LMFDB - Embedded newform 60.6.i.a.53.5

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			53.5
Root			$-5.69920 + 7.08001i$ of defining polynomial
Character	$\chi$	$=$	60.53
Dual form			60.6.i.a.17.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.876355 + 15.5638i) q^{3} +(55.7692 + 3.84667i) q^{5} +(151.287 - 151.287i) q^{7} +(-241.464 + 27.2788i) q^{9} +O(q^{10})$	\(q+(0.876355 + 15.5638i) q^{3} +(55.7692 + 3.84667i) q^{5} +(151.287 - 151.287i) q^{7} +(-241.464 + 27.2788i) q^{9} +504.939i q^{11} +(567.781 + 567.781i) q^{13} +(-10.9953 + 871.352i) q^{15} +(-91.1681 - 91.1681i) q^{17} -600.852i q^{19} +(2487.18 + 2222.02i) q^{21} +(-2156.65 + 2156.65i) q^{23} +(3095.41 + 429.052i) q^{25} +(-636.170 - 3734.19i) q^{27} +5818.05 q^{29} -2220.29 q^{31} +(-7858.78 + 442.506i) q^{33} +(9019.11 - 7855.21i) q^{35} +(-6791.46 + 6791.46i) q^{37} +(-8339.25 + 9334.40i) q^{39} -12164.1i q^{41} +(-5949.36 - 5949.36i) q^{43} +(-13571.2 + 592.485i) q^{45} +(-4500.58 - 4500.58i) q^{47} -28968.6i q^{49} +(1339.03 - 1498.82i) q^{51} +(26033.6 - 26033.6i) q^{53} +(-1942.34 + 28160.1i) q^{55} +(9351.54 - 526.559i) q^{57} -6530.45 q^{59} +28414.5 q^{61} +(-32403.5 + 40657.3i) q^{63} +(29480.6 + 33848.7i) q^{65} +(-12318.8 + 12318.8i) q^{67} +(-35455.7 - 31675.8i) q^{69} -69210.3i q^{71} +(-18264.0 - 18264.0i) q^{73} +(-3965.01 + 48552.3i) q^{75} +(76390.8 + 76390.8i) q^{77} +41121.4i q^{79} +(57560.7 - 13173.7i) q^{81} +(-56058.1 + 56058.1i) q^{83} +(-4733.68 - 5435.07i) q^{85} +(5098.67 + 90550.9i) q^{87} -54609.2 q^{89} +171796. q^{91} +(-1945.76 - 34556.1i) q^{93} +(2311.28 - 33509.0i) q^{95} +(17055.3 - 17055.3i) q^{97} +(-13774.2 - 121925. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.876355	+	15.5638i	0.0562182	+	0.998419i
$3$	0.876355	+	15.5638i	0.0562182	+	0.998419i
$4$		0			0
$5$	55.7692	+	3.84667i	0.997630	+	0.0688114i
$5$	55.7692	+	3.84667i	0.997630	+	0.0688114i
$6$		0			0
$7$	151.287	−	151.287i	1.16696	−	1.16696i	0.184044	−	0.982918i	$-0.441081\pi$
$7$	151.287	−	151.287i	1.16696	−	1.16696i	0.982918	−	0.184044i	$-0.0589190\pi$
$8$		0			0
$9$	−241.464	+	27.2788i	−0.993679	+	0.112259i
$10$		0			0
$11$			504.939i			1.25822i	0.777315	+	0.629111i	$0.216581\pi$
$11$			504.939i			1.25822i	−0.777315	+	0.629111i	$0.783419\pi$
$12$		0			0
$13$	567.781	+	567.781i	0.931799	+	0.931799i	0.997818	−	0.0660194i	$-0.0210299\pi$
$13$	567.781	+	567.781i	0.931799	+	0.931799i	−0.0660194	+	0.997818i	$0.521030\pi$
$14$		0			0
$15$	−10.9953	+	871.352i	−0.0126177	+	0.999920i
$16$		0			0
$17$	−91.1681	−	91.1681i	−0.0765104	−	0.0765104i	0.667816	−	0.744326i	$-0.267229\pi$
$17$	−91.1681	−	91.1681i	−0.0765104	−	0.0765104i	−0.744326	+	0.667816i	$0.767229\pi$
$18$		0			0
$19$		−	600.852i		−	0.381842i	−0.981605	−	0.190921i	$-0.938853\pi$
$19$		−	600.852i		−	0.381842i	0.981605	−	0.190921i	$-0.0611474\pi$
$20$		0			0
$21$	2487.18	+	2222.02i	1.23072	+	1.09951i
$22$		0			0
$23$	−2156.65	+	2156.65i	−0.850082	+	0.850082i	−0.990143	−	0.140061i	$-0.955270\pi$
$23$	−2156.65	+	2156.65i	−0.850082	+	0.850082i	0.140061	+	0.990143i	$0.455270\pi$
$24$		0			0
$25$	3095.41	+	429.052i	0.990530	+	0.137297i
$26$		0			0
$27$	−636.170	−	3734.19i	−0.167944	−	0.985797i
$28$		0			0
$29$	5818.05			1.28464			0.642321	−	0.766436i	$-0.277972\pi$
$29$	5818.05			1.28464			0.642321	+	0.766436i	$0.277972\pi$
$30$		0			0
$31$	−2220.29			−0.414959			−0.207479	−	0.978239i	$-0.566526\pi$
$31$	−2220.29			−0.414959			−0.207479	+	0.978239i	$0.566526\pi$
$32$		0			0
$33$	−7858.78	+	442.506i	−1.25623	+	0.0707350i
$34$		0			0
$35$	9019.11	−	7855.21i	1.24450	−	1.08390i
$36$		0			0
$37$	−6791.46	+	6791.46i	−0.815565	+	0.815565i	−0.985462	−	0.169896i	$-0.945657\pi$
$37$	−6791.46	+	6791.46i	−0.815565	+	0.815565i	0.169896	+	0.985462i	$0.445657\pi$
$38$		0			0
$39$	−8339.25	+	9334.40i	−0.877941	+	0.982709i
$40$		0			0
$41$		−	12164.1i		−	1.13011i	−0.825055	−	0.565053i	$-0.808856\pi$
$41$		−	12164.1i		−	1.13011i	0.825055	−	0.565053i	$-0.191144\pi$
$42$		0			0
$43$	−5949.36	−	5949.36i	−0.490681	−	0.490681i	0.417840	−	0.908521i	$-0.362787\pi$
$43$	−5949.36	−	5949.36i	−0.490681	−	0.490681i	−0.908521	+	0.417840i	$0.862787\pi$
$44$		0			0
$45$	−13571.2	+	592.485i	−0.999048	+	0.0436160i
$46$		0			0
$47$	−4500.58	−	4500.58i	−0.297183	−	0.297183i	0.542727	−	0.839909i	$-0.317392\pi$
$47$	−4500.58	−	4500.58i	−0.297183	−	0.297183i	−0.839909	+	0.542727i	$0.817392\pi$
$48$		0			0
$49$		−	28968.6i		−	1.72360i
$50$		0			0
$51$	1339.03	−	1498.82i	0.0720882	−	0.0806907i
$52$		0			0
$53$	26033.6	−	26033.6i	1.27305	−	1.27305i	0.328569	−	0.944480i	$-0.393434\pi$
$53$	26033.6	−	26033.6i	1.27305	−	1.27305i	0.944480	−	0.328569i	$-0.106566\pi$
$54$		0			0
$55$	−1942.34	+	28160.1i	−0.0865801	+	1.25524i
$56$		0			0
$57$	9351.54	−	526.559i	0.381238	−	0.0214664i
$58$		0			0
$59$	−6530.45			−0.244238			−0.122119	−	0.992515i	$-0.538969\pi$
$59$	−6530.45			−0.244238			−0.122119	+	0.992515i	$0.538969\pi$
$60$		0			0
$61$	28414.5			0.977722			0.488861	−	0.872362i	$-0.337412\pi$
$61$	28414.5			0.977722			0.488861	+	0.872362i	$0.337412\pi$
$62$		0			0
$63$	−32403.5	+	40657.3i	−1.02858	+	1.29059i
$64$		0			0
$65$	29480.6	+	33848.7i	0.865472	+	0.993709i
$66$		0			0
$67$	−12318.8	+	12318.8i	−0.335259	+	0.335259i	−0.854580	−	0.519321i	$-0.826185\pi$
$67$	−12318.8	+	12318.8i	−0.335259	+	0.335259i	0.519321	+	0.854580i	$0.326185\pi$
$68$		0			0
$69$	−35455.7	−	31675.8i	−0.896528	−	0.800948i
$70$		0			0
$71$		−	69210.3i		−	1.62939i	−0.579890	−	0.814695i	$-0.696905\pi$
$71$		−	69210.3i		−	1.62939i	0.579890	−	0.814695i	$-0.303095\pi$
$72$		0			0
$73$	−18264.0	−	18264.0i	−0.401133	−	0.401133i	0.477499	−	0.878632i	$-0.341543\pi$
$73$	−18264.0	−	18264.0i	−0.401133	−	0.401133i	−0.878632	+	0.477499i	$0.841543\pi$
$74$		0			0
$75$	−3965.01	+	48552.3i	−0.0813937	+	0.996682i
$76$		0			0
$77$	76390.8	+	76390.8i	1.46830	+	1.46830i
$78$		0			0
$79$			41121.4i			0.741311i	0.928770	+	0.370655i	$0.120867\pi$
$79$			41121.4i			0.741311i	−0.928770	+	0.370655i	$0.879133\pi$
$80$		0			0
$81$	57560.7	−	13173.7i	0.974796	−	0.223098i
$82$		0			0
$83$	−56058.1	+	56058.1i	−0.893189	+	0.893189i	−0.994822	−	0.101633i	$-0.967593\pi$
$83$	−56058.1	+	56058.1i	−0.893189	+	0.893189i	0.101633	+	0.994822i	$0.467593\pi$
$84$		0			0
$85$	−4733.68	−	5435.07i	−0.0710643	−	0.0815939i
$86$		0			0
$87$	5098.67	+	90550.9i	0.0722202	+	1.28261i
$88$		0			0
$89$	−54609.2			−0.730787			−0.365394	−	0.930853i	$-0.619066\pi$
$89$	−54609.2			−0.730787			−0.365394	+	0.930853i	$0.619066\pi$
$90$		0			0
$91$	171796.			2.17475
$92$		0			0
$93$	−1945.76	−	34556.1i	−0.0233282	−	0.414303i
$94$		0			0
$95$	2311.28	−	33509.0i	0.0262751	−	0.380937i
$96$		0			0
$97$	17055.3	−	17055.3i	0.184047	−	0.184047i	−0.609070	−	0.793117i	$-0.708457\pi$
$97$	17055.3	−	17055.3i	0.184047	−	0.184047i	0.793117	+	0.609070i	$0.208457\pi$
$98$		0			0
$99$	−13774.2	−	121925.i	−0.141246	−	1.25027i
$100$		0			0
$101$		−	44798.8i		−	0.436981i	−0.975839	−	0.218491i	$-0.929887\pi$
$101$		−	44798.8i		−	0.436981i	0.975839	−	0.218491i	$-0.0701133\pi$
$102$		0			0
$103$	−112985.	−	112985.i	−1.04937	−	1.04937i	−0.998716	−	0.0506522i	$-0.983870\pi$
$103$	−112985.	−	112985.i	−1.04937	−	1.04937i	−0.0506522	−	0.998716i	$-0.516130\pi$
$104$		0			0
$105$	130161.	+	133488.i	1.15214	+	1.18159i
$106$		0			0
$107$	−52567.6	−	52567.6i	−0.443873	−	0.443873i	0.449438	−	0.893311i	$-0.351624\pi$
$107$	−52567.6	−	52567.6i	−0.443873	−	0.443873i	−0.893311	+	0.449438i	$0.851624\pi$
$108$		0			0
$109$		−	10619.5i		−	0.0856125i	−0.999083	−	0.0428063i	$-0.986370\pi$
$109$		−	10619.5i		−	0.0856125i	0.999083	−	0.0428063i	$-0.0136298\pi$
$110$		0			0
$111$	−111653.	−	99749.2i	−0.860125	−	0.768426i
$112$		0			0
$113$	−53690.7	+	53690.7i	−0.395552	+	0.395552i	−0.876661	−	0.481109i	$-0.840234\pi$
$113$	−53690.7	+	53690.7i	−0.395552	+	0.395552i	0.481109	+	0.876661i	$0.340234\pi$
$114$		0			0
$115$	−128571.	+	111979.i	−0.906563	+	0.789572i
$116$		0			0
$117$	−152587.	−	121610.i	−1.03051	−	0.821307i
$118$		0			0
$119$	−27585.1			−0.178570
$120$		0			0
$121$	−93912.7			−0.583124
$122$		0			0
$123$	189319.	−	10660.0i	1.12832	−	0.0635325i
$124$		0			0
$125$	170978.	+	35834.9i	0.978735	+	0.205131i
$126$		0			0
$127$	−124569.	+	124569.i	−0.685333	+	0.685333i	−0.961197	−	0.275864i	$-0.911036\pi$
$127$	−124569.	+	124569.i	−0.685333	+	0.685333i	0.275864	+	0.961197i	$0.411036\pi$
$128$		0			0
$129$	87380.9	−	97808.4i	0.462320	−	0.517490i
$130$		0			0
$131$		−	46648.9i		−	0.237500i	−0.992924	−	0.118750i	$-0.962111\pi$
$131$		−	46648.9i		−	0.237500i	0.992924	−	0.118750i	$-0.0378887\pi$
$132$		0			0
$133$	−90901.1	−	90901.1i	−0.445595	−	0.445595i
$134$		0			0
$135$	−21114.5	−	210700.i	−0.0997117	−	0.995016i
$136$		0			0
$137$	−123029.	−	123029.i	−0.560025	−	0.560025i	0.369289	−	0.929315i	$-0.379601\pi$
$137$	−123029.	−	123029.i	−0.560025	−	0.560025i	−0.929315	+	0.369289i	$0.879601\pi$
$138$		0			0
$139$		−	88863.2i		−	0.390108i	−0.980793	−	0.195054i	$-0.937512\pi$
$139$		−	88863.2i		−	0.390108i	0.980793	−	0.195054i	$-0.0624882\pi$
$140$		0			0
$141$	66102.0	−	73990.2i	0.280006	−	0.313420i
$142$		0			0
$143$	−286695.	+	286695.i	−1.17241	+	1.17241i
$144$		0			0
$145$	324468.	+	22380.1i	1.28160	+	0.0883980i
$146$		0			0
$147$	450861.	−	25386.7i	1.72088	−	0.0968977i
$148$		0			0
$149$	−280995.			−1.03689			−0.518446	−	0.855110i	$-0.673489\pi$
$149$	−280995.			−1.03689			−0.518446	+	0.855110i	$0.673489\pi$
$150$		0			0
$151$	381934.			1.36316			0.681579	−	0.731745i	$-0.261294\pi$
$151$	381934.			1.36316			0.681579	+	0.731745i	$0.261294\pi$
$152$		0			0
$153$	24500.8	+	19526.9i	0.0846158	+	0.0674379i
$154$		0			0
$155$	−123824.	−	8540.72i	−0.413975	−	0.0285539i
$156$		0			0
$157$	−124075.	+	124075.i	−0.401731	+	0.401731i	−0.878843	−	0.477112i	$-0.841684\pi$
$157$	−124075.	+	124075.i	−0.401731	+	0.401731i	0.477112	+	0.878843i	$0.341684\pi$
$158$		0			0
$159$	427997.	+	382368.i	1.34260	+	1.19947i
$160$		0			0
$161$			652548.i			1.98403i
$162$		0			0
$163$	−131800.	−	131800.i	−0.388549	−	0.388549i	0.485621	−	0.874170i	$-0.338594\pi$
$163$	−131800.	−	131800.i	−0.388549	−	0.388549i	−0.874170	+	0.485621i	$0.838594\pi$
$164$		0			0
$165$	−439980.	−	5551.96i	−1.25812	−	0.0158758i
$166$		0			0
$167$	113051.	+	113051.i	0.313678	+	0.313678i	0.846333	−	0.532654i	$-0.178805\pi$
$167$	113051.	+	113051.i	0.313678	+	0.313678i	−0.532654	+	0.846333i	$0.678805\pi$
$168$		0			0
$169$			273457.i			0.736499i
$170$		0			0
$171$	16390.5	+	145084.i	0.0428650	+	0.379428i
$172$		0			0
$173$	177634.	−	177634.i	0.451245	−	0.451245i	−0.444523	−	0.895767i	$-0.646627\pi$
$173$	177634.	−	177634.i	0.451245	−	0.451245i	0.895767	+	0.444523i	$0.146627\pi$
$174$		0			0
$175$	533205.	−	403385.i	1.31613	−	0.995691i
$176$		0			0
$177$	−5722.99	−	101639.i	−0.0137306	−	0.243852i
$178$		0			0
$179$	224850.			0.524518			0.262259	−	0.964998i	$-0.415533\pi$
$179$	224850.			0.524518			0.262259	+	0.964998i	$0.415533\pi$
$180$		0			0
$181$	−430292.			−0.976263			−0.488132	−	0.872770i	$-0.662321\pi$
$181$	−430292.			−0.976263			−0.488132	+	0.872770i	$0.662321\pi$
$182$		0			0
$183$	24901.2	+	442238.i	0.0549658	+	0.976176i
$184$		0			0
$185$	−404879.	+	352630.i	−0.869753	+	0.757512i
$186$		0			0
$187$	46034.4	−	46034.4i	0.0962672	−	0.0962672i
$188$		0			0
$189$	−661180.	−	468691.i	−1.34637	−	0.954403i
$190$		0			0
$191$		−	479790.i		−	0.951629i	−0.879546	−	0.475814i	$-0.842153\pi$
$191$		−	479790.i		−	0.951629i	0.879546	−	0.475814i	$-0.157847\pi$
$192$		0			0
$193$	561095.	+	561095.i	1.08428	+	1.08428i	0.996105	+	0.0881793i	$0.0281048\pi$
$193$	561095.	+	561095.i	1.08428	+	1.08428i	0.0881793	+	0.996105i	$0.471895\pi$
$194$		0			0
$195$	−500980.	+	488494.i	−0.943482	+	0.919968i
$196$		0			0
$197$	264076.	+	264076.i	0.484801	+	0.484801i	0.906661	−	0.421860i	$-0.138623\pi$
$197$	264076.	+	264076.i	0.484801	+	0.484801i	−0.421860	+	0.906661i	$0.638623\pi$
$198$		0			0
$199$			111560.i			0.199699i	0.995003	+	0.0998494i	$0.0318361\pi$
$199$			111560.i			0.199699i	−0.995003	+	0.0998494i	$0.968164\pi$
$200$		0			0
$201$	−202523.	−	180931.i	−0.353576	−	0.315881i
$202$		0			0
$203$	880195.	−	880195.i	1.49913	−	1.49913i
$204$		0			0
$205$	46791.2	−	678380.i	0.0777642	−	1.12743i
$206$		0			0
$207$	461923.	−	579585.i	0.749280	−	0.940138i
$208$		0			0
$209$	303394.			0.480442
$210$		0			0
$211$	−932775.			−1.44235			−0.721175	−	0.692753i	$-0.756398\pi$
$211$	−932775.			−1.44235			−0.721175	+	0.692753i	$0.756398\pi$
$212$		0			0
$213$	1.07718e6	−	60652.8i	1.62681	−	0.0916013i
$214$		0			0
$215$	−308906.	−	354676.i	−0.455753	−	0.523282i
$216$		0			0
$217$	−335901.	+	335901.i	−0.484241	+	0.484241i
$218$		0			0
$219$	268251.	−	300263.i	0.377947	−	0.423049i
$220$		0			0
$221$		−	103527.i		−	0.142585i
$222$		0			0
$223$	−866194.	−	866194.i	−1.16642	−	1.16642i	−0.983044	−	0.183372i	$-0.941299\pi$
$223$	−866194.	−	866194.i	−1.16642	−	1.16642i	−0.183372	−	0.983044i	$-0.558701\pi$
$224$		0			0
$225$	−759133.	−	19161.5i	−0.999682	−	0.0252333i
$226$		0			0
$227$	−785260.	−	785260.i	−1.01146	−	1.01146i	−0.999934	−	0.0115270i	$-0.996331\pi$
$227$	−785260.	−	785260.i	−1.01146	−	1.01146i	−0.0115270	−	0.999934i	$-0.503669\pi$
$228$		0			0
$229$			1.35108e6i			1.70252i	0.524742	+	0.851261i	$0.324162\pi$
$229$			1.35108e6i			1.70252i	−0.524742	+	0.851261i	$0.675838\pi$
$230$		0			0
$231$	−1.12199e6	+	1.25588e6i	−1.38343	+	1.54852i
$232$		0			0
$233$	211648.	−	211648.i	0.255403	−	0.255403i	−0.567779	−	0.823181i	$-0.692197\pi$
$233$	211648.	−	211648.i	0.255403	−	0.255403i	0.823181	+	0.567779i	$0.192197\pi$
$234$		0			0
$235$	−233681.	−	268306.i	−0.276029	−	0.316928i
$236$		0			0
$237$	−640006.	+	36036.9i	−0.740138	+	0.0416751i
$238$		0			0
$239$	1.11134e6			1.25850			0.629251	−	0.777202i	$-0.283362\pi$
$239$	1.11134e6			1.25850			0.629251	+	0.777202i	$0.283362\pi$
$240$		0			0
$241$	501312.			0.555988			0.277994	−	0.960583i	$-0.410330\pi$
$241$	501312.			0.555988			0.277994	+	0.960583i	$0.410330\pi$
$242$		0			0
$243$	255477.	+	884319.i	0.277546	+	0.960712i
$244$		0			0
$245$	111433.	−	1.61555e6i	0.118603	−	1.71952i
$246$		0			0
$247$	341152.	−	341152.i	0.355800	−	0.355800i
$248$		0			0
$249$	−921604.	−	823351.i	−0.941989	−	0.841563i
$250$		0			0
$251$			66926.4i			0.0670522i	0.999438	+	0.0335261i	$0.0106737\pi$
$251$			66926.4i			0.0670522i	−0.999438	+	0.0335261i	$0.989326\pi$
$252$		0			0
$253$	−1.08898e6	−	1.08898e6i	−1.06959	−	1.06959i
$254$		0			0
$255$	80441.9	−	78437.1i	0.0774697	−	0.0755390i
$256$		0			0
$257$	1.10953e6	+	1.10953e6i	1.04787	+	1.04787i	0.998795	+	0.0490726i	$0.0156266\pi$
$257$	1.10953e6	+	1.10953e6i	1.04787	+	1.04787i	0.0490726	+	0.998795i	$0.484373\pi$
$258$		0			0
$259$			2.05492e6i			1.90347i
$260$		0			0
$261$	−1.40485e6	+	158709.i	−1.27652	+	0.144212i
$262$		0			0
$263$	−11345.4	+	11345.4i	−0.0101142	+	0.0101142i	−0.712146	−	0.702032i	$-0.752277\pi$
$263$	−11345.4	+	11345.4i	−0.0101142	+	0.0101142i	0.702032	+	0.712146i	$0.252277\pi$
$264$		0			0
$265$	1.55202e6	−	1.35173e6i	1.35763	−	1.18243i
$266$		0			0
$267$	−47857.1	−	849927.i	−0.0410835	−	0.729632i
$268$		0			0
$269$	1.52047e6			1.28115			0.640573	−	0.767897i	$-0.278697\pi$
$269$	1.52047e6			1.28115			0.640573	+	0.767897i	$0.278697\pi$
$270$		0			0
$271$	2.29409e6			1.89752			0.948761	−	0.315995i	$-0.102338\pi$
$271$	2.29409e6			1.89752			0.948761	+	0.315995i	$0.102338\pi$
$272$		0			0
$273$	150554.	+	2.67380e6i	0.122260	+	2.17131i
$274$		0			0
$275$	−216645.	+	1.56299e6i	−0.172750	+	1.24631i
$276$		0			0
$277$	−53946.6	+	53946.6i	−0.0422440	+	0.0422440i	−0.727913	−	0.685669i	$-0.759510\pi$
$277$	−53946.6	+	53946.6i	−0.0422440	+	0.0422440i	0.685669	+	0.727913i	$0.259510\pi$
$278$		0			0
$279$	536120.	−	60566.8i	0.412336	−	0.0465827i
$280$		0			0
$281$			2.07053e6i			1.56428i	0.623101	+	0.782141i	$0.285873\pi$
$281$			2.07053e6i			1.56428i	−0.623101	+	0.782141i	$0.714127\pi$
$282$		0			0
$283$	826504.	+	826504.i	0.613450	+	0.613450i	0.943843	−	0.330394i	$-0.107181\pi$
$283$	826504.	+	826504.i	0.613450	+	0.613450i	−0.330394	+	0.943843i	$0.607181\pi$
$284$		0			0
$285$	523553.	+	6606.54i	0.381811	+	0.00481795i
$286$		0			0
$287$	−1.84027e6	−	1.84027e6i	−1.31879	−	1.31879i
$288$		0			0
$289$		−	1.40323e6i		−	0.988292i
$290$		0			0
$291$	280391.	+	250498.i	0.194103	+	0.173409i
$292$		0			0
$293$	−476780.	+	476780.i	−0.324451	+	0.324451i	−0.850472	−	0.526021i	$-0.823683\pi$
$293$	−476780.	+	476780.i	−0.324451	+	0.324451i	0.526021	+	0.850472i	$0.323683\pi$
$294$		0			0
$295$	−364198.	−	25120.5i	−0.243659	−	0.0168064i
$296$		0			0
$297$	1.88554e6	−	321227.i	1.24035	−	0.211311i
$298$		0			0
$299$	−2.44901e6			−1.58421
$300$		0			0
$301$	−1.80012e6			−1.14521
$302$		0			0
$303$	697240.	−	39259.6i	0.436290	−	0.0245663i
$304$		0			0
$305$	1.58465e6	+	109301.i	0.975405	+	0.0672784i
$306$		0			0
$307$	−517400.	+	517400.i	−0.313314	+	0.313314i	−0.846192	−	0.532878i	$-0.821111\pi$
$307$	−517400.	+	517400.i	−0.313314	+	0.313314i	0.532878	+	0.846192i	$0.321111\pi$
$308$		0			0
$309$	1.65946e6	−	1.85749e6i	0.988715	−	1.10670i
$310$		0			0
$311$			580879.i			0.340553i	0.985396	+	0.170276i	$0.0544661\pi$
$311$			580879.i			0.340553i	−0.985396	+	0.170276i	$0.945534\pi$
$312$		0			0
$313$	−788946.	−	788946.i	−0.455184	−	0.455184i	0.441887	−	0.897071i	$-0.354309\pi$
$313$	−788946.	−	788946.i	−0.455184	−	0.455184i	−0.897071	+	0.441887i	$0.854309\pi$
$314$		0			0
$315$	−1.96351e6	+	2.14278e6i	−1.11495	+	1.21675i
$316$		0			0
$317$	−464640.	−	464640.i	−0.259698	−	0.259698i	0.565233	−	0.824931i	$-0.308786\pi$
$317$	−464640.	−	464640.i	−0.259698	−	0.259698i	−0.824931	+	0.565233i	$0.808786\pi$
$318$		0			0
$319$			2.93776e6i			1.61637i
$320$		0			0
$321$	772084.	−	864219.i	0.418217	−	0.468125i
$322$		0			0
$323$	−54778.5	+	54778.5i	−0.0292149	+	0.0292149i
$324$		0			0
$325$	1.51390e6	+	2.00112e6i	0.795042	+	1.05091i
$326$		0			0
$327$	165280.	−	9306.43i	0.0854771	−	0.00481298i
$328$		0			0
$329$	−1.36176e6			−0.693602
$330$		0			0
$331$	376906.			0.189088			0.0945439	−	0.995521i	$-0.469861\pi$
$331$	376906.			0.189088			0.0945439	+	0.995521i	$0.469861\pi$
$332$		0			0
$333$	1.45463e6	−	1.82516e6i	0.718856	−	0.901965i
$334$		0			0
$335$	−734394.	+	639622.i	−0.357534	+	0.311395i
$336$		0			0
$337$	−1.06686e6	+	1.06686e6i	−0.511719	+	0.511719i	−0.915053	−	0.403334i	$-0.867851\pi$
$337$	−1.06686e6	+	1.06686e6i	−0.511719	+	0.511719i	0.403334	+	0.915053i	$0.367851\pi$
$338$		0			0
$339$	−882684.	−	788580.i	−0.417163	−	0.372689i
$340$		0			0
$341$		−	1.12111e6i		−	0.522111i
$342$		0			0
$343$	−1.83989e6	−	1.83989e6i	−0.844416	−	0.844416i
$344$		0			0
$345$	−1.85549e6	−	1.90292e6i	−0.839289	−	0.860741i
$346$		0			0
$347$	1.95140e6	+	1.95140e6i	0.870005	+	0.870005i	0.992472	−	0.122468i	$-0.0390809\pi$
$347$	1.95140e6	+	1.95140e6i	0.870005	+	0.870005i	−0.122468	+	0.992472i	$0.539081\pi$
$348$		0			0
$349$		−	3.93764e6i		−	1.73050i	−0.501337	−	0.865252i	$-0.667158\pi$
$349$		−	3.93764e6i		−	1.73050i	0.501337	−	0.865252i	$-0.332842\pi$
$350$		0			0
$351$	1.75900e6	−	2.48141e6i	0.762074	−	1.07505i
$352$		0			0
$353$	−399857.	+	399857.i	−0.170792	+	0.170792i	−0.787327	−	0.616535i	$-0.788536\pi$
$353$	−399857.	+	399857.i	−0.170792	+	0.170792i	0.616535	+	0.787327i	$0.288536\pi$
$354$		0			0
$355$	266229.	−	3.85980e6i	0.112121	−	1.62553i
$356$		0			0
$357$	−24174.3	−	429329.i	−0.0100389	−	0.178287i
$358$		0			0
$359$	−610242.			−0.249900			−0.124950	−	0.992163i	$-0.539877\pi$
$359$	−610242.			−0.249900			−0.124950	+	0.992163i	$0.539877\pi$
$360$		0			0
$361$	2.11508e6			0.854197
$362$		0			0
$363$	−82300.8	−	1.46164e6i	−0.0327822	−	0.582202i
$364$		0			0
$365$	−948311.	−	1.08882e6i	−0.372579	−	0.427784i
$366$		0			0
$367$	−2.27572e6	+	2.27572e6i	−0.881969	+	0.881969i	−0.993735	−	0.111765i	$-0.964350\pi$
$367$	−2.27572e6	+	2.27572e6i	−0.881969	+	0.881969i	0.111765	+	0.993735i	$0.464350\pi$
$368$		0			0
$369$	331821.	+	2.93718e6i	0.126864	+	1.12296i
$370$		0			0
$371$		−	7.87711e6i		−	2.97120i
$372$		0			0
$373$	−1.84940e6	−	1.84940e6i	−0.688269	−	0.688269i	0.273580	−	0.961849i	$-0.411792\pi$
$373$	−1.84940e6	−	1.84940e6i	−0.688269	−	0.688269i	−0.961849	+	0.273580i	$0.911792\pi$
$374$		0			0
$375$	−407890.	+	2.69247e6i	−0.149784	+	0.988719i
$376$		0			0
$377$	3.30337e6	+	3.30337e6i	1.19703	+	1.19703i
$378$		0			0
$379$		−	193997.i		−	0.0693740i	−0.999398	−	0.0346870i	$-0.988957\pi$
$379$		−	193997.i		−	0.0693740i	0.999398	−	0.0346870i	$-0.0110434\pi$
$380$		0			0
$381$	−2.04794e6	−	1.82961e6i	−0.722778	−	0.645721i
$382$		0			0
$383$	−3.31948e6	+	3.31948e6i	−1.15631	+	1.15631i	−0.171045	+	0.985263i	$0.554714\pi$
$383$	−3.31948e6	+	3.31948e6i	−1.15631	+	1.15631i	−0.985263	+	0.171045i	$0.945286\pi$
$384$		0			0
$385$	3.96640e6	+	4.55410e6i	1.36378	+	1.56585i
$386$		0			0
$387$	1.59885e6	+	1.27426e6i	0.542662	+	0.432496i
$388$		0			0
$389$	−3.87517e6			−1.29842			−0.649212	−	0.760608i	$-0.724901\pi$
$389$	−3.87517e6			−1.29842			−0.649212	+	0.760608i	$0.724901\pi$
$390$		0			0
$391$	393236.			0.130080
$392$		0			0
$393$	726035.	−	40881.0i	0.237124	−	0.0133518i
$394$		0			0
$395$	−158181.	+	2.29331e6i	−0.0510106	+	0.739554i
$396$		0			0
$397$	−3.13355e6	+	3.13355e6i	−0.997837	+	0.997837i	−0.999998	−	0.00216047i	$-0.999312\pi$
$397$	−3.13355e6	+	3.13355e6i	−0.997837	+	0.997837i	0.00216047	+	0.999998i	$0.499312\pi$
$398$		0			0
$399$	1.33511e6	−	1.49443e6i	0.419840	−	0.469941i
$400$		0			0
$401$			2.10986e6i			0.655229i	0.944812	+	0.327614i	$0.106245\pi$
$401$			2.10986e6i			0.655229i	−0.944812	+	0.327614i	$0.893755\pi$
$402$		0			0
$403$	−1.26064e6	−	1.26064e6i	−0.386658	−	0.386658i
$404$		0			0
$405$	3.26079e6	−	513270.i	0.987837	−	0.155492i
$406$		0			0
$407$	−3.42928e6	−	3.42928e6i	−1.02616	−	1.02616i
$408$		0			0
$409$		−	1.18131e6i		−	0.349186i	−0.984641	−	0.174593i	$-0.944139\pi$
$409$		−	1.18131e6i		−	0.349186i	0.984641	−	0.174593i	$-0.0558609\pi$
$410$		0			0
$411$	1.80699e6	−	2.02262e6i	0.527656	−	0.590623i
$412$		0			0
$413$	−987973.	+	987973.i	−0.285017	+	0.285017i
$414$		0			0
$415$	−3.34195e6	+	2.91068e6i	−0.952533	+	0.829610i
$416$		0			0
$417$	1.38305e6	−	77875.7i	0.389491	−	0.0219312i
$418$		0			0
$419$	4.62127e6			1.28596			0.642978	−	0.765885i	$-0.277699\pi$
$419$	4.62127e6			1.28596			0.642978	+	0.765885i	$0.277699\pi$
$420$		0			0
$421$	5.46797e6			1.50356			0.751780	−	0.659414i	$-0.229196\pi$
$421$	5.46797e6			1.50356			0.751780	+	0.659414i	$0.229196\pi$
$422$		0			0
$423$	1.20950e6	+	963957.i	0.328666	+	0.261943i
$424$		0			0
$425$	−243087.	−	321318.i	−0.0652813	−	0.0862905i
$426$		0			0
$427$	4.29875e6	−	4.29875e6i	1.14096	−	1.14096i
$428$		0			0
$429$	−4.71331e6	−	4.21082e6i	−1.23647	−	1.10465i
$430$		0			0
$431$			7.10096e6i			1.84130i	0.390393	+	0.920648i	$0.372339\pi$
$431$			7.10096e6i			1.84130i	−0.390393	+	0.920648i	$0.627661\pi$
$432$		0			0
$433$	918303.	+	918303.i	0.235378	+	0.235378i	0.814933	−	0.579555i	$-0.196774\pi$
$433$	918303.	+	918303.i	0.235378	+	0.235378i	−0.579555	+	0.814933i	$0.696774\pi$
$434$		0			0
$435$	−63971.1	+	5.06957e6i	−0.0162092	+	1.28454i
$436$		0			0
$437$	1.29583e6	+	1.29583e6i	0.324597	+	0.324597i
$438$		0			0
$439$		−	688839.i		−	0.170591i	−0.996356	−	0.0852955i	$-0.972817\pi$
$439$		−	688839.i		−	0.170591i	0.996356	−	0.0852955i	$-0.0271834\pi$
$440$		0			0
$441$	790229.	+	6.99487e6i	0.193489	+	1.71271i
$442$		0			0
$443$	556700.	−	556700.i	0.134776	−	0.134776i	−0.636500	−	0.771276i	$-0.719619\pi$
$443$	556700.	−	556700.i	0.134776	−	0.134776i	0.771276	+	0.636500i	$0.219619\pi$
$444$		0			0
$445$	−3.04551e6	−	210064.i	−0.729055	−	0.0502865i
$446$		0			0
$447$	−246252.	−	4.37336e6i	−0.0582922	−	1.03525i
$448$		0			0
$449$	−5.83428e6			−1.36575			−0.682875	−	0.730535i	$-0.739271\pi$
$449$	−5.83428e6			−1.36575			−0.682875	+	0.730535i	$0.739271\pi$
$450$		0			0
$451$	6.14212e6			1.42192
$452$		0			0
$453$	334710.	+	5.94435e6i	0.0766342	+	1.36100i
$454$		0			0
$455$	9.58091e6	+	660842.i	2.16959	+	0.149647i
$456$		0			0
$457$	−538370.	+	538370.i	−0.120584	+	0.120584i	−0.764824	−	0.644240i	$-0.777174\pi$
$457$	−538370.	+	538370.i	−0.120584	+	0.120584i	0.644240	+	0.764824i	$0.277174\pi$
$458$		0			0
$459$	−282441.	+	398438.i	−0.0625743	+	0.0882732i
$460$		0			0
$461$		−	8.26708e6i		−	1.81176i	−0.423538	−	0.905878i	$-0.639212\pi$
$461$		−	8.26708e6i		−	1.81176i	0.423538	−	0.905878i	$-0.360788\pi$
$462$		0			0
$463$	228783.	+	228783.i	0.0495987	+	0.0495987i	0.731471	−	0.681872i	$-0.238834\pi$
$463$	228783.	+	228783.i	0.0495987	+	0.0495987i	−0.681872	+	0.731471i	$0.738834\pi$
$464$		0			0
$465$	24412.7	−	1.93465e6i	0.00523581	−	0.414926i
$466$		0			0
$467$	3.86350e6	+	3.86350e6i	0.819763	+	0.819763i	0.986073	−	0.166311i	$-0.0531854\pi$
$467$	3.86350e6	+	3.86350e6i	0.819763	+	0.819763i	−0.166311	+	0.986073i	$0.553185\pi$
$468$		0			0
$469$			3.72734e6i			0.782469i
$470$		0			0
$471$	−2.03981e6	−	1.82235e6i	−0.423680	−	0.378511i
$472$		0			0
$473$	3.00407e6	−	3.00407e6i	0.617386	−	0.617386i
$474$		0			0
$475$	257797.	−	1.85988e6i	0.0524256	−	0.378226i
$476$		0			0
$477$	−5.57602e6	+	6.99635e6i	−1.12209	+	1.40791i
$478$		0			0
$479$	4.63939e6			0.923895			0.461947	−	0.886907i	$-0.347151\pi$
$479$	4.63939e6			0.923895			0.461947	+	0.886907i	$0.347151\pi$
$480$		0			0
$481$	−7.71212e6			−1.51989
$482$		0			0
$483$	−1.01561e7	+	571863.i	−1.98089	+	0.111538i
$484$		0			0
$485$	1.01676e6	−	885552.i	0.196275	−	0.170946i
$486$		0			0
$487$	3.08733e6	−	3.08733e6i	0.589875	−	0.589875i	−0.347722	−	0.937598i	$-0.613045\pi$
$487$	3.08733e6	−	3.08733e6i	0.589875	−	0.589875i	0.937598	+	0.347722i	$0.113045\pi$
$488$		0			0
$489$	1.93580e6	−	2.16681e6i	0.366091	−	0.409778i
$490$		0			0
$491$			3.63927e6i			0.681256i	0.940198	+	0.340628i	$0.110640\pi$
$491$			3.63927e6i			0.681256i	−0.940198	+	0.340628i	$0.889360\pi$
$492$		0			0
$493$	−530420.	−	530420.i	−0.0982885	−	0.0982885i
$494$		0			0
$495$	−299169.	−	6.85263e6i	−0.0548786	−	1.25703i
$496$		0			0
$497$	−1.04706e7	−	1.04706e7i	−1.90144	−	1.90144i
$498$		0			0
$499$			6.06954e6i			1.09120i	0.838046	+	0.545600i	$0.183698\pi$
$499$			6.06954e6i			1.09120i	−0.838046	+	0.545600i	$0.816302\pi$
$500$		0			0
$501$	−1.66044e6	+	1.85858e6i	−0.295548	+	0.330817i
$502$		0			0
$503$	−163619.	+	163619.i	−0.0288346	+	0.0288346i	−0.721377	−	0.692543i	$-0.756491\pi$
$503$	−163619.	+	163619.i	−0.0288346	+	0.0288346i	0.692543	+	0.721377i	$0.256491\pi$
$504$		0			0
$505$	172326.	−	2.49839e6i	0.0300693	−	0.435946i
$506$		0			0
$507$	−4.25603e6	+	239645.i	−0.735334	+	0.0414046i
$508$		0			0
$509$	3.60298e6			0.616407			0.308203	−	0.951321i	$-0.400272\pi$
$509$	3.60298e6			0.616407			0.308203	+	0.951321i	$0.400272\pi$
$510$		0			0
$511$	−5.52620e6			−0.936213
$512$		0			0
$513$	−2.24370e6	+	382244.i	−0.376418	+	0.0641280i
$514$		0			0
$515$	−5.86647e6	−	6.73570e6i	−0.974673	−	1.11909i
$516$		0			0
$517$	2.27252e6	−	2.27252e6i	0.373922	−	0.373922i
$518$		0			0
$519$	2.92034e6	+	2.60900e6i	0.475899	+	0.425163i
$520$		0			0
$521$		−	3.06124e6i		−	0.494087i	−0.969004	−	0.247043i	$-0.920541\pi$
$521$		−	3.06124e6i		−	0.494087i	0.969004	−	0.247043i	$-0.0794590\pi$
$522$		0			0
$523$	−1.90090e6	−	1.90090e6i	−0.303882	−	0.303882i	0.538649	−	0.842530i	$-0.318935\pi$
$523$	−1.90090e6	−	1.90090e6i	−0.303882	−	0.303882i	−0.842530	+	0.538649i	$0.818935\pi$
$524$		0			0
$525$	6.74548e6	+	7.94519e6i	1.06811	+	1.25807i
$526$		0			0
$527$	202419.	+	202419.i	0.0317487	+	0.0317487i
$528$		0			0
$529$		−	2.86597e6i		−	0.445280i
$530$		0			0
$531$	1.57687e6	−	178143.i	0.242694	−	0.0274178i
$532$		0			0
$533$	6.90652e6	−	6.90652e6i	1.05303	−	1.05303i
$534$		0			0
$535$	−2.72944e6	−	3.13386e6i	−0.412277	−	0.473364i
$536$		0			0
$537$	197048.	+	3.49952e6i	0.0294875	+	0.523689i
$538$		0			0
$539$	1.46274e7			2.16867
$540$		0			0
$541$	−3.55404e6			−0.522071			−0.261036	−	0.965329i	$-0.584064\pi$
$541$	−3.55404e6			−0.522071			−0.261036	+	0.965329i	$0.584064\pi$
$542$		0			0
$543$	−377089.	−	6.69698e6i	−0.0548838	−	0.974720i
$544$		0			0
$545$	40849.7	−	592240.i	0.00589112	−	0.0854096i
$546$		0			0
$547$	−4.09378e6	+	4.09378e6i	−0.585001	+	0.585001i	−0.936273	−	0.351272i	$-0.885749\pi$
$547$	−4.09378e6	+	4.09378e6i	−0.585001	+	0.585001i	0.351272	+	0.936273i	$0.385749\pi$
$548$		0			0
$549$	−6.86108e6	+	775114.i	−0.971542	+	0.109758i
$550$		0			0
$551$		−	3.49578e6i		−	0.490530i
$552$		0			0
$553$	6.22114e6	+	6.22114e6i	0.865082	+	0.865082i
$554$		0			0
$555$	−5.84308e6	−	5.99243e6i	−0.805210	−	0.825791i
$556$		0			0
$557$	3.45849e6	+	3.45849e6i	0.472334	+	0.472334i	0.902669	−	0.430335i	$-0.141605\pi$
$557$	3.45849e6	+	3.45849e6i	0.472334	+	0.472334i	−0.430335	+	0.902669i	$0.641605\pi$
$558$		0			0
$559$		−	6.75586e6i		−	0.914432i
$560$		0			0
$561$	756812.	+	676127.i	0.101527	+	0.0907029i
$562$		0			0
$563$	2.34764e6	−	2.34764e6i	0.312149	−	0.312149i	−0.533593	−	0.845741i	$-0.679159\pi$
$563$	2.34764e6	−	2.34764e6i	0.312149	−	0.312149i	0.845741	+	0.533593i	$0.179159\pi$
$564$		0			0
$565$	−3.20082e6	+	2.78776e6i	−0.421833	+	0.367396i
$566$		0			0
$567$	6.71518e6	−	1.07012e7i	0.877203	−	1.39790i
$568$		0			0
$569$	−9.86323e6			−1.27714			−0.638570	−	0.769564i	$-0.720474\pi$
$569$	−9.86323e6			−1.27714			−0.638570	+	0.769564i	$0.720474\pi$
$570$		0			0
$571$	−1.01430e6			−0.130190			−0.0650949	−	0.997879i	$-0.520735\pi$
$571$	−1.01430e6			−0.130190			−0.0650949	+	0.997879i	$0.520735\pi$
$572$		0			0
$573$	7.46735e6	−	420466.i	0.950124	−	0.0534988i
$574$		0			0
$575$	−7.60104e6	+	5.75040e6i	−0.958745	+	0.725319i
$576$		0			0
$577$	4.10779e6	−	4.10779e6i	0.513652	−	0.513652i	−0.401991	−	0.915643i	$-0.631682\pi$
$577$	4.10779e6	−	4.10779e6i	0.513652	−	0.513652i	0.915643	+	0.401991i	$0.131682\pi$
$578$		0			0
$579$	−8.24105e6	+	9.22449e6i	−1.02161	+	1.14353i
$580$		0			0
$581$			1.69617e7i			2.08463i
$582$		0			0
$583$	1.31454e7	+	1.31454e7i	1.60178	+	1.60178i
$584$		0			0
$585$	−8.04186e6	−	7.36906e6i	−0.971554	−	0.890271i
$586$		0			0
$587$	6.58247e6	+	6.58247e6i	0.788486	+	0.788486i	0.981246	−	0.192760i	$-0.0617439\pi$
$587$	6.58247e6	+	6.58247e6i	0.788486	+	0.788486i	−0.192760	+	0.981246i	$0.561744\pi$
$588$		0			0
$589$			1.33406e6i			0.158449i
$590$		0			0
$591$	−3.87860e6	+	4.34145e6i	−0.456779	+	0.511289i
$592$		0			0
$593$	3.18682e6	−	3.18682e6i	0.372152	−	0.372152i	−0.496108	−	0.868261i	$-0.665238\pi$
$593$	3.18682e6	−	3.18682e6i	0.372152	−	0.372152i	0.868261	+	0.496108i	$0.165238\pi$
$594$		0			0
$595$	−1.53840e6	−	106111.i	−0.178146	−	0.0122876i
$596$		0			0
$597$	−1.73630e6	+	97766.0i	−0.199383	+	0.0112267i
$598$		0			0
$599$	−5.57885e6			−0.635298			−0.317649	−	0.948208i	$-0.602893\pi$
$599$	−5.57885e6			−0.635298			−0.317649	+	0.948208i	$0.602893\pi$
$600$		0			0
$601$	−1.45159e7			−1.63930			−0.819651	−	0.572863i	$-0.805833\pi$
$601$	−1.45159e7			−1.63930			−0.819651	+	0.572863i	$0.805833\pi$
$602$		0			0
$603$	2.63850e6	−	3.31058e6i	0.295504	−	0.370776i
$604$		0			0
$605$	−5.23744e6	−	361252.i	−0.581742	−	0.0401256i
$606$		0			0
$607$	121683.	−	121683.i	0.0134047	−	0.0134047i	−0.700373	−	0.713777i	$-0.746983\pi$
$607$	121683.	−	121683.i	0.0134047	−	0.0134047i	0.713777	+	0.700373i	$0.246983\pi$
$608$		0			0
$609$	1.44705e7	+	1.29278e7i	1.58104	+	1.41248i
$610$		0			0
$611$		−	5.11068e6i		−	0.553829i
$612$		0			0
$613$	5.08678e6	+	5.08678e6i	0.546754	+	0.546754i	0.925500	−	0.378747i	$-0.123645\pi$
$613$	5.08678e6	+	5.08678e6i	0.546754	+	0.546754i	−0.378747	+	0.925500i	$0.623645\pi$
$614$		0			0
$615$	1.05992e7	+	133748.i	1.13002	+	0.0142593i
$616$		0			0
$617$	−452387.	−	452387.i	−0.0478407	−	0.0478407i	0.682782	−	0.730622i	$-0.260770\pi$
$617$	−452387.	−	452387.i	−0.0478407	−	0.0478407i	−0.730622	+	0.682782i	$0.760770\pi$
$618$		0			0
$619$		−	1.04321e7i		−	1.09432i	−0.837029	−	0.547159i	$-0.815709\pi$
$619$		−	1.04321e7i		−	1.09432i	0.837029	−	0.547159i	$-0.184291\pi$
$620$		0			0
$621$	9.42536e6	+	6.68136e6i	0.980774	+	0.695242i
$622$		0			0
$623$	−8.26167e6	+	8.26167e6i	−0.852801	+	0.852801i
$624$		0			0
$625$	9.39745e6	+	2.65618e6i	0.962299	+	0.271993i
$626$		0			0
$627$	265880.	+	4.72196e6i	0.0270096	+	0.479682i
$628$		0			0
$629$	1.23833e6			0.124799
$630$		0			0
$631$	569289.			0.0569193			0.0284597	−	0.999595i	$-0.490940\pi$
$631$	569289.			0.0569193			0.0284597	+	0.999595i	$0.490940\pi$
$632$		0			0
$633$	−817442.	−	1.45175e7i	−0.0810863	−	1.44007i
$634$		0			0
$635$	−7.42631e6	+	6.46795e6i	−0.730867	+	0.636550i
$636$		0			0
$637$	1.64478e7	−	1.64478e7i	1.60605	−	1.60605i
$638$		0			0
$639$	1.88798e6	+	1.67118e7i	0.182913	+	1.61909i
$640$		0			0
$641$			4.83316e6i			0.464607i	0.972643	+	0.232304i	$0.0746263\pi$
$641$			4.83316e6i			0.464607i	−0.972643	+	0.232304i	$0.925374\pi$
$642$		0			0
$643$	6.92195e6	+	6.92195e6i	0.660239	+	0.660239i	0.955436	−	0.295197i	$-0.0953854\pi$
$643$	6.92195e6	+	6.92195e6i	0.660239	+	0.660239i	−0.295197	+	0.955436i	$0.595385\pi$
$644$		0			0
$645$	5.24940e6	−	5.11857e6i	0.496833	−	0.484450i
$646$		0			0
$647$	−30646.6	−	30646.6i	−0.00287820	−	0.00287820i	0.705666	−	0.708544i	$-0.250648\pi$
$647$	−30646.6	−	30646.6i	−0.00287820	−	0.00287820i	−0.708544	+	0.705666i	$0.750648\pi$
$648$		0			0
$649$		−	3.29748e6i		−	0.307306i
$650$		0			0
$651$	−5.52226e6	−	4.93353e6i	−0.510699	−	0.456252i
$652$		0			0
$653$	−1.22854e7	+	1.22854e7i	−1.12747	+	1.12747i	−0.136886	+	0.990587i	$0.543709\pi$
$653$	−1.22854e7	+	1.22854e7i	−1.12747	+	1.12747i	−0.990587	+	0.136886i	$0.956291\pi$
$654$		0			0
$655$	179443.	−	2.60157e6i	0.0163427	−	0.236937i
$656$		0			0
$657$	4.90831e6	+	3.91187e6i	0.443628	+	0.353566i
$658$		0			0
$659$	−8.98333e6			−0.805794			−0.402897	−	0.915245i	$-0.631997\pi$
$659$	−8.98333e6			−0.805794			−0.402897	+	0.915245i	$0.631997\pi$
$660$		0			0
$661$	3.77555e6			0.336106			0.168053	−	0.985778i	$-0.446252\pi$
$661$	3.77555e6			0.336106			0.168053	+	0.985778i	$0.446252\pi$
$662$		0			0
$663$	1.61127e6	−	90726.4i	0.142359	−	0.00801585i
$664$		0			0
$665$	−4.71982e6	−	5.41915e6i	−0.413877	−	0.475201i
$666$		0			0
$667$	−1.25475e7	+	1.25475e7i	−1.09205	+	1.09205i
$668$		0			0
$669$	1.27222e7	−	1.42404e7i	1.09900	−	1.23014i
$670$		0			0
$671$			1.43476e7i			1.23019i
$672$		0			0
$673$	−3.92841e6	−	3.92841e6i	−0.334333	−	0.334333i	0.519897	−	0.854229i	$-0.325970\pi$
$673$	−3.92841e6	−	3.92841e6i	−0.334333	−	0.334333i	−0.854229	+	0.519897i	$0.825970\pi$
$674$		0			0
$675$	−367043.	−	1.18318e7i	−0.0310069	−	0.999519i
$676$		0			0
$677$	−9.42349e6	−	9.42349e6i	−0.790206	−	0.790206i	0.191322	−	0.981527i	$-0.438723\pi$
$677$	−9.42349e6	−	9.42349e6i	−0.790206	−	0.790206i	−0.981527	+	0.191322i	$0.938723\pi$
$678$		0			0
$679$		−	5.16048e6i		−	0.429552i
$680$		0			0
$681$	1.15335e7	−	1.29098e7i	0.952998	−	1.06672i
$682$		0			0
$683$	9.25718e6	−	9.25718e6i	0.759323	−	0.759323i	−0.216876	−	0.976199i	$-0.569587\pi$
$683$	9.25718e6	−	9.25718e6i	0.759323	−	0.759323i	0.976199	+	0.216876i	$0.0695867\pi$
$684$		0			0
$685$	−6.38800e6	−	7.33451e6i	−0.520162	−	0.597234i
$686$		0			0
$687$	−2.10280e7	+	1.18403e6i	−1.69983	+	0.0957127i
$688$		0			0
$689$	2.95628e7			2.37245
$690$		0			0
$691$	−8.39289e6			−0.668677			−0.334339	−	0.942453i	$-0.608513\pi$
$691$	−8.39289e6			−0.668677			−0.334339	+	0.942453i	$0.608513\pi$
$692$		0			0
$693$	−2.05295e7	−	1.63618e7i	−1.62385	−	1.29419i
$694$		0			0
$695$	341828.	−	4.95583e6i	0.0268439	−	0.389183i
$696$		0			0
$697$	−1.10898e6	+	1.10898e6i	−0.0864649	+	0.0864649i
$698$		0			0
$699$	3.47953e6	+	3.10858e6i	0.269357	+	0.240640i
$700$		0			0
$701$		−	70263.9i		−	0.00540054i	−0.999996	−	0.00270027i	$-0.999140\pi$
$701$		−	70263.9i		−	0.00540054i	0.999996	−	0.00270027i	$-0.000859523\pi$
$702$		0			0
$703$	4.08066e6	+	4.08066e6i	0.311417	+	0.311417i
$704$		0			0
$705$	3.97107e6	−	3.87210e6i	0.300909	−	0.293409i
$706$		0			0
$707$	−6.77748e6	−	6.77748e6i	−0.509941	−	0.509941i
$708$		0			0
$709$			1.88394e7i			1.40751i	0.710444	+	0.703753i	$0.248494\pi$
$709$			1.88394e7i			1.40751i	−0.710444	+	0.703753i	$0.751506\pi$
$710$		0			0
$711$	−1.12174e6	−	9.92934e6i	−0.0832185	−	0.736625i
$712$		0			0
$713$	4.78839e6	−	4.78839e6i	0.352749	−	0.352749i
$714$		0			0
$715$	−1.70916e7	+	1.48859e7i	−1.25031	+	1.08896i
$716$		0			0
$717$	973931.	+	1.72967e7i	0.0707506	+	1.25651i
$718$		0			0
$719$	−2.51796e7			−1.81646			−0.908232	−	0.418467i	$-0.862568\pi$
$719$	−2.51796e7			−1.81646			−0.908232	+	0.418467i	$0.862568\pi$
$720$		0			0
$721$	−3.41864e7			−2.44915
$722$		0			0
$723$	439327.	+	7.80232e6i	0.0312566	+	0.555109i
$724$		0			0
$725$	1.80092e7	+	2.49624e6i	1.27248	+	0.176377i
$726$		0			0
$727$	6.41853e6	−	6.41853e6i	0.450401	−	0.450401i	−0.445087	−	0.895488i	$-0.646827\pi$
$727$	6.41853e6	−	6.41853e6i	0.450401	−	0.450401i	0.895488	+	0.445087i	$0.146827\pi$
$728$		0			0
$729$	−1.35395e7	+	4.75117e6i	−0.943590	+	0.331117i
$730$		0			0
$731$			1.08478e6i			0.0750844i
$732$		0			0
$733$	−204706.	−	204706.i	−0.0140725	−	0.0140725i	0.700036	−	0.714108i	$-0.253167\pi$
$733$	−204706.	−	204706.i	−0.0140725	−	0.0140725i	−0.714108	+	0.700036i	$0.753167\pi$
$734$		0			0
$735$	2.52418e7	+	318518.i	1.72346	+	0.0217478i
$736$		0			0
$737$	−6.22023e6	−	6.22023e6i	−0.421830	−	0.421830i
$738$		0			0
$739$		−	4.41366e6i		−	0.297295i	−0.988890	−	0.148648i	$-0.952508\pi$
$739$		−	4.41366e6i		−	0.297295i	0.988890	−	0.148648i	$-0.0474920\pi$
$740$		0			0
$741$	5.60859e6	+	5.01065e6i	0.375239	+	0.335235i
$742$		0			0
$743$	−2.20078e6	+	2.20078e6i	−0.146253	+	0.146253i	−0.776442	−	0.630189i	$-0.782977\pi$
$743$	−2.20078e6	+	2.20078e6i	−0.146253	+	0.146253i	0.630189	+	0.776442i	$0.282977\pi$
$744$		0			0
$745$	−1.56709e7	−	1.08090e6i	−1.03443	−	0.0713500i
$746$		0			0
$747$	1.20068e7	−	1.50652e7i	0.787275	−	0.987811i
$748$		0			0
$749$	−1.59056e7			−1.03597
$750$		0			0
$751$	1.91761e7			1.24068			0.620342	−	0.784331i	$-0.286994\pi$
$751$	1.91761e7			1.24068			0.620342	+	0.784331i	$0.286994\pi$
$752$		0			0
$753$	−1.04163e6	+	58651.2i	−0.0669462	+	0.00376955i
$754$		0			0
$755$	2.13002e7	+	1.46918e6i	1.35993	+	0.0938008i
$756$		0			0
$757$	1.86673e7	−	1.86673e7i	1.18397	−	1.18397i	0.205268	−	0.978706i	$-0.434193\pi$
$757$	1.86673e7	−	1.86673e7i	1.18397	−	1.18397i	0.978706	−	0.205268i	$-0.0658066\pi$
$758$		0			0
$759$	1.59943e7	−	1.79030e7i	1.00777	−	1.12803i
$760$		0			0
$761$		−	2.47189e7i		−	1.54727i	−0.633630	−	0.773636i	$-0.718436\pi$
$761$		−	2.47189e7i		−	1.54727i	0.633630	−	0.773636i	$-0.281564\pi$
$762$		0			0
$763$	−1.60659e6	−	1.60659e6i	−0.0999066	−	0.0999066i
$764$		0			0
$765$	1.29128e6	+	1.18324e6i	0.0797747	+	0.0731005i
$766$		0			0
$767$	−3.70787e6	−	3.70787e6i	−0.227581	−	0.227581i
$768$		0			0
$769$		−	2.40867e7i		−	1.46880i	−0.678718	−	0.734399i	$-0.737464\pi$
$769$		−	2.40867e7i		−	1.46880i	0.678718	−	0.734399i	$-0.262536\pi$
$770$		0			0
$771$	−1.62962e7	+	1.82409e7i	−0.987301	+	1.10512i
$772$		0			0
$773$	−1.74914e7	+	1.74914e7i	−1.05287	+	1.05287i	−0.0543506	+	0.998522i	$0.517309\pi$
$773$	−1.74914e7	+	1.74914e7i	−1.05287	+	1.05287i	−0.998522	+	0.0543506i	$0.982691\pi$
$774$		0			0
$775$	−6.87269e6	−	952619.i	−0.411029	−	0.0569724i
$776$		0			0
$777$	−3.19824e7	+	1.80084e6i	−1.90046	+	0.107010i
$778$		0			0
$779$	−7.30880e6			−0.431522
$780$		0			0
$781$	3.49470e7			2.05013
$782$		0			0
$783$	−3.70127e6	−	2.17257e7i	−0.215748	−	1.26640i
$784$		0			0
$785$	−7.39684e6	+	6.44229e6i	−0.428423	+	0.373135i
$786$		0			0
$787$	−35513.6	+	35513.6i	−0.00204389	+	0.00204389i	−0.708128	−	0.706084i	$-0.750460\pi$
$787$	−35513.6	+	35513.6i	−0.00204389	+	0.00204389i	0.706084	+	0.708128i	$0.250460\pi$
$788$		0			0
$789$	−186520.	−	166635.i	−0.0106668	−	0.00952958i
$790$		0			0
$791$			1.62454e7i			0.923188i
$792$		0			0
$793$	1.61332e7	+	1.61332e7i	0.911041	+	0.911041i
$794$		0			0
$795$	2.23982e7	+	2.29707e7i	1.25688	+	1.28901i
$796$		0			0
$797$	2.28117e7	+	2.28117e7i	1.27207	+	1.27207i	0.944998	+	0.327076i	$0.106063\pi$
$797$	2.28117e7	+	2.28117e7i	1.27207	+	1.27207i	0.327076	+	0.944998i	$0.393937\pi$
$798$		0			0
$799$			820618.i			0.0454752i
$800$		0			0
$801$	1.31862e7	−	1.48968e6i	0.726168	−	0.0820371i
$802$		0			0
$803$	9.22219e6	−	9.22219e6i	0.504714	−	0.504714i
$804$		0			0
$805$	−2.51014e6	+	3.63921e7i	−0.136524	+	1.97933i
$806$		0			0
$807$	1.33248e6	+	2.36644e7i	0.0720237	+	1.27912i
$808$		0			0
$809$	2.76782e7			1.48685			0.743424	−	0.668820i	$-0.233200\pi$
$809$	2.76782e7			1.48685			0.743424	+	0.668820i	$0.233200\pi$
$810$		0			0
$811$	2.48077e7			1.32445			0.662224	−	0.749306i	$-0.269613\pi$
$811$	2.48077e7			1.32445			0.662224	+	0.749306i	$0.269613\pi$
$812$		0			0
$813$	2.01043e6	+	3.57047e7i	0.106675	+	1.89452i
$814$		0			0
$815$	−6.84338e6	−	7.85736e6i	−0.360892	−	0.414365i
$816$		0			0
$817$	−3.57468e6	+	3.57468e6i	−0.187362	+	0.187362i
$818$		0			0
$819$	−4.14825e7	+	4.68639e6i	−2.16100	+	0.244134i
$820$		0			0
$821$		−	2.39255e7i		−	1.23880i	−0.785074	−	0.619402i	$-0.787375\pi$
$821$		−	2.39255e7i		−	1.23880i	0.785074	−	0.619402i	$-0.212625\pi$
$822$		0			0
$823$	−2.14187e7	−	2.14187e7i	−1.10228	−	1.10228i	−0.994135	−	0.108147i	$-0.965508\pi$
$823$	−2.14187e7	−	2.14187e7i	−1.10228	−	1.10228i	−0.108147	−	0.994135i	$-0.534492\pi$
$824$		0			0
$825$	−2.45160e7	−	2.00209e6i	−1.25405	−	0.102411i
$826$		0			0
$827$	9.79808e6	+	9.79808e6i	0.498170	+	0.498170i	0.910868	−	0.412698i	$-0.135414\pi$
$827$	9.79808e6	+	9.79808e6i	0.498170	+	0.498170i	−0.412698	+	0.910868i	$0.635414\pi$
$828$		0			0
$829$			5.48957e6i			0.277429i	0.990332	+	0.138714i	$0.0442970\pi$
$829$			5.48957e6i			0.277429i	−0.990332	+	0.138714i	$0.955703\pi$
$830$		0			0
$831$	−886891.	−	792338.i	−0.0445520	−	0.0398023i
$832$		0			0
$833$	−2.64101e6	+	2.64101e6i	−0.131874	+	0.131874i
$834$		0			0
$835$	5.86991e6	+	6.73966e6i	0.291350	+	0.334520i
$836$		0			0
$837$	1.41248e6	+	8.29098e6i	0.0696898	+	0.409065i
$838$		0			0
$839$	2.25564e7			1.10628			0.553139	−	0.833089i	$-0.313430\pi$
$839$	2.25564e7			1.10628			0.553139	+	0.833089i	$0.313430\pi$
$840$		0			0
$841$	1.33385e7			0.650305
$842$		0			0
$843$	−3.22253e7	+	1.81452e6i	−1.56181	+	0.0879411i
$844$		0			0
$845$	−1.05190e6	+	1.52505e7i	−0.0506795	+	0.734753i
$846$		0			0
$847$	−1.42078e7	+	1.42078e7i	−0.680484	+	0.680484i
$848$		0			0
$849$	−1.21392e7	+	1.35879e7i	−0.577992	+	0.646967i
$850$		0			0
$851$		−	2.92937e7i		−	1.38660i
$852$		0			0
$853$	−2.04195e7	−	2.04195e7i	−0.960889	−	0.960889i	0.0383747	−	0.999263i	$-0.487782\pi$
$853$	−2.04195e7	−	2.04195e7i	−0.960889	−	0.960889i	−0.999263	+	0.0383747i	$0.987782\pi$
$854$		0			0
$855$	355995.	+	8.15427e6i	0.0166544	+	0.381478i
$856$		0			0
$857$	1.82606e7	+	1.82606e7i	0.849301	+	0.849301i	0.990046	−	0.140744i	$-0.0449496\pi$
$857$	1.82606e7	+	1.82606e7i	0.849301	+	0.849301i	−0.140744	+	0.990046i	$0.544950\pi$
$858$		0			0
$859$		−	4.20747e7i		−	1.94553i	−0.231795	−	0.972765i	$-0.574460\pi$
$859$		−	4.20747e7i		−	1.94553i	0.231795	−	0.972765i	$-0.425540\pi$
$860$		0			0
$861$	2.70288e7	−	3.02543e7i	1.24257	−	1.39085i
$862$		0			0
$863$	−6.06377e6	+	6.06377e6i	−0.277151	+	0.277151i	−0.831971	−	0.554820i	$-0.812787\pi$
$863$	−6.06377e6	+	6.06377e6i	−0.277151	+	0.277151i	0.554820	+	0.831971i	$0.312787\pi$
$864$		0			0
$865$	1.05898e7	−	9.22323e6i	0.481226	−	0.419124i
$866$		0			0
$867$	2.18397e7	−	1.22973e6i	0.986729	−	0.0555600i
$868$		0			0
$869$	−2.07638e7			−0.932734
$870$		0			0
$871$	−1.39887e7			−0.624788
$872$		0			0
$873$	−3.65298e6	+	4.58348e6i	−0.162223	+	0.203545i
$874$		0			0
$875$	3.12881e7	−	2.04454e7i	1.38153	−	0.902766i
$876$		0			0
$877$	−1.55418e7	+	1.55418e7i	−0.682342	+	0.682342i	−0.960527	−	0.278185i	$-0.910267\pi$
$877$	−1.55418e7	+	1.55418e7i	−0.682342	+	0.682342i	0.278185	+	0.960527i	$0.410267\pi$
$878$		0			0
$879$	−7.83834e6	−	7.00268e6i	−0.342178	−	0.305698i
$880$		0			0
$881$		−	3.84506e6i		−	0.166902i	−0.996512	−	0.0834512i	$-0.973406\pi$
$881$		−	3.84506e6i		−	0.166902i	0.996512	−	0.0834512i	$-0.0265943\pi$
$882$		0			0
$883$	3.06162e7	+	3.06162e7i	1.32145	+	1.32145i	0.912605	+	0.408843i	$0.134068\pi$
$883$	3.06162e7	+	3.06162e7i	1.32145	+	1.32145i	0.408843	+	0.912605i	$0.365932\pi$
$884$		0			0
$885$	71804.3	−	5.69032e6i	0.00308171	−	0.244219i
$886$		0			0
$887$	6.56472e6	+	6.56472e6i	0.280161	+	0.280161i	0.833173	−	0.553012i	$-0.186522\pi$
$887$	6.56472e6	+	6.56472e6i	0.280161	+	0.280161i	−0.553012	+	0.833173i	$0.686522\pi$
$888$		0			0
$889$			3.76915e7i			1.59952i
$890$		0			0
$891$	6.65192e6	+	2.90647e7i	0.280707	+	1.22651i
$892$		0			0
$893$	−2.70418e6	+	2.70418e6i	−0.113477	+	0.113477i
$894$		0			0
$895$	1.25397e7	+	864925.i	0.523275	+	0.0360928i
$896$		0			0
$897$	−2.14620e6	−	3.81160e7i	−0.0890615	−	1.58171i
$898$		0			0
$899$	−1.29177e7			−0.533074
$900$		0			0
$901$	−4.74687e6			−0.194803
$902$		0			0
$903$	−1.57755e6	−	2.80168e7i	−0.0643817	−	1.14340i
$904$		0			0
$905$	−2.39971e7	−	1.65519e6i	−0.973949	−	0.0671781i
$906$		0			0
$907$	6.62226e6	−	6.62226e6i	0.267293	−	0.267293i	−0.560715	−	0.828009i	$-0.689474\pi$
$907$	6.62226e6	−	6.62226e6i	0.267293	−	0.267293i	0.828009	+	0.560715i	$0.189474\pi$
$908$		0			0
$909$	1.22206e6	+	1.08173e7i	0.0490549	+	0.434219i
$910$		0			0
$911$		−	2.25035e7i		−	0.898368i	−0.893439	−	0.449184i	$-0.851715\pi$
$911$		−	2.25035e7i		−	0.898368i	0.893439	−	0.449184i	$-0.148285\pi$
$912$		0			0
$913$	−2.83059e7	−	2.83059e7i	−1.12383	−	1.12383i
$914$		0			0
$915$	−312426.	+	2.47590e7i	−0.0123366	+	0.977644i
$916$		0			0
$917$	−7.05738e6	−	7.05738e6i	−0.277153	−	0.277153i
$918$		0			0
$919$		−	2.33232e7i		−	0.910960i	−0.890246	−	0.455480i	$-0.849468\pi$
$919$		−	2.33232e7i		−	0.910960i	0.890246	−	0.455480i	$-0.150532\pi$
$920$		0			0
$921$	−8.50614e6	−	7.59928e6i	−0.330433	−	0.295205i
$922$		0			0
$923$	3.92963e7	−	3.92963e7i	1.51826	−	1.51826i
$924$		0			0
$925$	−2.39362e7	+	1.81084e7i	−0.919816	+	0.695868i
$926$		0			0
$927$	3.03639e7	+	2.41997e7i	1.16054	+	0.924935i
$928$		0			0
$929$	7.09918e6			0.269879			0.134939	−	0.990854i	$-0.456916\pi$
$929$	7.09918e6			0.269879			0.134939	+	0.990854i	$0.456916\pi$
$930$		0			0
$931$	−1.74058e7			−0.658143
$932$		0			0
$933$	−9.04068e6	+	509056.i	−0.340014	+	0.0191453i
$934$		0			0
$935$	2.74438e6	−	2.39022e6i	0.102663	−	0.0894147i
$936$		0			0
$937$	6.75325e6	−	6.75325e6i	0.251284	−	0.251284i	−0.570213	−	0.821497i	$-0.693139\pi$
$937$	6.75325e6	−	6.75325e6i	0.251284	−	0.251284i	0.821497	+	0.570213i	$0.193139\pi$
$938$		0			0
$939$	1.15876e7	−	1.29704e7i	0.428874	−	0.480053i
$940$		0			0
$941$		−	1.55046e7i		−	0.570802i	−0.958408	−	0.285401i	$-0.907873\pi$
$941$		−	1.55046e7i		−	0.570802i	0.958408	−	0.285401i	$-0.0921268\pi$
$942$		0			0
$943$	2.62337e7	+	2.62337e7i	0.960683	+	0.960683i
$944$		0			0
$945$	−3.50705e7	−	2.86818e7i	−1.27751	−	1.04479i
$946$		0			0
$947$	−1.69942e7	−	1.69942e7i	−0.615779	−	0.615779i	0.328667	−	0.944446i	$-0.393401\pi$
$947$	−1.69942e7	−	1.69942e7i	−0.615779	−	0.615779i	−0.944446	+	0.328667i	$0.893401\pi$
$948$		0			0
$949$		−	2.07399e7i		−	0.747550i
$950$		0			0
$951$	6.82438e6	−	7.63876e6i	0.244688	−	0.273887i
$952$		0			0
$953$	1.69842e7	−	1.69842e7i	0.605779	−	0.605779i	−0.336062	−	0.941840i	$-0.609095\pi$
$953$	1.69842e7	−	1.69842e7i	0.605779	−	0.605779i	0.941840	+	0.336062i	$0.109095\pi$
$954$		0			0
$955$	1.84560e6	−	2.67575e7i	0.0654829	−	0.949373i
$956$		0			0
$957$	−4.57227e7	+	2.57452e6i	−1.61381	+	0.0908691i
$958$		0			0
$959$	−3.72255e7			−1.30706
$960$		0			0
$961$	−2.36995e7			−0.827809
$962$		0			0
$963$	1.41272e7	+	1.12592e7i	0.490896	+	0.391239i
$964$		0			0
$965$	2.91335e7	+	3.34502e7i	1.00710	+	1.15632i
$966$		0			0
$967$	−3.70755e7	+	3.70755e7i	−1.27503	+	1.27503i	−0.331615	+	0.943415i	$0.607594\pi$
$967$	−3.70755e7	+	3.70755e7i	−1.27503	+	1.27503i	−0.943415	+	0.331615i	$0.892406\pi$
$968$		0			0
$969$	−900568.	−	804557.i	−0.0308111	−	0.0275263i
$970$		0			0
$971$			1.45718e6i			0.0495982i	0.999692	+	0.0247991i	$0.00789460\pi$
$971$			1.45718e6i			0.0495982i	−0.999692	+	0.0247991i	$0.992105\pi$
$972$		0			0
$973$	−1.34439e7	−	1.34439e7i	−0.455241	−	0.455241i
$974$		0			0
$975$	−2.98183e7	+	2.53158e7i	−1.00455	+	0.852865i
$976$		0			0
$977$	−1.76383e7	−	1.76383e7i	−0.591182	−	0.591182i	0.346769	−	0.937951i	$-0.387279\pi$
$977$	−1.76383e7	−	1.76383e7i	−0.591182	−	0.591182i	−0.937951	+	0.346769i	$0.887279\pi$
$978$		0			0
$979$		−	2.75743e7i		−	0.919493i
$980$		0			0
$981$	289687.	+	2.56422e6i	0.00961073	+	0.0850713i
$982$		0			0
$983$	−2.17052e7	+	2.17052e7i	−0.716442	+	0.716442i	−0.967875	−	0.251433i	$-0.919098\pi$
$983$	−2.17052e7	+	2.17052e7i	−0.716442	+	0.716442i	0.251433	+	0.967875i	$0.419098\pi$
$984$		0			0
$985$	1.37115e7	+	1.57431e7i	0.450292	+	0.517011i
$986$		0			0
$987$	−1.19338e6	−	2.11941e7i	−0.0389930	−	0.692505i
$988$		0			0
$989$	2.56614e7			0.834238
$990$		0			0
$991$	−1.38843e7			−0.449095			−0.224548	−	0.974463i	$-0.572090\pi$
$991$	−1.38843e7			−0.449095			−0.224548	+	0.974463i	$0.572090\pi$
$992$		0			0
$993$	330304.	+	5.86609e6i	0.0106302	+	0.188789i
$994$		0			0
$995$	−429134.	+	6.22160e6i	−0.0137415	+	0.199225i
$996$		0			0
$997$	2.43827e7	−	2.43827e7i	0.776863	−	0.776863i	−0.202433	−	0.979296i	$-0.564885\pi$
$997$	2.43827e7	−	2.43827e7i	0.776863	−	0.776863i	0.979296	+	0.202433i	$0.0648849\pi$
$998$		0			0
$999$	2.96811e7	+	2.10401e7i	0.940951	+	0.667012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.6.i.a.53.5	yes	20
3.2	odd	2	inner	60.6.i.a.53.10	yes	20
5.2	odd	4	inner	60.6.i.a.17.10	yes	20
5.3	odd	4		300.6.i.d.257.1		20
5.4	even	2		300.6.i.d.293.6		20
15.2	even	4	inner	60.6.i.a.17.5	✓	20
15.8	even	4		300.6.i.d.257.6		20
15.14	odd	2		300.6.i.d.293.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.6.i.a.17.5	✓	20	15.2	even	4	inner
60.6.i.a.17.10	yes	20	5.2	odd	4	inner
60.6.i.a.53.5	yes	20	1.1	even	1	trivial
60.6.i.a.53.10	yes	20	3.2	odd	2	inner
300.6.i.d.257.1		20	5.3	odd	4
300.6.i.d.257.6		20	15.8	even	4
300.6.i.d.293.1		20	15.14	odd	2
300.6.i.d.293.6		20	5.4	even	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)

\(f(q)\)	\(=\)	\(q+(0.876355 + 15.5638i) q^{3} +(55.7692 + 3.84667i) q^{5} +(151.287 - 151.287i) q^{7} +(-241.464 + 27.2788i) q^{9} +O(q^{10})\)	\(q+(0.876355 + 15.5638i) q^{3} +(55.7692 + 3.84667i) q^{5} +(151.287 - 151.287i) q^{7} +(-241.464 + 27.2788i) q^{9} +504.939i q^{11} +(567.781 + 567.781i) q^{13} +(-10.9953 + 871.352i) q^{15} +(-91.1681 - 91.1681i) q^{17} -600.852i q^{19} +(2487.18 + 2222.02i) q^{21} +(-2156.65 + 2156.65i) q^{23} +(3095.41 + 429.052i) q^{25} +(-636.170 - 3734.19i) q^{27} +5818.05 q^{29} -2220.29 q^{31} +(-7858.78 + 442.506i) q^{33} +(9019.11 - 7855.21i) q^{35} +(-6791.46 + 6791.46i) q^{37} +(-8339.25 + 9334.40i) q^{39} -12164.1i q^{41} +(-5949.36 - 5949.36i) q^{43} +(-13571.2 + 592.485i) q^{45} +(-4500.58 - 4500.58i) q^{47} -28968.6i q^{49} +(1339.03 - 1498.82i) q^{51} +(26033.6 - 26033.6i) q^{53} +(-1942.34 + 28160.1i) q^{55} +(9351.54 - 526.559i) q^{57} -6530.45 q^{59} +28414.5 q^{61} +(-32403.5 + 40657.3i) q^{63} +(29480.6 + 33848.7i) q^{65} +(-12318.8 + 12318.8i) q^{67} +(-35455.7 - 31675.8i) q^{69} -69210.3i q^{71} +(-18264.0 - 18264.0i) q^{73} +(-3965.01 + 48552.3i) q^{75} +(76390.8 + 76390.8i) q^{77} +41121.4i q^{79} +(57560.7 - 13173.7i) q^{81} +(-56058.1 + 56058.1i) q^{83} +(-4733.68 - 5435.07i) q^{85} +(5098.67 + 90550.9i) q^{87} -54609.2 q^{89} +171796. q^{91} +(-1945.76 - 34556.1i) q^{93} +(2311.28 - 33509.0i) q^{95} +(17055.3 - 17055.3i) q^{97} +(-13774.2 - 121925. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} + 76 q^{7}+O(q^{10}) \) 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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