LMFDB - Embedded newform 800.2.y.e.101.3

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			101.3
Character	$\chi$	$=$	800.101
Dual form			800.2.y.e.301.3

$q$-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 $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

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

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	−0.902048	−	0.431635i	$-0.857937\pi$
$3$	−0.986257	−	2.38104i	−0.569416	−	1.37469i	0.332633	−	0.943057i	$-0.392063\pi$
$4$	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	−0.999984	−	0.00566848i	$-0.998196\pi$
$7$	−2.66071	−	2.66071i	−1.00565	−	1.00565i	−0.00566848	−	0.999984i	$-0.501804\pi$
$8$	−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	0.225018	+	0.974355i	$0.427756\pi$
$11$	−2.06648	+	4.98892i	−0.623067	+	1.50422i	−0.848084	+	0.529861i	$0.822244\pi$
$12$	−4.97875	−	1.33425i	−1.43724	−	0.385165i
$13$	3.28494	−	1.36067i	0.911077	−	0.377381i	0.122608	−	0.992455i	$-0.460874\pi$
$13$	3.28494	−	1.36067i	0.911077	−	0.377381i	0.788469	+	0.615075i	$0.210874\pi$
$14$	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	$0.287603\pi$
$17$			6.47754i			1.57103i	−0.618840	+	0.785517i	$0.712397\pi$
$18$	1.65570	−	4.87724i	0.390253	−	1.14958i
$19$	−1.25082	+	0.518105i	−0.286957	+	0.118861i	−0.521519	−	0.853240i	$-0.674634\pi$
$19$	−1.25082	+	0.518105i	−0.286957	+	0.118861i	0.234562	+	0.972101i	$0.424634\pi$
$20$		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	−0.986041	−	0.166503i	$-0.946753\pi$
$23$	−3.93037	+	3.93037i	−0.819538	+	0.819538i	0.166503	+	0.986041i	$0.446753\pi$
$24$	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	0.868774	−	0.495209i	$-0.164908\pi$
$29$	−0.515400	−	1.24429i	−0.0957074	−	0.231058i	−0.964481	+	0.264151i	$0.914908\pi$
$30$		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	0.589774	−	0.807569i	$-0.299217\pi$
$37$	2.65068	+	1.09795i	0.435769	+	0.180502i	−0.154004	+	0.988070i	$0.549217\pi$
$38$	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	0.0691302	−	0.997608i	$-0.477978\pi$
$41$	6.83045	−	6.83045i	1.06674	−	1.06674i	0.997608	−	0.0691302i	$-0.0220224\pi$
$42$	−0.896709	−	13.6851i	−0.138365	−	2.11165i
$43$	−0.124633	+	0.300891i	−0.0190064	+	0.0458854i	−0.933098	−	0.359623i	$-0.882905\pi$
$43$	−0.124633	+	0.300891i	−0.0190064	+	0.0458854i	0.914091	+	0.405508i	$0.132905\pi$
$44$	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	$-0.807586\pi$
$47$		−	7.79266i		−	1.13668i	0.822795	−	0.568338i	$-0.192414\pi$
$48$	−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	0.673633	+	0.739066i	$0.264733\pi$
$53$	−2.36819	+	5.71731i	−0.325296	+	0.785334i	−0.998929	+	0.0462678i	$0.985267\pi$
$54$	−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	−0.244162	−	0.969735i	$-0.578513\pi$
$59$	−8.46858	−	3.50780i	−1.10252	−	0.456677i	−0.858354	+	0.513058i	$0.828513\pi$
$60$		0			0
$61$	1.27530	+	3.07884i	0.163285	+	0.394205i	0.984252	−	0.176770i	$-0.0565650\pi$
$61$	1.27530	+	3.07884i	0.163285	+	0.394205i	−0.820967	+	0.570976i	$0.806565\pi$
$62$	−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	0.963322	+	0.268347i	$0.0864773\pi$
$67$	3.86267	+	9.32531i	0.471900	+	1.13927i	−0.491422	+	0.870922i	$0.663523\pi$
$68$	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	0.989550	+	0.144188i	$0.0460571\pi$
$71$	9.55305	+	9.55305i	1.13374	+	1.13374i	0.144188	+	0.989550i	$0.453943\pi$
$72$	−5.72257	−	8.56548i	−0.674411	−	1.00945i
$73$	−1.93135	+	1.93135i	−0.226047	+	0.226047i	−0.811039	−	0.584992i	$-0.801098\pi$
$73$	−1.93135	+	1.93135i	−0.226047	+	0.226047i	0.584992	+	0.811039i	$0.301098\pi$
$74$	−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	$0.115639\pi$
$79$			6.31686i			0.710702i	−0.934733	+	0.355351i	$0.884361\pi$
$80$		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	−0.915357	−	0.402644i	$-0.868091\pi$
$83$	−11.6422	+	4.82236i	−1.27790	+	0.529323i	−0.362542	+	0.931967i	$0.618091\pi$
$84$	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	0.806810	−	0.590811i	$-0.201192\pi$
$89$	2.03773	+	2.03773i	0.215999	+	0.215999i	−0.590811	+	0.806810i	$0.701192\pi$
$90$		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	0.471490	−	0.881872i	$-0.343717\pi$
$101$	1.82210	+	0.754738i	0.181306	+	0.0750992i	−0.290184	+	0.956971i	$0.593717\pi$
$102$	−15.5668	+	17.7498i	−1.54134	+	1.75749i
$103$	11.3691	+	11.3691i	1.12023	+	1.12023i	0.991707	+	0.128523i	$0.0410237\pi$
$103$	11.3691	+	11.3691i	1.12023	+	1.12023i	0.128523	+	0.991707i	$0.458976\pi$
$104$	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	−0.707094	−	0.707120i	$-0.749994\pi$
$107$	3.02985	−	7.31470i	0.292906	−	0.707139i	1.00000		1.87358e-5i	$-5.96377e-6\pi$
$108$	2.86601	−	1.65455i	0.275782	−	0.159209i
$109$	−13.5926	+	5.63022i	−1.30193	+	0.539277i	−0.922519	−	0.385951i	$-0.873874\pi$
$109$	−13.5926	+	5.63022i	−1.30193	+	0.539277i	−0.379411	+	0.925228i	$0.623874\pi$
$110$		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	$0.0893049\pi$
$113$			5.88683i			0.553787i	−0.960901	+	0.276893i	$0.910695\pi$
$114$	−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	0.730829	−	0.682561i	$-0.239134\pi$
$131$	−3.07413	−	7.42162i	−0.268588	−	0.648430i	−0.999417	+	0.0341310i	$0.989134\pi$
$132$	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	−0.992767	−	0.120054i	$-0.961693\pi$
$137$	−10.2148	+	10.2148i	−0.872713	+	0.872713i	0.120054	+	0.992767i	$0.461693\pi$
$138$	−20.2154	+	1.32461i	−1.72085	+	0.112758i
$139$	5.79595	−	13.9927i	0.491606	−	1.18684i	−0.462296	−	0.886725i	$-0.652974\pi$
$139$	5.79595	−	13.9927i	0.491606	−	1.18684i	0.953902	−	0.300117i	$-0.0970256\pi$
$140$		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	−0.992070	−	0.125687i	$-0.959887\pi$
$149$	−2.46202	+	5.94384i	−0.201697	+	0.486939i	0.790373	+	0.612625i	$0.209887\pi$
$150$		0			0
$151$	−8.46531	+	8.46531i	−0.688898	+	0.688898i	−0.961988	−	0.273091i	$-0.911954\pi$
$151$	−8.46531	+	8.46531i	−0.688898	+	0.688898i	0.273091	+	0.961988i	$0.411954\pi$
$152$	−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	0.844929	−	0.534878i	$-0.179642\pi$
$157$	−1.63819	−	3.95494i	−0.130742	−	0.315638i	−0.975671	+	0.219239i	$0.929642\pi$
$158$	−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	0.979071	−	0.203520i	$-0.0652383\pi$
$163$	1.82382	+	4.40309i	0.142852	+	0.344876i	−0.836218	+	0.548397i	$0.815238\pi$
$164$	−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	0.985254	+	0.171101i	$0.0547323\pi$
$167$	14.9434	+	14.9434i	1.15635	+	1.15635i	0.171101	+	0.985254i	$0.445268\pi$
$168$	−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	−0.208335	−	0.978058i	$-0.566804\pi$
$173$	4.41863	−	1.83025i	0.335942	−	0.139152i	0.544276	+	0.838906i	$0.316804\pi$
$174$	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	−0.852091	−	0.523394i	$-0.824666\pi$
$179$	−14.5098	+	6.01017i	−1.08452	+	0.449221i	−0.232424	+	0.972615i	$0.574666\pi$
$180$		0			0
$181$	0.857338	−	2.06980i	0.0637255	−	0.153847i	−0.888809	−	0.458278i	$-0.848466\pi$
$181$	0.857338	−	2.06980i	0.0637255	−	0.153847i	0.952534	+	0.304431i	$0.0984664\pi$
$182$	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	−0.168847	−	0.985642i	$-0.554004\pi$
$197$	−13.8279	−	5.72768i	−0.985194	−	0.408081i	−0.816347	+	0.577562i	$0.804004\pi$
$198$	20.9107	+	18.3389i	1.48606	+	1.30329i
$199$	1.24000	+	1.24000i	0.0879009	+	0.0879009i	0.749690	−	0.661789i	$-0.230203\pi$
$199$	1.24000	+	1.24000i	0.0879009	+	0.0879009i	−0.661789	+	0.749690i	$0.730203\pi$
$200$		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	−0.296410	−	0.955061i	$-0.595789\pi$
$211$	2.45961	−	1.01880i	0.169326	−	0.0701373i	0.465736	+	0.884924i	$0.345789\pi$
$212$	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	0.914760	−	0.403999i	$-0.132380\pi$
$227$	−0.267330	−	0.645391i	−0.0177433	−	0.0428361i	−0.932503	+	0.361163i	$0.882380\pi$
$228$	6.91877	−	0.910610i	0.458207	−	0.0603066i
$229$	−17.0305	−	7.05427i	−1.12541	−	0.466159i	−0.259190	−	0.965826i	$-0.583456\pi$
$229$	−17.0305	−	7.05427i	−1.12541	−	0.466159i	−0.866218	+	0.499667i	$0.833456\pi$
$230$		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	−0.459751	−	0.888048i	$-0.652061\pi$
$233$	6.53768	−	6.53768i	0.428297	−	0.428297i	0.888048	+	0.459751i	$0.152061\pi$
$234$	−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	$0.139075\pi$
$239$			13.0834i			0.846295i	−0.906061	+	0.423147i	$0.860925\pi$
$240$		0			0
$241$			16.8048i			1.08249i	0.840865	+	0.541245i	$0.182047\pi$
$241$			16.8048i			1.08249i	−0.840865	+	0.541245i	$0.817953\pi$
$242$	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	0.211457	−	0.977387i	$-0.432179\pi$
$251$	−5.23035	−	2.16648i	−0.330137	−	0.136747i	−0.541594	+	0.840640i	$0.682179\pi$
$252$	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	0.150496	−	0.988611i	$-0.451913\pi$
$263$	−13.5919	−	13.5919i	−0.838114	−	0.838114i	−0.988611	+	0.150496i	$0.951913\pi$
$264$	−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	−0.830543	−	0.556955i	$-0.811970\pi$
$269$	−16.7948	+	6.95665i	−1.02400	+	0.424154i	−0.193456	+	0.981109i	$0.561970\pi$
$270$		0			0
$271$			13.2078i			0.802320i	0.916008	+	0.401160i	$0.131393\pi$
$271$			13.2078i			0.802320i	−0.916008	+	0.401160i	$0.868607\pi$
$272$	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	0.696561	+	0.717497i	$0.254712\pi$
$277$	−5.04840	+	12.1879i	−0.303329	+	0.732301i	−0.999890	+	0.0148038i	$0.995288\pi$
$278$	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	0.492839	−	0.870121i	$-0.335959\pi$
$281$	−6.32440	−	6.32440i	−0.377282	−	0.377282i	−0.870121	+	0.492839i	$0.835959\pi$
$282$	18.7272	−	21.3535i	1.11519	−	1.27158i
$283$	7.92855	+	3.28411i	0.471303	+	0.195220i	0.605677	−	0.795711i	$-0.292902\pi$
$283$	7.92855	+	3.28411i	0.471303	+	0.195220i	−0.134374	+	0.990931i	$0.542902\pi$
$284$	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	−0.214034	−	0.976826i	$-0.568660\pi$
$293$	−18.0775	−	7.48795i	−1.05610	−	0.437451i	−0.842066	+	0.539375i	$0.818660\pi$
$294$	−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	−0.997367	−	0.0725248i	$-0.976894\pi$
$307$	−28.9336	+	11.9847i	−1.65133	+	0.684003i	−0.653962	+	0.756527i	$0.726894\pi$
$308$	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	−0.840311	−	0.542105i	$-0.817628\pi$
$311$	−5.25892	+	5.25892i	−0.298206	+	0.298206i	0.542105	+	0.840311i	$0.317628\pi$
$312$	21.5511	−	14.3982i	1.22009	−	0.815140i
$313$	13.6652	+	13.6652i	0.772405	+	0.772405i	0.978526	−	0.206122i	$-0.0660843\pi$
$313$	13.6652	+	13.6652i	0.772405	+	0.772405i	−0.206122	+	0.978526i	$0.566084\pi$
$314$	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	0.999522	−	0.0309297i	$-0.00984680\pi$
$317$	4.82293	+	11.6436i	0.270882	+	0.653968i	−0.728639	+	0.684898i	$0.759847\pi$
$318$	−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	0.376594	+	0.926378i	$0.377095\pi$
$331$	−9.91080	+	23.9268i	−0.544747	+	1.31513i	−0.921341	+	0.388756i	$0.872905\pi$
$332$	−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	$-0.832916\pi$
$337$		−	18.3992i		−	1.00227i	0.865370	−	0.501134i	$-0.167084\pi$
$338$	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	0.486610	−	0.873619i	$-0.338233\pi$
$347$	3.96687	+	1.64313i	0.212953	+	0.0882079i	−0.273657	+	0.961827i	$0.588233\pi$
$348$	0.905856	+	6.88266i	0.0485590	+	0.368949i
$349$	11.4421	+	27.6237i	0.612483	+	1.47867i	0.860264	+	0.509849i	$0.170299\pi$
$349$	11.4421	+	27.6237i	0.612483	+	1.47867i	−0.247781	+	0.968816i	$0.579701\pi$
$350$		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	0.946576	−	0.322480i	$-0.104516\pi$
$359$	11.8249	+	11.8249i	0.624097	+	0.624097i	−0.322480	+	0.946576i	$0.604516\pi$
$360$		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	$-0.653867\pi$
$367$		−	33.9246i		−	1.77085i	0.464781	−	0.885425i	$-0.346133\pi$
$368$	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	−0.677452	−	0.735567i	$-0.736916\pi$
$373$	6.21312	−	14.9998i	0.321703	−	0.776660i	0.999155	−	0.0410929i	$-0.0130840\pi$
$374$	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	0.905384	−	0.424594i	$-0.139583\pi$
$379$	24.2445	+	10.0424i	1.24535	+	0.515843i	0.339970	+	0.940436i	$0.389583\pi$
$380$		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	0.999158	+	0.0410229i	$0.0130617\pi$
$389$	34.2132	+	14.1716i	1.73468	+	0.718527i	0.735519	+	0.677504i	$0.236938\pi$
$390$		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	−0.272086	−	0.962273i	$-0.587714\pi$
$397$	4.30276	−	1.78226i	0.215949	−	0.0894491i	0.488036	+	0.872824i	$0.337714\pi$
$398$	−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	$-0.905313\pi$
$401$		−	11.7387i		−	0.586201i	0.956082	−	0.293100i	$-0.0946870\pi$
$402$	−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	0.314765	−	0.949170i	$-0.398074\pi$
$409$	−12.8300	−	12.8300i	−0.634405	−	0.634405i	−0.949170	+	0.314765i	$0.898074\pi$
$410$		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	0.763711	−	0.645558i	$-0.223375\pi$
$419$	−4.76515	−	11.5041i	−0.232793	−	0.562012i	−0.996504	+	0.0835464i	$0.973375\pi$
$420$		0			0
$421$	16.1536	+	6.69106i	0.787280	+	0.326102i	0.739849	−	0.672772i	$-0.234897\pi$
$421$	16.1536	+	6.69106i	0.787280	+	0.326102i	0.0474306	+	0.998875i	$0.484897\pi$
$422$	−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	$-0.837802\pi$
$431$		−	20.2537i		−	0.975586i	0.872959	−	0.487793i	$-0.162198\pi$
$432$	0.864396	−	6.56193i	0.0415883	−	0.315711i
$433$			26.2786i			1.26287i	0.775429	+	0.631434i	$0.217533\pi$
$433$			26.2786i			1.26287i	−0.775429	+	0.631434i	$0.782467\pi$
$434$	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	−0.608523	−	0.793536i	$-0.708238\pi$
$439$	3.87646	−	3.87646i	0.185013	−	0.185013i	0.793536	+	0.608523i	$0.208238\pi$
$440$		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	−0.291781	−	0.956485i	$-0.594248\pi$
$443$	−24.7191	−	10.2390i	−1.17444	−	0.486468i	−0.882657	+	0.470017i	$0.844248\pi$
$444$	−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	−0.557214	−	0.830369i	$-0.688130\pi$
$457$	5.83937	−	5.83937i	0.273154	−	0.273154i	0.830369	+	0.557214i	$0.188130\pi$
$458$	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	−0.526265	−	0.850320i	$-0.676408\pi$
$461$	−6.37952	+	2.64248i	−0.297124	+	0.123073i	0.229142	+	0.973393i	$0.426408\pi$
$462$	70.1267	+	23.8063i	3.26259	+	1.10757i
$463$		−	5.92393i		−	0.275309i	−0.990480	−	0.137654i	$-0.956044\pi$
$463$		−	5.92393i		−	0.275309i	0.990480	−	0.137654i	$-0.0439563\pi$
$464$	−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	−0.600074	−	0.799945i	$-0.704862\pi$
$467$	−9.91354	+	4.10632i	−0.458744	+	0.190018i	0.141330	+	0.989963i	$0.454862\pi$
$468$	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	0.378212	−	0.925719i	$-0.376539\pi$
$487$	−12.0824	−	12.0824i	−0.547506	−	0.547506i	−0.925719	+	0.378212i	$0.876539\pi$
$488$	−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	−0.995440	−	0.0953865i	$-0.969591\pi$
$491$	−4.96593	+	11.9888i	−0.224109	+	0.541048i	0.771331	+	0.636434i	$0.219591\pi$
$492$	−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	−0.504970	−	0.863137i	$-0.668497\pi$
$499$	−5.62274	+	2.32902i	−0.251708	+	0.104261i	0.253262	+	0.967398i	$0.418497\pi$
$500$		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	−0.987700	−	0.156361i	$-0.950024\pi$
$503$	−18.6450	+	18.6450i	−0.831339	+	0.831339i	0.156361	+	0.987700i	$0.450024\pi$
$504$	−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	−0.998760	−	0.0497872i	$-0.984146\pi$
$509$	−7.39404	−	17.8508i	−0.327735	−	0.791222i	0.671025	−	0.741435i	$-0.265854\pi$
$510$		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	−0.649250	−	0.760575i	$-0.724917\pi$
$521$	2.54106	−	2.54106i	0.111326	−	0.111326i	0.760575	+	0.649250i	$0.224917\pi$
$522$	−6.92203	+	0.453563i	−0.302969	+	0.0198519i
$523$	−1.93590	+	4.67367i	−0.0846509	+	0.204365i	−0.960537	−	0.278153i	$-0.910278\pi$
$523$	−1.93590	+	4.67367i	−0.0846509	+	0.204365i	0.875886	+	0.482518i	$0.160278\pi$
$524$	−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	−0.851140	−	0.524939i	$-0.824088\pi$
$541$	−14.4320	−	34.8420i	−0.620481	−	1.49797i	0.230659	−	0.973035i	$-0.425912\pi$
$542$	−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	0.746402	−	0.665496i	$-0.231780\pi$
$547$	−5.89286	−	14.2266i	−0.251961	−	0.608287i	−0.998362	+	0.0572089i	$0.981780\pi$
$548$	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	−0.585013	−	0.811024i	$-0.698911\pi$
$557$	−10.0351	+	4.15666i	−0.425199	+	0.176123i	0.159814	+	0.987147i	$0.448911\pi$
$558$	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	−0.774004	−	0.633181i	$-0.781749\pi$
$563$	−20.7280	+	8.58581i	−0.873580	+	0.361849i	−0.0995764	+	0.995030i	$0.531749\pi$
$564$	−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	0.293367	−	0.956000i	$-0.405224\pi$
$569$	−15.8062	−	15.8062i	−0.662632	−	0.662632i	−0.956000	+	0.293367i	$0.905224\pi$
$570$		0			0
$571$	6.01892	+	2.49312i	0.251884	+	0.104334i	0.505053	−	0.863088i	$-0.331473\pi$
$571$	6.01892	+	2.49312i	0.251884	+	0.104334i	−0.253169	+	0.967422i	$0.581473\pi$
$572$	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	0.572126	+	0.820166i	$0.306119\pi$
$587$	−9.99100	+	24.1204i	−0.412373	+	0.995556i	−0.984499	+	0.175390i	$0.943881\pi$
$588$	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	$0.124996\pi$
$593$			18.6374i			0.765345i	−0.923884	+	0.382673i	$0.875004\pi$
$594$	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	−0.255468	−	0.966818i	$-0.582230\pi$
$599$	17.4099	−	17.4099i	0.711350	−	0.711350i	0.966818	+	0.255468i	$0.0822295\pi$
$600$		0			0
$601$	−24.7490	−	24.7490i	−1.00953	−	1.00953i	−0.999954	−	0.00957803i	$-0.996951\pi$
$601$	−24.7490	−	24.7490i	−1.00953	−	1.00953i	−0.00957803	−	0.999954i	$-0.503049\pi$
$602$	−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	0.972104	−	0.234550i	$-0.0753618\pi$
$613$	36.9806	+	15.3179i	1.49363	+	0.618683i	0.521529	+	0.853234i	$0.325362\pi$
$614$	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	−0.287214	−	0.957866i	$-0.592729\pi$
$617$	16.6587	−	16.6587i	0.670652	−	0.670652i	0.957866	+	0.287214i	$0.0927292\pi$
$618$	3.83160	+	58.4758i	0.154130	+	2.35224i
$619$	−17.7139	+	42.7652i	−0.711983	+	1.71888i	−0.0169982	+	0.999856i	$0.505411\pi$
$619$	−17.7139	+	42.7652i	−0.711983	+	1.71888i	−0.694985	+	0.719024i	$0.744589\pi$
$620$		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	−0.712407	−	0.701766i	$-0.752395\pi$
$631$	−0.267293	+	0.267293i	−0.0106408	+	0.0106408i	0.701766	+	0.712407i	$0.252395\pi$
$632$	−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	0.996031	+	0.0890053i	$0.0283688\pi$
$643$	8.99345	+	21.7121i	0.354667	+	0.856242i	−0.641364	+	0.767237i	$0.721631\pi$
$644$	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	0.725126	−	0.688616i	$-0.241782\pi$
$647$	0.928657	+	0.928657i	0.0365093	+	0.0365093i	−0.688616	+	0.725126i	$0.741782\pi$
$648$	−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	−0.891541	−	0.452940i	$-0.850375\pi$
$653$	−30.7075	+	12.7195i	−1.20168	+	0.497751i	−0.310137	+	0.950692i	$0.600375\pi$
$654$	−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	−0.0154977	−	0.999880i	$-0.504933\pi$
$659$	17.4708	−	7.23664i	0.680566	−	0.281900i	0.696063	+	0.717980i	$0.254933\pi$
$660$		0			0
$661$	3.87034	−	9.34382i	0.150539	−	0.363432i	−0.830563	−	0.556924i	$-0.811981\pi$
$661$	3.87034	−	9.34382i	0.150539	−	0.363432i	0.981102	+	0.193492i	$0.0619813\pi$
$662$	−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	0.597405	−	0.801939i	$-0.296198\pi$
$677$	11.7809	+	4.87982i	0.452778	+	0.187547i	−0.144627	+	0.989486i	$0.546198\pi$
$678$	−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	−0.351816	−	0.936069i	$-0.614436\pi$
$683$	14.6053	−	35.2603i	0.558857	−	1.34920i	0.910672	−	0.413130i	$-0.135564\pi$
$684$	−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	−0.0171125	−	0.999854i	$-0.505447\pi$
$691$	17.8170	−	7.38004i	0.677790	−	0.280750i	0.694903	+	0.719104i	$0.255447\pi$
$692$	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	0.743631	−	0.668591i	$-0.233102\pi$
$701$	−6.75044	−	16.2970i	−0.254961	−	0.615529i	−0.998591	+	0.0530613i	$0.983102\pi$
$702$	−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	0.566775	−	0.823872i	$-0.308191\pi$
$709$	10.2509	+	4.24606i	0.384981	+	0.159464i	−0.181795	+	0.983336i	$0.558191\pi$
$710$		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	$0.100870\pi$
$719$			16.7114i			0.623232i	−0.950208	+	0.311616i	$0.899130\pi$
$720$		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	−0.576530	−	0.817076i	$-0.695594\pi$
$727$	6.48584	−	6.48584i	0.240546	−	0.240546i	0.817076	+	0.576530i	$0.195594\pi$
$728$	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	0.730749	−	0.682646i	$-0.239171\pi$
$733$	−7.27403	−	17.5611i	−0.268672	−	0.648632i	−0.999421	+	0.0340138i	$0.989171\pi$
$734$	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	0.808230	−	0.588867i	$-0.200426\pi$
$739$	−4.88417	−	11.7914i	−0.179667	−	0.433755i	−0.987897	+	0.155112i	$0.950426\pi$
$740$		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	−0.966650	−	0.256101i	$-0.917562\pi$
$743$	−33.3298	−	33.3298i	−1.22275	−	1.22275i	−0.256101	−	0.966650i	$-0.582438\pi$
$744$	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	$0.0371455\pi$
$751$			6.38146i			0.232863i	−0.993199	+	0.116431i	$0.962854\pi$
$752$	−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	−0.449517	−	0.893272i	$-0.648404\pi$
$757$	13.7562	−	33.2104i	0.499978	−	1.20705i	0.949495	−	0.313782i	$-0.101596\pi$
$758$	−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	0.530045	−	0.847970i	$-0.322175\pi$
$761$	−8.77034	−	8.77034i	−0.317925	−	0.317925i	−0.847970	+	0.530045i	$0.822175\pi$
$762$	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	0.229246	−	0.973368i	$-0.426374\pi$
$773$	−8.25543	−	3.41951i	−0.296927	−	0.122991i	−0.526174	+	0.850377i	$0.676374\pi$
$774$	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	−0.986306	−	0.164924i	$-0.947262\pi$
$787$	−43.9630	+	18.2101i	−1.56711	+	0.649119i	−0.580805	+	0.814043i	$0.697262\pi$
$788$	−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	0.955917	−	0.293636i	$-0.0948653\pi$
$797$	2.04252	+	4.93109i	0.0723499	+	0.174668i	−0.883567	+	0.468304i	$0.844865\pi$
$798$	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	−0.401051	−	0.916056i	$-0.631355\pi$
$809$	14.6482	−	14.6482i	0.515004	−	0.515004i	0.916056	+	0.401051i	$0.131355\pi$
$810$		0			0
$811$	−7.38535	+	17.8298i	−0.259335	+	0.626090i	−0.998895	−	0.0470010i	$-0.985034\pi$
$811$	−7.38535	+	17.8298i	−0.259335	+	0.626090i	0.739560	+	0.673091i	$0.235034\pi$
$812$	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	−0.957648	−	0.287942i	$-0.907029\pi$
$821$	−2.20294	+	5.31836i	−0.0768830	+	0.185612i	0.880765	+	0.473554i	$0.157029\pi$
$822$	−52.5390	+	3.44260i	−1.83251	+	0.120074i
$823$	−14.1449	+	14.1449i	−0.493061	+	0.493061i	−0.909269	−	0.416208i	$-0.863359\pi$
$823$	−14.1449	+	14.1449i	−0.493061	+	0.493061i	0.416208	+	0.909269i	$0.363359\pi$
$824$	−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	0.999961	+	0.00888040i	$0.00282676\pi$
$827$	49.2710	+	20.4087i	1.71332	+	0.709680i	0.713358	+	0.700800i	$0.247173\pi$
$828$	−32.1200	−	24.6485i	−1.11625	−	0.856594i
$829$	−5.39395	−	13.0222i	−0.187340	−	0.452278i	0.802106	−	0.597182i	$-0.203713\pi$
$829$	−5.39395	−	13.0222i	−0.187340	−	0.452278i	−0.989446	+	0.144903i	$0.953713\pi$
$830$		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	0.479803	−	0.877376i	$-0.340708\pi$
$839$	−11.5159	−	11.5159i	−0.397573	−	0.397573i	−0.877376	+	0.479803i	$0.840708\pi$
$840$		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	−0.599419	−	0.800435i	$-0.704602\pi$
$853$	11.4029	−	27.5290i	0.390427	−	0.942575i	0.989847	−	0.142140i	$-0.0453982\pi$
$854$	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	0.363389	−	0.931637i	$-0.381620\pi$
$857$	−16.6352	−	16.6352i	−0.568248	−	0.568248i	−0.931637	+	0.363389i	$0.881620\pi$
$858$	−46.1414	+	52.6122i	−1.57524	+	1.79615i
$859$	−21.0912	−	8.73628i	−0.719624	−	0.298078i	−0.00734363	−	0.999973i	$-0.502338\pi$
$859$	−21.0912	−	8.73628i	−0.719624	−	0.298078i	−0.712280	+	0.701895i	$0.752338\pi$
$860$		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	−0.978463	−	0.206424i	$-0.933817\pi$
$877$	−45.1432	+	18.6989i	−1.52438	+	0.631417i	−0.545913	+	0.837842i	$0.683817\pi$
$878$	−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	$-0.961402\pi$
$881$		−	7.18069i		−	0.241924i	0.992657	−	0.120962i	$-0.0385979\pi$
$882$	34.9148	+	11.8527i	1.17564	+	0.399101i
$883$	−29.2458	+	12.1140i	−0.984198	+	0.407668i	−0.815979	−	0.578081i	$-0.803802\pi$
$883$	−29.2458	+	12.1140i	−0.984198	+	0.407668i	−0.168219	+	0.985750i	$0.553802\pi$
$884$	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	−0.439976	−	0.898009i	$-0.645013\pi$
$887$	13.6414	−	13.6414i	0.458033	−	0.458033i	0.898009	+	0.439976i	$0.145013\pi$
$888$	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	−0.773135	−	0.634242i	$-0.781312\pi$
$907$	6.68678	−	16.1433i	0.222031	−	0.536030i	0.995166	+	0.0982121i	$0.0313124\pi$
$908$	−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	$0.221620\pi$
$911$			38.7147i			1.28268i	−0.767259	+	0.641338i	$0.778380\pi$
$912$	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	−0.833655	−	0.552285i	$-0.813756\pi$
$919$	−8.52974	+	8.52974i	−0.281370	+	0.281370i	0.552285	+	0.833655i	$0.313756\pi$
$920$		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	−0.912963	−	0.408043i	$-0.866211\pi$
$937$	−15.4558	+	15.4558i	−0.504920	+	0.504920i	0.408043	+	0.912963i	$0.366211\pi$
$938$	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	0.265859	−	0.964012i	$-0.414344\pi$
$941$	34.8326	−	14.4281i	1.13551	−	0.470343i	0.869650	+	0.493668i	$0.164344\pi$
$942$	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	−0.0406007	−	0.999175i	$-0.512927\pi$
$947$	19.6092	−	8.12240i	0.637214	−	0.263943i	0.677815	+	0.735233i	$0.262927\pi$
$948$	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	0.693693	−	0.720270i	$-0.255982\pi$
$953$	−0.820449	−	0.820449i	−0.0265769	−	0.0265769i	−0.720270	+	0.693693i	$0.755982\pi$
$954$	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	0.372115	−	0.928187i	$-0.378633\pi$
$967$	−17.2920	−	17.2920i	−0.556072	−	0.556072i	−0.928187	+	0.372115i	$0.878633\pi$
$968$	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	−0.827784	−	0.561048i	$-0.810398\pi$
$971$	4.80714	−	11.6055i	0.154268	−	0.372437i	0.982052	+	0.188611i	$0.0603984\pi$
$972$	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	$-0.885043\pi$
$977$		−	22.0892i		−	0.706697i	0.935492	−	0.353348i	$-0.114957\pi$
$978$	−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	−0.587137	−	0.809487i	$-0.699745\pi$
$983$	6.97130	−	6.97130i	0.222350	−	0.222350i	0.809487	+	0.587137i	$0.199745\pi$
$984$	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	0.415142	−	0.909757i	$-0.363732\pi$
$997$	2.06492	+	0.855318i	0.0653967	+	0.0270882i	−0.349745	+	0.936845i	$0.613732\pi$
$998$	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.101.3	yes	64
5.2	odd	4		800.2.ba.f.549.5		64
5.3	odd	4		800.2.ba.h.549.12		64
5.4	even	2		800.2.y.d.101.14	✓	64
32.13	even	8	inner	800.2.y.e.301.3	yes	64
160.13	odd	8		800.2.ba.f.749.5		64
160.77	odd	8		800.2.ba.h.749.12		64
160.109	even	8		800.2.y.d.301.14	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
800.2.y.d.101.14	✓	64	5.4	even	2
800.2.y.d.301.14	yes	64	160.109	even	8
800.2.y.e.101.3	yes	64	1.1	even	1	trivial
800.2.y.e.301.3	yes	64	32.13	even	8	inner
800.2.ba.f.549.5		64	5.2	odd	4
800.2.ba.f.749.5		64	160.13	odd	8
800.2.ba.h.549.12		64	5.3	odd	4
800.2.ba.h.749.12		64	160.77	odd	8

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

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Database

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