LMFDB - Embedded newform 1120.2.bz.e.591.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1120,2,Mod(271,1120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1120, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("1120.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.bz (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.94324502638$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			591.3
Character	$\chi$	$=$	1120.591
Dual form			1120.2.bz.e.271.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.94732 - 1.12428i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.47009 - 0.947962i) q^{7} +(1.02803 + 1.78060i) q^{9} +O(q^{10})$	\(q+(-1.94732 - 1.12428i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.47009 - 0.947962i) q^{7} +(1.02803 + 1.78060i) q^{9} +(-0.656783 + 1.13758i) q^{11} -3.02437 q^{13} +2.24857i q^{15} +(-0.313561 - 0.181034i) q^{17} +(-3.16395 + 1.82671i) q^{19} +(3.74428 + 4.62307i) q^{21} +(5.74815 - 3.31870i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.12251i q^{27} -3.35458i q^{29} +(-3.37591 + 5.84724i) q^{31} +(2.55793 - 1.47682i) q^{33} +(0.414089 + 2.61315i) q^{35} +(3.89163 - 2.24684i) q^{37} +(5.88941 + 3.40026i) q^{39} +4.07897i q^{41} +5.01967 q^{43} +(1.02803 - 1.78060i) q^{45} +(-6.23329 - 10.7964i) q^{47} +(5.20274 + 4.68311i) q^{49} +(0.407068 + 0.705063i) q^{51} +(-2.39639 - 1.38356i) q^{53} +1.31357 q^{55} +8.21496 q^{57} +(11.5288 + 6.65617i) q^{59} +(5.04721 + 8.74202i) q^{61} +(-0.851393 - 5.37279i) q^{63} +(1.51219 + 2.61918i) q^{65} +(0.897462 - 1.55445i) q^{67} -14.9246 q^{69} +12.4911i q^{71} +(7.83291 + 4.52233i) q^{73} +(1.94732 - 1.12428i) q^{75} +(2.70070 - 2.18733i) q^{77} +(7.89731 - 4.55951i) q^{79} +(5.47040 - 9.47500i) q^{81} +10.7568i q^{83} +0.362069i q^{85} +(-3.77150 + 6.53243i) q^{87} +(-1.99844 + 1.15380i) q^{89} +(7.47049 + 2.86699i) q^{91} +(13.1479 - 7.59096i) q^{93} +(3.16395 + 1.82671i) q^{95} +2.74318i q^{97} -2.70078 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9}+O(q^{10}) $ 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9	$ 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9} - 8 q^{11} + 20 q^{13} + 6 q^{17} - 18 q^{19} - 26 q^{21} - 18 q^{23} - 12 q^{25} + 6 q^{31} + 12 q^{33} + 8 q^{35} + 18 q^{39} - 32 q^{43} + 12 q^{45} + 8 q^{49} + 22 q^{51} + 30 q^{53} + 16 q^{55} - 44 q^{57} + 18 q^{59} + 22 q^{61} + 12 q^{63} - 10 q^{65} + 8 q^{67} - 12 q^{69} + 30 q^{73} + 12 q^{75} - 32 q^{77} - 6 q^{79} - 4 q^{81} - 14 q^{87} - 60 q^{89} - 18 q^{91} - 18 q^{93} + 18 q^{95} + 56 q^{99}+O(q^{100}) $ 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9 - 8 * q^11 + 20 * q^13 + 6 * q^17 - 18 * q^19 - 26 * q^21 - 18 * q^23 - 12 * q^25 + 6 * q^31 + 12 * q^33 + 8 * q^35 + 18 * q^39 - 32 * q^43 + 12 * q^45 + 8 * q^49 + 22 * q^51 + 30 * q^53 + 16 * q^55 - 44 * q^57 + 18 * q^59 + 22 * q^61 + 12 * q^63 - 10 * q^65 + 8 * q^67 - 12 * q^69 + 30 * q^73 + 12 * q^75 - 32 * q^77 - 6 * q^79 - 4 * q^81 - 14 * q^87 - 60 * q^89 - 18 * q^91 - 18 * q^93 + 18 * q^95 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.94732	−	1.12428i	−1.12428	−	0.649106i	−0.181793	−	0.983337i	$-0.558190\pi$
$3$	−1.94732	−	1.12428i	−1.12428	−	0.649106i	−0.942491	+	0.334231i	$0.891524\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−2.47009	−	0.947962i	−0.933608	−	0.358296i
$7$	−2.47009	−	0.947962i	−0.933608	−	0.358296i
$8$		0			0
$9$	1.02803	+	1.78060i	0.342677	+	0.593534i
$10$		0			0
$11$	−0.656783	+	1.13758i	−0.198028	+	0.342994i	−0.947889	−	0.318601i	$-0.896787\pi$
$11$	−0.656783	+	1.13758i	−0.198028	+	0.342994i	0.749861	+	0.661595i	$0.230120\pi$
$12$		0			0
$13$	−3.02437			−0.838810			−0.419405	−	0.907799i	$-0.637761\pi$
$13$	−3.02437			−0.838810			−0.419405	+	0.907799i	$0.637761\pi$
$14$		0			0
$15$			2.24857i			0.580578i
$16$		0			0
$17$	−0.313561	−	0.181034i	−0.0760497	−	0.0439073i	0.461493	−	0.887144i	$-0.347314\pi$
$17$	−0.313561	−	0.181034i	−0.0760497	−	0.0439073i	−0.537543	+	0.843237i	$0.680647\pi$
$18$		0			0
$19$	−3.16395	+	1.82671i	−0.725861	+	0.419076i	−0.816906	−	0.576771i	$-0.804313\pi$
$19$	−3.16395	+	1.82671i	−0.725861	+	0.419076i	0.0910453	+	0.995847i	$0.470979\pi$
$20$		0			0
$21$	3.74428	+	4.62307i	0.817069	+	1.00884i
$22$		0			0
$23$	5.74815	−	3.31870i	1.19857	−	0.691996i	0.238336	−	0.971183i	$-0.423398\pi$
$23$	5.74815	−	3.31870i	1.19857	−	0.691996i	0.960237	+	0.279186i	$0.0900647\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$			2.12251i			0.408476i
$28$		0			0
$29$		−	3.35458i		−	0.622929i	−0.950258	−	0.311465i	$-0.899180\pi$
$29$		−	3.35458i		−	0.622929i	0.950258	−	0.311465i	$-0.100820\pi$
$30$		0			0
$31$	−3.37591	+	5.84724i	−0.606330	+	1.05020i	0.385509	+	0.922704i	$0.374026\pi$
$31$	−3.37591	+	5.84724i	−0.606330	+	1.05020i	−0.991840	+	0.127491i	$0.959308\pi$
$32$		0			0
$33$	2.55793	−	1.47682i	0.445279	−	0.257082i
$34$		0			0
$35$	0.414089	+	2.61315i	0.0699938	+	0.441702i
$36$		0			0
$37$	3.89163	−	2.24684i	0.639781	−	0.369378i	−0.144749	−	0.989468i	$-0.546238\pi$
$37$	3.89163	−	2.24684i	0.639781	−	0.369378i	0.784530	+	0.620091i	$0.212904\pi$
$38$		0			0
$39$	5.88941	+	3.40026i	0.943061	+	0.544477i
$40$		0			0
$41$			4.07897i			0.637029i	0.947918	+	0.318514i	$0.103184\pi$
$41$			4.07897i			0.637029i	−0.947918	+	0.318514i	$0.896816\pi$
$42$		0			0
$43$	5.01967			0.765493			0.382746	−	0.923853i	$-0.374978\pi$
$43$	5.01967			0.765493			0.382746	+	0.923853i	$0.374978\pi$
$44$		0			0
$45$	1.02803	−	1.78060i	0.153250	−	0.265437i
$46$		0			0
$47$	−6.23329	−	10.7964i	−0.909219	−	1.57481i	−0.815151	−	0.579249i	$-0.803346\pi$
$47$	−6.23329	−	10.7964i	−0.909219	−	1.57481i	−0.0940684	−	0.995566i	$-0.529987\pi$
$48$		0			0
$49$	5.20274	+	4.68311i	0.743248	+	0.669016i
$50$		0			0
$51$	0.407068	+	0.705063i	0.0570010	+	0.0987286i
$52$		0			0
$53$	−2.39639	−	1.38356i	−0.329170	−	0.190046i	0.326303	−	0.945265i	$-0.394197\pi$
$53$	−2.39639	−	1.38356i	−0.329170	−	0.190046i	−0.655473	+	0.755219i	$0.727531\pi$
$54$		0			0
$55$	1.31357			0.177121
$56$		0			0
$57$	8.21496			1.08810
$58$		0			0
$59$	11.5288	+	6.65617i	1.50093	+	0.866559i	0.999999	+	0.00106912i	$0.000340311\pi$
$59$	11.5288	+	6.65617i	1.50093	+	0.866559i	0.500926	+	0.865490i	$0.332993\pi$
$60$		0			0
$61$	5.04721	+	8.74202i	0.646229	+	1.11930i	0.984016	+	0.178079i	$0.0569882\pi$
$61$	5.04721	+	8.74202i	0.646229	+	1.11930i	−0.337787	+	0.941222i	$0.609678\pi$
$62$		0			0
$63$	−0.851393	−	5.37279i	−0.107265	−	0.676908i
$64$		0			0
$65$	1.51219	+	2.61918i	0.187564	+	0.324870i
$66$		0			0
$67$	0.897462	−	1.55445i	0.109642	−	0.189906i	−0.805983	−	0.591939i	$-0.798363\pi$
$67$	0.897462	−	1.55445i	0.109642	−	0.189906i	0.915625	+	0.402032i	$0.131696\pi$
$68$		0			0
$69$	−14.9246			−1.79672
$70$		0			0
$71$			12.4911i			1.48242i	0.671276	+	0.741208i	$0.265747\pi$
$71$			12.4911i			1.48242i	−0.671276	+	0.741208i	$0.734253\pi$
$72$		0			0
$73$	7.83291	+	4.52233i	0.916772	+	0.529299i	0.882604	−	0.470117i	$-0.155788\pi$
$73$	7.83291	+	4.52233i	0.916772	+	0.529299i	0.0341685	+	0.999416i	$0.489122\pi$
$74$		0			0
$75$	1.94732	−	1.12428i	0.224857	−	0.129821i
$76$		0			0
$77$	2.70070	−	2.18733i	0.307774	−	0.249269i
$78$		0			0
$79$	7.89731	−	4.55951i	0.888517	−	0.512985i	0.0150598	−	0.999887i	$-0.495206\pi$
$79$	7.89731	−	4.55951i	0.888517	−	0.512985i	0.873457	+	0.486901i	$0.161873\pi$
$80$		0			0
$81$	5.47040	−	9.47500i	0.607822	−	1.05278i
$82$		0			0
$83$			10.7568i			1.18072i	0.807141	+	0.590359i	$0.201014\pi$
$83$			10.7568i			1.18072i	−0.807141	+	0.590359i	$0.798986\pi$
$84$		0			0
$85$			0.362069i			0.0392719i
$86$		0			0
$87$	−3.77150	+	6.53243i	−0.404347	+	0.700350i
$88$		0			0
$89$	−1.99844	+	1.15380i	−0.211834	+	0.122302i	−0.602163	−	0.798373i	$-0.705694\pi$
$89$	−1.99844	+	1.15380i	−0.211834	+	0.122302i	0.390329	+	0.920675i	$0.372361\pi$
$90$		0			0
$91$	7.47049	+	2.86699i	0.783120	+	0.300542i
$92$		0			0
$93$	13.1479	−	7.59096i	1.36338	−	0.787145i
$94$		0			0
$95$	3.16395	+	1.82671i	0.324615	+	0.187416i
$96$		0			0
$97$			2.74318i			0.278528i	0.990255	+	0.139264i	$0.0444737\pi$
$97$			2.74318i			0.278528i	−0.990255	+	0.139264i	$0.955526\pi$
$98$		0			0
$99$	−2.70078			−0.271438
$100$		0			0
$101$	−4.56687	+	7.91006i	−0.454421	+	0.787080i	−0.998655	−	0.0518536i	$-0.983487\pi$
$101$	−4.56687	+	7.91006i	−0.454421	+	0.787080i	0.544234	+	0.838934i	$0.316820\pi$
$102$		0			0
$103$	−8.96856	−	15.5340i	−0.883699	−	1.53061i	−0.847198	−	0.531278i	$-0.821712\pi$
$103$	−8.96856	−	15.5340i	−0.883699	−	1.53061i	−0.0365014	−	0.999334i	$-0.511621\pi$
$104$		0			0
$105$	2.13156	−	5.55418i	0.208019	−	0.542032i
$106$		0			0
$107$	7.57904	+	13.1273i	0.732694	+	1.26906i	0.955728	+	0.294252i	$0.0950706\pi$
$107$	7.57904	+	13.1273i	0.732694	+	1.26906i	−0.223034	+	0.974811i	$0.571596\pi$
$108$		0			0
$109$	−13.2526	−	7.65137i	−1.26937	−	0.732868i	−0.294497	−	0.955652i	$-0.595152\pi$
$109$	−13.2526	−	7.65137i	−1.26937	−	0.732868i	−0.974868	+	0.222784i	$0.928486\pi$
$110$		0			0
$111$	−10.1043			−0.959061
$112$		0			0
$113$	−15.2372			−1.43340			−0.716698	−	0.697384i	$-0.754347\pi$
$113$	−15.2372			−1.43340			−0.716698	+	0.697384i	$0.754347\pi$
$114$		0			0
$115$	−5.74815	−	3.31870i	−0.536018	−	0.309470i
$116$		0			0
$117$	−3.10915	−	5.38521i	−0.287441	−	0.497863i
$118$		0			0
$119$	0.602911	+	0.744416i	0.0552688	+	0.0682405i
$120$		0			0
$121$	4.63727	+	8.03199i	0.421570	+	0.730181i
$122$		0			0
$123$	4.58593	−	7.94306i	0.413499	−	0.716201i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$			9.07992i			0.805713i	0.915263	+	0.402856i	$0.131983\pi$
$127$			9.07992i			0.805713i	−0.915263	+	0.402856i	$0.868017\pi$
$128$		0			0
$129$	−9.77490	−	5.64354i	−0.860632	−	0.496886i
$130$		0			0
$131$	8.38219	−	4.83946i	0.732356	−	0.422826i	−0.0869277	−	0.996215i	$-0.527705\pi$
$131$	8.38219	−	4.83946i	0.732356	−	0.422826i	0.819283	+	0.573389i	$0.194372\pi$
$132$		0			0
$133$	9.54691	−	1.51284i	0.827822	−	0.131180i
$134$		0			0
$135$	1.83814	−	1.06125i	0.158202	−	0.0913381i
$136$		0			0
$137$	−10.9498	+	18.9657i	−0.935507	+	1.62035i	−0.161779	+	0.986827i	$0.551723\pi$
$137$	−10.9498	+	18.9657i	−0.935507	+	1.62035i	−0.773728	+	0.633518i	$0.781610\pi$
$138$		0			0
$139$		−	15.3183i		−	1.29928i	−0.760241	−	0.649641i	$-0.774919\pi$
$139$		−	15.3183i		−	1.29928i	0.760241	−	0.649641i	$-0.225081\pi$
$140$		0			0
$141$			28.0320i			2.36072i
$142$		0			0
$143$	1.98636	−	3.44047i	0.166108	−	0.287707i
$144$		0			0
$145$	−2.90515	+	1.67729i	−0.241259	+	0.139291i
$146$		0			0
$147$	−4.86624	−	14.9689i	−0.401360	−	1.23461i
$148$		0			0
$149$	10.3555	−	5.97873i	0.848352	−	0.489797i	−0.0117422	−	0.999931i	$-0.503738\pi$
$149$	10.3555	−	5.97873i	0.848352	−	0.489797i	0.860095	+	0.510135i	$0.170404\pi$
$150$		0			0
$151$	13.0976	+	7.56188i	1.06586	+	0.615377i	0.927049	−	0.374941i	$-0.122337\pi$
$151$	13.0976	+	7.56188i	1.06586	+	0.615377i	0.138816	+	0.990318i	$0.455670\pi$
$152$		0			0
$153$		−	0.744437i		−	0.0601841i
$154$		0			0
$155$	6.75181			0.542318
$156$		0			0
$157$	2.84274	−	4.92377i	0.226876	−	0.392960i	−0.730005	−	0.683442i	$-0.760482\pi$
$157$	2.84274	−	4.92377i	0.226876	−	0.392960i	0.956880	+	0.290482i	$0.0938156\pi$
$158$		0			0
$159$	3.11103	+	5.38846i	0.246720	+	0.427332i
$160$		0			0
$161$	−17.3445	+	2.74847i	−1.36694	+	0.216610i
$162$		0			0
$163$	−5.69372	−	9.86181i	−0.445966	−	0.772437i	0.552153	−	0.833743i	$-0.313807\pi$
$163$	−5.69372	−	9.86181i	−0.445966	−	0.772437i	−0.998119	+	0.0613066i	$0.980473\pi$
$164$		0			0
$165$	−2.55793	−	1.47682i	−0.199135	−	0.114971i
$166$		0			0
$167$	−5.82363			−0.450646			−0.225323	−	0.974284i	$-0.572344\pi$
$167$	−5.82363			−0.450646			−0.225323	+	0.974284i	$0.572344\pi$
$168$		0			0
$169$	−3.85317			−0.296398
$170$		0			0
$171$	−6.50529	−	3.75583i	−0.497472	−	0.287216i
$172$		0			0
$173$	0.665524	+	1.15272i	0.0505989	+	0.0876398i	0.890216	−	0.455540i	$-0.150554\pi$
$173$	0.665524	+	1.15272i	0.0505989	+	0.0876398i	−0.839617	+	0.543179i	$0.817220\pi$
$174$		0			0
$175$	2.05601	−	1.66518i	0.155419	−	0.125876i
$176$		0			0
$177$	−14.9669	−	25.9234i	−1.12498	−	1.94852i
$178$		0			0
$179$	−0.321093	+	0.556150i	−0.0239996	+	0.0415686i	−0.877776	−	0.479072i	$-0.840973\pi$
$179$	−0.321093	+	0.556150i	−0.0239996	+	0.0415686i	0.853776	+	0.520640i	$0.174307\pi$
$180$		0			0
$181$	−15.3953			−1.14432			−0.572162	−	0.820141i	$-0.693895\pi$
$181$	−15.3953			−1.14432			−0.572162	+	0.820141i	$0.693895\pi$
$182$		0			0
$183$		−	22.6980i		−	1.67788i
$184$		0			0
$185$	−3.89163	−	2.24684i	−0.286119	−	0.165191i
$186$		0			0
$187$	0.411883	−	0.237801i	0.0301199	−	0.0173897i
$188$		0			0
$189$	2.01205	−	5.24279i	0.146355	−	0.381357i
$190$		0			0
$191$	4.72451	−	2.72770i	0.341853	−	0.197369i	−0.319238	−	0.947675i	$-0.603427\pi$
$191$	4.72451	−	2.72770i	0.341853	−	0.197369i	0.661091	+	0.750305i	$0.270094\pi$
$192$		0			0
$193$	−0.821266	+	1.42248i	−0.0591160	+	0.102392i	−0.894069	−	0.447930i	$-0.852162\pi$
$193$	−0.821266	+	1.42248i	−0.0591160	+	0.102392i	0.834953	+	0.550322i	$0.185495\pi$
$194$		0			0
$195$		−	6.80051i		−	0.486995i
$196$		0			0
$197$			25.8538i			1.84201i	0.389555	+	0.921003i	$0.372629\pi$
$197$			25.8538i			1.84201i	−0.389555	+	0.921003i	$0.627371\pi$
$198$		0			0
$199$	−6.42513	+	11.1287i	−0.455465	+	0.788889i	−0.998715	−	0.0506821i	$-0.983860\pi$
$199$	−6.42513	+	11.1287i	−0.455465	+	0.788889i	0.543249	+	0.839571i	$0.317194\pi$
$200$		0			0
$201$	−3.49529	+	2.01800i	−0.246538	+	0.142339i
$202$		0			0
$203$	−3.18001	+	8.28612i	−0.223193	+	0.581572i
$204$		0			0
$205$	3.53249	−	2.03949i	0.246720	−	0.142444i
$206$		0			0
$207$	11.8186	+	6.82346i	0.821447	+	0.474263i
$208$		0			0
$209$		−	4.79901i		−	0.331954i
$210$		0			0
$211$	−27.2452			−1.87563			−0.937817	−	0.347130i	$-0.887156\pi$
$211$	−27.2452			−1.87563			−0.937817	+	0.347130i	$0.887156\pi$
$212$		0			0
$213$	14.0435	−	24.3241i	0.962245	−	1.66666i
$214$		0			0
$215$	−2.50984	−	4.34716i	−0.171169	−	0.296474i
$216$		0			0
$217$	13.8818	−	11.2430i	0.942356	−	0.763225i
$218$		0			0
$219$	−10.1688	−	17.6128i	−0.687142	−	1.19017i
$220$		0			0
$221$	0.948325	+	0.547515i	0.0637912	+	0.0368299i
$222$		0			0
$223$	−15.5595			−1.04194			−0.520971	−	0.853575i	$-0.674430\pi$
$223$	−15.5595			−1.04194			−0.520971	+	0.853575i	$0.674430\pi$
$224$		0			0
$225$	−2.05606			−0.137071
$226$		0			0
$227$	−14.7364	−	8.50808i	−0.978091	−	0.564701i	−0.0763977	−	0.997077i	$-0.524342\pi$
$227$	−14.7364	−	8.50808i	−0.978091	−	0.564701i	−0.901693	+	0.432376i	$0.857675\pi$
$228$		0			0
$229$	−2.15225	−	3.72781i	−0.142225	−	0.246341i	0.786109	−	0.618088i	$-0.212092\pi$
$229$	−2.15225	−	3.72781i	−0.142225	−	0.246341i	−0.928334	+	0.371747i	$0.878759\pi$
$230$		0			0
$231$	−7.71831	+	1.22307i	−0.507827	+	0.0804722i
$232$		0			0
$233$	2.00127	+	3.46631i	0.131108	+	0.227085i	0.924104	−	0.382141i	$-0.124813\pi$
$233$	2.00127	+	3.46631i	0.131108	+	0.227085i	−0.792996	+	0.609227i	$0.791480\pi$
$234$		0			0
$235$	−6.23329	+	10.7964i	−0.406615	+	0.704278i
$236$		0			0
$237$	−20.5048			−1.33193
$238$		0			0
$239$			14.5547i			0.941465i	0.882276	+	0.470732i	$0.156010\pi$
$239$			14.5547i			0.941465i	−0.882276	+	0.470732i	$0.843990\pi$
$240$		0			0
$241$	−6.38377	−	3.68567i	−0.411215	−	0.237415i	0.280097	−	0.959972i	$-0.409633\pi$
$241$	−6.38377	−	3.68567i	−0.411215	−	0.237415i	−0.691312	+	0.722557i	$0.742967\pi$
$242$		0			0
$243$	−15.7908	+	9.11681i	−1.01298	+	0.584843i
$244$		0			0
$245$	1.45432	−	6.84726i	0.0929133	−	0.437455i
$246$		0			0
$247$	9.56897	−	5.52465i	0.608859	−	0.351525i
$248$		0			0
$249$	12.0938	−	20.9470i	0.766411	−	1.32746i
$250$		0			0
$251$			10.8136i			0.682546i	0.939964	+	0.341273i	$0.110858\pi$
$251$			10.8136i			0.682546i	−0.939964	+	0.341273i	$0.889142\pi$
$252$		0			0
$253$			8.71866i			0.548138i
$254$		0			0
$255$	0.407068	−	0.705063i	0.0254916	−	0.0441528i
$256$		0			0
$257$	−2.68819	+	1.55202i	−0.167684	+	0.0968126i	−0.581494	−	0.813551i	$-0.697531\pi$
$257$	−2.68819	+	1.55202i	−0.167684	+	0.0968126i	0.413809	+	0.910364i	$0.364198\pi$
$258$		0			0
$259$	−11.7426	+	1.86078i	−0.729651	+	0.115623i
$260$		0			0
$261$	5.97317	−	3.44861i	0.369730	−	0.213464i
$262$		0			0
$263$	−5.41133	−	3.12423i	−0.333677	−	0.192648i	0.323796	−	0.946127i	$-0.395041\pi$
$263$	−5.41133	−	3.12423i	−0.333677	−	0.192648i	−0.657472	+	0.753479i	$0.728374\pi$
$264$		0			0
$265$			2.76712i			0.169983i
$266$		0			0
$267$	5.18879			0.317549
$268$		0			0
$269$	6.43871	−	11.1522i	0.392575	−	0.679960i	−0.600213	−	0.799840i	$-0.704918\pi$
$269$	6.43871	−	11.1522i	0.392575	−	0.679960i	0.992788	+	0.119880i	$0.0382510\pi$
$270$		0			0
$271$	2.05720	+	3.56317i	0.124966	+	0.216447i	0.921720	−	0.387857i	$-0.126785\pi$
$271$	2.05720	+	3.56317i	0.124966	+	0.216447i	−0.796754	+	0.604304i	$0.793451\pi$
$272$		0			0
$273$	−11.3241	−	13.9819i	−0.685366	−	0.846223i
$274$		0			0
$275$	−0.656783	−	1.13758i	−0.0396055	−	0.0685988i
$276$		0			0
$277$	−0.0523704	−	0.0302361i	−0.00314663	−	0.00181671i	0.498426	−	0.866932i	$-0.333912\pi$
$277$	−0.0523704	−	0.0302361i	−0.00314663	−	0.00181671i	−0.501572	+	0.865116i	$0.667245\pi$
$278$		0			0
$279$	−13.8822			−0.831103
$280$		0			0
$281$	20.2504			1.20804			0.604018	−	0.796971i	$-0.293566\pi$
$281$	20.2504			1.20804			0.604018	+	0.796971i	$0.293566\pi$
$282$		0			0
$283$	−0.856074	−	0.494255i	−0.0508883	−	0.0293804i	0.474340	−	0.880342i	$-0.342687\pi$
$283$	−0.856074	−	0.494255i	−0.0508883	−	0.0293804i	−0.525228	+	0.850961i	$0.676020\pi$
$284$		0			0
$285$	−4.10748	−	7.11437i	−0.243306	−	0.421419i
$286$		0			0
$287$	3.86671	−	10.0755i	0.228245	−	0.594735i
$288$		0			0
$289$	−8.43445	−	14.6089i	−0.496144	−	0.859347i
$290$		0			0
$291$	3.08412	−	5.34185i	0.180794	−	0.313145i
$292$		0			0
$293$	1.28131			0.0748550			0.0374275	−	0.999299i	$-0.488084\pi$
$293$	1.28131			0.0748550			0.0374275	+	0.999299i	$0.488084\pi$
$294$		0			0
$295$		−	13.3123i		−	0.775074i
$296$		0			0
$297$	−2.41453	−	1.39403i	−0.140105	−	0.0808896i
$298$		0			0
$299$	−17.3846	+	10.0370i	−1.00537	+	0.580453i
$300$		0			0
$301$	−12.3991	−	4.75846i	−0.714670	−	0.274273i
$302$		0			0
$303$	17.7863	−	10.2689i	1.02180	−	0.589935i
$304$		0			0
$305$	5.04721	−	8.74202i	0.289002	−	0.500567i
$306$		0			0
$307$		−	3.64739i		−	0.208168i	−0.994569	−	0.104084i	$-0.966809\pi$
$307$		−	3.64739i		−	0.208168i	0.994569	−	0.104084i	$-0.0331910\pi$
$308$		0			0
$309$			40.3329i			2.29446i
$310$		0			0
$311$	−10.8206	+	18.7418i	−0.613580	+	1.06275i	0.377051	+	0.926192i	$0.376938\pi$
$311$	−10.8206	+	18.7418i	−0.613580	+	1.06275i	−0.990632	+	0.136560i	$0.956395\pi$
$312$		0			0
$313$	21.5795	−	12.4589i	1.21974	−	0.704219i	0.254880	−	0.966973i	$-0.417964\pi$
$313$	21.5795	−	12.4589i	1.21974	−	0.704219i	0.964863	+	0.262754i	$0.0846308\pi$
$314$		0			0
$315$	−4.22728	+	3.42372i	−0.238180	+	0.192905i
$316$		0			0
$317$	−20.2359	+	11.6832i	−1.13656	+	0.656193i	−0.945576	−	0.325401i	$-0.894501\pi$
$317$	−20.2359	+	11.6832i	−1.13656	+	0.656193i	−0.190983	+	0.981593i	$0.561167\pi$
$318$		0			0
$319$	3.81611	+	2.20323i	0.213661	+	0.123357i
$320$		0			0
$321$		−	34.0840i		−	1.90238i
$322$		0			0
$323$	1.32279			0.0736019
$324$		0			0
$325$	1.51219	−	2.61918i	0.0838810	−	0.145286i
$326$		0			0
$327$	17.2046	+	29.7993i	0.951419	+	1.64791i
$328$		0			0
$329$	5.16227	+	32.5770i	0.284605	+	1.79603i
$330$		0			0
$331$	−2.24164	−	3.88263i	−0.123211	−	0.213409i	0.797821	−	0.602895i	$-0.205986\pi$
$331$	−2.24164	−	3.88263i	−0.123211	−	0.213409i	−0.921032	+	0.389486i	$0.872653\pi$
$332$		0			0
$333$	8.00145	+	4.61964i	0.438477	+	0.253155i
$334$		0			0
$335$	−1.79492			−0.0980671
$336$		0			0
$337$	22.5587			1.22885			0.614427	−	0.788974i	$-0.289387\pi$
$337$	22.5587			1.22885			0.614427	+	0.788974i	$0.289387\pi$
$338$		0			0
$339$	29.6717	+	17.1310i	1.61154	+	0.930426i
$340$		0			0
$341$	−4.43448	−	7.68074i	−0.240140	−	0.415935i
$342$		0			0
$343$	−8.41185	−	16.4997i	−0.454197	−	0.890901i
$344$		0			0
$345$	7.46232	+	12.9251i	0.401758	+	0.695865i
$346$		0			0
$347$	−8.80310	+	15.2474i	−0.472575	+	0.818524i	−0.999507	−	0.0313830i	$-0.990009\pi$
$347$	−8.80310	+	15.2474i	−0.472575	+	0.818524i	0.526932	+	0.849907i	$0.323342\pi$
$348$		0			0
$349$	14.8958			0.797356			0.398678	−	0.917091i	$-0.369469\pi$
$349$	14.8958			0.797356			0.398678	+	0.917091i	$0.369469\pi$
$350$		0			0
$351$		−	6.41925i		−	0.342634i
$352$		0			0
$353$	10.8891	+	6.28685i	0.579571	+	0.334615i	0.760963	−	0.648796i	$-0.224727\pi$
$353$	10.8891	+	6.28685i	0.579571	+	0.334615i	−0.181392	+	0.983411i	$0.558060\pi$
$354$		0			0
$355$	10.8176	−	6.24553i	0.574137	−	0.331478i
$356$		0			0
$357$	−0.337125	−	2.12746i	−0.0178425	−	0.112597i
$358$		0			0
$359$	4.78717	−	2.76387i	0.252657	−	0.145872i	−0.368323	−	0.929698i	$-0.620068\pi$
$359$	4.78717	−	2.76387i	0.252657	−	0.145872i	0.620980	+	0.783826i	$0.286735\pi$
$360$		0			0
$361$	−2.82627	+	4.89524i	−0.148751	+	0.257644i
$362$		0			0
$363$		−	20.8545i		−	1.09457i
$364$		0			0
$365$		−	9.04466i		−	0.473419i
$366$		0			0
$367$	−1.34845	+	2.33559i	−0.0703887	+	0.121917i	−0.899072	−	0.437801i	$-0.855757\pi$
$367$	−1.34845	+	2.33559i	−0.0703887	+	0.121917i	0.828683	+	0.559718i	$0.189091\pi$
$368$		0			0
$369$	−7.26303	+	4.19331i	−0.378098	+	0.218295i
$370$		0			0
$371$	4.60776	+	5.68921i	0.239223	+	0.295369i
$372$		0			0
$373$	10.2505	−	5.91815i	0.530753	−	0.306430i	−0.210570	−	0.977579i	$-0.567532\pi$
$373$	10.2505	−	5.91815i	0.530753	−	0.306430i	0.741323	+	0.671148i	$0.234199\pi$
$374$		0			0
$375$	−1.94732	−	1.12428i	−0.100559	−	0.0580578i
$376$		0			0
$377$			10.1455i			0.522519i
$378$		0			0
$379$	13.0284			0.669223			0.334611	−	0.942356i	$-0.391395\pi$
$379$	13.0284			0.669223			0.334611	+	0.942356i	$0.391395\pi$
$380$		0			0
$381$	10.2084	−	17.6815i	0.522993	−	0.905851i
$382$		0			0
$383$	13.7424	+	23.8025i	0.702204	+	1.21625i	0.967691	+	0.252138i	$0.0811338\pi$
$383$	13.7424	+	23.8025i	0.702204	+	1.21625i	−0.265487	+	0.964114i	$0.585533\pi$
$384$		0			0
$385$	−3.24463	−	1.24521i	−0.165362	−	0.0634618i
$386$		0			0
$387$	5.16038	+	8.93805i	0.262317	+	0.454346i
$388$		0			0
$389$	21.2638	+	12.2767i	1.07812	+	0.622452i	0.930388	−	0.366575i	$-0.119470\pi$
$389$	21.2638	+	12.2767i	1.07812	+	0.622452i	0.147731	+	0.989028i	$0.452803\pi$
$390$		0			0
$391$	−2.40319			−0.121535
$392$		0			0
$393$	−21.7637			−1.09783
$394$		0			0
$395$	−7.89731	−	4.55951i	−0.397357	−	0.229414i
$396$		0			0
$397$	17.4233	+	30.1781i	0.874451	+	1.51459i	0.857346	+	0.514740i	$0.172112\pi$
$397$	17.4233	+	30.1781i	0.874451	+	1.51459i	0.0171051	+	0.999854i	$0.494555\pi$
$398$		0			0
$399$	−20.2917	−	7.78747i	−1.01586	−	0.389861i
$400$		0			0
$401$	9.18494	+	15.9088i	0.458674	+	0.794447i	0.998891	−	0.0470788i	$-0.0149912\pi$
$401$	9.18494	+	15.9088i	0.458674	+	0.794447i	−0.540217	+	0.841526i	$0.681658\pi$
$402$		0			0
$403$	10.2100	−	17.6842i	0.508596	−	0.880914i
$404$		0			0
$405$	−10.9408			−0.543652
$406$		0			0
$407$			5.90274i			0.292588i
$408$		0			0
$409$	22.3382	+	12.8970i	1.10455	+	0.637715i	0.937413	−	0.348218i	$-0.113213\pi$
$409$	22.3382	+	12.8970i	1.10455	+	0.637715i	0.167141	+	0.985933i	$0.446547\pi$
$410$		0			0
$411$	42.6456	−	24.6214i	2.10355	−	1.21449i
$412$		0			0
$413$	−22.1675	−	27.3703i	−1.09079	−	1.34680i
$414$		0			0
$415$	9.31571	−	5.37842i	0.457290	−	0.264016i
$416$		0			0
$417$	−17.2221	+	29.8296i	−0.843372	+	1.46076i
$418$		0			0
$419$			8.97829i			0.438618i	0.975655	+	0.219309i	$0.0703803\pi$
$419$			8.97829i			0.438618i	−0.975655	+	0.219309i	$0.929620\pi$
$420$		0			0
$421$		−	13.7657i		−	0.670897i	−0.942058	−	0.335449i	$-0.891112\pi$
$421$		−	13.7657i		−	0.670897i	0.942058	−	0.335449i	$-0.108888\pi$
$422$		0			0
$423$	12.8161	−	22.1981i	0.623138	−	1.07931i
$424$		0			0
$425$	0.313561	−	0.181034i	0.0152099	−	0.00878146i
$426$		0			0
$427$	−4.17998	−	26.3782i	−0.202284	−	1.27653i
$428$		0			0
$429$	−7.73614	+	4.46646i	−0.373504	+	0.215643i
$430$		0			0
$431$	−19.0090	−	10.9749i	−0.915633	−	0.528641i	−0.0333938	−	0.999442i	$-0.510632\pi$
$431$	−19.0090	−	10.9749i	−0.915633	−	0.528641i	−0.882239	+	0.470801i	$0.843965\pi$
$432$		0			0
$433$			1.76054i			0.0846061i	0.999105	+	0.0423031i	$0.0134695\pi$
$433$			1.76054i			0.0846061i	−0.999105	+	0.0423031i	$0.986530\pi$
$434$		0			0
$435$	7.54300			0.361659
$436$		0			0
$437$	−12.1246	+	21.0004i	−0.579998	+	1.00459i
$438$		0			0
$439$	1.56542	+	2.71138i	0.0747133	+	0.129407i	0.900962	−	0.433899i	$-0.142862\pi$
$439$	1.56542	+	2.71138i	0.0747133	+	0.129407i	−0.826248	+	0.563306i	$0.809529\pi$
$440$		0			0
$441$	−2.99018	+	14.0784i	−0.142390	+	0.670400i
$442$		0			0
$443$	1.20461	+	2.08644i	0.0572326	+	0.0991298i	0.893222	−	0.449616i	$-0.148439\pi$
$443$	1.20461	+	2.08644i	0.0572326	+	0.0991298i	−0.835990	+	0.548745i	$0.815106\pi$
$444$		0			0
$445$	1.99844	+	1.15380i	0.0947350	+	0.0546953i
$446$		0			0
$447$	−26.8872			−1.27172
$448$		0			0
$449$	−22.8008			−1.07604			−0.538018	−	0.842933i	$-0.680827\pi$
$449$	−22.8008			−1.07604			−0.538018	+	0.842933i	$0.680827\pi$
$450$		0			0
$451$	−4.64017	−	2.67900i	−0.218497	−	0.126149i
$452$		0			0
$453$	−17.0034	−	29.4508i	−0.798890	−	1.38372i
$454$		0			0
$455$	−1.25236	−	7.90313i	−0.0587115	−	0.370504i
$456$		0			0
$457$	5.54897	+	9.61110i	0.259570	+	0.449588i	0.966127	−	0.258068i	$-0.0830859\pi$
$457$	5.54897	+	9.61110i	0.259570	+	0.449588i	−0.706557	+	0.707656i	$0.749753\pi$
$458$		0			0
$459$	0.384247	−	0.665535i	0.0179351	−	0.0310645i
$460$		0			0
$461$	−0.197161			−0.00918270			−0.00459135	−	0.999989i	$-0.501461\pi$
$461$	−0.197161			−0.00918270			−0.00459135	+	0.999989i	$0.501461\pi$
$462$		0			0
$463$			39.2085i			1.82217i	0.412214	+	0.911087i	$0.364756\pi$
$463$			39.2085i			1.82217i	−0.412214	+	0.911087i	$0.635244\pi$
$464$		0			0
$465$	−13.1479	−	7.59096i	−0.609720	−	0.352022i
$466$		0			0
$467$	−6.09296	+	3.51777i	−0.281949	+	0.162783i	−0.634305	−	0.773083i	$-0.718714\pi$
$467$	−6.09296	+	3.51777i	−0.281949	+	0.162783i	0.352357	+	0.935866i	$0.385380\pi$
$468$		0			0
$469$	−3.69037	+	2.98888i	−0.170406	+	0.138014i
$470$		0			0
$471$	−11.0714	+	6.39210i	−0.510145	+	0.294533i
$472$		0			0
$473$	−3.29684	+	5.71029i	−0.151589	+	0.262559i
$474$		0			0
$475$		−	3.65342i		−	0.167630i
$476$		0			0
$477$		−	5.68937i		−	0.260498i
$478$		0			0
$479$	14.9345	−	25.8674i	0.682377	−	1.18191i	−0.291877	−	0.956456i	$-0.594280\pi$
$479$	14.9345	−	25.8674i	0.682377	−	1.18191i	0.974254	−	0.225455i	$-0.0723868\pi$
$480$		0			0
$481$	−11.7698	+	6.79527i	−0.536654	+	0.309838i
$482$		0			0
$483$	36.8653	+	14.1480i	1.67743	+	0.643756i
$484$		0			0
$485$	2.37567	−	1.37159i	0.107873	−	0.0622808i
$486$		0			0
$487$	7.76585	+	4.48362i	0.351904	+	0.203172i	0.665524	−	0.746377i	$-0.268208\pi$
$487$	7.76585	+	4.48362i	0.351904	+	0.203172i	−0.313619	+	0.949549i	$0.601542\pi$
$488$		0			0
$489$			25.6054i			1.15792i
$490$		0			0
$491$	−28.3517			−1.27949			−0.639747	−	0.768585i	$-0.720961\pi$
$491$	−28.3517			−1.27949			−0.639747	+	0.768585i	$0.720961\pi$
$492$		0			0
$493$	−0.607294	+	1.05186i	−0.0273511	+	0.0473735i
$494$		0			0
$495$	1.35039	+	2.33894i	0.0606954	+	0.105128i
$496$		0			0
$497$	11.8410	−	30.8541i	0.531143	−	1.38399i
$498$		0			0
$499$	−1.33164	−	2.30647i	−0.0596125	−	0.103252i	0.834679	−	0.550737i	$-0.185653\pi$
$499$	−1.33164	−	2.30647i	−0.0596125	−	0.103252i	−0.894291	+	0.447485i	$0.852320\pi$
$500$		0			0
$501$	11.3405	+	6.54741i	0.506654	+	0.292517i
$502$		0			0
$503$	18.7909			0.837846			0.418923	−	0.908022i	$-0.362408\pi$
$503$	18.7909			0.837846			0.418923	+	0.908022i	$0.362408\pi$
$504$		0			0
$505$	9.13375			0.406446
$506$		0			0
$507$	7.50335	+	4.33206i	0.333236	+	0.192394i
$508$		0			0
$509$	9.94668	+	17.2282i	0.440879	+	0.763625i	0.997755	−	0.0669710i	$-0.0213335\pi$
$509$	9.94668	+	17.2282i	0.440879	+	0.763625i	−0.556876	+	0.830596i	$0.688000\pi$
$510$		0			0
$511$	−15.0610	−	18.5959i	−0.666261	−	0.822633i
$512$		0			0
$513$	−3.87720	−	6.71551i	−0.171183	−	0.296497i
$514$		0			0
$515$	−8.96856	+	15.5340i	−0.395202	+	0.684510i
$516$		0			0
$517$	16.3757			0.720202
$518$		0			0
$519$		−	2.99296i		−	0.131376i
$520$		0			0
$521$	−4.94160	−	2.85303i	−0.216495	−	0.124994i	0.387831	−	0.921730i	$-0.373224\pi$
$521$	−4.94160	−	2.85303i	−0.216495	−	0.124994i	−0.604326	+	0.796737i	$0.706558\pi$
$522$		0			0
$523$	−31.6069	+	18.2482i	−1.38207	+	0.797939i	−0.992405	−	0.123016i	$-0.960743\pi$
$523$	−31.6069	+	18.2482i	−1.38207	+	0.797939i	−0.389667	+	0.920956i	$0.627410\pi$
$524$		0			0
$525$	−5.87584	+	0.931107i	−0.256443	+	0.0406368i
$526$		0			0
$527$	2.11710	−	1.22231i	0.0922225	−	0.0532447i
$528$		0			0
$529$	10.5275	−	18.2342i	0.457718	−	0.792791i
$530$		0			0
$531$			27.3710i			1.18780i
$532$		0			0
$533$		−	12.3363i		−	0.534346i
$534$		0			0
$535$	7.57904	−	13.1273i	0.327671	−	0.567542i
$536$		0			0
$537$	1.25054	−	0.722001i	0.0539649	−	0.0311566i
$538$		0			0
$539$	−8.74449	+	2.84275i	−0.376652	+	0.122446i
$540$		0			0
$541$	−22.4500	+	12.9615i	−0.965200	+	0.557259i	−0.897770	−	0.440465i	$-0.854814\pi$
$541$	−22.4500	+	12.9615i	−0.965200	+	0.557259i	−0.0674307	+	0.997724i	$0.521480\pi$
$542$		0			0
$543$	29.9795	+	17.3087i	1.28655	+	0.742787i
$544$		0			0
$545$			15.3027i			0.655497i
$546$		0			0
$547$	46.3561			1.98205			0.991023	−	0.133693i	$-0.0426836\pi$
$547$	46.3561			1.98205			0.991023	+	0.133693i	$0.0426836\pi$
$548$		0			0
$549$	−10.3774	+	17.9742i	−0.442896	+	0.767118i
$550$		0			0
$551$	6.12783	+	10.6137i	0.261055	+	0.452160i
$552$		0			0
$553$	−23.8294	+	3.77609i	−1.01333	+	0.160576i
$554$		0			0
$555$	5.05217	+	8.75061i	0.214453	+	0.371443i
$556$		0			0
$557$	25.2643	+	14.5864i	1.07048	+	0.618044i	0.928313	−	0.371799i	$-0.121259\pi$
$557$	25.2643	+	14.5864i	1.07048	+	0.618044i	0.142170	+	0.989842i	$0.454592\pi$
$558$		0			0
$559$	−15.1814			−0.642103
$560$		0			0
$561$	−1.06942			−0.0451511
$562$		0			0
$563$	3.13167	+	1.80807i	0.131984	+	0.0762011i	0.564538	−	0.825407i	$-0.309054\pi$
$563$	3.13167	+	1.80807i	0.131984	+	0.0762011i	−0.432554	+	0.901608i	$0.642388\pi$
$564$		0			0
$565$	7.61860	+	13.1958i	0.320517	+	0.555152i
$566$		0			0
$567$	−22.4943	+	18.2184i	−0.944673	+	0.765102i
$568$		0			0
$569$	−4.64527	−	8.04584i	−0.194740	−	0.337299i	0.752075	−	0.659077i	$-0.229053\pi$
$569$	−4.64527	−	8.04584i	−0.194740	−	0.337299i	−0.946815	+	0.321778i	$0.895720\pi$
$570$		0			0
$571$	3.00801	−	5.21003i	0.125881	−	0.218033i	−0.796196	−	0.605039i	$-0.793157\pi$
$571$	3.00801	−	5.21003i	0.125881	−	0.218033i	0.922077	+	0.387006i	$0.126491\pi$
$572$		0			0
$573$	−12.2668			−0.512454
$574$		0			0
$575$			6.63740i			0.276799i
$576$		0			0
$577$	−31.1827	−	18.0033i	−1.29815	−	0.749488i	−0.318067	−	0.948068i	$-0.603034\pi$
$577$	−31.1827	−	18.0033i	−1.29815	−	0.749488i	−0.980085	+	0.198580i	$0.936367\pi$
$578$		0			0
$579$	3.19853	−	1.84667i	0.132927	−	0.0767452i
$580$		0			0
$581$	10.1971	−	26.5704i	0.423046	−	1.10233i
$582$		0			0
$583$	3.14782	−	1.81740i	0.130370	−	0.0752689i
$584$		0			0
$585$	−3.10915	+	5.38521i	−0.128548	+	0.222651i
$586$		0			0
$587$			30.4699i			1.25763i	0.777555	+	0.628814i	$0.216459\pi$
$587$			30.4699i			1.25763i	−0.777555	+	0.628814i	$0.783541\pi$
$588$		0			0
$589$		−	24.6672i		−	1.01639i
$590$		0			0
$591$	29.0670	−	50.3456i	1.19566	−	2.07094i
$592$		0			0
$593$	6.79176	−	3.92122i	0.278904	−	0.161025i	−0.354023	−	0.935237i	$-0.615187\pi$
$593$	6.79176	−	3.92122i	0.278904	−	0.161025i	0.632927	+	0.774211i	$0.281853\pi$
$594$		0			0
$595$	0.343227	−	0.894344i	0.0140709	−	0.0366645i
$596$		0			0
$597$	25.0235	−	14.4474i	1.02415	−	0.591291i
$598$		0			0
$599$	−8.87320	−	5.12294i	−0.362549	−	0.209318i	0.307649	−	0.951500i	$-0.400458\pi$
$599$	−8.87320	−	5.12294i	−0.362549	−	0.209318i	−0.670198	+	0.742182i	$0.733791\pi$
$600$		0			0
$601$		−	39.3191i		−	1.60386i	−0.597420	−	0.801929i	$-0.703807\pi$
$601$		−	39.3191i		−	1.60386i	0.597420	−	0.801929i	$-0.296193\pi$
$602$		0			0
$603$	3.69048			0.150288
$604$		0			0
$605$	4.63727	−	8.03199i	0.188532	−	0.326547i
$606$		0			0
$607$	8.11619	+	14.0577i	0.329426	+	0.570583i	0.982398	−	0.186799i	$-0.0598114\pi$
$607$	8.11619	+	14.0577i	0.329426	+	0.570583i	−0.652972	+	0.757382i	$0.726478\pi$
$608$		0			0
$609$	15.5084	−	12.5605i	0.628434	−	0.508976i
$610$		0			0
$611$	18.8518	+	32.6523i	0.762662	+	1.32097i
$612$		0			0
$613$	−19.2113	−	11.0917i	−0.775937	−	0.447988i	0.0590511	−	0.998255i	$-0.481192\pi$
$613$	−19.2113	−	11.0917i	−0.775937	−	0.447988i	−0.834989	+	0.550267i	$0.814526\pi$
$614$		0			0
$615$	−9.17185			−0.369845
$616$		0			0
$617$	6.15896			0.247951			0.123975	−	0.992285i	$-0.460436\pi$
$617$	6.15896			0.247951			0.123975	+	0.992285i	$0.460436\pi$
$618$		0			0
$619$	19.1120	+	11.0343i	0.768175	+	0.443506i	0.832223	−	0.554441i	$-0.187068\pi$
$619$	19.1120	+	11.0343i	0.768175	+	0.443506i	−0.0640481	+	0.997947i	$0.520401\pi$
$620$		0			0
$621$	7.04396	+	12.2005i	0.282664	+	0.489589i
$622$		0			0
$623$	6.03009	−	0.955550i	0.241590	−	0.0382833i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−5.39545	+	9.34520i	−0.215474	+	0.373211i
$628$		0			0
$629$	−1.62702			−0.0648735
$630$		0			0
$631$			31.8382i			1.26746i	0.773555	+	0.633729i	$0.218477\pi$
$631$			31.8382i			1.26746i	−0.773555	+	0.633729i	$0.781523\pi$
$632$		0			0
$633$	53.0550	+	30.6313i	2.10875	+	1.21749i
$634$		0			0
$635$	7.86344	−	4.53996i	0.312051	−	0.180163i
$636$		0			0
$637$	−15.7350	−	14.1635i	−0.623444	−	0.561177i
$638$		0			0
$639$	−22.2416	+	12.8412i	−0.879864	+	0.507990i
$640$		0			0
$641$	−3.82910	+	6.63219i	−0.151240	+	0.261956i	−0.931684	−	0.363271i	$-0.881660\pi$
$641$	−3.82910	+	6.63219i	−0.151240	+	0.261956i	0.780443	+	0.625226i	$0.214993\pi$
$642$		0			0
$643$		−	15.5274i		−	0.612340i	−0.951977	−	0.306170i	$-0.900952\pi$
$643$		−	15.5274i		−	0.612340i	0.951977	−	0.306170i	$-0.0990476\pi$
$644$		0			0
$645$			11.2871i			0.444428i
$646$		0			0
$647$	6.28748	−	10.8902i	0.247186	−	0.428139i	−0.715558	−	0.698554i	$-0.753827\pi$
$647$	6.28748	−	10.8902i	0.247186	−	0.428139i	0.962744	+	0.270414i	$0.0871607\pi$
$648$		0			0
$649$	−15.1439	+	8.74332i	−0.594449	+	0.343205i
$650$		0			0
$651$	−39.6725	+	6.28666i	−1.55489	+	0.246394i
$652$		0			0
$653$	−41.7322	+	24.0941i	−1.63311	+	0.942874i	−0.649979	+	0.759952i	$0.725222\pi$
$653$	−41.7322	+	24.0941i	−1.63311	+	0.942874i	−0.983127	+	0.182922i	$0.941444\pi$
$654$		0			0
$655$	−8.38219	−	4.83946i	−0.327519	−	0.189093i
$656$		0			0
$657$			18.5964i			0.725515i
$658$		0			0
$659$	−21.0948			−0.821736			−0.410868	−	0.911695i	$-0.634774\pi$
$659$	−21.0948			−0.821736			−0.410868	+	0.911695i	$0.634774\pi$
$660$		0			0
$661$	−10.4693	+	18.1334i	−0.407210	+	0.705308i	−0.994576	−	0.104013i	$-0.966832\pi$
$661$	−10.4693	+	18.1334i	−0.407210	+	0.705308i	0.587366	+	0.809321i	$0.300165\pi$
$662$		0			0
$663$	−1.23113	−	2.13237i	−0.0478130	−	0.0828145i
$664$		0			0
$665$	−6.08361	−	7.51145i	−0.235912	−	0.291282i
$666$		0			0
$667$	−11.1328	−	19.2826i	−0.431065	−	0.746626i
$668$		0			0
$669$	30.2993	+	17.4933i	1.17144	+	0.676330i
$670$		0			0
$671$	−13.2597			−0.511885
$672$		0			0
$673$	−6.93060			−0.267155			−0.133578	−	0.991038i	$-0.542647\pi$
$673$	−6.93060			−0.267155			−0.133578	+	0.991038i	$0.542647\pi$
$674$		0			0
$675$	−1.83814	−	1.06125i	−0.0707502	−	0.0408476i
$676$		0			0
$677$	−6.87785	−	11.9128i	−0.264337	−	0.457845i	0.703053	−	0.711138i	$-0.251820\pi$
$677$	−6.87785	−	11.9128i	−0.264337	−	0.457845i	−0.967390	+	0.253293i	$0.918486\pi$
$678$		0			0
$679$	2.60043	−	6.77593i	0.0997955	−	0.260036i
$680$		0			0
$681$	19.1310	+	33.1359i	0.733102	+	1.26977i
$682$		0			0
$683$	−2.06581	+	3.57808i	−0.0790459	+	0.136912i	−0.902839	−	0.429980i	$-0.858521\pi$
$683$	−2.06581	+	3.57808i	−0.0790459	+	0.136912i	0.823793	+	0.566891i	$0.191854\pi$
$684$		0			0
$685$	21.8997			0.836743
$686$		0			0
$687$			9.67899i			0.369276i
$688$		0			0
$689$	7.24759	+	4.18440i	0.276111	+	0.159413i
$690$		0			0
$691$	35.6084	−	20.5585i	1.35461	−	0.782082i	0.365716	−	0.930727i	$-0.380824\pi$
$691$	35.6084	−	20.5585i	1.35461	−	0.782082i	0.988891	+	0.148644i	$0.0474909\pi$
$692$		0			0
$693$	6.67118	+	2.56023i	0.253417	+	0.0972552i
$694$		0			0
$695$	−13.2660	+	7.65915i	−0.503210	+	0.290528i
$696$		0			0
$697$	0.738435	−	1.27901i	0.0279702	−	0.0484458i
$698$		0			0
$699$		−	9.00000i		−	0.340411i
$700$		0			0
$701$		−	0.155387i		−	0.00586887i	−0.999996	−	0.00293444i	$-0.999066\pi$
$701$		−	0.155387i		−	0.00586887i	0.999996	−	0.00293444i	$-0.000934061\pi$
$702$		0			0
$703$	−8.20863	+	14.2178i	−0.309594	+	0.536233i
$704$		0			0
$705$	24.2764	−	14.0160i	0.914303	−	0.527873i
$706$		0			0
$707$	18.7790	−	15.2094i	0.706258	−	0.572007i
$708$		0			0
$709$	−17.8060	+	10.2803i	−0.668717	+	0.386084i	−0.795590	−	0.605835i	$-0.792839\pi$
$709$	−17.8060	+	10.2803i	−0.668717	+	0.386084i	0.126874	+	0.991919i	$0.459506\pi$
$710$		0			0
$711$	16.2374	+	9.37465i	0.608949	+	0.351577i
$712$		0			0
$713$			44.8144i			1.67831i
$714$		0			0
$715$	−3.97271			−0.148571
$716$		0			0
$717$	16.3636	−	28.3426i	0.611110	−	1.05847i
$718$		0			0
$719$	−11.0943	−	19.2160i	−0.413749	−	0.716634i	0.581547	−	0.813513i	$-0.302448\pi$
$719$	−11.0943	−	19.2160i	−0.413749	−	0.716634i	−0.995296	+	0.0968783i	$0.969114\pi$
$720$		0			0
$721$	7.42756	+	46.8723i	0.276617	+	1.74562i
$722$		0			0
$723$	8.28749	+	14.3544i	0.308215	+	0.533844i
$724$		0			0
$725$	2.90515	+	1.67729i	0.107894	+	0.0622929i
$726$		0			0
$727$	30.9326			1.14723			0.573613	−	0.819127i	$-0.305542\pi$
$727$	30.9326			1.14723			0.573613	+	0.819127i	$0.305542\pi$
$728$		0			0
$729$	8.17716			0.302858
$730$		0			0
$731$	−1.57397	−	0.908734i	−0.0582155	−	0.0336107i
$732$		0			0
$733$	19.5494	+	33.8606i	0.722074	+	1.25067i	0.960167	+	0.279426i	$0.0901443\pi$
$733$	19.5494	+	33.8606i	0.722074	+	1.25067i	−0.238093	+	0.971242i	$0.576522\pi$
$734$		0			0
$735$	−10.5303	+	11.6987i	−0.388416	+	0.431514i
$736$		0			0
$737$	1.17888	+	2.04187i	0.0434244	+	0.0752133i
$738$		0			0
$739$	13.5525	−	23.4737i	0.498538	−	0.863494i	−0.501460	−	0.865181i	$-0.667204\pi$
$739$	13.5525	−	23.4737i	0.498538	−	0.863494i	0.999999	+	0.00168689i	$0.000536953\pi$
$740$		0			0
$741$	−24.8451			−0.912708
$742$		0			0
$743$		−	2.76625i		−	0.101484i	−0.998712	−	0.0507419i	$-0.983841\pi$
$743$		−	2.76625i		−	0.101484i	0.998712	−	0.0507419i	$-0.0161586\pi$
$744$		0			0
$745$	−10.3555	−	5.97873i	−0.379395	−	0.219044i
$746$		0			0
$747$	−19.1537	+	11.0584i	−0.700797	+	0.404605i
$748$		0			0
$749$	−6.27679	−	39.6103i	−0.229349	−	1.44733i
$750$		0			0
$751$	28.6416	−	16.5362i	1.04515	−	0.603415i	0.123860	−	0.992300i	$-0.460473\pi$
$751$	28.6416	−	16.5362i	1.04515	−	0.603415i	0.921287	+	0.388884i	$0.127139\pi$
$752$		0			0
$753$	12.1575	−	21.0574i	0.443045	−	0.767376i
$754$		0			0
$755$		−	15.1238i		−	0.550410i
$756$		0			0
$757$		−	28.5714i		−	1.03845i	−0.854639	−	0.519223i	$-0.826221\pi$
$757$		−	28.5714i		−	1.03845i	0.854639	−	0.519223i	$-0.173779\pi$
$758$		0			0
$759$	9.80226	−	16.9780i	0.355799	−	0.616263i
$760$		0			0
$761$	8.84164	−	5.10472i	0.320509	−	0.185046i	−0.331110	−	0.943592i	$-0.607423\pi$
$761$	8.84164	−	5.10472i	0.320509	−	0.185046i	0.651619	+	0.758546i	$0.274090\pi$
$762$		0			0
$763$	25.4819	+	31.4625i	0.922506	+	1.13902i
$764$		0			0
$765$	−0.644701	+	0.372218i	−0.0233092	+	0.0134576i
$766$		0			0
$767$	−34.8675	−	20.1307i	−1.25899	−	0.726879i
$768$		0			0
$769$			4.34684i			0.156751i	0.996924	+	0.0783755i	$0.0249733\pi$
$769$			4.34684i			0.156751i	−0.996924	+	0.0783755i	$0.975027\pi$
$770$		0			0
$771$	6.97967			0.251367
$772$		0			0
$773$	−8.02006	+	13.8911i	−0.288461	+	0.499630i	−0.973443	−	0.228931i	$-0.926477\pi$
$773$	−8.02006	+	13.8911i	−0.288461	+	0.499630i	0.684981	+	0.728561i	$0.259810\pi$
$774$		0			0
$775$	−3.37591	−	5.84724i	−0.121266	−	0.210039i
$776$		0			0
$777$	24.9587	+	9.57852i	0.895387	+	0.343628i
$778$		0			0
$779$	−7.45110	−	12.9057i	−0.266963	−	0.462394i
$780$		0			0
$781$	−14.2096	−	8.20392i	−0.508459	−	0.293559i
$782$		0			0
$783$	7.12011			0.254452
$784$		0			0
$785$	−5.68548			−0.202924
$786$		0			0
$787$	−10.1582	−	5.86482i	−0.362099	−	0.209058i	0.307902	−	0.951418i	$-0.400373\pi$
$787$	−10.1582	−	5.86482i	−0.362099	−	0.209058i	−0.670001	+	0.742360i	$0.733706\pi$
$788$		0			0
$789$	7.02505	+	12.1677i	0.250098	+	0.433183i
$790$		0			0
$791$	37.6373	+	14.4443i	1.33823	+	0.513580i
$792$		0			0
$793$	−15.2646	−	26.4391i	−0.542063	−	0.938881i
$794$		0			0
$795$	3.11103	−	5.38846i	0.110337	−	0.191109i
$796$		0			0
$797$	−13.4955			−0.478035			−0.239018	−	0.971015i	$-0.576825\pi$
$797$	−13.4955			−0.478035			−0.239018	+	0.971015i	$0.576825\pi$
$798$		0			0
$799$			4.51376i			0.159685i
$800$		0			0
$801$	−4.10891	−	2.37228i	−0.145181	−	0.0838205i
$802$		0			0
$803$	−10.2890	+	5.94038i	−0.363093	+	0.209632i
$804$		0			0
$805$	11.0525	+	13.6465i	0.389549	+	0.480977i
$806$		0			0
$807$	−25.0764	+	14.4779i	−0.882732	+	0.509646i
$808$		0			0
$809$	14.6739	−	25.4159i	0.515907	−	0.893577i	−0.483923	−	0.875111i	$-0.660788\pi$
$809$	14.6739	−	25.4159i	0.515907	−	0.893577i	0.999829	−	0.0184661i	$-0.00587829\pi$
$810$		0			0
$811$			10.1469i			0.356307i	0.984003	+	0.178154i	$0.0570124\pi$
$811$			10.1469i			0.356307i	−0.984003	+	0.178154i	$0.942988\pi$
$812$		0			0
$813$		−	9.25150i		−	0.324464i
$814$		0			0
$815$	−5.69372	+	9.86181i	−0.199442	+	0.345444i
$816$		0			0
$817$	−15.8820	+	9.16948i	−0.555641	+	0.320800i
$818$		0			0
$819$	2.57493	+	16.2493i	0.0899753	+	0.567798i
$820$		0			0
$821$	29.0738	−	16.7858i	1.01468	−	0.585827i	0.102123	−	0.994772i	$-0.467436\pi$
$821$	29.0738	−	16.7858i	1.01468	−	0.585827i	0.912559	+	0.408945i	$0.134103\pi$
$822$		0			0
$823$	−34.7158	−	20.0432i	−1.21012	−	0.698662i	−0.247333	−	0.968931i	$-0.579554\pi$
$823$	−34.7158	−	20.0432i	−1.21012	−	0.698662i	−0.962785	+	0.270268i	$0.912888\pi$
$824$		0			0
$825$			2.95365i			0.102833i
$826$		0			0
$827$	−0.365430			−0.0127073			−0.00635363	−	0.999980i	$-0.502022\pi$
$827$	−0.365430			−0.0127073			−0.00635363	+	0.999980i	$0.502022\pi$
$828$		0			0
$829$	6.58868	−	11.4119i	0.228834	−	0.396352i	−0.728629	−	0.684909i	$-0.759842\pi$
$829$	6.58868	−	11.4119i	0.228834	−	0.396352i	0.957463	+	0.288556i	$0.0931753\pi$
$830$		0			0
$831$	0.0679879	+	0.117759i	0.00235847	+	0.00408500i
$832$		0			0
$833$	−0.783571	−	2.41031i	−0.0271491	−	0.0835124i
$834$		0			0
$835$	2.91181	+	5.04341i	0.100767	+	0.174534i
$836$		0			0
$837$	−12.4108	−	7.16538i	−0.428980	−	0.247672i
$838$		0			0
$839$	34.9250			1.20575			0.602873	−	0.797837i	$-0.294023\pi$
$839$	34.9250			1.20575			0.602873	+	0.797837i	$0.294023\pi$
$840$		0			0
$841$	17.7468			0.611959
$842$		0			0
$843$	−39.4339	−	22.7672i	−1.35818	−	0.784143i
$844$		0			0
$845$	1.92659	+	3.33695i	0.0662766	+	0.114794i
$846$		0			0
$847$	−3.84048	−	24.2357i	−0.131961	−	0.832750i
$848$		0			0
$849$	1.11137	+	1.92494i	0.0381420	+	0.0660638i
$850$		0			0
$851$	14.9131	−	25.8303i	0.511216	−	0.885452i
$852$		0			0
$853$	−14.1386			−0.484095			−0.242048	−	0.970264i	$-0.577819\pi$
$853$	−14.1386			−0.484095			−0.242048	+	0.970264i	$0.577819\pi$
$854$		0			0
$855$			7.51166i			0.256893i
$856$		0			0
$857$	17.8449	+	10.3028i	0.609570	+	0.351936i	0.772797	−	0.634653i	$-0.218857\pi$
$857$	17.8449	+	10.3028i	0.609570	+	0.351936i	−0.163227	+	0.986589i	$0.552190\pi$
$858$		0			0
$859$	10.7747	−	6.22079i	0.367629	−	0.212251i	−0.304793	−	0.952419i	$-0.598587\pi$
$859$	10.7747	−	6.22079i	0.367629	−	0.212251i	0.672422	+	0.740168i	$0.265254\pi$
$860$		0			0
$861$	−18.8574	+	15.2728i	−0.642658	+	0.520497i
$862$		0			0
$863$	−44.8077	+	25.8697i	−1.52527	+	0.880616i	−0.525720	+	0.850658i	$0.676204\pi$
$863$	−44.8077	+	25.8697i	−1.52527	+	0.880616i	−0.999551	+	0.0299584i	$0.990463\pi$
$864$		0			0
$865$	0.665524	−	1.15272i	0.0226285	−	0.0391937i
$866$		0			0
$867$			37.9309i			1.28820i
$868$		0			0
$869$			11.9785i			0.406341i
$870$		0			0
$871$	−2.71426	+	4.70123i	−0.0919691	+	0.159295i
$872$		0			0
$873$	−4.88452	+	2.82008i	−0.165316	+	0.0954453i
$874$		0			0
$875$	−2.47009	−	0.947962i	−0.0835044	−	0.0320469i
$876$		0			0
$877$	25.3789	−	14.6525i	0.856985	−	0.494780i	−0.00601675	−	0.999982i	$-0.501915\pi$
$877$	25.3789	−	14.6525i	0.856985	−	0.494780i	0.863001	+	0.505202i	$0.168582\pi$
$878$		0			0
$879$	−2.49512	−	1.44056i	−0.0841583	−	0.0485888i
$880$		0			0
$881$		−	45.5762i		−	1.53550i	−0.640748	−	0.767751i	$-0.721376\pi$
$881$		−	45.5762i		−	1.53550i	0.640748	−	0.767751i	$-0.278624\pi$
$882$		0			0
$883$	21.7964			0.733509			0.366754	−	0.930318i	$-0.380469\pi$
$883$	21.7964			0.733509			0.366754	+	0.930318i	$0.380469\pi$
$884$		0			0
$885$	−14.9669	+	25.9234i	−0.503105	+	0.871404i
$886$		0			0
$887$	−19.1245	−	33.1245i	−0.642136	−	1.11221i	−0.984955	−	0.172811i	$-0.944715\pi$
$887$	−19.1245	−	33.1245i	−0.642136	−	1.11221i	0.342819	−	0.939402i	$-0.388618\pi$
$888$		0			0
$889$	8.60742	−	22.4283i	0.288684	−	0.752220i
$890$		0			0
$891$	7.18573	+	12.4461i	0.240731	+	0.416958i
$892$		0			0
$893$	39.4437	+	22.7728i	1.31993	+	0.762064i
$894$		0			0
$895$	0.642187			0.0214659
$896$		0			0
$897$	45.1377			1.50710
$898$		0			0
$899$	19.6150	+	11.3247i	0.654197	+	0.377701i
$900$		0			0
$901$	0.500943	+	0.867659i	0.0166888	+	0.0289059i
$902$		0			0
$903$	18.7951	+	23.2063i	0.625461	+	0.772258i
$904$		0			0
$905$	7.69765	+	13.3327i	0.255878	+	0.443195i
$906$		0			0
$907$	−12.8162	+	22.1983i	−0.425554	+	0.737082i	−0.996472	−	0.0839256i	$-0.973254\pi$
$907$	−12.8162	+	22.1983i	−0.425554	+	0.737082i	0.570918	+	0.821007i	$0.306588\pi$
$908$		0			0
$909$	−18.7796			−0.622879
$910$		0			0
$911$			24.8490i			0.823285i	0.911345	+	0.411642i	$0.135045\pi$
$911$			24.8490i			0.823285i	−0.911345	+	0.411642i	$0.864955\pi$
$912$		0			0
$913$	−12.2368	−	7.06492i	−0.404979	−	0.233815i
$914$		0			0
$915$	−19.6570	+	11.3490i	−0.649842	+	0.375186i
$916$		0			0
$917$	−25.2924	+	4.00793i	−0.835230	+	0.132354i
$918$		0			0
$919$	−7.19741	+	4.15543i	−0.237421	+	0.137075i	−0.613991	−	0.789313i	$-0.710437\pi$
$919$	−7.19741	+	4.15543i	−0.237421	+	0.137075i	0.376570	+	0.926388i	$0.377103\pi$
$920$		0			0
$921$	−4.10071	+	7.10264i	−0.135123	+	0.234040i
$922$		0			0
$923$		−	37.7776i		−	1.24346i
$924$		0			0
$925$			4.49367i			0.147751i
$926$		0			0
$927$	18.4399	−	31.9389i	0.605647	−	1.04901i
$928$		0			0
$929$	−16.8351	+	9.71975i	−0.552342	+	0.318895i	−0.750066	−	0.661363i	$-0.769978\pi$
$929$	−16.8351	+	9.71975i	−0.552342	+	0.318895i	0.197724	+	0.980258i	$0.436645\pi$
$930$		0			0
$931$	−25.0159	−	5.31325i	−0.819863	−	0.174135i
$932$		0			0
$933$	42.1423	−	24.3309i	1.37968	−	0.796558i
$934$		0			0
$935$	−0.411883	−	0.237801i	−0.0134700	−	0.00777692i
$936$		0			0
$937$		−	35.4081i		−	1.15673i	−0.815777	−	0.578367i	$-0.803690\pi$
$937$		−	35.4081i		−	1.15673i	0.815777	−	0.578367i	$-0.196310\pi$
$938$		0			0
$939$	−56.0294			−1.82845
$940$		0			0
$941$	2.43765	−	4.22213i	0.0794650	−	0.137637i	−0.823554	−	0.567238i	$-0.808012\pi$
$941$	2.43765	−	4.22213i	0.0794650	−	0.137637i	0.903019	+	0.429600i	$0.141345\pi$
$942$		0			0
$943$	13.5369	+	23.4466i	0.440822	+	0.763525i
$944$		0			0
$945$	−5.54642	+	0.878906i	−0.180425	+	0.0285908i
$946$		0			0
$947$	−20.0140	−	34.6653i	−0.650368	−	1.12647i	−0.983034	−	0.183426i	$-0.941281\pi$
$947$	−20.0140	−	34.6653i	−0.650368	−	1.12647i	0.332665	−	0.943045i	$-0.392052\pi$
$948$		0			0
$949$	−23.6896	−	13.6772i	−0.768998	−	0.443981i
$950$		0			0
$951$	52.5409			1.70375
$952$		0			0
$953$	11.5957			0.375622			0.187811	−	0.982205i	$-0.439861\pi$
$953$	11.5957			0.375622			0.187811	+	0.982205i	$0.439861\pi$
$954$		0			0
$955$	−4.72451	−	2.72770i	−0.152881	−	0.0882661i
$956$		0			0
$957$	−4.95411	−	8.58078i	−0.160144	−	0.277377i
$958$		0			0
$959$	45.0258	−	36.4670i	1.45396	−	1.17758i
$960$		0			0
$961$	−7.29347	−	12.6327i	−0.235273	−	0.407505i
$962$		0			0
$963$	−15.5830	+	26.9905i	−0.502155	+	0.869758i
$964$		0			0
$965$	1.64253			0.0528750
$966$		0			0
$967$		−	15.5545i		−	0.500200i	−0.968220	−	0.250100i	$-0.919536\pi$
$967$		−	15.5545i		−	0.500200i	0.968220	−	0.250100i	$-0.0804635\pi$
$968$		0			0
$969$	−2.57589	−	1.48719i	−0.0827495	−	0.0477755i
$970$		0			0
$971$	−22.8218	+	13.1762i	−0.732388	+	0.422844i	−0.819295	−	0.573372i	$-0.805635\pi$
$971$	−22.8218	+	13.1762i	−0.732388	+	0.422844i	0.0869072	+	0.996216i	$0.472302\pi$
$972$		0			0
$973$	−14.5212	+	37.8377i	−0.465527	+	1.21302i
$974$		0			0
$975$	−5.88941	+	3.40026i	−0.188612	+	0.108895i
$976$		0			0
$977$	−13.1466	+	22.7707i	−0.420598	+	0.728498i	−0.995998	−	0.0893746i	$-0.971513\pi$
$977$	−13.1466	+	22.7707i	−0.420598	+	0.728498i	0.575400	+	0.817872i	$0.304847\pi$
$978$		0			0
$979$		−	3.03118i		−	0.0968770i
$980$		0			0
$981$		−	31.4634i		−	1.00455i
$982$		0			0
$983$	−6.26335	+	10.8484i	−0.199770	+	0.346012i	−0.948454	−	0.316916i	$-0.897353\pi$
$983$	−6.26335	+	10.8484i	−0.199770	+	0.346012i	0.748684	+	0.662927i	$0.230686\pi$
$984$		0			0
$985$	22.3900	−	12.9269i	0.713406	−	0.411885i
$986$		0			0
$987$	26.5732	−	69.2417i	0.845836	−	2.20399i
$988$		0			0
$989$	28.8539	−	16.6588i	0.917499	−	0.529718i
$990$		0			0
$991$	3.08043	+	1.77849i	0.0978531	+	0.0564955i	0.548128	−	0.836394i	$-0.315341\pi$
$991$	3.08043	+	1.77849i	0.0978531	+	0.0564955i	−0.450275	+	0.892890i	$0.648674\pi$
$992$		0			0
$993$			10.0810i			0.319909i
$994$		0			0
$995$	12.8503			0.407381
$996$		0			0
$997$	10.5749	−	18.3163i	0.334910	−	0.580082i	−0.648557	−	0.761166i	$-0.724627\pi$
$997$	10.5749	−	18.3163i	0.334910	−	0.580082i	0.983468	+	0.181084i	$0.0579606\pi$
$998$		0			0
$999$	4.76892	+	8.26002i	0.150882	+	0.261335i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bz.e.591.3		24
4.3	odd	2		280.2.bj.f.171.8	yes	24
7.5	odd	6		1120.2.bz.f.271.3		24
8.3	odd	2		1120.2.bz.f.591.3		24
8.5	even	2		280.2.bj.e.171.9	yes	24
28.19	even	6		280.2.bj.e.131.9	✓	24
56.5	odd	6		280.2.bj.f.131.8	yes	24
56.19	even	6	inner	1120.2.bz.e.271.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.e.131.9	✓	24	28.19	even	6
280.2.bj.e.171.9	yes	24	8.5	even	2
280.2.bj.f.131.8	yes	24	56.5	odd	6
280.2.bj.f.171.8	yes	24	4.3	odd	2
1120.2.bz.e.271.3		24	56.19	even	6	inner
1120.2.bz.e.591.3		24	1.1	even	1	trivial
1120.2.bz.f.271.3		24	7.5	odd	6
1120.2.bz.f.591.3		24	8.3	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:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bz (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.94732 - 1.12428i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.47009 - 0.947962i) q^{7} +(1.02803 + 1.78060i) q^{9} +O(q^{10})\)	\(q+(-1.94732 - 1.12428i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.47009 - 0.947962i) q^{7} +(1.02803 + 1.78060i) q^{9} +(-0.656783 + 1.13758i) q^{11} -3.02437 q^{13} +2.24857i q^{15} +(-0.313561 - 0.181034i) q^{17} +(-3.16395 + 1.82671i) q^{19} +(3.74428 + 4.62307i) q^{21} +(5.74815 - 3.31870i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.12251i q^{27} -3.35458i q^{29} +(-3.37591 + 5.84724i) q^{31} +(2.55793 - 1.47682i) q^{33} +(0.414089 + 2.61315i) q^{35} +(3.89163 - 2.24684i) q^{37} +(5.88941 + 3.40026i) q^{39} +4.07897i q^{41} +5.01967 q^{43} +(1.02803 - 1.78060i) q^{45} +(-6.23329 - 10.7964i) q^{47} +(5.20274 + 4.68311i) q^{49} +(0.407068 + 0.705063i) q^{51} +(-2.39639 - 1.38356i) q^{53} +1.31357 q^{55} +8.21496 q^{57} +(11.5288 + 6.65617i) q^{59} +(5.04721 + 8.74202i) q^{61} +(-0.851393 - 5.37279i) q^{63} +(1.51219 + 2.61918i) q^{65} +(0.897462 - 1.55445i) q^{67} -14.9246 q^{69} +12.4911i q^{71} +(7.83291 + 4.52233i) q^{73} +(1.94732 - 1.12428i) q^{75} +(2.70070 - 2.18733i) q^{77} +(7.89731 - 4.55951i) q^{79} +(5.47040 - 9.47500i) q^{81} +10.7568i q^{83} +0.362069i q^{85} +(-3.77150 + 6.53243i) q^{87} +(-1.99844 + 1.15380i) q^{89} +(7.47049 + 2.86699i) q^{91} +(13.1479 - 7.59096i) q^{93} +(3.16395 + 1.82671i) q^{95} +2.74318i q^{97} -2.70078 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9}+O(q^{10}) \) 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9	\( 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9} - 8 q^{11} + 20 q^{13} + 6 q^{17} - 18 q^{19} - 26 q^{21} - 18 q^{23} - 12 q^{25} + 6 q^{31} + 12 q^{33} + 8 q^{35} + 18 q^{39} - 32 q^{43} + 12 q^{45} + 8 q^{49} + 22 q^{51} + 30 q^{53} + 16 q^{55} - 44 q^{57} + 18 q^{59} + 22 q^{61} + 12 q^{63} - 10 q^{65} + 8 q^{67} - 12 q^{69} + 30 q^{73} + 12 q^{75} - 32 q^{77} - 6 q^{79} - 4 q^{81} - 14 q^{87} - 60 q^{89} - 18 q^{91} - 18 q^{93} + 18 q^{95} + 56 q^{99}+O(q^{100}) \) 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9 - 8 * q^11 + 20 * q^13 + 6 * q^17 - 18 * q^19 - 26 * q^21 - 18 * q^23 - 12 * q^25 + 6 * q^31 + 12 * q^33 + 8 * q^35 + 18 * q^39 - 32 * q^43 + 12 * q^45 + 8 * q^49 + 22 * q^51 + 30 * q^53 + 16 * q^55 - 44 * q^57 + 18 * q^59 + 22 * q^61 + 12 * q^63 - 10 * q^65 + 8 * q^67 - 12 * q^69 + 30 * q^73 + 12 * q^75 - 32 * q^77 - 6 * q^79 - 4 * q^81 - 14 * q^87 - 60 * q^89 - 18 * q^91 - 18 * q^93 + 18 * q^95 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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