LMFDB - Embedded newform 156.3.l.a.47.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,3,Mod(47,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 1]))

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

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

chi := DirichletCharacter("156.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	156.l (of order $4$, degree $2$, 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:	$4.25069212402$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	156.47
Dual form			156.3.l.a.83.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41421 - 1.41421i) q^{2} +(-2.82843 + 1.00000i) q^{3} +4.00000i q^{4} +(-5.65685 + 5.65685i) q^{5} +(5.41421 + 2.58579i) q^{6} +(-3.00000 - 3.00000i) q^{7} +(5.65685 - 5.65685i) q^{8} +(7.00000 - 5.65685i) q^{9} +O(q^{10})$	\(q+(-1.41421 - 1.41421i) q^{2} +(-2.82843 + 1.00000i) q^{3} +4.00000i q^{4} +(-5.65685 + 5.65685i) q^{5} +(5.41421 + 2.58579i) q^{6} +(-3.00000 - 3.00000i) q^{7} +(5.65685 - 5.65685i) q^{8} +(7.00000 - 5.65685i) q^{9} +16.0000 q^{10} +(2.82843 - 2.82843i) q^{11} +(-4.00000 - 11.3137i) q^{12} -13.0000i q^{13} +8.48528i q^{14} +(10.3431 - 21.6569i) q^{15} -16.0000 q^{16} +28.2843 q^{17} +(-17.8995 - 1.89949i) q^{18} +(-17.0000 + 17.0000i) q^{19} +(-22.6274 - 22.6274i) q^{20} +(11.4853 + 5.48528i) q^{21} -8.00000 q^{22} -16.9706i q^{23} +(-10.3431 + 21.6569i) q^{24} -39.0000i q^{25} +(-18.3848 + 18.3848i) q^{26} +(-14.1421 + 23.0000i) q^{27} +(12.0000 - 12.0000i) q^{28} -22.6274i q^{29} +(-45.2548 + 16.0000i) q^{30} +(21.0000 - 21.0000i) q^{31} +(22.6274 + 22.6274i) q^{32} +(-5.17157 + 10.8284i) q^{33} +(-40.0000 - 40.0000i) q^{34} +33.9411 q^{35} +(22.6274 + 28.0000i) q^{36} +(21.0000 - 21.0000i) q^{37} +48.0833 q^{38} +(13.0000 + 36.7696i) q^{39} +64.0000i q^{40} +(-39.5980 + 39.5980i) q^{41} +(-8.48528 - 24.0000i) q^{42} +14.0000 q^{43} +(11.3137 + 11.3137i) q^{44} +(-7.59798 + 71.5980i) q^{45} +(-24.0000 + 24.0000i) q^{46} +(31.1127 - 31.1127i) q^{47} +(45.2548 - 16.0000i) q^{48} -31.0000i q^{49} +(-55.1543 + 55.1543i) q^{50} +(-80.0000 + 28.2843i) q^{51} +52.0000 q^{52} -50.9117i q^{53} +(52.5269 - 12.5269i) q^{54} +32.0000i q^{55} -33.9411 q^{56} +(31.0833 - 65.0833i) q^{57} +(-32.0000 + 32.0000i) q^{58} +(-36.7696 + 36.7696i) q^{59} +(86.6274 + 41.3726i) q^{60} +16.0000 q^{61} -59.3970 q^{62} +(-37.9706 - 4.02944i) q^{63} -64.0000i q^{64} +(73.5391 + 73.5391i) q^{65} +(22.6274 - 8.00000i) q^{66} +(1.00000 - 1.00000i) q^{67} +113.137i q^{68} +(16.9706 + 48.0000i) q^{69} +(-48.0000 - 48.0000i) q^{70} +(25.4558 + 25.4558i) q^{71} +(7.59798 - 71.5980i) q^{72} +(-7.00000 + 7.00000i) q^{73} -59.3970 q^{74} +(39.0000 + 110.309i) q^{75} +(-68.0000 - 68.0000i) q^{76} -16.9706 q^{77} +(33.6152 - 70.3848i) q^{78} -106.000i q^{79} +(90.5097 - 90.5097i) q^{80} +(17.0000 - 79.1960i) q^{81} +112.000 q^{82} +(-98.9949 - 98.9949i) q^{83} +(-21.9411 + 45.9411i) q^{84} +(-160.000 + 160.000i) q^{85} +(-19.7990 - 19.7990i) q^{86} +(22.6274 + 64.0000i) q^{87} -32.0000i q^{88} +(-79.1960 - 79.1960i) q^{89} +(112.000 - 90.5097i) q^{90} +(-39.0000 + 39.0000i) q^{91} +67.8823 q^{92} +(-38.3970 + 80.3970i) q^{93} -88.0000 q^{94} -192.333i q^{95} +(-86.6274 - 41.3726i) q^{96} +(-1.00000 - 1.00000i) q^{97} +(-43.8406 + 43.8406i) q^{98} +(3.79899 - 35.7990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 16 q^{6} - 12 q^{7} + 28 q^{9}+O(q^{10}) $ 4 * q + 16 * q^6 - 12 * q^7 + 28 * q^9	$ 4 q + 16 q^{6} - 12 q^{7} + 28 q^{9} + 64 q^{10} - 16 q^{12} + 64 q^{15} - 64 q^{16} - 32 q^{18} - 68 q^{19} + 12 q^{21} - 32 q^{22} - 64 q^{24} + 48 q^{28} + 84 q^{31} - 32 q^{33} - 160 q^{34} + 84 q^{37} + 52 q^{39} + 56 q^{43} + 128 q^{45} - 96 q^{46} - 320 q^{51} + 208 q^{52} + 80 q^{54} - 68 q^{57} - 128 q^{58} + 256 q^{60} + 64 q^{61} - 84 q^{63} + 4 q^{67} - 192 q^{70} - 128 q^{72} - 28 q^{73} + 156 q^{75} - 272 q^{76} + 208 q^{78} + 68 q^{81} + 448 q^{82} + 48 q^{84} - 640 q^{85} + 448 q^{90} - 156 q^{91} + 84 q^{93} - 352 q^{94} - 256 q^{96} - 4 q^{97} - 64 q^{99}+O(q^{100}) $ 4 * q + 16 * q^6 - 12 * q^7 + 28 * q^9 + 64 * q^10 - 16 * q^12 + 64 * q^15 - 64 * q^16 - 32 * q^18 - 68 * q^19 + 12 * q^21 - 32 * q^22 - 64 * q^24 + 48 * q^28 + 84 * q^31 - 32 * q^33 - 160 * q^34 + 84 * q^37 + 52 * q^39 + 56 * q^43 + 128 * q^45 - 96 * q^46 - 320 * q^51 + 208 * q^52 + 80 * q^54 - 68 * q^57 - 128 * q^58 + 256 * q^60 + 64 * q^61 - 84 * q^63 + 4 * q^67 - 192 * q^70 - 128 * q^72 - 28 * q^73 + 156 * q^75 - 272 * q^76 + 208 * q^78 + 68 * q^81 + 448 * q^82 + 48 * q^84 - 640 * q^85 + 448 * q^90 - 156 * q^91 + 84 * q^93 - 352 * q^94 - 256 * q^96 - 4 * q^97 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.41421	−	1.41421i	−0.707107	−	0.707107i
$2$	−1.41421	−	1.41421i	−0.707107	−	0.707107i
$3$	−2.82843	+	1.00000i	−0.942809	+	0.333333i
$3$	−2.82843	+	1.00000i	−0.942809	+	0.333333i
$4$			4.00000i			1.00000i
$5$	−5.65685	+	5.65685i	−1.13137	+	1.13137i	−0.141421	+	0.989949i	$0.545167\pi$
$5$	−5.65685	+	5.65685i	−1.13137	+	1.13137i	−0.989949	+	0.141421i	$0.954833\pi$
$6$	5.41421	+	2.58579i	0.902369	+	0.430964i
$7$	−3.00000	−	3.00000i	−0.428571	−	0.428571i	0.459570	−	0.888142i	$-0.348004\pi$
$7$	−3.00000	−	3.00000i	−0.428571	−	0.428571i	−0.888142	+	0.459570i	$0.848004\pi$
$8$	5.65685	−	5.65685i	0.707107	−	0.707107i
$9$	7.00000	−	5.65685i	0.777778	−	0.628539i
$10$	16.0000			1.60000
$11$	2.82843	−	2.82843i	0.257130	−	0.257130i	−0.566756	−	0.823886i	$-0.691802\pi$
$11$	2.82843	−	2.82843i	0.257130	−	0.257130i	0.823886	+	0.566756i	$0.191802\pi$
$12$	−4.00000	−	11.3137i	−0.333333	−	0.942809i
$13$		−	13.0000i		−	1.00000i
$13$		−	13.0000i		−	1.00000i
$14$			8.48528i			0.606092i
$15$	10.3431	−	21.6569i	0.689543	−	1.44379i
$16$	−16.0000			−1.00000
$17$	28.2843			1.66378			0.831890	−	0.554940i	$-0.187259\pi$
$17$	28.2843			1.66378			0.831890	+	0.554940i	$0.187259\pi$
$18$	−17.8995	−	1.89949i	−0.994416	−	0.105527i
$19$	−17.0000	+	17.0000i	−0.894737	+	0.894737i	−0.994965	−	0.100228i	$-0.968043\pi$
$19$	−17.0000	+	17.0000i	−0.894737	+	0.894737i	0.100228	+	0.994965i	$0.468043\pi$
$20$	−22.6274	−	22.6274i	−1.13137	−	1.13137i
$21$	11.4853	+	5.48528i	0.546918	+	0.261204i
$22$	−8.00000			−0.363636
$23$		−	16.9706i		−	0.737851i	−0.929459	−	0.368925i	$-0.879726\pi$
$23$		−	16.9706i		−	0.737851i	0.929459	−	0.368925i	$-0.120274\pi$
$24$	−10.3431	+	21.6569i	−0.430964	+	0.902369i
$25$		−	39.0000i		−	1.56000i
$26$	−18.3848	+	18.3848i	−0.707107	+	0.707107i
$27$	−14.1421	+	23.0000i	−0.523783	+	0.851852i
$28$	12.0000	−	12.0000i	0.428571	−	0.428571i
$29$		−	22.6274i		−	0.780256i	−0.920761	−	0.390128i	$-0.872431\pi$
$29$		−	22.6274i		−	0.780256i	0.920761	−	0.390128i	$-0.127569\pi$
$30$	−45.2548	+	16.0000i	−1.50849	+	0.533333i
$31$	21.0000	−	21.0000i	0.677419	−	0.677419i	−0.281996	−	0.959416i	$-0.590997\pi$
$31$	21.0000	−	21.0000i	0.677419	−	0.677419i	0.959416	+	0.281996i	$0.0909965\pi$
$32$	22.6274	+	22.6274i	0.707107	+	0.707107i
$33$	−5.17157	+	10.8284i	−0.156714	+	0.328134i
$34$	−40.0000	−	40.0000i	−1.17647	−	1.17647i
$35$	33.9411			0.969746
$36$	22.6274	+	28.0000i	0.628539	+	0.777778i
$37$	21.0000	−	21.0000i	0.567568	−	0.567568i	−0.363879	−	0.931446i	$-0.618548\pi$
$37$	21.0000	−	21.0000i	0.567568	−	0.567568i	0.931446	+	0.363879i	$0.118548\pi$
$38$	48.0833			1.26535
$39$	13.0000	+	36.7696i	0.333333	+	0.942809i
$40$			64.0000i			1.60000i
$41$	−39.5980	+	39.5980i	−0.965804	+	0.965804i	−0.999434	−	0.0336300i	$-0.989293\pi$
$41$	−39.5980	+	39.5980i	−0.965804	+	0.965804i	0.0336300	+	0.999434i	$0.489293\pi$
$42$	−8.48528	−	24.0000i	−0.202031	−	0.571429i
$43$	14.0000			0.325581			0.162791	−	0.986661i	$-0.447950\pi$
$43$	14.0000			0.325581			0.162791	+	0.986661i	$0.447950\pi$
$44$	11.3137	+	11.3137i	0.257130	+	0.257130i
$45$	−7.59798	+	71.5980i	−0.168844	+	1.59107i
$46$	−24.0000	+	24.0000i	−0.521739	+	0.521739i
$47$	31.1127	−	31.1127i	0.661972	−	0.661972i	−0.293872	−	0.955845i	$-0.594944\pi$
$47$	31.1127	−	31.1127i	0.661972	−	0.661972i	0.955845	+	0.293872i	$0.0949441\pi$
$48$	45.2548	−	16.0000i	0.942809	−	0.333333i
$49$		−	31.0000i		−	0.632653i
$50$	−55.1543	+	55.1543i	−1.10309	+	1.10309i
$51$	−80.0000	+	28.2843i	−1.56863	+	0.554594i
$52$	52.0000			1.00000
$53$		−	50.9117i		−	0.960598i	−0.877105	−	0.480299i	$-0.840528\pi$
$53$		−	50.9117i		−	0.960598i	0.877105	−	0.480299i	$-0.159472\pi$
$54$	52.5269	−	12.5269i	0.972721	−	0.231980i
$55$			32.0000i			0.581818i
$56$	−33.9411			−0.606092
$57$	31.0833	−	65.0833i	0.545320	−	1.14181i
$58$	−32.0000	+	32.0000i	−0.551724	+	0.551724i
$59$	−36.7696	+	36.7696i	−0.623213	+	0.623213i	−0.946352	−	0.323139i	$-0.895262\pi$
$59$	−36.7696	+	36.7696i	−0.623213	+	0.623213i	0.323139	+	0.946352i	$0.395262\pi$
$60$	86.6274	+	41.3726i	1.44379	+	0.689543i
$61$	16.0000			0.262295			0.131148	−	0.991363i	$-0.458134\pi$
$61$	16.0000			0.262295			0.131148	+	0.991363i	$0.458134\pi$
$62$	−59.3970			−0.958016
$63$	−37.9706	−	4.02944i	−0.602707	−	0.0639593i
$64$		−	64.0000i		−	1.00000i
$65$	73.5391	+	73.5391i	1.13137	+	1.13137i
$66$	22.6274	−	8.00000i	0.342840	−	0.121212i
$67$	1.00000	−	1.00000i	0.0149254	−	0.0149254i	−0.699605	−	0.714530i	$-0.746641\pi$
$67$	1.00000	−	1.00000i	0.0149254	−	0.0149254i	0.714530	+	0.699605i	$0.246641\pi$
$68$			113.137i			1.66378i
$69$	16.9706	+	48.0000i	0.245950	+	0.695652i
$70$	−48.0000	−	48.0000i	−0.685714	−	0.685714i
$71$	25.4558	+	25.4558i	0.358533	+	0.358533i	0.863272	−	0.504739i	$-0.168411\pi$
$71$	25.4558	+	25.4558i	0.358533	+	0.358533i	−0.504739	+	0.863272i	$0.668411\pi$
$72$	7.59798	−	71.5980i	0.105527	−	0.994416i
$73$	−7.00000	+	7.00000i	−0.0958904	+	0.0958904i	−0.753425	−	0.657534i	$-0.771599\pi$
$73$	−7.00000	+	7.00000i	−0.0958904	+	0.0958904i	0.657534	+	0.753425i	$0.271599\pi$
$74$	−59.3970			−0.802662
$75$	39.0000	+	110.309i	0.520000	+	1.47078i
$76$	−68.0000	−	68.0000i	−0.894737	−	0.894737i
$77$	−16.9706			−0.220397
$78$	33.6152	−	70.3848i	0.430964	−	0.902369i
$79$		−	106.000i		−	1.34177i	−0.741560	−	0.670886i	$-0.765914\pi$
$79$		−	106.000i		−	1.34177i	0.741560	−	0.670886i	$-0.234086\pi$
$80$	90.5097	−	90.5097i	1.13137	−	1.13137i
$81$	17.0000	−	79.1960i	0.209877	−	0.977728i
$82$	112.000			1.36585
$83$	−98.9949	−	98.9949i	−1.19271	−	1.19271i	−0.976303	−	0.216407i	$-0.930566\pi$
$83$	−98.9949	−	98.9949i	−1.19271	−	1.19271i	−0.216407	−	0.976303i	$-0.569434\pi$
$84$	−21.9411	+	45.9411i	−0.261204	+	0.546918i
$85$	−160.000	+	160.000i	−1.88235	+	1.88235i
$86$	−19.7990	−	19.7990i	−0.230221	−	0.230221i
$87$	22.6274	+	64.0000i	0.260085	+	0.735632i
$88$		−	32.0000i		−	0.363636i
$89$	−79.1960	−	79.1960i	−0.889842	−	0.889842i	0.104665	−	0.994508i	$-0.466623\pi$
$89$	−79.1960	−	79.1960i	−0.889842	−	0.889842i	−0.994508	+	0.104665i	$0.966623\pi$
$90$	112.000	−	90.5097i	1.24444	−	1.00566i
$91$	−39.0000	+	39.0000i	−0.428571	+	0.428571i
$92$	67.8823			0.737851
$93$	−38.3970	+	80.3970i	−0.412871	+	0.864484i
$94$	−88.0000			−0.936170
$95$		−	192.333i		−	2.02456i
$96$	−86.6274	−	41.3726i	−0.902369	−	0.430964i
$97$	−1.00000	−	1.00000i	−0.0103093	−	0.0103093i	0.701933	−	0.712243i	$-0.252320\pi$
$97$	−1.00000	−	1.00000i	−0.0103093	−	0.0103093i	−0.712243	+	0.701933i	$0.752320\pi$
$98$	−43.8406	+	43.8406i	−0.447353	+	0.447353i
$99$	3.79899	−	35.7990i	0.0383736	−	0.361606i
$100$	156.000			1.56000
$101$	−39.5980			−0.392059			−0.196030	−	0.980598i	$-0.562805\pi$
$101$	−39.5980			−0.392059			−0.196030	+	0.980598i	$0.562805\pi$
$102$	153.137	+	73.1371i	1.50134	+	0.717030i
$103$	70.0000			0.679612			0.339806	−	0.940496i	$-0.389639\pi$
$103$	70.0000			0.679612			0.339806	+	0.940496i	$0.389639\pi$
$104$	−73.5391	−	73.5391i	−0.707107	−	0.707107i
$105$	−96.0000	+	33.9411i	−0.914286	+	0.323249i
$106$	−72.0000	+	72.0000i	−0.679245	+	0.679245i
$107$	158.392			1.48030			0.740149	−	0.672443i	$-0.234755\pi$
$107$	158.392			1.48030			0.740149	+	0.672443i	$0.234755\pi$
$108$	−92.0000	−	56.5685i	−0.851852	−	0.523783i
$109$	−3.00000	−	3.00000i	−0.0275229	−	0.0275229i	0.693211	−	0.720734i	$-0.256195\pi$
$109$	−3.00000	−	3.00000i	−0.0275229	−	0.0275229i	−0.720734	+	0.693211i	$0.756195\pi$
$110$	45.2548	−	45.2548i	0.411408	−	0.411408i
$111$	−38.3970	+	80.3970i	−0.345919	+	0.724297i
$112$	48.0000	+	48.0000i	0.428571	+	0.428571i
$113$		−	16.9706i		−	0.150182i	−0.997177	−	0.0750910i	$-0.976075\pi$
$113$		−	16.9706i		−	0.150182i	0.997177	−	0.0750910i	$-0.0239247\pi$
$114$	−136.000	+	48.0833i	−1.19298	+	0.421783i
$115$	96.0000	+	96.0000i	0.834783	+	0.834783i
$116$	90.5097			0.780256
$117$	−73.5391	−	91.0000i	−0.628539	−	0.777778i
$118$	104.000			0.881356
$119$	−84.8528	−	84.8528i	−0.713049	−	0.713049i
$120$	−64.0000	−	181.019i	−0.533333	−	1.50849i
$121$			105.000i			0.867769i
$122$	−22.6274	−	22.6274i	−0.185471	−	0.185471i
$123$	72.4020	−	151.598i	0.588634	−	1.23250i
$124$	84.0000	+	84.0000i	0.677419	+	0.677419i
$125$	79.1960	+	79.1960i	0.633568	+	0.633568i
$126$	48.0000	+	59.3970i	0.380952	+	0.471405i
$127$	−224.000			−1.76378			−0.881890	−	0.471456i	$-0.843729\pi$
$127$	−224.000			−1.76378			−0.881890	+	0.471456i	$0.843729\pi$
$128$	−90.5097	+	90.5097i	−0.707107	+	0.707107i
$129$	−39.5980	+	14.0000i	−0.306961	+	0.108527i
$130$		−	208.000i		−	1.60000i
$131$	158.392			1.20910			0.604549	−	0.796568i	$-0.293353\pi$
$131$	158.392			1.20910			0.604549	+	0.796568i	$0.293353\pi$
$132$	−43.3137	−	20.6863i	−0.328134	−	0.156714i
$133$	102.000			0.766917
$134$	−2.82843			−0.0211077
$135$	−50.1076	−	210.108i	−0.371168	−	1.55635i
$136$	160.000	−	160.000i	1.17647	−	1.17647i
$137$	−67.8823	−	67.8823i	−0.495491	−	0.495491i	0.414540	−	0.910031i	$-0.363942\pi$
$137$	−67.8823	−	67.8823i	−0.495491	−	0.495491i	−0.910031	+	0.414540i	$0.863942\pi$
$138$	43.8823	−	91.8823i	0.317987	−	0.665813i
$139$		−	32.0000i		−	0.230216i	−0.993353	−	0.115108i	$-0.963279\pi$
$139$		−	32.0000i		−	0.230216i	0.993353	−	0.115108i	$-0.0367214\pi$
$140$			135.765i			0.969746i
$141$	−56.8873	+	119.113i	−0.403456	+	0.844771i
$142$		−	72.0000i		−	0.507042i
$143$	−36.7696	−	36.7696i	−0.257130	−	0.257130i
$144$	−112.000	+	90.5097i	−0.777778	+	0.628539i
$145$	128.000	+	128.000i	0.882759	+	0.882759i
$146$	19.7990			0.135610
$147$	31.0000	+	87.6812i	0.210884	+	0.596471i
$148$	84.0000	+	84.0000i	0.567568	+	0.567568i
$149$	79.1960	−	79.1960i	0.531517	−	0.531517i	−0.389507	−	0.921024i	$-0.627355\pi$
$149$	79.1960	−	79.1960i	0.531517	−	0.531517i	0.921024	+	0.389507i	$0.127355\pi$
$150$	100.846	−	211.154i	0.672304	−	1.40770i
$151$	141.000	+	141.000i	0.933775	+	0.933775i	0.997939	−	0.0641645i	$-0.0204382\pi$
$151$	141.000	+	141.000i	0.933775	+	0.933775i	−0.0641645	+	0.997939i	$0.520438\pi$
$152$			192.333i			1.26535i
$153$	197.990	−	160.000i	1.29405	−	1.04575i
$154$	24.0000	+	24.0000i	0.155844	+	0.155844i
$155$			237.588i			1.53283i
$156$	−147.078	+	52.0000i	−0.942809	+	0.333333i
$157$	102.000			0.649682			0.324841	−	0.945769i	$-0.394689\pi$
$157$	102.000			0.649682			0.324841	+	0.945769i	$0.394689\pi$
$158$	−149.907	+	149.907i	−0.948776	+	0.948776i
$159$	50.9117	+	144.000i	0.320199	+	0.905660i
$160$	−256.000			−1.60000
$161$	−50.9117	+	50.9117i	−0.316222	+	0.316222i
$162$	−136.042	+	87.9584i	−0.839763	+	0.542953i
$163$	−207.000	−	207.000i	−1.26994	−	1.26994i	−0.946119	−	0.323820i	$-0.895033\pi$
$163$	−207.000	−	207.000i	−1.26994	−	1.26994i	−0.323820	−	0.946119i	$-0.604967\pi$
$164$	−158.392	−	158.392i	−0.965804	−	0.965804i
$165$	−32.0000	−	90.5097i	−0.193939	−	0.548543i
$166$			280.000i			1.68675i
$167$	65.0538	−	65.0538i	0.389544	−	0.389544i	−0.484981	−	0.874525i	$-0.661173\pi$
$167$	65.0538	−	65.0538i	0.389544	−	0.389544i	0.874525	+	0.484981i	$0.161173\pi$
$168$	96.0000	−	33.9411i	0.571429	−	0.202031i
$169$	−169.000			−1.00000
$170$	452.548			2.66205
$171$	−22.8335	+	215.167i	−0.133529	+	1.25828i
$172$			56.0000i			0.325581i
$173$	−5.65685			−0.0326986			−0.0163493	−	0.999866i	$-0.505204\pi$
$173$	−5.65685			−0.0326986			−0.0163493	+	0.999866i	$0.505204\pi$
$174$	58.5097	−	122.510i	0.336262	−	0.704079i
$175$	−117.000	+	117.000i	−0.668571	+	0.668571i
$176$	−45.2548	+	45.2548i	−0.257130	+	0.257130i
$177$	67.2304	−	140.770i	0.379833	−	0.795308i
$178$			224.000i			1.25843i
$179$			277.186i			1.54852i	0.632865	+	0.774262i	$0.281879\pi$
$179$			277.186i			1.54852i	−0.632865	+	0.774262i	$0.718121\pi$
$180$	−286.392	−	30.3919i	−1.59107	−	0.168844i
$181$			64.0000i			0.353591i	0.984248	+	0.176796i	$0.0565731\pi$
$181$			64.0000i			0.353591i	−0.984248	+	0.176796i	$0.943427\pi$
$182$	110.309			0.606092
$183$	−45.2548	+	16.0000i	−0.247294	+	0.0874317i
$184$	−96.0000	−	96.0000i	−0.521739	−	0.521739i
$185$			237.588i			1.28426i
$186$	168.000	−	59.3970i	0.903226	−	0.319339i
$187$	80.0000	−	80.0000i	0.427807	−	0.427807i
$188$	124.451	+	124.451i	0.661972	+	0.661972i
$189$	111.426	−	26.5736i	0.589558	−	0.140601i
$190$	−272.000	+	272.000i	−1.43158	+	1.43158i
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$	64.0000	+	181.019i	0.333333	+	0.942809i
$193$	63.0000	−	63.0000i	0.326425	−	0.326425i	−0.524800	−	0.851225i	$-0.675860\pi$
$193$	63.0000	−	63.0000i	0.326425	−	0.326425i	0.851225	+	0.524800i	$0.175860\pi$
$194$			2.82843i			0.0145795i
$195$	−281.539	−	134.461i	−1.44379	−	0.689543i
$196$	124.000			0.632653
$197$	56.5685	−	56.5685i	0.287150	−	0.287150i	−0.548802	−	0.835952i	$-0.684916\pi$
$197$	56.5685	−	56.5685i	0.287150	−	0.287150i	0.835952	+	0.548802i	$0.184916\pi$
$198$	−56.0000	+	45.2548i	−0.282828	+	0.228560i
$199$	128.000			0.643216			0.321608	−	0.946873i	$-0.395777\pi$
$199$	128.000			0.643216			0.321608	+	0.946873i	$0.395777\pi$
$200$	−220.617	−	220.617i	−1.10309	−	1.10309i
$201$	−1.82843	+	3.82843i	−0.00909665	+	0.0190469i
$202$	56.0000	+	56.0000i	0.277228	+	0.277228i
$203$	−67.8823	+	67.8823i	−0.334395	+	0.334395i
$204$	−113.137	−	320.000i	−0.554594	−	1.56863i
$205$		−	448.000i		−	2.18537i
$206$	−98.9949	−	98.9949i	−0.480558	−	0.480558i
$207$	−96.0000	−	118.794i	−0.463768	−	0.573884i
$208$			208.000i			1.00000i
$209$			96.1665i			0.460127i
$210$	183.765	+	87.7645i	0.875069	+	0.417926i
$211$		−	158.000i		−	0.748815i	−0.927264	−	0.374408i	$-0.877846\pi$
$211$		−	158.000i		−	0.748815i	0.927264	−	0.374408i	$-0.122154\pi$
$212$	203.647			0.960598
$213$	−97.4558	−	46.5442i	−0.457539	−	0.218517i
$214$	−224.000	−	224.000i	−1.04673	−	1.04673i
$215$	−79.1960	+	79.1960i	−0.368353	+	0.368353i
$216$	50.1076	+	210.108i	0.231980	+	0.972721i
$217$	−126.000			−0.580645
$218$			8.48528i			0.0389233i
$219$	12.7990	−	26.7990i	0.0584429	−	0.122370i
$220$	−128.000			−0.581818
$221$		−	367.696i		−	1.66378i
$222$	168.000	−	59.3970i	0.756757	−	0.267554i
$223$	187.000	−	187.000i	0.838565	−	0.838565i	−0.150105	−	0.988670i	$-0.547961\pi$
$223$	187.000	−	187.000i	0.838565	−	0.838565i	0.988670	+	0.150105i	$0.0479612\pi$
$224$		−	135.765i		−	0.606092i
$225$	−220.617	−	273.000i	−0.980521	−	1.21333i
$226$	−24.0000	+	24.0000i	−0.106195	+	0.106195i
$227$	178.191	+	178.191i	0.784982	+	0.784982i	0.980667	−	0.195685i	$-0.0626930\pi$
$227$	178.191	+	178.191i	0.784982	+	0.784982i	−0.195685	+	0.980667i	$0.562693\pi$
$228$	260.333	+	124.333i	1.14181	+	0.545320i
$229$	133.000	−	133.000i	0.580786	−	0.580786i	−0.354333	−	0.935119i	$-0.615292\pi$
$229$	133.000	−	133.000i	0.580786	−	0.580786i	0.935119	+	0.354333i	$0.115292\pi$
$230$		−	271.529i		−	1.18056i
$231$	48.0000	−	16.9706i	0.207792	−	0.0734656i
$232$	−128.000	−	128.000i	−0.551724	−	0.551724i
$233$	−33.9411			−0.145670			−0.0728350	−	0.997344i	$-0.523205\pi$
$233$	−33.9411			−0.145670			−0.0728350	+	0.997344i	$0.523205\pi$
$234$	−24.6934	+	232.693i	−0.105527	+	0.994416i
$235$			352.000i			1.49787i
$236$	−147.078	−	147.078i	−0.623213	−	0.623213i
$237$	106.000	+	299.813i	0.447257	+	1.26503i
$238$			240.000i			1.00840i
$239$	−212.132	−	212.132i	−0.887582	−	0.887582i	0.106709	−	0.994290i	$-0.465969\pi$
$239$	−212.132	−	212.132i	−0.887582	−	0.887582i	−0.994290	+	0.106709i	$0.965969\pi$
$240$	−165.490	+	346.510i	−0.689543	+	1.44379i
$241$	−81.0000	+	81.0000i	−0.336100	+	0.336100i	−0.854897	−	0.518798i	$-0.826380\pi$
$241$	−81.0000	+	81.0000i	−0.336100	+	0.336100i	0.518798	+	0.854897i	$0.326380\pi$
$242$	148.492	−	148.492i	0.613605	−	0.613605i
$243$	31.1127	+	241.000i	0.128036	+	0.991770i
$244$			64.0000i			0.262295i
$245$	175.362	+	175.362i	0.715765	+	0.715765i
$246$	−316.784	+	112.000i	−1.28774	+	0.455285i
$247$	221.000	+	221.000i	0.894737	+	0.894737i
$248$		−	237.588i		−	0.958016i
$249$	378.995	+	181.005i	1.52207	+	0.726928i
$250$		−	224.000i		−	0.896000i
$251$		−	158.392i		−	0.631044i	−0.948918	−	0.315522i	$-0.897820\pi$
$251$		−	158.392i		−	0.631044i	0.948918	−	0.315522i	$-0.102180\pi$
$252$	16.1177	−	151.882i	0.0639593	−	0.602707i
$253$	−48.0000	−	48.0000i	−0.189723	−	0.189723i
$254$	316.784	+	316.784i	1.24718	+	1.24718i
$255$	292.548	−	612.548i	1.14725	−	2.40215i
$256$	256.000			1.00000
$257$	237.588			0.924466			0.462233	−	0.886758i	$-0.347048\pi$
$257$	237.588			0.924466			0.462233	+	0.886758i	$0.347048\pi$
$258$	75.7990	+	36.2010i	0.293795	+	0.140314i
$259$	−126.000			−0.486486
$260$	−294.156	+	294.156i	−1.13137	+	1.13137i
$261$	−128.000	−	158.392i	−0.490421	−	0.606866i
$262$	−224.000	−	224.000i	−0.854962	−	0.854962i
$263$	−277.186			−1.05394			−0.526969	−	0.849884i	$-0.676672\pi$
$263$	−277.186			−1.05394			−0.526969	+	0.849884i	$0.676672\pi$
$264$	32.0000	+	90.5097i	0.121212	+	0.342840i
$265$	288.000	+	288.000i	1.08679	+	1.08679i
$266$	−144.250	−	144.250i	−0.542292	−	0.542292i
$267$	303.196	+	144.804i	1.13557	+	0.542337i
$268$	4.00000	+	4.00000i	0.0149254	+	0.0149254i
$269$			248.902i			0.925285i	0.886545	+	0.462642i	$0.153099\pi$
$269$			248.902i			0.925285i	−0.886545	+	0.462642i	$0.846901\pi$
$270$	−226.274	+	368.000i	−0.838052	+	1.36296i
$271$	−101.000	−	101.000i	−0.372694	−	0.372694i	0.495764	−	0.868457i	$-0.334888\pi$
$271$	−101.000	−	101.000i	−0.372694	−	0.372694i	−0.868457	+	0.495764i	$0.834888\pi$
$272$	−452.548			−1.66378
$273$	71.3087	−	149.309i	0.261204	−	0.546918i
$274$			192.000i			0.700730i
$275$	−110.309	−	110.309i	−0.401122	−	0.401122i
$276$	−192.000	+	67.8823i	−0.695652	+	0.245950i
$277$		−	368.000i		−	1.32852i	−0.747502	−	0.664260i	$-0.768747\pi$
$277$		−	368.000i		−	1.32852i	0.747502	−	0.664260i	$-0.231253\pi$
$278$	−45.2548	+	45.2548i	−0.162787	+	0.162787i
$279$	28.2061	−	265.794i	0.101097	−	0.952666i
$280$	192.000	−	192.000i	0.685714	−	0.685714i
$281$	−96.1665	−	96.1665i	−0.342230	−	0.342230i	0.514975	−	0.857205i	$-0.327801\pi$
$281$	−96.1665	−	96.1665i	−0.342230	−	0.342230i	−0.857205	+	0.514975i	$0.827801\pi$
$282$	248.902	−	88.0000i	0.882630	−	0.312057i
$283$	224.000			0.791519			0.395760	−	0.918354i	$-0.370481\pi$
$283$	224.000			0.791519			0.395760	+	0.918354i	$0.370481\pi$
$284$	−101.823	+	101.823i	−0.358533	+	0.358533i
$285$	192.333	+	544.000i	0.674853	+	1.90877i
$286$			104.000i			0.363636i
$287$	237.588			0.827832
$288$	286.392	+	30.3919i	0.994416	+	0.105527i
$289$	511.000			1.76817
$290$		−	362.039i		−	1.24841i
$291$	3.82843	+	1.82843i	0.0131561	+	0.00628325i
$292$	−28.0000	−	28.0000i	−0.0958904	−	0.0958904i
$293$	−175.362	−	175.362i	−0.598507	−	0.598507i	0.341408	−	0.939915i	$-0.389096\pi$
$293$	−175.362	−	175.362i	−0.598507	−	0.598507i	−0.939915	+	0.341408i	$0.889096\pi$
$294$	80.1594	−	167.841i	0.272651	−	0.570886i
$295$		−	416.000i		−	1.41017i
$296$		−	237.588i		−	0.802662i
$297$	25.0538	+	105.054i	0.0843563	+	0.353717i
$298$	−224.000			−0.751678
$299$	−220.617			−0.737851
$300$	−441.235	+	156.000i	−1.47078	+	0.520000i
$301$	−42.0000	−	42.0000i	−0.139535	−	0.139535i
$302$		−	398.808i		−	1.32056i
$303$	112.000	−	39.5980i	0.369637	−	0.130686i
$304$	272.000	−	272.000i	0.894737	−	0.894737i
$305$	−90.5097	+	90.5097i	−0.296753	+	0.296753i
$306$	−506.274	−	53.7258i	−1.65449	−	0.175575i
$307$	−33.0000	−	33.0000i	−0.107492	−	0.107492i	0.651315	−	0.758807i	$-0.274218\pi$
$307$	−33.0000	−	33.0000i	−0.107492	−	0.107492i	−0.758807	+	0.651315i	$0.774218\pi$
$308$		−	67.8823i		−	0.220397i
$309$	−197.990	+	70.0000i	−0.640744	+	0.226537i
$310$	336.000	−	336.000i	1.08387	−	1.08387i
$311$		−	118.794i		−	0.381974i	−0.981593	−	0.190987i	$-0.938831\pi$
$311$		−	118.794i		−	0.381974i	0.981593	−	0.190987i	$-0.0611688\pi$
$312$	281.539	+	134.461i	0.902369	+	0.430964i
$313$	−528.000			−1.68690			−0.843450	−	0.537207i	$-0.819479\pi$
$313$	−528.000			−1.68690			−0.843450	+	0.537207i	$0.819479\pi$
$314$	−144.250	−	144.250i	−0.459394	−	0.459394i
$315$	237.588	−	192.000i	0.754247	−	0.609524i
$316$	424.000			1.34177
$317$	−45.2548	+	45.2548i	−0.142760	+	0.142760i	−0.774875	−	0.632115i	$-0.782187\pi$
$317$	−45.2548	+	45.2548i	−0.142760	+	0.142760i	0.632115	+	0.774875i	$0.282187\pi$
$318$	131.647	−	275.647i	0.413983	−	0.866814i
$319$	−64.0000	−	64.0000i	−0.200627	−	0.200627i
$320$	362.039	+	362.039i	1.13137	+	1.13137i
$321$	−448.000	+	158.392i	−1.39564	+	0.493433i
$322$	144.000			0.447205
$323$	−480.833	+	480.833i	−1.48865	+	1.48865i
$324$	316.784	+	68.0000i	0.977728	+	0.209877i
$325$	−507.000			−1.56000
$326$			585.484i			1.79596i
$327$	11.4853	+	5.48528i	0.0351232	+	0.0167746i
$328$			448.000i			1.36585i
$329$	−186.676			−0.567405
$330$	−82.7452	+	173.255i	−0.250743	+	0.525015i
$331$	−343.000	+	343.000i	−1.03625	+	1.03625i	−0.0369361	+	0.999318i	$0.511760\pi$
$331$	−343.000	+	343.000i	−1.03625	+	1.03625i	−0.999318	+	0.0369361i	$0.988240\pi$
$332$	395.980	−	395.980i	1.19271	−	1.19271i
$333$	28.2061	−	265.794i	0.0847029	−	0.798180i
$334$	−184.000			−0.550898
$335$			11.3137i			0.0337723i
$336$	−183.765	−	87.7645i	−0.546918	−	0.261204i
$337$			274.000i			0.813056i	0.913638	+	0.406528i	$0.133261\pi$
$337$			274.000i			0.813056i	−0.913638	+	0.406528i	$0.866739\pi$
$338$	239.002	+	239.002i	0.707107	+	0.707107i
$339$	16.9706	+	48.0000i	0.0500607	+	0.141593i
$340$	−640.000	−	640.000i	−1.88235	−	1.88235i
$341$		−	118.794i		−	0.348369i
$342$	336.583	−	272.000i	0.984160	−	0.795322i
$343$	−240.000	+	240.000i	−0.699708	+	0.699708i
$344$	79.1960	−	79.1960i	0.230221	−	0.230221i
$345$	−367.529	−	175.529i	−1.06530	−	0.508780i
$346$	8.00000	+	8.00000i	0.0231214	+	0.0231214i
$347$	356.382			1.02704			0.513518	−	0.858079i	$-0.328342\pi$
$347$	356.382			1.02704			0.513518	+	0.858079i	$0.328342\pi$
$348$	−256.000	+	90.5097i	−0.735632	+	0.260085i
$349$	99.0000	−	99.0000i	0.283668	−	0.283668i	−0.550902	−	0.834570i	$-0.685716\pi$
$349$	99.0000	−	99.0000i	0.283668	−	0.283668i	0.834570	+	0.550902i	$0.185716\pi$
$350$	330.926			0.945503
$351$	299.000	+	183.848i	0.851852	+	0.523783i
$352$	128.000			0.363636
$353$	79.1960	−	79.1960i	0.224351	−	0.224351i	−0.585977	−	0.810328i	$-0.699289\pi$
$353$	79.1960	−	79.1960i	0.224351	−	0.224351i	0.810328	+	0.585977i	$0.199289\pi$
$354$	−294.156	+	104.000i	−0.830950	+	0.293785i
$355$	−288.000			−0.811268
$356$	316.784	−	316.784i	0.889842	−	0.889842i
$357$	324.853	+	155.147i	0.909952	+	0.434586i
$358$	392.000	−	392.000i	1.09497	−	1.09497i
$359$	−336.583	+	336.583i	−0.937557	+	0.937557i	−0.998162	−	0.0606052i	$-0.980697\pi$
$359$	−336.583	+	336.583i	−0.937557	+	0.937557i	0.0606052	+	0.998162i	$0.480697\pi$
$360$	362.039	+	448.000i	1.00566	+	1.24444i
$361$		−	217.000i		−	0.601108i
$362$	90.5097	−	90.5097i	0.250027	−	0.250027i
$363$	−105.000	−	296.985i	−0.289256	−	0.818140i
$364$	−156.000	−	156.000i	−0.428571	−	0.428571i
$365$		−	79.1960i		−	0.216975i
$366$	86.6274	+	41.3726i	0.236687	+	0.113040i
$367$			352.000i			0.959128i	0.877507	+	0.479564i	$0.159205\pi$
$367$			352.000i			0.959128i	−0.877507	+	0.479564i	$0.840795\pi$
$368$			271.529i			0.737851i
$369$	−53.1859	+	501.186i	−0.144135	+	1.35823i
$370$	336.000	−	336.000i	0.908108	−	0.908108i
$371$	−152.735	+	152.735i	−0.411685	+	0.411685i
$372$	−321.588	−	153.588i	−0.864484	−	0.412871i
$373$	−576.000			−1.54424			−0.772118	−	0.635479i	$-0.780803\pi$
$373$	−576.000			−1.54424			−0.772118	+	0.635479i	$0.780803\pi$
$374$	−226.274			−0.605011
$375$	−303.196	−	144.804i	−0.808523	−	0.386144i
$376$		−	352.000i		−	0.936170i
$377$	−294.156			−0.780256
$378$	−195.161	−	120.000i	−0.516300	−	0.317460i
$379$	−7.00000	+	7.00000i	−0.0184697	+	0.0184697i	−0.716281	−	0.697812i	$-0.754157\pi$
$379$	−7.00000	+	7.00000i	−0.0184697	+	0.0184697i	0.697812	+	0.716281i	$0.254157\pi$
$380$	769.332			2.02456
$381$	633.568	−	224.000i	1.66291	−	0.587927i
$382$		0			0
$383$	336.583	+	336.583i	0.878806	+	0.878806i	0.993411	−	0.114605i	$-0.0365602\pi$
$383$	336.583	+	336.583i	0.878806	+	0.878806i	−0.114605	+	0.993411i	$0.536560\pi$
$384$	165.490	−	346.510i	0.430964	−	0.902369i
$385$	96.0000	−	96.0000i	0.249351	−	0.249351i
$386$	−178.191			−0.461634
$387$	98.0000	−	79.1960i	0.253230	−	0.204641i
$388$	4.00000	−	4.00000i	0.0103093	−	0.0103093i
$389$	−147.078			−0.378093			−0.189047	−	0.981968i	$-0.560540\pi$
$389$	−147.078			−0.378093			−0.189047	+	0.981968i	$0.560540\pi$
$390$	208.000	+	588.313i	0.533333	+	1.50849i
$391$		−	480.000i		−	1.22762i
$392$	−175.362	−	175.362i	−0.447353	−	0.447353i
$393$	−448.000	+	158.392i	−1.13995	+	0.403033i
$394$	−160.000			−0.406091
$395$	599.627	+	599.627i	1.51804	+	1.51804i
$396$	143.196	+	15.1960i	0.361606	+	0.0383736i
$397$	−413.000	+	413.000i	−1.04030	+	1.04030i	−0.0411493	+	0.999153i	$0.513102\pi$
$397$	−413.000	+	413.000i	−1.04030	+	1.04030i	−0.999153	+	0.0411493i	$0.986898\pi$
$398$	−181.019	−	181.019i	−0.454822	−	0.454822i
$399$	−288.500	+	102.000i	−0.723057	+	0.255639i
$400$			624.000i			1.56000i
$401$	203.647	+	203.647i	0.507847	+	0.507847i	0.913865	−	0.406018i	$-0.133083\pi$
$401$	203.647	+	203.647i	0.507847	+	0.507847i	−0.406018	+	0.913865i	$0.633083\pi$
$402$	8.00000	−	2.82843i	0.0199005	−	0.00703589i
$403$	−273.000	−	273.000i	−0.677419	−	0.677419i
$404$		−	158.392i		−	0.392059i
$405$	351.833	+	544.167i	0.868725	+	1.34362i
$406$	192.000			0.472906
$407$		−	118.794i		−	0.291877i
$408$	−292.548	+	612.548i	−0.717030	+	1.50134i
$409$	409.000	+	409.000i	1.00000	+	1.00000i	1.00000			$0$
$409$	409.000	+	409.000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$410$	−633.568	+	633.568i	−1.54529	+	1.54529i
$411$	259.882	+	124.118i	0.632317	+	0.301990i
$412$			280.000i			0.679612i
$413$	220.617			0.534182
$414$	−32.2355	+	303.765i	−0.0778635	+	0.733731i
$415$	1120.00			2.69880
$416$	294.156	−	294.156i	0.707107	−	0.707107i
$417$	32.0000	+	90.5097i	0.0767386	+	0.217050i
$418$	136.000	−	136.000i	0.325359	−	0.325359i
$419$	−11.3137			−0.0270017			−0.0135008	−	0.999909i	$-0.504298\pi$
$419$	−11.3137			−0.0270017			−0.0135008	+	0.999909i	$0.504298\pi$
$420$	−135.765	−	384.000i	−0.323249	−	0.914286i
$421$	21.0000	+	21.0000i	0.0498812	+	0.0498812i	0.731607	−	0.681726i	$-0.238770\pi$
$421$	21.0000	+	21.0000i	0.0498812	+	0.0498812i	−0.681726	+	0.731607i	$0.738770\pi$
$422$	−223.446	+	223.446i	−0.529492	+	0.529492i
$423$	41.7889	−	393.789i	0.0987917	−	0.930943i
$424$	−288.000	−	288.000i	−0.679245	−	0.679245i
$425$		−	1103.09i		−	2.59550i
$426$	72.0000	+	203.647i	0.169014	+	0.478044i
$427$	−48.0000	−	48.0000i	−0.112412	−	0.112412i
$428$			633.568i			1.48030i
$429$	140.770	+	67.2304i	0.328134	+	0.156714i
$430$	224.000			0.520930
$431$	178.191	+	178.191i	0.413436	+	0.413436i	0.882934	−	0.469498i	$-0.155565\pi$
$431$	178.191	+	178.191i	0.413436	+	0.413436i	−0.469498	+	0.882934i	$0.655565\pi$
$432$	226.274	−	368.000i	0.523783	−	0.851852i
$433$			734.000i			1.69515i	0.530676	+	0.847575i	$0.321938\pi$
$433$			734.000i			1.69515i	−0.530676	+	0.847575i	$0.678062\pi$
$434$	178.191	+	178.191i	0.410578	+	0.410578i
$435$	−490.039	−	234.039i	−1.12653	−	0.538020i
$436$	12.0000	−	12.0000i	0.0275229	−	0.0275229i
$437$	288.500	+	288.500i	0.660182	+	0.660182i
$438$	−56.0000	+	19.7990i	−0.127854	+	0.0452032i
$439$	−602.000			−1.37130			−0.685649	−	0.727932i	$-0.740482\pi$
$439$	−602.000			−1.37130			−0.685649	+	0.727932i	$0.740482\pi$
$440$	181.019	+	181.019i	0.411408	+	0.411408i
$441$	−175.362	−	217.000i	−0.397647	−	0.492063i
$442$	−520.000	+	520.000i	−1.17647	+	1.17647i
$443$	−135.765			−0.306466			−0.153233	−	0.988190i	$-0.548969\pi$
$443$	−135.765			−0.306466			−0.153233	+	0.988190i	$0.548969\pi$
$444$	−321.588	−	153.588i	−0.724297	−	0.345919i
$445$	896.000			2.01348
$446$	−528.916			−1.18591
$447$	−144.804	+	303.196i	−0.323946	+	0.678291i
$448$	−192.000	+	192.000i	−0.428571	+	0.428571i
$449$	395.980	+	395.980i	0.881915	+	0.881915i	0.993729	−	0.111814i	$-0.0356662\pi$
$449$	395.980	+	395.980i	0.881915	+	0.881915i	−0.111814	+	0.993729i	$0.535666\pi$
$450$	−74.0803	+	698.080i	−0.164623	+	1.55129i
$451$			224.000i			0.496674i
$452$	67.8823			0.150182
$453$	−539.808	−	257.808i	−1.19163	−	0.569113i
$454$		−	504.000i		−	1.11013i
$455$		−	441.235i		−	0.969746i
$456$	−192.333	−	544.000i	−0.421783	−	1.19298i
$457$	−233.000	−	233.000i	−0.509847	−	0.509847i	0.404633	−	0.914479i	$-0.367399\pi$
$457$	−233.000	−	233.000i	−0.509847	−	0.509847i	−0.914479	+	0.404633i	$0.867399\pi$
$458$	−376.181			−0.821355
$459$	−400.000	+	650.538i	−0.871460	+	1.41729i
$460$	−384.000	+	384.000i	−0.834783	+	0.834783i
$461$	−576.999	+	576.999i	−1.25163	+	1.25163i	−0.296634	+	0.954991i	$0.595864\pi$
$461$	−576.999	+	576.999i	−1.25163	+	1.25163i	−0.954991	+	0.296634i	$0.904136\pi$
$462$	−91.8823	−	43.8823i	−0.198879	−	0.0949832i
$463$	123.000	+	123.000i	0.265659	+	0.265659i	0.827348	−	0.561689i	$-0.189848\pi$
$463$	123.000	+	123.000i	0.265659	+	0.265659i	−0.561689	+	0.827348i	$0.689848\pi$
$464$			362.039i			0.780256i
$465$	−237.588	−	672.000i	−0.510942	−	1.44516i
$466$	48.0000	+	48.0000i	0.103004	+	0.103004i
$467$		−	395.980i		−	0.847922i	−0.905680	−	0.423961i	$-0.860639\pi$
$467$		−	395.980i		−	0.847922i	0.905680	−	0.423961i	$-0.139361\pi$
$468$	364.000	−	294.156i	0.777778	−	0.628539i
$469$	−6.00000			−0.0127932
$470$	497.803	−	497.803i	1.05916	−	1.05916i
$471$	−288.500	+	102.000i	−0.612526	+	0.216561i
$472$			416.000i			0.881356i
$473$	39.5980	−	39.5980i	0.0837167	−	0.0837167i
$474$	274.093	−	573.907i	0.578256	−	1.21077i
$475$	663.000	+	663.000i	1.39579	+	1.39579i
$476$	339.411	−	339.411i	0.713049	−	0.713049i
$477$	−288.000	−	356.382i	−0.603774	−	0.747132i
$478$			600.000i			1.25523i
$479$	353.553	−	353.553i	0.738107	−	0.738107i	−0.234104	−	0.972212i	$-0.575216\pi$
$479$	353.553	−	353.553i	0.738107	−	0.738107i	0.972212	+	0.234104i	$0.0752157\pi$
$480$	724.077	−	256.000i	1.50849	−	0.533333i
$481$	−273.000	−	273.000i	−0.567568	−	0.567568i
$482$	229.103			0.475317
$483$	93.0883	−	194.912i	0.192729	−	0.403544i
$484$	−420.000			−0.867769
$485$	11.3137			0.0233272
$486$	296.825	−	384.825i	0.610752	−	0.791822i
$487$	573.000	−	573.000i	1.17659	−	1.17659i	0.195984	−	0.980607i	$-0.437210\pi$
$487$	573.000	−	573.000i	1.17659	−	1.17659i	0.980607	−	0.195984i	$-0.0627902\pi$
$488$	90.5097	−	90.5097i	0.185471	−	0.185471i
$489$	792.484	+	378.484i	1.62062	+	0.773997i
$490$		−	496.000i		−	1.01224i
$491$		−	724.077i		−	1.47470i	−0.675511	−	0.737350i	$-0.736077\pi$
$491$		−	724.077i		−	1.47470i	0.675511	−	0.737350i	$-0.263923\pi$
$492$	606.392	+	289.608i	1.23250	+	0.588634i
$493$		−	640.000i		−	1.29817i
$494$		−	625.082i		−	1.26535i
$495$	181.019	+	224.000i	0.365696	+	0.452525i
$496$	−336.000	+	336.000i	−0.677419	+	0.677419i
$497$		−	152.735i		−	0.307314i
$498$	−280.000	−	791.960i	−0.562249	−	1.59028i
$499$	335.000	−	335.000i	0.671343	−	0.671343i	−0.286683	−	0.958026i	$-0.592553\pi$
$499$	335.000	−	335.000i	0.671343	−	0.671343i	0.958026	+	0.286683i	$0.0925526\pi$
$500$	−316.784	+	316.784i	−0.633568	+	0.633568i
$501$	−118.946	+	249.054i	−0.237418	+	0.497113i
$502$	−224.000	+	224.000i	−0.446215	+	0.446215i
$503$	−605.283			−1.20335			−0.601673	−	0.798742i	$-0.705499\pi$
$503$	−605.283			−1.20335			−0.601673	+	0.798742i	$0.705499\pi$
$504$	−237.588	+	192.000i	−0.471405	+	0.380952i
$505$	224.000	−	224.000i	0.443564	−	0.443564i
$506$			135.765i			0.268309i
$507$	478.004	−	169.000i	0.942809	−	0.333333i
$508$		−	896.000i		−	1.76378i
$509$	−548.715	+	548.715i	−1.07803	+	1.07803i	−0.0813388	+	0.996687i	$0.525920\pi$
$509$	−548.715	+	548.715i	−1.07803	+	1.07803i	−0.996687	+	0.0813388i	$0.974080\pi$
$510$	−1280.00	+	452.548i	−2.50980	+	0.887350i
$511$	42.0000			0.0821918
$512$	−362.039	−	362.039i	−0.707107	−	0.707107i
$513$	−150.584	−	631.416i	−0.293535	−	1.23083i
$514$	−336.000	−	336.000i	−0.653696	−	0.653696i
$515$	−395.980	+	395.980i	−0.768893	+	0.768893i
$516$	−56.0000	−	158.392i	−0.108527	−	0.306961i
$517$		−	176.000i		−	0.340426i
$518$	178.191	+	178.191i	0.343998	+	0.343998i
$519$	16.0000	−	5.65685i	0.0308285	−	0.0108995i
$520$	832.000			1.60000
$521$		−	593.970i		−	1.14006i	−0.821625	−	0.570028i	$-0.806932\pi$
$521$		−	593.970i		−	1.14006i	0.821625	−	0.570028i	$-0.193068\pi$
$522$	−42.9807	+	405.019i	−0.0823384	+	0.775899i
$523$		−	672.000i		−	1.28489i	−0.766330	−	0.642447i	$-0.777919\pi$
$523$		−	672.000i		−	1.28489i	0.766330	−	0.642447i	$-0.222081\pi$
$524$			633.568i			1.20910i
$525$	213.926	−	447.926i	0.407478	−	0.853192i
$526$	392.000	+	392.000i	0.745247	+	0.745247i
$527$	593.970	−	593.970i	1.12708	−	1.12708i
$528$	82.7452	−	173.255i	0.156714	−	0.328134i
$529$	241.000			0.455577
$530$		−	814.587i		−	1.53696i
$531$	−49.3869	+	465.387i	−0.0930073	+	0.876435i
$532$			408.000i			0.766917i
$533$	514.774	+	514.774i	0.965804	+	0.965804i
$534$	−224.000	−	633.568i	−0.419476	−	1.18646i
$535$	−896.000	+	896.000i	−1.67477	+	1.67477i
$536$		−	11.3137i		−	0.0211077i
$537$	−277.186	−	784.000i	−0.516175	−	1.45996i
$538$	352.000	−	352.000i	0.654275	−	0.654275i
$539$	−87.6812	−	87.6812i	−0.162674	−	0.162674i
$540$	840.431	−	200.431i	1.55635	−	0.371168i
$541$	429.000	−	429.000i	0.792976	−	0.792976i	−0.189001	−	0.981977i	$-0.560525\pi$
$541$	429.000	−	429.000i	0.792976	−	0.792976i	0.981977	+	0.189001i	$0.0605249\pi$
$542$			285.671i			0.527069i
$543$	−64.0000	−	181.019i	−0.117864	−	0.333369i
$544$	640.000	+	640.000i	1.17647	+	1.17647i
$545$	33.9411			0.0622773
$546$	−312.000	+	110.309i	−0.571429	+	0.202031i
$547$		−	32.0000i		−	0.0585009i	−0.999572	−	0.0292505i	$-0.990688\pi$
$547$		−	32.0000i		−	0.0585009i	0.999572	−	0.0292505i	$-0.00931204\pi$
$548$	271.529	−	271.529i	0.495491	−	0.495491i
$549$	112.000	−	90.5097i	0.204007	−	0.164863i
$550$			312.000i			0.567273i
$551$	384.666	+	384.666i	0.698124	+	0.698124i
$552$	367.529	+	175.529i	0.665813	+	0.317987i
$553$	−318.000	+	318.000i	−0.575045	+	0.575045i
$554$	−520.431	+	520.431i	−0.939405	+	0.939405i
$555$	−237.588	−	672.000i	−0.428086	−	1.21081i
$556$	128.000			0.230216
$557$	−367.696	−	367.696i	−0.660136	−	0.660136i	0.295276	−	0.955412i	$-0.404588\pi$
$557$	−367.696	−	367.696i	−0.660136	−	0.660136i	−0.955412	+	0.295276i	$0.904588\pi$
$558$	−415.779	+	336.000i	−0.745123	+	0.602151i
$559$		−	182.000i		−	0.325581i
$560$	−543.058			−0.969746
$561$	−146.274	+	306.274i	−0.260738	+	0.545943i
$562$			272.000i			0.483986i
$563$		−	435.578i		−	0.773673i	−0.922148	−	0.386836i	$-0.873568\pi$
$563$		−	435.578i		−	0.773673i	0.922148	−	0.386836i	$-0.126432\pi$
$564$	−476.451	−	227.549i	−0.844771	−	0.403456i
$565$	96.0000	+	96.0000i	0.169912	+	0.169912i
$566$	−316.784	−	316.784i	−0.559689	−	0.559689i
$567$	−288.588	+	186.588i	−0.508973	+	0.329079i
$568$	288.000			0.507042
$569$	588.313			1.03394			0.516971	−	0.856003i	$-0.327060\pi$
$569$	588.313			1.03394			0.516971	+	0.856003i	$0.327060\pi$
$570$	497.332	−	1041.33i	0.872513	−	1.82690i
$571$	−800.000			−1.40105			−0.700525	−	0.713627i	$-0.747051\pi$
$571$	−800.000			−1.40105			−0.700525	+	0.713627i	$0.747051\pi$
$572$	147.078	−	147.078i	0.257130	−	0.257130i
$573$		0			0
$574$	−336.000	−	336.000i	−0.585366	−	0.585366i
$575$	−661.852			−1.15105
$576$	−362.039	−	448.000i	−0.628539	−	0.777778i
$577$	273.000	+	273.000i	0.473137	+	0.473137i	0.902928	−	0.429791i	$-0.141413\pi$
$577$	273.000	+	273.000i	0.473137	+	0.473137i	−0.429791	+	0.902928i	$0.641413\pi$
$578$	−722.663	−	722.663i	−1.25028	−	1.25028i
$579$	−115.191	+	241.191i	−0.198948	+	0.416565i
$580$	−512.000	+	512.000i	−0.882759	+	0.882759i
$581$			593.970i			1.02232i
$582$	−2.82843	−	8.00000i	−0.00485984	−	0.0137457i
$583$	−144.000	−	144.000i	−0.246998	−	0.246998i
$584$			79.1960i			0.135610i
$585$	930.774	+	98.7737i	1.59107	+	0.168844i
$586$			496.000i			0.846416i
$587$	144.250	+	144.250i	0.245741	+	0.245741i	0.819220	−	0.573479i	$-0.194407\pi$
$587$	144.250	+	144.250i	0.245741	+	0.245741i	−0.573479	+	0.819220i	$0.694407\pi$
$588$	−350.725	+	124.000i	−0.596471	+	0.210884i
$589$			714.000i			1.21222i
$590$	−588.313	+	588.313i	−0.997140	+	0.997140i
$591$	−103.431	+	216.569i	−0.175011	+	0.366444i
$592$	−336.000	+	336.000i	−0.567568	+	0.567568i
$593$	45.2548	+	45.2548i	0.0763151	+	0.0763151i	0.744234	−	0.667919i	$-0.232815\pi$
$593$	45.2548	+	45.2548i	0.0763151	+	0.0763151i	−0.667919	+	0.744234i	$0.732815\pi$
$594$	113.137	−	184.000i	0.190466	−	0.309764i
$595$	960.000			1.61345
$596$	316.784	+	316.784i	0.531517	+	0.531517i
$597$	−362.039	+	128.000i	−0.606430	+	0.214405i
$598$	312.000	+	312.000i	0.521739	+	0.521739i
$599$	−480.833			−0.802726			−0.401363	−	0.915919i	$-0.631463\pi$
$599$	−480.833			−0.802726			−0.401363	+	0.915919i	$0.631463\pi$
$600$	844.617	+	403.383i	1.40770	+	0.672304i
$601$	496.000			0.825291			0.412646	−	0.910892i	$-0.364605\pi$
$601$	496.000			0.825291			0.412646	+	0.910892i	$0.364605\pi$
$602$			118.794i			0.197332i
$603$	1.34315	−	12.6569i	0.00222744	−	0.0209898i
$604$	−564.000	+	564.000i	−0.933775	+	0.933775i
$605$	−593.970	−	593.970i	−0.981768	−	0.981768i
$606$	−214.392	−	102.392i	−0.353782	−	0.168964i
$607$			448.000i			0.738056i	0.929418	+	0.369028i	$0.120309\pi$
$607$			448.000i			0.738056i	−0.929418	+	0.369028i	$0.879691\pi$
$608$	−769.332			−1.26535
$609$	124.118	−	259.882i	0.203806	−	0.426736i
$610$	256.000			0.419672
$611$	−404.465	−	404.465i	−0.661972	−	0.661972i
$612$	640.000	+	791.960i	1.04575	+	1.29405i
$613$	−203.000	−	203.000i	−0.331158	−	0.331158i	0.521868	−	0.853026i	$-0.325235\pi$
$613$	−203.000	−	203.000i	−0.331158	−	0.331158i	−0.853026	+	0.521868i	$0.825235\pi$
$614$			93.3381i			0.152016i
$615$	448.000	+	1267.14i	0.728455	+	2.06038i
$616$	−96.0000	+	96.0000i	−0.155844	+	0.155844i
$617$	475.176	−	475.176i	0.770139	−	0.770139i	−0.207992	−	0.978131i	$-0.566693\pi$
$617$	475.176	−	475.176i	0.770139	−	0.770139i	0.978131	+	0.207992i	$0.0666927\pi$
$618$	378.995	+	181.005i	0.613260	+	0.292888i
$619$	−343.000	−	343.000i	−0.554120	−	0.554120i	0.373508	−	0.927627i	$-0.378155\pi$
$619$	−343.000	−	343.000i	−0.554120	−	0.554120i	−0.927627	+	0.373508i	$0.878155\pi$
$620$	−950.352			−1.53283
$621$	390.323	+	240.000i	0.628539	+	0.386473i
$622$	−168.000	+	168.000i	−0.270096	+	0.270096i
$623$			475.176i			0.762722i
$624$	−208.000	−	588.313i	−0.333333	−	0.942809i
$625$	79.0000			0.126400
$626$	746.705	+	746.705i	1.19282	+	1.19282i
$627$	−96.1665	−	272.000i	−0.153376	−	0.433812i
$628$			408.000i			0.649682i
$629$	593.970	−	593.970i	0.944308	−	0.944308i
$630$	−607.529	−	64.4710i	−0.964332	−	0.102335i
$631$	−301.000	−	301.000i	−0.477021	−	0.477021i	0.427157	−	0.904178i	$-0.359515\pi$
$631$	−301.000	−	301.000i	−0.477021	−	0.477021i	−0.904178	+	0.427157i	$0.859515\pi$
$632$	−599.627	−	599.627i	−0.948776	−	0.948776i
$633$	158.000	+	446.891i	0.249605	+	0.705990i
$634$	128.000			0.201893
$635$	1267.14	−	1267.14i	1.99549	−	1.99549i
$636$	−576.000	+	203.647i	−0.905660	+	0.320199i
$637$	−403.000			−0.632653
$638$			181.019i			0.283729i
$639$	322.191	+	34.1909i	0.504211	+	0.0535069i
$640$		−	1024.00i		−	1.60000i
$641$	831.558			1.29728			0.648641	−	0.761095i	$-0.275338\pi$
$641$	831.558			1.29728			0.648641	+	0.761095i	$0.275338\pi$
$642$	857.568	+	409.568i	1.33578	+	0.637956i
$643$	−47.0000	+	47.0000i	−0.0730949	+	0.0730949i	−0.742709	−	0.669614i	$-0.766459\pi$
$643$	−47.0000	+	47.0000i	−0.0730949	+	0.0730949i	0.669614	+	0.742709i	$0.266459\pi$
$644$	−203.647	−	203.647i	−0.316222	−	0.316222i
$645$	144.804	−	303.196i	0.224502	−	0.470071i
$646$	1360.00			2.10526
$647$			192.333i			0.297269i	0.988892	+	0.148635i	$0.0474878\pi$
$647$			192.333i			0.297269i	−0.988892	+	0.148635i	$0.952512\pi$
$648$	−351.833	−	544.167i	−0.542953	−	0.839763i
$649$			208.000i			0.320493i
$650$	717.006	+	717.006i	1.10309	+	1.10309i
$651$	356.382	−	126.000i	0.547438	−	0.193548i
$652$	828.000	−	828.000i	1.26994	−	1.26994i
$653$		−	237.588i		−	0.363841i	−0.983313	−	0.181920i	$-0.941769\pi$
$653$		−	237.588i		−	0.363841i	0.983313	−	0.181920i	$-0.0582313\pi$
$654$	−8.48528	−	24.0000i	−0.0129744	−	0.0366972i
$655$	−896.000	+	896.000i	−1.36794	+	1.36794i
$656$	633.568	−	633.568i	0.965804	−	0.965804i
$657$	−9.40202	+	88.5980i	−0.0143105	+	0.134852i
$658$	264.000	+	264.000i	0.401216	+	0.401216i
$659$	288.500			0.437784			0.218892	−	0.975749i	$-0.429756\pi$
$659$	288.500			0.437784			0.218892	+	0.975749i	$0.429756\pi$
$660$	362.039	−	128.000i	0.548543	−	0.193939i
$661$	357.000	−	357.000i	0.540091	−	0.540091i	−0.383465	−	0.923556i	$-0.625269\pi$
$661$	357.000	−	357.000i	0.540091	−	0.540091i	0.923556	+	0.383465i	$0.125269\pi$
$662$	970.151			1.46548
$663$	367.696	+	1040.00i	0.554594	+	1.56863i
$664$	−1120.00			−1.68675
$665$	−576.999	+	576.999i	−0.867668	+	0.867668i
$666$	−415.779	+	336.000i	−0.624292	+	0.504505i
$667$	−384.000			−0.575712
$668$	260.215	+	260.215i	0.389544	+	0.389544i
$669$	−341.916	+	715.916i	−0.511085	+	1.07013i
$670$	16.0000	−	16.0000i	0.0238806	−	0.0238806i
$671$	45.2548	−	45.2548i	0.0674439	−	0.0674439i
$672$	135.765	+	384.000i	0.202031	+	0.571429i
$673$		−	1008.00i		−	1.49777i	−0.662699	−	0.748886i	$-0.730589\pi$
$673$		−	1008.00i		−	1.49777i	0.662699	−	0.748886i	$-0.269411\pi$
$674$	387.495	−	387.495i	0.574918	−	0.574918i
$675$	897.000	+	551.543i	1.32889	+	0.817101i
$676$		−	676.000i		−	1.00000i
$677$			1114.40i			1.64609i	0.567979	+	0.823043i	$0.307725\pi$
$677$			1114.40i			1.64609i	−0.567979	+	0.823043i	$0.692275\pi$
$678$	43.8823	−	91.8823i	0.0647231	−	0.135520i
$679$			6.00000i			0.00883652i
$680$			1810.19i			2.66205i
$681$	−682.191	−	325.809i	−1.00175	−	0.478427i
$682$	−168.000	+	168.000i	−0.246334	+	0.246334i
$683$	257.387	−	257.387i	0.376848	−	0.376848i	−0.493116	−	0.869964i	$-0.664142\pi$
$683$	257.387	−	257.387i	0.376848	−	0.376848i	0.869964	+	0.493116i	$0.164142\pi$
$684$	−860.666	−	91.3339i	−1.25828	−	0.133529i
$685$	768.000			1.12117
$686$	678.823			0.989537
$687$	−243.181	+	509.181i	−0.353975	+	0.741166i
$688$	−224.000			−0.325581
$689$	−661.852			−0.960598
$690$	271.529	+	768.000i	0.393520	+	1.11304i
$691$	879.000	−	879.000i	1.27207	−	1.27207i	0.327069	−	0.945000i	$-0.393939\pi$
$691$	879.000	−	879.000i	1.27207	−	1.27207i	0.945000	−	0.327069i	$-0.106061\pi$
$692$		−	22.6274i		−	0.0326986i
$693$	−118.794	+	96.0000i	−0.171420	+	0.138528i
$694$	−504.000	−	504.000i	−0.726225	−	0.726225i
$695$	181.019	+	181.019i	0.260459	+	0.260459i
$696$	490.039	+	234.039i	0.704079	+	0.336262i
$697$	−1120.00	+	1120.00i	−1.60689	+	1.60689i
$698$	−280.014			−0.401167
$699$	96.0000	−	33.9411i	0.137339	−	0.0485567i
$700$	−468.000	−	468.000i	−0.668571	−	0.668571i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	−162.850	−	682.850i	−0.231980	−	0.972721i
$703$			714.000i			1.01565i
$704$	−181.019	−	181.019i	−0.257130	−	0.257130i
$705$	−352.000	−	995.606i	−0.499291	−	1.41221i
$706$	−224.000			−0.317280
$707$	118.794	+	118.794i	0.168025	+	0.168025i
$708$	563.078	+	268.922i	0.795308	+	0.379833i
$709$	−245.000	+	245.000i	−0.345557	+	0.345557i	−0.858452	−	0.512895i	$-0.828573\pi$
$709$	−245.000	+	245.000i	−0.345557	+	0.345557i	0.512895	+	0.858452i	$0.328573\pi$
$710$	407.294	+	407.294i	0.573653	+	0.573653i
$711$	−599.627	−	742.000i	−0.843357	−	1.04360i
$712$	−896.000			−1.25843
$713$	−356.382	−	356.382i	−0.499834	−	0.499834i
$714$	−240.000	−	678.823i	−0.336134	−	0.950732i
$715$	416.000			0.581818
$716$	−1108.74			−1.54852
$717$	812.132	+	387.868i	1.13268	+	0.540960i
$718$	952.000			1.32591
$719$		−	118.794i		−	0.165221i	−0.996582	−	0.0826105i	$-0.973674\pi$
$719$		−	118.794i		−	0.165221i	0.996582	−	0.0826105i	$-0.0263257\pi$
$720$	121.568	−	1145.57i	0.168844	−	1.59107i
$721$	−210.000	−	210.000i	−0.291262	−	0.291262i
$722$	−306.884	+	306.884i	−0.425048	+	0.425048i
$723$	148.103	−	310.103i	0.204845	−	0.428911i
$724$	−256.000			−0.353591
$725$	−882.469			−1.21720
$726$	−271.508	+	568.492i	−0.373977	+	0.783047i
$727$	−1088.00			−1.49656			−0.748281	−	0.663382i	$-0.769120\pi$
$727$	−1088.00			−1.49656			−0.748281	+	0.663382i	$0.769120\pi$
$728$			441.235i			0.606092i
$729$	−329.000	−	650.538i	−0.451303	−	0.892371i
$730$	−112.000	+	112.000i	−0.153425	+	0.153425i
$731$	395.980			0.541696
$732$	−64.0000	−	181.019i	−0.0874317	−	0.247294i
$733$	−845.000	−	845.000i	−1.15280	−	1.15280i	−0.985990	−	0.166807i	$-0.946654\pi$
$733$	−845.000	−	845.000i	−1.15280	−	1.15280i	−0.166807	−	0.985990i	$-0.553346\pi$
$734$	497.803	−	497.803i	0.678206	−	0.678206i
$735$	−671.362	−	320.638i	−0.913418	−	0.436242i
$736$	384.000	−	384.000i	0.521739	−	0.521739i
$737$		−	5.65685i		−	0.00767551i
$738$	784.000	−	633.568i	1.06233	−	0.858493i
$739$	833.000	+	833.000i	1.12720	+	1.12720i	0.990631	+	0.136568i	$0.0436073\pi$
$739$	833.000	+	833.000i	1.12720	+	1.12720i	0.136568	+	0.990631i	$0.456393\pi$
$740$	−950.352			−1.28426
$741$	−846.082	−	404.082i	−1.14181	−	0.545320i
$742$	432.000			0.582210
$743$	500.632	+	500.632i	0.673798	+	0.673798i	0.958589	−	0.284792i	$-0.0919245\pi$
$743$	500.632	+	500.632i	0.673798	+	0.673798i	−0.284792	+	0.958589i	$0.591924\pi$
$744$	237.588	+	672.000i	0.319339	+	0.903226i
$745$			896.000i			1.20268i
$746$	814.587	+	814.587i	1.09194	+	1.09194i
$747$	−1252.96	−	132.965i	−1.67733	−	0.177998i
$748$	320.000	+	320.000i	0.427807	+	0.427807i
$749$	−475.176	−	475.176i	−0.634414	−	0.634414i
$750$	224.000	+	633.568i	0.298667	+	0.844757i
$751$	554.000			0.737683			0.368842	−	0.929492i	$-0.379754\pi$
$751$	554.000			0.737683			0.368842	+	0.929492i	$0.379754\pi$
$752$	−497.803	+	497.803i	−0.661972	+	0.661972i
$753$	158.392	+	448.000i	0.210348	+	0.594954i
$754$	416.000	+	416.000i	0.551724	+	0.551724i
$755$	−1595.23			−2.11289
$756$	106.294	+	445.706i	0.140601	+	0.589558i
$757$	−496.000			−0.655218			−0.327609	−	0.944813i	$-0.606243\pi$
$757$	−496.000			−0.655218			−0.327609	+	0.944813i	$0.606243\pi$
$758$	19.7990			0.0261200
$759$	183.765	+	87.7645i	0.242114	+	0.115632i
$760$	−1088.00	−	1088.00i	−1.43158	−	1.43158i
$761$	593.970	+	593.970i	0.780512	+	0.780512i	0.979917	−	0.199405i	$-0.0639010\pi$
$761$	593.970	+	593.970i	0.780512	+	0.780512i	−0.199405	+	0.979917i	$0.563901\pi$
$762$	−1212.78	−	579.216i	−1.59158	−	0.760126i
$763$			18.0000i			0.0235911i
$764$		0			0
$765$	−214.903	+	2025.10i	−0.280919	+	2.64719i
$766$		−	952.000i		−	1.24282i
$767$	478.004	+	478.004i	0.623213	+	0.623213i
$768$	−724.077	+	256.000i	−0.942809	+	0.333333i
$769$	497.000	+	497.000i	0.646294	+	0.646294i	0.952095	−	0.305801i	$-0.0989244\pi$
$769$	497.000	+	497.000i	0.646294	+	0.646294i	−0.305801	+	0.952095i	$0.598924\pi$
$770$	−271.529			−0.352635
$771$	−672.000	+	237.588i	−0.871595	+	0.308155i
$772$	252.000	+	252.000i	0.326425	+	0.326425i
$773$	395.980	−	395.980i	0.512264	−	0.512264i	−0.402956	−	0.915219i	$-0.632017\pi$
$773$	395.980	−	395.980i	0.512264	−	0.512264i	0.915219	+	0.402956i	$0.132017\pi$
$774$	−250.593	−	26.5929i	−0.323763	−	0.0343578i
$775$	−819.000	−	819.000i	−1.05677	−	1.05677i
$776$	−11.3137			−0.0145795
$777$	356.382	−	126.000i	0.458664	−	0.162162i
$778$	208.000	+	208.000i	0.267352	+	0.267352i
$779$		−	1346.33i		−	1.72828i
$780$	537.844	−	1126.16i	0.689543	−	1.44379i
$781$	144.000			0.184379
$782$	−678.823	+	678.823i	−0.868059	+	0.868059i
$783$	520.431	+	320.000i	0.664662	+	0.408685i
$784$			496.000i			0.632653i
$785$	−576.999	+	576.999i	−0.735031	+	0.735031i
$786$	857.568	+	409.568i	1.09105	+	0.521078i
$787$	−1.00000	−	1.00000i	−0.00127065	−	0.00127065i	0.706471	−	0.707742i	$-0.250286\pi$
$787$	−1.00000	−	1.00000i	−0.00127065	−	0.00127065i	−0.707742	+	0.706471i	$0.750286\pi$
$788$	226.274	+	226.274i	0.287150	+	0.287150i
$789$	784.000	−	277.186i	0.993663	−	0.351313i
$790$		−	1696.00i		−	2.14684i
$791$	−50.9117	+	50.9117i	−0.0643637	+	0.0643637i
$792$	−181.019	−	224.000i	−0.228560	−	0.282828i
$793$		−	208.000i		−	0.262295i
$794$	1168.14			1.47121
$795$	−1102.59	−	526.587i	−1.38690	−	0.662374i
$796$			512.000i			0.643216i
$797$	45.2548			0.0567815			0.0283907	−	0.999597i	$-0.490962\pi$
$797$	45.2548			0.0567815			0.0283907	+	0.999597i	$0.490962\pi$
$798$	552.250	+	263.750i	0.692042	+	0.330514i
$799$	880.000	−	880.000i	1.10138	−	1.10138i
$800$	882.469	−	882.469i	1.10309	−	1.10309i
$801$	−1002.37	−	106.372i	−1.25140	−	0.132799i
$802$		−	576.000i		−	0.718204i
$803$			39.5980i			0.0493126i
$804$	−15.3137	−	7.31371i	−0.0190469	−	0.00909665i
$805$		−	576.000i		−	0.715528i
$806$			772.161i			0.958016i
$807$	−248.902	−	704.000i	−0.308428	−	0.872367i
$808$	−224.000	+	224.000i	−0.277228	+	0.277228i
$809$			1397.24i			1.72712i	0.504243	+	0.863562i	$0.331772\pi$
$809$			1397.24i			1.72712i	−0.504243	+	0.863562i	$0.668228\pi$
$810$	272.000	−	1267.14i	0.335802	−	1.56436i
$811$	231.000	−	231.000i	0.284834	−	0.284834i	−0.550200	−	0.835033i	$-0.685448\pi$
$811$	231.000	−	231.000i	0.284834	−	0.284834i	0.835033	+	0.550200i	$0.185448\pi$
$812$	−271.529	−	271.529i	−0.334395	−	0.334395i
$813$	386.671	+	184.671i	0.475610	+	0.227148i
$814$	−168.000	+	168.000i	−0.206388	+	0.206388i
$815$	2341.94			2.87354
$816$	1280.00	−	452.548i	1.56863	−	0.554594i
$817$	−238.000	+	238.000i	−0.291310	+	0.291310i
$818$		−	1156.83i		−	1.41421i
$819$	−52.3827	+	493.617i	−0.0639593	+	0.602707i
$820$	1792.00			2.18537
$821$	956.008	−	956.008i	1.16444	−	1.16444i	0.180952	−	0.983492i	$-0.442082\pi$
$821$	956.008	−	956.008i	1.16444	−	1.16444i	0.983492	−	0.180952i	$-0.0579178\pi$
$822$	−192.000	−	543.058i	−0.233577	−	0.660655i
$823$	1274.00			1.54800			0.773998	−	0.633189i	$-0.218254\pi$
$823$	1274.00			1.54800			0.773998	+	0.633189i	$0.218254\pi$
$824$	395.980	−	395.980i	0.480558	−	0.480558i
$825$	422.309	+	201.691i	0.511889	+	0.244474i
$826$	−312.000	−	312.000i	−0.377724	−	0.377724i
$827$	−766.504	+	766.504i	−0.926849	+	0.926849i	−0.997501	−	0.0706524i	$-0.977492\pi$
$827$	−766.504	+	766.504i	−0.926849	+	0.926849i	0.0706524	+	0.997501i	$0.477492\pi$
$828$	475.176	−	384.000i	0.573884	−	0.463768i
$829$			1130.00i			1.36309i	0.731777	+	0.681544i	$0.238691\pi$
$829$			1130.00i			1.36309i	−0.731777	+	0.681544i	$0.761309\pi$
$830$	−1583.92	−	1583.92i	−1.90834	−	1.90834i
$831$	368.000	+	1040.86i	0.442840	+	1.25254i
$832$	−832.000			−1.00000
$833$		−	876.812i		−	1.05260i
$834$	82.7452	−	173.255i	0.0992148	−	0.207740i
$835$			736.000i			0.881437i
$836$	−384.666			−0.460127
$837$	186.015	+	779.985i	0.222240	+	0.931882i
$838$	16.0000	+	16.0000i	0.0190931	+	0.0190931i
$839$	−93.3381	+	93.3381i	−0.111249	+	0.111249i	−0.760540	−	0.649291i	$-0.775066\pi$
$839$	−93.3381	+	93.3381i	−0.111249	+	0.111249i	0.649291	+	0.760540i	$0.275066\pi$
$840$	−351.058	+	735.058i	−0.417926	+	0.875069i
$841$	329.000			0.391201
$842$		−	59.3970i		−	0.0705427i
$843$	368.167	+	175.833i	0.436734	+	0.208581i
$844$	632.000			0.748815
$845$	956.008	−	956.008i	1.13137	−	1.13137i
$846$	−616.000	+	497.803i	−0.728132	+	0.588420i
$847$	315.000	−	315.000i	0.371901	−	0.371901i
$848$			814.587i			0.960598i
$849$	−633.568	+	224.000i	−0.746252	+	0.263840i
$850$	−1560.00	+	1560.00i	−1.83529	+	1.83529i
$851$	−356.382	−	356.382i	−0.418780	−	0.418780i
$852$	186.177	−	389.823i	0.218517	−	0.457539i
$853$	21.0000	−	21.0000i	0.0246190	−	0.0246190i	−0.694690	−	0.719309i	$-0.744459\pi$
$853$	21.0000	−	21.0000i	0.0246190	−	0.0246190i	0.719309	+	0.694690i	$0.244459\pi$
$854$			135.765i			0.158975i
$855$	−1088.00	−	1346.33i	−1.27251	−	1.57466i
$856$	896.000	−	896.000i	1.04673	−	1.04673i
$857$	67.8823			0.0792092			0.0396046	−	0.999215i	$-0.487390\pi$
$857$	67.8823			0.0792092			0.0396046	+	0.999215i	$0.487390\pi$
$858$	−104.000	−	294.156i	−0.121212	−	0.342840i
$859$		−	14.0000i		−	0.0162980i	−0.999967	−	0.00814901i	$-0.997406\pi$
$859$		−	14.0000i		−	0.0162980i	0.999967	−	0.00814901i	$-0.00259394\pi$
$860$	−316.784	−	316.784i	−0.368353	−	0.368353i
$861$	−672.000	+	237.588i	−0.780488	+	0.275944i
$862$		−	504.000i		−	0.584687i
$863$	257.387	+	257.387i	0.298247	+	0.298247i	0.840327	−	0.542080i	$-0.182363\pi$
$863$	257.387	+	257.387i	0.298247	+	0.298247i	−0.542080	+	0.840327i	$0.682363\pi$
$864$	−840.431	+	200.431i	−0.972721	+	0.231980i
$865$	32.0000	−	32.0000i	0.0369942	−	0.0369942i
$866$	1038.03	−	1038.03i	1.19865	−	1.19865i
$867$	−1445.33	+	511.000i	−1.66704	+	0.589389i
$868$		−	504.000i		−	0.580645i
$869$	−299.813	−	299.813i	−0.345010	−	0.345010i
$870$	362.039	+	1024.00i	0.416136	+	1.17701i
$871$	−13.0000	−	13.0000i	−0.0149254	−	0.0149254i
$872$	−33.9411			−0.0389233
$873$	−12.6569	−	1.34315i	−0.0144981	−	0.00153854i
$874$		−	816.000i		−	0.933638i
$875$		−	475.176i		−	0.543058i
$876$	107.196	+	51.1960i	0.122370	+	0.0584429i
$877$	−819.000	−	819.000i	−0.933865	−	0.933865i	0.0640794	−	0.997945i	$-0.479589\pi$
$877$	−819.000	−	819.000i	−0.933865	−	0.933865i	−0.997945	+	0.0640794i	$0.979589\pi$
$878$	851.357	+	851.357i	0.969654	+	0.969654i
$879$	671.362	+	320.638i	0.763780	+	0.364775i
$880$		−	512.000i		−	0.581818i
$881$	−678.823			−0.770514			−0.385257	−	0.922809i	$-0.625887\pi$
$881$	−678.823			−0.770514			−0.385257	+	0.922809i	$0.625887\pi$
$882$	−58.8843	+	554.884i	−0.0667623	+	0.629121i
$883$	−1120.00			−1.26840			−0.634202	−	0.773168i	$-0.718671\pi$
$883$	−1120.00			−1.26840			−0.634202	+	0.773168i	$0.718671\pi$
$884$	1470.78			1.66378
$885$	416.000	+	1176.63i	0.470056	+	1.32952i
$886$	192.000	+	192.000i	0.216704	+	0.216704i
$887$	−871.156			−0.982137			−0.491069	−	0.871121i	$-0.663394\pi$
$887$	−871.156			−0.982137			−0.491069	+	0.871121i	$0.663394\pi$
$888$	237.588	+	672.000i	0.267554	+	0.756757i
$889$	672.000	+	672.000i	0.755906	+	0.755906i
$890$	−1267.14	−	1267.14i	−1.42375	−	1.42375i
$891$	−175.917	−	272.083i	−0.197437	−	0.305368i
$892$	748.000	+	748.000i	0.838565	+	0.838565i
$893$			1057.83i			1.18458i
$894$	633.568	−	224.000i	0.708689	−	0.250559i
$895$	−1568.00	−	1568.00i	−1.75196	−	1.75196i
$896$	543.058			0.606092
$897$	624.000	−	220.617i	0.695652	−	0.245950i
$898$		−	1120.00i		−	1.24722i
$899$	−475.176	−	475.176i	−0.528560	−	0.528560i
$900$	1092.00	−	882.469i	1.21333	−	0.980521i
$901$		−	1440.00i		−	1.59822i
$902$	316.784	−	316.784i	0.351202	−	0.351202i
$903$	160.794	+	76.7939i	0.178066	+	0.0850431i
$904$	−96.0000	−	96.0000i	−0.106195	−	0.106195i
$905$	−362.039	−	362.039i	−0.400043	−	0.400043i
$906$	398.808	+	1128.00i	0.440186	+	1.24503i
$907$	224.000			0.246968			0.123484	−	0.992347i	$-0.460593\pi$
$907$	224.000			0.246968			0.123484	+	0.992347i	$0.460593\pi$
$908$	−712.764	+	712.764i	−0.784982	+	0.784982i
$909$	−277.186	+	224.000i	−0.304935	+	0.246425i
$910$	−624.000	+	624.000i	−0.685714	+	0.685714i
$911$	−1663.12			−1.82559			−0.912796	−	0.408415i	$-0.866082\pi$
$911$	−1663.12			−1.82559			−0.912796	+	0.408415i	$0.866082\pi$
$912$	−497.332	+	1041.33i	−0.545320	+	1.14181i
$913$	−560.000			−0.613363
$914$			659.024i			0.721032i
$915$	165.490	−	346.510i	0.180864	−	0.378699i
$916$	532.000	+	532.000i	0.580786	+	0.580786i
$917$	−475.176	−	475.176i	−0.518185	−	0.518185i
$918$	1485.69	−	354.315i	1.61839	−	0.385964i
$919$			1190.00i			1.29489i	0.762114	+	0.647443i	$0.224162\pi$
$919$			1190.00i			1.29489i	−0.762114	+	0.647443i	$0.775838\pi$
$920$	1086.12			1.18056
$921$	126.338	+	60.3381i	0.137175	+	0.0655137i
$922$	1632.00			1.77007
$923$	330.926	−	330.926i	0.358533	−	0.358533i
$924$	67.8823	+	192.000i	0.0734656	+	0.207792i
$925$	−819.000	−	819.000i	−0.885405	−	0.885405i
$926$		−	347.897i		−	0.375698i
$927$	490.000	−	395.980i	0.528587	−	0.427163i
$928$	512.000	−	512.000i	0.551724	−	0.551724i
$929$	−237.588	+	237.588i	−0.255746	+	0.255746i	−0.823321	−	0.567576i	$-0.807881\pi$
$929$	−237.588	+	237.588i	−0.255746	+	0.255746i	0.567576	+	0.823321i	$0.307881\pi$
$930$	−614.352	+	1286.35i	−0.660593	+	1.38317i
$931$	527.000	+	527.000i	0.566058	+	0.566058i
$932$		−	135.765i		−	0.145670i
$933$	118.794	+	336.000i	0.127325	+	0.360129i
$934$	−560.000	+	560.000i	−0.599572	+	0.599572i
$935$			905.097i			0.968018i
$936$	−930.774	−	98.7737i	−0.994416	−	0.105527i
$937$	736.000			0.785486			0.392743	−	0.919648i	$-0.371526\pi$
$937$	736.000			0.785486			0.392743	+	0.919648i	$0.371526\pi$
$938$	8.48528	+	8.48528i	0.00904614	+	0.00904614i
$939$	1493.41	−	528.000i	1.59043	−	0.562300i
$940$	−1408.00			−1.49787
$941$	50.9117	−	50.9117i	0.0541038	−	0.0541038i	−0.679537	−	0.733641i	$-0.737819\pi$
$941$	50.9117	−	50.9117i	0.0541038	−	0.0541038i	0.733641	+	0.679537i	$0.237819\pi$
$942$	552.250	+	263.750i	0.586252	+	0.279990i
$943$	672.000	+	672.000i	0.712619	+	0.712619i
$944$	588.313	−	588.313i	0.623213	−	0.623213i
$945$	−480.000	+	780.646i	−0.507937	+	0.826080i
$946$	−112.000			−0.118393
$947$	523.259	−	523.259i	0.552544	−	0.552544i	−0.374630	−	0.927174i	$-0.622230\pi$
$947$	523.259	−	523.259i	0.552544	−	0.552544i	0.927174	+	0.374630i	$0.122230\pi$
$948$	−1199.25	+	424.000i	−1.26503	+	0.447257i
$949$	91.0000	+	91.0000i	0.0958904	+	0.0958904i
$950$		−	1875.25i		−	1.97394i
$951$	82.7452	−	173.255i	0.0870086	−	0.182182i
$952$	−960.000			−1.00840
$953$	−1482.10			−1.55519			−0.777595	−	0.628766i	$-0.783560\pi$
$953$	−1482.10			−1.55519			−0.777595	+	0.628766i	$0.783560\pi$
$954$	−96.7065	+	911.294i	−0.101369	+	0.955234i
$955$		0			0
$956$	848.528	−	848.528i	0.887582	−	0.887582i
$957$	245.019	+	117.019i	0.256029	+	0.122277i
$958$	−1000.00			−1.04384
$959$			407.294i			0.424706i
$960$	−1386.04	−	661.961i	−1.44379	−	0.689543i
$961$			79.0000i			0.0822060i
$962$			772.161i			0.802662i
$963$	1108.74	−	896.000i	1.15134	−	0.930426i
$964$	−324.000	−	324.000i	−0.336100	−	0.336100i
$965$			712.764i			0.738615i
$966$	−407.294	+	144.000i	−0.421629	+	0.149068i
$967$	1139.00	−	1139.00i	1.17787	−	1.17787i	0.197584	−	0.980286i	$-0.436691\pi$
$967$	1139.00	−	1139.00i	1.17787	−	1.17787i	0.980286	−	0.197584i	$-0.0633094\pi$
$968$	593.970	+	593.970i	0.613605	+	0.613605i
$969$	879.167	−	1840.83i	0.907293	−	1.89972i
$970$	−16.0000	−	16.0000i	−0.0164948	−	0.0164948i
$971$	333.754			0.343722			0.171861	−	0.985121i	$-0.445022\pi$
$971$	333.754			0.343722			0.171861	+	0.985121i	$0.445022\pi$
$972$	−964.000	+	124.451i	−0.991770	+	0.128036i
$973$	−96.0000	+	96.0000i	−0.0986639	+	0.0986639i
$974$	−1620.69			−1.66395
$975$	1434.01	−	507.000i	1.47078	−	0.520000i
$976$	−256.000			−0.262295
$977$	684.479	−	684.479i	0.700593	−	0.700593i	−0.263945	−	0.964538i	$-0.585024\pi$
$977$	684.479	−	684.479i	0.700593	−	0.700593i	0.964538	+	0.263945i	$0.0850237\pi$
$978$	−585.484	−	1656.00i	−0.598655	−	1.69325i
$979$	−448.000			−0.457610
$980$	−701.450	+	701.450i	−0.715765	+	0.715765i
$981$	−37.9706	−	4.02944i	−0.0387060	−	0.00410748i
$982$	−1024.00	+	1024.00i	−1.04277	+	1.04277i
$983$	−511.945	+	511.945i	−0.520799	+	0.520799i	−0.917813	−	0.397014i	$-0.870047\pi$
$983$	−511.945	+	511.945i	−0.520799	+	0.520799i	0.397014	+	0.917813i	$0.370047\pi$
$984$	−448.000	−	1267.14i	−0.455285	−	1.28774i
$985$			640.000i			0.649746i
$986$	−905.097	+	905.097i	−0.917948	+	0.917948i
$987$	528.000	−	186.676i	0.534954	−	0.189135i
$988$	−884.000	+	884.000i	−0.894737	+	0.894737i
$989$		−	237.588i		−	0.240230i
$990$	60.7838	−	572.784i	0.0613978	−	0.578570i
$991$			992.000i			1.00101i	0.865734	+	0.500505i	$0.166852\pi$
$991$			992.000i			1.00101i	−0.865734	+	0.500505i	$0.833148\pi$
$992$	950.352			0.958016
$993$	627.151	−	1313.15i	0.631572	−	1.32241i
$994$	−216.000	+	216.000i	−0.217304	+	0.217304i
$995$	−724.077	+	724.077i	−0.727716	+	0.727716i
$996$	−724.020	+	1515.98i	−0.726928	+	1.52207i
$997$	326.000			0.326981			0.163490	−	0.986545i	$-0.447725\pi$
$997$	326.000			0.326981			0.163490	+	0.986545i	$0.447725\pi$
$998$	−947.523			−0.949422
$999$	186.015	+	779.985i	0.186201	+	0.780766i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.3.l.a.47.1	✓	4
3.2	odd	2	inner	156.3.l.a.47.2	yes	4
4.3	odd	2		156.3.l.b.47.2	yes	4
12.11	even	2		156.3.l.b.47.1	yes	4
13.5	odd	4		156.3.l.b.83.1	yes	4
39.5	even	4		156.3.l.b.83.2	yes	4
52.31	even	4	inner	156.3.l.a.83.2	yes	4
156.83	odd	4	inner	156.3.l.a.83.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.l.a.47.1	✓	4	1.1	even	1	trivial
156.3.l.a.47.2	yes	4	3.2	odd	2	inner
156.3.l.a.83.1	yes	4	156.83	odd	4	inner
156.3.l.a.83.2	yes	4	52.31	even	4	inner
156.3.l.b.47.1	yes	4	12.11	even	2
156.3.l.b.47.2	yes	4	4.3	odd	2
156.3.l.b.83.1	yes	4	13.5	odd	4
156.3.l.b.83.2	yes	4	39.5	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	156.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 - 1.41421i) q^{2} +(-2.82843 + 1.00000i) q^{3} +4.00000i q^{4} +(-5.65685 + 5.65685i) q^{5} +(5.41421 + 2.58579i) q^{6} +(-3.00000 - 3.00000i) q^{7} +(5.65685 - 5.65685i) q^{8} +(7.00000 - 5.65685i) q^{9} +O(q^{10})\)	\(q+(-1.41421 - 1.41421i) q^{2} +(-2.82843 + 1.00000i) q^{3} +4.00000i q^{4} +(-5.65685 + 5.65685i) q^{5} +(5.41421 + 2.58579i) q^{6} +(-3.00000 - 3.00000i) q^{7} +(5.65685 - 5.65685i) q^{8} +(7.00000 - 5.65685i) q^{9} +16.0000 q^{10} +(2.82843 - 2.82843i) q^{11} +(-4.00000 - 11.3137i) q^{12} -13.0000i q^{13} +8.48528i q^{14} +(10.3431 - 21.6569i) q^{15} -16.0000 q^{16} +28.2843 q^{17} +(-17.8995 - 1.89949i) q^{18} +(-17.0000 + 17.0000i) q^{19} +(-22.6274 - 22.6274i) q^{20} +(11.4853 + 5.48528i) q^{21} -8.00000 q^{22} -16.9706i q^{23} +(-10.3431 + 21.6569i) q^{24} -39.0000i q^{25} +(-18.3848 + 18.3848i) q^{26} +(-14.1421 + 23.0000i) q^{27} +(12.0000 - 12.0000i) q^{28} -22.6274i q^{29} +(-45.2548 + 16.0000i) q^{30} +(21.0000 - 21.0000i) q^{31} +(22.6274 + 22.6274i) q^{32} +(-5.17157 + 10.8284i) q^{33} +(-40.0000 - 40.0000i) q^{34} +33.9411 q^{35} +(22.6274 + 28.0000i) q^{36} +(21.0000 - 21.0000i) q^{37} +48.0833 q^{38} +(13.0000 + 36.7696i) q^{39} +64.0000i q^{40} +(-39.5980 + 39.5980i) q^{41} +(-8.48528 - 24.0000i) q^{42} +14.0000 q^{43} +(11.3137 + 11.3137i) q^{44} +(-7.59798 + 71.5980i) q^{45} +(-24.0000 + 24.0000i) q^{46} +(31.1127 - 31.1127i) q^{47} +(45.2548 - 16.0000i) q^{48} -31.0000i q^{49} +(-55.1543 + 55.1543i) q^{50} +(-80.0000 + 28.2843i) q^{51} +52.0000 q^{52} -50.9117i q^{53} +(52.5269 - 12.5269i) q^{54} +32.0000i q^{55} -33.9411 q^{56} +(31.0833 - 65.0833i) q^{57} +(-32.0000 + 32.0000i) q^{58} +(-36.7696 + 36.7696i) q^{59} +(86.6274 + 41.3726i) q^{60} +16.0000 q^{61} -59.3970 q^{62} +(-37.9706 - 4.02944i) q^{63} -64.0000i q^{64} +(73.5391 + 73.5391i) q^{65} +(22.6274 - 8.00000i) q^{66} +(1.00000 - 1.00000i) q^{67} +113.137i q^{68} +(16.9706 + 48.0000i) q^{69} +(-48.0000 - 48.0000i) q^{70} +(25.4558 + 25.4558i) q^{71} +(7.59798 - 71.5980i) q^{72} +(-7.00000 + 7.00000i) q^{73} -59.3970 q^{74} +(39.0000 + 110.309i) q^{75} +(-68.0000 - 68.0000i) q^{76} -16.9706 q^{77} +(33.6152 - 70.3848i) q^{78} -106.000i q^{79} +(90.5097 - 90.5097i) q^{80} +(17.0000 - 79.1960i) q^{81} +112.000 q^{82} +(-98.9949 - 98.9949i) q^{83} +(-21.9411 + 45.9411i) q^{84} +(-160.000 + 160.000i) q^{85} +(-19.7990 - 19.7990i) q^{86} +(22.6274 + 64.0000i) q^{87} -32.0000i q^{88} +(-79.1960 - 79.1960i) q^{89} +(112.000 - 90.5097i) q^{90} +(-39.0000 + 39.0000i) q^{91} +67.8823 q^{92} +(-38.3970 + 80.3970i) q^{93} -88.0000 q^{94} -192.333i q^{95} +(-86.6274 - 41.3726i) q^{96} +(-1.00000 - 1.00000i) q^{97} +(-43.8406 + 43.8406i) q^{98} +(3.79899 - 35.7990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 16 q^{6} - 12 q^{7} + 28 q^{9}+O(q^{10}) \) 4 * q + 16 * q^6 - 12 * q^7 + 28 * q^9	\( 4 q + 16 q^{6} - 12 q^{7} + 28 q^{9} + 64 q^{10} - 16 q^{12} + 64 q^{15} - 64 q^{16} - 32 q^{18} - 68 q^{19} + 12 q^{21} - 32 q^{22} - 64 q^{24} + 48 q^{28} + 84 q^{31} - 32 q^{33} - 160 q^{34} + 84 q^{37} + 52 q^{39} + 56 q^{43} + 128 q^{45} - 96 q^{46} - 320 q^{51} + 208 q^{52} + 80 q^{54} - 68 q^{57} - 128 q^{58} + 256 q^{60} + 64 q^{61} - 84 q^{63} + 4 q^{67} - 192 q^{70} - 128 q^{72} - 28 q^{73} + 156 q^{75} - 272 q^{76} + 208 q^{78} + 68 q^{81} + 448 q^{82} + 48 q^{84} - 640 q^{85} + 448 q^{90} - 156 q^{91} + 84 q^{93} - 352 q^{94} - 256 q^{96} - 4 q^{97} - 64 q^{99}+O(q^{100}) \) 4 * q + 16 * q^6 - 12 * q^7 + 28 * q^9 + 64 * q^10 - 16 * q^12 + 64 * q^15 - 64 * q^16 - 32 * q^18 - 68 * q^19 + 12 * q^21 - 32 * q^22 - 64 * q^24 + 48 * q^28 + 84 * q^31 - 32 * q^33 - 160 * q^34 + 84 * q^37 + 52 * q^39 + 56 * q^43 + 128 * q^45 - 96 * q^46 - 320 * q^51 + 208 * q^52 + 80 * q^54 - 68 * q^57 - 128 * q^58 + 256 * q^60 + 64 * q^61 - 84 * q^63 + 4 * q^67 - 192 * q^70 - 128 * q^72 - 28 * q^73 + 156 * q^75 - 272 * q^76 + 208 * q^78 + 68 * q^81 + 448 * q^82 + 48 * q^84 - 640 * q^85 + 448 * q^90 - 156 * q^91 + 84 * q^93 - 352 * q^94 - 256 * q^96 - 4 * q^97 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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