LMFDB - Embedded newform 315.2.bf.b.109.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [315,2,Mod(109,315)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(315, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("315.109"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,8,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.27814731656356152999936.1
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:	$\Z[a_1, \ldots, a_{5}]$
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			109.5
Root			$2.07845 + 0.556918i$ of defining polynomial
Character	$\chi$	$=$	315.109
Dual form			315.2.bf.b.289.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.248840 - 0.143668i) q^{2} +(-0.958719 + 1.66055i) q^{4} +(-1.47507 - 1.68052i) q^{5} +(1.11487 + 2.39939i) q^{7} +1.12562i q^{8} +(-0.608495 - 0.206261i) q^{10} +(-1.66520 + 2.88421i) q^{11} +4.54754i q^{13} +(0.622139 + 0.436894i) q^{14} +(-1.75572 - 3.04100i) q^{16} +(4.80431 + 2.77377i) q^{17} +(-0.828617 - 1.43521i) q^{19} +(4.20477 - 0.838284i) q^{20} +0.956942i q^{22} +(-6.61094 + 3.81683i) q^{23} +(-0.648315 + 4.95779i) q^{25} +(0.653336 + 1.13161i) q^{26} +(-5.05315 - 0.449051i) q^{28} -0.118657 q^{29} +(3.13010 - 5.42150i) q^{31} +(-2.82342 - 1.63010i) q^{32} +1.59401 q^{34} +(2.38772 - 5.41284i) q^{35} +(6.71665 - 3.87786i) q^{37} +(-0.412386 - 0.238091i) q^{38} +(1.89163 - 1.66037i) q^{40} -0.0701896 q^{41} -2.92981i q^{43} +(-3.19291 - 5.53029i) q^{44} +(-1.09671 + 1.89956i) q^{46} +(5.53029 - 3.19291i) q^{47} +(-4.51415 + 5.35000i) q^{49} +(0.550949 + 1.32684i) q^{50} +(-7.55142 - 4.35981i) q^{52} +(-0.640682 - 0.369898i) q^{53} +(7.30326 - 1.45601i) q^{55} +(-2.70080 + 1.25492i) q^{56} +(-0.0295266 + 0.0170472i) q^{58} +(0.815051 - 1.41171i) q^{59} +(3.65901 + 6.33759i) q^{61} -1.79878i q^{62} +6.08612 q^{64} +(7.64225 - 6.70796i) q^{65} +(-2.62934 - 1.51805i) q^{67} +(-9.21197 + 5.31853i) q^{68} +(-0.183490 - 1.68997i) q^{70} +3.77048 q^{71} +(2.03961 + 1.17757i) q^{73} +(1.11425 - 1.92993i) q^{74} +3.17764 q^{76} +(-8.77681 - 0.779956i) q^{77} +(-5.97016 - 10.3406i) q^{79} +(-2.52065 + 7.43623i) q^{80} +(-0.0174660 + 0.0100840i) q^{82} +1.22411i q^{83} +(-2.42533 - 12.1653i) q^{85} +(-0.420920 - 0.729054i) q^{86} +(-3.24652 - 1.87438i) q^{88} +(6.50007 + 11.2585i) q^{89} +(-10.9113 + 5.06990i) q^{91} -14.6371i q^{92} +(0.917438 - 1.58905i) q^{94} +(-1.18963 + 3.50954i) q^{95} -3.04306i q^{97} +(-0.354679 + 1.97983i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 2 q^{5} - 4 q^{10} + 24 q^{14} - 24 q^{19} + 8 q^{20} - 4 q^{25} + 12 q^{26} - 24 q^{29} + 16 q^{31} + 16 q^{34} + 10 q^{35} + 32 q^{40} - 16 q^{41} - 20 q^{44} - 32 q^{46} - 40 q^{49}+ \cdots + 22 q^{95}+O(q^{100}) $ 16 * q + 8 * q^4 - 2 * q^5 - 4 * q^10 + 24 * q^14 - 24 * q^19 + 8 * q^20 - 4 * q^25 + 12 * q^26 - 24 * q^29 + 16 * q^31 + 16 * q^34 + 10 * q^35 + 32 * q^40 - 16 * q^41 - 20 * q^44 - 32 * q^46 - 40 * q^49 + 40 * q^50 + 8 * q^55 - 84 * q^56 - 4 * q^59 + 16 * q^61 + 16 * q^64 - 30 * q^65 + 16 * q^70 + 56 * q^71 - 40 * q^74 - 64 * q^76 - 16 * q^79 - 52 * q^80 - 64 * q^85 + 48 * q^86 - 16 * q^89 + 8 * q^91 - 32 * q^94 + 22 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.248840	−	0.143668i	0.175957	−	0.101589i	−0.409435	−	0.912339i	$-0.634274\pi$
$2$	0.248840	−	0.143668i	0.175957	−	0.101589i	0.585392	+	0.810751i	$0.300941\pi$
$3$		0			0
$3$		0			0
$4$	−0.958719	+	1.66055i	−0.479360	+	0.830275i
$5$	−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
$8$			1.12562i			0.397967i
$9$		0			0
$10$	−0.608495	−	0.206261i	−0.192423	−	0.0652254i
$11$	−1.66520	+	2.88421i	−0.502076	+	0.869621i	0.497921	+	0.867222i	$0.334097\pi$
$11$	−1.66520	+	2.88421i	−0.502076	+	0.869621i	−0.999997	+	0.00239862i	$0.999236\pi$
$12$		0			0
$13$			4.54754i			1.26126i	0.776083	+	0.630630i	$0.217204\pi$
$13$			4.54754i			1.26126i	−0.776083	+	0.630630i	$0.782796\pi$
$14$	0.622139	+	0.436894i	0.166274	+	0.116765i
$15$		0			0
$16$	−1.75572	−	3.04100i	−0.438931	−	0.760250i
$17$	4.80431	+	2.77377i	1.16522	+	0.672738i	0.952549	−	0.304386i	$-0.0984514\pi$
$17$	4.80431	+	2.77377i	1.16522	+	0.672738i	0.212668	+	0.977125i	$0.431785\pi$
$18$		0			0
$19$	−0.828617	−	1.43521i	−0.190098	−	0.329259i	0.755185	−	0.655512i	$-0.227547\pi$
$19$	−0.828617	−	1.43521i	−0.190098	−	0.329259i	−0.945282	+	0.326253i	$0.894214\pi$
$20$	4.20477	−	0.838284i	0.940216	−	0.187446i
$21$		0			0
$22$			0.956942i			0.204021i
$23$	−6.61094	+	3.81683i	−1.37848	+	0.795864i	−0.991976	−	0.126425i	$-0.959650\pi$
$23$	−6.61094	+	3.81683i	−1.37848	+	0.795864i	−0.386500	+	0.922289i	$0.626316\pi$
$24$		0			0
$25$	−0.648315	+	4.95779i	−0.129663	+	0.991558i
$26$	0.653336	+	1.13161i	0.128130	+	0.221927i
$27$		0			0
$28$	−5.05315	−	0.449051i	−0.954956	−	0.0848627i
$29$	−0.118657			−0.0220341			−0.0110170	−	0.999939i	$-0.503507\pi$
$29$	−0.118657			−0.0220341			−0.0110170	+	0.999939i	$0.503507\pi$
$30$		0			0
$31$	3.13010	−	5.42150i	0.562183	−	0.973729i	−0.435123	−	0.900371i	$-0.643295\pi$
$31$	3.13010	−	5.42150i	0.562183	−	0.973729i	0.997306	−	0.0733583i	$-0.0233717\pi$
$32$	−2.82342	−	1.63010i	−0.499115	−	0.288164i
$33$		0			0
$34$	1.59401			0.273370
$35$	2.38772	−	5.41284i	0.403599	−	0.914936i
$36$		0			0
$37$	6.71665	−	3.87786i	1.10421	−	0.637516i	0.166887	−	0.985976i	$-0.446628\pi$
$37$	6.71665	−	3.87786i	1.10421	−	0.637516i	0.937324	+	0.348460i	$0.113295\pi$
$38$	−0.412386	−	0.238091i	−0.0668979	−	0.0386235i
$39$		0			0
$40$	1.89163	−	1.66037i	0.299093	−	0.262528i
$41$	−0.0701896			−0.0109618			−0.00548089	−	0.999985i	$-0.501745\pi$
$41$	−0.0701896			−0.0109618			−0.00548089	+	0.999985i	$0.501745\pi$
$42$		0			0
$43$		−	2.92981i		−	0.446792i	−0.974728	−	0.223396i	$-0.928286\pi$
$43$		−	2.92981i		−	0.446792i	0.974728	−	0.223396i	$-0.0717143\pi$
$44$	−3.19291	−	5.53029i	−0.481350	−	0.833722i
$45$		0			0
$46$	−1.09671	+	1.89956i	−0.161701	+	0.280075i
$47$	5.53029	−	3.19291i	0.806675	−	0.465734i	−0.0391247	−	0.999234i	$-0.512457\pi$
$47$	5.53029	−	3.19291i	0.806675	−	0.465734i	0.845800	+	0.533500i	$0.179124\pi$
$48$		0			0
$49$	−4.51415	+	5.35000i	−0.644879	+	0.764285i
$50$	0.550949	+	1.32684i	0.0779159	+	0.187643i
$51$		0			0
$52$	−7.55142	−	4.35981i	−1.04719	−	0.604597i
$53$	−0.640682	−	0.369898i	−0.0880044	−	0.0508094i	0.455352	−	0.890311i	$-0.349513\pi$
$53$	−0.640682	−	0.369898i	−0.0880044	−	0.0508094i	−0.543356	+	0.839502i	$0.682847\pi$
$54$		0			0
$55$	7.30326	−	1.45601i	0.984772	−	0.196329i
$56$	−2.70080	+	1.25492i	−0.360910	+	0.167695i
$57$		0			0
$58$	−0.0295266	+	0.0170472i	−0.00387704	+	0.00223841i
$59$	0.815051	−	1.41171i	0.106111	−	0.183789i	−0.808081	−	0.589072i	$-0.799494\pi$
$59$	0.815051	−	1.41171i	0.106111	−	0.183789i	0.914191	+	0.405283i	$0.132827\pi$
$60$		0			0
$61$	3.65901	+	6.33759i	0.468488	+	0.811446i	0.999351	−	0.0360120i	$-0.0114655\pi$
$61$	3.65901	+	6.33759i	0.468488	+	0.811446i	−0.530863	+	0.847458i	$0.678132\pi$
$62$		−	1.79878i		−	0.228445i
$63$		0			0
$64$	6.08612			0.760765
$65$	7.64225	−	6.70796i	0.947904	−	0.832020i
$66$		0			0
$67$	−2.62934	−	1.51805i	−0.321224	−	0.185459i	0.330714	−	0.943731i	$-0.392711\pi$
$67$	−2.62934	−	1.51805i	−0.321224	−	0.185459i	−0.651938	+	0.758272i	$0.726044\pi$
$68$	−9.21197	+	5.31853i	−1.11712	+	0.644967i
$69$		0			0
$70$	−0.183490	−	1.68997i	−0.0219312	−	0.201990i
$71$	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	0.614588	−	0.788849i	$-0.289322\pi$
$73$	2.03961	+	1.17757i	0.238718	+	0.137824i	−0.375869	+	0.926673i	$0.622656\pi$
$74$	1.11425	−	1.92993i	0.129529	−	0.224350i
$75$		0			0
$76$	3.17764			0.364501
$77$	−8.77681	−	0.779956i	−1.00021	−	0.0888843i
$78$		0			0
$79$	−5.97016	−	10.3406i	−0.671696	−	1.16341i	−0.977423	−	0.211292i	$-0.932233\pi$
$79$	−5.97016	−	10.3406i	−0.671696	−	1.16341i	0.305727	−	0.952119i	$-0.401101\pi$
$80$	−2.52065	+	7.43623i	−0.281817	+	0.831396i
$81$		0			0
$82$	−0.0174660	+	0.0100840i	−0.00192880	+	0.00111359i
$83$			1.22411i			0.134363i	0.997741	+	0.0671817i	$0.0214007\pi$
$83$			1.22411i			0.134363i	−0.997741	+	0.0671817i	$0.978599\pi$
$84$		0			0
$85$	−2.42533	−	12.1653i	−0.263064	−	1.31951i
$86$	−0.420920	−	0.729054i	−0.0453889	−	0.0786160i
$87$		0			0
$88$	−3.24652	−	1.87438i	−0.346080	−	0.199810i
$89$	6.50007	+	11.2585i	0.689006	+	1.19339i	0.972160	+	0.234319i	$0.0752862\pi$
$89$	6.50007	+	11.2585i	0.689006	+	1.19339i	−0.283153	+	0.959075i	$0.591381\pi$
$90$		0			0
$91$	−10.9113	+	5.06990i	−1.14382	+	0.531470i
$92$		−	14.6371i		−	1.52602i
$93$		0			0
$94$	0.917438	−	1.58905i	0.0946265	−	0.163898i
$95$	−1.18963	+	3.50954i	−0.122053	+	0.360072i
$96$		0			0
$97$		−	3.04306i		−	0.308976i	−0.987995	−	0.154488i	$-0.950627\pi$
$97$		−	3.04306i		−	0.308976i	0.987995	−	0.154488i	$-0.0493728\pi$
$98$	−0.354679	+	1.97983i	−0.0358280	+	0.199993i
$99$		0			0
$100$	−7.61111	−	5.82969i	−0.761111	−	0.582969i
$101$	8.01983	−	13.8907i	0.798002	−	1.38218i	−0.122913	−	0.992417i	$-0.539224\pi$
$101$	8.01983	−	13.8907i	0.798002	−	1.38218i	0.920915	−	0.389763i	$-0.127443\pi$
$102$		0			0
$103$	−4.58293	+	2.64596i	−0.451570	+	0.260714i	−0.708493	−	0.705718i	$-0.750625\pi$
$103$	−4.58293	+	2.64596i	−0.451570	+	0.260714i	0.256923	+	0.966432i	$0.417291\pi$
$104$	−5.11880			−0.501940
$105$		0			0
$106$	−0.212570			−0.0206466
$107$	−4.47018	+	2.58086i	−0.432148	+	0.249501i	−0.700261	−	0.713886i	$-0.746933\pi$
$107$	−4.47018	+	2.58086i	−0.432148	+	0.249501i	0.268113	+	0.963387i	$0.413600\pi$
$108$		0			0
$109$	1.62043	−	2.80668i	0.155209	−	0.268831i	−0.777926	−	0.628356i	$-0.783728\pi$
$109$	1.62043	−	2.80668i	0.155209	−	0.268831i	0.933135	+	0.359525i	$0.117061\pi$
$110$	1.60816	−	1.41156i	0.153332	−	0.134587i
$111$		0			0
$112$	5.33915	−	7.60297i	0.504503	−	0.718413i
$113$			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
$116$	0.113759	−	0.197036i	0.0105622	−	0.0182943i
$117$		0			0
$118$		−	0.468387i		−	0.0431185i
$119$	−1.29920	+	14.6198i	−0.119097	+	1.34019i
$120$		0			0
$121$	−0.0457629	−	0.0792637i	−0.00416027	−	0.00720579i
$122$	1.82102	+	1.05136i	0.164867	+	0.0951861i
$123$		0			0
$124$	6.00178	+	10.3954i	0.538976	+	0.933533i
$125$	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	$0.737568\pi$
$128$	7.16131	−	4.13458i	0.632976	−	0.365449i
$129$		0			0
$130$	0.937979	−	2.76715i	0.0822662	−	0.242696i
$131$	−2.64893	−	4.58808i	−0.231438	−	0.400862i	0.726794	−	0.686856i	$-0.241010\pi$
$131$	−2.64893	−	4.58808i	−0.231438	−	0.400862i	−0.958231	+	0.285994i	$0.907676\pi$
$132$		0			0
$133$	2.51982	−	3.58824i	0.218496	−	0.311140i
$134$	−0.872379			−0.0753621
$135$		0			0
$136$	−3.12221	+	5.40783i	−0.267727	+	0.463718i
$137$	12.8779	+	7.43507i	1.10023	+	0.635221i	0.936283	−	0.351247i	$-0.114242\pi$
$137$	12.8779	+	7.43507i	1.10023	+	0.635221i	0.163952	+	0.986468i	$0.447576\pi$
$138$		0			0
$139$	9.51685			0.807209			0.403605	−	0.914934i	$-0.367757\pi$
$139$	9.51685			0.807209			0.403605	+	0.914934i	$0.367757\pi$
$140$	6.69913	+	9.15432i	0.566180	+	0.773681i
$141$		0			0
$142$	0.938247	−	0.541697i	0.0787359	−	0.0454582i
$143$	−13.1160	−	7.57255i	−1.09682	−	0.633249i
$144$		0			0
$145$	0.175028	+	0.199406i	0.0145353	+	0.0165598i
$146$	0.676716			0.0560054
$147$		0			0
$148$			14.8711i			1.22240i
$149$	−5.68502	−	9.84675i	−0.465735	−	0.806677i	0.533499	−	0.845801i	$-0.320877\pi$
$149$	−5.68502	−	9.84675i	−0.465735	−	0.806677i	−0.999234	+	0.0391236i	$0.987543\pi$
$150$		0			0
$151$	−4.47016	+	7.74255i	−0.363777	+	0.630080i	−0.988579	−	0.150703i	$-0.951846\pi$
$151$	−4.47016	+	7.74255i	−0.363777	+	0.630080i	0.624802	+	0.780783i	$0.285180\pi$
$152$	1.61550	−	0.932708i	0.131034	−	0.0756526i
$153$		0			0
$154$	−2.29608	+	1.06686i	−0.185023	+	0.0859701i
$155$	−13.7281	+	2.73690i	−1.10267	+	0.219833i
$156$		0			0
$157$	2.89800	+	1.67316i	0.231286	+	0.133533i	0.611165	−	0.791503i	$-0.290701\pi$
$157$	2.89800	+	1.67316i	0.231286	+	0.133533i	−0.379879	+	0.925036i	$0.624035\pi$
$158$	−2.97123	−	1.71544i	−0.236379	−	0.136473i
$159$		0			0
$160$	1.42533	+	7.14934i	0.112682	+	0.565205i
$161$	−16.5284	−	11.6070i	−1.30262	−	0.914758i
$162$		0			0
$163$	−13.6450	+	7.87793i	−1.06876	+	0.617047i	−0.927842	−	0.372974i	$-0.878338\pi$
$163$	−13.6450	+	7.87793i	−1.06876	+	0.617047i	−0.140916	+	0.990022i	$0.545005\pi$
$164$	0.0672922	−	0.116553i	0.00525463	−	0.00910129i
$165$		0			0
$166$	0.175865	+	0.304608i	0.0136498	+	0.0236421i
$167$			22.5942i			1.74839i	0.485577	+	0.874194i	$0.338610\pi$
$167$			22.5942i			1.74839i	−0.485577	+	0.874194i	$0.661390\pi$
$168$		0			0
$169$	−7.68012			−0.590779
$170$	−2.35128	−	2.67877i	−0.180335	−	0.205452i
$171$		0			0
$172$	4.86510	+	2.80887i	0.370960	+	0.214174i
$173$	7.38391	−	4.26310i	0.561388	−	0.324118i	−0.192314	−	0.981333i	$-0.561599\pi$
$173$	7.38391	−	4.26310i	0.561388	−	0.324118i	0.753703	+	0.657216i	$0.228266\pi$
$174$		0			0
$175$	−12.6185	+	3.97171i	−0.953866	+	0.300233i
$176$	11.6945			0.881506
$177$		0			0
$178$	3.23496	+	1.86770i	0.242470	+	0.139990i
$179$	5.89031	−	10.2023i	0.440262	−	0.762557i	−0.557446	−	0.830213i	$-0.688219\pi$
$179$	5.89031	−	10.2023i	0.440262	−	0.762557i	0.997709	+	0.0676564i	$0.0215522\pi$
$180$		0			0
$181$	9.08967			0.675630			0.337815	−	0.941213i	$-0.390312\pi$
$181$	9.08967			0.675630			0.337815	+	0.941213i	$0.390312\pi$
$182$	−1.98679	+	2.82920i	−0.147271	+	0.209714i
$183$		0			0
$184$	−4.29630	−	7.44141i	−0.316727	−	0.548588i
$185$	−16.4244	−	5.56736i	−1.20755	−	0.409320i
$186$		0			0
$187$	−16.0002	+	9.23775i	−1.17005	+	0.675531i
$188$			12.2444i			0.893016i
$189$		0			0
$190$	0.208182	+	1.04423i	0.0151031	+	0.0757562i
$191$	10.2478	+	17.7498i	0.741507	+	1.28433i	0.951809	+	0.306692i	$0.0992220\pi$
$191$	10.2478	+	17.7498i	0.741507	+	1.28433i	−0.210302	+	0.977637i	$0.567445\pi$
$192$		0			0
$193$	7.39842	+	4.27148i	0.532550	+	0.307468i	0.742054	−	0.670340i	$-0.233852\pi$
$193$	7.39842	+	4.27148i	0.532550	+	0.307468i	−0.209504	+	0.977808i	$0.567185\pi$
$194$	−0.437190	−	0.757235i	−0.0313884	−	0.0543663i
$195$		0			0
$196$	−4.55613	−	12.6251i	−0.325438	−	0.901794i
$197$		−	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	$-0.790433\pi$
$199$	1.89549	−	3.28309i	0.134368	−	0.232732i	0.925356	+	0.379100i	$0.123766\pi$
$200$	−5.58059	−	0.729756i	−0.394607	−	0.0516016i
$201$		0			0
$202$		−	4.60877i		−	0.324272i
$203$	−0.132287	−	0.284705i	−0.00928471	−	0.0199824i
$204$		0			0
$205$	0.103535	+	0.117955i	0.00723119	+	0.00823836i
$206$	−0.760278	+	1.31684i	−0.0529711	+	0.0917486i
$207$		0			0
$208$	13.8291	−	7.98422i	0.958874	−	0.553606i
$209$	5.51924			0.381774
$210$		0			0
$211$	−0.114416			−0.00787674			−0.00393837	−	0.999992i	$-0.501254\pi$
$211$	−0.114416			−0.00787674			−0.00393837	+	0.999992i	$0.501254\pi$
$212$	1.22847	−	0.709256i	0.0843715	−	0.0487119i
$213$		0			0
$214$	−0.741573	+	1.28444i	−0.0506929	+	0.0878026i
$215$	−4.92361	+	4.32169i	−0.335788	+	0.294737i
$216$		0			0
$217$	16.4979	+	1.46610i	1.11995	+	0.0995253i
$218$		−	0.931218i		−	0.0630700i
$219$		0			0
$220$	−4.58399	+	13.5233i	−0.309053	+	0.911744i
$221$	−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	$-0.0848431\pi$
$224$	0.763518	−	8.59183i	0.0510147	−	0.574066i
$225$		0			0
$226$	1.81895	+	3.15051i	0.120995	+	0.209569i
$227$	7.77575	+	4.48933i	0.516095	+	0.297967i	0.735335	−	0.677703i	$-0.237025\pi$
$227$	7.77575	+	4.48933i	0.516095	+	0.297967i	−0.219241	+	0.975671i	$0.570358\pi$
$228$		0			0
$229$	−2.54306	−	4.40471i	−0.168050	−	0.291071i	0.769684	−	0.638425i	$-0.220414\pi$
$229$	−2.54306	−	4.40471i	−0.168050	−	0.291071i	−0.937734	+	0.347354i	$0.887080\pi$
$230$	4.80999	−	0.958942i	0.317161	−	0.0632308i
$231$		0			0
$232$		−	0.133563i		−	0.00876883i
$233$	18.8952	−	10.9091i	1.23786	−	0.714681i	0.269207	−	0.963082i	$-0.413239\pi$
$233$	18.8952	−	10.9091i	1.23786	−	0.714681i	0.968657	+	0.248401i	$0.0799052\pi$
$234$		0			0
$235$	−13.5233	−	4.58399i	−0.882166	−	0.299027i
$236$	1.56281	+	2.70687i	0.101730	+	0.176202i
$237$		0			0
$238$	1.77710	+	3.82465i	0.115193	+	0.247915i
$239$	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	−0.154070	−	0.988060i	$-0.549238\pi$
$241$	12.0879	−	20.9368i	0.778650	−	1.34866i	0.932720	−	0.360601i	$-0.117428\pi$
$242$	−0.0227753	−	0.0131493i	−0.00146405	−	0.000845271i
$243$		0			0
$244$	−14.0319			−0.898297
$245$	15.6495	−	0.305506i	0.999810	−	0.0195180i
$246$		0			0
$247$	6.52666	−	3.76817i	0.415281	−	0.239763i
$248$	6.10255	+	3.52331i	0.387512	+	0.223730i
$249$		0			0
$250$	1.41709	−	2.88307i	0.0896249	−	0.182341i
$251$	−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
$254$	2.37735	+	4.11769i	0.149168	+	0.258367i
$255$		0			0
$256$	−4.89810	+	8.48376i	−0.306131	+	0.530235i
$257$	−6.35139	+	3.66697i	−0.396189	+	0.228740i	−0.684838	−	0.728695i	$-0.740127\pi$
$257$	−6.35139	+	3.66697i	−0.396189	+	0.228740i	0.288650	+	0.957435i	$0.406794\pi$
$258$		0			0
$259$	16.7927	+	11.7926i	1.04345	+	0.732755i
$260$	3.81213	+	19.1214i	0.236418	+	1.18586i
$261$		0			0
$262$	−1.31832	−	0.761132i	−0.0814460	−	0.0470229i
$263$	−8.21661	−	4.74386i	−0.506658	−	0.292519i	0.224801	−	0.974405i	$-0.427827\pi$
$263$	−8.21661	−	4.74386i	−0.506658	−	0.292519i	−0.731459	+	0.681886i	$0.761160\pi$
$264$		0			0
$265$	0.323431	+	1.62231i	0.0198682	+	0.0996575i
$266$	0.111519	−	1.25492i	0.00683766	−	0.0769438i
$267$		0			0
$268$	5.04159	−	2.91076i	0.307964	−	0.177803i
$269$	−8.02423	+	13.8984i	−0.489246	+	0.847399i	−0.999923	−	0.0123733i	$-0.996061\pi$
$269$	−8.02423	+	13.8984i	−0.489246	+	0.847399i	0.510677	+	0.859772i	$0.329395\pi$
$270$		0			0
$271$	−12.0845	−	20.9309i	−0.734080	−	1.27146i	−0.955126	−	0.296201i	$-0.904280\pi$
$271$	−12.0845	−	20.9309i	−0.734080	−	1.27146i	0.221045	−	0.975264i	$-0.429053\pi$
$272$		−	19.4799i		−	1.18114i
$273$		0			0
$274$	4.27272			0.258125
$275$	−13.2197	−	10.1256i	−0.797179	−	0.610595i
$276$		0			0
$277$	−20.1071	−	11.6088i	−1.20812	−	0.697508i	−0.245771	−	0.969328i	$-0.579041\pi$
$277$	−20.1071	−	11.6088i	−1.20812	−	0.697508i	−0.962348	+	0.271820i	$0.912374\pi$
$278$	2.36818	−	1.36727i	0.142034	−	0.0820032i
$279$		0			0
$280$	6.09280	+	2.68767i	0.364114	+	0.160619i
$281$	−12.4472			−0.742538			−0.371269	−	0.928525i	$-0.621077\pi$
$281$	−12.4472			−0.742538			−0.371269	+	0.928525i	$0.621077\pi$
$282$		0			0
$283$	−7.50649	−	4.33388i	−0.446215	−	0.257622i	0.260016	−	0.965604i	$-0.416272\pi$
$283$	−7.50649	−	4.33388i	−0.446215	−	0.257622i	−0.706230	+	0.707982i	$0.749606\pi$
$284$	−3.61483	+	6.26107i	−0.214501	+	0.371526i
$285$		0			0
$286$	−4.35173			−0.257323
$287$	−0.0782520	−	0.168412i	−0.00461907	−	0.00994107i
$288$		0			0
$289$	6.88760	+	11.9297i	0.405153	+	0.701746i
$290$	0.0722022	+	0.0244743i	0.00423986	+	0.00143718i
$291$		0			0
$292$	−3.91083	+	2.25792i	−0.228864	+	0.132135i
$293$		−	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
$296$	4.36500	+	7.56040i	0.253710	+	0.439439i
$297$		0			0
$298$	−2.82932	−	1.63351i	−0.163898	−	0.0946267i
$299$	−17.3572	−	30.0635i	−1.00379	−	1.73862i
$300$		0			0
$301$	7.02976	−	3.26634i	0.405189	−	0.188269i
$302$			2.56888i			0.147822i
$303$		0			0
$304$	−2.90964	+	5.03965i	−0.166879	+	0.289044i
$305$	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	$0.979577\pi$
$308$	9.70965	−	13.8266i	0.553259	−	0.787842i
$309$		0			0
$310$	−3.02289	+	2.65333i	−0.171689	+	0.150699i
$311$	14.2994	−	24.7672i	0.810843	−	1.40442i	−0.101432	−	0.994842i	$-0.532343\pi$
$311$	14.2994	−	24.7672i	0.810843	−	1.40442i	0.912275	−	0.409578i	$-0.134324\pi$
$312$		0			0
$313$	11.5429	−	6.66427i	0.652441	−	0.376687i	−0.136950	−	0.990578i	$-0.543730\pi$
$313$	11.5429	−	6.66427i	0.652441	−	0.376687i	0.789391	+	0.613891i	$0.210397\pi$
$314$	0.961518			0.0542616
$315$		0			0
$316$	22.8948			1.28794
$317$	−25.2815	+	14.5963i	−1.41995	+	0.819808i	−0.996294	−	0.0860147i	$-0.972587\pi$
$317$	−25.2815	+	14.5963i	−1.41995	+	0.819808i	−0.423656	+	0.905823i	$0.639253\pi$
$318$		0			0
$319$	0.197587	−	0.342231i	0.0110628	−	0.0191613i
$320$	−8.97747	−	10.2279i	−0.501856	−	0.571755i
$321$		0			0
$322$	−5.78047	−	0.513685i	−0.322133	−	0.0286266i
$323$		−	9.19357i		−	0.511544i
$324$		0			0
$325$	−22.5458	−	2.94824i	−1.25061	−	0.163539i
$326$	−2.26361	+	3.92069i	−0.125370	+	0.217147i
$327$		0			0
$328$		−	0.0790069i		−	0.00436243i
$329$	13.8266	+	9.70965i	0.762283	+	0.535310i
$330$		0			0
$331$	12.4457	+	21.5566i	0.684080	+	1.18486i	0.973725	+	0.227727i	$0.0731293\pi$
$331$	12.4457	+	21.5566i	0.684080	+	1.18486i	−0.289646	+	0.957134i	$0.593537\pi$
$332$	−2.03270	−	1.17358i	−0.111559	−	0.0644084i
$333$		0			0
$334$	3.24605	+	5.62233i	0.177616	+	0.307640i
$335$	1.32735	+	6.65789i	0.0725209	+	0.363759i
$336$		0			0
$337$			4.72659i			0.257474i	0.991679	+	0.128737i	$0.0410923\pi$
$337$			4.72659i			0.257474i	−0.991679	+	0.128737i	$0.958908\pi$
$338$	−1.91112	+	1.10339i	−0.103951	+	0.0600164i
$339$		0			0
$340$	22.5263	+	7.63570i	1.22166	+	0.414104i
$341$	10.4245	+	18.0557i	0.564517	+	0.977772i
$342$		0			0
$343$	−17.8694	−	4.86668i	−0.964857	−	0.262776i
$344$	3.29785			0.177808
$345$		0			0
$346$	1.22494	−	2.12166i	0.0658533	−	0.114061i
$347$	−12.2615	−	7.07915i	−0.658229	−	0.380029i	0.133373	−	0.991066i	$-0.457419\pi$
$347$	−12.2615	−	7.07915i	−0.658229	−	0.380029i	−0.791602	+	0.611037i	$0.790753\pi$
$348$		0			0
$349$	−5.04930			−0.270283			−0.135141	−	0.990826i	$-0.543149\pi$
$349$	−5.04930			−0.270283			−0.135141	+	0.990826i	$0.543149\pi$
$350$	−2.56937	+	2.80119i	−0.137339	+	0.149730i
$351$		0			0
$352$	9.40310	−	5.42888i	0.501187	−	0.289360i
$353$	13.9417	+	8.04924i	0.742042	+	0.428418i	0.822811	−	0.568315i	$-0.192404\pi$
$353$	13.9417	+	8.04924i	0.742042	+	0.428418i	−0.0807694	+	0.996733i	$0.525738\pi$
$354$		0			0
$355$	−5.56174	−	6.33638i	−0.295186	−	0.336300i
$356$	−24.9270			−1.32113
$357$		0			0
$358$		−	3.38499i		−	0.178902i
$359$	−0.153241	−	0.265421i	−0.00808776	−	0.0140084i	0.861953	−	0.506988i	$-0.169241\pi$
$359$	−0.153241	−	0.265421i	−0.00808776	−	0.0140084i	−0.870041	+	0.492979i	$0.835908\pi$
$360$		0			0
$361$	8.12679	−	14.0760i	0.427726	−	0.740843i
$362$	2.26188	−	1.30589i	0.118882	−	0.0686363i
$363$		0			0
$364$	2.04208	−	22.9794i	0.107034	−	1.20445i
$365$	−1.02964	−	5.16461i	−0.0538940	−	0.270328i
$366$		0			0
$367$	−20.4813	−	11.8249i	−1.06911	−	0.617253i	−0.141174	−	0.989985i	$-0.545088\pi$
$367$	−20.4813	−	11.8249i	−1.06911	−	0.617253i	−0.927939	+	0.372732i	$0.878421\pi$
$368$	23.2140	+	13.4026i	1.21011	+	0.698658i
$369$		0			0
$370$	−4.88690	+	0.974276i	−0.254058	+	0.0506502i
$371$	0.173255	−	1.94963i	0.00899496	−	0.101220i
$372$		0			0
$373$	16.3140	−	9.41887i	0.844705	−	0.487691i	−0.0141557	−	0.999900i	$-0.504506\pi$
$373$	16.3140	−	9.41887i	0.844705	−	0.487691i	0.858861	+	0.512209i	$0.171173\pi$
$374$	−2.65434	+	4.59744i	−0.137252	+	0.237728i
$375$		0			0
$376$	3.59401	+	6.22500i	0.185347	+	0.321030i
$377$		−	0.539598i		−	0.0277907i
$378$		0			0
$379$	−14.2534			−0.732147			−0.366074	−	0.930586i	$-0.619298\pi$
$379$	−14.2534			−0.732147			−0.366074	+	0.930586i	$0.619298\pi$
$380$	−4.68726	−	5.34010i	−0.240451	−	0.273941i
$381$		0			0
$382$	5.10014	+	2.94457i	0.260946	+	0.150657i
$383$	21.6995	−	12.5282i	1.10879	−	0.640161i	0.170276	−	0.985396i	$-0.445534\pi$
$383$	21.6995	−	12.5282i	1.10879	−	0.640161i	0.938516	+	0.345235i	$0.112201\pi$
$384$		0			0
$385$	11.6357	+	15.9001i	0.593010	+	0.810345i
$386$	2.45470			0.124941
$387$		0			0
$388$	5.05315	+	2.91744i	0.256535	+	0.148110i
$389$	6.73590	−	11.6669i	0.341524	−	0.591536i	−0.643192	−	0.765705i	$-0.722390\pi$
$389$	6.73590	−	11.6669i	0.341524	−	0.591536i	0.984716	+	0.174169i	$0.0557238\pi$
$390$		0			0
$391$	−42.3480			−2.14163
$392$	−6.02206	−	5.08122i	−0.304160	−	0.256640i
$393$		0			0
$394$	−1.98385	−	3.43613i	−0.0999449	−	0.173110i
$395$	−8.57123	+	25.2862i	−0.431265	+	1.27229i
$396$		0			0
$397$	15.9768	−	9.22418i	0.801850	−	0.462948i	−0.0422675	−	0.999106i	$-0.513458\pi$
$397$	15.9768	−	9.22418i	0.801850	−	0.462948i	0.844118	+	0.536158i	$0.180125\pi$
$398$		−	1.08929i		−	0.0546010i
$399$		0			0
$400$	16.2149	−	6.73298i	0.810745	−	0.336649i
$401$	12.7093	+	22.0131i	0.634670	+	1.09928i	0.986585	+	0.163249i	$0.0521973\pi$
$401$	12.7093	+	22.0131i	0.634670	+	1.09928i	−0.351915	+	0.936032i	$0.614469\pi$
$402$		0			0
$403$	24.6545	+	14.2343i	1.22813	+	0.709059i
$404$	15.3775	+	26.6346i	0.765060	+	1.32512i
$405$		0			0
$406$	−0.0738212	−	0.0518406i	−0.00366368	−	0.00257281i
$407$			25.8296i			1.28033i
$408$		0			0
$409$	−9.36556	+	16.2216i	−0.463097	+	0.802108i	−0.999113	−	0.0420997i	$-0.986595\pi$
$409$	−9.36556	+	16.2216i	−0.463097	+	0.802108i	0.536016	+	0.844208i	$0.319929\pi$
$410$	0.0427100	+	0.0144774i	0.00210930	+	0.000714986i
$411$		0			0
$412$		−	10.1469i		−	0.499903i
$413$	4.29592	+	0.381759i	0.211388	+	0.0187851i
$414$		0			0
$415$	2.05714	−	1.80565i	0.100981	−	0.0886360i
$416$	7.41296	−	12.8396i	0.363450	−	0.629514i
$417$		0			0
$418$	1.37341	−	0.792938i	0.0671756	−	0.0387839i
$419$	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	$0.627920\pi$
$422$	−0.0284714	+	0.0164380i	−0.00138596	+	0.000800187i
$423$		0			0
$424$	0.416364	−	0.721164i	0.0202204	−	0.0350228i
$425$	−16.8665	+	22.0205i	−0.818144	+	1.06815i
$426$		0			0
$427$	−11.1271	+	15.8450i	−0.538476	+	0.766791i
$428$		−	9.89727i		−	0.478403i
$429$		0			0
$430$	−0.604305	+	1.78277i	−0.0291422	+	0.0859730i
$431$	18.3063	−	31.7075i	0.881784	−	1.52729i	0.0324277	−	0.999474i	$-0.489676\pi$
$431$	18.3063	−	31.7075i	0.881784	−	1.52729i	0.849356	−	0.527820i	$-0.176991\pi$
$432$		0			0
$433$			18.0047i			0.865252i	0.901574	+	0.432626i	$0.142413\pi$
$433$			18.0047i			0.865252i	−0.901574	+	0.432626i	$0.857587\pi$
$434$	4.31598	−	2.00540i	0.207174	−	0.0962622i
$435$		0			0
$436$	3.10708	+	5.38163i	0.148802	+	0.257733i
$437$	10.9559	+	6.32538i	0.524090	+	0.302584i
$438$		0			0
$439$	−9.68731	−	16.7789i	−0.462350	−	0.800814i	0.536727	−	0.843756i	$-0.319660\pi$
$439$	−9.68731	−	16.7789i	−0.462350	−	0.800814i	−0.999078	+	0.0429418i	$0.986327\pi$
$440$	1.63892	+	8.22070i	0.0781324	+	0.391907i
$441$		0			0
$442$			7.24881i			0.344791i
$443$	−14.2396	+	8.22121i	−0.676542	+	0.390602i	−0.798551	−	0.601927i	$-0.794400\pi$
$443$	−14.2396	+	8.22121i	−0.676542	+	0.390602i	0.122009	+	0.992529i	$0.461066\pi$
$444$		0			0
$445$	9.33201	−	27.5306i	0.442380	−	1.30507i
$446$	−1.13020	−	1.95756i	−0.0535164	−	0.0926931i
$447$		0			0
$448$	6.78520	+	14.6030i	0.320571	+	0.689926i
$449$	−32.7245			−1.54436			−0.772182	−	0.635401i	$-0.780835\pi$
$449$	−32.7245			−1.54436			−0.772182	+	0.635401i	$0.780835\pi$
$450$		0			0
$451$	0.116880	−	0.202441i	0.00550365	−	0.00953259i
$452$	−21.0239	−	12.1381i	−0.988880	−	0.570930i
$453$		0			0
$454$	2.57989			0.121080
$455$	24.6151	+	10.8583i	1.15397	+	0.509043i
$456$		0			0
$457$	−32.4156	+	18.7152i	−1.51634	+	0.875459i	−0.516523	+	0.856273i	$0.672774\pi$
$457$	−32.4156	+	18.7152i	−1.51634	+	0.875459i	−0.999816	+	0.0191857i	$0.993893\pi$
$458$	−1.26563	−	0.730712i	−0.0591390	−	0.0341439i
$459$		0			0
$460$	−24.5979	+	21.5908i	−1.14688	+	1.00667i
$461$	−28.3604			−1.32088			−0.660438	−	0.750881i	$-0.729629\pi$
$461$	−28.3604			−1.32088			−0.660438	+	0.750881i	$0.729629\pi$
$462$		0			0
$463$			7.20833i			0.334999i	0.985872	+	0.167500i	$0.0535693\pi$
$463$			7.20833i			0.334999i	−0.985872	+	0.167500i	$0.946431\pi$
$464$	0.208329	+	0.360836i	0.00967143	+	0.0167514i
$465$		0			0
$466$	3.13458	−	5.42926i	0.145207	−	0.251506i
$467$	−10.4607	+	6.03950i	−0.484065	+	0.279475i	−0.722109	−	0.691779i	$-0.756827\pi$
$467$	−10.4607	+	6.03950i	−0.484065	+	0.279475i	0.238044	+	0.971254i	$0.423494\pi$
$468$		0			0
$469$	0.711033	−	8.00122i	0.0328325	−	0.369462i
$470$	−4.02372	+	0.802189i	−0.185601	+	0.0370022i
$471$		0			0
$472$	1.58905	+	0.917438i	0.0731419	+	0.0422285i
$473$	8.45018	+	4.87871i	0.388540	+	0.224323i
$474$		0			0
$475$	7.65266	−	3.17764i	0.351128	−	0.145800i
$476$	−23.0313	−	16.1737i	−1.05564	−	0.741319i
$477$		0			0
$478$	1.85362	−	1.07019i	0.0847827	−	0.0489493i
$479$	−10.0708	+	17.4432i	−0.460149	+	0.797001i	−0.998968	−	0.0454204i	$-0.985537\pi$
$479$	−10.0708	+	17.4432i	−0.460149	+	0.797001i	0.538819	+	0.842421i	$0.318871\pi$
$480$		0			0
$481$	17.6347	+	30.5443i	0.804075	+	1.39270i
$482$		−	6.94657i		−	0.316408i
$483$		0			0
$484$	0.175495			0.00797705
$485$	−5.11393	+	4.48874i	−0.232212	+	0.203823i
$486$		0			0
$487$	34.5887	+	19.9698i	1.56737	+	0.904919i	0.996475	+	0.0838930i	$0.0267354\pi$
$487$	34.5887	+	19.9698i	1.56737	+	0.904919i	0.570891	+	0.821026i	$0.306598\pi$
$488$	−7.13372	+	4.11866i	−0.322928	+	0.186443i
$489$		0			0
$490$	3.85033	−	2.32435i	0.173940	−	0.105004i
$491$	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
$494$	1.08273	−	1.87534i	0.0487143	−	0.0843757i
$495$		0			0
$496$	−21.9824			−0.987037
$497$	4.20358	+	9.04686i	0.188556	+	0.405807i
$498$		0			0
$499$	19.8929	+	34.4556i	0.890530	+	1.54244i	0.839241	+	0.543759i	$0.183000\pi$
$499$	19.8929	+	34.4556i	0.890530	+	1.54244i	0.0512890	+	0.998684i	$0.483667\pi$
$500$	1.43002	+	21.3899i	0.0639525	+	0.956584i
$501$		0			0
$502$	−1.49354	+	0.862295i	−0.0666599	+	0.0384861i
$503$		−	12.8734i		−	0.573995i	−0.957931	−	0.286997i	$-0.907343\pi$
$503$		−	12.8734i		−	0.573995i	0.957931	−	0.286997i	$-0.0926571\pi$
$504$		0			0
$505$	−35.1735	+	7.01237i	−1.56520	+	0.312046i
$506$	−3.65248	−	6.32628i	−0.162373	−	0.281238i
$507$		0			0
$508$	−27.4780	−	15.8644i	−1.21914	−	0.703871i
$509$	−16.6981	−	28.9219i	−0.740128	−	1.28194i	−0.952437	−	0.304737i	$-0.901431\pi$
$509$	−16.6981	−	28.9219i	−0.740128	−	1.28194i	0.212308	−	0.977203i	$-0.431902\pi$
$510$		0			0
$511$	−0.551558	+	6.20665i	−0.0243995	+	0.274566i
$512$			19.3531i			0.855296i
$513$		0			0
$514$	−1.05365	+	1.82498i	−0.0464746	+	0.0804965i
$515$	11.2068	+	3.79874i	0.493828	+	0.167392i
$516$		0			0
$517$			21.2673i			0.935335i
$518$	5.87290	+	0.521899i	0.258041	+	0.0229309i
$519$		0			0
$520$	7.55061	+	8.60227i	0.331116	+	0.377234i
$521$	6.77589	−	11.7362i	0.296857	−	0.514172i	−0.678558	−	0.734547i	$-0.737395\pi$
$521$	6.77589	−	11.7362i	0.296857	−	0.514172i	0.975415	+	0.220375i	$0.0707281\pi$
$522$		0			0
$523$	−17.5052	+	10.1066i	−0.765450	+	0.441933i	−0.831249	−	0.555900i	$-0.812374\pi$
$523$	−17.5052	+	10.1066i	−0.765450	+	0.441933i	0.0657991	+	0.997833i	$0.479040\pi$
$524$	10.1583			0.443768
$525$		0			0
$526$	−2.72616			−0.118866
$527$	30.0760	−	17.3644i	1.31013	−	0.756404i
$528$		0			0
$529$	17.6364	−	30.5471i	0.766798	−	1.32813i
$530$	0.313556	+	0.357228i	0.0136200	+	0.0155170i
$531$		0			0
$532$	3.54264	+	7.62441i	0.153593	+	0.330560i
$533$		−	0.319190i		−	0.0138257i
$534$		0			0
$535$	10.9310	+	3.70528i	0.472590	+	0.160193i
$536$	1.70875	−	2.95963i	0.0738066	−	0.127837i
$537$		0			0
$538$			4.61130i			0.198807i
$539$	−7.91354	−	21.9285i	−0.340860	−	0.944529i
$540$		0			0
$541$	16.4854	+	28.5535i	0.708762	+	1.22761i	0.965317	+	0.261082i	$0.0840794\pi$
$541$	16.4854	+	28.5535i	0.708762	+	1.22761i	−0.256554	+	0.966530i	$0.582587\pi$
$542$	−6.01421	−	3.47231i	−0.258332	−	0.149148i
$543$		0			0
$544$	−9.04306	−	15.6630i	−0.387718	−	0.671547i
$545$	−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	$-0.176452\pi$
$548$	−24.6926	+	14.2563i	−1.05482	+	0.608998i
$549$		0			0
$550$	−4.74432	−	0.620399i	−0.202298	−	0.0264539i
$551$	0.0983213	+	0.170297i	0.00418863	+	0.00725491i
$552$		0			0
$553$	18.1553	−	25.8532i	0.772041	−	1.09939i
$554$	−6.67127			−0.283435
$555$		0			0
$556$	−9.12399	+	15.8032i	−0.386943	+	0.670206i
$557$	20.7796	+	11.9971i	0.880460	+	0.508334i	0.870810	−	0.491620i	$-0.163595\pi$
$557$	20.7796	+	11.9971i	0.880460	+	0.508334i	0.00964963	+	0.999953i	$0.496928\pi$
$558$		0			0
$559$	13.3234			0.563521
$560$	−20.6526	+	2.24237i	−0.872732	+	0.0947575i
$561$		0			0
$562$	−3.09736	+	1.78826i	−0.130654	+	0.0754333i
$563$	−0.196151	−	0.113248i	−0.00826680	−	0.00477284i	0.495861	−	0.868402i	$-0.334853\pi$
$563$	−0.196151	−	0.113248i	−0.00826680	−	0.00477284i	−0.504128	+	0.863629i	$0.668186\pi$
$564$		0			0
$565$	21.2767	−	18.6756i	0.895119	−	0.785688i
$566$	−2.49056			−0.104686
$567$		0			0
$568$			4.24413i			0.178080i
$569$	6.40275	+	11.0899i	0.268417	+	0.464912i	0.968453	−	0.249195i	$-0.0801660\pi$
$569$	6.40275	+	11.0899i	0.268417	+	0.464912i	−0.700036	+	0.714108i	$0.746833\pi$
$570$		0			0
$571$	0.780149	−	1.35126i	0.0326482	−	0.0565484i	−0.849240	−	0.528008i	$-0.822939\pi$
$571$	0.780149	−	1.35126i	0.0326482	−	0.0565484i	0.881888	+	0.471459i	$0.156273\pi$
$572$	25.1492	−	14.5199i	1.05154	−	0.607107i
$573$		0			0
$574$	−0.0436677	−	0.0306655i	−0.00182265	−	0.00127995i
$575$	−14.6371	−	35.2502i	−0.610408	−	1.47003i
$576$		0			0
$577$	37.8018	+	21.8249i	1.57371	+	0.908581i	0.995709	+	0.0925443i	$0.0295000\pi$
$577$	37.8018	+	21.8249i	1.57371	+	0.908581i	0.578000	+	0.816037i	$0.303833\pi$
$578$	3.42782	+	1.97905i	0.142579	+	0.0823178i
$579$		0			0
$580$	−0.498926	+	0.0994684i	−0.0207168	+	0.00413020i
$581$	−2.93712	+	1.36472i	−0.121852	+	0.0566180i
$582$		0			0
$583$	2.13372	−	1.23191i	0.0883697	−	0.0510203i
$584$	−1.32550	+	2.29583i	−0.0548494	+	0.0950020i
$585$		0			0
$586$	−3.87994	−	6.72025i	−0.160279	−	0.277611i
$587$			13.6961i			0.565297i	0.959224	+	0.282648i	$0.0912129\pi$
$587$			13.6961i			0.565297i	−0.959224	+	0.282648i	$0.908787\pi$
$588$		0			0
$589$	−10.3746			−0.427479
$590$	−0.787135	+	0.690905i	−0.0324058	+	0.0284441i
$591$		0			0
$592$	−23.5852	−	13.6169i	−0.969344	−	0.559651i
$593$	−7.92838	+	4.57745i	−0.325579	+	0.187973i	−0.653877	−	0.756601i	$-0.726859\pi$
$593$	−7.92838	+	4.57745i	−0.325579	+	0.187973i	0.328297	+	0.944574i	$0.393525\pi$
$594$		0			0
$595$	26.4853	−	19.3820i	1.08579	−	0.794583i
$596$	21.8014			0.893018
$597$		0			0
$598$	−8.63833	−	4.98734i	−0.353247	−	0.203948i
$599$	−20.1368	+	34.8780i	−0.822767	+	1.42507i	0.0808467	+	0.996727i	$0.474238\pi$
$599$	−20.1368	+	34.8780i	−0.822767	+	1.42507i	−0.903614	+	0.428348i	$0.859096\pi$
$600$		0			0
$601$	−8.82450			−0.359959			−0.179980	−	0.983670i	$-0.557603\pi$
$601$	−8.82450			−0.359959			−0.179980	+	0.983670i	$0.557603\pi$
$602$	1.28002	−	1.82275i	0.0521696	−	0.0742897i
$603$		0			0
$604$	−8.57126	−	14.8459i	−0.348760	−	0.604070i
$605$	−0.0657008	+	0.193826i	−0.00267112	+	0.00788013i
$606$		0			0
$607$	24.3409	−	14.0532i	0.987966	−	0.570402i	0.0833003	−	0.996524i	$-0.473454\pi$
$607$	24.3409	−	14.0532i	0.987966	−	0.570402i	0.904666	+	0.426122i	$0.140121\pi$
$608$			5.40292i			0.219117i
$609$		0			0
$610$	−0.919292	−	4.61110i	−0.0372211	−	0.186698i
$611$	14.5199	+	25.1492i	0.587412	+	1.01743i
$612$		0			0
$613$	−1.83025	−	1.05670i	−0.0739232	−	0.0426796i	0.462583	−	0.886576i	$-0.346923\pi$
$613$	−1.83025	−	1.05670i	−0.0739232	−	0.0426796i	−0.536506	+	0.843896i	$0.680256\pi$
$614$	0.322795	+	0.559097i	0.0130269	+	0.0225633i
$615$		0			0
$616$	0.877935	−	9.87935i	0.0353730	−	0.398050i
$617$		−	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	$-0.928378\pi$
$619$	−7.31895	+	12.6768i	−0.294173	+	0.509523i	0.680619	+	0.732638i	$0.261711\pi$
$620$	8.61662	−	25.4201i	0.346052	−	1.02090i
$621$		0			0
$622$		−	8.21744i		−	0.329489i
$623$	−19.7667	+	28.1479i	−0.791937	+	1.12772i
$624$		0			0
$625$	−24.1594	−	6.42842i	−0.966375	−	0.257137i
$626$	1.91488	−	3.31668i	0.0765341	−	0.132561i
$627$		0			0
$628$	−5.55673	+	3.20818i	−0.221738	+	0.128020i
$629$	43.0252			1.71553
$630$		0			0
$631$	12.1251			0.482692			0.241346	−	0.970439i	$-0.422411\pi$
$631$	12.1251			0.482692			0.241346	+	0.970439i	$0.422411\pi$
$632$	11.6396	−	6.72014i	0.462999	−	0.267313i
$633$		0			0
$634$	−4.19403	+	7.26428i	−0.166566	+	0.288501i
$635$	27.8085	−	24.4088i	1.10355	−	0.968635i
$636$		0			0
$637$	−24.3293	−	20.5283i	−0.963963	−	0.813360i
$638$		−	0.113548i		−	0.00449540i
$639$		0			0
$640$	−17.5117	−	5.93593i	−0.692212	−	0.234638i
$641$	−6.52024	+	11.2934i	−0.257534	+	0.446062i	−0.965581	−	0.260104i	$-0.916243\pi$
$641$	−6.52024	+	11.2934i	−0.257534	+	0.446062i	0.708047	+	0.706166i	$0.249577\pi$
$642$		0			0
$643$		−	27.0185i		−	1.06550i	−0.846271	−	0.532752i	$-0.821158\pi$
$643$		−	27.0185i		−	1.06550i	0.846271	−	0.532752i	$-0.178842\pi$
$644$	35.1200	−	16.3184i	1.38392	−	0.643033i
$645$		0			0
$646$	−1.32082	−	2.28773i	−0.0519670	−	0.0900095i
$647$	−30.2927	−	17.4895i	−1.19093	−	0.687582i	−0.232411	−	0.972618i	$-0.574661\pi$
$647$	−30.2927	−	17.4895i	−1.19093	−	0.687582i	−0.958517	+	0.285035i	$0.907995\pi$
$648$		0			0
$649$	2.71444	+	4.70155i	0.106551	+	0.184552i
$650$	−6.03386	+	2.50546i	−0.236667	+	0.0982723i
$651$		0			0
$652$		−	30.2109i		−	1.18315i
$653$	28.0168	−	16.1755i	1.09638	−	0.632997i	0.161114	−	0.986936i	$-0.448491\pi$
$653$	28.0168	−	16.1755i	1.09638	−	0.632997i	0.935269	+	0.353939i	$0.115158\pi$
$654$		0			0
$655$	−3.80300	+	11.2193i	−0.148596	+	0.438376i
$656$	0.123234	+	0.213447i	0.00481146	+	0.00833370i
$657$		0			0
$658$	4.83557	+	0.429716i	0.188510	+	0.0167521i
$659$	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	−0.404114	−	0.914709i	$-0.632420\pi$
$661$	15.1715	−	26.2779i	0.590104	−	1.02209i	0.994218	−	0.107382i	$-0.0342467\pi$
$662$	6.19400	+	3.57611i	0.240737	+	0.138989i
$663$		0			0
$664$	−1.37788			−0.0534722
$665$	−9.74704	+	1.05829i	−0.377974	+	0.0410388i
$666$		0			0
$667$	0.784435	−	0.452894i	0.0303734	−	0.0175361i
$668$	−37.5187	−	21.6614i	−1.45164	−	0.838107i
$669$		0			0
$670$	1.28682	+	1.46605i	0.0497143	+	0.0566386i
$671$	−24.3719			−0.940867
$672$		0			0
$673$			40.5075i			1.56145i	0.624875	+	0.780725i	$0.285150\pi$
$673$			40.5075i			1.56145i	−0.624875	+	0.780725i	$0.714850\pi$
$674$	0.679059	+	1.17617i	0.0261564	+	0.0453042i
$675$		0			0
$676$	7.36308	−	12.7532i	0.283195	−	0.490509i
$677$	−20.2833	+	11.7105i	−0.779549	+	0.450073i	−0.836270	−	0.548317i	$-0.815269\pi$
$677$	−20.2833	+	11.7105i	−0.779549	+	0.450073i	0.0567215	+	0.998390i	$0.481935\pi$
$678$		0			0
$679$	7.30149	−	3.39260i	0.280205	−	0.130196i
$680$	13.6935	−	2.73000i	0.525121	−	0.104691i
$681$		0			0
$682$	5.18806	+	2.99533i	0.198661	+	0.114697i
$683$	−44.1887	−	25.5124i	−1.69083	−	0.976204i	−0.953845	−	0.300299i	$-0.902913\pi$
$683$	−44.1887	−	25.5124i	−1.69083	−	0.976204i	−0.736989	−	0.675904i	$-0.763753\pi$
$684$		0			0
$685$	−6.50107	−	32.6089i	−0.248393	−	1.24592i
$686$	−5.14581	+	1.35623i	−0.196468	+	0.0517812i
$687$		0			0
$688$	−8.90956	+	5.14393i	−0.339674	+	0.196111i
$689$	1.68212	−	2.91353i	0.0640838	−	0.110996i
$690$		0			0
$691$	−12.3057	−	21.3142i	−0.468133	−	0.810829i	0.531204	−	0.847244i	$-0.321740\pi$
$691$	−12.3057	−	21.3142i	−0.468133	−	0.810829i	−0.999337	+	0.0364144i	$0.988406\pi$
$692$			16.3485i			0.621476i
$693$		0			0
$694$	−4.06819			−0.154426
$695$	−14.0381	−	15.9933i	−0.532494	−	0.606660i
$696$		0			0
$697$	−0.337213	−	0.194690i	−0.0127728	−	0.00737441i
$698$	−1.25647	+	0.725422i	−0.0475580	+	0.0274576i
$699$		0			0
$700$	5.50234	−	24.7613i	0.207969	−	0.935891i
$701$	−25.7244			−0.971595			−0.485798	−	0.874071i	$-0.661471\pi$
$701$	−25.7244			−0.971595			−0.485798	+	0.874071i	$0.661471\pi$
$702$		0			0
$703$	−11.1311	−	6.42652i	−0.419816	−	0.242381i
$704$	−10.1346	+	17.5536i	−0.381962	+	0.661577i
$705$		0			0
$706$	4.62567			0.174089
$707$	42.2703	+	3.75638i	1.58974	+	0.141273i
$708$		0			0
$709$	5.85482	+	10.1408i	0.219882	+	0.380848i	0.954772	−	0.297339i	$-0.0960993\pi$
$709$	5.85482	+	10.1408i	0.219882	+	0.380848i	−0.734889	+	0.678187i	$0.762766\pi$
$710$	−2.29432	−	0.777702i	−0.0861042	−	0.0291867i
$711$		0			0
$712$	−12.6727	+	7.31661i	−0.474931	+	0.274202i
$713$			47.7883i			1.78968i
$714$		0			0
$715$	6.62129	+	33.2119i	0.247622	+	1.24205i
$716$	11.2943	+	19.5623i	0.422088	+	0.731077i
$717$		0			0
$718$	−0.0762651	−	0.0440317i	−0.00284619	−	0.00164325i
$719$	6.16037	+	10.6701i	0.229743	+	0.397927i	0.957732	−	0.287662i	$-0.0928781\pi$
$719$	6.16037	+	10.6701i	0.229743	+	0.397927i	−0.727989	+	0.685589i	$0.759545\pi$
$720$		0			0
$721$	−11.4580	−	8.04635i	−0.426719	−	0.299662i
$722$		−	4.67023i		−	0.173808i
$723$		0			0
$724$	−8.71444	+	15.0939i	−0.323870	+	0.560959i
$725$	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	$-0.106164\pi$
$728$	−5.70678	−	12.2820i	−0.211507	−	0.455202i
$729$		0			0
$730$	−0.998206	−	1.13724i	−0.0369452	−	0.0420910i
$731$	8.12662	−	14.0757i	0.300574	−	0.520609i
$732$		0			0
$733$	−8.69135	+	5.01795i	−0.321022	+	0.185342i	−0.651848	−	0.758349i	$-0.726006\pi$
$733$	−8.69135	+	5.01795i	−0.321022	+	0.185342i	0.330826	+	0.943692i	$0.392673\pi$
$734$	−6.79541			−0.250823
$735$		0			0
$736$	24.8873			0.917357
$737$	8.75672	−	5.05570i	0.322558	−	0.186229i
$738$		0			0
$739$	−15.5360	+	26.9092i	−0.571502	+	0.989870i	0.424910	+	0.905235i	$0.360306\pi$
$739$	−15.5360	+	26.9092i	−0.571502	+	0.989870i	−0.996412	+	0.0846345i	$0.973028\pi$
$740$	24.9913	−	21.9360i	0.918697	−	0.806383i
$741$		0			0
$742$	−0.236987	−	0.510038i	−0.00870005	−	0.0187241i
$743$		−	4.04189i		−	0.148283i	−0.997248	−	0.0741413i	$-0.976378\pi$
$743$		−	4.04189i		−	0.148283i	0.997248	−	0.0741413i	$-0.0236216\pi$
$744$		0			0
$745$	−8.16186	+	24.0785i	−0.299027	+	0.882168i
$746$	2.70638	−	4.68759i	0.0990876	−	0.171625i
$747$		0			0
$748$		−	35.4256i		−	1.29529i
$749$	−11.1761	−	7.84839i	−0.408367	−	0.286774i
$750$		0			0
$751$	−7.34725	−	12.7258i	−0.268105	−	0.464371i	0.700268	−	0.713881i	$-0.253064\pi$
$751$	−7.34725	−	12.7258i	−0.268105	−	0.464371i	−0.968372	+	0.249509i	$0.919731\pi$
$752$	−19.4193	−	11.2117i	−0.708149	−	0.408850i
$753$		0			0
$754$	−0.0775229	−	0.134274i	−0.00282322	−	0.00488996i
$755$	19.6054	−	3.90862i	0.713512	−	0.142249i
$756$		0			0
$757$		−	29.6087i		−	1.07615i	−0.842898	−	0.538073i	$-0.819153\pi$
$757$		−	29.6087i		−	1.07615i	0.842898	−	0.538073i	$-0.180847\pi$
$758$	−3.54681	+	2.04775i	−0.128826	+	0.0743778i
$759$		0			0
$760$	−3.95041	−	1.33907i	−0.143297	−	0.0485731i
$761$	−7.12611	−	12.3428i	−0.258321	−	0.447426i	0.707471	−	0.706742i	$-0.249836\pi$
$761$	−7.12611	−	12.3428i	−0.258321	−	0.447426i	−0.965792	+	0.259317i	$0.916503\pi$
$762$		0			0
$763$	8.54088	+	0.758990i	0.309200	+	0.0274773i
$764$	−39.2992			−1.42179
$765$		0			0
$766$	3.59980	−	6.23504i	0.130066	−	0.225281i
$767$	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	$0.378642\pi$
$770$	5.17977	+	2.28491i	0.186666	+	0.0823425i
$771$		0			0
$772$	−14.1860	+	8.19030i	−0.510566	+	0.294775i
$773$	36.8580	+	21.2800i	1.32569	+	0.765387i	0.984630	−	0.174655i	$-0.0558811\pi$
$773$	36.8580	+	21.2800i	1.32569	+	0.765387i	0.341059	+	0.940042i	$0.389214\pi$
$774$		0			0
$775$	24.8494	+	19.0332i	0.892615	+	0.683694i
$776$	3.42533			0.122962
$777$		0			0
$778$		−	3.87093i		−	0.138780i
$779$	0.0581603	+	0.100737i	0.00208381	+	0.00360926i
$780$		0			0
$781$	−6.27860	+	10.8748i	−0.224666	+	0.389133i
$782$	−10.5379	+	6.08405i	−0.376834	+	0.217565i
$783$		0			0
$784$	24.1949	+	4.33442i	0.864105	+	0.154801i
$785$	−1.46298	−	7.33819i	−0.0522159	−	0.261911i
$786$		0			0
$787$	21.8231	+	12.5996i	0.777909	+	0.449126i	0.835689	−	0.549203i	$-0.185069\pi$
$787$	21.8231	+	12.5996i	0.777909	+	0.449126i	−0.0577798	+	0.998329i	$0.518402\pi$
$788$	22.9298	+	13.2385i	0.816842	+	0.471604i
$789$		0			0
$790$	1.49995	+	7.52363i	0.0533657	+	0.267679i
$791$	−30.3782	+	14.1151i	−1.08012	+	0.501874i
$792$		0			0
$793$	−28.8205	+	16.6395i	−1.02344	+	0.590886i
$794$	2.65044	−	4.59069i	0.0940605	−	0.162918i
$795$		0			0
$796$	3.63449	+	6.29512i	0.128821	+	0.223125i
$797$		−	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
$800$	9.91217	−	12.9411i	0.350448	−	0.457537i
$801$		0			0
$802$	6.32515	+	3.65182i	0.223349	+	0.128950i
$803$	−6.79271	+	3.92177i	−0.239709	+	0.138396i
$804$		0			0
$805$	4.87477	+	44.8975i	0.171813	+	1.58243i
$806$	8.18003			0.288129
$807$		0			0
$808$	15.6357	+	9.02728i	0.550062	+	0.317579i
$809$	25.8890	−	44.8410i	0.910207	−	1.57653i	0.0964371	−	0.995339i	$-0.469255\pi$
$809$	25.8890	−	44.8410i	0.910207	−	1.57653i	0.813770	−	0.581187i	$-0.197411\pi$
$810$		0			0
$811$	12.0263			0.422299			0.211149	−	0.977454i	$-0.432279\pi$
$811$	12.0263			0.422299			0.211149	+	0.977454i	$0.432279\pi$
$812$	0.599592	+	0.0532831i	0.0210416	+	0.00186987i
$813$		0			0
$814$	3.71089	+	6.42744i	0.130067	+	0.225282i
$815$	33.3664	+	11.3102i	1.16877	+	0.396178i
$816$		0			0
$817$	−4.20488	+	2.42769i	−0.147110	+	0.0849341i
$818$			5.38212i			0.188182i
$819$		0			0
$820$	−0.295132	+	0.0588389i	−0.0103064	+	0.00205474i
$821$	4.03967	+	6.99692i	0.140985	+	0.244194i	0.927868	−	0.372909i	$-0.121640\pi$
$821$	4.03967	+	6.99692i	0.140985	+	0.244194i	−0.786882	+	0.617103i	$0.788306\pi$
$822$		0			0
$823$	−4.42994	−	2.55762i	−0.154418	−	0.0891532i	0.420800	−	0.907153i	$-0.361749\pi$
$823$	−4.42994	−	2.55762i	−0.154418	−	0.0891532i	−0.575218	+	0.818000i	$0.695083\pi$
$824$	−2.97834	−	5.15864i	−0.103755	−	0.179710i
$825$		0			0
$826$	1.12384	−	0.522188i	0.0391035	−	0.0181693i
$827$		−	0.705254i		−	0.0245241i	−0.999925	−	0.0122620i	$-0.996097\pi$
$827$		−	0.705254i		−	0.0245241i	0.999925	−	0.0122620i	$-0.00390323\pi$
$828$		0			0
$829$	12.4790	−	21.6143i	0.433415	−	0.750696i	−0.563750	−	0.825945i	$-0.690642\pi$
$829$	12.4790	−	21.6143i	0.433415	−	0.750696i	0.997165	+	0.0752491i	$0.0239752\pi$
$830$	0.252486	−	0.744864i	0.00876391	−	0.0258546i
$831$		0			0
$832$			27.6769i			0.959523i
$833$	−36.5270	+	13.1818i	−1.26559	+	0.456723i
$834$		0			0
$835$	37.9700	−	33.3280i	1.31401	−	1.15336i
$836$	−5.29140	+	9.16498i	−0.183007	+	0.316977i
$837$		0			0
$838$	0.509487	−	0.294152i	0.0175999	−	0.0101613i
$839$	−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
$842$	−3.99418	+	2.30604i	−0.137649	+	0.0794714i
$843$		0			0
$844$	0.109693	−	0.189994i	0.00377579	−	0.00653986i
$845$	11.3287	+	12.9066i	0.389721	+	0.444001i
$846$		0			0
$847$	0.139165	−	0.198172i	0.00478177	−	0.00680926i
$848$			2.59775i			0.0892071i
$849$		0			0
$850$	−1.03342	+	7.90275i	−0.0354460	+	0.271062i
$851$	−29.6023	+	51.2726i	−1.01475	+	1.75760i
$852$		0			0
$853$			32.5996i			1.11619i	0.829778	+	0.558094i	$0.188467\pi$
$853$			32.5996i			1.11619i	−0.829778	+	0.558094i	$0.811533\pi$
$854$	−0.492445	+	5.54146i	−0.0168511	+	0.189625i
$855$		0			0
$856$	−2.90507	−	5.03172i	−0.0992931	−	0.171981i
$857$	−27.4455	−	15.8456i	−0.937519	−	0.541277i	−0.0483371	−	0.998831i	$-0.515392\pi$
$857$	−27.4455	−	15.8456i	−0.937519	−	0.541277i	−0.889182	+	0.457554i	$0.848726\pi$
$858$		0			0
$859$	−21.8456	−	37.8377i	−0.745363	−	1.29101i	−0.950025	−	0.312174i	$-0.898943\pi$
$859$	−21.8456	−	37.8377i	−0.745363	−	1.29101i	0.204662	−	0.978833i	$-0.434390\pi$
$860$	−2.45601	−	12.3192i	−0.0837494	−	0.420081i
$861$		0			0
$862$		−	10.5201i		−	0.358317i
$863$	−33.6005	+	19.3992i	−1.14377	+	0.660358i	−0.947362	−	0.320164i	$-0.896262\pi$
$863$	−33.6005	+	19.3992i	−1.14377	+	0.660358i	−0.196411	+	0.980522i	$0.562929\pi$
$864$		0			0
$865$	−18.0561	−	6.12044i	−0.613924	−	0.208101i
$866$	2.58670	+	4.48030i	0.0878997	+	0.152247i
$867$		0			0
$868$	−18.2514	+	25.9901i	−0.619493	+	0.882160i
$869$	39.7660			1.34897
$870$		0			0
$871$	6.90338	−	11.9570i	0.233912	−	0.405148i
$872$	3.15925	+	1.82399i	0.106986	+	0.0617682i
$873$		0			0
$874$	3.63501			0.122956
$875$	25.2877	+	15.3470i	0.854881	+	0.518825i
$876$		0			0
$877$	3.72454	−	2.15036i	0.125769	−	0.0726127i	−0.435796	−	0.900046i	$-0.643533\pi$
$877$	3.72454	−	2.15036i	0.125769	−	0.0726127i	0.561565	+	0.827433i	$0.310200\pi$
$878$	−4.82118	−	2.78351i	−0.162707	−	0.0939390i
$879$		0			0
$880$	−17.2502	−	19.6529i	−0.581506	−	0.662498i
$881$	1.29308			0.0435650			0.0217825	−	0.999763i	$-0.493066\pi$
$881$	1.29308			0.0435650			0.0217825	+	0.999763i	$0.493066\pi$
$882$		0			0
$883$		−	1.49533i		−	0.0503218i	−0.999683	−	0.0251609i	$-0.991990\pi$
$883$		−	1.49533i		−	0.0503218i	0.999683	−	0.0251609i	$-0.00800981\pi$
$884$	−24.1862	−	41.8918i	−0.813471	−	1.40897i
$885$		0			0
$886$	−2.36225	+	4.09153i	−0.0793613	+	0.137458i
$887$	−8.73964	+	5.04584i	−0.293449	+	0.169423i	−0.639496	−	0.768794i	$-0.720857\pi$
$887$	−8.73964	+	5.04584i	−0.293449	+	0.169423i	0.346047	+	0.938217i	$0.387524\pi$
$888$		0			0
$889$	−39.7040	+	18.4483i	−1.33163	+	0.618736i
$890$	−1.63308	−	8.19142i	−0.0547410	−	0.274577i
$891$		0			0
$892$	13.0631	+	7.54198i	0.437385	+	0.252524i
$893$	−9.16498	−	5.29140i	−0.306694	−	0.177070i
$894$		0			0
$895$	−25.8339	+	5.15036i	−0.863531	+	0.172158i
$896$	17.9044	+	12.5733i	0.598143	+	0.420044i
$897$		0			0
$898$	−8.14317	+	4.70146i	−0.271741	+	0.156890i
$899$	−0.371409	+	0.643299i	−0.0123872	+	0.0214552i
$900$		0			0
$901$	−2.05202	−	3.55421i	−0.0683628	−	0.118408i
$902$		−	0.0671674i		−	0.00223643i
$903$		0			0
$904$	−14.2512			−0.473989
$905$	−13.4079	−	15.2754i	−0.445695	−	0.507772i
$906$		0			0
$907$	−3.69531	−	2.13349i	−0.122701	−	0.0708414i	0.437393	−	0.899270i	$-0.355902\pi$
$907$	−3.69531	−	2.13349i	−0.122701	−	0.0708414i	−0.560094	+	0.828429i	$0.689235\pi$
$908$	−14.9095	+	8.60802i	−0.494790	+	0.285667i
$909$		0			0
$910$	7.68520	−	0.834427i	0.254762	−	0.0276610i
$911$	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
$914$	−5.37754	+	9.31417i	−0.177873	+	0.308085i
$915$		0			0
$916$	9.75231			0.322226
$917$	8.05539	−	11.4709i	0.266012	−	0.378802i
$918$		0			0
$919$	−23.2822	−	40.3259i	−0.768008	−	1.33023i	−0.938642	−	0.344894i	$-0.887915\pi$
$919$	−23.2822	−	40.3259i	−0.768008	−	1.33023i	0.170634	−	0.985335i	$-0.445419\pi$
$920$	−6.16810	+	18.1967i	−0.203356	+	0.599926i
$921$		0			0
$922$	−7.05720	+	4.07448i	−0.232417	+	0.134186i
$923$			17.1464i			0.564381i
$924$		0			0
$925$	14.8711	+	35.8138i	0.488959	+	1.17755i
$926$	1.03561	+	1.79372i	0.0340321	+	0.0589453i
$927$		0			0
$928$	0.335019	+	0.193423i	0.0109975	+	0.00634943i
$929$	−3.69774	−	6.40467i	−0.121319	−	0.210130i	0.798969	−	0.601372i	$-0.205379\pi$
$929$	−3.69774	−	6.40467i	−0.121319	−	0.210130i	−0.920288	+	0.391242i	$0.872046\pi$
$930$		0			0
$931$	11.4188	+	2.04564i	0.374238	+	0.0670432i
$932$			41.8352i			1.37036i
$933$		0			0
$934$	−1.73537	+	3.00574i	−0.0567829	+	0.0983509i
$935$	39.1258	+	13.2624i	1.27955	+	0.433728i
$936$		0			0
$937$			44.1988i			1.44391i	0.691939	+	0.721956i	$0.256757\pi$
$937$			44.1988i			1.44391i	−0.691939	+	0.721956i	$0.743243\pi$
$938$	−0.972585	−	2.09318i	−0.0317560	−	0.0683447i
$939$		0			0
$940$	20.5770	−	18.0614i	0.671149	−	0.589099i
$941$	18.0180	−	31.2080i	0.587369	−	1.01735i	−0.407206	−	0.913336i	$-0.633497\pi$
$941$	18.0180	−	31.2080i	0.587369	−	1.01735i	0.994576	−	0.104017i	$-0.0331696\pi$
$942$		0			0
$943$	0.464020	−	0.267902i	0.0151106	−	0.00872408i
$944$	−5.72401			−0.186301
$945$		0			0
$946$	2.80366			0.0911548
$947$	29.6476	−	17.1170i	0.963417	−	0.556229i	0.0661943	−	0.997807i	$-0.478914\pi$
$947$	29.6476	−	17.1170i	0.963417	−	0.556229i	0.897223	+	0.441577i	$0.145581\pi$
$948$		0			0
$949$	−5.35504	+	9.27521i	−0.173832	+	0.301086i
$950$	1.44776	−	1.89017i	0.0469716	−	0.0613251i
$951$		0			0
$952$	−16.4563	−	1.46240i	−0.533353	−	0.0473967i
$953$			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
$956$	−7.14155	+	12.3695i	−0.230974	+	0.400059i
$957$		0			0
$958$			5.78743i			0.186983i
$959$	−3.48249	+	39.1883i	−0.112455	+	1.26545i
$960$		0			0
$961$	−4.09508	−	7.09289i	−0.132099	−	0.228803i
$962$	8.77646	+	5.06709i	0.282964	+	0.163370i
$963$		0			0
$964$	23.1778	+	40.1451i	0.746506	+	1.29299i
$965$	−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	$0.890218\pi$
$968$	0.0892209	−	0.0515117i	0.00286767	−	0.00165565i
$969$		0			0
$970$	−0.627664	+	1.85169i	−0.0201531	+	0.0594540i
$971$	22.3468	+	38.7058i	0.717144	+	1.24213i	0.962127	+	0.272602i	$0.0878843\pi$
$971$	22.3468	+	38.7058i	0.717144	+	1.24213i	−0.244983	+	0.969527i	$0.578782\pi$
$972$		0			0
$973$	10.6100	+	22.8346i	0.340141	+	0.732045i
$974$	11.4761			0.367718
$975$		0			0
$976$	12.8484	−	22.2541i	0.411268	−	0.712337i
$977$	−12.5029	−	7.21858i	−0.400005	−	0.230943i	0.286481	−	0.958086i	$-0.407514\pi$
$977$	−12.5029	−	7.21858i	−0.400005	−	0.230943i	−0.686486	+	0.727143i	$0.740848\pi$
$978$		0			0
$979$	−43.2956			−1.38373
$980$	−14.4962	+	26.2797i	−0.463063	+	0.839473i
$981$		0			0
$982$	7.86307	−	4.53974i	0.250921	−	0.144869i
$983$	14.5389	+	8.39401i	0.463717	+	0.267727i	0.713606	−	0.700547i	$-0.247061\pi$
$983$	14.5389	+	8.39401i	0.463717	+	0.267727i	−0.249889	+	0.968275i	$0.580394\pi$
$984$		0			0
$985$	−23.2056	+	20.3687i	−0.739393	+	0.649000i
$986$	−0.189140			−0.00602345
$987$		0			0
$988$			14.4505i			0.459730i
$989$	11.1826	+	19.3688i	0.355585	+	0.615892i
$990$		0			0
$991$	−20.0539	+	34.7344i	−0.637033	+	1.10337i	0.349048	+	0.937105i	$0.386505\pi$
$991$	−20.0539	+	34.7344i	−0.637033	+	1.10337i	−0.986081	+	0.166268i	$0.946828\pi$
$992$	−17.6752	+	10.2048i	−0.561188	+	0.324002i
$993$		0			0
$994$	2.34576	+	1.64730i	0.0744031	+	0.0522492i
$995$	−8.31330	+	1.65738i	−0.263549	+	0.0525425i
$996$		0			0
$997$	−44.4447	−	25.6602i	−1.40758	−	0.812666i	−0.412424	−	0.910992i	$-0.635318\pi$
$997$	−44.4447	−	25.6602i	−1.40758	−	0.812666i	−0.995154	+	0.0983259i	$0.968651\pi$
$998$	9.90032	+	5.71595i	0.313389	+	0.180935i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bf.b.109.5		16
3.2	odd	2		105.2.q.a.4.4	✓	16
5.4	even	2	inner	315.2.bf.b.109.4		16
7.2	even	3	inner	315.2.bf.b.289.4		16
7.3	odd	6		2205.2.d.o.1324.5		8
7.4	even	3		2205.2.d.s.1324.5		8
12.11	even	2		1680.2.di.d.529.7		16
15.2	even	4		525.2.i.k.151.2		8
15.8	even	4		525.2.i.h.151.3		8
15.14	odd	2		105.2.q.a.4.5	yes	16
21.2	odd	6		105.2.q.a.79.5	yes	16
21.5	even	6		735.2.q.g.79.5		16
21.11	odd	6		735.2.d.d.589.4		8
21.17	even	6		735.2.d.e.589.4		8
21.20	even	2		735.2.q.g.214.4		16
35.4	even	6		2205.2.d.s.1324.4		8
35.9	even	6	inner	315.2.bf.b.289.5		16
35.24	odd	6		2205.2.d.o.1324.4		8
60.59	even	2		1680.2.di.d.529.3		16
84.23	even	6		1680.2.di.d.289.3		16
105.2	even	12		525.2.i.k.226.2		8
105.17	odd	12		3675.2.a.bn.1.3		4
105.23	even	12		525.2.i.h.226.3		8
105.32	even	12		3675.2.a.bp.1.3		4
105.38	odd	12		3675.2.a.cb.1.2		4
105.44	odd	6		105.2.q.a.79.4	yes	16
105.53	even	12		3675.2.a.bz.1.2		4
105.59	even	6		735.2.d.e.589.5		8
105.74	odd	6		735.2.d.d.589.5		8
105.89	even	6		735.2.q.g.79.4		16
105.104	even	2		735.2.q.g.214.5		16
420.359	even	6		1680.2.di.d.289.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.4	✓	16	3.2	odd	2
105.2.q.a.4.5	yes	16	15.14	odd	2
105.2.q.a.79.4	yes	16	105.44	odd	6
105.2.q.a.79.5	yes	16	21.2	odd	6
315.2.bf.b.109.4		16	5.4	even	2	inner
315.2.bf.b.109.5		16	1.1	even	1	trivial
315.2.bf.b.289.4		16	7.2	even	3	inner
315.2.bf.b.289.5		16	35.9	even	6	inner
525.2.i.h.151.3		8	15.8	even	4
525.2.i.h.226.3		8	105.23	even	12
525.2.i.k.151.2		8	15.2	even	4
525.2.i.k.226.2		8	105.2	even	12
735.2.d.d.589.4		8	21.11	odd	6
735.2.d.d.589.5		8	105.74	odd	6
735.2.d.e.589.4		8	21.17	even	6
735.2.d.e.589.5		8	105.59	even	6
735.2.q.g.79.4		16	105.89	even	6
735.2.q.g.79.5		16	21.5	even	6
735.2.q.g.214.4		16	21.20	even	2
735.2.q.g.214.5		16	105.104	even	2
1680.2.di.d.289.3		16	84.23	even	6
1680.2.di.d.289.7		16	420.359	even	6
1680.2.di.d.529.3		16	60.59	even	2
1680.2.di.d.529.7		16	12.11	even	2
2205.2.d.o.1324.4		8	35.24	odd	6
2205.2.d.o.1324.5		8	7.3	odd	6
2205.2.d.s.1324.4		8	35.4	even	6
2205.2.d.s.1324.5		8	7.4	even	3
3675.2.a.bn.1.3		4	105.17	odd	12
3675.2.a.bp.1.3		4	105.32	even	12
3675.2.a.bz.1.2		4	105.53	even	12
3675.2.a.cb.1.2		4	105.38	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.248840 - 0.143668i) q^{2} +(-0.958719 + 1.66055i) q^{4} +(-1.47507 - 1.68052i) q^{5} +(1.11487 + 2.39939i) q^{7} +1.12562i q^{8} +(-0.608495 - 0.206261i) q^{10} +(-1.66520 + 2.88421i) q^{11} +4.54754i q^{13} +(0.622139 + 0.436894i) q^{14} +(-1.75572 - 3.04100i) q^{16} +(4.80431 + 2.77377i) q^{17} +(-0.828617 - 1.43521i) q^{19} +(4.20477 - 0.838284i) q^{20} +0.956942i q^{22} +(-6.61094 + 3.81683i) q^{23} +(-0.648315 + 4.95779i) q^{25} +(0.653336 + 1.13161i) q^{26} +(-5.05315 - 0.449051i) q^{28} -0.118657 q^{29} +(3.13010 - 5.42150i) q^{31} +(-2.82342 - 1.63010i) q^{32} +1.59401 q^{34} +(2.38772 - 5.41284i) q^{35} +(6.71665 - 3.87786i) q^{37} +(-0.412386 - 0.238091i) q^{38} +(1.89163 - 1.66037i) q^{40} -0.0701896 q^{41} -2.92981i q^{43} +(-3.19291 - 5.53029i) q^{44} +(-1.09671 + 1.89956i) q^{46} +(5.53029 - 3.19291i) q^{47} +(-4.51415 + 5.35000i) q^{49} +(0.550949 + 1.32684i) q^{50} +(-7.55142 - 4.35981i) q^{52} +(-0.640682 - 0.369898i) q^{53} +(7.30326 - 1.45601i) q^{55} +(-2.70080 + 1.25492i) q^{56} +(-0.0295266 + 0.0170472i) q^{58} +(0.815051 - 1.41171i) q^{59} +(3.65901 + 6.33759i) q^{61} -1.79878i q^{62} +6.08612 q^{64} +(7.64225 - 6.70796i) q^{65} +(-2.62934 - 1.51805i) q^{67} +(-9.21197 + 5.31853i) q^{68} +(-0.183490 - 1.68997i) q^{70} +3.77048 q^{71} +(2.03961 + 1.17757i) q^{73} +(1.11425 - 1.92993i) q^{74} +3.17764 q^{76} +(-8.77681 - 0.779956i) q^{77} +(-5.97016 - 10.3406i) q^{79} +(-2.52065 + 7.43623i) q^{80} +(-0.0174660 + 0.0100840i) q^{82} +1.22411i q^{83} +(-2.42533 - 12.1653i) q^{85} +(-0.420920 - 0.729054i) q^{86} +(-3.24652 - 1.87438i) q^{88} +(6.50007 + 11.2585i) q^{89} +(-10.9113 + 5.06990i) q^{91} -14.6371i q^{92} +(0.917438 - 1.58905i) q^{94} +(-1.18963 + 3.50954i) q^{95} -3.04306i q^{97} +(-0.354679 + 1.97983i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 2 q^{5} - 4 q^{10} + 24 q^{14} - 24 q^{19} + 8 q^{20} - 4 q^{25} + 12 q^{26} - 24 q^{29} + 16 q^{31} + 16 q^{34} + 10 q^{35} + 32 q^{40} - 16 q^{41} - 20 q^{44} - 32 q^{46} - 40 q^{49}+ \cdots + 22 q^{95}+O(q^{100}) \) 16 * q + 8 * q^4 - 2 * q^5 - 4 * q^10 + 24 * q^14 - 24 * q^19 + 8 * q^20 - 4 * q^25 + 12 * q^26 - 24 * q^29 + 16 * q^31 + 16 * q^34 + 10 * q^35 + 32 * q^40 - 16 * q^41 - 20 * q^44 - 32 * q^46 - 40 * q^49 + 40 * q^50 + 8 * q^55 - 84 * q^56 - 4 * q^59 + 16 * q^61 + 16 * q^64 - 30 * q^65 + 16 * q^70 + 56 * q^71 - 40 * q^74 - 64 * q^76 - 16 * q^79 - 52 * q^80 - 64 * q^85 + 48 * q^86 - 16 * q^89 + 8 * q^91 - 32 * q^94 + 22 * q^95

Introduction

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