LMFDB - Embedded newform 195.3.j.c.8.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,3,Mod(8,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 1]))

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

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

chi := DirichletCharacter("195.8");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	195.j (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:	$5.31336515503$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.2
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	195.8
Dual form			195.3.j.c.122.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.82843i q^{2} +(2.70711 + 1.29289i) q^{3} -4.00000 q^{4} +(-4.94975 - 0.707107i) q^{5} +(-3.65685 + 7.65685i) q^{6} +5.00000i q^{7} +(5.65685 + 7.00000i) q^{9} +O(q^{10})$	\(q+2.82843i q^{2} +(2.70711 + 1.29289i) q^{3} -4.00000 q^{4} +(-4.94975 - 0.707107i) q^{5} +(-3.65685 + 7.65685i) q^{6} +5.00000i q^{7} +(5.65685 + 7.00000i) q^{9} +(2.00000 - 14.0000i) q^{10} +(-9.19239 - 9.19239i) q^{11} +(-10.8284 - 5.17157i) q^{12} +13.0000i q^{13} -14.1421 q^{14} +(-12.4853 - 8.31371i) q^{15} -16.0000 q^{16} +(-13.4350 + 13.4350i) q^{17} +(-19.7990 + 16.0000i) q^{18} +(22.0000 - 22.0000i) q^{19} +(19.7990 + 2.82843i) q^{20} +(-6.46447 + 13.5355i) q^{21} +(26.0000 - 26.0000i) q^{22} +(14.8492 + 14.8492i) q^{23} +(24.0000 + 7.00000i) q^{25} -36.7696 q^{26} +(6.26346 + 26.2635i) q^{27} -20.0000i q^{28} +38.1838 q^{29} +(23.5147 - 35.3137i) q^{30} +(-13.0000 - 13.0000i) q^{31} -45.2548i q^{32} +(-13.0000 - 36.7696i) q^{33} +(-38.0000 - 38.0000i) q^{34} +(3.53553 - 24.7487i) q^{35} +(-22.6274 - 28.0000i) q^{36} +15.0000i q^{37} +(62.2254 + 62.2254i) q^{38} +(-16.8076 + 35.1924i) q^{39} +(-24.7487 + 24.7487i) q^{41} +(-38.2843 - 18.2843i) q^{42} +(17.0000 - 17.0000i) q^{43} +(36.7696 + 36.7696i) q^{44} +(-23.0503 - 38.6482i) q^{45} +(-42.0000 + 42.0000i) q^{46} +72.1249 q^{47} +(-43.3137 - 20.6863i) q^{48} +24.0000 q^{49} +(-19.7990 + 67.8823i) q^{50} +(-53.7401 + 19.0000i) q^{51} -52.0000i q^{52} +(9.19239 - 9.19239i) q^{53} +(-74.2843 + 17.7157i) q^{54} +(39.0000 + 52.0000i) q^{55} +(88.0000 - 31.1127i) q^{57} +108.000i q^{58} +(-48.0833 + 48.0833i) q^{59} +(49.9411 + 33.2548i) q^{60} +67.0000 q^{61} +(36.7696 - 36.7696i) q^{62} +(-35.0000 + 28.2843i) q^{63} +64.0000 q^{64} +(9.19239 - 64.3467i) q^{65} +(104.000 - 36.7696i) q^{66} -100.000 q^{67} +(53.7401 - 53.7401i) q^{68} +(21.0000 + 59.3970i) q^{69} +(70.0000 + 10.0000i) q^{70} +(37.4767 - 37.4767i) q^{71} -76.0000 q^{73} -42.4264 q^{74} +(55.9203 + 49.9792i) q^{75} +(-88.0000 + 88.0000i) q^{76} +(45.9619 - 45.9619i) q^{77} +(-99.5391 - 47.5391i) q^{78} +89.0000i q^{79} +(79.1960 + 11.3137i) q^{80} +(-17.0000 + 79.1960i) q^{81} +(-70.0000 - 70.0000i) q^{82} +93.3381 q^{83} +(25.8579 - 54.1421i) q^{84} +(76.0000 - 57.0000i) q^{85} +(48.0833 + 48.0833i) q^{86} +(103.368 + 49.3675i) q^{87} +(4.94975 - 4.94975i) q^{89} +(109.314 - 65.1960i) q^{90} -65.0000 q^{91} +(-59.3970 - 59.3970i) q^{92} +(-18.3848 - 52.0000i) q^{93} +204.000i q^{94} +(-124.451 + 93.3381i) q^{95} +(58.5097 - 122.510i) q^{96} -25.0000 q^{97} +67.8823i q^{98} +(12.3467 - 116.347i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{3} - 16 q^{4} + 8 q^{6}+O(q^{10}) $ 4 * q + 8 * q^3 - 16 * q^4 + 8 * q^6	$ 4 q + 8 q^{3} - 16 q^{4} + 8 q^{6} + 8 q^{10} - 32 q^{12} - 16 q^{15} - 64 q^{16} + 88 q^{19} - 40 q^{21} + 104 q^{22} + 96 q^{25} - 40 q^{27} + 128 q^{30} - 52 q^{31} - 52 q^{33} - 152 q^{34} - 104 q^{39} - 40 q^{42} + 68 q^{43} - 112 q^{45} - 168 q^{46} - 128 q^{48} + 96 q^{49} - 184 q^{54} + 156 q^{55} + 352 q^{57} + 64 q^{60} + 268 q^{61} - 140 q^{63} + 256 q^{64} + 416 q^{66} - 400 q^{67} + 84 q^{69} + 280 q^{70} - 304 q^{73} + 136 q^{75} - 352 q^{76} - 104 q^{78} - 68 q^{81} - 280 q^{82} + 160 q^{84} + 304 q^{85} + 108 q^{87} + 392 q^{90} - 260 q^{91} - 128 q^{96} - 100 q^{97} - 208 q^{99}+O(q^{100}) $ 4 * q + 8 * q^3 - 16 * q^4 + 8 * q^6 + 8 * q^10 - 32 * q^12 - 16 * q^15 - 64 * q^16 + 88 * q^19 - 40 * q^21 + 104 * q^22 + 96 * q^25 - 40 * q^27 + 128 * q^30 - 52 * q^31 - 52 * q^33 - 152 * q^34 - 104 * q^39 - 40 * q^42 + 68 * q^43 - 112 * q^45 - 168 * q^46 - 128 * q^48 + 96 * q^49 - 184 * q^54 + 156 * q^55 + 352 * q^57 + 64 * q^60 + 268 * q^61 - 140 * q^63 + 256 * q^64 + 416 * q^66 - 400 * q^67 + 84 * q^69 + 280 * q^70 - 304 * q^73 + 136 * q^75 - 352 * q^76 - 104 * q^78 - 68 * q^81 - 280 * q^82 + 160 * q^84 + 304 * q^85 + 108 * q^87 + 392 * q^90 - 260 * q^91 - 128 * q^96 - 100 * q^97 - 208 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$			2.82843i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$2$			2.82843i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$3$	2.70711	+	1.29289i	0.902369	+	0.430964i
$3$	2.70711	+	1.29289i	0.902369	+	0.430964i
$4$	−4.00000			−1.00000
$5$	−4.94975	−	0.707107i	−0.989949	−	0.141421i
$5$	−4.94975	−	0.707107i	−0.989949	−	0.141421i
$6$	−3.65685	+	7.65685i	−0.609476	+	1.27614i
$7$			5.00000i			0.714286i	0.934050	+	0.357143i	$0.116249\pi$
$7$			5.00000i			0.714286i	−0.934050	+	0.357143i	$0.883751\pi$
$8$		0			0
$9$	5.65685	+	7.00000i	0.628539	+	0.777778i
$10$	2.00000	−	14.0000i	0.200000	−	1.40000i
$11$	−9.19239	−	9.19239i	−0.835672	−	0.835672i	0.152614	−	0.988286i	$-0.451231\pi$
$11$	−9.19239	−	9.19239i	−0.835672	−	0.835672i	−0.988286	+	0.152614i	$0.951231\pi$
$12$	−10.8284	−	5.17157i	−0.902369	−	0.430964i
$13$			13.0000i			1.00000i
$13$			13.0000i			1.00000i
$14$	−14.1421			−1.01015
$15$	−12.4853	−	8.31371i	−0.832352	−	0.554247i
$16$	−16.0000			−1.00000
$17$	−13.4350	+	13.4350i	−0.790296	+	0.790296i	−0.981542	−	0.191246i	$-0.938747\pi$
$17$	−13.4350	+	13.4350i	−0.790296	+	0.790296i	0.191246	+	0.981542i	$0.438747\pi$
$18$	−19.7990	+	16.0000i	−1.09994	+	0.888889i
$19$	22.0000	−	22.0000i	1.15789	−	1.15789i	0.172967	−	0.984928i	$-0.444665\pi$
$19$	22.0000	−	22.0000i	1.15789	−	1.15789i	0.984928	−	0.172967i	$-0.0553354\pi$
$20$	19.7990	+	2.82843i	0.989949	+	0.141421i
$21$	−6.46447	+	13.5355i	−0.307832	+	0.644549i
$22$	26.0000	−	26.0000i	1.18182	−	1.18182i
$23$	14.8492	+	14.8492i	0.645619	+	0.645619i	0.951931	−	0.306312i	$-0.0990951\pi$
$23$	14.8492	+	14.8492i	0.645619	+	0.645619i	−0.306312	+	0.951931i	$0.599095\pi$
$24$		0			0
$25$	24.0000	+	7.00000i	0.960000	+	0.280000i
$26$	−36.7696			−1.41421
$27$	6.26346	+	26.2635i	0.231980	+	0.972721i
$28$		−	20.0000i		−	0.714286i
$29$	38.1838			1.31668			0.658341	−	0.752720i	$-0.271259\pi$
$29$	38.1838			1.31668			0.658341	+	0.752720i	$0.271259\pi$
$30$	23.5147	−	35.3137i	0.783824	−	1.17712i
$31$	−13.0000	−	13.0000i	−0.419355	−	0.419355i	0.465626	−	0.884981i	$-0.345829\pi$
$31$	−13.0000	−	13.0000i	−0.419355	−	0.419355i	−0.884981	+	0.465626i	$0.845829\pi$
$32$		−	45.2548i		−	1.41421i
$33$	−13.0000	−	36.7696i	−0.393939	−	1.11423i
$34$	−38.0000	−	38.0000i	−1.11765	−	1.11765i
$35$	3.53553	−	24.7487i	0.101015	−	0.707107i
$36$	−22.6274	−	28.0000i	−0.628539	−	0.777778i
$37$			15.0000i			0.405405i	0.979240	+	0.202703i	$0.0649725\pi$
$37$			15.0000i			0.405405i	−0.979240	+	0.202703i	$0.935027\pi$
$38$	62.2254	+	62.2254i	1.63751	+	1.63751i
$39$	−16.8076	+	35.1924i	−0.430964	+	0.902369i
$40$		0			0
$41$	−24.7487	+	24.7487i	−0.603628	+	0.603628i	−0.941273	−	0.337646i	$-0.890369\pi$
$41$	−24.7487	+	24.7487i	−0.603628	+	0.603628i	0.337646	+	0.941273i	$0.390369\pi$
$42$	−38.2843	−	18.2843i	−0.911530	−	0.435340i
$43$	17.0000	−	17.0000i	0.395349	−	0.395349i	−0.481240	−	0.876589i	$-0.659813\pi$
$43$	17.0000	−	17.0000i	0.395349	−	0.395349i	0.876589	+	0.481240i	$0.159813\pi$
$44$	36.7696	+	36.7696i	0.835672	+	0.835672i
$45$	−23.0503	−	38.6482i	−0.512228	−	0.858850i
$46$	−42.0000	+	42.0000i	−0.913043	+	0.913043i
$47$	72.1249			1.53457			0.767286	−	0.641305i	$-0.221607\pi$
$47$	72.1249			1.53457			0.767286	+	0.641305i	$0.221607\pi$
$48$	−43.3137	−	20.6863i	−0.902369	−	0.430964i
$49$	24.0000			0.489796
$50$	−19.7990	+	67.8823i	−0.395980	+	1.35765i
$51$	−53.7401	+	19.0000i	−1.05373	+	0.372549i
$52$		−	52.0000i		−	1.00000i
$53$	9.19239	−	9.19239i	0.173441	−	0.173441i	−0.615048	−	0.788490i	$-0.710863\pi$
$53$	9.19239	−	9.19239i	0.173441	−	0.173441i	0.788490	+	0.615048i	$0.210863\pi$
$54$	−74.2843	+	17.7157i	−1.37563	+	0.328069i
$55$	39.0000	+	52.0000i	0.709091	+	0.945455i
$56$		0			0
$57$	88.0000	−	31.1127i	1.54386	−	0.545837i
$58$			108.000i			1.86207i
$59$	−48.0833	+	48.0833i	−0.814971	+	0.814971i	−0.985374	−	0.170404i	$-0.945493\pi$
$59$	−48.0833	+	48.0833i	−0.814971	+	0.814971i	0.170404	+	0.985374i	$0.445493\pi$
$60$	49.9411	+	33.2548i	0.832352	+	0.554247i
$61$	67.0000			1.09836			0.549180	−	0.835704i	$-0.314940\pi$
$61$	67.0000			1.09836			0.549180	+	0.835704i	$0.314940\pi$
$62$	36.7696	−	36.7696i	0.593057	−	0.593057i
$63$	−35.0000	+	28.2843i	−0.555556	+	0.448957i
$64$	64.0000			1.00000
$65$	9.19239	−	64.3467i	0.141421	−	0.989949i
$66$	104.000	−	36.7696i	1.57576	−	0.557114i
$67$	−100.000			−1.49254			−0.746269	−	0.665645i	$-0.768157\pi$
$67$	−100.000			−1.49254			−0.746269	+	0.665645i	$0.768157\pi$
$68$	53.7401	−	53.7401i	0.790296	−	0.790296i
$69$	21.0000	+	59.3970i	0.304348	+	0.860826i
$70$	70.0000	+	10.0000i	1.00000	+	0.142857i
$71$	37.4767	−	37.4767i	0.527840	−	0.527840i	−0.392088	−	0.919928i	$-0.628247\pi$
$71$	37.4767	−	37.4767i	0.527840	−	0.527840i	0.919928	+	0.392088i	$0.128247\pi$
$72$		0			0
$73$	−76.0000			−1.04110			−0.520548	−	0.853832i	$-0.674272\pi$
$73$	−76.0000			−1.04110			−0.520548	+	0.853832i	$0.674272\pi$
$74$	−42.4264			−0.573330
$75$	55.9203	+	49.9792i	0.745604	+	0.666389i
$76$	−88.0000	+	88.0000i	−1.15789	+	1.15789i
$77$	45.9619	−	45.9619i	0.596908	−	0.596908i
$78$	−99.5391	−	47.5391i	−1.27614	−	0.609476i
$79$			89.0000i			1.12658i	0.826258	+	0.563291i	$0.190465\pi$
$79$			89.0000i			1.12658i	−0.826258	+	0.563291i	$0.809535\pi$
$80$	79.1960	+	11.3137i	0.989949	+	0.141421i
$81$	−17.0000	+	79.1960i	−0.209877	+	0.977728i
$82$	−70.0000	−	70.0000i	−0.853659	−	0.853659i
$83$	93.3381			1.12456			0.562278	−	0.826948i	$-0.309925\pi$
$83$	93.3381			1.12456			0.562278	+	0.826948i	$0.309925\pi$
$84$	25.8579	−	54.1421i	0.307832	−	0.644549i
$85$	76.0000	−	57.0000i	0.894118	−	0.670588i
$86$	48.0833	+	48.0833i	0.559108	+	0.559108i
$87$	103.368	+	49.3675i	1.18813	+	0.567443i
$88$		0			0
$89$	4.94975	−	4.94975i	0.0556151	−	0.0556151i	−0.678752	−	0.734367i	$-0.737479\pi$
$89$	4.94975	−	4.94975i	0.0556151	−	0.0556151i	0.734367	+	0.678752i	$0.237479\pi$
$90$	109.314	−	65.1960i	1.21460	−	0.724400i
$91$	−65.0000			−0.714286
$92$	−59.3970	−	59.3970i	−0.645619	−	0.645619i
$93$	−18.3848	−	52.0000i	−0.197686	−	0.559140i
$94$			204.000i			2.17021i
$95$	−124.451	+	93.3381i	−1.31001	+	0.982506i
$96$	58.5097	−	122.510i	0.609476	−	1.27614i
$97$	−25.0000			−0.257732			−0.128866	−	0.991662i	$-0.541134\pi$
$97$	−25.0000			−0.257732			−0.128866	+	0.991662i	$0.541134\pi$
$98$			67.8823i			0.692676i
$99$	12.3467	−	116.347i	0.124714	−	1.17522i
$100$	−96.0000	−	28.0000i	−0.960000	−	0.280000i
$101$	8.48528			0.0840127			0.0420063	−	0.999117i	$-0.486625\pi$
$101$	8.48528			0.0840127			0.0420063	+	0.999117i	$0.486625\pi$
$102$	−53.7401	−	152.000i	−0.526864	−	1.49020i
$103$	1.00000	−	1.00000i	0.00970874	−	0.00970874i	−0.702236	−	0.711944i	$-0.747815\pi$
$103$	1.00000	−	1.00000i	0.00970874	−	0.00970874i	0.711944	+	0.702236i	$0.247815\pi$
$104$		0			0
$105$	41.5685	−	62.4264i	0.395891	−	0.594537i
$106$	26.0000	+	26.0000i	0.245283	+	0.245283i
$107$	−41.7193	−	41.7193i	−0.389900	−	0.389900i	0.484752	−	0.874652i	$-0.338910\pi$
$107$	−41.7193	−	41.7193i	−0.389900	−	0.389900i	−0.874652	+	0.484752i	$0.838910\pi$
$108$	−25.0538	−	105.054i	−0.231980	−	0.972721i
$109$	99.0000	−	99.0000i	0.908257	−	0.908257i	−0.0878747	−	0.996132i	$-0.528007\pi$
$109$	99.0000	−	99.0000i	0.908257	−	0.908257i	0.996132	+	0.0878747i	$0.0280075\pi$
$110$	−147.078	+	110.309i	−1.33707	+	1.00281i
$111$	−19.3934	+	40.6066i	−0.174715	+	0.365825i
$112$		−	80.0000i		−	0.714286i
$113$	−14.1421	+	14.1421i	−0.125152	+	0.125152i	−0.766908	−	0.641757i	$-0.778206\pi$
$113$	−14.1421	+	14.1421i	−0.125152	+	0.125152i	0.641757	+	0.766908i	$0.278206\pi$
$114$	88.0000	+	248.902i	0.771930	+	2.18335i
$115$	−63.0000	−	84.0000i	−0.547826	−	0.730435i
$116$	−152.735			−1.31668
$117$	−91.0000	+	73.5391i	−0.777778	+	0.628539i
$118$	−136.000	−	136.000i	−1.15254	−	1.15254i
$119$	−67.1751	−	67.1751i	−0.564497	−	0.564497i
$120$		0			0
$121$			48.0000i			0.396694i
$122$			189.505i			1.55332i
$123$	−98.9949	+	35.0000i	−0.804837	+	0.284553i
$124$	52.0000	+	52.0000i	0.419355	+	0.419355i
$125$	−113.844	−	51.6188i	−0.910754	−	0.412950i
$126$	−80.0000	−	98.9949i	−0.634921	−	0.785674i
$127$	−156.000	−	156.000i	−1.22835	−	1.22835i	−0.964589	−	0.263757i	$-0.915038\pi$
$127$	−156.000	−	156.000i	−1.22835	−	1.22835i	−0.263757	−	0.964589i	$-0.584962\pi$
$128$		0			0
$129$	68.0000	−	24.0416i	0.527132	−	0.186369i
$130$	182.000	+	26.0000i	1.40000	+	0.200000i
$131$			70.7107i			0.539776i	0.962892	+	0.269888i	$0.0869867\pi$
$131$			70.7107i			0.539776i	−0.962892	+	0.269888i	$0.913013\pi$
$132$	52.0000	+	147.078i	0.393939	+	1.11423i
$133$	110.000	+	110.000i	0.827068	+	0.827068i
$134$		−	282.843i		−	2.11077i
$135$	−12.4315	−	134.426i	−0.0920849	−	0.995751i
$136$		0			0
$137$	56.5685			0.412909			0.206455	−	0.978456i	$-0.433807\pi$
$137$	56.5685			0.412909			0.206455	+	0.978456i	$0.433807\pi$
$138$	−168.000	+	59.3970i	−1.21739	+	0.430413i
$139$		−	223.000i		−	1.60432i	−0.597111	−	0.802158i	$-0.703685\pi$
$139$		−	223.000i		−	1.60432i	0.597111	−	0.802158i	$-0.296315\pi$
$140$	−14.1421	+	98.9949i	−0.101015	+	0.707107i
$141$	195.250	+	93.2498i	1.38475	+	0.661346i
$142$	106.000	+	106.000i	0.746479	+	0.746479i
$143$	119.501	−	119.501i	0.835672	−	0.835672i
$144$	−90.5097	−	112.000i	−0.628539	−	0.777778i
$145$	−189.000	−	27.0000i	−1.30345	−	0.186207i
$146$		−	214.960i		−	1.47233i
$147$	64.9706	+	31.0294i	0.441977	+	0.211085i
$148$		−	60.0000i		−	0.405405i
$149$	−53.0330	−	53.0330i	−0.355926	−	0.355926i	0.506383	−	0.862309i	$-0.330982\pi$
$149$	−53.0330	−	53.0330i	−0.355926	−	0.355926i	−0.862309	+	0.506383i	$0.830982\pi$
$150$	−141.362	+	158.167i	−0.942417	+	1.05444i
$151$	22.0000	−	22.0000i	0.145695	−	0.145695i	−0.630497	−	0.776192i	$-0.717149\pi$
$151$	22.0000	−	22.0000i	0.145695	−	0.145695i	0.776192	+	0.630497i	$0.217149\pi$
$152$		0			0
$153$	−170.045	−	18.0452i	−1.11141	−	0.117942i
$154$	130.000	+	130.000i	0.844156	+	0.844156i
$155$	55.1543	+	73.5391i	0.355834	+	0.474446i
$156$	67.2304	−	140.770i	0.430964	−	0.902369i
$157$	106.000	−	106.000i	0.675159	−	0.675159i	−0.283742	−	0.958901i	$-0.591576\pi$
$157$	106.000	−	106.000i	0.675159	−	0.675159i	0.958901	+	0.283742i	$0.0915758\pi$
$158$	−251.730			−1.59323
$159$	36.7696	−	13.0000i	0.231255	−	0.0817610i
$160$	−32.0000	+	224.000i	−0.200000	+	1.40000i
$161$	−74.2462	+	74.2462i	−0.461157	+	0.461157i
$162$	−224.000	−	48.0833i	−1.38272	−	0.296810i
$163$	271.000			1.66258			0.831288	−	0.555841i	$-0.187604\pi$
$163$	271.000			1.66258			0.831288	+	0.555841i	$0.187604\pi$
$164$	98.9949	−	98.9949i	0.603628	−	0.603628i
$165$	38.3467	+	191.192i	0.232404	+	1.15874i
$166$			264.000i			1.59036i
$167$	114.551			0.685936			0.342968	−	0.939347i	$-0.388568\pi$
$167$	114.551			0.685936			0.342968	+	0.939347i	$0.388568\pi$
$168$		0			0
$169$	−169.000			−1.00000
$170$	161.220	+	214.960i	0.948355	+	1.26447i
$171$	278.451	+	29.5492i	1.62837	+	0.172802i
$172$	−68.0000	+	68.0000i	−0.395349	+	0.395349i
$173$	−175.362	−	175.362i	−1.01366	−	1.01366i	−0.999905	−	0.0137505i	$-0.995623\pi$
$173$	−175.362	−	175.362i	−1.01366	−	1.01366i	−0.0137505	−	0.999905i	$-0.504377\pi$
$174$	−139.632	+	292.368i	−0.802485	+	1.68027i
$175$	−35.0000	+	120.000i	−0.200000	+	0.685714i
$176$	147.078	+	147.078i	0.835672	+	0.835672i
$177$	−192.333	+	68.0000i	−1.08663	+	0.384181i
$178$	14.0000	+	14.0000i	0.0786517	+	0.0786517i
$179$			83.4386i			0.466137i	0.972460	+	0.233069i	$0.0748767\pi$
$179$			83.4386i			0.466137i	−0.972460	+	0.233069i	$0.925123\pi$
$180$	92.2010	+	154.593i	0.512228	+	0.858850i
$181$		−	13.0000i		−	0.0718232i	−0.999355	−	0.0359116i	$-0.988567\pi$
$181$		−	13.0000i		−	0.0718232i	0.999355	−	0.0359116i	$-0.0114335\pi$
$182$		−	183.848i		−	1.01015i
$183$	181.376	+	86.6238i	0.991127	+	0.473354i
$184$		0			0
$185$	10.6066	−	74.2462i	0.0573330	−	0.401331i
$186$	147.078	−	52.0000i	0.790743	−	0.279570i
$187$	247.000			1.32086
$188$	−288.500			−1.53457
$189$	−131.317	+	31.3173i	−0.694800	+	0.165700i
$190$	−264.000	−	352.000i	−1.38947	−	1.85263i
$191$		−	57.9828i		−	0.303575i	−0.988413	−	0.151787i	$-0.951497\pi$
$191$		−	57.9828i		−	0.303575i	0.988413	−	0.151787i	$-0.0485029\pi$
$192$	173.255	+	82.7452i	0.902369	+	0.430964i
$193$	−99.0000			−0.512953			−0.256477	−	0.966550i	$-0.582562\pi$
$193$	−99.0000			−0.512953			−0.256477	+	0.966550i	$0.582562\pi$
$194$		−	70.7107i		−	0.364488i
$195$	108.078	−	162.309i	0.554247	−	0.832352i
$196$	−96.0000			−0.489796
$197$			93.3381i			0.473797i	0.971534	+	0.236899i	$0.0761310\pi$
$197$			93.3381i			0.473797i	−0.971534	+	0.236899i	$0.923869\pi$
$198$	329.078	+	34.9218i	1.66201	+	0.176373i
$199$	196.000			0.984925			0.492462	−	0.870334i	$-0.336097\pi$
$199$	196.000			0.984925			0.492462	+	0.870334i	$0.336097\pi$
$200$		0			0
$201$	−270.711	−	129.289i	−1.34682	−	0.643230i
$202$			24.0000i			0.118812i
$203$			190.919i			0.940487i
$204$	214.960	−	76.0000i	1.05373	−	0.372549i
$205$	140.000	−	105.000i	0.682927	−	0.512195i
$206$	2.82843	+	2.82843i	0.0137302	+	0.0137302i
$207$	−19.9447	+	187.945i	−0.0963512	+	0.907945i
$208$		−	208.000i		−	1.00000i
$209$	−404.465			−1.93524
$210$	176.569	+	117.574i	0.840803	+	0.559874i
$211$	16.0000			0.0758294			0.0379147	−	0.999281i	$-0.487928\pi$
$211$	16.0000			0.0758294			0.0379147	+	0.999281i	$0.487928\pi$
$212$	−36.7696	+	36.7696i	−0.173441	+	0.173441i
$213$	149.907	−	53.0000i	0.703787	−	0.248826i
$214$	118.000	−	118.000i	0.551402	−	0.551402i
$215$	−96.1665	+	72.1249i	−0.447286	+	0.335465i
$216$		0			0
$217$	65.0000	−	65.0000i	0.299539	−	0.299539i
$218$	280.014	+	280.014i	1.28447	+	1.28447i
$219$	−205.740	−	98.2599i	−0.939453	−	0.448675i
$220$	−156.000	−	208.000i	−0.709091	−	0.945455i
$221$	−174.655	−	174.655i	−0.790296	−	0.790296i
$222$	−114.853	−	54.8528i	−0.517355	−	0.247085i
$223$			80.0000i			0.358744i	0.983781	+	0.179372i	$0.0574066\pi$
$223$			80.0000i			0.358744i	−0.983781	+	0.179372i	$0.942593\pi$
$224$	226.274			1.01015
$225$	86.7645	+	207.598i	0.385620	+	0.922658i
$226$	−40.0000	−	40.0000i	−0.176991	−	0.176991i
$227$		−	127.279i		−	0.560701i	−0.959898	−	0.280351i	$-0.909549\pi$
$227$		−	127.279i		−	0.560701i	0.959898	−	0.280351i	$-0.0904508\pi$
$228$	−352.000	+	124.451i	−1.54386	+	0.545837i
$229$	48.0000	+	48.0000i	0.209607	+	0.209607i	0.804100	−	0.594493i	$-0.202647\pi$
$229$	48.0000	+	48.0000i	0.209607	+	0.209607i	−0.594493	+	0.804100i	$0.702647\pi$
$230$	237.588	−	178.191i	1.03299	−	0.774743i
$231$	183.848	−	65.0000i	0.795878	−	0.281385i
$232$		0			0
$233$	30.4056	+	30.4056i	0.130496	+	0.130496i	0.769338	−	0.638842i	$-0.220586\pi$
$233$	30.4056	+	30.4056i	0.130496	+	0.130496i	−0.638842	+	0.769338i	$0.720586\pi$
$234$	−208.000	−	257.387i	−0.888889	−	1.09994i
$235$	−357.000	−	51.0000i	−1.51915	−	0.217021i
$236$	192.333	−	192.333i	0.814971	−	0.814971i
$237$	−115.067	+	240.933i	−0.485517	+	1.01659i
$238$	190.000	−	190.000i	0.798319	−	0.798319i
$239$	−31.8198	−	31.8198i	−0.133137	−	0.133137i	0.637398	−	0.770535i	$-0.280011\pi$
$239$	−31.8198	−	31.8198i	−0.133137	−	0.133137i	−0.770535	+	0.637398i	$0.780011\pi$
$240$	199.765	+	133.019i	0.832352	+	0.554247i
$241$	−181.000	+	181.000i	−0.751037	+	0.751037i	−0.974673	−	0.223636i	$-0.928207\pi$
$241$	−181.000	+	181.000i	−0.751037	+	0.751037i	0.223636	+	0.974673i	$0.428207\pi$
$242$	−135.765			−0.561010
$243$	−148.413	+	192.413i	−0.610752	+	0.791822i
$244$	−268.000			−1.09836
$245$	−118.794	−	16.9706i	−0.484873	−	0.0692676i
$246$	−98.9949	−	280.000i	−0.402418	−	1.13821i
$247$	286.000	+	286.000i	1.15789	+	1.15789i
$248$		0			0
$249$	252.676	+	120.676i	1.01476	+	0.484643i
$250$	146.000	−	322.000i	0.584000	−	1.28800i
$251$	336.583			1.34097			0.670484	−	0.741924i	$-0.266087\pi$
$251$	336.583			1.34097			0.670484	+	0.741924i	$0.266087\pi$
$252$	140.000	−	113.137i	0.555556	−	0.448957i
$253$		−	273.000i		−	1.07905i
$254$	441.235	−	441.235i	1.73714	−	1.73714i
$255$	279.435	−	56.0452i	1.09582	−	0.219785i
$256$	256.000			1.00000
$257$	−147.078	+	147.078i	−0.572289	+	0.572289i	−0.932767	−	0.360479i	$-0.882613\pi$
$257$	−147.078	+	147.078i	−0.572289	+	0.572289i	0.360479	+	0.932767i	$0.382613\pi$
$258$	68.0000	+	192.333i	0.263566	+	0.745477i
$259$	−75.0000			−0.289575
$260$	−36.7696	+	257.387i	−0.141421	+	0.989949i
$261$	216.000	+	267.286i	0.827586	+	1.02409i
$262$	−200.000			−0.763359
$263$	192.333	−	192.333i	0.731304	−	0.731304i	−0.239574	−	0.970878i	$-0.577008\pi$
$263$	192.333	−	192.333i	0.731304	−	0.731304i	0.970878	+	0.239574i	$0.0770077\pi$
$264$		0			0
$265$	−52.0000	+	39.0000i	−0.196226	+	0.147170i
$266$	−311.127	+	311.127i	−1.16965	+	1.16965i
$267$	19.7990	−	7.00000i	0.0741535	−	0.0262172i
$268$	400.000			1.49254
$269$	−173.948			−0.646648			−0.323324	−	0.946288i	$-0.604800\pi$
$269$	−173.948			−0.646648			−0.323324	+	0.946288i	$0.604800\pi$
$270$	380.215	−	35.1615i	1.40820	−	0.130228i
$271$	−288.000	+	288.000i	−1.06273	+	1.06273i	−0.0648346	+	0.997896i	$0.520652\pi$
$271$	−288.000	+	288.000i	−1.06273	+	1.06273i	−0.997896	+	0.0648346i	$0.979348\pi$
$272$	214.960	−	214.960i	0.790296	−	0.790296i
$273$	−175.962	−	84.0381i	−0.644549	−	0.307832i
$274$			160.000i			0.583942i
$275$	−156.271	−	284.964i	−0.568257	−	1.03623i
$276$	−84.0000	−	237.588i	−0.304348	−	0.860826i
$277$	−177.000	−	177.000i	−0.638989	−	0.638989i	0.311317	−	0.950306i	$-0.399230\pi$
$277$	−177.000	−	177.000i	−0.638989	−	0.638989i	−0.950306	+	0.311317i	$0.899230\pi$
$278$	630.739			2.26885
$279$	17.4609	−	164.539i	0.0625839	−	0.589746i
$280$		0			0
$281$	−132.936	−	132.936i	−0.473082	−	0.473082i	0.429828	−	0.902911i	$-0.358574\pi$
$281$	−132.936	−	132.936i	−0.473082	−	0.473082i	−0.902911	+	0.429828i	$0.858574\pi$
$282$	−263.750	+	552.250i	−0.935284	+	1.95833i
$283$	−162.000	+	162.000i	−0.572438	+	0.572438i	−0.932809	−	0.360371i	$-0.882650\pi$
$283$	−162.000	+	162.000i	−0.572438	+	0.572438i	0.360371	+	0.932809i	$0.382650\pi$
$284$	−149.907	+	149.907i	−0.527840	+	0.527840i
$285$	−457.578	+	91.7746i	−1.60554	+	0.322016i
$286$	338.000	+	338.000i	1.18182	+	1.18182i
$287$	−123.744	−	123.744i	−0.431163	−	0.431163i
$288$	316.784	−	256.000i	1.09994	−	0.888889i
$289$		−	72.0000i		−	0.249135i
$290$	76.3675	−	534.573i	0.263336	−	1.84335i
$291$	−67.6777	−	32.3223i	−0.232569	−	0.111073i
$292$	304.000			1.04110
$293$		−	250.316i		−	0.854320i	−0.904176	−	0.427160i	$-0.859514\pi$
$293$		−	250.316i		−	0.854320i	0.904176	−	0.427160i	$-0.140486\pi$
$294$	−87.7645	+	183.765i	−0.298519	+	0.625049i
$295$	272.000	−	204.000i	0.922034	−	0.691525i
$296$		0			0
$297$	183.848	−	299.000i	0.619016	−	1.00673i
$298$	150.000	−	150.000i	0.503356	−	0.503356i
$299$	−193.040	+	193.040i	−0.645619	+	0.645619i
$300$	−223.681	−	199.917i	−0.745604	−	0.666389i
$301$	85.0000	+	85.0000i	0.282392	+	0.282392i
$302$	62.2254	+	62.2254i	0.206044	+	0.206044i
$303$	22.9706	+	10.9706i	0.0758104	+	0.0362065i
$304$	−352.000	+	352.000i	−1.15789	+	1.15789i
$305$	−331.633	−	47.3762i	−1.08732	−	0.155332i
$306$	51.0395	−	480.960i	0.166796	−	1.57177i
$307$			561.000i			1.82736i	0.406433	+	0.913681i	$0.366773\pi$
$307$			561.000i			1.82736i	−0.406433	+	0.913681i	$0.633227\pi$
$308$	−183.848	+	183.848i	−0.596908	+	0.596908i
$309$	4.00000	−	1.41421i	0.0129450	−	0.00457674i
$310$	−208.000	+	156.000i	−0.670968	+	0.503226i
$311$	−250.316			−0.804874			−0.402437	−	0.915448i	$-0.631837\pi$
$311$	−250.316			−0.804874			−0.402437	+	0.915448i	$0.631837\pi$
$312$		0			0
$313$	342.000	+	342.000i	1.09265	+	1.09265i	0.995245	+	0.0974071i	$0.0310549\pi$
$313$	342.000	+	342.000i	1.09265	+	1.09265i	0.0974071	+	0.995245i	$0.468945\pi$
$314$	299.813	+	299.813i	0.954819	+	0.954819i
$315$	193.241	−	115.251i	0.613464	−	0.365877i
$316$		−	356.000i		−	1.12658i
$317$			185.262i			0.584423i	0.956354	+	0.292211i	$0.0943911\pi$
$317$			185.262i			0.584423i	−0.956354	+	0.292211i	$0.905609\pi$
$318$	36.7696	+	104.000i	0.115628	+	0.327044i
$319$	−351.000	−	351.000i	−1.10031	−	1.10031i
$320$	−316.784	−	45.2548i	−0.989949	−	0.141421i
$321$	−59.0000	−	166.877i	−0.183801	−	0.519867i
$322$	−210.000	−	210.000i	−0.652174	−	0.652174i
$323$			591.141i			1.83016i
$324$	68.0000	−	316.784i	0.209877	−	0.977728i
$325$	−91.0000	+	312.000i	−0.280000	+	0.960000i
$326$			766.504i			2.35124i
$327$	396.000	−	140.007i	1.21101	−	0.428156i
$328$		0			0
$329$			360.624i			1.09612i
$330$	−540.774	+	108.461i	−1.63871	+	0.328669i
$331$	−156.000	−	156.000i	−0.471299	−	0.471299i	0.431036	−	0.902335i	$-0.358148\pi$
$331$	−156.000	−	156.000i	−0.471299	−	0.471299i	−0.902335	+	0.431036i	$0.858148\pi$
$332$	−373.352			−1.12456
$333$	−105.000	+	84.8528i	−0.315315	+	0.254813i
$334$			324.000i			0.970060i
$335$	494.975	+	70.7107i	1.47754	+	0.211077i
$336$	103.431	−	216.569i	0.307832	−	0.644549i
$337$	−251.000	−	251.000i	−0.744807	−	0.744807i	0.228692	−	0.973499i	$-0.426555\pi$
$337$	−251.000	−	251.000i	−0.744807	−	0.744807i	−0.973499	+	0.228692i	$0.926555\pi$
$338$		−	478.004i		−	1.41421i
$339$	−56.5685	+	20.0000i	−0.166869	+	0.0589971i
$340$	−304.000	+	228.000i	−0.894118	+	0.670588i
$341$			239.002i			0.700886i
$342$	−83.5778	+	787.578i	−0.244379	+	2.30286i
$343$			365.000i			1.06414i
$344$		0			0
$345$	−61.9447	−	308.849i	−0.179550	−	0.895215i
$346$	496.000	−	496.000i	1.43353	−	1.43353i
$347$	−99.7021	−	99.7021i	−0.287326	−	0.287326i	0.548696	−	0.836022i	$-0.315124\pi$
$347$	−99.7021	−	99.7021i	−0.287326	−	0.287326i	−0.836022	+	0.548696i	$0.815124\pi$
$348$	−413.470	−	197.470i	−1.18813	−	0.567443i
$349$	354.000	+	354.000i	1.01433	+	1.01433i	0.999896	+	0.0144308i	$0.00459362\pi$
$349$	354.000	+	354.000i	1.01433	+	1.01433i	0.0144308	+	0.999896i	$0.495406\pi$
$350$	−339.411	−	98.9949i	−0.969746	−	0.282843i
$351$	−341.425	+	81.4249i	−0.972721	+	0.231980i
$352$	−416.000	+	416.000i	−1.18182	+	1.18182i
$353$	−504.874			−1.43024			−0.715119	−	0.699002i	$-0.753628\pi$
$353$	−504.874			−1.43024			−0.715119	+	0.699002i	$0.753628\pi$
$354$	−192.333	−	544.000i	−0.543314	−	1.53672i
$355$	−212.000	+	159.000i	−0.597183	+	0.447887i
$356$	−19.7990	+	19.7990i	−0.0556151	+	0.0556151i
$357$	−95.0000	−	268.701i	−0.266106	−	0.752663i
$358$	−236.000			−0.659218
$359$	213.546	−	213.546i	0.594836	−	0.594836i	−0.344098	−	0.938934i	$-0.611815\pi$
$359$	213.546	−	213.546i	0.594836	−	0.594836i	0.938934	+	0.344098i	$0.111815\pi$
$360$		0			0
$361$		−	607.000i		−	1.68144i
$362$	36.7696			0.101573
$363$	−62.0589	+	129.941i	−0.170961	+	0.357965i
$364$	260.000			0.714286
$365$	376.181	+	53.7401i	1.03063	+	0.147233i
$366$	−245.009	+	513.009i	−0.669424	+	1.40166i
$367$	218.000	−	218.000i	0.594005	−	0.594005i	−0.344705	−	0.938711i	$-0.612021\pi$
$367$	218.000	−	218.000i	0.594005	−	0.594005i	0.938711	+	0.344705i	$0.112021\pi$
$368$	−237.588	−	237.588i	−0.645619	−	0.645619i
$369$	−313.241	−	33.2412i	−0.848892	−	0.0900844i
$370$	210.000	+	30.0000i	0.567568	+	0.0810811i
$371$	45.9619	+	45.9619i	0.123887	+	0.123887i
$372$	73.5391	+	208.000i	0.197686	+	0.559140i
$373$	171.000	+	171.000i	0.458445	+	0.458445i	0.898145	−	0.439700i	$-0.144915\pi$
$373$	171.000	+	171.000i	0.458445	+	0.458445i	−0.439700	+	0.898145i	$0.644915\pi$
$374$			698.621i			1.86797i
$375$	−241.451	−	286.926i	−0.643869	−	0.765136i
$376$		0			0
$377$			496.389i			1.31668i
$378$	−88.5786	−	371.421i	−0.234335	−	0.982596i
$379$	−103.000	+	103.000i	−0.271768	+	0.271768i	−0.829812	−	0.558044i	$-0.811552\pi$
$379$	−103.000	+	103.000i	−0.271768	+	0.271768i	0.558044	+	0.829812i	$0.311552\pi$
$380$	497.803	−	373.352i	1.31001	−	0.982506i
$381$	−220.617	−	624.000i	−0.579048	−	1.63780i
$382$	164.000			0.429319
$383$	492.146			1.28498			0.642489	−	0.766295i	$-0.277902\pi$
$383$	492.146			1.28498			0.642489	+	0.766295i	$0.277902\pi$
$384$		0			0
$385$	−260.000	+	195.000i	−0.675325	+	0.506494i
$386$		−	280.014i		−	0.725426i
$387$	215.167	+	22.8335i	0.555986	+	0.0590012i
$388$	100.000			0.257732
$389$			123.037i			0.316289i	0.987416	+	0.158145i	$0.0505512\pi$
$389$			123.037i			0.316289i	−0.987416	+	0.158145i	$0.949449\pi$
$390$	459.078	+	305.691i	1.17712	+	0.783824i
$391$	−399.000			−1.02046
$392$		0			0
$393$	−91.4214	+	191.421i	−0.232624	+	0.487077i
$394$	−264.000			−0.670051
$395$	62.9325	−	440.528i	0.159323	−	1.11526i
$396$	−49.3869	+	465.387i	−0.124714	+	1.17522i
$397$			191.000i			0.481108i	0.970636	+	0.240554i	$0.0773292\pi$
$397$			191.000i			0.481108i	−0.970636	+	0.240554i	$0.922671\pi$
$398$			554.372i			1.39289i
$399$	155.563	+	440.000i	0.389883	+	1.10276i
$400$	−384.000	−	112.000i	−0.960000	−	0.280000i
$401$	−400.222	−	400.222i	−0.998061	−	0.998061i	0.00193718	−	0.999998i	$-0.499383\pi$
$401$	−400.222	−	400.222i	−0.998061	−	0.998061i	−0.999998	+	0.00193718i	$0.999383\pi$
$402$	365.685	−	765.685i	0.909665	−	1.90469i
$403$	169.000	−	169.000i	0.419355	−	0.419355i
$404$	−33.9411			−0.0840127
$405$	140.146	−	379.979i	0.346039	−	0.938220i
$406$	−540.000			−1.33005
$407$	137.886	−	137.886i	0.338786	−	0.338786i
$408$		0			0
$409$	494.000	−	494.000i	1.20782	−	1.20782i	0.236094	−	0.971730i	$-0.424133\pi$
$409$	494.000	−	494.000i	1.20782	−	1.20782i	0.971730	−	0.236094i	$-0.0758672\pi$
$410$	296.985	+	395.980i	0.724353	+	0.965804i
$411$	153.137	+	73.1371i	0.372596	+	0.177949i
$412$	−4.00000	+	4.00000i	−0.00970874	+	0.00970874i
$413$	−240.416	−	240.416i	−0.582122	−	0.582122i
$414$	−531.588	−	56.4121i	−1.28403	−	0.136261i
$415$	−462.000	−	66.0000i	−1.11325	−	0.159036i
$416$	588.313			1.41421
$417$	288.315	−	603.685i	0.691403	−	1.44769i
$418$		−	1144.00i		−	2.73684i
$419$	541.644			1.29271			0.646353	−	0.763039i	$-0.276293\pi$
$419$	541.644			1.29271			0.646353	+	0.763039i	$0.276293\pi$
$420$	−166.274	+	249.706i	−0.395891	+	0.594537i
$421$	−38.0000	−	38.0000i	−0.0902613	−	0.0902613i	0.660534	−	0.750796i	$-0.270330\pi$
$421$	−38.0000	−	38.0000i	−0.0902613	−	0.0902613i	−0.750796	+	0.660534i	$0.770330\pi$
$422$			45.2548i			0.107239i
$423$	408.000	+	504.874i	0.964539	+	1.19356i
$424$		0			0
$425$	−416.486	+	228.395i	−0.979967	+	0.537401i
$426$	149.907	+	424.000i	0.351894	+	0.995305i
$427$			335.000i			0.784543i
$428$	166.877	+	166.877i	0.389900	+	0.389900i
$429$	478.004	−	169.000i	1.11423	−	0.393939i
$430$	−204.000	−	272.000i	−0.474419	−	0.632558i
$431$	370.524	−	370.524i	0.859684	−	0.859684i	−0.131616	−	0.991301i	$-0.542017\pi$
$431$	370.524	−	370.524i	0.859684	−	0.859684i	0.991301	+	0.131616i	$0.0420167\pi$
$432$	−100.215	−	420.215i	−0.231980	−	0.972721i
$433$	−238.000	+	238.000i	−0.549654	+	0.549654i	−0.926341	−	0.376687i	$-0.877063\pi$
$433$	−238.000	+	238.000i	−0.549654	+	0.549654i	0.376687	+	0.926341i	$0.377063\pi$
$434$	183.848	+	183.848i	0.423612	+	0.423612i
$435$	−476.735	−	317.449i	−1.09594	−	0.729767i
$436$	−396.000	+	396.000i	−0.908257	+	0.908257i
$437$	653.367			1.49512
$438$	277.921	−	581.921i	0.634523	−	1.32859i
$439$	333.000			0.758542			0.379271	−	0.925286i	$-0.376175\pi$
$439$	333.000			0.758542			0.379271	+	0.925286i	$0.376175\pi$
$440$		0			0
$441$	135.765	+	168.000i	0.307856	+	0.380952i
$442$	494.000	−	494.000i	1.11765	−	1.11765i
$443$	304.763	−	304.763i	0.687953	−	0.687953i	−0.273826	−	0.961779i	$-0.588289\pi$
$443$	304.763	−	304.763i	0.687953	−	0.687953i	0.961779	+	0.273826i	$0.0882894\pi$
$444$	77.5736	−	162.426i	0.174715	−	0.365825i
$445$	−28.0000	+	21.0000i	−0.0629213	+	0.0471910i
$446$	−226.274			−0.507341
$447$	−75.0000	−	212.132i	−0.167785	−	0.474568i
$448$			320.000i			0.714286i
$449$	−48.7904	+	48.7904i	−0.108665	+	0.108665i	−0.759349	−	0.650684i	$-0.774482\pi$
$449$	−48.7904	+	48.7904i	−0.108665	+	0.108665i	0.650684	+	0.759349i	$0.274482\pi$
$450$	−587.176	+	245.407i	−1.30484	+	0.545349i
$451$	455.000			1.00887
$452$	56.5685	−	56.5685i	0.125152	−	0.125152i
$453$	88.0000	−	31.1127i	0.194260	−	0.0686815i
$454$	360.000			0.792952
$455$	321.734	+	45.9619i	0.707107	+	0.101015i
$456$		0			0
$457$	413.000			0.903720			0.451860	−	0.892089i	$-0.350761\pi$
$457$	413.000			0.903720			0.451860	+	0.892089i	$0.350761\pi$
$458$	−135.765	+	135.765i	−0.296429	+	0.296429i
$459$	−437.000	−	268.701i	−0.952070	−	0.585404i
$460$	252.000	+	336.000i	0.547826	+	0.730435i
$461$	225.567	−	225.567i	0.489299	−	0.489299i	−0.418786	−	0.908085i	$-0.637544\pi$
$461$	225.567	−	225.567i	0.489299	−	0.489299i	0.908085	+	0.418786i	$0.137544\pi$
$462$	183.848	+	520.000i	0.397939	+	1.12554i
$463$	153.000			0.330454			0.165227	−	0.986256i	$-0.447164\pi$
$463$	153.000			0.330454			0.165227	+	0.986256i	$0.447164\pi$
$464$	−610.940			−1.31668
$465$	54.2304	+	270.387i	0.116625	+	0.581477i
$466$	−86.0000	+	86.0000i	−0.184549	+	0.184549i
$467$	−396.687	+	396.687i	−0.849437	+	0.849437i	−0.990063	−	0.140626i	$-0.955088\pi$
$467$	−396.687	+	396.687i	−0.849437	+	0.849437i	0.140626	+	0.990063i	$0.455088\pi$
$468$	364.000	−	294.156i	0.777778	−	0.628539i
$469$		−	500.000i		−	1.06610i
$470$	144.250	−	1009.75i	0.306914	−	2.14840i
$471$	424.000	−	149.907i	0.900212	−	0.318273i
$472$		0			0
$473$	−312.541			−0.660764
$474$	−681.460	−	325.460i	−1.43768	−	0.686625i
$475$	682.000	−	374.000i	1.43579	−	0.787368i
$476$	268.701	+	268.701i	0.564497	+	0.564497i
$477$	116.347	+	12.3467i	0.243913	+	0.0258841i
$478$	90.0000	−	90.0000i	0.188285	−	0.188285i
$479$	229.810	−	229.810i	0.479770	−	0.479770i	−0.425288	−	0.905058i	$-0.639827\pi$
$479$	229.810	−	229.810i	0.479770	−	0.479770i	0.905058	+	0.425288i	$0.139827\pi$
$480$	−376.235	+	565.019i	−0.783824	+	1.17712i
$481$	−195.000			−0.405405
$482$	−511.945	−	511.945i	−1.06213	−	1.06213i
$483$	−296.985	+	105.000i	−0.614875	+	0.217391i
$484$		−	192.000i		−	0.396694i
$485$	123.744	+	17.6777i	0.255142	+	0.0364488i
$486$	−544.225	−	419.775i	−1.11981	−	0.863734i
$487$	−65.0000			−0.133470			−0.0667351	−	0.997771i	$-0.521258\pi$
$487$	−65.0000			−0.133470			−0.0667351	+	0.997771i	$0.521258\pi$
$488$		0			0
$489$	733.626	+	350.374i	1.50026	+	0.716511i
$490$	48.0000	−	336.000i	0.0979592	−	0.685714i
$491$	69.2965			0.141133			0.0705667	−	0.997507i	$-0.477519\pi$
$491$	69.2965			0.141133			0.0705667	+	0.997507i	$0.477519\pi$
$492$	395.980	−	140.000i	0.804837	−	0.284553i
$493$	−513.000	+	513.000i	−1.04057	+	1.04057i
$494$	−808.930	+	808.930i	−1.63751	+	1.63751i
$495$	−143.383	+	567.156i	−0.289662	+	1.14577i
$496$	208.000	+	208.000i	0.419355	+	0.419355i
$497$	187.383	+	187.383i	0.377029	+	0.377029i
$498$	−341.324	+	714.676i	−0.685389	+	1.43509i
$499$	−111.000	+	111.000i	−0.222445	+	0.222445i	−0.809527	−	0.587082i	$-0.800276\pi$
$499$	−111.000	+	111.000i	−0.222445	+	0.222445i	0.587082	+	0.809527i	$0.300276\pi$
$500$	455.377	+	206.475i	0.910754	+	0.412950i
$501$	310.103	+	148.103i	0.618967	+	0.295614i
$502$			952.000i			1.89641i
$503$	−373.352	+	373.352i	−0.742251	+	0.742251i	−0.973011	−	0.230760i	$-0.925879\pi$
$503$	−373.352	+	373.352i	−0.742251	+	0.742251i	0.230760	+	0.973011i	$0.425879\pi$
$504$		0			0
$505$	−42.0000	−	6.00000i	−0.0831683	−	0.0118812i
$506$	772.161			1.52601
$507$	−457.501	−	218.499i	−0.902369	−	0.430964i
$508$	624.000	+	624.000i	1.22835	+	1.22835i
$509$	569.221	+	569.221i	1.11831	+	1.11831i	0.991989	+	0.126323i	$0.0403176\pi$
$509$	569.221	+	569.221i	1.11831	+	1.11831i	0.126323	+	0.991989i	$0.459682\pi$
$510$	158.520	+	790.362i	0.310823	+	1.54973i
$511$		−	380.000i		−	0.743640i
$512$			724.077i			1.41421i
$513$	715.592	+	440.000i	1.39492	+	0.857700i
$514$	−416.000	−	416.000i	−0.809339	−	0.809339i
$515$	−5.65685	+	4.24264i	−0.0109842	+	0.00823814i
$516$	−272.000	+	96.1665i	−0.527132	+	0.186369i
$517$	−663.000	−	663.000i	−1.28240	−	1.28240i
$518$		−	212.132i		−	0.409521i
$519$	−248.000	−	701.450i	−0.477842	−	1.35154i
$520$		0			0
$521$		−	439.820i		−	0.844185i	−0.906553	−	0.422093i	$-0.861296\pi$
$521$		−	439.820i		−	0.844185i	0.906553	−	0.422093i	$-0.138704\pi$
$522$	−756.000	+	610.940i	−1.44828	+	1.17038i
$523$	30.0000	+	30.0000i	0.0573614	+	0.0573614i	0.735206	−	0.677844i	$-0.237086\pi$
$523$	30.0000	+	30.0000i	0.0573614	+	0.0573614i	−0.677844	+	0.735206i	$0.737086\pi$
$524$		−	282.843i		−	0.539776i
$525$	−249.896	+	279.602i	−0.475992	+	0.532574i
$526$	544.000	+	544.000i	1.03422	+	1.03422i
$527$	349.311			0.662829
$528$	208.000	+	588.313i	0.393939	+	1.11423i
$529$		−	88.0000i		−	0.166352i
$530$	−110.309	−	147.078i	−0.208130	−	0.277506i
$531$	−608.583	−	64.5828i	−1.14611	−	0.121625i
$532$	−440.000	−	440.000i	−0.827068	−	0.827068i
$533$	−321.734	−	321.734i	−0.603628	−	0.603628i
$534$	19.7990	+	56.0000i	0.0370768	+	0.104869i
$535$	177.000	+	236.000i	0.330841	+	0.441121i
$536$		0			0
$537$	−107.877	+	225.877i	−0.200889	+	0.420628i
$538$		−	492.000i		−	0.914498i
$539$	−220.617	−	220.617i	−0.409309	−	0.409309i
$540$	49.7258	+	537.706i	0.0920849	+	0.995751i
$541$	−198.000	+	198.000i	−0.365989	+	0.365989i	−0.866012	−	0.500023i	$-0.833325\pi$
$541$	−198.000	+	198.000i	−0.365989	+	0.365989i	0.500023	+	0.866012i	$0.333325\pi$
$542$	−814.587	−	814.587i	−1.50293	−	1.50293i
$543$	16.8076	−	35.1924i	0.0309532	−	0.0648110i
$544$	608.000	+	608.000i	1.11765	+	1.11765i
$545$	−560.029	+	420.021i	−1.02758	+	0.770682i
$546$	237.696	−	497.696i	0.435340	−	0.911530i
$547$	57.0000	−	57.0000i	0.104205	−	0.104205i	−0.653082	−	0.757287i	$-0.726524\pi$
$547$	57.0000	−	57.0000i	0.104205	−	0.104205i	0.757287	+	0.653082i	$0.226524\pi$
$548$	−226.274			−0.412909
$549$	379.009	+	469.000i	0.690363	+	0.854281i
$550$	806.000	−	442.000i	1.46545	−	0.803636i
$551$	840.043	−	840.043i	1.52458	−	1.52458i
$552$		0			0
$553$	−445.000			−0.804702
$554$	500.632	−	500.632i	0.903667	−	0.903667i
$555$	124.706	−	187.279i	0.224695	−	0.337440i
$556$			892.000i			1.60432i
$557$	649.124			1.16539			0.582697	−	0.812690i	$-0.301998\pi$
$557$	649.124			1.16539			0.582697	+	0.812690i	$0.301998\pi$
$558$	465.387	+	49.3869i	0.834027	+	0.0885069i
$559$	221.000	+	221.000i	0.395349	+	0.395349i
$560$	−56.5685	+	395.980i	−0.101015	+	0.707107i
$561$	668.655	+	319.345i	1.19190	+	0.569242i
$562$	376.000	−	376.000i	0.669039	−	0.669039i
$563$	−396.687	−	396.687i	−0.704595	−	0.704595i	0.260798	−	0.965393i	$-0.416014\pi$
$563$	−396.687	−	396.687i	−0.704595	−	0.704595i	−0.965393	+	0.260798i	$0.916014\pi$
$564$	−780.999	−	372.999i	−1.38475	−	0.661346i
$565$	80.0000	−	60.0000i	0.141593	−	0.106195i
$566$	−458.205	−	458.205i	−0.809550	−	0.809550i
$567$	−395.980	−	85.0000i	−0.698377	−	0.149912i
$568$		0			0
$569$		−	878.227i		−	1.54346i	−0.635953	−	0.771728i	$-0.719393\pi$
$569$		−	878.227i		−	1.54346i	0.635953	−	0.771728i	$-0.280607\pi$
$570$	−259.578	−	1294.23i	−0.455400	−	2.27057i
$571$			753.000i			1.31874i	0.751819	+	0.659370i	$0.229177\pi$
$571$			753.000i			1.31874i	−0.751819	+	0.659370i	$0.770823\pi$
$572$	−478.004	+	478.004i	−0.835672	+	0.835672i
$573$	74.9655	−	156.966i	0.130830	−	0.273936i
$574$	350.000	−	350.000i	0.609756	−	0.609756i
$575$	252.437	+	460.327i	0.439021	+	0.800568i
$576$	362.039	+	448.000i	0.628539	+	0.777778i
$577$	−287.000			−0.497400			−0.248700	−	0.968581i	$-0.580003\pi$
$577$	−287.000			−0.497400			−0.248700	+	0.968581i	$0.580003\pi$
$578$	203.647			0.352330
$579$	−268.004	−	127.996i	−0.462873	−	0.221065i
$580$	756.000	+	108.000i	1.30345	+	0.186207i
$581$			466.690i			0.803254i
$582$	91.4214	−	191.421i	0.157081	−	0.328903i
$583$	−169.000			−0.289880
$584$		0			0
$585$	502.427	−	299.653i	0.858850	−	0.512228i
$586$	708.000			1.20819
$587$			972.979i			1.65755i	0.559586	+	0.828773i	$0.310960\pi$
$587$			972.979i			1.65755i	−0.559586	+	0.828773i	$0.689040\pi$
$588$	−259.882	−	124.118i	−0.441977	−	0.211085i
$589$	−572.000			−0.971138
$590$	576.999	+	769.332i	0.977965	+	1.30395i
$591$	−120.676	+	252.676i	−0.204190	+	0.427540i
$592$		−	240.000i		−	0.405405i
$593$			363.453i			0.612905i	0.951886	+	0.306453i	$0.0991421\pi$
$593$			363.453i			0.612905i	−0.951886	+	0.306453i	$0.900858\pi$
$594$	845.700	+	520.000i	1.42374	+	0.875421i
$595$	285.000	+	380.000i	0.478992	+	0.638655i
$596$	212.132	+	212.132i	0.355926	+	0.355926i
$597$	530.593	+	253.407i	0.888765	+	0.424467i
$598$	−546.000	−	546.000i	−0.913043	−	0.913043i
$599$	−72.1249			−0.120409			−0.0602044	−	0.998186i	$-0.519175\pi$
$599$	−72.1249			−0.120409			−0.0602044	+	0.998186i	$0.519175\pi$
$600$		0			0
$601$	−677.000			−1.12646			−0.563228	−	0.826302i	$-0.690441\pi$
$601$	−677.000			−1.12646			−0.563228	+	0.826302i	$0.690441\pi$
$602$	−240.416	+	240.416i	−0.399363	+	0.399363i
$603$	−565.685	−	700.000i	−0.938118	−	1.16086i
$604$	−88.0000	+	88.0000i	−0.145695	+	0.145695i
$605$	33.9411	−	237.588i	0.0561010	−	0.392707i
$606$	−31.0294	+	64.9706i	−0.0512037	+	0.107212i
$607$	−256.000	+	256.000i	−0.421746	+	0.421746i	−0.885805	−	0.464058i	$-0.846393\pi$
$607$	−256.000	+	256.000i	−0.421746	+	0.421746i	0.464058	+	0.885805i	$0.346393\pi$
$608$	−995.606	−	995.606i	−1.63751	−	1.63751i
$609$	−246.838	+	516.838i	−0.405316	+	0.848666i
$610$	134.000	−	938.000i	0.219672	−	1.53770i
$611$			937.624i			1.53457i
$612$	680.181	+	72.1808i	1.11141	+	0.117942i
$613$		−	221.000i		−	0.360522i	−0.983619	−	0.180261i	$-0.942306\pi$
$613$		−	221.000i		−	0.360522i	0.983619	−	0.180261i	$-0.0576942\pi$
$614$	−1586.75			−2.58428
$615$	514.749	−	103.241i	0.836990	−	0.167872i
$616$		0			0
$617$		−	770.746i		−	1.24918i	−0.780951	−	0.624592i	$-0.785265\pi$
$617$		−	770.746i		−	1.24918i	0.780951	−	0.624592i	$-0.214735\pi$
$618$	4.00000	+	11.3137i	0.00647249	+	0.0183070i
$619$	−644.000	−	644.000i	−1.04039	−	1.04039i	−0.999149	−	0.0412384i	$-0.986870\pi$
$619$	−644.000	−	644.000i	−1.04039	−	1.04039i	−0.0412384	−	0.999149i	$-0.513130\pi$
$620$	−220.617	−	294.156i	−0.355834	−	0.474446i
$621$	−296.985	+	483.000i	−0.478236	+	0.777778i
$622$		−	708.000i		−	1.13826i
$623$	24.7487	+	24.7487i	0.0397251	+	0.0397251i
$624$	268.922	−	563.078i	0.430964	−	0.902369i
$625$	527.000	+	336.000i	0.843200	+	0.537600i
$626$	−967.322	+	967.322i	−1.54524	+	1.54524i
$627$	−1094.93	−	522.930i	−1.74630	−	0.834019i
$628$	−424.000	+	424.000i	−0.675159	+	0.675159i
$629$	−201.525	−	201.525i	−0.320390	−	0.320390i
$630$	325.980	+	546.569i	0.517428	+	0.867569i
$631$	719.000	−	719.000i	1.13946	−	1.13946i	0.150914	−	0.988547i	$-0.451778\pi$
$631$	719.000	−	719.000i	1.13946	−	1.13946i	0.988547	−	0.150914i	$-0.0482218\pi$
$632$		0			0
$633$	43.3137	+	20.6863i	0.0684261	+	0.0326798i
$634$	−524.000			−0.826498
$635$	661.852	+	882.469i	1.04229	+	1.38972i
$636$	−147.078	+	52.0000i	−0.231255	+	0.0817610i
$637$			312.000i			0.489796i
$638$	992.778	−	992.778i	1.55608	−	1.55608i
$639$	474.337	+	50.3366i	0.742311	+	0.0787740i
$640$		0			0
$641$	831.558			1.29728			0.648641	−	0.761095i	$-0.275338\pi$
$641$	831.558			1.29728			0.648641	+	0.761095i	$0.275338\pi$
$642$	472.000	−	166.877i	0.735202	−	0.259933i
$643$		−	1039.00i		−	1.61586i	−0.589276	−	0.807932i	$-0.700587\pi$
$643$		−	1039.00i		−	1.61586i	0.589276	−	0.807932i	$-0.299413\pi$
$644$	296.985	−	296.985i	0.461157	−	0.461157i
$645$	−353.583	+	70.9167i	−0.548190	+	0.109948i
$646$	−1672.00			−2.58824
$647$	−632.861	+	632.861i	−0.978146	+	0.978146i	−0.999766	−	0.0216201i	$-0.993118\pi$
$647$	−632.861	+	632.861i	−0.978146	+	0.978146i	0.0216201	+	0.999766i	$0.493118\pi$
$648$		0			0
$649$	884.000			1.36210
$650$	−882.469	−	257.387i	−1.35765	−	0.395980i
$651$	260.000	−	91.9239i	0.399386	−	0.141204i
$652$	−1084.00			−1.66258
$653$	−325.269	+	325.269i	−0.498115	+	0.498115i	−0.910851	−	0.412736i	$-0.864573\pi$
$653$	−325.269	+	325.269i	−0.498115	+	0.498115i	0.412736	+	0.910851i	$0.364573\pi$
$654$	396.000	+	1120.06i	0.605505	+	1.71263i
$655$	50.0000	−	350.000i	0.0763359	−	0.534351i
$656$	395.980	−	395.980i	0.603628	−	0.603628i
$657$	−429.921	−	532.000i	−0.654370	−	0.809741i
$658$	−1020.00			−1.55015
$659$	1129.96			1.71465			0.857327	−	0.514773i	$-0.172124\pi$
$659$	1129.96			1.71465			0.857327	+	0.514773i	$0.172124\pi$
$660$	−153.387	−	764.770i	−0.232404	−	1.15874i
$661$	−97.0000	+	97.0000i	−0.146747	+	0.146747i	−0.776663	−	0.629916i	$-0.783089\pi$
$661$	−97.0000	+	97.0000i	−0.146747	+	0.146747i	0.629916	+	0.776663i	$0.283089\pi$
$662$	441.235	−	441.235i	0.666518	−	0.666518i
$663$	−247.000	−	698.621i	−0.372549	−	1.05373i
$664$		0			0
$665$	−466.690	−	622.254i	−0.701790	−	0.935720i
$666$	−240.000	−	296.985i	−0.360360	−	0.445923i
$667$	567.000	+	567.000i	0.850075	+	0.850075i
$668$	−458.205			−0.685936
$669$	−103.431	+	216.569i	−0.154606	+	0.323720i
$670$	−200.000	+	1400.00i	−0.298507	+	2.08955i
$671$	−615.890	−	615.890i	−0.917869	−	0.917869i
$672$	612.548	+	292.548i	0.911530	+	0.435340i
$673$	813.000	−	813.000i	1.20802	−	1.20802i	0.236358	−	0.971666i	$-0.424046\pi$
$673$	813.000	−	813.000i	1.20802	−	1.20802i	0.971666	−	0.236358i	$-0.0759537\pi$
$674$	709.935	−	709.935i	1.05332	−	1.05332i
$675$	−33.5212	+	674.167i	−0.0496611	+	0.998766i
$676$	676.000			1.00000
$677$	−716.299	−	716.299i	−1.05805	−	1.05805i	−0.998208	−	0.0598411i	$-0.980941\pi$
$677$	−716.299	−	716.299i	−1.05805	−	1.05805i	−0.0598411	−	0.998208i	$-0.519059\pi$
$678$	−56.5685	−	160.000i	−0.0834344	−	0.235988i
$679$		−	125.000i		−	0.184094i
$680$		0			0
$681$	164.558	−	344.558i	0.241642	−	0.505960i
$682$	−676.000			−0.991202
$683$		−	873.984i		−	1.27963i	−0.768531	−	0.639813i	$-0.779012\pi$
$683$		−	873.984i		−	1.27963i	0.768531	−	0.639813i	$-0.220988\pi$
$684$	−1113.80	−	118.197i	−1.62837	−	0.172802i
$685$	−280.000	−	40.0000i	−0.408759	−	0.0583942i
$686$	−1032.38			−1.50492
$687$	67.8823	+	192.000i	0.0988097	+	0.279476i
$688$	−272.000	+	272.000i	−0.395349	+	0.395349i
$689$	119.501	+	119.501i	0.173441	+	0.173441i
$690$	873.558	−	175.206i	1.26603	−	0.253922i
$691$	−396.000	−	396.000i	−0.573082	−	0.573082i	0.359906	−	0.932989i	$-0.382809\pi$
$691$	−396.000	−	396.000i	−0.573082	−	0.573082i	−0.932989	+	0.359906i	$0.882809\pi$
$692$	701.450	+	701.450i	1.01366	+	1.01366i
$693$	581.734	+	61.7336i	0.839442	+	0.0890817i
$694$	282.000	−	282.000i	0.406340	−	0.406340i
$695$	−157.685	+	1103.79i	−0.226885	+	1.58819i
$696$		0			0
$697$		−	665.000i		−	0.954089i
$698$	−1001.26	+	1001.26i	−1.43447	+	1.43447i
$699$	43.0000	+	121.622i	0.0615165	+	0.173995i
$700$	140.000	−	480.000i	0.200000	−	0.685714i
$701$	−1154.00			−1.64622			−0.823109	−	0.567884i	$-0.807762\pi$
$701$	−1154.00			−1.64622			−0.823109	+	0.567884i	$0.807762\pi$
$702$	−230.304	−	965.696i	−0.328069	−	1.37563i
$703$	330.000	+	330.000i	0.469417	+	0.469417i
$704$	−588.313	−	588.313i	−0.835672	−	0.835672i
$705$	−900.500	−	599.625i	−1.27730	−	0.850532i
$706$		−	1428.00i		−	2.02266i
$707$			42.4264i			0.0600091i
$708$	769.332	−	272.000i	1.08663	−	0.384181i
$709$	656.000	+	656.000i	0.925247	+	0.925247i	0.997394	−	0.0721472i	$-0.0229851\pi$
$709$	656.000	+	656.000i	0.925247	+	0.925247i	−0.0721472	+	0.997394i	$0.522985\pi$
$710$	−449.720	−	599.627i	−0.633408	−	0.844544i
$711$	−623.000	+	503.460i	−0.876231	+	0.708101i
$712$		0			0
$713$		−	386.080i		−	0.541487i
$714$	760.000	−	268.701i	1.06443	−	0.376331i
$715$	−676.000	+	507.000i	−0.945455	+	0.709091i
$716$		−	333.754i		−	0.466137i
$717$	−45.0000	−	127.279i	−0.0627615	−	0.177516i
$718$	604.000	+	604.000i	0.841226	+	0.841226i
$719$			359.210i			0.499597i	0.968298	+	0.249799i	$0.0803644\pi$
$719$			359.210i			0.499597i	−0.968298	+	0.249799i	$0.919636\pi$
$720$	368.804	+	618.372i	0.512228	+	0.858850i
$721$	5.00000	+	5.00000i	0.00693481	+	0.00693481i
$722$	1716.86			2.37792
$723$	−724.000	+	255.973i	−1.00138	+	0.354042i
$724$			52.0000i			0.0718232i
$725$	916.410	+	267.286i	1.26401	+	0.368671i
$726$	−367.529	−	175.529i	−0.506238	−	0.241775i
$727$	217.000	+	217.000i	0.298487	+	0.298487i	0.840421	−	0.541934i	$-0.182308\pi$
$727$	217.000	+	217.000i	0.298487	+	0.298487i	−0.541934	+	0.840421i	$0.682308\pi$
$728$		0			0
$729$	−650.538	+	329.000i	−0.892371	+	0.451303i
$730$	−152.000	+	1064.00i	−0.208219	+	1.45753i
$731$			456.791i			0.624885i
$732$	−725.505	−	346.495i	−0.991127	−	0.473354i
$733$			1049.00i			1.43111i	0.698559	+	0.715553i	$0.253825\pi$
$733$			1049.00i			1.43111i	−0.698559	+	0.715553i	$0.746175\pi$
$734$	616.597	+	616.597i	0.840051	+	0.840051i
$735$	−299.647	−	199.529i	−0.407683	−	0.271468i
$736$	672.000	−	672.000i	0.913043	−	0.913043i
$737$	919.239	+	919.239i	1.24727	+	1.24727i
$738$	94.0202	−	885.980i	0.127399	−	1.20051i
$739$	609.000	+	609.000i	0.824087	+	0.824087i	0.986691	−	0.162605i	$-0.0519895\pi$
$739$	609.000	+	609.000i	0.824087	+	0.824087i	−0.162605	+	0.986691i	$0.551990\pi$
$740$	−42.4264	+	296.985i	−0.0573330	+	0.401331i
$741$	404.465	+	1144.00i	0.545837	+	1.54386i
$742$	−130.000	+	130.000i	−0.175202	+	0.175202i
$743$	−562.857			−0.757546			−0.378773	−	0.925490i	$-0.623654\pi$
$743$	−562.857			−0.757546			−0.378773	+	0.925490i	$0.623654\pi$
$744$		0			0
$745$	225.000	+	300.000i	0.302013	+	0.402685i
$746$	−483.661	+	483.661i	−0.648339	+	0.648339i
$747$	528.000	+	653.367i	0.706827	+	0.874654i
$748$	−988.000			−1.32086
$749$	208.597	−	208.597i	0.278500	−	0.278500i
$750$	811.549	−	682.926i	1.08207	−	0.910568i
$751$			185.000i			0.246338i	0.992386	+	0.123169i	$0.0393058\pi$
$751$			185.000i			0.246338i	−0.992386	+	0.123169i	$0.960694\pi$
$752$	−1154.00			−1.53457
$753$	911.166	+	435.166i	1.21005	+	0.577909i
$754$	−1404.00			−1.86207
$755$	−124.451	+	93.3381i	−0.164835	+	0.123627i
$756$	525.269	−	125.269i	0.694800	−	0.165700i
$757$	493.000	−	493.000i	0.651255	−	0.651255i	−0.302040	−	0.953295i	$-0.597668\pi$
$757$	493.000	−	493.000i	0.651255	−	0.651255i	0.953295	+	0.302040i	$0.0976677\pi$
$758$	−291.328	−	291.328i	−0.384338	−	0.384338i
$759$	352.960	−	739.040i	0.465033	−	0.973702i
$760$		0			0
$761$	−618.011	−	618.011i	−0.812104	−	0.812104i	0.172845	−	0.984949i	$-0.444704\pi$
$761$	−618.011	−	618.011i	−0.812104	−	0.812104i	−0.984949	+	0.172845i	$0.944704\pi$
$762$	1764.94	−	624.000i	2.31619	−	0.818898i
$763$	495.000	+	495.000i	0.648755	+	0.648755i
$764$			231.931i			0.303575i
$765$	828.921	+	209.559i	1.08356	+	0.273934i
$766$			1392.00i			1.81723i
$767$	−625.082	−	625.082i	−0.814971	−	0.814971i
$768$	693.019	+	330.981i	0.902369	+	0.430964i
$769$	−897.000	+	897.000i	−1.16645	+	1.16645i	−0.183414	+	0.983036i	$0.558715\pi$

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:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	195.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.82843i q^{2} +(2.70711 + 1.29289i) q^{3} -4.00000 q^{4} +(-4.94975 - 0.707107i) q^{5} +(-3.65685 + 7.65685i) q^{6} +5.00000i q^{7} +(5.65685 + 7.00000i) q^{9} +O(q^{10})\)	\(q+2.82843i q^{2} +(2.70711 + 1.29289i) q^{3} -4.00000 q^{4} +(-4.94975 - 0.707107i) q^{5} +(-3.65685 + 7.65685i) q^{6} +5.00000i q^{7} +(5.65685 + 7.00000i) q^{9} +(2.00000 - 14.0000i) q^{10} +(-9.19239 - 9.19239i) q^{11} +(-10.8284 - 5.17157i) q^{12} +13.0000i q^{13} -14.1421 q^{14} +(-12.4853 - 8.31371i) q^{15} -16.0000 q^{16} +(-13.4350 + 13.4350i) q^{17} +(-19.7990 + 16.0000i) q^{18} +(22.0000 - 22.0000i) q^{19} +(19.7990 + 2.82843i) q^{20} +(-6.46447 + 13.5355i) q^{21} +(26.0000 - 26.0000i) q^{22} +(14.8492 + 14.8492i) q^{23} +(24.0000 + 7.00000i) q^{25} -36.7696 q^{26} +(6.26346 + 26.2635i) q^{27} -20.0000i q^{28} +38.1838 q^{29} +(23.5147 - 35.3137i) q^{30} +(-13.0000 - 13.0000i) q^{31} -45.2548i q^{32} +(-13.0000 - 36.7696i) q^{33} +(-38.0000 - 38.0000i) q^{34} +(3.53553 - 24.7487i) q^{35} +(-22.6274 - 28.0000i) q^{36} +15.0000i q^{37} +(62.2254 + 62.2254i) q^{38} +(-16.8076 + 35.1924i) q^{39} +(-24.7487 + 24.7487i) q^{41} +(-38.2843 - 18.2843i) q^{42} +(17.0000 - 17.0000i) q^{43} +(36.7696 + 36.7696i) q^{44} +(-23.0503 - 38.6482i) q^{45} +(-42.0000 + 42.0000i) q^{46} +72.1249 q^{47} +(-43.3137 - 20.6863i) q^{48} +24.0000 q^{49} +(-19.7990 + 67.8823i) q^{50} +(-53.7401 + 19.0000i) q^{51} -52.0000i q^{52} +(9.19239 - 9.19239i) q^{53} +(-74.2843 + 17.7157i) q^{54} +(39.0000 + 52.0000i) q^{55} +(88.0000 - 31.1127i) q^{57} +108.000i q^{58} +(-48.0833 + 48.0833i) q^{59} +(49.9411 + 33.2548i) q^{60} +67.0000 q^{61} +(36.7696 - 36.7696i) q^{62} +(-35.0000 + 28.2843i) q^{63} +64.0000 q^{64} +(9.19239 - 64.3467i) q^{65} +(104.000 - 36.7696i) q^{66} -100.000 q^{67} +(53.7401 - 53.7401i) q^{68} +(21.0000 + 59.3970i) q^{69} +(70.0000 + 10.0000i) q^{70} +(37.4767 - 37.4767i) q^{71} -76.0000 q^{73} -42.4264 q^{74} +(55.9203 + 49.9792i) q^{75} +(-88.0000 + 88.0000i) q^{76} +(45.9619 - 45.9619i) q^{77} +(-99.5391 - 47.5391i) q^{78} +89.0000i q^{79} +(79.1960 + 11.3137i) q^{80} +(-17.0000 + 79.1960i) q^{81} +(-70.0000 - 70.0000i) q^{82} +93.3381 q^{83} +(25.8579 - 54.1421i) q^{84} +(76.0000 - 57.0000i) q^{85} +(48.0833 + 48.0833i) q^{86} +(103.368 + 49.3675i) q^{87} +(4.94975 - 4.94975i) q^{89} +(109.314 - 65.1960i) q^{90} -65.0000 q^{91} +(-59.3970 - 59.3970i) q^{92} +(-18.3848 - 52.0000i) q^{93} +204.000i q^{94} +(-124.451 + 93.3381i) q^{95} +(58.5097 - 122.510i) q^{96} -25.0000 q^{97} +67.8823i q^{98} +(12.3467 - 116.347i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{3} - 16 q^{4} + 8 q^{6}+O(q^{10}) \) 4 * q + 8 * q^3 - 16 * q^4 + 8 * q^6	\( 4 q + 8 q^{3} - 16 q^{4} + 8 q^{6} + 8 q^{10} - 32 q^{12} - 16 q^{15} - 64 q^{16} + 88 q^{19} - 40 q^{21} + 104 q^{22} + 96 q^{25} - 40 q^{27} + 128 q^{30} - 52 q^{31} - 52 q^{33} - 152 q^{34} - 104 q^{39} - 40 q^{42} + 68 q^{43} - 112 q^{45} - 168 q^{46} - 128 q^{48} + 96 q^{49} - 184 q^{54} + 156 q^{55} + 352 q^{57} + 64 q^{60} + 268 q^{61} - 140 q^{63} + 256 q^{64} + 416 q^{66} - 400 q^{67} + 84 q^{69} + 280 q^{70} - 304 q^{73} + 136 q^{75} - 352 q^{76} - 104 q^{78} - 68 q^{81} - 280 q^{82} + 160 q^{84} + 304 q^{85} + 108 q^{87} + 392 q^{90} - 260 q^{91} - 128 q^{96} - 100 q^{97} - 208 q^{99}+O(q^{100}) \) 4 * q + 8 * q^3 - 16 * q^4 + 8 * q^6 + 8 * q^10 - 32 * q^12 - 16 * q^15 - 64 * q^16 + 88 * q^19 - 40 * q^21 + 104 * q^22 + 96 * q^25 - 40 * q^27 + 128 * q^30 - 52 * q^31 - 52 * q^33 - 152 * q^34 - 104 * q^39 - 40 * q^42 + 68 * q^43 - 112 * q^45 - 168 * q^46 - 128 * q^48 + 96 * q^49 - 184 * q^54 + 156 * q^55 + 352 * q^57 + 64 * q^60 + 268 * q^61 - 140 * q^63 + 256 * q^64 + 416 * q^66 - 400 * q^67 + 84 * q^69 + 280 * q^70 - 304 * q^73 + 136 * q^75 - 352 * q^76 - 104 * q^78 - 68 * q^81 - 280 * q^82 + 160 * q^84 + 304 * q^85 + 108 * q^87 + 392 * q^90 - 260 * q^91 - 128 * q^96 - 100 * q^97 - 208 * q^99

Introduction

L-functions

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