LMFDB - Embedded newform 850.2.v.c.193.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(107,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([4, 5]))

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

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

chi := DirichletCharacter("850.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.v (of order $16$, degree $8$, 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:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			193.3
Character	$\chi$	$=$	850.193
Dual form			850.2.v.c.207.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.923880 - 0.382683i) q^{2} +(0.856804 + 0.572498i) q^{3} +(0.707107 - 0.707107i) q^{4} +(1.01067 + 0.201035i) q^{6} +(1.64388 + 0.326988i) q^{7} +(0.382683 - 0.923880i) q^{8} +(-0.741692 - 1.79060i) q^{9} +O(q^{10})$	\(q+(0.923880 - 0.382683i) q^{2} +(0.856804 + 0.572498i) q^{3} +(0.707107 - 0.707107i) q^{4} +(1.01067 + 0.201035i) q^{6} +(1.64388 + 0.326988i) q^{7} +(0.382683 - 0.923880i) q^{8} +(-0.741692 - 1.79060i) q^{9} +(-1.12842 + 5.67293i) q^{11} +(1.01067 - 0.201035i) q^{12} +4.62429 q^{13} +(1.64388 - 0.326988i) q^{14} -1.00000i q^{16} +(3.82690 + 1.53454i) q^{17} +(-1.37047 - 1.37047i) q^{18} +(-0.932809 + 2.25200i) q^{19} +(1.22128 + 1.22128i) q^{21} +(1.12842 + 5.67293i) q^{22} +(-1.85758 - 2.78006i) q^{23} +(0.856804 - 0.572498i) q^{24} +(4.27229 - 1.76964i) q^{26} +(0.992735 - 4.99082i) q^{27} +(1.39361 - 0.931182i) q^{28} +(3.70873 - 5.55051i) q^{29} +(-0.914558 - 4.59779i) q^{31} +(-0.382683 - 0.923880i) q^{32} +(-4.21457 + 4.21457i) q^{33} +(4.12284 - 0.0467655i) q^{34} +(-1.79060 - 0.741692i) q^{36} +(0.910181 - 1.36218i) q^{37} +2.43755i q^{38} +(3.96211 + 2.64740i) q^{39} +(6.23402 + 9.32987i) q^{41} +(1.59568 + 0.660953i) q^{42} +(-9.87239 - 4.08928i) q^{43} +(3.21346 + 4.80928i) q^{44} +(-2.78006 - 1.85758i) q^{46} +2.54171i q^{47} +(0.572498 - 0.856804i) q^{48} +(-3.87174 - 1.60373i) q^{49} +(2.40039 + 3.50569i) q^{51} +(3.26987 - 3.26987i) q^{52} +(1.76263 + 4.25536i) q^{53} +(-0.992735 - 4.99082i) q^{54} +(0.931182 - 1.39361i) q^{56} +(-2.08850 + 1.39549i) q^{57} +(1.30233 - 6.54728i) q^{58} +(-9.68021 + 4.00967i) q^{59} +(3.66782 - 2.45076i) q^{61} +(-2.60444 - 3.89782i) q^{62} +(-0.633746 - 3.18606i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(-2.28091 + 5.50661i) q^{66} +(1.91399 + 1.91399i) q^{67} +(3.79111 - 1.62095i) q^{68} -3.44543i q^{69} +(-8.05408 + 1.60206i) q^{71} -1.93813 q^{72} +(5.37374 - 1.06890i) q^{73} +(0.319613 - 1.60680i) q^{74} +(0.932809 + 2.25200i) q^{76} +(-3.70996 + 8.95664i) q^{77} +(4.67362 + 0.929642i) q^{78} +(-4.50408 - 0.895917i) q^{79} +(-0.403592 + 0.403592i) q^{81} +(9.32987 + 6.23402i) q^{82} +(5.66048 - 2.34465i) q^{83} +1.72715 q^{84} -10.6858 q^{86} +(6.35531 - 2.63246i) q^{87} +(4.80928 + 3.21346i) q^{88} +(-10.2485 + 10.2485i) q^{89} +(7.60177 + 1.51209i) q^{91} +(-3.27931 - 0.652295i) q^{92} +(1.84863 - 4.46299i) q^{93} +(0.972672 + 2.34824i) q^{94} +(0.201035 - 1.01067i) q^{96} +(-9.36520 + 1.86285i) q^{97} -4.19074 q^{98} +(10.9949 - 2.18702i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 16 q^{18} + 8 q^{26} - 24 q^{27} + 8 q^{28} - 8 q^{29} - 16 q^{31} - 64 q^{33} + 24 q^{34} + 32 q^{37} - 32 q^{39} + 16 q^{41} + 24 q^{42} + 16 q^{43} - 16 q^{44} - 16 q^{49} + 32 q^{51} + 16 q^{52} - 16 q^{53} + 24 q^{54} + 8 q^{56} + 24 q^{57} + 16 q^{58} - 64 q^{59} - 24 q^{61} + 40 q^{62} + 24 q^{63} - 16 q^{67} + 8 q^{71} + 16 q^{72} - 32 q^{73} + 8 q^{74} - 24 q^{77} - 32 q^{78} + 72 q^{79} + 48 q^{81} - 48 q^{82} - 16 q^{83} - 64 q^{86} - 40 q^{87} - 32 q^{88} + 16 q^{89} + 48 q^{91} - 24 q^{92} + 8 q^{93} + 8 q^{94} + 48 q^{97} - 64 q^{99}+O(q^{100}) $ 32 * q - 16 * q^18 + 8 * q^26 - 24 * q^27 + 8 * q^28 - 8 * q^29 - 16 * q^31 - 64 * q^33 + 24 * q^34 + 32 * q^37 - 32 * q^39 + 16 * q^41 + 24 * q^42 + 16 * q^43 - 16 * q^44 - 16 * q^49 + 32 * q^51 + 16 * q^52 - 16 * q^53 + 24 * q^54 + 8 * q^56 + 24 * q^57 + 16 * q^58 - 64 * q^59 - 24 * q^61 + 40 * q^62 + 24 * q^63 - 16 * q^67 + 8 * q^71 + 16 * q^72 - 32 * q^73 + 8 * q^74 - 24 * q^77 - 32 * q^78 + 72 * q^79 + 48 * q^81 - 48 * q^82 - 16 * q^83 - 64 * q^86 - 40 * q^87 - 32 * q^88 + 16 * q^89 + 48 * q^91 - 24 * q^92 + 8 * q^93 + 8 * q^94 + 48 * q^97 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{15}{16}\right)$

Coefficient data

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

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

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

$2$	0.923880	−	0.382683i	0.653281	−	0.270598i
$2$	0.923880	−	0.382683i	0.653281	−	0.270598i
$3$	0.856804	+	0.572498i	0.494676	+	0.330532i	0.777758	−	0.628564i	$-0.216357\pi$
$3$	0.856804	+	0.572498i	0.494676	+	0.330532i	−0.283082	+	0.959096i	$0.591357\pi$
$4$	0.707107	−	0.707107i	0.353553	−	0.353553i
$5$		0			0
$5$		0			0
$6$	1.01067	+	0.201035i	0.412604	+	0.0820720i
$7$	1.64388	+	0.326988i	0.621328	+	0.123590i	0.495709	−	0.868489i	$-0.334908\pi$
$7$	1.64388	+	0.326988i	0.621328	+	0.123590i	0.125619	+	0.992079i	$0.459908\pi$
$8$	0.382683	−	0.923880i	0.135299	−	0.326641i
$9$	−0.741692	−	1.79060i	−0.247231	−	0.596867i
$10$		0			0
$11$	−1.12842	+	5.67293i	−0.340230	+	1.71045i	0.310017	+	0.950731i	$0.399665\pi$
$11$	−1.12842	+	5.67293i	−0.340230	+	1.71045i	−0.650247	+	0.759723i	$0.725335\pi$
$12$	1.01067	−	0.201035i	0.291755	−	0.0580337i
$13$	4.62429			1.28255			0.641274	−	0.767312i	$-0.278406\pi$
$13$	4.62429			1.28255			0.641274	+	0.767312i	$0.278406\pi$
$14$	1.64388	−	0.326988i	0.439345	−	0.0873912i
$15$		0			0
$16$		−	1.00000i		−	0.250000i
$17$	3.82690	+	1.53454i	0.928161	+	0.372180i
$17$	3.82690	+	1.53454i	0.928161	+	0.372180i
$18$	−1.37047	−	1.37047i	−0.323022	−	0.323022i
$19$	−0.932809	+	2.25200i	−0.214001	+	0.516644i	−0.994031	−	0.109098i	$-0.965204\pi$
$19$	−0.932809	+	2.25200i	−0.214001	+	0.516644i	0.780030	+	0.625742i	$0.215204\pi$
$20$		0			0
$21$	1.22128	+	1.22128i	0.266505	+	0.266505i
$22$	1.12842	+	5.67293i	0.240579	+	1.20947i
$23$	−1.85758	−	2.78006i	−0.387332	−	0.579684i	0.585650	−	0.810564i	$-0.300839\pi$
$23$	−1.85758	−	2.78006i	−0.387332	−	0.579684i	−0.972982	+	0.230881i	$0.925839\pi$
$24$	0.856804	−	0.572498i	0.174894	−	0.116861i
$25$		0			0
$26$	4.27229	−	1.76964i	0.837864	−	0.347055i
$27$	0.992735	−	4.99082i	0.191052	−	0.960483i
$28$	1.39361	−	0.931182i	0.263368	−	0.175977i
$29$	3.70873	−	5.55051i	0.688695	−	1.03070i	−0.308151	−	0.951337i	$-0.599710\pi$
$29$	3.70873	−	5.55051i	0.688695	−	1.03070i	0.996845	−	0.0793667i	$-0.0252898\pi$
$30$		0			0
$31$	−0.914558	−	4.59779i	−0.164260	−	0.825788i	−0.971769	−	0.235934i	$-0.924185\pi$
$31$	−0.914558	−	4.59779i	−0.164260	−	0.825788i	0.807510	−	0.589854i	$-0.200815\pi$
$32$	−0.382683	−	0.923880i	−0.0676495	−	0.163320i
$33$	−4.21457	+	4.21457i	−0.733663	+	0.733663i
$34$	4.12284	−	0.0467655i	0.707061	−	0.00802021i
$35$		0			0
$36$	−1.79060	−	0.741692i	−0.298434	−	0.123615i
$37$	0.910181	−	1.36218i	0.149633	−	0.223941i	−0.749079	−	0.662480i	$-0.769504\pi$
$37$	0.910181	−	1.36218i	0.149633	−	0.223941i	0.898712	+	0.438539i	$0.144504\pi$
$38$			2.43755i			0.395422i
$39$	3.96211	+	2.64740i	0.634445	+	0.423923i
$40$		0			0
$41$	6.23402	+	9.32987i	0.973591	+	1.45708i	0.887508	+	0.460793i	$0.152435\pi$
$41$	6.23402	+	9.32987i	0.973591	+	1.45708i	0.0860830	+	0.996288i	$0.472565\pi$
$42$	1.59568	+	0.660953i	0.246219	+	0.101987i
$43$	−9.87239	−	4.08928i	−1.50553	−	0.623609i	−0.530897	−	0.847436i	$-0.678145\pi$
$43$	−9.87239	−	4.08928i	−1.50553	−	0.623609i	−0.974629	+	0.223827i	$0.928145\pi$
$44$	3.21346	+	4.80928i	0.484447	+	0.725026i
$45$		0			0
$46$	−2.78006	−	1.85758i	−0.409898	−	0.273885i
$47$			2.54171i			0.370747i	0.982668	+	0.185374i	$0.0593495\pi$
$47$			2.54171i			0.370747i	−0.982668	+	0.185374i	$0.940650\pi$
$48$	0.572498	−	0.856804i	0.0826329	−	0.123669i
$49$	−3.87174	−	1.60373i	−0.553106	−	0.229104i
$50$		0			0
$51$	2.40039	+	3.50569i	0.336121	+	0.490895i
$52$	3.26987	−	3.26987i	0.453449	−	0.453449i
$53$	1.76263	+	4.25536i	0.242116	+	0.584519i	0.997493	−	0.0707718i	$-0.0225462\pi$
$53$	1.76263	+	4.25536i	0.242116	+	0.584519i	−0.755377	+	0.655290i	$0.772546\pi$
$54$	−0.992735	−	4.99082i	−0.135094	−	0.679164i
$55$		0			0
$56$	0.931182	−	1.39361i	0.124434	−	0.186229i
$57$	−2.08850	+	1.39549i	−0.276628	+	0.184837i
$58$	1.30233	−	6.54728i	0.171005	−	0.859699i
$59$	−9.68021	+	4.00967i	−1.26026	+	0.522015i	−0.909988	−	0.414635i	$-0.863909\pi$
$59$	−9.68021	+	4.00967i	−1.26026	+	0.522015i	−0.350268	+	0.936650i	$0.613909\pi$
$60$		0			0
$61$	3.66782	−	2.45076i	0.469616	−	0.313788i	−0.298148	−	0.954520i	$-0.596369\pi$
$61$	3.66782	−	2.45076i	0.469616	−	0.313788i	0.767765	+	0.640732i	$0.221369\pi$
$62$	−2.60444	−	3.89782i	−0.330764	−	0.495024i
$63$	−0.633746	−	3.18606i	−0.0798445	−	0.401405i
$64$	−0.707107	−	0.707107i	−0.0883883	−	0.0883883i
$65$		0			0
$66$	−2.28091	+	5.50661i	−0.280761	+	0.677816i
$67$	1.91399	+	1.91399i	0.233831	+	0.233831i	0.814290	−	0.580459i	$-0.197127\pi$
$67$	1.91399	+	1.91399i	0.233831	+	0.233831i	−0.580459	+	0.814290i	$0.697127\pi$
$68$	3.79111	−	1.62095i	0.459740	−	0.196569i
$69$		−	3.44543i		−	0.414781i
$70$		0			0
$71$	−8.05408	+	1.60206i	−0.955843	+	0.190129i	−0.648283	−	0.761400i	$-0.724513\pi$
$71$	−8.05408	+	1.60206i	−0.955843	+	0.190129i	−0.307560	+	0.951529i	$0.599513\pi$
$72$	−1.93813			−0.228411
$73$	5.37374	−	1.06890i	0.628949	−	0.125106i	0.129684	−	0.991555i	$-0.458604\pi$
$73$	5.37374	−	1.06890i	0.628949	−	0.125106i	0.499264	+	0.866450i	$0.333604\pi$
$74$	0.319613	−	1.60680i	0.0371543	−	0.186787i
$75$		0			0
$76$	0.932809	+	2.25200i	0.107001	+	0.258322i
$77$	−3.70996	+	8.95664i	−0.422789	+	1.02070i
$78$	4.67362	+	0.929642i	0.529184	+	0.105261i
$79$	−4.50408	−	0.895917i	−0.506749	−	0.100799i	−0.0649064	−	0.997891i	$-0.520675\pi$
$79$	−4.50408	−	0.895917i	−0.506749	−	0.100799i	−0.441842	+	0.897093i	$0.645675\pi$
$80$		0			0
$81$	−0.403592	+	0.403592i	−0.0448435	+	0.0448435i
$82$	9.32987	+	6.23402i	1.03031	+	0.688432i
$83$	5.66048	−	2.34465i	0.621318	−	0.257358i	−0.0497411	−	0.998762i	$-0.515840\pi$
$83$	5.66048	−	2.34465i	0.621318	−	0.257358i	0.671059	+	0.741404i	$0.265840\pi$
$84$	1.72715			0.188448
$85$		0			0
$86$	−10.6858			−1.15228
$87$	6.35531	−	2.63246i	0.681361	−	0.282229i
$88$	4.80928	+	3.21346i	0.512671	+	0.342556i
$89$	−10.2485	+	10.2485i	−1.08634	+	1.08634i	−0.0904408	+	0.995902i	$0.528828\pi$
$89$	−10.2485	+	10.2485i	−1.08634	+	1.08634i	−0.995902	+	0.0904408i	$0.971172\pi$
$90$		0			0
$91$	7.60177	+	1.51209i	0.796882	+	0.158510i
$92$	−3.27931	−	0.652295i	−0.341892	−	0.0680065i
$93$	1.84863	−	4.46299i	0.191694	−	0.462790i
$94$	0.972672	+	2.34824i	0.100323	+	0.242202i
$95$		0			0
$96$	0.201035	−	1.01067i	0.0205180	−	0.103151i
$97$	−9.36520	+	1.86285i	−0.950892	+	0.189144i	−0.646081	−	0.763269i	$-0.723593\pi$
$97$	−9.36520	+	1.86285i	−0.950892	+	0.189144i	−0.304811	+	0.952413i	$0.598593\pi$
$98$	−4.19074			−0.423329
$99$	10.9949	−	2.18702i	1.10503	−	0.219804i
$100$		0			0
$101$		−	8.75461i		−	0.871116i	−0.900161	−	0.435558i	$-0.856551\pi$
$101$		−	8.75461i		−	0.871116i	0.900161	−	0.435558i	$-0.143449\pi$
$102$	3.55924	+	2.32025i	0.352417	+	0.229739i
$103$	−6.22956	−	6.22956i	−0.613817	−	0.613817i	0.330122	−	0.943938i	$-0.392910\pi$
$103$	−6.22956	−	6.22956i	−0.613817	−	0.613817i	−0.943938	+	0.330122i	$0.892910\pi$
$104$	1.76964	−	4.27229i	0.173527	−	0.418932i
$105$		0			0
$106$	3.25691	+	3.25691i	0.316339	+	0.316339i
$107$	−2.54866	−	12.8130i	−0.246388	−	1.23868i	−0.883693	−	0.468066i	$-0.844951\pi$
$107$	−2.54866	−	12.8130i	−0.246388	−	1.23868i	0.637305	−	0.770612i	$-0.280049\pi$
$108$	−2.82707	−	4.23101i	−0.272035	−	0.407129i
$109$	−7.92144	+	5.29294i	−0.758737	+	0.506972i	−0.873740	−	0.486394i	$-0.838312\pi$
$109$	−7.92144	+	5.29294i	−0.758737	+	0.506972i	0.115003	+	0.993365i	$0.463312\pi$
$110$		0			0
$111$	1.55969	−	0.646046i	0.148040	−	0.0613200i
$112$	0.326988	−	1.64388i	0.0308974	−	0.155332i
$113$	5.75578	−	3.84589i	0.541458	−	0.361791i	−0.254566	−	0.967055i	$-0.581933\pi$
$113$	5.75578	−	3.84589i	0.541458	−	0.361791i	0.796024	+	0.605264i	$0.206933\pi$
$114$	−1.39549	+	2.08850i	−0.130700	+	0.195606i
$115$		0			0
$116$	−1.30233	−	6.54728i	−0.120919	−	0.607899i
$117$	−3.42980	−	8.28026i	−0.317085	−	0.765511i
$118$	−7.40891	+	7.40891i	−0.682045	+	0.682045i
$119$	5.78919	+	3.77394i	0.530694	+	0.345957i
$120$		0			0
$121$	−20.7462	−	8.59335i	−1.88602	−	0.781214i
$122$	2.45076	−	3.66782i	0.221881	−	0.332069i
$123$			11.5628i			1.04259i
$124$	−3.89782	−	2.60444i	−0.350035	−	0.233886i
$125$		0			0
$126$	−1.80476	−	2.70101i	−0.160780	−	0.240625i
$127$	−12.7690	−	5.28908i	−1.13306	−	0.469330i	−0.264242	−	0.964457i	$-0.585122\pi$
$127$	−12.7690	−	5.28908i	−1.13306	−	0.469330i	−0.868821	+	0.495127i	$0.835122\pi$
$128$	−0.923880	−	0.382683i	−0.0816602	−	0.0338248i
$129$	−6.11760	−	9.15563i	−0.538624	−	0.806108i
$130$		0			0
$131$	−0.0869490	−	0.0580974i	−0.00759677	−	0.00507600i	0.551766	−	0.833999i	$-0.313954\pi$
$131$	−0.0869490	−	0.0580974i	−0.00759677	−	0.00507600i	−0.559363	+	0.828923i	$0.688954\pi$
$132$			5.96031i			0.518778i
$133$	−2.26980	+	3.39700i	−0.196817	+	0.294557i
$134$	2.50074	+	1.03584i	0.216031	+	0.0894831i
$135$		0			0
$136$	2.88222	−	2.94836i	0.247148	−	0.252819i
$137$	−4.08626	+	4.08626i	−0.349112	+	0.349112i	−0.859779	−	0.510666i	$-0.829399\pi$
$137$	−4.08626	+	4.08626i	−0.349112	+	0.349112i	0.510666	+	0.859779i	$0.329399\pi$
$138$	−1.31851	−	3.18316i	−0.112239	−	0.270969i
$139$	−0.320189	−	1.60970i	−0.0271581	−	0.136533i	0.964828	−	0.262884i	$-0.0846735\pi$
$139$	−0.320189	−	1.60970i	−0.0271581	−	0.136533i	−0.991986	+	0.126351i	$0.959674\pi$
$140$		0			0
$141$	−1.45513	+	2.17775i	−0.122544	+	0.183400i
$142$	−6.82792	+	4.56227i	−0.572986	+	0.382857i
$143$	−5.21813	+	26.2333i	−0.436362	+	2.19374i
$144$	−1.79060	+	0.741692i	−0.149217	+	0.0618076i
$145$		0			0
$146$	4.55564	−	3.04398i	0.377027	−	0.251922i
$147$	−2.39919	−	3.59064i	−0.197882	−	0.296151i
$148$	−0.319613	−	1.60680i	−0.0262720	−	0.132078i
$149$	7.67572	+	7.67572i	0.628820	+	0.628820i	0.947771	−	0.318951i	$-0.103331\pi$
$149$	7.67572	+	7.67572i	0.628820	+	0.628820i	−0.318951	+	0.947771i	$0.603331\pi$
$150$		0			0
$151$	−3.20221	+	7.73081i	−0.260592	+	0.629124i	−0.998975	−	0.0452566i	$-0.985589\pi$
$151$	−3.20221	+	7.73081i	−0.260592	+	0.629124i	0.738384	+	0.674381i	$0.235589\pi$
$152$	1.72361	+	1.72361i	0.139803	+	0.139803i
$153$	−0.0906377	−	7.99062i	−0.00732763	−	0.646003i
$154$			9.69459i			0.781213i
$155$		0			0
$156$	4.67362	−	0.929642i	0.374189	−	0.0744309i
$157$	5.11593			0.408296			0.204148	−	0.978940i	$-0.434558\pi$
$157$	5.11593			0.408296			0.204148	+	0.978940i	$0.434558\pi$
$158$	−4.50408	+	0.895917i	−0.358325	+	0.0712754i
$159$	−0.925959	+	4.65511i	−0.0734333	+	0.369174i
$160$		0			0
$161$	−2.14459	−	5.17749i	−0.169017	−	0.408044i
$162$	−0.218422	+	0.527318i	−0.0171609	+	0.0414300i
$163$	−9.81857	−	1.95303i	−0.769050	−	0.152973i	−0.205053	−	0.978751i	$-0.565737\pi$
$163$	−9.81857	−	1.95303i	−0.769050	−	0.152973i	−0.563996	+	0.825777i	$0.690737\pi$
$164$	11.0053	+	2.18910i	0.859372	+	0.170940i
$165$		0			0
$166$	4.33234	−	4.33234i	0.336255	−	0.336255i
$167$	10.5435	+	7.04496i	0.815883	+	0.545156i	0.892049	−	0.451939i	$-0.149268\pi$
$167$	10.5435	+	7.04496i	0.815883	+	0.545156i	−0.0761654	+	0.997095i	$0.524268\pi$
$168$	1.59568	−	0.660953i	0.123109	−	0.0509936i
$169$	8.38405			0.644927
$170$		0			0
$171$	4.72429			0.361276
$172$	−9.87239	+	4.08928i	−0.752763	+	0.311805i
$173$	5.91996	+	3.95559i	0.450086	+	0.300738i	0.759877	−	0.650067i	$-0.225259\pi$
$173$	5.91996	+	3.95559i	0.450086	+	0.300738i	−0.309791	+	0.950805i	$0.600259\pi$
$174$	4.86415	−	4.86415i	0.368750	−	0.368750i
$175$		0			0
$176$	5.67293	+	1.12842i	0.427613	+	0.0850576i
$177$	−10.5896	−	2.10640i	−0.795960	−	0.158326i
$178$	−5.54647	+	13.3904i	−0.415725	+	1.00365i
$179$	−3.11798	−	7.52747i	−0.233049	−	0.562629i	0.763484	−	0.645826i	$-0.223487\pi$
$179$	−3.11798	−	7.52747i	−0.233049	−	0.562629i	−0.996533	+	0.0831969i	$0.973487\pi$
$180$		0			0
$181$	2.60085	−	13.0754i	0.193320	−	0.971883i	−0.755279	−	0.655403i	$-0.772499\pi$
$181$	2.60085	−	13.0754i	0.193320	−	0.971883i	0.948599	−	0.316480i	$-0.102501\pi$
$182$	7.60177	−	1.51209i	0.563481	−	0.112083i
$183$	4.54566			0.336025
$184$	−3.27931	+	0.652295i	−0.241754	+	0.0480879i
$185$		0			0
$186$		−	4.83071i		−	0.354204i
$187$	−13.0237	+	19.9782i	−0.952385	+	1.46095i
$188$	1.79726	+	1.79726i	0.131079	+	0.131079i
$189$	3.26387	−	7.87968i	0.237412	−	0.573163i
$190$		0			0
$191$	−12.4734	−	12.4734i	−0.902546	−	0.902546i	0.0931101	−	0.995656i	$-0.470319\pi$
$191$	−12.4734	−	12.4734i	−0.902546	−	0.902546i	−0.995656	+	0.0931101i	$0.970319\pi$
$192$	−0.201035	−	1.01067i	−0.0145084	−	0.0729387i
$193$	1.75845	+	2.63170i	0.126576	+	0.189434i	0.889345	−	0.457237i	$-0.151161\pi$
$193$	1.75845	+	2.63170i	0.126576	+	0.189434i	−0.762769	+	0.646671i	$0.776161\pi$
$194$	−7.93943	+	5.30496i	−0.570018	+	0.380874i
$195$		0			0
$196$	−3.87174	+	1.60373i	−0.276553	+	0.114552i
$197$	3.91682	−	19.6912i	0.279062	−	1.40294i	−0.545947	−	0.837820i	$-0.683830\pi$
$197$	3.91682	−	19.6912i	0.279062	−	1.40294i	0.825009	−	0.565120i	$-0.191170\pi$
$198$	9.32103	−	6.22811i	0.662417	−	0.442613i
$199$	−3.18389	+	4.76502i	−0.225700	+	0.337783i	−0.926986	−	0.375097i	$-0.877610\pi$
$199$	−3.18389	+	4.76502i	−0.225700	+	0.337783i	0.701286	+	0.712880i	$0.252610\pi$
$200$		0			0
$201$	0.544157	+	2.73566i	0.0383819	+	0.192959i
$202$	−3.35024	−	8.08820i	−0.235722	−	0.569084i
$203$	7.91166	−	7.91166i	0.555289	−	0.555289i
$204$	4.17623	+	0.781569i	0.292394	+	0.0547208i
$205$		0			0
$206$	−8.13931	−	3.37141i	−0.567093	−	0.234897i
$207$	−3.60024	+	5.38814i	−0.250234	+	0.374501i
$208$		−	4.62429i		−	0.320637i
$209$	−11.7229	−	7.83296i	−0.810887	−	0.541817i
$210$		0			0
$211$	10.6946	+	16.0056i	0.736246	+	1.10187i	0.990869	+	0.134830i	$0.0430488\pi$
$211$	10.6946	+	16.0056i	0.736246	+	1.10187i	−0.254622	+	0.967041i	$0.581951\pi$
$212$	4.25536	+	1.76263i	0.292259	+	0.121058i
$213$	−7.81793	−	3.23829i	−0.535676	−	0.221884i
$214$	−7.25797	−	10.8623i	−0.496145	−	0.742533i
$215$		0			0
$216$	−4.23101	−	2.82707i	−0.287884	−	0.192358i
$217$		−	7.85727i		−	0.533386i
$218$	−5.29294	+	7.92144i	−0.358483	+	0.536508i
$219$	5.21618	+	2.16061i	0.352477	+	0.146001i
$220$		0			0
$221$	17.6967	+	7.09614i	1.19041	+	0.477338i
$222$	1.19374	−	1.19374i	0.0801184	−	0.0801184i
$223$	1.65180	+	3.98779i	0.110612	+	0.267042i	0.969486	−	0.245145i	$-0.0788355\pi$
$223$	1.65180	+	3.98779i	0.110612	+	0.267042i	−0.858874	+	0.512187i	$0.828836\pi$
$224$	−0.326988	−	1.64388i	−0.0218478	−	0.109836i
$225$		0			0
$226$	3.84589	−	5.75578i	0.255825	−	0.382869i
$227$	16.3559	−	10.9287i	1.08558	−	0.725362i	0.121934	−	0.992538i	$-0.461091\pi$
$227$	16.3559	−	10.9287i	1.08558	−	0.725362i	0.963648	+	0.267176i	$0.0860905\pi$
$228$	−0.490031	+	2.46355i	−0.0324531	+	0.163153i
$229$	4.35060	−	1.80208i	0.287496	−	0.119085i	−0.234275	−	0.972170i	$-0.575272\pi$
$229$	4.35060	−	1.80208i	0.287496	−	0.119085i	0.521771	+	0.853086i	$0.325272\pi$
$230$		0			0
$231$	−8.30636	+	5.55013i	−0.546518	+	0.365172i
$232$	−3.70873	−	5.55051i	−0.243490	−	0.364409i
$233$	0.995617	+	5.00530i	0.0652250	+	0.327908i	0.999597	−	0.0283910i	$-0.00903836\pi$
$233$	0.995617	+	5.00530i	0.0652250	+	0.327908i	−0.934372	+	0.356299i	$0.884038\pi$
$234$	−6.33744	−	6.33744i	−0.414291	−	0.414291i
$235$		0			0
$236$	−4.00967	+	9.68021i	−0.261007	+	0.630128i
$237$	−3.34620	−	3.34620i	−0.217359	−	0.217359i
$238$	6.79274	+	1.27124i	0.440308	+	0.0824024i
$239$		−	2.61897i		−	0.169407i	−0.996406	−	0.0847037i	$-0.973006\pi$
$239$		−	2.61897i		−	0.169407i	0.996406	−	0.0847037i	$-0.0269944\pi$
$240$		0			0
$241$	3.94028	−	0.783771i	0.253816	−	0.0504871i	−0.0665423	−	0.997784i	$-0.521197\pi$
$241$	3.94028	−	0.783771i	0.253816	−	0.0504871i	0.320358	+	0.947296i	$0.396197\pi$
$242$	−22.4555			−1.44349
$243$	−15.5493	+	3.09295i	−0.997488	+	0.198413i
$244$	0.860592	−	4.32649i	0.0550938	−	0.276975i
$245$		0			0
$246$	4.42490	+	10.6827i	0.282122	+	0.681102i
$247$	−4.31358	+	10.4139i	−0.274466	+	0.662621i
$248$	−4.59779	−	0.914558i	−0.291960	−	0.0580745i
$249$	6.19222	+	1.23171i	0.392416	+	0.0780564i
$250$		0			0
$251$	−7.61296	+	7.61296i	−0.480526	+	0.480526i	−0.905300	−	0.424774i	$-0.860354\pi$
$251$	−7.61296	+	7.61296i	−0.480526	+	0.480526i	0.424774	+	0.905300i	$0.360354\pi$
$252$	−2.70101	−	1.80476i	−0.170148	−	0.113689i
$253$	17.8672	−	7.40086i	1.12330	−	0.465288i
$254$	−13.8210			−0.867208
$255$		0			0
$256$	−1.00000			−0.0625000
$257$	−0.611539	+	0.253308i	−0.0381467	+	0.0158009i	−0.401675	−	0.915782i	$-0.631572\pi$
$257$	−0.611539	+	0.253308i	−0.0381467	+	0.0158009i	0.363528	+	0.931583i	$0.381572\pi$
$258$	−9.15563	−	6.11760i	−0.570005	−	0.380865i
$259$	1.94164	−	1.94164i	0.120648	−	0.120648i
$260$		0			0
$261$	−12.6895	−	2.52410i	−0.785460	−	0.156238i
$262$	−0.102563	−	0.0204011i	−0.00633638	−	0.00126038i
$263$	−9.86725	+	23.8217i	−0.608441	+	1.46891i	0.256255	+	0.966609i	$0.417511\pi$
$263$	−9.86725	+	23.8217i	−0.608441	+	1.46891i	−0.864695	+	0.502297i	$0.832489\pi$
$264$	2.28091	+	5.50661i	0.140380	+	0.338908i
$265$		0			0
$266$	−0.797048	+	4.00703i	−0.0488702	+	0.245687i
$267$	−14.6482	+	2.91372i	−0.896458	+	0.178317i
$268$	2.70679			0.165343
$269$	−27.1342	+	5.39732i	−1.65440	+	0.329081i	−0.932017	−	0.362414i	$-0.881953\pi$
$269$	−27.1342	+	5.39732i	−1.65440	+	0.329081i	−0.722382	+	0.691494i	$0.756953\pi$
$270$		0			0
$271$		−	1.15983i		−	0.0704548i	−0.999379	−	0.0352274i	$-0.988784\pi$
$271$		−	1.15983i		−	0.0704548i	0.999379	−	0.0352274i	$-0.0112155\pi$
$272$	1.53454	−	3.82690i	0.0930450	−	0.232040i
$273$	5.64756	+	5.64756i	0.341806	+	0.341806i
$274$	−2.21147	+	5.33895i	−0.133600	+	0.322538i
$275$		0			0
$276$	−2.43629	−	2.43629i	−0.146647	−	0.146647i
$277$	−4.28548	−	21.5445i	−0.257489	−	1.29449i	−0.865641	−	0.500665i	$-0.833089\pi$
$277$	−4.28548	−	21.5445i	−0.257489	−	1.29449i	0.608152	−	0.793821i	$-0.291911\pi$
$278$	−0.911821	−	1.36464i	−0.0546874	−	0.0818455i
$279$	−7.55450	+	5.04776i	−0.452276	+	0.302201i
$280$		0			0
$281$	29.3623	−	12.1623i	1.75161	−	0.725539i	0.753963	−	0.656916i	$-0.228140\pi$
$281$	29.3623	−	12.1623i	1.75161	−	0.725539i	0.997643	−	0.0686226i	$-0.0218604\pi$
$282$	−0.510972	+	2.56883i	−0.0304280	+	0.152972i
$283$	15.9849	−	10.6808i	0.950205	−	0.634907i	0.0191622	−	0.999816i	$-0.493900\pi$
$283$	15.9849	−	10.6808i	0.950205	−	0.634907i	0.931043	+	0.364910i	$0.118900\pi$
$284$	−4.56227	+	6.82792i	−0.270721	+	0.405162i
$285$		0			0
$286$	5.21813	+	26.2333i	0.308554	+	1.55121i
$287$	7.19722	+	17.3756i	0.424838	+	1.02565i
$288$	−1.37047	+	1.37047i	−0.0807556	+	0.0807556i
$289$	12.2904	+	11.7451i	0.722964	+	0.690885i
$290$		0			0
$291$	−9.09061	−	3.76546i	−0.532901	−	0.220735i
$292$	3.04398	−	4.55564i	0.178135	−	0.266598i
$293$		−	0.480564i		−	0.0280748i	−0.999901	−	0.0140374i	$-0.995532\pi$
$293$		−	0.480564i		−	0.0280748i	0.999901	−	0.0140374i	$-0.00446840\pi$
$294$	−3.59064	−	2.39919i	−0.209411	−	0.139924i
$295$		0			0
$296$	−0.910181	−	1.36218i	−0.0529032	−	0.0791753i
$297$	27.1924	+	11.2634i	1.57786	+	0.653571i
$298$	10.0288	+	4.15407i	0.580954	+	0.240639i
$299$	−8.58999	−	12.8558i	−0.496772	−	0.743472i
$300$		0			0
$301$	−14.8919	−	9.95043i	−0.858353	−	0.573533i
$302$			8.36777i			0.481511i
$303$	5.01199	−	7.50098i	0.287932	−	0.430920i
$304$	2.25200	+	0.932809i	0.129161	+	0.0535003i
$305$		0			0
$306$	−3.14162	−	7.34768i	−0.179594	−	0.420039i
$307$	−10.5614	+	10.5614i	−0.602772	+	0.602772i	−0.941047	−	0.338275i	$-0.890156\pi$
$307$	−10.5614	+	10.5614i	−0.602772	+	0.602772i	0.338275	+	0.941047i	$0.390156\pi$
$308$	3.70996	+	8.95664i	0.211395	+	0.510352i
$309$	−1.77110	−	8.90392i	−0.100754	−	0.506526i
$310$		0			0
$311$	−8.98927	+	13.4534i	−0.509735	+	0.762872i	−0.993683	−	0.112225i	$-0.964202\pi$
$311$	−8.98927	+	13.4534i	−0.509735	+	0.762872i	0.483948	+	0.875097i	$0.339202\pi$
$312$	3.96211	−	2.64740i	0.224310	−	0.149879i
$313$	0.858633	−	4.31664i	0.0485328	−	0.243991i	−0.948902	−	0.315571i	$-0.897804\pi$
$313$	0.858633	−	4.31664i	0.0485328	−	0.243991i	0.997435	+	0.0715797i	$0.0228040\pi$
$314$	4.72650	−	1.95778i	0.266732	−	0.110484i
$315$		0			0
$316$	−3.81838	+	2.55136i	−0.214800	+	0.143525i
$317$	17.8387	+	26.6975i	1.00192	+	1.49948i	0.860448	+	0.509539i	$0.170184\pi$
$317$	17.8387	+	26.6975i	1.00192	+	1.49948i	0.141473	+	0.989942i	$0.454816\pi$
$318$	0.925959	+	4.65511i	0.0519252	+	0.261046i
$319$	27.3027	+	27.3027i	1.52866	+	1.52866i
$320$		0			0
$321$	5.15170	−	12.4373i	0.287540	−	0.694183i
$322$	−3.96268	−	3.96268i	−0.220832	−	0.220832i
$323$	−7.02555	+	7.18676i	−0.390912	+	0.399882i
$324$			0.570765i			0.0317092i
$325$		0			0
$326$	−9.81857	+	1.95303i	−0.543800	+	0.108169i
$327$	−9.81732			−0.542899
$328$	11.0053	−	2.18910i	0.607668	−	0.120873i
$329$	−0.831109	+	4.17827i	−0.0458205	+	0.230355i
$330$		0			0
$331$	−0.705646	−	1.70358i	−0.0387858	−	0.0936372i	0.903300	−	0.429010i	$-0.141138\pi$
$331$	−0.705646	−	1.70358i	−0.0387858	−	0.0936372i	−0.942085	+	0.335373i	$0.891138\pi$
$332$	2.34465	−	5.66048i	0.128679	−	0.310659i
$333$	−3.11420	−	0.619453i	−0.170657	−	0.0339458i
$334$	12.4369	+	2.47386i	0.680519	+	0.135364i
$335$		0			0
$336$	1.22128	−	1.22128i	0.0666263	−	0.0666263i
$337$	−10.4252	−	6.96587i	−0.567895	−	0.379455i	0.238223	−	0.971211i	$-0.423435\pi$
$337$	−10.4252	−	6.96587i	−0.567895	−	0.379455i	−0.806118	+	0.591755i	$0.798435\pi$
$338$	7.74585	−	3.20844i	0.421319	−	0.174516i
$339$	7.13334			0.387430
$340$		0			0
$341$	27.1150			1.46836
$342$	4.36468	−	1.80791i	0.236015	−	0.0977605i
$343$	−15.5956	−	10.4206i	−0.842081	−	0.562661i
$344$	−7.55600	+	7.55600i	−0.407392	+	0.407392i
$345$		0			0
$346$	6.98306	+	1.38902i	0.375412	+	0.0746741i
$347$	18.0345	+	3.58728i	0.968142	+	0.192575i	0.653744	−	0.756716i	$-0.273197\pi$
$347$	18.0345	+	3.58728i	0.968142	+	0.192575i	0.314398	+	0.949291i	$0.398197\pi$
$348$	2.63246	−	6.35531i	0.141114	−	0.340680i
$349$	0.302687	+	0.730751i	0.0162025	+	0.0391162i	0.931774	−	0.363040i	$-0.118261\pi$
$349$	0.302687	+	0.730751i	0.0162025	+	0.0391162i	−0.915571	+	0.402156i	$0.868261\pi$
$350$		0			0
$351$	4.59070	−	23.0790i	0.245033	−	1.23186i
$352$	5.67293	−	1.12842i	0.302368	−	0.0601448i
$353$	−22.0327			−1.17268			−0.586341	−	0.810064i	$-0.699432\pi$
$353$	−22.0327			−1.17268			−0.586341	+	0.810064i	$0.699432\pi$
$354$	−10.5896	+	2.10640i	−0.562829	+	0.111954i
$355$		0			0
$356$			14.4936i			0.768160i
$357$	2.79962	+	6.54783i	0.148172	+	0.346548i
$358$	−5.76127	−	5.76127i	−0.304493	−	0.304493i
$359$	10.0104	−	24.1672i	0.528328	−	1.27550i	−0.404289	−	0.914631i	$-0.632481\pi$
$359$	10.0104	−	24.1672i	0.528328	−	1.27550i	0.932618	−	0.360866i	$-0.117519\pi$
$360$		0			0
$361$	9.23366	+	9.23366i	0.485982	+	0.485982i
$362$	−2.60085	−	13.0754i	−0.136698	−	0.687225i
$363$	−12.8557	−	19.2400i	−0.674751	−	1.00984i
$364$	6.44447	−	4.30606i	0.337782	−	0.225699i
$365$		0			0
$366$	4.19964	−	1.73955i	0.219519	−	0.0909276i
$367$	3.20087	−	16.0919i	0.167084	−	0.839988i	−0.802768	−	0.596292i	$-0.796640\pi$
$367$	3.20087	−	16.0919i	0.167084	−	0.839988i	0.969852	−	0.243696i	$-0.0783599\pi$
$368$	−2.78006	+	1.85758i	−0.144921	+	0.0968331i
$369$	12.0824	−	18.0825i	0.628983	−	0.941339i
$370$		0			0
$371$	1.50610	+	7.57165i	0.0781926	+	0.393101i
$372$	−1.84863	−	4.46299i	−0.0958470	−	0.231395i
$373$	−0.608572	+	0.608572i	−0.0315107	+	0.0315107i	−0.722687	−	0.691176i	$-0.757093\pi$
$373$	−0.608572	+	0.608572i	−0.0315107	+	0.0315107i	0.691176	+	0.722687i	$0.257093\pi$
$374$	−4.38698	+	23.4414i	−0.226846	+	1.21212i
$375$		0			0
$376$	2.34824	+	0.972672i	0.121101	+	0.0501617i
$377$	17.1503	−	25.6672i	0.883283	−	1.32193i
$378$		−	8.52891i		−	0.438680i
$379$	−18.3579	−	12.2664i	−0.942984	−	0.630082i	−0.0138811	−	0.999904i	$-0.504419\pi$
$379$	−18.3579	−	12.2664i	−0.942984	−	0.630082i	−0.929103	+	0.369822i	$0.879419\pi$
$380$		0			0
$381$	−7.91251	−	11.8419i	−0.405370	−	0.606679i
$382$	−16.2973	−	6.75057i	−0.833844	−	0.345389i
$383$	27.9938	+	11.5954i	1.43041	+	0.592497i	0.957454	−	0.288587i	$-0.0931854\pi$
$383$	27.9938	+	11.5954i	1.43041	+	0.592497i	0.472960	+	0.881084i	$0.343185\pi$
$384$	−0.572498	−	0.856804i	−0.0292152	−	0.0437236i
$385$		0			0
$386$	2.63170	+	1.75845i	0.133950	+	0.0895026i
$387$			20.7105i			1.05277i
$388$	−5.30496	+	7.93943i	−0.269318	+	0.403064i
$389$	28.5851	+	11.8403i	1.44932	+	0.600329i	0.962039	−	0.272914i	$-0.0879873\pi$
$389$	28.5851	+	11.8403i	1.44932	+	0.600329i	0.487285	+	0.873243i	$0.337987\pi$
$390$		0			0
$391$	−2.84267	−	13.4896i	−0.143760	−	0.682197i
$392$	−2.96330	+	2.96330i	−0.149669	+	0.149669i
$393$	−0.0412375	−	0.0995562i	−0.00208016	−	0.00502195i
$394$	−3.91682	−	19.6912i	−0.197327	−	0.992028i
$395$		0			0
$396$	6.22811	−	9.32103i	0.312975	−	0.468399i
$397$	9.10159	−	6.08149i	0.456796	−	0.305221i	−0.305801	−	0.952095i	$-0.598924\pi$
$397$	9.10159	−	6.08149i	0.456796	−	0.305221i	0.762597	+	0.646874i	$0.223924\pi$
$398$	−1.11803	+	5.62073i	−0.0560419	+	0.281742i
$399$	−3.88955	+	1.61110i	−0.194721	+	0.0806560i
$400$		0			0
$401$	−12.1334	+	8.10725i	−0.605911	+	0.404857i	−0.820335	−	0.571884i	$-0.806213\pi$
$401$	−12.1334	+	8.10725i	−0.605911	+	0.404857i	0.214423	+	0.976741i	$0.431213\pi$
$402$	1.54963	+	2.31918i	0.0772884	+	0.115670i
$403$	−4.22918	−	21.2615i	−0.210671	−	1.05911i
$404$	−6.19044	−	6.19044i	−0.307986	−	0.307986i
$405$		0			0
$406$	4.28176	−	10.3371i	0.212500	−	0.513021i
$407$	6.70051	+	6.70051i	0.332132	+	0.332132i
$408$	4.15742	−	0.876098i	0.205823	−	0.0433733i
$409$		−	2.35457i		−	0.116426i	−0.998304	−	0.0582130i	$-0.981460\pi$
$409$		−	2.35457i		−	0.116426i	0.998304	−	0.0582130i	$-0.0185403\pi$
$410$		0			0
$411$	−5.84049	+	1.16175i	−0.288090	+	0.0573047i
$412$	−8.80993			−0.434034
$413$	−17.2242	+	3.42611i	−0.847547	+	0.168588i
$414$	−1.26424	+	6.35574i	−0.0621338	+	0.312368i
$415$		0			0
$416$	−1.76964	−	4.27229i	−0.0867637	−	0.209466i
$417$	0.647210	−	1.56250i	0.0316940	−	0.0765161i
$418$	−13.8280	−	2.75057i	−0.676352	−	0.134535i
$419$	26.7980	+	5.33045i	1.30917	+	0.260409i	0.799866	−	0.600179i	$-0.204904\pi$
$419$	26.7980	+	5.33045i	1.30917	+	0.260409i	0.509301	+	0.860589i	$0.329904\pi$
$420$		0			0
$421$	7.28333	−	7.28333i	0.354968	−	0.354968i	−0.506986	−	0.861954i	$-0.669241\pi$
$421$	7.28333	−	7.28333i	0.354968	−	0.354968i	0.861954	+	0.506986i	$0.169241\pi$
$422$	16.0056	+	10.6946i	0.779140	+	0.520605i
$423$	4.55120	−	1.88517i	0.221287	−	0.0916600i
$424$	4.60597			0.223686
$425$		0			0
$426$	−8.46207			−0.409989
$427$	6.83082	−	2.82942i	0.330567	−	0.136925i
$428$	−10.8623	−	7.25797i	−0.525050	−	0.350827i
$429$	−19.4894	+	19.4894i	−0.940958	+	0.940958i
$430$		0			0
$431$	16.9262	+	3.36683i	0.815307	+	0.162175i	0.585094	−	0.810966i	$-0.301058\pi$
$431$	16.9262	+	3.36683i	0.815307	+	0.162175i	0.230213	+	0.973140i	$0.426058\pi$
$432$	−4.99082	−	0.992735i	−0.240121	−	0.0477630i
$433$	9.81392	−	23.6929i	0.471627	−	1.13861i	−0.491817	−	0.870699i	$-0.663667\pi$
$433$	9.81392	−	23.6929i	0.471627	−	1.13861i	0.963444	−	0.267910i	$-0.0863329\pi$
$434$	−3.00685	−	7.25917i	−0.144333	−	0.348451i
$435$		0			0
$436$	−1.85863	+	9.34398i	−0.0890124	+	0.447495i
$437$	7.99347	−	1.59000i	0.382380	−	0.0760601i
$438$	5.64596			0.269774
$439$	34.5319	−	6.86883i	1.64812	−	0.327831i	0.718268	−	0.695767i	$-0.244935\pi$
$439$	34.5319	−	6.86883i	1.64812	−	0.327831i	0.929851	+	0.367936i	$0.119935\pi$
$440$		0			0
$441$			8.12222i			0.386772i
$442$	19.0652	−	0.216257i	0.906839	−	0.0102863i
$443$	−8.29543	−	8.29543i	−0.394128	−	0.394128i	0.482028	−	0.876156i	$-0.339900\pi$
$443$	−8.29543	−	8.29543i	−0.394128	−	0.394128i	−0.876156	+	0.482028i	$0.839900\pi$
$444$	0.646046	−	1.55969i	0.0306600	−	0.0740198i
$445$		0			0
$446$	3.05212	+	3.05212i	0.144522	+	0.144522i
$447$	2.18225	+	10.9709i	0.103217	+	0.518907i
$448$	−0.931182	−	1.39361i	−0.0439942	−	0.0658420i
$449$	−2.92263	+	1.95284i	−0.137928	+	0.0921603i	−0.622620	−	0.782525i	$-0.713932\pi$
$449$	−2.92263	+	1.95284i	−0.137928	+	0.0921603i	0.484692	+	0.874685i	$0.338932\pi$
$450$		0			0
$451$	−59.9623	+	24.8372i	−2.82352	+	1.16954i
$452$	1.35050	−	6.78941i	0.0635220	−	0.319347i
$453$	−7.16953	+	4.79053i	−0.336854	+	0.225079i
$454$	10.9287	−	16.3559i	0.512909	−	0.767622i
$455$		0			0
$456$	0.490031	+	2.46355i	0.0229478	+	0.115366i
$457$	13.2146	+	31.9028i	0.618152	+	1.49235i	0.853847	+	0.520524i	$0.174263\pi$
$457$	13.2146	+	31.9028i	0.618152	+	1.49235i	−0.235695	+	0.971827i	$0.575737\pi$
$458$	3.32980	−	3.32980i	0.155591	−	0.155591i
$459$	11.4577	−	17.5760i	0.534800	−	0.820377i
$460$		0			0
$461$	−0.00945111	−	0.00391478i	−0.000440182	−	0.000182329i	0.382463	−	0.923971i	$-0.375076\pi$
$461$	−0.00945111	−	0.00391478i	−0.000440182	−	0.000182329i	−0.382904	+	0.923788i	$0.625076\pi$
$462$	−5.55013	+	8.30636i	−0.258216	+	0.386447i
$463$			14.9029i			0.692597i	0.938124	+	0.346298i	$0.112562\pi$
$463$			14.9029i			0.692597i	−0.938124	+	0.346298i	$0.887438\pi$
$464$	−5.55051	−	3.70873i	−0.257676	−	0.172174i
$465$		0			0
$466$	2.83528	+	4.24329i	0.131342	+	0.196567i
$467$	−7.51619	−	3.11331i	−0.347808	−	0.144067i	0.201939	−	0.979398i	$-0.435276\pi$
$467$	−7.51619	−	3.11331i	−0.347808	−	0.144067i	−0.549747	+	0.835331i	$0.685276\pi$
$468$	−8.28026	−	3.42980i	−0.382755	−	0.158542i
$469$	2.52051	+	3.77221i	0.116386	+	0.174184i
$470$		0			0
$471$	4.38335	+	2.92886i	0.201974	+	0.134955i
$472$			10.4778i			0.482279i
$473$	34.3384	−	51.3910i	1.57888	−	2.36296i
$474$	−4.37202	−	1.81095i	−0.200814	−	0.0831797i
$475$		0			0
$476$	6.76216	−	1.42500i	0.309943	−	0.0653145i
$477$	6.31233	−	6.31233i	0.289022	−	0.289022i
$478$	−1.00224	−	2.41962i	−0.0458413	−	0.110671i
$479$	6.31687	+	31.7570i	0.288625	+	1.45102i	0.804296	+	0.594229i	$0.202543\pi$
$479$	6.31687	+	31.7570i	0.288625	+	1.45102i	−0.515671	+	0.856787i	$0.672457\pi$
$480$		0			0
$481$	4.20894	−	6.29913i	0.191911	−	0.287215i
$482$	3.34041	−	2.23199i	0.152151	−	0.101664i
$483$	1.12661	−	5.66387i	0.0512627	−	0.257715i
$484$	−20.7462	+	8.59335i	−0.943008	+	0.390607i
$485$		0			0
$486$	−13.1821	+	8.80797i	−0.597951	+	0.399538i
$487$	13.4875	+	20.1855i	0.611177	+	0.914691i	0.999978	−	0.00663048i	$-0.00211056\pi$
$487$	13.4875	+	20.1855i	0.611177	+	0.914691i	−0.388801	+	0.921322i	$0.627111\pi$
$488$	−0.860592	−	4.32649i	−0.0389572	−	0.195851i
$489$	−7.29448	−	7.29448i	−0.329868	−	0.329868i
$490$		0			0
$491$	−8.98813	+	21.6993i	−0.405629	+	0.979274i	0.580645	+	0.814157i	$0.302800\pi$
$491$	−8.98813	+	21.6993i	−0.405629	+	0.979274i	−0.986274	+	0.165118i	$0.947200\pi$
$492$	8.17616	+	8.17616i	0.368610	+	0.368610i
$493$	22.7104	−	15.5501i	1.02283	−	0.700341i
$494$			11.2719i			0.507148i
$495$		0			0
$496$	−4.59779	+	0.914558i	−0.206447	+	0.0410649i
$497$	−13.7638			−0.617390
$498$	6.19222	−	1.23171i	0.277480	−	0.0551942i
$499$	2.34595	−	11.7939i	0.105019	−	0.527967i	−0.892081	−	0.451875i	$-0.850755\pi$
$499$	2.34595	−	11.7939i	0.105019	−	0.527967i	0.997101	−	0.0760929i	$-0.0242445\pi$
$500$		0			0
$501$	5.00051	+	12.0723i	0.223406	+	0.539351i
$502$	−4.12011	+	9.94682i	−0.183889	+	0.443948i
$503$	22.9711	+	4.56923i	1.02423	+	0.203732i	0.678499	−	0.734601i	$-0.262631\pi$
$503$	22.9711	+	4.56923i	1.02423	+	0.203732i	0.345731	+	0.938334i	$0.387631\pi$
$504$	−3.18606	−	0.633746i	−0.141918	−	0.0282293i
$505$		0			0
$506$	13.6750	−	13.6750i	0.607928	−	0.607928i
$507$	7.18349	+	4.79985i	0.319030	+	0.213169i
$508$	−12.7690	+	5.28908i	−0.566531	+	0.234665i
$509$	−34.4909			−1.52878			−0.764392	−	0.644752i	$-0.776961\pi$
$509$	−34.4909			−1.52878			−0.764392	+	0.644752i	$0.776961\pi$
$510$		0			0
$511$	9.18329			0.406245
$512$	−0.923880	+	0.382683i	−0.0408301	+	0.0169124i
$513$	10.3133	+	6.89112i	0.455343	+	0.304250i
$514$	−0.468052	+	0.468052i	−0.0206449	+	0.0206449i
$515$		0			0
$516$	−10.7998	−	2.14821i	−0.475435	−	0.0945699i
$517$	−14.4190	−	2.86811i	−0.634146	−	0.126139i
$518$	1.05081	−	2.53688i	0.0461700	−	0.111464i
$519$	2.80767	+	6.77832i	0.123243	+	0.297535i
$520$		0			0
$521$	6.54790	−	32.9185i	0.286869	−	1.44219i	−0.521369	−	0.853331i	$-0.674578\pi$
$521$	6.54790	−	32.9185i	0.286869	−	1.44219i	0.808238	−	0.588856i	$-0.200422\pi$
$522$	−12.6895	+	2.52410i	−0.555404	+	0.110477i
$523$	18.1579			0.793991			0.396996	−	0.917820i	$-0.370053\pi$
$523$	18.1579			0.793991			0.396996	+	0.917820i	$0.370053\pi$
$524$	−0.102563	+	0.0204011i	−0.00448050	+	0.000891227i
$525$		0			0
$526$			25.7844i			1.12425i
$527$	3.55556	−	18.9987i	0.154883	−	0.827598i
$528$	4.21457	+	4.21457i	0.183416	+	0.183416i
$529$	4.52356	−	10.9208i	0.196677	−	0.474819i
$530$		0			0
$531$	14.3595	+	14.3595i	0.623147	+	0.623147i
$532$	0.797048	+	4.00703i	0.0345564	+	0.173727i
$533$	28.8279	+	43.1440i	1.24868	+	1.86878i
$534$	−12.4182	+	8.29757i	−0.537387	+	0.359071i
$535$		0			0
$536$	2.50074	−	1.03584i	0.108016	−	0.0447416i
$537$	1.63796	−	8.23460i	0.0706833	−	0.355349i
$538$	−23.0032	+	15.3703i	−0.991740	+	0.662659i
$539$	13.4668	−	20.1545i	0.580055	−	0.868114i
$540$		0			0
$541$	1.43320	+	7.20520i	0.0616182	+	0.309776i	0.999287	−	0.0377544i	$-0.0120205\pi$
$541$	1.43320	+	7.20520i	0.0616182	+	0.309776i	−0.937669	+	0.347530i	$0.887020\pi$
$542$	−0.443848	−	1.07154i	−0.0190649	−	0.0460268i
$543$	9.71403	−	9.71403i	0.416869	−	0.416869i
$544$	−0.0467655	−	4.12284i	−0.00200505	−	0.176765i
$545$		0			0
$546$	7.37889	+	3.05644i	0.315787	+	0.130803i
$547$	16.2036	−	24.2504i	0.692815	−	1.03687i	−0.303643	−	0.952786i	$-0.598203\pi$
$547$	16.2036	−	24.2504i	0.692815	−	1.03687i	0.996459	−	0.0840855i	$-0.0267969\pi$
$548$			5.77884i			0.246860i
$549$	−7.10873	−	4.74990i	−0.303393	−	0.202721i
$550$		0			0
$551$	9.04021	+	13.5296i	0.385126	+	0.576382i
$552$	−3.18316	−	1.31851i	−0.135484	−	0.0561195i
$553$	−7.11121	−	2.94556i	−0.302399	−	0.125258i
$554$	−12.2040	−	18.2646i	−0.518498	−	0.775988i
$555$		0			0
$556$	−1.36464	−	0.911821i	−0.0578735	−	0.0386698i
$557$			7.32927i			0.310551i	0.987871	+	0.155275i	$0.0496265\pi$
$557$			7.32927i			0.310551i	−0.987871	+	0.155275i	$0.950373\pi$
$558$	−5.04776	+	7.55450i	−0.213689	+	0.319808i
$559$	−45.6528	−	18.9100i	−1.93091	−	0.799808i
$560$		0			0
$561$	−22.5962	+	9.66135i	−0.954012	+	0.407903i
$562$	22.4729	−	22.4729i	0.947962	−	0.947962i
$563$	−11.8556	−	28.6219i	−0.499653	−	1.20627i	−0.949671	−	0.313249i	$-0.898583\pi$
$563$	−11.8556	−	28.6219i	−0.499653	−	1.20627i	0.450018	−	0.893019i	$-0.351417\pi$
$564$	0.510972	+	2.56883i	0.0215158	+	0.108167i
$565$		0			0
$566$	10.6808	−	15.9849i	0.448947	−	0.671897i
$567$	−0.795425	+	0.531486i	−0.0334047	+	0.0223203i
$568$	−1.60206	+	8.05408i	−0.0672208	+	0.337942i
$569$	25.5509	−	10.5835i	1.07115	−	0.443684i	0.223752	−	0.974646i	$-0.428169\pi$
$569$	25.5509	−	10.5835i	1.07115	−	0.443684i	0.847396	+	0.530962i	$0.178169\pi$
$570$		0			0
$571$	19.2218	−	12.8436i	0.804406	−	0.537487i	−0.0840429	−	0.996462i	$-0.526783\pi$
$571$	19.2218	−	12.8436i	0.804406	−	0.537487i	0.888449	+	0.458975i	$0.151783\pi$
$572$	14.8600	+	22.2395i	0.621326	+	0.929881i
$573$	−3.54627	−	17.8283i	−0.148147	−	0.744788i
$574$	13.2987	+	13.2987i	0.555078	+	0.555078i
$575$		0			0
$576$	−0.741692	+	1.79060i	−0.0309038	+	0.0746084i
$577$	−24.6305	−	24.6305i	−1.02538	−	1.02538i	−0.999669	−	0.0257102i	$-0.991815\pi$
$577$	−24.6305	−	24.6305i	−1.02538	−	1.02538i	−0.0257102	−	0.999669i	$-0.508185\pi$
$578$	15.8495	+	6.14768i	0.659251	+	0.255710i
$579$			3.26156i			0.135546i
$580$		0			0
$581$	10.0718	−	2.00341i	0.417849	−	0.0831153i
$582$	−9.83961			−0.407865
$583$	−26.1294	+	5.19745i	−1.08217	+	0.215256i
$584$	1.06890	−	5.37374i	0.0442315	−	0.222367i
$585$		0			0
$586$	−0.183904	−	0.443983i	−0.00759700	−	0.0183408i
$587$	4.24371	−	10.2452i	0.175157	−	0.422866i	−0.811782	−	0.583960i	$-0.801502\pi$
$587$	4.24371	−	10.2452i	0.175157	−	0.422866i	0.986939	+	0.161095i	$0.0515024\pi$
$588$	−4.23545	−	0.842484i	−0.174667	−	0.0347434i
$589$	11.2073	+	2.22928i	0.461791	+	0.0918558i
$590$		0			0
$591$	14.6291	−	14.6291i	0.601761	−	0.601761i
$592$	−1.36218	−	0.910181i	−0.0559854	−	0.0374082i
$593$	−42.6843	+	17.6804i	−1.75283	+	0.726048i	−0.755338	+	0.655336i	$0.772527\pi$
$593$	−42.6843	+	17.6804i	−1.75283	+	0.726048i	−0.997497	+	0.0707122i	$0.977473\pi$
$594$	29.4328			1.20764
$595$		0			0
$596$	10.8551			0.444643
$597$	−5.45593	+	2.25992i	−0.223296	+	0.0924923i
$598$	−12.8558	−	8.58999i	−0.525714	−	0.351271i
$599$	−29.0498	+	29.0498i	−1.18694	+	1.18694i	−0.209035	+	0.977908i	$0.567032\pi$
$599$	−29.0498	+	29.0498i	−1.18694	+	1.18694i	−0.977908	+	0.209035i	$0.932968\pi$
$600$		0			0
$601$	−13.6083	−	2.70685i	−0.555093	−	0.110415i	−0.0904304	−	0.995903i	$-0.528824\pi$
$601$	−13.6083	−	2.70685i	−0.555093	−	0.110415i	−0.464662	+	0.885488i	$0.653824\pi$
$602$	−17.5662	−	3.49413i	−0.715943	−	0.142410i
$603$	2.00760	−	4.84678i	0.0817558	−	0.197376i
$604$	3.20221	+	7.73081i	0.130296	+	0.314562i
$605$		0			0
$606$	1.75998	−	8.84801i	0.0714942	−	0.359426i
$607$	25.1950	−	5.01159i	1.02263	−	0.203414i	0.344835	−	0.938663i	$-0.387935\pi$
$607$	25.1950	−	5.01159i	1.02263	−	0.203414i	0.677797	+	0.735249i	$0.262935\pi$
$608$	2.43755			0.0988556
$609$	11.3081	−	2.24933i	0.458229	−	0.0911474i
$610$		0			0
$611$			11.7536i			0.475501i
$612$	−5.71431	−	5.58613i	−0.230987	−	0.225806i
$613$	14.4308	+	14.4308i	0.582856	+	0.582856i	0.935687	−	0.352831i	$-0.114781\pi$
$613$	14.4308	+	14.4308i	0.582856	+	0.582856i	−0.352831	+	0.935687i	$0.614781\pi$
$614$	−5.71580	+	13.7992i	−0.230671	+	0.556889i
$615$		0			0
$616$	6.85511	+	6.85511i	0.276200	+	0.276200i
$617$	3.04210	+	15.2937i	0.122470	+	0.615699i	0.992454	+	0.122619i	$0.0391292\pi$
$617$	3.04210	+	15.2937i	0.122470	+	0.615699i	−0.869984	+	0.493081i	$0.835871\pi$
$618$	−5.04366	−	7.54838i	−0.202886	−	0.303640i
$619$	−10.5371	+	7.04064i	−0.423520	+	0.282987i	−0.749010	−	0.662558i	$-0.769471\pi$
$619$	−10.5371	+	7.04064i	−0.423520	+	0.282987i	0.325490	+	0.945545i	$0.394471\pi$
$620$		0			0
$621$	−15.7189	+	6.51097i	−0.630777	+	0.261276i
$622$	−3.15661	+	15.8694i	−0.126569	+	0.636303i
$623$	−20.1985	+	13.4962i	−0.809236	+	0.540714i
$624$	2.64740	−	3.96211i	0.105981	−	0.158611i
$625$		0			0
$626$	−0.858633	−	4.31664i	−0.0343179	−	0.172528i
$627$	−5.55983	−	13.4226i	−0.222038	−	0.536048i
$628$	3.61751	−	3.61751i	0.144354	−	0.144354i
$629$	5.57350	−	3.81624i	0.222230	−	0.152163i
$630$		0			0
$631$	14.5366	+	6.02127i	0.578694	+	0.239703i	0.652778	−	0.757549i	$-0.273603\pi$
$631$	14.5366	+	6.02127i	0.578694	+	0.239703i	−0.0740843	+	0.997252i	$0.523603\pi$
$632$	−2.55136	+	3.81838i	−0.101488	+	0.151887i
$633$			19.8363i			0.788422i
$634$	26.6975	+	17.8387i	1.06029	+	0.708465i
$635$		0			0
$636$	2.63691	+	3.94641i	0.104560	+	0.156485i
$637$	−17.9041	−	7.41610i	−0.709384	−	0.293837i
$638$	35.6727	+	14.7761i	1.41230	+	0.584992i
$639$	8.84229	+	13.2334i	0.349795	+	0.523506i
$640$		0			0
$641$	−16.6671	−	11.1366i	−0.658310	−	0.439869i	0.181029	−	0.983478i	$-0.442057\pi$
$641$	−16.6671	−	11.1366i	−0.658310	−	0.439869i	−0.839338	+	0.543609i	$0.817057\pi$
$642$		−	13.4620i		−	0.531305i
$643$	−16.1042	+	24.1017i	−0.635089	+	0.950477i	0.364724	+	0.931116i	$0.381163\pi$
$643$	−16.1042	+	24.1017i	−0.635089	+	0.950477i	−0.999813	+	0.0193615i	$0.993837\pi$
$644$	−5.17749	−	2.14459i	−0.204022	−	0.0845086i
$645$		0			0
$646$	−3.74051	+	9.32826i	−0.147168	+	0.367015i
$647$	−0.105698	+	0.105698i	−0.00415541	+	0.00415541i	−0.709181	−	0.705026i	$-0.750935\pi$
$647$	−0.105698	+	0.105698i	−0.00415541	+	0.00415541i	0.705026	+	0.709181i	$0.250935\pi$
$648$	0.218422	+	0.527318i	0.00858044	+	0.0207150i
$649$	−11.8233	−	59.4398i	−0.464105	−	2.33321i
$650$		0			0
$651$	4.49827	−	6.73213i	0.176301	−	0.263853i
$652$	−8.32378	+	5.56177i	−0.325984	+	0.217816i
$653$	−6.59498	+	33.1552i	−0.258082	+	1.29746i	0.606545	+	0.795049i	$0.292555\pi$
$653$	−6.59498	+	33.1552i	−0.258082	+	1.29746i	−0.864627	+	0.502415i	$0.832445\pi$
$654$	−9.07002	+	3.75692i	−0.354666	+	0.146907i
$655$		0			0
$656$	9.32987	−	6.23402i	0.364270	−	0.243398i
$657$	−5.89964	−	8.82943i	−0.230167	−	0.344469i
$658$	0.831109	+	4.17827i	0.0324000	+	0.162886i
$659$	33.1839	+	33.1839i	1.29266	+	1.29266i	0.933134	+	0.359529i	$0.117063\pi$
$659$	33.1839	+	33.1839i	1.29266	+	1.29266i	0.359529	+	0.933134i	$0.382937\pi$
$660$		0			0
$661$	5.69800	−	13.7562i	0.221626	−	0.535054i	−0.773485	−	0.633815i	$-0.781488\pi$
$661$	5.69800	−	13.7562i	0.221626	−	0.535054i	0.995111	+	0.0987614i	$0.0314881\pi$
$662$	−1.30386	−	1.30386i	−0.0506761	−	0.0506761i
$663$	11.1001	+	16.2113i	0.431091	+	0.629596i
$664$		−	6.12686i		−	0.237768i
$665$		0			0
$666$	−3.11420	+	0.619453i	−0.120673	+	0.0240033i
$667$	−22.3201			−0.864236
$668$	12.4369	−	2.47386i	0.481200	−	0.0957166i
$669$	−0.867735	+	4.36240i	−0.0335486	+	0.168660i
$670$		0			0
$671$	9.76417	+	23.5728i	0.376941	+	0.910017i
$672$	0.660953	−	1.59568i	0.0254968	−	0.0615547i
$673$	−21.2609	−	4.22906i	−0.819547	−	0.163018i	−0.232527	−	0.972590i	$-0.574699\pi$
$673$	−21.2609	−	4.22906i	−0.819547	−	0.163018i	−0.587021	+	0.809572i	$0.699699\pi$
$674$	−12.2973	−	2.44609i	−0.473675	−	0.0942198i
$675$		0			0
$676$	5.92842	−	5.92842i	0.228016	−	0.228016i
$677$	−14.5209	−	9.70254i	−0.558083	−	0.372899i	0.244308	−	0.969698i	$-0.421439\pi$
$677$	−14.5209	−	9.70254i	−0.558083	−	0.372899i	−0.802391	+	0.596799i	$0.796439\pi$
$678$	6.59034	−	2.72981i	0.253101	−	0.104838i
$679$	−16.0044			−0.614192
$680$		0			0
$681$	20.2705			0.776766
$682$	25.0510	−	10.3765i	0.959252	−	0.397335i
$683$	−3.92593	−	2.62322i	−0.150222	−	0.100375i	0.478188	−	0.878258i	$-0.341294\pi$
$683$	−3.92593	−	2.62322i	−0.150222	−	0.100375i	−0.628410	+	0.777883i	$0.716294\pi$
$684$	3.34058	−	3.34058i	0.127730	−	0.127730i
$685$		0			0
$686$	−18.3962	−	3.65924i	−0.702371	−	0.139710i
$687$	4.75929	+	0.946682i	0.181578	+	0.0361182i
$688$	−4.08928	+	9.87239i	−0.155902	+	0.376381i
$689$	8.15090	+	19.6780i	0.310525	+	0.749673i
$690$		0			0
$691$	4.41342	−	22.1878i	0.167894	−	0.844062i	−0.801394	−	0.598136i	$-0.795908\pi$
$691$	4.41342	−	22.1878i	0.167894	−	0.844062i	0.969289	−	0.245926i	$-0.0790919\pi$
$692$	6.98306	−	1.38902i	0.265456	−	0.0528025i
$693$	18.7894			0.713751
$694$	18.0345	−	3.58728i	0.684580	−	0.136171i
$695$		0			0
$696$		−	6.87894i		−	0.260746i
$697$	9.53997	+	45.2709i	0.361352	+	1.71476i
$698$	0.559293	+	0.559293i	0.0211695	+	0.0211695i
$699$	−2.01248	+	4.85855i	−0.0761189	+	0.183767i
$700$		0			0
$701$	34.8429	+	34.8429i	1.31600	+	1.31600i	0.916916	+	0.399081i	$0.130671\pi$
$701$	34.8429	+	34.8429i	1.31600	+	1.31600i	0.399081	+	0.916916i	$0.369329\pi$
$702$	−4.59070	−	23.0790i	−0.173265	−	0.871060i
$703$	2.21861	+	3.32038i	0.0836765	+	0.125231i
$704$	4.80928	−	3.21346i	0.181257	−	0.121112i
$705$		0			0
$706$	−20.3556	+	8.43155i	−0.766092	+	0.317326i
$707$	2.86265	−	14.3915i	0.107661	−	0.541249i
$708$	−8.97740	+	5.99851i	−0.337391	+	0.225438i
$709$	−2.53326	+	3.79130i	−0.0951387	+	0.142385i	−0.875986	−	0.482337i	$-0.839788\pi$
$709$	−2.53326	+	3.79130i	−0.0951387	+	0.142385i	0.780847	+	0.624723i	$0.214788\pi$
$710$		0			0
$711$	1.73641	+	8.72951i	0.0651204	+	0.327382i
$712$	5.54647	+	13.3904i	0.207863	+	0.501825i
$713$	−11.0833	+	11.0833i	−0.415073	+	0.415073i
$714$	5.09226	+	4.97803i	0.190573	+	0.186298i
$715$		0			0
$716$	−7.52747	−	3.11798i	−0.281315	−	0.116524i
$717$	1.49936	−	2.24395i	0.0559945	−	0.0838017i
$718$		−	26.1584i		−	0.976223i
$719$	22.7552	+	15.2046i	0.848627	+	0.567034i	0.902096	−	0.431535i	$-0.142028\pi$
$719$	22.7552	+	15.2046i	0.848627	+	0.567034i	−0.0534694	+	0.998569i	$0.517028\pi$
$720$		0			0
$721$	−8.20365	−	12.2776i	−0.305520	−	0.457243i
$722$	12.0644	+	4.99722i	0.448989	+	0.185977i
$723$	3.82475	+	1.58426i	0.142244	+	0.0589194i
$724$	−7.40659	−	11.0848i	−0.275264	−	0.411962i
$725$		0			0
$726$	−19.2400	−	12.8557i	−0.714062	−	0.477121i
$727$			44.6488i			1.65593i	0.560777	+	0.827967i	$0.310502\pi$
$727$			44.6488i			1.65593i	−0.560777	+	0.827967i	$0.689498\pi$
$728$	4.30606	−	6.44447i	0.159593	−	0.238848i
$729$	−13.5115	−	5.59663i	−0.500424	−	0.207282i
$730$		0			0
$731$	−31.5056	−	30.7988i	−1.16527	−	1.13914i
$732$	3.21426	−	3.21426i	0.118803	−	0.118803i
$733$	−9.02065	−	21.7778i	−0.333185	−	0.804381i	−0.998336	−	0.0576712i	$-0.981632\pi$
$733$	−9.02065	−	21.7778i	−0.333185	−	0.804381i	0.665150	−	0.746710i	$-0.268368\pi$
$734$	−3.20087	−	16.0919i	−0.118146	−	0.593961i
$735$		0			0
$736$	−1.85758	+	2.78006i	−0.0684713	+	0.102475i
$737$	−13.0177	+	8.69814i	−0.479513	+	0.320400i
$738$	4.24276	−	21.3298i	0.156178	−	0.785161i
$739$	−25.2821	+	10.4722i	−0.930017	+	0.385226i	−0.795685	−	0.605711i	$-0.792889\pi$
$739$	−25.2821	+	10.4722i	−0.930017	+	0.385226i	−0.134332	+	0.990936i	$0.542889\pi$
$740$		0			0
$741$	−9.65782	+	6.45315i	−0.354789	+	0.237062i
$742$	4.28900	+	6.41894i	0.157454	+	0.235647i
$743$	3.46972	+	17.4435i	0.127292	+	0.639939i	0.990770	+	0.135553i	$0.0432811\pi$
$743$	3.46972	+	17.4435i	0.127292	+	0.639939i	−0.863478	+	0.504386i	$0.831719\pi$
$744$	−3.41582	−	3.41582i	−0.125230	−	0.125230i
$745$		0			0
$746$	−0.329357	+	0.795138i	−0.0120586	+	0.0291121i
$747$	−8.39666	−	8.39666i	−0.307218	−	0.307218i
$748$	4.91758	+	23.3358i	0.179805	+	0.853242i
$749$		−	21.8964i		−	0.800076i
$750$		0			0
$751$	−17.2734	+	3.43589i	−0.630314	+	0.125377i	−0.499901	−	0.866082i	$-0.666630\pi$
$751$	−17.2734	+	3.43589i	−0.630314	+	0.125377i	−0.130413	+	0.991460i	$0.541630\pi$
$752$	2.54171			0.0926868
$753$	−10.8812	+	2.16441i	−0.396534	+	0.0788754i
$754$	6.02237	−	30.2765i	0.219322	−	1.10260i
$755$		0			0
$756$	−3.26387	−	7.87968i	−0.118706	−	0.286581i
$757$	0.217531	−	0.525165i	0.00790628	−	0.0190875i	−0.919877	−	0.392207i	$-0.871712\pi$
$757$	0.217531	−	0.525165i	0.00790628	−	0.0190875i	0.927783	+	0.373119i	$0.121712\pi$
$758$	−21.6547	−	4.30738i	−0.786533	−	0.156451i
$759$	19.5457	+	3.88788i	0.709464	+	0.141121i
$760$		0			0
$761$	−6.97045	+	6.97045i	−0.252679	+	0.252679i	−0.822068	−	0.569389i	$-0.807180\pi$
$761$	−6.97045	+	6.97045i	−0.252679	+	0.252679i	0.569389	+	0.822068i	$0.307180\pi$
$762$	−11.8419	−	7.91251i	−0.428987	−	0.286640i
$763$	−14.7526	+	6.11073i	−0.534080	+	0.221223i
$764$	−17.6401			−0.638196
$765$		0			0
$766$	30.3002			1.09479
$767$	−44.7641	+	18.5419i	−1.61634	+	0.669509i
$768$	−0.856804	−	0.572498i	−0.0309172	−	0.0206582i
$769$	−36.4693	+	36.4693i	−1.31512	+	1.31512i	−0.397525	+	0.917591i	$0.630131\pi$
$769$	−36.4693	+	36.4693i	−1.31512	+	1.31512i	−0.917591	+	0.397525i	$0.869869\pi$
$770$		0			0
$771$	−0.668987	−	0.133070i	−0.0240930	−	0.00479239i
$772$	3.10430	+	0.617484i	0.111726	+	0.0222238i
$773$	−1.92767	+	4.65381i	−0.0693336	+	0.167386i	−0.954748	−	0.297417i	$-0.903875\pi$
$773$	−1.92767	+	4.65381i	−0.0693336	+	0.167386i	0.885414	+	0.464803i	$0.153875\pi$
$774$	7.92557	+	19.1340i	0.284879	+	0.687758i
$775$		0			0
$776$	−1.86285	+	9.36520i	−0.0668726	+	0.336191i
$777$	2.77519	−	0.552021i	0.0995596	−	0.0198036i
$778$	30.9403			1.10926
$779$	−26.8260	+	5.33603i	−0.961142	+	0.191183i
$780$		0			0
$781$		−	47.4980i		−	1.69961i
$782$	−7.78852	−	11.3749i	−0.278517	−	0.406765i
$783$	−24.0198	−	24.0198i	−0.858398	−	0.858398i
$784$	−1.60373	+	3.87174i	−0.0572760	+	0.138276i
$785$		0			0
$786$	−0.0761970	−	0.0761970i	−0.00271786	−	0.00271786i
$787$	1.02127	+	5.13427i	0.0364043	+	0.183017i	0.994709	−	0.102731i	$-0.0327580\pi$
$787$	1.02127	+	5.13427i	0.0364043	+	0.183017i	−0.958305	+	0.285748i	$0.907758\pi$
$788$	−11.1542	−	16.6934i	−0.397351	−	0.594677i
$789$	−22.0921	+	14.7615i	−0.786501	+	0.525523i
$790$		0			0
$791$	10.7194	−	4.44011i	0.381137	−	0.157872i
$792$	2.18702	−	10.9949i	0.0777125	−	0.390687i
$793$	16.9611	−	11.3330i	0.602305	−	0.402447i
$794$	6.08149	−	9.10159i	0.215824	−	0.323003i
$795$		0			0
$796$	1.11803	+	5.62073i	0.0396276	+	0.199221i
$797$	−8.71279	−	21.0345i	−0.308623	−	0.745081i	−0.999750	−	0.0223483i	$-0.992886\pi$
$797$	−8.71279	−	21.0345i	−0.308623	−	0.745081i	0.691128	−	0.722733i	$-0.257114\pi$
$798$	−2.97693	+	2.97693i	−0.105382	+	0.105382i
$799$	−3.90035	+	9.72690i	−0.137985	+	0.344113i
$800$		0			0
$801$	25.9523	+	10.7498i	0.916980	+	0.379825i
$802$	−8.10725	+	12.1334i	−0.286277	+	0.428444i
$803$			31.6910i			1.11835i
$804$	2.31918	+	1.54963i	0.0817913	+	0.0546512i
$805$		0			0
$806$	−12.0437	−	18.0247i	−0.424221	−	0.634892i
$807$	−26.3386	−	10.9098i	−0.927163	−	0.384043i
$808$	−8.08820	−	3.35024i	−0.284542	−	0.117861i
$809$	−10.5409	−	15.7756i	−0.370598	−	0.554640i	0.598560	−	0.801078i	$-0.295740\pi$
$809$	−10.5409	−	15.7756i	−0.370598	−	0.554640i	−0.969159	+	0.246438i	$0.920740\pi$
$810$		0			0
$811$	−38.9732	−	26.0410i	−1.36853	−	0.914424i	−0.368647	−	0.929569i	$-0.620179\pi$
$811$	−38.9732	−	26.0410i	−1.36853	−	0.914424i	−0.999885	+	0.0151451i	$0.995179\pi$
$812$		−	11.1888i		−	0.392649i
$813$	0.664001	−	0.993748i	0.0232875	−	0.0348523i
$814$	8.75464	+	3.62629i	0.306850	+	0.127101i
$815$		0			0
$816$	3.50569	−	2.40039i	0.122724	−	0.0840303i
$817$	18.4181	−	18.4181i	0.644368	−	0.644368i
$818$	−0.901056	−	2.17534i	−0.0315047	−	0.0760590i
$819$	−2.93063	−	14.7332i	−0.102404	−	0.514821i
$820$		0			0
$821$	−15.3189	+	22.9263i	−0.534632	+	0.800133i	−0.996211	−	0.0869661i	$-0.972283\pi$
$821$	−15.3189	+	22.9263i	−0.534632	+	0.800133i	0.461580	+	0.887099i	$0.347283\pi$
$822$	−4.95133	+	3.30837i	−0.172697	+	0.115393i
$823$	2.89100	−	14.5340i	0.100774	−	0.506624i	−0.897122	−	0.441783i	$-0.854346\pi$
$823$	2.89100	−	14.5340i	0.100774	−	0.506624i	0.997896	−	0.0648408i	$-0.0206540\pi$
$824$	−8.13931	+	3.37141i	−0.283546	+	0.117449i
$825$		0			0
$826$	−14.6020	+	9.75672i	−0.508067	+	0.339480i
$827$	−5.34655	−	8.00167i	−0.185918	−	0.278245i	0.726789	−	0.686861i	$-0.241012\pi$
$827$	−5.34655	−	8.00167i	−0.185918	−	0.278245i	−0.912707	+	0.408615i	$0.866012\pi$
$828$	1.26424	+	6.35574i	0.0439352	+	0.220877i
$829$	−17.9667	−	17.9667i	−0.624011	−	0.624011i	0.322544	−	0.946555i	$-0.395462\pi$
$829$	−17.9667	−	17.9667i	−0.624011	−	0.624011i	−0.946555	+	0.322544i	$0.895462\pi$
$830$		0			0
$831$	8.66239	−	20.9129i	0.300495	−	0.725459i
$832$	−3.26987	−	3.26987i	−0.113362	−	0.113362i
$833$	−12.3558	−	12.0786i	−0.428103	−	0.418500i
$834$		−	1.69124i		−	0.0585629i
$835$		0			0
$836$	−13.8280	+	2.75057i	−0.478253	+	0.0951304i
$837$	−23.8547			−0.824538
$838$	26.7980	−	5.33045i	0.925720	−	0.184137i
$839$	−1.70308	+	8.56197i	−0.0587969	+	0.295592i	−0.998984	−	0.0450665i	$-0.985650\pi$
$839$	−1.70308	+	8.56197i	−0.0587969	+	0.295592i	0.940187	+	0.340659i	$0.110650\pi$
$840$		0			0
$841$	−5.95566	−	14.3782i	−0.205368	−	0.495801i
$842$	3.94171	−	9.51613i	0.135840	−	0.327947i
$843$	32.1206	+	6.38918i	1.10629	+	0.220055i
$844$	18.8799	+	3.75544i	0.649873	+	0.129268i
$845$		0			0
$846$	3.48334	−	3.48334i	0.119760	−	0.119760i
$847$	−31.2943	−	20.9102i	−1.07528	−	0.718482i
$848$	4.25536	−	1.76263i	0.146130	−	0.0605289i
$849$	19.8107			0.679900
$850$		0			0
$851$	−5.47769			−0.187773
$852$	−7.81793	+	3.23829i	−0.267838	+	0.110942i
$853$	−1.58234	−	1.05729i	−0.0541784	−	0.0362009i	0.528186	−	0.849129i	$-0.322872\pi$
$853$	−1.58234	−	1.05729i	−0.0541784	−	0.0362009i	−0.582365	+	0.812928i	$0.697872\pi$
$854$	5.22808	−	5.22808i	0.178901	−	0.178901i
$855$		0			0
$856$	−12.8130	−	2.54866i	−0.437939	−	0.0871114i
$857$	−26.3520	−	5.24173i	−0.900166	−	0.179054i	−0.276748	−	0.960943i	$-0.589257\pi$
$857$	−26.3520	−	5.24173i	−0.900166	−	0.179054i	−0.623418	+	0.781888i	$0.714257\pi$
$858$	−10.5476	+	25.4641i	−0.360089	+	0.869331i
$859$	−3.39558	−	8.19765i	−0.115856	−	0.279700i	0.855306	−	0.518124i	$-0.173369\pi$
$859$	−3.39558	−	8.19765i	−0.115856	−	0.279700i	−0.971161	+	0.238424i	$0.923369\pi$
$860$		0			0
$861$	−3.78090	+	19.0079i	−0.128853	+	0.647787i
$862$	16.9262	−	3.36683i	0.576509	−	0.114675i
$863$	25.2274			0.858750			0.429375	−	0.903126i	$-0.358734\pi$
$863$	25.2274			0.858750			0.429375	+	0.903126i	$0.358734\pi$
$864$	−4.99082	+	0.992735i	−0.169791	+	0.0337735i
$865$		0			0
$866$		−	25.6450i		−	0.871453i
$867$	3.80643	+	17.0994i	0.129273	+	0.580727i
$868$	−5.55593	−	5.55593i	−0.188580	−	0.188580i
$869$	10.1650	−	24.5404i	0.344823	−	0.832476i
$870$		0			0
$871$	8.85083	+	8.85083i	0.299899	+	0.299899i
$872$	1.85863	+	9.34398i	0.0629413	+	0.316427i
$873$	10.2817	+	15.3877i	0.347984	+	0.520794i
$874$	6.77654	−	4.52794i	0.229220	−	0.153160i
$875$		0			0
$876$	5.21618	−	2.16061i	0.176239	−	0.0730004i
$877$	−0.972782	+	4.89051i	−0.0328485	+	0.165141i	−0.993728	−	0.111827i	$-0.964330\pi$
$877$	−0.972782	+	4.89051i	−0.0328485	+	0.165141i	0.960879	+	0.276968i	$0.0893296\pi$
$878$	29.2748	−	19.5608i	0.987975	−	0.660144i
$879$	0.275122	−	0.411749i	0.00927963	−	0.0138879i
$880$		0			0
$881$	−3.49273	−	17.5592i	−0.117673	−	0.591583i	−0.993955	−	0.109785i	$-0.964984\pi$
$881$	−3.49273	−	17.5592i	−0.117673	−	0.591583i	0.876282	−	0.481798i	$-0.160016\pi$
$882$	3.10824	+	7.50395i	0.104660	+	0.252671i
$883$	11.6480	−	11.6480i	0.391987	−	0.391987i	−0.483408	−	0.875395i	$-0.660601\pi$
$883$	11.6480	−	11.6480i	0.391987	−	0.391987i	0.875395	+	0.483408i	$0.160601\pi$
$884$	17.5312	−	7.49573i	0.589638	−	0.252109i
$885$		0			0
$886$	−10.8385	−	4.48945i	−0.364126	−	0.150826i
$887$	−9.14546	+	13.6871i	−0.307074	+	0.459569i	−0.952625	−	0.304149i	$-0.901628\pi$
$887$	−9.14546	+	13.6871i	−0.307074	+	0.459569i	0.645550	+	0.763718i	$0.276628\pi$
$888$		−	1.68820i		−	0.0566523i
$889$	−19.2612	−	12.8699i	−0.645999	−	0.431642i
$890$		0			0
$891$	−1.83413	−	2.74497i	−0.0614457	−	0.0919599i
$892$	3.98779	+	1.65180i	0.133521	+	0.0553062i
$893$	−5.72394	−	2.37093i	−0.191544	−	0.0793403i
$894$	6.21453	+	9.30070i	0.207845	+	0.311062i
$895$		0			0
$896$	−1.39361	−	0.931182i	−0.0465573	−	0.0311086i
$897$		−	15.9327i		−	0.531976i
$898$	−1.95284	+	2.92263i	−0.0651672	+	0.0975295i
$899$	−28.9120	−	11.9757i	−0.964268	−	0.399413i
$900$		0			0
$901$	0.215400	+	18.9897i	0.00717602	+	0.632638i
$902$	−45.8932	+	45.8932i	−1.52808	+	1.52808i
$903$	−7.06281	−	17.0511i	−0.235036	−	0.567426i
$904$	−1.35050	−	6.78941i	−0.0449169	−	0.225812i
$905$		0			0
$906$	−4.79053	+	7.16953i	−0.159155	+	0.238192i
$907$	36.8877	−	24.6476i	1.22484	−	0.818409i	0.236639	−	0.971598i	$-0.423954\pi$
$907$	36.8877	−	24.6476i	1.22484	−	0.818409i	0.988197	+	0.153189i	$0.0489542\pi$
$908$	3.83764	−	19.2931i	0.127357	−	0.640265i
$909$	−15.6760	+	6.49322i	−0.519941	+	0.215367i
$910$		0			0
$911$	−18.3469	+	12.2590i	−0.607860	+	0.406159i	−0.821054	−	0.570851i	$-0.806613\pi$
$911$	−18.3469	+	12.2590i	−0.607860	+	0.406159i	0.213194	+	0.977010i	$0.431613\pi$
$912$	1.39549	+	2.08850i	0.0462093	+	0.0691571i
$913$	6.91365	+	34.7573i	0.228808	+	1.15030i
$914$	24.4174	+	24.4174i	0.807655	+	0.807655i
$915$		0			0
$916$	1.80208	−	4.35060i	0.0595423	−	0.143748i
$917$	−0.123936	−	0.123936i	−0.00409274	−	0.00409274i
$918$	3.85949	−	20.6228i	0.127382	−	0.680653i
$919$			51.7535i			1.70719i	0.520937	+	0.853595i	$0.325583\pi$
$919$			51.7535i			1.70719i	−0.520937	+	0.853595i	$0.674417\pi$
$920$		0			0
$921$	−15.0954	+	3.00267i	−0.497412	+	0.0989414i
$922$	−0.0102298			−0.000336901
$923$	−37.2444	+	7.40837i	−1.22591	+	0.243849i
$924$	−1.94895	+	9.79802i	−0.0641157	+	0.322331i
$925$		0			0
$926$	5.70309	+	13.7685i	0.187415	+	0.452461i
$927$	−6.53425	+	15.7751i	−0.214613	+	0.518121i
$928$	−6.54728	−	1.30233i	−0.214925	−	0.0427512i
$929$	29.4582	+	5.85961i	0.966493	+	0.192247i	0.653013	−	0.757347i	$-0.273505\pi$
$929$	29.4582	+	5.85961i	0.966493	+	0.192247i	0.313481	+	0.949595i	$0.398505\pi$
$930$		0			0
$931$	7.22319	−	7.22319i	0.236731	−	0.236731i
$932$	4.24329	+	2.83528i	0.138994	+	0.0928726i
$933$	−15.4041	+	6.38058i	−0.504307	+	0.208891i
$934$	−8.13547			−0.266201
$935$		0			0
$936$	−8.96249			−0.292948
$937$	10.4831	−	4.34223i	0.342467	−	0.141854i	−0.204820	−	0.978800i	$-0.565661\pi$
$937$	10.4831	−	4.34223i	0.342467	−	0.141854i	0.547286	+	0.836945i	$0.315661\pi$
$938$	3.77221	+	2.52051i	0.123167	+	0.0822976i
$939$	3.20695	−	3.20695i	0.104655	−	0.104655i
$940$		0			0
$941$	5.10737	+	1.01592i	0.166495	+	0.0331180i	0.277634	−	0.960687i	$-0.410450\pi$
$941$	5.10737	+	1.01592i	0.166495	+	0.0331180i	−0.111139	+	0.993805i	$0.535450\pi$
$942$	5.17051	+	1.02848i	0.168464	+	0.0335096i
$943$	14.3575	−	34.6620i	0.467543	−	1.12875i
$944$	4.00967	+	9.68021i	0.130504	+	0.315064i
$945$		0			0
$946$	12.0580	−	60.6198i	0.392041	−	1.97092i
$947$	42.2326	−	8.40059i	1.37238	−	0.272983i	0.546795	−	0.837266i	$-0.315848\pi$
$947$	42.2326	−	8.40059i	1.37238	−	0.272983i	0.825581	+	0.564284i	$0.190848\pi$
$948$	−4.73224			−0.153696
$949$	24.8497	−	4.94292i	0.806656	−	0.160454i
$950$		0			0
$951$			33.0871i			1.07292i
$952$	5.70210	−	3.90429i	0.184806	−	0.126539i
$953$	24.6485	+	24.6485i	0.798443	+	0.798443i	0.982850	−	0.184407i	$-0.0590366\pi$
$953$	24.6485	+	24.6485i	0.798443	+	0.798443i	−0.184407	+	0.982850i	$0.559037\pi$
$954$	3.41621	−	8.24746i	0.110604	−	0.267021i
$955$		0			0
$956$	−1.85189	−	1.85189i	−0.0598945	−	0.0598945i
$957$	7.76231	+	39.0238i	0.250920	+	1.26146i
$958$	17.9889	+	26.9223i	0.581195	+	0.869820i
$959$	−8.05347	+	5.38115i	−0.260060	+	0.173767i
$960$		0			0
$961$	8.33696	−	3.45328i	0.268934	−	0.111396i
$962$	1.47798	−	7.43033i	0.0476521	−	0.239563i
$963$	−21.0526	+	14.0669i	−0.678412	+	0.453300i
$964$	2.23199	−	3.34041i	0.0718876	−	0.107587i
$965$		0			0
$966$	−1.12661	−	5.66387i	−0.0362482	−	0.182232i
$967$	−16.5968	−	40.0683i	−0.533718	−	1.28851i	−0.929045	−	0.369968i	$-0.879369\pi$
$967$	−16.5968	−	40.0683i	−0.533718	−	1.28851i	0.395327	−	0.918540i	$-0.370631\pi$
$968$	−15.8784	+	15.8784i	−0.510352	+	0.510352i
$969$	−10.1339	+	2.13553i	−0.325548	+	0.0686031i
$970$		0			0
$971$	−38.6703	−	16.0178i	−1.24099	−	0.514034i	−0.336965	−	0.941517i	$-0.609400\pi$
$971$	−38.6703	−	16.0178i	−1.24099	−	0.514034i	−0.904023	+	0.427483i	$0.859400\pi$
$972$	−8.80797	+	13.1821i	−0.282516	+	0.422815i
$973$		−	2.75085i		−	0.0881881i
$974$	20.1855	+	13.4875i	0.646784	+	0.432168i
$975$		0			0
$976$	−2.45076	−	3.66782i	−0.0784469	−	0.117404i
$977$	−22.8793	−	9.47693i	−0.731975	−	0.303194i	−0.0146115	−	0.999893i	$-0.504651\pi$
$977$	−22.8793	−	9.47693i	−0.731975	−	0.303194i	−0.717363	+	0.696699i	$0.754651\pi$
$978$	−9.53069	−	3.94774i	−0.304758	−	0.126235i
$979$	−46.5747	−	69.7039i	−1.48853	−	2.22775i
$980$		0			0
$981$	15.3528	+	10.2584i	0.490178	+	0.327526i
$982$			23.4871i			0.749504i
$983$	14.5707	−	21.8065i	0.464732	−	0.695521i	−0.522885	−	0.852403i	$-0.675144\pi$
$983$	14.5707	−	21.8065i	0.464732	−	0.695521i	0.987617	+	0.156882i	$0.0501444\pi$
$984$	10.6827	+	4.42490i	0.340551	+	0.141061i
$985$		0			0
$986$	15.0309	−	23.0573i	0.478683	−	0.734295i
$987$	−3.10415	+	3.10415i	−0.0988061	+	0.0988061i
$988$	4.31358	+	10.4139i	0.137233	+	0.331310i
$989$	6.97030	+	35.0421i	0.221643	+	1.11427i
$990$		0			0
$991$	2.70814	−	4.05303i	0.0860271	−	0.128749i	−0.785960	−	0.618277i	$-0.787831\pi$
$991$	2.70814	−	4.05303i	0.0860271	−	0.128749i	0.871987	+	0.489528i	$0.162831\pi$
$992$	−3.89782	+	2.60444i	−0.123756	+	0.0826911i
$993$	0.370696	−	1.86361i	0.0117637	−	0.0591400i
$994$	−12.7161	+	5.26717i	−0.403329	+	0.167064i
$995$		0			0
$996$	5.24951	−	3.50761i	0.166337	−	0.111143i
$997$	14.6581	+	21.9375i	0.464228	+	0.694767i	0.987539	−	0.157375i	$-0.0503033\pi$
$997$	14.6581	+	21.9375i	0.464228	+	0.694767i	−0.523311	+	0.852142i	$0.675303\pi$
$998$	−2.34595	−	11.7939i	−0.0742598	−	0.373329i
$999$	−5.89484	−	5.89484i	−0.186504	−	0.186504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.v.c.193.3		32
5.2	odd	4		850.2.s.c.57.3		32
5.3	odd	4		170.2.o.a.57.2	yes	32
5.4	even	2		170.2.r.a.23.2	yes	32
17.3	odd	16		850.2.s.c.343.3		32
85.3	even	16		170.2.r.a.37.2	yes	32
85.37	even	16	inner	850.2.v.c.207.3		32
85.54	odd	16		170.2.o.a.3.2	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.o.a.3.2	✓	32	85.54	odd	16
170.2.o.a.57.2	yes	32	5.3	odd	4
170.2.r.a.23.2	yes	32	5.4	even	2
170.2.r.a.37.2	yes	32	85.3	even	16
850.2.s.c.57.3		32	5.2	odd	4
850.2.s.c.343.3		32	17.3	odd	16
850.2.v.c.193.3		32	1.1	even	1	trivial
850.2.v.c.207.3		32	85.37	even	16	inner

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:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.v (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.923880 - 0.382683i) q^{2} +(0.856804 + 0.572498i) q^{3} +(0.707107 - 0.707107i) q^{4} +(1.01067 + 0.201035i) q^{6} +(1.64388 + 0.326988i) q^{7} +(0.382683 - 0.923880i) q^{8} +(-0.741692 - 1.79060i) q^{9} +O(q^{10})\)	\(q+(0.923880 - 0.382683i) q^{2} +(0.856804 + 0.572498i) q^{3} +(0.707107 - 0.707107i) q^{4} +(1.01067 + 0.201035i) q^{6} +(1.64388 + 0.326988i) q^{7} +(0.382683 - 0.923880i) q^{8} +(-0.741692 - 1.79060i) q^{9} +(-1.12842 + 5.67293i) q^{11} +(1.01067 - 0.201035i) q^{12} +4.62429 q^{13} +(1.64388 - 0.326988i) q^{14} -1.00000i q^{16} +(3.82690 + 1.53454i) q^{17} +(-1.37047 - 1.37047i) q^{18} +(-0.932809 + 2.25200i) q^{19} +(1.22128 + 1.22128i) q^{21} +(1.12842 + 5.67293i) q^{22} +(-1.85758 - 2.78006i) q^{23} +(0.856804 - 0.572498i) q^{24} +(4.27229 - 1.76964i) q^{26} +(0.992735 - 4.99082i) q^{27} +(1.39361 - 0.931182i) q^{28} +(3.70873 - 5.55051i) q^{29} +(-0.914558 - 4.59779i) q^{31} +(-0.382683 - 0.923880i) q^{32} +(-4.21457 + 4.21457i) q^{33} +(4.12284 - 0.0467655i) q^{34} +(-1.79060 - 0.741692i) q^{36} +(0.910181 - 1.36218i) q^{37} +2.43755i q^{38} +(3.96211 + 2.64740i) q^{39} +(6.23402 + 9.32987i) q^{41} +(1.59568 + 0.660953i) q^{42} +(-9.87239 - 4.08928i) q^{43} +(3.21346 + 4.80928i) q^{44} +(-2.78006 - 1.85758i) q^{46} +2.54171i q^{47} +(0.572498 - 0.856804i) q^{48} +(-3.87174 - 1.60373i) q^{49} +(2.40039 + 3.50569i) q^{51} +(3.26987 - 3.26987i) q^{52} +(1.76263 + 4.25536i) q^{53} +(-0.992735 - 4.99082i) q^{54} +(0.931182 - 1.39361i) q^{56} +(-2.08850 + 1.39549i) q^{57} +(1.30233 - 6.54728i) q^{58} +(-9.68021 + 4.00967i) q^{59} +(3.66782 - 2.45076i) q^{61} +(-2.60444 - 3.89782i) q^{62} +(-0.633746 - 3.18606i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(-2.28091 + 5.50661i) q^{66} +(1.91399 + 1.91399i) q^{67} +(3.79111 - 1.62095i) q^{68} -3.44543i q^{69} +(-8.05408 + 1.60206i) q^{71} -1.93813 q^{72} +(5.37374 - 1.06890i) q^{73} +(0.319613 - 1.60680i) q^{74} +(0.932809 + 2.25200i) q^{76} +(-3.70996 + 8.95664i) q^{77} +(4.67362 + 0.929642i) q^{78} +(-4.50408 - 0.895917i) q^{79} +(-0.403592 + 0.403592i) q^{81} +(9.32987 + 6.23402i) q^{82} +(5.66048 - 2.34465i) q^{83} +1.72715 q^{84} -10.6858 q^{86} +(6.35531 - 2.63246i) q^{87} +(4.80928 + 3.21346i) q^{88} +(-10.2485 + 10.2485i) q^{89} +(7.60177 + 1.51209i) q^{91} +(-3.27931 - 0.652295i) q^{92} +(1.84863 - 4.46299i) q^{93} +(0.972672 + 2.34824i) q^{94} +(0.201035 - 1.01067i) q^{96} +(-9.36520 + 1.86285i) q^{97} -4.19074 q^{98} +(10.9949 - 2.18702i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 16 q^{18} + 8 q^{26} - 24 q^{27} + 8 q^{28} - 8 q^{29} - 16 q^{31} - 64 q^{33} + 24 q^{34} + 32 q^{37} - 32 q^{39} + 16 q^{41} + 24 q^{42} + 16 q^{43} - 16 q^{44} - 16 q^{49} + 32 q^{51} + 16 q^{52} - 16 q^{53} + 24 q^{54} + 8 q^{56} + 24 q^{57} + 16 q^{58} - 64 q^{59} - 24 q^{61} + 40 q^{62} + 24 q^{63} - 16 q^{67} + 8 q^{71} + 16 q^{72} - 32 q^{73} + 8 q^{74} - 24 q^{77} - 32 q^{78} + 72 q^{79} + 48 q^{81} - 48 q^{82} - 16 q^{83} - 64 q^{86} - 40 q^{87} - 32 q^{88} + 16 q^{89} + 48 q^{91} - 24 q^{92} + 8 q^{93} + 8 q^{94} + 48 q^{97} - 64 q^{99}+O(q^{100}) \) 32 * q - 16 * q^18 + 8 * q^26 - 24 * q^27 + 8 * q^28 - 8 * q^29 - 16 * q^31 - 64 * q^33 + 24 * q^34 + 32 * q^37 - 32 * q^39 + 16 * q^41 + 24 * q^42 + 16 * q^43 - 16 * q^44 - 16 * q^49 + 32 * q^51 + 16 * q^52 - 16 * q^53 + 24 * q^54 + 8 * q^56 + 24 * q^57 + 16 * q^58 - 64 * q^59 - 24 * q^61 + 40 * q^62 + 24 * q^63 - 16 * q^67 + 8 * q^71 + 16 * q^72 - 32 * q^73 + 8 * q^74 - 24 * q^77 - 32 * q^78 + 72 * q^79 + 48 * q^81 - 48 * q^82 - 16 * q^83 - 64 * q^86 - 40 * q^87 - 32 * q^88 + 16 * q^89 + 48 * q^91 - 24 * q^92 + 8 * q^93 + 8 * q^94 + 48 * q^97 - 64 * q^99

Introduction

L-functions

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