LMFDB - Embedded newform 456.2.bk.a.253.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(61,456)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("456.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bk (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			253.10
Character	$\chi$	$=$	456.253
Dual form			456.2.bk.a.301.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.05105 + 0.946198i) q^{2} +(0.342020 - 0.939693i) q^{3} +(0.209419 - 1.98901i) q^{4} +(2.68674 - 0.473745i) q^{5} +(0.529654 + 1.31128i) q^{6} +(0.416079 - 0.720670i) q^{7} +(1.66188 + 2.28870i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(-2.37565 + 3.04012i) q^{10} +(1.90145 - 1.09780i) q^{11} +(-1.79743 - 0.877069i) q^{12} +(0.794462 + 2.18277i) q^{13} +(0.244576 + 1.15115i) q^{14} +(0.473745 - 2.68674i) q^{15} +(-3.91229 - 0.833070i) q^{16} +(1.80905 - 1.51798i) q^{17} +(1.41336 - 0.0492268i) q^{18} +(-3.91954 + 1.90715i) q^{19} +(-0.379628 - 5.44316i) q^{20} +(-0.534901 - 0.637470i) q^{21} +(-0.959784 + 2.95300i) q^{22} +(1.13751 - 6.45111i) q^{23} +(2.71907 - 0.778878i) q^{24} +(2.29569 - 0.835564i) q^{25} +(-2.90035 - 1.54248i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(-1.34628 - 0.978505i) q^{28} +(-1.10272 + 1.31417i) q^{29} +(2.04426 + 3.27216i) q^{30} +(2.45478 - 4.25180i) q^{31} +(4.90027 - 2.82620i) q^{32} +(-0.381263 - 2.16225i) q^{33} +(-0.465102 + 3.30719i) q^{34} +(0.776483 - 2.13337i) q^{35} +(-1.43893 + 1.38905i) q^{36} +1.34830i q^{37} +(2.31509 - 5.71317i) q^{38} +2.32285 q^{39} +(5.54931 + 5.36184i) q^{40} +(7.26475 + 2.64415i) q^{41} +(1.16538 + 0.163892i) q^{42} +(1.29888 - 0.229027i) q^{43} +(-1.78534 - 4.01190i) q^{44} +(-2.36268 - 1.36410i) q^{45} +(4.90845 + 7.85676i) q^{46} +(-4.64622 - 3.89864i) q^{47} +(-2.12091 + 3.39142i) q^{48} +(3.15376 + 5.46247i) q^{49} +(-1.62228 + 3.05040i) q^{50} +(-0.807698 - 2.21913i) q^{51} +(4.50791 - 1.12308i) q^{52} +(2.52243 + 0.444772i) q^{53} +(0.437138 - 1.34496i) q^{54} +(4.58863 - 3.85032i) q^{55} +(2.34087 - 0.245390i) q^{56} +(0.451575 + 4.33544i) q^{57} +(-0.0844500 - 2.42466i) q^{58} +(3.70993 + 4.42132i) q^{59} +(-5.24474 - 1.50494i) q^{60} +(1.61404 + 0.284599i) q^{61} +(1.44295 + 6.79157i) q^{62} +(-0.781973 + 0.284615i) q^{63} +(-2.47629 + 7.60710i) q^{64} +(3.16859 + 5.48816i) q^{65} +(2.44665 + 1.91189i) q^{66} +(-10.2547 + 12.2210i) q^{67} +(-2.64041 - 3.91611i) q^{68} +(-5.67301 - 3.27532i) q^{69} +(1.20247 + 2.97699i) q^{70} +(-1.67513 - 9.50011i) q^{71} +(0.198071 - 2.82148i) q^{72} +(-7.83683 - 2.85237i) q^{73} +(-1.27576 - 1.41713i) q^{74} -2.44302i q^{75} +(2.97251 + 8.19538i) q^{76} -1.82709i q^{77} +(-2.44144 + 2.19788i) q^{78} +(0.702586 + 0.255720i) q^{79} +(-10.9060 - 0.384818i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-10.1375 + 4.09475i) q^{82} +(1.96161 + 1.13253i) q^{83} +(-1.37995 + 0.930423i) q^{84} +(4.14133 - 4.93544i) q^{85} +(-1.14848 + 1.46972i) q^{86} +(0.857765 + 1.48569i) q^{87} +(5.67254 + 2.52743i) q^{88} +(0.0971828 - 0.0353716i) q^{89} +(3.77401 - 0.801831i) q^{90} +(1.90361 + 0.335658i) q^{91} +(-12.5931 - 3.61349i) q^{92} +(-3.15580 - 3.76094i) q^{93} +(8.57229 - 0.298570i) q^{94} +(-9.62729 + 6.98089i) q^{95} +(-0.979769 - 5.57136i) q^{96} +(-5.55990 + 4.66531i) q^{97} +(-8.48334 - 2.75726i) q^{98} +(-2.16225 - 0.381263i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.05105	+	0.946198i	−0.743206	+	0.669063i
$2$	−1.05105	+	0.946198i	−0.743206	+	0.669063i
$3$	0.342020	−	0.939693i	0.197465	−	0.542532i
$3$	0.342020	−	0.939693i	0.197465	−	0.542532i
$4$	0.209419	−	1.98901i	0.104709	−	0.994503i
$5$	2.68674	−	0.473745i	1.20155	−	0.211865i	0.463181	−	0.886264i	$-0.346708\pi$
$5$	2.68674	−	0.473745i	1.20155	−	0.211865i	0.738368	+	0.674399i	$0.235597\pi$
$6$	0.529654	+	1.31128i	0.216231	+	0.535330i
$7$	0.416079	−	0.720670i	0.157263	−	0.272388i	−0.776618	−	0.629972i	$-0.783066\pi$
$7$	0.416079	−	0.720670i	0.157263	−	0.272388i	0.933881	+	0.357585i	$0.116400\pi$
$8$	1.66188	+	2.28870i	0.587564	+	0.809177i
$9$	−0.766044	−	0.642788i	−0.255348	−	0.214263i
$10$	−2.37565	+	3.04012i	−0.751246	+	0.961371i
$11$	1.90145	−	1.09780i	0.573309	−	0.331000i	−0.185161	−	0.982708i	$-0.559281\pi$
$11$	1.90145	−	1.09780i	0.573309	−	0.331000i	0.758470	+	0.651708i	$0.225947\pi$
$12$	−1.79743	−	0.877069i	−0.518873	−	0.253188i
$13$	0.794462	+	2.18277i	0.220344	+	0.605390i	0.999777	−	0.0210947i	$-0.00671516\pi$
$13$	0.794462	+	2.18277i	0.220344	+	0.605390i	−0.779433	+	0.626485i	$0.784493\pi$
$14$	0.244576	+	1.15115i	0.0653657	+	0.307659i
$15$	0.473745	−	2.68674i	0.122321	−	0.693714i
$16$	−3.91229	−	0.833070i	−0.978072	−	0.208268i
$17$	1.80905	−	1.51798i	0.438760	−	0.368163i	−0.396485	−	0.918041i	$-0.629770\pi$
$17$	1.80905	−	1.51798i	0.438760	−	0.368163i	0.835245	+	0.549878i	$0.185326\pi$
$18$	1.41336	−	0.0492268i	0.333131	−	0.0116029i
$19$	−3.91954	+	1.90715i	−0.899204	+	0.437531i
$19$	−3.91954	+	1.90715i	−0.899204	+	0.437531i
$20$	−0.379628	−	5.44316i	−0.0848873	−	1.21713i
$21$	−0.534901	−	0.637470i	−0.116725	−	0.139107i
$22$	−0.959784	+	2.95300i	−0.204627	+	0.629581i
$23$	1.13751	−	6.45111i	0.237186	−	1.34515i	−0.600774	−	0.799419i	$-0.705141\pi$
$23$	1.13751	−	6.45111i	0.237186	−	1.34515i	0.837960	−	0.545731i	$-0.183748\pi$
$24$	2.71907	−	0.778878i	0.555028	−	0.158988i
$25$	2.29569	−	0.835564i	0.459138	−	0.167113i
$26$	−2.90035	−	1.54248i	−0.568805	−	0.302505i
$27$	−0.866025	+	0.500000i	−0.166667	+	0.0962250i
$28$	−1.34628	−	0.978505i	−0.254423	−	0.184920i
$29$	−1.10272	+	1.31417i	−0.204770	+	0.244036i	−0.858649	−	0.512563i	$-0.828696\pi$
$29$	−1.10272	+	1.31417i	−0.204770	+	0.244036i	0.653879	+	0.756599i	$0.273140\pi$
$30$	2.04426	+	3.27216i	0.373229	+	0.597412i
$31$	2.45478	−	4.25180i	0.440891	−	0.763646i	−0.556864	−	0.830603i	$-0.687996\pi$
$31$	2.45478	−	4.25180i	0.440891	−	0.763646i	0.997756	+	0.0669571i	$0.0213291\pi$
$32$	4.90027	−	2.82620i	0.866253	−	0.499606i
$33$	−0.381263	−	2.16225i	−0.0663694	−	0.376400i
$34$	−0.465102	+	3.30719i	−0.0797644	+	0.567179i
$35$	0.776483	−	2.13337i	0.131250	−	0.360605i
$36$	−1.43893	+	1.38905i	−0.239822	+	0.231509i
$37$			1.34830i			0.221659i	0.993839	+	0.110829i	$0.0353507\pi$
$37$			1.34830i			0.221659i	−0.993839	+	0.110829i	$0.964649\pi$
$38$	2.31509	−	5.71317i	0.375558	−	0.926799i
$39$	2.32285			0.371954
$40$	5.54931	+	5.36184i	0.877424	+	0.847781i
$41$	7.26475	+	2.64415i	1.13456	+	0.412947i	0.839947	−	0.542668i	$-0.182586\pi$
$41$	7.26475	+	2.64415i	1.13456	+	0.412947i	0.294616	+	0.955616i	$0.404808\pi$
$42$	1.16538	+	0.163892i	0.179822	+	0.0252890i
$43$	1.29888	−	0.229027i	0.198077	−	0.0349263i	−0.0737293	−	0.997278i	$-0.523490\pi$
$43$	1.29888	−	0.229027i	0.198077	−	0.0349263i	0.271806	+	0.962352i	$0.412379\pi$
$44$	−1.78534	−	4.01190i	−0.269150	−	0.604817i
$45$	−2.36268	−	1.36410i	−0.352208	−	0.203347i
$46$	4.90845	+	7.85676i	0.723712	+	1.15842i
$47$	−4.64622	−	3.89864i	−0.677720	−	0.568675i	0.237619	−	0.971358i	$-0.423633\pi$
$47$	−4.64622	−	3.89864i	−0.677720	−	0.568675i	−0.915339	+	0.402684i	$0.868077\pi$
$48$	−2.12091	+	3.39142i	−0.306127	+	0.489509i
$49$	3.15376	+	5.46247i	0.450537	+	0.780352i
$50$	−1.62228	+	3.05040i	−0.229425	+	0.431392i
$51$	−0.807698	−	2.21913i	−0.113100	−	0.310741i
$52$	4.50791	−	1.12308i	0.625135	−	0.155743i
$53$	2.52243	+	0.444772i	0.346482	+	0.0610941i	0.344181	−	0.938903i	$-0.388157\pi$
$53$	2.52243	+	0.444772i	0.346482	+	0.0610941i	0.00230071	+	0.999997i	$0.499268\pi$
$54$	0.437138	−	1.34496i	0.0594870	−	0.183026i
$55$	4.58863	−	3.85032i	0.618731	−	0.519177i
$56$	2.34087	−	0.245390i	0.312812	−	0.0327916i
$57$	0.451575	+	4.33544i	0.0598126	+	0.574244i
$58$	−0.0844500	−	2.42466i	−0.0110888	−	0.318373i
$59$	3.70993	+	4.42132i	0.482991	+	0.575607i	0.951421	−	0.307894i	$-0.0996244\pi$
$59$	3.70993	+	4.42132i	0.482991	+	0.575607i	−0.468429	+	0.883501i	$0.655180\pi$
$60$	−5.24474	−	1.50494i	−0.677093	−	0.194286i
$61$	1.61404	+	0.284599i	0.206657	+	0.0364392i	0.276018	−	0.961152i	$-0.410985\pi$
$61$	1.61404	+	0.284599i	0.206657	+	0.0364392i	−0.0693612	+	0.997592i	$0.522096\pi$
$62$	1.44295	+	6.79157i	0.183254	+	0.862530i
$63$	−0.781973	+	0.284615i	−0.0985193	+	0.0358581i
$64$	−2.47629	+	7.60710i	−0.309536	+	0.950888i
$65$	3.16859	+	5.48816i	0.393015	+	0.680722i
$66$	2.44665	+	1.91189i	0.301161	+	0.235337i
$67$	−10.2547	+	12.2210i	−1.25281	+	1.49304i	−0.454551	+	0.890721i	$0.650200\pi$
$67$	−10.2547	+	12.2210i	−1.25281	+	1.49304i	−0.798257	+	0.602317i	$0.794244\pi$
$68$	−2.64041	−	3.91611i	−0.320197	−	0.474898i
$69$	−5.67301	−	3.27532i	−0.682951	−	0.394302i
$70$	1.20247	+	2.97699i	0.143722	+	0.355818i
$71$	−1.67513	−	9.50011i	−0.198801	−	1.12746i	−0.906901	−	0.421344i	$-0.861559\pi$
$71$	−1.67513	−	9.50011i	−0.198801	−	1.12746i	0.708100	−	0.706112i	$-0.249552\pi$
$72$	0.198071	−	2.82148i	0.0233429	−	0.332515i
$73$	−7.83683	−	2.85237i	−0.917232	−	0.333845i	−0.160095	−	0.987102i	$-0.551180\pi$
$73$	−7.83683	−	2.85237i	−0.917232	−	0.333845i	−0.757137	+	0.653256i	$0.773402\pi$
$74$	−1.27576	−	1.41713i	−0.148304	−	0.164738i
$75$		−	2.44302i		−	0.282096i
$76$	2.97251	+	8.19538i	0.340970	+	0.940074i
$77$		−	1.82709i		−	0.208217i
$78$	−2.44144	+	2.19788i	−0.276438	+	0.248861i
$79$	0.702586	+	0.255720i	0.0790471	+	0.0287708i	0.381241	−	0.924476i	$-0.375497\pi$
$79$	0.702586	+	0.255720i	0.0790471	+	0.0287708i	−0.302194	+	0.953246i	$0.597719\pi$
$80$	−10.9060	−	0.384818i	−1.21933	−	0.0430239i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	−10.1375	+	4.09475i	−1.11950	+	0.452190i
$83$	1.96161	+	1.13253i	0.215314	+	0.124312i	0.603779	−	0.797152i	$-0.293661\pi$
$83$	1.96161	+	1.13253i	0.215314	+	0.124312i	−0.388464	+	0.921464i	$0.626994\pi$
$84$	−1.37995	+	0.930423i	−0.150565	+	0.101517i
$85$	4.14133	−	4.93544i	0.449190	−	0.535324i
$86$	−1.14848	+	1.46972i	−0.123844	+	0.158484i
$87$	0.857765	+	1.48569i	0.0919621	+	0.159283i
$88$	5.67254	+	2.52743i	0.604694	+	0.269425i
$89$	0.0971828	−	0.0353716i	0.0103014	−	0.00374939i	−0.336864	−	0.941553i	$-0.609366\pi$
$89$	0.0971828	−	0.0353716i	0.0103014	−	0.00374939i	0.347166	+	0.937804i	$0.387144\pi$
$90$	3.77401	−	0.801831i	0.397815	−	0.0845204i
$91$	1.90361	+	0.335658i	0.199553	+	0.0351865i
$92$	−12.5931	−	3.61349i	−1.31292	−	0.376732i
$93$	−3.15580	−	3.76094i	−0.327242	−	0.389991i
$94$	8.57229	−	0.298570i	0.884165	−	0.0307952i
$95$	−9.62729	+	6.98089i	−0.987739	+	0.716224i
$96$	−0.979769	−	5.57136i	−0.0999972	−	0.568625i
$97$	−5.55990	+	4.66531i	−0.564522	+	0.473690i	−0.879823	−	0.475301i	$-0.842339\pi$
$97$	−5.55990	+	4.66531i	−0.564522	+	0.473690i	0.315301	+	0.948992i	$0.397895\pi$
$98$	−8.48334	−	2.75726i	−0.856946	−	0.278525i
$99$	−2.16225	−	0.381263i	−0.217314	−	0.0383184i
$100$	−1.18118	−	4.74113i	−0.118118	−	0.474113i
$101$	−2.31210	−	6.35244i	−0.230062	−	0.632091i	0.769919	−	0.638141i	$-0.220296\pi$
$101$	−2.31210	−	6.35244i	−0.230062	−	0.632091i	−0.999982	+	0.00604996i	$0.998074\pi$
$102$	2.94867	+	1.56818i	0.291962	+	0.155273i
$103$	−8.41627	−	14.5774i	−0.829279	−	1.43635i	−0.898604	−	0.438760i	$-0.855418\pi$
$103$	−8.41627	−	14.5774i	−0.829279	−	1.43635i	0.0693251	−	0.997594i	$-0.477915\pi$
$104$	−3.67539	+	5.44579i	−0.360402	+	0.534003i
$105$	−1.73914	−	1.45931i	−0.169723	−	0.142414i
$106$	−3.07204	+	1.91924i	−0.298383	+	0.186413i
$107$	8.41888	+	4.86064i	0.813884	+	0.469896i	0.848303	−	0.529511i	$-0.177625\pi$
$107$	8.41888	+	4.86064i	0.813884	+	0.469896i	−0.0344187	+	0.999408i	$0.510958\pi$
$108$	0.813141	+	1.82724i	0.0782445	+	0.175826i
$109$	5.79986	−	1.02267i	0.555526	−	0.0979543i	0.111165	−	0.993802i	$-0.464542\pi$
$109$	5.79986	−	1.02267i	0.555526	−	0.0979543i	0.444361	+	0.895848i	$0.353431\pi$
$110$	−1.17973	+	8.38864i	−0.112482	+	0.799826i
$111$	1.26698	+	0.461145i	0.120257	+	0.0437699i
$112$	−2.22819	+	2.47284i	−0.210544	+	0.233662i
$113$	−3.70138			−0.348197			−0.174098	−	0.984728i	$-0.555701\pi$
$113$	−3.70138			−0.348197			−0.174098	+	0.984728i	$0.555701\pi$
$114$	−4.57682	−	4.12950i	−0.428658	−	0.386763i
$115$		−	17.8714i		−	1.66651i
$116$	2.38297	+	2.46853i	0.221253	+	0.229197i
$117$	0.794462	−	2.18277i	0.0734480	−	0.201797i
$118$	−8.08276	−	1.13671i	−0.744079	−	0.104642i
$119$	−0.341250	−	1.93533i	−0.0312824	−	0.177411i
$120$	6.93646	−	3.38079i	0.633209	−	0.308623i
$121$	−3.08965	+	5.35144i	−0.280878	+	0.486494i
$122$	−1.96573	+	1.22808i	−0.177969	+	0.111185i
$123$	4.96938	−	5.92228i	0.448074	−	0.533994i
$124$	−7.94278	−	5.77298i	−0.713283	−	0.518429i
$125$	−6.04132	+	3.48796i	−0.540352	+	0.311972i
$126$	0.552592	−	1.03905i	0.0492288	−	0.0925655i
$127$	−19.7109	+	7.17419i	−1.74906	+	0.636607i	−0.999674	−	0.0255238i	$-0.991875\pi$
$127$	−19.7109	+	7.17419i	−1.74906	+	0.636607i	−0.749389	+	0.662131i	$0.769652\pi$
$128$	−4.59512	−	10.3385i	−0.406155	−	0.913804i
$129$	0.229027	−	1.29888i	0.0201647	−	0.114360i
$130$	−8.52324	−	2.77022i	−0.747537	−	0.242965i
$131$	10.9514	+	13.0513i	0.956826	+	1.14030i	0.990031	+	0.140853i	$0.0449843\pi$
$131$	10.9514	+	13.0513i	0.956826	+	1.14030i	−0.0332043	+	0.999449i	$0.510571\pi$
$132$	−4.38057	+	0.305519i	−0.381280	+	0.0265920i
$133$	−0.256411	+	3.61822i	−0.0222336	+	0.313739i
$134$	−0.785337	−	22.5479i	−0.0678427	−	1.94784i
$135$	−2.08992	+	1.75365i	−0.179871	+	0.150930i
$136$	6.48062	+	1.61768i	0.555709	+	0.138715i
$137$	−3.53651	+	20.0565i	−0.302144	+	1.71354i	0.334508	+	0.942393i	$0.391430\pi$
$137$	−3.53651	+	20.0565i	−0.302144	+	1.71354i	−0.636652	+	0.771152i	$0.719681\pi$
$138$	9.06173	−	1.92527i	0.771386	−	0.163890i
$139$	−4.69766	−	12.9067i	−0.398451	−	1.09473i	−0.963039	−	0.269362i	$-0.913187\pi$
$139$	−4.69766	−	12.9067i	−0.398451	−	1.09473i	0.564588	−	0.825373i	$-0.309035\pi$
$140$	−4.08068	−	1.99120i	−0.344880	−	0.168287i
$141$	−5.25262	+	3.03260i	−0.442350	+	0.255391i
$142$	10.7496	+	8.40010i	0.902089	+	0.704921i
$143$	3.90688	+	3.27826i	0.326710	+	0.274142i
$144$	2.46150	+	3.15294i	0.205125	+	0.262745i
$145$	−2.34015	+	4.05325i	−0.194339	+	0.336604i
$146$	10.9358	−	4.41720i	0.905055	−	0.365570i
$147$	6.21169	−	1.09529i	0.512331	−	0.0903378i
$148$	2.68177	+	0.282359i	0.220440	+	0.0232097i
$149$	−6.82094	+	18.7404i	−0.558793	+	1.53527i	0.262598	+	0.964905i	$0.415421\pi$
$149$	−6.82094	+	18.7404i	−0.558793	+	1.53527i	−0.821391	+	0.570365i	$0.806802\pi$
$150$	2.31158	+	2.56774i	0.188740	+	0.209655i
$151$	8.76782			0.713515			0.356757	−	0.934197i	$-0.383882\pi$
$151$	8.76782			0.713515			0.356757	+	0.934197i	$0.383882\pi$
$152$	−10.8787	−	5.80118i	−0.882380	−	0.470538i
$153$	−2.36155			−0.190920
$154$	1.72879	+	1.92037i	0.139310	+	0.154748i
$155$	4.58109	−	12.5864i	0.367962	−	1.01097i
$156$	0.486449	−	4.62016i	0.0389471	−	0.369909i
$157$	5.61861	−	0.990712i	0.448414	−	0.0790674i	0.0551187	−	0.998480i	$-0.482446\pi$
$157$	5.61861	−	0.990712i	0.448414	−	0.0790674i	0.393295	+	0.919412i	$0.371335\pi$
$158$	−0.980416	+	0.396010i	−0.0779977	+	0.0315049i
$159$	1.28067	−	2.21818i	0.101564	−	0.175913i
$160$	11.8269	−	9.91475i	0.934995	−	0.783830i
$161$	−4.17583	−	3.50394i	−0.329102	−	0.276149i
$162$	−1.11434	−	0.870778i	−0.0875505	−	0.0684148i
$163$	−17.4908	+	10.0983i	−1.36999	+	0.790963i	−0.990926	−	0.134409i	$-0.957086\pi$
$163$	−17.4908	+	10.0983i	−1.36999	+	0.790963i	−0.379062	+	0.925371i	$0.623753\pi$
$164$	6.78061	−	13.8959i	0.529477	−	1.08509i
$165$	−2.04871	−	5.62879i	−0.159492	−	0.438201i
$166$	−3.13335	+	0.665716i	−0.243195	+	0.0516696i
$167$	−2.26163	+	12.8263i	−0.175010	+	0.992531i	0.763122	+	0.646254i	$0.223665\pi$
$167$	−2.26163	+	12.8263i	−0.175010	+	0.992531i	−0.938132	+	0.346277i	$0.887446\pi$
$168$	0.570034	−	2.28363i	0.0439791	−	0.176186i
$169$	5.82528	−	4.88799i	0.448098	−	0.375999i
$170$	0.317156	+	9.10592i	0.0243248	+	0.698392i
$171$	4.22843	+	1.05847i	0.323356	+	0.0809430i
$172$	−0.183527	−	2.63144i	−0.0139938	−	0.200645i
$173$	14.7162	+	17.5381i	1.11885	+	1.33340i	0.936702	+	0.350128i	$0.113862\pi$
$173$	14.7162	+	17.5381i	1.11885	+	1.33340i	0.182152	+	0.983270i	$0.441694\pi$
$174$	−2.30731	−	0.749924i	−0.174917	−	0.0568516i
$175$	0.353024	−	2.00210i	0.0266861	−	0.151344i
$176$	−8.35358	+	2.71088i	−0.629674	+	0.204340i
$177$	5.42355	−	1.97401i	0.407659	−	0.148376i
$178$	−0.0686755	+	0.129132i	−0.00514745	+	0.00967882i
$179$	−9.85353	+	5.68894i	−0.736487	+	0.425211i	−0.820791	−	0.571229i	$-0.806467\pi$
$179$	−9.85353	+	5.68894i	−0.736487	+	0.425211i	0.0843033	+	0.996440i	$0.473134\pi$
$180$	−3.20798	+	4.41372i	−0.239109	+	0.328979i
$181$	−11.4017	+	13.5880i	−0.847482	+	1.00999i	0.152284	+	0.988337i	$0.451337\pi$
$181$	−11.4017	+	13.5880i	−0.847482	+	1.00999i	−0.999766	+	0.0216527i	$0.993107\pi$
$182$	−2.31839	+	1.44840i	−0.171851	+	0.107363i
$183$	0.819471	−	1.41937i	0.0605770	−	0.104923i
$184$	16.6551	−	8.11759i	1.22783	−	0.598437i
$185$	0.638749	+	3.62253i	0.0469618	+	0.266334i
$186$	6.87551	+	0.966927i	0.504137	+	0.0708985i
$187$	1.77339	−	4.87234i	0.129683	−	0.356301i
$188$	−8.72742	+	8.42490i	−0.636512	+	0.614449i
$189$			0.832158i			0.0605306i
$190$	3.51347	−	16.4466i	0.254894	−	1.19316i
$191$	10.0802			0.729378			0.364689	−	0.931129i	$-0.381175\pi$
$191$	10.0802			0.729378			0.364689	+	0.931129i	$0.381175\pi$
$192$	6.30140	+	4.92873i	0.454764	+	0.355701i
$193$	20.8175	+	7.57694i	1.49847	+	0.545400i	0.955665	−	0.294456i	$-0.0951385\pi$
$193$	20.8175	+	7.57694i	1.49847	+	0.545400i	0.542809	+	0.839856i	$0.317361\pi$
$194$	1.42943	−	10.1642i	0.102627	−	0.729750i
$195$	6.24090	−	1.10044i	0.446920	−	0.0788041i
$196$	11.5253	−	5.12890i	0.823238	−	0.366350i
$197$	−15.6954	−	9.06176i	−1.11825	−	0.645624i	−0.177299	−	0.984157i	$-0.556736\pi$
$197$	−15.6954	−	9.06176i	−1.11825	−	0.645624i	−0.940954	+	0.338533i	$0.890069\pi$
$198$	2.63339	−	1.64519i	0.187147	−	0.116919i
$199$	5.53537	+	4.64473i	0.392392	+	0.329256i	0.817544	−	0.575866i	$-0.195335\pi$
$199$	5.53537	+	4.64473i	0.392392	+	0.329256i	−0.425152	+	0.905122i	$0.639779\pi$
$200$	5.72753	+	3.86554i	0.404997	+	0.273335i
$201$	7.97672	+	13.8161i	0.562634	+	0.974511i
$202$	8.44080	+	4.48904i	0.593893	+	0.315848i
$203$	0.488265	+	1.34150i	0.0342695	+	0.0941547i
$204$	−4.58301	+	1.14179i	−0.320875	+	0.0799411i
$205$	20.7712	+	3.66252i	1.45072	+	0.255801i
$206$	22.6390	+	7.35815i	1.57734	+	0.512666i
$207$	−5.01808	+	4.21067i	−0.348780	+	0.292661i
$208$	−1.28977	−	9.20145i	−0.0894292	−	0.638006i
$209$	−5.35914	+	7.92924i	−0.370699	+	0.548477i
$210$	3.20872	−	0.111759i	0.221423	−	0.00771209i
$211$	−6.29241	−	7.49900i	−0.433187	−	0.516253i	0.504652	−	0.863323i	$-0.331621\pi$
$211$	−6.29241	−	7.49900i	−0.433187	−	0.516253i	−0.937839	+	0.347070i	$0.887176\pi$
$212$	1.41290	−	4.92398i	0.0970382	−	0.338180i
$213$	−9.50011	−	1.67513i	−0.650937	−	0.114778i
$214$	−13.4478	+	2.85714i	−0.919274	+	0.195310i
$215$	3.38125	−	1.23068i	0.230600	−	0.0839314i
$216$	−2.58358	−	1.15113i	−0.175791	−	0.0783245i
$217$	−2.04276	−	3.53817i	−0.138672	−	0.240187i
$218$	−5.12831	+	6.56270i	−0.347333	+	0.444482i
$219$	−5.36071	+	6.38864i	−0.362243	+	0.431705i
$220$	−6.69737	−	9.93315i	−0.451536	−	0.669693i
$221$	4.75061	+	2.74276i	0.319560	+	0.184498i
$222$	−1.76800	+	0.714131i	−0.118660	+	0.0479294i
$223$	1.96186	+	11.1262i	0.131376	+	0.745069i	0.977315	+	0.211790i	$0.0679292\pi$
$223$	1.96186	+	11.1262i	0.131376	+	0.745069i	−0.845940	+	0.533279i	$0.820960\pi$
$224$	0.00214087	−	4.70740i	0.000143043	−	0.314526i
$225$	−2.29569	−	0.835564i	−0.153046	−	0.0557042i
$226$	3.89034	−	3.50224i	0.258782	−	0.232966i
$227$			6.26057i			0.415528i	0.978179	+	0.207764i	$0.0666187\pi$
$227$			6.26057i			0.415528i	−0.978179	+	0.207764i	$0.933381\pi$
$228$	8.71779	+	0.00973782i	0.577350	+	0.000644903i
$229$		−	15.9135i		−	1.05159i	−0.850610	−	0.525797i	$-0.823767\pi$
$229$		−	15.9135i		−	1.05159i	0.850610	−	0.525797i	$-0.176233\pi$
$230$	16.9099	+	18.7837i	1.11500	+	1.23856i
$231$	−1.71691	−	0.624902i	−0.112964	−	0.0411156i
$232$	−4.84034	−	0.339797i	−0.317784	−	0.0223088i
$233$	−3.63287	−	20.6030i	−0.237997	−	1.34975i	−0.836209	−	0.548411i	$-0.815233\pi$
$233$	−3.63287	−	20.6030i	−0.237997	−	1.34975i	0.598212	−	0.801338i	$-0.295878\pi$
$234$	1.23031	+	3.04592i	0.0804278	+	0.199118i
$235$	−14.3301	−	8.27352i	−0.934796	−	0.539705i
$236$	9.57095	−	6.45316i	0.623016	−	0.420065i
$237$	0.480597	−	0.572753i	0.0312181	−	0.0372043i
$238$	2.18987	+	1.71124i	0.141948	+	0.110923i
$239$	0.636007	+	1.10160i	0.0411399	+	0.0712564i	0.885862	−	0.463949i	$-0.153568\pi$
$239$	0.636007	+	1.10160i	0.0411399	+	0.0712564i	−0.844722	+	0.535205i	$0.820234\pi$
$240$	−4.09167	+	10.1166i	−0.264116	+	0.653027i
$241$	1.22529	−	0.445968i	0.0789277	−	0.0287273i	−0.302255	−	0.953227i	$-0.597739\pi$
$241$	1.22529	−	0.445968i	0.0789277	−	0.0287273i	0.381182	+	0.924500i	$0.375517\pi$
$242$	−1.81613	−	8.54806i	−0.116745	−	0.549490i
$243$	0.984808	+	0.173648i	0.0631754	+	0.0111395i
$244$	0.904080	−	3.15074i	0.0578778	−	0.201705i
$245$	11.0612	+	13.1822i	0.706671	+	0.842178i
$246$	0.380572	+	10.9266i	0.0242644	+	0.696657i
$247$	−7.27679	−	7.04027i	−0.463011	−	0.447962i
$248$	13.8107	−	1.44775i	0.876977	−	0.0919321i
$249$	1.73514	−	1.45596i	0.109960	−	0.0922676i
$250$	3.04944	−	9.38231i	0.192864	−	0.593389i
$251$	15.6643	+	2.76205i	0.988725	+	0.174339i	0.644546	−	0.764565i	$-0.277046\pi$
$251$	15.6643	+	2.76205i	0.988725	+	0.174339i	0.344178	+	0.938904i	$0.388157\pi$
$252$	0.402341	+	1.61495i	0.0253451	+	0.101732i
$253$	−4.91915	−	13.5152i	−0.309264	−	0.849696i
$254$	13.9290	−	26.1909i	0.873983	−	1.64336i
$255$	−3.22138	−	5.57959i	−0.201731	−	0.349408i
$256$	14.6120	+	6.51842i	0.913249	+	0.407401i
$257$	−16.6383	−	13.9612i	−1.03787	−	0.870877i	−0.0461045	−	0.998937i	$-0.514681\pi$
$257$	−16.6383	−	13.9612i	−1.03787	−	0.870877i	−0.991766	+	0.128059i	$0.959125\pi$
$258$	0.988277	+	1.58189i	0.0615274	+	0.0984844i
$259$	0.971677	+	0.560998i	0.0603771	+	0.0348587i
$260$	11.5795	−	5.15302i	0.718133	−	0.319577i
$261$	1.68947	−	0.297899i	0.104575	−	0.0184395i
$262$	−23.8596	−	3.35546i	−1.47405	−	0.207301i
$263$	21.5799	+	7.85443i	1.33067	+	0.484325i	0.906863	−	0.421426i	$-0.138470\pi$
$263$	21.5799	+	7.85443i	1.33067	+	0.484325i	0.423810	+	0.905751i	$0.360693\pi$
$264$	4.31513	−	4.46601i	0.265578	−	0.274864i
$265$	6.98782			0.429258
$266$	−3.15405	−	4.04555i	−0.193387	−	0.248049i
$267$		−	0.103420i		−	0.00632918i
$268$	22.1602	+	22.9559i	1.35365	+	1.40226i
$269$	5.50627	−	15.1283i	0.335723	−	0.922391i	−0.650870	−	0.759189i	$-0.725596\pi$
$269$	5.50627	−	15.1283i	0.335723	−	0.922391i	0.986593	−	0.163202i	$-0.0521822\pi$
$270$	0.537311	−	3.82065i	0.0326997	−	0.232517i
$271$	3.27466	+	18.5715i	0.198922	+	1.12814i	0.906722	+	0.421729i	$0.138576\pi$
$271$	3.27466	+	18.5715i	0.198922	+	1.12814i	−0.707800	+	0.706412i	$0.750312\pi$
$272$	−8.34211	+	4.43169i	−0.505815	+	0.268711i
$273$	0.966489	−	1.67401i	0.0584946	−	0.101316i
$274$	−15.2604	−	24.4267i	−0.921914	−	1.47567i
$275$	3.44786	−	4.10900i	0.207914	−	0.247782i
$276$	−7.70266	+	10.5977i	−0.463646	+	0.637909i
$277$	25.7551	−	14.8697i	1.54747	−	0.893433i	0.549137	−	0.835732i	$-0.314956\pi$
$277$	25.7551	−	14.8697i	1.54747	−	0.893433i	0.998334	−	0.0577006i	$-0.0183769\pi$
$278$	17.1498	+	9.12072i	1.02858	+	0.547024i
$279$	−4.61348	+	1.67917i	−0.276202	+	0.100529i
$280$	6.17307	−	1.76828i	0.368911	−	0.105675i
$281$	1.20743	−	6.84767i	0.0720291	−	0.408497i	−0.927380	−	0.374121i	$-0.877944\pi$
$281$	1.20743	−	6.84767i	0.0720291	−	0.408497i	0.999409	−	0.0343763i	$-0.0109445\pi$
$282$	2.65133	−	8.15744i	0.157885	−	0.485768i
$283$	−1.96136	−	2.33745i	−0.116590	−	0.138947i	0.704592	−	0.709612i	$-0.251130\pi$
$283$	−1.96136	−	2.33745i	−0.116590	−	0.138947i	−0.821183	+	0.570665i	$0.806685\pi$
$284$	−19.2466	+	1.34233i	−1.14207	+	0.0796528i
$285$	3.26716	+	11.4343i	0.193530	+	0.677309i
$286$	−7.20822	+	0.251060i	−0.426231	+	0.0148455i
$287$	4.92827	−	4.13531i	0.290907	−	0.244100i
$288$	−5.57047	−	0.984836i	−0.328243	−	0.0580320i
$289$	−1.98360	+	11.2495i	−0.116682	+	0.661738i
$290$	−1.37556	−	6.47442i	−0.0807760	−	0.380191i
$291$	2.48236	+	6.82022i	0.145518	+	0.399809i
$292$	−7.31457	+	14.9902i	−0.428053	+	0.877233i
$293$	−16.4827	+	9.51628i	−0.962929	+	0.555947i	−0.897073	−	0.441882i	$-0.854311\pi$
$293$	−16.4827	+	9.51628i	−0.962929	+	0.555947i	−0.0658556	+	0.997829i	$0.520978\pi$
$294$	−5.49244	+	7.02869i	−0.320326	+	0.409922i
$295$	12.0622	+	10.1214i	0.702288	+	0.589290i
$296$	−3.08585	+	2.24071i	−0.179361	+	0.130239i
$297$	−1.09780	+	1.90145i	−0.0637010	+	0.110333i
$298$	−10.5629	−	26.1510i	−0.611895	−	1.51489i
$299$	14.9850	−	2.64226i	0.866604	−	0.152806i
$300$	−4.85919	−	0.511615i	−0.280545	−	0.0295381i
$301$	0.375383	−	1.03136i	0.0216367	−	0.0594464i
$302$	−9.21543	+	8.29609i	−0.530288	+	0.477386i
$303$	−6.76012			−0.388359
$304$	16.9231	−	4.19607i	0.970609	−	0.240661i
$305$	4.47135			0.256029
$306$	2.48211	−	2.23449i	0.141893	−	0.127738i
$307$	−2.36076	+	6.48614i	−0.134736	+	0.370183i	−0.988651	−	0.150228i	$-0.951999\pi$
$307$	−2.36076	+	6.48614i	−0.134736	+	0.370183i	0.853916	+	0.520411i	$0.174221\pi$
$308$	−3.63410	−	0.382627i	−0.207072	−	0.0218022i
$309$	−16.5768	+	2.92294i	−0.943022	+	0.166280i
$310$	7.09430	+	17.5636i	0.402929	+	0.997546i
$311$	8.58360	−	14.8672i	0.486731	−	0.843044i	−0.513152	−	0.858298i	$-0.671522\pi$
$311$	8.58360	−	14.8672i	0.486731	−	0.843044i	0.999884	+	0.0152540i	$0.00485568\pi$
$312$	3.86031	+	5.31631i	0.218547	+	0.300977i
$313$	−20.4990	−	17.2007i	−1.15867	−	0.972242i	−0.158786	−	0.987313i	$-0.550758\pi$
$313$	−20.4990	−	17.2007i	−1.15867	−	0.972242i	−0.999886	+	0.0150713i	$0.995202\pi$
$314$	−4.96803	+	6.35760i	−0.280362	+	0.358780i
$315$	−1.96612	+	1.13514i	−0.110779	+	0.0639580i
$316$	0.655764	−	1.34389i	0.0368896	−	0.0756000i
$317$	−10.5906	−	29.0973i	−0.594825	−	1.63427i	−0.761431	−	0.648246i	$-0.775503\pi$
$317$	−10.5906	−	29.0973i	−0.594825	−	1.63427i	0.166606	−	0.986024i	$-0.446719\pi$
$318$	0.752792	+	3.54319i	0.0422145	+	0.198692i
$319$	−0.654069	+	3.70941i	−0.0366208	+	0.207687i
$320$	−3.04932	+	21.6115i	−0.170462	+	1.20812i
$321$	7.44694	−	6.24872i	0.415648	−	0.348770i
$322$	7.70443	−	0.268343i	0.429351	−	0.0149542i
$323$	−4.19564	+	9.39990i	−0.233452	+	0.523024i
$324$	1.99515	−	0.139150i	0.110842	−	0.00773056i
$325$	3.64768	+	4.34714i	0.202337	+	0.241136i
$326$	8.82874	−	27.1637i	0.488979	−	1.50446i
$327$	1.02267	−	5.79986i	0.0565539	−	0.320733i
$328$	6.02150	+	21.0211i	0.332482	+	1.16070i
$329$	−4.74282	+	1.72625i	−0.261480	+	0.0951710i
$330$	7.47926	+	3.97766i	0.411720	+	0.218963i
$331$	−21.6086	+	12.4757i	−1.18772	+	0.685728i	−0.957787	−	0.287479i	$-0.907183\pi$
$331$	−21.6086	+	12.4757i	−1.18772	+	0.685728i	−0.229929	+	0.973207i	$0.573849\pi$
$332$	2.66341	−	3.66447i	0.146174	−	0.201114i
$333$	0.866669	−	1.03286i	0.0474931	−	0.0566001i
$334$	−9.75916	−	15.6211i	−0.533997	−	0.854747i
$335$	−21.7620	+	37.6929i	−1.18899	+	2.05938i
$336$	1.56163	+	2.93958i	0.0851938	+	0.160367i
$337$	2.12310	+	12.0407i	0.115652	+	0.655898i	0.986425	+	0.164212i	$0.0525080\pi$
$337$	2.12310	+	12.0407i	0.115652	+	0.655898i	−0.870773	+	0.491686i	$0.836381\pi$
$338$	−1.49766	+	10.6494i	−0.0814621	+	0.579251i
$339$	−1.26595	+	3.47816i	−0.0687568	+	0.188908i
$340$	−8.94935	−	9.27070i	−0.485347	−	0.502774i
$341$		−	10.7795i		−	0.583741i
$342$	−5.44582	+	2.88843i	−0.294476	+	0.156188i
$343$	11.0740			0.597937
$344$	2.68276	+	2.59213i	0.144645	+	0.139758i
$345$	−16.7936	−	6.11237i	−0.904137	−	0.329079i
$346$	−32.0620	−	4.50900i	−1.72367	−	0.242405i
$347$	−26.6793	+	4.70428i	−1.43222	+	0.252539i	−0.835315	−	0.549772i	$-0.814715\pi$
$347$	−26.6793	+	4.70428i	−1.43222	+	0.252539i	−0.596906	+	0.802311i	$0.703603\pi$
$348$	3.13468	−	1.39497i	0.168037	−	0.0747781i
$349$	1.55663	+	0.898721i	0.0833245	+	0.0481074i	0.541083	−	0.840969i	$-0.318014\pi$
$349$	1.55663	+	0.898721i	0.0833245	+	0.0481074i	−0.457759	+	0.889076i	$0.651348\pi$
$350$	1.52333	+	2.43834i	0.0814256	+	0.130335i
$351$	−1.77941	−	1.49310i	−0.0949777	−	0.0796958i
$352$	6.21501	−	10.7534i	0.331261	−	0.573159i
$353$	−7.95961	−	13.7865i	−0.423647	−	0.733779i	0.572646	−	0.819803i	$-0.305917\pi$
$353$	−7.95961	−	13.7865i	−0.423647	−	0.733779i	−0.996293	+	0.0860242i	$0.972584\pi$
$354$	−3.83262	+	7.20654i	−0.203702	+	0.383023i
$355$	−9.00127	−	24.7308i	−0.477738	−	1.31257i
$356$	−0.0500025	−	0.200705i	−0.00265013	−	0.0106373i
$357$	−1.93533	−	0.341250i	−0.102428	−	0.0180609i
$358$	4.97371	−	15.3028i	0.262869	−	0.808776i
$359$	0.250006	−	0.209780i	0.0131948	−	0.0110718i	−0.636166	−	0.771552i	$-0.719481\pi$
$359$	0.250006	−	0.209780i	0.0131948	−	0.0110718i	0.649361	+	0.760480i	$0.275036\pi$
$360$	−0.804499	−	7.67444i	−0.0424008	−	0.404478i
$361$	11.7255	−	14.9503i	0.617134	−	0.786858i
$362$	−0.873180	−	25.0700i	−0.0458933	−	1.31765i
$363$	3.97198	+	4.73362i	0.208475	+	0.248451i
$364$	1.06628	−	3.71600i	0.0558882	−	0.194771i
$365$	−22.4069	−	3.95093i	−1.17283	−	0.206801i
$366$	0.481694	+	2.26721i	0.0251786	+	0.118509i
$367$	−18.8104	+	6.84644i	−0.981896	+	0.357381i	−0.782577	−	0.622554i	$-0.786095\pi$
$367$	−18.8104	+	6.84644i	−0.981896	+	0.357381i	−0.199319	+	0.979935i	$0.563873\pi$
$368$	−9.82448	+	24.2910i	−0.512136	+	1.26626i
$369$	−3.86549	−	6.69523i	−0.201230	−	0.348540i
$370$	−4.09899	−	3.20308i	−0.213096	−	0.166520i
$371$	1.37006	−	1.63278i	0.0711301	−	0.0847695i
$372$	−8.14142	+	5.48930i	−0.422113	+	0.284607i
$373$	−12.1008	−	6.98642i	−0.626557	−	0.361743i	0.152860	−	0.988248i	$-0.451152\pi$
$373$	−12.1008	−	6.98642i	−0.626557	−	0.361743i	−0.779418	+	0.626505i	$0.784485\pi$
$374$	2.74628	+	6.79906i	0.142007	+	0.351571i
$375$	1.21136	+	6.86994i	0.0625541	+	0.354762i
$376$	1.20134	−	17.1129i	0.0619544	−	0.882529i
$377$	−3.74460	−	1.36292i	−0.192857	−	0.0701941i
$378$	−0.787386	−	0.874641i	−0.0404988	−	0.0449867i
$379$			21.4431i			1.10146i	0.834683	+	0.550730i	$0.185651\pi$
$379$			21.4431i			1.10146i	−0.834683	+	0.550730i	$0.814349\pi$
$380$	11.8689	+	20.6107i	0.608861	+	1.05730i
$381$			20.9759i			1.07463i
$382$	−10.5948	+	9.53787i	−0.542078	+	0.488000i
$383$	−7.95424	−	2.89511i	−0.406443	−	0.147933i	0.130705	−	0.991421i	$-0.458276\pi$
$383$	−7.95424	−	2.89511i	−0.406443	−	0.147933i	−0.537148	+	0.843488i	$0.680498\pi$
$384$	−11.2866	+	0.782018i	−0.575969	+	0.0399072i
$385$	−0.865577	−	4.90893i	−0.0441139	−	0.250182i
$386$	−29.0495	+	11.7337i	−1.47858	+	0.597229i
$387$	−1.14221	−	0.659458i	−0.0580620	−	0.0335221i
$388$	8.11498	+	12.0357i	0.411976	+	0.611019i
$389$	21.3020	−	25.3868i	1.08006	−	1.28716i	0.124542	−	0.992214i	$-0.460254\pi$
$389$	21.3020	−	25.3868i	1.08006	−	1.28716i	0.955514	−	0.294946i	$-0.0953016\pi$
$390$	−5.51828	+	7.06175i	−0.279429	+	0.357586i
$391$	−7.73482	−	13.3971i	−0.391167	−	0.677521i
$392$	−7.26077	+	16.2960i	−0.366724	+	0.823071i
$393$	16.0098	−	5.82711i	0.807590	−	0.293939i
$394$	25.0709	−	5.32661i	1.26306	−	0.268351i
$395$	2.00881	+	0.354208i	0.101074	+	0.0178221i
$396$	−1.21115	+	4.22089i	−0.0608626	+	0.212108i
$397$	24.0674	+	28.6824i	1.20791	+	1.43953i	0.866182	+	0.499728i	$0.166567\pi$
$397$	24.0674	+	28.6824i	1.20791	+	1.43953i	0.341725	+	0.939800i	$0.388989\pi$
$398$	−10.2128	+	0.355709i	−0.511921	+	0.0178301i
$399$	3.31232	+	1.47845i	0.165823	+	0.0740151i
$400$	−9.67749	+	1.35649i	−0.483875	+	0.0678246i
$401$	17.9368	−	15.0508i	0.895722	−	0.751600i	−0.0736279	−	0.997286i	$-0.523458\pi$
$401$	17.9368	−	15.0508i	0.895722	−	0.751600i	0.969349	+	0.245686i	$0.0790133\pi$
$402$	−21.4567	−	6.97386i	−1.07016	−	0.347825i
$403$	11.2309	+	1.98031i	0.559452	+	0.0986465i
$404$	−13.1192	+	3.26846i	−0.652706	+	0.162612i
$405$	0.933096	+	2.56366i	0.0463659	+	0.127389i
$406$	−1.78251	−	0.947988i	−0.0884647	−	0.0470478i
$407$	1.48017	+	2.56372i	0.0733691	+	0.127079i
$408$	3.73662	−	5.53651i	0.184990	−	0.274098i
$409$	−9.36092	−	7.85474i	−0.462868	−	0.388392i	0.381317	−	0.924444i	$-0.375471\pi$
$409$	−9.36092	−	7.85474i	−0.462868	−	0.388392i	−0.844185	+	0.536052i	$0.819915\pi$
$410$	−25.2970	+	15.8041i	−1.24933	+	0.780511i
$411$	17.6374	+	10.1830i	0.869989	+	0.502289i
$412$	−30.7571	+	13.6872i	−1.51529	+	0.674321i
$413$	4.72993	−	0.834015i	0.232745	−	0.0410392i
$414$	1.29013	−	9.17372i	0.0634066	−	0.450864i
$415$	5.80687	+	2.11353i	0.285048	+	0.103749i
$416$	10.0620	+	8.45082i	0.493330	+	0.414336i
$417$	−13.7351			−0.672608
$418$	−1.86990	−	13.4048i	−0.0914600	−	0.655652i
$419$			13.1392i			0.641894i	0.947097	+	0.320947i	$0.104001\pi$
$419$			13.1392i			0.641894i	−0.947097	+	0.320947i	$0.895999\pi$
$420$	−3.26679	+	3.15355i	−0.159403	+	0.153878i
$421$	7.66851	−	21.0691i	0.373740	−	1.02684i	−0.600162	−	0.799878i	$-0.704897\pi$
$421$	7.66851	−	21.0691i	0.373740	−	1.02684i	0.973903	−	0.226965i	$-0.0728804\pi$
$422$	13.7092	+	1.92797i	0.667353	+	0.0938522i
$423$	1.05321	+	5.97306i	0.0512089	+	0.290420i
$424$	3.17403	+	6.51223i	0.154144	+	0.316262i
$425$	2.88466	−	4.99638i	0.139927	−	0.242360i
$426$	11.5701	−	7.22834i	0.560573	−	0.350214i
$427$	0.876671	−	1.04478i	0.0424251	−	0.0505603i
$428$	11.4309	−	15.7273i	0.552535	−	0.760208i
$429$	4.41679	−	2.55004i	0.213245	−	0.123117i
$430$	−2.38941	+	4.49284i	−0.115228	+	0.216664i
$431$	−14.0098	+	5.09916i	−0.674830	+	0.245618i	−0.656626	−	0.754216i	$-0.728017\pi$
$431$	−14.0098	+	5.09916i	−0.674830	+	0.245618i	−0.0182037	+	0.999834i	$0.505795\pi$
$432$	3.80468	−	1.23468i	0.183053	−	0.0594038i
$433$	4.77457	−	27.0779i	0.229451	−	1.30128i	−0.624539	−	0.780994i	$-0.714713\pi$
$433$	4.77457	−	27.0779i	0.229451	−	1.30128i	0.853990	−	0.520289i	$-0.174176\pi$
$434$	5.49486	+	1.78594i	0.263762	+	0.0857279i
$435$	3.00843	+	3.58531i	0.144243	+	0.171903i
$436$	−0.819501	−	11.7501i	−0.0392470	−	0.562729i
$437$	7.84476	+	27.4548i	0.375266	+	1.31334i
$438$	−0.410541	−	11.7871i	−0.0196164	−	0.563209i
$439$	4.48024	−	3.75937i	0.213830	−	0.179425i	−0.529581	−	0.848259i	$-0.677651\pi$
$439$	4.48024	−	3.75937i	0.213830	−	0.179425i	0.743411	+	0.668834i	$0.233206\pi$
$440$	16.4380	+	4.10322i	0.783651	+	0.195613i
$441$	1.09529	−	6.21169i	0.0521566	−	0.295795i
$442$	−7.58833	+	1.61223i	−0.360940	+	0.0766859i
$443$	−6.34469	−	17.4319i	−0.301445	−	0.828214i	−0.994250	−	0.107088i	$-0.965847\pi$
$443$	−6.34469	−	17.4319i	−0.301445	−	0.828214i	0.692804	−	0.721126i	$-0.256375\pi$
$444$	1.18255	−	2.42347i	0.0561213	−	0.115013i
$445$	0.244348	−	0.141074i	0.0115832	−	0.00668757i
$446$	−12.5896	−	9.83795i	−0.596137	−	0.465841i
$447$	15.2773	+	12.8192i	0.722591	+	0.606326i
$448$	4.45188	+	4.94974i	0.210331	+	0.233853i
$449$	−1.14255	+	1.97896i	−0.0539204	+	0.0933929i	−0.891726	−	0.452576i	$-0.850505\pi$
$449$	−1.14255	+	1.97896i	−0.0539204	+	0.0933929i	0.837805	+	0.545969i	$0.183838\pi$
$450$	3.20350	−	1.29396i	0.151014	−	0.0609978i
$451$	16.7163	−	2.94754i	0.787142	−	0.138794i
$452$	−0.775139	+	7.36207i	−0.0364595	+	0.346283i
$453$	2.99877	−	8.23905i	0.140894	−	0.387104i
$454$	−5.92373	−	6.58018i	−0.278015	−	0.308823i
$455$	5.27353			0.247227
$456$	−9.17206	+	8.23852i	−0.429521	+	0.385804i
$457$	−6.44697			−0.301577			−0.150788	−	0.988566i	$-0.548181\pi$
$457$	−6.44697			−0.301577			−0.150788	+	0.988566i	$0.548181\pi$
$458$	15.0573	+	16.7259i	0.703582	+	0.781550i
$459$	−0.807698	+	2.21913i	−0.0377001	+	0.103580i
$460$	−35.5463	−	3.74260i	−1.65735	−	0.174500i
$461$	−4.62630	+	0.815742i	−0.215468	+	0.0379929i	−0.280340	−	0.959901i	$-0.590447\pi$
$461$	−4.62630	+	0.815742i	−0.215468	+	0.0379929i	0.0648718	+	0.997894i	$0.479336\pi$
$462$	2.39584	−	0.967728i	0.111464	−	0.0450228i
$463$	0.181801	−	0.314888i	0.00844900	−	0.0146341i	−0.861770	−	0.507299i	$-0.830644\pi$
$463$	0.181801	−	0.314888i	0.00844900	−	0.0146341i	0.870219	+	0.492665i	$0.163977\pi$
$464$	5.40896	−	4.22278i	0.251105	−	0.196037i
$465$	−10.2606	−	8.60963i	−0.475822	−	0.399262i
$466$	23.3129	+	18.2174i	1.07995	+	0.843906i
$467$	16.1671	−	9.33405i	0.748122	−	0.431929i	−0.0768929	−	0.997039i	$-0.524500\pi$
$467$	16.1671	−	9.33405i	0.748122	−	0.431929i	0.825015	+	0.565111i	$0.191167\pi$
$468$	−4.17516	−	2.03730i	−0.192997	−	0.0941743i
$469$	4.54058	+	12.4752i	0.209665	+	0.576049i
$470$	22.8901	−	4.86327i	1.05584	−	0.224326i
$471$	0.990712	−	5.61861i	0.0456496	−	0.258892i
$472$	−3.95360	+	15.8386i	−0.181979	+	0.729031i
$473$	2.21833	−	1.86140i	0.101999	−	0.0855872i
$474$	0.0368057	+	1.05673i	0.00169054	+	0.0485374i
$475$	−7.40451	+	7.65325i	−0.339742	+	0.351155i
$476$	−3.92084	+	0.273455i	−0.179711	+	0.0125338i
$477$	−1.64640	−	1.96210i	−0.0753833	−	0.0898384i
$478$	−1.71080	−	0.556046i	−0.0782504	−	0.0254330i
$479$	−0.348974	+	1.97913i	−0.0159450	+	0.0904287i	−0.991742	−	0.128251i	$-0.959064\pi$
$479$	−0.348974	+	1.97913i	−0.0159450	+	0.0904287i	0.975797	+	0.218679i	$0.0701749\pi$
$480$	−5.27179	−	14.5047i	−0.240623	−	0.662044i
$481$	−2.94302	+	1.07117i	−0.134190	+	0.0488412i
$482$	−0.865866	+	1.62810i	−0.0394391	+	0.0741579i
$483$	−4.72084	+	2.72558i	−0.214806	+	0.124018i
$484$	9.99700	+	7.26603i	0.454409	+	0.330274i
$485$	−12.7279	+	15.1685i	−0.577942	+	0.688764i
$486$	−1.19939	+	0.749310i	−0.0544054	+	0.0339894i
$487$	10.0385	−	17.3872i	0.454888	−	0.787890i	−0.543793	−	0.839219i	$-0.683012\pi$
$487$	10.0385	−	17.3872i	0.454888	−	0.787890i	0.998682	+	0.0513293i	$0.0163458\pi$
$488$	2.03099	+	4.16703i	0.0919385	+	0.188633i
$489$	3.50712	+	19.8898i	0.158597	+	0.899450i
$490$	−24.0988	−	3.38910i	−1.08867	−	0.153104i
$491$	10.5245	−	28.9159i	0.474966	−	1.30496i	−0.438752	−	0.898608i	$-0.644579\pi$
$491$	10.5245	−	28.9159i	0.474966	−	1.30496i	0.913718	−	0.406350i	$-0.133199\pi$
$492$	−10.7388	−	11.1244i	−0.484141	−	0.501525i
$493$			4.05131i			0.182462i
$494$	14.3098	+	0.514409i	0.643827	+	0.0231444i
$495$	−5.99004			−0.269232
$496$	−13.1459	+	14.5893i	−0.590266	+	0.655078i
$497$	−7.54343	−	2.74558i	−0.338369	−	0.123156i
$498$	−0.446100	+	3.17208i	−0.0199902	+	0.142144i
$499$	16.1634	−	2.85004i	0.723573	−	0.127585i	0.200280	−	0.979739i	$-0.435815\pi$
$499$	16.1634	−	2.85004i	0.723573	−	0.127585i	0.523292	+	0.852153i	$0.324704\pi$
$500$	5.67240	+	12.7467i	0.253678	+	0.570048i
$501$	11.2793	+	6.51210i	0.503921	+	0.290939i
$502$	−19.0775	+	11.9185i	−0.851469	+	0.531949i
$503$	7.02476	+	5.89448i	0.313219	+	0.262822i	0.785821	−	0.618454i	$-0.212241\pi$
$503$	7.02476	+	5.89448i	0.313219	+	0.262822i	−0.472602	+	0.881276i	$0.656685\pi$
$504$	−1.95094	−	1.31670i	−0.0869020	−	0.0586506i
$505$	−9.22145	−	15.9720i	−0.410349	−	0.710746i
$506$	17.9584	+	9.55073i	0.798347	+	0.424582i
$507$	−2.60085	−	7.14576i	−0.115508	−	0.317355i
$508$	10.1417	+	40.7076i	0.449964	+	1.80611i
$509$	−4.78215	−	0.843223i	−0.211965	−	0.0373752i	0.0666571	−	0.997776i	$-0.478767\pi$
$509$	−4.78215	−	0.843223i	−0.211965	−	0.0373752i	−0.278622	+	0.960401i	$0.589878\pi$
$510$	8.66524	+	2.81638i	0.383703	+	0.124711i
$511$	−5.31636	+	4.46096i	−0.235182	+	0.197341i
$512$	−21.5257	+	6.97464i	−0.951309	+	0.308238i
$513$	2.44084	−	3.61141i	0.107766	−	0.159448i
$514$	30.6978	−	1.06920i	1.35402	−	0.0471602i
$515$	−29.5183	−	35.1786i	−1.30073	−	1.55015i
$516$	−2.53551	−	0.727546i	−0.111620	−	0.0320284i
$517$	−13.1145	−	2.31244i	−0.576775	−	0.101701i
$518$	−1.55210	+	0.329761i	−0.0681953	+	0.0144889i
$519$	21.5137	−	7.83034i	0.944346	−	0.343714i
$520$	−7.29492	+	16.3726i	−0.319903	+	0.717987i
$521$	17.0461	+	29.5247i	0.746803	+	1.29350i	0.949348	+	0.314228i	$0.101746\pi$
$521$	17.0461	+	29.5247i	0.746803	+	1.29350i	−0.202544	+	0.979273i	$0.564921\pi$
$522$	−1.49385	+	1.91168i	−0.0653839	+	0.0836719i
$523$	−22.1492	+	26.3963i	−0.968515	+	1.15423i	0.0194901	+	0.999810i	$0.493796\pi$
$523$	−22.1492	+	26.3963i	−0.968515	+	1.15423i	−0.988005	+	0.154421i	$0.950649\pi$
$524$	28.2526	−	19.0492i	1.23422	−	0.832166i
$525$	−1.76061	−	1.01649i	−0.0768395	−	0.0443633i
$526$	−30.1134	+	12.1634i	−1.31301	+	0.530350i
$527$	−2.01331	−	11.4180i	−0.0877010	−	0.497377i
$528$	−0.309696	+	8.77697i	−0.0134778	+	0.381969i
$529$	−18.7100	−	6.80989i	−0.813479	−	0.296082i
$530$	−7.34456	+	6.61186i	−0.319027	+	0.287201i
$531$		−	5.77162i		−	0.250467i
$532$	7.14296	+	1.26772i	0.309687	+	0.0549628i
$533$			17.9579i			0.777844i
$534$	0.0978555	+	0.108699i	0.00423462	+	0.00470389i
$535$	24.9221	+	9.07090i	1.07748	+	0.392169i
$536$	−45.0124	−	3.15991i	−1.94424	−	0.136487i
$537$	1.97575	+	11.2050i	0.0852598	+	0.483532i
$538$	8.52704	+	21.1107i	0.367627	+	0.910146i
$539$	11.9934	+	6.92441i	0.516594	+	0.298256i
$540$	3.05035	+	4.52410i	0.131266	+	0.194686i
$541$	−0.973825	+	1.16056i	−0.0418680	+	0.0498964i	−0.786572	−	0.617498i	$-0.788146\pi$
$541$	−0.973825	+	1.16056i	−0.0418680	+	0.0498964i	0.744704	+	0.667395i	$0.232591\pi$
$542$	−21.0142	−	16.4212i	−0.902637	−	0.705350i
$543$	8.86895	+	15.3615i	0.380603	+	0.659224i
$544$	4.57474	−	12.5512i	0.196140	−	0.538129i
$545$	15.0983	−	5.49532i	0.646738	−	0.235394i
$546$	0.568113	+	2.67396i	0.0243130	+	0.114435i
$547$	18.5142	+	3.26456i	0.791611	+	0.139582i	0.554811	−	0.831976i	$-0.312790\pi$
$547$	18.5142	+	3.26456i	0.791611	+	0.139582i	0.236800	+	0.971559i	$0.423902\pi$
$548$	39.1519	+	11.2343i	1.67249	+	0.479907i
$549$	−1.05349	−	1.25550i	−0.0449619	−	0.0535835i
$550$	0.264049	+	7.58114i	0.0112591	+	0.323261i
$551$	1.81583	−	7.25400i	0.0773571	−	0.309031i
$552$	−1.93167	−	18.4270i	−0.0822175	−	0.784306i
$553$	0.476621	−	0.399933i	0.0202680	−	0.0170069i
$554$	−13.0002	+	39.9982i	−0.552326	+	1.69936i
$555$	3.62253	+	0.638749i	0.153768	+	0.0271134i
$556$	−26.6553	+	6.64077i	−1.13044	+	0.281631i
$557$	−12.2457	−	33.6447i	−0.518865	−	1.42557i	−0.871772	−	0.489911i	$-0.837029\pi$
$557$	−12.2457	−	33.6447i	−0.518865	−	1.42557i	0.352907	−	0.935658i	$-0.385193\pi$
$558$	3.26018	−	6.13015i	0.138014	−	0.259510i
$559$	1.53182	+	2.65320i	0.0647892	+	0.112218i
$560$	−4.81507	+	7.69949i	−0.203474	+	0.325363i
$561$	−3.97197	−	3.33288i	−0.167697	−	0.140714i
$562$	5.21018	+	8.33972i	0.219778	+	0.351790i
$563$	6.15969	+	3.55630i	0.259600	+	0.149880i	0.624152	−	0.781303i	$-0.285445\pi$
$563$	6.15969	+	3.55630i	0.259600	+	0.149880i	−0.364552	+	0.931183i	$0.618778\pi$
$564$	4.93186	+	11.0826i	0.207669	+	0.466661i
$565$	−9.94466	+	1.75351i	−0.418375	+	0.0737708i
$566$	4.27318	+	0.600952i	0.179615	+	0.0252599i
$567$	0.781973	+	0.284615i	0.0328398	+	0.0119527i
$568$	18.9590	−	19.6219i	0.795503	−	0.823318i
$569$	29.4880			1.23620			0.618101	−	0.786098i	$-0.287902\pi$
$569$	29.4880			1.23620			0.618101	+	0.786098i	$0.287902\pi$
$570$	−14.2531	−	8.92665i	−0.596995	−	0.373896i
$571$		−	19.0587i		−	0.797581i	−0.917042	−	0.398791i	$-0.869430\pi$
$571$		−	19.0587i		−	0.797581i	0.917042	−	0.398791i	$-0.130570\pi$
$572$	7.33866	−	7.08428i	0.306845	−	0.296209i
$573$	3.44763	−	9.47229i	0.144027	−	0.395711i
$574$	−1.26704	+	9.00955i	−0.0528854	+	0.376051i
$575$	−2.77895	−	15.7602i	−0.115890	−	0.657247i
$576$	6.78670	−	4.23565i	0.282779	−	0.176485i
$577$	−2.57641	+	4.46247i	−0.107257	+	0.185775i	−0.914658	−	0.404228i	$-0.867540\pi$
$577$	−2.57641	+	4.46247i	−0.107257	+	0.185775i	0.807401	+	0.590003i	$0.200873\pi$
$578$	−8.55943	−	13.7007i	−0.356025	−	0.569875i
$579$	14.2400	−	16.9706i	0.591794	−	0.705272i
$580$	7.57187	+	5.50339i	0.314405	+	0.228516i
$581$	1.63237	−	0.942447i	0.0677220	−	0.0390993i
$582$	−9.06237	−	4.81960i	−0.375647	−	0.199779i
$583$	5.28455	−	1.92342i	0.218864	−	0.0796598i
$584$	−6.49568	−	22.6765i	−0.268793	−	0.938359i
$585$	1.10044	−	6.24090i	0.0454976	−	0.258030i
$586$	8.31987	−	25.5980i	0.343690	−	1.05744i
$587$	−8.34903	−	9.94999i	−0.344601	−	0.410680i	0.565710	−	0.824604i	$-0.308602\pi$
$587$	−8.34903	−	9.94999i	−0.344601	−	0.410680i	−0.910311	+	0.413924i	$0.864158\pi$
$588$	−0.877690	−	12.5845i	−0.0361953	−	0.518974i
$589$	−1.51277	+	21.3467i	−0.0623326	+	0.879577i
$590$	−22.2548	+	0.775129i	−0.916217	+	0.0319116i
$591$	−13.8834	+	11.6496i	−0.571088	+	0.479199i
$592$	1.12323	−	5.27493i	0.0461643	−	0.216798i
$593$	7.03653	−	39.9061i	0.288955	−	1.63875i	−0.401849	−	0.915706i	$-0.631632\pi$
$593$	7.03653	−	39.9061i	0.288955	−	1.63875i	0.690804	−	0.723042i	$-0.257257\pi$
$594$	−0.645302	−	3.03726i	−0.0264771	−	0.124620i
$595$	−1.83370	−	5.03806i	−0.0751746	−	0.206540i
$596$	35.8463	+	17.4915i	1.46832	+	0.716478i
$597$	6.25783	−	3.61296i	0.256116	−	0.147869i
$598$	−13.2499	+	16.9559i	−0.541828	+	0.693378i
$599$	5.67143	+	4.75890i	0.231728	+	0.194443i	0.751257	−	0.660010i	$-0.229448\pi$
$599$	5.67143	+	4.75890i	0.231728	+	0.194443i	−0.519528	+	0.854453i	$0.673892\pi$
$600$	5.59135	−	4.06002i	0.228266	−	0.165750i
$601$	21.1051	−	36.5551i	0.860895	−	1.49111i	−0.0101721	−	0.999948i	$-0.503238\pi$
$601$	21.1051	−	36.5551i	0.860895	−	1.49111i	0.871067	−	0.491165i	$-0.163429\pi$
$602$	0.581320	+	1.43920i	0.0236928	+	0.0586572i
$603$	15.7111	−	2.77029i	0.639804	−	0.112815i
$604$	1.83615	−	17.4392i	0.0747117	−	0.709592i
$605$	−5.76589	+	15.8416i	−0.234417	+	0.644054i
$606$	7.10524	−	6.39642i	0.288631	−	0.259837i
$607$	−38.6378			−1.56826			−0.784130	−	0.620597i	$-0.786890\pi$
$607$	−38.6378			−1.56826			−0.784130	+	0.620597i	$0.786890\pi$
$608$	−13.8168	+	20.4229i	−0.560345	+	0.828260i
$609$	1.42759			0.0578489
$610$	−4.69962	+	4.23078i	−0.190282	+	0.171299i
$611$	4.81857	−	13.2389i	0.194939	−	0.535589i
$612$	−0.494553	+	4.69714i	−0.0199911	+	0.189871i
$613$	5.24716	−	0.925216i	0.211931	−	0.0373691i	−0.0666746	−	0.997775i	$-0.521239\pi$
$613$	5.24716	−	0.925216i	0.211931	−	0.0373691i	0.278605	+	0.960406i	$0.410128\pi$
$614$	−3.65589	−	9.05101i	−0.147540	−	0.365269i
$615$	10.5458	−	18.2659i	0.425248	−	0.736551i
$616$	4.18166	−	3.03641i	0.168484	−	0.122341i
$617$	−0.440217	−	0.369386i	−0.0177225	−	0.0148709i	0.633883	−	0.773429i	$-0.281460\pi$
$617$	−0.440217	−	0.369386i	−0.0177225	−	0.0148709i	−0.651606	+	0.758558i	$0.725904\pi$
$618$	14.6574	−	18.7571i	0.589607	−	0.754521i
$619$	6.19900	−	3.57899i	0.249159	−	0.143852i	−0.370220	−	0.928944i	$-0.620718\pi$
$619$	6.19900	−	3.57899i	0.249159	−	0.143852i	0.619379	+	0.785092i	$0.287384\pi$
$620$	−24.0751	−	11.7477i	−0.966881	−	0.471797i
$621$	2.24045	+	6.15558i	0.0899061	+	0.247015i
$622$	5.04554	+	23.7480i	0.202308	+	0.952209i
$623$	0.0149444	−	0.0847541i	0.000598736	−	0.00339560i
$624$	−9.08766	−	1.93510i	−0.363798	−	0.0774659i
$625$	−23.9364	+	20.0850i	−0.957456	+	0.803401i
$626$	37.8208	−	1.31729i	1.51162	−	0.0526494i
$627$	5.61812	+	7.74790i	0.224366	+	0.309421i
$628$	−0.793890	−	11.3829i	−0.0316797	−	0.454228i
$629$	2.04668	+	2.43914i	0.0816065	+	0.0972549i
$630$	0.992429	−	3.05344i	0.0395393	−	0.121652i
$631$	4.67505	−	26.5135i	0.186111	−	1.05549i	−0.738409	−	0.674353i	$-0.764423\pi$
$631$	4.67505	−	26.5135i	0.186111	−	1.05549i	0.924520	−	0.381134i	$-0.124466\pi$
$632$	0.582349	+	2.03299i	0.0231646	+	0.0808678i
$633$	−9.19889	+	3.34812i	−0.365623	+	0.133076i
$634$	38.6631	+	20.5620i	1.53551	+	0.816623i
$635$	−49.5595	+	28.6132i	−1.96671	+	1.13548i
$636$	−4.14379	−	3.01179i	−0.164312	−	0.119425i
$637$	−9.41775	+	11.2236i	−0.373145	+	0.444697i
$638$	−2.82237	−	4.51766i	−0.111739	−	0.178856i
$639$	−4.82333	+	8.35426i	−0.190808	+	0.330489i
$640$	−17.2437	−	25.6000i	−0.681618	−	1.01193i
$641$	1.72190	+	9.76536i	0.0680108	+	0.385709i	0.999745	+	0.0225683i	$0.00718431\pi$
$641$	1.72190	+	9.76536i	0.0680108	+	0.385709i	−0.931734	+	0.363140i	$0.881705\pi$
$642$	−1.91459	+	13.6140i	−0.0755627	+	0.537302i
$643$	5.56630	−	15.2933i	0.219513	−	0.603108i	−0.780236	−	0.625485i	$-0.784901\pi$
$643$	5.56630	−	15.2933i	0.219513	−	0.603108i	0.999750	+	0.0223768i	$0.00712334\pi$
$644$	−7.84385	+	7.57196i	−0.309091	+	0.298377i
$645$		−	3.59825i		−	0.141681i
$646$	−4.48433	−	13.8497i	−0.176434	−	0.544909i
$647$	−10.5152			−0.413396			−0.206698	−	0.978405i	$-0.566272\pi$
$647$	−10.5152			−0.413396			−0.206698	+	0.978405i	$0.566272\pi$
$648$	−1.96535	+	2.03406i	−0.0772061	+	0.0799056i
$649$	11.9080	+	4.33415i	0.467429	+	0.170130i
$650$	−7.94715	−	1.11764i	−0.311713	−	0.0438373i
$651$	−4.02346	+	0.709444i	−0.157692	+	0.0278053i
$652$	16.4227	+	36.9041i	0.643164	+	1.44528i
$653$	−40.8418	−	23.5800i	−1.59826	−	0.922757i	−0.991822	−	0.127628i	$-0.959264\pi$
$653$	−40.8418	−	23.5800i	−1.59826	−	0.922757i	−0.606440	−	0.795129i	$-0.707403\pi$
$654$	4.41294	+	7.06361i	0.172560	+	0.276209i
$655$	35.6066	+	29.8774i	1.39126	+	1.16741i
$656$	−26.2190	−	16.3967i	−1.02368	−	0.640185i
$657$	4.16989	+	7.22246i	0.162683	+	0.281775i
$658$	3.35158	−	6.30202i	0.130658	−	0.245678i
$659$	−9.89275	−	27.1801i	−0.385367	−	1.05879i	−0.969063	−	0.246814i	$-0.920616\pi$
$659$	−9.89275	−	27.1801i	−0.385367	−	1.05879i	0.583696	−	0.811972i	$-0.301606\pi$
$660$	−11.6247	+	2.89613i	−0.452492	+	0.112732i
$661$	22.4860	+	3.96488i	0.874603	+	0.154216i	0.592891	−	0.805283i	$-0.297987\pi$
$661$	22.4860	+	3.96488i	0.874603	+	0.154216i	0.281712	+	0.959499i	$0.409098\pi$
$662$	10.9072	−	33.5586i	0.423922	−	1.30429i
$663$	4.20216	−	3.52603i	0.163198	−	0.136940i
$664$	0.667931	+	6.37167i	0.0259208	+	0.247269i
$665$	1.02520	+	9.84270i	0.0397557	+	0.381683i
$666$	0.0663723	+	1.90562i	0.00257188	+	0.0738414i
$667$	7.22352	+	8.60866i	0.279696	+	0.333329i
$668$	25.0380	+	7.18446i	0.968750	+	0.277975i
$669$	11.1262	+	1.96186i	0.430166	+	0.0758498i
$670$	−12.7920	−	60.2084i	−0.494197	−	2.32605i
$671$	3.38146	−	1.23075i	0.130540	−	0.0475126i
$672$	−4.42277	−	1.61204i	−0.170612	−	0.0621856i
$673$	−5.60370	−	9.70589i	−0.216007	−	0.374134i	0.737577	−	0.675263i	$-0.235970\pi$
$673$	−5.60370	−	9.70589i	−0.216007	−	0.374134i	−0.953583	+	0.301129i	$0.902637\pi$
$674$	−13.6244	−	10.6465i	−0.524790	−	0.410088i
$675$	−1.57035	+	1.87147i	−0.0604426	+	0.0720327i
$676$	−8.50232	−	12.6102i	−0.327012	−	0.485006i
$677$	−8.26938	−	4.77433i	−0.317818	−	0.183492i	0.332602	−	0.943067i	$-0.392074\pi$
$677$	−8.26938	−	4.77433i	−0.317818	−	0.183492i	−0.650420	+	0.759575i	$0.725407\pi$
$678$	−1.96045	−	4.85356i	−0.0752908	−	0.186400i
$679$	1.04879	+	5.94799i	0.0402489	+	0.228263i
$680$	18.1781	+	1.27612i	0.697100	+	0.0489371i
$681$	5.88301	+	2.14124i	0.225437	+	0.0820525i
$682$	10.1995	+	11.3298i	0.390559	+	0.433839i
$683$			44.5878i			1.70610i	0.521825	+	0.853052i	$0.325251\pi$
$683$			44.5878i			1.70610i	−0.521825	+	0.853052i	$0.674749\pi$
$684$	2.99081	−	8.18871i	0.114357	−	0.313103i
$685$			55.5621i			2.12292i
$686$	−11.6393	+	10.4782i	−0.444390	+	0.400058i
$687$	−14.9538	−	5.44273i	−0.570523	−	0.207653i
$688$	−5.27238	−	0.186036i	−0.201008	−	0.00709257i
$689$	1.03314	+	5.85922i	0.0393594	+	0.223219i
$690$	23.4345	−	9.46565i	0.892134	−	0.360351i
$691$	2.52946	+	1.46038i	0.0962252	+	0.0555557i	0.547340	−	0.836910i	$-0.315640\pi$
$691$	2.52946	+	1.46038i	0.0962252	+	0.0555557i	−0.451115	+	0.892466i	$0.648974\pi$
$692$	37.9653	−	25.5978i	1.44322	−	0.973084i
$693$	−1.17443	+	1.39963i	−0.0446130	+	0.0531677i
$694$	23.5901	−	30.1884i	0.895470	−	1.14593i
$695$	−18.7359	−	32.4516i	−0.710694	−	1.23096i
$696$	−1.97480	+	4.43221i	−0.0748545	+	0.168003i
$697$	17.1561	−	6.24430i	0.649833	−	0.236520i
$698$	−2.48647	+	0.528279i	−0.0941142	+	0.0199956i
$699$	−20.6030	−	3.63287i	−0.779278	−	0.137408i
$700$	−3.90825	−	1.12144i	−0.147718	−	0.0423865i
$701$	−7.66290	−	9.13229i	−0.289424	−	0.344922i	0.601667	−	0.798747i	$-0.294503\pi$
$701$	−7.66290	−	9.13229i	−0.289424	−	0.344922i	−0.891091	+	0.453825i	$0.850059\pi$
$702$	3.28302	−	0.114346i	0.123909	−	0.00431573i
$703$	−2.57141	−	5.28470i	−0.0969824	−	0.199316i
$704$	3.64256	+	17.1830i	0.137284	+	0.647609i
$705$	−12.6758	+	10.6362i	−0.477397	+	0.400583i
$706$	21.4107	+	6.95890i	0.805801	+	0.261902i
$707$	−5.54003	−	0.976856i	−0.208354	−	0.0367385i
$708$	−2.79052	−	11.2009i	−0.104874	−	0.420954i
$709$	−3.94862	−	10.8487i	−0.148294	−	0.407433i	0.843198	−	0.537603i	$-0.180670\pi$
$709$	−3.94862	−	10.8487i	−0.148294	−	0.407433i	−0.991492	+	0.130170i	$0.958448\pi$
$710$	32.8610	+	17.4763i	1.23325	+	0.655875i
$711$	−0.373838	−	0.647507i	−0.0140200	−	0.0242834i
$712$	0.242461	+	0.163639i	0.00908663	+	0.00613262i
$713$	−24.6365	−	20.6725i	−0.922646	−	0.774192i
$714$	2.35702	−	1.47253i	0.0882092	−	0.0551081i
$715$	12.0498	+	6.95698i	0.450639	+	0.260176i
$716$	9.25182	+	20.7901i	0.345757	+	0.776962i
$717$	1.25269	−	0.220883i	0.0467825	−	0.00824902i
$718$	−0.0642758	+	0.457045i	−0.00239875	+	0.0170568i
$719$	−9.22895	−	3.35906i	−0.344182	−	0.125272i	0.164145	−	0.986436i	$-0.447514\pi$
$719$	−9.22895	−	3.35906i	−0.344182	−	0.125272i	−0.508327	+	0.861164i	$0.669736\pi$
$720$	8.10711	+	7.30501i	0.302134	+	0.272242i
$721$	−14.0073			−0.521660
$722$	1.82179	+	26.8082i	0.0678000	+	0.997699i
$723$		−	1.30392i		−	0.0484935i
$724$	24.6389	+	25.5236i	0.915698	+	0.948578i
$725$	−1.43343	+	3.93833i	−0.0532364	+	0.146266i
$726$	−8.65370	−	1.21700i	−0.321169	−	0.0451671i
$727$	3.54316	+	20.0943i	0.131409	+	0.745255i	0.977294	+	0.211890i	$0.0679617\pi$
$727$	3.54316	+	20.0943i	0.131409	+	0.745255i	−0.845885	+	0.533365i	$0.820927\pi$
$728$	2.39536	+	4.91462i	0.0887780	+	0.182148i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	27.2891	−	17.0487i	1.01002	−	0.631000i
$731$	2.00208	−	2.38599i	0.0740497	−	0.0882490i
$732$	−2.65151	−	1.92717i	−0.0980027	−	0.0712304i
$733$	33.6518	−	19.4289i	1.24296	−	0.717622i	0.273262	−	0.961940i	$-0.411897\pi$
$733$	33.6518	−	19.4289i	1.24296	−	0.717622i	0.969695	+	0.244318i	$0.0785639\pi$
$734$	13.2926	−	24.9943i	0.490641	−	0.922558i
$735$	16.1703	−	5.88552i	0.596451	−	0.217091i
$736$	−12.6581	−	34.8270i	−0.466582	−	1.28374i
$737$	−6.08246	+	34.4954i	−0.224050	+	1.27065i
$738$	10.3978	+	3.37951i	0.382750	+	0.124402i
$739$	26.5600	+	31.6530i	0.977026	+	1.16437i	0.986391	+	0.164418i	$0.0525747\pi$
$739$	26.5600	+	31.6530i	0.977026	+	1.16437i	−0.00936460	+	0.999956i	$0.502981\pi$
$740$	7.33899	−	0.511851i	0.269787	−	0.0188160i
$741$	−9.10450	+	4.43003i	−0.334462	+	0.162741i
$742$	0.104924	+	3.01248i	0.00385188	+	0.110592i
$743$	31.2437	−	26.2165i	1.14622	−	0.961791i	0.146594	−	0.989197i	$-0.453169\pi$
$743$	31.2437	−	26.2165i	1.14622	−	0.961791i	0.999624	+	0.0274053i	$0.00872448\pi$
$744$	3.36308	−	13.4729i	0.123297	−	0.493941i
$745$	−9.44794	+	53.5819i	−0.346146	+	1.96309i
$746$	19.3291	−	4.10670i	0.707690	−	0.150357i
$747$	−0.774699	−	2.12847i	−0.0283448	−	0.0778766i
$748$	−9.31974	−	4.54764i	−0.340763	−	0.166278i
$749$	7.00584	−	4.04482i	0.255988	−	0.147795i
$750$	−7.77352	−	6.07448i	−0.283849	−	0.221809i
$751$	−13.0607	−	10.9592i	−0.476591	−	0.399907i	0.372601	−	0.927992i	$-0.378466\pi$
$751$	−13.0607	−	10.9592i	−0.476591	−	0.399907i	−0.849192	+	0.528084i	$0.822911\pi$
$752$	14.9295	+	19.1232i	0.544423	+	0.697352i
$753$	7.95299	−	13.7750i	0.289823	−	0.501989i
$754$	5.22536	−	2.11063i	0.190297	−	0.0768647i
$755$	23.5569	−	4.15371i	0.857322	−	0.151169i
$756$	1.65517	+	0.174269i	0.0601978	+	0.00633812i
$757$	−8.80227	+	24.1840i	−0.319924	+	0.878984i	0.670622	+	0.741800i	$0.266027\pi$
$757$	−8.80227	+	24.1840i	−0.319924	+	0.878984i	−0.990546	+	0.137184i	$0.956195\pi$
$758$	−20.2895	−	22.5378i	−0.736946	−	0.818611i
$759$	−14.3826			−0.522056
$760$	−31.9766	−	10.4325i	−1.15991	−	0.378428i
$761$	−29.2488			−1.06027			−0.530134	−	0.847914i	$-0.677858\pi$
$761$	−29.2488			−1.06027			−0.530134	+	0.847914i	$0.677858\pi$
$762$	−19.8474	−	22.0468i	−0.718995	−	0.798671i
$763$	1.67619	−	4.60530i	0.0606822	−	0.166723i
$764$	2.11098	−	20.0496i	0.0763727	−	0.725368i
$765$	−6.34488	+	1.11877i	−0.229400	+	0.0404493i
$766$	11.0997	−	4.48338i	0.401047	−	0.161991i
$767$	−6.70331	+	11.6105i	−0.242042	+	0.419230i
$768$	11.1229	−	11.5013i	0.401363	−	0.415019i
$769$	36.0775	+	30.2726i	1.30099	+	1.09166i	0.989974	+	0.141252i	$0.0451128\pi$
$769$	36.0775	+	30.2726i	1.30099	+	1.09166i	0.311013	+	0.950406i	$0.399332\pi$
$770$	5.55458	+	4.34053i	0.200173	+	0.156422i
$771$	−18.8099	+	10.8599i	−0.677422	+	0.391110i
$772$	19.4301	−	39.8193i	0.699306	−	1.43313i
$773$	−4.00409	−	11.0011i	−0.144017	−	0.395684i	0.846621	−	0.532196i	$-0.178633\pi$
$773$	−4.00409	−	11.0011i	−0.144017	−	0.395684i	−0.990638	+	0.136512i	$0.956411\pi$
$774$	1.82450	−	0.387637i	0.0655805	−	0.0139333i
$775$	2.08277	−	11.8120i	0.0748152	−	0.424298i
$776$	−19.9174	−	4.97174i	−0.714993	−	0.178475i
$777$	0.859499	−	0.721205i	0.0308343	−	0.0258731i
$778$	1.63138	+	46.8387i	0.0584878	+	1.67925i
$779$	−33.5173	+	3.49112i	−1.20088	+	0.125082i
$780$	−0.881819	−	12.6436i	−0.0315742	−	0.452715i
$781$	−13.6144	−	16.2250i	−0.487163	−	0.580578i
$782$	20.8060	+	6.76238i	0.744022	+	0.241822i
$783$	0.297899	−	1.68947i	0.0106460	−	0.0603766i
$784$	−7.78778	−	23.9980i	−0.278135	−	0.857073i
$785$	14.6264	−	5.32358i	0.522039	−	0.190007i
$786$	−11.3136	+	21.2731i	−0.403542	+	0.758785i
$787$	−20.1982	+	11.6614i	−0.719987	+	0.415684i	−0.814748	−	0.579816i	$-0.803125\pi$
$787$	−20.1982	+	11.6614i	−0.719987	+	0.415684i	0.0947611	+	0.995500i	$0.469791\pi$
$788$	−21.3108	+	29.3206i	−0.759166	+	1.04450i
$789$	14.7615	−	17.5921i	0.525524	−	0.626295i
$790$	−2.44652	+	1.52845i	−0.0870432	+	0.0543796i
$791$	−1.54007	+	2.66747i	−0.0547585	+	0.0948445i
$792$	−2.72081	−	5.58236i	−0.0966799	−	0.198360i
$793$	0.661082	+	3.74918i	0.0234757	+	0.133137i
$794$	−52.4353	−	7.37416i	−1.86086	−	0.261699i
$795$	2.38998	−	6.56640i	0.0847637	−	0.232886i
$796$	10.3976	−	10.0372i	0.368533	−	0.355759i
$797$		−	34.8857i		−	1.23572i	−0.786290	−	0.617858i	$-0.788001\pi$
$797$		−	34.8857i		−	1.23572i	0.786290	−	0.617858i	$-0.211999\pi$
$798$	−4.88032	+	1.58018i	−0.172761	+	0.0559377i
$799$	−14.3233			−0.506721
$800$	8.88803	−	10.5826i	0.314239	−	0.374150i
$801$	−0.0971828	−	0.0353716i	−0.00343378	−	0.00124980i
$802$	−4.61150	+	32.7909i	−0.162838	+	1.15789i
$803$	−18.0327	+	3.17965i	−0.636361	+	0.112208i
$804$	29.1507	−	12.9724i	1.02807	−	0.457501i
$805$	−12.8794	−	7.43590i	−0.453938	−	0.262081i
$806$	−13.6780	+	8.54526i	−0.481788	+	0.300994i
$807$	−12.3327	−	10.3484i	−0.434133	−	0.364281i
$808$	10.6964	−	15.8487i	0.376297	−	0.557556i
$809$	13.8411	+	23.9735i	0.486628	+	0.842864i	0.999882	−	0.0153728i	$-0.00489352\pi$
$809$	13.8411	+	23.9735i	0.486628	+	0.842864i	−0.513254	+	0.858237i	$0.671560\pi$
$810$	−3.40646	−	1.81165i	−0.119691	−	0.0636547i
$811$	5.55137	+	15.2523i	0.194935	+	0.535580i	0.998195	−	0.0600482i	$-0.0191255\pi$
$811$	5.55137	+	15.2523i	0.194935	+	0.535580i	−0.803260	+	0.595628i	$0.796903\pi$
$812$	2.77050	−	0.690227i	0.0972254	−	0.0242222i
$813$	18.5715	+	3.27466i	0.651332	+	0.114847i
$814$	−3.98152	−	1.29407i	−0.139552	−	0.0453573i
$815$	−42.2093	+	35.4178i	−1.47853	+	1.24063i
$816$	1.31125	+	9.35475i	0.0459031	+	0.327482i
$817$	−4.65421	+	3.37484i	−0.162830	+	0.118071i
$818$	17.2709	−	0.601542i	0.603864	−	0.0210324i
$819$	−1.24249	−	1.48075i	−0.0434163	−	0.0517415i
$820$	11.6346	−	40.5470i	0.406299	−	1.41596i
$821$	15.8357	+	2.79225i	0.552668	+	0.0974503i	0.443006	−	0.896519i	$-0.353912\pi$
$821$	15.8357	+	2.79225i	0.552668	+	0.0974503i	0.109662	+	0.993969i	$0.465023\pi$
$822$	−28.1729	+	5.98566i	−0.982644	+	0.208774i
$823$	4.25618	−	1.54912i	0.148361	−	0.0539991i	−0.266772	−	0.963760i	$-0.585957\pi$
$823$	4.25618	−	1.54912i	0.148361	−	0.0539991i	0.415133	+	0.909761i	$0.363735\pi$
$824$	19.3764	−	43.4882i	0.675010	−	1.51498i
$825$	−2.68196	−	4.64529i	−0.0933739	−	0.161728i
$826$	−4.18226	+	5.35204i	−0.145519	+	0.186221i
$827$	−0.361415	+	0.430717i	−0.0125676	+	0.0149775i	−0.772292	−	0.635268i	$-0.780890\pi$
$827$	−0.361415	+	0.430717i	−0.0125676	+	0.0149775i	0.759724	+	0.650246i	$0.225334\pi$
$828$	7.32416	+	10.8628i	0.254532	+	0.377508i
$829$	−32.9364	−	19.0158i	−1.14393	−	0.660447i	−0.196527	−	0.980498i	$-0.562966\pi$
$829$	−32.9364	−	19.0158i	−1.14393	−	0.660447i	−0.947400	+	0.320052i	$0.896300\pi$
$830$	−8.10313	+	3.27302i	−0.281264	+	0.113608i
$831$	−5.16419	−	29.2876i	−0.179144	−	1.01597i
$832$	−18.5718	+	0.638395i	−0.643863	+	0.0221324i
$833$	13.9972	+	5.09456i	0.484974	+	0.176516i
$834$	14.4362	−	12.9961i	0.499886	−	0.450017i
$835$			35.5325i			1.22965i
$836$	14.6490	+	12.3199i	0.506646	+	0.426092i
$837$			4.90956i			0.169699i
$838$	−12.4323	−	13.8100i	−0.429468	−	0.477059i
$839$	8.58932	+	3.12626i	0.296536	+	0.107930i	0.486004	−	0.873957i	$-0.338454\pi$
$839$	8.58932	+	3.12626i	0.296536	+	0.107930i	−0.189468	+	0.981887i	$0.560676\pi$
$840$	0.449678	−	6.40557i	0.0155154	−	0.221013i
$841$	4.52474	+	25.6611i	0.156026	+	0.884865i
$842$	11.8755	+	29.4006i	0.409257	+	1.01321i
$843$	−6.02174	−	3.47665i	−0.207400	−	0.119742i
$844$	−16.2333	+	10.9452i	−0.558774	+	0.376750i
$845$	13.3354	−	15.8925i	0.458751	−	0.546718i
$846$	−6.75868	−	5.28145i	−0.232368	−	0.181580i
$847$	2.57108	+	4.45324i	0.0883433	+	0.153015i
$848$	−9.49793	−	3.84143i	−0.326160	−	0.131915i
$849$	−2.86731	+	1.04362i	−0.0984058	+	0.0358168i
$850$	1.69564	+	7.98092i	0.0581599	+	0.273743i
$851$	8.69802	+	1.53370i	0.298164	+	0.0525744i
$852$	−5.32134	+	18.5450i	−0.182306	+	0.635340i
$853$	−2.90481	−	3.46182i	−0.0994590	−	0.118531i	0.714019	−	0.700126i	$-0.246873\pi$
$853$	−2.90481	−	3.46182i	−0.0994590	−	0.118531i	−0.813478	+	0.581596i	$0.802429\pi$
$854$	0.0671384	+	1.92762i	0.00229743	+	0.0659617i
$855$	11.8622	+	0.840630i	0.405677	+	0.0287489i
$856$	2.86665	+	27.3461i	0.0979800	+	0.934671i
$857$	12.5422	−	10.5242i	0.428434	−	0.359499i	−0.402927	−	0.915232i	$-0.632007\pi$
$857$	12.5422	−	10.5242i	0.428434	−	0.359499i	0.831360	+	0.555734i	$0.187563\pi$
$858$	−2.22944	+	6.85938i	−0.0761117	+	0.234175i
$859$	40.0543	+	7.06265i	1.36663	+	0.240974i	0.808363	−	0.588684i	$-0.200354\pi$
$859$	40.0543	+	7.06265i	1.36663	+	0.240974i	0.558271	+	0.829659i	$0.311465\pi$
$860$	−1.73972	−	6.98306i	−0.0593241	−	0.238120i
$861$	−2.20035	−	6.04542i	−0.0749878	−	0.206027i
$862$	9.90023	−	18.6155i	0.337203	−	0.634048i
$863$	21.1416	+	36.6183i	0.719668	+	1.24650i	0.961131	+	0.276092i	$0.0890393\pi$
$863$	21.1416	+	36.6183i	0.719668	+	1.24650i	−0.241463	+	0.970410i	$0.577627\pi$
$864$	−2.83065	+	4.89769i	−0.0963008	+	0.166623i
$865$	47.8473	+	40.1487i	1.62686	+	1.36510i
$866$	20.6028	+	32.9780i	0.700111	+	1.12064i
$867$	9.89268	+	5.71154i	0.335973	+	0.193974i
$868$	−7.46523	+	3.32211i	−0.253387	+	0.112760i
$869$	1.61666	−	0.285062i	0.0548416	−	0.00967005i
$870$	−6.55444	−	0.921774i	−0.222216	−	0.0312511i
$871$	−34.8226	−	12.6744i	−1.17992	−	0.429456i
$872$	11.9793	+	11.5746i	0.405670	+	0.391965i
$873$	7.25793			0.245644
$874$	−34.2229	−	21.4337i	−1.15761	−	0.725006i
$875$			5.80506i			0.196247i
$876$	11.5844	+	12.0004i	0.391401	+	0.405455i
$877$	3.05185	−	8.38488i	0.103053	−	0.283137i	−0.877441	−	0.479685i	$-0.840751\pi$
$877$	3.05185	−	8.38488i	0.103053	−	0.283137i	0.980494	+	0.196548i	$0.0629731\pi$
$878$	−1.15186	+	8.19049i	−0.0388733	+	0.276416i
$879$	3.30497	+	18.7434i	0.111474	+	0.632200i
$880$	−21.1596	+	11.2409i	−0.713292	+	0.378931i
$881$	−13.0100	+	22.5340i	−0.438318	+	0.759189i	−0.997560	−	0.0698154i	$-0.977759\pi$
$881$	−13.0100	+	22.5340i	−0.438318	+	0.759189i	0.559242	+	0.829005i	$0.311092\pi$
$882$	4.72628	+	7.56516i	0.159142	+	0.254732i
$883$	1.37044	−	1.63323i	0.0461191	−	0.0549626i	−0.742492	−	0.669855i	$-0.766356\pi$
$883$	1.37044	−	1.63323i	0.0461191	−	0.0549626i	0.788611	+	0.614893i	$0.210801\pi$
$884$	6.45024	−	8.87460i	0.216945	−	0.298485i
$885$	13.6365	−	7.87304i	0.458386	−	0.264649i
$886$	23.1626	+	12.3185i	0.778163	+	0.413848i
$887$	9.04654	−	3.29267i	0.303753	−	0.110557i	−0.185647	−	0.982617i	$-0.559438\pi$
$887$	9.04654	−	3.29267i	0.303753	−	0.110557i	0.489400	+	0.872059i	$0.337216\pi$
$888$	1.05016	+	3.66612i	0.0352410	+	0.123027i
$889$	−3.03108	+	17.1901i	−0.101659	+	0.576538i
$890$	−0.123338	+	0.379478i	−0.00413430	+	0.0127201i
$891$	1.41131	+	1.68193i	0.0472807	+	0.0563469i
$892$	22.5410	−	1.57210i	0.754729	−	0.0526378i
$893$	25.6463	+	6.41982i	0.858221	+	0.214831i
$894$	−28.1867	+	0.981734i	−0.942704	+	0.0328341i
$895$	−23.7788	+	19.9528i	−0.794838	+	0.666948i
$896$	−9.36259	−	0.990075i	−0.312782	−	0.0330761i
$897$	2.64226	−	14.9850i	0.0882223	−	0.500334i
$898$	−0.671606	−	3.16107i	−0.0224118	−	0.105486i
$899$	2.88066	+	7.91456i	0.0960755	+	0.263965i
$900$	−2.14270	+	4.39116i	−0.0714234	+	0.146372i
$901$	5.23835	−	3.02437i	0.174515	−	0.100756i
$902$	−14.7808	+	18.9150i	−0.492146	+	0.629800i
$903$	−0.840769	−	0.705489i	−0.0279791	−	0.0234772i
$904$	−6.15127	−	8.47135i	−0.204588	−	0.281753i
$905$	−24.1962	+	41.9090i	−0.804308	+	1.39310i
$906$	4.64391	+	11.4971i	0.154284	+	0.381966i
$907$	4.18018	−	0.737079i	0.138801	−	0.0244743i	−0.103816	−	0.994597i	$-0.533105\pi$
$907$	4.18018	−	0.737079i	0.138801	−	0.0244743i	0.242617	+	0.970122i	$0.421994\pi$
$908$	12.4523	+	1.31108i	0.413244	+	0.0435097i
$909$	−2.31210	+	6.35244i	−0.0766875	+	0.210697i
$910$	−5.54276	+	4.98981i	−0.183741	+	0.165411i
$911$	2.85176			0.0944832			0.0472416	−	0.998883i	$-0.484957\pi$
$911$	2.85176			0.0944832			0.0472416	+	0.998883i	$0.484957\pi$
$912$	1.84504	−	17.3377i	0.0610953	−	0.574109i
$913$	4.97320			0.164589
$914$	6.77610	−	6.10011i	0.224134	−	0.201774i
$915$	1.52929	−	4.20169i	0.0505568	−	0.138904i
$916$	−31.6520	−	3.33258i	−1.04581	−	0.110112i
$917$	13.9623	−	2.46194i	0.461077	−	0.0813004i
$918$	−1.25081	−	3.09666i	−0.0412827	−	0.102205i
$919$	−12.5839	+	21.7960i	−0.415106	+	0.718984i	−0.995440	−	0.0953946i	$-0.969589\pi$
$919$	−12.5839	+	21.7960i	−0.415106	+	0.718984i	0.580334	+	0.814379i	$0.302922\pi$
$920$	40.9022	−	29.7001i	1.34851	−	0.979185i
$921$	5.28755	+	4.43678i	0.174231	+	0.146197i
$922$	4.09063	−	5.23478i	0.134718	−	0.172398i
$923$	19.4057	−	11.2039i	0.638746	−	0.368780i
$924$	−1.60249	+	3.28407i	−0.0527179	+	0.108038i
$925$	1.12659	+	3.09527i	0.0370420	+	0.101772i
$926$	0.106865	+	0.502983i	0.00351179	+	0.0165291i
$927$	−2.92294	+	16.5768i	−0.0960019	+	0.544454i
$928$	−1.68952	+	9.55630i	−0.0554611	+	0.313701i
$929$	−22.3816	+	18.7804i	−0.734318	+	0.616166i	−0.931305	−	0.364240i	$-0.881329\pi$
$929$	−22.3816	+	18.7804i	−0.734318	+	0.616166i	0.196987	+	0.980406i	$0.436884\pi$
$930$	18.9308	−	0.659354i	0.620765	−	0.0216211i
$931$	−22.7790	−	15.3957i	−0.746552	−	0.504572i
$932$	−41.7403	+	2.91114i	−1.36725	+	0.0953575i
$933$	−11.0349	−	13.1508i	−0.361265	−	0.430539i
$934$	−8.16055	+	25.1078i	−0.267021	+	0.821553i
$935$	2.45639	−	13.9309i	0.0803325	−	0.455588i
$936$	6.31600	−	1.80922i	0.206445	−	0.0591361i
$937$	−14.9877	+	5.45508i	−0.489627	+	0.178210i	−0.575023	−	0.818137i	$-0.695007\pi$
$937$	−14.9877	+	5.45508i	−0.489627	+	0.178210i	0.0853955	+	0.996347i	$0.472785\pi$
$938$	−16.5764	−	8.81574i	−0.541237	−	0.287844i
$939$	−23.1745	+	13.3798i	−0.756270	+	0.436633i
$940$	−19.4571	+	26.7701i	−0.634620	+	0.873145i
$941$	−2.14637	+	2.55795i	−0.0699698	+	0.0833867i	−0.799894	−	0.600141i	$-0.795111\pi$
$941$	−2.14637	+	2.55795i	−0.0699698	+	0.0833867i	0.729924	+	0.683528i	$0.239555\pi$
$942$	4.27502	+	6.84285i	0.139288	+	0.222952i
$943$	25.3214	−	43.8580i	0.824579	−	1.42821i
$944$	−10.8310	−	20.3881i	−0.352520	−	0.663576i
$945$	0.394231	+	2.23579i	0.0128243	+	0.0727304i
$946$	−0.570326	+	4.05540i	−0.0185429	+	0.131853i
$947$	18.3886	−	50.5221i	0.597548	−	1.64175i	−0.158596	−	0.987344i	$-0.550697\pi$
$947$	18.3886	−	50.5221i	0.597548	−	1.64175i	0.756144	−	0.654405i	$-0.227081\pi$
$948$	−1.03856	−	1.07586i	−0.0337310	−	0.0349422i
$949$		−	19.3721i		−	0.628844i
$950$	0.541022	−	15.0501i	0.0175531	−	0.488290i
$951$	−30.9647			−1.00410
$952$	3.86226	−	3.99731i	0.125177	−	0.129553i
$953$	−45.1319	−	16.4267i	−1.46196	−	0.532112i	−0.516059	−	0.856553i	$-0.672601\pi$
$953$	−45.1319	−	16.4267i	−1.46196	−	0.532112i	−0.945906	+	0.324441i	$0.894824\pi$
$954$	3.58698	+	0.504450i	0.116133	+	0.0163322i
$955$	27.0829	−	4.77545i	0.876383	−	0.154530i
$956$	2.32427	−	1.03433i	0.0751724	−	0.0334525i
$957$	3.26200	+	1.88332i	0.105445	+	0.0608790i
$958$	−1.50586	−	2.41037i	−0.0486521	−	0.0778754i
$959$	12.9827	+	10.8938i	0.419232	+	0.351778i
$960$	19.2652	+	10.2570i	0.621782	+	0.331043i
$961$	3.44812	+	5.97232i	0.111230	+	0.192655i
$962$	2.07972	−	3.91053i	0.0670530	−	0.126081i
$963$	−3.32488	−	9.13502i	−0.107143	−	0.294372i
$964$	−0.630435	−	2.53050i	−0.0203050	−	0.0815019i
$965$	59.5207	+	10.4951i	1.91604	+	0.337850i
$966$	2.38291	−	7.33158i	0.0766689	−	0.235890i
$967$	30.1963	−	25.3377i	0.971046	−	0.814804i	−0.0116683	−	0.999932i	$-0.503714\pi$
$967$	30.1963	−	25.3377i	0.971046	−	0.814804i	0.982715	+	0.185127i	$0.0592698\pi$
$968$	−17.3825	+	1.82218i	−0.558694	+	0.0585669i
$969$	7.39802	+	7.15757i	0.237659	+	0.229934i
$970$	−0.974741	−	27.9859i	−0.0312970	−	0.898573i
$971$	−38.4624	−	45.8377i	−1.23432	−	1.47100i	−0.831314	−	0.555802i	$-0.812411\pi$
$971$	−38.4624	−	45.8377i	−1.23432	−	1.47100i	−0.403002	−	0.915199i	$-0.632033\pi$
$972$	0.551624	−	1.92242i	0.0176934	−	0.0616617i
$973$	−11.2561	−	1.98475i	−0.360854	−	0.0636282i
$974$	5.90075	+	27.7733i	0.189072	+	0.889913i
$975$	5.33255	−	1.94089i	0.170778	−	0.0621582i
$976$	−6.07751	−	2.45805i	−0.194536	−	0.0786801i
$977$	11.9475	+	20.6937i	0.382235	+	0.662051i	0.991381	−	0.131007i	$-0.0418210\pi$
$977$	11.9475	+	20.6937i	0.382235	+	0.662051i	−0.609146	+	0.793058i	$0.708488\pi$
$978$	−22.5059	−	17.5868i	−0.719659	−	0.562365i
$979$	0.145957	−	0.173945i	0.00466481	−	0.00555931i
$980$	28.5358	−	19.2401i	0.911543	−	0.614603i
$981$	−5.10032	−	2.94467i	−0.162841	−	0.0940160i
$982$	16.2984	+	40.3504i	0.520102	+	1.28763i
$983$	−4.88479	−	27.7030i	−0.155801	−	0.883589i	−0.958050	−	0.286600i	$-0.907475\pi$
$983$	−4.88479	−	27.7030i	−0.155801	−	0.883589i	0.802250	−	0.596989i	$-0.203636\pi$
$984$	21.8128	+	1.53128i	0.695368	+	0.0488156i
$985$	−46.4626	−	16.9110i	−1.48042	−	0.538829i
$986$	−3.83334	−	4.25814i	−0.122078	−	0.135607i
$987$			5.04721i			0.160654i
$988$	−15.5270	+	12.9992i	−0.493981	+	0.413560i
$989$		−	8.63974i		−	0.274728i
$990$	6.29584	−	5.66776i	0.200095	−	0.180133i
$991$	−35.5642	−	12.9443i	−1.12973	−	0.411189i	−0.291538	−	0.956559i	$-0.594167\pi$
$991$	−35.5642	−	12.9443i	−1.12973	−	0.411189i	−0.838196	+	0.545370i	$0.816389\pi$
$992$	0.0126307	−	27.7727i	0.000401025	−	0.881783i
$993$	4.33277	+	24.5724i	0.137496	+	0.779781i
$994$	10.5264	−	4.25183i	0.333877	−	0.134860i
$995$	17.0725	+	9.85684i	0.541236	+	0.312483i
$996$	−2.53254	−	3.75611i	−0.0802465	−	0.119017i
$997$	−14.0062	+	16.6919i	−0.443580	+	0.528639i	−0.940789	−	0.338992i	$-0.889914\pi$
$997$	−14.0062	+	16.6919i	−0.443580	+	0.528639i	0.497209	+	0.867631i	$0.334358\pi$
$998$	−14.2919	+	18.2893i	−0.452401	+	0.578938i
$999$	−0.674148	−	1.16766i	−0.0213291	−	0.0369431i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bk.a.253.10	yes	240
8.5	even	2	inner	456.2.bk.a.253.8	✓	240
19.16	even	9	inner	456.2.bk.a.301.8	yes	240
152.149	even	18	inner	456.2.bk.a.301.10	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bk.a.253.8	✓	240	8.5	even	2	inner
456.2.bk.a.253.10	yes	240	1.1	even	1	trivial
456.2.bk.a.301.8	yes	240	19.16	even	9	inner
456.2.bk.a.301.10	yes	240	152.149	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bk (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05105 + 0.946198i) q^{2} +(0.342020 - 0.939693i) q^{3} +(0.209419 - 1.98901i) q^{4} +(2.68674 - 0.473745i) q^{5} +(0.529654 + 1.31128i) q^{6} +(0.416079 - 0.720670i) q^{7} +(1.66188 + 2.28870i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(-2.37565 + 3.04012i) q^{10} +(1.90145 - 1.09780i) q^{11} +(-1.79743 - 0.877069i) q^{12} +(0.794462 + 2.18277i) q^{13} +(0.244576 + 1.15115i) q^{14} +(0.473745 - 2.68674i) q^{15} +(-3.91229 - 0.833070i) q^{16} +(1.80905 - 1.51798i) q^{17} +(1.41336 - 0.0492268i) q^{18} +(-3.91954 + 1.90715i) q^{19} +(-0.379628 - 5.44316i) q^{20} +(-0.534901 - 0.637470i) q^{21} +(-0.959784 + 2.95300i) q^{22} +(1.13751 - 6.45111i) q^{23} +(2.71907 - 0.778878i) q^{24} +(2.29569 - 0.835564i) q^{25} +(-2.90035 - 1.54248i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(-1.34628 - 0.978505i) q^{28} +(-1.10272 + 1.31417i) q^{29} +(2.04426 + 3.27216i) q^{30} +(2.45478 - 4.25180i) q^{31} +(4.90027 - 2.82620i) q^{32} +(-0.381263 - 2.16225i) q^{33} +(-0.465102 + 3.30719i) q^{34} +(0.776483 - 2.13337i) q^{35} +(-1.43893 + 1.38905i) q^{36} +1.34830i q^{37} +(2.31509 - 5.71317i) q^{38} +2.32285 q^{39} +(5.54931 + 5.36184i) q^{40} +(7.26475 + 2.64415i) q^{41} +(1.16538 + 0.163892i) q^{42} +(1.29888 - 0.229027i) q^{43} +(-1.78534 - 4.01190i) q^{44} +(-2.36268 - 1.36410i) q^{45} +(4.90845 + 7.85676i) q^{46} +(-4.64622 - 3.89864i) q^{47} +(-2.12091 + 3.39142i) q^{48} +(3.15376 + 5.46247i) q^{49} +(-1.62228 + 3.05040i) q^{50} +(-0.807698 - 2.21913i) q^{51} +(4.50791 - 1.12308i) q^{52} +(2.52243 + 0.444772i) q^{53} +(0.437138 - 1.34496i) q^{54} +(4.58863 - 3.85032i) q^{55} +(2.34087 - 0.245390i) q^{56} +(0.451575 + 4.33544i) q^{57} +(-0.0844500 - 2.42466i) q^{58} +(3.70993 + 4.42132i) q^{59} +(-5.24474 - 1.50494i) q^{60} +(1.61404 + 0.284599i) q^{61} +(1.44295 + 6.79157i) q^{62} +(-0.781973 + 0.284615i) q^{63} +(-2.47629 + 7.60710i) q^{64} +(3.16859 + 5.48816i) q^{65} +(2.44665 + 1.91189i) q^{66} +(-10.2547 + 12.2210i) q^{67} +(-2.64041 - 3.91611i) q^{68} +(-5.67301 - 3.27532i) q^{69} +(1.20247 + 2.97699i) q^{70} +(-1.67513 - 9.50011i) q^{71} +(0.198071 - 2.82148i) q^{72} +(-7.83683 - 2.85237i) q^{73} +(-1.27576 - 1.41713i) q^{74} -2.44302i q^{75} +(2.97251 + 8.19538i) q^{76} -1.82709i q^{77} +(-2.44144 + 2.19788i) q^{78} +(0.702586 + 0.255720i) q^{79} +(-10.9060 - 0.384818i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-10.1375 + 4.09475i) q^{82} +(1.96161 + 1.13253i) q^{83} +(-1.37995 + 0.930423i) q^{84} +(4.14133 - 4.93544i) q^{85} +(-1.14848 + 1.46972i) q^{86} +(0.857765 + 1.48569i) q^{87} +(5.67254 + 2.52743i) q^{88} +(0.0971828 - 0.0353716i) q^{89} +(3.77401 - 0.801831i) q^{90} +(1.90361 + 0.335658i) q^{91} +(-12.5931 - 3.61349i) q^{92} +(-3.15580 - 3.76094i) q^{93} +(8.57229 - 0.298570i) q^{94} +(-9.62729 + 6.98089i) q^{95} +(-0.979769 - 5.57136i) q^{96} +(-5.55990 + 4.66531i) q^{97} +(-8.48334 - 2.75726i) q^{98} +(-2.16225 - 0.381263i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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