LMFDB - Embedded newform 1008.2.q.g.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(529,1008)]

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, 4, 4]))

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

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

chi := DirichletCharacter("1008.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.q (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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.1
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	1008.529
Dual form			1008.2.q.g.625.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.71053 - 0.272169i) q^{3} +(1.59097 - 2.75564i) q^{5} +(2.56238 - 0.658939i) q^{7} +(2.85185 + 0.931107i) q^{9} +(1.59097 + 2.75564i) q^{11} +(2.85185 + 4.93955i) q^{13} +(-3.47141 + 4.28061i) q^{15} +(-0.760877 + 1.31788i) q^{17} +(0.641315 + 1.11079i) q^{19} +(-4.56238 + 0.429736i) q^{21} +(1.11956 - 1.93914i) q^{23} +(-2.56238 - 4.43818i) q^{25} +(-4.62476 - 2.36887i) q^{27} +(-3.54063 + 6.13255i) q^{29} +9.42107 q^{31} +(-1.97141 - 5.14663i) q^{33} +(2.26088 - 8.10936i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-3.53379 - 9.22544i) q^{39} +(-2.80150 - 4.85235i) q^{41} +(-3.41423 + 5.91362i) q^{43} +(7.10301 - 6.37731i) q^{45} +5.82846 q^{47} +(6.13160 - 3.37690i) q^{49} +(1.66019 - 2.04719i) q^{51} +(1.02859 - 1.78157i) q^{53} +10.1248 q^{55} +(-0.794668 - 2.07459i) q^{57} +1.12476 q^{59} +3.12476 q^{61} +(7.92107 + 0.506659i) q^{63} +18.1488 q^{65} -10.9669 q^{67} +(-2.44282 + 3.01225i) q^{69} -8.69002 q^{71} +(-2.48345 + 4.30146i) q^{73} +(3.17511 + 8.28905i) q^{75} +(5.89248 + 6.01266i) q^{77} +4.13844 q^{79} +(7.26608 + 5.31075i) q^{81} +(4.03379 - 6.98673i) q^{83} +(2.42107 + 4.19341i) q^{85} +(7.72545 - 9.52628i) q^{87} +(0.112725 + 0.195246i) q^{89} +(10.5624 + 10.7778i) q^{91} +(-16.1150 - 2.56412i) q^{93} +4.08126 q^{95} +(7.42107 - 12.8537i) q^{97} +(1.97141 + 9.34004i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{3} + q^{5} - 2 q^{7} + 8 q^{9} + q^{11} + 8 q^{13} - 12 q^{15} - 4 q^{17} + 3 q^{19} - 10 q^{21} + 7 q^{23} + 2 q^{25} + 7 q^{27} - 5 q^{29} + 40 q^{31} - 3 q^{33} + 13 q^{35} + 3 q^{37} + 5 q^{39}+ \cdots + 3 q^{99}+O(q^{100}) $ 6 * q - 2 * q^3 + q^5 - 2 * q^7 + 8 * q^9 + q^11 + 8 * q^13 - 12 * q^15 - 4 * q^17 + 3 * q^19 - 10 * q^21 + 7 * q^23 + 2 * q^25 + 7 * q^27 - 5 * q^29 + 40 * q^31 - 3 * q^33 + 13 * q^35 + 3 * q^37 + 5 * q^39 + 6 * q^43 + 9 * q^45 - 18 * q^47 + 12 * q^49 - 6 * q^51 + 15 * q^53 + 26 * q^55 + 22 * q^57 - 28 * q^59 - 16 * q^61 + 31 * q^63 + 24 * q^65 + 2 * q^67 + 3 * q^69 - 14 * q^71 + 19 * q^73 - 8 * q^75 + 10 * q^77 + 10 * q^79 + 8 * q^81 - 2 * q^83 - 2 * q^85 + 27 * q^87 - 9 * q^89 + 46 * q^91 - 38 * q^93 - 8 * q^95 + 28 * q^97 + 3 * q^99

Character values

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

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.71053	−	0.272169i	−0.987577	−	0.157137i
$3$	−1.71053	−	0.272169i	−0.987577	−	0.157137i
$4$		0			0
$5$	1.59097	−	2.75564i	0.711504	−	1.23236i	−0.252788	−	0.967522i	$-0.581348\pi$
$5$	1.59097	−	2.75564i	0.711504	−	1.23236i	0.964292	−	0.264840i	$-0.0853191\pi$
$6$		0			0
$7$	2.56238	−	0.658939i	0.968489	−	0.249055i
$7$	2.56238	−	0.658939i	0.968489	−	0.249055i
$8$		0			0
$9$	2.85185	+	0.931107i	0.950616	+	0.310369i
$10$		0			0
$11$	1.59097	+	2.75564i	0.479696	+	0.830858i	0.999729	−	0.0232884i	$-0.00741361\pi$
$11$	1.59097	+	2.75564i	0.479696	+	0.830858i	−0.520033	+	0.854146i	$0.674080\pi$
$12$		0			0
$13$	2.85185	+	4.93955i	0.790960	+	1.36998i	0.925373	+	0.379058i	$0.123752\pi$
$13$	2.85185	+	4.93955i	0.790960	+	1.36998i	−0.134412	+	0.990925i	$0.542915\pi$
$14$		0			0
$15$	−3.47141	+	4.28061i	−0.896314	+	1.10525i
$16$		0			0
$17$	−0.760877	+	1.31788i	−0.184540	+	0.319632i	−0.943421	−	0.331596i	$-0.892413\pi$
$17$	−0.760877	+	1.31788i	−0.184540	+	0.319632i	0.758882	+	0.651229i	$0.225746\pi$
$18$		0			0
$19$	0.641315	+	1.11079i	0.147128	+	0.254833i	0.930165	−	0.367142i	$-0.119664\pi$
$19$	0.641315	+	1.11079i	0.147128	+	0.254833i	−0.783037	+	0.621975i	$0.786330\pi$
$20$		0			0
$21$	−4.56238	+	0.429736i	−0.995593	+	0.0937761i
$22$		0			0
$23$	1.11956	−	1.93914i	0.233445	−	0.404338i	−0.725375	−	0.688354i	$-0.758334\pi$
$23$	1.11956	−	1.93914i	0.233445	−	0.404338i	0.958820	+	0.284016i	$0.0916669\pi$
$24$		0			0
$25$	−2.56238	−	4.43818i	−0.512476	−	0.887635i
$26$		0			0
$27$	−4.62476	−	2.36887i	−0.890036	−	0.455890i
$28$		0			0
$29$	−3.54063	+	6.13255i	−0.657478	+	1.13879i	0.323788	+	0.946130i	$0.395043\pi$
$29$	−3.54063	+	6.13255i	−0.657478	+	1.13879i	−0.981266	+	0.192656i	$0.938290\pi$
$30$		0			0
$31$	9.42107			1.69207			0.846037	−	0.533125i	$-0.178982\pi$
$31$	9.42107			1.69207			0.846037	+	0.533125i	$0.178982\pi$
$32$		0			0
$33$	−1.97141	−	5.14663i	−0.343178	−	0.895914i
$34$		0			0
$35$	2.26088	−	8.10936i	0.382158	−	1.37073i
$36$		0			0
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$		0			0
$39$	−3.53379	−	9.22544i	−0.565860	−	1.47725i
$40$		0			0
$41$	−2.80150	−	4.85235i	−0.437522	−	0.757810i	0.559976	−	0.828509i	$-0.310810\pi$
$41$	−2.80150	−	4.85235i	−0.437522	−	0.757810i	−0.997498	+	0.0706992i	$0.977477\pi$
$42$		0			0
$43$	−3.41423	+	5.91362i	−0.520665	+	0.901819i	0.479046	+	0.877790i	$0.340983\pi$
$43$	−3.41423	+	5.91362i	−0.520665	+	0.901819i	−0.999711	+	0.0240288i	$0.992351\pi$
$44$		0			0
$45$	7.10301	−	6.37731i	1.05885	−	0.950674i
$46$		0			0
$47$	5.82846			0.850168			0.425084	−	0.905154i	$-0.360245\pi$
$47$	5.82846			0.850168			0.425084	+	0.905154i	$0.360245\pi$
$48$		0			0
$49$	6.13160	−	3.37690i	0.875943	−	0.482415i
$50$		0			0
$51$	1.66019	−	2.04719i	0.232473	−	0.286663i
$52$		0			0
$53$	1.02859	−	1.78157i	0.141288	−	0.244717i	−0.786694	−	0.617343i	$-0.788209\pi$
$53$	1.02859	−	1.78157i	0.141288	−	0.244717i	0.927982	+	0.372626i	$0.121542\pi$
$54$		0			0
$55$	10.1248			1.36522
$56$		0			0
$57$	−0.794668	−	2.07459i	−0.105256	−	0.274786i
$58$		0			0
$59$	1.12476			0.146432			0.0732159	−	0.997316i	$-0.476674\pi$
$59$	1.12476			0.146432			0.0732159	+	0.997316i	$0.476674\pi$
$60$		0			0
$61$	3.12476			0.400085			0.200042	−	0.979787i	$-0.435892\pi$
$61$	3.12476			0.400085			0.200042	+	0.979787i	$0.435892\pi$
$62$		0			0
$63$	7.92107	+	0.506659i	0.997961	+	0.0638331i
$64$		0			0
$65$	18.1488			2.25109
$66$		0			0
$67$	−10.9669			−1.33982			−0.669910	−	0.742442i	$-0.733667\pi$
$67$	−10.9669			−1.33982			−0.669910	+	0.742442i	$0.733667\pi$
$68$		0			0
$69$	−2.44282	+	3.01225i	−0.294081	+	0.362632i
$70$		0			0
$71$	−8.69002			−1.03132			−0.515658	−	0.856794i	$-0.672452\pi$
$71$	−8.69002			−1.03132			−0.515658	+	0.856794i	$0.672452\pi$
$72$		0			0
$73$	−2.48345	+	4.30146i	−0.290666	+	0.503448i	−0.973967	−	0.226689i	$-0.927210\pi$
$73$	−2.48345	+	4.30146i	−0.290666	+	0.503448i	0.683302	+	0.730136i	$0.260543\pi$
$74$		0			0
$75$	3.17511	+	8.28905i	0.366630	+	0.957137i
$76$		0			0
$77$	5.89248	+	6.01266i	0.671510	+	0.685206i
$78$		0			0
$79$	4.13844			0.465610			0.232805	−	0.972523i	$-0.425210\pi$
$79$	4.13844			0.465610			0.232805	+	0.972523i	$0.425210\pi$
$80$		0			0
$81$	7.26608	+	5.31075i	0.807342	+	0.590084i
$82$		0			0
$83$	4.03379	−	6.98673i	0.442766	−	0.766893i	−0.555127	−	0.831765i	$-0.687331\pi$
$83$	4.03379	−	6.98673i	0.442766	−	0.766893i	0.997894	+	0.0648718i	$0.0206639\pi$
$84$		0			0
$85$	2.42107	+	4.19341i	0.262602	+	0.454839i
$86$		0			0
$87$	7.72545	−	9.52628i	0.828255	−	1.02132i
$88$		0			0
$89$	0.112725	+	0.195246i	0.0119488	+	0.0206960i	0.871938	−	0.489616i	$-0.162863\pi$
$89$	0.112725	+	0.195246i	0.0119488	+	0.0206960i	−0.859989	+	0.510312i	$0.829530\pi$
$90$		0			0
$91$	10.5624	+	10.7778i	1.10724	+	1.12982i
$92$		0			0
$93$	−16.1150	−	2.56412i	−1.67105	−	0.265887i
$94$		0			0
$95$	4.08126			0.418728
$96$		0			0
$97$	7.42107	−	12.8537i	0.753495	−	1.30509i	−0.192624	−	0.981273i	$-0.561700\pi$
$97$	7.42107	−	12.8537i	0.753495	−	1.30509i	0.946119	−	0.323819i	$-0.104967\pi$
$98$		0			0
$99$	1.97141	+	9.34004i	0.198134	+	0.938710i
$100$		0			0
$101$	−9.29467	−	16.0988i	−0.924854	−	1.60189i	−0.791796	−	0.610786i	$-0.790854\pi$
$101$	−9.29467	−	16.0988i	−0.924854	−	1.60189i	−0.133058	−	0.991108i	$-0.542480\pi$
$102$		0			0
$103$	−0.141315	+	0.244765i	−0.0139242	+	0.0241174i	−0.872904	−	0.487893i	$-0.837766\pi$
$103$	−0.141315	+	0.244765i	−0.0139242	+	0.0241174i	0.858979	+	0.512010i	$0.171099\pi$
$104$		0			0
$105$	−6.07442	+	13.2560i	−0.592803	+	1.29365i
$106$		0			0
$107$	−5.68878	−	9.85326i	−0.549955	−	0.952550i	−0.998277	−	0.0586780i	$-0.981311\pi$
$107$	−5.68878	−	9.85326i	−0.549955	−	0.952550i	0.448322	−	0.893872i	$-0.352022\pi$
$108$		0			0
$109$	−2.21053	+	3.82876i	−0.211731	+	0.366728i	−0.952256	−	0.305300i	$-0.901243\pi$
$109$	−2.21053	+	3.82876i	−0.211731	+	0.366728i	0.740526	+	0.672028i	$0.234577\pi$
$110$		0			0
$111$	−0.619562	−	1.61745i	−0.0588062	−	0.153522i
$112$		0			0
$113$	−1.60752	−	2.78431i	−0.151223	−	0.261926i	0.780454	−	0.625213i	$-0.214988\pi$
$113$	−1.60752	−	2.78431i	−0.151223	−	0.261926i	−0.931677	+	0.363287i	$0.881655\pi$
$114$		0			0
$115$	−3.56238	−	6.17023i	−0.332194	−	0.575377i
$116$		0			0
$117$	3.53379	+	16.7422i	0.326699	+	1.54782i
$118$		0			0
$119$	−1.08126	+	3.87828i	−0.0991186	+	0.355521i
$120$		0			0
$121$	0.437618	−	0.757977i	0.0397835	−	0.0689070i
$122$		0			0
$123$	3.47141	+	9.06259i	0.313007	+	0.817146i
$124$		0			0
$125$	−0.396990			−0.0355079
$126$		0			0
$127$	−20.1053			−1.78406			−0.892030	−	0.451976i	$-0.850719\pi$
$127$	−20.1053			−1.78406			−0.892030	+	0.451976i	$0.850719\pi$
$128$		0			0
$129$	7.44966	−	9.18620i	0.655906	−	0.808800i
$130$		0			0
$131$	3.18194	−	5.51129i	0.278008	−	0.481523i	−0.692882	−	0.721051i	$-0.743659\pi$
$131$	3.18194	−	5.51129i	0.278008	−	0.481523i	0.970890	+	0.239528i	$0.0769926\pi$
$132$		0			0
$133$	2.37524	+	2.42368i	0.205959	+	0.210160i
$134$		0			0
$135$	−13.8856	+	8.97539i	−1.19509	+	0.772479i
$136$		0			0
$137$	−1.37072	−	2.37416i	−0.117109	−	0.202838i	0.801512	−	0.597979i	$-0.204029\pi$
$137$	−1.37072	−	2.37416i	−0.117109	−	0.202838i	−0.918621	+	0.395140i	$0.870696\pi$
$138$		0			0
$139$	3.98345	+	6.89953i	0.337872	+	0.585211i	0.984032	−	0.177991i	$-0.0569597\pi$
$139$	3.98345	+	6.89953i	0.337872	+	0.585211i	−0.646161	+	0.763202i	$0.723626\pi$
$140$		0			0
$141$	−9.96978	−	1.58632i	−0.839607	−	0.133593i
$142$		0			0
$143$	−9.07442	+	15.7174i	−0.758841	+	1.31435i
$144$		0			0
$145$	11.2661	+	19.5134i	0.935597	+	1.62050i
$146$		0			0
$147$	−11.4074	+	4.10748i	−0.940866	+	0.338779i
$148$		0			0
$149$	11.6300	−	20.1437i	0.952764	−	1.65024i	0.213360	−	0.976974i	$-0.431559\pi$
$149$	11.6300	−	20.1437i	0.952764	−	1.65024i	0.739404	−	0.673262i	$-0.235107\pi$
$150$		0			0
$151$	−4.06238	−	7.03625i	−0.330592	−	0.572602i	0.652036	−	0.758188i	$-0.273915\pi$
$151$	−4.06238	−	7.03625i	−0.330592	−	0.572602i	−0.982628	+	0.185586i	$0.940582\pi$
$152$		0			0
$153$	−3.39699	+	3.04993i	−0.274630	+	0.246572i
$154$		0			0
$155$	14.9887	−	25.9611i	1.20392	−	2.08525i
$156$		0			0
$157$	−11.2632			−0.898901			−0.449451	−	0.893305i	$-0.648380\pi$
$157$	−11.2632			−0.898901			−0.449451	+	0.893305i	$0.648380\pi$
$158$		0			0
$159$	−2.24433	+	2.76748i	−0.177987	+	0.219476i
$160$		0			0
$161$	1.59097	−	5.70653i	0.125386	−	0.449738i
$162$		0			0
$163$	1.99028	+	3.44727i	0.155891	+	0.270011i	0.933383	−	0.358881i	$-0.116842\pi$
$163$	1.99028	+	3.44727i	0.155891	+	0.270011i	−0.777492	+	0.628893i	$0.783508\pi$
$164$		0			0
$165$	−17.3187	−	2.75564i	−1.34826	−	0.214527i
$166$		0			0
$167$	−2.61956	−	4.53721i	−0.202708	−	0.351100i	0.746692	−	0.665170i	$-0.231641\pi$
$167$	−2.61956	−	4.53721i	−0.202708	−	0.351100i	−0.949400	+	0.314070i	$0.898307\pi$
$168$		0			0
$169$	−9.76608	+	16.9153i	−0.751237	+	1.30118i
$170$		0			0
$171$	0.794668	+	3.76494i	0.0607698	+	0.287912i
$172$		0			0
$173$	2.55159			0.193994			0.0969968	−	0.995285i	$-0.469076\pi$
$173$	2.55159			0.193994			0.0969968	+	0.995285i	$0.469076\pi$
$174$		0			0
$175$	−9.49028	−	9.68385i	−0.717398	−	0.732030i
$176$		0			0
$177$	−1.92395	−	0.306125i	−0.144613	−	0.0230098i
$178$		0			0
$179$	−3.51887	+	6.09487i	−0.263013	+	0.455552i	−0.967041	−	0.254620i	$-0.918050\pi$
$179$	−3.51887	+	6.09487i	−0.263013	+	0.455552i	0.704028	+	0.710172i	$0.251383\pi$
$180$		0			0
$181$	−12.9669			−0.963822			−0.481911	−	0.876220i	$-0.660057\pi$
$181$	−12.9669			−0.963822			−0.481911	+	0.876220i	$0.660057\pi$
$182$		0			0
$183$	−5.34501	−	0.850463i	−0.395115	−	0.0628680i
$184$		0			0
$185$	3.18194			0.233941
$186$		0			0
$187$	−4.84213			−0.354092
$188$		0			0
$189$	−13.4114	−	3.02252i	−0.975532	−	0.219856i
$190$		0			0
$191$	−1.98057			−0.143309			−0.0716545	−	0.997430i	$-0.522828\pi$
$191$	−1.98057			−0.143309			−0.0716545	+	0.997430i	$0.522828\pi$
$192$		0			0
$193$	−4.54583			−0.327216			−0.163608	−	0.986525i	$-0.552313\pi$
$193$	−4.54583			−0.327216			−0.163608	+	0.986525i	$0.552313\pi$
$194$		0			0
$195$	−31.0442	−	4.93955i	−2.22312	−	0.353728i
$196$		0			0
$197$	−21.8148			−1.55424			−0.777120	−	0.629353i	$-0.783320\pi$
$197$	−21.8148			−1.55424			−0.777120	+	0.629353i	$0.783320\pi$
$198$		0			0
$199$	−6.14132	+	10.6371i	−0.435346	+	0.754042i	−0.997324	−	0.0731106i	$-0.976707\pi$
$199$	−6.14132	+	10.6371i	−0.435346	+	0.754042i	0.561978	+	0.827152i	$0.310041\pi$
$200$		0			0
$201$	18.7592	+	2.98485i	1.32317	+	0.210535i
$202$		0			0
$203$	−5.03147	+	18.0470i	−0.353140	+	1.26665i
$204$		0			0
$205$	−17.8285			−1.24519
$206$		0			0
$207$	4.99837	−	4.48769i	0.347410	−	0.311916i
$208$		0			0
$209$	−2.04063	+	3.53447i	−0.141153	+	0.244485i
$210$		0			0
$211$	8.32846	+	14.4253i	0.573355	+	0.993080i	0.996218	+	0.0868863i	$0.0276917\pi$
$211$	8.32846	+	14.4253i	0.573355	+	0.993080i	−0.422863	+	0.906193i	$0.638975\pi$
$212$		0			0
$213$	14.8646	+	2.36515i	1.01850	+	0.162058i
$214$		0			0
$215$	10.8639	+	18.8168i	0.740911	+	1.28330i
$216$		0			0
$217$	24.1404	−	6.20790i	1.63876	−	0.421420i
$218$		0			0
$219$	5.41874	−	6.68187i	0.366165	−	0.451519i
$220$		0			0
$221$	−8.67962			−0.583854
$222$		0			0
$223$	5.32846	−	9.22916i	0.356820	−	0.618031i	−0.630608	−	0.776102i	$-0.717194\pi$
$223$	5.32846	−	9.22916i	0.356820	−	0.618031i	0.987428	+	0.158071i	$0.0505276\pi$
$224$		0			0
$225$	−3.17511	−	15.0429i	−0.211674	−	1.00286i
$226$		0			0
$227$	−7.25404	−	12.5644i	−0.481468	−	0.833926i	0.518306	−	0.855195i	$-0.326563\pi$
$227$	−7.25404	−	12.5644i	−0.481468	−	0.833926i	−0.999774	+	0.0212688i	$0.993229\pi$
$228$		0			0
$229$	−5.12476	+	8.87635i	−0.338654	+	0.586566i	−0.984180	−	0.177173i	$-0.943305\pi$
$229$	−5.12476	+	8.87635i	−0.338654	+	0.586566i	0.645526	+	0.763738i	$0.276638\pi$
$230$		0			0
$231$	−8.44282	−	11.8886i	−0.555497	−	0.782212i
$232$		0			0
$233$	0.540628	+	0.936396i	0.0354177	+	0.0613453i	0.883191	−	0.469014i	$-0.155390\pi$
$233$	0.540628	+	0.936396i	0.0354177	+	0.0613453i	−0.847773	+	0.530359i	$0.822057\pi$
$234$		0			0
$235$	9.27292	−	16.0612i	0.604898	−	1.04771i
$236$		0			0
$237$	−7.07893	−	1.12635i	−0.459826	−	0.0731645i
$238$		0			0
$239$	6.16019	+	10.6698i	0.398470	+	0.690170i	0.993537	−	0.113506i	$-0.0362081\pi$
$239$	6.16019	+	10.6698i	0.398470	+	0.690170i	−0.595068	+	0.803676i	$0.702875\pi$
$240$		0			0
$241$	6.50000	+	11.2583i	0.418702	+	0.725213i	0.995809	−	0.0914555i	$-0.0291519\pi$
$241$	6.50000	+	11.2583i	0.418702	+	0.725213i	−0.577107	+	0.816668i	$0.695819\pi$
$242$		0			0
$243$	−10.9834	−	11.0618i	−0.704589	−	0.709616i
$244$		0			0
$245$	0.449657	−	22.2691i	0.0287275	−	1.42272i
$246$		0			0
$247$	−3.65787	+	6.33561i	−0.232744	+	0.403125i
$248$		0			0
$249$	−8.80150	+	10.8532i	−0.557773	+	0.687791i
$250$		0			0
$251$	−5.11109			−0.322609			−0.161305	−	0.986905i	$-0.551570\pi$
$251$	−5.11109			−0.322609			−0.161305	+	0.986905i	$0.551570\pi$
$252$		0			0
$253$	7.12476			0.447930
$254$		0			0
$255$	−3.00000	−	7.83191i	−0.187867	−	0.490453i
$256$		0			0
$257$	−3.83009	+	6.63392i	−0.238915	+	0.413813i	−0.960403	−	0.278614i	$-0.910125\pi$
$257$	−3.83009	+	6.63392i	−0.238915	+	0.413813i	0.721488	+	0.692427i	$0.243458\pi$
$258$		0			0
$259$	1.85185	+	1.88962i	0.115068	+	0.117415i
$260$		0			0
$261$	−15.8074	+	14.1924i	−0.978453	+	0.878487i
$262$		0			0
$263$	−1.54746	−	2.68029i	−0.0954208	−	0.165274i	0.814363	−	0.580355i	$-0.197086\pi$
$263$	−1.54746	−	2.68029i	−0.0954208	−	0.165274i	−0.909784	+	0.415082i	$0.863753\pi$
$264$		0			0
$265$	−3.27292	−	5.66886i	−0.201054	−	0.348235i
$266$		0			0
$267$	−0.139680	−	0.364654i	−0.00854830	−	0.0223165i
$268$		0			0
$269$	−13.4451	+	23.2877i	−0.819765	+	1.41987i	0.0860906	+	0.996287i	$0.472563\pi$
$269$	−13.4451	+	23.2877i	−0.819765	+	1.41987i	−0.905855	+	0.423587i	$0.860771\pi$
$270$		0			0
$271$	11.1082	+	19.2400i	0.674776	+	1.16875i	0.976534	+	0.215362i	$0.0690930\pi$
$271$	11.1082	+	19.2400i	0.674776	+	1.16875i	−0.301759	+	0.953384i	$0.597574\pi$
$272$		0			0
$273$	−15.1339	−	21.3106i	−0.915947	−	1.28977i
$274$		0			0
$275$	8.15335	−	14.1220i	0.491666	−	0.851590i
$276$		0			0
$277$	7.31875	+	12.6764i	0.439741	+	0.761653i	0.997669	−	0.0682357i	$-0.0217370\pi$
$277$	7.31875	+	12.6764i	0.439741	+	0.761653i	−0.557928	+	0.829889i	$0.688404\pi$
$278$		0			0
$279$	26.8675	+	8.77202i	1.60851	+	0.525167i
$280$		0			0
$281$	11.6992	−	20.2636i	0.697915	−	1.20882i	−0.271273	−	0.962502i	$-0.587445\pi$
$281$	11.6992	−	20.2636i	0.697915	−	1.20882i	0.969188	−	0.246322i	$-0.0792219\pi$
$282$		0			0
$283$	26.1248			1.55296			0.776478	−	0.630144i	$-0.217004\pi$
$283$	26.1248			1.55296			0.776478	+	0.630144i	$0.217004\pi$
$284$		0			0
$285$	−6.98113	−	1.11079i	−0.413526	−	0.0657975i
$286$		0			0
$287$	−10.3759	−	10.5876i	−0.612471	−	0.624963i
$288$		0			0
$289$	7.34213	+	12.7169i	0.431890	+	0.748056i
$290$		0			0
$291$	−16.1923	+	19.9668i	−0.949212	+	1.17048i
$292$		0			0
$293$	12.9315	+	22.3980i	0.755465	+	1.30850i	0.945143	+	0.326657i	$0.105922\pi$
$293$	12.9315	+	22.3980i	0.755465	+	1.30850i	−0.189678	+	0.981846i	$0.560745\pi$
$294$		0			0
$295$	1.78947	−	3.09945i	0.104187	−	0.180457i
$296$		0			0
$297$	−0.830095	−	16.5130i	−0.0481670	−	0.958182i
$298$		0			0
$299$	12.7713			0.738582
$300$		0			0
$301$	−4.85185	+	17.4027i	−0.279656	+	1.00308i
$302$		0			0
$303$	11.5172	+	30.0673i	0.661648	+	1.72732i
$304$		0			0
$305$	4.97141	−	8.61073i	0.284662	−	0.493049i
$306$		0			0
$307$	−3.53216			−0.201591			−0.100795	−	0.994907i	$-0.532139\pi$
$307$	−3.53216			−0.201591			−0.100795	+	0.994907i	$0.532139\pi$
$308$		0			0
$309$	0.308342	−	0.380217i	0.0175409	−	0.0216298i
$310$		0			0
$311$	−1.70370			−0.0966078			−0.0483039	−	0.998833i	$-0.515382\pi$
$311$	−1.70370			−0.0966078			−0.0483039	+	0.998833i	$0.515382\pi$
$312$		0			0
$313$	−2.84213			−0.160647			−0.0803234	−	0.996769i	$-0.525595\pi$
$313$	−2.84213			−0.160647			−0.0803234	+	0.996769i	$0.525595\pi$
$314$		0			0
$315$	13.9984	−	21.0216i	0.788719	−	1.18443i
$316$		0			0
$317$	−24.9201			−1.39965			−0.699827	−	0.714313i	$-0.746739\pi$
$317$	−24.9201			−1.39965			−0.699827	+	0.714313i	$0.746739\pi$
$318$		0			0
$319$	−22.5322			−1.26156
$320$		0			0
$321$	7.04910	+	18.4026i	0.393442	+	1.02713i
$322$		0			0
$323$	−1.95185			−0.108604
$324$		0			0
$325$	14.6150	−	25.3140i	0.810697	−	1.40417i
$326$		0			0
$327$	4.82326	−	5.94758i	0.266727	−	0.328902i
$328$		0			0
$329$	14.9347	−	3.84060i	0.823379	−	0.211739i
$330$		0			0
$331$	7.17154			0.394183			0.197092	−	0.980385i	$-0.436850\pi$
$331$	7.17154			0.394183			0.197092	+	0.980385i	$0.436850\pi$
$332$		0			0
$333$	0.619562	+	2.93533i	0.0339518	+	0.160855i
$334$		0			0
$335$	−17.4480	+	30.2209i	−0.953287	+	1.65114i
$336$		0			0
$337$	−10.9211	−	18.9158i	−0.594908	−	1.03041i	−0.993560	−	0.113309i	$-0.963855\pi$
$337$	−10.9211	−	18.9158i	−0.594908	−	1.03041i	0.398651	−	0.917103i	$-0.369478\pi$
$338$		0			0
$339$	1.99192	+	5.20018i	0.108186	+	0.282435i
$340$		0			0
$341$	14.9887	+	25.9611i	0.811681	+	1.40587i
$342$		0			0
$343$	13.4863	−	12.6933i	0.728193	−	0.685372i
$344$		0			0
$345$	4.41423	+	11.5239i	0.237654	+	0.620428i
$346$		0			0
$347$	2.11109			0.113329			0.0566646	−	0.998393i	$-0.481953\pi$
$347$	2.11109			0.113329			0.0566646	+	0.998393i	$0.481953\pi$
$348$		0			0
$349$	18.1082	−	31.3643i	0.969310	−	1.67889i	0.271751	−	0.962368i	$-0.412397\pi$
$349$	18.1082	−	31.3643i	0.969310	−	1.67889i	0.697559	−	0.716527i	$-0.254269\pi$
$350$		0			0
$351$	−1.48796	−	29.5999i	−0.0794215	−	1.57993i
$352$		0			0
$353$	5.24433	+	9.08344i	0.279127	+	0.483463i	0.971168	−	0.238396i	$-0.0766215\pi$
$353$	5.24433	+	9.08344i	0.279127	+	0.483463i	−0.692041	+	0.721858i	$0.743288\pi$
$354$		0			0
$355$	−13.8256	+	23.9466i	−0.733786	+	1.27095i
$356$		0			0
$357$	2.90507	−	6.33963i	0.153753	−	0.335529i
$358$		0			0
$359$	−16.2209	−	28.0955i	−0.856108	−	1.48282i	−0.875613	−	0.483013i	$-0.839542\pi$
$359$	−16.2209	−	28.0955i	−0.856108	−	1.48282i	0.0195047	−	0.999810i	$-0.493791\pi$
$360$		0			0
$361$	8.67743	−	15.0297i	0.456707	−	0.791039i
$362$		0			0
$363$	−0.954858	+	1.17744i	−0.0501171	+	0.0617995i
$364$		0			0
$365$	7.90219	+	13.6870i	0.413620	+	0.716410i
$366$		0			0
$367$	−9.05555	−	15.6847i	−0.472696	−	0.818733i	0.526816	−	0.849979i	$-0.323386\pi$
$367$	−9.05555	−	15.6847i	−0.472696	−	0.818733i	−0.999512	+	0.0312465i	$0.990052\pi$
$368$		0			0
$369$	−3.47141	−	16.4467i	−0.180714	−	0.856179i
$370$		0			0
$371$	1.46169	−	5.24284i	0.0758874	−	0.272195i
$372$		0			0
$373$	5.83530	−	10.1070i	0.302140	−	0.523322i	−0.674480	−	0.738293i	$-0.735632\pi$
$373$	5.83530	−	10.1070i	0.302140	−	0.523322i	0.976621	+	0.214971i	$0.0689656\pi$
$374$		0			0
$375$	0.679065	+	0.108048i	0.0350668	+	0.00557959i
$376$		0			0
$377$	−40.3893			−2.08016
$378$		0			0
$379$	−14.2690			−0.732947			−0.366474	−	0.930428i	$-0.619435\pi$
$379$	−14.2690			−0.732947			−0.366474	+	0.930428i	$0.619435\pi$
$380$		0			0
$381$	34.3908	+	5.47204i	1.76190	+	0.280341i
$382$		0			0
$383$	−0.824893	+	1.42876i	−0.0421501	+	0.0730061i	−0.886331	−	0.463053i	$-0.846754\pi$
$383$	−0.824893	+	1.42876i	−0.0421501	+	0.0730061i	0.844181	+	0.536059i	$0.180087\pi$
$384$		0			0
$385$	25.9435	−	6.67160i	1.32220	−	0.340016i
$386$		0			0
$387$	−15.2431	+	13.6857i	−0.774849	+	0.695685i
$388$		0			0
$389$	16.0338	+	27.7713i	0.812946	+	1.40806i	0.910794	+	0.412862i	$0.135471\pi$
$389$	16.0338	+	27.7713i	0.812946	+	1.40806i	−0.0978483	+	0.995201i	$0.531196\pi$
$390$		0			0
$391$	1.70370	+	2.95089i	0.0861596	+	0.149233i
$392$		0			0
$393$	−6.94282	+	8.56122i	−0.350219	+	0.431856i
$394$		0			0
$395$	6.58414	−	11.4041i	0.331284	−	0.573800i
$396$		0			0
$397$	−18.9669	−	32.8516i	−0.951921	−	1.64878i	−0.741261	−	0.671217i	$-0.765772\pi$
$397$	−18.9669	−	32.8516i	−0.951921	−	1.64878i	−0.210660	−	0.977559i	$-0.567561\pi$
$398$		0			0
$399$	−3.40327	−	4.79225i	−0.170377	−	0.239913i
$400$		0			0
$401$	−5.30959	+	9.19647i	−0.265148	+	0.459250i	−0.967602	−	0.252479i	$-0.918754\pi$
$401$	−5.30959	+	9.19647i	−0.265148	+	0.459250i	0.702454	+	0.711729i	$0.252087\pi$
$402$		0			0
$403$	26.8675	+	46.5358i	1.33836	+	2.31811i
$404$		0			0
$405$	26.1947	−	11.5735i	1.30162	−	0.575090i
$406$		0			0
$407$	−1.59097	+	2.75564i	−0.0788615	+	0.136592i
$408$		0			0
$409$	5.54583			0.274224			0.137112	−	0.990556i	$-0.456218\pi$
$409$	5.54583			0.274224			0.137112	+	0.990556i	$0.456218\pi$
$410$		0			0
$411$	1.69850	+	4.43415i	0.0837806	+	0.218721i
$412$		0			0
$413$	2.88207	−	0.741150i	0.141818	−	0.0364696i
$414$		0			0
$415$	−12.8353	−	22.2314i	−0.630060	−	1.09130i
$416$		0			0
$417$	−4.93598	−	12.8861i	−0.241716	−	0.631033i
$418$		0			0
$419$	−2.77455	−	4.80566i	−0.135546	−	0.234772i	0.790260	−	0.612772i	$-0.209945\pi$
$419$	−2.77455	−	4.80566i	−0.135546	−	0.234772i	−0.925806	+	0.378000i	$0.876612\pi$
$420$		0			0
$421$	−3.42107	+	5.92546i	−0.166733	+	0.288789i	−0.937269	−	0.348606i	$-0.886655\pi$
$421$	−3.42107	+	5.92546i	−0.166733	+	0.288789i	0.770537	+	0.637396i	$0.219988\pi$
$422$		0			0
$423$	16.6219	+	5.42692i	0.808184	+	0.263866i
$424$		0			0
$425$	7.79863			0.378289
$426$		0			0
$427$	8.00684	−	2.05903i	0.387478	−	0.0996433i
$428$		0			0
$429$	19.7999	−	24.4153i	0.955947	−	1.17878i
$430$		0			0
$431$	−16.5539	+	28.6722i	−0.797374	+	1.38109i	0.123947	+	0.992289i	$0.460445\pi$
$431$	−16.5539	+	28.6722i	−0.797374	+	1.38109i	−0.921321	+	0.388803i	$0.872889\pi$
$432$		0			0
$433$	−12.1111			−0.582022			−0.291011	−	0.956720i	$-0.593992\pi$
$433$	−12.1111			−0.582022			−0.291011	+	0.956720i	$0.593992\pi$
$434$		0			0
$435$	−13.9601	−	36.4446i	−0.669334	−	1.74739i
$436$		0			0
$437$	2.87197			0.137385
$438$		0			0
$439$	8.83422			0.421634			0.210817	−	0.977526i	$-0.432388\pi$
$439$	8.83422			0.421634			0.210817	+	0.977526i	$0.432388\pi$
$440$		0			0
$441$	20.6307	−	3.92124i	0.982412	−	0.186726i
$442$		0			0
$443$	−17.5185			−0.832328			−0.416164	−	0.909290i	$-0.636626\pi$
$443$	−17.5185			−0.832328			−0.416164	+	0.909290i	$0.636626\pi$
$444$		0			0
$445$	0.717370			0.0340066
$446$		0			0
$447$	−25.3759	+	31.2911i	−1.20024	+	1.48002i
$448$		0			0
$449$	31.2301			1.47384			0.736920	−	0.675980i	$-0.236280\pi$
$449$	31.2301			1.47384			0.736920	+	0.675980i	$0.236280\pi$
$450$		0			0
$451$	8.91423	−	15.4399i	0.419755	−	0.727036i
$452$		0			0
$453$	5.03379	+	13.1414i	0.236508	+	0.617437i
$454$		0			0
$455$	46.5043	−	11.9590i	2.18015	−	0.560645i
$456$		0			0
$457$	−32.1248			−1.50273			−0.751367	−	0.659885i	$-0.770605\pi$
$457$	−32.1248			−1.50273			−0.751367	+	0.659885i	$0.770605\pi$
$458$		0			0
$459$	6.64076	−	4.29245i	0.309964	−	0.200354i
$460$		0			0
$461$	1.23229	−	2.13438i	0.0573933	−	0.0994081i	−0.835901	−	0.548880i	$-0.815054\pi$
$461$	1.23229	−	2.13438i	0.0573933	−	0.0994081i	0.893295	+	0.449472i	$0.148388\pi$
$462$		0			0
$463$	−15.1735	−	26.2812i	−0.705171	−	1.22139i	−0.966630	−	0.256177i	$-0.917537\pi$
$463$	−15.1735	−	26.2812i	−0.705171	−	1.22139i	0.261459	−	0.965215i	$-0.415796\pi$
$464$		0			0
$465$	−32.7044	+	40.3279i	−1.51663	+	1.87016i
$466$		0			0
$467$	7.98181	+	13.8249i	0.369354	+	0.639740i	0.989465	−	0.144774i	$-0.0462456\pi$
$467$	7.98181	+	13.8249i	0.369354	+	0.639740i	−0.620110	+	0.784515i	$0.712912\pi$
$468$		0			0
$469$	−28.1014	+	7.22651i	−1.29760	+	0.333689i
$470$		0			0
$471$	19.2661	+	3.06549i	0.887734	+	0.141250i
$472$		0			0
$473$	−21.7278			−0.999044
$474$		0			0
$475$	3.28659	−	5.69254i	0.150799	−	0.261192i
$476$		0			0
$477$	4.59222	−	4.12304i	0.210263	−	0.188781i
$478$		0			0
$479$	−11.5865	−	20.0683i	−0.529399	−	0.916946i	−0.999412	−	0.0342863i	$-0.989084\pi$
$479$	−11.5865	−	20.0683i	−0.529399	−	0.916946i	0.470013	−	0.882659i	$-0.344249\pi$
$480$		0			0
$481$	−2.85185	+	4.93955i	−0.130033	+	0.225224i
$482$		0			0
$483$	−4.27455	+	9.32820i	−0.194499	+	0.424448i
$484$		0			0
$485$	−23.6134	−	40.8996i	−1.07223	−	1.85716i
$486$		0			0
$487$	−1.70658	+	2.95588i	−0.0773323	+	0.133943i	−0.902098	−	0.431531i	$-0.857974\pi$
$487$	−1.70658	+	2.95588i	−0.0773323	+	0.133943i	0.824766	+	0.565474i	$0.191307\pi$
$488$		0			0
$489$	−2.46621	−	6.43837i	−0.111526	−	0.291153i
$490$		0			0
$491$	9.58414	+	16.6002i	0.432526	+	0.749157i	0.997090	−	0.0762323i	$-0.0242890\pi$
$491$	9.58414	+	16.6002i	0.432526	+	0.749157i	−0.564564	+	0.825389i	$0.690956\pi$
$492$		0			0
$493$	−5.38796	−	9.33223i	−0.242662	−	0.420302i
$494$		0			0
$495$	28.8743	+	9.42724i	1.29780	+	0.423723i
$496$		0			0
$497$	−22.2672	+	5.72619i	−0.998819	+	0.256855i
$498$		0			0
$499$	20.5848	−	35.6540i	0.921503	−	1.59609i	0.124413	−	0.992231i	$-0.460295\pi$
$499$	20.5848	−	35.6540i	0.921503	−	1.59609i	0.797090	−	0.603860i	$-0.206371\pi$
$500$		0			0
$501$	3.24596	+	8.47402i	0.145019	+	0.378591i
$502$		0			0
$503$	26.4542			1.17953			0.589767	−	0.807574i	$-0.299220\pi$
$503$	26.4542			1.17953			0.589767	+	0.807574i	$0.299220\pi$
$504$		0			0
$505$	−59.1502			−2.63215
$506$		0			0
$507$	21.3090	−	26.2762i	0.946367	−	1.16697i
$508$		0			0
$509$	−6.38564	+	11.0603i	−0.283039	+	0.490237i	−0.972132	−	0.234436i	$-0.924676\pi$
$509$	−6.38564	+	11.0603i	−0.283039	+	0.490237i	0.689093	+	0.724673i	$0.258009\pi$
$510$		0			0
$511$	−3.52915	+	12.6584i	−0.156120	+	0.559975i
$512$		0			0
$513$	−0.334608	−	6.65634i	−0.0147733	−	0.293884i
$514$		0			0
$515$	0.449657	+	0.778828i	0.0198142	+	0.0343193i
$516$		0			0
$517$	9.27292	+	16.0612i	0.407822	+	0.706369i
$518$		0			0
$519$	−4.36458	−	0.694462i	−0.191584	−	0.0304835i
$520$		0			0
$521$	−3.40615	+	5.89962i	−0.149226	+	0.258467i	−0.930942	−	0.365168i	$-0.881012\pi$
$521$	−3.40615	+	5.89962i	−0.149226	+	0.258467i	0.781716	+	0.623635i	$0.214345\pi$
$522$		0			0
$523$	−14.7535	−	25.5538i	−0.645125	−	1.11739i	−0.984273	−	0.176656i	$-0.943472\pi$
$523$	−14.7535	−	25.5538i	−0.645125	−	1.11739i	0.339148	−	0.940733i	$-0.389861\pi$
$524$		0			0
$525$	13.5978	+	19.1475i	0.593457	+	0.835665i
$526$		0			0
$527$	−7.16827	+	12.4158i	−0.312255	+	0.540841i
$528$		0			0
$529$	8.99316	+	15.5766i	0.391007	+	0.677244i
$530$		0			0
$531$	3.20765	+	1.04728i	0.139200	+	0.0454479i
$532$		0			0
$533$	15.9789	−	27.6763i	0.692125	−	1.19879i
$534$		0			0
$535$	−36.2028			−1.56518
$536$		0			0
$537$	7.67799	−	9.46775i	0.331330	−	0.408564i
$538$		0			0
$539$	19.0607	+	11.5239i	0.821004	+	0.496371i
$540$		0			0
$541$	14.7008	+	25.4626i	0.632038	+	1.09472i	0.987135	+	0.159892i	$0.0511145\pi$
$541$	14.7008	+	25.4626i	0.632038	+	1.09472i	−0.355097	+	0.934829i	$0.615552\pi$
$542$		0			0
$543$	22.1803	+	3.52918i	0.951848	+	0.151452i
$544$		0			0
$545$	7.03379	+	12.1829i	0.301295	+	0.521857i
$546$		0			0
$547$	−17.6150	+	30.5102i	−0.753165	+	1.30452i	0.193116	+	0.981176i	$0.438141\pi$
$547$	−17.6150	+	30.5102i	−0.753165	+	1.30452i	−0.946281	+	0.323344i	$0.895193\pi$
$548$		0			0
$549$	8.91135	+	2.90949i	0.380327	+	0.124174i
$550$		0			0
$551$	−9.08263			−0.386933
$552$		0			0
$553$	10.6043	−	2.72698i	0.450939	−	0.115963i
$554$		0			0
$555$	−5.44282	−	0.866025i	−0.231035	−	0.0367607i
$556$		0			0
$557$	−3.36909	+	5.83543i	−0.142753	+	0.247255i	−0.928532	−	0.371252i	$-0.878929\pi$
$557$	−3.36909	+	5.83543i	−0.142753	+	0.247255i	0.785779	+	0.618507i	$0.212262\pi$
$558$		0			0
$559$	−38.9475			−1.64730
$560$		0			0
$561$	8.28263	+	1.31788i	0.349693	+	0.0556408i
$562$		0			0
$563$	1.45993			0.0615286			0.0307643	−	0.999527i	$-0.490206\pi$
$563$	1.45993			0.0615286			0.0307643	+	0.999527i	$0.490206\pi$
$564$		0			0
$565$	−10.2301			−0.430383
$566$		0			0
$567$	22.1179	+	8.82028i	0.928866	+	0.370417i
$568$		0			0
$569$	19.5653			0.820218			0.410109	−	0.912036i	$-0.365491\pi$
$569$	19.5653			0.820218			0.410109	+	0.912036i	$0.365491\pi$
$570$		0			0
$571$	21.9259			0.917569			0.458785	−	0.888547i	$-0.348285\pi$
$571$	21.9259			0.917569			0.458785	+	0.888547i	$0.348285\pi$
$572$		0			0
$573$	3.38783	+	0.539049i	0.141529	+	0.0225191i
$574$		0			0
$575$	−11.4750			−0.478540
$576$		0			0
$577$	12.3655	−	21.4177i	0.514783	−	0.891631i	−0.485069	−	0.874476i	$-0.661206\pi$
$577$	12.3655	−	21.4177i	0.514783	−	0.891631i	0.999853	−	0.0171554i	$-0.00546099\pi$
$578$		0			0
$579$	7.77579	+	1.23723i	0.323151	+	0.0514176i
$580$		0			0
$581$	5.73229	−	20.5607i	0.237815	−	0.853001i
$582$		0			0
$583$	6.54583			0.271101
$584$		0			0
$585$	51.7577	+	16.8985i	2.13992	+	0.698668i
$586$		0			0
$587$	18.0796	−	31.3148i	0.746226	−	1.29250i	−0.203394	−	0.979097i	$-0.565197\pi$
$587$	18.0796	−	31.3148i	0.746226	−	1.29250i	0.949620	−	0.313404i	$-0.101469\pi$
$588$		0			0
$589$	6.04187	+	10.4648i	0.248951	+	0.431196i
$590$		0			0
$591$	37.3149	+	5.93730i	1.53493	+	0.244228i
$592$		0			0
$593$	−7.55391	−	13.0838i	−0.310202	−	0.537285i	0.668204	−	0.743978i	$-0.267063\pi$
$593$	−7.55391	−	13.0838i	−0.310202	−	0.537285i	−0.978406	+	0.206693i	$0.933730\pi$
$594$		0			0
$595$	8.96690	+	9.14978i	0.367607	+	0.375105i
$596$		0			0
$597$	13.4000	−	16.5236i	0.548426	−	0.676265i
$598$		0			0
$599$	5.45417			0.222851			0.111426	−	0.993773i	$-0.464458\pi$
$599$	5.45417			0.222851			0.111426	+	0.993773i	$0.464458\pi$
$600$		0			0
$601$	−3.36840	+	5.83424i	−0.137400	+	0.237984i	−0.926512	−	0.376266i	$-0.877208\pi$
$601$	−3.36840	+	5.83424i	−0.137400	+	0.237984i	0.789112	+	0.614250i	$0.210541\pi$
$602$		0			0
$603$	−31.2759	−	10.2114i	−1.27365	−	0.415839i
$604$		0			0
$605$	−1.39248	−	2.41184i	−0.0566122	−	0.0980553i
$606$		0			0
$607$	3.33530	−	5.77690i	0.135376	−	0.234477i	−0.790365	−	0.612636i	$-0.790109\pi$
$607$	3.33530	−	5.77690i	0.135376	−	0.234477i	0.925741	+	0.378159i	$0.123443\pi$
$608$		0			0
$609$	13.5183	−	29.5006i	0.547790	−	1.19542i
$610$		0			0
$611$	16.6219	+	28.7899i	0.672449	+	1.16472i
$612$		0			0
$613$	0.654988	−	1.13447i	0.0264547	−	0.0458209i	−0.852495	−	0.522735i	$-0.824912\pi$
$613$	0.654988	−	1.13447i	0.0264547	−	0.0458209i	0.878950	+	0.476915i	$0.158245\pi$
$614$		0			0
$615$	30.4962	+	4.85235i	1.22972	+	0.195666i
$616$		0			0
$617$	17.2483	+	29.8749i	0.694390	+	1.20272i	0.970386	+	0.241560i	$0.0776589\pi$
$617$	17.2483	+	29.8749i	0.694390	+	1.20272i	−0.275996	+	0.961159i	$0.589008\pi$
$618$		0			0
$619$	−8.22421	−	14.2447i	−0.330559	−	0.572545i	0.652063	−	0.758165i	$-0.273904\pi$
$619$	−8.22421	−	14.2447i	−0.330559	−	0.572545i	−0.982622	+	0.185620i	$0.940571\pi$
$620$		0			0
$621$	−9.77128	+	6.31595i	−0.392108	+	0.253450i
$622$		0			0
$623$	0.417500	+	0.426015i	0.0167268	+	0.0170679i
$624$		0			0
$625$	12.1803	−	21.0969i	0.487212	−	0.843877i
$626$		0			0
$627$	4.45254	−	5.49044i	0.177817	−	0.219267i
$628$		0			0
$629$	−1.52175			−0.0606763
$630$		0			0
$631$	30.0118			1.19475			0.597375	−	0.801962i	$-0.296210\pi$
$631$	30.0118			1.19475			0.597375	+	0.801962i	$0.296210\pi$
$632$		0			0
$633$	−10.3200	−	26.9417i	−0.410183	−	1.07084i
$634$		0			0
$635$	−31.9870	+	55.4031i	−1.26937	+	2.19861i
$636$		0			0
$637$	34.1668	+	20.6569i	1.35374	+	0.818456i
$638$		0			0
$639$	−24.7826	−	8.09134i	−0.980386	−	0.320089i
$640$		0			0
$641$	−13.9497	−	24.1615i	−0.550978	−	0.954322i	−0.998204	−	0.0599014i	$-0.980921\pi$
$641$	−13.9497	−	24.1615i	−0.550978	−	0.954322i	0.447226	−	0.894421i	$-0.352412\pi$
$642$		0			0
$643$	−14.2524	−	24.6859i	−0.562060	−	0.973516i	−0.997317	−	0.0732100i	$-0.976676\pi$
$643$	−14.2524	−	24.6859i	−0.562060	−	0.973516i	0.435257	−	0.900306i	$-0.356658\pi$
$644$		0			0
$645$	−13.4617	−	35.1436i	−0.530054	−	1.38378i
$646$		0			0
$647$	−8.35705	+	14.4748i	−0.328550	+	0.569065i	−0.982224	−	0.187711i	$-0.939893\pi$
$647$	−8.35705	+	14.4748i	−0.328550	+	0.569065i	0.653675	+	0.756776i	$0.273226\pi$
$648$		0			0
$649$	1.78947	+	3.09945i	0.0702427	+	0.121664i
$650$		0			0
$651$	−42.9825	+	4.04857i	−1.68462	+	0.158676i
$652$		0			0
$653$	−19.0825	+	33.0519i	−0.746756	+	1.29342i	0.202614	+	0.979259i	$0.435056\pi$
$653$	−19.0825	+	33.0519i	−0.746756	+	1.29342i	−0.949370	+	0.314161i	$0.898277\pi$
$654$		0			0
$655$	−10.1248	−	17.5366i	−0.395607	−	0.685212i
$656$		0			0
$657$	−11.0875	+	9.95475i	−0.432566	+	0.388372i
$658$		0			0
$659$	−4.37072	+	7.57031i	−0.170259	+	0.294898i	−0.938510	−	0.345251i	$-0.887794\pi$
$659$	−4.37072	+	7.57031i	−0.170259	+	0.294898i	0.768251	+	0.640148i	$0.221127\pi$
$660$		0			0
$661$	−20.0837			−0.781167			−0.390584	−	0.920567i	$-0.627727\pi$
$661$	−20.0837			−0.781167			−0.390584	+	0.920567i	$0.627727\pi$
$662$		0			0
$663$	14.8468	+	2.36232i	0.576601	+	0.0917449i
$664$		0			0
$665$	10.4577	−	2.68930i	0.405534	−	0.104286i
$666$		0			0
$667$	7.92790	+	13.7315i	0.306970	+	0.531687i
$668$		0			0
$669$	−11.6264	+	14.3366i	−0.449503	+	0.554283i
$670$		0			0
$671$	4.97141	+	8.61073i	0.191919	+	0.332414i
$672$		0			0
$673$	−17.0264	+	29.4906i	−0.656319	+	1.13678i	0.325242	+	0.945631i	$0.394554\pi$
$673$	−17.0264	+	29.4906i	−0.656319	+	1.13678i	−0.981561	+	0.191148i	$0.938779\pi$
$674$		0			0
$675$	1.33693	+	26.5955i	0.0514585	+	1.02366i
$676$		0			0
$677$	−0.717370			−0.0275708			−0.0137854	−	0.999905i	$-0.504388\pi$
$677$	−0.717370			−0.0275708			−0.0137854	+	0.999905i	$0.504388\pi$
$678$		0			0
$679$	10.5458	−	37.8260i	0.404712	−	1.45163i
$680$		0			0
$681$	8.98865	+	23.4661i	0.344446	+	0.899223i
$682$		0			0
$683$	10.5270	−	18.2332i	0.402803	−	0.697675i	−0.591260	−	0.806481i	$-0.701369\pi$
$683$	10.5270	−	18.2332i	0.402803	−	0.697675i	0.994063	+	0.108806i	$0.0347027\pi$
$684$		0			0
$685$	−8.72313			−0.333294
$686$		0			0
$687$	11.1819	−	13.7885i	0.426618	−	0.526064i
$688$		0			0
$689$	11.7335			0.447012
$690$		0			0
$691$	−5.84789			−0.222464			−0.111232	−	0.993794i	$-0.535480\pi$
$691$	−5.84789			−0.222464			−0.111232	+	0.993794i	$0.535480\pi$
$692$		0			0
$693$	11.2060	+	22.6337i	0.425681	+	0.859784i
$694$		0			0
$695$	25.3502			0.961588
$696$		0			0
$697$	8.52640			0.322960
$698$		0			0
$699$	−0.669905	−	1.74888i	−0.0253381	−	0.0661486i
$700$		0			0
$701$	10.2711			0.387935			0.193967	−	0.981008i	$-0.437864\pi$
$701$	10.2711			0.387935			0.193967	+	0.981008i	$0.437864\pi$
$702$		0			0
$703$	−0.641315	+	1.11079i	−0.0241877	+	0.0418942i
$704$		0			0
$705$	−20.2330	+	24.9494i	−0.762018	+	0.939647i
$706$		0			0
$707$	−34.4246	−	35.1268i	−1.29467	−	1.32108i
$708$		0			0
$709$	43.4854			1.63313			0.816564	−	0.577255i	$-0.195876\pi$
$709$	43.4854			1.63313			0.816564	+	0.577255i	$0.195876\pi$
$710$		0			0
$711$	11.8022	+	3.85333i	0.442617	+	0.144511i
$712$		0			0
$713$	10.5475	−	18.2687i	0.395006	−	0.684170i
$714$		0			0
$715$	28.8743	+	50.0117i	1.07984	+	1.87033i
$716$		0			0
$717$	−7.63323	−	19.9276i	−0.285068	−	0.744210i
$718$		0			0
$719$	−25.4412	−	44.0654i	−0.948796	−	1.64336i	−0.747966	−	0.663737i	$-0.768969\pi$
$719$	−25.4412	−	44.0654i	−0.948796	−	1.64336i	−0.200830	−	0.979626i	$-0.564364\pi$
$720$		0			0
$721$	−0.200818	+	0.720299i	−0.00747886	+	0.0268253i
$722$		0			0
$723$	−8.05430	−	21.0268i	−0.299543	−	0.781997i
$724$		0			0
$725$	36.2898			1.34777
$726$		0			0
$727$	−6.07210	+	10.5172i	−0.225202	+	0.390061i	−0.956380	−	0.292126i	$-0.905637\pi$
$727$	−6.07210	+	10.5172i	−0.225202	+	0.390061i	0.731178	+	0.682186i	$0.238971\pi$
$728$		0			0
$729$	15.7769	+	21.9110i	0.584329	+	0.811517i
$730$		0			0
$731$	−5.19562	−	8.99907i	−0.192167	−	0.332843i
$732$		0			0
$733$	23.0848	−	39.9841i	0.852657	−	1.47685i	−0.0261440	−	0.999658i	$-0.508323\pi$
$733$	23.0848	−	39.9841i	0.852657	−	1.47685i	0.878801	−	0.477188i	$-0.158344\pi$
$734$		0			0
$735$	−6.83009	+	37.9696i	−0.251932	+	1.40053i
$736$		0			0
$737$	−17.4480	−	30.2209i	−0.642706	−	1.11320i
$738$		0			0
$739$	2.49604	−	4.32327i	0.0918184	−	0.159034i	−0.816458	−	0.577405i	$-0.804065\pi$
$739$	2.49604	−	4.32327i	0.0918184	−	0.159034i	0.908276	+	0.418371i	$0.137399\pi$
$740$		0			0
$741$	7.98126	−	9.84172i	0.293199	−	0.361545i
$742$		0			0
$743$	15.7060	+	27.2036i	0.576198	+	0.998004i	0.995910	+	0.0903470i	$0.0287976\pi$
$743$	15.7060	+	27.2036i	0.576198	+	0.998004i	−0.419712	+	0.907657i	$0.637869\pi$
$744$		0			0
$745$	−37.0059	−	64.0961i	−1.35579	−	2.34830i
$746$		0			0
$747$	18.0092	−	16.1692i	0.658921	−	0.591600i
$748$		0			0
$749$	−21.0695	−	21.4992i	−0.769863	−	0.785565i
$750$		0			0
$751$	1.64815	−	2.85468i	0.0601419	−	0.104169i	−0.834387	−	0.551179i	$-0.814178\pi$
$751$	1.64815	−	2.85468i	0.0601419	−	0.104169i	0.894529	+	0.447010i	$0.147511\pi$
$752$		0			0
$753$	8.74269	+	1.39108i	0.318601	+	0.0506937i
$754$		0			0
$755$	−25.8525			−0.940870
$756$		0			0
$757$	−10.1384			−0.368488			−0.184244	−	0.982881i	$-0.558984\pi$
$757$	−10.1384			−0.368488			−0.184244	+	0.982881i	$0.558984\pi$
$758$		0			0
$759$	−12.1871	−	1.93914i	−0.442365	−	0.0703862i
$760$		0			0
$761$	−7.03379	+	12.1829i	−0.254975	+	0.441629i	−0.964889	−	0.262659i	$-0.915400\pi$
$761$	−7.03379	+	12.1829i	−0.254975	+	0.441629i	0.709914	+	0.704288i	$0.248734\pi$
$762$		0			0
$763$	−3.14132	+	11.2673i	−0.113723	+	0.407905i
$764$		0			0
$765$	3.00000	+	14.2132i	0.108465	+	0.513881i
$766$		0			0
$767$	3.20765	+	5.55582i	0.115822	+	0.200609i
$768$		0			0
$769$	11.3461	+	19.6520i	0.409151	+	0.708669i	0.994795	−	0.101899i	$-0.0324918\pi$
$769$	11.3461	+	19.6520i	0.409151	+	0.708669i	−0.585644	+	0.810568i	$0.699158\pi$
$770$		0			0
$771$	8.35705	−	10.3051i	0.300972	−	0.371129i
$772$		0			0
$773$	0.327772	−	0.567717i	0.0117891	−	0.0204194i	−0.860071	−	0.510175i	$-0.829581\pi$
$773$	0.327772	−	0.567717i	0.0117891	−	0.0204194i	0.871860	+	0.489756i	$0.162914\pi$
$774$		0			0
$775$	−24.1404	−	41.8123i	−0.867148	−	1.50194i
$776$		0			0
$777$	−2.65335	−	3.73627i	−0.0951885	−	0.134038i
$778$		0			0
$779$	3.59329	−	6.22377i	0.128743	−	0.222990i
$780$		0			0
$781$	−13.8256	−	23.9466i	−0.494718	−	0.856877i
$782$		0			0
$783$	30.9018	−	19.9743i	1.10434	−	0.713823i
$784$		0			0
$785$	−17.9194	+	31.0374i	−0.639572	+	1.10777i
$786$		0			0
$787$	−0.540073			−0.0192515			−0.00962576	−	0.999954i	$-0.503064\pi$
$787$	−0.540073			−0.0192515			−0.00962576	+	0.999954i	$0.503064\pi$
$788$		0			0
$789$	1.91750	+	5.00589i	0.0682648	+	0.178215i
$790$		0			0
$791$	−5.95378	−	6.07521i	−0.211692	−	0.216010i
$792$		0			0
$793$	8.91135	+	15.4349i	0.316451	+	0.548110i
$794$		0			0
$795$	4.05555	+	10.5876i	0.143835	+	0.375502i
$796$		0			0
$797$	−12.5550	−	21.7459i	−0.444721	−	0.770279i	0.553312	−	0.832974i	$-0.313364\pi$
$797$	−12.5550	−	21.7459i	−0.444721	−	0.770279i	−0.998033	+	0.0626954i	$0.980030\pi$
$798$		0			0
$799$	−4.43474	+	7.68119i	−0.156890	+	0.271741i
$800$		0			0
$801$	0.139680	+	0.661770i	0.00493536	+	0.0233825i
$802$		0			0
$803$	−15.8044			−0.557725
$804$		0			0
$805$	−13.1940	−	13.4631i	−0.465027	−	0.474511i
$806$		0			0
$807$	29.3365	−	36.1750i	1.03270	−	1.27342i
$808$		0			0
$809$	−14.5865	+	25.2645i	−0.512833	+	0.888252i	0.487057	+	0.873370i	$0.338071\pi$
$809$	−14.5865	+	25.2645i	−0.512833	+	0.888252i	−0.999889	+	0.0148817i	$0.995263\pi$
$810$		0			0
$811$	15.4290			0.541785			0.270892	−	0.962610i	$-0.412681\pi$
$811$	15.4290			0.541785			0.270892	+	0.962610i	$0.412681\pi$
$812$		0			0
$813$	−13.7644	−	35.9339i	−0.482740	−	1.26026i
$814$		0			0
$815$	12.6659			0.443669
$816$		0			0
$817$	−8.75839			−0.306417
$818$		0			0
$819$	20.0870	+	40.5714i	0.701897	+	1.41768i
$820$		0			0
$821$	8.48727			0.296208			0.148104	−	0.988972i	$-0.452683\pi$
$821$	8.48727			0.296208			0.148104	+	0.988972i	$0.452683\pi$
$822$		0			0
$823$	−29.0974			−1.01427			−0.507136	−	0.861866i	$-0.669296\pi$
$823$	−29.0974			−1.01427			−0.507136	+	0.861866i	$0.669296\pi$
$824$		0			0
$825$	−17.7902	+	21.9371i	−0.619374	+	0.763752i
$826$		0			0
$827$	25.9396			0.902007			0.451003	−	0.892522i	$-0.351066\pi$
$827$	25.9396			0.902007			0.451003	+	0.892522i	$0.351066\pi$
$828$		0			0
$829$	3.10821	−	5.38358i	0.107953	−	0.186979i	−0.806988	−	0.590568i	$-0.798904\pi$
$829$	3.10821	−	5.38358i	0.107953	−	0.186979i	0.914941	+	0.403588i	$0.132237\pi$
$830$		0			0
$831$	−9.06883	−	23.6754i	−0.314594	−	0.821291i
$832$		0			0
$833$	−0.215047	+	10.6501i	−0.00745093	+	0.369004i
$834$		0			0
$835$	−16.6706			−0.576910
$836$		0			0
$837$	−43.5702	−	22.3173i	−1.50601	−	0.771399i
$838$		0			0
$839$	−21.2947	+	36.8834i	−0.735174	+	1.27336i	0.219474	+	0.975618i	$0.429566\pi$
$839$	−21.2947	+	36.8834i	−0.735174	+	1.27336i	−0.954647	+	0.297740i	$0.903767\pi$
$840$		0			0
$841$	−10.5721	−	18.3114i	−0.364555	−	0.631428i
$842$		0			0
$843$	−25.5270	+	31.4774i	−0.879195	+	1.08414i
$844$		0			0
$845$	31.0751	+	53.8237i	1.06902	+	1.85159i
$846$		0			0
$847$	0.621885	−	2.23059i	0.0213682	−	0.0766440i
$848$		0			0
$849$	−44.6873	−	7.11034i	−1.53366	−	0.244026i
$850$		0			0
$851$	2.23912			0.0767562
$852$		0			0
$853$	−10.6969	+	18.5275i	−0.366254	+	0.634370i	−0.988976	−	0.148073i	$-0.952693\pi$
$853$	−10.6969	+	18.5275i	−0.366254	+	0.634370i	0.622723	+	0.782442i	$0.286026\pi$
$854$		0			0
$855$	11.6391	+	3.80009i	0.398050	+	0.129960i
$856$		0			0
$857$	18.4218	+	31.9074i	0.629275	+	1.08994i	0.987697	+	0.156377i	$0.0499815\pi$
$857$	18.4218	+	31.9074i	0.629275	+	1.08994i	−0.358422	+	0.933560i	$0.616685\pi$
$858$		0			0
$859$	−8.81875	+	15.2745i	−0.300892	+	0.521160i	−0.976338	−	0.216249i	$-0.930618\pi$
$859$	−8.81875	+	15.2745i	−0.300892	+	0.521160i	0.675446	+	0.737409i	$0.263951\pi$
$860$		0			0
$861$	14.8668	+	20.9344i	0.506658	+	0.713441i
$862$		0			0
$863$	0.380438	+	0.658939i	0.0129503	+	0.0224305i	0.872428	−	0.488743i	$-0.162544\pi$
$863$	0.380438	+	0.658939i	0.0129503	+	0.0224305i	−0.859478	+	0.511173i	$0.829211\pi$
$864$		0			0
$865$	4.05950	−	7.03127i	0.138027	−	0.239070i
$866$		0			0
$867$	−9.09781	−	23.7511i	−0.308978	−	0.806628i
$868$		0			0
$869$	6.58414	+	11.4041i	0.223351	+	0.386856i
$870$		0			0
$871$	−31.2759	−	54.1715i	−1.05974	−	1.83553i
$872$		0			0
$873$	33.1319	−	29.7469i	1.12134	−	1.00678i
$874$		0			0
$875$	−1.01724	+	0.261592i	−0.0343890	+	0.00884343i
$876$		0			0
$877$	20.7495	−	35.9392i	0.700662	−	1.21358i	−0.267573	−	0.963538i	$-0.586222\pi$
$877$	20.7495	−	35.9392i	0.700662	−	1.21358i	0.968234	−	0.250044i	$-0.0804451\pi$
$878$		0			0
$879$	−16.0237	−	41.8320i	−0.540466	−	1.41096i
$880$		0			0
$881$	8.35486			0.281482			0.140741	−	0.990046i	$-0.455051\pi$
$881$	8.35486			0.281482			0.140741	+	0.990046i	$0.455051\pi$
$882$		0			0
$883$	−35.6181			−1.19864			−0.599322	−	0.800508i	$-0.704563\pi$
$883$	−35.6181			−1.19864			−0.599322	+	0.800508i	$0.704563\pi$
$884$		0			0
$885$	−3.90451	+	4.81467i	−0.131249	+	0.161843i
$886$		0			0
$887$	−18.5550	+	32.1382i	−0.623016	+	1.07909i	0.365905	+	0.930652i	$0.380759\pi$
$887$	−18.5550	+	32.1382i	−0.623016	+	1.07909i	−0.988921	+	0.148443i	$0.952574\pi$
$888$		0			0
$889$	−51.5175	+	13.2482i	−1.72784	+	0.444330i
$890$		0			0
$891$	−3.07442	+	28.4720i	−0.102997	+	0.953847i
$892$		0			0
$893$	3.73788	+	6.47420i	0.125083	+	0.216651i
$894$		0			0
$895$	11.1969	+	19.3935i	0.374270	+	0.648254i
$896$		0			0
$897$	−21.8457	−	3.47594i	−0.729407	−	0.116058i
$898$		0			0
$899$	−33.3565	+	57.7751i	−1.11250	+	1.92691i
$900$		0			0
$901$	1.56526	+	2.71111i	0.0521464	+	0.0903202i
$902$		0			0
$903$	13.0357	−	28.4474i	0.433802	−	0.946671i
$904$		0			0
$905$	−20.6300	+	35.7321i	−0.685763	+	1.18778i
$906$		0			0
$907$	−24.0751	−	41.6993i	−0.799401	−	1.38460i	−0.920007	−	0.391902i	$-0.871817\pi$
$907$	−24.0751	−	41.6993i	−0.799401	−	1.38460i	0.120606	−	0.992700i	$-0.461516\pi$
$908$		0			0
$909$	−11.5172	−	54.5658i	−0.382003	−	1.80983i
$910$		0			0
$911$	−17.4428	+	30.2119i	−0.577906	+	1.00096i	0.417813	+	0.908533i	$0.362797\pi$
$911$	−17.4428	+	30.2119i	−0.577906	+	1.00096i	−0.995719	+	0.0924301i	$0.970537\pi$
$912$		0			0
$913$	25.6706			0.849573
$914$		0			0
$915$	−10.8473	+	13.3759i	−0.358602	+	0.442193i
$916$		0			0
$917$	4.52175	−	16.2187i	0.149321	−	0.535590i
$918$		0			0
$919$	25.8675	+	44.8037i	0.853289	+	1.47794i	0.878224	+	0.478250i	$0.158729\pi$
$919$	25.8675	+	44.8037i	0.853289	+	1.47794i	−0.0249351	+	0.999689i	$0.507938\pi$
$920$		0			0
$921$	6.04187	+	0.961343i	0.199086	+	0.0316773i
$922$		0			0
$923$	−24.7826	−	42.9248i	−0.815730	−	1.41289i
$924$		0			0
$925$	2.56238	−	4.43818i	0.0842506	−	0.145926i
$926$		0			0
$927$	−0.630912	+	0.566453i	−0.0207219	+	0.0186048i
$928$		0			0
$929$	−50.8285			−1.66763			−0.833814	−	0.552046i	$-0.813847\pi$
$929$	−50.8285			−1.66763			−0.833814	+	0.552046i	$0.813847\pi$
$930$		0			0
$931$	7.68332	+	4.64526i	0.251811	+	0.152242i
$932$		0			0
$933$	2.91423	+	0.463693i	0.0954076	+	0.0151806i
$934$		0			0
$935$	−7.70370	+	13.3432i	−0.251938	+	0.436369i
$936$		0			0
$937$	2.54583			0.0831686			0.0415843	−	0.999135i	$-0.486759\pi$
$937$	2.54583			0.0831686			0.0415843	+	0.999135i	$0.486759\pi$
$938$		0			0
$939$	4.86156	+	0.773540i	0.158651	+	0.0252435i
$940$		0			0
$941$	1.15787			0.0377454			0.0188727	−	0.999822i	$-0.493992\pi$
$941$	1.15787			0.0377454			0.0188727	+	0.999822i	$0.493992\pi$
$942$		0			0
$943$	−12.5458			−0.408548
$944$		0			0
$945$	−29.6661	+	32.1482i	−0.965038	+	1.04578i
$946$		0			0
$947$	−9.81479			−0.318938			−0.159469	−	0.987203i	$-0.550978\pi$
$947$	−9.81479			−0.318938			−0.159469	+	0.987203i	$0.550978\pi$
$948$		0			0
$949$	−28.3297			−0.919620
$950$		0			0
$951$	42.6267	+	6.78248i	1.38227	+	0.219937i
$952$		0			0
$953$	6.53791			0.211784			0.105892	−	0.994378i	$-0.466230\pi$
$953$	6.53791			0.211784			0.105892	+	0.994378i	$0.466230\pi$
$954$		0			0
$955$	−3.15103	+	5.45774i	−0.101965	+	0.176608i
$956$		0			0
$957$	38.5420	+	6.13255i	1.24589	+	0.198237i
$958$		0			0
$959$	−5.07674	−	5.18029i	−0.163937	−	0.167280i
$960$		0			0
$961$	57.7565			1.86311
$962$		0			0
$963$	−7.04910	−	33.3969i	−0.227154	−	1.07620i
$964$		0			0
$965$	−7.23229	+	12.5267i	−0.232816	+	0.403248i
$966$		0			0
$967$	−14.4445	−	25.0185i	−0.464502	−	0.804542i	0.534677	−	0.845057i	$-0.320433\pi$
$967$	−14.4445	−	25.0185i	−0.464502	−	0.804542i	−0.999179	+	0.0405151i	$0.987100\pi$
$968$		0			0
$969$	3.33870	+	0.531232i	0.107254	+	0.0170656i
$970$		0			0
$971$	−2.66827	−	4.62158i	−0.0856289	−	0.148314i	0.820030	−	0.572320i	$-0.193957\pi$
$971$	−2.66827	−	4.62158i	−0.0856289	−	0.148314i	−0.905659	+	0.424007i	$0.860623\pi$
$972$		0			0
$973$	14.7535	+	15.0544i	0.472975	+	0.482622i
$974$		0			0
$975$	−31.8892	+	39.3227i	−1.02127	+	1.25933i
$976$		0			0
$977$	−48.0722			−1.53797			−0.768983	−	0.639269i	$-0.779237\pi$
$977$	−48.0722			−1.53797			−0.768983	+	0.639269i	$0.779237\pi$
$978$		0			0
$979$	−0.358685	+	0.621261i	−0.0114636	+	0.0198556i
$980$		0			0
$981$	−9.86909	+	8.86079i	−0.315096	+	0.282903i
$982$		0			0
$983$	14.7313	+	25.5154i	0.469857	+	0.813816i	0.999406	−	0.0344634i	$-0.0109722\pi$
$983$	14.7313	+	25.5154i	0.469857	+	0.813816i	−0.529549	+	0.848279i	$0.677639\pi$
$984$		0			0
$985$	−34.7067	+	60.1138i	−1.10585	+	1.91538i
$986$		0			0
$987$	−26.5917	+	2.50470i	−0.846422	+	0.0797255i
$988$		0			0
$989$	7.64488	+	13.2413i	0.243093	+	0.421050i
$990$		0			0
$991$	−15.4142	+	26.6982i	−0.489649	+	0.848097i	−0.999929	−	0.0119112i	$-0.996208\pi$
$991$	−15.4142	+	26.6982i	−0.489649	+	0.848097i	0.510280	+	0.860008i	$0.329542\pi$
$992$		0			0
$993$	−12.2672	−	1.95187i	−0.389286	−	0.0619407i
$994$		0			0
$995$	19.5413	+	33.8466i	0.619501	+	1.07301i
$996$		0			0
$997$	−2.77292	−	4.80283i	−0.0878191	−	0.152107i	0.818770	−	0.574122i	$-0.194656\pi$
$997$	−2.77292	−	4.80283i	−0.0878191	−	0.152107i	−0.906589	+	0.422015i	$0.861323\pi$
$998$		0			0
$999$	−0.260877	−	5.18960i	−0.00825377	−	0.164192i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.q.g.529.1		6
3.2	odd	2		3024.2.q.g.2881.1		6
4.3	odd	2		126.2.e.c.25.3	✓	6
7.2	even	3		1008.2.t.h.961.3		6
9.4	even	3		1008.2.t.h.193.3		6
9.5	odd	6		3024.2.t.h.1873.3		6
12.11	even	2		378.2.e.d.235.1		6
21.2	odd	6		3024.2.t.h.289.3		6
28.3	even	6		882.2.f.o.295.2		6
28.11	odd	6		882.2.f.n.295.2		6
28.19	even	6		882.2.h.p.79.3		6
28.23	odd	6		126.2.h.d.79.1	yes	6
28.27	even	2		882.2.e.o.655.1		6
36.7	odd	6		1134.2.g.m.487.3		6
36.11	even	6		1134.2.g.l.487.1		6
36.23	even	6		378.2.h.c.361.3		6
36.31	odd	6		126.2.h.d.67.1	yes	6
63.23	odd	6		3024.2.q.g.2305.1		6
63.58	even	3	inner	1008.2.q.g.625.1		6
84.11	even	6		2646.2.f.l.883.1		6
84.23	even	6		378.2.h.c.289.3		6
84.47	odd	6		2646.2.h.o.667.1		6
84.59	odd	6		2646.2.f.m.883.3		6
84.83	odd	2		2646.2.e.p.2125.3		6
252.11	even	6		7938.2.a.ca.1.3		3
252.23	even	6		378.2.e.d.37.1		6
252.31	even	6		882.2.f.o.589.2		6
252.59	odd	6		2646.2.f.m.1765.3		6
252.67	odd	6		882.2.f.n.589.2		6
252.79	odd	6		1134.2.g.m.163.3		6
252.95	even	6		2646.2.f.l.1765.1		6
252.103	even	6		882.2.e.o.373.1		6
252.115	even	6		7938.2.a.bw.1.3		3
252.131	odd	6		2646.2.e.p.1549.3		6
252.139	even	6		882.2.h.p.67.3		6
252.151	odd	6		7938.2.a.bv.1.1		3
252.167	odd	6		2646.2.h.o.361.1		6
252.191	even	6		1134.2.g.l.163.1		6
252.227	odd	6		7938.2.a.bz.1.1		3
252.247	odd	6		126.2.e.c.121.3	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.3	✓	6	4.3	odd	2
126.2.e.c.121.3	yes	6	252.247	odd	6
126.2.h.d.67.1	yes	6	36.31	odd	6
126.2.h.d.79.1	yes	6	28.23	odd	6
378.2.e.d.37.1		6	252.23	even	6
378.2.e.d.235.1		6	12.11	even	2
378.2.h.c.289.3		6	84.23	even	6
378.2.h.c.361.3		6	36.23	even	6
882.2.e.o.373.1		6	252.103	even	6
882.2.e.o.655.1		6	28.27	even	2
882.2.f.n.295.2		6	28.11	odd	6
882.2.f.n.589.2		6	252.67	odd	6
882.2.f.o.295.2		6	28.3	even	6
882.2.f.o.589.2		6	252.31	even	6
882.2.h.p.67.3		6	252.139	even	6
882.2.h.p.79.3		6	28.19	even	6
1008.2.q.g.529.1		6	1.1	even	1	trivial
1008.2.q.g.625.1		6	63.58	even	3	inner
1008.2.t.h.193.3		6	9.4	even	3
1008.2.t.h.961.3		6	7.2	even	3
1134.2.g.l.163.1		6	252.191	even	6
1134.2.g.l.487.1		6	36.11	even	6
1134.2.g.m.163.3		6	252.79	odd	6
1134.2.g.m.487.3		6	36.7	odd	6
2646.2.e.p.1549.3		6	252.131	odd	6
2646.2.e.p.2125.3		6	84.83	odd	2
2646.2.f.l.883.1		6	84.11	even	6
2646.2.f.l.1765.1		6	252.95	even	6
2646.2.f.m.883.3		6	84.59	odd	6
2646.2.f.m.1765.3		6	252.59	odd	6
2646.2.h.o.361.1		6	252.167	odd	6
2646.2.h.o.667.1		6	84.47	odd	6
3024.2.q.g.2305.1		6	63.23	odd	6
3024.2.q.g.2881.1		6	3.2	odd	2
3024.2.t.h.289.3		6	21.2	odd	6
3024.2.t.h.1873.3		6	9.5	odd	6
7938.2.a.bv.1.1		3	252.151	odd	6
7938.2.a.bw.1.3		3	252.115	even	6
7938.2.a.bz.1.1		3	252.227	odd	6
7938.2.a.ca.1.3		3	252.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.71053 - 0.272169i) q^{3} +(1.59097 - 2.75564i) q^{5} +(2.56238 - 0.658939i) q^{7} +(2.85185 + 0.931107i) q^{9} +(1.59097 + 2.75564i) q^{11} +(2.85185 + 4.93955i) q^{13} +(-3.47141 + 4.28061i) q^{15} +(-0.760877 + 1.31788i) q^{17} +(0.641315 + 1.11079i) q^{19} +(-4.56238 + 0.429736i) q^{21} +(1.11956 - 1.93914i) q^{23} +(-2.56238 - 4.43818i) q^{25} +(-4.62476 - 2.36887i) q^{27} +(-3.54063 + 6.13255i) q^{29} +9.42107 q^{31} +(-1.97141 - 5.14663i) q^{33} +(2.26088 - 8.10936i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-3.53379 - 9.22544i) q^{39} +(-2.80150 - 4.85235i) q^{41} +(-3.41423 + 5.91362i) q^{43} +(7.10301 - 6.37731i) q^{45} +5.82846 q^{47} +(6.13160 - 3.37690i) q^{49} +(1.66019 - 2.04719i) q^{51} +(1.02859 - 1.78157i) q^{53} +10.1248 q^{55} +(-0.794668 - 2.07459i) q^{57} +1.12476 q^{59} +3.12476 q^{61} +(7.92107 + 0.506659i) q^{63} +18.1488 q^{65} -10.9669 q^{67} +(-2.44282 + 3.01225i) q^{69} -8.69002 q^{71} +(-2.48345 + 4.30146i) q^{73} +(3.17511 + 8.28905i) q^{75} +(5.89248 + 6.01266i) q^{77} +4.13844 q^{79} +(7.26608 + 5.31075i) q^{81} +(4.03379 - 6.98673i) q^{83} +(2.42107 + 4.19341i) q^{85} +(7.72545 - 9.52628i) q^{87} +(0.112725 + 0.195246i) q^{89} +(10.5624 + 10.7778i) q^{91} +(-16.1150 - 2.56412i) q^{93} +4.08126 q^{95} +(7.42107 - 12.8537i) q^{97} +(1.97141 + 9.34004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{3} + q^{5} - 2 q^{7} + 8 q^{9} + q^{11} + 8 q^{13} - 12 q^{15} - 4 q^{17} + 3 q^{19} - 10 q^{21} + 7 q^{23} + 2 q^{25} + 7 q^{27} - 5 q^{29} + 40 q^{31} - 3 q^{33} + 13 q^{35} + 3 q^{37} + 5 q^{39}+ \cdots + 3 q^{99}+O(q^{100}) \) 6 * q - 2 * q^3 + q^5 - 2 * q^7 + 8 * q^9 + q^11 + 8 * q^13 - 12 * q^15 - 4 * q^17 + 3 * q^19 - 10 * q^21 + 7 * q^23 + 2 * q^25 + 7 * q^27 - 5 * q^29 + 40 * q^31 - 3 * q^33 + 13 * q^35 + 3 * q^37 + 5 * q^39 + 6 * q^43 + 9 * q^45 - 18 * q^47 + 12 * q^49 - 6 * q^51 + 15 * q^53 + 26 * q^55 + 22 * q^57 - 28 * q^59 - 16 * q^61 + 31 * q^63 + 24 * q^65 + 2 * q^67 + 3 * q^69 - 14 * q^71 + 19 * q^73 - 8 * q^75 + 10 * q^77 + 10 * q^79 + 8 * q^81 - 2 * q^83 - 2 * q^85 + 27 * q^87 - 9 * q^89 + 46 * q^91 - 38 * q^93 - 8 * q^95 + 28 * q^97 + 3 * q^99

Introduction

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