LMFDB - Embedded newform 1280.3.h.l.1279.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1280,3,Mod(1279,1280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1280, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1280.1279");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1280.h (of order $2$, degree $1$, 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:	$34.8774738381$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.493995311104.27
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 10x^{6} + 41x^{4} + 46x^{2} + 64 $ x^8 + 10x^6 + 41x^4 + 46*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	no (minimal twist has level 640)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1279.8
Root			$-0.707107 + 2.24979i$ of defining polynomial
Character	$\chi$	$=$	1280.1279
Dual form			1280.3.h.l.1279.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.62258 q^{3} +(-0.561553 + 4.96837i) q^{5} +6.45101 q^{7} +4.12311 q^{9} +O(q^{10})$	$q+3.62258 q^{3} +(-0.561553 + 4.96837i) q^{5} +6.45101 q^{7} +4.12311 q^{9} +3.94566i q^{11} -15.5167i q^{13} +(-2.03427 + 17.9983i) q^{15} +25.4535i q^{17} +32.0510i q^{19} +23.3693 q^{21} -15.2845 q^{23} +(-24.3693 - 5.58000i) q^{25} -17.6670 q^{27} +34.7386 q^{29} +20.2140i q^{31} +14.2935i q^{33} +(-3.62258 + 32.0510i) q^{35} +9.93673i q^{37} -56.2106i q^{39} +42.3542 q^{41} +52.9460 q^{43} +(-2.31534 + 20.4851i) q^{45} +21.6377 q^{47} -7.38447 q^{49} +92.2073i q^{51} -35.3902i q^{53} +(-19.6035 - 2.21569i) q^{55} +116.107i q^{57} -16.2684i q^{59} -77.3390 q^{61} +26.5982 q^{63} +(77.0928 + 8.71346i) q^{65} +14.0444 q^{67} -55.3693 q^{69} -107.990i q^{71} +93.7873i q^{73} +(-88.2799 - 20.2140i) q^{75} +25.4535i q^{77} +92.2073i q^{79} -101.108 q^{81} +26.7509 q^{83} +(-126.462 - 14.2935i) q^{85} +125.844 q^{87} -27.7538 q^{89} -100.099i q^{91} +73.2269i q^{93} +(-159.241 - 17.9983i) q^{95} +133.534i q^{97} +16.2684i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{5}+O(q^{10}) $ 8 * q + 12 * q^5	$ 8 q + 12 q^{5} + 88 q^{21} - 96 q^{25} + 80 q^{29} - 24 q^{41} - 68 q^{45} - 224 q^{49} + 8 q^{61} + 56 q^{65} - 344 q^{69} - 512 q^{81} - 352 q^{85} - 288 q^{89}+O(q^{100}) $ 8 * q + 12 * q^5 + 88 * q^21 - 96 * q^25 + 80 * q^29 - 24 * q^41 - 68 * q^45 - 224 * q^49 + 8 * q^61 + 56 * q^65 - 344 * q^69 - 512 * q^81 - 352 * q^85 - 288 * q^89

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$-1$	$1$	$-1$

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
$3$	3.62258			1.20753			0.603764	−	0.797163i	$-0.293667\pi$
$3$	3.62258			1.20753			0.603764	+	0.797163i	$0.293667\pi$
$4$		0			0
$5$	−0.561553	+	4.96837i	−0.112311	+	0.993673i
$5$	−0.561553	+	4.96837i	−0.112311	+	0.993673i
$6$		0			0
$7$	6.45101			0.921573			0.460786	−	0.887511i	$-0.347567\pi$
$7$	6.45101			0.921573			0.460786	+	0.887511i	$0.347567\pi$
$8$		0			0
$9$	4.12311			0.458123
$10$		0			0
$11$			3.94566i			0.358696i	0.983786	+	0.179348i	$0.0573988\pi$
$11$			3.94566i			0.358696i	−0.983786	+	0.179348i	$0.942601\pi$
$12$		0			0
$13$		−	15.5167i		−	1.19359i	−0.802392	−	0.596797i	$-0.796440\pi$
$13$		−	15.5167i		−	1.19359i	0.802392	−	0.596797i	$-0.203560\pi$
$14$		0			0
$15$	−2.03427	+	17.9983i	−0.135618	+	1.19989i
$16$		0			0
$17$			25.4535i			1.49726i	0.662987	+	0.748631i	$0.269289\pi$
$17$			25.4535i			1.49726i	−0.662987	+	0.748631i	$0.730711\pi$
$18$		0			0
$19$			32.0510i			1.68689i	0.537213	+	0.843447i	$0.319477\pi$
$19$			32.0510i			1.68689i	−0.537213	+	0.843447i	$0.680523\pi$
$20$		0			0
$21$	23.3693			1.11282
$22$		0			0
$23$	−15.2845			−0.664543			−0.332271	−	0.943184i	$-0.607815\pi$
$23$	−15.2845			−0.664543			−0.332271	+	0.943184i	$0.607815\pi$
$24$		0			0
$25$	−24.3693	−	5.58000i	−0.974773	−	0.223200i
$26$		0			0
$27$	−17.6670			−0.654332
$28$		0			0
$29$	34.7386			1.19788			0.598942	−	0.800792i	$-0.295588\pi$
$29$	34.7386			1.19788			0.598942	+	0.800792i	$0.295588\pi$
$30$		0			0
$31$			20.2140i			0.652065i	0.945359	+	0.326032i	$0.105712\pi$
$31$			20.2140i			0.652065i	−0.945359	+	0.326032i	$0.894288\pi$
$32$		0			0
$33$			14.2935i			0.433135i
$34$		0			0
$35$	−3.62258	+	32.0510i	−0.103502	+	0.915742i
$36$		0			0
$37$			9.93673i			0.268560i	0.990943	+	0.134280i	$0.0428722\pi$
$37$			9.93673i			0.268560i	−0.990943	+	0.134280i	$0.957128\pi$
$38$		0			0
$39$		−	56.2106i		−	1.44130i
$40$		0			0
$41$	42.3542			1.03303			0.516514	−	0.856279i	$-0.327229\pi$
$41$	42.3542			1.03303			0.516514	+	0.856279i	$0.327229\pi$
$42$		0			0
$43$	52.9460			1.23130			0.615651	−	0.788019i	$-0.288893\pi$
$43$	52.9460			1.23130			0.615651	+	0.788019i	$0.288893\pi$
$44$		0			0
$45$	−2.31534	+	20.4851i	−0.0514520	+	0.455224i
$46$		0			0
$47$	21.6377			0.460377			0.230189	−	0.973146i	$-0.426066\pi$
$47$	21.6377			0.460377			0.230189	+	0.973146i	$0.426066\pi$
$48$		0			0
$49$	−7.38447			−0.150704
$50$		0			0
$51$			92.2073i			1.80799i
$52$		0			0
$53$		−	35.3902i		−	0.667740i	−0.942619	−	0.333870i	$-0.891645\pi$
$53$		−	35.3902i		−	0.667740i	0.942619	−	0.333870i	$-0.108355\pi$
$54$		0			0
$55$	−19.6035	−	2.21569i	−0.356427	−	0.0402853i
$56$		0			0
$57$			116.107i			2.03697i
$58$		0			0
$59$		−	16.2684i		−	0.275735i	−0.990451	−	0.137867i	$-0.955975\pi$
$59$		−	16.2684i		−	0.275735i	0.990451	−	0.137867i	$-0.0440248\pi$
$60$		0			0
$61$	−77.3390			−1.26785			−0.633926	−	0.773393i	$-0.718558\pi$
$61$	−77.3390			−1.26785			−0.633926	+	0.773393i	$0.718558\pi$
$62$		0			0
$63$	26.5982			0.422194
$64$		0			0
$65$	77.0928	+	8.71346i	1.18604	+	0.134053i
$66$		0			0
$67$	14.0444			0.209617			0.104809	−	0.994492i	$-0.466577\pi$
$67$	14.0444			0.209617			0.104809	+	0.994492i	$0.466577\pi$
$68$		0			0
$69$	−55.3693			−0.802454
$70$		0			0
$71$		−	107.990i		−	1.52098i	−0.649347	−	0.760492i	$-0.724958\pi$
$71$		−	107.990i		−	1.52098i	0.649347	−	0.760492i	$-0.275042\pi$
$72$		0			0
$73$			93.7873i			1.28476i	0.766387	+	0.642379i	$0.222052\pi$
$73$			93.7873i			1.28476i	−0.766387	+	0.642379i	$0.777948\pi$
$74$		0			0
$75$	−88.2799	−	20.2140i	−1.17706	−	0.269520i
$76$		0			0
$77$			25.4535i			0.330564i
$78$		0			0
$79$			92.2073i			1.16718i	0.812048	+	0.583590i	$0.198353\pi$
$79$			92.2073i			1.16718i	−0.812048	+	0.583590i	$0.801647\pi$
$80$		0			0
$81$	−101.108			−1.24825
$82$		0			0
$83$	26.7509			0.322300			0.161150	−	0.986930i	$-0.448480\pi$
$83$	26.7509			0.322300			0.161150	+	0.986930i	$0.448480\pi$
$84$		0			0
$85$	−126.462	−	14.2935i	−1.48779	−	0.168158i
$86$		0			0
$87$	125.844			1.44648
$88$		0			0
$89$	−27.7538			−0.311840			−0.155920	−	0.987770i	$-0.549834\pi$
$89$	−27.7538			−0.311840			−0.155920	+	0.987770i	$0.549834\pi$
$90$		0			0
$91$		−	100.099i		−	1.09998i
$92$		0			0
$93$			73.2269i			0.787386i
$94$		0			0
$95$	−159.241	−	17.9983i	−1.67622	−	0.189456i
$96$		0			0
$97$			133.534i			1.37664i	0.725406	+	0.688321i	$0.241652\pi$
$97$			133.534i			1.37664i	−0.725406	+	0.688321i	$0.758348\pi$
$98$		0			0
$99$			16.2684i			0.164327i
$100$		0			0
$101$	148.708			1.47236			0.736180	−	0.676786i	$-0.236628\pi$
$101$	148.708			1.47236			0.736180	+	0.676786i	$0.236628\pi$
$102$		0			0
$103$	−146.089			−1.41834			−0.709168	−	0.705040i	$-0.750929\pi$
$103$	−146.089			−1.41834			−0.709168	+	0.705040i	$0.750929\pi$
$104$		0			0
$105$	−13.1231	+	116.107i	−0.124982	+	1.10578i
$106$		0			0
$107$	−35.2790			−0.329710			−0.164855	−	0.986318i	$-0.552716\pi$
$107$	−35.2790			−0.329710			−0.164855	+	0.986318i	$0.552716\pi$
$108$		0			0
$109$	−24.1383			−0.221452			−0.110726	−	0.993851i	$-0.535318\pi$
$109$	−24.1383			−0.221452			−0.110726	+	0.993851i	$0.535318\pi$
$110$		0			0
$111$			35.9966i			0.324294i
$112$		0			0
$113$			181.308i			1.60449i	0.596993	+	0.802246i	$0.296362\pi$
$113$			181.308i			1.60449i	−0.596993	+	0.802246i	$0.703638\pi$
$114$		0			0
$115$	8.58305	−	75.9389i	0.0746352	−	0.660338i
$116$		0			0
$117$		−	63.9771i		−	0.546813i
$118$		0			0
$119$			164.201i			1.37984i
$120$		0			0
$121$	105.432			0.871337
$122$		0			0
$123$	153.431			1.24741
$124$		0			0
$125$	41.4081	−	117.942i	0.331265	−	0.943538i
$126$		0			0
$127$	191.453			1.50751			0.753753	−	0.657158i	$-0.228242\pi$
$127$	191.453			1.50751			0.753753	+	0.657158i	$0.228242\pi$
$128$		0			0
$129$	191.801			1.48683
$130$		0			0
$131$		−	224.357i		−	1.71265i	−0.516439	−	0.856324i	$-0.672743\pi$
$131$		−	224.357i		−	1.71265i	0.516439	−	0.856324i	$-0.327257\pi$
$132$		0			0
$133$			206.761i			1.55460i
$134$		0			0
$135$	9.92093	−	87.7759i	0.0734884	−	0.650192i
$136$		0			0
$137$		−	55.8000i		−	0.407299i	−0.979044	−	0.203650i	$-0.934720\pi$
$137$		−	55.8000i		−	0.407299i	0.979044	−	0.203650i	$-0.0652803\pi$
$138$		0			0
$139$		−	115.395i		−	0.830183i	−0.909780	−	0.415092i	$-0.863750\pi$
$139$		−	115.395i		−	0.830183i	0.909780	−	0.415092i	$-0.136250\pi$
$140$		0			0
$141$	78.3845			0.555918
$142$		0			0
$143$	61.2237			0.428138
$144$		0			0
$145$	−19.5076	+	172.594i	−0.134535	+	1.19031i
$146$		0			0
$147$	−26.7509			−0.181979
$148$		0			0
$149$	52.6307			0.353226			0.176613	−	0.984280i	$-0.443486\pi$
$149$	52.6307			0.353226			0.176613	+	0.984280i	$0.443486\pi$
$150$		0			0
$151$			231.762i			1.53485i	0.641138	+	0.767425i	$0.278462\pi$
$151$			231.762i			1.53485i	−0.641138	+	0.767425i	$0.721538\pi$
$152$		0			0
$153$			104.947i			0.685930i
$154$		0			0
$155$	−100.431	−	11.3512i	−0.647939	−	0.0732338i
$156$		0			0
$157$		−	162.658i		−	1.03604i	−0.855370	−	0.518018i	$-0.826670\pi$
$157$		−	162.658i		−	1.03604i	0.855370	−	0.518018i	$-0.173330\pi$
$158$		0			0
$159$		−	128.204i		−	0.806314i
$160$		0			0
$161$	−98.6004			−0.612425
$162$		0			0
$163$	−293.319			−1.79951			−0.899753	−	0.436400i	$-0.856253\pi$
$163$	−293.319			−1.79951			−0.899753	+	0.436400i	$0.856253\pi$
$164$		0			0
$165$	−71.0152	−	8.02653i	−0.430395	−	0.0486457i
$166$		0			0
$167$	246.934			1.47865			0.739324	−	0.673350i	$-0.235145\pi$
$167$	246.934			1.47865			0.739324	+	0.673350i	$0.235145\pi$
$168$		0			0
$169$	−71.7689			−0.424668
$170$		0			0
$171$			132.150i			0.772804i
$172$		0			0
$173$		−	76.8967i		−	0.444490i	−0.974991	−	0.222245i	$-0.928662\pi$
$173$		−	76.8967i		−	0.444490i	0.974991	−	0.222245i	$-0.0713384\pi$
$174$		0			0
$175$	−157.207	−	35.9966i	−0.898324	−	0.205695i
$176$		0			0
$177$		−	58.9335i		−	0.332957i
$178$		0			0
$179$		−	284.999i		−	1.59217i	−0.605183	−	0.796086i	$-0.706900\pi$
$179$		−	284.999i		−	1.59217i	0.605183	−	0.796086i	$-0.293100\pi$
$180$		0			0
$181$	176.769			0.976624			0.488312	−	0.872669i	$-0.337613\pi$
$181$	176.769			0.976624			0.488312	+	0.872669i	$0.337613\pi$
$182$		0			0
$183$	−280.167			−1.53097
$184$		0			0
$185$	−49.3693	−	5.58000i	−0.266861	−	0.0301622i
$186$		0			0
$187$	−100.431			−0.537062
$188$		0			0
$189$	−113.970			−0.603014
$190$		0			0
$191$		−	265.271i		−	1.38885i	−0.719564	−	0.694426i	$-0.755659\pi$
$191$		−	265.271i		−	1.38885i	0.719564	−	0.694426i	$-0.244341\pi$
$192$		0			0
$193$			82.6273i			0.428121i	0.976820	+	0.214060i	$0.0686689\pi$
$193$			82.6273i			0.428121i	−0.976820	+	0.214060i	$0.931331\pi$
$194$		0			0
$195$	279.275	+	31.5652i	1.43218	+	0.161873i
$196$		0			0
$197$			180.771i			0.917621i	0.888534	+	0.458811i	$0.151724\pi$
$197$			180.771i			0.917621i	−0.888534	+	0.458811i	$0.848276\pi$
$198$		0			0
$199$		−	171.120i		−	0.859901i	−0.902852	−	0.429951i	$-0.858531\pi$
$199$		−	171.120i		−	0.859901i	0.902852	−	0.429951i	$-0.141469\pi$
$200$		0			0
$201$	50.8769			0.253119
$202$		0			0
$203$	224.099			1.10394
$204$		0			0
$205$	−23.7841	+	210.431i	−0.116020	+	1.02649i
$206$		0			0
$207$	−63.0196			−0.304442
$208$		0			0
$209$	−126.462			−0.605082
$210$		0			0
$211$		−	96.1529i		−	0.455701i	−0.973696	−	0.227851i	$-0.926830\pi$
$211$		−	96.1529i		−	0.455701i	0.973696	−	0.227851i	$-0.0731698\pi$
$212$		0			0
$213$		−	391.202i		−	1.83663i
$214$		0			0
$215$	−29.7320	+	263.055i	−0.138288	+	1.22351i
$216$		0			0
$217$			130.401i			0.600925i
$218$		0			0
$219$			339.752i			1.55138i
$220$		0			0
$221$	394.955			1.78712
$222$		0			0
$223$	79.8803			0.358208			0.179104	−	0.983830i	$-0.442680\pi$
$223$	79.8803			0.358208			0.179104	+	0.983830i	$0.442680\pi$
$224$		0			0
$225$	−100.477	−	23.0069i	−0.446566	−	0.102253i
$226$		0			0
$227$	229.897			1.01276			0.506381	−	0.862310i	$-0.330983\pi$
$227$	229.897			1.01276			0.506381	+	0.862310i	$0.330983\pi$
$228$		0			0
$229$	−132.277			−0.577627			−0.288813	−	0.957385i	$-0.593261\pi$
$229$	−132.277			−0.577627			−0.288813	+	0.957385i	$0.593261\pi$
$230$		0			0
$231$			92.2073i			0.399166i
$232$		0			0
$233$			81.2535i			0.348727i	0.984681	+	0.174364i	$0.0557868\pi$
$233$			81.2535i			0.348727i	−0.984681	+	0.174364i	$0.944213\pi$
$234$		0			0
$235$	−12.1507	+	107.504i	−0.0517052	+	0.457465i
$236$		0			0
$237$			334.028i			1.40940i
$238$		0			0
$239$		−	317.050i		−	1.32657i	−0.748368	−	0.663284i	$-0.769162\pi$
$239$		−	317.050i		−	1.32657i	0.748368	−	0.663284i	$-0.230838\pi$
$240$		0			0
$241$	446.725			1.85363			0.926816	−	0.375516i	$-0.122534\pi$
$241$	446.725			1.85363			0.926816	+	0.375516i	$0.122534\pi$
$242$		0			0
$243$	−207.269			−0.852960
$244$		0			0
$245$	4.14677	−	36.6888i	0.0169256	−	0.149750i
$246$		0			0
$247$	497.326			2.01347
$248$		0			0
$249$	96.9072			0.389186
$250$		0			0
$251$			253.434i			1.00970i	0.863208	+	0.504848i	$0.168451\pi$
$251$			253.434i			1.00970i	−0.863208	+	0.504848i	$0.831549\pi$
$252$		0			0
$253$		−	60.3073i		−	0.238369i
$254$		0			0
$255$	−458.119	−	51.7793i	−1.79655	−	0.203056i
$256$		0			0
$257$		−	85.7608i		−	0.333700i	−0.985982	−	0.166850i	$-0.946641\pi$
$257$		−	85.7608i		−	0.333700i	0.985982	−	0.166850i	$-0.0533595\pi$
$258$		0			0
$259$			64.1020i			0.247498i
$260$		0			0
$261$	143.231			0.548778
$262$		0			0
$263$	−302.587			−1.15052			−0.575260	−	0.817971i	$-0.695099\pi$
$263$	−302.587			−1.15052			−0.575260	+	0.817971i	$0.695099\pi$
$264$		0			0
$265$	175.831	+	19.8735i	0.663515	+	0.0749942i
$266$		0			0
$267$	−100.540			−0.376556
$268$		0			0
$269$	−173.339			−0.644383			−0.322191	−	0.946675i	$-0.604419\pi$
$269$	−173.339			−0.644383			−0.322191	+	0.946675i	$0.604419\pi$
$270$		0			0
$271$			195.766i			0.722383i	0.932492	+	0.361191i	$0.117630\pi$
$271$			195.766i			0.722383i	−0.932492	+	0.361191i	$0.882370\pi$
$272$		0			0
$273$		−	362.615i		−	1.32826i
$274$		0			0
$275$	22.0168	−	96.1529i	0.0800609	−	0.349647i
$276$		0			0
$277$		−	365.213i		−	1.31846i	−0.751943	−	0.659228i	$-0.770883\pi$
$277$		−	365.213i		−	1.31846i	0.751943	−	0.659228i	$-0.229117\pi$
$278$		0			0
$279$			83.3445i			0.298726i
$280$		0			0
$281$	−268.756			−0.956426			−0.478213	−	0.878244i	$-0.658715\pi$
$281$	−268.756			−0.956426			−0.478213	+	0.878244i	$0.658715\pi$
$282$		0			0
$283$	−43.6357			−0.154190			−0.0770949	−	0.997024i	$-0.524564\pi$
$283$	−43.6357			−0.154190			−0.0770949	+	0.997024i	$0.524564\pi$
$284$		0			0
$285$	−576.864	−	65.2004i	−2.02408	−	0.228773i
$286$		0			0
$287$	273.227			0.952011
$288$		0			0
$289$	−358.879			−1.24180
$290$		0			0
$291$			483.739i			1.66233i
$292$		0			0
$293$			226.098i			0.771667i	0.922569	+	0.385833i	$0.126086\pi$
$293$			226.098i			0.771667i	−0.922569	+	0.385833i	$0.873914\pi$
$294$		0			0
$295$	80.8271	+	9.13554i	0.273990	+	0.0309679i
$296$		0			0
$297$		−	69.7077i		−	0.234706i
$298$		0			0
$299$			237.165i			0.793195i
$300$		0			0
$301$	341.555			1.13473
$302$		0			0
$303$	538.708			1.77791
$304$		0			0
$305$	43.4299	−	384.248i	0.142393	−	1.25983i
$306$		0			0
$307$	172.436			0.561682			0.280841	−	0.959754i	$-0.409387\pi$
$307$	172.436			0.561682			0.280841	+	0.959754i	$0.409387\pi$
$308$		0			0
$309$	−529.218			−1.71268
$310$		0			0
$311$		−	78.9131i		−	0.253740i	−0.991919	−	0.126870i	$-0.959507\pi$
$311$		−	78.9131i		−	0.253740i	0.991919	−	0.126870i	$-0.0404931\pi$
$312$		0			0
$313$		−	338.922i		−	1.08282i	−0.840760	−	0.541408i	$-0.817891\pi$
$313$		−	338.922i		−	1.08282i	0.840760	−	0.541408i	$-0.182109\pi$
$314$		0			0
$315$	−14.9363	+	132.150i	−0.0474168	+	0.419522i
$316$		0			0
$317$		−	101.278i		−	0.319487i	−0.987159	−	0.159744i	$-0.948933\pi$
$317$		−	101.278i		−	0.319487i	0.987159	−	0.159744i	$-0.0510668\pi$
$318$		0			0
$319$			137.067i			0.429676i
$320$		0			0
$321$	−127.801			−0.398134
$322$		0			0
$323$	−815.808			−2.52572
$324$		0			0
$325$	−86.5834	+	378.132i	−0.266410	+	1.16348i
$326$		0			0
$327$	−87.4428			−0.267409
$328$		0			0
$329$	139.585			0.424271
$330$		0			0
$331$		−	153.335i		−	0.463248i	−0.972805	−	0.231624i	$-0.925596\pi$
$331$		−	153.335i		−	0.463248i	0.972805	−	0.231624i	$-0.0744039\pi$
$332$		0			0
$333$			40.9702i			0.123034i
$334$		0			0
$335$	−7.88666	+	69.7776i	−0.0235423	+	0.208291i
$336$		0			0
$337$			146.454i			0.434581i	0.976107	+	0.217291i	$0.0697219\pi$
$337$			146.454i			0.434581i	−0.976107	+	0.217291i	$0.930278\pi$
$338$		0			0
$339$			656.802i			1.93747i
$340$		0			0
$341$	−79.7575			−0.233893
$342$		0			0
$343$	−363.737			−1.06046
$344$		0			0
$345$	31.0928	−	275.095i	0.0901240	−	0.797377i
$346$		0			0
$347$	332.832			0.959169			0.479585	−	0.877496i	$-0.340787\pi$
$347$	332.832			0.959169			0.479585	+	0.877496i	$0.340787\pi$
$348$		0			0
$349$	−307.170			−0.880145			−0.440072	−	0.897962i	$-0.645047\pi$
$349$	−307.170			−0.880145			−0.440072	+	0.897962i	$0.645047\pi$
$350$		0			0
$351$			274.133i			0.781007i
$352$		0			0
$353$		−	177.788i		−	0.503650i	−0.967773	−	0.251825i	$-0.918969\pi$
$353$		−	177.788i		−	0.503650i	0.967773	−	0.251825i	$-0.0810308\pi$
$354$		0			0
$355$	536.533	+	60.6420i	1.51136	+	0.170823i
$356$		0			0
$357$			594.830i			1.66619i
$358$		0			0
$359$			447.742i			1.24719i	0.781746	+	0.623596i	$0.214329\pi$
$359$			447.742i			1.24719i	−0.781746	+	0.623596i	$0.785671\pi$
$360$		0			0
$361$	−666.265			−1.84561
$362$		0			0
$363$	381.935			1.05216
$364$		0			0
$365$	−465.970	−	52.6665i	−1.27663	−	0.144292i
$366$		0			0
$367$	−417.312			−1.13709			−0.568545	−	0.822652i	$-0.692494\pi$
$367$	−417.312			−1.13709			−0.568545	+	0.822652i	$0.692494\pi$
$368$		0			0
$369$	174.631			0.473254
$370$		0			0
$371$		−	228.302i		−	0.615371i
$372$		0			0
$373$		−	206.225i		−	0.552882i	−0.961031	−	0.276441i	$-0.910845\pi$
$373$		−	206.225i		−	0.552882i	0.961031	−	0.276441i	$-0.0891550\pi$
$374$		0			0
$375$	150.004	−	427.255i	0.400012	−	1.13935i
$376$		0			0
$377$		−	539.030i		−	1.42979i
$378$		0			0
$379$		−	573.943i		−	1.51436i	−0.653205	−	0.757181i	$-0.726576\pi$
$379$		−	573.943i		−	1.51436i	0.653205	−	0.757181i	$-0.273424\pi$
$380$		0			0
$381$	693.555			1.82035
$382$		0			0
$383$	−144.219			−0.376551			−0.188275	−	0.982116i	$-0.560290\pi$
$383$	−144.219			−0.376551			−0.188275	+	0.982116i	$0.560290\pi$
$384$		0			0
$385$	−126.462	−	14.2935i	−0.328473	−	0.0371259i
$386$		0			0
$387$	218.302			0.564087
$388$		0			0
$389$	470.358			1.20915			0.604573	−	0.796550i	$-0.293344\pi$
$389$	470.358			1.20915			0.604573	+	0.796550i	$0.293344\pi$
$390$		0			0
$391$		−	389.043i		−	0.994995i
$392$		0			0
$393$		−	812.751i		−	2.06807i
$394$		0			0
$395$	−458.119	−	51.7793i	−1.15980	−	0.131087i
$396$		0			0
$397$		−	337.011i		−	0.848895i	−0.905453	−	0.424448i	$-0.860468\pi$
$397$		−	337.011i		−	0.848895i	0.905453	−	0.424448i	$-0.139532\pi$
$398$		0			0
$399$			749.009i			1.87722i
$400$		0			0
$401$	228.739			0.570421			0.285210	−	0.958465i	$-0.407937\pi$
$401$	228.739			0.570421			0.285210	+	0.958465i	$0.407937\pi$
$402$		0			0
$403$	313.655			0.778301
$404$		0			0
$405$	56.7775	−	502.341i	0.140191	−	1.24035i
$406$		0			0
$407$	−39.2069			−0.0963315
$408$		0			0
$409$	576.263			1.40896			0.704478	−	0.709726i	$-0.251181\pi$
$409$	576.263			1.40896			0.704478	+	0.709726i	$0.251181\pi$
$410$		0			0
$411$		−	202.140i		−	0.491825i
$412$		0			0
$413$		−	104.947i		−	0.254110i
$414$		0			0
$415$	−15.0220	+	132.908i	−0.0361976	+	0.320260i
$416$		0			0
$417$		−	418.030i		−	1.00247i
$418$		0			0
$419$		−	435.905i		−	1.04035i	−0.854061	−	0.520173i	$-0.825867\pi$
$419$		−	435.905i		−	1.04035i	0.854061	−	0.520173i	$-0.174133\pi$
$420$		0			0
$421$	429.616			1.02046			0.510232	−	0.860037i	$-0.329559\pi$
$421$	429.616			1.02046			0.510232	+	0.860037i	$0.329559\pi$
$422$		0			0
$423$	89.2147			0.210909
$424$		0			0
$425$	142.030	−	620.283i	0.334189	−	1.45949i
$426$		0			0
$427$	−498.915			−1.16842
$428$		0			0
$429$	221.788			0.516988
$430$		0			0
$431$		−	690.856i		−	1.60291i	−0.598053	−	0.801457i	$-0.704059\pi$
$431$		−	690.856i		−	1.60291i	0.598053	−	0.801457i	$-0.295941\pi$
$432$		0			0
$433$		−	70.0935i		−	0.161879i	−0.996719	−	0.0809393i	$-0.974208\pi$
$433$		−	70.0935i		−	0.161879i	0.996719	−	0.0809393i	$-0.0257920\pi$
$434$		0			0
$435$	−70.6678	+	625.237i	−0.162455	+	1.43733i
$436$		0			0
$437$		−	489.883i		−	1.12101i
$438$		0			0
$439$		−	816.571i		−	1.86007i	−0.367469	−	0.930036i	$-0.619776\pi$
$439$		−	816.571i		−	1.86007i	0.367469	−	0.930036i	$-0.380224\pi$
$440$		0			0
$441$	−30.4470			−0.0690407
$442$		0			0
$443$	−199.242			−0.449756			−0.224878	−	0.974387i	$-0.572198\pi$
$443$	−199.242			−0.449756			−0.224878	+	0.974387i	$0.572198\pi$
$444$		0			0
$445$	15.5852	−	137.891i	0.0350230	−	0.309867i
$446$		0			0
$447$	190.659			0.426530
$448$		0			0
$449$	−3.00187			−0.00668567			−0.00334283	−	0.999994i	$-0.501064\pi$
$449$	−3.00187			−0.00668567			−0.00334283	+	0.999994i	$0.501064\pi$
$450$		0			0
$451$			167.115i			0.370543i
$452$		0			0
$453$			839.579i			1.85337i
$454$		0			0
$455$	497.326	+	56.2106i	1.09303	+	0.123540i
$456$		0			0
$457$			345.188i			0.755336i	0.925941	+	0.377668i	$0.123274\pi$
$457$			345.188i			0.755336i	−0.925941	+	0.377668i	$0.876726\pi$
$458$		0			0
$459$		−	449.685i		−	0.979706i
$460$		0			0
$461$	799.663			1.73463			0.867313	−	0.497763i	$-0.165845\pi$
$461$	799.663			1.73463			0.867313	+	0.497763i	$0.165845\pi$
$462$		0			0
$463$	245.737			0.530749			0.265375	−	0.964145i	$-0.414504\pi$
$463$	245.737			0.530749			0.265375	+	0.964145i	$0.414504\pi$
$464$		0			0
$465$	−363.818	−	41.1208i	−0.782405	−	0.0884318i
$466$		0			0
$467$	−331.439			−0.709719			−0.354860	−	0.934920i	$-0.615471\pi$
$467$	−331.439			−0.709719			−0.354860	+	0.934920i	$0.615471\pi$
$468$		0			0
$469$	90.6004			0.193178
$470$		0			0
$471$		−	589.240i		−	1.25104i
$472$		0			0
$473$			208.907i			0.441663i
$474$		0			0
$475$	178.844	−	781.060i	0.376515	−	1.64434i
$476$		0			0
$477$		−	145.918i		−	0.305907i
$478$		0			0
$479$			310.676i			0.648592i	0.945956	+	0.324296i	$0.105127\pi$
$479$			310.676i			0.648592i	−0.945956	+	0.324296i	$0.894873\pi$
$480$		0			0
$481$	154.186			0.320552
$482$		0			0
$483$	−357.188			−0.739520
$484$		0			0
$485$	−663.447	−	74.9865i	−1.36793	−	0.154611i
$486$		0			0
$487$	−173.615			−0.356498			−0.178249	−	0.983985i	$-0.557043\pi$
$487$	−173.615			−0.356498			−0.178249	+	0.983985i	$0.557043\pi$
$488$		0			0
$489$	−1062.57			−2.17295
$490$		0			0
$491$		−	470.930i		−	0.959125i	−0.877508	−	0.479563i	$-0.840795\pi$
$491$		−	470.930i		−	0.959125i	0.877508	−	0.479563i	$-0.159205\pi$
$492$		0			0
$493$			884.219i			1.79355i
$494$		0			0
$495$	−80.8271	−	9.13554i	−0.163287	−	0.0184556i
$496$		0			0
$497$		−	696.644i		−	1.40170i
$498$		0			0
$499$		−	114.424i		−	0.229307i	−0.993406	−	0.114653i	$-0.963424\pi$
$499$		−	114.424i		−	0.229307i	0.993406	−	0.114653i	$-0.0365757\pi$
$500$		0			0
$501$	894.540			1.78551
$502$		0			0
$503$	−279.067			−0.554806			−0.277403	−	0.960754i	$-0.589474\pi$
$503$	−279.067			−0.554806			−0.277403	+	0.960754i	$0.589474\pi$
$504$		0			0
$505$	−83.5076	+	738.837i	−0.165362	+	1.46304i
$506$		0			0
$507$	−259.989			−0.512799
$508$		0			0
$509$	−332.155			−0.652564			−0.326282	−	0.945272i	$-0.605796\pi$
$509$	−332.155			−0.652564			−0.326282	+	0.945272i	$0.605796\pi$
$510$		0			0
$511$			605.023i			1.18400i
$512$		0			0
$513$		−	566.243i		−	1.10379i
$514$		0			0
$515$	82.0364	−	725.821i	0.159294	−	1.40936i
$516$		0			0
$517$			85.3750i			0.165135i
$518$		0			0
$519$		−	278.565i		−	0.536734i
$520$		0			0
$521$	746.924			1.43364			0.716818	−	0.697260i	$-0.245598\pi$
$521$	746.924			1.43364			0.716818	+	0.697260i	$0.245598\pi$
$522$		0			0
$523$	584.018			1.11667			0.558335	−	0.829616i	$-0.311441\pi$
$523$	584.018			1.11667			0.558335	+	0.829616i	$0.311441\pi$
$524$		0			0
$525$	−569.494	−	130.401i	−1.08475	−	0.248382i
$526$		0			0
$527$	−514.517			−0.976312
$528$		0			0
$529$	−295.384			−0.558383
$530$		0			0
$531$		−	67.0761i		−	0.126320i
$532$		0			0
$533$		−	657.198i		−	1.23302i
$534$		0			0
$535$	19.8110	−	175.279i	0.0370300	−	0.327624i
$536$		0			0
$537$		−	1032.43i		−	1.92259i
$538$		0			0
$539$		−	29.1366i		−	0.0540567i
$540$		0			0
$541$	271.905			0.502598			0.251299	−	0.967910i	$-0.419142\pi$
$541$	271.905			0.502598			0.251299	+	0.967910i	$0.419142\pi$
$542$		0			0
$543$	640.360			1.17930
$544$		0			0
$545$	13.5549	−	119.928i	0.0248714	−	0.220051i
$546$		0			0
$547$	19.1146			0.0349445			0.0174722	−	0.999847i	$-0.494438\pi$
$547$	19.1146			0.0349445			0.0174722	+	0.999847i	$0.494438\pi$
$548$		0			0
$549$	−318.877			−0.580832
$550$		0			0
$551$			1113.41i			2.02070i
$552$		0			0
$553$			594.830i			1.07564i
$554$		0			0
$555$	−178.844	−	20.2140i	−0.322242	−	0.0364216i
$556$		0			0
$557$			868.015i			1.55837i	0.626791	+	0.779187i	$0.284368\pi$
$557$			868.015i			1.55837i	−0.626791	+	0.779187i	$0.715632\pi$
$558$		0			0
$559$		−	821.548i		−	1.46967i
$560$		0			0
$561$	−363.818			−0.648517
$562$		0			0
$563$	912.726			1.62118			0.810592	−	0.585612i	$-0.199146\pi$
$563$	912.726			1.62118			0.810592	+	0.585612i	$0.199146\pi$
$564$		0			0
$565$	−900.803	−	101.814i	−1.59434	−	0.180202i
$566$		0			0
$567$	−652.248			−1.15035
$568$		0			0
$569$	−115.434			−0.202871			−0.101436	−	0.994842i	$-0.532344\pi$
$569$	−115.434			−0.202871			−0.101436	+	0.994842i	$0.532344\pi$
$570$		0			0
$571$		−	347.158i		−	0.607982i	−0.952675	−	0.303991i	$-0.901681\pi$
$571$		−	347.158i		−	0.607982i	0.952675	−	0.303991i	$-0.0983193\pi$
$572$		0			0
$573$		−	960.965i		−	1.67708i
$574$		0			0
$575$	372.472	+	85.2874i	0.647778	+	0.148326i
$576$		0			0
$577$		−	70.4792i		−	0.122148i	−0.998133	−	0.0610738i	$-0.980547\pi$
$577$		−	70.4792i		−	0.122148i	0.998133	−	0.0610738i	$-0.0194525\pi$
$578$		0			0
$579$			299.324i			0.516968i
$580$		0			0
$581$	172.570			0.297022
$582$		0			0
$583$	139.638			0.239515
$584$		0			0
$585$	317.862	+	35.9265i	0.543353	+	0.0614129i
$586$		0			0
$587$	461.461			0.786134			0.393067	−	0.919510i	$-0.371414\pi$
$587$	461.461			0.786134			0.393067	+	0.919510i	$0.371414\pi$
$588$		0			0
$589$	−647.879			−1.09996
$590$		0			0
$591$			654.859i			1.10805i
$592$		0			0
$593$		−	222.428i		−	0.375090i	−0.982256	−	0.187545i	$-0.939947\pi$
$593$		−	222.428i		−	0.375090i	0.982256	−	0.187545i	$-0.0600531\pi$
$594$		0			0
$595$	−815.808	−	92.2073i	−1.37111	−	0.154970i
$596$		0			0
$597$		−	619.898i		−	1.03835i
$598$		0			0
$599$			206.571i			0.344861i	0.985022	+	0.172430i	$0.0551620\pi$
$599$			206.571i			0.344861i	−0.985022	+	0.172430i	$0.944838\pi$
$600$		0			0
$601$	102.941			0.171283			0.0856416	−	0.996326i	$-0.472706\pi$
$601$	102.941			0.171283			0.0856416	+	0.996326i	$0.472706\pi$
$602$		0			0
$603$	57.9064			0.0960306
$604$		0			0
$605$	−59.2055	+	523.824i	−0.0978604	+	0.865824i
$606$		0			0
$607$	−857.703			−1.41302			−0.706510	−	0.707703i	$-0.749731\pi$
$607$	−857.703			−1.41302			−0.706510	+	0.707703i	$0.749731\pi$
$608$		0			0
$609$	811.818			1.33303
$610$		0			0
$611$		−	335.747i		−	0.549504i
$612$		0			0
$613$		−	299.711i		−	0.488925i	−0.969659	−	0.244462i	$-0.921389\pi$
$613$		−	299.711i		−	0.488925i	0.969659	−	0.244462i	$-0.0786115\pi$
$614$		0			0
$615$	−86.1599	+	762.304i	−0.140097	+	1.23952i
$616$		0			0
$617$		−	189.334i		−	0.306863i	−0.988159	−	0.153431i	$-0.950968\pi$
$617$		−	189.334i		−	0.306863i	0.988159	−	0.153431i	$-0.0490324\pi$
$618$		0			0
$619$			269.762i			0.435803i	0.975971	+	0.217901i	$0.0699211\pi$
$619$			269.762i			0.435803i	−0.975971	+	0.217901i	$0.930079\pi$
$620$		0			0
$621$	270.030			0.434831
$622$		0			0
$623$	−179.040			−0.287384
$624$		0			0
$625$	562.727	+	271.962i	0.900364	+	0.435138i
$626$		0			0
$627$	−458.119			−0.730653
$628$		0			0
$629$	−252.924			−0.402105
$630$		0			0
$631$		−	569.026i		−	0.901785i	−0.892578	−	0.450892i	$-0.851106\pi$
$631$		−	569.026i		−	0.901785i	0.892578	−	0.450892i	$-0.148894\pi$
$632$		0			0
$633$		−	348.322i		−	0.550272i
$634$		0			0
$635$	−107.511	+	951.209i	−0.169309	+	1.49797i
$636$		0			0
$637$			114.583i			0.179879i
$638$		0			0
$639$		−	445.254i		−	0.696798i
$640$		0			0
$641$	−173.093			−0.270036			−0.135018	−	0.990843i	$-0.543109\pi$
$641$	−173.093			−0.270036			−0.135018	+	0.990843i	$0.543109\pi$
$642$		0			0
$643$	−551.298			−0.857384			−0.428692	−	0.903451i	$-0.641026\pi$
$643$	−551.298			−0.857384			−0.428692	+	0.903451i	$0.641026\pi$
$644$		0			0
$645$	−107.706	+	952.938i	−0.166987	+	1.47742i
$646$		0			0
$647$	−518.940			−0.802071			−0.401036	−	0.916062i	$-0.631350\pi$
$647$	−518.940			−0.802071			−0.401036	+	0.916062i	$0.631350\pi$
$648$		0			0
$649$	64.1893			0.0989050
$650$		0			0
$651$			472.388i			0.725634i
$652$		0			0
$653$			150.509i			0.230489i	0.993337	+	0.115245i	$0.0367652\pi$
$653$			150.509i			0.230489i	−0.993337	+	0.115245i	$0.963235\pi$
$654$		0			0
$655$	1114.69	+	125.988i	1.70181	+	0.192348i
$656$		0			0
$657$			386.695i			0.588577i
$658$		0			0
$659$		−	397.420i		−	0.603065i	−0.953456	−	0.301533i	$-0.902502\pi$
$659$		−	397.420i		−	0.603065i	0.953456	−	0.301533i	$-0.0974983\pi$
$660$		0			0
$661$	673.953			1.01960			0.509798	−	0.860294i	$-0.329720\pi$
$661$	673.953			1.01960			0.509798	+	0.860294i	$0.329720\pi$
$662$		0			0
$663$	1430.76			2.15800
$664$		0			0
$665$	−1027.27	−	116.107i	−1.54476	−	0.174597i
$666$		0			0
$667$	−530.962			−0.796045
$668$		0			0
$669$	289.373			0.432546
$670$		0			0
$671$		−	305.153i		−	0.454774i
$672$		0			0
$673$			1132.10i			1.68217i	0.540903	+	0.841085i	$0.318083\pi$
$673$			1132.10i			1.68217i	−0.540903	+	0.841085i	$0.681917\pi$
$674$		0			0
$675$	430.532	+	98.5816i	0.637825	+	0.146047i
$676$		0			0
$677$			1088.08i			1.60721i	0.595163	+	0.803605i	$0.297088\pi$
$677$			1088.08i			1.60721i	−0.595163	+	0.803605i	$0.702912\pi$
$678$		0			0
$679$			861.431i			1.26868i
$680$		0			0
$681$	832.820			1.22294
$682$		0			0
$683$	24.4045			0.0357313			0.0178657	−	0.999840i	$-0.494313\pi$
$683$	24.4045			0.0357313			0.0178657	+	0.999840i	$0.494313\pi$
$684$		0			0
$685$	277.235	+	31.3346i	0.404722	+	0.0457440i
$686$		0			0
$687$	−479.183			−0.697500
$688$		0			0
$689$	−549.140			−0.797010
$690$		0			0
$691$			349.646i			0.506001i	0.967466	+	0.253000i	$0.0814173\pi$
$691$			349.646i			0.506001i	−0.967466	+	0.253000i	$0.918583\pi$
$692$		0			0
$693$			104.947i			0.151439i
$694$		0			0
$695$	573.327	+	64.8007i	0.824931	+	0.0932384i
$696$		0			0
$697$			1078.06i			1.54671i
$698$		0			0
$699$			294.347i			0.421098i
$700$		0			0
$701$	−819.714			−1.16935			−0.584675	−	0.811268i	$-0.698778\pi$
$701$	−819.714			−1.16935			−0.584675	+	0.811268i	$0.698778\pi$
$702$		0			0
$703$	−318.482			−0.453033
$704$		0			0
$705$	−44.0170	+	389.443i	−0.0624355	+	0.552401i
$706$		0			0
$707$	959.319			1.35689
$708$		0			0
$709$	−719.231			−1.01443			−0.507215	−	0.861819i	$-0.669325\pi$
$709$	−719.231			−1.01443			−0.507215	+	0.861819i	$0.669325\pi$
$710$		0			0
$711$			380.180i			0.534712i
$712$		0			0
$713$		−	308.961i		−	0.433325i
$714$		0			0
$715$	−34.3803	+	304.182i	−0.0480844	+	0.425429i
$716$		0			0
$717$		−	1148.54i		−	1.60187i
$718$		0			0
$719$		−	600.046i		−	0.834556i	−0.908779	−	0.417278i	$-0.862984\pi$
$719$		−	600.046i		−	0.834556i	0.908779	−	0.417278i	$-0.137016\pi$
$720$		0			0
$721$	−942.419			−1.30710
$722$		0			0
$723$	1618.30			2.23831
$724$		0			0
$725$	−846.557	−	193.842i	−1.16766	−	0.267368i
$726$		0			0
$727$	−452.279			−0.622117			−0.311059	−	0.950391i	$-0.600684\pi$
$727$	−452.279			−0.622117			−0.311059	+	0.950391i	$0.600684\pi$
$728$		0			0
$729$	159.121			0.218273
$730$		0			0
$731$			1347.66i			1.84358i
$732$		0			0
$733$		−	773.541i		−	1.05531i	−0.849459	−	0.527654i	$-0.823072\pi$
$733$		−	773.541i		−	1.05531i	0.849459	−	0.527654i	$-0.176928\pi$
$734$		0			0
$735$	15.0220	−	132.908i	0.0204381	−	0.180827i
$736$		0			0
$737$			55.4142i			0.0751889i
$738$		0			0
$739$			34.5394i			0.0467381i	0.999727	+	0.0233690i	$0.00743927\pi$
$739$			34.5394i			0.0467381i	−0.999727	+	0.0233690i	$0.992561\pi$
$740$		0			0
$741$	1801.61			2.43132
$742$		0			0
$743$	396.078			0.533079			0.266539	−	0.963824i	$-0.414120\pi$
$743$	396.078			0.533079			0.266539	+	0.963824i	$0.414120\pi$
$744$		0			0
$745$	−29.5549	+	261.488i	−0.0396710	+	0.350991i
$746$		0			0
$747$	110.297			0.147653
$748$		0			0
$749$	−227.585			−0.303852
$750$		0			0
$751$		−	850.079i		−	1.13193i	−0.824429	−	0.565965i	$-0.808504\pi$
$751$		−	850.079i		−	1.13193i	0.824429	−	0.565965i	$-0.191496\pi$
$752$		0			0
$753$			918.084i			1.21924i
$754$		0			0
$755$	−1151.48	−	130.147i	−1.52514	−	0.172380i
$756$		0			0
$757$			458.313i			0.605433i	0.953081	+	0.302717i	$0.0978936\pi$
$757$			458.313i			0.605433i	−0.953081	+	0.302717i	$0.902106\pi$
$758$		0			0
$759$		−	218.468i		−	0.287837i
$760$		0			0
$761$	−788.678			−1.03637			−0.518185	−	0.855268i	$-0.673392\pi$
$761$	−788.678			−1.03637			−0.518185	+	0.855268i	$0.673392\pi$
$762$		0			0
$763$	−155.716			−0.204084
$764$		0			0
$765$	−521.417	−	58.9335i	−0.681590	−	0.0770372i
$766$		0			0
$767$	−252.432			−0.329116
$768$		0			0
$769$	980.098			1.27451			0.637255	−	0.770653i	$-0.280070\pi$
$769$	980.098			1.27451			0.637255	+	0.770653i	$0.280070\pi$
$770$		0			0
$771$		−	310.676i		−	0.402951i
$772$		0			0
$773$			193.305i			0.250071i	0.992152	+	0.125036i	$0.0399045\pi$
$773$			193.305i			0.250071i	−0.992152	+	0.125036i	$0.960095\pi$
$774$		0			0
$775$	112.794	−	492.602i	0.145541	−	0.635615i
$776$		0			0
$777$			232.215i			0.298861i
$778$		0			0
$779$			1357.49i			1.74261i
$780$		0			0
$781$	426.091			0.545571
$782$		0			0
$783$	−613.726			−0.783813
$784$		0			0
$785$	808.142	+	91.3408i	1.02948	+	0.116358i
$786$		0			0
$787$	−679.927			−0.863948			−0.431974	−	0.901886i	$-0.642183\pi$
$787$	−679.927			−0.863948			−0.431974	+	0.901886i	$0.642183\pi$
$788$		0			0
$789$	−1096.15			−1.38928
$790$		0			0
$791$			1169.62i			1.47866i
$792$		0			0
$793$			1200.05i			1.51330i
$794$		0			0
$795$	636.964	+	71.9933i	0.801212	+	0.0905576i
$796$		0			0
$797$		−	324.477i		−	0.407124i	−0.979062	−	0.203562i	$-0.934748\pi$
$797$		−	324.477i		−	0.407124i	0.979062	−	0.203562i	$-0.0652518\pi$
$798$		0			0
$799$			550.755i			0.689306i
$800$		0			0
$801$	−114.432			−0.142861
$802$		0			0
$803$	−370.052			−0.460837
$804$		0			0
$805$	55.3693	−	489.883i	0.0687818	−	0.608550i
$806$		0			0
$807$	−627.935			−0.778110
$808$		0			0
$809$	392.712			0.485429			0.242714	−	0.970098i	$-0.421962\pi$
$809$	392.712			0.485429			0.242714	+	0.970098i	$0.421962\pi$
$810$		0			0
$811$			606.480i			0.747818i	0.927465	+	0.373909i	$0.121983\pi$
$811$			606.480i			0.747818i	−0.927465	+	0.373909i	$0.878017\pi$
$812$		0			0
$813$			709.178i			0.872297i
$814$		0			0
$815$	164.714	−	1457.32i	0.202103	−	1.78812i
$816$		0			0
$817$			1696.97i			2.07707i
$818$		0			0
$819$		−	412.717i		−	0.503928i
$820$		0			0
$821$	750.634			0.914293			0.457146	−	0.889391i	$-0.348872\pi$
$821$	750.634			0.914293			0.457146	+	0.889391i	$0.348872\pi$
$822$		0			0
$823$	−557.389			−0.677265			−0.338632	−	0.940919i	$-0.609964\pi$
$823$	−557.389			−0.677265			−0.338632	+	0.940919i	$0.609964\pi$
$824$		0			0
$825$	79.7575	−	348.322i	0.0966758	−	0.422208i
$826$		0			0
$827$	1394.76			1.68652			0.843262	−	0.537502i	$-0.180632\pi$
$827$	1394.76			1.68652			0.843262	+	0.537502i	$0.180632\pi$
$828$		0			0
$829$	392.570			0.473547			0.236773	−	0.971565i	$-0.423910\pi$
$829$	392.570			0.473547			0.236773	+	0.971565i	$0.423910\pi$
$830$		0			0
$831$		−	1323.01i		−	1.59207i
$832$		0			0
$833$		−	187.960i		−	0.225643i
$834$		0			0
$835$	−138.667	+	1226.86i	−0.166068	+	1.46929i
$836$		0			0
$837$		−	357.120i		−	0.426667i
$838$		0			0
$839$			10.8057i			0.0128793i	0.999979	+	0.00643963i	$0.00204981\pi$
$839$			10.8057i			0.0128793i	−0.999979	+	0.00643963i	$0.997950\pi$
$840$		0			0
$841$	365.773			0.434926
$842$		0			0
$843$	−973.590			−1.15491
$844$		0			0
$845$	40.3021	−	356.574i	0.0476947	−	0.421981i
$846$		0			0
$847$	680.142			0.803001
$848$		0			0
$849$	−158.074			−0.186188
$850$		0			0
$851$		−	151.878i		−	0.178470i
$852$		0			0
$853$		−	222.965i		−	0.261389i	−0.991423	−	0.130695i	$-0.958279\pi$
$853$		−	222.965i		−	0.261389i	0.991423	−	0.130695i	$-0.0417207\pi$
$854$		0			0
$855$	−656.567	−	74.2090i	−0.767915	−	0.0867941i
$856$		0			0
$857$			1258.77i			1.46880i	0.678714	+	0.734402i	$0.262537\pi$
$857$			1258.77i			1.46880i	−0.678714	+	0.734402i	$0.737463\pi$
$858$		0			0
$859$			667.122i			0.776626i	0.921527	+	0.388313i	$0.126942\pi$
$859$			667.122i			0.776626i	−0.921527	+	0.388313i	$0.873058\pi$
$860$		0			0
$861$	989.788			1.14958
$862$		0			0
$863$	−235.010			−0.272317			−0.136159	−	0.990687i	$-0.543476\pi$
$863$	−235.010			−0.272317			−0.136159	+	0.990687i	$0.543476\pi$
$864$		0			0
$865$	382.051	+	43.1816i	0.441678	+	0.0499209i
$866$		0			0
$867$	−1300.07			−1.49950
$868$		0			0
$869$	−363.818			−0.418663
$870$		0			0
$871$		−	217.923i		−	0.250198i
$872$		0			0
$873$			550.576i			0.630671i
$874$		0			0
$875$	267.124	−	760.846i	0.305285	−	0.869539i
$876$		0			0
$877$			1577.19i			1.79840i	0.437543	+	0.899198i	$0.355849\pi$
$877$			1577.19i			1.79840i	−0.437543	+	0.899198i	$0.644151\pi$
$878$		0			0
$879$			819.060i			0.931809i
$880$		0			0
$881$	−220.324			−0.250084			−0.125042	−	0.992151i	$-0.539907\pi$
$881$	−220.324			−0.250084			−0.125042	+	0.992151i	$0.539907\pi$
$882$		0			0
$883$	1144.57			1.29623			0.648115	−	0.761542i	$-0.275558\pi$
$883$	1144.57			1.29623			0.648115	+	0.761542i	$0.275558\pi$
$884$		0			0
$885$	292.803	+	33.0943i	0.330851	+	0.0373946i
$886$		0			0
$887$	−773.413			−0.871942			−0.435971	−	0.899961i	$-0.643595\pi$
$887$	−773.413			−0.871942			−0.435971	+	0.899961i	$0.643595\pi$
$888$		0			0
$889$	1235.07			1.38928
$890$		0			0
$891$		−	398.937i		−	0.447741i
$892$		0			0
$893$			693.510i			0.776607i
$894$		0			0
$895$	1415.98	+	160.042i	1.58210	+	0.178818i
$896$		0			0
$897$			859.151i			0.957805i
$898$		0			0
$899$			702.207i			0.781098i
$900$		0			0
$901$	900.803			0.999781
$902$		0			0
$903$	1237.31			1.37022
$904$		0			0
$905$	−99.2651	+	878.253i	−0.109685	+	0.970445i
$906$		0			0
$907$	−271.474			−0.299310			−0.149655	−	0.988738i	$-0.547816\pi$
$907$	−271.474			−0.299310			−0.149655	+	0.988738i	$0.547816\pi$
$908$		0			0
$909$	613.140			0.674522
$910$		0			0
$911$			663.176i			0.727965i	0.931406	+	0.363983i	$0.118583\pi$
$911$			663.176i			0.727965i	−0.931406	+	0.363983i	$0.881417\pi$
$912$		0			0
$913$			105.550i			0.115608i
$914$		0			0
$915$	157.329	−	1391.97i	0.171944	−	1.52128i
$916$		0			0
$917$		−	1447.33i		−	1.57833i
$918$		0			0
$919$			1017.31i			1.10698i	0.832856	+	0.553490i	$0.186704\pi$
$919$			1017.31i			1.10698i	−0.832856	+	0.553490i	$0.813296\pi$
$920$		0			0
$921$	624.665			0.678246
$922$		0			0
$923$	−1675.65			−1.81544
$924$		0			0
$925$	55.4470	−	242.151i	0.0599427	−	0.261785i
$926$		0			0
$927$	−602.338			−0.649772
$928$		0			0
$929$	−800.790			−0.861991			−0.430996	−	0.902354i	$-0.641838\pi$
$929$	−800.790			−0.861991			−0.430996	+	0.902354i	$0.641838\pi$
$930$		0			0
$931$		−	236.680i		−	0.254221i
$932$		0			0
$933$		−	285.869i		−	0.306398i
$934$		0			0
$935$	56.3971	−	498.976i	0.0603177	−	0.533664i
$936$		0			0
$937$			795.927i			0.849441i	0.905324	+	0.424721i	$0.139628\pi$
$937$			795.927i			0.849441i	−0.905324	+	0.424721i	$0.860372\pi$
$938$		0			0
$939$		−	1227.77i		−	1.30753i
$940$		0			0
$941$	159.663			0.169674			0.0848368	−	0.996395i	$-0.472963\pi$
$941$	159.663			0.169674			0.0848368	+	0.996395i	$0.472963\pi$
$942$		0			0
$943$	−647.362			−0.686492
$944$		0			0
$945$	64.0000	−	566.243i	0.0677249	−	0.599199i
$946$		0			0
$947$	−138.776			−0.146543			−0.0732716	−	0.997312i	$-0.523344\pi$
$947$	−138.776			−0.146543			−0.0732716	+	0.997312i	$0.523344\pi$
$948$		0			0
$949$	1455.27			1.53348
$950$		0			0
$951$		−	366.886i		−	0.385790i
$952$		0			0
$953$		−	141.561i		−	0.148542i	−0.997238	−	0.0742711i	$-0.976337\pi$
$953$		−	141.561i		−	0.148542i	0.997238	−	0.0742711i	$-0.0236630\pi$
$954$		0			0
$955$	1317.96	+	148.963i	1.38006	+	0.155983i
$956$		0			0
$957$			496.535i			0.518846i
$958$		0			0
$959$		−	359.966i		−	0.375356i
$960$		0			0
$961$	552.394			0.574811
$962$		0			0
$963$	−145.459			−0.151048
$964$		0			0
$965$	−410.523	−	46.3996i	−0.425412	−	0.0480825i
$966$		0			0
$967$	278.872			0.288389			0.144194	−	0.989549i	$-0.453941\pi$
$967$	278.872			0.288389			0.144194	+	0.989549i	$0.453941\pi$
$968$		0			0
$969$	−2955.33			−3.04988
$970$		0			0
$971$		−	88.2616i		−	0.0908977i	−0.998967	−	0.0454488i	$-0.985528\pi$
$971$		−	88.2616i		−	0.0908977i	0.998967	−	0.0454488i	$-0.0144718\pi$
$972$		0			0
$973$		−	744.417i		−	0.765074i
$974$		0			0
$975$	−313.655	+	1369.81i	−0.321698	+	1.40494i
$976$		0			0
$977$		−	521.989i		−	0.534277i	−0.963658	−	0.267139i	$-0.913922\pi$
$977$		−	521.989i		−	0.534277i	0.963658	−	0.267139i	$-0.0860782\pi$
$978$		0			0
$979$		−	109.507i		−	0.111856i
$980$		0			0
$981$	−99.5246			−0.101452
$982$		0			0
$983$	1819.43			1.85090			0.925448	−	0.378876i	$-0.123689\pi$
$983$	1819.43			1.85090			0.925448	+	0.378876i	$0.123689\pi$
$984$		0			0
$985$	−898.138	−	101.513i	−0.911815	−	0.103059i
$986$		0			0
$987$	505.659			0.512319
$988$		0			0
$989$	−809.252			−0.818253
$990$		0			0
$991$			593.672i			0.599063i	0.954086	+	0.299532i	$0.0968304\pi$
$991$			593.672i			0.599063i	−0.954086	+	0.299532i	$0.903170\pi$
$992$		0			0
$993$		−	555.469i		−	0.559385i
$994$		0			0
$995$	850.189	+	96.0931i	0.854461	+	0.0965760i
$996$		0			0
$997$		−	639.235i		−	0.641158i	−0.947222	−	0.320579i	$-0.896122\pi$
$997$		−	639.235i		−	0.641158i	0.947222	−	0.320579i	$-0.103878\pi$
$998$		0			0
$999$		−	175.552i		−	0.175727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.3.h.l.1279.8		8
4.3	odd	2	inner	1280.3.h.l.1279.2		8
5.4	even	2	inner	1280.3.h.l.1279.1		8
8.3	odd	2		1280.3.h.h.1279.7		8
8.5	even	2		1280.3.h.h.1279.1		8
16.3	odd	4		640.3.e.i.319.4	yes	16
16.5	even	4		640.3.e.i.319.1	✓	16
16.11	odd	4		640.3.e.i.319.13	yes	16
16.13	even	4		640.3.e.i.319.16	yes	16
20.19	odd	2	inner	1280.3.h.l.1279.7		8
40.19	odd	2		1280.3.h.h.1279.2		8
40.29	even	2		1280.3.h.h.1279.8		8
80.19	odd	4		640.3.e.i.319.14	yes	16
80.29	even	4		640.3.e.i.319.2	yes	16
80.59	odd	4		640.3.e.i.319.3	yes	16
80.69	even	4		640.3.e.i.319.15	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.3.e.i.319.1	✓	16	16.5	even	4
640.3.e.i.319.2	yes	16	80.29	even	4
640.3.e.i.319.3	yes	16	80.59	odd	4
640.3.e.i.319.4	yes	16	16.3	odd	4
640.3.e.i.319.13	yes	16	16.11	odd	4
640.3.e.i.319.14	yes	16	80.19	odd	4
640.3.e.i.319.15	yes	16	80.69	even	4
640.3.e.i.319.16	yes	16	16.13	even	4
1280.3.h.h.1279.1		8	8.5	even	2
1280.3.h.h.1279.2		8	40.19	odd	2
1280.3.h.h.1279.7		8	8.3	odd	2
1280.3.h.h.1279.8		8	40.29	even	2
1280.3.h.l.1279.1		8	5.4	even	2	inner
1280.3.h.l.1279.2		8	4.3	odd	2	inner
1280.3.h.l.1279.7		8	20.19	odd	2	inner
1280.3.h.l.1279.8		8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1280.h (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+3.62258 q^{3} +(-0.561553 + 4.96837i) q^{5} +6.45101 q^{7} +4.12311 q^{9} +O(q^{10})\)	\(q+3.62258 q^{3} +(-0.561553 + 4.96837i) q^{5} +6.45101 q^{7} +4.12311 q^{9} +3.94566i q^{11} -15.5167i q^{13} +(-2.03427 + 17.9983i) q^{15} +25.4535i q^{17} +32.0510i q^{19} +23.3693 q^{21} -15.2845 q^{23} +(-24.3693 - 5.58000i) q^{25} -17.6670 q^{27} +34.7386 q^{29} +20.2140i q^{31} +14.2935i q^{33} +(-3.62258 + 32.0510i) q^{35} +9.93673i q^{37} -56.2106i q^{39} +42.3542 q^{41} +52.9460 q^{43} +(-2.31534 + 20.4851i) q^{45} +21.6377 q^{47} -7.38447 q^{49} +92.2073i q^{51} -35.3902i q^{53} +(-19.6035 - 2.21569i) q^{55} +116.107i q^{57} -16.2684i q^{59} -77.3390 q^{61} +26.5982 q^{63} +(77.0928 + 8.71346i) q^{65} +14.0444 q^{67} -55.3693 q^{69} -107.990i q^{71} +93.7873i q^{73} +(-88.2799 - 20.2140i) q^{75} +25.4535i q^{77} +92.2073i q^{79} -101.108 q^{81} +26.7509 q^{83} +(-126.462 - 14.2935i) q^{85} +125.844 q^{87} -27.7538 q^{89} -100.099i q^{91} +73.2269i q^{93} +(-159.241 - 17.9983i) q^{95} +133.534i q^{97} +16.2684i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{5}+O(q^{10}) \) 8 * q + 12 * q^5	\( 8 q + 12 q^{5} + 88 q^{21} - 96 q^{25} + 80 q^{29} - 24 q^{41} - 68 q^{45} - 224 q^{49} + 8 q^{61} + 56 q^{65} - 344 q^{69} - 512 q^{81} - 352 q^{85} - 288 q^{89}+O(q^{100}) \) 8 * q + 12 * q^5 + 88 * q^21 - 96 * q^25 + 80 * q^29 - 24 * q^41 - 68 * q^45 - 224 * q^49 + 8 * q^61 + 56 * q^65 - 344 * q^69 - 512 * q^81 - 352 * q^85 - 288 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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