LMFDB - Embedded newform 195.3.j.c.122.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [195,3,Mod(8,195)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [4,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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			122.2
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	195.122
Dual form			195.3.j.c.8.1

$q$-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} +(1.29289 - 2.70711i) q^{3} -4.00000 q^{4} +(4.94975 - 0.707107i) q^{5} +(7.65685 + 3.65685i) q^{6} -5.00000i q^{7} +(-5.65685 - 7.00000i) q^{9} +(2.00000 + 14.0000i) q^{10} +(9.19239 - 9.19239i) q^{11} +(-5.17157 + 10.8284i) q^{12} -13.0000i q^{13} +14.1421 q^{14} +(4.48528 - 14.3137i) 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} +(-13.5355 - 6.46447i) q^{21} +(26.0000 + 26.0000i) q^{22} +(-14.8492 + 14.8492i) q^{23} +(24.0000 - 7.00000i) q^{25} +36.7696 q^{26} +(-26.2635 + 6.26346i) q^{27} +20.0000i q^{28} -38.1838 q^{29} +(40.4853 + 12.6863i) 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} +(-35.1924 - 16.8076i) q^{39} +(24.7487 + 24.7487i) q^{41} +(18.2843 - 38.2843i) q^{42} +(17.0000 + 17.0000i) q^{43} +(-36.7696 + 36.7696i) q^{44} +(-32.9497 - 30.6482i) q^{45} +(-42.0000 - 42.0000i) q^{46} -72.1249 q^{47} +(-20.6863 + 43.3137i) 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} +(-17.7157 - 74.2843i) q^{54} +(39.0000 - 52.0000i) q^{55} +(88.0000 - 31.1127i) q^{57} -108.000i q^{58} +(48.0833 + 48.0833i) q^{59} +(-17.9411 + 57.2548i) 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} +(12.0797 - 74.0208i) q^{75} +(-88.0000 - 88.0000i) q^{76} +(-45.9619 - 45.9619i) q^{77} +(47.5391 - 99.5391i) 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} +(54.1421 + 25.8579i) q^{84} +(76.0000 + 57.0000i) q^{85} +(-48.0833 + 48.0833i) q^{86} +(-49.3675 + 103.368i) q^{87} +(-4.94975 - 4.94975i) q^{89} +(86.6863 - 93.1960i) 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} +(-122.510 - 58.5097i) q^{96} -25.0000 q^{97} +67.8823i q^{98} +(-116.347 - 12.3467i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

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

Coefficient data

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

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

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

$2$			2.82843i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$2$			2.82843i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$3$	1.29289	−	2.70711i	0.430964	−	0.902369i
$3$	1.29289	−	2.70711i	0.430964	−	0.902369i
$4$	−4.00000			−1.00000
$5$	4.94975	−	0.707107i	0.989949	−	0.141421i
$5$	4.94975	−	0.707107i	0.989949	−	0.141421i
$6$	7.65685	+	3.65685i	1.27614	+	0.609476i
$7$		−	5.00000i		−	0.714286i	−0.934050	−	0.357143i	$-0.883751\pi$
$7$		−	5.00000i		−	0.714286i	0.934050	−	0.357143i	$-0.116249\pi$
$8$		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	$-0.548769\pi$
$11$	9.19239	−	9.19239i	0.835672	−	0.835672i	0.988286	+	0.152614i	$0.0487692\pi$
$12$	−5.17157	+	10.8284i	−0.430964	+	0.902369i
$13$		−	13.0000i		−	1.00000i
$13$		−	13.0000i		−	1.00000i
$14$	14.1421			1.01015
$15$	4.48528	−	14.3137i	0.299019	−	0.954247i
$16$	−16.0000			−1.00000
$17$	13.4350	+	13.4350i	0.790296	+	0.790296i	0.981542	−	0.191246i	$-0.0612529\pi$
$17$	13.4350	+	13.4350i	0.790296	+	0.790296i	−0.191246	+	0.981542i	$0.561253\pi$
$18$	19.7990	−	16.0000i	1.09994	−	0.888889i
$19$	22.0000	+	22.0000i	1.15789	+	1.15789i	0.984928	+	0.172967i	$0.0553354\pi$
$19$	22.0000	+	22.0000i	1.15789	+	1.15789i	0.172967	+	0.984928i	$0.444665\pi$
$20$	−19.7990	+	2.82843i	−0.989949	+	0.141421i
$21$	−13.5355	−	6.46447i	−0.644549	−	0.307832i
$22$	26.0000	+	26.0000i	1.18182	+	1.18182i
$23$	−14.8492	+	14.8492i	−0.645619	+	0.645619i	−0.951931	−	0.306312i	$-0.900905\pi$
$23$	−14.8492	+	14.8492i	−0.645619	+	0.645619i	0.306312	+	0.951931i	$0.400905\pi$
$24$		0			0
$25$	24.0000	−	7.00000i	0.960000	−	0.280000i
$26$	36.7696			1.41421
$27$	−26.2635	+	6.26346i	−0.972721	+	0.231980i
$28$			20.0000i			0.714286i
$29$	−38.1838			−1.31668			−0.658341	−	0.752720i	$-0.728741\pi$
$29$	−38.1838			−1.31668			−0.658341	+	0.752720i	$0.728741\pi$
$30$	40.4853	+	12.6863i	1.34951	+	0.422876i
$31$	−13.0000	+	13.0000i	−0.419355	+	0.419355i	−0.884981	−	0.465626i	$-0.845829\pi$
$31$	−13.0000	+	13.0000i	−0.419355	+	0.419355i	0.465626	+	0.884981i	$0.345829\pi$
$32$		−	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	$-0.935027\pi$
$37$		−	15.0000i		−	0.405405i	0.979240	−	0.202703i	$-0.0649725\pi$
$38$	−62.2254	+	62.2254i	−1.63751	+	1.63751i
$39$	−35.1924	−	16.8076i	−0.902369	−	0.430964i
$40$		0			0
$41$	24.7487	+	24.7487i	0.603628	+	0.603628i	0.941273	−	0.337646i	$-0.109631\pi$
$41$	24.7487	+	24.7487i	0.603628	+	0.603628i	−0.337646	+	0.941273i	$0.609631\pi$
$42$	18.2843	−	38.2843i	0.435340	−	0.911530i
$43$	17.0000	+	17.0000i	0.395349	+	0.395349i	0.876589	−	0.481240i	$-0.159813\pi$
$43$	17.0000	+	17.0000i	0.395349	+	0.395349i	−0.481240	+	0.876589i	$0.659813\pi$
$44$	−36.7696	+	36.7696i	−0.835672	+	0.835672i
$45$	−32.9497	−	30.6482i	−0.732217	−	0.681072i
$46$	−42.0000	−	42.0000i	−0.913043	−	0.913043i
$47$	−72.1249			−1.53457			−0.767286	−	0.641305i	$-0.778393\pi$
$47$	−72.1249			−1.53457			−0.767286	+	0.641305i	$0.778393\pi$
$48$	−20.6863	+	43.3137i	−0.430964	+	0.902369i
$49$	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	$-0.289137\pi$
$53$	−9.19239	−	9.19239i	−0.173441	−	0.173441i	−0.788490	+	0.615048i	$0.789137\pi$
$54$	−17.7157	−	74.2843i	−0.328069	−	1.37563i
$55$	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	$-0.0545072\pi$
$59$	48.0833	+	48.0833i	0.814971	+	0.814971i	−0.170404	+	0.985374i	$0.554507\pi$
$60$	−17.9411	+	57.2548i	−0.299019	+	0.954247i
$61$	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	$-0.371753\pi$
$71$	−37.4767	−	37.4767i	−0.527840	−	0.527840i	−0.919928	+	0.392088i	$0.871753\pi$
$72$		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
$75$	12.0797	−	74.0208i	0.161063	−	0.986944i
$76$	−88.0000	−	88.0000i	−1.15789	−	1.15789i
$77$	−45.9619	−	45.9619i	−0.596908	−	0.596908i
$78$	47.5391	−	99.5391i	0.609476	−	1.27614i
$79$		−	89.0000i		−	1.12658i	−0.826258	−	0.563291i	$-0.809535\pi$
$79$		−	89.0000i		−	1.12658i	0.826258	−	0.563291i	$-0.190465\pi$
$80$	−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	$-0.690075\pi$
$83$	−93.3381			−1.12456			−0.562278	+	0.826948i	$0.690075\pi$
$84$	54.1421	+	25.8579i	0.644549	+	0.307832i
$85$	76.0000	+	57.0000i	0.894118	+	0.670588i
$86$	−48.0833	+	48.0833i	−0.559108	+	0.559108i
$87$	−49.3675	+	103.368i	−0.567443	+	1.18813i
$88$		0			0
$89$	−4.94975	−	4.94975i	−0.0556151	−	0.0556151i	0.678752	−	0.734367i	$-0.262521\pi$
$89$	−4.94975	−	4.94975i	−0.0556151	−	0.0556151i	−0.734367	+	0.678752i	$0.762521\pi$
$90$	86.6863	−	93.1960i	0.963181	−	1.03551i
$91$	−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
$96$	−122.510	−	58.5097i	−1.27614	−	0.609476i
$97$	−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
$99$	−116.347	−	12.3467i	−1.17522	−	0.124714i
$100$	−96.0000	+	28.0000i	−0.960000	+	0.280000i
$101$	−8.48528			−0.0840127			−0.0420063	−	0.999117i	$-0.513375\pi$
$101$	−8.48528			−0.0840127			−0.0420063	+	0.999117i	$0.513375\pi$
$102$	53.7401	+	152.000i	0.526864	+	1.49020i
$103$	1.00000	+	1.00000i	0.00970874	+	0.00970874i	0.711944	−	0.702236i	$-0.247815\pi$
$103$	1.00000	+	1.00000i	0.00970874	+	0.00970874i	−0.702236	+	0.711944i	$0.747815\pi$
$104$		0			0
$105$	−71.5685	−	22.4264i	−0.681605	−	0.213585i
$106$	26.0000	−	26.0000i	0.245283	−	0.245283i
$107$	41.7193	−	41.7193i	0.389900	−	0.389900i	−0.484752	−	0.874652i	$-0.661090\pi$
$107$	41.7193	−	41.7193i	0.389900	−	0.389900i	0.874652	+	0.484752i	$0.161090\pi$
$108$	105.054	−	25.0538i	0.972721	−	0.231980i
$109$	99.0000	+	99.0000i	0.908257	+	0.908257i	0.996132	−	0.0878747i	$-0.0280075\pi$
$109$	99.0000	+	99.0000i	0.908257	+	0.908257i	−0.0878747	+	0.996132i	$0.528007\pi$
$110$	147.078	+	110.309i	1.33707	+	1.00281i
$111$	−40.6066	−	19.3934i	−0.365825	−	0.174715i
$112$			80.0000i			0.714286i
$113$	14.1421	+	14.1421i	0.125152	+	0.125152i	0.766908	−	0.641757i	$-0.221794\pi$
$113$	14.1421	+	14.1421i	0.125152	+	0.125152i	−0.641757	+	0.766908i	$0.721794\pi$
$114$	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	−0.263757	+	0.964589i	$0.584962\pi$
$127$	−156.000	+	156.000i	−1.22835	+	1.22835i	−0.964589	+	0.263757i	$0.915038\pi$
$128$		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
$135$	−125.569	+	49.5736i	−0.930137	+	0.367212i
$136$		0			0
$137$	−56.5685			−0.412909			−0.206455	−	0.978456i	$-0.566193\pi$
$137$	−56.5685			−0.412909			−0.206455	+	0.978456i	$0.566193\pi$
$138$	−168.000	+	59.3970i	−1.21739	+	0.430413i
$139$			223.000i			1.60432i	0.597111	+	0.802158i	$0.296315\pi$
$139$			223.000i			1.60432i	−0.597111	+	0.802158i	$0.703685\pi$
$140$	14.1421	+	98.9949i	0.101015	+	0.707107i
$141$	−93.2498	+	195.250i	−0.661346	+	1.38475i
$142$	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
$147$	31.0294	−	64.9706i	0.211085	−	0.441977i
$148$			60.0000i			0.405405i
$149$	53.0330	−	53.0330i	0.355926	−	0.355926i	−0.506383	−	0.862309i	$-0.669018\pi$
$149$	53.0330	−	53.0330i	0.355926	−	0.355926i	0.862309	+	0.506383i	$0.169018\pi$
$150$	209.362	+	34.1665i	1.39575	+	0.227777i
$151$	22.0000	+	22.0000i	0.145695	+	0.145695i	0.776192	−	0.630497i	$-0.217149\pi$
$151$	22.0000	+	22.0000i	0.145695	+	0.145695i	−0.630497	+	0.776192i	$0.717149\pi$
$152$		0			0
$153$	18.0452	−	170.045i	0.117942	−	1.11141i
$154$	130.000	−	130.000i	0.844156	−	0.844156i
$155$	−55.1543	+	73.5391i	−0.355834	+	0.474446i
$156$	140.770	+	67.2304i	0.902369	+	0.430964i
$157$	106.000	+	106.000i	0.675159	+	0.675159i	0.958901	−	0.283742i	$-0.0915758\pi$
$157$	106.000	+	106.000i	0.675159	+	0.675159i	−0.283742	+	0.958901i	$0.591576\pi$
$158$	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
$165$	−90.3467	−	172.808i	−0.547556	−	1.04732i
$166$		−	264.000i		−	1.59036i
$167$	−114.551			−0.685936			−0.342968	−	0.939347i	$-0.611432\pi$
$167$	−114.551			−0.685936			−0.342968	+	0.939347i	$0.611432\pi$
$168$		0			0
$169$	−169.000			−1.00000
$170$	−161.220	+	214.960i	−0.948355	+	1.26447i
$171$	29.5492	−	278.451i	0.172802	−	1.62837i
$172$	−68.0000	−	68.0000i	−0.395349	−	0.395349i
$173$	175.362	−	175.362i	1.01366	−	1.01366i	0.0137505	−	0.999905i	$-0.495623\pi$
$173$	175.362	−	175.362i	1.01366	−	1.01366i	0.999905	−	0.0137505i	$-0.00437706\pi$
$174$	−292.368	−	139.632i	−1.68027	−	0.802485i
$175$	−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	$0.925123\pi$
$180$	131.799	+	122.593i	0.732217	+	0.681072i
$181$			13.0000i			0.0718232i	0.999355	+	0.0359116i	$0.0114335\pi$
$181$			13.0000i			0.0718232i	−0.999355	+	0.0359116i	$0.988567\pi$
$182$		−	183.848i		−	1.01015i
$183$	86.6238	−	181.376i	0.473354	−	0.991127i
$184$		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
$189$	31.3173	+	131.317i	0.165700	+	0.694800i
$190$	−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	$-0.0485029\pi$
$192$	82.7452	−	173.255i	0.430964	−	0.902369i
$193$	−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
$195$	−186.078	−	58.3087i	−0.954247	−	0.299019i
$196$	−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	$0.923869\pi$
$198$	34.9218	−	329.078i	0.176373	−	1.66201i
$199$	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
$201$	−129.289	+	270.711i	−0.643230	+	1.34682i
$202$		−	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
$207$	187.945	+	19.9447i	0.907945	+	0.0963512i
$208$			208.000i			1.00000i
$209$	404.465			1.93524
$210$	63.4315	−	202.426i	0.302055	−	0.963935i
$211$	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
$219$	−98.2599	+	205.740i	−0.448675	+	0.939453i
$220$	−156.000	+	208.000i	−0.709091	+	0.945455i
$221$	174.655	−	174.655i	0.790296	−	0.790296i
$222$	54.8528	−	114.853i	0.247085	−	0.517355i
$223$		−	80.0000i		−	0.358744i	−0.983781	−	0.179372i	$-0.942593\pi$
$223$		−	80.0000i		−	0.358744i	0.983781	−	0.179372i	$-0.0574066\pi$
$224$	−226.274			−1.01015
$225$	−184.765	−	128.402i	−0.821176	−	0.570676i
$226$	−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	−0.594493	−	0.804100i	$-0.702647\pi$
$229$	48.0000	−	48.0000i	0.209607	−	0.209607i	0.804100	+	0.594493i	$0.202647\pi$
$230$	−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	$-0.779414\pi$
$233$	−30.4056	+	30.4056i	−0.130496	+	0.130496i	0.638842	+	0.769338i	$0.279414\pi$
$234$	−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
$237$	−240.933	−	115.067i	−1.01659	−	0.485517i
$238$	190.000	+	190.000i	0.798319	+	0.798319i
$239$	31.8198	−	31.8198i	0.133137	−	0.133137i	−0.637398	−	0.770535i	$-0.719989\pi$
$239$	31.8198	−	31.8198i	0.133137	−	0.133137i	0.770535	+	0.637398i	$0.219989\pi$
$240$	−71.7645	+	229.019i	−0.299019	+	0.954247i
$241$	−181.000	−	181.000i	−0.751037	−	0.751037i	0.223636	−	0.974673i	$-0.428207\pi$
$241$	−181.000	−	181.000i	−0.751037	−	0.751037i	−0.974673	+	0.223636i	$0.928207\pi$
$242$	135.765			0.561010
$243$	192.413	+	148.413i	0.791822	+	0.610752i
$244$	−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
$249$	−120.676	+	252.676i	−0.484643	+	1.01476i
$250$	146.000	+	322.000i	0.584000	+	1.28800i
$251$	−336.583			−1.34097			−0.670484	−	0.741924i	$-0.733913\pi$
$251$	−336.583			−1.34097			−0.670484	+	0.741924i	$0.733913\pi$
$252$	140.000	−	113.137i	0.555556	−	0.448957i
$253$			273.000i			1.07905i
$254$	−441.235	−	441.235i	−1.73714	−	1.73714i
$255$	252.565	−	132.045i	0.990451	−	0.517824i
$256$	256.000			1.00000
$257$	147.078	+	147.078i	0.572289	+	0.572289i	0.932767	−	0.360479i	$-0.117387\pi$
$257$	147.078	+	147.078i	0.572289	+	0.572289i	−0.360479	+	0.932767i	$0.617387\pi$
$258$	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	$-0.422992\pi$
$263$	−192.333	−	192.333i	−0.731304	−	0.731304i	−0.970878	+	0.239574i	$0.922992\pi$
$264$		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	$-0.395200\pi$
$269$	173.948			0.646648			0.323324	+	0.946288i	$0.395200\pi$
$270$	−140.215	−	355.161i	−0.519316	−	1.31541i
$271$	−288.000	−	288.000i	−1.06273	−	1.06273i	−0.997896	−	0.0648346i	$-0.979348\pi$
$271$	−288.000	−	288.000i	−1.06273	−	1.06273i	−0.0648346	−	0.997896i	$-0.520652\pi$
$272$	−214.960	−	214.960i	−0.790296	−	0.790296i
$273$	−84.0381	+	175.962i	−0.307832	+	0.644549i
$274$		−	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	−0.950306	−	0.311317i	$-0.899230\pi$
$277$	−177.000	+	177.000i	−0.638989	+	0.638989i	0.311317	+	0.950306i	$0.399230\pi$
$278$	−630.739			−2.26885
$279$	164.539	+	17.4609i	0.589746	+	0.0625839i
$280$		0			0
$281$	132.936	−	132.936i	0.473082	−	0.473082i	−0.429828	−	0.902911i	$-0.641426\pi$
$281$	132.936	−	132.936i	0.473082	−	0.473082i	0.902911	+	0.429828i	$0.141426\pi$
$282$	−552.250	−	263.750i	−1.95833	−	0.935284i
$283$	−162.000	−	162.000i	−0.572438	−	0.572438i	0.360371	−	0.932809i	$-0.382650\pi$
$283$	−162.000	−	162.000i	−0.572438	−	0.572438i	−0.932809	+	0.360371i	$0.882650\pi$
$284$	149.907	+	149.907i	0.527840	+	0.527840i
$285$	413.578	−	216.225i	1.45115	−	0.758686i
$286$	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
$291$	−32.3223	+	67.6777i	−0.111073	+	0.232569i
$292$	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	$-0.140486\pi$
$294$	183.765	+	87.7645i	0.625049	+	0.298519i
$295$	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
$300$	−48.3188	+	296.083i	−0.161063	+	0.986944i
$301$	85.0000	−	85.0000i	0.282392	−	0.282392i
$302$	−62.2254	+	62.2254i	−0.206044	+	0.206044i
$303$	−10.9706	+	22.9706i	−0.0362065	+	0.0758104i
$304$	−352.000	−	352.000i	−1.15789	−	1.15789i
$305$	331.633	−	47.3762i	1.08732	−	0.155332i
$306$	480.960	+	51.0395i	1.57177	+	0.166796i
$307$		−	561.000i		−	1.82736i	−0.406433	−	0.913681i	$-0.633227\pi$
$307$		−	561.000i		−	1.82736i	0.406433	−	0.913681i	$-0.366773\pi$
$308$	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	$-0.368163\pi$
$311$	250.316			0.804874			0.402437	+	0.915448i	$0.368163\pi$
$312$		0			0
$313$	342.000	−	342.000i	1.09265	−	1.09265i	0.0974071	−	0.995245i	$-0.468945\pi$
$313$	342.000	−	342.000i	1.09265	−	1.09265i	0.995245	−	0.0974071i	$-0.0310549\pi$
$314$	−299.813	+	299.813i	−0.954819	+	0.954819i
$315$	−153.241	+	164.749i	−0.486480	+	0.523012i
$316$			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
$330$	488.774	−	255.539i	1.48113	−	0.774361i
$331$	−156.000	+	156.000i	−0.471299	+	0.471299i	−0.902335	−	0.431036i	$-0.858148\pi$
$331$	−156.000	+	156.000i	−0.471299	+	0.471299i	0.431036	+	0.902335i	$0.358148\pi$
$332$	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
$336$	216.569	+	103.431i	0.644549	+	0.307832i
$337$	−251.000	+	251.000i	−0.744807	+	0.744807i	−0.973499	−	0.228692i	$-0.926555\pi$
$337$	−251.000	+	251.000i	−0.744807	+	0.744807i	0.228692	+	0.973499i	$0.426555\pi$
$338$		−	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
$342$	787.578	+	83.5778i	2.30286	+	0.244379i
$343$		−	365.000i		−	1.06414i
$344$		0			0
$345$	145.945	+	279.151i	0.423028	+	0.809133i
$346$	496.000	+	496.000i	1.43353	+	1.43353i
$347$	99.7021	−	99.7021i	0.287326	−	0.287326i	−0.548696	−	0.836022i	$-0.684876\pi$
$347$	99.7021	−	99.7021i	0.287326	−	0.287326i	0.836022	+	0.548696i	$0.184876\pi$
$348$	197.470	−	413.470i	0.567443	−	1.18813i
$349$	354.000	−	354.000i	1.01433	−	1.01433i	0.0144308	−	0.999896i	$-0.495406\pi$
$349$	354.000	−	354.000i	1.01433	−	1.01433i	0.999896	−	0.0144308i	$-0.00459362\pi$
$350$	339.411	−	98.9949i	0.969746	−	0.282843i
$351$	81.4249	+	341.425i	0.231980	+	0.972721i
$352$	−416.000	−	416.000i	−1.18182	−	1.18182i
$353$	504.874			1.43024			0.715119	−	0.699002i	$-0.246372\pi$
$353$	504.874			1.43024			0.715119	+	0.699002i	$0.246372\pi$
$354$	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	$-0.388185\pi$
$359$	−213.546	−	213.546i	−0.594836	−	0.594836i	−0.938934	+	0.344098i	$0.888185\pi$
$360$		0			0
$361$			607.000i			1.68144i
$362$	−36.7696			−0.101573
$363$	−129.941	−	62.0589i	−0.357965	−	0.170961i
$364$	260.000			0.714286
$365$	−376.181	+	53.7401i	−1.03063	+	0.147233i
$366$	513.009	+	245.009i	1.40166	+	0.669424i
$367$	218.000	+	218.000i	0.594005	+	0.594005i	0.938711	−	0.344705i	$-0.112021\pi$
$367$	218.000	+	218.000i	0.594005	+	0.594005i	−0.344705	+	0.938711i	$0.612021\pi$
$368$	237.588	−	237.588i	0.645619	−	0.645619i
$369$	33.2412	−	313.241i	0.0900844	−	0.848892i
$370$	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	−0.439700	−	0.898145i	$-0.644915\pi$
$373$	171.000	−	171.000i	0.458445	−	0.458445i	0.898145	+	0.439700i	$0.144915\pi$
$374$			698.621i			1.86797i
$375$	7.45079	−	374.926i	0.0198688	−	0.999803i
$376$		0			0
$377$			496.389i			1.31668i
$378$	−371.421	+	88.5786i	−0.982596	+	0.234335i
$379$	−103.000	−	103.000i	−0.271768	−	0.271768i	0.558044	−	0.829812i	$-0.311552\pi$
$379$	−103.000	−	103.000i	−0.271768	−	0.271768i	−0.829812	+	0.558044i	$0.811552\pi$
$380$	−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	$-0.722098\pi$
$383$	−492.146			−1.28498			−0.642489	+	0.766295i	$0.722098\pi$
$384$		0			0
$385$	−260.000	−	195.000i	−0.675325	−	0.506494i
$386$		−	280.014i		−	0.725426i
$387$	22.8335	−	215.167i	0.0590012	−	0.555986i
$388$	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	$0.949449\pi$
$390$	164.922	−	526.309i	0.422876	−	1.34951i
$391$	−399.000			−1.02046
$392$		0			0
$393$	191.421	+	91.4214i	0.487077	+	0.232624i
$394$	−264.000			−0.670051
$395$	−62.9325	−	440.528i	−0.159323	−	1.11526i
$396$	465.387	+	49.3869i	1.17522	+	0.124714i
$397$		−	191.000i		−	0.481108i	−0.970636	−	0.240554i	$-0.922671\pi$
$397$		−	191.000i		−	0.481108i	0.970636	−	0.240554i	$-0.0773292\pi$
$398$			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	$-0.500617\pi$
$401$	400.222	−	400.222i	0.998061	−	0.998061i	0.999998	+	0.00193718i	$0.000616624\pi$
$402$	−765.685	−	365.685i	−1.90469	−	0.909665i
$403$	169.000	+	169.000i	0.419355	+	0.419355i
$404$	33.9411			0.0840127
$405$	−28.1457	+	404.021i	−0.0694956	+	0.997582i
$406$	−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	0.971730	+	0.236094i	$0.0758672\pi$
$409$	494.000	+	494.000i	1.20782	+	1.20782i	0.236094	+	0.971730i	$0.424133\pi$
$410$	−296.985	+	395.980i	−0.724353	+	0.965804i
$411$	−73.1371	+	153.137i	−0.177949	+	0.372596i
$412$	−4.00000	−	4.00000i	−0.00970874	−	0.00970874i
$413$	240.416	−	240.416i	0.582122	−	0.582122i
$414$	−56.4121	+	531.588i	−0.136261	+	1.28403i
$415$	−462.000	+	66.0000i	−1.11325	+	0.159036i
$416$	−588.313			−1.41421
$417$	603.685	+	288.315i	1.44769	+	0.691403i
$418$			1144.00i			2.73684i
$419$	−541.644			−1.29271			−0.646353	−	0.763039i	$-0.723707\pi$
$419$	−541.644			−1.29271			−0.646353	+	0.763039i	$0.723707\pi$
$420$	286.274	+	89.7056i	0.681605	+	0.213585i
$421$	−38.0000	+	38.0000i	−0.0902613	+	0.0902613i	−0.750796	−	0.660534i	$-0.770330\pi$
$421$	−38.0000	+	38.0000i	−0.0902613	+	0.0902613i	0.660534	+	0.750796i	$0.270330\pi$
$422$			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	$-0.457983\pi$
$431$	−370.524	−	370.524i	−0.859684	−	0.859684i	−0.991301	+	0.131616i	$0.957983\pi$
$432$	420.215	−	100.215i	0.972721	−	0.231980i
$433$	−238.000	−	238.000i	−0.549654	−	0.549654i	0.376687	−	0.926341i	$-0.377063\pi$
$433$	−238.000	−	238.000i	−0.549654	−	0.549654i	−0.926341	+	0.376687i	$0.877063\pi$
$434$	−183.848	+	183.848i	−0.423612	+	0.423612i
$435$	−171.265	+	546.551i	−0.393712	+	1.25644i
$436$	−396.000	−	396.000i	−0.908257	−	0.908257i
$437$	−653.367			−1.49512
$438$	−581.921	−	277.921i	−1.32859	−	0.634523i
$439$	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	$-0.411711\pi$
$443$	−304.763	−	304.763i	−0.687953	−	0.687953i	−0.961779	+	0.273826i	$0.911711\pi$
$444$	162.426	+	77.5736i	0.365825	+	0.174715i
$445$	−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	$-0.225518\pi$
$449$	48.7904	+	48.7904i	0.108665	+	0.108665i	−0.650684	+	0.759349i	$0.725518\pi$
$450$	363.176	−	522.593i	0.807057	−	1.16132i
$451$	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	$-0.362456\pi$
$461$	−225.567	−	225.567i	−0.489299	−	0.489299i	−0.908085	+	0.418786i	$0.862456\pi$
$462$	−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
$465$	127.770	+	244.387i	0.274773	+	0.525563i
$466$	−86.0000	−	86.0000i	−0.184549	−	0.184549i
$467$	396.687	+	396.687i	0.849437	+	0.849437i	0.990063	−	0.140626i	$-0.0449116\pi$
$467$	396.687	+	396.687i	0.849437	+	0.849437i	−0.140626	+	0.990063i	$0.544912\pi$
$468$	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
$474$	325.460	−	681.460i	0.686625	−	1.43768i
$475$	682.000	+	374.000i	1.43579	+	0.787368i
$476$	−268.701	+	268.701i	−0.564497	+	0.564497i
$477$	−12.3467	+	116.347i	−0.0258841	+	0.243913i
$478$	90.0000	+	90.0000i	0.188285	+	0.188285i
$479$	−229.810	−	229.810i	−0.479770	−	0.479770i	0.425288	−	0.905058i	$-0.360173\pi$
$479$	−229.810	−	229.810i	−0.479770	−	0.479770i	−0.905058	+	0.425288i	$0.860173\pi$
$480$	−647.765	−	202.981i	−1.34951	−	0.422876i
$481$	−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
$486$	−419.775	+	544.225i	−0.863734	+	1.11981i
$487$	−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
$489$	350.374	−	733.626i	0.716511	−	1.50026i
$490$	48.0000	+	336.000i	0.0979592	+	0.685714i
$491$	−69.2965			−0.141133			−0.0705667	−	0.997507i	$-0.522481\pi$
$491$	−69.2965			−0.141133			−0.0705667	+	0.997507i	$0.522481\pi$
$492$	−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
$495$	−584.617	+	21.1564i	−1.18105	+	0.0427402i
$496$	208.000	−	208.000i	0.419355	−	0.419355i
$497$	−187.383	+	187.383i	−0.377029	+	0.377029i
$498$	−714.676	−	341.324i	−1.43509	−	0.685389i
$499$	−111.000	−	111.000i	−0.222445	−	0.222445i	0.587082	−	0.809527i	$-0.300276\pi$
$499$	−111.000	−	111.000i	−0.222445	−	0.222445i	−0.809527	+	0.587082i	$0.800276\pi$
$500$	−455.377	+	206.475i	−0.910754	+	0.412950i
$501$	−148.103	+	310.103i	−0.295614	+	0.618967i
$502$		−	952.000i		−	1.89641i
$503$	373.352	+	373.352i	0.742251	+	0.742251i	0.973011	−	0.230760i	$-0.0741211\pi$
$503$	373.352	+	373.352i	0.742251	+	0.742251i	−0.230760	+	0.973011i	$0.574121\pi$
$504$		0			0
$505$	−42.0000	+	6.00000i	−0.0831683	+	0.0118812i
$506$	−772.161			−1.52601
$507$	−218.499	+	457.501i	−0.430964	+	0.902369i
$508$	624.000	−	624.000i	1.22835	−	1.22835i
$509$	−569.221	+	569.221i	−1.11831	+	1.11831i	−0.126323	+	0.991989i	$0.540318\pi$
$509$	−569.221	+	569.221i	−1.11831	+	1.11831i	−0.991989	+	0.126323i	$0.959682\pi$
$510$	373.480	+	714.362i	0.732314	+	1.40071i
$511$			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	−0.677844	−	0.735206i	$-0.737086\pi$
$523$	30.0000	−	30.0000i	0.0573614	−	0.0573614i	0.735206	+	0.677844i	$0.237086\pi$
$524$		−	282.843i		−	0.539776i
$525$	−370.104	−	60.3984i	−0.704960	−	0.115045i
$526$	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
$531$	64.5828	−	608.583i	0.121625	−	1.14611i
$532$	−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
$537$	225.877	+	107.877i	0.420628	+	0.200889i
$538$			492.000i			0.914498i
$539$	220.617	−	220.617i	0.409309	−	0.409309i
$540$	502.274	−	198.294i	0.930137	−	0.367212i
$541$	−198.000	−	198.000i	−0.365989	−	0.365989i	0.500023	−	0.866012i	$-0.333325\pi$
$541$	−198.000	−	198.000i	−0.365989	−	0.365989i	−0.866012	+	0.500023i	$0.833325\pi$
$542$	814.587	−	814.587i	1.50293	−	1.50293i
$543$	35.1924	+	16.8076i	0.0648110	+	0.0309532i
$544$	608.000	−	608.000i	1.11765	−	1.11765i
$545$	560.029	+	420.021i	1.02758	+	0.770682i
$546$	−497.696	−	237.696i	−0.911530	−	0.435340i
$547$	57.0000	+	57.0000i	0.104205	+	0.104205i	0.757287	−	0.653082i	$-0.226524\pi$
$547$	57.0000	+	57.0000i	0.104205	+	0.104205i	−0.653082	+	0.757287i	$0.726524\pi$
$548$	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
$555$	−214.706	−	67.2792i	−0.386857	−	0.121224i
$556$		−	892.000i		−	1.60432i
$557$	−649.124			−1.16539			−0.582697	−	0.812690i	$-0.698002\pi$
$557$	−649.124			−1.16539			−0.582697	+	0.812690i	$0.698002\pi$
$558$	−49.3869	+	465.387i	−0.0885069	+	0.834027i
$559$	221.000	−	221.000i	0.395349	−	0.395349i
$560$	56.5685	+	395.980i	0.101015	+	0.707107i
$561$	319.345	−	668.655i	0.569242	−	1.19190i
$562$	376.000	+	376.000i	0.669039	+	0.669039i
$563$	396.687	−	396.687i	0.704595	−	0.704595i	−0.260798	−	0.965393i	$-0.583986\pi$
$563$	396.687	−	396.687i	0.704595	−	0.704595i	0.965393	+	0.260798i	$0.0839858\pi$
$564$	372.999	−	780.999i	0.661346	−	1.38475i
$565$	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	$-0.280607\pi$
$570$	611.578	+	1169.77i	1.07294	+	2.05224i
$571$		−	753.000i		−	1.31874i	−0.751819	−	0.659370i	$-0.770823\pi$
$571$		−	753.000i		−	1.31874i	0.751819	−	0.659370i	$-0.229177\pi$
$572$	478.004	+	478.004i	0.835672	+	0.835672i
$573$	−156.966	−	74.9655i	−0.273936	−	0.130830i
$574$	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
$579$	−127.996	+	268.004i	−0.221065	+	0.462873i
$580$	756.000	−	108.000i	1.30345	−	0.186207i
$581$			466.690i			0.803254i
$582$	−191.421	−	91.4214i	−0.328903	−	0.157081i
$583$	−169.000			−0.289880
$584$		0			0
$585$	−398.427	+	428.347i	−0.681072	+	0.732217i
$586$	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	$0.689040\pi$
$588$	−124.118	+	259.882i	−0.211085	+	0.441977i
$589$	−572.000			−0.971138
$590$	−576.999	+	769.332i	−0.977965	+	1.30395i
$591$	252.676	+	120.676i	0.427540	+	0.204190i
$592$			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
$597$	253.407	−	530.593i	0.424467	−	0.888765i
$598$	−546.000	+	546.000i	−0.913043	+	0.913043i
$599$	72.1249			0.120409			0.0602044	−	0.998186i	$-0.480825\pi$
$599$	72.1249			0.120409			0.0602044	+	0.998186i	$0.480825\pi$
$600$		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
$606$	−64.9706	−	31.0294i	−0.107212	−	0.0512037i
$607$	−256.000	−	256.000i	−0.421746	−	0.421746i	0.464058	−	0.885805i	$-0.346393\pi$
$607$	−256.000	−	256.000i	−0.421746	−	0.421746i	−0.885805	+	0.464058i	$0.846393\pi$
$608$	995.606	−	995.606i	1.63751	−	1.63751i
$609$	516.838	+	246.838i	0.848666	+	0.405316i
$610$	134.000	+	938.000i	0.219672	+	1.53770i
$611$			937.624i			1.53457i
$612$	−72.1808	+	680.181i	−0.117942	+	1.11141i
$613$			221.000i			0.360522i	0.983619	+	0.180261i	$0.0576942\pi$
$613$			221.000i			0.360522i	−0.983619	+	0.180261i	$0.942306\pi$
$614$	1586.75			2.58428
$615$	465.251	−	243.241i	0.756506	−	0.395514i
$616$		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	−0.0412384	+	0.999149i	$0.513130\pi$
$619$	−644.000	+	644.000i	−1.04039	+	1.04039i	−0.999149	+	0.0412384i	$0.986870\pi$
$620$	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
$624$	563.078	+	268.922i	0.902369	+	0.430964i
$625$	527.000	−	336.000i	0.843200	−	0.537600i
$626$	967.322	+	967.322i	1.54524	+	1.54524i
$627$	522.930	−	1094.93i	0.834019	−	1.74630i
$628$	−424.000	−	424.000i	−0.675159	−	0.675159i
$629$	201.525	−	201.525i	0.320390	−	0.320390i
$630$	−465.980	−	433.431i	−0.739650	−	0.687986i
$631$	719.000	+	719.000i	1.13946	+	1.13946i	0.988547	+	0.150914i	$0.0482218\pi$
$631$	719.000	+	719.000i	1.13946	+	1.13946i	0.150914	+	0.988547i	$0.451778\pi$
$632$		0			0
$633$	20.6863	−	43.3137i	0.0326798	−	0.0684261i
$634$	−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
$639$	−50.3366	+	474.337i	−0.0787740	+	0.742311i
$640$		0			0
$641$	−831.558			−1.29728			−0.648641	−	0.761095i	$-0.724662\pi$
$641$	−831.558			−1.29728			−0.648641	+	0.761095i	$0.724662\pi$
$642$	472.000	−	166.877i	0.735202	−	0.259933i
$643$			1039.00i			1.61586i	0.589276	+	0.807932i	$0.299413\pi$
$643$			1039.00i			1.61586i	−0.589276	+	0.807932i	$0.700587\pi$
$644$	−296.985	−	296.985i	−0.461157	−	0.461157i
$645$	319.583	−	167.083i	0.495477	−	0.259044i
$646$	−1672.00			−2.58824
$647$	632.861	+	632.861i	0.978146	+	0.978146i	0.999766	−	0.0216201i	$-0.00688243\pi$
$647$	632.861	+	632.861i	0.978146	+	0.978146i	−0.0216201	+	0.999766i	$0.506882\pi$
$648$		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	$-0.135427\pi$
$653$	325.269	+	325.269i	0.498115	+	0.498115i	−0.412736	+	0.910851i	$0.635427\pi$
$654$	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	$-0.827876\pi$
$659$	−1129.96			−1.71465			−0.857327	+	0.514773i	$0.827876\pi$
$660$	361.387	+	691.230i	0.547556	+	1.04732i
$661$	−97.0000	−	97.0000i	−0.146747	−	0.146747i	0.629916	−	0.776663i	$-0.283089\pi$
$661$	−97.0000	−	97.0000i	−0.146747	−	0.146747i	−0.776663	+	0.629916i	$0.783089\pi$
$662$	−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
$669$	−216.569	−	103.431i	−0.323720	−	0.154606i
$670$	−200.000	−	1400.00i	−0.298507	−	2.08955i
$671$	615.890	−	615.890i	0.917869	−	0.917869i
$672$	−292.548	+	612.548i	−0.435340	+	0.911530i
$673$	813.000	+	813.000i	1.20802	+	1.20802i	0.971666	+	0.236358i	$0.0759537\pi$
$673$	813.000	+	813.000i	1.20802	+	1.20802i	0.236358	+	0.971666i	$0.424046\pi$
$674$	−709.935	−	709.935i	−1.05332	−	1.05332i
$675$	−586.479	+	334.167i	−0.868857	+	0.495062i
$676$	676.000			1.00000
$677$	716.299	−	716.299i	1.05805	−	1.05805i	0.0598411	−	0.998208i	$-0.480941\pi$
$677$	716.299	−	716.299i	1.05805	−	1.05805i	0.998208	−	0.0598411i	$-0.0190594\pi$
$678$	56.5685	+	160.000i	0.0834344	+	0.235988i
$679$			125.000i			0.184094i
$680$		0			0
$681$	−344.558	−	164.558i	−0.505960	−	0.241642i
$682$	−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	$-0.220988\pi$
$684$	−118.197	+	1113.80i	−0.172802	+	1.62837i
$685$	−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
$690$	−789.558	+	412.794i	−1.14429	+	0.598252i
$691$	−396.000	+	396.000i	−0.573082	+	0.573082i	−0.932989	−	0.359906i	$-0.882809\pi$
$691$	−396.000	+	396.000i	−0.573082	+	0.573082i	0.359906	+	0.932989i	$0.382809\pi$
$692$	−701.450	+	701.450i	−1.01366	+	1.01366i
$693$	−61.7336	+	581.734i	−0.0890817	+	0.839442i
$694$	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	$-0.192238\pi$
$701$	1154.00			1.64622			0.823109	+	0.567884i	$0.192238\pi$
$702$	−965.696	+	230.304i	−1.37563	+	0.328069i
$703$	330.000	−	330.000i	0.469417	−	0.469417i
$704$	588.313	−	588.313i	0.835672	−	0.835672i
$705$	−323.500	+	1032.37i	−0.458866	+	1.46436i
$706$			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	−0.0721472	−	0.997394i	$-0.522985\pi$
$709$	656.000	−	656.000i	0.925247	−	0.925247i	0.997394	+	0.0721472i	$0.0229851\pi$
$710$	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	$0.919636\pi$
$720$	527.196	+	490.372i	0.732217	+	0.681072i
$721$	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
$726$	175.529	−	367.529i	0.241775	−	0.506238i
$727$	217.000	−	217.000i	0.298487	−	0.298487i	−0.541934	−	0.840421i	$-0.682308\pi$
$727$	217.000	−	217.000i	0.298487	−	0.298487i	0.840421	+	0.541934i	$0.182308\pi$
$728$		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
$732$	−346.495	+	725.505i	−0.473354	+	0.991127i
$733$		−	1049.00i		−	1.43111i	−0.698559	−	0.715553i	$-0.746175\pi$
$733$		−	1049.00i		−	1.43111i	0.698559	−	0.715553i	$-0.253825\pi$
$734$	−616.597	+	616.597i	−0.840051	+	0.840051i
$735$	107.647	−	343.529i	0.146458	−	0.467386i
$736$	672.000	+	672.000i	0.913043	+	0.913043i
$737$	−919.239	+	919.239i	−1.24727	+	1.24727i
$738$	885.980	+	94.0202i	1.20051	+	0.127399i
$739$	609.000	−	609.000i	0.824087	−	0.824087i	−0.162605	−	0.986691i	$-0.551990\pi$
$739$	609.000	−	609.000i	0.824087	−	0.824087i	0.986691	+	0.162605i	$0.0519895\pi$
$740$	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	$-0.376346\pi$
$743$	562.857			0.757546			0.378773	+	0.925490i	$0.376346\pi$
$744$		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
$750$	1060.45	+	21.0740i	1.41393	+	0.0280987i
$751$		−	185.000i		−	0.246338i	−0.992386	−	0.123169i	$-0.960694\pi$
$751$		−	185.000i		−	0.246338i	0.992386	−	0.123169i	$-0.0393058\pi$
$752$	1154.00			1.53457
$753$	−435.166	+	911.166i	−0.577909	+	1.21005i
$754$	−1404.00			−1.86207
$755$	124.451	+	93.3381i	0.164835	+	0.123627i
$756$	−125.269	−	525.269i	−0.165700	−	0.694800i
$757$	493.000	+	493.000i	0.651255	+	0.651255i	0.953295	−	0.302040i	$-0.0976677\pi$
$757$	493.000	+	493.000i	0.651255	+	0.651255i	−0.302040	+	0.953295i	$0.597668\pi$
$758$	291.328	−	291.328i	0.384338	−	0.384338i
$759$	739.040	+	352.960i	0.973702	+	0.465033i
$760$		0			0
$761$	618.011	−	618.011i	0.812104	−	0.812104i	−0.172845	−	0.984949i	$-0.555296\pi$
$761$	618.011	−	618.011i	0.812104	−	0.812104i	0.984949	+	0.172845i	$0.0552959\pi$
$762$	−1764.94	+	624.000i	−2.31619	+	0.818898i
$763$	495.000	−	495.000i	0.648755	−	0.648755i
$764$			231.931i			0.303575i
$765$	−30.9209	−	854.441i	−0.0404195	−	1.11692i
$766$		−	1392.00i		−	1.81723i
$767$	625.082	−	625.082i	0.814971	−	0.814971i
$768$	330.981	−	693.019i	0.430964	−	0.902369i
$769$	−897.000	−	897.000i	−1.16645	−	1.16645i	−0.983036	−	0.183414i	$-0.941285\pi$
$769$	−897.000	−	897.000i	−1.16645	−	1.16645i	−0.183414	−	0.983036i	$-0.558715\pi$
$770$	551.543	−	735.391i	0.716290	−	0.955053i
$771$	588.313	−	208.000i	0.763052	−	0.269780i
$772$	396.000			0.512953
$773$	−540.230			−0.698874			−0.349437	−	0.936960i	$-0.613627\pi$
$773$	−540.230			−0.698874			−0.349437	+	0.936960i	$0.613627\pi$
$774$	608.583	+	64.5828i	0.786283	+	0.0834403i
$775$	−221.000	+	403.000i	−0.285161	+	0.520000i
$776$		0			0
$777$	−96.9670	+	203.033i	−0.124797	+	0.261304i
$778$	−348.000			−0.447301
$779$			1088.94i			1.39787i
$780$	744.313	+	233.235i	0.954247	+	0.299019i
$781$	−689.000			−0.882202
$782$		−	1128.54i		−	1.44315i
$783$	1002.84	−	239.162i	1.28076	−	0.305444i
$784$	−384.000			−0.489796
$785$	599.627	+	449.720i	0.763855	+	0.572892i
$786$	−258.579	+	541.421i	−0.328980	+	0.688831i
$787$			176.000i			0.223634i	0.993729	+	0.111817i	$0.0356671\pi$
$787$			176.000i			0.223634i	−0.993729	+	0.111817i	$0.964333\pi$
$788$		−	373.352i		−	0.473797i
$789$	−769.332	+	272.000i	−0.975072	+	0.344740i
$790$	1246.00	−	178.000i	1.57722	−	0.225316i
$791$	70.7107	−	70.7107i	0.0893940	−	0.0893940i
$792$		0			0
$793$		−	871.000i		−	1.09836i
$794$	540.230			0.680390
$795$	−172.808	+	90.3467i	−0.217368	+	0.113644i
$796$	−784.000			−0.984925
$797$	−946.816	−	946.816i	−1.18797	−	1.18797i	−0.977626	−	0.210348i	$-0.932540\pi$
$797$	−946.816	−	946.816i	−1.18797	−	1.18797i	−0.210348	−	0.977626i	$-0.567460\pi$
$798$	1244.51	−	440.000i	1.55953	−	0.551378i
$799$	−969.000	−	969.000i	−1.21277	−	1.21277i
$800$	−316.784	−	1086.12i	−0.395980	−	1.35765i
$801$	−6.64823	+	62.6482i	−0.00829992	+	0.0782125i
$802$	1132.00	+	1132.00i	1.41147	+	1.41147i
$803$	−698.621	+	698.621i	−0.870014	+	0.870014i
$804$	517.157	−	1082.84i	0.643230	−	1.34682i
$805$	420.000	+	315.000i	0.521739	+	0.391304i
$806$	−478.004	+	478.004i	−0.593057	+	0.593057i
$807$	224.897	−	470.897i	0.278682	−	0.583515i
$808$		0			0
$809$	1422.70			1.75859			0.879295	−	0.476278i	$-0.158014\pi$
$809$	1422.70			1.75859			0.879295	+	0.476278i	$0.158014\pi$
$810$	−1142.74	−	79.6081i	−1.41079	−	0.0982816i
$811$	639.000	−	639.000i	0.787916	−	0.787916i	−0.193236	−	0.981152i	$-0.561898\pi$
$811$	639.000	−	639.000i	0.787916	−	0.787916i	0.981152	+	0.193236i	$0.0618983\pi$
$812$		−	763.675i		−	0.940487i
$813$	−1152.00	+	407.294i	−1.41697	+	0.500976i
$814$	390.000	−	390.000i	0.479115	−	0.479115i
$815$	1341.38	−	191.626i	1.64587	−	0.235124i
$816$	−859.842	+	304.000i	−1.05373	+	0.372549i
$817$			748.000i			0.915545i
$818$	−1397.24	+	1397.24i	−1.70812	+	1.70812i
$819$	367.696	+	455.000i	0.448957	+	0.555556i
$820$	−560.000	−	420.000i	−0.682927	−	0.512195i
$821$	−31.8198	−	31.8198i	−0.0387574	−	0.0387574i	0.687463	−	0.726220i	$-0.258725\pi$
$821$	−31.8198	−	31.8198i	−0.0387574	−	0.0387574i	−0.726220	+	0.687463i	$0.758725\pi$
$822$	−433.137	−	206.863i	−0.526931	−	0.251658i
$823$	−54.0000	−	54.0000i	−0.0656136	−	0.0656136i	0.673539	−	0.739152i	$-0.264774\pi$
$823$	−54.0000	−	54.0000i	−0.0656136	−	0.0656136i	−0.739152	+	0.673539i	$0.764774\pi$
$824$		0			0
$825$	−569.387	−	791.469i	−0.690166	−	0.959357i
$826$	680.000	+	680.000i	0.823245	+	0.823245i
$827$	516.188			0.624169			0.312085	−	0.950054i	$-0.398973\pi$
$827$	516.188			0.624169			0.312085	+	0.950054i	$0.398973\pi$
$828$	−751.779	−	79.7788i	−0.907945	−	0.0963512i
$829$	748.000			0.902292			0.451146	−	0.892450i	$-0.351015\pi$
$829$	748.000			0.902292			0.451146	+	0.892450i	$0.351015\pi$
$830$	−186.676	−	1306.73i	−0.224911	−	1.57438i
$831$	250.316	+	708.000i	0.301222	+	0.851986i
$832$		−	832.000i		−	1.00000i
$833$	322.441	+	322.441i	0.387084	+	0.387084i
$834$	−815.478	+	1707.48i	−0.977792	+	2.04734i
$835$	−567.000	+	81.0000i	−0.679042	+	0.0970060i
$836$	−1617.86			−1.93524
$837$	260.000	−	422.850i	0.310633	−	0.505197i
$838$		−	1532.00i		−	1.82816i
$839$	242.538	+	242.538i	0.289079	+	0.289079i	0.836716	−	0.547637i	$-0.184472\pi$
$839$	242.538	+	242.538i	0.289079	+	0.289079i	−0.547637	+	0.836716i	$0.684472\pi$
$840$		0			0
$841$	617.000			0.733650
$842$	−107.480	−	107.480i	−0.127649	−	0.127649i
$843$	−188.000	−	531.744i	−0.223013	−	0.630776i
$844$	−64.0000			−0.0758294
$845$	−836.507	+	119.501i	−0.989949	+	0.141421i
$846$	−1428.00	+	1154.00i	−1.68794	+	1.36406i
$847$	−240.000			−0.283353
$848$	147.078	+	147.078i	0.173441	+	0.173441i
$849$	−648.000	+	229.103i	−0.763251	+	0.269850i
$850$	−646.000	+	1178.00i	−0.760000	+	1.38588i
$851$	222.739	+	222.739i	0.261738	+	0.261738i
$852$	599.627	−	212.000i	0.703787	−	0.248826i
$853$	−1129.00			−1.32356			−0.661782	−	0.749696i	$-0.730200\pi$
$853$	−1129.00			−1.32356			−0.661782	+	0.749696i	$0.730200\pi$
$854$	947.523			1.10951
$855$	−50.6333	−	1399.16i	−0.0592203	−	1.63644i
$856$		0			0
$857$	−456.084	−	456.084i	−0.532187	−	0.532187i	0.389036	−	0.921223i	$-0.372808\pi$
$857$	−456.084	−	456.084i	−0.532187	−	0.532187i	−0.921223	+	0.389036i	$0.872808\pi$
$858$	−478.004	−	1352.00i	−0.557114	−	1.57576i
$859$			1533.00i			1.78463i	0.451410	+	0.892317i	$0.350921\pi$
$859$			1533.00i			1.78463i	−0.451410	+	0.892317i	$0.649079\pi$
$860$	−384.666	−	288.500i	−0.447286	−	0.335465i
$861$	−175.000	−	494.975i	−0.203252	−	0.574884i
$862$	1048.00	−	1048.00i	1.21578	−	1.21578i
$863$	−793.374			−0.919321			−0.459660	−	0.888095i	$-0.652029\pi$
$863$	−793.374			−0.919321			−0.459660	+	0.888095i	$0.652029\pi$
$864$	283.452	+	1188.55i	0.328069	+	1.37563i
$865$	744.000	−	992.000i	0.860116	−	1.14682i
$866$	673.166	−	673.166i	0.777328	−	0.777328i
$867$	194.912	+	93.0883i	0.224812	+	0.107368i
$868$	−260.000	−	260.000i	−0.299539	−	0.299539i
$869$	−818.123	−	818.123i	−0.941453	−	0.941453i
$870$	−1545.88	−	484.410i	−1.77687	−	0.556794i
$871$			1300.00i			1.49254i
$872$		0			0
$873$	141.421	+	175.000i	0.161995	+	0.200458i
$874$		−	1848.00i		−	2.11442i
$875$	−258.094	−	569.221i	−0.294965	−	0.650538i
$876$	393.040	−	822.960i	0.448675	−	0.939453i
$877$	−460.000			−0.524515			−0.262258	−	0.964998i	$-0.584467\pi$
$877$	−460.000			−0.524515			−0.262258	+	0.964998i	$0.584467\pi$
$878$			941.866i			1.07274i
$879$	−677.632	−	323.632i	−0.770912	−	0.368182i
$880$	−624.000	+	832.000i	−0.709091	+	0.945455i
$881$	−162.635			−0.184602			−0.0923011	−	0.995731i	$-0.529422\pi$
$881$	−162.635			−0.184602			−0.0923011	+	0.995731i	$0.529422\pi$
$882$	475.176	−	384.000i	0.538748	−	0.435374i
$883$	783.000	+	783.000i	0.886750	+	0.886750i	0.994209	−	0.107460i	$-0.0342717\pi$
$883$	783.000	+	783.000i	0.886750	+	0.886750i	−0.107460	+	0.994209i	$0.534272\pi$
$884$	−698.621	+	698.621i	−0.790296	+	0.790296i
$885$	903.917	−	472.583i	1.02137	−	0.533992i
$886$	862.000	−	862.000i	0.972912	−	0.972912i
$887$	−389.616	+	389.616i	−0.439251	+	0.439251i	−0.891760	−	0.452509i	$-0.850529\pi$
$887$	−389.616	+	389.616i	−0.439251	+	0.439251i	0.452509	+	0.891760i	$0.350529\pi$
$888$		0			0
$889$	780.000	+	780.000i	0.877390	+	0.877390i
$890$	59.3970	−	79.1960i	0.0667382	−	0.0889842i
$891$	571.729	+	884.271i	0.641672	+	0.992447i
$892$			320.000i			0.358744i
$893$	−1586.75	−	1586.75i	−1.77687	−	1.77687i
$894$	600.000	−	212.132i	0.671141	−	0.237284i
$895$	59.0000	+	413.000i	0.0659218	+	0.461453i
$896$		0			0
$897$	772.161	−	273.000i	0.860826	−	0.304348i
$898$	−138.000	+	138.000i	−0.153675	+	0.153675i
$899$	496.389	−	496.389i	0.552157	−	0.552157i
$900$	739.058	+	513.608i	0.821176	+	0.570676i
$901$		−	247.000i		−	0.274140i
$902$			1286.93i			1.42676i
$903$	−120.208	−	340.000i	−0.133121	−	0.376523i
$904$		0			0
$905$	9.19239	+	64.3467i	0.0101573	+	0.0711013i
$906$	88.0000	+	248.902i	0.0971302	+	0.274726i
$907$	−39.0000	+	39.0000i	−0.0429989	+	0.0429989i	−0.728279	−	0.685280i	$-0.759680\pi$
$907$	−39.0000	+	39.0000i	−0.0429989	+	0.0429989i	0.685280	+	0.728279i	$0.259680\pi$
$908$			509.117i			0.560701i
$909$	48.0000	+	59.3970i	0.0528053	+	0.0653432i
$910$	−130.000	−	910.000i	−0.142857	−	1.00000i
$911$			93.3381i			0.102457i	0.998687	+	0.0512284i	$0.0163136\pi$
$911$			93.3381i			0.102457i	−0.998687	+	0.0512284i	$0.983686\pi$
$912$	−1408.00	+	497.803i	−1.54386	+	0.545837i
$913$	−858.000	+	858.000i	−0.939759	+	0.939759i
$914$			1168.14i			1.27805i
$915$	300.514	−	959.018i	0.328430	−	1.04811i
$916$	−192.000	+	192.000i	−0.209607	+	0.209607i
$917$	353.553			0.385554
$918$	760.000	−	1236.02i	0.827887	−	1.34643i
$919$			1139.00i			1.23939i	0.784842	+	0.619695i	$0.212744\pi$
$919$			1139.00i			1.23939i	−0.784842	+	0.619695i	$0.787256\pi$
$920$		0			0
$921$	−1518.69	−	725.313i	−1.64895	−	0.787528i
$922$	638.000	−	638.000i	0.691974	−	0.691974i
$923$	−487.197	+	487.197i	−0.527840	+	0.527840i
$924$	735.391	−	260.000i	0.795878	−	0.281385i
$925$	−105.000	−	360.000i	−0.113514	−	0.389189i
$926$			432.749i			0.467332i
$927$	1.34315	−	12.6569i	0.00144892	−	0.0136536i
$928$			1728.00i			1.86207i
$929$	−495.682	+	495.682i	−0.533565	+	0.533565i	−0.921631	−	0.388066i	$-0.873143\pi$
$929$	−495.682	+	495.682i	−0.533565	+	0.533565i	0.388066	+	0.921631i	$0.373143\pi$
$930$	−691.230	+	361.387i	−0.743259	+	0.388588i
$931$	528.000	+	528.000i	0.567132	+	0.567132i
$932$	121.622	−	121.622i	0.130496	−	0.130496i
$933$	323.632	−	677.632i	0.346872	−	0.726293i
$934$	−1122.00	+	1122.00i	−1.20128	+	1.20128i
$935$	1222.59	−	174.655i	1.30758	−	0.186797i
$936$		0			0
$937$	464.000	+	464.000i	0.495197	+	0.495197i	0.909939	−	0.414742i	$-0.136128\pi$
$937$	464.000	+	464.000i	0.495197	+	0.495197i	−0.414742	+	0.909939i	$0.636128\pi$
$938$	−1414.21			−1.50769
$939$	−483.661	−	1368.00i	−0.515081	−	1.45687i
$940$	1428.00	−	204.000i	1.51915	−	0.217021i
$941$	434.871	+	434.871i	0.462137	+	0.462137i	0.899355	−	0.437219i	$-0.144036\pi$
$941$	434.871	+	434.871i	0.462137	+	0.462137i	−0.437219	+	0.899355i	$0.644036\pi$
$942$	424.000	+	1199.25i	0.450106	+	1.27309i
$943$	−735.000			−0.779427
$944$	−769.332	−	769.332i	−0.814971	−	0.814971i
$945$	247.868	+	627.843i	0.262294	+	0.664384i
$946$			884.000i			0.934461i
$947$	−1480.68			−1.56355			−0.781775	−	0.623561i	$-0.785685\pi$
$947$	−1480.68			−1.56355			−0.781775	+	0.623561i	$0.785685\pi$
$948$	963.730	+	460.270i	1.01659	+	0.485517i
$949$			988.000i			1.04110i
$950$	−1057.83	+	1928.99i	−1.11351	+	2.03051i
$951$	501.524	+	239.524i	0.527365	+	0.251865i
$952$		0			0
$953$	−424.971	+	424.971i	−0.445930	+	0.445930i	−0.893999	−	0.448069i	$-0.852112\pi$
$953$	−424.971	+	424.971i	−0.445930	+	0.445930i	0.448069	+	0.893999i	$0.352112\pi$
$954$	−329.078	−	34.9218i	−0.344946	−	0.0366056i
$955$	−41.0000	−	287.000i	−0.0429319	−	0.300524i
$956$	−127.279	+	127.279i	−0.133137	+	0.133137i
$957$	496.389	+	1404.00i	0.518693	+	1.46708i
$958$	650.000	−	650.000i	0.678497	−	0.678497i
$959$			282.843i			0.294935i
$960$	287.058	−	916.077i	0.299019	−	0.954247i
$961$			623.000i			0.648283i
$962$		−	551.543i		−	0.573330i
$963$	−528.035	−	56.0351i	−0.548323	−	0.0581881i
$964$	724.000	+	724.000i	0.751037	+	0.751037i
$965$	−490.025	+	70.0036i	−0.507798	+	0.0725426i
$966$	296.985	+	840.000i	0.307438	+	0.869565i
$967$	−1236.00			−1.27818			−0.639090	−	0.769132i	$-0.720689\pi$
$967$	−1236.00			−1.27818			−0.639090	+	0.769132i	$0.720689\pi$
$968$		0			0
$969$	1600.28	+	764.283i	1.65148	+	0.788733i
$970$	−50.0000	−	350.000i	−0.0515464	−	0.360825i
$971$		−	93.3381i		−	0.0961257i	−0.998844	−	0.0480629i	$-0.984695\pi$
$971$		−	93.3381i		−	0.0961257i	0.998844	−	0.0480629i	$-0.0153048\pi$
$972$	−769.651	−	593.651i	−0.791822	−	0.610752i
$973$	1115.00			1.14594
$974$		−	183.848i		−	0.188755i
$975$	−962.271	−	157.036i	−0.986944	−	0.161063i
$976$	−1072.00			−1.09836
$977$		−	1551.39i		−	1.58791i	−0.607974	−	0.793957i	$-0.708017\pi$
$977$		−	1551.39i		−	1.58791i	0.607974	−	0.793957i	$-0.291983\pi$
$978$	2075.01	+	991.008i	2.12168	+	1.01330i
$979$	−91.0000			−0.0929520
$980$	−475.176	+	67.8823i	−0.484873	+	0.0692676i
$981$	132.971	−	1253.03i	0.135547	−	1.27730i
$982$		−	196.000i		−	0.199593i
$983$			1289.76i			1.31207i	0.754731	+	0.656034i	$0.227767\pi$
$983$			1289.76i			1.31207i	−0.754731	+	0.656034i	$0.772233\pi$
$984$		0			0
$985$	66.0000	+	462.000i	0.0670051	+	0.469036i
$986$	1450.98	−	1450.98i	1.47159	−	1.47159i
$987$	976.249	+	466.249i	0.989107	+	0.472390i
$988$	−1144.00	+	1144.00i	−1.15789	+	1.15789i
$989$	−504.874			−0.510490
$990$	−59.8394	−	1653.55i	−0.0604438	−	1.67025i
$991$	825.000			0.832492			0.416246	−	0.909252i	$-0.363345\pi$
$991$	825.000			0.832492			0.416246	+	0.909252i	$0.363345\pi$
$992$	588.313	+	588.313i	0.593057	+	0.593057i
$993$	220.617	+	624.000i	0.222173	+	0.628399i
$994$	−530.000	−	530.000i	−0.533199	−	0.533199i
$995$	970.151	−	138.593i	0.975026	−	0.139289i
$996$	482.705	−	1010.70i	0.484643	−	1.01476i
$997$	−927.000	−	927.000i	−0.929789	−	0.929789i	0.0679026	−	0.997692i	$-0.478369\pi$
$997$	−927.000	−	927.000i	−0.929789	−	0.929789i	−0.997692	+	0.0679026i	$0.978369\pi$
$998$	313.955	−	313.955i	0.314585	−	0.314585i
$999$	93.9518	+	393.952i	0.0940459	+	0.394346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.3.j.c.122.2	yes	4
3.2	odd	2	inner	195.3.j.c.122.1	yes	4
5.3	odd	4		195.3.u.c.83.2	yes	4
13.8	odd	4		195.3.u.c.47.1	yes	4
15.8	even	4		195.3.u.c.83.1	yes	4
39.8	even	4		195.3.u.c.47.2	yes	4
65.8	even	4	inner	195.3.j.c.8.2	yes	4
195.8	odd	4	inner	195.3.j.c.8.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.3.j.c.8.1	✓	4	195.8	odd	4	inner
195.3.j.c.8.2	yes	4	65.8	even	4	inner
195.3.j.c.122.1	yes	4	3.2	odd	2	inner
195.3.j.c.122.2	yes	4	1.1	even	1	trivial
195.3.u.c.47.1	yes	4	13.8	odd	4
195.3.u.c.47.2	yes	4	39.8	even	4
195.3.u.c.83.1	yes	4	15.8	even	4
195.3.u.c.83.2	yes	4	5.3	odd	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 $\F_{q}$
Belyi maps

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} +(1.29289 - 2.70711i) q^{3} -4.00000 q^{4} +(4.94975 - 0.707107i) q^{5} +(7.65685 + 3.65685i) q^{6} -5.00000i q^{7} +(-5.65685 - 7.00000i) q^{9} +(2.00000 + 14.0000i) q^{10} +(9.19239 - 9.19239i) q^{11} +(-5.17157 + 10.8284i) q^{12} -13.0000i q^{13} +14.1421 q^{14} +(4.48528 - 14.3137i) 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} +(-13.5355 - 6.46447i) q^{21} +(26.0000 + 26.0000i) q^{22} +(-14.8492 + 14.8492i) q^{23} +(24.0000 - 7.00000i) q^{25} +36.7696 q^{26} +(-26.2635 + 6.26346i) q^{27} +20.0000i q^{28} -38.1838 q^{29} +(40.4853 + 12.6863i) 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} +(-35.1924 - 16.8076i) q^{39} +(24.7487 + 24.7487i) q^{41} +(18.2843 - 38.2843i) q^{42} +(17.0000 + 17.0000i) q^{43} +(-36.7696 + 36.7696i) q^{44} +(-32.9497 - 30.6482i) q^{45} +(-42.0000 - 42.0000i) q^{46} -72.1249 q^{47} +(-20.6863 + 43.3137i) 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} +(-17.7157 - 74.2843i) q^{54} +(39.0000 - 52.0000i) q^{55} +(88.0000 - 31.1127i) q^{57} -108.000i q^{58} +(48.0833 + 48.0833i) q^{59} +(-17.9411 + 57.2548i) 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} +(12.0797 - 74.0208i) q^{75} +(-88.0000 - 88.0000i) q^{76} +(-45.9619 - 45.9619i) q^{77} +(47.5391 - 99.5391i) 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} +(54.1421 + 25.8579i) q^{84} +(76.0000 + 57.0000i) q^{85} +(-48.0833 + 48.0833i) q^{86} +(-49.3675 + 103.368i) q^{87} +(-4.94975 - 4.94975i) q^{89} +(86.6863 - 93.1960i) 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} +(-122.510 - 58.5097i) q^{96} -25.0000 q^{97} +67.8823i q^{98} +(-116.347 - 12.3467i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{3} - 16 q^{4} + 8 q^{6} + 8 q^{10} - 32 q^{12} - 16 q^{15} - 64 q^{16} + 88 q^{19} - 40 q^{21} + 104 q^{22} + 96 q^{25} - 40 q^{27} + 128 q^{30} - 52 q^{31} - 52 q^{33} - 152 q^{34} - 104 q^{39}+ \cdots - 208 q^{99}+O(q^{100}) \) 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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