LMFDB - Embedded newform 1148.2.n.a.141.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(57,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("1148.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.n (of order $5$, degree $4$, 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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.64000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 $ x^8 + 2x^6 + 4x^4 + 8*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.2
Root			$1.14412 - 0.831254i$ of defining polynomial
Character	$\chi$	$=$	1148.141
Dual form			1148.2.n.a.57.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.744002 q^{3} +(-1.95314 + 1.41904i) q^{5} +(0.309017 - 0.951057i) q^{7} -2.44646 q^{9} +O(q^{10})$	\(q-0.744002 q^{3} +(-1.95314 + 1.41904i) q^{5} +(0.309017 - 0.951057i) q^{7} -2.44646 q^{9} +(0.733196 + 0.532698i) q^{11} +(0.410927 + 1.26470i) q^{13} +(1.45314 - 1.05577i) q^{15} +(-1.87200 - 1.36009i) q^{17} +(2.10394 - 6.47527i) q^{19} +(-0.229909 + 0.707588i) q^{21} +(-0.125968 - 0.387689i) q^{23} +(0.255998 - 0.787881i) q^{25} +4.05218 q^{27} +(-2.89344 + 2.10221i) q^{29} +(6.04837 + 4.39440i) q^{31} +(-0.545499 - 0.396328i) q^{33} +(0.746033 + 2.29605i) q^{35} +(9.41776 - 6.84240i) q^{37} +(-0.305731 - 0.940942i) q^{39} +(3.06653 - 5.62107i) q^{41} +(2.06298 + 6.34921i) q^{43} +(4.77828 - 3.47162i) q^{45} +(-3.15231 - 9.70182i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(1.39277 + 1.01191i) q^{51} +(5.86474 - 4.26098i) q^{53} -2.18795 q^{55} +(-1.56534 + 4.81761i) q^{57} +(-1.69224 - 5.20817i) q^{59} +(3.33839 - 10.2745i) q^{61} +(-0.755998 + 2.32672i) q^{63} +(-2.59726 - 1.88702i) q^{65} +(-3.04973 + 2.21576i) q^{67} +(0.0937204 + 0.288442i) q^{69} +(5.60055 + 4.06904i) q^{71} +6.28470 q^{73} +(-0.190463 + 0.586185i) q^{75} +(0.733196 - 0.532698i) q^{77} +6.57951 q^{79} +4.32456 q^{81} -5.14066 q^{83} +5.58630 q^{85} +(2.15273 - 1.56405i) q^{87} +(-2.98210 + 9.17796i) q^{89} +1.32979 q^{91} +(-4.50000 - 3.26944i) q^{93} +(5.07936 + 15.6327i) q^{95} +(0.609430 - 0.442777i) q^{97} +(-1.79373 - 1.30322i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 2 q^{5} - 2 q^{7} + 12 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 - 2 * q^5 - 2 * q^7 + 12 * q^9	$ 8 q - 4 q^{3} - 2 q^{5} - 2 q^{7} + 12 q^{9} - 2 q^{15} - 14 q^{17} + 12 q^{19} - 4 q^{21} - 8 q^{23} + 4 q^{25} + 32 q^{27} + 2 q^{29} + 18 q^{31} + 14 q^{33} - 2 q^{35} + 14 q^{37} - 6 q^{39} - 22 q^{41} + 20 q^{43} + 10 q^{45} + 10 q^{47} - 2 q^{49} + 24 q^{51} - 8 q^{53} + 12 q^{55} + 34 q^{57} - 16 q^{59} + 14 q^{61} - 8 q^{63} + 2 q^{65} - 26 q^{67} + 28 q^{69} + 14 q^{71} - 40 q^{73} + 32 q^{75} - 72 q^{79} - 16 q^{81} - 8 q^{83} - 28 q^{85} - 14 q^{87} + 2 q^{89} + 20 q^{91} - 36 q^{93} - 8 q^{95} + 18 q^{97} - 14 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 - 2 * q^5 - 2 * q^7 + 12 * q^9 - 2 * q^15 - 14 * q^17 + 12 * q^19 - 4 * q^21 - 8 * q^23 + 4 * q^25 + 32 * q^27 + 2 * q^29 + 18 * q^31 + 14 * q^33 - 2 * q^35 + 14 * q^37 - 6 * q^39 - 22 * q^41 + 20 * q^43 + 10 * q^45 + 10 * q^47 - 2 * q^49 + 24 * q^51 - 8 * q^53 + 12 * q^55 + 34 * q^57 - 16 * q^59 + 14 * q^61 - 8 * q^63 + 2 * q^65 - 26 * q^67 + 28 * q^69 + 14 * q^71 - 40 * q^73 + 32 * q^75 - 72 * q^79 - 16 * q^81 - 8 * q^83 - 28 * q^85 - 14 * q^87 + 2 * q^89 + 20 * q^91 - 36 * q^93 - 8 * q^95 + 18 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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
$3$	−0.744002			−0.429550			−0.214775	−	0.976664i	$-0.568902\pi$
$3$	−0.744002			−0.429550			−0.214775	+	0.976664i	$0.568902\pi$
$4$		0			0
$5$	−1.95314	+	1.41904i	−0.873471	+	0.634614i	−0.931516	−	0.363700i	$-0.881513\pi$
$5$	−1.95314	+	1.41904i	−0.873471	+	0.634614i	0.0580453	+	0.998314i	$0.481513\pi$
$6$		0			0
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$		0			0
$9$	−2.44646			−0.815487
$10$		0			0
$11$	0.733196	+	0.532698i	0.221067	+	0.160614i	0.692807	−	0.721123i	$-0.256374\pi$
$11$	0.733196	+	0.532698i	0.221067	+	0.160614i	−0.471740	+	0.881738i	$0.656374\pi$
$12$		0			0
$13$	0.410927	+	1.26470i	0.113971	+	0.350766i	0.991731	−	0.128334i	$-0.0409631\pi$
$13$	0.410927	+	1.26470i	0.113971	+	0.350766i	−0.877760	+	0.479100i	$0.840963\pi$
$14$		0			0
$15$	1.45314	−	1.05577i	0.375199	−	0.272598i
$16$		0			0
$17$	−1.87200	−	1.36009i	−0.454027	−	0.329870i	0.337157	−	0.941449i	$-0.390535\pi$
$17$	−1.87200	−	1.36009i	−0.454027	−	0.329870i	−0.791184	+	0.611579i	$0.790535\pi$
$18$		0			0
$19$	2.10394	−	6.47527i	0.482677	−	1.48553i	−0.352640	−	0.935759i	$-0.614716\pi$
$19$	2.10394	−	6.47527i	0.482677	−	1.48553i	0.835317	−	0.549769i	$-0.185284\pi$
$20$		0			0
$21$	−0.229909	+	0.707588i	−0.0501703	+	0.154408i
$22$		0			0
$23$	−0.125968	−	0.387689i	−0.0262661	−	0.0808388i	0.937064	−	0.349157i	$-0.113532\pi$
$23$	−0.125968	−	0.387689i	−0.0262661	−	0.0808388i	−0.963330	+	0.268318i	$0.913532\pi$
$24$		0			0
$25$	0.255998	−	0.787881i	0.0511996	−	0.157576i
$26$		0			0
$27$	4.05218			0.779842
$28$		0			0
$29$	−2.89344	+	2.10221i	−0.537299	+	0.390370i	−0.823081	−	0.567924i	$-0.807747\pi$
$29$	−2.89344	+	2.10221i	−0.537299	+	0.390370i	0.285782	+	0.958295i	$0.407747\pi$
$30$		0			0
$31$	6.04837	+	4.39440i	1.08632	+	0.789257i	0.978774	−	0.204943i	$-0.0657008\pi$
$31$	6.04837	+	4.39440i	1.08632	+	0.789257i	0.107546	+	0.994200i	$0.465701\pi$
$32$		0			0
$33$	−0.545499	−	0.396328i	−0.0949592	−	0.0689919i
$34$		0			0
$35$	0.746033	+	2.29605i	0.126103	+	0.388104i
$36$		0			0
$37$	9.41776	−	6.84240i	1.54827	−	1.12488i	0.603399	−	0.797439i	$-0.293813\pi$
$37$	9.41776	−	6.84240i	1.54827	−	1.12488i	0.944871	−	0.327444i	$-0.106187\pi$
$38$		0			0
$39$	−0.305731	−	0.940942i	−0.0489561	−	0.150671i
$40$		0			0
$41$	3.06653	−	5.62107i	0.478911	−	0.877863i
$41$	3.06653	−	5.62107i	0.478911	−	0.877863i
$42$		0			0
$43$	2.06298	+	6.34921i	0.314602	+	0.968246i	0.975918	+	0.218138i	$0.0699983\pi$
$43$	2.06298	+	6.34921i	0.314602	+	0.968246i	−0.661316	+	0.750108i	$0.730002\pi$
$44$		0			0
$45$	4.77828	−	3.47162i	0.712304	−	0.517519i
$46$		0			0
$47$	−3.15231	−	9.70182i	−0.459812	−	1.41516i	−0.865392	−	0.501096i	$-0.832930\pi$
$47$	−3.15231	−	9.70182i	−0.459812	−	1.41516i	0.405580	−	0.914060i	$-0.367070\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$		0			0
$51$	1.39277	+	1.01191i	0.195027	+	0.141696i
$52$		0			0
$53$	5.86474	−	4.26098i	0.805584	−	0.585291i	−0.106963	−	0.994263i	$-0.534113\pi$
$53$	5.86474	−	4.26098i	0.805584	−	0.585291i	0.912547	+	0.408972i	$0.134113\pi$
$54$		0			0
$55$	−2.18795			−0.295023
$56$		0			0
$57$	−1.56534	+	4.81761i	−0.207334	+	0.638108i
$58$		0			0
$59$	−1.69224	−	5.20817i	−0.220311	−	0.678046i	−0.998734	−	0.0503066i	$-0.983980\pi$
$59$	−1.69224	−	5.20817i	−0.220311	−	0.678046i	0.778423	−	0.627740i	$-0.216020\pi$
$60$		0			0
$61$	3.33839	−	10.2745i	0.427437	−	1.31552i	−0.473204	−	0.880953i	$-0.656903\pi$
$61$	3.33839	−	10.2745i	0.427437	−	1.31552i	0.900641	−	0.434564i	$-0.143097\pi$
$62$		0			0
$63$	−0.755998	+	2.32672i	−0.0952468	+	0.293140i
$64$		0			0
$65$	−2.59726	−	1.88702i	−0.322151	−	0.234056i
$66$		0			0
$67$	−3.04973	+	2.21576i	−0.372584	+	0.270698i	−0.758282	−	0.651927i	$-0.773961\pi$
$67$	−3.04973	+	2.21576i	−0.372584	+	0.270698i	0.385698	+	0.922625i	$0.373961\pi$
$68$		0			0
$69$	0.0937204	+	0.288442i	0.0112826	+	0.0347243i
$70$		0			0
$71$	5.60055	+	4.06904i	0.664663	+	0.482906i	0.868234	−	0.496154i	$-0.165255\pi$
$71$	5.60055	+	4.06904i	0.664663	+	0.482906i	−0.203572	+	0.979060i	$0.565255\pi$
$72$		0			0
$73$	6.28470			0.735568			0.367784	−	0.929911i	$-0.380117\pi$
$73$	6.28470			0.735568			0.367784	+	0.929911i	$0.380117\pi$
$74$		0			0
$75$	−0.190463	+	0.586185i	−0.0219928	+	0.0676868i
$76$		0			0
$77$	0.733196	−	0.532698i	0.0835554	−	0.0607065i
$78$		0			0
$79$	6.57951			0.740253			0.370127	−	0.928981i	$-0.379314\pi$
$79$	6.57951			0.740253			0.370127	+	0.928981i	$0.379314\pi$
$80$		0			0
$81$	4.32456			0.480506
$82$		0			0
$83$	−5.14066			−0.564261			−0.282131	−	0.959376i	$-0.591041\pi$
$83$	−5.14066			−0.564261			−0.282131	+	0.959376i	$0.591041\pi$
$84$		0			0
$85$	5.58630			0.605919
$86$		0			0
$87$	2.15273	−	1.56405i	0.230797	−	0.167683i
$88$		0			0
$89$	−2.98210	+	9.17796i	−0.316102	+	0.972862i	0.659196	+	0.751971i	$0.270897\pi$
$89$	−2.98210	+	9.17796i	−0.316102	+	0.972862i	−0.975298	+	0.220891i	$0.929103\pi$
$90$		0			0
$91$	1.32979			0.139400
$92$		0			0
$93$	−4.50000	−	3.26944i	−0.466628	−	0.339025i
$94$		0			0
$95$	5.07936	+	15.6327i	0.521132	+	1.60388i
$96$		0			0
$97$	0.609430	−	0.442777i	0.0618783	−	0.0449572i	−0.556416	−	0.830904i	$-0.687824\pi$
$97$	0.609430	−	0.442777i	0.0618783	−	0.0449572i	0.618294	+	0.785947i	$0.287824\pi$
$98$		0			0
$99$	−1.79373	−	1.30322i	−0.180277	−	0.130979i
$100$		0			0
$101$	3.38045	−	10.4039i	0.336367	−	1.03523i	−0.629678	−	0.776856i	$-0.716813\pi$
$101$	3.38045	−	10.4039i	0.336367	−	1.03523i	0.966045	−	0.258375i	$-0.0831869\pi$
$102$		0			0
$103$	2.91876	−	8.98300i	0.287593	−	0.885122i	−0.698016	−	0.716082i	$-0.745933\pi$
$103$	2.91876	−	8.98300i	0.287593	−	0.885122i	0.985609	−	0.169039i	$-0.0540665\pi$
$104$		0			0
$105$	−0.555050	−	1.70827i	−0.0541673	−	0.166710i
$106$		0			0
$107$	1.39428	−	4.29116i	0.134790	−	0.414842i	−0.860767	−	0.508999i	$-0.830016\pi$
$107$	1.39428	−	4.29116i	0.134790	−	0.414842i	0.995557	+	0.0941569i	$0.0300156\pi$
$108$		0			0
$109$	−11.4049			−1.09239			−0.546197	−	0.837657i	$-0.683925\pi$
$109$	−11.4049			−1.09239			−0.546197	+	0.837657i	$0.683925\pi$
$110$		0			0
$111$	−7.00683	+	5.09076i	−0.665059	+	0.483193i
$112$		0			0
$113$	6.52431	+	4.74019i	0.613756	+	0.445920i	0.850735	−	0.525595i	$-0.176157\pi$
$113$	6.52431	+	4.74019i	0.613756	+	0.445920i	−0.236979	+	0.971515i	$0.576157\pi$
$114$		0			0
$115$	0.796180	+	0.578458i	0.0742441	+	0.0539415i
$116$		0			0
$117$	−1.00532	−	3.09405i	−0.0929416	−	0.286045i
$118$		0			0
$119$	−1.87200	+	1.36009i	−0.171606	+	0.124679i
$120$		0			0
$121$	−3.14538	−	9.68048i	−0.285943	−	0.880043i
$122$		0			0
$123$	−2.28150	+	4.18209i	−0.205716	+	0.377086i
$124$		0			0
$125$	−3.11213	−	9.57815i	−0.278357	−	0.856696i
$126$		0			0
$127$	−3.10191	+	2.25367i	−0.275250	+	0.199981i	−0.716843	−	0.697235i	$-0.754414\pi$
$127$	−3.10191	+	2.25367i	−0.275250	+	0.199981i	0.441593	+	0.897216i	$0.354414\pi$
$128$		0			0
$129$	−1.53486	−	4.72383i	−0.135137	−	0.415910i
$130$		0			0
$131$	6.12555	+	4.45048i	0.535192	+	0.388840i	0.822296	−	0.569060i	$-0.192693\pi$
$131$	6.12555	+	4.45048i	0.535192	+	0.388840i	−0.287104	+	0.957899i	$0.592693\pi$
$132$		0			0
$133$	−5.50819	−	4.00193i	−0.477621	−	0.347012i
$134$		0			0
$135$	−7.91447	+	5.75020i	−0.681169	+	0.494898i
$136$		0			0
$137$	−13.0054			−1.11113			−0.555563	−	0.831474i	$-0.687497\pi$
$137$	−13.0054			−1.11113			−0.555563	+	0.831474i	$0.687497\pi$
$138$		0			0
$139$	1.65789	−	5.10247i	0.140621	−	0.432786i	−0.855801	−	0.517305i	$-0.826935\pi$
$139$	1.65789	−	5.10247i	0.140621	−	0.432786i	0.996422	+	0.0845188i	$0.0269353\pi$
$140$		0			0
$141$	2.34533	+	7.21817i	0.197512	+	0.607880i
$142$		0			0
$143$	−0.372415	+	1.14618i	−0.0311429	+	0.0958480i
$144$		0			0
$145$	2.66818	−	8.21182i	0.221580	−	0.681954i
$146$		0			0
$147$	0.601910	+	0.437313i	0.0496447	+	0.0360690i
$148$		0			0
$149$	3.98716	−	2.89684i	0.326641	−	0.237319i	−0.412363	−	0.911020i	$-0.635296\pi$
$149$	3.98716	−	2.89684i	0.326641	−	0.237319i	0.739004	+	0.673701i	$0.235296\pi$
$150$		0			0
$151$	6.27744	+	19.3200i	0.510851	+	1.57224i	0.790707	+	0.612195i	$0.209713\pi$
$151$	6.27744	+	19.3200i	0.510851	+	1.57224i	−0.279856	+	0.960042i	$0.590287\pi$
$152$		0			0
$153$	4.57978	+	3.32740i	0.370253	+	0.269005i
$154$		0			0
$155$	−18.0491			−1.44974
$156$		0			0
$157$	3.01915	−	9.29200i	0.240955	−	0.741582i	−0.755321	−	0.655355i	$-0.772519\pi$
$157$	3.01915	−	9.29200i	0.240955	−	0.741582i	0.996276	−	0.0862272i	$-0.0274811\pi$
$158$		0			0
$159$	−4.36338	+	3.17018i	−0.346038	+	0.251411i
$160$		0			0
$161$	−0.407641			−0.0321266
$162$		0			0
$163$	3.73471			0.292525			0.146262	−	0.989246i	$-0.453276\pi$
$163$	3.73471			0.292525			0.146262	+	0.989246i	$0.453276\pi$
$164$		0			0
$165$	1.62784			0.126727
$166$		0			0
$167$	−13.8566			−1.07226			−0.536128	−	0.844136i	$-0.680114\pi$
$167$	−13.8566			−1.07226			−0.536128	+	0.844136i	$0.680114\pi$
$168$		0			0
$169$	9.08661	−	6.60181i	0.698970	−	0.507831i
$170$		0			0
$171$	−5.14721	+	15.8415i	−0.393617	+	1.21143i
$172$		0			0
$173$	−10.1371			−0.770711			−0.385355	−	0.922768i	$-0.625921\pi$
$173$	−10.1371			−0.770711			−0.385355	+	0.922768i	$0.625921\pi$
$174$		0			0
$175$	−0.670212	−	0.486937i	−0.0506632	−	0.0368090i
$176$		0			0
$177$	1.25903	+	3.87489i	0.0946344	+	0.291255i
$178$		0			0
$179$	2.66760	−	1.93812i	0.199385	−	0.144862i	−0.483613	−	0.875282i	$-0.660676\pi$
$179$	2.66760	−	1.93812i	0.199385	−	0.144862i	0.682998	+	0.730420i	$0.260676\pi$
$180$		0			0
$181$	−4.96832	−	3.60969i	−0.369292	−	0.268306i	0.387625	−	0.921817i	$-0.373295\pi$
$181$	−4.96832	−	3.60969i	−0.369292	−	0.268306i	−0.756917	+	0.653511i	$0.773295\pi$
$182$		0			0
$183$	−2.48377	+	7.64426i	−0.183606	+	0.565080i
$184$		0			0
$185$	−8.68456	+	26.7283i	−0.638502	+	1.96511i
$186$		0			0
$187$	−0.648027	−	1.99442i	−0.0473884	−	0.145847i
$188$		0			0
$189$	1.25219	−	3.85385i	0.0910835	−	0.280326i
$190$		0			0
$191$	−26.7405			−1.93487			−0.967436	−	0.253117i	$-0.918544\pi$
$191$	−26.7405			−1.93487			−0.967436	+	0.253117i	$0.918544\pi$
$192$		0			0
$193$	11.8992	−	8.64527i	0.856522	−	0.622300i	−0.0704144	−	0.997518i	$-0.522432\pi$
$193$	11.8992	−	8.64527i	0.856522	−	0.622300i	0.926937	+	0.375218i	$0.122432\pi$
$194$		0			0
$195$	1.93237	+	1.40395i	0.138380	+	0.100539i
$196$		0			0
$197$	12.8696	+	9.35034i	0.916924	+	0.666184i	0.942756	−	0.333482i	$-0.108224\pi$
$197$	12.8696	+	9.35034i	0.916924	+	0.666184i	−0.0258325	+	0.999666i	$0.508224\pi$
$198$		0			0
$199$	7.03041	+	21.6374i	0.498372	+	1.53383i	0.811634	+	0.584166i	$0.198578\pi$
$199$	7.03041	+	21.6374i	0.498372	+	1.53383i	−0.313262	+	0.949667i	$0.601422\pi$
$200$		0			0
$201$	2.26901	−	1.64853i	0.160043	−	0.116278i
$202$		0			0
$203$	1.10520	+	3.40145i	0.0775696	+	0.238735i
$204$		0			0
$205$	1.98716	+	15.3303i	0.138789	+	1.07071i
$206$		0			0
$207$	0.308176	+	0.948467i	0.0214197	+	0.0659230i
$208$		0			0
$209$	4.99196	−	3.62687i	0.345301	−	0.250876i
$210$		0			0
$211$	1.24106	+	3.81960i	0.0854384	+	0.262952i	0.984644	−	0.174574i	$-0.0558548\pi$
$211$	1.24106	+	3.81960i	0.0854384	+	0.262952i	−0.899206	+	0.437526i	$0.855855\pi$
$212$		0			0
$213$	−4.16682	−	3.02737i	−0.285506	−	0.207432i
$214$		0			0
$215$	−13.0391	−	9.47344i	−0.889258	−	0.646083i
$216$		0			0
$217$	6.04837	−	4.39440i	0.410590	−	0.298311i
$218$		0			0
$219$	−4.67583			−0.315963
$220$		0			0
$221$	0.950853	−	2.92642i	0.0639613	−	0.196853i
$222$		0			0
$223$	−5.83037	−	17.9440i	−0.390430	−	1.20162i	−0.932464	−	0.361264i	$-0.882345\pi$
$223$	−5.83037	−	17.9440i	−0.390430	−	1.20162i	0.542034	−	0.840357i	$-0.317655\pi$
$224$		0			0
$225$	−0.626289	+	1.92752i	−0.0417526	+	0.128501i
$226$		0			0
$227$	−1.69969	+	5.23112i	−0.112813	+	0.347201i	−0.991485	−	0.130225i	$-0.958430\pi$
$227$	−1.69969	+	5.23112i	−0.112813	+	0.347201i	0.878672	+	0.477426i	$0.158430\pi$
$228$		0			0
$229$	−3.95111	−	2.87065i	−0.261097	−	0.189698i	0.449534	−	0.893263i	$-0.351590\pi$
$229$	−3.95111	−	2.87065i	−0.261097	−	0.189698i	−0.710630	+	0.703566i	$0.751590\pi$
$230$		0			0
$231$	−0.545499	+	0.396328i	−0.0358912	+	0.0260765i
$232$		0			0
$233$	4.07243	+	12.5336i	0.266794	+	0.821107i	0.991275	+	0.131812i	$0.0420795\pi$
$233$	4.07243	+	12.5336i	0.266794	+	0.821107i	−0.724481	+	0.689295i	$0.757921\pi$
$234$		0			0
$235$	19.9242	+	14.4758i	1.29971	+	0.944294i
$236$		0			0
$237$	−4.89517			−0.317976
$238$		0			0
$239$	−4.65534	+	14.3277i	−0.301129	+	0.926780i	0.679964	+	0.733245i	$0.261995\pi$
$239$	−4.65534	+	14.3277i	−0.301129	+	0.926780i	−0.981093	+	0.193535i	$0.938005\pi$
$240$		0			0
$241$	−15.0751	+	10.9527i	−0.971074	+	0.705527i	−0.955696	−	0.294355i	$-0.904895\pi$
$241$	−15.0751	+	10.9527i	−0.971074	+	0.705527i	−0.0153783	+	0.999882i	$0.504895\pi$
$242$		0			0
$243$	−15.3740			−0.986243
$244$		0			0
$245$	2.41421			0.154238
$246$		0			0
$247$	9.05386			0.576083
$248$		0			0
$249$	3.82466			0.242378
$250$		0			0
$251$	16.0490	−	11.6603i	1.01301	−	0.735992i	0.0481689	−	0.998839i	$-0.484661\pi$
$251$	16.0490	−	11.6603i	1.01301	−	0.735992i	0.964838	+	0.262847i	$0.0846614\pi$
$252$		0			0
$253$	0.114162	−	0.351355i	0.00717732	−	0.0220895i
$254$		0			0
$255$	−4.15622			−0.260272
$256$		0			0
$257$	−7.74932	−	5.63021i	−0.483389	−	0.351203i	0.319247	−	0.947672i	$-0.396570\pi$
$257$	−7.74932	−	5.63021i	−0.483389	−	0.351203i	−0.802636	+	0.596469i	$0.796570\pi$
$258$		0			0
$259$	−3.59726	−	11.0712i	−0.223523	−	0.687933i
$260$		0			0
$261$	7.07869	−	5.14297i	0.438160	−	0.318342i
$262$		0			0
$263$	7.11423	+	5.16879i	0.438682	+	0.318721i	0.785111	−	0.619355i	$-0.212606\pi$
$263$	7.11423	+	5.16879i	0.438682	+	0.318721i	−0.346429	+	0.938076i	$0.612606\pi$
$264$		0			0
$265$	−5.40815	+	16.6446i	−0.332220	+	1.02247i
$266$		0			0
$267$	2.21869	−	6.82842i	0.135782	−	0.417893i
$268$		0			0
$269$	0.749799	+	2.30764i	0.0457160	+	0.140700i	0.971309	−	0.237821i	$-0.0764331\pi$
$269$	0.749799	+	2.30764i	0.0457160	+	0.140700i	−0.925593	+	0.378520i	$0.876433\pi$
$270$		0			0
$271$	−3.87378	+	11.9223i	−0.235315	+	0.724226i	0.761764	+	0.647854i	$0.224333\pi$
$271$	−3.87378	+	11.9223i	−0.235315	+	0.724226i	−0.997079	+	0.0763713i	$0.975667\pi$
$272$		0			0
$273$	−0.989365			−0.0598791
$274$		0			0
$275$	0.607399	−	0.441301i	0.0366275	−	0.0266115i
$276$		0			0
$277$	−21.0822	−	15.3171i	−1.26671	−	0.920317i	−0.267641	−	0.963519i	$-0.586244\pi$
$277$	−21.0822	−	15.3171i	−1.26671	−	0.920317i	−0.999066	+	0.0432018i	$0.986244\pi$
$278$		0			0
$279$	−14.7971	−	10.7507i	−0.885880	−	0.643629i
$280$		0			0
$281$	5.29211	+	16.2874i	0.315701	+	0.971627i	0.975465	+	0.220154i	$0.0706561\pi$
$281$	5.29211	+	16.2874i	0.315701	+	0.971627i	−0.659764	+	0.751473i	$0.729344\pi$
$282$		0			0
$283$	−5.62968	+	4.09020i	−0.334650	+	0.243137i	−0.742401	−	0.669956i	$-0.766313\pi$
$283$	−5.62968	+	4.09020i	−0.334650	+	0.243137i	0.407751	+	0.913093i	$0.366313\pi$
$284$		0			0
$285$	−3.77906	−	11.6307i	−0.223852	−	0.688946i
$286$		0			0
$287$	−4.39835	−	4.65345i	−0.259626	−	0.274684i
$288$		0			0
$289$	−3.59874	−	11.0758i	−0.211691	−	0.651517i
$290$		0			0
$291$	−0.453417	+	0.329427i	−0.0265798	+	0.0193113i
$292$		0			0
$293$	−9.74806	−	30.0015i	−0.569488	−	1.75270i	−0.654225	−	0.756300i	$-0.727005\pi$
$293$	−9.74806	−	30.0015i	−0.569488	−	1.75270i	0.0847365	−	0.996403i	$-0.472995\pi$
$294$		0			0
$295$	10.6958	+	7.77094i	0.622732	+	0.452442i
$296$		0			0
$297$	2.97104	+	2.15859i	0.172397	+	0.125254i
$298$		0			0
$299$	0.438549	−	0.318624i	0.0253619	−	0.0184265i
$300$		0			0
$301$	6.67596			0.384796
$302$		0			0
$303$	−2.51506	+	7.74056i	−0.144486	+	0.444683i
$304$		0			0
$305$	8.05959	+	24.8049i	0.461491	+	1.42032i
$306$		0			0
$307$	−3.94417	+	12.1389i	−0.225106	+	0.692805i	0.773175	+	0.634193i	$0.218667\pi$
$307$	−3.94417	+	12.1389i	−0.225106	+	0.692805i	−0.998281	+	0.0586119i	$0.981333\pi$
$308$		0			0
$309$	−2.17156	+	6.68337i	−0.123536	+	0.380204i
$310$		0			0
$311$	27.0046	+	19.6200i	1.53129	+	1.11255i	0.955516	+	0.294941i	$0.0952999\pi$
$311$	27.0046	+	19.6200i	1.53129	+	1.11255i	0.575776	+	0.817608i	$0.304700\pi$
$312$		0			0
$313$	12.3185	−	8.94995i	0.696285	−	0.505881i	−0.182435	−	0.983218i	$-0.558398\pi$
$313$	12.3185	−	8.94995i	0.696285	−	0.505881i	0.878720	+	0.477337i	$0.158398\pi$
$314$		0			0
$315$	−1.82514	−	5.61721i	−0.102835	−	0.316494i
$316$		0			0
$317$	−11.1153	−	8.07575i	−0.624298	−	0.453579i	0.230122	−	0.973162i	$-0.426087\pi$
$317$	−11.1153	−	8.07575i	−0.624298	−	0.453579i	−0.854420	+	0.519583i	$0.826087\pi$
$318$		0			0
$319$	−3.24130			−0.181478
$320$		0			0
$321$	−1.03735	+	3.19263i	−0.0578992	+	0.178195i
$322$		0			0
$323$	−12.7455	+	9.26016i	−0.709179	+	0.515249i
$324$		0			0
$325$	1.10163			0.0611076
$326$		0			0
$327$	8.48528			0.469237
$328$		0			0
$329$	−10.2011			−0.562405
$330$		0			0
$331$	−22.8047			−1.25346			−0.626731	−	0.779236i	$-0.715607\pi$
$331$	−22.8047			−1.25346			−0.626731	+	0.779236i	$0.715607\pi$
$332$		0			0
$333$	−23.0402	+	16.7397i	−1.26259	+	0.917328i
$334$		0			0
$335$	2.81230	−	8.65538i	0.153653	−	0.472894i
$336$		0			0
$337$	23.6332			1.28738			0.643692	−	0.765284i	$-0.277402\pi$
$337$	23.6332			1.28738			0.643692	+	0.765284i	$0.277402\pi$
$338$		0			0
$339$	−4.85410	−	3.52671i	−0.263639	−	0.191545i
$340$		0			0
$341$	2.09375	+	6.44391i	0.113383	+	0.348957i
$342$		0			0
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$		0			0
$345$	−0.592359	−	0.430374i	−0.0318915	−	0.0231706i
$346$		0			0
$347$	2.08759	−	6.42495i	0.112068	−	0.344910i	−0.879256	−	0.476349i	$-0.841960\pi$
$347$	2.08759	−	6.42495i	0.112068	−	0.344910i	0.991324	+	0.131439i	$0.0419599\pi$
$348$		0			0
$349$	7.50970	−	23.1125i	0.401985	−	1.23718i	−0.521402	−	0.853311i	$-0.674591\pi$
$349$	7.50970	−	23.1125i	0.401985	−	1.23718i	0.923387	−	0.383871i	$-0.125409\pi$
$350$		0			0
$351$	1.66515	+	5.12480i	0.0888791	+	0.273542i
$352$		0			0
$353$	−8.89599	+	27.3791i	−0.473486	+	1.45724i	0.374503	+	0.927226i	$0.377813\pi$
$353$	−8.89599	+	27.3791i	−0.473486	+	1.45724i	−0.847989	+	0.530014i	$0.822187\pi$
$354$		0			0
$355$	−16.7128			−0.887022
$356$		0			0
$357$	1.39277	−	1.01191i	0.0737133	−	0.0535559i
$358$		0			0
$359$	9.17738	+	6.66776i	0.484364	+	0.351911i	0.803013	−	0.595962i	$-0.203229\pi$
$359$	9.17738	+	6.66776i	0.484364	+	0.351911i	−0.318649	+	0.947873i	$0.603229\pi$
$360$		0			0
$361$	−22.1312	−	16.0792i	−1.16480	−	0.846276i
$362$		0			0
$363$	2.34017	+	7.20229i	0.122827	+	0.378022i
$364$		0			0
$365$	−12.2749	+	8.91823i	−0.642497	+	0.466801i
$366$		0			0
$367$	−7.10332	−	21.8618i	−0.370790	−	1.14117i	−0.946275	−	0.323362i	$-0.895187\pi$
$367$	−7.10332	−	21.8618i	−0.370790	−	1.14117i	0.575485	−	0.817812i	$-0.304813\pi$
$368$		0			0
$369$	−7.50214	+	13.7517i	−0.390546	+	0.715886i
$370$		0			0
$371$	−2.24013	−	6.89441i	−0.116302	−	0.357940i
$372$		0			0
$373$	9.51096	−	6.91011i	0.492459	−	0.357792i	−0.313670	−	0.949532i	$-0.601559\pi$
$373$	9.51096	−	6.91011i	0.492459	−	0.357792i	0.806129	+	0.591740i	$0.201559\pi$
$374$		0			0
$375$	2.31543	+	7.12617i	0.119568	+	0.367994i
$376$		0			0
$377$	−3.84767	−	2.79549i	−0.198165	−	0.143975i
$378$		0			0
$379$	−11.5754	−	8.41001i	−0.594588	−	0.431993i	0.249366	−	0.968409i	$-0.419778\pi$
$379$	−11.5754	−	8.41001i	−0.594588	−	0.431993i	−0.843954	+	0.536416i	$0.819778\pi$
$380$		0			0
$381$	2.30783	−	1.67673i	0.118234	−	0.0859017i
$382$		0			0
$383$	−3.74170			−0.191192			−0.0955961	−	0.995420i	$-0.530476\pi$
$383$	−3.74170			−0.191192			−0.0955961	+	0.995420i	$0.530476\pi$
$384$		0			0
$385$	−0.676115	+	2.08087i	−0.0344580	+	0.106051i
$386$		0			0
$387$	−5.04701	−	15.5331i	−0.256554	−	0.789592i
$388$		0			0
$389$	9.84430	−	30.2976i	0.499126	−	1.53615i	−0.311302	−	0.950311i	$-0.600765\pi$
$389$	9.84430	−	30.2976i	0.499126	−	1.53615i	0.810427	−	0.585839i	$-0.199235\pi$
$390$		0			0
$391$	−0.291480	+	0.897083i	−0.0147408	+	0.0453674i
$392$		0			0
$393$	−4.55742	−	3.31116i	−0.229892	−	0.167026i
$394$		0			0
$395$	−12.8507	+	9.33659i	−0.646589	+	0.469775i
$396$		0			0
$397$	−2.27999	−	7.01709i	−0.114429	−	0.352178i	0.877398	−	0.479763i	$-0.159277\pi$
$397$	−2.27999	−	7.01709i	−0.114429	−	0.352178i	−0.991828	+	0.127585i	$0.959277\pi$
$398$		0			0
$399$	4.09810	+	2.97745i	0.205162	+	0.149059i
$400$		0			0
$401$	−22.7535			−1.13626			−0.568128	−	0.822940i	$-0.692332\pi$
$401$	−22.7535			−1.13626			−0.568128	+	0.822940i	$0.692332\pi$
$402$		0			0
$403$	−3.07217	+	9.45518i	−0.153036	+	0.470996i
$404$		0			0
$405$	−8.44646	+	6.13671i	−0.419708	+	0.304936i
$406$		0			0
$407$	10.5500			0.522944
$408$		0			0
$409$	28.5678			1.41259			0.706294	−	0.707918i	$-0.250366\pi$
$409$	28.5678			1.41259			0.706294	+	0.707918i	$0.250366\pi$
$410$		0			0
$411$	9.67604			0.477284
$412$		0			0
$413$	−5.47620			−0.269466
$414$		0			0
$415$	10.0404	−	7.29480i	0.492866	−	0.358088i
$416$		0			0
$417$	−1.23348	+	3.79625i	−0.0604036	+	0.185903i
$418$		0			0
$419$	30.4659			1.48835			0.744177	−	0.667982i	$-0.232842\pi$
$419$	30.4659			1.48835			0.744177	+	0.667982i	$0.232842\pi$
$420$		0			0
$421$	8.27895	+	6.01501i	0.403491	+	0.293154i	0.770962	−	0.636882i	$-0.219776\pi$
$421$	8.27895	+	6.01501i	0.403491	+	0.293154i	−0.367470	+	0.930035i	$0.619776\pi$
$422$		0			0
$423$	7.71201	+	23.7351i	0.374971	+	1.15404i
$424$		0			0
$425$	−1.55082	+	1.12673i	−0.0752256	+	0.0546546i
$426$		0			0
$427$	−8.74002	−	6.35000i	−0.422959	−	0.307298i
$428$		0			0
$429$	0.277077	−	0.852757i	0.0133774	−	0.0411715i
$430$		0			0
$431$	10.5217	−	32.3826i	0.506814	−	1.55981i	−0.290885	−	0.956758i	$-0.593950\pi$
$431$	10.5217	−	32.3826i	0.506814	−	1.55981i	0.797699	−	0.603056i	$-0.206050\pi$
$432$		0			0
$433$	10.3613	+	31.8888i	0.497932	+	1.53248i	0.812337	+	0.583188i	$0.198195\pi$
$433$	10.3613	+	31.8888i	0.497932	+	1.53248i	−0.314405	+	0.949289i	$0.601805\pi$
$434$		0			0
$435$	−1.98513	+	6.10961i	−0.0951798	+	0.292933i
$436$		0			0
$437$	−2.77542			−0.132766
$438$		0			0
$439$	23.6765	−	17.2020i	1.13002	−	0.821005i	0.144319	−	0.989531i	$-0.453901\pi$
$439$	23.6765	−	17.2020i	1.13002	−	0.821005i	0.985697	+	0.168526i	$0.0539008\pi$
$440$		0			0
$441$	1.97923	+	1.43799i	0.0942490	+	0.0684759i
$442$		0			0
$443$	30.6965	+	22.3023i	1.45843	+	1.05961i	0.983768	+	0.179447i	$0.0574309\pi$
$443$	30.6965	+	22.3023i	1.45843	+	1.05961i	0.474665	+	0.880166i	$0.342569\pi$
$444$		0			0
$445$	−7.19943	−	22.1576i	−0.341286	−	1.05037i
$446$		0			0
$447$	−2.96646	+	2.15526i	−0.140309	+	0.101940i
$448$		0			0
$449$	8.12429	+	25.0040i	0.383409	+	1.18001i	0.937628	+	0.347640i	$0.113017\pi$
$449$	8.12429	+	25.0040i	0.383409	+	1.18001i	−0.554219	+	0.832371i	$0.686983\pi$
$450$		0			0
$451$	5.24269	−	2.48781i	0.246869	−	0.117146i
$452$		0			0
$453$	−4.67043	−	14.3741i	−0.219436	−	0.675354i
$454$		0			0
$455$	−2.59726	+	1.88702i	−0.121762	+	0.0884649i
$456$		0			0
$457$	−7.27425	−	22.3878i	−0.340275	−	1.04726i	−0.964065	−	0.265667i	$-0.914408\pi$
$457$	−7.27425	−	22.3878i	−0.340275	−	1.04726i	0.623790	−	0.781592i	$-0.285592\pi$
$458$		0			0
$459$	−7.58568	−	5.51132i	−0.354069	−	0.257246i
$460$		0			0
$461$	0.147665	+	0.107285i	0.00687745	+	0.00499676i	0.591219	−	0.806511i	$-0.298647\pi$
$461$	0.147665	+	0.107285i	0.00687745	+	0.00499676i	−0.584341	+	0.811508i	$0.698647\pi$
$462$		0			0
$463$	21.1429	−	15.3612i	0.982595	−	0.713897i	0.0243080	−	0.999705i	$-0.492262\pi$
$463$	21.1429	−	15.3612i	0.982595	−	0.713897i	0.958287	+	0.285807i	$0.0922618\pi$
$464$		0			0
$465$	13.4286			0.622736
$466$		0			0
$467$	6.49181	−	19.9797i	0.300405	−	0.924552i	−0.680947	−	0.732333i	$-0.738432\pi$
$467$	6.49181	−	19.9797i	0.300405	−	0.924552i	0.981352	−	0.192219i	$-0.0615684\pi$
$468$		0			0
$469$	1.16489	+	3.58518i	0.0537898	+	0.165548i
$470$		0			0
$471$	−2.24626	+	6.91327i	−0.103502	+	0.318547i
$472$		0			0
$473$	−1.86964	+	5.75416i	−0.0859662	+	0.264577i
$474$		0			0
$475$	−4.56313	−	3.31531i	−0.209371	−	0.152117i
$476$		0			0
$477$	−14.3479	+	10.4243i	−0.656943	+	0.477297i
$478$		0			0
$479$	−8.58985	−	26.4368i	−0.392480	−	1.20793i	−0.930907	−	0.365257i	$-0.880981\pi$
$479$	−8.58985	−	26.4368i	−0.392480	−	1.20793i	0.538426	−	0.842673i	$-0.319019\pi$
$480$		0			0
$481$	12.5236	+	9.09894i	0.571028	+	0.414876i
$482$		0			0
$483$	0.303286			0.0138000
$484$		0			0
$485$	−0.561985	+	1.72961i	−0.0255184	+	0.0785376i
$486$		0			0
$487$	16.4295	−	11.9367i	0.744491	−	0.540904i	−0.149623	−	0.988743i	$-0.547806\pi$
$487$	16.4295	−	11.9367i	0.744491	−	0.540904i	0.894114	+	0.447839i	$0.147806\pi$
$488$		0			0
$489$	−2.77863			−0.125654
$490$		0			0
$491$	25.2899			1.14132			0.570658	−	0.821188i	$-0.306688\pi$
$491$	25.2899			1.14132			0.570658	+	0.821188i	$0.306688\pi$
$492$		0			0
$493$	8.27572			0.372720
$494$		0			0
$495$	5.35274			0.240588
$496$		0			0
$497$	5.60055	−	4.06904i	0.251219	−	0.182521i
$498$		0			0
$499$	−3.38248	+	10.4102i	−0.151420	+	0.466024i	−0.997781	−	0.0665866i	$-0.978789\pi$
$499$	−3.38248	+	10.4102i	−0.151420	+	0.466024i	0.846360	+	0.532611i	$0.178789\pi$
$500$		0			0
$501$	10.3093			0.460588
$502$		0			0
$503$	−22.5116	−	16.3557i	−1.00374	−	0.729263i	−0.0408561	−	0.999165i	$-0.513009\pi$
$503$	−22.5116	−	16.3557i	−1.00374	−	0.729263i	−0.962888	+	0.269902i	$0.913009\pi$
$504$		0			0
$505$	8.16112	+	25.1173i	0.363165	+	1.11771i
$506$		0			0
$507$	−6.76045	+	4.91176i	−0.300242	+	0.218139i
$508$		0			0
$509$	17.1784	+	12.4809i	0.761421	+	0.553205i	0.899346	−	0.437238i	$-0.144043\pi$
$509$	17.1784	+	12.4809i	0.761421	+	0.553205i	−0.137925	+	0.990443i	$0.544043\pi$
$510$		0			0
$511$	1.94208	−	5.97710i	0.0859125	−	0.264411i
$512$		0			0
$513$	8.52554	−	26.2389i	0.376412	−	1.15848i
$514$		0			0
$515$	7.04650	+	21.6869i	0.310506	+	0.955639i
$516$		0			0
$517$	2.85688	−	8.79256i	0.125645	−	0.386696i
$518$		0			0
$519$	7.54203			0.331058
$520$		0			0
$521$	15.5440	−	11.2934i	0.680994	−	0.494771i	−0.192693	−	0.981259i	$-0.561722\pi$
$521$	15.5440	−	11.2934i	0.680994	−	0.494771i	0.873687	+	0.486488i	$0.161722\pi$
$522$		0			0
$523$	−27.2067	−	19.7668i	−1.18967	−	0.864342i	−0.196436	−	0.980517i	$-0.562937\pi$
$523$	−27.2067	−	19.7668i	−1.18967	−	0.864342i	−0.993229	+	0.116174i	$0.962937\pi$
$524$		0			0
$525$	0.498639	+	0.362282i	0.0217624	+	0.0158113i
$526$		0			0
$527$	−5.34579	−	16.4526i	−0.232866	−	0.716688i
$528$		0			0
$529$	18.4730	−	13.4214i	0.803172	−	0.583539i
$530$		0			0
$531$	4.14000	+	12.7416i	0.179660	+	0.552938i
$532$		0			0
$533$	8.36911	+	1.56840i	0.362506	+	0.0679348i
$534$		0			0
$535$	3.36610	+	10.3598i	0.145529	+	0.447893i
$536$		0			0
$537$	−1.98470	+	1.44197i	−0.0856460	+	0.0622254i
$538$		0			0
$539$	−0.280056	−	0.861923i	−0.0120629	−	0.0371257i
$540$		0			0
$541$	−8.45221	−	6.14089i	−0.363389	−	0.264017i	0.391075	−	0.920359i	$-0.372103\pi$
$541$	−8.45221	−	6.14089i	−0.363389	−	0.264017i	−0.754464	+	0.656341i	$0.772103\pi$
$542$		0			0
$543$	3.69644	+	2.68562i	0.158629	+	0.115251i
$544$		0			0
$545$	22.2754	−	16.1840i	0.954173	−	0.693247i
$546$		0			0
$547$	−4.45576			−0.190514			−0.0952572	−	0.995453i	$-0.530367\pi$
$547$	−4.45576			−0.190514			−0.0952572	+	0.995453i	$0.530367\pi$
$548$		0			0
$549$	−8.16725	+	25.1362i	−0.348570	+	1.07279i
$550$		0			0
$551$	7.52473	+	23.1587i	0.320564	+	0.986595i
$552$		0			0
$553$	2.03318	−	6.25749i	0.0864597	−	0.266096i
$554$		0			0
$555$	6.46133	−	19.8859i	0.274268	−	0.844111i
$556$		0			0
$557$	−35.8866	−	26.0732i	−1.52057	−	1.10476i	−0.961207	−	0.275830i	$-0.911047\pi$
$557$	−35.8866	−	26.0732i	−1.52057	−	1.10476i	−0.559359	−	0.828926i	$-0.688953\pi$
$558$		0			0
$559$	−7.18214	+	5.21813i	−0.303772	+	0.220703i
$560$		0			0
$561$	0.482133	+	1.48385i	0.0203557	+	0.0626483i
$562$		0			0
$563$	3.70287	+	2.69029i	0.156057	+	0.113382i	0.663074	−	0.748554i	$-0.269252\pi$
$563$	3.70287	+	2.69029i	0.156057	+	0.113382i	−0.507016	+	0.861937i	$0.669252\pi$
$564$		0			0
$565$	−19.4694			−0.819084
$566$		0			0
$567$	1.33636	−	4.11290i	0.0561219	−	0.172725i
$568$		0			0
$569$	−15.5803	+	11.3198i	−0.653162	+	0.474550i	−0.864347	−	0.502896i	$-0.832268\pi$
$569$	−15.5803	+	11.3198i	−0.653162	+	0.474550i	0.211185	+	0.977446i	$0.432268\pi$
$570$		0			0
$571$	34.5745			1.44690			0.723449	−	0.690378i	$-0.242556\pi$
$571$	34.5745			1.44690			0.723449	+	0.690378i	$0.242556\pi$
$572$		0			0
$573$	19.8949			0.831123
$574$		0			0
$575$	−0.337701			−0.0140831
$576$		0			0
$577$	−12.4692			−0.519100			−0.259550	−	0.965730i	$-0.583574\pi$
$577$	−12.4692			−0.519100			−0.259550	+	0.965730i	$0.583574\pi$
$578$		0			0
$579$	−8.85302	+	6.43209i	−0.367919	+	0.267309i
$580$		0			0
$581$	−1.58855	+	4.88906i	−0.0659043	+	0.202833i
$582$		0			0
$583$	6.56981			0.272094
$584$		0			0
$585$	6.35410	+	4.61653i	0.262710	+	0.190870i
$586$		0			0
$587$	−2.34836	−	7.22752i	−0.0969273	−	0.298312i	0.890824	−	0.454349i	$-0.150128\pi$
$587$	−2.34836	−	7.22752i	−0.0969273	−	0.298312i	−0.987751	+	0.156037i	$0.950128\pi$
$588$		0			0
$589$	41.1803	−	29.9193i	1.69681	−	1.23280i
$590$		0			0
$591$	−9.57504	−	6.95667i	−0.393864	−	0.286159i
$592$		0			0
$593$	5.88290	−	18.1057i	0.241582	−	0.743512i	−0.754598	−	0.656187i	$-0.772168\pi$
$593$	5.88290	−	18.1057i	0.241582	−	0.743512i	0.996180	−	0.0873250i	$-0.0278318\pi$
$594$		0			0
$595$	1.72626	−	5.31289i	0.0707698	−	0.217807i
$596$		0			0
$597$	−5.23064	−	16.0982i	−0.214076	−	0.658857i
$598$		0			0
$599$	−6.08611	+	18.7311i	−0.248672	+	0.765333i	0.746339	+	0.665566i	$0.231810\pi$
$599$	−6.08611	+	18.7311i	−0.248672	+	0.765333i	−0.995011	+	0.0997668i	$0.968190\pi$
$600$		0			0
$601$	−14.3058			−0.583546			−0.291773	−	0.956488i	$-0.594245\pi$
$601$	−14.3058			−0.583546			−0.291773	+	0.956488i	$0.594245\pi$
$602$		0			0
$603$	7.46105	−	5.42077i	0.303838	−	0.220751i
$604$		0			0
$605$	19.8803	+	14.4439i	0.808251	+	0.587229i
$606$		0			0
$607$	−7.85560	−	5.70743i	−0.318849	−	0.231657i	0.416835	−	0.908982i	$-0.363139\pi$
$607$	−7.85560	−	5.70743i	−0.318849	−	0.231657i	−0.735684	+	0.677325i	$0.763139\pi$
$608$		0			0
$609$	−0.822268	−	2.53068i	−0.0333200	−	0.102548i
$610$		0			0
$611$	10.9746	−	7.97348i	0.443983	−	0.322573i
$612$		0			0
$613$	−0.203300	−	0.625695i	−0.00821123	−	0.0252716i	0.946867	−	0.321626i	$-0.104229\pi$
$613$	−0.203300	−	0.625695i	−0.00821123	−	0.0252716i	−0.955078	+	0.296354i	$0.904229\pi$
$614$		0			0
$615$	−1.47845	−	11.4057i	−0.0596170	−	0.459924i
$616$		0			0
$617$	−2.11177	−	6.49936i	−0.0850166	−	0.261654i	0.899507	−	0.436906i	$-0.143926\pi$
$617$	−2.11177	−	6.49936i	−0.0850166	−	0.261654i	−0.984524	+	0.175252i	$0.943926\pi$
$618$		0			0
$619$	−13.3485	+	9.69827i	−0.536522	+	0.389806i	−0.822792	−	0.568343i	$-0.807585\pi$
$619$	−13.3485	+	9.69827i	−0.536522	+	0.389806i	0.286270	+	0.958149i	$0.407585\pi$
$620$		0			0
$621$	−0.510445	−	1.57099i	−0.0204834	−	0.0630415i
$622$		0			0
$623$	7.80724	+	5.67229i	0.312791	+	0.227256i
$624$		0			0
$625$	23.0213	+	16.7259i	0.920850	+	0.669037i
$626$		0			0
$627$	−3.71403	+	2.69840i	−0.148324	+	0.107764i
$628$		0			0
$629$	−26.9363			−1.07402
$630$		0			0
$631$	−12.5837	+	38.7287i	−0.500949	+	1.54176i	0.306526	+	0.951862i	$0.400833\pi$
$631$	−12.5837	+	38.7287i	−0.500949	+	1.54176i	−0.807475	+	0.589902i	$0.799167\pi$
$632$		0			0
$633$	−0.923354	−	2.84179i	−0.0367000	−	0.112951i
$634$		0			0
$635$	2.86042	−	8.80346i	0.113512	−	0.349355i
$636$		0			0
$637$	0.410927	−	1.26470i	0.0162815	−	0.0501094i
$638$		0			0
$639$	−13.7015	−	9.95474i	−0.542024	−	0.393803i
$640$		0			0
$641$	−19.0066	+	13.8091i	−0.750714	+	0.545426i	−0.896048	−	0.443957i	$-0.853574\pi$
$641$	−19.0066	+	13.8091i	−0.750714	+	0.545426i	0.145334	+	0.989383i	$0.453574\pi$
$642$		0			0
$643$	−4.77260	−	14.6886i	−0.188213	−	0.579260i	0.811776	−	0.583969i	$-0.198501\pi$
$643$	−4.77260	−	14.6886i	−0.188213	−	0.579260i	−0.999989	+	0.00470897i	$0.998501\pi$
$644$		0			0
$645$	9.70110	+	7.04826i	0.381980	+	0.277525i
$646$		0			0
$647$	10.3513			0.406950			0.203475	−	0.979080i	$-0.434776\pi$
$647$	10.3513			0.406950			0.203475	+	0.979080i	$0.434776\pi$
$648$		0			0
$649$	1.53364	−	4.72006i	0.0602007	−	0.185279i
$650$		0			0
$651$	−4.50000	+	3.26944i	−0.176369	+	0.128140i
$652$		0			0
$653$	8.31309			0.325316			0.162658	−	0.986682i	$-0.447993\pi$
$653$	8.31309			0.325316			0.162658	+	0.986682i	$0.447993\pi$
$654$		0			0
$655$	−18.2795			−0.714238
$656$		0			0
$657$	−15.3753			−0.599846
$658$		0			0
$659$	−18.2085			−0.709302			−0.354651	−	0.934999i	$-0.615400\pi$
$659$	−18.2085			−0.709302			−0.354651	+	0.934999i	$0.615400\pi$
$660$		0			0
$661$	−0.165000	+	0.119880i	−0.00641776	+	0.00466278i	−0.590990	−	0.806679i	$-0.701263\pi$
$661$	−0.165000	+	0.119880i	−0.00641776	+	0.00466278i	0.584572	+	0.811342i	$0.301263\pi$
$662$		0			0
$663$	−0.707436	+	2.17727i	−0.0274746	+	0.0845580i
$664$		0			0
$665$	16.4372			0.637406
$666$		0			0
$667$	1.17949	+	0.856946i	0.0456699	+	0.0331811i
$668$		0			0
$669$	4.33780	+	13.3504i	0.167709	+	0.516156i
$670$		0			0
$671$	7.92091	−	5.75487i	0.305783	−	0.222164i
$672$		0			0
$673$	−14.3793	−	10.4471i	−0.554280	−	0.402708i	0.275081	−	0.961421i	$-0.411295\pi$
$673$	−14.3793	−	10.4471i	−0.554280	−	0.402708i	−0.829361	+	0.558713i	$0.811295\pi$
$674$		0			0
$675$	1.03735	−	3.19263i	0.0399276	−	0.122885i
$676$		0			0
$677$	−6.63896	+	20.4326i	−0.255156	+	0.785289i	0.738643	+	0.674097i	$0.235467\pi$
$677$	−6.63896	+	20.4326i	−0.255156	+	0.785289i	−0.993799	+	0.111192i	$0.964533\pi$
$678$		0			0
$679$	−0.232782	−	0.716428i	−0.00893334	−	0.0274940i
$680$		0			0
$681$	1.26457	−	3.89196i	0.0484586	−	0.149140i
$682$		0			0
$683$	24.0253			0.919303			0.459652	−	0.888099i	$-0.347974\pi$
$683$	24.0253			0.919303			0.459652	+	0.888099i	$0.347974\pi$
$684$		0			0
$685$	25.4014	−	18.4552i	0.970536	−	0.705136i
$686$		0			0
$687$	2.93963	+	2.13577i	0.112154	+	0.0814846i
$688$		0			0
$689$	7.79886	+	5.66620i	0.297113	+	0.215865i
$690$		0			0
$691$	4.19633	+	12.9150i	0.159636	+	0.491309i	0.998601	−	0.0528761i	$-0.0168389\pi$
$691$	4.19633	+	12.9150i	0.159636	+	0.491309i	−0.838965	+	0.544185i	$0.816839\pi$
$692$		0			0
$693$	−1.79373	+	1.30322i	−0.0681383	+	0.0495054i
$694$		0			0
$695$	4.00251	+	12.3185i	0.151824	+	0.467266i
$696$		0			0
$697$	−13.3857	+	6.35190i	−0.507019	+	0.240595i
$698$		0			0
$699$	−3.02990	−	9.32506i	−0.114601	−	0.352706i
$700$		0			0
$701$	−29.8563	+	21.6919i	−1.12766	+	0.819291i	−0.985352	−	0.170532i	$-0.945451\pi$
$701$	−29.8563	+	21.6919i	−1.12766	+	0.819291i	−0.142305	+	0.989823i	$0.545451\pi$
$702$		0			0
$703$	−24.4920	−	75.3785i	−0.923731	−	2.84295i
$704$		0			0
$705$	−14.8236	−	10.7700i	−0.558290	−	0.405621i
$706$		0			0
$707$	−8.85012	−	6.42999i	−0.332843	−	0.241825i
$708$		0			0
$709$	−26.1746	+	19.0170i	−0.983008	+	0.714197i	−0.958379	−	0.285499i	$-0.907841\pi$
$709$	−26.1746	+	19.0170i	−0.983008	+	0.714197i	−0.0246292	+	0.999697i	$0.507841\pi$
$710$		0			0
$711$	−16.0965			−0.603667
$712$		0			0
$713$	0.941761	−	2.89844i	0.0352692	−	0.108548i
$714$		0			0
$715$	−0.899089	−	2.76711i	−0.0336240	−	0.103484i
$716$		0			0
$717$	3.46358	−	10.6598i	0.129350	−	0.398098i
$718$		0			0
$719$	1.63918	−	5.04487i	0.0611311	−	0.188142i	−0.915827	−	0.401573i	$-0.868464\pi$
$719$	1.63918	−	5.04487i	0.0611311	−	0.188142i	0.976958	+	0.213431i	$0.0684637\pi$
$720$		0			0
$721$	−7.64140	−	5.55180i	−0.284581	−	0.206760i
$722$		0			0
$723$	11.2159	−	8.14885i	0.417125	−	0.303059i
$724$		0			0
$725$	0.915575	+	2.81785i	0.0340036	+	0.104652i
$726$		0			0
$727$	14.7137	+	10.6901i	0.545701	+	0.396475i	0.826198	−	0.563380i	$-0.190499\pi$
$727$	14.7137	+	10.6901i	0.545701	+	0.396475i	−0.280497	+	0.959855i	$0.590499\pi$
$728$		0			0
$729$	−1.53537			−0.0568656
$730$		0			0
$731$	4.77358	−	14.6916i	0.176557	−	0.543387i
$732$		0			0
$733$	30.1976	−	21.9399i	1.11537	−	0.810367i	0.131873	−	0.991267i	$-0.457901\pi$
$733$	30.1976	−	21.9399i	1.11537	−	0.810367i	0.983502	+	0.180899i	$0.0579008\pi$
$734$		0			0
$735$	−1.79618			−0.0662531
$736$		0			0
$737$	−3.41638			−0.125844
$738$		0			0
$739$	35.7565			1.31532			0.657661	−	0.753314i	$-0.271546\pi$
$739$	35.7565			1.31532			0.657661	+	0.753314i	$0.271546\pi$
$740$		0			0
$741$	−6.73609			−0.247456
$742$		0			0
$743$	25.6981	−	18.6708i	0.942774	−	0.684965i	−0.00631314	−	0.999980i	$-0.502010\pi$
$743$	25.6981	−	18.6708i	0.942774	−	0.684965i	0.949087	+	0.315015i	$0.102010\pi$
$744$		0			0
$745$	−3.67675	+	11.3159i	−0.134706	+	0.414582i
$746$		0			0
$747$	12.5764			0.460148
$748$		0			0
$749$	−3.65028	−	2.65208i	−0.133378	−	0.0969051i
$750$		0			0
$751$	3.52691	+	10.8547i	0.128699	+	0.396094i	0.994557	−	0.104196i	$-0.0332269\pi$
$751$	3.52691	+	10.8547i	0.128699	+	0.396094i	−0.865858	+	0.500290i	$0.833227\pi$
$752$		0			0
$753$	−11.9405	+	8.67529i	−0.435137	+	0.316145i
$754$		0			0
$755$	−39.6765	−	28.8267i	−1.44398	−	1.04911i
$756$		0			0
$757$	−1.94666	+	5.99122i	−0.0707527	+	0.217755i	−0.980180	−	0.198108i	$-0.936520\pi$
$757$	−1.94666	+	5.99122i	−0.0707527	+	0.217755i	0.909427	+	0.415863i	$0.136520\pi$
$758$		0			0
$759$	−0.0849369	+	0.261409i	−0.00308301	+	0.00948854i
$760$		0			0
$761$	4.41766	+	13.5962i	0.160140	+	0.492861i	0.998645	−	0.0520328i	$-0.0165700\pi$
$761$	4.41766	+	13.5962i	0.160140	+	0.492861i	−0.838505	+	0.544894i	$0.816570\pi$
$762$		0			0
$763$	−3.52431	+	10.8467i	−0.127589	+	0.392678i
$764$		0			0
$765$	−13.6667			−0.494119
$766$		0			0
$767$	5.89141	−	4.28036i	0.212727	−	0.154555i
$768$		0			0
$769$	31.8936	+	23.1720i	1.15011	+	0.835605i	0.988496	−	0.151249i	$-0.0483295\pi$
$769$	31.8936	+	23.1720i	1.15011	+	0.835605i	0.161616	+	0.986854i	$0.448329\pi$
$770$		0			0
$771$	5.76551	+	4.18889i	0.207640	+	0.150859i
$772$		0			0
$773$	−5.10903	−	15.7240i	−0.183759	−	0.565552i	0.816166	−	0.577818i	$-0.196096\pi$
$773$	−5.10903	−	15.7240i	−0.183759	−	0.565552i	−0.999925	+	0.0122658i	$0.996096\pi$
$774$		0			0
$775$	5.01063	−	3.64044i	0.179987	−	0.130768i
$776$		0			0
$777$	2.67637	+	8.23702i	0.0960143	+	0.295501i
$778$		0			0
$779$	−29.9461	−	31.6830i	−1.07293	−	1.13516i
$780$		0			0
$781$	1.93873	+	5.96680i	0.0693732	+	0.213509i
$782$		0			0
$783$	−11.7247	+	8.51852i	−0.419008	+	0.304427i
$784$		0			0
$785$	7.28888	+	22.4329i	0.260151	+	0.800664i
$786$		0			0
$787$	13.0545	+	9.48467i	0.465344	+	0.338092i	0.795624	−	0.605791i	$-0.207143\pi$
$787$	13.0545	+	9.48467i	0.465344	+	0.338092i	−0.330280	+	0.943883i	$0.607143\pi$
$788$		0			0
$789$	−5.29300	−	3.84559i	−0.188436	−	0.136907i
$790$		0			0
$791$	6.52431	−	4.74019i	0.231978	−	0.168542i
$792$		0			0
$793$	14.3661			0.510154
$794$		0			0
$795$	4.02368	−	12.3836i	0.142705	−	0.439201i
$796$		0			0
$797$	−2.58937	−	7.96926i	−0.0917202	−	0.282286i	0.894665	−	0.446738i	$-0.147414\pi$
$797$	−2.58937	−	7.96926i	−0.0917202	−	0.282286i	−0.986385	+	0.164452i	$0.947414\pi$
$798$		0			0
$799$	−7.29420	+	22.4492i	−0.258050	+	0.794197i
$800$		0			0
$801$	7.29559	−	22.4535i	0.257777	−	0.793356i
$802$		0			0
$803$	4.60791	+	3.34784i	0.162610	+	0.118143i
$804$		0			0
$805$	0.796180	−	0.578458i	0.0280616	−	0.0203880i
$806$		0			0
$807$	−0.557852	−	1.71689i	−0.0196373	−	0.0604374i
$808$		0			0
$809$	−3.66938	−	2.66596i	−0.129009	−	0.0937303i	0.521410	−	0.853307i	$-0.325406\pi$
$809$	−3.66938	−	2.66596i	−0.129009	−	0.0937303i	−0.650418	+	0.759576i	$0.725406\pi$
$810$		0			0
$811$	36.9677			1.29811			0.649056	−	0.760741i	$-0.275164\pi$
$811$	36.9677			1.29811			0.649056	+	0.760741i	$0.275164\pi$
$812$		0			0
$813$	2.88210	−	8.87018i	0.101080	−	0.311091i
$814$		0			0
$815$	−7.29440	+	5.29969i	−0.255512	+	0.185640i
$816$		0			0
$817$	45.4532			1.59021
$818$		0			0
$819$	−3.25328			−0.113679
$820$		0			0
$821$	9.56794			0.333924			0.166962	−	0.985963i	$-0.446604\pi$
$821$	9.56794			0.333924			0.166962	+	0.985963i	$0.446604\pi$
$822$		0			0
$823$	32.6804			1.13917			0.569584	−	0.821933i	$-0.307104\pi$
$823$	32.6804			1.13917			0.569584	+	0.821933i	$0.307104\pi$
$824$		0			0
$825$	−0.451906	+	0.328329i	−0.0157334	+	0.0114309i
$826$		0			0
$827$	−2.05696	+	6.33068i	−0.0715276	+	0.220139i	−0.980429	−	0.196871i	$-0.936922\pi$
$827$	−2.05696	+	6.33068i	−0.0715276	+	0.220139i	0.908902	+	0.417010i	$0.136922\pi$
$828$		0			0
$829$	16.2644			0.564885			0.282443	−	0.959284i	$-0.408855\pi$
$829$	16.2644			0.564885			0.282443	+	0.959284i	$0.408855\pi$
$830$		0			0
$831$	15.6852	+	11.3960i	0.544114	+	0.395322i
$832$		0			0
$833$	0.715041	+	2.20067i	0.0247747	+	0.0762487i
$834$		0			0
$835$	27.0639	−	19.6631i	0.936585	−	0.680469i
$836$		0			0
$837$	24.5091	+	17.8069i	0.847158	+	0.615496i
$838$		0			0
$839$	−3.35668	+	10.3308i	−0.115885	+	0.356659i	−0.992131	−	0.125207i	$-0.960041\pi$
$839$	−3.35668	+	10.3308i	−0.115885	+	0.356659i	0.876245	+	0.481865i	$0.160041\pi$
$840$		0			0
$841$	−5.00877	+	15.4154i	−0.172716	+	0.531566i
$842$		0			0
$843$	−3.93734	−	12.1179i	−0.135609	−	0.417362i
$844$		0			0
$845$	−8.37919	+	25.7885i	−0.288253	+	0.887151i
$846$		0			0
$847$	−10.1787			−0.349743
$848$		0			0
$849$	4.18849	−	3.04312i	0.143749	−	0.104440i
$850$		0			0
$851$	−3.83906	−	2.78924i	−0.131601	−	0.0956140i
$852$		0			0
$853$	19.1065	+	13.8817i	0.654196	+	0.475301i	0.864698	−	0.502292i	$-0.167510\pi$
$853$	19.1065	+	13.8817i	0.654196	+	0.475301i	−0.210502	+	0.977593i	$0.567510\pi$
$854$		0			0
$855$	−12.4265	−	38.2447i	−0.424976	−	1.30794i
$856$		0			0
$857$	33.3729	−	24.2468i	1.14000	−	0.828256i	0.152878	−	0.988245i	$-0.451146\pi$
$857$	33.3729	−	24.2468i	1.14000	−	0.828256i	0.987119	+	0.159989i	$0.0511457\pi$
$858$		0			0
$859$	−7.14015	−	21.9751i	−0.243619	−	0.749782i	−0.995861	−	0.0908945i	$-0.971027\pi$
$859$	−7.14015	−	21.9751i	−0.243619	−	0.749782i	0.752242	−	0.658887i	$-0.228973\pi$
$860$		0			0
$861$	3.27238	+	3.46217i	0.111522	+	0.117991i
$862$		0			0
$863$	−9.90945	−	30.4981i	−0.337322	−	1.03817i	−0.965567	−	0.260154i	$-0.916227\pi$
$863$	−9.90945	−	30.4981i	−0.337322	−	1.03817i	0.628246	−	0.778015i	$-0.283773\pi$
$864$		0			0
$865$	19.7992	−	14.3850i	0.673193	−	0.489103i
$866$		0			0
$867$	2.67747	+	8.24041i	0.0909317	+	0.279859i
$868$		0			0
$869$	4.82407	+	3.50489i	0.163645	+	0.118895i
$870$		0			0
$871$	−4.05550	−	2.94649i	−0.137415	−	0.0998381i
$872$		0			0
$873$	−1.49095	+	1.08324i	−0.0504609	+	0.0366620i
$874$		0			0
$875$	−10.0711			−0.340464
$876$		0			0
$877$	9.28470	−	28.5754i	0.313522	−	0.964921i	−0.662837	−	0.748764i	$-0.730648\pi$
$877$	9.28470	−	28.5754i	0.313522	−	0.964921i	0.976359	−	0.216157i	$-0.0693524\pi$
$878$		0			0
$879$	7.25258	+	22.3211i	0.244623	+	0.752873i
$880$		0			0
$881$	−15.8100	+	48.6581i	−0.532651	+	1.63933i	0.216019	+	0.976389i	$0.430693\pi$
$881$	−15.8100	+	48.6581i	−0.532651	+	1.63933i	−0.748670	+	0.662943i	$0.769307\pi$
$882$		0			0
$883$	−13.3400	+	41.0563i	−0.448927	+	1.38165i	0.429193	+	0.903213i	$0.358798\pi$
$883$	−13.3400	+	41.0563i	−0.448927	+	1.38165i	−0.878119	+	0.478442i	$0.841202\pi$
$884$		0			0
$885$	−7.95768	−	5.78159i	−0.267495	−	0.194346i
$886$		0			0
$887$	−3.28142	+	2.38409i	−0.110179	+	0.0800499i	−0.641511	−	0.767114i	$-0.721692\pi$
$887$	−3.28142	+	2.38409i	−0.110179	+	0.0800499i	0.531331	+	0.847164i	$0.321692\pi$
$888$		0			0
$889$	1.18482	+	3.64651i	0.0397377	+	0.122300i
$890$		0			0
$891$	3.17074	+	2.30368i	0.106224	+	0.0771762i
$892$		0			0
$893$	−69.4541			−2.32419
$894$		0			0
$895$	−2.45992	+	7.57084i	−0.0822259	+	0.253065i
$896$		0			0
$897$	−0.326281	+	0.237057i	−0.0108942	+	0.00791511i
$898$		0			0
$899$	−26.7386			−0.891781
$900$		0			0
$901$	−16.7741			−0.558826
$902$		0			0
$903$	−4.96692			−0.165289
$904$		0			0
$905$	14.8261			0.492837
$906$		0			0
$907$	−41.5794	+	30.2092i	−1.38062	+	1.00308i	−0.383798	+	0.923417i	$0.625384\pi$
$907$	−41.5794	+	30.2092i	−1.38062	+	1.00308i	−0.996822	+	0.0796624i	$0.974616\pi$
$908$		0			0
$909$	−8.27013	+	25.4528i	−0.274303	+	0.844218i
$910$		0			0
$911$	7.15643			0.237103			0.118552	−	0.992948i	$-0.462175\pi$
$911$	7.15643			0.237103			0.118552	+	0.992948i	$0.462175\pi$
$912$		0			0
$913$	−3.76911	−	2.73842i	−0.124739	−	0.0906285i
$914$		0			0
$915$	−5.99635	−	18.4549i	−0.198233	−	0.610099i
$916$		0			0
$917$	6.12555	−	4.45048i	0.202284	−	0.146968i
$918$		0			0
$919$	22.8973	+	16.6359i	0.755313	+	0.548767i	0.897469	−	0.441077i	$-0.145404\pi$
$919$	22.8973	+	16.6359i	0.755313	+	0.548767i	−0.142156	+	0.989844i	$0.545404\pi$
$920$		0			0
$921$	2.93447	−	9.03138i	0.0966942	−	0.297594i
$922$		0			0
$923$	−2.84471	+	8.75511i	−0.0936347	+	0.288178i
$924$		0			0
$925$	−2.98007	−	9.17171i	−0.0979841	−	0.301564i
$926$		0			0
$927$	−7.14062	+	21.9766i	−0.234529	+	0.721805i
$928$		0			0
$929$	−45.3018			−1.48631			−0.743153	−	0.669122i	$-0.766670\pi$
$929$	−45.3018			−1.48631			−0.743153	+	0.669122i	$0.766670\pi$
$930$		0			0
$931$	−5.50819	+	4.00193i	−0.180524	+	0.131158i
$932$		0			0
$933$	−20.0915	−	14.5973i	−0.657766	−	0.477895i
$934$		0			0
$935$	4.09585	+	2.97581i	0.133949	+	0.0973193i
$936$		0			0
$937$	−11.2538	−	34.6356i	−0.367646	−	1.13150i	−0.948308	−	0.317352i	$-0.897206\pi$
$937$	−11.2538	−	34.6356i	−0.367646	−	1.13150i	0.580662	−	0.814145i	$-0.302794\pi$
$938$		0			0
$939$	−9.16502	+	6.65878i	−0.299089	+	0.217301i
$940$		0			0
$941$	4.36065	+	13.4207i	0.142153	+	0.437502i	0.996634	−	0.0819808i	$-0.0261246\pi$
$941$	4.36065	+	13.4207i	0.142153	+	0.437502i	−0.854481	+	0.519483i	$0.826125\pi$
$942$		0			0
$943$	−2.56551	−	0.480785i	−0.0835446	−	0.0156565i
$944$		0			0
$945$	3.02306	+	9.30402i	0.0983401	+	0.302660i
$946$		0			0
$947$	−29.6712	+	21.5574i	−0.964184	+	0.700521i	−0.954119	−	0.299428i	$-0.903204\pi$
$947$	−29.6712	+	21.5574i	−0.964184	+	0.700521i	−0.0100655	+	0.999949i	$0.503204\pi$
$948$		0			0
$949$	2.58255	+	7.94828i	0.0838332	+	0.258012i
$950$		0			0
$951$	8.26981	+	6.00837i	0.268167	+	0.194835i
$952$		0			0
$953$	1.29584	+	0.941480i	0.0419763	+	0.0304975i	0.608576	−	0.793496i	$-0.291741\pi$
$953$	1.29584	+	0.941480i	0.0419763	+	0.0304975i	−0.566599	+	0.823993i	$0.691741\pi$
$954$		0			0
$955$	52.2278	−	37.9457i	1.69005	−	1.22790i
$956$		0			0
$957$	2.41153			0.0779538
$958$		0			0
$959$	−4.01889	+	12.3689i	−0.129777	+	0.399412i
$960$		0			0
$961$	7.69253	+	23.6752i	0.248146	+	0.763715i
$962$		0			0
$963$	−3.41106	+	10.4982i	−0.109920	+	0.338299i
$964$		0			0
$965$	−10.9728	+	33.7708i	−0.353227	+	1.08712i
$966$		0			0
$967$	−25.6746	−	18.6537i	−0.825641	−	0.599863i	0.0926819	−	0.995696i	$-0.470456\pi$
$967$	−25.6746	−	18.6537i	−0.825641	−	0.599863i	−0.918323	+	0.395833i	$0.870456\pi$
$968$		0			0
$969$	9.48269	−	6.88957i	0.304628	−	0.221325i
$970$		0			0
$971$	13.9268	+	42.8623i	0.446932	+	1.37552i	0.880351	+	0.474323i	$0.157307\pi$
$971$	13.9268	+	42.8623i	0.446932	+	1.37552i	−0.433419	+	0.901193i	$0.642693\pi$
$972$		0			0
$973$	−4.34042	−	3.15350i	−0.139148	−	0.101097i
$974$		0			0
$975$	−0.819617			−0.0262487
$976$		0			0
$977$	3.71331	−	11.4284i	0.118799	−	0.365626i	−0.873921	−	0.486067i	$-0.838431\pi$
$977$	3.71331	−	11.4284i	0.118799	−	0.365626i	0.992720	+	0.120441i	$0.0384309\pi$
$978$		0			0
$979$	−7.07554	+	5.14068i	−0.226135	+	0.164297i
$980$		0			0
$981$	27.9017			0.890832
$982$		0			0
$983$	1.26624			0.0403866			0.0201933	−	0.999796i	$-0.493572\pi$
$983$	1.26624			0.0403866			0.0201933	+	0.999796i	$0.493572\pi$
$984$		0			0
$985$	−38.4047			−1.22368
$986$		0			0
$987$	7.58964			0.241581
$988$		0			0
$989$	2.20165	−	1.59959i	0.0700085	−	0.0508641i
$990$		0			0
$991$	−7.50432	+	23.0959i	−0.238383	+	0.733666i	0.758272	+	0.651938i	$0.226044\pi$
$991$	−7.50432	+	23.0959i	−0.238383	+	0.733666i	−0.996655	+	0.0817278i	$0.973956\pi$
$992$		0			0
$993$	16.9668			0.538424
$994$		0			0
$995$	−44.4356	−	32.2844i	−1.40870	−	1.02348i
$996$		0			0
$997$	−3.26818	−	10.0584i	−0.103504	−	0.318554i	0.885872	−	0.463930i	$-0.153561\pi$
$997$	−3.26818	−	10.0584i	−0.103504	−	0.318554i	−0.989377	+	0.145376i	$0.953561\pi$
$998$		0			0
$999$	38.1624	−	27.7266i	1.20741	−	0.877231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.a.141.2	yes	8
41.16	even	5	inner	1148.2.n.a.57.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.a.57.2	✓	8	41.16	even	5	inner
1148.2.n.a.141.2	yes	8	1.1	even	1	trivial

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.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-0.744002 q^{3} +(-1.95314 + 1.41904i) q^{5} +(0.309017 - 0.951057i) q^{7} -2.44646 q^{9} +O(q^{10})\)	\(q-0.744002 q^{3} +(-1.95314 + 1.41904i) q^{5} +(0.309017 - 0.951057i) q^{7} -2.44646 q^{9} +(0.733196 + 0.532698i) q^{11} +(0.410927 + 1.26470i) q^{13} +(1.45314 - 1.05577i) q^{15} +(-1.87200 - 1.36009i) q^{17} +(2.10394 - 6.47527i) q^{19} +(-0.229909 + 0.707588i) q^{21} +(-0.125968 - 0.387689i) q^{23} +(0.255998 - 0.787881i) q^{25} +4.05218 q^{27} +(-2.89344 + 2.10221i) q^{29} +(6.04837 + 4.39440i) q^{31} +(-0.545499 - 0.396328i) q^{33} +(0.746033 + 2.29605i) q^{35} +(9.41776 - 6.84240i) q^{37} +(-0.305731 - 0.940942i) q^{39} +(3.06653 - 5.62107i) q^{41} +(2.06298 + 6.34921i) q^{43} +(4.77828 - 3.47162i) q^{45} +(-3.15231 - 9.70182i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(1.39277 + 1.01191i) q^{51} +(5.86474 - 4.26098i) q^{53} -2.18795 q^{55} +(-1.56534 + 4.81761i) q^{57} +(-1.69224 - 5.20817i) q^{59} +(3.33839 - 10.2745i) q^{61} +(-0.755998 + 2.32672i) q^{63} +(-2.59726 - 1.88702i) q^{65} +(-3.04973 + 2.21576i) q^{67} +(0.0937204 + 0.288442i) q^{69} +(5.60055 + 4.06904i) q^{71} +6.28470 q^{73} +(-0.190463 + 0.586185i) q^{75} +(0.733196 - 0.532698i) q^{77} +6.57951 q^{79} +4.32456 q^{81} -5.14066 q^{83} +5.58630 q^{85} +(2.15273 - 1.56405i) q^{87} +(-2.98210 + 9.17796i) q^{89} +1.32979 q^{91} +(-4.50000 - 3.26944i) q^{93} +(5.07936 + 15.6327i) q^{95} +(0.609430 - 0.442777i) q^{97} +(-1.79373 - 1.30322i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 2 q^{5} - 2 q^{7} + 12 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 - 2 * q^5 - 2 * q^7 + 12 * q^9	\( 8 q - 4 q^{3} - 2 q^{5} - 2 q^{7} + 12 q^{9} - 2 q^{15} - 14 q^{17} + 12 q^{19} - 4 q^{21} - 8 q^{23} + 4 q^{25} + 32 q^{27} + 2 q^{29} + 18 q^{31} + 14 q^{33} - 2 q^{35} + 14 q^{37} - 6 q^{39} - 22 q^{41} + 20 q^{43} + 10 q^{45} + 10 q^{47} - 2 q^{49} + 24 q^{51} - 8 q^{53} + 12 q^{55} + 34 q^{57} - 16 q^{59} + 14 q^{61} - 8 q^{63} + 2 q^{65} - 26 q^{67} + 28 q^{69} + 14 q^{71} - 40 q^{73} + 32 q^{75} - 72 q^{79} - 16 q^{81} - 8 q^{83} - 28 q^{85} - 14 q^{87} + 2 q^{89} + 20 q^{91} - 36 q^{93} - 8 q^{95} + 18 q^{97} - 14 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 - 2 * q^5 - 2 * q^7 + 12 * q^9 - 2 * q^15 - 14 * q^17 + 12 * q^19 - 4 * q^21 - 8 * q^23 + 4 * q^25 + 32 * q^27 + 2 * q^29 + 18 * q^31 + 14 * q^33 - 2 * q^35 + 14 * q^37 - 6 * q^39 - 22 * q^41 + 20 * q^43 + 10 * q^45 + 10 * q^47 - 2 * q^49 + 24 * q^51 - 8 * q^53 + 12 * q^55 + 34 * q^57 - 16 * q^59 + 14 * q^61 - 8 * q^63 + 2 * q^65 - 26 * q^67 + 28 * q^69 + 14 * q^71 - 40 * q^73 + 32 * q^75 - 72 * q^79 - 16 * q^81 - 8 * q^83 - 28 * q^85 - 14 * q^87 + 2 * q^89 + 20 * q^91 - 36 * q^93 - 8 * q^95 + 18 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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