LMFDB - Embedded newform 1680.2.bl.c.127.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1680,2,Mod(127,1680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1680, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1680.127"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.bl (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,0,0,0,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.1
Root			$-1.35818 - 0.394157i$ of defining polynomial
Character	$\chi$	$=$	1680.127
Dual form			1680.2.bl.c.463.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{3} +(-1.75233 - 1.38900i) q^{5} +(0.707107 - 0.707107i) q^{7} +1.00000i q^{9} +2.82843i q^{11} +(-0.363328 + 0.363328i) q^{13} +(0.256912 + 2.22126i) q^{15} +(3.86799 + 3.86799i) q^{17} +0.900390 q^{19} -1.00000 q^{21} +(-4.40621 - 4.40621i) q^{23} +(1.14134 + 4.86799i) q^{25} +(0.707107 - 0.707107i) q^{27} -4.28267i q^{29} +10.8131i q^{31} +(2.00000 - 2.00000i) q^{33} +(-2.22126 + 0.256912i) q^{35} +(1.00000 + 1.00000i) q^{37} +0.513824 q^{39} +9.06068 q^{41} +(2.12792 + 2.12792i) q^{43} +(1.38900 - 1.75233i) q^{45} +(-4.95634 + 4.95634i) q^{47} -1.00000i q^{49} -5.47017i q^{51} +(8.64600 - 8.64600i) q^{53} +(3.92870 - 4.95634i) q^{55} +(-0.636672 - 0.636672i) q^{57} -6.05661 q^{59} +11.2920 q^{61} +(0.707107 + 0.707107i) q^{63} +(1.14134 - 0.132007i) q^{65} +(4.95634 - 4.95634i) q^{67} +6.23132i q^{69} -8.18453i q^{71} +(9.91934 - 9.91934i) q^{73} +(2.63514 - 4.24924i) q^{75} +(2.00000 + 2.00000i) q^{77} +6.05661 q^{79} -1.00000 q^{81} +(-6.75712 - 6.75712i) q^{83} +(-1.40535 - 12.1507i) q^{85} +(-3.02831 + 3.02831i) q^{87} +14.5140i q^{89} +0.513824i q^{91} +(7.64600 - 7.64600i) q^{93} +(-1.57778 - 1.25065i) q^{95} +(8.64600 + 8.64600i) q^{97} -2.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{13} - 4 q^{17} - 12 q^{21} - 20 q^{25} + 24 q^{33} + 12 q^{37} + 16 q^{41} + 4 q^{45} + 28 q^{53} - 16 q^{57} - 16 q^{61} - 20 q^{65} + 60 q^{73} + 24 q^{77} - 12 q^{81} - 84 q^{85} + 16 q^{93}+ \cdots + 28 q^{97}+O(q^{100}) $ 12 * q + 4 * q^13 - 4 * q^17 - 12 * q^21 - 20 * q^25 + 24 * q^33 + 12 * q^37 + 16 * q^41 + 4 * q^45 + 28 * q^53 - 16 * q^57 - 16 * q^61 - 20 * q^65 + 60 * q^73 + 24 * q^77 - 12 * q^81 - 84 * q^85 + 16 * q^93 + 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$-1$

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
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		0			0
$5$	−1.75233	−	1.38900i	−0.783667	−	0.621181i
$5$	−1.75233	−	1.38900i	−0.783667	−	0.621181i
$6$		0			0
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$			2.82843i			0.852803i	0.904534	+	0.426401i	$0.140219\pi$
$11$			2.82843i			0.852803i	−0.904534	+	0.426401i	$0.859781\pi$
$12$		0			0
$13$	−0.363328	+	0.363328i	−0.100769	+	0.100769i	−0.755694	−	0.654925i	$-0.772700\pi$
$13$	−0.363328	+	0.363328i	−0.100769	+	0.100769i	0.654925	+	0.755694i	$0.272700\pi$
$14$		0			0
$15$	0.256912	+	2.22126i	0.0663344	+	0.573527i
$16$		0			0
$17$	3.86799	+	3.86799i	0.938126	+	0.938126i	0.998194	−	0.0600683i	$-0.0191318\pi$
$17$	3.86799	+	3.86799i	0.938126	+	0.938126i	−0.0600683	+	0.998194i	$0.519132\pi$
$18$		0			0
$19$	0.900390			0.206564			0.103282	−	0.994652i	$-0.467066\pi$
$19$	0.900390			0.206564			0.103282	+	0.994652i	$0.467066\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$		0			0
$23$	−4.40621	−	4.40621i	−0.918758	−	0.918758i	0.0781810	−	0.996939i	$-0.475089\pi$
$23$	−4.40621	−	4.40621i	−0.918758	−	0.918758i	−0.996939	+	0.0781810i	$0.975089\pi$
$24$		0			0
$25$	1.14134	+	4.86799i	0.228267	+	0.973599i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$		−	4.28267i		−	0.795272i	−0.917543	−	0.397636i	$-0.869831\pi$
$29$		−	4.28267i		−	0.795272i	0.917543	−	0.397636i	$-0.130169\pi$
$30$		0			0
$31$			10.8131i			1.94209i	0.238905	+	0.971043i	$0.423212\pi$
$31$			10.8131i			1.94209i	−0.238905	+	0.971043i	$0.576788\pi$
$32$		0			0
$33$	2.00000	−	2.00000i	0.348155	−	0.348155i
$34$		0			0
$35$	−2.22126	+	0.256912i	−0.375461	+	0.0434260i
$36$		0			0
$37$	1.00000	+	1.00000i	0.164399	+	0.164399i	0.784512	−	0.620113i	$-0.212913\pi$
$37$	1.00000	+	1.00000i	0.164399	+	0.164399i	−0.620113	+	0.784512i	$0.712913\pi$
$38$		0			0
$39$	0.513824			0.0822776
$40$		0			0
$41$	9.06068			1.41504			0.707520	−	0.706693i	$-0.249814\pi$
$41$	9.06068			1.41504			0.707520	+	0.706693i	$0.249814\pi$
$42$		0			0
$43$	2.12792	+	2.12792i	0.324504	+	0.324504i	0.850492	−	0.525988i	$-0.176304\pi$
$43$	2.12792	+	2.12792i	0.324504	+	0.324504i	−0.525988	+	0.850492i	$0.676304\pi$
$44$		0			0
$45$	1.38900	−	1.75233i	0.207060	−	0.261222i
$46$		0			0
$47$	−4.95634	+	4.95634i	−0.722957	+	0.722957i	−0.969206	−	0.246249i	$-0.920802\pi$
$47$	−4.95634	+	4.95634i	−0.722957	+	0.722957i	0.246249	+	0.969206i	$0.420802\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$		−	5.47017i		−	0.765977i
$52$		0			0
$53$	8.64600	−	8.64600i	1.18762	−	1.18762i	0.209896	−	0.977724i	$-0.432688\pi$
$53$	8.64600	−	8.64600i	1.18762	−	1.18762i	0.977724	−	0.209896i	$-0.0673125\pi$
$54$		0			0
$55$	3.92870	−	4.95634i	0.529745	−	0.668313i
$56$		0			0
$57$	−0.636672	−	0.636672i	−0.0843292	−	0.0843292i
$58$		0			0
$59$	−6.05661			−0.788504			−0.394252	−	0.919002i	$-0.628996\pi$
$59$	−6.05661			−0.788504			−0.394252	+	0.919002i	$0.628996\pi$
$60$		0			0
$61$	11.2920			1.44579			0.722896	−	0.690957i	$-0.242810\pi$
$61$	11.2920			1.44579			0.722896	+	0.690957i	$0.242810\pi$
$62$		0			0
$63$	0.707107	+	0.707107i	0.0890871	+	0.0890871i
$64$		0			0
$65$	1.14134	−	0.132007i	0.141565	−	0.0163735i
$66$		0			0
$67$	4.95634	−	4.95634i	0.605514	−	0.605514i	−0.336257	−	0.941770i	$-0.609161\pi$
$67$	4.95634	−	4.95634i	0.605514	−	0.605514i	0.941770	+	0.336257i	$0.109161\pi$
$68$		0			0
$69$			6.23132i			0.750163i
$70$		0			0
$71$		−	8.18453i		−	0.971325i	−0.874146	−	0.485662i	$-0.838578\pi$
$71$		−	8.18453i		−	0.971325i	0.874146	−	0.485662i	$-0.161422\pi$
$72$		0			0
$73$	9.91934	−	9.91934i	1.16097	−	1.16097i	0.176708	−	0.984263i	$-0.443455\pi$
$73$	9.91934	−	9.91934i	1.16097	−	1.16097i	0.984263	−	0.176708i	$-0.0565449\pi$
$74$		0			0
$75$	2.63514	−	4.24924i	0.304280	−	0.490660i
$76$		0			0
$77$	2.00000	+	2.00000i	0.227921	+	0.227921i
$78$		0			0
$79$	6.05661			0.681422			0.340711	−	0.940168i	$-0.389332\pi$
$79$	6.05661			0.681422			0.340711	+	0.940168i	$0.389332\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−6.75712	−	6.75712i	−0.741691	−	0.741691i	0.231213	−	0.972903i	$-0.425731\pi$
$83$	−6.75712	−	6.75712i	−0.741691	−	0.741691i	−0.972903	+	0.231213i	$0.925731\pi$
$84$		0			0
$85$	−1.40535	−	12.1507i	−0.152432	−	1.31792i
$86$		0			0
$87$	−3.02831	+	3.02831i	−0.324669	+	0.324669i
$88$		0			0
$89$			14.5140i			1.53848i	0.638960	+	0.769240i	$0.279365\pi$
$89$			14.5140i			1.53848i	−0.638960	+	0.769240i	$0.720635\pi$
$90$		0			0
$91$			0.513824i			0.0538634i
$92$		0			0
$93$	7.64600	−	7.64600i	0.792853	−	0.792853i
$94$		0			0
$95$	−1.57778	−	1.25065i	−0.161877	−	0.128313i
$96$		0			0
$97$	8.64600	+	8.64600i	0.877868	+	0.877868i	0.993314	−	0.115445i	$-0.0368296\pi$
$97$	8.64600	+	8.64600i	0.877868	+	0.877868i	−0.115445	+	0.993314i	$0.536830\pi$
$98$		0			0
$99$	−2.82843			−0.284268
$100$		0			0
$101$	−10.7780			−1.07245			−0.536226	−	0.844074i	$-0.680150\pi$
$101$	−10.7780			−1.07245			−0.536226	+	0.844074i	$0.680150\pi$
$102$		0			0
$103$	11.8407	+	11.8407i	1.16670	+	1.16670i	0.982978	+	0.183723i	$0.0588150\pi$
$103$	11.8407	+	11.8407i	1.16670	+	1.16670i	0.183723	+	0.982978i	$0.441185\pi$
$104$		0			0
$105$	1.75233	+	1.38900i	0.171010	+	0.135553i
$106$		0			0
$107$	−1.25065	+	1.25065i	−0.120904	+	0.120904i	−0.764970	−	0.644066i	$-0.777246\pi$
$107$	−1.25065	+	1.25065i	−0.120904	+	0.120904i	0.644066	+	0.764970i	$0.277246\pi$
$108$		0			0
$109$		−	4.82936i		−	0.462569i	−0.972886	−	0.231284i	$-0.925707\pi$
$109$		−	4.82936i		−	0.462569i	0.972886	−	0.231284i	$-0.0742928\pi$
$110$		0			0
$111$		−	1.41421i		−	0.134231i
$112$		0			0
$113$	3.63667	−	3.63667i	0.342109	−	0.342109i	−0.515051	−	0.857160i	$-0.672227\pi$
$113$	3.63667	−	3.63667i	0.342109	−	0.342109i	0.857160	+	0.515051i	$0.172227\pi$
$114$		0			0
$115$	1.60090	+	13.8414i	0.149285	+	1.29072i
$116$		0			0
$117$	−0.363328	−	0.363328i	−0.0335897	−	0.0335897i
$118$		0			0
$119$	5.47017			0.501449
$120$		0			0
$121$	3.00000			0.272727
$122$		0			0
$123$	−6.40687	−	6.40687i	−0.577688	−	0.577688i
$124$		0			0
$125$	4.76166	−	10.1157i	0.425896	−	0.904772i
$126$		0			0
$127$	10.6858	−	10.6858i	0.948213	−	0.948213i	−0.0505103	−	0.998724i	$-0.516085\pi$
$127$	10.6858	−	10.6858i	0.948213	−	0.948213i	0.998724	+	0.0505103i	$0.0160848\pi$
$128$		0			0
$129$		−	3.00933i		−	0.264957i
$130$		0			0
$131$			11.7135i			1.02341i	0.859161	+	0.511705i	$0.170986\pi$
$131$			11.7135i			1.02341i	−0.859161	+	0.511705i	$0.829014\pi$
$132$		0			0
$133$	0.636672	−	0.636672i	0.0552064	−	0.0552064i
$134$		0			0
$135$	−2.22126	+	0.256912i	−0.191176	+	0.0221115i
$136$		0			0
$137$	2.91002	+	2.91002i	0.248619	+	0.248619i	0.820404	−	0.571784i	$-0.193749\pi$
$137$	2.91002	+	2.91002i	0.248619	+	0.248619i	−0.571784	+	0.820404i	$0.693749\pi$
$138$		0			0
$139$	1.30015			0.110277			0.0551386	−	0.998479i	$-0.482440\pi$
$139$	1.30015			0.110277			0.0551386	+	0.998479i	$0.482440\pi$
$140$		0			0
$141$	7.00933			0.590292
$142$		0			0
$143$	−1.02765	−	1.02765i	−0.0859362	−	0.0859362i
$144$		0			0
$145$	−5.94865	+	7.50466i	−0.494008	+	0.623228i
$146$		0			0
$147$	−0.707107	+	0.707107i	−0.0583212	+	0.0583212i
$148$		0			0
$149$			11.4533i			0.938292i	0.883121	+	0.469146i	$0.155438\pi$
$149$			11.4533i			0.938292i	−0.883121	+	0.469146i	$0.844562\pi$
$150$		0			0
$151$			5.91137i			0.481060i	0.970642	+	0.240530i	$0.0773213\pi$
$151$			5.91137i			0.481060i	−0.970642	+	0.240530i	$0.922679\pi$
$152$		0			0
$153$	−3.86799	+	3.86799i	−0.312709	+	0.312709i
$154$		0			0
$155$	15.0194	−	18.9481i	1.20639	−	1.52195i
$156$		0			0
$157$	2.08066	+	2.08066i	0.166054	+	0.166054i	0.785243	−	0.619188i	$-0.212538\pi$
$157$	2.08066	+	2.08066i	0.166054	+	0.166054i	−0.619188	+	0.785243i	$0.712538\pi$
$158$		0			0
$159$	−12.2273			−0.969687
$160$		0			0
$161$	−6.23132			−0.491097
$162$		0			0
$163$	−4.88372	−	4.88372i	−0.382523	−	0.382523i	0.489488	−	0.872010i	$-0.337184\pi$
$163$	−4.88372	−	4.88372i	−0.382523	−	0.382523i	−0.872010	+	0.489488i	$0.837184\pi$
$164$		0			0
$165$	−6.28267	+	0.726656i	−0.489105	+	0.0565701i
$166$		0			0
$167$	10.9403	−	10.9403i	0.846589	−	0.846589i	−0.143117	−	0.989706i	$-0.545713\pi$
$167$	10.9403	−	10.9403i	0.846589	−	0.846589i	0.989706	+	0.143117i	$0.0457126\pi$
$168$		0			0
$169$			12.7360i			0.979691i
$170$		0			0
$171$			0.900390i			0.0688545i
$172$		0			0
$173$	4.13201	−	4.13201i	0.314151	−	0.314151i	−0.532365	−	0.846515i	$-0.678696\pi$
$173$	4.13201	−	4.13201i	0.314151	−	0.314151i	0.846515	+	0.532365i	$0.178696\pi$
$174$		0			0
$175$	4.24924	+	2.63514i	0.321212	+	0.199198i
$176$		0			0
$177$	4.28267	+	4.28267i	0.321905	+	0.321905i
$178$		0			0
$179$	11.6408			0.870078			0.435039	−	0.900412i	$-0.356735\pi$
$179$	11.6408			0.870078			0.435039	+	0.900412i	$0.356735\pi$
$180$		0			0
$181$	−17.5747			−1.30632			−0.653158	−	0.757222i	$-0.726556\pi$
$181$	−17.5747			−1.30632			−0.653158	+	0.757222i	$0.726556\pi$
$182$		0			0
$183$	−7.98465	−	7.98465i	−0.590242	−	0.590242i
$184$		0			0
$185$	−0.363328	−	3.14134i	−0.0267124	−	0.230956i
$186$		0			0
$187$	−10.9403	+	10.9403i	−0.800037	+	0.800037i
$188$		0			0
$189$		−	1.00000i		−	0.0727393i
$190$		0			0
$191$			5.02897i			0.363883i	0.983309	+	0.181942i	$0.0582382\pi$
$191$			5.02897i			0.363883i	−0.983309	+	0.181942i	$0.941762\pi$
$192$		0			0
$193$	1.44398	−	1.44398i	0.103940	−	0.103940i	−0.653224	−	0.757165i	$-0.726584\pi$
$193$	1.44398	−	1.44398i	0.103940	−	0.103940i	0.757165	+	0.653224i	$0.226584\pi$
$194$		0			0
$195$	−0.900390	−	0.713703i	−0.0644783	−	0.0511093i
$196$		0			0
$197$	2.80731	+	2.80731i	0.200013	+	0.200013i	0.800005	−	0.599993i	$-0.204830\pi$
$197$	2.80731	+	2.80731i	0.200013	+	0.200013i	−0.599993	+	0.800005i	$0.704830\pi$
$198$		0			0
$199$	−12.4686			−0.883877			−0.441938	−	0.897045i	$-0.645709\pi$
$199$	−12.4686			−0.883877			−0.441938	+	0.897045i	$0.645709\pi$
$200$		0			0
$201$	−7.00933			−0.494400
$202$		0			0
$203$	−3.02831	−	3.02831i	−0.212545	−	0.212545i
$204$		0			0
$205$	−15.8773	−	12.5853i	−1.10892	−	0.878997i
$206$		0			0
$207$	4.40621	−	4.40621i	0.306253	−	0.306253i
$208$		0			0
$209$			2.54669i			0.176158i
$210$		0			0
$211$			5.65685i			0.389434i	0.980859	+	0.194717i	$0.0623788\pi$
$211$			5.65685i			0.389434i	−0.980859	+	0.194717i	$0.937621\pi$
$212$		0			0
$213$	−5.78734	+	5.78734i	−0.396542	+	0.396542i
$214$		0			0
$215$	−0.773132	−	6.68450i	−0.0527272	−	0.455879i
$216$		0			0
$217$	7.64600	+	7.64600i	0.519044	+	0.519044i
$218$		0			0
$219$	−14.0281			−0.947929
$220$		0			0
$221$	−2.81070			−0.189068
$222$		0			0
$223$	20.3260	+	20.3260i	1.36113	+	1.36113i	0.872480	+	0.488650i	$0.162511\pi$
$223$	20.3260	+	20.3260i	1.36113	+	1.36113i	0.488650	+	0.872480i	$0.337489\pi$
$224$		0			0
$225$	−4.86799	+	1.14134i	−0.324533	+	0.0760891i
$226$		0			0
$227$	−17.7701	+	17.7701i	−1.17944	+	1.17944i	−0.199555	+	0.979887i	$0.563950\pi$
$227$	−17.7701	+	17.7701i	−1.17944	+	1.17944i	−0.979887	+	0.199555i	$0.936050\pi$
$228$		0			0
$229$		−	1.73599i		−	0.114717i	−0.998354	−	0.0573586i	$-0.981732\pi$
$229$		−	1.73599i		−	0.114717i	0.998354	−	0.0573586i	$-0.0182678\pi$
$230$		0			0
$231$		−	2.82843i		−	0.186097i
$232$		0			0
$233$	−10.0993	+	10.0993i	−0.661628	+	0.661628i	−0.955764	−	0.294136i	$-0.904968\pi$
$233$	−10.0993	+	10.0993i	−0.661628	+	0.661628i	0.294136	+	0.955764i	$0.404968\pi$
$234$		0			0
$235$	15.5695	−	1.80078i	1.01564	−	0.117470i
$236$		0			0
$237$	−4.28267	−	4.28267i	−0.278189	−	0.278189i
$238$		0			0
$239$	−16.3427			−1.05712			−0.528560	−	0.848896i	$-0.677268\pi$
$239$	−16.3427			−1.05712			−0.528560	+	0.848896i	$0.677268\pi$
$240$		0			0
$241$	−7.71733			−0.497117			−0.248558	−	0.968617i	$-0.579957\pi$
$241$	−7.71733			−0.497117			−0.248558	+	0.968617i	$0.579957\pi$
$242$		0			0
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		0			0
$245$	−1.38900	+	1.75233i	−0.0887402	+	0.111952i
$246$		0			0
$247$	−0.327137	+	0.327137i	−0.0208152	+	0.0208152i
$248$		0			0
$249$			9.55602i			0.605588i
$250$		0			0
$251$		−	13.9140i		−	0.878244i	−0.898427	−	0.439122i	$-0.855290\pi$
$251$		−	13.9140i		−	0.878244i	0.898427	−	0.439122i	$-0.144710\pi$
$252$		0			0
$253$	12.4626	−	12.4626i	0.783520	−	0.783520i
$254$		0			0
$255$	−7.59808	+	9.58555i	−0.475810	+	0.600270i
$256$		0			0
$257$	−1.08998	−	1.08998i	−0.0679914	−	0.0679914i	0.672293	−	0.740285i	$-0.265309\pi$
$257$	−1.08998	−	1.08998i	−0.0679914	−	0.0679914i	−0.740285	+	0.672293i	$0.765309\pi$
$258$		0			0
$259$	1.41421			0.0878750
$260$		0			0
$261$	4.28267			0.265091
$262$		0			0
$263$	−4.07907	−	4.07907i	−0.251526	−	0.251526i	0.570070	−	0.821596i	$-0.306916\pi$
$263$	−4.07907	−	4.07907i	−0.251526	−	0.251526i	−0.821596	+	0.570070i	$0.806916\pi$
$264$		0			0
$265$	−27.1600	+	3.14134i	−1.66843	+	0.192971i
$266$		0			0
$267$	10.2629	−	10.2629i	0.628082	−	0.628082i
$268$		0			0
$269$		−	16.6940i		−	1.01785i	−0.860811	−	0.508924i	$-0.830043\pi$
$269$		−	16.6940i		−	1.01785i	0.860811	−	0.508924i	$-0.169957\pi$
$270$		0			0
$271$		−	22.3813i		−	1.35957i	−0.733413	−	0.679784i	$-0.762074\pi$
$271$		−	22.3813i		−	1.35957i	0.733413	−	0.679784i	$-0.237926\pi$
$272$		0			0
$273$	0.363328	−	0.363328i	0.0219896	−	0.0219896i
$274$		0			0
$275$	−13.7688	+	3.22819i	−0.830288	+	0.194667i
$276$		0			0
$277$	2.71733	+	2.71733i	0.163268	+	0.163268i	0.784013	−	0.620745i	$-0.213170\pi$
$277$	2.71733	+	2.71733i	0.163268	+	0.163268i	−0.620745	+	0.784013i	$0.713170\pi$
$278$		0			0
$279$	−10.8131			−0.647362
$280$		0			0
$281$	−8.28267			−0.494103			−0.247051	−	0.969002i	$-0.579462\pi$
$281$	−8.28267			−0.494103			−0.247051	+	0.969002i	$0.579462\pi$
$282$		0			0
$283$	4.90171	+	4.90171i	0.291376	+	0.291376i	0.837624	−	0.546248i	$-0.183944\pi$
$283$	4.90171	+	4.90171i	0.291376	+	0.291376i	−0.546248	+	0.837624i	$0.683944\pi$
$284$		0			0
$285$	0.231321	+	2.00000i	0.0137023	+	0.118470i
$286$		0			0
$287$	6.40687	−	6.40687i	0.378185	−	0.378185i
$288$		0			0
$289$			12.9227i			0.760161i
$290$		0			0
$291$		−	12.2273i		−	0.716776i
$292$		0			0
$293$	16.8260	−	16.8260i	0.982984	−	0.982984i	−0.0168740	−	0.999858i	$-0.505371\pi$
$293$	16.8260	−	16.8260i	0.982984	−	0.982984i	0.999858	+	0.0168740i	$0.00537141\pi$
$294$		0			0
$295$	10.6132	+	8.41266i	0.617924	+	0.489804i
$296$		0			0
$297$	2.00000	+	2.00000i	0.116052	+	0.116052i
$298$		0			0
$299$	3.20180			0.185165
$300$		0			0
$301$	3.00933			0.173455
$302$		0			0
$303$	7.62120	+	7.62120i	0.437827	+	0.437827i
$304$		0			0
$305$	−19.7873	−	15.6846i	−1.13302	−	0.898100i
$306$		0			0
$307$	−3.85607	+	3.85607i	−0.220078	+	0.220078i	−0.808531	−	0.588453i	$-0.799737\pi$
$307$	−3.85607	+	3.85607i	−0.220078	+	0.220078i	0.588453	+	0.808531i	$0.299737\pi$
$308$		0			0
$309$		−	16.7453i		−	0.952608i
$310$		0			0
$311$			33.0851i			1.87608i	0.346521	+	0.938042i	$0.387363\pi$
$311$			33.0851i			1.87608i	−0.346521	+	0.938042i	$0.612637\pi$
$312$		0			0
$313$	15.6367	−	15.6367i	0.883837	−	0.883837i	−0.110085	−	0.993922i	$-0.535112\pi$
$313$	15.6367	−	15.6367i	0.883837	−	0.883837i	0.993922	+	0.110085i	$0.0351124\pi$
$314$		0			0
$315$	−0.256912	−	2.22126i	−0.0144753	−	0.125154i
$316$		0			0
$317$	10.3633	+	10.3633i	0.582063	+	0.582063i	0.935470	−	0.353407i	$-0.114977\pi$
$317$	10.3633	+	10.3633i	0.582063	+	0.582063i	−0.353407	+	0.935470i	$0.614977\pi$
$318$		0			0
$319$	12.1132			0.678210
$320$		0			0
$321$	1.76868			0.0987180
$322$		0			0
$323$	3.48270	+	3.48270i	0.193783	+	0.193783i
$324$		0			0
$325$	−2.18336	−	1.35400i	−0.121111	−	0.0751064i
$326$		0			0
$327$	−3.41487	+	3.41487i	−0.188843	+	0.188843i
$328$		0			0
$329$			7.00933i			0.386437i
$330$		0			0
$331$			33.3396i			1.83251i	0.400594	+	0.916256i	$0.368804\pi$
$331$			33.3396i			1.83251i	−0.400594	+	0.916256i	$0.631196\pi$
$332$		0			0
$333$	−1.00000	+	1.00000i	−0.0547997	+	0.0547997i
$334$		0			0
$335$	−15.5695	+	1.80078i	−0.850655	+	0.0983871i
$336$		0			0
$337$	−14.1893	−	14.1893i	−0.772940	−	0.772940i	0.205679	−	0.978619i	$-0.434060\pi$
$337$	−14.1893	−	14.1893i	−0.772940	−	0.772940i	−0.978619	+	0.205679i	$0.934060\pi$
$338$		0			0
$339$	−5.14303			−0.279331
$340$		0			0
$341$	−30.5840			−1.65622
$342$		0			0
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$		0			0
$345$	8.65533	−	10.9193i	0.465987	−	0.587878i
$346$		0			0
$347$	2.67805	−	2.67805i	0.143765	−	0.143765i	−0.631561	−	0.775326i	$-0.717585\pi$
$347$	2.67805	−	2.67805i	0.143765	−	0.143765i	0.775326	+	0.631561i	$0.217585\pi$
$348$		0			0
$349$			15.8200i			0.846827i	0.905937	+	0.423413i	$0.139168\pi$
$349$			15.8200i			0.846827i	−0.905937	+	0.423413i	$0.860832\pi$
$350$		0			0
$351$			0.513824i			0.0274259i
$352$		0			0
$353$	3.53397	−	3.53397i	0.188094	−	0.188094i	−0.606778	−	0.794872i	$-0.707538\pi$
$353$	3.53397	−	3.53397i	0.188094	−	0.188094i	0.794872	+	0.606778i	$0.207538\pi$
$354$		0			0
$355$	−11.3683	+	14.3420i	−0.603369	+	0.761195i
$356$		0			0
$357$	−3.86799	−	3.86799i	−0.204716	−	0.204716i
$358$		0			0
$359$	9.88630			0.521779			0.260890	−	0.965369i	$-0.415984\pi$
$359$	9.88630			0.521779			0.260890	+	0.965369i	$0.415984\pi$
$360$		0			0
$361$	−18.1893			−0.957331
$362$		0			0
$363$	−2.12132	−	2.12132i	−0.111340	−	0.111340i
$364$		0			0
$365$	−31.1600	+	3.60398i	−1.63099	+	0.188641i
$366$		0			0
$367$	−11.2128	+	11.2128i	−0.585305	+	0.585305i	−0.936356	−	0.351051i	$-0.885824\pi$
$367$	−11.2128	+	11.2128i	−0.585305	+	0.585305i	0.351051	+	0.936356i	$0.385824\pi$
$368$		0			0
$369$			9.06068i			0.471680i
$370$		0			0
$371$		−	12.2273i		−	0.634809i
$372$		0			0
$373$	−14.3947	+	14.3947i	−0.745330	+	0.745330i	−0.973598	−	0.228269i	$-0.926694\pi$
$373$	−14.3947	+	14.3947i	−0.745330	+	0.745330i	0.228269	+	0.973598i	$0.426694\pi$
$374$		0			0
$375$	−10.5199	+	3.78585i	−0.543243	+	0.195500i
$376$		0			0
$377$	1.55602	+	1.55602i	0.0801389	+	0.0801389i
$378$		0			0
$379$	30.1378			1.54808			0.774038	−	0.633139i	$-0.218234\pi$
$379$	30.1378			1.54808			0.774038	+	0.633139i	$0.218234\pi$
$380$		0			0
$381$	−15.1120			−0.774213
$382$		0			0
$383$	−15.8967	−	15.8967i	−0.812282	−	0.812282i	0.172693	−	0.984976i	$-0.444753\pi$
$383$	−15.8967	−	15.8967i	−0.812282	−	0.812282i	−0.984976	+	0.172693i	$0.944753\pi$
$384$		0			0
$385$	−0.726656	−	6.28267i	−0.0370338	−	0.320195i
$386$		0			0
$387$	−2.12792	+	2.12792i	−0.108168	+	0.108168i
$388$		0			0
$389$			3.55602i			0.180297i	0.995928	+	0.0901486i	$0.0287342\pi$
$389$			3.55602i			0.180297i	−0.995928	+	0.0901486i	$0.971266\pi$
$390$		0			0
$391$		−	34.0864i		−	1.72382i
$392$		0			0
$393$	8.28267	−	8.28267i	0.417806	−	0.417806i
$394$		0			0
$395$	−10.6132	−	8.41266i	−0.534008	−	0.423287i
$396$		0			0
$397$	13.1086	+	13.1086i	0.657904	+	0.657904i	0.954884	−	0.296980i	$-0.0959794\pi$
$397$	13.1086	+	13.1086i	0.657904	+	0.657904i	−0.296980	+	0.954884i	$0.595979\pi$
$398$		0			0
$399$	−0.900390			−0.0450759
$400$		0			0
$401$	2.99067			0.149347			0.0746735	−	0.997208i	$-0.476209\pi$
$401$	2.99067			0.149347			0.0746735	+	0.997208i	$0.476209\pi$
$402$		0			0
$403$	−3.92870	−	3.92870i	−0.195702	−	0.195702i
$404$		0			0
$405$	1.75233	+	1.38900i	0.0870741	+	0.0690202i
$406$		0			0
$407$	−2.82843	+	2.82843i	−0.140200	+	0.140200i
$408$		0			0
$409$			33.9346i			1.67796i	0.544163	+	0.838979i	$0.316847\pi$
$409$			33.9346i			1.67796i	−0.544163	+	0.838979i	$0.683153\pi$
$410$		0			0
$411$		−	4.11538i		−	0.202997i
$412$		0			0
$413$	−4.28267	+	4.28267i	−0.210737	+	0.210737i
$414$		0			0
$415$	2.45505	+	21.2264i	0.120514	+	1.04196i
$416$		0			0
$417$	−0.919344	−	0.919344i	−0.0450205	−	0.0450205i
$418$		0			0
$419$	38.1970			1.86604			0.933022	−	0.359820i	$-0.117162\pi$
$419$	38.1970			1.86604			0.933022	+	0.359820i	$0.117162\pi$
$420$		0			0
$421$	−30.8667			−1.50435			−0.752175	−	0.658964i	$-0.770995\pi$
$421$	−30.8667			−1.50435			−0.752175	+	0.658964i	$0.770995\pi$
$422$		0			0
$423$	−4.95634	−	4.95634i	−0.240986	−	0.240986i
$424$		0			0
$425$	−14.4147	+	23.2440i	−0.699215	+	1.12750i
$426$		0			0
$427$	7.98465	−	7.98465i	0.386404	−	0.386404i
$428$		0			0
$429$			1.45331i			0.0701666i
$430$		0			0
$431$		−	14.6409i		−	0.705227i	−0.935769	−	0.352614i	$-0.885293\pi$
$431$		−	14.6409i		−	0.705227i	0.935769	−	0.352614i	$-0.114707\pi$
$432$		0			0
$433$	−8.66466	+	8.66466i	−0.416397	+	0.416397i	−0.883960	−	0.467563i	$-0.845132\pi$
$433$	−8.66466	+	8.66466i	−0.416397	+	0.416397i	0.467563	+	0.883960i	$0.345132\pi$
$434$		0			0
$435$	9.51293	−	1.10027i	0.456110	−	0.0527539i
$436$		0			0
$437$	−3.96731	−	3.96731i	−0.189782	−	0.189782i
$438$		0			0
$439$	8.61254			0.411054			0.205527	−	0.978651i	$-0.434109\pi$
$439$	8.61254			0.411054			0.205527	+	0.978651i	$0.434109\pi$
$440$		0			0
$441$	1.00000			0.0476190
$442$		0			0
$443$	6.13437	+	6.13437i	0.291453	+	0.291453i	0.837654	−	0.546201i	$-0.183927\pi$
$443$	6.13437	+	6.13437i	0.291453	+	0.291453i	−0.546201	+	0.837654i	$0.683927\pi$
$444$		0			0
$445$	20.1600	−	25.4333i	0.955675	−	1.20566i
$446$		0			0
$447$	8.09872	−	8.09872i	0.383056	−	0.383056i
$448$		0			0
$449$			24.5467i			1.15843i	0.815175	+	0.579215i	$0.196641\pi$
$449$			24.5467i			1.15843i	−0.815175	+	0.579215i	$0.803359\pi$
$450$		0			0
$451$			25.6275i			1.20675i
$452$		0			0
$453$	4.17997	−	4.17997i	0.196392	−	0.196392i
$454$		0			0
$455$	0.713703	−	0.900390i	0.0334589	−	0.0422109i
$456$		0			0
$457$	−18.0280	−	18.0280i	−0.843314	−	0.843314i	0.145975	−	0.989288i	$-0.453368\pi$
$457$	−18.0280	−	18.0280i	−0.843314	−	0.843314i	−0.989288	+	0.145975i	$0.953368\pi$
$458$		0			0
$459$	5.47017			0.255326
$460$		0			0
$461$	−2.21266			−0.103054			−0.0515270	−	0.998672i	$-0.516409\pi$
$461$	−2.21266			−0.103054			−0.0515270	+	0.998672i	$0.516409\pi$
$462$		0			0
$463$	−22.3993	−	22.3993i	−1.04098	−	1.04098i	−0.999124	−	0.0418597i	$-0.986672\pi$
$463$	−22.3993	−	22.3993i	−1.04098	−	1.04098i	−0.0418597	−	0.999124i	$-0.513328\pi$
$464$		0			0
$465$	−24.0187	+	2.77801i	−1.11384	+	0.128827i
$466$		0			0
$467$	4.65559	−	4.65559i	0.215435	−	0.215435i	−0.591136	−	0.806572i	$-0.701321\pi$
$467$	4.65559	−	4.65559i	0.215435	−	0.215435i	0.806572	+	0.591136i	$0.201321\pi$
$468$		0			0
$469$		−	7.00933i		−	0.323661i
$470$		0			0
$471$		−	2.94249i		−	0.135583i
$472$		0			0
$473$	−6.01866	+	6.01866i	−0.276738	+	0.276738i
$474$		0			0
$475$	1.02765	+	4.38309i	0.0471517	+	0.201110i
$476$		0			0
$477$	8.64600	+	8.64600i	0.395873	+	0.395873i
$478$		0			0
$479$	−25.7367			−1.17594			−0.587971	−	0.808882i	$-0.700073\pi$
$479$	−25.7367			−1.17594			−0.587971	+	0.808882i	$0.700073\pi$
$480$		0			0
$481$	−0.726656			−0.0331327
$482$		0			0
$483$	4.40621	+	4.40621i	0.200489	+	0.200489i
$484$		0			0
$485$	−3.14134	−	27.1600i	−0.142641	−	1.23327i
$486$		0			0
$487$	19.8980	−	19.8980i	0.901664	−	0.901664i	−0.0939158	−	0.995580i	$-0.529938\pi$
$487$	19.8980	−	19.8980i	0.901664	−	0.901664i	0.995580	+	0.0939158i	$0.0299385\pi$
$488$		0			0
$489$			6.90663i			0.312328i
$490$		0			0
$491$			15.0972i			0.681325i	0.940186	+	0.340663i	$0.110651\pi$
$491$			15.0972i			0.681325i	−0.940186	+	0.340663i	$0.889349\pi$
$492$		0			0
$493$	16.5653	−	16.5653i	0.746066	−	0.746066i
$494$		0			0
$495$	4.95634	+	3.92870i	0.222771	+	0.176582i
$496$		0			0
$497$	−5.78734	−	5.78734i	−0.259598	−	0.259598i
$498$		0			0
$499$	−24.4810			−1.09592			−0.547959	−	0.836505i	$-0.684595\pi$
$499$	−24.4810			−1.09592			−0.547959	+	0.836505i	$0.684595\pi$
$500$		0			0
$501$	−15.4720			−0.691237
$502$		0			0
$503$	−5.72948	−	5.72948i	−0.255465	−	0.255465i	0.567742	−	0.823207i	$-0.307817\pi$
$503$	−5.72948	−	5.72948i	−0.255465	−	0.255465i	−0.823207	+	0.567742i	$0.807817\pi$
$504$		0			0
$505$	18.8867	+	14.9707i	0.840445	+	0.666187i
$506$		0			0
$507$	9.00570	−	9.00570i	0.399957	−	0.399957i
$508$		0			0
$509$		−	4.07001i		−	0.180400i	−0.995924	−	0.0902000i	$-0.971249\pi$
$509$		−	4.07001i		−	0.180400i	0.995924	−	0.0902000i	$-0.0287506\pi$
$510$		0			0
$511$		−	14.0281i		−	0.620565i
$512$		0			0
$513$	0.636672	−	0.636672i	0.0281097	−	0.0281097i
$514$		0			0
$515$	−4.30207	−	37.1957i	−0.189572	−	1.63904i
$516$		0			0
$517$	−14.0187	−	14.0187i	−0.616540	−	0.616540i
$518$		0			0
$519$	−5.84354			−0.256503
$520$		0			0
$521$	13.3247			0.583765			0.291883	−	0.956454i	$-0.405718\pi$
$521$	13.3247			0.583765			0.291883	+	0.956454i	$0.405718\pi$
$522$		0			0
$523$	11.5862	+	11.5862i	0.506630	+	0.506630i	0.913490	−	0.406861i	$-0.133377\pi$
$523$	11.5862	+	11.5862i	0.506630	+	0.506630i	−0.406861	+	0.913490i	$0.633377\pi$
$524$		0			0
$525$	−1.14134	−	4.86799i	−0.0498120	−	0.212457i
$526$		0			0
$527$	−41.8249	+	41.8249i	−1.82192	+	1.82192i
$528$		0			0
$529$			15.8294i			0.688233i
$530$		0			0
$531$		−	6.05661i		−	0.262835i
$532$		0			0
$533$	−3.29200	+	3.29200i	−0.142592	+	0.142592i
$534$		0			0
$535$	3.92870	−	0.454395i	0.169852	−	0.0196452i
$536$		0			0
$537$	−8.23132	−	8.23132i	−0.355208	−	0.355208i
$538$		0			0
$539$	2.82843			0.121829
$540$		0			0
$541$	−37.3947			−1.60772			−0.803862	−	0.594816i	$-0.797225\pi$
$541$	−37.3947			−1.60772			−0.803862	+	0.594816i	$0.797225\pi$
$542$		0			0
$543$	12.4272	+	12.4272i	0.533301	+	0.533301i
$544$		0			0
$545$	−6.70800	+	8.46264i	−0.287339	+	0.362500i
$546$		0			0
$547$	21.9269	−	21.9269i	0.937527	−	0.937527i	−0.0606333	−	0.998160i	$-0.519312\pi$
$547$	21.9269	−	21.9269i	0.937527	−	0.937527i	0.998160	+	0.0606333i	$0.0193120\pi$
$548$		0			0
$549$			11.2920i			0.481931i
$550$		0			0
$551$		−	3.85607i		−	0.164274i
$552$		0			0
$553$	4.28267	−	4.28267i	0.182118	−	0.182118i
$554$		0			0
$555$	−1.96435	+	2.47817i	−0.0833819	+	0.105193i
$556$		0			0
$557$	22.0993	+	22.0993i	0.936378	+	0.936378i	0.998094	−	0.0617158i	$-0.0196572\pi$
$557$	22.0993	+	22.0993i	0.936378	+	0.936378i	−0.0617158	+	0.998094i	$0.519657\pi$
$558$		0			0
$559$	−1.54626			−0.0654000
$560$		0			0
$561$	15.4720			0.653227
$562$		0			0
$563$	−7.63953	−	7.63953i	−0.321968	−	0.321968i	0.527554	−	0.849522i	$-0.323109\pi$
$563$	−7.63953	−	7.63953i	−0.321968	−	0.321968i	−0.849522	+	0.527554i	$0.823109\pi$
$564$		0			0
$565$	−11.4240	+	1.32131i	−0.480612	+	0.0555877i
$566$		0			0
$567$	−0.707107	+	0.707107i	−0.0296957	+	0.0296957i
$568$		0			0
$569$		−	0.0840454i		−	0.00352337i	−0.999998	−	0.00176168i	$-0.999439\pi$
$569$		−	0.0840454i		−	0.00352337i	0.999998	−	0.00176168i	$-0.000560761\pi$
$570$		0			0
$571$		−	15.5695i		−	0.651565i	−0.945445	−	0.325783i	$-0.894372\pi$
$571$		−	15.5695i		−	0.651565i	0.945445	−	0.325783i	$-0.105628\pi$
$572$		0			0
$573$	3.55602	−	3.55602i	0.148555	−	0.148555i
$574$		0			0
$575$	16.4204	−	26.4784i	0.684779	−	1.10422i
$576$		0			0
$577$	9.19269	+	9.19269i	0.382697	+	0.382697i	0.872073	−	0.489376i	$-0.162775\pi$
$577$	9.19269	+	9.19269i	0.382697	+	0.382697i	−0.489376	+	0.872073i	$0.662775\pi$
$578$		0			0
$579$	−2.04210			−0.0848669
$580$		0			0
$581$	−9.55602			−0.396450
$582$		0			0
$583$	24.4546	+	24.4546i	1.01281	+	1.01281i
$584$		0			0
$585$	0.132007	+	1.14134i	0.00545783	+	0.0471884i
$586$		0			0
$587$	−21.1538	+	21.1538i	−0.873110	+	0.873110i	−0.992810	−	0.119700i	$-0.961807\pi$
$587$	−21.1538	+	21.1538i	−0.873110	+	0.873110i	0.119700	+	0.992810i	$0.461807\pi$
$588$		0			0
$589$			9.73599i			0.401164i
$590$		0			0
$591$		−	3.97014i		−	0.163310i
$592$		0			0
$593$	5.58532	−	5.58532i	0.229362	−	0.229362i	−0.583064	−	0.812426i	$-0.698146\pi$
$593$	5.58532	−	5.58532i	0.229362	−	0.229362i	0.812426	+	0.583064i	$0.198146\pi$
$594$		0			0
$595$	−9.58555	−	7.59808i	−0.392969	−	0.311491i
$596$		0			0
$597$	8.81664	+	8.81664i	0.360841	+	0.360841i
$598$		0			0
$599$	29.7117			1.21399			0.606993	−	0.794707i	$-0.292376\pi$
$599$	29.7117			1.21399			0.606993	+	0.794707i	$0.292376\pi$
$600$		0			0
$601$	23.6519			0.964783			0.482391	−	0.875956i	$-0.339768\pi$
$601$	23.6519			0.964783			0.482391	+	0.875956i	$0.339768\pi$
$602$		0			0
$603$	4.95634	+	4.95634i	0.201838	+	0.201838i
$604$		0			0
$605$	−5.25700	−	4.16701i	−0.213727	−	0.169413i
$606$		0			0
$607$	7.21152	−	7.21152i	0.292706	−	0.292706i	−0.545442	−	0.838149i	$-0.683638\pi$
$607$	7.21152	−	7.21152i	0.292706	−	0.292706i	0.838149	+	0.545442i	$0.183638\pi$
$608$		0			0
$609$			4.28267i			0.173543i
$610$		0			0
$611$		−	3.60156i		−	0.145703i
$612$		0			0
$613$	−0.614625	+	0.614625i	−0.0248245	+	0.0248245i	−0.719410	−	0.694586i	$-0.755588\pi$
$613$	−0.614625	+	0.614625i	−0.0248245	+	0.0248245i	0.694586	+	0.719410i	$0.255588\pi$
$614$		0			0
$615$	2.32780	+	20.1261i	0.0938658	+	0.811564i
$616$		0			0
$617$	0.381986	+	0.381986i	0.0153782	+	0.0153782i	0.714754	−	0.699376i	$-0.246539\pi$
$617$	0.381986	+	0.381986i	0.0153782	+	0.0153782i	−0.699376	+	0.714754i	$0.746539\pi$
$618$		0			0
$619$	−40.1514			−1.61382			−0.806910	−	0.590674i	$-0.798862\pi$
$619$	−40.1514			−1.61382			−0.806910	+	0.590674i	$0.798862\pi$
$620$		0			0
$621$	−6.23132			−0.250054
$622$		0			0
$623$	10.2629	+	10.2629i	0.411176	+	0.411176i
$624$		0			0
$625$	−22.3947	+	11.1120i	−0.895788	+	0.444481i
$626$		0			0
$627$	1.80078	−	1.80078i	0.0719162	−	0.0719162i
$628$		0			0
$629$			7.73599i			0.308454i
$630$		0			0
$631$		−	20.3704i		−	0.810932i	−0.914110	−	0.405466i	$-0.867109\pi$
$631$		−	20.3704i		−	0.810932i	0.914110	−	0.405466i	$-0.132891\pi$
$632$		0			0
$633$	4.00000	−	4.00000i	0.158986	−	0.158986i
$634$		0			0
$635$	−33.5678	+	3.88246i	−1.33210	+	0.154071i
$636$		0			0
$637$	0.363328	+	0.363328i	0.0143956	+	0.0143956i
$638$		0			0
$639$	8.18453			0.323775
$640$		0			0
$641$	−16.2827			−0.643127			−0.321563	−	0.946888i	$-0.604208\pi$
$641$	−16.2827			−0.643127			−0.321563	+	0.946888i	$0.604208\pi$
$642$		0			0
$643$	16.5708	+	16.5708i	0.653489	+	0.653489i	0.953831	−	0.300343i	$-0.0971010\pi$
$643$	16.5708	+	16.5708i	0.653489	+	0.653489i	−0.300343	+	0.953831i	$0.597101\pi$
$644$		0			0
$645$	−4.17997	+	5.27334i	−0.164586	+	0.207638i
$646$		0			0
$647$	−14.7964	+	14.7964i	−0.581707	+	0.581707i	−0.935372	−	0.353665i	$-0.884935\pi$
$647$	−14.7964	+	14.7964i	−0.581707	+	0.581707i	0.353665	+	0.935372i	$0.384935\pi$
$648$		0			0
$649$		−	17.1307i		−	0.672438i
$650$		0			0
$651$		−	10.8131i		−	0.423798i
$652$		0			0
$653$	29.7767	−	29.7767i	1.16525	−	1.16525i	0.181943	−	0.983309i	$-0.441761\pi$
$653$	29.7767	−	29.7767i	1.16525	−	1.16525i	0.983309	−	0.181943i	$-0.0582386\pi$
$654$		0			0
$655$	16.2701	−	20.5259i	0.635724	−	0.802013i
$656$		0			0
$657$	9.91934	+	9.91934i	0.386990	+	0.386990i
$658$		0			0
$659$	38.6693			1.50634			0.753172	−	0.657824i	$-0.228523\pi$
$659$	38.6693			1.50634			0.753172	+	0.657824i	$0.228523\pi$
$660$		0			0
$661$	19.8573			0.772361			0.386181	−	0.922423i	$-0.373794\pi$
$661$	19.8573			0.772361			0.386181	+	0.922423i	$0.373794\pi$
$662$		0			0
$663$	1.98747	+	1.98747i	0.0771868	+	0.0771868i
$664$		0			0
$665$	−2.00000	+	0.231321i	−0.0775567	+	0.00897024i
$666$		0			0
$667$	−18.8703	+	18.8703i	−0.730663	+	0.730663i
$668$		0			0
$669$		−	28.7453i		−	1.11136i
$670$		0			0
$671$			31.9386i			1.23298i
$672$		0			0
$673$	2.98134	−	2.98134i	0.114922	−	0.114922i	−0.647307	−	0.762229i	$-0.724105\pi$
$673$	2.98134	−	2.98134i	0.114922	−	0.114922i	0.762229	+	0.647307i	$0.224105\pi$
$674$		0			0
$675$	4.24924	+	2.63514i	0.163553	+	0.101427i
$676$		0			0
$677$	−20.4333	−	20.4333i	−0.785317	−	0.785317i	0.195406	−	0.980723i	$-0.437398\pi$
$677$	−20.4333	−	20.4333i	−0.785317	−	0.785317i	−0.980723	+	0.195406i	$0.937398\pi$
$678$		0			0
$679$	12.2273			0.469240
$680$		0			0
$681$	25.1307			0.963010
$682$		0			0
$683$	−14.1370	−	14.1370i	−0.540937	−	0.540937i	0.382866	−	0.923804i	$-0.374937\pi$
$683$	−14.1370	−	14.1370i	−0.540937	−	0.540937i	−0.923804	+	0.382866i	$0.874937\pi$
$684$		0			0
$685$	−1.05729	−	9.14134i	−0.0403970	−	0.349272i
$686$		0			0
$687$	−1.22753	+	1.22753i	−0.0468331	+	0.0468331i
$688$		0			0
$689$			6.28267i			0.239351i
$690$		0			0
$691$			8.01104i			0.304754i	0.988322	+	0.152377i	$0.0486928\pi$
$691$			8.01104i			0.304754i	−0.988322	+	0.152377i	$0.951307\pi$
$692$		0			0
$693$	−2.00000	+	2.00000i	−0.0759737	+	0.0759737i
$694$		0			0
$695$	−2.27829	−	1.80591i	−0.0864206	−	0.0685021i
$696$		0			0
$697$	35.0466	+	35.0466i	1.32749	+	1.32749i
$698$		0			0
$699$	14.2826			0.540217
$700$		0			0
$701$	37.4134			1.41308			0.706542	−	0.707672i	$-0.250254\pi$
$701$	37.4134			1.41308			0.706542	+	0.707672i	$0.250254\pi$
$702$		0			0
$703$	0.900390	+	0.900390i	0.0339588	+	0.0339588i
$704$		0			0
$705$	−12.2827	−	9.73599i	−0.462592	−	0.366678i
$706$		0			0
$707$	−7.62120	+	7.62120i	−0.286625	+	0.286625i
$708$		0			0
$709$		−	20.9253i		−	0.785866i	−0.919567	−	0.392933i	$-0.871461\pi$
$709$		−	20.9253i		−	0.785866i	0.919567	−	0.392933i	$-0.128539\pi$
$710$		0			0
$711$			6.05661i			0.227141i
$712$		0			0
$713$	47.6447	−	47.6447i	1.78431	−	1.78431i
$714$		0			0
$715$	0.373373	+	3.22819i	0.0139634	+	0.120727i
$716$		0			0
$717$	11.5560	+	11.5560i	0.431567	+	0.431567i
$718$		0			0
$719$	27.1378			1.01207			0.506034	−	0.862514i	$-0.331111\pi$
$719$	27.1378			1.01207			0.506034	+	0.862514i	$0.331111\pi$
$720$		0			0
$721$	16.7453			0.623628
$722$		0			0
$723$	5.45697	+	5.45697i	0.202947	+	0.202947i
$724$		0			0
$725$	20.8480	−	4.88797i	0.774276	−	0.181535i
$726$		0			0
$727$	17.3967	−	17.3967i	0.645208	−	0.645208i	−0.306623	−	0.951831i	$-0.599199\pi$
$727$	17.3967	−	17.3967i	0.645208	−	0.645208i	0.951831	+	0.306623i	$0.0991991\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$			16.4615i			0.608852i
$732$		0			0
$733$	26.5874	−	26.5874i	0.982028	−	0.982028i	−0.0178136	−	0.999841i	$-0.505671\pi$
$733$	26.5874	−	26.5874i	0.982028	−	0.982028i	0.999841	+	0.0178136i	$0.00567055\pi$
$734$		0			0
$735$	2.22126	−	0.256912i	0.0819324	−	0.00947634i
$736$		0			0
$737$	14.0187	+	14.0187i	0.516384	+	0.516384i
$738$		0			0
$739$	−46.0544			−1.69414			−0.847068	−	0.531484i	$-0.821635\pi$
$739$	−46.0544			−1.69414			−0.847068	+	0.531484i	$0.821635\pi$
$740$		0			0
$741$	0.462642			0.0169956
$742$		0			0
$743$	−25.9597	−	25.9597i	−0.952371	−	0.952371i	0.0465456	−	0.998916i	$-0.485179\pi$
$743$	−25.9597	−	25.9597i	−0.952371	−	0.952371i	−0.998916	+	0.0465456i	$0.985179\pi$
$744$		0			0
$745$	15.9087	−	20.0700i	0.582850	−	0.735308i
$746$		0			0
$747$	6.75712	−	6.75712i	0.247230	−	0.247230i
$748$		0			0
$749$			1.76868i			0.0646261i
$750$		0			0
$751$		−	32.5401i		−	1.18741i	−0.804685	−	0.593703i	$-0.797666\pi$
$751$		−	32.5401i		−	1.18741i	0.804685	−	0.593703i	$-0.202334\pi$
$752$		0			0
$753$	−9.83869	+	9.83869i	−0.358542	+	0.358542i
$754$		0			0
$755$	8.21092	−	10.3587i	0.298826	−	0.376991i
$756$		0			0
$757$	−6.73599	−	6.73599i	−0.244824	−	0.244824i	0.574019	−	0.818842i	$-0.305384\pi$
$757$	−6.73599	−	6.73599i	−0.244824	−	0.244824i	−0.818842	+	0.574019i	$0.805384\pi$
$758$		0			0
$759$	−17.6248			−0.639741
$760$		0			0
$761$	40.6940			1.47515			0.737577	−	0.675262i	$-0.235970\pi$
$761$	40.6940			1.47515			0.737577	+	0.675262i	$0.235970\pi$
$762$		0			0
$763$	−3.41487	−	3.41487i	−0.123627	−	0.123627i
$764$		0			0
$765$	12.1507	−	1.40535i	0.439308	−	0.0508106i
$766$		0			0
$767$	2.20054	−	2.20054i	0.0794568	−	0.0794568i
$768$		0			0
$769$		−	15.2920i		−	0.551444i	−0.961237	−	0.275722i	$-0.911083\pi$
$769$		−	15.2920i		−	0.551444i	0.961237	−	0.275722i	$-0.0889169\pi$
$770$		0			0
$771$			1.54147i			0.0555147i
$772$		0			0
$773$	−30.6460	+	30.6460i	−1.10226	+	1.10226i	−0.108122	+	0.994138i	$0.534484\pi$
$773$	−30.6460	+	30.6460i	−1.10226	+	1.10226i	−0.994138	+	0.108122i	$0.965516\pi$
$774$		0			0
$775$	−52.6380	+	12.3414i	−1.89081	+	0.443315i
$776$		0			0
$777$	−1.00000	−	1.00000i	−0.0358748	−	0.0358748i
$778$		0			0
$779$	8.15814			0.292296
$780$		0			0
$781$	23.1493			0.828349
$782$		0			0
$783$	−3.02831	−	3.02831i	−0.108223	−	0.108223i
$784$		0			0
$785$	−0.755961	−	6.53604i	−0.0269814	−	0.233281i
$786$		0			0
$787$	−29.3563	+	29.3563i	−1.04644	+	1.04644i	−0.0475709	+	0.998868i	$0.515148\pi$
$787$	−29.3563	+	29.3563i	−1.04644	+	1.04644i	−0.998868	+	0.0475709i	$0.984852\pi$
$788$		0			0
$789$			5.76868i			0.205370i
$790$		0			0
$791$		−	5.14303i		−	0.182865i
$792$		0			0
$793$	−4.10270	+	4.10270i	−0.145691	+	0.145691i
$794$		0			0
$795$	21.4263	+	16.9838i	0.759912	+	0.602352i
$796$		0			0
$797$	9.32131	+	9.32131i	0.330178	+	0.330178i	0.852654	−	0.522476i	$-0.174992\pi$
$797$	9.32131	+	9.32131i	0.330178	+	0.330178i	−0.522476	+	0.852654i	$0.674992\pi$
$798$		0			0
$799$	−38.3422			−1.35645
$800$		0			0
$801$	−14.5140			−0.512827
$802$		0			0
$803$	28.0561	+	28.0561i	0.990080	+	0.990080i
$804$		0			0
$805$	10.9193	+	8.65533i	0.384856	+	0.305060i
$806$		0			0
$807$	−11.8044	+	11.8044i	−0.415535	+	0.415535i
$808$		0			0
$809$		−	7.85735i		−	0.276250i	−0.990415	−	0.138125i	$-0.955893\pi$
$809$		−	7.85735i		−	0.276250i	0.990415	−	0.138125i	$-0.0441075\pi$
$810$		0			0
$811$		−	28.2927i		−	0.993490i	−0.867897	−	0.496745i	$-0.834528\pi$
$811$		−	28.2927i		−	0.993490i	0.867897	−	0.496745i	$-0.165472\pi$
$812$		0			0
$813$	−15.8260	+	15.8260i	−0.555041	+	0.555041i
$814$		0			0
$815$	1.77439	+	15.3414i	0.0621543	+	0.537386i
$816$		0			0
$817$	1.91595	+	1.91595i	0.0670308	+	0.0670308i
$818$		0			0
$819$	−0.513824			−0.0179545
$820$		0			0
$821$	−1.59597			−0.0556997			−0.0278498	−	0.999612i	$-0.508866\pi$
$821$	−1.59597			−0.0556997			−0.0278498	+	0.999612i	$0.508866\pi$
$822$		0			0
$823$	10.5406	+	10.5406i	0.367421	+	0.367421i	0.866536	−	0.499115i	$-0.166341\pi$
$823$	10.5406	+	10.5406i	0.367421	+	0.367421i	−0.499115	+	0.866536i	$0.666341\pi$
$824$		0			0
$825$	12.0187	+	7.45331i	0.418436	+	0.259491i
$826$		0			0
$827$	37.4451	−	37.4451i	1.30209	−	1.30209i	0.375115	−	0.926978i	$-0.377603\pi$
$827$	37.4451	−	37.4451i	1.30209	−	1.30209i	0.926978	−	0.375115i	$-0.122397\pi$
$828$		0			0
$829$		−	19.7614i		−	0.686343i	−0.939273	−	0.343171i	$-0.888499\pi$
$829$		−	19.7614i		−	0.686343i	0.939273	−	0.343171i	$-0.111501\pi$
$830$		0			0
$831$		−	3.84288i		−	0.133308i
$832$		0			0
$833$	3.86799	−	3.86799i	0.134018	−	0.134018i
$834$		0			0
$835$	−34.3673	+	3.97493i	−1.18933	+	0.137558i
$836$		0			0
$837$	7.64600	+	7.64600i	0.264284	+	0.264284i
$838$		0			0
$839$	22.6274			0.781185			0.390593	−	0.920564i	$-0.372270\pi$
$839$	22.6274			0.781185			0.390593	+	0.920564i	$0.372270\pi$
$840$		0			0
$841$	10.6587			0.367542
$842$		0			0
$843$	5.85673	+	5.85673i	0.201717	+	0.201717i
$844$		0			0
$845$	17.6903	−	22.3177i	0.608566	−	0.767751i
$846$		0			0
$847$	2.12132	−	2.12132i	0.0728894	−	0.0728894i
$848$		0			0
$849$		−	6.93206i		−	0.237908i
$850$		0			0
$851$		−	8.81242i		−	0.302086i
$852$		0			0
$853$	−26.3047	+	26.3047i	−0.900656	+	0.900656i	−0.995493	−	0.0948364i	$-0.969767\pi$
$853$	−26.3047	+	26.3047i	−0.900656	+	0.900656i	0.0948364	+	0.995493i	$0.469767\pi$
$854$		0			0
$855$	1.25065	−	1.57778i	0.0427712	−	0.0539590i
$856$		0			0
$857$	−0.891358	−	0.891358i	−0.0304482	−	0.0304482i	0.691719	−	0.722167i	$-0.256854\pi$
$857$	−0.891358	−	0.891358i	−0.0304482	−	0.0304482i	−0.722167	+	0.691719i	$0.756854\pi$
$858$		0			0
$859$	29.9842			1.02305			0.511523	−	0.859269i	$-0.329081\pi$
$859$	29.9842			1.02305			0.511523	+	0.859269i	$0.329081\pi$
$860$		0			0
$861$	−9.06068			−0.308787
$862$		0			0
$863$	16.5194	+	16.5194i	0.562328	+	0.562328i	0.929968	−	0.367640i	$-0.119834\pi$
$863$	16.5194	+	16.5194i	0.562328	+	0.562328i	−0.367640	+	0.929968i	$0.619834\pi$
$864$		0			0
$865$	−12.9800	+	1.50127i	−0.441334	+	0.0510449i
$866$		0			0
$867$	9.13775	−	9.13775i	0.310334	−	0.310334i
$868$		0			0
$869$			17.1307i			0.581119i
$870$		0			0
$871$			3.60156i			0.122034i
$872$		0			0
$873$	−8.64600	+	8.64600i	−0.292623	+	0.292623i
$874$		0			0
$875$	−3.78585	−	10.5199i	−0.127985	−	0.355636i
$876$		0			0
$877$	36.8387	+	36.8387i	1.24395	+	1.24395i	0.958347	+	0.285607i	$0.0921953\pi$
$877$	36.8387	+	36.8387i	1.24395	+	1.24395i	0.285607	+	0.958347i	$0.407805\pi$
$878$		0			0
$879$	−23.7955			−0.802603
$880$		0			0
$881$	3.04202			0.102488			0.0512442	−	0.998686i	$-0.483681\pi$
$881$	3.04202			0.102488			0.0512442	+	0.998686i	$0.483681\pi$
$882$		0			0
$883$	−8.85865	−	8.85865i	−0.298117	−	0.298117i	0.542159	−	0.840276i	$-0.317607\pi$
$883$	−8.85865	−	8.85865i	−0.298117	−	0.298117i	−0.840276	+	0.542159i	$0.817607\pi$
$884$		0			0
$885$	−1.55602	−	13.4533i	−0.0523049	−	0.452228i
$886$		0			0
$887$	−36.2407	+	36.2407i	−1.21684	+	1.21684i	−0.248111	+	0.968732i	$0.579810\pi$
$887$	−36.2407	+	36.2407i	−1.21684	+	1.21684i	−0.968732	+	0.248111i	$0.920190\pi$
$888$		0			0
$889$		−	15.1120i		−	0.506841i
$890$		0			0
$891$		−	2.82843i		−	0.0947559i
$892$		0			0
$893$	−4.46264	+	4.46264i	−0.149337	+	0.149337i
$894$		0			0
$895$	−20.3986	−	16.1692i	−0.681851	−	0.540476i
$896$		0			0
$897$	−2.26401	−	2.26401i	−0.0755933	−	0.0755933i
$898$		0			0
$899$	46.3089			1.54449
$900$		0			0
$901$	66.8853			2.22827
$902$		0			0
$903$	−2.12792	−	2.12792i	−0.0708126	−	0.0708126i
$904$		0			0
$905$	30.7967	+	24.4113i	1.02372	+	0.811459i
$906$		0			0
$907$	−16.3691	+	16.3691i	−0.543526	+	0.543526i	−0.924561	−	0.381035i	$-0.875568\pi$
$907$	−16.3691	+	16.3691i	−0.543526	+	0.543526i	0.381035	+	0.924561i	$0.375568\pi$
$908$		0			0
$909$		−	10.7780i		−	0.357484i
$910$		0			0
$911$			54.3944i			1.80217i	0.433646	+	0.901083i	$0.357227\pi$
$911$			54.3944i			1.80217i	−0.433646	+	0.901083i	$0.642773\pi$
$912$		0			0
$913$	19.1120	−	19.1120i	0.632516	−	0.632516i
$914$		0			0
$915$	2.90105	+	25.0825i	0.0959057	+	0.829201i
$916$		0			0
$917$	8.28267	+	8.28267i	0.273518	+	0.273518i
$918$		0			0
$919$	−2.05529			−0.0677979			−0.0338990	−	0.999425i	$-0.510792\pi$
$919$	−2.05529			−0.0677979			−0.0338990	+	0.999425i	$0.510792\pi$
$920$		0			0
$921$	5.45331			0.179693
$922$		0			0
$923$	2.97367	+	2.97367i	0.0978796	+	0.0978796i
$924$		0			0
$925$	−3.72666	+	6.00933i	−0.122532	+	0.197586i
$926$		0			0
$927$	−11.8407	+	11.8407i	−0.388900	+	0.388900i
$928$		0			0
$929$			19.8060i			0.649814i	0.945746	+	0.324907i	$0.105333\pi$
$929$			19.8060i			0.649814i	−0.945746	+	0.324907i	$0.894667\pi$
$930$		0			0
$931$		−	0.900390i		−	0.0295091i
$932$		0			0
$933$	23.3947	−	23.3947i	0.765908	−	0.765908i
$934$		0			0
$935$	34.3673	−	3.97493i	1.12393	−	0.129994i
$936$		0			0
$937$	−30.7674	−	30.7674i	−1.00513	−	1.00513i	−0.999987	−	0.00513907i	$-0.998364\pi$
$937$	−30.7674	−	30.7674i	−1.00513	−	1.00513i	−0.00513907	−	0.999987i	$-0.501636\pi$
$938$		0			0
$939$	−22.1136			−0.721650
$940$		0			0
$941$	−18.2500			−0.594932			−0.297466	−	0.954732i	$-0.596142\pi$
$941$	−18.2500			−0.594932			−0.297466	+	0.954732i	$0.596142\pi$
$942$		0			0
$943$	−39.9233	−	39.9233i	−1.30008	−	1.30008i
$944$		0			0
$945$	−1.38900	+	1.75233i	−0.0451843	+	0.0570034i
$946$		0			0
$947$	−0.923508	+	0.923508i	−0.0300100	+	0.0300100i	−0.721953	−	0.691943i	$-0.756755\pi$
$947$	−0.923508	+	0.923508i	−0.0300100	+	0.0300100i	0.691943	+	0.721953i	$0.256755\pi$
$948$		0			0
$949$			7.20796i			0.233980i
$950$		0			0
$951$		−	14.6560i		−	0.475252i
$952$		0			0
$953$	29.7580	−	29.7580i	0.963957	−	0.963957i	−0.0354155	−	0.999373i	$-0.511275\pi$
$953$	29.7580	−	29.7580i	0.963957	−	0.963957i	0.999373	+	0.0354155i	$0.0112755\pi$
$954$		0			0
$955$	6.98525	−	8.81242i	0.226037	−	0.285163i
$956$		0			0
$957$	−8.56534	−	8.56534i	−0.276878	−	0.276878i
$958$		0			0
$959$	4.11538			0.132893
$960$		0			0
$961$	−85.9226			−2.77170
$962$		0			0
$963$	−1.25065	−	1.25065i	−0.0403015	−	0.0403015i
$964$		0			0
$965$	−4.53604	+	0.524640i	−0.146020	+	0.0168888i
$966$		0			0
$967$	20.3806	−	20.3806i	0.655397	−	0.655397i	−0.298890	−	0.954287i	$-0.596616\pi$
$967$	20.3806	−	20.3806i	0.655397	−	0.655397i	0.954287	+	0.298890i	$0.0966164\pi$
$968$		0			0
$969$		−	4.92528i		−	0.158223i
$970$		0			0
$971$		−	18.5168i		−	0.594233i	−0.954841	−	0.297117i	$-0.903975\pi$
$971$		−	18.5168i		−	0.594233i	0.954841	−	0.297117i	$-0.0960250\pi$
$972$		0			0
$973$	0.919344	−	0.919344i	0.0294728	−	0.0294728i
$974$		0			0
$975$	0.586446	+	2.50129i	0.0187813	+	0.0801054i
$976$		0			0
$977$	−30.4006	−	30.4006i	−0.972603	−	0.972603i	0.0270318	−	0.999635i	$-0.491394\pi$
$977$	−30.4006	−	30.4006i	−0.972603	−	0.972603i	−0.999635	+	0.0270318i	$0.991394\pi$
$978$		0			0
$979$	−41.0518			−1.31202
$980$		0			0
$981$	4.82936			0.154190
$982$		0			0
$983$	14.9680	+	14.9680i	0.477406	+	0.477406i	0.904301	−	0.426895i	$-0.140393\pi$
$983$	14.9680	+	14.9680i	0.477406	+	0.477406i	−0.426895	+	0.904301i	$0.640393\pi$
$984$		0			0
$985$	−1.01998	−	8.81871i	−0.0324991	−	0.280988i
$986$		0			0
$987$	4.95634	−	4.95634i	0.157762	−	0.157762i
$988$		0			0
$989$		−	18.7521i		−	0.596282i
$990$		0			0
$991$		−	7.85739i		−	0.249598i	−0.992182	−	0.124799i	$-0.960171\pi$
$991$		−	7.85739i		−	0.249598i	0.992182	−	0.124799i	$-0.0398287\pi$
$992$		0			0
$993$	23.5747	−	23.5747i	0.748120	−	0.748120i
$994$		0			0
$995$	21.8492	+	17.3190i	0.692665	+	0.549048i
$996$		0			0
$997$	35.3913	+	35.3913i	1.12085	+	1.12085i	0.991613	+	0.129241i	$0.0412541\pi$
$997$	35.3913	+	35.3913i	1.12085	+	1.12085i	0.129241	+	0.991613i	$0.458746\pi$
$998$		0			0
$999$	1.41421			0.0447437

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.bl.c.127.1	✓	12
4.3	odd	2	inner	1680.2.bl.c.127.4	yes	12
5.3	odd	4	inner	1680.2.bl.c.463.4	yes	12
20.3	even	4	inner	1680.2.bl.c.463.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1680.2.bl.c.127.1	✓	12	1.1	even	1	trivial
1680.2.bl.c.127.4	yes	12	4.3	odd	2	inner
1680.2.bl.c.463.1	yes	12	20.3	even	4	inner
1680.2.bl.c.463.4	yes	12	5.3	odd	4	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{3} +(-1.75233 - 1.38900i) q^{5} +(0.707107 - 0.707107i) q^{7} +1.00000i q^{9} +2.82843i q^{11} +(-0.363328 + 0.363328i) q^{13} +(0.256912 + 2.22126i) q^{15} +(3.86799 + 3.86799i) q^{17} +0.900390 q^{19} -1.00000 q^{21} +(-4.40621 - 4.40621i) q^{23} +(1.14134 + 4.86799i) q^{25} +(0.707107 - 0.707107i) q^{27} -4.28267i q^{29} +10.8131i q^{31} +(2.00000 - 2.00000i) q^{33} +(-2.22126 + 0.256912i) q^{35} +(1.00000 + 1.00000i) q^{37} +0.513824 q^{39} +9.06068 q^{41} +(2.12792 + 2.12792i) q^{43} +(1.38900 - 1.75233i) q^{45} +(-4.95634 + 4.95634i) q^{47} -1.00000i q^{49} -5.47017i q^{51} +(8.64600 - 8.64600i) q^{53} +(3.92870 - 4.95634i) q^{55} +(-0.636672 - 0.636672i) q^{57} -6.05661 q^{59} +11.2920 q^{61} +(0.707107 + 0.707107i) q^{63} +(1.14134 - 0.132007i) q^{65} +(4.95634 - 4.95634i) q^{67} +6.23132i q^{69} -8.18453i q^{71} +(9.91934 - 9.91934i) q^{73} +(2.63514 - 4.24924i) q^{75} +(2.00000 + 2.00000i) q^{77} +6.05661 q^{79} -1.00000 q^{81} +(-6.75712 - 6.75712i) q^{83} +(-1.40535 - 12.1507i) q^{85} +(-3.02831 + 3.02831i) q^{87} +14.5140i q^{89} +0.513824i q^{91} +(7.64600 - 7.64600i) q^{93} +(-1.57778 - 1.25065i) q^{95} +(8.64600 + 8.64600i) q^{97} -2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{13} - 4 q^{17} - 12 q^{21} - 20 q^{25} + 24 q^{33} + 12 q^{37} + 16 q^{41} + 4 q^{45} + 28 q^{53} - 16 q^{57} - 16 q^{61} - 20 q^{65} + 60 q^{73} + 24 q^{77} - 12 q^{81} - 84 q^{85} + 16 q^{93}+ \cdots + 28 q^{97}+O(q^{100}) \) 12 * q + 4 * q^13 - 4 * q^17 - 12 * q^21 - 20 * q^25 + 24 * q^33 + 12 * q^37 + 16 * q^41 + 4 * q^45 + 28 * q^53 - 16 * q^57 - 16 * q^61 - 20 * q^65 + 60 * q^73 + 24 * q^77 - 12 * q^81 - 84 * q^85 + 16 * q^93 + 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more