$
$462$	−6.06756	+	3.09158i	−0.0131332	+	0.00669172i
$463$	−135.158	−	265.262i	−0.291917	−	0.572919i	0.697744	−	0.716347i	$-0.254187\pi$
$463$	−135.158	−	265.262i	−0.291917	−	0.572919i	−0.989661	+	0.143428i	$0.954187\pi$
$464$	183.218	−	59.5313i	0.394867	−	0.128300i
$465$		0			0
$466$	−132.775	+	408.640i	−0.284925	+	0.876910i
$467$	35.1679	+	222.042i	0.0753060	+	0.475464i	0.996304	+	0.0858964i	$0.0273754\pi$
$467$	35.1679	+	222.042i	0.0753060	+	0.475464i	−0.920998	+	0.389567i	$0.872625\pi$
$468$	44.8286	−	44.8286i	0.0957876	−	0.0957876i
$469$	95.0955	−	130.888i	0.202762	−	0.279078i
$470$		0			0
$471$	−328.354	+	238.563i	−0.697142	+	0.506504i
$472$	−218.827	−	34.6587i	−0.463616	−	0.0734295i
$473$	−13.8026	−	7.03277i	−0.0291810	−	0.0148684i
$474$			84.0608i			0.177343i
$475$		0			0
$476$	110.640			0.232437
$477$	76.5589	−	150.255i	0.160501	−	0.315001i
$478$	−63.4148	+	400.385i	−0.132667	+	0.837626i
$479$	135.106	+	185.957i	0.282058	+	0.388219i	0.926414	−	0.376506i	$-0.122875\pi$
$479$	135.106	+	185.957i	0.282058	+	0.388219i	−0.644356	+	0.764725i	$0.722875\pi$
$480$		0			0
$481$	179.195	+	130.193i	0.372546	+	0.270671i
$482$	59.4679	+	59.4679i	0.123377	+	0.123377i
$483$	−259.207	+	41.0544i	−0.536661	+	0.0849987i
$484$	−229.148	−	74.4547i	−0.473446	−	0.153832i
$485$		0			0
$486$	58.7824	+	180.914i	0.120951	+	0.372250i
$487$	−394.215	+	200.863i	−0.809477	+	0.412449i	−0.809187	−	0.587551i	$-0.800092\pi$
$487$	−394.215	+	200.863i	−0.809477	+	0.412449i	−0.000289730		1.00000i	$0.500092\pi$
$488$	83.4475	+	163.775i	0.170999	+	0.335604i
$489$	129.233	−	41.9903i	0.264280	−	0.0858696i
$490$		0			0
$491$	220.205	−	677.722i	0.448483	−	1.38029i	−0.430135	−	0.902764i	$-0.641534\pi$
$491$	220.205	−	677.722i	0.448483	−	1.38029i	0.878618	−	0.477524i	$-0.158466\pi$
$492$	5.20738	+	32.8781i	0.0105841	+	0.0668254i
$493$	721.569	−	721.569i	1.46363	−	1.46363i
$494$	78.5765	−	108.151i	0.159062	−	0.218930i
$495$		0			0
$496$	−126.486	+	91.8976i	−0.255012	+	0.185277i
$497$	−137.974	−	21.8529i	−0.277613	−	0.0439697i
$498$	165.431	+	84.2915i	0.332191	+	0.169260i
$499$		−	413.251i		−	0.828158i	−0.910241	−	0.414079i	$-0.864104\pi$
$499$		−	413.251i		−	0.828158i	0.910241	−	0.414079i	$-0.135896\pi$
$500$		0			0
$501$	669.973			1.33727
$502$	−83.9815	+	164.823i	−0.167294	+	0.328333i
$503$	39.0001	−	246.237i	0.0775350	−	0.489537i	−0.918111	−	0.396323i	$-0.870286\pi$
$503$	39.0001	−	246.237i	0.0775350	−	0.489537i	0.995646	−	0.0932137i	$-0.0297140\pi$
$504$	−11.1966	−	15.4108i	−0.0222154	−	0.0305769i
$505$		0			0
$506$	33.0342	+	24.0007i	0.0652849	+	0.0474322i
$507$	32.2243	+	32.2243i	0.0635587	+	0.0635587i
$508$	46.2563	−	7.32627i	0.0910557	−	0.0144218i
$509$	318.506	+	103.489i	0.625749	+	0.203318i	0.604691	−	0.796460i	$-0.293297\pi$
$509$	318.506	+	103.489i	0.625749	+	0.203318i	0.0210580	+	0.999778i	$0.493297\pi$
$510$		0			0
$511$	−27.4507	−	84.4844i	−0.0537195	−	0.165332i
$512$	−20.1612	+	10.2726i	−0.0393773	+	0.0200637i
$513$	102.464	+	201.096i	0.199734	+	0.392001i
$514$	−123.515	+	40.1325i	−0.240302	+	0.0780789i
$515$		0			0
$516$	−33.3301	+	102.580i	−0.0645932	+	0.198798i
$517$	−9.57014	−	60.4235i	−0.0185109	−	0.116873i
$518$	47.0598	−	47.0598i	0.0908490	−	0.0908490i
$519$	−61.4916	+	84.6359i	−0.118481	+	0.163075i
$520$		0			0
$521$	−208.409	+	151.418i	−0.400018	+	0.290630i	−0.769548	−	0.638589i	$-0.779519\pi$
$521$	−208.409	+	151.418i	−0.400018	+	0.290630i	0.369530	+	0.929219i	$0.379519\pi$
$522$	−173.527	−	27.4840i	−0.332428	−	0.0526514i
$523$	−689.071	−	351.099i	−1.31753	−	0.671317i	−0.353087	−	0.935591i	$-0.614868\pi$
$523$	−689.071	−	351.099i	−1.31753	−	0.671317i	−0.964448	+	0.264273i	$0.914868\pi$
$524$		−	217.274i		−	0.414644i
$525$		0			0
$526$	−221.371			−0.420857
$527$	−375.978	+	737.898i	−0.713430	+	1.40019i
$528$	1.15403	−	7.28629i	0.00218567	−	0.0137998i
$529$	614.011	+	845.113i	1.16070	+	1.59757i
$530$		0			0
$531$	163.464	+	118.764i	0.307842	+	0.223661i
$532$	−28.4025	−	28.4025i	−0.0533881	−	0.0533881i
$533$	−79.7262	+	12.6274i	−0.149580	+	0.0236912i
$534$	−512.344	−	166.471i	−0.959446	−	0.311743i
$535$		0			0
$536$	54.1598	+	166.687i	0.101044	+	0.310982i
$537$	326.186	−	166.200i	0.607424	−	0.309498i
$538$	−212.627	−	417.304i	−0.395217	−	0.775657i
$539$	29.2002	−	9.48773i	0.0541748	−	0.0176025i
$540$		0			0
$541$	19.0936	−	58.7641i	0.0352932	−	0.108621i	−0.931858	−	0.362823i	$-0.881813\pi$
$541$	19.0936	−	58.7641i	0.0352932	−	0.108621i	0.967151	+	0.254202i	$0.0818128\pi$
$542$	−41.5082	−	262.072i	−0.0765833	−	0.483528i
$543$	77.7356	−	77.7356i	0.143159	−	0.143159i
$544$	−70.4504	+	96.9667i	−0.129504	+	0.178248i
$545$		0			0
$546$	−93.0165	+	67.5804i	−0.170360	+	0.123774i
$547$	−84.3244	−	13.3557i	−0.154158	−	0.0244162i	0.0788784	−	0.996884i	$-0.474866\pi$
$547$	−84.3244	−	13.3557i	−0.154158	−	0.0244162i	−0.233036	+	0.972468i	$0.574866\pi$
$548$	28.5570	+	14.5505i	0.0521113	+	0.0265520i
$549$		−	167.630i		−	0.305337i
$550$		0			0
$551$	−370.469			−0.672357
$552$	129.070	−	253.315i	0.233823	−	0.458904i
$553$	−9.58114	+	60.4930i	−0.0173258	+	0.109391i
$554$	−233.322	−	321.140i	−0.421159	−	0.579675i
$555$		0			0
$556$	−323.404	−	234.967i	−0.581662	−	0.422602i
$557$	−59.2331	−	59.2331i	−0.106343	−	0.106343i	0.651933	−	0.758276i	$-0.273958\pi$
$557$	−59.2331	−	59.2331i	−0.106343	−	0.106343i	−0.758276	+	0.651933i	$0.773958\pi$
$558$	140.828	−	22.3050i	0.252381	−	0.0399732i
$559$	−248.745	−	80.8223i	−0.444983	−	0.144584i
$560$		0			0
$561$	−12.0753	−	37.1640i	−0.0215246	−	0.0662460i
$562$	−395.338	+	201.435i	−0.703449	+	0.358425i
$563$	129.457	+	254.074i	0.229942	+	0.451286i	0.976933	−	0.213548i	$-0.0685021\pi$
$563$	129.457	+	254.074i	0.229942	+	0.451286i	−0.746991	+	0.664834i	$0.768502\pi$
$564$	−405.104	+	131.626i	−0.718270	+	0.233380i
$565$		0			0
$566$	−41.2973	+	127.100i	−0.0729634	+	0.224558i
$567$	−20.8838	−	131.855i	−0.0368321	−	0.232549i
$568$	107.008	−	107.008i	0.188394	−	0.188394i
$569$	−139.865	+	192.508i	−0.245809	+	0.338327i	−0.914038	−	0.405629i	$-0.867053\pi$
$569$	−139.865	+	192.508i	−0.245809	+	0.338327i	0.668229	+	0.743955i	$0.267053\pi$
$570$		0			0
$571$	774.265	−	562.537i	1.35598	−	0.985178i	0.357292	−	0.933993i	$-0.383700\pi$
$571$	774.265	−	562.537i	1.35598	−	0.985178i	0.998689	−	0.0511852i	$-0.0162999\pi$
$572$	17.6685	+	2.79842i	0.0308891	+	0.00489235i
$573$	−356.035	−	181.409i	−0.621353	−	0.316595i
$574$			24.2537i			0.0422539i
$575$		0			0
$576$	20.6357			0.0358259
$577$	458.043	−	898.960i	0.793836	−	1.55799i	−0.0355856	−	0.999367i	$-0.511330\pi$
$577$	458.043	−	898.960i	0.793836	−	1.55799i	0.829421	−	0.558624i	$-0.188670\pi$
$578$	−35.3819	+	223.393i	−0.0612144	+	0.386492i
$579$	−160.244	−	220.557i	−0.276760	−	0.380928i
$580$		0			0
$581$	109.442	+	79.5146i	0.188369	+	0.136858i
$582$	−161.692	−	161.692i	−0.277821	−	0.277821i
$583$	46.9981	−	7.44376i	0.0806142	−	0.0127680i
$584$	91.5229	+	29.7376i	0.156717	+	0.0509205i
$585$		0			0
$586$	61.8790	+	190.444i	0.105596	+	0.324990i
$587$	6.40101	−	3.26148i	0.0109046	−	0.00555618i	−0.448530	−	0.893768i	$-0.648052\pi$
$587$	6.40101	−	3.26148i	0.0109046	−	0.00555618i	0.459434	+	0.888212i	$0.348052\pi$
$588$	−97.0513	−	190.474i	−0.165053	−	0.323935i
$589$	285.944	−	92.9088i	0.485473	−	0.157740i
$590$		0			0
$591$	−29.8675	+	91.9228i	−0.0505373	+	0.155538i
$592$	11.2785	+	71.2095i	0.0190515	+	0.120286i
$593$	−161.092	+	161.092i	−0.271655	+	0.271655i	−0.829766	−	0.558111i	$-0.811526\pi$
$593$	−161.092	+	161.092i	−0.271655	+	0.271655i	0.558111	+	0.829766i	$0.311526\pi$
$594$	−17.7521	+	24.4336i	−0.0298856	+	0.0411340i
$595$		0			0
$596$	−450.596	+	327.377i	−0.756033	+	0.549290i
$597$	−504.301	−	79.8735i	−0.844726	−	0.133791i
$598$	614.264	+	312.983i	1.02720	+	0.523384i
$599$			1018.75i			1.70076i	0.526173	+	0.850378i	$0.323627\pi$
$599$			1018.75i			1.70076i	−0.526173	+	0.850378i	$0.676373\pi$
$600$		0			0
$601$	56.8591			0.0946075			0.0473038	−	0.998881i	$-0.484937\pi$
$601$	56.8591			0.0946075			0.0473038	+	0.998881i	$0.484937\pi$
$602$	−35.6773	+	70.0207i	−0.0592647	+	0.116314i
$603$	25.0041	−	157.870i	0.0414662	−	0.261807i
$604$	−254.859	−	350.784i	−0.421953	−	0.580768i
$605$		0			0
$606$	−174.010	−	126.426i	−0.287145	−	0.208623i
$607$	171.454	+	171.454i	0.282462	+	0.282462i	0.834090	−	0.551628i	$-0.185993\pi$
$607$	171.454	+	171.454i	0.282462	+	0.282462i	−0.551628	+	0.834090i	$0.685993\pi$
$608$	42.9778	−	6.80701i	0.0706871	−	0.0111957i
$609$	303.031	+	98.4606i	0.497587	+	0.161676i
$610$		0			0
$611$	−319.181	−	982.338i	−0.522391	−	1.60776i
$612$	97.3937	−	49.6246i	0.159140	−	0.0810859i
$613$	−274.017	−	537.789i	−0.447010	−	0.877307i	−0.999054	−	0.0434918i	$-0.986152\pi$
$613$	−274.017	−	537.789i	−0.447010	−	0.877307i	0.552043	−	0.833815i	$-0.313848\pi$
$614$	−510.554	+	165.889i	−0.831521	+	0.270177i
$615$		0			0
$616$	1.66096	−	5.11192i	0.00269637	−	0.00829857i
$617$	21.8733	+	138.102i	0.0354510	+	0.223829i	0.999053	−	0.0435126i	$-0.0138549\pi$
$617$	21.8733	+	138.102i	0.0354510	+	0.223829i	−0.963602	+	0.267341i	$0.913855\pi$
$618$	−94.9007	+	94.9007i	−0.153561	+	0.153561i
$619$	97.5904	−	134.322i	0.157658	−	0.216998i	−0.722879	−	0.690974i	$-0.757182\pi$
$619$	97.5904	−	134.322i	0.157658	−	0.216998i	0.880538	+	0.473976i	$0.157182\pi$
$620$		0			0
$621$	−941.632	+	684.136i	−1.51632	+	1.10167i
$622$	−111.707	−	17.6926i	−0.179593	−	0.0284447i
$623$	−349.726	−	178.194i	−0.561358	−	0.286026i
$624$		−	124.553i		−	0.199605i
$625$		0			0
$626$	−235.332			−0.375930
$627$	−6.44054	+	12.6403i	−0.0102720	+	0.0201599i
$628$	50.1143	−	316.409i	0.0797998	−	0.503836i
$629$	224.474	+	308.962i	0.356875	+	0.491196i
$630$		0			0
$631$	−583.662	−	424.055i	−0.924979	−	0.672037i	0.0197794	−	0.999804i	$-0.493704\pi$
$631$	−583.662	−	424.055i	−0.924979	−	0.672037i	−0.944758	+	0.327768i	$0.893704\pi$
$632$	−46.9162	−	46.9162i	−0.0742345	−	0.0742345i
$633$	−54.9873	+	8.70913i	−0.0868677	+	0.0137585i
$634$	648.410	+	210.681i	1.02273	+	0.332305i
$635$		0			0
$636$	−102.380	−	315.095i	−0.160975	−	0.495432i
$637$	461.881	−	235.340i	0.725087	−	0.369451i
$638$	−22.5064	−	44.1712i	−0.0352764	−	0.0692339i
$639$	−131.257	+	42.6479i	−0.205410	+	0.0667416i
$640$		0			0
$641$	295.691	−	910.042i	0.461296	−	1.41972i	−0.402286	−	0.915514i	$-0.631784\pi$
$641$	295.691	−	910.042i	0.461296	−	1.41972i	0.863582	−	0.504209i	$-0.168216\pi$
$642$	7.50541	+	47.3873i	0.0116907	+	0.0738120i
$643$	−47.9432	+	47.9432i	−0.0745618	+	0.0745618i	−0.743404	−	0.668842i	$-0.766790\pi$
$643$	−47.9432	+	47.9432i	−0.0745618	+	0.0745618i	0.668842	+	0.743404i	$0.266790\pi$
$644$	121.756	−	167.583i	0.189062	−	0.260222i
$645$		0			0
$646$	186.471	−	135.479i	0.288655	−	0.209720i
$647$	979.858	+	155.194i	1.51446	+	0.239867i	0.857669	−	0.514203i	$-0.171912\pi$
$647$	979.858	+	155.194i	1.51446	+	0.239867i	0.656794	+	0.754070i	$0.271912\pi$
$648$	128.858	+	65.6564i	0.198855	+	0.101322i
$649$			57.0133i			0.0878479i
$650$		0			0
$651$	−258.585			−0.397211
$652$	−48.6920	+	95.5634i	−0.0746810	+	0.146570i
$653$	47.8858	−	302.339i	0.0733320	−	0.463000i	−0.923509	−	0.383577i	$-0.874692\pi$
$653$	47.8858	−	302.339i	0.0733320	−	0.463000i	0.996841	−	0.0794232i	$-0.0253078\pi$
$654$	354.100	+	487.377i	0.541438	+	0.745225i
$655$		0			0
$656$	−21.2564	−	15.4437i	−0.0324030	−	0.0235422i
$657$	−62.0574	−	62.0574i	−0.0944557	−	0.0944557i
$658$	−306.529	+	48.5494i	−0.465850	+	0.0737833i
$659$	535.335	+	173.941i	0.812345	+	0.263947i	0.685591	−	0.727987i	$-0.259544\pi$
$659$	535.335	+	173.941i	0.812345	+	0.263947i	0.126754	+	0.991934i	$0.459544\pi$
$660$		0			0
$661$	357.954	+	1101.67i	0.541534	+	1.66667i	0.729092	+	0.684415i	$0.239943\pi$
$661$	357.954	+	1101.67i	0.541534	+	1.66667i	−0.187559	+	0.982253i	$0.560057\pi$
$662$	−341.504	+	174.005i	−0.515866	+	0.262847i
$663$	−299.524	−	587.850i	−0.451771	−	0.886651i
$664$	−139.376	+	45.2860i	−0.209903	+	0.0682018i
$665$		0			0
$666$	20.3182	−	62.5330i	0.0305078	−	0.0938934i
$667$	−298.872	−	1887.00i	−0.448083	−	2.82909i
$668$	−373.927	+	373.927i	−0.559771	+	0.559771i
$669$	−624.077	+	858.969i	−0.932851	+	1.28396i
$670$		0			0
$671$	38.2666	−	27.8023i	0.0570292	−	0.0414342i
$672$	−36.9634	−	5.85443i	−0.0550051	−	0.00871195i
$673$	−36.9443	−	18.8241i	−0.0548950	−	0.0279704i	0.426328	−	0.904569i	$-0.359807\pi$
$673$	−36.9443	−	18.8241i	−0.0548950	−	0.0279704i	−0.481223	+	0.876598i	$0.659807\pi$
$674$			561.161i			0.832583i
$675$		0			0
$676$	−35.9702			−0.0532103
$677$	109.815	−	215.524i	0.162209	−	0.318352i	−0.795569	−	0.605863i	$-0.792828\pi$
$677$	109.815	−	215.524i	0.162209	−	0.318352i	0.957777	+	0.287511i	$0.0928278\pi$
$678$	67.7897	−	428.007i	0.0999848	−	0.631279i
$679$	−97.9293	−	134.788i	−0.144226	−	0.198510i
$680$		0			0
$681$	226.397	+	164.487i	0.332447	+	0.241537i
$682$	28.4490	+	28.4490i	0.0417140	+	0.0417140i
$683$	−1069.27	+	169.356i	−1.56555	+	0.247959i	−0.878174	−	0.478341i	$-0.841238\pi$
$683$	−1069.27	+	169.356i	−1.56555	+	0.247959i	−0.687377	+	0.726300i	$0.741238\pi$
$684$	−37.7412	−	12.2629i	−0.0551772	−	0.0179281i
$685$		0			0
$686$	−104.041	−	320.205i	−0.151663	−	0.466771i
$687$	−30.2539	+	15.4152i	−0.0440378	+	0.0224384i
$688$	−38.6497	−	75.8542i	−0.0561768	−	0.110253i
$689$	764.074	−	248.263i	1.10896	−	0.360323i
$690$		0			0
$691$	−60.8202	+	187.185i	−0.0880177	+	0.270891i	−0.985371	−	0.170422i	$-0.945487\pi$
$691$	−60.8202	+	187.185i	−0.0880177	+	0.270891i	0.897353	+	0.441313i	$0.145487\pi$
$692$	−12.9174	−	81.5570i	−0.0186667	−	0.117857i
$693$	−3.46615	+	3.46615i	−0.00500167	+	0.00500167i
$694$	−99.3339	+	136.721i	−0.143132	+	0.197005i
$695$		0			0
$696$	−279.249	+	202.886i	−0.401219	+	0.291503i
$697$	−137.462	−	21.7718i	−0.197219	−	0.0312364i
$698$	356.010	+	181.396i	0.510043	+	0.259880i
$699$		−	769.849i		−	1.10136i
$700$		0			0
$701$	179.635			0.256255			0.128127	−	0.991758i	$-0.459103\pi$
$701$	179.635			0.256255			0.128127	+	0.991758i	$0.459103\pi$
$702$	−231.497	+	454.339i	−0.329768	+	0.647206i
$703$	21.6890	−	136.939i	0.0308521	−	0.194792i
$704$	3.42255	+	4.71073i	0.00486157	+	0.00669138i
$705$		0			0
$706$	−465.569	−	338.255i	−0.659446	−	0.479115i
$707$	−110.814	−	110.814i	−0.156738	−	0.156738i
$708$	392.076	−	62.0988i	0.553780	−	0.0877101i
$709$	65.4964	+	21.2811i	0.0923785	+	0.0300156i	0.354842	−	0.934926i	$-0.384535\pi$
$709$	65.4964	+	21.2811i	0.0923785	+	0.0300156i	−0.262463	+	0.964942i	$0.584535\pi$
$710$		0			0
$711$	18.6984	+	57.5479i	0.0262988	+	0.0809394i
$712$	378.862	−	193.040i	0.532109	−	0.271123i
$713$	703.918	+	1381.52i	0.987262	+	1.93761i
$714$	−188.534	+	61.2583i	−0.264053	+	0.0857959i
$715$		0			0
$716$	−89.2919	+	274.812i	−0.124709	+	0.383816i
$717$	−113.622	−	717.379i	−0.158468	−	1.00053i
$718$	−567.178	+	567.178i	−0.789941	+	0.789941i
$719$	−666.444	+	917.282i	−0.926904	+	1.27577i	0.0341503	+	0.999417i	$0.489128\pi$
$719$	−666.444	+	917.282i	−0.926904	+	1.27577i	−0.961055	+	0.276358i	$0.910872\pi$
$720$		0			0
$721$	−79.1103	+	57.4770i	−0.109723	+	0.0797185i
$722$	421.597	+	66.7745i	0.583930	+	0.0924854i
$723$	−134.261	−	68.4092i	−0.185699	−	0.0946186i
$724$			86.7719i			0.119851i
$725$		0			0
$726$	431.698			0.594626
$727$	−322.113	+	632.182i	−0.443071	+	0.869577i	0.556186	+	0.831058i	$0.312264\pi$
$727$	−322.113	+	632.182i	−0.443071	+	0.869577i	−0.999258	+	0.0385192i	$0.987736\pi$
$728$	14.1964	−	89.6327i	0.0195006	−	0.123122i
$729$	−470.821	−	648.029i	−0.645845	−	0.888929i
$730$		0			0
$731$	−364.827	−	265.062i	−0.499079	−	0.362602i
$732$	−232.875	−	232.875i	−0.318135	−	0.318135i
$733$	−971.877	+	153.930i	−1.32589	+	0.210000i	−0.778905	−	0.627142i	$-0.784225\pi$
$733$	−971.877	+	153.930i	−1.32589	+	0.210000i	−0.546985	+	0.837142i	$0.684225\pi$
$734$	539.799	+	175.391i	0.735422	+	0.238953i
$735$		0			0
$736$	69.3437	+	213.418i	0.0942170	+	0.289970i
$737$	40.1857	−	20.4756i	0.0545260	−	0.0277824i
$738$	10.8784	+	21.3500i	0.0147403	+	0.0289295i
$739$	−1239.16	+	402.628i	−1.67681	+	0.544828i	−0.984288	−	0.176571i	$-0.943500\pi$
$739$	−1239.16	+	402.628i	−1.67681	+	0.544828i	−0.692520	+	0.721399i	$0.743500\pi$
$740$		0			0
$741$	−74.0162	+	227.798i	−0.0998869	+	0.307420i
$742$	−37.7623	−	238.422i	−0.0508926	−	0.321323i
$743$	314.184	−	314.184i	0.422859	−	0.422859i	−0.463328	−	0.886187i	$-0.653345\pi$
$743$	314.184	−	314.184i	0.422859	−	0.422859i	0.886187	+	0.463328i	$0.153345\pi$
$744$	164.655	−	226.628i	0.221310	−	0.304608i
$745$		0			0
$746$	471.958	−	342.898i	0.632652	−	0.459649i
$747$	132.004	+	20.9073i	0.176712	+	0.0279884i
$748$	27.4816	+	14.0026i	0.0367401	+	0.0187200i
$749$			34.9569i			0.0466715i
$750$		0			0
$751$	87.3707			0.116339			0.0581696	−	0.998307i	$-0.481474\pi$
$751$	87.3707			0.116339			0.0581696	+	0.998307i	$0.481474\pi$
$752$	152.634	−	299.561i	0.202971	−	0.398353i
$753$	51.8489	−	327.361i	0.0688565	−	0.434743i
$754$	−491.979	−	677.151i	−0.652492	−	0.898078i
$755$		0			0
$756$	123.952	+	90.0564i	0.163958	+	0.119122i
$757$	436.322	+	436.322i	0.576382	+	0.576382i	0.933905	−	0.357522i	$-0.116378\pi$
$757$	436.322	+	436.322i	0.576382	+	0.576382i	−0.357522	+	0.933905i	$0.616378\pi$
$758$	−163.508	+	25.8971i	−0.215710	+	0.0341651i
$759$	−69.5797	−	22.6078i	−0.0916728	−	0.0297863i
$760$		0			0
$761$	328.146	+	1009.93i	0.431203	+	1.32711i	0.896928	+	0.442177i	$0.145794\pi$
$761$	328.146	+	1009.93i	0.431203	+	1.32711i	−0.465724	+	0.884930i	$0.654206\pi$
$762$	−74.7656	+	38.0950i	−0.0981176	+	0.0499934i
$763$	199.272	+	391.093i	0.261169	+	0.512573i
$764$	299.960	−	97.4628i	0.392617	−	0.127569i
$765$		0			0
$766$	40.0180	−	123.163i	0.0522428	−	0.160787i
$767$	150.584	+	950.747i	0.196328	+	1.23957i
$768$	28.6675	−	28.6675i	0.0373275	−	0.0373275i
$769$	495.875	−	682.513i	0.644831	−	0.887534i	−0.354031	−	0.935234i	$-0.615189\pi$
$769$	495.875	−	682.513i	0.644831	−	0.887534i	0.998862	+	0.0477002i	$0.0151892\pi$
$770$		0			0
$771$	188.253	−	136.774i	0.244168	−	0.177398i
$772$	212.534	+	33.6620i	0.275303	+	0.0436037i
$773$	497.779	+	253.631i	0.643958	+	0.328113i	0.745291	−	0.666740i	$-0.232311\pi$
$773$	497.779	+	253.631i	0.643958	+	0.328113i	−0.101333	+	0.994853i	$0.532311\pi$
$774$			77.6397i			0.100310i
$775$		0			0
$776$	180.488			0.232587
$777$	−54.1355	+	106.247i	−0.0696724	+	0.136740i
$778$	−47.9695	+	302.868i	−0.0616575	+	0.389290i
$779$	29.6988	+	40.8769i	0.0381243	+	0.0524736i
$780$		0			0
$781$	−31.5053	−	22.8899i	−0.0403397	−	0.0293085i
$782$	840.504	+	840.504i	1.07481	+	1.07481i
$783$	1395.72	−	221.060i	1.78252	−	0.282324i
$784$	160.474	+	52.1412i	0.204687	+	0.0665067i
$785$		0			0
$786$	120.298	+	370.240i	0.153051	+	0.471044i
$787$	−479.262	+	244.196i	−0.608973	+	0.310287i	−0.731146	−	0.682221i	$-0.761014\pi$
$787$	−479.262	+	244.196i	−0.608973	+	0.310287i	0.122172	+	0.992509i	$0.461014\pi$
$788$	−34.6344	−	67.9739i	−0.0439523	−	0.0862613i
$789$	377.222	−	122.567i	0.478102	−	0.155345i
$790$		0			0
$791$	97.5674	−	300.282i	0.123347	−	0.379623i
$792$	−0.830708	−	5.24489i	−0.00104887	−	0.00662233i
$793$	564.698	−	564.698i	0.712104	−	0.712104i
$794$	−113.126	+	155.705i	−0.142476	+	0.196102i
$795$		0			0
$796$	326.041	−	236.883i	0.409599	−	0.297591i
$797$	−1006.27	−	159.378i	−1.26258	−	0.199972i	−0.510978	−	0.859594i	$-0.670717\pi$
$797$	−1006.27	−	159.378i	−1.26258	−	0.199972i	−0.751598	+	0.659622i	$0.770717\pi$
$798$	64.1242	+	32.6729i	0.0803562	+	0.0409435i
$799$		−	1780.88i		−	2.22889i
$800$		0			0
$801$	−387.780			−0.484119
$802$	−15.3010	+	30.0299i	−0.0190786	+	0.0374438i
$803$	3.87393	−	24.4590i	0.00482432	−	0.0304596i
$804$	−184.580	−	254.052i	−0.229577	−	0.315985i
$805$		0			0
$806$	549.551	+	399.272i	0.681825	+	0.495375i
$807$	593.372	+	593.372i	0.735281	+	0.735281i
$808$	167.680	−	26.5579i	0.207525	−	0.0328687i
$809$	509.810	+	165.647i	0.630173	+	0.204756i	0.606652	−	0.794968i	$-0.292512\pi$
$809$	509.810	+	165.647i	0.630173	+	0.204756i	0.0235211	+	0.999723i	$0.492512\pi$
$810$		0			0
$811$	−337.483	−	1038.67i	−0.416132	−	1.28072i	−0.911234	−	0.411889i	$-0.864869\pi$
$811$	−337.483	−	1038.67i	−0.416132	−	1.28072i	0.495102	−	0.868835i	$-0.335131\pi$
$812$	−224.081	+	114.175i	−0.275962	+	0.140610i
$813$	215.833	+	423.596i	0.265477	+	0.521029i
$814$	17.6449	−	5.73319i	0.0216768	−	0.00704323i
$815$		0			0
$816$	66.3618	−	204.240i	0.0813257	−	0.250295i
$817$	25.6106	+	161.699i	0.0313472	+	0.197918i
$818$	−302.022	+	302.022i	−0.369220	+	0.369220i
$819$	−48.6464	+	66.9560i	−0.0593973	+	0.0817534i
$820$		0			0
$821$	−353.280	+	256.673i	−0.430304	+	0.312634i	−0.781770	−	0.623566i	$-0.785683\pi$
$821$	−353.280	+	256.673i	−0.430304	+	0.312634i	0.351466	+	0.936200i	$0.385683\pi$
$822$	−56.7181	−	8.98326i	−0.0690001	−	0.0109285i
$823$	302.881	+	154.326i	0.368021	+	0.187516i	0.628214	−	0.778041i	$-0.283786\pi$
$823$	302.881	+	154.326i	0.368021	+	0.187516i	−0.260193	+	0.965557i	$0.583786\pi$
$824$		−	105.932i		−	0.128559i
$825$		0			0
$826$	289.229			0.350156
$827$	−599.324	+	1176.24i	−0.724696	+	1.42230i	0.174458	+	0.984665i	$0.444183\pi$
$827$	−599.324	+	1176.24i	−0.724696	+	1.42230i	−0.899154	+	0.437632i	$0.855817\pi$
$828$	32.0142	−	202.129i	0.0386645	−	0.244118i
$829$	−94.2063	−	129.664i	−0.113638	−	0.156410i	0.748409	−	0.663238i	$-0.230818\pi$
$829$	−94.2063	−	129.664i	−0.113638	−	0.156410i	−0.862047	+	0.506828i	$0.830818\pi$
$830$		0			0
$831$	575.393	+	418.048i	0.692411	+	0.503066i
$832$	69.5160	+	69.5160i	0.0835529	+	0.0835529i
$833$	882.773	−	139.817i	1.05975	−	0.167848i
$834$	681.185	+	221.330i	0.816768	+	0.265384i
$835$		0			0
$836$	−3.46021	−	10.6494i	−0.00413901	−	0.0127386i
$837$	−1021.83	+	520.650i	−1.22083	+	0.622044i
$838$	−436.999	−	857.658i	−0.521478	−	1.02346i
$839$	−556.528	+	180.827i	−0.663323	+	0.215527i	−0.621279	−	0.783589i	$-0.713387\pi$
$839$	−556.528	+	180.827i	−0.663323	+	0.215527i	−0.0420436	+	0.999116i	$0.513387\pi$
$840$		0			0
$841$	−456.900	+	1406.19i	−0.543282	+	1.67205i
$842$	−59.7518	−	377.258i	−0.0709642	−	0.448050i
$843$	562.139	−	562.139i	0.666831	−	0.666831i
$844$	25.8289	−	35.5504i	0.0306029	−	0.0421213i
$845$		0			0
$846$	−248.055	+	180.222i	−0.293209	+	0.213029i
$847$	310.664	+	49.2044i	0.366782	+	0.0580926i
$848$	233.002	+	118.721i	0.274767	+	0.140001i
$849$		−	239.447i		−	0.282034i
$850$		0			0
$851$	715.002			0.840191
$852$	−123.097	+	241.591i	−0.144480	+	0.283558i
$853$	−116.308	+	734.339i	−0.136352	+	0.860890i	0.820782	+	0.571242i	$0.193538\pi$
$853$	−116.308	+	734.339i	−0.136352	+	0.860890i	−0.957133	+	0.289648i	$0.906462\pi$
$854$	−141.042	−	194.127i	−0.165154	−	0.227315i
$855$		0			0
$856$	−30.6368	−	22.2590i	−0.0357907	−	0.0260035i
$857$	818.405	+	818.405i	0.954964	+	0.954964i	0.999029	−	0.0440643i	$-0.0140306\pi$
$857$	818.405	+	818.405i	0.954964	+	0.954964i	−0.0440643	+	0.999029i	$0.514031\pi$
$858$	−31.6571	+	5.01399i	−0.0368964	+	0.00584382i
$859$	749.275	+	243.454i	0.872264	+	0.283416i	0.710742	−	0.703453i	$-0.248359\pi$
$859$	749.275	+	243.454i	0.872264	+	0.283416i	0.161523	+	0.986869i	$0.448359\pi$
$860$		0			0
$861$	−13.4286	−	41.3290i	−0.0155965	−	0.0480012i
$862$	1041.73	−	530.789i	1.20851	−	0.615764i
$863$	478.974	+	940.039i	0.555010	+	1.08927i	0.982676	+	0.185332i	$0.0593361\pi$
$863$	478.974	+	940.039i	0.555010	+	1.08927i	−0.427666	+	0.903937i	$0.640664\pi$
$864$	−157.854	+	51.2899i	−0.182701	+	0.0593633i
$865$		0			0
$866$	318.382	−	979.880i	0.367647	−	1.13150i
$867$	−63.3945	−	400.257i	−0.0731194	−	0.461658i
$868$	144.322	−	144.322i	0.166269	−	0.166269i
$869$	−10.0358	+	13.8131i	−0.0115487	+	0.0158954i
$870$		0			0
$871$	616.051	−	447.587i	0.707292	−	0.513878i
$872$	−469.648	−	74.3849i	−0.538587	−	0.0853038i
$873$	−146.661	−	74.7273i	−0.167996	−	0.0855982i
$874$		−	431.533i		−	0.493744i
$875$		0			0
$876$	−172.423			−0.196829
$877$	−309.296	+	607.027i	−0.352674	+	0.692163i	−0.997386	−	0.0722637i	$-0.976978\pi$
$877$	−309.296	+	607.027i	−0.352674	+	0.692163i	0.644711	+	0.764426i	$0.276978\pi$
$878$	109.877	−	693.739i	0.125145	−	0.790135i
$879$	−210.887	−	290.261i	−0.239917	−	0.330217i
$880$		0			0
$881$	−1031.43	−	749.378i	−1.17075	−	0.850599i	−0.179651	−	0.983730i	$-0.557497\pi$
$881$	−1031.43	−	749.378i	−1.17075	−	0.850599i	−0.991098	+	0.133131i	$0.957497\pi$
$882$	−108.810	−	108.810i	−0.123367	−	0.123367i
$883$	−1008.24	+	159.690i	−1.14184	+	0.180849i	−0.698571	−	0.715541i	$-0.746180\pi$
$883$	−1008.24	+	159.690i	−1.14184	+	0.180849i	−0.443266	+	0.896390i	$0.646180\pi$
$884$	495.263	+	160.921i	0.560253	+	0.182037i
$885$		0			0
$886$	227.229	+	699.338i	0.256466	+	0.789320i
$887$	47.4677	−	24.1860i	0.0535149	−	0.0272672i	−0.427028	−	0.904238i	$-0.640440\pi$
$887$	47.4677	−	24.1860i	0.0535149	−	0.0272672i	0.480543	+	0.876971i	$0.340440\pi$
$888$	−58.6456	−	115.098i	−0.0660423	−	0.129615i
$889$	−58.1459	+	18.8927i	−0.0654059	+	0.0212517i
$890$		0			0
$891$	11.5003	−	35.3942i	0.0129072	−	0.0397242i
$892$	−131.098	−	827.722i	−0.146971	−	0.927939i
$893$	−457.171	+	457.171i	−0.511950	+	0.511950i
$894$	586.568	−	807.342i	0.656116	−	0.903067i
$895$		0			0
$896$	23.8976	−	17.3626i	0.0266714	−	0.0193779i
$897$	−1220.01	−	193.231i	−1.36011	−	0.215420i
$898$	−54.7762	−	27.9098i	−0.0609980	−	0.0310800i
$899$		−	1882.47i		−	2.09396i
$900$		0			0
$901$	1385.19			1.53739
$902$	−3.06955	+	6.02432i	−0.00340304	+	0.00667885i
$903$	22.0267	−	139.071i	0.0243928	−	0.154010i
$904$	201.046	+	276.715i	0.222395	+	0.306101i
$905$		0			0
$906$	628.507	+	456.637i	0.693717	+	0.504015i
$907$	−545.754	−	545.754i	−0.601714	−	0.601714i	0.339053	−	0.940767i	$-0.389893\pi$
$907$	−545.754	−	545.754i	−0.601714	−	0.601714i	−0.940767	+	0.339053i	$0.889893\pi$
$908$	−218.161	+	34.5533i	−0.240265	+	0.0380543i
$909$	−147.249	−	47.8441i	−0.161990	−	0.0526338i
$910$		0			0
$911$	286.195	+	880.816i	0.314154	+	0.966868i	0.976101	+	0.217317i	$0.0697305\pi$
$911$	286.195	+	880.816i	0.314154	+	0.966868i	−0.661947	+	0.749551i	$0.730270\pi$
$912$	−69.4665	+	35.3950i	−0.0761694	+	0.0388103i
$913$	17.1208	+	33.6015i	0.0187522	+	0.0368033i
$914$	−344.533	+	111.945i	−0.376951	+	0.122479i
$915$		0			0
$916$	8.28186	−	25.4889i	0.00904133	−	0.0278264i
$917$	44.3712	+	280.149i	0.0483873	+	0.305506i
$918$	−621.676	+	621.676i	−0.677207	+	0.677207i
$919$	−921.461	+	1268.28i	−1.00268	+	1.38007i	−0.0790096	+	0.996874i	$0.525176\pi$
$919$	−921.461	+	1268.28i	−1.00268	+	1.38007i	−0.923668	+	0.383194i	$0.874824\pi$
$920$		0			0
$921$	778.150	−	565.359i	0.844897	−	0.613854i
$922$	−290.219	−	45.9661i	−0.314771	−	0.0498548i
$923$	−585.836	−	298.498i	−0.634708	−	0.323400i
$924$			9.63049i			0.0104226i
$925$		0			0
$926$	−421.025			−0.454671
$927$	−43.8592	+	86.0785i	−0.0473131	+	0.0928571i
$928$	42.6197	−	269.090i	0.0459264	−	0.289968i
$929$	166.174	+	228.719i	0.178874	+	0.246199i	0.889034	−	0.457842i	$-0.151377\pi$
$929$	166.174	+	228.719i	0.178874	+	0.246199i	−0.710160	+	0.704041i	$0.751377\pi$
$930$		0			0
$931$	−262.510	−	190.725i	−0.281966	−	0.204860i
$932$	429.670	+	429.670i	0.461019	+	0.461019i
$933$	200.147	−	31.7002i	0.214520	−	0.0339766i
$934$	302.368	+	98.2453i	0.323734	+	0.105188i
$935$		0			0
$936$	−27.7056	−	85.2690i	−0.0296000	−	0.0910994i
$937$	1611.51	−	821.106i	1.71986	−	0.876314i	0.741079	−	0.671418i	$-0.234315\pi$
$937$	1611.51	−	821.106i	1.71986	−	0.876314i	0.978784	−	0.204895i	$-0.0656854\pi$
$938$	−103.873	−	203.862i	−0.110739	−	0.217337i
$939$	401.013	−	130.297i	0.427064	−	0.138762i
$940$		0			0
$941$	364.832	−	1122.84i	0.387707	−	1.19324i	−0.546790	−	0.837270i	$-0.684150\pi$
$941$	364.832	−	1122.84i	0.387707	−	1.19324i	0.934497	−	0.355970i	$-0.115850\pi$
$942$	89.7909	+	566.917i	0.0953194	+	0.601823i
$943$	−184.249	+	184.249i	−0.195386	+	0.195386i
$944$	−184.168	+	253.485i	−0.195093	+	0.268523i
$945$		0			0
$946$	−17.7236	+	12.8770i	−0.0187353	+	0.0136120i
$947$	1291.80	+	204.601i	1.36410	+	0.216052i	0.795195	−	0.606354i	$-0.207368\pi$
$947$	1291.80	+	204.601i	1.36410	+	0.216052i	0.568902	+	0.822405i	$0.307368\pi$
$948$	105.923	+	53.9704i	0.111733	+	0.0569308i
$949$		−	418.108i		−	0.440577i
$950$		0			0
$951$	−1221.56			−1.28450
$952$	71.0352	−	139.414i	0.0746168	−	0.146444i
$953$	−186.161	+	1175.37i	−0.195342	+	1.23334i	0.673850	+	0.738868i	$0.264639\pi$
$953$	−186.161	+	1175.37i	−0.195342	+	1.23334i	−0.869192	+	0.494474i	$0.835361\pi$
$954$	−140.179	−	192.940i	−0.146938	−	0.202243i
$955$		0			0
$956$	463.800	+	336.971i	0.485147	+	0.352480i
$957$	62.8079	+	62.8079i	0.0656300	+	0.0656300i
$958$	321.063	−	50.8513i	0.335138	−	0.0530807i
$959$	−39.7923	−	12.9293i	−0.0414936	−	0.0134821i
$960$		0			0
$961$	175.134	+	539.006i	0.182241	+	0.560881i
$962$	279.102	−	142.210i	0.290127	−	0.147827i
$963$	15.6790	+	30.7718i	0.0162814	+	0.0319541i
$964$	113.115	−	36.7532i	0.117339	−	0.0381257i
$965$		0			0
$966$	−114.690	+	352.978i	−0.118726	+	0.365402i
$967$	−65.5712	−	414.000i	−0.0678089	−	0.428129i	−0.998116	−	0.0613481i	$-0.980460\pi$
$967$	−65.5712	−	414.000i	−0.0678089	−	0.428129i	0.930308	−	0.366780i	$-0.119540\pi$
$968$	−240.940	+	240.940i	−0.248905	+	0.248905i
$969$	−242.741	+	334.104i	−0.250507	+	0.344793i
$970$		0			0
$971$	−878.393	+	638.190i	−0.904627	+	0.657250i	−0.939650	−	0.342136i	$-0.888850\pi$
$971$	−878.393	+	638.190i	−0.904627	+	0.657250i	0.0350230	+	0.999387i	$0.488850\pi$
$972$	265.705	+	42.0835i	0.273359	+	0.0432958i
$973$	464.976	+	236.917i	0.477879	+	0.243491i
$974$			625.702i			0.642405i
$975$		0			0
$976$	259.945			0.266337
$977$	−216.788	+	425.470i	−0.221891	+	0.435486i	−0.974937	−	0.222483i	$-0.928584\pi$
$977$	−216.788	+	425.470i	−0.221891	+	0.435486i	0.753046	+	0.657968i	$0.228584\pi$
$978$	30.0617	−	189.802i	0.0307379	−	0.194072i
$979$	−64.3153	−	88.5225i	−0.0656949	−	0.0904213i
$980$		0			0
$981$	350.829	+	254.892i	0.357623	+	0.259829i
$982$	−712.599	−	712.599i	−0.725661	−	0.725661i
$983$	352.898	−	55.8936i	0.359001	−	0.0568602i	0.0256713	−	0.999670i	$-0.491828\pi$
$983$	352.898	−	55.8936i	0.359001	−	0.0568602i	0.333330	+	0.942810i	$0.391828\pi$
$984$	44.7722	+	14.5474i	0.0455002	+	0.0147839i
$985$		0			0
$986$	−445.954	−	1372.51i	−0.452286	−	1.39199i
$987$	495.454	−	252.446i	0.501979	−	0.255771i
$988$	−85.8293	−	168.450i	−0.0868718	−	0.170495i
$989$	−802.962	+	260.898i	−0.811893	+	0.263800i
$990$		0			0
$991$	−326.239	+	1004.06i	−0.329202	+	1.01318i	0.640307	+	0.768119i	$0.278807\pi$
$991$	−326.239	+	1004.06i	−0.329202	+	1.01318i	−0.969508	+	0.245059i	$0.921193\pi$
$992$	34.5886	+	218.384i	0.0348675	+	0.220145i
$993$	485.590	−	485.590i	0.489013	−	0.489013i
$994$	−116.121	+	159.827i	−0.116822	+	0.160792i
$995$		0			0
$996$	212.427	−	154.337i	0.213280	−	0.154957i
$997$	−991.318	−	157.009i	−0.994301	−	0.157482i	−0.361978	−	0.932187i	$-0.617898\pi$
$997$	−991.318	−	157.009i	−0.994301	−	0.157482i	−0.632323	+	0.774705i	$0.717898\pi$
$998$	−520.726	−	265.323i	−0.521770	−	0.265855i
$999$			528.849i			0.529379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.3.f.c.107.1		16
5.2	odd	4		50.3.f.a.33.2	✓	16
5.3	odd	4		250.3.f.b.143.1		16
5.4	even	2		250.3.f.a.107.2		16
20.7	even	4		400.3.bg.a.33.1		16
25.3	odd	20	inner	250.3.f.c.243.1		16
25.4	even	10		50.3.f.a.47.2	yes	16
25.21	even	5		250.3.f.b.7.1		16
25.22	odd	20		250.3.f.a.243.2		16
100.79	odd	10		400.3.bg.a.97.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.a.33.2	✓	16	5.2	odd	4
50.3.f.a.47.2	yes	16	25.4	even	10
250.3.f.a.107.2		16	5.4	even	2
250.3.f.a.243.2		16	25.22	odd	20
250.3.f.b.7.1		16	25.21	even	5
250.3.f.b.143.1		16	5.3	odd	4
250.3.f.c.107.1		16	1.1	even	1	trivial
250.3.f.c.243.1		16	25.3	odd	20	inner
400.3.bg.a.33.1		16	20.7	even	4
400.3.bg.a.97.1		16	100.79	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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	250.f (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.642040 - 1.26007i) q^{2} +(-0.396386 + 2.50268i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(2.89907 + 2.10629i) q^{6} +(1.84619 + 1.84619i) q^{7} +(-2.79360 + 0.442463i) q^{8} +(2.45322 + 0.797099i) q^{9} +O(q^{10})\)	\(q+(0.642040 - 1.26007i) q^{2} +(-0.396386 + 2.50268i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(2.89907 + 2.10629i) q^{6} +(1.84619 + 1.84619i) q^{7} +(-2.79360 + 0.442463i) q^{8} +(2.45322 + 0.797099i) q^{9} +(0.224918 + 0.692225i) q^{11} +(4.51540 - 2.30071i) q^{12} +(5.57900 + 10.9494i) q^{13} +(3.51167 - 1.14101i) q^{14} +(-1.23607 + 3.80423i) q^{16} +(3.31453 + 20.9271i) q^{17} +(2.57947 - 2.57947i) q^{18} +(4.52135 - 6.22310i) q^{19} +(-5.35223 + 3.88862i) q^{21} +(1.01666 + 0.161023i) q^{22} +(35.3452 + 18.0093i) q^{23} -7.16689i q^{24} +17.3790 q^{26} +(-13.3205 + 26.1430i) q^{27} +(0.816872 - 5.15753i) q^{28} +(-28.3088 - 38.9637i) q^{29} +(31.6215 + 22.9744i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-1.82157 + 0.288509i) q^{33} +(28.4978 + 9.25950i) q^{34} +(-1.59420 - 4.90644i) q^{36} +(16.0598 - 8.18285i) q^{37} +(-4.93868 - 9.69270i) q^{38} +(-29.6143 + 9.62228i) q^{39} +(-2.02980 + 6.24709i) q^{41} +(1.46361 + 9.24086i) q^{42} +(-15.0496 + 15.0496i) q^{43} +(0.855637 - 1.17768i) q^{44} +(45.3860 - 32.9749i) q^{46} +(-83.0166 - 13.1485i) q^{47} +(-9.03080 - 4.60142i) q^{48} -42.1832i q^{49} -53.6878 q^{51} +(11.1580 - 21.8988i) q^{52} +(10.2271 - 64.5712i) q^{53} +(24.3898 + 33.5696i) q^{54} +(-5.97440 - 4.34066i) q^{56} +(13.7822 + 13.7822i) q^{57} +(-67.2725 + 10.6549i) q^{58} +(74.4974 + 24.2057i) q^{59} +(-20.0819 - 61.8056i) q^{61} +(49.2517 - 25.0950i) q^{62} +(3.05752 + 6.00071i) q^{63} +(7.60845 - 2.47214i) q^{64} +(-0.805979 + 2.48055i) q^{66} +(-9.69353 - 61.2025i) q^{67} +(29.9644 - 29.9644i) q^{68} +(-59.0818 + 81.3191i) q^{69} +(-43.2855 + 31.4488i) q^{71} +(-7.20601 - 1.14132i) q^{72} +(-30.3151 - 15.4463i) q^{73} -25.4902i q^{74} -15.3843 q^{76} +(-0.862739 + 1.69322i) q^{77} +(-6.88879 + 43.4941i) q^{78} +(13.7883 + 18.9780i) q^{79} +(-41.3660 - 30.0541i) q^{81} +(6.56858 + 6.56858i) q^{82} +(51.1748 - 8.10529i) q^{83} +(12.5839 + 4.08874i) q^{84} +(9.30114 + 28.6260i) q^{86} +(108.735 - 55.4032i) q^{87} +(-0.934615 - 1.83428i) q^{88} +(-142.975 + 46.4555i) q^{89} +(-9.91480 + 30.5146i) q^{91} +(-12.4112 - 78.3609i) q^{92} +(-70.0319 + 70.0319i) q^{93} +(-69.8680 + 96.1651i) q^{94} +(-11.5963 + 8.42518i) q^{96} +(-63.0263 - 9.98239i) q^{97} +(-53.1539 - 27.0833i) q^{98} +1.87746i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 2 q^{3} + 4 q^{6} + 2 q^{7} - 8 q^{8} + 40 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 2 * q^3 + 4 * q^6 + 2 * q^7 - 8 * q^8 + 40 * q^9	\( 16 q + 4 q^{2} - 2 q^{3} + 4 q^{6} + 2 q^{7} - 8 q^{8} + 40 q^{9} + 32 q^{11} + 16 q^{12} + 8 q^{13} + 30 q^{14} + 16 q^{16} - 8 q^{17} + 16 q^{18} - 30 q^{19} - 68 q^{21} + 8 q^{22} - 42 q^{23} - 56 q^{26} + 40 q^{27} - 4 q^{28} - 100 q^{29} + 132 q^{31} + 64 q^{32} - 134 q^{33} - 100 q^{34} + 48 q^{36} + 82 q^{37} - 20 q^{38} + 320 q^{39} - 88 q^{41} + 128 q^{42} + 78 q^{43} - 40 q^{44} - 26 q^{46} - 168 q^{47} - 32 q^{48} - 168 q^{51} + 16 q^{52} + 518 q^{53} - 80 q^{54} + 48 q^{56} - 280 q^{57} - 80 q^{58} + 350 q^{59} + 372 q^{61} + 158 q^{62} - 142 q^{63} - 202 q^{66} - 158 q^{67} + 196 q^{68} + 30 q^{69} + 122 q^{71} - 68 q^{72} - 352 q^{73} + 40 q^{76} - 96 q^{77} - 158 q^{78} - 760 q^{79} - 144 q^{81} - 352 q^{82} - 32 q^{83} + 20 q^{84} + 264 q^{86} + 440 q^{87} + 244 q^{88} - 550 q^{89} - 798 q^{91} + 436 q^{92} - 54 q^{93} - 190 q^{94} - 16 q^{96} - 618 q^{97} - 336 q^{98}+O(q^{100}) \) 16 * q + 4 * q^2 - 2 * q^3 + 4 * q^6 + 2 * q^7 - 8 * q^8 + 40 * q^9 + 32 * q^11 + 16 * q^12 + 8 * q^13 + 30 * q^14 + 16 * q^16 - 8 * q^17 + 16 * q^18 - 30 * q^19 - 68 * q^21 + 8 * q^22 - 42 * q^23 - 56 * q^26 + 40 * q^27 - 4 * q^28 - 100 * q^29 + 132 * q^31 + 64 * q^32 - 134 * q^33 - 100 * q^34 + 48 * q^36 + 82 * q^37 - 20 * q^38 + 320 * q^39 - 88 * q^41 + 128 * q^42 + 78 * q^43 - 40 * q^44 - 26 * q^46 - 168 * q^47 - 32 * q^48 - 168 * q^51 + 16 * q^52 + 518 * q^53 - 80 * q^54 + 48 * q^56 - 280 * q^57 - 80 * q^58 + 350 * q^59 + 372 * q^61 + 158 * q^62 - 142 * q^63 - 202 * q^66 - 158 * q^67 + 196 * q^68 + 30 * q^69 + 122 * q^71 - 68 * q^72 - 352 * q^73 + 40 * q^76 - 96 * q^77 - 158 * q^78 - 760 * q^79 - 144 * q^81 - 352 * q^82 - 32 * q^83 + 20 * q^84 + 264 * q^86 + 440 * q^87 + 244 * q^88 - 550 * q^89 - 798 * q^91 + 436 * q^92 - 54 * q^93 - 190 * q^94 - 16 * q^96 - 618 * q^97 - 336 * q^98

Introduction

L-functions

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