LMFDB - Embedded newform 450.6.f.e.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,6,Mod(107,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([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("450.107");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	450.f (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:	$72.1727189158$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3457x^{8} + 2937456x^{4} + 12960000 $ x^12 + 3457x^8 + 2937456x^4 + 12960000
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{4}\cdot 5^{8} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.3
Root			$4.70903 - 4.70903i$ of defining polynomial
Character	$\chi$	$=$	450.107
Dual form			450.6.f.e.143.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.82843 + 2.82843i) q^{2} -16.0000i q^{4} +(103.048 + 103.048i) q^{7} +(45.2548 + 45.2548i) q^{8} +O(q^{10})$	\(q+(-2.82843 + 2.82843i) q^{2} -16.0000i q^{4} +(103.048 + 103.048i) q^{7} +(45.2548 + 45.2548i) q^{8} -744.757i q^{11} +(-301.835 + 301.835i) q^{13} -582.927 q^{14} -256.000 q^{16} +(-566.318 + 566.318i) q^{17} +282.904i q^{19} +(2106.49 + 2106.49i) q^{22} +(3525.74 + 3525.74i) q^{23} -1707.44i q^{26} +(1648.77 - 1648.77i) q^{28} +6543.59 q^{29} -6418.84 q^{31} +(724.077 - 724.077i) q^{32} -3203.58i q^{34} +(-7026.43 - 7026.43i) q^{37} +(-800.174 - 800.174i) q^{38} -4019.24i q^{41} +(4303.95 - 4303.95i) q^{43} -11916.1 q^{44} -19944.6 q^{46} +(1270.82 - 1270.82i) q^{47} +4430.74i q^{49} +(4829.36 + 4829.36i) q^{52} +(452.023 + 452.023i) q^{53} +9326.83i q^{56} +(-18508.1 + 18508.1i) q^{58} +13652.9 q^{59} +27543.3 q^{61} +(18155.2 - 18155.2i) q^{62} +4096.00i q^{64} +(-24369.6 - 24369.6i) q^{67} +(9061.09 + 9061.09i) q^{68} +17922.9i q^{71} +(-1389.99 + 1389.99i) q^{73} +39747.5 q^{74} +4526.47 q^{76} +(76745.6 - 76745.6i) q^{77} +54864.2i q^{79} +(11368.1 + 11368.1i) q^{82} +(19422.4 + 19422.4i) q^{83} +24346.8i q^{86} +(33703.9 - 33703.9i) q^{88} +141941. q^{89} -62207.0 q^{91} +(56411.8 - 56411.8i) q^{92} +7188.87i q^{94} +(121179. + 121179. i) q^{97} +(-12532.0 - 12532.0i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 144 q^{7}+O(q^{10}) $ 12 * q - 144 * q^7	$ 12 q - 144 q^{7} + 276 q^{13} - 3072 q^{16} - 384 q^{22} - 2304 q^{28} - 58512 q^{31} - 25764 q^{37} - 16080 q^{43} - 60672 q^{46} - 4416 q^{52} - 23952 q^{58} - 145200 q^{61} - 33552 q^{67} + 158988 q^{73} - 86016 q^{76} + 75024 q^{82} - 6144 q^{88} - 465024 q^{91} + 631116 q^{97}+O(q^{100}) $ 12 * q - 144 * q^7 + 276 * q^13 - 3072 * q^16 - 384 * q^22 - 2304 * q^28 - 58512 * q^31 - 25764 * q^37 - 16080 * q^43 - 60672 * q^46 - 4416 * q^52 - 23952 * q^58 - 145200 * q^61 - 33552 * q^67 + 158988 * q^73 - 86016 * q^76 + 75024 * q^82 - 6144 * q^88 - 465024 * q^91 + 631116 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−2.82843	+	2.82843i	−0.500000	+	0.500000i
$2$	−2.82843	+	2.82843i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	16.0000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	103.048	+	103.048i	0.794866	+	0.794866i	0.982281	−	0.187415i	$-0.0600108\pi$
$7$	103.048	+	103.048i	0.794866	+	0.794866i	−0.187415	+	0.982281i	$0.560011\pi$
$8$	45.2548	+	45.2548i	0.250000	+	0.250000i
$9$		0			0
$10$		0			0
$11$		−	744.757i		−	1.85581i	−0.372820	−	0.927904i	$-0.621609\pi$
$11$		−	744.757i		−	1.85581i	0.372820	−	0.927904i	$-0.378391\pi$
$12$		0			0
$13$	−301.835	+	301.835i	−0.495349	+	0.495349i	−0.909987	−	0.414637i	$-0.863908\pi$
$13$	−301.835	+	301.835i	−0.495349	+	0.495349i	0.414637	+	0.909987i	$0.363908\pi$
$14$	−582.927			−0.794866
$15$		0			0
$16$	−256.000			−0.250000
$17$	−566.318	+	566.318i	−0.475268	+	0.475268i	−0.903614	−	0.428347i	$-0.859096\pi$
$17$	−566.318	+	566.318i	−0.475268	+	0.475268i	0.428347	+	0.903614i	$0.359096\pi$
$18$		0			0
$19$			282.904i			0.179786i	0.995951	+	0.0898929i	$0.0286525\pi$
$19$			282.904i			0.179786i	−0.995951	+	0.0898929i	$0.971348\pi$
$20$		0			0
$21$		0			0
$22$	2106.49	+	2106.49i	0.927904	+	0.927904i
$23$	3525.74	+	3525.74i	1.38973	+	1.38973i	0.825869	+	0.563861i	$0.190685\pi$
$23$	3525.74	+	3525.74i	1.38973	+	1.38973i	0.563861	+	0.825869i	$0.309315\pi$
$24$		0			0
$25$		0			0
$26$		−	1707.44i		−	0.495349i
$27$		0			0
$28$	1648.77	−	1648.77i	0.397433	−	0.397433i
$29$	6543.59			1.44485			0.722423	−	0.691452i	$-0.243029\pi$
$29$	6543.59			1.44485			0.722423	+	0.691452i	$0.243029\pi$
$30$		0			0
$31$	−6418.84			−1.19964			−0.599822	−	0.800133i	$-0.704762\pi$
$31$	−6418.84			−1.19964			−0.599822	+	0.800133i	$0.704762\pi$
$32$	724.077	−	724.077i	0.125000	−	0.125000i
$33$		0			0
$34$		−	3203.58i		−	0.475268i
$35$		0			0
$36$		0			0
$37$	−7026.43	−	7026.43i	−0.843782	−	0.843782i	0.145566	−	0.989349i	$-0.453500\pi$
$37$	−7026.43	−	7026.43i	−0.843782	−	0.843782i	−0.989349	+	0.145566i	$0.953500\pi$
$38$	−800.174	−	800.174i	−0.0898929	−	0.0898929i
$39$		0			0
$40$		0			0
$41$		−	4019.24i		−	0.373409i	−0.982416	−	0.186704i	$-0.940219\pi$
$41$		−	4019.24i		−	0.373409i	0.982416	−	0.186704i	$-0.0597806\pi$
$42$		0			0
$43$	4303.95	−	4303.95i	0.354974	−	0.354974i	−0.506983	−	0.861956i	$-0.669239\pi$
$43$	4303.95	−	4303.95i	0.354974	−	0.354974i	0.861956	+	0.506983i	$0.169239\pi$
$44$	−11916.1			−0.927904
$45$		0			0
$46$	−19944.6			−1.38973
$47$	1270.82	−	1270.82i	0.0839153	−	0.0839153i	−0.663903	−	0.747818i	$-0.731101\pi$
$47$	1270.82	−	1270.82i	0.0839153	−	0.0839153i	0.747818	+	0.663903i	$0.231101\pi$
$48$		0			0
$49$			4430.74i			0.263624i
$50$		0			0
$51$		0			0
$52$	4829.36	+	4829.36i	0.247675	+	0.247675i
$53$	452.023	+	452.023i	0.0221040	+	0.0221040i	0.718072	−	0.695968i	$-0.245025\pi$
$53$	452.023	+	452.023i	0.0221040	+	0.0221040i	−0.695968	+	0.718072i	$0.745025\pi$
$54$		0			0
$55$		0			0
$56$			9326.83i			0.397433i
$57$		0			0
$58$	−18508.1	+	18508.1i	−0.722423	+	0.722423i
$59$	13652.9			0.510616			0.255308	−	0.966860i	$-0.417823\pi$
$59$	13652.9			0.510616			0.255308	+	0.966860i	$0.417823\pi$
$60$		0			0
$61$	27543.3			0.947745			0.473873	−	0.880593i	$-0.342856\pi$
$61$	27543.3			0.947745			0.473873	+	0.880593i	$0.342856\pi$
$62$	18155.2	−	18155.2i	0.599822	−	0.599822i
$63$		0			0
$64$			4096.00i			0.125000i
$65$		0			0
$66$		0			0
$67$	−24369.6	−	24369.6i	−0.663226	−	0.663226i	0.292913	−	0.956139i	$-0.405375\pi$
$67$	−24369.6	−	24369.6i	−0.663226	−	0.663226i	−0.956139	+	0.292913i	$0.905375\pi$
$68$	9061.09	+	9061.09i	0.237634	+	0.237634i
$69$		0			0
$70$		0			0
$71$			17922.9i			0.421951i	0.977491	+	0.210976i	$0.0676641\pi$
$71$			17922.9i			0.421951i	−0.977491	+	0.210976i	$0.932336\pi$
$72$		0			0
$73$	−1389.99	+	1389.99i	−0.0305283	+	0.0305283i	−0.722206	−	0.691678i	$-0.756872\pi$
$73$	−1389.99	+	1389.99i	−0.0305283	+	0.0305283i	0.691678	+	0.722206i	$0.256872\pi$
$74$	39747.5			0.843782
$75$		0			0
$76$	4526.47			0.0898929
$77$	76745.6	−	76745.6i	1.47512	−	1.47512i
$78$		0			0
$79$			54864.2i			0.989056i	0.869162	+	0.494528i	$0.164659\pi$
$79$			54864.2i			0.989056i	−0.869162	+	0.494528i	$0.835341\pi$
$80$		0			0
$81$		0			0
$82$	11368.1	+	11368.1i	0.186704	+	0.186704i
$83$	19422.4	+	19422.4i	0.309463	+	0.309463i	0.844701	−	0.535238i	$-0.179778\pi$
$83$	19422.4	+	19422.4i	0.309463	+	0.309463i	−0.535238	+	0.844701i	$0.679778\pi$
$84$		0			0
$85$		0			0
$86$			24346.8i			0.354974i
$87$		0			0
$88$	33703.9	−	33703.9i	0.463952	−	0.463952i
$89$	141941.			1.89948			0.949739	−	0.313044i	$-0.101349\pi$
$89$	141941.			1.89948			0.949739	+	0.313044i	$0.101349\pi$
$90$		0			0
$91$	−62207.0			−0.787473
$92$	56411.8	−	56411.8i	0.694865	−	0.694865i
$93$		0			0
$94$			7188.87i			0.0839153i
$95$		0			0
$96$		0			0
$97$	121179.	+	121179.i	1.30767	+	1.30767i	0.923089	+	0.384585i	$0.125656\pi$
$97$	121179.	+	121179.i	1.30767	+	1.30767i	0.384585	+	0.923089i	$0.374344\pi$
$98$	−12532.0	−	12532.0i	−0.131812	−	0.131812i
$99$		0			0
$100$		0			0
$101$		−	89431.2i		−	0.872339i	−0.899864	−	0.436170i	$-0.856335\pi$
$101$		−	89431.2i		−	0.872339i	0.899864	−	0.436170i	$-0.143665\pi$
$102$		0			0
$103$	−34487.5	+	34487.5i	−0.320309	+	0.320309i	−0.848886	−	0.528577i	$-0.822726\pi$
$103$	−34487.5	+	34487.5i	−0.320309	+	0.320309i	0.528577	+	0.848886i	$0.322726\pi$
$104$	−27319.0			−0.247675
$105$		0			0
$106$	−2557.03			−0.0221040
$107$	−87052.5	+	87052.5i	−0.735059	+	0.735059i	−0.971617	−	0.236559i	$-0.923980\pi$
$107$	−87052.5	+	87052.5i	−0.735059	+	0.735059i	0.236559	+	0.971617i	$0.423980\pi$
$108$		0			0
$109$			213367.i			1.72013i	0.510185	+	0.860065i	$0.329577\pi$
$109$			213367.i			1.72013i	−0.510185	+	0.860065i	$0.670423\pi$
$110$		0			0
$111$		0			0
$112$	−26380.3	−	26380.3i	−0.198717	−	0.198717i
$113$	92875.0	+	92875.0i	0.684231	+	0.684231i	0.960951	−	0.276720i	$-0.0892473\pi$
$113$	92875.0	+	92875.0i	0.684231	+	0.684231i	−0.276720	+	0.960951i	$0.589247\pi$
$114$		0			0
$115$		0			0
$116$		−	104698.i		−	0.722423i
$117$		0			0
$118$	−38616.2	+	38616.2i	−0.255308	+	0.255308i
$119$	−116716.			−0.755548
$120$		0			0
$121$	−393612.			−2.44402
$122$	−77904.2	+	77904.2i	−0.473873	+	0.473873i
$123$		0			0
$124$			102701.i			0.599822i
$125$		0			0
$126$		0			0
$127$	128111.	+	128111.i	0.704817	+	0.704817i	0.965440	−	0.260624i	$-0.0839282\pi$
$127$	128111.	+	128111.i	0.704817	+	0.704817i	−0.260624	+	0.965440i	$0.583928\pi$
$128$	−11585.2	−	11585.2i	−0.0625000	−	0.0625000i
$129$		0			0
$130$		0			0
$131$			270354.i			1.37643i	0.725507	+	0.688215i	$0.241605\pi$
$131$			270354.i			1.37643i	−0.725507	+	0.688215i	$0.758395\pi$
$132$		0			0
$133$	−29152.7	+	29152.7i	−0.142906	+	0.142906i
$134$	137855.			0.663226
$135$		0			0
$136$	−51257.3			−0.237634
$137$	60081.8	−	60081.8i	0.273490	−	0.273490i	−0.557013	−	0.830504i	$-0.688053\pi$
$137$	60081.8	−	60081.8i	0.273490	−	0.273490i	0.830504	+	0.557013i	$0.188053\pi$
$138$		0			0
$139$		−	192670.i		−	0.845819i	−0.906172	−	0.422910i	$-0.861009\pi$
$139$		−	192670.i		−	0.845819i	0.906172	−	0.422910i	$-0.138991\pi$
$140$		0			0
$141$		0			0
$142$	−50693.6	−	50693.6i	−0.210976	−	0.210976i
$143$	224794.	+	224794.i	0.919273	+	0.919273i
$144$		0			0
$145$		0			0
$146$		−	7862.94i		−	0.0305283i
$147$		0			0
$148$	−112423.	+	112423.i	−0.421891	+	0.421891i
$149$	406382.			1.49958			0.749788	−	0.661678i	$-0.230155\pi$
$149$	406382.			1.49958			0.749788	+	0.661678i	$0.230155\pi$
$150$		0			0
$151$	211613.			0.755267			0.377634	−	0.925955i	$-0.376738\pi$
$151$	211613.			0.755267			0.377634	+	0.925955i	$0.376738\pi$
$152$	−12802.8	+	12802.8i	−0.0449464	+	0.0449464i
$153$		0			0
$154$			434139.i			1.47512i
$155$		0			0
$156$		0			0
$157$	297822.	+	297822.i	0.964292	+	0.964292i	0.999384	−	0.0350925i	$-0.0111726\pi$
$157$	297822.	+	297822.i	0.964292	+	0.964292i	−0.0350925	+	0.999384i	$0.511173\pi$
$158$	−155179.	−	155179.i	−0.494528	−	0.494528i
$159$		0			0
$160$		0			0
$161$			726640.i			2.20930i
$162$		0			0
$163$	−21493.5	+	21493.5i	−0.0633635	+	0.0633635i	−0.738078	−	0.674715i	$-0.764267\pi$
$163$	−21493.5	+	21493.5i	−0.0633635	+	0.0633635i	0.674715	+	0.738078i	$0.264267\pi$
$164$	−64307.9			−0.186704
$165$		0			0
$166$	−109870.			−0.309463
$167$	231934.	−	231934.i	0.643537	−	0.643537i	−0.307886	−	0.951423i	$-0.599622\pi$
$167$	231934.	−	231934.i	0.643537	−	0.643537i	0.951423	+	0.307886i	$0.0996216\pi$
$168$		0			0
$169$			189084.i			0.509258i
$170$		0			0
$171$		0			0
$172$	−68863.2	−	68863.2i	−0.177487	−	0.177487i
$173$	−428012.	−	428012.i	−1.08728	−	1.08728i	−0.995808	−	0.0914698i	$-0.970844\pi$
$173$	−428012.	−	428012.i	−1.08728	−	1.08728i	−0.0914698	−	0.995808i	$-0.529156\pi$
$174$		0			0
$175$		0			0
$176$			190658.i			0.463952i
$177$		0			0
$178$	−401471.	+	401471.i	−0.949739	+	0.949739i
$179$	242661.			0.566066			0.283033	−	0.959110i	$-0.408659\pi$
$179$	242661.			0.566066			0.283033	+	0.959110i	$0.408659\pi$
$180$		0			0
$181$	68244.2			0.154835			0.0774176	−	0.996999i	$-0.475333\pi$
$181$	68244.2			0.154835			0.0774176	+	0.996999i	$0.475333\pi$
$182$	175948.	−	175948.i	0.393736	−	0.393736i
$183$		0			0
$184$			319114.i			0.694865i
$185$		0			0
$186$		0			0
$187$	421769.	+	421769.i	0.882005	+	0.882005i
$188$	−20333.2	−	20333.2i	−0.0419576	−	0.0419576i
$189$		0			0
$190$		0			0
$191$			105778.i			0.209803i	0.994483	+	0.104901i	$0.0334527\pi$
$191$			105778.i			0.209803i	−0.994483	+	0.104901i	$0.966547\pi$
$192$		0			0
$193$	−27490.4	+	27490.4i	−0.0531236	+	0.0531236i	−0.733170	−	0.680046i	$-0.761960\pi$
$193$	−27490.4	+	27490.4i	−0.0531236	+	0.0531236i	0.680046	+	0.733170i	$0.261960\pi$
$194$	−685495.			−1.30767
$195$		0			0
$196$	70891.8			0.131812
$197$	−178152.	+	178152.i	−0.327059	+	0.327059i	−0.851467	−	0.524408i	$-0.824287\pi$
$197$	−178152.	+	178152.i	−0.327059	+	0.327059i	0.524408	+	0.851467i	$0.324287\pi$
$198$		0			0
$199$			757628.i			1.35620i	0.734970	+	0.678100i	$0.237196\pi$
$199$			757628.i			1.35620i	−0.734970	+	0.678100i	$0.762804\pi$
$200$		0			0
$201$		0			0
$202$	252950.	+	252950.i	0.436170	+	0.436170i
$203$	674304.	+	674304.i	1.14846	+	1.14846i
$204$		0			0
$205$		0			0
$206$		−	195091.i		−	0.320309i
$207$		0			0
$208$	77269.8	−	77269.8i	0.123837	−	0.123837i
$209$	210695.			0.333648
$210$		0			0
$211$	840932.			1.30033			0.650167	−	0.759791i	$-0.274699\pi$
$211$	840932.			1.30033			0.650167	+	0.759791i	$0.274699\pi$
$212$	7232.37	−	7232.37i	0.0110520	−	0.0110520i
$213$		0			0
$214$		−	492443.i		−	0.735059i
$215$		0			0
$216$		0			0
$217$	−661448.	−	661448.i	−0.953557	−	0.953557i
$218$	−603493.	−	603493.i	−0.860065	−	0.860065i
$219$		0			0
$220$		0			0
$221$		−	341870.i		−	0.470847i
$222$		0			0
$223$	−600800.	+	600800.i	−0.809036	+	0.809036i	−0.984488	−	0.175452i	$-0.943861\pi$
$223$	−600800.	+	600800.i	−0.809036	+	0.809036i	0.175452	+	0.984488i	$0.443861\pi$
$224$	149229.			0.198717
$225$		0			0
$226$	−525381.			−0.684231
$227$	−642116.	+	642116.i	−0.827082	+	0.827082i	−0.987112	−	0.160030i	$-0.948841\pi$
$227$	−642116.	+	642116.i	−0.827082	+	0.827082i	0.160030	+	0.987112i	$0.448841\pi$
$228$		0			0
$229$		−	217938.i		−	0.274628i	−0.990528	−	0.137314i	$-0.956153\pi$
$229$		−	217938.i		−	0.274628i	0.990528	−	0.137314i	$-0.0438469\pi$
$230$		0			0
$231$		0			0
$232$	296129.	+	296129.i	0.361211	+	0.361211i
$233$	63784.0	+	63784.0i	0.0769701	+	0.0769701i	0.744544	−	0.667574i	$-0.232667\pi$
$233$	63784.0	+	63784.0i	0.0769701	+	0.0769701i	−0.667574	+	0.744544i	$0.732667\pi$
$234$		0			0
$235$		0			0
$236$		−	218446.i		−	0.255308i
$237$		0			0
$238$	330122.	−	330122.i	0.377774	−	0.377774i
$239$	772095.			0.874331			0.437165	−	0.899381i	$-0.355982\pi$
$239$	772095.			0.874331			0.437165	+	0.899381i	$0.355982\pi$
$240$		0			0
$241$	−1.36558e6			−1.51451			−0.757257	−	0.653117i	$-0.773461\pi$
$241$	−1.36558e6			−1.51451			−0.757257	+	0.653117i	$0.773461\pi$
$242$	1.11330e6	−	1.11330e6i	1.22201	−	1.22201i
$243$		0			0
$244$		−	440693.i		−	0.473873i
$245$		0			0
$246$		0			0
$247$	−85390.4	−	85390.4i	−0.0890568	−	0.0890568i
$248$	−290484.	−	290484.i	−0.299911	−	0.299911i
$249$		0			0
$250$		0			0
$251$		−	782791.i		−	0.784263i	−0.919909	−	0.392131i	$-0.871738\pi$
$251$		−	782791.i		−	0.784263i	0.919909	−	0.392131i	$-0.128262\pi$
$252$		0			0
$253$	2.62582e6	−	2.62582e6i	2.57907	−	2.57907i
$254$	−724704.			−0.704817
$255$		0			0
$256$	65536.0			0.0625000
$257$	−1.31783e6	+	1.31783e6i	−1.24459	+	1.24459i	−0.286510	+	0.958077i	$0.592495\pi$
$257$	−1.31783e6	+	1.31783e6i	−1.24459	+	1.24459i	−0.958077	+	0.286510i	$0.907505\pi$
$258$		0			0
$259$		−	1.44812e6i		−	1.34139i
$260$		0			0
$261$		0			0
$262$	−764676.	−	764676.i	−0.688215	−	0.688215i
$263$	1.26266e6	+	1.26266e6i	1.12563	+	1.12563i	0.990879	+	0.134752i	$0.0430239\pi$
$263$	1.26266e6	+	1.26266e6i	1.12563	+	1.12563i	0.134752	+	0.990879i	$0.456976\pi$
$264$		0			0
$265$		0			0
$266$		−	164912.i		−	0.142906i
$267$		0			0
$268$	−389913.	+	389913.i	−0.331613	+	0.331613i
$269$	323403.			0.272498			0.136249	−	0.990675i	$-0.456495\pi$
$269$	323403.			0.272498			0.136249	+	0.990675i	$0.456495\pi$
$270$		0			0
$271$	1.17418e6			0.971203			0.485602	−	0.874180i	$-0.338601\pi$
$271$	1.17418e6			0.971203			0.485602	+	0.874180i	$0.338601\pi$
$272$	144977.	−	144977.i	0.118817	−	0.118817i
$273$		0			0
$274$			339874.i			0.273490i
$275$		0			0
$276$		0			0
$277$	182207.	+	182207.i	0.142681	+	0.142681i	0.774839	−	0.632158i	$-0.217831\pi$
$277$	182207.	+	182207.i	0.142681	+	0.142681i	−0.632158	+	0.774839i	$0.717831\pi$
$278$	544954.	+	544954.i	0.422910	+	0.422910i
$279$		0			0
$280$		0			0
$281$		−	464741.i		−	0.351111i	−0.984469	−	0.175556i	$-0.943828\pi$
$281$		−	464741.i		−	0.351111i	0.984469	−	0.175556i	$-0.0561722\pi$
$282$		0			0
$283$	−72230.5	+	72230.5i	−0.0536110	+	0.0536110i	−0.733404	−	0.679793i	$-0.762070\pi$
$283$	−72230.5	+	72230.5i	−0.0536110	+	0.0536110i	0.679793	+	0.733404i	$0.262070\pi$
$284$	286766.			0.210976
$285$		0			0
$286$	−1.27163e6			−0.919273
$287$	414174.	−	414174.i	0.296810	−	0.296810i
$288$		0			0
$289$			778424.i			0.548241i
$290$		0			0
$291$		0			0
$292$	22239.8	+	22239.8i	0.0152642	+	0.0152642i
$293$	−430913.	−	430913.i	−0.293238	−	0.293238i	0.545120	−	0.838358i	$-0.316484\pi$
$293$	−430913.	−	430913.i	−0.293238	−	0.293238i	−0.838358	+	0.545120i	$0.816484\pi$
$294$		0			0
$295$		0			0
$296$		−	635960.i		−	0.421891i
$297$		0			0
$298$	−1.14942e6	+	1.14942e6i	−0.749788	+	0.749788i
$299$	−2.12839e6			−1.37680
$300$		0			0
$301$	887026.			0.564313
$302$	−598533.	+	598533.i	−0.377634	+	0.377634i
$303$		0			0
$304$		−	72423.5i		−	0.0449464i
$305$		0			0
$306$		0			0
$307$	−520866.	−	520866.i	−0.315414	−	0.315414i	0.531589	−	0.847002i	$-0.321595\pi$
$307$	−520866.	−	520866.i	−0.315414	−	0.315414i	−0.847002	+	0.531589i	$0.821595\pi$
$308$	−1.22793e6	−	1.22793e6i	−0.737559	−	0.737559i
$309$		0			0
$310$		0			0
$311$		−	1.65179e6i		−	0.968396i	−0.874958	−	0.484198i	$-0.839111\pi$
$311$		−	1.65179e6i		−	0.968396i	0.874958	−	0.484198i	$-0.160889\pi$
$312$		0			0
$313$	−808852.	+	808852.i	−0.466668	+	0.466668i	−0.900833	−	0.434165i	$-0.857043\pi$
$313$	−808852.	+	808852.i	−0.466668	+	0.466668i	0.434165	+	0.900833i	$0.357043\pi$
$314$	−1.68474e6			−0.964292
$315$		0			0
$316$	877827.			0.494528
$317$	1.04885e6	−	1.04885e6i	0.586227	−	0.586227i	−0.350381	−	0.936607i	$-0.613948\pi$
$317$	1.04885e6	−	1.04885e6i	0.586227	−	0.586227i	0.936607	+	0.350381i	$0.113948\pi$
$318$		0			0
$319$		−	4.87339e6i		−	2.68135i
$320$		0			0
$321$		0			0
$322$	−2.05525e6	−	2.05525e6i	−1.10465	−	1.10465i
$323$	−160214.	−	160214.i	−0.0854464	−	0.0854464i
$324$		0			0
$325$		0			0
$326$		−	121586.i		−	0.0633635i
$327$		0			0
$328$	181890.	−	181890.i	0.0933522	−	0.0933522i
$329$	261912.			0.133403
$330$		0			0
$331$	772673.			0.387637			0.193819	−	0.981037i	$-0.437913\pi$
$331$	772673.			0.387637			0.193819	+	0.981037i	$0.437913\pi$
$332$	310759.	−	310759.i	0.154731	−	0.154731i
$333$		0			0
$334$			1.31202e6i			0.643537i
$335$		0			0
$336$		0			0
$337$	−485089.	−	485089.i	−0.232673	−	0.232673i	0.581134	−	0.813808i	$-0.302609\pi$
$337$	−485089.	−	485089.i	−0.232673	−	0.232673i	−0.813808	+	0.581134i	$0.802609\pi$
$338$	−534810.	−	534810.i	−0.254629	−	0.254629i
$339$		0			0
$340$		0			0
$341$			4.78048e6i			2.22631i
$342$		0			0
$343$	1.27535e6	−	1.27535e6i	0.585320	−	0.585320i
$344$	389549.			0.177487
$345$		0			0
$346$	2.42120e6			1.08728
$347$	1.31517e6	−	1.31517e6i	0.586352	−	0.586352i	−0.350289	−	0.936642i	$-0.613917\pi$
$347$	1.31517e6	−	1.31517e6i	0.586352	−	0.586352i	0.936642	+	0.350289i	$0.113917\pi$
$348$		0			0
$349$		−	4.36535e6i		−	1.91847i	−0.282604	−	0.959237i	$-0.591198\pi$
$349$		−	4.36535e6i		−	1.91847i	0.282604	−	0.959237i	$-0.408802\pi$
$350$		0			0
$351$		0			0
$352$	−539262.	−	539262.i	−0.231976	−	0.231976i
$353$	1.99522e6	+	1.99522e6i	0.852223	+	0.852223i	0.990407	−	0.138184i	$-0.0441265\pi$
$353$	1.99522e6	+	1.99522e6i	0.852223	+	0.852223i	−0.138184	+	0.990407i	$0.544127\pi$
$354$		0			0
$355$		0			0
$356$		−	2.27106e6i		−	0.949739i
$357$		0			0
$358$	−686348.	+	686348.i	−0.283033	+	0.283033i
$359$	1.45280e6			0.594934			0.297467	−	0.954732i	$-0.403858\pi$
$359$	1.45280e6			0.594934			0.297467	+	0.954732i	$0.403858\pi$
$360$		0			0
$361$	2.39606e6			0.967677
$362$	−193024.	+	193024.i	−0.0774176	+	0.0774176i
$363$		0			0
$364$			995312.i			0.393736i
$365$		0			0
$366$		0			0
$367$	−2.63291e6	−	2.63291e6i	−1.02040	−	1.02040i	−0.999787	−	0.0206148i	$-0.993438\pi$
$367$	−2.63291e6	−	2.63291e6i	−1.02040	−	1.02040i	−0.0206148	−	0.999787i	$-0.506562\pi$
$368$	−902589.	−	902589.i	−0.347433	−	0.347433i
$369$		0			0
$370$		0			0
$371$			93160.0i			0.0351394i
$372$		0			0
$373$	1.50759e6	−	1.50759e6i	0.561061	−	0.561061i	−0.368548	−	0.929609i	$-0.620145\pi$
$373$	1.50759e6	−	1.50759e6i	0.561061	−	0.561061i	0.929609	+	0.368548i	$0.120145\pi$
$374$	−2.38589e6			−0.882005
$375$		0			0
$376$	115022.			0.0419576
$377$	−1.97509e6	+	1.97509e6i	−0.715703	+	0.715703i
$378$		0			0
$379$		−	773746.i		−	0.276694i	−0.990384	−	0.138347i	$-0.955821\pi$
$379$		−	773746.i		−	0.276694i	0.990384	−	0.138347i	$-0.0441790\pi$
$380$		0			0
$381$		0			0
$382$	−299185.	−	299185.i	−0.104901	−	0.104901i
$383$	−2.82130e6	−	2.82130e6i	−0.982772	−	0.982772i	0.0170818	−	0.999854i	$-0.494562\pi$
$383$	−2.82130e6	−	2.82130e6i	−0.982772	−	0.982772i	−0.999854	+	0.0170818i	$0.994562\pi$
$384$		0			0
$385$		0			0
$386$		−	155509.i		−	0.0531236i
$387$		0			0
$388$	1.93887e6	−	1.93887e6i	0.653837	−	0.653837i
$389$	−2.37203e6			−0.794778			−0.397389	−	0.917650i	$-0.630084\pi$
$389$	−2.37203e6			−0.794778			−0.397389	+	0.917650i	$0.630084\pi$
$390$		0			0
$391$	−3.99338e6			−1.32099
$392$	−200512.	+	200512.i	−0.0659061	+	0.0659061i
$393$		0			0
$394$		−	1.00778e6i		−	0.327059i
$395$		0			0
$396$		0			0
$397$	1.98940e6	+	1.98940e6i	0.633498	+	0.633498i	0.948944	−	0.315446i	$-0.102154\pi$
$397$	1.98940e6	+	1.98940e6i	0.633498	+	0.633498i	−0.315446	+	0.948944i	$0.602154\pi$
$398$	−2.14290e6	−	2.14290e6i	−0.678100	−	0.678100i
$399$		0			0
$400$		0			0
$401$		−	868678.i		−	0.269773i	−0.990861	−	0.134886i	$-0.956933\pi$
$401$		−	868678.i		−	0.269773i	0.990861	−	0.134886i	$-0.0430669\pi$
$402$		0			0
$403$	1.93743e6	−	1.93743e6i	0.594243	−	0.594243i
$404$	−1.43090e6			−0.436170
$405$		0			0
$406$	−3.81444e6			−1.14846
$407$	−5.23298e6	+	5.23298e6i	−1.56590	+	1.56590i
$408$		0			0
$409$			1.60852e6i			0.475464i	0.971331	+	0.237732i	$0.0764040\pi$
$409$			1.60852e6i			0.475464i	−0.971331	+	0.237732i	$0.923596\pi$
$410$		0			0
$411$		0			0
$412$	551800.	+	551800.i	0.160154	+	0.160154i
$413$	1.40690e6	+	1.40690e6i	0.405871	+	0.405871i
$414$		0			0
$415$		0			0
$416$			437104.i			0.123837i
$417$		0			0
$418$	−595935.	+	595935.i	−0.166824	+	0.166824i
$419$	−386112.			−0.107443			−0.0537215	−	0.998556i	$-0.517108\pi$
$419$	−386112.			−0.107443			−0.0537215	+	0.998556i	$0.517108\pi$
$420$		0			0
$421$	5.36712e6			1.47583			0.737915	−	0.674894i	$-0.235811\pi$
$421$	5.36712e6			1.47583			0.737915	+	0.674894i	$0.235811\pi$
$422$	−2.37852e6	+	2.37852e6i	−0.650167	+	0.650167i
$423$		0			0
$424$			40912.4i			0.0110520i
$425$		0			0
$426$		0			0
$427$	2.83828e6	+	2.83828e6i	0.753330	+	0.753330i
$428$	1.39284e6	+	1.39284e6i	0.367529	+	0.367529i
$429$		0			0
$430$		0			0
$431$		−	3.40932e6i		−	0.884046i	−0.897004	−	0.442023i	$-0.854261\pi$
$431$		−	3.40932e6i		−	0.884046i	0.897004	−	0.442023i	$-0.145739\pi$
$432$		0			0
$433$	−2.74187e6	+	2.74187e6i	−0.702792	+	0.702792i	−0.965009	−	0.262217i	$-0.915546\pi$
$433$	−2.74187e6	+	2.74187e6i	−0.702792	+	0.702792i	0.262217	+	0.965009i	$0.415546\pi$
$434$	3.74172e6			0.953557
$435$		0			0
$436$	3.41387e6			0.860065
$437$	−997446.	+	997446.i	−0.249854	+	0.249854i
$438$		0			0
$439$			6.42105e6i			1.59017i	0.606495	+	0.795087i	$0.292575\pi$
$439$			6.42105e6i			1.59017i	−0.606495	+	0.795087i	$0.707425\pi$
$440$		0			0
$441$		0			0
$442$	966953.	+	966953.i	0.235424	+	0.235424i
$443$	2.88801e6	+	2.88801e6i	0.699180	+	0.699180i	0.964234	−	0.265054i	$-0.0853898\pi$
$443$	2.88801e6	+	2.88801e6i	0.699180	+	0.699180i	−0.265054	+	0.964234i	$0.585390\pi$
$444$		0			0
$445$		0			0
$446$		−	3.39864e6i		−	0.809036i
$447$		0			0
$448$	−422084.	+	422084.i	−0.0993583	+	0.0993583i
$449$	−2.70977e6			−0.634332			−0.317166	−	0.948370i	$-0.602731\pi$
$449$	−2.70977e6			−0.634332			−0.317166	+	0.948370i	$0.602731\pi$
$450$		0			0
$451$	−2.99336e6			−0.692974
$452$	1.48600e6	−	1.48600e6i	0.342116	−	0.342116i
$453$		0			0
$454$		−	3.63235e6i		−	0.827082i
$455$		0			0
$456$		0			0
$457$	2.63241e6	+	2.63241e6i	0.589607	+	0.589607i	0.937525	−	0.347918i	$-0.113111\pi$
$457$	2.63241e6	+	2.63241e6i	0.589607	+	0.589607i	−0.347918	+	0.937525i	$0.613111\pi$
$458$	616422.	+	616422.i	0.137314	+	0.137314i
$459$		0			0
$460$		0			0
$461$		−	4.96571e6i		−	1.08825i	−0.839004	−	0.544126i	$-0.816861\pi$
$461$		−	4.96571e6i		−	1.08825i	0.839004	−	0.544126i	$-0.183139\pi$
$462$		0			0
$463$	851371.	−	851371.i	0.184572	−	0.184572i	−0.608773	−	0.793345i	$-0.708338\pi$
$463$	851371.	−	851371.i	0.184572	−	0.184572i	0.793345	+	0.608773i	$0.208338\pi$
$464$	−1.67516e6			−0.361211
$465$		0			0
$466$	−360817.			−0.0769701
$467$	2.86333e6	−	2.86333e6i	0.607546	−	0.607546i	−0.334758	−	0.942304i	$-0.608654\pi$
$467$	2.86333e6	−	2.86333e6i	0.607546	−	0.607546i	0.942304	+	0.334758i	$0.108654\pi$
$468$		0			0
$469$		−	5.02247e6i		−	1.05435i
$470$		0			0
$471$		0			0
$472$	617859.	+	617859.i	0.127654	+	0.127654i
$473$	−3.20540e6	−	3.20540e6i	−0.658763	−	0.658763i
$474$		0			0
$475$		0			0
$476$			1.86745e6i			0.377774i
$477$		0			0
$478$	−2.18381e6	+	2.18381e6i	−0.437165	+	0.437165i
$479$	3.88850e6			0.774361			0.387180	−	0.922004i	$-0.373449\pi$
$479$	3.88850e6			0.774361			0.387180	+	0.922004i	$0.373449\pi$
$480$		0			0
$481$	4.24165e6			0.835934
$482$	3.86243e6	−	3.86243e6i	0.757257	−	0.757257i
$483$		0			0
$484$			6.29779e6i			1.22201i
$485$		0			0
$486$		0			0
$487$	−2.14170e6	−	2.14170e6i	−0.409200	−	0.409200i	0.472259	−	0.881460i	$-0.343439\pi$
$487$	−2.14170e6	−	2.14170e6i	−0.409200	−	0.409200i	−0.881460	+	0.472259i	$0.843439\pi$
$488$	1.24647e6	+	1.24647e6i	0.236936	+	0.236936i
$489$		0			0
$490$		0			0
$491$			7.55003e6i			1.41334i	0.707546	+	0.706668i	$0.249802\pi$
$491$			7.55003e6i			1.41334i	−0.707546	+	0.706668i	$0.750198\pi$
$492$		0			0
$493$	−3.70576e6	+	3.70576e6i	−0.686688	+	0.686688i
$494$	483041.			0.0890568
$495$		0			0
$496$	1.64322e6			0.299911
$497$	−1.84692e6	+	1.84692e6i	−0.335395	+	0.335395i
$498$		0			0
$499$			521365.i			0.0937326i	0.998901	+	0.0468663i	$0.0149235\pi$
$499$			521365.i			0.0937326i	−0.998901	+	0.0468663i	$0.985077\pi$
$500$		0			0
$501$		0			0
$502$	2.21407e6	+	2.21407e6i	0.392131	+	0.392131i
$503$	−5.01780e6	−	5.01780e6i	−0.884287	−	0.884287i	0.109680	−	0.993967i	$-0.465017\pi$
$503$	−5.01780e6	−	5.01780e6i	−0.884287	−	0.884287i	−0.993967	+	0.109680i	$0.965017\pi$
$504$		0			0
$505$		0			0
$506$			1.48539e7i			2.57907i
$507$		0			0
$508$	2.04977e6	−	2.04977e6i	0.352408	−	0.352408i
$509$	284518.			0.0486761			0.0243380	−	0.999704i	$-0.492252\pi$
$509$	284518.			0.0486761			0.0243380	+	0.999704i	$0.492252\pi$
$510$		0			0
$511$	−286470.			−0.0485319
$512$	−185364.	+	185364.i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	7.45475e6i		−	1.24459i
$515$		0			0
$516$		0			0
$517$	−946455.	−	946455.i	−0.155731	−	0.155731i
$518$	4.09590e6	+	4.09590e6i	0.670694	+	0.670694i
$519$		0			0
$520$		0			0
$521$			3.00835e6i			0.485550i	0.970083	+	0.242775i	$0.0780576\pi$
$521$			3.00835e6i			0.485550i	−0.970083	+	0.242775i	$0.921942\pi$
$522$		0			0
$523$	395738.	−	395738.i	0.0632635	−	0.0632635i	−0.674767	−	0.738031i	$-0.735756\pi$
$523$	395738.	−	395738.i	0.0632635	−	0.0632635i	0.738031	+	0.674767i	$0.235756\pi$
$524$	4.32566e6			0.688215
$525$		0			0
$526$	−7.14267e6			−1.12563
$527$	3.63511e6	−	3.63511e6i	0.570152	−	0.570152i
$528$		0			0
$529$			1.84253e7i			2.86270i
$530$		0			0
$531$		0			0
$532$	466443.	+	466443.i	0.0714528	+	0.0714528i
$533$	1.21315e6	+	1.21315e6i	0.184968	+	0.184968i
$534$		0			0
$535$		0			0
$536$		−	2.20568e6i		−	0.331613i
$537$		0			0
$538$	−914721.	+	914721.i	−0.136249	+	0.136249i
$539$	3.29982e6			0.489236
$540$		0			0
$541$	−1.89254e6			−0.278004			−0.139002	−	0.990292i	$-0.544389\pi$
$541$	−1.89254e6			−0.278004			−0.139002	+	0.990292i	$0.544389\pi$
$542$	−3.32107e6	+	3.32107e6i	−0.485602	+	0.485602i
$543$		0			0
$544$			820116.i			0.118817i
$545$		0			0
$546$		0			0
$547$	−5.48168e6	−	5.48168e6i	−0.783331	−	0.783331i	0.197060	−	0.980391i	$-0.436861\pi$
$547$	−5.48168e6	−	5.48168e6i	−0.783331	−	0.783331i	−0.980391	+	0.197060i	$0.936861\pi$
$548$	−961310.	−	961310.i	−0.136745	−	0.136745i
$549$		0			0
$550$		0			0
$551$			1.85121e6i			0.259763i
$552$		0			0
$553$	−5.65364e6	+	5.65364e6i	−0.786168	+	0.786168i
$554$	−1.03072e6			−0.142681
$555$		0			0
$556$	−3.08272e6			−0.422910
$557$	881422.	−	881422.i	0.120378	−	0.120378i	−0.644352	−	0.764729i	$-0.722873\pi$
$557$	881422.	−	881422.i	0.120378	−	0.120378i	0.764729	+	0.644352i	$0.222873\pi$
$558$		0			0
$559$			2.59817e6i			0.351672i
$560$		0			0
$561$		0			0
$562$	1.31449e6	+	1.31449e6i	0.175556	+	0.175556i
$563$	−4.65833e6	−	4.65833e6i	−0.619382	−	0.619382i	0.325991	−	0.945373i	$-0.394302\pi$
$563$	−4.65833e6	−	4.65833e6i	−0.619382	−	0.619382i	−0.945373	+	0.325991i	$0.894302\pi$
$564$		0			0
$565$		0			0
$566$		−	408597.i		−	0.0536110i
$567$		0			0
$568$	−811097.	+	811097.i	−0.105488	+	0.105488i
$569$	−5.23579e6			−0.677957			−0.338978	−	0.940794i	$-0.610081\pi$
$569$	−5.23579e6			−0.677957			−0.338978	+	0.940794i	$0.610081\pi$
$570$		0			0
$571$	−1.08355e7			−1.39078			−0.695392	−	0.718630i	$-0.744769\pi$
$571$	−1.08355e7			−1.39078			−0.695392	+	0.718630i	$0.744769\pi$
$572$	3.59670e6	−	3.59670e6i	0.459636	−	0.459636i
$573$		0			0
$574$			2.34292e6i			0.296810i
$575$		0			0
$576$		0			0
$577$	3.55499e6	+	3.55499e6i	0.444528	+	0.444528i	0.893530	−	0.449003i	$-0.148221\pi$
$577$	3.55499e6	+	3.55499e6i	0.444528	+	0.444528i	−0.449003	+	0.893530i	$0.648221\pi$
$578$	−2.20172e6	−	2.20172e6i	−0.274121	−	0.274121i
$579$		0			0
$580$		0			0
$581$			4.00288e6i			0.491963i
$582$		0			0
$583$	336647.	−	336647.i	0.0410208	−	0.0410208i
$584$	−125807.			−0.0152642
$585$		0			0
$586$	2.43761e6			0.293238
$587$	9.52451e6	−	9.52451e6i	1.14090	−	1.14090i	0.152614	−	0.988286i	$-0.451231\pi$
$587$	9.52451e6	−	9.52451e6i	1.14090	−	1.14090i	0.988286	−	0.152614i	$-0.0487690\pi$
$588$		0			0
$589$		−	1.81592e6i		−	0.215679i
$590$		0			0
$591$		0			0
$592$	1.79877e6	+	1.79877e6i	0.210946	+	0.210946i
$593$	6.05271e6	+	6.05271e6i	0.706827	+	0.706827i	0.965867	−	0.259040i	$-0.0834061\pi$
$593$	6.05271e6	+	6.05271e6i	0.706827	+	0.706827i	−0.259040	+	0.965867i	$0.583406\pi$
$594$		0			0
$595$		0			0
$596$		−	6.50211e6i		−	0.749788i
$597$		0			0
$598$	6.01998e6	−	6.01998e6i	0.688402	−	0.688402i
$599$	1.13352e7			1.29081			0.645407	−	0.763838i	$-0.276688\pi$
$599$	1.13352e7			1.29081			0.645407	+	0.763838i	$0.276688\pi$
$600$		0			0
$601$	−1.33968e7			−1.51292			−0.756459	−	0.654041i	$-0.773072\pi$
$601$	−1.33968e7			−1.51292			−0.756459	+	0.654041i	$0.773072\pi$
$602$	−2.50889e6	+	2.50889e6i	−0.282157	+	0.282157i
$603$		0			0
$604$		−	3.38581e6i		−	0.377634i
$605$		0			0
$606$		0			0
$607$	−1.22734e6	−	1.22734e6i	−0.135205	−	0.135205i	0.636265	−	0.771470i	$-0.280478\pi$
$607$	−1.22734e6	−	1.22734e6i	−0.135205	−	0.135205i	−0.771470	+	0.636265i	$0.780478\pi$
$608$	204844.	+	204844.i	0.0224732	+	0.0224732i
$609$		0			0
$610$		0			0
$611$			767159.i			0.0831347i
$612$		0			0
$613$	−8.42422e6	+	8.42422e6i	−0.905479	+	0.905479i	−0.995903	−	0.0904240i	$-0.971178\pi$
$613$	−8.42422e6	+	8.42422e6i	−0.905479	+	0.905479i	0.0904240	+	0.995903i	$0.471178\pi$
$614$	2.94646e6			0.315414
$615$		0			0
$616$	6.94622e6			0.737559
$617$	608492.	−	608492.i	0.0643491	−	0.0643491i	−0.674200	−	0.738549i	$-0.735511\pi$
$617$	608492.	−	608492.i	0.0643491	−	0.0643491i	0.738549	+	0.674200i	$0.235511\pi$
$618$		0			0
$619$			4.53768e6i			0.476001i	0.971265	+	0.238000i	$0.0764920\pi$
$619$			4.53768e6i			0.476001i	−0.971265	+	0.238000i	$0.923508\pi$
$620$		0			0
$621$		0			0
$622$	4.67196e6	+	4.67196e6i	0.484198	+	0.484198i
$623$	1.46268e7	+	1.46268e7i	1.50983	+	1.50983i
$624$		0			0
$625$		0			0
$626$		−	4.57556e6i		−	0.466668i
$627$		0			0
$628$	4.76516e6	−	4.76516e6i	0.482146	−	0.482146i
$629$	7.95839e6			0.802045
$630$		0			0
$631$	4.73983e6			0.473903			0.236952	−	0.971521i	$-0.423852\pi$
$631$	4.73983e6			0.473903			0.236952	+	0.971521i	$0.423852\pi$
$632$	−2.48287e6	+	2.48287e6i	−0.247264	+	0.247264i
$633$		0			0
$634$			5.93320e6i			0.586227i
$635$		0			0
$636$		0			0
$637$	−1.33735e6	−	1.33735e6i	−0.130586	−	0.130586i
$638$	1.37840e7	+	1.37840e7i	1.34068	+	1.34068i
$639$		0			0
$640$		0			0
$641$		−	8.51535e6i		−	0.818573i	−0.912406	−	0.409287i	$-0.865778\pi$
$641$		−	8.51535e6i		−	0.818573i	0.912406	−	0.409287i	$-0.134222\pi$
$642$		0			0
$643$	6.83215e6	−	6.83215e6i	0.651673	−	0.651673i	−0.301722	−	0.953396i	$-0.597562\pi$
$643$	6.83215e6	−	6.83215e6i	0.651673	−	0.651673i	0.953396	+	0.301722i	$0.0975616\pi$
$644$	1.16262e7			1.10465
$645$		0			0
$646$	906306.			0.0854464
$647$	7.55983e6	−	7.55983e6i	0.709989	−	0.709989i	−0.256544	−	0.966533i	$-0.582584\pi$
$647$	7.55983e6	−	7.55983e6i	0.709989	−	0.709989i	0.966533	+	0.256544i	$0.0825839\pi$
$648$		0			0
$649$		−	1.01681e7i		−	0.947605i
$650$		0			0
$651$		0			0
$652$	343897.	+	343897.i	0.0316817	+	0.0316817i
$653$	−8.56784e6	−	8.56784e6i	−0.786300	−	0.786300i	0.194586	−	0.980886i	$-0.437664\pi$
$653$	−8.56784e6	−	8.56784e6i	−0.786300	−	0.786300i	−0.980886	+	0.194586i	$0.937664\pi$
$654$		0			0
$655$		0			0
$656$			1.02893e6i			0.0933522i
$657$		0			0
$658$	−740798.	+	740798.i	−0.0667014	+	0.0667014i
$659$	−1.85670e6			−0.166544			−0.0832718	−	0.996527i	$-0.526537\pi$
$659$	−1.85670e6			−0.166544			−0.0832718	+	0.996527i	$0.526537\pi$
$660$		0			0
$661$	2.58327e6			0.229967			0.114984	−	0.993367i	$-0.463318\pi$
$661$	2.58327e6			0.229967			0.114984	+	0.993367i	$0.463318\pi$
$662$	−2.18545e6	+	2.18545e6i	−0.193819	+	0.193819i
$663$		0			0
$664$			1.75792e6i			0.154731i
$665$		0			0
$666$		0			0
$667$	2.30710e7	+	2.30710e7i	2.00795	+	2.00795i
$668$	−3.71095e6	−	3.71095e6i	−0.321769	−	0.321769i
$669$		0			0
$670$		0			0
$671$		−	2.05131e7i		−	1.75883i
$672$		0			0
$673$	−4.77133e6	+	4.77133e6i	−0.406071	+	0.406071i	−0.880366	−	0.474295i	$-0.842703\pi$
$673$	−4.77133e6	+	4.77133e6i	−0.406071	+	0.406071i	0.474295	+	0.880366i	$0.342703\pi$
$674$	2.74408e6			0.232673
$675$		0			0
$676$	3.02534e6			0.254629
$677$	1.24737e7	−	1.24737e7i	1.04598	−	1.04598i	0.0470935	−	0.998890i	$-0.485004\pi$
$677$	1.24737e7	−	1.24737e7i	1.04598	−	1.04598i	0.998890	−	0.0470935i	$-0.0149959\pi$
$678$		0			0
$679$			2.49746e7i			2.07885i
$680$		0			0
$681$		0			0
$682$	−1.35212e7	−	1.35212e7i	−1.11315	−	1.11315i
$683$	2.99944e6	+	2.99944e6i	0.246030	+	0.246030i	0.819339	−	0.573309i	$-0.194341\pi$
$683$	2.99944e6	+	2.99944e6i	0.246030	+	0.246030i	−0.573309	+	0.819339i	$0.694341\pi$
$684$		0			0
$685$		0			0
$686$			7.21446e6i			0.585320i
$687$		0			0
$688$	−1.10181e6	+	1.10181e6i	−0.0887434	+	0.0887434i
$689$	−272873.			−0.0218984
$690$		0			0
$691$	−2.35493e7			−1.87622			−0.938108	−	0.346343i	$-0.887423\pi$
$691$	−2.35493e7			−1.87622			−0.938108	+	0.346343i	$0.887423\pi$
$692$	−6.84819e6	+	6.84819e6i	−0.543639	+	0.543639i
$693$		0			0
$694$			7.43973e6i			0.586352i
$695$		0			0
$696$		0			0
$697$	2.27617e6	+	2.27617e6i	0.177469	+	0.177469i
$698$	1.23471e7	+	1.23471e7i	0.959237	+	0.959237i
$699$		0			0
$700$		0			0
$701$			2.55909e6i			0.196694i	0.995152	+	0.0983469i	$0.0313555\pi$
$701$			2.55909e6i			0.196694i	−0.995152	+	0.0983469i	$0.968645\pi$
$702$		0			0
$703$	1.98781e6	−	1.98781e6i	0.151700	−	0.151700i
$704$	3.05052e6			0.231976
$705$		0			0
$706$	−1.12866e7			−0.852223
$707$	9.21569e6	−	9.21569e6i	0.693393	−	0.693393i
$708$		0			0
$709$			2.92286e6i			0.218369i	0.994021	+	0.109185i	$0.0348240\pi$
$709$			2.92286e6i			0.218369i	−0.994021	+	0.109185i	$0.965176\pi$
$710$		0			0
$711$		0			0
$712$	6.42353e6	+	6.42353e6i	0.474869	+	0.474869i
$713$	−2.26312e7	−	2.26312e7i	−1.66718	−	1.66718i
$714$		0			0
$715$		0			0
$716$		−	3.88257e6i		−	0.283033i
$717$		0			0
$718$	−4.10913e6	+	4.10913e6i	−0.297467	+	0.297467i
$719$	−1.94781e7			−1.40516			−0.702578	−	0.711606i	$-0.747968\pi$
$719$	−1.94781e7			−1.40516			−0.702578	+	0.711606i	$0.747968\pi$
$720$		0			0
$721$	−7.10773e6			−0.509205
$722$	−6.77709e6	+	6.77709e6i	−0.483839	+	0.483839i
$723$		0			0
$724$		−	1.09191e6i		−	0.0774176i
$725$		0			0
$726$		0			0
$727$	−1.36184e7	−	1.36184e7i	−0.955630	−	0.955630i	0.0434265	−	0.999057i	$-0.486173\pi$
$727$	−1.36184e7	−	1.36184e7i	−0.955630	−	0.955630i	−0.999057	+	0.0434265i	$0.986173\pi$
$728$	−2.81517e6	−	2.81517e6i	−0.196868	−	0.196868i
$729$		0			0
$730$		0			0
$731$			4.87481e6i			0.337415i
$732$		0			0
$733$	1.32962e7	−	1.32962e7i	0.914044	−	0.914044i	−0.0825431	−	0.996587i	$-0.526304\pi$
$733$	1.32962e7	−	1.32962e7i	0.914044	−	0.914044i	0.996587	+	0.0825431i	$0.0263042\pi$
$734$	1.48940e7			1.02040
$735$		0			0
$736$	5.10582e6			0.347433
$737$	−1.81494e7	+	1.81494e7i	−1.23082	+	1.23082i
$738$		0			0
$739$		−	1.64692e7i		−	1.10933i	−0.832073	−	0.554666i	$-0.812846\pi$
$739$		−	1.64692e7i		−	1.10933i	0.832073	−	0.554666i	$-0.187154\pi$
$740$		0			0
$741$		0			0
$742$	−263496.	−	263496.i	−0.0175697	−	0.0175697i
$743$	−6.90258e6	−	6.90258e6i	−0.458711	−	0.458711i	0.439521	−	0.898232i	$-0.355148\pi$
$743$	−6.90258e6	−	6.90258e6i	−0.458711	−	0.458711i	−0.898232	+	0.439521i	$0.855148\pi$
$744$		0			0
$745$		0			0
$746$			8.52819e6i			0.561061i
$747$		0			0
$748$	6.74831e6	−	6.74831e6i	0.441003	−	0.441003i
$749$	−1.79412e7			−1.16855
$750$		0			0
$751$	2.31540e7			1.49805			0.749023	−	0.662544i	$-0.230523\pi$
$751$	2.31540e7			1.49805			0.749023	+	0.662544i	$0.230523\pi$
$752$	−325331.	+	325331.i	−0.0209788	+	0.0209788i
$753$		0			0
$754$		−	1.11728e7i		−	0.715703i
$755$		0			0
$756$		0			0
$757$	−1.12366e7	−	1.12366e7i	−0.712682	−	0.712682i	0.254414	−	0.967096i	$-0.418118\pi$
$757$	−1.12366e7	−	1.12366e7i	−0.712682	−	0.712682i	−0.967096	+	0.254414i	$0.918118\pi$
$758$	2.18848e6	+	2.18848e6i	0.138347	+	0.138347i
$759$		0			0
$760$		0			0
$761$			321915.i			0.0201502i	0.999949	+	0.0100751i	$0.00320706\pi$
$761$			321915.i			0.0201502i	−0.999949	+	0.0100751i	$0.996793\pi$
$762$		0			0
$763$	−2.19870e7	+	2.19870e7i	−1.36727	+	1.36727i
$764$	1.69245e6			0.104901
$765$		0			0
$766$	1.59597e7			0.982772
$767$	−4.12092e6	+	4.12092e6i	−0.252933	+	0.252933i
$768$		0			0
$769$		−	1.20479e7i		−	0.734678i	−0.930087	−	0.367339i	$-0.880269\pi$
$769$		−	1.20479e7i		−	0.734678i	0.930087	−	0.367339i	$-0.119731\pi$
$770$		0			0
$771$		0			0
$772$	439846.	+	439846.i	0.0265618	+	0.0265618i
$773$	−5.01112e6	−	5.01112e6i	−0.301638	−	0.301638i	0.540017	−	0.841654i	$-0.318418\pi$
$773$	−5.01112e6	−	5.01112e6i	−0.301638	−	0.301638i	−0.841654	+	0.540017i	$0.818418\pi$
$774$		0			0
$775$		0			0
$776$			1.09679e7i			0.653837i
$777$		0			0
$778$	6.70911e6	−	6.70911e6i	0.397389	−	0.397389i
$779$	1.13706e6			0.0671336
$780$		0			0
$781$	1.33482e7			0.783060
$782$	1.12950e7	−	1.12950e7i	0.660494	−	0.660494i
$783$		0			0
$784$		−	1.13427e6i		−	0.0659061i
$785$		0			0
$786$		0			0
$787$	−4.08074e6	−	4.08074e6i	−0.234856	−	0.234856i	0.579860	−	0.814716i	$-0.303107\pi$
$787$	−4.08074e6	−	4.08074e6i	−0.234856	−	0.234856i	−0.814716	+	0.579860i	$0.803107\pi$
$788$	2.85044e6	+	2.85044e6i	0.163530	+	0.163530i
$789$		0			0
$790$		0			0
$791$			1.91412e7i			1.08774i
$792$		0			0
$793$	−8.31354e6	+	8.31354e6i	−0.469465	+	0.469465i
$794$	−1.12537e7			−0.633498
$795$		0			0
$796$	1.21221e7			0.678100
$797$	−8.30424e6	+	8.30424e6i	−0.463078	+	0.463078i	−0.899663	−	0.436585i	$-0.856188\pi$
$797$	−8.30424e6	+	8.30424e6i	−0.463078	+	0.463078i	0.436585	+	0.899663i	$0.356188\pi$
$798$		0			0
$799$			1.43938e6i			0.0797644i
$800$		0			0
$801$		0			0
$802$	2.45699e6	+	2.45699e6i	0.134886	+	0.134886i
$803$	1.03520e6	+	1.03520e6i	0.0566547	+	0.0566547i
$804$		0			0
$805$		0			0
$806$			1.09598e7i			0.594243i
$807$		0			0
$808$	4.04719e6	−	4.04719e6i	0.218085	−	0.218085i
$809$	−2.89113e7			−1.55309			−0.776545	−	0.630062i	$-0.783029\pi$
$809$	−2.89113e7			−1.55309			−0.776545	+	0.630062i	$0.783029\pi$
$810$		0			0
$811$	−3.75545e6			−0.200498			−0.100249	−	0.994962i	$-0.531964\pi$
$811$	−3.75545e6			−0.200498			−0.100249	+	0.994962i	$0.531964\pi$
$812$	1.07889e7	−	1.07889e7i	0.574229	−	0.574229i
$813$		0			0
$814$		−	2.96022e7i		−	1.56590i
$815$		0			0
$816$		0			0
$817$	1.21761e6	+	1.21761e6i	0.0638192	+	0.0638192i
$818$	−4.54957e6	−	4.54957e6i	−0.237732	−	0.237732i
$819$		0			0
$820$		0			0
$821$			3.14204e7i			1.62687i	0.581654	+	0.813436i	$0.302406\pi$
$821$			3.14204e7i			1.62687i	−0.581654	+	0.813436i	$0.697594\pi$
$822$		0			0
$823$	1.21173e6	−	1.21173e6i	0.0623600	−	0.0623600i	−0.675239	−	0.737599i	$-0.735960\pi$
$823$	1.21173e6	−	1.21173e6i	0.0623600	−	0.0623600i	0.737599	+	0.675239i	$0.235960\pi$
$824$	−3.12145e6			−0.160154
$825$		0			0
$826$	−7.95864e6			−0.405871
$827$	2.86118e6	−	2.86118e6i	0.145473	−	0.145473i	−0.630619	−	0.776092i	$-0.717199\pi$
$827$	2.86118e6	−	2.86118e6i	0.145473	−	0.145473i	0.776092	+	0.630619i	$0.217199\pi$
$828$		0			0
$829$			2.07617e7i			1.04925i	0.851335	+	0.524623i	$0.175794\pi$
$829$			2.07617e7i			1.04925i	−0.851335	+	0.524623i	$0.824206\pi$
$830$		0			0
$831$		0			0
$832$	−1.23632e6	−	1.23632e6i	−0.0619187	−	0.0619187i
$833$	−2.50921e6	−	2.50921e6i	−0.125292	−	0.125292i
$834$		0			0
$835$		0			0
$836$		−	3.37112e6i		−	0.166824i
$837$		0			0
$838$	1.09209e6	−	1.09209e6i	0.0537215	−	0.0537215i
$839$	1.24202e7			0.609147			0.304574	−	0.952489i	$-0.401486\pi$
$839$	1.24202e7			0.609147			0.304574	+	0.952489i	$0.401486\pi$
$840$		0			0
$841$	2.23075e7			1.08758
$842$	−1.51805e7	+	1.51805e7i	−0.737915	+	0.737915i
$843$		0			0
$844$		−	1.34549e7i		−	0.650167i
$845$		0			0
$846$		0			0
$847$	−4.05609e7	−	4.05609e7i	−1.94267	−	1.94267i
$848$	−115718.	−	115718.i	−0.00552600	−	0.00552600i
$849$		0			0
$850$		0			0
$851$		−	4.95467e7i		−	2.34526i
$852$		0			0
$853$	−1.42853e7	+	1.42853e7i	−0.672227	+	0.672227i	−0.958229	−	0.286002i	$-0.907673\pi$
$853$	−1.42853e7	+	1.42853e7i	−0.672227	+	0.672227i	0.286002	+	0.958229i	$0.407673\pi$
$854$	−1.60557e7			−0.753330
$855$		0			0
$856$	−7.87910e6			−0.367529
$857$	−1.41765e7	+	1.41765e7i	−0.659350	+	0.659350i	−0.955226	−	0.295876i	$-0.904388\pi$
$857$	−1.41765e7	+	1.41765e7i	−0.659350	+	0.659350i	0.295876	+	0.955226i	$0.404388\pi$
$858$		0			0
$859$		−	2.81052e7i		−	1.29958i	−0.760112	−	0.649792i	$-0.774856\pi$
$859$		−	2.81052e7i		−	1.29958i	0.760112	−	0.649792i	$-0.225144\pi$
$860$		0			0
$861$		0			0
$862$	9.64302e6	+	9.64302e6i	0.442023	+	0.442023i
$863$	1.39692e6	+	1.39692e6i	0.0638475	+	0.0638475i	0.738310	−	0.674462i	$-0.235624\pi$
$863$	1.39692e6	+	1.39692e6i	0.0638475	+	0.0638475i	−0.674462	+	0.738310i	$0.735624\pi$
$864$		0			0
$865$		0			0
$866$		−	1.55103e7i		−	0.702792i
$867$		0			0
$868$	−1.05832e7	+	1.05832e7i	−0.476778	+	0.476778i
$869$	4.08605e7			1.83550
$870$		0			0
$871$	1.47112e7			0.657057
$872$	−9.65589e6	+	9.65589e6i	−0.430032	+	0.430032i
$873$		0			0
$874$		−	5.64241e6i		−	0.249854i
$875$		0			0
$876$		0			0
$877$	2.50455e7	+	2.50455e7i	1.09959	+	1.09959i	0.994458	+	0.105131i	$0.0335263\pi$
$877$	2.50455e7	+	2.50455e7i	1.09959	+	1.09959i	0.105131	+	0.994458i	$0.466474\pi$
$878$	−1.81615e7	−	1.81615e7i	−0.795087	−	0.795087i
$879$		0			0
$880$		0			0
$881$		−	947233.i		−	0.0411166i	−0.999789	−	0.0205583i	$-0.993456\pi$
$881$		−	947233.i		−	0.0411166i	0.999789	−	0.0205583i	$-0.00654437\pi$
$882$		0			0
$883$	2.11113e7	−	2.11113e7i	0.911199	−	0.911199i	−0.0851672	−	0.996367i	$-0.527142\pi$
$883$	2.11113e7	−	2.11113e7i	0.911199	−	0.911199i	0.996367	+	0.0851672i	$0.0271425\pi$
$884$	−5.46991e6			−0.235424
$885$		0			0
$886$	−1.63370e7			−0.699180
$887$	−1.07682e7	+	1.07682e7i	−0.459553	+	0.459553i	−0.898509	−	0.438956i	$-0.855348\pi$
$887$	−1.07682e7	+	1.07682e7i	−0.459553	+	0.459553i	0.438956	+	0.898509i	$0.355348\pi$
$888$		0			0
$889$			2.64031e7i			1.12047i
$890$		0			0
$891$		0			0
$892$	9.61281e6	+	9.61281e6i	0.404518	+	0.404518i
$893$	359522.	+	359522.i	0.0150868	+	0.0150868i
$894$		0			0
$895$		0			0
$896$		−	2.38767e6i		−	0.0993583i
$897$		0			0
$898$	7.66439e6	−	7.66439e6i	0.317166	−	0.317166i
$899$	−4.20023e7			−1.73330
$900$		0			0
$901$	−511978.			−0.0210106
$902$	8.46649e6	−	8.46649e6i	0.346487	−	0.346487i
$903$		0			0
$904$			8.40609e6i			0.342116i
$905$		0			0
$906$		0			0
$907$	678139.	+	678139.i	0.0273716	+	0.0273716i	0.720660	−	0.693289i	$-0.243839\pi$
$907$	678139.	+	678139.i	0.0273716	+	0.0273716i	−0.693289	+	0.720660i	$0.743839\pi$
$908$	1.02739e7	+	1.02739e7i	0.413541	+	0.413541i
$909$		0			0
$910$		0			0
$911$		−	4.26770e7i		−	1.70372i	−0.523771	−	0.851859i	$-0.675475\pi$
$911$		−	4.26770e7i		−	1.70372i	0.523771	−	0.851859i	$-0.324525\pi$
$912$		0			0
$913$	1.44650e7	−	1.44650e7i	0.574303	−	0.574303i
$914$	−1.48911e7			−0.589607
$915$		0			0
$916$	−3.48701e6			−0.137314
$917$	−2.78594e7	+	2.78594e7i	−1.09408	+	1.09408i
$918$		0			0
$919$		−	2.12124e7i		−	0.828516i	−0.910159	−	0.414258i	$-0.864041\pi$
$919$		−	2.12124e7i		−	0.828516i	0.910159	−	0.414258i	$-0.135959\pi$
$920$		0			0
$921$		0			0
$922$	1.40452e7	+	1.40452e7i	0.544126	+	0.544126i
$923$	−5.40976e6	−	5.40976e6i	−0.209013	−	0.209013i
$924$		0			0
$925$		0			0
$926$			4.81608e6i			0.184572i
$927$		0			0
$928$	4.73807e6	−	4.73807e6i	0.180606	−	0.180606i
$929$	−4.17745e7			−1.58808			−0.794040	−	0.607866i	$-0.792026\pi$
$929$	−4.17745e7			−1.58808			−0.794040	+	0.607866i	$0.792026\pi$
$930$		0			0
$931$	−1.25347e6			−0.0473959
$932$	1.02054e6	−	1.02054e6i	0.0384851	−	0.0384851i
$933$		0			0
$934$			1.61975e7i			0.607546i
$935$		0			0
$936$		0			0
$937$	9.35181e6	+	9.35181e6i	0.347974	+	0.347974i	0.859354	−	0.511380i	$-0.170866\pi$
$937$	9.35181e6	+	9.35181e6i	0.347974	+	0.347974i	−0.511380	+	0.859354i	$0.670866\pi$
$938$	1.42057e7	+	1.42057e7i	0.527176	+	0.527176i
$939$		0			0
$940$		0			0
$941$		−	2.12220e7i		−	0.781291i	−0.920541	−	0.390646i	$-0.872252\pi$
$941$		−	2.12220e7i		−	0.781291i	0.920541	−	0.390646i	$-0.127748\pi$
$942$		0			0
$943$	1.41708e7	−	1.41708e7i	0.518938	−	0.518938i
$944$	−3.49514e6			−0.127654
$945$		0			0
$946$	1.81325e7			0.658763
$947$	−1.14035e6	+	1.14035e6i	−0.0413202	+	0.0413202i	−0.727465	−	0.686145i	$-0.759302\pi$
$947$	−1.14035e6	+	1.14035e6i	−0.0413202	+	0.0413202i	0.686145	+	0.727465i	$0.259302\pi$
$948$		0			0
$949$		−	839093.i		−	0.0302444i
$950$		0			0
$951$		0			0
$952$	−5.28195e6	−	5.28195e6i	−0.188887	−	0.188887i
$953$	−1.20675e7	−	1.20675e7i	−0.430413	−	0.430413i	0.458356	−	0.888769i	$-0.348439\pi$
$953$	−1.20675e7	−	1.20675e7i	−0.430413	−	0.430413i	−0.888769	+	0.458356i	$0.848439\pi$
$954$		0			0
$955$		0			0
$956$		−	1.23535e7i		−	0.437165i
$957$		0			0
$958$	−1.09983e7	+	1.09983e7i	−0.387180	+	0.387180i
$959$	1.23826e7			0.434776
$960$		0			0
$961$	1.25724e7			0.439147
$962$	−1.19972e7	+	1.19972e7i	−0.417967	+	0.417967i
$963$		0			0
$964$			2.18492e7i			0.757257i
$965$		0			0
$966$		0			0
$967$	−3.02688e7	−	3.02688e7i	−1.04095	−	1.04095i	−0.999125	−	0.0418240i	$-0.986683\pi$
$967$	−3.02688e7	−	3.02688e7i	−1.04095	−	1.04095i	−0.0418240	−	0.999125i	$-0.513317\pi$
$968$	−1.78128e7	−	1.78128e7i	−0.611005	−	0.611005i
$969$		0			0
$970$		0			0
$971$			1.67488e7i			0.570079i	0.958516	+	0.285039i	$0.0920067\pi$
$971$			1.67488e7i			0.570079i	−0.958516	+	0.285039i	$0.907993\pi$
$972$		0			0
$973$	1.98543e7	−	1.98543e7i	0.672313	−	0.672313i
$974$	1.21153e7			0.409200
$975$		0			0
$976$	−7.05109e6			−0.236936
$977$	2.50120e7	−	2.50120e7i	0.838326	−	0.838326i	−0.150313	−	0.988639i	$-0.548028\pi$
$977$	2.50120e7	−	2.50120e7i	0.838326	−	0.838326i	0.988639	+	0.150313i	$0.0480280\pi$
$978$		0			0
$979$		−	1.05712e8i		−	3.52506i
$980$		0			0
$981$		0			0
$982$	−2.13547e7	−	2.13547e7i	−0.706668	−	0.706668i
$983$	2.18441e7	+	2.18441e7i	0.721024	+	0.721024i	0.968814	−	0.247790i	$-0.0797042\pi$
$983$	2.18441e7	+	2.18441e7i	0.721024	+	0.721024i	−0.247790	+	0.968814i	$0.579704\pi$
$984$		0			0
$985$		0			0
$986$		−	2.09629e7i		−	0.686688i
$987$		0			0
$988$	−1.36625e6	+	1.36625e6i	−0.0445284	+	0.0445284i
$989$	3.03492e7			0.986636
$990$		0			0
$991$	2.39866e6			0.0775863			0.0387931	−	0.999247i	$-0.487649\pi$
$991$	2.39866e6			0.0775863			0.0387931	+	0.999247i	$0.487649\pi$
$992$	−4.64774e6	+	4.64774e6i	−0.149956	+	0.149956i
$993$		0			0
$994$		−	1.04477e7i		−	0.335395i
$995$		0			0
$996$		0			0
$997$	1.02022e7	+	1.02022e7i	0.325055	+	0.325055i	0.850702	−	0.525648i	$-0.176177\pi$
$997$	1.02022e7	+	1.02022e7i	0.325055	+	0.325055i	−0.525648	+	0.850702i	$0.676177\pi$
$998$	−1.47464e6	−	1.47464e6i	−0.0468663	−	0.0468663i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.6.f.e.107.3		12
3.2	odd	2	inner	450.6.f.e.107.6		12
5.2	odd	4		90.6.f.c.53.2	yes	12
5.3	odd	4	inner	450.6.f.e.143.6		12
5.4	even	2		90.6.f.c.17.5	yes	12
15.2	even	4		90.6.f.c.53.5	yes	12
15.8	even	4	inner	450.6.f.e.143.3		12
15.14	odd	2		90.6.f.c.17.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.6.f.c.17.2	✓	12	15.14	odd	2
90.6.f.c.17.5	yes	12	5.4	even	2
90.6.f.c.53.2	yes	12	5.2	odd	4
90.6.f.c.53.5	yes	12	15.2	even	4
450.6.f.e.107.3		12	1.1	even	1	trivial
450.6.f.e.107.6		12	3.2	odd	2	inner
450.6.f.e.143.3		12	15.8	even	4	inner
450.6.f.e.143.6		12	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	450.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.82843 + 2.82843i) q^{2} -16.0000i q^{4} +(103.048 + 103.048i) q^{7} +(45.2548 + 45.2548i) q^{8} +O(q^{10})\)	\(q+(-2.82843 + 2.82843i) q^{2} -16.0000i q^{4} +(103.048 + 103.048i) q^{7} +(45.2548 + 45.2548i) q^{8} -744.757i q^{11} +(-301.835 + 301.835i) q^{13} -582.927 q^{14} -256.000 q^{16} +(-566.318 + 566.318i) q^{17} +282.904i q^{19} +(2106.49 + 2106.49i) q^{22} +(3525.74 + 3525.74i) q^{23} -1707.44i q^{26} +(1648.77 - 1648.77i) q^{28} +6543.59 q^{29} -6418.84 q^{31} +(724.077 - 724.077i) q^{32} -3203.58i q^{34} +(-7026.43 - 7026.43i) q^{37} +(-800.174 - 800.174i) q^{38} -4019.24i q^{41} +(4303.95 - 4303.95i) q^{43} -11916.1 q^{44} -19944.6 q^{46} +(1270.82 - 1270.82i) q^{47} +4430.74i q^{49} +(4829.36 + 4829.36i) q^{52} +(452.023 + 452.023i) q^{53} +9326.83i q^{56} +(-18508.1 + 18508.1i) q^{58} +13652.9 q^{59} +27543.3 q^{61} +(18155.2 - 18155.2i) q^{62} +4096.00i q^{64} +(-24369.6 - 24369.6i) q^{67} +(9061.09 + 9061.09i) q^{68} +17922.9i q^{71} +(-1389.99 + 1389.99i) q^{73} +39747.5 q^{74} +4526.47 q^{76} +(76745.6 - 76745.6i) q^{77} +54864.2i q^{79} +(11368.1 + 11368.1i) q^{82} +(19422.4 + 19422.4i) q^{83} +24346.8i q^{86} +(33703.9 - 33703.9i) q^{88} +141941. q^{89} -62207.0 q^{91} +(56411.8 - 56411.8i) q^{92} +7188.87i q^{94} +(121179. + 121179. i) q^{97} +(-12532.0 - 12532.0i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 144 q^{7}+O(q^{10}) \) 12 * q - 144 * q^7	\( 12 q - 144 q^{7} + 276 q^{13} - 3072 q^{16} - 384 q^{22} - 2304 q^{28} - 58512 q^{31} - 25764 q^{37} - 16080 q^{43} - 60672 q^{46} - 4416 q^{52} - 23952 q^{58} - 145200 q^{61} - 33552 q^{67} + 158988 q^{73} - 86016 q^{76} + 75024 q^{82} - 6144 q^{88} - 465024 q^{91} + 631116 q^{97}+O(q^{100}) \) 12 * q - 144 * q^7 + 276 * q^13 - 3072 * q^16 - 384 * q^22 - 2304 * q^28 - 58512 * q^31 - 25764 * q^37 - 16080 * q^43 - 60672 * q^46 - 4416 * q^52 - 23952 * q^58 - 145200 * q^61 - 33552 * q^67 + 158988 * q^73 - 86016 * q^76 + 75024 * q^82 - 6144 * q^88 - 465024 * q^91 + 631116 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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