LMFDB - Embedded newform 1428.2.q.e.613.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1428,2,Mod(205,1428)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1428, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1428.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1428 = 2^{2} \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1428.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.4026374086$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			613.2
Root			$-1.38232 - 0.298668i$ of defining polynomial
Character	$\chi$	$=$	1428.613
Dual form			1428.2.q.e.205.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(-1.14553 - 1.98411i) q^{5} +(-2.63641 - 0.222079i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} +(-1.14553 - 1.98411i) q^{5} +(-2.63641 - 0.222079i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-0.736790 + 1.27616i) q^{11} -4.89962 q^{13} +2.29105 q^{15} +(0.500000 - 0.866025i) q^{17} +(2.93017 + 5.07520i) q^{19} +(1.51053 - 2.17216i) q^{21} +(3.91693 + 6.78433i) q^{23} +(-0.124459 + 0.215569i) q^{25} +1.00000 q^{27} +3.08215 q^{29} +(4.81482 - 8.33951i) q^{31} +(-0.736790 - 1.27616i) q^{33} +(2.57945 + 5.48533i) q^{35} +(-0.852138 - 1.47595i) q^{37} +(2.44981 - 4.24320i) q^{39} +7.79458 q^{41} +10.9324 q^{43} +(-1.14553 + 1.98411i) q^{45} +(-3.34944 - 5.80139i) q^{47} +(6.90136 + 1.17099i) q^{49} +(0.500000 + 0.866025i) q^{51} +(-5.35086 + 9.26796i) q^{53} +3.37605 q^{55} -5.86033 q^{57} +(2.81340 - 4.87295i) q^{59} +(2.14695 + 3.71862i) q^{61} +(1.12588 + 2.39424i) q^{63} +(5.61265 + 9.72139i) q^{65} +(2.48411 - 4.30261i) q^{67} -7.83387 q^{69} -2.74357 q^{71} +(4.45357 - 7.71381i) q^{73} +(-0.124459 - 0.215569i) q^{75} +(2.22589 - 3.20086i) q^{77} +(2.00444 + 3.47179i) q^{79} +(-0.500000 + 0.866025i) q^{81} -4.57743 q^{83} -2.29105 q^{85} +(-1.54108 + 2.66922i) q^{87} +(-0.0396544 - 0.0686835i) q^{89} +(12.9174 + 1.08810i) q^{91} +(4.81482 + 8.33951i) q^{93} +(6.71316 - 11.6275i) q^{95} -4.56388 q^{97} +1.47358 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 2 q^{5} + 3 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 - 2 * q^5 + 3 * q^7 - 4 * q^9	$ 8 q - 4 q^{3} - 2 q^{5} + 3 q^{7} - 4 q^{9} - q^{11} - 20 q^{13} + 4 q^{15} + 4 q^{17} + 9 q^{19} + 5 q^{23} - 18 q^{25} + 8 q^{27} + 10 q^{29} + 24 q^{31} - q^{33} - 18 q^{35} - 2 q^{37} + 10 q^{39} - 28 q^{43} - 2 q^{45} + 2 q^{47} + 5 q^{49} + 4 q^{51} + 15 q^{53} - 60 q^{55} - 18 q^{57} + 37 q^{59} - 19 q^{61} - 3 q^{63} + 21 q^{65} - 2 q^{67} - 10 q^{69} - 22 q^{71} + 9 q^{73} - 18 q^{75} + 13 q^{77} + 9 q^{79} - 4 q^{81} + 16 q^{83} - 4 q^{85} - 5 q^{87} - 22 q^{89} + 7 q^{91} + 24 q^{93} - 33 q^{95} + 26 q^{97} + 2 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 - 2 * q^5 + 3 * q^7 - 4 * q^9 - q^11 - 20 * q^13 + 4 * q^15 + 4 * q^17 + 9 * q^19 + 5 * q^23 - 18 * q^25 + 8 * q^27 + 10 * q^29 + 24 * q^31 - q^33 - 18 * q^35 - 2 * q^37 + 10 * q^39 - 28 * q^43 - 2 * q^45 + 2 * q^47 + 5 * q^49 + 4 * q^51 + 15 * q^53 - 60 * q^55 - 18 * q^57 + 37 * q^59 - 19 * q^61 - 3 * q^63 + 21 * q^65 - 2 * q^67 - 10 * q^69 - 22 * q^71 + 9 * q^73 - 18 * q^75 + 13 * q^77 + 9 * q^79 - 4 * q^81 + 16 * q^83 - 4 * q^85 - 5 * q^87 - 22 * q^89 + 7 * q^91 + 24 * q^93 - 33 * q^95 + 26 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1428\mathbb{Z}\right)^\times$.

$n$	$409$	$715$	$953$	$1261$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$	−1.14553	−	1.98411i	−0.512295	−	0.887321i	−0.999898	−	0.0142554i	$-0.995462\pi$
$5$	−1.14553	−	1.98411i	−0.512295	−	0.887321i	0.487604	−	0.873065i	$-0.337871\pi$
$6$		0			0
$7$	−2.63641	−	0.222079i	−0.996471	−	0.0839380i
$7$	−2.63641	−	0.222079i	−0.996471	−	0.0839380i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−0.736790	+	1.27616i	−0.222151	+	0.384776i	−0.955461	−	0.295118i	$-0.904641\pi$
$11$	−0.736790	+	1.27616i	−0.222151	+	0.384776i	0.733310	+	0.679894i	$0.237974\pi$
$12$		0			0
$13$	−4.89962			−1.35891			−0.679456	−	0.733717i	$-0.737784\pi$
$13$	−4.89962			−1.35891			−0.679456	+	0.733717i	$0.737784\pi$
$14$		0			0
$15$	2.29105			0.591547
$16$		0			0
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$18$		0			0
$19$	2.93017	+	5.07520i	0.672226	+	1.16433i	0.977271	+	0.211992i	$0.0679952\pi$
$19$	2.93017	+	5.07520i	0.672226	+	1.16433i	−0.305045	+	0.952338i	$0.598671\pi$
$20$		0			0
$21$	1.51053	−	2.17216i	0.329625	−	0.474005i
$22$		0			0
$23$	3.91693	+	6.78433i	0.816737	+	1.41463i	0.908074	+	0.418810i	$0.137553\pi$
$23$	3.91693	+	6.78433i	0.816737	+	1.41463i	−0.0913370	+	0.995820i	$0.529114\pi$
$24$		0			0
$25$	−0.124459	+	0.215569i	−0.0248918	+	0.0431139i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	3.08215			0.572341			0.286171	−	0.958179i	$-0.407618\pi$
$29$	3.08215			0.572341			0.286171	+	0.958179i	$0.407618\pi$
$30$		0			0
$31$	4.81482	−	8.33951i	0.864767	−	1.49782i	−0.00251105	−	0.999997i	$-0.500799\pi$
$31$	4.81482	−	8.33951i	0.864767	−	1.49782i	0.867278	−	0.497824i	$-0.165867\pi$
$32$		0			0
$33$	−0.736790	−	1.27616i	−0.128259	−	0.222151i
$34$		0			0
$35$	2.57945	+	5.48533i	0.436007	+	0.927190i
$36$		0			0
$37$	−0.852138	−	1.47595i	−0.140091	−	0.242644i	0.787440	−	0.616391i	$-0.211406\pi$
$37$	−0.852138	−	1.47595i	−0.140091	−	0.242644i	−0.927531	+	0.373747i	$0.878073\pi$
$38$		0			0
$39$	2.44981	−	4.24320i	0.392284	−	0.679456i
$40$		0			0
$41$	7.79458			1.21731			0.608654	−	0.793436i	$-0.291710\pi$
$41$	7.79458			1.21731			0.608654	+	0.793436i	$0.291710\pi$
$42$		0			0
$43$	10.9324			1.66718			0.833589	−	0.552386i	$-0.186282\pi$
$43$	10.9324			1.66718			0.833589	+	0.552386i	$0.186282\pi$
$44$		0			0
$45$	−1.14553	+	1.98411i	−0.170765	+	0.295774i
$46$		0			0
$47$	−3.34944	−	5.80139i	−0.488566	−	0.846220i	0.511348	−	0.859374i	$-0.329146\pi$
$47$	−3.34944	−	5.80139i	−0.488566	−	0.846220i	−0.999913	+	0.0131534i	$0.995813\pi$
$48$		0			0
$49$	6.90136	+	1.17099i	0.985909	+	0.167284i
$50$		0			0
$51$	0.500000	+	0.866025i	0.0700140	+	0.121268i
$52$		0			0
$53$	−5.35086	+	9.26796i	−0.734997	+	1.27305i	0.219728	+	0.975561i	$0.429483\pi$
$53$	−5.35086	+	9.26796i	−0.734997	+	1.27305i	−0.954725	+	0.297491i	$0.903850\pi$
$54$		0			0
$55$	3.37605			0.455226
$56$		0			0
$57$	−5.86033			−0.776220
$58$		0			0
$59$	2.81340	−	4.87295i	0.366273	−	0.634404i	−0.622706	−	0.782456i	$-0.713967\pi$
$59$	2.81340	−	4.87295i	0.366273	−	0.634404i	0.988980	+	0.148052i	$0.0473002\pi$
$60$		0			0
$61$	2.14695	+	3.71862i	0.274888	+	0.476121i	0.970107	−	0.242678i	$-0.0780257\pi$
$61$	2.14695	+	3.71862i	0.274888	+	0.476121i	−0.695218	+	0.718798i	$0.744692\pi$
$62$		0			0
$63$	1.12588	+	2.39424i	0.141848	+	0.301646i
$64$		0			0
$65$	5.61265	+	9.72139i	0.696163	+	1.20579i
$66$		0			0
$67$	2.48411	−	4.30261i	0.303483	−	0.525648i	−0.673440	−	0.739242i	$-0.735184\pi$
$67$	2.48411	−	4.30261i	0.303483	−	0.525648i	0.976922	+	0.213595i	$0.0685172\pi$
$68$		0			0
$69$	−7.83387			−0.943087
$70$		0			0
$71$	−2.74357			−0.325601			−0.162801	−	0.986659i	$-0.552053\pi$
$71$	−2.74357			−0.325601			−0.162801	+	0.986659i	$0.552053\pi$
$72$		0			0
$73$	4.45357	−	7.71381i	0.521251	−	0.902833i	−0.478444	−	0.878118i	$-0.658799\pi$
$73$	4.45357	−	7.71381i	0.521251	−	0.902833i	0.999695	−	0.0247149i	$-0.00786780\pi$
$74$		0			0
$75$	−0.124459	−	0.215569i	−0.0143713	−	0.0248918i
$76$		0			0
$77$	2.22589	−	3.20086i	0.253664	−	0.364771i
$78$		0			0
$79$	2.00444	+	3.47179i	0.225517	+	0.390607i	0.956474	−	0.291816i	$-0.0942596\pi$
$79$	2.00444	+	3.47179i	0.225517	+	0.390607i	−0.730957	+	0.682423i	$0.760926\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−4.57743			−0.502438			−0.251219	−	0.967930i	$-0.580831\pi$
$83$	−4.57743			−0.502438			−0.251219	+	0.967930i	$0.580831\pi$
$84$		0			0
$85$	−2.29105			−0.248499
$86$		0			0
$87$	−1.54108	+	2.66922i	−0.165221	+	0.286171i
$88$		0			0
$89$	−0.0396544	−	0.0686835i	−0.00420336	−	0.00728043i	0.863916	−	0.503636i	$-0.168005\pi$
$89$	−0.0396544	−	0.0686835i	−0.00420336	−	0.00728043i	−0.868119	+	0.496355i	$0.834671\pi$
$90$		0			0
$91$	12.9174	+	1.08810i	1.35412	+	0.114064i
$92$		0			0
$93$	4.81482	+	8.33951i	0.499274	+	0.864767i
$94$		0			0
$95$	6.71316	−	11.6275i	0.688756	−	1.19296i
$96$		0			0
$97$	−4.56388			−0.463392			−0.231696	−	0.972788i	$-0.574427\pi$
$97$	−4.56388			−0.463392			−0.231696	+	0.972788i	$0.574427\pi$
$98$		0			0
$99$	1.47358			0.148100
$100$		0			0
$101$	−4.92371	+	8.52811i	−0.489927	+	0.848579i	−0.999933	−	0.0115922i	$-0.996310\pi$
$101$	−4.92371	+	8.52811i	−0.489927	+	0.848579i	0.510006	+	0.860171i	$0.329643\pi$
$102$		0			0
$103$	6.75996	+	11.7086i	0.666079	+	1.15368i	0.978992	+	0.203900i	$0.0653618\pi$
$103$	6.75996	+	11.7086i	0.666079	+	1.15368i	−0.312913	+	0.949782i	$0.601305\pi$
$104$		0			0
$105$	−6.04016	−	0.508795i	−0.589459	−	0.0496533i
$106$		0			0
$107$	6.62318	+	11.4717i	0.640287	+	1.10901i	0.985369	+	0.170437i	$0.0545179\pi$
$107$	6.62318	+	11.4717i	0.640287	+	1.10901i	−0.345082	+	0.938573i	$0.612149\pi$
$108$		0			0
$109$	8.34440	−	14.4529i	0.799248	−	1.38434i	−0.120858	−	0.992670i	$-0.538564\pi$
$109$	8.34440	−	14.4529i	0.799248	−	1.38434i	0.920106	−	0.391669i	$-0.128102\pi$
$110$		0			0
$111$	1.70428			0.161763
$112$		0			0
$113$	−6.70491			−0.630745			−0.315372	−	0.948968i	$-0.602129\pi$
$113$	−6.70491			−0.630745			−0.315372	+	0.948968i	$0.602129\pi$
$114$		0			0
$115$	8.97390	−	15.5432i	0.836820	−	1.44941i
$116$		0			0
$117$	2.44981	+	4.24320i	0.226485	+	0.392284i
$118$		0			0
$119$	−1.51053	+	2.17216i	−0.138470	+	0.199122i
$120$		0			0
$121$	4.41428	+	7.64576i	0.401298	+	0.695069i
$122$		0			0
$123$	−3.89729	+	6.75030i	−0.351407	+	0.608654i
$124$		0			0
$125$	−10.8850			−0.973582
$126$		0			0
$127$	−15.0539			−1.33581			−0.667907	−	0.744245i	$-0.732810\pi$
$127$	−15.0539			−1.33581			−0.667907	+	0.744245i	$0.732810\pi$
$128$		0			0
$129$	−5.46621	+	9.46775i	−0.481273	+	0.833589i
$130$		0			0
$131$	6.58155	+	11.3996i	0.575033	+	0.995986i	0.996038	+	0.0889281i	$0.0283441\pi$
$131$	6.58155	+	11.3996i	0.575033	+	0.995986i	−0.421005	+	0.907058i	$0.638323\pi$
$132$		0			0
$133$	−6.59804	−	14.0311i	−0.572123	−	1.21665i
$134$		0			0
$135$	−1.14553	−	1.98411i	−0.0985912	−	0.170765i
$136$		0			0
$137$	−7.55477	+	13.0852i	−0.645447	+	1.11795i	0.338750	+	0.940876i	$0.389996\pi$
$137$	−7.55477	+	13.0852i	−0.645447	+	1.11795i	−0.984198	+	0.177072i	$0.943338\pi$
$138$		0			0
$139$	1.49465			0.126774			0.0633871	−	0.997989i	$-0.479810\pi$
$139$	1.49465			0.126774			0.0633871	+	0.997989i	$0.479810\pi$
$140$		0			0
$141$	6.69887			0.564147
$142$		0			0
$143$	3.60999	−	6.25269i	0.301883	−	0.522877i
$144$		0			0
$145$	−3.53069	−	6.11533i	−0.293207	−	0.507850i
$146$		0			0
$147$	−4.46478	+	5.39126i	−0.368249	+	0.444664i
$148$		0			0
$149$	9.74732	+	16.8829i	0.798532	+	1.38310i	0.920572	+	0.390573i	$0.127723\pi$
$149$	9.74732	+	16.8829i	0.798532	+	1.38310i	−0.122040	+	0.992525i	$0.538944\pi$
$150$		0			0
$151$	−1.26056	+	2.18335i	−0.102583	+	0.177679i	−0.912748	−	0.408523i	$-0.866044\pi$
$151$	−1.26056	+	2.18335i	−0.102583	+	0.177679i	0.810165	+	0.586202i	$0.199377\pi$
$152$		0			0
$153$	−1.00000			−0.0808452
$154$		0			0
$155$	−22.0620			−1.77206
$156$		0			0
$157$	−1.59767	+	2.76725i	−0.127508	+	0.220851i	−0.922711	−	0.385493i	$-0.874031\pi$
$157$	−1.59767	+	2.76725i	−0.127508	+	0.220851i	0.795202	+	0.606344i	$0.207365\pi$
$158$		0			0
$159$	−5.35086	−	9.26796i	−0.424351	−	0.734997i
$160$		0			0
$161$	−8.82000	−	18.7562i	−0.695113	−	1.47819i
$162$		0			0
$163$	10.0381	+	17.3866i	0.786248	+	1.36182i	0.928251	+	0.371955i	$0.121312\pi$
$163$	10.0381	+	17.3866i	0.786248	+	1.36182i	−0.142003	+	0.989866i	$0.545354\pi$
$164$		0			0
$165$	−1.68802	+	2.92374i	−0.131413	+	0.227613i
$166$		0			0
$167$	12.8056			0.990925			0.495462	−	0.868629i	$-0.334999\pi$
$167$	12.8056			0.990925			0.495462	+	0.868629i	$0.334999\pi$
$168$		0			0
$169$	11.0063			0.846640
$170$		0			0
$171$	2.93017	−	5.07520i	0.224075	−	0.388110i
$172$		0			0
$173$	−5.76907	−	9.99232i	−0.438614	−	0.759702i	0.558969	−	0.829189i	$-0.311197\pi$
$173$	−5.76907	−	9.99232i	−0.438614	−	0.759702i	−0.997583	+	0.0694866i	$0.977864\pi$
$174$		0			0
$175$	0.375999	−	0.540690i	0.0284229	−	0.0408724i
$176$		0			0
$177$	2.81340	+	4.87295i	0.211468	+	0.366273i
$178$		0			0
$179$	3.45425	−	5.98294i	0.258183	−	0.447186i	−0.707572	−	0.706641i	$-0.750210\pi$
$179$	3.45425	−	5.98294i	0.258183	−	0.447186i	0.965755	+	0.259455i	$0.0835430\pi$
$180$		0			0
$181$	−6.80677			−0.505943			−0.252971	−	0.967474i	$-0.581408\pi$
$181$	−6.80677			−0.505943			−0.252971	+	0.967474i	$0.581408\pi$
$182$		0			0
$183$	−4.29390			−0.317414
$184$		0			0
$185$	−1.95229	+	3.38147i	−0.143535	+	0.248610i
$186$		0			0
$187$	0.736790	+	1.27616i	0.0538794	+	0.0933219i
$188$		0			0
$189$	−2.63641	−	0.222079i	−0.191771	−	0.0161539i
$190$		0			0
$191$	−13.6956	−	23.7215i	−0.990980	−	1.71643i	−0.611543	−	0.791211i	$-0.709451\pi$
$191$	−13.6956	−	23.7215i	−0.990980	−	1.71643i	−0.379437	−	0.925218i	$-0.623882\pi$
$192$		0			0
$193$	7.27585	−	12.6021i	0.523727	−	0.907121i	−0.475892	−	0.879504i	$-0.657875\pi$
$193$	7.27585	−	12.6021i	0.523727	−	0.907121i	0.999619	−	0.0276176i	$-0.00879207\pi$
$194$		0			0
$195$	−11.2253			−0.803860
$196$		0			0
$197$	12.9356			0.921623			0.460812	−	0.887498i	$-0.347558\pi$
$197$	12.9356			0.921623			0.460812	+	0.887498i	$0.347558\pi$
$198$		0			0
$199$	−2.51264	+	4.35201i	−0.178116	+	0.308506i	−0.941235	−	0.337752i	$-0.890334\pi$
$199$	−2.51264	+	4.35201i	−0.178116	+	0.308506i	0.763119	+	0.646258i	$0.223667\pi$
$200$		0			0
$201$	2.48411	+	4.30261i	0.175216	+	0.303483i
$202$		0			0
$203$	−8.12583	−	0.684482i	−0.570322	−	0.0480412i
$204$		0			0
$205$	−8.92889	−	15.4653i	−0.623621	−	1.08014i
$206$		0			0
$207$	3.91693	−	6.78433i	0.272246	−	0.471543i
$208$		0			0
$209$	−8.63567			−0.597342
$210$		0			0
$211$	19.4352			1.33797			0.668987	−	0.743274i	$-0.266728\pi$
$211$	19.4352			1.33797			0.668987	+	0.743274i	$0.266728\pi$
$212$		0			0
$213$	1.37178	−	2.37600i	0.0939930	−	0.162801i
$214$		0			0
$215$	−12.5234	−	21.6911i	−0.854086	−	1.47932i
$216$		0			0
$217$	−14.5459	+	20.9171i	−0.987439	+	1.41995i
$218$		0			0
$219$	4.45357	+	7.71381i	0.300944	+	0.521251i
$220$		0			0
$221$	−2.44981	+	4.24320i	−0.164792	+	0.285428i
$222$		0			0
$223$	23.0892			1.54617			0.773084	−	0.634304i	$-0.218713\pi$
$223$	23.0892			1.54617			0.773084	+	0.634304i	$0.218713\pi$
$224$		0			0
$225$	0.248918			0.0165945
$226$		0			0
$227$	3.68014	−	6.37419i	0.244260	−	0.423070i	−0.717664	−	0.696390i	$-0.754788\pi$
$227$	3.68014	−	6.37419i	0.244260	−	0.423070i	0.961923	+	0.273320i	$0.0881217\pi$
$228$		0			0
$229$	4.51694	+	7.82358i	0.298488	+	0.516996i	0.975790	−	0.218708i	$-0.0701844\pi$
$229$	4.51694	+	7.82358i	0.298488	+	0.516996i	−0.677302	+	0.735705i	$0.736851\pi$
$230$		0			0
$231$	1.65908	+	3.52811i	0.109159	+	0.232132i
$232$		0			0
$233$	7.33181	+	12.6991i	0.480323	+	0.831944i	0.999745	−	0.0225739i	$-0.00718611\pi$
$233$	7.33181	+	12.6991i	0.480323	+	0.831944i	−0.519422	+	0.854518i	$0.673853\pi$
$234$		0			0
$235$	−7.67373	+	13.2913i	−0.500579	+	0.867028i
$236$		0			0
$237$	−4.00888			−0.260405
$238$		0			0
$239$	14.0768			0.910549			0.455275	−	0.890351i	$-0.349541\pi$
$239$	14.0768			0.910549			0.455275	+	0.890351i	$0.349541\pi$
$240$		0			0
$241$	5.82746	−	10.0934i	0.375379	−	0.650176i	−0.615004	−	0.788524i	$-0.710846\pi$
$241$	5.82746	−	10.0934i	0.375379	−	0.650176i	0.990384	+	0.138348i	$0.0441791\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−5.58233	−	15.0344i	−0.356642	−	0.960516i
$246$		0			0
$247$	−14.3567	−	24.8666i	−0.913496	−	1.58222i
$248$		0			0
$249$	2.28872	−	3.96417i	0.145041	−	0.251219i
$250$		0			0
$251$	−14.4043			−0.909194			−0.454597	−	0.890697i	$-0.650217\pi$
$251$	−14.4043			−0.909194			−0.454597	+	0.890697i	$0.650217\pi$
$252$		0			0
$253$	−11.5438			−0.725754
$254$		0			0
$255$	1.14553	−	1.98411i	0.0717356	−	0.124250i
$256$		0			0
$257$	3.33859	+	5.78260i	0.208255	+	0.360709i	0.951165	−	0.308683i	$-0.0998882\pi$
$257$	3.33859	+	5.78260i	0.208255	+	0.360709i	−0.742910	+	0.669392i	$0.766555\pi$
$258$		0			0
$259$	1.91881	+	4.08045i	0.119229	+	0.253547i
$260$		0			0
$261$	−1.54108	−	2.66922i	−0.0953902	−	0.165221i
$262$		0			0
$263$	−10.3664	+	17.9551i	−0.639218	+	1.10716i	0.346386	+	0.938092i	$0.387409\pi$
$263$	−10.3664	+	17.9551i	−0.639218	+	1.10716i	−0.985605	+	0.169067i	$0.945925\pi$
$264$		0			0
$265$	24.5182			1.50614
$266$		0			0
$267$	0.0793088			0.00485362
$268$		0			0
$269$	−1.66691	+	2.88717i	−0.101633	+	0.176034i	−0.912358	−	0.409394i	$-0.865740\pi$
$269$	−1.66691	+	2.88717i	−0.101633	+	0.176034i	0.810724	+	0.585428i	$0.199073\pi$
$270$		0			0
$271$	−10.0917	−	17.4794i	−0.613028	−	1.06180i	−0.990727	−	0.135868i	$-0.956618\pi$
$271$	−10.0917	−	17.4794i	−0.613028	−	1.06180i	0.377698	−	0.925929i	$-0.376716\pi$
$272$		0			0
$273$	−7.40105	+	10.6428i	−0.447932	+	0.644130i
$274$		0			0
$275$	−0.183400	−	0.317659i	−0.0110595	−	0.0191555i
$276$		0			0
$277$	3.18427	−	5.51531i	0.191324	−	0.331383i	−0.754365	−	0.656455i	$-0.772055\pi$
$277$	3.18427	−	5.51531i	0.191324	−	0.331383i	0.945689	+	0.325072i	$0.105389\pi$
$278$		0			0
$279$	−9.62964			−0.576511
$280$		0			0
$281$	−0.681848			−0.0406757			−0.0203378	−	0.999793i	$-0.506474\pi$
$281$	−0.681848			−0.0406757			−0.0203378	+	0.999793i	$0.506474\pi$
$282$		0			0
$283$	16.5110	−	28.5980i	0.981479	−	1.69997i	0.324838	−	0.945770i	$-0.394690\pi$
$283$	16.5110	−	28.5980i	0.981479	−	1.69997i	0.656642	−	0.754203i	$-0.271976\pi$
$284$		0			0
$285$	6.71316	+	11.6275i	0.397654	+	0.688756i
$286$		0			0
$287$	−20.5497	−	1.73101i	−1.21301	−	0.102178i
$288$		0			0
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$		0			0
$291$	2.28194	−	3.95244i	0.133770	−	0.231696i
$292$		0			0
$293$	−11.7974			−0.689213			−0.344606	−	0.938747i	$-0.611988\pi$
$293$	−11.7974			−0.689213			−0.344606	+	0.938747i	$0.611988\pi$
$294$		0			0
$295$	−12.8913			−0.750559
$296$		0			0
$297$	−0.736790	+	1.27616i	−0.0427529	+	0.0740502i
$298$		0			0
$299$	−19.1915	−	33.2407i	−1.10987	−	1.92236i
$300$		0			0
$301$	−28.8224	−	2.42786i	−1.66129	−	0.139940i
$302$		0			0
$303$	−4.92371	−	8.52811i	−0.282860	−	0.489927i
$304$		0			0
$305$	4.91877	−	8.51956i	0.281648	−	0.487828i
$306$		0			0
$307$	0.370361			0.0211376			0.0105688	−	0.999944i	$-0.496636\pi$
$307$	0.370361			0.0211376			0.0105688	+	0.999944i	$0.496636\pi$
$308$		0			0
$309$	−13.5199			−0.769121
$310$		0			0
$311$	15.3878	−	26.6525i	0.872563	−	1.51132i	0.0132262	−	0.999913i	$-0.495790\pi$
$311$	15.3878	−	26.6525i	0.872563	−	1.51132i	0.859337	−	0.511410i	$-0.170877\pi$
$312$		0			0
$313$	−9.11751	−	15.7920i	−0.515352	−	0.892616i	−0.999841	−	0.0178189i	$-0.994328\pi$
$313$	−9.11751	−	15.7920i	−0.515352	−	0.892616i	0.484489	−	0.874797i	$-0.339006\pi$
$314$		0			0
$315$	3.46071	−	4.97654i	0.194989	−	0.280396i
$316$		0			0
$317$	4.82362	+	8.35475i	0.270921	+	0.469249i	0.969098	−	0.246676i	$-0.0793384\pi$
$317$	4.82362	+	8.35475i	0.270921	+	0.469249i	−0.698177	+	0.715925i	$0.746005\pi$
$318$		0			0
$319$	−2.27090	+	3.93331i	−0.127146	+	0.220223i
$320$		0			0
$321$	−13.2464			−0.739340
$322$		0			0
$323$	5.86033			0.326078
$324$		0			0
$325$	0.609803	−	1.05621i	0.0338258	−	0.0585879i
$326$		0			0
$327$	8.34440	+	14.4529i	0.461446	+	0.799248i
$328$		0			0
$329$	7.54213	+	16.0387i	0.415811	+	0.884243i
$330$		0			0
$331$	4.91428	+	8.51178i	0.270113	+	0.467850i	0.968891	−	0.247489i	$-0.0796055\pi$
$331$	4.91428	+	8.51178i	0.270113	+	0.467850i	−0.698777	+	0.715339i	$0.746272\pi$
$332$		0			0
$333$	−0.852138	+	1.47595i	−0.0466969	+	0.0808813i
$334$		0			0
$335$	−11.3825			−0.621891
$336$		0			0
$337$	−2.77288			−0.151048			−0.0755241	−	0.997144i	$-0.524063\pi$
$337$	−2.77288			−0.151048			−0.0755241	+	0.997144i	$0.524063\pi$
$338$		0			0
$339$	3.35245	−	5.80662i	0.182080	−	0.315372i
$340$		0			0
$341$	7.09502	+	12.2889i	0.384217	+	0.665483i
$342$		0			0
$343$	−17.9348	−	4.61985i	−0.968388	−	0.249449i
$344$		0			0
$345$	8.97390	+	15.5432i	0.483138	+	0.836820i
$346$		0			0
$347$	−12.8910	+	22.3278i	−0.692024	+	1.19862i	0.279150	+	0.960247i	$0.409947\pi$
$347$	−12.8910	+	22.3278i	−0.692024	+	1.19862i	−0.971174	+	0.238373i	$0.923386\pi$
$348$		0			0
$349$	−25.0403			−1.34038			−0.670188	−	0.742191i	$-0.733787\pi$
$349$	−25.0403			−1.34038			−0.670188	+	0.742191i	$0.733787\pi$
$350$		0			0
$351$	−4.89962			−0.261523
$352$		0			0
$353$	1.49391	−	2.58752i	0.0795125	−	0.137720i	−0.823527	−	0.567277i	$-0.807997\pi$
$353$	1.49391	−	2.58752i	0.0795125	−	0.137720i	0.903040	+	0.429557i	$0.141330\pi$
$354$		0			0
$355$	3.14282	+	5.44353i	0.166804	+	0.288913i
$356$		0			0
$357$	−1.12588	−	2.39424i	−0.0595879	−	0.126717i
$358$		0			0
$359$	7.29759	+	12.6398i	0.385152	+	0.667103i	0.991790	−	0.127875i	$-0.0408156\pi$
$359$	7.29759	+	12.6398i	0.385152	+	0.667103i	−0.606638	+	0.794978i	$0.707482\pi$
$360$		0			0
$361$	−7.67176	+	13.2879i	−0.403777	+	0.699362i
$362$		0			0
$363$	−8.82856			−0.463379
$364$		0			0
$365$	−20.4067			−1.06814
$366$		0			0
$367$	17.2481	−	29.8746i	0.900343	−	1.55944i	0.0732945	−	0.997310i	$-0.476649\pi$
$367$	17.2481	−	29.8746i	0.900343	−	1.55944i	0.827049	−	0.562130i	$-0.190018\pi$
$368$		0			0
$369$	−3.89729	−	6.75030i	−0.202885	−	0.351407i
$370$		0			0
$371$	16.1653	−	23.2459i	0.839261	−	1.20687i
$372$		0			0
$373$	−12.8167	−	22.1992i	−0.663624	−	1.14943i	−0.979657	−	0.200682i	$-0.935684\pi$
$373$	−12.8167	−	22.1992i	−0.663624	−	1.14943i	0.316033	−	0.948748i	$-0.397649\pi$
$374$		0			0
$375$	5.44249	−	9.42666i	0.281049	−	0.486791i
$376$		0			0
$377$	−15.1014			−0.777761
$378$		0			0
$379$	19.1496			0.983647			0.491823	−	0.870695i	$-0.336331\pi$
$379$	19.1496			0.983647			0.491823	+	0.870695i	$0.336331\pi$
$380$		0			0
$381$	7.52693	−	13.0370i	0.385616	−	0.667907i
$382$		0			0
$383$	15.1587	+	26.2556i	0.774572	+	1.34160i	0.935035	+	0.354556i	$0.115368\pi$
$383$	15.1587	+	26.2556i	0.774572	+	1.34160i	−0.160463	+	0.987042i	$0.551299\pi$
$384$		0			0
$385$	−8.90066	−	0.749750i	−0.453620	−	0.0382108i
$386$		0			0
$387$	−5.46621	−	9.46775i	−0.277863	−	0.481273i
$388$		0			0
$389$	−18.1607	+	31.4552i	−0.920784	+	1.59484i	−0.122578	+	0.992459i	$0.539116\pi$
$389$	−18.1607	+	31.4552i	−0.920784	+	1.59484i	−0.798206	+	0.602385i	$0.794217\pi$
$390$		0			0
$391$	7.83387			0.396176
$392$		0			0
$393$	−13.1631			−0.663991
$394$		0			0
$395$	4.59227	−	7.95405i	0.231062	−	0.400212i
$396$		0			0
$397$	2.27141	+	3.93419i	0.113999	+	0.197451i	0.917379	−	0.398015i	$-0.130301\pi$
$397$	2.27141	+	3.93419i	0.113999	+	0.197451i	−0.803380	+	0.595466i	$0.796967\pi$
$398$		0			0
$399$	15.4503	+	1.30146i	0.773481	+	0.0651544i
$400$		0			0
$401$	−9.54479	−	16.5321i	−0.476644	−	0.825571i	0.522998	−	0.852334i	$-0.324814\pi$
$401$	−9.54479	−	16.5321i	−0.476644	−	0.825571i	−0.999642	+	0.0267626i	$0.991480\pi$
$402$		0			0
$403$	−23.5908	+	40.8605i	−1.17514	+	2.03541i
$404$		0			0
$405$	2.29105			0.113843
$406$		0			0
$407$	2.51139			0.124485
$408$		0			0
$409$	6.41753	−	11.1155i	0.317327	−	0.549626i	−0.662603	−	0.748971i	$-0.730548\pi$
$409$	6.41753	−	11.1155i	0.317327	−	0.549626i	0.979929	+	0.199345i	$0.0638815\pi$
$410$		0			0
$411$	−7.55477	−	13.0852i	−0.372649	−	0.645447i
$412$		0			0
$413$	−8.49946	+	12.2223i	−0.418231	+	0.601421i
$414$		0			0
$415$	5.24357	+	9.08212i	0.257396	+	0.445824i
$416$		0			0
$417$	−0.747323	+	1.29440i	−0.0365966	+	0.0633871i
$418$		0			0
$419$	4.15303			0.202889			0.101444	−	0.994841i	$-0.467654\pi$
$419$	4.15303			0.202889			0.101444	+	0.994841i	$0.467654\pi$
$420$		0			0
$421$	38.0557			1.85472			0.927360	−	0.374170i	$-0.122072\pi$
$421$	38.0557			1.85472			0.927360	+	0.374170i	$0.122072\pi$
$422$		0			0
$423$	−3.34944	+	5.80139i	−0.162855	+	0.282073i
$424$		0			0
$425$	0.124459	+	0.215569i	0.00603715	+	0.0104567i
$426$		0			0
$427$	−4.83442	−	10.2806i	−0.233954	−	0.497514i
$428$		0			0
$429$	3.60999	+	6.25269i	0.174292	+	0.301883i
$430$		0			0
$431$	3.32572	−	5.76031i	0.160194	−	0.277464i	−0.774744	−	0.632275i	$-0.782121\pi$
$431$	3.32572	−	5.76031i	0.160194	−	0.277464i	0.934938	+	0.354811i	$0.115455\pi$
$432$		0			0
$433$	−13.9664			−0.671182			−0.335591	−	0.942008i	$-0.608936\pi$
$433$	−13.9664			−0.671182			−0.335591	+	0.942008i	$0.608936\pi$
$434$		0			0
$435$	7.06137			0.338567
$436$		0			0
$437$	−22.9545	+	39.7584i	−1.09806	+	1.90190i
$438$		0			0
$439$	9.63371	+	16.6861i	0.459792	+	0.796383i	0.998950	−	0.0458217i	$-0.0145906\pi$
$439$	9.63371	+	16.6861i	0.459792	+	0.796383i	−0.539158	+	0.842205i	$0.681257\pi$
$440$		0			0
$441$	−2.43658	−	6.56225i	−0.116028	−	0.312488i
$442$		0			0
$443$	9.09411	+	15.7515i	0.432074	+	0.748374i	0.997052	−	0.0767319i	$-0.0244486\pi$
$443$	9.09411	+	15.7515i	0.432074	+	0.748374i	−0.564978	+	0.825106i	$0.691115\pi$
$444$		0			0
$445$	−0.0908503	+	0.157357i	−0.00430672	+	0.00745946i
$446$		0			0
$447$	−19.4946			−0.922065
$448$		0			0
$449$	23.1290			1.09152			0.545762	−	0.837941i	$-0.316240\pi$
$449$	23.1290			1.09152			0.545762	+	0.837941i	$0.316240\pi$
$450$		0			0
$451$	−5.74297	+	9.94711i	−0.270426	+	0.468391i
$452$		0			0
$453$	−1.26056	−	2.18335i	−0.0592262	−	0.102583i
$454$		0			0
$455$	−12.6383	−	26.8761i	−0.592495	−	1.25997i
$456$		0			0
$457$	−4.71655	−	8.16930i	−0.220631	−	0.382144i	0.734369	−	0.678751i	$-0.237478\pi$
$457$	−4.71655	−	8.16930i	−0.220631	−	0.382144i	−0.955000	+	0.296607i	$0.904145\pi$
$458$		0			0
$459$	0.500000	−	0.866025i	0.0233380	−	0.0404226i
$460$		0			0
$461$	33.7016			1.56964			0.784820	−	0.619723i	$-0.212755\pi$
$461$	33.7016			1.56964			0.784820	+	0.619723i	$0.212755\pi$
$462$		0			0
$463$	−7.72955			−0.359222			−0.179611	−	0.983738i	$-0.557484\pi$
$463$	−7.72955			−0.359222			−0.179611	+	0.983738i	$0.557484\pi$
$464$		0			0
$465$	11.0310	−	19.1063i	0.511550	−	0.886031i
$466$		0			0
$467$	9.79449	+	16.9646i	0.453235	+	0.785026i	0.998585	−	0.0531823i	$-0.0169364\pi$
$467$	9.79449	+	16.9646i	0.453235	+	0.785026i	−0.545350	+	0.838209i	$0.683603\pi$
$468$		0			0
$469$	−7.50467	+	10.7918i	−0.346534	+	0.498319i
$470$		0			0
$471$	−1.59767	−	2.76725i	−0.0736170	−	0.127508i
$472$		0			0
$473$	−8.05489	+	13.9515i	−0.370364	+	0.641490i
$474$		0			0
$475$	−1.45874			−0.0669317
$476$		0			0
$477$	10.7017			0.489998
$478$		0			0
$479$	−16.6433	+	28.8271i	−0.760453	+	1.31714i	0.182164	+	0.983268i	$0.441690\pi$
$479$	−16.6433	+	28.8271i	−0.760453	+	1.31714i	−0.942617	+	0.333875i	$0.891643\pi$
$480$		0			0
$481$	4.17515	+	7.23158i	0.190371	+	0.329732i
$482$		0			0
$483$	20.6533	+	1.73974i	0.939758	+	0.0791608i
$484$		0			0
$485$	5.22804	+	9.05524i	0.237393	+	0.411177i
$486$		0			0
$487$	−6.20058	+	10.7397i	−0.280975	+	0.486663i	−0.971625	−	0.236526i	$-0.923991\pi$
$487$	−6.20058	+	10.7397i	−0.280975	+	0.486663i	0.690650	+	0.723189i	$0.257324\pi$
$488$		0			0
$489$	−20.0763			−0.907881
$490$		0			0
$491$	17.6678			0.797338			0.398669	−	0.917095i	$-0.369472\pi$
$491$	17.6678			0.797338			0.398669	+	0.917095i	$0.369472\pi$
$492$		0			0
$493$	1.54108	−	2.66922i	0.0694066	−	0.120216i
$494$		0			0
$495$	−1.68802	−	2.92374i	−0.0758710	−	0.131413i
$496$		0			0
$497$	7.23317	+	0.609289i	0.324452	+	0.0273303i
$498$		0			0
$499$	6.80677	+	11.7897i	0.304713	+	0.527778i	0.977197	−	0.212333i	$-0.0681062\pi$
$499$	6.80677	+	11.7897i	0.304713	+	0.527778i	−0.672485	+	0.740111i	$0.734773\pi$
$500$		0			0
$501$	−6.40278	+	11.0899i	−0.286055	+	0.495462i
$502$		0			0
$503$	14.1267			0.629877			0.314938	−	0.949112i	$-0.398016\pi$
$503$	14.1267			0.629877			0.314938	+	0.949112i	$0.398016\pi$
$504$		0			0
$505$	22.5609			1.00395
$506$		0			0
$507$	−5.50316	+	9.53175i	−0.244404	+	0.423320i
$508$		0			0
$509$	3.22173	+	5.58019i	0.142801	+	0.247338i	0.928550	−	0.371207i	$-0.121056\pi$
$509$	3.22173	+	5.58019i	0.142801	+	0.247338i	−0.785750	+	0.618545i	$0.787723\pi$
$510$		0			0
$511$	−13.4545	+	19.3478i	−0.595194	+	0.855894i
$512$		0			0
$513$	2.93017	+	5.07520i	0.129370	+	0.224075i
$514$		0			0
$515$	15.4874	−	26.8250i	0.682457	−	1.18205i
$516$		0			0
$517$	9.87133			0.434140
$518$		0			0
$519$	11.5381			0.506468
$520$		0			0
$521$	11.1903	−	19.3822i	0.490256	−	0.849149i	−0.509681	−	0.860364i	$-0.670236\pi$
$521$	11.1903	−	19.3822i	0.490256	−	0.849149i	0.999937	+	0.0112146i	$0.00356979\pi$
$522$		0			0
$523$	−6.07399	−	10.5205i	−0.265597	−	0.460027i	0.702123	−	0.712056i	$-0.252236\pi$
$523$	−6.07399	−	10.5205i	−0.265597	−	0.460027i	−0.967720	+	0.252028i	$0.918902\pi$
$524$		0			0
$525$	0.280252	+	0.595970i	0.0122312	+	0.0260103i
$526$		0			0
$527$	−4.81482	−	8.33951i	−0.209737	−	0.363275i
$528$		0			0
$529$	−19.1847	+	33.2289i	−0.834118	+	1.44474i
$530$		0			0
$531$	−5.62680			−0.244182
$532$		0			0
$533$	−38.1905			−1.65421
$534$		0			0
$535$	15.1740	−	26.2822i	0.656031	−	1.13628i
$536$		0			0
$537$	3.45425	+	5.98294i	0.149062	+	0.258183i
$538$		0			0
$539$	−6.57922	+	7.94446i	−0.283387	+	0.342192i
$540$		0			0
$541$	−4.27485	−	7.40426i	−0.183790	−	0.318334i	0.759378	−	0.650650i	$-0.225503\pi$
$541$	−4.27485	−	7.40426i	−0.183790	−	0.318334i	−0.943168	+	0.332316i	$0.892170\pi$
$542$		0			0
$543$	3.40338	−	5.89483i	0.146053	−	0.252971i
$544$		0			0
$545$	−38.2349			−1.63780
$546$		0			0
$547$	−22.3676			−0.956370			−0.478185	−	0.878259i	$-0.658705\pi$
$547$	−22.3676			−0.956370			−0.478185	+	0.878259i	$0.658705\pi$
$548$		0			0
$549$	2.14695	−	3.71862i	0.0916295	−	0.158707i
$550$		0			0
$551$	9.03122	+	15.6425i	0.384743	+	0.666394i
$552$		0			0
$553$	−4.51352	−	9.59822i	−0.191934	−	0.408158i
$554$		0			0
$555$	−1.95229	−	3.38147i	−0.0828702	−	0.143535i
$556$		0			0
$557$	19.0216	−	32.9463i	0.805970	−	1.39598i	−0.109664	−	0.993969i	$-0.534978\pi$
$557$	19.0216	−	32.9463i	0.805970	−	1.39598i	0.915634	−	0.402012i	$-0.131689\pi$
$558$		0			0
$559$	−53.5647			−2.26555
$560$		0			0
$561$	−1.47358			−0.0622146
$562$		0			0
$563$	14.4512	−	25.0303i	0.609047	−	1.05490i	−0.382351	−	0.924017i	$-0.624885\pi$
$563$	14.4512	−	25.0303i	0.609047	−	1.05490i	0.991398	−	0.130883i	$-0.0417812\pi$
$564$		0			0
$565$	7.68064	+	13.3033i	0.323127	+	0.559673i
$566$		0			0
$567$	1.51053	−	2.17216i	0.0634364	−	0.0912222i
$568$		0			0
$569$	−15.7795	−	27.3308i	−0.661509	−	1.14577i	−0.980219	−	0.197916i	$-0.936583\pi$
$569$	−15.7795	−	27.3308i	−0.661509	−	1.14577i	0.318710	−	0.947852i	$-0.396751\pi$
$570$		0			0
$571$	0.831448	−	1.44011i	0.0347950	−	0.0602667i	−0.848103	−	0.529831i	$-0.822255\pi$
$571$	0.831448	−	1.44011i	0.0347950	−	0.0602667i	0.882899	+	0.469564i	$0.155589\pi$
$572$		0			0
$573$	27.3912			1.14429
$574$		0			0
$575$	−1.94999			−0.0813202
$576$		0			0
$577$	−3.24998	+	5.62912i	−0.135298	+	0.234343i	−0.925711	−	0.378231i	$-0.876533\pi$
$577$	−3.24998	+	5.62912i	−0.135298	+	0.234343i	0.790413	+	0.612574i	$0.209866\pi$
$578$		0			0
$579$	7.27585	+	12.6021i	0.302374	+	0.523727i
$580$		0			0
$581$	12.0680	+	1.01655i	0.500665	+	0.0421737i
$582$		0			0
$583$	−7.88492	−	13.6571i	−0.326560	−	0.565618i
$584$		0			0
$585$	5.61265	−	9.72139i	0.232054	−	0.401930i
$586$		0			0
$587$	−18.7633			−0.774446			−0.387223	−	0.921986i	$-0.626566\pi$
$587$	−18.7633			−0.774446			−0.387223	+	0.921986i	$0.626566\pi$
$588$		0			0
$589$	56.4329			2.32528
$590$		0			0
$591$	−6.46780	+	11.2026i	−0.266050	+	0.460812i
$592$		0			0
$593$	−9.49743	−	16.4500i	−0.390013	−	0.675522i	0.602438	−	0.798166i	$-0.294196\pi$
$593$	−9.49743	−	16.4500i	−0.390013	−	0.675522i	−0.992451	+	0.122644i	$0.960863\pi$
$594$		0			0
$595$	6.04016	+	0.508795i	0.247622	+	0.0208586i
$596$		0			0
$597$	−2.51264	−	4.35201i	−0.102835	−	0.178116i
$598$		0			0
$599$	10.0649	−	17.4329i	0.411240	−	0.712288i	−0.583786	−	0.811908i	$-0.698429\pi$
$599$	10.0649	−	17.4329i	0.411240	−	0.712288i	0.995026	+	0.0996196i	$0.0317626\pi$
$600$		0			0
$601$	31.6416			1.29069			0.645345	−	0.763891i	$-0.276714\pi$
$601$	31.6416			1.29069			0.645345	+	0.763891i	$0.276714\pi$
$602$		0			0
$603$	−4.96823			−0.202322
$604$		0			0
$605$	10.1133	−	17.5168i	0.411166	−	0.712160i
$606$		0			0
$607$	−17.4993	−	30.3097i	−0.710275	−	1.23023i	−0.964754	−	0.263154i	$-0.915237\pi$
$607$	−17.4993	−	30.3097i	−0.710275	−	1.23023i	0.254479	−	0.967078i	$-0.418096\pi$
$608$		0			0
$609$	4.65569	−	6.69494i	0.188658	−	0.271292i
$610$		0			0
$611$	16.4110	+	28.4247i	0.663917	+	1.14994i
$612$		0			0
$613$	17.3880	−	30.1170i	0.702296	−	1.21641i	−0.265362	−	0.964149i	$-0.585492\pi$
$613$	17.3880	−	30.1170i	0.702296	−	1.21641i	0.967658	−	0.252264i	$-0.0811751\pi$
$614$		0			0
$615$	17.8578			0.720095
$616$		0			0
$617$	11.1428			0.448592			0.224296	−	0.974521i	$-0.427992\pi$
$617$	11.1428			0.448592			0.224296	+	0.974521i	$0.427992\pi$
$618$		0			0
$619$	−1.03580	+	1.79407i	−0.0416325	+	0.0721096i	−0.886091	−	0.463512i	$-0.846589\pi$
$619$	−1.03580	+	1.79407i	−0.0416325	+	0.0721096i	0.844458	+	0.535621i	$0.179923\pi$
$620$		0			0
$621$	3.91693	+	6.78433i	0.157181	+	0.272246i
$622$		0			0
$623$	0.0892923	+	0.189885i	0.00357742	+	0.00760756i
$624$		0			0
$625$	13.0913	+	22.6748i	0.523653	+	0.906993i
$626$		0			0
$627$	4.31784	−	7.47871i	0.172438	−	0.298671i
$628$		0			0
$629$	−1.70428			−0.0679539
$630$		0			0
$631$	29.4945			1.17416			0.587078	−	0.809530i	$-0.300278\pi$
$631$	29.4945			1.17416			0.587078	+	0.809530i	$0.300278\pi$
$632$		0			0
$633$	−9.71760	+	16.8314i	−0.386240	+	0.668987i
$634$		0			0
$635$	17.2446	+	29.8685i	0.684330	+	1.18529i
$636$		0			0
$637$	−33.8141	−	5.73739i	−1.33976	−	0.227324i
$638$		0			0
$639$	1.37178	+	2.37600i	0.0542669	+	0.0939930i
$640$		0			0
$641$	8.17643	−	14.1620i	0.322950	−	0.559365i	−0.658146	−	0.752891i	$-0.728659\pi$
$641$	8.17643	−	14.1620i	0.322950	−	0.559365i	0.981095	+	0.193525i	$0.0619922\pi$
$642$		0			0
$643$	7.59072			0.299349			0.149674	−	0.988735i	$-0.452177\pi$
$643$	7.59072			0.299349			0.149674	+	0.988735i	$0.452177\pi$
$644$		0			0
$645$	25.0467			0.986214
$646$		0			0
$647$	5.93140	−	10.2735i	0.233187	−	0.403892i	−0.725557	−	0.688162i	$-0.758418\pi$
$647$	5.93140	−	10.2735i	0.233187	−	0.403892i	0.958744	+	0.284270i	$0.0917511\pi$
$648$		0			0
$649$	4.14577	+	7.18068i	0.162736	+	0.281866i
$650$		0			0
$651$	−10.8418	−	23.0557i	−0.424925	−	0.903623i
$652$		0			0
$653$	21.5339	+	37.2979i	0.842688	+	1.45958i	0.887614	+	0.460588i	$0.152361\pi$
$653$	21.5339	+	37.2979i	0.842688	+	1.45958i	−0.0449267	+	0.998990i	$0.514305\pi$
$654$		0			0
$655$	15.0787	−	26.1170i	0.589173	−	1.02048i
$656$		0			0
$657$	−8.90714			−0.347501
$658$		0			0
$659$	−41.4674			−1.61534			−0.807670	−	0.589635i	$-0.799271\pi$
$659$	−41.4674			−1.61534			−0.807670	+	0.589635i	$0.799271\pi$
$660$		0			0
$661$	−17.3849	+	30.1115i	−0.676193	+	1.17120i	0.299925	+	0.953963i	$0.403038\pi$
$661$	−17.3849	+	30.1115i	−0.676193	+	1.17120i	−0.976119	+	0.217238i	$0.930295\pi$
$662$		0			0
$663$	−2.44981	−	4.24320i	−0.0951428	−	0.164792i
$664$		0			0
$665$	−20.2809	+	29.1642i	−0.786460	+	1.13094i
$666$		0			0
$667$	12.0726	+	20.9103i	0.467452	+	0.809651i
$668$		0			0
$669$	−11.5446	+	19.9958i	−0.446340	+	0.773084i
$670$		0			0
$671$	−6.32740			−0.244267
$672$		0			0
$673$	22.4767			0.866413			0.433207	−	0.901295i	$-0.357382\pi$
$673$	22.4767			0.866413			0.433207	+	0.901295i	$0.357382\pi$
$674$		0			0
$675$	−0.124459	+	0.215569i	−0.00479043	+	0.00829727i
$676$		0			0
$677$	−15.0843	−	26.1267i	−0.579735	−	1.00413i	−0.995509	−	0.0946633i	$-0.969823\pi$
$677$	−15.0843	−	26.1267i	−0.579735	−	1.00413i	0.415774	−	0.909468i	$-0.363511\pi$
$678$		0			0
$679$	12.0323	+	1.01354i	0.461757	+	0.0388962i
$680$		0			0
$681$	3.68014	+	6.37419i	0.141023	+	0.244260i
$682$		0			0
$683$	−21.5045	+	37.2469i	−0.822846	+	1.42521i	0.0807077	+	0.996738i	$0.474282\pi$
$683$	−21.5045	+	37.2469i	−0.822846	+	1.42521i	−0.903554	+	0.428474i	$0.859051\pi$
$684$		0			0
$685$	34.6167			1.32264
$686$		0			0
$687$	−9.03389			−0.344664
$688$		0			0
$689$	26.2172	−	45.4095i	0.998796	−	1.72996i
$690$		0			0
$691$	17.3479	+	30.0475i	0.659946	+	1.14306i	0.980629	+	0.195874i	$0.0627542\pi$
$691$	17.3479	+	30.0475i	0.659946	+	1.14306i	−0.320683	+	0.947187i	$0.603912\pi$
$692$		0			0
$693$	−3.88497	−	0.327251i	−0.147578	−	0.0124313i
$694$		0			0
$695$	−1.71216	−	2.96554i	−0.0649458	−	0.112489i
$696$		0			0
$697$	3.89729	−	6.75030i	0.147620	−	0.255686i
$698$		0			0
$699$	−14.6636			−0.554629
$700$		0			0
$701$	19.2181			0.725856			0.362928	−	0.931817i	$-0.381777\pi$
$701$	19.2181			0.725856			0.362928	+	0.931817i	$0.381777\pi$
$702$		0			0
$703$	4.99381	−	8.64954i	0.188345	−	0.326223i
$704$		0			0
$705$	−7.67373	−	13.2913i	−0.289009	−	0.500579i
$706$		0			0
$707$	14.8748	−	21.3902i	0.559426	−	0.804461i
$708$		0			0
$709$	−17.2125	−	29.8129i	−0.646428	−	1.11965i	−0.983970	−	0.178336i	$-0.942929\pi$
$709$	−17.2125	−	29.8129i	−0.646428	−	1.11965i	0.337542	−	0.941311i	$-0.390405\pi$
$710$		0			0
$711$	2.00444	−	3.47179i	0.0751723	−	0.130202i
$712$		0			0
$713$	75.4373			2.82515
$714$		0			0
$715$	−16.5414			−0.618612
$716$		0			0
$717$	−7.03838	+	12.1908i	−0.262853	+	0.455275i
$718$		0			0
$719$	17.0972	+	29.6132i	0.637618	+	1.10439i	0.985954	+	0.167017i	$0.0534136\pi$
$719$	17.0972	+	29.6132i	0.637618	+	1.10439i	−0.348336	+	0.937370i	$0.613253\pi$
$720$		0			0
$721$	−15.2218	−	32.3699i	−0.566890	−	1.20552i
$722$		0			0
$723$	5.82746	+	10.0934i	0.216725	+	0.375379i
$724$		0			0
$725$	−0.383602	+	0.664418i	−0.0142466	+	0.0246759i
$726$		0			0
$727$	25.8650			0.959280			0.479640	−	0.877465i	$-0.340767\pi$
$727$	25.8650			0.959280			0.479640	+	0.877465i	$0.340767\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	5.46621	−	9.46775i	0.202175	−	0.350177i
$732$		0			0
$733$	−8.82649	−	15.2879i	−0.326014	−	0.564673i	0.655703	−	0.755019i	$-0.272372\pi$
$733$	−8.82649	−	15.2879i	−0.326014	−	0.564673i	−0.981717	+	0.190346i	$0.939039\pi$
$734$		0			0
$735$	15.8114	+	2.68279i	0.583211	+	0.0989561i
$736$		0			0
$737$	3.66054	+	6.34024i	0.134838	+	0.233546i
$738$		0			0
$739$	−11.6434	+	20.1669i	−0.428309	+	0.741852i	−0.996723	−	0.0808900i	$-0.974224\pi$
$739$	−11.6434	+	20.1669i	−0.428309	+	0.741852i	0.568414	+	0.822742i	$0.307557\pi$
$740$		0			0
$741$	28.7134			1.05481
$742$		0			0
$743$	24.9103			0.913869			0.456935	−	0.889500i	$-0.348947\pi$
$743$	24.9103			0.913869			0.456935	+	0.889500i	$0.348947\pi$
$744$		0			0
$745$	22.3316	−	38.6795i	0.818167	−	1.41711i
$746$		0			0
$747$	2.28872	+	3.96417i	0.0837397	+	0.145041i
$748$		0			0
$749$	−14.9138	−	31.7150i	−0.544939	−	1.15884i
$750$		0			0
$751$	13.7399	+	23.7983i	0.501378	+	0.868412i	0.999999	+	0.00159176i	$0.000506674\pi$
$751$	13.7399	+	23.7983i	0.501378	+	0.868412i	−0.498621	+	0.866820i	$0.666160\pi$
$752$		0			0
$753$	7.20217	−	12.4745i	0.262462	−	0.454597i
$754$		0			0
$755$	5.77601			0.210210
$756$		0			0
$757$	−10.2235			−0.371578			−0.185789	−	0.982590i	$-0.559484\pi$
$757$	−10.2235			−0.371578			−0.185789	+	0.982590i	$0.559484\pi$
$758$		0			0
$759$	5.77191	−	9.99725i	0.209507	−	0.362877i
$760$		0			0
$761$	−3.91324	−	6.77792i	−0.141855	−	0.245700i	0.786340	−	0.617794i	$-0.211973\pi$
$761$	−3.91324	−	6.77792i	−0.141855	−	0.245700i	−0.928195	+	0.372094i	$0.878640\pi$
$762$		0			0
$763$	−25.2090	+	36.2508i	−0.912627	+	1.31237i
$764$		0			0
$765$	1.14553	+	1.98411i	0.0414166	+	0.0717356i
$766$		0			0
$767$	−13.7846	+	23.8756i	−0.497733	+	0.862098i
$768$		0			0
$769$	−44.2965			−1.59737			−0.798686	−	0.601749i	$-0.794471\pi$
$769$	−44.2965			−1.59737			−0.798686	+	0.601749i	$0.794471\pi$
$770$		0			0
$771$	−6.67718			−0.240473
$772$		0			0
$773$	−14.8262	+	25.6798i	−0.533262	+	0.923637i	0.465983	+	0.884794i	$0.345701\pi$
$773$	−14.8262	+	25.6798i	−0.533262	+	0.923637i	−0.999245	+	0.0388437i	$0.987633\pi$
$774$		0			0
$775$	1.19850	+	2.07586i	0.0430512	+	0.0745669i
$776$		0			0
$777$	−4.49318	−	0.378484i	−0.161192	−	0.0135780i
$778$		0			0
$779$	22.8394	+	39.5590i	0.818307	+	1.41735i
$780$		0			0
$781$	2.02143	−	3.50122i	0.0723325	−	0.125284i
$782$		0			0
$783$	3.08215			0.110147
$784$		0			0
$785$	7.32071			0.261287
$786$		0			0
$787$	−22.0083	+	38.1195i	−0.784511	+	1.35881i	0.144780	+	0.989464i	$0.453753\pi$
$787$	−22.0083	+	38.1195i	−0.784511	+	1.35881i	−0.929291	+	0.369349i	$0.879581\pi$
$788$		0			0
$789$	−10.3664	−	17.9551i	−0.369053	−	0.639218i
$790$		0			0
$791$	17.6769	+	1.48902i	0.628519	+	0.0529435i
$792$		0			0
$793$	−10.5192	−	18.2199i	−0.373549	−	0.647006i
$794$		0			0
$795$	−12.2591	+	21.2334i	−0.434785	+	0.753070i
$796$		0			0
$797$	13.9946			0.495714			0.247857	−	0.968797i	$-0.420274\pi$
$797$	13.9946			0.495714			0.247857	+	0.968797i	$0.420274\pi$
$798$		0			0
$799$	−6.69887			−0.236989
$800$		0			0
$801$	−0.0396544	+	0.0686835i	−0.00140112	+	0.00242681i
$802$		0			0
$803$	6.56269	+	11.3669i	0.231592	+	0.401130i
$804$		0			0
$805$	−27.1107	+	38.9855i	−0.955528	+	1.37406i
$806$		0			0
$807$	−1.66691	−	2.88717i	−0.0586779	−	0.101633i
$808$		0			0
$809$	22.7492	−	39.4027i	0.799818	−	1.38532i	−0.119917	−	0.992784i	$-0.538263\pi$
$809$	22.7492	−	39.4027i	0.799818	−	1.38532i	0.919735	−	0.392541i	$-0.128404\pi$
$810$		0			0
$811$	40.5999			1.42565			0.712827	−	0.701340i	$-0.247414\pi$
$811$	40.5999			1.42565			0.712827	+	0.701340i	$0.247414\pi$
$812$		0			0
$813$	20.1834			0.707864
$814$		0			0
$815$	22.9979	−	39.8335i	0.805581	−	1.39531i
$816$		0			0
$817$	32.0338	+	55.4842i	1.12072	+	1.94115i
$818$		0			0
$819$	−5.51639	−	11.7309i	−0.192758	−	0.409910i
$820$		0			0
$821$	−11.4594	−	19.8483i	−0.399937	−	0.692711i	0.593781	−	0.804627i	$-0.297635\pi$
$821$	−11.4594	−	19.8483i	−0.399937	−	0.692711i	−0.993718	+	0.111916i	$0.964301\pi$
$822$		0			0
$823$	−10.7534	+	18.6254i	−0.374838	+	0.649239i	−0.990303	−	0.138925i	$-0.955635\pi$
$823$	−10.7534	+	18.6254i	−0.374838	+	0.649239i	0.615464	+	0.788165i	$0.288968\pi$
$824$		0			0
$825$	0.366801			0.0127704
$826$		0			0
$827$	3.07905			0.107069			0.0535345	−	0.998566i	$-0.482951\pi$
$827$	3.07905			0.107069			0.0535345	+	0.998566i	$0.482951\pi$
$828$		0			0
$829$	−22.5949	+	39.1355i	−0.784753	+	1.35923i	0.144394	+	0.989520i	$0.453877\pi$
$829$	−22.5949	+	39.1355i	−0.784753	+	1.35923i	−0.929147	+	0.369711i	$0.879457\pi$
$830$		0			0
$831$	3.18427	+	5.51531i	0.110461	+	0.191324i
$832$		0			0
$833$	4.46478	−	5.39126i	0.154696	−	0.186796i
$834$		0			0
$835$	−14.6691	−	25.4076i	−0.507645	−	0.879268i
$836$		0			0
$837$	4.81482	−	8.33951i	0.166425	−	0.288256i
$838$		0			0
$839$	−46.4316			−1.60300			−0.801499	−	0.597996i	$-0.795964\pi$
$839$	−46.4316			−1.60300			−0.801499	+	0.597996i	$0.795964\pi$
$840$		0			0
$841$	−19.5003			−0.672425
$842$		0			0
$843$	0.340924	−	0.590498i	0.0117421	−	0.0203378i
$844$		0			0
$845$	−12.6080	−	21.8377i	−0.433729	−	0.751241i
$846$		0			0
$847$	−9.93991	−	21.1377i	−0.341539	−	0.726300i
$848$		0			0
$849$	16.5110	+	28.5980i	0.566657	+	0.981479i
$850$		0			0
$851$	6.67553	−	11.5624i	0.228834	−	0.396353i
$852$		0			0
$853$	−15.1781			−0.519690			−0.259845	−	0.965650i	$-0.583671\pi$
$853$	−15.1781			−0.519690			−0.259845	+	0.965650i	$0.583671\pi$
$854$		0			0
$855$	−13.4263			−0.459171
$856$		0			0
$857$	−25.8579	+	44.7871i	−0.883288	+	1.52990i	−0.0356237	+	0.999365i	$0.511342\pi$
$857$	−25.8579	+	44.7871i	−0.883288	+	1.52990i	−0.847664	+	0.530534i	$0.821992\pi$
$858$		0			0
$859$	24.6169	+	42.6378i	0.839919	+	1.45478i	0.889961	+	0.456036i	$0.150731\pi$
$859$	24.6169	+	42.6378i	0.839919	+	1.45478i	−0.0500422	+	0.998747i	$0.515936\pi$
$860$		0			0
$861$	11.7740	−	16.9311i	0.401256	−	0.577010i
$862$		0			0
$863$	−13.5101	−	23.4002i	−0.459890	−	0.796553i	0.539065	−	0.842264i	$-0.318778\pi$
$863$	−13.5101	−	23.4002i	−0.459890	−	0.796553i	−0.998955	+	0.0457115i	$0.985445\pi$
$864$		0			0
$865$	−13.2172	+	22.8929i	−0.449400	+	0.778383i
$866$		0			0
$867$	1.00000			0.0339618
$868$		0			0
$869$	−5.90740			−0.200395
$870$		0			0
$871$	−12.1712	+	21.0812i	−0.412406	+	0.714308i
$872$		0			0
$873$	2.28194	+	3.95244i	0.0772320	+	0.133770i
$874$		0			0
$875$	28.6973	+	2.41733i	0.970146	+	0.0817205i
$876$		0			0
$877$	0.774566	+	1.34159i	0.0261552	+	0.0453022i	0.878807	−	0.477178i	$-0.158340\pi$
$877$	0.774566	+	1.34159i	0.0261552	+	0.0453022i	−0.852652	+	0.522480i	$0.825007\pi$
$878$		0			0
$879$	5.89871	−	10.2169i	0.198959	−	0.344606i
$880$		0			0
$881$	−8.30444			−0.279784			−0.139892	−	0.990167i	$-0.544675\pi$
$881$	−8.30444			−0.279784			−0.139892	+	0.990167i	$0.544675\pi$
$882$		0			0
$883$	−13.3328			−0.448685			−0.224342	−	0.974510i	$-0.572023\pi$
$883$	−13.3328			−0.448685			−0.224342	+	0.974510i	$0.572023\pi$
$884$		0			0
$885$	6.44564	−	11.1642i	0.216668	−	0.375280i
$886$		0			0
$887$	−23.1013	−	40.0126i	−0.775665	−	1.34349i	−0.934420	−	0.356173i	$-0.884081\pi$
$887$	−23.1013	−	40.0126i	−0.775665	−	1.34349i	0.158755	−	0.987318i	$-0.449252\pi$
$888$		0			0
$889$	39.6882	+	3.34315i	1.33110	+	0.112126i
$890$		0			0
$891$	−0.736790	−	1.27616i	−0.0246834	−	0.0427529i
$892$		0			0
$893$	19.6288	−	33.9981i	0.656853	−	1.13770i
$894$		0			0
$895$	−15.8277			−0.529063
$896$		0			0
$897$	38.3830			1.28157
$898$		0			0
$899$	14.8400	−	25.7037i	0.494942	−	0.857265i
$900$		0			0
$901$	5.35086	+	9.26796i	0.178263	+	0.308760i
$902$		0			0
$903$	16.5138	−	23.7470i	0.549544	−	0.790250i
$904$		0			0
$905$	7.79733	+	13.5054i	0.259192	+	0.448934i
$906$		0			0
$907$	−27.4169	+	47.4874i	−0.910363	+	1.57679i	−0.0968108	+	0.995303i	$0.530864\pi$
$907$	−27.4169	+	47.4874i	−0.910363	+	1.57679i	−0.813552	+	0.581492i	$0.802469\pi$
$908$		0			0
$909$	9.84742			0.326618
$910$		0			0
$911$	22.7887			0.755023			0.377512	−	0.926005i	$-0.376780\pi$
$911$	22.7887			0.755023			0.377512	+	0.926005i	$0.376780\pi$
$912$		0			0
$913$	3.37261	−	5.84152i	0.111617	−	0.193326i
$914$		0			0
$915$	4.91877	+	8.51956i	0.162609	+	0.281648i
$916$		0			0
$917$	−14.8201	−	31.5157i	−0.489403	−	1.04074i
$918$		0			0
$919$	−18.4818	−	32.0114i	−0.609659	−	1.05596i	−0.991297	−	0.131648i	$-0.957973\pi$
$919$	−18.4818	−	32.0114i	−0.609659	−	1.05596i	0.381638	−	0.924312i	$-0.375360\pi$
$920$		0			0
$921$	−0.185180	+	0.320742i	−0.00610190	+	0.0105688i
$922$		0			0
$923$	13.4424			0.442463
$924$		0			0
$925$	0.424225			0.0139484
$926$		0			0
$927$	6.75996	−	11.7086i	0.222026	−	0.384561i
$928$		0			0
$929$	1.80566	+	3.12749i	0.0592418	+	0.102610i	0.894125	−	0.447817i	$-0.147798\pi$
$929$	1.80566	+	3.12749i	0.0592418	+	0.102610i	−0.834883	+	0.550427i	$0.814465\pi$
$930$		0			0
$931$	14.2792	+	38.4570i	0.467981	+	1.26038i
$932$		0			0
$933$	15.3878	+	26.6525i	0.503774	+	0.872563i
$934$		0			0
$935$	1.68802	−	2.92374i	0.0552043	−	0.0956166i
$936$		0			0
$937$	−38.8014			−1.26759			−0.633794	−	0.773502i	$-0.718503\pi$
$937$	−38.8014			−1.26759			−0.633794	+	0.773502i	$0.718503\pi$
$938$		0			0
$939$	18.2350			0.595077
$940$		0			0
$941$	−16.9819	+	29.4134i	−0.553593	+	0.958851i	0.444419	+	0.895819i	$0.353410\pi$
$941$	−16.9819	+	29.4134i	−0.553593	+	0.958851i	−0.998012	+	0.0630316i	$0.979923\pi$
$942$		0			0
$943$	30.5308	+	52.8809i	0.994221	+	1.72204i
$944$		0			0
$945$	2.57945	+	5.48533i	0.0839096	+	0.178438i
$946$		0			0
$947$	−1.22488	−	2.12156i	−0.0398034	−	0.0689415i	0.845437	−	0.534075i	$-0.179340\pi$
$947$	−1.22488	−	2.12156i	−0.0398034	−	0.0689415i	−0.885241	+	0.465133i	$0.846006\pi$
$948$		0			0
$949$	−21.8208	+	37.7948i	−0.708334	+	1.22687i
$950$		0			0
$951$	−9.64723			−0.312833
$952$		0			0
$953$	37.0641			1.20062			0.600312	−	0.799766i	$-0.295043\pi$
$953$	37.0641			1.20062			0.600312	+	0.799766i	$0.295043\pi$
$954$		0			0
$955$	−31.3774	+	54.3472i	−1.01535	+	1.75863i
$956$		0			0
$957$	−2.27090	−	3.93331i	−0.0734078	−	0.127146i
$958$		0			0
$959$	22.8235	−	32.8204i	0.737008	−	1.05982i
$960$		0			0
$961$	−30.8650	−	53.4597i	−0.995644	−	1.72451i
$962$		0			0
$963$	6.62318	−	11.4717i	0.213429	−	0.369670i
$964$		0			0
$965$	−33.3387			−1.07321
$966$		0			0
$967$	−19.1733			−0.616573			−0.308287	−	0.951294i	$-0.599756\pi$
$967$	−19.1733			−0.616573			−0.308287	+	0.951294i	$0.599756\pi$
$968$		0			0
$969$	−2.93017	+	5.07520i	−0.0941305	+	0.163039i
$970$		0			0
$971$	8.21647	+	14.2313i	0.263679	+	0.456705i	0.967217	−	0.253953i	$-0.0817307\pi$
$971$	8.21647	+	14.2313i	0.263679	+	0.456705i	−0.703538	+	0.710658i	$0.748397\pi$
$972$		0			0
$973$	−3.94051	−	0.331930i	−0.126327	−	0.0106412i
$974$		0			0
$975$	0.609803	+	1.05621i	0.0195293	+	0.0338258i
$976$		0			0
$977$	8.75786	−	15.1691i	0.280189	−	0.485301i	−0.691242	−	0.722623i	$-0.742936\pi$
$977$	8.75786	−	15.1691i	0.280189	−	0.485301i	0.971431	+	0.237322i	$0.0762696\pi$
$978$		0			0
$979$	0.116868			0.00373512
$980$		0			0
$981$	−16.6888			−0.532832
$982$		0			0
$983$	10.2905	−	17.8237i	0.328216	−	0.568487i	−0.653942	−	0.756545i	$-0.726886\pi$
$983$	10.2905	−	17.8237i	0.328216	−	0.568487i	0.982158	+	0.188058i	$0.0602193\pi$
$984$		0			0
$985$	−14.8181	−	25.6656i	−0.472143	−	0.817775i
$986$		0			0
$987$	−17.6610	−	1.48768i	−0.562156	−	0.0473534i
$988$		0			0
$989$	42.8215	+	74.1691i	1.36165	+	2.35844i
$990$		0			0
$991$	6.75057	−	11.6923i	0.214439	−	0.371419i	−0.738660	−	0.674078i	$-0.764541\pi$
$991$	6.75057	−	11.6923i	0.214439	−	0.371419i	0.953099	+	0.302659i	$0.0978743\pi$
$992$		0			0
$993$	−9.82856			−0.311900
$994$		0			0
$995$	11.5132			0.364992
$996$		0			0
$997$	7.88437	−	13.6561i	0.249700	−	0.432494i	−0.713742	−	0.700409i	$-0.753001\pi$
$997$	7.88437	−	13.6561i	0.249700	−	0.432494i	0.963443	+	0.267915i	$0.0863345\pi$
$998$		0			0
$999$	−0.852138	−	1.47595i	−0.0269604	−	0.0466969i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1428.2.q.e.613.2	yes	8
7.2	even	3	inner	1428.2.q.e.205.2	✓	8
7.3	odd	6		9996.2.a.z.1.2		4
7.4	even	3		9996.2.a.bd.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1428.2.q.e.205.2	✓	8	7.2	even	3	inner
1428.2.q.e.613.2	yes	8	1.1	even	1	trivial
9996.2.a.z.1.2		4	7.3	odd	6
9996.2.a.bd.1.3		4	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1428 = 2^{2} \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1428.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-1.14553 - 1.98411i) q^{5} +(-2.63641 - 0.222079i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-1.14553 - 1.98411i) q^{5} +(-2.63641 - 0.222079i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-0.736790 + 1.27616i) q^{11} -4.89962 q^{13} +2.29105 q^{15} +(0.500000 - 0.866025i) q^{17} +(2.93017 + 5.07520i) q^{19} +(1.51053 - 2.17216i) q^{21} +(3.91693 + 6.78433i) q^{23} +(-0.124459 + 0.215569i) q^{25} +1.00000 q^{27} +3.08215 q^{29} +(4.81482 - 8.33951i) q^{31} +(-0.736790 - 1.27616i) q^{33} +(2.57945 + 5.48533i) q^{35} +(-0.852138 - 1.47595i) q^{37} +(2.44981 - 4.24320i) q^{39} +7.79458 q^{41} +10.9324 q^{43} +(-1.14553 + 1.98411i) q^{45} +(-3.34944 - 5.80139i) q^{47} +(6.90136 + 1.17099i) q^{49} +(0.500000 + 0.866025i) q^{51} +(-5.35086 + 9.26796i) q^{53} +3.37605 q^{55} -5.86033 q^{57} +(2.81340 - 4.87295i) q^{59} +(2.14695 + 3.71862i) q^{61} +(1.12588 + 2.39424i) q^{63} +(5.61265 + 9.72139i) q^{65} +(2.48411 - 4.30261i) q^{67} -7.83387 q^{69} -2.74357 q^{71} +(4.45357 - 7.71381i) q^{73} +(-0.124459 - 0.215569i) q^{75} +(2.22589 - 3.20086i) q^{77} +(2.00444 + 3.47179i) q^{79} +(-0.500000 + 0.866025i) q^{81} -4.57743 q^{83} -2.29105 q^{85} +(-1.54108 + 2.66922i) q^{87} +(-0.0396544 - 0.0686835i) q^{89} +(12.9174 + 1.08810i) q^{91} +(4.81482 + 8.33951i) q^{93} +(6.71316 - 11.6275i) q^{95} -4.56388 q^{97} +1.47358 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 2 q^{5} + 3 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 - 2 * q^5 + 3 * q^7 - 4 * q^9	\( 8 q - 4 q^{3} - 2 q^{5} + 3 q^{7} - 4 q^{9} - q^{11} - 20 q^{13} + 4 q^{15} + 4 q^{17} + 9 q^{19} + 5 q^{23} - 18 q^{25} + 8 q^{27} + 10 q^{29} + 24 q^{31} - q^{33} - 18 q^{35} - 2 q^{37} + 10 q^{39} - 28 q^{43} - 2 q^{45} + 2 q^{47} + 5 q^{49} + 4 q^{51} + 15 q^{53} - 60 q^{55} - 18 q^{57} + 37 q^{59} - 19 q^{61} - 3 q^{63} + 21 q^{65} - 2 q^{67} - 10 q^{69} - 22 q^{71} + 9 q^{73} - 18 q^{75} + 13 q^{77} + 9 q^{79} - 4 q^{81} + 16 q^{83} - 4 q^{85} - 5 q^{87} - 22 q^{89} + 7 q^{91} + 24 q^{93} - 33 q^{95} + 26 q^{97} + 2 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 - 2 * q^5 + 3 * q^7 - 4 * q^9 - q^11 - 20 * q^13 + 4 * q^15 + 4 * q^17 + 9 * q^19 + 5 * q^23 - 18 * q^25 + 8 * q^27 + 10 * q^29 + 24 * q^31 - q^33 - 18 * q^35 - 2 * q^37 + 10 * q^39 - 28 * q^43 - 2 * q^45 + 2 * q^47 + 5 * q^49 + 4 * q^51 + 15 * q^53 - 60 * q^55 - 18 * q^57 + 37 * q^59 - 19 * q^61 - 3 * q^63 + 21 * q^65 - 2 * q^67 - 10 * q^69 - 22 * q^71 + 9 * q^73 - 18 * q^75 + 13 * q^77 + 9 * q^79 - 4 * q^81 + 16 * q^83 - 4 * q^85 - 5 * q^87 - 22 * q^89 + 7 * q^91 + 24 * q^93 - 33 * q^95 + 26 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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