LMFDB - Embedded newform 669.2.m.b.19.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [669,2,Mod(19,669)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("669.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(669, base_ring=CyclotomicField(222)) chi = DirichletCharacter(H, H._module([0, 172])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 669 = 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	669.m (of order $111$, degree $72$, minimal)

Newform invariants

comment:select newform

sage:traces = [1368] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.34199189522$
Analytic rank:	$0$
Dimension:	$1368$
Relative dimension:	$19$ over $\Q(\zeta_{111})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{111}]$

Embedding invariants

Embedding label			19.9
Character	$\chi$	$=$	669.19
Dual form			669.2.m.b.493.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0440153 - 0.343722i) q^{2} +(-0.759946 + 0.649986i) q^{3} +(1.81926 - 0.473698i) q^{4} +(-3.74410 + 0.533405i) q^{5} +(0.256864 + 0.232601i) q^{6} +(-1.52315 + 2.05943i) q^{7} +(-0.501306 - 1.24755i) q^{8} +(0.155037 - 0.987909i) q^{9} +(0.348140 + 1.26345i) q^{10} +(1.22602 - 0.394524i) q^{11} +(-1.07464 + 1.54248i) q^{12} +(1.56024 - 0.551267i) q^{13} +(0.774914 + 0.432893i) q^{14} +(2.49861 - 2.83897i) q^{15} +(2.87565 - 1.60643i) q^{16} +(0.784242 - 3.63890i) q^{17} +(-0.346390 - 0.00980636i) q^{18} +(-3.84459 - 4.12671i) q^{19} +(-6.55881 + 2.74397i) q^{20} +(-0.181091 - 2.55508i) q^{21} +(-0.189570 - 0.404043i) q^{22} +(-2.80015 - 3.57012i) q^{23} +(1.19186 + 0.622228i) q^{24} +(8.93268 - 2.59793i) q^{25} +(-0.258157 - 0.512024i) q^{26} +(0.524307 + 0.851529i) q^{27} +(-1.79545 + 4.46815i) q^{28} +(-3.46172 - 2.06449i) q^{29} +(-1.08579 - 0.733868i) q^{30} +(1.07488 - 10.8154i) q^{31} +(-2.27771 - 3.07967i) q^{32} +(-0.675271 + 1.09671i) q^{33} +(-1.28529 - 0.109394i) q^{34} +(4.60431 - 8.52318i) q^{35} +(-0.185919 - 1.87070i) q^{36} +(-1.30025 + 1.17743i) q^{37} +(-1.24922 + 1.50311i) q^{38} +(-0.827381 + 1.43307i) q^{39} +(2.54239 + 4.40355i) q^{40} +(-11.9870 - 2.05537i) q^{41} +(-0.870267 + 0.174708i) q^{42} +(2.68571 + 10.9476i) q^{43} +(2.04355 - 1.29850i) q^{44} +(-0.0535171 + 3.78152i) q^{45} +(-1.10388 + 1.11961i) q^{46} +(0.838089 - 0.899591i) q^{47} +(-1.14118 + 3.08993i) q^{48} +(0.128477 + 0.419520i) q^{49} +(-1.28614 - 2.95601i) q^{50} +(1.76925 + 3.27511i) q^{51} +(2.57734 - 1.74198i) q^{52} +(6.72840 - 0.381271i) q^{53} +(0.269612 - 0.217696i) q^{54} +(-4.37988 + 2.13110i) q^{55} +(3.33281 + 0.867796i) q^{56} +(5.60398 + 0.637155i) q^{57} +(-0.557240 + 1.28074i) q^{58} +(1.22867 - 0.104575i) q^{59} +(3.20080 - 6.34841i) q^{60} +(0.0873457 - 0.469421i) q^{61} +(-3.76480 + 0.106582i) q^{62} +(1.79839 + 1.82402i) q^{63} +(3.79785 - 3.63994i) q^{64} +(-5.54764 + 2.89624i) q^{65} +(0.406685 + 0.183833i) q^{66} +(0.607534 - 2.20482i) q^{67} +(-0.296999 - 6.99159i) q^{68} +(4.44849 + 0.893042i) q^{69} +(-3.13226 - 1.20745i) q^{70} +(-1.90993 + 4.07077i) q^{71} +(-1.31019 + 0.301829i) q^{72} +(-0.155831 - 0.0758218i) q^{73} +(0.461940 + 0.395099i) q^{74} +(-5.09974 + 7.78040i) q^{75} +(-8.94911 - 5.68639i) q^{76} +(-1.05491 + 3.12582i) q^{77} +(0.528994 + 0.221312i) q^{78} +(-5.74684 - 15.5605i) q^{79} +(-9.90982 + 7.54852i) q^{80} +(-0.951927 - 0.306324i) q^{81} +(-0.178866 + 4.21065i) q^{82} +(2.04880 - 8.35142i) q^{83} +(-1.53979 - 4.56258i) q^{84} +(-0.995276 + 14.0427i) q^{85} +(3.64472 - 1.40500i) q^{86} +(3.97261 - 0.681172i) q^{87} +(-1.10680 - 1.33174i) q^{88} +(5.19121 + 0.739568i) q^{89} +(1.30215 - 0.148050i) q^{90} +(-1.24118 + 4.05287i) q^{91} +(-6.78535 - 5.16854i) q^{92} +(6.21300 + 8.91778i) q^{93} +(-0.346098 - 0.248474i) q^{94} +(16.5957 + 13.4001i) q^{95} +(3.73268 + 0.859902i) q^{96} +(-1.84781 + 2.35591i) q^{97} +(0.138543 - 0.0626255i) q^{98} +(-0.199676 - 1.27236i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1368 q - 2 q^{2} + 19 q^{3} - 38 q^{4} + q^{5} + q^{6} + 4 q^{7} + 19 q^{9} - 5 q^{10} - 4 q^{11} + 19 q^{12} - 12 q^{13} - 8 q^{14} - 2 q^{15} - 30 q^{16} + 8 q^{17} + q^{18} - 71 q^{19} + 10 q^{20}+ \cdots - 4 q^{99}+O(q^{100}) $ 1368 * q - 2 * q^2 + 19 * q^3 - 38 * q^4 + q^5 + q^6 + 4 * q^7 + 19 * q^9 - 5 * q^10 - 4 * q^11 + 19 * q^12 - 12 * q^13 - 8 * q^14 - 2 * q^15 - 30 * q^16 + 8 * q^17 + q^18 - 71 * q^19 + 10 * q^20 - 2 * q^21 + 5 * q^22 + 6 * q^23 + 20 * q^25 - 38 * q^27 - 24 * q^28 + 71 * q^29 + 10 * q^30 + 2 * q^31 + 8 * q^32 + 8 * q^33 - 130 * q^34 + 11 * q^35 + 19 * q^36 + 18 * q^37 - 6 * q^38 - 68 * q^39 - 223 * q^40 - 236 * q^41 - 70 * q^42 + 10 * q^43 - 172 * q^44 + q^45 + 4 * q^46 + 11 * q^47 + 15 * q^48 + 10 * q^49 + 9 * q^50 - 78 * q^51 + 530 * q^52 + 24 * q^53 - 2 * q^54 - 4 * q^55 - 22 * q^56 + 3 * q^57 - 52 * q^58 - 34 * q^59 - 20 * q^60 - 12 * q^61 + 5 * q^62 - 2 * q^63 - 214 * q^64 - 106 * q^65 + 138 * q^66 - 12 * q^67 - 144 * q^68 + 6 * q^69 - 67 * q^70 + 8 * q^71 + 17 * q^73 - 8 * q^74 + 20 * q^75 + 26 * q^76 - 142 * q^77 - 74 * q^78 - 14 * q^79 + 977 * q^80 + 19 * q^81 - 194 * q^82 - 130 * q^83 + 12 * q^84 - 52 * q^85 + 15 * q^86 + 6 * q^87 + 62 * q^88 - 22 * q^89 - 5 * q^90 - 4 * q^91 + 32 * q^92 + 2 * q^93 + 417 * q^94 - 74 * q^95 - 4 * q^96 - 15 * q^97 - 80 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/669\mathbb{Z}\right)^\times$.

$n$	$224$	$226$
$\chi(n)$	$1$	$e\left(\frac{86}{111}\right)$

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 $

$2$	−0.0440153	−	0.343722i	−0.0311235	−	0.243048i	0.968866	−	0.247585i	$-0.0796369\pi$
$2$	−0.0440153	−	0.343722i	−0.0311235	−	0.243048i	−0.999990	+	0.00453692i	$0.998556\pi$
$3$	−0.759946	+	0.649986i	−0.438755	+	0.375270i
$3$	−0.759946	+	0.649986i	−0.438755	+	0.375270i
$4$	1.81926	−	0.473698i	0.909629	−	0.236849i
$5$	−3.74410	+	0.533405i	−1.67441	+	0.238546i	−0.912483	−	0.409115i	$-0.865838\pi$
$5$	−3.74410	+	0.533405i	−1.67441	+	0.238546i	−0.761929	+	0.647661i	$0.775747\pi$
$6$	0.256864	+	0.232601i	0.104864	+	0.0949589i
$7$	−1.52315	+	2.05943i	−0.575696	+	0.778393i	−0.991366	−	0.131123i	$-0.958142\pi$
$7$	−1.52315	+	2.05943i	−0.575696	+	0.778393i	0.415670	+	0.909516i	$0.363547\pi$
$8$	−0.501306	−	1.24755i	−0.177239	−	0.441075i
$9$	0.155037	−	0.987909i	0.0516789	−	0.329303i
$10$	0.348140	+	1.26345i	0.110092	+	0.399538i
$11$	1.22602	−	0.394524i	0.369658	−	0.118953i	−0.115666	−	0.993288i	$-0.536900\pi$
$11$	1.22602	−	0.394524i	0.369658	−	0.118953i	0.485323	+	0.874335i	$0.338702\pi$
$12$	−1.07464	+	1.54248i	−0.310222	+	0.445275i
$13$	1.56024	−	0.551267i	0.432732	−	0.152894i	−0.107884	−	0.994164i	$-0.534407\pi$
$13$	1.56024	−	0.551267i	0.432732	−	0.152894i	0.540616	+	0.841269i	$0.318191\pi$
$14$	0.774914	+	0.432893i	0.207104	+	0.115696i
$15$	2.49861	−	2.83897i	0.645138	−	0.733019i
$16$	2.87565	−	1.60643i	0.718911	−	0.401608i
$17$	0.784242	−	3.63890i	0.190207	−	0.882562i	−0.777184	−	0.629273i	$-0.783353\pi$
$17$	0.784242	−	3.63890i	0.190207	−	0.882562i	0.967391	−	0.253289i	$-0.0815123\pi$
$18$	−0.346390	−	0.00980636i	−0.0816448	−	0.00231138i
$19$	−3.84459	−	4.12671i	−0.882008	−	0.946733i	0.116914	−	0.993142i	$-0.462700\pi$
$19$	−3.84459	−	4.12671i	−0.882008	−	0.946733i	−0.998923	+	0.0464088i	$0.985222\pi$
$20$	−6.55881	+	2.74397i	−1.46659	+	0.613571i
$21$	−0.181091	−	2.55508i	−0.0395174	−	0.557565i
$22$	−0.189570	−	0.404043i	−0.0404164	−	0.0861423i
$23$	−2.80015	−	3.57012i	−0.583871	−	0.744421i	0.401310	−	0.915942i	$-0.368555\pi$
$23$	−2.80015	−	3.57012i	−0.583871	−	0.744421i	−0.985180	+	0.171521i	$0.945132\pi$
$24$	1.19186	+	0.622228i	0.243286	+	0.127012i
$25$	8.93268	−	2.59793i	1.78654	−	0.519585i
$26$	−0.258157	−	0.512024i	−0.0506287	−	0.100416i
$27$	0.524307	+	0.851529i	0.100903	+	0.163877i
$28$	−1.79545	+	4.46815i	−0.339309	+	0.844402i
$29$	−3.46172	−	2.06449i	−0.642826	−	0.383365i	0.153573	−	0.988137i	$-0.450922\pi$
$29$	−3.46172	−	2.06449i	−0.642826	−	0.383365i	−0.796399	+	0.604772i	$0.793264\pi$
$30$	−1.08579	−	0.733868i	−0.198238	−	0.133985i
$31$	1.07488	−	10.8154i	0.193055	−	1.94250i	−0.120015	−	0.992772i	$-0.538294\pi$
$31$	1.07488	−	10.8154i	0.193055	−	1.94250i	0.313069	−	0.949730i	$-0.398643\pi$
$32$	−2.27771	−	3.07967i	−0.402646	−	0.544413i
$33$	−0.675271	+	1.09671i	−0.117550	+	0.190913i
$34$	−1.28529	−	0.109394i	−0.220425	−	0.0187609i
$35$	4.60431	−	8.52318i	0.778270	−	1.44068i
$36$	−0.185919	−	1.87070i	−0.0309865	−	0.311784i
$37$	−1.30025	+	1.17743i	−0.213760	+	0.193569i	−0.771097	−	0.636718i	$-0.780292\pi$
$37$	−1.30025	+	1.17743i	−0.213760	+	0.193569i	0.557337	+	0.830286i	$0.311823\pi$
$38$	−1.24922	+	1.50311i	−0.202650	+	0.243836i
$39$	−0.827381	+	1.43307i	−0.132487	+	0.229474i
$40$	2.54239	+	4.40355i	0.401987	+	0.696262i
$41$	−11.9870	−	2.05537i	−1.87205	−	0.320995i	−0.883091	−	0.469201i	$-0.844542\pi$
$41$	−11.9870	−	2.05537i	−1.87205	−	0.320995i	−0.988956	+	0.148207i	$0.952650\pi$
$42$	−0.870267	+	0.174708i	−0.134285	+	0.0269580i
$43$	2.68571	+	10.9476i	0.409567	+	1.66950i	0.701198	+	0.712966i	$0.252649\pi$
$43$	2.68571	+	10.9476i	0.409567	+	1.66950i	−0.291631	+	0.956531i	$0.594198\pi$
$44$	2.04355	−	1.29850i	0.308077	−	0.195757i
$45$	−0.0535171	+	3.78152i	−0.00797786	+	0.563716i
$46$	−1.10388	+	1.11961i	−0.162758	+	0.165078i
$47$	0.838089	−	0.899591i	0.122248	−	0.131219i	−0.667604	−	0.744517i	$-0.732680\pi$
$47$	0.838089	−	0.899591i	0.122248	−	0.131219i	0.789852	+	0.613298i	$0.210157\pi$
$48$	−1.14118	+	3.08993i	−0.164715	+	0.445993i
$49$	0.128477	+	0.419520i	0.0183538	+	0.0599314i
$50$	−1.28614	−	2.95601i	−0.181887	−	0.418043i
$51$	1.76925	+	3.27511i	0.247745	+	0.458607i
$52$	2.57734	−	1.74198i	0.357413	−	0.241569i
$53$	6.72840	−	0.381271i	0.924217	−	0.0523715i	0.411959	−	0.911203i	$-0.364845\pi$
$53$	6.72840	−	0.381271i	0.924217	−	0.0523715i	0.512259	+	0.858831i	$0.328809\pi$
$54$	0.269612	−	0.217696i	0.0366895	−	0.0296247i
$55$	−4.37988	+	2.13110i	−0.590583	+	0.287357i
$56$	3.33281	+	0.867796i	0.445365	+	0.115964i
$57$	5.60398	+	0.637155i	0.742266	+	0.0843932i
$58$	−0.557240	+	1.28074i	−0.0731692	+	0.168169i
$59$	1.22867	−	0.104575i	0.159959	−	0.0136145i	−0.00455270	−	0.999990i	$-0.501449\pi$
$59$	1.22867	−	0.104575i	0.159959	−	0.0136145i	0.164512	+	0.986375i	$0.447395\pi$
$60$	3.20080	−	6.34841i	0.413221	−	0.819576i
$61$	0.0873457	−	0.469421i	0.0111835	−	0.0601032i	−0.977075	−	0.212897i	$-0.931710\pi$
$61$	0.0873457	−	0.469421i	0.0111835	−	0.0601032i	0.988258	+	0.152794i	$0.0488271\pi$
$62$	−3.76480	+	0.106582i	−0.478130	+	0.0135360i
$63$	1.79839	+	1.82402i	0.226576	+	0.229805i
$64$	3.79785	−	3.63994i	0.474731	−	0.454993i
$65$	−5.54764	+	2.89624i	−0.688100	+	0.359234i
$66$	0.406685	+	0.183833i	0.0500595	+	0.0226283i
$67$	0.607534	−	2.20482i	0.0742220	−	0.269362i	−0.917505	−	0.397723i	$-0.869800\pi$
$67$	0.607534	−	2.20482i	0.0742220	−	0.269362i	0.991728	+	0.128361i	$0.0409716\pi$
$68$	−0.296999	−	6.99159i	−0.0360164	−	0.847855i
$69$	4.44849	+	0.893042i	0.535535	+	0.107510i
$70$	−3.13226	−	1.20745i	−0.374377	−	0.144318i
$71$	−1.90993	+	4.07077i	−0.226667	+	0.483112i	−0.985821	−	0.167800i	$-0.946334\pi$
$71$	−1.90993	+	4.07077i	−0.226667	+	0.483112i	0.759154	+	0.650911i	$0.225613\pi$
$72$	−1.31019	+	0.301829i	−0.154407	+	0.0355709i
$73$	−0.155831	−	0.0758218i	−0.0182386	−	0.00887426i	0.428381	−	0.903598i	$-0.359084\pi$
$73$	−0.155831	−	0.0758218i	−0.0182386	−	0.00887426i	−0.446620	+	0.894724i	$0.647372\pi$
$74$	0.461940	+	0.395099i	0.0536994	+	0.0459294i
$75$	−5.09974	+	7.78040i	−0.588867	+	0.898403i
$76$	−8.94911	−	5.68639i	−1.02653	−	0.652273i
$77$	−1.05491	+	3.12582i	−0.120218	+	0.356220i
$78$	0.528994	+	0.221312i	0.0598967	+	0.0250587i
$79$	−5.74684	−	15.5605i	−0.646570	−	1.75070i	−0.660536	−	0.750794i	$-0.729671\pi$
$79$	−5.74684	−	15.5605i	−0.646570	−	1.75070i	0.0139665	−	0.999902i	$-0.495554\pi$
$80$	−9.90982	+	7.54852i	−1.10795	+	0.843950i
$81$	−0.951927	−	0.306324i	−0.105770	−	0.0340360i
$82$	−0.178866	+	4.21065i	−0.0197524	+	0.464988i
$83$	2.04880	−	8.35142i	0.224885	−	0.916688i	−0.743801	−	0.668401i	$-0.766979\pi$
$83$	2.04880	−	8.35142i	0.224885	−	0.916688i	0.968686	−	0.248287i	$-0.0798676\pi$
$84$	−1.53979	−	4.56258i	−0.168005	−	0.497818i
$85$	−0.995276	+	14.0427i	−0.107953	+	1.52315i
$86$	3.64472	−	1.40500i	0.393021	−	0.151505i
$87$	3.97261	−	0.681172i	0.425909	−	0.0730294i
$88$	−1.10680	−	1.33174i	−0.117985	−	0.141964i
$89$	5.19121	+	0.739568i	0.550267	+	0.0783940i	0.410619	−	0.911807i	$-0.365313\pi$
$89$	5.19121	+	0.739568i	0.550267	+	0.0783940i	0.139648	+	0.990201i	$0.455403\pi$
$90$	1.30215	−	0.148050i	0.137258	−	0.0156058i
$91$	−1.24118	+	4.05287i	−0.130111	+	0.424856i
$92$	−6.78535	−	5.16854i	−0.707421	−	0.538858i
$93$	6.21300	+	8.91778i	0.644258	+	0.924731i
$94$	−0.346098	−	0.248474i	−0.0356973	−	0.0256281i
$95$	16.5957	+	13.4001i	1.70268	+	1.37482i
$96$	3.73268	+	0.859902i	0.380965	+	0.0877634i
$97$	−1.84781	+	2.35591i	−0.187617	+	0.239207i	−0.871513	−	0.490373i	$-0.836861\pi$
$97$	−1.84781	+	2.35591i	−0.187617	+	0.239207i	0.683896	+	0.729579i	$0.260284\pi$
$98$	0.138543	−	0.0626255i	0.0139950	−	0.00632613i
$99$	−0.199676	−	1.27236i	−0.0200682	−	0.127877i
$100$	15.0202	−	8.95769i	1.50202	−	0.895769i
$101$	−16.8212	−	0.953186i	−1.67377	−	0.0948456i	−0.806034	−	0.591870i	$-0.798390\pi$
$101$	−16.8212	−	0.953186i	−1.67377	−	0.0948456i	−0.867737	+	0.497024i	$0.834426\pi$
$102$	1.04785	−	0.752285i	0.103753	−	0.0744873i
$103$	−9.57108	−	3.38168i	−0.943066	−	0.333207i	−0.183045	−	0.983105i	$-0.558595\pi$
$103$	−9.57108	−	3.38168i	−0.943066	−	0.333207i	−0.760021	+	0.649898i	$0.774812\pi$
$104$	−1.46989	−	1.67012i	−0.144135	−	0.163769i
$105$	2.04092	+	9.46989i	0.199173	+	0.924167i
$106$	−0.427204	−	2.29592i	−0.0414937	−	0.222999i
$107$	12.7159	+	3.69822i	1.22930	+	0.357521i	0.829199	−	0.558953i	$-0.188797\pi$
$107$	12.7159	+	3.69822i	1.22930	+	0.357521i	0.400096	+	0.916473i	$0.368977\pi$
$108$	1.35722	+	1.30079i	0.130598	+	0.125168i
$109$	−0.147346	−	10.4115i	−0.0141132	−	0.997241i	−0.873761	−	0.486355i	$-0.838326\pi$
$109$	−0.147346	−	10.4115i	−0.0141132	−	0.997241i	0.859648	−	0.510887i	$-0.170683\pi$
$110$	0.925287	+	1.41166i	0.0882226	+	0.134596i
$111$	0.222807	−	1.73993i	0.0211479	−	0.165147i
$112$	−1.07170	+	8.36903i	−0.101266	+	0.790799i
$113$	7.89688	+	12.0478i	0.742876	+	1.13337i	0.986542	+	0.163506i	$0.0522803\pi$
$113$	7.89688	+	12.0478i	0.742876	+	1.13337i	−0.243667	+	0.969859i	$0.578350\pi$
$114$	−0.0276571	−	1.95426i	−0.00259033	−	0.183033i
$115$	12.3883	+	11.8733i	1.15522	+	1.10719i
$116$	−7.27571	−	2.11602i	−0.675533	−	0.196468i
$117$	−0.302708	−	1.62684i	−0.0279853	−	0.150401i
$118$	−0.0900250	−	0.417718i	−0.00828748	−	0.0384540i
$119$	6.29955	+	7.15768i	0.577479	+	0.656143i
$120$	−4.79432	−	1.69394i	−0.437660	−	0.154635i
$121$	−7.58818	+	5.44778i	−0.689834	+	0.495252i
$122$	−0.165195	−	0.00936090i	−0.0149560	−	0.000847496i
$123$	10.4454	−	6.22938i	0.941830	−	0.561684i
$124$	−3.16774	−	20.1852i	−0.284472	−	1.81268i
$125$	−14.8282	+	6.70277i	−1.32627	+	0.599514i
$126$	0.547799	−	0.698430i	0.0488018	−	0.0622211i
$127$	−4.68571	−	1.07945i	−0.415790	−	0.0957861i	0.0114282	−	0.999935i	$-0.496362\pi$
$127$	−4.68571	−	1.07945i	−0.415790	−	0.0957861i	−0.427218	+	0.904149i	$0.640506\pi$
$128$	−7.37874	−	5.95791i	−0.652194	−	0.526610i
$129$	−9.15680	−	6.57393i	−0.806211	−	0.578803i
$130$	1.23968	+	1.77937i	0.108727	+	0.156061i
$131$	−2.28589	−	1.74121i	−0.199719	−	0.152130i	0.501298	−	0.865275i	$-0.332856\pi$
$131$	−2.28589	−	1.74121i	−0.199719	−	0.152130i	−0.701017	+	0.713144i	$0.747270\pi$
$132$	−0.708983	+	2.31507i	−0.0617091	+	0.201501i
$133$	14.3546	−	1.63207i	1.24470	−	0.141518i
$134$	−0.784587	−	0.111777i	−0.0677780	−	0.00965602i
$135$	−2.41727	−	2.90854i	−0.208045	−	0.250327i
$136$	−4.93285	+	0.845822i	−0.422988	+	0.0725286i
$137$	2.47017	−	0.952224i	0.211041	−	0.0813540i	−0.251861	−	0.967764i	$-0.581042\pi$
$137$	2.47017	−	0.952224i	0.211041	−	0.0813540i	0.462902	+	0.886410i	$0.346808\pi$
$138$	0.111157	−	1.56835i	0.00946228	−	0.133507i
$139$	5.73520	+	16.9940i	0.486453	+	1.44142i	0.858313	+	0.513127i	$0.171513\pi$
$139$	5.73520	+	16.9940i	0.486453	+	1.44142i	−0.371860	+	0.928289i	$0.621280\pi$
$140$	4.33901	−	17.6869i	0.366714	−	1.49482i
$141$	−0.0521812	+	1.22839i	−0.00439445	+	0.103449i
$142$	1.48328	+	0.477310i	0.124474	+	0.0400549i
$143$	1.69539	−	1.29141i	0.141775	−	0.107993i
$144$	−1.14118	−	3.08993i	−0.0950981	−	0.257494i
$145$	14.0622	+	5.88314i	1.16781	+	0.488568i
$146$	−0.0192027	+	0.0568997i	−0.00158922	+	0.00470905i
$147$	−0.370317	−	0.235305i	−0.0305432	−	0.0194076i
$148$	−1.80774	+	2.75798i	−0.148596	+	0.226704i
$149$	4.46982	+	3.82306i	0.366182	+	0.313197i	0.813931	−	0.580962i	$-0.197324\pi$
$149$	4.46982	+	3.82306i	0.366182	+	0.313197i	−0.447749	+	0.894159i	$0.647774\pi$
$150$	2.89876	+	1.41044i	0.236683	+	0.115162i
$151$	3.92477	−	0.904154i	0.319393	−	0.0735790i	−0.0617599	−	0.998091i	$-0.519671\pi$
$151$	3.92477	−	0.904154i	0.319393	−	0.0735790i	0.381153	+	0.924512i	$0.375527\pi$
$152$	−3.22096	+	6.86506i	−0.261255	+	0.556830i
$153$	−3.47331	−	1.33892i	−0.280801	−	0.108245i
$154$	1.12084	+	0.225011i	0.0903201	+	0.0181319i
$155$	1.74452	+	41.0673i	0.140123	+	3.29860i
$156$	−0.826380	+	2.99905i	−0.0661633	+	0.240116i
$157$	−0.834583	−	0.377255i	−0.0666070	−	0.0301082i	0.378323	−	0.925674i	$-0.376501\pi$
$157$	−0.834583	−	0.377255i	−0.0666070	−	0.0301082i	−0.444930	+	0.895566i	$0.646771\pi$
$158$	−5.09555	+	2.66022i	−0.405380	+	0.211635i
$159$	−4.86541	+	4.66311i	−0.385852	+	0.369809i
$160$	10.1707	+	10.3156i	0.804063	+	0.815522i
$161$	11.6175	−	0.328893i	0.915584	−	0.0259204i
$162$	−0.0633909	+	0.340681i	−0.00498046	+	0.0267664i
$163$	−0.106716	+	0.211659i	−0.00835868	+	0.0165784i	−0.897067	−	0.441895i	$-0.854306\pi$
$163$	−0.106716	+	0.211659i	−0.00835868	+	0.0165784i	0.888708	+	0.458474i	$0.151604\pi$
$164$	−22.7810	+	1.93895i	−1.77890	+	0.151406i
$165$	1.94329	−	4.46638i	0.151285	−	0.347707i
$166$	−2.96074	−	0.336627i	−0.229798	−	0.0261273i
$167$	−3.99703	−	1.04075i	−0.309299	−	0.0805353i	0.0940900	−	0.995564i	$-0.470006\pi$
$167$	−3.99703	−	1.04075i	−0.309299	−	0.0805353i	−0.403389	+	0.915028i	$0.632168\pi$
$168$	−3.09681	+	1.50680i	−0.238924	+	0.116252i
$169$	−7.98402	+	6.44664i	−0.614155	+	0.495896i
$170$	4.87059	−	0.275996i	0.373557	−	0.0211679i
$171$	−4.67287	+	3.15831i	−0.357343	+	0.241522i
$172$	10.0719	+	18.6443i	0.767973	+	1.42162i
$173$	7.56000	+	17.3756i	0.574776	+	1.32104i	0.923421	+	0.383788i	$0.125381\pi$
$173$	7.56000	+	17.3756i	0.574776	+	1.32104i	−0.348645	+	0.937255i	$0.613358\pi$
$174$	−0.408989	−	1.33549i	−0.0310054	−	0.101243i
$175$	−8.25555	+	22.3533i	−0.624061	+	1.68975i
$176$	2.89181	−	3.10402i	0.217978	−	0.233974i
$177$	−0.865750	+	0.878089i	−0.0650738	+	0.0660012i
$178$	0.0257130	−	1.81688i	0.00192727	−	0.136181i
$179$	19.2184	−	12.2116i	1.43645	−	0.912740i	0.436536	−	0.899687i	$-0.356205\pi$
$179$	19.2184	−	12.2116i	1.43645	−	0.912740i	0.999915	−	0.0130534i	$-0.00415515\pi$
$180$	1.69394	+	6.90492i	0.126259	+	0.514663i
$181$	1.22343	−	0.245607i	0.0909372	−	0.0182558i	−0.151145	−	0.988512i	$-0.548296\pi$
$181$	1.22343	−	0.245607i	0.0909372	−	0.0182558i	0.242082	+	0.970256i	$0.422170\pi$
$182$	1.44769	+	0.248231i	0.107310	+	0.0184001i
$183$	0.238739	+	0.413508i	0.0176481	+	0.0305674i
$184$	−3.05017	+	5.28304i	−0.224861	+	0.389471i
$185$	4.24022	−	5.10198i	0.311747	−	0.375105i
$186$	2.79177	−	2.52806i	0.204702	−	0.185367i
$187$	−0.474138	−	4.77075i	−0.0346724	−	0.348871i
$188$	1.09857	−	2.03359i	0.0801212	−	0.148315i
$189$	−2.55227	−	0.217230i	−0.185650	−	0.0158011i
$190$	3.87544	−	6.29412i	0.281154	−	0.456623i
$191$	2.00755	+	2.71438i	0.145261	+	0.196406i	0.870608	−	0.491978i	$-0.163726\pi$
$191$	2.00755	+	2.71438i	0.145261	+	0.196406i	−0.725347	+	0.688384i	$0.758321\pi$
$192$	−0.520249	+	5.23471i	−0.0375457	+	0.377783i
$193$	−16.4198	−	11.0978i	−1.18192	−	0.798838i	−0.198486	−	0.980104i	$-0.563602\pi$
$193$	−16.4198	−	11.0978i	−1.18192	−	0.798838i	−0.983434	+	0.181265i	$0.941981\pi$
$194$	0.891110	+	0.531436i	0.0639780	+	0.0381549i
$195$	2.33339	−	5.80687i	0.167098	−	0.415839i
$196$	0.432458	+	0.702356i	0.0308898	+	0.0501683i
$197$	−6.88012	−	13.6459i	−0.490188	−	0.972230i	−0.994099	−	0.108475i	$-0.965403\pi$
$197$	−6.88012	−	13.6459i	−0.490188	−	0.972230i	0.503911	−	0.863756i	$-0.331894\pi$
$198$	−0.428548	+	0.124636i	−0.0304556	+	0.00885751i
$199$	−23.1440	−	12.0827i	−1.64064	−	0.856521i	−0.995735	−	0.0922544i	$-0.970593\pi$
$199$	−23.1440	−	12.0827i	−1.64064	−	0.856521i	−0.644900	−	0.764267i	$-0.723101\pi$
$200$	−7.71905	−	9.84160i	−0.545819	−	0.695906i
$201$	0.971412	+	2.07044i	0.0685181	+	0.146037i
$202$	0.412759	+	5.82376i	0.0290416	+	0.409759i
$203$	9.52439	−	3.98467i	0.668481	−	0.279669i
$204$	4.77014	+	5.12019i	0.333976	+	0.358485i
$205$	45.9767	+	1.30161i	3.21115	+	0.0909083i
$206$	−0.741082	+	3.43863i	−0.0516336	+	0.239581i
$207$	−3.96108	+	2.21279i	−0.275314	+	0.153800i
$208$	3.60112	−	4.09167i	0.249693	−	0.283706i
$209$	−6.34161	−	3.54263i	−0.438658	−	0.245049i
$210$	3.16518	−	1.11833i	0.218418	−	0.0771720i
$211$	9.84879	−	14.1364i	0.678019	−	0.973189i	−0.321634	−	0.946864i	$-0.604232\pi$
$211$	9.84879	−	14.1364i	0.678019	−	0.973189i	0.999653	−	0.0263247i	$-0.00838039\pi$
$212$	12.0601	−	3.88086i	0.828291	−	0.266539i
$213$	−1.19450	−	4.33500i	−0.0818456	−	0.297029i
$214$	0.711464	−	4.53352i	0.0486347	−	0.309905i
$215$	−15.8951	−	39.5564i	−1.08404	−	2.69773i
$216$	0.799486	−	1.08098i	0.0543981	−	0.0735511i
$217$	20.6364	+	18.6871i	1.40089	+	1.26856i
$218$	−3.57218	+	0.508912i	−0.241938	+	0.0344678i
$219$	0.167706	−	0.0436672i	0.0113325	−	0.00295076i
$220$	−6.95864	+	5.95176i	−0.469151	+	0.401268i
$221$	−0.782400	−	6.10987i	−0.0526299	−	0.410995i
$222$	−0.607858			−0.0407968
$223$	−12.8459	+	7.61465i	−0.860225	+	0.509915i
$223$	−12.8459	+	7.61465i	−0.860225	+	0.509915i
$224$	9.81166			0.655569
$225$	−1.18162	−	9.22745i	−0.0787747	−	0.615163i
$226$	3.79352	−	3.24462i	0.252341	−	0.215829i
$227$	−27.5062	+	7.16205i	−1.82565	+	0.475362i	−0.996495	−	0.0836576i	$-0.973340\pi$
$227$	−27.5062	+	7.16205i	−1.82565	+	0.475362i	−0.829154	+	0.559020i	$0.811178\pi$
$228$	10.4969	−	1.49545i	0.695175	−	0.0990385i
$229$	14.0822	+	12.7520i	0.930576	+	0.842676i	0.987807	−	0.155685i	$-0.0497585\pi$
$229$	14.0822	+	12.7520i	0.930576	+	0.842676i	−0.0572306	+	0.998361i	$0.518227\pi$
$230$	3.53582	−	4.78075i	0.233145	−	0.315233i
$231$	−1.23006	−	3.06113i	−0.0809322	−	0.201407i
$232$	−0.840164	+	5.35361i	−0.0551595	+	0.351482i
$233$	4.26608	+	15.4822i	0.279480	+	1.01427i	0.959645	+	0.281214i	$0.0907371\pi$
$233$	4.26608	+	15.4822i	0.279480	+	1.01427i	−0.680165	+	0.733059i	$0.738092\pi$
$234$	−0.545857	+	0.175653i	−0.0356838	+	0.0114828i
$235$	−2.65804	+	3.81520i	−0.173392	+	0.248876i
$236$	2.18573	−	0.772268i	0.142279	−	0.0502703i
$237$	14.4814	+	8.08980i	0.940669	+	0.525489i
$238$	2.18297	−	2.48034i	0.141501	−	0.160777i
$239$	−11.0322	+	6.16293i	−0.713610	+	0.398647i	−0.801908	−	0.597447i	$-0.796182\pi$
$239$	−11.0322	+	6.16293i	−0.713610	+	0.398647i	0.0882976	+	0.996094i	$0.471857\pi$
$240$	2.62450	−	12.1777i	0.169411	−	0.786068i
$241$	13.1264	+	0.371611i	0.845547	+	0.0239376i	0.448417	−	0.893825i	$-0.351988\pi$
$241$	13.1264	+	0.371611i	0.845547	+	0.0239376i	0.397130	+	0.917762i	$0.370006\pi$
$242$	2.20652	+	2.36844i	0.141840	+	0.152249i
$243$	0.922520	−	0.385950i	0.0591797	−	0.0247587i
$244$	−0.0634596	−	0.895374i	−0.00406258	−	0.0573205i
$245$	−0.704803	−	1.50219i	−0.0450282	−	0.0959716i
$246$	−2.60093	−	3.31612i	−0.165829	−	0.211428i
$247$	−8.27339	−	4.31926i	−0.526423	−	0.274828i
$248$	−14.0316	+	4.08086i	−0.891006	+	0.259135i
$249$	3.87133	+	7.67832i	0.245336	+	0.486594i
$250$	2.95655	+	4.80175i	0.186989	+	0.303689i
$251$	0.258063	−	0.642215i	0.0162888	−	0.0405363i	−0.919523	−	0.393036i	$-0.871425\pi$
$251$	0.258063	−	0.642215i	0.0162888	−	0.0405363i	0.935812	+	0.352499i	$0.114668\pi$
$252$	4.13577	+	2.46647i	0.260529	+	0.155373i
$253$	−4.84152	−	3.27230i	−0.304384	−	0.205727i
$254$	−0.164789	+	1.65809i	−0.0103398	+	0.104038i
$255$	−8.37121	−	11.3186i	−0.524225	−	0.708799i
$256$	3.79315	−	6.16046i	0.237072	−	0.385029i
$257$	−11.7850	−	1.00305i	−0.735128	−	0.0625687i	−0.288740	−	0.957408i	$-0.593236\pi$
$257$	−11.7850	−	1.00305i	−0.735128	−	0.0625687i	−0.446389	+	0.894839i	$0.647290\pi$
$258$	−1.85656	+	3.43674i	−0.115585	+	0.213962i
$259$	−0.444366	−	4.47118i	−0.0276116	−	0.277826i
$260$	−8.72065	+	7.89691i	−0.540831	+	0.489746i
$261$	−2.57622	+	3.09980i	−0.159464	+	0.191873i
$262$	−0.497879	+	0.862351i	−0.0307590	+	0.0532762i
$263$	−7.13738	−	12.3623i	−0.440110	−	0.762292i	0.557587	−	0.830118i	$-0.311727\pi$
$263$	−7.13738	−	12.3623i	−0.440110	−	0.762292i	−0.997697	+	0.0678258i	$0.978394\pi$
$264$	1.70672	+	0.292646i	0.105041	+	0.0180111i
$265$	−24.9884	+	5.01648i	−1.53503	+	0.308160i
$266$	−1.19280	−	4.86214i	−0.0731351	−	0.298117i
$267$	−4.42575	+	2.81218i	−0.270851	+	0.172103i
$268$	0.0608396	−	4.29893i	0.00371637	−	0.262599i
$269$	12.4298	−	12.6069i	0.757855	−	0.768657i	−0.220545	−	0.975377i	$-0.570783\pi$
$269$	12.4298	−	12.6069i	0.757855	−	0.768657i	0.978400	+	0.206720i	$0.0662790\pi$
$270$	−0.893332	+	0.958888i	−0.0543665	+	0.0583561i
$271$	6.41835	−	17.3788i	0.389887	−	1.05568i	−0.580528	−	0.814240i	$-0.697154\pi$
$271$	6.41835	−	17.3788i	0.389887	−	1.05568i	0.970415	−	0.241444i	$-0.0776210\pi$
$272$	−3.59044	−	11.7240i	−0.217702	−	0.710872i
$273$	−1.69108	−	3.88671i	−0.102349	−	0.235234i
$274$	−0.436026	−	0.807140i	−0.0263413	−	0.0487611i
$275$	9.92666	−	6.70925i	0.598600	−	0.404583i
$276$	8.51598	−	0.482565i	0.512602	−	0.0290470i
$277$	−10.2453	+	8.27253i	−0.615583	+	0.497048i	−0.884763	−	0.466042i	$-0.845680\pi$
$277$	−10.2453	+	8.27253i	−0.615583	+	0.497048i	0.269180	+	0.963090i	$0.413247\pi$
$278$	5.58879	−	2.71931i	0.335193	−	0.163093i
$279$	−10.5180	−	2.73867i	−0.629695	−	0.163960i
$280$	−12.9412	−	1.47138i	−0.773387	−	0.0879316i
$281$	7.91594	−	18.1937i	0.472226	−	1.08534i	−0.503031	−	0.864268i	$-0.667782\pi$
$281$	7.91594	−	18.1937i	0.472226	−	1.08534i	0.975257	−	0.221076i	$-0.0709569\pi$
$282$	0.424520	−	0.0361320i	0.0252798	−	0.00215163i
$283$	−4.50459	+	8.93433i	−0.267770	+	0.531091i	−0.986412	−	0.164290i	$-0.947467\pi$
$283$	−4.50459	+	8.93433i	−0.267770	+	0.531091i	0.718642	+	0.695380i	$0.244764\pi$
$284$	−1.54635	+	8.31052i	−0.0917588	+	0.493139i
$285$	−21.3217	+	0.603622i	−1.26299	+	0.0357555i
$286$	−0.518510	−	0.525900i	−0.0306601	−	0.0310971i
$287$	22.4908	−	21.5557i	1.32759	−	1.27239i
$288$	−3.39556	+	1.77271i	−0.200085	+	0.104458i
$289$	2.86435	+	1.29477i	0.168491	+	0.0761628i
$290$	1.40321	−	5.09245i	0.0823993	−	0.299039i
$291$	−0.127074	−	2.99142i	−0.00744920	−	0.175360i
$292$	−0.319413	−	0.0641227i	−0.0186922	−	0.00375250i
$293$	9.88594	+	3.81092i	0.577543	+	0.222636i	0.630801	−	0.775945i	$-0.282726\pi$
$293$	9.88594	+	3.81092i	0.577543	+	0.222636i	−0.0532583	+	0.998581i	$0.516961\pi$
$294$	−0.0645797	+	0.137643i	−0.00376636	+	0.00802751i
$295$	−4.54448	+	1.04692i	−0.264590	+	0.0609539i
$296$	2.12073	+	1.03187i	0.123265	+	0.0599764i
$297$	0.978757	+	0.837136i	0.0567933	+	0.0485756i
$298$	1.11733	−	1.70465i	0.0647251	−	0.0987476i
$299$	−6.33699	−	4.02661i	−0.366477	−	0.232865i
$300$	−5.59219	+	16.5703i	−0.322865	+	0.956686i
$301$	−26.6366	−	11.1438i	−1.53531	−	0.642319i
$302$	−0.483527	−	1.30923i	−0.0278239	−	0.0753378i
$303$	13.4028	−	10.2092i	0.769968	−	0.586501i
$304$	−17.6849	−	5.69090i	−1.01430	−	0.326396i
$305$	−0.0766393	+	1.80415i	−0.00438836	+	0.103305i
$306$	−0.307338	+	1.25279i	−0.0175693	+	0.0716170i
$307$	−7.01612	−	20.7896i	−0.400431	−	1.18652i	−0.938993	−	0.343937i	$-0.888239\pi$
$307$	−7.01612	−	20.7896i	−0.400431	−	1.18652i	0.538561	−	0.842586i	$-0.318968\pi$
$308$	−0.438459	+	6.18637i	−0.0249835	+	0.352501i
$309$	9.47155	−	3.65117i	0.538817	−	0.207708i
$310$	14.0389	−	2.40722i	0.797357	−	0.136721i
$311$	4.75548	+	5.72195i	0.269658	+	0.324462i	0.886592	−	0.462553i	$-0.153067\pi$
$311$	4.75548	+	5.72195i	0.269658	+	0.324462i	−0.616933	+	0.787016i	$0.711625\pi$
$312$	2.20259	+	0.313793i	0.124697	+	0.0177650i
$313$	20.5935	−	2.34141i	1.16401	−	0.132345i	0.490447	−	0.871471i	$-0.336833\pi$
$313$	20.5935	−	2.34141i	1.16401	−	0.132345i	0.673567	+	0.739126i	$0.264761\pi$
$314$	−0.0929364	+	0.303469i	−0.00524471	+	0.0171258i
$315$	−7.70628	−	5.87004i	−0.434200	−	0.330739i
$316$	−17.8260	−	25.5864i	−1.00279	−	1.43935i
$317$	4.97198	+	3.56953i	0.279254	+	0.200485i	0.714144	−	0.699999i	$-0.246816\pi$
$317$	4.97198	+	3.56953i	0.279254	+	0.200485i	−0.434890	+	0.900484i	$0.643213\pi$
$318$	1.81697	+	1.46710i	0.101890	+	0.0822708i
$319$	−5.05861	−	1.16536i	−0.283228	−	0.0652476i
$320$	−12.2780	+	15.6541i	−0.686358	+	0.875090i
$321$	−12.0672	+	5.45472i	−0.673526	+	0.304453i
$322$	−0.624394	−	3.97870i	−0.0347961	−	0.221724i
$323$	−18.0318	+	10.7537i	−1.00331	+	0.598352i
$324$	−1.87691	−	0.106356i	−0.104273	−	0.00590869i
$325$	12.5050	−	8.97768i	0.693650	−	0.497992i
$326$	0.0774491	+	0.0273645i	0.00428951	+	0.00151558i
$327$	6.87931	+	7.81641i	0.380427	+	0.432249i
$328$	3.44496	+	15.9847i	0.190216	+	0.882606i
$329$	0.576113	+	3.09620i	0.0317621	+	0.170699i
$330$	−1.62073	−	0.471362i	−0.0892181	−	0.0259476i
$331$	−20.9950	−	20.1221i	−1.15399	−	1.10601i	−0.992886	−	0.119071i	$-0.962008\pi$
$331$	−20.9950	−	20.1221i	−1.15399	−	1.10601i	−0.161103	−	0.986938i	$-0.551505\pi$
$332$	−0.228756	−	16.1639i	−0.0125546	−	0.887110i
$333$	0.961608	+	1.46707i	0.0526958	+	0.0803951i
$334$	−0.181797	+	1.41968i	−0.00994746	+	0.0776812i
$335$	−1.09860	+	8.57914i	−0.0600230	+	0.468729i
$336$	−4.62532	−	7.05660i	−0.252332	−	0.384969i
$337$	0.339699	+	24.0032i	0.0185046	+	1.30754i	0.765815	+	0.643061i	$0.222336\pi$
$337$	0.339699	+	24.0032i	0.0185046	+	1.30754i	−0.747311	+	0.664475i	$0.768655\pi$
$338$	2.56727	+	2.46053i	0.139641	+	0.133835i
$339$	−13.8321	−	4.02285i	−0.751258	−	0.218491i
$340$	4.84134	+	26.0188i	0.262558	+	1.41107i
$341$	−2.94911	−	13.6839i	−0.159703	−	0.741025i
$342$	1.29126	+	1.46715i	0.0698232	+	0.0793345i
$343$	−17.9659	−	6.34775i	−0.970066	−	0.342746i
$344$	12.3113	−	8.83867i	0.663783	−	0.476549i
$345$	−17.1319	−	0.970794i	−0.922352	−	0.0522658i
$346$	5.63962	−	3.36333i	0.303188	−	0.180814i
$347$	1.67017	+	10.6425i	0.0896596	+	0.571320i	0.990537	+	0.137246i	$0.0438251\pi$
$347$	1.67017	+	10.6425i	0.0896596	+	0.571320i	−0.900877	+	0.434074i	$0.857076\pi$
$348$	6.90454	−	3.12105i	0.370122	−	0.167306i
$349$	−5.53374	+	7.05538i	−0.296214	+	0.377666i	−0.911960	−	0.410279i	$-0.865431\pi$
$349$	−5.53374	+	7.05538i	−0.296214	+	0.377666i	0.615746	+	0.787945i	$0.288855\pi$
$350$	8.04668	+	1.85373i	0.430113	+	0.0990858i
$351$	1.28746	+	1.03956i	0.0687198	+	0.0554873i
$352$	−4.00751	−	2.87711i	−0.213601	−	0.153350i
$353$	14.1183	+	20.2645i	0.751440	+	1.07857i	0.994101	+	0.108461i	$0.0345924\pi$
$353$	14.1183	+	20.2645i	0.751440	+	1.07857i	−0.242661	+	0.970111i	$0.578020\pi$
$354$	0.339925	+	0.258928i	0.0180668	+	0.0137619i
$355$	4.97961	−	16.2601i	0.264290	−	0.862998i
$356$	9.79448	−	1.11360i	0.519107	−	0.0590207i
$357$	−9.43971	−	1.34483i	−0.499602	−	0.0711761i
$358$	−5.04331	−	6.06828i	−0.266547	−	0.320719i
$359$	−9.50382	+	1.62959i	−0.501593	+	0.0860067i	−0.414234	−	0.910170i	$-0.635951\pi$
$359$	−9.50382	+	1.62959i	−0.501593	+	0.0860067i	−0.0873582	+	0.996177i	$0.527842\pi$
$360$	4.74447	−	1.82894i	0.250055	−	0.0963935i
$361$	−0.905679	+	12.7786i	−0.0476673	+	0.672555i
$362$	−0.138270	−	0.409711i	−0.00726732	−	0.0215339i
$363$	2.22563	−	9.07223i	0.116815	−	0.476168i
$364$	−0.338186	+	7.96116i	−0.0177258	+	0.417278i
$365$	0.623889	+	0.200763i	0.0326558	+	0.0105084i
$366$	0.131624	−	0.100261i	0.00688008	−	0.00524070i
$367$	−6.18043	−	16.7346i	−0.322616	−	0.873537i	−0.991493	−	0.130164i	$-0.958450\pi$
$367$	−6.18043	−	16.7346i	−0.322616	−	0.873537i	0.668876	−	0.743374i	$-0.266775\pi$
$368$	−13.7874	−	5.76815i	−0.718717	−	0.300686i
$369$	−3.88893	+	11.5234i	−0.202450	+	0.599882i
$370$	−1.94030	−	1.23289i	−0.100871	−	0.0640949i
$371$	−9.46316	+	14.4374i	−0.491303	+	0.749554i
$372$	15.5274	+	13.2807i	0.805058	+	0.688570i
$373$	8.70300	+	4.23458i	0.450624	+	0.219258i	0.648878	−	0.760893i	$-0.275239\pi$
$373$	8.70300	+	4.23458i	0.450624	+	0.219258i	−0.198253	+	0.980151i	$0.563527\pi$
$374$	−1.61894	+	0.372957i	−0.0837134	+	0.0192852i
$375$	6.91193	−	14.7319i	0.356930	−	0.760750i
$376$	−1.54242	−	0.594586i	−0.0795444	−	0.0306635i
$377$	−6.53920	−	1.31276i	−0.336786	−	0.0676104i
$378$	0.0376721	+	0.886831i	0.00193764	+	0.0456137i
$379$	2.68449	−	9.74238i	0.137893	−	0.500432i	−0.862087	−	0.506760i	$-0.830843\pi$
$379$	2.68449	−	9.74238i	0.137893	−	0.500432i	0.999980	+	0.00632767i	$0.00201417\pi$
$380$	36.5395	+	16.5169i	1.87444	+	0.847299i
$381$	4.26252	−	2.22532i	0.218376	−	0.114007i
$382$	0.844630	−	0.809513i	0.0432150	−	0.0414183i
$383$	2.42131	+	2.45581i	0.123723	+	0.125486i	0.771184	−	0.636612i	$-0.219665\pi$
$383$	2.42131	+	2.45581i	0.123723	+	0.125486i	−0.647461	+	0.762098i	$0.724169\pi$
$384$	9.48000	−	0.268381i	0.483774	−	0.0136957i
$385$	2.28236	−	12.2661i	0.116320	−	0.625136i
$386$	−3.09184	+	6.13230i	−0.157371	+	0.312126i
$387$	11.2316	−	0.955953i	0.570936	−	0.0485938i
$388$	−2.24565	+	5.16132i	−0.114006	+	0.262026i
$389$	24.3185	+	2.76493i	1.23299	+	0.140187i	0.705091	−	0.709117i	$-0.250906\pi$
$389$	24.3185	+	2.76493i	1.23299	+	0.140187i	0.527904	+	0.849304i	$0.322978\pi$
$390$	−2.09865	−	0.546447i	−0.106269	−	0.0276704i
$391$	−15.1873	+	7.38961i	−0.768054	+	0.373708i
$392$	0.458965	−	0.370589i	0.0231813	−	0.0187176i
$393$	2.86892	−	0.162570i	0.144718	−	0.00820055i
$394$	−4.38756	+	2.96548i	−0.221042	+	0.149398i
$395$	29.8168	+	55.1948i	1.50025	+	2.77715i
$396$	−0.965976	−	2.22016i	−0.0485421	−	0.111567i
$397$	−9.80421	−	32.0141i	−0.492059	−	1.60674i	−0.764537	−	0.644580i	$-0.777032\pi$
$397$	−9.80421	−	32.0141i	−0.492059	−	1.60674i	0.272477	−	0.962162i	$-0.412157\pi$
$398$	−3.13440	+	8.48693i	−0.157113	+	0.425411i
$399$	−9.84788	+	10.5706i	−0.493011	+	0.529189i
$400$	21.5138	−	21.8205i	1.07569	−	1.09102i
$401$	0.0622691	−	4.39994i	0.00310957	−	0.219722i	−0.992291	−	0.123926i	$-0.960451\pi$
$401$	0.0622691	−	4.39994i	0.00310957	−	0.219722i	0.995401	−	0.0957960i	$-0.0305397\pi$
$402$	0.668897	−	0.425026i	0.0333616	−	0.0211984i
$403$	−4.28510	−	17.4671i	−0.213456	−	0.870100i
$404$	−31.0536	+	6.23407i	−1.54497	+	0.310157i
$405$	3.72750	+	0.639145i	0.185221	+	0.0317594i
$406$	−1.78884	−	3.09835i	−0.0887784	−	0.153769i
$407$	−1.12960	+	1.95653i	−0.0559923	+	0.0969815i
$408$	3.19893	−	3.84906i	0.158370	−	0.190557i
$409$	18.1561	−	16.4411i	0.897761	−	0.812960i	−0.0852780	−	0.996357i	$-0.527178\pi$
$409$	18.1561	−	16.4411i	0.897761	−	0.812960i	0.983039	+	0.183397i	$0.0587094\pi$
$410$	−1.57629	−	15.8605i	−0.0778472	−	0.783293i
$411$	−1.25827	+	2.32922i	−0.0620658	+	0.114892i
$412$	−19.0142	−	1.61834i	−0.936760	−	0.0797301i
$413$	−1.65608	+	2.68965i	−0.0814904	+	0.132349i
$414$	0.934932	+	1.26411i	0.0459494	+	0.0621277i
$415$	−3.21622	+	32.3614i	−0.157878	+	1.58856i
$416$	−5.25149	−	3.54939i	−0.257475	−	0.174023i
$417$	−15.4043	−	9.18676i	−0.754353	−	0.449878i
$418$	−0.938553	+	2.33568i	−0.0459061	+	0.114242i
$419$	15.1182	+	24.5535i	0.738572	+	1.19952i	0.973762	+	0.227568i	$0.0730775\pi$
$419$	15.1182	+	24.5535i	0.738572	+	1.19952i	−0.235190	+	0.971949i	$0.575571\pi$
$420$	8.19883	+	16.2614i	0.400062	+	0.793475i
$421$	−4.10112	+	1.19274i	−0.199876	+	0.0581308i	−0.377684	−	0.925934i	$-0.623280\pi$
$421$	−4.10112	+	1.19274i	−0.199876	+	0.0581308i	0.177808	+	0.984065i	$0.443099\pi$
$422$	−5.29248	−	2.76303i	−0.257634	−	0.134502i
$423$	−0.758779	−	0.967425i	−0.0368931	−	0.0470378i
$424$	−3.84865	−	8.20288i	−0.186907	−	0.398367i
$425$	−2.44820	−	34.5425i	−0.118755	−	1.67556i
$426$	−1.43746	+	0.601381i	−0.0696450	+	0.0291370i
$427$	0.833701	+	0.894881i	0.0403456	+	0.0433063i
$428$	24.8854	+	0.704511i	1.20288	+	0.0340538i
$429$	−0.449003	+	2.08338i	−0.0216781	+	0.100587i
$430$	−12.8968	+	7.20457i	−0.621938	+	0.347435i
$431$	11.0507	−	12.5561i	0.532296	−	0.604805i	−0.420919	−	0.907098i	$-0.638293\pi$
$431$	11.0507	−	12.5561i	0.532296	−	0.604805i	0.953215	+	0.302293i	$0.0977520\pi$
$432$	2.87565	+	1.60643i	0.138355	+	0.0772895i
$433$	27.2656	−	9.63356i	1.31030	−	0.462959i	0.415570	−	0.909561i	$-0.363582\pi$
$433$	27.2656	−	9.63356i	1.31030	−	0.462959i	0.894733	+	0.446602i	$0.147366\pi$
$434$	5.51485	−	7.91569i	0.264721	−	0.379965i
$435$	−14.5105	+	4.66939i	−0.695725	+	0.223880i
$436$	−5.19997	−	18.8714i	−0.249033	−	0.903777i
$437$	−3.96746	+	25.2810i	−0.189789	+	1.20936i
$438$	−0.0223910	−	0.0557222i	−0.00106988	−	0.00266251i
$439$	−9.23531	+	12.4870i	−0.440777	+	0.595970i	−0.967126	−	0.254299i	$-0.918155\pi$
$439$	−9.23531	+	12.4870i	−0.440777	+	0.595970i	0.526348	+	0.850269i	$0.323561\pi$
$440$	4.85431	+	4.39578i	0.231420	+	0.209561i
$441$	0.434366	−	0.0618821i	0.0206841	−	0.00294677i
$442$	−2.06566	+	0.537856i	−0.0982534	+	0.0255832i
$443$	16.6760	−	14.2631i	0.792303	−	0.677661i	−0.158534	−	0.987354i	$-0.550677\pi$
$443$	16.6760	−	14.2631i	0.792303	−	0.677661i	0.950837	+	0.309693i	$0.100226\pi$
$444$	−0.418858	−	3.27092i	−0.0198781	−	0.155231i
$445$	−19.8309			−0.940074
$446$	3.18274	+	4.08025i	0.150707	+	0.193206i
$447$	−5.88176			−0.278198
$448$	1.71153	+	13.3656i	0.0808622	+	0.631465i
$449$	−20.4922	+	17.5271i	−0.967088	+	0.827155i	−0.984977	−	0.172685i	$-0.944756\pi$
$449$	−20.4922	+	17.5271i	−0.967088	+	0.827155i	0.0178895	+	0.999840i	$0.494305\pi$
$450$	−3.11966	+	0.812298i	−0.147062	+	0.0382921i
$451$	−15.5071	+	2.20922i	−0.730200	+	0.104028i
$452$	20.0735	+	18.1774i	0.944178	+	0.854993i
$453$	−2.39492	+	3.23815i	−0.112523	+	0.152142i
$454$	3.67245	+	9.13923i	0.172356	+	0.428925i
$455$	2.48527	−	15.8364i	0.116511	−	0.742421i
$456$	−2.01443	−	7.31065i	−0.0943344	−	0.342353i
$457$	3.24583	−	1.04449i	0.151833	−	0.0488590i	−0.229432	−	0.973325i	$-0.573687\pi$
$457$	3.24583	−	1.04449i	0.151833	−	0.0488590i	0.381265	+	0.924466i	$0.375489\pi$
$458$	3.76331	−	5.40163i	0.175848	−	0.252402i
$459$	3.50981	−	1.24009i	0.163824	−	0.0578827i
$460$	28.1619	+	15.7322i	1.31306	+	0.733518i
$461$	7.21530	−	8.19817i	0.336050	−	0.381827i	−0.557965	−	0.829865i	$-0.688418\pi$
$461$	7.21530	−	8.19817i	0.336050	−	0.381827i	0.894015	+	0.448038i	$0.147877\pi$
$462$	−0.998035	+	0.557536i	−0.0464328	+	0.0259389i
$463$	7.84664	−	36.4085i	0.364664	−	1.69205i	−0.307421	−	0.951574i	$-0.599466\pi$
$463$	7.84664	−	36.4085i	0.364664	−	1.69205i	0.672085	−	0.740474i	$-0.265399\pi$
$464$	−13.2711	−	0.375709i	−0.616097	−	0.0174418i
$465$	−28.0189	−	30.0750i	−1.29934	−	1.39469i
$466$	5.13380	−	2.14780i	0.237819	−	0.0994949i
$467$	0.0521919	+	0.736395i	0.00241516	+	0.0340763i	0.998560	−	0.0536491i	$-0.0170852\pi$
$467$	0.0521919	+	0.736395i	0.00241516	+	0.0340763i	−0.996145	+	0.0877254i	$0.972040\pi$
$468$	−1.32133	−	2.81625i	−0.0610787	−	0.130181i
$469$	3.61532	+	4.60945i	0.166940	+	0.212845i
$470$	1.42836	+	0.745700i	0.0658854	+	0.0343966i
$471$	0.879449	−	0.255773i	0.0405229	−	0.0117854i
$472$	−0.746403	−	1.48040i	−0.0343560	−	0.0681410i
$473$	7.61182	+	12.3624i	0.349992	+	0.568423i
$474$	2.14324	−	5.33365i	0.0984422	−	0.244983i
$475$	−45.0633	−	26.8747i	−2.06765	−	1.23309i
$476$	14.8511	+	10.0376i	0.680698	+	0.460072i
$477$	0.666489	−	6.70616i	0.0305164	−	0.307054i
$478$	2.60392	+	3.52073i	0.119100	+	0.161034i
$479$	5.20625	−	8.45549i	0.237880	−	0.386341i	−0.710389	−	0.703809i	$-0.751481\pi$
$479$	5.20625	−	8.45549i	0.237880	−	0.386341i	0.948269	+	0.317468i	$0.102832\pi$
$480$	−14.4342	−	1.22853i	−0.658827	−	0.0560745i
$481$	−1.37962	+	2.55386i	−0.0629053	+	0.116446i
$482$	−0.450032	−	4.52819i	−0.0204984	−	0.206254i
$483$	−8.61487	+	7.80113i	−0.391990	+	0.354964i
$484$	−11.2243	+	13.5054i	−0.510194	+	0.613883i
$485$	5.66173	−	9.80640i	0.257086	−	0.445286i
$486$	−0.173264	−	0.300103i	−0.00785943	−	0.0136129i
$487$	−14.8635	−	2.54861i	−0.673530	−	0.115488i	−0.177935	−	0.984042i	$-0.556942\pi$
$487$	−14.8635	−	2.54861i	−0.673530	−	0.115488i	−0.495595	+	0.868554i	$0.665050\pi$
$488$	−0.629413	+	0.126356i	−0.0284922	+	0.00571986i
$489$	−0.0564769	−	0.230214i	−0.00255397	−	0.0104106i
$490$	−0.485315	+	0.308376i	−0.0219243	+	0.0139310i
$491$	0.289262	−	20.4393i	0.0130542	−	0.922411i	−0.880653	−	0.473761i	$-0.842896\pi$
$491$	0.289262	−	20.4393i	0.0130542	−	0.922411i	0.893708	−	0.448650i	$-0.148095\pi$
$492$	16.0520	−	16.2808i	0.723682	−	0.733996i
$493$	−10.2273	+	10.9778i	−0.460614	+	0.494415i
$494$	−1.12047	+	3.03386i	−0.0504123	+	0.136500i
$495$	1.42629	+	4.65732i	0.0641069	+	0.209331i
$496$	−14.2832	−	32.8280i	−0.641335	−	1.47402i
$497$	−5.47437	−	10.1338i	−0.245559	−	0.454562i
$498$	2.46881	−	1.66862i	0.110630	−	0.0747728i
$499$	8.71100	−	0.493616i	0.389958	−	0.0220973i	0.139493	−	0.990223i	$-0.455453\pi$
$499$	8.71100	−	0.493616i	0.389958	−	0.0220973i	0.250465	+	0.968126i	$0.419417\pi$
$500$	−23.8012	+	19.2182i	−1.06442	+	0.859462i
$501$	3.71400	−	1.80710i	0.165929	−	0.0807354i
$502$	−0.232102	−	0.0604347i	−0.0103592	−	0.00269733i
$503$	44.0834	+	5.01213i	1.96558	+	0.223480i	0.999408	−	0.0344164i	$-0.0109572\pi$
$503$	44.0834	+	5.01213i	1.96558	+	0.223480i	0.966173	+	0.257896i	$0.0830293\pi$
$504$	1.37401	−	3.15797i	0.0612033	−	0.140667i
$505$	63.4886	−	5.40368i	2.82521	−	0.240460i
$506$	−0.911658	+	1.80817i	−0.0405282	+	0.0803828i
$507$	1.87720	−	10.0886i	0.0833692	−	0.448050i
$508$	−9.03586	+	0.255807i	−0.400902	+	0.0113496i
$509$	19.7397	+	20.0210i	0.874947	+	0.887417i	0.994428	−	0.105419i	$-0.0336185\pi$
$509$	19.7397	+	20.0210i	0.874947	+	0.887417i	−0.119481	+	0.992837i	$0.538123\pi$
$510$	−3.52199	+	3.37556i	−0.155957	+	0.149472i
$511$	0.393503	−	0.205435i	0.0174075	−	0.00908790i
$512$	−19.5683	−	8.84541i	−0.864803	−	0.390916i
$513$	1.49827	−	5.43744i	0.0661504	−	0.240069i
$514$	0.173950	+	4.09491i	0.00767260	+	0.180619i
$515$	37.6389	+	7.55607i	1.65857	+	0.332960i
$516$	−19.7726	−	7.62213i	−0.870442	−	0.335545i
$517$	0.672600	−	1.43356i	0.0295809	−	0.0630478i
$518$	−1.51728	+	0.349539i	−0.0666656	+	0.0153579i
$519$	−17.0391	−	8.29063i	−0.747933	−	0.363918i
$520$	6.39426	+	5.46905i	0.280407	+	0.239834i
$521$	21.7190	−	33.1355i	0.951528	−	1.45169i	0.0602776	−	0.998182i	$-0.480801\pi$
$521$	21.7190	−	33.1355i	0.951528	−	1.45169i	0.891250	−	0.453512i	$-0.149829\pi$
$522$	1.17886	+	0.749064i	0.0515973	+	0.0327856i
$523$	−4.94378	+	14.6490i	−0.216176	+	0.640555i	0.783637	+	0.621219i	$0.213362\pi$
$523$	−4.94378	+	14.6490i	−0.216176	+	0.640555i	−0.999813	+	0.0193359i	$0.993845\pi$
$524$	−4.98344	−	2.08489i	−0.217702	−	0.0910790i
$525$	−8.25555	−	22.3533i	−0.360302	−	0.975577i
$526$	−3.93504	+	2.99740i	−0.171576	+	0.130693i
$527$	−38.5131	−	12.3933i	−1.67766	−	0.539860i
$528$	−0.180050	+	4.23852i	−0.00783568	+	0.184458i
$529$	0.575022	−	2.34393i	0.0250010	−	0.101910i
$530$	2.82415	+	8.36827i	0.122673	+	0.363494i
$531$	0.0871780	−	1.23003i	0.00378320	−	0.0533786i
$532$	25.3416	−	9.76888i	1.09870	−	0.423535i
$533$	−19.8356	+	3.40115i	−0.859174	+	0.147320i
$534$	1.16141	+	1.39745i	0.0502591	+	0.0604735i
$535$	−49.5823	−	7.06377i	−2.14363	−	0.305393i
$536$	−3.05519	+	0.347365i	−0.131964	+	0.0150039i
$537$	−6.66756	+	21.7719i	−0.287727	+	0.939526i
$538$	−4.88037	−	3.71748i	−0.210408	−	0.160272i
$539$	0.323025	+	0.463651i	0.0139137	+	0.0199709i
$540$	−5.77541	−	4.14633i	−0.248534	−	0.178430i
$541$	3.45931	+	2.79320i	0.148727	+	0.120089i	0.699708	−	0.714429i	$-0.253314\pi$
$541$	3.45931	+	2.79320i	0.148727	+	0.120089i	−0.550980	+	0.834518i	$0.685746\pi$
$542$	−6.25596	−	1.44120i	−0.268717	−	0.0619046i
$543$	−0.770104	+	0.981863i	−0.0330483	+	0.0421358i
$544$	−12.9929	+	5.87314i	−0.557064	+	0.251809i
$545$	6.10523	+	38.9031i	0.261519	+	1.66643i
$546$	−1.26151	+	0.752336i	−0.0539878	+	0.0321970i
$547$	29.1383	+	1.65115i	1.24587	+	0.0705979i	0.667145	−	0.744928i	$-0.267516\pi$
$547$	29.1383	+	1.65115i	1.24587	+	0.0705979i	0.578720	+	0.815526i	$0.303552\pi$
$548$	4.04282	−	2.90246i	0.172701	−	0.123987i
$549$	−0.450204	−	0.159067i	−0.0192142	−	0.00678882i
$550$	−2.74304	−	3.11670i	−0.116964	−	0.132897i
$551$	4.78934	+	22.2226i	0.204033	+	0.946716i
$552$	−1.11594	−	5.99739i	−0.0474976	−	0.255266i
$553$	40.7992	+	11.8658i	1.73496	+	0.504584i
$554$	3.29440	+	3.15743i	0.139966	+	0.134146i
$555$	0.0938764	+	6.63331i	0.00398483	+	0.281568i
$556$	18.4839	+	28.1998i	0.783890	+	1.19594i
$557$	−2.18390	+	17.0544i	−0.0925349	+	0.722618i	0.877487	+	0.479601i	$0.159218\pi$
$557$	−2.18390	+	17.0544i	−0.0925349	+	0.722618i	−0.970022	+	0.243018i	$0.921863\pi$
$558$	−0.478388	+	3.73580i	−0.0202518	+	0.158149i
$559$	10.2254	+	15.6004i	0.432489	+	0.659825i
$560$	−0.451544	−	31.9061i	−0.0190812	−	1.34828i
$561$	3.46124	+	3.31733i	0.146134	+	0.140058i
$562$	−6.60199	−	1.92008i	−0.278488	−	0.0809938i
$563$	−5.35267	−	28.7668i	−0.225588	−	1.21238i	−0.886791	−	0.462170i	$-0.847071\pi$
$563$	−5.35267	−	28.7668i	−0.225588	−	1.21238i	0.661203	−	0.750207i	$-0.270046\pi$
$564$	0.486953	+	2.25947i	0.0205044	+	0.0951409i
$565$	−35.9931	−	40.8961i	−1.51424	−	1.72051i
$566$	3.26919	+	1.15508i	0.137414	+	0.0485516i
$567$	2.08078	−	1.49385i	0.0873846	−	0.0627360i
$568$	6.03595	+	0.342032i	0.253263	+	0.0143513i
$569$	14.0452	−	8.37621i	0.588805	−	0.351149i	−0.186770	−	0.982404i	$-0.559802\pi$
$569$	14.0452	−	8.37621i	0.588805	−	0.351149i	0.775576	+	0.631255i	$0.217460\pi$
$570$	1.14596	+	7.30218i	0.0479990	+	0.305854i
$571$	15.3876	−	6.95562i	0.643950	−	0.291084i	−0.0633563	−	0.997991i	$-0.520180\pi$
$571$	15.3876	−	6.95562i	0.643950	−	0.291084i	0.707306	+	0.706907i	$0.249910\pi$
$572$	2.47261	−	3.15252i	0.103385	−	0.131813i
$573$	−3.28994	−	0.757908i	−0.137439	−	0.0316621i
$574$	−8.39910	−	6.78180i	−0.350572	−	0.283067i
$575$	−34.2877	−	24.6162i	−1.42990	−	1.02656i
$576$	−3.00713	−	4.31625i	−0.125297	−	0.179844i
$577$	10.6576	+	8.11811i	0.443681	+	0.337961i	0.803753	−	0.594963i	$-0.202833\pi$
$577$	10.6576	+	8.11811i	0.443681	+	0.337961i	−0.360072	+	0.932925i	$0.617248\pi$
$578$	0.318965	−	1.04153i	0.0132672	−	0.0433219i
$579$	19.6916	−	2.23887i	0.818353	−	0.0930441i
$580$	28.3697	+	4.04170i	1.17799	+	0.167822i
$581$	14.0786	+	16.9398i	0.584077	+	0.702782i
$582$	−1.02262	+	0.175346i	−0.0423891	+	0.00726833i
$583$	8.09871	−	3.12196i	0.335414	−	0.129298i
$584$	−0.0164725	+	0.232416i	−0.000681636	+	0.00961745i
$585$	2.00113	+	5.92958i	0.0827366	+	0.245158i
$586$	0.874762	−	3.56575i	0.0361361	−	0.147300i
$587$	1.02149	−	24.0466i	0.0421613	−	0.992511i	−0.846058	−	0.533091i	$-0.821030\pi$
$587$	1.02149	−	24.0466i	0.0421613	−	0.992511i	0.888219	−	0.459420i	$-0.151943\pi$
$588$	−0.785166	−	0.252661i	−0.0323797	−	0.0104196i
$589$	−48.7645	+	37.1450i	−2.00931	+	1.53053i
$590$	0.559875	+	1.51596i	0.0230497	+	0.0624109i
$591$	14.0982	+	5.89817i	0.579921	+	0.242618i
$592$	−1.84760	+	5.47464i	−0.0759357	+	0.225006i
$593$	21.0932	+	13.4029i	0.866196	+	0.550393i	0.893413	−	0.449237i	$-0.148304\pi$
$593$	21.0932	+	13.4029i	0.866196	+	0.550393i	−0.0272169	+	0.999630i	$0.508664\pi$
$594$	0.244662	−	0.373267i	0.0100386	−	0.0153153i
$595$	−27.4041	−	23.4388i	−1.12346	−	0.960899i
$596$	9.94273	+	4.83779i	0.407270	+	0.198164i
$597$	25.4418	−	5.86106i	1.04126	−	0.239877i
$598$	−1.10511	+	2.35539i	−0.0451912	+	0.0963192i
$599$	−8.47559	−	3.26724i	−0.346303	−	0.133496i	0.180290	−	0.983614i	$-0.442297\pi$
$599$	−8.47559	−	3.26724i	−0.346303	−	0.133496i	−0.526593	+	0.850118i	$0.676531\pi$
$600$	12.2630	+	2.46181i	0.500633	+	0.100503i
$601$	0.319363	+	7.51804i	0.0130271	+	0.306667i	0.993776	+	0.111395i	$0.0355320\pi$
$601$	0.319363	+	7.51804i	0.0130271	+	0.306667i	−0.980749	+	0.195272i	$0.937441\pi$
$602$	−2.65796	+	9.64609i	−0.108330	+	0.393145i
$603$	−2.08398	−	0.942016i	−0.0848660	−	0.0383619i
$604$	6.71187	−	3.50404i	0.273102	−	0.142578i
$605$	25.5050	−	24.4446i	1.03693	−	0.993813i
$606$	−4.09904	−	4.15746i	−0.166512	−	0.168885i
$607$	4.34948	−	0.123135i	0.176540	−	0.00499788i	0.0600816	−	0.998193i	$-0.480864\pi$
$607$	4.34948	−	0.123135i	0.176540	−	0.00499788i	0.116458	+	0.993196i	$0.462846\pi$
$608$	−3.95205	+	21.2395i	−0.160277	+	0.861375i
$609$	−4.64805	+	9.21885i	−0.188348	+	0.373567i
$610$	0.623499	−	0.0530676i	0.0252447	−	0.00214864i
$611$	0.811704	−	1.86559i	0.0328380	−	0.0754736i
$612$	−6.95310	−	0.790544i	−0.281062	−	0.0319559i
$613$	44.9789	+	11.7116i	1.81668	+	0.473027i	0.995256	−	0.0972886i	$-0.0310170\pi$
$613$	44.9789	+	11.7116i	1.81668	+	0.473027i	0.821426	+	0.570316i	$0.193179\pi$
$614$	−6.83701	+	3.32665i	−0.275919	+	0.134253i
$615$	−35.7858	+	28.8950i	−1.44302	+	1.16516i
$616$	4.42844	−	0.250941i	0.178427	−	0.0101107i
$617$	−18.5178	+	12.5159i	−0.745499	+	0.503869i	−0.872850	−	0.487988i	$-0.837731\pi$
$617$	−18.5178	+	12.5159i	−0.745499	+	0.503869i	0.127351	+	0.991858i	$0.459352\pi$
$618$	−1.67188	−	3.09487i	−0.0672529	−	0.124494i
$619$	7.09024	+	16.2959i	0.284981	+	0.654988i	0.998980	−	0.0451582i	$-0.0143792\pi$
$619$	7.09024	+	16.2959i	0.284981	+	0.654988i	−0.713999	+	0.700147i	$0.753118\pi$
$620$	22.6272	+	73.8856i	0.908730	+	2.96732i
$621$	1.57192	−	4.25625i	0.0630791	−	0.170797i
$622$	1.75745	−	1.88641i	0.0704672	−	0.0756383i
$623$	−9.43007	+	9.56448i	−0.377808	+	0.383193i
$624$	−0.0771316	+	5.45012i	−0.00308773	+	0.218180i
$625$	12.6840	−	8.05959i	0.507360	−	0.322384i
$626$	−1.71123	−	6.97538i	−0.0683943	−	0.278792i
$627$	7.12194	−	1.42974i	0.284423	−	0.0570985i
$628$	−1.69703	−	0.290984i	−0.0677187	−	0.0116115i
$629$	3.26484	+	5.65487i	0.130178	+	0.225474i
$630$	−1.67847	+	2.90719i	−0.0668717	+	0.115825i
$631$	−9.00078	+	10.8301i	−0.358315	+	0.431138i	−0.917396	−	0.397976i	$-0.869713\pi$
$631$	−9.00078	+	10.8301i	−0.358315	+	0.431138i	0.559081	+	0.829113i	$0.311154\pi$
$632$	−16.5316	+	14.9701i	−0.657592	+	0.595477i
$633$	1.70389	+	17.1445i	0.0677237	+	0.681431i
$634$	1.00808	−	1.86609i	0.0400361	−	0.0741120i
$635$	18.1196	+	1.54220i	0.719053	+	0.0612004i
$636$	−6.64252	+	10.7881i	−0.263393	+	0.427778i
$637$	0.431722	+	0.583726i	0.0171054	+	0.0231281i
$638$	−0.177903	+	1.79005i	−0.00704326	+	0.0708687i
$639$	3.72544	+	2.51796i	0.147376	+	0.0996089i
$640$	30.8047	+	18.3712i	1.21766	+	0.726184i
$641$	−6.42601	+	15.9917i	−0.253812	+	0.631635i	−0.999395	−	0.0347772i	$-0.988928\pi$
$641$	−6.42601	+	15.9917i	−0.253812	+	0.631635i	0.745583	+	0.666413i	$0.232171\pi$
$642$	2.40605	+	3.90767i	0.0949592	+	0.154224i
$643$	19.5041	+	38.6841i	0.769167	+	1.52555i	0.848792	+	0.528727i	$0.177330\pi$
$643$	19.5041	+	38.6841i	0.769167	+	1.52555i	−0.0796252	+	0.996825i	$0.525372\pi$
$644$	20.9794	−	6.10151i	0.826703	−	0.240433i
$645$	37.7905	+	19.7292i	1.48800	+	0.776835i
$646$	4.48996	+	5.72459i	0.176655	+	0.225231i
$647$	−19.5844	−	41.7415i	−0.769941	−	1.64103i	−0.767515	−	0.641031i	$-0.778507\pi$
$647$	−19.5844	−	41.7415i	−0.769941	−	1.64103i	−0.00242664	−	0.999997i	$-0.500772\pi$
$648$	0.0950530	+	1.34114i	0.00373404	+	0.0526849i
$649$	1.46511	−	0.612950i	0.0575106	−	0.0240604i
$650$	−3.63623	−	3.90307i	−0.142625	−	0.153091i
$651$	−27.8289	−	0.787842i	−1.09070	−	0.0308779i
$652$	−0.0938821	+	0.435615i	−0.00367671	+	0.0170600i
$653$	−18.9931	+	10.6102i	−0.743259	+	0.415209i	−0.812931	−	0.582361i	$-0.802129\pi$
$653$	−18.9931	+	10.6102i	−0.743259	+	0.415209i	0.0696717	+	0.997570i	$0.477805\pi$
$654$	2.38388	−	2.70861i	0.0932169	−	0.105915i
$655$	9.48738	+	5.29997i	0.370702	+	0.207087i
$656$	−37.7720	+	13.3457i	−1.47475	+	0.521062i
$657$	−0.0990644	+	0.142191i	−0.00386487	+	0.00554741i
$658$	1.03887	−	0.334303i	0.0404995	−	0.0130325i
$659$	6.66845	+	24.2007i	0.259766	+	0.942727i	0.970863	+	0.239634i	$0.0770273\pi$
$659$	6.66845	+	24.2007i	0.259766	+	0.942727i	−0.711097	+	0.703093i	$0.751802\pi$
$660$	1.41963	−	9.04604i	0.0552591	−	0.352116i
$661$	16.3914	+	40.7917i	0.637553	+	1.58661i	0.800070	+	0.599907i	$0.204796\pi$
$661$	16.3914	+	40.7917i	0.637553	+	1.58661i	−0.162517	+	0.986706i	$0.551961\pi$
$662$	−5.99229	+	8.10211i	−0.232897	+	0.314898i
$663$	4.56591	+	4.13463i	0.177325	+	0.160576i
$664$	−11.4459	+	1.63064i	−0.444186	+	0.0632812i
$665$	−52.8744	+	13.7674i	−2.05038	+	0.533877i
$666$	0.461940	−	0.395099i	0.0178998	−	0.0153098i
$667$	2.32287	+	18.1396i	0.0899419	+	0.702369i
$668$	−7.76463			−0.300423
$669$	4.81277	−	14.1364i	0.186073	−	0.546544i
$670$	2.99719			0.115792
$671$	−0.0781107	−	0.609978i	−0.00301543	−	0.0235479i
$672$	−7.45633	+	6.37744i	−0.287634	+	0.246015i
$673$	−5.95885	+	1.55156i	−0.229697	+	0.0598084i	−0.365046	−	0.930990i	$-0.618947\pi$
$673$	−5.95885	+	1.55156i	−0.229697	+	0.0598084i	0.135349	+	0.990798i	$0.456784\pi$
$674$	8.23546	−	1.17327i	0.317218	−	0.0451926i
$675$	6.89568	+	6.24433i	0.265415	+	0.240344i
$676$	−11.4712	+	15.5101i	−0.441201	+	0.596543i
$677$	1.41129	+	3.51213i	0.0542403	+	0.134982i	0.952551	−	0.304378i	$-0.0984485\pi$
$677$	1.41129	+	3.51213i	0.0542403	+	0.134982i	−0.898311	+	0.439360i	$0.855205\pi$
$678$	−0.773916	+	4.93147i	−0.0297221	+	0.189392i
$679$	−2.03736	−	7.39385i	−0.0781865	−	0.283750i
$680$	18.0179	−	5.79804i	0.690955	−	0.222345i
$681$	16.2480	−	23.3214i	0.622624	−	0.893678i
$682$	−4.57365	+	1.61597i	−0.175134	+	0.0618788i
$683$	−33.9788	−	18.9817i	−1.30016	−	0.726315i	−0.324563	−	0.945864i	$-0.605217\pi$
$683$	−33.9788	−	18.9817i	−1.30016	−	0.726315i	−0.975602	+	0.219549i	$0.929541\pi$
$684$	−7.00507	+	7.95931i	−0.267846	+	0.304332i
$685$	−8.74065	+	4.88282i	−0.333963	+	0.186563i
$686$	−1.39109	+	6.45466i	−0.0531119	+	0.246440i
$687$	−18.9903	−	0.537619i	−0.724526	−	0.0205115i
$688$	25.3098	+	27.1671i	0.964926	+	1.03574i
$689$	10.2877	−	4.30402i	0.391931	−	0.163970i
$690$	0.420384	+	5.93135i	0.0160037	+	0.225803i
$691$	3.94876	+	8.41626i	0.150218	+	0.320170i	0.966151	−	0.257976i	$-0.0830557\pi$
$691$	3.94876	+	8.41626i	0.150218	+	0.320170i	−0.815933	+	0.578146i	$0.803776\pi$
$692$	21.9844	+	28.0296i	0.835721	+	1.06552i
$693$	2.92447	+	1.52677i	0.111091	+	0.0579972i
$694$	3.58455	−	1.04251i	0.136068	−	0.0395731i
$695$	−30.5378	−	60.5682i	−1.15837	−	2.29748i
$696$	−2.84129	−	4.61455i	−0.107699	−	0.174914i
$697$	−16.8800	+	42.0074i	−0.639374	+	1.59114i
$698$	2.66866	+	1.59152i	0.101010	+	0.0602400i
$699$	−13.3052	−	8.99276i	−0.503249	−	0.340137i
$700$	−4.43027	+	44.5770i	−0.167448	+	1.68485i
$701$	17.1857	+	23.2365i	0.649093	+	0.877632i	0.998232	−	0.0594392i	$-0.0189313\pi$
$701$	17.1857	+	23.2365i	0.649093	+	0.877632i	−0.349139	+	0.937071i	$0.613526\pi$
$702$	0.300650	−	0.488286i	0.0113473	−	0.0184292i
$703$	9.85785	+	0.839026i	0.371796	+	0.0316445i
$704$	3.22018	−	5.96097i	0.121365	−	0.224662i
$705$	−0.459856	−	4.62703i	−0.0173192	−	0.174264i
$706$	6.34394	−	5.74471i	0.238757	−	0.216205i
$707$	27.5842	−	33.1903i	1.03741	−	1.24825i
$708$	−1.15907	+	2.00758i	−0.0435607	+	0.0754493i
$709$	−4.41130	−	7.64059i	−0.165670	−	0.286948i	0.771223	−	0.636565i	$-0.219645\pi$
$709$	−4.41130	−	7.64059i	−0.165670	−	0.286948i	−0.936893	+	0.349616i	$0.886312\pi$
$710$	−5.80814	−	0.995906i	−0.217976	−	0.0373757i
$711$	−16.2634	+	3.26490i	−0.609923	+	0.122443i
$712$	−1.67974	−	6.84704i	−0.0629509	−	0.256604i
$713$	−41.6221	+	26.4472i	−1.55876	+	0.990457i
$714$	−0.0467566	+	3.30383i	−0.00174982	+	0.123643i
$715$	−5.65885	+	5.73951i	−0.211629	+	0.214645i
$716$	29.1786	−	31.3198i	1.09046	−	1.17048i
$717$	4.37802	−	11.8542i	0.163500	−	0.442705i
$718$	0.978440	+	3.19494i	0.0365151	+	0.119234i
$719$	1.39814	+	3.21344i	0.0521419	+	0.119841i	0.941077	−	0.338192i	$-0.109815\pi$
$719$	1.39814	+	3.21344i	0.0521419	+	0.119841i	−0.888935	+	0.458033i	$0.848554\pi$
$720$	5.92087	+	10.9603i	0.220658	+	0.408466i
$721$	21.5425	−	14.5602i	0.802285	−	0.542250i
$722$	4.43213	−	0.251150i	0.164947	−	0.00934685i
$723$	−10.2169	+	8.24958i	−0.379971	+	0.306805i
$724$	2.10940	−	1.02636i	0.0783953	−	0.0381444i
$725$	−36.2858	−	9.44810i	−1.34762	−	0.350894i
$726$	−3.21628	−	0.365681i	−0.119367	−	0.0135717i
$727$	5.16747	−	11.8767i	0.191651	−	0.440483i	−0.794298	−	0.607528i	$-0.792161\pi$
$727$	5.16747	−	11.8767i	0.191651	−	0.440483i	0.985949	+	0.167045i	$0.0534225\pi$
$728$	5.67836	−	0.483300i	0.210454	−	0.0179123i
$729$	−0.450204	+	0.892926i	−0.0166742	+	0.0330713i
$730$	0.0415461	−	0.223281i	0.00153769	−	0.00826399i
$731$	41.9435	−	1.18743i	1.55134	−	0.0439187i
$732$	0.630206	+	0.639188i	0.0232931	+	0.0236251i
$733$	−20.4962	+	19.6440i	−0.757044	+	0.725568i	−0.967731	−	0.251985i	$-0.918916\pi$
$733$	−20.4962	+	19.6440i	−0.757044	+	0.725568i	0.210687	+	0.977554i	$0.432430\pi$
$734$	−5.48000	+	2.86093i	−0.202271	+	0.105599i
$735$	1.51202	+	0.683475i	0.0557716	+	0.0252103i
$736$	−4.61685	+	16.7552i	−0.170179	+	0.617605i
$737$	−0.125010	−	2.94284i	−0.00460481	−	0.108401i
$738$	4.13200	+	0.829507i	0.152101	+	0.0305346i
$739$	−4.37903	−	1.68807i	−0.161085	−	0.0620965i	0.277804	−	0.960638i	$-0.410394\pi$
$739$	−4.37903	−	1.68807i	−0.161085	−	0.0620965i	−0.438889	+	0.898541i	$0.644628\pi$
$740$	5.29726	−	11.2904i	0.194731	−	0.415043i
$741$	9.09479	−	2.09518i	0.334106	−	0.0769684i
$742$	5.37898	+	2.61723i	0.197469	+	0.0960814i
$743$	8.26238	+	7.06686i	0.303117	+	0.259258i	0.788487	−	0.615051i	$-0.210865\pi$
$743$	8.26238	+	7.06686i	0.303117	+	0.259258i	−0.485370	+	0.874309i	$0.661315\pi$
$744$	8.01075	−	12.2216i	0.293688	−	0.448064i
$745$	−18.7747	−	11.9297i	−0.687851	−	0.437070i
$746$	1.07245	−	3.17780i	0.0392653	−	0.116347i
$747$	−7.93280	−	3.31880i	−0.290246	−	0.121429i
$748$	−3.12247	−	8.45462i	−0.114169	−	0.309132i
$749$	−26.9845	+	20.5547i	−0.985992	+	0.751051i
$750$	−5.36789	−	1.72735i	−0.196008	−	0.0630740i
$751$	0.117603	−	2.76846i	0.00429138	−	0.101022i	−0.995676	−	0.0928981i	$-0.970387\pi$
$751$	0.117603	−	2.76846i	0.00429138	−	0.101022i	0.999967	−	0.00812427i	$-0.00258606\pi$
$752$	0.964915	−	3.93324i	0.0351868	−	0.143430i
$753$	0.221317	+	0.655786i	0.00806522	+	0.0238982i
$754$	−0.163398	+	2.30545i	−0.00595061	+	0.0839594i
$755$	−14.2124	+	5.47873i	−0.517243	+	0.199391i
$756$	−4.74613	+	0.813806i	−0.172615	+	0.0295978i
$757$	4.91658	+	5.91580i	0.178696	+	0.215013i	0.850865	−	0.525385i	$-0.176079\pi$
$757$	4.91658	+	5.91580i	0.178696	+	0.215013i	−0.672169	+	0.740398i	$0.734637\pi$
$758$	−3.46683	−	0.493903i	−0.125921	−	0.0179394i
$759$	5.80624	−	0.660150i	0.210753	−	0.0239619i
$760$	8.39775	−	27.4215i	0.304618	−	0.994683i
$761$	−15.4706	−	11.7843i	−0.560809	−	0.427180i	0.286654	−	0.958034i	$-0.407457\pi$
$761$	−15.4706	−	11.7843i	−0.560809	−	0.427180i	−0.847463	+	0.530854i	$0.821871\pi$
$762$	−0.952508	−	1.36717i	−0.0345057	−	0.0495275i
$763$	21.6662	+	15.5548i	0.784370	+	0.563122i
$764$	4.93805	+	3.98720i	0.178652	+	0.144252i
$765$	13.7186	+	3.16037i	0.495997	+	0.114264i
$766$	0.737543	−	0.940349i	0.0266485	−	0.0339762i
$767$	1.85937	−	0.840488i	0.0671379	−	0.0303482i
$768$	1.12163	+	7.14711i	0.0404732	+	0.257899i
$769$	−18.9984	+	11.3302i	−0.685099	+	0.408576i	−0.812252	−	0.583307i	$-0.801758\pi$
$769$	−18.9984	+	11.3302i	−0.685099	+	0.408576i	0.127153	+	0.991883i	$0.459416\pi$
$770$	−4.31657	−	0.244602i	−0.155558	−	0.00881484i
$771$	9.60794	−	6.89782i	0.346022	−	0.248419i
$772$	−35.1288	−	12.4118i	−1.26431	−	0.446710i
$773$	30.1460	+	34.2525i	1.08428	+	1.23198i	0.971168	+	0.238394i	$0.0766210\pi$
$773$	30.1460	+	34.2525i	1.08428	+	1.23198i	0.113108	+	0.993583i	$0.463920\pi$
$774$	−0.822946	−	3.81848i	−0.0295802	−	0.137252i
$775$	−18.4960	−	99.4029i	−0.664396	−	3.57066i
$776$	3.86544	+	1.12420i	0.138761	+	0.0403564i
$777$	3.24390	+	3.10903i	0.116374	+	0.111536i
$778$	−0.120018	−	8.48048i	−0.00430285	−	0.304040i
$779$	37.6029	+	57.3688i	1.34727	+	2.05545i
$780$	1.49434	−	11.6695i	0.0535060	−	0.417836i
$781$	−0.735592	+	5.74434i	−0.0263215	+	0.205549i
$782$	3.20844	+	4.89495i	0.114734	+	0.175043i
$783$	−0.0570362	−	4.03018i	−0.00203831	−	0.144027i
$784$	1.04338	+	1.00000i	0.0372637	+	0.0357143i
$785$	3.32599	+	0.967310i	0.118710	+	0.0345248i
$786$	−0.182155	−	0.978954i	−0.00649726	−	0.0349181i
$787$	6.45623	+	29.9570i	0.230140	+	1.06785i	0.933933	+	0.357448i	$0.116353\pi$
$787$	6.45623	+	29.9570i	0.230140	+	1.06785i	−0.703793	+	0.710405i	$0.748512\pi$
$788$	−18.9808	−	21.5663i	−0.676161	−	0.768268i
$789$	13.4593	+	4.75549i	0.479166	+	0.169300i
$790$	17.6593	−	12.6781i	0.628288	−	0.451066i
$791$	−36.8398	−	2.08756i	−1.30987	−	0.0742251i
$792$	−1.48723	+	0.886947i	−0.0528464	+	0.0315163i
$793$	−0.122496	−	0.780560i	−0.00434998	−	0.0277185i
$794$	−10.5724	+	4.77903i	−0.375201	+	0.169602i
$795$	15.7292	−	20.0544i	0.557858	−	0.711256i
$796$	−47.8285	−	11.0183i	−1.69524	−	0.390534i
$797$	−34.6269	−	27.9593i	−1.22655	−	0.990368i	−0.999866	−	0.0163997i	$-0.994780\pi$
$797$	−34.6269	−	27.9593i	−1.22655	−	0.990368i	−0.226683	−	0.973969i	$-0.572788\pi$
$798$	4.06679	+	2.91967i	0.143963	+	0.103355i
$799$	−2.61625	−	3.75522i	−0.0925564	−	0.132850i
$800$	−28.3468	−	21.5924i	−1.00221	−	0.763405i
$801$	1.53545	−	5.01378i	0.0542526	−	0.177153i
$802$	−1.51510	+	0.172261i	−0.0534999	+	0.00608276i
$803$	−0.220964	−	0.0314798i	−0.00779766	−	0.00111090i
$804$	2.74801	+	3.30650i	0.0969149	+	0.116611i
$805$	−43.3215	+	7.42821i	−1.52688	+	0.261810i
$806$	−5.81523	+	2.24170i	−0.204833	+	0.0789607i
$807$	−1.25163	+	17.6597i	−0.0440595	+	0.621652i
$808$	7.24342	+	21.4631i	0.254823	+	0.755069i
$809$	10.6166	−	43.2757i	0.373258	−	1.52149i	−0.417107	−	0.908858i	$-0.636956\pi$
$809$	10.6166	−	43.2757i	0.373258	−	1.52149i	0.790365	−	0.612636i	$-0.209891\pi$
$810$	0.0556208	−	1.30936i	0.00195432	−	0.0460061i
$811$	−26.7256	−	8.60011i	−0.938461	−	0.301991i	−0.202707	−	0.979239i	$-0.564974\pi$
$811$	−26.7256	−	8.60011i	−0.938461	−	0.301991i	−0.735754	+	0.677249i	$0.763172\pi$
$812$	15.4398	−	11.7608i	0.541831	−	0.412724i
$813$	6.41835	+	17.3788i	0.225101	+	0.609500i
$814$	0.722221	+	0.302152i	0.0253138	+	0.0105904i
$815$	0.286657	−	0.849397i	0.0100411	−	0.0297531i
$816$	10.3490	+	6.57588i	0.362287	+	0.230202i
$817$	34.8523	−	53.1722i	1.21933	−	1.86026i
$818$	−6.45031	−	5.51698i	−0.225530	−	0.192897i
$819$	3.81144	+	1.85451i	0.133182	+	0.0648019i
$820$	84.2600	−	19.4111i	2.94249	−	0.677865i
$821$	10.6028	−	22.5984i	0.370040	−	0.788691i	−0.629888	−	0.776686i	$-0.716899\pi$
$821$	10.6028	−	22.5984i	0.370040	−	0.788691i	0.999928	−	0.0120050i	$-0.00382140\pi$
$822$	0.855986	+	0.329973i	0.0298559	+	0.0115091i
$823$	−24.5051	−	4.91944i	−0.854193	−	0.171481i	−0.249928	−	0.968264i	$-0.580407\pi$
$823$	−24.5051	−	4.91944i	−0.854193	−	0.171481i	−0.604265	+	0.796783i	$0.706533\pi$
$824$	0.579235	+	13.6356i	0.0201786	+	0.475020i
$825$	−3.18281	+	11.5509i	−0.110811	+	0.402149i
$826$	0.997383	+	0.450846i	0.0347034	+	0.0156869i
$827$	26.5982	−	13.8861i	0.924912	−	0.482866i	0.0676283	−	0.997711i	$-0.478457\pi$
$827$	26.5982	−	13.8861i	0.924912	−	0.482866i	0.857283	+	0.514845i	$0.172150\pi$
$828$	−6.15803	+	5.90199i	−0.214006	+	0.205108i
$829$	−25.3528	−	25.7141i	−0.880538	−	0.893088i	0.114414	−	0.993433i	$-0.463501\pi$
$829$	−25.3528	−	25.7141i	−0.880538	−	0.893088i	−0.994953	+	0.100345i	$0.968005\pi$
$830$	11.2649	−	0.318911i	0.391010	−	0.0110696i
$831$	2.40888	−	12.9460i	0.0835630	−	0.449092i
$832$	3.91897	−	7.77281i	0.135866	−	0.269474i
$833$	1.62735	−	0.138508i	0.0563842	−	0.00479900i
$834$	−2.47966	+	5.69916i	−0.0858638	+	0.197346i
$835$	15.5204	+	1.76462i	0.537106	+	0.0610672i
$836$	−13.2152	−	3.44096i	−0.457056	−	0.119008i
$837$	9.77319	−	4.75530i	0.337811	−	0.164367i
$838$	7.77415	−	6.27718i	0.268553	−	0.216842i
$839$	8.79127	−	0.498165i	0.303508	−	0.0171985i	0.0958365	−	0.995397i	$-0.469447\pi$
$839$	8.79127	−	0.498165i	0.303508	−	0.0171985i	0.207672	+	0.978199i	$0.433411\pi$
$840$	10.7910	−	7.29346i	0.372326	−	0.251648i
$841$	−6.06205	−	11.2217i	−0.209036	−	0.386954i
$842$	0.590484	+	1.35715i	0.0203494	+	0.0467703i
$843$	5.80995	+	18.9715i	0.200105	+	0.653412i
$844$	11.2211	−	30.3831i	0.386247	−	1.04583i
$845$	26.4543	−	28.3956i	0.910055	−	0.976838i
$846$	−0.299127	+	0.303390i	−0.0102842	+	0.0104308i
$847$	0.338595	−	23.9251i	0.0116342	−	0.822077i
$848$	18.7360	−	11.9051i	0.643398	−	0.408824i
$849$	−2.38394	−	9.71753i	−0.0818166	−	0.333505i
$850$	−11.7653	+	2.36190i	−0.403545	+	0.0810124i
$851$	7.84446	+	1.34507i	0.268905	+	0.0461083i
$852$	−4.22658	−	7.32065i	−0.144800	−	0.250801i
$853$	−18.5102	+	32.0606i	−0.633778	+	1.09773i	0.352995	+	0.935625i	$0.385163\pi$
$853$	−18.5102	+	32.0606i	−0.633778	+	1.09773i	−0.986773	+	0.162110i	$0.948170\pi$
$854$	0.270895	−	0.325950i	0.00926982	−	0.0111538i
$855$	15.8110	−	14.3175i	0.540726	−	0.489650i
$856$	−1.76086	−	17.7177i	−0.0601851	−	0.605578i
$857$	19.1463	−	35.4424i	0.654026	−	1.21069i	−0.311466	−	0.950257i	$-0.600820\pi$
$857$	19.1463	−	35.4424i	0.654026	−	1.21069i	0.965492	−	0.260431i	$-0.0838647\pi$
$858$	0.735867	+	0.0626315i	0.0251221	+	0.00213821i
$859$	9.83625	−	15.9751i	0.335609	−	0.545063i	−0.638935	−	0.769261i	$-0.720625\pi$
$859$	9.83625	−	15.9751i	0.335609	−	0.545063i	0.974544	+	0.224198i	$0.0719761\pi$
$860$	−47.6550	−	64.4339i	−1.62502	−	2.19718i
$861$	−3.08091	+	30.9999i	−0.104997	+	1.05647i
$862$	−4.80220	−	3.24572i	−0.163564	−	0.110550i
$863$	25.9920	+	15.5010i	0.884777	+	0.527659i	0.881419	−	0.472335i	$-0.156589\pi$
$863$	25.9920	+	15.5010i	0.884777	+	0.527659i	0.00335766	+	0.999994i	$0.498931\pi$
$864$	1.42821	−	3.55423i	0.0485886	−	0.120917i
$865$	−37.5736	−	61.0234i	−1.27754	−	2.07486i
$866$	−4.51137	−	8.94777i	−0.153303	−	0.304058i
$867$	−3.01833	+	0.877833i	−0.102508	+	0.0298128i
$868$	46.3950	+	24.2213i	1.57475	+	0.822123i
$869$	−13.1847	−	16.8102i	−0.447261	−	0.570247i
$870$	2.24365	+	4.78205i	0.0760670	+	0.162127i
$871$	−0.267550	−	3.77497i	−0.00906560	−	0.127910i
$872$	−12.9150	+	5.40318i	−0.437357	+	0.182975i
$873$	2.04095	+	2.19072i	0.0690756	+	0.0741446i
$874$	8.86427	+	0.250949i	0.299838	+	0.00848848i
$875$	8.78165	−	40.7470i	0.296874	−	1.37750i
$876$	0.284415	−	0.158884i	0.00960951	−	0.00536819i
$877$	28.5355	−	32.4226i	0.963575	−	1.09483i	−0.0318693	−	0.999492i	$-0.510146\pi$
$877$	28.5355	−	32.4226i	0.963575	−	1.09483i	0.995445	−	0.0953421i	$-0.0303945\pi$
$878$	4.69854	+	2.62476i	0.158568	+	0.0885814i
$879$	−9.98982	+	3.52963i	−0.336948	+	0.119051i
$880$	−9.17152	+	13.1643i	−0.309172	+	0.443767i
$881$	−38.2091	+	12.2954i	−1.28730	+	0.414244i	−0.869336	−	0.494221i	$-0.835453\pi$
$881$	−38.2091	+	12.2954i	−1.28730	+	0.414244i	−0.417961	+	0.908465i	$0.637255\pi$
$882$	−0.0403890	−	0.146577i	−0.00135997	−	0.00493551i
$883$	7.10778	−	45.2915i	0.239196	−	1.52418i	−0.509038	−	0.860744i	$-0.669999\pi$
$883$	7.10778	−	45.2915i	0.239196	−	1.52418i	0.748234	−	0.663435i	$-0.230902\pi$
$884$	−4.31762	−	10.7448i	−0.145217	−	0.361387i
$885$	2.77308	−	3.74945i	0.0932160	−	0.126036i
$886$	−5.63654	−	5.10413i	−0.189363	−	0.171476i
$887$	−37.3079	+	5.31508i	−1.25268	+	0.178463i	−0.735564	−	0.677455i	$-0.763083\pi$
$887$	−37.3079	+	5.31508i	−1.25268	+	0.178463i	−0.517111	+	0.855918i	$0.672993\pi$
$888$	−2.28234	+	0.594275i	−0.0765904	+	0.0199426i
$889$	9.36011	−	8.00575i	0.313928	−	0.268504i
$890$	0.872862	+	6.81631i	0.0292584	+	0.228483i
$891$	−1.28793			−0.0431473
$892$	−19.7630	+	19.9381i	−0.661713	+	0.667577i
$893$	−6.93446			−0.232053
$894$	0.258887	+	2.02169i	0.00865849	+	0.0676154i
$895$	−65.4418	+	55.9727i	−2.18748	+	1.87096i
$896$	23.5088	−	6.12123i	0.785375	−	0.204496i
$897$	7.43301	−	1.05895i	0.248181	−	0.0353572i
$898$	6.92642	+	6.27216i	0.231138	+	0.209305i
$899$	−26.0492	+	35.2208i	−0.868789	+	1.17468i
$900$	−6.52070	−	16.2274i	−0.217357	−	0.540913i
$901$	3.88930	−	24.7830i	0.129571	−	0.825641i
$902$	1.44191	+	5.23288i	0.0480103	+	0.174236i
$903$	27.4857	−	8.84473i	0.914668	−	0.294334i
$904$	11.0715	−	15.8914i	0.368233	−	0.528540i
$905$	−4.44965	+	1.57216i	−0.147911	+	0.0522604i
$906$	1.21844	+	0.680660i	0.0404798	+	0.0226134i
$907$	−13.5926	+	15.4441i	−0.451333	+	0.512814i	−0.931191	−	0.364532i	$-0.881229\pi$
$907$	−13.5926	+	15.4441i	−0.451333	+	0.512814i	0.479857	+	0.877347i	$0.340688\pi$
$908$	−46.6482	+	26.0592i	−1.54807	+	0.864806i
$909$	−3.54956	+	16.4700i	−0.117731	+	0.546276i
$910$	−5.55270	−	0.157198i	−0.184070	−	0.00521107i
$911$	−33.9745	−	36.4677i	−1.12563	−	1.20823i	−0.975602	−	0.219545i	$-0.929543\pi$
$911$	−33.9745	−	36.4677i	−1.12563	−	1.20823i	−0.150023	−	0.988682i	$-0.547935\pi$
$912$	17.1386	−	7.17019i	0.567516	−	0.237429i
$913$	−0.782974	−	11.0473i	−0.0259127	−	0.365611i
$914$	−0.501879	−	1.06969i	−0.0166007	−	0.0353822i
$915$	−1.11443	−	1.42087i	−0.0368419	−	0.0469726i
$916$	31.6597	+	16.5285i	1.04607	+	0.546116i
$917$	7.06767	−	2.05552i	0.233395	−	0.0678791i
$918$	−0.580733	−	1.15182i	−0.0191670	−	0.0380156i
$919$	14.3512	+	23.3077i	0.473401	+	0.768852i	0.996515	−	0.0834107i	$-0.0265813\pi$
$919$	14.3512	+	23.3077i	0.473401	+	0.768852i	−0.523114	+	0.852262i	$0.675230\pi$
$920$	8.60212	−	21.4072i	0.283604	−	0.705775i
$921$	18.8448	+	11.2386i	0.620958	+	0.370324i
$922$	−3.13547	−	2.11921i	−0.103261	−	0.0697925i
$923$	−0.735869	+	7.40426i	−0.0242214	+	0.243714i
$924$	−3.68785	−	4.98630i	−0.121321	−	0.164037i
$925$	−8.55584	+	13.8956i	−0.281314	+	0.456884i
$926$	−12.8598	−	1.09453i	−0.422598	−	0.0359684i
$927$	−4.82466	+	8.93107i	−0.158462	+	0.293335i
$928$	1.52687	+	15.3633i	0.0501219	+	0.504323i
$929$	3.52668	−	3.19356i	0.115707	−	0.104777i	−0.611330	−	0.791376i	$-0.709365\pi$
$929$	3.52668	−	3.19356i	0.115707	−	0.104777i	0.727037	+	0.686598i	$0.240897\pi$
$930$	−9.10417	+	10.9545i	−0.298538	+	0.359211i
$931$	1.23730	−	2.14307i	0.0405509	−	0.0702361i
$932$	15.0950	+	26.1453i	0.494453	+	0.856418i
$933$	−7.33310	−	1.25739i	−0.240075	−	0.0411650i
$934$	0.250818	−	0.0503522i	0.00820701	−	0.00164757i
$935$	4.31996	+	17.6092i	0.141278	+	0.575884i
$936$	−1.87781	+	1.19319i	−0.0613782	+	0.0390006i
$937$	0.522401	−	36.9129i	0.0170661	−	1.20589i	−0.789124	−	0.614234i	$-0.789465\pi$
$937$	0.522401	−	36.9129i	0.0170661	−	1.20589i	0.806190	−	0.591657i	$-0.201526\pi$
$938$	1.42524	−	1.44555i	0.0465357	−	0.0471990i
$939$	−14.1281	+	15.1648i	−0.461052	+	0.494886i
$940$	−3.02841	+	8.19994i	−0.0987760	+	0.267453i
$941$	8.64924	+	28.2427i	0.281957	+	0.920687i	0.979035	+	0.203692i	$0.0652940\pi$
$941$	8.64924	+	28.2427i	0.281957	+	0.920687i	−0.697078	+	0.716995i	$0.745517\pi$
$942$	−0.126624	−	0.291028i	−0.00412564	−	0.00948220i
$943$	26.2273	+	48.5502i	0.854079	+	1.58101i
$944$	3.36522	−	2.27450i	0.109529	−	0.0740285i
$945$	9.67180	−	0.548061i	0.314624	−	0.0178284i
$946$	3.91418	−	3.16048i	0.127261	−	0.102756i
$947$	−21.9097	+	10.6605i	−0.711969	+	0.346419i	−0.757762	−	0.652532i	$-0.773707\pi$
$947$	−21.9097	+	10.6605i	−0.711969	+	0.346419i	0.0457925	+	0.998951i	$0.485419\pi$
$948$	30.1776	+	7.85763i	0.980122	+	0.255204i
$949$	−0.284931	−	0.0323957i	−0.00924925	−	0.00105161i
$950$	−7.25393	+	16.6722i	−0.235349	+	0.540916i
$951$	−6.09858	+	0.519066i	−0.197760	+	0.0168319i
$952$	5.77155	−	11.4472i	0.187057	−	0.371005i
$953$	2.83092	−	15.2142i	0.0917025	−	0.492836i	−0.905891	−	0.423510i	$-0.860798\pi$
$953$	2.83092	−	15.2142i	0.0917025	−	0.492836i	0.997594	−	0.0693264i	$-0.0220850\pi$
$954$	−2.33439	+	0.0660870i	−0.0755786	+	0.00213965i
$955$	−8.96432	−	9.09209i	−0.290079	−	0.294213i
$956$	−17.1510	+	16.4379i	−0.554702	+	0.531639i
$957$	4.60174	−	2.40242i	0.148753	−	0.0776591i
$958$	−3.13549	−	1.41733i	−0.101303	−	0.0457919i
$959$	−1.80140	+	6.53754i	−0.0581703	+	0.211108i
$960$	−0.844355	−	19.8768i	−0.0272514	−	0.641520i
$961$	−85.4238	−	17.1490i	−2.75561	−	0.553193i
$962$	0.938542	+	0.361797i	0.0302598	+	0.0116648i
$963$	5.62494	−	11.9888i	0.181261	−	0.386334i
$964$	24.0564	−	5.54190i	0.774804	−	0.178493i
$965$	67.3968	+	32.7929i	2.16958	+	1.05564i
$966$	3.06060	+	2.61775i	0.0984733	+	0.0842247i
$967$	4.86483	−	7.42201i	0.156442	−	0.238676i	−0.749572	−	0.661923i	$-0.769741\pi$
$967$	4.86483	−	7.42201i	0.156442	−	0.238676i	0.906014	+	0.423247i	$0.139110\pi$
$968$	10.6004	+	6.73562i	0.340709	+	0.216491i
$969$	6.71342	−	19.8926i	0.215666	−	0.639044i
$970$	−3.61988	−	1.51443i	−0.116227	−	0.0486253i
$971$	20.8788	+	56.5328i	0.670032	+	1.81422i	0.574017	+	0.818844i	$0.305384\pi$
$971$	20.8788	+	56.5328i	0.670032	+	1.81422i	0.0960149	+	0.995380i	$0.469390\pi$
$972$	1.49548	−	1.13914i	0.0479675	−	0.0365379i
$973$	−43.7337	−	14.0732i	−1.40204	−	0.451166i
$974$	−0.221789	+	5.22109i	−0.00710659	+	0.167295i
$975$	−3.66773	+	14.9506i	−0.117461	+	0.478802i
$976$	−0.502918	−	1.49020i	−0.0160980	−	0.0477003i
$977$	1.07496	−	15.1670i	0.0343910	−	0.485236i	−0.950347	−	0.311192i	$-0.899272\pi$
$977$	1.07496	−	15.1670i	0.0343910	−	0.485236i	0.984738	−	0.174043i	$-0.0556833\pi$
$978$	−0.0766437	+	0.0295453i	−0.00245080	+	0.000944754i
$979$	6.65628	−	1.14133i	0.212736	−	0.0364772i
$980$	−1.99380	−	2.39901i	−0.0636897	−	0.0766337i
$981$	−10.3085	−	1.46860i	−0.329124	−	0.0468888i
$982$	−7.03815	+	0.800214i	−0.224596	+	0.0255359i
$983$	12.0261	−	39.2693i	0.383572	−	1.25250i	−0.530757	−	0.847524i	$-0.678092\pi$
$983$	12.0261	−	39.2693i	0.383572	−	1.25250i	0.914329	−	0.404971i	$-0.132719\pi$
$984$	−13.0078	−	9.90832i	−0.414674	−	0.315866i
$985$	33.0386	+	47.4217i	1.05270	+	1.51098i
$986$	4.22346	+	3.03215i	0.134502	+	0.0965633i
$987$	−2.45030	−	1.97848i	−0.0779939	−	0.0629757i
$988$	−17.0975	−	3.93877i	−0.543943	−	0.125309i
$989$	31.5639	−	40.2432i	1.00367	−	1.27966i
$990$	1.53804	−	0.695240i	0.0488823	−	0.0220962i
$991$	7.48338	+	47.6848i	0.237717	+	1.51476i	0.753161	+	0.657836i	$0.228528\pi$
$991$	7.48338	+	47.6848i	0.237717	+	1.51476i	−0.515444	+	0.856923i	$0.672373\pi$
$992$	−35.7561	+	21.3240i	−1.13526	+	0.677039i
$993$	29.0341	+	1.64524i	0.921370	+	0.0522102i
$994$	−3.24224	+	2.32770i	−0.102838	+	0.0738302i
$995$	93.0984	+	32.8938i	2.95142	+	1.04280i
$996$	10.6802	+	12.1350i	0.338414	+	0.384513i
$997$	2.07301	+	9.61878i	0.0656528	+	0.304630i	0.998442	−	0.0557912i	$-0.0177681\pi$
$997$	2.07301	+	9.61878i	0.0656528	+	0.304630i	−0.932790	+	0.360421i	$0.882633\pi$
$998$	−0.553084	−	2.97243i	−0.0175076	−	0.0940908i
$999$	−1.68435	−	0.489865i	−0.0532904	−	0.0154987i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	669.2.m.b.19.9	✓	1368
223.47	even	111	inner	669.2.m.b.493.9	yes	1368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
669.2.m.b.19.9	✓	1368	1.1	even	1	trivial
669.2.m.b.493.9	yes	1368	223.47	even	111	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 669 = 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	669.m (of order \(111\), degree \(72\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0440153 - 0.343722i) q^{2} +(-0.759946 + 0.649986i) q^{3} +(1.81926 - 0.473698i) q^{4} +(-3.74410 + 0.533405i) q^{5} +(0.256864 + 0.232601i) q^{6} +(-1.52315 + 2.05943i) q^{7} +(-0.501306 - 1.24755i) q^{8} +(0.155037 - 0.987909i) q^{9} +(0.348140 + 1.26345i) q^{10} +(1.22602 - 0.394524i) q^{11} +(-1.07464 + 1.54248i) q^{12} +(1.56024 - 0.551267i) q^{13} +(0.774914 + 0.432893i) q^{14} +(2.49861 - 2.83897i) q^{15} +(2.87565 - 1.60643i) q^{16} +(0.784242 - 3.63890i) q^{17} +(-0.346390 - 0.00980636i) q^{18} +(-3.84459 - 4.12671i) q^{19} +(-6.55881 + 2.74397i) q^{20} +(-0.181091 - 2.55508i) q^{21} +(-0.189570 - 0.404043i) q^{22} +(-2.80015 - 3.57012i) q^{23} +(1.19186 + 0.622228i) q^{24} +(8.93268 - 2.59793i) q^{25} +(-0.258157 - 0.512024i) q^{26} +(0.524307 + 0.851529i) q^{27} +(-1.79545 + 4.46815i) q^{28} +(-3.46172 - 2.06449i) q^{29} +(-1.08579 - 0.733868i) q^{30} +(1.07488 - 10.8154i) q^{31} +(-2.27771 - 3.07967i) q^{32} +(-0.675271 + 1.09671i) q^{33} +(-1.28529 - 0.109394i) q^{34} +(4.60431 - 8.52318i) q^{35} +(-0.185919 - 1.87070i) q^{36} +(-1.30025 + 1.17743i) q^{37} +(-1.24922 + 1.50311i) q^{38} +(-0.827381 + 1.43307i) q^{39} +(2.54239 + 4.40355i) q^{40} +(-11.9870 - 2.05537i) q^{41} +(-0.870267 + 0.174708i) q^{42} +(2.68571 + 10.9476i) q^{43} +(2.04355 - 1.29850i) q^{44} +(-0.0535171 + 3.78152i) q^{45} +(-1.10388 + 1.11961i) q^{46} +(0.838089 - 0.899591i) q^{47} +(-1.14118 + 3.08993i) q^{48} +(0.128477 + 0.419520i) q^{49} +(-1.28614 - 2.95601i) q^{50} +(1.76925 + 3.27511i) q^{51} +(2.57734 - 1.74198i) q^{52} +(6.72840 - 0.381271i) q^{53} +(0.269612 - 0.217696i) q^{54} +(-4.37988 + 2.13110i) q^{55} +(3.33281 + 0.867796i) q^{56} +(5.60398 + 0.637155i) q^{57} +(-0.557240 + 1.28074i) q^{58} +(1.22867 - 0.104575i) q^{59} +(3.20080 - 6.34841i) q^{60} +(0.0873457 - 0.469421i) q^{61} +(-3.76480 + 0.106582i) q^{62} +(1.79839 + 1.82402i) q^{63} +(3.79785 - 3.63994i) q^{64} +(-5.54764 + 2.89624i) q^{65} +(0.406685 + 0.183833i) q^{66} +(0.607534 - 2.20482i) q^{67} +(-0.296999 - 6.99159i) q^{68} +(4.44849 + 0.893042i) q^{69} +(-3.13226 - 1.20745i) q^{70} +(-1.90993 + 4.07077i) q^{71} +(-1.31019 + 0.301829i) q^{72} +(-0.155831 - 0.0758218i) q^{73} +(0.461940 + 0.395099i) q^{74} +(-5.09974 + 7.78040i) q^{75} +(-8.94911 - 5.68639i) q^{76} +(-1.05491 + 3.12582i) q^{77} +(0.528994 + 0.221312i) q^{78} +(-5.74684 - 15.5605i) q^{79} +(-9.90982 + 7.54852i) q^{80} +(-0.951927 - 0.306324i) q^{81} +(-0.178866 + 4.21065i) q^{82} +(2.04880 - 8.35142i) q^{83} +(-1.53979 - 4.56258i) q^{84} +(-0.995276 + 14.0427i) q^{85} +(3.64472 - 1.40500i) q^{86} +(3.97261 - 0.681172i) q^{87} +(-1.10680 - 1.33174i) q^{88} +(5.19121 + 0.739568i) q^{89} +(1.30215 - 0.148050i) q^{90} +(-1.24118 + 4.05287i) q^{91} +(-6.78535 - 5.16854i) q^{92} +(6.21300 + 8.91778i) q^{93} +(-0.346098 - 0.248474i) q^{94} +(16.5957 + 13.4001i) q^{95} +(3.73268 + 0.859902i) q^{96} +(-1.84781 + 2.35591i) q^{97} +(0.138543 - 0.0626255i) q^{98} +(-0.199676 - 1.27236i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1368 q - 2 q^{2} + 19 q^{3} - 38 q^{4} + q^{5} + q^{6} + 4 q^{7} + 19 q^{9} - 5 q^{10} - 4 q^{11} + 19 q^{12} - 12 q^{13} - 8 q^{14} - 2 q^{15} - 30 q^{16} + 8 q^{17} + q^{18} - 71 q^{19} + 10 q^{20}+ \cdots - 4 q^{99}+O(q^{100}) \) 1368 * q - 2 * q^2 + 19 * q^3 - 38 * q^4 + q^5 + q^6 + 4 * q^7 + 19 * q^9 - 5 * q^10 - 4 * q^11 + 19 * q^12 - 12 * q^13 - 8 * q^14 - 2 * q^15 - 30 * q^16 + 8 * q^17 + q^18 - 71 * q^19 + 10 * q^20 - 2 * q^21 + 5 * q^22 + 6 * q^23 + 20 * q^25 - 38 * q^27 - 24 * q^28 + 71 * q^29 + 10 * q^30 + 2 * q^31 + 8 * q^32 + 8 * q^33 - 130 * q^34 + 11 * q^35 + 19 * q^36 + 18 * q^37 - 6 * q^38 - 68 * q^39 - 223 * q^40 - 236 * q^41 - 70 * q^42 + 10 * q^43 - 172 * q^44 + q^45 + 4 * q^46 + 11 * q^47 + 15 * q^48 + 10 * q^49 + 9 * q^50 - 78 * q^51 + 530 * q^52 + 24 * q^53 - 2 * q^54 - 4 * q^55 - 22 * q^56 + 3 * q^57 - 52 * q^58 - 34 * q^59 - 20 * q^60 - 12 * q^61 + 5 * q^62 - 2 * q^63 - 214 * q^64 - 106 * q^65 + 138 * q^66 - 12 * q^67 - 144 * q^68 + 6 * q^69 - 67 * q^70 + 8 * q^71 + 17 * q^73 - 8 * q^74 + 20 * q^75 + 26 * q^76 - 142 * q^77 - 74 * q^78 - 14 * q^79 + 977 * q^80 + 19 * q^81 - 194 * q^82 - 130 * q^83 + 12 * q^84 - 52 * q^85 + 15 * q^86 + 6 * q^87 + 62 * q^88 - 22 * q^89 - 5 * q^90 - 4 * q^91 + 32 * q^92 + 2 * q^93 + 417 * q^94 - 74 * q^95 - 4 * q^96 - 15 * q^97 - 80 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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