LMFDB - Embedded newform 676.2.e.g.653.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [676,2,Mod(529,676)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(676, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("676.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$676 = 2^{2} \cdot 13^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	676.e (of order $3$ , degree $2$ , not 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:	$5.39788717664$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1$ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			653.2
Root			$0.900969 - 1.56052i$ of defining polynomial
Character	$\chi$	$=$	676.653
Dual form			676.2.e.g.529.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.678448 - 1.17511i) q^{3} +4.24698 q^{5} +(1.06853 - 1.85075i) q^{7} +(0.579417 - 1.00358i) q^{9} +(-1.67845 - 2.90716i) q^{11} +(-2.88135 - 4.99065i) q^{15} +(0.0304995 - 0.0528266i) q^{17} +(-3.09299 + 5.35722i) q^{19} -2.89977 q^{21} +(2.54892 + 4.41485i) q^{23} +13.0368 q^{25} -5.64310 q^{27} +(1.06853 + 1.85075i) q^{29} -2.85086 q^{31} +(-2.27748 + 3.94471i) q^{33} +(4.53803 - 7.86010i) q^{35} +(-1.73609 - 3.00700i) q^{37} +(-2.69806 - 4.67318i) q^{41} +(4.30678 - 7.45957i) q^{43} +(2.46077 - 4.26218i) q^{45} -6.96077 q^{47} +(1.21648 + 2.10701i) q^{49} -0.0827692 q^{51} +0.0217703 q^{53} +(-7.12833 - 12.3466i) q^{55} +8.39373 q^{57} +(2.90581 - 5.03302i) q^{59} +(-5.33997 + 9.24910i) q^{61} +(-1.23825 - 2.14471i) q^{63} +(3.70291 + 6.41362i) q^{67} +(3.45862 - 5.99050i) q^{69} +(-0.0244587 + 0.0423637i) q^{71} +4.51573 q^{73} +(-8.84481 - 15.3197i) q^{75} -7.17390 q^{77} +12.8170 q^{79} +(2.09030 + 3.62051i) q^{81} +3.55496 q^{83} +(0.129531 - 0.224354i) q^{85} +(1.44989 - 2.51128i) q^{87} +(-1.17360 - 2.03274i) q^{89} +(1.93416 + 3.35006i) q^{93} +(-13.1359 + 22.7520i) q^{95} +(1.71164 - 2.96464i) q^{97} -3.89008 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$6 q + 16 q^{5} + q^{7} - 5 q^{9} - 6 q^{11} + 10 q^{17} - 4 q^{19} + 28 q^{21} - 3 q^{23} + 22 q^{25} - 42 q^{27} + q^{29} + 10 q^{31} - 14 q^{33} + 12 q^{35} - 4 q^{37} - 25 q^{41} - 5 q^{43} - 11 q^{45}+ \cdots - 22 q^{99}+O(q^{100})$ 6 * q + 16 * q^5 + q^7 - 5 * q^9 - 6 * q^11 + 10 * q^17 - 4 * q^19 + 28 * q^21 - 3 * q^23 + 22 * q^25 - 42 * q^27 + q^29 + 10 * q^31 - 14 * q^33 + 12 * q^35 - 4 * q^37 - 25 * q^41 - 5 * q^43 - 11 * q^45 - 16 * q^47 - 12 * q^49 - 14 * q^51 - 6 * q^53 - 16 * q^55 - 14 * q^57 - 9 * q^59 - 8 * q^61 + 18 * q^63 + 9 * q^67 + 14 * q^69 + 9 * q^71 + 2 * q^73 - 7 * q^75 + 24 * q^77 + 18 * q^79 + q^81 + 22 * q^83 + 15 * q^85 - 14 * q^87 - 25 * q^89 + 14 * q^93 - 27 * q^95 + 13 * q^97 - 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/676\mathbb{Z}\right)^\times$ .

$n$	$339$	$509$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$		0			0
$2$		0			0
$3$	−0.678448	−	1.17511i	−0.391702	−	0.678448i	0.600972	−	0.799270i	$-0.294780\pi$
$3$	−0.678448	−	1.17511i	−0.391702	−	0.678448i	−0.992674	+	0.120822i	$0.961447\pi$
$4$		0			0
$5$	4.24698			1.89931			0.949654	−	0.313302i	$-0.101435\pi$
$5$	4.24698			1.89931			0.949654	+	0.313302i	$0.101435\pi$
$6$		0			0
$7$	1.06853	−	1.85075i	0.403867	−	0.699518i	−0.590322	−	0.807168i	$-0.700999\pi$
$7$	1.06853	−	1.85075i	0.403867	−	0.699518i	0.994189	+	0.107650i	$0.0343325\pi$
$8$		0			0
$9$	0.579417	−	1.00358i	0.193139	−	0.334526i
$10$		0			0
$11$	−1.67845	−	2.90716i	−0.506071	−	0.876541i	−0.999975	−	0.00702454i	$-0.997764\pi$
$11$	−1.67845	−	2.90716i	−0.506071	−	0.876541i	0.493904	−	0.869516i	$-0.335569\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	−2.88135	−	4.99065i	−0.743963	−	1.28858i
$16$		0			0
$17$	0.0304995	−	0.0528266i	0.00739721	−	0.0128123i	−0.862303	−	0.506392i	$-0.830979\pi$
$17$	0.0304995	−	0.0528266i	0.00739721	−	0.0128123i	0.869700	+	0.493580i	$0.164312\pi$
$18$		0			0
$19$	−3.09299	+	5.35722i	−0.709581	+	1.22903i	0.255432	+	0.966827i	$0.417782\pi$
$19$	−3.09299	+	5.35722i	−0.709581	+	1.22903i	−0.965013	+	0.262203i	$0.915551\pi$
$20$		0			0
$21$	−2.89977			−0.632782
$22$		0			0
$23$	2.54892	+	4.41485i	0.531486	+	0.920561i	0.999325	+	0.0367468i	$0.0116995\pi$
$23$	2.54892	+	4.41485i	0.531486	+	0.920561i	−0.467839	+	0.883814i	$0.654967\pi$
$24$		0			0
$25$	13.0368			2.60737
$26$		0			0
$27$	−5.64310			−1.08602
$28$		0			0
$29$	1.06853	+	1.85075i	0.198421	+	0.343676i	0.948017	−	0.318220i	$-0.103085\pi$
$29$	1.06853	+	1.85075i	0.198421	+	0.343676i	−0.749595	+	0.661896i	$0.769752\pi$
$30$		0			0
$31$	−2.85086			−0.512029			−0.256014	−	0.966673i	$-0.582409\pi$
$31$	−2.85086			−0.512029			−0.256014	+	0.966673i	$0.582409\pi$
$32$		0			0
$33$	−2.27748	+	3.94471i	−0.396458	+	0.686686i
$34$		0			0
$35$	4.53803	−	7.86010i	0.767067	−	1.32860i
$36$		0			0
$37$	−1.73609	−	3.00700i	−0.285412	−	0.494348i	0.687297	−	0.726377i	$-0.258797\pi$
$37$	−1.73609	−	3.00700i	−0.285412	−	0.494348i	−0.972709	+	0.232028i	$0.925464\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.69806	−	4.67318i	−0.421367	−	0.729828i	0.574707	−	0.818359i	$-0.305116\pi$
$41$	−2.69806	−	4.67318i	−0.421367	−	0.729828i	−0.996073	+	0.0885311i	$0.971783\pi$
$42$		0			0
$43$	4.30678	−	7.45957i	0.656778	−	1.13757i	−0.324667	−	0.945828i	$-0.605252\pi$
$43$	4.30678	−	7.45957i	0.656778	−	1.13757i	0.981445	−	0.191745i	$-0.0614145\pi$
$44$		0			0
$45$	2.46077	−	4.26218i	0.366830	−	0.635368i
$46$		0			0
$47$	−6.96077			−1.01533			−0.507666	−	0.861554i	$-0.669492\pi$
$47$	−6.96077			−1.01533			−0.507666	+	0.861554i	$0.669492\pi$
$48$		0			0
$49$	1.21648	+	2.10701i	0.173783	+	0.301001i
$50$		0			0
$51$	−0.0827692			−0.0115900
$52$		0			0
$53$	0.0217703			0.00299038			0.00149519	−	0.999999i	$-0.499524\pi$
$53$	0.0217703			0.00299038			0.00149519	+	0.999999i	$0.499524\pi$
$54$		0			0
$55$	−7.12833	−	12.3466i	−0.961184	−	1.66482i
$56$		0			0
$57$	8.39373			1.11178
$58$		0			0
$59$	2.90581	−	5.03302i	0.378305	−	0.655243i	−0.612511	−	0.790462i	$-0.709841\pi$
$59$	2.90581	−	5.03302i	0.378305	−	0.655243i	0.990816	+	0.135219i	$0.0431738\pi$
$60$		0			0
$61$	−5.33997	+	9.24910i	−0.683713	+	1.18423i	0.290126	+	0.956988i	$0.406303\pi$
$61$	−5.33997	+	9.24910i	−0.683713	+	1.18423i	−0.973839	+	0.227237i	$0.927031\pi$
$62$		0			0
$63$	−1.23825	−	2.14471i	−0.156005	−	0.270208i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	3.70291	+	6.41362i	0.452382	+	0.783549i	0.998533	−	0.0541378i	$-0.0172410\pi$
$67$	3.70291	+	6.41362i	0.452382	+	0.783549i	−0.546151	+	0.837686i	$0.683908\pi$
$68$		0			0
$69$	3.45862	−	5.99050i	0.416368	−	0.721171i
$70$		0			0
$71$	−0.0244587	+	0.0423637i	−0.00290271	+	0.00502764i	−0.867473	−	0.497484i	$-0.834257\pi$
$71$	−0.0244587	+	0.0423637i	−0.00290271	+	0.00502764i	0.864570	+	0.502512i	$0.167591\pi$
$72$		0			0
$73$	4.51573			0.528526			0.264263	−	0.964451i	$-0.414871\pi$
$73$	4.51573			0.528526			0.264263	+	0.964451i	$0.414871\pi$
$74$		0			0
$75$	−8.84481	−	15.3197i	−1.02131	−	1.76896i
$76$		0			0
$77$	−7.17390			−0.817542
$78$		0			0
$79$	12.8170			1.44203			0.721013	−	0.692922i	$-0.243677\pi$
$79$	12.8170			1.44203			0.721013	+	0.692922i	$0.243677\pi$
$80$		0			0
$81$	2.09030	+	3.62051i	0.232256	+	0.402279i
$82$		0			0
$83$	3.55496			0.390207			0.195104	−	0.980783i	$-0.437496\pi$
$83$	3.55496			0.390207			0.195104	+	0.980783i	$0.437496\pi$
$84$		0			0
$85$	0.129531	−	0.224354i	0.0140496	−	0.0243346i
$86$		0			0
$87$	1.44989	−	2.51128i	0.155444	−	0.269237i
$88$		0			0
$89$	−1.17360	−	2.03274i	−0.124402	−	0.215470i	0.797097	−	0.603851i	$-0.206368\pi$
$89$	−1.17360	−	2.03274i	−0.124402	−	0.215470i	−0.921499	+	0.388381i	$0.873034\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.93416	+	3.35006i	0.200563	+	0.347385i
$94$		0			0
$95$	−13.1359	+	22.7520i	−1.34771	+	2.33430i
$96$		0			0
$97$	1.71164	−	2.96464i	0.173790	−	0.301014i	−0.765952	−	0.642898i	$-0.777732\pi$
$97$	1.71164	−	2.96464i	0.173790	−	0.301014i	0.939742	+	0.341885i	$0.111065\pi$
$98$		0			0
$99$	−3.89008			−0.390968
$100$		0			0
$101$	5.68933	+	9.85421i	0.566110	+	0.980531i	0.996945	+	0.0781005i	$0.0248855\pi$
$101$	5.68933	+	9.85421i	0.566110	+	0.980531i	−0.430836	+	0.902430i	$0.641781\pi$
$102$		0			0
$103$	−6.07606			−0.598692			−0.299346	−	0.954145i	$-0.596769\pi$
$103$	−6.07606			−0.598692			−0.299346	+	0.954145i	$0.596769\pi$
$104$		0			0
$105$	−12.3153			−1.20185
$106$		0			0
$107$	8.01842	+	13.8883i	0.775170	+	1.34263i	0.934699	+	0.355440i	$0.115669\pi$
$107$	8.01842	+	13.8883i	0.775170	+	1.34263i	−0.159529	+	0.987193i	$0.550998\pi$
$108$		0			0
$109$	−14.9095			−1.42807			−0.714034	−	0.700111i	$-0.753134\pi$
$109$	−14.9095			−1.42807			−0.714034	+	0.700111i	$0.753134\pi$
$110$		0			0
$111$	−2.35570	+	4.08019i	−0.223593	+	0.387275i
$112$		0			0
$113$	−4.12229	+	7.14002i	−0.387793	+	0.671677i	−0.992152	−	0.125035i	$-0.960096\pi$
$113$	−4.12229	+	7.14002i	−0.387793	+	0.671677i	0.604360	+	0.796712i	$0.293429\pi$
$114$		0			0
$115$	10.8252	+	18.7498i	1.00946	+	1.74843i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.0651793	−	0.112894i	−0.00597498	−	0.0103490i
$120$		0			0
$121$	−0.134375	+	0.232744i	−0.0122159	+	0.0211586i
$122$		0			0
$123$	−3.66099	+	6.34102i	−0.330100	+	0.571751i
$124$		0			0
$125$	34.1323			3.05288
$126$		0			0
$127$	3.32155	+	5.75310i	0.294740	+	0.510505i	0.974924	−	0.222536i	$-0.0714336\pi$
$127$	3.32155	+	5.75310i	0.294740	+	0.510505i	−0.680184	+	0.733041i	$0.738100\pi$
$128$		0			0
$129$	−11.6877			−1.02905
$130$		0			0
$131$	7.86294			0.686988			0.343494	−	0.939155i	$-0.388390\pi$
$131$	7.86294			0.686988			0.343494	+	0.939155i	$0.388390\pi$
$132$		0			0
$133$	6.60992	+	11.4487i	0.573152	+	0.992729i
$134$		0			0
$135$	−23.9661			−2.06268
$136$		0			0
$137$	0.493959	−	0.855562i	0.0422018	−	0.0730956i	−0.844153	−	0.536102i	$-0.819896\pi$
$137$	0.493959	−	0.855562i	0.0422018	−	0.0730956i	0.886355	+	0.463007i	$0.153229\pi$
$138$		0			0
$139$	6.01842	−	10.4242i	0.510476	−	0.884170i	−0.489451	−	0.872031i	$-0.662803\pi$
$139$	6.01842	−	10.4242i	0.510476	−	0.884170i	0.999926	−	0.0121387i	$-0.00386395\pi$
$140$		0			0
$141$	4.72252	+	8.17965i	0.397708	+	0.688850i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	4.53803	+	7.86010i	0.376863	+	0.652746i
$146$		0			0
$147$	1.65064	−	2.85899i	0.136142	−	0.235805i
$148$		0			0
$149$	−1.17964	+	2.04320i	−0.0966402	+	0.167386i	−0.910292	−	0.413967i	$-0.864143\pi$
$149$	−1.17964	+	2.04320i	−0.0966402	+	0.167386i	0.813652	+	0.581353i	$0.197476\pi$
$150$		0			0
$151$	−7.43967			−0.605431			−0.302716	−	0.953081i	$-0.597893\pi$
$151$	−7.43967			−0.605431			−0.302716	+	0.953081i	$0.597893\pi$
$152$		0			0
$153$	−0.0353438	−	0.0612173i	−0.00285738	−	0.00494912i
$154$		0			0
$155$	−12.1075			−0.972500
$156$		0			0
$157$	−10.9487			−0.873801			−0.436900	−	0.899510i	$-0.643924\pi$
$157$	−10.9487			−0.873801			−0.436900	+	0.899510i	$0.643924\pi$
$158$		0			0
$159$	−0.0147700	−	0.0255824i	−0.00117134	−	0.00202881i
$160$		0			0
$161$	10.8944			0.858599
$162$		0			0
$163$	−3.51238	+	6.08362i	−0.275111	+	0.476506i	−0.970163	−	0.242454i	$-0.922048\pi$
$163$	−3.51238	+	6.08362i	−0.275111	+	0.476506i	0.695052	+	0.718959i	$0.255381\pi$
$164$		0			0
$165$	−9.67241	+	16.7531i	−0.752996	+	1.30423i
$166$		0			0
$167$	7.74094	+	13.4077i	0.599012	+	1.03752i	0.992967	+	0.118389i	$0.0377731\pi$
$167$	7.74094	+	13.4077i	0.599012	+	1.03752i	−0.393955	+	0.919130i	$0.628894\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	3.58426	+	6.20812i	0.274095	+	0.474747i
$172$		0			0
$173$	−6.89008	+	11.9340i	−0.523843	+	0.907323i	0.475771	+	0.879569i	$0.342169\pi$
$173$	−6.89008	+	11.9340i	−0.523843	+	0.907323i	−0.999615	+	0.0277544i	$0.991164\pi$
$174$		0			0
$175$	13.9303	−	24.1279i	1.05303	−	1.82390i
$176$		0			0
$177$	−7.88577			−0.592731
$178$		0			0
$179$	−11.0613	−	19.1587i	−0.826760	−	1.43199i	−0.900567	−	0.434718i	$-0.856848\pi$
$179$	−11.0613	−	19.1587i	−0.826760	−	1.43199i	0.0738068	−	0.997273i	$-0.476485\pi$
$180$		0			0
$181$	−13.6407			−1.01391			−0.506953	−	0.861974i	$-0.669228\pi$
$181$	−13.6407			−1.01391			−0.506953	+	0.861974i	$0.669228\pi$
$182$		0			0
$183$	14.4916			1.07125
$184$		0			0
$185$	−7.37316	−	12.7707i	−0.542085	−	0.938919i
$186$		0			0
$187$	−0.204767			−0.0149740
$188$		0			0
$189$	−6.02984	+	10.4440i	−0.438606	+	0.759688i
$190$		0			0
$191$	−2.24578	+	3.88981i	−0.162499	+	0.281457i	−0.935764	−	0.352626i	$-0.885289\pi$
$191$	−2.24578	+	3.88981i	−0.162499	+	0.281457i	0.773265	+	0.634083i	$0.218622\pi$
$192$		0			0
$193$	−12.8877	−	22.3221i	−0.927676	−	1.60678i	−0.787199	−	0.616698i	$-0.788470\pi$
$193$	−12.8877	−	22.3221i	−0.927676	−	1.60678i	−0.140477	−	0.990084i	$-0.544864\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	9.31163	+	16.1282i	0.663426	+	1.14909i	0.979710	+	0.200423i	$0.0642315\pi$
$197$	9.31163	+	16.1282i	0.663426	+	1.14909i	−0.316284	+	0.948665i	$0.602435\pi$
$198$		0			0
$199$	5.98307	−	10.3630i	0.424129	−	0.734613i	−0.572210	−	0.820107i	$-0.693914\pi$
$199$	5.98307	−	10.3630i	0.424129	−	0.734613i	0.996339	+	0.0854945i	$0.0272470\pi$
$200$		0			0
$201$	5.02446	−	8.70262i	0.354398	−	0.613835i
$202$		0			0
$203$	4.56704			0.320543
$204$		0			0
$205$	−11.4586	−	19.8469i	−0.800304	−	1.38617i
$206$		0			0
$207$	5.90754			0.410603
$208$		0			0
$209$	20.7657			1.43639
$210$		0			0
$211$	−1.48039	−	2.56410i	−0.101914	−	0.176520i	0.810559	−	0.585657i	$-0.199163\pi$
$211$	−1.48039	−	2.56410i	−0.101914	−	0.176520i	−0.912473	+	0.409137i	$0.865830\pi$
$212$		0			0
$213$	0.0663757			0.00454799
$214$		0			0
$215$	18.2908	−	31.6806i	1.24742	−	2.16060i
$216$		0			0
$217$	−3.04623	+	5.27622i	−0.206791	+	0.358173i
$218$		0			0
$219$	−3.06369	−	5.30646i	−0.207025	−	0.358577i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	2.72132	+	4.71347i	0.182233	+	0.315637i	0.942641	−	0.333809i	$-0.108334\pi$
$223$	2.72132	+	4.71347i	0.182233	+	0.315637i	−0.760407	+	0.649446i	$0.775001\pi$
$224$		0			0
$225$	7.55376	−	13.0835i	0.503584	−	0.872233i
$226$		0			0
$227$	−11.2240	+	19.4406i	−0.744964	+	1.29032i	0.205248	+	0.978710i	$0.434200\pi$
$227$	−11.2240	+	19.4406i	−0.744964	+	1.29032i	−0.950212	+	0.311605i	$0.899133\pi$
$228$		0			0
$229$	−16.6136			−1.09786			−0.548928	−	0.835870i	$-0.684964\pi$
$229$	−16.6136			−1.09786			−0.548928	+	0.835870i	$0.684964\pi$
$230$		0			0
$231$	4.86712	+	8.43009i	0.320233	+	0.554659i
$232$		0			0
$233$	9.73125			0.637515			0.318758	−	0.947836i	$-0.396734\pi$
$233$	9.73125			0.637515			0.318758	+	0.947836i	$0.396734\pi$
$234$		0			0
$235$	−29.5623			−1.92843
$236$		0			0
$237$	−8.69567	−	15.0613i	−0.564844	−	0.978339i
$238$		0			0
$239$	−2.82908			−0.182998			−0.0914991	−	0.995805i	$-0.529166\pi$
$239$	−2.82908			−0.182998			−0.0914991	+	0.995805i	$0.529166\pi$
$240$		0			0
$241$	−9.17241	+	15.8871i	−0.590847	+	1.02338i	0.403272	+	0.915080i	$0.367873\pi$
$241$	−9.17241	+	15.8871i	−0.590847	+	1.02338i	−0.994119	+	0.108296i	$0.965460\pi$
$242$		0			0
$243$	−5.62833	+	9.74856i	−0.361058	+	0.625370i
$244$		0			0
$245$	5.16637	+	8.94841i	0.330067	+	0.571693i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−2.41185	−	4.17745i	−0.152845	−	0.264735i
$250$		0			0
$251$	1.26875	−	2.19754i	0.0800828	−	0.138707i	−0.823203	−	0.567748i	$-0.807815\pi$
$251$	1.26875	−	2.19754i	0.0800828	−	0.138707i	0.903285	+	0.429040i	$0.141148\pi$
$252$		0			0
$253$	8.55645	−	14.8202i	0.537939	−	0.931738i
$254$		0			0
$255$	−0.351519			−0.0220130
$256$		0			0
$257$	11.7431	+	20.3396i	0.732514	+	1.26875i	0.955805	+	0.294000i	$0.0949865\pi$
$257$	11.7431	+	20.3396i	0.732514	+	1.26875i	−0.223291	+	0.974752i	$0.571680\pi$
$258$		0			0
$259$	−7.42029			−0.461074
$260$		0			0
$261$	2.47650			0.153292
$262$		0			0
$263$	7.90462	+	13.6912i	0.487420	+	0.844235i	0.999895	−	0.0144662i	$-0.00460491\pi$
$263$	7.90462	+	13.6912i	0.487420	+	0.844235i	−0.512476	+	0.858702i	$0.671272\pi$
$264$		0			0
$265$	0.0924579			0.00567964
$266$		0			0
$267$	−1.59246	+	2.75822i	−0.0974568	+	0.168800i
$268$		0			0
$269$	15.4291	−	26.7239i	0.940727	−	1.62939i	0.176639	−	0.984276i	$-0.443477\pi$
$269$	15.4291	−	26.7239i	0.940727	−	1.62939i	0.764088	−	0.645112i	$-0.223189\pi$
$270$		0			0
$271$	−8.09664	−	14.0238i	−0.491836	−	0.851885i	0.508120	−	0.861286i	$-0.330341\pi$
$271$	−8.09664	−	14.0238i	−0.491836	−	0.851885i	−0.999956	+	0.00940175i	$0.997007\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−21.8817	−	37.9001i	−1.31951	−	2.28546i
$276$		0			0
$277$	−6.55376	+	11.3514i	−0.393777	+	0.682042i	−0.992944	−	0.118582i	$-0.962165\pi$
$277$	−6.55376	+	11.3514i	−0.393777	+	0.682042i	0.599167	+	0.800624i	$0.295499\pi$
$278$		0			0
$279$	−1.65183	+	2.86106i	−0.0988927	+	0.171287i
$280$		0			0
$281$	14.2687			0.851202			0.425601	−	0.904911i	$-0.360063\pi$
$281$	14.2687			0.851202			0.425601	+	0.904911i	$0.360063\pi$
$282$		0			0
$283$	3.97823	+	6.89050i	0.236481	+	0.409597i	0.959702	−	0.281019i	$-0.0906725\pi$
$283$	3.97823	+	6.89050i	0.236481	+	0.409597i	−0.723221	+	0.690617i	$0.757339\pi$
$284$		0			0
$285$	35.6480			2.11161
$286$		0			0
$287$	−11.5319			−0.680704
$288$		0			0
$289$	8.49814	+	14.7192i	0.499891	+	0.865836i
$290$		0			0
$291$	−4.64502			−0.272296
$292$		0			0
$293$	−9.81498	+	17.0000i	−0.573397	+	0.993153i	0.422817	+	0.906215i	$0.361041\pi$
$293$	−9.81498	+	17.0000i	−0.573397	+	0.993153i	−0.996214	+	0.0869378i	$0.972292\pi$
$294$		0			0
$295$	12.3409	−	21.3751i	0.718517	−	1.24451i
$296$		0			0
$297$	9.47166	+	16.4054i	0.549601	+	0.951937i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−9.20387	−	15.9416i	−0.530502	−	0.918856i
$302$		0			0
$303$	7.71983	−	13.3711i	0.443493	−	0.768152i
$304$		0			0
$305$	−22.6787	+	39.2807i	−1.29858	+	2.24921i
$306$		0			0
$307$	−15.6775			−0.894765			−0.447382	−	0.894343i	$-0.647644\pi$
$307$	−15.6775			−0.894765			−0.447382	+	0.894343i	$0.647644\pi$
$308$		0			0
$309$	4.12229	+	7.14002i	0.234509	+	0.406182i
$310$		0			0
$311$	16.4983			0.935531			0.467766	−	0.883853i	$-0.345059\pi$
$311$	16.4983			0.935531			0.467766	+	0.883853i	$0.345059\pi$
$312$		0			0
$313$	−11.3937			−0.644012			−0.322006	−	0.946738i	$-0.604357\pi$
$313$	−11.3937			−0.644012			−0.322006	+	0.946738i	$0.604357\pi$
$314$		0			0
$315$	−5.25882	−	9.10855i	−0.296301	−	0.513209i
$316$		0			0
$317$	25.4470			1.42924			0.714622	−	0.699511i	$-0.246599\pi$
$317$	25.4470			1.42924			0.714622	+	0.699511i	$0.246599\pi$
$318$		0			0
$319$	3.58695	−	6.21278i	0.200831	−	0.347849i
$320$		0			0
$321$	10.8802	−	18.8450i	0.607271	−	1.05182i
$322$		0			0
$323$	0.188669	+	0.326784i	0.0104978	+	0.0181828i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	10.1153	+	17.5202i	0.559377	+	0.968869i
$328$		0			0
$329$	−7.43780	+	12.8827i	−0.410059	+	0.710244i
$330$		0			0
$331$	−4.47770	+	7.75560i	−0.246117	+	0.426286i	−0.962445	−	0.271477i	$-0.912488\pi$
$331$	−4.47770	+	7.75560i	−0.246117	+	0.426286i	0.716328	+	0.697763i	$0.245821\pi$
$332$		0			0
$333$	−4.02369			−0.220497
$334$		0			0
$335$	15.7262	+	27.2385i	0.859212	+	1.48820i
$336$		0			0
$337$	19.3110			1.05194			0.525968	−	0.850505i	$-0.323703\pi$
$337$	19.3110			1.05194			0.525968	+	0.850505i	$0.323703\pi$
$338$		0			0
$339$	11.1870			0.607597
$340$		0			0
$341$	4.78501	+	8.28788i	0.259123	+	0.448814i
$342$		0			0
$343$	20.1588			1.08847
$344$		0			0
$345$	14.6887	−	25.4415i	0.790811	−	1.36973i
$346$		0			0
$347$	−18.0206	+	31.2125i	−0.967395	+	1.67558i	−0.264357	+	0.964425i	$0.585160\pi$
$347$	−18.0206	+	31.2125i	−0.967395	+	1.67558i	−0.703038	+	0.711153i	$0.748173\pi$
$348$		0			0
$349$	−11.6208	−	20.1278i	−0.622047	−	1.07742i	−0.989104	−	0.147219i	$-0.952968\pi$
$349$	−11.6208	−	20.1278i	−0.622047	−	1.07742i	0.367057	−	0.930199i	$-0.380365\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−12.1174	−	20.9880i	−0.644947	−	1.11708i	−0.984314	−	0.176426i	$-0.943546\pi$
$353$	−12.1174	−	20.9880i	−0.644947	−	1.11708i	0.339367	−	0.940654i	$-0.389787\pi$
$354$		0			0
$355$	−0.103875	+	0.179918i	−0.00551314	+	0.00954903i
$356$		0			0
$357$	−0.0884415	+	0.153185i	−0.00468082	+	0.00810742i
$358$		0			0
$359$	17.7332			0.935921			0.467960	−	0.883749i	$-0.344989\pi$
$359$	17.7332			0.935921			0.467960	+	0.883749i	$0.344989\pi$
$360$		0			0
$361$	−9.63318	−	16.6852i	−0.507009	−	0.878166i
$362$		0			0
$363$	0.364666			0.0191400
$364$		0			0
$365$	19.1782			1.00383
$366$		0			0
$367$	−15.1042	−	26.1612i	−0.788431	−	1.36560i	−0.926928	−	0.375240i	$-0.877560\pi$
$367$	−15.1042	−	26.1612i	−0.788431	−	1.36560i	0.138496	−	0.990363i	$-0.455773\pi$
$368$		0			0
$369$	−6.25321			−0.325529
$370$		0			0
$371$	0.0232622	−	0.0402913i	0.00120771	−	0.00209182i
$372$		0			0
$373$	0.340634	−	0.589995i	0.0176374	−	0.0305488i	−0.857072	−	0.515197i	$-0.827719\pi$
$373$	0.340634	−	0.589995i	0.0176374	−	0.0305488i	0.874709	+	0.484648i	$0.161052\pi$
$374$		0			0
$375$	−23.1570	−	40.1091i	−1.19582	−	2.07122i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−18.2479	−	31.6064i	−0.937334	−	1.62351i	−0.770419	−	0.637538i	$-0.779953\pi$
$379$	−18.2479	−	31.6064i	−0.937334	−	1.62351i	−0.166915	−	0.985971i	$-0.553381\pi$
$380$		0			0
$381$	4.50700	−	7.80635i	0.230901	−	0.399932i
$382$		0			0
$383$	2.60388	−	4.51004i	0.133052	−	0.230453i	−0.791800	−	0.610781i	$-0.790856\pi$
$383$	2.60388	−	4.51004i	0.133052	−	0.230453i	0.924852	+	0.380328i	$0.124189\pi$
$384$		0			0
$385$	−30.4674			−1.55276
$386$		0			0
$387$	−4.99084	−	8.64440i	−0.253699	−	0.439419i
$388$		0			0
$389$	−17.5254			−0.888574			−0.444287	−	0.895885i	$-0.646543\pi$
$389$	−17.5254			−0.888574			−0.444287	+	0.895885i	$0.646543\pi$
$390$		0			0
$391$	0.310962			0.0157260
$392$		0			0
$393$	−5.33459	−	9.23979i	−0.269095	−	0.466086i
$394$		0			0
$395$	54.4336			2.73885
$396$		0			0
$397$	14.9025	−	25.8118i	0.747933	−	1.29546i	−0.200879	−	0.979616i	$-0.564380\pi$
$397$	14.9025	−	25.8118i	0.747933	−	1.29546i	0.948812	−	0.315842i	$-0.102287\pi$
$398$		0			0
$399$	8.96897	−	15.5347i	0.449010	−	0.777708i
$400$		0			0
$401$	−8.16703	−	14.1457i	−0.407842	−	0.706403i	0.586806	−	0.809728i	$-0.300385\pi$
$401$	−8.16703	−	14.1457i	−0.407842	−	0.706403i	−0.994648	+	0.103325i	$0.967052\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	8.87747	+	15.3762i	0.441125	+	0.764051i
$406$		0			0
$407$	−5.82789	+	10.0942i	−0.288878	+	0.500351i
$408$		0			0
$409$	4.74914	−	8.22574i	0.234830	−	0.406737i	−0.724394	−	0.689387i	$-0.757880\pi$
$409$	4.74914	−	8.22574i	0.234830	−	0.406737i	0.959223	+	0.282650i	$0.0912134\pi$
$410$		0			0
$411$	−1.34050			−0.0661221
$412$		0			0
$413$	−6.20991	−	10.7559i	−0.305570	−	0.529262i
$414$		0			0
$415$	15.0978			0.741124
$416$		0			0
$417$	−16.3327			−0.799817
$418$		0			0
$419$	−6.22252	−	10.7777i	−0.303990	−	0.526526i	0.673046	−	0.739601i	$-0.264986\pi$
$419$	−6.22252	−	10.7777i	−0.303990	−	0.526526i	−0.977036	+	0.213075i	$0.931652\pi$
$420$		0			0
$421$	3.65578			0.178172			0.0890858	−	0.996024i	$-0.471605\pi$
$421$	3.65578			0.178172			0.0890858	+	0.996024i	$0.471605\pi$
$422$		0			0
$423$	−4.03319	+	6.98569i	−0.196100	+	0.339656i
$424$		0			0
$425$	0.397616	−	0.688692i	0.0192872	−	0.0334065i
$426$		0			0
$427$	11.4119	+	19.7659i	0.552258	+	0.956539i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	17.8110	+	30.8495i	0.857924	+	1.48597i	0.873906	+	0.486095i	$0.161579\pi$
$431$	17.8110	+	30.8495i	0.857924	+	1.48597i	−0.0159818	+	0.999872i	$0.505087\pi$
$432$		0			0
$433$	17.3463	−	30.0447i	0.833610	−	1.44386i	−0.0615466	−	0.998104i	$-0.519603\pi$
$433$	17.3463	−	30.0447i	0.833610	−	1.44386i	0.895157	−	0.445751i	$-0.147063\pi$
$434$		0			0
$435$	6.15764	−	10.6653i	0.295236	−	0.511364i
$436$		0			0
$437$	−31.5351			−1.50853
$438$		0			0
$439$	−4.74429	−	8.21735i	−0.226433	−	0.392193i	0.730316	−	0.683110i	$-0.239373\pi$
$439$	−4.74429	−	8.21735i	−0.226433	−	0.392193i	−0.956748	+	0.290917i	$0.906040\pi$
$440$		0			0
$441$	2.81940			0.134257
$442$		0			0
$443$	14.1849			0.673946			0.336973	−	0.941514i	$-0.390597\pi$
$443$	14.1849			0.673946			0.336973	+	0.941514i	$0.390597\pi$
$444$		0			0
$445$	−4.98427	−	8.63301i	−0.236277	−	0.409244i
$446$		0			0
$447$	3.20131			0.151417
$448$		0			0
$449$	3.49947	−	6.06126i	0.165150	−	0.286048i	−0.771558	−	0.636158i	$-0.780522\pi$
$449$	3.49947	−	6.06126i	0.165150	−	0.286048i	0.936709	+	0.350110i	$0.113856\pi$
$450$		0			0
$451$	−9.05711	+	15.6874i	−0.426483	+	0.738690i
$452$		0			0
$453$	5.04743	+	8.74240i	0.237149	+	0.410754i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.60656	−	2.78265i	−0.0751519	−	0.130167i	0.826000	−	0.563669i	$-0.190611\pi$
$457$	−1.60656	−	2.78265i	−0.0751519	−	0.130167i	−0.901152	+	0.433503i	$0.857277\pi$
$458$		0			0
$459$	−0.172112	+	0.298106i	−0.00803348	+	0.0139144i
$460$		0			0
$461$	−7.76391	+	13.4475i	−0.361601	+	0.626312i	−0.988225	−	0.153011i	$-0.951103\pi$
$461$	−7.76391	+	13.4475i	−0.361601	+	0.626312i	0.626623	+	0.779322i	$0.284436\pi$
$462$		0			0
$463$	32.0834			1.49104			0.745520	−	0.666483i	$-0.232201\pi$
$463$	32.0834			1.49104			0.745520	+	0.666483i	$0.232201\pi$
$464$		0			0
$465$	8.21432	+	14.2276i	0.380930	+	0.659790i
$466$		0			0
$467$	7.24459			0.335239			0.167620	−	0.985852i	$-0.446392\pi$
$467$	7.24459			0.335239			0.167620	+	0.985852i	$0.446392\pi$
$468$		0			0
$469$	15.8267			0.730809
$470$		0			0
$471$	7.42812	+	12.8659i	0.342270	+	0.592828i
$472$		0			0
$473$	−28.9148			−1.32951
$474$		0			0
$475$	−40.3228	+	69.8412i	−1.85014	+	3.20453i
$476$		0			0
$477$	0.0126141	−	0.0218482i	0.000577558	−	0.00100036i
$478$		0			0
$479$	−2.89104	−	5.00743i	−0.132095	−	0.228795i	0.792389	−	0.610016i	$-0.208837\pi$
$479$	−2.89104	−	5.00743i	−0.132095	−	0.228795i	−0.924484	+	0.381221i	$0.875504\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−7.39128	−	12.8021i	−0.336315	−	0.582514i
$484$		0			0
$485$	7.26928	−	12.5908i	0.330081	−	0.571717i
$486$		0			0
$487$	−2.07391	+	3.59211i	−0.0939778	+	0.162774i	−0.909182	−	0.416400i	$-0.863292\pi$
$487$	−2.07391	+	3.59211i	−0.0939778	+	0.162774i	0.815204	+	0.579174i	$0.196625\pi$
$488$		0			0
$489$	9.53186			0.431046
$490$		0			0
$491$	−3.59688	−	6.22997i	−0.162325	−	0.281155i	0.773377	−	0.633946i	$-0.218566\pi$
$491$	−3.59688	−	6.22997i	−0.162325	−	0.281155i	−0.935702	+	0.352791i	$0.885233\pi$
$492$		0			0
$493$	0.130359			0.00587105
$494$		0			0
$495$	−16.5211			−0.742569
$496$		0			0
$497$	0.0522697	+	0.0905338i	0.00234462	+	0.00406100i
$498$		0			0
$499$	−41.5066			−1.85809			−0.929046	−	0.369964i	$-0.879370\pi$
$499$	−41.5066			−1.85809			−0.929046	+	0.369964i	$0.879370\pi$
$500$		0			0
$501$	10.5036	−	18.1929i	0.469268	−	0.812797i
$502$		0			0
$503$	12.9303	−	22.3959i	0.576532	−	0.998583i	−0.419341	−	0.907829i	$-0.637739\pi$
$503$	12.9303	−	22.3959i	0.576532	−	0.998583i	0.995873	−	0.0907545i	$-0.0289278\pi$
$504$		0			0
$505$	24.1625	+	41.8506i	1.07522	+	1.86233i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−17.6962	−	30.6507i	−0.784370	−	1.35857i	−0.929374	−	0.369138i	$-0.879653\pi$
$509$	−17.6962	−	30.6507i	−0.784370	−	1.35857i	0.145004	−	0.989431i	$-0.453680\pi$
$510$		0			0
$511$	4.82520	−	8.35749i	0.213454	−	0.369714i
$512$		0			0
$513$	17.4541	−	30.2313i	0.770616	−	1.33475i
$514$		0			0
$515$	−25.8049			−1.13710
$516$		0			0
$517$	11.6833	+	20.2361i	0.513831	+	0.889981i
$518$		0			0
$519$	18.6983			0.820762
$520$		0			0
$521$	−34.2620			−1.50105			−0.750524	−	0.660844i	$-0.770199\pi$
$521$	−34.2620			−1.50105			−0.750524	+	0.660844i	$0.770199\pi$
$522$		0			0
$523$	7.30141	+	12.6464i	0.319268	+	0.552989i	0.980336	−	0.197338i	$-0.0632296\pi$
$523$	7.30141	+	12.6464i	0.319268	+	0.552989i	−0.661067	+	0.750327i	$0.729896\pi$
$524$		0			0
$525$	−37.8039			−1.64990
$526$		0			0
$527$	−0.0869495	+	0.150601i	−0.00378758	+	0.00656028i
$528$		0			0
$529$	−1.49396	+	2.58761i	−0.0649547	+	0.112505i
$530$		0			0
$531$	−3.36735	−	5.83243i	−0.146131	−	0.253106i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	34.0541	+	58.9834i	1.47229	+	2.55007i
$536$		0			0
$537$	−15.0090	+	25.9964i	−0.647687	+	1.12183i
$538$		0			0
$539$	4.08360	−	7.07300i	0.175893	−	0.304656i
$540$		0			0
$541$	18.8866			0.811999			0.406000	−	0.913873i	$-0.366923\pi$
$541$	18.8866			0.811999			0.406000	+	0.913873i	$0.366923\pi$
$542$		0			0
$543$	9.25451	+	16.0293i	0.397149	+	0.687882i
$544$		0			0
$545$	−63.3202			−2.71234
$546$		0			0
$547$	−34.6752			−1.48260			−0.741301	−	0.671172i	$-0.765791\pi$
$547$	−34.6752			−1.48260			−0.741301	+	0.671172i	$0.765791\pi$
$548$		0			0
$549$	6.18814	+	10.7182i	0.264103	+	0.457440i
$550$		0			0
$551$	−13.2198			−0.563184
$552$		0			0
$553$	13.6954	−	23.7211i	0.582387	−	1.00872i
$554$		0			0
$555$	−10.0046	+	17.3285i	−0.424672	+	0.735553i
$556$		0			0
$557$	2.12833	+	3.68638i	0.0901804	+	0.156197i	0.907587	−	0.419864i	$-0.137922\pi$
$557$	2.12833	+	3.68638i	0.0901804	+	0.156197i	−0.817407	+	0.576061i	$0.804589\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.138924	+	0.240623i	0.00586537	+	0.0101591i
$562$		0			0
$563$	−10.5685	+	18.3052i	−0.445411	+	0.771474i	−0.998081	−	0.0619264i	$-0.980276\pi$
$563$	−10.5685	+	18.3052i	−0.445411	+	0.771474i	0.552670	+	0.833400i	$0.313609\pi$
$564$		0			0
$565$	−17.5073	+	30.3235i	−0.736537	+	1.27572i
$566$		0			0
$567$	8.93422			0.375202
$568$		0			0
$569$	−17.7397	−	30.7261i	−0.743689	−	1.28811i	−0.950805	−	0.309790i	$-0.899741\pi$
$569$	−17.7397	−	30.7261i	−0.743689	−	1.28811i	0.207116	−	0.978316i	$-0.433592\pi$
$570$		0			0
$571$	3.94033			0.164898			0.0824488	−	0.996595i	$-0.473726\pi$
$571$	3.94033			0.164898			0.0824488	+	0.996595i	$0.473726\pi$
$572$		0			0
$573$	6.09459			0.254605
$574$		0			0
$575$	33.2298	+	57.5557i	1.38578	+	2.40024i
$576$		0			0
$577$	−16.6256			−0.692135			−0.346067	−	0.938210i	$-0.612483\pi$
$577$	−16.6256			−0.692135			−0.346067	+	0.938210i	$0.612483\pi$
$578$		0			0
$579$	−17.4873	+	30.2888i	−0.726745	+	1.25876i
$580$		0			0
$581$	3.79859	−	6.57934i	0.157592	−	0.272957i
$582$		0			0
$583$	−0.0365403	−	0.0632896i	−0.00151334	−	0.00262119i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.00149	+	6.93079i	0.165159	+	0.286064i	0.936712	−	0.350101i	$-0.113853\pi$
$587$	4.00149	+	6.93079i	0.165159	+	0.286064i	−0.771553	+	0.636166i	$0.780520\pi$
$588$		0			0
$589$	8.81767	−	15.2726i	0.363326	−	0.629298i
$590$		0			0
$591$	12.6349	−	21.8843i	0.519731	−	0.900200i
$592$		0			0
$593$	15.8345			0.650243			0.325122	−	0.945672i	$-0.394595\pi$
$593$	15.8345			0.650243			0.325122	+	0.945672i	$0.394595\pi$
$594$		0			0
$595$	−0.276815	−	0.479458i	−0.0113483	−	0.0196559i
$596$		0			0
$597$	−16.2368			−0.664529
$598$		0			0
$599$	25.9226			1.05917			0.529585	−	0.848257i	$-0.322348\pi$
$599$	25.9226			1.05917			0.529585	+	0.848257i	$0.322348\pi$
$600$		0			0
$601$	−10.0308	−	17.3738i	−0.409165	−	0.708694i	0.585632	−	0.810577i	$-0.300847\pi$
$601$	−10.0308	−	17.3738i	−0.409165	−	0.708694i	−0.994796	+	0.101883i	$0.967513\pi$
$602$		0			0
$603$	8.58211			0.349490
$604$		0			0
$605$	−0.570688	+	0.988460i	−0.0232018	+	0.0401866i
$606$		0			0
$607$	−20.8807	+	36.1664i	−0.847521	+	1.46795i	0.0358926	+	0.999356i	$0.488573\pi$
$607$	−20.8807	+	36.1664i	−0.847521	+	1.46795i	−0.883414	+	0.468594i	$0.844761\pi$
$608$		0			0
$609$	−3.09850	−	5.36676i	−0.125558	−	0.217472i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	6.20895	+	10.7542i	0.250777	+	0.434359i	0.963740	−	0.266843i	$-0.0859806\pi$
$613$	6.20895	+	10.7542i	0.250777	+	0.434359i	−0.712963	+	0.701202i	$0.752647\pi$
$614$		0			0
$615$	−15.5481	+	26.9302i	−0.626962	+	1.08593i
$616$		0			0
$617$	8.60992	−	14.9128i	0.346622	−	0.600367i	−0.639025	−	0.769186i	$-0.720662\pi$
$617$	8.60992	−	14.9128i	0.346622	−	0.600367i	0.985647	+	0.168819i	$0.0539953\pi$
$618$		0			0
$619$	42.6136			1.71278			0.856392	−	0.516326i	$-0.172701\pi$
$619$	42.6136			1.71278			0.856392	+	0.516326i	$0.172701\pi$
$620$		0			0
$621$	−14.3838	−	24.9135i	−0.577202	−	0.999744i
$622$		0			0
$623$	−5.01613			−0.200967
$624$		0			0
$625$	79.7749			3.19100
$626$		0			0
$627$	−14.0884	−	24.4019i	−0.562638	−	0.974518i
$628$		0			0
$629$	−0.211800			−0.00844501
$630$		0			0
$631$	13.4303	−	23.2619i	0.534651	−	0.926042i	−0.464529	−	0.885558i	$-0.653777\pi$
$631$	13.4303	−	23.2619i	0.534651	−	0.926042i	0.999180	−	0.0404845i	$-0.0128901\pi$
$632$		0			0
$633$	−2.00873	+	3.47922i	−0.0798398	+	0.138287i
$634$		0			0
$635$	14.1066	+	24.4333i	0.559802	+	0.969605i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	0.0283435	+	0.0490924i	0.00112125	+	0.00194207i
$640$		0			0
$641$	−16.6523	+	28.8426i	−0.657725	+	1.13921i	0.323479	+	0.946236i	$0.395148\pi$
$641$	−16.6523	+	28.8426i	−0.657725	+	1.13921i	−0.981203	+	0.192977i	$0.938186\pi$
$642$		0			0
$643$	−15.3373	+	26.5650i	−0.604843	+	1.04762i	0.387233	+	0.921982i	$0.373431\pi$
$643$	−15.3373	+	26.5650i	−0.604843	+	1.04762i	−0.992076	+	0.125637i	$0.959902\pi$
$644$		0			0
$645$	−49.6375			−1.95447
$646$		0			0
$647$	1.62804	+	2.81985i	0.0640048	+	0.110860i	0.896252	−	0.443545i	$-0.146279\pi$
$647$	1.62804	+	2.81985i	0.0640048	+	0.110860i	−0.832247	+	0.554405i	$0.812946\pi$
$648$		0			0
$649$	−19.5090			−0.765796
$650$		0			0
$651$	8.26683			0.324003
$652$		0			0
$653$	−7.40917	−	12.8331i	−0.289943	−	0.502196i	0.683853	−	0.729620i	$-0.260303\pi$
$653$	−7.40917	−	12.8331i	−0.289943	−	0.502196i	−0.973796	+	0.227424i	$0.926970\pi$
$654$		0			0
$655$	33.3937			1.30480
$656$		0			0
$657$	2.61649	−	4.53189i	0.102079	−	0.176806i
$658$		0			0
$659$	−15.2696	+	26.4477i	−0.594818	+	1.03026i	0.398754	+	0.917058i	$0.369443\pi$
$659$	−15.2696	+	26.4477i	−0.594818	+	1.03026i	−0.993572	+	0.113198i	$0.963891\pi$
$660$		0			0
$661$	9.68382	+	16.7729i	0.376657	+	0.652389i	0.990574	−	0.136982i	$-0.0437402\pi$
$661$	9.68382	+	16.7729i	0.376657	+	0.652389i	−0.613916	+	0.789371i	$0.710407\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	28.0722	+	48.6224i	1.08859	+	1.88550i
$666$		0			0
$667$	−5.44720	+	9.43482i	−0.210916	+	0.365318i
$668$		0			0
$669$	3.69255	−	6.39569i	0.142762	−	0.247272i
$670$		0			0
$671$	35.8514			1.38403
$672$		0			0
$673$	−20.7729	−	35.9798i	−0.800738	−	1.38692i	−0.919131	−	0.393951i	$-0.871108\pi$
$673$	−20.7729	−	35.9798i	−0.800738	−	1.38692i	0.118394	−	0.992967i	$-0.462226\pi$
$674$		0			0
$675$	−73.5682			−2.83164
$676$		0			0
$677$	−40.6064			−1.56063			−0.780315	−	0.625387i	$-0.784941\pi$
$677$	−40.6064			−1.56063			−0.780315	+	0.625387i	$0.784941\pi$
$678$		0			0
$679$	−3.65787	−	6.33562i	−0.140376	−	0.243139i
$680$		0			0
$681$	30.4596			1.16722
$682$		0			0
$683$	1.20291	−	2.08350i	0.0460279	−	0.0797227i	−0.842094	−	0.539331i	$-0.818677\pi$
$683$	1.20291	−	2.08350i	0.0460279	−	0.0797227i	0.888122	+	0.459609i	$0.152010\pi$
$684$		0			0
$685$	2.09783	−	3.63356i	0.0801541	−	0.138831i
$686$		0			0
$687$	11.2714	+	19.5227i	0.430032	+	0.744838i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−3.40635	−	5.89996i	−0.129583	−	0.224445i	0.793932	−	0.608007i	$-0.208031\pi$
$691$	−3.40635	−	5.89996i	−0.129583	−	0.224445i	−0.923515	+	0.383562i	$0.874697\pi$
$692$		0			0
$693$	−4.15668	+	7.19958i	−0.157899	+	0.273489i
$694$		0			0
$695$	25.5601	−	44.2714i	0.969550	−	1.67931i
$696$		0			0
$697$	−0.329158			−0.0124677
$698$		0			0
$699$	−6.60215	−	11.4353i	−0.249716	−	0.432521i
$700$		0			0
$701$	−12.7802			−0.482700			−0.241350	−	0.970438i	$-0.577590\pi$
$701$	−12.7802			−0.482700			−0.241350	+	0.970438i	$0.577590\pi$
$702$		0			0
$703$	21.4789			0.810092
$704$		0			0
$705$	20.0565	+	34.7388i	0.755370	+	1.30834i
$706$		0			0
$707$	24.3169			0.914532
$708$		0			0
$709$	2.47070	−	4.27937i	0.0927890	−	0.160715i	−0.815895	−	0.578201i	$-0.803755\pi$
$709$	2.47070	−	4.27937i	0.0927890	−	0.160715i	0.908684	+	0.417485i	$0.137088\pi$
$710$		0			0
$711$	7.42639	−	12.8629i	0.278511	−	0.482396i
$712$		0			0
$713$	−7.26659	−	12.5861i	−0.272136	−	0.471354i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.91939	+	3.32448i	0.0716808	+	0.124155i
$718$		0			0
$719$	18.8077	−	32.5760i	0.701410	−	1.21488i	−0.266561	−	0.963818i	$-0.585887\pi$
$719$	18.8077	−	32.5760i	0.701410	−	1.21488i	0.967971	−	0.251060i	$-0.0807793\pi$
$720$		0			0
$721$	−6.49247	+	11.2453i	−0.241792	+	0.418796i
$722$		0			0
$723$	24.8920			0.925744
$724$		0			0
$725$	13.9303	+	24.1279i	0.517357	+	0.896089i
$726$		0			0
$727$	−17.1879			−0.637464			−0.318732	−	0.947845i	$-0.603257\pi$
$727$	−17.1879			−0.637464			−0.318732	+	0.947845i	$0.603257\pi$
$728$		0			0
$729$	27.8159			1.03022
$730$		0			0
$731$	−0.262709	−	0.455025i	−0.00971665	−	0.0168297i
$732$		0			0
$733$	−19.2597			−0.711371			−0.355686	−	0.934606i	$-0.615753\pi$
$733$	−19.2597			−0.711371			−0.355686	+	0.934606i	$0.615753\pi$
$734$		0			0
$735$	7.01022	−	12.1421i	0.258576	−	0.447867i
$736$		0			0
$737$	12.4303	−	21.5299i	0.457875	−	0.793063i
$738$		0			0
$739$	−9.03923	−	15.6564i	−0.332513	−	0.575930i	0.650491	−	0.759514i	$-0.274563\pi$
$739$	−9.03923	−	15.6564i	−0.332513	−	0.575930i	−0.983004	+	0.183584i	$0.941230\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−16.4110	−	28.4246i	−0.602059	−	1.04280i	−0.992509	−	0.122173i	$-0.961014\pi$
$743$	−16.4110	−	28.4246i	−0.602059	−	1.04280i	0.390449	−	0.920624i	$-0.372320\pi$
$744$		0			0
$745$	−5.00993	+	8.67745i	−0.183549	+	0.317917i
$746$		0			0
$747$	2.05980	−	3.56768i	0.0753642	−	0.130535i
$748$		0			0
$749$	34.2717			1.25226
$750$		0			0
$751$	16.5851	+	28.7262i	0.605198	+	1.04823i	0.992020	+	0.126080i	$0.0402396\pi$
$751$	16.5851	+	28.7262i	0.605198	+	1.04823i	−0.386822	+	0.922155i	$0.626427\pi$
$752$		0			0
$753$	−3.44312			−0.125474
$754$		0			0
$755$	−31.5961			−1.14990
$756$		0			0
$757$	0.368313	+	0.637938i	0.0133866	+	0.0231862i	0.872641	−	0.488362i	$-0.162405\pi$
$757$	0.368313	+	0.637938i	0.0133866	+	0.0231862i	−0.859255	+	0.511548i	$0.829072\pi$
$758$		0			0
$759$	−23.2204			−0.842848
$760$		0			0
$761$	−18.1908	+	31.5074i	−0.659417	+	1.14214i	0.321350	+	0.946961i	$0.395863\pi$
$761$	−18.1908	+	31.5074i	−0.659417	+	1.14214i	−0.980767	+	0.195183i	$0.937470\pi$
$762$		0			0
$763$	−15.9312	+	27.5937i	−0.576749	+	0.998959i
$764$		0			0
$765$	−0.150104	−	0.259988i	−0.00542704	−	0.00939990i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	5.72617	+	9.91802i	0.206491	+	0.357653i	0.950607	−	0.310398i	$-0.100462\pi$
$769$	5.72617	+	9.91802i	0.206491	+	0.357653i	−0.744116	+	0.668051i	$0.767129\pi$
$770$		0			0
$771$	15.9342	−	27.5988i	0.573855	−	0.993945i
$772$		0			0
$773$	−3.78866	+	6.56215i	−0.136269	+	0.236024i	−0.926081	−	0.377324i	$-0.876844\pi$
$773$	−3.78866	+	6.56215i	−0.136269	+	0.236024i	0.789813	+	0.613348i	$0.210178\pi$
$774$		0			0
$775$	−37.1661			−1.33505
$776$		0			0
$777$	5.03428	+	8.71963i	0.180604	+	0.312815i
$778$		0			0
$779$	33.3803			1.19597
$780$		0			0
$781$	0.164210			0.00587591
$782$		0			0
$783$	−6.02984	−	10.4440i	−0.215489	−	0.373237i
$784$		0			0
$785$	−46.4989			−1.65962
$786$		0			0
$787$	15.2533	−	26.4195i	0.543722	−	0.941754i	−0.454964	−	0.890510i	$-0.650348\pi$
$787$	15.2533	−	26.4195i	0.543722	−	0.941754i	0.998686	−	0.0512444i	$-0.0163187\pi$
$788$		0			0
$789$	10.7257	−	18.5775i	0.381847	−	0.661378i
$790$		0			0
$791$	8.80960	+	15.2587i	0.313233	+	0.542536i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−0.0627278	−	0.108648i	−0.00222473	−	0.00385334i
$796$		0			0
$797$	−18.1218	+	31.3878i	−0.641906	+	1.11181i	0.343101	+	0.939298i	$0.388523\pi$
$797$	−18.1218	+	31.3878i	−0.641906	+	1.11181i	−0.985007	+	0.172515i	$0.944811\pi$
$798$		0			0
$799$	−0.212300	+	0.367714i	−0.00751063	+	0.0130088i
$800$		0			0
$801$	−2.72002			−0.0961073
$802$		0			0
$803$	−7.57942	−	13.1279i	−0.267472	−	0.463275i
$804$		0			0
$805$	46.2683			1.63074
$806$		0			0
$807$	−41.8713			−1.47394
$808$		0			0
$809$	−11.1618	−	19.3328i	−0.392429	−	0.679706i	0.600341	−	0.799744i	$-0.295032\pi$
$809$	−11.1618	−	19.3328i	−0.392429	−	0.679706i	−0.992769	+	0.120038i	$0.961698\pi$
$810$		0			0
$811$	−39.4922			−1.38676			−0.693379	−	0.720573i	$-0.743879\pi$
$811$	−39.4922			−1.38676			−0.693379	+	0.720573i	$0.743879\pi$
$812$		0			0
$813$	−10.9863	+	19.0288i	−0.385306	+	0.667370i
$814$		0			0
$815$	−14.9170	+	25.8370i	−0.522520	+	0.905030i
$816$		0			0
$817$	26.6417	+	46.1447i	0.932074	+	1.61440i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.69149	−	9.85795i	−0.198634	−	0.344045i	0.749452	−	0.662059i	$-0.230317\pi$
$821$	−5.69149	−	9.85795i	−0.198634	−	0.344045i	−0.948086	+	0.318014i	$0.896984\pi$
$822$		0			0
$823$	−12.8424	+	22.2437i	−0.447659	+	0.775368i	−0.998233	−	0.0594185i	$-0.981075\pi$
$823$	−12.8424	+	22.2437i	−0.447659	+	0.775368i	0.550574	+	0.834786i	$0.314409\pi$
$824$		0			0
$825$	−29.6911	+	51.4265i	−1.03371	+	1.79044i
$826$		0			0
$827$	−36.7251			−1.27706			−0.638529	−	0.769598i	$-0.720457\pi$
$827$	−36.7251			−1.27706			−0.638529	+	0.769598i	$0.720457\pi$
$828$		0			0
$829$	5.79039	+	10.0292i	0.201109	+	0.348330i	0.948886	−	0.315619i	$-0.102212\pi$
$829$	5.79039	+	10.0292i	0.201109	+	0.348330i	−0.747777	+	0.663950i	$0.768879\pi$
$830$		0			0
$831$	17.7855			0.616974
$832$		0			0
$833$	0.148408			0.00514203
$834$		0			0
$835$	32.8756	+	56.9422i	1.13771	+	1.97057i
$836$		0			0
$837$	16.0877			0.556071
$838$		0			0
$839$	−6.72886	+	11.6547i	−0.232306	+	0.402366i	−0.958486	−	0.285139i	$-0.907960\pi$
$839$	−6.72886	+	11.6547i	−0.232306	+	0.402366i	0.726180	+	0.687504i	$0.241294\pi$
$840$		0			0
$841$	12.2165	−	21.1596i	0.421258	−	0.729640i
$842$		0			0
$843$	−9.68060	−	16.7673i	−0.333418	−	0.577496i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.287168	+	0.497389i	0.00986720	+	0.0170905i
$848$		0			0
$849$	5.39804	−	9.34969i	0.185260	−	0.320880i
$850$		0			0
$851$	8.85032	−	15.3292i	0.303385	−	0.525478i
$852$		0			0
$853$	−5.34050			−0.182855			−0.0914277	−	0.995812i	$-0.529143\pi$
$853$	−5.34050			−0.182855			−0.0914277	+	0.995812i	$0.529143\pi$
$854$		0			0
$855$	15.2223	+	26.3658i	0.520591	+	0.901690i
$856$		0			0
$857$	49.3381			1.68536			0.842679	−	0.538417i	$-0.180977\pi$
$857$	49.3381			1.68536			0.842679	+	0.538417i	$0.180977\pi$
$858$		0			0
$859$	−4.92500			−0.168039			−0.0840194	−	0.996464i	$-0.526776\pi$
$859$	−4.92500			−0.168039			−0.0840194	+	0.996464i	$0.526776\pi$
$860$		0			0
$861$	7.82377	+	13.5512i	0.266633	+	0.461822i
$862$		0			0
$863$	−40.0315			−1.36269			−0.681343	−	0.731964i	$-0.738604\pi$
$863$	−40.0315			−1.36269			−0.681343	+	0.731964i	$0.738604\pi$
$864$		0			0
$865$	−29.2620	+	50.6833i	−0.994939	+	1.72329i
$866$		0			0
$867$	11.5311	−	19.9724i	0.391616	−	0.678299i
$868$		0			0
$869$	−21.5127	−	37.2610i	−0.729767	−	1.26399i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−1.98350	−	3.43552i	−0.0671313	−	0.116275i
$874$		0			0
$875$	36.4714	−	63.1704i	1.23296	−	2.13555i
$876$		0			0
$877$	14.4690	−	25.0610i	0.488582	−	0.846249i	−0.511331	−	0.859384i	$-0.670848\pi$
$877$	14.4690	−	25.0610i	0.488582	−	0.846249i	0.999914	+	0.0131342i	$0.00418086\pi$
$878$		0			0
$879$	26.6358			0.898404
$880$		0			0
$881$	−10.8346	−	18.7661i	−0.365027	−	0.632245i	0.623754	−	0.781621i	$-0.285607\pi$
$881$	−10.8346	−	18.7661i	−0.365027	−	0.632245i	−0.988780	+	0.149376i	$0.952273\pi$
$882$		0			0
$883$	11.7614			0.395802			0.197901	−	0.980222i	$-0.436588\pi$
$883$	11.7614			0.395802			0.197901	+	0.980222i	$0.436588\pi$
$884$		0			0
$885$	−33.4907			−1.12578
$886$		0			0
$887$	−13.4242	−	23.2515i	−0.450742	−	0.780707i	0.547691	−	0.836681i	$-0.315507\pi$
$887$	−13.4242	−	23.2515i	−0.450742	−	0.780707i	−0.998432	+	0.0559736i	$0.982174\pi$
$888$		0			0
$889$	14.1967			0.476143
$890$		0			0
$891$	7.01693	−	12.1537i	0.235076	−	0.407163i
$892$		0			0
$893$	21.5296	−	37.2904i	0.720461	−	1.24787i
$894$		0			0
$895$	−46.9771	−	81.3667i	−1.57027	−	2.71979i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−3.04623	−	5.27622i	−0.101597	−	0.175972i
$900$		0			0
$901$	0.000663981	−	0.00115005i	2.21204e−5	−	3.83137e-5i
$902$		0			0
$903$	−12.4887	+	21.6310i	−0.415598	+	0.719836i
$904$		0			0
$905$	−57.9318			−1.92572
$906$		0			0
$907$	−8.21528	−	14.2293i	−0.272784	−	0.472476i	0.696790	−	0.717276i	$-0.254611\pi$
$907$	−8.21528	−	14.2293i	−0.272784	−	0.472476i	−0.969574	+	0.244800i	$0.921278\pi$
$908$		0			0
$909$	13.1860			0.437351
$910$		0			0
$911$	26.0519			0.863138			0.431569	−	0.902080i	$-0.357960\pi$
$911$	26.0519			0.863138			0.431569	+	0.902080i	$0.357960\pi$
$912$		0			0
$913$	−5.96681	−	10.3348i	−0.197473	−	0.342033i
$914$		0			0
$915$	61.5454			2.03463
$916$		0			0
$917$	8.40180	−	14.5523i	0.277452	−	0.480561i
$918$		0			0
$919$	−2.18478	+	3.78416i	−0.0720694	+	0.124828i	−0.899808	−	0.436286i	$-0.856294\pi$
$919$	−2.18478	+	3.78416i	−0.0720694	+	0.124828i	0.827739	+	0.561114i	$0.189627\pi$
$920$		0			0
$921$	10.6364	+	18.4228i	0.350481	+	0.607051i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−22.6332	−	39.2018i	−0.744174	−	1.28895i
$926$		0			0
$927$	−3.52057	+	6.09781i	−0.115631	+	0.200278i
$928$		0			0
$929$	16.1434	−	27.9612i	0.529648	−	0.917377i	−0.469754	−	0.882797i	$-0.655657\pi$
$929$	16.1434	−	27.9612i	0.529648	−	0.917377i	0.999402	−	0.0345796i	$-0.0110092\pi$
$930$		0			0
$931$	−15.0502			−0.493252
$932$		0			0
$933$	−11.1932	−	19.3872i	−0.366450	−	0.634709i
$934$		0			0
$935$	−0.869641			−0.0284403
$936$		0			0
$937$	−48.5730			−1.58681			−0.793405	−	0.608693i	$-0.791694\pi$
$937$	−48.5730			−1.58681			−0.793405	+	0.608693i	$0.791694\pi$
$938$		0			0
$939$	7.73005	+	13.3888i	0.252261	+	0.436928i
$940$		0			0
$941$	4.82849			0.157404			0.0787022	−	0.996898i	$-0.474922\pi$
$941$	4.82849			0.157404			0.0787022	+	0.996898i	$0.474922\pi$
$942$		0			0
$943$	13.7543	−	23.8231i	0.447901	−	0.775787i
$944$		0			0
$945$	−25.6086	+	44.3554i	−0.833047	+	1.44288i
$946$		0			0
$947$	17.5532	+	30.4031i	0.570403	+	0.987968i	0.996524	+	0.0833014i	$0.0265464\pi$
$947$	17.5532	+	30.4031i	0.570403	+	0.987968i	−0.426121	+	0.904666i	$0.640120\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−17.2644	−	29.9029i	−0.559838	−	0.969667i
$952$		0			0
$953$	14.0933	−	24.4103i	0.456526	−	0.790727i	−0.542248	−	0.840218i	$-0.682427\pi$
$953$	14.0933	−	24.4103i	0.456526	−	0.790727i	0.998775	+	0.0494916i	$0.0157601\pi$
$954$		0			0
$955$	−9.53780	+	16.5199i	−0.308636	+	0.534573i
$956$		0			0
$957$	−9.73423			−0.314663
$958$		0			0
$959$	−1.05562	−	1.82839i	−0.0340878	−	0.0590418i
$960$		0			0
$961$	−22.8726			−0.737827
$962$		0			0
$963$	18.5840			0.598862
$964$		0			0
$965$	−54.7338	−	94.8017i	−1.76194	−	3.05177i
$966$		0			0
$967$	44.6674			1.43641			0.718203	−	0.695834i	$-0.244965\pi$
$967$	44.6674			1.43641			0.718203	+	0.695834i	$0.244965\pi$
$968$		0			0
$969$	0.256004	−	0.443412i	0.00822404	−	0.0142445i
$970$		0			0
$971$	7.45539	−	12.9131i	0.239255	−	0.414402i	−0.721246	−	0.692679i	$-0.756430\pi$
$971$	7.45539	−	12.9131i	0.239255	−	0.414402i	0.960501	+	0.278277i	$0.0897635\pi$
$972$		0			0
$973$	−12.8617	−	22.2772i	−0.412328	−	0.714174i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	17.6063	+	30.4951i	0.563276	+	0.975623i	0.997208	+	0.0746773i	$0.0237927\pi$
$977$	17.6063	+	30.4951i	0.563276	+	0.975623i	−0.433931	+	0.900946i	$0.642874\pi$
$978$		0			0
$979$	−3.93967	+	6.82370i	−0.125912	+	0.218086i
$980$		0			0
$981$	−8.63879	+	14.9628i	−0.275815	+	0.477726i
$982$		0			0
$983$	−30.5646			−0.974861			−0.487430	−	0.873162i	$-0.662066\pi$
$983$	−30.5646			−0.974861			−0.487430	+	0.873162i	$0.662066\pi$
$984$		0			0
$985$	39.5463	+	68.4962i	1.26005	+	2.18247i
$986$		0			0
$987$	20.1847			0.642485
$988$		0			0
$989$	43.9105			1.39627
$990$		0			0
$991$	−31.2869	−	54.1906i	−0.993862	−	1.72142i	−0.592736	−	0.805397i	$-0.701952\pi$
$991$	−31.2869	−	54.1906i	−0.993862	−	1.72142i	−0.401126	−	0.916023i	$-0.631381\pi$
$992$		0			0
$993$	12.1515			0.385617
$994$		0			0
$995$	25.4100	−	44.0114i	0.805551	−	1.39526i
$996$		0			0
$997$	0.942222	−	1.63198i	0.0298405	−	0.0516852i	−0.850720	−	0.525620i	$-0.823833\pi$
$997$	0.942222	−	1.63198i	0.0298405	−	0.0516852i	0.880560	+	0.473935i	$0.157167\pi$
$998$		0			0
$999$	9.79696	+	16.9688i	0.309962	+	0.536870i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	676.2.e.g.653.2		6
13.2	odd	12		676.2.d.e.337.3		6
13.3	even	3		676.2.a.h.1.2	yes	3
13.4	even	6		676.2.e.f.529.2		6
13.5	odd	4		676.2.h.e.361.3		12
13.6	odd	12		676.2.h.e.485.3		12
13.7	odd	12		676.2.h.e.485.4		12
13.8	odd	4		676.2.h.e.361.4		12
13.9	even	3	inner	676.2.e.g.529.2		6
13.10	even	6		676.2.a.g.1.2	✓	3
13.11	odd	12		676.2.d.e.337.4		6
13.12	even	2		676.2.e.f.653.2		6
39.2	even	12		6084.2.b.p.4393.6		6
39.11	even	12		6084.2.b.p.4393.1		6
39.23	odd	6		6084.2.a.bc.1.3		3
39.29	odd	6		6084.2.a.x.1.1		3
52.3	odd	6		2704.2.a.y.1.2		3
52.11	even	12		2704.2.f.n.337.4		6
52.15	even	12		2704.2.f.n.337.3		6
52.23	odd	6		2704.2.a.x.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
676.2.a.g.1.2	✓	3	13.10	even	6
676.2.a.h.1.2	yes	3	13.3	even	3
676.2.d.e.337.3		6	13.2	odd	12
676.2.d.e.337.4		6	13.11	odd	12
676.2.e.f.529.2		6	13.4	even	6
676.2.e.f.653.2		6	13.12	even	2
676.2.e.g.529.2		6	13.9	even	3	inner
676.2.e.g.653.2		6	1.1	even	1	trivial
676.2.h.e.361.3		12	13.5	odd	4
676.2.h.e.361.4		12	13.8	odd	4
676.2.h.e.485.3		12	13.6	odd	12
676.2.h.e.485.4		12	13.7	odd	12
2704.2.a.x.1.2		3	52.23	odd	6
2704.2.a.y.1.2		3	52.3	odd	6
2704.2.f.n.337.3		6	52.15	even	12
2704.2.f.n.337.4		6	52.11	even	12
6084.2.a.x.1.1		3	39.29	odd	6
6084.2.a.bc.1.3		3	39.23	odd	6
6084.2.b.p.4393.1		6	39.11	even	12
6084.2.b.p.4393.6		6	39.2	even	12

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	676.2.e.g.653.2

Level	$676$
Weight	$2$
Character	676.653
Analytic conductor	$5.398$
Analytic rank	$0$
Dimension	$6$
Inner twists	$2$