LMFDB - Embedded newform 60.6.i.a.53.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,6,Mod(17,60)]

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, 2, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("60.17");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	60.i (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:	$9.62302918878$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 2 x^{18} - 382 x^{17} + 117610 x^{16} - 661518 x^{15} + 1160778 x^{14} + \cdots + 48\!\cdots\!00 $ x^20 - 2x^19 + 2x^18 - 382x^17 + 117610x^16 - 661518x^15 + 1160778x^14 - 161859774x^13 + 12872525097x^12 - 60314430972x^11 + 238998177000x^10 - 23647959230160x^9 + 244333990200544x^8 + 369253960052800x^7 + 17753999958800000x^6 - 195554595639827200x^5 + 1195920778734496000x^4 - 5202205084237824000x^3 + 36839424090977280000x^2 - 600638984600463360000*x + 4896482487496796160000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{23}\cdot 3^{14}\cdot 5^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.4
Root			$6.78762 - 2.77873i$ of defining polynomial
Character	$\chi$	$=$	60.53
Dual form			60.6.i.a.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.90111 - 12.0403i) q^{3} +(51.4858 + 21.7765i) q^{5} +(56.0116 - 56.0116i) q^{7} +(-46.9362 + 238.424i) q^{9} +O(q^{10})$	\(q+(-9.90111 - 12.0403i) q^{3} +(51.4858 + 21.7765i) q^{5} +(56.0116 - 56.0116i) q^{7} +(-46.9362 + 238.424i) q^{9} -616.203i q^{11} +(-323.806 - 323.806i) q^{13} +(-247.572 - 835.514i) q^{15} +(-1378.31 - 1378.31i) q^{17} +256.440i q^{19} +(-1228.97 - 119.818i) q^{21} +(2641.63 - 2641.63i) q^{23} +(2176.57 + 2242.36i) q^{25} +(3335.41 - 1795.54i) q^{27} +381.009 q^{29} -7358.84 q^{31} +(-7419.24 + 6101.09i) q^{33} +(4103.54 - 1664.07i) q^{35} +(6067.48 - 6067.48i) q^{37} +(-692.674 + 7104.76i) q^{39} +1462.80i q^{41} +(3450.11 + 3450.11i) q^{43} +(-7608.58 + 11253.3i) q^{45} +(6963.19 + 6963.19i) q^{47} +10532.4i q^{49} +(-2948.43 + 30242.0i) q^{51} +(5262.26 - 5262.26i) q^{53} +(13418.7 - 31725.7i) q^{55} +(3087.61 - 2539.04i) q^{57} +33815.5 q^{59} -31177.0 q^{61} +(10725.5 + 15983.5i) q^{63} +(-9620.07 - 23722.8i) q^{65} +(-15756.9 + 15756.9i) q^{67} +(-57961.0 - 5650.87i) q^{69} -75916.6i q^{71} +(51080.6 + 51080.6i) q^{73} +(5448.11 - 48408.3i) q^{75} +(-34514.5 - 34514.5i) q^{77} +42068.3i q^{79} +(-54643.0 - 22381.4i) q^{81} +(48969.9 - 48969.9i) q^{83} +(-40948.7 - 100978. i) q^{85} +(-3772.42 - 4587.46i) q^{87} -21879.1 q^{89} -36273.8 q^{91} +(72860.7 + 88602.4i) q^{93} +(-5584.36 + 13203.0i) q^{95} +(63524.7 - 63524.7i) q^{97} +(146917. + 28922.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} + 76 q^{7}+O(q^{10}) $ 20 * q + 2 * q^3 + 76 * q^7	$ 20 q + 2 q^{3} + 76 q^{7} + 1068 q^{13} - 130 q^{15} + 2180 q^{21} + 4060 q^{25} + 1454 q^{27} - 4720 q^{31} - 460 q^{33} - 612 q^{37} - 24012 q^{43} - 18860 q^{45} - 31700 q^{51} + 19200 q^{55} + 33476 q^{57} + 59880 q^{61} + 67208 q^{63} - 80804 q^{67} - 56956 q^{73} - 102470 q^{75} - 9980 q^{81} + 239260 q^{85} + 71540 q^{87} + 218520 q^{91} + 307928 q^{93} - 151164 q^{97}+O(q^{100}) $ 20 * q + 2 * q^3 + 76 * q^7 + 1068 * q^13 - 130 * q^15 + 2180 * q^21 + 4060 * q^25 + 1454 * q^27 - 4720 * q^31 - 460 * q^33 - 612 * q^37 - 24012 * q^43 - 18860 * q^45 - 31700 * q^51 + 19200 * q^55 + 33476 * q^57 + 59880 * q^61 + 67208 * q^63 - 80804 * q^67 - 56956 * q^73 - 102470 * q^75 - 9980 * q^81 + 239260 * q^85 + 71540 * q^87 + 218520 * q^91 + 307928 * q^93 - 151164 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$37$	$41$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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
$3$	−9.90111	−	12.0403i	−0.635156	−	0.772384i
$3$	−9.90111	−	12.0403i	−0.635156	−	0.772384i
$4$		0			0
$5$	51.4858	+	21.7765i	0.921006	+	0.389549i
$5$	51.4858	+	21.7765i	0.921006	+	0.389549i
$6$		0			0
$7$	56.0116	−	56.0116i	0.432049	−	0.432049i	−0.457276	−	0.889325i	$-0.651175\pi$
$7$	56.0116	−	56.0116i	0.432049	−	0.432049i	0.889325	+	0.457276i	$0.151175\pi$
$8$		0			0
$9$	−46.9362	+	238.424i	−0.193153	+	0.981169i
$10$		0			0
$11$		−	616.203i		−	1.53547i	−0.640767	−	0.767736i	$-0.721383\pi$
$11$		−	616.203i		−	1.53547i	0.640767	−	0.767736i	$-0.278617\pi$
$12$		0			0
$13$	−323.806	−	323.806i	−0.531407	−	0.531407i	0.389584	−	0.920991i	$-0.372619\pi$
$13$	−323.806	−	323.806i	−0.531407	−	0.531407i	−0.920991	+	0.389584i	$0.872619\pi$
$14$		0			0
$15$	−247.572	−	835.514i	−0.284101	−	0.958794i
$16$		0			0
$17$	−1378.31	−	1378.31i	−1.15671	−	1.15671i	−0.985179	−	0.171532i	$-0.945128\pi$
$17$	−1378.31	−	1378.31i	−1.15671	−	1.15671i	−0.171532	−	0.985179i	$-0.554872\pi$
$18$		0			0
$19$			256.440i			0.162968i	0.996675	+	0.0814839i	$0.0259659\pi$
$19$			256.440i			0.162968i	−0.996675	+	0.0814839i	$0.974034\pi$
$20$		0			0
$21$	−1228.97	−	119.818i	−0.608126	−	0.0592889i
$22$		0			0
$23$	2641.63	−	2641.63i	1.04124	−	1.04124i	0.0421311	−	0.999112i	$-0.486585\pi$
$23$	2641.63	−	2641.63i	1.04124	−	1.04124i	0.999112	−	0.0421311i	$-0.0134147\pi$
$24$		0			0
$25$	2176.57	+	2242.36i	0.696503	+	0.717554i
$26$		0			0
$27$	3335.41	−	1795.54i	0.880521	−	0.474007i
$28$		0			0
$29$	381.009			0.0841280			0.0420640	−	0.999115i	$-0.486607\pi$
$29$	381.009			0.0841280			0.0420640	+	0.999115i	$0.486607\pi$
$30$		0			0
$31$	−7358.84			−1.37532			−0.687662	−	0.726031i	$-0.741363\pi$
$31$	−7358.84			−1.37532			−0.687662	+	0.726031i	$0.741363\pi$
$32$		0			0
$33$	−7419.24	+	6101.09i	−1.18597	+	0.975264i
$34$		0			0
$35$	4103.54	−	1664.07i	0.566224	−	0.229615i
$36$		0			0
$37$	6067.48	−	6067.48i	0.728625	−	0.728625i	−0.241721	−	0.970346i	$-0.577712\pi$
$37$	6067.48	−	6067.48i	0.728625	−	0.728625i	0.970346	+	0.241721i	$0.0777119\pi$
$38$		0			0
$39$	−692.674	+	7104.76i	−0.0729235	+	0.747976i
$40$		0			0
$41$			1462.80i			0.135902i	0.997689	+	0.0679508i	$0.0216461\pi$
$41$			1462.80i			0.135902i	−0.997689	+	0.0679508i	$0.978354\pi$
$42$		0			0
$43$	3450.11	+	3450.11i	0.284552	+	0.284552i	0.834921	−	0.550369i	$-0.185513\pi$
$43$	3450.11	+	3450.11i	0.284552	+	0.284552i	−0.550369	+	0.834921i	$0.685513\pi$
$44$		0			0
$45$	−7608.58	+	11253.3i	−0.560108	+	0.828419i
$46$		0			0
$47$	6963.19	+	6963.19i	0.459794	+	0.459794i	0.898588	−	0.438794i	$-0.144594\pi$
$47$	6963.19	+	6963.19i	0.459794	+	0.459794i	−0.438794	+	0.898588i	$0.644594\pi$
$48$		0			0
$49$			10532.4i			0.626668i
$50$		0			0
$51$	−2948.43	+	30242.0i	−0.158732	+	1.62812i
$52$		0			0
$53$	5262.26	−	5262.26i	0.257325	−	0.257325i	−0.566640	−	0.823965i	$-0.691757\pi$
$53$	5262.26	−	5262.26i	0.257325	−	0.257325i	0.823965	+	0.566640i	$0.191757\pi$
$54$		0			0
$55$	13418.7	−	31725.7i	0.598142	−	1.41418i
$56$		0			0
$57$	3087.61	−	2539.04i	0.125874	−	0.103510i
$58$		0			0
$59$	33815.5			1.26470			0.632348	−	0.774684i	$-0.282091\pi$
$59$	33815.5			1.26470			0.632348	+	0.774684i	$0.282091\pi$
$60$		0			0
$61$	−31177.0			−1.07278			−0.536388	−	0.843971i	$-0.680212\pi$
$61$	−31177.0			−1.07278			−0.536388	+	0.843971i	$0.680212\pi$
$62$		0			0
$63$	10725.5	+	15983.5i	0.340461	+	0.507364i
$64$		0			0
$65$	−9620.07	−	23722.8i	−0.282420	−	0.696438i
$66$		0			0
$67$	−15756.9	+	15756.9i	−0.428830	+	0.428830i	−0.888230	−	0.459400i	$-0.848065\pi$
$67$	−15756.9	+	15756.9i	−0.428830	+	0.428830i	0.459400	+	0.888230i	$0.348065\pi$
$68$		0			0
$69$	−57961.0	−	5650.87i	−1.46559	−	0.142887i
$70$		0			0
$71$		−	75916.6i		−	1.78727i	−0.448791	−	0.893637i	$-0.648145\pi$
$71$		−	75916.6i		−	1.78727i	0.448791	−	0.893637i	$-0.351855\pi$
$72$		0			0
$73$	51080.6	+	51080.6i	1.12189	+	1.12189i	0.991458	+	0.130428i	$0.0416352\pi$
$73$	51080.6	+	51080.6i	1.12189	+	1.12189i	0.130428	+	0.991458i	$0.458365\pi$
$74$		0			0
$75$	5448.11	−	48408.3i	0.111839	−	0.993726i
$76$		0			0
$77$	−34514.5	−	34514.5i	−0.663399	−	0.663399i
$78$		0			0
$79$			42068.3i			0.758380i	0.925319	+	0.379190i	$0.123797\pi$
$79$			42068.3i			0.758380i	−0.925319	+	0.379190i	$0.876203\pi$
$80$		0			0
$81$	−54643.0	−	22381.4i	−0.925384	−	0.379031i
$82$		0			0
$83$	48969.9	−	48969.9i	0.780251	−	0.780251i	−0.199622	−	0.979873i	$-0.563971\pi$
$83$	48969.9	−	48969.9i	0.780251	−	0.780251i	0.979873	+	0.199622i	$0.0639714\pi$
$84$		0			0
$85$	−40948.7	−	100978.i	−0.614741	−	1.51593i
$86$		0			0
$87$	−3772.42	−	4587.46i	−0.0534345	−	0.0649791i
$88$		0			0
$89$	−21879.1			−0.292788			−0.146394	−	0.989226i	$-0.546767\pi$
$89$	−21879.1			−0.292788			−0.146394	+	0.989226i	$0.546767\pi$
$90$		0			0
$91$	−36273.8			−0.459187
$92$		0			0
$93$	72860.7	+	88602.4i	0.873546	+	1.06228i
$94$		0			0
$95$	−5584.36	+	13203.0i	−0.0634840	+	0.150094i
$96$		0			0
$97$	63524.7	−	63524.7i	0.685509	−	0.685509i	−0.275727	−	0.961236i	$-0.588919\pi$
$97$	63524.7	−	63524.7i	0.685509	−	0.685509i	0.961236	+	0.275727i	$0.0889186\pi$
$98$		0			0
$99$	146917.	+	28922.2i	1.50656	+	0.296581i
$100$		0			0
$101$			155948.i			1.52117i	0.649240	+	0.760584i	$0.275087\pi$
$101$			155948.i			1.52117i	−0.649240	+	0.760584i	$0.724913\pi$
$102$		0			0
$103$	−23215.6	−	23215.6i	−0.215619	−	0.215619i	0.591030	−	0.806649i	$-0.298721\pi$
$103$	−23215.6	−	23215.6i	−0.215619	−	0.215619i	−0.806649	+	0.591030i	$0.798721\pi$
$104$		0			0
$105$	−60665.3	−	32931.6i	−0.536992	−	0.291500i
$106$		0			0
$107$	52970.3	+	52970.3i	0.447273	+	0.447273i	0.894447	−	0.447174i	$-0.147569\pi$
$107$	52970.3	+	52970.3i	0.447273	+	0.447273i	−0.447174	+	0.894447i	$0.647569\pi$
$108$		0			0
$109$			164337.i			1.32485i	0.749127	+	0.662427i	$0.230473\pi$
$109$			164337.i			1.32485i	−0.749127	+	0.662427i	$0.769527\pi$
$110$		0			0
$111$	−133129.	−	12979.3i	−1.02557	−	0.0999872i
$112$		0			0
$113$	−83175.2	+	83175.2i	−0.612770	+	0.612770i	−0.943667	−	0.330897i	$-0.892649\pi$
$113$	−83175.2	+	83175.2i	−0.612770	+	0.612770i	0.330897	+	0.943667i	$0.392649\pi$
$114$		0			0
$115$	193532.	−	78481.0i	1.36461	−	0.553375i
$116$		0			0
$117$	92401.5	−	62005.0i	0.624043	−	0.418757i
$118$		0			0
$119$	−154403.			−0.999511
$120$		0			0
$121$	−218655.			−1.35767
$122$		0			0
$123$	17612.5	−	14483.3i	0.104968	−	0.0863188i
$124$		0			0
$125$	63231.9	+	162848.i	0.361960	+	0.932193i
$126$		0			0
$127$	24604.9	−	24604.9i	0.135367	−	0.135367i	−0.636177	−	0.771543i	$-0.719485\pi$
$127$	24604.9	−	24604.9i	0.135367	−	0.135367i	0.771543	+	0.636177i	$0.219485\pi$
$128$		0			0
$129$	7380.34	−	75700.2i	0.0390483	−	0.400518i
$130$		0			0
$131$			212325.i			1.08099i	0.841347	+	0.540496i	$0.181763\pi$
$131$			212325.i			1.08099i	−0.841347	+	0.540496i	$0.818237\pi$
$132$		0			0
$133$	14363.6	+	14363.6i	0.0704101	+	0.0704101i
$134$		0			0
$135$	210827.	−	19811.2i	0.995614	−	0.0935572i
$136$		0			0
$137$	26773.9	+	26773.9i	0.121874	+	0.121874i	0.765413	−	0.643539i	$-0.222535\pi$
$137$	26773.9	+	26773.9i	0.121874	+	0.121874i	−0.643539	+	0.765413i	$0.722535\pi$
$138$		0			0
$139$			180163.i			0.790913i	0.918485	+	0.395457i	$0.129414\pi$
$139$			180163.i			0.790913i	−0.918485	+	0.395457i	$0.870586\pi$
$140$		0			0
$141$	14895.4	−	152782.i	0.0630963	−	0.647179i
$142$		0			0
$143$	−199530.	+	199530.i	−0.815960	+	0.815960i
$144$		0			0
$145$	19616.6	+	8297.04i	0.0774824	+	0.0327720i
$146$		0			0
$147$	126813.	−	104282.i	0.484028	−	0.398032i
$148$		0			0
$149$	300303.			1.10814			0.554070	−	0.832470i	$-0.313074\pi$
$149$	300303.			1.10814			0.554070	+	0.832470i	$0.313074\pi$
$150$		0			0
$151$	−11066.3			−0.0394968			−0.0197484	−	0.999805i	$-0.506287\pi$
$151$	−11066.3			−0.0394968			−0.0197484	+	0.999805i	$0.506287\pi$
$152$		0			0
$153$	393315.	−	263930.i	1.35835	−	0.911506i
$154$		0			0
$155$	−378876.	−	160250.i	−1.26668	−	0.535757i
$156$		0			0
$157$	44512.4	−	44512.4i	0.144123	−	0.144123i	−0.631364	−	0.775487i	$-0.717505\pi$
$157$	44512.4	−	44512.4i	0.144123	−	0.144123i	0.775487	+	0.631364i	$0.217505\pi$
$158$		0			0
$159$	−115461.	−	11256.8i	−0.362195	−	0.0353120i
$160$		0			0
$161$		−	295924.i		−	0.899736i
$162$		0			0
$163$	−264018.	−	264018.i	−0.778330	−	0.778330i	0.201216	−	0.979547i	$-0.435511\pi$
$163$	−264018.	−	264018.i	−0.778330	−	0.778330i	−0.979547	+	0.201216i	$0.935511\pi$
$164$		0			0
$165$	−514846.	+	152554.i	−1.47220	+	0.436229i
$166$		0			0
$167$	−303339.	−	303339.i	−0.841660	−	0.841660i	0.147414	−	0.989075i	$-0.452905\pi$
$167$	−303339.	−	303339.i	−0.841660	−	0.841660i	−0.989075	+	0.147414i	$0.952905\pi$
$168$		0			0
$169$		−	161592.i		−	0.435213i
$170$		0			0
$171$	−61141.5	−	12036.3i	−0.159899	−	0.0314777i
$172$		0			0
$173$	125811.	−	125811.i	0.319596	−	0.319596i	−0.529016	−	0.848612i	$-0.677439\pi$
$173$	125811.	−	125811.i	0.319596	−	0.319596i	0.848612	+	0.529016i	$0.177439\pi$
$174$		0			0
$175$	247511.	+	3684.74i	0.610942	+	0.00909519i
$176$		0			0
$177$	−334811.	−	407148.i	−0.803280	−	0.976831i
$178$		0			0
$179$	−444862.			−1.03775			−0.518875	−	0.854850i	$-0.673649\pi$
$179$	−444862.			−1.03775			−0.518875	+	0.854850i	$0.673649\pi$
$180$		0			0
$181$	741760.			1.68293			0.841467	−	0.540308i	$-0.181692\pi$
$181$	741760.			1.68293			0.841467	+	0.540308i	$0.181692\pi$
$182$		0			0
$183$	308686.	+	375379.i	0.681381	+	0.828595i
$184$		0			0
$185$	444517.	−	180261.i	0.954903	−	0.387232i
$186$		0			0
$187$	−849318.	+	849318.i	−1.77610	+	1.77610i
$188$		0			0
$189$	86250.6	−	287392.i	0.175634	−	0.585222i
$190$		0			0
$191$		−	381675.i		−	0.757025i	−0.925596	−	0.378513i	$-0.876436\pi$
$191$		−	381675.i		−	0.757025i	0.925596	−	0.378513i	$-0.123564\pi$
$192$		0			0
$193$	−351676.	−	351676.i	−0.679594	−	0.679594i	0.280314	−	0.959908i	$-0.409561\pi$
$193$	−351676.	−	351676.i	−0.679594	−	0.679594i	−0.959908	+	0.280314i	$0.909561\pi$
$194$		0			0
$195$	−190379.	+	350710.i	−0.358537	+	0.660483i
$196$		0			0
$197$	766300.	+	766300.i	1.40680	+	1.40680i	0.775694	+	0.631109i	$0.217400\pi$
$197$	766300.	+	766300.i	1.40680	+	1.40680i	0.631109	+	0.775694i	$0.282600\pi$
$198$		0			0
$199$		−	536580.i		−	0.960509i	−0.877129	−	0.480255i	$-0.840544\pi$
$199$		−	536580.i		−	0.960509i	0.877129	−	0.480255i	$-0.159456\pi$
$200$		0			0
$201$	345729.	+	33706.7i	0.603595	+	0.0588472i
$202$		0			0
$203$	21340.9	−	21340.9i	0.0363474	−	0.0363474i
$204$		0			0
$205$	−31854.6	+	75313.3i	−0.0529404	+	0.125166i
$206$		0			0
$207$	505840.	+	753816.i	0.820516	+	1.22275i
$208$		0			0
$209$	158019.			0.250232
$210$		0			0
$211$	1.10664e6			1.71120			0.855602	−	0.517634i	$-0.173187\pi$
$211$	1.10664e6			1.71120			0.855602	+	0.517634i	$0.173187\pi$
$212$		0			0
$213$	−914057.	+	751659.i	−1.38046	+	1.13520i
$214$		0			0
$215$	102500.	+	252763.i	0.151227	+	0.372921i
$216$		0			0
$217$	−412180.	+	412180.i	−0.594207	+	0.594207i
$218$		0			0
$219$	109270.	−	1.12078e6i	0.153953	−	1.57910i
$220$		0			0
$221$			892612.i			1.22937i
$222$		0			0
$223$	−501399.	−	501399.i	−0.675183	−	0.675183i	0.283723	−	0.958906i	$-0.408430\pi$
$223$	−501399.	−	501399.i	−0.675183	−	0.675183i	−0.958906	+	0.283723i	$0.908430\pi$
$224$		0			0
$225$	−636791.	+	413699.i	−0.838573	+	0.544789i
$226$		0			0
$227$	−686298.	−	686298.i	−0.883992	−	0.883992i	0.109946	−	0.993938i	$-0.464932\pi$
$227$	−686298.	−	686298.i	−0.883992	−	0.883992i	−0.993938	+	0.109946i	$0.964932\pi$
$228$		0			0
$229$			1.02915e6i			1.29685i	0.761279	+	0.648424i	$0.224572\pi$
$229$			1.02915e6i			1.29685i	−0.761279	+	0.648424i	$0.775428\pi$
$230$		0			0
$231$	−73832.1	+	757295.i	−0.0910364	+	0.933760i
$232$		0			0
$233$	768347.	−	768347.i	0.927187	−	0.927187i	−0.0703361	−	0.997523i	$-0.522407\pi$
$233$	768347.	−	768347.i	0.927187	−	0.927187i	0.997523	+	0.0703361i	$0.0224072\pi$
$234$		0			0
$235$	206872.	+	510139.i	0.244361	+	0.602586i
$236$		0			0
$237$	506513.	−	416522.i	0.585760	−	0.481690i
$238$		0			0
$239$	518074.			0.586675			0.293337	−	0.956009i	$-0.405234\pi$
$239$	518074.			0.586675			0.293337	+	0.956009i	$0.405234\pi$
$240$		0			0
$241$	1.07418e6			1.19133			0.595666	−	0.803232i	$-0.296888\pi$
$241$	1.07418e6			1.19133			0.595666	+	0.803232i	$0.296888\pi$
$242$		0			0
$243$	271548.	+	879517.i	0.295006	+	0.955495i
$244$		0			0
$245$	−229358.	+	542269.i	−0.244118	+	0.577164i
$246$		0			0
$247$	83037.0	−	83037.0i	0.0866022	−	0.0866022i
$248$		0			0
$249$	−1.07447e6	−	104755.i	−1.09823	−	0.107072i
$250$		0			0
$251$		−	914663.i		−	0.916382i	−0.888854	−	0.458191i	$-0.848497\pi$
$251$		−	914663.i		−	0.916382i	0.888854	−	0.458191i	$-0.151503\pi$
$252$		0			0
$253$	−1.62778e6	−	1.62778e6i	−1.59880	−	1.59880i
$254$		0			0
$255$	−810367.	+	1.49283e6i	−0.780425	+	1.43767i
$256$		0			0
$257$	−101079.	−	101079.i	−0.0954619	−	0.0954619i	0.657763	−	0.753225i	$-0.271503\pi$
$257$	−101079.	−	101079.i	−0.0954619	−	0.0954619i	−0.753225	+	0.657763i	$0.771503\pi$
$258$		0			0
$259$		−	679698.i		−	0.629603i
$260$		0			0
$261$	−17883.1	+	90841.8i	−0.0162496	+	0.0825438i
$262$		0			0
$263$	8443.27	−	8443.27i	0.00752699	−	0.00752699i	−0.703333	−	0.710860i	$-0.748306\pi$
$263$	8443.27	−	8443.27i	0.00752699	−	0.00752699i	0.710860	+	0.703333i	$0.248306\pi$
$264$		0			0
$265$	385525.	−	156338.i	0.337239	−	0.136757i
$266$		0			0
$267$	216627.	+	263430.i	0.185966	+	0.226145i
$268$		0			0
$269$	630649.			0.531382			0.265691	−	0.964058i	$-0.414400\pi$
$269$	630649.			0.531382			0.265691	+	0.964058i	$0.414400\pi$
$270$		0			0
$271$	−458865.			−0.379544			−0.189772	−	0.981828i	$-0.560775\pi$
$271$	−458865.			−0.379544			−0.189772	+	0.981828i	$0.560775\pi$
$272$		0			0
$273$	359151.	+	436747.i	0.291656	+	0.354669i
$274$		0			0
$275$	1.38175e6	−	1.34121e6i	1.10178	−	1.06946i
$276$		0			0
$277$	358085.	−	358085.i	0.280405	−	0.280405i	−0.552865	−	0.833271i	$-0.686466\pi$
$277$	358085.	−	358085.i	0.280405	−	0.280405i	0.833271	+	0.552865i	$0.186466\pi$
$278$		0			0
$279$	345396.	−	1.75452e6i	0.265648	−	1.34943i
$280$		0			0
$281$		−	2.32732e6i		−	1.75829i	−0.476556	−	0.879144i	$-0.658115\pi$
$281$		−	2.32732e6i		−	1.75829i	0.476556	−	0.879144i	$-0.341885\pi$
$282$		0			0
$283$	−12977.6	−	12977.6i	−0.00963229	−	0.00963229i	0.702274	−	0.711907i	$-0.252168\pi$
$283$	−12977.6	−	12977.6i	−0.00963229	−	0.00963229i	−0.711907	+	0.702274i	$0.752168\pi$
$284$		0			0
$285$	214259.	−	63487.3i	0.156253	−	0.0462993i
$286$		0			0
$287$	81933.6	+	81933.6i	0.0587161	+	0.0587161i
$288$		0			0
$289$			2.37962e6i			1.67596i
$290$		0			0
$291$	−1.39382e6	−	135890.i	−0.964881	−	0.0940705i
$292$		0			0
$293$	−779591.	+	779591.i	−0.530515	+	0.530515i	−0.920726	−	0.390211i	$-0.872402\pi$
$293$	−779591.	+	779591.i	−0.530515	+	0.530515i	0.390211	+	0.920726i	$0.372402\pi$
$294$		0			0
$295$	1.74102e6	+	736383.i	1.16479	+	0.492661i
$296$		0			0
$297$	−1.10641e6	−	2.05529e6i	−0.727825	−	1.35201i
$298$		0			0
$299$	−1.71075e6			−1.10665
$300$		0			0
$301$	386492.			0.245881
$302$		0			0
$303$	1.87766e6	−	1.54406e6i	1.17492	−	0.966179i
$304$		0			0
$305$	−1.60517e6	−	678924.i	−0.988033	−	0.417899i
$306$		0			0
$307$	−1.17490e6	+	1.17490e6i	−0.711470	+	0.711470i	−0.966843	−	0.255373i	$-0.917802\pi$
$307$	−1.17490e6	+	1.17490e6i	−0.711470	+	0.711470i	0.255373	+	0.966843i	$0.417802\pi$
$308$		0			0
$309$	−49662.0	+	509383.i	−0.0295888	+	0.303493i
$310$		0			0
$311$			1.66861e6i			0.978258i	0.872211	+	0.489129i	$0.162685\pi$
$311$			1.66861e6i			0.978258i	−0.872211	+	0.489129i	$0.837315\pi$
$312$		0			0
$313$	−1.86555e6	−	1.86555e6i	−1.07633	−	1.07633i	−0.996835	−	0.0794979i	$-0.974668\pi$
$313$	−1.86555e6	−	1.86555e6i	−1.07633	−	1.07633i	−0.0794979	−	0.996835i	$-0.525332\pi$
$314$		0			0
$315$	204149.	+	1.05649e6i	0.115923	+	0.599912i
$316$		0			0
$317$	−449760.	−	449760.i	−0.251381	−	0.251381i	0.570156	−	0.821537i	$-0.306883\pi$
$317$	−449760.	−	449760.i	−0.251381	−	0.251381i	−0.821537	+	0.570156i	$0.806883\pi$
$318$		0			0
$319$		−	234779.i		−	0.129176i
$320$		0			0
$321$	113312.	−	1.16224e6i	0.0613781	−	0.629555i
$322$		0			0
$323$	353454.	−	353454.i	0.188507	−	0.188507i
$324$		0			0
$325$	21301.7	−	1.43088e6i	0.0111868	−	0.751440i
$326$		0			0
$327$	1.97866e6	−	1.62711e6i	1.02330	−	0.841489i
$328$		0			0
$329$	780039.			0.397307
$330$		0			0
$331$	−918132.			−0.460612			−0.230306	−	0.973118i	$-0.573973\pi$
$331$	−918132.			−0.460612			−0.230306	+	0.973118i	$0.573973\pi$
$332$		0			0
$333$	1.16185e6	+	1.73142e6i	0.574168	+	0.855640i
$334$		0			0
$335$	−1.15439e6	+	468128.i	−0.562005	+	0.227904i
$336$		0			0
$337$	−284329.	+	284329.i	−0.136379	+	0.136379i	−0.772001	−	0.635622i	$-0.780744\pi$
$337$	−284329.	+	284329.i	−0.136379	+	0.136379i	0.635622	+	0.772001i	$0.280744\pi$
$338$		0			0
$339$	1.82498e6	+	177925.i	0.862499	+	0.0840888i
$340$		0			0
$341$			4.53454e6i			2.11177i
$342$		0			0
$343$	1.53132e6	+	1.53132e6i	0.702800	+	0.702800i
$344$		0			0
$345$	−2.86111e6	−	1.55312e6i	−1.29416	−	0.702520i
$346$		0			0
$347$	2.36134e6	+	2.36134e6i	1.05277	+	1.05277i	0.998528	+	0.0542447i	$0.0172751\pi$
$347$	2.36134e6	+	2.36134e6i	1.05277	+	1.05277i	0.0542447	+	0.998528i	$0.482725\pi$
$348$		0			0
$349$			2.67825e6i			1.17703i	0.808487	+	0.588514i	$0.200287\pi$
$349$			2.67825e6i			1.17703i	−0.808487	+	0.588514i	$0.799713\pi$
$350$		0			0
$351$	−1.66143e6	−	498620.i	−0.719806	−	0.216024i
$352$		0			0
$353$	−2.48203e6	+	2.48203e6i	−1.06016	+	1.06016i	−0.0620850	+	0.998071i	$0.519775\pi$
$353$	−2.48203e6	+	2.48203e6i	−1.06016	+	1.06016i	−0.998071	+	0.0620850i	$0.980225\pi$
$354$		0			0
$355$	1.65320e6	−	3.90863e6i	0.696231	−	1.64609i
$356$		0			0
$357$	1.52876e6	+	1.85905e6i	0.634846	+	0.772006i
$358$		0			0
$359$	1.03055e6			0.422020			0.211010	−	0.977484i	$-0.432325\pi$
$359$	1.03055e6			0.422020			0.211010	+	0.977484i	$0.432325\pi$
$360$		0			0
$361$	2.41034e6			0.973441
$362$		0			0
$363$	2.16492e6	+	2.63266e6i	0.862334	+	1.04864i
$364$		0			0
$365$	1.51757e6	+	3.74228e6i	0.596233	+	1.47029i
$366$		0			0
$367$	−781513.	+	781513.i	−0.302880	+	0.302880i	−0.842140	−	0.539259i	$-0.818704\pi$
$367$	−781513.	+	781513.i	−0.302880	+	0.302880i	0.539259	+	0.842140i	$0.318704\pi$
$368$		0			0
$369$	−348766.	−	68658.1i	−0.133342	−	0.0262498i
$370$		0			0
$371$		−	589495.i		−	0.222354i
$372$		0			0
$373$	1.19110e6	+	1.19110e6i	0.443279	+	0.443279i	0.893112	−	0.449833i	$-0.148517\pi$
$373$	1.19110e6	+	1.19110e6i	0.443279	+	0.443279i	−0.449833	+	0.893112i	$0.648517\pi$
$374$		0			0
$375$	1.33466e6	−	2.37370e6i	0.490110	−	0.871661i
$376$		0			0
$377$	−123373.	−	123373.i	−0.0447062	−	0.0447062i
$378$		0			0
$379$		−	2.99522e6i		−	1.07110i	−0.844503	−	0.535551i	$-0.820104\pi$
$379$		−	2.99522e6i		−	1.07110i	0.844503	−	0.535551i	$-0.179896\pi$
$380$		0			0
$381$	−539866.	−	52633.9i	−0.190534	−	0.0185760i
$382$		0			0
$383$	72587.9	−	72587.9i	0.0252853	−	0.0252853i	−0.694351	−	0.719636i	$-0.744309\pi$
$383$	72587.9	−	72587.9i	0.0252853	−	0.0252853i	0.719636	+	0.694351i	$0.244309\pi$
$384$		0			0
$385$	−1.02540e6	−	2.52861e6i	−0.352567	−	0.869420i
$386$		0			0
$387$	−984524.	+	660654.i	−0.334156	+	0.224232i
$388$		0			0
$389$	−5.47068e6			−1.83302			−0.916510	−	0.400011i	$-0.869006\pi$
$389$	−5.47068e6			−1.83302			−0.916510	+	0.400011i	$0.869006\pi$
$390$		0			0
$391$	−7.28197e6			−2.40883
$392$		0			0
$393$	2.55645e6	−	2.10225e6i	0.834941	−	0.686599i
$394$		0			0
$395$	−916098.	+	2.16592e6i	−0.295426	+	0.698472i
$396$		0			0
$397$	957388.	−	957388.i	0.304868	−	0.304868i	−0.538047	−	0.842915i	$-0.680838\pi$
$397$	957388.	−	957388.i	0.304868	−	0.304868i	0.842915	+	0.538047i	$0.180838\pi$
$398$		0			0
$399$	30726.1	−	315158.i	0.00966218	−	0.0991050i
$400$		0			0
$401$		−	1.26667e6i		−	0.393370i	−0.980467	−	0.196685i	$-0.936982\pi$
$401$		−	1.26667e6i		−	0.393370i	0.980467	−	0.196685i	$-0.0630177\pi$
$402$		0			0
$403$	2.38284e6	+	2.38284e6i	0.730857	+	0.730857i
$404$		0			0
$405$	−2.32595e6	−	2.34226e6i	−0.704633	−	0.709572i
$406$		0			0
$407$	−3.73880e6	−	3.73880e6i	−1.11878	−	1.11878i
$408$		0			0
$409$			4.60839e6i			1.36220i	0.732190	+	0.681101i	$0.238498\pi$
$409$			4.60839e6i			1.36220i	−0.732190	+	0.681101i	$0.761502\pi$
$410$		0			0
$411$	57273.8	−	587457.i	0.0167244	−	0.171542i
$412$		0			0
$413$	1.89406e6	−	1.89406e6i	0.546410	−	0.546410i
$414$		0			0
$415$	3.58765e6	−	1.45486e6i	1.02256	−	0.414669i
$416$		0			0
$417$	2.16921e6	−	1.78381e6i	0.610888	−	0.502353i
$418$		0			0
$419$	2.24477e6			0.624651			0.312325	−	0.949975i	$-0.398892\pi$
$419$	2.24477e6			0.624651			0.312325	+	0.949975i	$0.398892\pi$
$420$		0			0
$421$	−688460.			−0.189310			−0.0946550	−	0.995510i	$-0.530175\pi$
$421$	−688460.			−0.189310			−0.0946550	+	0.995510i	$0.530175\pi$
$422$		0			0
$423$	−1.98702e6	+	1.33337e6i	−0.539947	+	0.362325i
$424$		0			0
$425$	90672.6	−	6.09065e6i	0.0243503	−	1.63565i
$426$		0			0
$427$	−1.74627e6	+	1.74627e6i	−0.463492	+	0.463492i
$428$		0			0
$429$	4.37797e6	+	426828.i	1.14850	+	0.111972i
$430$		0			0
$431$			937065.i			0.242983i	0.992592	+	0.121492i	$0.0387678\pi$
$431$			937065.i			0.242983i	−0.992592	+	0.121492i	$0.961232\pi$
$432$		0			0
$433$	−1.41482e6	−	1.41482e6i	−0.362645	−	0.362645i	0.502141	−	0.864786i	$-0.332546\pi$
$433$	−1.41482e6	−	1.41482e6i	−0.362645	−	0.362645i	−0.864786	+	0.502141i	$0.832546\pi$
$434$		0			0
$435$	−94327.2	−	318339.i	−0.0239009	−	0.0806615i
$436$		0			0
$437$	677419.	+	677419.i	0.169689	+	0.169689i
$438$		0			0
$439$			4.73461e6i			1.17253i	0.810120	+	0.586264i	$0.199402\pi$
$439$			4.73461e6i			1.17253i	−0.810120	+	0.586264i	$0.800598\pi$
$440$		0			0
$441$	−2.51118e6	−	494350.i	−0.614867	−	0.121043i
$442$		0			0
$443$	1.73457e6	−	1.73457e6i	0.419934	−	0.419934i	−0.465247	−	0.885181i	$-0.654034\pi$
$443$	1.73457e6	−	1.73457e6i	0.419934	−	0.419934i	0.885181	+	0.465247i	$0.154034\pi$
$444$		0			0
$445$	−1.12646e6	−	476449.i	−0.269660	−	0.114055i
$446$		0			0
$447$	−2.97334e6	−	3.61573e6i	−0.703842	−	0.855909i
$448$		0			0
$449$	4.89094e6			1.14492			0.572462	−	0.819931i	$-0.305988\pi$
$449$	4.89094e6			1.14492			0.572462	+	0.819931i	$0.305988\pi$
$450$		0			0
$451$	901379.			0.208673
$452$		0			0
$453$	109569.	+	133242.i	0.0250866	+	0.0305067i
$454$		0			0
$455$	−1.86759e6	−	789916.i	−0.422914	−	0.178876i
$456$		0			0
$457$	5.42002e6	−	5.42002e6i	1.21398	−	1.21398i	0.244268	−	0.969708i	$-0.421452\pi$
$457$	5.42002e6	−	5.42002e6i	1.21398	−	1.21398i	0.969708	−	0.244268i	$-0.0785477\pi$
$458$		0			0
$459$	−7.07204e6	−	2.12242e6i	−1.56680	−	0.470218i
$460$		0			0
$461$		−	5.42757e6i		−	1.18947i	−0.803922	−	0.594735i	$-0.797257\pi$
$461$		−	5.42757e6i		−	1.18947i	0.803922	−	0.594735i	$-0.202743\pi$
$462$		0			0
$463$	−2.02984e6	−	2.02984e6i	−0.440058	−	0.440058i	0.451974	−	0.892031i	$-0.350720\pi$
$463$	−2.02984e6	−	2.02984e6i	−0.440058	−	0.440058i	−0.892031	+	0.451974i	$0.850720\pi$
$464$		0			0
$465$	1.82184e6	+	6.14841e6i	0.390731	+	1.31865i
$466$		0			0
$467$	2.16522e6	+	2.16522e6i	0.459421	+	0.459421i	0.898465	−	0.439044i	$-0.144683\pi$
$467$	2.16522e6	+	2.16522e6i	0.459421	+	0.459421i	−0.439044	+	0.898465i	$0.644683\pi$
$468$		0			0
$469$			1.76514e6i			0.370551i
$470$		0			0
$471$	−976663.	−	95219.2i	−0.202858	−	0.0197775i
$472$		0			0
$473$	2.12597e6	−	2.12597e6i	0.436922	−	0.436922i
$474$		0			0
$475$	−575030.	+	558160.i	−0.116938	+	0.113508i
$476$		0			0
$477$	1.00766e6	+	1.50164e6i	0.202776	+	0.302183i
$478$		0			0
$479$	−5.20850e6			−1.03723			−0.518614	−	0.855009i	$-0.673552\pi$
$479$	−5.20850e6			−1.03723			−0.518614	+	0.855009i	$0.673552\pi$
$480$		0			0
$481$	−3.92938e6			−0.774392
$482$		0			0
$483$	−3.56300e6	+	2.92997e6i	−0.694941	+	0.571473i
$484$		0			0
$485$	4.65396e6	−	1.88727e6i	0.898397	−	0.364318i
$486$		0			0
$487$	446510.	−	446510.i	0.0853118	−	0.0853118i	−0.663163	−	0.748475i	$-0.730786\pi$
$487$	446510.	−	446510.i	0.0853118	−	0.0853118i	0.748475	+	0.663163i	$0.230786\pi$
$488$		0			0
$489$	−564777.	+	5.79291e6i	−0.106808	+	1.09553i
$490$		0			0
$491$			303583.i			0.0568295i	0.999596	+	0.0284148i	$0.00904592\pi$
$491$			303583.i			0.0568295i	−0.999596	+	0.0284148i	$0.990954\pi$
$492$		0			0
$493$	−525149.	−	525149.i	−0.0973118	−	0.0973118i
$494$		0			0
$495$	6.93434e6	+	4.68842e6i	1.27201	+	0.860030i
$496$		0			0
$497$	−4.25221e6	−	4.25221e6i	−0.772190	−	0.772190i
$498$		0			0
$499$		−	6.40003e6i		−	1.15062i	−0.817937	−	0.575308i	$-0.804882\pi$
$499$		−	6.40003e6i		−	1.15062i	0.817937	−	0.575308i	$-0.195118\pi$
$500$		0			0
$501$	−648891.	+	6.65567e6i	−0.115499	+	1.18467i
$502$		0			0
$503$	−5.22988e6	+	5.22988e6i	−0.921662	+	0.921662i	−0.997147	−	0.0754852i	$-0.975949\pi$
$503$	−5.22988e6	+	5.22988e6i	−0.921662	+	0.921662i	0.0754852	+	0.997147i	$0.475949\pi$
$504$		0			0
$505$	−3.39600e6	+	8.02912e6i	−0.592570	+	1.40100i
$506$		0			0
$507$	−1.94561e6	+	1.59994e6i	−0.336152	+	0.276429i
$508$		0			0
$509$	7.48590e6			1.28071			0.640353	−	0.768080i	$-0.278788\pi$
$509$	7.48590e6			1.28071			0.640353	+	0.768080i	$0.278788\pi$
$510$		0			0
$511$	5.72221e6			0.969419
$512$		0			0
$513$	460448.	+	855333.i	0.0772480	+	0.143497i
$514$		0			0
$515$	−689721.	−	1.70083e6i	−0.114592	−	0.282581i
$516$		0			0
$517$	4.29074e6	−	4.29074e6i	0.706001	−	0.706001i
$518$		0			0
$519$	−2.76046e6	−	269129.i	−0.449845	−	0.0438573i
$520$		0			0
$521$			1.59522e6i			0.257470i	0.991679	+	0.128735i	$0.0410917\pi$
$521$			1.59522e6i			0.257470i	−0.991679	+	0.128735i	$0.958908\pi$
$522$		0			0
$523$	1.71677e6	+	1.71677e6i	0.274447	+	0.274447i	0.830888	−	0.556440i	$-0.187833\pi$
$523$	1.71677e6	+	1.71677e6i	0.274447	+	0.274447i	−0.556440	+	0.830888i	$0.687833\pi$
$524$		0			0
$525$	−2.40627e6	−	3.01658e6i	−0.381018	−	0.477658i
$526$		0			0
$527$	1.01428e7	+	1.01428e7i	1.59085	+	1.59085i
$528$		0			0
$529$		−	7.52006e6i		−	1.16837i
$530$		0			0
$531$	−1.58717e6	+	8.06243e6i	−0.244280	+	1.24088i
$532$		0			0
$533$	473663.	−	473663.i	0.0722190	−	0.0722190i
$534$		0			0
$535$	1.57371e6	+	3.88072e6i	0.237706	+	0.586176i
$536$		0			0
$537$	4.40462e6	+	5.35626e6i	0.659133	+	0.801541i
$538$		0			0
$539$	6.49009e6			0.962230
$540$		0			0
$541$	−1.05415e6			−0.154849			−0.0774245	−	0.996998i	$-0.524670\pi$
$541$	−1.05415e6			−0.154849			−0.0774245	+	0.996998i	$0.524670\pi$
$542$		0			0
$543$	−7.34425e6	−	8.93099e6i	−1.06893	−	1.29987i
$544$		0			0
$545$	−3.57867e6	+	8.46100e6i	−0.516096	+	1.22020i
$546$		0			0
$547$	−7.50469e6	+	7.50469e6i	−1.07242	+	1.07242i	−0.0752551	+	0.997164i	$0.523977\pi$
$547$	−7.50469e6	+	7.50469e6i	−1.07242	+	1.07242i	−0.997164	+	0.0752551i	$0.976023\pi$
$548$		0			0
$549$	1.46333e6	−	7.43333e6i	0.207210	−	1.05257i
$550$		0			0
$551$			97706.1i			0.0137102i
$552$		0			0
$553$	2.35631e6	+	2.35631e6i	0.327657	+	0.327657i
$554$		0			0
$555$	−6.57160e6	−	3.56733e6i	−0.905604	−	0.491598i
$556$		0			0
$557$	−4.27281e6	−	4.27281e6i	−0.583546	−	0.583546i	0.352330	−	0.935876i	$-0.385390\pi$
$557$	−4.27281e6	−	4.27281e6i	−0.583546	−	0.583546i	−0.935876	+	0.352330i	$0.885390\pi$
$558$		0			0
$559$		−	2.23434e6i		−	0.302426i
$560$		0			0
$561$	1.86352e7	+	1.81683e6i	2.49993	+	0.243729i
$562$		0			0
$563$	6.78859e6	−	6.78859e6i	0.902628	−	0.902628i	−0.0930348	−	0.995663i	$-0.529657\pi$
$563$	6.78859e6	−	6.78859e6i	0.902628	−	0.902628i	0.995663	+	0.0930348i	$0.0296568\pi$
$564$		0			0
$565$	−6.09360e6	+	2.47108e6i	−0.803069	+	0.325661i
$566$		0			0
$567$	−4.31426e6	+	1.80702e6i	−0.563571	+	0.236051i
$568$		0			0
$569$	−8.49421e6			−1.09987			−0.549936	−	0.835207i	$-0.685348\pi$
$569$	−8.49421e6			−1.09987			−0.549936	+	0.835207i	$0.685348\pi$
$570$		0			0
$571$	1.25808e7			1.61480			0.807398	−	0.590007i	$-0.200875\pi$
$571$	1.25808e7			1.61480			0.807398	+	0.590007i	$0.200875\pi$
$572$		0			0
$573$	−4.59547e6	+	3.77901e6i	−0.584714	+	0.480829i
$574$		0			0
$575$	1.16732e7	+	173780.i	1.47238	+	0.0219195i
$576$		0			0
$577$	−4.93393e6	+	4.93393e6i	−0.616955	+	0.616955i	−0.944749	−	0.327794i	$-0.893695\pi$
$577$	−4.93393e6	+	4.93393e6i	−0.616955	+	0.616955i	0.327794	+	0.944749i	$0.393695\pi$
$578$		0			0
$579$	−752292.	+	7.71626e6i	−0.0932589	+	0.956556i
$580$		0			0
$581$		−	5.48577e6i		−	0.674213i
$582$		0			0
$583$	−3.24262e6	−	3.24262e6i	−0.395115	−	0.395115i
$584$		0			0
$585$	6.10761e6	−	1.18020e6i	0.737873	−	0.142582i
$586$		0			0
$587$	−1.05978e7	−	1.05978e7i	−1.26946	−	1.26946i	−0.946368	−	0.323091i	$-0.895278\pi$
$587$	−1.05978e7	−	1.05978e7i	−1.26946	−	1.26946i	−0.323091	−	0.946368i	$-0.604722\pi$
$588$		0			0
$589$		−	1.88710e6i		−	0.224134i
$590$		0			0
$591$	1.63924e6	−	1.68137e7i	0.193052	−	1.98013i
$592$		0			0
$593$	−410012.	+	410012.i	−0.0478807	+	0.0478807i	−0.730642	−	0.682761i	$-0.760779\pi$
$593$	−410012.	+	410012.i	−0.0478807	+	0.0478807i	0.682761	+	0.730642i	$0.260779\pi$
$594$		0			0
$595$	−7.94954e6	−	3.36235e6i	−0.920555	−	0.389359i
$596$		0			0
$597$	−6.46056e6	+	5.31273e6i	−0.741882	+	0.610073i
$598$		0			0
$599$	−3.14687e6			−0.358354			−0.179177	−	0.983817i	$-0.557343\pi$
$599$	−3.14687e6			−0.358354			−0.179177	+	0.983817i	$0.557343\pi$
$600$		0			0
$601$	4.12306e6			0.465622			0.232811	−	0.972522i	$-0.425208\pi$
$601$	4.12306e6			0.465622			0.232811	+	0.972522i	$0.425208\pi$
$602$		0			0
$603$	−3.01726e6	−	4.49641e6i	−0.337925	−	0.503584i
$604$		0			0
$605$	−1.12576e7	−	4.76152e6i	−1.25042	−	0.528880i
$606$		0			0
$607$	138597.	−	138597.i	0.0152680	−	0.0152680i	−0.699432	−	0.714700i	$-0.746563\pi$
$607$	138597.	−	138597.i	0.0152680	−	0.0152680i	0.714700	+	0.699432i	$0.246563\pi$
$608$		0			0
$609$	−468250.	−	45651.7i	−0.0511604	−	0.00498786i
$610$		0			0
$611$		−	4.50945e6i		−	0.488676i
$612$		0			0
$613$	2.87301e6	+	2.87301e6i	0.308806	+	0.308806i	0.844446	−	0.535640i	$-0.179930\pi$
$613$	2.87301e6	+	2.87301e6i	0.308806	+	0.308806i	−0.535640	+	0.844446i	$0.679930\pi$
$614$		0			0
$615$	1.22219e6	−	362147.i	0.130302	−	0.0386098i
$616$		0			0
$617$	6.00454e6	+	6.00454e6i	0.634990	+	0.634990i	0.949315	−	0.314325i	$-0.101778\pi$
$617$	6.00454e6	+	6.00454e6i	0.634990	+	0.634990i	−0.314325	+	0.949315i	$0.601778\pi$
$618$		0			0
$619$		−	1.13901e7i		−	1.19482i	−0.801937	−	0.597409i	$-0.796197\pi$
$619$		−	1.13901e7i		−	1.19482i	0.801937	−	0.597409i	$-0.203803\pi$
$620$		0			0
$621$	4.06777e6	−	1.35541e7i	0.423279	−	1.41039i
$622$		0			0
$623$	−1.22548e6	+	1.22548e6i	−0.126499	+	0.126499i
$624$		0			0
$625$	−290701.	+	9.76130e6i	−0.0297677	+	0.999557i
$626$		0			0
$627$	−1.56456e6	−	1.90259e6i	−0.158937	−	0.193275i
$628$		0			0
$629$	−1.67257e7			−1.68562
$630$		0			0
$631$	−2.66614e6			−0.266569			−0.133284	−	0.991078i	$-0.542552\pi$
$631$	−2.66614e6			−0.266569			−0.133284	+	0.991078i	$0.542552\pi$
$632$		0			0
$633$	−1.09570e7	−	1.33243e7i	−1.08688	−	1.32171i
$634$		0			0
$635$	1.80261e6	−	730995.i	0.177406	−	0.0719416i
$636$		0			0
$637$	3.41046e6	−	3.41046e6i	0.333015	−	0.333015i
$638$		0			0
$639$	1.81003e7	+	3.56324e6i	1.75362	+	0.345217i
$640$		0			0
$641$			6.50816e6i			0.625624i	0.949815	+	0.312812i	$0.101271\pi$
$641$			6.50816e6i			0.625624i	−0.949815	+	0.312812i	$0.898729\pi$
$642$		0			0
$643$	6.81712e6	+	6.81712e6i	0.650239	+	0.650239i	0.953051	−	0.302811i	$-0.0979252\pi$
$643$	6.81712e6	+	6.81712e6i	0.650239	+	0.650239i	−0.302811	+	0.953051i	$0.597925\pi$
$644$		0			0
$645$	2.02846e6	−	3.73676e6i	0.191985	−	0.353669i
$646$		0			0
$647$	4.91694e6	+	4.91694e6i	0.461779	+	0.461779i	0.899238	−	0.437459i	$-0.144122\pi$
$647$	4.91694e6	+	4.91694e6i	0.461779	+	0.461779i	−0.437459	+	0.899238i	$0.644122\pi$
$648$		0			0
$649$		−	2.08372e7i		−	1.94190i
$650$		0			0
$651$	9.04381e6	+	881721.i	0.836371	+	0.0815415i
$652$		0			0
$653$	−251758.	+	251758.i	−0.0231047	+	0.0231047i	−0.718565	−	0.695460i	$-0.755201\pi$
$653$	−251758.	+	251758.i	−0.0231047	+	0.0231047i	0.695460	+	0.718565i	$0.255201\pi$
$654$		0			0
$655$	−4.62368e6	+	1.09317e7i	−0.421100	+	0.995600i
$656$		0			0
$657$	−1.45764e7	+	9.78131e6i	−1.31745	+	0.884064i
$658$		0			0
$659$	1.12808e7			1.01187			0.505936	−	0.862571i	$-0.331147\pi$
$659$	1.12808e7			1.01187			0.505936	+	0.862571i	$0.331147\pi$
$660$		0			0
$661$	1.01880e6			0.0906950			0.0453475	−	0.998971i	$-0.485560\pi$
$661$	1.01880e6			0.0906950			0.0453475	+	0.998971i	$0.485560\pi$
$662$		0			0
$663$	1.07473e7	−	8.83784e6i	0.949544	−	0.780841i
$664$		0			0
$665$	426733.	+	1.05231e6i	0.0374199	+	0.0922763i
$666$		0			0
$667$	1.00649e6	−	1.00649e6i	0.0875977	−	0.0875977i
$668$		0			0
$669$	−1.07257e6	+	1.10014e7i	−0.0926536	+	0.950348i
$670$		0			0
$671$			1.92113e7i			1.64722i
$672$		0			0
$673$	1.76092e6	+	1.76092e6i	0.149865	+	0.149865i	0.778058	−	0.628193i	$-0.216205\pi$
$673$	1.76092e6	+	1.76092e6i	0.149865	+	0.149865i	−0.628193	+	0.778058i	$0.716205\pi$
$674$		0			0
$675$	1.12860e7	+	3.57106e6i	0.953411	+	0.301674i
$676$		0			0
$677$	−5.23077e6	−	5.23077e6i	−0.438626	−	0.438626i	0.452924	−	0.891549i	$-0.350381\pi$
$677$	−5.23077e6	−	5.23077e6i	−0.438626	−	0.438626i	−0.891549	+	0.452924i	$0.850381\pi$
$678$		0			0
$679$		−	7.11624e6i		−	0.592347i
$680$		0			0
$681$	−1.46810e6	+	1.50583e7i	−0.121308	+	1.24425i
$682$		0			0
$683$	−8.63973e6	+	8.63973e6i	−0.708677	+	0.708677i	−0.966257	−	0.257580i	$-0.917075\pi$
$683$	−8.63973e6	+	8.63973e6i	−0.708677	+	0.708677i	0.257580	+	0.966257i	$0.417075\pi$
$684$		0			0
$685$	795435.	+	1.96152e6i	0.0647707	+	0.159722i
$686$		0			0
$687$	1.23912e7	−	1.01897e7i	1.00166	−	0.823701i
$688$		0			0
$689$	−3.40791e6			−0.273489
$690$		0			0
$691$	−9.88818e6			−0.787809			−0.393905	−	0.919151i	$-0.628876\pi$
$691$	−9.88818e6			−0.787809			−0.393905	+	0.919151i	$0.628876\pi$
$692$		0			0
$693$	9.84906e6	−	6.60910e6i	0.779043	−	0.522769i
$694$		0			0
$695$	−3.92331e6	+	9.27584e6i	−0.308100	+	0.728435i
$696$		0			0
$697$	2.01619e6	−	2.01619e6i	0.157199	−	0.157199i
$698$		0			0
$699$	−1.68586e7	−	1.64362e6i	−1.30505	−	0.127235i
$700$		0			0
$701$		−	1.61068e6i		−	0.123798i	−0.998082	−	0.0618991i	$-0.980284\pi$
$701$		−	1.61068e6i		−	0.123798i	0.998082	−	0.0618991i	$-0.0197157\pi$
$702$		0			0
$703$	1.55594e6	+	1.55594e6i	0.118742	+	0.118742i
$704$		0			0
$705$	4.09395e6	−	7.54173e6i	0.310220	−	0.571476i
$706$		0			0
$707$	8.73491e6	+	8.73491e6i	0.657219	+	0.657219i
$708$		0			0
$709$			1.99678e7i			1.49182i	0.666049	+	0.745908i	$0.267984\pi$
$709$			1.99678e7i			1.49182i	−0.666049	+	0.745908i	$0.732016\pi$
$710$		0			0
$711$	−1.00301e7	−	1.97452e6i	−0.744099	−	0.146483i
$712$		0			0
$713$	−1.94393e7	+	1.94393e7i	−1.43205	+	1.43205i
$714$		0			0
$715$	−1.46180e7	+	5.92791e6i	−1.06936	+	0.433647i
$716$		0			0
$717$	−5.12951e6	−	6.23776e6i	−0.372630	−	0.453138i
$718$		0			0
$719$	8.21981e6			0.592979			0.296490	−	0.955036i	$-0.404184\pi$
$719$	8.21981e6			0.592979			0.296490	+	0.955036i	$0.404184\pi$
$720$		0			0
$721$	−2.60069e6			−0.186316
$722$		0			0
$723$	−1.06355e7	−	1.29334e7i	−0.756682	−	0.920166i
$724$		0			0
$725$	829294.	+	854359.i	0.0585954	+	0.0603664i
$726$		0			0
$727$	1.42367e7	−	1.42367e7i	0.999020	−	0.999020i	−0.000979495	−	1.00000i	$-0.500312\pi$
$727$	1.42367e7	−	1.42367e7i	0.999020	−	0.999020i	1.00000		0.000979495i	$0.000311783\pi$
$728$		0			0
$729$	7.90100e6	−	1.19777e7i	0.550634	−	0.834747i
$730$		0			0
$731$		−	9.51064e6i		−	0.658289i
$732$		0			0
$733$	−4.76397e6	−	4.76397e6i	−0.327499	−	0.327499i	0.524136	−	0.851635i	$-0.324388\pi$
$733$	−4.76397e6	−	4.76397e6i	−0.327499	−	0.327499i	−0.851635	+	0.524136i	$0.824388\pi$
$734$		0			0
$735$	8.79997e6	−	2.60753e6i	0.600845	−	0.178037i
$736$		0			0
$737$	9.70947e6	+	9.70947e6i	0.658456	+	0.658456i
$738$		0			0
$739$			1.49992e7i			1.01031i	0.863028	+	0.505157i	$0.168565\pi$
$739$			1.49992e7i			1.01031i	−0.863028	+	0.505157i	$0.831435\pi$
$740$		0			0
$741$	−1.82195e6	−	177629.i	−0.121896	−	0.0118842i
$742$		0			0
$743$	−6.28423e6	+	6.28423e6i	−0.417619	+	0.417619i	−0.884382	−	0.466764i	$-0.845420\pi$
$743$	−6.28423e6	+	6.28423e6i	−0.417619	+	0.417619i	0.466764	+	0.884382i	$0.345420\pi$
$744$		0			0
$745$	1.54614e7	+	6.53955e6i	1.02060	+	0.431675i
$746$		0			0
$747$	9.37715e6	+	1.39741e7i	0.614850	+	0.916266i
$748$		0			0
$749$	5.93390e6			0.386488
$750$		0			0
$751$	5.31885e6			0.344126			0.172063	−	0.985086i	$-0.444957\pi$
$751$	5.31885e6			0.344126			0.172063	+	0.985086i	$0.444957\pi$
$752$		0			0
$753$	−1.10128e7	+	9.05618e6i	−0.707799	+	0.582046i
$754$		0			0
$755$	−569759.	−	240986.i	−0.0363768	−	0.0153859i
$756$		0			0
$757$	1.38183e7	−	1.38183e7i	0.876423	−	0.876423i	−0.116740	−	0.993163i	$-0.537244\pi$
$757$	1.38183e7	−	1.38183e7i	0.876423	−	0.876423i	0.993163	+	0.116740i	$0.0372444\pi$
$758$		0			0
$759$	−3.48208e6	+	3.57157e7i	−0.219399	+	2.25037i
$760$		0			0
$761$			6.28201e6i			0.393221i	0.980482	+	0.196611i	$0.0629935\pi$
$761$			6.28201e6i			0.393221i	−0.980482	+	0.196611i	$0.937007\pi$
$762$		0			0
$763$	9.20475e6	+	9.20475e6i	0.572401	+	0.572401i
$764$		0			0
$765$	2.59976e7	−	5.02362e6i	1.60612	−	0.310358i
$766$		0			0
$767$	−1.09497e7	−	1.09497e7i	−0.672068	−	0.672068i
$768$		0			0
$769$			77953.3i			0.00475356i	0.999997	+	0.00237678i	$0.000756553\pi$
$769$			77953.3i			0.00475356i	−0.999997	+	0.00237678i	$0.999243\pi$
$770$		0			0
$771$	−216225.	+	2.21782e6i	−0.0131000	+	0.134366i
$772$		0			0
$773$	1.35614e7	−	1.35614e7i	0.816313	−	0.816313i	−0.169259	−	0.985572i	$-0.554137\pi$
$773$	1.35614e7	−	1.35614e7i	0.816313	−	0.816313i	0.985572	+	0.169259i	$0.0541374\pi$
$774$		0			0
$775$	−1.60170e7	−	1.65011e7i	−0.957917	−	0.986870i
$776$		0			0
$777$	−8.18375e6	+	6.72977e6i	−0.486295	+	0.399896i
$778$		0			0
$779$	−375120.			−0.0221476
$780$		0			0
$781$	−4.67800e7			−2.74431
$782$		0			0
$783$	1.27082e6	−	684117.i	0.0740765	−	0.0398773i
$784$		0			0
$785$	3.26108e6	−	1.32243e6i	0.188880	−	0.0765948i
$786$		0			0
$787$	2.89852e6	−	2.89852e6i	0.166817	−	0.166817i	−0.618762	−	0.785579i	$-0.712365\pi$
$787$	2.89852e6	−	2.89852e6i	0.166817	−	0.166817i	0.785579	+	0.618762i	$0.212365\pi$
$788$		0			0
$789$	−185257.	−	18061.5i	−0.0105945	−	0.00103291i
$790$		0			0
$791$			9.31755e6i			0.529494i
$792$		0			0
$793$	1.00953e7	+	1.00953e7i	0.570081	+	0.570081i
$794$		0			0
$795$	−5.69947e6	−	3.09390e6i	−0.319828	−	0.173616i
$796$		0			0
$797$	−1.24492e7	−	1.24492e7i	−0.694219	−	0.694219i	0.268939	−	0.963157i	$-0.413327\pi$
$797$	−1.24492e7	−	1.24492e7i	−0.694219	−	0.694219i	−0.963157	+	0.268939i	$0.913327\pi$
$798$		0			0
$799$		−	1.91949e7i		−	1.06370i
$800$		0			0
$801$	1.02692e6	−	5.21649e6i	0.0565529	−	0.287275i
$802$		0			0
$803$	3.14760e7	−	3.14760e7i	1.72262	−	1.72262i
$804$		0			0
$805$	6.44417e6	−	1.52359e7i	0.350491	−	0.828662i
$806$		0			0
$807$	−6.24413e6	−	7.59319e6i	−0.337511	−	0.410431i
$808$		0			0
$809$	4.88806e6			0.262582			0.131291	−	0.991344i	$-0.458088\pi$
$809$	4.88806e6			0.262582			0.131291	+	0.991344i	$0.458088\pi$
$810$		0			0
$811$	6.56543e6			0.350518			0.175259	−	0.984522i	$-0.443924\pi$
$811$	6.56543e6			0.350518			0.175259	+	0.984522i	$0.443924\pi$
$812$		0			0
$813$	4.54327e6	+	5.52486e6i	0.241070	+	0.293153i
$814$		0			0
$815$	−7.84378e6	−	1.93425e7i	−0.413649	−	1.02004i
$816$		0			0
$817$	−884747.	+	884747.i	−0.0463728	+	0.0463728i
$818$		0			0
$819$	1.70255e6	−	8.64855e6i	0.0886934	−	0.450540i
$820$		0			0
$821$		−	1.76992e7i		−	0.916424i	−0.888843	−	0.458212i	$-0.848490\pi$
$821$		−	1.76992e7i		−	0.916424i	0.888843	−	0.458212i	$-0.151510\pi$
$822$		0			0
$823$	1.74735e7	+	1.74735e7i	0.899249	+	0.899249i	0.995370	−	0.0961203i	$-0.0306434\pi$
$823$	1.74735e7	+	1.74735e7i	0.899249	+	0.899249i	−0.0961203	+	0.995370i	$0.530643\pi$
$824$		0			0
$825$	−2.98293e7	−	3.35714e6i	−1.52584	−	0.171725i
$826$		0			0
$827$	−1.27114e7	−	1.27114e7i	−0.646294	−	0.646294i	0.305801	−	0.952095i	$-0.401076\pi$
$827$	−1.27114e7	−	1.27114e7i	−0.646294	−	0.646294i	−0.952095	+	0.305801i	$0.901076\pi$
$828$		0			0
$829$			5.67658e6i			0.286880i	0.989659	+	0.143440i	$0.0458164\pi$
$829$			5.67658e6i			0.286880i	−0.989659	+	0.143440i	$0.954184\pi$
$830$		0			0
$831$	−7.85687e6	−	766001.i	−0.394682	−	0.0384793i
$832$		0			0
$833$	1.45169e7	−	1.45169e7i	0.724873	−	0.724873i
$834$		0			0
$835$	−9.01199e6	−	2.22233e7i	−0.447306	−	1.10304i
$836$		0			0
$837$	−2.45447e7	+	1.32131e7i	−1.21100	+	0.651914i
$838$		0			0
$839$	−3.51049e7			−1.72172			−0.860861	−	0.508841i	$-0.830074\pi$
$839$	−3.51049e7			−1.72172			−0.860861	+	0.508841i	$0.830074\pi$
$840$		0			0
$841$	−2.03660e7			−0.992922
$842$		0			0
$843$	−2.80215e7	+	2.30430e7i	−1.35807	+	1.11679i
$844$		0			0
$845$	3.51890e6	−	8.31968e6i	0.169537	−	0.400834i
$846$		0			0
$847$	−1.22472e7	+	1.22472e7i	−0.586581	+	0.586581i
$848$		0			0
$849$	−27761.3	+	284747.i	−0.00132181	+	0.0135578i
$850$		0			0
$851$		−	3.20561e7i		−	1.51735i
$852$		0			0
$853$	1.52150e7	+	1.52150e7i	0.715977	+	0.715977i	0.967779	−	0.251801i	$-0.0810230\pi$
$853$	1.52150e7	+	1.52150e7i	0.715977	+	0.715977i	−0.251801	+	0.967779i	$0.581023\pi$
$854$		0			0
$855$	−2.88581e6	−	1.95114e6i	−0.135006	−	0.0912797i
$856$		0			0
$857$	2.09661e7	+	2.09661e7i	0.975136	+	0.975136i	0.999698	−	0.0245623i	$-0.00781920\pi$
$857$	2.09661e7	+	2.09661e7i	0.975136	+	0.975136i	−0.0245623	+	0.999698i	$0.507819\pi$
$858$		0			0
$859$			2.09600e7i			0.969188i	0.874739	+	0.484594i	$0.161033\pi$
$859$			2.09600e7i			0.969188i	−0.874739	+	0.484594i	$0.838967\pi$
$860$		0			0
$861$	175269.	−	1.79774e6i	0.00805745	−	0.0826453i
$862$		0			0
$863$	733482.	−	733482.i	0.0335245	−	0.0335245i	−0.690146	−	0.723670i	$-0.742454\pi$
$863$	733482.	−	733482.i	0.0335245	−	0.0335245i	0.723670	+	0.690146i	$0.242454\pi$
$864$		0			0
$865$	9.21716e6	−	3.73774e6i	0.418848	−	0.169851i
$866$		0			0
$867$	2.86513e7	−	2.35609e7i	1.29448	−	1.06450i
$868$		0			0
$869$	2.59226e7			1.16447
$870$		0			0
$871$	1.02044e7			0.455766
$872$		0			0
$873$	1.21642e7	+	1.81274e7i	0.540192	+	0.805008i
$874$		0			0
$875$	1.26631e7	+	5.57963e6i	0.559138	+	0.246369i
$876$		0			0
$877$	3.51575e6	−	3.51575e6i	0.154354	−	0.154354i	−0.625705	−	0.780060i	$-0.715189\pi$
$877$	3.51575e6	−	3.51575e6i	0.154354	−	0.154354i	0.780060	+	0.625705i	$0.215189\pi$
$878$		0			0
$879$	1.71053e7	+	1.66767e6i	0.746721	+	0.0728011i
$880$		0			0
$881$			878251.i			0.0381223i	0.999818	+	0.0190611i	$0.00606772\pi$
$881$			878251.i			0.0381223i	−0.999818	+	0.0190611i	$0.993932\pi$
$882$		0			0
$883$	1.79607e7	+	1.79607e7i	0.775214	+	0.775214i	0.979013	−	0.203798i	$-0.0653287\pi$
$883$	1.79607e7	+	1.79607e7i	0.775214	+	0.775214i	−0.203798	+	0.979013i	$0.565329\pi$
$884$		0			0
$885$	−8.37177e6	−	2.82533e7i	−0.359302	−	1.21258i
$886$		0			0
$887$	−1.40908e7	−	1.40908e7i	−0.601349	−	0.601349i	0.339321	−	0.940670i	$-0.389803\pi$
$887$	−1.40908e7	−	1.40908e7i	−0.601349	−	0.601349i	−0.940670	+	0.339321i	$0.889803\pi$
$888$		0			0
$889$		−	2.75632e6i		−	0.116970i
$890$		0			0
$891$	−1.37915e7	+	3.36712e7i	−0.581991	+	1.42090i
$892$		0			0
$893$	−1.78564e6	+	1.78564e6i	−0.0749317	+	0.0749317i
$894$		0			0
$895$	−2.29041e7	−	9.68752e6i	−0.955773	−	0.404255i
$896$		0			0
$897$	1.69383e7	+	2.05979e7i	0.702894	+	0.854756i
$898$		0			0
$899$	−2.80379e6			−0.115703
$900$		0			0
$901$	−1.45060e7			−0.595302
$902$		0			0
$903$	−3.82670e6	−	4.65347e6i	−0.156173	−	0.189914i
$904$		0			0
$905$	3.81901e7	+	1.61529e7i	1.54999	+	0.655586i
$906$		0			0
$907$	5.21671e6	−	5.21671e6i	0.210561	−	0.210561i	−0.593945	−	0.804506i	$-0.702430\pi$
$907$	5.21671e6	−	5.21671e6i	0.210561	−	0.210561i	0.804506	+	0.593945i	$0.202430\pi$
$908$		0			0
$909$	−3.71818e7	−	7.31961e6i	−1.49252	−	0.293818i
$910$		0			0
$911$			2.36471e6i			0.0944021i	0.998885	+	0.0472010i	$0.0150301\pi$
$911$			2.36471e6i			0.0944021i	−0.998885	+	0.0472010i	$0.984970\pi$
$912$		0			0
$913$	−3.01754e7	−	3.01754e7i	−1.19805	−	1.19805i
$914$		0			0
$915$	7.71853e6	+	2.60488e7i	0.304777	+	1.02857i
$916$		0			0
$917$	1.18927e7	+	1.18927e7i	0.467041	+	0.467041i
$918$		0			0
$919$			1.72028e7i			0.671908i	0.941878	+	0.335954i	$0.109059\pi$
$919$			1.72028e7i			0.671908i	−0.941878	+	0.335954i	$0.890941\pi$
$920$		0			0
$921$	2.57790e7	+	2.51331e6i	1.00142	+	0.0976330i
$922$		0			0
$923$	−2.45823e7	+	2.45823e7i	−0.949770	+	0.949770i
$924$		0			0
$925$	2.68117e7	+	399151.i	1.03032	+	0.0153385i
$926$		0			0
$927$	6.62482e6	−	4.44551e6i	0.253206	−	0.169911i
$928$		0			0
$929$	3.23733e7			1.23069			0.615344	−	0.788258i	$-0.289017\pi$
$929$	3.23733e7			1.23069			0.615344	+	0.788258i	$0.289017\pi$
$930$		0			0
$931$	−2.70093e6			−0.102127
$932$		0			0
$933$	2.00905e7	−	1.65211e7i	0.755591	−	0.621347i
$934$		0			0
$935$	−6.22230e7	+	2.52327e7i	−2.32767	+	0.943918i
$936$		0			0
$937$	−1.53693e7	+	1.53693e7i	−0.571882	+	0.571882i	−0.932654	−	0.360772i	$-0.882513\pi$
$937$	−1.53693e7	+	1.53693e7i	−0.571882	+	0.571882i	0.360772	+	0.932654i	$0.382513\pi$
$938$		0			0
$939$	−3.99072e6	+	4.09328e7i	−0.147702	+	1.51498i
$940$		0			0
$941$			3.45303e7i			1.27124i	0.772003	+	0.635619i	$0.219255\pi$
$941$			3.45303e7i			1.27124i	−0.772003	+	0.635619i	$0.780745\pi$
$942$		0			0
$943$	3.86417e6	+	3.86417e6i	0.141507	+	0.141507i
$944$		0			0
$945$	1.06991e7	−	1.29184e7i	0.389733	−	0.470575i
$946$		0			0
$947$	2.20443e7	+	2.20443e7i	0.798769	+	0.798769i	0.982901	−	0.184132i	$-0.0589475\pi$
$947$	2.20443e7	+	2.20443e7i	0.798769	+	0.798769i	−0.184132	+	0.982901i	$0.558947\pi$
$948$		0			0
$949$		−	3.30805e7i		−	1.19236i
$950$		0			0
$951$	−962109.	+	9.86835e6i	−0.0344964	+	0.353829i
$952$		0			0
$953$	1.46652e7	−	1.46652e7i	0.523064	−	0.523064i	−0.395431	−	0.918495i	$-0.629405\pi$
$953$	1.46652e7	−	1.46652e7i	0.523064	−	0.523064i	0.918495	+	0.395431i	$0.129405\pi$
$954$		0			0
$955$	8.31153e6	−	1.96508e7i	0.294899	−	0.697225i
$956$		0			0
$957$	−2.82680e6	+	2.32457e6i	−0.0997736	+	0.0820471i
$958$		0			0
$959$	2.99930e6			0.105311
$960$		0			0
$961$	2.55234e7			0.891517
$962$		0			0
$963$	−1.51156e7	+	1.01432e7i	−0.525243	+	0.352458i
$964$		0			0
$965$	−1.04481e7	−	2.57646e7i	−0.361175	−	0.890646i
$966$		0			0
$967$	1.51230e6	−	1.51230e6i	0.0520081	−	0.0520081i	−0.680624	−	0.732633i	$-0.738291\pi$
$967$	1.51230e6	−	1.51230e6i	0.0520081	−	0.0520081i	0.732633	+	0.680624i	$0.238291\pi$
$968$		0			0
$969$	−7.75527e6	−	756095.i	−0.265331	−	0.0258683i
$970$		0			0
$971$		−	1.56209e6i		−	0.0531688i	−0.999647	−	0.0265844i	$-0.991537\pi$
$971$		−	1.56209e6i		−	0.0531688i	0.999647	−	0.0265844i	$-0.00846307\pi$
$972$		0			0
$973$	1.00912e7	+	1.00912e7i	0.341713	+	0.341713i
$974$		0			0
$975$	−1.74391e7	+	1.39108e7i	−0.587505	+	0.468641i
$976$		0			0
$977$	−2.74017e7	−	2.74017e7i	−0.918421	−	0.918421i	0.0784935	−	0.996915i	$-0.474989\pi$
$977$	−2.74017e7	−	2.74017e7i	−0.918421	−	0.918421i	−0.996915	+	0.0784935i	$0.974989\pi$
$978$		0			0
$979$			1.34819e7i			0.449568i
$980$		0			0
$981$	−3.91818e7	−	7.71333e6i	−1.29990	−	0.255899i
$982$		0			0
$983$	−1.94825e7	+	1.94825e7i	−0.643074	+	0.643074i	−0.951310	−	0.308236i	$-0.900261\pi$
$983$	−1.94825e7	+	1.94825e7i	−0.643074	+	0.643074i	0.308236	+	0.951310i	$0.400261\pi$
$984$		0			0
$985$	2.27663e7	+	5.61409e7i	0.747655	+	1.84369i
$986$		0			0
$987$	−7.72325e6	−	9.39188e6i	−0.252352	−	0.306874i
$988$		0			0
$989$	1.82278e7			0.592576
$990$		0			0
$991$	1.01093e7			0.326991			0.163495	−	0.986544i	$-0.447723\pi$
$991$	1.01093e7			0.326991			0.163495	+	0.986544i	$0.447723\pi$
$992$		0			0
$993$	9.09053e6	+	1.10546e7i	0.292561	+	0.355769i
$994$		0			0
$995$	1.16848e7	−	2.76262e7i	0.374166	−	0.884634i
$996$		0			0
$997$	−2.66908e6	+	2.66908e6i	−0.0850401	+	0.0850401i	−0.748347	−	0.663307i	$-0.769152\pi$
$997$	−2.66908e6	+	2.66908e6i	−0.0850401	+	0.0850401i	0.663307	+	0.748347i	$0.269152\pi$
$998$		0			0
$999$	9.34314e6	−	3.11319e7i	0.296196	−	0.986943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.6.i.a.53.4	yes	20
3.2	odd	2	inner	60.6.i.a.53.2	yes	20
5.2	odd	4	inner	60.6.i.a.17.2	✓	20
5.3	odd	4		300.6.i.d.257.9		20
5.4	even	2		300.6.i.d.293.7		20
15.2	even	4	inner	60.6.i.a.17.4	yes	20
15.8	even	4		300.6.i.d.257.7		20
15.14	odd	2		300.6.i.d.293.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.6.i.a.17.2	✓	20	5.2	odd	4	inner
60.6.i.a.17.4	yes	20	15.2	even	4	inner
60.6.i.a.53.2	yes	20	3.2	odd	2	inner
60.6.i.a.53.4	yes	20	1.1	even	1	trivial
300.6.i.d.257.7		20	15.8	even	4
300.6.i.d.257.9		20	5.3	odd	4
300.6.i.d.293.7		20	5.4	even	2
300.6.i.d.293.9		20	15.14	odd	2

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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	60.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.90111 - 12.0403i) q^{3} +(51.4858 + 21.7765i) q^{5} +(56.0116 - 56.0116i) q^{7} +(-46.9362 + 238.424i) q^{9} +O(q^{10})\)	\(q+(-9.90111 - 12.0403i) q^{3} +(51.4858 + 21.7765i) q^{5} +(56.0116 - 56.0116i) q^{7} +(-46.9362 + 238.424i) q^{9} -616.203i q^{11} +(-323.806 - 323.806i) q^{13} +(-247.572 - 835.514i) q^{15} +(-1378.31 - 1378.31i) q^{17} +256.440i q^{19} +(-1228.97 - 119.818i) q^{21} +(2641.63 - 2641.63i) q^{23} +(2176.57 + 2242.36i) q^{25} +(3335.41 - 1795.54i) q^{27} +381.009 q^{29} -7358.84 q^{31} +(-7419.24 + 6101.09i) q^{33} +(4103.54 - 1664.07i) q^{35} +(6067.48 - 6067.48i) q^{37} +(-692.674 + 7104.76i) q^{39} +1462.80i q^{41} +(3450.11 + 3450.11i) q^{43} +(-7608.58 + 11253.3i) q^{45} +(6963.19 + 6963.19i) q^{47} +10532.4i q^{49} +(-2948.43 + 30242.0i) q^{51} +(5262.26 - 5262.26i) q^{53} +(13418.7 - 31725.7i) q^{55} +(3087.61 - 2539.04i) q^{57} +33815.5 q^{59} -31177.0 q^{61} +(10725.5 + 15983.5i) q^{63} +(-9620.07 - 23722.8i) q^{65} +(-15756.9 + 15756.9i) q^{67} +(-57961.0 - 5650.87i) q^{69} -75916.6i q^{71} +(51080.6 + 51080.6i) q^{73} +(5448.11 - 48408.3i) q^{75} +(-34514.5 - 34514.5i) q^{77} +42068.3i q^{79} +(-54643.0 - 22381.4i) q^{81} +(48969.9 - 48969.9i) q^{83} +(-40948.7 - 100978. i) q^{85} +(-3772.42 - 4587.46i) q^{87} -21879.1 q^{89} -36273.8 q^{91} +(72860.7 + 88602.4i) q^{93} +(-5584.36 + 13203.0i) q^{95} +(63524.7 - 63524.7i) q^{97} +(146917. + 28922.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} + 76 q^{7}+O(q^{10}) \) 20 * q + 2 * q^3 + 76 * q^7	\( 20 q + 2 q^{3} + 76 q^{7} + 1068 q^{13} - 130 q^{15} + 2180 q^{21} + 4060 q^{25} + 1454 q^{27} - 4720 q^{31} - 460 q^{33} - 612 q^{37} - 24012 q^{43} - 18860 q^{45} - 31700 q^{51} + 19200 q^{55} + 33476 q^{57} + 59880 q^{61} + 67208 q^{63} - 80804 q^{67} - 56956 q^{73} - 102470 q^{75} - 9980 q^{81} + 239260 q^{85} + 71540 q^{87} + 218520 q^{91} + 307928 q^{93} - 151164 q^{97}+O(q^{100}) \) 20 * q + 2 * q^3 + 76 * q^7 + 1068 * q^13 - 130 * q^15 + 2180 * q^21 + 4060 * q^25 + 1454 * q^27 - 4720 * q^31 - 460 * q^33 - 612 * q^37 - 24012 * q^43 - 18860 * q^45 - 31700 * q^51 + 19200 * q^55 + 33476 * q^57 + 59880 * q^61 + 67208 * q^63 - 80804 * q^67 - 56956 * q^73 - 102470 * q^75 - 9980 * q^81 + 239260 * q^85 + 71540 * q^87 + 218520 * q^91 + 307928 * q^93 - 151164 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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