LMFDB - Embedded newform 800.2.y.e.301.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [800,2,Mod(101,800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(800, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("800.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.y (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			301.3
Character	$\chi$	$=$	800.301
Dual form			800.2.y.e.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26838 - 0.625467i) q^{2} +(-0.986257 + 2.38104i) q^{3} +(1.21758 + 1.58666i) q^{4} +(2.74021 - 2.40319i) q^{6} +(-2.66071 + 2.66071i) q^{7} +(-0.551955 - 2.77405i) q^{8} +(-2.57531 - 2.57531i) q^{9} +O(q^{10})$	\(q+(-1.26838 - 0.625467i) q^{2} +(-0.986257 + 2.38104i) q^{3} +(1.21758 + 1.58666i) q^{4} +(2.74021 - 2.40319i) q^{6} +(-2.66071 + 2.66071i) q^{7} +(-0.551955 - 2.77405i) q^{8} +(-2.57531 - 2.57531i) q^{9} +(-2.06648 - 4.98892i) q^{11} +(-4.97875 + 1.33425i) q^{12} +(3.28494 + 1.36067i) q^{13} +(5.03897 - 1.71061i) q^{14} +(-1.03499 + 3.86378i) q^{16} -6.47754i q^{17} +(1.65570 + 4.87724i) q^{18} +(-1.25082 - 0.518105i) q^{19} +(-3.71110 - 8.95938i) q^{21} +(-0.499321 + 7.62037i) q^{22} +(-3.93037 - 3.93037i) q^{23} +(7.14948 + 1.42170i) q^{24} +(-3.31550 - 3.78046i) q^{26} +(1.52870 - 0.633209i) q^{27} +(-7.46127 - 0.982010i) q^{28} +(-0.515400 + 1.24429i) q^{29} +4.32793 q^{31} +(3.72942 - 4.25340i) q^{32} +13.9169 q^{33} +(-4.05149 + 8.21599i) q^{34} +(0.950490 - 7.22178i) q^{36} +(2.65068 - 1.09795i) q^{37} +(1.26245 + 1.43950i) q^{38} +(-6.47958 + 6.47958i) q^{39} +(6.83045 + 6.83045i) q^{41} +(-0.896709 + 13.6851i) q^{42} +(-0.124633 - 0.300891i) q^{43} +(5.39962 - 9.35322i) q^{44} +(2.52689 + 7.44352i) q^{46} +7.79266i q^{47} +(-8.17904 - 6.27502i) q^{48} -7.15871i q^{49} +(15.4232 + 6.38852i) q^{51} +(1.84077 + 6.86880i) q^{52} +(-2.36819 - 5.71731i) q^{53} +(-2.33503 - 0.153002i) q^{54} +(8.84952 + 5.91234i) q^{56} +(2.46725 - 2.46725i) q^{57} +(1.43198 - 1.25586i) q^{58} +(-8.46858 + 3.50780i) q^{59} +(1.27530 - 3.07884i) q^{61} +(-5.48947 - 2.70698i) q^{62} +13.7043 q^{63} +(-7.39069 + 3.06230i) q^{64} +(-17.6519 - 8.70454i) q^{66} +(3.86267 - 9.32531i) q^{67} +(10.2777 - 7.88694i) q^{68} +(13.2347 - 5.48199i) q^{69} +(9.55305 - 9.55305i) q^{71} +(-5.72257 + 8.56548i) q^{72} +(-1.93135 - 1.93135i) q^{73} +(-4.04880 - 0.265296i) q^{74} +(-0.700914 - 2.61546i) q^{76} +(18.7723 + 7.77576i) q^{77} +(12.2713 - 4.16582i) q^{78} -6.31686i q^{79} -6.66170i q^{81} +(-4.39140 - 12.9358i) q^{82} +(-11.6422 - 4.82236i) q^{83} +(9.69693 - 16.7970i) q^{84} +(-0.0301150 + 0.459598i) q^{86} +(-2.45437 - 2.45437i) q^{87} +(-12.6989 + 8.48617i) q^{88} +(2.03773 - 2.03773i) q^{89} +(-12.3606 + 5.11992i) q^{91} +(1.45061 - 11.0217i) q^{92} +(-4.26845 + 10.3050i) q^{93} +(4.87405 - 9.88407i) q^{94} +(6.44932 + 13.0748i) q^{96} +1.02663 q^{97} +(-4.47754 + 9.07998i) q^{98} +(-7.52618 + 18.1698i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 16 q^{14} + 20 q^{16} + 20 q^{18} - 4 q^{22} + 8 q^{23} - 28 q^{24} + 24 q^{27} - 20 q^{28} - 20 q^{32} - 20 q^{34} + 12 q^{36} - 20 q^{38} + 24 q^{39} - 100 q^{42} + 8 q^{43} + 40 q^{44} + 32 q^{46} + 16 q^{51} - 88 q^{52} - 32 q^{53} + 76 q^{54} + 48 q^{56} + 72 q^{58} + 32 q^{59} - 32 q^{61} - 48 q^{62} + 80 q^{63} + 48 q^{64} + 16 q^{66} - 40 q^{67} + 48 q^{68} - 32 q^{69} + 32 q^{71} - 36 q^{72} + 8 q^{74} + 16 q^{77} + 36 q^{78} + 40 q^{83} + 56 q^{84} - 84 q^{86} - 40 q^{88} + 48 q^{91} + 4 q^{92} + 32 q^{94} - 100 q^{96} - 40 q^{98} - 64 q^{99}+O(q^{100}) $ 64 * q - 16 * q^14 + 20 * q^16 + 20 * q^18 - 4 * q^22 + 8 * q^23 - 28 * q^24 + 24 * q^27 - 20 * q^28 - 20 * q^32 - 20 * q^34 + 12 * q^36 - 20 * q^38 + 24 * q^39 - 100 * q^42 + 8 * q^43 + 40 * q^44 + 32 * q^46 + 16 * q^51 - 88 * q^52 - 32 * q^53 + 76 * q^54 + 48 * q^56 + 72 * q^58 + 32 * q^59 - 32 * q^61 - 48 * q^62 + 80 * q^63 + 48 * q^64 + 16 * q^66 - 40 * q^67 + 48 * q^68 - 32 * q^69 + 32 * q^71 - 36 * q^72 + 8 * q^74 + 16 * q^77 + 36 * q^78 + 40 * q^83 + 56 * q^84 - 84 * q^86 - 40 * q^88 + 48 * q^91 + 4 * q^92 + 32 * q^94 - 100 * q^96 - 40 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.26838	−	0.625467i	−0.896881	−	0.442272i
$2$	−1.26838	−	0.625467i	−0.896881	−	0.442272i
$3$	−0.986257	+	2.38104i	−0.569416	+	1.37469i	0.332633	+	0.943057i	$0.392063\pi$
$3$	−0.986257	+	2.38104i	−0.569416	+	1.37469i	−0.902048	+	0.431635i	$0.857937\pi$
$4$	1.21758	+	1.58666i	0.608791	+	0.793330i
$5$		0			0
$5$		0			0
$6$	2.74021	−	2.40319i	1.11869	−	0.981098i
$7$	−2.66071	+	2.66071i	−1.00565	+	1.00565i	−0.00566848	+	0.999984i	$0.501804\pi$
$7$	−2.66071	+	2.66071i	−1.00565	+	1.00565i	−0.999984	+	0.00566848i	$0.998196\pi$
$8$	−0.551955	−	2.77405i	−0.195146	−	0.980774i
$9$	−2.57531	−	2.57531i	−0.858435	−	0.858435i
$10$		0			0
$11$	−2.06648	−	4.98892i	−0.623067	−	1.50422i	−0.848084	−	0.529861i	$-0.822244\pi$
$11$	−2.06648	−	4.98892i	−0.623067	−	1.50422i	0.225018	−	0.974355i	$-0.427756\pi$
$12$	−4.97875	+	1.33425i	−1.43724	+	0.385165i
$13$	3.28494	+	1.36067i	0.911077	+	0.377381i	0.788469	−	0.615075i	$-0.210874\pi$
$13$	3.28494	+	1.36067i	0.911077	+	0.377381i	0.122608	+	0.992455i	$0.460874\pi$
$14$	5.03897	−	1.71061i	1.34672	−	0.457179i
$15$		0			0
$16$	−1.03499	+	3.86378i	−0.258747	+	0.965945i
$17$		−	6.47754i		−	1.57103i	−0.618840	−	0.785517i	$-0.712397\pi$
$17$		−	6.47754i		−	1.57103i	0.618840	−	0.785517i	$-0.287603\pi$
$18$	1.65570	+	4.87724i	0.390253	+	1.14958i
$19$	−1.25082	−	0.518105i	−0.286957	−	0.118861i	0.234562	−	0.972101i	$-0.424634\pi$
$19$	−1.25082	−	0.518105i	−0.286957	−	0.118861i	−0.521519	+	0.853240i	$0.674634\pi$
$20$		0			0
$21$	−3.71110	−	8.95938i	−0.809827	−	1.95510i
$22$	−0.499321	+	7.62037i	−0.106456	+	1.62467i
$23$	−3.93037	−	3.93037i	−0.819538	−	0.819538i	0.166503	−	0.986041i	$-0.446753\pi$
$23$	−3.93037	−	3.93037i	−0.819538	−	0.819538i	−0.986041	+	0.166503i	$0.946753\pi$
$24$	7.14948	+	1.42170i	1.45938	+	0.290203i
$25$		0			0
$26$	−3.31550	−	3.78046i	−0.650223	−	0.741409i
$27$	1.52870	−	0.633209i	0.294199	−	0.121861i
$28$	−7.46127	−	0.982010i	−1.41005	−	0.185582i
$29$	−0.515400	+	1.24429i	−0.0957074	+	0.231058i	−0.964481	−	0.264151i	$-0.914908\pi$
$29$	−0.515400	+	1.24429i	−0.0957074	+	0.231058i	0.868774	+	0.495209i	$0.164908\pi$
$30$		0			0
$31$	4.32793			0.777319			0.388660	−	0.921381i	$-0.372938\pi$
$31$	4.32793			0.777319			0.388660	+	0.921381i	$0.372938\pi$
$32$	3.72942	−	4.25340i	0.659275	−	0.751902i
$33$	13.9169			2.42262
$34$	−4.05149	+	8.21599i	−0.694824	+	1.40903i
$35$		0			0
$36$	0.950490	−	7.22178i	0.158415	−	1.20363i
$37$	2.65068	−	1.09795i	0.435769	−	0.180502i	−0.154004	−	0.988070i	$-0.549217\pi$
$37$	2.65068	−	1.09795i	0.435769	−	0.180502i	0.589774	+	0.807569i	$0.299217\pi$
$38$	1.26245	+	1.43950i	0.204797	+	0.233517i
$39$	−6.47958	+	6.47958i	−1.03756	+	1.03756i
$40$		0			0
$41$	6.83045	+	6.83045i	1.06674	+	1.06674i	0.997608	+	0.0691302i	$0.0220224\pi$
$41$	6.83045	+	6.83045i	1.06674	+	1.06674i	0.0691302	+	0.997608i	$0.477978\pi$
$42$	−0.896709	+	13.6851i	−0.138365	+	2.11165i
$43$	−0.124633	−	0.300891i	−0.0190064	−	0.0458854i	0.914091	−	0.405508i	$-0.132905\pi$
$43$	−0.124633	−	0.300891i	−0.0190064	−	0.0458854i	−0.933098	+	0.359623i	$0.882905\pi$
$44$	5.39962	−	9.35322i	0.814023	−	1.41005i
$45$		0			0
$46$	2.52689	+	7.44352i	0.372570	+	1.09749i
$47$			7.79266i			1.13668i	0.822795	+	0.568338i	$0.192414\pi$
$47$			7.79266i			1.13668i	−0.822795	+	0.568338i	$0.807586\pi$
$48$	−8.17904	−	6.27502i	−1.18054	−	0.905721i
$49$		−	7.15871i		−	1.02267i
$50$		0			0
$51$	15.4232	+	6.38852i	2.15969	+	0.894571i
$52$	1.84077	+	6.86880i	0.255268	+	0.952531i
$53$	−2.36819	−	5.71731i	−0.325296	−	0.785334i	−0.998929	−	0.0462678i	$-0.985267\pi$
$53$	−2.36819	−	5.71731i	−0.325296	−	0.785334i	0.673633	−	0.739066i	$-0.264733\pi$
$54$	−2.33503	−	0.153002i	−0.317757	−	0.0208209i
$55$		0			0
$56$	8.84952	+	5.91234i	1.18257	+	0.790069i
$57$	2.46725	−	2.46725i	0.326795	−	0.326795i
$58$	1.43198	−	1.25586i	0.188029	−	0.164903i
$59$	−8.46858	+	3.50780i	−1.10252	+	0.456677i	−0.858354	−	0.513058i	$-0.828513\pi$
$59$	−8.46858	+	3.50780i	−1.10252	+	0.456677i	−0.244162	+	0.969735i	$0.578513\pi$
$60$		0			0
$61$	1.27530	−	3.07884i	0.163285	−	0.394205i	−0.820967	−	0.570976i	$-0.806565\pi$
$61$	1.27530	−	3.07884i	0.163285	−	0.394205i	0.984252	+	0.176770i	$0.0565650\pi$
$62$	−5.48947	−	2.70698i	−0.697163	−	0.343786i
$63$	13.7043			1.72658
$64$	−7.39069	+	3.06230i	−0.923836	+	0.382788i
$65$		0			0
$66$	−17.6519	−	8.70454i	−2.17280	−	1.07146i
$67$	3.86267	−	9.32531i	0.471900	−	1.13927i	−0.491422	−	0.870922i	$-0.663523\pi$
$67$	3.86267	−	9.32531i	0.471900	−	1.13927i	0.963322	−	0.268347i	$-0.0864773\pi$
$68$	10.2777	−	7.88694i	1.24635	−	0.956432i
$69$	13.2347	−	5.48199i	1.59327	−	0.659954i
$70$		0			0
$71$	9.55305	−	9.55305i	1.13374	−	1.13374i	0.144188	−	0.989550i	$-0.453943\pi$
$71$	9.55305	−	9.55305i	1.13374	−	1.13374i	0.989550	−	0.144188i	$-0.0460571\pi$
$72$	−5.72257	+	8.56548i	−0.674411	+	1.00945i
$73$	−1.93135	−	1.93135i	−0.226047	−	0.226047i	0.584992	−	0.811039i	$-0.301098\pi$
$73$	−1.93135	−	1.93135i	−0.226047	−	0.226047i	−0.811039	+	0.584992i	$0.801098\pi$
$74$	−4.04880	−	0.265296i	−0.470664	−	0.0308401i
$75$		0			0
$76$	−0.700914	−	2.61546i	−0.0804004	−	0.300013i
$77$	18.7723	+	7.77576i	2.13931	+	0.886130i
$78$	12.2713	−	4.16582i	1.38946	−	0.471686i
$79$		−	6.31686i		−	0.710702i	−0.934733	−	0.355351i	$-0.884361\pi$
$79$		−	6.31686i		−	0.710702i	0.934733	−	0.355351i	$-0.115639\pi$
$80$		0			0
$81$		−	6.66170i		−	0.740188i
$82$	−4.39140	−	12.9358i	−0.484949	−	1.42853i
$83$	−11.6422	−	4.82236i	−1.27790	−	0.529323i	−0.362542	−	0.931967i	$-0.618091\pi$
$83$	−11.6422	−	4.82236i	−1.27790	−	0.529323i	−0.915357	+	0.402644i	$0.868091\pi$
$84$	9.69693	−	16.7970i	1.05802	−	1.83271i
$85$		0			0
$86$	−0.0301150	+	0.459598i	−0.00324738	+	0.0495598i
$87$	−2.45437	−	2.45437i	−0.263136	−	0.263136i
$88$	−12.6989	+	8.48617i	−1.35371	+	0.904629i
$89$	2.03773	−	2.03773i	0.215999	−	0.215999i	−0.590811	−	0.806810i	$-0.701192\pi$
$89$	2.03773	−	2.03773i	0.215999	−	0.215999i	0.806810	+	0.590811i	$0.201192\pi$
$90$		0			0
$91$	−12.3606	+	5.11992i	−1.29574	+	0.536713i
$92$	1.45061	−	11.0217i	0.151237	−	1.14909i
$93$	−4.26845	+	10.3050i	−0.442618	+	1.06857i
$94$	4.87405	−	9.88407i	0.502720	−	1.01946i
$95$		0			0
$96$	6.44932	+	13.0748i	0.658231	+	1.33444i
$97$	1.02663			0.104238			0.0521190	−	0.998641i	$-0.483402\pi$
$97$	1.02663			0.104238			0.0521190	+	0.998641i	$0.483402\pi$
$98$	−4.47754	+	9.07998i	−0.452300	+	0.917217i
$99$	−7.52618	+	18.1698i	−0.756410	+	1.82613i
$100$		0			0
$101$	1.82210	−	0.754738i	0.181306	−	0.0750992i	−0.290184	−	0.956971i	$-0.593717\pi$
$101$	1.82210	−	0.754738i	0.181306	−	0.0750992i	0.471490	+	0.881872i	$0.343717\pi$
$102$	−15.5668	−	17.7498i	−1.54134	−	1.75749i
$103$	11.3691	−	11.3691i	1.12023	−	1.12023i	0.128523	−	0.991707i	$-0.458976\pi$
$103$	11.3691	−	11.3691i	1.12023	−	1.12023i	0.991707	−	0.128523i	$-0.0410237\pi$
$104$	1.96141	−	9.86360i	0.192332	−	0.967205i
$105$		0			0
$106$	−0.572224	+	8.73296i	−0.0555793	+	0.848220i
$107$	3.02985	+	7.31470i	0.292906	+	0.707139i	1.00000		1.87358e-5i	$5.96377e-6\pi$
$107$	3.02985	+	7.31470i	0.292906	+	0.707139i	−0.707094	+	0.707120i	$0.749994\pi$
$108$	2.86601	+	1.65455i	0.275782	+	0.159209i
$109$	−13.5926	−	5.63022i	−1.30193	−	0.539277i	−0.379411	−	0.925228i	$-0.623874\pi$
$109$	−13.5926	−	5.63022i	−1.30193	−	0.539277i	−0.922519	+	0.385951i	$0.873874\pi$
$110$		0			0
$111$			7.39422i			0.701829i
$112$	−7.52659	−	13.0342i	−0.711196	−	1.23161i
$113$		−	5.88683i		−	0.553787i	−0.960901	−	0.276893i	$-0.910695\pi$
$113$		−	5.88683i		−	0.553787i	0.960901	−	0.276893i	$-0.0893049\pi$
$114$	−4.67260	+	1.58623i	−0.437629	+	0.148564i
$115$		0			0
$116$	−2.60180	+	0.697256i	−0.241571	+	0.0647386i
$117$	−4.95559	−	11.9638i	−0.458144	−	1.10606i
$118$	12.9354	+	0.847588i	1.19080	+	0.0780268i
$119$	17.2348	+	17.2348i	1.57991	+	1.57991i
$120$		0			0
$121$	−12.8408	+	12.8408i	−1.16735	+	1.16735i
$122$	−3.54328	+	3.10749i	−0.320793	+	0.281339i
$123$	−23.0001	+	9.52697i	−2.07385	+	0.859018i
$124$	5.26961	+	6.86696i	0.473225	+	0.616671i
$125$		0			0
$126$	−17.3822	−	8.57156i	−1.54853	−	0.763616i
$127$	12.5359			1.11238			0.556191	−	0.831054i	$-0.312262\pi$
$127$	12.5359			1.11238			0.556191	+	0.831054i	$0.312262\pi$
$128$	11.2896	+	0.738468i	0.997868	+	0.0652720i
$129$	0.839352			0.0739009
$130$		0			0
$131$	−3.07413	+	7.42162i	−0.268588	+	0.648430i	−0.999417	−	0.0341310i	$-0.989134\pi$
$131$	−3.07413	+	7.42162i	−0.268588	+	0.648430i	0.730829	+	0.682561i	$0.239134\pi$
$132$	16.9449	+	22.0814i	1.47487	+	1.92194i
$133$	4.70658	−	1.94953i	0.408112	−	0.169046i
$134$	−10.7320	+	9.41208i	−0.927105	+	0.813080i
$135$		0			0
$136$	−17.9690	+	3.57531i	−1.54083	+	0.306580i
$137$	−10.2148	−	10.2148i	−0.872713	−	0.872713i	0.120054	−	0.992767i	$-0.461693\pi$
$137$	−10.2148	−	10.2148i	−0.872713	−	0.872713i	−0.992767	+	0.120054i	$0.961693\pi$
$138$	−20.2154	−	1.32461i	−1.72085	−	0.112758i
$139$	5.79595	+	13.9927i	0.491606	+	1.18684i	0.953902	+	0.300117i	$0.0970256\pi$
$139$	5.79595	+	13.9927i	0.491606	+	1.18684i	−0.462296	+	0.886725i	$0.652974\pi$
$140$		0			0
$141$	−18.5546	−	7.68557i	−1.56258	−	0.647242i
$142$	−18.0920	+	6.14180i	−1.51825	+	0.515408i
$143$		−	19.2001i		−	1.60559i
$144$	12.6158	−	7.28501i	1.05132	−	0.607084i
$145$		0			0
$146$	1.24169	+	3.65768i	0.102763	+	0.302712i
$147$	17.0452	+	7.06033i	1.40586	+	0.582327i
$148$	4.96949	+	2.86889i	0.408490	+	0.235821i
$149$	−2.46202	−	5.94384i	−0.201697	−	0.486939i	0.790373	−	0.612625i	$-0.209887\pi$
$149$	−2.46202	−	5.94384i	−0.201697	−	0.486939i	−0.992070	+	0.125687i	$0.959887\pi$
$150$		0			0
$151$	−8.46531	−	8.46531i	−0.688898	−	0.688898i	0.273091	−	0.961988i	$-0.411954\pi$
$151$	−8.46531	−	8.46531i	−0.688898	−	0.688898i	−0.961988	+	0.273091i	$0.911954\pi$
$152$	−0.746854	+	3.75579i	−0.0605779	+	0.304635i
$153$	−16.6816	+	16.6816i	−1.34863	+	1.34863i
$154$	−18.9470	−	21.6041i	−1.52679	−	1.74091i
$155$		0			0
$156$	−18.1703	−	2.39148i	−1.45479	−	0.191471i
$157$	−1.63819	+	3.95494i	−0.130742	+	0.315638i	−0.975671	−	0.219239i	$-0.929642\pi$
$157$	−1.63819	+	3.95494i	−0.130742	+	0.315638i	0.844929	+	0.534878i	$0.179642\pi$
$158$	−3.95099	+	8.01219i	−0.314324	+	0.637415i
$159$	15.9488			1.26482
$160$		0			0
$161$	20.9151			1.64834
$162$	−4.16667	+	8.44957i	−0.327365	+	0.663861i
$163$	1.82382	−	4.40309i	0.142852	−	0.344876i	−0.836218	−	0.548397i	$-0.815238\pi$
$163$	1.82382	−	4.40309i	0.142852	−	0.344876i	0.979071	+	0.203520i	$0.0652383\pi$
$164$	−2.52097	+	19.1543i	−0.196855	+	1.49570i
$165$		0			0
$166$	11.7505	+	13.3984i	0.912019	+	1.03992i
$167$	14.9434	−	14.9434i	1.15635	−	1.15635i	0.171101	−	0.985254i	$-0.445268\pi$
$167$	14.9434	−	14.9434i	1.15635	−	1.15635i	0.985254	−	0.171101i	$-0.0547323\pi$
$168$	−22.8054	+	15.2399i	−1.75947	+	1.17579i
$169$	−0.252992	−	0.252992i	−0.0194609	−	0.0194609i
$170$		0			0
$171$	1.88695	+	4.55551i	0.144299	+	0.348369i
$172$	0.325661	−	0.564110i	0.0248314	−	0.0430130i
$173$	4.41863	+	1.83025i	0.335942	+	0.139152i	0.544276	−	0.838906i	$-0.316804\pi$
$173$	4.41863	+	1.83025i	0.335942	+	0.139152i	−0.208335	+	0.978058i	$0.566804\pi$
$174$	1.57795	+	4.64821i	0.119624	+	0.352380i
$175$		0			0
$176$	21.4149	−	2.82096i	1.61421	−	0.212638i
$177$		−	23.6236i		−	1.77566i
$178$	−3.85915	+	1.31008i	−0.289255	+	0.0981950i
$179$	−14.5098	−	6.01017i	−1.08452	−	0.449221i	−0.232424	−	0.972615i	$-0.574666\pi$
$179$	−14.5098	−	6.01017i	−1.08452	−	0.449221i	−0.852091	+	0.523394i	$0.824666\pi$
$180$		0			0
$181$	0.857338	+	2.06980i	0.0637255	+	0.153847i	0.952534	−	0.304431i	$-0.0984664\pi$
$181$	0.857338	+	2.06980i	0.0637255	+	0.153847i	−0.888809	+	0.458278i	$0.848466\pi$
$182$	18.8803	+	1.23712i	1.39950	+	0.0917016i
$183$	6.07306	+	6.07306i	0.448934	+	0.448934i
$184$	−8.73365	+	13.0724i	−0.643853	+	0.963711i
$185$		0			0
$186$	11.8594	−	10.4008i	0.869576	−	0.762626i
$187$	−32.3159	+	13.3857i	−2.36317	+	0.978859i
$188$	−12.3643	+	9.48821i	−0.901760	+	0.691999i
$189$	−2.38264	+	5.75221i	−0.173312	+	0.418412i
$190$		0			0
$191$	2.71021			0.196104			0.0980521	−	0.995181i	$-0.468739\pi$
$191$	2.71021			0.196104			0.0980521	+	0.995181i	$0.468739\pi$
$192$	−0.00232266	−	20.6177i	−0.000167624	−	1.48796i
$193$	−23.4863			−1.69058			−0.845290	−	0.534308i	$-0.820572\pi$
$193$	−23.4863			−1.69058			−0.845290	+	0.534308i	$0.820572\pi$
$194$	−1.30215	−	0.642120i	−0.0934891	−	0.0461016i
$195$		0			0
$196$	11.3585	−	8.71633i	0.811318	−	0.622595i
$197$	−13.8279	+	5.72768i	−0.985194	+	0.408081i	−0.816347	−	0.577562i	$-0.804004\pi$
$197$	−13.8279	+	5.72768i	−0.985194	+	0.408081i	−0.168847	+	0.985642i	$0.554004\pi$
$198$	20.9107	−	18.3389i	1.48606	−	1.30329i
$199$	1.24000	−	1.24000i	0.0879009	−	0.0879009i	−0.661789	−	0.749690i	$-0.730203\pi$
$199$	1.24000	−	1.24000i	0.0879009	−	0.0879009i	0.749690	+	0.661789i	$0.230203\pi$
$200$		0			0
$201$	18.3943	+	18.3943i	1.29743	+	1.29743i
$202$	−2.78318	−	0.182367i	−0.195824	−	0.0128313i
$203$	−1.93935	−	4.68201i	−0.136116	−	0.328613i
$204$	8.64266	+	32.2500i	0.605107	+	2.25795i
$205$		0			0
$206$	−21.5313	+	7.30935i	−1.50016	+	0.509267i
$207$			20.2438i			1.40704i
$208$	−8.65718	+	11.2840i	−0.600267	+	0.782405i
$209$			7.31087i			0.505703i
$210$		0			0
$211$	2.45961	+	1.01880i	0.169326	+	0.0701373i	0.465736	−	0.884924i	$-0.345789\pi$
$211$	2.45961	+	1.01880i	0.169326	+	0.0701373i	−0.296410	+	0.955061i	$0.595789\pi$
$212$	6.18797	−	10.7188i	0.424992	−	0.736171i
$213$	13.3244	+	32.1679i	0.912972	+	2.20411i
$214$	0.732100	−	11.1729i	0.0500453	−	0.763764i
$215$		0			0
$216$	−2.60033	−	3.89119i	−0.176930	−	0.264762i
$217$	−11.5154	+	11.5154i	−0.781713	+	0.781713i
$218$	13.7190	+	15.6430i	0.929170	+	1.05948i
$219$	6.50342	−	2.69380i	0.439460	−	0.182030i
$220$		0			0
$221$	8.81376	−	21.2783i	0.592878	−	1.43133i
$222$	4.62484	−	9.37870i	0.310399	−	0.629457i
$223$	23.5742			1.57864			0.789322	−	0.613980i	$-0.210432\pi$
$223$	23.5742			1.57864			0.789322	+	0.613980i	$0.210432\pi$
$224$	1.39414	+	21.2399i	0.0931500	+	1.41915i
$225$		0			0
$226$	−3.68202	+	7.46675i	−0.244924	+	0.496681i
$227$	−0.267330	+	0.645391i	−0.0177433	+	0.0428361i	−0.932503	−	0.361163i	$-0.882380\pi$
$227$	−0.267330	+	0.645391i	−0.0177433	+	0.0428361i	0.914760	+	0.403999i	$0.132380\pi$
$228$	6.91877	+	0.910610i	0.458207	+	0.0603066i
$229$	−17.0305	+	7.05427i	−1.12541	+	0.466159i	−0.866218	−	0.499667i	$-0.833456\pi$
$229$	−17.0305	+	7.05427i	−1.12541	+	0.466159i	−0.259190	+	0.965826i	$0.583456\pi$
$230$		0			0
$231$	−37.0287	+	37.0287i	−2.43631	+	2.43631i
$232$	3.73619	+	0.742955i	0.245293	+	0.0487774i
$233$	6.53768	+	6.53768i	0.428297	+	0.428297i	0.888048	−	0.459751i	$-0.152061\pi$
$233$	6.53768	+	6.53768i	0.428297	+	0.428297i	−0.459751	+	0.888048i	$0.652061\pi$
$234$	−1.19741	+	18.2743i	−0.0782774	+	1.19463i
$235$		0			0
$236$	−15.8769	−	9.16573i	−1.03350	−	0.596638i
$237$	15.0407	+	6.23005i	0.976996	+	0.404685i
$238$	−11.0805	−	32.6401i	−0.718243	−	2.11575i
$239$		−	13.0834i		−	0.846295i	−0.906061	−	0.423147i	$-0.860925\pi$
$239$		−	13.0834i		−	0.846295i	0.906061	−	0.423147i	$-0.139075\pi$
$240$		0			0
$241$		−	16.8048i		−	1.08249i	−0.840865	−	0.541245i	$-0.817953\pi$
$241$		−	16.8048i		−	1.08249i	0.840865	−	0.541245i	$-0.182047\pi$
$242$	24.3185	−	8.25554i	1.56325	−	0.530686i
$243$	20.4478	+	8.46977i	1.31173	+	0.543336i
$244$	6.43786	−	1.72528i	0.412142	−	0.110450i
$245$		0			0
$246$	35.1318	+	2.30199i	2.23992	+	0.146770i
$247$	−3.40388	−	3.40388i	−0.216584	−	0.216584i
$248$	−2.38882	−	12.0059i	−0.151690	−	0.762375i
$249$	22.9644	−	22.9644i	1.45531	−	1.45531i
$250$		0			0
$251$	−5.23035	+	2.16648i	−0.330137	+	0.136747i	−0.541594	−	0.840640i	$-0.682179\pi$
$251$	−5.23035	+	2.16648i	−0.330137	+	0.136747i	0.211457	+	0.977387i	$0.432179\pi$
$252$	16.6861	+	21.7440i	1.05112	+	1.36974i
$253$	−11.4863	+	27.7303i	−0.722136	+	1.74339i
$254$	−15.9003	−	7.84080i	−0.997675	−	0.491976i
$255$		0			0
$256$	−13.8576	−	7.99792i	−0.866100	−	0.499870i
$257$	22.5243			1.40503			0.702514	−	0.711670i	$-0.252061\pi$
$257$	22.5243			1.40503			0.702514	+	0.711670i	$0.252061\pi$
$258$	−1.06462	−	0.524987i	−0.0662803	−	0.0326843i
$259$	−4.13137	+	9.97400i	−0.256711	+	0.619754i
$260$		0			0
$261$	4.53173	−	1.87711i	0.280507	−	0.116190i
$262$	8.54115	−	7.49067i	0.527674	−	0.462775i
$263$	−13.5919	+	13.5919i	−0.838114	+	0.838114i	−0.988611	−	0.150496i	$-0.951913\pi$
$263$	−13.5919	+	13.5919i	−0.838114	+	0.838114i	0.150496	+	0.988611i	$0.451913\pi$
$264$	−7.68149	−	38.6061i	−0.472763	−	2.37604i
$265$		0			0
$266$	−7.18910	−	0.471063i	−0.440792	−	0.0288827i
$267$	2.84218	+	6.86163i	0.173939	+	0.419925i
$268$	19.4992	−	5.22559i	1.19111	−	0.319204i
$269$	−16.7948	−	6.95665i	−1.02400	−	0.424154i	−0.193456	−	0.981109i	$-0.561970\pi$
$269$	−16.7948	−	6.95665i	−1.02400	−	0.424154i	−0.830543	+	0.556955i	$0.811970\pi$
$270$		0			0
$271$		−	13.2078i		−	0.802320i	−0.916008	−	0.401160i	$-0.868607\pi$
$271$		−	13.2078i		−	0.802320i	0.916008	−	0.401160i	$-0.131393\pi$
$272$	25.0278	+	6.70416i	1.51753	+	0.406499i
$273$		−	34.4805i		−	2.08686i
$274$	6.56727	+	19.3454i	0.396743	+	1.16870i
$275$		0			0
$276$	24.8124	+	14.3242i	1.49353	+	0.862216i
$277$	−5.04840	−	12.1879i	−0.303329	−	0.732301i	−0.999890	−	0.0148038i	$-0.995288\pi$
$277$	−5.04840	−	12.1879i	−0.303329	−	0.732301i	0.696561	−	0.717497i	$-0.254712\pi$
$278$	1.40047	−	21.3732i	0.0839947	−	1.28188i
$279$	−11.1457	−	11.1457i	−0.667278	−	0.667278i
$280$		0			0
$281$	−6.32440	+	6.32440i	−0.377282	+	0.377282i	−0.870121	−	0.492839i	$-0.835959\pi$
$281$	−6.32440	+	6.32440i	−0.377282	+	0.377282i	0.492839	+	0.870121i	$0.335959\pi$
$282$	18.7272	+	21.3535i	1.11519	+	1.27158i
$283$	7.92855	−	3.28411i	0.471303	−	0.195220i	−0.134374	−	0.990931i	$-0.542902\pi$
$283$	7.92855	−	3.28411i	0.471303	−	0.195220i	0.605677	+	0.795711i	$0.292902\pi$
$284$	26.7891	+	3.52583i	1.58964	+	0.209219i
$285$		0			0
$286$	−12.0090	+	24.3530i	−0.710107	+	1.44002i
$287$	−36.3477			−2.14553
$288$	−20.5582	+	1.34939i	−1.21140	+	0.0795138i
$289$	−24.9585			−1.46815
$290$		0			0
$291$	−1.01252	+	2.44443i	−0.0593548	+	0.143295i
$292$	0.712819	−	5.41597i	0.0417146	−	0.316946i
$293$	−18.0775	+	7.48795i	−1.05610	+	0.437451i	−0.842066	−	0.539375i	$-0.818660\pi$
$293$	−18.0775	+	7.48795i	−1.05610	+	0.437451i	−0.214034	+	0.976826i	$0.568660\pi$
$294$	−17.2037	−	19.6164i	−1.00334	−	1.14405i
$295$		0			0
$296$	−4.50882	−	6.74710i	−0.262070	−	0.392167i
$297$	−6.31806	−	6.31806i	−0.366611	−	0.366611i
$298$	−0.594896	+	9.07897i	−0.0344614	+	0.525931i
$299$	−7.56309	−	18.2589i	−0.437385	−	1.05594i
$300$		0			0
$301$	1.13219	+	0.468970i	0.0652586	+	0.0270310i
$302$	5.44247	+	16.0320i	0.313179	+	0.922539i
$303$			5.08285i			0.292002i
$304$	3.29642	−	4.29665i	0.189063	−	0.246430i
$305$		0			0
$306$	31.5925	−	10.7249i	1.80602	−	0.613100i
$307$	−28.9336	−	11.9847i	−1.65133	−	0.684003i	−0.653962	−	0.756527i	$-0.726894\pi$
$307$	−28.9336	−	11.9847i	−1.65133	−	0.684003i	−0.997367	+	0.0725248i	$0.976894\pi$
$308$	10.5194	+	39.2530i	0.599397	+	2.23665i
$309$	15.8574	+	38.2831i	0.902094	+	2.17785i
$310$		0			0
$311$	−5.25892	−	5.25892i	−0.298206	−	0.298206i	0.542105	−	0.840311i	$-0.317628\pi$
$311$	−5.25892	−	5.25892i	−0.298206	−	0.298206i	−0.840311	+	0.542105i	$0.817628\pi$
$312$	21.5511	+	14.3982i	1.22009	+	0.815140i
$313$	13.6652	−	13.6652i	0.772405	−	0.772405i	−0.206122	−	0.978526i	$-0.566084\pi$
$313$	13.6652	−	13.6652i	0.772405	−	0.772405i	0.978526	+	0.206122i	$0.0660843\pi$
$314$	4.55153	−	3.99174i	0.256858	−	0.225267i
$315$		0			0
$316$	10.0227	−	7.69130i	0.563822	−	0.432669i
$317$	4.82293	−	11.6436i	0.270882	−	0.653968i	−0.728639	−	0.684898i	$-0.759847\pi$
$317$	4.82293	−	11.6436i	0.270882	−	0.653968i	0.999522	+	0.0309297i	$0.00984680\pi$
$318$	−20.2291	−	9.97543i	−1.13439	−	0.559394i
$319$	7.27271			0.407194
$320$		0			0
$321$	−20.4048			−1.13888
$322$	−26.5283	−	13.0817i	−1.47837	−	0.729015i
$323$	−3.35604	+	8.10221i	−0.186735	+	0.450819i
$324$	10.5699	−	8.11116i	0.587214	−	0.450620i
$325$		0			0
$326$	−5.06728	+	4.44406i	−0.280651	+	0.246133i
$327$	26.8115	−	26.8115i	1.48268	−	1.48268i
$328$	15.1779	−	22.7181i	0.838060	−	1.25440i
$329$	−20.7340	−	20.7340i	−1.14310	−	1.14310i
$330$		0			0
$331$	−9.91080	−	23.9268i	−0.544747	−	1.31513i	−0.921341	−	0.388756i	$-0.872905\pi$
$331$	−9.91080	−	23.9268i	−0.544747	−	1.31513i	0.376594	−	0.926378i	$-0.377095\pi$
$332$	−6.52390	−	24.3439i	−0.358045	−	1.33604i
$333$	−9.65387	−	3.99876i	−0.529029	−	0.219131i
$334$	−28.3005	+	9.60732i	−1.54854	+	0.525689i
$335$		0			0
$336$	38.4580	−	5.06603i	2.09806	−	0.276375i
$337$			18.3992i			1.00227i	0.865370	+	0.501134i	$0.167084\pi$
$337$			18.3992i			1.00227i	−0.865370	+	0.501134i	$0.832916\pi$
$338$	0.162652	+	0.479128i	0.00884711	+	0.0260612i
$339$	14.0168	+	5.80593i	0.761286	+	0.315335i
$340$		0			0
$341$	−8.94357	−	21.5917i	−0.484322	−	1.16926i
$342$	0.455943	−	6.95835i	0.0246546	−	0.376265i
$343$	0.422294	+	0.422294i	0.0228017	+	0.0228017i
$344$	−0.765894	+	0.511817i	−0.0412943	+	0.0275953i
$345$		0			0
$346$	−4.45974	−	5.08516i	−0.239757	−	0.273380i
$347$	3.96687	−	1.64313i	0.212953	−	0.0882079i	−0.273657	−	0.961827i	$-0.588233\pi$
$347$	3.96687	−	1.64313i	0.212953	−	0.0882079i	0.486610	+	0.873619i	$0.338233\pi$
$348$	0.905856	−	6.88266i	0.0485590	−	0.368949i
$349$	11.4421	−	27.6237i	0.612483	−	1.47867i	−0.247781	−	0.968816i	$-0.579701\pi$
$349$	11.4421	−	27.6237i	0.612483	−	1.47867i	0.860264	−	0.509849i	$-0.170299\pi$
$350$		0			0
$351$	5.88328			0.314026
$352$	−28.9266	−	9.81624i	−1.54179	−	0.523207i
$353$	−9.94577			−0.529360			−0.264680	−	0.964336i	$-0.585266\pi$
$353$	−9.94577			−0.529360			−0.264680	+	0.964336i	$0.585266\pi$
$354$	−14.7758	+	29.9637i	−0.785324	+	1.59255i
$355$		0			0
$356$	5.71429	+	0.752082i	0.302857	+	0.0398602i
$357$	−58.0347	+	24.0388i	−3.07152	+	1.27227i
$358$	14.6448	+	16.6986i	0.774003	+	0.882548i
$359$	11.8249	−	11.8249i	0.624097	−	0.624097i	−0.322480	−	0.946576i	$-0.604516\pi$
$359$	11.8249	−	11.8249i	0.624097	−	0.624097i	0.946576	+	0.322480i	$0.104516\pi$
$360$		0			0
$361$	−12.1389	−	12.1389i	−0.638891	−	0.638891i
$362$	0.207158	−	3.16153i	0.0108880	−	0.166166i
$363$	−17.9101	−	43.2388i	−0.940035	−	2.26945i
$364$	−23.1736	−	13.3781i	−1.21463	−	0.701204i
$365$		0			0
$366$	−3.90446	−	11.5015i	−0.204089	−	0.601191i
$367$			33.9246i			1.77085i	0.464781	+	0.885425i	$0.346133\pi$
$367$			33.9246i			1.77085i	−0.464781	+	0.885425i	$0.653867\pi$
$368$	19.2540	−	11.1182i	1.00368	−	0.579577i
$369$		−	35.1810i		−	1.83145i
$370$		0			0
$371$	21.5132	+	8.91104i	1.11691	+	0.462638i
$372$	−21.5477	+	5.77455i	−1.11719	+	0.299396i
$373$	6.21312	+	14.9998i	0.321703	+	0.776660i	0.999155	+	0.0410929i	$0.0130840\pi$
$373$	6.21312	+	14.9998i	0.321703	+	0.776660i	−0.677452	+	0.735567i	$0.736916\pi$
$374$	49.3612	+	3.23437i	2.55241	+	0.167245i
$375$		0			0
$376$	21.6172	−	4.30120i	1.11482	−	0.221817i
$377$	−3.38611	+	3.38611i	−0.174394	+	0.174394i
$378$	6.61992	−	5.80573i	0.340492	−	0.298615i
$379$	24.2445	−	10.0424i	1.24535	−	0.515843i	0.339970	−	0.940436i	$-0.389583\pi$
$379$	24.2445	−	10.0424i	1.24535	−	0.515843i	0.905384	+	0.424594i	$0.139583\pi$
$380$		0			0
$381$	−12.3636	+	29.8485i	−0.633408	+	1.52918i
$382$	−3.43758	−	1.69515i	−0.175882	−	0.0867313i
$383$	−1.54204			−0.0787944			−0.0393972	−	0.999224i	$-0.512544\pi$
$383$	−1.54204			−0.0787944			−0.0393972	+	0.999224i	$0.512544\pi$
$384$	−12.8927	+	26.1526i	−0.657930	+	1.33459i
$385$		0			0
$386$	29.7896	+	14.6899i	1.51625	+	0.747696i
$387$	−0.453918	+	1.09585i	−0.0230739	+	0.0557054i
$388$	1.25000	+	1.62891i	0.0634592	+	0.0826952i
$389$	34.2132	−	14.1716i	1.73468	−	0.718527i	0.735519	−	0.677504i	$-0.236938\pi$
$389$	34.2132	−	14.1716i	1.73468	−	0.718527i	0.999158	−	0.0410229i	$-0.0130617\pi$
$390$		0			0
$391$	−25.4591	+	25.4591i	−1.28752	+	1.28752i
$392$	−19.8586	+	3.95129i	−1.00301	+	0.199570i
$393$	−14.6392	−	14.6392i	−0.738452	−	0.738452i
$394$	21.1215	+	1.38398i	1.06408	+	0.0697237i
$395$		0			0
$396$	−37.9931	+	10.1817i	−1.90922	+	0.511652i
$397$	4.30276	+	1.78226i	0.215949	+	0.0894491i	0.488036	−	0.872824i	$-0.337714\pi$
$397$	4.30276	+	1.78226i	0.215949	+	0.0894491i	−0.272086	+	0.962273i	$0.587714\pi$
$398$	−2.34836	+	0.797211i	−0.117713	+	0.0399606i
$399$			13.1293i			0.657285i
$400$		0			0
$401$			11.7387i			0.586201i	0.956082	+	0.293100i	$0.0946870\pi$
$401$			11.7387i			0.586201i	−0.956082	+	0.293100i	$0.905313\pi$
$402$	−11.8260	−	34.8360i	−0.589826	−	1.73746i
$403$	14.2170	+	5.88886i	0.708198	+	0.293345i
$404$	3.41607	+	1.97210i	0.169956	+	0.0981155i
$405$		0			0
$406$	−0.468604	+	7.15157i	−0.0232564	+	0.354927i
$407$	−10.9551	−	10.9551i	−0.543027	−	0.543027i
$408$	9.20912	−	46.3110i	0.455919	−	2.29274i
$409$	−12.8300	+	12.8300i	−0.634405	+	0.634405i	−0.949170	−	0.314765i	$-0.898074\pi$
$409$	−12.8300	+	12.8300i	−0.634405	+	0.634405i	0.314765	+	0.949170i	$0.398074\pi$
$410$		0			0
$411$	34.3964	−	14.2474i	1.69665	−	0.702774i
$412$	31.8817	+	4.19609i	1.57070	+	0.206726i
$413$	13.1992	−	31.8656i	0.649489	−	1.56801i
$414$	12.6618	−	25.6769i	0.622295	−	1.26195i
$415$		0			0
$416$	18.0384	−	8.89765i	0.884404	−	0.436243i
$417$	−39.0333			−1.91147
$418$	4.57271	−	9.27297i	0.223658	−	0.453556i
$419$	−4.76515	+	11.5041i	−0.232793	+	0.562012i	−0.996504	−	0.0835464i	$-0.973375\pi$
$419$	−4.76515	+	11.5041i	−0.232793	+	0.562012i	0.763711	+	0.645558i	$0.223375\pi$
$420$		0			0
$421$	16.1536	−	6.69106i	0.787280	−	0.326102i	0.0474306	−	0.998875i	$-0.484897\pi$
$421$	16.1536	−	6.69106i	0.787280	−	0.326102i	0.739849	+	0.672772i	$0.234897\pi$
$422$	−2.48249	−	2.83063i	−0.120846	−	0.137793i
$423$	20.0685	−	20.0685i	0.975763	−	0.975763i
$424$	−14.5530	+	9.72517i	−0.706755	+	0.472296i
$425$		0			0
$426$	3.21956	−	49.1352i	0.155988	−	2.38061i
$427$	4.79870	+	11.5851i	0.232225	+	0.560642i
$428$	−7.91686	+	13.7136i	−0.382676	+	0.662871i
$429$	45.7160	+	18.9362i	2.20719	+	0.914248i
$430$		0			0
$431$			20.2537i			0.975586i	0.872959	+	0.487793i	$0.162198\pi$
$431$			20.2537i			0.975586i	−0.872959	+	0.487793i	$0.837802\pi$
$432$	0.864396	+	6.56193i	0.0415883	+	0.315711i
$433$		−	26.2786i		−	1.26287i	−0.775429	−	0.631434i	$-0.782467\pi$
$433$		−	26.2786i		−	1.26287i	0.775429	−	0.631434i	$-0.217533\pi$
$434$	21.8083	−	7.40339i	1.04683	−	0.355374i
$435$		0			0
$436$	−7.61681	−	28.4220i	−0.364779	−	1.36117i
$437$	2.87982	+	6.95251i	0.137761	+	0.332584i
$438$	−9.93370	−	0.650902i	−0.474650	−	0.0311013i
$439$	3.87646	+	3.87646i	0.185013	+	0.185013i	0.793536	−	0.608523i	$-0.208238\pi$
$439$	3.87646	+	3.87646i	0.185013	+	0.185013i	−0.608523	+	0.793536i	$0.708238\pi$
$440$		0			0
$441$	−18.4359	+	18.4359i	−0.877899	+	0.877899i
$442$	−24.4881	+	21.4763i	−1.16478	+	1.02152i
$443$	−24.7191	+	10.2390i	−1.17444	+	0.486468i	−0.882657	−	0.470017i	$-0.844248\pi$
$443$	−24.7191	+	10.2390i	−1.17444	+	0.486468i	−0.291781	+	0.956485i	$0.594248\pi$
$444$	−11.7321	+	9.00308i	−0.556782	+	0.427267i
$445$		0			0
$446$	−29.9010	−	14.7449i	−1.41586	−	0.698189i
$447$	16.5807			0.784239
$448$	11.5166	−	27.8123i	0.544107	−	1.31401i
$449$	16.6479			0.785665			0.392832	−	0.919610i	$-0.371495\pi$
$449$	16.6479			0.785665			0.392832	+	0.919610i	$0.371495\pi$
$450$		0			0
$451$	19.9616	−	48.1916i	0.939955	−	2.26925i
$452$	9.34041	−	7.16770i	0.439336	−	0.337140i
$453$	28.5052	−	11.8072i	1.33929	−	0.554752i
$454$	0.742746	−	0.651396i	0.0348588	−	0.0305715i
$455$		0			0
$456$	−8.20609	−	5.48246i	−0.384285	−	0.256740i
$457$	5.83937	+	5.83937i	0.273154	+	0.273154i	0.830369	−	0.557214i	$-0.188130\pi$
$457$	5.83937	+	5.83937i	0.273154	+	0.273154i	−0.557214	+	0.830369i	$0.688130\pi$
$458$	26.0134	+	1.70452i	1.21553	+	0.0796469i
$459$	−4.10164	−	9.90223i	−0.191448	−	0.462196i
$460$		0			0
$461$	−6.37952	−	2.64248i	−0.297124	−	0.123073i	0.229142	−	0.973393i	$-0.426408\pi$
$461$	−6.37952	−	2.64248i	−0.297124	−	0.123073i	−0.526265	+	0.850320i	$0.676408\pi$
$462$	70.1267	−	23.8063i	3.26259	−	1.10757i
$463$			5.92393i			0.275309i	0.990480	+	0.137654i	$0.0439563\pi$
$463$			5.92393i			0.275309i	−0.990480	+	0.137654i	$0.956044\pi$
$464$	−4.27422	−	3.27921i	−0.198426	−	0.152234i
$465$		0			0
$466$	−4.20317	−	12.3814i	−0.194708	−	0.573556i
$467$	−9.91354	−	4.10632i	−0.458744	−	0.190018i	0.141330	−	0.989963i	$-0.454862\pi$
$467$	−9.91354	−	4.10632i	−0.458744	−	0.190018i	−0.600074	+	0.799945i	$0.704862\pi$
$468$	12.9487	−	22.4298i	0.598555	−	1.03682i
$469$	14.5345	+	35.0894i	0.671140	+	1.62028i
$470$		0			0
$471$	−7.80117	−	7.80117i	−0.359459	−	0.359459i
$472$	14.4051	+	21.5561i	0.663048	+	0.992201i
$473$	−1.24357	+	1.24357i	−0.0571794	+	0.0571794i
$474$	−15.1806	−	17.3095i	−0.697268	−	0.795052i
$475$		0			0
$476$	−6.36100	+	48.3306i	−0.291556	+	2.21523i
$477$	−8.62502	+	20.8226i	−0.394913	+	0.953404i
$478$	−8.18323	+	16.5947i	−0.374292	+	0.759026i
$479$	5.94147			0.271473			0.135736	−	0.990745i	$-0.456660\pi$
$479$	5.94147			0.271473			0.135736	+	0.990745i	$0.456660\pi$
$480$		0			0
$481$	10.2013			0.465137
$482$	−10.5108	+	21.3149i	−0.478755	+	0.970865i
$483$	−20.6277	+	49.7996i	−0.938592	+	2.26596i
$484$	−36.0088	−	4.73927i	−1.63676	−	0.215421i
$485$		0			0
$486$	−20.6381	−	23.5323i	−0.936163	−	1.06745i
$487$	−12.0824	+	12.0824i	−0.547506	+	0.547506i	−0.925719	−	0.378212i	$-0.876539\pi$
$487$	−12.0824	+	12.0824i	−0.547506	+	0.547506i	0.378212	+	0.925719i	$0.376539\pi$
$488$	−9.24477	−	1.83836i	−0.418491	−	0.0832185i
$489$	8.68515	+	8.68515i	0.392756	+	0.392756i
$490$		0			0
$491$	−4.96593	−	11.9888i	−0.224109	−	0.541048i	0.771331	−	0.636434i	$-0.219591\pi$
$491$	−4.96593	−	11.9888i	−0.224109	−	0.541048i	−0.995440	+	0.0953865i	$0.969591\pi$
$492$	−43.1206	−	24.8936i	−1.94403	−	1.12229i
$493$	8.05991	+	3.33853i	0.363000	+	0.150360i
$494$	2.18841	+	6.44644i	0.0984610	+	0.290039i
$495$		0			0
$496$	−4.47935	+	16.7222i	−0.201129	+	0.750848i
$497$			50.8357i			2.28029i
$498$	−43.4911	+	14.7642i	−1.94888	+	0.661598i
$499$	−5.62274	−	2.32902i	−0.251708	−	0.104261i	0.253262	−	0.967398i	$-0.418497\pi$
$499$	−5.62274	−	2.32902i	−0.251708	−	0.104261i	−0.504970	+	0.863137i	$0.668497\pi$
$500$		0			0
$501$	20.8427	+	50.3188i	0.931184	+	2.24808i
$502$	7.98914	+	0.523485i	0.356573	+	0.0233643i
$503$	−18.6450	−	18.6450i	−0.831339	−	0.831339i	0.156361	−	0.987700i	$-0.450024\pi$
$503$	−18.6450	−	18.6450i	−0.831339	−	0.831339i	−0.987700	+	0.156361i	$0.950024\pi$
$504$	−7.56414	−	38.0163i	−0.336933	−	1.69338i
$505$		0			0
$506$	31.9134	−	27.9883i	1.41872	−	1.24423i
$507$	0.851898	−	0.352868i	0.0378341	−	0.0156714i
$508$	15.2635	+	19.8903i	0.677209	+	0.882487i
$509$	−7.39404	+	17.8508i	−0.327735	+	0.791222i	0.671025	+	0.741435i	$0.265854\pi$
$509$	−7.39404	+	17.8508i	−0.327735	+	0.791222i	−0.998760	+	0.0497872i	$0.984146\pi$
$510$		0			0
$511$	10.2775			0.454650
$512$	12.5743	+	18.8119i	0.555711	+	0.831376i
$513$	−2.24019			−0.0989070
$514$	−28.5694	−	14.0882i	−1.26014	−	0.621404i
$515$		0			0
$516$	1.02198	+	1.33177i	0.0449902	+	0.0586278i
$517$	38.8770	−	16.1034i	1.70981	−	0.708225i
$518$	11.4786	−	10.0668i	0.504339	−	0.442310i
$519$	−8.71580	+	8.71580i	−0.382581	+	0.382581i
$520$		0			0
$521$	2.54106	+	2.54106i	0.111326	+	0.111326i	0.760575	−	0.649250i	$-0.224917\pi$
$521$	2.54106	+	2.54106i	0.111326	+	0.111326i	−0.649250	+	0.760575i	$0.724917\pi$
$522$	−6.92203	−	0.453563i	−0.302969	−	0.0198519i
$523$	−1.93590	−	4.67367i	−0.0846509	−	0.204365i	0.875886	−	0.482518i	$-0.160278\pi$
$523$	−1.93590	−	4.67367i	−0.0846509	−	0.204365i	−0.960537	+	0.278153i	$0.910278\pi$
$524$	−15.5186	+	4.15882i	−0.677933	+	0.181679i
$525$		0			0
$526$	25.7411	−	8.73845i	1.12236	−	0.381015i
$527$		−	28.0343i		−	1.22119i
$528$	−14.4038	+	53.7717i	−0.626844	+	2.34011i
$529$			7.89558i			0.343286i
$530$		0			0
$531$	30.8429	+	12.7755i	1.33847	+	0.554411i
$532$	8.82389	+	5.09403i	0.382564	+	0.220854i
$533$	13.1436	+	31.7316i	0.569315	+	1.37445i
$534$	0.686753	−	10.4808i	0.0297187	−	0.453551i
$535$		0			0
$536$	−28.0009	−	5.56808i	−1.20945	−	0.240505i
$537$	28.6208	−	28.6208i	1.23508	−	1.23508i
$538$	16.9511	+	19.3283i	0.730814	+	0.833302i
$539$	−35.7142	+	14.7933i	−1.53832	+	0.637194i
$540$		0			0
$541$	−14.4320	+	34.8420i	−0.620481	+	1.49797i	0.230659	+	0.973035i	$0.425912\pi$
$541$	−14.4320	+	34.8420i	−0.620481	+	1.49797i	−0.851140	+	0.524939i	$0.824088\pi$
$542$	−8.26107	+	16.7526i	−0.354843	+	0.719585i
$543$	−5.77382			−0.247778
$544$	−27.5515	−	24.1575i	−1.18126	−	1.03574i
$545$		0			0
$546$	−21.5664	+	43.7345i	−0.922958	+	1.87166i
$547$	−5.89286	+	14.2266i	−0.251961	+	0.608287i	−0.998362	−	0.0572089i	$-0.981780\pi$
$547$	−5.89286	+	14.2266i	−0.251961	+	0.608287i	0.746402	+	0.665496i	$0.231780\pi$
$548$	3.77008	−	28.6449i	0.161050	−	1.22365i
$549$	−11.2132	+	4.64468i	−0.478570	+	0.198230i
$550$		0			0
$551$	1.28934	−	1.28934i	0.0549278	−	0.0549278i
$552$	−22.5123	−	33.6879i	−0.958186	−	1.43385i
$553$	16.8073	+	16.8073i	0.714719	+	0.714719i
$554$	−1.21984	+	18.6165i	−0.0518261	+	0.790941i
$555$		0			0
$556$	−15.1446	+	26.2334i	−0.642273	+	1.11255i
$557$	−10.0351	−	4.15666i	−0.425199	−	0.176123i	0.159814	−	0.987147i	$-0.448911\pi$
$557$	−10.0351	−	4.15666i	−0.425199	−	0.176123i	−0.585013	+	0.811024i	$0.698911\pi$
$558$	7.16576	+	21.1083i	0.303351	+	0.893588i
$559$		−	1.15799i		−	0.0489778i
$560$		0			0
$561$		−	90.1471i		−	3.80601i
$562$	11.9775	−	4.06605i	0.505238	−	0.171516i
$563$	−20.7280	−	8.58581i	−0.873580	−	0.361849i	−0.0995764	−	0.995030i	$-0.531749\pi$
$563$	−20.7280	−	8.58581i	−0.873580	−	0.361849i	−0.774004	+	0.633181i	$0.781749\pi$
$564$	−10.3974	−	38.7977i	−0.437808	−	1.63368i
$565$		0			0
$566$	−12.1105	−	0.793537i	−0.509043	−	0.0333549i
$567$	17.7248	+	17.7248i	0.744372	+	0.744372i
$568$	−31.7735	−	21.2278i	−1.33319	−	0.890698i
$569$	−15.8062	+	15.8062i	−0.662632	+	0.662632i	−0.956000	−	0.293367i	$-0.905224\pi$
$569$	−15.8062	+	15.8062i	−0.662632	+	0.662632i	0.293367	+	0.956000i	$0.405224\pi$
$570$		0			0
$571$	6.01892	−	2.49312i	0.251884	−	0.104334i	−0.253169	−	0.967422i	$-0.581473\pi$
$571$	6.01892	−	2.49312i	0.251884	−	0.104334i	0.505053	+	0.863088i	$0.331473\pi$
$572$	30.4640	−	23.3777i	1.27376	−	0.977469i
$573$	−2.67297	+	6.45311i	−0.111665	+	0.269583i
$574$	46.1027	+	22.7343i	1.92429	+	0.948910i
$575$		0			0
$576$	26.9197	+	11.1469i	1.12165	+	0.464456i
$577$	17.1520			0.714046			0.357023	−	0.934096i	$-0.383792\pi$
$577$	17.1520			0.714046			0.357023	+	0.934096i	$0.383792\pi$
$578$	31.6569	+	15.6107i	1.31675	+	0.649320i
$579$	23.1635	−	55.9217i	0.962643	−	2.32402i
$580$		0			0
$581$	43.8074	−	18.1456i	1.81744	−	0.752807i
$582$	2.81317	−	2.46718i	0.116610	−	0.102268i
$583$	−23.6294	+	23.6294i	−0.978630	+	0.978630i
$584$	−4.29164	+	6.42367i	−0.177589	+	0.265814i
$585$		0			0
$586$	27.6127	+	1.80931i	1.14067	+	0.0747418i
$587$	−9.99100	−	24.1204i	−0.412373	−	0.995556i	−0.984499	−	0.175390i	$-0.943881\pi$
$587$	−9.99100	−	24.1204i	−0.412373	−	0.995556i	0.572126	−	0.820166i	$-0.306119\pi$
$588$	9.55152	+	35.6414i	0.393898	+	1.46983i
$589$	−5.41344	−	2.24232i	−0.223057	−	0.0923932i
$590$		0			0
$591$		−	38.5736i		−	1.58670i
$592$	1.49881	+	11.3780i	0.0616008	+	0.467633i
$593$		−	18.6374i		−	0.765345i	−0.923884	−	0.382673i	$-0.875004\pi$
$593$		−	18.6374i		−	0.765345i	0.923884	−	0.382673i	$-0.124996\pi$
$594$	4.06197	+	11.9654i	0.166665	+	0.490948i
$595$		0			0
$596$	6.43315	−	11.1435i	0.263512	−	0.456456i
$597$	1.72952	+	4.17543i	0.0707845	+	0.170889i
$598$	−1.82746	+	27.8897i	−0.0747306	+	1.14050i
$599$	17.4099	+	17.4099i	0.711350	+	0.711350i	0.966818	−	0.255468i	$-0.0822295\pi$
$599$	17.4099	+	17.4099i	0.711350	+	0.711350i	−0.255468	+	0.966818i	$0.582230\pi$
$600$		0			0
$601$	−24.7490	+	24.7490i	−1.00953	+	1.00953i	−0.00957803	+	0.999954i	$0.503049\pi$
$601$	−24.7490	+	24.7490i	−1.00953	+	1.00953i	−0.999954	+	0.00957803i	$0.996951\pi$
$602$	−1.14273	−	1.30298i	−0.0465742	−	0.0531056i
$603$	−33.9631	+	14.0680i	−1.38308	+	0.572892i
$604$	3.12437	−	23.7388i	0.127129	−	0.965918i
$605$		0			0
$606$	3.17915	−	6.44699i	0.129144	−	0.261891i
$607$	21.2313			0.861753			0.430877	−	0.902411i	$-0.358204\pi$
$607$	21.2313			0.861753			0.430877	+	0.902411i	$0.358204\pi$
$608$	−6.86853	+	3.38798i	−0.278556	+	0.137401i
$609$	13.0607			0.529248
$610$		0			0
$611$	−10.6032	+	25.5984i	−0.428960	+	1.03560i
$612$	−46.7794	−	6.15684i	−1.89094	−	0.248875i
$613$	36.9806	−	15.3179i	1.49363	−	0.618683i	0.521529	−	0.853234i	$-0.325362\pi$
$613$	36.9806	−	15.3179i	1.49363	−	0.618683i	0.972104	+	0.234550i	$0.0753618\pi$
$614$	29.2028	+	33.2982i	1.17853	+	1.34381i
$615$		0			0
$616$	11.2088	−	56.3672i	0.451617	−	2.27110i
$617$	16.6587	+	16.6587i	0.670652	+	0.670652i	0.957866	−	0.287214i	$-0.0927292\pi$
$617$	16.6587	+	16.6587i	0.670652	+	0.670652i	−0.287214	+	0.957866i	$0.592729\pi$
$618$	3.83160	−	58.4758i	0.154130	−	2.35224i
$619$	−17.7139	−	42.7652i	−0.711983	−	1.71888i	−0.694985	−	0.719024i	$-0.744589\pi$
$619$	−17.7139	−	42.7652i	−0.711983	−	1.71888i	−0.0169982	−	0.999856i	$-0.505411\pi$
$620$		0			0
$621$	−8.49711	−	3.51962i	−0.340977	−	0.141237i
$622$	3.38103	+	9.95959i	0.135567	+	0.399343i
$623$			10.8436i			0.434439i
$624$	−18.3294	−	31.7420i	−0.733764	−	1.27070i
$625$		0			0
$626$	−25.8799	+	8.78558i	−1.03437	+	0.351142i
$627$	−17.4074	−	7.21040i	−0.695186	−	0.287956i
$628$	−8.26978	+	2.21621i	−0.330000	+	0.0884365i
$629$	−7.11200	−	17.1699i	−0.283574	−	0.684608i
$630$		0			0
$631$	−0.267293	−	0.267293i	−0.0106408	−	0.0106408i	0.701766	−	0.712407i	$-0.252395\pi$
$631$	−0.267293	−	0.267293i	−0.0106408	−	0.0106408i	−0.712407	+	0.701766i	$0.752395\pi$
$632$	−17.5233	+	3.48662i	−0.697038	+	0.138690i
$633$	−4.85161	+	4.85161i	−0.192834	+	0.192834i
$634$	−13.4000	+	11.7519i	−0.532181	+	0.466728i
$635$		0			0
$636$	19.4189	+	25.3053i	0.770011	+	1.00342i
$637$	9.74061	−	23.5159i	0.385937	−	0.931735i
$638$	−9.22457	−	4.54884i	−0.365204	−	0.180090i
$639$	−49.2041			−1.94648
$640$		0			0
$641$	4.73635			0.187075			0.0935373	−	0.995616i	$-0.470183\pi$
$641$	4.73635			0.187075			0.0935373	+	0.995616i	$0.470183\pi$
$642$	25.8810	+	12.7625i	1.02144	+	0.503696i
$643$	8.99345	−	21.7121i	0.354667	−	0.856242i	−0.641364	−	0.767237i	$-0.721631\pi$
$643$	8.99345	−	21.7121i	0.354667	−	0.856242i	0.996031	−	0.0890053i	$-0.0283688\pi$
$644$	25.4659	+	33.1852i	1.00350	+	1.30768i
$645$		0			0
$646$	9.32440	−	8.17759i	0.366864	−	0.321743i
$647$	0.928657	−	0.928657i	0.0365093	−	0.0365093i	−0.688616	−	0.725126i	$-0.741782\pi$
$647$	0.928657	−	0.928657i	0.0365093	−	0.0365093i	0.725126	+	0.688616i	$0.241782\pi$
$648$	−18.4799	+	3.67696i	−0.725958	+	0.144444i
$649$	35.0003	+	35.0003i	1.37388	+	1.37388i
$650$		0			0
$651$	−16.0614	−	38.7756i	−0.629494	−	1.51973i
$652$	9.20685	−	2.46734i	0.360568	−	0.0966285i
$653$	−30.7075	−	12.7195i	−1.20168	−	0.497751i	−0.310137	−	0.950692i	$-0.600375\pi$
$653$	−30.7075	−	12.7195i	−1.20168	−	0.497751i	−0.891541	+	0.452940i	$0.850375\pi$
$654$	−50.7769	+	17.2375i	−1.98554	+	0.674040i
$655$		0			0
$656$	−33.4608	+	19.3220i	−1.30642	+	0.754396i
$657$			9.94763i			0.388094i
$658$	13.3302	+	39.2670i	0.519665	+	1.53079i
$659$	17.4708	+	7.23664i	0.680566	+	0.281900i	0.696063	−	0.717980i	$-0.254933\pi$
$659$	17.4708	+	7.23664i	0.680566	+	0.281900i	−0.0154977	+	0.999880i	$0.504933\pi$
$660$		0			0
$661$	3.87034	+	9.34382i	0.150539	+	0.363432i	0.981102	−	0.193492i	$-0.0619813\pi$
$661$	3.87034	+	9.34382i	0.150539	+	0.363432i	−0.830563	+	0.556924i	$0.811981\pi$
$662$	−2.39474	+	36.5472i	−0.0930741	+	1.42045i
$663$	41.9717	+	41.9717i	1.63005	+	1.63005i
$664$	−6.95149	+	34.9578i	−0.269770	+	1.35663i
$665$		0			0
$666$	9.74369	+	11.1101i	0.377560	+	0.430509i
$667$	6.91622	−	2.86479i	0.267797	−	0.110925i
$668$	41.9049	+	5.51528i	1.62135	+	0.213393i
$669$	−23.2502	+	56.1309i	−0.898904	+	2.17015i
$670$		0			0
$671$	−17.9955			−0.694708
$672$	−51.9480	−	17.6285i	−2.00394	−	0.680036i
$673$	41.3179			1.59269			0.796345	−	0.604843i	$-0.206764\pi$
$673$	41.3179			1.59269			0.796345	+	0.604843i	$0.206764\pi$
$674$	11.5081	−	23.3372i	0.443275	−	0.898915i
$675$		0			0
$676$	0.0933739	−	0.709451i	0.00359130	−	0.0272866i
$677$	11.7809	−	4.87982i	0.452778	−	0.187547i	−0.144627	−	0.989486i	$-0.546198\pi$
$677$	11.7809	−	4.87982i	0.452778	−	0.187547i	0.597405	+	0.801939i	$0.296198\pi$
$678$	−14.1472	−	16.1311i	−0.543319	−	0.619513i
$679$	−2.73155	+	2.73155i	−0.104827	+	0.104827i
$680$		0			0
$681$	−1.27304	−	1.27304i	−0.0487831	−	0.0487831i
$682$	−2.16103	+	32.9804i	−0.0827500	+	1.26289i
$683$	14.6053	+	35.2603i	0.558857	+	1.34920i	0.910672	+	0.413130i	$0.135564\pi$
$683$	14.6053	+	35.2603i	0.558857	+	1.34920i	−0.351816	+	0.936069i	$0.614436\pi$
$684$	−4.93053	+	8.54067i	−0.188524	+	0.326561i
$685$		0			0
$686$	−0.271499	−	0.799760i	−0.0103659	−	0.0305350i
$687$		−	47.5076i		−	1.81253i
$688$	1.29157	−	0.170137i	0.0492407	−	0.00648642i
$689$		−	22.0033i		−	0.838260i
$690$		0			0
$691$	17.8170	+	7.38004i	0.677790	+	0.280750i	0.694903	−	0.719104i	$-0.255447\pi$
$691$	17.8170	+	7.38004i	0.677790	+	0.280750i	−0.0171125	+	0.999854i	$0.505447\pi$
$692$	2.47605	+	9.23935i	0.0941252	+	0.351227i
$693$	−28.3196	−	68.3695i	−1.07577	−	2.59714i
$694$	−6.05923	−	0.397028i	−0.230005	−	0.0150710i
$695$		0			0
$696$	−5.45385	+	8.16325i	−0.206728	+	0.309427i
$697$	44.2445	−	44.2445i	1.67588	−	1.67588i
$698$	−31.7907	+	27.8808i	−1.20330	+	1.05530i
$699$	−22.0143	+	9.11861i	−0.832656	+	0.344897i
$700$		0			0
$701$	−6.75044	+	16.2970i	−0.254961	+	0.615529i	−0.998591	−	0.0530613i	$-0.983102\pi$
$701$	−6.75044	+	16.2970i	−0.254961	+	0.615529i	0.743631	+	0.668591i	$0.233102\pi$
$702$	−7.46224	−	3.67979i	−0.281644	−	0.138885i
$703$	−3.88437			−0.146502
$704$	30.5503	+	30.5434i	1.15141	+	1.15115i
$705$		0			0
$706$	12.6150	+	6.22075i	0.474773	+	0.234121i
$707$	−2.83993	+	6.85620i	−0.106807	+	0.257854i
$708$	37.4826	−	28.7637i	1.40868	−	1.08101i
$709$	10.2509	−	4.24606i	0.384981	−	0.159464i	−0.181795	−	0.983336i	$-0.558191\pi$
$709$	10.2509	−	4.24606i	0.384981	−	0.159464i	0.566775	+	0.823872i	$0.308191\pi$
$710$		0			0
$711$	−16.2678	+	16.2678i	−0.610092	+	0.610092i
$712$	−6.77749	−	4.52802i	−0.253997	−	0.169695i
$713$	−17.0104	−	17.0104i	−0.637043	−	0.637043i
$714$	88.6456	+	5.80847i	3.31748	+	0.217376i
$715$		0			0
$716$	−8.13081	−	30.3400i	−0.303863	−	1.13386i
$717$	31.1520	+	12.9036i	1.16339	+	0.481894i
$718$	−22.3946	+	7.60243i	−0.835761	+	0.283720i
$719$		−	16.7114i		−	0.623232i	−0.950208	−	0.311616i	$-0.899130\pi$
$719$		−	16.7114i		−	0.623232i	0.950208	−	0.311616i	$-0.100870\pi$
$720$		0			0
$721$			60.4996i			2.25312i
$722$	7.80429	+	22.9893i	0.290446	+	0.855572i
$723$	40.0128	+	16.5738i	1.48809	+	0.616387i
$724$	−2.24019	+	3.88046i	−0.0832559	+	0.144216i
$725$		0			0
$726$	−4.32760	+	66.0454i	−0.160612	+	2.45117i
$727$	6.48584	+	6.48584i	0.240546	+	0.240546i	0.817076	−	0.576530i	$-0.195594\pi$
$727$	6.48584	+	6.48584i	0.240546	+	0.240546i	−0.576530	+	0.817076i	$0.695594\pi$
$728$	21.0254	+	31.4629i	0.779253	+	1.16609i
$729$	−26.2021	+	26.2021i	−0.970447	+	0.970447i
$730$		0			0
$731$	−1.94903	+	0.807316i	−0.0720876	+	0.0298597i
$732$	−2.24144	+	17.0303i	−0.0828459	+	0.629460i
$733$	−7.27403	+	17.5611i	−0.268672	+	0.648632i	−0.999421	−	0.0340138i	$-0.989171\pi$
$733$	−7.27403	+	17.5611i	−0.268672	+	0.648632i	0.730749	+	0.682646i	$0.239171\pi$
$734$	21.2187	−	43.0294i	0.783198	−	1.58824i
$735$		0			0
$736$	−31.3754	+	2.05941i	−1.15651	+	0.0759109i
$737$	−54.5054			−2.00773
$738$	−22.0046	+	44.6230i	−0.809999	+	1.64259i
$739$	−4.88417	+	11.7914i	−0.179667	+	0.433755i	−0.987897	−	0.155112i	$-0.950426\pi$
$739$	−4.88417	+	11.7914i	−0.179667	+	0.433755i	0.808230	+	0.588867i	$0.200426\pi$
$740$		0			0
$741$	11.4619	−	4.74766i	0.421062	−	0.174410i
$742$	−21.7133	−	24.7584i	−0.797121	−	0.908908i
$743$	−33.3298	+	33.3298i	−1.22275	+	1.22275i	−0.256101	+	0.966650i	$0.582438\pi$
$743$	−33.3298	+	33.3298i	−1.22275	+	1.22275i	−0.966650	+	0.256101i	$0.917562\pi$
$744$	30.9424	+	6.15302i	1.13440	+	0.225581i
$745$		0			0
$746$	1.50127	−	22.9115i	0.0549654	−	0.838851i
$747$	17.5632	+	42.4013i	0.642604	+	1.55138i
$748$	−60.5858	−	34.9762i	−2.21524	−	1.27886i
$749$	−27.5238	−	11.4007i	−1.00570	−	0.416574i
$750$		0			0
$751$		−	6.38146i		−	0.232863i	−0.993199	−	0.116431i	$-0.962854\pi$
$751$		−	6.38146i		−	0.232863i	0.993199	−	0.116431i	$-0.0371455\pi$
$752$	−30.1091	−	8.06530i	−1.09797	−	0.294111i
$753$		−	14.5904i		−	0.531702i
$754$	6.41279	−	2.17698i	0.233540	−	0.0792810i
$755$		0			0
$756$	−12.0279	+	3.22334i	−0.437450	+	0.117232i
$757$	13.7562	+	33.2104i	0.499978	+	1.20705i	0.949495	+	0.313782i	$0.101596\pi$
$757$	13.7562	+	33.2104i	0.499978	+	1.20705i	−0.449517	+	0.893272i	$0.648404\pi$
$758$	−37.0324	−	2.42653i	−1.34508	−	0.0881357i
$759$	−54.6984	−	54.6984i	−1.98543	−	1.98543i
$760$		0			0
$761$	−8.77034	+	8.77034i	−0.317925	+	0.317925i	−0.847970	−	0.530045i	$-0.822175\pi$
$761$	−8.77034	+	8.77034i	−0.317925	+	0.317925i	0.530045	+	0.847970i	$0.322175\pi$
$762$	34.3510	−	30.1262i	1.24441	−	1.09136i
$763$	51.1462	−	21.1854i	1.85162	−	0.766964i
$764$	3.29991	+	4.30019i	0.119386	+	0.155575i
$765$		0			0
$766$	1.95589	+	0.964493i	0.0706692	+	0.0348486i
$767$	−32.5917			−1.17682
$768$	32.7105	−	25.1075i	1.18034	−	0.905987i
$769$	−14.8635			−0.535992			−0.267996	−	0.963420i	$-0.586361\pi$
$769$	−14.8635			−0.535992			−0.267996	+	0.963420i	$0.586361\pi$
$770$		0			0
$771$	−22.2148	+	53.6312i	−0.800045	+	1.93148i
$772$	−28.5965	−	37.2648i	−1.02921	−	1.34119i
$773$	−8.25543	+	3.41951i	−0.296927	+	0.122991i	−0.526174	−	0.850377i	$-0.676374\pi$
$773$	−8.25543	+	3.41951i	−0.296927	+	0.122991i	0.229246	+	0.973368i	$0.426374\pi$
$774$	1.26116	−	1.10605i	0.0453315	−	0.0397562i
$775$		0			0
$776$	−0.566651	−	2.84791i	−0.0203416	−	0.102234i
$777$	−19.6739	−	19.6739i	−0.705796	−	0.705796i
$778$	−52.2592	−	3.42426i	−1.87358	−	0.122766i
$779$	−5.00475	−	12.0825i	−0.179314	−	0.432902i
$780$		0			0
$781$	−67.4006	−	27.9182i	−2.41178	−	0.998993i
$782$	48.2157	−	16.3680i	1.72419	−	0.585320i
$783$			2.22850i			0.0796401i
$784$	27.6597	+	7.40917i	0.987847	+	0.264613i
$785$		0			0
$786$	9.41178	+	27.7245i	0.335707	+	0.988900i
$787$	−43.9630	−	18.2101i	−1.56711	−	0.649119i	−0.580805	−	0.814043i	$-0.697262\pi$
$787$	−43.9630	−	18.2101i	−1.56711	−	0.649119i	−0.986306	+	0.164924i	$0.947262\pi$
$788$	−25.9244	−	14.9662i	−0.923520	−	0.533148i
$789$	−18.9577	−	45.7680i	−0.674913	−	1.62938i
$790$		0			0
$791$	15.6631	+	15.6631i	0.556917	+	0.556917i
$792$	54.5580	+	10.8491i	1.93864	+	0.385505i
$793$	8.37855	−	8.37855i	0.297531	−	0.297531i
$794$	−4.34279	−	4.95182i	−0.154120	−	0.175733i
$795$		0			0
$796$	3.47725	+	0.457656i	0.123248	+	0.0162212i
$797$	2.04252	−	4.93109i	0.0723499	−	0.174668i	−0.883567	−	0.468304i	$-0.844865\pi$
$797$	2.04252	−	4.93109i	0.0723499	−	0.174668i	0.955917	+	0.293636i	$0.0948653\pi$
$798$	8.21192	−	16.6529i	0.290699	−	0.589507i
$799$	50.4773			1.78576
$800$		0			0
$801$	−10.4955			−0.370842
$802$	7.34214	−	14.8891i	0.259260	−	0.525752i
$803$	−5.64425	+	13.6264i	−0.199181	+	0.480866i
$804$	−6.78895	+	51.5821i	−0.239428	+	1.81916i
$805$		0			0
$806$	−14.3493	−	16.3616i	−0.505431	−	0.576312i
$807$	33.1281	−	33.1281i	1.16616	−	1.16616i
$808$	−3.09940	−	4.63801i	−0.109036	−	0.163165i
$809$	14.6482	+	14.6482i	0.515004	+	0.515004i	0.916056	−	0.401051i	$-0.131355\pi$
$809$	14.6482	+	14.6482i	0.515004	+	0.515004i	−0.401051	+	0.916056i	$0.631355\pi$
$810$		0			0
$811$	−7.38535	−	17.8298i	−0.259335	−	0.626090i	0.739560	−	0.673091i	$-0.235034\pi$
$811$	−7.38535	−	17.8298i	−0.259335	−	0.626090i	−0.998895	+	0.0470010i	$0.985034\pi$
$812$	5.06744	−	8.77783i	0.177832	−	0.308041i
$813$	31.4484	+	13.0263i	1.10294	+	0.456854i
$814$	7.04322	+	20.7474i	0.246865	+	0.727196i
$815$		0			0
$816$	−40.6467	+	52.9800i	−1.42292	+	1.85467i
$817$			0.440932i			0.0154263i
$818$	24.2982	−	8.24862i	0.849565	−	0.288406i
$819$	45.0176	+	18.6469i	1.57304	+	0.651576i
$820$		0			0
$821$	−2.20294	−	5.31836i	−0.0768830	−	0.185612i	0.880765	−	0.473554i	$-0.157029\pi$
$821$	−2.20294	−	5.31836i	−0.0768830	−	0.185612i	−0.957648	+	0.287942i	$0.907029\pi$
$822$	−52.5390	−	3.44260i	−1.83251	−	0.120074i
$823$	−14.1449	−	14.1449i	−0.493061	−	0.493061i	0.416208	−	0.909269i	$-0.363359\pi$
$823$	−14.1449	−	14.1449i	−0.493061	−	0.493061i	−0.909269	+	0.416208i	$0.863359\pi$
$824$	−37.8136	−	25.2632i	−1.31730	−	0.880085i
$825$		0			0
$826$	−36.6725	+	32.1621i	−1.27600	+	1.11906i
$827$	49.2710	−	20.4087i	1.71332	−	0.709680i	0.713358	−	0.700800i	$-0.247173\pi$
$827$	49.2710	−	20.4087i	1.71332	−	0.709680i	0.999961	−	0.00888040i	$-0.00282676\pi$
$828$	−32.1200	+	24.6485i	−1.11625	+	0.856594i
$829$	−5.39395	+	13.0222i	−0.187340	+	0.452278i	−0.989446	−	0.144903i	$-0.953713\pi$
$829$	−5.39395	+	13.0222i	−0.187340	+	0.452278i	0.802106	+	0.597182i	$0.203713\pi$
$830$		0			0
$831$	33.9989			1.17941
$832$	−28.4447	+	0.00320440i	−0.986143	+	0.000111093i
$833$	−46.3708			−1.60665
$834$	49.5091	+	24.4141i	1.71436	+	0.845389i
$835$		0			0
$836$	−11.5999	+	8.90159i	−0.401190	+	0.307868i
$837$	6.61612	−	2.74049i	0.228686	−	0.0947250i
$838$	13.2395	−	11.6111i	0.457350	−	0.401100i
$839$	−11.5159	+	11.5159i	−0.397573	+	0.397573i	−0.877376	−	0.479803i	$-0.840708\pi$
$839$	−11.5159	+	11.5159i	−0.397573	+	0.397573i	0.479803	+	0.877376i	$0.340708\pi$
$840$		0			0
$841$	19.2235	+	19.2235i	0.662879	+	0.662879i
$842$	−24.6740	−	1.61675i	−0.850322	−	0.0557170i
$843$	−8.82113	−	21.2961i	−0.303816	−	0.733477i
$844$	1.37828	+	5.14304i	0.0474424	+	0.177031i
$845$		0			0
$846$	−38.0067	+	12.9023i	−1.30670	+	0.443591i
$847$		−	68.3312i		−	2.34789i
$848$	24.5415	−	3.23282i	0.842758	−	0.111016i
$849$			22.1171i			0.759058i
$850$		0			0
$851$	−14.7335	−	6.10281i	−0.505058	−	0.209202i
$852$	−34.8160	+	60.3084i	−1.19278	+	2.06613i
$853$	11.4029	+	27.5290i	0.390427	+	0.942575i	0.989847	+	0.142140i	$0.0453982\pi$
$853$	11.4029	+	27.5290i	0.390427	+	0.942575i	−0.599419	+	0.800435i	$0.704602\pi$
$854$	1.15951	−	17.6957i	0.0396775	−	0.605536i
$855$		0			0
$856$	18.6190	−	12.4423i	0.636384	−	0.425270i
$857$	−16.6352	+	16.6352i	−0.568248	+	0.568248i	−0.931637	−	0.363389i	$-0.881620\pi$
$857$	−16.6352	+	16.6352i	−0.568248	+	0.568248i	0.363389	+	0.931637i	$0.381620\pi$
$858$	−46.1414	−	52.6122i	−1.57524	−	1.79615i
$859$	−21.0912	+	8.73628i	−0.719624	+	0.298078i	−0.712280	−	0.701895i	$-0.752338\pi$
$859$	−21.0912	+	8.73628i	−0.719624	+	0.298078i	−0.00734363	+	0.999973i	$0.502338\pi$
$860$		0			0
$861$	35.8481	−	86.5451i	1.22170	−	2.94945i
$862$	12.6680	−	25.6894i	0.431474	−	0.874985i
$863$	8.05843			0.274312			0.137156	−	0.990549i	$-0.456204\pi$
$863$	8.05843			0.274312			0.137156	+	0.990549i	$0.456204\pi$
$864$	3.00789	−	8.86369i	0.102330	−	0.301549i
$865$		0			0
$866$	−16.4364	+	33.3313i	−0.558531	+	1.13264i
$867$	24.6155	−	59.4271i	0.835986	−	2.01825i
$868$	−32.2918	−	4.25007i	−1.09606	−	0.144257i
$869$	−31.5143	+	13.0536i	−1.06905	+	0.442815i
$870$		0			0
$871$	25.3773	−	25.3773i	0.859876	−	0.859876i
$872$	−8.11603	+	40.8140i	−0.274843	+	1.38214i
$873$	−2.64388	−	2.64388i	−0.0894816	−	0.0894816i
$874$	0.695849	−	10.6197i	0.0235375	−	0.359216i
$875$		0			0
$876$	12.1926	+	7.03879i	0.411950	+	0.237819i
$877$	−45.1432	−	18.6989i	−1.52438	−	0.631417i	−0.545913	−	0.837842i	$-0.683817\pi$
$877$	−45.1432	−	18.6989i	−1.52438	−	0.631417i	−0.978463	+	0.206424i	$0.933817\pi$
$878$	−2.49223	−	7.34142i	−0.0841087	−	0.247761i
$879$		−	50.4283i		−	1.70090i
$880$		0			0
$881$			7.18069i			0.241924i	0.992657	+	0.120962i	$0.0385979\pi$
$881$			7.18069i			0.241924i	−0.992657	+	0.120962i	$0.961402\pi$
$882$	34.9148	−	11.8527i	1.17564	−	0.399101i
$883$	−29.2458	−	12.1140i	−0.984198	−	0.407668i	−0.168219	−	0.985750i	$-0.553802\pi$
$883$	−29.2458	−	12.1140i	−0.984198	−	0.407668i	−0.815979	+	0.578081i	$0.803802\pi$
$884$	44.4929	−	11.9236i	1.49646	−	0.401035i
$885$		0			0
$886$	37.7573	+	2.47403i	1.26848	+	0.0831168i
$887$	13.6414	+	13.6414i	0.458033	+	0.458033i	0.898009	−	0.439976i	$-0.145013\pi$
$887$	13.6414	+	13.6414i	0.458033	+	0.458033i	−0.439976	+	0.898009i	$0.645013\pi$
$888$	20.5119	−	4.08128i	0.688336	−	0.136959i
$889$	−33.3544	+	33.3544i	−1.11867	+	1.11867i
$890$		0			0
$891$	−33.2347	+	13.7662i	−1.11340	+	0.461187i
$892$	28.7035	+	37.4042i	0.961064	+	1.25239i
$893$	4.03742	−	9.74718i	0.135107	−	0.326177i
$894$	−21.0306	−	10.3707i	−0.703369	−	0.346847i
$895$		0			0
$896$	−32.0031	+	28.0734i	−1.06915	+	0.937867i
$897$	50.9343			1.70065
$898$	−21.1159	−	10.4127i	−0.704648	−	0.347477i
$899$	−2.23062	+	5.38519i	−0.0743952	+	0.179606i
$900$		0			0
$901$	−37.0341	+	15.3400i	−1.23379	+	0.511051i
$902$	−55.4612	+	48.6400i	−1.84665	+	1.61953i
$903$	−2.23327	+	2.23327i	−0.0743186	+	0.0743186i
$904$	−16.3304	+	3.24927i	−0.543140	+	0.108069i
$905$		0			0
$906$	−43.5405	−	2.85297i	−1.44654	−	0.0947837i
$907$	6.68678	+	16.1433i	0.222031	+	0.536030i	0.995166	−	0.0982121i	$-0.0313124\pi$
$907$	6.68678	+	16.1433i	0.222031	+	0.536030i	−0.773135	+	0.634242i	$0.781312\pi$
$908$	−1.34951	+	0.361655i	−0.0447851	+	0.0120019i
$909$	−6.63614	−	2.74878i	−0.220107	−	0.0911713i
$910$		0			0
$911$		−	38.7147i		−	1.28268i	−0.767259	−	0.641338i	$-0.778380\pi$
$911$		−	38.7147i		−	1.28268i	0.767259	−	0.641338i	$-0.221620\pi$
$912$	6.97935	+	12.0865i	0.231109	+	0.400224i
$913$			68.0474i			2.25204i
$914$	−3.75421	−	11.0589i	−0.124178	−	0.365795i
$915$		0			0
$916$	−31.9288	−	18.4325i	−1.05496	−	0.609027i
$917$	−11.5674	−	27.9261i	−0.381988	−	0.922201i
$918$	−0.991075	+	15.1252i	−0.0327104	+	0.499207i
$919$	−8.52974	−	8.52974i	−0.281370	−	0.281370i	0.552285	−	0.833655i	$-0.313756\pi$
$919$	−8.52974	−	8.52974i	−0.281370	−	0.281370i	−0.833655	+	0.552285i	$0.813756\pi$
$920$		0			0
$921$	57.0720	−	57.0720i	1.88059	−	1.88059i
$922$	6.43888	+	7.34185i	0.212053	+	0.241791i
$923$	44.3797	−	18.3827i	1.46077	−	0.605073i
$924$	−103.838	−	13.6665i	−3.41600	−	0.449595i
$925$		0			0
$926$	3.70522	−	7.51381i	0.121761	−	0.246919i
$927$	−58.5578			−1.92329
$928$	3.37030	+	6.83268i	0.110636	+	0.224294i
$929$	−11.5216			−0.378012			−0.189006	−	0.981976i	$-0.560526\pi$
$929$	−11.5216			−0.378012			−0.189006	+	0.981976i	$0.560526\pi$
$930$		0			0
$931$	−3.70896	+	8.95423i	−0.121556	+	0.293463i
$932$	−2.41292	+	18.3332i	−0.0790377	+	0.600525i
$933$	17.7083	−	7.33502i	0.579744	−	0.240138i
$934$	10.0058	+	11.4090i	0.327399	+	0.373313i
$935$		0			0
$936$	−30.4530	+	20.3505i	−0.995388	+	0.665178i
$937$	−15.4558	−	15.4558i	−0.504920	−	0.504920i	0.408043	−	0.912963i	$-0.366211\pi$
$937$	−15.4558	−	15.4558i	−0.504920	−	0.504920i	−0.912963	+	0.408043i	$0.866211\pi$
$938$	3.51196	−	53.5975i	0.114669	−	1.75002i
$939$	19.0600	+	46.0148i	0.621999	+	1.50164i
$940$		0			0
$941$	34.8326	+	14.4281i	1.13551	+	0.470343i	0.869650	−	0.493668i	$-0.164344\pi$
$941$	34.8326	+	14.4281i	1.13551	+	0.470343i	0.265859	+	0.964012i	$0.414344\pi$
$942$	5.01549	+	14.7742i	0.163413	+	0.481371i
$943$		−	53.6924i		−	1.74847i
$944$	−4.78851	−	36.3513i	−0.155853	−	1.18313i
$945$		0			0
$946$	2.35513	−	0.799509i	0.0765719	−	0.0259943i
$947$	19.6092	+	8.12240i	0.637214	+	0.263943i	0.677815	−	0.735233i	$-0.262927\pi$
$947$	19.6092	+	8.12240i	0.637214	+	0.263943i	−0.0406007	+	0.999175i	$0.512927\pi$
$948$	8.42828	+	31.4500i	0.273738	+	1.02145i
$949$	−3.71644	−	8.97228i	−0.120641	−	0.291252i
$950$		0			0
$951$	22.9671	+	22.9671i	0.744760	+	0.744760i
$952$	38.2974	−	57.3231i	1.24123	−	1.85785i
$953$	−0.820449	+	0.820449i	−0.0265769	+	0.0265769i	−0.720270	−	0.693693i	$-0.755982\pi$
$953$	−0.820449	+	0.820449i	−0.0265769	+	0.0265769i	0.693693	+	0.720270i	$0.255982\pi$
$954$	23.9637	−	21.0164i	0.775853	−	0.680431i
$955$		0			0
$956$	20.7589	−	15.9301i	0.671391	−	0.515217i
$957$	−7.17276	+	17.3166i	−0.231862	+	0.559765i
$958$	−7.53605	−	3.71619i	−0.243479	−	0.120065i
$959$	54.3574			1.75529
$960$		0			0
$961$	−12.2690			−0.395775
$962$	−12.9391	−	6.38055i	−0.417173	−	0.205717i
$963$	11.0348	−	26.6404i	0.355592	−	0.858474i
$964$	26.6635	−	20.4612i	0.858773	−	0.659011i
$965$		0			0
$966$	57.3118	−	50.2630i	1.84398	−	1.61718i
$967$	−17.2920	+	17.2920i	−0.556072	+	0.556072i	−0.928187	−	0.372115i	$-0.878633\pi$
$967$	−17.2920	+	17.2920i	−0.556072	+	0.556072i	0.372115	+	0.928187i	$0.378633\pi$
$968$	42.7086	+	28.5335i	1.37271	+	0.917101i
$969$	−15.9817	−	15.9817i	−0.513407	−	0.513407i
$970$		0			0
$971$	4.80714	+	11.6055i	0.154268	+	0.372437i	0.982052	−	0.188611i	$-0.0603984\pi$
$971$	4.80714	+	11.6055i	0.154268	+	0.372437i	−0.827784	+	0.561048i	$0.810398\pi$
$972$	11.4583	+	42.7564i	0.367524	+	1.37141i
$973$	−52.6517	−	21.8090i	−1.68794	−	0.699166i
$974$	22.8823	−	7.76796i	0.733195	−	0.248901i
$975$		0			0
$976$	10.5761	+	8.11403i	0.338531	+	0.259724i
$977$			22.0892i			0.706697i	0.935492	+	0.353348i	$0.114957\pi$
$977$			22.0892i			0.706697i	−0.935492	+	0.353348i	$0.885043\pi$
$978$	−5.58381	−	16.4484i	−0.178551	−	0.525960i
$979$	−14.3770	−	5.95514i	−0.459490	−	0.190327i
$980$		0			0
$981$	20.5055	+	49.5045i	0.654689	+	1.58056i
$982$	−1.19991	+	18.3124i	−0.0382908	+	0.584373i
$983$	6.97130	+	6.97130i	0.222350	+	0.222350i	0.809487	−	0.587137i	$-0.199745\pi$
$983$	6.97130	+	6.97130i	0.222350	+	0.222350i	−0.587137	+	0.809487i	$0.699745\pi$
$984$	39.1233	+	58.5450i	1.24721	+	1.86635i
$985$		0			0
$986$	−8.13491	−	9.27573i	−0.259068	−	0.295399i
$987$	69.8174	−	28.9193i	2.22231	−	0.920512i
$988$	1.25630	−	9.54531i	0.0399682	−	0.303677i
$989$	−0.692758	+	1.67247i	−0.0220284	+	0.0531813i
$990$		0			0
$991$	60.5799			1.92439			0.962193	−	0.272370i	$-0.0878075\pi$
$991$	60.5799			1.92439			0.962193	+	0.272370i	$0.0878075\pi$
$992$	16.1407	−	18.4084i	0.512467	−	0.584468i
$993$	66.7451			2.11809
$994$	31.7961	−	64.4791i	1.00851	−	2.04515i
$995$		0			0
$996$	64.3979	+	8.47568i	2.04052	+	0.268562i
$997$	2.06492	−	0.855318i	0.0653967	−	0.0270882i	−0.349745	−	0.936845i	$-0.613732\pi$
$997$	2.06492	−	0.855318i	0.0653967	−	0.0270882i	0.415142	+	0.909757i	$0.363732\pi$
$998$	5.67506	+	6.47092i	0.179641	+	0.204833i
$999$	3.35687	−	3.35687i	0.106207	−	0.106207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.y.e.301.3	yes	64
5.2	odd	4		800.2.ba.h.749.12		64
5.3	odd	4		800.2.ba.f.749.5		64
5.4	even	2		800.2.y.d.301.14	yes	64
32.5	even	8	inner	800.2.y.e.101.3	yes	64
160.37	odd	8		800.2.ba.f.549.5		64
160.69	even	8		800.2.y.d.101.14	✓	64
160.133	odd	8		800.2.ba.h.549.12		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
800.2.y.d.101.14	✓	64	160.69	even	8
800.2.y.d.301.14	yes	64	5.4	even	2
800.2.y.e.101.3	yes	64	32.5	even	8	inner
800.2.y.e.301.3	yes	64	1.1	even	1	trivial
800.2.ba.f.549.5		64	160.37	odd	8
800.2.ba.f.749.5		64	5.3	odd	4
800.2.ba.h.549.12		64	160.133	odd	8
800.2.ba.h.749.12		64	5.2	odd	4

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:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.y (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26838 - 0.625467i) q^{2} +(-0.986257 + 2.38104i) q^{3} +(1.21758 + 1.58666i) q^{4} +(2.74021 - 2.40319i) q^{6} +(-2.66071 + 2.66071i) q^{7} +(-0.551955 - 2.77405i) q^{8} +(-2.57531 - 2.57531i) q^{9} +O(q^{10})\)	\(q+(-1.26838 - 0.625467i) q^{2} +(-0.986257 + 2.38104i) q^{3} +(1.21758 + 1.58666i) q^{4} +(2.74021 - 2.40319i) q^{6} +(-2.66071 + 2.66071i) q^{7} +(-0.551955 - 2.77405i) q^{8} +(-2.57531 - 2.57531i) q^{9} +(-2.06648 - 4.98892i) q^{11} +(-4.97875 + 1.33425i) q^{12} +(3.28494 + 1.36067i) q^{13} +(5.03897 - 1.71061i) q^{14} +(-1.03499 + 3.86378i) q^{16} -6.47754i q^{17} +(1.65570 + 4.87724i) q^{18} +(-1.25082 - 0.518105i) q^{19} +(-3.71110 - 8.95938i) q^{21} +(-0.499321 + 7.62037i) q^{22} +(-3.93037 - 3.93037i) q^{23} +(7.14948 + 1.42170i) q^{24} +(-3.31550 - 3.78046i) q^{26} +(1.52870 - 0.633209i) q^{27} +(-7.46127 - 0.982010i) q^{28} +(-0.515400 + 1.24429i) q^{29} +4.32793 q^{31} +(3.72942 - 4.25340i) q^{32} +13.9169 q^{33} +(-4.05149 + 8.21599i) q^{34} +(0.950490 - 7.22178i) q^{36} +(2.65068 - 1.09795i) q^{37} +(1.26245 + 1.43950i) q^{38} +(-6.47958 + 6.47958i) q^{39} +(6.83045 + 6.83045i) q^{41} +(-0.896709 + 13.6851i) q^{42} +(-0.124633 - 0.300891i) q^{43} +(5.39962 - 9.35322i) q^{44} +(2.52689 + 7.44352i) q^{46} +7.79266i q^{47} +(-8.17904 - 6.27502i) q^{48} -7.15871i q^{49} +(15.4232 + 6.38852i) q^{51} +(1.84077 + 6.86880i) q^{52} +(-2.36819 - 5.71731i) q^{53} +(-2.33503 - 0.153002i) q^{54} +(8.84952 + 5.91234i) q^{56} +(2.46725 - 2.46725i) q^{57} +(1.43198 - 1.25586i) q^{58} +(-8.46858 + 3.50780i) q^{59} +(1.27530 - 3.07884i) q^{61} +(-5.48947 - 2.70698i) q^{62} +13.7043 q^{63} +(-7.39069 + 3.06230i) q^{64} +(-17.6519 - 8.70454i) q^{66} +(3.86267 - 9.32531i) q^{67} +(10.2777 - 7.88694i) q^{68} +(13.2347 - 5.48199i) q^{69} +(9.55305 - 9.55305i) q^{71} +(-5.72257 + 8.56548i) q^{72} +(-1.93135 - 1.93135i) q^{73} +(-4.04880 - 0.265296i) q^{74} +(-0.700914 - 2.61546i) q^{76} +(18.7723 + 7.77576i) q^{77} +(12.2713 - 4.16582i) q^{78} -6.31686i q^{79} -6.66170i q^{81} +(-4.39140 - 12.9358i) q^{82} +(-11.6422 - 4.82236i) q^{83} +(9.69693 - 16.7970i) q^{84} +(-0.0301150 + 0.459598i) q^{86} +(-2.45437 - 2.45437i) q^{87} +(-12.6989 + 8.48617i) q^{88} +(2.03773 - 2.03773i) q^{89} +(-12.3606 + 5.11992i) q^{91} +(1.45061 - 11.0217i) q^{92} +(-4.26845 + 10.3050i) q^{93} +(4.87405 - 9.88407i) q^{94} +(6.44932 + 13.0748i) q^{96} +1.02663 q^{97} +(-4.47754 + 9.07998i) q^{98} +(-7.52618 + 18.1698i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 16 q^{14} + 20 q^{16} + 20 q^{18} - 4 q^{22} + 8 q^{23} - 28 q^{24} + 24 q^{27} - 20 q^{28} - 20 q^{32} - 20 q^{34} + 12 q^{36} - 20 q^{38} + 24 q^{39} - 100 q^{42} + 8 q^{43} + 40 q^{44} + 32 q^{46} + 16 q^{51} - 88 q^{52} - 32 q^{53} + 76 q^{54} + 48 q^{56} + 72 q^{58} + 32 q^{59} - 32 q^{61} - 48 q^{62} + 80 q^{63} + 48 q^{64} + 16 q^{66} - 40 q^{67} + 48 q^{68} - 32 q^{69} + 32 q^{71} - 36 q^{72} + 8 q^{74} + 16 q^{77} + 36 q^{78} + 40 q^{83} + 56 q^{84} - 84 q^{86} - 40 q^{88} + 48 q^{91} + 4 q^{92} + 32 q^{94} - 100 q^{96} - 40 q^{98} - 64 q^{99}+O(q^{100}) \) 64 * q - 16 * q^14 + 20 * q^16 + 20 * q^18 - 4 * q^22 + 8 * q^23 - 28 * q^24 + 24 * q^27 - 20 * q^28 - 20 * q^32 - 20 * q^34 + 12 * q^36 - 20 * q^38 + 24 * q^39 - 100 * q^42 + 8 * q^43 + 40 * q^44 + 32 * q^46 + 16 * q^51 - 88 * q^52 - 32 * q^53 + 76 * q^54 + 48 * q^56 + 72 * q^58 + 32 * q^59 - 32 * q^61 - 48 * q^62 + 80 * q^63 + 48 * q^64 + 16 * q^66 - 40 * q^67 + 48 * q^68 - 32 * q^69 + 32 * q^71 - 36 * q^72 + 8 * q^74 + 16 * q^77 + 36 * q^78 + 40 * q^83 + 56 * q^84 - 84 * q^86 - 40 * q^88 + 48 * q^91 + 4 * q^92 + 32 * q^94 - 100 * q^96 - 40 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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