LMFDB - Embedded newform 60.5.k.a.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,5,Mod(13,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("60.13");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	60.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.20219778503$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 8x^{6} + 28x^{5} + 97x^{4} - 168x^{3} + 288x^{2} + 864x + 1296 $ x^8 - 4x^7 + 8x^6 + 28x^5 + 97x^4 - 168x^3 + 288x^2 + 864*x + 1296
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 3^{2}\cdot 5^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.3
Root			$3.17086 - 3.17086i$ of defining polynomial
Character	$\chi$	$=$	60.37
Dual form			60.5.k.a.13.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.67423 - 3.67423i) q^{3} +(-21.4961 - 12.7640i) q^{5} +(-29.2390 - 29.2390i) q^{7} -27.0000i q^{9} +O(q^{10})$	\(q+(3.67423 - 3.67423i) q^{3} +(-21.4961 - 12.7640i) q^{5} +(-29.2390 - 29.2390i) q^{7} -27.0000i q^{9} -100.806 q^{11} +(65.5718 - 65.5718i) q^{13} +(-125.879 + 32.0836i) q^{15} +(-206.336 - 206.336i) q^{17} -260.194i q^{19} -214.862 q^{21} +(210.067 - 210.067i) q^{23} +(299.160 + 548.751i) q^{25} +(-99.2043 - 99.2043i) q^{27} +503.161i q^{29} +1252.33 q^{31} +(-370.386 + 370.386i) q^{33} +(255.317 + 1001.73i) q^{35} +(1812.07 + 1812.07i) q^{37} -481.852i q^{39} -3129.49 q^{41} +(2140.10 - 2140.10i) q^{43} +(-344.628 + 580.393i) q^{45} +(838.104 + 838.104i) q^{47} -691.158i q^{49} -1516.26 q^{51} +(883.512 - 883.512i) q^{53} +(2166.94 + 1286.69i) q^{55} +(-956.012 - 956.012i) q^{57} -4933.68i q^{59} -5873.12 q^{61} +(-789.454 + 789.454i) q^{63} +(-2246.49 + 572.576i) q^{65} +(-932.560 - 932.560i) q^{67} -1543.67i q^{69} -4439.96 q^{71} +(-412.029 + 412.029i) q^{73} +(3115.43 + 917.056i) q^{75} +(2947.48 + 2947.48i) q^{77} -8658.90i q^{79} -729.000 q^{81} +(5223.10 - 5223.10i) q^{83} +(1801.74 + 7069.09i) q^{85} +(1848.73 + 1848.73i) q^{87} +5102.20i q^{89} -3834.51 q^{91} +(4601.37 - 4601.37i) q^{93} +(-3321.11 + 5593.13i) q^{95} +(-2418.77 - 2418.77i) q^{97} +2721.77i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{5} - 140 q^{7}+O(q^{10}) $ 8 * q + 12 * q^5 - 140 * q^7	$ 8 q + 12 q^{5} - 140 q^{7} + 288 q^{11} + 300 q^{13} - 144 q^{15} - 1020 q^{17} + 792 q^{21} + 1320 q^{23} - 2036 q^{25} + 1472 q^{31} - 180 q^{33} + 1416 q^{35} - 300 q^{37} - 3480 q^{41} - 6360 q^{43} + 648 q^{45} + 4800 q^{47} + 2232 q^{51} + 3900 q^{53} + 11172 q^{55} + 360 q^{57} - 11544 q^{61} - 3780 q^{63} - 16380 q^{65} - 920 q^{67} - 3600 q^{71} + 2960 q^{73} + 15912 q^{75} + 19800 q^{77} - 5832 q^{81} + 12720 q^{83} + 1396 q^{85} - 19620 q^{87} + 32400 q^{91} - 14760 q^{93} - 37200 q^{95} - 15600 q^{97}+O(q^{100}) $ 8 * q + 12 * q^5 - 140 * q^7 + 288 * q^11 + 300 * q^13 - 144 * q^15 - 1020 * q^17 + 792 * q^21 + 1320 * q^23 - 2036 * q^25 + 1472 * q^31 - 180 * q^33 + 1416 * q^35 - 300 * q^37 - 3480 * q^41 - 6360 * q^43 + 648 * q^45 + 4800 * q^47 + 2232 * q^51 + 3900 * q^53 + 11172 * q^55 + 360 * q^57 - 11544 * q^61 - 3780 * q^63 - 16380 * q^65 - 920 * q^67 - 3600 * q^71 + 2960 * q^73 + 15912 * q^75 + 19800 * q^77 - 5832 * q^81 + 12720 * q^83 + 1396 * q^85 - 19620 * q^87 + 32400 * q^91 - 14760 * q^93 - 37200 * q^95 - 15600 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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
$2$		0			0
$3$	3.67423	−	3.67423i	0.408248	−	0.408248i
$3$	3.67423	−	3.67423i	0.408248	−	0.408248i
$4$		0			0
$5$	−21.4961	−	12.7640i	−0.859842	−	0.510560i
$5$	−21.4961	−	12.7640i	−0.859842	−	0.510560i
$6$		0			0
$7$	−29.2390	−	29.2390i	−0.596715	−	0.596715i	0.342722	−	0.939437i	$-0.388651\pi$
$7$	−29.2390	−	29.2390i	−0.596715	−	0.596715i	−0.939437	+	0.342722i	$0.888651\pi$
$8$		0			0
$9$		−	27.0000i		−	0.333333i
$10$		0			0
$11$	−100.806			−0.833109			−0.416555	−	0.909111i	$-0.636763\pi$
$11$	−100.806			−0.833109			−0.416555	+	0.909111i	$0.636763\pi$
$12$		0			0
$13$	65.5718	−	65.5718i	0.387999	−	0.387999i	−0.485974	−	0.873973i	$-0.661535\pi$
$13$	65.5718	−	65.5718i	0.387999	−	0.387999i	0.873973	+	0.485974i	$0.161535\pi$
$14$		0			0
$15$	−125.879	+	32.0836i	−0.559464	+	0.142594i
$16$		0			0
$17$	−206.336	−	206.336i	−0.713967	−	0.713967i	0.253396	−	0.967363i	$-0.418452\pi$
$17$	−206.336	−	206.336i	−0.713967	−	0.713967i	−0.967363	+	0.253396i	$0.918452\pi$
$18$		0			0
$19$		−	260.194i		−	0.720758i	−0.932806	−	0.360379i	$-0.882647\pi$
$19$		−	260.194i		−	0.720758i	0.932806	−	0.360379i	$-0.117353\pi$
$20$		0			0
$21$	−214.862			−0.487216
$22$		0			0
$23$	210.067	−	210.067i	0.397101	−	0.397101i	−0.480108	−	0.877209i	$-0.659403\pi$
$23$	210.067	−	210.067i	0.397101	−	0.397101i	0.877209	+	0.480108i	$0.159403\pi$
$24$		0			0
$25$	299.160	+	548.751i	0.478657	+	0.878002i
$26$		0			0
$27$	−99.2043	−	99.2043i	−0.136083	−	0.136083i
$28$		0			0
$29$			503.161i			0.598289i	0.954208	+	0.299145i	$0.0967013\pi$
$29$			503.161i			0.598289i	−0.954208	+	0.299145i	$0.903299\pi$
$30$		0			0
$31$	1252.33			1.30316			0.651578	−	0.758581i	$-0.274107\pi$
$31$	1252.33			1.30316			0.651578	+	0.758581i	$0.274107\pi$
$32$		0			0
$33$	−370.386	+	370.386i	−0.340115	+	0.340115i
$34$		0			0
$35$	255.317	+	1001.73i	0.208422	+	0.817739i
$36$		0			0
$37$	1812.07	+	1812.07i	1.32364	+	1.32364i	0.910805	+	0.412838i	$0.135462\pi$
$37$	1812.07	+	1812.07i	1.32364	+	1.32364i	0.412838	+	0.910805i	$0.364538\pi$
$38$		0			0
$39$		−	481.852i		−	0.316800i
$40$		0			0
$41$	−3129.49			−1.86168			−0.930842	−	0.365423i	$-0.880924\pi$
$41$	−3129.49			−1.86168			−0.930842	+	0.365423i	$0.880924\pi$
$42$		0			0
$43$	2140.10	−	2140.10i	1.15744	−	1.15744i	0.172413	−	0.985025i	$-0.444844\pi$
$43$	2140.10	−	2140.10i	1.15744	−	1.15744i	0.985025	−	0.172413i	$-0.0551563\pi$
$44$		0			0
$45$	−344.628	+	580.393i	−0.170187	+	0.286614i
$46$		0			0
$47$	838.104	+	838.104i	0.379404	+	0.379404i	0.870887	−	0.491483i	$-0.163545\pi$
$47$	838.104	+	838.104i	0.379404	+	0.379404i	−0.491483	+	0.870887i	$0.663545\pi$
$48$		0			0
$49$		−	691.158i		−	0.287863i
$50$		0			0
$51$	−1516.26			−0.582951
$52$		0			0
$53$	883.512	−	883.512i	0.314529	−	0.314529i	−0.532132	−	0.846661i	$-0.678609\pi$
$53$	883.512	−	883.512i	0.314529	−	0.314529i	0.846661	+	0.532132i	$0.178609\pi$
$54$		0			0
$55$	2166.94	+	1286.69i	0.716342	+	0.425352i
$56$		0			0
$57$	−956.012	−	956.012i	−0.294248	−	0.294248i
$58$		0			0
$59$		−	4933.68i		−	1.41732i	−0.705551	−	0.708659i	$-0.749300\pi$
$59$		−	4933.68i		−	1.41732i	0.705551	−	0.708659i	$-0.250700\pi$
$60$		0			0
$61$	−5873.12			−1.57837			−0.789186	−	0.614154i	$-0.789497\pi$
$61$	−5873.12			−1.57837			−0.789186	+	0.614154i	$0.789497\pi$
$62$		0			0
$63$	−789.454	+	789.454i	−0.198905	+	0.198905i
$64$		0			0
$65$	−2246.49	+	572.576i	−0.531714	+	0.135521i
$66$		0			0
$67$	−932.560	−	932.560i	−0.207743	−	0.207743i	0.595564	−	0.803308i	$-0.296929\pi$
$67$	−932.560	−	932.560i	−0.207743	−	0.207743i	−0.803308	+	0.595564i	$0.796929\pi$
$68$		0			0
$69$		−	1543.67i		−	0.324232i
$70$		0			0
$71$	−4439.96			−0.880769			−0.440385	−	0.897809i	$-0.645158\pi$
$71$	−4439.96			−0.880769			−0.440385	+	0.897809i	$0.645158\pi$
$72$		0			0
$73$	−412.029	+	412.029i	−0.0773183	+	0.0773183i	−0.744708	−	0.667390i	$-0.767411\pi$
$73$	−412.029	+	412.029i	−0.0773183	+	0.0773183i	0.667390	+	0.744708i	$0.267411\pi$
$74$		0			0
$75$	3115.43	+	917.056i	0.553854	+	0.163032i
$76$		0			0
$77$	2947.48	+	2947.48i	0.497129	+	0.497129i
$78$		0			0
$79$		−	8658.90i		−	1.38742i	−0.720254	−	0.693711i	$-0.755975\pi$
$79$		−	8658.90i		−	1.38742i	0.720254	−	0.693711i	$-0.244025\pi$
$80$		0			0
$81$	−729.000			−0.111111
$82$		0			0
$83$	5223.10	−	5223.10i	0.758180	−	0.758180i	−0.217811	−	0.975991i	$-0.569892\pi$
$83$	5223.10	−	5223.10i	0.758180	−	0.758180i	0.975991	+	0.217811i	$0.0698917\pi$
$84$		0			0
$85$	1801.74	+	7069.09i	0.249376	+	0.978421i
$86$		0			0
$87$	1848.73	+	1848.73i	0.244251	+	0.244251i
$88$		0			0
$89$			5102.20i			0.644136i	0.946717	+	0.322068i	$0.104378\pi$
$89$			5102.20i			0.644136i	−0.946717	+	0.322068i	$0.895622\pi$
$90$		0			0
$91$	−3834.51			−0.463049
$92$		0			0
$93$	4601.37	−	4601.37i	0.532012	−	0.532012i
$94$		0			0
$95$	−3321.11	+	5593.13i	−0.367990	+	0.619738i
$96$		0			0
$97$	−2418.77	−	2418.77i	−0.257070	−	0.257070i	0.566791	−	0.823861i	$-0.308185\pi$
$97$	−2418.77	−	2418.77i	−0.257070	−	0.257070i	−0.823861	+	0.566791i	$0.808185\pi$
$98$		0			0
$99$			2721.77i			0.277703i
$100$		0			0
$101$	4380.82			0.429450			0.214725	−	0.976675i	$-0.431114\pi$
$101$	4380.82			0.429450			0.214725	+	0.976675i	$0.431114\pi$
$102$		0			0
$103$	−6844.96	+	6844.96i	−0.645203	+	0.645203i	−0.951830	−	0.306627i	$-0.900800\pi$
$103$	−6844.96	+	6844.96i	−0.645203	+	0.645203i	0.306627	+	0.951830i	$0.400800\pi$
$104$		0			0
$105$	4618.69	+	2742.50i	0.418929	+	0.248753i
$106$		0			0
$107$	12713.4	+	12713.4i	1.11044	+	1.11044i	0.993091	+	0.117350i	$0.0374398\pi$
$107$	12713.4	+	12713.4i	1.11044	+	1.11044i	0.117350	+	0.993091i	$0.462560\pi$
$108$		0			0
$109$			11845.5i			0.997011i	0.866887	+	0.498505i	$0.166118\pi$
$109$			11845.5i			0.997011i	−0.866887	+	0.498505i	$0.833882\pi$
$110$		0			0
$111$	13315.9			1.08075
$112$		0			0
$113$	16798.8	−	16798.8i	1.31559	−	1.31559i	0.398367	−	0.917226i	$-0.369577\pi$
$113$	16798.8	−	16798.8i	1.31559	−	1.31559i	0.917226	−	0.398367i	$-0.130423\pi$
$114$		0			0
$115$	−7196.89	+	1834.31i	−0.544188	+	0.138700i
$116$		0			0
$117$	−1770.44	−	1770.44i	−0.129333	−	0.129333i
$118$		0			0
$119$			12066.1i			0.852069i
$120$		0			0
$121$	−4479.11			−0.305929
$122$		0			0
$123$	−11498.5	+	11498.5i	−0.760029	+	0.760029i
$124$		0			0
$125$	573.499	−	15614.5i	0.0367039	−	0.999326i
$126$		0			0
$127$	−14949.7	−	14949.7i	−0.926882	−	0.926882i	0.0706214	−	0.997503i	$-0.477502\pi$
$127$	−14949.7	−	14949.7i	−0.926882	−	0.926882i	−0.997503	+	0.0706214i	$0.977502\pi$
$128$		0			0
$129$		−	15726.5i		−	0.945044i
$130$		0			0
$131$	−3761.56			−0.219193			−0.109596	−	0.993976i	$-0.534956\pi$
$131$	−3761.56			−0.219193			−0.109596	+	0.993976i	$0.534956\pi$
$132$		0			0
$133$	−7607.81	+	7607.81i	−0.430087	+	0.430087i
$134$		0			0
$135$	866.257	+	3398.75i	0.0475312	+	0.186488i
$136$		0			0
$137$	−13779.0	−	13779.0i	−0.734139	−	0.734139i	0.237298	−	0.971437i	$-0.423738\pi$
$137$	−13779.0	−	13779.0i	−0.734139	−	0.734139i	−0.971437	+	0.237298i	$0.923738\pi$
$138$		0			0
$139$		−	25283.6i		−	1.30861i	−0.756232	−	0.654303i	$-0.772962\pi$
$139$		−	25283.6i		−	1.30861i	0.756232	−	0.654303i	$-0.227038\pi$
$140$		0			0
$141$	6158.78			0.309782
$142$		0			0
$143$	−6610.04	+	6610.04i	−0.323245	+	0.323245i
$144$		0			0
$145$	6422.36	−	10816.0i	0.305463	−	0.514434i
$146$		0			0
$147$	−2539.48	−	2539.48i	−0.117519	−	0.117519i
$148$		0			0
$149$			13593.6i			0.612295i	0.951984	+	0.306147i	$0.0990400\pi$
$149$			13593.6i			0.612295i	−0.951984	+	0.306147i	$0.900960\pi$
$150$		0			0
$151$	17658.0			0.774440			0.387220	−	0.921987i	$-0.373435\pi$
$151$	17658.0			0.774440			0.387220	+	0.921987i	$0.373435\pi$
$152$		0			0
$153$	−5571.08	+	5571.08i	−0.237989	+	0.237989i
$154$		0			0
$155$	−26920.2	−	15984.8i	−1.12051	−	0.665340i
$156$		0			0
$157$	2986.67	+	2986.67i	0.121168	+	0.121168i	0.765091	−	0.643923i	$-0.222694\pi$
$157$	2986.67	+	2986.67i	0.121168	+	0.121168i	−0.643923	+	0.765091i	$0.722694\pi$
$158$		0			0
$159$		−	6492.46i		−	0.256812i
$160$		0			0
$161$	−12284.3			−0.473913
$162$		0			0
$163$	−14591.9	+	14591.9i	−0.549207	+	0.549207i	−0.926211	−	0.377005i	$-0.876954\pi$
$163$	−14591.9	+	14591.9i	−0.549207	+	0.549207i	0.377005	+	0.926211i	$0.376954\pi$
$164$		0			0
$165$	12689.4	−	3234.22i	0.466095	−	0.118796i
$166$		0			0
$167$	4074.21	+	4074.21i	0.146087	+	0.146087i	0.776367	−	0.630281i	$-0.217060\pi$
$167$	4074.21	+	4074.21i	0.146087	+	0.146087i	−0.630281	+	0.776367i	$0.717060\pi$
$168$		0			0
$169$			19961.7i			0.698914i
$170$		0			0
$171$	−7025.23			−0.240253
$172$		0			0
$173$	10988.5	−	10988.5i	0.367152	−	0.367152i	−0.499286	−	0.866437i	$-0.666404\pi$
$173$	10988.5	−	10988.5i	0.367152	−	0.367152i	0.866437	+	0.499286i	$0.166404\pi$
$174$		0			0
$175$	7297.80	−	24792.1i	0.238295	−	0.809539i
$176$		0			0
$177$	−18127.5	−	18127.5i	−0.578618	−	0.578618i
$178$		0			0
$179$			55895.4i			1.74450i	0.489063	+	0.872248i	$0.337339\pi$
$179$			55895.4i			1.74450i	−0.489063	+	0.872248i	$0.662661\pi$
$180$		0			0
$181$	61470.9			1.87634			0.938171	−	0.346171i	$-0.112518\pi$
$181$	61470.9			1.87634			0.938171	+	0.346171i	$0.112518\pi$
$182$		0			0
$183$	−21579.2	+	21579.2i	−0.644368	+	0.644368i
$184$		0			0
$185$	−15823.0	−	62081.5i	−0.462324	−	1.81392i
$186$		0			0
$187$	20800.0	+	20800.0i	0.594812	+	0.594812i
$188$		0			0
$189$			5801.28i			0.162405i
$190$		0			0
$191$	21064.5			0.577411			0.288706	−	0.957418i	$-0.406775\pi$
$191$	21064.5			0.577411			0.288706	+	0.957418i	$0.406775\pi$
$192$		0			0
$193$	−16416.6	+	16416.6i	−0.440726	+	0.440726i	−0.892256	−	0.451530i	$-0.850878\pi$
$193$	−16416.6	+	16416.6i	−0.440726	+	0.440726i	0.451530	+	0.892256i	$0.350878\pi$
$194$		0			0
$195$	−6150.36	+	10357.9i	−0.161745	+	0.272398i
$196$		0			0
$197$	37084.2	+	37084.2i	0.955556	+	0.955556i	0.999054	−	0.0434975i	$-0.0138500\pi$
$197$	37084.2	+	37084.2i	0.955556	+	0.955556i	−0.0434975	+	0.999054i	$0.513850\pi$
$198$		0			0
$199$		−	15577.7i		−	0.393366i	−0.980467	−	0.196683i	$-0.936983\pi$
$199$		−	15577.7i		−	0.393366i	0.980467	−	0.196683i	$-0.0630170\pi$
$200$		0			0
$201$	−6852.89			−0.169622
$202$		0			0
$203$	14712.0	−	14712.0i	0.357008	−	0.357008i
$204$		0			0
$205$	67271.7	+	39944.8i	1.60075	+	0.950501i
$206$		0			0
$207$	−5671.80	−	5671.80i	−0.132367	−	0.132367i
$208$		0			0
$209$			26229.1i			0.600470i
$210$		0			0
$211$	71670.6			1.60981			0.804907	−	0.593401i	$-0.202215\pi$
$211$	71670.6			1.60981			0.804907	+	0.593401i	$0.202215\pi$
$212$		0			0
$213$	−16313.4	+	16313.4i	−0.359573	+	0.359573i
$214$		0			0
$215$	−73320.0	+	18687.5i	−1.58615	+	0.404272i
$216$		0			0
$217$	−36617.0	−	36617.0i	−0.777613	−	0.777613i
$218$		0			0
$219$			3027.78i			0.0631301i
$220$		0			0
$221$	−27059.7			−0.554036
$222$		0			0
$223$	10834.2	−	10834.2i	0.217864	−	0.217864i	−0.589734	−	0.807598i	$-0.700767\pi$
$223$	10834.2	−	10834.2i	0.217864	−	0.217864i	0.807598	+	0.589734i	$0.200767\pi$
$224$		0			0
$225$	14816.3	−	8077.33i	0.292667	−	0.159552i
$226$		0			0
$227$	8536.10	+	8536.10i	0.165656	+	0.165656i	0.785067	−	0.619411i	$-0.212628\pi$
$227$	8536.10	+	8536.10i	0.165656	+	0.165656i	−0.619411	+	0.785067i	$0.712628\pi$
$228$		0			0
$229$			53172.3i			1.01395i	0.861962	+	0.506973i	$0.169235\pi$
$229$			53172.3i			1.01395i	−0.861962	+	0.506973i	$0.830765\pi$
$230$		0			0
$231$	21659.4			0.405904
$232$		0			0
$233$	−8276.62	+	8276.62i	−0.152455	+	0.152455i	−0.779213	−	0.626759i	$-0.784381\pi$
$233$	−8276.62	+	8276.62i	−0.152455	+	0.152455i	0.626759	+	0.779213i	$0.284381\pi$
$234$		0			0
$235$	−7318.36	−	28713.5i	−0.132519	−	0.519936i
$236$		0			0
$237$	−31814.8	−	31814.8i	−0.566412	−	0.566412i
$238$		0			0
$239$		−	64206.9i		−	1.12405i	−0.827120	−	0.562025i	$-0.810022\pi$
$239$		−	64206.9i		−	1.12405i	0.827120	−	0.562025i	$-0.189978\pi$
$240$		0			0
$241$	−52792.1			−0.908940			−0.454470	−	0.890762i	$-0.650171\pi$
$241$	−52792.1			−0.908940			−0.454470	+	0.890762i	$0.650171\pi$
$242$		0			0
$243$	−2678.52	+	2678.52i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	−8821.94	+	14857.2i	−0.146971	+	0.247516i
$246$		0			0
$247$	−17061.4	−	17061.4i	−0.279653	−	0.279653i
$248$		0			0
$249$		−	38381.8i		−	0.619051i
$250$		0			0
$251$	7619.52			0.120943			0.0604714	−	0.998170i	$-0.480740\pi$
$251$	7619.52			0.120943			0.0604714	+	0.998170i	$0.480740\pi$
$252$		0			0
$253$	−21176.0	+	21176.0i	−0.330829	+	0.330829i
$254$		0			0
$255$	32593.5	+	19353.5i	0.501246	+	0.297632i
$256$		0			0
$257$	−56900.1	−	56900.1i	−0.861483	−	0.861483i	0.130027	−	0.991510i	$-0.458494\pi$
$257$	−56900.1	−	56900.1i	−0.861483	−	0.861483i	−0.991510	+	0.130027i	$0.958494\pi$
$258$		0			0
$259$		−	105966.i		−	1.57967i
$260$		0			0
$261$	13585.4			0.199430
$262$		0			0
$263$	78565.0	−	78565.0i	1.13584	−	1.13584i	0.146653	−	0.989188i	$-0.453150\pi$
$263$	78565.0	−	78565.0i	1.13584	−	1.13584i	0.989188	−	0.146653i	$-0.0468502\pi$
$264$		0			0
$265$	−30269.2	+	7714.86i	−0.431031	+	0.109859i
$266$		0			0
$267$	18746.7	+	18746.7i	0.262967	+	0.262967i
$268$		0			0
$269$			108837.i			1.50409i	0.659114	+	0.752043i	$0.270932\pi$
$269$			108837.i			1.50409i	−0.659114	+	0.752043i	$0.729068\pi$
$270$		0			0
$271$	−51081.3			−0.695542			−0.347771	−	0.937580i	$-0.613061\pi$
$271$	−51081.3			−0.695542			−0.347771	+	0.937580i	$0.613061\pi$
$272$		0			0
$273$	−14088.9	+	14088.9i	−0.189039	+	0.189039i
$274$		0			0
$275$	−30157.2	−	55317.5i	−0.398773	−	0.731472i
$276$		0			0
$277$	−37506.3	−	37506.3i	−0.488815	−	0.488815i	0.419117	−	0.907932i	$-0.362340\pi$
$277$	−37506.3	−	37506.3i	−0.488815	−	0.488815i	−0.907932	+	0.419117i	$0.862340\pi$
$278$		0			0
$279$		−	33813.0i		−	0.434386i
$280$		0			0
$281$	−101190.			−1.28152			−0.640758	−	0.767743i	$-0.721380\pi$
$281$	−101190.			−1.28152			−0.640758	+	0.767743i	$0.721380\pi$
$282$		0			0
$283$	−4039.24	+	4039.24i	−0.0504344	+	0.0504344i	−0.731874	−	0.681440i	$-0.761354\pi$
$283$	−4039.24	+	4039.24i	−0.0504344	+	0.0504344i	0.681440	+	0.731874i	$0.261354\pi$
$284$		0			0
$285$	8347.94	+	32753.0i	0.102776	+	0.403238i
$286$		0			0
$287$	91503.2	+	91503.2i	1.11089	+	1.11089i
$288$		0			0
$289$			1628.37i			0.0194966i
$290$		0			0
$291$	−17774.3			−0.209897
$292$		0			0
$293$	92563.9	−	92563.9i	1.07822	−	1.07822i	0.0815481	−	0.996669i	$-0.474014\pi$
$293$	92563.9	−	92563.9i	1.07822	−	1.07822i	0.996669	−	0.0815481i	$-0.0259864\pi$
$294$		0			0
$295$	−62973.6	+	106055.i	−0.723626	+	1.21867i
$296$		0			0
$297$	10000.4	+	10000.4i	0.113372	+	0.113372i
$298$		0			0
$299$		−	27548.9i		−	0.308150i
$300$		0			0
$301$	−125149.			−1.38132
$302$		0			0
$303$	16096.2	−	16096.2i	0.175322	−	0.175322i
$304$		0			0
$305$	126249.	+	74964.6i	1.35715	+	0.805854i
$306$		0			0
$307$	82316.5	+	82316.5i	0.873394	+	0.873394i	0.992841	−	0.119447i	$-0.0381121\pi$
$307$	82316.5	+	82316.5i	0.873394	+	0.873394i	−0.119447	+	0.992841i	$0.538112\pi$
$308$		0			0
$309$			50300.0i			0.526806i
$310$		0			0
$311$	66895.0			0.691628			0.345814	−	0.938303i	$-0.387603\pi$
$311$	66895.0			0.691628			0.345814	+	0.938303i	$0.387603\pi$
$312$		0			0
$313$	12902.7	−	12902.7i	0.131702	−	0.131702i	−0.638183	−	0.769885i	$-0.720314\pi$
$313$	12902.7	−	12902.7i	0.131702	−	0.131702i	0.769885	+	0.638183i	$0.220314\pi$
$314$		0			0
$315$	27046.7	−	6893.55i	0.272580	−	0.0694739i
$316$		0			0
$317$	87261.9	+	87261.9i	0.868373	+	0.868373i	0.992292	−	0.123919i	$-0.0395464\pi$
$317$	87261.9	+	87261.9i	0.868373	+	0.868373i	−0.123919	+	0.992292i	$0.539546\pi$
$318$		0			0
$319$		−	50721.8i		−	0.498440i
$320$		0			0
$321$	93424.2			0.906671
$322$		0			0
$323$	−53687.4	+	53687.4i	−0.514597	+	0.514597i
$324$		0			0
$325$	55599.1	+	16366.1i	0.526382	+	0.154946i
$326$		0			0
$327$	43523.1	+	43523.1i	0.407028	+	0.407028i
$328$		0			0
$329$		−	49010.7i		−	0.452792i
$330$		0			0
$331$	−89537.0			−0.817234			−0.408617	−	0.912706i	$-0.633989\pi$
$331$	−89537.0			−0.817234			−0.408617	+	0.912706i	$0.633989\pi$
$332$		0			0
$333$	48925.8	−	48925.8i	0.441214	−	0.441214i
$334$		0			0
$335$	8143.16	+	31949.6i	0.0725610	+	0.284692i
$336$		0			0
$337$	−10633.8	−	10633.8i	−0.0936326	−	0.0936326i	0.658739	−	0.752372i	$-0.271090\pi$
$337$	−10633.8	−	10633.8i	−0.0936326	−	0.0936326i	−0.752372	+	0.658739i	$0.771090\pi$
$338$		0			0
$339$		−	123446.i		−	1.07418i
$340$		0			0
$341$	−126243.			−1.08567
$342$		0			0
$343$	−90411.7	+	90411.7i	−0.768487	+	0.768487i
$344$		0			0
$345$	−19703.4	+	33182.8i	−0.165540	+	0.278788i
$346$		0			0
$347$	−37803.6	−	37803.6i	−0.313960	−	0.313960i	0.532482	−	0.846442i	$-0.321260\pi$
$347$	−37803.6	−	37803.6i	−0.313960	−	0.313960i	−0.846442	+	0.532482i	$0.821260\pi$
$348$		0			0
$349$		−	68613.6i		−	0.563325i	−0.959514	−	0.281663i	$-0.909114\pi$
$349$		−	68613.6i		−	0.563325i	0.959514	−	0.281663i	$-0.0908859\pi$
$350$		0			0
$351$	−13010.0			−0.105600
$352$		0			0
$353$	31348.2	−	31348.2i	0.251572	−	0.251572i	−0.570043	−	0.821615i	$-0.693073\pi$
$353$	31348.2	−	31348.2i	0.251572	−	0.251572i	0.821615	+	0.570043i	$0.193073\pi$
$354$		0			0
$355$	95441.6	+	56671.7i	0.757323	+	0.449686i
$356$		0			0
$357$	44333.9	+	44333.9i	0.347856	+	0.347856i
$358$		0			0
$359$			85046.4i			0.659883i	0.944001	+	0.329941i	$0.107029\pi$
$359$			85046.4i			0.659883i	−0.944001	+	0.329941i	$0.892971\pi$
$360$		0			0
$361$	62620.3			0.480508
$362$		0			0
$363$	−16457.3	+	16457.3i	−0.124895	+	0.124895i
$364$		0			0
$365$	14116.1	−	3597.86i	0.105957	−	0.0270059i
$366$		0			0
$367$	−19597.4	−	19597.4i	−0.145501	−	0.145501i	0.630604	−	0.776105i	$-0.282807\pi$
$367$	−19597.4	−	19597.4i	−0.145501	−	0.145501i	−0.776105	+	0.630604i	$0.782807\pi$
$368$		0			0
$369$			84496.2i			0.620561i
$370$		0			0
$371$	−51666.0			−0.375368
$372$		0			0
$373$	88837.3	−	88837.3i	0.638525	−	0.638525i	−0.311667	−	0.950191i	$-0.600887\pi$
$373$	88837.3	−	88837.3i	0.638525	−	0.638525i	0.950191	+	0.311667i	$0.100887\pi$
$374$		0			0
$375$	−55264.1	−	59478.4i	−0.392989	−	0.422958i
$376$		0			0
$377$	32993.2	+	32993.2i	0.232136	+	0.232136i
$378$		0			0
$379$			55861.4i			0.388896i	0.980913	+	0.194448i	$0.0622916\pi$
$379$			55861.4i			0.388896i	−0.980913	+	0.194448i	$0.937708\pi$
$380$		0			0
$381$	−109857.			−0.756796
$382$		0			0
$383$	77604.9	−	77604.9i	0.529044	−	0.529044i	−0.391244	−	0.920287i	$-0.627955\pi$
$383$	77604.9	−	77604.9i	0.529044	−	0.529044i	0.920287	+	0.391244i	$0.127955\pi$
$384$		0			0
$385$	−25737.5	−	100981.i	−0.173638	−	0.681266i
$386$		0			0
$387$	−57782.8	−	57782.8i	−0.385813	−	0.385813i
$388$		0			0
$389$		−	210631.i		−	1.39195i	−0.718067	−	0.695974i	$-0.754973\pi$
$389$		−	210631.i		−	1.39195i	0.718067	−	0.695974i	$-0.245027\pi$
$390$		0			0
$391$	−86688.7			−0.567034
$392$		0			0
$393$	−13820.9	+	13820.9i	−0.0894850	+	0.0894850i
$394$		0			0
$395$	−110522.	+	186132.i	−0.708362	+	1.19296i
$396$		0			0
$397$	−47327.7	−	47327.7i	−0.300285	−	0.300285i	0.540840	−	0.841125i	$-0.318106\pi$
$397$	−47327.7	−	47327.7i	−0.300285	−	0.300285i	−0.841125	+	0.540840i	$0.818106\pi$
$398$		0			0
$399$			55905.7i			0.351164i
$400$		0			0
$401$	−16778.8			−0.104345			−0.0521726	−	0.998638i	$-0.516615\pi$
$401$	−16778.8			−0.104345			−0.0521726	+	0.998638i	$0.516615\pi$
$402$		0			0
$403$	82117.7	−	82117.7i	0.505623	−	0.505623i
$404$		0			0
$405$	15670.6	+	9304.96i	0.0955380	+	0.0567289i
$406$		0			0
$407$	−182667.	−	182667.i	−1.10274	−	1.10274i
$408$		0			0
$409$		−	33710.4i		−	0.201520i	−0.994911	−	0.100760i	$-0.967873\pi$
$409$		−	33710.4i		−	0.201520i	0.994911	−	0.100760i	$-0.0321274\pi$
$410$		0			0
$411$	−101255.			−0.599422
$412$		0			0
$413$	−144256.	+	144256.i	−0.845735	+	0.845735i
$414$		0			0
$415$	−178944.	+	45608.4i	−1.03901	+	0.264818i
$416$		0			0
$417$	−92897.9	−	92897.9i	−0.534237	−	0.534237i
$418$		0			0
$419$		−	293984.i		−	1.67454i	−0.546789	−	0.837270i	$-0.684150\pi$
$419$		−	293984.i		−	1.67454i	0.546789	−	0.837270i	$-0.315850\pi$
$420$		0			0
$421$	90452.8			0.510338			0.255169	−	0.966896i	$-0.417869\pi$
$421$	90452.8			0.510338			0.255169	+	0.966896i	$0.417869\pi$
$422$		0			0
$423$	22628.8	−	22628.8i	0.126468	−	0.126468i
$424$		0			0
$425$	51499.7	−	174955.i	0.285119	−	0.968609i
$426$		0			0
$427$	171724.	+	171724.i	0.941838	+	0.941838i
$428$		0			0
$429$			48573.7i			0.263929i
$430$		0			0
$431$	193225.			1.04018			0.520091	−	0.854111i	$-0.325898\pi$
$431$	193225.			1.04018			0.520091	+	0.854111i	$0.325898\pi$
$432$		0			0
$433$	233890.	−	233890.i	1.24749	−	1.24749i	0.290661	−	0.956826i	$-0.406125\pi$
$433$	233890.	−	233890.i	1.24749	−	1.24749i	0.956826	−	0.290661i	$-0.0938753\pi$
$434$		0			0
$435$	−16143.2	−	63337.7i	−0.0853123	−	0.334722i
$436$		0			0
$437$	−54658.0	−	54658.0i	−0.286214	−	0.286214i
$438$		0			0
$439$			256431.i			1.33058i	0.746583	+	0.665292i	$0.231693\pi$
$439$			256431.i			1.33058i	−0.746583	+	0.665292i	$0.768307\pi$
$440$		0			0
$441$	−18661.3			−0.0959542
$442$		0			0
$443$	−271033.	+	271033.i	−1.38107	+	1.38107i	−0.538333	+	0.842732i	$0.680946\pi$
$443$	−271033.	+	271033.i	−1.38107	+	1.38107i	−0.842732	+	0.538333i	$0.819054\pi$
$444$		0			0
$445$	65124.5	−	109677.i	0.328870	−	0.553855i
$446$		0			0
$447$	49945.9	+	49945.9i	0.249968	+	0.249968i
$448$		0			0
$449$			346521.i			1.71885i	0.511265	+	0.859423i	$0.329177\pi$
$449$			346521.i			1.71885i	−0.511265	+	0.859423i	$0.670823\pi$
$450$		0			0
$451$	315472.			1.55099
$452$		0			0
$453$	64879.7	−	64879.7i	0.316164	−	0.316164i
$454$		0			0
$455$	82426.8	+	48943.7i	0.398149	+	0.236414i
$456$		0			0
$457$	37089.6	+	37089.6i	0.177590	+	0.177590i	0.790305	−	0.612714i	$-0.209922\pi$
$457$	37089.6	+	37089.6i	0.177590	+	0.177590i	−0.612714	+	0.790305i	$0.709922\pi$
$458$		0			0
$459$			40938.9i			0.194317i
$460$		0			0
$461$	178438.			0.839627			0.419813	−	0.907610i	$-0.362096\pi$
$461$	178438.			0.839627			0.419813	+	0.907610i	$0.362096\pi$
$462$		0			0
$463$	−137047.	+	137047.i	−0.639303	+	0.639303i	−0.950383	−	0.311081i	$-0.899309\pi$
$463$	−137047.	+	137047.i	−0.639303	+	0.639303i	0.311081	+	0.950383i	$0.399309\pi$
$464$		0			0
$465$	−157643.	+	40179.4i	−0.729070	+	0.185822i
$466$		0			0
$467$	−137506.	−	137506.i	−0.630503	−	0.630503i	0.317691	−	0.948194i	$-0.397092\pi$
$467$	−137506.	−	137506.i	−0.630503	−	0.630503i	−0.948194	+	0.317691i	$0.897092\pi$
$468$		0			0
$469$			54534.3i			0.247927i
$470$		0			0
$471$	21947.5			0.0989334
$472$		0			0
$473$	−215736.	+	215736.i	−0.964272	+	0.964272i
$474$		0			0
$475$	142782.	−	77839.6i	0.632827	−	0.344995i
$476$		0			0
$477$	−23854.8	−	23854.8i	−0.104843	−	0.104843i
$478$		0			0
$479$			17228.2i			0.0750879i	0.999295	+	0.0375439i	$0.0119534\pi$
$479$			17228.2i			0.0750879i	−0.999295	+	0.0375439i	$0.988047\pi$
$480$		0			0
$481$	237641.			1.02714
$482$		0			0
$483$	−45135.4	+	45135.4i	−0.193474	+	0.193474i
$484$		0			0
$485$	21120.8	+	82867.2i	0.0897898	+	0.352289i
$486$		0			0
$487$	55195.9	+	55195.9i	0.232728	+	0.232728i	0.813830	−	0.581102i	$-0.197378\pi$
$487$	55195.9	+	55195.9i	0.232728	+	0.232728i	−0.581102	+	0.813830i	$0.697378\pi$
$488$		0			0
$489$			107228.i			0.448425i
$490$		0			0
$491$	99534.3			0.412867			0.206433	−	0.978461i	$-0.433814\pi$
$491$	99534.3			0.412867			0.206433	+	0.978461i	$0.433814\pi$
$492$		0			0
$493$	103820.	−	103820.i	0.427159	−	0.427159i
$494$		0			0
$495$	34740.6	−	58507.2i	0.141784	−	0.238781i
$496$		0			0
$497$	129820.	+	129820.i	0.525568	+	0.525568i
$498$		0			0
$499$			222798.i			0.894769i	0.894342	+	0.447385i	$0.147645\pi$
$499$			222798.i			0.894769i	−0.894342	+	0.447385i	$0.852355\pi$
$500$		0			0
$501$	29939.2			0.119279
$502$		0			0
$503$	−18900.9	+	18900.9i	−0.0747045	+	0.0747045i	−0.743472	−	0.668767i	$-0.766822\pi$
$503$	−18900.9	+	18900.9i	−0.0747045	+	0.0747045i	0.668767	+	0.743472i	$0.266822\pi$
$504$		0			0
$505$	−94170.3	−	55916.8i	−0.369259	−	0.219260i
$506$		0			0
$507$	73343.9	+	73343.9i	0.285330	+	0.285330i
$508$		0			0
$509$		−	294705.i		−	1.13750i	−0.822510	−	0.568750i	$-0.807427\pi$
$509$		−	294705.i		−	1.13750i	0.822510	−	0.568750i	$-0.192573\pi$
$510$		0			0
$511$	24094.7			0.0922739
$512$		0			0
$513$	−25812.3	+	25812.3i	−0.0980827	+	0.0980827i
$514$		0			0
$515$	234509.	−	59770.5i	0.884187	−	0.225358i
$516$		0			0
$517$	−84486.0	−	84486.0i	−0.316085	−	0.316085i
$518$		0			0
$519$		−	80748.6i		−	0.299778i
$520$		0			0
$521$	284288.			1.04733			0.523664	−	0.851925i	$-0.324565\pi$
$521$	284288.			1.04733			0.523664	+	0.851925i	$0.324565\pi$
$522$		0			0
$523$	−121118.	+	121118.i	−0.442796	+	0.442796i	−0.892951	−	0.450154i	$-0.851369\pi$
$523$	−121118.	+	121118.i	−0.442796	+	0.442796i	0.450154	+	0.892951i	$0.351369\pi$
$524$		0			0
$525$	−64278.2	−	117906.i	−0.233209	−	0.427776i
$526$		0			0
$527$	−258402.	−	258402.i	−0.930411	−	0.930411i
$528$		0			0
$529$			191585.i			0.684621i
$530$		0			0
$531$	−133209.			−0.472439
$532$		0			0
$533$	−205206.	+	205206.i	−0.722331	+	0.722331i
$534$		0			0
$535$	−111014.	−	435563.i	−0.387857	−	1.52175i
$536$		0			0
$537$	205373.	+	205373.i	0.712188	+	0.712188i
$538$		0			0
$539$			69673.0i			0.239821i
$540$		0			0
$541$	−434885.			−1.48587			−0.742933	−	0.669366i	$-0.766566\pi$
$541$	−434885.			−1.48587			−0.742933	+	0.669366i	$0.766566\pi$
$542$		0			0
$543$	225858.	−	225858.i	0.766014	−	0.766014i
$544$		0			0
$545$	151196.	−	254631.i	0.509034	−	0.857272i
$546$		0			0
$547$	7758.44	+	7758.44i	0.0259298	+	0.0259298i	0.719953	−	0.694023i	$-0.244163\pi$
$547$	7758.44	+	7758.44i	0.0259298	+	0.0259298i	−0.694023	+	0.719953i	$0.744163\pi$
$548$		0			0
$549$			158574.i			0.526124i
$550$		0			0
$551$	130919.			0.431222
$552$		0			0
$553$	−253178.	+	253178.i	−0.827895	+	0.827895i
$554$		0			0
$555$	−286240.	−	169964.i	−0.929274	−	0.551788i
$556$		0			0
$557$	−22166.3	−	22166.3i	−0.0714470	−	0.0714470i	0.670480	−	0.741927i	$-0.266088\pi$
$557$	−22166.3	−	22166.3i	−0.0714470	−	0.0714470i	−0.741927	+	0.670480i	$0.766088\pi$
$558$		0			0
$559$		−	280661.i		−	0.898168i
$560$		0			0
$561$	152848.			0.485662
$562$		0			0
$563$	253305.	−	253305.i	0.799147	−	0.799147i	−0.183814	−	0.982961i	$-0.558844\pi$
$563$	253305.	−	253305.i	0.799147	−	0.799147i	0.982961	+	0.183814i	$0.0588445\pi$
$564$		0			0
$565$	−575528.	+	146688.i	−1.80289	+	0.459513i
$566$		0			0
$567$	21315.3	+	21315.3i	0.0663017	+	0.0663017i
$568$		0			0
$569$			4947.07i			0.0152800i	0.999971	+	0.00764001i	$0.00243191\pi$
$569$			4947.07i			0.0152800i	−0.999971	+	0.00764001i	$0.997568\pi$
$570$		0			0
$571$	−205345.			−0.629813			−0.314907	−	0.949123i	$-0.601973\pi$
$571$	−205345.			−0.629813			−0.314907	+	0.949123i	$0.601973\pi$
$572$		0			0
$573$	77396.1	−	77396.1i	0.235727	−	0.235727i
$574$		0			0
$575$	178118.	+	52430.7i	0.538731	+	0.158581i
$576$		0			0
$577$	−178874.	−	178874.i	−0.537274	−	0.537274i	0.385453	−	0.922727i	$-0.374045\pi$
$577$	−178874.	−	178874.i	−0.537274	−	0.537274i	−0.922727	+	0.385453i	$0.874045\pi$
$578$		0			0
$579$			120637.i			0.359851i
$580$		0			0
$581$	−305437.			−0.904835
$582$		0			0
$583$	−89063.4	+	89063.4i	−0.262037	+	0.262037i
$584$		0			0
$585$	15459.5	+	60655.3i	0.0451736	+	0.177238i
$586$		0			0
$587$	−240208.	−	240208.i	−0.697126	−	0.697126i	0.266663	−	0.963790i	$-0.414079\pi$
$587$	−240208.	−	240208.i	−0.697126	−	0.697126i	−0.963790	+	0.266663i	$0.914079\pi$
$588$		0			0
$589$		−	325849.i		−	0.939260i
$590$		0			0
$591$	272512.			0.780208
$592$		0			0
$593$	−481681.	+	481681.i	−1.36978	+	1.36978i	−0.509025	+	0.860752i	$0.669994\pi$
$593$	−481681.	+	481681.i	−1.36978	+	1.36978i	−0.860752	+	0.509025i	$0.830006\pi$
$594$		0			0
$595$	154012.	−	259375.i	0.435033	−	0.732645i
$596$		0			0
$597$	−57236.1	−	57236.1i	−0.160591	−	0.160591i
$598$		0			0
$599$			154606.i			0.430896i	0.976515	+	0.215448i	$0.0691211\pi$
$599$			154606.i			0.430896i	−0.976515	+	0.215448i	$0.930879\pi$
$600$		0			0
$601$	439313.			1.21626			0.608128	−	0.793839i	$-0.291921\pi$
$601$	439313.			1.21626			0.608128	+	0.793839i	$0.291921\pi$
$602$		0			0
$603$	−25179.1	+	25179.1i	−0.0692478	+	0.0692478i
$604$		0			0
$605$	96283.2	+	57171.4i	0.263051	+	0.156195i
$606$		0			0
$607$	−37796.8	−	37796.8i	−0.102584	−	0.102584i	0.653952	−	0.756536i	$-0.273110\pi$
$607$	−37796.8	−	37796.8i	−0.102584	−	0.102584i	−0.756536	+	0.653952i	$0.773110\pi$
$608$		0			0
$609$		−	108110.i		−	0.291496i
$610$		0			0
$611$	109912.			0.294417
$612$		0			0
$613$	140335.	−	140335.i	0.373461	−	0.373461i	−0.495275	−	0.868736i	$-0.664933\pi$
$613$	140335.	−	140335.i	0.373461	−	0.373461i	0.868736	+	0.495275i	$0.164933\pi$
$614$		0			0
$615$	393939.	−	100405.i	1.04155	−	0.265464i
$616$		0			0
$617$	54366.7	+	54366.7i	0.142811	+	0.142811i	0.774898	−	0.632086i	$-0.217801\pi$
$617$	54366.7	+	54366.7i	0.142811	+	0.142811i	−0.632086	+	0.774898i	$0.717801\pi$
$618$		0			0
$619$			273964.i			0.715011i	0.933911	+	0.357505i	$0.116373\pi$
$619$			273964.i			0.715011i	−0.933911	+	0.357505i	$0.883627\pi$
$620$		0			0
$621$	−41679.0			−0.108077
$622$		0			0
$623$	149183.	−	149183.i	0.384365	−	0.384365i
$624$		0			0
$625$	−211631.	+	328329.i	−0.541776	+	0.840523i
$626$		0			0
$627$	96371.9	+	96371.9i	0.245141	+	0.245141i
$628$		0			0
$629$		−	747790.i		−	1.89007i
$630$		0			0
$631$	−770840.			−1.93600			−0.968001	−	0.250947i	$-0.919258\pi$
$631$	−770840.			−1.93600			−0.968001	+	0.250947i	$0.919258\pi$
$632$		0			0
$633$	263334.	−	263334.i	0.657204	−	0.657204i
$634$		0			0
$635$	130541.	+	512177.i	0.323743	+	1.27020i
$636$		0			0
$637$	−45320.5	−	45320.5i	−0.111690	−	0.111690i
$638$		0			0
$639$			119879.i			0.293590i
$640$		0			0
$641$	404369.			0.984152			0.492076	−	0.870552i	$-0.336238\pi$
$641$	404369.			0.984152			0.492076	+	0.870552i	$0.336238\pi$
$642$		0			0
$643$	438578.	−	438578.i	1.06078	−	1.06078i	0.0627491	−	0.998029i	$-0.480013\pi$
$643$	438578.	−	438578.i	1.06078	−	1.06078i	0.998029	−	0.0627491i	$-0.0199868\pi$
$644$		0			0
$645$	−200733.	+	338057.i	−0.482502	+	0.812588i
$646$		0			0
$647$	190458.	+	190458.i	0.454978	+	0.454978i	0.897003	−	0.442025i	$-0.145740\pi$
$647$	190458.	+	190458.i	0.454978	+	0.454978i	−0.442025	+	0.897003i	$0.645740\pi$
$648$		0			0
$649$			497346.i			1.18078i
$650$		0			0
$651$	−269079.			−0.634919
$652$		0			0
$653$	−184154.	+	184154.i	−0.431872	+	0.431872i	−0.889265	−	0.457393i	$-0.848783\pi$
$653$	−184154.	+	184154.i	−0.431872	+	0.431872i	0.457393	+	0.889265i	$0.348783\pi$
$654$		0			0
$655$	80858.8	+	48012.6i	0.188471	+	0.111911i
$656$		0			0
$657$	11124.8	+	11124.8i	0.0257728	+	0.0257728i
$658$		0			0
$659$			136158.i			0.313525i	0.987636	+	0.156762i	$0.0501057\pi$
$659$			136158.i			0.313525i	−0.987636	+	0.156762i	$0.949894\pi$
$660$		0			0
$661$	−302378.			−0.692065			−0.346032	−	0.938223i	$-0.612471\pi$
$661$	−302378.			−0.692065			−0.346032	+	0.938223i	$0.612471\pi$
$662$		0			0
$663$	−99423.6	+	99423.6i	−0.226184	+	0.226184i
$664$		0			0
$665$	260644.	−	66431.7i	0.589392	−	0.150222i
$666$		0			0
$667$	105697.	+	105697.i	0.237582	+	0.237582i
$668$		0			0
$669$		−	79614.5i		−	0.177885i
$670$		0			0
$671$	592047.			1.31496
$672$		0			0
$673$	−273891.	+	273891.i	−0.604710	+	0.604710i	−0.941559	−	0.336849i	$-0.890639\pi$
$673$	−273891.	+	273891.i	−0.604710	+	0.604710i	0.336849	+	0.941559i	$0.390639\pi$
$674$		0			0
$675$	24760.5	−	84116.5i	0.0543441	−	0.184618i
$676$		0			0
$677$	178343.	+	178343.i	0.389116	+	0.389116i	0.874372	−	0.485256i	$-0.161274\pi$
$677$	178343.	+	178343.i	0.389116	+	0.389116i	−0.485256	+	0.874372i	$0.661274\pi$
$678$		0			0
$679$			141445.i			0.306795i
$680$		0			0
$681$	62727.3			0.135258
$682$		0			0
$683$	238606.	−	238606.i	0.511494	−	0.511494i	−0.403490	−	0.914984i	$-0.632203\pi$
$683$	238606.	−	238606.i	0.511494	−	0.511494i	0.914984	+	0.403490i	$0.132203\pi$
$684$		0			0
$685$	120319.	+	472071.i	0.256421	+	1.00607i
$686$		0			0
$687$	195367.	+	195367.i	0.413941	+	0.413941i
$688$		0			0
$689$		−	115867.i		−	0.244074i
$690$		0			0
$691$	207226.			0.433998			0.216999	−	0.976172i	$-0.430373\pi$
$691$	207226.			0.433998			0.216999	+	0.976172i	$0.430373\pi$
$692$		0			0
$693$	79581.8	−	79581.8i	0.165710	−	0.165710i
$694$		0			0
$695$	−322720.	+	543497.i	−0.668123	+	1.12520i
$696$		0			0
$697$	645727.	+	645727.i	1.32918	+	1.32918i
$698$		0			0
$699$			60820.5i			0.124479i
$700$		0			0
$701$	−472139.			−0.960803			−0.480401	−	0.877049i	$-0.659509\pi$
$701$	−472139.			−0.960803			−0.480401	+	0.877049i	$0.659509\pi$
$702$		0			0
$703$	471488.	−	471488.i	0.954025	−	0.954025i
$704$		0			0
$705$	−132389.	−	78610.7i	−0.266364	−	0.158162i
$706$		0			0
$707$	−128091.	−	128091.i	−0.256259	−	0.256259i
$708$		0			0
$709$		−	180630.i		−	0.359333i	−0.983728	−	0.179667i	$-0.942498\pi$
$709$		−	180630.i		−	0.359333i	0.983728	−	0.179667i	$-0.0575019\pi$
$710$		0			0
$711$	−233790.			−0.462474
$712$		0			0
$713$	263073.	−	263073.i	0.517485	−	0.517485i
$714$		0			0
$715$	226460.	−	57719.2i	0.442976	−	0.112904i
$716$		0			0
$717$	−235911.	−	235911.i	−0.458892	−	0.458892i
$718$		0			0
$719$		−	71380.5i		−	0.138077i	−0.997614	−	0.0690386i	$-0.978007\pi$
$719$		−	71380.5i		−	0.138077i	0.997614	−	0.0690386i	$-0.0219932\pi$
$720$		0			0
$721$	400280.			0.770004
$722$		0			0
$723$	−193971.	+	193971.i	−0.371073	+	0.371073i
$724$		0			0
$725$	−276111.	+	150526.i	−0.525299	+	0.286375i
$726$		0			0
$727$	−520312.	−	520312.i	−0.984453	−	0.984453i	0.0154283	−	0.999881i	$-0.495089\pi$
$727$	−520312.	−	520312.i	−0.984453	−	0.984453i	−0.999881	+	0.0154283i	$0.995089\pi$
$728$		0			0
$729$			19683.0i			0.0370370i
$730$		0			0
$731$	−883162.			−1.65274
$732$		0			0
$733$	304781.	−	304781.i	0.567258	−	0.567258i	−0.364101	−	0.931359i	$-0.618624\pi$
$733$	304781.	−	304781.i	0.567258	−	0.567258i	0.931359	+	0.364101i	$0.118624\pi$
$734$		0			0
$735$	22174.8	+	87002.6i	0.0410474	+	0.161049i
$736$		0			0
$737$	94007.8	+	94007.8i	0.173073	+	0.173073i
$738$		0			0
$739$		−	422739.i		−	0.774076i	−0.922064	−	0.387038i	$-0.873498\pi$
$739$		−	422739.i		−	0.774076i	0.922064	−	0.387038i	$-0.126502\pi$
$740$		0			0
$741$	−125375.			−0.228336
$742$		0			0
$743$	−309220.	+	309220.i	−0.560131	+	0.560131i	−0.929344	−	0.369214i	$-0.879627\pi$
$743$	−309220.	+	309220.i	−0.560131	+	0.560131i	0.369214	+	0.929344i	$0.379627\pi$
$744$		0			0
$745$	173508.	−	292208.i	0.312613	−	0.526477i
$746$		0			0
$747$	−141024.	−	141024.i	−0.252727	−	0.252727i
$748$		0			0
$749$		−	743457.i		−	1.32523i
$750$		0			0
$751$	−830203.			−1.47199			−0.735994	−	0.676988i	$-0.763285\pi$
$751$	−830203.			−1.47199			−0.735994	+	0.676988i	$0.763285\pi$
$752$		0			0
$753$	27995.9	−	27995.9i	0.0493747	−	0.0493747i
$754$		0			0
$755$	−379578.	−	225387.i	−0.665896	−	0.395398i
$756$		0			0
$757$	319294.	+	319294.i	0.557184	+	0.557184i	0.928505	−	0.371321i	$-0.121095\pi$
$757$	319294.	+	319294.i	0.557184	+	0.557184i	−0.371321	+	0.928505i	$0.621095\pi$
$758$		0			0
$759$			155611.i			0.270120i
$760$		0			0
$761$	−668943.			−1.15510			−0.577550	−	0.816355i	$-0.695991\pi$
$761$	−668943.			−1.15510			−0.577550	+	0.816355i	$0.695991\pi$
$762$		0			0
$763$	346351.	−	346351.i	0.594931	−	0.594931i
$764$		0			0
$765$	190866.	−	48646.9i	0.326140	−	0.0831252i
$766$		0			0
$767$	−323510.	−	323510.i	−0.549917	−	0.549917i
$768$		0			0
$769$		−	831330.i		−	1.40579i	−0.711293	−	0.702896i	$-0.751890\pi$
$769$		−	831330.i		−	1.40579i	0.711293	−	0.702896i	$-0.248110\pi$
$770$		0			0
$771$	−418129.			−0.703398
$772$		0			0
$773$	457925.	−	457925.i	0.766364	−	0.766364i	−0.211100	−	0.977464i	$-0.567705\pi$
$773$	457925.	−	457925.i	0.766364	−	0.766364i	0.977464	+	0.211100i	$0.0677047\pi$
$774$		0			0
$775$	374649.	+	687220.i	0.623765	+	1.14417i
$776$		0			0
$777$	−389344.	−	389344.i	−0.644899	−	0.644899i
$778$		0			0
$779$			814273.i			1.34182i
$780$		0			0
$781$	447575.			0.733777
$782$		0			0
$783$	49915.8	−	49915.8i	0.0814169	−	0.0814169i
$784$		0			0
$785$	−26079.8	−	102324.i	−0.0423218	−	0.166049i
$786$		0			0
$787$	440089.	+	440089.i	0.710544	+	0.710544i	0.966649	−	0.256105i	$-0.0824394\pi$
$787$	440089.	+	440089.i	0.710544	+	0.710544i	−0.256105	+	0.966649i	$0.582439\pi$
$788$		0			0
$789$		−	577333.i		−	0.927411i
$790$		0			0
$791$	−982362.			−1.57007
$792$		0			0
$793$	−385111.	+	385111.i	−0.612406	+	0.612406i
$794$		0			0
$795$	−82869.8	+	139562.i	−0.131118	+	0.220818i
$796$		0			0
$797$	874514.	+	874514.i	1.37673	+	1.37673i	0.850080	+	0.526654i	$0.176554\pi$
$797$	874514.	+	874514.i	1.37673	+	1.37673i	0.526654	+	0.850080i	$0.323446\pi$
$798$		0			0
$799$		−	345862.i		−	0.541764i
$800$		0			0
$801$	137759.			0.214712
$802$		0			0
$803$	41535.1	−	41535.1i	0.0644146	−	0.0644146i
$804$		0			0
$805$	264064.	+	156797.i	0.407490	+	0.241961i
$806$		0			0
$807$	399893.	+	399893.i	0.614041	+	0.614041i
$808$		0			0
$809$		−	900682.i		−	1.37618i	−0.725627	−	0.688088i	$-0.758450\pi$
$809$		−	900682.i		−	1.37618i	0.725627	−	0.688088i	$-0.241550\pi$
$810$		0			0
$811$	560145.			0.851645			0.425822	−	0.904807i	$-0.359985\pi$
$811$	560145.			0.851645			0.425822	+	0.904807i	$0.359985\pi$
$812$		0			0
$813$	−187685.	+	187685.i	−0.283954	+	0.283954i
$814$		0			0
$815$	499918.	−	127417.i	0.752634	−	0.191828i
$816$		0			0
$817$	−556841.	−	556841.i	−0.834232	−	0.834232i
$818$		0			0
$819$			103532.i			0.154350i
$820$		0			0
$821$	−391487.			−0.580805			−0.290403	−	0.956905i	$-0.593789\pi$
$821$	−391487.			−0.580805			−0.290403	+	0.956905i	$0.593789\pi$
$822$		0			0
$823$	−877887.	+	877887.i	−1.29610	+	1.29610i	−0.365154	+	0.930947i	$0.618983\pi$
$823$	−877887.	+	877887.i	−1.29610	+	1.29610i	−0.930947	+	0.365154i	$0.881017\pi$
$824$		0			0
$825$	−314054.	−	92444.9i	−0.461420	−	0.135824i
$826$		0			0
$827$	−796044.	−	796044.i	−1.16393	−	1.16393i	−0.983608	−	0.180320i	$-0.942287\pi$
$827$	−796044.	−	796044.i	−1.16393	−	1.16393i	−0.180320	−	0.983608i	$-0.557713\pi$
$828$		0			0
$829$			83808.3i			0.121949i	0.998139	+	0.0609745i	$0.0194208\pi$
$829$			83808.3i			0.121949i	−0.998139	+	0.0609745i	$0.980579\pi$
$830$		0			0
$831$	−275614.			−0.399116
$832$		0			0
$833$	−142611.	+	142611.i	−0.205524	+	0.205524i
$834$		0			0
$835$	−35576.2	−	139583.i	−0.0510254	−	0.200198i
$836$		0			0
$837$	−124237.	−	124237.i	−0.177337	−	0.177337i
$838$		0			0
$839$			1.03825e6i			1.47495i	0.675372	+	0.737477i	$0.263983\pi$
$839$			1.03825e6i			1.47495i	−0.675372	+	0.737477i	$0.736017\pi$
$840$		0			0
$841$	454110.			0.642050
$842$		0			0
$843$	−371795.	+	371795.i	−0.523176	+	0.523176i
$844$		0			0
$845$	254791.	−	429097.i	0.356838	−	0.600956i
$846$		0			0
$847$	130965.	+	130965.i	0.182553	+	0.182553i
$848$		0			0
$849$			29682.2i			0.0411795i
$850$		0			0
$851$	761309.			1.05124
$852$		0			0
$853$	417742.	−	417742.i	0.574130	−	0.574130i	−0.359150	−	0.933280i	$-0.616933\pi$
$853$	417742.	−	417742.i	0.574130	−	0.574130i	0.933280	+	0.359150i	$0.116933\pi$
$854$		0			0
$855$	151015.	+	89670.0i	0.206579	+	0.122663i
$856$		0			0
$857$	295564.	+	295564.i	0.402430	+	0.402430i	0.879088	−	0.476659i	$-0.158152\pi$
$857$	295564.	+	295564.i	0.402430	+	0.402430i	−0.476659	+	0.879088i	$0.658152\pi$
$858$		0			0
$859$			156574.i			0.212194i	0.994356	+	0.106097i	$0.0338354\pi$
$859$			156574.i			0.212194i	−0.994356	+	0.106097i	$0.966165\pi$
$860$		0			0
$861$	672409.			0.907041
$862$		0			0
$863$	852253.	−	852253.i	1.14432	−	1.14432i	0.156667	−	0.987652i	$-0.449925\pi$
$863$	852253.	−	852253.i	1.14432	−	1.14432i	0.987652	−	0.156667i	$-0.0500748\pi$
$864$		0			0
$865$	−376466.	+	95952.0i	−0.503146	+	0.128239i
$866$		0			0
$867$	5983.02	+	5983.02i	0.00795944	+	0.00795944i
$868$		0			0
$869$			872871.i			1.15587i
$870$		0			0
$871$	−122299.			−0.161208
$872$		0			0
$873$	−65306.8	+	65306.8i	−0.0856900	+	0.0856900i
$874$		0			0
$875$	−473321.	+	439783.i	−0.618215	+	0.574411i
$876$		0			0
$877$	673537.	+	673537.i	0.875713	+	0.875713i	0.993088	−	0.117374i	$-0.0374477\pi$
$877$	673537.	+	673537.i	0.875713	+	0.875713i	−0.117374	+	0.993088i	$0.537448\pi$
$878$		0			0
$879$		−	680203.i		−	0.880361i
$880$		0			0
$881$	801878.			1.03313			0.516567	−	0.856247i	$-0.327210\pi$
$881$	801878.			1.03313			0.516567	+	0.856247i	$0.327210\pi$
$882$		0			0
$883$	419877.	−	419877.i	0.538519	−	0.538519i	−0.384575	−	0.923094i	$-0.625652\pi$
$883$	419877.	−	419877.i	0.538519	−	0.538519i	0.923094	+	0.384575i	$0.125652\pi$
$884$		0			0
$885$	158290.	+	621050.i	0.202101	+	0.792939i
$886$		0			0
$887$	700728.	+	700728.i	0.890640	+	0.890640i	0.994583	−	0.103943i	$-0.0331461\pi$
$887$	700728.	+	700728.i	0.890640	+	0.890640i	−0.103943	+	0.994583i	$0.533146\pi$
$888$		0			0
$889$			874228.i			1.10617i
$890$		0			0
$891$	73487.7			0.0925677
$892$		0			0
$893$	218069.	−	218069.i	0.273458	−	0.273458i
$894$		0			0
$895$	713449.	−	1.20153e6i	0.890670	−	1.49999i
$896$		0			0
$897$	−101221.	−	101221.i	−0.125802	−	0.125802i
$898$		0			0
$899$			630126.i			0.779665i
$900$		0			0
$901$	−364601.			−0.449126
$902$		0			0
$903$	−459827.	+	459827.i	−0.563922	+	0.563922i
$904$		0			0
$905$	−1.32138e6	−	784614.i	−1.61336	−	0.957986i
$906$		0			0
$907$	−226251.	−	226251.i	−0.275027	−	0.275027i	0.556093	−	0.831120i	$-0.312300\pi$
$907$	−226251.	−	226251.i	−0.275027	−	0.275027i	−0.831120	+	0.556093i	$0.812300\pi$
$908$		0			0
$909$		−	118282.i		−	0.143150i
$910$		0			0
$911$	840996.			1.01334			0.506672	−	0.862139i	$-0.330875\pi$
$911$	840996.			1.01334			0.506672	+	0.862139i	$0.330875\pi$
$912$		0			0
$913$	−526521.	+	526521.i	−0.631647	+	0.631647i
$914$		0			0
$915$	739306.	−	188431.i	0.883043	−	0.225066i
$916$		0			0
$917$	109985.	+	109985.i	0.130796	+	0.130796i
$918$		0			0
$919$		−	131956.i		−	0.156242i	−0.996944	−	0.0781208i	$-0.975108\pi$
$919$		−	131956.i		−	0.156242i	0.996944	−	0.0781208i	$-0.0248920\pi$
$920$		0			0
$921$	604900.			0.713123
$922$		0			0
$923$	−291136.	+	291136.i	−0.341737	+	0.341737i
$924$		0			0
$925$	−452275.	+	1.53647e6i	−0.528591	+	1.79573i
$926$		0			0
$927$	184814.	+	184814.i	0.215068	+	0.215068i
$928$		0			0
$929$			789125.i			0.914354i	0.889376	+	0.457177i	$0.151139\pi$
$929$			789125.i			0.914354i	−0.889376	+	0.457177i	$0.848861\pi$
$930$		0			0
$931$	−179835.			−0.207479
$932$		0			0
$933$	245788.	−	245788.i	0.282356	−	0.282356i
$934$		0			0
$935$	−181626.	−	712609.i	−0.207757	−	0.815132i
$936$		0			0
$937$	−979642.	−	979642.i	−1.11580	−	1.11580i	−0.992350	−	0.123454i	$-0.960603\pi$
$937$	−979642.	−	979642.i	−1.11580	−	1.11580i	−0.123454	−	0.992350i	$-0.539397\pi$
$938$		0			0
$939$		−	94815.1i		−	0.107534i
$940$		0			0
$941$	−961058.			−1.08535			−0.542675	−	0.839942i	$-0.682589\pi$
$941$	−961058.			−1.08535			−0.542675	+	0.839942i	$0.682589\pi$
$942$		0			0
$943$	−657401.	+	657401.i	−0.739277	+	0.739277i
$944$		0			0
$945$	74047.5	−	124705.i	0.0829176	−	0.139643i
$946$		0			0
$947$	−96791.3	−	96791.3i	−0.107929	−	0.107929i	0.651080	−	0.759009i	$-0.274316\pi$
$947$	−96791.3	−	96791.3i	−0.107929	−	0.107929i	−0.759009	+	0.651080i	$0.774316\pi$
$948$		0			0
$949$			54035.0i			0.0599988i
$950$		0			0
$951$	641242.			0.709024
$952$		0			0
$953$	280586.	−	280586.i	0.308944	−	0.308944i	−0.535556	−	0.844500i	$-0.679898\pi$
$953$	280586.	−	280586.i	0.308944	−	0.308944i	0.844500	+	0.535556i	$0.179898\pi$
$954$		0			0
$955$	−452804.	−	268868.i	−0.496482	−	0.294803i
$956$		0			0
$957$	−186364.	−	186364.i	−0.203487	−	0.203487i
$958$		0			0
$959$			805772.i			0.876143i
$960$		0			0
$961$	644819.			0.698218
$962$		0			0
$963$	343263.	−	343263.i	0.370147	−	0.370147i
$964$		0			0
$965$	562433.	−	143350.i	0.603972	−	0.153938i
$966$		0			0
$967$	−1.05482e6	−	1.05482e6i	−1.12805	−	1.12805i	−0.990495	−	0.137551i	$-0.956077\pi$
$967$	−1.05482e6	−	1.05482e6i	−1.12805	−	1.12805i	−0.137551	−	0.990495i	$-0.543923\pi$
$968$		0			0
$969$			394520.i			0.420167i
$970$		0			0
$971$	494524.			0.524504			0.262252	−	0.964999i	$-0.415535\pi$
$971$	494524.			0.524504			0.262252	+	0.964999i	$0.415535\pi$
$972$		0			0
$973$	−739268.	+	739268.i	−0.780865	+	0.780865i
$974$		0			0
$975$	264417.	−	144151.i	0.278151	−	0.151638i
$976$		0			0
$977$	−391473.	−	391473.i	−0.410121	−	0.410121i	0.471660	−	0.881781i	$-0.343655\pi$
$977$	−391473.	−	391473.i	−0.410121	−	0.410121i	−0.881781	+	0.471660i	$0.843655\pi$
$978$		0			0
$979$		−	514333.i		−	0.536635i
$980$		0			0
$981$	319828.			0.332337
$982$		0			0
$983$	657131.	−	657131.i	0.680057	−	0.680057i	−0.279956	−	0.960013i	$-0.590320\pi$
$983$	657131.	−	657131.i	0.680057	−	0.680057i	0.960013	+	0.279956i	$0.0903200\pi$
$984$		0			0
$985$	−323821.	−	1.27051e6i	−0.333758	−	1.30950i
$986$		0			0
$987$	−180077.	−	180077.i	−0.184852	−	0.184852i
$988$		0			0
$989$		−	899128.i		−	0.919240i
$990$		0			0
$991$	443257.			0.451344			0.225672	−	0.974203i	$-0.427542\pi$
$991$	443257.			0.451344			0.225672	+	0.974203i	$0.427542\pi$
$992$		0			0
$993$	−328980.	+	328980.i	−0.333634	+	0.333634i
$994$		0			0
$995$	−198834.	+	334859.i	−0.200837	+	0.338233i
$996$		0			0
$997$	−667384.	−	667384.i	−0.671407	−	0.671407i	0.286634	−	0.958040i	$-0.407464\pi$
$997$	−667384.	−	667384.i	−0.671407	−	0.671407i	−0.958040	+	0.286634i	$0.907464\pi$
$998$		0			0
$999$		−	359530.i		−	0.360250i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.5.k.a.37.3	yes	8
3.2	odd	2		180.5.l.b.37.4		8
4.3	odd	2		240.5.bg.d.97.1		8
5.2	odd	4		300.5.k.d.193.2		8
5.3	odd	4	inner	60.5.k.a.13.3	✓	8
5.4	even	2		300.5.k.d.157.2		8
15.2	even	4		900.5.l.k.793.3		8
15.8	even	4		180.5.l.b.73.4		8
15.14	odd	2		900.5.l.k.757.3		8
20.3	even	4		240.5.bg.d.193.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.k.a.13.3	✓	8	5.3	odd	4	inner
60.5.k.a.37.3	yes	8	1.1	even	1	trivial
180.5.l.b.37.4		8	3.2	odd	2
180.5.l.b.73.4		8	15.8	even	4
240.5.bg.d.97.1		8	4.3	odd	2
240.5.bg.d.193.1		8	20.3	even	4
300.5.k.d.157.2		8	5.4	even	2
300.5.k.d.193.2		8	5.2	odd	4
900.5.l.k.757.3		8	15.14	odd	2
900.5.l.k.793.3		8	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	60.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.67423 - 3.67423i) q^{3} +(-21.4961 - 12.7640i) q^{5} +(-29.2390 - 29.2390i) q^{7} -27.0000i q^{9} +O(q^{10})\)	\(q+(3.67423 - 3.67423i) q^{3} +(-21.4961 - 12.7640i) q^{5} +(-29.2390 - 29.2390i) q^{7} -27.0000i q^{9} -100.806 q^{11} +(65.5718 - 65.5718i) q^{13} +(-125.879 + 32.0836i) q^{15} +(-206.336 - 206.336i) q^{17} -260.194i q^{19} -214.862 q^{21} +(210.067 - 210.067i) q^{23} +(299.160 + 548.751i) q^{25} +(-99.2043 - 99.2043i) q^{27} +503.161i q^{29} +1252.33 q^{31} +(-370.386 + 370.386i) q^{33} +(255.317 + 1001.73i) q^{35} +(1812.07 + 1812.07i) q^{37} -481.852i q^{39} -3129.49 q^{41} +(2140.10 - 2140.10i) q^{43} +(-344.628 + 580.393i) q^{45} +(838.104 + 838.104i) q^{47} -691.158i q^{49} -1516.26 q^{51} +(883.512 - 883.512i) q^{53} +(2166.94 + 1286.69i) q^{55} +(-956.012 - 956.012i) q^{57} -4933.68i q^{59} -5873.12 q^{61} +(-789.454 + 789.454i) q^{63} +(-2246.49 + 572.576i) q^{65} +(-932.560 - 932.560i) q^{67} -1543.67i q^{69} -4439.96 q^{71} +(-412.029 + 412.029i) q^{73} +(3115.43 + 917.056i) q^{75} +(2947.48 + 2947.48i) q^{77} -8658.90i q^{79} -729.000 q^{81} +(5223.10 - 5223.10i) q^{83} +(1801.74 + 7069.09i) q^{85} +(1848.73 + 1848.73i) q^{87} +5102.20i q^{89} -3834.51 q^{91} +(4601.37 - 4601.37i) q^{93} +(-3321.11 + 5593.13i) q^{95} +(-2418.77 - 2418.77i) q^{97} +2721.77i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{5} - 140 q^{7}+O(q^{10}) \) 8 * q + 12 * q^5 - 140 * q^7	\( 8 q + 12 q^{5} - 140 q^{7} + 288 q^{11} + 300 q^{13} - 144 q^{15} - 1020 q^{17} + 792 q^{21} + 1320 q^{23} - 2036 q^{25} + 1472 q^{31} - 180 q^{33} + 1416 q^{35} - 300 q^{37} - 3480 q^{41} - 6360 q^{43} + 648 q^{45} + 4800 q^{47} + 2232 q^{51} + 3900 q^{53} + 11172 q^{55} + 360 q^{57} - 11544 q^{61} - 3780 q^{63} - 16380 q^{65} - 920 q^{67} - 3600 q^{71} + 2960 q^{73} + 15912 q^{75} + 19800 q^{77} - 5832 q^{81} + 12720 q^{83} + 1396 q^{85} - 19620 q^{87} + 32400 q^{91} - 14760 q^{93} - 37200 q^{95} - 15600 q^{97}+O(q^{100}) \) 8 * q + 12 * q^5 - 140 * q^7 + 288 * q^11 + 300 * q^13 - 144 * q^15 - 1020 * q^17 + 792 * q^21 + 1320 * q^23 - 2036 * q^25 + 1472 * q^31 - 180 * q^33 + 1416 * q^35 - 300 * q^37 - 3480 * q^41 - 6360 * q^43 + 648 * q^45 + 4800 * q^47 + 2232 * q^51 + 3900 * q^53 + 11172 * q^55 + 360 * q^57 - 11544 * q^61 - 3780 * q^63 - 16380 * q^65 - 920 * q^67 - 3600 * q^71 + 2960 * q^73 + 15912 * q^75 + 19800 * q^77 - 5832 * q^81 + 12720 * q^83 + 1396 * q^85 - 19620 * q^87 + 32400 * q^91 - 14760 * q^93 - 37200 * q^95 - 15600 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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