LMFDB - Embedded newform 1512.2.j.d.323.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(323,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1512.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.j (of order $2$, degree $1$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.6
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.d.323.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29821 + 0.560940i) q^{2} +(1.37069 - 1.45643i) q^{4} +0.530075 q^{5} -1.00000i q^{7} +(-0.962474 + 2.65963i) q^{8} +O(q^{10})$	\(q+(-1.29821 + 0.560940i) q^{2} +(1.37069 - 1.45643i) q^{4} +0.530075 q^{5} -1.00000i q^{7} +(-0.962474 + 2.65963i) q^{8} +(-0.688148 + 0.297340i) q^{10} -0.905144i q^{11} -4.38398i q^{13} +(0.560940 + 1.29821i) q^{14} +(-0.242402 - 3.99265i) q^{16} +1.25430i q^{17} +0.00364927 q^{19} +(0.726570 - 0.772020i) q^{20} +(0.507731 + 1.17507i) q^{22} -0.778929 q^{23} -4.71902 q^{25} +(2.45915 + 5.69133i) q^{26} +(-1.45643 - 1.37069i) q^{28} -5.43228 q^{29} -3.49953i q^{31} +(2.55432 + 5.04732i) q^{32} +(-0.703586 - 1.62834i) q^{34} -0.530075i q^{35} -5.34322i q^{37} +(-0.00473751 + 0.00204702i) q^{38} +(-0.510183 + 1.40980i) q^{40} -1.74538i q^{41} -0.259493 q^{43} +(-1.31828 - 1.24067i) q^{44} +(1.01121 - 0.436933i) q^{46} +3.75927 q^{47} -1.00000 q^{49} +(6.12627 - 2.64709i) q^{50} +(-6.38498 - 6.00909i) q^{52} -3.08087 q^{53} -0.479794i q^{55} +(2.65963 + 0.962474i) q^{56} +(7.05223 - 3.04718i) q^{58} +5.73302i q^{59} +0.555629i q^{61} +(1.96302 + 4.54312i) q^{62} +(-6.14729 - 5.11965i) q^{64} -2.32384i q^{65} +11.5465 q^{67} +(1.82680 + 1.71926i) q^{68} +(0.297340 + 0.688148i) q^{70} -16.0043 q^{71} -13.1552 q^{73} +(2.99723 + 6.93662i) q^{74} +(0.00500203 - 0.00531492i) q^{76} -0.905144 q^{77} +1.96889i q^{79} +(-0.128491 - 2.11640i) q^{80} +(0.979053 + 2.26587i) q^{82} -5.82561i q^{83} +0.664872i q^{85} +(0.336876 - 0.145560i) q^{86} +(2.40735 + 0.871177i) q^{88} +1.94491i q^{89} -4.38398 q^{91} +(-1.06767 + 1.13446i) q^{92} +(-4.88032 + 2.10872i) q^{94} +0.00193439 q^{95} -13.8042 q^{97} +(1.29821 - 0.560940i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4}+O(q^{10}) $ 48 * q - 4 * q^4	$ 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) $ 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	−1.29821	+	0.560940i	−0.917972	+	0.396644i
$2$	−1.29821	+	0.560940i	−0.917972	+	0.396644i
$3$		0			0
$3$		0			0
$4$	1.37069	−	1.45643i	0.685346	−	0.728217i
$5$	0.530075			0.237057			0.118528	−	0.992951i	$-0.462182\pi$
$5$	0.530075			0.237057			0.118528	+	0.992951i	$0.462182\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−0.962474	+	2.65963i	−0.340286	+	0.940322i
$9$		0			0
$10$	−0.688148	+	0.297340i	−0.217612	+	0.0940272i
$11$		−	0.905144i		−	0.272911i	−0.990646	−	0.136456i	$-0.956429\pi$
$11$		−	0.905144i		−	0.272911i	0.990646	−	0.136456i	$-0.0435711\pi$
$12$		0			0
$13$		−	4.38398i		−	1.21590i	−0.793976	−	0.607949i	$-0.791992\pi$
$13$		−	4.38398i		−	1.21590i	0.793976	−	0.607949i	$-0.208008\pi$
$14$	0.560940	+	1.29821i	0.149917	+	0.346961i
$15$		0			0
$16$	−0.242402	−	3.99265i	−0.0606005	−	0.998162i
$17$			1.25430i			0.304212i	0.988364	+	0.152106i	$0.0486055\pi$
$17$			1.25430i			0.304212i	−0.988364	+	0.152106i	$0.951395\pi$
$18$		0			0
$19$	0.00364927			0.000837200			0.000418600	−	1.00000i	$-0.499867\pi$
$19$	0.00364927			0.000837200			0.000418600		1.00000i	$0.499867\pi$
$20$	0.726570	−	0.772020i	0.162466	−	0.172629i
$21$		0			0
$22$	0.507731	+	1.17507i	0.108249	+	0.250525i
$23$	−0.778929			−0.162418			−0.0812090	−	0.996697i	$-0.525878\pi$
$23$	−0.778929			−0.162418			−0.0812090	+	0.996697i	$0.525878\pi$
$24$		0			0
$25$	−4.71902			−0.943804
$26$	2.45915	+	5.69133i	0.482279	+	1.11616i
$27$		0			0
$28$	−1.45643	−	1.37069i	−0.275240	−	0.259037i
$29$	−5.43228			−1.00875			−0.504375	−	0.863485i	$-0.668277\pi$
$29$	−5.43228			−1.00875			−0.504375	+	0.863485i	$0.668277\pi$
$30$		0			0
$31$		−	3.49953i		−	0.628533i	−0.949335	−	0.314267i	$-0.898241\pi$
$31$		−	3.49953i		−	0.628533i	0.949335	−	0.314267i	$-0.101759\pi$
$32$	2.55432	+	5.04732i	0.451545	+	0.892248i
$33$		0			0
$34$	−0.703586	−	1.62834i	−0.120664	−	0.279258i
$35$		−	0.530075i		−	0.0895990i
$36$		0			0
$37$		−	5.34322i		−	0.878421i	−0.898384	−	0.439210i	$-0.855258\pi$
$37$		−	5.34322i		−	0.878421i	0.898384	−	0.439210i	$-0.144742\pi$
$38$	−0.00473751	+	0.00204702i	−0.000768526	+	0.000332071i
$39$		0			0
$40$	−0.510183	+	1.40980i	−0.0806671	+	0.222910i
$41$		−	1.74538i		−	0.272582i	−0.990669	−	0.136291i	$-0.956482\pi$
$41$		−	1.74538i		−	0.272582i	0.990669	−	0.136291i	$-0.0435183\pi$
$42$		0			0
$43$	−0.259493			−0.0395723			−0.0197862	−	0.999804i	$-0.506299\pi$
$43$	−0.259493			−0.0395723			−0.0197862	+	0.999804i	$0.506299\pi$
$44$	−1.31828	−	1.24067i	−0.198739	−	0.187039i
$45$		0			0
$46$	1.01121	−	0.436933i	0.149095	−	0.0644222i
$47$	3.75927			0.548346			0.274173	−	0.961680i	$-0.411596\pi$
$47$	3.75927			0.548346			0.274173	+	0.961680i	$0.411596\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	6.12627	−	2.64709i	0.866386	−	0.374355i
$51$		0			0
$52$	−6.38498	−	6.00909i	−0.885438	−	0.833312i
$53$	−3.08087			−0.423190			−0.211595	−	0.977357i	$-0.567866\pi$
$53$	−3.08087			−0.423190			−0.211595	+	0.977357i	$0.567866\pi$
$54$		0			0
$55$		−	0.479794i		−	0.0646955i
$56$	2.65963	+	0.962474i	0.355408	+	0.128616i
$57$		0			0
$58$	7.05223	−	3.04718i	0.926004	−	0.400115i
$59$			5.73302i			0.746376i	0.927756	+	0.373188i	$0.121735\pi$
$59$			5.73302i			0.746376i	−0.927756	+	0.373188i	$0.878265\pi$
$60$		0			0
$61$			0.555629i			0.0711410i	0.999367	+	0.0355705i	$0.0113248\pi$
$61$			0.555629i			0.0711410i	−0.999367	+	0.0355705i	$0.988675\pi$
$62$	1.96302	+	4.54312i	0.249304	+	0.576976i
$63$		0			0
$64$	−6.14729	−	5.11965i	−0.768411	−	0.639956i
$65$		−	2.32384i		−	0.288237i
$66$		0			0
$67$	11.5465			1.41063			0.705313	−	0.708896i	$-0.250806\pi$
$67$	11.5465			1.41063			0.705313	+	0.708896i	$0.250806\pi$
$68$	1.82680	+	1.71926i	0.221532	+	0.208491i
$69$		0			0
$70$	0.297340	+	0.688148i	0.0355390	+	0.0822494i
$71$	−16.0043			−1.89936			−0.949681	−	0.313218i	$-0.898593\pi$
$71$	−16.0043			−1.89936			−0.949681	+	0.313218i	$0.898593\pi$
$72$		0			0
$73$	−13.1552			−1.53970			−0.769851	−	0.638224i	$-0.779669\pi$
$73$	−13.1552			−1.53970			−0.769851	+	0.638224i	$0.779669\pi$
$74$	2.99723	+	6.93662i	0.348421	+	0.806366i
$75$		0			0
$76$	0.00500203	−	0.00531492i	0.000573772	−	0.000609663i
$77$	−0.905144			−0.103151
$78$		0			0
$79$			1.96889i			0.221517i	0.993847	+	0.110759i	$0.0353280\pi$
$79$			1.96889i			0.221517i	−0.993847	+	0.110759i	$0.964672\pi$
$80$	−0.128491	−	2.11640i	−0.0143658	−	0.236621i
$81$		0			0
$82$	0.979053	+	2.26587i	0.108118	+	0.250223i
$83$		−	5.82561i		−	0.639444i	−0.947511	−	0.319722i	$-0.896411\pi$
$83$		−	5.82561i		−	0.639444i	0.947511	−	0.319722i	$-0.103589\pi$
$84$		0			0
$85$			0.664872i			0.0721155i
$86$	0.336876	−	0.145560i	0.0363263	−	0.0156961i
$87$		0			0
$88$	2.40735	+	0.871177i	0.256624	+	0.0928678i
$89$			1.94491i			0.206160i	0.994673	+	0.103080i	$0.0328697\pi$
$89$			1.94491i			0.206160i	−0.994673	+	0.103080i	$0.967130\pi$
$90$		0			0
$91$	−4.38398			−0.459566
$92$	−1.06767	+	1.13446i	−0.111313	+	0.118276i
$93$		0			0
$94$	−4.88032	+	2.10872i	−0.503366	+	0.217498i
$95$	0.00193439			0.000198464
$96$		0			0
$97$	−13.8042			−1.40161			−0.700803	−	0.713355i	$-0.747175\pi$
$97$	−13.8042			−1.40161			−0.700803	+	0.713355i	$0.747175\pi$
$98$	1.29821	−	0.560940i	0.131139	−	0.0566635i
$99$		0			0
$100$	−6.46833	+	6.87294i	−0.646833	+	0.687294i
$101$	−5.41639			−0.538951			−0.269475	−	0.963007i	$-0.586850\pi$
$101$	−5.41639			−0.538951			−0.269475	+	0.963007i	$0.586850\pi$
$102$		0			0
$103$		−	2.14390i		−	0.211245i	−0.994406	−	0.105623i	$-0.966316\pi$
$103$		−	2.14390i		−	0.211245i	0.994406	−	0.105623i	$-0.0336835\pi$
$104$	11.6598	+	4.21947i	1.14334	+	0.413753i
$105$		0			0
$106$	3.99961	−	1.72818i	0.388477	−	0.167856i
$107$		−	9.10325i		−	0.880045i	−0.897987	−	0.440022i	$-0.854971\pi$
$107$		−	9.10325i		−	0.880045i	0.897987	−	0.440022i	$-0.145029\pi$
$108$		0			0
$109$		−	1.29567i		−	0.124103i	−0.998073	−	0.0620515i	$-0.980236\pi$
$109$		−	1.29567i		−	0.124103i	0.998073	−	0.0620515i	$-0.0197643\pi$
$110$	0.269136	+	0.622873i	0.0256611	+	0.0593886i
$111$		0			0
$112$	−3.99265	+	0.242402i	−0.377270	+	0.0229049i
$113$		−	14.0728i		−	1.32386i	−0.749567	−	0.661928i	$-0.769738\pi$
$113$		−	14.0728i		−	1.32386i	0.749567	−	0.661928i	$-0.230262\pi$
$114$		0			0
$115$	−0.412891			−0.0385023
$116$	−7.44599	+	7.91176i	−0.691343	+	0.734588i
$117$		0			0
$118$	−3.21588	−	7.44266i	−0.296046	−	0.685152i
$119$	1.25430			0.114981
$120$		0			0
$121$	10.1807			0.925519
$122$	−0.311675	−	0.721323i	−0.0282177	−	0.0653055i
$123$		0			0
$124$	−5.09683	−	4.79678i	−0.457709	−	0.430763i
$125$	−5.15181			−0.460792
$126$		0			0
$127$		−	11.5015i		−	1.02060i	−0.859997	−	0.510298i	$-0.829535\pi$
$127$		−	11.5015i		−	1.02060i	0.859997	−	0.510298i	$-0.170465\pi$
$128$	10.8523	+	3.19812i	0.959215	+	0.282676i
$129$		0			0
$130$	1.30353	+	3.01683i	0.114328	+	0.264594i
$131$		−	10.2828i		−	0.898411i	−0.893429	−	0.449205i	$-0.851707\pi$
$131$		−	10.2828i		−	0.898411i	0.893429	−	0.449205i	$-0.148293\pi$
$132$		0			0
$133$		−	0.00364927i		−	0.000316432i
$134$	−14.9897	+	6.47688i	−1.29492	+	0.559517i
$135$		0			0
$136$	−3.33597	−	1.20723i	−0.286057	−	0.103519i
$137$		−	19.3027i		−	1.64914i	−0.565761	−	0.824570i	$-0.691417\pi$
$137$		−	19.3027i		−	1.64914i	0.565761	−	0.824570i	$-0.308583\pi$
$138$		0			0
$139$	15.3098			1.29856			0.649280	−	0.760550i	$-0.275070\pi$
$139$	15.3098			1.29856			0.649280	+	0.760550i	$0.275070\pi$
$140$	−0.772020	−	0.726570i	−0.0652476	−	0.0614064i
$141$		0			0
$142$	20.7769	−	8.97746i	1.74356	−	0.753372i
$143$	−3.96814			−0.331832
$144$		0			0
$145$	−2.87952			−0.239131
$146$	17.0782	−	7.37929i	1.41340	−	0.610714i
$147$		0			0
$148$	−7.78206	−	7.32392i	−0.639681	−	0.602022i
$149$	−1.53793			−0.125992			−0.0629962	−	0.998014i	$-0.520066\pi$
$149$	−1.53793			−0.125992			−0.0629962	+	0.998014i	$0.520066\pi$
$150$		0			0
$151$			10.1304i			0.824398i	0.911094	+	0.412199i	$0.135239\pi$
$151$			10.1304i			0.824398i	−0.911094	+	0.412199i	$0.864761\pi$
$152$	−0.00351232	+	0.00970571i	−0.000284887	+	0.000787237i
$153$		0			0
$154$	1.17507	−	0.507731i	0.0946895	−	0.0409142i
$155$		−	1.85501i		−	0.148998i
$156$		0			0
$157$		−	2.61643i		−	0.208814i	−0.994535	−	0.104407i	$-0.966706\pi$
$157$		−	2.61643i		−	0.208814i	0.994535	−	0.104407i	$-0.0332945\pi$
$158$	−1.10443	−	2.55603i	−0.0878636	−	0.203347i
$159$		0			0
$160$	1.35398	+	2.67546i	0.107042	+	0.211514i
$161$			0.778929i			0.0613882i
$162$		0			0
$163$	14.4604			1.13262			0.566312	−	0.824191i	$-0.308370\pi$
$163$	14.4604			1.13262			0.566312	+	0.824191i	$0.308370\pi$
$164$	−2.54203	−	2.39238i	−0.198499	−	0.186813i
$165$		0			0
$166$	3.26782	+	7.56286i	0.253632	+	0.586992i
$167$	−7.65107			−0.592058			−0.296029	−	0.955179i	$-0.595662\pi$
$167$	−7.65107			−0.592058			−0.296029	+	0.955179i	$0.595662\pi$
$168$		0			0
$169$	−6.21931			−0.478409
$170$	−0.372953	−	0.863143i	−0.0286042	−	0.0662000i
$171$		0			0
$172$	−0.355685	+	0.377935i	−0.0271208	+	0.0288172i
$173$	9.98644			0.759255			0.379628	−	0.925139i	$-0.376052\pi$
$173$	9.98644			0.759255			0.379628	+	0.925139i	$0.376052\pi$
$174$		0			0
$175$			4.71902i			0.356724i
$176$	−3.61392	+	0.219409i	−0.272410	+	0.0165386i
$177$		0			0
$178$	−1.09098	−	2.52490i	−0.0817721	−	0.189249i
$179$		−	16.1143i		−	1.20444i	−0.798331	−	0.602219i	$-0.794283\pi$
$179$		−	16.1143i		−	1.20444i	0.798331	−	0.602219i	$-0.205717\pi$
$180$		0			0
$181$		−	20.4077i		−	1.51689i	−0.651736	−	0.758446i	$-0.725959\pi$
$181$		−	20.4077i		−	1.51689i	0.651736	−	0.758446i	$-0.274041\pi$
$182$	5.69133	−	2.45915i	0.421869	−	0.182284i
$183$		0			0
$184$	0.749699	−	2.07167i	0.0552685	−	0.152725i
$185$		−	2.83231i		−	0.208236i
$186$		0			0
$187$	1.13532			0.0830228
$188$	5.15280	−	5.47513i	0.375807	−	0.399315i
$189$		0			0
$190$	−0.00251124	+	0.00108507i	−0.000182184	+	7.87196e-5i
$191$	4.05526			0.293428			0.146714	−	0.989179i	$-0.453130\pi$
$191$	4.05526			0.293428			0.146714	+	0.989179i	$0.453130\pi$
$192$		0			0
$193$	−5.82186			−0.419066			−0.209533	−	0.977802i	$-0.567194\pi$
$193$	−5.82186			−0.419066			−0.209533	+	0.977802i	$0.567194\pi$
$194$	17.9208	−	7.74334i	1.28664	−	0.555939i
$195$		0			0
$196$	−1.37069	+	1.45643i	−0.0979066	+	0.104031i
$197$	−15.4557			−1.10118			−0.550588	−	0.834777i	$-0.685596\pi$
$197$	−15.4557			−1.10118			−0.550588	+	0.834777i	$0.685596\pi$
$198$		0			0
$199$			13.6803i			0.969771i	0.874578	+	0.484885i	$0.161139\pi$
$199$			13.6803i			0.969771i	−0.874578	+	0.484885i	$0.838861\pi$
$200$	4.54193	−	12.5509i	0.321163	−	0.887480i
$201$		0			0
$202$	7.03160	−	3.03827i	0.494742	−	0.213772i
$203$			5.43228i			0.381271i
$204$		0			0
$205$		−	0.925182i		−	0.0646175i
$206$	1.20260	+	2.78324i	0.0837892	+	0.193917i
$207$		0			0
$208$	−17.5037	+	1.06269i	−1.21366	+	0.0736841i
$209$		−	0.00330311i		−	0.000228481i
$210$		0			0
$211$	10.9961			0.757000			0.378500	−	0.925601i	$-0.376440\pi$
$211$	10.9961			0.757000			0.378500	+	0.925601i	$0.376440\pi$
$212$	−4.22292	+	4.48708i	−0.290032	+	0.308174i
$213$		0			0
$214$	5.10638	+	11.8179i	0.349065	+	0.807857i
$215$	−0.137551			−0.00938089
$216$		0			0
$217$	−3.49953			−0.237563
$218$	0.726795	+	1.68206i	0.0492248	+	0.113923i
$219$		0			0
$220$	−0.698789	−	0.657651i	−0.0471123	−	0.0443388i
$221$	5.49882			0.369891
$222$		0			0
$223$			18.7956i			1.25864i	0.777144	+	0.629322i	$0.216668\pi$
$223$			18.7956i			1.25864i	−0.777144	+	0.629322i	$0.783332\pi$
$224$	5.04732	−	2.55432i	0.337238	−	0.170668i
$225$		0			0
$226$	7.89399	+	18.2694i	0.525100	+	1.21526i
$227$		−	18.8278i		−	1.24965i	−0.780767	−	0.624823i	$-0.785171\pi$
$227$		−	18.8278i		−	1.24965i	0.780767	−	0.624823i	$-0.214829\pi$
$228$		0			0
$229$		−	15.7721i		−	1.04225i	−0.853480	−	0.521126i	$-0.825512\pi$
$229$		−	15.7721i		−	1.04225i	0.853480	−	0.521126i	$-0.174488\pi$
$230$	0.536019	−	0.231607i	0.0353440	−	0.0152717i
$231$		0			0
$232$	5.22843	−	14.4479i	0.343263	−	0.948549i
$233$			4.23089i			0.277175i	0.990350	+	0.138587i	$0.0442562\pi$
$233$			4.23089i			0.277175i	−0.990350	+	0.138587i	$0.955744\pi$
$234$		0			0
$235$	1.99269			0.129989
$236$	8.34977	+	7.85821i	0.543524	+	0.511526i
$237$		0			0
$238$	−1.62834	+	0.703586i	−0.105550	+	0.0456067i
$239$	−7.80160			−0.504644			−0.252322	−	0.967643i	$-0.581194\pi$
$239$	−7.80160			−0.504644			−0.252322	+	0.967643i	$0.581194\pi$
$240$		0			0
$241$	−20.2165			−1.30226			−0.651129	−	0.758967i	$-0.725704\pi$
$241$	−20.2165			−1.30226			−0.651129	+	0.758967i	$0.725704\pi$
$242$	−13.2167	+	5.71077i	−0.849601	+	0.367102i
$243$		0			0
$244$	0.809237	+	0.761597i	0.0518061	+	0.0487562i
$245$	−0.530075			−0.0338653
$246$		0			0
$247$		−	0.0159983i		−	0.00101795i
$248$	9.30745	+	3.36820i	0.591024	+	0.213881i
$249$		0			0
$250$	6.68813	−	2.88986i	0.422994	−	0.182771i
$251$			12.7749i			0.806345i	0.915124	+	0.403172i	$0.132093\pi$
$251$			12.7749i			0.806345i	−0.915124	+	0.403172i	$0.867907\pi$
$252$		0			0
$253$			0.705043i			0.0443257i
$254$	6.45167	+	14.9314i	0.404814	+	0.936879i
$255$		0			0
$256$	−15.8825	+	1.93565i	−0.992655	+	0.120978i
$257$		−	20.3263i		−	1.26792i	−0.773365	−	0.633961i	$-0.781428\pi$
$257$		−	20.3263i		−	1.26792i	0.773365	−	0.633961i	$-0.218572\pi$
$258$		0			0
$259$	−5.34322			−0.332012
$260$	−3.38452	−	3.18527i	−0.209899	−	0.197542i
$261$		0			0
$262$	5.76802	+	13.3492i	0.356350	+	0.824716i
$263$	4.85204			0.299190			0.149595	−	0.988747i	$-0.452203\pi$
$263$	4.85204			0.299190			0.149595	+	0.988747i	$0.452203\pi$
$264$		0			0
$265$	−1.63309			−0.100320
$266$	0.00204702	+	0.00473751i	0.000125511	+	0.000290476i
$267$		0			0
$268$	15.8267	−	16.8167i	0.966768	−	1.02724i
$269$	−31.3976			−1.91435			−0.957174	−	0.289514i	$-0.906506\pi$
$269$	−31.3976			−1.91435			−0.957174	+	0.289514i	$0.906506\pi$
$270$		0			0
$271$			24.4088i			1.48273i	0.671103	+	0.741364i	$0.265821\pi$
$271$			24.4088i			1.48273i	−0.671103	+	0.741364i	$0.734179\pi$
$272$	5.00797	−	0.304045i	0.303653	−	0.0184354i
$273$		0			0
$274$	10.8276	+	25.0589i	0.654122	+	1.51386i
$275$			4.27139i			0.257575i
$276$		0			0
$277$			12.8387i			0.771402i	0.922624	+	0.385701i	$0.126040\pi$
$277$			12.8387i			0.771402i	−0.922624	+	0.385701i	$0.873960\pi$
$278$	−19.8753	+	8.58787i	−1.19204	+	0.515066i
$279$		0			0
$280$	1.40980	+	0.510183i	0.0842520	+	0.0304893i
$281$			27.8988i			1.66431i	0.554547	+	0.832153i	$0.312892\pi$
$281$			27.8988i			1.66431i	−0.554547	+	0.832153i	$0.687108\pi$
$282$		0			0
$283$	6.65773			0.395761			0.197880	−	0.980226i	$-0.436594\pi$
$283$	6.65773			0.395761			0.197880	+	0.980226i	$0.436594\pi$
$284$	−21.9370	+	23.3092i	−1.30172	+	1.38315i
$285$		0			0
$286$	5.15147	−	2.22589i	0.304613	−	0.131619i
$287$	−1.74538			−0.103026
$288$		0			0
$289$	15.4267			0.907455
$290$	3.73821	−	1.61524i	0.219515	−	0.0948499i
$291$		0			0
$292$	−18.0318	+	19.1597i	−1.05523	+	1.12124i
$293$	24.0566			1.40540			0.702699	−	0.711487i	$-0.251978\pi$
$293$	24.0566			1.40540			0.702699	+	0.711487i	$0.251978\pi$
$294$		0			0
$295$			3.03893i			0.176933i
$296$	14.2110	+	5.14271i	0.825998	+	0.298914i
$297$		0			0
$298$	1.99656	−	0.862688i	0.115657	−	0.0499742i
$299$			3.41481i			0.197484i
$300$		0			0
$301$			0.259493i			0.0149569i
$302$	−5.68253	−	13.1513i	−0.326993	−	0.756774i
$303$		0			0
$304$	−0.000884591	−	0.0145702i	−5.07348e−5	−	0.000835661i
$305$			0.294525i			0.0168645i
$306$		0			0
$307$	23.6311			1.34870			0.674350	−	0.738411i	$-0.264424\pi$
$307$	23.6311			1.34870			0.674350	+	0.738411i	$0.264424\pi$
$308$	−1.24067	+	1.31828i	−0.0706940	+	0.0751161i
$309$		0			0
$310$	1.04055	+	2.40819i	0.0590993	+	0.136776i
$311$	−25.7037			−1.45752			−0.728761	−	0.684768i	$-0.759904\pi$
$311$	−25.7037			−1.45752			−0.728761	+	0.684768i	$0.759904\pi$
$312$		0			0
$313$	−9.99902			−0.565178			−0.282589	−	0.959241i	$-0.591193\pi$
$313$	−9.99902			−0.565178			−0.282589	+	0.959241i	$0.591193\pi$
$314$	1.46766	+	3.39668i	0.0828250	+	0.191686i
$315$		0			0
$316$	2.86756	+	2.69874i	0.161313	+	0.151816i
$317$	23.7177			1.33212			0.666059	−	0.745899i	$-0.267980\pi$
$317$	23.7177			1.33212			0.666059	+	0.745899i	$0.267980\pi$
$318$		0			0
$319$			4.91700i			0.275299i
$320$	−3.25852	−	2.71380i	−0.182157	−	0.151706i
$321$		0			0
$322$	−0.436933	−	1.01121i	−0.0243493	−	0.0563527i
$323$			0.00457727i			0.000254686i
$324$		0			0
$325$			20.6881i			1.14757i
$326$	−18.7726	+	8.11140i	−1.03972	+	0.449249i
$327$		0			0
$328$	4.64207	+	1.67988i	0.256315	+	0.0927559i
$329$		−	3.75927i		−	0.207255i
$330$		0			0
$331$	12.8674			0.707254			0.353627	−	0.935386i	$-0.384948\pi$
$331$	12.8674			0.707254			0.353627	+	0.935386i	$0.384948\pi$
$332$	−8.48462	−	7.98512i	−0.465654	−	0.438241i
$333$		0			0
$334$	9.93269	−	4.29179i	0.543493	−	0.234836i
$335$	6.12050			0.334398
$336$		0			0
$337$	−10.2878			−0.560412			−0.280206	−	0.959940i	$-0.590403\pi$
$337$	−10.2878			−0.560412			−0.280206	+	0.959940i	$0.590403\pi$
$338$	8.07397	−	3.48866i	0.439166	−	0.189758i
$339$		0			0
$340$	0.968342	+	0.911335i	0.0525157	+	0.0494241i
$341$	−3.16758			−0.171534
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	0.249755	−	0.690156i	0.0134659	−	0.0372107i
$345$		0			0
$346$	−12.9645	+	5.60179i	−0.696975	+	0.301154i
$347$			2.21263i			0.118780i	0.998235	+	0.0593901i	$0.0189156\pi$
$347$			2.21263i			0.118780i	−0.998235	+	0.0593901i	$0.981084\pi$
$348$		0			0
$349$			8.10593i			0.433900i	0.976183	+	0.216950i	$0.0696109\pi$
$349$			8.10593i			0.433900i	−0.976183	+	0.216950i	$0.930389\pi$
$350$	−2.64709	−	6.12627i	−0.141493	−	0.327463i
$351$		0			0
$352$	4.56855	−	2.31203i	0.243505	−	0.123232i
$353$			16.8821i			0.898546i	0.893395	+	0.449273i	$0.148317\pi$
$353$			16.8821i			0.898546i	−0.893395	+	0.449273i	$0.851683\pi$
$354$		0			0
$355$	−8.48349			−0.450257
$356$	2.83263	+	2.66587i	0.150129	+	0.141291i
$357$		0			0
$358$	9.03915	+	20.9197i	0.477734	+	1.10564i
$359$	6.06059			0.319866			0.159933	−	0.987128i	$-0.448872\pi$
$359$	6.06059			0.319866			0.159933	+	0.987128i	$0.448872\pi$
$360$		0			0
$361$	−19.0000			−0.999999
$362$	11.4475	+	26.4935i	0.601667	+	1.39247i
$363$		0			0
$364$	−6.00909	+	6.38498i	−0.314962	+	0.334664i
$365$	−6.97325			−0.364997
$366$		0			0
$367$		−	4.36701i		−	0.227956i	−0.993483	−	0.113978i	$-0.963641\pi$
$367$		−	4.36701i		−	0.227956i	0.993483	−	0.113978i	$-0.0363594\pi$
$368$	0.188814	+	3.10999i	0.00984262	+	0.162120i
$369$		0			0
$370$	1.58876	+	3.67693i	0.0825955	+	0.191154i
$371$			3.08087i			0.159951i
$372$		0			0
$373$		−	10.3873i		−	0.537835i	−0.963163	−	0.268918i	$-0.913334\pi$
$373$		−	10.3873i		−	0.537835i	0.963163	−	0.268918i	$-0.0866660\pi$
$374$	−1.47388	+	0.636846i	−0.0762127	+	0.0329305i
$375$		0			0
$376$	−3.61820	+	9.99827i	−0.186594	+	0.515621i
$377$			23.8150i			1.22654i
$378$		0			0
$379$	28.3525			1.45637			0.728186	−	0.685380i	$-0.240364\pi$
$379$	28.3525			1.45637			0.728186	+	0.685380i	$0.240364\pi$
$380$	0.00265145	−	0.00281731i	0.000136016	−	0.000144525i
$381$		0			0
$382$	−5.26458	+	2.27476i	−0.269359	+	0.116387i
$383$	26.3164			1.34470			0.672352	−	0.740232i	$-0.265284\pi$
$383$	26.3164			1.34470			0.672352	+	0.740232i	$0.265284\pi$
$384$		0			0
$385$	−0.479794			−0.0244526
$386$	7.55798	−	3.26571i	0.384691	−	0.166220i
$387$		0			0
$388$	−18.9213	+	20.1049i	−0.960586	+	1.02067i
$389$	17.5966			0.892182			0.446091	−	0.894988i	$-0.352816\pi$
$389$	17.5966			0.892182			0.446091	+	0.894988i	$0.352816\pi$
$390$		0			0
$391$		−	0.977009i		−	0.0494095i
$392$	0.962474	−	2.65963i	0.0486123	−	0.134332i
$393$		0			0
$394$	20.0648	−	8.66974i	1.01085	−	0.436775i
$395$			1.04366i			0.0525121i
$396$		0			0
$397$			5.06951i			0.254431i	0.991875	+	0.127216i	$0.0406040\pi$
$397$			5.06951i			0.254431i	−0.991875	+	0.127216i	$0.959396\pi$
$398$	−7.67383	−	17.7599i	−0.384654	−	0.890223i
$399$		0			0
$400$	1.14390	+	18.8414i	0.0571950	+	0.942069i
$401$		−	16.6708i		−	0.832498i	−0.909251	−	0.416249i	$-0.863345\pi$
$401$		−	16.6708i		−	0.832498i	0.909251	−	0.416249i	$-0.136655\pi$
$402$		0			0
$403$	−15.3419			−0.764233
$404$	−7.42420	+	7.88861i	−0.369368	+	0.392473i
$405$		0			0
$406$	−3.04718	−	7.05223i	−0.151229	−	0.349996i
$407$	−4.83639			−0.239731
$408$		0			0
$409$	−5.09197			−0.251782			−0.125891	−	0.992044i	$-0.540179\pi$
$409$	−5.09197			−0.251782			−0.125891	+	0.992044i	$0.540179\pi$
$410$	0.518972	+	1.20108i	0.0256302	+	0.0593171i
$411$		0			0
$412$	−3.12246	−	2.93863i	−0.153832	−	0.144776i
$413$	5.73302			0.282104
$414$		0			0
$415$		−	3.08801i		−	0.151584i
$416$	22.1274	−	11.1981i	1.08488	−	0.549033i
$417$		0			0
$418$	0.00185285	+	0.00428813i	9.06258e−5	+	0.000209739i
$419$			37.4571i			1.82990i	0.403570	+	0.914949i	$0.367769\pi$
$419$			37.4571i			1.82990i	−0.403570	+	0.914949i	$0.632231\pi$
$420$		0			0
$421$			35.9612i			1.75264i	0.481728	+	0.876321i	$0.340009\pi$
$421$			35.9612i			1.75264i	−0.481728	+	0.876321i	$0.659991\pi$
$422$	−14.2752	+	6.16813i	−0.694905	+	0.300260i
$423$		0			0
$424$	2.96525	−	8.19398i	0.144005	−	0.397935i
$425$		−	5.91906i		−	0.287116i
$426$		0			0
$427$	0.555629			0.0268888
$428$	−13.2583	−	12.4778i	−0.640864	−	0.603136i
$429$		0			0
$430$	0.178570	−	0.0771577i	0.00861140	−	0.00372088i
$431$	20.6573			0.995025			0.497513	−	0.867457i	$-0.334247\pi$
$431$	20.6573			0.995025			0.497513	+	0.867457i	$0.334247\pi$
$432$		0			0
$433$	23.8116			1.14431			0.572157	−	0.820144i	$-0.306107\pi$
$433$	23.8116			1.14431			0.572157	+	0.820144i	$0.306107\pi$
$434$	4.54312	−	1.96302i	0.218077	−	0.0942282i
$435$		0			0
$436$	−1.88706	−	1.77597i	−0.0903740	−	0.0850536i
$437$	−0.00284252			−0.000135976
$438$		0			0
$439$			26.5607i			1.26767i	0.773467	+	0.633836i	$0.218521\pi$
$439$			26.5607i			1.26767i	−0.773467	+	0.633836i	$0.781479\pi$
$440$	1.27608	+	0.461789i	0.0608346	+	0.0220149i
$441$		0			0
$442$	−7.13862	+	3.08451i	−0.339549	+	0.146715i
$443$			0.346564i			0.0164658i	0.999966	+	0.00823288i	$0.00262064\pi$
$443$			0.346564i			0.0164658i	−0.999966	+	0.00823288i	$0.997379\pi$
$444$		0			0
$445$			1.03095i			0.0488716i
$446$	−10.5432	−	24.4006i	−0.499234	−	1.15540i
$447$		0			0
$448$	−5.11965	+	6.14729i	−0.241881	+	0.290432i
$449$			10.4601i			0.493641i	0.969061	+	0.246821i	$0.0793859\pi$
$449$			10.4601i			0.493641i	−0.969061	+	0.246821i	$0.920614\pi$
$450$		0			0
$451$	−1.57982			−0.0743908
$452$	−20.4961	−	19.2895i	−0.964055	−	0.907300i
$453$		0			0
$454$	10.5613	+	24.4424i	0.495665	+	1.14714i
$455$	−2.32384			−0.108943
$456$		0			0
$457$	−11.0889			−0.518717			−0.259359	−	0.965781i	$-0.583511\pi$
$457$	−11.0889			−0.518717			−0.259359	+	0.965781i	$0.583511\pi$
$458$	8.84721	+	20.4755i	0.413403	+	0.956758i
$459$		0			0
$460$	−0.565947	+	0.601349i	−0.0263874	+	0.0280380i
$461$	−37.8447			−1.76261			−0.881303	−	0.472553i	$-0.843333\pi$
$461$	−37.8447			−1.76261			−0.881303	+	0.472553i	$0.843333\pi$
$462$		0			0
$463$		−	18.1959i		−	0.845634i	−0.906215	−	0.422817i	$-0.861041\pi$
$463$		−	18.1959i		−	0.845634i	0.906215	−	0.422817i	$-0.138959\pi$
$464$	1.31680	+	21.6892i	0.0611307	+	1.00690i
$465$		0			0
$466$	−2.37327	−	5.49258i	−0.109940	−	0.254439i
$467$		−	6.19184i		−	0.286524i	−0.989685	−	0.143262i	$-0.954241\pi$
$467$		−	6.19184i		−	0.286524i	0.989685	−	0.143262i	$-0.0457592\pi$
$468$		0			0
$469$		−	11.5465i		−	0.533167i
$470$	−2.58693	+	1.11778i	−0.119326	+	0.0515594i
$471$		0			0
$472$	−15.2477	−	5.51788i	−0.701834	−	0.253981i
$473$			0.234879i			0.0107997i
$474$		0			0
$475$	−0.0172210			−0.000790152
$476$	1.71926	−	1.82680i	0.0788020	−	0.0837314i
$477$		0			0
$478$	10.1281	−	4.37623i	0.463249	−	0.200164i
$479$	−4.17517			−0.190769			−0.0953843	−	0.995441i	$-0.530408\pi$
$479$	−4.17517			−0.190769			−0.0953843	+	0.995441i	$0.530408\pi$
$480$		0			0
$481$	−23.4246			−1.06807
$482$	26.2452	−	11.3402i	1.19544	−	0.516533i
$483$		0			0
$484$	13.9546	−	14.8275i	0.634301	−	0.673979i
$485$	−7.31727			−0.332260
$486$		0			0
$487$		−	16.4966i		−	0.747534i	−0.927523	−	0.373767i	$-0.878066\pi$
$487$		−	16.4966i		−	0.747534i	0.927523	−	0.373767i	$-0.121934\pi$
$488$	−1.47777	−	0.534778i	−0.0668955	−	0.0242083i
$489$		0			0
$490$	0.688148	−	0.297340i	0.0310874	−	0.0134325i
$491$			25.1039i			1.13292i	0.824089	+	0.566461i	$0.191688\pi$
$491$			25.1039i			1.13292i	−0.824089	+	0.566461i	$0.808312\pi$
$492$		0			0
$493$		−	6.81370i		−	0.306873i
$494$	0.00897410	+	0.0207692i	0.000403764	+	0.000934450i
$495$		0			0
$496$	−13.9724	+	0.848293i	−0.627378	+	0.0380895i
$497$			16.0043i			0.717892i
$498$		0			0
$499$	37.1869			1.66472			0.832358	−	0.554238i	$-0.186990\pi$
$499$	37.1869			1.66472			0.832358	+	0.554238i	$0.186990\pi$
$500$	−7.06155	+	7.50327i	−0.315802	+	0.335557i
$501$		0			0
$502$	−7.16595	−	16.5845i	−0.319832	−	0.740202i
$503$	−8.24722			−0.367725			−0.183863	−	0.982952i	$-0.558860\pi$
$503$	−8.24722			−0.367725			−0.183863	+	0.982952i	$0.558860\pi$
$504$		0			0
$505$	−2.87109			−0.127762
$506$	−0.395487	−	0.915294i	−0.0175815	−	0.0406898i
$507$		0			0
$508$	−16.7512	−	15.7651i	−0.743216	−	0.699462i
$509$	29.7128			1.31700			0.658498	−	0.752582i	$-0.271192\pi$
$509$	29.7128			1.31700			0.658498	+	0.752582i	$0.271192\pi$
$510$		0			0
$511$			13.1552i			0.581953i
$512$	19.5330	−	11.4220i	0.863245	−	0.504786i
$513$		0			0
$514$	11.4019	+	26.3878i	0.502914	+	1.16392i
$515$		−	1.13643i		−	0.0500771i
$516$		0			0
$517$		−	3.40268i		−	0.149650i
$518$	6.93662	−	2.99723i	0.304778	−	0.131691i
$519$		0			0
$520$	6.18056	+	2.23663i	0.271036	+	0.0980829i
$521$			9.22757i			0.404267i	0.979358	+	0.202134i	$0.0647875\pi$
$521$			9.22757i			0.404267i	−0.979358	+	0.202134i	$0.935212\pi$
$522$		0			0
$523$	1.55380			0.0679431			0.0339716	−	0.999423i	$-0.489184\pi$
$523$	1.55380			0.0679431			0.0339716	+	0.999423i	$0.489184\pi$
$524$	−14.9762	−	14.0945i	−0.654238	−	0.615723i
$525$		0			0
$526$	−6.29896	+	2.72170i	−0.274648	+	0.118672i
$527$	4.38945			0.191207
$528$		0			0
$529$	−22.3933			−0.973620
$530$	2.12009	−	0.916066i	0.0920910	−	0.0397914i
$531$		0			0
$532$	−0.00531492	−	0.00500203i	−0.000230431	−	0.000216865i
$533$	−7.65171			−0.331433
$534$		0			0
$535$		−	4.82541i		−	0.208621i
$536$	−11.1132	+	30.7094i	−0.480016	+	1.32644i
$537$		0			0
$538$	40.7607	−	17.6122i	1.75732	−	0.759315i
$539$			0.905144i			0.0389873i
$540$		0			0
$541$		−	7.33522i		−	0.315366i	−0.987490	−	0.157683i	$-0.949598\pi$
$541$		−	7.33522i		−	0.315366i	0.987490	−	0.157683i	$-0.0504024\pi$
$542$	−13.6919	−	31.6877i	−0.588116	−	1.36110i
$543$		0			0
$544$	−6.33084	+	3.20388i	−0.271433	+	0.137365i
$545$		−	0.686805i		−	0.0294195i
$546$		0			0
$547$	21.4488			0.917086			0.458543	−	0.888672i	$-0.348372\pi$
$547$	21.4488			0.917086			0.458543	+	0.888672i	$0.348372\pi$
$548$	−28.1131	−	26.4580i	−1.20093	−	1.13023i
$549$		0			0
$550$	−2.39600	−	5.54516i	−0.102166	−	0.236446i
$551$	−0.0198238			−0.000844524
$552$		0			0
$553$	1.96889			0.0837256
$554$	−7.20173	−	16.6673i	−0.305972	−	0.708126i
$555$		0			0
$556$	20.9850	−	22.2977i	0.889963	−	0.945633i
$557$	29.9101			1.26733			0.633666	−	0.773607i	$-0.281549\pi$
$557$	29.9101			1.26733			0.633666	+	0.773607i	$0.281549\pi$
$558$		0			0
$559$			1.13761i			0.0481159i
$560$	−2.11640	+	0.128491i	−0.0894344	+	0.00542975i
$561$		0			0
$562$	−15.6496	−	36.2185i	−0.660137	−	1.52779i
$563$			42.7436i			1.80143i	0.434414	+	0.900713i	$0.356956\pi$
$563$			42.7436i			1.80143i	−0.434414	+	0.900713i	$0.643044\pi$
$564$		0			0
$565$		−	7.45963i		−	0.313829i
$566$	−8.64312	+	3.73458i	−0.363297	+	0.156976i
$567$		0			0
$568$	15.4037	−	42.5656i	0.646326	−	1.78601i
$569$			20.9180i			0.876927i	0.898749	+	0.438464i	$0.144477\pi$
$569$			20.9180i			0.876927i	−0.898749	+	0.438464i	$0.855523\pi$
$570$		0			0
$571$	−5.23949			−0.219266			−0.109633	−	0.993972i	$-0.534968\pi$
$571$	−5.23949			−0.219266			−0.109633	+	0.993972i	$0.534968\pi$
$572$	−5.43910	+	5.77933i	−0.227420	+	0.241646i
$573$		0			0
$574$	2.26587	−	0.979053i	0.0945755	−	0.0408649i
$575$	3.67578			0.153291
$576$		0			0
$577$	−5.71213			−0.237799			−0.118900	−	0.992906i	$-0.537937\pi$
$577$	−5.71213			−0.237799			−0.118900	+	0.992906i	$0.537937\pi$
$578$	−20.0271	+	8.65347i	−0.833019	+	0.359937i
$579$		0			0
$580$	−3.94693	+	4.19383i	−0.163887	+	0.174139i
$581$	−5.82561			−0.241687
$582$		0			0
$583$			2.78863i			0.115493i
$584$	12.6615	−	34.9880i	0.523939	−	1.44782i
$585$		0			0
$586$	−31.2304	+	13.4943i	−1.29012	+	0.557444i
$587$		−	28.8731i		−	1.19172i	−0.803088	−	0.595860i	$-0.796811\pi$
$587$		−	28.8731i		−	1.19172i	0.803088	−	0.595860i	$-0.203189\pi$
$588$		0			0
$589$		−	0.0127707i		−	0.000526208i
$590$	−1.70466	−	3.94517i	−0.0701797	−	0.162420i
$591$		0			0
$592$	−21.3336	+	1.29521i	−0.876806	+	0.0532328i
$593$			32.7752i			1.34592i	0.739680	+	0.672958i	$0.234977\pi$
$593$			32.7752i			1.34592i	−0.739680	+	0.672958i	$0.765023\pi$
$594$		0			0
$595$	0.664872			0.0272571
$596$	−2.10803	+	2.23990i	−0.0863484	+	0.0917498i
$597$		0			0
$598$	−1.91551	−	4.43314i	−0.0783308	−	0.181285i
$599$	18.9096			0.772625			0.386313	−	0.922368i	$-0.373749\pi$
$599$	18.9096			0.772625			0.386313	+	0.922368i	$0.373749\pi$
$600$		0			0
$601$	36.4186			1.48555			0.742773	−	0.669543i	$-0.233510\pi$
$601$	36.4186			1.48555			0.742773	+	0.669543i	$0.233510\pi$
$602$	−0.145560	−	0.336876i	−0.00593258	−	0.0137301i
$603$		0			0
$604$	14.7542	+	13.8856i	0.600341	+	0.564998i
$605$	5.39654			0.219401
$606$		0			0
$607$		−	8.21476i		−	0.333427i	−0.986005	−	0.166713i	$-0.946685\pi$
$607$		−	8.21476i		−	0.333427i	0.986005	−	0.166713i	$-0.0533155\pi$
$608$	0.00932142	+	0.0184190i	0.000378033	+	0.000746990i
$609$		0			0
$610$	−0.165211	−	0.382355i	−0.00668919	−	0.0154811i
$611$		−	16.4806i		−	0.666732i
$612$		0			0
$613$		−	27.6348i		−	1.11616i	−0.829787	−	0.558080i	$-0.811538\pi$
$613$		−	27.6348i		−	1.11616i	0.829787	−	0.558080i	$-0.188462\pi$
$614$	−30.6782	+	13.2557i	−1.23807	+	0.534955i
$615$		0			0
$616$	0.871177	−	2.40735i	0.0351007	−	0.0969949i
$617$		−	23.3314i		−	0.939287i	−0.882856	−	0.469643i	$-0.844383\pi$
$617$		−	23.3314i		−	0.939287i	0.882856	−	0.469643i	$-0.155617\pi$
$618$		0			0
$619$	−22.9819			−0.923719			−0.461859	−	0.886953i	$-0.652818\pi$
$619$	−22.9819			−0.923719			−0.461859	+	0.886953i	$0.652818\pi$
$620$	−2.70170	−	2.54265i	−0.108503	−	0.102115i
$621$		0			0
$622$	33.3688	−	14.4182i	1.33797	−	0.578118i
$623$	1.94491			0.0779211
$624$		0			0
$625$	20.8643			0.834570
$626$	12.9808	−	5.60885i	0.518818	−	0.224175i
$627$		0			0
$628$	−3.81067	−	3.58633i	−0.152062	−	0.143110i
$629$	6.70199			0.267226
$630$		0			0
$631$		−	44.4382i		−	1.76906i	−0.466486	−	0.884528i	$-0.654480\pi$
$631$		−	44.4382i		−	1.76906i	0.466486	−	0.884528i	$-0.345520\pi$
$632$	−5.23652	−	1.89500i	−0.208297	−	0.0753791i
$633$		0			0
$634$	−30.7905	+	13.3042i	−1.22285	+	0.528377i
$635$		−	6.09668i		−	0.241939i
$636$		0			0
$637$			4.38398i			0.173700i
$638$	−2.75814	−	6.38329i	−0.109196	−	0.252717i
$639$		0			0
$640$	5.75252	+	1.69524i	0.227388	+	0.0670103i
$641$		−	37.6567i		−	1.48735i	−0.668541	−	0.743675i	$-0.733081\pi$
$641$		−	37.6567i		−	1.48735i	0.668541	−	0.743675i	$-0.266919\pi$
$642$		0			0
$643$	−22.1342			−0.872886			−0.436443	−	0.899732i	$-0.643762\pi$
$643$	−22.1342			−0.872886			−0.436443	+	0.899732i	$0.643762\pi$
$644$	1.13446	+	1.06767i	0.0447040	+	0.0420722i
$645$		0			0
$646$	−0.00256757	−	0.00594225i	−0.000101020	−	0.000233795i
$647$	20.8560			0.819936			0.409968	−	0.912100i	$-0.365540\pi$
$647$	20.8560			0.819936			0.409968	+	0.912100i	$0.365540\pi$
$648$		0			0
$649$	5.18921			0.203694
$650$	−11.6048	−	26.8575i	−0.455177	−	1.05344i
$651$		0			0
$652$	19.8207	−	21.0606i	0.776240	−	0.824796i
$653$	12.5052			0.489366			0.244683	−	0.969603i	$-0.421316\pi$
$653$	12.5052			0.489366			0.244683	+	0.969603i	$0.421316\pi$
$654$		0			0
$655$		−	5.45065i		−	0.212974i
$656$	−6.96869	+	0.423084i	−0.272081	+	0.0165186i
$657$		0			0
$658$	2.10872	+	4.88032i	0.0822066	+	0.190255i
$659$			27.7704i			1.08178i	0.841092	+	0.540891i	$0.181913\pi$
$659$			27.7704i			1.08178i	−0.841092	+	0.540891i	$0.818087\pi$
$660$		0			0
$661$			17.8134i			0.692862i	0.938075	+	0.346431i	$0.112607\pi$
$661$			17.8134i			0.692862i	−0.938075	+	0.346431i	$0.887393\pi$
$662$	−16.7045	+	7.21782i	−0.649240	+	0.280528i
$663$		0			0
$664$	15.4940	+	5.60700i	0.601283	+	0.217594i
$665$		−	0.00193439i		−	7.50123e-5i
$666$		0			0
$667$	4.23136			0.163839
$668$	−10.4873	+	11.1433i	−0.405765	+	0.431147i
$669$		0			0
$670$	−7.94568	+	3.43323i	−0.306969	+	0.132637i
$671$	0.502924			0.0194152
$672$		0			0
$673$	−16.2911			−0.627975			−0.313987	−	0.949427i	$-0.601665\pi$
$673$	−16.2911			−0.627975			−0.313987	+	0.949427i	$0.601665\pi$
$674$	13.3557	−	5.77083i	0.514442	−	0.222284i
$675$		0			0
$676$	−8.52477	+	9.05802i	−0.327876	+	0.348385i
$677$	4.61803			0.177485			0.0887426	−	0.996055i	$-0.471715\pi$
$677$	4.61803			0.177485			0.0887426	+	0.996055i	$0.471715\pi$
$678$		0			0
$679$			13.8042i			0.529757i
$680$	−1.76832	−	0.639922i	−0.0678118	−	0.0245399i
$681$		0			0
$682$	4.11217	−	1.77682i	0.157463	−	0.0680379i
$683$		−	30.9791i		−	1.18538i	−0.805429	−	0.592692i	$-0.798065\pi$
$683$		−	30.9791i		−	1.18538i	0.805429	−	0.592692i	$-0.201935\pi$
$684$		0			0
$685$		−	10.2319i		−	0.390940i
$686$	−0.560940	−	1.29821i	−0.0214168	−	0.0495658i
$687$		0			0
$688$	0.0629017	+	1.03606i	0.00239810	+	0.0394996i
$689$			13.5065i			0.514556i
$690$		0			0
$691$	−29.0382			−1.10467			−0.552333	−	0.833624i	$-0.686262\pi$
$691$	−29.0382			−1.10467			−0.552333	+	0.833624i	$0.686262\pi$
$692$	13.6883	−	14.5446i	0.520353	−	0.552903i
$693$		0			0
$694$	−1.24115	−	2.87246i	−0.0471135	−	0.109037i
$695$	8.11534			0.307832
$696$		0			0
$697$	2.18923			0.0829228
$698$	−4.54694	−	10.5232i	−0.172104	−	0.398309i
$699$		0			0
$700$	6.87294	+	6.46833i	0.259773	+	0.244480i
$701$	27.6010			1.04248			0.521238	−	0.853411i	$-0.325470\pi$
$701$	27.6010			1.04248			0.521238	+	0.853411i	$0.325470\pi$
$702$		0			0
$703$		−	0.0194989i		−	0.000735413i
$704$	−4.63402	+	5.56418i	−0.174651	+	0.209708i
$705$		0			0
$706$	−9.46987	−	21.9166i	−0.356403	−	0.824840i
$707$			5.41639i			0.203704i
$708$		0			0
$709$		−	37.8212i		−	1.42040i	−0.703998	−	0.710202i	$-0.748604\pi$
$709$		−	37.8212i		−	1.42040i	0.703998	−	0.710202i	$-0.251396\pi$
$710$	11.0133	−	4.75873i	0.413323	−	0.178592i
$711$		0			0
$712$	−5.17274	−	1.87192i	−0.193857	−	0.0701533i
$713$			2.72588i			0.102085i
$714$		0			0
$715$	−2.10341			−0.0786631
$716$	−23.4694	−	22.0877i	−0.877093	−	0.825458i
$717$		0			0
$718$	−7.86792	+	3.39963i	−0.293628	+	0.126873i
$719$	41.2974			1.54013			0.770067	−	0.637963i	$-0.220223\pi$
$719$	41.2974			1.54013			0.770067	+	0.637963i	$0.220223\pi$
$720$		0			0
$721$	−2.14390			−0.0798432
$722$	24.6660	−	10.6579i	0.917972	−	0.396644i
$723$		0			0
$724$	−29.7225	−	27.9727i	−1.10463	−	1.03960i
$725$	25.6350			0.952061
$726$		0			0
$727$			11.9168i			0.441971i	0.975277	+	0.220985i	$0.0709273\pi$
$727$			11.9168i			0.441971i	−0.975277	+	0.220985i	$0.929073\pi$
$728$	4.21947	−	11.6598i	0.156384	−	0.432140i
$729$		0			0
$730$	9.05274	−	3.91158i	0.335057	−	0.144774i
$731$		−	0.325482i		−	0.0120384i
$732$		0			0
$733$		−	47.2142i		−	1.74390i	−0.489597	−	0.871949i	$-0.662856\pi$
$733$		−	47.2142i		−	1.74390i	0.489597	−	0.871949i	$-0.337144\pi$
$734$	2.44963	+	5.66929i	0.0904175	+	0.209257i
$735$		0			0
$736$	−1.98964	−	3.93151i	−0.0733391	−	0.144917i
$737$		−	10.4512i		−	0.384976i
$738$		0			0
$739$	−13.4529			−0.494874			−0.247437	−	0.968904i	$-0.579588\pi$
$739$	−13.4529			−0.494874			−0.247437	+	0.968904i	$0.579588\pi$
$740$	−4.12507	−	3.88223i	−0.151641	−	0.142713i
$741$		0			0
$742$	−1.72818	−	3.99961i	−0.0634436	−	0.146830i
$743$	−10.7698			−0.395106			−0.197553	−	0.980292i	$-0.563299\pi$
$743$	−10.7698			−0.395106			−0.197553	+	0.980292i	$0.563299\pi$
$744$		0			0
$745$	−0.815220			−0.0298673
$746$	5.82667	+	13.4849i	0.213329	+	0.493718i
$747$		0			0
$748$	1.55618	−	1.65352i	0.0568994	−	0.0604587i
$749$	−9.10325			−0.332626
$750$		0			0
$751$			14.1004i			0.514530i	0.966341	+	0.257265i	$0.0828213\pi$
$751$			14.1004i			0.514530i	−0.966341	+	0.257265i	$0.917179\pi$
$752$	−0.911255	−	15.0094i	−0.0332300	−	0.547338i
$753$		0			0
$754$	−13.3588	−	30.9169i	−0.486499	−	1.12593i
$755$			5.36986i			0.195429i
$756$		0			0
$757$			13.8374i			0.502929i	0.967866	+	0.251465i	$0.0809122\pi$
$757$			13.8374i			0.502929i	−0.967866	+	0.251465i	$0.919088\pi$
$758$	−36.8075	+	15.9041i	−1.33691	+	0.577661i
$759$		0			0
$760$	−0.00186180	+	0.00514476i	−6.75344e−5	+	0.000186620i
$761$		−	33.1367i		−	1.20121i	−0.799548	−	0.600603i	$-0.794927\pi$
$761$		−	33.1367i		−	1.20121i	0.799548	−	0.600603i	$-0.205073\pi$
$762$		0			0
$763$	−1.29567			−0.0469066
$764$	5.55852	−	5.90622i	0.201100	−	0.213680i
$765$		0			0
$766$	−34.1641	+	14.7619i	−1.23440	+	0.533369i
$767$	25.1335			0.907517
$768$		0			0
$769$	30.1190			1.08612			0.543060	−	0.839694i	$-0.317266\pi$
$769$	30.1190			1.08612			0.543060	+	0.839694i	$0.317266\pi$
$770$	0.622873	−	0.269136i	0.0224468	−	0.00969898i
$771$		0			0
$772$	−7.97998	+	8.47915i	−0.287206	+	0.305171i
$773$	16.0579			0.577561			0.288780	−	0.957395i	$-0.406750\pi$
$773$	16.0579			0.577561			0.288780	+	0.957395i	$0.406750\pi$
$774$		0			0
$775$			16.5143i			0.593212i
$776$	13.2862	−	36.7141i	0.476947	−	1.31796i
$777$		0			0
$778$	−22.8440	+	9.87063i	−0.818999	+	0.353879i
$779$		−	0.00636936i		−	0.000228206i
$780$		0			0
$781$			14.4862i			0.518357i
$782$	0.548044	+	1.26836i	0.0195980	+	0.0453565i
$783$		0			0
$784$	0.242402	+	3.99265i	0.00865722	+	0.142595i
$785$		−	1.38691i		−	0.0495008i
$786$		0			0
$787$	11.2848			0.402258			0.201129	−	0.979565i	$-0.435539\pi$
$787$	11.2848			0.402258			0.201129	+	0.979565i	$0.435539\pi$
$788$	−21.1851	+	22.5103i	−0.754687	+	0.801895i
$789$		0			0
$790$	−0.585430	−	1.35489i	−0.0208287	−	0.0482047i
$791$	−14.0728			−0.500371
$792$		0			0
$793$	2.43587			0.0865002
$794$	−2.84369	−	6.58128i	−0.100919	−	0.233561i
$795$		0			0
$796$	19.9245	+	18.7515i	0.706204	+	0.664629i
$797$	−39.3545			−1.39401			−0.697004	−	0.717068i	$-0.745484\pi$
$797$	−39.3545			−1.39401			−0.697004	+	0.717068i	$0.745484\pi$
$798$		0			0
$799$			4.71524i			0.166813i
$800$	−12.0539	−	23.8184i	−0.426170	−	0.842108i
$801$		0			0
$802$	9.35129	+	21.6421i	0.330206	+	0.764210i
$803$			11.9074i			0.420202i
$804$		0			0
$805$			0.412891i			0.0145525i
$806$	19.9169	−	8.60586i	0.701544	−	0.303129i
$807$		0			0
$808$	5.21313	−	14.4056i	0.183397	−	0.506787i
$809$		−	0.183323i		−	0.00644529i	−0.999995	−	0.00322265i	$-0.998974\pi$
$809$		−	0.183323i		−	0.00644529i	0.999995	−	0.00322265i	$-0.00102580\pi$
$810$		0			0
$811$	−46.7136			−1.64033			−0.820167	−	0.572124i	$-0.806120\pi$
$811$	−46.7136			−1.64033			−0.820167	+	0.572124i	$0.806120\pi$
$812$	7.91176	+	7.44599i	0.277648	+	0.261303i
$813$		0			0
$814$	6.27864	−	2.71292i	0.220066	−	0.0950879i
$815$	7.66508			0.268496
$816$		0			0
$817$	−0.000946960	0		−3.31299e−5	0
$818$	6.61044	−	2.85629i	0.231129	−	0.0998678i
$819$		0			0
$820$	−1.34747	−	1.26814i	−0.0470556	−	0.0442854i
$821$	−19.7408			−0.688959			−0.344480	−	0.938794i	$-0.611945\pi$
$821$	−19.7408			−0.688959			−0.344480	+	0.938794i	$0.611945\pi$
$822$		0			0
$823$		−	11.6881i		−	0.407421i	−0.979031	−	0.203711i	$-0.934700\pi$
$823$		−	11.6881i		−	0.407421i	0.979031	−	0.203711i	$-0.0653002\pi$
$824$	5.70200	+	2.06345i	0.198639	+	0.0718837i
$825$		0			0
$826$	−7.44266	+	3.21588i	−0.258963	+	0.111895i
$827$		−	30.8036i		−	1.07115i	−0.844489	−	0.535573i	$-0.820096\pi$
$827$		−	30.8036i		−	1.07115i	0.844489	−	0.535573i	$-0.179904\pi$
$828$		0			0
$829$			33.2395i			1.15446i	0.816583	+	0.577228i	$0.195866\pi$
$829$			33.2395i			1.15446i	−0.816583	+	0.577228i	$0.804134\pi$
$830$	1.73219	+	4.00888i	0.0601251	+	0.139150i
$831$		0			0
$832$	−22.4445	+	26.9496i	−0.778122	+	0.934310i
$833$		−	1.25430i		−	0.0434588i
$834$		0			0
$835$	−4.05564			−0.140351
$836$	−0.00481077	−	0.00452755i	−0.000166384	−	0.000156589i
$837$		0			0
$838$	−21.0112	−	48.6271i	−0.725819	−	1.67980i
$839$	−42.9568			−1.48303			−0.741517	−	0.670934i	$-0.765893\pi$
$839$	−42.9568			−1.48303			−0.741517	+	0.670934i	$0.765893\pi$
$840$		0			0
$841$	0.509663			0.0175746
$842$	−20.1721	−	46.6852i	−0.695176	−	1.60888i
$843$		0			0
$844$	15.0722	−	16.0150i	0.518807	−	0.551260i
$845$	−3.29670			−0.113410
$846$		0			0
$847$		−	10.1807i		−	0.349813i
$848$	0.746809	+	12.3008i	0.0256455	+	0.422412i
$849$		0			0
$850$	3.32024	+	7.68417i	0.113883	+	0.263565i
$851$			4.16199i			0.142671i
$852$		0			0
$853$		−	31.5917i		−	1.08168i	−0.841126	−	0.540840i	$-0.818107\pi$
$853$		−	31.5917i		−	1.08168i	0.841126	−	0.540840i	$-0.181893\pi$
$854$	−0.721323	+	0.311675i	−0.0246832	+	0.0106653i
$855$		0			0
$856$	24.2113	+	8.76164i	0.827526	+	0.299467i
$857$			37.4806i			1.28031i	0.768245	+	0.640156i	$0.221130\pi$
$857$			37.4806i			1.28031i	−0.768245	+	0.640156i	$0.778870\pi$
$858$		0			0
$859$	−41.4525			−1.41434			−0.707171	−	0.707042i	$-0.750029\pi$
$859$	−41.4525			−1.41434			−0.707171	+	0.707042i	$0.750029\pi$
$860$	−0.188540	+	0.200334i	−0.00642916	+	0.00683132i
$861$		0			0
$862$	−26.8174	+	11.5875i	−0.913405	+	0.394671i
$863$	43.8203			1.49166			0.745830	−	0.666136i	$-0.232053\pi$
$863$	43.8203			1.49166			0.745830	+	0.666136i	$0.232053\pi$
$864$		0			0
$865$	5.29356			0.179987
$866$	−30.9125	+	13.3569i	−1.05045	+	0.453886i
$867$		0			0
$868$	−4.79678	+	5.09683i	−0.162813	+	0.172998i
$869$	1.78213			0.0604545
$870$		0			0
$871$		−	50.6195i		−	1.71518i
$872$	3.44602	+	1.24705i	0.116697	+	0.0422305i
$873$		0			0
$874$	0.00369019	−	0.00159448i	0.000124822	−	5.39342e-5i
$875$			5.15181i			0.174163i
$876$		0			0
$877$		−	33.3035i		−	1.12458i	−0.826940	−	0.562289i	$-0.809921\pi$
$877$		−	33.3035i		−	1.12458i	0.826940	−	0.562289i	$-0.190079\pi$
$878$	−14.8989	−	34.4813i	−0.502815	−	1.16369i
$879$		0			0
$880$	−1.91565	+	0.116303i	−0.0645765	+	0.00392058i
$881$			35.6627i			1.20151i	0.799434	+	0.600754i	$0.205133\pi$
$881$			35.6627i			1.20151i	−0.799434	+	0.600754i	$0.794867\pi$
$882$		0			0
$883$	8.32201			0.280058			0.140029	−	0.990147i	$-0.455280\pi$
$883$	8.32201			0.280058			0.140029	+	0.990147i	$0.455280\pi$
$884$	7.53719	−	8.00867i	0.253503	−	0.269361i
$885$		0			0
$886$	−0.194402	−	0.449913i	−0.00653105	−	0.0151151i
$887$	−43.3551			−1.45572			−0.727861	−	0.685725i	$-0.759485\pi$
$887$	−43.3551			−1.45572			−0.727861	+	0.685725i	$0.759485\pi$
$888$		0			0
$889$	−11.5015			−0.385749
$890$	−0.578299	−	1.33838i	−0.0193846	−	0.0448628i
$891$		0			0
$892$	27.3745	+	25.7630i	0.916567	+	0.862608i
$893$	0.0137186			0.000459075
$894$		0			0
$895$		−	8.54178i		−	0.285520i
$896$	3.19812	−	10.8523i	0.106842	−	0.362549i
$897$		0			0
$898$	−5.86747	−	13.5794i	−0.195800	−	0.453149i
$899$			19.0104i			0.634032i
$900$		0			0
$901$		−	3.86433i		−	0.128739i
$902$	2.05094	−	0.886184i	0.0682887	−	0.0295067i
$903$		0			0
$904$	37.4284	+	13.5447i	1.24485	+	0.450489i
$905$		−	10.8176i		−	0.359590i
$906$		0			0
$907$	−7.89354			−0.262101			−0.131050	−	0.991376i	$-0.541835\pi$
$907$	−7.89354			−0.262101			−0.131050	+	0.991376i	$0.541835\pi$
$908$	−27.4215	−	25.8071i	−0.910013	−	0.856440i
$909$		0			0
$910$	3.01683	−	1.30353i	0.100007	−	0.0432118i
$911$	47.9212			1.58770			0.793850	−	0.608113i	$-0.208073\pi$
$911$	47.9212			1.58770			0.793850	+	0.608113i	$0.208073\pi$
$912$		0			0
$913$	−5.27302			−0.174511
$914$	14.3957	−	6.22021i	0.476168	−	0.205746i
$915$		0			0
$916$	−22.9711	−	21.6187i	−0.758985	−	0.714303i
$917$	−10.2828			−0.339567
$918$		0			0
$919$			22.2192i			0.732943i	0.930429	+	0.366471i	$0.119434\pi$
$919$			22.2192i			0.732943i	−0.930429	+	0.366471i	$0.880566\pi$
$920$	0.397397	−	1.09814i	0.0131018	−	0.0362046i
$921$		0			0
$922$	49.1304	−	21.2286i	1.61802	−	0.699127i
$923$			70.1627i			2.30943i
$924$		0			0
$925$			25.2148i			0.829057i
$926$	10.2068	+	23.6220i	0.335416	+	0.776268i
$927$		0			0
$928$	−13.8758	−	27.4184i	−0.455496	−	0.900055i
$929$			34.2658i			1.12422i	0.827061	+	0.562112i	$0.190011\pi$
$929$			34.2658i			1.12422i	−0.827061	+	0.562112i	$0.809989\pi$
$930$		0			0
$931$	−0.00364927			−0.000119600
$932$	6.16201	+	5.79925i	0.201843	+	0.189961i
$933$		0			0
$934$	3.47325	+	8.03830i	0.113648	+	0.263021i
$935$	0.601805			0.0196811
$936$		0			0
$937$	5.43172			0.177447			0.0887233	−	0.996056i	$-0.471721\pi$
$937$	5.43172			0.177447			0.0887233	+	0.996056i	$0.471721\pi$
$938$	6.47688	+	14.9897i	0.211478	+	0.489432i
$939$		0			0
$940$	2.73137	−	2.90223i	0.0890875	−	0.0946603i
$941$	18.1273			0.590932			0.295466	−	0.955353i	$-0.404525\pi$
$941$	18.1273			0.590932			0.295466	+	0.955353i	$0.404525\pi$
$942$		0			0
$943$			1.35953i			0.0442723i
$944$	22.8899	−	1.38970i	0.745004	−	0.0452308i
$945$		0			0
$946$	−0.131753	−	0.304922i	−0.00428365	−	0.00991385i
$947$			11.9799i			0.389295i	0.980873	+	0.194647i	$0.0623562\pi$
$947$			11.9799i			0.389295i	−0.980873	+	0.194647i	$0.937644\pi$
$948$		0			0
$949$			57.6723i			1.87212i
$950$	0.0223564	−	0.00965993i	0.000725338	−	0.000313410i
$951$		0			0
$952$	−1.20723	+	3.33597i	−0.0391265	+	0.108119i
$953$			22.7578i			0.737197i	0.929589	+	0.368599i	$0.120162\pi$
$953$			22.7578i			0.737197i	−0.929589	+	0.368599i	$0.879838\pi$
$954$		0			0
$955$	2.14959			0.0695592
$956$	−10.6936	+	11.3625i	−0.345856	+	0.367490i
$957$		0			0
$958$	5.42025	−	2.34202i	0.175120	−	0.0756673i
$959$	−19.3027			−0.623316
$960$		0			0
$961$	18.7533			0.604946
$962$	30.4100	−	13.1398i	0.980459	−	0.423644i
$963$		0			0
$964$	−27.7106	+	29.4440i	−0.892498	+	0.948327i
$965$	−3.08602			−0.0993425
$966$		0			0
$967$		−	41.9989i		−	1.35060i	−0.737545	−	0.675298i	$-0.764015\pi$
$967$		−	41.9989i		−	1.35060i	0.737545	−	0.675298i	$-0.235985\pi$
$968$	−9.79867	+	27.0770i	−0.314941	+	0.870286i
$969$		0			0
$970$	9.49935	−	4.10455i	0.305006	−	0.131789i
$971$		−	36.5508i		−	1.17297i	−0.809959	−	0.586486i	$-0.800511\pi$
$971$		−	36.5508i		−	1.17297i	0.809959	−	0.586486i	$-0.199489\pi$
$972$		0			0
$973$		−	15.3098i		−	0.490809i
$974$	9.25362	+	21.4161i	0.296505	+	0.686215i
$975$		0			0
$976$	2.21843	−	0.134686i	0.0710103	−	0.00431118i
$977$		−	30.6094i		−	0.979281i	−0.871925	−	0.489640i	$-0.837128\pi$
$977$		−	30.6094i		−	0.979281i	0.871925	−	0.489640i	$-0.162872\pi$
$978$		0			0
$979$	1.76042			0.0562633
$980$	−0.726570	+	0.772020i	−0.0232094	+	0.0246613i
$981$		0			0
$982$	−14.0818	−	32.5901i	−0.449367	−	1.03999i
$983$	−36.1930			−1.15438			−0.577189	−	0.816610i	$-0.695850\pi$
$983$	−36.1930			−1.15438			−0.577189	+	0.816610i	$0.695850\pi$
$984$		0			0
$985$	−8.19270			−0.261041
$986$	3.82207	+	8.84560i	0.121720	+	0.281701i
$987$		0			0
$988$	−0.0233005	−	0.0219288i	−0.000741288	−	0.000697648i
$989$	0.202127			0.00642726
$990$		0			0
$991$		−	52.1154i		−	1.65550i	−0.561097	−	0.827750i	$-0.689621\pi$
$991$		−	52.1154i		−	1.65550i	0.561097	−	0.827750i	$-0.310379\pi$
$992$	17.6632	−	8.93892i	0.560808	−	0.283811i
$993$		0			0
$994$	−8.97746	−	20.7769i	−0.284748	−	0.659005i
$995$			7.25159i			0.229891i
$996$		0			0
$997$			20.2906i			0.642609i	0.946976	+	0.321305i	$0.104121\pi$
$997$			20.2906i			0.642609i	−0.946976	+	0.321305i	$0.895879\pi$
$998$	−48.2764	+	20.8596i	−1.52816	+	0.660300i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.d.323.6	yes	48
3.2	odd	2	inner	1512.2.j.d.323.43	yes	48
4.3	odd	2		6048.2.j.d.5615.27		48
8.3	odd	2	inner	1512.2.j.d.323.44	yes	48
8.5	even	2		6048.2.j.d.5615.21		48
12.11	even	2		6048.2.j.d.5615.22		48
24.5	odd	2		6048.2.j.d.5615.28		48
24.11	even	2	inner	1512.2.j.d.323.5	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.d.323.5	✓	48	24.11	even	2	inner
1512.2.j.d.323.6	yes	48	1.1	even	1	trivial
1512.2.j.d.323.43	yes	48	3.2	odd	2	inner
1512.2.j.d.323.44	yes	48	8.3	odd	2	inner
6048.2.j.d.5615.21		48	8.5	even	2
6048.2.j.d.5615.22		48	12.11	even	2
6048.2.j.d.5615.27		48	4.3	odd	2
6048.2.j.d.5615.28		48	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29821 + 0.560940i) q^{2} +(1.37069 - 1.45643i) q^{4} +0.530075 q^{5} -1.00000i q^{7} +(-0.962474 + 2.65963i) q^{8} +O(q^{10})\)	\(q+(-1.29821 + 0.560940i) q^{2} +(1.37069 - 1.45643i) q^{4} +0.530075 q^{5} -1.00000i q^{7} +(-0.962474 + 2.65963i) q^{8} +(-0.688148 + 0.297340i) q^{10} -0.905144i q^{11} -4.38398i q^{13} +(0.560940 + 1.29821i) q^{14} +(-0.242402 - 3.99265i) q^{16} +1.25430i q^{17} +0.00364927 q^{19} +(0.726570 - 0.772020i) q^{20} +(0.507731 + 1.17507i) q^{22} -0.778929 q^{23} -4.71902 q^{25} +(2.45915 + 5.69133i) q^{26} +(-1.45643 - 1.37069i) q^{28} -5.43228 q^{29} -3.49953i q^{31} +(2.55432 + 5.04732i) q^{32} +(-0.703586 - 1.62834i) q^{34} -0.530075i q^{35} -5.34322i q^{37} +(-0.00473751 + 0.00204702i) q^{38} +(-0.510183 + 1.40980i) q^{40} -1.74538i q^{41} -0.259493 q^{43} +(-1.31828 - 1.24067i) q^{44} +(1.01121 - 0.436933i) q^{46} +3.75927 q^{47} -1.00000 q^{49} +(6.12627 - 2.64709i) q^{50} +(-6.38498 - 6.00909i) q^{52} -3.08087 q^{53} -0.479794i q^{55} +(2.65963 + 0.962474i) q^{56} +(7.05223 - 3.04718i) q^{58} +5.73302i q^{59} +0.555629i q^{61} +(1.96302 + 4.54312i) q^{62} +(-6.14729 - 5.11965i) q^{64} -2.32384i q^{65} +11.5465 q^{67} +(1.82680 + 1.71926i) q^{68} +(0.297340 + 0.688148i) q^{70} -16.0043 q^{71} -13.1552 q^{73} +(2.99723 + 6.93662i) q^{74} +(0.00500203 - 0.00531492i) q^{76} -0.905144 q^{77} +1.96889i q^{79} +(-0.128491 - 2.11640i) q^{80} +(0.979053 + 2.26587i) q^{82} -5.82561i q^{83} +0.664872i q^{85} +(0.336876 - 0.145560i) q^{86} +(2.40735 + 0.871177i) q^{88} +1.94491i q^{89} -4.38398 q^{91} +(-1.06767 + 1.13446i) q^{92} +(-4.88032 + 2.10872i) q^{94} +0.00193439 q^{95} -13.8042 q^{97} +(1.29821 - 0.560940i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4}+O(q^{10}) \) 48 * q - 4 * q^4	\( 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) \) 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * q^94

Introduction

L-functions

Modular forms

Varieties

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Database

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