LMFDB - Embedded newform 1680.2.di.d.289.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1680,2,Mod(289,1680)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1680, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 3, 2]))

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

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

chi := DirichletCharacter("1680.289");

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.di (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 4 x^{13} - 14 x^{12} + 38 x^{11} - 40 x^{10} + 64 x^{9} + 291 x^{8} + \cdots + 1 $ x^16 - 2x^15 + 2x^14 - 4x^13 - 14x^12 + 38x^11 - 40x^10 + 64x^9 + 291x^8 - 630x^7 + 584x^6 - 800x^5 + 734x^4 - 188x^3 + 32x^2 - 8*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.7
Root			$2.07845 - 0.556918i$ of defining polynomial
Character	$\chi$	$=$	1680.289
Dual form			1680.2.di.d.529.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{3} +(1.47507 - 1.68052i) q^{5} +(-1.11487 + 2.39939i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{3} +(1.47507 - 1.68052i) q^{5} +(-1.11487 + 2.39939i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-1.66520 - 2.88421i) q^{11} -4.54754i q^{13} +(0.437190 - 2.19291i) q^{15} +(-4.80431 + 2.77377i) q^{17} +(0.828617 - 1.43521i) q^{19} +(0.234193 + 2.63537i) q^{21} +(-6.61094 - 3.81683i) q^{23} +(-0.648315 - 4.95779i) q^{25} -1.00000i q^{27} +0.118657 q^{29} +(-3.13010 - 5.42150i) q^{31} +(-2.88421 - 1.66520i) q^{33} +(2.38772 + 5.41284i) q^{35} +(6.71665 + 3.87786i) q^{37} +(-2.27377 - 3.93829i) q^{39} +0.0701896 q^{41} -2.92981i q^{43} +(-0.717839 - 2.11771i) q^{45} +(5.53029 + 3.19291i) q^{47} +(-4.51415 - 5.35000i) q^{49} +(-2.77377 + 4.80431i) q^{51} +(0.640682 - 0.369898i) q^{53} +(-7.30326 - 1.45601i) q^{55} -1.65723i q^{57} +(0.815051 + 1.41171i) q^{59} +(3.65901 - 6.33759i) q^{61} +(1.52050 + 2.16520i) q^{63} +(-7.64225 - 6.70796i) q^{65} +(2.62934 - 1.51805i) q^{67} -7.63366 q^{69} +3.77048 q^{71} +(2.03961 - 1.17757i) q^{73} +(-3.04035 - 3.96942i) q^{75} +(8.77681 - 0.779956i) q^{77} +(5.97016 - 10.3406i) q^{79} +(-0.500000 - 0.866025i) q^{81} -1.22411i q^{83} +(-2.42533 + 12.1653i) q^{85} +(0.102760 - 0.0593285i) q^{87} +(-6.50007 + 11.2585i) q^{89} +(10.9113 + 5.06990i) q^{91} +(-5.42150 - 3.13010i) q^{93} +(-1.18963 - 3.50954i) q^{95} +3.04306i q^{97} -3.33039 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{5} + 8 q^{9}+O(q^{10}) $ 16 * q + 2 * q^5 + 8 * q^9	$ 16 q + 2 q^{5} + 8 q^{9} + 4 q^{15} + 24 q^{19} - 4 q^{21} - 4 q^{25} + 24 q^{29} - 16 q^{31} + 10 q^{35} + 4 q^{39} + 16 q^{41} - 2 q^{45} - 40 q^{49} - 4 q^{51} - 8 q^{55} - 4 q^{59} + 16 q^{61} + 30 q^{65} + 40 q^{69} + 56 q^{71} - 8 q^{75} + 16 q^{79} - 8 q^{81} - 64 q^{85} + 16 q^{89} - 8 q^{91} + 22 q^{95}+O(q^{100}) $ 16 * q + 2 * q^5 + 8 * q^9 + 4 * q^15 + 24 * q^19 - 4 * q^21 - 4 * q^25 + 24 * q^29 - 16 * q^31 + 10 * q^35 + 4 * q^39 + 16 * q^41 - 2 * q^45 - 40 * q^49 - 4 * q^51 - 8 * q^55 - 4 * q^59 + 16 * q^61 + 30 * q^65 + 40 * q^69 + 56 * q^71 - 8 * q^75 + 16 * q^79 - 8 * q^81 - 64 * q^85 + 16 * q^89 - 8 * q^91 + 22 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$1$	$1$

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
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$		0			0
$5$	1.47507	−	1.68052i	0.659673	−	0.751553i
$5$	1.47507	−	1.68052i	0.659673	−	0.751553i
$6$		0			0
$7$	−1.11487	+	2.39939i	−0.421380	+	0.906884i
$7$	−1.11487	+	2.39939i	−0.421380	+	0.906884i
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−1.66520	−	2.88421i	−0.502076	−	0.869621i	−0.999997	−	0.00239862i	$-0.999236\pi$
$11$	−1.66520	−	2.88421i	−0.502076	−	0.869621i	0.497921	−	0.867222i	$-0.334097\pi$
$12$		0			0
$13$		−	4.54754i		−	1.26126i	−0.776083	−	0.630630i	$-0.782796\pi$
$13$		−	4.54754i		−	1.26126i	0.776083	−	0.630630i	$-0.217204\pi$
$14$		0			0
$15$	0.437190	−	2.19291i	0.112882	−	0.566208i
$16$		0			0
$17$	−4.80431	+	2.77377i	−1.16522	+	0.672738i	−0.952549	−	0.304386i	$-0.901549\pi$
$17$	−4.80431	+	2.77377i	−1.16522	+	0.672738i	−0.212668	+	0.977125i	$0.568215\pi$
$18$		0			0
$19$	0.828617	−	1.43521i	0.190098	−	0.329259i	−0.755185	−	0.655512i	$-0.772453\pi$
$19$	0.828617	−	1.43521i	0.190098	−	0.329259i	0.945282	+	0.326253i	$0.105786\pi$
$20$		0			0
$21$	0.234193	+	2.63537i	0.0511052	+	0.575084i
$22$		0			0
$23$	−6.61094	−	3.81683i	−1.37848	−	0.795864i	−0.386500	−	0.922289i	$-0.626316\pi$
$23$	−6.61094	−	3.81683i	−1.37848	−	0.795864i	−0.991976	+	0.126425i	$0.959650\pi$
$24$		0			0
$25$	−0.648315	−	4.95779i	−0.129663	−	0.991558i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	0.118657			0.0220341			0.0110170	−	0.999939i	$-0.496493\pi$
$29$	0.118657			0.0220341			0.0110170	+	0.999939i	$0.496493\pi$
$30$		0			0
$31$	−3.13010	−	5.42150i	−0.562183	−	0.973729i	−0.997306	−	0.0733583i	$-0.976628\pi$
$31$	−3.13010	−	5.42150i	−0.562183	−	0.973729i	0.435123	−	0.900371i	$-0.356705\pi$
$32$		0			0
$33$	−2.88421	−	1.66520i	−0.502076	−	0.289874i
$34$		0			0
$35$	2.38772	+	5.41284i	0.403599	+	0.914936i
$36$		0			0
$37$	6.71665	+	3.87786i	1.10421	+	0.637516i	0.937324	−	0.348460i	$-0.113295\pi$
$37$	6.71665	+	3.87786i	1.10421	+	0.637516i	0.166887	+	0.985976i	$0.446628\pi$
$38$		0			0
$39$	−2.27377	−	3.93829i	−0.364095	−	0.630630i
$40$		0			0
$41$	0.0701896			0.0109618			0.00548089	−	0.999985i	$-0.498255\pi$
$41$	0.0701896			0.0109618			0.00548089	+	0.999985i	$0.498255\pi$
$42$		0			0
$43$		−	2.92981i		−	0.446792i	−0.974728	−	0.223396i	$-0.928286\pi$
$43$		−	2.92981i		−	0.446792i	0.974728	−	0.223396i	$-0.0717143\pi$
$44$		0			0
$45$	−0.717839	−	2.11771i	−0.107009	−	0.315690i
$46$		0			0
$47$	5.53029	+	3.19291i	0.806675	+	0.465734i	0.845800	−	0.533500i	$-0.179124\pi$
$47$	5.53029	+	3.19291i	0.806675	+	0.465734i	−0.0391247	+	0.999234i	$0.512457\pi$
$48$		0			0
$49$	−4.51415	−	5.35000i	−0.644879	−	0.764285i
$50$		0			0
$51$	−2.77377	+	4.80431i	−0.388406	+	0.672738i
$52$		0			0
$53$	0.640682	−	0.369898i	0.0880044	−	0.0508094i	−0.455352	−	0.890311i	$-0.650487\pi$
$53$	0.640682	−	0.369898i	0.0880044	−	0.0508094i	0.543356	+	0.839502i	$0.317153\pi$
$54$		0			0
$55$	−7.30326	−	1.45601i	−0.984772	−	0.196329i
$56$		0			0
$57$		−	1.65723i		−	0.219506i
$58$		0			0
$59$	0.815051	+	1.41171i	0.106111	+	0.183789i	0.914191	−	0.405283i	$-0.132827\pi$
$59$	0.815051	+	1.41171i	0.106111	+	0.183789i	−0.808081	+	0.589072i	$0.799494\pi$
$60$		0			0
$61$	3.65901	−	6.33759i	0.468488	−	0.811446i	−0.530863	−	0.847458i	$-0.678132\pi$
$61$	3.65901	−	6.33759i	0.468488	−	0.811446i	0.999351	+	0.0360120i	$0.0114655\pi$
$62$		0			0
$63$	1.52050	+	2.16520i	0.191565	+	0.272789i
$64$		0			0
$65$	−7.64225	−	6.70796i	−0.947904	−	0.832020i
$66$		0			0
$67$	2.62934	−	1.51805i	0.321224	−	0.185459i	−0.330714	−	0.943731i	$-0.607289\pi$
$67$	2.62934	−	1.51805i	0.321224	−	0.185459i	0.651938	+	0.758272i	$0.273956\pi$
$68$		0			0
$69$	−7.63366			−0.918984
$70$		0			0
$71$	3.77048			0.447474			0.223737	−	0.974650i	$-0.428174\pi$
$71$	3.77048			0.447474			0.223737	+	0.974650i	$0.428174\pi$
$72$		0			0
$73$	2.03961	−	1.17757i	0.238718	−	0.137824i	−0.375869	−	0.926673i	$-0.622656\pi$
$73$	2.03961	−	1.17757i	0.238718	−	0.137824i	0.614588	+	0.788849i	$0.289322\pi$
$74$		0			0
$75$	−3.04035	−	3.96942i	−0.351070	−	0.458349i
$76$		0			0
$77$	8.77681	−	0.779956i	1.00021	−	0.0888843i
$78$		0			0
$79$	5.97016	−	10.3406i	0.671696	−	1.16341i	−0.305727	−	0.952119i	$-0.598899\pi$
$79$	5.97016	−	10.3406i	0.671696	−	1.16341i	0.977423	−	0.211292i	$-0.0677672\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	1.22411i		−	0.134363i	−0.997741	−	0.0671817i	$-0.978599\pi$
$83$		−	1.22411i		−	0.134363i	0.997741	−	0.0671817i	$-0.0214007\pi$
$84$		0			0
$85$	−2.42533	+	12.1653i	−0.263064	+	1.31951i
$86$		0			0
$87$	0.102760	−	0.0593285i	0.0110170	−	0.00636069i
$88$		0			0
$89$	−6.50007	+	11.2585i	−0.689006	+	1.19339i	0.283153	+	0.959075i	$0.408619\pi$
$89$	−6.50007	+	11.2585i	−0.689006	+	1.19339i	−0.972160	+	0.234319i	$0.924714\pi$
$90$		0			0
$91$	10.9113	+	5.06990i	1.14382	+	0.531470i
$92$		0			0
$93$	−5.42150	−	3.13010i	−0.562183	−	0.324576i
$94$		0			0
$95$	−1.18963	−	3.50954i	−0.122053	−	0.360072i
$96$		0			0
$97$			3.04306i			0.308976i	0.987995	+	0.154488i	$0.0493728\pi$
$97$			3.04306i			0.308976i	−0.987995	+	0.154488i	$0.950627\pi$
$98$		0			0
$99$	−3.33039			−0.334717
$100$		0			0
$101$	−8.01983	−	13.8907i	−0.798002	−	1.38218i	−0.920915	−	0.389763i	$-0.872557\pi$
$101$	−8.01983	−	13.8907i	−0.798002	−	1.38218i	0.122913	−	0.992417i	$-0.460776\pi$
$102$		0			0
$103$	4.58293	+	2.64596i	0.451570	+	0.260714i	0.708493	−	0.705718i	$-0.249375\pi$
$103$	4.58293	+	2.64596i	0.451570	+	0.260714i	−0.256923	+	0.966432i	$0.582709\pi$
$104$		0			0
$105$	4.77425	+	3.49379i	0.465919	+	0.340959i
$106$		0			0
$107$	−4.47018	−	2.58086i	−0.432148	−	0.249501i	0.268113	−	0.963387i	$-0.413600\pi$
$107$	−4.47018	−	2.58086i	−0.432148	−	0.249501i	−0.700261	+	0.713886i	$0.746933\pi$
$108$		0			0
$109$	1.62043	+	2.80668i	0.155209	+	0.268831i	0.933135	−	0.359525i	$-0.117061\pi$
$109$	1.62043	+	2.80668i	0.155209	+	0.268831i	−0.777926	+	0.628356i	$0.783728\pi$
$110$		0			0
$111$	7.75572			0.736141
$112$		0			0
$113$			12.6608i			1.19103i	0.803345	+	0.595513i	$0.203051\pi$
$113$			12.6608i			1.19103i	−0.803345	+	0.595513i	$0.796949\pi$
$114$		0			0
$115$	−16.1659	+	5.47973i	−1.50748	+	0.510988i
$116$		0			0
$117$	−3.93829	−	2.27377i	−0.364095	−	0.210210i
$118$		0			0
$119$	−1.29920	−	14.6198i	−0.119097	−	1.34019i
$120$		0			0
$121$	−0.0457629	+	0.0792637i	−0.00416027	+	0.00720579i
$122$		0			0
$123$	0.0607860	−	0.0350948i	0.00548089	−	0.00316439i
$124$		0			0
$125$	−9.28799	−	6.22360i	−0.830743	−	0.556656i
$126$		0			0
$127$			16.5475i			1.46836i	0.678957	+	0.734178i	$0.262432\pi$
$127$			16.5475i			1.46836i	−0.678957	+	0.734178i	$0.737568\pi$
$128$		0			0
$129$	−1.46491	−	2.53729i	−0.128978	−	0.223396i
$130$		0			0
$131$	−2.64893	+	4.58808i	−0.231438	+	0.400862i	−0.958231	−	0.285994i	$-0.907676\pi$
$131$	−2.64893	+	4.58808i	−0.231438	+	0.400862i	0.726794	+	0.686856i	$0.241010\pi$
$132$		0			0
$133$	2.51982	+	3.58824i	0.218496	+	0.311140i
$134$		0			0
$135$	−1.68052	−	1.47507i	−0.144636	−	0.126954i
$136$		0			0
$137$	−12.8779	+	7.43507i	−1.10023	+	0.635221i	−0.936283	−	0.351247i	$-0.885758\pi$
$137$	−12.8779	+	7.43507i	−1.10023	+	0.635221i	−0.163952	+	0.986468i	$0.552424\pi$
$138$		0			0
$139$	−9.51685			−0.807209			−0.403605	−	0.914934i	$-0.632243\pi$
$139$	−9.51685			−0.807209			−0.403605	+	0.914934i	$0.632243\pi$
$140$		0			0
$141$	6.38582			0.537783
$142$		0			0
$143$	−13.1160	+	7.57255i	−1.09682	+	0.633249i
$144$		0			0
$145$	0.175028	−	0.199406i	0.0145353	−	0.0165598i
$146$		0			0
$147$	−6.58437	−	2.37616i	−0.543069	−	0.195982i
$148$		0			0
$149$	5.68502	−	9.84675i	0.465735	−	0.806677i	−0.533499	−	0.845801i	$-0.679123\pi$
$149$	5.68502	−	9.84675i	0.465735	−	0.806677i	0.999234	+	0.0391236i	$0.0124566\pi$
$150$		0			0
$151$	4.47016	+	7.74255i	0.363777	+	0.630080i	0.988579	−	0.150703i	$-0.0481538\pi$
$151$	4.47016	+	7.74255i	0.363777	+	0.630080i	−0.624802	+	0.780783i	$0.714820\pi$
$152$		0			0
$153$			5.54754i			0.448492i
$154$		0			0
$155$	−13.7281	−	2.73690i	−1.10267	−	0.219833i
$156$		0			0
$157$	2.89800	−	1.67316i	0.231286	−	0.133533i	−0.379879	−	0.925036i	$-0.624035\pi$
$157$	2.89800	−	1.67316i	0.231286	−	0.133533i	0.611165	+	0.791503i	$0.290701\pi$
$158$		0			0
$159$	0.369898	−	0.640682i	0.0293348	−	0.0508094i
$160$		0			0
$161$	16.5284	−	11.6070i	1.30262	−	0.914758i
$162$		0			0
$163$	13.6450	+	7.87793i	1.06876	+	0.617047i	0.927842	−	0.372974i	$-0.121662\pi$
$163$	13.6450	+	7.87793i	1.06876	+	0.617047i	0.140916	+	0.990022i	$0.454995\pi$
$164$		0			0
$165$	−7.05282	+	2.39069i	−0.549061	+	0.186115i
$166$		0			0
$167$		−	22.5942i		−	1.74839i	−0.485577	−	0.874194i	$-0.661390\pi$
$167$		−	22.5942i		−	1.74839i	0.485577	−	0.874194i	$-0.338610\pi$
$168$		0			0
$169$	−7.68012			−0.590779
$170$		0			0
$171$	−0.828617	−	1.43521i	−0.0633659	−	0.109753i
$172$		0			0
$173$	−7.38391	−	4.26310i	−0.561388	−	0.324118i	0.192314	−	0.981333i	$-0.438401\pi$
$173$	−7.38391	−	4.26310i	−0.561388	−	0.324118i	−0.753703	+	0.657216i	$0.771734\pi$
$174$		0			0
$175$	12.6185	+	3.97171i	0.953866	+	0.300233i
$176$		0			0
$177$	1.41171	+	0.815051i	0.106111	+	0.0612630i
$178$		0			0
$179$	5.89031	+	10.2023i	0.440262	+	0.762557i	0.997709	−	0.0676564i	$-0.0215522\pi$
$179$	5.89031	+	10.2023i	0.440262	+	0.762557i	−0.557446	+	0.830213i	$0.688219\pi$
$180$		0			0
$181$	9.08967			0.675630			0.337815	−	0.941213i	$-0.390312\pi$
$181$	9.08967			0.675630			0.337815	+	0.941213i	$0.390312\pi$
$182$		0			0
$183$		−	7.31802i		−	0.540964i
$184$		0			0
$185$	16.4244	−	5.56736i	1.20755	−	0.409320i
$186$		0			0
$187$	16.0002	+	9.23775i	1.17005	+	0.675531i
$188$		0			0
$189$	2.39939	+	1.11487i	0.174530	+	0.0810945i
$190$		0			0
$191$	10.2478	−	17.7498i	0.741507	−	1.28433i	−0.210302	−	0.977637i	$-0.567445\pi$
$191$	10.2478	−	17.7498i	0.741507	−	1.28433i	0.951809	−	0.306692i	$-0.0992220\pi$
$192$		0			0
$193$	7.39842	−	4.27148i	0.532550	−	0.307468i	−0.209504	−	0.977808i	$-0.567185\pi$
$193$	7.39842	−	4.27148i	0.532550	−	0.307468i	0.742054	+	0.670340i	$0.233852\pi$
$194$		0			0
$195$	−9.97236	−	1.98814i	−0.714135	−	0.142374i
$196$		0			0
$197$		−	13.8086i		−	0.983820i	−0.870646	−	0.491910i	$-0.836299\pi$
$197$		−	13.8086i		−	0.983820i	0.870646	−	0.491910i	$-0.163701\pi$
$198$		0			0
$199$	−1.89549	−	3.28309i	−0.134368	−	0.232732i	0.790988	−	0.611832i	$-0.209567\pi$
$199$	−1.89549	−	3.28309i	−0.134368	−	0.232732i	−0.925356	+	0.379100i	$0.876234\pi$
$200$		0			0
$201$	1.51805	−	2.62934i	0.107075	−	0.185459i
$202$		0			0
$203$	−0.132287	+	0.284705i	−0.00928471	+	0.0199824i
$204$		0			0
$205$	0.103535	−	0.117955i	0.00723119	−	0.00823836i
$206$		0			0
$207$	−6.61094	+	3.81683i	−0.459492	+	0.265288i
$208$		0			0
$209$	−5.51924			−0.381774
$210$		0			0
$211$	0.114416			0.00787674			0.00393837	−	0.999992i	$-0.498746\pi$
$211$	0.114416			0.00787674			0.00393837	+	0.999992i	$0.498746\pi$
$212$		0			0
$213$	3.26533	−	1.88524i	0.223737	−	0.129175i
$214$		0			0
$215$	−4.92361	−	4.32169i	−0.335788	−	0.294737i
$216$		0			0
$217$	16.4979	−	1.46610i	1.11995	−	0.0995253i
$218$		0			0
$219$	1.17757	−	2.03961i	0.0795728	−	0.137824i
$220$		0			0
$221$	12.6138	+	21.8478i	0.848498	+	1.46964i
$222$		0			0
$223$		−	7.86673i		−	0.526795i	−0.964687	−	0.263398i	$-0.915157\pi$
$223$		−	7.86673i		−	0.526795i	0.964687	−	0.263398i	$-0.0848431\pi$
$224$		0			0
$225$	−4.61773	−	1.91744i	−0.307849	−	0.127829i
$226$		0			0
$227$	7.77575	−	4.48933i	0.516095	−	0.297967i	−0.219241	−	0.975671i	$-0.570358\pi$
$227$	7.77575	−	4.48933i	0.516095	−	0.297967i	0.735335	+	0.677703i	$0.237025\pi$
$228$		0			0
$229$	−2.54306	+	4.40471i	−0.168050	+	0.291071i	−0.937734	−	0.347354i	$-0.887080\pi$
$229$	−2.54306	+	4.40471i	−0.168050	+	0.291071i	0.769684	+	0.638425i	$0.220414\pi$
$230$		0			0
$231$	7.21096	−	5.06387i	0.474446	−	0.333178i
$232$		0			0
$233$	−18.8952	−	10.9091i	−1.23786	−	0.714681i	−0.269207	−	0.963082i	$-0.586761\pi$
$233$	−18.8952	−	10.9091i	−1.23786	−	0.714681i	−0.968657	+	0.248401i	$0.920095\pi$
$234$		0			0
$235$	13.5233	−	4.58399i	0.882166	−	0.299027i
$236$		0			0
$237$		−	11.9403i		−	0.775608i
$238$		0			0
$239$	7.44905			0.481839			0.240920	−	0.970545i	$-0.422551\pi$
$239$	7.44905			0.481839			0.240920	+	0.970545i	$0.422551\pi$
$240$		0			0
$241$	12.0879	+	20.9368i	0.778650	+	1.34866i	0.932720	+	0.360601i	$0.117428\pi$
$241$	12.0879	+	20.9368i	0.778650	+	1.34866i	−0.154070	+	0.988060i	$0.549238\pi$
$242$		0			0
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	−15.6495	−	0.305506i	−0.999810	−	0.0195180i
$246$		0			0
$247$	−6.52666	−	3.76817i	−0.415281	−	0.239763i
$248$		0			0
$249$	−0.612055	−	1.06011i	−0.0387874	−	0.0671817i
$250$		0			0
$251$	−6.00200			−0.378843			−0.189421	−	0.981896i	$-0.560661\pi$
$251$	−6.00200			−0.378843			−0.189421	+	0.981896i	$0.560661\pi$
$252$		0			0
$253$			25.4231i			1.59834i
$254$		0			0
$255$	3.98224	+	11.7481i	0.249377	+	0.735694i
$256$		0			0
$257$	6.35139	+	3.66697i	0.396189	+	0.228740i	0.684838	−	0.728695i	$-0.259873\pi$
$257$	6.35139	+	3.66697i	0.396189	+	0.228740i	−0.288650	+	0.957435i	$0.593206\pi$
$258$		0			0
$259$	−16.7927	+	11.7926i	−1.04345	+	0.732755i
$260$		0			0
$261$	0.0593285	−	0.102760i	0.00367234	−	0.00636069i
$262$		0			0
$263$	−8.21661	+	4.74386i	−0.506658	+	0.292519i	−0.731459	−	0.681886i	$-0.761160\pi$
$263$	−8.21661	+	4.74386i	−0.506658	+	0.292519i	0.224801	+	0.974405i	$0.427827\pi$
$264$		0			0
$265$	0.323431	−	1.62231i	0.0198682	−	0.0996575i
$266$		0			0
$267$			13.0001i			0.795596i
$268$		0			0
$269$	8.02423	+	13.8984i	0.489246	+	0.847399i	0.999923	−	0.0123733i	$-0.00393863\pi$
$269$	8.02423	+	13.8984i	0.489246	+	0.847399i	−0.510677	+	0.859772i	$0.670605\pi$
$270$		0			0
$271$	12.0845	−	20.9309i	0.734080	−	1.27146i	−0.221045	−	0.975264i	$-0.570947\pi$
$271$	12.0845	−	20.9309i	0.734080	−	1.27146i	0.955126	−	0.296201i	$-0.0957198\pi$
$272$		0			0
$273$	11.9844	−	1.06500i	0.725331	−	0.0644570i
$274$		0			0
$275$	−13.2197	+	10.1256i	−0.797179	+	0.610595i
$276$		0			0
$277$	−20.1071	+	11.6088i	−1.20812	+	0.697508i	−0.962348	−	0.271820i	$-0.912374\pi$
$277$	−20.1071	+	11.6088i	−1.20812	+	0.697508i	−0.245771	+	0.969328i	$0.579041\pi$
$278$		0			0
$279$	−6.26020			−0.374789
$280$		0			0
$281$	12.4472			0.742538			0.371269	−	0.928525i	$-0.378923\pi$
$281$	12.4472			0.742538			0.371269	+	0.928525i	$0.378923\pi$
$282$		0			0
$283$	7.50649	−	4.33388i	0.446215	−	0.257622i	−0.260016	−	0.965604i	$-0.583728\pi$
$283$	7.50649	−	4.33388i	0.446215	−	0.257622i	0.706230	+	0.707982i	$0.250394\pi$
$284$		0			0
$285$	−2.78502	−	2.44454i	−0.164970	−	0.144802i
$286$		0			0
$287$	−0.0782520	+	0.168412i	−0.00461907	+	0.00994107i
$288$		0			0
$289$	6.88760	−	11.9297i	0.405153	−	0.701746i
$290$		0			0
$291$	1.52153	+	2.63537i	0.0891936	+	0.154488i
$292$		0			0
$293$		−	27.0063i		−	1.57772i	−0.614571	−	0.788862i	$-0.710671\pi$
$293$		−	27.0063i		−	1.57772i	0.614571	−	0.788862i	$-0.289329\pi$
$294$		0			0
$295$	3.57467	+	0.712664i	0.208125	+	0.0414929i
$296$		0			0
$297$	−2.88421	+	1.66520i	−0.167359	+	0.0966245i
$298$		0			0
$299$	−17.3572	+	30.0635i	−1.00379	+	1.73862i
$300$		0			0
$301$	7.02976	+	3.26634i	0.405189	+	0.188269i
$302$		0			0
$303$	−13.8907	−	8.01983i	−0.798002	−	0.460727i
$304$		0			0
$305$	−5.25316	−	15.4975i	−0.300795	−	0.887382i
$306$		0			0
$307$			2.24681i			0.128232i	0.997942	+	0.0641161i	$0.0204228\pi$
$307$			2.24681i			0.128232i	−0.997942	+	0.0641161i	$0.979577\pi$
$308$		0			0
$309$	5.29191			0.301046
$310$		0			0
$311$	14.2994	+	24.7672i	0.810843	+	1.40442i	0.912275	+	0.409578i	$0.134324\pi$
$311$	14.2994	+	24.7672i	0.810843	+	1.40442i	−0.101432	+	0.994842i	$0.532343\pi$
$312$		0			0
$313$	11.5429	+	6.66427i	0.652441	+	0.376687i	0.789391	−	0.613891i	$-0.210397\pi$
$313$	11.5429	+	6.66427i	0.652441	+	0.376687i	−0.136950	+	0.990578i	$0.543730\pi$
$314$		0			0
$315$	5.88151	+	0.638590i	0.331386	+	0.0359804i
$316$		0			0
$317$	25.2815	+	14.5963i	1.41995	+	0.819808i	0.996294	−	0.0860147i	$-0.0274132\pi$
$317$	25.2815	+	14.5963i	1.41995	+	0.819808i	0.423656	+	0.905823i	$0.360747\pi$
$318$		0			0
$319$	−0.197587	−	0.342231i	−0.0110628	−	0.0191613i
$320$		0			0
$321$	−5.16172			−0.288099
$322$		0			0
$323$			9.19357i			0.511544i
$324$		0			0
$325$	−22.5458	+	2.94824i	−1.25061	+	0.163539i
$326$		0			0
$327$	2.80668	+	1.62043i	0.155209	+	0.0896102i
$328$		0			0
$329$	−13.8266	+	9.70965i	−0.762283	+	0.535310i
$330$		0			0
$331$	−12.4457	+	21.5566i	−0.684080	+	1.18486i	0.289646	+	0.957134i	$0.406463\pi$
$331$	−12.4457	+	21.5566i	−0.684080	+	1.18486i	−0.973725	+	0.227727i	$0.926871\pi$
$332$		0			0
$333$	6.71665	−	3.87786i	0.368070	−	0.212505i
$334$		0			0
$335$	1.32735	−	6.65789i	0.0725209	−	0.363759i
$336$		0			0
$337$		−	4.72659i		−	0.257474i	−0.991679	−	0.128737i	$-0.958908\pi$
$337$		−	4.72659i		−	0.257474i	0.991679	−	0.128737i	$-0.0410923\pi$
$338$		0			0
$339$	6.33039	+	10.9646i	0.343820	+	0.595513i
$340$		0			0
$341$	−10.4245	+	18.0557i	−0.564517	+	0.977772i
$342$		0			0
$343$	17.8694	−	4.86668i	0.964857	−	0.262776i
$344$		0			0
$345$	−11.2602	+	12.8285i	−0.606229	+	0.690665i
$346$		0			0
$347$	−12.2615	+	7.07915i	−0.658229	+	0.380029i	−0.791602	−	0.611037i	$-0.790753\pi$
$347$	−12.2615	+	7.07915i	−0.658229	+	0.380029i	0.133373	+	0.991066i	$0.457419\pi$
$348$		0			0
$349$	−5.04930			−0.270283			−0.135141	−	0.990826i	$-0.543149\pi$
$349$	−5.04930			−0.270283			−0.135141	+	0.990826i	$0.543149\pi$
$350$		0			0
$351$	−4.54754			−0.242730
$352$		0			0
$353$	−13.9417	+	8.04924i	−0.742042	+	0.428418i	−0.822811	−	0.568315i	$-0.807596\pi$
$353$	−13.9417	+	8.04924i	−0.742042	+	0.428418i	0.0807694	+	0.996733i	$0.474262\pi$
$354$		0			0
$355$	5.56174	−	6.33638i	0.295186	−	0.336300i
$356$		0			0
$357$	−8.43504	−	12.0115i	−0.446430	−	0.635717i
$358$		0			0
$359$	−0.153241	+	0.265421i	−0.00808776	+	0.0140084i	−0.870041	−	0.492979i	$-0.835908\pi$
$359$	−0.153241	+	0.265421i	−0.00808776	+	0.0140084i	0.861953	+	0.506988i	$0.169241\pi$
$360$		0			0
$361$	8.12679	+	14.0760i	0.427726	+	0.740843i
$362$		0			0
$363$			0.0915259i			0.00480386i
$364$		0			0
$365$	1.02964	−	5.16461i	0.0538940	−	0.270328i
$366$		0			0
$367$	20.4813	−	11.8249i	1.06911	−	0.617253i	0.141174	−	0.989985i	$-0.454912\pi$
$367$	20.4813	−	11.8249i	1.06911	−	0.617253i	0.927939	+	0.372732i	$0.121579\pi$
$368$		0			0
$369$	0.0350948	−	0.0607860i	0.00182696	−	0.00316439i
$370$		0			0
$371$	0.173255	+	1.94963i	0.00899496	+	0.101220i
$372$		0			0
$373$	16.3140	+	9.41887i	0.844705	+	0.487691i	0.858861	−	0.512209i	$-0.171173\pi$
$373$	16.3140	+	9.41887i	0.844705	+	0.487691i	−0.0141557	+	0.999900i	$0.504506\pi$
$374$		0			0
$375$	−11.1554	−	0.745798i	−0.576064	−	0.0385128i
$376$		0			0
$377$		−	0.539598i		−	0.0277907i
$378$		0			0
$379$	14.2534			0.732147			0.366074	−	0.930586i	$-0.380702\pi$
$379$	14.2534			0.732147			0.366074	+	0.930586i	$0.380702\pi$
$380$		0			0
$381$	8.27377	+	14.3306i	0.423878	+	0.734178i
$382$		0			0
$383$	21.6995	+	12.5282i	1.10879	+	0.640161i	0.938516	−	0.345235i	$-0.112201\pi$
$383$	21.6995	+	12.5282i	1.10879	+	0.640161i	0.170276	+	0.985396i	$0.445534\pi$
$384$		0			0
$385$	11.6357	−	15.9001i	0.593010	−	0.810345i
$386$		0			0
$387$	−2.53729	−	1.46491i	−0.128978	−	0.0744653i
$388$		0			0
$389$	−6.73590	−	11.6669i	−0.341524	−	0.591536i	0.643192	−	0.765705i	$-0.277610\pi$
$389$	−6.73590	−	11.6669i	−0.341524	−	0.591536i	−0.984716	+	0.174169i	$0.944276\pi$
$390$		0			0
$391$	42.3480			2.14163
$392$		0			0
$393$			5.29785i			0.267241i
$394$		0			0
$395$	−8.57123	−	25.2862i	−0.431265	−	1.27229i
$396$		0			0
$397$	15.9768	+	9.22418i	0.801850	+	0.462948i	0.844118	−	0.536158i	$-0.180125\pi$
$397$	15.9768	+	9.22418i	0.801850	+	0.462948i	−0.0422675	+	0.999106i	$0.513458\pi$
$398$		0			0
$399$	3.97635	+	1.84759i	0.199067	+	0.0924953i
$400$		0			0
$401$	−12.7093	+	22.0131i	−0.634670	+	1.09928i	0.351915	+	0.936032i	$0.385531\pi$
$401$	−12.7093	+	22.0131i	−0.634670	+	1.09928i	−0.986585	+	0.163249i	$0.947803\pi$
$402$		0			0
$403$	−24.6545	+	14.2343i	−1.22813	+	0.709059i
$404$		0			0
$405$	−2.19291	−	0.437190i	−0.108967	−	0.0217241i
$406$		0			0
$407$		−	25.8296i		−	1.28033i
$408$		0			0
$409$	−9.36556	−	16.2216i	−0.463097	−	0.802108i	0.536016	−	0.844208i	$-0.319929\pi$
$409$	−9.36556	−	16.2216i	−0.463097	−	0.802108i	−0.999113	+	0.0420997i	$0.986595\pi$
$410$		0			0
$411$	−7.43507	+	12.8779i	−0.366745	+	0.635221i
$412$		0			0
$413$	−4.29592	+	0.381759i	−0.211388	+	0.0187851i
$414$		0			0
$415$	−2.05714	−	1.80565i	−0.100981	−	0.0886360i
$416$		0			0
$417$	−8.24184	+	4.75843i	−0.403605	+	0.233021i
$418$		0			0
$419$	2.04745			0.100024			0.0500121	−	0.998749i	$-0.484074\pi$
$419$	2.04745			0.100024			0.0500121	+	0.998749i	$0.484074\pi$
$420$		0			0
$421$	−16.0512			−0.782287			−0.391144	−	0.920330i	$-0.627920\pi$
$421$	−16.0512			−0.782287			−0.391144	+	0.920330i	$0.627920\pi$
$422$		0			0
$423$	5.53029	−	3.19291i	0.268892	−	0.155245i
$424$		0			0
$425$	16.8665	+	22.0205i	0.818144	+	1.06815i
$426$		0			0
$427$	11.1271	+	15.8450i	0.538476	+	0.766791i
$428$		0			0
$429$	−7.57255	+	13.1160i	−0.365606	+	0.633249i
$430$		0			0
$431$	18.3063	+	31.7075i	0.881784	+	1.52729i	0.849356	+	0.527820i	$0.176991\pi$
$431$	18.3063	+	31.7075i	0.881784	+	1.52729i	0.0324277	+	0.999474i	$0.489676\pi$
$432$		0			0
$433$		−	18.0047i		−	0.865252i	−0.901574	−	0.432626i	$-0.857587\pi$
$433$		−	18.0047i		−	0.865252i	0.901574	−	0.432626i	$-0.142413\pi$
$434$		0			0
$435$	0.0518757	−	0.260205i	0.00248725	−	0.0124759i
$436$		0			0
$437$	−10.9559	+	6.32538i	−0.524090	+	0.302584i
$438$		0			0
$439$	9.68731	−	16.7789i	0.462350	−	0.800814i	−0.536727	−	0.843756i	$-0.680340\pi$
$439$	9.68731	−	16.7789i	0.462350	−	0.800814i	0.999078	+	0.0429418i	$0.0136730\pi$
$440$		0			0
$441$	−6.89031	+	1.23437i	−0.328110	+	0.0587796i
$442$		0			0
$443$	−14.2396	−	8.22121i	−0.676542	−	0.390602i	0.122009	−	0.992529i	$-0.461066\pi$
$443$	−14.2396	−	8.22121i	−0.676542	−	0.390602i	−0.798551	+	0.601927i	$0.794400\pi$
$444$		0			0
$445$	9.33201	+	27.5306i	0.442380	+	1.30507i
$446$		0			0
$447$		−	11.3700i		−	0.537785i
$448$		0			0
$449$	32.7245			1.54436			0.772182	−	0.635401i	$-0.219165\pi$
$449$	32.7245			1.54436			0.772182	+	0.635401i	$0.219165\pi$
$450$		0			0
$451$	−0.116880	−	0.202441i	−0.00550365	−	0.00953259i
$452$		0			0
$453$	7.74255	+	4.47016i	0.363777	+	0.210027i
$454$		0			0
$455$	24.6151	−	10.8583i	1.15397	−	0.509043i
$456$		0			0
$457$	−32.4156	−	18.7152i	−1.51634	−	0.875459i	−0.999816	−	0.0191857i	$-0.993893\pi$
$457$	−32.4156	−	18.7152i	−1.51634	−	0.875459i	−0.516523	−	0.856273i	$-0.672774\pi$
$458$		0			0
$459$	2.77377	+	4.80431i	0.129469	+	0.224246i
$460$		0			0
$461$	28.3604			1.32088			0.660438	−	0.750881i	$-0.270371\pi$
$461$	28.3604			1.32088			0.660438	+	0.750881i	$0.270371\pi$
$462$		0			0
$463$			7.20833i			0.334999i	0.985872	+	0.167500i	$0.0535693\pi$
$463$			7.20833i			0.334999i	−0.985872	+	0.167500i	$0.946431\pi$
$464$		0			0
$465$	−13.2573	+	4.49382i	−0.614793	+	0.208396i
$466$		0			0
$467$	−10.4607	−	6.03950i	−0.484065	−	0.279475i	0.238044	−	0.971254i	$-0.423494\pi$
$467$	−10.4607	−	6.03950i	−0.484065	−	0.279475i	−0.722109	+	0.691779i	$0.756827\pi$
$468$		0			0
$469$	0.711033	+	8.00122i	0.0328325	+	0.369462i
$470$		0			0
$471$	1.67316	−	2.89800i	0.0770952	−	0.133533i
$472$		0			0
$473$	−8.45018	+	4.87871i	−0.388540	+	0.224323i
$474$		0			0
$475$	−7.65266	−	3.17764i	−0.351128	−	0.145800i
$476$		0			0
$477$		−	0.739795i		−	0.0338729i
$478$		0			0
$479$	−10.0708	−	17.4432i	−0.460149	−	0.797001i	0.538819	−	0.842421i	$-0.318871\pi$
$479$	−10.0708	−	17.4432i	−0.460149	−	0.797001i	−0.998968	+	0.0454204i	$0.985537\pi$
$480$		0			0
$481$	17.6347	−	30.5443i	0.804075	−	1.39270i
$482$		0			0
$483$	8.51050	−	18.3161i	0.387241	−	0.833413i
$484$		0			0
$485$	5.11393	+	4.48874i	0.232212	+	0.203823i
$486$		0			0
$487$	−34.5887	+	19.9698i	−1.56737	+	0.904919i	−0.570891	+	0.821026i	$0.693402\pi$
$487$	−34.5887	+	19.9698i	−1.56737	+	0.904919i	−0.996475	+	0.0838930i	$0.973265\pi$
$488$		0			0
$489$	15.7559			0.712505
$490$		0			0
$491$	31.5989			1.42604			0.713019	−	0.701145i	$-0.247327\pi$
$491$	31.5989			1.42604			0.713019	+	0.701145i	$0.247327\pi$
$492$		0			0
$493$	−0.570066	+	0.329127i	−0.0256745	+	0.0148232i
$494$		0			0
$495$	−4.91258	+	5.59680i	−0.220804	+	0.251558i
$496$		0			0
$497$	−4.20358	+	9.04686i	−0.188556	+	0.405807i
$498$		0			0
$499$	−19.8929	+	34.4556i	−0.890530	+	1.54244i	−0.0512890	+	0.998684i	$0.516333\pi$
$499$	−19.8929	+	34.4556i	−0.890530	+	1.54244i	−0.839241	+	0.543759i	$0.817000\pi$
$500$		0			0
$501$	−11.2971	−	19.5671i	−0.504716	−	0.874194i
$502$		0			0
$503$			12.8734i			0.573995i	0.957931	+	0.286997i	$0.0926571\pi$
$503$			12.8734i			0.573995i	−0.957931	+	0.286997i	$0.907343\pi$
$504$		0			0
$505$	−35.1735	−	7.01237i	−1.56520	−	0.312046i
$506$		0			0
$507$	−6.65118	+	3.84006i	−0.295389	+	0.170543i
$508$		0			0
$509$	16.6981	−	28.9219i	0.740128	−	1.28194i	−0.212308	−	0.977203i	$-0.568098\pi$
$509$	16.6981	−	28.9219i	0.740128	−	1.28194i	0.952437	−	0.304737i	$-0.0985685\pi$
$510$		0			0
$511$	0.551558	+	6.20665i	0.0243995	+	0.274566i
$512$		0			0
$513$	−1.43521	−	0.828617i	−0.0633659	−	0.0365843i
$514$		0			0
$515$	11.2068	−	3.79874i	0.493828	−	0.167392i
$516$		0			0
$517$		−	21.2673i		−	0.935335i
$518$		0			0
$519$	−8.52620			−0.374259
$520$		0			0
$521$	−6.77589	−	11.7362i	−0.296857	−	0.514172i	0.678558	−	0.734547i	$-0.262605\pi$
$521$	−6.77589	−	11.7362i	−0.296857	−	0.514172i	−0.975415	+	0.220375i	$0.929272\pi$
$522$		0			0
$523$	17.5052	+	10.1066i	0.765450	+	0.441933i	0.831249	−	0.555900i	$-0.187626\pi$
$523$	17.5052	+	10.1066i	0.765450	+	0.441933i	−0.0657991	+	0.997833i	$0.520960\pi$
$524$		0			0
$525$	12.9138	−	2.86963i	0.563603	−	0.125241i
$526$		0			0
$527$	30.0760	+	17.3644i	1.31013	+	0.756404i
$528$		0			0
$529$	17.6364	+	30.5471i	0.766798	+	1.32813i
$530$		0			0
$531$	1.63010			0.0707404
$532$		0			0
$533$		−	0.319190i		−	0.0138257i
$534$		0			0
$535$	−10.9310	+	3.70528i	−0.472590	+	0.160193i
$536$		0			0
$537$	10.2023	+	5.89031i	0.440262	+	0.254186i
$538$		0			0
$539$	−7.91354	+	21.9285i	−0.340860	+	0.944529i
$540$		0			0
$541$	16.4854	−	28.5535i	0.708762	−	1.22761i	−0.256554	−	0.966530i	$-0.582587\pi$
$541$	16.4854	−	28.5535i	0.708762	−	1.22761i	0.965317	−	0.261082i	$-0.0840794\pi$
$542$		0			0
$543$	7.87189	−	4.54484i	0.337815	−	0.195038i
$544$		0			0
$545$	7.10694	+	1.41688i	0.304428	+	0.0606923i
$546$		0			0
$547$		−	24.6221i		−	1.05277i	−0.850248	−	0.526383i	$-0.823548\pi$
$547$		−	24.6221i		−	1.05277i	0.850248	−	0.526383i	$-0.176452\pi$
$548$		0			0
$549$	−3.65901	−	6.33759i	−0.156163	−	0.270482i
$550$		0			0
$551$	0.0983213	−	0.170297i	0.00418863	−	0.00725491i
$552$		0			0
$553$	18.1553	+	25.8532i	0.772041	+	1.09939i
$554$		0			0
$555$	11.4403	−	13.0337i	0.485612	−	0.553248i
$556$		0			0
$557$	−20.7796	+	11.9971i	−0.880460	+	0.508334i	−0.870810	−	0.491620i	$-0.836405\pi$
$557$	−20.7796	+	11.9971i	−0.880460	+	0.508334i	−0.00964963	+	0.999953i	$0.503072\pi$
$558$		0			0
$559$	−13.3234			−0.563521
$560$		0			0
$561$	18.4755			0.780036
$562$		0			0
$563$	−0.196151	+	0.113248i	−0.00826680	+	0.00477284i	−0.504128	−	0.863629i	$-0.668186\pi$
$563$	−0.196151	+	0.113248i	−0.00826680	+	0.00477284i	0.495861	+	0.868402i	$0.334853\pi$
$564$		0			0
$565$	21.2767	+	18.6756i	0.895119	+	0.785688i
$566$		0			0
$567$	2.63537	−	0.234193i	0.110675	−	0.00983520i
$568$		0			0
$569$	−6.40275	+	11.0899i	−0.268417	+	0.464912i	−0.968453	−	0.249195i	$-0.919834\pi$
$569$	−6.40275	+	11.0899i	−0.268417	+	0.464912i	0.700036	+	0.714108i	$0.253167\pi$
$570$		0			0
$571$	−0.780149	−	1.35126i	−0.0326482	−	0.0565484i	0.849240	−	0.528008i	$-0.177061\pi$
$571$	−0.780149	−	1.35126i	−0.0326482	−	0.0565484i	−0.881888	+	0.471459i	$0.843727\pi$
$572$		0			0
$573$		−	20.4957i		−	0.856219i
$574$		0			0
$575$	−14.6371	+	35.2502i	−0.610408	+	1.47003i
$576$		0			0
$577$	37.8018	−	21.8249i	1.57371	−	0.908581i	0.578000	−	0.816037i	$-0.303833\pi$
$577$	37.8018	−	21.8249i	1.57371	−	0.908581i	0.995709	−	0.0925443i	$-0.0295000\pi$
$578$		0			0
$579$	4.27148	−	7.39842i	0.177517	−	0.307468i
$580$		0			0
$581$	2.93712	+	1.36472i	0.121852	+	0.0566180i
$582$		0			0
$583$	−2.13372	−	1.23191i	−0.0883697	−	0.0510203i
$584$		0			0
$585$	−9.63038	+	3.26440i	−0.398167	+	0.134966i
$586$		0			0
$587$		−	13.6961i		−	0.565297i	−0.959224	−	0.282648i	$-0.908787\pi$
$587$		−	13.6961i		−	0.565297i	0.959224	−	0.282648i	$-0.0912129\pi$
$588$		0			0
$589$	−10.3746			−0.427479
$590$		0			0
$591$	−6.90429	−	11.9586i	−0.284004	−	0.491910i
$592$		0			0
$593$	7.92838	+	4.57745i	0.325579	+	0.187973i	0.653877	−	0.756601i	$-0.273141\pi$
$593$	7.92838	+	4.57745i	0.325579	+	0.187973i	−0.328297	+	0.944574i	$0.606475\pi$
$594$		0			0
$595$	−26.4853	−	19.3820i	−1.08579	−	0.794583i
$596$		0			0
$597$	−3.28309	−	1.89549i	−0.134368	−	0.0775773i
$598$		0			0
$599$	−20.1368	−	34.8780i	−0.822767	−	1.42507i	−0.903614	−	0.428348i	$-0.859096\pi$
$599$	−20.1368	−	34.8780i	−0.822767	−	1.42507i	0.0808467	−	0.996727i	$-0.474238\pi$
$600$		0			0
$601$	−8.82450			−0.359959			−0.179980	−	0.983670i	$-0.557603\pi$
$601$	−8.82450			−0.359959			−0.179980	+	0.983670i	$0.557603\pi$
$602$		0			0
$603$		−	3.03610i		−	0.123639i
$604$		0			0
$605$	0.0657008	+	0.193826i	0.00267112	+	0.00788013i
$606$		0			0
$607$	−24.3409	−	14.0532i	−0.987966	−	0.570402i	−0.0833003	−	0.996524i	$-0.526546\pi$
$607$	−24.3409	−	14.0532i	−0.987966	−	0.570402i	−0.904666	+	0.426122i	$0.859879\pi$
$608$		0			0
$609$	0.0277887	+	0.312705i	0.00112606	+	0.0126714i
$610$		0			0
$611$	14.5199	−	25.1492i	0.587412	−	1.01743i
$612$		0			0
$613$	−1.83025	+	1.05670i	−0.0739232	+	0.0426796i	−0.536506	−	0.843896i	$-0.680256\pi$
$613$	−1.83025	+	1.05670i	−0.0739232	+	0.0426796i	0.462583	+	0.886576i	$0.346923\pi$
$614$		0			0
$615$	0.0306862	−	0.153920i	0.00123739	−	0.00620664i
$616$		0			0
$617$		−	18.0390i		−	0.726221i	−0.931746	−	0.363111i	$-0.881715\pi$
$617$		−	18.0390i		−	0.726221i	0.931746	−	0.363111i	$-0.118285\pi$
$618$		0			0
$619$	7.31895	+	12.6768i	0.294173	+	0.509523i	0.974792	−	0.223114i	$-0.0716223\pi$
$619$	7.31895	+	12.6768i	0.294173	+	0.509523i	−0.680619	+	0.732638i	$0.738289\pi$
$620$		0			0
$621$	−3.81683	+	6.61094i	−0.153164	+	0.265288i
$622$		0			0
$623$	−19.7667	−	28.1479i	−0.791937	−	1.12772i
$624$		0			0
$625$	−24.1594	+	6.42842i	−0.966375	+	0.257137i
$626$		0			0
$627$	−4.77980	+	2.75962i	−0.190887	+	0.110209i
$628$		0			0
$629$	−43.0252			−1.71553
$630$		0			0
$631$	−12.1251			−0.482692			−0.241346	−	0.970439i	$-0.577589\pi$
$631$	−12.1251			−0.482692			−0.241346	+	0.970439i	$0.577589\pi$
$632$		0			0
$633$	0.0990874	−	0.0572082i	0.00393837	−	0.00227382i
$634$		0			0
$635$	27.8085	+	24.4088i	1.10355	+	0.968635i
$636$		0			0
$637$	−24.3293	+	20.5283i	−0.963963	+	0.813360i
$638$		0			0
$639$	1.88524	−	3.26533i	0.0745790	−	0.129175i
$640$		0			0
$641$	6.52024	+	11.2934i	0.257534	+	0.446062i	0.965581	−	0.260104i	$-0.0837567\pi$
$641$	6.52024	+	11.2934i	0.257534	+	0.446062i	−0.708047	+	0.706166i	$0.750423\pi$
$642$		0			0
$643$		−	27.0185i		−	1.06550i	−0.846271	−	0.532752i	$-0.821158\pi$
$643$		−	27.0185i		−	1.06550i	0.846271	−	0.532752i	$-0.178842\pi$
$644$		0			0
$645$	−6.42482	−	1.28088i	−0.252977	−	0.0504347i
$646$		0			0
$647$	−30.2927	+	17.4895i	−1.19093	+	0.687582i	−0.958517	−	0.285035i	$-0.907995\pi$
$647$	−30.2927	+	17.4895i	−1.19093	+	0.687582i	−0.232411	+	0.972618i	$0.574661\pi$
$648$		0			0
$649$	2.71444	−	4.70155i	0.106551	−	0.184552i
$650$		0			0
$651$	13.5546	−	9.51864i	0.531246	−	0.373065i
$652$		0			0
$653$	−28.0168	−	16.1755i	−1.09638	−	0.632997i	−0.161114	−	0.986936i	$-0.551509\pi$
$653$	−28.0168	−	16.1755i	−1.09638	−	0.632997i	−0.935269	+	0.353939i	$0.884842\pi$
$654$		0			0
$655$	3.80300	+	11.2193i	0.148596	+	0.438376i
$656$		0			0
$657$		−	2.35514i		−	0.0918827i
$658$		0			0
$659$	8.54282			0.332781			0.166390	−	0.986060i	$-0.446789\pi$
$659$	8.54282			0.332781			0.166390	+	0.986060i	$0.446789\pi$
$660$		0			0
$661$	15.1715	+	26.2779i	0.590104	+	1.02209i	0.994218	+	0.107382i	$0.0342467\pi$
$661$	15.1715	+	26.2779i	0.590104	+	1.02209i	−0.404114	+	0.914709i	$0.632420\pi$
$662$		0			0
$663$	21.8478	+	12.6138i	0.848498	+	0.489881i
$664$		0			0
$665$	9.74704	+	1.05829i	0.377974	+	0.0410388i
$666$		0			0
$667$	−0.784435	−	0.452894i	−0.0303734	−	0.0175361i
$668$		0			0
$669$	−3.93337	−	6.81279i	−0.152073	−	0.263398i
$670$		0			0
$671$	−24.3719			−0.940867
$672$		0			0
$673$		−	40.5075i		−	1.56145i	−0.624875	−	0.780725i	$-0.714850\pi$
$673$		−	40.5075i		−	1.56145i	0.624875	−	0.780725i	$-0.285150\pi$
$674$		0			0
$675$	−4.95779	+	0.648315i	−0.190825	+	0.0249537i
$676$		0			0
$677$	20.2833	+	11.7105i	0.779549	+	0.450073i	0.836270	−	0.548317i	$-0.184731\pi$
$677$	20.2833	+	11.7105i	0.779549	+	0.450073i	−0.0567215	+	0.998390i	$0.518065\pi$
$678$		0			0
$679$	−7.30149	−	3.39260i	−0.280205	−	0.130196i
$680$		0			0
$681$	4.48933	−	7.77575i	0.172032	−	0.297967i
$682$		0			0
$683$	−44.1887	+	25.5124i	−1.69083	+	0.976204i	−0.736989	+	0.675904i	$0.763753\pi$
$683$	−44.1887	+	25.5124i	−1.69083	+	0.976204i	−0.953845	+	0.300299i	$0.902913\pi$
$684$		0			0
$685$	−6.50107	+	32.6089i	−0.248393	+	1.24592i
$686$		0			0
$687$			5.08612i			0.194047i
$688$		0			0
$689$	−1.68212	−	2.91353i	−0.0640838	−	0.110996i
$690$		0			0
$691$	12.3057	−	21.3142i	0.468133	−	0.810829i	−0.531204	−	0.847244i	$-0.678260\pi$
$691$	12.3057	−	21.3142i	0.468133	−	0.810829i	0.999337	+	0.0364144i	$0.0115936\pi$
$692$		0			0
$693$	3.71294	−	7.99092i	0.141043	−	0.303550i
$694$		0			0
$695$	−14.0381	+	15.9933i	−0.532494	+	0.606660i
$696$		0			0
$697$	−0.337213	+	0.194690i	−0.0127728	+	0.00737441i
$698$		0			0
$699$	−21.8183			−0.825243
$700$		0			0
$701$	25.7244			0.971595			0.485798	−	0.874071i	$-0.338529\pi$
$701$	25.7244			0.971595			0.485798	+	0.874071i	$0.338529\pi$
$702$		0			0
$703$	11.1311	−	6.42652i	0.419816	−	0.242381i
$704$		0			0
$705$	9.41956	−	10.7315i	0.354761	−	0.404173i
$706$		0			0
$707$	42.2703	−	3.75638i	1.58974	−	0.141273i
$708$		0			0
$709$	5.85482	−	10.1408i	0.219882	−	0.380848i	−0.734889	−	0.678187i	$-0.762766\pi$
$709$	5.85482	−	10.1408i	0.219882	−	0.380848i	0.954772	+	0.297339i	$0.0960993\pi$
$710$		0			0
$711$	−5.97016	−	10.3406i	−0.223899	−	0.387804i
$712$		0			0
$713$			47.7883i			1.78968i
$714$		0			0
$715$	−6.62129	+	33.2119i	−0.247622	+	1.24205i
$716$		0			0
$717$	6.45107	−	3.72453i	0.240920	−	0.139095i
$718$		0			0
$719$	6.16037	−	10.6701i	0.229743	−	0.397927i	−0.727989	−	0.685589i	$-0.759545\pi$
$719$	6.16037	−	10.6701i	0.229743	−	0.397927i	0.957732	+	0.287662i	$0.0928781\pi$
$720$		0			0
$721$	−11.4580	+	8.04635i	−0.426719	+	0.299662i
$722$		0			0
$723$	20.9368	+	12.0879i	0.778650	+	0.449554i
$724$		0			0
$725$	−0.0769272	−	0.588277i	−0.00285700	−	0.0218481i
$726$		0			0
$727$		−	17.6540i		−	0.654751i	−0.944894	−	0.327376i	$-0.893836\pi$
$727$		−	17.6540i		−	0.654751i	0.944894	−	0.327376i	$-0.106164\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	8.12662	+	14.0757i	0.300574	+	0.520609i
$732$		0			0
$733$	−8.69135	−	5.01795i	−0.321022	−	0.185342i	0.330826	−	0.943692i	$-0.392673\pi$
$733$	−8.69135	−	5.01795i	−0.321022	−	0.185342i	−0.651848	+	0.758349i	$0.726006\pi$
$734$		0			0
$735$	−13.7056	+	7.56017i	−0.505539	+	0.278861i
$736$		0			0
$737$	−8.75672	−	5.05570i	−0.322558	−	0.186229i
$738$		0			0
$739$	15.5360	+	26.9092i	0.571502	+	0.989870i	0.996412	+	0.0846345i	$0.0269723\pi$
$739$	15.5360	+	26.9092i	0.571502	+	0.989870i	−0.424910	+	0.905235i	$0.639694\pi$
$740$		0			0
$741$	−7.53634			−0.276854
$742$		0			0
$743$			4.04189i			0.148283i	0.997248	+	0.0741413i	$0.0236216\pi$
$743$			4.04189i			0.148283i	−0.997248	+	0.0741413i	$0.976378\pi$
$744$		0			0
$745$	−8.16186	−	24.0785i	−0.299027	−	0.882168i
$746$		0			0
$747$	−1.06011	−	0.612055i	−0.0387874	−	0.0223939i
$748$		0			0
$749$	11.1761	−	7.84839i	0.408367	−	0.286774i
$750$		0			0
$751$	7.34725	−	12.7258i	0.268105	−	0.464371i	−0.700268	−	0.713881i	$-0.746936\pi$
$751$	7.34725	−	12.7258i	0.268105	−	0.464371i	0.968372	+	0.249509i	$0.0802693\pi$
$752$		0			0
$753$	−5.19789	+	3.00100i	−0.189421	+	0.109363i
$754$		0			0
$755$	19.6054	+	3.90862i	0.713512	+	0.142249i
$756$		0			0
$757$			29.6087i			1.07615i	0.842898	+	0.538073i	$0.180847\pi$
$757$			29.6087i			1.07615i	−0.842898	+	0.538073i	$0.819153\pi$
$758$		0			0
$759$	12.7115	+	22.0170i	0.461400	+	0.799168i
$760$		0			0
$761$	7.12611	−	12.3428i	0.258321	−	0.447426i	−0.707471	−	0.706742i	$-0.750164\pi$
$761$	7.12611	−	12.3428i	0.258321	−	0.447426i	0.965792	+	0.259317i	$0.0834974\pi$
$762$		0			0
$763$	−8.54088	+	0.758990i	−0.309200	+	0.0274773i
$764$		0			0
$765$	9.32277	+	8.18303i	0.337065	+	0.295858i
$766$		0			0
$767$	6.41981	−	3.70648i	0.231806	−	0.133833i
$768$		0			0
$769$	20.6367			0.744178			0.372089	−	0.928197i	$-0.378642\pi$
$769$	20.6367			0.744178			0.372089	+	0.928197i	$0.378642\pi$
$770$		0			0
$771$	7.33395			0.264126
$772$		0			0
$773$	−36.8580	+	21.2800i	−1.32569	+	0.765387i	−0.984630	−	0.174655i	$-0.944119\pi$
$773$	−36.8580	+	21.2800i	−1.32569	+	0.765387i	−0.341059	+	0.940042i	$0.610786\pi$
$774$		0			0
$775$	−24.8494	+	19.0332i	−0.892615	+	0.683694i
$776$		0			0
$777$	−8.64659	+	18.6090i	−0.310195	+	0.667594i
$778$		0			0
$779$	0.0581603	−	0.100737i	0.00208381	−	0.00360926i
$780$		0			0
$781$	−6.27860	−	10.8748i	−0.224666	−	0.389133i
$782$		0			0
$783$		−	0.118657i		−	0.00424046i
$784$		0			0
$785$	1.46298	−	7.33819i	0.0522159	−	0.261911i
$786$		0			0
$787$	−21.8231	+	12.5996i	−0.777909	+	0.449126i	−0.835689	−	0.549203i	$-0.814931\pi$
$787$	−21.8231	+	12.5996i	−0.777909	+	0.449126i	0.0577798	+	0.998329i	$0.481598\pi$
$788$		0			0
$789$	−4.74386	+	8.21661i	−0.168886	+	0.292519i
$790$		0			0
$791$	−30.3782	−	14.1151i	−1.08012	−	0.501874i
$792$		0			0
$793$	−28.8205	−	16.6395i	−1.02344	−	0.590886i
$794$		0			0
$795$	−0.531054	−	1.56667i	−0.0188345	−	0.0555642i
$796$		0			0
$797$		−	51.7211i		−	1.83205i	−0.401116	−	0.916027i	$-0.631377\pi$
$797$		−	51.7211i		−	1.83205i	0.401116	−	0.916027i	$-0.368623\pi$
$798$		0			0
$799$	−35.4256			−1.25327
$800$		0			0
$801$	6.50007	+	11.2585i	0.229669	+	0.397798i
$802$		0			0
$803$	−6.79271	−	3.92177i	−0.239709	−	0.138396i
$804$		0			0
$805$	4.87477	−	44.8975i	0.171813	−	1.58243i
$806$		0			0
$807$	13.8984	+	8.02423i	0.489246	+	0.282466i
$808$		0			0
$809$	−25.8890	−	44.8410i	−0.910207	−	1.57653i	−0.813770	−	0.581187i	$-0.802589\pi$
$809$	−25.8890	−	44.8410i	−0.910207	−	1.57653i	−0.0964371	−	0.995339i	$-0.530745\pi$
$810$		0			0
$811$	−12.0263			−0.422299			−0.211149	−	0.977454i	$-0.567721\pi$
$811$	−12.0263			−0.422299			−0.211149	+	0.977454i	$0.567721\pi$
$812$		0			0
$813$		−	24.1690i		−	0.847643i
$814$		0			0
$815$	33.3664	−	11.3102i	1.16877	−	0.396178i
$816$		0			0
$817$	−4.20488	−	2.42769i	−0.147110	−	0.0849341i
$818$		0			0
$819$	9.84632	−	6.91454i	0.344058	−	0.241613i
$820$		0			0
$821$	−4.03967	+	6.99692i	−0.140985	+	0.244194i	−0.927868	−	0.372909i	$-0.878360\pi$
$821$	−4.03967	+	6.99692i	−0.140985	+	0.244194i	0.786882	+	0.617103i	$0.211694\pi$
$822$		0			0
$823$	4.42994	−	2.55762i	0.154418	−	0.0891532i	−0.420800	−	0.907153i	$-0.638251\pi$
$823$	4.42994	−	2.55762i	0.154418	−	0.0891532i	0.575218	+	0.818000i	$0.304917\pi$
$824$		0			0
$825$	−6.38582	+	15.3789i	−0.222326	+	0.535423i
$826$		0			0
$827$			0.705254i			0.0245241i	0.999925	+	0.0122620i	$0.00390323\pi$
$827$			0.705254i			0.0245241i	−0.999925	+	0.0122620i	$0.996097\pi$
$828$		0			0
$829$	12.4790	+	21.6143i	0.433415	+	0.750696i	0.997165	−	0.0752491i	$-0.0239752\pi$
$829$	12.4790	+	21.6143i	0.433415	+	0.750696i	−0.563750	+	0.825945i	$0.690642\pi$
$830$		0			0
$831$	−11.6088	+	20.1071i	−0.402706	+	0.697508i
$832$		0			0
$833$	36.5270	+	13.1818i	1.26559	+	0.456723i
$834$		0			0
$835$	−37.9700	−	33.3280i	−1.31401	−	1.15336i
$836$		0			0
$837$	−5.42150	+	3.13010i	−0.187394	+	0.108192i
$838$		0			0
$839$	−11.6389			−0.401819			−0.200909	−	0.979610i	$-0.564390\pi$
$839$	−11.6389			−0.401819			−0.200909	+	0.979610i	$0.564390\pi$
$840$		0			0
$841$	−28.9859			−0.999514
$842$		0			0
$843$	10.7796	−	6.22360i	0.371269	−	0.214352i
$844$		0			0
$845$	−11.3287	+	12.9066i	−0.389721	+	0.444001i
$846$		0			0
$847$	−0.139165	−	0.198172i	−0.00478177	−	0.00680926i
$848$		0			0
$849$	4.33388	−	7.50649i	0.148738	−	0.257622i
$850$		0			0
$851$	−29.6023	−	51.2726i	−1.01475	−	1.75760i
$852$		0			0
$853$		−	32.5996i		−	1.11619i	−0.829778	−	0.558094i	$-0.811533\pi$
$853$		−	32.5996i		−	1.11619i	0.829778	−	0.558094i	$-0.188467\pi$
$854$		0			0
$855$	−3.63417	−	0.724526i	−0.124286	−	0.0247783i
$856$		0			0
$857$	27.4455	−	15.8456i	0.937519	−	0.541277i	0.0483371	−	0.998831i	$-0.484608\pi$
$857$	27.4455	−	15.8456i	0.937519	−	0.541277i	0.889182	+	0.457554i	$0.151274\pi$
$858$		0			0
$859$	21.8456	−	37.8377i	0.745363	−	1.29101i	−0.204662	−	0.978833i	$-0.565610\pi$
$859$	21.8456	−	37.8377i	0.745363	−	1.29101i	0.950025	−	0.312174i	$-0.101057\pi$
$860$		0			0
$861$	0.0164380	+	0.184975i	0.000560204	+	0.00630394i
$862$		0			0
$863$	−33.6005	−	19.3992i	−1.14377	−	0.660358i	−0.196411	−	0.980522i	$-0.562929\pi$
$863$	−33.6005	−	19.3992i	−1.14377	−	0.660358i	−0.947362	+	0.320164i	$0.896262\pi$
$864$		0			0
$865$	−18.0561	+	6.12044i	−0.613924	+	0.208101i
$866$		0			0
$867$		−	13.7752i		−	0.467830i
$868$		0			0
$869$	−39.7660			−1.34897
$870$		0			0
$871$	−6.90338	−	11.9570i	−0.233912	−	0.405148i
$872$		0			0
$873$	2.63537	+	1.52153i	0.0891936	+	0.0514960i
$874$		0			0
$875$	25.2877	−	15.3470i	0.854881	−	0.518825i
$876$		0			0
$877$	3.72454	+	2.15036i	0.125769	+	0.0726127i	0.561565	−	0.827433i	$-0.310200\pi$
$877$	3.72454	+	2.15036i	0.125769	+	0.0726127i	−0.435796	+	0.900046i	$0.643533\pi$
$878$		0			0
$879$	−13.5031	−	23.3881i	−0.455450	−	0.788862i
$880$		0			0
$881$	−1.29308			−0.0435650			−0.0217825	−	0.999763i	$-0.506934\pi$
$881$	−1.29308			−0.0435650			−0.0217825	+	0.999763i	$0.506934\pi$
$882$		0			0
$883$		−	1.49533i		−	0.0503218i	−0.999683	−	0.0251609i	$-0.991990\pi$
$883$		−	1.49533i		−	0.0503218i	0.999683	−	0.0251609i	$-0.00800981\pi$
$884$		0			0
$885$	3.45209	−	1.17015i	0.116041	−	0.0393342i
$886$		0			0
$887$	−8.73964	−	5.04584i	−0.293449	−	0.169423i	0.346047	−	0.938217i	$-0.387524\pi$
$887$	−8.73964	−	5.04584i	−0.293449	−	0.169423i	−0.639496	+	0.768794i	$0.720857\pi$
$888$		0			0
$889$	−39.7040	−	18.4483i	−1.33163	−	0.618736i
$890$		0			0
$891$	−1.66520	+	2.88421i	−0.0557862	+	0.0966245i
$892$		0			0
$893$	9.16498	−	5.29140i	0.306694	−	0.177070i
$894$		0			0
$895$	25.8339	+	5.15036i	0.863531	+	0.172158i
$896$		0			0
$897$			34.7144i			1.15908i
$898$		0			0
$899$	−0.371409	−	0.643299i	−0.0123872	−	0.0214552i
$900$		0			0
$901$	−2.05202	+	3.55421i	−0.0683628	+	0.118408i
$902$		0			0
$903$	7.72112	−	0.686142i	0.256943	−	0.0228334i
$904$		0			0
$905$	13.4079	−	15.2754i	0.445695	−	0.507772i
$906$		0			0
$907$	3.69531	−	2.13349i	0.122701	−	0.0708414i	−0.437393	−	0.899270i	$-0.644098\pi$
$907$	3.69531	−	2.13349i	0.122701	−	0.0708414i	0.560094	+	0.828429i	$0.310765\pi$
$908$		0			0
$909$	−16.0397			−0.532002
$910$		0			0
$911$	28.5451			0.945742			0.472871	−	0.881132i	$-0.343218\pi$
$911$	28.5451			0.945742			0.472871	+	0.881132i	$0.343218\pi$
$912$		0			0
$913$	−3.53058	+	2.03838i	−0.116845	+	0.0674606i
$914$		0			0
$915$	−12.2981	−	10.7946i	−0.406563	−	0.356859i
$916$		0			0
$917$	−8.05539	−	11.4709i	−0.266012	−	0.378802i
$918$		0			0
$919$	23.2822	−	40.3259i	0.768008	−	1.33023i	−0.170634	−	0.985335i	$-0.554581\pi$
$919$	23.2822	−	40.3259i	0.768008	−	1.33023i	0.938642	−	0.344894i	$-0.112085\pi$
$920$		0			0
$921$	1.12341	+	1.94580i	0.0370175	+	0.0641161i
$922$		0			0
$923$		−	17.1464i		−	0.564381i
$924$		0			0
$925$	14.8711	−	35.8138i	0.488959	−	1.17755i
$926$		0			0
$927$	4.58293	−	2.64596i	0.150523	−	0.0869046i
$928$		0			0
$929$	3.69774	−	6.40467i	0.121319	−	0.210130i	−0.798969	−	0.601372i	$-0.794621\pi$
$929$	3.69774	−	6.40467i	0.121319	−	0.210130i	0.920288	+	0.391242i	$0.127954\pi$
$930$		0			0
$931$	−11.4188	+	2.04564i	−0.374238	+	0.0670432i
$932$		0			0
$933$	24.7672	+	14.2994i	0.810843	+	0.468140i
$934$		0			0
$935$	39.1258	−	13.2624i	1.27955	−	0.433728i
$936$		0			0
$937$		−	44.1988i		−	1.44391i	−0.691939	−	0.721956i	$-0.743243\pi$
$937$		−	44.1988i		−	1.44391i	0.691939	−	0.721956i	$-0.256757\pi$
$938$		0			0
$939$	13.3285			0.434960
$940$		0			0
$941$	−18.0180	−	31.2080i	−0.587369	−	1.01735i	−0.994576	−	0.104017i	$-0.966830\pi$
$941$	−18.0180	−	31.2080i	−0.587369	−	1.01735i	0.407206	−	0.913336i	$-0.366503\pi$
$942$		0			0
$943$	−0.464020	−	0.267902i	−0.0151106	−	0.00872408i
$944$		0			0
$945$	5.41284	−	2.38772i	0.176080	−	0.0776726i
$946$		0			0
$947$	29.6476	+	17.1170i	0.963417	+	0.556229i	0.897223	−	0.441577i	$-0.145581\pi$
$947$	29.6476	+	17.1170i	0.963417	+	0.556229i	0.0661943	+	0.997807i	$0.478914\pi$
$948$		0			0
$949$	−5.35504	−	9.27521i	−0.173832	−	0.301086i
$950$		0			0
$951$	29.1925			0.946633
$952$		0			0
$953$			30.9689i			1.00318i	0.865105	+	0.501591i	$0.167252\pi$
$953$			30.9689i			1.00318i	−0.865105	+	0.501591i	$0.832748\pi$
$954$		0			0
$955$	−14.7126	−	43.4039i	−0.476088	−	1.40452i
$956$		0			0
$957$	−0.342231	−	0.197587i	−0.0110628	−	0.00638709i
$958$		0			0
$959$	−3.48249	−	39.1883i	−0.112455	−	1.26545i
$960$		0			0
$961$	−4.09508	+	7.09289i	−0.132099	+	0.228803i
$962$		0			0
$963$	−4.47018	+	2.58086i	−0.144049	+	0.0831670i
$964$		0			0
$965$	3.73490	−	18.7340i	0.120231	−	0.603068i
$966$		0			0
$967$			21.0270i			0.676184i	0.941113	+	0.338092i	$0.109782\pi$
$967$			21.0270i			0.676184i	−0.941113	+	0.338092i	$0.890218\pi$
$968$		0			0
$969$	4.59678	+	7.96187i	0.147670	+	0.255772i
$970$		0			0
$971$	22.3468	−	38.7058i	0.717144	−	1.24213i	−0.244983	−	0.969527i	$-0.578782\pi$
$971$	22.3468	−	38.7058i	0.717144	−	1.24213i	0.962127	−	0.272602i	$-0.0878843\pi$
$972$		0			0
$973$	10.6100	−	22.8346i	0.340141	−	0.732045i
$974$		0			0
$975$	−18.0511	+	13.8261i	−0.578097	+	0.442790i
$976$		0			0
$977$	12.5029	−	7.21858i	0.400005	−	0.230943i	−0.286481	−	0.958086i	$-0.592486\pi$
$977$	12.5029	−	7.21858i	0.400005	−	0.230943i	0.686486	+	0.727143i	$0.259152\pi$
$978$		0			0
$979$	43.2956			1.38373
$980$		0			0
$981$	3.24087			0.103473
$982$		0			0
$983$	14.5389	−	8.39401i	0.463717	−	0.267727i	−0.249889	−	0.968275i	$-0.580394\pi$
$983$	14.5389	−	8.39401i	0.463717	−	0.267727i	0.713606	+	0.700547i	$0.247061\pi$
$984$		0			0
$985$	−23.2056	−	20.3687i	−0.739393	−	0.649000i
$986$		0			0
$987$	−7.11934	+	15.3221i	−0.226611	+	0.487707i
$988$		0			0
$989$	−11.1826	+	19.3688i	−0.355585	+	0.615892i
$990$		0			0
$991$	20.0539	+	34.7344i	0.637033	+	1.10337i	0.986081	+	0.166268i	$0.0531718\pi$
$991$	20.0539	+	34.7344i	0.637033	+	1.10337i	−0.349048	+	0.937105i	$0.613495\pi$
$992$		0			0
$993$			24.8915i			0.789907i
$994$		0			0
$995$	−8.31330	−	1.65738i	−0.263549	−	0.0525425i
$996$		0			0
$997$	−44.4447	+	25.6602i	−1.40758	+	0.812666i	−0.995154	−	0.0983259i	$-0.968651\pi$
$997$	−44.4447	+	25.6602i	−1.40758	+	0.812666i	−0.412424	+	0.910992i	$0.635318\pi$
$998$		0			0
$999$	3.87786	−	6.71665i	0.122690	−	0.212505i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.di.d.289.7		16
4.3	odd	2		105.2.q.a.79.4	yes	16
5.4	even	2	inner	1680.2.di.d.289.3		16
7.4	even	3	inner	1680.2.di.d.529.3		16
12.11	even	2		315.2.bf.b.289.5		16
20.3	even	4		525.2.i.k.226.2		8
20.7	even	4		525.2.i.h.226.3		8
20.19	odd	2		105.2.q.a.79.5	yes	16
28.3	even	6		735.2.q.g.214.5		16
28.11	odd	6		105.2.q.a.4.5	yes	16
28.19	even	6		735.2.d.e.589.5		8
28.23	odd	6		735.2.d.d.589.5		8
28.27	even	2		735.2.q.g.79.4		16
35.4	even	6	inner	1680.2.di.d.529.7		16
60.59	even	2		315.2.bf.b.289.4		16
84.11	even	6		315.2.bf.b.109.4		16
84.23	even	6		2205.2.d.s.1324.4		8
84.47	odd	6		2205.2.d.o.1324.4		8
140.19	even	6		735.2.d.e.589.4		8
140.23	even	12		3675.2.a.bp.1.3		4
140.39	odd	6		105.2.q.a.4.4	✓	16
140.47	odd	12		3675.2.a.cb.1.2		4
140.59	even	6		735.2.q.g.214.4		16
140.67	even	12		525.2.i.h.151.3		8
140.79	odd	6		735.2.d.d.589.4		8
140.103	odd	12		3675.2.a.bn.1.3		4
140.107	even	12		3675.2.a.bz.1.2		4
140.123	even	12		525.2.i.k.151.2		8
140.139	even	2		735.2.q.g.79.5		16
420.179	even	6		315.2.bf.b.109.5		16
420.299	odd	6		2205.2.d.o.1324.5		8
420.359	even	6		2205.2.d.s.1324.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.4	✓	16	140.39	odd	6
105.2.q.a.4.5	yes	16	28.11	odd	6
105.2.q.a.79.4	yes	16	4.3	odd	2
105.2.q.a.79.5	yes	16	20.19	odd	2
315.2.bf.b.109.4		16	84.11	even	6
315.2.bf.b.109.5		16	420.179	even	6
315.2.bf.b.289.4		16	60.59	even	2
315.2.bf.b.289.5		16	12.11	even	2
525.2.i.h.151.3		8	140.67	even	12
525.2.i.h.226.3		8	20.7	even	4
525.2.i.k.151.2		8	140.123	even	12
525.2.i.k.226.2		8	20.3	even	4
735.2.d.d.589.4		8	140.79	odd	6
735.2.d.d.589.5		8	28.23	odd	6
735.2.d.e.589.4		8	140.19	even	6
735.2.d.e.589.5		8	28.19	even	6
735.2.q.g.79.4		16	28.27	even	2
735.2.q.g.79.5		16	140.139	even	2
735.2.q.g.214.4		16	140.59	even	6
735.2.q.g.214.5		16	28.3	even	6
1680.2.di.d.289.3		16	5.4	even	2	inner
1680.2.di.d.289.7		16	1.1	even	1	trivial
1680.2.di.d.529.3		16	7.4	even	3	inner
1680.2.di.d.529.7		16	35.4	even	6	inner
2205.2.d.o.1324.4		8	84.47	odd	6
2205.2.d.o.1324.5		8	420.299	odd	6
2205.2.d.s.1324.4		8	84.23	even	6
2205.2.d.s.1324.5		8	420.359	even	6
3675.2.a.bn.1.3		4	140.103	odd	12
3675.2.a.bp.1.3		4	140.23	even	12
3675.2.a.bz.1.2		4	140.107	even	12
3675.2.a.cb.1.2		4	140.47	odd	12

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:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.di (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{3} +(1.47507 - 1.68052i) q^{5} +(-1.11487 + 2.39939i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{3} +(1.47507 - 1.68052i) q^{5} +(-1.11487 + 2.39939i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-1.66520 - 2.88421i) q^{11} -4.54754i q^{13} +(0.437190 - 2.19291i) q^{15} +(-4.80431 + 2.77377i) q^{17} +(0.828617 - 1.43521i) q^{19} +(0.234193 + 2.63537i) q^{21} +(-6.61094 - 3.81683i) q^{23} +(-0.648315 - 4.95779i) q^{25} -1.00000i q^{27} +0.118657 q^{29} +(-3.13010 - 5.42150i) q^{31} +(-2.88421 - 1.66520i) q^{33} +(2.38772 + 5.41284i) q^{35} +(6.71665 + 3.87786i) q^{37} +(-2.27377 - 3.93829i) q^{39} +0.0701896 q^{41} -2.92981i q^{43} +(-0.717839 - 2.11771i) q^{45} +(5.53029 + 3.19291i) q^{47} +(-4.51415 - 5.35000i) q^{49} +(-2.77377 + 4.80431i) q^{51} +(0.640682 - 0.369898i) q^{53} +(-7.30326 - 1.45601i) q^{55} -1.65723i q^{57} +(0.815051 + 1.41171i) q^{59} +(3.65901 - 6.33759i) q^{61} +(1.52050 + 2.16520i) q^{63} +(-7.64225 - 6.70796i) q^{65} +(2.62934 - 1.51805i) q^{67} -7.63366 q^{69} +3.77048 q^{71} +(2.03961 - 1.17757i) q^{73} +(-3.04035 - 3.96942i) q^{75} +(8.77681 - 0.779956i) q^{77} +(5.97016 - 10.3406i) q^{79} +(-0.500000 - 0.866025i) q^{81} -1.22411i q^{83} +(-2.42533 + 12.1653i) q^{85} +(0.102760 - 0.0593285i) q^{87} +(-6.50007 + 11.2585i) q^{89} +(10.9113 + 5.06990i) q^{91} +(-5.42150 - 3.13010i) q^{93} +(-1.18963 - 3.50954i) q^{95} +3.04306i q^{97} -3.33039 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{5} + 8 q^{9}+O(q^{10}) \) 16 * q + 2 * q^5 + 8 * q^9	\( 16 q + 2 q^{5} + 8 q^{9} + 4 q^{15} + 24 q^{19} - 4 q^{21} - 4 q^{25} + 24 q^{29} - 16 q^{31} + 10 q^{35} + 4 q^{39} + 16 q^{41} - 2 q^{45} - 40 q^{49} - 4 q^{51} - 8 q^{55} - 4 q^{59} + 16 q^{61} + 30 q^{65} + 40 q^{69} + 56 q^{71} - 8 q^{75} + 16 q^{79} - 8 q^{81} - 64 q^{85} + 16 q^{89} - 8 q^{91} + 22 q^{95}+O(q^{100}) \) 16 * q + 2 * q^5 + 8 * q^9 + 4 * q^15 + 24 * q^19 - 4 * q^21 - 4 * q^25 + 24 * q^29 - 16 * q^31 + 10 * q^35 + 4 * q^39 + 16 * q^41 - 2 * q^45 - 40 * q^49 - 4 * q^51 - 8 * q^55 - 4 * q^59 + 16 * q^61 + 30 * q^65 + 40 * q^69 + 56 * q^71 - 8 * q^75 + 16 * q^79 - 8 * q^81 - 64 * q^85 + 16 * q^89 - 8 * q^91 + 22 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more