LMFDB - Embedded newform 51.3.f.a.47.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,3,Mod(38,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.38"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	51.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.38964934824$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 62 x^{18} + 1545 x^{16} + 20120 x^{14} + 149608 x^{12} + 655792 x^{10} + 1690896 x^{8} + \cdots + 36864 $ x^20 + 62x^18 + 1545x^16 + 20120x^14 + 149608x^12 + 655792x^10 + 1690896x^8 + 2476352x^6 + 1880640x^4 + 593152*x^2 + 36864
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.8
Root			$-1.52557i$ of defining polynomial
Character	$\chi$	$=$	51.47
Dual form			51.3.f.a.38.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.52557 q^{2} +(-0.805308 + 2.88989i) q^{3} +2.37853 q^{4} +(0.0213954 - 0.0213954i) q^{5} +(-2.03387 + 7.29864i) q^{6} +(6.89994 - 6.89994i) q^{7} -4.09515 q^{8} +(-7.70296 - 4.65451i) q^{9} +(0.0540358 - 0.0540358i) q^{10} +(-2.99781 - 2.99781i) q^{11} +(-1.91545 + 6.87369i) q^{12} -5.86939 q^{13} +(17.4263 - 17.4263i) q^{14} +(0.0446006 + 0.0790604i) q^{15} -19.8567 q^{16} +(16.8769 + 2.04180i) q^{17} +(-19.4544 - 11.7553i) q^{18} +22.1601i q^{19} +(0.0508896 - 0.0508896i) q^{20} +(14.3835 + 25.4967i) q^{21} +(-7.57118 - 7.57118i) q^{22} +(-4.33017 - 4.33017i) q^{23} +(3.29786 - 11.8345i) q^{24} +24.9991i q^{25} -14.8236 q^{26} +(19.6543 - 18.5124i) q^{27} +(16.4117 - 16.4117i) q^{28} +(2.07869 - 2.07869i) q^{29} +(0.112642 + 0.199673i) q^{30} +(-35.3313 - 35.3313i) q^{31} -33.7690 q^{32} +(11.0775 - 6.24918i) q^{33} +(42.6240 + 5.15673i) q^{34} -0.295254i q^{35} +(-18.3217 - 11.0709i) q^{36} +(33.3847 + 33.3847i) q^{37} +55.9671i q^{38} +(4.72667 - 16.9619i) q^{39} +(-0.0876174 + 0.0876174i) q^{40} +(44.4867 + 44.4867i) q^{41} +(36.3266 + 64.3938i) q^{42} +19.1248i q^{43} +(-7.13037 - 7.13037i) q^{44} +(-0.264393 + 0.0652228i) q^{45} +(-10.9362 - 10.9362i) q^{46} -79.9440i q^{47} +(15.9908 - 57.3838i) q^{48} -46.2184i q^{49} +63.1371i q^{50} +(-19.4917 + 47.1283i) q^{51} -13.9605 q^{52} -54.2306 q^{53} +(49.6384 - 46.7545i) q^{54} -0.128279 q^{55} +(-28.2563 + 28.2563i) q^{56} +(-64.0404 - 17.8458i) q^{57} +(5.24989 - 5.24989i) q^{58} +5.34420 q^{59} +(0.106084 + 0.188047i) q^{60} +(44.0138 - 44.0138i) q^{61} +(-89.2317 - 89.2317i) q^{62} +(-85.2658 + 21.0341i) q^{63} -5.85937 q^{64} +(-0.125578 + 0.125578i) q^{65} +(27.9770 - 15.7828i) q^{66} -105.233 q^{67} +(40.1423 + 4.85649i) q^{68} +(16.0008 - 9.02659i) q^{69} -0.745687i q^{70} +(33.6145 - 33.6145i) q^{71} +(31.5447 + 19.0609i) q^{72} +(-20.6784 - 20.6784i) q^{73} +(84.3155 + 84.3155i) q^{74} +(-72.2447 - 20.1320i) q^{75} +52.7085i q^{76} -41.3694 q^{77} +(11.9376 - 42.8386i) q^{78} +(-17.7033 + 17.7033i) q^{79} +(-0.424843 + 0.424843i) q^{80} +(37.6711 + 71.7070i) q^{81} +(112.354 + 112.354i) q^{82} +86.0948 q^{83} +(34.2116 + 60.6446i) q^{84} +(0.404775 - 0.317404i) q^{85} +48.3010i q^{86} +(4.33320 + 7.68118i) q^{87} +(12.2765 + 12.2765i) q^{88} -87.8261i q^{89} +(-0.667745 + 0.164725i) q^{90} +(-40.4985 + 40.4985i) q^{91} +(-10.2994 - 10.2994i) q^{92} +(130.556 - 73.6510i) q^{93} -201.904i q^{94} +(0.474126 + 0.474126i) q^{95} +(27.1945 - 97.5889i) q^{96} +(66.3611 + 66.3611i) q^{97} -116.728i q^{98} +(9.13865 + 37.0453i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{3} + 24 q^{4} - 2 q^{6} - 4 q^{7} - 16 q^{10} - 42 q^{12} - 12 q^{13} - 64 q^{16} - 4 q^{18} + 88 q^{21} - 40 q^{22} - 82 q^{24} + 54 q^{27} - 160 q^{28} + 48 q^{31} + 264 q^{33} + 152 q^{34}+ \cdots - 864 q^{99}+O(q^{100}) $ 20 * q - 6 * q^3 + 24 * q^4 - 2 * q^6 - 4 * q^7 - 16 * q^10 - 42 * q^12 - 12 * q^13 - 64 * q^16 - 4 * q^18 + 88 * q^21 - 40 * q^22 - 82 * q^24 + 54 * q^27 - 160 * q^28 + 48 * q^31 + 264 * q^33 + 152 * q^34 + 32 * q^37 + 56 * q^39 + 52 * q^40 + 64 * q^45 + 388 * q^46 - 230 * q^48 - 298 * q^51 + 64 * q^52 - 254 * q^54 - 204 * q^55 - 24 * q^57 + 396 * q^58 - 336 * q^61 - 400 * q^63 - 480 * q^64 - 408 * q^67 - 132 * q^69 + 276 * q^72 - 88 * q^73 - 358 * q^75 + 380 * q^78 - 172 * q^79 + 388 * q^81 + 372 * q^82 + 1320 * q^84 + 648 * q^85 - 156 * q^88 + 672 * q^90 - 124 * q^91 + 194 * q^96 + 688 * q^97 - 864 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	2.52557			1.26279			0.631394	−	0.775462i	$-0.282483\pi$
$2$	2.52557			1.26279			0.631394	+	0.775462i	$0.282483\pi$
$3$	−0.805308	+	2.88989i	−0.268436	+	0.963297i
$3$	−0.805308	+	2.88989i	−0.268436	+	0.963297i
$4$	2.37853			0.594632
$5$	0.0213954	−	0.0213954i	0.00427909	−	0.00427909i	−0.704964	−	0.709243i	$-0.749037\pi$
$5$	0.0213954	−	0.0213954i	0.00427909	−	0.00427909i	0.709243	+	0.704964i	$0.249037\pi$
$6$	−2.03387	+	7.29864i	−0.338978	+	1.21644i
$7$	6.89994	−	6.89994i	0.985706	−	0.985706i	−0.0141932	−	0.999899i	$-0.504518\pi$
$7$	6.89994	−	6.89994i	0.985706	−	0.985706i	0.999899	+	0.0141932i	$0.00451800\pi$
$8$	−4.09515			−0.511893
$9$	−7.70296	−	4.65451i	−0.855884	−	0.517168i
$10$	0.0540358	−	0.0540358i	0.00540358	−	0.00540358i
$11$	−2.99781	−	2.99781i	−0.272528	−	0.272528i	0.557589	−	0.830117i	$-0.311726\pi$
$11$	−2.99781	−	2.99781i	−0.272528	−	0.272528i	−0.830117	+	0.557589i	$0.811726\pi$
$12$	−1.91545	+	6.87369i	−0.159621	+	0.572808i
$13$	−5.86939			−0.451492			−0.225746	−	0.974186i	$-0.572482\pi$
$13$	−5.86939			−0.451492			−0.225746	+	0.974186i	$0.572482\pi$
$14$	17.4263	−	17.4263i	1.24474	−	1.24474i
$15$	0.0446006	+	0.0790604i	0.00297337	+	0.00527069i
$16$	−19.8567			−1.24104
$17$	16.8769	+	2.04180i	0.992761	+	0.120106i
$17$	16.8769	+	2.04180i	0.992761	+	0.120106i
$18$	−19.4544	−	11.7553i	−1.08080	−	0.653073i
$19$			22.1601i			1.16632i	0.812356	+	0.583162i	$0.198185\pi$
$19$			22.1601i			1.16632i	−0.812356	+	0.583162i	$0.801815\pi$
$20$	0.0508896	−	0.0508896i	0.00254448	−	0.00254448i
$21$	14.3835	+	25.4967i	0.684929	+	1.21413i
$22$	−7.57118	−	7.57118i	−0.344145	−	0.344145i
$23$	−4.33017	−	4.33017i	−0.188268	−	0.188268i	0.606679	−	0.794947i	$-0.292501\pi$
$23$	−4.33017	−	4.33017i	−0.188268	−	0.188268i	−0.794947	+	0.606679i	$0.792501\pi$
$24$	3.29786	−	11.8345i	0.137411	−	0.493106i
$25$			24.9991i			0.999963i
$26$	−14.8236			−0.570138
$27$	19.6543	−	18.5124i	0.727937	−	0.685644i
$28$	16.4117	−	16.4117i	0.586133	−	0.586133i
$29$	2.07869	−	2.07869i	0.0716790	−	0.0716790i	−0.670358	−	0.742037i	$-0.733860\pi$
$29$	2.07869	−	2.07869i	0.0716790	−	0.0716790i	0.742037	+	0.670358i	$0.233860\pi$
$30$	0.112642	+	0.199673i	0.00375474	+	0.00665577i
$31$	−35.3313	−	35.3313i	−1.13972	−	1.13972i	−0.988501	−	0.151218i	$-0.951681\pi$
$31$	−35.3313	−	35.3313i	−1.13972	−	1.13972i	−0.151218	−	0.988501i	$-0.548319\pi$
$32$	−33.7690			−1.05528
$33$	11.0775	−	6.24918i	0.335682	−	0.189369i
$34$	42.6240	+	5.15673i	1.25365	+	0.151668i
$35$		−	0.295254i		−	0.00843584i
$36$	−18.3217	−	11.0709i	−0.508936	−	0.307525i
$37$	33.3847	+	33.3847i	0.902288	+	0.902288i	0.995634	−	0.0933453i	$-0.0297561\pi$
$37$	33.3847	+	33.3847i	0.902288	+	0.902288i	−0.0933453	+	0.995634i	$0.529756\pi$
$38$			55.9671i			1.47282i
$39$	4.72667	−	16.9619i	0.121197	−	0.434921i
$40$	−0.0876174	+	0.0876174i	−0.00219044	+	0.00219044i
$41$	44.4867	+	44.4867i	1.08504	+	1.08504i	0.996031	+	0.0890098i	$0.0283702\pi$
$41$	44.4867	+	44.4867i	1.08504	+	1.08504i	0.0890098	+	0.996031i	$0.471630\pi$
$42$	36.3266	+	64.3938i	0.864920	+	1.53318i
$43$			19.1248i			0.444762i	0.974960	+	0.222381i	$0.0713829\pi$
$43$			19.1248i			0.444762i	−0.974960	+	0.222381i	$0.928617\pi$
$44$	−7.13037	−	7.13037i	−0.162054	−	0.162054i
$45$	−0.264393	+	0.0652228i	−0.00587541	+	0.00144940i
$46$	−10.9362	−	10.9362i	−0.237743	−	0.237743i
$47$		−	79.9440i		−	1.70094i	−0.526027	−	0.850468i	$-0.676319\pi$
$47$		−	79.9440i		−	1.70094i	0.526027	−	0.850468i	$-0.323681\pi$
$48$	15.9908	−	57.3838i	0.333141	−	1.19550i
$49$		−	46.2184i		−	0.943233i
$50$			63.1371i			1.26274i
$51$	−19.4917	+	47.1283i	−0.382191	+	0.924083i
$52$	−13.9605			−0.268472
$53$	−54.2306			−1.02322			−0.511610	−	0.859218i	$-0.670951\pi$
$53$	−54.2306			−1.02322			−0.511610	+	0.859218i	$0.670951\pi$
$54$	49.6384	−	46.7545i	0.919229	−	0.865823i
$55$	−0.128279			−0.00233234
$56$	−28.2563	+	28.2563i	−0.504576	+	0.504576i
$57$	−64.0404	−	17.8458i	−1.12352	−	0.313083i
$58$	5.24989	−	5.24989i	0.0905153	−	0.0905153i
$59$	5.34420			0.0905796			0.0452898	−	0.998974i	$-0.485579\pi$
$59$	5.34420			0.0905796			0.0452898	+	0.998974i	$0.485579\pi$
$60$	0.106084	+	0.188047i	0.00176806	+	0.00313412i
$61$	44.0138	−	44.0138i	0.721537	−	0.721537i	−0.247381	−	0.968918i	$-0.579570\pi$
$61$	44.0138	−	44.0138i	0.721537	−	0.721537i	0.968918	+	0.247381i	$0.0795700\pi$
$62$	−89.2317	−	89.2317i	−1.43922	−	1.43922i
$63$	−85.2658	+	21.0341i	−1.35343	+	0.333875i
$64$	−5.85937			−0.0915526
$65$	−0.125578	+	0.125578i	−0.00193197	+	0.00193197i
$66$	27.9770	−	15.7828i	0.423895	−	0.239133i
$67$	−105.233			−1.57064			−0.785320	−	0.619090i	$-0.787502\pi$
$67$	−105.233			−1.57064			−0.785320	+	0.619090i	$0.787502\pi$
$68$	40.1423	+	4.85649i	0.590328	+	0.0714189i
$69$	16.0008	−	9.02659i	0.231896	−	0.130820i
$70$		−	0.745687i		−	0.0106527i
$71$	33.6145	−	33.6145i	0.473444	−	0.473444i	−0.429584	−	0.903027i	$-0.641340\pi$
$71$	33.6145	−	33.6145i	0.473444	−	0.473444i	0.903027	+	0.429584i	$0.141340\pi$
$72$	31.5447	+	19.0609i	0.438121	+	0.264735i
$73$	−20.6784	−	20.6784i	−0.283266	−	0.283266i	0.551144	−	0.834410i	$-0.314191\pi$
$73$	−20.6784	−	20.6784i	−0.283266	−	0.283266i	−0.834410	+	0.551144i	$0.814191\pi$
$74$	84.3155	+	84.3155i	1.13940	+	1.13940i
$75$	−72.2447	−	20.1320i	−0.963262	−	0.268426i
$76$			52.7085i			0.693533i
$77$	−41.3694			−0.537265
$78$	11.9376	−	42.8386i	0.153046	−	0.549213i
$79$	−17.7033	+	17.7033i	−0.224093	+	0.224093i	−0.810219	−	0.586127i	$-0.800652\pi$
$79$	−17.7033	+	17.7033i	−0.224093	+	0.224093i	0.586127	+	0.810219i	$0.300652\pi$
$80$	−0.424843	+	0.424843i	−0.00531054	+	0.00531054i
$81$	37.6711	+	71.7070i	0.465075	+	0.885271i
$82$	112.354	+	112.354i	1.37018	+	1.37018i
$83$	86.0948			1.03729			0.518644	−	0.854991i	$-0.326437\pi$
$83$	86.0948			1.03729			0.518644	+	0.854991i	$0.326437\pi$
$84$	34.2116	+	60.6446i	0.407281	+	0.721959i
$85$	0.404775	−	0.317404i	0.00476205	−	0.00373416i
$86$			48.3010i			0.561640i
$87$	4.33320	+	7.68118i	0.0498069	+	0.0882894i
$88$	12.2765	+	12.2765i	0.139505	+	0.139505i
$89$		−	87.8261i		−	0.986810i	−0.869800	−	0.493405i	$-0.835752\pi$
$89$		−	87.8261i		−	0.986810i	0.869800	−	0.493405i	$-0.164248\pi$
$90$	−0.667745	+	0.164725i	−0.00741939	+	0.00183028i
$91$	−40.4985	+	40.4985i	−0.445038	+	0.445038i
$92$	−10.2994	−	10.2994i	−0.111950	−	0.111950i
$93$	130.556	−	73.6510i	1.40383	−	0.791946i
$94$		−	201.904i		−	2.14792i
$95$	0.474126	+	0.474126i	0.00499080	+	0.00499080i
$96$	27.1945	−	97.5889i	0.283276	−	1.01655i
$97$	66.3611	+	66.3611i	0.684135	+	0.684135i	0.960929	−	0.276794i	$-0.0892720\pi$
$97$	66.3611	+	66.3611i	0.684135	+	0.684135i	−0.276794	+	0.960929i	$0.589272\pi$
$98$		−	116.728i		−	1.19110i
$99$	9.13865	+	37.0453i	0.0923096	+	0.374195i
$100$			59.4610i			0.594610i
$101$			144.531i			1.43100i	0.698611	+	0.715502i	$0.253802\pi$
$101$			144.531i			1.43100i	−0.698611	+	0.715502i	$0.746198\pi$
$102$	−49.2278	+	119.026i	−0.482626	+	1.16692i
$103$	82.6992			0.802905			0.401453	−	0.915880i	$-0.368505\pi$
$103$	82.6992			0.802905			0.401453	+	0.915880i	$0.368505\pi$
$104$	24.0360			0.231116
$105$	0.853253	+	0.237771i	0.00812622	+	0.00226448i
$106$	−136.964			−1.29211
$107$	−62.5184	+	62.5184i	−0.584284	+	0.584284i	−0.936078	−	0.351793i	$-0.885572\pi$
$107$	−62.5184	+	62.5184i	−0.584284	+	0.584284i	0.351793	+	0.936078i	$0.385572\pi$
$108$	46.7483	−	44.0323i	0.432855	−	0.407706i
$109$	66.9748	−	66.9748i	0.614448	−	0.614448i	−0.329654	−	0.944102i	$-0.606932\pi$
$109$	66.9748	−	66.9748i	0.614448	−	0.614448i	0.944102	+	0.329654i	$0.106932\pi$
$110$	−0.323977			−0.00294525
$111$	−123.363	+	69.5932i	−1.11138	+	0.626965i
$112$	−137.010	+	137.010i	−1.22331	+	1.22331i
$113$	−90.9854	−	90.9854i	−0.805180	−	0.805180i	0.178720	−	0.983900i	$-0.442804\pi$
$113$	−90.9854	−	90.9854i	−0.805180	−	0.805180i	−0.983900	+	0.178720i	$0.942804\pi$
$114$	−161.739	−	45.0708i	−1.41876	−	0.395358i
$115$	−0.185291			−0.00161123
$116$	4.94422	−	4.94422i	0.0426226	−	0.0426226i
$117$	45.2117	+	27.3192i	0.386425	+	0.233497i
$118$	13.4972			0.114383
$119$	130.538	−	102.362i	1.09696	−	0.860181i
$120$	−0.182646	−	0.323764i	−0.00152205	−	0.00269803i
$121$		−	103.026i		−	0.851457i
$122$	111.160	−	111.160i	0.911148	−	0.911148i
$123$	−164.387	+	92.7362i	−1.33648	+	0.753953i
$124$	−84.0364	−	84.0364i	−0.677713	−	0.677713i
$125$	1.06975	+	1.06975i	0.00855801	+	0.00855801i
$126$	−215.345	+	53.1232i	−1.70909	+	0.421613i
$127$		−	126.106i		−	0.992960i	−0.868048	−	0.496480i	$-0.834626\pi$
$127$		−	126.106i		−	0.992960i	0.868048	−	0.496480i	$-0.165374\pi$
$128$	120.278			0.939671
$129$	−55.2685	−	15.4013i	−0.428438	−	0.119390i
$130$	−0.317157	+	0.317157i	−0.00243967	+	0.00243967i
$131$	137.002	−	137.002i	1.04581	−	1.04581i	0.0469159	−	0.998899i	$-0.485061\pi$
$131$	137.002	−	137.002i	1.04581	−	1.04581i	0.998899	−	0.0469159i	$-0.0149393\pi$
$132$	26.3481	−	14.8639i	0.199607	−	0.112605i
$133$	152.904	+	152.904i	1.14965	+	1.14965i
$134$	−265.773			−1.98338
$135$	0.0244312	−	0.816593i	0.000180972	−	0.00604883i
$136$	−69.1135	−	8.36149i	−0.508188	−	0.0614815i
$137$			192.929i			1.40824i	0.710079	+	0.704122i	$0.248659\pi$
$137$			192.929i			1.40824i	−0.710079	+	0.704122i	$0.751341\pi$
$138$	40.4113	−	22.7973i	0.292836	−	0.165198i
$139$	−19.3326	−	19.3326i	−0.139084	−	0.139084i	0.634137	−	0.773221i	$-0.281355\pi$
$139$	−19.3326	−	19.3326i	−0.139084	−	0.139084i	−0.773221	+	0.634137i	$0.781355\pi$
$140$		−	0.702271i		−	0.00501622i
$141$	231.029	+	64.3796i	1.63851	+	0.456593i
$142$	84.8959	−	84.8959i	0.597859	−	0.597859i
$143$	17.5953	+	17.5953i	0.123044	+	0.123044i
$144$	152.955	+	92.4233i	1.06219	+	0.641828i
$145$		−	0.0889489i		−	0.000613441i
$146$	−52.2249	−	52.2249i	−0.357705	−	0.357705i
$147$	133.566	+	37.2201i	0.908614	+	0.253198i
$148$	79.4064	+	79.4064i	0.536530	+	0.536530i
$149$			92.8272i			0.623001i	0.950246	+	0.311501i	$0.100832\pi$
$149$			92.8272i			0.623001i	−0.950246	+	0.311501i	$0.899168\pi$
$150$	−182.459	−	50.8448i	−1.21640	−	0.338965i
$151$		−	10.0788i		−	0.0667469i	−0.999443	−	0.0333735i	$-0.989375\pi$
$151$		−	10.0788i		−	0.0667469i	0.999443	−	0.0333735i	$-0.0106251\pi$
$152$		−	90.7490i		−	0.597033i
$153$	−120.499	−	94.2818i	−0.787573	−	0.616221i
$154$	−104.481			−0.678451
$155$	−1.51185			−0.00975390
$156$	11.2425	−	40.3444i	0.0720675	−	0.258618i
$157$	−28.7471			−0.183103			−0.0915513	−	0.995800i	$-0.529183\pi$
$157$	−28.7471			−0.183103			−0.0915513	+	0.995800i	$0.529183\pi$
$158$	−44.7110	+	44.7110i	−0.282981	+	0.282981i
$159$	43.6724	−	156.721i	0.274669	−	0.985665i
$160$	−0.722503	+	0.722503i	−0.00451564	+	0.00451564i
$161$	−59.7558			−0.371154
$162$	95.1411	+	181.101i	0.587291	+	1.11791i
$163$	21.0297	−	21.0297i	0.129017	−	0.129017i	−0.639650	−	0.768666i	$-0.720921\pi$
$163$	21.0297	−	21.0297i	0.129017	−	0.129017i	0.768666	+	0.639650i	$0.220921\pi$
$164$	105.813	+	105.813i	0.645200	+	0.645200i
$165$	0.103304	−	0.370712i	0.000626084	−	0.00224674i
$166$	217.439			1.30987
$167$	−167.822	+	167.822i	−1.00492	+	1.00492i	−0.00493391	+	0.999988i	$0.501571\pi$
$167$	−167.822	+	167.822i	−1.00492	+	1.00492i	−0.999988	+	0.00493391i	$0.998429\pi$
$168$	−58.9026	−	104.413i	−0.350611	−	0.621504i
$169$	−134.550			−0.796155
$170$	1.02229	−	0.801628i	0.00601346	−	0.00471546i
$171$	103.145	−	170.699i	0.603185	−	0.998238i
$172$			45.4888i			0.264470i
$173$	−172.379	+	172.379i	−0.996409	+	0.996409i	−0.999994	−	0.00358423i	$-0.998859\pi$
$173$	−172.379	+	172.379i	−0.996409	+	0.996409i	0.00358423	+	0.999994i	$0.498859\pi$
$174$	10.9438	+	19.3994i	0.0628956	+	0.111491i
$175$	172.492	+	172.492i	0.985670	+	0.985670i
$176$	59.5266	+	59.5266i	0.338219	+	0.338219i
$177$	−4.30373	+	15.4442i	−0.0243148	+	0.0872551i
$178$		−	221.811i		−	1.24613i
$179$	−121.348			−0.677923			−0.338962	−	0.940800i	$-0.610076\pi$
$179$	−121.348			−0.677923			−0.338962	+	0.940800i	$0.610076\pi$
$180$	−0.628867	+	0.155134i	−0.00349371	+	0.000861858i
$181$	30.5988	−	30.5988i	0.169054	−	0.169054i	−0.617509	−	0.786563i	$-0.711858\pi$
$181$	30.5988	−	30.5988i	0.169054	−	0.169054i	0.786563	+	0.617509i	$0.211858\pi$
$182$	−102.282	+	102.282i	−0.561989	+	0.561989i
$183$	91.7504	+	162.640i	0.501368	+	0.888741i
$184$	17.7327	+	17.7327i	0.0963732	+	0.0963732i
$185$	1.42856			0.00772194
$186$	329.729	−	186.011i	1.77274	−	1.00006i
$187$	−44.4729	−	56.7147i	−0.237823	−	0.303287i
$188$		−	190.149i		−	1.01143i
$189$	7.87896	−	263.348i	0.0416876	−	1.39338i
$190$	1.19744	+	1.19744i	0.00630232	+	0.00630232i
$191$		−	27.2933i		−	0.142897i	−0.997444	−	0.0714485i	$-0.977238\pi$
$191$		−	27.2933i		−	0.142897i	0.997444	−	0.0714485i	$-0.0227622\pi$
$192$	4.71860	−	16.9329i	0.0245760	−	0.0881924i
$193$	−203.823	+	203.823i	−1.05608	+	1.05608i	−0.0577462	+	0.998331i	$0.518391\pi$
$193$	−203.823	+	203.823i	−1.05608	+	1.05608i	−0.998331	+	0.0577462i	$0.981609\pi$
$194$	167.600	+	167.600i	0.863917	+	0.863917i
$195$	−0.261778	−	0.464037i	−0.00134245	−	0.00237967i
$196$		−	109.932i		−	0.560877i
$197$	−25.6048	−	25.6048i	−0.129974	−	0.129974i	0.639127	−	0.769101i	$-0.279296\pi$
$197$	−25.6048	−	25.6048i	−0.129974	−	0.129974i	−0.769101	+	0.639127i	$0.779296\pi$
$198$	23.0804	+	93.5607i	0.116567	+	0.472529i
$199$	−30.4685	−	30.4685i	−0.153108	−	0.153108i	0.626397	−	0.779504i	$-0.284529\pi$
$199$	−30.4685	−	30.4685i	−0.153108	−	0.153108i	−0.779504	+	0.626397i	$0.784529\pi$
$200$		−	102.375i		−	0.511875i
$201$	84.7449	−	304.112i	0.421617	−	1.51299i
$202$			365.025i			1.80705i
$203$		−	28.6857i		−	0.141309i
$204$	−46.3616	+	112.096i	−0.227263	+	0.549490i
$205$	1.90362			0.00928596
$206$	208.863			1.01390
$207$	13.2003	+	53.5099i	0.0637695	+	0.258502i
$208$	116.547			0.560322
$209$	66.4318	−	66.4318i	0.317856	−	0.317856i
$210$	2.15496	+	0.600508i	0.0102617	+	0.00285956i
$211$	79.4704	−	79.4704i	0.376637	−	0.376637i	−0.493250	−	0.869887i	$-0.664191\pi$
$211$	79.4704	−	79.4704i	0.376637	−	0.376637i	0.869887	+	0.493250i	$0.164191\pi$
$212$	−128.989			−0.608439
$213$	70.0722	+	124.212i	0.328978	+	0.583156i
$214$	−157.895	+	157.895i	−0.737827	+	0.737827i
$215$	0.409182	+	0.409182i	0.00190317	+	0.00190317i
$216$	−80.4872	+	75.8110i	−0.372626	+	0.350977i
$217$	−487.567			−2.24685
$218$	169.150	−	169.150i	0.775917	−	0.775917i
$219$	76.4109	−	43.1059i	0.348908	−	0.196831i
$220$	−0.305115			−0.00138688
$221$	−99.0574	−	11.9841i	−0.448224	−	0.0542269i
$222$	−311.563	+	175.763i	−1.40344	+	0.791724i
$223$			239.323i			1.07320i	0.843837	+	0.536600i	$0.180291\pi$
$223$			239.323i			1.07320i	−0.843837	+	0.536600i	$0.819709\pi$
$224$	−233.004	+	233.004i	−1.04020	+	1.04020i
$225$	116.358	−	192.567i	0.517149	−	0.855853i
$226$	−229.790	−	229.790i	−1.01677	−	1.01677i
$227$	4.78777	+	4.78777i	0.0210915	+	0.0210915i	0.717574	−	0.696482i	$-0.245253\pi$
$227$	4.78777	+	4.78777i	0.0210915	+	0.0210915i	−0.696482	+	0.717574i	$0.745253\pi$
$228$	−152.322	−	42.4466i	−0.668079	−	0.186169i
$229$		−	64.0470i		−	0.279681i	−0.990174	−	0.139841i	$-0.955341\pi$
$229$		−	64.0470i		−	0.279681i	0.990174	−	0.139841i	$-0.0446590\pi$
$230$	−0.467968			−0.00203464
$231$	33.3151	−	119.553i	0.144221	−	0.517546i
$232$	−8.51254	+	8.51254i	−0.0366920	+	0.0366920i
$233$	117.441	−	117.441i	0.504041	−	0.504041i	−0.408650	−	0.912691i	$-0.634000\pi$
$233$	117.441	−	117.441i	0.504041	−	0.504041i	0.912691	+	0.408650i	$0.134000\pi$
$234$	114.186	+	68.9966i	0.487972	+	0.294857i
$235$	−1.71044	−	1.71044i	−0.00727845	−	0.00727845i
$236$	12.7113			0.0538616
$237$	−36.9040	−	65.4173i	−0.155713	−	0.276022i
$238$	329.684	−	258.522i	1.38523	−	1.08623i
$239$		−	159.936i		−	0.669189i	−0.942362	−	0.334595i	$-0.891401\pi$
$239$		−	159.936i		−	0.669189i	0.942362	−	0.334595i	$-0.108599\pi$
$240$	−0.885621	−	1.56988i	−0.00369009	−	0.00654117i
$241$	−85.4402	−	85.4402i	−0.354524	−	0.354524i	0.507266	−	0.861790i	$-0.330656\pi$
$241$	−85.4402	−	85.4402i	−0.354524	−	0.354524i	−0.861790	+	0.507266i	$0.830656\pi$
$242$		−	260.201i		−	1.07521i
$243$	−237.562	+	51.1191i	−0.977623	+	0.210367i
$244$	104.688	−	104.688i	0.429049	−	0.429049i
$245$	−0.988862	−	0.988862i	−0.00403617	−	0.00403617i
$246$	−415.172	+	234.212i	−1.68769	+	0.952082i
$247$		−	130.067i		−	0.526585i
$248$	144.687	+	144.687i	0.583414	+	0.583414i
$249$	−69.3329	+	248.805i	−0.278445	+	0.999216i
$250$	2.70174	+	2.70174i	0.0108070	+	0.0108070i
$251$			175.660i			0.699840i	0.936780	+	0.349920i	$0.113791\pi$
$251$			175.660i			0.699840i	−0.936780	+	0.349920i	$0.886209\pi$
$252$	−202.807	+	50.0302i	−0.804790	+	0.198533i
$253$			25.9620i			0.102617i
$254$		−	318.490i		−	1.25390i
$255$	0.591295	+	1.42536i	0.00231880	+	0.00558966i
$256$	327.208			1.27816
$257$	−125.343			−0.487717			−0.243859	−	0.969811i	$-0.578413\pi$
$257$	−125.343			−0.487717			−0.243859	+	0.969811i	$0.578413\pi$
$258$	−139.585	−	38.8972i	−0.541026	−	0.150764i
$259$	460.705			1.77878
$260$	−0.298691	+	0.298691i	−0.00114881	+	0.00114881i
$261$	−25.6873	+	6.33677i	−0.0984189	+	0.0242788i
$262$	346.008	−	346.008i	1.32064	−	1.32064i
$263$	−208.112			−0.791300			−0.395650	−	0.918401i	$-0.629481\pi$
$263$	−208.112			−0.791300			−0.395650	+	0.918401i	$0.629481\pi$
$264$	−45.3640	+	25.5913i	−0.171833	+	0.0969368i
$265$	−1.16029	+	1.16029i	−0.00437844	+	0.00437844i
$266$	386.170	+	386.170i	1.45177	+	1.45177i
$267$	253.808	+	70.7271i	0.950591	+	0.264895i
$268$	−250.299			−0.933953
$269$	8.40323	−	8.40323i	0.0312388	−	0.0312388i	−0.691315	−	0.722554i	$-0.742968\pi$
$269$	8.40323	−	8.40323i	0.0312388	−	0.0312388i	0.722554	+	0.691315i	$0.242968\pi$
$270$	0.0617028	−	2.06237i	0.000228529	−	0.00763839i
$271$	−304.338			−1.12302			−0.561510	−	0.827470i	$-0.689779\pi$
$271$	−304.338			−1.12302			−0.561510	+	0.827470i	$0.689779\pi$
$272$	−335.121	−	40.5435i	−1.23206	−	0.149057i
$273$	−84.4225	−	149.650i	−0.309240	−	0.548169i
$274$			487.258i			1.77831i
$275$	74.9424	−	74.9424i	0.272518	−	0.272518i
$276$	38.0584	−	21.4700i	0.137893	−	0.0777899i
$277$	−34.0345	−	34.0345i	−0.122868	−	0.122868i	0.642999	−	0.765867i	$-0.277690\pi$
$277$	−34.0345	−	34.0345i	−0.122868	−	0.122868i	−0.765867	+	0.642999i	$0.777690\pi$
$278$	−48.8260	−	48.8260i	−0.175633	−	0.175633i
$279$	107.705	+	436.605i	0.386041	+	1.56489i
$280$			1.20911i			0.00431825i
$281$	283.239			1.00797			0.503983	−	0.863713i	$-0.331867\pi$
$281$	283.239			1.00797			0.503983	+	0.863713i	$0.331867\pi$
$282$	583.482	+	162.595i	2.06909	+	0.576579i
$283$	−62.0769	+	62.0769i	−0.219353	+	0.219353i	−0.808226	−	0.588873i	$-0.799572\pi$
$283$	−62.0769	+	62.0769i	−0.219353	+	0.219353i	0.588873	+	0.808226i	$0.299572\pi$
$284$	79.9530	−	79.9530i	0.281525	−	0.281525i
$285$	−1.75199	+	0.988355i	−0.00614733	+	0.00346791i
$286$	44.4383	+	44.4383i	0.155379	+	0.155379i
$287$	613.911			2.13906
$288$	260.121	+	157.178i	0.903199	+	0.545758i
$289$	280.662	+	68.9188i	0.971149	+	0.238473i
$290$		−	0.224647i		−	0.000774645i
$291$	−245.218	+	138.335i	−0.842672	+	0.475379i
$292$	−49.1842	−	49.1842i	−0.168439	−	0.168439i
$293$			219.206i			0.748144i	0.927400	+	0.374072i	$0.122039\pi$
$293$			219.206i			0.748144i	−0.927400	+	0.374072i	$0.877961\pi$
$294$	337.332	+	94.0021i	1.14739	+	0.319735i
$295$	0.114341	−	0.114341i	0.000387598	−	0.000387598i
$296$	−136.715	−	136.715i	−0.461876	−	0.461876i
$297$	−114.416	−	3.42316i	−0.385240	−	0.0115258i
$298$			234.442i			0.786718i
$299$	25.4154	+	25.4154i	0.0850015	+	0.0850015i
$300$	−171.836	−	47.8845i	−0.572787	−	0.159615i
$301$	131.960	+	131.960i	0.438404	+	0.438404i
$302$		−	25.4547i		−	0.0842872i
$303$	−417.680	−	116.392i	−1.37848	−	0.384133i
$304$		−	440.028i		−	1.44746i
$305$		−	1.88339i		−	0.00617504i
$306$	−304.329	−	238.116i	−0.994538	−	0.778156i
$307$	90.9488			0.296250			0.148125	−	0.988969i	$-0.452676\pi$
$307$	90.9488			0.296250			0.148125	+	0.988969i	$0.452676\pi$
$308$	−98.3983			−0.319475
$309$	−66.5984	+	238.992i	−0.215529	+	0.773436i
$310$	−3.81830			−0.0123171
$311$	255.834	−	255.834i	0.822616	−	0.822616i	−0.163867	−	0.986483i	$-0.552397\pi$
$311$	255.834	−	255.834i	0.822616	−	0.822616i	0.986483	+	0.163867i	$0.0523967\pi$
$312$	−19.3564	+	69.4615i	−0.0620398	+	0.222633i
$313$	−45.8906	+	45.8906i	−0.146615	+	0.146615i	−0.776604	−	0.629989i	$-0.783059\pi$
$313$	−45.8906	+	45.8906i	−0.146615	+	0.146615i	0.629989	+	0.776604i	$0.283059\pi$
$314$	−72.6030			−0.231220
$315$	−1.37426	+	2.27433i	−0.00436274	+	0.00722010i
$316$	−42.1078	+	42.1078i	−0.133253	+	0.133253i
$317$	−122.939	−	122.939i	−0.387819	−	0.387819i	0.486090	−	0.873909i	$-0.338423\pi$
$317$	−122.939	−	122.939i	−0.387819	−	0.387819i	−0.873909	+	0.486090i	$0.838423\pi$
$318$	110.298	−	395.810i	0.346849	−	1.24469i
$319$	−12.4630			−0.0390690
$320$	−0.125364	+	0.125364i	−0.000391761	+	0.000391761i
$321$	−130.325	−	231.018i	−0.405997	−	0.719683i
$322$	−150.918			−0.468689
$323$	−45.2467	+	373.995i	−0.140083	+	1.15788i
$324$	89.6017	+	170.557i	0.276549	+	0.526411i
$325$		−	146.729i		−	0.451475i
$326$	53.1121	−	53.1121i	0.162921	−	0.162921i
$327$	139.615	+	247.485i	0.426956	+	0.756836i
$328$	−182.179	−	182.179i	−0.555425	−	0.555425i
$329$	−551.609	−	551.609i	−1.67662	−	1.67662i
$330$	0.260902	−	0.936260i	0.000790611	−	0.00283715i
$331$			32.9705i			0.0996086i	0.998759	+	0.0498043i	$0.0158598\pi$
$331$			32.9705i			0.0996086i	−0.998759	+	0.0498043i	$0.984140\pi$
$332$	204.779			0.616804
$333$	−101.771	−	412.550i	−0.305620	−	1.23889i
$334$	−423.847	+	423.847i	−1.26900	+	1.26900i
$335$	−2.25150	+	2.25150i	−0.00672090	+	0.00672090i
$336$	−285.609	−	506.280i	−0.850028	−	1.50679i
$337$	−322.331	−	322.331i	−0.956470	−	0.956470i	0.0426210	−	0.999091i	$-0.486429\pi$
$337$	−322.331	−	322.331i	−0.956470	−	0.956470i	−0.999091	+	0.0426210i	$0.986429\pi$
$338$	−339.817			−1.00537
$339$	336.209	−	189.667i	0.991767	−	0.559489i
$340$	0.962768	−	0.754955i	0.00283167	−	0.00222045i
$341$			211.833i			0.621210i
$342$	260.499	−	431.112i	0.761694	−	1.26056i
$343$	19.1928	+	19.1928i	0.0559558	+	0.0559558i
$344$		−	78.3187i		−	0.227671i
$345$	0.149217	−	0.535472i	0.000432512	−	0.00155209i
$346$	−435.356	+	435.356i	−1.25825	+	1.25825i
$347$	−285.050	−	285.050i	−0.821469	−	0.821469i	0.164850	−	0.986319i	$-0.447286\pi$
$347$	−285.050	−	285.050i	−0.821469	−	0.821469i	−0.986319	+	0.164850i	$0.947286\pi$
$348$	10.3066	+	18.2699i	0.0296168	+	0.0524997i
$349$			4.65073i			0.0133259i	0.999978	+	0.00666294i	$0.00212090\pi$
$349$			4.65073i			0.0133259i	−0.999978	+	0.00666294i	$0.997879\pi$
$350$	435.642	+	435.642i	1.24469	+	1.24469i
$351$	−115.359	+	108.657i	−0.328657	+	0.309563i
$352$	101.233	+	101.233i	0.287594	+	0.287594i
$353$			382.110i			1.08246i	0.840873	+	0.541232i	$0.182042\pi$
$353$			382.110i			1.08246i	−0.840873	+	0.541232i	$0.817958\pi$
$354$	−10.8694	+	39.0054i	−0.0307045	+	0.110185i
$355$		−	1.43839i		−	0.00405181i
$356$		−	208.897i		−	0.586789i
$357$	190.690	+	459.674i	0.534147	+	1.28760i
$358$	−306.474			−0.856073
$359$	−77.1661			−0.214947			−0.107474	−	0.994208i	$-0.534276\pi$
$359$	−77.1661			−0.214947			−0.107474	+	0.994208i	$0.534276\pi$
$360$	1.08273	−	0.267097i	0.00300758	−	0.000741936i
$361$	−130.072			−0.360310
$362$	77.2795	−	77.2795i	0.213479	−	0.213479i
$363$	297.735	+	82.9680i	0.820207	+	0.228562i
$364$	−96.3268	+	96.3268i	−0.264634	+	0.264634i
$365$	−0.884847			−0.00242424
$366$	231.722	+	410.759i	0.633121	+	1.12229i
$367$	226.575	−	226.575i	0.617370	−	0.617370i	−0.327486	−	0.944856i	$-0.606201\pi$
$367$	226.575	−	226.575i	0.617370	−	0.617370i	0.944856	+	0.327486i	$0.106201\pi$
$368$	85.9829	+	85.9829i	0.233649	+	0.233649i
$369$	−135.615	−	549.742i	−0.367521	−	1.48982i
$370$	3.60793			0.00975117
$371$	−374.188	+	374.188i	−1.00859	+	1.00859i
$372$	310.531	−	175.181i	0.834762	−	0.470917i
$373$	446.563			1.19722			0.598610	−	0.801040i	$-0.295720\pi$
$373$	446.563			1.19722			0.598610	+	0.801040i	$0.295720\pi$
$374$	−112.320	−	143.237i	−0.300320	−	0.382987i
$375$	−3.95295	+	2.22999i	−0.0105412	+	0.00594663i
$376$			327.382i			0.870698i
$377$	−12.2006	+	12.2006i	−0.0323625	+	0.0323625i
$378$	19.8989	−	665.105i	0.0526426	−	1.75954i
$379$	219.441	+	219.441i	0.578999	+	0.578999i	0.934627	−	0.355628i	$-0.115733\pi$
$379$	219.441	+	219.441i	0.578999	+	0.578999i	−0.355628	+	0.934627i	$0.615733\pi$
$380$	1.12772	+	1.12772i	0.00296769	+	0.00296769i
$381$	364.433	+	101.554i	0.956516	+	0.266546i
$382$		−	68.9314i		−	0.180449i
$383$	280.815			0.733197			0.366599	−	0.930379i	$-0.380522\pi$
$383$	280.815			0.733197			0.366599	+	0.930379i	$0.380522\pi$
$384$	−96.8608	+	347.590i	−0.252242	+	0.905183i
$385$	−0.885115	+	0.885115i	−0.00229900	+	0.00229900i
$386$	−514.770	+	514.770i	−1.33360	+	1.33360i
$387$	89.0164	−	147.317i	0.230016	−	0.380665i
$388$	157.842	+	157.842i	0.406809	+	0.406809i
$389$	403.158			1.03640			0.518199	−	0.855260i	$-0.326603\pi$
$389$	403.158			1.03640			0.518199	+	0.855260i	$0.326603\pi$
$390$	−0.661141	−	1.17196i	−0.00169523	−	0.00300502i
$391$	−64.2386	−	81.9213i	−0.164293	−	0.209517i
$392$			189.271i			0.482835i
$393$	285.592	+	506.249i	0.726696	+	1.28817i
$394$	−64.6669	−	64.6669i	−0.164129	−	0.164129i
$395$			0.757540i			0.00191782i
$396$	21.7365	+	88.1133i	0.0548903	+	0.222508i
$397$	525.784	−	525.784i	1.32439	−	1.32439i	0.414214	−	0.910179i	$-0.364056\pi$
$397$	525.784	−	525.784i	1.32439	−	1.32439i	0.910179	−	0.414214i	$-0.135944\pi$
$398$	−76.9504	−	76.9504i	−0.193343	−	0.193343i
$399$	−565.010	+	318.741i	−1.41606	+	0.798849i
$400$		−	496.400i		−	1.24100i
$401$	−294.784	−	294.784i	−0.735122	−	0.735122i	0.236508	−	0.971630i	$-0.423997\pi$
$401$	−294.784	−	294.784i	−0.735122	−	0.735122i	−0.971630	+	0.236508i	$0.923997\pi$
$402$	214.030	−	768.057i	0.532412	−	1.91059i
$403$	207.373	+	207.373i	0.514573	+	0.514573i
$404$			343.772i			0.850920i
$405$	2.34019	+	0.728212i	0.00577825	+	0.00179806i
$406$		−	72.4478i		−	0.178443i
$407$		−	200.162i		−	0.491797i
$408$	79.8215	−	192.997i	0.195641	−	0.473032i
$409$	−95.6272			−0.233807			−0.116904	−	0.993143i	$-0.537297\pi$
$409$	−95.6272			−0.233807			−0.116904	+	0.993143i	$0.537297\pi$
$410$	4.80774			0.0117262
$411$	−557.545	−	155.368i	−1.35656	−	0.378024i
$412$	196.702			0.477433
$413$	36.8747	−	36.8747i	0.0892849	−	0.0892849i
$414$	33.3383	+	135.143i	0.0805273	+	0.326433i
$415$	1.84204	−	1.84204i	0.00443864	−	0.00443864i
$416$	198.204			0.476451
$417$	71.4379	−	40.3005i	0.171314	−	0.0966438i
$418$	167.779	−	167.779i	0.401384	−	0.401384i
$419$	−8.23730	−	8.23730i	−0.0196594	−	0.0196594i	0.697209	−	0.716868i	$-0.254425\pi$
$419$	−8.23730	−	8.23730i	−0.0196594	−	0.0196594i	−0.716868	+	0.697209i	$0.754425\pi$
$420$	2.02949	+	0.565545i	0.00483211	+	0.00134654i
$421$	215.261			0.511308			0.255654	−	0.966768i	$-0.417709\pi$
$421$	215.261			0.511308			0.255654	+	0.966768i	$0.417709\pi$
$422$	200.709	−	200.709i	0.475613	−	0.475613i
$423$	−372.100	+	615.805i	−0.879669	+	1.45580i
$424$	222.082			0.523779
$425$	−51.0432	+	421.908i	−0.120102	+	0.992725i
$426$	176.973	+	313.707i	0.415429	+	0.736403i
$427$		−	607.385i		−	1.42245i
$428$	−148.702	+	148.702i	−0.347434	+	0.347434i
$429$	−65.0182	+	36.6789i	−0.151558	+	0.0854986i
$430$	1.03342	+	1.03342i	0.00240330	+	0.00240330i
$431$	561.869	+	561.869i	1.30364	+	1.30364i	0.925919	+	0.377722i	$0.123292\pi$
$431$	561.869	+	561.869i	1.30364	+	1.30364i	0.377722	+	0.925919i	$0.376708\pi$
$432$	−390.270	+	367.595i	−0.903402	+	0.850915i
$433$			51.2892i			0.118451i	0.998245	+	0.0592254i	$0.0188631\pi$
$433$			51.2892i			0.118451i	−0.998245	+	0.0592254i	$0.981137\pi$
$434$	−1231.39			−2.83730
$435$	0.257053	+	0.0716313i	0.000590926	+	0.000164670i
$436$	159.301	−	159.301i	0.365370	−	0.365370i
$437$	95.9571	−	95.9571i	0.219581	−	0.219581i
$438$	192.981	−	108.867i	0.440597	−	0.248555i
$439$	455.275	+	455.275i	1.03707	+	1.03707i	0.999286	+	0.0377871i	$0.0120309\pi$
$439$	455.275	+	455.275i	1.03707	+	1.03707i	0.0377871	+	0.999286i	$0.487969\pi$
$440$	0.525320			0.00119391
$441$	−215.124	+	356.018i	−0.487810	+	0.807298i
$442$	−250.177	−	30.2669i	−0.566011	−	0.0684771i
$443$		−	715.488i		−	1.61510i	−0.589801	−	0.807549i	$-0.700794\pi$
$443$		−	715.488i		−	1.61510i	0.589801	−	0.807549i	$-0.299206\pi$
$444$	−293.423	+	165.529i	−0.660862	+	0.372814i
$445$	−1.87908	−	1.87908i	−0.00422264	−	0.00422264i
$446$			604.429i			1.35522i
$447$	−268.261	−	74.7545i	−0.600136	−	0.167236i
$448$	−40.4293	+	40.4293i	−0.0902440	+	0.0902440i
$449$	−207.961	−	207.961i	−0.463164	−	0.463164i	0.436527	−	0.899691i	$-0.356208\pi$
$449$	−207.961	−	207.961i	−0.463164	−	0.463164i	−0.899691	+	0.436527i	$0.856208\pi$
$450$	293.872	−	486.342i	0.653049	−	1.08076i
$451$		−	266.725i		−	0.591407i
$452$	−216.411	−	216.411i	−0.478786	−	0.478786i
$453$	29.1266	+	8.11653i	0.0642971	+	0.0179173i
$454$	12.0919	+	12.0919i	0.0266341	+	0.0266341i
$455$			1.73296i			0.00380871i
$456$	262.255	+	73.0810i	0.575121	+	0.160265i
$457$			688.667i			1.50693i	0.657488	+	0.753465i	$0.271619\pi$
$457$			688.667i			1.50693i	−0.657488	+	0.753465i	$0.728381\pi$
$458$		−	161.756i		−	0.353178i
$459$	369.503	−	272.302i	0.805017	−	0.593251i
$460$	−0.440721			−0.000958089
$461$	413.461			0.896879			0.448439	−	0.893813i	$-0.351980\pi$
$461$	413.461			0.896879			0.448439	+	0.893813i	$0.351980\pi$
$462$	84.1398	−	301.940i	0.182121	−	0.653550i
$463$	−866.659			−1.87183			−0.935917	−	0.352220i	$-0.885427\pi$
$463$	−866.659			−1.87183			−0.935917	+	0.352220i	$0.885427\pi$
$464$	−41.2759	+	41.2759i	−0.0889568	+	0.0889568i
$465$	1.21751	−	4.36910i	0.00261830	−	0.00939591i
$466$	296.607	−	296.607i	0.636496	−	0.636496i
$467$	747.435			1.60050			0.800252	−	0.599664i	$-0.204699\pi$
$467$	747.435			1.60050			0.800252	+	0.599664i	$0.204699\pi$
$468$	107.537	+	64.9794i	0.229781	+	0.138845i
$469$	−726.101	+	726.101i	−1.54819	+	1.54819i
$470$	−4.31983	−	4.31983i	−0.00919113	−	0.00919113i
$471$	23.1503	−	83.0760i	0.0491513	−	0.176382i
$472$	−21.8853			−0.0463671
$473$	57.3323	−	57.3323i	0.121210	−	0.121210i
$474$	−93.2039	−	165.216i	−0.196633	−	0.348558i
$475$	−553.983			−1.16628
$476$	310.489	−	243.470i	0.652288	−	0.511491i
$477$	417.736	+	252.417i	0.875758	+	0.529176i
$478$		−	403.931i		−	0.845044i
$479$	452.004	−	452.004i	0.943641	−	0.943641i	−0.0548535	−	0.998494i	$-0.517469\pi$
$479$	452.004	−	452.004i	0.943641	−	0.943641i	0.998494	+	0.0548535i	$0.0174692\pi$
$480$	−1.50612	−	2.66979i	−0.00313775	−	0.00556207i
$481$	−195.948	−	195.948i	−0.407376	−	0.407376i
$482$	−215.786	−	215.786i	−0.447688	−	0.447688i
$483$	48.1218	−	172.688i	0.0996311	−	0.357532i
$484$		−	245.051i		−	0.506304i
$485$	2.83965			0.00585494
$486$	−599.981	+	129.105i	−1.23453	+	0.265649i
$487$	57.3670	−	57.3670i	0.117797	−	0.117797i	−0.645751	−	0.763548i	$-0.723456\pi$
$487$	57.3670	−	57.3670i	0.117797	−	0.117797i	0.763548	+	0.645751i	$0.223456\pi$
$488$	−180.243	+	180.243i	−0.369350	+	0.369350i
$489$	43.8382	+	77.7091i	0.0896487	+	0.158914i
$490$	−2.49745	−	2.49745i	−0.00509683	−	0.00509683i
$491$	−213.710			−0.435255			−0.217628	−	0.976032i	$-0.569832\pi$
$491$	−213.710			−0.435255			−0.217628	+	0.976032i	$0.569832\pi$
$492$	−391.000	+	220.576i	−0.794715	+	0.448325i
$493$	39.3262	−	30.8376i	0.0797691	−	0.0625510i
$494$		−	328.493i		−	0.664966i
$495$	0.988125	+	0.597074i	0.00199621	+	0.00120621i
$496$	701.563	+	701.563i	1.41444	+	1.41444i
$497$		−	463.876i		−	0.933352i
$498$	−175.105	+	628.375i	−0.351617	+	1.26180i
$499$	−181.080	+	181.080i	−0.362885	+	0.362885i	−0.864874	−	0.501989i	$-0.832602\pi$
$499$	−181.080	+	181.080i	−0.362885	+	0.362885i	0.501989	+	0.864874i	$0.332602\pi$
$500$	2.54444	+	2.54444i	0.00508887	+	0.00508887i
$501$	−349.839	−	620.136i	−0.698281	−	1.23780i
$502$			443.642i			0.883750i
$503$	−297.442	−	297.442i	−0.591337	−	0.591337i	0.346656	−	0.937992i	$-0.387317\pi$
$503$	−297.442	−	297.442i	−0.591337	−	0.591337i	−0.937992	+	0.346656i	$0.887317\pi$
$504$	349.176	−	86.1378i	0.692810	−	0.170908i
$505$	3.09231	+	3.09231i	0.00612338	+	0.00612338i
$506$			65.5690i			0.129583i
$507$	108.354	−	388.836i	0.213717	−	0.766934i
$508$		−	299.947i		−	0.590446i
$509$			966.463i			1.89875i	0.314147	+	0.949374i	$0.398282\pi$
$509$			966.463i			1.89875i	−0.314147	+	0.949374i	$0.601718\pi$
$510$	1.49336	+	3.59986i	0.00292816	+	0.00705855i
$511$	−285.360			−0.558434
$512$	345.277			0.674370
$513$	410.237	+	435.542i	0.799683	+	0.849009i
$514$	−316.564			−0.615883
$515$	1.76939	−	1.76939i	0.00343570	−	0.00343570i
$516$	−131.458	−	36.6325i	−0.254763	−	0.0709932i
$517$	−239.657	+	239.657i	−0.463552	+	0.463552i
$518$	1163.54			2.24622
$519$	−359.338	−	636.974i	−0.692366	−	1.22731i
$520$	0.514261	−	0.514261i	0.000988964	−	0.000988964i
$521$	231.742	+	231.742i	0.444803	+	0.444803i	0.893622	−	0.448819i	$-0.148155\pi$
$521$	231.742	+	231.742i	0.444803	+	0.444803i	−0.448819	+	0.893622i	$0.648155\pi$
$522$	−64.8753	+	16.0040i	−0.124282	+	0.0306590i
$523$	60.6041			0.115878			0.0579389	−	0.998320i	$-0.481547\pi$
$523$	60.6041			0.115878			0.0579389	+	0.998320i	$0.481547\pi$
$524$	325.863	−	325.863i	0.621875	−	0.621875i
$525$	−637.393	+	359.575i	−1.21408	+	0.684904i
$526$	−525.602			−0.999244
$527$	−524.144	−	668.423i	−0.994581	−	1.26835i
$528$	−219.963	+	124.088i	−0.416596	+	0.235015i
$529$		−	491.499i		−	0.929110i
$530$	−2.93039	+	2.93039i	−0.00552904	+	0.00552904i
$531$	−41.1661	−	24.8746i	−0.0775257	−	0.0468449i
$532$	363.686	+	363.686i	0.683620	+	0.683620i
$533$	−261.110	−	261.110i	−0.489887	−	0.489887i
$534$	641.011	+	178.627i	1.20039	+	0.334507i
$535$			2.67522i			0.00500041i
$536$	430.944			0.804000
$537$	97.7228	−	350.683i	0.181979	−	0.653042i
$538$	21.2230	−	21.2230i	0.0394479	−	0.0394479i
$539$	−138.554	+	138.554i	−0.257057	+	0.257057i
$540$	0.0581103	−	1.94229i	0.000107612	−	0.00359683i
$541$	418.241	+	418.241i	0.773089	+	0.773089i	0.978645	−	0.205556i	$-0.0659003\pi$
$541$	418.241	+	418.241i	0.773089	+	0.773089i	−0.205556	+	0.978645i	$0.565900\pi$
$542$	−768.629			−1.41813
$543$	63.7857	+	113.069i	0.117469	+	0.208230i
$544$	−569.918	−	68.9497i	−1.04764	−	0.126746i
$545$		−	2.86591i		−	0.00525855i
$546$	−213.215	−	377.952i	−0.390504	−	0.692220i
$547$	−486.262	−	486.262i	−0.888962	−	0.888962i	0.105462	−	0.994423i	$-0.466368\pi$
$547$	−486.262	−	486.262i	−0.888962	−	0.888962i	−0.994423	+	0.105462i	$0.966368\pi$
$548$			458.888i			0.837387i
$549$	−543.899	+	134.174i	−0.990708	+	0.244396i
$550$	189.273	−	189.273i	0.344132	−	0.344132i
$551$	46.0641	+	46.0641i	0.0836008	+	0.0836008i
$552$	−65.5258	+	36.9652i	−0.118706	+	0.0669660i
$553$			244.304i			0.441779i
$554$	−85.9566	−	85.9566i	−0.155156	−	0.155156i
$555$	−1.15043	+	4.12838i	−0.00207285	+	0.00743852i
$556$	−45.9832	−	45.9832i	−0.0827036	−	0.0827036i
$557$		−	30.5161i		−	0.0547866i	−0.999625	−	0.0273933i	$-0.991279\pi$
$557$		−	30.5161i		−	0.0547866i	0.999625	−	0.0273933i	$-0.00872065\pi$
$558$	272.018	+	1102.68i	0.487488	+	1.97613i
$559$		−	112.251i		−	0.200806i
$560$			5.86278i			0.0104693i
$561$	199.714	−	82.8489i	0.355996	−	0.147681i
$562$	715.340			1.27285
$563$	−948.258			−1.68430			−0.842148	−	0.539247i	$-0.818709\pi$
$563$	−948.258			−1.68430			−0.842148	+	0.539247i	$0.818709\pi$
$564$	549.510	+	153.129i	0.974309	+	0.271505i
$565$	−3.89334			−0.00689087
$566$	−156.780	+	156.780i	−0.276996	+	0.276996i
$567$	754.702	+	234.846i	1.33104	+	0.414190i
$568$	−137.656	+	137.656i	−0.242353	+	0.242353i
$569$	24.1937			0.0425197			0.0212598	−	0.999774i	$-0.493232\pi$
$569$	24.1937			0.0425197			0.0212598	+	0.999774i	$0.493232\pi$
$570$	−4.42478	+	2.49616i	−0.00776277	+	0.00437924i
$571$	−147.329	+	147.329i	−0.258018	+	0.258018i	−0.824248	−	0.566229i	$-0.808402\pi$
$571$	−147.329	+	147.329i	−0.258018	+	0.258018i	0.566229	+	0.824248i	$0.308402\pi$
$572$	41.8509	+	41.8509i	0.0731660	+	0.0731660i
$573$	78.8748	+	21.9796i	0.137652	+	0.0383587i
$574$	1550.48			2.70118
$575$	108.250	−	108.250i	0.188261	−	0.188261i
$576$	45.1344	+	27.2725i	0.0783584	+	0.0473481i
$577$	460.540			0.798164			0.399082	−	0.916915i	$-0.369329\pi$
$577$	460.540			0.798164			0.399082	+	0.916915i	$0.369329\pi$
$578$	708.833	+	174.060i	1.22635	+	0.301141i
$579$	−424.886	−	753.167i	−0.733827	−	1.30081i
$580$		−	0.211568i		−	0.000364772i
$581$	594.049	−	594.049i	1.02246	−	1.02246i
$582$	−619.315	+	349.376i	−1.06412	+	0.600303i
$583$	162.573	+	162.573i	0.278856	+	0.278856i
$584$	84.6812	+	84.6812i	0.145002	+	0.145002i
$585$	1.55183	−	0.382818i	0.00265270	−	0.000654390i
$586$			553.622i			0.944747i
$587$	−398.312			−0.678556			−0.339278	−	0.940686i	$-0.610183\pi$
$587$	−398.312			−0.678556			−0.339278	+	0.940686i	$0.610183\pi$
$588$	317.691	+	88.5290i	0.540291	+	0.150560i
$589$	782.946	−	782.946i	1.32928	−	1.32928i
$590$	0.288778	−	0.288778i	0.000489454	−	0.000489454i
$591$	94.6150	−	53.3754i	0.160093	−	0.0903138i
$592$	−662.910	−	662.910i	−1.11978	−	1.11978i
$593$	455.426			0.768003			0.384001	−	0.923333i	$-0.374546\pi$
$593$	455.426			0.768003			0.384001	+	0.923333i	$0.374546\pi$
$594$	−288.967	−	8.64545i	−0.486476	−	0.0145546i
$595$	0.602851	−	4.98299i	0.00101320	−	0.00837477i
$596$			220.792i			0.370457i
$597$	112.587	−	63.5141i	0.188588	−	0.106389i
$598$	64.1886	+	64.1886i	0.107339	+	0.107339i
$599$			578.376i			0.965569i	0.875739	+	0.482784i	$0.160375\pi$
$599$			578.376i			0.965569i	−0.875739	+	0.482784i	$0.839625\pi$
$600$	295.853	+	82.4434i	0.493088	+	0.137406i
$601$	441.494	−	441.494i	0.734600	−	0.734600i	−0.236928	−	0.971527i	$-0.576140\pi$
$601$	441.494	−	441.494i	0.734600	−	0.734600i	0.971527	+	0.236928i	$0.0761404\pi$
$602$	333.274	+	333.274i	0.553612	+	0.553612i
$603$	810.604	+	489.807i	1.34429	+	0.812284i
$604$		−	23.9727i		−	0.0396899i
$605$	−2.20429	−	2.20429i	−0.00364346	−	0.00364346i
$606$	−1054.88	−	293.957i	−1.74073	−	0.485078i
$607$	91.3692	+	91.3692i	0.150526	+	0.150526i	0.778353	−	0.627827i	$-0.216055\pi$
$607$	91.3692	+	91.3692i	0.150526	+	0.150526i	−0.627827	+	0.778353i	$0.716055\pi$
$608$		−	748.327i		−	1.23080i
$609$	82.8985	+	23.1008i	0.136122	+	0.0379324i
$610$		−	4.75663i		−	0.00779776i
$611$			469.223i			0.767958i
$612$	−286.610	−	224.252i	−0.468316	−	0.366425i
$613$	−135.981			−0.221828			−0.110914	−	0.993830i	$-0.535378\pi$
$613$	−135.981			−0.221828			−0.110914	+	0.993830i	$0.535378\pi$
$614$	229.698			0.374101
$615$	−1.53300	+	5.50126i	−0.00249269	+	0.00894514i
$616$	169.414			0.275022
$617$	−150.969	+	150.969i	−0.244683	+	0.244683i	−0.818784	−	0.574101i	$-0.805352\pi$
$617$	−150.969	+	150.969i	−0.244683	+	0.244683i	0.574101	+	0.818784i	$0.305352\pi$
$618$	−168.199	+	603.592i	−0.272167	+	0.976686i
$619$	−861.159	+	861.159i	−1.39121	+	1.39121i	−0.568588	+	0.822622i	$0.692510\pi$
$619$	−861.159	+	861.159i	−1.39121	+	1.39121i	−0.822622	+	0.568588i	$0.807490\pi$
$620$	−3.59599			−0.00579998
$621$	−165.268	−	4.94457i	−0.266132	−	0.00796226i
$622$	646.127	−	646.127i	1.03879	−	1.03879i
$623$	−605.995	−	605.995i	−0.972704	−	0.972704i
$624$	−93.8562	+	336.808i	−0.150411	+	0.539756i
$625$	−624.931			−0.999890
$626$	−115.900	+	115.900i	−0.185144	+	0.185144i
$627$	138.483	+	245.479i	0.220866	+	0.391513i
$628$	−68.3758			−0.108879
$629$	495.266	+	631.596i	0.787387	+	1.00413i
$630$	−3.47081	+	5.74400i	−0.00550922	+	0.00911745i
$631$			26.1221i			0.0413980i	0.999786	+	0.0206990i	$0.00658916\pi$
$631$			26.1221i			0.0413980i	−0.999786	+	0.0206990i	$0.993411\pi$
$632$	72.4977	−	72.4977i	0.114711	−	0.114711i
$633$	165.663	+	293.659i	0.261711	+	0.463917i
$634$	−310.491	−	310.491i	−0.489733	−	0.489733i
$635$	−2.69809	−	2.69809i	−0.00424896	−	0.00424896i
$636$	103.876	−	372.765i	0.163327	−	0.586108i
$637$			271.274i			0.425862i
$638$	−31.4763			−0.0493359
$639$	−415.390	+	102.472i	−0.650063	+	0.160363i
$640$	2.57340	−	2.57340i	0.00402093	−	0.00402093i
$641$	−478.801	+	478.801i	−0.746959	+	0.746959i	−0.973907	−	0.226948i	$-0.927125\pi$
$641$	−478.801	+	478.801i	−0.746959	+	0.746959i	0.226948	+	0.973907i	$0.427125\pi$
$642$	−329.145	−	583.454i	−0.512687	−	0.908806i
$643$	13.1640	+	13.1640i	0.0204727	+	0.0204727i	0.717269	−	0.696796i	$-0.245392\pi$
$643$	13.1640	+	13.1640i	0.0204727	+	0.0204727i	−0.696796	+	0.717269i	$0.745392\pi$
$644$	−142.131			−0.220700
$645$	−1.51201	+	0.852975i	−0.00234420	+	0.00132244i
$646$	−114.274	+	944.553i	−0.176894	+	1.46216i
$647$			775.698i			1.19892i	0.800406	+	0.599458i	$0.204617\pi$
$647$			775.698i			1.19892i	−0.800406	+	0.599458i	$0.795383\pi$
$648$	−154.269	−	293.651i	−0.238069	−	0.453164i
$649$	−16.0209	−	16.0209i	−0.0246855	−	0.0246855i
$650$		−	370.576i		−	0.570117i
$651$	392.642	−	1409.02i	0.603137	−	2.16439i
$652$	50.0198	−	50.0198i	0.0767175	−	0.0767175i
$653$	−378.601	−	378.601i	−0.579787	−	0.579787i	0.355057	−	0.934845i	$-0.384461\pi$
$653$	−378.601	−	378.601i	−0.579787	−	0.579787i	−0.934845	+	0.355057i	$0.884461\pi$
$654$	352.607	+	625.043i	0.539155	+	0.955723i
$655$		−	5.86242i		−	0.00895026i
$656$	−883.359	−	883.359i	−1.34658	−	1.34658i
$657$	63.0371	+	255.533i	0.0959468	+	0.388939i
$658$	−1393.13	−	1393.13i	−2.11722	−	2.11722i
$659$			393.519i			0.597146i	0.954387	+	0.298573i	$0.0965106\pi$
$659$			393.519i			0.597146i	−0.954387	+	0.298573i	$0.903489\pi$
$660$	0.245711	−	0.881748i	0.000372290	−	0.00133598i
$661$		−	198.424i		−	0.300188i	−0.988672	−	0.150094i	$-0.952042\pi$
$661$		−	198.424i		−	0.300188i	0.988672	−	0.150094i	$-0.0479577\pi$
$662$			83.2694i			0.125785i
$663$	114.405	−	276.614i	0.172556	−	0.417216i
$664$	−352.571			−0.530980
$665$	6.54288			0.00983892
$666$	−257.031	−	1041.93i	−0.385933	−	1.56445i
$667$	−18.0021			−0.0269897
$668$	−399.169	+	399.169i	−0.597559	+	0.597559i
$669$	−691.619	−	192.729i	−1.03381	−	0.288086i
$670$	−5.68634	+	5.68634i	−0.00848707	+	0.00848707i
$671$	−263.889			−0.393278
$672$	−485.717	−	860.998i	−0.722794	−	1.28125i
$673$	316.549	−	316.549i	0.470355	−	0.470355i	−0.431674	−	0.902029i	$-0.642077\pi$
$673$	316.549	−	316.549i	0.470355	−	0.470355i	0.902029	+	0.431674i	$0.142077\pi$
$674$	−814.070	−	814.070i	−1.20782	−	1.20782i
$675$	462.793	+	491.339i	0.685619	+	0.727910i
$676$	−320.032			−0.473419
$677$	351.749	−	351.749i	0.519570	−	0.519570i	−0.397871	−	0.917441i	$-0.630251\pi$
$677$	351.749	−	351.749i	0.519570	−	0.519570i	0.917441	+	0.397871i	$0.130251\pi$
$678$	849.121	−	479.017i	1.25239	−	0.706515i
$679$	915.775			1.34871
$680$	−1.65761	+	1.29982i	−0.00243766	+	0.00191149i
$681$	−17.6918	+	9.98050i	−0.0259791	+	0.0146557i
$682$			534.999i			0.784456i
$683$	−751.652	+	751.652i	−1.10051	+	1.10051i	−0.106166	+	0.994348i	$0.533858\pi$
$683$	−751.652	+	751.652i	−1.10051	+	1.10051i	−0.994348	+	0.106166i	$0.966142\pi$
$684$	245.332	−	406.012i	0.358673	−	0.593584i
$685$	4.12781	+	4.12781i	0.00602600	+	0.00602600i
$686$	48.4730	+	48.4730i	0.0706603	+	0.0706603i
$687$	185.089	+	51.5776i	0.269416	+	0.0750766i
$688$		−	379.755i		−	0.551969i
$689$	318.301			0.461975
$690$	0.376858	−	1.35238i	0.000546171	−	0.00195996i
$691$	676.031	−	676.031i	0.978337	−	0.978337i	−0.0214328	−	0.999770i	$-0.506823\pi$
$691$	676.031	−	676.031i	0.978337	−	0.978337i	0.999770	+	0.0214328i	$0.00682281\pi$
$692$	−410.008	+	410.008i	−0.592497	+	0.592497i
$693$	318.667	+	192.554i	0.459836	+	0.277856i
$694$	−719.915	−	719.915i	−1.03734	−	1.03734i
$695$	−0.827259			−0.00119030
$696$	−17.7451	−	31.4555i	−0.0254958	−	0.0451947i
$697$	659.966	+	841.632i	0.946866	+	1.20751i
$698$			11.7458i			0.0168278i
$699$	244.817	+	433.970i	0.350238	+	0.620844i
$700$	410.278	+	410.278i	0.586111	+	0.586111i
$701$		−	776.727i		−	1.10803i	−0.832508	−	0.554014i	$-0.813096\pi$
$701$		−	776.727i		−	1.10803i	0.832508	−	0.554014i	$-0.186904\pi$
$702$	−291.347	+	274.420i	−0.415024	+	0.390912i
$703$	−739.809	+	739.809i	−1.05236	+	1.05236i
$704$	17.5652	+	17.5652i	0.0249506	+	0.0249506i
$705$	6.32040	−	3.56555i	0.00896511	−	0.00505751i
$706$			965.047i			1.36692i
$707$	997.258	+	997.258i	1.41055	+	1.41055i
$708$	−10.2365	+	36.7344i	−0.0144584	+	0.0518847i
$709$	−368.649	−	368.649i	−0.519956	−	0.519956i	0.397602	−	0.917558i	$-0.369843\pi$
$709$	−368.649	−	368.649i	−0.519956	−	0.519956i	−0.917558	+	0.397602i	$0.869843\pi$
$710$		−	3.63277i		−	0.00511658i
$711$	218.768	−	53.9676i	0.307691	−	0.0759038i
$712$			359.661i			0.505141i
$713$			305.980i			0.429145i
$714$	481.603	+	1160.94i	0.674514	+	1.62597i
$715$	0.752918			0.00105303
$716$	−288.630			−0.403115
$717$	462.198	+	128.798i	0.644628	+	0.179635i
$718$	−194.889			−0.271433
$719$	485.521	−	485.521i	0.675273	−	0.675273i	−0.283654	−	0.958927i	$-0.591547\pi$
$719$	485.521	−	485.521i	0.675273	−	0.675273i	0.958927	+	0.283654i	$0.0915466\pi$
$720$	5.24998	−	1.29511i	0.00729164	−	0.00179877i
$721$	570.620	−	570.620i	0.791428	−	0.791428i
$722$	−328.507			−0.454995
$723$	315.719	−	178.107i	0.436679	−	0.246345i
$724$	72.7801	−	72.7801i	0.100525	−	0.100525i
$725$	51.9653	+	51.9653i	0.0716763	+	0.0716763i
$726$	751.952	+	209.542i	1.03575	+	0.288625i
$727$	−756.846			−1.04105			−0.520527	−	0.853845i	$-0.674264\pi$
$727$	−756.846			−1.04105			−0.520527	+	0.853845i	$0.674264\pi$
$728$	165.847	−	165.847i	0.227812	−	0.227812i
$729$	43.5821	−	727.696i	0.0597834	−	0.998211i
$730$	−2.23475			−0.00306130
$731$	−39.0490	+	322.767i	−0.0534186	+	0.441542i
$732$	218.231	+	386.843i	0.298130	+	0.528474i
$733$			385.816i			0.526353i	0.964748	+	0.263176i	$0.0847701\pi$
$733$			385.816i			0.526353i	−0.964748	+	0.263176i	$0.915230\pi$
$734$	572.232	−	572.232i	0.779607	−	0.779607i
$735$	3.65405	−	2.06137i	0.00497149	−	0.00280458i
$736$	146.226	+	146.226i	0.198676	+	0.198676i
$737$	315.468	+	315.468i	0.428043	+	0.428043i
$738$	−342.506	−	1388.42i	−0.464101	−	1.88132i
$739$			1032.78i			1.39754i	0.715347	+	0.698770i	$0.246269\pi$
$739$			1032.78i			1.39754i	−0.715347	+	0.698770i	$0.753731\pi$
$740$	3.39787			0.00459171
$741$	375.879	+	104.744i	0.507258	+	0.141355i
$742$	−945.041	+	945.041i	−1.27364	+	1.27364i
$743$	805.346	−	805.346i	1.08391	−	1.08391i	0.0877707	−	0.996141i	$-0.472026\pi$
$743$	805.346	−	805.346i	1.08391	−	1.08391i	0.996141	−	0.0877707i	$-0.0279743\pi$
$744$	−534.646	+	301.612i	−0.718611	+	0.405392i
$745$	1.98608	+	1.98608i	0.00266588	+	0.00266588i
$746$	1127.83			1.51184
$747$	−663.185	−	400.729i	−0.887798	−	0.536451i
$748$	−105.780	−	134.898i	−0.141417	−	0.180344i
$749$			862.747i			1.15187i
$750$	−9.98346	+	5.63200i	−0.0133113	+	0.00750933i
$751$	115.715	+	115.715i	0.154082	+	0.154082i	0.779938	−	0.625856i	$-0.215250\pi$
$751$	115.715	+	115.715i	0.154082	+	0.154082i	−0.625856	+	0.779938i	$0.715250\pi$
$752$			1587.42i			2.11094i
$753$	−507.638	−	141.460i	−0.674154	−	0.187862i
$754$	−30.8137	+	30.8137i	−0.0408669	+	0.0408669i
$755$	−0.215640	−	0.215640i	−0.000285616	−	0.000285616i
$756$	18.7403	−	626.381i	0.0247888	−	0.828546i
$757$		−	229.198i		−	0.302772i	−0.988475	−	0.151386i	$-0.951626\pi$
$757$		−	229.198i		−	0.302772i	0.988475	−	0.151386i	$-0.0483736\pi$
$758$	554.214	+	554.214i	0.731153	+	0.731153i
$759$	−75.0274	−	20.9074i	−0.0988503	−	0.0275460i
$760$	−1.94161	−	1.94161i	−0.00255476	−	0.00255476i
$761$		−	1423.20i		−	1.87017i	−0.354424	−	0.935085i	$-0.615323\pi$
$761$		−	1423.20i		−	1.87017i	0.354424	−	0.935085i	$-0.384677\pi$
$762$	920.402	+	256.483i	1.20788	+	0.336591i
$763$		−	924.244i		−	1.21133i
$764$		−	64.9180i		−	0.0849712i
$765$	−4.59532	+	0.560922i	−0.00600696	+	0.000733232i
$766$	709.218			0.925872
$767$	−31.3672			−0.0408960
$768$	−263.504	+	945.597i	−0.343104	+	1.23125i
$769$	1003.32			1.30470			0.652351	−	0.757917i	$-0.273783\pi$
$769$	1003.32			1.30470			0.652351	+	0.757917i	$0.273783\pi$
$770$	−2.23543	+	2.23543i	−0.00290315	+	0.00290315i
$771$	100.940	−	362.229i	0.130921	−	0.469817i
$772$	−484.799	+	484.799i	−0.627978	+	0.627978i
$773$	−942.731			−1.21957			−0.609787	−	0.792565i	$-0.708745\pi$
$773$	−942.731			−1.21957			−0.609787	+	0.792565i	$0.708745\pi$
$774$	224.818	−	372.061i	0.290462	−	0.480698i
$775$	883.249	−	883.249i	1.13968	−	1.13968i
$776$	−271.758	−	271.758i	−0.350204	−	0.350204i
$777$	−371.009	+	1331.39i	−0.477490	+	1.71350i
$778$	1018.21			1.30875
$779$	−985.831	+	985.831i	−1.26551	+	1.26551i
$780$	−0.622647	−	1.10372i	−0.000798266	−	0.00141503i
$781$	−201.539			−0.258053
$782$	−162.239	−	206.898i	−0.207467	−	0.264576i
$783$	2.37363	−	79.3367i	0.00303146	−	0.101324i
$784$			917.746i			1.17059i
$785$	−0.615056	+	0.615056i	−0.000783511	+	0.000783511i
$786$	721.283	+	1278.57i	0.917663	+	1.62668i
$787$	538.253	+	538.253i	0.683930	+	0.683930i	0.960883	−	0.276953i	$-0.0893247\pi$
$787$	538.253	+	538.253i	0.683930	+	0.683930i	−0.276953	+	0.960883i	$0.589325\pi$
$788$	−60.9018	−	60.9018i	−0.0772866	−	0.0772866i
$789$	167.594	−	601.421i	0.212413	−	0.762257i
$790$			1.91322i			0.00242180i
$791$	−1255.59			−1.58734
$792$	−37.4241	−	151.706i	−0.0472527	−	0.191548i
$793$	−258.334	+	258.334i	−0.325768	+	0.325768i
$794$	1327.91	−	1327.91i	1.67243	−	1.67243i
$795$	−2.41872	−	4.28750i	−0.00304241	−	0.00539308i
$796$	−72.4701	−	72.4701i	−0.0910428	−	0.0910428i
$797$	−1413.34			−1.77332			−0.886661	−	0.462421i	$-0.846981\pi$
$797$	−1413.34			−1.77332			−0.886661	+	0.462421i	$0.846981\pi$
$798$	−1426.97	+	805.003i	−1.78819	+	1.00878i
$799$	163.230	−	1349.21i	0.204293	−	1.68862i
$800$		−	844.195i		−	1.05524i
$801$	−408.787	+	676.520i	−0.510346	+	0.844595i
$802$	−744.499	−	744.499i	−0.928303	−	0.928303i
$803$			123.980i			0.154396i
$804$	201.568	−	723.338i	0.250707	−	0.899675i
$805$	−1.27850	+	1.27850i	−0.00158820	+	0.00158820i
$806$	523.736	+	523.736i	0.649797	+	0.649797i
$807$	17.5172	+	31.0516i	0.0217066	+	0.0384779i
$808$		−	591.877i		−	0.732521i
$809$	327.290	+	327.290i	0.404561	+	0.404561i	0.879837	−	0.475276i	$-0.157652\pi$
$809$	327.290	+	327.290i	0.404561	+	0.404561i	−0.475276	+	0.879837i	$0.657652\pi$
$810$	5.91033	+	1.83915i	0.00729670	+	0.00227056i
$811$	−436.722	−	436.722i	−0.538498	−	0.538498i	0.384589	−	0.923088i	$-0.374343\pi$
$811$	−436.722	−	436.722i	−0.538498	−	0.538498i	−0.923088	+	0.384589i	$0.874343\pi$
$812$		−	68.2297i		−	0.0840267i
$813$	245.086	−	879.505i	0.301459	−	1.08180i
$814$		−	505.523i		−	0.621036i
$815$		−	0.899880i		−	0.00110415i
$816$	387.042	−	935.812i	0.474316	−	1.14683i
$817$	−423.807			−0.518736
$818$	−241.514			−0.295249
$819$	500.459	−	123.457i	0.611061	−	0.150742i
$820$	4.52782			0.00552173
$821$	156.578	−	156.578i	0.190716	−	0.190716i	−0.605290	−	0.796005i	$-0.706943\pi$
$821$	156.578	−	156.578i	0.190716	−	0.190716i	0.796005	+	0.605290i	$0.206943\pi$
$822$	−1408.12	−	392.393i	−1.71304	−	0.477364i
$823$	221.300	−	221.300i	0.268895	−	0.268895i	−0.559760	−	0.828655i	$-0.689107\pi$
$823$	221.300	−	221.300i	0.268895	−	0.268895i	0.828655	+	0.559760i	$0.189107\pi$
$824$	−338.666			−0.411002
$825$	156.224	+	276.927i	0.189362	+	0.335669i
$826$	93.1297	−	93.1297i	0.112748	−	0.112748i
$827$	−431.211	−	431.211i	−0.521415	−	0.521415i	0.396583	−	0.917999i	$-0.370196\pi$
$827$	−431.211	−	431.211i	−0.521415	−	0.521415i	−0.917999	+	0.396583i	$0.870196\pi$
$828$	31.3972	+	127.275i	0.0379194	+	0.153714i
$829$	−846.071			−1.02059			−0.510296	−	0.859999i	$-0.670464\pi$
$829$	−846.071			−1.02059			−0.510296	+	0.859999i	$0.670464\pi$
$830$	4.65220	−	4.65220i	0.00560506	−	0.00560506i
$831$	125.764	−	70.9477i	0.151341	−	0.0853763i
$832$	34.3909			0.0413353
$833$	94.3689	−	780.025i	0.113288	−	0.936405i
$834$	180.422	−	101.782i	0.216333	−	0.122041i
$835$			7.18124i			0.00860029i
$836$	158.010	−	158.010i	0.189007	−	0.189007i
$837$	−1348.48	−	40.3443i	−1.61108	−	0.0482011i
$838$	−20.8039	−	20.8039i	−0.0248257	−	0.0248257i
$839$	746.151	+	746.151i	0.889333	+	0.889333i	0.994459	−	0.105126i	$-0.0335245\pi$
$839$	746.151	+	746.151i	0.889333	+	0.889333i	−0.105126	+	0.994459i	$0.533524\pi$
$840$	−3.49420	−	0.973707i	−0.00415976	−	0.00115917i
$841$			832.358i			0.989724i
$842$	543.657			0.645673
$843$	−228.094	+	818.529i	−0.270575	+	0.970972i
$844$	189.023	−	189.023i	0.223961	−	0.223961i
$845$	−2.87876	+	2.87876i	−0.00340682	+	0.00340682i
$846$	−939.766	+	1555.26i	−1.11083	+	1.83837i
$847$	−710.876	−	710.876i	−0.839286	−	0.839286i
$848$	1076.84			1.26986
$849$	−129.404	−	229.386i	−0.152420	−	0.270184i
$850$	−128.913	+	1065.56i	−0.151663	+	1.25360i
$851$		−	289.122i		−	0.339744i
$852$	166.669	+	295.443i	0.195621	+	0.346764i
$853$	−308.095	−	308.095i	−0.361190	−	0.361190i	0.503061	−	0.864251i	$-0.332207\pi$
$853$	−308.095	−	308.095i	−0.361190	−	0.361190i	−0.864251	+	0.503061i	$0.832207\pi$
$854$		−	1534.00i		−	1.79625i
$855$	−1.44535	−	5.85899i	−0.00169046	−	0.00685262i
$856$	256.022	−	256.022i	0.299091	−	0.299091i
$857$	531.097	+	531.097i	0.619717	+	0.619717i	0.945459	−	0.325742i	$-0.105614\pi$
$857$	531.097	+	531.097i	0.619717	+	0.619717i	−0.325742	+	0.945459i	$0.605614\pi$
$858$	−164.208	+	92.6353i	−0.191385	+	0.107967i
$859$			1037.60i			1.20791i	0.797017	+	0.603956i	$0.206410\pi$
$859$			1037.60i			1.20791i	−0.797017	+	0.603956i	$0.793590\pi$
$860$	0.973252	+	0.973252i	0.00113169	+	0.00113169i
$861$	−494.388	+	1774.14i	−0.574202	+	2.06055i
$862$	1419.04	+	1419.04i	1.64622	+	1.64622i
$863$		−	1270.43i		−	1.47210i	−0.676925	−	0.736052i	$-0.736688\pi$
$863$		−	1270.43i		−	1.47210i	0.676925	−	0.736052i	$-0.263312\pi$
$864$	−663.706	+	625.146i	−0.768179	+	0.723548i
$865$			7.37624i			0.00852744i
$866$			129.535i			0.149578i
$867$	−425.187	+	755.582i	−0.490412	+	0.871491i
$868$	−1159.69			−1.33605
$869$	106.142			0.122143
$870$	0.649206	+	0.180910i	0.000746214	+	0.000207943i
$871$	617.653			0.709131
$872$	−274.272	+	274.272i	−0.314532	+	0.314532i
$873$	−202.298	−	820.055i	−0.231728	−	0.939353i
$874$	242.347	−	242.347i	0.277285	−	0.277285i
$875$	14.7624			0.0168714
$876$	181.746	−	102.529i	0.207472	−	0.117042i
$877$	−38.0693	+	38.0693i	−0.0434085	+	0.0434085i	−0.728478	−	0.685069i	$-0.759772\pi$
$877$	−38.0693	+	38.0693i	−0.0434085	+	0.0434085i	0.685069	+	0.728478i	$0.259772\pi$
$878$	1149.83	+	1149.83i	1.30960	+	1.30960i
$879$	−633.482	−	176.529i	−0.720685	−	0.200829i
$880$	2.54719			0.00289454
$881$	354.173	−	354.173i	0.402013	−	0.402013i	−0.476929	−	0.878942i	$-0.658250\pi$
$881$	354.173	−	354.173i	0.402013	−	0.402013i	0.878942	+	0.476929i	$0.158250\pi$
$882$	−543.312	+	899.151i	−0.616000	+	1.01945i
$883$	1084.70			1.22843			0.614215	−	0.789139i	$-0.289473\pi$
$883$	1084.70			1.22843			0.614215	+	0.789139i	$0.289473\pi$
$884$	−235.611	−	28.5046i	−0.266528	−	0.0322451i
$885$	0.238354	+	0.422514i	0.000269327	+	0.000477417i
$886$		−	1807.02i		−	2.03952i
$887$	−109.008	+	109.008i	−0.122895	+	0.122895i	−0.765880	−	0.642984i	$-0.777696\pi$
$887$	−109.008	+	109.008i	−0.122895	+	0.122895i	0.642984	+	0.765880i	$0.277696\pi$
$888$	505.190	−	284.994i	0.568908	−	0.320939i
$889$	−870.124	−	870.124i	−0.978767	−	0.978767i
$890$	−4.74575	−	4.74575i	−0.00533230	−	0.00533230i
$891$	102.033	−	327.894i	0.114515	−	0.368007i
$892$			569.238i			0.638159i
$893$	1771.57			1.98384
$894$	−677.512	−	188.798i	−0.757844	−	0.211184i
$895$	−2.59630	+	2.59630i	−0.00290089	+	0.00290089i
$896$	829.910	−	829.910i	0.926239	−	0.926239i
$897$	−93.9152	+	52.9806i	−0.104699	+	0.0590643i
$898$	−525.220	−	525.220i	−0.584878	−	0.584878i
$899$	−146.885			−0.163388
$900$	276.762	−	458.026i	0.307513	−	0.508918i
$901$	−915.247	−	110.728i	−1.01581	−	0.122895i
$902$		−	673.633i		−	0.746822i
$903$	−487.618	+	275.081i	−0.539998	+	0.304630i
$904$	372.598	+	372.598i	0.412166	+	0.412166i
$905$		−	1.30935i		−	0.00144679i
$906$	73.5614	+	20.4989i	0.0811936	+	0.0226257i
$907$	−660.017	+	660.017i	−0.727693	+	0.727693i	−0.970160	−	0.242467i	$-0.922043\pi$
$907$	−660.017	+	660.017i	−0.727693	+	0.727693i	0.242467	+	0.970160i	$0.422043\pi$
$908$	11.3878	+	11.3878i	0.0125417	+	0.0125417i
$909$	672.722	−	1113.32i	0.740069	−	1.22477i
$910$			4.37673i			0.00480960i
$911$	−101.875	−	101.875i	−0.111828	−	0.111828i	0.648979	−	0.760807i	$-0.275196\pi$
$911$	−101.875	−	101.875i	−0.111828	−	0.111828i	−0.760807	+	0.648979i	$0.775196\pi$
$912$	1271.63	+	354.358i	1.39433	+	0.388550i
$913$	−258.096	−	258.096i	−0.282690	−	0.282690i
$914$			1739.28i			1.90293i
$915$	5.44278	+	1.51671i	0.00594840	+	0.00165760i
$916$		−	152.338i		−	0.166307i
$917$		−	1890.61i		−	2.06173i
$918$	933.207	−	687.720i	1.01657	−	0.749151i
$919$	164.434			0.178927			0.0894634	−	0.995990i	$-0.471485\pi$
$919$	164.434			0.178927			0.0894634	+	0.995990i	$0.471485\pi$
$920$	0.758796			0.000824778
$921$	−73.2418	+	262.832i	−0.0795243	+	0.285377i
$922$	1044.23			1.13257
$923$	−197.297	+	197.297i	−0.213756	+	0.213756i
$924$	79.2409	−	284.360i	0.0857586	−	0.307749i
$925$	−834.586	+	834.586i	−0.902255	+	0.902255i
$926$	−2188.81			−2.36373
$927$	−637.029	−	384.924i	−0.687194	−	0.415237i
$928$	−70.1953	+	70.1953i	−0.0756415	+	0.0756415i
$929$	230.277	+	230.277i	0.247876	+	0.247876i	0.820099	−	0.572222i	$-0.193919\pi$
$929$	230.277	+	230.277i	0.247876	+	0.247876i	−0.572222	+	0.820099i	$0.693919\pi$
$930$	3.07491	−	11.0345i	0.00330636	−	0.0118650i
$931$	1024.21			1.10011
$932$	279.338	−	279.338i	0.299719	−	0.299719i
$933$	533.307	+	945.356i	0.571604	+	1.01324i
$934$	1887.70			2.02110
$935$	−2.16495	−	0.261920i	−0.00231546	−	0.000280128i
$936$	−185.149	−	111.876i	−0.197808	−	0.119526i
$937$		−	1116.40i		−	1.19147i	−0.803183	−	0.595733i	$-0.796862\pi$
$937$		−	1116.40i		−	1.19147i	0.803183	−	0.595733i	$-0.203138\pi$
$938$	−1833.82	+	1833.82i	−1.95503	+	1.95503i
$939$	−95.6627	−	169.575i	−0.101877	−	0.180591i
$940$	−4.06832	−	4.06832i	−0.00432800	−	0.00432800i
$941$	−1117.63	−	1117.63i	−1.18770	−	1.18770i	−0.977701	−	0.210003i	$-0.932652\pi$
$941$	−1117.63	−	1117.63i	−1.18770	−	1.18770i	−0.210003	−	0.977701i	$-0.567348\pi$
$942$	58.4678	−	209.815i	0.0620677	−	0.222733i
$943$		−	385.269i		−	0.408557i
$944$	−106.118			−0.112413
$945$	−5.46587	−	5.80302i	−0.00578399	−	0.00614076i
$946$	144.797	−	144.797i	0.153062	−	0.153062i
$947$	−1056.51	+	1056.51i	−1.11564	+	1.11564i	−0.123264	+	0.992374i	$0.539336\pi$
$947$	−1056.51	+	1056.51i	−1.11564	+	1.11564i	−0.992374	+	0.123264i	$0.960664\pi$
$948$	−87.7773	−	155.597i	−0.0925921	−	0.164132i
$949$	121.370	+	121.370i	0.127892	+	0.127892i
$950$	−1399.13			−1.47276
$951$	454.283	−	256.276i	0.477690	−	0.269480i
$952$	−534.573	+	419.186i	−0.561527	+	0.440321i
$953$			753.109i			0.790251i	0.918627	+	0.395126i	$0.129299\pi$
$953$			753.109i			0.790251i	−0.918627	+	0.395126i	$0.870701\pi$
$954$	1055.02	+	637.498i	1.10590	+	0.668237i
$955$	−0.583953	−	0.583953i	−0.000611469	−	0.000611469i
$956$		−	380.413i		−	0.397921i
$957$	10.0366	−	36.0168i	0.0104875	−	0.0376351i
$958$	1141.57	−	1141.57i	1.19162	−	1.19162i
$959$	1331.20	+	1331.20i	1.38812	+	1.38812i
$960$	−0.261331	−	0.463244i	−0.000272220	−	0.000482546i
$961$			1535.60i			1.59791i
$962$	−494.881	−	494.881i	−0.514429	−	0.514429i
$963$	772.569	−	190.584i	0.802253	−	0.197907i
$964$	−203.222	−	203.222i	−0.210811	−	0.210811i
$965$			8.72176i			0.00903809i
$966$	121.535	−	436.136i	0.125813	−	0.451487i
$967$			473.999i			0.490174i	0.969501	+	0.245087i	$0.0788166\pi$
$967$			473.999i			0.490174i	−0.969501	+	0.245087i	$0.921183\pi$
$968$			421.908i			0.435855i
$969$	−1044.37	−	431.940i	−1.07778	−	0.445758i
$970$	7.17174			0.00739355
$971$	994.798			1.02451			0.512254	−	0.858834i	$-0.328811\pi$
$971$	994.798			1.02451			0.512254	+	0.858834i	$0.328811\pi$
$972$	−565.049	+	121.588i	−0.581326	+	0.125091i
$973$	−266.788			−0.274191
$974$	144.885	−	144.885i	0.148752	−	0.148752i
$975$	424.032	+	118.162i	0.434905	+	0.121192i
$976$	−873.969	+	873.969i	−0.895460	+	0.895460i
$977$	−12.3001			−0.0125897			−0.00629484	−	0.999980i	$-0.502004\pi$
$977$	−12.3001			−0.0125897			−0.00629484	+	0.999980i	$0.502004\pi$
$978$	110.717	+	196.260i	0.113207	+	0.200675i
$979$	−263.286	+	263.286i	−0.268933	+	0.268933i
$980$	−2.35204	−	2.35204i	−0.00240004	−	0.00240004i
$981$	−827.639	+	204.169i	−0.843668	+	0.208123i
$982$	−539.742			−0.549635
$983$	−327.122	+	327.122i	−0.332779	+	0.332779i	−0.853641	−	0.520862i	$-0.825611\pi$
$983$	−327.122	+	327.122i	−0.332779	+	0.332779i	0.520862	+	0.853641i	$0.325611\pi$
$984$	673.190	−	379.768i	0.684136	−	0.385943i
$985$	−1.09565			−0.00111234
$986$	99.3212	−	77.8828i	0.100731	−	0.0789886i
$987$	2038.31	−	1149.87i	2.06515	−	1.16502i
$988$		−	309.367i		−	0.313125i
$989$	82.8134	−	82.8134i	0.0837345	−	0.0837345i
$990$	2.49558	+	1.50796i	0.00252079	+	0.00152319i
$991$	1169.11	+	1169.11i	1.17972	+	1.17972i	0.979815	+	0.199908i	$0.0640645\pi$
$991$	1169.11	+	1169.11i	1.17972	+	1.17972i	0.199908	+	0.979815i	$0.435936\pi$
$992$	1193.10	+	1193.10i	1.20272	+	1.20272i
$993$	−95.2811	−	26.5514i	−0.0959527	−	0.0267386i
$994$		−	1171.55i		−	1.17863i
$995$	−1.30377			−0.00131032
$996$	−164.910	+	591.789i	−0.165573	+	0.594166i
$997$	−277.371	+	277.371i	−0.278205	+	0.278205i	−0.832392	−	0.554187i	$-0.813029\pi$
$997$	−277.371	+	277.371i	−0.278205	+	0.278205i	0.554187	+	0.832392i	$0.313029\pi$
$998$	−457.330	+	457.330i	−0.458247	+	0.458247i
$999$	1274.18	+	38.1216i	1.27546	+	0.0381597i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.3.f.a.47.8	yes	20
3.2	odd	2	inner	51.3.f.a.47.3	yes	20
17.4	even	4	inner	51.3.f.a.38.3	✓	20
51.38	odd	4	inner	51.3.f.a.38.8	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.3.f.a.38.3	✓	20	17.4	even	4	inner
51.3.f.a.38.8	yes	20	51.38	odd	4	inner
51.3.f.a.47.3	yes	20	3.2	odd	2	inner
51.3.f.a.47.8	yes	20	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	51.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.52557 q^{2} +(-0.805308 + 2.88989i) q^{3} +2.37853 q^{4} +(0.0213954 - 0.0213954i) q^{5} +(-2.03387 + 7.29864i) q^{6} +(6.89994 - 6.89994i) q^{7} -4.09515 q^{8} +(-7.70296 - 4.65451i) q^{9} +(0.0540358 - 0.0540358i) q^{10} +(-2.99781 - 2.99781i) q^{11} +(-1.91545 + 6.87369i) q^{12} -5.86939 q^{13} +(17.4263 - 17.4263i) q^{14} +(0.0446006 + 0.0790604i) q^{15} -19.8567 q^{16} +(16.8769 + 2.04180i) q^{17} +(-19.4544 - 11.7553i) q^{18} +22.1601i q^{19} +(0.0508896 - 0.0508896i) q^{20} +(14.3835 + 25.4967i) q^{21} +(-7.57118 - 7.57118i) q^{22} +(-4.33017 - 4.33017i) q^{23} +(3.29786 - 11.8345i) q^{24} +24.9991i q^{25} -14.8236 q^{26} +(19.6543 - 18.5124i) q^{27} +(16.4117 - 16.4117i) q^{28} +(2.07869 - 2.07869i) q^{29} +(0.112642 + 0.199673i) q^{30} +(-35.3313 - 35.3313i) q^{31} -33.7690 q^{32} +(11.0775 - 6.24918i) q^{33} +(42.6240 + 5.15673i) q^{34} -0.295254i q^{35} +(-18.3217 - 11.0709i) q^{36} +(33.3847 + 33.3847i) q^{37} +55.9671i q^{38} +(4.72667 - 16.9619i) q^{39} +(-0.0876174 + 0.0876174i) q^{40} +(44.4867 + 44.4867i) q^{41} +(36.3266 + 64.3938i) q^{42} +19.1248i q^{43} +(-7.13037 - 7.13037i) q^{44} +(-0.264393 + 0.0652228i) q^{45} +(-10.9362 - 10.9362i) q^{46} -79.9440i q^{47} +(15.9908 - 57.3838i) q^{48} -46.2184i q^{49} +63.1371i q^{50} +(-19.4917 + 47.1283i) q^{51} -13.9605 q^{52} -54.2306 q^{53} +(49.6384 - 46.7545i) q^{54} -0.128279 q^{55} +(-28.2563 + 28.2563i) q^{56} +(-64.0404 - 17.8458i) q^{57} +(5.24989 - 5.24989i) q^{58} +5.34420 q^{59} +(0.106084 + 0.188047i) q^{60} +(44.0138 - 44.0138i) q^{61} +(-89.2317 - 89.2317i) q^{62} +(-85.2658 + 21.0341i) q^{63} -5.85937 q^{64} +(-0.125578 + 0.125578i) q^{65} +(27.9770 - 15.7828i) q^{66} -105.233 q^{67} +(40.1423 + 4.85649i) q^{68} +(16.0008 - 9.02659i) q^{69} -0.745687i q^{70} +(33.6145 - 33.6145i) q^{71} +(31.5447 + 19.0609i) q^{72} +(-20.6784 - 20.6784i) q^{73} +(84.3155 + 84.3155i) q^{74} +(-72.2447 - 20.1320i) q^{75} +52.7085i q^{76} -41.3694 q^{77} +(11.9376 - 42.8386i) q^{78} +(-17.7033 + 17.7033i) q^{79} +(-0.424843 + 0.424843i) q^{80} +(37.6711 + 71.7070i) q^{81} +(112.354 + 112.354i) q^{82} +86.0948 q^{83} +(34.2116 + 60.6446i) q^{84} +(0.404775 - 0.317404i) q^{85} +48.3010i q^{86} +(4.33320 + 7.68118i) q^{87} +(12.2765 + 12.2765i) q^{88} -87.8261i q^{89} +(-0.667745 + 0.164725i) q^{90} +(-40.4985 + 40.4985i) q^{91} +(-10.2994 - 10.2994i) q^{92} +(130.556 - 73.6510i) q^{93} -201.904i q^{94} +(0.474126 + 0.474126i) q^{95} +(27.1945 - 97.5889i) q^{96} +(66.3611 + 66.3611i) q^{97} -116.728i q^{98} +(9.13865 + 37.0453i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3} + 24 q^{4} - 2 q^{6} - 4 q^{7} - 16 q^{10} - 42 q^{12} - 12 q^{13} - 64 q^{16} - 4 q^{18} + 88 q^{21} - 40 q^{22} - 82 q^{24} + 54 q^{27} - 160 q^{28} + 48 q^{31} + 264 q^{33} + 152 q^{34}+ \cdots - 864 q^{99}+O(q^{100}) \) 20 * q - 6 * q^3 + 24 * q^4 - 2 * q^6 - 4 * q^7 - 16 * q^10 - 42 * q^12 - 12 * q^13 - 64 * q^16 - 4 * q^18 + 88 * q^21 - 40 * q^22 - 82 * q^24 + 54 * q^27 - 160 * q^28 + 48 * q^31 + 264 * q^33 + 152 * q^34 + 32 * q^37 + 56 * q^39 + 52 * q^40 + 64 * q^45 + 388 * q^46 - 230 * q^48 - 298 * q^51 + 64 * q^52 - 254 * q^54 - 204 * q^55 - 24 * q^57 + 396 * q^58 - 336 * q^61 - 400 * q^63 - 480 * q^64 - 408 * q^67 - 132 * q^69 + 276 * q^72 - 88 * q^73 - 358 * q^75 + 380 * q^78 - 172 * q^79 + 388 * q^81 + 372 * q^82 + 1320 * q^84 + 648 * q^85 - 156 * q^88 + 672 * q^90 - 124 * q^91 + 194 * q^96 + 688 * q^97 - 864 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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