LMFDB - Embedded newform 1218.2.i.d.697.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1218,2,Mod(697,1218)] 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("1218.697"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1218, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1218 = 2 \cdot 3 \cdot 7 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1218.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,3,-3,-3,1] 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:	$9.72577896619$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1783323.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 $ x^6 - x^5 + 5x^4 - 2x^3 + 19x^2 - 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			697.1
Root			$-0.956115 - 1.65604i$ of defining polynomial
Character	$\chi$	$=$	1218.697
Dual form			1218.2.i.d.1045.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.956115 - 1.65604i) q^{5} -1.00000 q^{6} +(-2.58392 + 0.568650i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.956115 - 1.65604i) q^{10} +(1.17169 - 2.02943i) q^{11} +(-0.500000 - 0.866025i) q^{12} +1.91223 q^{13} +(-1.78442 - 1.95341i) q^{14} +1.91223 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.69665 - 4.67074i) q^{17} +(0.500000 - 0.866025i) q^{18} +(3.11274 + 5.39142i) q^{19} +1.91223 q^{20} +(0.799494 - 2.52206i) q^{21} +2.34338 q^{22} +(1.11274 + 1.92731i) q^{23} +(0.500000 - 0.866025i) q^{24} +(0.671690 - 1.16340i) q^{25} +(0.956115 + 1.65604i) q^{26} +1.00000 q^{27} +(0.799494 - 2.52206i) q^{28} +1.00000 q^{29} +(0.956115 + 1.65604i) q^{30} +(-1.44105 + 2.49596i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.17169 + 2.02943i) q^{33} +5.39331 q^{34} +(3.41223 + 3.73538i) q^{35} +1.00000 q^{36} +(0.612735 + 1.06129i) q^{37} +(-3.11274 + 5.39142i) q^{38} +(-0.956115 + 1.65604i) q^{39} +(0.956115 + 1.65604i) q^{40} +12.3933 q^{41} +(2.58392 - 0.568650i) q^{42} +0.313241 q^{43} +(1.17169 + 2.02943i) q^{44} +(-0.956115 + 1.65604i) q^{45} +(-1.11274 + 1.92731i) q^{46} +(-0.0288161 - 0.0499109i) q^{47} +1.00000 q^{48} +(6.35327 - 2.93869i) q^{49} +1.34338 q^{50} +(2.69665 + 4.67074i) q^{51} +(-0.956115 + 1.65604i) q^{52} +(-2.56885 + 4.44938i) q^{53} +(0.500000 + 0.866025i) q^{54} -4.48108 q^{55} +(2.58392 - 0.568650i) q^{56} -6.22547 q^{57} +(0.500000 + 0.866025i) q^{58} +(0.343380 - 0.594751i) q^{59} +(-0.956115 + 1.65604i) q^{60} +(1.14287 + 1.97952i) q^{61} -2.88209 q^{62} +(1.78442 + 1.95341i) q^{63} +1.00000 q^{64} +(-1.82831 - 3.16673i) q^{65} +(-1.17169 + 2.02943i) q^{66} +(3.18158 - 5.51067i) q^{67} +(2.69665 + 4.67074i) q^{68} -2.22547 q^{69} +(-1.52882 + 4.82277i) q^{70} -1.37087 q^{71} +(0.500000 + 0.866025i) q^{72} +(5.45611 - 9.45027i) q^{73} +(-0.612735 + 1.06129i) q^{74} +(0.671690 + 1.16340i) q^{75} -6.22547 q^{76} +(-1.87352 + 5.91015i) q^{77} -1.91223 q^{78} +(-5.50989 - 9.54342i) q^{79} +(-0.956115 + 1.65604i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.19665 + 10.7329i) q^{82} +17.8168 q^{83} +(1.78442 + 1.95341i) q^{84} -10.3132 q^{85} +(0.156620 + 0.271275i) q^{86} +(-0.500000 + 0.866025i) q^{87} +(-1.17169 + 2.02943i) q^{88} +(1.14155 + 1.97722i) q^{89} -1.91223 q^{90} +(-4.94105 + 1.08739i) q^{91} -2.22547 q^{92} +(-1.44105 - 2.49596i) q^{93} +(0.0288161 - 0.0499109i) q^{94} +(5.95226 - 10.3096i) q^{95} +(0.500000 + 0.866025i) q^{96} -9.36581 q^{97} +(5.72162 + 4.03275i) q^{98} -2.34338 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + q^{5} - 6 q^{6} - 4 q^{7} - 6 q^{8} - 3 q^{9} - q^{10} + 9 q^{11} - 3 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 8 q^{19} - 2 q^{20}+ \cdots - 18 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + q^5 - 6 * q^6 - 4 * q^7 - 6 * q^8 - 3 * q^9 - q^10 + 9 * q^11 - 3 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 8 * q^19 - 2 * q^20 + 2 * q^21 + 18 * q^22 - 4 * q^23 + 3 * q^24 + 6 * q^25 - q^26 + 6 * q^27 + 2 * q^28 + 6 * q^29 - q^30 + 4 * q^31 + 3 * q^32 + 9 * q^33 - 12 * q^34 + 7 * q^35 + 6 * q^36 - 7 * q^37 - 8 * q^38 + q^39 - q^40 + 30 * q^41 + 4 * q^42 - 6 * q^43 + 9 * q^44 + q^45 + 4 * q^46 - q^47 + 6 * q^48 + 12 * q^49 + 12 * q^50 - 6 * q^51 + q^52 + 2 * q^53 + 3 * q^54 + 4 * q^55 + 4 * q^56 - 16 * q^57 + 3 * q^58 + 6 * q^59 + q^60 + 8 * q^61 + 8 * q^62 + 2 * q^63 + 6 * q^64 - 9 * q^65 - 9 * q^66 - 9 * q^67 - 6 * q^68 + 8 * q^69 - 10 * q^70 - 2 * q^71 + 3 * q^72 + 26 * q^73 + 7 * q^74 + 6 * q^75 - 16 * q^76 - 27 * q^77 + 2 * q^78 - 3 * q^79 + q^80 - 3 * q^81 + 15 * q^82 + 30 * q^83 + 2 * q^84 - 54 * q^85 - 3 * q^86 - 3 * q^87 - 9 * q^88 - 3 * q^89 + 2 * q^90 - 17 * q^91 + 8 * q^92 + 4 * q^93 + q^94 + 4 * q^95 + 3 * q^96 - 22 * q^97 - 12 * q^98 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1218\mathbb{Z}\right)^\times$.

$n$	$379$	$407$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.956115	−	1.65604i	−0.427587	−	0.740603i	0.569071	−	0.822289i	$-0.307303\pi$
$5$	−0.956115	−	1.65604i	−0.427587	−	0.740603i	−0.996658	+	0.0816854i	$0.973970\pi$
$6$	−1.00000			−0.408248
$7$	−2.58392	+	0.568650i	−0.976630	+	0.214929i
$7$	−2.58392	+	0.568650i	−0.976630	+	0.214929i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.956115	−	1.65604i	0.302350	−	0.523686i
$11$	1.17169	−	2.02943i	0.353278	−	0.611895i	−0.633544	−	0.773707i	$-0.718400\pi$
$11$	1.17169	−	2.02943i	0.353278	−	0.611895i	0.986822	+	0.161812i	$0.0517337\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	1.91223			0.530357			0.265178	−	0.964199i	$-0.414569\pi$
$13$	1.91223			0.530357			0.265178	+	0.964199i	$0.414569\pi$
$14$	−1.78442	−	1.95341i	−0.476908	−	0.522072i
$15$	1.91223			0.493735
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.69665	−	4.67074i	0.654035	−	1.13282i	−0.328100	−	0.944643i	$-0.606408\pi$
$17$	2.69665	−	4.67074i	0.654035	−	1.13282i	0.982135	−	0.188178i	$-0.0602583\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	3.11274	+	5.39142i	0.714110	+	1.23688i	0.963302	+	0.268421i	$0.0865019\pi$
$19$	3.11274	+	5.39142i	0.714110	+	1.23688i	−0.249191	+	0.968454i	$0.580165\pi$
$20$	1.91223			0.427587
$21$	0.799494	−	2.52206i	0.174464	−	0.550360i
$22$	2.34338			0.499610
$23$	1.11274	+	1.92731i	0.232021	+	0.401873i	0.958403	−	0.285419i	$-0.0921328\pi$
$23$	1.11274	+	1.92731i	0.232021	+	0.401873i	−0.726382	+	0.687292i	$0.758799\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	0.671690	−	1.16340i	0.134338	−	0.232680i
$26$	0.956115	+	1.65604i	0.187509	+	0.324776i
$27$	1.00000			0.192450
$28$	0.799494	−	2.52206i	0.151090	−	0.476625i
$29$	1.00000			0.185695
$29$	1.00000			0.185695
$30$	0.956115	+	1.65604i	0.174562	+	0.302350i
$31$	−1.44105	+	2.49596i	−0.258819	+	0.448288i	−0.965926	−	0.258819i	$-0.916667\pi$
$31$	−1.44105	+	2.49596i	−0.258819	+	0.448288i	0.707107	+	0.707107i	$0.250000\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.17169	+	2.02943i	0.203965	+	0.353278i
$34$	5.39331			0.924945
$35$	3.41223	+	3.73538i	0.576772	+	0.631394i
$36$	1.00000			0.166667
$37$	0.612735	+	1.06129i	0.100733	+	0.174475i	0.911987	−	0.410219i	$-0.134548\pi$
$37$	0.612735	+	1.06129i	0.100733	+	0.174475i	−0.811254	+	0.584694i	$0.801215\pi$
$38$	−3.11274	+	5.39142i	−0.504952	+	0.874603i
$39$	−0.956115	+	1.65604i	−0.153101	+	0.265178i
$40$	0.956115	+	1.65604i	0.151175	+	0.261843i
$41$	12.3933			1.93551			0.967755	−	0.251894i	$-0.0810535\pi$
$41$	12.3933			1.93551			0.967755	+	0.251894i	$0.0810535\pi$
$42$	2.58392	−	0.568650i	0.398707	−	0.0877446i
$43$	0.313241			0.0477688			0.0238844	−	0.999715i	$-0.492397\pi$
$43$	0.313241			0.0477688			0.0238844	+	0.999715i	$0.492397\pi$
$44$	1.17169	+	2.02943i	0.176639	+	0.305948i
$45$	−0.956115	+	1.65604i	−0.142529	+	0.246868i
$46$	−1.11274	+	1.92731i	−0.164064	+	0.284167i
$47$	−0.0288161	−	0.0499109i	−0.00420325	−	0.00728025i	0.863916	−	0.503636i	$-0.168005\pi$
$47$	−0.0288161	−	0.0499109i	−0.00420325	−	0.00728025i	−0.868119	+	0.496355i	$0.834671\pi$
$48$	1.00000			0.144338
$49$	6.35327	−	2.93869i	0.907611	−	0.419813i
$50$	1.34338			0.189983
$51$	2.69665	+	4.67074i	0.377607	+	0.654035i
$52$	−0.956115	+	1.65604i	−0.132589	+	0.229651i
$53$	−2.56885	+	4.44938i	−0.352859	+	0.611169i	−0.986749	−	0.162254i	$-0.948124\pi$
$53$	−2.56885	+	4.44938i	−0.352859	+	0.611169i	0.633890	+	0.773423i	$0.281457\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−4.48108			−0.604229
$56$	2.58392	−	0.568650i	0.345291	−	0.0759890i
$57$	−6.22547			−0.824584
$58$	0.500000	+	0.866025i	0.0656532	+	0.113715i
$59$	0.343380	−	0.594751i	0.0447042	−	0.0774300i	−0.842808	−	0.538215i	$-0.819099\pi$
$59$	0.343380	−	0.594751i	0.0447042	−	0.0774300i	0.887512	+	0.460785i	$0.152432\pi$
$60$	−0.956115	+	1.65604i	−0.123434	+	0.213794i
$61$	1.14287	+	1.97952i	0.146330	+	0.253451i	0.929868	−	0.367892i	$-0.119921\pi$
$61$	1.14287	+	1.97952i	0.146330	+	0.253451i	−0.783538	+	0.621343i	$0.786587\pi$
$62$	−2.88209			−0.366026
$63$	1.78442	+	1.95341i	0.224816	+	0.246107i
$64$	1.00000			0.125000
$65$	−1.82831	−	3.16673i	−0.226774	−	0.392784i
$66$	−1.17169	+	2.02943i	−0.144225	+	0.249805i
$67$	3.18158	−	5.51067i	0.388692	−	0.673235i	−0.603582	−	0.797301i	$-0.706260\pi$
$67$	3.18158	−	5.51067i	0.388692	−	0.673235i	0.992274	+	0.124066i	$0.0395935\pi$
$68$	2.69665	+	4.67074i	0.327017	+	0.566411i
$69$	−2.22547			−0.267915
$70$	−1.52882	+	4.82277i	−0.182728	+	0.576431i
$71$	−1.37087			−0.162693			−0.0813463	−	0.996686i	$-0.525922\pi$
$71$	−1.37087			−0.162693			−0.0813463	+	0.996686i	$0.525922\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	5.45611	−	9.45027i	0.638590	−	1.10607i	−0.347152	−	0.937809i	$-0.612851\pi$
$73$	5.45611	−	9.45027i	0.638590	−	1.10607i	0.985742	−	0.168261i	$-0.0538153\pi$
$74$	−0.612735	+	1.06129i	−0.0712290	+	0.123372i
$75$	0.671690	+	1.16340i	0.0775601	+	0.134338i
$76$	−6.22547			−0.714110
$77$	−1.87352	+	5.91015i	−0.213507	+	0.673525i
$78$	−1.91223			−0.216517
$79$	−5.50989	−	9.54342i	−0.619912	−	1.07372i	−0.989501	−	0.144523i	$-0.953835\pi$
$79$	−5.50989	−	9.54342i	−0.619912	−	1.07372i	0.369590	−	0.929195i	$-0.379498\pi$
$80$	−0.956115	+	1.65604i	−0.106897	+	0.185151i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	6.19665	+	10.7329i	0.684306	+	1.18525i
$83$	17.8168			1.95564			0.977821	−	0.209440i	$-0.0671642\pi$
$83$	17.8168			1.95564			0.977821	+	0.209440i	$0.0671642\pi$
$84$	1.78442	+	1.95341i	0.194697	+	0.213135i
$85$	−10.3132			−1.11863
$86$	0.156620	+	0.271275i	0.0168888	+	0.0292523i
$87$	−0.500000	+	0.866025i	−0.0536056	+	0.0928477i
$88$	−1.17169	+	2.02943i	−0.124903	+	0.216338i
$89$	1.14155	+	1.97722i	0.121004	+	0.209585i	0.920164	−	0.391533i	$-0.128055\pi$
$89$	1.14155	+	1.97722i	0.121004	+	0.209585i	−0.799160	+	0.601119i	$0.794722\pi$
$90$	−1.91223			−0.201567
$91$	−4.94105	+	1.08739i	−0.517962	+	0.113989i
$92$	−2.22547			−0.232021
$93$	−1.44105	−	2.49596i	−0.149429	−	0.258819i
$94$	0.0288161	−	0.0499109i	0.00297215	−	0.00514791i
$95$	5.95226	−	10.3096i	0.610689	−	1.05774i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−9.36581			−0.950954			−0.475477	−	0.879728i	$-0.657725\pi$
$97$	−9.36581			−0.950954			−0.475477	+	0.879728i	$0.657725\pi$
$98$	5.72162	+	4.03275i	0.577971	+	0.407369i
$99$	−2.34338			−0.235519
$100$	0.671690	+	1.16340i	0.0671690	+	0.116340i
$101$	8.97723	−	15.5490i	0.893267	−	1.54718i	0.0573332	−	0.998355i	$-0.481740\pi$
$101$	8.97723	−	15.5490i	0.893267	−	1.54718i	0.835934	−	0.548830i	$-0.184926\pi$
$102$	−2.69665	+	4.67074i	−0.267009	+	0.462472i
$103$	8.53871	+	14.7895i	0.841344	+	1.45725i	0.888759	+	0.458376i	$0.151569\pi$
$103$	8.53871	+	14.7895i	0.841344	+	1.45725i	−0.0474144	+	0.998875i	$0.515098\pi$
$104$	−1.91223			−0.187509
$105$	−4.94105	+	1.08739i	−0.482197	+	0.106118i
$106$	−5.13770			−0.499017
$107$	−6.54003	−	11.3277i	−0.632249	−	1.09509i	−0.987091	−	0.160161i	$-0.948799\pi$
$107$	−6.54003	−	11.3277i	−0.632249	−	1.09509i	0.354842	−	0.934926i	$-0.384535\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	4.14155	−	7.17338i	0.396689	−	0.687085i	−0.596626	−	0.802519i	$-0.703493\pi$
$109$	4.14155	−	7.17338i	0.396689	−	0.687085i	0.993315	+	0.115434i	$0.0368259\pi$
$110$	−2.24054	−	3.88073i	−0.213627	−	0.370013i
$111$	−1.22547			−0.116316
$112$	1.78442	+	1.95341i	0.168612	+	0.184580i
$113$	−10.1678			−0.956510			−0.478255	−	0.878221i	$-0.658730\pi$
$113$	−10.1678			−0.956510			−0.478255	+	0.878221i	$0.658730\pi$
$114$	−3.11274	−	5.39142i	−0.291534	−	0.504952i
$115$	2.12780	−	3.68547i	0.198419	−	0.343671i
$116$	−0.500000	+	0.866025i	−0.0464238	+	0.0804084i
$117$	−0.956115	−	1.65604i	−0.0883928	−	0.153101i
$118$	0.686759			0.0632213
$119$	−4.31192	+	13.6023i	−0.395273	+	1.24692i
$120$	−1.91223			−0.174562
$121$	2.75429	+	4.77056i	0.250390	+	0.433688i
$122$	−1.14287	+	1.97952i	−0.103471	+	0.179217i
$123$	−6.19665	+	10.7329i	−0.558733	+	0.967755i
$124$	−1.44105	−	2.49596i	−0.129410	−	0.224144i
$125$	−12.1300			−1.08494
$126$	−0.799494	+	2.52206i	−0.0712246	+	0.224683i
$127$	4.10756			0.364487			0.182244	−	0.983253i	$-0.441664\pi$
$127$	4.10756			0.364487			0.182244	+	0.983253i	$0.441664\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−0.156620	+	0.271275i	−0.0137897	+	0.0238844i
$130$	1.82831	−	3.16673i	0.160353	−	0.277740i
$131$	7.97723	+	13.8170i	0.696974	+	1.20719i	0.969511	+	0.245048i	$0.0788039\pi$
$131$	7.97723	+	13.8170i	0.696974	+	1.20719i	−0.272537	+	0.962145i	$0.587863\pi$
$132$	−2.34338			−0.203965
$133$	−11.1089	−	12.1609i	−0.963262	−	1.05449i
$134$	6.36317			0.549694
$135$	−0.956115	−	1.65604i	−0.0822892	−	0.142529i
$136$	−2.69665	+	4.67074i	−0.231236	+	0.400513i
$137$	4.71558	−	8.16762i	0.402879	−	0.697807i	−0.591193	−	0.806530i	$-0.701343\pi$
$137$	4.71558	−	8.16762i	0.402879	−	0.697807i	0.994072	+	0.108723i	$0.0346763\pi$
$138$	−1.11274	−	1.92731i	−0.0947223	−	0.164064i
$139$	−14.8442			−1.25907			−0.629536	−	0.776971i	$-0.716755\pi$
$139$	−14.8442			−1.25907			−0.629536	+	0.776971i	$0.716755\pi$
$140$	−4.94105	+	1.08739i	−0.417595	+	0.0919012i
$141$	0.0576321			0.00485350
$142$	−0.685436	−	1.18721i	−0.0575206	−	0.0996285i
$143$	2.24054	−	3.88073i	0.187363	−	0.324523i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−0.956115	−	1.65604i	−0.0794010	−	0.137527i
$146$	10.9122			0.903103
$147$	−0.631656	+	6.97144i	−0.0520981	+	0.574995i
$148$	−1.22547			−0.100733
$149$	9.63770	+	16.6930i	0.789551	+	1.36754i	0.926242	+	0.376929i	$0.123020\pi$
$149$	9.63770	+	16.6930i	0.789551	+	1.36754i	−0.136691	+	0.990614i	$0.543647\pi$
$150$	−0.671690	+	1.16340i	−0.0548432	+	0.0949913i
$151$	−2.19665	+	3.80472i	−0.178761	+	0.309623i	−0.941456	−	0.337135i	$-0.890542\pi$
$151$	−2.19665	+	3.80472i	−0.178761	+	0.309623i	0.762695	+	0.646758i	$0.223876\pi$
$152$	−3.11274	−	5.39142i	−0.252476	−	0.437302i
$153$	−5.39331			−0.436023
$154$	−6.05510	+	1.33256i	−0.487934	+	0.107381i
$155$	5.51122			0.442672
$156$	−0.956115	−	1.65604i	−0.0765504	−	0.132589i
$157$	2.54389	−	4.40614i	0.203024	−	0.351648i	−0.746477	−	0.665411i	$-0.768256\pi$
$157$	2.54389	−	4.40614i	0.203024	−	0.351648i	0.949501	+	0.313763i	$0.101590\pi$
$158$	5.50989	−	9.54342i	0.438344	−	0.759234i
$159$	−2.56885	−	4.44938i	−0.203723	−	0.352859i
$160$	−1.91223			−0.151175
$161$	−3.97118	−	4.34727i	−0.312973	−	0.342613i
$162$	−1.00000			−0.0785674
$163$	−8.46216	−	14.6569i	−0.662807	−	1.14802i	−0.979875	−	0.199613i	$-0.936032\pi$
$163$	−8.46216	−	14.6569i	−0.662807	−	1.14802i	0.317067	−	0.948403i	$-0.397302\pi$
$164$	−6.19665	+	10.7329i	−0.483877	+	0.838100i
$165$	2.24054	−	3.88073i	0.174426	−	0.302114i
$166$	8.90838	+	15.4298i	0.691424	+	1.19758i
$167$	24.3055			1.88082			0.940409	−	0.340044i	$-0.110442\pi$
$167$	24.3055			1.88082			0.940409	+	0.340044i	$0.110442\pi$
$168$	−0.799494	+	2.52206i	−0.0616823	+	0.194581i
$169$	−9.34338			−0.718722
$170$	−5.15662	−	8.93153i	−0.395495	−	0.685017i
$171$	3.11274	−	5.39142i	0.238037	−	0.412292i
$172$	−0.156620	+	0.271275i	−0.0119422	+	0.0206845i
$173$	7.01375	+	12.1482i	0.533245	+	0.923608i	0.999246	+	0.0388236i	$0.0123611\pi$
$173$	7.01375	+	12.1482i	0.533245	+	0.923608i	−0.466001	+	0.884784i	$0.654306\pi$
$174$	−1.00000			−0.0758098
$175$	−1.07402	+	3.38809i	−0.0811886	+	0.256116i
$176$	−2.34338			−0.176639
$177$	0.343380	+	0.594751i	0.0258100	+	0.0447042i
$178$	−1.14155	+	1.97722i	−0.0855629	+	0.148199i
$179$	4.89848	−	8.48442i	0.366130	−	0.634155i	−0.622827	−	0.782360i	$-0.714016\pi$
$179$	4.89848	−	8.48442i	0.366130	−	0.634155i	0.988957	+	0.148204i	$0.0473493\pi$
$180$	−0.956115	−	1.65604i	−0.0712646	−	0.123434i
$181$	5.54641			0.412262			0.206131	−	0.978524i	$-0.433913\pi$
$181$	5.54641			0.412262			0.206131	+	0.978524i	$0.433913\pi$
$182$	−3.41223	−	3.73538i	−0.252931	−	0.276885i
$183$	−2.28575			−0.168967
$184$	−1.11274	−	1.92731i	−0.0820319	−	0.142083i
$185$	1.17169	−	2.02943i	0.0861443	−	0.149206i
$186$	1.44105	−	2.49596i	0.105663	−	0.183013i
$187$	−6.31928	−	10.9453i	−0.462112	−	0.800401i
$188$	0.0576321			0.00420325
$189$	−2.58392	+	0.568650i	−0.187952	+	0.0413632i
$190$	11.9045			0.863645
$191$	6.50604	+	11.2688i	0.470761	+	0.815382i	0.999441	−	0.0334397i	$-0.0106462\pi$
$191$	6.50604	+	11.2688i	0.470761	+	0.815382i	−0.528680	+	0.848821i	$0.677313\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	2.47504	−	4.28689i	0.178157	−	0.308577i	−0.763092	−	0.646290i	$-0.776320\pi$
$193$	2.47504	−	4.28689i	0.178157	−	0.308577i	0.941249	+	0.337713i	$0.109653\pi$
$194$	−4.68291	−	8.11103i	−0.336213	−	0.582338i
$195$	3.65662			0.261856
$196$	−0.631656	+	6.97144i	−0.0451183	+	0.497960i
$197$	−9.73933			−0.693899			−0.346949	−	0.937884i	$-0.612782\pi$
$197$	−9.73933			−0.693899			−0.346949	+	0.937884i	$0.612782\pi$
$198$	−1.17169	−	2.02943i	−0.0832684	−	0.144225i
$199$	−5.55125	+	9.61505i	−0.393518	+	0.681593i	−0.992911	−	0.118862i	$-0.962075\pi$
$199$	−5.55125	+	9.61505i	−0.393518	+	0.681593i	0.599393	+	0.800455i	$0.295409\pi$
$200$	−0.671690	+	1.16340i	−0.0474956	+	0.0822649i
$201$	3.18158	+	5.51067i	0.224412	+	0.388692i
$202$	17.9545			1.26327
$203$	−2.58392	+	0.568650i	−0.181356	+	0.0399114i
$204$	−5.39331			−0.377607
$205$	−11.8494	−	20.5238i	−0.827600	−	1.43344i
$206$	−8.53871	+	14.7895i	−0.594920	+	1.03043i
$207$	1.11274	−	1.92731i	0.0773404	−	0.133958i
$208$	−0.956115	−	1.65604i	−0.0662946	−	0.114826i
$209$	14.5886			1.00912
$210$	−3.41223	−	3.73538i	−0.235466	−	0.257765i
$211$	−15.8520			−1.09129			−0.545647	−	0.838015i	$-0.683716\pi$
$211$	−15.8520			−1.09129			−0.545647	+	0.838015i	$0.683716\pi$
$212$	−2.56885	−	4.44938i	−0.176429	−	0.305585i
$213$	0.685436	−	1.18721i	0.0469653	−	0.0813463i
$214$	6.54003	−	11.3277i	0.447067	−	0.774344i
$215$	−0.299494	−	0.518739i	−0.0204253	−	0.0353777i
$216$	−1.00000			−0.0680414
$217$	2.30421	−	7.26882i	0.156420	−	0.493440i
$218$	8.28310			0.561002
$219$	5.45611	+	9.45027i	0.368690	+	0.638590i
$220$	2.24054	−	3.88073i	0.151057	−	0.261639i
$221$	5.15662	−	8.93153i	0.346872	−	0.600800i
$222$	−0.612735	−	1.06129i	−0.0411241	−	0.0712290i
$223$	−24.2479			−1.62376			−0.811880	−	0.583824i	$-0.801556\pi$
$223$	−24.2479			−1.62376			−0.811880	+	0.583824i	$0.801556\pi$
$224$	−0.799494	+	2.52206i	−0.0534185	+	0.168513i
$225$	−1.34338			−0.0895586
$226$	−5.08392	−	8.80561i	−0.338177	−	0.585740i
$227$	−1.68544	+	2.91926i	−0.111866	+	0.193758i	−0.916523	−	0.399983i	$-0.869016\pi$
$227$	−1.68544	+	2.91926i	−0.111866	+	0.193758i	0.804656	+	0.593741i	$0.202350\pi$
$228$	3.11274	−	5.39142i	0.206146	−	0.357055i
$229$	−3.46601	−	6.00330i	−0.229040	−	0.396710i	0.728484	−	0.685063i	$-0.240225\pi$
$229$	−3.46601	−	6.00330i	−0.229040	−	0.396710i	−0.957524	+	0.288354i	$0.906892\pi$
$230$	4.25561			0.280607
$231$	−4.18158	−	4.57759i	−0.275128	−	0.301183i
$232$	−1.00000			−0.0656532
$233$	−8.43334	−	14.6070i	−0.552487	−	0.956935i	−0.998094	−	0.0617065i	$-0.980346\pi$
$233$	−8.43334	−	14.6070i	−0.552487	−	0.956935i	0.445608	−	0.895228i	$-0.352988\pi$
$234$	0.956115	−	1.65604i	0.0625032	−	0.108259i
$235$	−0.0551029	+	0.0954410i	−0.00359452	+	0.00622589i
$236$	0.343380	+	0.594751i	0.0223521	+	0.0387150i
$237$	11.0198			0.715812
$238$	−13.9359	+	3.06690i	−0.903328	+	0.198798i
$239$	−4.56115			−0.295036			−0.147518	−	0.989059i	$-0.547128\pi$
$239$	−4.56115			−0.295036			−0.147518	+	0.989059i	$0.547128\pi$
$240$	−0.956115	−	1.65604i	−0.0617169	−	0.106897i
$241$	12.5925	−	21.8108i	0.811154	−	1.40496i	−0.100903	−	0.994896i	$-0.532173\pi$
$241$	12.5925	−	21.8108i	0.811154	−	1.40496i	0.912057	−	0.410063i	$-0.134493\pi$
$242$	−2.75429	+	4.77056i	−0.177052	+	0.306663i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−2.28575			−0.146330
$245$	−10.9410	−	7.71155i	−0.698998	−	0.492673i
$246$	−12.3933			−0.790168
$247$	5.95226	+	10.3096i	0.378733	+	0.655986i
$248$	1.44105	−	2.49596i	0.0915065	−	0.158494i
$249$	−8.90838	+	15.4298i	−0.564545	+	0.977821i
$250$	−6.06500	−	10.5049i	−0.383584	−	0.664387i
$251$	13.0499			0.823704			0.411852	−	0.911251i	$-0.364882\pi$
$251$	13.0499			0.823704			0.411852	+	0.911251i	$0.364882\pi$
$252$	−2.58392	+	0.568650i	−0.162772	+	0.0358216i
$253$	5.21512			0.327872
$254$	2.05378	+	3.55725i	0.128866	+	0.223202i
$255$	5.15662	−	8.93153i	0.322920	−	0.559314i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.42212	−	7.65934i	−0.275845	−	0.477777i	0.694503	−	0.719489i	$-0.255624\pi$
$257$	−4.42212	−	7.65934i	−0.275845	−	0.477777i	−0.970348	+	0.241713i	$0.922291\pi$
$258$	−0.313241			−0.0195015
$259$	−2.18676	−	2.39385i	−0.135879	−	0.148747i
$260$	3.65662			0.226774
$261$	−0.500000	−	0.866025i	−0.0309492	−	0.0536056i
$262$	−7.97723	+	13.8170i	−0.492835	+	0.853615i
$263$	15.6300	−	27.0719i	0.963787	−	1.66933i	0.250947	−	0.968001i	$-0.419258\pi$
$263$	15.6300	−	27.0719i	0.963787	−	1.66933i	0.712840	−	0.701327i	$-0.247409\pi$
$264$	−1.17169	−	2.02943i	−0.0721125	−	0.124903i
$265$	9.82446			0.603512
$266$	4.97723	−	15.7010i	0.305173	−	0.962692i
$267$	−2.28310			−0.139724
$268$	3.18158	+	5.51067i	0.194346	+	0.336618i
$269$	−2.81709	+	4.87935i	−0.171761	+	0.297499i	−0.939036	−	0.343820i	$-0.888279\pi$
$269$	−2.81709	+	4.87935i	−0.171761	+	0.297499i	0.767274	+	0.641319i	$0.221612\pi$
$270$	0.956115	−	1.65604i	0.0581873	−	0.100783i
$271$	2.01892	+	3.49687i	0.122641	+	0.212420i	0.920808	−	0.390016i	$-0.127530\pi$
$271$	2.01892	+	3.49687i	0.122641	+	0.212420i	−0.798168	+	0.602436i	$0.794197\pi$
$272$	−5.39331			−0.327017
$273$	1.52882	−	4.82277i	0.0925282	−	0.291887i
$274$	9.43115			0.569757
$275$	−1.57402	−	2.72629i	−0.0949172	−	0.164401i
$276$	1.11274	−	1.92731i	0.0669788	−	0.116011i
$277$	2.78828	−	4.82944i	0.167531	−	0.290173i	−0.770020	−	0.638020i	$-0.779754\pi$
$277$	2.78828	−	4.82944i	0.167531	−	0.290173i	0.937551	+	0.347847i	$0.113087\pi$
$278$	−7.42212	−	12.8555i	−0.445149	−	0.771021i
$279$	2.88209			0.172546
$280$	−3.41223	−	3.73538i	−0.203920	−	0.223231i
$281$	2.73669			0.163257			0.0816285	−	0.996663i	$-0.473988\pi$
$281$	2.73669			0.163257			0.0816285	+	0.996663i	$0.473988\pi$
$282$	0.0288161	+	0.0499109i	0.00171597	+	0.00297215i
$283$	−0.0976657	+	0.169162i	−0.00580562	+	0.0100556i	−0.868914	−	0.494964i	$-0.835181\pi$
$283$	−0.0976657	+	0.169162i	−0.00580562	+	0.0100556i	0.863108	+	0.505019i	$0.168515\pi$
$284$	0.685436	−	1.18721i	0.0406732	−	0.0704480i
$285$	5.95226	+	10.3096i	0.352582	+	0.610689i
$286$	4.48108			0.264972
$287$	−32.0233	+	7.04745i	−1.89028	+	0.415998i
$288$	−1.00000			−0.0589256
$289$	−6.04389	−	10.4683i	−0.355523	−	0.615783i
$290$	0.956115	−	1.65604i	0.0561450	−	0.0972460i
$291$	4.68291	−	8.11103i	0.274517	−	0.475477i
$292$	5.45611	+	9.45027i	0.319295	+	0.553035i
$293$	−15.8717			−0.927237			−0.463619	−	0.886035i	$-0.653449\pi$
$293$	−15.8717			−0.927237			−0.463619	+	0.886035i	$0.653449\pi$
$294$	−6.35327	+	2.93869i	−0.370530	+	0.171388i
$295$	−1.31324			−0.0764598
$296$	−0.612735	−	1.06129i	−0.0356145	−	0.0616861i
$297$	1.17169	−	2.02943i	0.0679883	−	0.117759i
$298$	−9.63770	+	16.6930i	−0.558297	+	0.966999i
$299$	2.12780	+	3.68547i	0.123054	+	0.213136i
$300$	−1.34338			−0.0775601
$301$	−0.809389	+	0.178124i	−0.0466524	+	0.0102669i
$302$	−4.39331			−0.252806
$303$	8.97723	+	15.5490i	0.515728	+	0.893267i
$304$	3.11274	−	5.39142i	0.178528	−	0.309219i
$305$	2.18544	−	3.78529i	0.125138	−	0.216745i
$306$	−2.69665	−	4.67074i	−0.154157	−	0.267009i
$307$	−8.45359			−0.482472			−0.241236	−	0.970467i	$-0.577553\pi$
$307$	−8.45359			−0.482472			−0.241236	+	0.970467i	$0.577553\pi$
$308$	−4.18158	−	4.57759i	−0.238268	−	0.260832i
$309$	−17.0774			−0.971501
$310$	2.75561	+	4.77285i	0.156508	+	0.271080i
$311$	7.13385	−	12.3562i	0.404523	−	0.700655i	−0.589743	−	0.807591i	$-0.700771\pi$
$311$	7.13385	−	12.3562i	0.404523	−	0.700655i	0.994266	+	0.106936i	$0.0341041\pi$
$312$	0.956115	−	1.65604i	0.0541293	−	0.0937547i
$313$	6.72932	+	11.6555i	0.380364	+	0.658809i	0.991114	−	0.133014i	$-0.0424655\pi$
$313$	6.72932	+	11.6555i	0.380364	+	0.658809i	−0.610750	+	0.791823i	$0.709132\pi$
$314$	5.08777			0.287120
$315$	1.52882	−	4.82277i	0.0861390	−	0.271732i
$316$	11.0198			0.619912
$317$	−3.50989	−	6.07932i	−0.197135	−	0.341448i	0.750463	−	0.660912i	$-0.229831\pi$
$317$	−3.50989	−	6.07932i	−0.197135	−	0.341448i	−0.947598	+	0.319464i	$0.896497\pi$
$318$	2.56885	−	4.44938i	0.144054	−	0.249509i
$319$	1.17169	−	2.02943i	0.0656020	−	0.113626i
$320$	−0.956115	−	1.65604i	−0.0534484	−	0.0925754i
$321$	13.0801			0.730058
$322$	1.77925	−	5.61278i	0.0991537	−	0.312788i
$323$	33.5759			1.86821
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	1.28442	−	2.22469i	0.0712471	−	0.123404i
$326$	8.46216	−	14.6569i	0.468676	−	0.811770i
$327$	4.14155	+	7.17338i	0.229028	+	0.396689i
$328$	−12.3933			−0.684306
$329$	0.102840	+	0.112579i	0.00566976	+	0.00620670i
$330$	4.48108			0.246675
$331$	14.8344	+	25.6939i	0.815370	+	1.41226i	0.909062	+	0.416661i	$0.136800\pi$
$331$	14.8344	+	25.6939i	0.815370	+	1.41226i	−0.0936923	+	0.995601i	$0.529867\pi$
$332$	−8.90838	+	15.4298i	−0.488911	+	0.846818i
$333$	0.612735	−	1.06129i	0.0335777	−	0.0581582i
$334$	12.1528	+	21.0492i	0.664970	+	1.15176i
$335$	−12.1678			−0.664800
$336$	−2.58392	+	0.568650i	−0.140964	+	0.0310224i
$337$	−32.0147			−1.74395			−0.871977	−	0.489547i	$-0.837162\pi$
$337$	−32.0147			−1.74395			−0.871977	+	0.489547i	$0.837162\pi$
$338$	−4.67169	−	8.09160i	−0.254106	−	0.440125i
$339$	5.08392	−	8.80561i	0.276121	−	0.478255i
$340$	5.15662	−	8.93153i	0.279657	−	0.484380i
$341$	3.37692	+	5.84899i	0.182870	+	0.316741i
$342$	6.22547			0.336635
$343$	−14.7453	+	11.2061i	−0.796169	+	0.605074i
$344$	−0.313241			−0.0168888
$345$	2.12780	+	3.68547i	0.114557	+	0.198419i
$346$	−7.01375	+	12.1482i	−0.377061	+	0.653089i
$347$	−8.15277	+	14.1210i	−0.437664	+	0.758056i	−0.997509	−	0.0705417i	$-0.977527\pi$
$347$	−8.15277	+	14.1210i	−0.437664	+	0.758056i	0.559845	+	0.828597i	$0.310861\pi$
$348$	−0.500000	−	0.866025i	−0.0268028	−	0.0464238i
$349$	−4.97251			−0.266172			−0.133086	−	0.991104i	$-0.542489\pi$
$349$	−4.97251			−0.266172			−0.133086	+	0.991104i	$0.542489\pi$
$350$	−3.47118	+	0.763913i	−0.185543	+	0.0408329i
$351$	1.91223			0.102067
$352$	−1.17169	−	2.02943i	−0.0624513	−	0.108169i
$353$	−5.14759	+	8.91589i	−0.273979	+	0.474545i	−0.969877	−	0.243595i	$-0.921673\pi$
$353$	−5.14759	+	8.91589i	−0.273979	+	0.474545i	0.695898	+	0.718140i	$0.255006\pi$
$354$	−0.343380	+	0.594751i	−0.0182504	+	0.0316107i
$355$	1.31071	+	2.27022i	0.0695654	+	0.120491i
$356$	−2.28310			−0.121004
$357$	−9.62395	−	10.5354i	−0.509354	−	0.557591i
$358$	9.79696			0.517786
$359$	4.05895	+	7.03032i	0.214223	+	0.371046i	0.953032	−	0.302869i	$-0.0979446\pi$
$359$	4.05895	+	7.03032i	0.214223	+	0.371046i	−0.738809	+	0.673915i	$0.764611\pi$
$360$	0.956115	−	1.65604i	0.0503917	−	0.0872809i
$361$	−9.87824	+	17.1096i	−0.519907	+	0.900506i
$362$	2.77321	+	4.80334i	0.145757	+	0.252458i
$363$	−5.50857			−0.289125
$364$	1.52882	−	4.82277i	0.0801317	−	0.252782i
$365$	−20.8667			−1.09221
$366$	−1.14287	−	1.97952i	−0.0597390	−	0.103471i
$367$	−16.4635	+	28.5156i	−0.859387	+	1.48850i	0.0131282	+	0.999914i	$0.495821\pi$
$367$	−16.4635	+	28.5156i	−0.859387	+	1.48850i	−0.872515	+	0.488588i	$0.837512\pi$
$368$	1.11274	−	1.92731i	0.0580053	−	0.100468i
$369$	−6.19665	−	10.7329i	−0.322585	−	0.558733i
$370$	2.34338			0.121827
$371$	4.10756	−	12.9576i	0.213254	−	0.672726i
$372$	2.88209			0.149429
$373$	9.14892	+	15.8464i	0.473713	+	0.820495i	0.999547	−	0.0300922i	$-0.00958009\pi$
$373$	9.14892	+	15.8464i	0.473713	+	0.820495i	−0.525834	+	0.850587i	$0.676247\pi$
$374$	6.31928	−	10.9453i	0.326762	−	0.565969i
$375$	6.06500	−	10.5049i	0.313195	−	0.542470i
$376$	0.0288161	+	0.0499109i	0.00148607	+	0.00257396i
$377$	1.91223			0.0984848
$378$	−1.78442	−	1.95341i	−0.0917809	−	0.100473i
$379$	22.0044			1.13029			0.565145	−	0.824992i	$-0.308820\pi$
$379$	22.0044			1.13029			0.565145	+	0.824992i	$0.308820\pi$
$380$	5.95226	+	10.3096i	0.305345	+	0.528872i
$381$	−2.05378	+	3.55725i	−0.105218	+	0.182244i
$382$	−6.50604	+	11.2688i	−0.332878	+	0.576562i
$383$	−11.4622	−	19.8530i	−0.585689	−	1.01444i	−0.994789	−	0.101953i	$-0.967491\pi$
$383$	−11.4622	−	19.8530i	−0.585689	−	1.01444i	0.409100	−	0.912489i	$-0.365843\pi$
$384$	−1.00000			−0.0510310
$385$	11.5787	−	2.54817i	0.590107	−	0.129867i
$386$	4.95007			0.251952
$387$	−0.156620	−	0.271275i	−0.00796146	−	0.0137897i
$388$	4.68291	−	8.11103i	0.237739	−	0.411775i
$389$	−5.23536	+	9.06792i	−0.265444	+	0.459762i	−0.967680	−	0.252182i	$-0.918852\pi$
$389$	−5.23536	+	9.06792i	−0.265444	+	0.459762i	0.702236	+	0.711944i	$0.252185\pi$
$390$	1.82831	+	3.16673i	0.0925801	+	0.160353i
$391$	12.0026			0.607000
$392$	−6.35327	+	2.93869i	−0.320889	+	0.148426i
$393$	−15.9545			−0.804796
$394$	−4.86967	−	8.43451i	−0.245330	−	0.424924i
$395$	−10.5362	+	18.2492i	−0.530133	+	0.918217i
$396$	1.17169	−	2.02943i	0.0588796	−	0.101983i
$397$	1.86098	+	3.22331i	0.0933998	+	0.161773i	0.908940	−	0.416928i	$-0.136893\pi$
$397$	1.86098	+	3.22331i	0.0933998	+	0.161773i	−0.815540	+	0.578701i	$0.803560\pi$
$398$	−11.1025			−0.556518
$399$	16.0861	−	3.54011i	0.805313	−	0.177227i
$400$	−1.34338			−0.0671690
$401$	8.85460	+	15.3366i	0.442177	+	0.765874i	0.997851	−	0.0655269i	$-0.0208728\pi$
$401$	8.85460	+	15.3366i	0.442177	+	0.765874i	−0.555673	+	0.831401i	$0.687539\pi$
$402$	−3.18158	+	5.51067i	−0.158683	+	0.274847i
$403$	−2.75561	+	4.77285i	−0.137267	+	0.237753i
$404$	8.97723	+	15.5490i	0.446634	+	0.773592i
$405$	1.91223			0.0950194
$406$	−1.78442	−	1.95341i	−0.0885595	−	0.0969463i
$407$	2.87174			0.142347
$408$	−2.69665	−	4.67074i	−0.133504	−	0.231236i
$409$	−13.1791	+	22.8268i	−0.651662	+	1.12871i	0.331057	+	0.943611i	$0.392595\pi$
$409$	−13.1791	+	22.8268i	−0.651662	+	1.12871i	−0.982719	+	0.185102i	$0.940739\pi$
$410$	11.8494	−	20.5238i	0.585201	−	1.01360i
$411$	4.71558	+	8.16762i	0.232602	+	0.402879i
$412$	−17.0774			−0.841344
$413$	−0.549060	+	1.73205i	−0.0270175	+	0.0852286i
$414$	2.22547			0.109376
$415$	−17.0349	−	29.5052i	−0.836208	−	1.44836i
$416$	0.956115	−	1.65604i	0.0468774	−	0.0811940i
$417$	7.42212	−	12.8555i	0.363463	−	0.629536i
$418$	7.29432	+	12.6341i	0.356777	+	0.617956i
$419$	35.0543			1.71252			0.856258	−	0.516549i	$-0.172784\pi$
$419$	35.0543			1.71252			0.856258	+	0.516549i	$0.172784\pi$
$420$	1.52882	−	4.82277i	0.0745986	−	0.235327i
$421$	−9.42851			−0.459517			−0.229759	−	0.973248i	$-0.573794\pi$
$421$	−9.42851			−0.459517			−0.229759	+	0.973248i	$0.573794\pi$
$422$	−7.92598	−	13.7282i	−0.385830	−	0.668278i
$423$	−0.0288161	+	0.0499109i	−0.00140108	+	0.00242675i
$424$	2.56885	−	4.44938i	0.124754	−	0.216081i
$425$	−3.62263	−	6.27458i	−0.175723	−	0.304362i
$426$	1.37087			0.0664190
$427$	−4.07874	−	4.46501i	−0.197384	−	0.216077i
$428$	13.0801			0.632249
$429$	2.24054	+	3.88073i	0.108174	+	0.187363i
$430$	0.299494	−	0.518739i	0.0144429	−	0.0250158i
$431$	−7.87053	+	13.6322i	−0.379110	+	0.656638i	−0.990933	−	0.134357i	$-0.957103\pi$
$431$	−7.87053	+	13.6322i	−0.379110	+	0.656638i	0.611823	+	0.790995i	$0.290437\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	1.69711			0.0815578			0.0407789	−	0.999168i	$-0.487016\pi$
$433$	1.69711			0.0815578			0.0407789	+	0.999168i	$0.487016\pi$
$434$	7.44709	−	1.63890i	0.357472	−	0.0786697i
$435$	1.91223			0.0916844
$436$	4.14155	+	7.17338i	0.198344	+	0.343542i
$437$	−6.92730	+	11.9984i	−0.331378	+	0.573963i
$438$	−5.45611	+	9.45027i	−0.260703	+	0.451551i
$439$	12.2956	+	21.2967i	0.586839	+	1.01643i	0.994643	+	0.103366i	$0.0329612\pi$
$439$	12.2956	+	21.2967i	0.586839	+	1.01643i	−0.407804	+	0.913069i	$0.633705\pi$
$440$	4.48108			0.213627
$441$	−5.72162	−	4.03275i	−0.272458	−	0.192036i
$442$	10.3132			0.490551
$443$	−10.6240	−	18.4012i	−0.504759	−	0.874269i	−0.999985	−	0.00550422i	$-0.998248\pi$
$443$	−10.6240	−	18.4012i	−0.504759	−	0.874269i	0.495226	−	0.868764i	$-0.335085\pi$
$444$	0.612735	−	1.06129i	0.0290791	−	0.0503665i
$445$	2.18291	−	3.78091i	0.103480	−	0.179232i
$446$	−12.1240	−	20.9993i	−0.574086	−	0.994346i
$447$	−19.2754			−0.911695
$448$	−2.58392	+	0.568650i	−0.122079	+	0.0268662i
$449$	−31.3330			−1.47870			−0.739349	−	0.673323i	$-0.764866\pi$
$449$	−31.3330			−1.47870			−0.739349	+	0.673323i	$0.764866\pi$
$450$	−0.671690	−	1.16340i	−0.0316638	−	0.0548432i
$451$	14.5211	−	25.1513i	0.683772	−	1.18433i
$452$	5.08392	−	8.80561i	0.239127	−	0.414181i
$453$	−2.19665	−	3.80472i	−0.103208	−	0.178761i
$454$	−3.37087			−0.158203
$455$	6.52496	+	7.14290i	0.305895	+	0.334864i
$456$	6.22547			0.291534
$457$	−11.8705	−	20.5604i	−0.555280	−	0.961774i	−0.997882	−	0.0650551i	$-0.979278\pi$
$457$	−11.8705	−	20.5604i	−0.555280	−	0.961774i	0.442601	−	0.896718i	$-0.354056\pi$
$458$	3.46601	−	6.00330i	0.161956	−	0.280516i
$459$	2.69665	−	4.67074i	0.125869	−	0.218012i
$460$	2.12780	+	3.68547i	0.0992094	+	0.171836i
$461$	10.2332			0.476606			0.238303	−	0.971191i	$-0.423409\pi$
$461$	10.2332			0.476606			0.238303	+	0.971191i	$0.423409\pi$
$462$	1.87352	−	5.91015i	0.0871640	−	0.274965i
$463$	24.8770			1.15613			0.578067	−	0.815989i	$-0.303807\pi$
$463$	24.8770			1.15613			0.578067	+	0.815989i	$0.303807\pi$
$464$	−0.500000	−	0.866025i	−0.0232119	−	0.0402042i
$465$	−2.75561	+	4.77285i	−0.127788	+	0.221336i
$466$	8.43334	−	14.6070i	0.390667	−	0.676655i
$467$	0.540034	+	0.935366i	0.0249898	+	0.0432836i	0.878250	−	0.478202i	$-0.158711\pi$
$467$	0.540034	+	0.935366i	0.0249898	+	0.0432836i	−0.853260	+	0.521486i	$0.825378\pi$
$468$	1.91223			0.0883928
$469$	−5.08732	+	16.0483i	−0.234910	+	0.741043i
$470$	−0.110206			−0.00508342
$471$	2.54389	+	4.40614i	0.117216	+	0.203024i
$472$	−0.343380	+	0.594751i	−0.0158053	+	0.0273756i
$473$	0.367021	−	0.635699i	0.0168756	−	0.0292295i
$474$	5.50989	+	9.54342i	0.253078	+	0.438344i
$475$	8.36317			0.383729
$476$	−9.62395	−	10.5354i	−0.441113	−	0.482888i
$477$	5.13770			0.235239
$478$	−2.28057	−	3.95007i	−0.104311	−	0.180672i
$479$	−8.09514	+	14.0212i	−0.369876	+	0.640644i	−0.989546	−	0.144218i	$-0.953933\pi$
$479$	−8.09514	+	14.0212i	−0.369876	+	0.640644i	0.619670	+	0.784863i	$0.287267\pi$
$480$	0.956115	−	1.65604i	0.0436405	−	0.0755875i
$481$	1.17169	+	2.02943i	0.0534245	+	0.0925339i
$482$	25.1850			1.14714
$483$	5.75043	−	1.26551i	0.261654	−	0.0575829i
$484$	−5.50857			−0.250390
$485$	8.95479	+	15.5102i	0.406616	+	0.704280i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	2.22932	−	3.86130i	0.101020	−	0.174972i	−0.811085	−	0.584928i	$-0.801123\pi$
$487$	2.22932	−	3.86130i	0.101020	−	0.174972i	0.912105	+	0.409956i	$0.134456\pi$
$488$	−1.14287	−	1.97952i	−0.0517355	−	0.0896085i
$489$	16.9243			0.765344
$490$	1.20787	−	13.3310i	0.0545661	−	0.602233i
$491$	13.5337			0.610765			0.305383	−	0.952230i	$-0.401216\pi$
$491$	13.5337			0.610765			0.305383	+	0.952230i	$0.401216\pi$
$492$	−6.19665	−	10.7329i	−0.279367	−	0.483877i
$493$	2.69665	−	4.67074i	0.121451	−	0.210360i
$494$	−5.95226	+	10.3096i	−0.267805	+	0.463852i
$495$	2.24054	+	3.88073i	0.100705	+	0.174426i
$496$	2.88209			0.129410
$497$	3.54222	−	0.779547i	0.158890	−	0.0349675i
$498$	−17.8168			−0.798388
$499$	2.12010	+	3.67212i	0.0949087	+	0.164387i	0.909571	−	0.415550i	$-0.136411\pi$
$499$	2.12010	+	3.67212i	0.0949087	+	0.164387i	−0.814662	+	0.579936i	$0.803077\pi$
$500$	6.06500	−	10.5049i	0.271235	−	0.469793i
$501$	−12.1528	+	21.0492i	−0.542946	+	0.940409i
$502$	6.52496	+	11.3016i	0.291223	+	0.504414i
$503$	5.02243			0.223939			0.111970	−	0.993712i	$-0.464284\pi$
$503$	5.02243			0.223939			0.111970	+	0.993712i	$0.464284\pi$
$504$	−1.78442	−	1.95341i	−0.0794846	−	0.0870120i
$505$	−34.3330			−1.52780
$506$	2.60756	+	4.51643i	0.115920	+	0.200780i
$507$	4.67169	−	8.09160i	0.207477	−	0.359361i
$508$	−2.05378	+	3.55725i	−0.0911218	+	0.157828i
$509$	−13.9057	−	24.0854i	−0.616361	−	1.06757i	−0.990144	−	0.140052i	$-0.955273\pi$
$509$	−13.9057	−	24.0854i	−0.616361	−	1.06757i	0.373783	−	0.927516i	$-0.378060\pi$
$510$	10.3132			0.456678
$511$	−8.72426	+	27.5213i	−0.385939	+	1.21747i
$512$	−1.00000			−0.0441942
$513$	3.11274	+	5.39142i	0.137431	+	0.238037i
$514$	4.42212	−	7.65934i	0.195052	−	0.337839i
$515$	16.3280	−	28.2809i	0.719496	−	1.24620i
$516$	−0.156620	−	0.271275i	−0.00689483	−	0.0119422i
$517$	−0.135054			−0.00593966
$518$	0.979756	−	3.09071i	0.0430480	−	0.135798i
$519$	−14.0275			−0.615739
$520$	1.82831	+	3.16673i	0.0801767	+	0.138870i
$521$	−15.1201	+	26.1888i	−0.662424	+	1.14735i	0.317553	+	0.948240i	$0.397139\pi$
$521$	−15.1201	+	26.1888i	−0.662424	+	1.14735i	−0.979977	+	0.199111i	$0.936195\pi$
$522$	0.500000	−	0.866025i	0.0218844	−	0.0379049i
$523$	−15.4045	−	26.6814i	−0.673593	−	1.16670i	−0.976878	−	0.213797i	$-0.931417\pi$
$523$	−15.4045	−	26.6814i	−0.673593	−	1.16670i	0.303285	−	0.952900i	$-0.401917\pi$
$524$	−15.9545			−0.696974
$525$	−2.39716	−	2.62418i	−0.104621	−	0.114528i
$526$	31.2600			1.36300
$527$	7.77200	+	13.4615i	0.338554	+	0.586392i
$528$	1.17169	−	2.02943i	0.0509913	−	0.0883194i
$529$	9.02364	−	15.6294i	0.392332	−	0.679539i
$530$	4.91223	+	8.50823i	0.213374	+	0.369574i
$531$	−0.686759			−0.0298028
$532$	16.0861	−	3.54011i	0.697421	−	0.153483i
$533$	23.6988			1.02651
$534$	−1.14155	−	1.97722i	−0.0493997	−	0.0855629i
$535$	−12.5060	+	21.6611i	−0.540683	+	0.936491i
$536$	−3.18158	+	5.51067i	−0.137424	+	0.238025i
$537$	4.89848	+	8.48442i	0.211385	+	0.366130i
$538$	−5.63419			−0.242907
$539$	1.48021	−	16.3367i	0.0637572	−	0.703673i
$540$	1.91223			0.0822892
$541$	6.95359	+	12.0440i	0.298958	+	0.517810i	0.975898	−	0.218228i	$-0.0700276\pi$
$541$	6.95359	+	12.0440i	0.298958	+	0.517810i	−0.676940	+	0.736038i	$0.736694\pi$
$542$	−2.01892	+	3.49687i	−0.0867201	+	0.150204i
$543$	−2.77321	+	4.80334i	−0.119010	+	0.206131i
$544$	−2.69665	−	4.67074i	−0.115618	−	0.200256i
$545$	−15.8392			−0.678476
$546$	4.94105	−	1.08739i	0.211457	−	0.0465360i
$547$	−18.6885			−0.799062			−0.399531	−	0.916720i	$-0.630827\pi$
$547$	−18.6885			−0.799062			−0.399531	+	0.916720i	$0.630827\pi$
$548$	4.71558	+	8.16762i	0.201439	+	0.348903i
$549$	1.14287	−	1.97952i	0.0487767	−	0.0844837i
$550$	1.57402	−	2.72629i	0.0671166	−	0.116249i
$551$	3.11274	+	5.39142i	0.132607	+	0.229682i
$552$	2.22547			0.0947223
$553$	19.6640	+	21.5262i	0.836198	+	0.915388i
$554$	5.57655			0.236925
$555$	1.17169	+	2.02943i	0.0497355	+	0.0861443i
$556$	7.42212	−	12.8555i	0.314768	−	0.545194i
$557$	−4.52243	+	7.83309i	−0.191622	+	0.331899i	−0.945788	−	0.324785i	$-0.894708\pi$
$557$	−4.52243	+	7.83309i	−0.191622	+	0.331899i	0.754166	+	0.656684i	$0.228041\pi$
$558$	1.44105	+	2.49596i	0.0610043	+	0.105663i
$559$	0.598988			0.0253345
$560$	1.52882	−	4.82277i	0.0646043	−	0.203799i
$561$	12.6386			0.533601
$562$	1.36834	+	2.37004i	0.0577201	+	0.0999741i
$563$	8.14287	−	14.1039i	0.343181	−	0.594407i	−0.641840	−	0.766838i	$-0.721829\pi$
$563$	8.14287	−	14.1039i	0.343181	−	0.594407i	0.985022	+	0.172431i	$0.0551622\pi$
$564$	−0.0288161	+	0.0499109i	−0.00121337	+	0.00210163i
$565$	9.72162	+	16.8383i	0.408992	+	0.708394i
$566$	−0.195331			−0.00821039
$567$	0.799494	−	2.52206i	0.0335756	−	0.105917i
$568$	1.37087			0.0575206
$569$	8.98625	+	15.5646i	0.376723	+	0.652504i	0.990583	−	0.136911i	$-0.0437174\pi$
$569$	8.98625	+	15.5646i	0.376723	+	0.652504i	−0.613860	+	0.789415i	$0.710384\pi$
$570$	−5.95226	+	10.3096i	−0.249313	+	0.431823i
$571$	−3.88594	+	6.73065i	−0.162622	+	0.281669i	−0.935808	−	0.352510i	$-0.885328\pi$
$571$	−3.88594	+	6.73065i	−0.162622	+	0.281669i	0.773186	+	0.634179i	$0.218662\pi$
$572$	2.24054	+	3.88073i	0.0936817	+	0.162261i
$573$	−13.0121			−0.543588
$574$	−22.1149	−	24.2093i	−0.923059	−	1.01048i
$575$	2.98965			0.124677
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−15.4320	+	26.7290i	−0.642443	+	1.11274i	0.342442	+	0.939539i	$0.388746\pi$
$577$	−15.4320	+	26.7290i	−0.642443	+	1.11274i	−0.984886	+	0.173206i	$0.944587\pi$
$578$	6.04389	−	10.4683i	0.251392	−	0.435425i
$579$	2.47504	+	4.28689i	0.102859	+	0.178157i
$580$	1.91223			0.0794010
$581$	−46.0371	+	10.1315i	−1.90994	+	0.420325i
$582$	9.36581			0.388226
$583$	6.01979	+	10.4266i	0.249314	+	0.431825i
$584$	−5.45611	+	9.45027i	−0.225776	+	0.391055i
$585$	−1.82831	+	3.16673i	−0.0755913	+	0.130928i
$586$	−7.93587	−	13.7453i	−0.327828	−	0.567814i
$587$	−8.56115			−0.353356			−0.176678	−	0.984269i	$-0.556535\pi$
$587$	−8.56115			−0.353356			−0.176678	+	0.984269i	$0.556535\pi$
$588$	−5.72162	−	4.03275i	−0.235956	−	0.166308i
$589$	−17.9424			−0.739302
$590$	−0.656620	−	1.13730i	−0.0270326	−	0.0468219i
$591$	4.86967	−	8.43451i	0.200311	−	0.346949i
$592$	0.612735	−	1.06129i	0.0251833	−	0.0436187i
$593$	−14.5826	−	25.2578i	−0.598835	−	1.03721i	−0.992993	−	0.118171i	$-0.962297\pi$
$593$	−14.5826	−	25.2578i	−0.598835	−	1.03721i	0.394158	−	0.919043i	$-0.371036\pi$
$594$	2.34338			0.0961500
$595$	26.6486	−	5.86462i	1.09249	−	0.240426i
$596$	−19.2754			−0.789551
$597$	−5.55125	−	9.61505i	−0.227198	−	0.393518i
$598$	−2.12780	+	3.68547i	−0.0870124	+	0.150710i
$599$	−11.4833	+	19.8896i	−0.469194	+	0.812667i	−0.999380	−	0.0352140i	$-0.988789\pi$
$599$	−11.4833	+	19.8896i	−0.469194	+	0.812667i	0.530186	+	0.847881i	$0.322122\pi$
$600$	−0.671690	−	1.16340i	−0.0274216	−	0.0474956i
$601$	16.2151			0.661429			0.330714	−	0.943731i	$-0.392710\pi$
$601$	16.2151			0.661429			0.330714	+	0.943731i	$0.392710\pi$
$602$	−0.558955	−	0.611889i	−0.0227813	−	0.0249387i
$603$	−6.36317			−0.259128
$604$	−2.19665	−	3.80472i	−0.0893806	−	0.154812i
$605$	5.26683	−	9.12241i	0.214127	−	0.370879i
$606$	−8.97723	+	15.5490i	−0.364675	+	0.631635i
$607$	24.0474	+	41.6513i	0.976054	+	1.69057i	0.676413	+	0.736523i	$0.263534\pi$
$607$	24.0474	+	41.6513i	0.976054	+	1.69057i	0.299641	+	0.954052i	$0.403133\pi$
$608$	6.22547			0.252476
$609$	0.799494	−	2.52206i	0.0323971	−	0.102199i
$610$	4.37087			0.176971
$611$	−0.0551029	−	0.0954410i	−0.00222922	−	0.00386113i
$612$	2.69665	−	4.67074i	0.109006	−	0.188804i
$613$	16.7479	−	29.0082i	0.676442	−	1.17163i	−0.299604	−	0.954064i	$-0.596854\pi$
$613$	16.7479	−	29.0082i	0.676442	−	1.17163i	0.976045	−	0.217567i	$-0.0698122\pi$
$614$	−4.22679	−	7.32102i	−0.170579	−	0.295452i
$615$	23.6988			0.955630
$616$	1.87352	−	5.91015i	0.0754862	−	0.238127i
$617$	−8.69885			−0.350202			−0.175101	−	0.984550i	$-0.556025\pi$
$617$	−8.69885			−0.350202			−0.175101	+	0.984550i	$0.556025\pi$
$618$	−8.53871	−	14.7895i	−0.343477	−	0.594920i
$619$	−7.45226	+	12.9077i	−0.299532	+	0.518804i	−0.976029	−	0.217641i	$-0.930164\pi$
$619$	−7.45226	+	12.9077i	−0.299532	+	0.518804i	0.676497	+	0.736445i	$0.263497\pi$
$620$	−2.75561	+	4.77285i	−0.110668	+	0.191682i
$621$	1.11274	+	1.92731i	0.0446525	+	0.0773404i
$622$	14.2677			0.572082
$623$	−4.07402	−	4.45984i	−0.163222	−	0.178680i
$624$	1.91223			0.0765504
$625$	8.23922	+	14.2707i	0.329569	+	0.570830i
$626$	−6.72932	+	11.6555i	−0.268958	+	0.465849i
$627$	−7.29432	+	12.6341i	−0.291307	+	0.504559i
$628$	2.54389	+	4.40614i	0.101512	+	0.175824i
$629$	6.60934			0.263532
$630$	4.94105	−	1.08739i	0.196856	−	0.0433226i
$631$	−23.5035			−0.935660			−0.467830	−	0.883818i	$-0.654964\pi$
$631$	−23.5035			−0.935660			−0.467830	+	0.883818i	$0.654964\pi$
$632$	5.50989	+	9.54342i	0.219172	+	0.379617i
$633$	7.92598	−	13.7282i	0.315029	−	0.545647i
$634$	3.50989	−	6.07932i	0.139396	−	0.241440i
$635$	−3.92730	−	6.80228i	−0.155850	−	0.269940i
$636$	5.13770			0.203723
$637$	12.1489	−	5.61945i	0.481358	−	0.222651i
$638$	2.34338			0.0927753
$639$	0.685436	+	1.18721i	0.0271154	+	0.0469653i
$640$	0.956115	−	1.65604i	0.0377937	−	0.0654607i
$641$	−7.89331	+	13.6716i	−0.311767	+	0.539996i	−0.978745	−	0.205081i	$-0.934254\pi$
$641$	−7.89331	+	13.6716i	−0.311767	+	0.539996i	0.666978	+	0.745077i	$0.267587\pi$
$642$	6.54003	+	11.3277i	0.258115	+	0.447067i
$643$	46.8909			1.84919			0.924597	−	0.380946i	$-0.124402\pi$
$643$	46.8909			1.84919			0.924597	+	0.380946i	$0.124402\pi$
$644$	5.75043	−	1.26551i	0.226599	−	0.0498682i
$645$	0.598988			0.0235851
$646$	16.7879	+	29.0776i	0.660513	+	1.14404i
$647$	−18.2402	+	31.5930i	−0.717096	+	1.24205i	0.245049	+	0.969511i	$0.421196\pi$
$647$	−18.2402	+	31.5930i	−0.717096	+	1.24205i	−0.962145	+	0.272537i	$0.912137\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−0.804669	−	1.39373i	−0.0315860	−	0.0547086i
$650$	2.56885			0.100759
$651$	5.14287	+	5.62992i	0.201565	+	0.220654i
$652$	16.9243			0.662807
$653$	16.1390	+	27.9536i	0.631569	+	1.09391i	0.987231	+	0.159295i	$0.0509220\pi$
$653$	16.1390	+	27.9536i	0.631569	+	1.09391i	−0.355662	+	0.934615i	$0.615745\pi$
$654$	−4.14155	+	7.17338i	−0.161947	+	0.280501i
$655$	15.2543	−	26.4212i	0.596034	−	1.03236i
$656$	−6.19665	−	10.7329i	−0.241939	−	0.419050i
$657$	−10.9122			−0.425727
$658$	−0.0460765	+	0.145352i	−0.00179625	+	0.00566641i
$659$	25.5062			0.993579			0.496789	−	0.867871i	$-0.334512\pi$
$659$	25.5062			0.993579			0.496789	+	0.867871i	$0.334512\pi$
$660$	2.24054	+	3.88073i	0.0872129	+	0.151057i
$661$	−1.23317	+	2.13592i	−0.0479649	+	0.0830776i	−0.889011	−	0.457886i	$-0.848607\pi$
$661$	−1.23317	+	2.13592i	−0.0479649	+	0.0830776i	0.841046	+	0.540963i	$0.181940\pi$
$662$	−14.8344	+	25.6939i	−0.576554	+	0.998620i
$663$	5.15662	+	8.93153i	0.200267	+	0.346872i
$664$	−17.8168			−0.691424
$665$	−9.51760	+	30.0240i	−0.369077	+	1.16428i
$666$	1.22547			0.0474860
$667$	1.11274	+	1.92731i	0.0430853	+	0.0746259i
$668$	−12.1528	+	21.0492i	−0.470205	+	0.814418i
$669$	12.1240	−	20.9993i	0.468739	−	0.811880i
$670$	−6.08392	−	10.5377i	−0.235042	−	0.407105i
$671$	5.35637			0.206781
$672$	−1.78442	−	1.95341i	−0.0688357	−	0.0753546i
$673$	0.170251			0.00656270			0.00328135	−	0.999995i	$-0.498956\pi$
$673$	0.170251			0.00656270			0.00328135	+	0.999995i	$0.498956\pi$
$674$	−16.0074	−	27.7256i	−0.616581	−	1.06795i
$675$	0.671690	−	1.16340i	0.0258534	−	0.0447793i
$676$	4.67169	−	8.09160i	0.179680	−	0.311216i
$677$	−3.34591	−	5.79528i	−0.128594	−	0.222731i	0.794538	−	0.607214i	$-0.207713\pi$
$677$	−3.34591	−	5.79528i	−0.128594	−	0.222731i	−0.923132	+	0.384483i	$0.874380\pi$
$678$	10.1678			0.390493
$679$	24.2005	−	5.32587i	0.928730	−	0.204388i
$680$	10.3132			0.395495
$681$	−1.68544	−	2.91926i	−0.0645861	−	0.111866i
$682$	−3.37692	+	5.84899i	−0.129309	+	0.223969i
$683$	−0.299494	+	0.518739i	−0.0114598	+	0.0198490i	−0.871698	−	0.490043i	$-0.836981\pi$
$683$	−0.299494	+	0.518739i	−0.0114598	+	0.0198490i	0.860239	+	0.509892i	$0.170315\pi$
$684$	3.11274	+	5.39142i	0.119018	+	0.206146i
$685$	−18.0345			−0.689064
$686$	−17.0774	−	7.16671i	−0.652019	−	0.273626i
$687$	6.93202			0.264473
$688$	−0.156620	−	0.271275i	−0.00597110	−	0.0103422i
$689$	−4.91223	+	8.50823i	−0.187141	+	0.324138i
$690$	−2.12780	+	3.68547i	−0.0810041	+	0.140303i
$691$	−2.50517	−	4.33909i	−0.0953013	−	0.165067i	0.814433	−	0.580258i	$-0.197048\pi$
$691$	−2.50517	−	4.33909i	−0.0953013	−	0.165067i	−0.909734	+	0.415191i	$0.863715\pi$
$692$	−14.0275			−0.533245
$693$	6.05510	−	1.33256i	0.230014	−	0.0506199i
$694$	−16.3055			−0.618950
$695$	14.1928	+	24.5827i	0.538364	+	0.932473i
$696$	0.500000	−	0.866025i	0.0189525	−	0.0328266i
$697$	33.4205	−	57.8859i	1.26589	−	2.19259i
$698$	−2.48625	−	4.30632i	−0.0941061	−	0.162997i
$699$	16.8667			0.637957
$700$	−2.39716	−	2.62418i	−0.0906041	−	0.0991846i
$701$	32.9665			1.24513			0.622565	−	0.782568i	$-0.286091\pi$
$701$	32.9665			1.24513			0.622565	+	0.782568i	$0.286091\pi$
$702$	0.956115	+	1.65604i	0.0360862	+	0.0625032i
$703$	−3.81456	+	6.60702i	−0.143869	+	0.249188i
$704$	1.17169	−	2.02943i	0.0441597	−	0.0764869i
$705$	−0.0551029	−	0.0954410i	−0.00207530	−	0.00359452i
$706$	−10.2952			−0.387465
$707$	−14.3545	+	45.2823i	−0.539856	+	1.70302i
$708$	−0.686759			−0.0258100
$709$	−7.65277	−	13.2550i	−0.287406	−	0.497801i	0.685784	−	0.727805i	$-0.259459\pi$
$709$	−7.65277	−	13.2550i	−0.287406	−	0.497801i	−0.973190	+	0.230004i	$0.926126\pi$
$710$	−1.31071	+	2.27022i	−0.0491901	+	0.0851998i
$711$	−5.50989	+	9.54342i	−0.206637	+	0.357906i
$712$	−1.14155	−	1.97722i	−0.0427814	−	0.0740996i
$713$	−6.41401			−0.240206
$714$	4.31192	−	13.6023i	0.161369	−	0.509052i
$715$	−8.56885			−0.320457
$716$	4.89848	+	8.48442i	0.183065	+	0.317078i
$717$	2.28057	−	3.95007i	0.0851696	−	0.147518i
$718$	−4.05895	+	7.03032i	−0.151479	+	0.262369i
$719$	−7.01375	−	12.1482i	−0.261569	−	0.453050i	0.705090	−	0.709118i	$-0.250906\pi$
$719$	−7.01375	−	12.1482i	−0.261569	−	0.453050i	−0.966659	+	0.256067i	$0.917573\pi$
$720$	1.91223			0.0712646
$721$	−30.4734	−	33.3593i	−1.13489	−	1.24236i
$722$	−19.7565			−0.735260
$723$	12.5925	+	21.8108i	0.468320	+	0.811154i
$724$	−2.77321	+	4.80334i	−0.103065	+	0.178515i
$725$	0.671690	−	1.16340i	0.0249459	−	0.0432076i
$726$	−2.75429	−	4.77056i	−0.102221	−	0.177052i
$727$	−32.7384			−1.21420			−0.607100	−	0.794625i	$-0.707667\pi$
$727$	−32.7384			−1.21420			−0.607100	+	0.794625i	$0.707667\pi$
$728$	4.94105	−	1.08739i	0.183127	−	0.0403013i
$729$	1.00000			0.0370370
$730$	−10.4333	−	18.0711i	−0.386155	−	0.668841i
$731$	0.844702	−	1.46307i	0.0312424	−	0.0541135i
$732$	1.14287	−	1.97952i	0.0422418	−	0.0731650i
$733$	22.3340	+	38.6836i	0.824926	+	1.42881i	0.901976	+	0.431786i	$0.142116\pi$
$733$	22.3340	+	38.6836i	0.824926	+	1.42881i	−0.0770504	+	0.997027i	$0.524550\pi$
$734$	−32.9270			−1.21536
$735$	12.1489	−	5.61945i	0.448120	−	0.207277i
$736$	2.22547			0.0820319
$737$	−7.45566	−	12.9136i	−0.274633	−	0.475678i
$738$	6.19665	−	10.7329i	0.228102	−	0.395084i
$739$	−7.64759	+	13.2460i	−0.281321	+	0.487263i	−0.971710	−	0.236175i	$-0.924106\pi$
$739$	−7.64759	+	13.2460i	−0.281321	+	0.487263i	0.690389	+	0.723438i	$0.257439\pi$
$740$	1.17169	+	2.02943i	0.0430722	+	0.0746032i
$741$	−11.9045			−0.437324
$742$	13.2754	−	2.92155i	0.487355	−	0.107254i
$743$	−35.5233			−1.30322			−0.651612	−	0.758553i	$-0.725907\pi$
$743$	−35.5233			−1.30322			−0.651612	+	0.758553i	$0.725907\pi$
$744$	1.44105	+	2.49596i	0.0528313	+	0.0915065i
$745$	18.4295	−	31.9208i	0.675204	−	1.16949i
$746$	−9.14892	+	15.8464i	−0.334966	+	0.580178i
$747$	−8.90838	−	15.4298i	−0.325940	−	0.564545i
$748$	12.6386			0.462112
$749$	23.3404	+	25.5508i	0.852840	+	0.933606i
$750$	12.1300			0.442925
$751$	−0.502529	−	0.870406i	−0.0183376	−	0.0317616i	0.856711	−	0.515797i	$-0.172504\pi$
$751$	−0.502529	−	0.870406i	−0.0183376	−	0.0317616i	−0.875049	+	0.484035i	$0.839171\pi$
$752$	−0.0288161	+	0.0499109i	−0.00105081	+	0.00182006i
$753$	−6.52496	+	11.3016i	−0.237783	+	0.411852i
$754$	0.956115	+	1.65604i	0.0348196	+	0.0603094i
$755$	8.40101			0.305744
$756$	0.799494	−	2.52206i	0.0290773	−	0.0917266i
$757$	−30.2151			−1.09819			−0.549094	−	0.835761i	$-0.685027\pi$
$757$	−30.2151			−1.09819			−0.549094	+	0.835761i	$0.685027\pi$
$758$	11.0022	+	19.0564i	0.399618	+	0.692158i
$759$	−2.60756	+	4.51643i	−0.0946485	+	0.163936i
$760$	−5.95226	+	10.3096i	−0.215911	+	0.373969i
$761$	−0.581728	−	1.00758i	−0.0210876	−	0.0365248i	0.855289	−	0.518151i	$-0.173380\pi$
$761$	−0.581728	−	1.00758i	−0.0210876	−	0.0365248i	−0.876377	+	0.481626i	$0.840046\pi$
$762$	−4.10756			−0.148801
$763$	−6.62229	+	20.8905i	−0.239743	+	0.756288i
$764$	−13.0121			−0.470761
$765$	5.15662	+	8.93153i	0.186438	+	0.322920i
$766$	11.4622	−	19.8530i	0.414145	−	0.717319i
$767$	0.656620	−	1.13730i	0.0237092	−	0.0410655i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	34.9116			1.25894			0.629471	−	0.777024i	$-0.283271\pi$
$769$	34.9116			1.25894			0.629471	+	0.777024i	$0.283271\pi$
$770$	7.99615	+	8.75340i	0.288161	+	0.315451i
$771$	8.84425			0.318518
$772$	2.47504	+	4.28689i	0.0890785	+	0.154288i
$773$	15.1687	−	26.2730i	0.545580	−	0.944973i	−0.452990	−	0.891516i	$-0.649643\pi$
$773$	15.1687	−	26.2730i	0.545580	−	0.944973i	0.998570	−	0.0534573i	$-0.0170241\pi$
$774$	0.156620	−	0.271275i	0.00562961	−	0.00975076i
$775$	1.93587	+	3.35303i	0.0695385	+	0.120444i
$776$	9.36581			0.336213
$777$	3.16652	−	0.696864i	0.113598	−	0.0249998i
$778$	−10.4707			−0.375394
$779$	38.5771	+	66.8175i	1.38217	+	2.39398i
$780$	−1.82831	+	3.16673i	−0.0654640	+	0.113387i
$781$	−1.60624	+	2.78209i	−0.0574757	+	0.0995508i
$782$	6.00132	+	10.3946i	0.214607	+	0.371710i
$783$	1.00000			0.0357371
$784$	−5.72162	−	4.03275i	−0.204344	−	0.144027i
$785$	−9.72898			−0.347242
$786$	−7.97723	−	13.8170i	−0.284538	−	0.492835i
$787$	9.52243	−	16.4933i	0.339438	−	0.587924i	−0.644889	−	0.764276i	$-0.723096\pi$
$787$	9.52243	−	16.4933i	0.339438	−	0.587924i	0.984327	+	0.176352i	$0.0564297\pi$
$788$	4.86967	−	8.43451i	0.173475	−	0.300467i
$789$	15.6300	+	27.0719i	0.556443	+	0.963787i
$790$	−21.0724			−0.749721
$791$	26.2729	−	5.78194i	0.934156	−	0.205582i
$792$	2.34338			0.0832684
$793$	2.18544	+	3.78529i	0.0776071	+	0.134419i
$794$	−1.86098	+	3.22331i	−0.0660436	+	0.114391i
$795$	−4.91223	+	8.50823i	−0.174219	+	0.301756i
$796$	−5.55125	−	9.61505i	−0.196759	−	0.340796i
$797$	20.3012			0.719104			0.359552	−	0.933125i	$-0.382930\pi$
$797$	20.3012			0.719104			0.359552	+	0.933125i	$0.382930\pi$
$798$	11.1089	+	12.1609i	0.393250	+	0.430492i
$799$	−0.310828			−0.0109963
$800$	−0.671690	−	1.16340i	−0.0237478	−	0.0411324i
$801$	1.14155	−	1.97722i	0.0403347	−	0.0698618i
$802$	−8.85460	+	15.3366i	−0.312667	+	0.541555i
$803$	−12.7857	−	22.1456i	−0.451199	−	0.781500i
$804$	−6.36317			−0.224412
$805$	−3.40233	+	10.7329i	−0.119917	+	0.378286i
$806$	−5.51122			−0.194124
$807$	−2.81709	−	4.87935i	−0.0991664	−	0.171761i
$808$	−8.97723	+	15.5490i	−0.315818	+	0.547012i
$809$	−4.58139	+	7.93520i	−0.161073	+	0.278987i	−0.935254	−	0.353978i	$-0.884829\pi$
$809$	−4.58139	+	7.93520i	−0.161073	+	0.278987i	0.774181	+	0.632965i	$0.218162\pi$
$810$	0.956115	+	1.65604i	0.0335944	+	0.0581873i
$811$	42.6757			1.49855			0.749274	−	0.662260i	$-0.230403\pi$
$811$	42.6757			1.49855			0.749274	+	0.662260i	$0.230403\pi$
$812$	0.799494	−	2.52206i	0.0280567	−	0.0885071i
$813$	−4.03784			−0.141613
$814$	1.43587	+	2.48700i	0.0503272	+	0.0871693i
$815$	−16.1816	+	28.0273i	−0.566816	+	0.981754i
$816$	2.69665	−	4.67074i	0.0944018	−	0.163509i
$817$	0.975036	+	1.68881i	0.0341122	+	0.0590840i
$818$	−26.3581			−0.921590
$819$	3.41223	+	3.73538i	0.119233	+	0.130525i
$820$	23.6988			0.827600
$821$	4.88594	+	8.46270i	0.170521	+	0.295350i	0.938602	−	0.345002i	$-0.112122\pi$
$821$	4.88594	+	8.46270i	0.170521	+	0.295350i	−0.768081	+	0.640352i	$0.778788\pi$
$822$	−4.71558	+	8.16762i	−0.164475	+	0.284878i
$823$	−0.553780	+	0.959176i	−0.0193036	+	0.0334348i	−0.875516	−	0.483189i	$-0.839478\pi$
$823$	−0.553780	+	0.959176i	−0.0193036	+	0.0334348i	0.856212	+	0.516624i	$0.172812\pi$
$824$	−8.53871	−	14.7895i	−0.297460	−	0.515216i
$825$	3.14805			0.109601
$826$	−1.77453	+	0.390526i	−0.0617438	+	0.0135881i
$827$	−50.5378			−1.75737			−0.878686	−	0.477401i	$-0.841579\pi$
$827$	−50.5378			−1.75737			−0.878686	+	0.477401i	$0.841579\pi$
$828$	1.11274	+	1.92731i	0.0386702	+	0.0669788i
$829$	−4.31709	+	7.47742i	−0.149939	+	0.259702i	−0.931205	−	0.364497i	$-0.881241\pi$
$829$	−4.31709	+	7.47742i	−0.149939	+	0.259702i	0.781266	+	0.624198i	$0.214574\pi$
$830$	17.0349	−	29.5052i	0.591289	−	1.02414i
$831$	2.78828	+	4.82944i	0.0967242	+	0.167531i
$832$	1.91223			0.0662946
$833$	3.40672	−	37.5991i	0.118036	−	1.30273i
$834$	14.8442			0.514014
$835$	−23.2389	−	40.2509i	−0.804215	−	1.39294i
$836$	−7.29432	+	12.6341i	−0.252279	+	0.436961i
$837$	−1.44105	+	2.49596i	−0.0498098	+	0.0862731i
$838$	17.5272	+	30.3579i	0.605466	+	1.04870i
$839$	−2.15311			−0.0743335			−0.0371667	−	0.999309i	$-0.511833\pi$
$839$	−2.15311			−0.0743335			−0.0371667	+	0.999309i	$0.511833\pi$
$840$	4.94105	−	1.08739i	0.170482	−	0.0375185i
$841$	1.00000			0.0344828
$842$	−4.71425	−	8.16532i	−0.162464	−	0.281396i
$843$	−1.36834	+	2.37004i	−0.0471283	+	0.0816285i
$844$	7.92598	−	13.7282i	0.272823	−	0.472544i
$845$	8.93334	+	15.4730i	0.307316	+	0.532287i
$846$	−0.0576321			−0.00198143
$847$	−9.82963	−	10.7605i	−0.337750	−	0.369736i
$848$	5.13770			0.176429
$849$	−0.0976657	−	0.169162i	−0.00335188	−	0.00580562i
$850$	3.62263	−	6.27458i	0.124255	−	0.215216i
$851$	−1.36362	+	2.36187i	−0.0467444	+	0.0809637i
$852$	0.685436	+	1.18721i	0.0234827	+	0.0406732i
$853$	33.7437			1.15536			0.577681	−	0.816262i	$-0.303958\pi$
$853$	33.7437			1.15536			0.577681	+	0.816262i	$0.303958\pi$
$854$	1.82744	−	5.76480i	0.0625338	−	0.197267i
$855$	−11.9045			−0.407126
$856$	6.54003	+	11.3277i	0.223534	+	0.387172i
$857$	−3.20919	+	5.55849i	−0.109624	+	0.189874i	−0.915618	−	0.402049i	$-0.868298\pi$
$857$	−3.20919	+	5.55849i	−0.109624	+	0.189874i	0.805994	+	0.591924i	$0.201631\pi$
$858$	−2.24054	+	3.88073i	−0.0764908	+	0.132486i
$859$	−26.8955	−	46.5844i	−0.917663	−	1.58944i	−0.802956	−	0.596039i	$-0.796740\pi$
$859$	−26.8955	−	46.5844i	−0.917663	−	1.58944i	−0.114707	−	0.993399i	$-0.536593\pi$
$860$	0.598988			0.0204253
$861$	9.90838	−	31.2567i	0.337677	−	1.06523i
$862$	−15.7411			−0.536143
$863$	−18.9369	−	32.7996i	−0.644618	−	1.11651i	−0.984390	−	0.176003i	$-0.943683\pi$
$863$	−18.9369	−	32.7996i	−0.644618	−	1.11651i	0.339772	−	0.940508i	$-0.389650\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	13.4119	−	23.2301i	0.456018	−	0.789846i
$866$	0.848554	+	1.46974i	0.0288350	+	0.0499438i
$867$	12.0878			0.410522
$868$	5.14287	+	5.62992i	0.174561	+	0.191092i
$869$	−25.8236			−0.876004
$870$	0.956115	+	1.65604i	0.0324153	+	0.0561450i
$871$	6.08392	−	10.5377i	0.206146	−	0.357055i
$872$	−4.14155	+	7.17338i	−0.140251	+	0.242921i
$873$	4.68291	+	8.11103i	0.158492	+	0.274517i
$874$	−13.8546			−0.468639
$875$	31.3429	−	6.89772i	1.05958	−	0.233186i
$876$	−10.9122			−0.368690
$877$	−6.06885	−	10.5116i	−0.204930	−	0.354950i	0.745180	−	0.666863i	$-0.232364\pi$
$877$	−6.06885	−	10.5116i	−0.204930	−	0.354950i	−0.950111	+	0.311913i	$0.899030\pi$
$878$	−12.2956	+	21.2967i	−0.414958	+	0.718728i
$879$	7.93587	−	13.7453i	0.267670	−	0.463619i
$880$	2.24054	+	3.88073i	0.0755286	+	0.130819i
$881$	21.1403			0.712236			0.356118	−	0.934441i	$-0.384100\pi$
$881$	21.1403			0.712236			0.356118	+	0.934441i	$0.384100\pi$
$882$	0.631656	−	6.97144i	0.0212690	−	0.234741i
$883$	40.4657			1.36178			0.680889	−	0.732387i	$-0.261594\pi$
$883$	40.4657			1.36178			0.680889	+	0.732387i	$0.261594\pi$
$884$	5.15662	+	8.93153i	0.173436	+	0.300400i
$885$	0.656620	−	1.13730i	0.0220721	−	0.0382299i
$886$	10.6240	−	18.4012i	0.356919	−	0.618201i
$887$	−5.54774	−	9.60896i	−0.186275	−	0.322637i	0.757731	−	0.652568i	$-0.226308\pi$
$887$	−5.54774	−	9.60896i	−0.186275	−	0.322637i	−0.944005	+	0.329930i	$0.892975\pi$
$888$	1.22547			0.0411241
$889$	−10.6136	+	2.33576i	−0.355969	+	0.0783390i
$890$	4.36581			0.146342
$891$	1.17169	+	2.02943i	0.0392531	+	0.0679883i
$892$	12.1240	−	20.9993i	0.405940	−	0.703109i
$893$	0.179394	−	0.310719i	0.00600317	−	0.0103978i
$894$	−9.63770	−	16.6930i	−0.322333	−	0.558297i
$895$	−18.7340			−0.626210
$896$	−1.78442	−	1.95341i	−0.0596134	−	0.0652590i
$897$	−4.25561			−0.142091
$898$	−15.6665	−	27.1352i	−0.522798	−	0.905513i
$899$	−1.44105	+	2.49596i	−0.0480615	+	0.0832450i
$900$	0.671690	−	1.16340i	0.0223897	−	0.0387800i
$901$	13.8546	+	23.9969i	0.461564	+	0.799452i
$902$	29.0422			0.967000
$903$	0.250434	−	0.790014i	0.00833393	−	0.0262900i
$904$	10.1678			0.338177
$905$	−5.30301	−	9.18508i	−0.176278	−	0.305322i
$906$	2.19665	−	3.80472i	0.0729789	−	0.126403i
$907$	7.40320	−	12.8227i	0.245819	−	0.425772i	−0.716542	−	0.697544i	$-0.754276\pi$
$907$	7.40320	−	12.8227i	0.245819	−	0.425772i	0.962362	+	0.271772i	$0.0876097\pi$
$908$	−1.68544	−	2.91926i	−0.0559332	−	0.0968791i
$909$	−17.9545			−0.595512
$910$	−2.92345	+	9.22223i	−0.0969113	+	0.305714i
$911$	−17.6445			−0.584590			−0.292295	−	0.956328i	$-0.594419\pi$
$911$	−17.6445			−0.584590			−0.292295	+	0.956328i	$0.594419\pi$
$912$	3.11274	+	5.39142i	0.103073	+	0.178528i
$913$	20.8757	−	36.1578i	0.690885	−	1.19665i
$914$	11.8705	−	20.5604i	0.392642	−	0.680077i
$915$	2.18544	+	3.78529i	0.0722483	+	0.125138i
$916$	6.93202			0.229040
$917$	−28.4695	−	31.1657i	−0.940146	−	1.02918i
$918$	5.39331			0.178006
$919$	3.62516	+	6.27896i	0.119583	+	0.207124i	0.919602	−	0.392850i	$-0.128511\pi$
$919$	3.62516	+	6.27896i	0.119583	+	0.207124i	−0.800020	+	0.599974i	$0.795178\pi$
$920$	−2.12780	+	3.68547i	−0.0701516	+	0.121506i
$921$	4.22679	−	7.32102i	0.139278	−	0.241236i
$922$	5.11659	+	8.86219i	0.168506	+	0.291861i
$923$	−2.62142			−0.0862852
$924$	6.05510	−	1.33256i	0.199198	−	0.0438381i
$925$	1.64627			0.0541291
$926$	12.4385	+	21.5441i	0.408755	+	0.707984i
$927$	8.53871	−	14.7895i	0.280448	−	0.485750i
$928$	0.500000	−	0.866025i	0.0164133	−	0.0284287i
$929$	−29.0233	−	50.2698i	−0.952224	−	1.64930i	−0.740597	−	0.671949i	$-0.765457\pi$
$929$	−29.0233	−	50.2698i	−0.952224	−	1.64930i	−0.211626	−	0.977351i	$-0.567876\pi$
$930$	−5.51122			−0.180720
$931$	35.6198	+	25.1058i	1.16739	+	0.822809i
$932$	16.8667			0.552487
$933$	7.13385	+	12.3562i	0.233552	+	0.404523i
$934$	−0.540034	+	0.935366i	−0.0176704	+	0.0306061i
$935$	−12.0839	+	20.9300i	−0.395186	+	0.684483i
$936$	0.956115	+	1.65604i	0.0312516	+	0.0541293i
$937$	−25.2428			−0.824648			−0.412324	−	0.911037i	$-0.635283\pi$
$937$	−25.2428			−0.824648			−0.412324	+	0.911037i	$0.635283\pi$
$938$	−16.4419	+	3.61842i	−0.536848	+	0.118145i
$939$	−13.4586			−0.439206
$940$	−0.0551029	−	0.0954410i	−0.00179726	−	0.00311294i
$941$	2.75429	−	4.77056i	0.0897872	−	0.155516i	−0.817634	−	0.575738i	$-0.804715\pi$
$941$	2.75429	−	4.77056i	0.0897872	−	0.155516i	0.907421	+	0.420223i	$0.138048\pi$
$942$	−2.54389	+	4.40614i	−0.0828843	+	0.143560i
$943$	13.7905	+	23.8858i	0.449079	+	0.777828i
$944$	−0.686759			−0.0223521
$945$	3.41223	+	3.73538i	0.111000	+	0.121512i
$946$	0.734042			0.0238658
$947$	−8.72294	−	15.1086i	−0.283457	−	0.490963i	0.688776	−	0.724974i	$-0.258148\pi$
$947$	−8.72294	−	15.1086i	−0.283457	−	0.490963i	−0.972234	+	0.234011i	$0.924815\pi$
$948$	−5.50989	+	9.54342i	−0.178953	+	0.309956i
$949$	10.4333	−	18.0711i	0.338681	−	0.586612i
$950$	4.18158	+	7.24272i	0.135669	+	0.234985i
$951$	7.01979			0.227632
$952$	4.31192	−	13.6023i	0.139750	−	0.440852i
$953$	9.10492			0.294937			0.147469	−	0.989067i	$-0.452887\pi$
$953$	9.10492			0.294937			0.147469	+	0.989067i	$0.452887\pi$
$954$	2.56885	+	4.44938i	0.0831696	+	0.144054i
$955$	12.4410	−	21.5485i	0.402583	−	0.697294i
$956$	2.28057	−	3.95007i	0.0737590	−	0.127754i
$957$	1.17169	+	2.02943i	0.0378754	+	0.0656020i
$958$	−16.1903			−0.523084
$959$	−7.54015	+	23.7860i	−0.243484	+	0.768089i
$960$	1.91223			0.0617169
$961$	11.3468	+	19.6532i	0.366025	+	0.633974i
$962$	−1.17169	+	2.02943i	−0.0377768	+	0.0654313i
$963$	−6.54003	+	11.3277i	−0.210750	+	0.365029i
$964$	12.5925	+	21.8108i	0.405577	+	0.702480i
$965$	−9.46567			−0.304711
$966$	3.97118	+	4.34727i	0.127771	+	0.139871i
$967$	−31.9897			−1.02872			−0.514359	−	0.857575i	$-0.671970\pi$
$967$	−31.9897			−1.02872			−0.514359	+	0.857575i	$0.671970\pi$
$968$	−2.75429	−	4.77056i	−0.0885261	−	0.153332i
$969$	−16.7879	+	29.0776i	−0.539306	+	0.934106i
$970$	−8.95479	+	15.5102i	−0.287521	+	0.498001i
$971$	18.0886	+	31.3304i	0.580492	+	1.00544i	0.995421	+	0.0955879i	$0.0304731\pi$
$971$	18.0886	+	31.3304i	0.580492	+	1.00544i	−0.414929	+	0.909854i	$0.636194\pi$
$972$	1.00000			0.0320750
$973$	38.3563	−	8.44118i	1.22965	−	0.270612i
$974$	4.45864			0.142864
$975$	1.28442	+	2.22469i	0.0411345	+	0.0712471i
$976$	1.14287	−	1.97952i	0.0365825	−	0.0633627i
$977$	−11.3469	+	19.6534i	−0.363019	+	0.628768i	−0.988456	−	0.151507i	$-0.951587\pi$
$977$	−11.3469	+	19.6534i	−0.363019	+	0.628768i	0.625437	+	0.780275i	$0.284921\pi$
$978$	8.46216	+	14.6569i	0.270590	+	0.468676i
$979$	5.35017			0.170992
$980$	12.1489	−	5.61945i	0.388083	−	0.179507i
$981$	−8.28310			−0.264459
$982$	6.76683	+	11.7205i	0.215938	+	0.374016i
$983$	9.43115	−	16.3352i	0.300807	−	0.521013i	−0.675512	−	0.737349i	$-0.736077\pi$
$983$	9.43115	−	16.3352i	0.300807	−	0.521013i	0.976319	+	0.216336i	$0.0694107\pi$
$984$	6.19665	−	10.7329i	0.197542	−	0.342153i
$985$	9.31192	+	16.1287i	0.296702	+	0.513904i
$986$	5.39331			0.171758
$987$	−0.148917	+	0.0327725i	−0.00474007	+	0.00104316i
$988$	−11.9045			−0.378733
$989$	0.348554	+	0.603713i	0.0110834	+	0.0191970i
$990$	−2.24054	+	3.88073i	−0.0712090	+	0.123338i
$991$	−7.43587	+	12.8793i	−0.236208	+	0.409125i	−0.959623	−	0.281289i	$-0.909238\pi$
$991$	−7.43587	+	12.8793i	−0.236208	+	0.409125i	0.723415	+	0.690414i	$0.242571\pi$
$992$	1.44105	+	2.49596i	0.0457532	+	0.0792469i
$993$	−29.6687			−0.941508
$994$	2.44622	+	2.67788i	0.0775894	+	0.0849373i
$995$	21.2305			0.673053
$996$	−8.90838	−	15.4298i	−0.282273	−	0.488911i
$997$	10.9298	−	18.9310i	0.346151	−	0.599551i	−0.639411	−	0.768865i	$-0.720822\pi$
$997$	10.9298	−	18.9310i	0.346151	−	0.599551i	0.985562	+	0.169314i	$0.0541551\pi$
$998$	−2.12010	+	3.67212i	−0.0671106	+	0.116239i
$999$	0.612735	+	1.06129i	0.0193861	+	0.0335777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1218.2.i.d.697.1	✓	6
7.2	even	3	inner	1218.2.i.d.1045.1	yes	6
7.3	odd	6		8526.2.a.bp.1.1		3
7.4	even	3		8526.2.a.bs.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1218.2.i.d.697.1	✓	6	1.1	even	1	trivial
1218.2.i.d.1045.1	yes	6	7.2	even	3	inner
8526.2.a.bp.1.1		3	7.3	odd	6
8526.2.a.bs.1.3		3	7.4	even	3

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:	\( N \)	\(=\)	\( 1218 = 2 \cdot 3 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1218.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.956115 - 1.65604i) q^{5} -1.00000 q^{6} +(-2.58392 + 0.568650i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.956115 - 1.65604i) q^{10} +(1.17169 - 2.02943i) q^{11} +(-0.500000 - 0.866025i) q^{12} +1.91223 q^{13} +(-1.78442 - 1.95341i) q^{14} +1.91223 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.69665 - 4.67074i) q^{17} +(0.500000 - 0.866025i) q^{18} +(3.11274 + 5.39142i) q^{19} +1.91223 q^{20} +(0.799494 - 2.52206i) q^{21} +2.34338 q^{22} +(1.11274 + 1.92731i) q^{23} +(0.500000 - 0.866025i) q^{24} +(0.671690 - 1.16340i) q^{25} +(0.956115 + 1.65604i) q^{26} +1.00000 q^{27} +(0.799494 - 2.52206i) q^{28} +1.00000 q^{29} +(0.956115 + 1.65604i) q^{30} +(-1.44105 + 2.49596i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.17169 + 2.02943i) q^{33} +5.39331 q^{34} +(3.41223 + 3.73538i) q^{35} +1.00000 q^{36} +(0.612735 + 1.06129i) q^{37} +(-3.11274 + 5.39142i) q^{38} +(-0.956115 + 1.65604i) q^{39} +(0.956115 + 1.65604i) q^{40} +12.3933 q^{41} +(2.58392 - 0.568650i) q^{42} +0.313241 q^{43} +(1.17169 + 2.02943i) q^{44} +(-0.956115 + 1.65604i) q^{45} +(-1.11274 + 1.92731i) q^{46} +(-0.0288161 - 0.0499109i) q^{47} +1.00000 q^{48} +(6.35327 - 2.93869i) q^{49} +1.34338 q^{50} +(2.69665 + 4.67074i) q^{51} +(-0.956115 + 1.65604i) q^{52} +(-2.56885 + 4.44938i) q^{53} +(0.500000 + 0.866025i) q^{54} -4.48108 q^{55} +(2.58392 - 0.568650i) q^{56} -6.22547 q^{57} +(0.500000 + 0.866025i) q^{58} +(0.343380 - 0.594751i) q^{59} +(-0.956115 + 1.65604i) q^{60} +(1.14287 + 1.97952i) q^{61} -2.88209 q^{62} +(1.78442 + 1.95341i) q^{63} +1.00000 q^{64} +(-1.82831 - 3.16673i) q^{65} +(-1.17169 + 2.02943i) q^{66} +(3.18158 - 5.51067i) q^{67} +(2.69665 + 4.67074i) q^{68} -2.22547 q^{69} +(-1.52882 + 4.82277i) q^{70} -1.37087 q^{71} +(0.500000 + 0.866025i) q^{72} +(5.45611 - 9.45027i) q^{73} +(-0.612735 + 1.06129i) q^{74} +(0.671690 + 1.16340i) q^{75} -6.22547 q^{76} +(-1.87352 + 5.91015i) q^{77} -1.91223 q^{78} +(-5.50989 - 9.54342i) q^{79} +(-0.956115 + 1.65604i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.19665 + 10.7329i) q^{82} +17.8168 q^{83} +(1.78442 + 1.95341i) q^{84} -10.3132 q^{85} +(0.156620 + 0.271275i) q^{86} +(-0.500000 + 0.866025i) q^{87} +(-1.17169 + 2.02943i) q^{88} +(1.14155 + 1.97722i) q^{89} -1.91223 q^{90} +(-4.94105 + 1.08739i) q^{91} -2.22547 q^{92} +(-1.44105 - 2.49596i) q^{93} +(0.0288161 - 0.0499109i) q^{94} +(5.95226 - 10.3096i) q^{95} +(0.500000 + 0.866025i) q^{96} -9.36581 q^{97} +(5.72162 + 4.03275i) q^{98} -2.34338 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + q^{5} - 6 q^{6} - 4 q^{7} - 6 q^{8} - 3 q^{9} - q^{10} + 9 q^{11} - 3 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 8 q^{19} - 2 q^{20}+ \cdots - 18 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + q^5 - 6 * q^6 - 4 * q^7 - 6 * q^8 - 3 * q^9 - q^10 + 9 * q^11 - 3 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 8 * q^19 - 2 * q^20 + 2 * q^21 + 18 * q^22 - 4 * q^23 + 3 * q^24 + 6 * q^25 - q^26 + 6 * q^27 + 2 * q^28 + 6 * q^29 - q^30 + 4 * q^31 + 3 * q^32 + 9 * q^33 - 12 * q^34 + 7 * q^35 + 6 * q^36 - 7 * q^37 - 8 * q^38 + q^39 - q^40 + 30 * q^41 + 4 * q^42 - 6 * q^43 + 9 * q^44 + q^45 + 4 * q^46 - q^47 + 6 * q^48 + 12 * q^49 + 12 * q^50 - 6 * q^51 + q^52 + 2 * q^53 + 3 * q^54 + 4 * q^55 + 4 * q^56 - 16 * q^57 + 3 * q^58 + 6 * q^59 + q^60 + 8 * q^61 + 8 * q^62 + 2 * q^63 + 6 * q^64 - 9 * q^65 - 9 * q^66 - 9 * q^67 - 6 * q^68 + 8 * q^69 - 10 * q^70 - 2 * q^71 + 3 * q^72 + 26 * q^73 + 7 * q^74 + 6 * q^75 - 16 * q^76 - 27 * q^77 + 2 * q^78 - 3 * q^79 + q^80 - 3 * q^81 + 15 * q^82 + 30 * q^83 + 2 * q^84 - 54 * q^85 - 3 * q^86 - 3 * q^87 - 9 * q^88 - 3 * q^89 + 2 * q^90 - 17 * q^91 + 8 * q^92 + 4 * q^93 + q^94 + 4 * q^95 + 3 * q^96 - 22 * q^97 - 12 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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