LMFDB - Embedded newform 735.2.q.g.214.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(79,735)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("735.79"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.q (of order $6$, degree $2$, not 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:	$5.86900454856$
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			214.5
Root			$2.07845 + 0.556918i$ of defining polynomial
Character	$\chi$	$=$	735.214
Dual form			735.2.q.g.79.5

$q$-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} +(-0.866025 - 0.500000i) q^{3} +(-0.958719 + 1.66055i) q^{4} +(-0.717839 - 2.11771i) q^{5} -0.287336 q^{6} +1.12562i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.482874 - 0.423842i) q^{10} +(1.66520 - 2.88421i) q^{11} +(1.66055 - 0.958719i) q^{12} +4.54754i q^{13} +(-0.437190 + 2.19291i) q^{15} +(-1.75572 - 3.04100i) q^{16} +(-4.80431 - 2.77377i) q^{17} +(0.248840 + 0.143668i) q^{18} +(0.828617 + 1.43521i) q^{19} +(4.20477 + 0.838284i) q^{20} -0.956942i q^{22} +(-6.61094 + 3.81683i) q^{23} +(0.562810 - 0.974816i) q^{24} +(-3.96942 + 3.04035i) q^{25} +(0.653336 + 1.13161i) q^{26} -1.00000i q^{27} +0.118657 q^{29} +(0.206261 + 0.608495i) q^{30} +(-3.13010 + 5.42150i) q^{31} +(-2.82342 - 1.63010i) q^{32} +(-2.88421 + 1.66520i) q^{33} -1.59401 q^{34} -1.91744 q^{36} +(-6.71665 + 3.87786i) q^{37} +(0.412386 + 0.238091i) q^{38} +(2.27377 - 3.93829i) q^{39} +(2.38374 - 0.808014i) q^{40} -0.0701896 q^{41} +2.92981i q^{43} +(3.19291 + 5.53029i) q^{44} +(1.47507 - 1.68052i) q^{45} +(-1.09671 + 1.89956i) q^{46} +(-5.53029 + 3.19291i) q^{47} +3.51145i q^{48} +(-0.550949 + 1.32684i) q^{50} +(2.77377 + 4.80431i) q^{51} +(-7.55142 - 4.35981i) q^{52} +(-0.640682 - 0.369898i) q^{53} +(-0.143668 - 0.248840i) q^{54} +(-7.30326 - 1.45601i) q^{55} -1.65723i q^{57} +(0.0295266 - 0.0170472i) q^{58} +(0.815051 - 1.41171i) q^{59} +(-3.22230 - 2.82836i) q^{60} +(-3.65901 - 6.33759i) q^{61} +1.79878i q^{62} +6.08612 q^{64} +(9.63038 - 3.26440i) q^{65} +(-0.478471 + 0.828736i) q^{66} +(2.62934 + 1.51805i) q^{67} +(9.21197 - 5.31853i) q^{68} +7.63366 q^{69} -3.77048 q^{71} +(-0.974816 + 0.562810i) q^{72} +(2.03961 + 1.17757i) q^{73} +(-1.11425 + 1.92993i) q^{74} +(4.95779 - 0.648315i) q^{75} -3.17764 q^{76} -1.30667i q^{78} +(-5.97016 - 10.3406i) q^{79} +(-5.17964 + 5.90106i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.0174660 + 0.0100840i) q^{82} -1.22411i q^{83} +(-2.42533 + 12.1653i) q^{85} +(0.420920 + 0.729054i) q^{86} +(-0.102760 - 0.0593285i) q^{87} +(3.24652 + 1.87438i) q^{88} +(6.50007 + 11.2585i) q^{89} +(0.125620 - 0.630102i) q^{90} -14.6371i q^{92} +(5.42150 - 3.13010i) q^{93} +(-0.917438 + 1.58905i) q^{94} +(2.44454 - 2.78502i) q^{95} +(1.63010 + 2.82342i) q^{96} -3.04306i q^{97} +3.33039 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 2 q^{5} + 8 q^{6} + 8 q^{9} + 4 q^{10} - 4 q^{15} + 24 q^{19} + 8 q^{20} + 12 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} - 12 q^{30} - 16 q^{31} - 16 q^{34} + 16 q^{36} - 4 q^{39} - 32 q^{40}+ \cdots - 8 q^{96}+O(q^{100}) $ 16 * q + 8 * q^4 - 2 * q^5 + 8 * q^6 + 8 * q^9 + 4 * q^10 - 4 * q^15 + 24 * q^19 + 8 * q^20 + 12 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 - 12 * q^30 - 16 * q^31 - 16 * q^34 + 16 * q^36 - 4 * q^39 - 32 * q^40 - 16 * q^41 + 20 * q^44 + 2 * q^45 - 32 * q^46 - 40 * q^50 + 4 * q^51 + 4 * q^54 - 8 * q^55 - 4 * q^59 + 16 * q^60 - 16 * q^61 + 16 * q^64 + 30 * q^65 - 28 * q^66 - 40 * q^69 - 56 * q^71 + 40 * q^74 - 8 * q^75 + 64 * q^76 - 16 * q^79 - 52 * q^80 - 8 * q^81 - 64 * q^85 - 48 * q^86 - 16 * q^89 + 8 * q^90 + 32 * q^94 - 22 * q^95 - 8 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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 $

$2$	0.248840	−	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	$0.300941\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.958719	+	1.66055i	−0.479360	+	0.830275i
$5$	−0.717839	−	2.11771i	−0.321027	−	0.947070i
$5$	−0.717839	−	2.11771i	−0.321027	−	0.947070i
$6$	−0.287336			−0.117304
$7$		0			0
$7$		0			0
$8$			1.12562i			0.397967i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.482874	−	0.423842i	−0.152698	−	0.134030i
$11$	1.66520	−	2.88421i	0.502076	−	0.869621i	−0.497921	−	0.867222i	$-0.665903\pi$
$11$	1.66520	−	2.88421i	0.502076	−	0.869621i	0.999997	−	0.00239862i	$-0.000763504\pi$
$12$	1.66055	−	0.958719i	0.479360	−	0.276758i
$13$			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			0
$15$	−0.437190	+	2.19291i	−0.112882	+	0.566208i
$16$	−1.75572	−	3.04100i	−0.438931	−	0.760250i
$17$	−4.80431	−	2.77377i	−1.16522	−	0.672738i	−0.212668	−	0.977125i	$-0.568215\pi$
$17$	−4.80431	−	2.77377i	−1.16522	−	0.672738i	−0.952549	+	0.304386i	$0.901549\pi$
$18$	0.248840	+	0.143668i	0.0586522	+	0.0338629i
$19$	0.828617	+	1.43521i	0.190098	+	0.329259i	0.945282	−	0.326253i	$-0.105786\pi$
$19$	0.828617	+	1.43521i	0.190098	+	0.329259i	−0.755185	+	0.655512i	$0.772453\pi$
$20$	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	$0.626316\pi$
$24$	0.562810	−	0.974816i	0.114883	−	0.198983i
$25$	−3.96942	+	3.04035i	−0.793883	+	0.608070i
$26$	0.653336	+	1.13161i	0.128130	+	0.221927i
$27$		−	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	$0.496493\pi$
$30$	0.206261	+	0.608495i	0.0376579	+	0.111095i
$31$	−3.13010	+	5.42150i	−0.562183	+	0.973729i	0.435123	+	0.900371i	$0.356705\pi$
$31$	−3.13010	+	5.42150i	−0.562183	+	0.973729i	−0.997306	+	0.0733583i	$0.976628\pi$
$32$	−2.82342	−	1.63010i	−0.499115	−	0.288164i
$33$	−2.88421	+	1.66520i	−0.502076	+	0.289874i
$34$	−1.59401			−0.273370
$35$		0			0
$36$	−1.91744			−0.319573
$37$	−6.71665	+	3.87786i	−1.10421	+	0.637516i	−0.937324	−	0.348460i	$-0.886705\pi$
$37$	−6.71665	+	3.87786i	−1.10421	+	0.637516i	−0.166887	+	0.985976i	$0.553372\pi$
$38$	0.412386	+	0.238091i	0.0668979	+	0.0386235i
$39$	2.27377	−	3.93829i	0.364095	−	0.630630i
$40$	2.38374	−	0.808014i	0.376902	−	0.127758i
$41$	−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	$0.0717143\pi$
$43$			2.92981i			0.446792i	−0.974728	+	0.223396i	$0.928286\pi$
$44$	3.19291	+	5.53029i	0.481350	+	0.833722i
$45$	1.47507	−	1.68052i	0.219891	−	0.250518i
$46$	−1.09671	+	1.89956i	−0.161701	+	0.280075i
$47$	−5.53029	+	3.19291i	−0.806675	+	0.465734i	−0.845800	−	0.533500i	$-0.820876\pi$
$47$	−5.53029	+	3.19291i	−0.806675	+	0.465734i	0.0391247	+	0.999234i	$0.487543\pi$
$48$			3.51145i			0.506833i
$49$		0			0
$50$	−0.550949	+	1.32684i	−0.0779159	+	0.187643i
$51$	2.77377	+	4.80431i	0.388406	+	0.672738i
$52$	−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	$0.682847\pi$
$54$	−0.143668	−	0.248840i	−0.0195507	−	0.0338629i
$55$	−7.30326	−	1.45601i	−0.984772	−	0.196329i
$56$		0			0
$57$		−	1.65723i		−	0.219506i
$58$	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	$0.132827\pi$
$60$	−3.22230	−	2.82836i	−0.415997	−	0.365140i
$61$	−3.65901	−	6.33759i	−0.468488	−	0.811446i	0.530863	−	0.847458i	$-0.321868\pi$
$61$	−3.65901	−	6.33759i	−0.468488	−	0.811446i	−0.999351	+	0.0360120i	$0.988535\pi$
$62$			1.79878i			0.228445i
$63$		0			0
$64$	6.08612			0.760765
$65$	9.63038	−	3.26440i	1.19450	−	0.404899i
$66$	−0.478471	+	0.828736i	−0.0588957	+	0.102010i
$67$	2.62934	+	1.51805i	0.321224	+	0.185459i	0.651938	−	0.758272i	$-0.273956\pi$
$67$	2.62934	+	1.51805i	0.321224	+	0.185459i	−0.330714	+	0.943731i	$0.607289\pi$
$68$	9.21197	−	5.31853i	1.11712	−	0.644967i
$69$	7.63366			0.918984
$70$		0			0
$71$	−3.77048			−0.447474			−0.223737	−	0.974650i	$-0.571826\pi$
$71$	−3.77048			−0.447474			−0.223737	+	0.974650i	$0.571826\pi$
$72$	−0.974816	+	0.562810i	−0.114883	+	0.0663278i
$73$	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
$75$	4.95779	−	0.648315i	0.572476	−	0.0748610i
$76$	−3.17764			−0.364501
$77$		0			0
$78$		−	1.30667i		−	0.147951i
$79$	−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	$-0.401101\pi$
$80$	−5.17964	+	5.90106i	−0.579101	+	0.659759i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.0174660	+	0.0100840i	−0.00192880	+	0.00111359i
$83$		−	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
$86$	0.420920	+	0.729054i	0.0453889	+	0.0786160i
$87$	−0.102760	−	0.0593285i	−0.0110170	−	0.00636069i
$88$	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	$0.591381\pi$
$90$	0.125620	−	0.630102i	0.0132415	−	0.0664186i
$91$		0			0
$92$		−	14.6371i		−	1.52602i
$93$	5.42150	−	3.13010i	0.562183	−	0.324576i
$94$	−0.917438	+	1.58905i	−0.0946265	+	0.163898i
$95$	2.44454	−	2.78502i	0.250805	−	0.285737i
$96$	1.63010	+	2.82342i	0.166372	+	0.288164i
$97$		−	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			0
$99$	3.33039			0.334717
$100$	−1.24310	−	9.50626i	−0.124310	−	0.950626i
$101$	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	$-0.127443\pi$
$102$	1.38045	+	0.797004i	0.136685	+	0.0789151i
$103$	−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	$0.413600\pi$
$108$	1.66055	+	0.958719i	0.159787	+	0.0922528i
$109$	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	$0.117061\pi$
$110$	−2.02653	+	0.686930i	−0.193222	+	0.0654962i
$111$	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	$0.796949\pi$
$114$	−0.238091	−	0.412386i	−0.0222993	−	0.0386235i
$115$	12.8285	+	11.2602i	1.19627	+	1.05002i
$116$	−0.113759	+	0.197036i	−0.0105622	+	0.0182943i
$117$	−3.93829	+	2.27377i	−0.364095	+	0.210210i
$118$		−	0.468387i		−	0.0431185i
$119$		0			0
$120$	−2.46839	−	0.492110i	−0.225332	−	0.0449233i
$121$	−0.0457629	−	0.0792637i	−0.00416027	−	0.00720579i
$122$	−1.82102	−	1.05136i	−0.164867	−	0.0951861i
$123$	0.0607860	+	0.0350948i	0.00548089	+	0.00316439i
$124$	−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	$-0.737568\pi$
$127$		−	16.5475i		−	1.46836i	0.678957	−	0.734178i	$-0.262432\pi$
$128$	7.16131	−	4.13458i	0.632976	−	0.365449i
$129$	1.46491	−	2.53729i	0.128978	−	0.223396i
$130$	1.92744	−	2.19589i	0.169047	−	0.192592i
$131$	−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	$0.907676\pi$
$132$		−	6.38582i		−	0.555815i
$133$		0			0
$134$	0.872379			0.0753621
$135$	−2.11771	+	0.717839i	−0.182264	+	0.0617817i
$136$	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	$0.447576\pi$
$138$	1.89956	−	1.09671i	0.161701	−	0.0933583i
$139$	−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
$142$	−0.938247	+	0.541697i	−0.0787359	+	0.0454582i
$143$	13.1160	+	7.57255i	1.09682	+	0.633249i
$144$	1.75572	−	3.04100i	0.146310	−	0.253417i
$145$	−0.0851767	−	0.251282i	−0.00707354	−	0.0208678i
$146$	0.676716			0.0560054
$147$		0			0
$148$		−	14.8711i		−	1.22240i
$149$	5.68502	+	9.84675i	0.465735	+	0.806677i	0.999234	−	0.0391236i	$-0.0124566\pi$
$149$	5.68502	+	9.84675i	0.465735	+	0.806677i	−0.533499	+	0.845801i	$0.679123\pi$
$150$	1.14056	−	0.873602i	0.0931259	−	0.0713293i
$151$	−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
$153$		−	5.54754i		−	0.448492i
$154$		0			0
$155$	13.7281	+	2.73690i	1.10267	+	0.219833i
$156$	4.35981	+	7.55142i	0.349064	+	0.604597i
$157$	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
$159$	0.369898	+	0.640682i	0.0293348	+	0.0508094i
$160$	−1.42533	+	7.14934i	−0.112682	+	0.565205i
$161$		0			0
$162$			0.287336i			0.0225752i
$163$	13.6450	−	7.87793i	1.06876	−	0.617047i	0.140916	−	0.990022i	$-0.454995\pi$
$163$	13.6450	−	7.87793i	1.06876	−	0.617047i	0.927842	+	0.372974i	$0.121662\pi$
$164$	0.0672922	−	0.116553i	0.00525463	−	0.00910129i
$165$	5.59680	+	4.91258i	0.435711	+	0.382444i
$166$	−0.175865	−	0.304608i	−0.0136498	−	0.0236421i
$167$		−	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
$170$	1.14424	+	3.37565i	0.0877592	+	0.258900i
$171$	−0.828617	+	1.43521i	−0.0633659	+	0.109753i
$172$	−4.86510	−	2.80887i	−0.370960	−	0.214174i
$173$	−7.38391	+	4.26310i	−0.561388	+	0.324118i	−0.753703	−	0.657216i	$-0.771734\pi$
$173$	−7.38391	+	4.26310i	−0.561388	+	0.324118i	0.192314	+	0.981333i	$0.438401\pi$
$174$	−0.0340944			−0.00258469
$175$		0			0
$176$	−11.6945			−0.881506
$177$	−1.41171	+	0.815051i	−0.106111	+	0.0612630i
$178$	3.23496	+	1.86770i	0.242470	+	0.139990i
$179$	−5.89031	+	10.2023i	−0.440262	+	0.762557i	−0.997709	−	0.0676564i	$-0.978448\pi$
$179$	−5.89031	+	10.2023i	−0.440262	+	0.762557i	0.557446	+	0.830213i	$0.311781\pi$
$180$	1.37641	+	4.06058i	0.102592	+	0.302658i
$181$	−9.08967			−0.675630			−0.337815	−	0.941213i	$-0.609688\pi$
$181$	−9.08967			−0.675630			−0.337815	+	0.941213i	$0.609688\pi$
$182$		0			0
$183$			7.31802i			0.540964i
$184$	−4.29630	−	7.44141i	−0.316727	−	0.548588i
$185$	13.0337	+	11.4403i	0.958254	+	0.841105i
$186$	0.899391	−	1.55779i	0.0659465	−	0.114223i
$187$	−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	$-0.900778\pi$
$191$	−10.2478	−	17.7498i	−0.741507	−	1.28433i	0.210302	−	0.977637i	$-0.432555\pi$
$192$	−5.27073	−	3.04306i	−0.380382	−	0.219614i
$193$	−7.39842	−	4.27148i	−0.532550	−	0.307468i	0.209504	−	0.977808i	$-0.432815\pi$
$193$	−7.39842	−	4.27148i	−0.532550	−	0.307468i	−0.742054	+	0.670340i	$0.766148\pi$
$194$	−0.437190	−	0.757235i	−0.0313884	−	0.0543663i
$195$	−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	$-0.163701\pi$
$198$	0.828736	−	0.478471i	0.0588957	−	0.0340034i
$199$	−1.89549	+	3.28309i	−0.134368	+	0.232732i	−0.925356	−	0.379100i	$-0.876234\pi$
$199$	−1.89549	+	3.28309i	−0.134368	+	0.232732i	0.790988	+	0.611832i	$0.209567\pi$
$200$	−3.42228	−	4.46805i	−0.241992	−	0.315939i
$201$	−1.51805	−	2.62934i	−0.107075	−	0.185459i
$202$		−	4.60877i		−	0.324272i
$203$		0			0
$204$	−10.6371			−0.744744
$205$	0.0503848	+	0.148642i	0.00351903	+	0.0103816i
$206$	−0.760278	+	1.31684i	−0.0529711	+	0.0917486i
$207$	−6.61094	−	3.81683i	−0.459492	−	0.265288i
$208$	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
$213$	3.26533	+	1.88524i	0.223737	+	0.129175i
$214$	−0.741573	+	1.28444i	−0.0506929	+	0.0878026i
$215$	6.20450	−	2.10313i	0.423143	−	0.143432i
$216$	1.12562			0.0765888
$217$		0			0
$218$		−	0.931218i		−	0.0630700i
$219$	−1.17757	−	2.03961i	−0.0795728	−	0.137824i
$220$	9.41956	−	10.7315i	0.635067	−	0.723519i
$221$	12.6138	−	21.8478i	0.848498	−	1.46964i
$222$	1.92993	−	1.11425i	0.129529	−	0.0747835i
$223$		−	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
$226$	1.81895	+	3.15051i	0.120995	+	0.209569i
$227$	−7.77575	−	4.48933i	−0.516095	−	0.297967i	0.219241	−	0.975671i	$-0.429642\pi$
$227$	−7.77575	−	4.48933i	−0.516095	−	0.297967i	−0.735335	+	0.677703i	$0.762975\pi$
$228$	2.75192	+	1.58882i	0.182250	+	0.105222i
$229$	2.54306	+	4.40471i	0.168050	+	0.291071i	0.937734	−	0.347354i	$-0.112920\pi$
$229$	2.54306	+	4.40471i	0.168050	+	0.291071i	−0.769684	+	0.638425i	$0.779586\pi$
$230$	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	$0.0799052\pi$
$234$	−0.653336	+	1.13161i	−0.0427099	+	0.0739757i
$235$	10.7315	+	9.41956i	0.700048	+	0.614465i
$236$	1.56281	+	2.70687i	0.101730	+	0.176202i
$237$			11.9403i			0.775608i
$238$		0			0
$239$	−7.44905			−0.481839			−0.240920	−	0.970545i	$-0.577449\pi$
$239$	−7.44905			−0.481839			−0.240920	+	0.970545i	$0.577449\pi$
$240$	7.43623	−	2.52065i	0.480007	−	0.162707i
$241$	−12.0879	+	20.9368i	−0.778650	+	1.34866i	0.154070	+	0.988060i	$0.450762\pi$
$241$	−12.0879	+	20.9368i	−0.778650	+	1.34866i	−0.932720	+	0.360601i	$0.882572\pi$
$242$	−0.0227753	−	0.0131493i	−0.00146405	−	0.000845271i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	14.0319			0.898297
$245$		0			0
$246$	0.0201680			0.00128586
$247$	−6.52666	+	3.76817i	−0.415281	+	0.239763i
$248$	−6.10255	−	3.52331i	−0.387512	−	0.223730i
$249$	−0.612055	+	1.06011i	−0.0387874	+	0.0671817i
$250$	3.20536	+	0.214294i	0.202725	+	0.0135532i
$251$	−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
$255$	8.18303	−	9.32277i	0.512441	−	0.583814i
$256$	−4.89810	+	8.48376i	−0.306131	+	0.530235i
$257$	6.35139	−	3.66697i	0.396189	−	0.228740i	−0.288650	−	0.957435i	$-0.593206\pi$
$257$	6.35139	−	3.66697i	0.396189	−	0.228740i	0.684838	+	0.728695i	$0.259873\pi$
$258$		−	0.841839i		−	0.0524106i
$259$		0			0
$260$	−3.81213	+	19.1214i	−0.236418	+	1.18586i
$261$	0.0593285	+	0.102760i	0.00367234	+	0.00636069i
$262$	−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	$0.761160\pi$
$264$	−1.87438	−	3.24652i	−0.115360	−	0.199810i
$265$	−0.323431	+	1.62231i	−0.0198682	+	0.0996575i
$266$		0			0
$267$		−	13.0001i		−	0.795596i
$268$	−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	$0.329395\pi$
$270$	−0.423842	+	0.482874i	−0.0257942	+	0.0293868i
$271$	12.0845	+	20.9309i	0.734080	+	1.27146i	0.955126	+	0.296201i	$0.0957198\pi$
$271$	12.0845	+	20.9309i	0.734080	+	1.27146i	−0.221045	+	0.975264i	$0.570947\pi$
$272$			19.4799i			1.18114i
$273$		0			0
$274$	4.27272			0.258125
$275$	2.15914	+	16.5114i	0.130201	+	0.995675i
$276$	−7.31853	+	12.6761i	−0.440524	+	0.763010i
$277$	20.1071	+	11.6088i	1.20812	+	0.697508i	0.962348	−	0.271820i	$-0.0876257\pi$
$277$	20.1071	+	11.6088i	1.20812	+	0.697508i	0.245771	+	0.969328i	$0.420959\pi$
$278$	−2.36818	+	1.36727i	−0.142034	+	0.0820032i
$279$	−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	$0.378923\pi$
$282$	1.58905	−	0.917438i	0.0946265	−	0.0546326i
$283$	−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
$285$	−3.50954	+	1.18963i	−0.207887	+	0.0704674i
$286$	4.35173			0.257323
$287$		0			0
$288$		−	3.26020i		−	0.192109i
$289$	6.88760	+	11.9297i	0.405153	+	0.701746i
$290$	−0.0572965	−	0.0502918i	−0.00336456	−	0.00295324i
$291$	−1.52153	+	2.63537i	−0.0891936	+	0.154488i
$292$	−3.91083	+	2.25792i	−0.228864	+	0.132135i
$293$			27.0063i			1.57772i	0.614571	+	0.788862i	$0.289329\pi$
$293$			27.0063i			1.57772i	−0.614571	+	0.788862i	$0.710671\pi$
$294$		0			0
$295$	−3.57467	−	0.712664i	−0.208125	−	0.0414929i
$296$	−4.36500	−	7.56040i	−0.253710	−	0.439439i
$297$	−2.88421	−	1.66520i	−0.167359	−	0.0966245i
$298$	2.82932	+	1.63351i	0.163898	+	0.0946267i
$299$	−17.3572	−	30.0635i	−1.00379	−	1.73862i
$300$	−3.67657	+	8.85421i	−0.212267	+	0.511198i
$301$		0			0
$302$			2.56888i			0.147822i
$303$	−13.8907	+	8.01983i	−0.798002	+	0.460727i
$304$	2.90964	−	5.03965i	0.166879	−	0.289044i
$305$	−10.7946	+	12.2981i	−0.618098	+	0.704187i
$306$	−0.797004	−	1.38045i	−0.0455617	−	0.0789151i
$307$			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
$310$	3.80930	−	1.29123i	0.216354	−	0.0733372i
$311$	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	$-0.134324\pi$
$312$	4.43301	+	2.55940i	0.250970	+	0.144898i
$313$	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	$0.639253\pi$
$318$	0.184091	+	0.106285i	0.0103233	+	0.00596016i
$319$	0.197587	−	0.342231i	0.0110628	−	0.0191613i
$320$	−4.36885	−	12.8886i	−0.244226	−	0.720497i
$321$	5.16172			0.288099
$322$		0			0
$323$		−	9.19357i		−	0.511544i
$324$	−0.958719	−	1.66055i	−0.0532622	−	0.0922528i
$325$	−13.8261	−	18.0511i	−0.766935	−	1.00129i
$326$	2.26361	−	3.92069i	0.125370	−	0.217147i
$327$	−2.80668	+	1.62043i	−0.155209	+	0.0896102i
$328$		−	0.0790069i		−	0.00436243i
$329$		0			0
$330$	2.09849	+	0.418365i	0.115518	+	0.0230302i
$331$	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
$333$	−6.71665	−	3.87786i	−0.368070	−	0.212505i
$334$	−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	$-0.958908\pi$
$337$		−	4.72659i		−	0.257474i	0.991679	−	0.128737i	$-0.0410923\pi$
$338$	−1.91112	+	1.10339i	−0.103951	+	0.0600164i
$339$	6.33039	−	10.9646i	0.343820	−	0.595513i
$340$	−17.8758	−	15.6905i	−0.969453	−	0.850934i
$341$	10.4245	+	18.0557i	0.564517	+	0.977772i
$342$			0.476183i			0.0257490i
$343$		0			0
$344$	−3.29785			−0.177808
$345$	−5.47973	−	16.1659i	−0.295019	−	0.870342i
$346$	−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	$0.790753\pi$
$348$	0.197036	−	0.113759i	0.0105622	−	0.00609811i
$349$	5.04930			0.270283			0.135141	−	0.990826i	$-0.456851\pi$
$349$	5.04930			0.270283			0.135141	+	0.990826i	$0.456851\pi$
$350$		0			0
$351$	4.54754			0.242730
$352$	−9.40310	+	5.42888i	−0.501187	+	0.289360i
$353$	−13.9417	−	8.04924i	−0.742042	−	0.428418i	0.0807694	−	0.996733i	$-0.474262\pi$
$353$	−13.9417	−	8.04924i	−0.742042	−	0.428418i	−0.822811	+	0.568315i	$0.807596\pi$
$354$	−0.234193	+	0.405635i	−0.0124472	+	0.0215592i
$355$	2.70660	+	7.98480i	0.143651	+	0.423789i
$356$	−24.9270			−1.32113
$357$		0			0
$358$			3.38499i			0.178902i
$359$	0.153241	+	0.265421i	0.00808776	+	0.0140084i	0.870041	−	0.492979i	$-0.164092\pi$
$359$	0.153241	+	0.265421i	0.00808776	+	0.0140084i	−0.861953	+	0.506988i	$0.830759\pi$
$360$	1.89163	+	1.66037i	0.0996977	+	0.0875093i
$361$	8.12679	−	14.0760i	0.427726	−	0.740843i
$362$	−2.26188	+	1.30589i	−0.118882	+	0.0686363i
$363$			0.0915259i			0.00480386i
$364$		0			0
$365$	1.02964	−	5.16461i	0.0538940	−	0.270328i
$366$	1.05136	+	1.82102i	0.0549557	+	0.0951861i
$367$	−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
$369$	−0.0350948	−	0.0607860i	−0.00182696	−	0.00316439i
$370$	4.88690	+	0.974276i	0.254058	+	0.0506502i
$371$		0			0
$372$			12.0036i			0.622355i
$373$	−16.3140	+	9.41887i	−0.844705	+	0.487691i	−0.858861	−	0.512209i	$-0.828827\pi$
$373$	−16.3140	+	9.41887i	−0.844705	+	0.487691i	0.0141557	+	0.999900i	$0.495494\pi$
$374$	−2.65434	+	4.59744i	−0.137252	+	0.237728i
$375$	−4.93184	−	10.0338i	−0.254679	−	0.518143i
$376$	−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	$0.619298\pi$
$380$	2.28103	+	6.72933i	0.117015	+	0.345208i
$381$	−8.27377	+	14.3306i	−0.423878	+	0.734178i
$382$	−5.10014	−	2.94457i	−0.260946	−	0.150657i
$383$	−21.6995	+	12.5282i	−1.10879	+	0.640161i	−0.938516	−	0.345235i	$-0.887799\pi$
$383$	−21.6995	+	12.5282i	−1.10879	+	0.640161i	−0.170276	+	0.985396i	$0.554466\pi$
$384$	−8.26917			−0.421984
$385$		0			0
$386$	−2.45470			−0.124941
$387$	−2.53729	+	1.46491i	−0.128978	+	0.0744653i
$388$	5.05315	+	2.91744i	0.256535	+	0.148110i
$389$	−6.73590	+	11.6669i	−0.341524	+	0.591536i	−0.984716	−	0.174169i	$-0.944276\pi$
$389$	−6.73590	+	11.6669i	−0.341524	+	0.591536i	0.643192	+	0.765705i	$0.277610\pi$
$390$	−2.76715	+	0.937979i	−0.140120	+	0.0474964i
$391$	42.3480			2.14163
$392$		0			0
$393$			5.29785i			0.267241i
$394$	−1.98385	−	3.43613i	−0.0999449	−	0.173110i
$395$	−17.6129	+	20.0660i	−0.886199	+	1.00963i
$396$	−3.19291	+	5.53029i	−0.160450	+	0.277907i
$397$	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	$-0.947803\pi$
$401$	−12.7093	−	22.0131i	−0.634670	−	1.09928i	0.351915	−	0.936032i	$-0.385531\pi$
$402$	−0.755502	−	0.436189i	−0.0376810	−	0.0217552i
$403$	−24.6545	−	14.2343i	−1.22813	−	0.709059i
$404$	15.3775	+	26.6346i	0.765060	+	1.32512i
$405$	2.19291	+	0.437190i	0.108967	+	0.0217241i
$406$		0			0
$407$			25.8296i			1.28033i
$408$	−5.40783	+	3.12221i	−0.267727	+	0.154573i
$409$	9.36556	−	16.2216i	0.463097	−	0.802108i	−0.536016	−	0.844208i	$-0.680071\pi$
$409$	9.36556	−	16.2216i	0.463097	−	0.802108i	0.999113	+	0.0420997i	$0.0134047\pi$
$410$	0.0338928	+	0.0297493i	0.00167385	+	0.00146921i
$411$	−7.43507	−	12.8779i	−0.366745	−	0.635221i
$412$		−	10.1469i		−	0.499903i
$413$		0			0
$414$	−2.19342			−0.107801
$415$	−2.59231	+	0.878713i	−0.127252	+	0.0431343i
$416$	7.41296	−	12.8396i	0.363450	−	0.629514i
$417$	8.24184	+	4.75843i	0.403605	+	0.233021i
$418$	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
$423$	−5.53029	−	3.19291i	−0.268892	−	0.155245i
$424$	0.416364	−	0.721164i	0.0202204	−	0.0350228i
$425$	27.5035	−	3.59655i	1.33412	−	0.174458i
$426$	1.08339			0.0524906
$427$		0			0
$428$		−	9.89727i		−	0.478403i
$429$	−7.57255	−	13.1160i	−0.365606	−	0.633249i
$430$	1.24178	−	1.41473i	0.0598837	−	0.0682244i
$431$	−18.3063	+	31.7075i	−0.881784	+	1.52729i	−0.0324277	+	0.999474i	$0.510324\pi$
$431$	−18.3063	+	31.7075i	−0.881784	+	1.52729i	−0.849356	+	0.527820i	$0.823009\pi$
$432$	−3.04100	+	1.75572i	−0.146310	+	0.0844722i
$433$			18.0047i			0.865252i	0.901574	+	0.432626i	$0.142413\pi$
$433$			18.0047i			0.865252i	−0.901574	+	0.432626i	$0.857587\pi$
$434$		0			0
$435$	−0.0518757	+	0.260205i	−0.00248725	+	0.0124759i
$436$	3.10708	+	5.38163i	0.148802	+	0.257733i
$437$	−10.9559	−	6.32538i	−0.524090	−	0.302584i
$438$	−0.586053	−	0.338358i	−0.0280027	−	0.0161674i
$439$	9.68731	+	16.7789i	0.462350	+	0.800814i	0.999078	−	0.0429418i	$-0.0136730\pi$
$439$	9.68731	+	16.7789i	0.462350	+	0.800814i	−0.536727	+	0.843756i	$0.680340\pi$
$440$	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	$0.461066\pi$
$444$	−7.43556	+	12.8788i	−0.352876	+	0.611199i
$445$	19.1762	−	21.8470i	0.909038	−	1.03565i
$446$	−1.13020	−	1.95756i	−0.0535164	−	0.0926931i
$447$		−	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	$0.219165\pi$
$450$	−1.42455	+	0.186284i	−0.0671540	+	0.00878152i
$451$	−0.116880	+	0.202441i	−0.00550365	+	0.00953259i
$452$	−21.0239	−	12.1381i	−0.988880	−	0.570930i
$453$	7.74255	−	4.47016i	0.363777	−	0.210027i
$454$	−2.57989			−0.121080
$455$		0			0
$456$	1.86542			0.0873561
$457$	32.4156	−	18.7152i	1.51634	−	0.875459i	0.516523	−	0.856273i	$-0.327226\pi$
$457$	32.4156	−	18.7152i	1.51634	−	0.875459i	0.999816	−	0.0191857i	$-0.00610737\pi$
$458$	1.26563	+	0.730712i	0.0591390	+	0.0341439i
$459$	−2.77377	+	4.80431i	−0.129469	+	0.224246i
$460$	−30.9971	+	10.5071i	−1.44525	+	0.489894i
$461$	−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	$-0.946431\pi$
$463$		−	7.20833i		−	0.334999i	0.985872	−	0.167500i	$-0.0535693\pi$
$464$	−0.208329	−	0.360836i	−0.00967143	−	0.0167514i
$465$	−10.5204	−	9.23426i	−0.487873	−	0.428229i
$466$	3.13458	−	5.42926i	0.145207	−	0.251506i
$467$	10.4607	−	6.03950i	0.484065	−	0.279475i	−0.238044	−	0.971254i	$-0.576506\pi$
$467$	10.4607	−	6.03950i	0.484065	−	0.279475i	0.722109	+	0.691779i	$0.243173\pi$
$468$		−	8.71963i		−	0.403065i
$469$		0			0
$470$	4.02372	+	0.802189i	0.185601	+	0.0370022i
$471$	−1.67316	−	2.89800i	−0.0770952	−	0.133533i
$472$	1.58905	+	0.917438i	0.0731419	+	0.0422285i
$473$	8.45018	+	4.87871i	0.388540	+	0.224323i
$474$	1.71544	+	2.97123i	0.0787929	+	0.136473i
$475$	−7.65266	−	3.17764i	−0.351128	−	0.145800i
$476$		0			0
$477$		−	0.739795i		−	0.0338729i
$478$	−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	$0.318871\pi$
$480$	4.80904	−	5.47885i	0.219502	−	0.250074i
$481$	−17.6347	−	30.5443i	−0.804075	−	1.39270i
$482$			6.94657i			0.316408i
$483$		0			0
$484$	0.175495			0.00797705
$485$	−6.44432	+	2.18443i	−0.292622	+	0.0991896i
$486$	0.143668	−	0.248840i	0.00651691	−	0.0112876i
$487$	−34.5887	−	19.9698i	−1.56737	−	0.904919i	−0.996475	−	0.0838930i	$-0.973265\pi$
$487$	−34.5887	−	19.9698i	−1.56737	−	0.904919i	−0.570891	−	0.821026i	$-0.693402\pi$
$488$	7.13372	−	4.11866i	0.322928	−	0.186443i
$489$	−15.7559			−0.712505
$490$		0			0
$491$	−31.5989			−1.42604			−0.713019	−	0.701145i	$-0.752673\pi$
$491$	−31.5989			−1.42604			−0.713019	+	0.701145i	$0.752673\pi$
$492$	−0.116553	+	0.0672922i	−0.00525463	+	0.00303376i
$493$	−0.570066	−	0.329127i	−0.0256745	−	0.0148232i
$494$	−1.08273	+	1.87534i	−0.0487143	+	0.0843757i
$495$	−2.39069	−	7.05282i	−0.107453	−	0.317001i
$496$	21.9824			0.987037
$497$		0			0
$498$			0.351730i			0.0157614i
$499$	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	$0.483667\pi$
$500$	−19.2392	+	9.45650i	−0.860402	+	0.422907i
$501$	−11.2971	+	19.5671i	−0.504716	+	0.874194i
$502$	−1.49354	+	0.862295i	−0.0666599	+	0.0384861i
$503$			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
$506$	3.65248	+	6.32628i	0.162373	+	0.281238i
$507$	6.65118	+	3.84006i	0.295389	+	0.170543i
$508$	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	$-0.431902\pi$
$510$	0.696884	−	3.49552i	0.0308585	−	0.154784i
$511$		0			0
$512$			19.3531i			0.855296i
$513$	1.43521	−	0.828617i	0.0633659	−	0.0365843i
$514$	1.05365	−	1.82498i	0.0464746	−	0.0804965i
$515$	8.89318	+	7.80596i	0.391880	+	0.343972i
$516$	2.80887	+	4.86510i	0.123653	+	0.214174i
$517$			21.2673i			0.935335i
$518$		0			0
$519$	8.52620			0.374259
$520$	3.67448	+	10.8402i	0.161136	+	0.475372i
$521$	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	$0.0707281\pi$
$522$	0.0295266	+	0.0170472i	0.00129235	+	0.000746136i
$523$	−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
$528$	10.1277	+	5.84725i	0.440753	+	0.254469i
$529$	17.6364	−	30.5471i	0.766798	−	1.32813i
$530$	0.152591	+	0.450162i	0.00662812	+	0.0195538i
$531$	1.63010			0.0707404
$532$		0			0
$533$		−	0.319190i		−	0.0138257i
$534$	−1.86770	−	3.23496i	−0.0808235	−	0.139990i
$535$	8.67438	+	7.61391i	0.375026	+	0.329178i
$536$	−1.70875	+	2.95963i	−0.0738066	+	0.127837i
$537$	10.2023	−	5.89031i	0.440262	−	0.254186i
$538$			4.61130i			0.198807i
$539$		0			0
$540$	0.838284	−	4.20477i	0.0360740	−	0.180945i
$541$	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
$543$	7.87189	+	4.54484i	0.337815	+	0.195038i
$544$	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	$0.176452\pi$
$547$			24.6221i			1.05277i	−0.850248	+	0.526383i	$0.823548\pi$
$548$	−24.6926	+	14.2563i	−1.05482	+	0.608998i
$549$	3.65901	−	6.33759i	0.156163	−	0.270482i
$550$	2.90944	+	3.79850i	0.124059	+	0.161969i
$551$	0.0983213	+	0.170297i	0.00418863	+	0.00725491i
$552$			8.59260i			0.365725i
$553$		0			0
$554$	6.67127			0.283435
$555$	−5.56736	−	16.4244i	−0.236321	−	0.697177i
$556$	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	$0.496928\pi$
$558$	−1.55779	+	0.899391i	−0.0659465	+	0.0380742i
$559$	−13.3234			−0.563521
$560$		0			0
$561$	18.4755			0.780036
$562$	3.09736	−	1.78826i	0.130654	−	0.0754333i
$563$	0.196151	+	0.113248i	0.00826680	+	0.00477284i	0.504128	−	0.863629i	$-0.331814\pi$
$563$	0.196151	+	0.113248i	0.00826680	+	0.00477284i	−0.495861	+	0.868402i	$0.665147\pi$
$564$	−6.12221	+	10.6040i	−0.257792	+	0.446508i
$565$	26.8119	−	9.08840i	1.12799	−	0.382352i
$566$	−2.49056			−0.104686
$567$		0			0
$568$		−	4.24413i		−	0.178080i
$569$	−6.40275	−	11.0899i	−0.268417	−	0.464912i	0.700036	−	0.714108i	$-0.253167\pi$
$569$	−6.40275	−	11.0899i	−0.268417	−	0.464912i	−0.968453	+	0.249195i	$0.919834\pi$
$570$	−0.702404	+	0.800236i	−0.0294205	+	0.0335182i
$571$	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
$573$			20.4957i			0.856219i
$574$		0			0
$575$	14.6371	−	35.2502i	0.610408	−	1.47003i
$576$	3.04306	+	5.27073i	0.126794	+	0.219614i
$577$	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
$579$	4.27148	+	7.39842i	0.177517	+	0.307468i
$580$	0.498926	+	0.0994684i	0.0207168	+	0.00413020i
$581$		0			0
$582$			0.874380i			0.0362442i
$583$	−2.13372	+	1.23191i	−0.0883697	+	0.0510203i
$584$	−1.32550	+	2.29583i	−0.0548494	+	0.0950020i
$585$	7.64225	+	6.70796i	0.315968	+	0.277340i
$586$	3.87994	+	6.72025i	0.160279	+	0.277611i
$587$		−	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
$590$	−0.991909	+	0.336226i	−0.0408362	+	0.0138422i
$591$	−6.90429	+	11.9586i	−0.284004	+	0.491910i
$592$	23.5852	+	13.6169i	0.969344	+	0.559651i
$593$	7.92838	−	4.57745i	0.325579	−	0.187973i	−0.328297	−	0.944574i	$-0.606475\pi$
$593$	7.92838	−	4.57745i	0.325579	−	0.187973i	0.653877	+	0.756601i	$0.273141\pi$
$594$	−0.956942			−0.0392638
$595$		0			0
$596$	−21.8014			−0.893018
$597$	3.28309	−	1.89549i	0.134368	−	0.0775773i
$598$	−8.63833	−	4.98734i	−0.353247	−	0.203948i
$599$	20.1368	−	34.8780i	0.822767	−	1.42507i	−0.0808467	−	0.996727i	$-0.525762\pi$
$599$	20.1368	−	34.8780i	0.822767	−	1.42507i	0.903614	−	0.428348i	$-0.140904\pi$
$600$	0.729756	+	5.58059i	0.0297922	+	0.227827i
$601$	8.82450			0.359959			0.179980	−	0.983670i	$-0.442397\pi$
$601$	8.82450			0.359959			0.179980	+	0.983670i	$0.442397\pi$
$602$		0			0
$603$			3.03610i			0.123639i
$604$	−8.57126	−	14.8459i	−0.348760	−	0.604070i
$605$	−0.135007	+	0.153811i	−0.00548883	+	0.00625332i
$606$	−2.30438	+	3.99131i	−0.0936092	+	0.162136i
$607$	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
$612$	9.21197	+	5.31853i	0.372372	+	0.214989i
$613$	1.83025	+	1.05670i	0.0739232	+	0.0426796i	0.536506	−	0.843896i	$-0.319744\pi$
$613$	1.83025	+	1.05670i	0.0739232	+	0.0426796i	−0.462583	+	0.886576i	$0.653077\pi$
$614$	0.322795	+	0.559097i	0.0130269	+	0.0225633i
$615$	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	$-0.118285\pi$
$618$	1.31684	−	0.760278i	0.0529711	−	0.0305829i
$619$	7.31895	−	12.6768i	0.294173	−	0.509523i	−0.680619	−	0.732638i	$-0.738289\pi$
$619$	7.31895	−	12.6768i	0.294173	−	0.509523i	0.974792	+	0.223114i	$0.0716223\pi$
$620$	−17.7061	+	20.1722i	−0.711095	+	0.810137i
$621$	3.81683	+	6.61094i	0.153164	+	0.265288i
$622$		−	8.21744i		−	0.329489i
$623$		0			0
$624$	−15.9684			−0.639249
$625$	6.51251	−	24.1368i	0.260501	−	0.965474i
$626$	1.91488	−	3.31668i	0.0765341	−	0.132561i
$627$	−4.77980	−	2.75962i	−0.190887	−	0.110209i
$628$	−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
$633$	0.0990874	+	0.0572082i	0.00393837	+	0.00227382i
$634$	−4.19403	+	7.26428i	−0.166566	+	0.288501i
$635$	−35.0429	+	11.8785i	−1.39064	+	0.471383i
$636$	−1.41851			−0.0562477
$637$		0			0
$638$		−	0.113548i		−	0.00449540i
$639$	−1.88524	−	3.26533i	−0.0745790	−	0.129175i
$640$	−13.8965	−	12.1976i	−0.549308	−	0.482154i
$641$	6.52024	−	11.2934i	0.257534	−	0.446062i	−0.708047	−	0.706166i	$-0.750423\pi$
$641$	6.52024	−	11.2934i	0.257534	−	0.446062i	0.965581	+	0.260104i	$0.0837567\pi$
$642$	1.28444	−	0.741573i	0.0506929	−	0.0292675i
$643$		−	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
$646$	−1.32082	−	2.28773i	−0.0519670	−	0.0900095i
$647$	30.2927	+	17.4895i	1.19093	+	0.687582i	0.958517	−	0.285035i	$-0.0920054\pi$
$647$	30.2927	+	17.4895i	1.19093	+	0.687582i	0.232411	+	0.972618i	$0.425339\pi$
$648$	−0.974816	−	0.562810i	−0.0382944	−	0.0221093i
$649$	−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	$0.115158\pi$
$654$	−0.465609	+	0.806458i	−0.0182067	+	0.0315350i
$655$	−7.81473	+	8.90317i	−0.305347	+	0.347875i
$656$	0.123234	+	0.213447i	0.00481146	+	0.00833370i
$657$			2.35514i			0.0918827i
$658$		0			0
$659$	−8.54282			−0.332781			−0.166390	−	0.986060i	$-0.553211\pi$
$659$	−8.54282			−0.332781			−0.166390	+	0.986060i	$0.553211\pi$
$660$	−13.5233	+	4.58399i	−0.526395	+	0.178432i
$661$	−15.1715	+	26.2779i	−0.590104	+	1.02209i	0.404114	+	0.914709i	$0.367580\pi$
$661$	−15.1715	+	26.2779i	−0.590104	+	1.02209i	−0.994218	+	0.107382i	$0.965753\pi$
$662$	6.19400	+	3.57611i	0.240737	+	0.138989i
$663$	−21.8478	+	12.6138i	−0.848498	+	0.489881i
$664$	1.37788			0.0534722
$665$		0			0
$666$	−2.22850			−0.0863525
$667$	−0.784435	+	0.452894i	−0.0303734	+	0.0175361i
$668$	37.5187	+	21.6614i	1.45164	+	0.838107i
$669$	−3.93337	+	6.81279i	−0.152073	+	0.263398i
$670$	−0.626227	−	1.84745i	−0.0241933	−	0.0713731i
$671$	−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	$-0.285150\pi$
$674$	−0.679059	−	1.17617i	−0.0261564	−	0.0453042i
$675$	3.04035	+	3.96942i	0.117023	+	0.152783i
$676$	7.36308	−	12.7532i	0.283195	−	0.490509i
$677$	20.2833	−	11.7105i	0.779549	−	0.450073i	−0.0567215	−	0.998390i	$-0.518065\pi$
$677$	20.2833	−	11.7105i	0.779549	−	0.450073i	0.836270	+	0.548317i	$0.184731\pi$
$678$		−	3.63790i		−	0.139713i
$679$		0			0
$680$	−13.6935	−	2.73000i	−0.525121	−	0.104691i
$681$	4.48933	+	7.77575i	0.172032	+	0.297967i
$682$	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	$-0.763753\pi$
$684$	−1.58882	−	2.75192i	−0.0607501	−	0.105222i
$685$	6.50107	−	32.6089i	0.248393	−	1.24592i
$686$		0			0
$687$		−	5.08612i		−	0.194047i
$688$	8.90956	−	5.14393i	0.339674	−	0.196111i
$689$	1.68212	−	2.91353i	0.0640838	−	0.110996i
$690$	−3.68610	−	3.23546i	−0.140327	−	0.123172i
$691$	12.3057	+	21.3142i	0.468133	+	0.810829i	0.999337	−	0.0364144i	$-0.0115936\pi$
$691$	12.3057	+	21.3142i	0.468133	+	0.810829i	−0.531204	+	0.847244i	$0.678260\pi$
$692$		−	16.3485i		−	0.621476i
$693$		0			0
$694$	−4.06819			−0.154426
$695$	6.83157	+	20.1540i	0.259136	+	0.764483i
$696$	0.0667814	−	0.115669i	0.00253134	−	0.00438441i
$697$	0.337213	+	0.194690i	0.0127728	+	0.00737441i
$698$	1.25647	−	0.725422i	0.0475580	−	0.0274576i
$699$	−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	$0.338529\pi$
$702$	1.13161	−	0.653336i	0.0427099	−	0.0246586i
$703$	−11.1311	−	6.42652i	−0.419816	−	0.242381i
$704$	10.1346	−	17.5536i	0.381962	−	0.661577i
$705$	−4.58399	−	13.5233i	−0.172643	−	0.509319i
$706$	−4.62567			−0.174089
$707$		0			0
$708$		−	3.12562i		−	0.117468i
$709$	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	$0.762766\pi$
$710$	1.82067	+	1.59809i	0.0683285	+	0.0599751i
$711$	5.97016	−	10.3406i	0.223899	−	0.387804i
$712$	−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
$717$	6.45107	+	3.72453i	0.240920	+	0.139095i
$718$	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	$0.759545\pi$
$720$	−7.70029	−	1.53517i	−0.286973	−	0.0572123i
$721$		0			0
$722$		−	4.67023i		−	0.173808i
$723$	20.9368	−	12.0879i	0.778650	−	0.449554i
$724$	8.71444	−	15.0939i	0.323870	−	0.560959i
$725$	−0.470999	+	0.360759i	−0.0174925	+	0.0133983i
$726$	0.0131493	+	0.0227753i	0.000488017	+	0.000845271i
$727$		−	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
$730$	−0.485773	−	1.43309i	−0.0179793	−	0.0530410i
$731$	8.12662	−	14.0757i	0.300574	−	0.520609i
$732$	−12.1519	−	7.01593i	−0.449149	−	0.259316i
$733$	−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
$738$	−0.0174660	−	0.0100840i	−0.000642932	−	0.000371197i
$739$	−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	$0.973028\pi$
$740$	−31.4928	+	10.6751i	−1.15770	+	0.392423i
$741$	7.53634			0.276854
$742$		0			0
$743$		−	4.04189i		−	0.148283i	−0.997248	−	0.0741413i	$-0.976378\pi$
$743$		−	4.04189i		−	0.148283i	0.997248	−	0.0741413i	$-0.0236216\pi$
$744$	3.52331	+	6.10255i	0.129171	+	0.223730i
$745$	16.7717	−	19.1076i	0.614466	−	0.700049i
$746$	−2.70638	+	4.68759i	−0.0990876	+	0.171625i
$747$	1.06011	−	0.612055i	0.0387874	−	0.0223939i
$748$		−	35.4256i		−	1.29529i
$749$		0			0
$750$	−2.66877	−	1.78826i	−0.0974498	−	0.0652981i
$751$	−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
$753$	5.19789	+	3.00100i	0.189421	+	0.109363i
$754$	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	$0.180847\pi$
$757$			29.6087i			1.07615i	−0.842898	+	0.538073i	$0.819153\pi$
$758$	−3.54681	+	2.04775i	−0.128826	+	0.0743778i
$759$	12.7115	−	22.0170i	0.461400	−	0.799168i
$760$	3.13487	+	2.75163i	0.113714	+	0.0998120i
$761$	−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	$0.916503\pi$
$762$			4.75470i			0.172245i
$763$		0			0
$764$	39.2992			1.42179
$765$	−11.7481	+	3.98224i	−0.424753	+	0.143978i
$766$	−3.59980	+	6.23504i	−0.130066	+	0.225281i
$767$	6.41981	+	3.70648i	0.231806	+	0.133833i
$768$	8.48376	−	4.89810i	0.306131	−	0.176745i
$769$	−20.6367			−0.744178			−0.372089	−	0.928197i	$-0.621358\pi$
$769$	−20.6367			−0.744178			−0.372089	+	0.928197i	$0.621358\pi$
$770$		0			0
$771$	−7.33395			−0.264126
$772$	14.1860	−	8.19030i	0.510566	−	0.294775i
$773$	−36.8580	−	21.2800i	−1.32569	−	0.765387i	−0.341059	−	0.940042i	$-0.610786\pi$
$773$	−36.8580	−	21.2800i	−1.32569	−	0.765387i	−0.984630	+	0.174655i	$0.944119\pi$
$774$	−0.420920	+	0.729054i	−0.0151296	+	0.0262053i
$775$	−4.05858	−	31.0368i	−0.145789	−	1.11487i
$776$	3.42533			0.122962
$777$		0			0
$778$			3.87093i			0.138780i
$779$	−0.0581603	−	0.100737i	−0.00208381	−	0.00360926i
$780$	12.8621	−	14.6535i	0.460537	−	0.524681i
$781$	−6.27860	+	10.8748i	−0.224666	+	0.389133i
$782$	10.5379	−	6.08405i	0.376834	−	0.217565i
$783$		−	0.118657i		−	0.00424046i
$784$		0			0
$785$	1.46298	−	7.33819i	0.0522159	−	0.261911i
$786$	0.761132	+	1.31832i	0.0271487	+	0.0470229i
$787$	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
$789$	4.74386	+	8.21661i	0.168886	+	0.292519i
$790$	−1.49995	+	7.52363i	−0.0533657	+	0.267679i
$791$		0			0
$792$			3.74876i			0.133206i
$793$	28.8205	−	16.6395i	1.02344	−	0.590886i
$794$	2.65044	−	4.59069i	0.0940605	−	0.162918i
$795$	1.09125	−	1.24324i	0.0387027	−	0.0440933i
$796$	−3.63449	−	6.29512i	−0.128821	−	0.223125i
$797$			51.7211i			1.83205i	0.401116	+	0.916027i	$0.368623\pi$
$797$			51.7211i			1.83205i	−0.401116	+	0.916027i	$0.631377\pi$
$798$		0			0
$799$	35.4256			1.25327
$800$	16.1634	−	2.11364i	0.571463	−	0.0747284i
$801$	−6.50007	+	11.2585i	−0.229669	+	0.397798i
$802$	−6.32515	−	3.65182i	−0.223349	−	0.128950i
$803$	6.79271	−	3.92177i	0.239709	−	0.138396i
$804$	5.82152			0.205309
$805$		0			0
$806$	−8.18003			−0.288129
$807$	13.8984	−	8.02423i	0.489246	−	0.282466i
$808$	15.6357	+	9.02728i	0.550062	+	0.317579i
$809$	−25.8890	+	44.8410i	−0.910207	+	1.57653i	−0.0964371	+	0.995339i	$0.530745\pi$
$809$	−25.8890	+	44.8410i	−0.910207	+	1.57653i	−0.813770	+	0.581187i	$0.802589\pi$
$810$	0.608495	−	0.206261i	0.0213803	−	0.00724726i
$811$	−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
$814$	3.71089	+	6.42744i	0.130067	+	0.225282i
$815$	−26.4781	−	23.2411i	−0.927487	−	0.814099i
$816$	9.73994	−	16.8701i	0.340966	−	0.590571i
$817$	−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	0.786882	−	0.617103i	$-0.211694\pi$
$821$	−4.03967	−	6.99692i	−0.140985	−	0.244194i	−0.927868	+	0.372909i	$0.878360\pi$
$822$	−3.70029	−	2.13636i	−0.129062	−	0.0745142i
$823$	4.42994	+	2.55762i	0.154418	+	0.0891532i	0.575218	−	0.818000i	$-0.304917\pi$
$823$	4.42994	+	2.55762i	0.154418	+	0.0891532i	−0.420800	+	0.907153i	$0.638251\pi$
$824$	−2.97834	−	5.15864i	−0.103755	−	0.179710i
$825$	6.38582	−	15.3789i	0.222326	−	0.535423i
$826$		0			0
$827$		−	0.705254i		−	0.0245241i	−0.999925	−	0.0122620i	$-0.996097\pi$
$827$		−	0.705254i		−	0.0245241i	0.999925	−	0.0122620i	$-0.00390323\pi$
$828$	12.6761	−	7.31853i	0.440524	−	0.254337i
$829$	−12.4790	+	21.6143i	−0.433415	+	0.750696i	−0.997165	−	0.0752491i	$-0.976025\pi$
$829$	−12.4790	+	21.6143i	−0.433415	+	0.750696i	0.563750	+	0.825945i	$0.309358\pi$
$830$	−0.518828	+	0.591091i	−0.0180088	+	0.0205171i
$831$	−11.6088	−	20.1071i	−0.402706	−	0.697508i
$832$			27.6769i			0.959523i
$833$		0			0
$834$	2.73453			0.0946891
$835$	−47.8479	+	16.2190i	−1.65585	+	0.561280i
$836$	−5.29140	+	9.16498i	−0.183007	+	0.316977i
$837$	5.42150	+	3.13010i	0.187394	+	0.108192i
$838$	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
$843$	−10.7796	−	6.22360i	−0.371269	−	0.214352i
$844$	0.109693	−	0.189994i	0.00377579	−	0.00653986i
$845$	5.51309	+	16.2643i	0.189656	+	0.559509i
$846$	−1.83488			−0.0630843
$847$		0			0
$848$			2.59775i			0.0892071i
$849$	4.33388	+	7.50649i	0.148738	+	0.257622i
$850$	6.32728	−	4.84634i	0.217024	−	0.166228i
$851$	29.6023	−	51.2726i	1.01475	−	1.75760i
$852$	−6.26107	+	3.61483i	−0.214501	+	0.123842i
$853$			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			0
$855$	3.63417	+	0.724526i	0.124286	+	0.0247783i
$856$	−2.90507	−	5.03172i	−0.0992931	−	0.171981i
$857$	27.4455	+	15.8456i	0.937519	+	0.541277i	0.889182	−	0.457554i	$-0.151274\pi$
$857$	27.4455	+	15.8456i	0.937519	+	0.541277i	0.0483371	+	0.998831i	$0.484608\pi$
$858$	−3.76871	−	2.17587i	−0.128662	−	0.0742828i
$859$	21.8456	+	37.8377i	0.745363	+	1.29101i	0.950025	+	0.312174i	$0.101057\pi$
$859$	21.8456	+	37.8377i	0.745363	+	1.29101i	−0.204662	+	0.978833i	$0.565610\pi$
$860$	−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	$0.562929\pi$
$864$	−1.63010	+	2.82342i	−0.0554572	+	0.0960547i
$865$	14.3285	+	12.5768i	0.487183	+	0.427623i
$866$	2.58670	+	4.48030i	0.0878997	+	0.152247i
$867$		−	13.7752i		−	0.467830i
$868$		0			0
$869$	−39.7660			−1.34897
$870$	0.0244743	+	0.0722022i	0.000829757	+	0.00244788i
$871$	−6.90338	+	11.9570i	−0.233912	+	0.405148i
$872$	3.15925	+	1.82399i	0.106986	+	0.0617682i
$873$	2.63537	−	1.52153i	0.0891936	−	0.0514960i
$874$	−3.63501			−0.122956
$875$		0			0
$876$	4.51583			0.152576
$877$	−3.72454	+	2.15036i	−0.125769	+	0.0726127i	−0.561565	−	0.827433i	$-0.689800\pi$
$877$	−3.72454	+	2.15036i	−0.125769	+	0.0726127i	0.435796	+	0.900046i	$0.356467\pi$
$878$	4.82118	+	2.78351i	0.162707	+	0.0939390i
$879$	13.5031	−	23.3881i	0.455450	−	0.788862i
$880$	8.39476	+	24.7656i	0.282987	+	0.834848i
$881$	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	$0.00800981\pi$
$883$			1.49533i			0.0503218i	−0.999683	+	0.0251609i	$0.991990\pi$
$884$	24.1862	+	41.8918i	0.813471	+	1.40897i
$885$	2.73942	+	2.40452i	0.0920847	+	0.0808271i
$886$	−2.36225	+	4.09153i	−0.0793613	+	0.137458i
$887$	8.73964	−	5.04584i	0.293449	−	0.169423i	−0.346047	−	0.938217i	$-0.612476\pi$
$887$	8.73964	−	5.04584i	0.293449	−	0.169423i	0.639496	+	0.768794i	$0.279143\pi$
$888$			8.73000i			0.292960i
$889$		0			0
$890$	1.63308	−	8.19142i	0.0547410	−	0.274577i
$891$	1.66520	+	2.88421i	0.0557862	+	0.0966245i
$892$	13.0631	+	7.54198i	0.437385	+	0.252524i
$893$	−9.16498	−	5.29140i	−0.306694	−	0.177070i
$894$	−1.63351	−	2.82932i	−0.0546328	−	0.0946267i
$895$	25.8339	+	5.15036i	0.863531	+	0.172158i
$896$		0			0
$897$			34.7144i			1.15908i
$898$	8.14317	−	4.70146i	0.271741	−	0.156890i
$899$	−0.371409	+	0.643299i	−0.0123872	+	0.0214552i
$900$	7.61111	−	5.82969i	0.253704	−	0.194323i
$901$	2.05202	+	3.55421i	0.0683628	+	0.118408i
$902$			0.0671674i			0.00223643i
$903$		0			0
$904$	−14.2512			−0.473989
$905$	6.52492	+	19.2493i	0.216896	+	0.639869i
$906$	1.28444	−	2.22471i	0.0426726	−	0.0739111i
$907$	3.69531	+	2.13349i	0.122701	+	0.0708414i	0.560094	−	0.828429i	$-0.310765\pi$
$907$	3.69531	+	2.13349i	0.122701	+	0.0708414i	−0.437393	+	0.899270i	$0.644098\pi$
$908$	14.9095	−	8.60802i	0.494790	−	0.285667i
$909$	16.0397			0.532002
$910$		0			0
$911$	−28.5451			−0.945742			−0.472871	−	0.881132i	$-0.656782\pi$
$911$	−28.5451			−0.945742			−0.472871	+	0.881132i	$0.656782\pi$
$912$	−5.03965	+	2.90964i	−0.166879	+	0.0963479i
$913$	−3.53058	−	2.03838i	−0.116845	−	0.0674606i
$914$	5.37754	−	9.31417i	0.177873	−	0.308085i
$915$	15.4975	−	5.25316i	0.512331	−	0.173664i
$916$	−9.75231			−0.322226
$917$		0			0
$918$			1.59401i			0.0526101i
$919$	−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	$-0.445419\pi$
$920$	−12.6747	+	14.4401i	−0.417873	+	0.476075i
$921$	1.12341	−	1.94580i	0.0370175	−	0.0641161i
$922$	−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
$927$	−4.58293	−	2.64596i	−0.150523	−	0.0869046i
$928$	−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	$0.872046\pi$
$930$	−3.94457	−	0.786409i	−0.129348	−	0.0257874i
$931$		0			0
$932$			41.8352i			1.37036i
$933$	−24.7672	+	14.2994i	−0.810843	+	0.468140i
$934$	1.73537	−	3.00574i	0.0567829	−	0.0983509i
$935$	31.0485	+	27.2527i	1.01539	+	0.891259i
$936$	−2.55940	−	4.43301i	−0.0836567	−	0.144898i
$937$			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			0
$939$	−13.3285			−0.434960
$940$	−25.9302	+	8.78952i	−0.845749	+	0.286683i
$941$	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	$-0.0331696\pi$
$942$	−0.832699	−	0.480759i	−0.0271308	−	0.0156640i
$943$	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	$0.145581\pi$
$948$	−19.8275	−	11.4474i	−0.643968	−	0.371795i
$949$	−5.35504	+	9.27521i	−0.173832	+	0.301086i
$950$	−2.36081	+	0.308716i	−0.0765949	+	0.0100161i
$951$	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	$0.832748\pi$
$954$	−0.106285	−	0.184091i	−0.00344110	−	0.00596016i
$955$	−30.2326	+	34.4434i	−0.978305	+	1.11456i
$956$	7.14155	−	12.3695i	0.230974	−	0.400059i
$957$	−0.342231	+	0.197587i	−0.0110628	+	0.00638709i
$958$			5.78743i			0.186983i
$959$		0			0
$960$	−2.66079	+	13.3463i	−0.0858766	+	0.430751i
$961$	−4.09508	−	7.09289i	−0.132099	−	0.228803i
$962$	−8.77646	−	5.06709i	−0.282964	−	0.163370i
$963$	−4.47018	−	2.58086i	−0.144049	−	0.0831670i
$964$	−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	$-0.890218\pi$
$967$		−	21.0270i		−	0.676184i	0.941113	−	0.338092i	$-0.109782\pi$
$968$	0.0892209	−	0.0515117i	0.00286767	−	0.00165565i
$969$	−4.59678	+	7.96187i	−0.147670	+	0.255772i
$970$	−1.28977	+	1.46942i	−0.0414122	+	0.0471801i
$971$	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	$0.578782\pi$
$972$			1.91744i			0.0615019i
$973$		0			0
$974$	−11.4761			−0.367718
$975$	2.94824	+	22.5458i	0.0944192	+	0.722042i
$976$	−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	$0.740848\pi$
$978$	−3.92069	+	2.26361i	−0.125370	+	0.0723824i
$979$	43.2956			1.38373
$980$		0			0
$981$	3.24087			0.103473
$982$	−7.86307	+	4.53974i	−0.250921	+	0.144869i
$983$	−14.5389	−	8.39401i	−0.463717	−	0.267727i	0.249889	−	0.968275i	$-0.419606\pi$
$983$	−14.5389	−	8.39401i	−0.463717	−	0.267727i	−0.713606	+	0.700547i	$0.752939\pi$
$984$	−0.0395034	+	0.0684220i	−0.00125932	+	0.00218121i
$985$	−29.2426	+	9.91233i	−0.931747	+	0.315833i
$986$	−0.189140			−0.00602345
$987$		0			0
$988$		−	14.4505i		−	0.459730i
$989$	−11.1826	−	19.3688i	−0.355585	−	0.615892i
$990$	−1.60816	−	1.41156i	−0.0511108	−	0.0448623i
$991$	−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
$993$		−	24.8915i		−	0.789907i
$994$		0			0
$995$	8.31330	+	1.65738i	0.263549	+	0.0525425i
$996$	−1.17358	−	2.03270i	−0.0371862	−	0.0644084i
$997$	−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
$999$	3.87786	+	6.71665i	0.122690	+	0.212505i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.q.g.214.5		16
5.4	even	2	inner	735.2.q.g.214.4		16
7.2	even	3	inner	735.2.q.g.79.4		16
7.3	odd	6		735.2.d.d.589.5		8
7.4	even	3		735.2.d.e.589.5		8
7.5	odd	6		105.2.q.a.79.4	yes	16
7.6	odd	2		105.2.q.a.4.5	yes	16
21.5	even	6		315.2.bf.b.289.5		16
21.11	odd	6		2205.2.d.o.1324.4		8
21.17	even	6		2205.2.d.s.1324.4		8
21.20	even	2		315.2.bf.b.109.4		16
28.19	even	6		1680.2.di.d.289.7		16
28.27	even	2		1680.2.di.d.529.3		16
35.3	even	12		3675.2.a.bp.1.3		4
35.4	even	6		735.2.d.e.589.4		8
35.9	even	6	inner	735.2.q.g.79.5		16
35.12	even	12		525.2.i.h.226.3		8
35.13	even	4		525.2.i.k.151.2		8
35.17	even	12		3675.2.a.bz.1.2		4
35.18	odd	12		3675.2.a.bn.1.3		4
35.19	odd	6		105.2.q.a.79.5	yes	16
35.24	odd	6		735.2.d.d.589.4		8
35.27	even	4		525.2.i.h.151.3		8
35.32	odd	12		3675.2.a.cb.1.2		4
35.33	even	12		525.2.i.k.226.2		8
35.34	odd	2		105.2.q.a.4.4	✓	16
105.59	even	6		2205.2.d.s.1324.5		8
105.74	odd	6		2205.2.d.o.1324.5		8
105.89	even	6		315.2.bf.b.289.4		16
105.104	even	2		315.2.bf.b.109.5		16
140.19	even	6		1680.2.di.d.289.3		16
140.139	even	2		1680.2.di.d.529.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.4	✓	16	35.34	odd	2
105.2.q.a.4.5	yes	16	7.6	odd	2
105.2.q.a.79.4	yes	16	7.5	odd	6
105.2.q.a.79.5	yes	16	35.19	odd	6
315.2.bf.b.109.4		16	21.20	even	2
315.2.bf.b.109.5		16	105.104	even	2
315.2.bf.b.289.4		16	105.89	even	6
315.2.bf.b.289.5		16	21.5	even	6
525.2.i.h.151.3		8	35.27	even	4
525.2.i.h.226.3		8	35.12	even	12
525.2.i.k.151.2		8	35.13	even	4
525.2.i.k.226.2		8	35.33	even	12
735.2.d.d.589.4		8	35.24	odd	6
735.2.d.d.589.5		8	7.3	odd	6
735.2.d.e.589.4		8	35.4	even	6
735.2.d.e.589.5		8	7.4	even	3
735.2.q.g.79.4		16	7.2	even	3	inner
735.2.q.g.79.5		16	35.9	even	6	inner
735.2.q.g.214.4		16	5.4	even	2	inner
735.2.q.g.214.5		16	1.1	even	1	trivial
1680.2.di.d.289.3		16	140.19	even	6
1680.2.di.d.289.7		16	28.19	even	6
1680.2.di.d.529.3		16	28.27	even	2
1680.2.di.d.529.7		16	140.139	even	2
2205.2.d.o.1324.4		8	21.11	odd	6
2205.2.d.o.1324.5		8	105.74	odd	6
2205.2.d.s.1324.4		8	21.17	even	6
2205.2.d.s.1324.5		8	105.59	even	6
3675.2.a.bn.1.3		4	35.18	odd	12
3675.2.a.bp.1.3		4	35.3	even	12
3675.2.a.bz.1.2		4	35.17	even	12
3675.2.a.cb.1.2		4	35.32	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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.248840 - 0.143668i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.958719 + 1.66055i) q^{4} +(-0.717839 - 2.11771i) q^{5} -0.287336 q^{6} +1.12562i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.482874 - 0.423842i) q^{10} +(1.66520 - 2.88421i) q^{11} +(1.66055 - 0.958719i) q^{12} +4.54754i q^{13} +(-0.437190 + 2.19291i) q^{15} +(-1.75572 - 3.04100i) q^{16} +(-4.80431 - 2.77377i) q^{17} +(0.248840 + 0.143668i) q^{18} +(0.828617 + 1.43521i) q^{19} +(4.20477 + 0.838284i) q^{20} -0.956942i q^{22} +(-6.61094 + 3.81683i) q^{23} +(0.562810 - 0.974816i) q^{24} +(-3.96942 + 3.04035i) q^{25} +(0.653336 + 1.13161i) q^{26} -1.00000i q^{27} +0.118657 q^{29} +(0.206261 + 0.608495i) q^{30} +(-3.13010 + 5.42150i) q^{31} +(-2.82342 - 1.63010i) q^{32} +(-2.88421 + 1.66520i) q^{33} -1.59401 q^{34} -1.91744 q^{36} +(-6.71665 + 3.87786i) q^{37} +(0.412386 + 0.238091i) q^{38} +(2.27377 - 3.93829i) q^{39} +(2.38374 - 0.808014i) q^{40} -0.0701896 q^{41} +2.92981i q^{43} +(3.19291 + 5.53029i) q^{44} +(1.47507 - 1.68052i) q^{45} +(-1.09671 + 1.89956i) q^{46} +(-5.53029 + 3.19291i) q^{47} +3.51145i q^{48} +(-0.550949 + 1.32684i) q^{50} +(2.77377 + 4.80431i) q^{51} +(-7.55142 - 4.35981i) q^{52} +(-0.640682 - 0.369898i) q^{53} +(-0.143668 - 0.248840i) q^{54} +(-7.30326 - 1.45601i) q^{55} -1.65723i q^{57} +(0.0295266 - 0.0170472i) q^{58} +(0.815051 - 1.41171i) q^{59} +(-3.22230 - 2.82836i) q^{60} +(-3.65901 - 6.33759i) q^{61} +1.79878i q^{62} +6.08612 q^{64} +(9.63038 - 3.26440i) q^{65} +(-0.478471 + 0.828736i) q^{66} +(2.62934 + 1.51805i) q^{67} +(9.21197 - 5.31853i) q^{68} +7.63366 q^{69} -3.77048 q^{71} +(-0.974816 + 0.562810i) q^{72} +(2.03961 + 1.17757i) q^{73} +(-1.11425 + 1.92993i) q^{74} +(4.95779 - 0.648315i) q^{75} -3.17764 q^{76} -1.30667i q^{78} +(-5.97016 - 10.3406i) q^{79} +(-5.17964 + 5.90106i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.0174660 + 0.0100840i) q^{82} -1.22411i q^{83} +(-2.42533 + 12.1653i) q^{85} +(0.420920 + 0.729054i) q^{86} +(-0.102760 - 0.0593285i) q^{87} +(3.24652 + 1.87438i) q^{88} +(6.50007 + 11.2585i) q^{89} +(0.125620 - 0.630102i) q^{90} -14.6371i q^{92} +(5.42150 - 3.13010i) q^{93} +(-0.917438 + 1.58905i) q^{94} +(2.44454 - 2.78502i) q^{95} +(1.63010 + 2.82342i) q^{96} -3.04306i q^{97} +3.33039 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 2 q^{5} + 8 q^{6} + 8 q^{9} + 4 q^{10} - 4 q^{15} + 24 q^{19} + 8 q^{20} + 12 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} - 12 q^{30} - 16 q^{31} - 16 q^{34} + 16 q^{36} - 4 q^{39} - 32 q^{40}+ \cdots - 8 q^{96}+O(q^{100}) \) 16 * q + 8 * q^4 - 2 * q^5 + 8 * q^6 + 8 * q^9 + 4 * q^10 - 4 * q^15 + 24 * q^19 + 8 * q^20 + 12 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 - 12 * q^30 - 16 * q^31 - 16 * q^34 + 16 * q^36 - 4 * q^39 - 32 * q^40 - 16 * q^41 + 20 * q^44 + 2 * q^45 - 32 * q^46 - 40 * q^50 + 4 * q^51 + 4 * q^54 - 8 * q^55 - 4 * q^59 + 16 * q^60 - 16 * q^61 + 16 * q^64 + 30 * q^65 - 28 * q^66 - 40 * q^69 - 56 * q^71 + 40 * q^74 - 8 * q^75 + 64 * q^76 - 16 * q^79 - 52 * q^80 - 8 * q^81 - 64 * q^85 - 48 * q^86 - 16 * q^89 + 8 * q^90 + 32 * q^94 - 22 * q^95 - 8 * q^96

Introduction

L-functions

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