LMFDB - Embedded newform 975.2.i.d.451.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(451,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("975.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.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:	$7.78541419707$
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:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	975.451
Dual form			975.2.i.d.601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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	$-0.833333\pi$
$2$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$3$	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
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	0.755929	−	0.654654i	$-0.227186\pi$
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	−0.944911	+	0.327327i	$0.893852\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.0829925	+	0.996550i	$0.526448\pi$
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.821541	+	0.570149i	$0.806886\pi$
$12$	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			0
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	0.998899	−	0.0469020i	$-0.0149348\pi$
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	−0.540068	+	0.841621i	$0.681602\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$		0			0
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$		0			0
$25$		0			0
$26$		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	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$		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			0
$36$	1.00000	−	1.73205i	0.166667	−	0.288675i
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$		0			0
$39$	1.00000	+	3.46410i	0.160128	+	0.554700i
$40$		0			0
$41$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$41$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$42$		0			0
$43$	5.50000	+	9.52628i	0.838742	+	1.45274i	0.890947	+	0.454108i	$0.150042\pi$
$43$	5.50000	+	9.52628i	0.838742	+	1.45274i	−0.0522047	+	0.998636i	$0.516625\pi$
$44$	−12.0000			−1.80907
$45$		0			0
$46$		0			0
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$	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
$55$		0			0
$56$		0			0
$57$	4.00000			0.529813
$58$		0			0
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$		0			0
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$		0			0
$63$	−0.500000	+	0.866025i	−0.0629941	+	0.109109i
$64$	−8.00000			−1.00000
$65$		0			0
$66$		0			0
$67$	5.50000	−	9.52628i	0.671932	−	1.16382i	−0.305424	−	0.952217i	$-0.598798\pi$
$67$	5.50000	−	9.52628i	0.671932	−	1.16382i	0.977356	−	0.211604i	$-0.0678686\pi$
$68$		0			0
$69$	3.00000	+	5.19615i	0.361158	+	0.625543i
$70$		0			0
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$		0			0
$73$	−5.00000			−0.585206			−0.292603	−	0.956234i	$-0.594521\pi$
$73$	−5.00000			−0.585206			−0.292603	+	0.956234i	$0.594521\pi$
$74$		0			0
$75$		0			0
$76$	−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	$0.287620\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$	−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	0.350304	+	0.936636i	$0.386078\pi$
$89$	−6.00000	+	10.3923i	−0.635999	+	1.10158i	−0.986303	+	0.164946i	$0.947255\pi$
$90$		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
$95$		0			0
$96$		0			0
$97$	8.50000	+	14.7224i	0.863044	+	1.49484i	0.868976	+	0.494854i	$0.164778\pi$
$97$	8.50000	+	14.7224i	0.863044	+	1.49484i	−0.00593185	+	0.999982i	$0.501888\pi$
$98$		0			0
$99$	6.00000			0.603023
$100$		0			0
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	−0.975796	−	0.218685i	$-0.929823\pi$
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	0.677284	+	0.735721i	$0.263157\pi$
$102$		0			0
$103$	13.0000			1.28093			0.640464	−	0.767988i	$-0.278742\pi$
$103$	13.0000			1.28093			0.640464	+	0.767988i	$0.278742\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.00000	−	15.5885i	0.870063	−	1.50699i	0.00813215	−	0.999967i	$-0.497411\pi$
$107$	9.00000	−	15.5885i	0.870063	−	1.50699i	0.861931	−	0.507026i	$-0.169255\pi$
$108$	−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	$-0.257736\pi$
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	−0.971930	+	0.235269i	$0.924403\pi$
$114$		0			0
$115$		0			0
$116$	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
$125$		0			0
$126$		0			0
$127$	−0.500000	+	0.866025i	−0.0443678	+	0.0768473i	−0.887357	−	0.461084i	$-0.847461\pi$
$127$	−0.500000	+	0.866025i	−0.0443678	+	0.0768473i	0.842989	+	0.537931i	$0.180794\pi$
$128$		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
$135$		0			0
$136$		0			0
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	0.999893	+	0.0146279i	$0.00465636\pi$
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	−0.487278	+	0.873247i	$0.662010\pi$
$138$		0			0
$139$	9.50000	+	16.4545i	0.805779	+	1.39565i	0.915764	+	0.401718i	$0.131587\pi$
$139$	9.50000	+	16.4545i	0.805779	+	1.39565i	−0.109984	+	0.993933i	$0.535080\pi$
$140$		0			0
$141$	−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
$145$		0			0
$146$		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	−0.650183	−	0.759778i	$-0.725308\pi$
$149$	−12.0000	−	20.7846i	−0.983078	−	1.70274i	−0.332896	−	0.942964i	$-0.608026\pi$
$150$		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
$155$		0			0
$156$	−5.00000	+	5.19615i	−0.400320	+	0.416025i
$157$	1.00000			0.0798087			0.0399043	−	0.999204i	$-0.487295\pi$
$157$	1.00000			0.0798087			0.0399043	+	0.999204i	$0.487295\pi$
$158$		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	$-0.0249005\pi$
$163$	5.50000	+	9.52628i	0.430793	+	0.746156i	−0.566149	+	0.824303i	$0.691567\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$		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	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		0			0
$175$		0			0
$176$	−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	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		0			0
$181$	−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
$185$		0			0
$186$		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	0.736839	−	0.676068i	$-0.236317\pi$
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	−0.953912	+	0.300088i	$0.902984\pi$
$192$	−4.00000	+	6.92820i	−0.288675	+	0.500000i
$193$	−6.50000	+	11.2583i	−0.467880	+	0.810392i	−0.999326	−	0.0366998i	$-0.988315\pi$
$193$	−6.50000	+	11.2583i	−0.467880	+	0.810392i	0.531446	+	0.847092i	$0.321649\pi$
$194$		0			0
$195$		0			0
$196$	12.0000			0.857143
$197$	6.00000	−	10.3923i	0.427482	−	0.740421i	−0.569166	−	0.822222i	$-0.692734\pi$
$197$	6.00000	−	10.3923i	0.427482	−	0.740421i	0.996649	+	0.0818013i	$0.0260673\pi$
$198$		0			0
$199$	−8.50000	−	14.7224i	−0.602549	−	1.04365i	−0.992434	−	0.122782i	$-0.960818\pi$
$199$	−8.50000	−	14.7224i	−0.602549	−	1.04365i	0.389885	−	0.920864i	$-0.372515\pi$
$200$		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	−0.550743	−	0.834675i	$-0.685655\pi$
$211$	6.50000	−	11.2583i	0.447478	−	0.775055i	0.998221	+	0.0596196i	$0.0189888\pi$
$212$		0			0
$213$	6.00000			0.411113
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−2.50000	−	4.33013i	−0.169711	−	0.293948i
$218$		0			0
$219$	−2.50000	+	4.33013i	−0.168934	+	0.292603i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	4.00000	−	6.92820i	0.267860	−	0.463947i	−0.700449	−	0.713702i	$-0.747017\pi$
$223$	4.00000	−	6.92820i	0.267860	−	0.463947i	0.968309	+	0.249756i	$0.0803503\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$227$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$228$	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	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$		0			0
$236$	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	$0.5\pi$
$240$		0			0
$241$	11.0000	+	19.0526i	0.708572	+	1.22728i	0.965387	+	0.260822i	$0.0839937\pi$
$241$	11.0000	+	19.0526i	0.708572	+	1.22728i	−0.256814	+	0.966461i	$0.582673\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−1.00000	+	1.73205i	−0.0640184	+	0.110883i
$245$		0			0
$246$		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	$-0.166667\pi$
$251$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$252$	−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	$-0.955440\pi$
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	0.615948	+	0.787787i	$0.288773\pi$
$258$		0			0
$259$	−2.00000			−0.124274
$260$		0			0
$261$	−6.00000			−0.371391
$262$		0			0
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	−0.619586	−	0.784929i	$-0.712699\pi$
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	0.989561	+	0.144112i	$0.0460326\pi$
$264$		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	0.956176	+	0.292791i	$0.0945841\pi$
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	−0.224523	+	0.974469i	$0.572083\pi$
$270$		0			0
$271$	3.50000	−	6.06218i	0.212610	−	0.368251i	−0.739921	−	0.672694i	$-0.765137\pi$
$271$	3.50000	−	6.06218i	0.212610	−	0.368251i	0.952531	+	0.304443i	$0.0984703\pi$
$272$		0			0
$273$	2.50000	−	2.59808i	0.151307	−	0.157243i
$274$		0			0
$275$		0			0
$276$	−6.00000	+	10.3923i	−0.361158	+	0.625543i
$277$	−5.00000	−	8.66025i	−0.300421	−	0.520344i	0.675810	−	0.737075i	$-0.263794\pi$
$277$	−5.00000	−	8.66025i	−0.300421	−	0.520344i	−0.976231	+	0.216731i	$0.930460\pi$
$278$		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	−0.290269	−	0.956945i	$-0.593745\pi$
$283$	11.5000	−	19.9186i	0.683604	−	1.18404i	0.973873	−	0.227092i	$-0.0729218\pi$
$284$	−6.00000	+	10.3923i	−0.356034	+	0.616670i
$285$		0			0
$286$		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	$-0.110589\pi$
$293$	3.00000	+	5.19615i	0.175262	+	0.303562i	−0.764990	+	0.644042i	$0.777256\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	3.00000	−	5.19615i	0.174078	−	0.301511i
$298$		0			0
$299$	−6.00000	−	20.7846i	−0.346989	−	1.20201i
$300$		0			0
$301$	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			0
$306$		0			0
$307$	25.0000			1.42683			0.713413	−	0.700744i	$-0.247149\pi$
$307$	25.0000			1.42683			0.713413	+	0.700744i	$0.247149\pi$
$308$	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	$-0.725239\pi$
$313$	−23.0000			−1.30004			−0.650018	+	0.759918i	$0.725239\pi$
$314$		0			0
$315$		0			0
$316$	11.0000	+	19.0526i	0.618798	+	1.07179i
$317$	12.0000			0.673987			0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000			0.673987			0.336994	+	0.941507i	$0.390590\pi$
$318$		0			0
$319$	18.0000	+	31.1769i	1.00781	+	1.74557i
$320$		0			0
$321$	−9.00000	−	15.5885i	−0.502331	−	0.870063i
$322$		0			0
$323$		0			0
$324$	−2.00000			−0.111111
$325$		0			0
$326$		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	0.946038	−	0.324057i	$-0.105047\pi$
$331$	3.50000	+	6.06218i	0.192377	+	0.333207i	−0.753660	+	0.657264i	$0.771714\pi$
$332$	−12.0000	−	20.7846i	−0.658586	−	1.14070i
$333$	−2.00000			−0.109599
$334$		0			0
$335$		0			0
$336$	2.00000	−	3.46410i	0.109109	−	0.188982i
$337$	7.00000			0.381314			0.190657	−	0.981657i	$-0.438938\pi$
$337$	7.00000			0.381314			0.190657	+	0.981657i	$0.438938\pi$
$338$		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
$345$		0			0
$346$		0			0
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$	6.00000	−	10.3923i	0.321634	−	0.557086i
$349$	−5.50000	+	9.52628i	−0.294408	+	0.509930i	−0.974847	−	0.222875i	$-0.928456\pi$
$349$	−5.50000	+	9.52628i	−0.294408	+	0.509930i	0.680439	+	0.732805i	$0.261789\pi$
$350$		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	$-0.992342\pi$
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	0.520689	+	0.853746i	$0.325675\pi$
$354$		0			0
$355$		0			0
$356$	−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
$365$		0			0
$366$		0			0
$367$	2.50000	−	4.33013i	0.130499	−	0.226031i	−0.793370	−	0.608740i	$-0.791675\pi$
$367$	2.50000	−	4.33013i	0.130499	−	0.226031i	0.923869	+	0.382709i	$0.125009\pi$
$368$	−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	0.993484	+	0.113975i	$0.0363585\pi$
$373$	11.5000	+	19.9186i	0.595447	+	1.03135i	−0.398036	+	0.917370i	$0.630308\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.00000	+	20.7846i	0.309016	+	1.07046i
$378$		0			0
$379$	0.500000	−	0.866025i	0.0256833	−	0.0444847i	−0.852898	−	0.522077i	$-0.825157\pi$
$379$	0.500000	−	0.866025i	0.0256833	−	0.0444847i	0.878581	+	0.477593i	$0.158491\pi$
$380$		0			0
$381$	0.500000	+	0.866025i	0.0256158	+	0.0443678i
$382$		0			0
$383$	12.0000	+	20.7846i	0.613171	+	1.06204i	0.990702	+	0.136047i	$0.0434398\pi$
$383$	12.0000	+	20.7846i	0.613171	+	1.06204i	−0.377531	+	0.925997i	$0.623227\pi$
$384$		0			0
$385$		0			0
$386$		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
$395$		0			0
$396$	6.00000	+	10.3923i	0.301511	+	0.522233i
$397$	−6.50000	−	11.2583i	−0.326226	−	0.565039i	0.655534	−	0.755166i	$-0.272444\pi$
$397$	−6.50000	−	11.2583i	−0.326226	−	0.565039i	−0.981760	+	0.190126i	$0.939110\pi$
$398$		0			0
$399$	−2.00000	−	3.46410i	−0.100125	−	0.173422i
$400$		0			0
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	−0.676425	−	0.736512i	$-0.736472\pi$
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	0.976050	+	0.217545i	$0.0698049\pi$
$402$		0			0
$403$	−12.5000	+	12.9904i	−0.622669	+	0.647097i
$404$	−12.0000			−0.597022
$405$		0			0
$406$		0			0
$407$	6.00000	+	10.3923i	0.297409	+	0.515127i
$408$		0			0
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	0.797574	−	0.603220i	$-0.206116\pi$
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	−0.921192	+	0.389109i	$0.872783\pi$
$410$		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
$415$		0			0
$416$		0			0
$417$	19.0000			0.930434
$418$		0			0
$419$	12.0000	−	20.7846i	0.586238	−	1.01539i	−0.408481	−	0.912767i	$-0.633942\pi$
$419$	12.0000	−	20.7846i	0.586238	−	1.01539i	0.994720	−	0.102628i	$-0.0327251\pi$
$420$		0			0
$421$	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	0.417687	+	0.908591i	$0.362841\pi$
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	−0.995706	+	0.0925683i	$0.970492\pi$
$432$	2.00000	−	3.46410i	0.0962250	−	0.166667i
$433$	5.50000	+	9.52628i	0.264313	+	0.457804i	0.967383	−	0.253317i	$-0.0815214\pi$
$433$	5.50000	+	9.52628i	0.264313	+	0.457804i	−0.703070	+	0.711120i	$0.748188\pi$
$434$		0			0
$435$		0			0
$436$	−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	−0.966906	−	0.255134i	$-0.917881\pi$
$439$	−5.50000	+	9.52628i	−0.262501	+	0.454665i	0.704405	+	0.709798i	$0.251214\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$		0			0
$443$	36.0000			1.71041			0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000			1.71041			0.855206	+	0.518289i	$0.173431\pi$
$444$	2.00000	−	3.46410i	0.0949158	−	0.164399i
$445$		0			0
$446$		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	0.786513	−	0.617574i	$-0.211885\pi$
$449$	−3.00000	−	5.19615i	−0.141579	−	0.245222i	−0.928091	+	0.372353i	$0.878551\pi$
$450$		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
$455$		0			0
$456$		0			0
$457$	−15.5000	+	26.8468i	−0.725059	+	1.25584i	0.233890	+	0.972263i	$0.424854\pi$
$457$	−15.5000	+	26.8468i	−0.725059	+	1.25584i	−0.958950	+	0.283577i	$0.908479\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$461$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$462$		0			0
$463$	19.0000			0.883005			0.441502	−	0.897260i	$-0.354446\pi$
$463$	19.0000			0.883005			0.441502	+	0.897260i	$0.354446\pi$
$464$	12.0000	+	20.7846i	0.557086	+	0.964901i
$465$		0			0
$466$		0			0
$467$	−42.0000			−1.94353			−0.971764	−	0.235954i	$-0.924178\pi$
$467$	−42.0000			−1.94353			−0.971764	+	0.235954i	$0.924178\pi$
$468$	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
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$		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
$485$		0			0
$486$		0			0
$487$	−14.0000	−	24.2487i	−0.634401	−	1.09881i	−0.986642	−	0.162905i	$-0.947914\pi$
$487$	−14.0000	−	24.2487i	−0.634401	−	1.09881i	0.352241	−	0.935909i	$-0.385420\pi$
$488$		0			0
$489$	11.0000			0.497437
$490$		0			0
$491$	−15.0000	+	25.9808i	−0.676941	+	1.17250i	0.298957	+	0.954267i	$0.403361\pi$
$491$	−15.0000	+	25.9808i	−0.676941	+	1.17250i	−0.975898	+	0.218229i	$0.929972\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−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	$0.853055\pi$
$500$		0			0
$501$	6.00000	+	10.3923i	0.268060	+	0.464294i
$502$		0			0
$503$	21.0000	+	36.3731i	0.936344	+	1.62179i	0.772220	+	0.635355i	$0.219146\pi$
$503$	21.0000	+	36.3731i	0.936344	+	1.62179i	0.164124	+	0.986440i	$0.447520\pi$
$504$		0			0
$505$		0			0
$506$		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	−0.594675	−	0.803966i	$-0.702719\pi$
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	0.993593	+	0.113020i	$0.0360525\pi$
$510$		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
$515$		0			0
$516$	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	$-0.861206\pi$
$523$	−2.00000	+	3.46410i	−0.0874539	+	0.151475i	0.818980	+	0.573822i	$0.194540\pi$
$524$	18.0000	+	31.1769i	0.786334	+	1.36197i
$525$		0			0
$526$		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
$535$		0			0
$536$		0			0
$537$	−6.00000	−	10.3923i	−0.258919	−	0.448461i
$538$		0			0
$539$	18.0000	+	31.1769i	0.775315	+	1.34288i
$540$		0			0
$541$	−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
$545$		0			0
$546$		0			0
$547$	7.00000			0.299298			0.149649	−	0.988739i	$-0.452186\pi$
$547$	7.00000			0.299298			0.149649	+	0.988739i	$0.452186\pi$
$548$	−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
$555$		0			0
$556$	−19.0000	+	32.9090i	−0.805779	+	1.39565i
$557$	−6.00000	+	10.3923i	−0.254228	+	0.440336i	−0.964686	−	0.263404i	$-0.915155\pi$
$557$	−6.00000	+	10.3923i	−0.254228	+	0.440336i	0.710457	+	0.703740i	$0.248488\pi$
$558$		0			0
$559$	−38.5000	−	9.52628i	−1.62838	−	0.402919i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	21.0000	+	36.3731i	0.885044	+	1.53294i	0.845663	+	0.533718i	$0.179206\pi$
$563$	21.0000	+	36.3731i	0.885044	+	1.53294i	0.0393818	+	0.999224i	$0.487461\pi$
$564$	−12.0000			−0.505291
$565$		0			0
$566$		0			0
$567$	1.00000			0.0419961
$568$		0			0
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	0.358954	+	0.933355i	$0.383134\pi$
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	−0.987786	+	0.155815i	$0.950200\pi$
$570$		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
$575$		0			0
$576$	4.00000	+	6.92820i	0.166667	+	0.288675i
$577$	−14.0000			−0.582828			−0.291414	−	0.956597i	$-0.594126\pi$
$577$	−14.0000			−0.582828			−0.291414	+	0.956597i	$0.594126\pi$
$578$		0			0
$579$	6.50000	+	11.2583i	0.270131	+	0.467880i
$580$		0			0
$581$	6.00000	+	10.3923i	0.248922	+	0.431145i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	21.0000	−	36.3731i	0.866763	−	1.50128i	0.00147660	−	0.999999i	$-0.499530\pi$
$587$	21.0000	−	36.3731i	0.866763	−	1.50128i	0.865286	−	0.501278i	$-0.167137\pi$
$588$	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	$-0.288762\pi$
$593$	30.0000			1.23195			0.615976	+	0.787765i	$0.288762\pi$
$594$		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	0.469095	+	0.883148i	$0.344580\pi$
$601$	−13.0000	+	22.5167i	−0.530281	+	0.918474i	−0.999376	+	0.0353259i	$0.988753\pi$
$602$		0			0
$603$	−11.0000			−0.447955
$604$	−16.0000	−	27.7128i	−0.651031	−	1.12762i
$605$		0			0
$606$		0			0
$607$	−20.0000	−	34.6410i	−0.811775	−	1.40604i	−0.911621	−	0.411033i	$-0.865168\pi$
$607$	−20.0000	−	34.6410i	−0.811775	−	1.40604i	0.0998457	−	0.995003i	$-0.468165\pi$
$608$		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	$-0.679574\pi$
$613$	11.5000	−	19.9186i	0.464481	−	0.804504i	0.999178	+	0.0405396i	$0.0129077\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.00000	+	5.19615i	0.120775	+	0.209189i	0.920074	−	0.391745i	$-0.128129\pi$
$617$	3.00000	+	5.19615i	0.120775	+	0.209189i	−0.799298	+	0.600935i	$0.794795\pi$
$618$		0			0
$619$	−19.0000			−0.763674			−0.381837	−	0.924230i	$-0.624709\pi$
$619$	−19.0000			−0.763674			−0.381837	+	0.924230i	$0.624709\pi$
$620$		0			0
$621$	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
$625$		0			0
$626$		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	0.954074	+	0.299571i	$0.0968437\pi$
$631$	18.5000	+	32.0429i	0.736473	+	1.27561i	−0.217601	+	0.976038i	$0.569823\pi$
$632$		0			0
$633$	−6.50000	−	11.2583i	−0.258352	−	0.447478i
$634$		0			0
$635$		0			0
$636$		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	0.993899	+	0.110291i	$0.0351782\pi$
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	−0.401435	+	0.915888i	$0.631488\pi$
$642$		0			0
$643$	5.50000	+	9.52628i	0.216899	+	0.375680i	0.953858	−	0.300257i	$-0.0970725\pi$
$643$	5.50000	+	9.52628i	0.216899	+	0.375680i	−0.736959	+	0.675937i	$0.763739\pi$
$644$	6.00000	+	10.3923i	0.236433	+	0.409514i
$645$		0			0
$646$		0			0
$647$	−3.00000	+	5.19615i	−0.117942	+	0.204282i	−0.918952	−	0.394369i	$-0.870963\pi$
$647$	−3.00000	+	5.19615i	−0.117942	+	0.204282i	0.801010	+	0.598651i	$0.204296\pi$
$648$		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	0.172211	−	0.985060i	$-0.444909\pi$
$653$	24.0000	−	41.5692i	0.939193	−	1.62673i	0.766982	−	0.641669i	$-0.221758\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	2.50000	+	4.33013i	0.0975343	+	0.168934i
$658$		0			0
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	0.968052	+	0.250748i	$0.0806766\pi$
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	−0.266872	+	0.963732i	$0.585990\pi$
$660$		0			0
$661$	24.5000	−	42.4352i	0.952940	−	1.65054i	0.213925	−	0.976850i	$-0.431375\pi$
$661$	24.5000	−	42.4352i	0.952940	−	1.65054i	0.739014	−	0.673690i	$-0.235292\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		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	$-0.765333\pi$
$673$	5.50000	−	9.52628i	0.212009	−	0.367211i	0.952343	+	0.305028i	$0.0986659\pi$
$674$		0			0
$675$		0			0
$676$	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	$-0.0547574\pi$
$683$	9.00000	+	15.5885i	0.344375	+	0.596476i	−0.640865	+	0.767654i	$0.721424\pi$
$684$	8.00000			0.305888
$685$		0			0
$686$		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	−0.909652	−	0.415371i	$-0.863652\pi$
$691$	−2.50000	+	4.33013i	−0.0951045	+	0.164726i	0.814548	+	0.580097i	$0.196985\pi$
$692$	6.00000	−	10.3923i	0.228086	−	0.395056i
$693$	−3.00000	−	5.19615i	−0.113961	−	0.197386i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$	3.00000	−	5.19615i	0.113470	−	0.196537i
$700$		0			0
$701$	−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
$705$		0			0
$706$		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	0.987421	−	0.158114i	$-0.0505412\pi$
$709$	9.50000	+	16.4545i	0.356780	+	0.617961i	−0.630641	+	0.776075i	$0.717208\pi$
$710$		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
$715$		0			0
$716$	24.0000			0.896922
$717$		0			0
$718$		0			0
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	0.804648	−	0.593753i	$-0.202354\pi$
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	−0.916529	+	0.399969i	$0.869021\pi$
$720$		0			0
$721$	−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
$725$		0			0
$726$		0			0
$727$	25.0000			0.927199			0.463599	−	0.886045i	$-0.346558\pi$
$727$	25.0000			0.927199			0.463599	+	0.886045i	$0.346558\pi$
$728$		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	$-0.679903\pi$
$733$	−29.0000			−1.07114			−0.535570	+	0.844491i	$0.679903\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	33.0000	+	57.1577i	1.21557	+	2.10543i
$738$		0			0
$739$	−10.0000	+	17.3205i	−0.367856	+	0.637145i	−0.989230	−	0.146369i	$-0.953241\pi$
$739$	−10.0000	+	17.3205i	−0.367856	+	0.637145i	0.621374	+	0.783514i	$0.286575\pi$
$740$		0			0
$741$	−10.0000	+	10.3923i	−0.367359	+	0.381771i
$742$		0			0
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	−0.805735	−	0.592277i	$-0.798229\pi$
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	0.915794	+	0.401648i	$0.131563\pi$
$744$		0			0
$745$		0			0
$746$		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	−0.227153	−	0.973859i	$-0.572942\pi$
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	0.956963	−	0.290209i	$-0.0937250\pi$
$752$	12.0000	−	20.7846i	0.437595	−	0.757937i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−1.00000	+	1.73205i	−0.0363696	+	0.0629941i
$757$	7.00000	−	12.1244i	0.254419	−	0.440667i	−0.710318	−	0.703881i	$-0.751449\pi$
$757$	7.00000	−	12.1244i	0.254419	−	0.440667i	0.964738	+	0.263213i	$0.0847823\pi$
$758$		0			0
$759$	−36.0000			−1.30672
$760$		0			0
$761$	−24.0000	−	41.5692i	−0.869999	−	1.50688i	−0.861996	−	0.506915i	$-0.830786\pi$
$761$	−24.0000	−	41.5692i	−0.869999	−	1.50688i	−0.00800331	−	0.999968i	$-0.502548\pi$
$762$		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	0.288230	+	0.957561i	$0.406933\pi$
$769$	−19.0000	+	32.9090i	−0.685158	+	1.18673i	−0.973387	+	0.229166i	$0.926400\pi$
$770$		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	$-0.271596\pi$
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	−0.981250	+	0.192740i	$0.938263\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1.00000	+	1.73205i	−0.0358748	+	0.0621370i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	−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
$785$		0			0
$786$		0			0
$787$	−6.50000	−	11.2583i	−0.231700	−	0.401316i	0.726609	−	0.687052i	$-0.241095\pi$
$787$	−6.50000	−	11.2583i	−0.231700	−	0.401316i	−0.958308	+	0.285736i	$0.907762\pi$
$788$	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	$-0.0984960\pi$
$797$	6.00000	+	10.3923i	0.212531	+	0.368114i	−0.739975	+	0.672634i	$0.765163\pi$
$798$		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
$805$		0			0
$806$		0			0
$807$	24.0000			0.844840
$808$		0			0
$809$	12.0000	−	20.7846i	0.421898	−	0.730748i	−0.574228	−	0.818696i	$-0.694698\pi$
$809$	12.0000	−	20.7846i	0.421898	−	0.730748i	0.996125	+	0.0879478i	$0.0280309\pi$
$810$		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
$815$		0			0
$816$		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	−0.808915	−	0.587925i	$-0.799945\pi$
$821$	3.00000	−	5.19615i	0.104701	−	0.181347i	0.913616	+	0.406578i	$0.133278\pi$
$822$		0			0
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	0.692240	−	0.721668i	$-0.256624\pi$
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	−0.971102	+	0.238664i	$0.923291\pi$
$824$		0			0
$825$		0			0
$826$		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	−0.460657	−	0.887578i	$-0.652386\pi$
$829$	15.5000	−	26.8468i	0.538337	−	0.932427i	0.998994	−	0.0448490i	$-0.0142807\pi$
$830$		0			0
$831$	−10.0000			−0.346896
$832$	20.0000	−	20.7846i	0.693375	−	0.720577i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	−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	0.978517	−	0.206165i	$-0.0660984\pi$
$839$	9.00000	+	15.5885i	0.310715	+	0.538173i	−0.667803	+	0.744338i	$0.732765\pi$
$840$		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			0
$846$		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	$-0.704510\pi$
$853$	−35.0000			−1.19838			−0.599189	+	0.800608i	$0.704510\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−42.0000			−1.43469			−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000			−1.43469			−0.717346	+	0.696717i	$0.754643\pi$
$858$		0			0
$859$	−13.0000			−0.443554			−0.221777	−	0.975097i	$-0.571186\pi$
$859$	−13.0000			−0.443554			−0.221777	+	0.975097i	$0.571186\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	54.0000			1.83818			0.919091	−	0.394046i	$-0.128925\pi$
$863$	54.0000			1.83818			0.919091	+	0.394046i	$0.128925\pi$
$864$		0			0
$865$		0			0
$866$		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			0
$876$	−10.0000			−0.337869
$877$	−23.0000	−	39.8372i	−0.776655	−	1.34521i	−0.933860	−	0.357640i	$-0.883582\pi$
$877$	−23.0000	−	39.8372i	−0.776655	−	1.34521i	0.157205	−	0.987566i	$-0.449752\pi$
$878$		0			0
$879$	6.00000			0.202375
$880$		0			0
$881$	24.0000	−	41.5692i	0.808581	−	1.40050i	−0.105267	−	0.994444i	$-0.533570\pi$
$881$	24.0000	−	41.5692i	0.808581	−	1.40050i	0.913847	−	0.406059i	$-0.133097\pi$
$882$		0			0
$883$	7.00000			0.235569			0.117784	−	0.993039i	$-0.462421\pi$
$883$	7.00000			0.235569			0.117784	+	0.993039i	$0.462421\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−21.0000	+	36.3731i	−0.705111	+	1.22129i	0.261540	+	0.965193i	$0.415770\pi$
$887$	−21.0000	+	36.3731i	−0.705111	+	1.22129i	−0.966651	+	0.256096i	$0.917564\pi$
$888$		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
$895$		0			0
$896$		0			0
$897$	−21.0000	−	5.19615i	−0.701170	−	0.173494i
$898$		0			0
$899$	15.0000	−	25.9808i	0.500278	−	0.866507i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−5.50000	−	9.52628i	−0.183029	−	0.317015i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	−0.999195	−	0.0401089i	$-0.987230\pi$
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	0.534333	+	0.845274i	$0.320563\pi$
$908$		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
$915$		0			0
$916$	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	0.967274	−	0.253735i	$-0.0816592\pi$
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	−0.703378	+	0.710816i	$0.748326\pi$
$920$		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
$925$		0			0
$926$		0			0
$927$	−6.50000	−	11.2583i	−0.213488	−	0.369772i
$928$		0			0
$929$	−6.00000	−	10.3923i	−0.196854	−	0.340960i	0.750653	−	0.660697i	$-0.229739\pi$
$929$	−6.00000	−	10.3923i	−0.196854	−	0.340960i	−0.947507	+	0.319736i	$0.896406\pi$
$930$		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	$-0.573441\pi$
$937$	−14.0000			−0.457360			−0.228680	+	0.973502i	$0.573441\pi$
$938$		0			0
$939$	−11.5000	+	19.9186i	−0.375288	+	0.650018i
$940$		0			0
$941$	−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			0
$946$		0			0
$947$	−24.0000	+	41.5692i	−0.779895	+	1.35082i	0.152106	+	0.988364i	$0.451394\pi$
$947$	−24.0000	+	41.5692i	−0.779895	+	1.35082i	−0.932002	+	0.362454i	$0.881939\pi$
$948$	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	−0.974902	−	0.222633i	$-0.928535\pi$
$953$	−21.0000	−	36.3731i	−0.680257	−	1.17824i	0.294646	−	0.955607i	$-0.404798\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	36.0000			1.16371
$958$		0			0
$959$	6.00000	−	10.3923i	0.193750	−	0.335585i
$960$		0			0
$961$	−6.00000			−0.193548
$962$		0			0
$963$	−18.0000			−0.580042
$964$	−22.0000	+	38.1051i	−0.708572	+	1.22728i
$965$		0			0
$966$		0			0
$967$	4.00000			0.128631			0.0643157	−	0.997930i	$-0.479514\pi$
$967$	4.00000			0.128631			0.0643157	+	0.997930i	$0.479514\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	0.753545	−	0.657396i	$-0.228342\pi$
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	−0.946094	+	0.323891i	$0.895009\pi$
$972$	−1.00000	+	1.73205i	−0.0320750	+	0.0555556i
$973$	9.50000	−	16.4545i	0.304556	−	0.527506i
$974$		0			0
$975$		0			0
$976$	−4.00000			−0.128037
$977$	24.0000	−	41.5692i	0.767828	−	1.32992i	−0.170910	−	0.985287i	$-0.554671\pi$
$977$	24.0000	−	41.5692i	0.767828	−	1.32992i	0.938738	−	0.344631i	$-0.111996\pi$
$978$		0			0
$979$	−36.0000	−	62.3538i	−1.15056	−	1.99284i
$980$		0			0
$981$	3.50000	+	6.06218i	0.111746	+	0.193550i
$982$		0			0
$983$	42.0000			1.33959			0.669796	−	0.742545i	$-0.266382\pi$
$983$	42.0000			1.33959			0.669796	+	0.742545i	$0.266382\pi$
$984$		0			0
$985$		0			0
$986$		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	0.491698	+	0.870766i	$0.336377\pi$
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	−0.999954	+	0.00956046i	$0.996957\pi$
$992$		0			0
$993$	7.00000			0.222138
$994$		0			0
$995$		0			0
$996$	−24.0000			−0.760469
$997$	−24.5000	−	42.4352i	−0.775923	−	1.34394i	−0.934274	−	0.356555i	$-0.883951\pi$
$997$	−24.5000	−	42.4352i	−0.775923	−	1.34394i	0.158352	−	0.987383i	$-0.449382\pi$
$998$		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	975.2.i.d.451.1		2
5.2	odd	4		975.2.bb.b.724.1		4
5.3	odd	4		975.2.bb.b.724.2		4
5.4	even	2		195.2.i.b.61.1	yes	2
13.3	even	3	inner	975.2.i.d.601.1		2
15.14	odd	2		585.2.j.a.451.1		2
65.3	odd	12		975.2.bb.b.874.1		4
65.4	even	6		2535.2.a.i.1.1		1
65.9	even	6		2535.2.a.h.1.1		1
65.29	even	6		195.2.i.b.16.1	✓	2
65.42	odd	12		975.2.bb.b.874.2		4
195.29	odd	6		585.2.j.a.406.1		2
195.74	odd	6		7605.2.a.l.1.1		1
195.134	odd	6		7605.2.a.k.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.b.16.1	✓	2	65.29	even	6
195.2.i.b.61.1	yes	2	5.4	even	2
585.2.j.a.406.1		2	195.29	odd	6
585.2.j.a.451.1		2	15.14	odd	2
975.2.i.d.451.1		2	1.1	even	1	trivial
975.2.i.d.601.1		2	13.3	even	3	inner
975.2.bb.b.724.1		4	5.2	odd	4
975.2.bb.b.724.2		4	5.3	odd	4
975.2.bb.b.874.1		4	65.3	odd	12
975.2.bb.b.874.2		4	65.42	odd	12
2535.2.a.h.1.1		1	65.9	even	6
2535.2.a.i.1.1		1	65.4	even	6
7605.2.a.k.1.1		1	195.134	odd	6
7605.2.a.l.1.1		1	195.74	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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.i (of order \(3\), degree \(2\), minimal)

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

Introduction

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