LMFDB - Embedded newform 1512.2.j.c.323.12

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:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.12
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.c.323.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.971008 + 1.02818i) q^{2} +(-0.114288 - 1.99673i) q^{4} -2.21305 q^{5} -1.00000i q^{7} +(2.16396 + 1.82133i) q^{8} +O(q^{10})$	\(q+(-0.971008 + 1.02818i) q^{2} +(-0.114288 - 1.99673i) q^{4} -2.21305 q^{5} -1.00000i q^{7} +(2.16396 + 1.82133i) q^{8} +(2.14889 - 2.27540i) q^{10} +2.42373i q^{11} -1.11593i q^{13} +(1.02818 + 0.971008i) q^{14} +(-3.97388 + 0.456405i) q^{16} +0.701326i q^{17} +0.938340 q^{19} +(0.252925 + 4.41886i) q^{20} +(-2.49201 - 2.35346i) q^{22} -4.30502 q^{23} -0.102426 q^{25} +(1.14737 + 1.08358i) q^{26} +(-1.99673 + 0.114288i) q^{28} +4.26130 q^{29} -7.02221i q^{31} +(3.38940 - 4.52901i) q^{32} +(-0.721086 - 0.680993i) q^{34} +2.21305i q^{35} +3.12583i q^{37} +(-0.911135 + 0.964777i) q^{38} +(-4.78895 - 4.03070i) q^{40} +0.157922i q^{41} +7.08975 q^{43} +(4.83953 - 0.277003i) q^{44} +(4.18020 - 4.42631i) q^{46} +0.867970 q^{47} -1.00000 q^{49} +(0.0994564 - 0.105312i) q^{50} +(-2.22822 + 0.127538i) q^{52} +3.91444 q^{53} -5.36382i q^{55} +(1.82133 - 2.16396i) q^{56} +(-4.13775 + 4.38136i) q^{58} +7.28820i q^{59} +4.57877i q^{61} +(7.22006 + 6.81862i) q^{62} +(1.36548 + 7.88260i) q^{64} +2.46961i q^{65} +15.1677 q^{67} +(1.40036 - 0.0801531i) q^{68} +(-2.27540 - 2.14889i) q^{70} +6.93451 q^{71} +7.02133 q^{73} +(-3.21390 - 3.03520i) q^{74} +(-0.107241 - 1.87361i) q^{76} +2.42373 q^{77} +6.65903i q^{79} +(8.79437 - 1.01005i) q^{80} +(-0.162371 - 0.153343i) q^{82} +8.41084i q^{83} -1.55207i q^{85} +(-6.88420 + 7.28950i) q^{86} +(-4.41441 + 5.24486i) q^{88} -7.34335i q^{89} -1.11593 q^{91} +(0.492011 + 8.59596i) q^{92} +(-0.842806 + 0.892426i) q^{94} -2.07659 q^{95} +7.99425 q^{97} +(0.971008 - 1.02818i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4}+O(q^{10}) $ 32 * q + 8 * q^4	$ 32 q + 8 q^{4} - 8 q^{10} - 8 q^{16} - 64 q^{19} + 24 q^{22} - 16 q^{25} - 8 q^{28} + 8 q^{34} - 24 q^{40} - 48 q^{43} - 8 q^{46} - 32 q^{49} - 24 q^{52} - 96 q^{58} - 40 q^{64} + 16 q^{67} - 16 q^{70} - 16 q^{73} + 16 q^{76} + 24 q^{82} + 72 q^{88} + 16 q^{91} - 56 q^{94} + 64 q^{97}+O(q^{100}) $ 32 * q + 8 * q^4 - 8 * q^10 - 8 * q^16 - 64 * q^19 + 24 * q^22 - 16 * q^25 - 8 * q^28 + 8 * q^34 - 24 * q^40 - 48 * q^43 - 8 * q^46 - 32 * q^49 - 24 * q^52 - 96 * q^58 - 40 * q^64 + 16 * q^67 - 16 * q^70 - 16 * q^73 + 16 * q^76 + 24 * q^82 + 72 * q^88 + 16 * q^91 - 56 * q^94 + 64 * q^97

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 $

$2$	−0.971008	+	1.02818i	−0.686606	+	0.727030i
$2$	−0.971008	+	1.02818i	−0.686606	+	0.727030i
$3$		0			0
$3$		0			0
$4$	−0.114288	−	1.99673i	−0.0571440	−	0.998366i
$5$	−2.21305			−0.989704			−0.494852	−	0.868977i	$-0.664778\pi$
$5$	−2.21305			−0.989704			−0.494852	+	0.868977i	$0.664778\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.16396	+	1.82133i	0.765077	+	0.643939i
$9$		0			0
$10$	2.14889	−	2.27540i	0.679537	−	0.719544i
$11$			2.42373i			0.730781i	0.930854	+	0.365390i	$0.119065\pi$
$11$			2.42373i			0.730781i	−0.930854	+	0.365390i	$0.880935\pi$
$12$		0			0
$13$		−	1.11593i		−	0.309504i	−0.987953	−	0.154752i	$-0.950542\pi$
$13$		−	1.11593i		−	0.309504i	0.987953	−	0.154752i	$-0.0494579\pi$
$14$	1.02818	+	0.971008i	0.274791	+	0.259513i
$15$		0			0
$16$	−3.97388	+	0.456405i	−0.993469	+	0.114101i
$17$			0.701326i			0.170097i	0.996377	+	0.0850483i	$0.0271044\pi$
$17$			0.701326i			0.170097i	−0.996377	+	0.0850483i	$0.972896\pi$
$18$		0			0
$19$	0.938340			0.215270			0.107635	−	0.994190i	$-0.465672\pi$
$19$	0.938340			0.215270			0.107635	+	0.994190i	$0.465672\pi$
$20$	0.252925	+	4.41886i	0.0565557	+	0.988087i
$21$		0			0
$22$	−2.49201	−	2.35346i	−0.531299	−	0.501759i
$23$	−4.30502			−0.897658			−0.448829	−	0.893618i	$-0.648159\pi$
$23$	−4.30502			−0.897658			−0.448829	+	0.893618i	$0.648159\pi$
$24$		0			0
$25$	−0.102426			−0.0204852
$26$	1.14737	+	1.08358i	0.225019	+	0.212508i
$27$		0			0
$28$	−1.99673	+	0.114288i	−0.377347	+	0.0215984i
$29$	4.26130			0.791303			0.395652	−	0.918401i	$-0.370519\pi$
$29$	4.26130			0.791303			0.395652	+	0.918401i	$0.370519\pi$
$30$		0			0
$31$		−	7.02221i		−	1.26123i	−0.776098	−	0.630613i	$-0.782804\pi$
$31$		−	7.02221i		−	1.26123i	0.776098	−	0.630613i	$-0.217196\pi$
$32$	3.38940	−	4.52901i	0.599167	−	0.800624i
$33$		0			0
$34$	−0.721086	−	0.680993i	−0.123665	−	0.116789i
$35$			2.21305i			0.374073i
$36$		0			0
$37$			3.12583i			0.513883i	0.966427	+	0.256941i	$0.0827148\pi$
$37$			3.12583i			0.513883i	−0.966427	+	0.256941i	$0.917285\pi$
$38$	−0.911135	+	0.964777i	−0.147806	+	0.156508i
$39$		0			0
$40$	−4.78895	−	4.03070i	−0.757200	−	0.637309i
$41$			0.157922i			0.0246632i	0.999924	+	0.0123316i	$0.00392537\pi$
$41$			0.157922i			0.0246632i	−0.999924	+	0.0123316i	$0.996075\pi$
$42$		0			0
$43$	7.08975			1.08118			0.540588	−	0.841287i	$-0.318202\pi$
$43$	7.08975			1.08118			0.540588	+	0.841287i	$0.318202\pi$
$44$	4.83953	−	0.277003i	0.729587	−	0.0417597i
$45$		0			0
$46$	4.18020	−	4.42631i	0.616337	−	0.652624i
$47$	0.867970			0.126607			0.0633033	−	0.997994i	$-0.479836\pi$
$47$	0.867970			0.126607			0.0633033	+	0.997994i	$0.479836\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	0.0994564	−	0.105312i	0.0140653	−	0.0148933i
$51$		0			0
$52$	−2.22822	+	0.127538i	−0.308998	+	0.0176863i
$53$	3.91444			0.537689			0.268845	−	0.963184i	$-0.413358\pi$
$53$	3.91444			0.537689			0.268845	+	0.963184i	$0.413358\pi$
$54$		0			0
$55$		−	5.36382i		−	0.723257i
$56$	1.82133	−	2.16396i	0.243386	−	0.289172i
$57$		0			0
$58$	−4.13775	+	4.38136i	−0.543314	+	0.575301i
$59$			7.28820i			0.948843i	0.880298	+	0.474421i	$0.157343\pi$
$59$			7.28820i			0.948843i	−0.880298	+	0.474421i	$0.842657\pi$
$60$		0			0
$61$			4.57877i			0.586251i	0.956074	+	0.293126i	$0.0946955\pi$
$61$			4.57877i			0.586251i	−0.956074	+	0.293126i	$0.905305\pi$
$62$	7.22006	+	6.81862i	0.916948	+	0.865965i
$63$		0			0
$64$	1.36548	+	7.88260i	0.170686	+	0.985326i
$65$			2.46961i			0.306318i
$66$		0			0
$67$	15.1677			1.85303			0.926513	−	0.376264i	$-0.122791\pi$
$67$	15.1677			1.85303			0.926513	+	0.376264i	$0.122791\pi$
$68$	1.40036	−	0.0801531i	0.169819	−	0.00971999i
$69$		0			0
$70$	−2.27540	−	2.14889i	−0.271962	−	0.256841i
$71$	6.93451			0.822975			0.411487	−	0.911416i	$-0.365009\pi$
$71$	6.93451			0.822975			0.411487	+	0.911416i	$0.365009\pi$
$72$		0			0
$73$	7.02133			0.821785			0.410893	−	0.911684i	$-0.365217\pi$
$73$	7.02133			0.821785			0.410893	+	0.911684i	$0.365217\pi$
$74$	−3.21390	−	3.03520i	−0.373608	−	0.352835i
$75$		0			0
$76$	−0.107241	−	1.87361i	−0.0123014	−	0.214918i
$77$	2.42373			0.276209
$78$		0			0
$79$			6.65903i			0.749200i	0.927187	+	0.374600i	$0.122220\pi$
$79$			6.65903i			0.749200i	−0.927187	+	0.374600i	$0.877780\pi$
$80$	8.79437	−	1.01005i	0.983241	−	0.112926i
$81$		0			0
$82$	−0.162371	−	0.153343i	−0.0179309	−	0.0169339i
$83$			8.41084i			0.923210i	0.887086	+	0.461605i	$0.152726\pi$
$83$			8.41084i			0.923210i	−0.887086	+	0.461605i	$0.847274\pi$
$84$		0			0
$85$		−	1.55207i		−	0.168345i
$86$	−6.88420	+	7.28950i	−0.742342	+	0.786047i
$87$		0			0
$88$	−4.41441	+	5.24486i	−0.470578	+	0.559104i
$89$		−	7.34335i		−	0.778393i	−0.921155	−	0.389197i	$-0.872753\pi$
$89$		−	7.34335i		−	0.778393i	0.921155	−	0.389197i	$-0.127247\pi$
$90$		0			0
$91$	−1.11593			−0.116982
$92$	0.492011	+	8.59596i	0.0512957	+	0.896191i
$93$		0			0
$94$	−0.842806	+	0.892426i	−0.0869288	+	0.0920467i
$95$	−2.07659			−0.213054
$96$		0			0
$97$	7.99425			0.811693			0.405846	−	0.913941i	$-0.366977\pi$
$97$	7.99425			0.811693			0.405846	+	0.913941i	$0.366977\pi$
$98$	0.971008	−	1.02818i	0.0980866	−	0.103861i
$99$		0			0
$100$	0.0117061	+	0.204517i	0.00117061	+	0.0204517i
$101$	15.6519			1.55742			0.778709	−	0.627385i	$-0.215875\pi$
$101$	15.6519			1.55742			0.778709	+	0.627385i	$0.215875\pi$
$102$		0			0
$103$		−	4.90314i		−	0.483121i	−0.970386	−	0.241560i	$-0.922341\pi$
$103$		−	4.90314i		−	0.483121i	0.970386	−	0.241560i	$-0.0776592\pi$
$104$	2.03249	−	2.41484i	0.199302	−	0.236795i
$105$		0			0
$106$	−3.80095	+	4.02473i	−0.369181	+	0.390916i
$107$			15.1434i			1.46397i	0.681320	+	0.731986i	$0.261406\pi$
$107$			15.1434i			1.46397i	−0.681320	+	0.731986i	$0.738594\pi$
$108$		0			0
$109$		−	2.72939i		−	0.261428i	−0.991420	−	0.130714i	$-0.958273\pi$
$109$		−	2.72939i		−	0.261428i	0.991420	−	0.130714i	$-0.0417270\pi$
$110$	5.51494	+	5.20831i	0.525829	+	0.496593i
$111$		0			0
$112$	0.456405	+	3.97388i	0.0431262	+	0.375496i
$113$		−	2.84331i		−	0.267476i	−0.991017	−	0.133738i	$-0.957302\pi$
$113$		−	2.84331i		−	0.267476i	0.991017	−	0.133738i	$-0.0426980\pi$
$114$		0			0
$115$	9.52720			0.888416
$116$	−0.487015	−	8.50867i	−0.0452182	−	0.790010i
$117$		0			0
$118$	−7.49355	−	7.07690i	−0.689837	−	0.651481i
$119$	0.701326			0.0642905
$120$		0			0
$121$	5.12555			0.465959
$122$	−4.70778	−	4.44602i	−0.426222	−	0.402524i
$123$		0			0
$124$	−14.0215	+	0.802554i	−1.25916	+	0.0720715i
$125$	11.2919			1.00998
$126$		0			0
$127$			10.4243i			0.925006i	0.886618	+	0.462503i	$0.153049\pi$
$127$			10.4243i			0.925006i	−0.886618	+	0.462503i	$0.846951\pi$
$128$	−9.43059	−	6.25011i	−0.833555	−	0.552437i
$129$		0			0
$130$	−2.53919	−	2.39801i	−0.222702	−	0.210320i
$131$		−	21.3573i		−	1.86600i	−0.359881	−	0.932998i	$-0.617183\pi$
$131$		−	21.3573i		−	1.86600i	0.359881	−	0.932998i	$-0.382817\pi$
$132$		0			0
$133$		−	0.938340i		−	0.0813644i
$134$	−14.7279	+	15.5950i	−1.27230	+	1.34720i
$135$		0			0
$136$	−1.27735	+	1.51764i	−0.109532	+	0.130137i
$137$		−	11.2577i		−	0.961812i	−0.876772	−	0.480906i	$-0.840308\pi$
$137$		−	11.2577i		−	0.961812i	0.876772	−	0.480906i	$-0.159692\pi$
$138$		0			0
$139$	8.11586			0.688379			0.344189	−	0.938900i	$-0.388154\pi$
$139$	8.11586			0.688379			0.344189	+	0.938900i	$0.388154\pi$
$140$	4.41886	−	0.252925i	0.373462	−	0.0213760i
$141$		0			0
$142$	−6.73346	+	7.12989i	−0.565059	+	0.598327i
$143$	2.70472			0.226180
$144$		0			0
$145$	−9.43045			−0.783156
$146$	−6.81777	+	7.21916i	−0.564243	+	0.597462i
$147$		0			0
$148$	6.24144	−	0.357245i	0.513043	−	0.0293653i
$149$	−4.90580			−0.401899			−0.200949	−	0.979602i	$-0.564403\pi$
$149$	−4.90580			−0.401899			−0.200949	+	0.979602i	$0.564403\pi$
$150$		0			0
$151$			18.9521i			1.54230i	0.636654	+	0.771150i	$0.280318\pi$
$151$			18.9521i			1.54230i	−0.636654	+	0.771150i	$0.719682\pi$
$152$	2.03053	+	1.70903i	0.164698	+	0.138621i
$153$		0			0
$154$	−2.35346	+	2.49201i	−0.189647	+	0.200812i
$155$			15.5405i			1.24824i
$156$		0			0
$157$			10.0907i			0.805326i	0.915348	+	0.402663i	$0.131915\pi$
$157$			10.0907i			0.805326i	−0.915348	+	0.402663i	$0.868085\pi$
$158$	−6.84665	−	6.46597i	−0.544690	−	0.514405i
$159$		0			0
$160$	−7.50090	+	10.0229i	−0.592998	+	0.792381i
$161$			4.30502i			0.339283i
$162$		0			0
$163$	−19.9762			−1.56466			−0.782330	−	0.622864i	$-0.785969\pi$
$163$	−19.9762			−1.56466			−0.782330	+	0.622864i	$0.785969\pi$
$164$	0.315327	−	0.0180485i	0.0246229	−	0.00140935i
$165$		0			0
$166$	−8.64782	−	8.16699i	−0.671201	−	0.633881i
$167$	−13.8623			−1.07270			−0.536348	−	0.843997i	$-0.680197\pi$
$167$	−13.8623			−1.07270			−0.536348	+	0.843997i	$0.680197\pi$
$168$		0			0
$169$	11.7547			0.904207
$170$	1.59580	+	1.50707i	0.122392	+	0.115587i
$171$		0			0
$172$	−0.810273	−	14.1563i	−0.0617827	−	1.07941i
$173$	21.4796			1.63306			0.816531	−	0.577301i	$-0.195894\pi$
$173$	21.4796			1.63306			0.816531	+	0.577301i	$0.195894\pi$
$174$		0			0
$175$			0.102426i			0.00774268i
$176$	−1.10620	−	9.63159i	−0.0833830	−	0.726008i
$177$		0			0
$178$	7.55025	+	7.13045i	0.565915	+	0.534450i
$179$			3.94291i			0.294707i	0.989084	+	0.147354i	$0.0470755\pi$
$179$			3.94291i			0.294707i	−0.989084	+	0.147354i	$0.952925\pi$
$180$		0			0
$181$		−	11.7849i		−	0.875962i	−0.898984	−	0.437981i	$-0.855694\pi$
$181$		−	11.7849i		−	0.875962i	0.898984	−	0.437981i	$-0.144306\pi$
$182$	1.08358	−	1.14737i	0.0803203	−	0.0850491i
$183$		0			0
$184$	−9.31590	−	7.84087i	−0.686777	−	0.578037i
$185$		−	6.91760i		−	0.508592i
$186$		0			0
$187$	−1.69982			−0.124303
$188$	−0.0991986	−	1.73310i	−0.00723480	−	0.126400i
$189$		0			0
$190$	2.01638	−	2.13510i	0.146284	−	0.154896i
$191$	−16.6064			−1.20160			−0.600798	−	0.799401i	$-0.705150\pi$
$191$	−16.6064			−1.20160			−0.600798	+	0.799401i	$0.705150\pi$
$192$		0			0
$193$	6.90416			0.496972			0.248486	−	0.968635i	$-0.420067\pi$
$193$	6.90416			0.496972			0.248486	+	0.968635i	$0.420067\pi$
$194$	−7.76247	+	8.21948i	−0.557313	+	0.590125i
$195$		0			0
$196$	0.114288	+	1.99673i	0.00816343	+	0.142624i
$197$	−8.98273			−0.639993			−0.319997	−	0.947419i	$-0.603682\pi$
$197$	−8.98273			−0.639993			−0.319997	+	0.947419i	$0.603682\pi$
$198$		0			0
$199$		−	11.4427i		−	0.811153i	−0.914061	−	0.405577i	$-0.867071\pi$
$199$		−	11.4427i		−	0.811153i	0.914061	−	0.405577i	$-0.132929\pi$
$200$	−0.221646	−	0.186552i	−0.0156728	−	0.0131912i
$201$		0			0
$202$	−15.1981	+	16.0928i	−1.06933	+	1.13229i
$203$		−	4.26130i		−	0.299085i
$204$		0			0
$205$		−	0.349488i		−	0.0244093i
$206$	5.04129	+	4.76099i	0.351243	+	0.331714i
$207$		0			0
$208$	0.509317	+	4.43458i	0.0353148	+	0.307483i
$209$			2.27428i			0.157315i
$210$		0			0
$211$	23.8035			1.63870			0.819351	−	0.573292i	$-0.194334\pi$
$211$	23.8035			1.63870			0.819351	+	0.573292i	$0.194334\pi$
$212$	−0.447373	−	7.81608i	−0.0307257	−	0.536811i
$213$		0			0
$214$	−15.5701	−	14.7044i	−1.06435	−	1.00517i
$215$	−15.6899			−1.07004
$216$		0			0
$217$	−7.02221			−0.476698
$218$	2.80629	+	2.65026i	0.190066	+	0.179498i
$219$		0			0
$220$	−10.7101	+	0.613020i	−0.722075	+	0.0413298i
$221$	0.782633			0.0526456
$222$		0			0
$223$			4.42841i			0.296549i	0.988946	+	0.148274i	$0.0473718\pi$
$223$			4.42841i			0.296549i	−0.988946	+	0.148274i	$0.952628\pi$
$224$	−4.52901	−	3.38940i	−0.302607	−	0.226464i
$225$		0			0
$226$	2.92342	+	2.76087i	0.194463	+	0.183651i
$227$			6.46751i			0.429264i	0.976695	+	0.214632i	$0.0688552\pi$
$227$			6.46751i			0.429264i	−0.976695	+	0.214632i	$0.931145\pi$
$228$		0			0
$229$			11.4715i			0.758056i	0.925385	+	0.379028i	$0.123742\pi$
$229$			11.4715i			0.758056i	−0.925385	+	0.379028i	$0.876258\pi$
$230$	−9.25098	+	9.79563i	−0.609992	+	0.645905i
$231$		0			0
$232$	9.22130	+	7.76125i	0.605408	+	0.509551i
$233$			19.8678i			1.30158i	0.759256	+	0.650792i	$0.225563\pi$
$233$			19.8678i			1.30158i	−0.759256	+	0.650792i	$0.774437\pi$
$234$		0			0
$235$	−1.92086			−0.125303
$236$	14.5526	−	0.832953i	0.947292	−	0.0542207i
$237$		0			0
$238$	−0.680993	+	0.721086i	−0.0441422	+	0.0467411i
$239$	−10.2210			−0.661138			−0.330569	−	0.943782i	$-0.607241\pi$
$239$	−10.2210			−0.661138			−0.330569	+	0.943782i	$0.607241\pi$
$240$		0			0
$241$	28.1808			1.81529			0.907643	−	0.419744i	$-0.137880\pi$
$241$	28.1808			1.81529			0.907643	+	0.419744i	$0.137880\pi$
$242$	−4.97695	+	5.26997i	−0.319931	+	0.338766i
$243$		0			0
$244$	9.14258	−	0.523298i	0.585293	−	0.0335007i
$245$	2.21305			0.141386
$246$		0			0
$247$		−	1.04712i		−	0.0666269i
$248$	12.7898	−	15.1958i	0.812152	−	0.964935i
$249$		0			0
$250$	−10.9645	+	11.6101i	−0.693458	+	0.734284i
$251$			4.62338i			0.291825i	0.989297	+	0.145913i	$0.0466118\pi$
$251$			4.62338i			0.291825i	−0.989297	+	0.145913i	$0.953388\pi$
$252$		0			0
$253$		−	10.4342i		−	0.655991i
$254$	−10.7180	−	10.1221i	−0.672507	−	0.635115i
$255$		0			0
$256$	15.5834	−	3.62739i	0.973962	−	0.226712i
$257$		−	29.6682i		−	1.85065i	−0.379174	−	0.925326i	$-0.623792\pi$
$257$		−	29.6682i		−	1.85065i	0.379174	−	0.925326i	$-0.376208\pi$
$258$		0			0
$259$	3.12583			0.194230
$260$	4.93115	−	0.282247i	0.305817	−	0.0175042i
$261$		0			0
$262$	21.9590	+	20.7381i	1.35663	+	1.28120i
$263$	−15.8635			−0.978185			−0.489093	−	0.872232i	$-0.662672\pi$
$263$	−15.8635			−0.978185			−0.489093	+	0.872232i	$0.662672\pi$
$264$		0			0
$265$	−8.66283			−0.532153
$266$	0.964777	+	0.911135i	0.0591543	+	0.0558653i
$267$		0			0
$268$	−1.73348	−	30.2858i	−0.105889	−	1.85000i
$269$	−3.13803			−0.191329			−0.0956644	−	0.995414i	$-0.530498\pi$
$269$	−3.13803			−0.191329			−0.0956644	+	0.995414i	$0.530498\pi$
$270$		0			0
$271$			22.7174i			1.37998i	0.723817	+	0.689992i	$0.242386\pi$
$271$			22.7174i			1.37998i	−0.723817	+	0.689992i	$0.757614\pi$
$272$	−0.320089	−	2.78698i	−0.0194082	−	0.168986i
$273$		0			0
$274$	11.5749	+	10.9313i	0.699266	+	0.660386i
$275$		−	0.248252i		−	0.0149702i
$276$		0			0
$277$			24.8267i			1.49169i	0.666119	+	0.745845i	$0.267954\pi$
$277$			24.8267i			1.49169i	−0.666119	+	0.745845i	$0.732046\pi$
$278$	−7.88057	+	8.34453i	−0.472645	+	0.500472i
$279$		0			0
$280$	−4.03070	+	4.78895i	−0.240880	+	0.286195i
$281$		−	30.2207i		−	1.80282i	−0.432970	−	0.901408i	$-0.642535\pi$
$281$		−	30.2207i		−	1.80282i	0.432970	−	0.901408i	$-0.357465\pi$
$282$		0			0
$283$	−14.9803			−0.890488			−0.445244	−	0.895409i	$-0.646883\pi$
$283$	−14.9803			−0.890488			−0.445244	+	0.895409i	$0.646883\pi$
$284$	−0.792531	−	13.8464i	−0.0470280	−	0.821630i
$285$		0			0
$286$	−2.62630	+	2.78092i	−0.155296	+	0.164439i
$287$	0.157922			0.00932182
$288$		0			0
$289$	16.5081			0.971067
$290$	9.15704	−	9.69616i	0.537720	−	0.569378i
$291$		0			0
$292$	−0.802454	−	14.0197i	−0.0469601	−	0.820442i
$293$	−7.58993			−0.443408			−0.221704	−	0.975114i	$-0.571162\pi$
$293$	−7.58993			−0.443408			−0.221704	+	0.975114i	$0.571162\pi$
$294$		0			0
$295$		−	16.1291i		−	0.939074i
$296$	−5.69318	+	6.76418i	−0.330909	+	0.393160i
$297$		0			0
$298$	4.76357	−	5.04402i	0.275946	−	0.292192i
$299$			4.80411i			0.277829i
$300$		0			0
$301$		−	7.08975i		−	0.408646i
$302$	−19.4861	−	18.4026i	−1.12130	−	1.05895i
$303$		0			0
$304$	−3.72885	+	0.428263i	−0.213864	+	0.0245626i
$305$		−	10.1330i		−	0.580216i
$306$		0			0
$307$	−18.1246			−1.03443			−0.517214	−	0.855856i	$-0.673031\pi$
$307$	−18.1246			−1.03443			−0.517214	+	0.855856i	$0.673031\pi$
$308$	−0.277003	−	4.83953i	−0.0157837	−	0.275758i
$309$		0			0
$310$	−15.9783	−	15.0899i	−0.907508	−	0.857050i
$311$	17.0291			0.965631			0.482816	−	0.875722i	$-0.339614\pi$
$311$	17.0291			0.965631			0.482816	+	0.875722i	$0.339614\pi$
$312$		0			0
$313$	7.44270			0.420686			0.210343	−	0.977628i	$-0.432542\pi$
$313$	7.44270			0.420686			0.210343	+	0.977628i	$0.432542\pi$
$314$	−10.3750	−	9.79815i	−0.585496	−	0.552942i
$315$		0			0
$316$	13.2963	−	0.761047i	0.747975	−	0.0428123i
$317$	2.40549			0.135106			0.0675528	−	0.997716i	$-0.478481\pi$
$317$	2.40549			0.135106			0.0675528	+	0.997716i	$0.478481\pi$
$318$		0			0
$319$			10.3282i			0.578269i
$320$	−3.02188	−	17.4446i	−0.168928	−	0.975181i
$321$		0			0
$322$	−4.42631	−	4.18020i	−0.246669	−	0.232954i
$323$			0.658082i			0.0366167i
$324$		0			0
$325$			0.114301i			0.00634025i
$326$	19.3971	−	20.5391i	1.07431	−	1.13755i
$327$		0			0
$328$	−0.287628	+	0.341737i	−0.0158816	+	0.0188693i
$329$		−	0.867970i		−	0.0478528i
$330$		0			0
$331$	14.3776			0.790265			0.395133	−	0.918624i	$-0.370699\pi$
$331$	14.3776			0.790265			0.395133	+	0.918624i	$0.370699\pi$
$332$	16.7942	−	0.961258i	0.921701	−	0.0527559i
$333$		0			0
$334$	13.4604	−	14.2529i	0.736520	−	0.779882i
$335$	−33.5667			−1.83395
$336$		0			0
$337$	20.4430			1.11360			0.556800	−	0.830646i	$-0.312029\pi$
$337$	20.4430			1.11360			0.556800	+	0.830646i	$0.312029\pi$
$338$	−11.4139	+	12.0859i	−0.620834	+	0.657385i
$339$		0			0
$340$	−3.09906	+	0.177383i	−0.168070	+	0.00961992i
$341$	17.0199			0.921679
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	15.3420	+	12.9128i	0.827183	+	0.696211i
$345$		0			0
$346$	−20.8568	+	22.0848i	−1.12127	+	1.18728i
$347$			6.62453i			0.355623i	0.984065	+	0.177812i	$0.0569018\pi$
$347$			6.62453i			0.355623i	−0.984065	+	0.177812i	$0.943098\pi$
$348$		0			0
$349$		−	33.7876i		−	1.80861i	−0.426889	−	0.904304i	$-0.640391\pi$
$349$		−	33.7876i		−	1.80861i	0.426889	−	0.904304i	$-0.359609\pi$
$350$	−0.105312	−	0.0994564i	−0.00562915	−	0.00531617i
$351$		0			0
$352$	10.9771	+	8.21498i	0.585081	+	0.437860i
$353$		−	26.5976i		−	1.41565i	−0.706390	−	0.707823i	$-0.749677\pi$
$353$		−	26.5976i		−	1.41565i	0.706390	−	0.707823i	$-0.250323\pi$
$354$		0			0
$355$	−15.3464			−0.814501
$356$	−14.6627	+	0.839256i	−0.777122	+	0.0444805i
$357$		0			0
$358$	−4.05400	−	3.82860i	−0.214261	−	0.202348i
$359$	−29.7098			−1.56802			−0.784012	−	0.620746i	$-0.786830\pi$
$359$	−29.7098			−1.56802			−0.784012	+	0.620746i	$0.786830\pi$
$360$		0			0
$361$	−18.1195			−0.953659
$362$	12.1169	+	11.4432i	0.636850	+	0.601441i
$363$		0			0
$364$	0.127538	+	2.22822i	0.00668479	+	0.116790i
$365$	−15.5385			−0.813324
$366$		0			0
$367$		−	15.6932i		−	0.819176i	−0.912271	−	0.409588i	$-0.865672\pi$
$367$		−	15.6932i		−	0.819176i	0.912271	−	0.409588i	$-0.134328\pi$
$368$	17.1076	−	1.96483i	0.891795	−	0.102424i
$369$		0			0
$370$	7.11251	+	6.71705i	0.369762	+	0.349203i
$371$		−	3.91444i		−	0.203227i
$372$		0			0
$373$		−	11.0269i		−	0.570951i	−0.958386	−	0.285475i	$-0.907849\pi$
$373$		−	11.0269i		−	0.570951i	0.958386	−	0.285475i	$-0.0921515\pi$
$374$	1.65054	−	1.74771i	0.0853474	−	0.0903722i
$375$		0			0
$376$	1.87826	+	1.58086i	0.0968637	+	0.0815268i
$377$		−	4.75533i		−	0.244912i
$378$		0			0
$379$	−7.84736			−0.403092			−0.201546	−	0.979479i	$-0.564597\pi$
$379$	−7.84736			−0.403092			−0.201546	+	0.979479i	$0.564597\pi$
$380$	0.237329	+	4.14639i	0.0121747	+	0.212705i
$381$		0			0
$382$	16.1249	−	17.0743i	0.825023	−	0.873596i
$383$	3.26238			0.166700			0.0833500	−	0.996520i	$-0.473438\pi$
$383$	3.26238			0.166700			0.0833500	+	0.996520i	$0.473438\pi$
$384$		0			0
$385$	−5.36382			−0.273365
$386$	−6.70399	+	7.09868i	−0.341224	+	0.361313i
$387$		0			0
$388$	−0.913646	−	15.9624i	−0.0463833	−	0.810366i
$389$	1.15697			0.0586609			0.0293304	−	0.999570i	$-0.490662\pi$
$389$	1.15697			0.0586609			0.0293304	+	0.999570i	$0.490662\pi$
$390$		0			0
$391$		−	3.01922i		−	0.152688i
$392$	−2.16396	−	1.82133i	−0.109297	−	0.0919913i
$393$		0			0
$394$	8.72231	−	9.23582i	0.439423	−	0.465294i
$395$		−	14.7367i		−	0.741486i
$396$		0			0
$397$			2.41295i			0.121103i	0.998165	+	0.0605513i	$0.0192859\pi$
$397$			2.41295i			0.121103i	−0.998165	+	0.0605513i	$0.980714\pi$
$398$	11.7651	+	11.1110i	0.589732	+	0.556943i
$399$		0			0
$400$	0.407028	−	0.0467477i	0.0203514	−	0.00233739i
$401$			7.48047i			0.373557i	0.982402	+	0.186778i	$0.0598047\pi$
$401$			7.48047i			0.373557i	−0.982402	+	0.186778i	$0.940195\pi$
$402$		0			0
$403$	−7.83631			−0.390355
$404$	−1.78882	−	31.2526i	−0.0889971	−	1.55487i
$405$		0			0
$406$	4.38136	+	4.13775i	0.217443	+	0.205353i
$407$	−7.57615			−0.375536
$408$		0			0
$409$	−7.49823			−0.370764			−0.185382	−	0.982667i	$-0.559352\pi$
$409$	−7.49823			−0.370764			−0.185382	+	0.982667i	$0.559352\pi$
$410$	0.359335	+	0.339355i	0.0177463	+	0.0167596i
$411$		0			0
$412$	−9.79026	+	0.560370i	−0.482331	+	0.0276075i
$413$	7.28820			0.358629
$414$		0			0
$415$		−	18.6136i		−	0.913705i
$416$	−5.05408	−	3.78235i	−0.247797	−	0.185445i
$417$		0			0
$418$	−2.33836	−	2.20834i	−0.114373	−	0.108014i
$419$		−	26.7682i		−	1.30771i	−0.756619	−	0.653856i	$-0.773150\pi$
$419$		−	26.7682i		−	1.30771i	0.756619	−	0.653856i	$-0.226850\pi$
$420$		0			0
$421$		−	28.1616i		−	1.37251i	−0.727359	−	0.686257i	$-0.759253\pi$
$421$		−	28.1616i		−	1.37251i	0.727359	−	0.686257i	$-0.240747\pi$
$422$	−23.1134	+	24.4742i	−1.12514	+	1.19139i
$423$		0			0
$424$	8.47070	+	7.12950i	0.411374	+	0.346239i
$425$		−	0.0718340i		−	0.00348446i
$426$		0			0
$427$	4.57877			0.221582
$428$	30.2374	−	1.73071i	1.46158	−	0.0836571i
$429$		0			0
$430$	15.2350	−	16.1320i	0.734699	−	0.777954i
$431$	29.9359			1.44196			0.720980	−	0.692955i	$-0.243692\pi$
$431$	29.9359			1.44196			0.720980	+	0.692955i	$0.243692\pi$
$432$		0			0
$433$	−39.1106			−1.87954			−0.939768	−	0.341814i	$-0.888959\pi$
$433$	−39.1106			−1.87954			−0.939768	+	0.341814i	$0.888959\pi$
$434$	6.81862	−	7.22006i	0.327304	−	0.346574i
$435$		0			0
$436$	−5.44986	+	0.311937i	−0.261001	+	0.0149391i
$437$	−4.03957			−0.193239
$438$		0			0
$439$		−	31.4351i		−	1.50031i	−0.661260	−	0.750157i	$-0.729978\pi$
$439$		−	31.4351i		−	1.50031i	0.661260	−	0.750157i	$-0.270022\pi$
$440$	9.76930	−	11.6071i	0.465733	−	0.553347i
$441$		0			0
$442$	−0.759943	+	0.804684i	−0.0361468	+	0.0382749i
$443$			24.2344i			1.15141i	0.817656	+	0.575707i	$0.195273\pi$
$443$			24.2344i			1.15141i	−0.817656	+	0.575707i	$0.804727\pi$
$444$		0			0
$445$			16.2512i			0.770379i
$446$	−4.55318	−	4.30002i	−0.215600	−	0.203612i
$447$		0			0
$448$	7.88260	−	1.36548i	0.372418	−	0.0645131i
$449$		−	22.6066i		−	1.06687i	−0.845841	−	0.533435i	$-0.820901\pi$
$449$		−	22.6066i		−	1.06687i	0.845841	−	0.533435i	$-0.179099\pi$
$450$		0			0
$451$	−0.382759			−0.0180234
$452$	−5.67732	+	0.324956i	−0.267039	+	0.0152846i
$453$		0			0
$454$	−6.64974	−	6.28001i	−0.312088	−	0.294735i
$455$	2.46961			0.115777
$456$		0			0
$457$	−9.35271			−0.437502			−0.218751	−	0.975781i	$-0.570198\pi$
$457$	−9.35271			−0.437502			−0.218751	+	0.975781i	$0.570198\pi$
$458$	−11.7947	−	11.1389i	−0.551129	−	0.520486i
$459$		0			0
$460$	−1.08884	−	19.0233i	−0.0507676	−	0.886964i
$461$	11.5898			0.539789			0.269895	−	0.962890i	$-0.413011\pi$
$461$	11.5898			0.539789			0.269895	+	0.962890i	$0.413011\pi$
$462$		0			0
$463$			17.8299i			0.828625i	0.910135	+	0.414312i	$0.135978\pi$
$463$			17.8299i			0.828625i	−0.910135	+	0.414312i	$0.864022\pi$
$464$	−16.9339	+	1.94488i	−0.786135	+	0.0902887i
$465$		0			0
$466$	−20.4276	−	19.2918i	−0.946290	−	0.893676i
$467$		−	3.50180i		−	0.162044i	−0.996712	−	0.0810221i	$-0.974182\pi$
$467$		−	3.50180i		−	0.162044i	0.996712	−	0.0810221i	$-0.0258184\pi$
$468$		0			0
$469$		−	15.1677i		−	0.700378i
$470$	1.86517	−	1.97498i	0.0860338	−	0.0910990i
$471$		0			0
$472$	−13.2742	+	15.7714i	−0.610997	+	0.725938i
$473$			17.1836i			0.790103i
$474$		0			0
$475$	−0.0961103			−0.00440985
$476$	−0.0801531	−	1.40036i	−0.00367381	−	0.0641854i
$477$		0			0
$478$	9.92462	−	10.5089i	0.453942	−	0.480667i
$479$	−18.2987			−0.836087			−0.418043	−	0.908427i	$-0.637284\pi$
$479$	−18.2987			−0.836087			−0.418043	+	0.908427i	$0.637284\pi$
$480$		0			0
$481$	3.48822			0.159049
$482$	−27.3638	+	28.9748i	−1.24639	+	1.31977i
$483$		0			0
$484$	−0.585789	−	10.2344i	−0.0266268	−	0.465198i
$485$	−17.6916			−0.803336
$486$		0			0
$487$			24.3559i			1.10367i	0.833953	+	0.551836i	$0.186072\pi$
$487$			24.3559i			1.10367i	−0.833953	+	0.551836i	$0.813928\pi$
$488$	−8.33947	+	9.90830i	−0.377510	+	0.448527i
$489$		0			0
$490$	−2.14889	+	2.27540i	−0.0970767	+	0.102792i
$491$			25.8479i			1.16650i	0.812292	+	0.583250i	$0.198219\pi$
$491$			25.8479i			1.16650i	−0.812292	+	0.583250i	$0.801781\pi$
$492$		0			0
$493$			2.98856i			0.134598i
$494$	1.07663	+	1.01677i	0.0484398	+	0.0457465i
$495$		0			0
$496$	3.20497	+	27.9054i	0.143907	+	1.25299i
$497$		−	6.93451i		−	0.311055i
$498$		0			0
$499$	−13.5430			−0.606270			−0.303135	−	0.952948i	$-0.598033\pi$
$499$	−13.5430			−0.606270			−0.303135	+	0.952948i	$0.598033\pi$
$500$	−1.29053	−	22.5469i	−0.0577142	−	1.00833i
$501$		0			0
$502$	−4.75365	−	4.48934i	−0.212166	−	0.200369i
$503$	17.6930			0.788890			0.394445	−	0.918920i	$-0.370937\pi$
$503$	17.6930			0.788890			0.394445	+	0.918920i	$0.370937\pi$
$504$		0			0
$505$	−34.6383			−1.54138
$506$	10.7282	+	10.1317i	0.476925	+	0.450408i
$507$		0			0
$508$	20.8145	−	1.19137i	0.923494	−	0.0528585i
$509$	12.0147			0.532544			0.266272	−	0.963898i	$-0.414208\pi$
$509$	12.0147			0.532544			0.266272	+	0.963898i	$0.414208\pi$
$510$		0			0
$511$		−	7.02133i		−	0.310606i
$512$	−11.4020	+	19.5447i	−0.503902	+	0.863761i
$513$		0			0
$514$	30.5041	+	28.8080i	1.34548	+	1.27067i
$515$			10.8509i			0.478147i
$516$		0			0
$517$			2.10372i			0.0925216i
$518$	−3.03520	+	3.21390i	−0.133359	+	0.141211i
$519$		0			0
$520$	−4.49799	+	5.34415i	−0.197250	+	0.234357i
$521$		−	17.5217i		−	0.767638i	−0.923408	−	0.383819i	$-0.874609\pi$
$521$		−	17.5217i		−	0.767638i	0.923408	−	0.383819i	$-0.125391\pi$
$522$		0			0
$523$	−5.61428			−0.245495			−0.122748	−	0.992438i	$-0.539171\pi$
$523$	−5.61428			−0.245495			−0.122748	+	0.992438i	$0.539171\pi$
$524$	−42.6448	+	2.44088i	−1.86295	+	0.106630i
$525$		0			0
$526$	15.4036	−	16.3105i	0.671628	−	0.711170i
$527$	4.92486			0.214530
$528$		0			0
$529$	−4.46684			−0.194210
$530$	8.41168	−	8.90691i	0.365380	−	0.386891i
$531$		0			0
$532$	−1.87361	+	0.107241i	−0.0812314	+	0.00464948i
$533$	0.176230			0.00763337
$534$		0			0
$535$		−	33.5131i		−	1.44890i
$536$	32.8223	+	27.6254i	1.41771	+	1.19323i
$537$		0			0
$538$	3.04705	−	3.22644i	0.131368	−	0.139102i
$539$		−	2.42373i		−	0.104397i
$540$		0			0
$541$			34.1532i			1.46836i	0.678954	+	0.734181i	$0.262433\pi$
$541$			34.1532i			1.46836i	−0.678954	+	0.734181i	$0.737567\pi$
$542$	−23.3575	−	22.0588i	−1.00329	−	0.947505i
$543$		0			0
$544$	3.17631	+	2.37707i	0.136183	+	0.101916i
$545$			6.04027i			0.258737i
$546$		0			0
$547$	21.6399			0.925255			0.462627	−	0.886553i	$-0.346907\pi$
$547$	21.6399			0.925255			0.462627	+	0.886553i	$0.346907\pi$
$548$	−22.4787	+	1.28662i	−0.960240	+	0.0549618i
$549$		0			0
$550$	0.255247	+	0.241055i	0.0108838	+	0.0102786i
$551$	3.99855			0.170344
$552$		0			0
$553$	6.65903			0.283171
$554$	−25.5262	−	24.1069i	−1.08450	−	1.02420i
$555$		0			0
$556$	−0.927546	−	16.2052i	−0.0393367	−	0.687254i
$557$	25.9554			1.09976			0.549882	−	0.835242i	$-0.314673\pi$
$557$	25.9554			1.09976			0.549882	+	0.835242i	$0.314673\pi$
$558$		0			0
$559$		−	7.91168i		−	0.334629i
$560$	−1.01005	−	8.79437i	−0.0426822	−	0.371630i
$561$		0			0
$562$	31.0722	+	29.3445i	1.31070	+	1.23782i
$563$			13.9262i			0.586921i	0.955971	+	0.293460i	$0.0948069\pi$
$563$			13.9262i			0.586921i	−0.955971	+	0.293460i	$0.905193\pi$
$564$		0			0
$565$			6.29237i			0.264722i
$566$	14.5460	−	15.4024i	0.611415	−	0.647411i
$567$		0			0
$568$	15.0060	+	12.6301i	0.629639	+	0.529945i
$569$		−	18.6130i		−	0.780296i	−0.920752	−	0.390148i	$-0.872424\pi$
$569$		−	18.6130i		−	0.780296i	0.920752	−	0.390148i	$-0.127576\pi$
$570$		0			0
$571$	4.69112			0.196317			0.0981586	−	0.995171i	$-0.468705\pi$
$571$	4.69112			0.196317			0.0981586	+	0.995171i	$0.468705\pi$
$572$	−0.309117	−	5.40059i	−0.0129248	−	0.225810i
$573$		0			0
$574$	−0.153343	+	0.162371i	−0.00640042	+	0.00677724i
$575$	0.440945			0.0183887
$576$		0			0
$577$	−9.27967			−0.386318			−0.193159	−	0.981167i	$-0.561873\pi$
$577$	−9.27967			−0.386318			−0.193159	+	0.981167i	$0.561873\pi$
$578$	−16.0295	+	16.9733i	−0.666741	+	0.705995i
$579$		0			0
$580$	1.07779	+	18.8301i	0.0447527	+	0.781877i
$581$	8.41084			0.348940
$582$		0			0
$583$			9.48752i			0.392933i
$584$	15.1939	+	12.7882i	0.628729	+	0.529179i
$585$		0			0
$586$	7.36988	−	7.80377i	0.304447	−	0.322371i
$587$			34.3528i			1.41789i	0.705264	+	0.708945i	$0.250829\pi$
$587$			34.3528i			1.41789i	−0.705264	+	0.708945i	$0.749171\pi$
$588$		0			0
$589$		−	6.58922i		−	0.271504i
$590$	16.5836	+	15.6615i	0.682734	+	0.644774i
$591$		0			0
$592$	−1.42664	−	12.4217i	−0.0586347	−	0.510527i
$593$			44.4288i			1.82447i	0.409666	+	0.912236i	$0.365645\pi$
$593$			44.4288i			1.82447i	−0.409666	+	0.912236i	$0.634355\pi$
$594$		0			0
$595$	−1.55207			−0.0636285
$596$	0.560674	+	9.79557i	0.0229661	+	0.401242i
$597$		0			0
$598$	−4.93947	−	4.66483i	−0.201990	−	0.190759i
$599$	13.8604			0.566322			0.283161	−	0.959072i	$-0.408617\pi$
$599$	13.8604			0.566322			0.283161	+	0.959072i	$0.408617\pi$
$600$		0			0
$601$	−6.51128			−0.265601			−0.132800	−	0.991143i	$-0.542397\pi$
$601$	−6.51128			−0.265601			−0.132800	+	0.991143i	$0.542397\pi$
$602$	7.28950	+	6.88420i	0.297098	+	0.280579i
$603$		0			0
$604$	37.8422	−	2.16600i	1.53978	−	0.0881331i
$605$	−11.3431			−0.461162
$606$		0			0
$607$			43.5994i			1.76964i	0.465929	+	0.884822i	$0.345720\pi$
$607$			43.5994i			1.76964i	−0.465929	+	0.884822i	$0.654280\pi$
$608$	3.18041	−	4.24975i	0.128983	−	0.172350i
$609$		0			0
$610$	10.4185	+	9.83925i	0.421834	+	0.398380i
$611$		−	0.968597i		−	0.0391852i
$612$		0			0
$613$			22.4072i			0.905017i	0.891760	+	0.452508i	$0.149471\pi$
$613$			22.4072i			0.905017i	−0.891760	+	0.452508i	$0.850529\pi$
$614$	17.5992	−	18.6353i	0.710245	−	0.752060i
$615$		0			0
$616$	5.24486	+	4.41441i	0.211321	+	0.177862i
$617$			30.5128i			1.22840i	0.789151	+	0.614199i	$0.210521\pi$
$617$			30.5128i			1.22840i	−0.789151	+	0.614199i	$0.789479\pi$
$618$		0			0
$619$	−13.5504			−0.544637			−0.272319	−	0.962207i	$-0.587790\pi$
$619$	−13.5504			−0.544637			−0.272319	+	0.962207i	$0.587790\pi$
$620$	31.0302	−	1.77609i	1.24620	−	0.0713294i
$621$		0			0
$622$	−16.5354	+	17.5089i	−0.663008	+	0.702042i
$623$	−7.34335			−0.294205
$624$		0			0
$625$	−24.4774			−0.979095
$626$	−7.22692	+	7.65240i	−0.288846	+	0.305851i
$627$		0			0
$628$	20.1484	−	1.15325i	0.804010	−	0.0460195i
$629$	−2.19222			−0.0874097
$630$		0			0
$631$		−	26.5393i		−	1.05651i	−0.849085	−	0.528257i	$-0.822846\pi$
$631$		−	26.5393i		−	1.05651i	0.849085	−	0.528257i	$-0.177154\pi$
$632$	−12.1283	+	14.4099i	−0.482439	+	0.573195i
$633$		0			0
$634$	−2.33575	+	2.47326i	−0.0927644	+	0.0982258i
$635$		−	23.0694i		−	0.915482i
$636$		0			0
$637$			1.11593i			0.0442149i
$638$	−10.6192	−	10.0288i	−0.420419	−	0.397043i
$639$		0			0
$640$	20.8703	+	13.8318i	0.824973	+	0.546749i
$641$		−	10.3318i		−	0.408083i	−0.978962	−	0.204041i	$-0.934592\pi$
$641$		−	10.3318i		−	0.408083i	0.978962	−	0.204041i	$-0.0654077\pi$
$642$		0			0
$643$	13.5130			0.532901			0.266450	−	0.963849i	$-0.414149\pi$
$643$	13.5130			0.532901			0.266450	+	0.963849i	$0.414149\pi$
$644$	8.59596	−	0.492011i	0.338728	−	0.0193880i
$645$		0			0
$646$	−0.676624	−	0.639003i	−0.0266214	−	0.0251412i
$647$	8.31247			0.326797			0.163399	−	0.986560i	$-0.447754\pi$
$647$	8.31247			0.326797			0.163399	+	0.986560i	$0.447754\pi$
$648$		0			0
$649$	−17.6646			−0.693396
$650$	−0.117521	−	0.110987i	−0.00460955	−	0.00435326i
$651$		0			0
$652$	2.28304	+	39.8872i	0.0894109	+	1.56210i
$653$	−2.56899			−0.100533			−0.0502663	−	0.998736i	$-0.516007\pi$
$653$	−2.56899			−0.100533			−0.0502663	+	0.998736i	$0.516007\pi$
$654$		0			0
$655$			47.2647i			1.84678i
$656$	−0.0720762	−	0.627561i	−0.00281410	−	0.0245021i
$657$		0			0
$658$	0.892426	+	0.842806i	0.0347904	+	0.0328560i
$659$			12.7747i			0.497632i	0.968551	+	0.248816i	$0.0800414\pi$
$659$			12.7747i			0.497632i	−0.968551	+	0.248816i	$0.919959\pi$
$660$		0			0
$661$		−	25.8624i		−	1.00593i	−0.864307	−	0.502965i	$-0.832242\pi$
$661$		−	25.8624i		−	1.00593i	0.864307	−	0.502965i	$-0.167758\pi$
$662$	−13.9608	+	14.7827i	−0.542601	+	0.574546i
$663$		0			0
$664$	−15.3190	+	18.2008i	−0.594491	+	0.706326i
$665$			2.07659i			0.0805267i
$666$		0			0
$667$	−18.3450			−0.710320
$668$	1.58429	+	27.6793i	0.0612981	+	1.07094i
$669$		0			0
$670$	32.5936	−	34.5125i	1.25920	−	1.33333i
$671$	−11.0977			−0.428421
$672$		0			0
$673$	−33.9446			−1.30847			−0.654235	−	0.756292i	$-0.727009\pi$
$673$	−33.9446			−1.30847			−0.654235	+	0.756292i	$0.727009\pi$
$674$	−19.8503	+	21.0190i	−0.764605	+	0.809621i
$675$		0			0
$676$	−1.34342	−	23.4710i	−0.0516700	−	0.902730i
$677$	34.1280			1.31165			0.655823	−	0.754915i	$-0.272322\pi$
$677$	34.1280			1.31165			0.655823	+	0.754915i	$0.272322\pi$
$678$		0			0
$679$		−	7.99425i		−	0.306791i
$680$	2.82683	−	3.35862i	0.108404	−	0.128797i
$681$		0			0
$682$	−16.5265	+	17.4994i	−0.632831	+	0.670088i
$683$		−	6.80951i		−	0.260559i	−0.991477	−	0.130279i	$-0.958413\pi$
$683$		−	6.80951i		−	0.260559i	0.991477	−	0.130279i	$-0.0415874\pi$
$684$		0			0
$685$			24.9139i			0.951910i
$686$	−1.02818	−	0.971008i	−0.0392559	−	0.0370732i
$687$		0			0
$688$	−28.1738	+	3.23579i	−1.07412	+	0.123363i
$689$		−	4.36825i		−	0.166417i
$690$		0			0
$691$	−5.06521			−0.192690			−0.0963448	−	0.995348i	$-0.530715\pi$
$691$	−5.06521			−0.192690			−0.0963448	+	0.995348i	$0.530715\pi$
$692$	−2.45486	−	42.8890i	−0.0933197	−	1.63039i
$693$		0			0
$694$	−6.81117	−	6.43247i	−0.258549	−	0.244173i
$695$	−17.9608			−0.681291
$696$		0			0
$697$	−0.110755			−0.00419513
$698$	34.7396	+	32.8080i	1.31491	+	1.24180i
$699$		0			0
$700$	0.204517	−	0.0117061i	0.00773002	−	0.000442447i
$701$	−44.7933			−1.69182			−0.845910	−	0.533326i	$-0.820942\pi$
$701$	−44.7933			−1.69182			−0.845910	+	0.533326i	$0.820942\pi$
$702$		0			0
$703$			2.93309i			0.110624i
$704$	−19.1053	+	3.30956i	−0.720057	+	0.124734i
$705$		0			0
$706$	27.3470	+	25.8265i	1.02922	+	0.971992i
$707$		−	15.6519i		−	0.588649i
$708$		0			0
$709$			40.5597i			1.52325i	0.648018	+	0.761625i	$0.275598\pi$
$709$			40.5597i			1.52325i	−0.648018	+	0.761625i	$0.724402\pi$
$710$	14.9015	−	15.7788i	0.559242	−	0.592167i
$711$		0			0
$712$	13.3747	−	15.8907i	0.501238	−	0.595531i
$713$			30.2307i			1.13215i
$714$		0			0
$715$	−5.98566			−0.223851
$716$	7.87294	−	0.450627i	0.294225	−	0.0168407i
$717$		0			0
$718$	28.8484	−	30.5469i	1.07661	−	1.14000i
$719$	13.2926			0.495729			0.247864	−	0.968795i	$-0.420271\pi$
$719$	13.2926			0.495729			0.247864	+	0.968795i	$0.420271\pi$
$720$		0			0
$721$	−4.90314			−0.182603
$722$	17.5942	−	18.6300i	0.654788	−	0.693338i
$723$		0			0
$724$	−23.5312	+	1.34687i	−0.874530	+	0.0500559i
$725$	−0.436468			−0.0162100
$726$		0			0
$727$		−	28.6102i		−	1.06109i	−0.847656	−	0.530546i	$-0.821987\pi$
$727$		−	28.6102i		−	1.06109i	0.847656	−	0.530546i	$-0.178013\pi$
$728$	−2.41484	−	2.03249i	−0.0894999	−	0.0753290i
$729$		0			0
$730$	15.0880	−	15.9763i	0.558433	−	0.591311i
$731$			4.97222i			0.183904i
$732$		0			0
$733$			33.9007i			1.25215i	0.779763	+	0.626075i	$0.215340\pi$
$733$			33.9007i			1.25215i	−0.779763	+	0.626075i	$0.784660\pi$
$734$	16.1353	+	15.2382i	0.595565	+	0.562452i
$735$		0			0
$736$	−14.5914	+	19.4975i	−0.537847	+	0.718686i
$737$			36.7623i			1.35416i
$738$		0			0
$739$	−11.1200			−0.409055			−0.204528	−	0.978861i	$-0.565566\pi$
$739$	−11.1200			−0.409055			−0.204528	+	0.978861i	$0.565566\pi$
$740$	−13.8126	+	0.790599i	−0.507761	+	0.0290630i
$741$		0			0
$742$	4.02473	+	3.80095i	0.147752	+	0.139537i
$743$	45.7857			1.67971			0.839857	−	0.542808i	$-0.182639\pi$
$743$	45.7857			1.67971			0.839857	+	0.542808i	$0.182639\pi$
$744$		0			0
$745$	10.8568			0.397761
$746$	11.3376	+	10.7072i	0.415098	+	0.392018i
$747$		0			0
$748$	0.194269	+	3.39409i	0.00710319	+	0.124100i
$749$	15.1434			0.553329
$750$		0			0
$751$			13.8013i			0.503616i	0.967777	+	0.251808i	$0.0810252\pi$
$751$			13.8013i			0.503616i	−0.967777	+	0.251808i	$0.918975\pi$
$752$	−3.44921	+	0.396146i	−0.125780	+	0.0144460i
$753$		0			0
$754$	4.88931	+	4.61746i	0.178058	+	0.168158i
$755$		−	41.9418i		−	1.52642i
$756$		0			0
$757$			5.94985i			0.216251i	0.994137	+	0.108126i	$0.0344848\pi$
$757$			5.94985i			0.216251i	−0.994137	+	0.108126i	$0.965515\pi$
$758$	7.61985	−	8.06846i	0.276765	−	0.293060i
$759$		0			0
$760$	−4.49366	−	3.78216i	−0.163002	−	0.137193i
$761$			38.1237i			1.38198i	0.722864	+	0.690991i	$0.242825\pi$
$761$			38.1237i			1.38198i	−0.722864	+	0.690991i	$0.757175\pi$
$762$		0			0
$763$	−2.72939			−0.0988106
$764$	1.89791	+	33.1585i	0.0686640	+	1.19963i
$765$		0			0
$766$	−3.16780	+	3.35430i	−0.114457	+	0.121196i
$767$	8.13314			0.293671
$768$		0			0
$769$	15.5207			0.559689			0.279845	−	0.960045i	$-0.409717\pi$
$769$	15.5207			0.559689			0.279845	+	0.960045i	$0.409717\pi$
$770$	5.20831	−	5.51494i	0.187694	−	0.198745i
$771$		0			0
$772$	−0.789062	−	13.7858i	−0.0283990	−	0.496160i
$773$	39.6525			1.42620			0.713101	−	0.701061i	$-0.247290\pi$
$773$	39.6525			1.42620			0.713101	+	0.701061i	$0.247290\pi$
$774$		0			0
$775$			0.719256i			0.0258365i
$776$	17.2993	+	14.5602i	0.621007	+	0.522680i
$777$		0			0
$778$	−1.12343	+	1.18957i	−0.0402769	+	0.0426482i
$779$			0.148184i			0.00530925i
$780$		0			0
$781$			16.8073i			0.601414i
$782$	3.10429	+	2.93169i	0.111009	+	0.104837i
$783$		0			0
$784$	3.97388	−	0.456405i	0.141924	−	0.0163002i
$785$		−	22.3312i		−	0.797035i
$786$		0			0
$787$	−50.2403			−1.79087			−0.895436	−	0.445189i	$-0.853136\pi$
$787$	−50.2403			−1.79087			−0.895436	+	0.445189i	$0.853136\pi$
$788$	1.02662	+	17.9361i	0.0365718	+	0.638948i
$789$		0			0
$790$	15.1520	+	14.3095i	0.539082	+	0.509109i
$791$	−2.84331			−0.101096
$792$		0			0
$793$	5.10960			0.181447
$794$	−2.48094	−	2.34299i	−0.0880451	−	0.0831498i
$795$		0			0
$796$	−22.8481	+	1.30777i	−0.809828	+	0.0463525i
$797$	1.78519			0.0632345			0.0316173	−	0.999500i	$-0.489934\pi$
$797$	1.78519			0.0632345			0.0316173	+	0.999500i	$0.489934\pi$
$798$		0			0
$799$			0.608730i			0.0215353i
$800$	−0.347163	+	0.463889i	−0.0122741	+	0.0164009i
$801$		0			0
$802$	−7.69123	−	7.26359i	−0.271587	−	0.256486i
$803$			17.0178i			0.600545i
$804$		0			0
$805$		−	9.52720i		−	0.335790i
$806$	7.60912	−	8.05710i	0.268020	−	0.283799i
$807$		0			0
$808$	33.8701	+	28.5073i	1.19154	+	1.00288i
$809$		−	31.9043i		−	1.12169i	−0.827919	−	0.560847i	$-0.810476\pi$
$809$		−	31.9043i		−	1.12169i	0.827919	−	0.560847i	$-0.189524\pi$
$810$		0			0
$811$	−12.5528			−0.440789			−0.220394	−	0.975411i	$-0.570734\pi$
$811$	−12.5528			−0.440789			−0.220394	+	0.975411i	$0.570734\pi$
$812$	−8.50867	+	0.487015i	−0.298596	+	0.0170909i
$813$		0			0
$814$	7.35650	−	7.78961i	0.257845	−	0.273026i
$815$	44.2084			1.54855
$816$		0			0
$817$	6.65259			0.232745
$818$	7.28084	−	7.70950i	0.254569	−	0.269556i
$819$		0			0
$820$	−0.697834	+	0.0399423i	−0.0243694	+	0.00139484i
$821$	42.1349			1.47052			0.735260	−	0.677786i	$-0.237060\pi$
$821$	42.1349			1.47052			0.735260	+	0.677786i	$0.237060\pi$
$822$		0			0
$823$			1.50592i			0.0524931i	0.999656	+	0.0262465i	$0.00835549\pi$
$823$			1.50592i			0.0524931i	−0.999656	+	0.0262465i	$0.991645\pi$
$824$	8.93026	−	10.6102i	0.311100	−	0.369625i
$825$		0			0
$826$	−7.07690	+	7.49355i	−0.246237	+	0.260734i
$827$			40.6098i			1.41214i	0.708141	+	0.706071i	$0.249534\pi$
$827$			40.6098i			1.41214i	−0.708141	+	0.706071i	$0.750466\pi$
$828$		0			0
$829$		−	35.4547i		−	1.23139i	−0.787984	−	0.615696i	$-0.788875\pi$
$829$		−	35.4547i		−	1.23139i	0.787984	−	0.615696i	$-0.211125\pi$
$830$	19.1380	+	18.0739i	0.664290	+	0.627355i
$831$		0			0
$832$	8.79646	−	1.52379i	0.304962	−	0.0528279i
$833$		−	0.701326i		−	0.0242995i
$834$		0			0
$835$	30.6779			1.06165
$836$	4.54112	−	0.259923i	0.157058	−	0.00898961i
$837$		0			0
$838$	27.5224	+	25.9921i	0.950745	+	0.897883i
$839$	−31.8372			−1.09914			−0.549571	−	0.835447i	$-0.685209\pi$
$839$	−31.8372			−1.09914			−0.549571	+	0.835447i	$0.685209\pi$
$840$		0			0
$841$	−10.8413			−0.373839
$842$	28.9551	+	27.3452i	0.997858	+	0.942377i
$843$		0			0
$844$	−2.72046	−	47.5293i	−0.0936420	−	1.63602i
$845$	−26.0137			−0.894898
$846$		0			0
$847$		−	5.12555i		−	0.176116i
$848$	−15.5555	+	1.78657i	−0.534178	+	0.0613510i
$849$		0			0
$850$	0.0738579	+	0.0697514i	0.00253331	+	0.00239245i
$851$		−	13.4567i		−	0.461291i
$852$		0			0
$853$		−	30.0499i		−	1.02889i	−0.857523	−	0.514445i	$-0.827998\pi$
$853$		−	30.0499i		−	1.02889i	0.857523	−	0.514445i	$-0.172002\pi$
$854$	−4.44602	+	4.70778i	−0.152140	+	0.161097i
$855$		0			0
$856$	−27.5813	+	32.7699i	−0.942708	+	1.12005i
$857$		−	26.7594i		−	0.914085i	−0.889445	−	0.457043i	$-0.848909\pi$
$857$		−	26.7594i		−	0.914085i	0.889445	−	0.457043i	$-0.151091\pi$
$858$		0			0
$859$	−3.98544			−0.135981			−0.0679907	−	0.997686i	$-0.521659\pi$
$859$	−3.98544			−0.135981			−0.0679907	+	0.997686i	$0.521659\pi$
$860$	1.79317	+	31.3286i	0.0611466	+	1.06830i
$861$		0			0
$862$	−29.0680	+	30.7793i	−0.990059	+	1.04835i
$863$	−33.1318			−1.12782			−0.563910	−	0.825836i	$-0.690704\pi$
$863$	−33.1318			−1.12782			−0.563910	+	0.825836i	$0.690704\pi$
$864$		0			0
$865$	−47.5353			−1.61625
$866$	37.9767	−	40.2125i	1.29050	−	1.36648i
$867$		0			0
$868$	0.802554	+	14.0215i	0.0272404	+	0.475920i
$869$	−16.1397			−0.547501
$870$		0			0
$871$		−	16.9261i		−	0.573519i
$872$	4.97113	−	5.90631i	0.168344	−	0.200013i
$873$		0			0
$874$	3.92245	−	4.15338i	0.132679	−	0.140490i
$875$		−	11.2919i		−	0.381736i
$876$		0			0
$877$		−	4.35210i		−	0.146960i	−0.997297	−	0.0734800i	$-0.976589\pi$
$877$		−	4.35210i		−	0.146960i	0.997297	−	0.0734800i	$-0.0234105\pi$
$878$	32.3208	+	30.5237i	1.09077	+	1.03013i
$879$		0			0
$880$	2.44807	+	21.3151i	0.0825245	+	0.718534i
$881$			37.2945i			1.25648i	0.778018	+	0.628242i	$0.216225\pi$
$881$			37.2945i			1.25648i	−0.778018	+	0.628242i	$0.783775\pi$
$882$		0			0
$883$	−44.7359			−1.50548			−0.752742	−	0.658315i	$-0.771269\pi$
$883$	−44.7359			−1.50548			−0.752742	+	0.658315i	$0.771269\pi$
$884$	−0.0894455	−	1.56271i	−0.00300838	−	0.0525596i
$885$		0			0
$886$	−24.9173	−	23.5318i	−0.837112	−	0.790568i
$887$	3.69357			0.124018			0.0620090	−	0.998076i	$-0.480249\pi$
$887$	3.69357			0.124018			0.0620090	+	0.998076i	$0.480249\pi$
$888$		0			0
$889$	10.4243			0.349619
$890$	−16.7090	−	15.7800i	−0.560089	−	0.528947i
$891$		0			0
$892$	8.84236	−	0.506114i	0.296064	−	0.0169460i
$893$	0.814451			0.0272546
$894$		0			0
$895$		−	8.72584i		−	0.291673i
$896$	−6.25011	+	9.43059i	−0.208802	+	0.315054i
$897$		0			0
$898$	23.2435	+	21.9511i	0.775645	+	0.732519i
$899$		−	29.9237i		−	0.998012i
$900$		0			0
$901$			2.74530i			0.0914591i
$902$	0.371662	−	0.393543i	0.0123750	−	0.0131035i
$903$		0			0
$904$	5.17861	−	6.15282i	0.172238	−	0.204640i
$905$			26.0804i			0.866943i
$906$		0			0
$907$	−9.61629			−0.319304			−0.159652	−	0.987173i	$-0.551037\pi$
$907$	−9.61629			−0.319304			−0.159652	+	0.987173i	$0.551037\pi$
$908$	12.9139	−	0.739159i	0.428563	−	0.0245299i
$909$		0			0
$910$	−2.39801	+	2.53919i	−0.0794933	+	0.0841735i
$911$	53.1598			1.76126			0.880632	−	0.473802i	$-0.157119\pi$
$911$	53.1598			1.76126			0.880632	+	0.473802i	$0.157119\pi$
$912$		0			0
$913$	−20.3856			−0.674664
$914$	9.08156	−	9.61623i	0.300391	−	0.318077i
$915$		0			0
$916$	22.9054	−	1.31105i	0.756817	−	0.0433183i
$917$	−21.3573			−0.705280
$918$		0			0
$919$		−	33.3183i		−	1.09907i	−0.835471	−	0.549534i	$-0.814805\pi$
$919$		−	33.3183i		−	1.09907i	0.835471	−	0.549534i	$-0.185195\pi$
$920$	20.6165	+	17.3522i	0.679707	+	0.572085i
$921$		0			0
$922$	−11.2538	+	11.9163i	−0.370623	+	0.392443i
$923$		−	7.73845i		−	0.254714i
$924$		0			0
$925$		−	0.320166i		−	0.0105270i
$926$	−18.3322	−	17.3129i	−0.602435	−	0.568939i
$927$		0			0
$928$	14.4433	−	19.2995i	0.474123	−	0.633536i
$929$			13.5434i			0.444343i	0.975008	+	0.222172i	$0.0713146\pi$
$929$			13.5434i			0.444343i	−0.975008	+	0.222172i	$0.928685\pi$
$930$		0			0
$931$	−0.938340			−0.0307528
$932$	39.6707	−	2.27065i	1.29946	−	0.0743777i
$933$		0			0
$934$	3.60047	+	3.40028i	0.117811	+	0.111261i
$935$	3.76178			0.123024
$936$		0			0
$937$	42.3432			1.38329			0.691647	−	0.722236i	$-0.256886\pi$
$937$	42.3432			1.38329			0.691647	+	0.722236i	$0.256886\pi$
$938$	15.5950	+	14.7279i	0.509195	+	0.480884i
$939$		0			0
$940$	0.219531	+	3.83544i	0.00716031	+	0.125098i
$941$	−60.9773			−1.98780			−0.993902	−	0.110267i	$-0.964829\pi$
$941$	−60.9773			−1.98780			−0.993902	+	0.110267i	$0.964829\pi$
$942$		0			0
$943$		−	0.679855i		−	0.0221391i
$944$	−3.32637	−	28.9624i	−0.108264	−	0.942646i
$945$		0			0
$946$	−17.6677	−	16.6854i	−0.574428	−	0.542489i
$947$		−	39.4879i		−	1.28318i	−0.767047	−	0.641591i	$-0.778275\pi$
$947$		−	39.4879i		−	1.28318i	0.767047	−	0.641591i	$-0.221725\pi$
$948$		0			0
$949$		−	7.83534i		−	0.254346i
$950$	0.0933239	−	0.0988183i	0.00302783	−	0.00320609i
$951$		0			0
$952$	1.51764	+	1.27735i	0.0491871	+	0.0413991i
$953$		−	25.8210i		−	0.836425i	−0.908349	−	0.418213i	$-0.862657\pi$
$953$		−	25.8210i		−	0.836425i	0.908349	−	0.418213i	$-0.137343\pi$
$954$		0			0
$955$	36.7507			1.18922
$956$	1.16813	+	20.4085i	0.0377801	+	0.660058i
$957$		0			0
$958$	17.7681	−	18.8142i	0.574062	−	0.607860i
$959$	−11.2577			−0.363531
$960$		0			0
$961$	−18.3114			−0.590690
$962$	−3.38708	+	3.58650i	−0.109204	+	0.115633i
$963$		0			0
$964$	−3.22073	−	56.2695i	−0.103733	−	1.81232i
$965$	−15.2792			−0.491856
$966$		0			0
$967$		−	4.92813i		−	0.158478i	−0.996856	−	0.0792390i	$-0.974751\pi$
$967$		−	4.92813i		−	0.158478i	0.996856	−	0.0792390i	$-0.0252490\pi$
$968$	11.0915	+	9.33534i	0.356495	+	0.300049i
$969$		0			0
$970$	17.1787	−	18.1901i	0.551575	−	0.584049i
$971$		−	20.9043i		−	0.670850i	−0.942067	−	0.335425i	$-0.891120\pi$
$971$		−	20.9043i		−	0.670850i	0.942067	−	0.335425i	$-0.108880\pi$
$972$		0			0
$973$		−	8.11586i		−	0.260183i
$974$	−25.0421	−	23.6498i	−0.802402	−	0.757787i
$975$		0			0
$976$	−2.08977	−	18.1955i	−0.0668920	−	0.582423i
$977$			16.6995i			0.534266i	0.963660	+	0.267133i	$0.0860763\pi$
$977$			16.6995i			0.534266i	−0.963660	+	0.267133i	$0.913924\pi$
$978$		0			0
$979$	17.7983			0.568835
$980$	−0.252925	−	4.41886i	−0.00807938	−	0.141155i
$981$		0			0
$982$	−26.5762	−	25.0985i	−0.848081	−	0.800927i
$983$	27.7932			0.886465			0.443232	−	0.896407i	$-0.353832\pi$
$983$	27.7932			0.886465			0.443232	+	0.896407i	$0.353832\pi$
$984$		0			0
$985$	19.8792			0.633404
$986$	−3.07276	−	2.90191i	−0.0978567	−	0.0924158i
$987$		0			0
$988$	−2.09083	+	0.119674i	−0.0665181	+	0.00380733i
$989$	−30.5215			−0.970526
$990$		0			0
$991$			38.3482i			1.21817i	0.793104	+	0.609086i	$0.208464\pi$
$991$			38.3482i			1.21817i	−0.793104	+	0.609086i	$0.791536\pi$
$992$	−31.8037	−	23.8011i	−1.00977	−	0.755685i
$993$		0			0
$994$	7.12989	+	6.73346i	0.226146	+	0.213572i
$995$			25.3233i			0.802802i
$996$		0			0
$997$			27.7418i			0.878590i	0.898343	+	0.439295i	$0.144772\pi$
$997$			27.7418i			0.878590i	−0.898343	+	0.439295i	$0.855228\pi$
$998$	13.1504	−	13.9246i	0.416269	−	0.440776i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.c.323.12	yes	32
3.2	odd	2	inner	1512.2.j.c.323.21	yes	32
4.3	odd	2		6048.2.j.c.5615.5		32
8.3	odd	2	inner	1512.2.j.c.323.22	yes	32
8.5	even	2		6048.2.j.c.5615.27		32
12.11	even	2		6048.2.j.c.5615.28		32
24.5	odd	2		6048.2.j.c.5615.6		32
24.11	even	2	inner	1512.2.j.c.323.11	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.c.323.11	✓	32	24.11	even	2	inner
1512.2.j.c.323.12	yes	32	1.1	even	1	trivial
1512.2.j.c.323.21	yes	32	3.2	odd	2	inner
1512.2.j.c.323.22	yes	32	8.3	odd	2	inner
6048.2.j.c.5615.5		32	4.3	odd	2
6048.2.j.c.5615.6		32	24.5	odd	2
6048.2.j.c.5615.27		32	8.5	even	2
6048.2.j.c.5615.28		32	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.971008 + 1.02818i) q^{2} +(-0.114288 - 1.99673i) q^{4} -2.21305 q^{5} -1.00000i q^{7} +(2.16396 + 1.82133i) q^{8} +O(q^{10})\)	\(q+(-0.971008 + 1.02818i) q^{2} +(-0.114288 - 1.99673i) q^{4} -2.21305 q^{5} -1.00000i q^{7} +(2.16396 + 1.82133i) q^{8} +(2.14889 - 2.27540i) q^{10} +2.42373i q^{11} -1.11593i q^{13} +(1.02818 + 0.971008i) q^{14} +(-3.97388 + 0.456405i) q^{16} +0.701326i q^{17} +0.938340 q^{19} +(0.252925 + 4.41886i) q^{20} +(-2.49201 - 2.35346i) q^{22} -4.30502 q^{23} -0.102426 q^{25} +(1.14737 + 1.08358i) q^{26} +(-1.99673 + 0.114288i) q^{28} +4.26130 q^{29} -7.02221i q^{31} +(3.38940 - 4.52901i) q^{32} +(-0.721086 - 0.680993i) q^{34} +2.21305i q^{35} +3.12583i q^{37} +(-0.911135 + 0.964777i) q^{38} +(-4.78895 - 4.03070i) q^{40} +0.157922i q^{41} +7.08975 q^{43} +(4.83953 - 0.277003i) q^{44} +(4.18020 - 4.42631i) q^{46} +0.867970 q^{47} -1.00000 q^{49} +(0.0994564 - 0.105312i) q^{50} +(-2.22822 + 0.127538i) q^{52} +3.91444 q^{53} -5.36382i q^{55} +(1.82133 - 2.16396i) q^{56} +(-4.13775 + 4.38136i) q^{58} +7.28820i q^{59} +4.57877i q^{61} +(7.22006 + 6.81862i) q^{62} +(1.36548 + 7.88260i) q^{64} +2.46961i q^{65} +15.1677 q^{67} +(1.40036 - 0.0801531i) q^{68} +(-2.27540 - 2.14889i) q^{70} +6.93451 q^{71} +7.02133 q^{73} +(-3.21390 - 3.03520i) q^{74} +(-0.107241 - 1.87361i) q^{76} +2.42373 q^{77} +6.65903i q^{79} +(8.79437 - 1.01005i) q^{80} +(-0.162371 - 0.153343i) q^{82} +8.41084i q^{83} -1.55207i q^{85} +(-6.88420 + 7.28950i) q^{86} +(-4.41441 + 5.24486i) q^{88} -7.34335i q^{89} -1.11593 q^{91} +(0.492011 + 8.59596i) q^{92} +(-0.842806 + 0.892426i) q^{94} -2.07659 q^{95} +7.99425 q^{97} +(0.971008 - 1.02818i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4}+O(q^{10}) \) 32 * q + 8 * q^4	\( 32 q + 8 q^{4} - 8 q^{10} - 8 q^{16} - 64 q^{19} + 24 q^{22} - 16 q^{25} - 8 q^{28} + 8 q^{34} - 24 q^{40} - 48 q^{43} - 8 q^{46} - 32 q^{49} - 24 q^{52} - 96 q^{58} - 40 q^{64} + 16 q^{67} - 16 q^{70} - 16 q^{73} + 16 q^{76} + 24 q^{82} + 72 q^{88} + 16 q^{91} - 56 q^{94} + 64 q^{97}+O(q^{100}) \) 32 * q + 8 * q^4 - 8 * q^10 - 8 * q^16 - 64 * q^19 + 24 * q^22 - 16 * q^25 - 8 * q^28 + 8 * q^34 - 24 * q^40 - 48 * q^43 - 8 * q^46 - 32 * q^49 - 24 * q^52 - 96 * q^58 - 40 * q^64 + 16 * q^67 - 16 * q^70 - 16 * q^73 + 16 * q^76 + 24 * q^82 + 72 * q^88 + 16 * q^91 - 56 * q^94 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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