LMFDB - Embedded newform 114.2.l.b.59.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(29,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 17]))

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

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

chi := DirichletCharacter("114.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.l (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + \cdots + 19683 $ x^18 - x^15 - 18x^14 + 36x^13 + 10x^12 + 18x^11 + 90x^10 - 567x^9 + 270x^8 + 162x^7 + 270x^6 + 2916x^5 - 4374x^4 - 729x^3 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			59.3
Root			$-1.72388 + 0.168030i$ of defining polynomial
Character	$\chi$	$=$	114.59
Dual form			114.2.l.b.29.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.173648 - 0.984808i) q^{2} +(1.67739 + 0.431705i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(1.14133 + 3.13578i) q^{5} +(0.716422 - 1.57694i) q^{6} +(-1.07356 - 1.85947i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.62726 + 1.44827i) q^{9} +(3.28633 - 0.579469i) q^{10} +(-5.41799 - 3.12808i) q^{11} +(-1.42858 - 0.979371i) q^{12} +(-2.56208 - 3.05336i) q^{13} +(-2.01764 + 0.734361i) q^{14} +(0.560722 + 5.75264i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-0.403611 - 0.0711674i) q^{17} +(1.88249 - 2.33586i) q^{18} +(4.34640 - 0.329887i) q^{19} -3.33703i q^{20} +(-0.998042 - 3.58251i) q^{21} +(-4.02138 + 4.79249i) q^{22} +(-0.280411 + 0.770422i) q^{23} +(-1.21256 + 1.23681i) q^{24} +(-4.70025 + 3.94398i) q^{25} +(-3.45187 + 1.99294i) q^{26} +(3.78171 + 3.56352i) q^{27} +(0.372845 + 2.11451i) q^{28} +(0.805141 + 4.56618i) q^{29} +(5.76261 + 0.446732i) q^{30} +(-2.02597 + 1.16970i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-7.73767 - 7.58597i) q^{33} +(-0.140172 + 0.385121i) q^{34} +(4.60559 - 5.48872i) q^{35} +(-1.97348 - 2.25951i) q^{36} +6.01346i q^{37} +(0.429869 - 4.33765i) q^{38} +(-2.97944 - 6.22774i) q^{39} +(-3.28633 - 0.579469i) q^{40} +(0.926617 + 0.777524i) q^{41} +(-3.70139 + 0.360783i) q^{42} +(5.87377 - 2.13788i) q^{43} +(4.02138 + 4.79249i) q^{44} +(-1.54289 + 9.89147i) q^{45} +(0.710025 + 0.409933i) q^{46} +(-7.59919 + 1.33994i) q^{47} +(1.00746 + 1.40891i) q^{48} +(1.19492 - 2.06967i) q^{49} +(3.06787 + 5.31371i) q^{50} +(-0.646288 - 0.293616i) q^{51} +(1.36325 + 3.74550i) q^{52} +(-0.220516 - 0.0802612i) q^{53} +(4.16607 - 3.10546i) q^{54} +(3.62525 - 20.5598i) q^{55} +2.14713 q^{56} +(7.43301 + 1.32301i) q^{57} +4.63662 q^{58} +(0.930375 - 5.27642i) q^{59} +(1.44061 - 5.59749i) q^{60} +(7.30705 + 2.65955i) q^{61} +(0.800119 + 2.19831i) q^{62} +(-0.127515 - 6.44012i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(6.65050 - 11.5190i) q^{65} +(-8.81436 + 6.30282i) q^{66} +(3.48689 - 0.614832i) q^{67} +(0.354929 + 0.204918i) q^{68} +(-0.802953 + 1.17124i) q^{69} +(-4.60559 - 5.48872i) q^{70} +(4.19799 - 1.52794i) q^{71} +(-2.56787 + 1.55114i) q^{72} +(-4.33185 - 3.63485i) q^{73} +(5.92210 + 1.04423i) q^{74} +(-9.58679 + 4.58646i) q^{75} +(-4.19711 - 1.17656i) q^{76} +13.4328i q^{77} +(-6.65050 + 1.85274i) q^{78} +(-8.05412 + 9.59853i) q^{79} +(-1.14133 + 3.13578i) q^{80} +(4.80501 + 7.60999i) q^{81} +(0.926617 - 0.777524i) q^{82} +(8.01579 - 4.62792i) q^{83} +(-0.287438 + 3.70781i) q^{84} +(-0.237488 - 1.34686i) q^{85} +(-1.08543 - 6.15577i) q^{86} +(-0.620710 + 8.00685i) q^{87} +(5.41799 - 3.12808i) q^{88} +(-5.61888 + 4.71480i) q^{89} +(9.47328 + 3.23709i) q^{90} +(-2.92708 + 8.04207i) q^{91} +(0.527000 - 0.628054i) q^{92} +(-3.90331 + 1.08741i) q^{93} +7.71642i q^{94} +(5.99513 + 13.2528i) q^{95} +(1.56245 - 0.747499i) q^{96} +(-16.0734 - 2.83418i) q^{97} +(-1.83073 - 1.53616i) q^{98} +(-9.70416 - 16.0650i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9} - 12 q^{13} - 12 q^{14} + 18 q^{15} + 6 q^{17} - 6 q^{19} - 24 q^{22} + 3 q^{24} - 18 q^{25} + 18 q^{26} - 6 q^{27} + 6 q^{28} - 6 q^{29} - 24 q^{33} - 6 q^{34} - 24 q^{35}+ \cdots - 102 q^{99}+O(q^{100}) $ 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9 - 12 * q^13 - 12 * q^14 + 18 * q^15 + 6 * q^17 - 6 * q^19 - 24 * q^22 + 3 * q^24 - 18 * q^25 + 18 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 - 24 * q^33 - 6 * q^34 - 24 * q^35 + 3 * q^38 + 6 * q^39 + 3 * q^41 - 6 * q^43 + 24 * q^44 - 54 * q^45 + 18 * q^46 + 30 * q^47 + 21 * q^49 + 3 * q^50 + 42 * q^51 - 6 * q^52 - 60 * q^53 + 54 * q^54 + 30 * q^55 + 12 * q^57 + 12 * q^58 + 3 * q^59 + 24 * q^60 + 54 * q^61 + 6 * q^62 - 18 * q^63 - 9 * q^64 + 24 * q^65 - 27 * q^66 - 15 * q^67 - 27 * q^68 + 30 * q^69 + 24 * q^70 + 36 * q^71 + 6 * q^72 - 42 * q^73 + 6 * q^74 - 24 * q^78 - 6 * q^79 - 3 * q^81 + 3 * q^82 + 36 * q^83 - 30 * q^84 - 6 * q^86 - 60 * q^89 - 18 * q^91 - 66 * q^93 + 6 * q^95 + 9 * q^97 + 12 * q^98 - 102 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$-1$	$e\left(\frac{1}{18}\right)$

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 $

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$	1.67739	+	0.431705i	0.968440	+	0.249245i
$3$	1.67739	+	0.431705i	0.968440	+	0.249245i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	1.14133	+	3.13578i	0.510418	+	1.40236i	0.880802	+	0.473484i	$0.157004\pi$
$5$	1.14133	+	3.13578i	0.510418	+	1.40236i	−0.370384	+	0.928879i	$0.620774\pi$
$6$	0.716422	−	1.57694i	0.292478	−	0.643783i
$7$	−1.07356	−	1.85947i	−0.405769	−	0.702812i	0.588642	−	0.808394i	$-0.299663\pi$
$7$	−1.07356	−	1.85947i	−0.405769	−	0.702812i	−0.994411	+	0.105582i	$0.966330\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	2.62726	+	1.44827i	0.875754	+	0.482758i
$10$	3.28633	−	0.579469i	1.03923	−	0.183244i
$11$	−5.41799	−	3.12808i	−1.63359	−	0.943151i	−0.982975	−	0.183740i	$-0.941180\pi$
$11$	−5.41799	−	3.12808i	−1.63359	−	0.943151i	−0.650611	−	0.759412i	$-0.725487\pi$
$12$	−1.42858	−	0.979371i	−0.412395	−	0.282720i
$13$	−2.56208	−	3.05336i	−0.710592	−	0.846850i	0.283089	−	0.959094i	$-0.408641\pi$
$13$	−2.56208	−	3.05336i	−0.710592	−	0.846850i	−0.993681	+	0.112243i	$0.964196\pi$
$14$	−2.01764	+	0.734361i	−0.539237	+	0.196266i
$15$	0.560722	+	5.75264i	0.144778	+	1.48532i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−0.403611	−	0.0711674i	−0.0978899	−	0.0172606i	0.124489	−	0.992221i	$-0.460271\pi$
$17$	−0.403611	−	0.0711674i	−0.0978899	−	0.0172606i	−0.222379	+	0.974960i	$0.571382\pi$
$18$	1.88249	−	2.33586i	0.443707	−	0.550567i
$19$	4.34640	−	0.329887i	0.997132	−	0.0756812i
$19$	4.34640	−	0.329887i	0.997132	−	0.0756812i
$20$		−	3.33703i		−	0.746182i
$21$	−0.998042	−	3.58251i	−0.217791	−	0.781768i
$22$	−4.02138	+	4.79249i	−0.857361	+	1.02176i
$23$	−0.280411	+	0.770422i	−0.0584697	+	0.160644i	−0.965488	−	0.260446i	$-0.916130\pi$
$23$	−0.280411	+	0.770422i	−0.0584697	+	0.160644i	0.907019	+	0.421090i	$0.138353\pi$
$24$	−1.21256	+	1.23681i	−0.247513	+	0.252462i
$25$	−4.70025	+	3.94398i	−0.940051	+	0.788796i
$26$	−3.45187	+	1.99294i	−0.676968	+	0.390848i
$27$	3.78171	+	3.56352i	0.727790	+	0.685800i
$28$	0.372845	+	2.11451i	0.0704610	+	0.399604i
$29$	0.805141	+	4.56618i	0.149511	+	0.847919i	0.963634	+	0.267226i	$0.0861071\pi$
$29$	0.805141	+	4.56618i	0.149511	+	0.847919i	−0.814123	+	0.580693i	$0.802782\pi$
$30$	5.76261	+	0.446732i	1.05210	+	0.0815616i
$31$	−2.02597	+	1.16970i	−0.363875	+	0.210084i	−0.670779	−	0.741657i	$-0.734040\pi$
$31$	−2.02597	+	1.16970i	−0.363875	+	0.210084i	0.306904	+	0.951740i	$0.400707\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	−7.73767	−	7.58597i	−1.34695	−	1.32055i
$34$	−0.140172	+	0.385121i	−0.0240394	+	0.0660477i
$35$	4.60559	−	5.48872i	0.778486	−	0.927764i
$36$	−1.97348	−	2.25951i	−0.328913	−	0.376585i
$37$			6.01346i			0.988607i	0.869289	+	0.494303i	$0.164577\pi$
$37$			6.01346i			0.988607i	−0.869289	+	0.494303i	$0.835423\pi$
$38$	0.429869	−	4.33765i	0.0697340	−	0.703660i
$39$	−2.97944	−	6.22774i	−0.477093	−	0.997236i
$40$	−3.28633	−	0.579469i	−0.519614	−	0.0916220i
$41$	0.926617	+	0.777524i	0.144713	+	0.121429i	0.712270	−	0.701905i	$-0.247667\pi$
$41$	0.926617	+	0.777524i	0.144713	+	0.121429i	−0.567557	+	0.823334i	$0.692111\pi$
$42$	−3.70139	+	0.360783i	−0.571137	+	0.0556700i
$43$	5.87377	−	2.13788i	0.895741	−	0.326023i	0.147196	−	0.989107i	$-0.452975\pi$
$43$	5.87377	−	2.13788i	0.895741	−	0.326023i	0.748545	+	0.663084i	$0.230753\pi$
$44$	4.02138	+	4.79249i	0.606246	+	0.722496i
$45$	−1.54289	+	9.89147i	−0.230001	+	1.47453i
$46$	0.710025	+	0.409933i	0.104687	+	0.0604413i
$47$	−7.59919	+	1.33994i	−1.10846	+	0.195451i	−0.697767	−	0.716325i	$-0.745823\pi$
$47$	−7.59919	+	1.33994i	−1.10846	+	0.195451i	−0.410689	+	0.911776i	$0.634712\pi$
$48$	1.00746	+	1.40891i	0.145414	+	0.203359i
$49$	1.19492	−	2.06967i	0.170703	−	0.295666i
$50$	3.06787	+	5.31371i	0.433863	+	0.751472i
$51$	−0.646288	−	0.293616i	−0.0904984	−	0.0411145i
$52$	1.36325	+	3.74550i	0.189049	+	0.519408i
$53$	−0.220516	−	0.0802612i	−0.0302902	−	0.0110247i	0.326831	−	0.945083i	$-0.394019\pi$
$53$	−0.220516	−	0.0802612i	−0.0302902	−	0.0110247i	−0.357121	+	0.934058i	$0.616242\pi$
$54$	4.16607	−	3.10546i	0.566930	−	0.422599i
$55$	3.62525	−	20.5598i	0.488828	−	2.77228i
$56$	2.14713			0.286922
$57$	7.43301	+	1.32301i	0.984526	+	0.175237i
$58$	4.63662			0.608819
$59$	0.930375	−	5.27642i	0.121124	−	0.686931i	−0.862410	−	0.506210i	$-0.831046\pi$
$59$	0.930375	−	5.27642i	0.121124	−	0.686931i	0.983534	−	0.180721i	$-0.0578430\pi$
$60$	1.44061	−	5.59749i	0.185982	−	0.722633i
$61$	7.30705	+	2.65955i	0.935572	+	0.340520i	0.764416	−	0.644723i	$-0.223027\pi$
$61$	7.30705	+	2.65955i	0.935572	+	0.340520i	0.171156	+	0.985244i	$0.445250\pi$
$62$	0.800119	+	2.19831i	0.101615	+	0.279186i
$63$	−0.127515	−	6.44012i	−0.0160654	−	0.811379i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	6.65050	−	11.5190i	0.824893	−	1.42876i
$66$	−8.81436	+	6.30282i	−1.08497	+	0.775824i
$67$	3.48689	−	0.614832i	0.425991	−	0.0751137i	0.0434574	−	0.999055i	$-0.486163\pi$
$67$	3.48689	−	0.614832i	0.425991	−	0.0751137i	0.382534	+	0.923942i	$0.375052\pi$
$68$	0.354929	+	0.204918i	0.0430415	+	0.0248500i
$69$	−0.802953	+	1.17124i	−0.0966642	+	0.141001i
$70$	−4.60559	−	5.48872i	−0.550473	−	0.656028i
$71$	4.19799	−	1.52794i	0.498210	−	0.181334i	−0.0806788	−	0.996740i	$-0.525709\pi$
$71$	4.19799	−	1.52794i	0.498210	−	0.181334i	0.578889	+	0.815407i	$0.303487\pi$
$72$	−2.56787	+	1.55114i	−0.302627	+	0.182803i
$73$	−4.33185	−	3.63485i	−0.507005	−	0.425427i	0.353069	−	0.935597i	$-0.385138\pi$
$73$	−4.33185	−	3.63485i	−0.507005	−	0.425427i	−0.860074	+	0.510170i	$0.829583\pi$
$74$	5.92210	+	1.04423i	0.688430	+	0.121389i
$75$	−9.58679	+	4.58646i	−1.10699	+	0.529599i
$76$	−4.19711	−	1.17656i	−0.481441	−	0.134961i
$77$			13.4328i			1.53081i
$78$	−6.65050	+	1.85274i	−0.753020	+	0.209782i
$79$	−8.05412	+	9.59853i	−0.906159	+	1.07992i	0.0903059	+	0.995914i	$0.471216\pi$
$79$	−8.05412	+	9.59853i	−0.906159	+	1.07992i	−0.996465	+	0.0840047i	$0.973229\pi$
$80$	−1.14133	+	3.13578i	−0.127605	+	0.350591i
$81$	4.80501	+	7.60999i	0.533889	+	0.845554i
$82$	0.926617	−	0.777524i	0.102328	−	0.0858631i
$83$	8.01579	−	4.62792i	0.879848	−	0.507980i	0.00923947	−	0.999957i	$-0.497059\pi$
$83$	8.01579	−	4.62792i	0.879848	−	0.507980i	0.870608	+	0.491977i	$0.163726\pi$
$84$	−0.287438	+	3.70781i	−0.0313621	+	0.404555i
$85$	−0.237488	−	1.34686i	−0.0257591	−	0.146087i
$86$	−1.08543	−	6.15577i	−0.117045	−	0.663794i
$87$	−0.620710	+	8.00685i	−0.0665471	+	0.858424i
$88$	5.41799	−	3.12808i	0.577560	−	0.333454i
$89$	−5.61888	+	4.71480i	−0.595600	+	0.499767i	−0.890028	−	0.455906i	$-0.849315\pi$
$89$	−5.61888	+	4.71480i	−0.595600	+	0.499767i	0.294428	+	0.955674i	$0.404871\pi$
$90$	9.47328	+	3.23709i	0.998571	+	0.341219i
$91$	−2.92708	+	8.04207i	−0.306841	+	0.843038i
$92$	0.527000	−	0.628054i	0.0549435	−	0.0654792i
$93$	−3.90331	+	1.08741i	−0.404754	+	0.112759i
$94$			7.71642i			0.795888i
$95$	5.99513	+	13.2528i	0.615087	+	1.35971i
$96$	1.56245	−	0.747499i	0.159467	−	0.0762913i
$97$	−16.0734	−	2.83418i	−1.63201	−	0.287767i	−0.718786	−	0.695231i	$-0.755302\pi$
$97$	−16.0734	−	2.83418i	−1.63201	−	0.287767i	−0.913221	+	0.407464i	$0.866413\pi$
$98$	−1.83073	−	1.53616i	−0.184931	−	0.155176i
$99$	−9.70416	−	16.0650i	−0.975305	−	1.61459i
$100$	5.76571	−	2.09855i	0.576571	−	0.209855i
$101$	−3.69207	−	4.40004i	−0.367375	−	0.437820i	0.550412	−	0.834893i	$-0.314471\pi$
$101$	−3.69207	−	4.40004i	−0.367375	−	0.437820i	−0.917787	+	0.397073i	$0.870026\pi$
$102$	−0.401382	+	0.585484i	−0.0397428	+	0.0579715i
$103$	−0.957127	−	0.552597i	−0.0943085	−	0.0544490i	0.452104	−	0.891965i	$-0.350674\pi$
$103$	−0.957127	−	0.552597i	−0.0943085	−	0.0544490i	−0.546413	+	0.837516i	$0.684007\pi$
$104$	3.92533	−	0.692141i	0.384910	−	0.0678700i
$105$	10.0949	−	7.21847i	0.985158	−	0.704450i
$106$	−0.117334	+	0.203228i	−0.0113965	+	0.0197393i
$107$	−3.47626	−	6.02105i	−0.336062	−	0.582077i	0.647626	−	0.761958i	$-0.275762\pi$
$107$	−3.47626	−	6.02105i	−0.336062	−	0.582077i	−0.983688	+	0.179881i	$0.942429\pi$
$108$	−2.33485	−	4.64203i	−0.224671	−	0.446680i
$109$	2.42887	+	6.67327i	0.232644	+	0.639183i	0.999998	−	0.00204008i	$-0.000649379\pi$
$109$	2.42887	+	6.67327i	0.232644	+	0.639183i	−0.767354	+	0.641223i	$0.778427\pi$
$110$	−19.6179	−	7.14034i	−1.87050	−	0.680805i
$111$	−2.59604	+	10.0869i	−0.246405	+	0.957407i
$112$	0.372845	−	2.11451i	0.0352305	−	0.199802i
$113$	2.33000			0.219188			0.109594	−	0.993976i	$-0.465045\pi$
$113$	2.33000			0.219188			0.109594	+	0.993976i	$0.465045\pi$
$114$	2.59364	−	7.09035i	0.242917	−	0.664072i
$115$	−2.73592			−0.255125
$116$	0.805141	−	4.56618i	0.0747555	−	0.423960i
$117$	−2.30914	−	11.7326i	−0.213480	−	1.08468i
$118$	−5.03470	−	1.83248i	−0.463482	−	0.168693i
$119$	0.300968	+	0.826903i	0.0275897	+	0.0758021i
$120$	−5.26229	−	2.39072i	−0.480379	−	0.218242i
$121$	14.0697	+	24.3695i	1.27907	+	2.21541i
$122$	3.88800	−	6.73422i	0.352003	−	0.609687i
$123$	1.21863	+	1.70423i	0.109881	+	0.153666i
$124$	2.30385	−	0.406231i	0.206892	−	0.0364806i
$125$	−3.28225	−	1.89501i	−0.293573	−	0.169495i
$126$	−6.36442	−	0.992737i	−0.566988	−	0.0884401i
$127$	0.792153	+	0.944052i	0.0702922	+	0.0837710i	0.800045	−	0.599941i	$-0.204809\pi$
$127$	0.792153	+	0.944052i	0.0702922	+	0.0837710i	−0.729752	+	0.683712i	$0.760365\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	10.7755	−	1.05031i	0.948732	−	0.0924749i
$130$	−10.1892	−	8.54971i	−0.893648	−	0.749859i
$131$	6.34320	+	1.11848i	0.554208	+	0.0977218i	0.443736	−	0.896157i	$-0.353653\pi$
$131$	6.34320	+	1.11848i	0.554208	+	0.0977218i	0.110472	+	0.993879i	$0.464764\pi$
$132$	4.67647	+	9.77492i	0.407035	+	0.850798i
$133$	−5.27955	−	7.72783i	−0.457795	−	0.670088i
$134$		−	3.54068i		−	0.305868i
$135$	−6.85823	+	15.9258i	−0.590262	+	1.37067i
$136$	0.263438	−	0.313953i	0.0225896	−	0.0269213i
$137$	3.68452	−	10.1231i	0.314790	−	0.864878i	−0.676882	−	0.736091i	$-0.736669\pi$
$137$	3.68452	−	10.1231i	0.314790	−	0.864878i	0.991672	−	0.128787i	$-0.0411084\pi$
$138$	1.01402	+	0.994138i	0.0863189	+	0.0846267i
$139$	6.45972	−	5.42035i	0.547906	−	0.459748i	−0.326325	−	0.945258i	$-0.605810\pi$
$139$	6.45972	−	5.42035i	0.547906	−	0.459748i	0.874231	+	0.485510i	$0.161366\pi$
$140$	−6.20509	+	3.58251i	−0.524426	+	0.302777i
$141$	−13.3253	−	1.03301i	−1.12219	−	0.0869948i
$142$	−0.775757	−	4.39954i	−0.0651001	−	0.369201i
$143$	4.33014	+	24.5575i	0.362105	+	2.05360i
$144$	1.08167	+	2.79821i	0.0901389	+	0.233184i
$145$	−13.3996	+	7.73627i	−1.11278	+	0.642462i
$146$	−4.33185	+	3.63485i	−0.358506	+	0.300823i
$147$	2.89783	−	2.95578i	0.239009	−	0.243788i
$148$	2.05672	−	5.65080i	0.169062	−	0.464493i
$149$	−3.41271	+	4.06711i	−0.279580	+	0.333190i	−0.887500	−	0.460808i	$-0.847560\pi$
$149$	−3.41271	+	4.06711i	−0.279580	+	0.333190i	0.607920	+	0.793998i	$0.292004\pi$
$150$	2.85206	+	10.2376i	0.232869	+	0.835894i
$151$		−	2.55987i		−	0.208319i	−0.994561	−	0.104160i	$-0.966785\pi$
$151$		−	2.55987i		−	0.208319i	0.994561	−	0.104160i	$-0.0332153\pi$
$152$	−1.88751	+	3.92903i	−0.153097	+	0.318687i
$153$	−0.957320	−	0.771514i	−0.0773948	−	0.0623732i
$154$	13.2287	+	2.33258i	1.06600	+	0.187964i
$155$	−5.98021	−	5.01799i	−0.480342	−	0.403055i
$156$	0.669749	+	6.87119i	0.0536229	+	0.550135i
$157$	15.7565	−	5.73489i	1.25750	−	0.457694i	0.374573	−	0.927197i	$-0.377789\pi$
$157$	15.7565	−	5.73489i	1.25750	−	0.457694i	0.882931	+	0.469503i	$0.155567\pi$
$158$	8.05412	+	9.59853i	0.640751	+	0.763618i
$159$	−0.335241	−	0.229827i	−0.0265864	−	0.0182265i
$160$	2.88995	+	1.66851i	0.228471	+	0.131908i
$161$	1.73361	−	0.305683i	0.136628	−	0.0240912i
$162$	8.32876	−	3.41055i	0.654369	−	0.267958i
$163$	5.28499	−	9.15387i	0.413952	−	0.716987i	−0.581365	−	0.813643i	$-0.697481\pi$
$163$	5.28499	−	9.15387i	0.413952	−	0.716987i	0.995318	+	0.0966559i	$0.0308146\pi$
$164$	−0.604806	−	1.04755i	−0.0472274	−	0.0818003i
$165$	14.9567	−	32.9217i	1.16438	−	2.56295i
$166$	−3.16568	−	8.69765i	−0.245705	−	0.675068i
$167$	−10.5199	−	3.82893i	−0.814054	−	0.296292i	−0.0987568	−	0.995112i	$-0.531487\pi$
$167$	−10.5199	−	3.82893i	−0.814054	−	0.296292i	−0.715298	+	0.698820i	$0.753709\pi$
$168$	3.60157	+	0.926926i	0.277867	+	0.0715139i
$169$	−0.501366	+	2.84339i	−0.0385666	+	0.218722i
$170$	−1.36764			−0.104893
$171$	11.8969	+	5.42808i	0.909778	+	0.415095i
$172$	−6.25073			−0.476614
$173$	3.80558	−	21.5825i	0.289333	−	1.64089i	−0.400051	−	0.916493i	$-0.631007\pi$
$173$	3.80558	−	21.5825i	0.289333	−	1.64089i	0.689384	−	0.724396i	$-0.257881\pi$
$174$	7.77742	+	2.00165i	0.589605	+	0.151745i
$175$	12.3797	+	4.50585i	0.935819	+	0.340610i
$176$	−2.13973	−	5.87886i	−0.161288	−	0.443136i
$177$	3.83846	−	8.44895i	0.288516	−	0.635062i
$178$	3.66746	+	6.35223i	0.274888	+	0.476120i
$179$	−10.6934	+	18.5215i	−0.799263	+	1.38436i	0.120833	+	0.992673i	$0.461443\pi$
$179$	−10.6934	+	18.5215i	−0.799263	+	1.38436i	−0.920097	+	0.391692i	$0.871890\pi$
$180$	4.83293	−	8.76724i	0.360225	−	0.653472i
$181$	−18.0057	+	3.17489i	−1.33835	+	0.235988i	−0.796578	−	0.604536i	$-0.793359\pi$
$181$	−18.0057	+	3.17489i	−1.33835	+	0.235988i	−0.541775	+	0.840523i	$0.682248\pi$
$182$	7.41162	+	4.27910i	0.549386	+	0.317188i
$183$	11.1086	+	7.61559i	0.821173	+	0.562961i
$184$	−0.527000	−	0.628054i	−0.0388509	−	0.0463008i
$185$	−18.8569	+	6.86334i	−1.38639	+	0.504603i
$186$	0.393089	+	4.03283i	0.0288227	+	0.295702i
$187$	1.96414	+	1.64811i	0.143632	+	0.120522i
$188$	7.59919	+	1.33994i	0.554228	+	0.0977253i
$189$	2.56634	−	10.8576i	0.186674	−	0.789776i
$190$	14.0925	−	3.60272i	1.02238	−	0.261369i
$191$			3.46116i			0.250441i	0.992129	+	0.125220i	$0.0399638\pi$
$191$			3.46116i			0.250441i	−0.992129	+	0.125220i	$0.960036\pi$
$192$	−0.464826	−	1.66851i	−0.0335460	−	0.120415i
$193$	6.64414	−	7.91818i	0.478256	−	0.569963i	−0.471934	−	0.881634i	$-0.656444\pi$
$193$	6.64414	−	7.91818i	0.478256	−	0.569963i	0.950190	+	0.311671i	$0.100889\pi$
$194$	−5.58224	+	15.3371i	−0.400781	+	1.10114i
$195$	16.1283	−	16.4508i	1.15497	−	1.17806i
$196$	−1.83073	+	1.53616i	−0.130766	+	0.109726i
$197$	10.2877	−	5.93959i	0.732966	−	0.423178i	−0.0865400	−	0.996248i	$-0.527581\pi$
$197$	10.2877	−	5.93959i	0.732966	−	0.423178i	0.819506	+	0.573070i	$0.194248\pi$
$198$	−17.5061	+	6.76707i	−1.24410	+	0.480915i
$199$	4.24330	+	24.0650i	0.300800	+	1.70592i	0.642645	+	0.766164i	$0.277837\pi$
$199$	4.24330	+	24.0650i	0.300800	+	1.70592i	−0.341845	+	0.939756i	$0.611052\pi$
$200$	−1.06546	−	6.04253i	−0.0753395	−	0.427271i
$201$	6.11429	+	0.473995i	0.431269	+	0.0334330i
$202$	−4.97432	+	2.87192i	−0.349992	+	0.202068i
$203$	7.62630	−	6.39922i	0.535261	−	0.449137i
$204$	0.506890	+	0.496952i	0.0354894	+	0.0347936i
$205$	−1.38057	+	3.79308i	−0.0964230	+	0.264920i
$206$	−0.710405	+	0.846628i	−0.0494963	+	0.0589874i
$207$	−1.85249	+	1.61799i	−0.128757	+	0.112458i
$208$		−	3.98588i		−	0.276371i
$209$	−24.5807	−	11.8085i	−1.70028	−	0.816814i
$210$	−5.35585	−	11.1950i	−0.369588	−	0.772527i
$211$	−16.3173	−	2.87718i	−1.12333	−	0.198074i	−0.419028	−	0.907973i	$-0.637629\pi$
$211$	−16.3173	−	2.87718i	−1.12333	−	0.198074i	−0.704303	+	0.709900i	$0.748740\pi$
$212$	0.179766	+	0.150842i	0.0123464	+	0.0103598i
$213$	7.70128	−	0.750660i	0.527683	−	0.0514344i
$214$	−6.53323	+	2.37790i	−0.446602	+	0.162550i
$215$	13.4078	+	15.9788i	0.914405	+	1.08975i
$216$	−4.97695	+	1.49330i	−0.338639	+	0.101606i
$217$	4.35002	+	2.51149i	0.295299	+	0.170491i
$218$	6.99366	−	1.23317i	0.473670	−	0.0835208i
$219$	−5.69701	−	7.96714i	−0.384968	−	0.538370i
$220$	−10.4385	+	18.0800i	−0.703762	+	1.21895i
$221$	0.816781	+	1.41471i	0.0549426	+	0.0951634i
$222$	9.48286	+	4.30817i	0.636448	+	0.289146i
$223$	−4.05122	−	11.1306i	−0.271290	−	0.745362i	−0.998275	−	0.0587091i	$-0.981302\pi$
$223$	−4.05122	−	11.1306i	−0.271290	−	0.745362i	0.726986	−	0.686653i	$-0.240921\pi$
$224$	−2.01764	−	0.734361i	−0.134809	−	0.0490665i
$225$	−18.0608	+	3.55461i	−1.20405	+	0.236974i
$226$	0.404601	−	2.29460i	0.0269136	−	0.152635i
$227$	−23.0722			−1.53135			−0.765676	−	0.643226i	$-0.777595\pi$
$227$	−23.0722			−1.53135			−0.765676	+	0.643226i	$0.777595\pi$
$228$	−6.53225	−	3.78547i	−0.432609	−	0.250699i
$229$	14.0461			0.928192			0.464096	−	0.885785i	$-0.346379\pi$
$229$	14.0461			0.928192			0.464096	+	0.885785i	$0.346379\pi$
$230$	−0.475087	+	2.69435i	−0.0313263	+	0.177660i
$231$	−5.79899	+	22.5320i	−0.381546	+	1.48249i
$232$	−4.35700	−	1.58582i	−0.286051	−	0.104114i
$233$	−8.06779	−	22.1661i	−0.528539	−	1.45215i	−0.860792	−	0.508958i	$-0.830031\pi$
$233$	−8.06779	−	22.1661i	−0.528539	−	1.45215i	0.332253	−	0.943190i	$-0.392191\pi$
$234$	−11.9553	+	0.236716i	−0.781543	+	0.0154746i
$235$	−12.8749	−	22.3001i	−0.839869	−	1.45470i
$236$	−2.67891	+	4.64000i	−0.174382	+	0.302038i
$237$	−17.6536	+	12.6235i	−1.14673	+	0.819981i
$238$	0.866603	−	0.152806i	0.0561735	−	0.00990491i
$239$	−23.6023	−	13.6268i	−1.52670	−	0.881443i	−0.999497	−	0.0317050i	$-0.989906\pi$
$239$	−23.6023	−	13.6268i	−1.52670	−	0.881443i	−0.527206	−	0.849738i	$-0.676760\pi$
$240$	−3.26819	+	4.76720i	−0.210960	+	0.307721i
$241$	13.6728	+	16.2946i	0.880739	+	1.04962i	0.998399	+	0.0565704i	$0.0180165\pi$
$241$	13.6728	+	16.2946i	0.880739	+	1.04962i	−0.117659	+	0.993054i	$0.537539\pi$
$242$	26.4425	−	9.62427i	1.69979	−	0.618672i
$243$	4.77459	+	14.8392i	0.306290	+	0.951938i
$244$	−5.95676	−	4.99832i	−0.381343	−	0.319985i
$245$	7.85381	+	1.38484i	0.501762	+	0.0884741i
$246$	1.88996	−	0.904184i	0.120499	−	0.0576487i
$247$	−12.1431	−	12.4259i	−0.772645	−	0.790643i
$248$		−	2.33939i		−	0.148552i
$249$	15.4435	−	4.30236i	0.978692	−	0.272651i
$250$	−2.43617	+	2.90332i	−0.154077	+	0.183622i
$251$	0.848967	−	2.33252i	0.0535863	−	0.147227i	−0.910012	−	0.414583i	$-0.863928\pi$
$251$	0.848967	−	2.33252i	0.0535863	−	0.147227i	0.963598	+	0.267355i	$0.0861498\pi$
$252$	−2.08283	+	6.09535i	−0.131206	+	0.383971i
$253$	3.92920	−	3.29699i	0.247027	−	0.207280i
$254$	1.06727	−	0.616186i	0.0669662	−	0.0386629i
$255$	0.183087	−	2.36173i	0.0114654	−	0.147897i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	1.95465	+	11.0854i	0.121928	+	0.691488i	0.983085	+	0.183149i	$0.0586291\pi$
$257$	1.95465	+	11.0854i	0.121928	+	0.691488i	−0.861157	+	0.508339i	$0.830260\pi$
$258$	0.836793	−	10.7942i	0.0520964	−	0.672018i
$259$	11.1818	−	6.45583i	0.694805	−	0.401146i
$260$	−10.1892	+	8.54971i	−0.631904	+	0.530231i
$261$	−4.49777	+	13.1626i	−0.278405	+	0.814746i
$262$	2.20297	−	6.05261i	0.136100	−	0.373931i
$263$	7.57578	−	9.02847i	0.467143	−	0.556719i	−0.480109	−	0.877209i	$-0.659403\pi$
$263$	7.57578	−	9.02847i	0.467143	−	0.556719i	0.947252	+	0.320490i	$0.103847\pi$
$264$	10.4385	−	2.90803i	0.642444	−	0.178977i
$265$		−	0.783093i		−	0.0481050i
$266$	−8.52721	+	3.85742i	−0.522837	+	0.236513i
$267$	−11.4604	+	5.48285i	−0.701367	+	0.335545i
$268$	−3.48689	−	0.614832i	−0.212996	−	0.0375569i
$269$	8.96522	+	7.52271i	0.546619	+	0.458668i	0.873794	−	0.486296i	$-0.161652\pi$
$269$	8.96522	+	7.52271i	0.546619	+	0.458668i	−0.327175	+	0.944964i	$0.606097\pi$
$270$	14.4929	+	9.51952i	0.882009	+	0.579339i
$271$	−29.1999	+	10.6279i	−1.77377	+	0.645598i	−0.773841	+	0.633380i	$0.781667\pi$
$271$	−29.1999	+	10.6279i	−1.77377	+	0.645598i	−0.999925	+	0.0122180i	$0.996111\pi$
$272$	−0.263438	−	0.313953i	−0.0159733	−	0.0190362i
$273$	−8.38165	+	12.2260i	−0.507280	+	0.739954i
$274$	−9.32954	−	5.38641i	−0.563618	−	0.325405i
$275$	37.8030	−	6.66569i	2.27961	−	0.401956i
$276$	1.15512	−	0.825982i	0.0695299	−	0.0497183i
$277$	1.91965	−	3.32494i	0.115341	−	0.199776i	−0.802575	−	0.596551i	$-0.796537\pi$
$277$	1.91965	−	3.32494i	0.115341	−	0.199776i	0.917916	+	0.396775i	$0.129871\pi$
$278$	−4.21628	−	7.30281i	−0.252876	−	0.437994i
$279$	−7.01680	+	0.138933i	−0.420085	+	0.00831773i
$280$	2.45058	+	6.73292i	0.146450	+	0.402369i
$281$	23.0658	+	8.39528i	1.37599	+	0.500820i	0.920961	−	0.389655i	$-0.127406\pi$
$281$	23.0658	+	8.39528i	1.37599	+	0.500820i	0.455031	+	0.890475i	$0.349628\pi$
$282$	−3.33122	+	12.9434i	−0.198371	+	0.770770i
$283$	−4.03563	+	22.8872i	−0.239894	+	1.36050i	0.592165	+	0.805817i	$0.298273\pi$
$283$	−4.03563	+	22.8872i	−0.239894	+	1.36050i	−0.832059	+	0.554688i	$0.812838\pi$
$284$	−4.46741			−0.265092
$285$	4.33484	+	24.8183i	0.256774	+	1.47011i
$286$	24.9363			1.47451
$287$	0.450998	−	2.55773i	0.0266215	−	0.150978i
$288$	2.94353	−	0.579329i	0.173449	−	0.0341373i
$289$	−15.8169	−	5.75689i	−0.930408	−	0.338641i
$290$	5.29192	+	14.5394i	0.310752	+	0.853785i
$291$	−25.7378	−	11.6930i	−1.50878	−	0.685455i
$292$	2.82741	+	4.89723i	0.165462	+	0.286588i
$293$	5.48661	−	9.50309i	0.320531	−	0.555177i	−0.660066	−	0.751207i	$-0.729472\pi$
$293$	5.48661	−	9.50309i	0.320531	−	0.555177i	0.980598	+	0.196031i	$0.0628052\pi$
$294$	−2.40767	−	3.36707i	−0.140418	−	0.196372i
$295$	17.6075	−	3.10468i	1.02515	−	0.180762i
$296$	−5.20781	−	3.00673i	−0.302698	−	0.174763i
$297$	−9.34230	−	31.1366i	−0.542095	−	1.80673i
$298$	3.41271	+	4.06711i	0.197693	+	0.235601i
$299$	3.07081	−	1.11768i	0.177590	−	0.0646374i
$300$	10.5773	−	1.03099i	0.610680	−	0.0595243i
$301$	−10.2812	−	8.62693i	−0.592597	−	0.497248i
$302$	−2.52098	−	0.444517i	−0.145066	−	0.0255791i
$303$	−4.29352	−	8.97446i	−0.246656	−	0.515569i
$304$	3.54158	+	2.54110i	0.203124	+	0.145742i
$305$			25.9487i			1.48582i
$306$	−0.926030	+	0.808805i	−0.0529376	+	0.0462363i
$307$	−0.351542	+	0.418952i	−0.0200636	+	0.0239108i	−0.775983	−	0.630754i	$-0.782746\pi$
$307$	−0.351542	+	0.418952i	−0.0200636	+	0.0239108i	0.755919	+	0.654665i	$0.227190\pi$
$308$	4.59428	−	12.6227i	0.261783	−	0.719243i
$309$	−1.36691	−	1.34012i	−0.0777610	−	0.0762366i
$310$	−5.98021	+	5.01799i	−0.339653	+	0.285003i
$311$	12.1908	−	7.03836i	0.691277	−	0.399109i	−0.112813	−	0.993616i	$-0.535986\pi$
$311$	12.1908	−	7.03836i	0.691277	−	0.399109i	0.804090	+	0.594507i	$0.202653\pi$
$312$	6.88310	+	0.533595i	0.389679	+	0.0302088i
$313$	−3.23018	−	18.3193i	−0.182580	−	1.03547i	−0.929025	−	0.370018i	$-0.879352\pi$
$313$	−3.23018	−	18.3193i	−0.182580	−	1.03547i	0.746444	−	0.665448i	$-0.231759\pi$
$314$	−2.91168	−	16.5130i	−0.164316	−	0.931880i
$315$	20.0493	−	7.75016i	1.12965	−	0.436672i
$316$	10.8513	−	6.26499i	0.610433	−	0.352433i
$317$	−20.8301	+	17.4785i	−1.16993	+	0.981690i	−0.999993	−	0.00376423i	$-0.998802\pi$
$317$	−20.8301	+	17.4785i	−1.16993	+	0.981690i	−0.169940	+	0.985454i	$0.554357\pi$
$318$	−0.284549	+	0.290239i	−0.0159567	+	0.0162758i
$319$	9.92113	−	27.2581i	0.555477	−	1.52616i
$320$	2.14500	−	2.55631i	0.119909	−	0.142902i
$321$	−3.23171	−	11.6004i	−0.180377	−	0.647469i
$322$		−	1.76036i		−	0.0981009i
$323$	−1.77773	−	0.176176i	−0.0989155	−	0.00980270i
$324$	−1.91246	−	8.79446i	−0.106248	−	0.488581i
$325$	24.0848	+	4.24680i	1.33598	+	0.235570i
$326$	−8.09708	−	6.79425i	−0.448456	−	0.376299i
$327$	1.19328	+	12.2422i	0.0659883	+	0.676996i
$328$	−1.13666	+	0.413712i	−0.0627618	+	0.0228434i
$329$	10.6498	+	12.6919i	0.587142	+	0.699729i
$330$	−29.8244	−	20.4463i	−1.64178	−	1.12553i
$331$	25.4221	+	14.6775i	1.39733	+	0.806746i	0.994112	−	0.108360i	$-0.0345598\pi$
$331$	25.4221	+	14.6775i	1.39733	+	0.806746i	0.403214	+	0.915106i	$0.367893\pi$
$332$	−9.11522	+	1.60726i	−0.500263	+	0.0882098i
$333$	−8.70914	+	15.7989i	−0.477258	+	0.865776i
$334$	−5.59752	+	9.69519i	−0.306283	+	0.530497i
$335$	5.90767	+	10.2324i	0.322770	+	0.559055i
$336$	1.53825	−	3.38589i	0.0839184	−	0.184716i
$337$	4.60842	+	12.6615i	0.251037	+	0.689717i	0.999643	+	0.0267031i	$0.00850087\pi$
$337$	4.60842	+	12.6615i	0.251037	+	0.689717i	−0.748607	+	0.663014i	$0.769277\pi$
$338$	2.71313	+	0.987499i	0.147575	+	0.0537129i
$339$	3.90832	+	1.00587i	0.212271	+	0.0546316i
$340$	−0.237488	+	1.34686i	−0.0128796	+	0.0730437i
$341$	14.6356			0.792562
$342$	7.41148	−	10.7736i	0.400767	−	0.582568i
$343$	−20.1612			−1.08860
$344$	−1.08543	+	6.15577i	−0.0585224	+	0.331897i
$345$	−4.58919	−	1.18111i	−0.247074	−	0.0635888i
$346$	−20.5938	−	7.49553i	−1.10713	−	0.402962i
$347$	2.06013	+	5.66016i	0.110594	+	0.303854i	0.982627	−	0.185594i	$-0.0594208\pi$
$347$	2.06013	+	5.66016i	0.110594	+	0.303854i	−0.872033	+	0.489447i	$0.837199\pi$
$348$	3.32178	−	7.31168i	0.178066	−	0.391947i
$349$	−14.3065	−	24.7795i	−0.765808	−	1.32642i	−0.939818	−	0.341675i	$-0.889006\pi$
$349$	−14.3065	−	24.7795i	−0.765808	−	1.32642i	0.174010	−	0.984744i	$-0.444328\pi$
$350$	6.58711	−	11.4092i	0.352096	−	0.609848i
$351$	1.19169	−	20.6769i	0.0636078	−	1.10365i
$352$	−6.16111	+	1.08637i	−0.328388	+	0.0579037i
$353$	14.6066	+	8.43315i	0.777433	+	0.448851i	0.835520	−	0.549460i	$-0.185167\pi$
$353$	14.6066	+	8.43315i	0.777433	+	0.448851i	−0.0580867	+	0.998312i	$0.518500\pi$
$354$	−7.65405	−	5.24729i	−0.406808	−	0.278890i
$355$	9.58259	+	11.4201i	0.508591	+	0.606115i
$356$	6.89257	−	2.50869i	0.365306	−	0.132960i
$357$	0.147862	+	1.51697i	0.00782569	+	0.0802864i
$358$	16.3833	+	13.7472i	0.865882	+	0.726561i
$359$	−16.2813	−	2.87084i	−0.859295	−	0.151517i	−0.273397	−	0.961901i	$-0.588147\pi$
$359$	−16.2813	−	2.87084i	−0.859295	−	0.151517i	−0.585898	+	0.810385i	$0.699258\pi$
$360$	−7.79482	−	6.28192i	−0.410823	−	0.331086i
$361$	18.7823	−	2.86764i	0.988545	−	0.150928i
$362$			18.2835i			0.960958i
$363$	13.0800	+	46.9511i	0.686521	+	2.46429i
$364$	5.50110	−	6.55596i	0.288336	−	0.343626i
$365$	6.45403	−	17.7323i	0.337819	−	0.928151i
$366$	9.42888	−	9.61743i	0.492856	−	0.502711i
$367$	−7.32428	+	6.14580i	−0.382324	+	0.320808i	−0.813614	−	0.581405i	$-0.802503\pi$
$367$	−7.32428	+	6.14580i	−0.382324	+	0.320808i	0.431290	+	0.902213i	$0.358059\pi$
$368$	−0.710025	+	0.409933i	−0.0370126	+	0.0213692i
$369$	1.30840	+	3.38475i	0.0681124	+	0.176203i
$370$	3.48461	+	19.7622i	0.181156	+	1.02739i
$371$	0.0874947	+	0.496207i	0.00454250	+	0.0257618i
$372$	4.03982	+	0.313177i	0.209455	+	0.0162375i
$373$	3.75197	−	2.16620i	0.194270	−	0.112162i	−0.399710	−	0.916642i	$-0.630889\pi$
$373$	3.75197	−	2.16620i	0.194270	−	0.112162i	0.593980	+	0.804480i	$0.297556\pi$
$374$	1.96414	−	1.64811i	0.101563	−	0.0852217i
$375$	−4.68752	−	4.59562i	−0.242062	−	0.237317i
$376$	2.63917	−	7.25106i	0.136105	−	0.373945i
$377$	11.8794	−	14.1573i	0.611819	−	0.729138i
$378$	−10.2470	−	4.41276i	−0.527051	−	0.226968i
$379$		−	5.96818i		−	0.306565i	−0.988182	−	0.153282i	$-0.951016\pi$
$379$		−	5.96818i		−	0.306565i	0.988182	−	0.153282i	$-0.0489844\pi$
$380$	−1.10084	−	14.5040i	−0.0564719	−	0.744042i
$381$	0.921197	+	1.92552i	0.0471943	+	0.0986472i
$382$	3.40858	+	0.601025i	0.174398	+	0.0307511i
$383$	3.37004	+	2.82780i	0.172201	+	0.144494i	0.724815	−	0.688944i	$-0.241925\pi$
$383$	3.37004	+	2.82780i	0.172201	+	0.144494i	−0.552614	+	0.833437i	$0.686370\pi$
$384$	−1.72388	+	0.168030i	−0.0879714	+	0.00857477i
$385$	−42.1222	+	15.3312i	−2.14675	+	0.781351i
$386$	−6.64414	−	7.91818i	−0.338178	−	0.403025i
$387$	18.5282	+	2.89006i	0.941839	+	0.146910i
$388$	14.1347	+	8.16068i	0.717582	+	0.414296i
$389$	−14.5009	+	2.55689i	−0.735223	+	0.129640i	−0.528708	−	0.848804i	$-0.677323\pi$
$389$	−14.5009	+	2.55689i	−0.735223	+	0.129640i	−0.206515	+	0.978443i	$0.566212\pi$
$390$	−13.4002	−	18.7399i	−0.678546	−	0.948932i
$391$	0.168006	−	0.290994i	0.00849641	−	0.0147162i
$392$	1.19492	+	2.06967i	0.0603527	+	0.104534i
$393$	10.1572	+	4.61451i	0.512361	+	0.232771i
$394$	−4.06292	−	11.1628i	−0.204687	−	0.562373i
$395$	−39.2913	−	14.3009i	−1.97696	−	0.719554i
$396$	3.62437	+	18.4152i	0.182132	+	0.925398i
$397$	1.74751	−	9.91059i	0.0877048	−	0.497398i	−0.909035	−	0.416719i	$-0.863180\pi$
$397$	1.74751	−	9.91059i	0.0877048	−	0.497398i	0.996740	−	0.0806794i	$-0.0257090\pi$
$398$	24.4362			1.22488
$399$	−5.51971	−	15.2418i	−0.276331	−	0.763043i
$400$	−6.13575			−0.306787
$401$	−2.58090	+	14.6370i	−0.128884	+	0.730937i	0.850041	+	0.526717i	$0.176577\pi$
$401$	−2.58090	+	14.6370i	−0.128884	+	0.730937i	−0.978925	+	0.204221i	$0.934534\pi$
$402$	1.52853	−	5.93909i	0.0762361	−	0.296215i
$403$	8.76220	+	3.18918i	0.436476	+	0.158864i
$404$	1.96451	+	5.39745i	0.0977381	+	0.268533i
$405$	−18.3791	+	23.7529i	−0.913267	+	1.18029i
$406$	−4.97771	−	8.62165i	−0.247040	−	0.427885i
$407$	18.8106	−	32.5809i	0.932405	−	1.61497i
$408$	0.577423	−	0.412894i	0.0285867	−	0.0204413i
$409$	−9.81162	+	1.73005i	−0.485153	+	0.0855456i	−0.410874	−	0.911692i	$-0.634777\pi$
$409$	−9.81162	+	1.73005i	−0.485153	+	0.0855456i	−0.0742787	+	0.997238i	$0.523665\pi$
$410$	3.49572	+	2.01825i	0.172641	+	0.0996745i
$411$	10.5506	−	15.3898i	0.520422	−	0.759123i
$412$	0.710405	+	0.846628i	0.0349992	+	0.0417104i
$413$	−10.8101	+	3.93457i	−0.531932	+	0.193607i
$414$	1.27173	+	2.10531i	0.0625019	+	0.103470i
$415$	23.6608	+	19.8538i	1.16146	+	0.974583i
$416$	−3.92533	−	0.692141i	−0.192455	−	0.0339350i
$417$	13.1754	−	6.30333i	0.645204	−	0.308676i
$418$	−15.8975	+	22.1567i	−0.777574	+	1.08372i
$419$			8.34847i			0.407849i	0.978987	+	0.203925i	$0.0653698\pi$
$419$			8.34847i			0.407849i	−0.978987	+	0.203925i	$0.934630\pi$
$420$	−11.9549	+	3.33049i	−0.583341	+	0.162511i
$421$	23.4446	−	27.9402i	1.14262	−	1.36172i	0.220234	−	0.975447i	$-0.429318\pi$
$421$	23.4446	−	27.9402i	1.14262	−	1.36172i	0.922384	−	0.386273i	$-0.126238\pi$
$422$	−5.66695	+	15.5698i	−0.275863	+	0.757926i
$423$	−21.9057	−	7.48533i	−1.06509	−	0.363949i
$424$	0.179766	−	0.150842i	0.00873021	−	0.00732552i
$425$	2.17775	−	1.25733i	0.105637	−	0.0609893i
$426$	0.598057	−	7.71463i	0.0289760	−	0.373775i
$427$	−2.89924	−	16.4424i	−0.140304	−	0.795705i
$428$	1.20729	+	6.84689i	0.0583566	+	0.330957i
$429$	−3.33825	+	43.0617i	−0.161172	+	2.07904i
$430$	18.0643	−	10.4294i	0.871138	−	0.502952i
$431$	8.05751	−	6.76105i	0.388116	−	0.325668i	−0.427762	−	0.903891i	$-0.640698\pi$
$431$	8.05751	−	6.76105i	0.388116	−	0.325668i	0.815879	+	0.578223i	$0.196254\pi$
$432$	0.606372	+	5.16065i	0.0291741	+	0.248292i
$433$	−12.6127	+	34.6530i	−0.606126	+	1.66532i	0.132485	+	0.991185i	$0.457704\pi$
$433$	−12.6127	+	34.6530i	−0.606126	+	1.66532i	−0.738611	+	0.674132i	$0.764518\pi$
$434$	3.22870	−	3.84782i	0.154983	−	0.184701i
$435$	−25.8161	+	7.19205i	−1.23779	+	0.344832i
$436$		−	7.10155i		−	0.340102i
$437$	−0.964625	+	3.44107i	−0.0461443	+	0.164608i
$438$	−8.83538	+	4.22698i	−0.422171	+	0.201973i
$439$	13.1107	+	2.31177i	0.625739	+	0.110335i	0.477522	−	0.878620i	$-0.341535\pi$
$439$	13.1107	+	2.31177i	0.625739	+	0.110335i	0.148218	+	0.988955i	$0.452646\pi$
$440$	15.9927	+	13.4195i	0.762421	+	0.639747i
$441$	6.13681	−	3.70698i	0.292229	−	0.176523i
$442$	1.53505	−	0.558711i	0.0730147	−	0.0265752i
$443$	4.79891	+	5.71912i	0.228003	+	0.271724i	0.867902	−	0.496736i	$-0.165468\pi$
$443$	4.79891	+	5.71912i	0.228003	+	0.271724i	−0.639899	+	0.768459i	$0.721024\pi$
$444$	5.88941	−	8.59069i	0.279499	−	0.407696i
$445$	−21.1976	−	12.2384i	−1.00486	−	0.580156i
$446$	−11.6650	+	2.05686i	−0.552354	+	0.0973950i
$447$	−7.48023	+	5.34883i	−0.353803	+	0.252991i
$448$	−1.07356	+	1.85947i	−0.0507211	+	0.0878516i
$449$	12.1781	+	21.0931i	0.574722	+	0.995447i	0.996072	+	0.0885490i	$0.0282230\pi$
$449$	12.1781	+	21.0931i	0.574722	+	0.995447i	−0.421350	+	0.906898i	$0.638444\pi$
$450$	0.364394	+	18.4036i	0.0171777	+	0.867555i
$451$	−2.58825	−	7.11115i	−0.121876	−	0.334851i
$452$	−2.18949	−	0.796908i	−0.102985	−	0.0374834i
$453$	1.10511	−	4.29390i	0.0519226	−	0.201745i
$454$	−4.00644	+	22.7216i	−0.188031	+	1.06638i
$455$	−28.5589			−1.33886
$456$	−4.86227	+	5.77567i	−0.227697	+	0.270470i
$457$	−34.8127			−1.62847			−0.814236	−	0.580534i	$-0.802844\pi$
$457$	−34.8127			−1.62847			−0.814236	+	0.580534i	$0.802844\pi$
$458$	2.43908	−	13.8327i	0.113971	−	0.646360i
$459$	−1.27273	−	1.70741i	−0.0594060	−	0.0796950i
$460$	2.57092	+	0.935738i	0.119870	+	0.0436290i
$461$	0.765028	+	2.10190i	0.0356309	+	0.0978951i	0.956232	−	0.292608i	$-0.0945232\pi$
$461$	0.765028	+	2.10190i	0.0356309	+	0.0978951i	−0.920601	+	0.390503i	$0.872301\pi$
$462$	21.1827	+	9.62353i	0.985507	+	0.447727i
$463$	1.84091	+	3.18854i	0.0855541	+	0.148184i	0.905627	−	0.424075i	$-0.139401\pi$
$463$	1.84091	+	3.18854i	0.0855541	+	0.148184i	−0.820073	+	0.572259i	$0.806067\pi$
$464$	−2.31831	+	4.01543i	−0.107625	+	0.186412i
$465$	−7.86484	−	10.9988i	−0.364723	−	0.510058i
$466$	−23.2303	+	4.09613i	−1.07612	+	0.189749i
$467$	−11.3948	−	6.57879i	−0.527288	−	0.304430i	0.212623	−	0.977134i	$-0.431799\pi$
$467$	−11.3948	−	6.57879i	−0.527288	−	0.304430i	−0.739911	+	0.672704i	$0.765133\pi$
$468$	−1.84290	+	11.8148i	−0.0851879	+	0.546138i
$469$	−4.88666	−	5.82369i	−0.225645	−	0.268913i
$470$	−24.1970	+	8.80698i	−1.11612	+	0.406236i
$471$	28.9055	−	2.81748i	1.33190	−	0.129823i
$472$	4.10432	+	3.44394i	0.188917	+	0.158520i
$473$	−38.5115	−	6.79061i	−1.77076	−	0.312233i
$474$	9.36615	+	19.5775i	0.430202	+	0.899223i
$475$	−19.1281	+	18.6927i	−0.877658	+	0.857678i
$476$		−	0.879972i		−	0.0403335i
$477$	−0.463112	−	0.530234i	−0.0212045	−	0.0242778i
$478$	−17.5182	+	20.8774i	−0.801266	+	0.954911i
$479$	−11.4643	+	31.4978i	−0.523816	+	1.43917i	0.342424	+	0.939546i	$0.388752\pi$
$479$	−11.4643	+	31.4978i	−0.523816	+	1.43917i	−0.866240	+	0.499628i	$0.833470\pi$
$480$	4.12726	+	4.04635i	0.188383	+	0.184690i
$481$	18.3613	−	15.4069i	0.837202	−	0.702496i
$482$	18.4213	−	10.6355i	0.839065	−	0.484434i
$483$	3.03991	+	0.235661i	0.138321	+	0.0107229i
$484$	−4.88637	−	27.7120i	−0.222108	−	1.25964i
$485$	−9.45772	−	53.6374i	−0.429453	−	2.43555i
$486$	15.4429	−	2.12524i	0.700504	−	0.0964030i
$487$	−15.2052	+	8.77875i	−0.689015	+	0.397803i	−0.803243	−	0.595651i	$-0.796894\pi$
$487$	−15.2052	+	8.77875i	−0.689015	+	0.397803i	0.114228	+	0.993455i	$0.463561\pi$
$488$	−5.95676	+	4.99832i	−0.269650	+	0.226263i
$489$	12.8168	−	13.0730i	0.579594	−	0.591183i
$490$	2.72760	−	7.49402i	0.123220	−	0.338545i
$491$	15.8204	−	18.8540i	0.713964	−	0.850869i	−0.280065	−	0.959981i	$-0.590356\pi$
$491$	15.8204	−	18.8540i	0.713964	−	0.850869i	0.994030	+	0.109112i	$0.0348006\pi$
$492$	−0.562260	−	2.01825i	−0.0253486	−	0.0909899i
$493$		−	1.90026i		−	0.0855834i
$494$	−14.3458	+	9.80084i	−0.645447	+	0.440961i
$495$	39.3007	−	48.7656i	1.76643	−	2.19185i
$496$	−2.30385	−	0.406231i	−0.103446	−	0.0182403i
$497$	−7.34797	−	6.16568i	−0.329602	−	0.276569i
$498$	−1.55526	−	15.9560i	−0.0696930	−	0.715004i
$499$	13.8001	−	5.02282i	0.617777	−	0.224852i	−0.0141259	−	0.999900i	$-0.504497\pi$
$499$	13.8001	−	5.02282i	0.617777	−	0.224852i	0.631902	+	0.775048i	$0.282274\pi$
$500$	2.43617	+	2.90332i	0.108949	+	0.129840i
$501$	−15.9930	−	10.9641i	−0.714514	−	0.489840i
$502$	−2.14966	−	1.24111i	−0.0959440	−	0.0553933i
$503$	−4.24201	+	0.747980i	−0.189142	+	0.0333508i	−0.267417	−	0.963581i	$-0.586170\pi$
$503$	−4.24201	+	0.747980i	−0.189142	+	0.0333508i	0.0782748	+	0.996932i	$0.475059\pi$
$504$	5.64107	+	3.10963i	0.251273	+	0.138514i
$505$	9.58368	−	16.5994i	0.426468	−	0.738665i
$506$	−2.56461	−	4.44203i	−0.114011	−	0.197472i
$507$	−2.06849	+	4.55303i	−0.0918650	+	0.202207i
$508$	−0.421496	−	1.15805i	−0.0187009	−	0.0513802i
$509$	−4.35756	−	1.58602i	−0.193145	−	0.0702991i	0.243637	−	0.969867i	$-0.421660\pi$
$509$	−4.35756	−	1.58602i	−0.193145	−	0.0702991i	−0.436782	+	0.899567i	$0.643882\pi$
$510$	−2.29406	−	0.590416i	−0.101583	−	0.0261440i
$511$	−2.10837	+	11.9572i	−0.0932690	+	0.528955i
$512$	1.00000			0.0441942
$513$	17.6124	+	14.2409i	0.777605	+	0.628753i
$514$	11.2564			0.496498
$515$	0.640425	−	3.63203i	0.0282205	−	0.160047i
$516$	−10.4849	−	2.69847i	−0.461572	−	0.118794i
$517$	45.3638	+	16.5111i	1.99510	+	0.726156i
$518$	−4.41605	−	12.1330i	−0.194030	−	0.533093i
$519$	15.7007	−	34.5594i	0.689185	−	1.51699i
$520$	6.65050	+	11.5190i	0.291644	+	0.505141i
$521$	−0.205968	+	0.356747i	−0.00902363	+	0.0156294i	−0.870502	−	0.492165i	$-0.836206\pi$
$521$	−0.205968	+	0.356747i	−0.00902363	+	0.0156294i	0.861478	+	0.507794i	$0.169539\pi$
$522$	12.1816	+	6.71510i	0.533175	+	0.293912i
$523$	−19.2248	+	3.38986i	−0.840643	+	0.148228i	−0.577359	−	0.816490i	$-0.695917\pi$
$523$	−19.2248	+	3.38986i	−0.840643	+	0.148228i	−0.263284	+	0.964718i	$0.584806\pi$
$524$	−5.57811	−	3.22053i	−0.243681	−	0.140689i
$525$	18.8204	+	12.9025i	0.821390	+	0.563109i
$526$	−7.57578	−	9.02847i	−0.330320	−	0.393660i
$527$	0.900948	−	0.327918i	0.0392459	−	0.0142843i
$528$	−1.05122	−	10.7849i	−0.0457487	−	0.469351i
$529$	17.1041	+	14.3520i	0.743657	+	0.624002i
$530$	−0.771196	−	0.135983i	−0.0334986	−	0.00590671i
$531$	10.0860	−	12.5151i	0.437697	−	0.543109i
$532$	2.31808	+	9.06750i	0.100502	+	0.393126i
$533$		−	4.82137i		−	0.208837i
$534$	3.40947	+	12.2384i	0.147542	+	0.529608i
$535$	14.9131	−	17.7728i	0.644751	−	0.768385i
$536$	−1.21098	+	3.32715i	−0.0523065	+	0.143711i
$537$	−25.9328	+	26.4514i	−1.11908	+	1.14146i
$538$	8.96522	−	7.52271i	0.386518	−	0.324327i
$539$	−12.9481	+	7.47562i	−0.557716	+	0.321998i
$540$	11.8916	−	12.6197i	0.511731	−	0.543064i
$541$	−3.15633	−	17.9005i	−0.135701	−	0.769601i	−0.974369	−	0.224957i	$-0.927776\pi$
$541$	−3.15633	−	17.9005i	−0.135701	−	0.769601i	0.838667	−	0.544644i	$-0.183335\pi$
$542$	5.39592	+	30.6018i	0.231775	+	1.31446i
$543$	−31.5732	−	2.44763i	−1.35493	−	0.105038i
$544$	−0.354929	+	0.204918i	−0.0152175	+	0.00878581i
$545$	−18.1538	+	15.2328i	−0.777622	+	0.652502i
$546$	10.5848	+	10.3773i	0.452990	+	0.444109i
$547$	1.42436	−	3.91340i	0.0609014	−	0.167325i	−0.905510	−	0.424324i	$-0.860512\pi$
$547$	1.42436	−	3.91340i	0.0609014	−	0.167325i	0.966412	+	0.256999i	$0.0827338\pi$
$548$	−6.92464	+	8.25246i	−0.295806	+	0.352528i
$549$	15.3458	+	17.5699i	0.654942	+	0.749867i
$550$		−	38.3862i		−	1.63679i
$551$	5.00579	+	19.5808i	0.213254	+	0.834172i
$552$	−0.612849	−	1.28100i	−0.0260846	−	0.0545229i
$553$	26.4948	+	4.67174i	1.12667	+	0.198663i
$554$	−2.94108	−	2.46786i	−0.124955	−	0.104849i
$555$	−34.5932	+	3.37188i	−1.46840	+	0.143128i
$556$	−7.92402	+	2.88411i	−0.336053	+	0.122313i
$557$	9.16196	+	10.9188i	0.388205	+	0.462644i	0.924386	−	0.381459i	$-0.124578\pi$
$557$	9.16196	+	10.9188i	0.388205	+	0.462644i	−0.536181	+	0.844103i	$0.680134\pi$
$558$	−1.08163	+	6.93432i	−0.0457891	+	0.293553i
$559$	−21.5767	−	12.4573i	−0.912599	−	0.526889i
$560$	7.05617	−	1.24419i	0.298178	−	0.0525767i
$561$	2.58313	+	3.61245i	0.109060	+	0.152518i
$562$	12.2731	−	21.2576i	0.517708	−	0.896697i
$563$	−3.28307	−	5.68645i	−0.138365	−	0.239655i	0.788513	−	0.615018i	$-0.210851\pi$
$563$	−3.28307	−	5.68645i	−0.138365	−	0.239655i	−0.926878	+	0.375363i	$0.877518\pi$
$564$	12.1683	+	5.52821i	0.512379	+	0.232780i
$565$	2.65930	+	7.30637i	0.111878	+	0.307381i
$566$	21.8387	+	7.94865i	0.917950	+	0.334107i
$567$	8.99204	−	17.1046i	0.377630	−	0.718324i
$568$	−0.775757	+	4.39954i	−0.0325501	+	0.184601i
$569$	45.7506			1.91797			0.958983	−	0.283465i	$-0.0914840\pi$
$569$	45.7506			1.91797			0.958983	+	0.283465i	$0.0914840\pi$
$570$	25.1940	+	0.0406643i	1.05526	+	0.00170324i
$571$	5.82547			0.243788			0.121894	−	0.992543i	$-0.461103\pi$
$571$	5.82547			0.243788			0.121894	+	0.992543i	$0.461103\pi$
$572$	4.33014	−	24.5575i	0.181052	−	1.02680i
$573$	−1.49420	+	5.80571i	−0.0624212	+	0.242537i
$574$	−2.44056	−	0.888292i	−0.101867	−	0.0370766i
$575$	−1.72053	−	4.72712i	−0.0717510	−	0.197134i
$576$	−0.0593887	−	2.99941i	−0.00247453	−	0.124976i
$577$	−17.9425	−	31.0773i	−0.746956	−	1.29377i	−0.949276	−	0.314446i	$-0.898181\pi$
$577$	−17.9425	−	31.0773i	−0.746956	−	1.29377i	0.202320	−	0.979319i	$-0.435152\pi$
$578$	−8.41602	+	14.5770i	−0.350060	+	0.606322i
$579$	14.5631	−	10.4135i	0.605223	−	0.432772i
$580$	15.2375	−	2.68678i	0.632702	−	0.111562i
$581$	−17.2109	−	9.93674i	−0.714030	−	0.412245i
$582$	−15.9847	+	23.3163i	−0.662586	+	0.966493i
$583$	0.943689	+	1.12464i	0.0390836	+	0.0465780i
$584$	5.31380	−	1.93407i	0.219887	−	0.0800322i
$585$	34.1553	−	20.6317i	1.41215	−	0.853015i
$586$	−8.40598	−	7.05345i	−0.347248	−	0.291376i
$587$	29.5771	+	5.21525i	1.22078	+	0.215256i	0.746661	−	0.665205i	$-0.231656\pi$
$587$	29.5771	+	5.21525i	1.22078	+	0.215256i	0.474118	+	0.880461i	$0.342767\pi$
$588$	−3.73401	+	1.78641i	−0.153988	+	0.0736701i
$589$	−8.41982	+	5.75231i	−0.346932	+	0.237020i
$590$		−	17.8792i		−	0.736074i
$591$	19.8206	−	5.52176i	0.815309	−	0.227135i
$592$	−3.86538	+	4.60658i	−0.158866	+	0.189329i
$593$	−0.268437	+	0.737526i	−0.0110234	+	0.0302866i	−0.945082	−	0.326832i	$-0.894019\pi$
$593$	−0.268437	+	0.737526i	−0.0110234	+	0.0302866i	0.934059	+	0.357119i	$0.116241\pi$
$594$	−32.2858	+	3.79356i	−1.32470	+	0.155651i
$595$	−2.24948	+	1.88754i	−0.0922198	+	0.0773816i
$596$	4.59793	−	2.65462i	0.188339	−	0.108737i
$597$	−3.27130	+	42.1981i	−0.133886	+	1.72706i
$598$	−0.567463	−	3.21824i	−0.0232053	−	0.131604i
$599$	−2.35948	−	13.3813i	−0.0964057	−	0.546744i	−0.994308	−	0.106548i	$-0.966020\pi$
$599$	−2.35948	−	13.3813i	−0.0964057	−	0.546744i	0.897902	−	0.440196i	$-0.145091\pi$
$600$	0.821399	−	10.5956i	0.0335335	−	0.432565i
$601$	1.41283	−	0.815696i	0.0576304	−	0.0332729i	−0.470908	−	0.882182i	$-0.656074\pi$
$601$	1.41283	−	0.815696i	0.0576304	−	0.0332729i	0.528538	+	0.848909i	$0.322740\pi$
$602$	−10.2812	+	8.62693i	−0.419029	+	0.351607i
$603$	10.0514	+	3.43464i	0.409325	+	0.139869i
$604$	−0.875527	+	2.40549i	−0.0356247	+	0.0978781i
$605$	−60.3592	+	71.9333i	−2.45395	+	2.92450i
$606$	−9.58368	+	2.66989i	−0.389310	+	0.108457i
$607$			23.6670i			0.960615i	0.877100	+	0.480308i	$0.159475\pi$
$607$			23.6670i			0.960615i	−0.877100	+	0.480308i	$0.840525\pi$
$608$	3.11749	−	3.04652i	0.126431	−	0.123553i
$609$	15.5548	−	7.44167i	0.630314	−	0.301552i
$610$	25.5545	+	4.50595i	1.03467	+	0.182441i
$611$	23.5610	+	19.7700i	0.953177	+	0.799811i
$612$	0.635714	+	1.05241i	0.0256972	+	0.0425411i
$613$	14.7136	−	5.35532i	0.594278	−	0.216299i	−0.0273321	−	0.999626i	$-0.508701\pi$
$613$	14.7136	−	5.35532i	0.594278	−	0.216299i	0.621610	+	0.783327i	$0.286479\pi$
$614$	0.351542	+	0.418952i	0.0141871	+	0.0169075i
$615$	−3.95324	+	5.76646i	−0.159410	+	0.232526i
$616$	−11.6331	−	6.71638i	−0.468712	−	0.270611i
$617$	19.6258	−	3.46056i	0.790105	−	0.139317i	0.235988	−	0.971756i	$-0.424167\pi$
$617$	19.6258	−	3.46056i	0.790105	−	0.139317i	0.554117	+	0.832439i	$0.313056\pi$
$618$	−1.55712	+	1.11344i	−0.0626365	+	0.0447891i
$619$	−3.55524	+	6.15786i	−0.142897	+	0.247505i	−0.928587	−	0.371116i	$-0.878975\pi$
$619$	−3.55524	+	6.15786i	−0.142897	+	0.247505i	0.785689	+	0.618621i	$0.212309\pi$
$620$	3.90331	+	6.76072i	0.156761	+	0.271517i
$621$	−3.80585	+	1.91426i	−0.152723	+	0.0768168i
$622$	−4.81452	−	13.2278i	−0.193045	−	0.530386i
$623$	14.7992	+	5.38648i	0.592919	+	0.215805i
$624$	1.72073	−	6.68587i	0.0688841	−	0.267649i
$625$	−3.13111	+	17.7574i	−0.125244	+	0.710297i
$626$	−18.6019			−0.743480
$627$	−36.1335	−	30.4191i	−1.44303	−	1.21482i
$628$	−16.7677			−0.669104
$629$	0.427962	−	2.42710i	0.0170640	−	0.0967746i
$630$	−4.15090	−	21.0905i	−0.165376	−	0.840264i
$631$	−1.16675	−	0.424661i	−0.0464474	−	0.0169055i	0.318692	−	0.947858i	$-0.396756\pi$
$631$	−1.16675	−	0.424661i	−0.0464474	−	0.0169055i	−0.365139	+	0.930953i	$0.618979\pi$
$632$	−4.28551	−	11.7743i	−0.170468	−	0.468358i
$633$	−26.1284	−	11.8704i	−1.03851	−	0.471807i
$634$	13.5959	+	23.5487i	0.539960	+	0.935239i
$635$	−2.05623	+	3.56149i	−0.0815989	+	0.141334i
$636$	0.236418	+	0.330626i	0.00937460	+	0.0131102i
$637$	−9.38092	+	1.65411i	−0.371685	+	0.0655382i
$638$	−25.1212	−	14.5037i	−0.994557	−	0.574208i
$639$	13.2421	+	2.06553i	0.523849	+	0.0817112i
$640$	−2.14500	−	2.55631i	−0.0847885	−	0.101047i
$641$	−7.06477	+	2.57137i	−0.279042	+	0.101563i	−0.477750	−	0.878496i	$-0.658548\pi$
$641$	−7.06477	+	2.57137i	−0.279042	+	0.101563i	0.198708	+	0.980059i	$0.436325\pi$
$642$	−11.9853	+	1.16823i	−0.473022	+	0.0461065i
$643$	−9.31005	−	7.81206i	−0.367153	−	0.308078i	0.440481	−	0.897762i	$-0.354808\pi$
$643$	−9.31005	−	7.81206i	−0.367153	−	0.308078i	−0.807634	+	0.589684i	$0.799252\pi$
$644$	−1.73361	−	0.305683i	−0.0683139	−	0.0120456i
$645$	15.5920	+	32.5909i	0.613933	+	1.28327i
$646$	−0.482199	+	1.72013i	−0.0189719	+	0.0676776i
$647$		−	38.1298i		−	1.49904i	−0.661983	−	0.749519i	$-0.730285\pi$
$647$		−	38.1298i		−	1.49904i	0.661983	−	0.749519i	$-0.269715\pi$
$648$	−8.99295	+	0.356262i	−0.353276	+	0.0139953i
$649$	−21.5458	+	25.6773i	−0.845747	+	1.00792i
$650$	8.36457	−	22.9815i	0.328085	−	0.901407i
$651$	6.21245	+	6.09066i	0.243485	+	0.238712i
$652$	−8.09708	+	6.79425i	−0.317106	+	0.266084i
$653$	39.7547	−	22.9524i	1.55572	−	0.898196i	0.558063	−	0.829798i	$-0.311545\pi$
$653$	39.7547	−	22.9524i	1.55572	−	0.898196i	0.997658	−	0.0683980i	$-0.0217888\pi$
$654$	12.2634	+	0.950692i	0.479539	+	0.0371750i
$655$	3.73239	+	21.1674i	0.145836	+	0.827080i
$656$	0.210047	+	1.19124i	0.00820096	+	0.0465099i
$657$	−6.11664	−	15.8234i	−0.238633	−	0.617330i
$658$	14.3484	−	8.28407i	0.559360	−	0.322947i
$659$	−14.3577	+	12.0475i	−0.559295	+	0.469304i	−0.878074	−	0.478525i	$-0.841172\pi$
$659$	−14.3577	+	12.0475i	−0.559295	+	0.469304i	0.318779	+	0.947829i	$0.396727\pi$
$660$	−25.3146	+	25.8208i	−0.985369	+	1.00507i
$661$	4.05073	−	11.1293i	0.157555	−	0.432879i	−0.835649	−	0.549263i	$-0.814908\pi$
$661$	4.05073	−	11.1293i	0.157555	−	0.432879i	0.993204	+	0.116385i	$0.0371306\pi$
$662$	18.8690	−	22.4872i	0.733364	−	0.873989i
$663$	0.759323	+	2.72562i	0.0294896	+	0.105854i
$664$			9.25584i			0.359196i
$665$	18.2071	−	25.3755i	0.706039	−	0.984020i
$666$	14.0466	+	11.3203i	0.544294	+	0.438652i
$667$	−3.74366	−	0.660108i	−0.144955	−	0.0255595i
$668$	8.57590	+	7.19604i	0.331812	+	0.278423i
$669$	−1.99031	−	20.4193i	−0.0769500	−	0.789456i
$670$	11.1028	−	4.04108i	0.428938	−	0.156121i
$671$	−31.2703	−	37.2665i	−1.20718	−	1.43866i
$672$	−3.06734	−	2.10283i	−0.118325	−	0.0811186i
$673$	−9.02264	−	5.20922i	−0.347797	−	0.200801i	0.315917	−	0.948787i	$-0.397688\pi$
$673$	−9.02264	−	5.20922i	−0.347797	−	0.200801i	−0.663715	+	0.747986i	$0.731021\pi$
$674$	13.2694	−	2.33976i	0.511119	−	0.0901240i
$675$	−31.8294	−	1.83445i	−1.22512	−	0.0706082i
$676$	1.44363	−	2.50044i	0.0555241	−	0.0961706i
$677$	10.3670	+	17.9562i	0.398437	+	0.690112i	0.993533	−	0.113542i	$-0.0362196\pi$
$677$	10.3670	+	17.9562i	0.398437	+	0.690112i	−0.595097	+	0.803654i	$0.702886\pi$
$678$	1.66926	−	3.67427i	0.0641077	−	0.141110i
$679$	11.9858	+	32.9306i	0.459972	+	1.26376i
$680$	1.28516	+	0.467759i	0.0492836	+	0.0179377i
$681$	−38.7009	−	9.96036i	−1.48302	−	0.381682i
$682$	2.54145	−	14.4133i	0.0973170	−	0.551912i
$683$	−2.79983			−0.107132			−0.0535662	−	0.998564i	$-0.517059\pi$
$683$	−2.79983			−0.107132			−0.0535662	+	0.998564i	$0.517059\pi$
$684$	−9.32291	−	9.16970i	−0.356470	−	0.350612i
$685$	35.9492			1.37355
$686$	−3.50095	+	19.8549i	−0.133667	+	0.758064i
$687$	23.5608	+	6.06377i	0.898899	+	0.231347i
$688$	5.87377	+	2.13788i	0.223935	+	0.0815058i
$689$	0.319912	+	0.878950i	0.0121877	+	0.0334853i
$690$	−1.96007	+	4.31437i	−0.0746186	+	0.164245i
$691$	−4.20182	−	7.27776i	−0.159845	−	0.276859i	0.774968	−	0.632001i	$-0.217766\pi$
$691$	−4.20182	−	7.27776i	−0.159845	−	0.276859i	−0.934813	+	0.355142i	$0.884433\pi$
$692$	−10.9577	+	18.9794i	−0.416551	+	0.721487i
$693$	−19.4543	+	35.2914i	−0.739009	+	1.34061i
$694$	5.93191	−	1.04596i	0.225172	−	0.0397040i
$695$	24.3697	+	14.0698i	0.924395	+	0.533700i
$696$	−6.62378	−	4.54097i	−0.251074	−	0.172125i
$697$	−0.318658	−	0.379762i	−0.0120700	−	0.0143845i
$698$	−26.8874	+	9.78621i	−1.01770	+	0.370413i
$699$	−3.96361	−	40.6640i	−0.149918	−	1.53805i
$700$	−10.0920	−	8.46823i	−0.381443	−	0.320069i
$701$	14.9472	+	2.63560i	0.564549	+	0.0995451i	0.448636	−	0.893714i	$-0.351910\pi$
$701$	14.9472	+	2.63560i	0.564549	+	0.0995451i	0.115912	+	0.993259i	$0.463021\pi$
$702$	−20.1559	−	4.76410i	−0.760734	−	0.179809i
$703$	1.98376	+	26.1369i	0.0748190	+	0.985771i
$704$			6.25616i			0.235788i
$705$	−11.9692	−	42.9640i	−0.450787	−	1.61812i
$706$	10.8414	−	12.9203i	0.408023	−	0.486263i
$707$	−4.21806	+	11.5890i	−0.158636	+	0.435850i
$708$	−6.49668	+	6.62659i	−0.244160	+	0.249042i
$709$	−29.3000	+	24.5857i	−1.10039	+	0.923334i	−0.997451	−	0.0713544i	$-0.977268\pi$
$709$	−29.3000	+	24.5857i	−1.10039	+	0.923334i	−0.102935	+	0.994688i	$0.532823\pi$
$710$	12.9106	−	7.45393i	0.484526	−	0.279741i
$711$	−35.0616	+	13.5533i	−1.31491	+	0.508287i
$712$	−1.27370	−	7.22349i	−0.0477338	−	0.270712i
$713$	−0.333055	−	1.88885i	−0.0124730	−	0.0707380i
$714$	1.51960	+	0.117803i	0.0568695	+	0.00440866i
$715$	−72.0647	+	41.6065i	−2.69507	+	1.55600i
$716$	16.3833	−	13.7472i	0.612271	−	0.513756i
$717$	−33.7074	−	33.0466i	−1.25883	−	1.23415i
$718$	−5.65444	+	15.5354i	−0.211022	+	0.579778i
$719$	24.9620	−	29.7485i	0.930924	−	1.10943i	−0.0628501	−	0.998023i	$-0.520019\pi$
$719$	24.9620	−	29.7485i	0.930924	−	1.10943i	0.993775	−	0.111410i	$-0.0355365\pi$
$720$	−7.54004	+	6.58555i	−0.281001	+	0.245429i
$721$			2.37299i			0.0883749i
$722$	0.437448	−	18.9950i	0.0162801	−	0.706919i
$723$	15.9001	+	33.2349i	0.591330	+	1.23602i
$724$	18.0057	+	3.17489i	0.669177	+	0.117994i
$725$	−21.7933	−	18.2868i	−0.809383	−	0.679153i
$726$	48.5091	−	4.72829i	1.80034	−	0.175483i
$727$	35.9582	−	13.0877i	1.33361	−	0.485396i	0.425818	−	0.904809i	$-0.359986\pi$
$727$	35.9582	−	13.0877i	1.33361	−	0.485396i	0.907796	+	0.419413i	$0.137764\pi$
$728$	−5.50110	−	6.55596i	−0.203884	−	0.242980i
$729$	1.60266	+	26.9524i	0.0593577	+	0.998237i
$730$	−16.3422	−	9.43516i	−0.604851	−	0.349211i
$731$	−2.52286	+	0.444849i	−0.0933114	+	0.0164533i
$732$	−7.83401	−	10.9557i	−0.289553	−	0.404934i
$733$	−7.71039	+	13.3548i	−0.284790	+	0.493270i	−0.972558	−	0.232660i	$-0.925257\pi$
$733$	−7.71039	+	13.3548i	−0.284790	+	0.493270i	0.687768	+	0.725930i	$0.258590\pi$
$734$	4.78059	+	8.28022i	0.176455	+	0.305628i
$735$	12.5761	+	5.71344i	0.463875	+	0.210744i
$736$	0.280411	+	0.770422i	0.0103361	+	0.0283981i
$737$	−20.8152	−	7.57610i	−0.766736	−	0.279069i
$738$	3.56053	−	0.700763i	0.131065	−	0.0257955i
$739$	−4.98207	+	28.2547i	−0.183268	+	1.03937i	0.744892	+	0.667185i	$0.232501\pi$
$739$	−4.98207	+	28.2547i	−0.183268	+	1.03937i	−0.928160	+	0.372181i	$0.878610\pi$
$740$	20.0671			0.737680
$741$	−15.0043	−	26.0853i	−0.551196	−	0.958269i
$742$	0.503862			0.0184974
$743$	−4.95784	+	28.1173i	−0.181886	+	1.03152i	0.748006	+	0.663691i	$0.231011\pi$
$743$	−4.95784	+	28.1173i	−0.181886	+	1.03152i	−0.929892	+	0.367833i	$0.880100\pi$
$744$	1.00993	−	3.92407i	0.0370257	−	0.143863i
$745$	−16.6486	−	6.05959i	−0.609957	−	0.222006i
$746$	−1.48177	−	4.07112i	−0.0542514	−	0.149054i
$747$	27.7621	−	0.549693i	1.01576	−	0.0201122i
$748$	−1.28200	−	2.22049i	−0.0468746	−	0.0811892i
$749$	−7.46397	+	12.9280i	−0.272727	+	0.472378i
$750$	−5.33978	+	3.81828i	−0.194981	+	0.139424i
$751$	12.4716	−	2.19908i	0.455096	−	0.0802457i	0.0585987	−	0.998282i	$-0.481337\pi$
$751$	12.4716	−	2.19908i	0.455096	−	0.0802457i	0.396497	+	0.918036i	$0.370226\pi$
$752$	−6.68262	−	3.85821i	−0.243690	−	0.140694i
$753$	2.43101	−	3.54603i	0.0885908	−	0.129225i
$754$	−11.8794	−	14.1573i	−0.432622	−	0.515578i
$755$	8.02719	−	2.92166i	0.292139	−	0.106330i
$756$	−6.12510	+	9.32509i	−0.222768	+	0.339150i
$757$	38.4432	+	32.2577i	1.39724	+	1.17243i	0.962308	+	0.271963i	$0.0876729\pi$
$757$	38.4432	+	32.2577i	1.39724	+	1.17243i	0.434934	+	0.900462i	$0.356772\pi$
$758$	−5.87751	−	1.03636i	−0.213481	−	0.0376424i
$759$	8.01413	−	3.83408i	0.290894	−	0.139168i
$760$	−14.4749	−	1.43448i	−0.525058	−	0.0520342i
$761$		−	26.6803i		−	0.967159i	−0.875300	−	0.483580i	$-0.839336\pi$
$761$		−	26.6803i		−	0.967159i	0.875300	−	0.483580i	$-0.160664\pi$
$762$	2.05623	−	0.572839i	0.0744893	−	0.0207518i
$763$	9.80118	−	11.6806i	0.354826	−	0.422866i
$764$	1.18379	−	3.25243i	0.0428279	−	0.117669i
$765$	1.32668	−	3.88250i	0.0479662	−	0.140372i
$766$	3.37004	−	2.82780i	0.121764	−	0.102172i
$767$	−18.4945	+	10.6778i	−0.667798	+	0.385553i
$768$	−0.133871	+	1.72687i	−0.00483066	+	0.0623130i
$769$	−6.83201	−	38.7463i	−0.246369	−	1.39723i	−0.817292	−	0.576223i	$-0.804526\pi$
$769$	−6.83201	−	38.7463i	−0.246369	−	1.39723i	0.570924	−	0.821003i	$-0.306585\pi$
$770$	7.78387	+	44.1445i	0.280511	+	1.59086i
$771$	−1.50691	+	19.4383i	−0.0542699	+	0.700054i
$772$	−8.95163	+	5.16822i	−0.322176	+	0.186008i
$773$	−2.48012	+	2.08107i	−0.0892039	+	0.0748509i	−0.686299	−	0.727319i	$-0.740766\pi$
$773$	−2.48012	+	2.08107i	−0.0892039	+	0.0748509i	0.597095	+	0.802170i	$0.296321\pi$
$774$	6.06354	−	17.7448i	0.217949	−	0.637824i
$775$	4.90933	−	13.4883i	0.176348	−	0.484513i
$776$	10.4912	−	12.5029i	0.376611	−	0.448828i
$777$	21.5433	−	6.00168i	0.772861	−	0.215309i
$778$			14.7246i			0.527901i
$779$	4.28394	+	3.07375i	0.153488	+	0.110128i
$780$	−20.7821	+	9.94248i	−0.744119	+	0.355998i
$781$	−27.5242	−	4.85326i	−0.984893	−	0.173663i
$782$	−0.257400	−	0.215984i	−0.00920459	−	0.00772357i
$783$	−13.2269	+	20.1371i	−0.472690	+	0.719642i
$784$	2.24572	−	0.817375i	0.0802042	−	0.0291919i
$785$	35.9667	+	42.8634i	1.28371	+	1.52986i
$786$	6.30818	−	9.20154i	0.225005	−	0.328208i
$787$	−22.8624	−	13.1996i	−0.814956	−	0.470515i	0.0337179	−	0.999431i	$-0.489265\pi$
$787$	−22.8624	−	13.1996i	−0.814956	−	0.470515i	−0.848674	+	0.528916i	$0.822599\pi$
$788$	−11.6987	+	2.06280i	−0.416749	+	0.0734842i
$789$	16.6052	−	11.8737i	0.591160	−	0.422716i
$790$	−20.9065	+	36.2110i	−0.743818	+	1.28833i
$791$	−2.50141	−	4.33256i	−0.0889397	−	0.154048i
$792$	18.7648	−	0.371545i	0.666778	−	0.0132023i
$793$	−10.6007	−	29.1251i	−0.376440	−	1.03426i
$794$	−9.45658	−	3.44191i	−0.335601	−	0.122149i
$795$	0.338065	−	1.31355i	0.0119899	−	0.0465869i
$796$	4.24330	−	24.0650i	0.150400	−	0.852960i
$797$	9.50783			0.336785			0.168392	−	0.985720i	$-0.446142\pi$
$797$	9.50783			0.336785			0.168392	+	0.985720i	$0.446142\pi$
$798$	−15.9687	+	2.78915i	−0.565286	+	0.0987347i
$799$	3.16247			0.111880
$800$	−1.06546	+	6.04253i	−0.0376697	+	0.213636i
$801$	−21.5906	+	4.24933i	−0.762865	+	0.150143i
$802$	13.9665	+	5.08338i	0.493173	+	0.179500i
$803$	12.0998	+	33.2440i	0.426993	+	1.17315i
$804$	−5.58344	−	2.53662i	−0.196913	−	0.0894597i
$805$	2.93718	+	5.08734i	0.103522	+	0.179305i
$806$	4.66227	−	8.07529i	0.164221	−	0.284440i
$807$	11.7906	+	16.4888i	0.415047	+	0.580434i
$808$	5.65658	−	0.997408i	0.198998	−	0.0350887i
$809$	31.3018	+	18.0721i	1.10051	+	0.635380i	0.936355	−	0.351054i	$-0.114177\pi$
$809$	31.3018	+	18.0721i	1.10051	+	0.635380i	0.164156	+	0.986434i	$0.447510\pi$
$810$	20.2006	+	22.2246i	0.709776	+	0.780892i
$811$	16.3764	+	19.5167i	0.575054	+	0.685323i	0.972660	−	0.232233i	$-0.0746033\pi$
$811$	16.3764	+	19.5167i	0.575054	+	0.685323i	−0.397606	+	0.917556i	$0.630159\pi$
$812$	−9.35504	+	3.40496i	−0.328297	+	0.119491i
$813$	−53.5676	+	5.22135i	−1.87870	+	0.183121i
$814$	−28.8195	−	24.1824i	−1.01012	−	0.847593i
$815$	34.7364	+	6.12497i	1.21676	+	0.214548i
$816$	−0.306353	−	0.640349i	−0.0107245	−	0.0224167i
$817$	24.8245	−	11.2297i	0.868498	−	0.392879i
$818$			9.96298i			0.348347i
$819$	−19.3373	+	16.8894i	−0.675701	+	0.590164i
$820$	2.59462	−	3.09214i	0.0906080	−	0.107982i
$821$	3.53702	−	9.71788i	0.123443	−	0.339156i	−0.862543	−	0.505983i	$-0.831130\pi$
$821$	3.53702	−	9.71788i	0.123443	−	0.339156i	0.985986	+	0.166827i	$0.0533520\pi$
$822$	−13.3239	−	13.0627i	−0.464725	−	0.455614i
$823$	11.1336	−	9.34221i	0.388093	−	0.325649i	−0.427776	−	0.903885i	$-0.640703\pi$
$823$	11.1336	−	9.34221i	0.388093	−	0.325649i	0.815870	+	0.578235i	$0.196259\pi$
$824$	0.957127	−	0.552597i	0.0333431	−	0.0192506i
$825$	66.2879	+	5.13880i	2.30785	+	0.178910i
$826$	1.99763	+	11.3291i	0.0695065	+	0.394191i
$827$	4.21974	+	23.9313i	0.146735	+	0.832174i	0.965958	+	0.258699i	$0.0832938\pi$
$827$	4.21974	+	23.9313i	0.146735	+	0.832174i	−0.819223	+	0.573475i	$0.805595\pi$
$828$	2.29416	−	0.886822i	0.0797276	−	0.0308192i
$829$	43.3587	−	25.0331i	1.50591	−	0.869437i	0.505932	−	0.862573i	$-0.331149\pi$
$829$	43.3587	−	25.0331i	1.50591	−	0.869437i	0.999976	−	0.00686327i	$-0.00218466\pi$
$830$	23.6608	−	19.8538i	0.821279	−	0.689134i
$831$	4.65540	−	4.74849i	0.161494	−	0.164723i
$832$	−1.36325	+	3.74550i	−0.0472623	+	0.129852i
$833$	−0.629576	+	0.750299i	−0.0218135	+	0.0259963i
$834$	−3.91968	−	14.0698i	−0.135727	−	0.487199i
$835$		−	37.3582i		−	1.29283i
$836$	19.0595	+	19.5035i	0.659186	+	0.674542i
$837$	−11.8299	−	2.79614i	−0.408900	−	0.0966488i
$838$	8.22164	+	1.44970i	0.284012	+	0.0500789i
$839$	−25.2797	−	21.2122i	−0.872752	−	0.732326i	0.0919238	−	0.995766i	$-0.470698\pi$
$839$	−25.2797	−	21.2122i	−0.872752	−	0.732326i	−0.964676	+	0.263440i	$0.915143\pi$
$840$	1.20394	+	12.3516i	0.0415399	+	0.426172i
$841$	7.04931	−	2.56574i	0.243080	−	0.0884737i
$842$	−23.4446	−	27.9402i	−0.807954	−	0.962882i
$843$	35.0661	+	24.0398i	1.20774	+	0.827974i
$844$	14.3492	+	8.28452i	0.493920	+	0.285165i
$845$	−9.48847	+	1.67307i	−0.326413	+	0.0575555i
$846$	−11.1755	+	20.2731i	−0.384221	+	0.697002i
$847$	30.2095	−	52.3245i	1.03801	−	1.79789i
$848$	−0.117334	−	0.203228i	−0.00402927	−	0.00697889i
$849$	−16.6499	+	36.6485i	−0.571422	+	1.25777i
$850$	−0.860063	−	2.36300i	−0.0294999	−	0.0810503i
$851$	−4.63290	−	1.68624i	−0.158814	−	0.0578035i
$852$	−7.49358	−	1.92860i	−0.256726	−	0.0660728i
$853$	5.13243	−	29.1074i	0.175731	−	0.996620i	−0.761566	−	0.648088i	$-0.775569\pi$
$853$	5.13243	−	29.1074i	0.175731	−	0.996620i	0.937297	−	0.348532i	$-0.113320\pi$
$854$	−16.6961			−0.571328
$855$	−3.44297	+	43.5012i	−0.117747	+	1.48771i
$856$	6.95251			0.237632
$857$	8.49473	−	48.1760i	0.290175	−	1.64566i	−0.396019	−	0.918242i	$-0.629608\pi$
$857$	8.49473	−	48.1760i	0.290175	−	1.64566i	0.686193	−	0.727419i	$-0.259280\pi$
$858$	41.8279	+	10.7651i	1.42798	+	0.367515i
$859$	−36.8403	−	13.4088i	−1.25698	−	0.457502i	−0.374222	−	0.927339i	$-0.622090\pi$
$859$	−36.8403	−	13.4088i	−1.25698	−	0.457502i	−0.882753	+	0.469837i	$0.844313\pi$
$860$	−7.13415	−	19.6009i	−0.243272	−	0.668386i
$861$	1.86068	−	4.09562i	0.0634120	−	0.139578i
$862$	−5.25916	−	9.10914i	−0.179128	−	0.310258i
$863$	17.6337	−	30.5424i	0.600257	−	1.03967i	−0.392525	−	0.919741i	$-0.628398\pi$
$863$	17.6337	−	30.5424i	0.600257	−	1.03967i	0.992782	−	0.119934i	$-0.0382682\pi$
$864$	5.18754	+	0.298978i	0.176484	+	0.0101714i
$865$	72.0215	−	12.6993i	2.44880	−	0.431790i
$866$	31.9364	+	18.4385i	1.08524	+	0.626565i
$867$	−24.0459	−	16.4848i	−0.816640	−	0.559853i
$868$	−3.22870	−	3.84782i	−0.109589	−	0.130604i
$869$	73.6621	−	26.8108i	2.49882	−	0.909494i
$870$	2.59986	+	26.6728i	0.0881434	+	0.904293i
$871$	−10.8110	−	9.07148i	−0.366316	−	0.307375i
$872$	−6.99366	−	1.23317i	−0.236835	−	0.0417604i
$873$	−38.1244	−	30.7248i	−1.29031	−	1.03988i
$874$	3.22128	+	1.54750i	0.108962	+	0.0523451i
$875$			8.13764i			0.275102i
$876$	2.62851	+	9.43516i	0.0888093	+	0.318784i
$877$	14.4779	−	17.2541i	0.488883	−	0.582628i	−0.464050	−	0.885809i	$-0.653604\pi$
$877$	14.4779	−	17.2541i	0.488883	−	0.582628i	0.952933	+	0.303181i	$0.0980486\pi$
$878$	4.55330	−	12.5101i	0.153666	−	0.422195i
$879$	13.3057	−	13.5718i	0.448791	−	0.457765i
$880$	15.9927	−	13.4195i	0.539113	−	0.452370i
$881$	−47.0165	+	27.1450i	−1.58403	+	0.914539i	−0.589765	+	0.807575i	$0.700780\pi$
$881$	−47.0165	+	27.1450i	−1.58403	+	0.914539i	−0.994263	+	0.106964i	$0.965887\pi$
$882$	−2.58501	−	6.68729i	−0.0870419	−	0.225173i
$883$	4.51473	+	25.6043i	0.151933	+	0.861653i	0.961537	+	0.274677i	$0.0885708\pi$
$883$	4.51473	+	25.6043i	0.151933	+	0.861653i	−0.809604	+	0.586977i	$0.800318\pi$
$884$	−0.283665	−	1.60874i	−0.00954068	−	0.0541079i
$885$	30.8750	+	2.39350i	1.03785	+	0.0804568i
$886$	6.46556	−	3.73289i	0.217215	−	0.125409i
$887$	−4.19836	+	3.52284i	−0.140967	+	0.118286i	−0.710545	−	0.703652i	$-0.751551\pi$
$887$	−4.19836	+	3.52284i	−0.140967	+	0.118286i	0.569577	+	0.821938i	$0.307107\pi$
$888$	−7.43750	−	7.29169i	−0.249586	−	0.244693i
$889$	0.905006	−	2.48648i	0.0303529	−	0.0833939i
$890$	−15.7334	+	18.7503i	−0.527385	+	0.628513i
$891$	−2.22883	−	56.2613i	−0.0746687	−	1.88482i
$892$			11.8450i			0.396599i
$893$	−32.5871	+	8.33079i	−1.09048	+	0.278779i
$894$	3.96864	+	8.29540i	0.132731	+	0.277440i
$895$	−70.2842	−	12.3930i	−2.34934	−	0.414252i
$896$	1.64480	+	1.38015i	0.0549487	+	0.0461075i
$897$	5.63345	−	0.549105i	0.188096	−	0.0183341i
$898$	22.8874	−	8.33033i	0.763763	−	0.277987i
$899$	−6.97224	−	8.30919i	−0.232537	−	0.277127i
$900$	18.1873	+	2.83690i	0.606244	+	0.0945633i
$901$	0.0832905	+	0.0480878i	0.00277481	+	0.00160204i
$902$	−7.45256	+	1.31409i	−0.248143	+	0.0437543i
$903$	−13.5212	−	18.9091i	−0.449958	−	0.629257i
$904$	−1.16500	+	2.01784i	−0.0387474	+	0.0671124i
$905$	−30.5062	−	52.8383i	−1.01406	−	1.75640i
$906$	−4.03676	−	1.83395i	−0.134112	−	0.0609288i
$907$	20.0545	+	55.0993i	0.665899	+	1.82954i	0.547928	+	0.836526i	$0.315417\pi$
$907$	20.0545	+	55.0993i	0.665899	+	1.82954i	0.117971	+	0.993017i	$0.462361\pi$
$908$	21.6807	+	7.89114i	0.719500	+	0.261877i
$909$	−3.32758	−	16.9072i	−0.110369	−	0.560776i
$910$	−4.95921	+	28.1251i	−0.164396	+	0.932336i
$911$	−2.91388			−0.0965412			−0.0482706	−	0.998834i	$-0.515371\pi$
$911$	−2.91388			−0.0965412			−0.0482706	+	0.998834i	$0.515371\pi$
$912$	4.84360	+	5.79133i	0.160388	+	0.191770i
$913$	−57.9060			−1.91641
$914$	−6.04517	+	34.2839i	−0.199956	+	1.13401i
$915$	−11.2022	+	43.5261i	−0.370333	+	1.43893i
$916$	−13.1990	−	4.80405i	−0.436108	−	0.158730i
$917$	−4.73006	−	12.9957i	−0.156200	−	0.429157i
$918$	−1.90248	+	0.956907i	−0.0627911	+	0.0315826i
$919$	2.94881	+	5.10749i	0.0972722	+	0.168480i	0.910555	−	0.413389i	$-0.135655\pi$
$919$	2.94881	+	5.10749i	0.0972722	+	0.168480i	−0.813282	+	0.581869i	$0.802322\pi$
$920$	1.36796	−	2.36937i	0.0451002	−	0.0781159i
$921$	−0.770536	+	0.550982i	−0.0253900	+	0.0181555i
$922$	2.20281	−	0.388415i	0.0725457	−	0.0127918i
$923$	−15.4209	−	8.90328i	−0.507586	−	0.293055i
$924$	13.1557	−	19.1897i	0.432789	−	0.631296i
$925$	−23.7170	−	28.2648i	−0.779809	−	0.929340i
$926$	3.45977	−	1.25925i	0.113695	−	0.0413816i
$927$	−1.71431	−	2.83800i	−0.0563053	−	0.0932121i
$928$	3.55186	+	2.98036i	0.116596	+	0.0978353i
$929$	−22.4137	−	3.95214i	−0.735369	−	0.129665i	−0.206593	−	0.978427i	$-0.566238\pi$
$929$	−22.4137	−	3.95214i	−0.735369	−	0.129665i	−0.528776	+	0.848762i	$0.677349\pi$
$930$	−12.1974	+	5.83543i	−0.399969	+	0.191351i
$931$	4.51085	−	9.38978i	0.147837	−	0.307738i
$932$			23.5886i			0.772672i
$933$	23.4872	−	6.54323i	0.768936	−	0.214216i
$934$	−8.45753	+	10.0793i	−0.276739	+	0.329804i
$935$	−2.92637	+	8.04015i	−0.0957027	+	0.262941i
$936$	11.3153	+	3.86651i	0.369851	+	0.126381i
$937$	−33.5028	+	28.1122i	−1.09449	+	0.918384i	−0.997042	−	0.0768570i	$-0.975512\pi$
$937$	−33.5028	+	28.1122i	−1.09449	+	0.918384i	−0.0974452	+	0.995241i	$0.531067\pi$
$938$	−6.58377	+	3.80114i	−0.214968	+	0.124112i
$939$	2.49025	−	32.1230i	0.0812663	−	1.04829i
$940$	4.47142	+	25.3587i	0.145842	+	0.827110i
$941$	1.06108	+	6.01769i	0.0345903	+	0.196171i	0.997206	−	0.0746992i	$-0.0237997\pi$
$941$	1.06108	+	6.01769i	0.0345903	+	0.196171i	−0.962616	+	0.270870i	$0.912689\pi$
$942$	2.24471	−	28.9556i	0.0731366	−	0.943425i
$943$	−0.858855	+	0.495860i	−0.0279682	+	0.0161474i
$944$	4.10432	−	3.44394i	0.133584	−	0.112091i
$945$	36.9762	−	4.34467i	1.20283	−	0.141332i
$946$	−13.3749	+	36.7472i	−0.434855	+	1.19475i
$947$	−19.9420	+	23.7660i	−0.648029	+	0.772291i	−0.985615	−	0.169004i	$-0.945945\pi$
$947$	−19.9420	+	23.7660i	−0.648029	+	0.772291i	0.337586	+	0.941295i	$0.390389\pi$
$948$	20.9065	−	5.82427i	0.679010	−	0.189163i
$949$			22.5395i			0.731662i
$950$	15.0871	+	22.0835i	0.489491	+	0.716482i
$951$	−42.4857	+	20.3258i	−1.37769	+	0.659109i
$952$	−0.866603	−	0.152806i	−0.0280868	−	0.00495246i
$953$	−38.1684	−	32.0271i	−1.23640	−	1.03746i	−0.997797	−	0.0663415i	$-0.978867\pi$
$953$	−38.1684	−	32.0271i	−1.23640	−	1.03746i	−0.238599	−	0.971118i	$-0.576688\pi$
$954$	−0.602598	+	0.364003i	−0.0195098	+	0.0117850i
$955$	−10.8534	+	3.95033i	−0.351209	+	0.127830i
$956$	17.5182	+	20.8774i	0.566580	+	0.675224i
$957$	28.4090	−	41.4394i	0.918334	−	1.33954i
$958$	29.0286	+	16.7597i	0.937871	+	0.541480i
$959$	−22.7792	+	4.01659i	−0.735579	+	0.129702i
$960$	4.70157	−	3.36192i	0.151742	−	0.108505i
$961$	−12.7636	+	22.1072i	−0.411730	+	0.713137i
$962$	−11.9845	−	20.7577i	−0.386395	−	0.669255i
$963$	−0.412901	−	20.8535i	−0.0133055	−	0.671993i
$964$	−7.27512	−	19.9882i	−0.234316	−	0.643777i
$965$	32.4128	+	11.7973i	1.04341	+	0.379769i
$966$	0.759955	−	2.95280i	0.0244512	−	0.0950049i
$967$	−1.94625	+	11.0377i	−0.0625873	+	0.354950i	0.937390	+	0.348280i	$0.113234\pi$
$967$	−1.94625	+	11.0377i	−0.0625873	+	0.354950i	−0.999978	+	0.00666987i	$0.997877\pi$
$968$	−28.1395			−0.904438
$969$	−2.90589	−	1.06297i	−0.0933505	−	0.0341475i
$970$	−54.4648			−1.74876
$971$	−8.32593	+	47.2187i	−0.267192	+	1.51532i	0.495528	+	0.868592i	$0.334974\pi$
$971$	−8.32593	+	47.2187i	−0.267192	+	1.51532i	−0.762720	+	0.646729i	$0.776137\pi$
$972$	0.588677	−	15.5773i	0.0188818	−	0.499643i
$973$	−17.0139	−	6.19254i	−0.545440	−	0.198524i
$974$	6.00502	+	16.4987i	0.192413	+	0.528651i
$975$	38.5662	+	17.5211i	1.23511	+	0.561123i
$976$	3.88800	+	6.73422i	0.124452	+	0.215557i
$977$	−5.39563	+	9.34550i	−0.172621	+	0.298989i	−0.939336	−	0.343000i	$-0.888557\pi$
$977$	−5.39563	+	9.34550i	−0.172621	+	0.298989i	0.766714	+	0.641989i	$0.221890\pi$
$978$	−10.6488	−	14.8921i	−0.340512	−	0.476198i
$979$	45.1913	−	7.96844i	1.44432	−	0.254672i
$980$	−6.90653	−	3.98749i	−0.220621	−	0.127376i
$981$	−3.28344	+	21.0501i	−0.104832	+	0.672078i
$982$	−15.8204	−	18.8540i	−0.504849	−	0.601656i
$983$	34.3549	−	12.5042i	1.09575	−	0.398821i	0.270003	−	0.962860i	$-0.412975\pi$
$983$	34.3549	−	12.5042i	1.09575	−	0.398821i	0.825748	+	0.564039i	$0.190753\pi$
$984$	−2.08523	+	0.203252i	−0.0664746	+	0.00647943i
$985$	30.3669	+	25.4808i	0.967569	+	0.811887i
$986$	−1.87139	−	0.329977i	−0.0595972	−	0.0105086i
$987$	12.3847	+	25.8869i	0.394208	+	0.823988i
$988$	7.16083	+	15.8297i	0.227816	+	0.503611i
$989$			5.12476i			0.162958i
$990$	−41.2002	−	47.1717i	−1.30943	−	1.49921i
$991$	−3.96786	+	4.72871i	−0.126043	+	0.150213i	−0.825375	−	0.564584i	$-0.809036\pi$
$991$	−3.96786	+	4.72871i	−0.126043	+	0.150213i	0.699332	+	0.714797i	$0.253481\pi$
$992$	−0.800119	+	2.19831i	−0.0254038	+	0.0697964i
$993$	36.3064	+	35.5947i	1.15215	+	1.12956i
$994$	−7.34797	+	6.16568i	−0.233063	+	0.195563i
$995$	−70.6194	+	40.7721i	−2.23879	+	1.29256i
$996$	−15.9836	−	1.23909i	−0.506461	−	0.0392621i
$997$	3.18227	+	18.0475i	0.100783	+	0.571571i	0.992821	+	0.119610i	$0.0381643\pi$
$997$	3.18227	+	18.0475i	0.100783	+	0.571571i	−0.892038	+	0.451961i	$0.850725\pi$
$998$	−2.55015	−	14.4626i	−0.0807237	−	0.457807i
$999$	−21.4291	+	22.7412i	−0.677986	+	0.719498i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.l.b.59.3	yes	18
3.2	odd	2		114.2.l.a.59.1	yes	18
4.3	odd	2		912.2.cc.c.401.1		18
12.11	even	2		912.2.cc.d.401.3		18
19.10	odd	18		114.2.l.a.29.1	✓	18
57.29	even	18	inner	114.2.l.b.29.3	yes	18
76.67	even	18		912.2.cc.d.257.3		18
228.143	odd	18		912.2.cc.c.257.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.29.1	✓	18	19.10	odd	18
114.2.l.a.59.1	yes	18	3.2	odd	2
114.2.l.b.29.3	yes	18	57.29	even	18	inner
114.2.l.b.59.3	yes	18	1.1	even	1	trivial
912.2.cc.c.257.1		18	228.143	odd	18
912.2.cc.c.401.1		18	4.3	odd	2
912.2.cc.d.257.3		18	76.67	even	18
912.2.cc.d.401.3		18	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(1.67739 + 0.431705i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(1.14133 + 3.13578i) q^{5} +(0.716422 - 1.57694i) q^{6} +(-1.07356 - 1.85947i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.62726 + 1.44827i) q^{9} +(3.28633 - 0.579469i) q^{10} +(-5.41799 - 3.12808i) q^{11} +(-1.42858 - 0.979371i) q^{12} +(-2.56208 - 3.05336i) q^{13} +(-2.01764 + 0.734361i) q^{14} +(0.560722 + 5.75264i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-0.403611 - 0.0711674i) q^{17} +(1.88249 - 2.33586i) q^{18} +(4.34640 - 0.329887i) q^{19} -3.33703i q^{20} +(-0.998042 - 3.58251i) q^{21} +(-4.02138 + 4.79249i) q^{22} +(-0.280411 + 0.770422i) q^{23} +(-1.21256 + 1.23681i) q^{24} +(-4.70025 + 3.94398i) q^{25} +(-3.45187 + 1.99294i) q^{26} +(3.78171 + 3.56352i) q^{27} +(0.372845 + 2.11451i) q^{28} +(0.805141 + 4.56618i) q^{29} +(5.76261 + 0.446732i) q^{30} +(-2.02597 + 1.16970i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-7.73767 - 7.58597i) q^{33} +(-0.140172 + 0.385121i) q^{34} +(4.60559 - 5.48872i) q^{35} +(-1.97348 - 2.25951i) q^{36} +6.01346i q^{37} +(0.429869 - 4.33765i) q^{38} +(-2.97944 - 6.22774i) q^{39} +(-3.28633 - 0.579469i) q^{40} +(0.926617 + 0.777524i) q^{41} +(-3.70139 + 0.360783i) q^{42} +(5.87377 - 2.13788i) q^{43} +(4.02138 + 4.79249i) q^{44} +(-1.54289 + 9.89147i) q^{45} +(0.710025 + 0.409933i) q^{46} +(-7.59919 + 1.33994i) q^{47} +(1.00746 + 1.40891i) q^{48} +(1.19492 - 2.06967i) q^{49} +(3.06787 + 5.31371i) q^{50} +(-0.646288 - 0.293616i) q^{51} +(1.36325 + 3.74550i) q^{52} +(-0.220516 - 0.0802612i) q^{53} +(4.16607 - 3.10546i) q^{54} +(3.62525 - 20.5598i) q^{55} +2.14713 q^{56} +(7.43301 + 1.32301i) q^{57} +4.63662 q^{58} +(0.930375 - 5.27642i) q^{59} +(1.44061 - 5.59749i) q^{60} +(7.30705 + 2.65955i) q^{61} +(0.800119 + 2.19831i) q^{62} +(-0.127515 - 6.44012i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(6.65050 - 11.5190i) q^{65} +(-8.81436 + 6.30282i) q^{66} +(3.48689 - 0.614832i) q^{67} +(0.354929 + 0.204918i) q^{68} +(-0.802953 + 1.17124i) q^{69} +(-4.60559 - 5.48872i) q^{70} +(4.19799 - 1.52794i) q^{71} +(-2.56787 + 1.55114i) q^{72} +(-4.33185 - 3.63485i) q^{73} +(5.92210 + 1.04423i) q^{74} +(-9.58679 + 4.58646i) q^{75} +(-4.19711 - 1.17656i) q^{76} +13.4328i q^{77} +(-6.65050 + 1.85274i) q^{78} +(-8.05412 + 9.59853i) q^{79} +(-1.14133 + 3.13578i) q^{80} +(4.80501 + 7.60999i) q^{81} +(0.926617 - 0.777524i) q^{82} +(8.01579 - 4.62792i) q^{83} +(-0.287438 + 3.70781i) q^{84} +(-0.237488 - 1.34686i) q^{85} +(-1.08543 - 6.15577i) q^{86} +(-0.620710 + 8.00685i) q^{87} +(5.41799 - 3.12808i) q^{88} +(-5.61888 + 4.71480i) q^{89} +(9.47328 + 3.23709i) q^{90} +(-2.92708 + 8.04207i) q^{91} +(0.527000 - 0.628054i) q^{92} +(-3.90331 + 1.08741i) q^{93} +7.71642i q^{94} +(5.99513 + 13.2528i) q^{95} +(1.56245 - 0.747499i) q^{96} +(-16.0734 - 2.83418i) q^{97} +(-1.83073 - 1.53616i) q^{98} +(-9.70416 - 16.0650i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9} - 12 q^{13} - 12 q^{14} + 18 q^{15} + 6 q^{17} - 6 q^{19} - 24 q^{22} + 3 q^{24} - 18 q^{25} + 18 q^{26} - 6 q^{27} + 6 q^{28} - 6 q^{29} - 24 q^{33} - 6 q^{34} - 24 q^{35}+ \cdots - 102 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9 - 12 * q^13 - 12 * q^14 + 18 * q^15 + 6 * q^17 - 6 * q^19 - 24 * q^22 + 3 * q^24 - 18 * q^25 + 18 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 - 24 * q^33 - 6 * q^34 - 24 * q^35 + 3 * q^38 + 6 * q^39 + 3 * q^41 - 6 * q^43 + 24 * q^44 - 54 * q^45 + 18 * q^46 + 30 * q^47 + 21 * q^49 + 3 * q^50 + 42 * q^51 - 6 * q^52 - 60 * q^53 + 54 * q^54 + 30 * q^55 + 12 * q^57 + 12 * q^58 + 3 * q^59 + 24 * q^60 + 54 * q^61 + 6 * q^62 - 18 * q^63 - 9 * q^64 + 24 * q^65 - 27 * q^66 - 15 * q^67 - 27 * q^68 + 30 * q^69 + 24 * q^70 + 36 * q^71 + 6 * q^72 - 42 * q^73 + 6 * q^74 - 24 * q^78 - 6 * q^79 - 3 * q^81 + 3 * q^82 + 36 * q^83 - 30 * q^84 - 6 * q^86 - 60 * q^89 - 18 * q^91 - 66 * q^93 + 6 * q^95 + 9 * q^97 + 12 * q^98 - 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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