LMFDB - Embedded newform 1008.2.r.n.337.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(337,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("1008.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.r (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.6095158642368.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} + 6x^{8} - 7x^{7} + 25x^{6} - 66x^{5} + 75x^{4} - 63x^{3} + 162x^{2} - 324x + 243 $ x^10 - 4x^9 + 6x^8 - 7x^7 + 25x^6 - 66x^5 + 75x^4 - 63x^3 + 162x^2 - 324*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			337.5
Root			$-1.28430 + 1.16214i$ of defining polynomial
Character	$\chi$	$=$	1008.337
Dual form			1008.2.r.n.673.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.58317 + 0.702538i) q^{3} +(-1.53571 + 2.65993i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(2.01288 + 2.22448i) q^{9} +O(q^{10})$	\(q+(1.58317 + 0.702538i) q^{3} +(-1.53571 + 2.65993i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(2.01288 + 2.22448i) q^{9} +(2.86748 + 4.96662i) q^{11} +(1.44746 - 2.50708i) q^{13} +(-4.30001 + 3.13224i) q^{15} -4.02576 q^{17} +0.899439 q^{19} +(-0.183172 - 1.72234i) q^{21} +(-1.86147 + 3.22416i) q^{23} +(-2.21683 - 3.83966i) q^{25} +(1.62396 + 4.93586i) q^{27} +(-4.43290 - 7.67800i) q^{29} +(-0.651412 + 1.12828i) q^{31} +(1.05048 + 9.87753i) q^{33} +3.07143 q^{35} -3.56450 q^{37} +(4.05291 - 2.95225i) q^{39} +(-4.99831 + 8.65733i) q^{41} +(2.55085 + 4.41820i) q^{43} +(-9.00818 + 1.93797i) q^{45} +(5.40094 + 9.35469i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-6.37349 - 2.82825i) q^{51} +8.43366 q^{53} -17.6145 q^{55} +(1.42397 + 0.631889i) q^{57} +(2.79513 - 4.84131i) q^{59} +(-2.33253 - 4.04006i) q^{61} +(0.920014 - 2.85545i) q^{63} +(4.44578 + 7.70031i) q^{65} +(-4.21515 + 7.30085i) q^{67} +(-5.21212 + 3.79665i) q^{69} +3.17199 q^{71} +8.54922 q^{73} +(-0.812122 - 7.63626i) q^{75} +(2.86748 - 4.96662i) q^{77} +(-0.689381 - 1.19404i) q^{79} +(-0.896613 + 8.95523i) q^{81} +(-6.44654 - 11.1657i) q^{83} +(6.18242 - 10.7083i) q^{85} +(-1.62396 - 15.2699i) q^{87} +5.27216 q^{89} -2.89493 q^{91} +(-1.82396 + 1.32862i) q^{93} +(-1.38128 + 2.39245i) q^{95} +(-8.60488 - 14.9041i) q^{97} +(-5.27624 + 16.3759i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{5} - 5 q^{7}+O(q^{10}) $ 10 * q - 3 * q^5 - 5 * q^7	$ 10 q - 3 q^{5} - 5 q^{7} - 4 q^{11} - 3 q^{13} - 15 q^{15} - 2 q^{19} - 8 q^{23} - 10 q^{25} + 9 q^{27} - 9 q^{29} + 3 q^{31} + 30 q^{33} + 6 q^{35} - 6 q^{37} + 18 q^{39} - 12 q^{41} + 5 q^{43} - 9 q^{45} - 3 q^{47} - 5 q^{49} - 9 q^{51} + 60 q^{53} - 44 q^{55} - 21 q^{57} - 7 q^{59} - 14 q^{61} - 6 q^{63} - 11 q^{65} + 8 q^{67} + 21 q^{69} + 18 q^{71} + 30 q^{73} + 51 q^{75} - 4 q^{77} + 3 q^{79} - 12 q^{81} - 20 q^{83} - 21 q^{85} - 9 q^{87} - 24 q^{89} + 6 q^{91} - 39 q^{93} + 12 q^{95} - 37 q^{97} - 60 q^{99}+O(q^{100}) $ 10 * q - 3 * q^5 - 5 * q^7 - 4 * q^11 - 3 * q^13 - 15 * q^15 - 2 * q^19 - 8 * q^23 - 10 * q^25 + 9 * q^27 - 9 * q^29 + 3 * q^31 + 30 * q^33 + 6 * q^35 - 6 * q^37 + 18 * q^39 - 12 * q^41 + 5 * q^43 - 9 * q^45 - 3 * q^47 - 5 * q^49 - 9 * q^51 + 60 * q^53 - 44 * q^55 - 21 * q^57 - 7 * q^59 - 14 * q^61 - 6 * q^63 - 11 * q^65 + 8 * q^67 + 21 * q^69 + 18 * q^71 + 30 * q^73 + 51 * q^75 - 4 * q^77 + 3 * q^79 - 12 * q^81 - 20 * q^83 - 21 * q^85 - 9 * q^87 - 24 * q^89 + 6 * q^91 - 39 * q^93 + 12 * q^95 - 37 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.58317	+	0.702538i	0.914046	+	0.405610i
$3$	1.58317	+	0.702538i	0.914046	+	0.405610i
$4$		0			0
$5$	−1.53571	+	2.65993i	−0.686792	+	1.18956i	0.286078	+	0.958206i	$0.407648\pi$
$5$	−1.53571	+	2.65993i	−0.686792	+	1.18956i	−0.972870	+	0.231352i	$0.925685\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$		0			0
$9$	2.01288	+	2.22448i	0.670961	+	0.741493i
$10$		0			0
$11$	2.86748	+	4.96662i	0.864577	+	1.49749i	0.867466	+	0.497496i	$0.165747\pi$
$11$	2.86748	+	4.96662i	0.864577	+	1.49749i	−0.00288940	+	0.999996i	$0.500920\pi$
$12$		0			0
$13$	1.44746	−	2.50708i	0.401454	−	0.695339i	−0.592448	−	0.805609i	$-0.701838\pi$
$13$	1.44746	−	2.50708i	0.401454	−	0.695339i	0.993902	+	0.110270i	$0.0351716\pi$
$14$		0			0
$15$	−4.30001	+	3.13224i	−1.11026	+	0.808741i
$16$		0			0
$17$	−4.02576			−0.976391			−0.488196	−	0.872734i	$-0.662345\pi$
$17$	−4.02576			−0.976391			−0.488196	+	0.872734i	$0.662345\pi$
$18$		0			0
$19$	0.899439			0.206345			0.103173	−	0.994663i	$-0.467101\pi$
$19$	0.899439			0.206345			0.103173	+	0.994663i	$0.467101\pi$
$20$		0			0
$21$	−0.183172	−	1.72234i	−0.0399714	−	0.375845i
$22$		0			0
$23$	−1.86147	+	3.22416i	−0.388143	+	0.672284i	−0.992200	−	0.124658i	$-0.960217\pi$
$23$	−1.86147	+	3.22416i	−0.388143	+	0.672284i	0.604057	+	0.796941i	$0.293550\pi$
$24$		0			0
$25$	−2.21683	−	3.83966i	−0.443366	−	0.767933i
$26$		0			0
$27$	1.62396	+	4.93586i	0.312532	+	0.949907i
$28$		0			0
$29$	−4.43290	−	7.67800i	−0.823168	−	1.42577i	−0.903311	−	0.428986i	$-0.858871\pi$
$29$	−4.43290	−	7.67800i	−0.823168	−	1.42577i	0.0801431	−	0.996783i	$-0.474462\pi$
$30$		0			0
$31$	−0.651412	+	1.12828i	−0.116997	+	0.202645i	−0.918576	−	0.395244i	$-0.870660\pi$
$31$	−0.651412	+	1.12828i	−0.116997	+	0.202645i	0.801579	+	0.597889i	$0.203993\pi$
$32$		0			0
$33$	1.05048	+	9.87753i	0.182865	+	1.71946i
$34$		0			0
$35$	3.07143			0.519166
$36$		0			0
$37$	−3.56450			−0.586000			−0.293000	−	0.956112i	$-0.594654\pi$
$37$	−3.56450			−0.586000			−0.293000	+	0.956112i	$0.594654\pi$
$38$		0			0
$39$	4.05291	−	2.95225i	0.648984	−	0.472738i
$40$		0			0
$41$	−4.99831	+	8.65733i	−0.780606	+	1.35205i	0.150984	+	0.988536i	$0.451756\pi$
$41$	−4.99831	+	8.65733i	−0.780606	+	1.35205i	−0.931589	+	0.363512i	$0.881577\pi$
$42$		0			0
$43$	2.55085	+	4.41820i	0.389001	+	0.673770i	0.992315	−	0.123734i	$-0.0394869\pi$
$43$	2.55085	+	4.41820i	0.389001	+	0.673770i	−0.603314	+	0.797503i	$0.706154\pi$
$44$		0			0
$45$	−9.00818	+	1.93797i	−1.34286	+	0.288896i
$46$		0			0
$47$	5.40094	+	9.35469i	0.787807	+	1.36452i	0.927308	+	0.374300i	$0.122117\pi$
$47$	5.40094	+	9.35469i	0.787807	+	1.36452i	−0.139500	+	0.990222i	$0.544550\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$	−6.37349	−	2.82825i	−0.892467	−	0.396034i
$52$		0			0
$53$	8.43366			1.15845			0.579226	−	0.815167i	$-0.303355\pi$
$53$	8.43366			1.15845			0.579226	+	0.815167i	$0.303355\pi$
$54$		0			0
$55$	−17.6145			−2.37514
$56$		0			0
$57$	1.42397	+	0.631889i	0.188609	+	0.0836958i
$58$		0			0
$59$	2.79513	−	4.84131i	0.363895	−	0.630285i	−0.624703	−	0.780862i	$-0.714780\pi$
$59$	2.79513	−	4.84131i	0.363895	−	0.630285i	0.988598	+	0.150578i	$0.0481133\pi$
$60$		0			0
$61$	−2.33253	−	4.04006i	−0.298650	−	0.517277i	0.677177	−	0.735820i	$-0.263203\pi$
$61$	−2.33253	−	4.04006i	−0.298650	−	0.517277i	−0.975827	+	0.218543i	$0.929870\pi$
$62$		0			0
$63$	0.920014	−	2.85545i	0.115911	−	0.359752i
$64$		0			0
$65$	4.44578	+	7.70031i	0.551431	+	0.955106i
$66$		0			0
$67$	−4.21515	+	7.30085i	−0.514962	+	0.891940i	0.484887	+	0.874577i	$0.338861\pi$
$67$	−4.21515	+	7.30085i	−0.514962	+	0.891940i	−0.999849	+	0.0173636i	$0.994473\pi$
$68$		0			0
$69$	−5.21212	+	3.79665i	−0.627466	+	0.457064i
$70$		0			0
$71$	3.17199			0.376446			0.188223	−	0.982126i	$-0.439727\pi$
$71$	3.17199			0.376446			0.188223	+	0.982126i	$0.439727\pi$
$72$		0			0
$73$	8.54922			1.00061			0.500305	−	0.865849i	$-0.333221\pi$
$73$	8.54922			1.00061			0.500305	+	0.865849i	$0.333221\pi$
$74$		0			0
$75$	−0.812122	−	7.63626i	−0.0937757	−	0.881760i
$76$		0			0
$77$	2.86748	−	4.96662i	0.326779	−	0.565999i
$78$		0			0
$79$	−0.689381	−	1.19404i	−0.0775615	−	0.134340i	0.824636	−	0.565664i	$-0.191380\pi$
$79$	−0.689381	−	1.19404i	−0.0775615	−	0.134340i	−0.902197	+	0.431324i	$0.858047\pi$
$80$		0			0
$81$	−0.896613	+	8.95523i	−0.0996236	+	0.995025i
$82$		0			0
$83$	−6.44654	−	11.1657i	−0.707600	−	1.22560i	−0.965745	−	0.259493i	$-0.916445\pi$
$83$	−6.44654	−	11.1657i	−0.707600	−	1.22560i	0.258145	−	0.966106i	$-0.416889\pi$
$84$		0			0
$85$	6.18242	−	10.7083i	0.670578	−	1.16147i
$86$		0			0
$87$	−1.62396	−	15.2699i	−0.174107	−	1.63710i
$88$		0			0
$89$	5.27216			0.558848			0.279424	−	0.960168i	$-0.409857\pi$
$89$	5.27216			0.558848			0.279424	+	0.960168i	$0.409857\pi$
$90$		0			0
$91$	−2.89493			−0.303471
$92$		0			0
$93$	−1.82396	+	1.32862i	−0.189136	+	0.137772i
$94$		0			0
$95$	−1.38128	+	2.39245i	−0.141716	+	0.245460i
$96$		0			0
$97$	−8.60488	−	14.9041i	−0.873694	−	1.51328i	−0.858148	−	0.513403i	$-0.828385\pi$
$97$	−8.60488	−	14.9041i	−0.873694	−	1.51328i	−0.0155457	−	0.999879i	$-0.504949\pi$
$98$		0			0
$99$	−5.27624	+	16.3759i	−0.530282	+	1.64584i
$100$		0			0
$101$	2.28975	+	3.96596i	0.227838	+	0.394628i	0.957167	−	0.289536i	$-0.0935009\pi$
$101$	2.28975	+	3.96596i	0.227838	+	0.394628i	−0.729329	+	0.684163i	$0.760168\pi$
$102$		0			0
$103$	7.88036	−	13.6492i	0.776475	−	1.34489i	−0.157487	−	0.987521i	$-0.550339\pi$
$103$	7.88036	−	13.6492i	0.776475	−	1.34489i	0.933962	−	0.357373i	$-0.116327\pi$
$104$		0			0
$105$	4.86260	+	2.15779i	0.474542	+	0.210579i
$106$		0			0
$107$	20.0118			1.93462			0.967309	−	0.253602i	$-0.0816152\pi$
$107$	20.0118			1.93462			0.967309	+	0.253602i	$0.0816152\pi$
$108$		0			0
$109$	12.6590			1.21251			0.606257	−	0.795269i	$-0.292670\pi$
$109$	12.6590			1.21251			0.606257	+	0.795269i	$0.292670\pi$
$110$		0			0
$111$	−5.64322	−	2.50419i	−0.535631	−	0.237688i
$112$		0			0
$113$	6.04917	−	10.4775i	0.569058	−	0.985637i	−0.427602	−	0.903967i	$-0.640641\pi$
$113$	6.04917	−	10.4775i	0.569058	−	0.985637i	0.996659	−	0.0816695i	$-0.0260252\pi$
$114$		0			0
$115$	−5.71737	−	9.90277i	−0.533147	−	0.923438i
$116$		0			0
$117$	8.49052	−	1.82660i	0.784949	−	0.168870i
$118$		0			0
$119$	2.01288	+	3.48641i	0.184521	+	0.319599i
$120$		0			0
$121$	−10.9449	+	18.9571i	−0.994987	+	1.72337i
$122$		0			0
$123$	−13.9953	+	10.1946i	−1.26191	+	0.919213i
$124$		0			0
$125$	−1.73947			−0.155583
$126$		0			0
$127$	3.74870			0.332644			0.166322	−	0.986072i	$-0.446811\pi$
$127$	3.74870			0.332644			0.166322	+	0.986072i	$0.446811\pi$
$128$		0			0
$129$	0.934488	+	8.78686i	0.0822771	+	0.773639i
$130$		0			0
$131$	3.75086	−	6.49668i	0.327714	−	0.567617i	−0.654344	−	0.756197i	$-0.727055\pi$
$131$	3.75086	−	6.49668i	0.327714	−	0.567617i	0.982058	+	0.188580i	$0.0603884\pi$
$132$		0			0
$133$	−0.449719	−	0.778937i	−0.0389956	−	0.0675424i
$134$		0			0
$135$	−15.6230	−	3.26044i	−1.34461	−	0.280614i
$136$		0			0
$137$	0.243515	+	0.421780i	0.0208049	+	0.0360351i	0.876240	−	0.481874i	$-0.160044\pi$
$137$	0.243515	+	0.421780i	0.0208049	+	0.0360351i	−0.855436	+	0.517909i	$0.826710\pi$
$138$		0			0
$139$	−1.59257	+	2.75842i	−0.135080	+	0.233966i	−0.925628	−	0.378434i	$-0.876463\pi$
$139$	−1.59257	+	2.75842i	−0.135080	+	0.233966i	0.790548	+	0.612400i	$0.209796\pi$
$140$		0			0
$141$	1.97860	+	18.6045i	0.166628	+	1.56678i
$142$		0			0
$143$	16.6023			1.38835
$144$		0			0
$145$	27.2306			2.26138
$146$		0			0
$147$	−1.40000	+	1.01980i	−0.115470	+	0.0841117i
$148$		0			0
$149$	−7.32874	+	12.6938i	−0.600394	+	1.03991i	0.392367	+	0.919809i	$0.371656\pi$
$149$	−7.32874	+	12.6938i	−0.600394	+	1.03991i	−0.992761	+	0.120104i	$0.961677\pi$
$150$		0			0
$151$	0.328832	+	0.569554i	0.0267600	+	0.0463496i	0.879095	−	0.476646i	$-0.158148\pi$
$151$	0.328832	+	0.569554i	0.0267600	+	0.0463496i	−0.852335	+	0.522996i	$0.824814\pi$
$152$		0			0
$153$	−8.10339	−	8.95523i	−0.655120	−	0.723987i
$154$		0			0
$155$	−2.00077	−	3.46543i	−0.160705	−	0.278350i
$156$		0			0
$157$	−8.18467	+	14.1763i	−0.653208	+	1.13139i	0.329132	+	0.944284i	$0.393244\pi$
$157$	−8.18467	+	14.1763i	−0.653208	+	1.13139i	−0.982340	+	0.187106i	$0.940089\pi$
$158$		0			0
$159$	13.3520	+	5.92496i	1.05888	+	0.469880i
$160$		0			0
$161$	3.72294			0.293409
$162$		0			0
$163$	21.2855			1.66721			0.833606	−	0.552360i	$-0.186273\pi$
$163$	21.2855			1.66721			0.833606	+	0.552360i	$0.186273\pi$
$164$		0			0
$165$	−27.8868	−	12.3748i	−2.17099	−	0.963380i
$166$		0			0
$167$	−5.82623	+	10.0913i	−0.450847	+	0.780890i	−0.998439	−	0.0558557i	$-0.982211\pi$
$167$	−5.82623	+	10.0913i	−0.450847	+	0.780890i	0.547592	+	0.836746i	$0.315545\pi$
$168$		0			0
$169$	2.30970	+	4.00052i	0.177669	+	0.307732i
$170$		0			0
$171$	1.81046	+	2.00078i	0.138450	+	0.153004i
$172$		0			0
$173$	−10.4166	−	18.0422i	−0.791963	−	1.37172i	−0.924750	−	0.380575i	$-0.875726\pi$
$173$	−10.4166	−	18.0422i	−0.791963	−	1.37172i	0.132787	−	0.991145i	$-0.457607\pi$
$174$		0			0
$175$	−2.21683	+	3.83966i	−0.167577	+	0.290251i
$176$		0			0
$177$	7.82638	−	5.70095i	0.588267	−	0.428510i
$178$		0			0
$179$	13.9982			1.04627			0.523136	−	0.852249i	$-0.324762\pi$
$179$	13.9982			1.04627			0.523136	+	0.852249i	$0.324762\pi$
$180$		0			0
$181$	−12.5929			−0.936020			−0.468010	−	0.883723i	$-0.655029\pi$
$181$	−12.5929			−0.936020			−0.468010	+	0.883723i	$0.655029\pi$
$182$		0			0
$183$	−0.854507	−	8.03481i	−0.0631670	−	0.593950i
$184$		0			0
$185$	5.47405	−	9.48133i	0.402460	−	0.697081i
$186$		0			0
$187$	−11.5438	−	19.9944i	−0.844165	−	1.46214i
$188$		0			0
$189$	3.46260	−	3.87432i	0.251867	−	0.281816i
$190$		0			0
$191$	−4.30807	−	7.46179i	−0.311721	−	0.539916i	0.667014	−	0.745045i	$-0.267572\pi$
$191$	−4.30807	−	7.46179i	−0.311721	−	0.539916i	−0.978735	+	0.205129i	$0.934239\pi$
$192$		0			0
$193$	6.34671	−	10.9928i	0.456846	−	0.791281i	−0.541946	−	0.840413i	$-0.682312\pi$
$193$	6.34671	−	10.9928i	0.456846	−	0.791281i	0.998792	+	0.0491322i	$0.0156456\pi$
$194$		0			0
$195$	1.62868	+	15.3143i	0.116632	+	1.09668i
$196$		0			0
$197$	8.97559			0.639484			0.319742	−	0.947505i	$-0.396404\pi$
$197$	8.97559			0.639484			0.319742	+	0.947505i	$0.396404\pi$
$198$		0			0
$199$	−8.43366			−0.597846			−0.298923	−	0.954277i	$-0.596627\pi$
$199$	−8.43366			−0.597846			−0.298923	+	0.954277i	$0.596627\pi$
$200$		0			0
$201$	−11.8024	+	8.59721i	−0.832479	+	0.606401i
$202$		0			0
$203$	−4.43290	+	7.67800i	−0.311128	+	0.538890i
$204$		0			0
$205$	−15.3520	−	26.5904i	−1.07223	−	1.85715i
$206$		0			0
$207$	−10.9190	+	2.34905i	−0.758923	+	0.163271i
$208$		0			0
$209$	2.57912	+	4.46717i	0.178401	+	0.309000i
$210$		0			0
$211$	12.4303	−	21.5300i	0.855740	−	1.48219i	−0.0202163	−	0.999796i	$-0.506435\pi$
$211$	12.4303	−	21.5300i	0.855740	−	1.48219i	0.875957	−	0.482390i	$-0.160231\pi$
$212$		0			0
$213$	5.02181	+	2.22844i	0.344089	+	0.152690i
$214$		0			0
$215$	−15.6695			−1.06865
$216$		0			0
$217$	1.30282			0.0884415
$218$		0			0
$219$	13.5349	+	6.00615i	0.914604	+	0.405858i
$220$		0			0
$221$	−5.82715	+	10.0929i	−0.391976	+	0.678923i
$222$		0			0
$223$	11.8796	+	20.5761i	0.795516	+	1.37787i	0.922511	+	0.385972i	$0.126134\pi$
$223$	11.8796	+	20.5761i	0.795516	+	1.37787i	−0.126994	+	0.991903i	$0.540533\pi$
$224$		0			0
$225$	4.07903	−	12.6601i	0.271935	−	0.844006i
$226$		0			0
$227$	−7.56512	−	13.1032i	−0.502115	−	0.869688i	−0.999997	−	0.00244376i	$-0.999222\pi$
$227$	−7.56512	−	13.1032i	−0.502115	−	0.869688i	0.497882	−	0.867245i	$-0.334111\pi$
$228$		0			0
$229$	7.96769	−	13.8004i	0.526520	−	0.911959i	−0.473003	−	0.881061i	$-0.656830\pi$
$229$	7.96769	−	13.8004i	0.526520	−	0.911959i	0.999523	−	0.0308980i	$-0.00983671\pi$
$230$		0			0
$231$	8.02895	−	5.84851i	0.528266	−	0.384804i
$232$		0			0
$233$	26.5211			1.73746			0.868728	−	0.495289i	$-0.164938\pi$
$233$	26.5211			1.73746			0.868728	+	0.495289i	$0.164938\pi$
$234$		0			0
$235$	−33.1772			−2.16424
$236$		0			0
$237$	−0.252550	−	2.37470i	−0.0164049	−	0.154253i
$238$		0			0
$239$	−1.96280	+	3.39966i	−0.126963	+	0.219906i	−0.922498	−	0.386001i	$-0.873856\pi$
$239$	−1.96280	+	3.39966i	−0.126963	+	0.219906i	0.795536	+	0.605907i	$0.207190\pi$
$240$		0			0
$241$	−1.07398	−	1.86018i	−0.0691810	−	0.119825i	0.829360	−	0.558715i	$-0.188705\pi$
$241$	−1.07398	−	1.86018i	−0.0691810	−	0.119825i	−0.898541	+	0.438890i	$0.855372\pi$
$242$		0			0
$243$	−7.71088	+	13.5478i	−0.494653	+	0.869091i
$244$		0			0
$245$	−1.53571	−	2.65993i	−0.0981131	−	0.169937i
$246$		0			0
$247$	1.30190	−	2.25496i	0.0828382	−	0.143480i
$248$		0			0
$249$	−2.36165	−	22.2063i	−0.149663	−	1.40726i
$250$		0			0
$251$	−7.64783			−0.482727			−0.241363	−	0.970435i	$-0.577595\pi$
$251$	−7.64783			−0.482727			−0.241363	+	0.970435i	$0.577595\pi$
$252$		0			0
$253$	−21.3509			−1.34232
$254$		0			0
$255$	17.3108	−	12.6097i	1.08404	−	0.789648i
$256$		0			0
$257$	−1.86916	+	3.23749i	−0.116595	+	0.201949i	−0.918416	−	0.395615i	$-0.870531\pi$
$257$	−1.86916	+	3.23749i	−0.116595	+	0.201949i	0.801821	+	0.597564i	$0.203865\pi$
$258$		0			0
$259$	1.78225	+	3.08695i	0.110744	+	0.191813i
$260$		0			0
$261$	8.15666	−	25.3158i	0.504884	−	1.56701i
$262$		0			0
$263$	7.02999	+	12.1763i	0.433488	+	0.750822i	0.997171	−	0.0751686i	$-0.0239495\pi$
$263$	7.02999	+	12.1763i	0.433488	+	0.750822i	−0.563683	+	0.825991i	$0.690616\pi$
$264$		0			0
$265$	−12.9517	+	22.4330i	−0.795616	+	1.37805i
$266$		0			0
$267$	8.34675	+	3.70389i	0.510813	+	0.226674i
$268$		0			0
$269$	3.21969			0.196308			0.0981540	−	0.995171i	$-0.468706\pi$
$269$	3.21969			0.196308			0.0981540	+	0.995171i	$0.468706\pi$
$270$		0			0
$271$	23.1135			1.40405			0.702024	−	0.712153i	$-0.252280\pi$
$271$	23.1135			1.40405			0.702024	+	0.712153i	$0.252280\pi$
$272$		0			0
$273$	−4.58317	−	2.03380i	−0.277386	−	0.123091i
$274$		0			0
$275$	12.7134	−	22.0203i	0.766648	−	1.32787i
$276$		0			0
$277$	−1.20313	−	2.08388i	−0.0722890	−	0.125208i	0.827615	−	0.561296i	$-0.189697\pi$
$277$	−1.20313	−	2.08388i	−0.0722890	−	0.125208i	−0.899904	+	0.436088i	$0.856364\pi$
$278$		0			0
$279$	−3.82105	+	0.822040i	−0.228760	+	0.0492142i
$280$		0			0
$281$	6.72895	+	11.6549i	0.401415	+	0.695272i	0.993897	−	0.110312i	$-0.0351851\pi$
$281$	6.72895	+	11.6549i	0.401415	+	0.695272i	−0.592482	+	0.805584i	$0.701852\pi$
$282$		0			0
$283$	7.12782	−	12.3457i	0.423705	−	0.733878i	−0.572594	−	0.819839i	$-0.694063\pi$
$283$	7.12782	−	12.3457i	0.423705	−	0.733878i	0.996298	+	0.0859612i	$0.0273961\pi$
$284$		0			0
$285$	−3.86759	+	2.81726i	−0.229096	+	0.166880i
$286$		0			0
$287$	9.99663			0.590082
$288$		0			0
$289$	−0.793225			−0.0466603
$290$		0			0
$291$	−3.15234	−	29.6410i	−0.184794	−	1.73759i
$292$		0			0
$293$	13.3154	−	23.0629i	0.777891	−	1.34735i	−0.155263	−	0.987873i	$-0.549623\pi$
$293$	13.3154	−	23.0629i	0.777891	−	1.34735i	0.933155	−	0.359474i	$-0.117044\pi$
$294$		0			0
$295$	8.58504	+	14.8697i	0.499840	+	0.865749i
$296$		0			0
$297$	−19.8579	+	22.2191i	−1.15227	+	1.28928i
$298$		0			0
$299$	5.38882	+	9.33371i	0.311643	+	0.539782i
$300$		0			0
$301$	2.55085	−	4.41820i	0.147029	−	0.254661i
$302$		0			0
$303$	0.838834	+	7.88744i	0.0481898	+	0.453122i
$304$		0			0
$305$	14.3284			0.820441
$306$		0			0
$307$	2.05604			0.117344			0.0586722	−	0.998277i	$-0.481313\pi$
$307$	2.05604			0.117344			0.0586722	+	0.998277i	$0.481313\pi$
$308$		0			0
$309$	22.0650	−	16.0728i	1.25524	−	0.914349i
$310$		0			0
$311$	−10.3726	+	17.9658i	−0.588174	+	1.01875i	0.406297	+	0.913741i	$0.366820\pi$
$311$	−10.3726	+	17.9658i	−0.588174	+	1.01875i	−0.994472	+	0.105007i	$0.966514\pi$
$312$		0			0
$313$	−4.54999	−	7.88081i	−0.257180	−	0.445450i	0.708305	−	0.705906i	$-0.249460\pi$
$313$	−4.54999	−	7.88081i	−0.257180	−	0.445450i	−0.965485	+	0.260457i	$0.916127\pi$
$314$		0			0
$315$	6.18242	+	6.83232i	0.348340	+	0.384958i
$316$		0			0
$317$	10.9007	+	18.8806i	0.612247	+	1.06044i	0.990861	+	0.134888i	$0.0430675\pi$
$317$	10.9007	+	18.8806i	0.612247	+	1.06044i	−0.378614	+	0.925555i	$0.623599\pi$
$318$		0			0
$319$	25.4225	−	44.0330i	1.42338	−	2.46537i
$320$		0			0
$321$	31.6822	+	14.0591i	1.76833	+	0.784701i
$322$		0			0
$323$	−3.62093			−0.201474
$324$		0			0
$325$	−12.8351			−0.711965
$326$		0			0
$327$	20.0414	+	8.89344i	1.10829	+	0.491808i
$328$		0			0
$329$	5.40094	−	9.35469i	0.297763	−	0.515741i
$330$		0			0
$331$	−1.45105	−	2.51330i	−0.0797572	−	0.138144i	0.823388	−	0.567479i	$-0.192081\pi$
$331$	−1.45105	−	2.51330i	−0.0797572	−	0.138144i	−0.903145	+	0.429335i	$0.858748\pi$
$332$		0			0
$333$	−7.17491	−	7.92915i	−0.393183	−	0.434515i
$334$		0			0
$335$	−12.9465	−	22.4240i	−0.707343	−	1.22515i
$336$		0			0
$337$	10.4494	−	18.0989i	0.569216	−	0.985912i	−0.427427	−	0.904050i	$-0.640580\pi$
$337$	10.4494	−	18.0989i	0.569216	−	0.985912i	0.996644	−	0.0818620i	$-0.0260867\pi$
$338$		0			0
$339$	16.9377	−	12.3379i	0.919929	−	0.670102i
$340$		0			0
$341$	−7.47164			−0.404612
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	−2.09452	−	19.6945i	−0.112765	−	1.06032i
$346$		0			0
$347$	−11.9519	+	20.7013i	−0.641611	+	1.11130i	0.343462	+	0.939166i	$0.388400\pi$
$347$	−11.9519	+	20.7013i	−0.641611	+	1.11130i	−0.985073	+	0.172136i	$0.944933\pi$
$348$		0			0
$349$	−1.08701	−	1.88276i	−0.0581865	−	0.100782i	0.835465	−	0.549544i	$-0.185198\pi$
$349$	−1.08701	−	1.88276i	−0.0581865	−	0.100782i	−0.893651	+	0.448762i	$0.851865\pi$
$350$		0			0
$351$	14.7252	+	3.07308i	0.785975	+	0.164029i
$352$		0			0
$353$	−6.11627	−	10.5937i	−0.325536	−	0.563845i	0.656085	−	0.754687i	$-0.272211\pi$
$353$	−6.11627	−	10.5937i	−0.325536	−	0.563845i	−0.981621	+	0.190842i	$0.938878\pi$
$354$		0			0
$355$	−4.87126	+	8.43728i	−0.258540	+	0.447804i
$356$		0			0
$357$	0.737406	+	6.93373i	0.0390277	+	0.366972i
$358$		0			0
$359$	−18.4590			−0.974231			−0.487116	−	0.873337i	$-0.661951\pi$
$359$	−18.4590			−0.974231			−0.487116	+	0.873337i	$0.661951\pi$
$360$		0			0
$361$	−18.1910			−0.957422
$362$		0			0
$363$	−30.6457	+	22.3231i	−1.60848	+	1.17166i
$364$		0			0
$365$	−13.1292	+	22.7404i	−0.687211	+	1.19028i
$366$		0			0
$367$	2.49144	+	4.31530i	0.130052	+	0.225257i	0.923696	−	0.383125i	$-0.125152\pi$
$367$	2.49144	+	4.31530i	0.130052	+	0.225257i	−0.793644	+	0.608382i	$0.791819\pi$
$368$		0			0
$369$	−29.3191	+	6.30755i	−1.52629	+	0.328358i
$370$		0			0
$371$	−4.21683	−	7.30377i	−0.218927	−	0.379193i
$372$		0			0
$373$	11.4442	−	19.8220i	0.592561	−	1.02635i	−0.401325	−	0.915936i	$-0.631450\pi$
$373$	11.4442	−	19.8220i	0.592561	−	1.02635i	0.993886	−	0.110410i	$-0.0352163\pi$
$374$		0			0
$375$	−2.75388	−	1.22204i	−0.142210	−	0.0631059i
$376$		0			0
$377$	−25.6658			−1.32186
$378$		0			0
$379$	−28.7312			−1.47582			−0.737911	−	0.674897i	$-0.764188\pi$
$379$	−28.7312			−1.47582			−0.737911	+	0.674897i	$0.764188\pi$
$380$		0			0
$381$	5.93485	+	2.63360i	0.304052	+	0.134924i
$382$		0			0
$383$	−7.38186	+	12.7858i	−0.377195	+	0.653321i	−0.990653	−	0.136406i	$-0.956445\pi$
$383$	−7.38186	+	12.7858i	−0.377195	+	0.653321i	0.613458	+	0.789728i	$0.289778\pi$
$384$		0			0
$385$	8.80725	+	15.2546i	0.448859	+	0.777446i
$386$		0			0
$387$	−4.69364	+	14.5676i	−0.238591	+	0.740515i
$388$		0			0
$389$	−10.5774	−	18.3207i	−0.536297	−	0.928894i	−0.999099	−	0.0424324i	$-0.986489\pi$
$389$	−10.5774	−	18.3207i	−0.536297	−	0.928894i	0.462802	−	0.886462i	$-0.346844\pi$
$390$		0			0
$391$	7.49384	−	12.9797i	0.378980	−	0.656412i
$392$		0			0
$393$	10.5024	−	7.65025i	0.529777	−	0.385904i
$394$		0			0
$395$	4.23477			0.213074
$396$		0			0
$397$	9.75888			0.489784			0.244892	−	0.969550i	$-0.421247\pi$
$397$	9.75888			0.489784			0.244892	+	0.969550i	$0.421247\pi$
$398$		0			0
$399$	−0.164752	−	1.54914i	−0.00824791	−	0.0775539i
$400$		0			0
$401$	−10.4740	+	18.1414i	−0.523045	+	0.905940i	0.476596	+	0.879123i	$0.341871\pi$
$401$	−10.4740	+	18.1414i	−0.523045	+	0.905940i	−0.999640	+	0.0268172i	$0.991463\pi$
$402$		0			0
$403$	1.88579	+	3.26629i	0.0939380	+	0.162705i
$404$		0			0
$405$	−22.4434	−	16.1376i	−1.11522	−	0.801883i
$406$		0			0
$407$	−10.2211	−	17.7035i	−0.506642	−	0.877530i
$408$		0			0
$409$	−13.0911	+	22.6745i	−0.647316	+	1.12118i	0.336446	+	0.941703i	$0.390775\pi$
$409$	−13.0911	+	22.6745i	−0.647316	+	1.12118i	−0.983761	+	0.179481i	$0.942558\pi$
$410$		0			0
$411$	0.0892101	+	0.838829i	0.00440041	+	0.0413764i
$412$		0			0
$413$	−5.59026			−0.275079
$414$		0			0
$415$	39.6002			1.94390
$416$		0			0
$417$	−4.45921	+	3.24821i	−0.218369	+	0.159066i
$418$		0			0
$419$	1.86859	−	3.23650i	0.0912867	−	0.158113i	−0.816766	−	0.576969i	$-0.804235\pi$
$419$	1.86859	−	3.23650i	0.0912867	−	0.158113i	0.908053	+	0.418856i	$0.137569\pi$
$420$		0			0
$421$	14.8220	+	25.6724i	0.722380	+	1.25120i	0.960044	+	0.279851i	$0.0902850\pi$
$421$	14.8220	+	25.6724i	0.722380	+	1.25120i	−0.237664	+	0.971347i	$0.576382\pi$
$422$		0			0
$423$	−9.93787	+	30.8442i	−0.483196	+	1.49969i
$424$		0			0
$425$	8.92444	+	15.4576i	0.432899	+	0.749803i
$426$		0			0
$427$	−2.33253	+	4.04006i	−0.112879	+	0.195512i
$428$		0			0
$429$	26.2843	+	11.6637i	1.26902	+	0.563130i
$430$		0			0
$431$	−37.0811			−1.78614			−0.893068	−	0.449922i	$-0.851452\pi$
$431$	−37.0811			−1.78614			−0.893068	+	0.449922i	$0.851452\pi$
$432$		0			0
$433$	0.249834			0.0120063			0.00600313	−	0.999982i	$-0.498089\pi$
$433$	0.249834			0.0120063			0.00600313	+	0.999982i	$0.498089\pi$
$434$		0			0
$435$	43.1108	+	19.1305i	2.06701	+	0.917239i
$436$		0			0
$437$	−1.67428	+	2.89993i	−0.0800916	+	0.138723i
$438$		0			0
$439$	−1.53346	−	2.65603i	−0.0731879	−	0.126765i	0.827109	−	0.562042i	$-0.189984\pi$
$439$	−1.53346	−	2.65603i	−0.0731879	−	0.126765i	−0.900297	+	0.435276i	$0.856651\pi$
$440$		0			0
$441$	−2.93290	+	0.630967i	−0.139662	+	0.0300461i
$442$		0			0
$443$	−19.2949	−	33.4198i	−0.916730	−	1.58782i	−0.804348	−	0.594159i	$-0.797485\pi$
$443$	−19.2949	−	33.4198i	−0.916730	−	1.58782i	−0.112382	−	0.993665i	$-0.535848\pi$
$444$		0			0
$445$	−8.09653	+	14.0236i	−0.383812	+	0.664782i
$446$		0			0
$447$	−20.5205	+	14.9477i	−0.970587	+	0.707002i
$448$		0			0
$449$	−0.651903			−0.0307652			−0.0153826	−	0.999882i	$-0.504897\pi$
$449$	−0.651903			−0.0307652			−0.0153826	+	0.999882i	$0.504897\pi$
$450$		0			0
$451$	−57.3302			−2.69957
$452$		0			0
$453$	0.120465	+	1.13272i	0.00565996	+	0.0532198i
$454$		0			0
$455$	4.44578	−	7.70031i	0.208421	−	0.360996i
$456$		0			0
$457$	12.2796	+	21.2690i	0.574417	+	0.994920i	0.996105	+	0.0881789i	$0.0281047\pi$
$457$	12.2796	+	21.2690i	0.574417	+	0.994920i	−0.421687	+	0.906741i	$0.638562\pi$
$458$		0			0
$459$	−6.53769	−	19.8706i	−0.305153	−	0.927481i
$460$		0			0
$461$	−15.4863	−	26.8231i	−0.721269	−	1.24927i	−0.960491	−	0.278310i	$-0.910226\pi$
$461$	−15.4863	−	26.8231i	−0.721269	−	1.24927i	0.239222	−	0.970965i	$-0.423108\pi$
$462$		0			0
$463$	−1.22554	+	2.12271i	−0.0569559	+	0.0986505i	−0.893098	−	0.449863i	$-0.851473\pi$
$463$	−1.22554	+	2.12271i	−0.0569559	+	0.0986505i	0.836142	+	0.548514i	$0.184806\pi$
$464$		0			0
$465$	−0.732968	−	6.89199i	−0.0339906	−	0.319608i
$466$		0			0
$467$	11.1442			0.515692			0.257846	−	0.966186i	$-0.416987\pi$
$467$	11.1442			0.515692			0.257846	+	0.966186i	$0.416987\pi$
$468$		0			0
$469$	8.43029			0.389275
$470$		0			0
$471$	−22.9171	+	16.6935i	−1.05597	+	0.769194i
$472$		0			0
$473$	−14.6290	+	25.3382i	−0.672643	+	1.16505i
$474$		0			0
$475$	−1.99390	−	3.45354i	−0.0914866	−	0.158459i
$476$		0			0
$477$	16.9760	+	18.7605i	0.777276	+	0.858984i
$478$		0			0
$479$	10.7763	+	18.6651i	0.492383	+	0.852832i	0.999962	−	0.00877317i	$-0.00279262\pi$
$479$	10.7763	+	18.6651i	0.492383	+	0.852832i	−0.507579	+	0.861605i	$0.669459\pi$
$480$		0			0
$481$	−5.15948	+	8.93648i	−0.235252	+	0.407469i
$482$		0			0
$483$	5.89406	+	2.61550i	0.268189	+	0.119010i
$484$		0			0
$485$	52.8585			2.40018
$486$		0			0
$487$	12.6363			0.572607			0.286304	−	0.958139i	$-0.407573\pi$
$487$	12.6363			0.572607			0.286304	+	0.958139i	$0.407573\pi$
$488$		0			0
$489$	33.6987	+	14.9539i	1.52391	+	0.676238i
$490$		0			0
$491$	5.77170	−	9.99687i	0.260473	−	0.451152i	−0.705895	−	0.708317i	$-0.749455\pi$
$491$	5.77170	−	9.99687i	0.260473	−	0.451152i	0.966368	+	0.257164i	$0.0827882\pi$
$492$		0			0
$493$	17.8458	+	30.9098i	0.803734	+	1.39211i
$494$		0			0
$495$	−35.4559	−	39.1831i	−1.59362	−	1.76115i
$496$		0			0
$497$	−1.58599	−	2.74702i	−0.0711416	−	0.123221i
$498$		0			0
$499$	1.10170	−	1.90820i	0.0493190	−	0.0854229i	−0.840312	−	0.542103i	$-0.817628\pi$
$499$	1.10170	−	1.90820i	0.0493190	−	0.0854229i	0.889631	+	0.456680i	$0.150962\pi$
$500$		0			0
$501$	−16.3135	+	11.8832i	−0.728832	+	0.530901i
$502$		0			0
$503$	−7.98086			−0.355849			−0.177925	−	0.984044i	$-0.556938\pi$
$503$	−7.98086			−0.355849			−0.177925	+	0.984044i	$0.556938\pi$
$504$		0			0
$505$	−14.0656			−0.625910
$506$		0			0
$507$	0.846143	+	7.95616i	0.0375785	+	0.353346i
$508$		0			0
$509$	8.97939	−	15.5528i	0.398004	−	0.689364i	−0.595475	−	0.803374i	$-0.703036\pi$
$509$	8.97939	−	15.5528i	0.398004	−	0.689364i	0.993480	+	0.114010i	$0.0363695\pi$
$510$		0			0
$511$	−4.27461	−	7.40384i	−0.189098	−	0.327527i
$512$		0			0
$513$	1.46066	+	4.43951i	0.0644895	+	0.196009i
$514$		0			0
$515$	24.2039	+	41.9225i	1.06655	+	1.84732i
$516$		0			0
$517$	−30.9741	+	53.6488i	−1.36224	+	2.35947i
$518$		0			0
$519$	−3.81607	−	35.8820i	−0.167507	−	1.57504i
$520$		0			0
$521$	−9.10139			−0.398739			−0.199370	−	0.979924i	$-0.563889\pi$
$521$	−9.10139			−0.398739			−0.199370	+	0.979924i	$0.563889\pi$
$522$		0			0
$523$	−7.26754			−0.317787			−0.158894	−	0.987296i	$-0.550793\pi$
$523$	−7.26754			−0.317787			−0.158894	+	0.987296i	$0.550793\pi$
$524$		0			0
$525$	−6.20714	+	4.52145i	−0.270902	+	0.197332i
$526$		0			0
$527$	2.62243	−	4.54219i	0.114235	−	0.197861i
$528$		0			0
$529$	4.56986	+	7.91523i	0.198690	+	0.344141i
$530$		0			0
$531$	16.3957	−	3.52727i	0.711511	−	0.153071i
$532$		0			0
$533$	14.4698	+	25.0624i	0.626755	+	1.08557i
$534$		0			0
$535$	−30.7324	+	53.2302i	−1.32868	+	2.30134i
$536$		0			0
$537$	22.1615	+	9.83423i	0.956340	+	0.424378i
$538$		0			0
$539$	−5.73496			−0.247022
$540$		0			0
$541$	−14.1645			−0.608979			−0.304490	−	0.952516i	$-0.598486\pi$
$541$	−14.1645			−0.608979			−0.304490	+	0.952516i	$0.598486\pi$
$542$		0			0
$543$	−19.9367	−	8.84696i	−0.855566	−	0.379659i
$544$		0			0
$545$	−19.4406	+	33.6721i	−0.832745	+	1.44236i
$546$		0			0
$547$	14.4689	+	25.0609i	0.618645	+	1.07152i	0.989733	+	0.142927i	$0.0456514\pi$
$547$	14.4689	+	25.0609i	0.618645	+	1.07152i	−0.371088	+	0.928598i	$0.621015\pi$
$548$		0			0
$549$	4.29192	−	13.3208i	0.183175	−	0.568519i
$550$		0			0
$551$	−3.98712	−	6.90589i	−0.169857	−	0.294201i
$552$		0			0
$553$	−0.689381	+	1.19404i	−0.0293155	+	0.0507759i
$554$		0			0
$555$	15.3274	−	11.1649i	0.650610	−	0.473922i
$556$		0			0
$557$	12.6737			0.537002			0.268501	−	0.963279i	$-0.413472\pi$
$557$	12.6737			0.537002			0.268501	+	0.963279i	$0.413472\pi$
$558$		0			0
$559$	14.7691			0.624664
$560$		0			0
$561$	−4.22899	−	39.7646i	−0.178548	−	1.67886i
$562$		0			0
$563$	−6.27850	+	10.8747i	−0.264607	+	0.458313i	−0.967461	−	0.253022i	$-0.918576\pi$
$563$	−6.27850	+	10.8747i	−0.264607	+	0.458313i	0.702854	+	0.711335i	$0.251909\pi$
$564$		0			0
$565$	18.5796	+	32.1808i	0.781648	+	1.35385i
$566$		0			0
$567$	8.20376	−	3.70112i	0.344526	−	0.155433i
$568$		0			0
$569$	−12.4534	−	21.5700i	−0.522075	−	0.904261i	−0.999670	−	0.0256807i	$-0.991825\pi$
$569$	−12.4534	−	21.5700i	−0.522075	−	0.904261i	0.477595	−	0.878580i	$-0.341509\pi$
$570$		0			0
$571$	−3.74023	+	6.47827i	−0.156524	+	0.271107i	−0.933613	−	0.358283i	$-0.883362\pi$
$571$	−3.74023	+	6.47827i	−0.156524	+	0.271107i	0.777089	+	0.629391i	$0.216695\pi$
$572$		0			0
$573$	−1.57823	−	14.8399i	−0.0659316	−	0.619946i
$574$		0			0
$575$	16.5063			0.688358
$576$		0			0
$577$	−0.153516			−0.00639096			−0.00319548	−	0.999995i	$-0.501017\pi$
$577$	−0.153516			−0.00639096			−0.00319548	+	0.999995i	$0.501017\pi$
$578$		0			0
$579$	17.7708	−	12.9448i	0.738530	−	0.537966i
$580$		0			0
$581$	−6.44654	+	11.1657i	−0.267448	+	0.463233i
$582$		0			0
$583$	24.1833	+	41.8868i	1.00157	+	1.73477i
$584$		0			0
$585$	−8.18036	+	25.3894i	−0.338216	+	1.04972i
$586$		0			0
$587$	−10.0759	−	17.4519i	−0.415875	−	0.720317i	0.579645	−	0.814869i	$-0.303191\pi$
$587$	−10.0759	−	17.4519i	−0.415875	−	0.720317i	−0.995520	+	0.0945525i	$0.969858\pi$
$588$		0			0
$589$	−0.585905	+	1.01482i	−0.0241418	+	0.0418148i
$590$		0			0
$591$	14.2099	+	6.30569i	0.584518	+	0.259381i
$592$		0			0
$593$	−8.17775			−0.335820			−0.167910	−	0.985802i	$-0.553702\pi$
$593$	−8.17775			−0.335820			−0.167910	+	0.985802i	$0.553702\pi$
$594$		0			0
$595$	−12.3648			−0.506909
$596$		0			0
$597$	−13.3520	−	5.92496i	−0.546459	−	0.242493i
$598$		0			0
$599$	−16.1323	+	27.9420i	−0.659148	+	1.14168i	0.321689	+	0.946845i	$0.395750\pi$
$599$	−16.1323	+	27.9420i	−0.659148	+	1.14168i	−0.980837	+	0.194832i	$0.937584\pi$
$600$		0			0
$601$	−12.8203	−	22.2054i	−0.522950	−	0.905777i	−0.999643	−	0.0267067i	$-0.991498\pi$
$601$	−12.8203	−	22.2054i	−0.522950	−	0.905777i	0.476693	−	0.879070i	$-0.341835\pi$
$602$		0			0
$603$	−24.7252	+	5.31924i	−1.00689	+	0.216616i
$604$		0			0
$605$	−33.6163	−	58.2252i	−1.36670	−	2.36719i
$606$		0			0
$607$	−14.9054	+	25.8168i	−0.604990	+	1.04787i	0.387063	+	0.922053i	$0.373490\pi$
$607$	−14.9054	+	25.8168i	−0.604990	+	1.04787i	−0.992053	+	0.125820i	$0.959844\pi$
$608$		0			0
$609$	−12.4121	+	9.04134i	−0.502965	+	0.366374i
$610$		0			0
$611$	31.2706			1.26507
$612$		0			0
$613$	29.4212			1.18831			0.594156	−	0.804350i	$-0.297486\pi$
$613$	29.4212			1.18831			0.594156	+	0.804350i	$0.297486\pi$
$614$		0			0
$615$	−5.62409	−	52.8825i	−0.226785	−	2.13243i
$616$		0			0
$617$	14.7229	−	25.5008i	0.592721	−	1.02662i	−0.401143	−	0.916016i	$-0.631387\pi$
$617$	14.7229	−	25.5008i	0.592721	−	1.02662i	0.993864	−	0.110608i	$-0.0352798\pi$
$618$		0			0
$619$	2.56660	+	4.44548i	0.103160	+	0.178679i	0.912985	−	0.407993i	$-0.133771\pi$
$619$	2.56660	+	4.44548i	0.103160	+	0.178679i	−0.809825	+	0.586672i	$0.800438\pi$
$620$		0			0
$621$	−18.9370	−	3.95204i	−0.759914	−	0.158590i
$622$		0			0
$623$	−2.63608	−	4.56582i	−0.105612	−	0.182926i
$624$		0			0
$625$	13.7555	−	23.8252i	0.550219	−	0.953007i
$626$		0			0
$627$	0.944844	+	8.88423i	0.0377334	+	0.354802i
$628$		0			0
$629$	14.3498			0.572165
$630$		0			0
$631$	15.6329			0.622338			0.311169	−	0.950355i	$-0.399280\pi$
$631$	15.6329			0.622338			0.311169	+	0.950355i	$0.399280\pi$
$632$		0			0
$633$	34.8050	−	25.3529i	1.38338	−	1.00769i
$634$		0			0
$635$	−5.75693	+	9.97130i	−0.228457	+	0.395699i
$636$		0			0
$637$	1.44746	+	2.50708i	0.0573506	+	0.0993341i
$638$		0			0
$639$	6.38484	+	7.05602i	0.252580	+	0.279132i
$640$		0			0
$641$	0.617855	+	1.07016i	0.0244038	+	0.0422686i	0.877969	−	0.478717i	$-0.158898\pi$
$641$	0.617855	+	1.07016i	0.0244038	+	0.0422686i	−0.853566	+	0.520985i	$0.825565\pi$
$642$		0			0
$643$	−6.17709	+	10.6990i	−0.243601	+	0.421929i	−0.961737	−	0.273974i	$-0.911662\pi$
$643$	−6.17709	+	10.6990i	−0.243601	+	0.421929i	0.718137	+	0.695902i	$0.244995\pi$
$644$		0			0
$645$	−24.8076	−	11.0084i	−0.976797	−	0.433456i
$646$		0			0
$647$	−27.1060			−1.06565			−0.532824	−	0.846226i	$-0.678869\pi$
$647$	−27.1060			−1.06565			−0.532824	+	0.846226i	$0.678869\pi$
$648$		0			0
$649$	32.0599			1.25846
$650$		0			0
$651$	2.06260	+	0.915283i	0.0808396	+	0.0358728i
$652$		0			0
$653$	−23.3811	+	40.4972i	−0.914973	+	1.58478i	−0.108032	+	0.994147i	$0.534455\pi$
$653$	−23.3811	+	40.4972i	−0.914973	+	1.58478i	−0.806941	+	0.590632i	$0.798879\pi$
$654$		0			0
$655$	11.5205	+	19.9541i	0.450143	+	0.779670i
$656$		0			0
$657$	17.2086	+	19.0176i	0.671370	+	0.741946i
$658$		0			0
$659$	−2.51052	−	4.34835i	−0.0977960	−	0.169388i	0.812976	−	0.582297i	$-0.197846\pi$
$659$	−2.51052	−	4.34835i	−0.0977960	−	0.169388i	−0.910772	+	0.412909i	$0.864513\pi$
$660$		0			0
$661$	10.4204	−	18.0487i	0.405308	−	0.702014i	−0.589049	−	0.808097i	$-0.700498\pi$
$661$	10.4204	−	18.0487i	0.405308	−	0.702014i	0.994357	+	0.106083i	$0.0338310\pi$
$662$		0			0
$663$	−16.3160	+	11.8851i	−0.633662	+	0.461577i
$664$		0			0
$665$	2.76256			0.107127
$666$		0			0
$667$	33.0068			1.27803
$668$		0			0
$669$	4.35201	+	40.9214i	0.168259	+	1.58211i
$670$		0			0
$671$	13.3770	−	23.1696i	0.516412	−	0.894451i
$672$		0			0
$673$	−3.60931	−	6.25150i	−0.139129	−	0.240978i	0.788038	−	0.615626i	$-0.211097\pi$
$673$	−3.60931	−	6.25150i	−0.139129	−	0.240978i	−0.927167	+	0.374648i	$0.877763\pi$
$674$		0			0
$675$	15.3520	−	17.1774i	0.590899	−	0.661160i
$676$		0			0
$677$	7.02316	+	12.1645i	0.269922	+	0.467518i	0.968841	−	0.247682i	$-0.0796688\pi$
$677$	7.02316	+	12.1645i	0.269922	+	0.467518i	−0.698920	+	0.715200i	$0.746335\pi$
$678$		0			0
$679$	−8.60488	+	14.9041i	−0.330225	+	0.571967i
$680$		0			0
$681$	−2.77143	−	26.0594i	−0.106202	−	0.998598i
$682$		0			0
$683$	17.4730			0.668585			0.334292	−	0.942469i	$-0.391503\pi$
$683$	17.4730			0.668585			0.334292	+	0.942469i	$0.391503\pi$
$684$		0			0
$685$	−1.49588			−0.0571545
$686$		0			0
$687$	22.3096	−	16.2509i	0.851163	−	0.620011i
$688$		0			0
$689$	12.2074	−	21.1439i	0.465066	−	0.805517i
$690$		0			0
$691$	−0.120365	−	0.208479i	−0.00457891	−	0.00793091i	0.863727	−	0.503960i	$-0.168124\pi$
$691$	−0.120365	−	0.208479i	−0.00457891	−	0.00793091i	−0.868306	+	0.496029i	$0.834791\pi$
$692$		0			0
$693$	16.8200	−	3.61857i	0.638940	−	0.137458i
$694$		0			0
$695$	−4.89147	−	8.47227i	−0.185544	−	0.321372i
$696$		0			0
$697$	20.1220	−	34.8524i	0.762176	−	1.32013i
$698$		0			0
$699$	41.9876	+	18.6321i	1.58812	+	0.704730i
$700$		0			0
$701$	−22.4403			−0.847558			−0.423779	−	0.905766i	$-0.639297\pi$
$701$	−22.4403			−0.847558			−0.423779	+	0.905766i	$0.639297\pi$
$702$		0			0
$703$	−3.20605			−0.120918
$704$		0			0
$705$	−52.5252	−	23.3082i	−1.97821	−	0.877837i
$706$		0			0
$707$	2.28975	−	3.96596i	0.0861148	−	0.149155i
$708$		0			0
$709$	−5.61430	−	9.72424i	−0.210849	−	0.365202i	0.741131	−	0.671360i	$-0.234290\pi$
$709$	−5.61430	−	9.72424i	−0.210849	−	0.365202i	−0.951981	+	0.306158i	$0.900956\pi$
$710$		0			0
$711$	1.26848	−	3.93698i	0.0475718	−	0.147648i
$712$		0			0
$713$	−2.42517	−	4.20052i	−0.0908233	−	0.157311i
$714$		0			0
$715$	−25.4963	+	44.1610i	−0.953509	+	1.65153i
$716$		0			0
$717$	−5.49584	+	4.00332i	−0.205246	+	0.149507i
$718$		0			0
$719$	19.2391			0.717499			0.358749	−	0.933434i	$-0.383203\pi$
$719$	19.2391			0.717499			0.358749	+	0.933434i	$0.383203\pi$
$720$		0			0
$721$	−15.7607			−0.586960
$722$		0			0
$723$	−0.393445	−	3.69950i	−0.0146324	−	0.137586i
$724$		0			0
$725$	−19.6540	+	34.0417i	−0.729930	+	1.26428i
$726$		0			0
$727$	−1.90232	−	3.29491i	−0.0705531	−	0.122202i	0.828591	−	0.559855i	$-0.189143\pi$
$727$	−1.90232	−	3.29491i	−0.0705531	−	0.122202i	−0.899144	+	0.437653i	$0.855810\pi$
$728$		0			0
$729$	−21.7255	+	16.0313i	−0.804648	+	0.593753i
$730$		0			0
$731$	−10.2691	−	17.7866i	−0.379817	−	0.657863i
$732$		0			0
$733$	12.3542	−	21.3980i	0.456311	−	0.790354i	−0.542451	−	0.840087i	$-0.682504\pi$
$733$	12.3542	−	21.3980i	0.456311	−	0.790354i	0.998763	+	0.0497330i	$0.0158370\pi$
$734$		0			0
$735$	−0.562599	−	5.29003i	−0.0207518	−	0.195126i
$736$		0			0
$737$	−48.3473			−1.78090
$738$		0			0
$739$	24.0248			0.883766			0.441883	−	0.897073i	$-0.354311\pi$
$739$	24.0248			0.883766			0.441883	+	0.897073i	$0.354311\pi$
$740$		0			0
$741$	3.64534	−	2.65537i	0.133915	−	0.0975473i
$742$		0			0
$743$	9.01288	−	15.6108i	0.330651	−	0.572704i	−0.651989	−	0.758228i	$-0.726065\pi$
$743$	9.01288	−	15.6108i	0.330651	−	0.572704i	0.982640	+	0.185525i	$0.0593985\pi$
$744$		0			0
$745$	−22.5097	−	38.9879i	−0.824692	−	1.42841i
$746$		0			0
$747$	11.8618	−	36.8155i	0.434001	−	1.34701i
$748$		0			0
$749$	−10.0059	−	17.3308i	−0.365608	−	0.633252i
$750$		0			0
$751$	−8.13086	+	14.0831i	−0.296699	+	0.513898i	−0.975379	−	0.220536i	$-0.929219\pi$
$751$	−8.13086	+	14.0831i	−0.296699	+	0.513898i	0.678680	+	0.734435i	$0.262553\pi$
$752$		0			0
$753$	−12.1079	−	5.37289i	−0.441235	−	0.195799i
$754$		0			0
$755$	−2.01997			−0.0735141
$756$		0			0
$757$	−27.4472			−0.997586			−0.498793	−	0.866721i	$-0.666223\pi$
$757$	−27.4472			−0.997586			−0.498793	+	0.866721i	$0.666223\pi$
$758$		0			0
$759$	−33.8022	−	14.9998i	−1.22694	−	0.544458i
$760$		0			0
$761$	18.4990	−	32.0413i	0.670590	−	1.16150i	−0.307147	−	0.951662i	$-0.599374\pi$
$761$	18.4990	−	32.0413i	0.670590	−	1.16150i	0.977737	−	0.209834i	$-0.0672923\pi$
$762$		0			0
$763$	−6.32951	−	10.9630i	−0.229144	−	0.396888i
$764$		0			0
$765$	36.2648	−	7.80181i	1.31116	−	0.282075i
$766$		0			0
$767$	−8.09170	−	14.0152i	−0.292174	−	0.506061i
$768$		0			0
$769$	−9.37354	+	16.2354i	−0.338019	+	0.585465i	−0.984060	−	0.177837i	$-0.943090\pi$
$769$	−9.37354	+	16.2354i	−0.338019	+	0.585465i	0.646041	+	0.763302i	$0.276423\pi$
$770$		0			0
$771$	−5.23367	+	3.81235i	−0.188486	+	0.137298i
$772$		0			0
$773$	−20.7391			−0.745933			−0.372967	−	0.927845i	$-0.621659\pi$
$773$	−20.7391			−0.745933			−0.372967	+	0.927845i	$0.621659\pi$
$774$		0			0
$775$	5.77628			0.207490
$776$		0			0
$777$	0.652916	+	6.13927i	0.0234232	+	0.220245i
$778$		0			0
$779$	−4.49568	+	7.78674i	−0.161074	+	0.278989i
$780$		0			0
$781$	9.09561	+	15.7541i	0.325466	+	0.563724i
$782$		0			0
$783$	30.6987	−	34.3490i	1.09708	−	1.22753i
$784$		0			0
$785$	−25.1386	−	43.5414i	−0.897236	−	1.55406i
$786$		0			0
$787$	11.4574	−	19.8448i	0.408412	−	0.707391i	−0.586300	−	0.810094i	$-0.699416\pi$
$787$	11.4574	−	19.8448i	0.408412	−	0.707391i	0.994712	+	0.102703i	$0.0327492\pi$
$788$		0			0
$789$	2.57539	+	24.2160i	0.0916863	+	0.862113i
$790$		0			0
$791$	−12.0983			−0.430167
$792$		0			0
$793$	−13.5050			−0.479577
$794$		0			0
$795$	−36.2648	+	26.4163i	−1.28618	+	0.936889i
$796$		0			0
$797$	7.10542	−	12.3069i	0.251687	−	0.435935i	−0.712303	−	0.701872i	$-0.752348\pi$
$797$	7.10542	−	12.3069i	0.251687	−	0.435935i	0.963990	+	0.265937i	$0.0856813\pi$
$798$		0			0
$799$	−21.7429	−	37.6598i	−0.769208	−	1.33231i
$800$		0			0
$801$	10.6122	+	11.7278i	0.374965	+	0.414382i
$802$		0			0
$803$	24.5147	+	42.4607i	0.865105	+	1.49841i
$804$		0			0
$805$	−5.71737	+	9.90277i	−0.201511	+	0.349027i
$806$		0			0
$807$	5.09733	+	2.26195i	0.179435	+	0.0796246i
$808$		0			0
$809$	−36.2465			−1.27436			−0.637179	−	0.770716i	$-0.719899\pi$
$809$	−36.2465			−1.27436			−0.637179	+	0.770716i	$0.719899\pi$
$810$		0			0
$811$	−38.7558			−1.36090			−0.680449	−	0.732795i	$-0.738215\pi$
$811$	−38.7558			−1.36090			−0.680449	+	0.732795i	$0.738215\pi$
$812$		0			0
$813$	36.5928	+	16.2381i	1.28336	+	0.569496i
$814$		0			0
$815$	−32.6885	+	56.6181i	−1.14503	+	1.98325i
$816$		0			0
$817$	2.29433	+	3.97390i	0.0802686	+	0.139029i
$818$		0			0
$819$	−5.82715	−	6.43970i	−0.203617	−	0.225021i
$820$		0			0
$821$	6.63984	+	11.5005i	0.231732	+	0.401372i	0.958318	−	0.285704i	$-0.0922274\pi$
$821$	6.63984	+	11.5005i	0.231732	+	0.401372i	−0.726586	+	0.687076i	$0.758894\pi$
$822$		0			0
$823$	21.0617	−	36.4799i	0.734165	−	1.27161i	−0.220924	−	0.975291i	$-0.570907\pi$
$823$	21.0617	−	36.4799i	0.734165	−	1.27161i	0.955089	−	0.296320i	$-0.0957594\pi$
$824$		0			0
$825$	35.5977	−	25.9303i	1.23935	−	0.902778i
$826$		0			0
$827$	10.5251			0.365993			0.182997	−	0.983114i	$-0.441420\pi$
$827$	10.5251			0.365993			0.182997	+	0.983114i	$0.441420\pi$
$828$		0			0
$829$	54.4042			1.88954			0.944768	−	0.327739i	$-0.106287\pi$
$829$	54.4042			1.88954			0.944768	+	0.327739i	$0.106287\pi$
$830$		0			0
$831$	−0.440759	−	4.14439i	−0.0152897	−	0.143767i
$832$		0			0
$833$	2.01288	−	3.48641i	0.0697422	−	0.120797i
$834$		0			0
$835$	−17.8948	−	30.9947i	−0.619276	−	1.07262i
$836$		0			0
$837$	−6.62690	−	1.38300i	−0.229059	−	0.0478034i
$838$		0			0
$839$	−1.77133	−	3.06803i	−0.0611530	−	0.105920i	0.833828	−	0.552024i	$-0.186144\pi$
$839$	−1.77133	−	3.06803i	−0.0611530	−	0.105920i	−0.894981	+	0.446104i	$0.852811\pi$
$840$		0			0
$841$	−24.8011	+	42.9568i	−0.855212	+	1.48127i
$842$		0			0
$843$	2.46511	+	23.1790i	0.0849028	+	0.798329i
$844$		0			0
$845$	−14.1881			−0.488087
$846$		0			0
$847$	21.8897			0.752140
$848$		0			0
$849$	19.9579	−	14.5379i	0.684954	−	0.498939i
$850$		0			0
$851$	6.63521	−	11.4925i	0.227452	−	0.393958i
$852$		0			0
$853$	−8.89877	−	15.4131i	−0.304688	−	0.527735i	0.672504	−	0.740094i	$-0.265219\pi$
$853$	−8.89877	−	15.4131i	−0.304688	−	0.527735i	−0.977192	+	0.212359i	$0.931886\pi$
$854$		0			0
$855$	−8.10230	+	1.74309i	−0.277093	+	0.0596123i
$856$		0			0
$857$	−17.7640	−	30.7682i	−0.606808	−	1.05102i	−0.991763	−	0.128087i	$-0.959116\pi$
$857$	−17.7640	−	30.7682i	−0.606808	−	1.05102i	0.384955	−	0.922935i	$-0.374217\pi$
$858$		0			0
$859$	−13.9097	+	24.0923i	−0.474592	+	0.822017i	−0.999577	−	0.0290944i	$-0.990738\pi$
$859$	−13.9097	+	24.0923i	−0.474592	+	0.822017i	0.524985	+	0.851112i	$0.324071\pi$
$860$		0			0
$861$	15.8264	+	7.02301i	0.539362	+	0.239343i
$862$		0			0
$863$	−17.8384			−0.607226			−0.303613	−	0.952795i	$-0.598193\pi$
$863$	−17.8384			−0.607226			−0.303613	+	0.952795i	$0.598193\pi$
$864$		0			0
$865$	63.9879			2.17565
$866$		0			0
$867$	−1.25581	−	0.557270i	−0.0426497	−	0.0189259i
$868$		0			0
$869$	3.95357	−	6.84779i	0.134116	−	0.232295i
$870$		0			0
$871$	12.2025	+	21.1354i	0.413467	+	0.716146i
$872$		0			0
$873$	15.8332	−	49.1416i	0.535874	−	1.66319i
$874$		0			0
$875$	0.869734	+	1.50642i	0.0294024	+	0.0509264i
$876$		0			0
$877$	17.9657	−	31.1175i	0.606658	−	1.05076i	−0.385129	−	0.922863i	$-0.625843\pi$
$877$	17.9657	−	31.1175i	0.606658	−	1.05076i	0.991787	−	0.127900i	$-0.0408237\pi$
$878$		0			0
$879$	37.2831	−	27.1580i	1.25753	−	0.916017i
$880$		0			0
$881$	−53.6578			−1.80778			−0.903888	−	0.427770i	$-0.859299\pi$
$881$	−53.6578			−1.80778			−0.903888	+	0.427770i	$0.859299\pi$
$882$		0			0
$883$	5.70179			0.191881			0.0959403	−	0.995387i	$-0.469414\pi$
$883$	5.70179			0.191881			0.0959403	+	0.995387i	$0.469414\pi$
$884$		0			0
$885$	3.14507	+	29.5727i	0.105721	+	0.994075i
$886$		0			0
$887$	−18.1234	+	31.3906i	−0.608524	+	1.05399i	0.382960	+	0.923765i	$0.374905\pi$
$887$	−18.1234	+	31.3906i	−0.608524	+	1.05399i	−0.991484	+	0.130229i	$0.958429\pi$
$888$		0			0
$889$	−1.87435	−	3.24647i	−0.0628637	−	0.108883i
$890$		0			0
$891$	−47.0482	+	21.2258i	−1.57617	+	0.711090i
$892$		0			0
$893$	4.85781	+	8.41397i	0.162560	+	0.281563i
$894$		0			0
$895$	−21.4972	+	37.2342i	−0.718571	+	1.24460i
$896$		0			0
$897$	1.97416	+	18.5627i	0.0659153	+	0.619792i
$898$		0			0
$899$	11.5506			0.385233
$900$		0			0
$901$	−33.9519			−1.13110
$902$		0			0
$903$	7.14240	−	5.20272i	0.237684	−	0.173136i
$904$		0			0
$905$	19.3390	−	33.4962i	0.642851	−	1.11345i
$906$		0			0
$907$	−28.9777	−	50.1909i	−0.962190	−	1.66656i	−0.716983	−	0.697090i	$-0.754478\pi$
$907$	−28.9777	−	50.1909i	−0.962190	−	1.66656i	−0.245206	−	0.969471i	$-0.578856\pi$
$908$		0			0
$909$	−4.21320	+	13.0765i	−0.139743	+	0.433720i
$910$		0			0
$911$	−11.9811	−	20.7519i	−0.396952	−	0.687541i	0.596396	−	0.802690i	$-0.296599\pi$
$911$	−11.9811	−	20.7519i	−0.396952	−	0.687541i	−0.993348	+	0.115149i	$0.963265\pi$
$912$		0			0
$913$	36.9706	−	64.0350i	1.22355	−	2.11925i
$914$		0			0
$915$	22.6843	+	10.0662i	0.749921	+	0.332779i
$916$		0			0
$917$	−7.50172			−0.247729
$918$		0			0
$919$	18.5705			0.612583			0.306291	−	0.951938i	$-0.400912\pi$
$919$	18.5705			0.612583			0.306291	+	0.951938i	$0.400912\pi$
$920$		0			0
$921$	3.25507	+	1.44444i	0.107258	+	0.0475961i
$922$		0			0
$923$	4.59134	−	7.95243i	0.151126	−	0.261757i
$924$		0			0
$925$	7.90189	+	13.6865i	0.259813	+	0.450008i
$926$		0			0
$927$	46.2246	−	9.94450i	1.51821	−	0.326620i
$928$		0			0
$929$	18.5380	+	32.1087i	0.608211	+	1.05345i	0.991535	+	0.129839i	$0.0414459\pi$
$929$	18.5380	+	32.1087i	0.608211	+	1.05345i	−0.383324	+	0.923614i	$0.625221\pi$
$930$		0			0
$931$	−0.449719	+	0.778937i	−0.0147390	+	0.0255286i
$932$		0			0
$933$	−29.0432	+	21.1559i	−0.950833	+	0.692613i
$934$		0			0
$935$	70.9118			2.31906
$936$		0			0
$937$	−12.1388			−0.396559			−0.198279	−	0.980146i	$-0.563535\pi$
$937$	−12.1388			−0.396559			−0.198279	+	0.980146i	$0.563535\pi$
$938$		0			0
$939$	−1.66686	−	15.6732i	−0.0543959	−	0.511476i
$940$		0			0
$941$	5.06687	−	8.77608i	0.165175	−	0.286092i	−0.771542	−	0.636178i	$-0.780514\pi$
$941$	5.06687	−	8.77608i	0.165175	−	0.286092i	0.936718	+	0.350086i	$0.113848\pi$
$942$		0			0
$943$	−18.6084	−	32.2307i	−0.605974	−	1.04958i
$944$		0			0
$945$	4.98788	+	15.1601i	0.162256	+	0.493159i
$946$		0			0
$947$	3.59014	+	6.21831i	0.116664	+	0.202068i	0.918444	−	0.395552i	$-0.129447\pi$
$947$	3.59014	+	6.21831i	0.116664	+	0.202068i	−0.801780	+	0.597620i	$0.796113\pi$
$948$		0			0
$949$	12.3747	−	21.4336i	0.401699	−	0.695764i
$950$		0			0
$951$	3.99342	+	37.5495i	0.129495	+	1.21763i
$952$		0			0
$953$	−5.23901			−0.169708			−0.0848541	−	0.996393i	$-0.527042\pi$
$953$	−5.23901			−0.169708			−0.0848541	+	0.996393i	$0.527042\pi$
$954$		0			0
$955$	26.4638			0.856349
$956$		0			0
$957$	71.1830	−	51.8517i	2.30102	−	1.67613i
$958$		0			0
$959$	0.243515	−	0.421780i	0.00786350	−	0.0136200i
$960$		0			0
$961$	14.6513	+	25.3768i	0.472623	+	0.818608i
$962$		0			0
$963$	40.2815	+	44.5159i	1.29805	+	1.43451i
$964$		0			0
$965$	19.4935	+	33.7637i	0.627517	+	1.08689i
$966$		0			0
$967$	10.9993	−	19.0513i	0.353713	−	0.612648i	−0.633184	−	0.774001i	$-0.718252\pi$
$967$	10.9993	−	19.0513i	0.353713	−	0.612648i	0.986897	+	0.161353i	$0.0515858\pi$
$968$		0			0
$969$	−5.73256	−	2.54384i	−0.184156	−	0.0817198i
$970$		0			0
$971$	21.7786			0.698909			0.349454	−	0.936953i	$-0.386367\pi$
$971$	21.7786			0.698909			0.349454	+	0.936953i	$0.386367\pi$
$972$		0			0
$973$	3.18515			0.102111
$974$		0			0
$975$	−20.3202	−	9.01716i	−0.650769	−	0.288780i
$976$		0			0
$977$	−13.5221	+	23.4209i	−0.432610	+	0.749302i	−0.997097	−	0.0761396i	$-0.975741\pi$
$977$	−13.5221	+	23.4209i	−0.432610	+	0.749302i	0.564487	+	0.825442i	$0.309074\pi$
$978$		0			0
$979$	15.1178	+	26.1848i	0.483167	+	0.836870i
$980$		0			0
$981$	25.4811	+	28.1597i	0.813549	+	0.899071i
$982$		0			0
$983$	−19.2381	−	33.3213i	−0.613600	−	1.06279i	−0.990628	−	0.136584i	$-0.956388\pi$
$983$	−19.2381	−	33.3213i	−0.613600	−	1.06279i	0.377029	−	0.926201i	$-0.376946\pi$
$984$		0			0
$985$	−13.7839	+	23.8745i	−0.439193	+	0.760704i
$986$		0			0
$987$	15.1226	−	11.0158i	0.481359	−	0.350635i
$988$		0			0
$989$	−18.9933			−0.603953
$990$		0			0
$991$	−3.35307			−0.106514			−0.0532568	−	0.998581i	$-0.516960\pi$
$991$	−3.35307			−0.106514			−0.0532568	+	0.998581i	$0.516960\pi$
$992$		0			0
$993$	−0.531585	−	4.99841i	−0.0168693	−	0.158620i
$994$		0			0
$995$	12.9517	−	22.4330i	0.410596	−	0.711173i
$996$		0			0
$997$	11.7713	+	20.3886i	0.372802	+	0.645712i	0.989995	−	0.141099i	$-0.0450636\pi$
$997$	11.7713	+	20.3886i	0.372802	+	0.645712i	−0.617193	+	0.786812i	$0.711730\pi$
$998$		0			0
$999$	−5.78861	−	17.5939i	−0.183144	−	0.556646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.r.n.337.5		10
3.2	odd	2		3024.2.r.n.1009.4		10
4.3	odd	2		504.2.r.f.337.1	yes	10
9.2	odd	6		3024.2.r.n.2017.4		10
9.4	even	3		9072.2.a.cn.1.4		5
9.5	odd	6		9072.2.a.cm.1.2		5
9.7	even	3	inner	1008.2.r.n.673.5		10
12.11	even	2		1512.2.r.f.1009.4		10
36.7	odd	6		504.2.r.f.169.1	✓	10
36.11	even	6		1512.2.r.f.505.4		10
36.23	even	6		4536.2.a.bc.1.2		5
36.31	odd	6		4536.2.a.bd.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.r.f.169.1	✓	10	36.7	odd	6
504.2.r.f.337.1	yes	10	4.3	odd	2
1008.2.r.n.337.5		10	1.1	even	1	trivial
1008.2.r.n.673.5		10	9.7	even	3	inner
1512.2.r.f.505.4		10	36.11	even	6
1512.2.r.f.1009.4		10	12.11	even	2
3024.2.r.n.1009.4		10	3.2	odd	2
3024.2.r.n.2017.4		10	9.2	odd	6
4536.2.a.bc.1.2		5	36.23	even	6
4536.2.a.bd.1.4		5	36.31	odd	6
9072.2.a.cm.1.2		5	9.5	odd	6
9072.2.a.cn.1.4		5	9.4	even	3

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.58317 + 0.702538i) q^{3} +(-1.53571 + 2.65993i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(2.01288 + 2.22448i) q^{9} +O(q^{10})\)	\(q+(1.58317 + 0.702538i) q^{3} +(-1.53571 + 2.65993i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(2.01288 + 2.22448i) q^{9} +(2.86748 + 4.96662i) q^{11} +(1.44746 - 2.50708i) q^{13} +(-4.30001 + 3.13224i) q^{15} -4.02576 q^{17} +0.899439 q^{19} +(-0.183172 - 1.72234i) q^{21} +(-1.86147 + 3.22416i) q^{23} +(-2.21683 - 3.83966i) q^{25} +(1.62396 + 4.93586i) q^{27} +(-4.43290 - 7.67800i) q^{29} +(-0.651412 + 1.12828i) q^{31} +(1.05048 + 9.87753i) q^{33} +3.07143 q^{35} -3.56450 q^{37} +(4.05291 - 2.95225i) q^{39} +(-4.99831 + 8.65733i) q^{41} +(2.55085 + 4.41820i) q^{43} +(-9.00818 + 1.93797i) q^{45} +(5.40094 + 9.35469i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-6.37349 - 2.82825i) q^{51} +8.43366 q^{53} -17.6145 q^{55} +(1.42397 + 0.631889i) q^{57} +(2.79513 - 4.84131i) q^{59} +(-2.33253 - 4.04006i) q^{61} +(0.920014 - 2.85545i) q^{63} +(4.44578 + 7.70031i) q^{65} +(-4.21515 + 7.30085i) q^{67} +(-5.21212 + 3.79665i) q^{69} +3.17199 q^{71} +8.54922 q^{73} +(-0.812122 - 7.63626i) q^{75} +(2.86748 - 4.96662i) q^{77} +(-0.689381 - 1.19404i) q^{79} +(-0.896613 + 8.95523i) q^{81} +(-6.44654 - 11.1657i) q^{83} +(6.18242 - 10.7083i) q^{85} +(-1.62396 - 15.2699i) q^{87} +5.27216 q^{89} -2.89493 q^{91} +(-1.82396 + 1.32862i) q^{93} +(-1.38128 + 2.39245i) q^{95} +(-8.60488 - 14.9041i) q^{97} +(-5.27624 + 16.3759i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{5} - 5 q^{7}+O(q^{10}) \) 10 * q - 3 * q^5 - 5 * q^7	\( 10 q - 3 q^{5} - 5 q^{7} - 4 q^{11} - 3 q^{13} - 15 q^{15} - 2 q^{19} - 8 q^{23} - 10 q^{25} + 9 q^{27} - 9 q^{29} + 3 q^{31} + 30 q^{33} + 6 q^{35} - 6 q^{37} + 18 q^{39} - 12 q^{41} + 5 q^{43} - 9 q^{45} - 3 q^{47} - 5 q^{49} - 9 q^{51} + 60 q^{53} - 44 q^{55} - 21 q^{57} - 7 q^{59} - 14 q^{61} - 6 q^{63} - 11 q^{65} + 8 q^{67} + 21 q^{69} + 18 q^{71} + 30 q^{73} + 51 q^{75} - 4 q^{77} + 3 q^{79} - 12 q^{81} - 20 q^{83} - 21 q^{85} - 9 q^{87} - 24 q^{89} + 6 q^{91} - 39 q^{93} + 12 q^{95} - 37 q^{97} - 60 q^{99}+O(q^{100}) \) 10 * q - 3 * q^5 - 5 * q^7 - 4 * q^11 - 3 * q^13 - 15 * q^15 - 2 * q^19 - 8 * q^23 - 10 * q^25 + 9 * q^27 - 9 * q^29 + 3 * q^31 + 30 * q^33 + 6 * q^35 - 6 * q^37 + 18 * q^39 - 12 * q^41 + 5 * q^43 - 9 * q^45 - 3 * q^47 - 5 * q^49 - 9 * q^51 + 60 * q^53 - 44 * q^55 - 21 * q^57 - 7 * q^59 - 14 * q^61 - 6 * q^63 - 11 * q^65 + 8 * q^67 + 21 * q^69 + 18 * q^71 + 30 * q^73 + 51 * q^75 - 4 * q^77 + 3 * q^79 - 12 * q^81 - 20 * q^83 - 21 * q^85 - 9 * q^87 - 24 * q^89 + 6 * q^91 - 39 * q^93 + 12 * q^95 - 37 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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