LMFDB - Embedded newform 1148.2.i.d.821.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(165,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1148.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 14 x^{14} - 8 x^{13} + 136 x^{12} - 87 x^{11} + 706 x^{10} - 568 x^{9} + 2685 x^{8} + \cdots + 121 $ x^16 + 14x^14 - 8x^13 + 136x^12 - 87x^11 + 706x^10 - 568x^9 + 2685x^8 - 2100x^7 + 5529x^6 - 4919x^5 + 8145x^4 - 5182x^3 + 2775x^2 - 660x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			821.2
Root			$1.12452 + 1.94772i$ of defining polynomial
Character	$\chi$	$=$	1148.821
Dual form			1148.2.i.d.165.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12452 - 1.94772i) q^{3} +(0.735486 - 1.27390i) q^{5} +(0.221110 + 2.63650i) q^{7} +(-1.02909 + 1.78243i) q^{9} +O(q^{10})$	\(q+(-1.12452 - 1.94772i) q^{3} +(0.735486 - 1.27390i) q^{5} +(0.221110 + 2.63650i) q^{7} +(-1.02909 + 1.78243i) q^{9} +(0.247127 + 0.428036i) q^{11} +5.52254 q^{13} -3.30827 q^{15} +(2.12812 + 3.68601i) q^{17} +(0.480467 - 0.832194i) q^{19} +(4.88653 - 3.39545i) q^{21} +(1.15001 - 1.99187i) q^{23} +(1.41812 + 2.45626i) q^{25} -2.11820 q^{27} +1.25851 q^{29} +(4.13238 + 7.15750i) q^{31} +(0.555797 - 0.962669i) q^{33} +(3.52125 + 1.65743i) q^{35} +(4.11309 - 7.12407i) q^{37} +(-6.21020 - 10.7564i) q^{39} +1.00000 q^{41} +5.33579 q^{43} +(1.51376 + 2.62191i) q^{45} +(-1.83383 + 3.17628i) q^{47} +(-6.90222 + 1.16591i) q^{49} +(4.78622 - 8.28998i) q^{51} +(-4.27318 - 7.40136i) q^{53} +0.727033 q^{55} -2.16118 q^{57} +(-0.736223 - 1.27518i) q^{59} +(3.11685 - 5.39855i) q^{61} +(-4.92691 - 2.31907i) q^{63} +(4.06175 - 7.03516i) q^{65} +(-1.95758 - 3.39063i) q^{67} -5.17281 q^{69} -10.1617 q^{71} +(-0.387918 - 0.671894i) q^{73} +(3.18941 - 5.52421i) q^{75} +(-1.07387 + 0.746191i) q^{77} +(4.99271 - 8.64763i) q^{79} +(5.46922 + 9.47297i) q^{81} -7.68368 q^{83} +6.26081 q^{85} +(-1.41522 - 2.45123i) q^{87} +(3.41540 - 5.91564i) q^{89} +(1.22109 + 14.5601i) q^{91} +(9.29389 - 16.0975i) q^{93} +(-0.706754 - 1.22413i) q^{95} -6.83506 q^{97} -1.01726 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^9	$ 16 q - 4 q^{9} + 8 q^{11} - 14 q^{13} - 2 q^{15} + q^{17} - 4 q^{19} + 13 q^{21} + 3 q^{23} + 4 q^{25} - 24 q^{27} - 8 q^{29} - 4 q^{31} - 23 q^{33} + 12 q^{35} + 31 q^{37} - 5 q^{39} + 16 q^{41} - 16 q^{43} - q^{45} - 24 q^{47} + 16 q^{49} + 23 q^{51} + q^{53} + 4 q^{55} - 30 q^{57} - 4 q^{59} + 4 q^{61} + 23 q^{63} + 24 q^{65} - 42 q^{69} + 16 q^{71} - 11 q^{73} + 15 q^{75} + 25 q^{77} - 14 q^{79} + 28 q^{81} - 84 q^{83} - 40 q^{85} - 25 q^{87} + 11 q^{89} + 7 q^{91} + 27 q^{93} + 15 q^{95} - 32 q^{97} - 16 q^{99}+O(q^{100}) $ 16 * q - 4 * q^9 + 8 * q^11 - 14 * q^13 - 2 * q^15 + q^17 - 4 * q^19 + 13 * q^21 + 3 * q^23 + 4 * q^25 - 24 * q^27 - 8 * q^29 - 4 * q^31 - 23 * q^33 + 12 * q^35 + 31 * q^37 - 5 * q^39 + 16 * q^41 - 16 * q^43 - q^45 - 24 * q^47 + 16 * q^49 + 23 * q^51 + q^53 + 4 * q^55 - 30 * q^57 - 4 * q^59 + 4 * q^61 + 23 * q^63 + 24 * q^65 - 42 * q^69 + 16 * q^71 - 11 * q^73 + 15 * q^75 + 25 * q^77 - 14 * q^79 + 28 * q^81 - 84 * q^83 - 40 * q^85 - 25 * q^87 + 11 * q^89 + 7 * q^91 + 27 * q^93 + 15 * q^95 - 32 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.12452	−	1.94772i	−0.649241	−	1.12452i	−0.983304	−	0.181968i	$-0.941753\pi$
$3$	−1.12452	−	1.94772i	−0.649241	−	1.12452i	0.334063	−	0.942551i	$-0.391580\pi$
$4$		0			0
$5$	0.735486	−	1.27390i	0.328919	−	0.569705i	−0.653378	−	0.757032i	$-0.726649\pi$
$5$	0.735486	−	1.27390i	0.328919	−	0.569705i	0.982298	+	0.187326i	$0.0599822\pi$
$6$		0			0
$7$	0.221110	+	2.63650i	0.0835717	+	0.996502i
$7$	0.221110	+	2.63650i	0.0835717	+	0.996502i
$8$		0			0
$9$	−1.02909	+	1.78243i	−0.343029	+	0.594144i
$10$		0			0
$11$	0.247127	+	0.428036i	0.0745114	+	0.129058i	0.900874	−	0.434081i	$-0.142927\pi$
$11$	0.247127	+	0.428036i	0.0745114	+	0.129058i	−0.826362	+	0.563139i	$0.809594\pi$
$12$		0			0
$13$	5.52254			1.53168			0.765838	−	0.643033i	$-0.222324\pi$
$13$	5.52254			1.53168			0.765838	+	0.643033i	$0.222324\pi$
$14$		0			0
$15$	−3.30827			−0.854193
$16$		0			0
$17$	2.12812	+	3.68601i	0.516145	+	0.893989i	0.999824	+	0.0187440i	$0.00596676\pi$
$17$	2.12812	+	3.68601i	0.516145	+	0.893989i	−0.483679	+	0.875245i	$0.660700\pi$
$18$		0			0
$19$	0.480467	−	0.832194i	0.110227	−	0.190918i	−0.805635	−	0.592412i	$-0.798176\pi$
$19$	0.480467	−	0.832194i	0.110227	−	0.190918i	0.915862	+	0.401494i	$0.131509\pi$
$20$		0			0
$21$	4.88653	−	3.39545i	1.06633	−	0.740948i
$22$		0			0
$23$	1.15001	−	1.99187i	0.239793	−	0.415333i	−0.720862	−	0.693079i	$-0.756254\pi$
$23$	1.15001	−	1.99187i	0.239793	−	0.415333i	0.960655	+	0.277746i	$0.0895872\pi$
$24$		0			0
$25$	1.41812	+	2.45626i	0.283624	+	0.491251i
$26$		0			0
$27$	−2.11820			−0.407648
$28$		0			0
$29$	1.25851			0.233699			0.116850	−	0.993150i	$-0.462720\pi$
$29$	1.25851			0.233699			0.116850	+	0.993150i	$0.462720\pi$
$30$		0			0
$31$	4.13238	+	7.15750i	0.742198	+	1.28552i	0.951492	+	0.307672i	$0.0995500\pi$
$31$	4.13238	+	7.15750i	0.742198	+	1.28552i	−0.209294	+	0.977853i	$0.567117\pi$
$32$		0			0
$33$	0.555797	−	0.962669i	0.0967518	−	0.167579i
$34$		0			0
$35$	3.52125	+	1.65743i	0.595201	+	0.280158i
$36$		0			0
$37$	4.11309	−	7.12407i	0.676187	−	1.17119i	−0.299933	−	0.953960i	$-0.596964\pi$
$37$	4.11309	−	7.12407i	0.676187	−	1.17119i	0.976120	−	0.217230i	$-0.0697022\pi$
$38$		0			0
$39$	−6.21020	−	10.7564i	−0.994428	−	1.72240i
$40$		0			0
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$		0			0
$43$	5.33579			0.813700			0.406850	−	0.913495i	$-0.366627\pi$
$43$	5.33579			0.813700			0.406850	+	0.913495i	$0.366627\pi$
$44$		0			0
$45$	1.51376	+	2.62191i	0.225658	+	0.390851i
$46$		0			0
$47$	−1.83383	+	3.17628i	−0.267491	+	0.463308i	−0.968213	−	0.250126i	$-0.919528\pi$
$47$	−1.83383	+	3.17628i	−0.267491	+	0.463308i	0.700722	+	0.713434i	$0.252861\pi$
$48$		0			0
$49$	−6.90222	+	1.16591i	−0.986032	+	0.166559i
$50$		0			0
$51$	4.78622	−	8.28998i	0.670205	−	1.16083i
$52$		0			0
$53$	−4.27318	−	7.40136i	−0.586966	−	1.01665i	−0.994627	−	0.103521i	$-0.966989\pi$
$53$	−4.27318	−	7.40136i	−0.586966	−	1.01665i	0.407661	−	0.913133i	$-0.366344\pi$
$54$		0			0
$55$	0.727033			0.0980331
$56$		0			0
$57$	−2.16118			−0.286255
$58$		0			0
$59$	−0.736223	−	1.27518i	−0.0958481	−	0.166014i	0.814114	−	0.580705i	$-0.197223\pi$
$59$	−0.736223	−	1.27518i	−0.0958481	−	0.166014i	−0.909962	+	0.414691i	$0.863890\pi$
$60$		0			0
$61$	3.11685	−	5.39855i	0.399072	−	0.691213i	−0.594539	−	0.804066i	$-0.702666\pi$
$61$	3.11685	−	5.39855i	0.399072	−	0.691213i	0.993612	+	0.112853i	$0.0359989\pi$
$62$		0			0
$63$	−4.92691	−	2.31907i	−0.620733	−	0.292175i
$64$		0			0
$65$	4.06175	−	7.03516i	0.503798	−	0.872604i
$66$		0			0
$67$	−1.95758	−	3.39063i	−0.239157	−	0.414232i	0.721316	−	0.692606i	$-0.243538\pi$
$67$	−1.95758	−	3.39063i	−0.239157	−	0.414232i	−0.960473	+	0.278375i	$0.910204\pi$
$68$		0			0
$69$	−5.17281			−0.622733
$70$		0			0
$71$	−10.1617			−1.20597			−0.602987	−	0.797751i	$-0.706023\pi$
$71$	−10.1617			−1.20597			−0.602987	+	0.797751i	$0.706023\pi$
$72$		0			0
$73$	−0.387918	−	0.671894i	−0.0454024	−	0.0786392i	0.842431	−	0.538804i	$-0.181124\pi$
$73$	−0.387918	−	0.671894i	−0.0454024	−	0.0786392i	−0.887834	+	0.460165i	$0.847790\pi$
$74$		0			0
$75$	3.18941	−	5.52421i	0.368281	−	0.637881i
$76$		0			0
$77$	−1.07387	+	0.746191i	−0.122379	+	0.0850364i
$78$		0			0
$79$	4.99271	−	8.64763i	0.561724	−	0.972935i	−0.435622	−	0.900130i	$-0.643472\pi$
$79$	4.99271	−	8.64763i	0.561724	−	0.972935i	0.997346	−	0.0728051i	$-0.0231951\pi$
$80$		0			0
$81$	5.46922	+	9.47297i	0.607691	+	1.05255i
$82$		0			0
$83$	−7.68368			−0.843393			−0.421697	−	0.906737i	$-0.638565\pi$
$83$	−7.68368			−0.843393			−0.421697	+	0.906737i	$0.638565\pi$
$84$		0			0
$85$	6.26081			0.679080
$86$		0			0
$87$	−1.41522	−	2.45123i	−0.151727	−	0.262799i
$88$		0			0
$89$	3.41540	−	5.91564i	0.362031	−	0.627057i	−0.626264	−	0.779611i	$-0.715417\pi$
$89$	3.41540	−	5.91564i	0.362031	−	0.627057i	0.988295	+	0.152555i	$0.0487500\pi$
$90$		0			0
$91$	1.22109	+	14.5601i	0.128005	+	1.52632i
$92$		0			0
$93$	9.29389	−	16.0975i	0.963732	−	1.66923i
$94$		0			0
$95$	−0.706754	−	1.22413i	−0.0725115	−	0.125594i
$96$		0			0
$97$	−6.83506			−0.693995			−0.346998	−	0.937866i	$-0.612799\pi$
$97$	−6.83506			−0.693995			−0.346998	+	0.937866i	$0.612799\pi$
$98$		0			0
$99$	−1.01726			−0.102238
$100$		0			0
$101$	−1.24772	−	2.16111i	−0.124152	−	0.215038i	0.797249	−	0.603651i	$-0.206288\pi$
$101$	−1.24772	−	2.16111i	−0.124152	−	0.215038i	−0.921401	+	0.388612i	$0.872955\pi$
$102$		0			0
$103$	1.13955	−	1.97377i	0.112284	−	0.194481i	−0.804407	−	0.594079i	$-0.797517\pi$
$103$	1.13955	−	1.97377i	0.112284	−	0.194481i	0.916691	+	0.399598i	$0.130850\pi$
$104$		0			0
$105$	−0.731492	−	8.72225i	−0.0713863	−	0.851204i
$106$		0			0
$107$	3.02994	−	5.24800i	0.292915	−	0.507344i	−0.681583	−	0.731741i	$-0.738708\pi$
$107$	3.02994	−	5.24800i	0.292915	−	0.507344i	0.974498	+	0.224397i	$0.0720413\pi$
$108$		0			0
$109$	2.77659	+	4.80919i	0.265949	+	0.460637i	0.967812	−	0.251675i	$-0.0809814\pi$
$109$	2.77659	+	4.80919i	0.265949	+	0.460637i	−0.701863	+	0.712312i	$0.747648\pi$
$110$		0			0
$111$	−18.5010			−1.75603
$112$		0			0
$113$	9.60020			0.903111			0.451555	−	0.892243i	$-0.350869\pi$
$113$	9.60020			0.903111			0.451555	+	0.892243i	$0.350869\pi$
$114$		0			0
$115$	−1.69163	−	2.92998i	−0.157745	−	0.273222i
$116$		0			0
$117$	−5.68317	+	9.84354i	−0.525409	+	0.910036i
$118$		0			0
$119$	−9.24761	+	6.42579i	−0.847727	+	0.589052i
$120$		0			0
$121$	5.37786	−	9.31472i	0.488896	−	0.846793i
$122$		0			0
$123$	−1.12452	−	1.94772i	−0.101394	−	0.175620i
$124$		0			0
$125$	11.5269			1.03100
$126$		0			0
$127$	4.29583			0.381193			0.190596	−	0.981668i	$-0.438958\pi$
$127$	4.29583			0.381193			0.190596	+	0.981668i	$0.438958\pi$
$128$		0			0
$129$	−6.00020	−	10.3927i	−0.528288	−	0.915022i
$130$		0			0
$131$	−6.43217	+	11.1408i	−0.561981	+	0.973379i	0.435343	+	0.900265i	$0.356627\pi$
$131$	−6.43217	+	11.1408i	−0.561981	+	0.973379i	−0.997324	+	0.0731146i	$0.976706\pi$
$132$		0			0
$133$	2.30031	+	1.08274i	0.199462	+	0.0938858i
$134$		0			0
$135$	−1.55791	+	2.69838i	−0.134083	+	0.232239i
$136$		0			0
$137$	9.91997	+	17.1819i	0.847520	+	1.46795i	0.883415	+	0.468592i	$0.155239\pi$
$137$	9.91997	+	17.1819i	0.847520	+	1.46795i	−0.0358948	+	0.999356i	$0.511428\pi$
$138$		0			0
$139$	10.3831			0.880685			0.440342	−	0.897830i	$-0.354857\pi$
$139$	10.3831			0.880685			0.440342	+	0.897830i	$0.354857\pi$
$140$		0			0
$141$	8.24869			0.694665
$142$		0			0
$143$	1.36477	+	2.36384i	0.114127	+	0.197674i
$144$		0			0
$145$	0.925615	−	1.60321i	0.0768682	−	0.133140i
$146$		0			0
$147$	10.0326	+	12.1325i	0.827471	+	1.00067i
$148$		0			0
$149$	8.19926	−	14.2015i	0.671710	−	1.16344i	−0.305710	−	0.952125i	$-0.598894\pi$
$149$	8.19926	−	14.2015i	0.671710	−	1.16344i	0.977419	−	0.211310i	$-0.0677730\pi$
$150$		0			0
$151$	1.44633	+	2.50512i	0.117701	+	0.203864i	0.918856	−	0.394593i	$-0.129114\pi$
$151$	1.44633	+	2.50512i	0.117701	+	0.203864i	−0.801155	+	0.598456i	$0.795781\pi$
$152$		0			0
$153$	−8.76008			−0.708211
$154$		0			0
$155$	12.1572			0.976494
$156$		0			0
$157$	10.7590	+	18.6352i	0.858665	+	1.48725i	0.873203	+	0.487357i	$0.162039\pi$
$157$	10.7590	+	18.6352i	0.858665	+	1.48725i	−0.0145378	+	0.999894i	$0.504628\pi$
$158$		0			0
$159$	−9.61054	+	16.6459i	−0.762165	+	1.32011i
$160$		0			0
$161$	5.50583	+	2.59156i	0.433920	+	0.204244i
$162$		0			0
$163$	−2.01866	+	3.49643i	−0.158114	+	0.273861i	−0.934188	−	0.356780i	$-0.883875\pi$
$163$	−2.01866	+	3.49643i	−0.158114	+	0.273861i	0.776075	+	0.630641i	$0.217208\pi$
$164$		0			0
$165$	−0.817562	−	1.41606i	−0.0636471	−	0.110240i
$166$		0			0
$167$	−15.8080			−1.22326			−0.611630	−	0.791144i	$-0.709486\pi$
$167$	−15.8080			−1.22326			−0.611630	+	0.791144i	$0.709486\pi$
$168$		0			0
$169$	17.4984			1.34603
$170$		0			0
$171$	0.988885	+	1.71280i	0.0756220	+	0.130981i
$172$		0			0
$173$	−6.97356	+	12.0786i	−0.530190	+	0.918316i	0.469189	+	0.883098i	$0.344546\pi$
$173$	−6.97356	+	12.0786i	−0.530190	+	0.918316i	−0.999380	+	0.0352188i	$0.988787\pi$
$174$		0			0
$175$	−6.16235	+	4.28197i	−0.465830	+	0.323687i
$176$		0			0
$177$	−1.65579	+	2.86792i	−0.124457	+	0.215566i
$178$		0			0
$179$	−8.22591	−	14.2477i	−0.614833	−	1.06492i	−0.990414	−	0.138133i	$-0.955890\pi$
$179$	−8.22591	−	14.2477i	−0.614833	−	1.06492i	0.375580	−	0.926790i	$-0.377443\pi$
$180$		0			0
$181$	1.78054			0.132347			0.0661733	−	0.997808i	$-0.478921\pi$
$181$	1.78054			0.132347			0.0661733	+	0.997808i	$0.478921\pi$
$182$		0			0
$183$	−14.0198			−1.03638
$184$		0			0
$185$	−6.05024	−	10.4793i	−0.444822	−	0.770455i
$186$		0			0
$187$	−1.05183	+	1.82182i	−0.0769174	+	0.133225i
$188$		0			0
$189$	−0.468356	−	5.58463i	−0.0340679	−	0.406222i
$190$		0			0
$191$	−11.1268	+	19.2722i	−0.805107	+	1.39449i	0.111112	+	0.993808i	$0.464559\pi$
$191$	−11.1268	+	19.2722i	−0.805107	+	1.39449i	−0.916219	+	0.400678i	$0.868775\pi$
$192$		0			0
$193$	2.17412	+	3.76569i	0.156497	+	0.271061i	0.933603	−	0.358309i	$-0.116647\pi$
$193$	2.17412	+	3.76569i	0.156497	+	0.271061i	−0.777106	+	0.629370i	$0.783313\pi$
$194$		0			0
$195$	−18.2701			−1.30835
$196$		0			0
$197$	−18.5511			−1.32171			−0.660854	−	0.750514i	$-0.729806\pi$
$197$	−18.5511			−1.32171			−0.660854	+	0.750514i	$0.729806\pi$
$198$		0			0
$199$	3.01494	+	5.22203i	0.213724	+	0.370180i	0.952877	−	0.303357i	$-0.0981075\pi$
$199$	3.01494	+	5.22203i	0.213724	+	0.370180i	−0.739153	+	0.673537i	$0.764774\pi$
$200$		0			0
$201$	−4.40268	+	7.62566i	−0.310541	+	0.537873i
$202$		0			0
$203$	0.278269	+	3.31805i	0.0195306	+	0.232882i
$204$		0			0
$205$	0.735486	−	1.27390i	0.0513686	−	0.0889730i
$206$		0			0
$207$	2.36691	+	4.09961i	0.164512	+	0.284943i
$208$		0			0
$209$	0.474945			0.0328526
$210$		0			0
$211$	−7.97038			−0.548704			−0.274352	−	0.961629i	$-0.588463\pi$
$211$	−7.97038			−0.548704			−0.274352	+	0.961629i	$0.588463\pi$
$212$		0			0
$213$	11.4270	+	19.7922i	0.782968	+	1.35614i
$214$		0			0
$215$	3.92440	−	6.79726i	0.267642	−	0.463569i
$216$		0			0
$217$	−17.9570	+	12.4776i	−1.21900	+	0.847035i
$218$		0			0
$219$	−0.872443	+	1.51112i	−0.0589542	+	0.102112i
$220$		0			0
$221$	11.7526	+	20.3561i	0.790567	+	1.36930i
$222$		0			0
$223$	−18.1994			−1.21872			−0.609360	−	0.792894i	$-0.708573\pi$
$223$	−18.1994			−1.21872			−0.609360	+	0.792894i	$0.708573\pi$
$224$		0			0
$225$	−5.83748			−0.389165
$226$		0			0
$227$	1.28970	+	2.23383i	0.0856004	+	0.148264i	0.905647	−	0.424033i	$-0.139386\pi$
$227$	1.28970	+	2.23383i	0.0856004	+	0.148264i	−0.820047	+	0.572297i	$0.806053\pi$
$228$		0			0
$229$	−11.2766	+	19.5317i	−0.745180	+	1.29069i	0.204930	+	0.978777i	$0.434303\pi$
$229$	−11.2766	+	19.5317i	−0.745180	+	1.29069i	−0.950111	+	0.311913i	$0.899030\pi$
$230$		0			0
$231$	2.66096	+	1.25250i	0.175079	+	0.0824085i
$232$		0			0
$233$	0.774942	−	1.34224i	0.0507682	−	0.0879330i	−0.839525	−	0.543322i	$-0.817166\pi$
$233$	0.774942	−	1.34224i	0.0507682	−	0.0879330i	0.890293	+	0.455389i	$0.150500\pi$
$234$		0			0
$235$	2.69751	+	4.67222i	0.175966	+	0.304782i
$236$		0			0
$237$	−22.4576			−1.45878
$238$		0			0
$239$	16.3710			1.05895			0.529477	−	0.848324i	$-0.322388\pi$
$239$	16.3710			1.05895			0.529477	+	0.848324i	$0.322388\pi$
$240$		0			0
$241$	−5.88014	−	10.1847i	−0.378773	−	0.656054i	0.612111	−	0.790772i	$-0.290321\pi$
$241$	−5.88014	−	10.1847i	−0.378773	−	0.656054i	−0.990884	+	0.134718i	$0.956987\pi$
$242$		0			0
$243$	9.12318	−	15.8018i	0.585253	−	1.01369i
$244$		0			0
$245$	−3.59124	+	9.65025i	−0.229436	+	0.616532i
$246$		0			0
$247$	2.65340	−	4.59582i	0.168832	−	0.292425i
$248$		0			0
$249$	8.64044	+	14.9657i	0.547566	+	0.948412i
$250$		0			0
$251$	15.1858			0.958517			0.479259	−	0.877674i	$-0.340906\pi$
$251$	15.1858			0.958517			0.479259	+	0.877674i	$0.340906\pi$
$252$		0			0
$253$	1.13679			0.0714692
$254$		0			0
$255$	−7.04040	−	12.1943i	−0.440887	−	0.763639i
$256$		0			0
$257$	−0.0473438	+	0.0820019i	−0.00295323	+	0.00511514i	−0.867498	−	0.497440i	$-0.834273\pi$
$257$	−0.0473438	+	0.0820019i	−0.00295323	+	0.00511514i	0.864545	+	0.502555i	$0.167607\pi$
$258$		0			0
$259$	19.6920	+	9.26893i	1.22360	+	0.575943i
$260$		0			0
$261$	−1.29511	+	2.24320i	−0.0801656	+	0.138851i
$262$		0			0
$263$	−8.95875	−	15.5170i	−0.552420	−	0.956819i	−0.998099	−	0.0616267i	$-0.980371\pi$
$263$	−8.95875	−	15.5170i	−0.552420	−	0.956819i	0.445679	−	0.895193i	$-0.352962\pi$
$264$		0			0
$265$	−12.5714			−0.772258
$266$		0			0
$267$	−15.3627			−0.940183
$268$		0			0
$269$	−16.1780	−	28.0212i	−0.986393	−	1.70848i	−0.635576	−	0.772038i	$-0.719237\pi$
$269$	−16.1780	−	28.0212i	−0.986393	−	1.70848i	−0.350817	−	0.936444i	$-0.614096\pi$
$270$		0			0
$271$	8.49051	−	14.7060i	0.515762	−	0.893325i	−0.484071	−	0.875029i	$-0.660842\pi$
$271$	8.49051	−	14.7060i	0.515762	−	0.893325i	0.999833	−	0.0182965i	$-0.00582429\pi$
$272$		0			0
$273$	26.9860	−	18.7515i	1.63327	−	1.13489i
$274$		0			0
$275$	−0.700910	+	1.21401i	−0.0422665	+	0.0732077i
$276$		0			0
$277$	0.211304	+	0.365990i	0.0126960	+	0.0219902i	0.872304	−	0.488965i	$-0.162625\pi$
$277$	0.211304	+	0.365990i	0.0126960	+	0.0219902i	−0.859608	+	0.510955i	$0.829292\pi$
$278$		0			0
$279$	−17.0103			−1.01838
$280$		0			0
$281$	−10.4772			−0.625016			−0.312508	−	0.949915i	$-0.601169\pi$
$281$	−10.4772			−0.625016			−0.312508	+	0.949915i	$0.601169\pi$
$282$		0			0
$283$	13.7671	+	23.8454i	0.818372	+	1.41746i	0.906881	+	0.421387i	$0.138456\pi$
$283$	13.7671	+	23.8454i	0.818372	+	1.41746i	−0.0885089	+	0.996075i	$0.528210\pi$
$284$		0			0
$285$	−1.58952	+	2.75313i	−0.0941549	+	0.163081i
$286$		0			0
$287$	0.221110	+	2.63650i	0.0130517	+	0.155627i
$288$		0			0
$289$	−0.557791	+	0.966123i	−0.0328113	+	0.0568308i
$290$		0			0
$291$	7.68616	+	13.3128i	0.450571	+	0.780411i
$292$		0			0
$293$	22.6387			1.32257			0.661283	−	0.750137i	$-0.270012\pi$
$293$	22.6387			1.32257			0.661283	+	0.750137i	$0.270012\pi$
$294$		0			0
$295$	−2.16593			−0.126105
$296$		0			0
$297$	−0.523464	−	0.906666i	−0.0303745	−	0.0526101i
$298$		0			0
$299$	6.35095	−	11.0002i	0.367285	−	0.636156i
$300$		0			0
$301$	1.17980	+	14.0678i	0.0680023	+	0.810854i
$302$		0			0
$303$	−2.80616	+	4.86042i	−0.161210	+	0.279224i
$304$		0			0
$305$	−4.58481	−	7.94112i	−0.262525	−	0.454707i
$306$		0			0
$307$	−9.00706			−0.514060			−0.257030	−	0.966403i	$-0.582744\pi$
$307$	−9.00706			−0.514060			−0.257030	+	0.966403i	$0.582744\pi$
$308$		0			0
$309$	−5.12580			−0.291597
$310$		0			0
$311$	12.9014	+	22.3459i	0.731573	+	1.26712i	0.956211	+	0.292679i	$0.0945467\pi$
$311$	12.9014	+	22.3459i	0.731573	+	1.26712i	−0.224638	+	0.974442i	$0.572120\pi$
$312$		0			0
$313$	2.65320	−	4.59548i	0.149968	−	0.259752i	−0.781247	−	0.624221i	$-0.785416\pi$
$313$	2.65320	−	4.59548i	0.149968	−	0.259752i	0.931215	+	0.364469i	$0.118750\pi$
$314$		0			0
$315$	−6.57794	+	4.57075i	−0.370625	+	0.257532i
$316$		0			0
$317$	−1.36857	+	2.37044i	−0.0768668	+	0.133137i	−0.901897	−	0.431952i	$-0.857825\pi$
$317$	−1.36857	+	2.37044i	−0.0768668	+	0.133137i	0.825030	+	0.565089i	$0.191158\pi$
$318$		0			0
$319$	0.311011	+	0.538686i	0.0174133	+	0.0301606i
$320$		0			0
$321$	−13.6289			−0.760690
$322$		0			0
$323$	4.08997			0.227572
$324$		0			0
$325$	7.83162	+	13.5648i	0.434420	+	0.752438i
$326$		0			0
$327$	6.24465	−	10.8161i	0.345330	−	0.598129i
$328$		0			0
$329$	−8.77973	−	4.13257i	−0.484042	−	0.227836i
$330$		0			0
$331$	5.77447	−	10.0017i	0.317394	−	0.549742i	−0.662550	−	0.749018i	$-0.730526\pi$
$331$	5.77447	−	10.0017i	0.317394	−	0.549742i	0.979943	+	0.199276i	$0.0638590\pi$
$332$		0			0
$333$	8.46545	+	14.6626i	0.463904	+	0.803505i
$334$		0			0
$335$	−5.75910			−0.314653
$336$		0			0
$337$	−31.6744			−1.72541			−0.862706	−	0.505705i	$-0.831232\pi$
$337$	−31.6744			−1.72541			−0.862706	+	0.505705i	$0.831232\pi$
$338$		0			0
$339$	−10.7956	−	18.6985i	−0.586337	−	1.01557i
$340$		0			0
$341$	−2.04244	+	3.53762i	−0.110605	+	0.191573i
$342$		0			0
$343$	−4.60007	−	17.9399i	−0.248380	−	0.968663i
$344$		0			0
$345$	−3.80453	+	6.58964i	−0.204829	+	0.354774i
$346$		0			0
$347$	4.07049	+	7.05030i	0.218515	+	0.378480i	0.954354	−	0.298677i	$-0.0965453\pi$
$347$	4.07049	+	7.05030i	0.218515	+	0.378480i	−0.735839	+	0.677157i	$0.763212\pi$
$348$		0			0
$349$	4.07115			0.217924			0.108962	−	0.994046i	$-0.465247\pi$
$349$	4.07115			0.217924			0.108962	+	0.994046i	$0.465247\pi$
$350$		0			0
$351$	−11.6979			−0.624385
$352$		0			0
$353$	−15.2796	−	26.4651i	−0.813252	−	1.40859i	−0.910576	−	0.413341i	$-0.864362\pi$
$353$	−15.2796	−	26.4651i	−0.813252	−	1.40859i	0.0973245	−	0.995253i	$-0.468972\pi$
$354$		0			0
$355$	−7.47380	+	12.9450i	−0.396668	+	0.687050i
$356$		0			0
$357$	22.9148	+	10.7859i	1.21278	+	0.570848i
$358$		0			0
$359$	14.5051	−	25.1236i	0.765550	−	1.32597i	−0.174405	−	0.984674i	$-0.555800\pi$
$359$	14.5051	−	25.1236i	0.765550	−	1.32597i	0.939955	−	0.341297i	$-0.110866\pi$
$360$		0			0
$361$	9.03830	+	15.6548i	0.475700	+	0.823937i
$362$		0			0
$363$	−24.1900			−1.26965
$364$		0			0
$365$	−1.14123			−0.0597349
$366$		0			0
$367$	−8.22199	−	14.2409i	−0.429185	−	0.743369i	0.567616	−	0.823293i	$-0.307866\pi$
$367$	−8.22199	−	14.2409i	−0.429185	−	0.743369i	−0.996801	+	0.0799237i	$0.974532\pi$
$368$		0			0
$369$	−1.02909	+	1.78243i	−0.0535721	+	0.0927896i
$370$		0			0
$371$	18.5688	−	12.9027i	0.964044	−	0.669876i
$372$		0			0
$373$	−13.2182	+	22.8946i	−0.684413	+	1.18544i	0.289208	+	0.957266i	$0.406608\pi$
$373$	−13.2182	+	22.8946i	−0.684413	+	1.18544i	−0.973621	+	0.228171i	$0.926725\pi$
$374$		0			0
$375$	−12.9622	−	22.4512i	−0.669366	−	1.15938i
$376$		0			0
$377$	6.95016			0.357951
$378$		0			0
$379$	−15.6085			−0.801756			−0.400878	−	0.916132i	$-0.631295\pi$
$379$	−15.6085			−0.801756			−0.400878	+	0.916132i	$0.631295\pi$
$380$		0			0
$381$	−4.83074	−	8.36709i	−0.247486	−	0.428659i
$382$		0			0
$383$	1.68236	−	2.91393i	0.0859645	−	0.148895i	−0.819837	−	0.572597i	$-0.805936\pi$
$383$	1.68236	−	2.91393i	0.0859645	−	0.148895i	0.905802	+	0.423702i	$0.139270\pi$
$384$		0			0
$385$	0.160754	+	1.91682i	0.00819279	+	0.0976901i
$386$		0			0
$387$	−5.49099	+	9.51068i	−0.279123	+	0.483455i
$388$		0			0
$389$	0.612558	+	1.06098i	0.0310579	+	0.0537939i	0.881137	−	0.472862i	$-0.156779\pi$
$389$	0.612558	+	1.06098i	0.0310579	+	0.0537939i	−0.850079	+	0.526656i	$0.823446\pi$
$390$		0			0
$391$	9.78940			0.495071
$392$		0			0
$393$	28.9324			1.45945
$394$		0			0
$395$	−7.34414	−	12.7204i	−0.369524	−	0.640034i
$396$		0			0
$397$	−18.2659	+	31.6375i	−0.916742	+	1.58784i	−0.112410	+	0.993662i	$0.535857\pi$
$397$	−18.2659	+	31.6375i	−0.916742	+	1.58784i	−0.804331	+	0.594181i	$0.797476\pi$
$398$		0			0
$399$	−0.477858	−	5.69794i	−0.0239228	−	0.285254i
$400$		0			0
$401$	14.9933	−	25.9691i	0.748728	−	1.29684i	−0.199704	−	0.979856i	$-0.563998\pi$
$401$	14.9933	−	25.9691i	0.748728	−	1.29684i	0.948433	−	0.316979i	$-0.102668\pi$
$402$		0			0
$403$	22.8212	+	39.5276i	1.13681	+	1.96901i
$404$		0			0
$405$	16.0901			0.799526
$406$		0			0
$407$	4.06581			0.201535
$408$		0			0
$409$	18.5125	+	32.0646i	0.915386	+	1.58549i	0.806336	+	0.591458i	$0.201447\pi$
$409$	18.5125	+	32.0646i	0.915386	+	1.58549i	0.109050	+	0.994036i	$0.465219\pi$
$410$		0			0
$411$	22.3104	−	38.6427i	1.10049	−	1.90610i
$412$		0			0
$413$	3.19921	−	2.22300i	0.157423	−	0.109387i
$414$		0			0
$415$	−5.65124	+	9.78823i	−0.277408	+	0.480485i
$416$		0			0
$417$	−11.6760	−	20.2235i	−0.571777	−	0.990347i
$418$		0			0
$419$	24.4042			1.19222			0.596112	−	0.802901i	$-0.296711\pi$
$419$	24.4042			1.19222			0.596112	+	0.802901i	$0.296711\pi$
$420$		0			0
$421$	−2.51451			−0.122550			−0.0612750	−	0.998121i	$-0.519517\pi$
$421$	−2.51451			−0.122550			−0.0612750	+	0.998121i	$0.519517\pi$
$422$		0			0
$423$	−3.77433	−	6.53734i	−0.183514	−	0.317856i
$424$		0			0
$425$	−6.03586	+	10.4544i	−0.292782	+	0.507114i
$426$		0			0
$427$	14.9224	+	7.02390i	0.722147	+	0.339910i
$428$		0			0
$429$	3.06941	−	5.31637i	0.148193	−	0.256677i
$430$		0			0
$431$	−8.91625	−	15.4434i	−0.429481	−	0.743882i	0.567347	−	0.823479i	$-0.307970\pi$
$431$	−8.91625	−	15.4434i	−0.429481	−	0.743882i	−0.996827	+	0.0795969i	$0.974637\pi$
$432$		0			0
$433$	−26.2172			−1.25992			−0.629960	−	0.776628i	$-0.716929\pi$
$433$	−26.2172			−1.25992			−0.629960	+	0.776628i	$0.716929\pi$
$434$		0			0
$435$	−4.16349			−0.199624
$436$		0			0
$437$	−1.10508	−	1.91405i	−0.0528631	−	0.0915617i
$438$		0			0
$439$	−6.03303	+	10.4495i	−0.287941	+	0.498728i	−0.973318	−	0.229460i	$-0.926304\pi$
$439$	−6.03303	+	10.4495i	−0.287941	+	0.498728i	0.685377	+	0.728188i	$0.259637\pi$
$440$		0			0
$441$	5.02483	−	13.5026i	0.239278	−	0.642979i
$442$		0			0
$443$	15.5949	−	27.0112i	0.740937	−	1.28334i	−0.211131	−	0.977458i	$-0.567715\pi$
$443$	15.5949	−	27.0112i	0.740937	−	1.28334i	0.952069	−	0.305884i	$-0.0989519\pi$
$444$		0			0
$445$	−5.02395	−	8.70174i	−0.238158	−	0.412502i
$446$		0			0
$447$	−36.8809			−1.74441
$448$		0			0
$449$	−12.5606			−0.592770			−0.296385	−	0.955069i	$-0.595781\pi$
$449$	−12.5606			−0.592770			−0.296385	+	0.955069i	$0.595781\pi$
$450$		0			0
$451$	0.247127	+	0.428036i	0.0116367	+	0.0201554i
$452$		0			0
$453$	3.25286	−	5.63411i	0.152832	−	0.264714i
$454$		0			0
$455$	19.4463	+	9.15325i	0.911655	+	0.429111i
$456$		0			0
$457$	0.104526	−	0.181044i	0.00488950	−	0.00846887i	−0.863570	−	0.504228i	$-0.831777\pi$
$457$	0.104526	−	0.181044i	0.00488950	−	0.00846887i	0.868460	+	0.495760i	$0.165110\pi$
$458$		0			0
$459$	−4.50779	−	7.80772i	−0.210406	−	0.364433i
$460$		0			0
$461$	−10.3033			−0.479873			−0.239936	−	0.970789i	$-0.577127\pi$
$461$	−10.3033			−0.479873			−0.239936	+	0.970789i	$0.577127\pi$
$462$		0			0
$463$	−8.65140			−0.402065			−0.201032	−	0.979585i	$-0.564430\pi$
$463$	−8.65140			−0.402065			−0.201032	+	0.979585i	$0.564430\pi$
$464$		0			0
$465$	−13.6711	−	23.6790i	−0.633980	−	1.09809i
$466$		0			0
$467$	−11.3792	+	19.7093i	−0.526566	+	0.912040i	0.472954	+	0.881087i	$0.343188\pi$
$467$	−11.3792	+	19.7093i	−0.526566	+	0.912040i	−0.999521	+	0.0309530i	$0.990146\pi$
$468$		0			0
$469$	8.50655	−	5.91086i	0.392796	−	0.272938i
$470$		0			0
$471$	24.1975	−	41.9113i	1.11496	−	1.93117i
$472$		0			0
$473$	1.31862	+	2.28391i	0.0606300	+	0.105014i
$474$		0			0
$475$	2.72544			0.125052
$476$		0			0
$477$	17.5899			0.805385
$478$		0			0
$479$	−0.884953	−	1.53278i	−0.0404345	−	0.0700347i	0.845100	−	0.534608i	$-0.179541\pi$
$479$	−0.884953	−	1.53278i	−0.0404345	−	0.0700347i	−0.885534	+	0.464574i	$0.846208\pi$
$480$		0			0
$481$	22.7147	−	39.3430i	1.03570	−	1.79388i
$482$		0			0
$483$	−1.14376	−	13.6381i	−0.0520429	−	0.620555i
$484$		0			0
$485$	−5.02709	+	8.70718i	−0.228269	+	0.395373i
$486$		0			0
$487$	13.5661	+	23.4971i	0.614738	+	1.06476i	0.990430	+	0.138013i	$0.0440716\pi$
$487$	13.5661	+	23.4971i	0.614738	+	1.06476i	−0.375692	+	0.926744i	$0.622595\pi$
$488$		0			0
$489$	9.08010			0.410616
$490$		0			0
$491$	−0.410698			−0.0185345			−0.00926727	−	0.999957i	$-0.502950\pi$
$491$	−0.410698			−0.0185345			−0.00926727	+	0.999957i	$0.502950\pi$
$492$		0			0
$493$	2.67826	+	4.63888i	0.120623	+	0.208925i
$494$		0			0
$495$	−0.748180	+	1.29589i	−0.0336282	+	0.0582457i
$496$		0			0
$497$	−2.24686	−	26.7913i	−0.100785	−	1.20176i
$498$		0			0
$499$	10.1026	−	17.4982i	0.452255	−	0.783328i	−0.546271	−	0.837608i	$-0.683953\pi$
$499$	10.1026	−	17.4982i	0.452255	−	0.783328i	0.998526	+	0.0542805i	$0.0172865\pi$
$500$		0			0
$501$	17.7764	+	30.7896i	0.794191	+	1.37558i
$502$		0			0
$503$	−38.0193			−1.69520			−0.847599	−	0.530638i	$-0.821952\pi$
$503$	−38.0193			−1.69520			−0.847599	+	0.530638i	$0.821952\pi$
$504$		0			0
$505$	−3.67071			−0.163345
$506$		0			0
$507$	−19.6773	−	34.0821i	−0.873900	−	1.51364i
$508$		0			0
$509$	−21.6299	+	37.4642i	−0.958730	+	1.66057i	−0.233139	+	0.972443i	$0.574900\pi$
$509$	−21.6299	+	37.4642i	−0.958730	+	1.66057i	−0.725591	+	0.688126i	$0.758434\pi$
$510$		0			0
$511$	1.68567	−	1.17131i	0.0745698	−	0.0518156i
$512$		0			0
$513$	−1.01773	+	1.76276i	−0.0449338	+	0.0778276i
$514$		0			0
$515$	−1.67625	−	2.90335i	−0.0738645	−	0.127937i
$516$		0			0
$517$	−1.81275			−0.0797246
$518$		0			0
$519$	31.3676			1.37689
$520$		0			0
$521$	−2.35210	−	4.07395i	−0.103047	−	0.178483i	0.809891	−	0.586580i	$-0.199526\pi$
$521$	−2.35210	−	4.07395i	−0.103047	−	0.178483i	−0.912939	+	0.408097i	$0.866193\pi$
$522$		0			0
$523$	−8.59410	+	14.8854i	−0.375794	+	0.650894i	−0.990446	−	0.137905i	$-0.955963\pi$
$523$	−8.59410	+	14.8854i	−0.375794	+	0.650894i	0.614652	+	0.788799i	$0.289297\pi$
$524$		0			0
$525$	15.2698	+	7.18740i	0.666428	+	0.313684i
$526$		0			0
$527$	−17.5884	+	30.4640i	−0.766164	+	1.32703i
$528$		0			0
$529$	8.85498	+	15.3373i	0.384999	+	0.666838i
$530$		0			0
$531$	3.03055			0.131515
$532$		0			0
$533$	5.52254			0.239208
$534$		0			0
$535$	−4.45695	−	7.71967i	−0.192691	−	0.333750i
$536$		0			0
$537$	−18.5004	+	32.0436i	−0.798351	+	1.38278i
$538$		0			0
$539$	−2.20477	−	2.66627i	−0.0949663	−	0.114844i
$540$		0			0
$541$	9.71714	−	16.8306i	0.417772	−	0.723603i	−0.577943	−	0.816077i	$-0.696144\pi$
$541$	9.71714	−	16.8306i	0.417772	−	0.723603i	0.995715	+	0.0924744i	$0.0294776\pi$
$542$		0			0
$543$	−2.00225	−	3.46800i	−0.0859249	−	0.148826i
$544$		0			0
$545$	8.16857			0.349903
$546$		0			0
$547$	−24.8699			−1.06336			−0.531681	−	0.846945i	$-0.678439\pi$
$547$	−24.8699			−1.06336			−0.531681	+	0.846945i	$0.678439\pi$
$548$		0			0
$549$	6.41503	+	11.1112i	0.273787	+	0.474213i
$550$		0			0
$551$	0.604672	−	1.04732i	0.0257599	−	0.0446175i
$552$		0			0
$553$	23.9034	+	11.2512i	1.01648	+	0.478449i
$554$		0			0
$555$	−13.6072	+	23.5684i	−0.577594	+	1.00042i
$556$		0			0
$557$	−10.8840	−	18.8516i	−0.461169	−	0.798768i	0.537851	−	0.843040i	$-0.319236\pi$
$557$	−10.8840	−	18.8516i	−0.461169	−	0.798768i	−0.999020	+	0.0442721i	$0.985903\pi$
$558$		0			0
$559$	29.4671			1.24633
$560$		0			0
$561$	4.73121			0.199752
$562$		0			0
$563$	−17.3695	−	30.0848i	−0.732036	−	1.26792i	−0.956011	−	0.293329i	$-0.905237\pi$
$563$	−17.3695	−	30.0848i	−0.732036	−	1.26792i	0.223975	−	0.974595i	$-0.428097\pi$
$564$		0			0
$565$	7.06082	−	12.2297i	0.297051	−	0.514507i
$566$		0			0
$567$	−23.7661	+	16.5141i	−0.998084	+	0.693529i
$568$		0			0
$569$	19.1067	−	33.0937i	0.800993	−	1.38736i	−0.117970	−	0.993017i	$-0.537639\pi$
$569$	19.1067	−	33.0937i	0.800993	−	1.38736i	0.918963	−	0.394343i	$-0.129028\pi$
$570$		0			0
$571$	22.8229	+	39.5304i	0.955109	+	1.65430i	0.734119	+	0.679021i	$0.237595\pi$
$571$	22.8229	+	39.5304i	0.955109	+	1.65430i	0.220990	+	0.975276i	$0.429071\pi$
$572$		0			0
$573$	50.0492			2.09083
$574$		0			0
$575$	6.52338			0.272044
$576$		0			0
$577$	2.59966	+	4.50274i	0.108225	+	0.187452i	0.915051	−	0.403337i	$-0.132150\pi$
$577$	2.59966	+	4.50274i	0.108225	+	0.187452i	−0.806826	+	0.590789i	$0.798817\pi$
$578$		0			0
$579$	4.88969	−	8.46919i	0.203209	−	0.351968i
$580$		0			0
$581$	−1.69894	−	20.2580i	−0.0704838	−	0.840443i
$582$		0			0
$583$	2.11203	−	3.65814i	0.0874713	−	0.151505i
$584$		0			0
$585$	8.35979	+	14.4796i	0.345635	+	0.598657i
$586$		0			0
$587$	−12.2599			−0.506020			−0.253010	−	0.967464i	$-0.581421\pi$
$587$	−12.2599			−0.506020			−0.253010	+	0.967464i	$0.581421\pi$
$588$		0			0
$589$	7.94190			0.327240
$590$		0			0
$591$	20.8610	+	36.1324i	0.858108	+	1.48629i
$592$		0			0
$593$	−6.23297	+	10.7958i	−0.255957	+	0.443331i	−0.965155	−	0.261679i	$-0.915724\pi$
$593$	−6.23297	+	10.7958i	−0.255957	+	0.443331i	0.709198	+	0.705010i	$0.249057\pi$
$594$		0			0
$595$	1.38433	+	16.5066i	0.0567519	+	0.676705i
$596$		0			0
$597$	6.78072	−	11.7445i	0.277516	−	0.480672i
$598$		0			0
$599$	21.4454	+	37.1445i	0.876235	+	1.51768i	0.855441	+	0.517900i	$0.173286\pi$
$599$	21.4454	+	37.1445i	0.876235	+	1.51768i	0.0207938	+	0.999784i	$0.493381\pi$
$600$		0			0
$601$	2.40756			0.0982066			0.0491033	−	0.998794i	$-0.484364\pi$
$601$	2.40756			0.0982066			0.0491033	+	0.998794i	$0.484364\pi$
$602$		0			0
$603$	8.05809			0.328151
$604$		0			0
$605$	−7.91068	−	13.7017i	−0.321615	−	0.557053i
$606$		0			0
$607$	3.51826	−	6.09380i	0.142802	−	0.247340i	−0.785749	−	0.618545i	$-0.787722\pi$
$607$	3.51826	−	6.09380i	0.142802	−	0.247340i	0.928551	+	0.371206i	$0.121056\pi$
$608$		0			0
$609$	6.14973	−	4.27320i	0.249200	−	0.173159i
$610$		0			0
$611$	−10.1274	+	17.5411i	−0.409710	+	0.709638i
$612$		0			0
$613$	−15.2736	−	26.4547i	−0.616897	−	1.06850i	−0.990049	−	0.140726i	$-0.955056\pi$
$613$	−15.2736	−	26.4547i	−0.616897	−	1.06850i	0.373152	−	0.927770i	$-0.378277\pi$
$614$		0			0
$615$	−3.30827			−0.133402
$616$		0			0
$617$	−16.2455			−0.654018			−0.327009	−	0.945021i	$-0.606041\pi$
$617$	−16.2455			−0.654018			−0.327009	+	0.945021i	$0.606041\pi$
$618$		0			0
$619$	−13.1570	−	22.7886i	−0.528825	−	0.915952i	−0.999435	−	0.0336109i	$-0.989299\pi$
$619$	−13.1570	−	22.7886i	−0.528825	−	0.915952i	0.470610	−	0.882342i	$-0.344034\pi$
$620$		0			0
$621$	−2.43594	+	4.21918i	−0.0977511	+	0.169310i
$622$		0			0
$623$	16.3517	+	7.69667i	0.655119	+	0.308361i
$624$		0			0
$625$	1.38727	−	2.40282i	0.0554909	−	0.0961130i
$626$		0			0
$627$	−0.534085	−	0.925062i	−0.0213293	−	0.0369434i
$628$		0			0
$629$	35.0126			1.39604
$630$		0			0
$631$	33.3206			1.32647			0.663237	−	0.748410i	$-0.269182\pi$
$631$	33.3206			1.32647			0.663237	+	0.748410i	$0.269182\pi$
$632$		0			0
$633$	8.96285	+	15.5241i	0.356241	+	0.617028i
$634$		0			0
$635$	3.15952	−	5.47245i	0.125382	−	0.217168i
$636$		0			0
$637$	−38.1178	+	6.43879i	−1.51028	+	0.255114i
$638$		0			0
$639$	10.4573	−	18.1126i	0.413684	−	0.716522i
$640$		0			0
$641$	−17.1231	−	29.6581i	−0.676322	−	1.17142i	−0.976081	−	0.217409i	$-0.930239\pi$
$641$	−17.1231	−	29.6581i	−0.676322	−	1.17142i	0.299758	−	0.954015i	$-0.403094\pi$
$642$		0			0
$643$	17.7446			0.699777			0.349889	−	0.936791i	$-0.386219\pi$
$643$	17.7446			0.699777			0.349889	+	0.936791i	$0.386219\pi$
$644$		0			0
$645$	−17.6523			−0.695057
$646$		0			0
$647$	−7.17566	−	12.4286i	−0.282104	−	0.488619i	0.689799	−	0.724001i	$-0.257699\pi$
$647$	−7.17566	−	12.4286i	−0.282104	−	0.488619i	−0.971903	+	0.235382i	$0.924366\pi$
$648$		0			0
$649$	0.363881	−	0.630260i	0.0142836	−	0.0247399i
$650$		0			0
$651$	44.4959	+	20.9440i	1.74393	+	0.820860i
$652$		0			0
$653$	−15.5483	+	26.9305i	−0.608452	+	1.05387i	0.383043	+	0.923730i	$0.374876\pi$
$653$	−15.5483	+	26.9305i	−0.608452	+	1.05387i	−0.991496	+	0.130140i	$0.958457\pi$
$654$		0			0
$655$	9.46154	+	16.3879i	0.369693	+	0.640327i
$656$		0			0
$657$	1.59681			0.0622973
$658$		0			0
$659$	−24.5409			−0.955980			−0.477990	−	0.878365i	$-0.658634\pi$
$659$	−24.5409			−0.955980			−0.477990	+	0.878365i	$0.658634\pi$
$660$		0			0
$661$	−13.2992	−	23.0350i	−0.517281	−	0.895956i	−0.999799	−	0.0200702i	$-0.993611\pi$
$661$	−13.2992	−	23.0350i	−0.517281	−	0.895956i	0.482518	−	0.875886i	$-0.339722\pi$
$662$		0			0
$663$	26.4321	−	45.7817i	1.02654	−	1.77802i
$664$		0			0
$665$	3.07115	−	2.13402i	0.119094	−	0.0827539i
$666$		0			0
$667$	1.44729	−	2.50678i	0.0560393	−	0.0970630i
$668$		0			0
$669$	20.4655	+	35.4473i	0.791243	+	1.37047i
$670$		0			0
$671$	3.08103			0.118942
$672$		0			0
$673$	−20.9351			−0.806988			−0.403494	−	0.914982i	$-0.632204\pi$
$673$	−20.9351			−0.806988			−0.403494	+	0.914982i	$0.632204\pi$
$674$		0			0
$675$	−3.00387	−	5.20285i	−0.115619	−	0.200258i
$676$		0			0
$677$	1.41343	−	2.44814i	0.0543227	−	0.0940896i	−0.837585	−	0.546307i	$-0.816033\pi$
$677$	1.41343	−	2.44814i	0.0543227	−	0.0940896i	0.891908	+	0.452217i	$0.149367\pi$
$678$		0			0
$679$	−1.51130	−	18.0206i	−0.0579984	−	0.691568i
$680$		0			0
$681$	2.90058	−	5.02396i	0.111151	−	0.192519i
$682$		0			0
$683$	−7.35578	−	12.7406i	−0.281461	−	0.487505i	0.690284	−	0.723539i	$-0.257486\pi$
$683$	−7.35578	−	12.7406i	−0.281461	−	0.487505i	−0.971745	+	0.236034i	$0.924152\pi$
$684$		0			0
$685$	29.1840			1.11506
$686$		0			0
$687$	50.7231			1.93521
$688$		0			0
$689$	−23.5988	−	40.8743i	−0.899042	−	1.55719i
$690$		0			0
$691$	−4.74185	+	8.21312i	−0.180388	+	0.312442i	−0.942013	−	0.335577i	$-0.891069\pi$
$691$	−4.74185	+	8.21312i	−0.180388	+	0.312442i	0.761624	+	0.648019i	$0.224402\pi$
$692$		0			0
$693$	−0.224926	−	2.68200i	−0.00854423	−	0.101881i
$694$		0			0
$695$	7.63664	−	13.2271i	0.289674	−	0.501731i
$696$		0			0
$697$	2.12812	+	3.68601i	0.0806083	+	0.139618i
$698$		0			0
$699$	−3.48575			−0.131843
$700$		0			0
$701$	6.62883			0.250367			0.125184	−	0.992134i	$-0.460048\pi$
$701$	6.62883			0.250367			0.125184	+	0.992134i	$0.460048\pi$
$702$		0			0
$703$	−3.95241	−	6.84577i	−0.149068	−	0.258193i
$704$		0			0
$705$	6.06680	−	10.5080i	0.228489	−	0.395754i
$706$		0			0
$707$	5.42187	−	3.76744i	0.203910	−	0.141689i
$708$		0			0
$709$	14.7298	−	25.5128i	0.553191	−	0.958155i	−0.444851	−	0.895605i	$-0.646743\pi$
$709$	14.7298	−	25.5128i	0.553191	−	0.958155i	0.998042	−	0.0625502i	$-0.0199234\pi$
$710$		0			0
$711$	10.2759	+	17.7983i	0.385375	+	0.667490i
$712$		0			0
$713$	19.0091			0.711895
$714$		0			0
$715$	4.01506			0.150155
$716$		0			0
$717$	−18.4096	−	31.8863i	−0.687517	−	1.19081i
$718$		0			0
$719$	−8.02658	+	13.9024i	−0.299341	+	0.518473i	−0.975985	−	0.217836i	$-0.930100\pi$
$719$	−8.02658	+	13.9024i	−0.299341	+	0.518473i	0.676644	+	0.736310i	$0.263433\pi$
$720$		0			0
$721$	5.45579	+	2.56801i	0.203184	+	0.0956377i
$722$		0			0
$723$	−13.2247	+	22.9058i	−0.491831	+	0.851875i
$724$		0			0
$725$	1.78472	+	3.09122i	0.0662827	+	0.114805i
$726$		0			0
$727$	41.7494			1.54840			0.774199	−	0.632942i	$-0.218153\pi$
$727$	41.7494			1.54840			0.774199	+	0.632942i	$0.218153\pi$
$728$		0			0
$729$	−8.22146			−0.304498
$730$		0			0
$731$	11.3552	+	19.6678i	0.419987	+	0.727440i
$732$		0			0
$733$	−7.63490	+	13.2240i	−0.282002	+	0.488441i	−0.971878	−	0.235486i	$-0.924332\pi$
$733$	−7.63490	+	13.2240i	−0.282002	+	0.488441i	0.689876	+	0.723927i	$0.257665\pi$
$734$		0			0
$735$	22.8344	−	3.85715i	0.842261	−	0.142273i
$736$		0			0
$737$	0.967541	−	1.67583i	0.0356398	−	0.0617300i
$738$		0			0
$739$	−25.7304	−	44.5664i	−0.946508	−	1.63940i	−0.752703	−	0.658360i	$-0.771250\pi$
$739$	−25.7304	−	44.5664i	−0.946508	−	1.63940i	−0.193805	−	0.981040i	$-0.562083\pi$
$740$		0			0
$741$	−11.9352			−0.438450
$742$		0			0
$743$	−14.2055			−0.521148			−0.260574	−	0.965454i	$-0.583912\pi$
$743$	−14.2055			−0.521148			−0.260574	+	0.965454i	$0.583912\pi$
$744$		0			0
$745$	−12.0609	−	20.8901i	−0.441877	−	0.765353i
$746$		0			0
$747$	7.90717	−	13.6956i	0.289308	−	0.501097i
$748$		0			0
$749$	14.5063	+	6.82803i	0.530048	+	0.249491i
$750$		0			0
$751$	−24.0768	+	41.7023i	−0.878576	+	1.52174i	−0.0256728	+	0.999670i	$0.508173\pi$
$751$	−24.0768	+	41.7023i	−0.878576	+	1.52174i	−0.852904	+	0.522068i	$0.825161\pi$
$752$		0			0
$753$	−17.0767	−	29.5777i	−0.622309	−	1.07787i
$754$		0			0
$755$	4.25503			0.154856
$756$		0			0
$757$	−20.7677			−0.754816			−0.377408	−	0.926047i	$-0.623185\pi$
$757$	−20.7677			−0.754816			−0.377408	+	0.926047i	$0.623185\pi$
$758$		0			0
$759$	−1.27834	−	2.21415i	−0.0464008	−	0.0803685i
$760$		0			0
$761$	3.90446	−	6.76273i	0.141537	−	0.245149i	−0.786539	−	0.617541i	$-0.788129\pi$
$761$	3.90446	−	6.76273i	0.141537	−	0.245149i	0.928075	+	0.372392i	$0.121462\pi$
$762$		0			0
$763$	−12.0655	+	8.38382i	−0.436800	+	0.303515i
$764$		0			0
$765$	−6.44292	+	11.1595i	−0.232944	+	0.403471i
$766$		0			0
$767$	−4.06582	−	7.04221i	−0.146808	−	0.254279i
$768$		0			0
$769$	−6.74705			−0.243305			−0.121652	−	0.992573i	$-0.538819\pi$
$769$	−6.74705			−0.243305			−0.121652	+	0.992573i	$0.538819\pi$
$770$		0			0
$771$	0.212956			0.00766943
$772$		0			0
$773$	12.0211	+	20.8212i	0.432369	+	0.748885i	0.997077	−	0.0764061i	$-0.0243445\pi$
$773$	12.0211	+	20.8212i	0.432369	+	0.748885i	−0.564708	+	0.825291i	$0.691011\pi$
$774$		0			0
$775$	−11.7204	+	20.3004i	−0.421010	+	0.729211i
$776$		0			0
$777$	−4.09075	−	48.7777i	−0.146755	−	1.74989i
$778$		0			0
$779$	0.480467	−	0.832194i	0.0172145	−	0.0298164i
$780$		0			0
$781$	−2.51123	−	4.34958i	−0.0898589	−	0.155640i
$782$		0			0
$783$	−2.66578			−0.0952671
$784$		0			0
$785$	31.6525			1.12973
$786$		0			0
$787$	−16.3714	−	28.3560i	−0.583576	−	1.01078i	−0.995051	−	0.0993620i	$-0.968320\pi$
$787$	−16.3714	−	28.3560i	−0.583576	−	1.01078i	0.411476	−	0.911421i	$-0.365014\pi$
$788$		0			0
$789$	−20.1486	+	34.8983i	−0.717308	+	1.24241i
$790$		0			0
$791$	2.12270	+	25.3109i	0.0754745	+	0.899952i
$792$		0			0
$793$	17.2129	−	29.8137i	0.611250	−	1.05872i
$794$		0			0
$795$	14.1368	+	24.4857i	0.501382	+	0.868419i
$796$		0			0
$797$	−50.3514			−1.78354			−0.891769	−	0.452491i	$-0.850535\pi$
$797$	−50.3514			−1.78354			−0.891769	+	0.452491i	$0.850535\pi$
$798$		0			0
$799$	−15.6104			−0.552257
$800$		0			0
$801$	7.02948	+	12.1754i	0.248374	+	0.430197i
$802$		0			0
$803$	0.191730	−	0.332086i	0.00676600	−	0.0117190i
$804$		0			0
$805$	7.35085	−	5.10781i	0.259083	−	0.180027i
$806$		0			0
$807$	−36.3850	+	63.0207i	−1.28081	+	2.21844i
$808$		0			0
$809$	−20.1863	−	34.9637i	−0.709712	−	1.22926i	−0.964964	−	0.262383i	$-0.915492\pi$
$809$	−20.1863	−	34.9637i	−0.709712	−	1.22926i	0.255252	−	0.966875i	$-0.417842\pi$
$810$		0			0
$811$	46.0779			1.61801			0.809007	−	0.587799i	$-0.200006\pi$
$811$	46.0779			1.61801			0.809007	+	0.587799i	$0.200006\pi$
$812$		0			0
$813$	−38.1910			−1.33942
$814$		0			0
$815$	2.96940	+	5.14315i	0.104013	+	0.180157i
$816$		0			0
$817$	2.56367	−	4.44041i	0.0896916	−	0.155350i
$818$		0			0
$819$	−27.2091	−	12.8072i	−0.950762	−	0.447518i
$820$		0			0
$821$	−8.08693	+	14.0070i	−0.282236	+	0.488847i	−0.971935	−	0.235249i	$-0.924409\pi$
$821$	−8.08693	+	14.0070i	−0.282236	+	0.488847i	0.689699	+	0.724096i	$0.257743\pi$
$822$		0			0
$823$	−2.81340	−	4.87295i	−0.0980689	−	0.169860i	0.812816	−	0.582520i	$-0.197933\pi$
$823$	−2.81340	−	4.87295i	−0.0980689	−	0.169860i	−0.910885	+	0.412660i	$0.864600\pi$
$824$		0			0
$825$	3.15275			0.109765
$826$		0			0
$827$	−8.75878			−0.304573			−0.152286	−	0.988336i	$-0.548664\pi$
$827$	−8.75878			−0.304573			−0.152286	+	0.988336i	$0.548664\pi$
$828$		0			0
$829$	−9.80296	−	16.9792i	−0.340471	−	0.589713i	0.644049	−	0.764984i	$-0.277253\pi$
$829$	−9.80296	−	16.9792i	−0.340471	−	0.589713i	−0.984520	+	0.175271i	$0.943920\pi$
$830$		0			0
$831$	0.475231	−	0.823125i	0.0164856	−	0.0285539i
$832$		0			0
$833$	−18.9863	−	22.9605i	−0.657837	−	0.795533i
$834$		0			0
$835$	−11.6266	+	20.1378i	−0.402354	+	0.696898i
$836$		0			0
$837$	−8.75323	−	15.1610i	−0.302556	−	0.524042i
$838$		0			0
$839$	9.03213			0.311824			0.155912	−	0.987771i	$-0.450168\pi$
$839$	9.03213			0.311824			0.155912	+	0.987771i	$0.450168\pi$
$840$		0			0
$841$	−27.4162			−0.945385
$842$		0			0
$843$	11.7818	+	20.4067i	0.405786	+	0.702843i
$844$		0			0
$845$	12.8698	−	22.2912i	0.442736	−	0.766842i
$846$		0			0
$847$	25.7473	+	12.1191i	0.884688	+	0.416418i
$848$		0			0
$849$	30.9628	−	53.6292i	1.06264	−	1.84055i
$850$		0			0
$851$	−9.46014	−	16.3854i	−0.324289	−	0.561686i
$852$		0			0
$853$	−23.1999			−0.794348			−0.397174	−	0.917743i	$-0.630009\pi$
$853$	−23.1999			−0.794348			−0.397174	+	0.917743i	$0.630009\pi$
$854$		0			0
$855$	2.90925			0.0994941
$856$		0			0
$857$	−2.78332	−	4.82085i	−0.0950763	−	0.164677i	0.814564	−	0.580073i	$-0.196976\pi$
$857$	−2.78332	−	4.82085i	−0.0950763	−	0.164677i	−0.909640	+	0.415397i	$0.863643\pi$
$858$		0			0
$859$	13.3020	−	23.0398i	0.453860	−	0.786108i	−0.544762	−	0.838591i	$-0.683380\pi$
$859$	13.3020	−	23.0398i	0.453860	−	0.786108i	0.998622	+	0.0524826i	$0.0167134\pi$
$860$		0			0
$861$	4.88653	−	3.39545i	0.166532	−	0.115717i
$862$		0			0
$863$	2.63236	−	4.55938i	0.0896066	−	0.155203i	−0.817738	−	0.575590i	$-0.804772\pi$
$863$	2.63236	−	4.55938i	0.0896066	−	0.155203i	0.907345	+	0.420387i	$0.138106\pi$
$864$		0			0
$865$	10.2579	+	17.7672i	0.348780	+	0.604104i
$866$		0			0
$867$	2.50899			0.0852097
$868$		0			0
$869$	4.93533			0.167420
$870$		0			0
$871$	−10.8108	−	18.7249i	−0.366311	−	0.634469i
$872$		0			0
$873$	7.03387	−	12.1830i	0.238061	−	0.412333i
$874$		0			0
$875$	2.54871	+	30.3906i	0.0861621	+	1.02739i
$876$		0			0
$877$	−14.9460	+	25.8873i	−0.504691	+	0.874151i	0.495294	+	0.868725i	$0.335060\pi$
$877$	−14.9460	+	25.8873i	−0.504691	+	0.874151i	−0.999985	+	0.00542540i	$0.998273\pi$
$878$		0			0
$879$	−25.4576	−	44.0939i	−0.858665	−	1.48725i
$880$		0			0
$881$	−6.34231			−0.213678			−0.106839	−	0.994276i	$-0.534073\pi$
$881$	−6.34231			−0.213678			−0.106839	+	0.994276i	$0.534073\pi$
$882$		0			0
$883$	−15.9746			−0.537587			−0.268794	−	0.963198i	$-0.586625\pi$
$883$	−15.9746			−0.537587			−0.268794	+	0.963198i	$0.586625\pi$
$884$		0			0
$885$	2.43563	+	4.21863i	0.0818727	+	0.141808i
$886$		0			0
$887$	6.77839	−	11.7405i	0.227596	−	0.394208i	−0.729499	−	0.683982i	$-0.760247\pi$
$887$	6.77839	−	11.7405i	0.227596	−	0.394208i	0.957095	+	0.289774i	$0.0935801\pi$
$888$		0			0
$889$	0.949850	+	11.3259i	0.0318569	+	0.379859i
$890$		0			0
$891$	−2.70318	+	4.68204i	−0.0905599	+	0.156854i
$892$		0			0
$893$	1.76219	+	3.05220i	0.0589693	+	0.102138i
$894$		0			0
$895$	−24.2002			−0.808923
$896$		0			0
$897$	−28.5670			−0.953826
$898$		0			0
$899$	5.20064	+	9.00777i	0.173451	+	0.300426i
$900$		0			0
$901$	18.1877	−	31.5020i	0.605919	−	1.04948i
$902$		0			0
$903$	26.0735	−	18.1174i	0.867671	−	0.602910i
$904$		0			0
$905$	1.30956	−	2.26823i	0.0435314	−	0.0753985i
$906$		0			0
$907$	−14.2253	−	24.6390i	−0.472344	−	0.818123i	0.527155	−	0.849769i	$-0.323259\pi$
$907$	−14.2253	−	24.6390i	−0.472344	−	0.818123i	−0.999499	+	0.0316455i	$0.989925\pi$
$908$		0			0
$909$	5.13604			0.170352
$910$		0			0
$911$	27.8892			0.924011			0.462006	−	0.886877i	$-0.347130\pi$
$911$	27.8892			0.924011			0.462006	+	0.886877i	$0.347130\pi$
$912$		0			0
$913$	−1.89884	−	3.28889i	−0.0628424	−	0.108846i
$914$		0			0
$915$	−10.3114	+	17.8599i	−0.340885	+	0.590429i
$916$		0			0
$917$	−30.7950	−	14.4950i	−1.01694	−	0.478668i
$918$		0			0
$919$	−14.6711	+	25.4111i	−0.483955	+	0.838234i	−0.999830	−	0.0184294i	$-0.994133\pi$
$919$	−14.6711	+	25.4111i	−0.483955	+	0.838234i	0.515875	+	0.856664i	$0.327467\pi$
$920$		0			0
$921$	10.1286	+	17.5433i	0.333749	+	0.578071i
$922$		0			0
$923$	−56.1185			−1.84716
$924$		0			0
$925$	23.3314			0.767132
$926$		0			0
$927$	2.34540	+	4.06235i	0.0770331	+	0.133425i
$928$		0			0
$929$	−22.8697	+	39.6114i	−0.750329	+	1.29961i	0.197334	+	0.980336i	$0.436772\pi$
$929$	−22.8697	+	39.6114i	−0.750329	+	1.29961i	−0.947663	+	0.319272i	$0.896562\pi$
$930$		0			0
$931$	−2.34603	+	6.30417i	−0.0768880	+	0.206611i
$932$		0			0
$933$	29.0158	−	50.2568i	0.949935	−	1.64534i
$934$		0			0
$935$	1.54721	+	2.67985i	0.0505993	+	0.0876405i
$936$		0			0
$937$	8.24433			0.269331			0.134665	−	0.990891i	$-0.457004\pi$
$937$	8.24433			0.269331			0.134665	+	0.990891i	$0.457004\pi$
$938$		0			0
$939$	−11.9343			−0.389462
$940$		0			0
$941$	5.11811	+	8.86482i	0.166846	+	0.288985i	0.937309	−	0.348499i	$-0.113309\pi$
$941$	5.11811	+	8.86482i	0.166846	+	0.288985i	−0.770464	+	0.637484i	$0.779975\pi$
$942$		0			0
$943$	1.15001	−	1.99187i	0.0374493	−	0.0648641i
$944$		0			0
$945$	−7.45873	−	3.51078i	−0.242633	−	0.114206i
$946$		0			0
$947$	−5.51873	+	9.55872i	−0.179335	+	0.310617i	−0.941653	−	0.336586i	$-0.890728\pi$
$947$	−5.51873	+	9.55872i	−0.179335	+	0.310617i	0.762318	+	0.647202i	$0.224061\pi$
$948$		0			0
$949$	−2.14229	−	3.71056i	−0.0695418	−	0.120450i
$950$		0			0
$951$	6.15595			0.199620
$952$		0			0
$953$	0.620938			0.0201141			0.0100571	−	0.999949i	$-0.496799\pi$
$953$	0.620938			0.0201141			0.0100571	+	0.999949i	$0.496799\pi$
$954$		0			0
$955$	16.3672	+	28.3488i	0.529630	+	0.917347i
$956$		0			0
$957$	0.699475	−	1.21153i	0.0226108	−	0.0391631i
$958$		0			0
$959$	−43.1066	+	29.9530i	−1.39198	+	0.967234i
$960$		0			0
$961$	−18.6532	+	32.3083i	−0.601716	+	1.04220i
$962$		0			0
$963$	6.23614	+	10.8013i	0.200957	+	0.348067i
$964$		0			0
$965$	6.39616			0.205900
$966$		0			0
$967$	15.9164			0.511836			0.255918	−	0.966698i	$-0.417622\pi$
$967$	15.9164			0.511836			0.255918	+	0.966698i	$0.417622\pi$
$968$		0			0
$969$	−4.59925	−	7.96613i	−0.147749	−	0.255909i
$970$		0			0
$971$	17.3535	−	30.0571i	0.556899	−	0.964577i	−0.440854	−	0.897579i	$-0.645324\pi$
$971$	17.3535	−	30.0571i	0.556899	−	0.964577i	0.997753	−	0.0669986i	$-0.0213423\pi$
$972$		0			0
$973$	2.29581	+	27.3751i	0.0736003	+	0.877604i
$974$		0			0
$975$	17.6136	−	30.5077i	0.564087	−	0.977028i
$976$		0			0
$977$	12.0728	+	20.9106i	0.386242	+	0.668991i	0.991941	−	0.126703i	$-0.0404396\pi$
$977$	12.0728	+	20.9106i	0.386242	+	0.668991i	−0.605699	+	0.795694i	$0.707106\pi$
$978$		0			0
$979$	3.37614			0.107902
$980$		0			0
$981$	−11.4294			−0.364913
$982$		0			0
$983$	−3.54460	−	6.13942i	−0.113055	−	0.195817i	0.803946	−	0.594703i	$-0.202730\pi$
$983$	−3.54460	−	6.13942i	−0.113055	−	0.195817i	−0.917001	+	0.398886i	$0.869397\pi$
$984$		0			0
$985$	−13.6441	+	23.6322i	−0.434736	+	0.752984i
$986$		0			0
$987$	1.82387	+	21.7476i	0.0580543	+	0.692235i
$988$		0			0
$989$	6.13619	−	10.6282i	0.195119	−	0.337957i
$990$		0			0
$991$	−24.5531	−	42.5273i	−0.779956	−	1.35092i	−0.931966	−	0.362545i	$-0.881908\pi$
$991$	−24.5531	−	42.5273i	−0.779956	−	1.35092i	0.152010	−	0.988379i	$-0.451425\pi$
$992$		0			0
$993$	−25.9740			−0.824260
$994$		0			0
$995$	8.86979			0.281191
$996$		0			0
$997$	11.9228	+	20.6509i	0.377599	+	0.654021i	0.990712	−	0.135974i	$-0.0434164\pi$
$997$	11.9228	+	20.6509i	0.377599	+	0.654021i	−0.613113	+	0.789995i	$0.710083\pi$
$998$		0			0
$999$	−8.71235	+	15.0902i	−0.275647	+	0.477434i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.i.d.821.2	yes	16
7.2	even	3		8036.2.a.m.1.7		8
7.4	even	3	inner	1148.2.i.d.165.2	✓	16
7.5	odd	6		8036.2.a.n.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.i.d.165.2	✓	16	7.4	even	3	inner
1148.2.i.d.821.2	yes	16	1.1	even	1	trivial
8036.2.a.m.1.7		8	7.2	even	3
8036.2.a.n.1.2		8	7.5	odd	6

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12452 - 1.94772i) q^{3} +(0.735486 - 1.27390i) q^{5} +(0.221110 + 2.63650i) q^{7} +(-1.02909 + 1.78243i) q^{9} +O(q^{10})\)	\(q+(-1.12452 - 1.94772i) q^{3} +(0.735486 - 1.27390i) q^{5} +(0.221110 + 2.63650i) q^{7} +(-1.02909 + 1.78243i) q^{9} +(0.247127 + 0.428036i) q^{11} +5.52254 q^{13} -3.30827 q^{15} +(2.12812 + 3.68601i) q^{17} +(0.480467 - 0.832194i) q^{19} +(4.88653 - 3.39545i) q^{21} +(1.15001 - 1.99187i) q^{23} +(1.41812 + 2.45626i) q^{25} -2.11820 q^{27} +1.25851 q^{29} +(4.13238 + 7.15750i) q^{31} +(0.555797 - 0.962669i) q^{33} +(3.52125 + 1.65743i) q^{35} +(4.11309 - 7.12407i) q^{37} +(-6.21020 - 10.7564i) q^{39} +1.00000 q^{41} +5.33579 q^{43} +(1.51376 + 2.62191i) q^{45} +(-1.83383 + 3.17628i) q^{47} +(-6.90222 + 1.16591i) q^{49} +(4.78622 - 8.28998i) q^{51} +(-4.27318 - 7.40136i) q^{53} +0.727033 q^{55} -2.16118 q^{57} +(-0.736223 - 1.27518i) q^{59} +(3.11685 - 5.39855i) q^{61} +(-4.92691 - 2.31907i) q^{63} +(4.06175 - 7.03516i) q^{65} +(-1.95758 - 3.39063i) q^{67} -5.17281 q^{69} -10.1617 q^{71} +(-0.387918 - 0.671894i) q^{73} +(3.18941 - 5.52421i) q^{75} +(-1.07387 + 0.746191i) q^{77} +(4.99271 - 8.64763i) q^{79} +(5.46922 + 9.47297i) q^{81} -7.68368 q^{83} +6.26081 q^{85} +(-1.41522 - 2.45123i) q^{87} +(3.41540 - 5.91564i) q^{89} +(1.22109 + 14.5601i) q^{91} +(9.29389 - 16.0975i) q^{93} +(-0.706754 - 1.22413i) q^{95} -6.83506 q^{97} -1.01726 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^9	\( 16 q - 4 q^{9} + 8 q^{11} - 14 q^{13} - 2 q^{15} + q^{17} - 4 q^{19} + 13 q^{21} + 3 q^{23} + 4 q^{25} - 24 q^{27} - 8 q^{29} - 4 q^{31} - 23 q^{33} + 12 q^{35} + 31 q^{37} - 5 q^{39} + 16 q^{41} - 16 q^{43} - q^{45} - 24 q^{47} + 16 q^{49} + 23 q^{51} + q^{53} + 4 q^{55} - 30 q^{57} - 4 q^{59} + 4 q^{61} + 23 q^{63} + 24 q^{65} - 42 q^{69} + 16 q^{71} - 11 q^{73} + 15 q^{75} + 25 q^{77} - 14 q^{79} + 28 q^{81} - 84 q^{83} - 40 q^{85} - 25 q^{87} + 11 q^{89} + 7 q^{91} + 27 q^{93} + 15 q^{95} - 32 q^{97} - 16 q^{99}+O(q^{100}) \) 16 * q - 4 * q^9 + 8 * q^11 - 14 * q^13 - 2 * q^15 + q^17 - 4 * q^19 + 13 * q^21 + 3 * q^23 + 4 * q^25 - 24 * q^27 - 8 * q^29 - 4 * q^31 - 23 * q^33 + 12 * q^35 + 31 * q^37 - 5 * q^39 + 16 * q^41 - 16 * q^43 - q^45 - 24 * q^47 + 16 * q^49 + 23 * q^51 + q^53 + 4 * q^55 - 30 * q^57 - 4 * q^59 + 4 * q^61 + 23 * q^63 + 24 * q^65 - 42 * q^69 + 16 * q^71 - 11 * q^73 + 15 * q^75 + 25 * q^77 - 14 * q^79 + 28 * q^81 - 84 * q^83 - 40 * q^85 - 25 * q^87 + 11 * q^89 + 7 * q^91 + 27 * q^93 + 15 * q^95 - 32 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more