LMFDB - Embedded newform 224.6.p.a.31.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,6,Mod(31,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("224.31");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	224.p (of order $6$, 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:	$35.9259756381$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.16
Character	$\chi$	$=$	224.31
Dual form			224.6.p.a.159.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.76024 + 6.51293i) q^{3} +(-83.0525 + 47.9504i) q^{5} +(105.609 + 75.1911i) q^{7} +(93.2211 + 161.464i) q^{9} +(-66.6527 - 38.4820i) q^{11} +825.530i q^{13} -721.221i q^{15} +(585.759 + 338.188i) q^{17} +(1308.05 + 2265.60i) q^{19} +(-886.831 + 405.089i) q^{21} +(632.641 - 365.255i) q^{23} +(3035.98 - 5258.48i) q^{25} -3229.62 q^{27} -2552.11 q^{29} +(-3444.22 + 5965.56i) q^{31} +(501.261 - 289.403i) q^{33} +(-12376.6 - 1180.81i) q^{35} +(-2784.93 - 4823.64i) q^{37} +(-5376.62 - 3104.19i) q^{39} -13932.4i q^{41} -2424.13i q^{43} +(-15484.5 - 8939.98i) q^{45} +(3096.66 + 5363.57i) q^{47} +(5499.59 + 15881.7i) q^{49} +(-4405.19 + 2543.34i) q^{51} +(-7424.20 + 12859.1i) q^{53} +7380.90 q^{55} -19674.3 q^{57} +(-1749.75 + 3030.66i) q^{59} +(37115.3 - 21428.5i) q^{61} +(-2295.63 + 24061.4i) q^{63} +(-39584.5 - 68562.4i) q^{65} +(-9630.25 - 5560.03i) q^{67} +5493.80i q^{69} -17066.1i q^{71} +(-34535.4 - 19939.0i) q^{73} +(22832.1 + 39546.3i) q^{75} +(-4145.64 - 9075.74i) q^{77} +(-62493.2 + 36080.5i) q^{79} +(-10508.6 + 18201.4i) q^{81} -117067. q^{83} -64865.0 q^{85} +(9596.57 - 16621.7i) q^{87} +(124994. - 72165.5i) q^{89} +(-62072.5 + 87183.5i) q^{91} +(-25902.2 - 44863.9i) q^{93} +(-217273. - 125443. i) q^{95} -38041.3i q^{97} -14349.3i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 3240 q^{9} + 6856 q^{21} + 27728 q^{25} - 15920 q^{29} - 28296 q^{33} - 2152 q^{37} + 35400 q^{45} + 29280 q^{49} - 17512 q^{53} - 108368 q^{57} + 37704 q^{61} + 18216 q^{65} + 157704 q^{73} + 28224 q^{77}+ \cdots + 39400 q^{93}+O(q^{100}) $ 80 * q - 3240 * q^9 + 6856 * q^21 + 27728 * q^25 - 15920 * q^29 - 28296 * q^33 - 2152 * q^37 + 35400 * q^45 + 29280 * q^49 - 17512 * q^53 - 108368 * q^57 + 37704 * q^61 + 18216 * q^65 + 157704 * q^73 + 28224 * q^77 - 273136 * q^81 + 230704 * q^85 + 28440 * q^89 + 39400 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.76024	+	6.51293i	−0.241220	+	0.417805i	−0.961062	−	0.276333i	$-0.910881\pi$
$3$	−3.76024	+	6.51293i	−0.241220	+	0.417805i	0.719842	+	0.694138i	$0.244214\pi$
$4$		0			0
$5$	−83.0525	+	47.9504i	−1.48569	+	0.857763i	−0.999867	−	0.0162949i	$-0.994813\pi$
$5$	−83.0525	+	47.9504i	−1.48569	+	0.857763i	−0.485822	+	0.874058i	$0.661480\pi$
$6$		0			0
$7$	105.609	+	75.1911i	0.814623	+	0.579991i
$7$	105.609	+	75.1911i	0.814623	+	0.579991i
$8$		0			0
$9$	93.2211	+	161.464i	0.383626	+	0.664460i
$10$		0			0
$11$	−66.6527	−	38.4820i	−0.166087	−	0.0958905i	0.414652	−	0.909980i	$-0.363903\pi$
$11$	−66.6527	−	38.4820i	−0.166087	−	0.0958905i	−0.580740	+	0.814089i	$0.697237\pi$
$12$		0			0
$13$			825.530i			1.35480i	0.735616	+	0.677399i	$0.236893\pi$
$13$			825.530i			1.35480i	−0.735616	+	0.677399i	$0.763107\pi$
$14$		0			0
$15$		−	721.221i		−	0.827638i
$16$		0			0
$17$	585.759	+	338.188i	0.491582	+	0.283815i	0.725231	−	0.688506i	$-0.241733\pi$
$17$	585.759	+	338.188i	0.491582	+	0.283815i	−0.233648	+	0.972321i	$0.575066\pi$
$18$		0			0
$19$	1308.05	+	2265.60i	0.831265	+	1.43979i	0.897036	+	0.441958i	$0.145716\pi$
$19$	1308.05	+	2265.60i	0.831265	+	1.43979i	−0.0657710	+	0.997835i	$0.520951\pi$
$20$		0			0
$21$	−886.831	+	405.089i	−0.438826	+	0.200448i
$22$		0			0
$23$	632.641	−	365.255i	0.249366	−	0.143972i	−0.370108	−	0.928989i	$-0.620679\pi$
$23$	632.641	−	365.255i	0.249366	−	0.143972i	0.619474	+	0.785017i	$0.287346\pi$
$24$		0			0
$25$	3035.98	−	5258.48i	0.971515	−	1.68271i
$26$		0			0
$27$	−3229.62			−0.852592
$28$		0			0
$29$	−2552.11			−0.563514			−0.281757	−	0.959486i	$-0.590917\pi$
$29$	−2552.11			−0.563514			−0.281757	+	0.959486i	$0.590917\pi$
$30$		0			0
$31$	−3444.22	+	5965.56i	−0.643704	+	1.11493i	0.340895	+	0.940101i	$0.389270\pi$
$31$	−3444.22	+	5965.56i	−0.643704	+	1.11493i	−0.984599	+	0.174827i	$0.944063\pi$
$32$		0			0
$33$	501.261	−	289.403i	0.0801270	−	0.0462614i
$34$		0			0
$35$	−12376.6	−	1180.81i	−1.70777	−	0.162934i
$36$		0			0
$37$	−2784.93	−	4823.64i	−0.334434	−	0.579256i	0.648942	−	0.760838i	$-0.275212\pi$
$37$	−2784.93	−	4823.64i	−0.334434	−	0.579256i	−0.983376	+	0.181582i	$0.941878\pi$
$38$		0			0
$39$	−5376.62	−	3104.19i	−0.566041	−	0.326804i
$40$		0			0
$41$		−	13932.4i		−	1.29439i	−0.762323	−	0.647197i	$-0.775941\pi$
$41$		−	13932.4i		−	1.29439i	0.762323	−	0.647197i	$-0.224059\pi$
$42$		0			0
$43$		−	2424.13i		−	0.199933i	−0.994991	−	0.0999665i	$-0.968126\pi$
$43$		−	2424.13i		−	0.199933i	0.994991	−	0.0999665i	$-0.0318736\pi$
$44$		0			0
$45$	−15484.5	−	8939.98i	−1.13990	−	0.658120i
$46$		0			0
$47$	3096.66	+	5363.57i	0.204479	+	0.354168i	0.949967	−	0.312351i	$-0.101117\pi$
$47$	3096.66	+	5363.57i	0.204479	+	0.354168i	−0.745488	+	0.666520i	$0.767783\pi$
$48$		0			0
$49$	5499.59	+	15881.7i	0.327220	+	0.944948i
$50$		0			0
$51$	−4405.19	+	2543.34i	−0.237159	+	0.136924i
$52$		0			0
$53$	−7424.20	+	12859.1i	−0.363045	+	0.628812i	−0.988460	−	0.151480i	$-0.951596\pi$
$53$	−7424.20	+	12859.1i	−0.363045	+	0.628812i	0.625416	+	0.780292i	$0.284929\pi$
$54$		0			0
$55$	7380.90			0.329005
$56$		0			0
$57$	−19674.3			−0.802070
$58$		0			0
$59$	−1749.75	+	3030.66i	−0.0654404	+	0.113346i	−0.896889	−	0.442255i	$-0.854179\pi$
$59$	−1749.75	+	3030.66i	−0.0654404	+	0.113346i	0.831449	+	0.555601i	$0.187512\pi$
$60$		0			0
$61$	37115.3	−	21428.5i	1.27711	−	0.737341i	0.300795	−	0.953689i	$-0.402748\pi$
$61$	37115.3	−	21428.5i	1.27711	−	0.737341i	0.976316	+	0.216348i	$0.0694147\pi$
$62$		0			0
$63$	−2295.63	+	24061.4i	−0.0728704	+	0.763784i
$64$		0			0
$65$	−39584.5	−	68562.4i	−1.16210	−	2.01281i
$66$		0			0
$67$	−9630.25	−	5560.03i	−0.262090	−	0.151318i	0.363198	−	0.931712i	$-0.381685\pi$
$67$	−9630.25	−	5560.03i	−0.262090	−	0.151318i	−0.625288	+	0.780394i	$0.715018\pi$
$68$		0			0
$69$			5493.80i			0.138915i
$70$		0			0
$71$		−	17066.1i		−	0.401779i	−0.979614	−	0.200890i	$-0.935617\pi$
$71$		−	17066.1i		−	0.401779i	0.979614	−	0.200890i	$-0.0643832\pi$
$72$		0			0
$73$	−34535.4	−	19939.0i	−0.758503	−	0.437922i	0.0702553	−	0.997529i	$-0.477619\pi$
$73$	−34535.4	−	19939.0i	−0.758503	−	0.437922i	−0.828758	+	0.559607i	$0.810952\pi$
$74$		0			0
$75$	22832.1	+	39546.3i	0.468697	+	0.811807i
$76$		0			0
$77$	−4145.64	−	9075.74i	−0.0796828	−	0.174444i
$78$		0			0
$79$	−62493.2	+	36080.5i	−1.12659	+	0.650436i	−0.943075	−	0.332581i	$-0.892080\pi$
$79$	−62493.2	+	36080.5i	−1.12659	+	0.650436i	−0.183513	+	0.983017i	$0.558747\pi$
$80$		0			0
$81$	−10508.6	+	18201.4i	−0.177964	+	0.308242i
$82$		0			0
$83$	−117067.			−1.86525			−0.932626	−	0.360844i	$-0.882489\pi$
$83$	−117067.			−1.86525			−0.932626	+	0.360844i	$0.882489\pi$
$84$		0			0
$85$	−64865.0			−0.973785
$86$		0			0
$87$	9596.57	−	16621.7i	0.135931	−	0.235439i
$88$		0			0
$89$	124994.	−	72165.5i	1.67269	−	0.965727i	0.706565	−	0.707648i	$-0.250244\pi$
$89$	124994.	−	72165.5i	1.67269	−	0.965727i	0.966124	−	0.258079i	$-0.0830896\pi$
$90$		0			0
$91$	−62072.5	+	87183.5i	−0.785771	+	1.10365i
$92$		0			0
$93$	−25902.2	−	44863.9i	−0.310548	−	0.537885i
$94$		0			0
$95$	−217273.	−	125443.i	−2.47000	−	1.42606i
$96$		0			0
$97$		−	38041.3i		−	0.410512i	−0.978708	−	0.205256i	$-0.934197\pi$
$97$		−	38041.3i		−	0.410512i	0.978708	−	0.205256i	$-0.0658028\pi$
$98$		0			0
$99$		−	14349.3i		−	0.147144i
$100$		0			0
$101$	−22428.8	−	12949.3i	−0.218778	−	0.126311i	0.386607	−	0.922245i	$-0.373647\pi$
$101$	−22428.8	−	12949.3i	−0.218778	−	0.126311i	−0.605384	+	0.795933i	$0.706980\pi$
$102$		0			0
$103$	92348.3	+	159952.i	0.857701	+	1.48558i	0.874117	+	0.485716i	$0.161441\pi$
$103$	92348.3	+	159952.i	0.857701	+	1.48558i	−0.0164162	+	0.999865i	$0.505226\pi$
$104$		0			0
$105$	54229.4	−	76167.5i	0.480023	−	0.674212i
$106$		0			0
$107$	196004.	−	113163.i	1.65503	−	0.955532i	0.680072	−	0.733145i	$-0.261948\pi$
$107$	196004.	−	113163.i	1.65503	−	0.955532i	0.974958	−	0.222387i	$-0.0713849\pi$
$108$		0			0
$109$	−82540.8	+	142965.i	−0.665430	+	1.15256i	0.313738	+	0.949509i	$0.398418\pi$
$109$	−82540.8	+	142965.i	−0.665430	+	1.15256i	−0.979169	+	0.203049i	$0.934915\pi$
$110$		0			0
$111$	41888.1			0.322688
$112$		0			0
$113$	213968.			1.57635			0.788175	−	0.615451i	$-0.211026\pi$
$113$	213968.			1.57635			0.788175	+	0.615451i	$0.211026\pi$
$114$		0			0
$115$	−35028.3	+	60670.7i	−0.246987	+	0.427794i
$116$		0			0
$117$	−133293.	+	76956.8i	−0.900208	+	0.519736i
$118$		0			0
$119$	36432.7	+	79759.6i	0.235844	+	0.516316i
$120$		0			0
$121$	−77563.8	−	134344.i	−0.481610	−	0.834173i
$122$		0			0
$123$	90740.8	+	52389.2i	0.540804	+	0.312233i
$124$		0			0
$125$			282616.i			1.61779i
$126$		0			0
$127$			56131.3i			0.308813i	0.988007	+	0.154406i	$0.0493465\pi$
$127$			56131.3i			0.308813i	−0.988007	+	0.154406i	$0.950653\pi$
$128$		0			0
$129$	15788.2	+	9115.32i	0.0835330	+	0.0482278i
$130$		0			0
$131$	−66886.6	−	115851.i	−0.340534	−	0.589823i	0.643998	−	0.765027i	$-0.277275\pi$
$131$	−66886.6	−	115851.i	−0.340534	−	0.589823i	−0.984532	+	0.175205i	$0.943941\pi$
$132$		0			0
$133$	−32211.5	+	337622.i	−0.157900	+	1.65501i
$134$		0			0
$135$	268228.	−	154861.i	1.26669	−	0.731322i
$136$		0			0
$137$	58529.6	−	101376.i	0.266424	−	0.461461i	−0.701511	−	0.712658i	$-0.747491\pi$
$137$	58529.6	−	101376.i	0.266424	−	0.461461i	0.967936	+	0.251198i	$0.0808244\pi$
$138$		0			0
$139$	422270.			1.85376			0.926879	−	0.375360i	$-0.122481\pi$
$139$	422270.			1.85376			0.926879	+	0.375360i	$0.122481\pi$
$140$		0			0
$141$	−46576.8			−0.197298
$142$		0			0
$143$	31768.0	−	55023.8i	0.129912	−	0.225015i
$144$		0			0
$145$	211959.	−	122375.i	0.837207	−	0.483361i
$146$		0			0
$147$	−124117.	−	23900.8i	−0.473736	−	0.0912260i
$148$		0			0
$149$	−56607.5	−	98047.1i	−0.208886	−	0.361801i	0.742478	−	0.669870i	$-0.233650\pi$
$149$	−56607.5	−	98047.1i	−0.208886	−	0.361801i	−0.951364	+	0.308070i	$0.900317\pi$
$150$		0			0
$151$	−197701.	−	114143.i	−0.705614	−	0.407387i	0.103821	−	0.994596i	$-0.466893\pi$
$151$	−197701.	−	114143.i	−0.705614	−	0.407387i	−0.809435	+	0.587209i	$0.800226\pi$
$152$		0			0
$153$			126105.i			0.435516i
$154$		0			0
$155$		−	660606.i		−	2.20858i
$156$		0			0
$157$	276244.	+	159489.i	0.894424	+	0.516396i	0.875387	−	0.483423i	$-0.160607\pi$
$157$	276244.	+	159489.i	0.894424	+	0.516396i	0.0190371	+	0.999819i	$0.493940\pi$
$158$		0			0
$159$	−55833.6	−	96706.7i	−0.175147	−	0.303364i
$160$		0			0
$161$	94276.6	+	8994.66i	0.286642	+	0.0273476i
$162$		0			0
$163$	−254311.	+	146826.i	−0.749714	+	0.432847i	−0.825590	−	0.564270i	$-0.809158\pi$
$163$	−254311.	+	146826.i	−0.749714	+	0.432847i	0.0758768	+	0.997117i	$0.475824\pi$
$164$		0			0
$165$	−27754.0	+	48071.3i	−0.0793626	+	0.137460i
$166$		0			0
$167$	−67687.4			−0.187809			−0.0939045	−	0.995581i	$-0.529935\pi$
$167$	−67687.4			−0.187809			−0.0939045	+	0.995581i	$0.529935\pi$
$168$		0			0
$169$	−310207.			−0.835477
$170$		0			0
$171$	−243875.	+	422404.i	−0.637790	+	1.10468i
$172$		0			0
$173$	−81640.7	+	47135.3i	−0.207392	+	0.119738i	−0.600099	−	0.799926i	$-0.704872\pi$
$173$	−81640.7	+	47135.3i	−0.207392	+	0.119738i	0.392707	+	0.919664i	$0.371539\pi$
$174$		0			0
$175$	716018.	−	327064.i	1.76738	−	0.807306i
$176$		0			0
$177$	−13159.0	−	22792.0i	−0.0315711	−	0.0546827i
$178$		0			0
$179$	502677.	+	290221.i	1.17262	+	0.677011i	0.954295	−	0.298866i	$-0.0966083\pi$
$179$	502677.	+	290221.i	1.17262	+	0.677011i	0.218322	+	0.975877i	$0.429942\pi$
$180$		0			0
$181$		−	12998.7i		−	0.0294919i	−0.999891	−	0.0147459i	$-0.995306\pi$
$181$		−	12998.7i		−	0.0294919i	0.999891	−	0.0147459i	$-0.00469395\pi$
$182$		0			0
$183$			322306.i			0.711445i
$184$		0			0
$185$	462591.	+	267077.i	0.993728	+	0.573729i
$186$		0			0
$187$	−26028.3	−	45082.3i	−0.0544304	−	0.0942762i
$188$		0			0
$189$	−341077.	−	242838.i	−0.694541	−	0.494496i
$190$		0			0
$191$	−221458.	+	127859.i	−0.439247	+	0.253599i	−0.703278	−	0.710915i	$-0.748281\pi$
$191$	−221458.	+	127859.i	−0.439247	+	0.253599i	0.264031	+	0.964514i	$0.414948\pi$
$192$		0			0
$193$	−69367.4	+	120148.i	−0.134049	+	0.232179i	−0.925234	−	0.379398i	$-0.876131\pi$
$193$	−69367.4	+	120148.i	−0.134049	+	0.232179i	0.791185	+	0.611577i	$0.209464\pi$
$194$		0			0
$195$	595390.			1.12128
$196$		0			0
$197$	837884.			1.53822			0.769110	−	0.639117i	$-0.220700\pi$
$197$	837884.			1.53822			0.769110	+	0.639117i	$0.220700\pi$
$198$		0			0
$199$	382374.	−	662292.i	0.684473	−	1.18554i	−0.289130	−	0.957290i	$-0.593366\pi$
$199$	382374.	−	662292.i	0.684473	−	1.18554i	0.973602	−	0.228251i	$-0.0733008\pi$
$200$		0			0
$201$	72424.2	−	41814.1i	0.126443	−	0.0730017i
$202$		0			0
$203$	−269526.	−	191896.i	−0.459051	−	0.326833i
$204$		0			0
$205$	668064.	+	1.15712e6i	1.11028	+	1.92307i
$206$		0			0
$207$	117951.	+	68099.0i	0.191327	+	0.110462i
$208$		0			0
$209$		−	201345.i		−	0.318842i
$210$		0			0
$211$		−	281749.i		−	0.435669i	−0.975986	−	0.217835i	$-0.930101\pi$
$211$		−	281749.i		−	0.435669i	0.975986	−	0.217835i	$-0.0698993\pi$
$212$		0			0
$213$	111150.	+	64172.6i	0.167865	+	0.0969171i
$214$		0			0
$215$	116238.	+	201330.i	0.171495	+	0.297038i
$216$		0			0
$217$	−812298.	+	371043.i	−1.17102	+	0.534903i
$218$		0			0
$219$	259723.	−	149951.i	0.365932	−	0.211271i
$220$		0			0
$221$	−279184.	+	483561.i	−0.384512	+	0.665995i
$222$		0			0
$223$	669475.			0.901513			0.450757	−	0.892647i	$-0.351154\pi$
$223$	669475.			0.901513			0.450757	+	0.892647i	$0.351154\pi$
$224$		0			0
$225$	1.13207e6			1.49079
$226$		0			0
$227$	−434773.	+	753049.i	−0.560012	+	0.969970i	0.437482	+	0.899227i	$0.355870\pi$
$227$	−434773.	+	753049.i	−0.560012	+	0.969970i	−0.997495	+	0.0707430i	$0.977463\pi$
$228$		0			0
$229$	−989258.	+	571149.i	−1.24658	+	0.719715i	−0.970426	−	0.241398i	$-0.922394\pi$
$229$	−989258.	+	571149.i	−1.24658	+	0.719715i	−0.276156	+	0.961113i	$0.589061\pi$
$230$		0			0
$231$	74698.3	+	7126.75i	0.0921045	+	0.00878743i
$232$		0			0
$233$	198626.	+	344030.i	0.239688	+	0.415152i	0.960625	−	0.277849i	$-0.0896215\pi$
$233$	198626.	+	344030.i	0.239688	+	0.415152i	−0.720937	+	0.693001i	$0.756288\pi$
$234$		0			0
$235$	−514371.	−	296972.i	−0.607585	−	0.350789i
$236$		0			0
$237$		−	542686.i		−	0.627592i
$238$		0			0
$239$			965243.i			1.09305i	0.837441	+	0.546527i	$0.184051\pi$
$239$			965243.i			1.09305i	−0.837441	+	0.546527i	$0.815949\pi$
$240$		0			0
$241$	−256209.	−	147922.i	−0.284153	−	0.164056i	0.351149	−	0.936319i	$-0.385791\pi$
$241$	−256209.	−	147922.i	−0.284153	−	0.164056i	−0.635302	+	0.772264i	$0.719124\pi$
$242$		0			0
$243$	−471428.	−	816537.i	−0.512153	−	0.887075i
$244$		0			0
$245$	−1.21829e6	−	1.05531e6i	−1.29669	−	1.12322i
$246$		0			0
$247$	−1.87032e6	+	1.07983e6i	−1.95063	+	1.12620i
$248$		0			0
$249$	440199.	−	762447.i	0.449936	−	0.779312i
$250$		0			0
$251$	328861.			0.329479			0.164740	−	0.986337i	$-0.447322\pi$
$251$	328861.			0.329479			0.164740	+	0.986337i	$0.447322\pi$
$252$		0			0
$253$	−56222.9			−0.0552220
$254$		0			0
$255$	243908.	−	422461.i	0.234896	−	0.406852i
$256$		0			0
$257$	−9335.17	+	5389.66i	−0.00881636	+	0.00509013i	−0.504402	−	0.863469i	$-0.668287\pi$
$257$	−9335.17	+	5389.66i	−0.00881636	+	0.00509013i	0.495585	+	0.868559i	$0.334954\pi$
$258$		0			0
$259$	68580.8	−	718822.i	0.0635262	−	0.665843i
$260$		0			0
$261$	−237911.	−	412073.i	−0.216179	−	0.374432i
$262$		0			0
$263$	−1.29629e6	−	748413.i	−1.15561	−	0.667194i	−0.205365	−	0.978685i	$-0.565838\pi$
$263$	−1.29629e6	−	748413.i	−1.15561	−	0.667194i	−0.950249	+	0.311492i	$0.899171\pi$
$264$		0			0
$265$		−	1.42397e6i		−	1.24563i
$266$		0			0
$267$			1.08544e6i			0.931810i
$268$		0			0
$269$	−913977.	−	527685.i	−0.770113	−	0.444625i	0.0628017	−	0.998026i	$-0.479996\pi$
$269$	−913977.	−	527685.i	−0.770113	−	0.444625i	−0.832915	+	0.553401i	$0.813330\pi$
$270$		0			0
$271$	100026.	+	173251.i	0.0827353	+	0.143302i	0.904424	−	0.426635i	$-0.140301\pi$
$271$	100026.	+	173251.i	0.0827353	+	0.143302i	−0.821689	+	0.569937i	$0.806968\pi$
$272$		0			0
$273$	−334413.	−	732106.i	−0.271566	−	0.594521i
$274$		0			0
$275$	−404713.	+	233661.i	−0.322712	+	0.186318i
$276$		0			0
$277$	947536.	−	1.64118e6i	0.741987	−	1.28516i	−0.209603	−	0.977787i	$-0.567217\pi$
$277$	947536.	−	1.64118e6i	0.741987	−	1.28516i	0.951589	−	0.307372i	$-0.0994496\pi$
$278$		0			0
$279$	−1.28429e6			−0.987766
$280$		0			0
$281$	−833472.			−0.629688			−0.314844	−	0.949143i	$-0.601952\pi$
$281$	−833472.			−0.629688			−0.314844	+	0.949143i	$0.601952\pi$
$282$		0			0
$283$	−895615.	+	1.55125e6i	−0.664745	+	1.15137i	0.314609	+	0.949221i	$0.398127\pi$
$283$	−895615.	+	1.55125e6i	−0.664745	+	1.15137i	−0.979354	+	0.202151i	$0.935207\pi$
$284$		0			0
$285$	1.63400e6	−	943391.i	1.19163	−	0.687986i
$286$		0			0
$287$	1.04759e6	−	1.47139e6i	0.750737	−	1.05444i
$288$		0			0
$289$	−481186.	−	833439.i	−0.338898	−	0.586988i
$290$		0			0
$291$	247761.	+	143045.i	0.171514	+	0.0990237i
$292$		0			0
$293$		−	1.18104e6i		−	0.803700i	−0.915705	−	0.401850i	$-0.868367\pi$
$293$		−	1.18104e6i		−	0.803700i	0.915705	−	0.401850i	$-0.131633\pi$
$294$		0			0
$295$		−	335605.i		−	0.224530i
$296$		0			0
$297$	215263.	+	124282.i	0.141605	+	0.0817555i
$298$		0			0
$299$	301529.	+	522264.i	0.195052	+	0.337841i
$300$		0			0
$301$	182273.	−	256010.i	0.115959	−	0.162870i
$302$		0			0
$303$	168676.	−	97384.9i	0.105547	−	0.0609376i
$304$		0			0
$305$	−2.05502e6	+	3.55939e6i	−1.26493	+	2.19092i
$306$		0			0
$307$	485375.			0.293922			0.146961	−	0.989142i	$-0.453051\pi$
$307$	485375.			0.293922			0.146961	+	0.989142i	$0.453051\pi$
$308$		0			0
$309$	−1.38901e6			−0.827577
$310$		0			0
$311$	−1.61012e6	+	2.78881e6i	−0.943968	+	1.63500i	−0.186164	+	0.982519i	$0.559605\pi$
$311$	−1.61012e6	+	2.78881e6i	−0.943968	+	1.63500i	−0.757804	+	0.652482i	$0.773728\pi$
$312$		0			0
$313$	−1.35853e6	+	784348.i	−0.783806	+	0.452531i	−0.837778	−	0.546012i	$-0.816145\pi$
$313$	−1.35853e6	+	784348.i	−0.783806	+	0.452531i	0.0539712	+	0.998542i	$0.482812\pi$
$314$		0			0
$315$	−963098.	−	2.10844e6i	−0.546883	−	1.19725i
$316$		0			0
$317$	−1.08063e6	−	1.87171e6i	−0.603989	−	1.04614i	−0.992210	−	0.124574i	$-0.960244\pi$
$317$	−1.08063e6	−	1.87171e6i	−0.603989	−	1.04614i	0.388221	−	0.921566i	$-0.373090\pi$
$318$		0			0
$319$	170105.	+	98210.3i	0.0935925	+	0.0540356i
$320$		0			0
$321$			1.70208e6i			0.921973i
$322$		0			0
$323$			1.76946e6i			0.943702i
$324$		0			0
$325$	4.34103e6	+	2.50629e6i	2.27973	+	1.31621i
$326$		0			0
$327$	−620747.	−	1.07517e6i	−0.321030	−	0.556040i
$328$		0			0
$329$	−76257.3	+	799284.i	−0.0388411	+	0.407109i
$330$		0			0
$331$	1.79033e6	−	1.03365e6i	0.898179	−	0.518564i	0.0215698	−	0.999767i	$-0.493134\pi$
$331$	1.79033e6	−	1.03365e6i	0.898179	−	0.518564i	0.876609	+	0.481204i	$0.159800\pi$
$332$		0			0
$333$	519228.	−	899330.i	0.256595	−	0.444435i
$334$		0			0
$335$	1.06642e6			0.519179
$336$		0			0
$337$	−2.49561e6			−1.19702			−0.598511	−	0.801115i	$-0.704241\pi$
$337$	−2.49561e6			−1.19702			−0.598511	+	0.801115i	$0.704241\pi$
$338$		0			0
$339$	−804572.	+	1.39356e6i	−0.380247	+	0.658607i
$340$		0			0
$341$	459133.	−	265080.i	0.213822	−	0.123450i
$342$		0			0
$343$	−613359.	+	2.09078e6i	−0.281501	+	0.959561i
$344$		0			0
$345$	−263430.	−	456274.i	−0.119156	−	0.206385i
$346$		0			0
$347$	−1.95020e6	−	1.12595e6i	−0.869470	−	0.501989i	−0.00229771	−	0.999997i	$-0.500731\pi$
$347$	−1.95020e6	−	1.12595e6i	−0.869470	−	0.501989i	−0.867172	+	0.498009i	$0.834065\pi$
$348$		0			0
$349$		−	4.17219e6i		−	1.83358i	−0.399368	−	0.916791i	$-0.630770\pi$
$349$		−	4.17219e6i		−	1.83358i	0.399368	−	0.916791i	$-0.369230\pi$
$350$		0			0
$351$		−	2.66614e6i		−	1.15509i
$352$		0			0
$353$	401593.	+	231860.i	0.171534	+	0.0990351i	0.583309	−	0.812250i	$-0.301758\pi$
$353$	401593.	+	231860.i	0.171534	+	0.0990351i	−0.411775	+	0.911286i	$0.635091\pi$
$354$		0			0
$355$	818325.	+	1.41738e6i	0.344631	+	0.596919i
$356$		0			0
$357$	−656465.	−	62631.4i	−0.272610	−	0.0260089i
$358$		0			0
$359$	1.51847e6	−	876687.i	0.621826	−	0.359011i	−0.155754	−	0.987796i	$-0.549781\pi$
$359$	1.51847e6	−	876687.i	0.621826	−	0.359011i	0.777580	+	0.628784i	$0.216447\pi$
$360$		0			0
$361$	−2.18392e6	+	3.78267e6i	−0.882002	+	1.52767i
$362$		0			0
$363$	1.16664e6			0.464696
$364$		0			0
$365$	3.82433e6			1.50253
$366$		0			0
$367$	−1.74921e6	+	3.02973e6i	−0.677919	+	1.17419i	0.297687	+	0.954663i	$0.403785\pi$
$367$	−1.74921e6	+	3.02973e6i	−0.677919	+	1.17419i	−0.975606	+	0.219527i	$0.929549\pi$
$368$		0			0
$369$	2.24958e6	−	1.29879e6i	0.860072	−	0.496563i
$370$		0			0
$371$	−1.75095e6	+	799804.i	−0.660450	+	0.301682i
$372$		0			0
$373$	99389.7	+	172148.i	0.0369887	+	0.0640663i	0.883927	−	0.467625i	$-0.154890\pi$
$373$	99389.7	+	172148.i	0.0369887	+	0.0640663i	−0.846938	+	0.531691i	$0.821557\pi$
$374$		0			0
$375$	−1.84066e6	−	1.06271e6i	−0.675921	−	0.390243i
$376$		0			0
$377$		−	2.10684e6i		−	0.763447i
$378$		0			0
$379$			1.20610e6i			0.431307i	0.976470	+	0.215654i	$0.0691882\pi$
$379$			1.20610e6i			0.431307i	−0.976470	+	0.215654i	$0.930812\pi$
$380$		0			0
$381$	−365579.	−	211067.i	−0.129024	−	0.0744918i
$382$		0			0
$383$	2.02976e6	+	3.51565e6i	0.707046	+	1.22464i	0.965948	+	0.258737i	$0.0833062\pi$
$383$	2.02976e6	+	3.51565e6i	0.707046	+	1.22464i	−0.258901	+	0.965904i	$0.583360\pi$
$384$		0			0
$385$	779491.	+	554978.i	0.268015	+	0.190820i
$386$		0			0
$387$	391409.	−	225980.i	0.132847	−	0.0766995i
$388$		0			0
$389$	−782149.	+	1.35472e6i	−0.262069	+	0.453917i	−0.966792	−	0.255566i	$-0.917738\pi$
$389$	−782149.	+	1.35472e6i	−0.262069	+	0.453917i	0.704723	+	0.709483i	$0.251071\pi$
$390$		0			0
$391$	494099.			0.163445
$392$		0			0
$393$	1.00604e6			0.328575
$394$		0			0
$395$	3.46015e6	−	5.99315e6i	1.11584	−	1.93269i
$396$		0			0
$397$	471426.	−	272178.i	0.150120	−	0.0866716i	−0.423059	−	0.906102i	$-0.639044\pi$
$397$	471426.	−	272178.i	0.150120	−	0.0866716i	0.573178	+	0.819431i	$0.305710\pi$
$398$		0			0
$399$	−2.07779e6	−	1.47933e6i	−0.653384	−	0.465194i
$400$		0			0
$401$	−1.63637e6	−	2.83427e6i	−0.508183	−	0.880199i	−0.999955	−	0.00947500i	$-0.996984\pi$
$401$	−1.63637e6	−	2.83427e6i	−0.508183	−	0.880199i	0.491772	−	0.870724i	$-0.336349\pi$
$402$		0			0
$403$	−4.92475e6	−	2.84330e6i	−1.51050	−	0.872089i
$404$		0			0
$405$		−	2.01556e6i		−	0.610603i
$406$		0			0
$407$			428678.i			0.128276i
$408$		0			0
$409$	4.13542e6	+	2.38758e6i	1.22239	+	0.705749i	0.965428	−	0.260671i	$-0.0839439\pi$
$409$	4.13542e6	+	2.38758e6i	1.22239	+	0.705749i	0.256966	+	0.966421i	$0.417277\pi$
$410$		0			0
$411$	440171.	+	762399.i	0.128534	+	0.222627i
$412$		0			0
$413$	−412668.	+	188499.i	−0.119049	+	0.0543795i
$414$		0			0
$415$	9.72267e6	−	5.61339e6i	2.77118	−	1.59994i
$416$		0			0
$417$	−1.58784e6	+	2.75022e6i	−0.447163	+	0.774510i
$418$		0			0
$419$	−4.20477e6			−1.17006			−0.585029	−	0.811012i	$-0.698917\pi$
$419$	−4.20477e6			−1.17006			−0.585029	+	0.811012i	$0.698917\pi$
$420$		0			0
$421$	−1.14368e6			−0.314484			−0.157242	−	0.987560i	$-0.550260\pi$
$421$	−1.14368e6			−0.314484			−0.157242	+	0.987560i	$0.550260\pi$
$422$		0			0
$423$	−577348.	+	999996.i	−0.156887	+	0.271736i
$424$		0			0
$425$	3.55671e6	−	2.05347e6i	0.955159	−	0.551461i
$426$		0			0
$427$	5.53096e6	+	527693.i	1.46801	+	0.140059i
$428$		0			0
$429$	238911.	+	413806.i	0.0626748	+	0.108556i
$430$		0			0
$431$	−1.66344e6	−	960389.i	−0.431335	−	0.249031i	0.268580	−	0.963257i	$-0.413446\pi$
$431$	−1.66344e6	−	960389.i	−0.431335	−	0.249031i	−0.699915	+	0.714226i	$0.746779\pi$
$432$		0			0
$433$			3.16538e6i			0.811346i	0.914018	+	0.405673i	$0.132963\pi$
$433$			3.16538e6i			0.811346i	−0.914018	+	0.405673i	$0.867037\pi$
$434$		0			0
$435$			1.84064e6i			0.466385i
$436$		0			0
$437$	1.65505e6	+	955542.i	0.414578	+	0.239357i
$438$		0			0
$439$	3.67448e6	+	6.36439e6i	0.909986	+	1.57614i	0.814080	+	0.580752i	$0.197241\pi$
$439$	3.67448e6	+	6.36439e6i	0.909986	+	1.57614i	0.0959059	+	0.995390i	$0.469425\pi$
$440$		0			0
$441$	−2.05165e6	+	2.36850e6i	−0.502350	+	0.579931i
$442$		0			0
$443$	3.00808e6	−	1.73672e6i	0.728250	−	0.420455i	−0.0895317	−	0.995984i	$-0.528537\pi$
$443$	3.00808e6	−	1.73672e6i	0.728250	−	0.420455i	0.817782	+	0.575529i	$0.195204\pi$
$444$		0			0
$445$	−6.92073e6	+	1.19871e7i	−1.65673	+	2.86954i
$446$		0			0
$447$	851433.			0.201549
$448$		0			0
$449$	−2.15654e6			−0.504827			−0.252413	−	0.967620i	$-0.581224\pi$
$449$	−2.15654e6			−0.504827			−0.252413	+	0.967620i	$0.581224\pi$
$450$		0			0
$451$	−536146.	+	928632.i	−0.124120	+	0.214982i
$452$		0			0
$453$	1.48681e6	−	858411.i	0.340416	−	0.196539i
$454$		0			0
$455$	974795.	−	1.02172e7i	0.220742	−	2.31368i
$456$		0			0
$457$	2.13065e6	+	3.69039e6i	0.477222	+	0.826573i	0.999659	−	0.0261046i	$-0.00831030\pi$
$457$	2.13065e6	+	3.69039e6i	0.477222	+	0.826573i	−0.522437	+	0.852678i	$0.674977\pi$
$458$		0			0
$459$	−1.89177e6	−	1.09222e6i	−0.419119	−	0.241979i
$460$		0			0
$461$			2.43908e6i			0.534532i	0.963623	+	0.267266i	$0.0861202\pi$
$461$			2.43908e6i			0.534532i	−0.963623	+	0.267266i	$0.913880\pi$
$462$		0			0
$463$		−	5.34064e6i		−	1.15782i	−0.815392	−	0.578910i	$-0.803478\pi$
$463$		−	5.34064e6i		−	1.15782i	0.815392	−	0.578910i	$-0.196522\pi$
$464$		0			0
$465$	4.30249e6	+	2.48404e6i	0.922756	+	0.532754i
$466$		0			0
$467$	1.60738e6	+	2.78406e6i	0.341056	+	0.590727i	0.984629	−	0.174658i	$-0.0558820\pi$
$467$	1.60738e6	+	2.78406e6i	0.341056	+	0.590727i	−0.643573	+	0.765385i	$0.722549\pi$
$468$		0			0
$469$	−598978.	−	1.31130e6i	−0.125742	−	0.275277i
$470$		0			0
$471$	−2.07749e6	+	1.19944e6i	−0.431506	+	0.249130i
$472$		0			0
$473$	−93285.3	+	161575.i	−0.0191717	+	0.0332063i
$474$		0			0
$475$	1.58848e7			3.23034
$476$		0			0
$477$	−2.76837e6			−0.557094
$478$		0			0
$479$	140771.	−	243823.i	0.0280334	−	0.0485552i	−0.851668	−	0.524081i	$-0.824409\pi$
$479$	140771.	−	243823.i	0.0280334	−	0.0485552i	0.879702	+	0.475526i	$0.157742\pi$
$480$		0			0
$481$	3.98206e6	−	2.29904e6i	0.784774	−	0.453090i
$482$		0			0
$483$	−413085.	+	580195.i	−0.0805696	+	0.113163i
$484$		0			0
$485$	1.82410e6	+	3.15943e6i	0.352122	+	0.609894i
$486$		0			0
$487$	6.02329e6	+	3.47755e6i	1.15083	+	0.664432i	0.949089	−	0.315007i	$-0.102007\pi$
$487$	6.02329e6	+	3.47755e6i	1.15083	+	0.664432i	0.201741	+	0.979439i	$0.435340\pi$
$488$		0			0
$489$		−	2.20841e6i		−	0.417645i
$490$		0			0
$491$			3.27128e6i			0.612370i	0.951972	+	0.306185i	$0.0990526\pi$
$491$			3.27128e6i			0.612370i	−0.951972	+	0.306185i	$0.900947\pi$
$492$		0			0
$493$	−1.49492e6	−	863093.i	−0.277014	−	0.159934i
$494$		0			0
$495$	688056.	+	1.19175e6i	0.126215	+	0.218611i
$496$		0			0
$497$	1.28322e6	−	1.80233e6i	0.233028	−	0.327298i
$498$		0			0
$499$	−873610.	+	504379.i	−0.157060	+	0.0906788i	−0.576470	−	0.817118i	$-0.695570\pi$
$499$	−873610.	+	504379.i	−0.157060	+	0.0906788i	0.419410	+	0.907797i	$0.362237\pi$
$500$		0			0
$501$	254521.	−	440844.i	0.0453033	−	0.0784676i
$502$		0			0
$503$	1.40846e6			0.248213			0.124107	−	0.992269i	$-0.460394\pi$
$503$	1.40846e6			0.248213			0.124107	+	0.992269i	$0.460394\pi$
$504$		0			0
$505$	2.48369e6			0.433381
$506$		0			0
$507$	1.16645e6	−	2.02036e6i	0.201534	−	0.349066i
$508$		0			0
$509$	8.88556e6	−	5.13008e6i	1.52016	−	0.877667i	0.520447	−	0.853894i	$-0.325765\pi$
$509$	8.88556e6	−	5.13008e6i	1.52016	−	0.877667i	0.999717	−	0.0237729i	$-0.00756785\pi$
$510$		0			0
$511$	−2.14802e6	−	4.70250e6i	−0.363903	−	0.796666i
$512$		0			0
$513$	−4.22449e6	−	7.31703e6i	−0.708730	−	1.22756i
$514$		0			0
$515$	−1.53395e7	−	8.85627e6i	−2.54855	−	1.47141i
$516$		0			0
$517$		−	476662.i		−	0.0784304i
$518$		0			0
$519$		−	708961.i		−	0.115532i
$520$		0			0
$521$	−2.77627e6	−	1.60288e6i	−0.448092	−	0.258706i	0.258932	−	0.965896i	$-0.416629\pi$
$521$	−2.77627e6	−	1.60288e6i	−0.448092	−	0.258706i	−0.707024	+	0.707189i	$0.749963\pi$
$522$		0			0
$523$	−2.06331e6	−	3.57375e6i	−0.329845	−	0.571308i	0.652636	−	0.757672i	$-0.273663\pi$
$523$	−2.06331e6	−	3.57375e6i	−0.329845	−	0.571308i	−0.982481	+	0.186363i	$0.940330\pi$
$524$		0			0
$525$	−562255.	+	5.89322e6i	−0.0890298	+	0.933157i
$526$		0			0
$527$	−4.03496e6	+	2.32958e6i	−0.632867	+	0.365386i
$528$		0			0
$529$	−2.95135e6	+	5.11189e6i	−0.458544	+	0.794222i
$530$		0			0
$531$	−652455.			−0.100419
$532$		0			0
$533$	1.15016e7			1.75364
$534$		0			0
$535$	−1.08524e7	+	1.87970e7i	−1.63924	+	2.83925i
$536$		0			0
$537$	−3.78038e6	+	2.18260e6i	−0.565717	+	0.326617i
$538$		0			0
$539$	244598.	−	1.27020e6i	0.0362644	−	0.188321i
$540$		0			0
$541$	−2.34437e6	−	4.06057e6i	−0.344376	−	0.596476i	0.640864	−	0.767654i	$-0.278576\pi$
$541$	−2.34437e6	−	4.06057e6i	−0.344376	−	0.596476i	−0.985240	+	0.171178i	$0.945243\pi$
$542$		0			0
$543$	84659.5	+	48878.2i	0.0123219	+	0.00711402i
$544$		0			0
$545$		−	1.58315e7i		−	2.28313i
$546$		0			0
$547$			1.04708e7i			1.49627i	0.663547	+	0.748135i	$0.269050\pi$
$547$			1.04708e7i			1.49627i	−0.663547	+	0.748135i	$0.730950\pi$
$548$		0			0
$549$	6.91987e6	+	3.99519e6i	0.979866	+	0.565726i
$550$		0			0
$551$	−3.33828e6	−	5.78207e6i	−0.468429	−	0.811343i
$552$		0			0
$553$	−9.31279e6	−	888506.i	−1.29499	−	0.123551i
$554$		0			0
$555$	−3.47891e6	+	2.00855e6i	−0.479414	+	0.276790i
$556$		0			0
$557$	2.07829e6	−	3.59970e6i	0.283836	−	0.491619i	−0.688490	−	0.725246i	$-0.741726\pi$
$557$	2.07829e6	−	3.59970e6i	0.283836	−	0.491619i	0.972326	+	0.233627i	$0.0750594\pi$
$558$		0			0
$559$	2.00119e6			0.270869
$560$		0			0
$561$	391491.			0.0525187
$562$		0			0
$563$	417869.	−	723770.i	0.0555609	−	0.0962343i	−0.836907	−	0.547345i	$-0.815639\pi$
$563$	417869.	−	723770.i	0.0555609	−	0.0962343i	0.892468	+	0.451111i	$0.148972\pi$
$564$		0			0
$565$	−1.77706e7	+	1.02598e7i	−2.34197	+	1.35213i
$566$		0			0
$567$	−2.47839e6	+	1.13208e6i	−0.323751	+	0.147884i
$568$		0			0
$569$	4.57516e6	+	7.92441e6i	0.592414	+	1.02609i	0.993906	+	0.110229i	$0.0351584\pi$
$569$	4.57516e6	+	7.92441e6i	0.592414	+	1.02609i	−0.401492	+	0.915863i	$0.631508\pi$
$570$		0			0
$571$	8.37615e6	+	4.83597e6i	1.07511	+	0.620717i	0.929574	−	0.368636i	$-0.120175\pi$
$571$	8.37615e6	+	4.83597e6i	1.07511	+	0.620717i	0.145539	+	0.989352i	$0.453508\pi$
$572$		0			0
$573$		−	1.92313e6i		−	0.244693i
$574$		0			0
$575$		−	4.43563e6i		−	0.559482i
$576$		0			0
$577$	5.45355e6	+	3.14861e6i	0.681930	+	0.393712i	0.800582	−	0.599223i	$-0.204524\pi$
$577$	5.45355e6	+	3.14861e6i	0.681930	+	0.393712i	−0.118652	+	0.992936i	$0.537857\pi$
$578$		0			0
$579$	−521677.	−	903571.i	−0.0646703	−	0.112012i
$580$		0			0
$581$	−1.23633e7	−	8.80237e6i	−1.51948	−	1.08183i
$582$		0			0
$583$	989687.	−	571396.i	0.120594	−	0.0696251i
$584$		0			0
$585$	7.38022e6	−	1.27829e7i	0.891620	−	1.54433i
$586$		0			0
$587$	6.49226e6			0.777679			0.388839	−	0.921306i	$-0.372876\pi$
$587$	6.49226e6			0.777679			0.388839	+	0.921306i	$0.372876\pi$
$588$		0			0
$589$	−1.80208e7			−2.14035
$590$		0			0
$591$	−3.15065e6	+	5.45708e6i	−0.371049	+	0.642676i
$592$		0			0
$593$	2.50110e6	−	1.44401e6i	0.292075	−	0.168630i	−0.346802	−	0.937938i	$-0.612732\pi$
$593$	2.50110e6	−	1.44401e6i	0.292075	−	0.168630i	0.638877	+	0.769309i	$0.279399\pi$
$594$		0			0
$595$	−6.85034e6	−	4.87727e6i	−0.793267	−	0.564787i
$596$		0			0
$597$	2.87564e6	+	4.98076e6i	0.330217	+	0.571952i
$598$		0			0
$599$	−9.12438e6	−	5.26796e6i	−1.03905	−	0.599895i	−0.119485	−	0.992836i	$-0.538124\pi$
$599$	−9.12438e6	−	5.26796e6i	−1.03905	−	0.599895i	−0.919564	+	0.392941i	$0.871458\pi$
$600$		0			0
$601$		−	5.13446e6i		−	0.579841i	−0.957051	−	0.289920i	$-0.906371\pi$
$601$		−	5.13446e6i		−	0.579841i	0.957051	−	0.289920i	$-0.0936288\pi$
$602$		0			0
$603$		−	2.07325e6i		−	0.232198i
$604$		0			0
$605$	1.28837e7	+	7.43843e6i	1.43105	+	0.826214i
$606$		0			0
$607$	2.10630e6	+	3.64822e6i	0.232033	+	0.401892i	0.958406	−	0.285408i	$-0.0921291\pi$
$607$	2.10630e6	+	3.64822e6i	0.232033	+	0.401892i	−0.726374	+	0.687300i	$0.758796\pi$
$608$		0			0
$609$	2.26329e6	−	1.03383e6i	0.247285	−	0.112955i
$610$		0			0
$611$	−4.42779e6	+	2.55639e6i	−0.479826	+	0.277028i
$612$		0			0
$613$	−1.54486e6	+	2.67578e6i	−0.166050	+	0.287607i	−0.937028	−	0.349255i	$-0.886435\pi$
$613$	−1.54486e6	+	2.67578e6i	−0.166050	+	0.287607i	0.770978	+	0.636862i	$0.219768\pi$
$614$		0			0
$615$	−1.00483e7			−1.07129
$616$		0			0
$617$	1.16142e7			1.22822			0.614109	−	0.789221i	$-0.289515\pi$
$617$	1.16142e7			1.22822			0.614109	+	0.789221i	$0.289515\pi$
$618$		0			0
$619$	−2.81419e6	+	4.87431e6i	−0.295207	+	0.511313i	−0.975033	−	0.222060i	$-0.928722\pi$
$619$	−2.81419e6	+	4.87431e6i	−0.295207	+	0.511313i	0.679826	+	0.733373i	$0.262055\pi$
$620$		0			0
$621$	−2.04319e6	+	1.17963e6i	−0.212608	+	0.122749i
$622$		0			0
$623$	1.86267e7	+	1.77712e6i	1.92272	+	0.183442i
$624$		0			0
$625$	−4.06413e6	−	7.03927e6i	−0.416166	−	0.720822i
$626$		0			0
$627$	1.31135e6	+	757106.i	0.133214	+	0.0769109i
$628$		0			0
$629$		−	3.76732e6i		−	0.379669i
$630$		0			0
$631$		−	4.97513e6i		−	0.497429i	−0.968577	−	0.248714i	$-0.919992\pi$
$631$		−	4.97513e6i		−	0.497429i	0.968577	−	0.248714i	$-0.0800080\pi$
$632$		0			0
$633$	1.83502e6	+	1.05945e6i	0.182025	+	0.105092i
$634$		0			0
$635$	−2.69152e6	−	4.66184e6i	−0.264888	−	0.458800i
$636$		0			0
$637$	−1.31109e7	+	4.54008e6i	−1.28021	+	0.443317i
$638$		0			0
$639$	2.75555e6	−	1.59092e6i	0.266966	−	0.154133i
$640$		0			0
$641$	−1.72514e6	+	2.98804e6i	−0.165836	+	0.287237i	−0.936952	−	0.349458i	$-0.886366\pi$
$641$	−1.72514e6	+	2.98804e6i	−0.165836	+	0.287237i	0.771116	+	0.636695i	$0.219699\pi$
$642$		0			0
$643$	9.77674e6			0.932538			0.466269	−	0.884643i	$-0.345598\pi$
$643$	9.77674e6			0.932538			0.466269	+	0.884643i	$0.345598\pi$
$644$		0			0
$645$	−1.74833e6			−0.165472
$646$		0			0
$647$	−3.15431e6	+	5.46342e6i	−0.296240	+	0.513102i	−0.975273	−	0.221006i	$-0.929066\pi$
$647$	−3.15431e6	+	5.46342e6i	−0.296240	+	0.513102i	0.679033	+	0.734108i	$0.262399\pi$
$648$		0			0
$649$	233251.	−	134668.i	0.0217376	−	0.0125502i
$650$		0			0
$651$	637859.	−	6.68566e6i	0.0589892	−	0.618289i
$652$		0			0
$653$	−5.85654e6	−	1.01438e7i	−0.537475	−	0.930934i	−0.999039	−	0.0438270i	$-0.986045\pi$
$653$	−5.85654e6	−	1.01438e7i	−0.537475	−	0.930934i	0.461564	−	0.887107i	$-0.347288\pi$
$654$		0			0
$655$	1.11102e7	+	6.41448e6i	1.01186	+	0.584196i
$656$		0			0
$657$		−	7.43495e6i		−	0.671993i
$658$		0			0
$659$			1.94632e7i			1.74582i	0.487878	+	0.872912i	$0.337771\pi$
$659$			1.94632e7i			1.74582i	−0.487878	+	0.872912i	$0.662229\pi$
$660$		0			0
$661$	−8.26727e6	−	4.77311e6i	−0.735968	−	0.424911i	0.0846337	−	0.996412i	$-0.473028\pi$
$661$	−8.26727e6	−	4.77311e6i	−0.735968	−	0.424911i	−0.820601	+	0.571501i	$0.806361\pi$
$662$		0			0
$663$	−2.09960e6	−	3.63662e6i	−0.185504	−	0.321302i
$664$		0			0
$665$	−1.35139e7	−	2.95849e7i	−1.18502	−	2.59428i
$666$		0			0
$667$	−1.61457e6	+	932172.i	−0.140521	+	0.0811300i
$668$		0			0
$669$	−2.51739e6	+	4.36024e6i	−0.217463	+	0.376657i
$670$		0			0
$671$	−3.29845e6			−0.282816
$672$		0			0
$673$	1.46910e7			1.25030			0.625149	−	0.780505i	$-0.285038\pi$
$673$	1.46910e7			1.25030			0.625149	+	0.780505i	$0.285038\pi$
$674$		0			0
$675$	−9.80506e6	+	1.69829e7i	−0.828306	+	1.43467i
$676$		0			0
$677$	−3.98711e6	+	2.30196e6i	−0.334339	+	0.193031i	−0.657766	−	0.753223i	$-0.728498\pi$
$677$	−3.98711e6	+	2.30196e6i	−0.334339	+	0.193031i	0.323427	+	0.946253i	$0.395165\pi$
$678$		0			0
$679$	2.86037e6	−	4.01751e6i	0.238094	−	0.334413i
$680$		0			0
$681$	−3.26970e6	−	5.66329e6i	−0.270172	−	0.467952i
$682$		0			0
$683$	−1.78042e7	−	1.02793e7i	−1.46040	−	0.843162i	−0.461371	−	0.887207i	$-0.652642\pi$
$683$	−1.78042e7	−	1.02793e7i	−1.46040	−	0.843162i	−0.999030	+	0.0440450i	$0.985975\pi$
$684$		0			0
$685$			1.12261e7i			0.914116i
$686$		0			0
$687$		−	8.59063e6i		−	0.694438i
$688$		0			0
$689$	−1.06156e7	−	6.12890e6i	−0.851913	−	0.491852i
$690$		0			0
$691$	−5.93846e6	−	1.02857e7i	−0.473128	−	0.819481i	0.526399	−	0.850238i	$-0.323542\pi$
$691$	−5.93846e6	−	1.02857e7i	−0.473128	−	0.819481i	−0.999527	+	0.0307562i	$0.990208\pi$
$692$		0			0
$693$	1.07894e6	−	1.51542e6i	0.0853424	−	0.119867i
$694$		0			0
$695$	−3.50706e7	+	2.02480e7i	−2.75411	+	1.59009i
$696$		0			0
$697$	4.71177e6	−	8.16102e6i	0.367368	−	0.636301i
$698$		0			0
$699$	−2.98753e6			−0.231270
$700$		0			0
$701$	1.03169e7			0.792962			0.396481	−	0.918043i	$-0.370231\pi$
$701$	1.03169e7			0.792962			0.396481	+	0.918043i	$0.370231\pi$
$702$		0			0
$703$	7.28564e6	−	1.26191e7i	0.556006	−	0.963030i
$704$		0			0
$705$	3.86832e6	−	2.23338e6i	0.293123	−	0.169235i
$706$		0			0
$707$	−1.39502e6	−	3.05401e6i	−0.104962	−	0.229785i
$708$		0			0
$709$	659220.	+	1.14180e6i	0.0492510	+	0.0853052i	0.889600	−	0.456741i	$-0.150983\pi$
$709$	659220.	+	1.14180e6i	0.0492510	+	0.0853052i	−0.840349	+	0.542046i	$0.817650\pi$
$710$		0			0
$711$	−1.16514e7	−	6.72692e6i	−0.864377	−	0.499048i
$712$		0			0
$713$			5.03207e6i			0.370700i
$714$		0			0
$715$			6.09316e6i			0.445736i
$716$		0			0
$717$	−6.28657e6	−	3.62955e6i	−0.456684	−	0.263666i
$718$		0			0
$719$	2.83122e6	+	4.90381e6i	0.204245	+	0.353762i	0.949892	−	0.312579i	$-0.101193\pi$
$719$	2.83122e6	+	4.90381e6i	0.204245	+	0.353762i	−0.745647	+	0.666341i	$0.767859\pi$
$720$		0			0
$721$	−2.27414e6	+	2.38362e7i	−0.162922	+	1.70765i
$722$		0			0
$723$	1.92682e6	−	1.11245e6i	0.137086	−	0.0791469i
$724$		0			0
$725$	−7.74817e6	+	1.34202e7i	−0.547462	+	0.948232i
$726$		0			0
$727$	2.87224e6			0.201551			0.100775	−	0.994909i	$-0.467868\pi$
$727$	2.87224e6			0.201551			0.100775	+	0.994909i	$0.467868\pi$
$728$		0			0
$729$	1.98357e6			0.138238
$730$		0			0
$731$	819811.	−	1.41995e6i	0.0567440	−	0.0982836i
$732$		0			0
$733$	1.84388e7	−	1.06457e7i	1.26758	−	0.731835i	0.293047	−	0.956098i	$-0.405331\pi$
$733$	1.84388e7	−	1.06457e7i	1.26758	−	0.731835i	0.974529	+	0.224263i	$0.0719976\pi$
$734$		0			0
$735$	1.14542e7	−	3.96642e6i	0.782075	−	0.270820i
$736$		0			0
$737$	427922.	+	741182.i	0.0290199	+	0.0502639i
$738$		0			0
$739$	6.94113e6	+	4.00746e6i	0.467540	+	0.269935i	0.715209	−	0.698910i	$-0.246331\pi$
$739$	6.94113e6	+	4.00746e6i	0.467540	+	0.269935i	−0.247669	+	0.968845i	$0.579665\pi$
$740$		0			0
$741$		−	1.62417e7i		−	1.08664i
$742$		0			0
$743$		−	2.03855e6i		−	0.135472i	−0.997703	−	0.0677360i	$-0.978422\pi$
$743$		−	2.03855e6i		−	0.135472i	0.997703	−	0.0677360i	$-0.0215776\pi$
$744$		0			0
$745$	9.40280e6	+	5.42871e6i	0.620678	+	0.358349i
$746$		0			0
$747$	−1.09131e7	−	1.89020e7i	−0.715559	−	1.23939i
$748$		0			0
$749$	2.92087e7	+	2.78672e6i	1.90243	+	0.181505i
$750$		0			0
$751$	8.84867e6	−	5.10878e6i	0.572503	−	0.330535i	−0.185645	−	0.982617i	$-0.559438\pi$
$751$	8.84867e6	−	5.10878e6i	0.572503	−	0.330535i	0.758149	+	0.652082i	$0.226104\pi$
$752$		0			0
$753$	−1.23660e6	+	2.14185e6i	−0.0794769	+	0.137658i
$754$		0			0
$755$	2.18928e7			1.39776
$756$		0			0
$757$	1.71925e7			1.09043			0.545217	−	0.838295i	$-0.316447\pi$
$757$	1.71925e7			1.09043			0.545217	+	0.838295i	$0.316447\pi$
$758$		0			0
$759$	211412.	−	366176.i	0.0133206	−	0.0230720i
$760$		0			0
$761$	−2.27259e7	+	1.31208e7i	−1.42252	+	0.821293i	−0.996514	−	0.0834273i	$-0.973413\pi$
$761$	−2.27259e7	+	1.31208e7i	−1.42252	+	0.821293i	−0.426007	+	0.904720i	$0.640080\pi$
$762$		0			0
$763$	−1.94668e7	+	8.89206e6i	−1.21055	+	0.552957i
$764$		0			0
$765$	−6.04679e6	−	1.04733e7i	−0.373569	−	0.647041i
$766$		0			0
$767$	−2.50190e6	−	1.44447e6i	−0.153561	−	0.0886585i
$768$		0			0
$769$			2.33601e7i			1.42449i	0.701933	+	0.712243i	$0.252321\pi$
$769$			2.33601e7i			1.42449i	−0.701933	+	0.712243i	$0.747679\pi$
$770$		0			0
$771$		−	81065.8i		−	0.00491136i
$772$		0			0
$773$	−6.57520e6	−	3.79619e6i	−0.395786	−	0.228507i	0.288878	−	0.957366i	$-0.406718\pi$
$773$	−6.57520e6	−	3.79619e6i	−0.395786	−	0.228507i	−0.684664	+	0.728859i	$0.740051\pi$
$774$		0			0
$775$	2.09132e7	+	3.62227e7i	1.25074	+	2.16634i
$776$		0			0
$777$	4.42376e6	+	3.14961e6i	0.262869	+	0.187156i
$778$		0			0
$779$	3.15653e7	−	1.82242e7i	1.86366	−	1.07598i
$780$		0			0
$781$	−656736.	+	1.13750e6i	−0.0385268	+	0.0667304i
$782$		0			0
$783$	8.24234e6			0.480448
$784$		0			0
$785$	−3.05903e7			−1.77178
$786$		0			0
$787$	−573125.	+	992682.i	−0.0329847	+	0.0571312i	−0.882047	−	0.471162i	$-0.843835\pi$
$787$	−573125.	+	992682.i	−0.0329847	+	0.0571312i	0.849062	+	0.528294i	$0.177168\pi$
$788$		0			0
$789$	9.74873e6	−	5.62843e6i	0.557514	−	0.321881i
$790$		0			0
$791$	2.25970e7	+	1.60885e7i	1.28413	+	0.914269i
$792$		0			0
$793$	1.76899e7	+	3.06398e7i	0.998947	+	1.73023i
$794$		0			0
$795$	9.27425e6	+	5.35449e6i	0.520428	+	0.300469i
$796$		0			0
$797$			7.81993e6i			0.436071i	0.975941	+	0.218035i	$0.0699648\pi$
$797$			7.81993e6i			0.436071i	−0.975941	+	0.218035i	$0.930035\pi$
$798$		0			0
$799$			4.18901e6i			0.232137i
$800$		0			0
$801$	2.33042e7	+	1.34547e7i	1.28337	+	0.740956i
$802$		0			0
$803$	1.53458e6	+	2.65798e6i	0.0839850	+	0.145466i
$804$		0			0
$805$	−8.26121e6	+	3.77357e6i	−0.449318	+	0.205240i
$806$		0			0
$807$	6.87356e6	−	3.96845e6i	0.371533	−	0.214505i
$808$		0			0
$809$	−1.15628e7	+	2.00273e7i	−0.621141	+	1.07585i	0.368132	+	0.929773i	$0.379997\pi$
$809$	−1.15628e7	+	2.00273e7i	−0.621141	+	1.07585i	−0.989274	+	0.146075i	$0.953336\pi$
$810$		0			0
$811$	3.10201e7			1.65612			0.828058	−	0.560642i	$-0.189446\pi$
$811$	3.10201e7			1.65612			0.828058	+	0.560642i	$0.189446\pi$
$812$		0			0
$813$	−1.50449e6			−0.0798296
$814$		0			0
$815$	1.40808e7	−	2.43886e7i	0.742561	−	1.28615i
$816$		0			0
$817$	5.49212e6	−	3.17087e6i	0.287862	−	0.166197i
$818$		0			0
$819$	−1.98634e7	−	1.89511e6i	−1.03477	−	0.0987247i
$820$		0			0
$821$	1.25924e7	+	2.18106e7i	0.652002	+	1.12930i	0.982636	+	0.185542i	$0.0594040\pi$
$821$	1.25924e7	+	2.18106e7i	0.652002	+	1.12930i	−0.330634	+	0.943759i	$0.607263\pi$
$822$		0			0
$823$	−1.40883e7	−	8.13389e6i	−0.725036	−	0.418600i	0.0915675	−	0.995799i	$-0.470812\pi$
$823$	−1.40883e7	−	8.13389e6i	−0.725036	−	0.418600i	−0.816603	+	0.577199i	$0.804146\pi$
$824$		0			0
$825$		−	3.51449e6i		−	0.179774i
$826$		0			0
$827$		−	1.06196e7i		−	0.539939i	−0.962869	−	0.269970i	$-0.912986\pi$
$827$		−	1.06196e7i		−	0.539939i	0.962869	−	0.269970i	$-0.0870137\pi$
$828$		0			0
$829$	7.86782e6	+	4.54249e6i	0.397620	+	0.229566i	0.685457	−	0.728114i	$-0.259603\pi$
$829$	7.86782e6	+	4.54249e6i	0.397620	+	0.229566i	−0.287837	+	0.957680i	$0.592936\pi$
$830$		0			0
$831$	7.12593e6	+	1.23425e7i	0.357964	+	0.620011i
$832$		0			0
$833$	−2.14958e6	+	1.11628e7i	−0.107335	+	0.557390i
$834$		0			0
$835$	5.62161e6	−	3.24564e6i	0.279026	−	0.161096i
$836$		0			0
$837$	1.11235e7	−	1.92665e7i	0.548817	−	0.950579i
$838$		0			0
$839$	−4.00717e7			−1.96532			−0.982660	−	0.185419i	$-0.940636\pi$
$839$	−4.00717e7			−1.96532			−0.982660	+	0.185419i	$0.940636\pi$
$840$		0			0
$841$	−1.39979e7			−0.682452
$842$		0			0
$843$	3.13406e6	−	5.42835e6i	0.151893	−	0.263087i
$844$		0			0
$845$	2.57634e7	−	1.48745e7i	1.24126	−	0.716641i
$846$		0			0
$847$	1.91006e6	−	2.00201e7i	0.0914826	−	0.958866i
$848$		0			0
$849$	−6.73546e6	−	1.16662e7i	−0.320699	−	0.555468i
$850$		0			0
$851$	−3.52372e6	−	2.03442e6i	−0.166793	−	0.0962978i
$852$		0			0
$853$			1.27239e7i			0.598751i	0.954135	+	0.299376i	$0.0967784\pi$
$853$			1.27239e7i			0.598751i	−0.954135	+	0.299376i	$0.903222\pi$
$854$		0			0
$855$		−	4.67757e7i		−	2.18829i
$856$		0			0
$857$	−1.94382e7	−	1.12226e7i	−0.904073	−	0.521967i	−0.0255535	−	0.999673i	$-0.508135\pi$
$857$	−1.94382e7	−	1.12226e7i	−0.904073	−	0.521967i	−0.878519	+	0.477707i	$0.841468\pi$
$858$		0			0
$859$	1.42985e7	+	2.47656e7i	0.661159	+	1.14516i	0.980311	+	0.197458i	$0.0632686\pi$
$859$	1.42985e7	+	2.47656e7i	0.661159	+	1.14516i	−0.319152	+	0.947703i	$0.603398\pi$
$860$		0			0
$861$	5.64385e6	+	1.23557e7i	0.259459	+	0.568014i
$862$		0			0
$863$	7.12829e6	−	4.11552e6i	0.325805	−	0.188104i	−0.328172	−	0.944618i	$-0.606433\pi$
$863$	7.12829e6	−	4.11552e6i	0.325805	−	0.188104i	0.653977	+	0.756514i	$0.273099\pi$
$864$		0			0
$865$	4.52031e6	−	7.82941e6i	0.205413	−	0.355786i
$866$		0			0
$867$	7.23752e6			0.326995
$868$		0			0
$869$	5.55379e6			0.249482
$870$		0			0
$871$	4.58997e6	−	7.95006e6i	0.205005	−	0.355079i
$872$		0			0
$873$	6.14229e6	−	3.54625e6i	0.272769	−	0.157483i
$874$		0			0
$875$	−2.12502e7	+	2.98469e7i	−0.938305	+	1.31789i
$876$		0			0
$877$	−1.42657e7	−	2.47088e7i	−0.626315	−	1.08481i	−0.988285	−	0.152619i	$-0.951229\pi$
$877$	−1.42657e7	−	2.47088e7i	−0.626315	−	1.08481i	0.361970	−	0.932190i	$-0.382104\pi$
$878$		0			0
$879$	7.69201e6	+	4.44098e6i	0.335790	+	0.193868i
$880$		0			0
$881$			2.30793e7i			1.00180i	0.865504	+	0.500902i	$0.166998\pi$
$881$			2.30793e7i			1.00180i	−0.865504	+	0.500902i	$0.833002\pi$
$882$		0			0
$883$		−	3.04072e7i		−	1.31243i	−0.754575	−	0.656213i	$-0.772157\pi$
$883$		−	3.04072e7i		−	1.31243i	0.754575	−	0.656213i	$-0.227843\pi$
$884$		0			0
$885$	2.18577e6	+	1.26196e6i	0.0938095	+	0.0541610i
$886$		0			0
$887$	4.60945e6	+	7.98380e6i	0.196716	+	0.340722i	0.947462	−	0.319869i	$-0.103639\pi$
$887$	4.60945e6	+	7.98380e6i	0.196716	+	0.340722i	−0.750746	+	0.660591i	$0.770306\pi$
$888$		0			0
$889$	−4.22057e6	+	5.92797e6i	−0.179109	+	0.251566i
$890$		0			0
$891$	1.40085e6	−	808782.i	0.0591150	−	0.0341301i
$892$		0			0
$893$	−8.10115e6	+	1.40316e7i	−0.339952	+	0.588815i
$894$		0			0
$895$	−5.56648e7			−2.32286
$896$		0			0
$897$	−4.53529e6			−0.188202
$898$		0			0
$899$	8.79003e6	−	1.52248e7i	0.362736	−	0.628278i
$900$		0			0
$901$	−8.69758e6	+	5.02155e6i	−0.356933	+	0.206075i
$902$		0			0
$903$	981987.	+	2.14979e6i	0.0400762	+	0.0877359i
$904$		0			0
$905$	623291.	+	1.07957e6i	0.0252970	+	0.0438158i
$906$		0			0
$907$	1.63082e7	+	9.41554e6i	0.658245	+	0.380038i	0.791608	−	0.611029i	$-0.209244\pi$
$907$	1.63082e7	+	9.41554e6i	0.658245	+	0.380038i	−0.133363	+	0.991067i	$0.542578\pi$
$908$		0			0
$909$		−	4.82859e6i		−	0.193825i
$910$		0			0
$911$			1.00944e7i			0.402983i	0.979490	+	0.201491i	$0.0645788\pi$
$911$			1.00944e7i			0.402983i	−0.979490	+	0.201491i	$0.935421\pi$
$912$		0			0
$913$	7.80280e6	+	4.50495e6i	0.309795	+	0.178860i
$914$		0			0
$915$	−1.54547e7	−	2.67684e7i	−0.610251	−	1.05699i
$916$		0			0
$917$	1.64713e6	−	1.72642e7i	0.0646851	−	0.677990i
$918$		0			0
$919$	3.77800e7	−	2.18123e7i	1.47561	−	0.851946i	0.475992	−	0.879449i	$-0.342089\pi$
$919$	3.77800e7	−	2.18123e7i	1.47561	−	0.851946i	0.999622	+	0.0275034i	$0.00875571\pi$
$920$		0			0
$921$	−1.82513e6	+	3.16122e6i	−0.0708998	+	0.122802i
$922$		0			0
$923$	1.40885e7			0.544329
$924$		0			0
$925$	−3.38200e7			−1.29963
$926$		0			0
$927$	−1.72176e7	+	2.98218e7i	−0.658073	+	1.13982i
$928$		0			0
$929$	2.33559e7	−	1.34846e7i	0.887888	−	0.512622i	0.0146366	−	0.999893i	$-0.495341\pi$
$929$	2.33559e7	−	1.34846e7i	0.887888	−	0.512622i	0.873251	+	0.487271i	$0.162008\pi$
$930$		0			0
$931$	−2.87880e7	+	3.32340e7i	−1.08852	+	1.25663i
$932$		0			0
$933$	−1.21089e7	−	2.09732e7i	−0.455408	−	0.788789i
$934$		0			0
$935$	4.32343e6	+	2.49613e6i	0.161733	+	0.0933767i
$936$		0			0
$937$		−	3.76491e6i		−	0.140090i	−0.997544	−	0.0700448i	$-0.977686\pi$
$937$		−	3.76491e6i		−	0.140090i	0.997544	−	0.0700448i	$-0.0223142\pi$
$938$		0			0
$939$		−	1.17974e7i		−	0.436638i
$940$		0			0
$941$	−1.63557e7	−	9.44296e6i	−0.602136	−	0.347644i	0.167745	−	0.985830i	$-0.446351\pi$
$941$	−1.63557e7	−	9.44296e6i	−0.602136	−	0.347644i	−0.769882	+	0.638187i	$0.779685\pi$
$942$		0			0
$943$	−5.08888e6	−	8.81420e6i	−0.186356	−	0.322778i
$944$		0			0
$945$	3.99715e7	+	3.81357e6i	1.45603	+	0.138916i
$946$		0			0
$947$	1.51749e6	−	876121.i	0.0549857	−	0.0317460i	−0.472255	−	0.881462i	$-0.656560\pi$
$947$	1.51749e6	−	876121.i	0.0549857	−	0.0317460i	0.527241	+	0.849716i	$0.323227\pi$
$948$		0			0
$949$	1.64602e7	−	2.85100e7i	0.593295	−	1.02762i
$950$		0			0
$951$	1.62537e7			0.582777
$952$		0			0
$953$	4.38471e7			1.56390			0.781949	−	0.623342i	$-0.214226\pi$
$953$	4.38471e7			1.56390			0.781949	+	0.623342i	$0.214226\pi$
$954$		0			0
$955$	1.22618e7	−	2.12380e7i	0.435056	−	0.753539i
$956$		0			0
$957$	−1.27927e6	+	738589.i	−0.0451527	+	0.0260689i
$958$		0			0
$959$	1.38038e7	−	6.30535e6i	0.484678	−	0.221392i
$960$		0			0
$961$	−9.41068e6	−	1.62998e7i	−0.328710	−	0.569342i
$962$		0			0
$963$	3.65435e7	+	2.10984e7i	1.26983	+	0.733134i
$964$		0			0
$965$		−	1.33048e7i		−	0.459928i
$966$		0			0
$967$			3.75521e7i			1.29142i	0.763582	+	0.645711i	$0.223439\pi$
$967$			3.75521e7i			1.29142i	−0.763582	+	0.645711i	$0.776561\pi$
$968$		0			0
$969$	−1.15244e7	−	6.65361e6i	−0.394284	−	0.227640i
$970$		0			0
$971$	−3.76332e6	−	6.51826e6i	−0.128092	−	0.221862i	0.794845	−	0.606812i	$-0.207552\pi$
$971$	−3.76332e6	−	6.51826e6i	−0.128092	−	0.221862i	−0.922937	+	0.384950i	$0.874219\pi$
$972$		0			0
$973$	4.45956e7	+	3.17510e7i	1.51011	+	1.07516i
$974$		0			0
$975$	−3.26467e7	+	1.88486e7i	−1.09983	+	0.634990i
$976$		0			0
$977$	−2.29454e7	+	3.97426e7i	−0.769058	+	1.33205i	0.169016	+	0.985613i	$0.445941\pi$
$977$	−2.29454e7	+	3.97426e7i	−0.769058	+	1.33205i	−0.938074	+	0.346435i	$0.887392\pi$
$978$		0			0
$979$	−1.11083e7			−0.370416
$980$		0			0
$981$	−3.07782e7			−1.02111
$982$		0			0
$983$	1.99948e7	−	3.46320e7i	0.659984	−	1.14313i	−0.320636	−	0.947203i	$-0.603897\pi$
$983$	1.99948e7	−	3.46320e7i	0.659984	−	1.14313i	0.980619	−	0.195923i	$-0.0627701\pi$
$984$		0			0
$985$	−6.95884e7	+	4.01769e7i	−2.28532	+	1.31943i
$986$		0			0
$987$	−4.91894e6	−	3.50216e6i	−0.160723	−	0.114431i
$988$		0			0
$989$	−885426.	−	1.53360e6i	−0.0287847	−	0.0498565i
$990$		0			0
$991$	5.98801e6	+	3.45718e6i	0.193686	+	0.111825i	0.593707	−	0.804681i	$-0.297664\pi$
$991$	5.98801e6	+	3.45718e6i	0.193686	+	0.111825i	−0.400021	+	0.916506i	$0.630997\pi$
$992$		0			0
$993$			1.55471e7i			0.500351i
$994$		0			0
$995$			7.33400e7i			2.34846i
$996$		0			0
$997$	1.21562e7	+	7.01839e6i	0.387311	+	0.223614i	0.680995	−	0.732289i	$-0.261548\pi$
$997$	1.21562e7	+	7.01839e6i	0.387311	+	0.223614i	−0.293683	+	0.955903i	$0.594881\pi$
$998$		0			0
$999$	8.99425e6	+	1.55785e7i	0.285135	+	0.493869i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.6.p.a.31.16	✓	80
4.3	odd	2	inner	224.6.p.a.31.25	yes	80
7.5	odd	6	inner	224.6.p.a.159.25	yes	80
28.19	even	6	inner	224.6.p.a.159.16	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.6.p.a.31.16	✓	80	1.1	even	1	trivial
224.6.p.a.31.25	yes	80	4.3	odd	2	inner
224.6.p.a.159.16	yes	80	28.19	even	6	inner
224.6.p.a.159.25	yes	80	7.5	odd	6	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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	224.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.76024 + 6.51293i) q^{3} +(-83.0525 + 47.9504i) q^{5} +(105.609 + 75.1911i) q^{7} +(93.2211 + 161.464i) q^{9} +(-66.6527 - 38.4820i) q^{11} +825.530i q^{13} -721.221i q^{15} +(585.759 + 338.188i) q^{17} +(1308.05 + 2265.60i) q^{19} +(-886.831 + 405.089i) q^{21} +(632.641 - 365.255i) q^{23} +(3035.98 - 5258.48i) q^{25} -3229.62 q^{27} -2552.11 q^{29} +(-3444.22 + 5965.56i) q^{31} +(501.261 - 289.403i) q^{33} +(-12376.6 - 1180.81i) q^{35} +(-2784.93 - 4823.64i) q^{37} +(-5376.62 - 3104.19i) q^{39} -13932.4i q^{41} -2424.13i q^{43} +(-15484.5 - 8939.98i) q^{45} +(3096.66 + 5363.57i) q^{47} +(5499.59 + 15881.7i) q^{49} +(-4405.19 + 2543.34i) q^{51} +(-7424.20 + 12859.1i) q^{53} +7380.90 q^{55} -19674.3 q^{57} +(-1749.75 + 3030.66i) q^{59} +(37115.3 - 21428.5i) q^{61} +(-2295.63 + 24061.4i) q^{63} +(-39584.5 - 68562.4i) q^{65} +(-9630.25 - 5560.03i) q^{67} +5493.80i q^{69} -17066.1i q^{71} +(-34535.4 - 19939.0i) q^{73} +(22832.1 + 39546.3i) q^{75} +(-4145.64 - 9075.74i) q^{77} +(-62493.2 + 36080.5i) q^{79} +(-10508.6 + 18201.4i) q^{81} -117067. q^{83} -64865.0 q^{85} +(9596.57 - 16621.7i) q^{87} +(124994. - 72165.5i) q^{89} +(-62072.5 + 87183.5i) q^{91} +(-25902.2 - 44863.9i) q^{93} +(-217273. - 125443. i) q^{95} -38041.3i q^{97} -14349.3i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 3240 q^{9} + 6856 q^{21} + 27728 q^{25} - 15920 q^{29} - 28296 q^{33} - 2152 q^{37} + 35400 q^{45} + 29280 q^{49} - 17512 q^{53} - 108368 q^{57} + 37704 q^{61} + 18216 q^{65} + 157704 q^{73} + 28224 q^{77}+ \cdots + 39400 q^{93}+O(q^{100}) \) 80 * q - 3240 * q^9 + 6856 * q^21 + 27728 * q^25 - 15920 * q^29 - 28296 * q^33 - 2152 * q^37 + 35400 * q^45 + 29280 * q^49 - 17512 * q^53 - 108368 * q^57 + 37704 * q^61 + 18216 * q^65 + 157704 * q^73 + 28224 * q^77 - 273136 * q^81 + 230704 * q^85 + 28440 * q^89 + 39400 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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