LMFDB - Embedded newform 80.6.n.c.63.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(47,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("80.47");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	80.n (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:	$12.8307055850$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{155})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 77x^{2} + 1521 $ x^4 - 77*x^2 + 1521
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			63.2
Root			$-6.22495 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	80.63
Dual form			80.6.n.c.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(12.4499 - 12.4499i) q^{3} +(55.0000 - 10.0000i) q^{5} +(136.949 + 136.949i) q^{7} -67.0000i q^{9} +O(q^{10})$	\(q+(12.4499 - 12.4499i) q^{3} +(55.0000 - 10.0000i) q^{5} +(136.949 + 136.949i) q^{7} -67.0000i q^{9} +124.499i q^{11} +(165.000 + 165.000i) q^{13} +(560.245 - 809.243i) q^{15} +(1265.00 - 1265.00i) q^{17} -2738.98 q^{19} +3410.00 q^{21} +(-535.346 + 535.346i) q^{23} +(2925.00 - 1100.00i) q^{25} +(2191.18 + 2191.18i) q^{27} -2596.00i q^{29} -7096.44i q^{31} +(1550.00 + 1550.00i) q^{33} +(8901.68 + 6162.70i) q^{35} +(1385.00 - 1385.00i) q^{37} +4108.47 q^{39} +2178.00 q^{41} +(-13831.8 + 13831.8i) q^{43} +(-670.000 - 3685.00i) q^{45} +(-4942.61 - 4942.61i) q^{47} +20703.0i q^{49} -31498.2i q^{51} +(-23915.0 - 23915.0i) q^{53} +(1244.99 + 6847.44i) q^{55} +(-34100.0 + 34100.0i) q^{57} -27140.8 q^{59} -35882.0 q^{61} +(9175.58 - 9175.58i) q^{63} +(10725.0 + 7425.00i) q^{65} +(26829.5 + 26829.5i) q^{67} +13330.0i q^{69} +67105.0i q^{71} +(-21615.0 - 21615.0i) q^{73} +(22721.1 - 50110.8i) q^{75} +(-17050.0 + 17050.0i) q^{77} +21911.8 q^{79} +70841.0 q^{81} +(38756.5 - 38756.5i) q^{83} +(56925.0 - 82225.0i) q^{85} +(-32319.9 - 32319.9i) q^{87} +114424. i q^{89} +45193.1i q^{91} +(-88350.0 - 88350.0i) q^{93} +(-150644. + 27389.8i) q^{95} +(-615.000 + 615.000i) q^{97} +8341.43 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 220 q^{5}+O(q^{10}) $ 4 * q + 220 * q^5	$ 4 q + 220 q^{5} + 660 q^{13} + 5060 q^{17} + 13640 q^{21} + 11700 q^{25} + 6200 q^{33} + 5540 q^{37} + 8712 q^{41} - 2680 q^{45} - 95660 q^{53} - 136400 q^{57} - 143528 q^{61} + 42900 q^{65} - 86460 q^{73} - 68200 q^{77} + 283364 q^{81} + 227700 q^{85} - 353400 q^{93} - 2460 q^{97}+O(q^{100}) $ 4 * q + 220 * q^5 + 660 * q^13 + 5060 * q^17 + 13640 * q^21 + 11700 * q^25 + 6200 * q^33 + 5540 * q^37 + 8712 * q^41 - 2680 * q^45 - 95660 * q^53 - 136400 * q^57 - 143528 * q^61 + 42900 * q^65 - 86460 * q^73 - 68200 * q^77 + 283364 * q^81 + 227700 * q^85 - 353400 * q^93 - 2460 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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
$3$	12.4499	−	12.4499i	0.798661	−	0.798661i	−0.184223	−	0.982884i	$-0.558977\pi$
$3$	12.4499	−	12.4499i	0.798661	−	0.798661i	0.982884	+	0.184223i	$0.0589769\pi$
$4$		0			0
$5$	55.0000	−	10.0000i	0.983870	−	0.178885i
$5$	55.0000	−	10.0000i	0.983870	−	0.178885i
$6$		0			0
$7$	136.949	+	136.949i	1.05636	+	1.05636i	0.998314	+	0.0580499i	$0.0184883\pi$
$7$	136.949	+	136.949i	1.05636	+	1.05636i	0.0580499	+	0.998314i	$0.481512\pi$
$8$		0			0
$9$		−	67.0000i		−	0.275720i
$10$		0			0
$11$			124.499i			0.310230i	0.987896	+	0.155115i	$0.0495749\pi$
$11$			124.499i			0.310230i	−0.987896	+	0.155115i	$0.950425\pi$
$12$		0			0
$13$	165.000	+	165.000i	0.270786	+	0.270786i	0.829416	−	0.558631i	$-0.188673\pi$
$13$	165.000	+	165.000i	0.270786	+	0.270786i	−0.558631	+	0.829416i	$0.688673\pi$
$14$		0			0
$15$	560.245	−	809.243i	0.642910	−	0.928648i
$16$		0			0
$17$	1265.00	−	1265.00i	1.06162	−	1.06162i	0.0636453	−	0.997973i	$-0.479727\pi$
$17$	1265.00	−	1265.00i	1.06162	−	1.06162i	0.997973	−	0.0636453i	$-0.0202726\pi$
$18$		0			0
$19$	−2738.98			−1.74062			−0.870311	−	0.492502i	$-0.836082\pi$
$19$	−2738.98			−1.74062			−0.870311	+	0.492502i	$0.836082\pi$
$20$		0			0
$21$	3410.00			1.68735
$22$		0			0
$23$	−535.346	+	535.346i	−0.211016	+	0.211016i	−0.804699	−	0.593683i	$-0.797673\pi$
$23$	−535.346	+	535.346i	−0.211016	+	0.211016i	0.593683	+	0.804699i	$0.297673\pi$
$24$		0			0
$25$	2925.00	−	1100.00i	0.936000	−	0.352000i
$26$		0			0
$27$	2191.18	+	2191.18i	0.578454	+	0.578454i
$28$		0			0
$29$		−	2596.00i		−	0.573205i	−0.958050	−	0.286602i	$-0.907474\pi$
$29$		−	2596.00i		−	0.573205i	0.958050	−	0.286602i	$-0.0925258\pi$
$30$		0			0
$31$		−	7096.44i		−	1.32628i	−0.748494	−	0.663142i	$-0.769223\pi$
$31$		−	7096.44i		−	1.32628i	0.748494	−	0.663142i	$-0.230777\pi$
$32$		0			0
$33$	1550.00	+	1550.00i	0.247769	+	0.247769i
$34$		0			0
$35$	8901.68	+	6162.70i	1.22829	+	0.850356i
$36$		0			0
$37$	1385.00	−	1385.00i	0.166320	−	0.166320i	−0.619039	−	0.785360i	$-0.712478\pi$
$37$	1385.00	−	1385.00i	0.166320	−	0.166320i	0.785360	+	0.619039i	$0.212478\pi$
$38$		0			0
$39$	4108.47			0.432532
$40$		0			0
$41$	2178.00			0.202348			0.101174	−	0.994869i	$-0.467740\pi$
$41$	2178.00			0.202348			0.101174	+	0.994869i	$0.467740\pi$
$42$		0			0
$43$	−13831.8	+	13831.8i	−1.14080	+	1.14080i	−0.152494	+	0.988304i	$0.548730\pi$
$43$	−13831.8	+	13831.8i	−1.14080	+	1.14080i	−0.988304	+	0.152494i	$0.951270\pi$
$44$		0			0
$45$	−670.000	−	3685.00i	−0.0493223	−	0.271273i
$46$		0			0
$47$	−4942.61	−	4942.61i	−0.326371	−	0.326371i	0.524834	−	0.851205i	$-0.324128\pi$
$47$	−4942.61	−	4942.61i	−0.326371	−	0.326371i	−0.851205	+	0.524834i	$0.824128\pi$
$48$		0			0
$49$			20703.0i			1.23181i
$50$		0			0
$51$		−	31498.2i		−	1.69575i
$52$		0			0
$53$	−23915.0	−	23915.0i	−1.16945	−	1.16945i	−0.982339	−	0.187108i	$-0.940089\pi$
$53$	−23915.0	−	23915.0i	−1.16945	−	1.16945i	−0.187108	−	0.982339i	$-0.559911\pi$
$54$		0			0
$55$	1244.99	+	6847.44i	0.0554957	+	0.305226i
$56$		0			0
$57$	−34100.0	+	34100.0i	−1.39017	+	1.39017i
$58$		0			0
$59$	−27140.8			−1.01506			−0.507531	−	0.861634i	$-0.669442\pi$
$59$	−27140.8			−1.01506			−0.507531	+	0.861634i	$0.669442\pi$
$60$		0			0
$61$	−35882.0			−1.23467			−0.617337	−	0.786699i	$-0.711788\pi$
$61$	−35882.0			−1.23467			−0.617337	+	0.786699i	$0.711788\pi$
$62$		0			0
$63$	9175.58	−	9175.58i	0.291261	−	0.291261i
$64$		0			0
$65$	10725.0	+	7425.00i	0.314857	+	0.217978i
$66$		0			0
$67$	26829.5	+	26829.5i	0.730174	+	0.730174i	0.970654	−	0.240480i	$-0.0773050\pi$
$67$	26829.5	+	26829.5i	0.730174	+	0.730174i	−0.240480	+	0.970654i	$0.577305\pi$
$68$		0			0
$69$			13330.0i			0.337060i
$70$		0			0
$71$			67105.0i			1.57982i	0.613220	+	0.789912i	$0.289874\pi$
$71$			67105.0i			1.57982i	−0.613220	+	0.789912i	$0.710126\pi$
$72$		0			0
$73$	−21615.0	−	21615.0i	−0.474732	−	0.474732i	0.428710	−	0.903442i	$-0.358968\pi$
$73$	−21615.0	−	21615.0i	−0.474732	−	0.474732i	−0.903442	+	0.428710i	$0.858968\pi$
$74$		0			0
$75$	22721.1	−	50110.8i	0.466418	−	1.02868i
$76$		0			0
$77$	−17050.0	+	17050.0i	−0.327716	+	0.327716i
$78$		0			0
$79$	21911.8			0.395012			0.197506	−	0.980302i	$-0.436716\pi$
$79$	21911.8			0.395012			0.197506	+	0.980302i	$0.436716\pi$
$80$		0			0
$81$	70841.0			1.19970
$82$		0			0
$83$	38756.5	−	38756.5i	0.617518	−	0.617518i	−0.327376	−	0.944894i	$-0.606164\pi$
$83$	38756.5	−	38756.5i	0.617518	−	0.617518i	0.944894	+	0.327376i	$0.106164\pi$
$84$		0			0
$85$	56925.0	−	82225.0i	0.854586	−	1.23440i
$86$		0			0
$87$	−32319.9	−	32319.9i	−0.457796	−	0.457796i
$88$		0			0
$89$			114424.i			1.53124i	0.643296	+	0.765618i	$0.277567\pi$
$89$			114424.i			1.53124i	−0.643296	+	0.765618i	$0.722433\pi$
$90$		0			0
$91$			45193.1i			0.572096i
$92$		0			0
$93$	−88350.0	−	88350.0i	−1.05925	−	1.05925i
$94$		0			0
$95$	−150644.	+	27389.8i	−1.71255	+	0.311372i
$96$		0			0
$97$	−615.000	+	615.000i	−0.00663660	+	0.00663660i	−0.710417	−	0.703781i	$-0.751494\pi$
$97$	−615.000	+	615.000i	−0.00663660	+	0.00663660i	0.703781	+	0.710417i	$0.251494\pi$
$98$		0			0
$99$	8341.43			0.0855367
$100$		0			0
$101$	146982.			1.43371			0.716854	−	0.697223i	$-0.245581\pi$
$101$	146982.			1.43371			0.716854	+	0.697223i	$0.245581\pi$
$102$		0			0
$103$	−1929.73	+	1929.73i	−0.0179227	+	0.0179227i	−0.716011	−	0.698089i	$-0.754034\pi$
$103$	−1929.73	+	1929.73i	−0.0179227	+	0.0179227i	0.698089	+	0.716011i	$0.254034\pi$
$104$		0			0
$105$	187550.	−	34100.0i	1.66014	−	0.301843i
$106$		0			0
$107$	−61216.2	−	61216.2i	−0.516900	−	0.516900i	0.399732	−	0.916632i	$-0.369103\pi$
$107$	−61216.2	−	61216.2i	−0.516900	−	0.516900i	−0.916632	+	0.399732i	$0.869103\pi$
$108$		0			0
$109$		−	94204.0i		−	0.759457i	−0.925098	−	0.379728i	$-0.876017\pi$
$109$		−	94204.0i		−	0.759457i	0.925098	−	0.379728i	$-0.123983\pi$
$110$		0			0
$111$		−	34486.2i		−	0.265667i
$112$		0			0
$113$	11705.0	+	11705.0i	0.0862334	+	0.0862334i	0.748908	−	0.662674i	$-0.230579\pi$
$113$	11705.0	+	11705.0i	0.0862334	+	0.0862334i	−0.662674	+	0.748908i	$0.730579\pi$
$114$		0			0
$115$	−24090.6	+	34797.5i	−0.169864	+	0.245360i
$116$		0			0
$117$	11055.0	−	11055.0i	0.0746610	−	0.0746610i
$118$		0			0
$119$	346481.			2.24291
$120$		0			0
$121$	145551.			0.903757
$122$		0			0
$123$	27115.9	−	27115.9i	0.161607	−	0.161607i
$124$		0			0
$125$	149875.	−	89750.0i	0.857935	−	0.513759i
$126$		0			0
$127$	−61216.2	−	61216.2i	−0.336788	−	0.336788i	0.518369	−	0.855157i	$-0.326539\pi$
$127$	−61216.2	−	61216.2i	−0.336788	−	0.336788i	−0.855157	+	0.518369i	$0.826539\pi$
$128$		0			0
$129$			344410.i			1.82222i
$130$		0			0
$131$			228705.i			1.16439i	0.813051	+	0.582193i	$0.197805\pi$
$131$			228705.i			1.16439i	−0.813051	+	0.582193i	$0.802195\pi$
$132$		0			0
$133$	−375100.	−	375100.i	−1.83873	−	1.83873i
$134$		0			0
$135$	142427.	+	98603.2i	0.672601	+	0.465647i
$136$		0			0
$137$	−243055.	+	243055.i	−1.10638	+	1.10638i	−0.112754	+	0.993623i	$0.535967\pi$
$137$	−243055.	+	243055.i	−1.10638	+	1.10638i	−0.993623	+	0.112754i	$0.964033\pi$
$138$		0			0
$139$	−304027.			−1.33467			−0.667336	−	0.744757i	$-0.732565\pi$
$139$	−304027.			−1.33467			−0.667336	+	0.744757i	$0.732565\pi$
$140$		0			0
$141$	−123070.			−0.521320
$142$		0			0
$143$	−20542.3	+	20542.3i	−0.0840059	+	0.0840059i
$144$		0			0
$145$	−25960.0	−	142780.i	−0.102538	−	0.563959i
$146$		0			0
$147$	257750.	+	257750.i	0.983798	+	0.983798i
$148$		0			0
$149$			348876.i			1.28738i	0.765288	+	0.643688i	$0.222597\pi$
$149$			348876.i			1.28738i	−0.765288	+	0.643688i	$0.777403\pi$
$150$		0			0
$151$		−	502602.i		−	1.79383i	−0.442199	−	0.896917i	$-0.645802\pi$
$151$		−	502602.i		−	1.79383i	0.442199	−	0.896917i	$-0.354198\pi$
$152$		0			0
$153$	−84755.0	−	84755.0i	−0.292709	−	0.292709i
$154$		0			0
$155$	−70964.4	−	390304.i	−0.237253	−	1.30489i
$156$		0			0
$157$	−221935.	+	221935.i	−0.718583	+	0.718583i	−0.968315	−	0.249732i	$-0.919657\pi$
$157$	−221935.	+	221935.i	−0.718583	+	0.718583i	0.249732	+	0.968315i	$0.419657\pi$
$158$		0			0
$159$	−595479.			−1.86799
$160$		0			0
$161$	−146630.			−0.445819
$162$		0			0
$163$	−30664.1	+	30664.1i	−0.0903985	+	0.0903985i	−0.750860	−	0.660461i	$-0.770361\pi$
$163$	−30664.1	+	30664.1i	−0.0903985	+	0.0903985i	0.660461	+	0.750860i	$0.270361\pi$
$164$		0			0
$165$	100750.	+	69750.0i	0.288095	+	0.199450i
$166$		0			0
$167$	−25061.6	−	25061.6i	−0.0695374	−	0.0695374i	0.671483	−	0.741020i	$-0.265658\pi$
$167$	−25061.6	−	25061.6i	−0.0695374	−	0.0695374i	−0.741020	+	0.671483i	$0.765658\pi$
$168$		0			0
$169$		−	316843.i		−	0.853350i
$170$		0			0
$171$			183512.i			0.479925i
$172$		0			0
$173$	−16555.0	−	16555.0i	−0.0420546	−	0.0420546i	0.685767	−	0.727821i	$-0.259467\pi$
$173$	−16555.0	−	16555.0i	−0.0420546	−	0.0420546i	−0.727821	+	0.685767i	$0.759467\pi$
$174$		0			0
$175$	551219.	+	249932.i	1.36060	+	0.616916i
$176$		0			0
$177$	−337900.	+	337900.i	−0.810690	+	0.810690i
$178$		0			0
$179$	84908.3			0.198070			0.0990348	−	0.995084i	$-0.468424\pi$
$179$	84908.3			0.198070			0.0990348	+	0.995084i	$0.468424\pi$
$180$		0			0
$181$	−114378.			−0.259505			−0.129753	−	0.991546i	$-0.541418\pi$
$181$	−114378.			−0.259505			−0.129753	+	0.991546i	$0.541418\pi$
$182$		0			0
$183$	−446727.	+	446727.i	−0.986086	+	0.986086i
$184$		0			0
$185$	62325.0	−	90025.0i	0.133885	−	0.193390i
$186$		0			0
$187$	157491.	+	157491.i	0.329346	+	0.329346i
$188$		0			0
$189$			600160.i			1.22212i
$190$		0			0
$191$		−	428401.i		−	0.849703i	−0.905263	−	0.424851i	$-0.860326\pi$
$191$		−	428401.i		−	0.849703i	0.905263	−	0.424851i	$-0.139674\pi$
$192$		0			0
$193$	−522335.	−	522335.i	−1.00938	−	1.00938i	−0.999956	−	0.00942713i	$-0.996999\pi$
$193$	−522335.	−	522335.i	−1.00938	−	1.00938i	−0.00942713	−	0.999956i	$-0.503001\pi$
$194$		0			0
$195$	225966.	−	41084.7i	0.425555	−	0.0773737i
$196$		0			0
$197$	301345.	−	301345.i	0.553221	−	0.553221i	−0.374148	−	0.927369i	$-0.622065\pi$
$197$	301345.	−	301345.i	0.553221	−	0.553221i	0.927369	+	0.374148i	$0.122065\pi$
$198$		0			0
$199$	736536.			1.31844			0.659221	−	0.751949i	$-0.270886\pi$
$199$	736536.			1.31844			0.659221	+	0.751949i	$0.270886\pi$
$200$		0			0
$201$	668050.			1.16632
$202$		0			0
$203$	355519.	−	355519.i	0.605513	−	0.605513i
$204$		0			0
$205$	119790.	−	21780.0i	0.199084	−	0.0361971i
$206$		0			0
$207$	35868.2	+	35868.2i	0.0581813	+	0.0581813i
$208$		0			0
$209$		−	341000.i		−	0.539994i
$210$		0			0
$211$		−	516297.i		−	0.798351i	−0.916875	−	0.399175i	$-0.869296\pi$
$211$		−	516297.i		−	0.798351i	0.916875	−	0.399175i	$-0.130704\pi$
$212$		0			0
$213$	835450.	+	835450.i	1.26174	+	1.26174i
$214$		0			0
$215$	−622433.	+	899069.i	−0.918325	+	1.32647i
$216$		0			0
$217$	971850.	−	971850.i	1.40104	−	1.40104i
$218$		0			0
$219$	−538209.			−0.758300
$220$		0			0
$221$	417450.			0.574942
$222$		0			0
$223$	−361284.	+	361284.i	−0.486504	+	0.486504i	−0.907201	−	0.420697i	$-0.861785\pi$
$223$	−361284.	+	361284.i	−0.486504	+	0.486504i	0.420697	+	0.907201i	$0.361785\pi$
$224$		0			0
$225$	−73700.0	−	195975.i	−0.0970535	−	0.258074i
$226$		0			0
$227$	−717475.	−	717475.i	−0.924150	−	0.924150i	0.0731699	−	0.997319i	$-0.476688\pi$
$227$	−717475.	−	717475.i	−0.924150	−	0.924150i	−0.997319	+	0.0731699i	$0.976688\pi$
$228$		0			0
$229$		−	903276.i		−	1.13823i	−0.822256	−	0.569117i	$-0.807285\pi$
$229$		−	903276.i		−	1.13823i	0.822256	−	0.569117i	$-0.192715\pi$
$230$		0			0
$231$			424542.i			0.523468i
$232$		0			0
$233$	703065.	+	703065.i	0.848410	+	0.848410i	0.989935	−	0.141525i	$-0.0452005\pi$
$233$	703065.	+	703065.i	0.848410	+	0.848410i	−0.141525	+	0.989935i	$0.545201\pi$
$234$		0			0
$235$	−321270.	−	222417.i	−0.379490	−	0.262724i
$236$		0			0
$237$	272800.	−	272800.i	0.315481	−	0.315481i
$238$		0			0
$239$	580663.			0.657551			0.328776	−	0.944408i	$-0.393364\pi$
$239$	580663.			0.657551			0.328776	+	0.944408i	$0.393364\pi$
$240$		0			0
$241$	−670582.			−0.743720			−0.371860	−	0.928289i	$-0.621280\pi$
$241$	−670582.			−0.743720			−0.371860	+	0.928289i	$0.621280\pi$
$242$		0			0
$243$	349506.	−	349506.i	0.379699	−	0.379699i
$244$		0			0
$245$	207030.	+	1.13866e6i	0.220353	+	1.21194i
$246$		0			0
$247$	−451931.	−	451931.i	−0.471335	−	0.471335i
$248$		0			0
$249$		−	965030.i		−	0.986376i
$250$		0			0
$251$			1.23117e6i			1.23349i	0.787165	+	0.616743i	$0.211548\pi$
$251$			1.23117e6i			1.23349i	−0.787165	+	0.616743i	$0.788452\pi$
$252$		0			0
$253$	−66650.0	−	66650.0i	−0.0654634	−	0.0654634i
$254$		0			0
$255$	−314982.	−	1.73240e6i	−0.303344	−	1.66839i
$256$		0			0
$257$	−599895.	+	599895.i	−0.566555	+	0.566555i	−0.931162	−	0.364606i	$-0.881204\pi$
$257$	−599895.	+	599895.i	−0.566555	+	0.566555i	0.364606	+	0.931162i	$0.381204\pi$
$258$		0			0
$259$	379348.			0.351390
$260$		0			0
$261$	−173932.			−0.158044
$262$		0			0
$263$	940976.	−	940976.i	0.838859	−	0.838859i	−0.149850	−	0.988709i	$-0.547879\pi$
$263$	940976.	−	940976.i	0.838859	−	0.838859i	0.988709	+	0.149850i	$0.0478789\pi$
$264$		0			0
$265$	−1.55448e6	−	1.07618e6i	−1.35978	−	0.941387i
$266$		0			0
$267$	1.42457e6	+	1.42457e6i	1.22294	+	1.22294i
$268$		0			0
$269$			1.02604e6i			0.864534i	0.901746	+	0.432267i	$0.142286\pi$
$269$			1.02604e6i			0.864534i	−0.901746	+	0.432267i	$0.857714\pi$
$270$		0			0
$271$			1.65023e6i			1.36497i	0.730901	+	0.682484i	$0.239100\pi$
$271$			1.65023e6i			1.36497i	−0.730901	+	0.682484i	$0.760900\pi$
$272$		0			0
$273$	562650.	+	562650.i	0.456911	+	0.456911i
$274$		0			0
$275$	136949.	+	364160.i	0.109201	+	0.290376i
$276$		0			0
$277$	868065.	−	868065.i	0.679756	−	0.679756i	−0.280189	−	0.959945i	$-0.590397\pi$
$277$	868065.	−	868065.i	0.679756	−	0.679756i	0.959945	+	0.280189i	$0.0903972\pi$
$278$		0			0
$279$	−475462.			−0.365683
$280$		0			0
$281$	−215182.			−0.162570			−0.0812850	−	0.996691i	$-0.525902\pi$
$281$	−215182.			−0.162570			−0.0812850	+	0.996691i	$0.525902\pi$
$282$		0			0
$283$	−115722.	+	115722.i	−0.0858913	+	0.0858913i	−0.748747	−	0.662856i	$-0.769344\pi$
$283$	−115722.	+	115722.i	−0.0858913	+	0.0858913i	0.662856	+	0.748747i	$0.269344\pi$
$284$		0			0
$285$	−1.53450e6	+	2.21650e6i	−1.11906	+	1.61643i
$286$		0			0
$287$	298275.	+	298275.i	0.213753	+	0.213753i
$288$		0			0
$289$		−	1.78059e6i		−	1.25407i
$290$		0			0
$291$			15313.4i			0.0106008i
$292$		0			0
$293$	1.06760e6	+	1.06760e6i	0.726510	+	0.726510i	0.969923	−	0.243413i	$-0.0782670\pi$
$293$	1.06760e6	+	1.06760e6i	0.726510	+	0.726510i	−0.243413	+	0.969923i	$0.578267\pi$
$294$		0			0
$295$	−1.49274e6	+	271408.i	−0.998688	+	0.181580i
$296$		0			0
$297$	−272800.	+	272800.i	−0.179454	+	0.179454i
$298$		0			0
$299$	−176664.			−0.114280
$300$		0			0
$301$	−3.78851e6			−2.41020
$302$		0			0
$303$	1.82991e6	−	1.82991e6i	1.14505	−	1.14505i
$304$		0			0
$305$	−1.97351e6	+	358820.i	−1.21476	+	0.220865i
$306$		0			0
$307$	−1.43947e6	−	1.43947e6i	−0.871679	−	0.871679i	0.120976	−	0.992655i	$-0.461397\pi$
$307$	−1.43947e6	−	1.43947e6i	−0.871679	−	0.871679i	−0.992655	+	0.120976i	$0.961397\pi$
$308$		0			0
$309$			48050.0i			0.0286284i
$310$		0			0
$311$		−	929883.i		−	0.545164i	−0.962133	−	0.272582i	$-0.912122\pi$
$311$		−	929883.i		−	0.545164i	0.962133	−	0.272582i	$-0.0878776\pi$
$312$		0			0
$313$	708225.	+	708225.i	0.408611	+	0.408611i	0.881254	−	0.472643i	$-0.156700\pi$
$313$	708225.	+	708225.i	0.408611	+	0.408611i	−0.472643	+	0.881254i	$0.656700\pi$
$314$		0			0
$315$	412901.	−	596412.i	0.234460	−	0.338665i
$316$		0			0
$317$	−141175.	+	141175.i	−0.0789059	+	0.0789059i	−0.745458	−	0.666552i	$-0.767769\pi$
$317$	−141175.	+	141175.i	−0.0789059	+	0.0789059i	0.666552	+	0.745458i	$0.267769\pi$
$318$		0			0
$319$	323199.			0.177825
$320$		0			0
$321$	−1.52427e6			−0.825656
$322$		0			0
$323$	−3.46481e6	+	3.46481e6i	−1.84788	+	1.84788i
$324$		0			0
$325$	664125.	+	301125.i	0.348772	+	0.158139i
$326$		0			0
$327$	−1.17283e6	−	1.17283e6i	−0.606549	−	0.606549i
$328$		0			0
$329$		−	1.35377e6i		−	0.689533i
$330$		0			0
$331$		−	1.86138e6i		−	0.933826i	−0.884303	−	0.466913i	$-0.845366\pi$
$331$		−	1.86138e6i		−	0.933826i	0.884303	−	0.466913i	$-0.154634\pi$
$332$		0			0
$333$	−92795.0	−	92795.0i	−0.0458579	−	0.0458579i
$334$		0			0
$335$	1.74392e6	+	1.20733e6i	0.849013	+	0.587778i
$336$		0			0
$337$	−472175.	+	472175.i	−0.226479	+	0.226479i	−0.811220	−	0.584741i	$-0.801196\pi$
$337$	−472175.	+	472175.i	−0.226479	+	0.226479i	0.584741	+	0.811220i	$0.301196\pi$
$338$		0			0
$339$	291452.			0.137743
$340$		0			0
$341$	883500.			0.411453
$342$		0			0
$343$	−533553.	+	533553.i	−0.244874	+	0.244874i
$344$		0			0
$345$	133300.	+	733150.i	0.0602952	+	0.331623i
$346$		0			0
$347$	351822.	+	351822.i	0.156855	+	0.156855i	0.781172	−	0.624316i	$-0.214622\pi$
$347$	351822.	+	351822.i	0.156855	+	0.156855i	−0.624316	+	0.781172i	$0.714622\pi$
$348$		0			0
$349$		−	821876.i		−	0.361196i	−0.983557	−	0.180598i	$-0.942197\pi$
$349$		−	821876.i		−	0.361196i	0.983557	−	0.180598i	$-0.0578033\pi$
$350$		0			0
$351$			723090.i			0.313274i
$352$		0			0
$353$	2.27222e6	+	2.27222e6i	0.970543	+	0.970543i	0.999578	−	0.0290358i	$-0.00924370\pi$
$353$	2.27222e6	+	2.27222e6i	0.970543	+	0.970543i	−0.0290358	+	0.999578i	$0.509244\pi$
$354$		0			0
$355$	671050.	+	3.69077e6i	0.282608	+	1.55434i
$356$		0			0
$357$	4.31365e6	−	4.31365e6i	1.79132	−	1.79132i
$358$		0			0
$359$	553274.			0.226571			0.113285	−	0.993562i	$-0.463863\pi$
$359$	553274.			0.226571			0.113285	+	0.993562i	$0.463863\pi$
$360$		0			0
$361$	5.02590e6			2.02977
$362$		0			0
$363$	1.81210e6	−	1.81210e6i	0.721796	−	0.721796i
$364$		0			0
$365$	−1.40498e6	−	972675.i	−0.551997	−	0.382152i
$366$		0			0
$367$	2.92795e6	+	2.92795e6i	1.13475	+	1.13475i	0.989377	+	0.145370i	$0.0464373\pi$
$367$	2.92795e6	+	2.92795e6i	1.13475	+	1.13475i	0.145370	+	0.989377i	$0.453563\pi$
$368$		0			0
$369$		−	145926.i		−	0.0557913i
$370$		0			0
$371$		−	6.55027e6i		−	2.47072i
$372$		0			0
$373$	−444675.	−	444675.i	−0.165490	−	0.165490i	0.619504	−	0.784994i	$-0.287334\pi$
$373$	−444675.	−	444675.i	−0.165490	−	0.165490i	−0.784994	+	0.619504i	$0.787334\pi$
$374$		0			0
$375$	748550.	−	2.98331e6i	0.274880	−	1.09552i
$376$		0			0
$377$	428340.	−	428340.i	0.155216	−	0.155216i
$378$		0			0
$379$	1.96086e6			0.701210			0.350605	−	0.936523i	$-0.385976\pi$
$379$	1.96086e6			0.701210			0.350605	+	0.936523i	$0.385976\pi$
$380$		0			0
$381$	−1.52427e6			−0.537959
$382$		0			0
$383$	−3.16241e6	+	3.16241e6i	−1.10159	+	1.10159i	−0.107375	+	0.994219i	$0.534245\pi$
$383$	−3.16241e6	+	3.16241e6i	−1.10159	+	1.10159i	−0.994219	+	0.107375i	$0.965755\pi$
$384$		0			0
$385$	−767250.	+	1.10825e6i	−0.263806	+	0.381053i
$386$		0			0
$387$	926733.	+	926733.i	0.314541	+	0.314541i
$388$		0			0
$389$		−	3.04000e6i		−	1.01859i	−0.860591	−	0.509296i	$-0.829906\pi$
$389$		−	3.04000e6i		−	1.01859i	0.860591	−	0.509296i	$-0.170094\pi$
$390$		0			0
$391$			1.35442e6i			0.448036i
$392$		0			0
$393$	2.84735e6	+	2.84735e6i	0.929950	+	0.929950i
$394$		0			0
$395$	1.20515e6	−	219118.i	0.388641	−	0.0706620i
$396$		0			0
$397$	893025.	−	893025.i	0.284372	−	0.284372i	−0.550478	−	0.834850i	$-0.685554\pi$
$397$	893025.	−	893025.i	0.284372	−	0.284372i	0.834850	+	0.550478i	$0.185554\pi$
$398$		0			0
$399$	−9.33991e6			−2.93705
$400$		0			0
$401$	1.78048e6			0.552938			0.276469	−	0.961023i	$-0.410836\pi$
$401$	1.78048e6			0.552938			0.276469	+	0.961023i	$0.410836\pi$
$402$		0			0
$403$	1.17091e6	−	1.17091e6i	0.359139	−	0.359139i
$404$		0			0
$405$	3.89626e6	−	708410.i	1.18035	−	0.214609i
$406$		0			0
$407$	172431.	+	172431.i	0.0515976	+	0.0515976i
$408$		0			0
$409$			1.98018e6i			0.585323i	0.956216	+	0.292661i	$0.0945409\pi$
$409$			1.98018e6i			0.585323i	−0.956216	+	0.292661i	$0.905459\pi$
$410$		0			0
$411$			6.05202e6i			1.76724i
$412$		0			0
$413$	−3.71690e6	−	3.71690e6i	−1.07227	−	1.07227i
$414$		0			0
$415$	1.74404e6	−	2.51917e6i	0.497093	−	0.718023i
$416$		0			0
$417$	−3.78510e6	+	3.78510e6i	−1.06595	+	1.06595i
$418$		0			0
$419$	−988771.			−0.275144			−0.137572	−	0.990492i	$-0.543930\pi$
$419$	−988771.			−0.275144			−0.137572	+	0.990492i	$0.543930\pi$
$420$		0			0
$421$	−339922.			−0.0934704			−0.0467352	−	0.998907i	$-0.514882\pi$
$421$	−339922.			−0.0934704			−0.0467352	+	0.998907i	$0.514882\pi$
$422$		0			0
$423$	−331155.	+	331155.i	−0.0899871	+	0.0899871i
$424$		0			0
$425$	2.30862e6	−	5.09162e6i	0.619985	−	1.36736i
$426$		0			0
$427$	−4.91400e6	−	4.91400e6i	−1.30426	−	1.30426i
$428$		0			0
$429$			511500.i			0.134185i
$430$		0			0
$431$		−	3.78390e6i		−	0.981174i	−0.871392	−	0.490587i	$-0.836782\pi$
$431$		−	3.78390e6i		−	0.981174i	0.871392	−	0.490587i	$-0.163218\pi$
$432$		0			0
$433$	1.43578e6	+	1.43578e6i	0.368019	+	0.368019i	0.866754	−	0.498736i	$-0.166202\pi$
$433$	1.43578e6	+	1.43578e6i	0.368019	+	0.368019i	−0.498736	+	0.866754i	$0.666202\pi$
$434$		0			0
$435$	−2.10080e6	−	1.45440e6i	−0.532305	−	0.368519i
$436$		0			0
$437$	1.46630e6	−	1.46630e6i	0.367299	−	0.367299i
$438$		0			0
$439$	1.15585e6			0.286246			0.143123	−	0.989705i	$-0.454286\pi$
$439$	1.15585e6			0.286246			0.143123	+	0.989705i	$0.454286\pi$
$440$		0			0
$441$	1.38710e6			0.339634
$442$		0			0
$443$	1.62886e6	−	1.62886e6i	0.394343	−	0.394343i	−0.481889	−	0.876232i	$-0.660049\pi$
$443$	1.62886e6	−	1.62886e6i	0.394343	−	0.394343i	0.876232	+	0.481889i	$0.160049\pi$
$444$		0			0
$445$	1.14424e6	+	6.29332e6i	0.273916	+	1.50654i
$446$		0			0
$447$	4.34347e6	+	4.34347e6i	1.02818	+	1.02818i
$448$		0			0
$449$			3.44694e6i			0.806896i	0.915003	+	0.403448i	$0.132188\pi$
$449$			3.44694e6i			0.806896i	−0.915003	+	0.403448i	$0.867812\pi$
$450$		0			0
$451$			271159.i			0.0627744i
$452$		0			0
$453$	−6.25735e6	−	6.25735e6i	−1.43267	−	1.43267i
$454$		0			0
$455$	451931.	+	2.48562e6i	0.102340	+	0.562868i
$456$		0			0
$457$	−3.65997e6	+	3.65997e6i	−0.819762	+	0.819762i	−0.986073	−	0.166312i	$-0.946814\pi$
$457$	−3.65997e6	+	3.65997e6i	−0.819762	+	0.819762i	0.166312	+	0.986073i	$0.446814\pi$
$458$		0			0
$459$	5.54369e6			1.22819
$460$		0			0
$461$	−6.06802e6			−1.32983			−0.664913	−	0.746921i	$-0.731531\pi$
$461$	−6.06802e6			−1.32983			−0.664913	+	0.746921i	$0.731531\pi$
$462$		0			0
$463$	2.75786e6	−	2.75786e6i	0.597889	−	0.597889i	−0.341862	−	0.939750i	$-0.611057\pi$
$463$	2.75786e6	−	2.75786e6i	0.597889	−	0.597889i	0.939750	+	0.341862i	$0.111057\pi$
$464$		0			0
$465$	−5.74275e6	−	3.97575e6i	−1.23165	−	0.852681i
$466$		0			0
$467$	1.36375e6	+	1.36375e6i	0.289363	+	0.289363i	0.836828	−	0.547466i	$-0.184407\pi$
$467$	1.36375e6	+	1.36375e6i	0.289363	+	0.289363i	−0.547466	+	0.836828i	$0.684407\pi$
$468$		0			0
$469$			7.34855e6i			1.54266i
$470$		0			0
$471$			5.52614e6i			1.14781i
$472$		0			0
$473$	−1.72205e6	−	1.72205e6i	−0.353910	−	0.353910i
$474$		0			0
$475$	−8.01151e6	+	3.01288e6i	−1.62922	+	0.612699i
$476$		0			0
$477$	−1.60230e6	+	1.60230e6i	−0.322440	+	0.322440i
$478$		0			0
$479$	4.26185e6			0.848710			0.424355	−	0.905496i	$-0.360501\pi$
$479$	4.26185e6			0.848710			0.424355	+	0.905496i	$0.360501\pi$
$480$		0			0
$481$	457050.			0.0900743
$482$		0			0
$483$	−1.82553e6	+	1.82553e6i	−0.356058	+	0.356058i
$484$		0			0
$485$	−27675.0	+	39975.0i	−0.00534236	+	0.00771674i
$486$		0			0
$487$	−3.18983e6	−	3.18983e6i	−0.609459	−	0.609459i	0.333346	−	0.942805i	$-0.391822\pi$
$487$	−3.18983e6	−	3.18983e6i	−0.609459	−	0.609459i	−0.942805	+	0.333346i	$0.891822\pi$
$488$		0			0
$489$			763530.i			0.144396i
$490$		0			0
$491$			3.82772e6i			0.716534i	0.933619	+	0.358267i	$0.116632\pi$
$491$			3.82772e6i			0.716534i	−0.933619	+	0.358267i	$0.883368\pi$
$492$		0			0
$493$	−3.28394e6	−	3.28394e6i	−0.608524	−	0.608524i
$494$		0			0
$495$	458779.	−	83414.3i	0.0841570	−	0.0153013i
$496$		0			0
$497$	−9.18995e6	+	9.18995e6i	−1.66887	+	1.66887i
$498$		0			0
$499$	7.12159e6			1.28034			0.640171	−	0.768233i	$-0.278864\pi$
$499$	7.12159e6			1.28034			0.640171	+	0.768233i	$0.278864\pi$
$500$		0			0
$501$	−624030.			−0.111074
$502$		0			0
$503$	3.86511e6	−	3.86511e6i	0.681148	−	0.681148i	−0.279111	−	0.960259i	$-0.590040\pi$
$503$	3.86511e6	−	3.86511e6i	0.681148	−	0.681148i	0.960259	+	0.279111i	$0.0900396\pi$
$504$		0			0
$505$	8.08401e6	−	1.46982e6i	1.41058	−	0.256469i
$506$		0			0
$507$	−3.94466e6	−	3.94466e6i	−0.681538	−	0.681538i
$508$		0			0
$509$			73964.0i			0.0126539i	0.999980	+	0.00632697i	$0.00201395\pi$
$509$			73964.0i			0.0126539i	−0.999980	+	0.00632697i	$0.997986\pi$
$510$		0			0
$511$		−	5.92030e6i		−	1.00298i
$512$		0			0
$513$	−6.00160e6	−	6.00160e6i	−1.00687	−	1.00687i
$514$		0			0
$515$	−86838.0	+	125433.i	−0.0144275	+	0.0208398i
$516$		0			0
$517$	615350.	−	615350.i	0.101250	−	0.101250i
$518$		0			0
$519$	−412216.			−0.0671748
$520$		0			0
$521$	8.64492e6			1.39530			0.697649	−	0.716440i	$-0.254230\pi$
$521$	8.64492e6			1.39530			0.697649	+	0.716440i	$0.254230\pi$
$522$		0			0
$523$	−4.65366e6	+	4.65366e6i	−0.743944	+	0.743944i	−0.973335	−	0.229390i	$-0.926327\pi$
$523$	−4.65366e6	+	4.65366e6i	−0.743944	+	0.743944i	0.229390	+	0.973335i	$0.426327\pi$
$524$		0			0
$525$	9.97425e6	−	3.75100e6i	1.57936	−	0.593949i
$526$		0			0
$527$	−8.97700e6	−	8.97700e6i	−1.40801	−	1.40801i
$528$		0			0
$529$			5.86315e6i			0.910945i
$530$		0			0
$531$			1.81843e6i			0.279873i
$532$		0			0
$533$	359370.	+	359370.i	0.0547928	+	0.0547928i
$534$		0			0
$535$	−3.97905e6	−	2.75473e6i	−0.601028	−	0.416097i
$536$		0			0
$537$	1.05710e6	−	1.05710e6i	0.158190	−	0.158190i
$538$		0			0
$539$	−2.57750e6			−0.382144
$540$		0			0
$541$	−459778.			−0.0675391			−0.0337695	−	0.999430i	$-0.510751\pi$
$541$	−459778.			−0.0675391			−0.0337695	+	0.999430i	$0.510751\pi$
$542$		0			0
$543$	−1.42399e6	+	1.42399e6i	−0.207257	+	0.207257i
$544$		0			0
$545$	−942040.	−	5.18122e6i	−0.135856	−	0.747207i
$546$		0			0
$547$	5.91742e6	+	5.91742e6i	0.845599	+	0.845599i	0.989580	−	0.143981i	$-0.0459906\pi$
$547$	5.91742e6	+	5.91742e6i	0.845599	+	0.845599i	−0.143981	+	0.989580i	$0.545991\pi$
$548$		0			0
$549$			2.40409e6i			0.340424i
$550$		0			0
$551$			7.11039e6i			0.997733i
$552$		0			0
$553$	3.00080e6	+	3.00080e6i	0.417277	+	0.417277i
$554$		0			0
$555$	−344862.	−	1.89674e6i	−0.0475240	−	0.261382i
$556$		0			0
$557$	939785.	−	939785.i	0.128348	−	0.128348i	−0.640014	−	0.768363i	$-0.721072\pi$
$557$	939785.	−	939785.i	0.128348	−	0.128348i	0.768363	+	0.640014i	$0.221072\pi$
$558$		0			0
$559$	−4.56451e6			−0.617823
$560$		0			0
$561$	3.92150e6			0.526072
$562$		0			0
$563$	6.79746e6	−	6.79746e6i	0.903807	−	0.903807i	−0.0919563	−	0.995763i	$-0.529312\pi$
$563$	6.79746e6	−	6.79746e6i	0.903807	−	0.903807i	0.995763	+	0.0919563i	$0.0293120\pi$
$564$		0			0
$565$	760825.	+	526725.i	0.100268	+	0.0694165i
$566$		0			0
$567$	9.70160e6	+	9.70160e6i	1.26732	+	1.26732i
$568$		0			0
$569$		−	1.05783e7i		−	1.36973i	−0.728669	−	0.684866i	$-0.759861\pi$
$569$		−	1.05783e7i		−	1.36973i	0.728669	−	0.684866i	$-0.240139\pi$
$570$		0			0
$571$		−	138318.i		−	0.0177537i	−0.999961	−	0.00887687i	$-0.997174\pi$
$571$		−	138318.i		−	0.0177537i	0.999961	−	0.00887687i	$-0.00282563\pi$
$572$		0			0
$573$	−5.33355e6	−	5.33355e6i	−0.678625	−	0.678625i
$574$		0			0
$575$	−977006.	+	2.15477e6i	−0.123233	+	0.271788i
$576$		0			0
$577$	2.30082e6	−	2.30082e6i	0.287703	−	0.287703i	−0.548468	−	0.836171i	$-0.684789\pi$
$577$	2.30082e6	−	2.30082e6i	0.287703	−	0.287703i	0.836171	+	0.548468i	$0.184789\pi$
$578$		0			0
$579$	−1.30060e7			−1.61231
$580$		0			0
$581$	1.06153e7			1.30465
$582$		0			0
$583$	2.97739e6	−	2.97739e6i	0.362798	−	0.362798i
$584$		0			0
$585$	497475.	−	718575.i	0.0601010	−	0.0868125i
$586$		0			0
$587$	2.89977e6	+	2.89977e6i	0.347351	+	0.347351i	0.859122	−	0.511771i	$-0.171010\pi$
$587$	2.89977e6	+	2.89977e6i	0.347351	+	0.347351i	−0.511771	+	0.859122i	$0.671010\pi$
$588$		0			0
$589$			1.94370e7i			2.30856i
$590$		0			0
$591$		−	7.50343e6i		−	0.883672i
$592$		0			0
$593$	−2.96786e6	−	2.96786e6i	−0.346582	−	0.346582i	0.512253	−	0.858835i	$-0.328811\pi$
$593$	−2.96786e6	−	2.96786e6i	−0.346582	−	0.346582i	−0.858835	+	0.512253i	$0.828811\pi$
$594$		0			0
$595$	1.90564e7	−	3.46481e6i	2.20673	−	0.401224i
$596$		0			0
$597$	9.16980e6	−	9.16980e6i	1.05299	−	1.05299i
$598$		0			0
$599$	7.81704e6			0.890175			0.445088	−	0.895487i	$-0.353173\pi$
$599$	7.81704e6			0.890175			0.445088	+	0.895487i	$0.353173\pi$
$600$		0			0
$601$	8.56898e6			0.967705			0.483852	−	0.875150i	$-0.339237\pi$
$601$	8.56898e6			0.967705			0.483852	+	0.875150i	$0.339237\pi$
$602$		0			0
$603$	1.79758e6	−	1.79758e6i	0.201324	−	0.201324i
$604$		0			0
$605$	8.00530e6	−	1.45551e6i	0.889180	−	0.161669i
$606$		0			0
$607$	3.00534e6	+	3.00534e6i	0.331072	+	0.331072i	0.852993	−	0.521922i	$-0.174785\pi$
$607$	3.00534e6	+	3.00534e6i	0.331072	+	0.331072i	−0.521922	+	0.852993i	$0.674785\pi$
$608$		0			0
$609$		−	8.85236e6i		−	0.967199i
$610$		0			0
$611$		−	1.63106e6i		−	0.176753i
$612$		0			0
$613$	4.50004e6	+	4.50004e6i	0.483688	+	0.483688i	0.906307	−	0.422619i	$-0.138889\pi$
$613$	4.50004e6	+	4.50004e6i	0.483688	+	0.483688i	−0.422619	+	0.906307i	$0.638889\pi$
$614$		0			0
$615$	1.22021e6	−	1.76253e6i	0.130091	−	0.187910i
$616$		0			0
$617$	−6.72666e6	+	6.72666e6i	−0.711355	+	0.711355i	−0.966819	−	0.255464i	$-0.917772\pi$
$617$	−6.72666e6	+	6.72666e6i	−0.711355	+	0.711355i	0.255464	+	0.966819i	$0.417772\pi$
$618$		0			0
$619$	−5.77103e6			−0.605378			−0.302689	−	0.953089i	$-0.597884\pi$
$619$	−5.77103e6			−0.605378			−0.302689	+	0.953089i	$0.597884\pi$
$620$		0			0
$621$	−2.34608e6			−0.244126
$622$		0			0
$623$	−1.56702e7	+	1.56702e7i	−1.61754	+	1.61754i
$624$		0			0
$625$	7.34562e6	−	6.43500e6i	0.752192	−	0.658944i
$626$		0			0
$627$	−4.24542e6	−	4.24542e6i	−0.431272	−	0.431272i
$628$		0			0
$629$		−	3.50405e6i		−	0.353137i
$630$		0			0
$631$			5.11778e6i			0.511692i	0.966718	+	0.255846i	$0.0823539\pi$
$631$			5.11778e6i			0.511692i	−0.966718	+	0.255846i	$0.917646\pi$
$632$		0			0
$633$	−6.42785e6	−	6.42785e6i	−0.637612	−	0.637612i
$634$		0			0
$635$	−3.97905e6	−	2.75473e6i	−0.391602	−	0.271109i
$636$		0			0
$637$	−3.41600e6	+	3.41600e6i	−0.333556	+	0.333556i
$638$		0			0
$639$	4.49603e6			0.435589
$640$		0			0
$641$	−3.85882e6			−0.370945			−0.185473	−	0.982649i	$-0.559382\pi$
$641$	−3.85882e6			−0.370945			−0.185473	+	0.982649i	$0.559382\pi$
$642$		0			0
$643$	−1.00447e7	+	1.00447e7i	−0.958094	+	0.958094i	−0.999157	−	0.0410627i	$-0.986926\pi$
$643$	−1.00447e7	+	1.00447e7i	−0.958094	+	0.958094i	0.0410627	+	0.999157i	$0.486926\pi$
$644$		0			0
$645$	3.44410e6	+	1.89426e7i	0.325969	+	1.79283i
$646$		0			0
$647$	−4.19418e6	−	4.19418e6i	−0.393901	−	0.393901i	0.482174	−	0.876075i	$-0.339847\pi$
$647$	−4.19418e6	−	4.19418e6i	−0.393901	−	0.393901i	−0.876075	+	0.482174i	$0.839847\pi$
$648$		0			0
$649$		−	3.37900e6i		−	0.314903i
$650$		0			0
$651$		−	2.41989e7i		−	2.23791i
$652$		0			0
$653$	2.20820e6	+	2.20820e6i	0.202655	+	0.202655i	0.801136	−	0.598482i	$-0.204229\pi$
$653$	2.20820e6	+	2.20820e6i	0.202655	+	0.202655i	−0.598482	+	0.801136i	$0.704229\pi$
$654$		0			0
$655$	2.28705e6	+	1.25788e7i	0.208292	+	1.14560i
$656$		0			0
$657$	−1.44820e6	+	1.44820e6i	−0.130893	+	0.130893i
$658$		0			0
$659$	−1.30512e7			−1.17068			−0.585340	−	0.810788i	$-0.699039\pi$
$659$	−1.30512e7			−1.17068			−0.585340	+	0.810788i	$0.699039\pi$
$660$		0			0
$661$	−1.60587e7			−1.42958			−0.714788	−	0.699341i	$-0.753477\pi$
$661$	−1.60587e7			−1.42958			−0.714788	+	0.699341i	$0.753477\pi$
$662$		0			0
$663$	5.19721e6	−	5.19721e6i	0.459184	−	0.459184i
$664$		0			0
$665$	−2.43815e7	−	1.68795e7i	−2.13799	−	1.48015i
$666$		0			0
$667$	1.38976e6	+	1.38976e6i	0.120955	+	0.120955i
$668$		0			0
$669$			8.99589e6i			0.777103i
$670$		0			0
$671$		−	4.46727e6i		−	0.383033i
$672$		0			0
$673$	7.35410e6	+	7.35410e6i	0.625882	+	0.625882i	0.947029	−	0.321148i	$-0.104069\pi$
$673$	7.35410e6	+	7.35410e6i	0.625882	+	0.625882i	−0.321148	+	0.947029i	$0.604069\pi$
$674$		0			0
$675$	8.81951e6	+	3.99891e6i	0.745049	+	0.337817i
$676$		0			0
$677$	−7.18218e6	+	7.18218e6i	−0.602260	+	0.602260i	−0.940912	−	0.338651i	$-0.890029\pi$
$677$	−7.18218e6	+	7.18218e6i	−0.602260	+	0.602260i	0.338651	+	0.940912i	$0.390029\pi$
$678$		0			0
$679$	−168447.			−0.0140213
$680$		0			0
$681$	−1.78650e7			−1.47617
$682$		0			0
$683$	6.97644e6	−	6.97644e6i	0.572245	−	0.572245i	−0.360510	−	0.932755i	$-0.617397\pi$
$683$	6.97644e6	−	6.97644e6i	0.572245	−	0.572245i	0.932755	+	0.360510i	$0.117397\pi$
$684$		0			0
$685$	−1.09375e7	+	1.57986e7i	−0.890616	+	1.28645i
$686$		0			0
$687$	−1.12457e7	−	1.12457e7i	−0.909064	−	0.909064i
$688$		0			0
$689$		−	7.89195e6i		−	0.633339i
$690$		0			0
$691$		−	7.72529e6i		−	0.615488i	−0.951469	−	0.307744i	$-0.900426\pi$
$691$		−	7.72529e6i		−	0.615488i	0.951469	−	0.307744i	$-0.0995740\pi$
$692$		0			0
$693$	1.14235e6	+	1.14235e6i	0.0903579	+	0.0903579i
$694$		0			0
$695$	−1.67215e7	+	3.04027e6i	−1.31314	+	0.238753i
$696$		0			0
$697$	2.75517e6	−	2.75517e6i	0.214816	−	0.214816i
$698$		0			0
$699$	1.75062e7			1.35518
$700$		0			0
$701$	6.60460e6			0.507635			0.253817	−	0.967252i	$-0.418314\pi$
$701$	6.60460e6			0.507635			0.253817	+	0.967252i	$0.418314\pi$
$702$		0			0
$703$	−3.79348e6	+	3.79348e6i	−0.289501	+	0.289501i
$704$		0			0
$705$	−6.76885e6	+	1.23070e6i	−0.512911	+	0.0932566i
$706$		0			0
$707$	2.01290e7	+	2.01290e7i	1.51452	+	1.51452i
$708$		0			0
$709$			1.65072e6i			0.123327i	0.998097	+	0.0616636i	$0.0196406\pi$
$709$			1.65072e6i			0.123327i	−0.998097	+	0.0616636i	$0.980359\pi$
$710$		0			0
$711$		−	1.46809e6i		−	0.108913i
$712$		0			0
$713$	3.79905e6	+	3.79905e6i	0.279867	+	0.279867i
$714$		0			0
$715$	−924405.	+	1.33525e6i	−0.0676234	+	0.0976783i
$716$		0			0
$717$	7.22920e6	−	7.22920e6i	0.525161	−	0.525161i
$718$		0			0
$719$	2.08929e7			1.50722			0.753611	−	0.657321i	$-0.228310\pi$
$719$	2.08929e7			1.50722			0.753611	+	0.657321i	$0.228310\pi$
$720$		0			0
$721$	−528550.			−0.0378659
$722$		0			0
$723$	−8.34868e6	+	8.34868e6i	−0.593980	+	0.593980i
$724$		0			0
$725$	−2.85560e6	−	7.59330e6i	−0.201768	−	0.536520i
$726$		0			0
$727$	−7.86800e6	−	7.86800e6i	−0.552113	−	0.552113i	0.374937	−	0.927050i	$-0.377664\pi$
$727$	−7.86800e6	−	7.86800e6i	−0.552113	−	0.552113i	−0.927050	+	0.374937i	$0.877664\pi$
$728$		0			0
$729$			8.51173e6i			0.593197i
$730$		0			0
$731$			3.49946e7i			2.42218i
$732$		0			0
$733$	−7.35047e6	−	7.35047e6i	−0.505307	−	0.505307i	0.407775	−	0.913082i	$-0.366305\pi$
$733$	−7.35047e6	−	7.35047e6i	−0.505307	−	0.505307i	−0.913082	+	0.407775i	$0.866305\pi$
$734$		0			0
$735$	1.67538e7	+	1.15988e7i	1.14392	+	0.791942i
$736$		0			0
$737$	−3.34025e6	+	3.34025e6i	−0.226522	+	0.226522i
$738$		0			0
$739$	−1.69954e7			−1.14477			−0.572386	−	0.819984i	$-0.693982\pi$
$739$	−1.69954e7			−1.14477			−0.572386	+	0.819984i	$0.693982\pi$
$740$		0			0
$741$	−1.12530e7			−0.752875
$742$		0			0
$743$	1.13579e7	−	1.13579e7i	0.754787	−	0.754787i	−0.220582	−	0.975369i	$-0.570796\pi$
$743$	1.13579e7	−	1.13579e7i	0.754787	−	0.754787i	0.975369	+	0.220582i	$0.0707955\pi$
$744$		0			0
$745$	3.48876e6	+	1.91882e7i	0.230293	+	1.26661i
$746$		0			0
$747$	−2.59669e6	−	2.59669e6i	−0.170262	−	0.170262i
$748$		0			0
$749$		−	1.67670e7i		−	1.09207i
$750$		0			0
$751$			28759.3i			0.00186071i	1.00000		0.000930353i	$0.000296141\pi$
$751$			28759.3i			0.00186071i	−1.00000		0.000930353i	$0.999704\pi$
$752$		0			0
$753$	1.53280e7	+	1.53280e7i	0.985137	+	0.985137i
$754$		0			0
$755$	−5.02602e6	−	2.76431e7i	−0.320891	−	1.76490i
$756$		0			0
$757$	2.57294e6	−	2.57294e6i	0.163189	−	0.163189i	−0.620789	−	0.783978i	$-0.713188\pi$
$757$	2.57294e6	−	2.57294e6i	0.163189	−	0.163189i	0.783978	+	0.620789i	$0.213188\pi$
$758$		0			0
$759$	−1.65957e6			−0.104566
$760$		0			0
$761$	1.02148e6			0.0639395			0.0319697	−	0.999489i	$-0.489822\pi$
$761$	1.02148e6			0.0639395			0.0319697	+	0.999489i	$0.489822\pi$
$762$		0			0
$763$	1.29011e7	−	1.29011e7i	0.802263	−	0.802263i
$764$		0			0
$765$	−5.50908e6	−	3.81397e6i	−0.340349	−	0.235627i
$766$		0			0
$767$	−4.47823e6	−	4.47823e6i	−0.274864	−	0.274864i
$768$		0			0
$769$		−	2.69757e7i		−	1.64497i	−0.568790	−	0.822483i	$-0.692588\pi$
$769$		−	2.69757e7i		−	1.64497i	0.568790	−	0.822483i	$-0.307412\pi$
$770$		0			0
$771$			1.49373e7i			0.904972i
$772$		0			0
$773$	2.18892e7	+	2.18892e7i	1.31759	+	1.31759i	0.915678	+	0.401912i	$0.131654\pi$
$773$	2.18892e7	+	2.18892e7i	1.31759	+	1.31759i	0.401912	+	0.915678i	$0.368346\pi$
$774$		0			0
$775$	−7.80609e6	−	2.07571e7i	−0.466852	−	1.24140i
$776$		0			0
$777$	4.72285e6	−	4.72285e6i	0.280641	−	0.280641i
$778$		0			0
$779$	−5.96549e6			−0.352211
$780$		0			0
$781$	−8.35450e6			−0.490109
$782$		0			0
$783$	5.68831e6	−	5.68831e6i	0.331573	−	0.331573i
$784$		0			0
$785$	−9.98708e6	+	1.44258e7i	−0.578448	+	0.835536i
$786$		0			0
$787$	−3.54739e6	−	3.54739e6i	−0.204161	−	0.204161i	0.597619	−	0.801780i	$-0.296113\pi$
$787$	−3.54739e6	−	3.54739e6i	−0.204161	−	0.204161i	−0.801780	+	0.597619i	$0.796113\pi$
$788$		0			0
$789$		−	2.34301e7i		−	1.33993i
$790$		0			0
$791$			3.20597e6i			0.182188i
$792$		0			0
$793$	−5.92053e6	−	5.92053e6i	−0.334332	−	0.334332i
$794$		0			0
$795$	−3.27513e7	+	5.95479e6i	−1.83785	+	0.334155i
$796$		0			0
$797$	1.54117e7	−	1.54117e7i	0.859419	−	0.859419i	−0.131851	−	0.991270i	$-0.542092\pi$
$797$	1.54117e7	−	1.54117e7i	0.859419	−	0.859419i	0.991270	+	0.131851i	$0.0420920\pi$
$798$		0			0
$799$	−1.25048e7			−0.692963
$800$		0			0
$801$	7.66641e6			0.422193
$802$		0			0
$803$	2.69105e6	−	2.69105e6i	0.147276	−	0.147276i
$804$		0			0
$805$	−8.06465e6	+	1.46630e6i	−0.438627	+	0.0797504i
$806$		0			0
$807$	1.27740e7	+	1.27740e7i	0.690470	+	0.690470i
$808$		0			0
$809$			1.66604e7i			0.894983i	0.894288	+	0.447491i	$0.147683\pi$
$809$			1.66604e7i			0.894983i	−0.894288	+	0.447491i	$0.852317\pi$
$810$		0			0
$811$			2.08751e7i			1.11449i	0.830348	+	0.557246i	$0.188142\pi$
$811$			2.08751e7i			1.11449i	−0.830348	+	0.557246i	$0.811858\pi$
$812$		0			0
$813$	2.05452e7	+	2.05452e7i	1.09015	+	1.09015i
$814$		0			0
$815$	−1.37988e6	+	1.99317e6i	−0.0727694	+	0.105111i
$816$		0			0
$817$	3.78851e7	−	3.78851e7i	1.98570	−	1.98570i
$818$		0			0
$819$	3.02794e6			0.157738
$820$		0			0
$821$	1.05967e7			0.548673			0.274336	−	0.961634i	$-0.411542\pi$
$821$	1.05967e7			0.548673			0.274336	+	0.961634i	$0.411542\pi$
$822$		0			0
$823$	−4.69106e6	+	4.69106e6i	−0.241419	+	0.241419i	−0.817437	−	0.576018i	$-0.804606\pi$
$823$	−4.69106e6	+	4.69106e6i	−0.241419	+	0.241419i	0.576018	+	0.817437i	$0.304606\pi$
$824$		0			0
$825$	6.23875e6	+	2.82875e6i	0.319126	+	0.144697i
$826$		0			0
$827$	−1.09854e7	−	1.09854e7i	−0.558535	−	0.558535i	0.370355	−	0.928890i	$-0.379236\pi$
$827$	−1.09854e7	−	1.09854e7i	−0.558535	−	0.558535i	−0.928890	+	0.370355i	$0.879236\pi$
$828$		0			0
$829$		−	1.57558e7i		−	0.796259i	−0.917329	−	0.398129i	$-0.869659\pi$
$829$		−	1.57558e7i		−	0.796259i	0.917329	−	0.398129i	$-0.130341\pi$
$830$		0			0
$831$		−	2.16146e7i		−	1.08579i
$832$		0			0
$833$	2.61893e7	+	2.61893e7i	1.30771	+	1.30771i
$834$		0			0
$835$	−1.62901e6	−	1.12777e6i	−0.0808550	−	0.0559765i
$836$		0			0
$837$	1.55496e7	−	1.55496e7i	0.767195	−	0.767195i
$838$		0			0
$839$	857051.			0.0420341			0.0210171	−	0.999779i	$-0.493310\pi$
$839$	857051.			0.0420341			0.0210171	+	0.999779i	$0.493310\pi$
$840$		0			0
$841$	1.37719e7			0.671436
$842$		0			0
$843$	−2.67899e6	+	2.67899e6i	−0.129838	+	0.129838i
$844$		0			0
$845$	−3.16843e6	−	1.74264e7i	−0.152652	−	0.839586i
$846$		0			0
$847$	1.99330e7	+	1.99330e7i	0.954696	+	0.954696i
$848$		0			0
$849$			2.88145e6i			0.137196i
$850$		0			0
$851$			1.48291e6i			0.0701924i
$852$		0			0
$853$	−2.23144e7	−	2.23144e7i	−1.05006	−	1.05006i	−0.998679	−	0.0513788i	$-0.983638\pi$
$853$	−2.23144e7	−	2.23144e7i	−1.05006	−	1.05006i	−0.0513788	−	0.998679i	$-0.516362\pi$
$854$		0			0
$855$	1.83512e6	+	1.00931e7i	0.0858515	+	0.472183i
$856$		0			0
$857$	−2.93450e7	+	2.93450e7i	−1.36484	+	1.36484i	−0.497209	+	0.867631i	$0.665642\pi$
$857$	−2.93450e7	+	2.93450e7i	−1.36484	+	1.36484i	−0.867631	+	0.497209i	$0.834358\pi$
$858$		0			0
$859$	4.00795e7			1.85327			0.926636	−	0.375961i	$-0.122687\pi$
$859$	4.00795e7			1.85327			0.926636	+	0.375961i	$0.122687\pi$
$860$		0			0
$861$	7.42698e6			0.341432
$862$		0			0
$863$	2.97399e6	−	2.97399e6i	0.135929	−	0.135929i	−0.635868	−	0.771798i	$-0.719358\pi$
$863$	2.97399e6	−	2.97399e6i	0.135929	−	0.135929i	0.771798	+	0.635868i	$0.219358\pi$
$864$		0			0
$865$	−1.07608e6	−	744975.i	−0.0488993	−	0.0338533i
$866$		0			0
$867$	−2.21682e7	−	2.21682e7i	−1.00157	−	1.00157i
$868$		0			0
$869$			2.72800e6i			0.122545i
$870$		0			0
$871$			8.85375e6i			0.395441i
$872$		0			0
$873$	41205.0	+	41205.0i	0.00182985	+	0.00182985i
$874$		0			0
$875$	3.28164e7	+	8.23405e6i	1.44901	+	0.363575i
$876$		0			0
$877$	7.28414e6	−	7.28414e6i	0.319801	−	0.319801i	−0.528890	−	0.848691i	$-0.677391\pi$
$877$	7.28414e6	−	7.28414e6i	0.319801	−	0.319801i	0.848691	+	0.528890i	$0.177391\pi$
$878$		0			0
$879$	2.65832e7			1.16047
$880$		0			0
$881$	5.53982e6			0.240467			0.120234	−	0.992746i	$-0.461636\pi$
$881$	5.53982e6			0.240467			0.120234	+	0.992746i	$0.461636\pi$
$882$		0			0
$883$	2.65177e7	−	2.65177e7i	1.14455	−	1.14455i	0.156940	−	0.987608i	$-0.449837\pi$
$883$	2.65177e7	−	2.65177e7i	1.14455	−	1.14455i	0.987608	−	0.156940i	$-0.0501630\pi$
$884$		0			0
$885$	−1.52055e7	+	2.19635e7i	−0.652593	+	0.942635i
$886$		0			0
$887$	−1.90456e7	−	1.90456e7i	−0.812804	−	0.812804i	0.172249	−	0.985053i	$-0.444897\pi$
$887$	−1.90456e7	−	1.90456e7i	−0.812804	−	0.812804i	−0.985053	+	0.172249i	$0.944897\pi$
$888$		0			0
$889$		−	1.67670e7i		−	0.711541i
$890$		0			0
$891$			8.81963e6i			0.372183i
$892$		0			0
$893$	1.35377e7	+	1.35377e7i	0.568089	+	0.568089i
$894$		0			0
$895$	4.66996e6	−	849083.i	0.194875	−	0.0354318i
$896$		0			0
$897$	−2.19945e6	+	2.19945e6i	−0.0912710	+	0.0912710i
$898$		0			0
$899$	−1.84224e7			−0.760232
$900$		0			0
$901$	−6.05049e7			−2.48301
$902$		0			0
$903$	−4.71666e7	+	4.71666e7i	−1.92493	+	1.92493i
$904$		0			0
$905$	−6.29079e6	+	1.14378e6i	−0.255319	+	0.0464217i
$906$		0			0
$907$	1.57179e7	+	1.57179e7i	0.634419	+	0.634419i	0.949173	−	0.314754i	$-0.101922\pi$
$907$	1.57179e7	+	1.57179e7i	0.634419	+	0.634419i	−0.314754	+	0.949173i	$0.601922\pi$
$908$		0			0
$909$		−	9.84779e6i		−	0.395302i
$910$		0			0
$911$		−	2.48003e7i		−	0.990060i	−0.868876	−	0.495030i	$-0.835157\pi$
$911$		−	2.48003e7i		−	0.990060i	0.868876	−	0.495030i	$-0.164843\pi$
$912$		0			0
$913$	4.82515e6	+	4.82515e6i	0.191573	+	0.191573i
$914$		0			0
$915$	−2.01027e7	+	2.90373e7i	−0.793784	+	1.14658i
$916$		0			0
$917$	−3.13208e7	+	3.13208e7i	−1.23001	+	1.23001i
$918$		0			0
$919$	−2.20049e7			−0.859472			−0.429736	−	0.902955i	$-0.641393\pi$
$919$	−2.20049e7			−0.859472			−0.429736	+	0.902955i	$0.641393\pi$
$920$		0			0
$921$	−3.58425e7			−1.39235
$922$		0			0
$923$	−1.10723e7	+	1.10723e7i	−0.427794	+	0.427794i
$924$		0			0
$925$	2.52763e6	−	5.57463e6i	0.0971311	−	0.214221i
$926$		0			0
$927$	129292.	+	129292.i	0.00494166	+	0.00494166i
$928$		0			0
$929$		−	1.02722e6i		−	0.0390504i	−0.999809	−	0.0195252i	$-0.993785\pi$
$929$		−	1.02722e6i		−	0.0390504i	0.999809	−	0.0195252i	$-0.00621546\pi$
$930$		0			0
$931$		−	5.67051e7i		−	2.14411i
$932$		0			0
$933$	−1.15770e7	−	1.15770e7i	−0.435402	−	0.435402i
$934$		0			0
$935$	1.02369e7	+	7.08711e6i	0.382949	+	0.265118i
$936$		0			0
$937$	2.34206e6	−	2.34206e6i	0.0871465	−	0.0871465i	−0.662190	−	0.749336i	$-0.730373\pi$
$937$	2.34206e6	−	2.34206e6i	0.0871465	−	0.0871465i	0.749336	+	0.662190i	$0.230373\pi$
$938$		0			0
$939$	1.76347e7			0.652684
$940$		0			0
$941$	5.25523e7			1.93472			0.967359	−	0.253410i	$-0.0815521\pi$
$941$	5.25523e7			1.93472			0.967359	+	0.253410i	$0.0815521\pi$
$942$		0			0
$943$	−1.16598e6	+	1.16598e6i	−0.0426985	+	0.0426985i
$944$		0			0
$945$	6.00160e6	+	3.30088e7i	0.218619	+	1.20240i
$946$		0			0
$947$	1.44462e7	+	1.44462e7i	0.523454	+	0.523454i	0.918613	−	0.395159i	$-0.129310\pi$
$947$	1.44462e7	+	1.44462e7i	0.523454	+	0.523454i	−0.395159	+	0.918613i	$0.629310\pi$
$948$		0			0
$949$		−	7.13295e6i		−	0.257101i
$950$		0			0
$951$			3.51523e6i			0.126038i
$952$		0			0
$953$	6.37070e6	+	6.37070e6i	0.227225	+	0.227225i	0.811532	−	0.584308i	$-0.198634\pi$
$953$	6.37070e6	+	6.37070e6i	0.227225	+	0.227225i	−0.584308	+	0.811532i	$0.698634\pi$
$954$		0			0
$955$	−4.28401e6	−	2.35621e7i	−0.151999	−	0.835997i
$956$		0			0
$957$	4.02380e6	−	4.02380e6i	0.142022	−	0.142022i
$958$		0			0
$959$	−6.65722e7			−2.33747
$960$		0			0
$961$	−2.17303e7			−0.759029
$962$		0			0
$963$	−4.10148e6	+	4.10148e6i	−0.142520	+	0.142520i
$964$		0			0
$965$	−3.39518e7	−	2.35051e7i	−1.17367	−	0.812537i
$966$		0			0
$967$	−4.86757e6	−	4.86757e6i	−0.167397	−	0.167397i	0.618437	−	0.785834i	$-0.287766\pi$
$967$	−4.86757e6	−	4.86757e6i	−0.167397	−	0.167397i	−0.785834	+	0.618437i	$0.787766\pi$
$968$		0			0
$969$			8.62730e7i			2.95165i
$970$		0			0
$971$		−	4.34769e7i		−	1.47983i	−0.672703	−	0.739913i	$-0.734867\pi$
$971$		−	4.34769e7i		−	1.47983i	0.672703	−	0.739913i	$-0.265133\pi$
$972$		0			0
$973$	−4.16361e7	−	4.16361e7i	−1.40990	−	1.40990i
$974$		0			0
$975$	1.20173e7	−	4.51931e6i	0.404850	−	0.152251i
$976$		0			0
$977$	−1.12987e7	+	1.12987e7i	−0.378697	+	0.378697i	−0.870632	−	0.491935i	$-0.836290\pi$
$977$	−1.12987e7	+	1.12987e7i	−0.378697	+	0.378697i	0.491935	+	0.870632i	$0.336290\pi$
$978$		0			0
$979$	−1.42457e7			−0.475036
$980$		0			0
$981$	−6.31167e6			−0.209398
$982$		0			0
$983$	3.39231e7	−	3.39231e7i	1.11972	−	1.11972i	0.127943	−	0.991782i	$-0.459163\pi$
$983$	3.39231e7	−	3.39231e7i	1.11972	−	1.11972i	0.991782	−	0.127943i	$-0.0408374\pi$
$984$		0			0
$985$	1.35605e7	−	1.95874e7i	0.445334	−	0.643260i
$986$		0			0
$987$	−1.68543e7	−	1.68543e7i	−0.550704	−	0.550704i
$988$		0			0
$989$		−	1.48096e7i		−	0.481453i
$990$		0			0
$991$			4.46333e7i			1.44369i	0.692054	+	0.721846i	$0.256706\pi$
$991$			4.46333e7i			1.44369i	−0.692054	+	0.721846i	$0.743294\pi$
$992$		0			0
$993$	−2.31740e7	−	2.31740e7i	−0.745811	−	0.745811i
$994$		0			0
$995$	4.05095e7	−	7.36536e6i	1.29718	−	0.235850i
$996$		0			0
$997$	−1.89060e7	+	1.89060e7i	−0.602367	+	0.602367i	−0.940940	−	0.338573i	$-0.890056\pi$
$997$	−1.89060e7	+	1.89060e7i	−0.602367	+	0.602367i	0.338573	+	0.940940i	$0.390056\pi$
$998$		0			0
$999$	6.06958e6			0.192417

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.n.c.63.2	yes	4
4.3	odd	2	inner	80.6.n.c.63.1	yes	4
5.2	odd	4	inner	80.6.n.c.47.1	✓	4
5.3	odd	4		400.6.n.b.207.2		4
5.4	even	2		400.6.n.b.143.1		4
20.3	even	4		400.6.n.b.207.1		4
20.7	even	4	inner	80.6.n.c.47.2	yes	4
20.19	odd	2		400.6.n.b.143.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.n.c.47.1	✓	4	5.2	odd	4	inner
80.6.n.c.47.2	yes	4	20.7	even	4	inner
80.6.n.c.63.1	yes	4	4.3	odd	2	inner
80.6.n.c.63.2	yes	4	1.1	even	1	trivial
400.6.n.b.143.1		4	5.4	even	2
400.6.n.b.143.2		4	20.19	odd	2
400.6.n.b.207.1		4	20.3	even	4
400.6.n.b.207.2		4	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	80.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(12.4499 - 12.4499i) q^{3} +(55.0000 - 10.0000i) q^{5} +(136.949 + 136.949i) q^{7} -67.0000i q^{9} +O(q^{10})\)	\(q+(12.4499 - 12.4499i) q^{3} +(55.0000 - 10.0000i) q^{5} +(136.949 + 136.949i) q^{7} -67.0000i q^{9} +124.499i q^{11} +(165.000 + 165.000i) q^{13} +(560.245 - 809.243i) q^{15} +(1265.00 - 1265.00i) q^{17} -2738.98 q^{19} +3410.00 q^{21} +(-535.346 + 535.346i) q^{23} +(2925.00 - 1100.00i) q^{25} +(2191.18 + 2191.18i) q^{27} -2596.00i q^{29} -7096.44i q^{31} +(1550.00 + 1550.00i) q^{33} +(8901.68 + 6162.70i) q^{35} +(1385.00 - 1385.00i) q^{37} +4108.47 q^{39} +2178.00 q^{41} +(-13831.8 + 13831.8i) q^{43} +(-670.000 - 3685.00i) q^{45} +(-4942.61 - 4942.61i) q^{47} +20703.0i q^{49} -31498.2i q^{51} +(-23915.0 - 23915.0i) q^{53} +(1244.99 + 6847.44i) q^{55} +(-34100.0 + 34100.0i) q^{57} -27140.8 q^{59} -35882.0 q^{61} +(9175.58 - 9175.58i) q^{63} +(10725.0 + 7425.00i) q^{65} +(26829.5 + 26829.5i) q^{67} +13330.0i q^{69} +67105.0i q^{71} +(-21615.0 - 21615.0i) q^{73} +(22721.1 - 50110.8i) q^{75} +(-17050.0 + 17050.0i) q^{77} +21911.8 q^{79} +70841.0 q^{81} +(38756.5 - 38756.5i) q^{83} +(56925.0 - 82225.0i) q^{85} +(-32319.9 - 32319.9i) q^{87} +114424. i q^{89} +45193.1i q^{91} +(-88350.0 - 88350.0i) q^{93} +(-150644. + 27389.8i) q^{95} +(-615.000 + 615.000i) q^{97} +8341.43 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 220 q^{5}+O(q^{10}) \) 4 * q + 220 * q^5	\( 4 q + 220 q^{5} + 660 q^{13} + 5060 q^{17} + 13640 q^{21} + 11700 q^{25} + 6200 q^{33} + 5540 q^{37} + 8712 q^{41} - 2680 q^{45} - 95660 q^{53} - 136400 q^{57} - 143528 q^{61} + 42900 q^{65} - 86460 q^{73} - 68200 q^{77} + 283364 q^{81} + 227700 q^{85} - 353400 q^{93} - 2460 q^{97}+O(q^{100}) \) 4 * q + 220 * q^5 + 660 * q^13 + 5060 * q^17 + 13640 * q^21 + 11700 * q^25 + 6200 * q^33 + 5540 * q^37 + 8712 * q^41 - 2680 * q^45 - 95660 * q^53 - 136400 * q^57 - 143528 * q^61 + 42900 * q^65 - 86460 * q^73 - 68200 * q^77 + 283364 * q^81 + 227700 * q^85 - 353400 * q^93 - 2460 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more