LMFDB - Embedded newform 195.2.i.b.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,2,Mod(16,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("195.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.i (of order $3$, 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:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	195.16
Dual form			195.2.i.b.61.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-3.00000 - 5.19615i) q^{11} -2.00000 q^{12} +(2.50000 + 2.59808i) q^{13} +(0.500000 + 0.866025i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(2.00000 - 3.46410i) q^{19} +(-1.00000 + 1.73205i) q^{20} -1.00000 q^{21} +(3.00000 + 5.19615i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(3.00000 + 5.19615i) q^{29} +5.00000 q^{31} +(-3.00000 + 5.19615i) q^{33} +(-0.500000 + 0.866025i) q^{35} +(1.00000 + 1.73205i) q^{36} +(-1.00000 - 1.73205i) q^{37} +(1.00000 - 3.46410i) q^{39} +(-5.50000 + 9.52628i) q^{43} -12.0000 q^{44} +(0.500000 - 0.866025i) q^{45} +6.00000 q^{47} +(-2.00000 + 3.46410i) q^{48} +(3.00000 + 5.19615i) q^{49} +(7.00000 - 1.73205i) q^{52} +(3.00000 + 5.19615i) q^{55} -4.00000 q^{57} +(-3.00000 + 5.19615i) q^{59} +2.00000 q^{60} +(0.500000 - 0.866025i) q^{61} +(0.500000 + 0.866025i) q^{63} -8.00000 q^{64} +(-2.50000 - 2.59808i) q^{65} +(-5.50000 - 9.52628i) q^{67} +(3.00000 - 5.19615i) q^{69} +(3.00000 - 5.19615i) q^{71} +5.00000 q^{73} +(-0.500000 - 0.866025i) q^{75} +(-4.00000 - 6.92820i) q^{76} -6.00000 q^{77} +11.0000 q^{79} +(2.00000 + 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} +(-1.00000 + 1.73205i) q^{84} +(3.00000 - 5.19615i) q^{87} +(-6.00000 - 10.3923i) q^{89} +(3.50000 - 0.866025i) q^{91} +12.0000 q^{92} +(-2.50000 - 4.33013i) q^{93} +(-2.00000 + 3.46410i) q^{95} +(-8.50000 + 14.7224i) q^{97} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} + 2 q^{4} - 2 q^{5} + q^{7} - q^{9}+O(q^{10}) $ 2 * q - q^3 + 2 * q^4 - 2 * q^5 + q^7 - q^9	$ 2 q - q^{3} + 2 q^{4} - 2 q^{5} + q^{7} - q^{9} - 6 q^{11} - 4 q^{12} + 5 q^{13} + q^{15} - 4 q^{16} + 4 q^{19} - 2 q^{20} - 2 q^{21} + 6 q^{23} + 2 q^{25} + 2 q^{27} - 2 q^{28} + 6 q^{29} + 10 q^{31} - 6 q^{33} - q^{35} + 2 q^{36} - 2 q^{37} + 2 q^{39} - 11 q^{43} - 24 q^{44} + q^{45} + 12 q^{47} - 4 q^{48} + 6 q^{49} + 14 q^{52} + 6 q^{55} - 8 q^{57} - 6 q^{59} + 4 q^{60} + q^{61} + q^{63} - 16 q^{64} - 5 q^{65} - 11 q^{67} + 6 q^{69} + 6 q^{71} + 10 q^{73} - q^{75} - 8 q^{76} - 12 q^{77} + 22 q^{79} + 4 q^{80} - q^{81} + 24 q^{83} - 2 q^{84} + 6 q^{87} - 12 q^{89} + 7 q^{91} + 24 q^{92} - 5 q^{93} - 4 q^{95} - 17 q^{97} + 12 q^{99}+O(q^{100}) $ 2 * q - q^3 + 2 * q^4 - 2 * q^5 + q^7 - q^9 - 6 * q^11 - 4 * q^12 + 5 * q^13 + q^15 - 4 * q^16 + 4 * q^19 - 2 * q^20 - 2 * q^21 + 6 * q^23 + 2 * q^25 + 2 * q^27 - 2 * q^28 + 6 * q^29 + 10 * q^31 - 6 * q^33 - q^35 + 2 * q^36 - 2 * q^37 + 2 * q^39 - 11 * q^43 - 24 * q^44 + q^45 + 12 * q^47 - 4 * q^48 + 6 * q^49 + 14 * q^52 + 6 * q^55 - 8 * q^57 - 6 * q^59 + 4 * q^60 + q^61 + q^63 - 16 * q^64 - 5 * q^65 - 11 * q^67 + 6 * q^69 + 6 * q^71 + 10 * q^73 - q^75 - 8 * q^76 - 12 * q^77 + 22 * q^79 + 4 * q^80 - q^81 + 24 * q^83 - 2 * q^84 + 6 * q^87 - 12 * q^89 + 7 * q^91 + 24 * q^92 - 5 * q^93 - 4 * q^95 - 17 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$2$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	0.944911	+	0.327327i	$0.106148\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.821541	−	0.570149i	$-0.806886\pi$
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.0829925	−	0.996550i	$-0.526448\pi$
$12$	−2.00000			−0.577350
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$14$		0			0
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$	−1.00000	+	1.73205i	−0.223607	+	0.387298i
$21$	−1.00000			−0.218218
$22$		0			0
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$	−1.00000	−	1.73205i	−0.188982	−	0.327327i
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	0.997738	+	0.0672232i	$0.0214140\pi$
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	−0.440652	+	0.897678i	$0.645253\pi$
$30$		0			0
$31$	5.00000			0.898027			0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000			0.898027			0.449013	+	0.893525i	$0.351776\pi$
$32$		0			0
$33$	−3.00000	+	5.19615i	−0.522233	+	0.904534i
$34$		0			0
$35$	−0.500000	+	0.866025i	−0.0845154	+	0.146385i
$36$	1.00000	+	1.73205i	0.166667	+	0.288675i
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$		0			0
$39$	1.00000	−	3.46410i	0.160128	−	0.554700i
$40$		0			0
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$		0			0
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	0.0522047	+	0.998636i	$0.483375\pi$
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	−0.890947	+	0.454108i	$0.849958\pi$
$44$	−12.0000			−1.80907
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$		0			0
$47$	6.00000			0.875190			0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000			0.875190			0.437595	+	0.899172i	$0.355830\pi$
$48$	−2.00000	+	3.46410i	−0.288675	+	0.500000i
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$		0			0
$51$		0			0
$52$	7.00000	−	1.73205i	0.970725	−	0.240192i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$		0			0
$55$	3.00000	+	5.19615i	0.404520	+	0.700649i
$56$		0			0
$57$	−4.00000			−0.529813
$58$		0			0
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	−0.992524	−	0.122047i	$-0.961054\pi$
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	0.601958	+	0.798528i	$0.294388\pi$
$60$	2.00000			0.258199
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$		0			0
$63$	0.500000	+	0.866025i	0.0629941	+	0.109109i
$64$	−8.00000			−1.00000
$65$	−2.50000	−	2.59808i	−0.310087	−	0.322252i
$66$		0			0
$67$	−5.50000	−	9.52628i	−0.671932	−	1.16382i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−5.50000	−	9.52628i	−0.671932	−	1.16382i	0.305424	−	0.952217i	$-0.401202\pi$
$68$		0			0
$69$	3.00000	−	5.19615i	0.361158	−	0.625543i
$70$		0			0
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	−0.631260	−	0.775571i	$-0.717462\pi$
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	0.987294	+	0.158901i	$0.0507952\pi$
$72$		0			0
$73$	5.00000			0.585206			0.292603	−	0.956234i	$-0.405479\pi$
$73$	5.00000			0.585206			0.292603	+	0.956234i	$0.405479\pi$
$74$		0			0
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$	−4.00000	−	6.92820i	−0.458831	−	0.794719i
$77$	−6.00000			−0.683763
$78$		0			0
$79$	11.0000			1.23760			0.618798	−	0.785550i	$-0.287620\pi$
$79$	11.0000			1.23760			0.618798	+	0.785550i	$0.287620\pi$
$80$	2.00000	+	3.46410i	0.223607	+	0.387298i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$	−1.00000	+	1.73205i	−0.109109	+	0.188982i
$85$		0			0
$86$		0			0
$87$	3.00000	−	5.19615i	0.321634	−	0.557086i
$88$		0			0
$89$	−6.00000	−	10.3923i	−0.635999	−	1.10158i	−0.986303	−	0.164946i	$-0.947255\pi$
$89$	−6.00000	−	10.3923i	−0.635999	−	1.10158i	0.350304	−	0.936636i	$-0.386078\pi$
$90$		0			0
$91$	3.50000	−	0.866025i	0.366900	−	0.0907841i
$92$	12.0000			1.25109
$93$	−2.50000	−	4.33013i	−0.259238	−	0.449013i
$94$		0			0
$95$	−2.00000	+	3.46410i	−0.205196	+	0.355409i
$96$		0			0
$97$	−8.50000	+	14.7224i	−0.863044	+	1.49484i	0.00593185	+	0.999982i	$0.498112\pi$
$97$	−8.50000	+	14.7224i	−0.863044	+	1.49484i	−0.868976	+	0.494854i	$0.835222\pi$
$98$		0			0
$99$	6.00000			0.603023
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$		0			0
$103$	−13.0000			−1.28093			−0.640464	−	0.767988i	$-0.721258\pi$
$103$	−13.0000			−1.28093			−0.640464	+	0.767988i	$0.721258\pi$
$104$		0			0
$105$	1.00000			0.0975900
$106$		0			0
$107$	−9.00000	−	15.5885i	−0.870063	−	1.50699i	−0.861931	−	0.507026i	$-0.830745\pi$
$107$	−9.00000	−	15.5885i	−0.870063	−	1.50699i	−0.00813215	−	0.999967i	$-0.502589\pi$
$108$	1.00000	−	1.73205i	0.0962250	−	0.166667i
$109$	−7.00000			−0.670478			−0.335239	−	0.942133i	$-0.608817\pi$
$109$	−7.00000			−0.670478			−0.335239	+	0.942133i	$0.608817\pi$
$110$		0			0
$111$	−1.00000	+	1.73205i	−0.0949158	+	0.164399i
$112$	−4.00000			−0.377964
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	−0.689714	−	0.724082i	$-0.742264\pi$
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	0.971930	+	0.235269i	$0.0755971\pi$
$114$		0			0
$115$	−3.00000	−	5.19615i	−0.279751	−	0.484544i
$116$	12.0000			1.11417
$117$	−3.50000	+	0.866025i	−0.323575	+	0.0800641i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$		0			0
$123$		0			0
$124$	5.00000	−	8.66025i	0.449013	−	0.777714i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	0.500000	+	0.866025i	0.0443678	+	0.0768473i	0.887357	−	0.461084i	$-0.152539\pi$
$127$	0.500000	+	0.866025i	0.0443678	+	0.0768473i	−0.842989	+	0.537931i	$0.819206\pi$
$128$		0			0
$129$	11.0000			0.968496
$130$		0			0
$131$	18.0000			1.57267			0.786334	−	0.617802i	$-0.211977\pi$
$131$	18.0000			1.57267			0.786334	+	0.617802i	$0.211977\pi$
$132$	6.00000	+	10.3923i	0.522233	+	0.904534i
$133$	−2.00000	−	3.46410i	−0.173422	−	0.300376i
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$		0			0
$139$	9.50000	−	16.4545i	0.805779	−	1.39565i	−0.109984	−	0.993933i	$-0.535080\pi$
$139$	9.50000	−	16.4545i	0.805779	−	1.39565i	0.915764	−	0.401718i	$-0.131587\pi$
$140$	1.00000	+	1.73205i	0.0845154	+	0.146385i
$141$	−3.00000	−	5.19615i	−0.252646	−	0.437595i
$142$		0			0
$143$	6.00000	−	20.7846i	0.501745	−	1.73810i
$144$	4.00000			0.333333
$145$	−3.00000	−	5.19615i	−0.249136	−	0.431517i
$146$		0			0
$147$	3.00000	−	5.19615i	0.247436	−	0.428571i
$148$	−4.00000			−0.328798
$149$	−12.0000	+	20.7846i	−0.983078	+	1.70274i	−0.332896	+	0.942964i	$0.608026\pi$
$149$	−12.0000	+	20.7846i	−0.983078	+	1.70274i	−0.650183	+	0.759778i	$0.725308\pi$
$150$		0			0
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−5.00000			−0.401610
$156$	−5.00000	−	5.19615i	−0.400320	−	0.416025i
$157$	−1.00000			−0.0798087			−0.0399043	−	0.999204i	$-0.512705\pi$
$157$	−1.00000			−0.0798087			−0.0399043	+	0.999204i	$0.512705\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	6.00000			0.472866
$162$		0			0
$163$	−5.50000	+	9.52628i	−0.430793	+	0.746156i	−0.996942	−	0.0781474i	$-0.975100\pi$
$163$	−5.50000	+	9.52628i	−0.430793	+	0.746156i	0.566149	+	0.824303i	$0.308433\pi$
$164$		0			0
$165$	3.00000	−	5.19615i	0.233550	−	0.404520i
$166$		0			0
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	0.999169	−	0.0407502i	$-0.0129748\pi$
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	−0.534875	+	0.844931i	$0.679641\pi$
$168$		0			0
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$		0			0
$171$	2.00000	+	3.46410i	0.152944	+	0.264906i
$172$	11.0000	+	19.0526i	0.838742	+	1.45274i
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		0			0
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$	−12.0000	+	20.7846i	−0.904534	+	1.56670i
$177$	6.00000			0.450988
$178$		0			0
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	0.998286	−	0.0585225i	$-0.0186389\pi$
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	−0.549825	+	0.835280i	$0.685306\pi$
$180$	−1.00000	−	1.73205i	−0.0745356	−	0.129099i
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$	−1.00000			−0.0739221
$184$		0			0
$185$	1.00000	+	1.73205i	0.0735215	+	0.127343i
$186$		0			0
$187$		0			0
$188$	6.00000	−	10.3923i	0.437595	−	0.757937i
$189$	0.500000	−	0.866025i	0.0363696	−	0.0629941i
$190$		0			0
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	−0.953912	−	0.300088i	$-0.902984\pi$
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	0.736839	+	0.676068i	$0.236317\pi$
$192$	4.00000	+	6.92820i	0.288675	+	0.500000i
$193$	6.50000	+	11.2583i	0.467880	+	0.810392i	0.999326	−	0.0366998i	$-0.0116845\pi$
$193$	6.50000	+	11.2583i	0.467880	+	0.810392i	−0.531446	+	0.847092i	$0.678351\pi$
$194$		0			0
$195$	−1.00000	+	3.46410i	−0.0716115	+	0.248069i
$196$	12.0000			0.857143
$197$	−6.00000	−	10.3923i	−0.427482	−	0.740421i	0.569166	−	0.822222i	$-0.307266\pi$
$197$	−6.00000	−	10.3923i	−0.427482	−	0.740421i	−0.996649	+	0.0818013i	$0.973933\pi$
$198$		0			0
$199$	−8.50000	+	14.7224i	−0.602549	+	1.04365i	0.389885	+	0.920864i	$0.372515\pi$
$199$	−8.50000	+	14.7224i	−0.602549	+	1.04365i	−0.992434	+	0.122782i	$0.960818\pi$
$200$		0			0
$201$	−5.50000	+	9.52628i	−0.387940	+	0.671932i
$202$		0			0
$203$	6.00000			0.421117
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−6.00000			−0.417029
$208$	4.00000	−	13.8564i	0.277350	−	0.960769i
$209$	−24.0000			−1.66011
$210$		0			0
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	0.998221	−	0.0596196i	$-0.0189888\pi$
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	−0.550743	+	0.834675i	$0.685655\pi$
$212$		0			0
$213$	−6.00000			−0.411113
$214$		0			0
$215$	5.50000	−	9.52628i	0.375097	−	0.649687i
$216$		0			0
$217$	2.50000	−	4.33013i	0.169711	−	0.293948i
$218$		0			0
$219$	−2.50000	−	4.33013i	−0.168934	−	0.292603i
$220$	12.0000			0.809040
$221$		0			0
$222$		0			0
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	0.700449	−	0.713702i	$-0.252983\pi$
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	−0.968309	+	0.249756i	$0.919650\pi$
$224$		0			0
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$		0			0
$227$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$227$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$228$	−4.00000	+	6.92820i	−0.264906	+	0.458831i
$229$	14.0000			0.925146			0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000			0.925146			0.462573	+	0.886581i	$0.346926\pi$
$230$		0			0
$231$	3.00000	+	5.19615i	0.197386	+	0.341882i
$232$		0			0
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$		0			0
$235$	−6.00000			−0.391397
$236$	6.00000	+	10.3923i	0.390567	+	0.676481i
$237$	−5.50000	−	9.52628i	−0.357263	−	0.618798i
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$	2.00000	−	3.46410i	0.129099	−	0.223607i
$241$	11.0000	−	19.0526i	0.708572	−	1.22728i	−0.256814	−	0.966461i	$-0.582673\pi$
$241$	11.0000	−	19.0526i	0.708572	−	1.22728i	0.965387	−	0.260822i	$-0.0839937\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−1.00000	−	1.73205i	−0.0640184	−	0.110883i
$245$	−3.00000	−	5.19615i	−0.191663	−	0.331970i
$246$		0			0
$247$	14.0000	−	3.46410i	0.890799	−	0.220416i
$248$		0			0
$249$	−6.00000	−	10.3923i	−0.380235	−	0.658586i
$250$		0			0
$251$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$251$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$252$	2.00000			0.125988
$253$	18.0000	−	31.1769i	1.13165	−	1.96008i
$254$		0			0
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	6.00000	+	10.3923i	0.374270	+	0.648254i	0.990217	−	0.139533i	$-0.0445601\pi$
$257$	6.00000	+	10.3923i	0.374270	+	0.648254i	−0.615948	+	0.787787i	$0.711227\pi$
$258$		0			0
$259$	−2.00000			−0.124274
$260$	−7.00000	+	1.73205i	−0.434122	+	0.107417i
$261$	−6.00000			−0.371391
$262$		0			0
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	0.619586	−	0.784929i	$-0.287301\pi$
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−6.00000	+	10.3923i	−0.367194	+	0.635999i
$268$	−22.0000			−1.34386
$269$	12.0000	−	20.7846i	0.731653	−	1.26726i	−0.224523	−	0.974469i	$-0.572083\pi$
$269$	12.0000	−	20.7846i	0.731653	−	1.26726i	0.956176	−	0.292791i	$-0.0945841\pi$
$270$		0			0
$271$	3.50000	+	6.06218i	0.212610	+	0.368251i	0.952531	−	0.304443i	$-0.0984703\pi$
$271$	3.50000	+	6.06218i	0.212610	+	0.368251i	−0.739921	+	0.672694i	$0.765137\pi$
$272$		0			0
$273$	−2.50000	−	2.59808i	−0.151307	−	0.157243i
$274$		0			0
$275$	−3.00000	−	5.19615i	−0.180907	−	0.313340i
$276$	−6.00000	−	10.3923i	−0.361158	−	0.625543i
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	−0.675810	−	0.737075i	$-0.736206\pi$
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	0.976231	+	0.216731i	$0.0695395\pi$
$278$		0			0
$279$	−2.50000	+	4.33013i	−0.149671	+	0.259238i
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	−11.5000	−	19.9186i	−0.683604	−	1.18404i	−0.973873	−	0.227092i	$-0.927078\pi$
$283$	−11.5000	−	19.9186i	−0.683604	−	1.18404i	0.290269	−	0.956945i	$-0.406255\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$	4.00000			0.236940
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$	17.0000			0.996558
$292$	5.00000	−	8.66025i	0.292603	−	0.506803i
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	−0.940252	−	0.340480i	$-0.889411\pi$
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	0.764990	+	0.644042i	$0.222744\pi$
$294$		0			0
$295$	3.00000	−	5.19615i	0.174667	−	0.302532i
$296$		0			0
$297$	−3.00000	−	5.19615i	−0.174078	−	0.301511i
$298$		0			0
$299$	−6.00000	+	20.7846i	−0.346989	+	1.20201i
$300$	−2.00000			−0.115470
$301$	5.50000	+	9.52628i	0.317015	+	0.549086i
$302$		0			0
$303$	−3.00000	+	5.19615i	−0.172345	+	0.298511i
$304$	−16.0000			−0.917663
$305$	−0.500000	+	0.866025i	−0.0286299	+	0.0495885i
$306$		0			0
$307$	−25.0000			−1.42683			−0.713413	−	0.700744i	$-0.752851\pi$
$307$	−25.0000			−1.42683			−0.713413	+	0.700744i	$0.752851\pi$
$308$	−6.00000	+	10.3923i	−0.341882	+	0.592157i
$309$	6.50000	+	11.2583i	0.369772	+	0.640464i
$310$		0			0
$311$	12.0000			0.680458			0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000			0.680458			0.340229	+	0.940343i	$0.389495\pi$
$312$		0			0
$313$	23.0000			1.30004			0.650018	−	0.759918i	$-0.274761\pi$
$313$	23.0000			1.30004			0.650018	+	0.759918i	$0.274761\pi$
$314$		0			0
$315$	−0.500000	−	0.866025i	−0.0281718	−	0.0487950i
$316$	11.0000	−	19.0526i	0.618798	−	1.07179i
$317$	−12.0000			−0.673987			−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000			−0.673987			−0.336994	+	0.941507i	$0.609410\pi$
$318$		0			0
$319$	18.0000	−	31.1769i	1.00781	−	1.74557i
$320$	8.00000			0.447214
$321$	−9.00000	+	15.5885i	−0.502331	+	0.870063i
$322$		0			0
$323$		0			0
$324$	−2.00000			−0.111111
$325$	2.50000	+	2.59808i	0.138675	+	0.144115i
$326$		0			0
$327$	3.50000	+	6.06218i	0.193550	+	0.335239i
$328$		0			0
$329$	3.00000	−	5.19615i	0.165395	−	0.286473i
$330$		0			0
$331$	3.50000	−	6.06218i	0.192377	−	0.333207i	−0.753660	−	0.657264i	$-0.771714\pi$
$331$	3.50000	−	6.06218i	0.192377	−	0.333207i	0.946038	+	0.324057i	$0.105047\pi$
$332$	12.0000	−	20.7846i	0.658586	−	1.14070i
$333$	2.00000			0.109599
$334$		0			0
$335$	5.50000	+	9.52628i	0.300497	+	0.520476i
$336$	2.00000	+	3.46410i	0.109109	+	0.188982i
$337$	−7.00000			−0.381314			−0.190657	−	0.981657i	$-0.561062\pi$
$337$	−7.00000			−0.381314			−0.190657	+	0.981657i	$0.561062\pi$
$338$		0			0
$339$	−6.00000			−0.325875
$340$		0			0
$341$	−15.0000	−	25.9808i	−0.812296	−	1.40694i
$342$		0			0
$343$	13.0000			0.701934
$344$		0			0
$345$	−3.00000	+	5.19615i	−0.161515	+	0.279751i
$346$		0			0
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	−0.980921	−	0.194409i	$-0.937721\pi$
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	0.658824	+	0.752297i	$0.271054\pi$
$348$	−6.00000	−	10.3923i	−0.321634	−	0.557086i
$349$	−5.50000	−	9.52628i	−0.294408	−	0.509930i	0.680439	−	0.732805i	$-0.261789\pi$
$349$	−5.50000	−	9.52628i	−0.294408	−	0.509930i	−0.974847	+	0.222875i	$0.928456\pi$
$350$		0			0
$351$	2.50000	+	2.59808i	0.133440	+	0.138675i
$352$		0			0
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	0.999711	−	0.0240566i	$-0.00765819\pi$
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	−0.520689	+	0.853746i	$0.674325\pi$
$354$		0			0
$355$	−3.00000	+	5.19615i	−0.159223	+	0.275783i
$356$	−24.0000			−1.27200
$357$		0			0
$358$		0			0
$359$	12.0000			0.633336			0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000			0.633336			0.316668	+	0.948536i	$0.397436\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$		0			0
$363$	25.0000			1.31216
$364$	2.00000	−	6.92820i	0.104828	−	0.363137i
$365$	−5.00000			−0.261712
$366$		0			0
$367$	−2.50000	−	4.33013i	−0.130499	−	0.226031i	0.793370	−	0.608740i	$-0.208325\pi$
$367$	−2.50000	−	4.33013i	−0.130499	−	0.226031i	−0.923869	+	0.382709i	$0.874991\pi$
$368$	12.0000	−	20.7846i	0.625543	−	1.08347i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−10.0000			−0.518476
$373$	−11.5000	+	19.9186i	−0.595447	+	1.03135i	0.398036	+	0.917370i	$0.369692\pi$
$373$	−11.5000	+	19.9186i	−0.595447	+	1.03135i	−0.993484	+	0.113975i	$0.963641\pi$
$374$		0			0
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$		0			0
$377$	−6.00000	+	20.7846i	−0.309016	+	1.07046i
$378$		0			0
$379$	0.500000	+	0.866025i	0.0256833	+	0.0444847i	0.878581	−	0.477593i	$-0.158491\pi$
$379$	0.500000	+	0.866025i	0.0256833	+	0.0444847i	−0.852898	+	0.522077i	$0.825157\pi$
$380$	4.00000	+	6.92820i	0.205196	+	0.355409i
$381$	0.500000	−	0.866025i	0.0256158	−	0.0443678i
$382$		0			0
$383$	−12.0000	+	20.7846i	−0.613171	+	1.06204i	0.377531	+	0.925997i	$0.376773\pi$
$383$	−12.0000	+	20.7846i	−0.613171	+	1.06204i	−0.990702	+	0.136047i	$0.956560\pi$
$384$		0			0
$385$	6.00000			0.305788
$386$		0			0
$387$	−5.50000	−	9.52628i	−0.279581	−	0.484248i
$388$	17.0000	+	29.4449i	0.863044	+	1.49484i
$389$	24.0000			1.21685			0.608424	−	0.793612i	$-0.291802\pi$
$389$	24.0000			1.21685			0.608424	+	0.793612i	$0.291802\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−9.00000	−	15.5885i	−0.453990	−	0.786334i
$394$		0			0
$395$	−11.0000			−0.553470
$396$	6.00000	−	10.3923i	0.301511	−	0.522233i
$397$	6.50000	−	11.2583i	0.326226	−	0.565039i	−0.655534	−	0.755166i	$-0.727556\pi$
$397$	6.50000	−	11.2583i	0.326226	−	0.565039i	0.981760	+	0.190126i	$0.0608897\pi$
$398$		0			0
$399$	−2.00000	+	3.46410i	−0.100125	+	0.173422i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	6.00000	+	10.3923i	0.299626	+	0.518967i	0.976050	−	0.217545i	$-0.0698049\pi$
$401$	6.00000	+	10.3923i	0.299626	+	0.518967i	−0.676425	+	0.736512i	$0.736472\pi$
$402$		0			0
$403$	12.5000	+	12.9904i	0.622669	+	0.647097i
$404$	−12.0000			−0.597022
$405$	0.500000	+	0.866025i	0.0248452	+	0.0430331i
$406$		0			0
$407$	−6.00000	+	10.3923i	−0.297409	+	0.515127i
$408$		0			0
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	−0.921192	−	0.389109i	$-0.872783\pi$
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	0.797574	+	0.603220i	$0.206116\pi$
$410$		0			0
$411$	12.0000			0.591916
$412$	−13.0000	+	22.5167i	−0.640464	+	1.10932i
$413$	3.00000	+	5.19615i	0.147620	+	0.255686i
$414$		0			0
$415$	−12.0000			−0.589057
$416$		0			0
$417$	−19.0000			−0.930434
$418$		0			0
$419$	12.0000	+	20.7846i	0.586238	+	1.01539i	0.994720	+	0.102628i	$0.0327251\pi$
$419$	12.0000	+	20.7846i	0.586238	+	1.01539i	−0.408481	+	0.912767i	$0.633942\pi$
$420$	1.00000	−	1.73205i	0.0487950	−	0.0845154i
$421$	17.0000			0.828529			0.414265	−	0.910156i	$-0.364039\pi$
$421$	17.0000			0.828529			0.414265	+	0.910156i	$0.364039\pi$
$422$		0			0
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−0.500000	−	0.866025i	−0.0241967	−	0.0419099i
$428$	−36.0000			−1.74013
$429$	−21.0000	+	5.19615i	−1.01389	+	0.250873i
$430$		0			0
$431$	−12.0000	−	20.7846i	−0.578020	−	1.00116i	−0.995706	−	0.0925683i	$-0.970492\pi$
$431$	−12.0000	−	20.7846i	−0.578020	−	1.00116i	0.417687	−	0.908591i	$-0.362841\pi$
$432$	−2.00000	−	3.46410i	−0.0962250	−	0.166667i
$433$	−5.50000	+	9.52628i	−0.264313	+	0.457804i	−0.967383	−	0.253317i	$-0.918479\pi$
$433$	−5.50000	+	9.52628i	−0.264313	+	0.457804i	0.703070	+	0.711120i	$0.251812\pi$
$434$		0			0
$435$	−3.00000	+	5.19615i	−0.143839	+	0.249136i
$436$	−7.00000	+	12.1244i	−0.335239	+	0.580651i
$437$	24.0000			1.14808
$438$		0			0
$439$	−5.50000	−	9.52628i	−0.262501	−	0.454665i	0.704405	−	0.709798i	$-0.251214\pi$
$439$	−5.50000	−	9.52628i	−0.262501	−	0.454665i	−0.966906	+	0.255134i	$0.917881\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$		0			0
$443$	−36.0000			−1.71041			−0.855206	−	0.518289i	$-0.826569\pi$
$443$	−36.0000			−1.71041			−0.855206	+	0.518289i	$0.826569\pi$
$444$	2.00000	+	3.46410i	0.0949158	+	0.164399i
$445$	6.00000	+	10.3923i	0.284427	+	0.492642i
$446$		0			0
$447$	24.0000			1.13516
$448$	−4.00000	+	6.92820i	−0.188982	+	0.327327i
$449$	−3.00000	+	5.19615i	−0.141579	+	0.245222i	−0.928091	−	0.372353i	$-0.878551\pi$
$449$	−3.00000	+	5.19615i	−0.141579	+	0.245222i	0.786513	+	0.617574i	$0.211885\pi$
$450$		0			0
$451$		0			0
$452$	−6.00000	−	10.3923i	−0.282216	−	0.488813i
$453$	8.00000	+	13.8564i	0.375873	+	0.651031i
$454$		0			0
$455$	−3.50000	+	0.866025i	−0.164083	+	0.0405999i
$456$		0			0
$457$	15.5000	+	26.8468i	0.725059	+	1.25584i	0.958950	+	0.283577i	$0.0915211\pi$
$457$	15.5000	+	26.8468i	0.725059	+	1.25584i	−0.233890	+	0.972263i	$0.575146\pi$
$458$		0			0
$459$		0			0
$460$	−12.0000			−0.559503
$461$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$461$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$462$		0			0
$463$	−19.0000			−0.883005			−0.441502	−	0.897260i	$-0.645554\pi$
$463$	−19.0000			−0.883005			−0.441502	+	0.897260i	$0.645554\pi$
$464$	12.0000	−	20.7846i	0.557086	−	0.964901i
$465$	2.50000	+	4.33013i	0.115935	+	0.200805i
$466$		0			0
$467$	42.0000			1.94353			0.971764	−	0.235954i	$-0.0758216\pi$
$467$	42.0000			1.94353			0.971764	+	0.235954i	$0.0758216\pi$
$468$	−2.00000	+	6.92820i	−0.0924500	+	0.320256i
$469$	−11.0000			−0.507933
$470$		0			0
$471$	0.500000	+	0.866025i	0.0230388	+	0.0399043i
$472$		0			0
$473$	66.0000			3.03468
$474$		0			0
$475$	2.00000	−	3.46410i	0.0917663	−	0.158944i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$		0			0
$481$	2.00000	−	6.92820i	0.0911922	−	0.315899i
$482$		0			0
$483$	−3.00000	−	5.19615i	−0.136505	−	0.236433i
$484$	25.0000	+	43.3013i	1.13636	+	1.96824i
$485$	8.50000	−	14.7224i	0.385965	−	0.668511i
$486$		0			0
$487$	14.0000	−	24.2487i	0.634401	−	1.09881i	−0.352241	−	0.935909i	$-0.614580\pi$
$487$	14.0000	−	24.2487i	0.634401	−	1.09881i	0.986642	−	0.162905i	$-0.0520863\pi$
$488$		0			0
$489$	11.0000			0.497437
$490$		0			0
$491$	−15.0000	−	25.9808i	−0.676941	−	1.17250i	−0.975898	−	0.218229i	$-0.929972\pi$
$491$	−15.0000	−	25.9808i	−0.676941	−	1.17250i	0.298957	−	0.954267i	$-0.403361\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−6.00000			−0.269680
$496$	−10.0000	−	17.3205i	−0.449013	−	0.777714i
$497$	−3.00000	−	5.19615i	−0.134568	−	0.233079i
$498$		0			0
$499$	−40.0000			−1.79065			−0.895323	−	0.445418i	$-0.853055\pi$
$499$	−40.0000			−1.79065			−0.895323	+	0.445418i	$0.853055\pi$
$500$	−1.00000	+	1.73205i	−0.0447214	+	0.0774597i
$501$	6.00000	−	10.3923i	0.268060	−	0.464294i
$502$		0			0
$503$	−21.0000	+	36.3731i	−0.936344	+	1.62179i	−0.164124	+	0.986440i	$0.552480\pi$
$503$	−21.0000	+	36.3731i	−0.936344	+	1.62179i	−0.772220	+	0.635355i	$0.780854\pi$
$504$		0			0
$505$	3.00000	+	5.19615i	0.133498	+	0.231226i
$506$		0			0
$507$	11.5000	−	6.06218i	0.510733	−	0.269231i
$508$	2.00000			0.0887357
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	0.993593	−	0.113020i	$-0.0360525\pi$
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	−0.594675	+	0.803966i	$0.702719\pi$
$510$		0			0
$511$	2.50000	−	4.33013i	0.110593	−	0.191554i
$512$		0			0
$513$	2.00000	−	3.46410i	0.0883022	−	0.152944i
$514$		0			0
$515$	13.0000			0.572848
$516$	11.0000	−	19.0526i	0.484248	−	0.838742i
$517$	−18.0000	−	31.1769i	−0.791639	−	1.37116i
$518$		0			0
$519$	−6.00000			−0.263371
$520$		0			0
$521$	−36.0000			−1.57719			−0.788594	−	0.614914i	$-0.789191\pi$
$521$	−36.0000			−1.57719			−0.788594	+	0.614914i	$0.789191\pi$
$522$		0			0
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	0.906434	−	0.422347i	$-0.138794\pi$
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	−0.818980	+	0.573822i	$0.805460\pi$
$524$	18.0000	−	31.1769i	0.786334	−	1.36197i
$525$	−1.00000			−0.0436436
$526$		0			0
$527$		0			0
$528$	24.0000			1.04447
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$	−3.00000	−	5.19615i	−0.130189	−	0.225494i
$532$	−8.00000			−0.346844
$533$		0			0
$534$		0			0
$535$	9.00000	+	15.5885i	0.389104	+	0.673948i
$536$		0			0
$537$	6.00000	−	10.3923i	0.258919	−	0.448461i
$538$		0			0
$539$	18.0000	−	31.1769i	0.775315	−	1.34288i
$540$	−1.00000	+	1.73205i	−0.0430331	+	0.0745356i
$541$	−7.00000			−0.300954			−0.150477	−	0.988614i	$-0.548081\pi$
$541$	−7.00000			−0.300954			−0.150477	+	0.988614i	$0.548081\pi$
$542$		0			0
$543$	5.00000	+	8.66025i	0.214571	+	0.371647i
$544$		0			0
$545$	7.00000			0.299847
$546$		0			0
$547$	−7.00000			−0.299298			−0.149649	−	0.988739i	$-0.547814\pi$
$547$	−7.00000			−0.299298			−0.149649	+	0.988739i	$0.547814\pi$
$548$	12.0000	+	20.7846i	0.512615	+	0.887875i
$549$	0.500000	+	0.866025i	0.0213395	+	0.0369611i
$550$		0			0
$551$	24.0000			1.02243
$552$		0			0
$553$	5.50000	−	9.52628i	0.233884	−	0.405099i
$554$		0			0
$555$	1.00000	−	1.73205i	0.0424476	−	0.0735215i
$556$	−19.0000	−	32.9090i	−0.805779	−	1.39565i
$557$	6.00000	+	10.3923i	0.254228	+	0.440336i	0.964686	−	0.263404i	$-0.0848453\pi$
$557$	6.00000	+	10.3923i	0.254228	+	0.440336i	−0.710457	+	0.703740i	$0.751512\pi$
$558$		0			0
$559$	−38.5000	+	9.52628i	−1.62838	+	0.402919i
$560$	4.00000			0.169031
$561$		0			0
$562$		0			0
$563$	−21.0000	+	36.3731i	−0.885044	+	1.53294i	−0.0393818	+	0.999224i	$0.512539\pi$
$563$	−21.0000	+	36.3731i	−0.885044	+	1.53294i	−0.845663	+	0.533718i	$0.820794\pi$
$564$	−12.0000			−0.505291
$565$	−3.00000	+	5.19615i	−0.126211	+	0.218604i
$566$		0			0
$567$	−1.00000			−0.0419961
$568$		0			0
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	−0.987786	−	0.155815i	$-0.950200\pi$
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	0.358954	−	0.933355i	$-0.383134\pi$
$570$		0			0
$571$	−28.0000			−1.17176			−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000			−1.17176			−0.585882	+	0.810397i	$0.699252\pi$
$572$	−30.0000	−	31.1769i	−1.25436	−	1.30357i
$573$	6.00000			0.250654
$574$		0			0
$575$	3.00000	+	5.19615i	0.125109	+	0.216695i
$576$	4.00000	−	6.92820i	0.166667	−	0.288675i
$577$	14.0000			0.582828			0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000			0.582828			0.291414	+	0.956597i	$0.405874\pi$
$578$		0			0
$579$	6.50000	−	11.2583i	0.270131	−	0.467880i
$580$	−12.0000			−0.498273
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	3.50000	−	0.866025i	0.144707	−	0.0358057i
$586$		0			0
$587$	−21.0000	−	36.3731i	−0.866763	−	1.50128i	−0.865286	−	0.501278i	$-0.832863\pi$
$587$	−21.0000	−	36.3731i	−0.866763	−	1.50128i	−0.00147660	−	0.999999i	$-0.500470\pi$
$588$	−6.00000	−	10.3923i	−0.247436	−	0.428571i
$589$	10.0000	−	17.3205i	0.412043	−	0.713679i
$590$		0			0
$591$	−6.00000	+	10.3923i	−0.246807	+	0.427482i
$592$	−4.00000	+	6.92820i	−0.164399	+	0.284747i
$593$	−30.0000			−1.23195			−0.615976	−	0.787765i	$-0.711238\pi$
$593$	−30.0000			−1.23195			−0.615976	+	0.787765i	$0.711238\pi$
$594$		0			0
$595$		0			0
$596$	24.0000	+	41.5692i	0.983078	+	1.70274i
$597$	17.0000			0.695764
$598$		0			0
$599$	18.0000			0.735460			0.367730	−	0.929933i	$-0.380135\pi$
$599$	18.0000			0.735460			0.367730	+	0.929933i	$0.380135\pi$
$600$		0			0
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	−0.999376	−	0.0353259i	$-0.988753\pi$
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	0.469095	−	0.883148i	$-0.344580\pi$
$602$		0			0
$603$	11.0000			0.447955
$604$	−16.0000	+	27.7128i	−0.651031	+	1.12762i
$605$	12.5000	−	21.6506i	0.508197	−	0.880223i
$606$		0			0
$607$	20.0000	−	34.6410i	0.811775	−	1.40604i	−0.0998457	−	0.995003i	$-0.531835\pi$
$607$	20.0000	−	34.6410i	0.811775	−	1.40604i	0.911621	−	0.411033i	$-0.134832\pi$
$608$		0			0
$609$	−3.00000	−	5.19615i	−0.121566	−	0.210559i
$610$		0			0
$611$	15.0000	+	15.5885i	0.606835	+	0.630641i
$612$		0			0
$613$	−11.5000	−	19.9186i	−0.464481	−	0.804504i	0.534697	−	0.845044i	$-0.320426\pi$
$613$	−11.5000	−	19.9186i	−0.464481	−	0.804504i	−0.999178	+	0.0405396i	$0.987092\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	−0.920074	−	0.391745i	$-0.871871\pi$
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	0.799298	+	0.600935i	$0.205205\pi$
$618$		0			0
$619$	−19.0000			−0.763674			−0.381837	−	0.924230i	$-0.624709\pi$
$619$	−19.0000			−0.763674			−0.381837	+	0.924230i	$0.624709\pi$
$620$	−5.00000	+	8.66025i	−0.200805	+	0.347804i
$621$	3.00000	+	5.19615i	0.120386	+	0.208514i
$622$		0			0
$623$	−12.0000			−0.480770
$624$	−14.0000	+	3.46410i	−0.560449	+	0.138675i
$625$	1.00000			0.0400000
$626$		0			0
$627$	12.0000	+	20.7846i	0.479234	+	0.830057i
$628$	−1.00000	+	1.73205i	−0.0399043	+	0.0691164i
$629$		0			0
$630$		0			0
$631$	18.5000	−	32.0429i	0.736473	−	1.27561i	−0.217601	−	0.976038i	$-0.569823\pi$
$631$	18.5000	−	32.0429i	0.736473	−	1.27561i	0.954074	−	0.299571i	$-0.0968437\pi$
$632$		0			0
$633$	6.50000	−	11.2583i	0.258352	−	0.447478i
$634$		0			0
$635$	−0.500000	−	0.866025i	−0.0198419	−	0.0343672i
$636$		0			0
$637$	−6.00000	+	20.7846i	−0.237729	+	0.823516i
$638$		0			0
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$		0			0
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$		0			0
$643$	−5.50000	+	9.52628i	−0.216899	+	0.375680i	−0.953858	−	0.300257i	$-0.902928\pi$
$643$	−5.50000	+	9.52628i	−0.216899	+	0.375680i	0.736959	+	0.675937i	$0.236261\pi$
$644$	6.00000	−	10.3923i	0.236433	−	0.409514i
$645$	−11.0000			−0.433125
$646$		0			0
$647$	3.00000	+	5.19615i	0.117942	+	0.204282i	0.918952	−	0.394369i	$-0.129037\pi$
$647$	3.00000	+	5.19615i	0.117942	+	0.204282i	−0.801010	+	0.598651i	$0.795704\pi$
$648$		0			0
$649$	36.0000			1.41312
$650$		0			0
$651$	−5.00000			−0.195965
$652$	11.0000	+	19.0526i	0.430793	+	0.746156i
$653$	−24.0000	−	41.5692i	−0.939193	−	1.62673i	−0.766982	−	0.641669i	$-0.778242\pi$
$653$	−24.0000	−	41.5692i	−0.939193	−	1.62673i	−0.172211	−	0.985060i	$-0.555091\pi$
$654$		0			0
$655$	−18.0000			−0.703318
$656$		0			0
$657$	−2.50000	+	4.33013i	−0.0975343	+	0.168934i
$658$		0			0
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	−0.266872	−	0.963732i	$-0.585990\pi$
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	0.968052	−	0.250748i	$-0.0806766\pi$
$660$	−6.00000	−	10.3923i	−0.233550	−	0.404520i
$661$	24.5000	+	42.4352i	0.952940	+	1.65054i	0.739014	+	0.673690i	$0.235292\pi$
$661$	24.5000	+	42.4352i	0.952940	+	1.65054i	0.213925	+	0.976850i	$0.431375\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.00000	+	3.46410i	0.0775567	+	0.134332i
$666$		0			0
$667$	−18.0000	+	31.1769i	−0.696963	+	1.20717i
$668$	24.0000			0.928588
$669$	−4.00000	+	6.92820i	−0.154649	+	0.267860i
$670$		0			0
$671$	−6.00000			−0.231627
$672$		0			0
$673$	−5.50000	−	9.52628i	−0.212009	−	0.367211i	0.740334	−	0.672239i	$-0.234667\pi$
$673$	−5.50000	−	9.52628i	−0.212009	−	0.367211i	−0.952343	+	0.305028i	$0.901334\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$	22.0000	+	13.8564i	0.846154	+	0.532939i
$677$		0			0			−	1.00000i	$-0.5\pi$
$677$		0			0				1.00000i	$0.5\pi$
$678$		0			0
$679$	8.50000	+	14.7224i	0.326200	+	0.564995i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−9.00000	+	15.5885i	−0.344375	+	0.596476i	−0.985240	−	0.171178i	$-0.945243\pi$
$683$	−9.00000	+	15.5885i	−0.344375	+	0.596476i	0.640865	+	0.767654i	$0.278576\pi$
$684$	8.00000			0.305888
$685$	6.00000	−	10.3923i	0.229248	−	0.397070i
$686$		0			0
$687$	−7.00000	−	12.1244i	−0.267067	−	0.462573i
$688$	44.0000			1.67748
$689$		0			0
$690$		0			0
$691$	−2.50000	−	4.33013i	−0.0951045	−	0.164726i	0.814548	−	0.580097i	$-0.196985\pi$
$691$	−2.50000	−	4.33013i	−0.0951045	−	0.164726i	−0.909652	+	0.415371i	$0.863652\pi$
$692$	−6.00000	−	10.3923i	−0.228086	−	0.395056i
$693$	3.00000	−	5.19615i	0.113961	−	0.197386i
$694$		0			0
$695$	−9.50000	+	16.4545i	−0.360356	+	0.624154i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	3.00000	+	5.19615i	0.113470	+	0.196537i
$700$	−1.00000	−	1.73205i	−0.0377964	−	0.0654654i
$701$	−12.0000			−0.453234			−0.226617	−	0.973984i	$-0.572767\pi$
$701$	−12.0000			−0.453234			−0.226617	+	0.973984i	$0.572767\pi$
$702$		0			0
$703$	−8.00000			−0.301726
$704$	24.0000	+	41.5692i	0.904534	+	1.56670i
$705$	3.00000	+	5.19615i	0.112987	+	0.195698i
$706$		0			0
$707$	−6.00000			−0.225653
$708$	6.00000	−	10.3923i	0.225494	−	0.390567i
$709$	9.50000	−	16.4545i	0.356780	−	0.617961i	−0.630641	−	0.776075i	$-0.717208\pi$
$709$	9.50000	−	16.4545i	0.356780	−	0.617961i	0.987421	+	0.158114i	$0.0505412\pi$
$710$		0			0
$711$	−5.50000	+	9.52628i	−0.206266	+	0.357263i
$712$		0			0
$713$	15.0000	+	25.9808i	0.561754	+	0.972987i
$714$		0			0
$715$	−6.00000	+	20.7846i	−0.224387	+	0.777300i
$716$	24.0000			0.896922
$717$		0			0
$718$		0			0
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	−0.916529	−	0.399969i	$-0.869021\pi$
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	0.804648	+	0.593753i	$0.202354\pi$
$720$	−4.00000			−0.149071
$721$	−6.50000	+	11.2583i	−0.242073	+	0.419282i
$722$		0			0
$723$	−22.0000			−0.818189
$724$	−10.0000	+	17.3205i	−0.371647	+	0.643712i
$725$	3.00000	+	5.19615i	0.111417	+	0.192980i
$726$		0			0
$727$	−25.0000			−0.927199			−0.463599	−	0.886045i	$-0.653442\pi$
$727$	−25.0000			−0.927199			−0.463599	+	0.886045i	$0.653442\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$		0			0
$732$	−1.00000	+	1.73205i	−0.0369611	+	0.0640184i
$733$	29.0000			1.07114			0.535570	−	0.844491i	$-0.320097\pi$
$733$	29.0000			1.07114			0.535570	+	0.844491i	$0.320097\pi$
$734$		0			0
$735$	−3.00000	+	5.19615i	−0.110657	+	0.191663i
$736$		0			0
$737$	−33.0000	+	57.1577i	−1.21557	+	2.10543i
$738$		0			0
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	0.621374	−	0.783514i	$-0.286575\pi$
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	−0.989230	+	0.146369i	$0.953241\pi$
$740$	4.00000			0.147043
$741$	−10.0000	−	10.3923i	−0.367359	−	0.381771i
$742$		0			0
$743$	−3.00000	−	5.19615i	−0.110059	−	0.190628i	0.805735	−	0.592277i	$-0.201771\pi$
$743$	−3.00000	−	5.19615i	−0.110059	−	0.190628i	−0.915794	+	0.401648i	$0.868437\pi$
$744$		0			0
$745$	12.0000	−	20.7846i	0.439646	−	0.761489i
$746$		0			0
$747$	−6.00000	+	10.3923i	−0.219529	+	0.380235i
$748$		0			0
$749$	−18.0000			−0.657706
$750$		0			0
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	0.956963	+	0.290209i	$0.0937250\pi$
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	−0.227153	+	0.973859i	$0.572942\pi$
$752$	−12.0000	−	20.7846i	−0.437595	−	0.757937i
$753$		0			0
$754$		0			0
$755$	16.0000			0.582300
$756$	−1.00000	−	1.73205i	−0.0363696	−	0.0629941i
$757$	−7.00000	−	12.1244i	−0.254419	−	0.440667i	0.710318	−	0.703881i	$-0.248551\pi$
$757$	−7.00000	−	12.1244i	−0.254419	−	0.440667i	−0.964738	+	0.263213i	$0.915218\pi$
$758$		0			0
$759$	−36.0000			−1.30672
$760$		0			0
$761$	−24.0000	+	41.5692i	−0.869999	+	1.50688i	−0.00800331	+	0.999968i	$0.502548\pi$
$761$	−24.0000	+	41.5692i	−0.869999	+	1.50688i	−0.861996	+	0.506915i	$0.830786\pi$
$762$		0			0
$763$	−3.50000	+	6.06218i	−0.126709	+	0.219466i
$764$	6.00000	+	10.3923i	0.217072	+	0.375980i
$765$		0			0
$766$		0			0
$767$	−21.0000	+	5.19615i	−0.758266	+	0.187622i
$768$	16.0000			0.577350
$769$	−19.0000	−	32.9090i	−0.685158	−	1.18673i	−0.973387	−	0.229166i	$-0.926400\pi$
$769$	−19.0000	−	32.9090i	−0.685158	−	1.18673i	0.288230	−	0.957561i	$-0.406933\pi$
$770$		0			0
$771$	6.00000	−	10.3923i	0.216085	−	0.374270i
$772$	26.0000			0.935760
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	−0.657542	−	0.753418i	$-0.728404\pi$
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	0.981250	+	0.192740i	$0.0617373\pi$
$774$		0			0
$775$	5.00000			0.179605
$776$		0			0
$777$	1.00000	+	1.73205i	0.0358748	+	0.0621370i
$778$		0			0
$779$		0			0
$780$	5.00000	+	5.19615i	0.179029	+	0.186052i
$781$	−36.0000			−1.28818
$782$		0			0
$783$	3.00000	+	5.19615i	0.107211	+	0.185695i
$784$	12.0000	−	20.7846i	0.428571	−	0.742307i
$785$	1.00000			0.0356915
$786$		0			0
$787$	6.50000	−	11.2583i	0.231700	−	0.401316i	−0.726609	−	0.687052i	$-0.758905\pi$
$787$	6.50000	−	11.2583i	0.231700	−	0.401316i	0.958308	+	0.285736i	$0.0922379\pi$
$788$	−24.0000			−0.854965
$789$	−6.00000	+	10.3923i	−0.213606	+	0.369976i
$790$		0			0
$791$	−3.00000	−	5.19615i	−0.106668	−	0.184754i
$792$		0			0
$793$	3.50000	−	0.866025i	0.124289	−	0.0307535i
$794$		0			0
$795$		0			0
$796$	17.0000	+	29.4449i	0.602549	+	1.04365i
$797$	−6.00000	+	10.3923i	−0.212531	+	0.368114i	−0.952506	−	0.304520i	$-0.901504\pi$
$797$	−6.00000	+	10.3923i	−0.212531	+	0.368114i	0.739975	+	0.672634i	$0.234837\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	12.0000			0.423999
$802$		0			0
$803$	−15.0000	−	25.9808i	−0.529339	−	0.916841i
$804$	11.0000	+	19.0526i	0.387940	+	0.671932i
$805$	−6.00000			−0.211472
$806$		0			0
$807$	−24.0000			−0.844840
$808$		0			0
$809$	12.0000	+	20.7846i	0.421898	+	0.730748i	0.996125	−	0.0879478i	$-0.0280309\pi$
$809$	12.0000	+	20.7846i	0.421898	+	0.730748i	−0.574228	+	0.818696i	$0.694698\pi$
$810$		0			0
$811$	5.00000			0.175574			0.0877869	−	0.996139i	$-0.472021\pi$
$811$	5.00000			0.175574			0.0877869	+	0.996139i	$0.472021\pi$
$812$	6.00000	−	10.3923i	0.210559	−	0.364698i
$813$	3.50000	−	6.06218i	0.122750	−	0.212610i
$814$		0			0
$815$	5.50000	−	9.52628i	0.192657	−	0.333691i
$816$		0			0
$817$	22.0000	+	38.1051i	0.769683	+	1.33313i
$818$		0			0
$819$	−1.00000	+	3.46410i	−0.0349428	+	0.121046i
$820$		0			0
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	0.913616	−	0.406578i	$-0.133278\pi$
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	−0.808915	+	0.587925i	$0.799945\pi$
$822$		0			0
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	−0.692240	−	0.721668i	$-0.743376\pi$
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	0.971102	+	0.238664i	$0.0767093\pi$
$824$		0			0
$825$	−3.00000	+	5.19615i	−0.104447	+	0.180907i
$826$		0			0
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$	−6.00000	+	10.3923i	−0.208514	+	0.361158i
$829$	15.5000	+	26.8468i	0.538337	+	0.932427i	0.998994	+	0.0448490i	$0.0142807\pi$
$829$	15.5000	+	26.8468i	0.538337	+	0.932427i	−0.460657	+	0.887578i	$0.652386\pi$
$830$		0			0
$831$	−10.0000			−0.346896
$832$	−20.0000	−	20.7846i	−0.693375	−	0.720577i
$833$		0			0
$834$		0			0
$835$	−6.00000	−	10.3923i	−0.207639	−	0.359641i
$836$	−24.0000	+	41.5692i	−0.830057	+	1.43770i
$837$	5.00000			0.172825
$838$		0			0
$839$	9.00000	−	15.5885i	0.310715	−	0.538173i	−0.667803	−	0.744338i	$-0.732765\pi$
$839$	9.00000	−	15.5885i	0.310715	−	0.538173i	0.978517	+	0.206165i	$0.0660984\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$		0			0
$843$	3.00000	+	5.19615i	0.103325	+	0.178965i
$844$	26.0000			0.894957
$845$	0.500000	−	12.9904i	0.0172005	−	0.446883i
$846$		0			0
$847$	12.5000	+	21.6506i	0.429505	+	0.743925i
$848$		0			0
$849$	−11.5000	+	19.9186i	−0.394679	+	0.683604i
$850$		0			0
$851$	6.00000	−	10.3923i	0.205677	−	0.356244i
$852$	−6.00000	+	10.3923i	−0.205557	+	0.356034i
$853$	35.0000			1.19838			0.599189	−	0.800608i	$-0.295490\pi$
$853$	35.0000			1.19838			0.599189	+	0.800608i	$0.295490\pi$
$854$		0			0
$855$	−2.00000	−	3.46410i	−0.0683986	−	0.118470i
$856$		0			0
$857$	42.0000			1.43469			0.717346	−	0.696717i	$-0.245357\pi$
$857$	42.0000			1.43469			0.717346	+	0.696717i	$0.245357\pi$
$858$		0			0
$859$	−13.0000			−0.443554			−0.221777	−	0.975097i	$-0.571186\pi$
$859$	−13.0000			−0.443554			−0.221777	+	0.975097i	$0.571186\pi$
$860$	−11.0000	−	19.0526i	−0.375097	−	0.649687i
$861$		0			0
$862$		0			0
$863$	−54.0000			−1.83818			−0.919091	−	0.394046i	$-0.871075\pi$
$863$	−54.0000			−1.83818			−0.919091	+	0.394046i	$0.871075\pi$
$864$		0			0
$865$	−3.00000	+	5.19615i	−0.102003	+	0.176674i
$866$		0			0
$867$	8.50000	−	14.7224i	0.288675	−	0.500000i
$868$	−5.00000	−	8.66025i	−0.169711	−	0.293948i
$869$	−33.0000	−	57.1577i	−1.11945	−	1.93894i
$870$		0			0
$871$	11.0000	−	38.1051i	0.372721	−	1.29114i
$872$		0			0
$873$	−8.50000	−	14.7224i	−0.287681	−	0.498279i
$874$		0			0
$875$	−0.500000	+	0.866025i	−0.0169031	+	0.0292770i
$876$	−10.0000			−0.337869
$877$	23.0000	−	39.8372i	0.776655	−	1.34521i	−0.157205	−	0.987566i	$-0.550248\pi$
$877$	23.0000	−	39.8372i	0.776655	−	1.34521i	0.933860	−	0.357640i	$-0.116418\pi$
$878$		0			0
$879$	6.00000			0.202375
$880$	12.0000	−	20.7846i	0.404520	−	0.700649i
$881$	24.0000	+	41.5692i	0.808581	+	1.40050i	0.913847	+	0.406059i	$0.133097\pi$
$881$	24.0000	+	41.5692i	0.808581	+	1.40050i	−0.105267	+	0.994444i	$0.533570\pi$
$882$		0			0
$883$	−7.00000			−0.235569			−0.117784	−	0.993039i	$-0.537579\pi$
$883$	−7.00000			−0.235569			−0.117784	+	0.993039i	$0.537579\pi$
$884$		0			0
$885$	−6.00000			−0.201688
$886$		0			0
$887$	21.0000	+	36.3731i	0.705111	+	1.22129i	0.966651	+	0.256096i	$0.0824362\pi$
$887$	21.0000	+	36.3731i	0.705111	+	1.22129i	−0.261540	+	0.965193i	$0.584230\pi$
$888$		0			0
$889$	1.00000			0.0335389
$890$		0			0
$891$	−3.00000	+	5.19615i	−0.100504	+	0.174078i
$892$	−16.0000			−0.535720
$893$	12.0000	−	20.7846i	0.401565	−	0.695530i
$894$		0			0
$895$	−6.00000	−	10.3923i	−0.200558	−	0.347376i
$896$		0			0
$897$	21.0000	−	5.19615i	0.701170	−	0.173494i
$898$		0			0
$899$	15.0000	+	25.9808i	0.500278	+	0.866507i
$900$	1.00000	+	1.73205i	0.0333333	+	0.0577350i
$901$		0			0
$902$		0			0
$903$	5.50000	−	9.52628i	0.183029	−	0.317015i
$904$		0			0
$905$	10.0000			0.332411
$906$		0			0
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	0.999195	−	0.0401089i	$-0.0127705\pi$
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	−0.534333	+	0.845274i	$0.679437\pi$
$908$		0			0
$909$	6.00000			0.199007
$910$		0			0
$911$	−36.0000			−1.19273			−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000			−1.19273			−0.596367	+	0.802712i	$0.703390\pi$
$912$	8.00000	+	13.8564i	0.264906	+	0.458831i
$913$	−36.0000	−	62.3538i	−1.19143	−	2.06361i
$914$		0			0
$915$	1.00000			0.0330590
$916$	14.0000	−	24.2487i	0.462573	−	0.801200i
$917$	9.00000	−	15.5885i	0.297206	−	0.514776i
$918$		0			0
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$		0			0
$921$	12.5000	+	21.6506i	0.411889	+	0.713413i
$922$		0			0
$923$	21.0000	−	5.19615i	0.691223	−	0.171033i
$924$	12.0000			0.394771
$925$	−1.00000	−	1.73205i	−0.0328798	−	0.0569495i
$926$		0			0
$927$	6.50000	−	11.2583i	0.213488	−	0.369772i
$928$		0			0
$929$	−6.00000	+	10.3923i	−0.196854	+	0.340960i	−0.947507	−	0.319736i	$-0.896406\pi$
$929$	−6.00000	+	10.3923i	−0.196854	+	0.340960i	0.750653	+	0.660697i	$0.229739\pi$
$930$		0			0
$931$	24.0000			0.786568
$932$	−6.00000	+	10.3923i	−0.196537	+	0.340411i
$933$	−6.00000	−	10.3923i	−0.196431	−	0.340229i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	14.0000			0.457360			0.228680	−	0.973502i	$-0.426559\pi$
$937$	14.0000			0.457360			0.228680	+	0.973502i	$0.426559\pi$
$938$		0			0
$939$	−11.5000	−	19.9186i	−0.375288	−	0.650018i
$940$	−6.00000	+	10.3923i	−0.195698	+	0.338960i
$941$	−18.0000			−0.586783			−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000			−0.586783			−0.293392	+	0.955992i	$0.594784\pi$
$942$		0			0
$943$		0			0
$944$	24.0000			0.781133
$945$	−0.500000	+	0.866025i	−0.0162650	+	0.0281718i
$946$		0			0
$947$	24.0000	+	41.5692i	0.779895	+	1.35082i	0.932002	+	0.362454i	$0.118061\pi$
$947$	24.0000	+	41.5692i	0.779895	+	1.35082i	−0.152106	+	0.988364i	$0.548606\pi$
$948$	−22.0000			−0.714527
$949$	12.5000	+	12.9904i	0.405767	+	0.421686i
$950$		0			0
$951$	6.00000	+	10.3923i	0.194563	+	0.336994i
$952$		0			0
$953$	21.0000	−	36.3731i	0.680257	−	1.17824i	−0.294646	−	0.955607i	$-0.595202\pi$
$953$	21.0000	−	36.3731i	0.680257	−	1.17824i	0.974902	−	0.222633i	$-0.0714650\pi$
$954$		0			0
$955$	3.00000	−	5.19615i	0.0970777	−	0.168144i
$956$		0			0
$957$	−36.0000			−1.16371
$958$		0			0
$959$	6.00000	+	10.3923i	0.193750	+	0.335585i
$960$	−4.00000	−	6.92820i	−0.129099	−	0.223607i
$961$	−6.00000			−0.193548
$962$		0			0
$963$	18.0000			0.580042
$964$	−22.0000	−	38.1051i	−0.708572	−	1.22728i
$965$	−6.50000	−	11.2583i	−0.209242	−	0.362418i
$966$		0			0
$967$	−4.00000			−0.128631			−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000			−0.128631			−0.0643157	+	0.997930i	$0.520486\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	−0.946094	−	0.323891i	$-0.895009\pi$
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	0.753545	+	0.657396i	$0.228342\pi$
$972$	1.00000	+	1.73205i	0.0320750	+	0.0555556i
$973$	−9.50000	−	16.4545i	−0.304556	−	0.527506i
$974$		0			0
$975$	1.00000	−	3.46410i	0.0320256	−	0.110940i
$976$	−4.00000			−0.128037
$977$	−24.0000	−	41.5692i	−0.767828	−	1.32992i	−0.938738	−	0.344631i	$-0.888004\pi$
$977$	−24.0000	−	41.5692i	−0.767828	−	1.32992i	0.170910	−	0.985287i	$-0.445329\pi$
$978$		0			0
$979$	−36.0000	+	62.3538i	−1.15056	+	1.99284i
$980$	−12.0000			−0.383326
$981$	3.50000	−	6.06218i	0.111746	−	0.193550i
$982$		0			0
$983$	−42.0000			−1.33959			−0.669796	−	0.742545i	$-0.733618\pi$
$983$	−42.0000			−1.33959			−0.669796	+	0.742545i	$0.733618\pi$
$984$		0			0
$985$	6.00000	+	10.3923i	0.191176	+	0.331126i
$986$		0			0
$987$	−6.00000			−0.190982
$988$	8.00000	−	27.7128i	0.254514	−	0.881662i
$989$	−66.0000			−2.09868
$990$		0			0
$991$	−16.0000	−	27.7128i	−0.508257	−	0.880327i	−0.999954	−	0.00956046i	$-0.996957\pi$
$991$	−16.0000	−	27.7128i	−0.508257	−	0.880327i	0.491698	−	0.870766i	$-0.336377\pi$
$992$		0			0
$993$	−7.00000			−0.222138
$994$		0			0
$995$	8.50000	−	14.7224i	0.269468	−	0.466732i
$996$	−24.0000			−0.760469
$997$	24.5000	−	42.4352i	0.775923	−	1.34394i	−0.158352	−	0.987383i	$-0.550618\pi$
$997$	24.5000	−	42.4352i	0.775923	−	1.34394i	0.934274	−	0.356555i	$-0.116049\pi$
$998$		0			0
$999$	−1.00000	−	1.73205i	−0.0316386	−	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.i.b.16.1	✓	2
3.2	odd	2		585.2.j.a.406.1		2
5.2	odd	4		975.2.bb.b.874.1		4
5.3	odd	4		975.2.bb.b.874.2		4
5.4	even	2		975.2.i.d.601.1		2
13.3	even	3		2535.2.a.h.1.1		1
13.9	even	3	inner	195.2.i.b.61.1	yes	2
13.10	even	6		2535.2.a.i.1.1		1
39.23	odd	6		7605.2.a.k.1.1		1
39.29	odd	6		7605.2.a.l.1.1		1
39.35	odd	6		585.2.j.a.451.1		2
65.9	even	6		975.2.i.d.451.1		2
65.22	odd	12		975.2.bb.b.724.2		4
65.48	odd	12		975.2.bb.b.724.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.b.16.1	✓	2	1.1	even	1	trivial
195.2.i.b.61.1	yes	2	13.9	even	3	inner
585.2.j.a.406.1		2	3.2	odd	2
585.2.j.a.451.1		2	39.35	odd	6
975.2.i.d.451.1		2	65.9	even	6
975.2.i.d.601.1		2	5.4	even	2
975.2.bb.b.724.1		4	65.48	odd	12
975.2.bb.b.724.2		4	65.22	odd	12
975.2.bb.b.874.1		4	5.2	odd	4
975.2.bb.b.874.2		4	5.3	odd	4
2535.2.a.h.1.1		1	13.3	even	3
2535.2.a.i.1.1		1	13.10	even	6
7605.2.a.k.1.1		1	39.23	odd	6
7605.2.a.l.1.1		1	39.29	odd	6

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-3.00000 - 5.19615i) q^{11} -2.00000 q^{12} +(2.50000 + 2.59808i) q^{13} +(0.500000 + 0.866025i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(2.00000 - 3.46410i) q^{19} +(-1.00000 + 1.73205i) q^{20} -1.00000 q^{21} +(3.00000 + 5.19615i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(3.00000 + 5.19615i) q^{29} +5.00000 q^{31} +(-3.00000 + 5.19615i) q^{33} +(-0.500000 + 0.866025i) q^{35} +(1.00000 + 1.73205i) q^{36} +(-1.00000 - 1.73205i) q^{37} +(1.00000 - 3.46410i) q^{39} +(-5.50000 + 9.52628i) q^{43} -12.0000 q^{44} +(0.500000 - 0.866025i) q^{45} +6.00000 q^{47} +(-2.00000 + 3.46410i) q^{48} +(3.00000 + 5.19615i) q^{49} +(7.00000 - 1.73205i) q^{52} +(3.00000 + 5.19615i) q^{55} -4.00000 q^{57} +(-3.00000 + 5.19615i) q^{59} +2.00000 q^{60} +(0.500000 - 0.866025i) q^{61} +(0.500000 + 0.866025i) q^{63} -8.00000 q^{64} +(-2.50000 - 2.59808i) q^{65} +(-5.50000 - 9.52628i) q^{67} +(3.00000 - 5.19615i) q^{69} +(3.00000 - 5.19615i) q^{71} +5.00000 q^{73} +(-0.500000 - 0.866025i) q^{75} +(-4.00000 - 6.92820i) q^{76} -6.00000 q^{77} +11.0000 q^{79} +(2.00000 + 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} +(-1.00000 + 1.73205i) q^{84} +(3.00000 - 5.19615i) q^{87} +(-6.00000 - 10.3923i) q^{89} +(3.50000 - 0.866025i) q^{91} +12.0000 q^{92} +(-2.50000 - 4.33013i) q^{93} +(-2.00000 + 3.46410i) q^{95} +(-8.50000 + 14.7224i) q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} + 2 q^{4} - 2 q^{5} + q^{7} - q^{9}+O(q^{10}) \) 2 * q - q^3 + 2 * q^4 - 2 * q^5 + q^7 - q^9	\( 2 q - q^{3} + 2 q^{4} - 2 q^{5} + q^{7} - q^{9} - 6 q^{11} - 4 q^{12} + 5 q^{13} + q^{15} - 4 q^{16} + 4 q^{19} - 2 q^{20} - 2 q^{21} + 6 q^{23} + 2 q^{25} + 2 q^{27} - 2 q^{28} + 6 q^{29} + 10 q^{31} - 6 q^{33} - q^{35} + 2 q^{36} - 2 q^{37} + 2 q^{39} - 11 q^{43} - 24 q^{44} + q^{45} + 12 q^{47} - 4 q^{48} + 6 q^{49} + 14 q^{52} + 6 q^{55} - 8 q^{57} - 6 q^{59} + 4 q^{60} + q^{61} + q^{63} - 16 q^{64} - 5 q^{65} - 11 q^{67} + 6 q^{69} + 6 q^{71} + 10 q^{73} - q^{75} - 8 q^{76} - 12 q^{77} + 22 q^{79} + 4 q^{80} - q^{81} + 24 q^{83} - 2 q^{84} + 6 q^{87} - 12 q^{89} + 7 q^{91} + 24 q^{92} - 5 q^{93} - 4 q^{95} - 17 q^{97} + 12 q^{99}+O(q^{100}) \) 2 * q - q^3 + 2 * q^4 - 2 * q^5 + q^7 - q^9 - 6 * q^11 - 4 * q^12 + 5 * q^13 + q^15 - 4 * q^16 + 4 * q^19 - 2 * q^20 - 2 * q^21 + 6 * q^23 + 2 * q^25 + 2 * q^27 - 2 * q^28 + 6 * q^29 + 10 * q^31 - 6 * q^33 - q^35 + 2 * q^36 - 2 * q^37 + 2 * q^39 - 11 * q^43 - 24 * q^44 + q^45 + 12 * q^47 - 4 * q^48 + 6 * q^49 + 14 * q^52 + 6 * q^55 - 8 * q^57 - 6 * q^59 + 4 * q^60 + q^61 + q^63 - 16 * q^64 - 5 * q^65 - 11 * q^67 + 6 * q^69 + 6 * q^71 + 10 * q^73 - q^75 - 8 * q^76 - 12 * q^77 + 22 * q^79 + 4 * q^80 - q^81 + 24 * q^83 - 2 * q^84 + 6 * q^87 - 12 * q^89 + 7 * q^91 + 24 * q^92 - 5 * q^93 - 4 * q^95 - 17 * q^97 + 12 * q^99

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