LMFDB - Embedded newform 462.2.u.b.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(13,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("462.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.u (of order $10$, degree $4$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			13.8
Character	$\chi$	$=$	462.13
Dual form			462.2.u.b.391.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(3.18685 - 1.03547i) q^{5} +(0.309017 + 0.951057i) q^{6} +(-1.29336 - 2.30808i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.951057 + 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(3.18685 - 1.03547i) q^{5} +(0.309017 + 0.951057i) q^{6} +(-1.29336 - 2.30808i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +3.35085 q^{10} +(0.695687 + 3.24284i) q^{11} +1.00000i q^{12} +(1.25628 - 3.86645i) q^{13} +(-0.516820 - 2.59478i) q^{14} +(2.71089 + 1.96958i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-1.34308 - 4.13359i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(-6.45286 + 4.68828i) q^{19} +(3.18685 + 1.03547i) q^{20} +(1.10706 - 2.40300i) q^{21} +(-0.340455 + 3.29910i) q^{22} +1.33151 q^{23} +(-0.309017 + 0.951057i) q^{24} +(5.03871 - 3.66084i) q^{25} +(2.38960 - 3.28900i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(0.310307 - 2.62749i) q^{28} +(-5.08234 + 6.99524i) q^{29} +(1.96958 + 2.71089i) q^{30} +(4.15890 + 1.35131i) q^{31} +1.00000i q^{32} +(-2.21460 + 2.46892i) q^{33} -4.34631i q^{34} +(-6.51167 - 6.01626i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-4.73950 - 3.44345i) q^{37} +(-7.58579 + 2.46477i) q^{38} +(3.86645 - 1.25628i) q^{39} +(2.71089 + 1.96958i) q^{40} +(-3.41909 + 2.48412i) q^{41} +(1.79544 - 1.94329i) q^{42} +7.53044i q^{43} +(-1.34327 + 3.03243i) q^{44} +3.35085i q^{45} +(1.26634 + 0.411458i) q^{46} +(1.67901 + 2.31096i) q^{47} +(-0.587785 + 0.809017i) q^{48} +(-3.65446 + 5.97034i) q^{49} +(5.92336 - 1.92462i) q^{50} +(2.55470 - 3.51624i) q^{51} +(3.28900 - 2.38960i) q^{52} +(4.02534 - 12.3887i) q^{53} -1.00000 q^{54} +(5.57491 + 9.61407i) q^{55} +(1.10706 - 2.40300i) q^{56} +(-7.58579 - 2.46477i) q^{57} +(-6.99524 + 5.08234i) q^{58} +(1.54007 - 2.11973i) q^{59} +(1.03547 + 3.18685i) q^{60} +(2.11173 + 6.49924i) q^{61} +(3.53777 + 2.57034i) q^{62} +(2.59478 - 0.516820i) q^{63} +(-0.309017 + 0.951057i) q^{64} -13.6226i q^{65} +(-2.86915 + 1.66373i) q^{66} -1.42737 q^{67} +(1.34308 - 4.13359i) q^{68} +(0.782639 + 1.07721i) q^{69} +(-4.33384 - 7.73402i) q^{70} +(-3.40310 - 10.4737i) q^{71} +(-0.951057 + 0.309017i) q^{72} +(-6.22243 - 4.52086i) q^{73} +(-3.44345 - 4.73950i) q^{74} +(5.92336 + 1.92462i) q^{75} -7.97617 q^{76} +(6.58496 - 5.79985i) q^{77} +4.06542 q^{78} +(8.00297 + 2.60032i) q^{79} +(1.96958 + 2.71089i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-4.01938 + 1.30598i) q^{82} +(-5.05077 - 15.5447i) q^{83} +(2.30808 - 1.29336i) q^{84} +(-8.56040 - 11.7824i) q^{85} +(-2.32703 + 7.16188i) q^{86} -8.64659 q^{87} +(-2.21460 + 2.46892i) q^{88} +8.96914i q^{89} +(-1.03547 + 3.18685i) q^{90} +(-10.5489 + 2.10109i) q^{91} +(1.07721 + 0.782639i) q^{92} +(1.35131 + 4.15890i) q^{93} +(0.882707 + 2.71669i) q^{94} +(-15.7097 + 21.6226i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(3.40913 + 1.10769i) q^{97} +(-5.32053 + 4.54884i) q^{98} +(-3.29910 - 0.340455i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} + 10 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) $ 32 * q + 8 * q^4 + 10 * q^5 - 8 * q^6 - 10 * q^7 + 8 * q^9	$ 32 q + 8 q^{4} + 10 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{9} + 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} - 12 q^{17} - 16 q^{19} + 10 q^{20} - 8 q^{21} - 4 q^{22} + 8 q^{23} + 8 q^{24} + 6 q^{25} + 10 q^{28} + 20 q^{29} - 50 q^{31} - 16 q^{33} - 12 q^{35} - 8 q^{36} - 16 q^{37} + 6 q^{40} + 40 q^{41} + 12 q^{44} + 52 q^{49} + 40 q^{51} - 32 q^{54} - 40 q^{55} - 8 q^{56} + 10 q^{58} + 60 q^{59} + 4 q^{60} - 4 q^{61} + 20 q^{62} - 10 q^{63} + 8 q^{64} + 8 q^{66} - 16 q^{67} + 12 q^{68} + 30 q^{69} - 28 q^{70} - 48 q^{71} - 74 q^{73} - 40 q^{74} - 24 q^{76} + 6 q^{77} - 60 q^{79} - 8 q^{81} + 20 q^{82} + 4 q^{83} - 2 q^{84} - 10 q^{85} - 36 q^{86} + 20 q^{87} - 16 q^{88} - 4 q^{90} - 20 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} - 8 q^{96} + 60 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) $ 32 * q + 8 * q^4 + 10 * q^5 - 8 * q^6 - 10 * q^7 + 8 * q^9 + 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 - 12 * q^17 - 16 * q^19 + 10 * q^20 - 8 * q^21 - 4 * q^22 + 8 * q^23 + 8 * q^24 + 6 * q^25 + 10 * q^28 + 20 * q^29 - 50 * q^31 - 16 * q^33 - 12 * q^35 - 8 * q^36 - 16 * q^37 + 6 * q^40 + 40 * q^41 + 12 * q^44 + 52 * q^49 + 40 * q^51 - 32 * q^54 - 40 * q^55 - 8 * q^56 + 10 * q^58 + 60 * q^59 + 4 * q^60 - 4 * q^61 + 20 * q^62 - 10 * q^63 + 8 * q^64 + 8 * q^66 - 16 * q^67 + 12 * q^68 + 30 * q^69 - 28 * q^70 - 48 * q^71 - 74 * q^73 - 40 * q^74 - 24 * q^76 + 6 * q^77 - 60 * q^79 - 8 * q^81 + 20 * q^82 + 4 * q^83 - 2 * q^84 - 10 * q^85 - 36 * q^86 + 20 * q^87 - 16 * q^88 - 4 * q^90 - 20 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 - 8 * q^96 + 60 * q^97 - 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	3.18685	−	1.03547i	1.42520	−	0.463076i	0.507950	−	0.861386i	$-0.330403\pi$
$5$	3.18685	−	1.03547i	1.42520	−	0.463076i	0.917251	+	0.398310i	$0.130403\pi$
$6$	0.309017	+	0.951057i	0.126156	+	0.388267i
$7$	−1.29336	−	2.30808i	−0.488843	−	0.872372i
$7$	−1.29336	−	2.30808i	−0.488843	−	0.872372i
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$	3.35085			1.05963
$11$	0.695687	+	3.24284i	0.209758	+	0.977753i
$11$	0.695687	+	3.24284i	0.209758	+	0.977753i
$12$			1.00000i			0.288675i
$13$	1.25628	−	3.86645i	0.348431	−	1.07236i	−0.611291	−	0.791406i	$-0.709349\pi$
$13$	1.25628	−	3.86645i	0.348431	−	1.07236i	0.959721	−	0.280953i	$-0.0906507\pi$
$14$	−0.516820	−	2.59478i	−0.138126	−	0.693485i
$15$	2.71089	+	1.96958i	0.699950	+	0.508543i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−1.34308	−	4.13359i	−0.325746	−	1.00254i	−0.971103	−	0.238661i	$-0.923291\pi$
$17$	−1.34308	−	4.13359i	−0.325746	−	1.00254i	0.645357	−	0.763881i	$-0.276709\pi$
$18$	−0.587785	+	0.809017i	−0.138542	+	0.190687i
$19$	−6.45286	+	4.68828i	−1.48039	+	1.07556i	−0.502956	+	0.864312i	$0.667754\pi$
$19$	−6.45286	+	4.68828i	−1.48039	+	1.07556i	−0.977432	+	0.211253i	$0.932246\pi$
$20$	3.18685	+	1.03547i	0.712600	+	0.231538i
$21$	1.10706	−	2.40300i	0.241580	−	0.524378i
$22$	−0.340455	+	3.29910i	−0.0725852	+	0.703371i
$23$	1.33151			0.277638			0.138819	−	0.990318i	$-0.455669\pi$
$23$	1.33151			0.277638			0.138819	+	0.990318i	$0.455669\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	5.03871	−	3.66084i	1.00774	−	0.732167i
$26$	2.38960	−	3.28900i	0.468638	−	0.645025i
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	0.310307	−	2.62749i	0.0586425	−	0.496549i
$29$	−5.08234	+	6.99524i	−0.943766	+	1.29898i	0.0104750	+	0.999945i	$0.496666\pi$
$29$	−5.08234	+	6.99524i	−0.943766	+	1.29898i	−0.954241	+	0.299038i	$0.903334\pi$
$30$	1.96958	+	2.71089i	0.359594	+	0.494939i
$31$	4.15890	+	1.35131i	0.746961	+	0.242702i	0.657673	−	0.753304i	$-0.271541\pi$
$31$	4.15890	+	1.35131i	0.746961	+	0.242702i	0.0892877	+	0.996006i	$0.471541\pi$
$32$			1.00000i			0.176777i
$33$	−2.21460	+	2.46892i	−0.385512	+	0.429783i
$34$		−	4.34631i		−	0.745386i
$35$	−6.51167	−	6.01626i	−1.10067	−	1.01693i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	−4.73950	−	3.44345i	−0.779169	−	0.566099i	0.125561	−	0.992086i	$-0.459927\pi$
$37$	−4.73950	−	3.44345i	−0.779169	−	0.566099i	−0.904729	+	0.425987i	$0.859927\pi$
$38$	−7.58579	+	2.46477i	−1.23058	+	0.399839i
$39$	3.86645	−	1.25628i	0.619127	−	0.201167i
$40$	2.71089	+	1.96958i	0.428630	+	0.311418i
$41$	−3.41909	+	2.48412i	−0.533972	+	0.387954i	−0.821842	−	0.569716i	$-0.807053\pi$
$41$	−3.41909	+	2.48412i	−0.533972	+	0.387954i	0.287869	+	0.957670i	$0.407053\pi$
$42$	1.79544	−	1.94329i	0.277043	−	0.299856i
$43$			7.53044i			1.14838i	0.818721	+	0.574191i	$0.194683\pi$
$43$			7.53044i			1.14838i	−0.818721	+	0.574191i	$0.805317\pi$
$44$	−1.34327	+	3.03243i	−0.202506	+	0.457156i
$45$			3.35085i			0.499515i
$46$	1.26634	+	0.411458i	0.186711	+	0.0606661i
$47$	1.67901	+	2.31096i	0.244909	+	0.337088i	0.913720	−	0.406344i	$-0.133197\pi$
$47$	1.67901	+	2.31096i	0.244909	+	0.337088i	−0.668811	+	0.743432i	$0.733197\pi$
$48$	−0.587785	+	0.809017i	−0.0848395	+	0.116772i
$49$	−3.65446	+	5.97034i	−0.522065	+	0.852906i
$50$	5.92336	−	1.92462i	0.837689	−	0.272182i
$51$	2.55470	−	3.51624i	0.357729	−	0.492372i
$52$	3.28900	−	2.38960i	0.456102	−	0.331377i
$53$	4.02534	−	12.3887i	0.552923	−	1.70172i	−0.148444	−	0.988921i	$-0.547427\pi$
$53$	4.02534	−	12.3887i	0.552923	−	1.70172i	0.701367	−	0.712800i	$-0.252573\pi$
$54$	−1.00000			−0.136083
$55$	5.57491	+	9.61407i	0.751721	+	1.29636i
$56$	1.10706	−	2.40300i	0.147937	−	0.321115i
$57$	−7.58579	−	2.46477i	−1.00476	−	0.326467i
$58$	−6.99524	+	5.08234i	−0.918520	+	0.667344i
$59$	1.54007	−	2.11973i	0.200500	−	0.275965i	−0.696913	−	0.717156i	$-0.745444\pi$
$59$	1.54007	−	2.11973i	0.200500	−	0.275965i	0.897413	+	0.441191i	$0.145444\pi$
$60$	1.03547	+	3.18685i	0.133678	+	0.411420i
$61$	2.11173	+	6.49924i	0.270380	+	0.832143i	0.990405	+	0.138195i	$0.0441302\pi$
$61$	2.11173	+	6.49924i	0.270380	+	0.832143i	−0.720025	+	0.693948i	$0.755870\pi$
$62$	3.53777	+	2.57034i	0.449298	+	0.326434i
$63$	2.59478	−	0.516820i	0.326912	−	0.0651132i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$		−	13.6226i		−	1.68968i
$66$	−2.86915	+	1.66373i	−0.353167	+	0.204791i
$67$	−1.42737			−0.174381			−0.0871907	−	0.996192i	$-0.527789\pi$
$67$	−1.42737			−0.174381			−0.0871907	+	0.996192i	$0.527789\pi$
$68$	1.34308	−	4.13359i	0.162873	−	0.501271i
$69$	0.782639	+	1.07721i	0.0942187	+	0.129681i
$70$	−4.33384	−	7.73402i	−0.517993	−	0.924392i
$71$	−3.40310	−	10.4737i	−0.403874	−	1.24300i	−0.921832	−	0.387590i	$-0.873308\pi$
$71$	−3.40310	−	10.4737i	−0.403874	−	1.24300i	0.517958	−	0.855406i	$-0.326692\pi$
$72$	−0.951057	+	0.309017i	−0.112083	+	0.0364180i
$73$	−6.22243	−	4.52086i	−0.728280	−	0.529127i	0.160739	−	0.986997i	$-0.448612\pi$
$73$	−6.22243	−	4.52086i	−0.728280	−	0.529127i	−0.889019	+	0.457870i	$0.848612\pi$
$74$	−3.44345	−	4.73950i	−0.400293	−	0.550956i
$75$	5.92336	+	1.92462i	0.683970	+	0.222235i
$76$	−7.97617			−0.914930
$77$	6.58496	−	5.79985i	0.750426	−	0.660955i
$78$	4.06542			0.460319
$79$	8.00297	+	2.60032i	0.900404	+	0.292559i	0.722404	−	0.691471i	$-0.243037\pi$
$79$	8.00297	+	2.60032i	0.900404	+	0.292559i	0.178000	+	0.984030i	$0.443037\pi$
$80$	1.96958	+	2.71089i	0.220206	+	0.303087i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−4.01938	+	1.30598i	−0.443867	+	0.144221i
$83$	−5.05077	−	15.5447i	−0.554394	−	1.70625i	−0.697537	−	0.716549i	$-0.745721\pi$
$83$	−5.05077	−	15.5447i	−0.554394	−	1.70625i	0.143143	−	0.989702i	$-0.454279\pi$
$84$	2.30808	−	1.29336i	0.251832	−	0.141117i
$85$	−8.56040	−	11.7824i	−0.928506	−	1.27798i
$86$	−2.32703	+	7.16188i	−0.250931	+	0.772285i
$87$	−8.64659			−0.927012
$88$	−2.21460	+	2.46892i	−0.236077	+	0.263187i
$89$			8.96914i			0.950727i	0.879789	+	0.475364i	$0.157683\pi$
$89$			8.96914i			0.950727i	−0.879789	+	0.475364i	$0.842317\pi$
$90$	−1.03547	+	3.18685i	−0.109148	+	0.335923i
$91$	−10.5489	+	2.10109i	−1.10582	+	0.220254i
$92$	1.07721	+	0.782639i	0.112307	+	0.0815958i
$93$	1.35131	+	4.15890i	0.140124	+	0.431258i
$94$	0.882707	+	2.71669i	0.0910443	+	0.280206i
$95$	−15.7097	+	21.6226i	−1.61178	+	2.21843i
$96$	−0.809017	+	0.587785i	−0.0825700	+	0.0599906i
$97$	3.40913	+	1.10769i	0.346145	+	0.112469i	0.476930	−	0.878941i	$-0.341750\pi$
$97$	3.40913	+	1.10769i	0.346145	+	0.112469i	−0.130785	+	0.991411i	$0.541750\pi$
$98$	−5.32053	+	4.54884i	−0.537455	+	0.459502i
$99$	−3.29910	−	0.340455i	−0.331572	−	0.0342170i
$100$	6.22819			0.622819
$101$	2.93130	−	9.02160i	0.291675	−	0.897683i	−0.692643	−	0.721280i	$-0.743554\pi$
$101$	2.93130	−	9.02160i	0.291675	−	0.897683i	0.984318	−	0.176402i	$-0.0564460\pi$
$102$	3.51624	−	2.55470i	0.348160	−	0.252953i
$103$	−7.73913	+	10.6520i	−0.762559	+	1.04957i	0.234438	+	0.972131i	$0.424675\pi$
$103$	−7.73913	+	10.6520i	−0.762559	+	1.04957i	−0.996997	+	0.0774410i	$0.975325\pi$
$104$	3.86645	−	1.25628i	0.379136	−	0.123189i
$105$	1.03979	−	8.80432i	0.101473	−	0.859214i
$106$	7.65665	−	10.5385i	0.743679	−	1.02359i
$107$	−9.11004	−	12.5389i	−0.880701	−	1.21218i	−0.976226	−	0.216754i	$-0.930453\pi$
$107$	−9.11004	−	12.5389i	−0.880701	−	1.21218i	0.0955251	−	0.995427i	$-0.469547\pi$
$108$	−0.951057	−	0.309017i	−0.0915155	−	0.0297352i
$109$		−	9.74058i		−	0.932979i	−0.884527	−	0.466489i	$-0.845519\pi$
$109$		−	9.74058i		−	0.932979i	0.884527	−	0.466489i	$-0.154481\pi$
$110$	2.33114	+	10.8663i	0.222266	+	1.03606i
$111$		−	5.85834i		−	0.556049i
$112$	1.79544	−	1.94329i	0.169654	−	0.183624i
$113$	9.62643	−	6.99401i	0.905578	−	0.657941i	−0.0343143	−	0.999411i	$-0.510925\pi$
$113$	9.62643	−	6.99401i	0.905578	−	0.657941i	0.939893	+	0.341470i	$0.110925\pi$
$114$	−6.45286	−	4.68828i	−0.604366	−	0.439097i
$115$	4.24330	−	1.37873i	0.395690	−	0.128567i
$116$	−8.22339	+	2.67194i	−0.763523	+	0.248084i
$117$	3.28900	+	2.38960i	0.304068	+	0.220918i
$118$	2.11973	−	1.54007i	0.195137	−	0.141775i
$119$	−7.80356	+	8.44615i	−0.715351	+	0.774257i
$120$			3.35085i			0.305889i
$121$	−10.0320	+	4.51201i	−0.912003	+	0.410183i
$122$			6.83371i			0.618695i
$123$	−4.01938	−	1.30598i	−0.362416	−	0.117756i
$124$	2.57034	+	3.53777i	0.230824	+	0.317701i
$125$	2.41901	−	3.32948i	0.216363	−	0.297798i
$126$	2.62749	+	0.310307i	0.234076	+	0.0276443i
$127$	10.0435	−	3.26334i	0.891218	−	0.289574i	0.172611	−	0.984990i	$-0.444780\pi$
$127$	10.0435	−	3.26334i	0.891218	−	0.289574i	0.718608	+	0.695416i	$0.244780\pi$
$128$	−0.587785	+	0.809017i	−0.0519534	+	0.0715077i
$129$	−6.09226	+	4.42628i	−0.536393	+	0.389712i
$130$	4.20962	−	12.9559i	0.369208	−	1.13631i
$131$	1.47125			0.128544			0.0642720	−	0.997932i	$-0.479527\pi$
$131$	1.47125			0.128544			0.0642720	+	0.997932i	$0.479527\pi$
$132$	−3.24284	+	0.695687i	−0.282253	+	0.0605518i
$133$	19.1668	+	8.83009i	1.66197	+	0.765666i
$134$	−1.35751	−	0.441082i	−0.117271	−	0.0381037i
$135$	−2.71089	+	1.96958i	−0.233317	+	0.169514i
$136$	2.55470	−	3.51624i	0.219063	−	0.301515i
$137$	2.83922	+	8.73822i	0.242571	+	0.746557i	0.996026	+	0.0890578i	$0.0283856\pi$
$137$	2.83922	+	8.73822i	0.242571	+	0.746557i	−0.753455	+	0.657499i	$0.771614\pi$
$138$	0.411458	+	1.26634i	0.0350256	+	0.107798i
$139$	−0.651883	−	0.473621i	−0.0552920	−	0.0401720i	0.559796	−	0.828630i	$-0.310880\pi$
$139$	−0.651883	−	0.473621i	−0.0552920	−	0.0401720i	−0.615088	+	0.788459i	$0.710880\pi$
$140$	−1.73179	−	8.69472i	−0.146363	−	0.734838i
$141$	−0.882707	+	2.71669i	−0.0743374	+	0.228787i
$142$		−	11.0127i		−	0.924163i
$143$	13.4123	+	1.38409i	1.12159	+	0.115744i
$144$	−1.00000			−0.0833333
$145$	−8.95328	+	27.5553i	−0.743529	+	2.28835i
$146$	−4.52086	−	6.22243i	−0.374149	−	0.514972i
$147$	−6.97814	+	0.552761i	−0.575547	+	0.0455909i
$148$	−1.81033	−	5.57162i	−0.148808	−	0.457984i
$149$	10.5048	−	3.41323i	0.860590	−	0.279623i	0.154715	−	0.987959i	$-0.450554\pi$
$149$	10.5048	−	3.41323i	0.860590	−	0.279623i	0.705875	+	0.708336i	$0.250554\pi$
$150$	5.03871	+	3.66084i	0.411409	+	0.298906i
$151$	7.41822	+	10.2103i	0.603686	+	0.830902i	0.996039	−	0.0889122i	$-0.0283390\pi$
$151$	7.41822	+	10.2103i	0.603686	+	0.830902i	−0.392354	+	0.919814i	$0.628339\pi$
$152$	−7.58579	−	2.46477i	−0.615289	−	0.199919i
$153$	4.34631			0.351378
$154$	8.05492	−	3.48112i	0.649084	−	0.280517i
$155$	14.6530			1.17696
$156$	3.86645	+	1.25628i	0.309564	+	0.100583i
$157$	−0.0381184	−	0.0524654i	−0.00304218	−	0.00418720i	0.807493	−	0.589877i	$-0.200824\pi$
$157$	−0.0381184	−	0.0524654i	−0.00304218	−	0.00418720i	−0.810535	+	0.585690i	$0.800824\pi$
$158$	6.80773	+	4.94611i	0.541594	+	0.393491i
$159$	12.3887	−	4.02534i	0.982489	−	0.319230i
$160$	1.03547	+	3.18685i	0.0818610	+	0.251942i
$161$	−1.72211	−	3.07322i	−0.135721	−	0.242204i
$162$	−0.587785	−	0.809017i	−0.0461808	−	0.0635624i
$163$	−4.04450	+	12.4477i	−0.316790	+	0.974978i	0.658222	+	0.752824i	$0.271309\pi$
$163$	−4.04450	+	12.4477i	−0.316790	+	0.974978i	−0.975012	+	0.222154i	$0.928691\pi$
$164$	−4.22623			−0.330013
$165$	−4.50110	+	10.1612i	−0.350410	+	0.791049i
$166$		−	16.3446i		−	1.26859i
$167$	−0.490022	+	1.50813i	−0.0379190	+	0.116703i	−0.968224	−	0.250083i	$-0.919542\pi$
$167$	−0.490022	+	1.50813i	−0.0379190	+	0.116703i	0.930305	+	0.366786i	$0.119542\pi$
$168$	2.59478	−	0.516820i	0.200192	−	0.0398735i
$169$	−2.85394	−	2.07351i	−0.219534	−	0.159501i
$170$	−4.50047	−	13.8510i	−0.345170	−	1.06233i
$171$	−2.46477	−	7.58579i	−0.188486	−	0.580100i
$172$	−4.42628	+	6.09226i	−0.337501	+	0.464530i
$173$	−6.33012	+	4.59910i	−0.481270	+	0.349663i	−0.801817	−	0.597569i	$-0.796133\pi$
$173$	−6.33012	+	4.59910i	−0.481270	+	0.349663i	0.320547	+	0.947233i	$0.396133\pi$
$174$	−8.22339	−	2.67194i	−0.623414	−	0.202559i
$175$	−14.9663	−	6.89497i	−1.13135	−	0.521211i
$176$	−2.86915	+	1.66373i	−0.216270	+	0.125408i
$177$	2.62013			0.196941
$178$	−2.77162	+	8.53016i	−0.207741	+	0.639363i
$179$	−8.31217	+	6.03915i	−0.621281	+	0.451387i	−0.853369	−	0.521308i	$-0.825444\pi$
$179$	−8.31217	+	6.03915i	−0.621281	+	0.451387i	0.232088	+	0.972695i	$0.425444\pi$
$180$	−1.96958	+	2.71089i	−0.146804	+	0.202058i
$181$	3.21311	−	1.04400i	0.238829	−	0.0776002i	−0.187157	−	0.982330i	$-0.559927\pi$
$181$	3.21311	−	1.04400i	0.238829	−	0.0776002i	0.425986	+	0.904730i	$0.359927\pi$
$182$	−10.6819	−	1.26153i	−0.791792	−	0.0935108i
$183$	−4.01675	+	5.52859i	−0.296927	+	0.408685i
$184$	0.782639	+	1.07721i	0.0576969	+	0.0794130i
$185$	−18.6696	−	6.06613i	−1.37262	−	0.445991i
$186$			4.37293i			0.320639i
$187$	12.4702	−	7.23109i	0.911911	−	0.528790i
$188$			2.85650i			0.208332i
$189$	1.94329	+	1.79544i	0.141354	+	0.130599i
$190$	−21.6226	+	15.7097i	−1.56867	+	1.13970i
$191$	3.94217	+	2.86415i	0.285245	+	0.207243i	0.721202	−	0.692725i	$-0.243590\pi$
$191$	3.94217	+	2.86415i	0.285245	+	0.207243i	−0.435957	+	0.899968i	$0.643590\pi$
$192$	−0.951057	+	0.309017i	−0.0686366	+	0.0223014i
$193$	23.3253	−	7.57885i	1.67899	−	0.545537i	0.694276	−	0.719709i	$-0.255725\pi$
$193$	23.3253	−	7.57885i	1.67899	−	0.545537i	0.984715	+	0.174172i	$0.0557248\pi$
$194$	2.89998	+	2.10696i	0.208207	+	0.151271i
$195$	11.0209	−	8.00717i	0.789225	−	0.573406i
$196$	−6.46579	+	2.68207i	−0.461842	+	0.191577i
$197$			3.63422i			0.258928i	0.991584	+	0.129464i	$0.0413256\pi$
$197$			3.63422i			0.258928i	−0.991584	+	0.129464i	$0.958674\pi$
$198$	−3.03243	−	1.34327i	−0.215505	−	0.0954621i
$199$		−	9.89059i		−	0.701125i	−0.936539	−	0.350563i	$-0.885990\pi$
$199$		−	9.89059i		−	0.701125i	0.936539	−	0.350563i	$-0.114010\pi$
$200$	5.92336	+	1.92462i	0.418845	+	0.136091i
$201$	−0.838989	−	1.15477i	−0.0591777	−	0.0814511i
$202$	5.57565	−	7.67423i	0.392302	−	0.539957i
$203$	22.7188	+	2.68310i	1.59455	+	0.188316i
$204$	4.13359	−	1.34308i	0.289409	−	0.0940347i
$205$	−8.32390	+	11.4569i	−0.581366	+	0.800182i
$206$	−10.6520	+	7.73913i	−0.742159	+	0.539210i
$207$	−0.411458	+	1.26634i	−0.0285983	+	0.0880165i
$208$	4.06542			0.281886
$209$	−19.6925	−	17.6640i	−1.36216	−	1.22185i
$210$	3.70959	−	8.05210i	0.255986	−	0.555647i
$211$	6.08793	+	1.97809i	0.419111	+	0.136177i	0.510978	−	0.859594i	$-0.329283\pi$
$211$	6.08793	+	1.97809i	0.419111	+	0.136177i	−0.0918671	+	0.995771i	$0.529283\pi$
$212$	10.5385	−	7.65665i	0.723785	−	0.525861i
$213$	6.47308	−	8.90944i	0.443528	−	0.610465i
$214$	−4.78943	−	14.7404i	−0.327399	−	1.00763i
$215$	7.79754	+	23.9984i	0.531788	+	1.63667i
$216$	−0.809017	−	0.587785i	−0.0550466	−	0.0399937i
$217$	−2.26002	−	11.3468i	−0.153420	−	0.770271i
$218$	3.01001	−	9.26385i	0.203863	−	0.627427i
$219$		−	7.69135i		−	0.519733i
$220$	−1.14081	+	11.0548i	−0.0769136	+	0.745314i
$221$	−17.6696			−1.18859
$222$	1.81033	−	5.57162i	0.121501	−	0.373942i
$223$	−4.91386	−	6.76334i	−0.329056	−	0.452907i	0.612149	−	0.790742i	$-0.290305\pi$
$223$	−4.91386	−	6.76334i	−0.329056	−	0.452907i	−0.941205	+	0.337835i	$0.890305\pi$
$224$	2.30808	−	1.29336i	0.154215	−	0.0864160i
$225$	1.92462	+	5.92336i	0.128308	+	0.394890i
$226$	11.3165	−	3.67697i	0.752766	−	0.244588i
$227$	12.3732	+	8.98966i	0.821239	+	0.596665i	0.917067	−	0.398733i	$-0.130550\pi$
$227$	12.3732	+	8.98966i	0.821239	+	0.596665i	−0.0958282	+	0.995398i	$0.530550\pi$
$228$	−4.68828	−	6.45286i	−0.310489	−	0.427351i
$229$	0.824290	+	0.267828i	0.0544706	+	0.0176986i	0.336126	−	0.941817i	$-0.390883\pi$
$229$	0.824290	+	0.267828i	0.0544706	+	0.0176986i	−0.281655	+	0.959516i	$0.590883\pi$
$230$	4.46167			0.294194
$231$	8.56272	+	1.91828i	0.563386	+	0.126213i
$232$	−8.64659			−0.567676
$233$	14.5931	+	4.74160i	0.956028	+	0.310632i	0.745163	−	0.666883i	$-0.232372\pi$
$233$	14.5931	+	4.74160i	0.956028	+	0.310632i	0.210865	+	0.977515i	$0.432372\pi$
$234$	2.38960	+	3.28900i	0.156213	+	0.215008i
$235$	7.74367	+	5.62610i	0.505141	+	0.367007i
$236$	2.49189	−	0.809664i	0.162208	−	0.0527046i
$237$	2.60032	+	8.00297i	0.168909	+	0.519849i
$238$	−10.0316	+	5.62133i	−0.650254	+	0.364377i
$239$	−10.3144	−	14.1965i	−0.667182	−	0.918297i	0.332510	−	0.943100i	$-0.392104\pi$
$239$	−10.3144	−	14.1965i	−0.667182	−	0.918297i	−0.999692	+	0.0248024i	$0.992104\pi$
$240$	−1.03547	+	3.18685i	−0.0668392	+	0.205710i
$241$	20.8041			1.34011			0.670055	−	0.742312i	$-0.266271\pi$
$241$	20.8041			1.34011			0.670055	+	0.742312i	$0.266271\pi$
$242$	−10.9353	+	1.19110i	−0.702949	+	0.0765671i
$243$		−	1.00000i		−	0.0641500i
$244$	−2.11173	+	6.49924i	−0.135190	+	0.416072i
$245$	−5.46409	+	22.8106i	−0.349088	+	1.45732i
$246$	−3.41909	−	2.48412i	−0.217993	−	0.158381i
$247$	10.0203	+	30.8395i	0.637579	+	1.96227i
$248$	1.35131	+	4.15890i	0.0858082	+	0.264090i
$249$	9.60714	−	13.2231i	0.608828	−	0.837980i
$250$	3.32948	−	2.41901i	0.210575	−	0.152992i
$251$	5.86531	+	1.90575i	0.370215	+	0.120290i	0.488215	−	0.872724i	$-0.337648\pi$
$251$	5.86531	+	1.90575i	0.370215	+	0.120290i	−0.118000	+	0.993014i	$0.537648\pi$
$252$	2.40300	+	1.10706i	0.151375	+	0.0697382i
$253$	0.926312	+	4.31786i	0.0582367	+	0.271462i
$254$	10.5604			0.662617
$255$	4.50047	−	13.8510i	0.281830	−	0.867385i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−7.70597	+	10.6064i	−0.480685	+	0.661606i	−0.978636	−	0.205599i	$-0.934086\pi$
$257$	−7.70597	+	10.6064i	−0.480685	+	0.661606i	0.497951	+	0.867205i	$0.334086\pi$
$258$	−7.16188	+	2.32703i	−0.445879	+	0.144875i
$259$	−1.81788	+	15.3927i	−0.112958	+	0.956459i
$260$	8.00717	−	11.0209i	0.496584	−	0.683489i
$261$	−5.08234	−	6.99524i	−0.314589	−	0.432994i
$262$	1.39924	+	0.454642i	0.0864456	+	0.0280879i
$263$		−	3.63307i		−	0.224024i	−0.993707	−	0.112012i	$-0.964270\pi$
$263$		−	3.63307i		−	0.224024i	0.993707	−	0.112012i	$-0.0357296\pi$
$264$	−3.29910	−	0.340455i	−0.203046	−	0.0209536i
$265$		−	43.6490i		−	2.68134i
$266$	15.5000	+	14.3208i	0.950368	+	0.878063i
$267$	−7.25619	+	5.27193i	−0.444071	+	0.322637i
$268$	−1.15477	−	0.838989i	−0.0705387	−	0.0512494i
$269$	3.02434	−	0.982667i	0.184397	−	0.0599142i	−0.215363	−	0.976534i	$-0.569093\pi$
$269$	3.02434	−	0.982667i	0.184397	−	0.0599142i	0.399760	+	0.916620i	$0.369093\pi$
$270$	−3.18685	+	1.03547i	−0.193945	+	0.0630166i
$271$	24.4388	+	17.7558i	1.48455	+	1.07859i	0.976054	+	0.217526i	$0.0697987\pi$
$271$	24.4388	+	17.7558i	1.48455	+	1.07859i	0.508497	+	0.861064i	$0.330201\pi$
$272$	3.51624	−	2.55470i	0.213203	−	0.154901i
$273$	−7.90030	−	7.29924i	−0.478148	−	0.441770i
$274$			9.18791i			0.555062i
$275$	15.3769	+	13.7929i	0.927260	+	0.831745i
$276$			1.33151i			0.0801472i
$277$	−21.8573	−	7.10188i	−1.31328	−	0.426710i	−0.433098	−	0.901347i	$-0.642579\pi$
$277$	−21.8573	−	7.10188i	−1.31328	−	0.426710i	−0.880182	+	0.474637i	$0.842579\pi$
$278$	−0.473621	−	0.651883i	−0.0284059	−	0.0390973i
$279$	−2.57034	+	3.53777i	−0.153882	+	0.211801i
$280$	1.03979	−	8.80432i	0.0621394	−	0.526159i
$281$	16.2054	−	5.26544i	0.966731	−	0.314110i	0.217236	−	0.976119i	$-0.430296\pi$
$281$	16.2054	−	5.26544i	0.966731	−	0.314110i	0.749496	+	0.662009i	$0.230296\pi$
$282$	−1.67901	+	2.31096i	−0.0999835	+	0.137616i
$283$	−14.0633	+	10.2176i	−0.835974	+	0.607371i	−0.921243	−	0.388987i	$-0.872825\pi$
$283$	−14.0633	+	10.2176i	−0.835974	+	0.607371i	0.0852690	+	0.996358i	$0.472825\pi$
$284$	3.40310	−	10.4737i	0.201937	−	0.621498i
$285$	−26.7269			−1.58317
$286$	12.3281	+	5.46097i	0.728976	+	0.322914i
$287$	10.1556	+	4.67869i	0.599469	+	0.276174i
$288$	−0.951057	−	0.309017i	−0.0560415	−	0.0182090i
$289$	−1.52938	+	1.11116i	−0.0899635	+	0.0653623i
$290$	−17.0301	+	23.4400i	−1.00004	+	1.37644i
$291$	1.10769	+	3.40913i	0.0649342	+	0.199847i
$292$	−2.37676	−	7.31490i	−0.139089	−	0.428072i
$293$	2.17095	+	1.57729i	0.126828	+	0.0921461i	0.649391	−	0.760455i	$-0.275024\pi$
$293$	2.17095	+	1.57729i	0.126828	+	0.0921461i	−0.522563	+	0.852601i	$0.675024\pi$
$294$	−6.80742	−	1.63066i	−0.397017	−	0.0951019i
$295$	2.71306	−	8.34994i	0.157961	−	0.486153i
$296$		−	5.85834i		−	0.340509i
$297$	−1.66373	−	2.86915i	−0.0965395	−	0.166485i
$298$	11.0454			0.639845
$299$	1.67275	−	5.14820i	0.0967376	−	0.297728i
$300$	3.66084	+	5.03871i	0.211358	+	0.290910i
$301$	17.3809	−	9.73955i	1.00182	−	0.561378i
$302$	3.89999	+	12.0029i	0.224419	+	0.690691i
$303$	9.02160	−	2.93130i	0.518277	−	0.168398i
$304$	−6.45286	−	4.68828i	−0.370097	−	0.268891i
$305$	13.4595	+	18.5255i	0.770691	+	1.06076i
$306$	4.13359	+	1.34308i	0.236301	+	0.0767790i
$307$	−27.8314			−1.58842			−0.794212	−	0.607641i	$-0.792116\pi$
$307$	−27.8314			−1.58842			−0.794212	+	0.607641i	$0.792116\pi$
$308$	8.73641	−	0.821637i	0.497803	−	0.0468171i
$309$	−13.1666			−0.749021
$310$	13.9358	+	4.52803i	0.791503	+	0.257175i
$311$	−0.364789	−	0.502088i	−0.0206853	−	0.0284708i	0.798549	−	0.601930i	$-0.205601\pi$
$311$	−0.364789	−	0.502088i	−0.0206853	−	0.0284708i	−0.819234	+	0.573459i	$0.805601\pi$
$312$	3.28900	+	2.38960i	0.186203	+	0.135284i
$313$	10.5475	−	3.42710i	0.596182	−	0.193711i	0.00464514	−	0.999989i	$-0.498521\pi$
$313$	10.5475	−	3.42710i	0.596182	−	0.193711i	0.591537	+	0.806278i	$0.298521\pi$
$314$	−0.0200400	−	0.0616768i	−0.00113092	−	0.00348062i
$315$	7.73402	−	4.33384i	0.435763	−	0.244184i
$316$	4.94611	+	6.80773i	0.278240	+	0.382965i
$317$	−4.05992	+	12.4952i	−0.228028	+	0.701798i	0.769942	+	0.638114i	$0.220285\pi$
$317$	−4.05992	+	12.4952i	−0.228028	+	0.701798i	−0.997970	+	0.0636843i	$0.979715\pi$
$318$	13.0263			0.730477
$319$	−26.2202	−	11.6147i	−1.46805	−	0.650299i
$320$			3.35085i			0.187318i
$321$	4.78943	−	14.7404i	0.267320	−	0.822727i
$322$	−0.688149	−	3.45497i	−0.0383490	−	0.192538i
$323$	28.0461	+	20.3767i	1.56053	+	1.13379i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	−7.82438	−	24.0810i	−0.434018	−	1.33577i
$326$	−7.69310	+	10.5886i	−0.426081	+	0.586450i
$327$	7.88030	−	5.72537i	0.435781	−	0.316614i
$328$	−4.01938	−	1.30598i	−0.221933	−	0.0721105i
$329$	3.16231	−	6.86418i	0.174344	−	0.378434i
$330$	−7.42079	+	8.27297i	−0.408501	+	0.455412i
$331$	−16.3939			−0.901092			−0.450546	−	0.892753i	$-0.648771\pi$
$331$	−16.3939			−0.901092			−0.450546	+	0.892753i	$0.648771\pi$
$332$	5.05077	−	15.5447i	0.277197	−	0.853125i
$333$	4.73950	−	3.44345i	0.259723	−	0.188700i
$334$	−0.932077	+	1.28289i	−0.0510010	+	0.0701969i
$335$	−4.54882	+	1.47800i	−0.248528	+	0.0807518i
$336$	2.62749	+	0.310307i	0.143341	+	0.0169286i
$337$	−20.1910	+	27.7905i	−1.09987	+	1.51384i	−0.264318	+	0.964436i	$0.585147\pi$
$337$	−20.1910	+	27.7905i	−1.09987	+	1.51384i	−0.835554	+	0.549408i	$0.814853\pi$
$338$	−2.07351	−	2.85394i	−0.112784	−	0.155234i
$339$	11.3165	+	3.67697i	0.614631	+	0.199706i
$340$		−	14.5638i		−	0.789835i
$341$	−1.48878	+	14.4267i	−0.0806222	+	0.781252i
$342$		−	7.97617i		−	0.431302i
$343$	18.5065	+	0.712992i	0.999259	+	0.0384979i
$344$	−6.09226	+	4.42628i	−0.328472	+	0.238649i
$345$	3.60957	+	2.62251i	0.194333	+	0.141191i
$346$	−7.44150	+	2.41789i	−0.400057	+	0.129987i
$347$	22.5095	−	7.31378i	1.20837	−	0.392625i	0.365539	−	0.930796i	$-0.380885\pi$
$347$	22.5095	−	7.31378i	1.20837	−	0.392625i	0.842835	+	0.538172i	$0.180885\pi$
$348$	−6.99524	−	5.08234i	−0.374984	−	0.272442i
$349$	−0.432192	+	0.314006i	−0.0231347	+	0.0168084i	−0.599293	−	0.800530i	$-0.704551\pi$
$349$	−0.432192	+	0.314006i	−0.0231347	+	0.0168084i	0.576158	+	0.817338i	$0.304551\pi$
$350$	−12.1032	−	11.1824i	−0.646942	−	0.597722i
$351$			4.06542i			0.216996i
$352$	−3.24284	+	0.695687i	−0.172844	+	0.0370803i
$353$			20.1854i			1.07436i	0.843467	+	0.537180i	$0.180511\pi$
$353$			20.1854i			1.07436i	−0.843467	+	0.537180i	$0.819489\pi$
$354$	2.49189	+	0.809664i	0.132442	+	0.0430332i
$355$	−21.6903	−	29.8542i	−1.15120	−	1.58449i
$356$	−5.27193	+	7.25619i	−0.279412	+	0.384577i
$357$	−11.4199	−	1.34869i	−0.604405	−	0.0713803i
$358$	−9.77154	+	3.17497i	−0.516442	+	0.167802i
$359$	−3.36003	+	4.62468i	−0.177336	+	0.244081i	−0.888427	−	0.459018i	$-0.848201\pi$
$359$	−3.36003	+	4.62468i	−0.177336	+	0.244081i	0.711091	+	0.703100i	$0.248201\pi$
$360$	−2.71089	+	1.96958i	−0.142877	+	0.103806i
$361$	13.7881	−	42.4355i	0.725691	−	2.23345i
$362$	3.37847			0.177568
$363$	−9.54698	−	5.46400i	−0.501086	−	0.286785i
$364$	−9.76922	−	4.50066i	−0.512046	−	0.235899i
$365$	−24.5111	−	7.96415i	−1.28297	−	0.416863i
$366$	−5.52859	+	4.01675i	−0.288984	+	0.209959i
$367$	−8.70219	+	11.9775i	−0.454250	+	0.625222i	−0.973304	−	0.229520i	$-0.926284\pi$
$367$	−8.70219	+	11.9775i	−0.454250	+	0.625222i	0.519054	+	0.854742i	$0.326284\pi$
$368$	0.411458	+	1.26634i	0.0214487	+	0.0660124i
$369$	−1.30598	−	4.01938i	−0.0679864	−	0.209241i
$370$	−15.8813	−	11.5385i	−0.825632	−	0.599857i
$371$	−33.8003	+	6.73223i	−1.75483	+	0.349520i
$372$	−1.35131	+	4.15890i	−0.0700621	+	0.215629i
$373$			6.75795i			0.349913i	0.984576	+	0.174957i	$0.0559785\pi$
$373$			6.75795i			0.349913i	−0.984576	+	0.174957i	$0.944021\pi$
$374$	14.0944	−	3.02367i	0.728804	−	0.156350i
$375$	4.11546			0.212522
$376$	−0.882707	+	2.71669i	−0.0455221	+	0.140103i
$377$	20.6619	+	28.4386i	1.06414	+	1.46466i
$378$	1.29336	+	2.30808i	0.0665231	+	0.118715i
$379$	7.28121	+	22.4093i	0.374011	+	1.15109i	0.944144	+	0.329534i	$0.106892\pi$
$379$	7.28121	+	22.4093i	0.374011	+	1.15109i	−0.570133	+	0.821553i	$0.693108\pi$
$380$	−25.4188	+	8.25908i	−1.30396	+	0.423682i
$381$	8.54353	+	6.20724i	0.437698	+	0.318006i
$382$	2.86415	+	3.94217i	0.146543	+	0.201699i
$383$	−12.7244	−	4.13441i	−0.650187	−	0.211259i	−0.0346906	−	0.999398i	$-0.511045\pi$
$383$	−12.7244	−	4.13441i	−0.650187	−	0.211259i	−0.615497	+	0.788139i	$0.711045\pi$
$384$	−1.00000			−0.0510310
$385$	14.9797	−	25.3018i	0.763436	−	1.28950i
$386$	24.5257			1.24832
$387$	−7.16188	−	2.32703i	−0.364059	−	0.118290i
$388$	2.10696	+	2.89998i	0.106965	+	0.147224i
$389$	−13.9570	−	10.1404i	−0.707649	−	0.514137i	0.174765	−	0.984610i	$-0.444083\pi$
$389$	−13.9570	−	10.1404i	−0.707649	−	0.514137i	−0.882414	+	0.470473i	$0.844083\pi$
$390$	12.9559	−	4.20962i	0.656047	−	0.213162i
$391$	−1.78832	−	5.50389i	−0.0904394	−	0.278344i
$392$	−6.97814	+	0.552761i	−0.352449	+	0.0279186i
$393$	0.864781	+	1.19027i	0.0436224	+	0.0600411i
$394$	−1.12304	+	3.45635i	−0.0565777	+	0.174128i
$395$	28.1968			1.41873
$396$	−2.46892	−	2.21460i	−0.124068	−	0.111288i
$397$		−	16.3142i		−	0.818786i	−0.912358	−	0.409393i	$-0.865740\pi$
$397$		−	16.3142i		−	0.818786i	0.912358	−	0.409393i	$-0.134260\pi$
$398$	3.05636	−	9.40651i	0.153201	−	0.471506i
$399$	4.12225	+	20.6964i	0.206370	+	1.03612i
$400$	5.03871	+	3.66084i	0.251935	+	0.183042i
$401$	−4.41908	−	13.6005i	−0.220679	−	0.679179i	−0.998702	−	0.0509430i	$-0.983777\pi$
$401$	−4.41908	−	13.6005i	−0.220679	−	0.679179i	0.778023	−	0.628236i	$-0.216223\pi$
$402$	−0.441082	−	1.35751i	−0.0219992	−	0.0677066i
$403$	10.4495	−	14.3825i	0.520528	−	0.716445i
$404$	7.67423	−	5.57565i	0.381807	−	0.277399i
$405$	−3.18685	−	1.03547i	−0.158356	−	0.0514529i
$406$	20.7778	+	9.57228i	1.03118	+	0.475064i
$407$	7.86934	−	17.7650i	0.390069	−	0.880579i
$408$	4.34631			0.215174
$409$	−5.52485	+	17.0038i	−0.273186	+	0.840782i	0.716507	+	0.697580i	$0.245740\pi$
$409$	−5.52485	+	17.0038i	−0.273186	+	0.840782i	−0.989694	+	0.143202i	$0.954260\pi$
$410$	−11.4569	+	8.32390i	−0.565814	+	0.411088i
$411$	−5.40052	+	7.43318i	−0.266388	+	0.366652i
$412$	−12.5222	+	4.06870i	−0.616923	+	0.200450i
$413$	−6.88436	−	0.813044i	−0.338757	−	0.0400073i
$414$	−0.782639	+	1.07721i	−0.0384646	+	0.0529420i
$415$	−32.1921	−	44.3086i	−1.58025	−	2.17502i
$416$	3.86645	+	1.25628i	0.189568	+	0.0615944i
$417$		−	0.805771i		−	0.0394588i
$418$	−13.2702	−	22.8848i	−0.649067	−	1.11933i
$419$			18.6363i			0.910444i	0.890378	+	0.455222i	$0.150440\pi$
$419$			18.6363i			0.910444i	−0.890378	+	0.455222i	$0.849560\pi$
$420$	6.01626	−	6.51167i	0.293563	−	0.317737i
$421$	10.9174	−	7.93199i	0.532084	−	0.386582i	−0.289053	−	0.957313i	$-0.593340\pi$
$421$	10.9174	−	7.93199i	0.532084	−	0.386582i	0.821137	+	0.570732i	$0.193340\pi$
$422$	5.17870	+	3.76255i	0.252095	+	0.183158i
$423$	−2.71669	+	0.882707i	−0.132090	+	0.0429187i
$424$	12.3887	−	4.02534i	0.601649	−	0.195488i
$425$	−21.8998	−	15.9111i	−1.06230	−	0.771803i
$426$	8.90944	−	6.47308i	0.431664	−	0.313622i
$427$	12.2695	−	13.2799i	0.593765	−	0.642659i
$428$		−	15.4989i		−	0.749169i
$429$	6.76377	+	11.6643i	0.326558	+	0.563157i
$430$			25.2334i			1.21686i
$431$	−29.9821	−	9.74178i	−1.44419	−	0.469245i	−0.520987	−	0.853564i	$-0.674436\pi$
$431$	−29.9821	−	9.74178i	−1.44419	−	0.469245i	−0.923200	+	0.384319i	$0.874436\pi$
$432$	−0.587785	−	0.809017i	−0.0282798	−	0.0389238i
$433$	21.5925	−	29.7196i	1.03767	−	1.42823i	0.138643	−	0.990342i	$-0.455726\pi$
$433$	21.5925	−	29.7196i	1.03767	−	1.42823i	0.899029	−	0.437890i	$-0.144274\pi$
$434$	1.35695	−	11.4898i	0.0651357	−	0.551529i
$435$	−27.5553	+	8.95328i	−1.32118	+	0.429277i
$436$	5.72537	−	7.88030i	0.274196	−	0.377398i
$437$	−8.59202	+	6.24247i	−0.411012	+	0.298618i
$438$	2.37676	−	7.31490i	0.113566	−	0.349520i
$439$	16.8116			0.802374			0.401187	−	0.915996i	$-0.368598\pi$
$439$	16.8116			0.802374			0.401187	+	0.915996i	$0.368598\pi$
$440$	−4.50110	+	10.1612i	−0.214581	+	0.484417i
$441$	−4.54884	−	5.32053i	−0.216611	−	0.253359i
$442$	−16.8048	−	5.46021i	−0.799322	−	0.259715i
$443$	6.82698	−	4.96009i	0.324360	−	0.235661i	−0.413674	−	0.910425i	$-0.635755\pi$
$443$	6.82698	−	4.96009i	0.324360	−	0.235661i	0.738034	+	0.674764i	$0.235755\pi$
$444$	3.44345	−	4.73950i	0.163419	−	0.224927i
$445$	9.28727	+	28.5833i	0.440259	+	1.35498i
$446$	−2.58337	−	7.95079i	−0.122326	−	0.376481i
$447$	8.93595	+	6.49235i	0.422656	+	0.307078i
$448$	2.59478	−	0.516820i	0.122592	−	0.0244174i
$449$	10.1726	−	31.3081i	0.480076	−	1.47752i	−0.358912	−	0.933372i	$-0.616852\pi$
$449$	10.1726	−	31.3081i	0.480076	−	1.47752i	0.838988	−	0.544151i	$-0.183148\pi$
$450$			6.22819i			0.293599i
$451$	−10.4342	−	9.35940i	−0.491328	−	0.440717i
$452$	11.8989			0.559678
$453$	−3.89999	+	12.0029i	−0.183237	+	0.563947i
$454$	8.98966	+	12.3732i	0.421906	+	0.580704i
$455$	−31.4421	+	17.6189i	−1.47403	+	0.825987i
$456$	−2.46477	−	7.58579i	−0.115424	−	0.355237i
$457$	−11.5893	+	3.76560i	−0.542126	+	0.176147i	−0.567263	−	0.823537i	$-0.691998\pi$
$457$	−11.5893	+	3.76560i	−0.542126	+	0.176147i	0.0251371	+	0.999684i	$0.491998\pi$
$458$	0.701183	+	0.509439i	0.0327641	+	0.0238045i
$459$	2.55470	+	3.51624i	0.119243	+	0.164124i
$460$	4.24330	+	1.37873i	0.197845	+	0.0642837i
$461$	−17.6247			−0.820865			−0.410433	−	0.911891i	$-0.634622\pi$
$461$	−17.6247			−0.820865			−0.410433	+	0.911891i	$0.634622\pi$
$462$	7.55085	+	4.47042i	0.351297	+	0.207983i
$463$	−9.39398			−0.436575			−0.218288	−	0.975884i	$-0.570047\pi$
$463$	−9.39398			−0.436575			−0.218288	+	0.975884i	$0.570047\pi$
$464$	−8.22339	−	2.67194i	−0.381761	−	0.124042i
$465$	8.61283	+	11.8545i	0.399410	+	0.549741i
$466$	12.4137	+	9.01905i	0.575052	+	0.417800i
$467$	−24.4180	+	7.93389i	−1.12993	+	0.367137i	−0.813550	−	0.581495i	$-0.802468\pi$
$467$	−24.4180	+	7.93389i	−1.12993	+	0.367137i	−0.316381	+	0.948632i	$0.602468\pi$
$468$	1.25628	+	3.86645i	0.0580718	+	0.178727i
$469$	1.84610	+	3.29449i	0.0852451	+	0.152125i
$470$	5.62610	+	7.74367i	0.259513	+	0.357189i
$471$	0.0200400	−	0.0616768i	0.000923395	−	0.00284192i
$472$	2.62013			0.120601
$473$	−24.4200	+	5.23883i	−1.12283	+	0.240882i
$474$			8.41482i			0.386505i
$475$	−15.3511	+	47.2457i	−0.704355	+	2.16778i
$476$	−11.2777	+	2.24626i	−0.516914	+	0.102957i
$477$	10.5385	+	7.65665i	0.482523	+	0.350574i
$478$	−5.42259	−	16.6890i	−0.248024	−	0.763338i
$479$	−4.17403	−	12.8463i	−0.190716	−	0.586964i	0.809284	−	0.587418i	$-0.199856\pi$
$479$	−4.17403	−	12.8463i	−0.190716	−	0.586964i	−1.00000		0.000453914i	$0.999856\pi$
$480$	−1.96958	+	2.71089i	−0.0898986	+	0.123735i
$481$	−19.2681	+	13.9991i	−0.878548	+	0.638303i
$482$	19.7859	+	6.42882i	0.901221	+	0.292825i
$483$	1.47405	−	3.19961i	0.0670718	−	0.145587i
$484$	−10.7682	−	2.24639i	−0.489463	−	0.102109i
$485$	12.0114			0.545408
$486$	0.309017	−	0.951057i	0.0140173	−	0.0431408i
$487$	−12.8400	+	9.32882i	−0.581837	+	0.422729i	−0.839386	−	0.543536i	$-0.817085\pi$
$487$	−12.8400	+	9.32882i	−0.581837	+	0.422729i	0.257549	+	0.966265i	$0.417085\pi$
$488$	−4.01675	+	5.52859i	−0.181830	+	0.250267i
$489$	−12.4477	+	4.04450i	−0.562904	+	0.182899i
$490$	−12.2455	+	20.0057i	−0.553197	+	0.903766i
$491$	16.8799	−	23.2333i	0.761781	−	1.04850i	−0.235282	−	0.971927i	$-0.575601\pi$
$491$	16.8799	−	23.2333i	0.761781	−	1.04850i	0.997064	−	0.0765752i	$-0.0243985\pi$
$492$	−2.48412	−	3.41909i	−0.111993	−	0.154145i
$493$	35.7414	+	11.6131i	1.60971	+	0.523027i
$494$			32.4265i			1.45894i
$495$	−10.8663	+	2.33114i	−0.488402	+	0.104777i
$496$			4.37293i			0.196350i
$497$	−19.7726	+	21.4008i	−0.886924	+	0.959958i
$498$	13.2231	−	9.60714i	0.592541	−	0.430506i
$499$	−31.1600	−	22.6391i	−1.39491	−	1.01346i	−0.995306	−	0.0967776i	$-0.969146\pi$
$499$	−31.1600	−	22.6391i	−1.39491	−	1.01346i	−0.399607	−	0.916686i	$-0.630854\pi$
$500$	3.91404	−	1.27175i	0.175041	−	0.0568743i
$501$	−1.50813	+	0.490022i	−0.0673784	+	0.0218926i
$502$	4.98933	+	3.62496i	0.222685	+	0.161790i
$503$	8.90773	−	6.47185i	0.397176	−	0.288565i	−0.371214	−	0.928547i	$-0.621058\pi$
$503$	8.90773	−	6.47185i	0.397176	−	0.288565i	0.768390	+	0.639982i	$0.221058\pi$
$504$	1.94329	+	1.79544i	0.0865611	+	0.0799754i
$505$		−	31.7857i		−	1.41445i
$506$	−0.453318	+	4.39278i	−0.0201524	+	0.195283i
$507$		−	3.52767i		−	0.156669i
$508$	10.0435	+	3.26334i	0.445609	+	0.144787i
$509$	12.2189	+	16.8179i	0.541595	+	0.745442i	0.988842	−	0.148969i	$-0.0475954\pi$
$509$	12.2189	+	16.8179i	0.541595	+	0.745442i	−0.447247	+	0.894411i	$0.647595\pi$
$510$	8.56040	−	11.7824i	0.379061	−	0.521733i
$511$	−2.38668	+	20.2089i	−0.105580	+	0.893991i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	4.68828	−	6.45286i	0.206992	−	0.284901i
$514$	−10.6064	+	7.70597i	−0.467826	+	0.339896i
$515$	−13.6336	+	41.9599i	−0.600768	+	1.84897i
$516$	−7.53044			−0.331509
$517$	−6.32600	+	7.05246i	−0.278217	+	0.310167i
$518$	−6.48553	+	14.0776i	−0.284958	+	0.618535i
$519$	−7.44150	−	2.41789i	−0.326646	−	0.106134i
$520$	11.0209	−	8.00717i	0.483300	−	0.351138i
$521$	21.4609	−	29.5384i	0.940218	−	1.29410i	−0.0155198	−	0.999880i	$-0.504940\pi$
$521$	21.4609	−	29.5384i	0.940218	−	1.29410i	0.955738	−	0.294220i	$-0.0950597\pi$
$522$	−2.67194	−	8.22339i	−0.116948	−	0.359928i
$523$	−5.06088	−	15.5758i	−0.221297	−	0.681081i	−0.998646	−	0.0520126i	$-0.983436\pi$
$523$	−5.06088	−	15.5758i	−0.221297	−	0.681081i	0.777350	−	0.629069i	$-0.216564\pi$
$524$	1.19027	+	0.864781i	0.0519971	+	0.0377781i
$525$	−3.21885	−	16.1608i	−0.140482	−	0.705315i
$526$	1.12268	−	3.45525i	0.0489511	−	0.150656i
$527$		−	19.0061i		−	0.827919i
$528$	−3.03243	−	1.34327i	−0.131970	−	0.0584584i
$529$	−21.2271			−0.922917
$530$	13.4883	−	41.5127i	0.585894	−	1.80320i
$531$	1.54007	+	2.11973i	0.0668334	+	0.0919883i
$532$	10.3160	+	18.4096i	0.447257	+	0.798159i
$533$	5.30935	+	16.3405i	0.229973	+	0.707785i
$534$	−8.53016	+	2.77162i	−0.369136	+	0.119940i
$535$	−42.0160	−	30.5264i	−1.81651	−	1.31977i
$536$	−0.838989	−	1.15477i	−0.0362388	−	0.0498784i
$537$	−9.77154	−	3.17497i	−0.421673	−	0.137010i
$538$	3.17998			0.137099
$539$	−21.9032	−	7.69733i	−0.943439	−	0.331547i
$540$	−3.35085			−0.144198
$541$	−9.80091	−	3.18451i	−0.421374	−	0.136913i	0.0906520	−	0.995883i	$-0.471105\pi$
$541$	−9.80091	−	3.18451i	−0.421374	−	0.136913i	−0.512026	+	0.858970i	$0.671105\pi$
$542$	17.7558	+	24.4388i	0.762678	+	1.04974i
$543$	2.73324	+	1.98581i	0.117294	+	0.0852194i
$544$	4.13359	−	1.34308i	0.177226	−	0.0575842i
$545$	−10.0861	−	31.0417i	−0.432040	−	1.32968i
$546$	−5.25804	−	9.38332i	−0.225024	−	0.401569i
$547$	−1.55026	−	2.13375i	−0.0662844	−	0.0912326i	0.774588	−	0.632466i	$-0.217957\pi$
$547$	−1.55026	−	2.13375i	−0.0662844	−	0.0912326i	−0.840872	+	0.541234i	$0.817957\pi$
$548$	−2.83922	+	8.73822i	−0.121285	+	0.373278i
$549$	−6.83371			−0.291656
$550$	10.3620	+	17.8696i	0.441838	+	0.761961i
$551$		−	68.9667i		−	2.93808i
$552$	−0.411458	+	1.26634i	−0.0175128	+	0.0538989i
$553$	−4.34895	−	21.8346i	−0.184936	−	0.928503i
$554$	−18.5930	−	13.5086i	−0.789939	−	0.573924i
$555$	−6.06613	−	18.6696i	−0.257493	−	0.792482i
$556$	−0.248997	−	0.766334i	−0.0105598	−	0.0324998i
$557$	12.2515	−	16.8628i	0.519114	−	0.714499i	−0.466309	−	0.884622i	$-0.654417\pi$
$557$	12.2515	−	16.8628i	0.519114	−	0.714499i	0.985423	+	0.170123i	$0.0544166\pi$
$558$	−3.53777	+	2.57034i	−0.149766	+	0.108811i
$559$	29.1161	+	9.46038i	1.23148	+	0.400132i
$560$	3.70959	−	8.05210i	0.156759	−	0.340263i
$561$	13.1799	+	5.83827i	0.556455	+	0.246492i
$562$	17.0393			0.718761
$563$	11.3867	−	35.0447i	0.479893	−	1.47696i	−0.359351	−	0.933202i	$-0.617002\pi$
$563$	11.3867	−	35.0447i	0.479893	−	1.47696i	0.839244	−	0.543755i	$-0.182998\pi$
$564$	−2.31096	+	1.67901i	−0.0973089	+	0.0706990i
$565$	23.4359	−	32.2567i	0.985955	−	1.35705i
$566$	−16.5324	+	5.37169i	−0.694907	+	0.225789i
$567$	−0.310307	+	2.62749i	−0.0130317	+	0.110344i
$568$	6.47308	−	8.90944i	0.271605	−	0.373832i
$569$	2.28389	+	3.14351i	0.0957457	+	0.131783i	0.854202	−	0.519941i	$-0.174046\pi$
$569$	2.28389	+	3.14351i	0.0957457	+	0.131783i	−0.758456	+	0.651724i	$0.774046\pi$
$570$	−25.4188	−	8.25908i	−1.06468	−	0.345935i
$571$			2.92993i			0.122614i	0.998119	+	0.0613069i	$0.0195268\pi$
$571$			2.92993i			0.122614i	−0.998119	+	0.0613069i	$0.980473\pi$
$572$	10.0372	+	9.00328i	0.419676	+	0.376446i
$573$			4.87279i			0.203564i
$574$	8.21280	+	7.58796i	0.342795	+	0.316715i
$575$	6.70907	−	4.87442i	0.279787	−	0.203277i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	−17.5272	+	5.69493i	−0.729666	+	0.237083i	−0.650209	−	0.759755i	$-0.725319\pi$
$577$	−17.5272	+	5.69493i	−0.729666	+	0.237083i	−0.0794571	+	0.996838i	$0.525319\pi$
$578$	−1.79789	+	0.584171i	−0.0747825	+	0.0242983i
$579$	19.8417	+	14.4158i	0.824592	+	0.599101i
$580$	−23.4400	+	17.0301i	−0.973292	+	0.707138i
$581$	−29.3459	+	31.7624i	−1.21747	+	1.31773i
$582$			3.58458i			0.148585i
$583$	42.9750	+	4.43486i	1.77984	+	0.183673i
$584$		−	7.69135i		−	0.318270i
$585$	12.9559	+	4.20962i	0.535660	+	0.174046i
$586$	1.57729	+	2.17095i	0.0651572	+	0.0896811i
$587$	12.1267	−	16.6910i	0.500523	−	0.688910i	−0.481763	−	0.876302i	$-0.660003\pi$
$587$	12.1267	−	16.6910i	0.500523	−	0.688910i	0.982285	+	0.187392i	$0.0600033\pi$
$588$	−5.97034	−	3.65446i	−0.246213	−	0.150707i
$589$	−33.1721	+	10.7783i	−1.36683	+	0.444111i
$590$	5.16055	−	7.10289i	0.212456	−	0.292421i
$591$	−2.94015	+	2.13614i	−0.120941	+	0.0878691i
$592$	1.81033	−	5.57162i	0.0744040	−	0.228992i
$593$	11.9095			0.489063			0.244532	−	0.969641i	$-0.421366\pi$
$593$	11.9095			0.489063			0.244532	+	0.969641i	$0.421366\pi$
$594$	−0.695687	−	3.24284i	−0.0285444	−	0.133055i
$595$	−16.1230	+	34.9969i	−0.660979	+	1.43473i
$596$	10.5048	+	3.41323i	0.430295	+	0.139811i
$597$	8.00165	−	5.81354i	0.327486	−	0.237932i
$598$	3.18176	−	4.37932i	0.130112	−	0.179084i
$599$	1.11447	+	3.42999i	0.0455361	+	0.140146i	0.971240	−	0.238104i	$-0.0765260\pi$
$599$	1.11447	+	3.42999i	0.0455361	+	0.140146i	−0.925703	+	0.378250i	$0.876526\pi$
$600$	1.92462	+	5.92336i	0.0785721	+	0.241820i
$601$	38.8729	+	28.2428i	1.58566	+	1.15205i	0.909822	+	0.414998i	$0.136218\pi$
$601$	38.8729	+	28.2428i	1.58566	+	1.15205i	0.675837	+	0.737051i	$0.263782\pi$
$602$	19.5399	−	3.89188i	0.796385	−	0.158621i
$603$	0.441082	−	1.35751i	0.0179623	−	0.0552822i
$604$			12.6206i			0.513526i
$605$	−27.2985	+	24.7669i	−1.10984	+	1.00692i
$606$	9.48587			0.385337
$607$	−3.41023	+	10.4956i	−0.138417	+	0.426004i	−0.996106	−	0.0881655i	$-0.971900\pi$
$607$	−3.41023	+	10.4956i	−0.138417	+	0.426004i	0.857689	+	0.514169i	$0.171900\pi$
$608$	−4.68828	−	6.45286i	−0.190135	−	0.261698i
$609$	11.1831	+	19.9570i	0.453163	+	0.808699i
$610$	7.07610	+	21.7780i	0.286503	+	0.881765i
$611$	11.0445	−	3.58858i	0.446813	−	0.145178i
$612$	3.51624	+	2.55470i	0.142136	+	0.103268i
$613$	6.75980	+	9.30406i	0.273026	+	0.375788i	0.923408	−	0.383819i	$-0.125391\pi$
$613$	6.75980	+	9.30406i	0.273026	+	0.375788i	−0.650383	+	0.759607i	$0.725391\pi$
$614$	−26.4693	−	8.60038i	−1.06821	−	0.347083i
$615$	−14.1615			−0.571045
$616$	8.56272	+	1.91828i	0.345002	+	0.0772896i
$617$	−2.23443			−0.0899547			−0.0449773	−	0.998988i	$-0.514322\pi$
$617$	−2.23443			−0.0899547			−0.0449773	+	0.998988i	$0.514322\pi$
$618$	−12.5222	−	4.06870i	−0.503715	−	0.163667i
$619$	−14.3148	−	19.7026i	−0.575359	−	0.791913i	0.417818	−	0.908531i	$-0.362795\pi$
$619$	−14.3148	−	19.7026i	−0.575359	−	0.791913i	−0.993177	+	0.116617i	$0.962795\pi$
$620$	11.8545	+	8.61283i	0.476090	+	0.345899i
$621$	−1.26634	+	0.411458i	−0.0508163	+	0.0165112i
$622$	−0.191781	−	0.590240i	−0.00768970	−	0.0236665i
$623$	20.7015	−	11.6003i	0.829387	−	0.464756i
$624$	2.38960	+	3.28900i	0.0956604	+	0.131665i
$625$	−5.36164	+	16.5014i	−0.214466	+	0.660057i
$626$	11.0903			0.443259
$627$	2.71553	−	26.3142i	0.108448	−	1.05089i
$628$		−	0.0648508i		−	0.00258783i
$629$	−7.86825	+	24.2160i	−0.313728	+	0.965554i
$630$	8.69472	−	1.73179i	0.346406	−	0.0689960i
$631$	23.8486	+	17.3270i	0.949396	+	0.689776i	0.950664	−	0.310223i	$-0.100404\pi$
$631$	23.8486	+	17.3270i	0.949396	+	0.689776i	−0.00126809	+	0.999999i	$0.500404\pi$
$632$	2.60032	+	8.00297i	0.103435	+	0.318341i
$633$	1.97809	+	6.08793i	0.0786220	+	0.241974i
$634$	−7.72243	+	10.6290i	−0.306697	+	0.422132i
$635$	28.6281	−	20.7995i	1.13607	−	0.825403i
$636$	12.3887	+	4.02534i	0.491245	+	0.159615i
$637$	18.4930	+	21.6302i	0.732718	+	0.857020i
$638$	−21.3477	−	19.1487i	−0.845164	−	0.758105i
$639$	11.0127			0.435654
$640$	−1.03547	+	3.18685i	−0.0409305	+	0.125971i
$641$	26.4650	−	19.2279i	1.04530	−	0.759458i	0.0739901	−	0.997259i	$-0.476427\pi$
$641$	26.4650	−	19.2279i	1.04530	−	0.759458i	0.971314	+	0.237801i	$0.0764267\pi$
$642$	9.11004	−	12.5389i	0.359545	−	0.494871i
$643$	−33.1283	+	10.7640i	−1.30645	+	0.424492i	−0.877821	−	0.478988i	$-0.841004\pi$
$643$	−33.1283	+	10.7640i	−1.30645	+	0.424492i	−0.428630	+	0.903480i	$0.641004\pi$
$644$	0.413175	−	3.49852i	0.0162814	−	0.137861i
$645$	−14.8318	+	20.4142i	−0.584002	+	0.803809i
$646$	20.3767	+	28.0461i	0.801711	+	1.10346i
$647$	−10.4783	−	3.40462i	−0.411946	−	0.133849i	0.0957099	−	0.995409i	$-0.469488\pi$
$647$	−10.4783	−	3.40462i	−0.411946	−	0.133849i	−0.507656	+	0.861560i	$0.669488\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	7.94535	+	3.51954i	0.311882	+	0.138154i
$650$		−	25.3202i		−	0.993140i
$651$	7.85135	−	8.49787i	0.307718	−	0.333058i
$652$	−10.5886	+	7.69310i	−0.414683	+	0.301285i
$653$	−1.53109	−	1.11240i	−0.0599163	−	0.0435317i	0.557424	−	0.830228i	$-0.311790\pi$
$653$	−1.53109	−	1.11240i	−0.0599163	−	0.0435317i	−0.617340	+	0.786696i	$0.711790\pi$
$654$	9.26385	−	3.01001i	0.362245	−	0.117701i
$655$	4.68866	−	1.52344i	0.183201	−	0.0595256i
$656$	−3.41909	−	2.48412i	−0.133493	−	0.0969884i
$657$	6.22243	−	4.52086i	0.242760	−	0.176376i
$658$	5.12869	−	5.55101i	0.199937	−	0.216401i
$659$		−	18.1765i		−	0.708055i	−0.935235	−	0.354028i	$-0.884812\pi$
$659$		−	18.1765i		−	0.708055i	0.935235	−	0.354028i	$-0.115188\pi$
$660$	−9.61407	+	5.57491i	−0.374227	+	0.217003i
$661$			33.3978i			1.29902i	0.760351	+	0.649512i	$0.225027\pi$
$661$			33.3978i			1.29902i	−0.760351	+	0.649512i	$0.774973\pi$
$662$	−15.5915	−	5.06600i	−0.605983	−	0.196896i
$663$	−10.3859	−	14.2950i	−0.403356	−	0.555172i
$664$	9.60714	−	13.2231i	0.372829	−	0.513156i
$665$	70.2248	+	8.29356i	2.72320	+	0.321610i
$666$	5.57162	−	1.81033i	0.215896	−	0.0701488i
$667$	−6.76716	+	9.31420i	−0.262025	+	0.360647i
$668$	−1.28289	+	0.932077i	−0.0496367	+	0.0360632i
$669$	2.58337	−	7.95079i	0.0998787	−	0.307395i
$670$	−4.78291			−0.184780
$671$	−19.6069	+	11.3695i	−0.756916	+	0.438913i
$672$	2.40300	+	1.10706i	0.0926978	+	0.0427057i
$673$	18.2164	+	5.91888i	0.702192	+	0.228156i	0.638285	−	0.769800i	$-0.279644\pi$
$673$	18.2164	+	5.91888i	0.702192	+	0.228156i	0.0639066	+	0.997956i	$0.479644\pi$
$674$	−27.7905	+	20.1910i	−1.07045	+	0.777727i
$675$	−3.66084	+	5.03871i	−0.140906	+	0.193940i
$676$	−1.09011	−	3.35501i	−0.0419273	−	0.129039i
$677$	14.6937	+	45.2227i	0.564727	+	1.73805i	0.668762	+	0.743476i	$0.266824\pi$
$677$	14.6937	+	45.2227i	0.564727	+	1.73805i	−0.104036	+	0.994574i	$0.533176\pi$
$678$	9.62643	+	6.99401i	0.369701	+	0.268603i
$679$	−1.85258	−	9.30119i	−0.0710955	−	0.356947i
$680$	4.50047	−	13.8510i	0.172585	−	0.531163i
$681$			15.2941i			0.586072i
$682$	−5.87403	+	13.2606i	−0.224928	+	0.507774i
$683$	28.8662			1.10453			0.552267	−	0.833667i	$-0.313763\pi$
$683$	28.8662			1.10453			0.552267	+	0.833667i	$0.313763\pi$
$684$	2.46477	−	7.58579i	0.0942430	−	0.290050i
$685$	18.0963	+	24.9074i	0.691425	+	0.951665i
$686$	17.3804	+	6.39693i	0.663588	+	0.244236i
$687$	0.267828	+	0.824290i	0.0102183	+	0.0314486i
$688$	−7.16188	+	2.32703i	−0.273044	+	0.0887174i
$689$	−42.8434	−	31.1275i	−1.63220	−	1.18586i
$690$	2.62251	+	3.60957i	0.0998371	+	0.137414i
$691$	10.2129	+	3.31838i	0.388518	+	0.126237i	0.496761	−	0.867887i	$-0.334522\pi$
$691$	10.2129	+	3.31838i	0.388518	+	0.126237i	−0.108243	+	0.994124i	$0.534522\pi$
$692$	−7.82445			−0.297441
$693$	3.48112	+	8.05492i	0.132237	+	0.305981i
$694$	23.6679			0.898421
$695$	−2.56787	−	0.834351i	−0.0974049	−	0.0316488i
$696$	−5.08234	−	6.99524i	−0.192645	−	0.265154i
$697$	14.8604	+	10.7967i	0.562879	+	0.408956i
$698$	−0.508073	+	0.165083i	−0.0192308	+	0.00624848i
$699$	4.74160	+	14.5931i	0.179344	+	0.551963i
$700$	−8.05527	−	14.3751i	−0.304460	−	0.543329i
$701$	11.7169	+	16.1270i	0.442542	+	0.609107i	0.970775	−	0.239993i	$-0.0771450\pi$
$701$	11.7169	+	16.1270i	0.442542	+	0.609107i	−0.528232	+	0.849100i	$0.677145\pi$
$702$	−1.25628	+	3.86645i	−0.0474154	+	0.145930i
$703$	46.7272			1.76235
$704$	−3.29910	−	0.340455i	−0.124340	−	0.0128314i
$705$			9.57170i			0.360491i
$706$	−6.23763	+	19.1975i	−0.234756	+	0.722506i
$707$	−24.6138	+	4.90249i	−0.925696	+	0.184377i
$708$	2.11973	+	1.54007i	0.0796642	+	0.0578795i
$709$	−5.38972	−	16.5879i	−0.202415	−	0.622970i	−0.999810	−	0.0195117i	$-0.993789\pi$
$709$	−5.38972	−	16.5879i	−0.202415	−	0.622970i	0.797394	−	0.603459i	$-0.206211\pi$
$710$	−11.4033	−	35.0957i	−0.427957	−	1.31712i
$711$	−4.94611	+	6.80773i	−0.185493	+	0.255310i
$712$	−7.25619	+	5.27193i	−0.271937	+	0.197574i
$713$	5.53760	+	1.79927i	0.207385	+	0.0673834i
$714$	−10.4442	−	4.81162i	−0.390864	−	0.180070i
$715$	44.1760	−	9.47709i	1.65209	−	0.354423i
$716$	−10.2744			−0.383973
$717$	5.42259	−	16.6890i	0.202510	−	0.623263i
$718$	−4.62468	+	3.36003i	−0.172592	+	0.125395i
$719$	15.8269	−	21.7838i	0.590243	−	0.812400i	−0.404528	−	0.914526i	$-0.632564\pi$
$719$	15.8269	−	21.7838i	0.590243	−	0.812400i	0.994772	+	0.102125i	$0.0325642\pi$
$720$	−3.18685	+	1.03547i	−0.118767	+	0.0385897i
$721$	34.5951	+	4.08568i	1.28839	+	0.152159i
$722$	26.2266	−	36.0978i	0.976053	−	1.34342i
$723$	12.2283	+	16.8309i	0.454777	+	0.625947i
$724$	3.21311	+	1.04400i	0.119414	+	0.0388001i
$725$			53.8526i			2.00003i
$726$	−7.39124	−	8.14675i	−0.274315	−	0.302354i
$727$		−	32.3887i		−	1.20123i	−0.799538	−	0.600616i	$-0.794922\pi$
$727$		−	32.3887i		−	1.20123i	0.799538	−	0.600616i	$-0.205078\pi$
$728$	−7.90030	−	7.29924i	−0.292805	−	0.270528i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	−20.8504	−	15.1487i	−0.771709	−	0.560679i
$731$	31.1277	−	10.1140i	1.15130	−	0.374080i
$732$	−6.49924	+	2.11173i	−0.240219	+	0.0780519i
$733$	−23.8571	−	17.3332i	−0.881183	−	0.640217i	0.0523810	−	0.998627i	$-0.483319\pi$
$733$	−23.8571	−	17.3332i	−0.881183	−	0.640217i	−0.933564	+	0.358410i	$0.883319\pi$
$734$	−11.9775	+	8.70219i	−0.442099	+	0.321204i
$735$	−21.6659	+	8.98721i	−0.799159	+	0.331498i
$736$			1.33151i			0.0490799i
$737$	−0.993005	−	4.62874i	−0.0365778	−	0.170502i
$738$		−	4.22623i		−	0.155570i
$739$	21.9304	+	7.12561i	0.806721	+	0.262120i	0.683209	−	0.730223i	$-0.260584\pi$
$739$	21.9304	+	7.12561i	0.806721	+	0.262120i	0.123513	+	0.992343i	$0.460584\pi$
$740$	−11.5385	−	15.8813i	−0.424163	−	0.583810i
$741$	−19.0598	+	26.2336i	−0.700180	+	0.963716i
$742$	−34.2264	−	4.04214i	−1.25649	−	0.148392i
$743$	−16.2910	+	5.29326i	−0.597658	+	0.194191i	−0.592196	−	0.805794i	$-0.701739\pi$
$743$	−16.2910	+	5.29326i	−0.597658	+	0.194191i	−0.00546257	+	0.999985i	$0.501739\pi$
$744$	−2.57034	+	3.53777i	−0.0942333	+	0.129701i
$745$	29.9430	−	21.7549i	1.09703	−	0.797037i
$746$	−2.08832	+	6.42719i	−0.0764589	+	0.235316i
$747$	16.3446			0.598019
$748$	14.3389	+	1.47972i	0.524283	+	0.0541040i
$749$	−17.1582	+	37.2440i	−0.626948	+	1.36087i
$750$	3.91404	+	1.27175i	0.142921	+	0.0464377i
$751$	−4.96767	+	3.60922i	−0.181273	+	0.131702i	−0.674721	−	0.738073i	$-0.735736\pi$
$751$	−4.96767	+	3.60922i	−0.181273	+	0.131702i	0.493448	+	0.869775i	$0.335736\pi$
$752$	−1.67901	+	2.31096i	−0.0612272	+	0.0842719i
$753$	1.90575	+	5.86531i	0.0694495	+	0.213744i
$754$	10.8626	+	33.4316i	0.395592	+	1.21751i
$755$	34.2132	+	24.8573i	1.24514	+	0.904650i
$756$	0.516820	+	2.59478i	0.0187966	+	0.0943713i
$757$	−3.87785	+	11.9348i	−0.140943	+	0.433777i	−0.996467	−	0.0839857i	$-0.973235\pi$
$757$	−3.87785	+	11.9348i	−0.140943	+	0.433777i	0.855524	+	0.517763i	$0.173235\pi$
$758$			23.5625i			0.855829i
$759$	−2.94875	+	3.28738i	−0.107033	+	0.119324i
$760$	−26.7269			−0.969488
$761$	5.19652	−	15.9933i	0.188374	−	0.579755i	−0.811616	−	0.584191i	$-0.801412\pi$
$761$	5.19652	−	15.9933i	0.188374	−	0.579755i	0.999990	+	0.00443571i	$0.00141193\pi$
$762$	6.20724	+	8.54353i	0.224864	+	0.309499i
$763$	−22.4820	+	12.5981i	−0.813904	+	0.456080i
$764$	1.50577	+	4.63429i	0.0544770	+	0.167663i
$765$	13.8510	−	4.50047i	0.500785	−	0.162715i
$766$	−10.8240	−	7.86412i	−0.391088	−	0.284142i
$767$	−6.26105	−	8.61759i	−0.226073	−	0.311163i
$768$	−0.951057	−	0.309017i	−0.0343183	−	0.0111507i
$769$	1.89877			0.0684712			0.0342356	−	0.999414i	$-0.489100\pi$
$769$	1.89877			0.0684712			0.0342356	+	0.999414i	$0.489100\pi$
$770$	22.0652	−	19.4344i	0.795175	−	0.700368i
$771$	−13.1102			−0.472151
$772$	23.3253	+	7.57885i	0.839496	+	0.272769i
$773$	−21.9537	−	30.2167i	−0.789620	−	1.08682i	−0.994155	−	0.107960i	$-0.965568\pi$
$773$	−21.9537	−	30.2167i	−0.789620	−	1.08682i	0.204535	−	0.978859i	$-0.434432\pi$
$774$	−6.09226	−	4.42628i	−0.218982	−	0.159099i
$775$	25.9024	−	8.41620i	0.930442	−	0.302319i
$776$	1.10769	+	3.40913i	0.0397639	+	0.122381i
$777$	−13.5215	+	7.57693i	−0.485082	+	0.271821i
$778$	−10.1404	−	13.9570i	−0.363550	−	0.500383i
$779$	10.4167	−	32.0593i	0.373217	−	1.14864i
$780$	13.6226			0.487768
$781$	31.5970	−	18.3221i	1.13063	−	0.655617i
$782$		−	5.78714i		−	0.206948i
$783$	2.67194	−	8.22339i	0.0954874	−	0.293880i
$784$	−6.80742	−	1.63066i	−0.243122	−	0.0582378i
$785$	−0.175804	−	0.127729i	−0.00627470	−	0.00455884i
$786$	0.454642	+	1.39924i	0.0162165	+	0.0499094i
$787$	−13.7204	−	42.2270i	−0.489078	−	1.50523i	−0.825986	−	0.563691i	$-0.809381\pi$
$787$	−13.7204	−	42.2270i	−0.489078	−	1.50523i	0.336907	−	0.941538i	$-0.390619\pi$
$788$	−2.13614	+	2.94015i	−0.0760969	+	0.104738i
$789$	2.93921	−	2.13546i	0.104639	−	0.0760245i
$790$	26.8167	+	8.71328i	0.954097	+	0.310005i
$791$	−28.5931	−	13.1728i	−1.01666	−	0.468371i
$792$	−1.66373	−	2.86915i	−0.0591181	−	0.101951i
$793$	27.7819			0.986565
$794$	5.04137	−	15.5157i	0.178911	−	0.550633i
$795$	35.3128	−	25.6563i	1.25242	−	0.909934i
$796$	5.81354	−	8.00165i	0.206055	−	0.283611i
$797$	43.7952	−	14.2299i	1.55131	−	0.504050i	0.596838	−	0.802362i	$-0.296424\pi$
$797$	43.7952	−	14.2299i	1.55131	−	0.504050i	0.954468	+	0.298312i	$0.0964237\pi$
$798$	−2.47506	+	20.9573i	−0.0876162	+	0.741881i
$799$	7.29749	−	10.0441i	0.258167	−	0.355336i
$800$	3.66084	+	5.03871i	0.129430	+	0.178145i
$801$	−8.53016	−	2.77162i	−0.301398	−	0.0979303i
$802$		−	14.3005i		−	0.504967i
$803$	10.3316	−	23.3235i	0.364593	−	0.823067i
$804$		−	1.42737i		−	0.0503396i
$805$	−8.67033	−	8.01068i	−0.305589	−	0.282340i
$806$	14.3825	−	10.4495i	0.506603	−	0.368069i
$807$	2.57265	+	1.86914i	0.0905617	+	0.0657970i
$808$	9.02160	−	2.93130i	0.317379	−	0.103123i
$809$	−48.7918	+	15.8534i	−1.71543	+	0.557377i	−0.991222	−	0.132206i	$-0.957794\pi$
$809$	−48.7918	+	15.8534i	−1.71543	+	0.557377i	−0.724207	+	0.689583i	$0.757794\pi$
$810$	−2.71089	−	1.96958i	−0.0952511	−	0.0692040i
$811$	−10.5956	+	7.69812i	−0.372060	+	0.270318i	−0.758065	−	0.652179i	$-0.773855\pi$
$811$	−10.5956	+	7.69812i	−0.372060	+	0.270318i	0.386004	+	0.922497i	$0.373855\pi$
$812$	16.8028	+	15.5245i	0.589664	+	0.544802i
$813$			30.2080i			1.05944i
$814$	12.9739	−	14.4638i	0.454734	−	0.506955i
$815$			43.8568i			1.53624i
$816$	4.13359	+	1.34308i	0.144704	+	0.0470173i
$817$	−35.3048	−	48.5929i	−1.23516	−	1.70005i
$818$	−10.5089	+	14.4643i	−0.367435	+	0.505731i
$819$	1.26153	−	10.6819i	0.0440814	−	0.373255i
$820$	−13.4683	+	4.37613i	−0.470335	+	0.152821i
$821$	−17.0606	+	23.4820i	−0.595421	+	0.819526i	−0.995279	−	0.0970505i	$-0.969059\pi$
$821$	−17.0606	+	23.4820i	−0.595421	+	0.819526i	0.399859	+	0.916577i	$0.369059\pi$
$822$	−7.43318	+	5.40052i	−0.259262	+	0.188365i
$823$	−10.8010	+	33.2420i	−0.376498	+	1.15874i	0.565964	+	0.824430i	$0.308504\pi$
$823$	−10.8010	+	33.2420i	−0.376498	+	1.15874i	−0.942462	+	0.334312i	$0.891496\pi$
$824$	−13.1666			−0.458680
$825$	−2.12042	+	20.5474i	−0.0738234	+	0.715370i
$826$	−6.29617	−	2.90064i	−0.219072	−	0.100926i
$827$	−5.30991	−	1.72530i	−0.184644	−	0.0599944i	0.215236	−	0.976562i	$-0.430948\pi$
$827$	−5.30991	−	1.72530i	−0.184644	−	0.0599944i	−0.399879	+	0.916568i	$0.630948\pi$
$828$	−1.07721	+	0.782639i	−0.0374357	+	0.0271986i
$829$	−3.11236	+	4.28379i	−0.108097	+	0.148782i	−0.859638	−	0.510904i	$-0.829311\pi$
$829$	−3.11236	+	4.28379i	−0.108097	+	0.148782i	0.751541	+	0.659686i	$0.229311\pi$
$830$	−16.9244	−	52.0879i	−0.587454	−	1.80800i
$831$	−7.10188	−	21.8573i	−0.246361	−	0.758222i
$832$	3.28900	+	2.38960i	0.114025	+	0.0828443i
$833$	29.5872	+	7.08734i	1.02513	+	0.245562i
$834$	0.248997	−	0.766334i	0.00862206	−	0.0265360i
$835$			5.31359i			0.183884i
$836$	−5.54892	−	25.8655i	−0.191914	−	0.894576i
$837$	−4.37293			−0.151150
$838$	−5.75894	+	17.7242i	−0.198939	+	0.612272i
$839$	−8.33019	−	11.4655i	−0.287590	−	0.395834i	0.640639	−	0.767842i	$-0.278669\pi$
$839$	−8.33019	−	11.4655i	−0.287590	−	0.395834i	−0.928230	+	0.372008i	$0.878669\pi$
$840$	7.73402	−	4.33384i	0.266849	−	0.149532i
$841$	−14.1417	−	43.5237i	−0.487645	−	1.50082i
$842$	12.8342	−	4.17009i	0.442297	−	0.143711i
$843$	13.7851	+	10.0155i	0.474785	+	0.344951i
$844$	3.76255	+	5.17870i	0.129512	+	0.178258i
$845$	−11.2421	−	3.65279i	−0.386741	−	0.125660i
$846$	−2.85650			−0.0982085
$847$	23.3891	+	17.3191i	0.803658	+	0.595091i
$848$	13.0263			0.447324
$849$	−16.5324	−	5.37169i	−0.567389	−	0.184356i
$850$	−15.9111	−	21.8998i	−0.545747	−	0.751157i
$851$	−6.31067	−	4.58497i	−0.216327	−	0.157171i
$852$	10.4737	−	3.40310i	0.358822	−	0.116588i
$853$	7.08231	+	21.7971i	0.242494	+	0.746319i	0.996039	+	0.0889222i	$0.0283423\pi$
$853$	7.08231	+	21.7971i	0.242494	+	0.746319i	−0.753545	+	0.657396i	$0.771658\pi$
$854$	15.7727	−	8.83843i	0.539732	−	0.302445i
$855$	−15.7097	−	21.6226i	−0.537261	−	0.739476i
$856$	4.78943	−	14.7404i	0.163699	−	0.503815i
$857$	−1.97573			−0.0674897			−0.0337448	−	0.999430i	$-0.510743\pi$
$857$	−1.97573			−0.0674897			−0.0337448	+	0.999430i	$0.510743\pi$
$858$	2.82826	+	13.1835i	0.0965554	+	0.450078i
$859$			16.0866i			0.548867i	0.961606	+	0.274433i	$0.0884902\pi$
$859$			16.0866i			0.548867i	−0.961606	+	0.274433i	$0.911510\pi$
$860$	−7.79754	+	23.9984i	−0.265894	+	0.818337i
$861$	2.18420	+	10.9661i	0.0744373	+	0.373725i
$862$	−25.5043	−	18.5300i	−0.868680	−	0.631133i
$863$	2.70910	+	8.33775i	0.0922188	+	0.283820i	0.986519	−	0.163647i	$-0.0523259\pi$
$863$	2.70910	+	8.33775i	0.0922188	+	0.283820i	−0.894300	+	0.447468i	$0.852326\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	−15.4109	+	21.2113i	−0.523986	+	0.721205i
$866$	29.7196	−	21.5925i	1.00991	−	0.733745i
$867$	−1.79789	−	0.584171i	−0.0610597	−	0.0198395i
$868$	4.84109	−	10.5082i	0.164317	−	0.356670i
$869$	−2.86487	+	27.7614i	−0.0971839	+	0.941740i
$870$	−28.9734			−0.982291
$871$	−1.79319	+	5.51886i	−0.0607598	+	0.187000i
$872$	7.88030	−	5.72537i	0.266861	−	0.193886i
$873$	−2.10696	+	2.89998i	−0.0713098	+	0.0981495i
$874$	−10.1005	+	3.28186i	−0.341655	+	0.111011i
$875$	−10.8133	−	1.27706i	−0.365558	−	0.0431724i
$876$	4.52086	−	6.22243i	0.152746	−	0.210236i
$877$	28.2777	+	38.9209i	0.954870	+	1.31427i	0.949330	+	0.314281i	$0.101763\pi$
$877$	28.2777	+	38.9209i	0.954870	+	1.31427i	0.00553948	+	0.999985i	$0.498237\pi$
$878$	15.9888	+	5.19507i	0.539595	+	0.175325i
$879$			2.68344i			0.0905103i
$880$	−7.42079	+	8.27297i	−0.250155	+	0.278882i
$881$			27.7281i			0.934182i	0.884209	+	0.467091i	$0.154698\pi$
$881$			27.7281i			0.934182i	−0.884209	+	0.467091i	$0.845302\pi$
$882$	−2.68207	−	6.46579i	−0.0903100	−	0.217715i
$883$	−32.0456	+	23.2825i	−1.07842	+	0.783518i	−0.977407	−	0.211367i	$-0.932208\pi$
$883$	−32.0456	+	23.2825i	−1.07842	+	0.783518i	−0.101013	+	0.994885i	$0.532208\pi$
$884$	−14.2950	−	10.3859i	−0.480793	−	0.349317i
$885$	8.34994	−	2.71306i	0.280680	−	0.0911986i
$886$	8.02560	−	2.60768i	0.269625	−	0.0876066i
$887$	−34.8003	−	25.2839i	−1.16848	−	0.848950i	−0.177653	−	0.984093i	$-0.556850\pi$
$887$	−34.8003	−	25.2839i	−1.16848	−	0.848950i	−0.990826	+	0.135144i	$0.956850\pi$
$888$	4.73950	−	3.44345i	0.159047	−	0.115555i
$889$	−20.5219	−	18.9606i	−0.688282	−	0.635917i
$890$			30.0542i			1.00742i
$891$	1.34327	−	3.03243i	0.0450013	−	0.101590i
$892$		−	8.35995i		−	0.279912i
$893$	−21.6688	−	7.04063i	−0.725119	−	0.235606i
$894$	6.49235	+	8.93595i	0.217137	+	0.298863i
$895$	−20.2363	+	27.8528i	−0.676424	+	0.931017i
$896$	2.62749	+	0.310307i	0.0877783	+	0.0103666i
$897$	5.14820	−	1.67275i	0.171893	−	0.0558515i
$898$	19.3495	−	26.6323i	0.645701	−	0.888731i
$899$	−30.5897	+	22.2247i	−1.02022	+	0.741235i
$900$	−1.92462	+	5.92336i	−0.0641538	+	0.197445i
$901$	−56.6162			−1.88616
$902$	−7.03131	−	12.1257i	−0.234117	−	0.403741i
$903$	18.0957	+	8.33664i	0.602186	+	0.277426i
$904$	11.3165	+	3.67697i	0.376383	+	0.122294i
$905$	9.15866	−	6.65416i	0.304444	−	0.221192i
$906$	−7.41822	+	10.2103i	−0.246454	+	0.339214i
$907$	−15.6556	−	48.1830i	−0.519835	−	1.59989i	−0.774308	−	0.632809i	$-0.781902\pi$
$907$	−15.6556	−	48.1830i	−0.519835	−	1.59989i	0.254473	−	0.967080i	$-0.418098\pi$
$908$	4.72615	+	14.5456i	0.156843	+	0.482712i
$909$	7.67423	+	5.57565i	0.254538	+	0.184933i
$910$	−35.3477	+	7.04044i	−1.17177	+	0.233388i
$911$	−18.2798	+	56.2593i	−0.605635	+	1.86395i	−0.113271	+	0.993564i	$0.536133\pi$
$911$	−18.2798	+	56.2593i	−0.605635	+	1.86395i	−0.492364	+	0.870390i	$0.663867\pi$
$912$		−	7.97617i		−	0.264117i
$913$	46.8952	−	27.1931i	1.55200	−	0.899960i
$914$	−12.1857			−0.403069
$915$	−7.07610	+	21.7780i	−0.233929	+	0.719958i
$916$	0.509439	+	0.701183i	0.0168323	+	0.0231677i
$917$	−1.90285	−	3.39577i	−0.0628378	−	0.112138i
$918$	1.34308	+	4.13359i	0.0443284	+	0.136429i
$919$	1.38918	−	0.451373i	0.0458249	−	0.0148894i	−0.286015	−	0.958225i	$-0.592331\pi$
$919$	1.38918	−	0.451373i	0.0458249	−	0.0148894i	0.331840	+	0.943336i	$0.392331\pi$
$920$	3.60957	+	2.62251i	0.119004	+	0.0864614i
$921$	−16.3589	−	22.5161i	−0.539044	−	0.741931i
$922$	−16.7621	−	5.44634i	−0.552031	−	0.179366i
$923$	−44.7712			−1.47366
$924$	5.79985	+	6.58496i	0.190801	+	0.216629i
$925$	−36.4868			−1.19968
$926$	−8.93421	−	2.90290i	−0.293596	−	0.0953952i
$927$	−7.73913	−	10.6520i	−0.254186	−	0.349857i
$928$	−6.99524	−	5.08234i	−0.229630	−	0.166836i
$929$	−15.5035	+	5.03739i	−0.508653	+	0.165271i	−0.552089	−	0.833785i	$-0.686169\pi$
$929$	−15.5035	+	5.03739i	−0.508653	+	0.165271i	0.0434367	+	0.999056i	$0.486169\pi$
$930$	4.52803	+	13.9358i	0.148480	+	0.456974i
$931$	−4.40892	−	55.6589i	−0.144496	−	1.82415i
$932$	9.01905	+	12.4137i	0.295429	+	0.406623i
$933$	0.191781	−	0.590240i	0.00627862	−	0.0193236i
$934$	−25.6746			−0.840099
$935$	32.2530	−	35.9569i	1.05479	−	1.17592i
$936$			4.06542i			0.132883i
$937$	3.92764	−	12.0880i	0.128310	−	0.394899i	−0.866179	−	0.499733i	$-0.833431\pi$
$937$	3.92764	−	12.0880i	0.128310	−	0.394899i	0.994490	+	0.104835i	$0.0334314\pi$
$938$	0.737695	+	3.70372i	0.0240866	+	0.120931i
$939$	8.97227	+	6.51874i	0.292799	+	0.212731i
$940$	2.95782	+	9.10323i	0.0964734	+	0.296915i
$941$	0.949834	+	2.92329i	0.0309637	+	0.0952965i	0.965344	−	0.260981i	$-0.0840459\pi$
$941$	0.949834	+	2.92329i	0.0309637	+	0.0952965i	−0.934380	+	0.356277i	$0.884046\pi$
$942$	0.0381184	−	0.0524654i	0.00124196	−	0.00170942i
$943$	−4.55254	+	3.30761i	−0.148251	+	0.107711i
$944$	2.49189	+	0.809664i	0.0811041	+	0.0263523i
$945$	8.05210	+	3.70959i	0.261935	+	0.120673i
$946$	−24.8437	−	2.56378i	−0.807739	−	0.0833556i
$947$	−28.0790			−0.912444			−0.456222	−	0.889866i	$-0.650798\pi$
$947$	−28.0790			−0.912444			−0.456222	+	0.889866i	$0.650798\pi$
$948$	−2.60032	+	8.00297i	−0.0844545	+	0.259924i
$949$	−25.2968	+	18.3792i	−0.821169	+	0.596614i
$950$	−29.1995	+	40.1896i	−0.947356	+	1.30392i
$951$	−12.4952	+	4.05992i	−0.405183	+	0.131652i
$952$	−11.4199	−	1.34869i	−0.370121	−	0.0437113i
$953$	10.4437	−	14.3745i	0.338304	−	0.465635i	−0.605641	−	0.795738i	$-0.707083\pi$
$953$	10.4437	−	14.3745i	0.338304	−	0.465635i	0.943945	+	0.330103i	$0.107083\pi$
$954$	7.65665	+	10.5385i	0.247893	+	0.341196i
$955$	15.5288	+	5.04562i	0.502501	+	0.163272i
$956$		−	17.5479i		−	0.567539i
$957$	−6.01532	−	28.0395i	−0.194448	−	0.906389i
$958$		−	13.5074i		−	0.436405i
$959$	16.4964	−	17.8548i	0.532696	−	0.576561i
$960$	−2.71089	+	1.96958i	−0.0874937	+	0.0635679i
$961$	−9.60911	−	6.98143i	−0.309971	−	0.225207i
$962$	−22.6510	+	7.35975i	−0.730297	+	0.237288i
$963$	14.7404	−	4.78943i	0.475001	−	0.154337i
$964$	16.8309	+	12.2283i	0.542086	+	0.393848i
$965$	66.4865	−	48.3052i	2.14027	−	1.55500i
$966$	2.39064	−	2.58750i	0.0769177	−	0.0832515i
$967$		−	1.58866i		−	0.0510879i	−0.999674	−	0.0255440i	$-0.991868\pi$
$967$		−	1.58866i		−	0.0510879i	0.999674	−	0.0255440i	$-0.00813178\pi$
$968$	−9.54698	−	5.46400i	−0.306851	−	0.175620i
$969$			34.6669i			1.11366i
$970$	11.4235	+	3.71172i	0.366786	+	0.119176i
$971$	16.1386	+	22.2129i	0.517912	+	0.712845i	0.985228	−	0.171245i	$-0.0547791\pi$
$971$	16.1386	+	22.2129i	0.517912	+	0.712845i	−0.467316	+	0.884090i	$0.654779\pi$
$972$	0.587785	−	0.809017i	0.0188532	−	0.0259492i
$973$	−0.250036	+	2.11716i	−0.00801580	+	0.0678729i
$974$	−15.0943	+	4.90445i	−0.483654	+	0.157149i
$975$	14.8828	−	20.4845i	0.476633	−	0.656028i
$976$	−5.52859	+	4.01675i	−0.176966	+	0.128573i
$977$	3.71451	−	11.4321i	0.118838	−	0.365745i	−0.873890	−	0.486123i	$-0.838411\pi$
$977$	3.71451	−	11.4321i	0.118838	−	0.365745i	0.992728	+	0.120378i	$0.0384107\pi$
$978$	−13.0883			−0.418517
$979$	−29.0855	+	6.23972i	−0.929577	+	0.199422i
$980$	−17.8283	+	15.2425i	−0.569504	+	0.486903i
$981$	9.26385	+	3.01001i	0.295772	+	0.0961021i
$982$	23.2333	−	16.8799i	0.741403	−	0.538661i
$983$	−7.93650	+	10.9236i	−0.253135	+	0.348410i	−0.916606	−	0.399792i	$-0.869083\pi$
$983$	−7.93650	+	10.9236i	−0.253135	+	0.348410i	0.663471	+	0.748202i	$0.269083\pi$
$984$	−1.30598	−	4.01938i	−0.0416330	−	0.128133i
$985$	3.76312	+	11.5817i	0.119903	+	0.369024i
$986$	30.4035	+	22.0894i	0.968244	+	0.703470i
$987$	7.41200	−	1.47630i	0.235927	−	0.0469910i
$988$	−10.0203	+	30.8395i	−0.318790	+	0.981134i
$989$			10.0268i			0.318834i
$990$	−11.0548	−	1.14081i	−0.351345	−	0.0362574i
$991$	−43.4002			−1.37865			−0.689327	−	0.724450i	$-0.742094\pi$
$991$	−43.4002			−1.37865			−0.689327	+	0.724450i	$0.742094\pi$
$992$	−1.35131	+	4.15890i	−0.0429041	+	0.132045i
$993$	−9.63611	−	13.2630i	−0.305793	−	0.420887i
$994$	−25.4181	+	14.2433i	−0.806213	+	0.451770i
$995$	−10.2414	−	31.5198i	−0.324674	−	0.999244i
$996$	15.5447	−	5.05077i	0.492552	−	0.160040i
$997$	15.7084	+	11.4128i	0.497489	+	0.361447i	0.808057	−	0.589104i	$-0.200519\pi$
$997$	15.7084	+	11.4128i	0.497489	+	0.361447i	−0.310568	+	0.950551i	$0.600519\pi$
$998$	−22.6391	−	31.1600i	−0.716627	−	0.986353i
$999$	5.57162	+	1.81033i	0.176278	+	0.0572762i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.u.b.13.8	yes	32
7.6	odd	2		462.2.u.a.13.5	✓	32
11.6	odd	10		462.2.u.a.391.5	yes	32
77.6	even	10	inner	462.2.u.b.391.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.u.a.13.5	✓	32	7.6	odd	2
462.2.u.a.391.5	yes	32	11.6	odd	10
462.2.u.b.13.8	yes	32	1.1	even	1	trivial
462.2.u.b.391.8	yes	32	77.6	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(3.18685 - 1.03547i) q^{5} +(0.309017 + 0.951057i) q^{6} +(-1.29336 - 2.30808i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.951057 + 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(3.18685 - 1.03547i) q^{5} +(0.309017 + 0.951057i) q^{6} +(-1.29336 - 2.30808i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +3.35085 q^{10} +(0.695687 + 3.24284i) q^{11} +1.00000i q^{12} +(1.25628 - 3.86645i) q^{13} +(-0.516820 - 2.59478i) q^{14} +(2.71089 + 1.96958i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-1.34308 - 4.13359i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(-6.45286 + 4.68828i) q^{19} +(3.18685 + 1.03547i) q^{20} +(1.10706 - 2.40300i) q^{21} +(-0.340455 + 3.29910i) q^{22} +1.33151 q^{23} +(-0.309017 + 0.951057i) q^{24} +(5.03871 - 3.66084i) q^{25} +(2.38960 - 3.28900i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(0.310307 - 2.62749i) q^{28} +(-5.08234 + 6.99524i) q^{29} +(1.96958 + 2.71089i) q^{30} +(4.15890 + 1.35131i) q^{31} +1.00000i q^{32} +(-2.21460 + 2.46892i) q^{33} -4.34631i q^{34} +(-6.51167 - 6.01626i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-4.73950 - 3.44345i) q^{37} +(-7.58579 + 2.46477i) q^{38} +(3.86645 - 1.25628i) q^{39} +(2.71089 + 1.96958i) q^{40} +(-3.41909 + 2.48412i) q^{41} +(1.79544 - 1.94329i) q^{42} +7.53044i q^{43} +(-1.34327 + 3.03243i) q^{44} +3.35085i q^{45} +(1.26634 + 0.411458i) q^{46} +(1.67901 + 2.31096i) q^{47} +(-0.587785 + 0.809017i) q^{48} +(-3.65446 + 5.97034i) q^{49} +(5.92336 - 1.92462i) q^{50} +(2.55470 - 3.51624i) q^{51} +(3.28900 - 2.38960i) q^{52} +(4.02534 - 12.3887i) q^{53} -1.00000 q^{54} +(5.57491 + 9.61407i) q^{55} +(1.10706 - 2.40300i) q^{56} +(-7.58579 - 2.46477i) q^{57} +(-6.99524 + 5.08234i) q^{58} +(1.54007 - 2.11973i) q^{59} +(1.03547 + 3.18685i) q^{60} +(2.11173 + 6.49924i) q^{61} +(3.53777 + 2.57034i) q^{62} +(2.59478 - 0.516820i) q^{63} +(-0.309017 + 0.951057i) q^{64} -13.6226i q^{65} +(-2.86915 + 1.66373i) q^{66} -1.42737 q^{67} +(1.34308 - 4.13359i) q^{68} +(0.782639 + 1.07721i) q^{69} +(-4.33384 - 7.73402i) q^{70} +(-3.40310 - 10.4737i) q^{71} +(-0.951057 + 0.309017i) q^{72} +(-6.22243 - 4.52086i) q^{73} +(-3.44345 - 4.73950i) q^{74} +(5.92336 + 1.92462i) q^{75} -7.97617 q^{76} +(6.58496 - 5.79985i) q^{77} +4.06542 q^{78} +(8.00297 + 2.60032i) q^{79} +(1.96958 + 2.71089i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-4.01938 + 1.30598i) q^{82} +(-5.05077 - 15.5447i) q^{83} +(2.30808 - 1.29336i) q^{84} +(-8.56040 - 11.7824i) q^{85} +(-2.32703 + 7.16188i) q^{86} -8.64659 q^{87} +(-2.21460 + 2.46892i) q^{88} +8.96914i q^{89} +(-1.03547 + 3.18685i) q^{90} +(-10.5489 + 2.10109i) q^{91} +(1.07721 + 0.782639i) q^{92} +(1.35131 + 4.15890i) q^{93} +(0.882707 + 2.71669i) q^{94} +(-15.7097 + 21.6226i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(3.40913 + 1.10769i) q^{97} +(-5.32053 + 4.54884i) q^{98} +(-3.29910 - 0.340455i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} + 10 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) \) 32 * q + 8 * q^4 + 10 * q^5 - 8 * q^6 - 10 * q^7 + 8 * q^9	\( 32 q + 8 q^{4} + 10 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{9} + 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} - 12 q^{17} - 16 q^{19} + 10 q^{20} - 8 q^{21} - 4 q^{22} + 8 q^{23} + 8 q^{24} + 6 q^{25} + 10 q^{28} + 20 q^{29} - 50 q^{31} - 16 q^{33} - 12 q^{35} - 8 q^{36} - 16 q^{37} + 6 q^{40} + 40 q^{41} + 12 q^{44} + 52 q^{49} + 40 q^{51} - 32 q^{54} - 40 q^{55} - 8 q^{56} + 10 q^{58} + 60 q^{59} + 4 q^{60} - 4 q^{61} + 20 q^{62} - 10 q^{63} + 8 q^{64} + 8 q^{66} - 16 q^{67} + 12 q^{68} + 30 q^{69} - 28 q^{70} - 48 q^{71} - 74 q^{73} - 40 q^{74} - 24 q^{76} + 6 q^{77} - 60 q^{79} - 8 q^{81} + 20 q^{82} + 4 q^{83} - 2 q^{84} - 10 q^{85} - 36 q^{86} + 20 q^{87} - 16 q^{88} - 4 q^{90} - 20 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} - 8 q^{96} + 60 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) 32 * q + 8 * q^4 + 10 * q^5 - 8 * q^6 - 10 * q^7 + 8 * q^9 + 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 - 12 * q^17 - 16 * q^19 + 10 * q^20 - 8 * q^21 - 4 * q^22 + 8 * q^23 + 8 * q^24 + 6 * q^25 + 10 * q^28 + 20 * q^29 - 50 * q^31 - 16 * q^33 - 12 * q^35 - 8 * q^36 - 16 * q^37 + 6 * q^40 + 40 * q^41 + 12 * q^44 + 52 * q^49 + 40 * q^51 - 32 * q^54 - 40 * q^55 - 8 * q^56 + 10 * q^58 + 60 * q^59 + 4 * q^60 - 4 * q^61 + 20 * q^62 - 10 * q^63 + 8 * q^64 + 8 * q^66 - 16 * q^67 + 12 * q^68 + 30 * q^69 - 28 * q^70 - 48 * q^71 - 74 * q^73 - 40 * q^74 - 24 * q^76 + 6 * q^77 - 60 * q^79 - 8 * q^81 + 20 * q^82 + 4 * q^83 - 2 * q^84 - 10 * q^85 - 36 * q^86 + 20 * q^87 - 16 * q^88 - 4 * q^90 - 20 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 - 8 * q^96 + 60 * q^97 - 40 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more