LMFDB - Embedded newform 770.2.bv.a.423.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(3,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 10, 48]))

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

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

chi := DirichletCharacter("770.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bv (of order $60$, degree $16$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$48$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			423.29
Character	$\chi$	$=$	770.423
Dual form			770.2.bv.a.537.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0523360 + 0.998630i) q^{2} +(-0.798767 + 2.08086i) q^{3} +(-0.994522 + 0.104528i) q^{4} +(1.05151 - 1.97341i) q^{5} +(-2.11981 - 0.688769i) q^{6} +(-2.58843 + 0.547767i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-1.46252 - 1.31686i) q^{9} +O(q^{10})$	\(q+(0.0523360 + 0.998630i) q^{2} +(-0.798767 + 2.08086i) q^{3} +(-0.994522 + 0.104528i) q^{4} +(1.05151 - 1.97341i) q^{5} +(-2.11981 - 0.688769i) q^{6} +(-2.58843 + 0.547767i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-1.46252 - 1.31686i) q^{9} +(2.02573 + 0.946785i) q^{10} +(-3.30764 + 0.243981i) q^{11} +(0.576883 - 2.15296i) q^{12} +(-1.09645 - 0.558667i) q^{13} +(-0.682484 - 2.55621i) q^{14} +(3.26647 + 3.76433i) q^{15} +(0.978148 - 0.207912i) q^{16} +(0.404210 - 7.71279i) q^{17} +(1.23851 - 1.52943i) q^{18} +(-0.691534 + 6.57950i) q^{19} +(-0.839469 + 2.07251i) q^{20} +(0.927724 - 5.82369i) q^{21} +(-0.416755 - 3.29034i) q^{22} +(2.13119 - 7.95372i) q^{23} +(2.18020 + 0.463415i) q^{24} +(-2.78867 - 4.15010i) q^{25} +(0.500518 - 1.12418i) q^{26} +(-2.04950 + 1.04427i) q^{27} +(2.51699 - 0.815331i) q^{28} +(0.0506664 + 0.0697363i) q^{29} +(-3.58822 + 3.45901i) q^{30} +(1.46780 - 6.90545i) q^{31} +(0.258819 + 0.965926i) q^{32} +(2.13434 - 7.07762i) q^{33} +7.72338 q^{34} +(-1.64078 + 5.68400i) q^{35} +(1.59215 + 1.15677i) q^{36} +(-8.35863 + 3.20858i) q^{37} +(-6.60668 - 0.346241i) q^{38} +(2.03831 - 1.83531i) q^{39} +(-2.11360 - 0.729852i) q^{40} +(2.67042 - 3.67551i) q^{41} +(5.86426 + 0.621664i) q^{42} +(2.42512 + 2.42512i) q^{43} +(3.26402 - 0.588387i) q^{44} +(-4.13654 + 1.50146i) q^{45} +(8.05436 + 1.71201i) q^{46} +(-3.93579 + 3.18714i) q^{47} +(-0.348677 + 2.20146i) q^{48} +(6.39990 - 2.83571i) q^{49} +(3.99846 - 3.00205i) q^{50} +(15.7264 + 7.00183i) q^{51} +(1.14884 + 0.440997i) q^{52} +(-2.14960 - 3.31010i) q^{53} +(-1.15010 - 1.99204i) q^{54} +(-2.99653 + 6.78386i) q^{55} +(0.945942 + 2.47087i) q^{56} +(-13.1387 - 6.69448i) q^{57} +(-0.0669891 + 0.0542467i) q^{58} +(-0.587019 - 5.58511i) q^{59} +(-3.64206 - 3.40227i) q^{60} +(2.21078 + 10.4009i) q^{61} +(6.97280 + 1.10438i) q^{62} +(4.50695 + 2.60746i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-2.25540 + 1.57629i) q^{65} +(7.17962 + 1.76100i) q^{66} +(-3.22223 - 12.0255i) q^{67} +(0.404210 + 7.71279i) q^{68} +(14.8483 + 10.7879i) q^{69} +(-5.76208 - 1.34105i) q^{70} +(-3.42723 + 10.5479i) q^{71} +(-1.07185 + 1.65051i) q^{72} +(0.806350 + 0.652969i) q^{73} +(-3.64164 - 8.17925i) q^{74} +(10.8633 - 2.48786i) q^{75} -6.61574i q^{76} +(8.42793 - 2.44334i) q^{77} +(1.93947 + 1.93947i) q^{78} +(1.17312 + 1.05628i) q^{79} +(0.618234 - 2.14890i) q^{80} +(-1.15305 - 10.9705i) q^{81} +(3.81024 + 2.47440i) q^{82} +(1.33387 + 2.61787i) q^{83} +(-0.313900 + 5.88876i) q^{84} +(-14.7954 - 8.90772i) q^{85} +(-2.29488 + 2.54872i) q^{86} +(-0.185582 + 0.0497266i) q^{87} +(0.758406 + 3.22875i) q^{88} +(-4.13544 - 7.16280i) q^{89} +(-1.71589 - 4.05229i) q^{90} +(3.14409 + 0.845472i) q^{91} +(-1.28813 + 8.13292i) q^{92} +(13.1968 + 8.57013i) q^{93} +(-3.38876 - 3.76359i) q^{94} +(12.2569 + 8.28307i) q^{95} +(-2.21669 - 0.232984i) q^{96} +(-3.88182 + 7.61850i) q^{97} +(3.16677 + 6.24272i) q^{98} +(5.15876 + 3.99886i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) $ 768 * q + 24 * q^5 + 4 * q^7	$ 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) $ 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.0523360	+	0.998630i	0.0370071	+	0.706138i
$2$	0.0523360	+	0.998630i	0.0370071	+	0.706138i
$3$	−0.798767	+	2.08086i	−0.461169	+	1.20139i	0.484077	+	0.875025i	$0.339155\pi$
$3$	−0.798767	+	2.08086i	−0.461169	+	1.20139i	−0.945246	+	0.326360i	$0.894178\pi$
$4$	−0.994522	+	0.104528i	−0.497261	+	0.0522642i
$5$	1.05151	−	1.97341i	0.470248	−	0.882534i
$5$	1.05151	−	1.97341i	0.470248	−	0.882534i
$6$	−2.11981	−	0.688769i	−0.865410	−	0.281189i
$7$	−2.58843	+	0.547767i	−0.978333	+	0.207037i
$7$	−2.58843	+	0.547767i	−0.978333	+	0.207037i
$8$	−0.156434	−	0.987688i	−0.0553079	−	0.349201i
$9$	−1.46252	−	1.31686i	−0.487505	−	0.438952i
$10$	2.02573	+	0.946785i	0.640593	+	0.299400i
$11$	−3.30764	+	0.243981i	−0.997291	+	0.0735631i
$11$	−3.30764	+	0.243981i	−0.997291	+	0.0735631i
$12$	0.576883	−	2.15296i	0.166532	−	0.621505i
$13$	−1.09645	−	0.558667i	−0.304099	−	0.154946i	0.295282	−	0.955410i	$-0.404587\pi$
$13$	−1.09645	−	0.558667i	−0.304099	−	0.154946i	−0.599381	+	0.800464i	$0.704587\pi$
$14$	−0.682484	−	2.55621i	−0.182402	−	0.683176i
$15$	3.26647	+	3.76433i	0.843400	+	0.971946i
$16$	0.978148	−	0.207912i	0.244537	−	0.0519779i
$17$	0.404210	−	7.71279i	0.0980354	−	1.87063i	−0.300911	−	0.953652i	$-0.597291\pi$
$17$	0.404210	−	7.71279i	0.0980354	−	1.87063i	0.398946	−	0.916974i	$-0.369376\pi$
$18$	1.23851	−	1.52943i	0.291919	−	0.360490i
$19$	−0.691534	+	6.57950i	−0.158649	+	1.50944i	0.568341	+	0.822793i	$0.307585\pi$
$19$	−0.691534	+	6.57950i	−0.158649	+	1.50944i	−0.726990	+	0.686648i	$0.759081\pi$
$20$	−0.839469	+	2.07251i	−0.187711	+	0.463427i
$21$	0.927724	−	5.82369i	0.202446	−	1.27083i
$22$	−0.416755	−	3.29034i	−0.0888525	−	0.701502i
$23$	2.13119	−	7.95372i	0.444385	−	1.65847i	−0.273171	−	0.961965i	$-0.588073\pi$
$23$	2.13119	−	7.95372i	0.444385	−	1.65847i	0.717556	−	0.696501i	$-0.245261\pi$
$24$	2.18020	+	0.463415i	0.445031	+	0.0945942i
$25$	−2.78867	−	4.15010i	−0.557734	−	0.830020i
$26$	0.500518	−	1.12418i	0.0981597	−	0.220470i
$27$	−2.04950	+	1.04427i	−0.394426	+	0.200970i
$28$	2.51699	−	0.815331i	0.475666	−	0.154083i
$29$	0.0506664	+	0.0697363i	0.00940852	+	0.0129497i	0.813695	−	0.581292i	$-0.197452\pi$
$29$	0.0506664	+	0.0697363i	0.00940852	+	0.0129497i	−0.804287	+	0.594241i	$0.797452\pi$
$30$	−3.58822	+	3.45901i	−0.655116	+	0.631526i
$31$	1.46780	−	6.90545i	0.263624	−	1.24025i	−0.624637	−	0.780915i	$-0.714753\pi$
$31$	1.46780	−	6.90545i	0.263624	−	1.24025i	0.888261	−	0.459339i	$-0.151914\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	2.13434	−	7.07762i	0.371542	−	1.23206i
$34$	7.72338			1.32455
$35$	−1.64078	+	5.68400i	−0.277342	+	0.960771i
$36$	1.59215	+	1.15677i	0.265359	+	0.192795i
$37$	−8.35863	+	3.20858i	−1.37415	+	0.527487i	−0.929700	−	0.368317i	$-0.879934\pi$
$37$	−8.35863	+	3.20858i	−1.37415	+	0.527487i	−0.444449	+	0.895804i	$0.646601\pi$
$38$	−6.60668	−	0.346241i	−1.07174	−	0.0561678i
$39$	2.03831	−	1.83531i	0.326392	−	0.293884i
$40$	−2.11360	−	0.729852i	−0.334190	−	0.115400i
$41$	2.67042	−	3.67551i	0.417049	−	0.574019i	−0.547871	−	0.836563i	$-0.684561\pi$
$41$	2.67042	−	3.67551i	0.417049	−	0.574019i	0.964920	+	0.262544i	$0.0845615\pi$
$42$	5.86426	+	0.621664i	0.904876	+	0.0959248i
$43$	2.42512	+	2.42512i	0.369827	+	0.369827i	0.867414	−	0.497587i	$-0.165780\pi$
$43$	2.42512	+	2.42512i	0.369827	+	0.369827i	−0.497587	+	0.867414i	$0.665780\pi$
$44$	3.26402	−	0.588387i	0.492069	−	0.0887027i
$45$	−4.13654	+	1.50146i	−0.616639	+	0.223824i
$46$	8.05436	+	1.71201i	1.18755	+	0.252422i
$47$	−3.93579	+	3.18714i	−0.574094	+	0.464892i	−0.871866	−	0.489745i	$-0.837090\pi$
$47$	−3.93579	+	3.18714i	−0.574094	+	0.464892i	0.297772	+	0.954637i	$0.403757\pi$
$48$	−0.348677	+	2.20146i	−0.0503272	+	0.317754i
$49$	6.39990	−	2.83571i	0.914272	−	0.405102i
$50$	3.99846	−	3.00205i	0.565468	−	0.424553i
$51$	15.7264	+	7.00183i	2.20213	+	0.980453i
$52$	1.14884	+	0.440997i	0.159315	+	0.0611553i
$53$	−2.14960	−	3.31010i	−0.295271	−	0.454677i	0.659635	−	0.751586i	$-0.270711\pi$
$53$	−2.14960	−	3.31010i	−0.295271	−	0.454677i	−0.954906	+	0.296909i	$0.904044\pi$
$54$	−1.15010	−	1.99204i	−0.156509	−	0.271082i
$55$	−2.99653	+	6.78386i	−0.404052	+	0.914736i
$56$	0.945942	+	2.47087i	0.126407	+	0.330184i
$57$	−13.1387	−	6.69448i	−1.74026	−	0.886705i
$58$	−0.0669891	+	0.0542467i	−0.00879610	+	0.00712294i
$59$	−0.587019	−	5.58511i	−0.0764233	−	0.727119i	−0.963900	−	0.266266i	$-0.914210\pi$
$59$	−0.587019	−	5.58511i	−0.0764233	−	0.727119i	0.887476	−	0.460853i	$-0.152457\pi$
$60$	−3.64206	−	3.40227i	−0.470188	−	0.439231i
$61$	2.21078	+	10.4009i	0.283061	+	1.33170i	0.858062	+	0.513546i	$0.171669\pi$
$61$	2.21078	+	10.4009i	0.283061	+	1.33170i	−0.575000	+	0.818153i	$0.694998\pi$
$62$	6.97280	+	1.10438i	0.885547	+	0.140257i
$63$	4.50695	+	2.60746i	0.567822	+	0.328510i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$	−2.25540	+	1.57629i	−0.279748	+	0.195515i
$66$	7.17962	+	1.76100i	0.883750	+	0.216765i
$67$	−3.22223	−	12.0255i	−0.393658	−	1.46915i	−0.824054	−	0.566511i	$-0.808293\pi$
$67$	−3.22223	−	12.0255i	−0.393658	−	1.46915i	0.430397	−	0.902640i	$-0.358374\pi$
$68$	0.404210	+	7.71279i	0.0490177	+	0.935313i
$69$	14.8483	+	10.7879i	1.78752	+	1.29871i
$70$	−5.76208	−	1.34105i	−0.688700	−	0.160287i
$71$	−3.42723	+	10.5479i	−0.406737	+	1.25181i	0.512699	+	0.858568i	$0.328646\pi$
$71$	−3.42723	+	10.5479i	−0.406737	+	1.25181i	−0.919436	+	0.393239i	$0.871354\pi$
$72$	−1.07185	+	1.65051i	−0.126319	+	0.194515i
$73$	0.806350	+	0.652969i	0.0943761	+	0.0764242i	0.675347	−	0.737500i	$-0.263994\pi$
$73$	0.806350	+	0.652969i	0.0943761	+	0.0764242i	−0.580971	+	0.813924i	$0.697327\pi$
$74$	−3.64164	−	8.17925i	−0.423332	−	0.950818i
$75$	10.8633	−	2.48786i	1.25438	−	0.287274i
$76$		−	6.61574i		−	0.758878i
$77$	8.42793	−	2.44334i	0.960452	−	0.278445i
$78$	1.93947	+	1.93947i	0.219602	+	0.219602i
$79$	1.17312	+	1.05628i	0.131986	+	0.118841i	0.732480	−	0.680788i	$-0.238363\pi$
$79$	1.17312	+	1.05628i	0.131986	+	0.118841i	−0.600494	+	0.799629i	$0.705029\pi$
$80$	0.618234	−	2.14890i	0.0691207	−	0.240255i
$81$	−1.15305	−	10.9705i	−0.128117	−	1.21895i
$82$	3.81024	+	2.47440i	0.420770	+	0.273251i
$83$	1.33387	+	2.61787i	0.146411	+	0.287348i	0.952552	−	0.304375i	$-0.0984477\pi$
$83$	1.33387	+	2.61787i	0.146411	+	0.287348i	−0.806141	+	0.591724i	$0.798448\pi$
$84$	−0.313900	+	5.88876i	−0.0342493	+	0.642517i
$85$	−14.7954	−	8.90772i	−1.60479	−	0.966178i
$86$	−2.29488	+	2.54872i	−0.247463	+	0.274835i
$87$	−0.185582	+	0.0497266i	−0.0198965	+	0.00533125i
$88$	0.758406	+	3.22875i	0.0808463	+	0.344186i
$89$	−4.13544	−	7.16280i	−0.438356	−	0.759255i	0.559207	−	0.829028i	$-0.311106\pi$
$89$	−4.13544	−	7.16280i	−0.438356	−	0.759255i	−0.997563	+	0.0697732i	$0.977772\pi$
$90$	−1.71589	−	4.05229i	−0.180871	−	0.427149i
$91$	3.14409	+	0.845472i	0.329590	+	0.0886295i
$92$	−1.28813	+	8.13292i	−0.134297	+	0.847916i
$93$	13.1968	+	8.57013i	1.36845	+	0.888681i
$94$	−3.38876	−	3.76359i	−0.349523	−	0.388185i
$95$	12.2569	+	8.28307i	1.25753	+	0.849825i
$96$	−2.21669	−	0.232984i	−0.226240	−	0.0237788i
$97$	−3.88182	+	7.61850i	−0.394139	+	0.773541i	−0.999753	−	0.0222171i	$-0.992927\pi$
$97$	−3.88182	+	7.61850i	−0.394139	+	0.773541i	0.605614	+	0.795758i	$0.292927\pi$
$98$	3.16677	+	6.24272i	0.319892	+	0.630610i
$99$	5.15876	+	3.99886i	0.518475	+	0.401900i
$100$	3.20719	+	3.83587i	0.320719	+	0.383587i
$101$	−2.70910	+	12.7453i	−0.269565	+	1.26820i	0.609991	+	0.792409i	$0.291173\pi$
$101$	−2.70910	+	12.7453i	−0.269565	+	1.26820i	−0.879556	+	0.475796i	$0.842160\pi$
$102$	−6.16918	+	16.0713i	−0.610840	+	1.59129i
$103$	−2.49890	+	0.959239i	−0.246224	+	0.0945166i	−0.478350	−	0.878169i	$-0.658765\pi$
$103$	−2.49890	+	0.959239i	−0.246224	+	0.0945166i	0.232126	+	0.972686i	$0.425432\pi$
$104$	−0.380267	+	1.17034i	−0.0372883	+	0.114761i
$105$	−10.5170	−	7.95443i	−1.02635	−	0.776273i
$106$	3.19306	−	2.31990i	0.310138	−	0.225328i
$107$	−6.53172	−	8.06601i	−0.631446	−	0.779770i	0.356546	−	0.934278i	$-0.383954\pi$
$107$	−6.53172	−	8.06601i	−0.631446	−	0.779770i	−0.987992	+	0.154507i	$0.950621\pi$
$108$	1.92912	−	1.25278i	0.185629	−	0.120549i
$109$	−6.64522	−	3.83662i	−0.636497	−	0.367482i	0.146767	−	0.989171i	$-0.453113\pi$
$109$	−6.64522	−	3.83662i	−0.636497	−	0.367482i	−0.783264	+	0.621689i	$0.786447\pi$
$110$	−6.93139	−	2.63738i	−0.660882	−	0.251465i
$111$		−	19.9560i		−	1.89414i
$112$	−2.41798	+	1.07396i	−0.228477	+	0.101480i
$113$	−0.944760	−	5.96498i	−0.0888756	−	0.561138i	−0.991438	−	0.130579i	$-0.958316\pi$
$113$	−0.944760	−	5.96498i	−0.0888756	−	0.561138i	0.902562	−	0.430559i	$-0.141684\pi$
$114$	5.99768	−	13.4710i	0.561734	−	1.26168i
$115$	−13.4550	−	12.5691i	−1.25468	−	1.17208i
$116$	−0.0576783	−	0.0640582i	−0.00535529	−	0.00594766i
$117$	0.867886	+	2.26092i	0.0802361	+	0.209022i
$118$	5.54673	−	0.878516i	0.510618	−	0.0808740i
$119$	3.17855	+	20.1854i	0.291377	+	1.85039i
$120$	3.20700	−	3.81513i	0.292757	−	0.348272i
$121$	10.8809	−	1.61400i	0.989177	−	0.146728i
$122$	−10.2709	+	2.75209i	−0.929888	+	0.249163i
$123$	5.51519	+	8.49265i	0.497288	+	0.765756i
$124$	−0.737941	+	7.02104i	−0.0662691	+	0.630508i
$125$	−11.1221	+	1.13932i	−0.994794	+	0.101904i
$126$	−2.36802	+	4.63723i	−0.210960	+	0.413118i
$127$	−6.53232	−	12.8204i	−0.579650	−	1.13763i	−0.975641	−	0.219373i	$-0.929599\pi$
$127$	−6.53232	−	12.8204i	−0.579650	−	1.13763i	0.395991	−	0.918254i	$-0.370401\pi$
$128$	−0.358368	−	0.933580i	−0.0316756	−	0.0825176i
$129$	−6.98344	+	3.10923i	−0.614858	+	0.273752i
$130$	−1.69217	−	2.16981i	−0.148413	−	0.190305i
$131$	−6.71345	+	3.87601i	−0.586557	+	0.338649i	−0.763735	−	0.645530i	$-0.776636\pi$
$131$	−6.71345	+	3.87601i	−0.586557	+	0.338649i	0.177178	+	0.984179i	$0.443303\pi$
$132$	−1.38284	+	7.26195i	−0.120361	+	0.632071i
$133$	−1.81405	−	17.4094i	−0.157298	−	1.50958i
$134$	11.8404	−	3.84718i	1.02285	−	0.332346i
$135$	−0.0942885	+	5.14255i	−0.00811506	+	0.442601i
$136$	−7.68107	+	0.807313i	−0.658646	+	0.0692265i
$137$	−14.3782	−	0.753529i	−1.22841	−	0.0643783i	−0.572940	−	0.819598i	$-0.694197\pi$
$137$	−14.3782	−	0.753529i	−1.22841	−	0.0643783i	−0.655472	+	0.755219i	$0.727530\pi$
$138$	−9.99601	+	15.3925i	−0.850917	+	1.31030i
$139$	−2.50567	+	1.82047i	−0.212528	+	0.154410i	−0.688957	−	0.724803i	$-0.741931\pi$
$139$	−2.50567	+	1.82047i	−0.212528	+	0.154410i	0.476429	+	0.879213i	$0.341931\pi$
$140$	1.03765	−	5.82437i	0.0876976	−	0.492249i
$141$	−3.48821	−	10.7356i	−0.293760	−	0.904102i
$142$	−10.7128	−	2.87049i	−0.899001	−	0.240886i
$143$	3.76295	+	1.58036i	0.314674	+	0.132156i
$144$	−1.70435	−	0.984005i	−0.142029	−	0.0820004i
$145$	0.190894	−	0.0266572i	0.0158529	−	0.00221376i
$146$	−0.609873	+	0.839418i	−0.0504735	+	0.0694708i
$147$	0.788684	+	15.5824i	0.0650496	+	1.28521i
$148$	7.97745	−	4.06471i	0.655742	−	0.334117i
$149$	−2.39566	−	11.2707i	−0.196260	−	0.923331i	−0.960474	−	0.278368i	$-0.910206\pi$
$149$	−2.39566	−	11.2707i	−0.196260	−	0.923331i	0.764214	−	0.644962i	$-0.223127\pi$
$150$	3.05299	+	10.7182i	0.249276	+	0.875136i
$151$	−5.20294	+	2.31650i	−0.423409	+	0.188514i	−0.607369	−	0.794420i	$-0.707775\pi$
$151$	−5.20294	+	2.31650i	−0.423409	+	0.188514i	0.183960	+	0.982934i	$0.441108\pi$
$152$	6.60668	−	0.346241i	0.535872	−	0.0280839i
$153$	−10.7478	+	10.7478i	−0.868908	+	0.868908i
$154$	2.88108	+	8.28851i	0.232164	+	0.667907i
$155$	−12.0839	−	10.1577i	−0.970598	−	0.815885i
$156$	−1.83531	+	2.03831i	−0.146942	+	0.163196i
$157$	2.32996	+	0.894389i	0.185951	+	0.0713800i	0.449562	−	0.893249i	$-0.351580\pi$
$157$	2.32996	+	0.894389i	0.185951	+	0.0713800i	−0.263611	+	0.964629i	$0.584913\pi$
$158$	−0.993437	+	1.22679i	−0.0790336	+	0.0975983i
$159$	8.60489	−	1.82903i	0.682412	−	0.145051i
$160$	2.17831	+	0.504922i	0.172211	+	0.0399176i
$161$	−1.15965	+	21.7550i	−0.0913931	+	1.71454i
$162$	10.8952	−	1.72562i	0.856004	−	0.135578i
$163$	−19.6411	+	1.02935i	−1.53841	+	0.0806247i	−0.802581	−	0.596543i	$-0.796541\pi$
$163$	−19.6411	+	1.02935i	−1.53841	+	0.0806247i	−0.735829	+	0.677168i	$0.763207\pi$
$164$	−2.27159	+	3.93451i	−0.177382	+	0.307234i
$165$	−11.7227	−	11.6541i	−0.912614	−	0.907270i
$166$	−2.54447	+	1.46905i	−0.197489	+	0.114020i
$167$	−2.25840	+	4.43236i	−0.174760	+	0.342986i	−0.961727	−	0.274009i	$-0.911650\pi$
$167$	−2.25840	+	4.43236i	−0.174760	+	0.342986i	0.786967	+	0.616995i	$0.211650\pi$
$168$	−5.89712	−	0.00527548i	−0.454973	−	0.000407012i
$169$	−6.75112	−	9.29212i	−0.519317	−	0.714779i
$170$	8.12118	−	15.2414i	0.622866	−	1.16896i
$171$	9.67563	−	8.71198i	0.739914	−	0.666222i
$172$	−2.66533	−	2.15834i	−0.203229	−	0.164572i
$173$	3.87708	+	4.78779i	0.294769	+	0.364009i	0.902917	−	0.429814i	$-0.141421\pi$
$173$	3.87708	+	4.78779i	0.294769	+	0.364009i	−0.608149	+	0.793823i	$0.708088\pi$
$174$	−0.0593711	−	0.182725i	−0.00450091	−	0.0138524i
$175$	9.49155	+	9.21469i	0.717494	+	0.696565i
$176$	−3.18463	+	0.926346i	−0.240051	+	0.0698260i
$177$	12.0907	+	3.23970i	0.908795	+	0.243511i
$178$	6.93655	−	4.50465i	0.519916	−	0.337638i
$179$	−6.14209	−	13.7954i	−0.459081	−	1.03111i	−0.983707	−	0.179780i	$-0.942461\pi$
$179$	−6.14209	−	13.7954i	−0.459081	−	1.03111i	0.524626	−	0.851333i	$-0.324205\pi$
$180$	3.95693	−	1.92562i	0.294932	−	0.143527i
$181$	9.00581	+	2.92617i	0.669397	+	0.217500i	0.623947	−	0.781466i	$-0.285528\pi$
$181$	9.00581	+	2.92617i	0.669397	+	0.217500i	0.0454494	+	0.998967i	$0.485528\pi$
$182$	−0.679764	+	3.18403i	−0.0503875	+	0.236016i
$183$	−23.4087	−	3.70758i	−1.73042	−	0.274072i
$184$	−8.18919	−	0.860719i	−0.603715	−	0.0634530i
$185$	−2.45732	+	19.8688i	−0.180666	+	1.46078i
$186$	−7.86771	+	13.6273i	−0.576889	+	0.999201i
$187$	0.544794	+	25.6097i	0.0398393	+	1.87277i
$188$	3.58108	−	3.58108i	0.261177	−	0.261177i
$189$	4.73296	−	3.82567i	0.344272	−	0.278277i
$190$	−7.63024	+	12.6736i	−0.553556	+	0.919439i
$191$	11.1487	+	4.96370i	0.806688	+	0.359161i	0.768290	−	0.640102i	$-0.221108\pi$
$191$	11.1487	+	4.96370i	0.806688	+	0.359161i	0.0383982	+	0.999263i	$0.487774\pi$
$192$	0.116652	−	2.22585i	0.00841862	−	0.160637i
$193$	0.224873	−	4.29083i	0.0161867	−	0.308861i	−0.978523	−	0.206137i	$-0.933911\pi$
$193$	0.224873	−	4.29083i	0.0161867	−	0.308861i	0.994710	−	0.102724i	$-0.0327558\pi$
$194$	−7.81122	−	3.47778i	−0.560813	−	0.249690i
$195$	−1.47851	−	5.95226i	−0.105878	−	0.426250i
$196$	−6.06843	+	3.48915i	−0.433459	+	0.249225i
$197$	6.36388	−	6.36388i	0.453408	−	0.453408i	−0.443076	−	0.896484i	$-0.646113\pi$
$197$	6.36388	−	6.36388i	0.453408	−	0.453408i	0.896484	+	0.443076i	$0.146113\pi$
$198$	−3.72339	+	5.36098i	−0.264610	+	0.380988i
$199$	−12.5918	+	21.8097i	−0.892612	+	1.54605i	−0.0558787	+	0.998438i	$0.517796\pi$
$199$	−12.5918	+	21.8097i	−0.892612	+	1.54605i	−0.836733	+	0.547611i	$0.815537\pi$
$200$	−3.66276	+	3.40355i	−0.258996	+	0.240668i
$201$	27.5972	+	2.90059i	1.94656	+	0.204592i
$202$	−12.8696	−	2.03835i	−0.905503	−	0.143418i
$203$	−0.169346	−	0.152754i	−0.0118857	−	0.0107212i
$204$	−16.3721	−	5.31962i	−1.14628	−	0.372448i
$205$	−4.44532	−	9.13465i	−0.310475	−	0.637991i
$206$	−1.08871	−	2.44527i	−0.0758538	−	0.170370i
$207$	−13.5908	+	8.82598i	−0.944627	+	0.613448i
$208$	−1.18864	−	0.318495i	−0.0824173	−	0.0220837i
$209$	0.682069	−	21.9313i	0.0471797	−	1.51702i
$210$	7.39311	−	10.9189i	0.510173	−	0.753475i
$211$	0.704694	+	2.16883i	0.0485132	+	0.149308i	0.972379	−	0.233409i	$-0.0749882\pi$
$211$	0.704694	+	2.16883i	0.0485132	+	0.149308i	−0.923865	+	0.382718i	$0.874988\pi$
$212$	2.48383	+	3.06727i	0.170590	+	0.210661i
$213$	−19.2112	−	15.5569i	−1.31633	−	1.06594i
$214$	7.71311	−	6.94492i	0.527257	−	0.474745i
$215$	7.33578	−	2.23572i	0.500296	−	0.152475i
$216$	1.35203	+	1.86091i	0.0919938	+	0.126619i
$217$	−0.0167093	+	18.6782i	−0.00113430	+	1.26796i
$218$	3.48358	−	6.83691i	0.235938	−	0.463054i
$219$	−2.00282	+	1.15633i	−0.135338	+	0.0781376i
$220$	2.27101	−	7.05992i	0.153111	−	0.475980i
$221$	−4.75208	+	8.23084i	−0.319659	+	0.553666i
$222$	19.9287	−	1.04442i	1.33753	−	0.0700968i
$223$	3.23067	−	0.511688i	0.216342	−	0.0342652i	−0.0473226	−	0.998880i	$-0.515069\pi$
$223$	3.23067	−	0.511688i	0.216342	−	0.0342652i	0.263664	+	0.964615i	$0.415069\pi$
$224$	−1.19904	−	2.35846i	−0.0801140	−	0.157581i
$225$	−1.38661	+	9.74186i	−0.0924407	+	0.649457i
$226$	5.90736	−	1.25565i	0.392952	−	0.0835245i
$227$	7.98301	−	9.85819i	0.529851	−	0.654311i	−0.440004	−	0.897996i	$-0.645023\pi$
$227$	7.98301	−	9.85819i	0.529851	−	0.654311i	0.969854	+	0.243685i	$0.0783562\pi$
$228$	13.7664	+	5.28444i	0.911705	+	0.349971i
$229$	14.7752	−	16.4095i	0.976371	−	1.08437i	−0.0200466	−	0.999799i	$-0.506381\pi$
$229$	14.7752	−	16.4095i	0.976371	−	1.08437i	0.996417	−	0.0845707i	$-0.0269519\pi$
$230$	11.8477	−	14.0943i	0.781214	−	0.929354i
$231$	−1.64770	+	19.4890i	−0.108411	+	1.28228i
$232$	0.0609518	−	0.0609518i	0.00400168	−	0.00400168i
$233$	28.5545	−	1.49648i	1.87067	−	0.0980377i	0.916999	−	0.398888i	$-0.130604\pi$
$233$	28.5545	−	1.49648i	1.87067	−	0.0980377i	0.953671	+	0.300851i	$0.0972706\pi$
$234$	−2.21240	+	0.985024i	−0.144629	+	0.0643931i
$235$	2.15101	+	11.1182i	0.140317	+	0.725272i
$236$	1.16761	+	5.49315i	0.0760047	+	0.357574i
$237$	−3.13502	+	1.59737i	−0.203641	+	0.103761i
$238$	−19.9914	+	4.23061i	−1.29585	+	0.274230i
$239$	−5.17261	+	7.11949i	−0.334588	+	0.460522i	−0.942851	−	0.333214i	$-0.891867\pi$
$239$	−5.17261	+	7.11949i	−0.334588	+	0.460522i	0.608263	+	0.793736i	$0.291867\pi$
$240$	3.97774	+	3.00293i	0.256762	+	0.193839i
$241$	3.06616	+	1.77025i	0.197509	+	0.114032i	0.595493	−	0.803361i	$-0.296957\pi$
$241$	3.06616	+	1.77025i	0.197509	+	0.114032i	−0.397984	+	0.917392i	$0.630290\pi$
$242$	2.18126	+	10.7816i	0.140216	+	0.693065i
$243$	17.0837	+	4.57756i	1.09592	+	0.293651i
$244$	−3.28586	−	10.1128i	−0.210356	−	0.647408i
$245$	1.13353	−	15.6114i	0.0724185	−	0.997374i
$246$	−8.19237	+	5.95210i	−0.522326	+	0.379492i
$247$	4.43398	−	6.82773i	0.282128	−	0.434438i
$248$	−7.05004	−	0.369477i	−0.447678	−	0.0234618i
$249$	−6.51287	+	0.684530i	−0.412736	+	0.0433803i
$250$	−1.71984	−	11.0473i	−0.108773	−	0.698691i
$251$	8.37125	−	2.71998i	0.528388	−	0.171684i	−0.0326605	−	0.999467i	$-0.510398\pi$
$251$	8.37125	−	2.71998i	0.528388	−	0.171684i	0.561049	+	0.827783i	$0.310398\pi$
$252$	−4.75481	−	2.12208i	−0.299525	−	0.133678i
$253$	−5.10866	+	26.8280i	−0.321179	+	1.68666i
$254$	12.4610	−	7.19434i	0.781870	−	0.451413i
$255$	30.3538	−	23.6721i	1.90083	−	1.48240i
$256$	0.913545	−	0.406737i	0.0570966	−	0.0254210i
$257$	3.48731	+	9.08476i	0.217533	+	0.566692i	0.998310	−	0.0581179i	$-0.0185099\pi$
$257$	3.48731	+	9.08476i	0.217533	+	0.566692i	−0.780777	+	0.624810i	$0.785177\pi$
$258$	−3.47045	−	6.81115i	−0.216061	−	0.424044i
$259$	19.8781	−	12.8837i	1.23517	−	0.800557i
$260$	2.07828	−	1.80341i	0.128889	−	0.111843i
$261$	0.0177322	−	0.168711i	0.00109760	−	0.0104429i
$262$	−4.22205	−	6.50139i	−0.260839	−	0.401657i
$263$	18.6269	−	4.99105i	1.14858	−	0.307762i	0.366185	−	0.930542i	$-0.380664\pi$
$263$	18.6269	−	4.99105i	1.14858	−	0.307762i	0.782397	+	0.622780i	$0.213997\pi$
$264$	−7.32437	−	1.00088i	−0.450784	−	0.0616001i
$265$	−8.79250	+	0.761452i	−0.540119	+	0.0467756i
$266$	17.2906	−	2.72270i	1.06015	−	0.166940i
$267$	18.2080	−	2.88387i	1.11431	−	0.176490i
$268$	4.46158	+	11.6228i	0.272535	+	0.709977i
$269$	20.2850	+	22.5288i	1.23680	+	1.37360i	0.902244	+	0.431226i	$0.141919\pi$
$269$	20.2850	+	22.5288i	1.23680	+	1.37360i	0.334554	+	0.942377i	$0.391414\pi$
$270$	−5.14044	+	0.174981i	−0.312837	+	0.0106490i
$271$	5.18094	−	11.6366i	0.314720	−	0.706872i	−0.685046	−	0.728499i	$-0.740218\pi$
$271$	5.18094	−	11.6366i	0.314720	−	0.706872i	0.999766	+	0.0216276i	$0.00688480\pi$
$272$	−1.20820	−	7.62829i	−0.0732580	−	0.462533i
$273$	−4.27071	+	5.86708i	−0.258475	+	0.355092i
$274$		−	14.3979i		−	0.869810i
$275$	10.2365	+	13.0466i	0.617281	+	0.786743i
$276$	−15.8946	−	9.17673i	−0.956740	−	0.552374i
$277$	−22.8007	+	14.8070i	−1.36996	+	0.889665i	−0.999236	−	0.0390769i	$-0.987558\pi$
$277$	−22.8007	+	14.8070i	−1.36996	+	0.889665i	−0.370727	+	0.928742i	$0.620892\pi$
$278$	−1.94911	−	2.40696i	−0.116900	−	0.144360i
$279$	−11.2402	+	8.16645i	−0.672930	+	0.488912i
$280$	5.87069	+	0.731406i	0.350841	+	0.0437098i
$281$	−0.163707	+	0.503839i	−0.00976596	+	0.0300565i	−0.955821	−	0.293950i	$-0.905030\pi$
$281$	−0.163707	+	0.503839i	−0.00976596	+	0.0300565i	0.946055	+	0.324007i	$0.105030\pi$
$282$	10.5383	−	4.04529i	0.627549	−	0.240894i
$283$	4.74183	−	12.3529i	0.281872	−	0.734303i	−0.717418	−	0.696643i	$-0.754676\pi$
$283$	4.74183	−	12.3529i	0.281872	−	0.734303i	0.999291	−	0.0376599i	$-0.0119904\pi$
$284$	2.30589	−	10.8484i	0.136830	−	0.643733i
$285$	−27.0263	+	18.8886i	−1.60090	+	1.11887i
$286$	−1.38125	+	3.84050i	−0.0816753	+	0.227094i
$287$	−4.89885	+	10.9766i	−0.289170	+	0.647926i
$288$	0.893458	−	1.75351i	0.0526475	−	0.103327i
$289$	−42.4169	−	4.45819i	−2.49511	−	0.262247i
$290$	0.0366113	+	0.189237i	0.00214989	+	0.0111124i
$291$	−12.7524	−	14.1629i	−0.747557	−	0.830246i
$292$	−0.870186	−	0.565106i	−0.0509238	−	0.0330703i
$293$	−3.51049	+	22.1643i	−0.205085	+	1.29486i	0.643357	+	0.765566i	$0.277541\pi$
$293$	−3.51049	+	22.1643i	−0.205085	+	1.29486i	−0.848442	+	0.529289i	$0.822459\pi$
$294$	−15.5197	+	1.60312i	−0.905130	+	0.0934960i
$295$	−11.6389	−	4.71435i	−0.677646	−	0.274480i
$296$	4.47665	+	7.75379i	0.260200	+	0.450680i
$297$	6.52422	−	3.95411i	0.378574	−	0.229441i
$298$	11.1299	−	2.98224i	0.644736	−	0.172756i
$299$	−6.78023	+	7.53020i	−0.392111	+	0.435483i
$300$	−10.5437	+	3.60976i	−0.608742	+	0.208409i
$301$	−7.60565	−	4.94884i	−0.438382	−	0.285247i
$302$	−2.58563	−	5.07458i	−0.148786	−	0.292009i
$303$	−24.3572	−	15.8178i	−1.39929	−	0.908708i
$304$	0.691534	+	6.57950i	0.0396622	+	0.377360i
$305$	22.8499	+	6.57385i	1.30838	+	0.376418i
$306$	−11.2956	−	10.1706i	−0.645724	−	0.581413i
$307$	5.25416	+	5.25416i	0.299871	+	0.299871i	0.840963	−	0.541092i	$-0.181989\pi$
$307$	5.25416	+	5.25416i	0.299871	+	0.299871i	−0.541092	+	0.840963i	$0.681989\pi$
$308$	−8.12637	+	3.31092i	−0.463043	+	0.188657i
$309$		−	5.96608i		−	0.339398i
$310$	9.51134	−	12.5989i	0.540208	−	0.715570i
$311$	3.92391	+	8.81324i	0.222504	+	0.499753i	0.989960	−	0.141349i	$-0.0451441\pi$
$311$	3.92391	+	8.81324i	0.222504	+	0.499753i	−0.767455	+	0.641102i	$0.778477\pi$
$312$	−2.13157	−	1.72611i	−0.120677	−	0.0977220i
$313$	−6.24079	+	9.60998i	−0.352751	+	0.543188i	−0.969852	−	0.243696i	$-0.921640\pi$
$313$	−6.24079	+	9.60998i	−0.352751	+	0.543188i	0.617101	+	0.786884i	$0.288307\pi$
$314$	−0.771222	+	2.37358i	−0.0435226	+	0.133949i
$315$	9.88467	−	6.15227i	0.556938	−	0.346641i
$316$	−1.27710	−	0.927870i	−0.0718427	−	0.0521968i
$317$	1.10420	+	21.0693i	0.0620178	+	1.18337i	0.835477	+	0.549525i	$0.185191\pi$
$317$	1.10420	+	21.0693i	0.0620178	+	1.18337i	−0.773459	+	0.633846i	$0.781475\pi$
$318$	2.27687	+	8.49738i	0.127680	+	0.476509i
$319$	−0.184601	−	0.218301i	−0.0103356	−	0.0122225i
$320$	−0.390226	+	2.20175i	−0.0218143	+	0.123082i
$321$	22.0016	−	7.14874i	1.22801	−	0.399004i
$322$	−21.7859	−	0.0194894i	−1.21408	−	0.00108610i
$323$	50.4668	+	7.99316i	2.80805	+	0.444751i
$324$	2.29347	+	10.7899i	0.127415	+	0.599440i
$325$	0.739099	+	6.10830i	0.0409979	+	0.338828i
$326$	−2.05587	−	19.5603i	−0.113864	−	1.08335i
$327$	13.2915	−	10.7632i	0.735020	−	0.595207i
$328$	−4.04801	−	2.06256i	−0.223514	−	0.113886i
$329$	8.44169	−	10.4056i	0.465406	−	0.573678i
$330$	11.0246	−	12.3166i	0.606884	−	0.678007i
$331$	−14.7466	−	25.5419i	−0.810548	−	1.40391i	−0.912481	−	0.409118i	$-0.865836\pi$
$331$	−14.7466	−	25.5419i	−0.810548	−	1.40391i	0.101934	−	0.994791i	$-0.467497\pi$
$332$	−1.60020	−	2.46410i	−0.0878226	−	0.135235i
$333$	16.4499	+	6.31451i	0.901447	+	0.346033i
$334$	−4.54448	−	2.02333i	−0.248663	−	0.110712i
$335$	−27.1194	−	6.28614i	−1.48169	−	0.343449i
$336$	−0.303363	−	5.88932i	−0.0165498	−	0.321289i
$337$	−1.81525	+	11.4610i	−0.0988829	+	0.624322i	0.887620	+	0.460577i	$0.152357\pi$
$337$	−1.81525	+	11.4610i	−0.0988829	+	0.624322i	−0.986503	+	0.163745i	$0.947643\pi$
$338$	8.92606	−	7.22818i	0.485514	−	0.393161i
$339$	13.1669	+	2.79872i	0.715130	+	0.152006i
$340$	15.6455	+	7.31238i	0.848497	+	0.396569i
$341$	−3.17015	+	23.1988i	−0.171673	+	1.25629i
$342$	9.20642	+	9.20642i	0.497826	+	0.497826i
$343$	−15.0124	+	10.8457i	−0.810592	+	0.585612i
$344$	2.01589	−	2.77464i	0.108690	−	0.149598i
$345$	36.9019	−	17.9581i	1.98673	−	0.966833i
$346$	−4.57832	+	4.12234i	−0.246132	+	0.221618i
$347$	−1.51476	−	0.0793851i	−0.0813165	−	0.00426162i	0.0116343	−	0.999932i	$-0.496297\pi$
$347$	−1.51476	−	0.0793851i	−0.0813165	−	0.00426162i	−0.0929508	+	0.995671i	$0.529630\pi$
$348$	0.179368	−	0.0688528i	0.00961512	−	0.00369090i
$349$	−9.57341	−	6.95549i	−0.512453	−	0.372319i	0.301300	−	0.953529i	$-0.402579\pi$
$349$	−9.57341	−	6.95549i	−0.512453	−	0.372319i	−0.813753	+	0.581210i	$0.802579\pi$
$350$	−8.70531	+	9.96080i	−0.465318	+	0.532427i
$351$	2.83057			0.151084
$352$	−1.09175	−	3.13179i	−0.0581903	−	0.166925i
$353$	−3.16173	−	11.7998i	−0.168282	−	0.628038i	−0.997599	−	0.0692585i	$-0.977937\pi$
$353$	−3.16173	−	11.7998i	−0.168282	−	0.628038i	0.829317	−	0.558779i	$-0.188730\pi$
$354$	−2.60248	+	12.2437i	−0.138320	+	0.650746i
$355$	17.2116	+	17.8545i	0.913496	+	0.947619i
$356$	4.86150	+	6.69129i	0.257659	+	0.354638i
$357$	−44.5419	−	9.50933i	−2.35741	−	0.503287i
$358$	13.4550	−	6.85566i	0.711119	−	0.362333i
$359$	−8.19201	+	18.3996i	−0.432358	+	0.971091i	0.557650	+	0.830076i	$0.311703\pi$
$359$	−8.19201	+	18.3996i	−0.432358	+	0.971091i	−0.990007	+	0.141015i	$0.954963\pi$
$360$	2.13007	+	3.85073i	0.112264	+	0.202951i
$361$	−24.2268	−	5.14957i	−1.27510	−	0.271030i
$362$	−2.45083	+	9.14661i	−0.128813	+	0.480735i
$363$	−5.33283	+	23.9309i	−0.279901	+	1.25605i
$364$	−3.21524	−	0.512193i	−0.168524	−	0.0268462i
$365$	2.13646	−	0.904654i	0.111827	−	0.0473518i
$366$	2.47738	−	23.5707i	0.129495	−	1.23206i
$367$	11.6412	−	14.3757i	0.607666	−	0.750405i	−0.376740	−	0.926319i	$-0.622955\pi$
$367$	11.6412	−	14.3757i	0.607666	−	0.750405i	0.984405	+	0.175914i	$0.0562882\pi$
$368$	0.430950	−	8.22302i	0.0224648	−	0.428654i
$369$	−8.74565	+	1.85895i	−0.455280	+	0.0967728i
$370$	−19.9702	−	1.41410i	−1.03820	−	0.0735158i
$371$	7.37726	+	7.39047i	0.383008	+	0.383694i
$372$	−14.0204	−	7.14373i	−0.726922	−	0.370385i
$373$	−4.83340	+	18.0385i	−0.250264	+	0.933998i	0.720400	+	0.693559i	$0.243958\pi$
$373$	−4.83340	+	18.0385i	−0.250264	+	0.933998i	−0.970664	+	0.240439i	$0.922709\pi$
$374$	−25.5461	+	1.88436i	−1.32096	+	0.0974378i
$375$	6.51324	−	24.0537i	0.336342	−	1.24213i
$376$	3.76359	+	3.38876i	0.194093	+	0.174762i
$377$	−0.0165936	−	0.104768i	−0.000854613	−	0.00539582i
$378$	4.06813	+	4.52625i	0.209242	+	0.232805i
$379$	7.88302	+	2.56135i	0.404923	+	0.131568i	0.504395	−	0.863473i	$-0.331715\pi$
$379$	7.88302	+	2.56135i	0.404923	+	0.131568i	−0.0994720	+	0.995040i	$0.531715\pi$
$380$	−13.0556	−	6.95650i	−0.669736	−	0.356861i
$381$	31.8953	−	3.35233i	1.63405	−	0.171745i
$382$	−4.37342	+	11.3932i	−0.223764	+	0.582925i
$383$	−1.28108	−	24.4445i	−0.0654601	−	1.24905i	−0.811978	−	0.583688i	$-0.801609\pi$
$383$	−1.28108	−	24.4445i	−0.0654601	−	1.24905i	0.746518	−	0.665366i	$-0.231724\pi$
$384$	2.22890			0.113743
$385$	4.04032	−	19.2009i	0.205914	−	0.978570i
$386$	4.29672			0.218697
$387$	−0.353245	−	6.74031i	−0.0179564	−	0.342629i
$388$	3.06420	−	7.98252i	0.155561	−	0.405251i
$389$	−4.01828	+	0.422338i	−0.203735	+	0.0214134i	−0.205846	−	0.978584i	$-0.565995\pi$
$389$	−4.01828	+	0.422338i	−0.203735	+	0.0214134i	0.00211123	+	0.999998i	$0.499328\pi$
$390$	5.86672	−	1.78800i	0.297073	−	0.0905387i
$391$	−60.4840	−	19.6524i	−3.05881	−	0.993866i
$392$	−3.80196	−	5.87751i	−0.192028	−	0.296859i
$393$	−2.70295	−	17.0658i	−0.136346	−	0.860855i
$394$	6.68822	+	6.02210i	0.336948	+	0.303389i
$395$	3.31801	−	1.20435i	0.166947	−	0.0605976i
$396$	−5.54850	−	3.43771i	−0.278822	−	0.172752i
$397$	2.25599	−	8.41946i	0.113225	−	0.422561i	−0.885923	−	0.463832i	$-0.846474\pi$
$397$	2.25599	−	8.41946i	0.113225	−	0.422561i	0.999148	+	0.0412713i	$0.0131408\pi$
$398$	−22.4388	−	11.4331i	−1.12476	−	0.573092i
$399$	37.6754	+	10.1312i	1.88613	+	0.507196i
$400$	−3.59058	−	3.47961i	−0.179529	−	0.173981i
$401$	15.3694	−	3.26687i	0.767512	−	0.163140i	0.192514	−	0.981294i	$-0.438336\pi$
$401$	15.3694	−	3.26687i	0.767512	−	0.163140i	0.574998	+	0.818155i	$0.305003\pi$
$402$	−1.45228	+	27.7112i	−0.0724333	+	1.38211i
$403$	−5.46721	+	6.75144i	−0.272341	+	0.336313i
$404$	1.36201	−	12.9587i	0.0677625	−	0.644717i
$405$	−22.8618	−	9.26016i	−1.13601	−	0.460141i
$406$	0.143682	−	0.177108i	0.00713081	−	0.00878972i
$407$	26.8645	−	12.6522i	1.33162	−	0.627144i
$408$	4.45548	−	16.6281i	0.220579	−	0.823213i
$409$	−10.3516	−	2.20030i	−0.511855	−	0.108798i	−0.0552584	−	0.998472i	$-0.517598\pi$
$409$	−10.3516	−	2.20030i	−0.511855	−	0.108798i	−0.456596	+	0.889674i	$0.650932\pi$
$410$	8.88948	−	4.91730i	0.439020	−	0.242848i
$411$	13.0528	−	29.3171i	0.643848	−	1.44611i
$412$	2.38495	−	1.21519i	0.117498	−	0.0598681i
$413$	4.57880	+	14.1351i	0.225308	+	0.695543i
$414$	−9.52517	−	13.1103i	−0.468137	−	0.644335i
$415$	6.56869	+	0.120437i	0.322444	+	0.00591200i
$416$	0.255850	−	1.20368i	0.0125441	−	0.0590152i
$417$	−1.78671	−	6.66807i	−0.0874953	−	0.326537i
$418$	21.9370	−	0.466663i	1.07297	−	0.0228252i
$419$	31.6099			1.54424			0.772122	−	0.635475i	$-0.219196\pi$
$419$	31.6099			1.54424			0.772122	+	0.635475i	$0.219196\pi$
$420$	11.2909	+	6.81153i	0.550937	+	0.332368i
$421$	0.266392	+	0.193545i	0.0129831	+	0.00943281i	0.594258	−	0.804275i	$-0.297446\pi$
$421$	0.266392	+	0.193545i	0.0129831	+	0.00943281i	−0.581275	+	0.813707i	$0.697446\pi$
$422$	−2.12897	+	0.817236i	−0.103637	+	0.0397824i
$423$	9.95316	+	0.521623i	0.483939	+	0.0253622i
$424$	−2.93308	+	2.64095i	−0.142443	+	0.128256i
$425$	−33.1361	+	19.8309i	−1.60734	+	0.961940i
$426$	14.5302	−	19.9990i	0.703988	−	0.968957i
$427$	−11.4197	−	25.7110i	−0.552639	−	1.24424i
$428$	7.33907	+	7.33907i	0.354747	+	0.354747i
$429$	−6.29423	+	6.56784i	−0.303888	+	0.317098i
$430$	2.61658	+	7.20872i	0.126183	+	0.347635i
$431$	−6.11026	−	1.29878i	−0.294321	−	0.0625599i	0.0583847	−	0.998294i	$-0.481405\pi$
$431$	−6.11026	−	1.29878i	−0.294321	−	0.0625599i	−0.352706	+	0.935734i	$0.614738\pi$
$432$	−1.78760	+	1.44757i	−0.0860058	+	0.0696461i
$433$	2.56333	−	16.1842i	0.123186	−	0.777765i	−0.846316	−	0.532681i	$-0.821184\pi$
$433$	2.56333	−	16.1842i	0.123186	−	0.777765i	0.969502	−	0.245084i	$-0.0788155\pi$
$434$	−18.6535	+	0.960858i	−0.895398	+	0.0461226i
$435$	−0.0970101	+	0.418517i	−0.00465128	+	0.0200664i
$436$	7.00986	+	3.12099i	0.335711	+	0.149468i
$437$	50.8578	+	19.5225i	2.43286	+	0.933886i
$438$	−1.25957	−	1.93956i	−0.0601844	−	0.0926758i
$439$	18.8821	+	32.7048i	0.901195	+	1.56092i	0.825945	+	0.563751i	$0.190642\pi$
$439$	18.8821	+	32.7048i	0.901195	+	1.56092i	0.0752506	+	0.997165i	$0.476024\pi$
$440$	7.16910	+	1.89841i	0.341774	+	0.0905030i
$441$	−13.0942	−	4.28047i	−0.623532	−	0.203832i
$442$	−8.46827	−	4.31480i	−0.402794	−	0.205234i
$443$	12.1565	−	9.84414i	0.577573	−	0.467709i	−0.295470	−	0.955352i	$-0.595476\pi$
$443$	12.1565	−	9.84414i	0.577573	−	0.467709i	0.873043	+	0.487643i	$0.162143\pi$
$444$	2.08597	+	19.8467i	0.0989960	+	0.941884i
$445$	−18.4836	+	0.629182i	−0.876205	+	0.0298261i
$446$	0.680067	+	3.19946i	0.0322021	+	0.151499i
$447$	25.3663	+	4.01763i	1.19978	+	0.190027i
$448$	2.29247	−	1.32083i	0.108309	−	0.0624031i
$449$	−1.52976	+	0.497049i	−0.0721938	+	0.0234572i	−0.344891	−	0.938643i	$-0.612084\pi$
$449$	−1.52976	+	0.497049i	−0.0721938	+	0.0234572i	0.272697	+	0.962100i	$0.412084\pi$
$450$	−9.80108	−	0.874860i	−0.462027	−	0.0412413i
$451$	−7.93602	+	12.8088i	−0.373693	+	0.603143i
$452$	1.56309	+	5.83355i	0.0735218	+	0.274387i
$453$	−0.664370	−	12.6769i	−0.0312148	−	0.595615i
$454$	10.2625	+	7.45613i	0.481642	+	0.349933i
$455$	4.97449	−	5.31555i	0.233208	−	0.249197i
$456$	−4.55672	+	14.0241i	−0.213388	+	0.656741i
$457$	10.1450	−	15.6220i	0.474565	−	0.730766i	−0.517611	−	0.855616i	$-0.673178\pi$
$457$	10.1450	−	15.6220i	0.474565	−	0.730766i	0.992176	+	0.124850i	$0.0398451\pi$
$458$	17.1603	+	13.8961i	0.801847	+	0.649323i
$459$	7.22582	+	16.2295i	0.337273	+	0.757526i
$460$	14.6951	+	11.0938i	0.685162	+	0.517252i
$461$		−	7.91220i		−	0.368508i	−0.982879	−	0.184254i	$-0.941013\pi$
$461$		−	7.91220i		−	0.368508i	0.982879	−	0.184254i	$-0.0589869\pi$
$462$	−19.5485	−	0.625469i	−0.909481	−	0.0290994i
$463$	22.6366	+	22.6366i	1.05201	+	1.05201i	0.998571	+	0.0534397i	$0.0170185\pi$
$463$	22.6366	+	22.6366i	1.05201	+	1.05201i	0.0534397	+	0.998571i	$0.482982\pi$
$464$	0.0640582	+	0.0576783i	0.00297383	+	0.00267765i
$465$	30.7889	−	17.0312i	1.42780	−	0.789802i
$466$	2.98886	+	28.4371i	0.138456	+	1.31732i
$467$	−17.0801	−	11.0919i	−0.790371	−	0.513273i	0.0851994	−	0.996364i	$-0.472847\pi$
$467$	−17.0801	−	11.0919i	−0.790371	−	0.513273i	−0.875570	+	0.483091i	$0.839514\pi$
$468$	−1.09946	−	2.15782i	−0.0508227	−	0.0997451i
$469$	14.9277	+	29.3621i	0.689296	+	1.35582i
$470$	−10.9904	+	2.72995i	−0.506949	+	0.125923i
$471$	−3.72220	+	4.13392i	−0.171510	+	0.190481i
$472$	−5.42452	+	1.45350i	−0.249684	+	0.0669026i
$473$	−8.61310	−	7.42974i	−0.396031	−	0.341620i
$474$	−1.75926	−	3.04712i	−0.0808054	−	0.139959i
$475$	29.2341	−	15.4781i	1.34135	−	0.710185i
$476$	−5.27108	−	19.7426i	−0.241600	−	0.904900i
$477$	−1.21509	+	7.67180i	−0.0556353	+	0.351267i
$478$	−7.38045	−	4.79292i	−0.337574	−	0.219223i
$479$	−4.03303	−	4.47913i	−0.184274	−	0.204657i	0.643929	−	0.765085i	$-0.277303\pi$
$479$	−4.03303	−	4.47913i	−0.184274	−	0.204657i	−0.828203	+	0.560428i	$0.810637\pi$
$480$	−2.79064	+	4.12945i	−0.127375	+	0.188483i
$481$	10.9573	+	1.15166i	0.499610	+	0.0525112i
$482$	−1.60735	+	3.15460i	−0.0732128	+	0.143688i
$483$	−44.3429	−	19.7903i	−2.01767	−	0.900489i
$484$	−10.6526	+	2.74253i	−0.484210	+	0.124660i
$485$	10.9526	+	15.6713i	0.497334	+	0.711597i
$486$	−3.67720	+	17.2998i	−0.166801	+	0.784737i
$487$	9.89891	−	25.7875i	0.448562	−	1.16855i	−0.503866	−	0.863782i	$-0.668089\pi$
$487$	9.89891	−	25.7875i	0.448562	−	1.16855i	0.952428	−	0.304763i	$-0.0985773\pi$
$488$	9.92701	−	3.81062i	0.449375	−	0.172499i
$489$	13.5467	−	41.6926i	0.612605	−	1.88540i
$490$	15.6493	+	0.314939i	0.706964	+	0.0142275i
$491$	15.5764	−	11.3169i	0.702951	−	0.510724i	−0.177941	−	0.984041i	$-0.556944\pi$
$491$	15.5764	−	11.3169i	0.702951	−	0.510724i	0.880892	+	0.473317i	$0.156944\pi$
$492$	−6.37270	−	7.86963i	−0.287304	−	0.354790i
$493$	0.558342	−	0.362591i	0.0251464	−	0.0163303i
$494$	7.05043	+	4.07057i	0.317214	+	0.183144i
$495$	13.3158	−	5.97551i	0.598503	−	0.268579i
$496$		−	7.05972i		−	0.316991i
$497$	3.09332	−	29.1798i	0.138754	−	1.30889i
$498$	−1.02445	−	6.46812i	−0.0459067	−	0.289843i
$499$	7.90036	−	17.7445i	0.353669	−	0.794353i	−0.645854	−	0.763461i	$-0.723499\pi$
$499$	7.90036	−	17.7445i	0.353669	−	0.794353i	0.999523	−	0.0308920i	$-0.00983480\pi$
$500$	10.9421	−	2.29566i	0.489346	−	0.102665i
$501$	−7.41918	−	8.23983i	−0.331464	−	0.368129i
$502$	3.15437	+	8.21742i	0.140787	+	0.366761i
$503$	−4.36843	+	0.691891i	−0.194778	+	0.0308499i	−0.253061	−	0.967450i	$-0.581437\pi$
$503$	−4.36843	+	0.691891i	−0.194778	+	0.0308499i	0.0582829	+	0.998300i	$0.481437\pi$
$504$	1.87032	−	4.85936i	0.0833107	−	0.216453i
$505$	22.3030	+	18.7479i	0.992471	+	0.834271i
$506$	−27.0586	−	3.69759i	−1.20290	−	0.164378i
$507$	24.7282	−	6.62590i	1.09822	−	0.294266i
$508$	7.83664	+	12.0674i	0.347695	+	0.535403i
$509$	1.28992	−	12.2728i	0.0571746	−	0.543980i	−0.928019	−	0.372534i	$-0.878489\pi$
$509$	1.28992	−	12.2728i	0.0571746	−	0.543980i	0.985193	−	0.171447i	$-0.0548442\pi$
$510$	25.2282	+	29.0733i	1.11712	+	1.28739i
$511$	−2.44485	−	1.24847i	−0.108154	−	0.0552291i
$512$	0.453990	+	0.891007i	0.0200637	+	0.0393773i
$513$	−5.45349	−	14.2068i	−0.240778	−	0.627247i
$514$	−8.88980	+	3.95799i	−0.392112	+	0.174580i
$515$	−0.734644	+	5.94000i	−0.0323723	+	0.261747i
$516$	6.62018	−	3.82217i	0.291437	−	0.168261i
$517$	12.2406	−	11.5022i	0.538340	−	0.505865i
$518$	13.9064	+	19.1766i	0.611013	+	0.842572i
$519$	−13.0596	+	4.24332i	−0.573253	+	0.186261i
$520$	1.90971	+	1.98104i	0.0837462	+	0.0868745i
$521$	−3.08307	+	0.324044i	−0.135072	+	0.0141966i	−0.171823	−	0.985128i	$-0.554966\pi$
$521$	−3.08307	+	0.324044i	−0.135072	+	0.0141966i	0.0367512	+	0.999324i	$0.488299\pi$
$522$	0.169408	+	0.00887828i	0.00741477	+	0.000388592i
$523$	−3.29628	+	5.07582i	−0.144136	+	0.221950i	−0.903364	−	0.428875i	$-0.858910\pi$
$523$	−3.29628	+	5.07582i	−0.144136	+	0.221950i	0.759228	+	0.650825i	$0.225577\pi$
$524$	6.27152	−	4.55652i	0.273972	−	0.199053i
$525$	−26.7560	+	12.3902i	−1.16773	+	0.540753i
$526$	5.95907	+	18.3401i	0.259828	+	0.799668i
$527$	−52.6670	−	14.1121i	−2.29421	−	0.614731i
$528$	0.616183	−	7.36671i	0.0268159	−	0.320595i
$529$	−38.8012	−	22.4019i	−1.68701	−	0.973994i
$530$	−1.22057	−	8.74060i	−0.0530183	−	0.379667i
$531$	−6.49626	+	8.94133i	−0.281914	+	0.388021i
$532$	3.62389	+	17.1244i	0.157115	+	0.742435i
$533$	−4.98136	+	2.53813i	−0.215767	+	0.109939i
$534$	3.83285	+	18.0322i	0.165864	+	0.780328i
$535$	−22.7857	+	4.40829i	−0.985110	+	0.190587i
$536$	−11.3734	+	5.06376i	−0.491256	+	0.218721i
$537$	33.6123	−	1.76155i	1.45048	−	0.0760164i
$538$	−21.4363	+	21.4363i	−0.924182	+	0.924182i
$539$	−20.4767	+	10.9410i	−0.881994	+	0.471261i
$540$	−0.443771	−	5.12424i	−0.0190969	−	0.220512i
$541$	21.3559	−	23.7181i	0.918160	−	1.01972i	−0.0815744	−	0.996667i	$-0.525995\pi$
$541$	21.3559	−	23.7181i	0.918160	−	1.01972i	0.999734	−	0.0230526i	$-0.00733852\pi$
$542$	11.8918	+	4.56483i	0.510796	+	0.196076i
$543$	−13.2825	+	16.4025i	−0.570006	+	0.703899i
$544$	7.55460	−	1.60578i	0.323901	−	0.0688473i
$545$	−14.5587	+	9.07950i	−0.623627	+	0.388923i
$546$	−6.08255	−	3.95779i	−0.260309	−	0.169378i
$547$	4.38340	−	0.694263i	0.187421	−	0.0296845i	−0.0620183	−	0.998075i	$-0.519754\pi$
$547$	4.38340	−	0.694263i	0.187421	−	0.0296845i	0.249439	+	0.968390i	$0.419754\pi$
$548$	14.3782	−	0.753529i	0.614206	−	0.0321892i
$549$	10.4632	−	18.1228i	0.446558	−	0.773461i
$550$	−12.4930	+	10.9052i	−0.532705	+	0.465001i
$551$	−0.493868	+	0.285135i	−0.0210395	+	0.0121471i
$552$	8.33230	−	16.3531i	0.354646	−	0.696032i
$553$	−3.61513	−	2.09151i	−0.153731	−	0.0889400i
$554$	−15.9800	−	21.9946i	−0.678924	−	0.934459i
$555$	−39.3814	−	20.9839i	−1.67165	−	0.890717i
$556$	2.30165	−	2.07241i	0.0976116	−	0.0878899i
$557$	−5.44537	−	4.40958i	−0.230728	−	0.186840i	0.506984	−	0.861956i	$-0.330760\pi$
$557$	−5.44537	−	4.40958i	−0.230728	−	0.186840i	−0.737712	+	0.675116i	$0.764094\pi$
$558$	−8.74352	−	10.7973i	−0.370143	−	0.457088i
$559$	−1.30418	−	4.01385i	−0.0551609	−	0.169768i
$560$	−0.423155	+	5.90093i	−0.0178816	+	0.249360i
$561$	−53.7255	−	19.3226i	−2.26829	−	0.815800i
$562$	−0.511716	−	0.137114i	−0.0215855	−	0.00578380i
$563$	−28.4849	+	18.4983i	−1.20050	+	0.779611i	−0.980621	−	0.195917i	$-0.937232\pi$
$563$	−28.4849	+	18.4983i	−1.20050	+	0.779611i	−0.219876	+	0.975528i	$0.570565\pi$
$564$	4.59128	+	10.3122i	0.193328	+	0.434221i
$565$	−12.7648	−	4.40782i	−0.537017	−	0.185438i
$566$	12.5841	+	4.08883i	0.528950	+	0.171866i
$567$	8.99389	+	27.7648i	0.377708	+	1.16601i
$568$	10.9542	+	1.73497i	0.459628	+	0.0727979i
$569$	−4.13585	−	0.434695i	−0.173384	−	0.0182234i	0.0174387	−	0.999848i	$-0.494449\pi$
$569$	−4.13585	−	0.434695i	−0.173384	−	0.0182234i	−0.190822	+	0.981625i	$0.561115\pi$
$570$	−20.2772	−	26.0007i	−0.849318	−	1.08905i
$571$	−11.7464	+	20.3454i	−0.491573	+	0.851429i	−0.999953	−	0.00970350i	$-0.996911\pi$
$571$	−11.7464	+	20.3454i	−0.491573	+	0.851429i	0.508380	+	0.861133i	$0.330245\pi$
$572$	−3.90753	−	1.17836i	−0.163382	−	0.0492699i
$573$	−19.2340	+	19.2340i	−0.803510	+	0.803510i
$574$	−11.2179	−	4.31767i	−0.468226	−	0.180216i
$575$	−38.9519	+	13.3356i	−1.62441	+	0.556134i
$576$	1.79787	+	0.800462i	0.0749111	+	0.0333526i
$577$	−0.644661	+	12.3009i	−0.0268376	+	0.512092i	0.951828	+	0.306632i	$0.0992022\pi$
$577$	−0.644661	+	12.3009i	−0.0268376	+	0.512092i	−0.978666	+	0.205459i	$0.934131\pi$
$578$	2.23216	−	42.5921i	0.0928455	−	1.77160i
$579$	8.74899	+	3.89530i	0.363596	+	0.161883i
$580$	−0.187062	+	0.0464651i	−0.00776733	+	0.00192936i
$581$	−4.88661	−	6.04551i	−0.202731	−	0.250810i
$582$	13.4761	−	13.4761i	0.558603	−	0.558603i
$583$	7.91772	+	10.4242i	0.327918	+	0.431724i
$584$	0.518789	−	0.898569i	0.0214676	−	0.0371830i
$585$	5.37431	+	0.664681i	0.222200	+	0.0274812i
$586$	−22.3177	−	2.34568i	−0.921936	−	0.0968993i
$587$	7.63165	+	1.20873i	0.314992	+	0.0498898i	0.311929	−	0.950105i	$-0.399025\pi$
$587$	7.63165	+	1.20873i	0.314992	+	0.0498898i	0.00306314	+	0.999995i	$0.499025\pi$
$588$	−2.41317	−	15.4146i	−0.0995173	−	0.635686i
$589$	44.4194	+	14.4327i	1.83027	+	0.594690i
$590$	4.09876	−	11.8697i	0.168743	−	0.488669i
$591$	8.15909	+	18.3256i	0.335620	+	0.753815i
$592$	−7.50887	+	4.87632i	−0.308613	+	0.200415i
$593$	23.3383	+	6.25348i	0.958390	+	0.256800i	0.703919	−	0.710281i	$-0.251432\pi$
$593$	23.3383	+	6.25348i	0.958390	+	0.256800i	0.254471	+	0.967080i	$0.418099\pi$
$594$	4.29015	+	6.30834i	0.176027	+	0.258834i
$595$	43.1763	+	14.9525i	1.77005	+	0.612994i
$596$	3.56064	+	10.9585i	0.145850	+	0.448879i
$597$	−35.3250	−	43.6227i	−1.44576	−	1.78536i
$598$	−7.87473	−	6.37683i	−0.322022	−	0.260768i
$599$	−8.06549	+	7.26220i	−0.329547	+	0.296725i	−0.817249	−	0.576285i	$-0.804502\pi$
$599$	−8.06549	+	7.26220i	−0.329547	+	0.296725i	0.487702	+	0.873010i	$0.337835\pi$
$600$	−4.15662	−	10.3403i	−0.169694	−	0.422143i
$601$	23.0402	+	31.7121i	0.939830	+	1.29357i	0.955899	+	0.293694i	$0.0948848\pi$
$601$	23.0402	+	31.7121i	0.939830	+	1.29357i	−0.0160692	+	0.999871i	$0.505115\pi$
$602$	4.54401	−	7.85423i	0.185200	−	0.320114i
$603$	−11.1233	+	21.8307i	−0.452976	+	0.889016i
$604$	4.93230	−	2.84766i	0.200692	−	0.115870i
$605$	8.25630	−	23.1697i	0.335666	−	0.941981i
$606$	14.5213	−	25.1517i	0.589889	−	1.02172i
$607$	5.78053	−	0.302945i	0.234625	−	0.0122962i	0.0653387	−	0.997863i	$-0.479187\pi$
$607$	5.78053	−	0.302945i	0.234625	−	0.0122962i	0.169286	+	0.985567i	$0.445854\pi$
$608$	−6.53429	+	1.03493i	−0.265001	+	0.0419720i
$609$	0.453127	−	0.230370i	0.0183616	−	0.00933505i
$610$	−5.36897	+	23.1626i	−0.217383	+	0.937826i
$611$	6.09593	−	1.29573i	0.246615	−	0.0524196i
$612$	9.56547	−	11.8124i	0.386661	−	0.477487i
$613$	11.1719	+	4.28849i	0.451229	+	0.173211i	0.573360	−	0.819303i	$-0.305640\pi$
$613$	11.1719	+	4.28849i	0.451229	+	0.173211i	−0.122131	+	0.992514i	$0.538973\pi$
$614$	−4.97198	+	5.52194i	−0.200653	+	0.222847i
$615$	22.5587	−	1.95364i	0.909655	−	0.0787783i
$616$	−3.73168	−	7.94195i	−0.150354	−	0.319990i
$617$	−10.8209	+	10.8209i	−0.435633	+	0.435633i	−0.890539	−	0.454906i	$-0.849673\pi$
$617$	−10.8209	+	10.8209i	−0.435633	+	0.435633i	0.454906	+	0.890539i	$0.349673\pi$
$618$	5.95790	−	0.312240i	0.239662	−	0.0125601i
$619$	−5.70202	+	2.53870i	−0.229183	+	0.102039i	−0.518116	−	0.855310i	$-0.673366\pi$
$619$	−5.70202	+	2.53870i	−0.229183	+	0.102039i	0.288932	+	0.957349i	$0.406700\pi$
$620$	13.0794	+	8.83893i	0.525282	+	0.354980i
$621$	3.93797	+	18.5267i	0.158025	+	0.743451i
$622$	−8.59580	+	4.37978i	−0.344660	+	0.175613i
$623$	14.6278	+	16.2751i	0.586052	+	0.652049i
$624$	1.61219	−	2.21899i	0.0645393	−	0.0888307i
$625$	−9.44666	+	23.1465i	−0.377866	+	0.925860i
$626$	−9.92343	−	5.72929i	−0.396620	−	0.228989i
$627$	45.0912	+	18.9373i	1.80077	+	0.756284i
$628$	−2.41069	−	0.645942i	−0.0961969	−	0.0257759i
$629$	21.3684	+	65.7653i	0.852015	+	2.62223i
$630$	6.66116	+	9.54914i	0.265387	+	0.380447i
$631$	1.66017	−	1.20618i	0.0660903	−	0.0480174i	−0.554250	−	0.832351i	$-0.686995\pi$
$631$	1.66017	−	1.20618i	0.0660903	−	0.0480174i	0.620340	+	0.784333i	$0.286995\pi$
$632$	0.859760	−	1.32391i	0.0341994	−	0.0526625i
$633$	−5.07591	−	0.266017i	−0.201749	−	0.0105732i
$634$	−20.9827	+	2.20537i	−0.833328	+	0.0875863i
$635$	−32.1687	−	0.589811i	−1.27657	−	0.0234059i
$636$	−8.36657	+	2.71846i	−0.331756	+	0.107794i
$637$	−8.60137	−	0.466212i	−0.340799	−	0.0184720i
$638$	0.208341	−	0.195773i	0.00824828	−	0.00775071i
$639$	18.9025	−	10.9133i	0.747770	−	0.431725i
$640$	−2.21916	−	0.274460i	−0.0877200	−	0.0108490i
$641$	19.2670	−	8.57821i	0.761000	−	0.338819i	0.0107227	−	0.999943i	$-0.496587\pi$
$641$	19.2670	−	8.57821i	0.761000	−	0.338819i	0.750277	+	0.661124i	$0.229920\pi$
$642$	8.29042	+	21.5973i	0.327197	+	0.852377i
$643$	2.60368	+	5.11001i	0.102679	+	0.201519i	0.936631	−	0.350319i	$-0.113927\pi$
$643$	2.60368	+	5.11001i	0.102679	+	0.201519i	−0.833951	+	0.551838i	$0.813927\pi$
$644$	−1.12072	−	21.7571i	−0.0441627	−	0.857349i
$645$	−1.20736	+	17.0505i	−0.0475399	+	0.671365i
$646$	−5.34097	+	50.8160i	−0.210138	+	1.99933i
$647$	−24.9631	−	38.4397i	−0.981399	−	1.51122i	−0.854596	−	0.519294i	$-0.826195\pi$
$647$	−24.9631	−	38.4397i	−0.981399	−	1.51122i	−0.126803	−	0.991928i	$-0.540472\pi$
$648$	−10.6551	+	2.85502i	−0.418572	+	0.112156i
$649$	3.30431	+	18.3303i	0.129705	+	0.719527i
$650$	−6.06125	+	1.05777i	−0.237742	+	0.0414892i
$651$	−38.8535	−	14.9543i	−1.52279	−	0.586107i
$652$	19.4259	−	3.07676i	0.760777	−	0.120495i
$653$	6.10212	+	15.8966i	0.238794	+	0.622080i	0.999639	−	0.0268532i	$-0.00854865\pi$
$653$	6.10212	+	15.8966i	0.238794	+	0.622080i	−0.760845	+	0.648934i	$0.775215\pi$
$654$	11.4441	+	12.7099i	0.447499	+	0.496998i
$655$	0.589711	+	17.3240i	0.0230419	+	0.676905i
$656$	1.84788	−	4.15041i	0.0721476	−	0.162046i
$657$	−0.319433	−	2.01682i	−0.0124623	−	0.0786838i
$658$	10.8331	+	7.88554i	0.422319	+	0.307410i
$659$			6.24936i			0.243441i	0.992564	+	0.121720i	$0.0388411\pi$
$659$			6.24936i			0.243441i	−0.992564	+	0.121720i	$0.961159\pi$
$660$	12.8767	+	10.3649i	0.501225	+	0.403453i
$661$	−38.8479	−	22.4288i	−1.51101	−	0.872380i	−0.999917	−	0.0128526i	$-0.995909\pi$
$661$	−38.8479	−	22.4288i	−1.51101	−	0.872380i	−0.511089	−	0.859528i	$-0.670758\pi$
$662$	24.7351	−	16.0632i	0.961357	−	0.624313i
$663$	−13.3314	−	16.4629i	−0.517750	−	0.639368i
$664$	2.37697	−	1.72697i	0.0922445	−	0.0670195i
$665$	−36.2632	−	14.7262i	−1.40623	−	0.571057i
$666$	−5.44494	+	16.7578i	−0.210987	+	0.649351i
$667$	0.662644	−	0.254365i	0.0256577	−	0.00984905i
$668$	1.78272	−	4.64414i	0.0689755	−	0.179687i
$669$	−1.51580	+	7.13129i	−0.0586043	+	0.275712i
$670$	4.85821	−	27.4113i	0.187689	−	1.05899i
$671$	−9.85009	−	33.8630i	−0.380258	−	1.30727i
$672$	5.86537	−	0.611170i	0.226261	−	0.0235764i
$673$	8.05245	−	15.8038i	0.310399	−	0.609193i	−0.682126	−	0.731235i	$-0.738944\pi$
$673$	8.05245	−	15.8038i	0.310399	−	0.609193i	0.992525	+	0.122042i	$0.0389444\pi$
$674$	−11.5403	−	1.21294i	−0.444517	−	0.0467206i
$675$	10.0492	+	5.59350i	0.386794	+	0.215294i
$676$	7.68543	+	8.53554i	0.295593	+	0.328290i
$677$	−8.84162	−	5.74181i	−0.339811	−	0.220676i	0.363440	−	0.931618i	$-0.381602\pi$
$677$	−8.84162	−	5.74181i	−0.339811	−	0.220676i	−0.703251	+	0.710942i	$0.748269\pi$
$678$	−2.10578	+	13.2954i	−0.0808719	+	0.510605i
$679$	5.87464	−	21.8463i	0.225448	−	0.838382i
$680$	−6.48354	+	16.0068i	−0.248632	+	0.613831i
$681$	14.1370	+	24.4859i	0.541729	+	0.938303i
$682$	−23.3330	−	1.95167i	−0.893465	−	0.0747333i
$683$	4.84229	−	1.29749i	0.185285	−	0.0496470i	−0.164983	−	0.986296i	$-0.552757\pi$
$683$	4.84229	−	1.29749i	0.185285	−	0.0496470i	0.350268	+	0.936649i	$0.386090\pi$
$684$	−8.71198	+	9.67563i	−0.333111	+	0.369957i
$685$	−16.6058	+	27.5817i	−0.634474	+	1.05384i
$686$	−11.6165	−	14.4242i	−0.443520	−	0.550717i
$687$	22.3439	+	43.8524i	0.852474	+	1.67307i
$688$	2.87634	+	1.86791i	0.109659	+	0.0712136i
$689$	0.507681	+	4.83026i	0.0193411	+	0.184018i
$690$	19.8648	+	35.9115i	0.756240	+	1.36713i
$691$	14.5596	+	13.1095i	0.553874	+	0.498710i	0.897870	−	0.440261i	$-0.145114\pi$
$691$	14.5596	+	13.1095i	0.553874	+	0.498710i	−0.343996	+	0.938971i	$0.611781\pi$
$692$	−4.35630	−	4.35630i	−0.165602	−	0.165602i
$693$	−15.5435	−	7.52494i	−0.590450	−	0.285849i
$694$		−	1.51684i		−	0.0575783i
$695$	0.957809	+	6.85894i	0.0363318	+	0.260174i
$696$	0.0781459	+	0.175518i	0.00296211	+	0.00665301i
$697$	−27.2691	−	22.0821i	−1.03289	−	0.836417i
$698$	6.44493	−	9.92432i	0.243944	−	0.375641i
$699$	−19.6945	+	60.6134i	−0.744914	+	2.29261i
$700$	−10.4028	−	8.17207i	−0.393187	−	0.308875i
$701$	25.6887	+	18.6639i	0.970248	+	0.704927i	0.955508	−	0.294965i	$-0.0953079\pi$
$701$	25.6887	+	18.6639i	0.970248	+	0.704927i	0.0147401	+	0.999891i	$0.495308\pi$
$702$	0.148140	+	2.82669i	0.00559120	+	0.106686i
$703$	−15.3306	−	57.2144i	−0.578203	−	2.15788i
$704$	3.07036	−	1.25416i	0.115718	−	0.0472678i
$705$	−24.8536	−	4.40491i	−0.936041	−	0.165898i
$706$	11.6181	−	3.77495i	0.437253	−	0.142072i
$707$	0.0308402	−	34.4742i	0.00115986	−	1.29654i
$708$	−12.3631	−	1.95813i	−0.464635	−	0.0735910i
$709$	−4.11588	−	19.3637i	−0.154575	−	0.727219i	−0.985341	−	0.170597i	$-0.945430\pi$
$709$	−4.11588	−	19.3637i	−0.154575	−	0.727219i	0.830766	−	0.556622i	$-0.187903\pi$
$710$	−16.9293	+	18.1224i	−0.635344	+	0.680123i
$711$	−0.324736	−	3.08965i	−0.0121785	−	0.115871i
$712$	−6.42769	+	5.20504i	−0.240888	+	0.195067i
$713$	−51.7958	−	26.3913i	−1.93977	−	0.988362i
$714$	7.16516	−	44.9786i	0.268149	−	1.68328i
$715$	7.07546	−	5.76408i	0.264607	−	0.215564i
$716$	7.55045	+	13.0778i	0.282174	+	0.488739i
$717$	−10.6830	−	16.4503i	−0.398962	−	0.614348i
$718$	−18.8031	−	7.21783i	−0.701725	−	0.269367i
$719$	−28.1055	−	12.5134i	−1.04816	−	0.466670i	−0.190929	−	0.981604i	$-0.561150\pi$
$719$	−28.1055	−	12.5134i	−1.04816	−	0.466670i	−0.857230	+	0.514934i	$0.827817\pi$
$720$	−3.73397	+	2.32868i	−0.139157	+	0.0867848i
$721$	5.94278	−	3.85174i	0.221321	−	0.143446i
$722$	3.87458	−	24.4631i	0.144197	−	0.910424i
$723$	−6.13279	+	4.96623i	−0.228081	+	0.184696i
$724$	−9.26234	−	1.96877i	−0.344232	−	0.0731688i
$725$	0.148121	−	0.404742i	0.00550107	−	0.0150317i
$726$	−24.1772	−	4.07307i	−0.897302	−	0.151166i
$727$	0.282731	+	0.282731i	0.0104859	+	0.0104859i	0.712330	−	0.701844i	$-0.247640\pi$
$727$	0.282731	+	0.282731i	0.0104859	+	0.0104859i	−0.701844	+	0.712330i	$0.747640\pi$
$728$	0.343219	−	3.23764i	0.0127205	−	0.119995i
$729$	−3.71964	+	5.11965i	−0.137765	+	0.189617i
$730$	1.01523	+	2.08618i	0.0375753	+	0.0772130i
$731$	19.6847	−	17.7242i	0.728065	−	0.655553i
$732$	23.6680	+	1.24039i	0.874796	+	0.0458461i
$733$	−26.2372	+	10.0715i	−0.969093	+	0.372000i	−0.790866	−	0.611989i	$-0.790370\pi$
$733$	−26.2372	+	10.0715i	−0.969093	+	0.372000i	−0.178227	+	0.983989i	$0.557036\pi$
$734$	14.9652	+	10.8729i	0.552377	+	0.401325i
$735$	31.5797	+	14.8286i	1.16483	+	0.546960i
$736$	8.23430			0.303520
$737$	13.5920	+	38.9899i	0.500666	+	1.43621i
$738$	−2.31411	−	8.63638i	−0.0851836	−	0.317909i
$739$	7.59940	−	35.7524i	0.279549	−	1.31517i	−0.584348	−	0.811503i	$-0.698650\pi$
$739$	7.59940	−	35.7524i	0.279549	−	1.31517i	0.863896	−	0.503670i	$-0.168017\pi$
$740$	0.367007	−	20.0168i	0.0134915	−	0.735833i
$741$	10.6658	+	14.6803i	0.391819	+	0.539293i
$742$	−6.99425	+	7.75394i	−0.256767	+	0.284656i
$743$	−35.5114	+	18.0939i	−1.30279	+	0.663802i	−0.961149	−	0.276030i	$-0.910981\pi$
$743$	−35.5114	+	18.0939i	−1.30279	+	0.663802i	−0.341636	+	0.939832i	$0.610981\pi$
$744$	6.40017	−	14.3750i	0.234642	−	0.527014i
$745$	−24.7607	−	7.12359i	−0.907162	−	0.260988i
$746$	−18.2667	−	3.88271i	−0.668793	−	0.142156i
$747$	1.49655	−	5.58519i	0.0547558	−	0.204351i
$748$	−3.21876	−	25.4125i	−0.117689	−	0.929173i
$749$	21.3252	+	17.3004i	0.779205	+	0.632143i
$750$	24.3616	+	5.24544i	0.889559	+	0.191536i
$751$	4.33778	−	41.2712i	0.158288	−	1.50601i	−0.570516	−	0.821286i	$-0.693257\pi$
$751$	4.33778	−	41.2712i	0.158288	−	1.50601i	0.728804	−	0.684722i	$-0.240076\pi$
$752$	−3.18714	+	3.93579i	−0.116223	+	0.143523i
$753$	−1.02677	+	19.5920i	−0.0374177	+	0.713973i
$754$	0.103756	−	0.0220540i	0.00377856	−	0.000803158i
$755$	−0.899533	+	12.7033i	−0.0327374	+	0.462322i
$756$	−4.30714	+	4.29944i	−0.156649	+	0.156369i
$757$	−5.82823	−	2.96963i	−0.211831	−	0.107933i	0.344856	−	0.938656i	$-0.387928\pi$
$757$	−5.82823	−	2.96963i	−0.211831	−	0.107933i	−0.556687	+	0.830722i	$0.687928\pi$
$758$	−2.14527	+	8.00627i	−0.0779198	+	0.290801i
$759$	−51.7447	−	32.0598i	−1.87821	−	1.16370i
$760$	6.26369	−	13.4017i	0.227208	−	0.486132i
$761$	10.3120	+	9.28498i	0.373810	+	0.336580i	0.834527	−	0.550967i	$-0.185741\pi$
$761$	10.3120	+	9.28498i	0.373810	+	0.336580i	−0.460717	+	0.887547i	$0.652408\pi$
$762$	5.01701	+	31.6761i	0.181747	+	1.14751i
$763$	19.3022	+	6.29078i	0.698788	+	0.227741i
$764$	−11.6064	−	3.77116i	−0.419906	−	0.136436i
$765$	9.90839	+	32.5111i	0.358239	+	1.17544i
$766$	24.3439	−	2.55865i	0.879582	−	0.0924478i
$767$	−2.47658	+	6.45172i	−0.0894243	+	0.232958i
$768$	0.116652	+	2.22585i	0.00420931	+	0.0803184i
$769$	43.6017			1.57232			0.786159	−	0.618025i	$-0.212067\pi$
$769$	43.6017			1.57232			0.786159	+	0.618025i	$0.212067\pi$
$770$	19.3861	+	3.02988i	0.698626	+	0.109189i
$771$	−21.6897			−0.781134
$772$	0.224873	+	4.29083i	0.00809335	+	0.154430i
$773$	3.92095	−	10.2144i	0.141027	−	0.367388i	−0.844817	−	0.535056i	$-0.820290\pi$
$773$	3.92095	−	10.2144i	0.141027	−	0.367388i	0.985843	+	0.167668i	$0.0536238\pi$
$774$	6.71259	−	0.705521i	0.241279	−	0.0253594i
$775$	−32.7515	+	13.1655i	−1.17647	+	0.472918i
$776$	8.13195	+	2.64223i	0.291920	+	0.0948506i
$777$	10.9313	+	51.6547i	0.392157	+	1.85310i
$778$	−0.632060	−	3.99067i	−0.0226604	−	0.143072i
$779$	22.3364	+	20.1118i	0.800284	+	0.720579i
$780$	2.09259	+	5.76511i	0.0749266	+	0.206424i
$781$	8.76253	−	35.7249i	0.313548	−	1.27834i
$782$	16.4600	−	61.4296i	0.588609	−	2.19672i
$783$	−0.176664	−	0.0900150i	−0.00631347	−	0.00321687i
$784$	5.67047	−	4.10436i	0.202517	−	0.146584i
$785$	4.21496	−	3.65751i	0.150438	−	0.130542i
$786$	16.9009	−	3.59240i	0.602836	−	0.128137i
$787$	−1.76148	+	33.6110i	−0.0627899	+	1.19810i	0.767603	+	0.640925i	$0.221449\pi$
$787$	−1.76148	+	33.6110i	−0.0627899	+	1.19810i	−0.830393	+	0.557178i	$0.811884\pi$
$788$	−5.66381	+	6.99422i	−0.201765	+	0.249159i
$789$	−4.49285	+	42.7466i	−0.159950	+	1.52182i
$790$	1.37635	+	3.25043i	0.0489685	+	0.115645i
$791$	5.71286	+	14.9224i	0.203126	+	0.530580i
$792$	3.14261	−	5.72081i	0.111668	−	0.203280i
$793$	3.38664	−	12.6391i	0.120263	−	0.448828i
$794$	8.52599	+	1.81226i	0.302576	+	0.0643145i
$795$	5.43869	−	18.9042i	0.192890	−	0.670462i
$796$	10.2431	−	23.0064i	0.363058	−	0.815441i
$797$	2.45695	−	1.25188i	0.0870296	−	0.0443438i	−0.409934	−	0.912115i	$-0.634448\pi$
$797$	2.45695	−	1.25188i	0.0870296	−	0.0443438i	0.496964	+	0.867771i	$0.334448\pi$
$798$	−8.14557	+	38.1540i	−0.288350	+	1.35064i
$799$	22.9909	+	31.6442i	0.813358	+	1.11949i
$800$	3.28693	−	3.76777i	0.116210	−	0.133211i
$801$	−3.38422	+	15.9215i	−0.119575	+	0.562558i
$802$	4.06677	+	15.1774i	0.143602	+	0.535932i
$803$	−2.82643	−	1.96305i	−0.0997424	−	0.0692746i
$804$	−27.7492			−0.978640
$805$	41.7121	+	25.1640i	1.47016	+	0.886915i
$806$	−7.02832	−	5.10637i	−0.247562	−	0.179864i
$807$	−63.0822	+	24.2150i	−2.22060	+	0.852408i
$808$	13.0122	+	0.681939i	0.457767	+	0.0239905i
$809$	14.0166	−	12.6206i	0.492799	−	0.443718i	−0.384880	−	0.922966i	$-0.625757\pi$
$809$	14.0166	−	12.6206i	0.492799	−	0.443718i	0.877679	+	0.479248i	$0.159091\pi$
$810$	8.05097	−	23.3151i	0.282882	−	0.819208i
$811$	−3.68294	+	5.06913i	−0.129325	+	0.178001i	−0.868769	−	0.495217i	$-0.835089\pi$
$811$	−3.68294	+	5.06913i	−0.129325	+	0.178001i	0.739444	+	0.673218i	$0.235089\pi$
$812$	0.184385	+	0.134216i	0.00647064	+	0.00471005i
$813$	20.0757	+	20.0757i	0.704087	+	0.704087i
$814$	14.0408	+	26.1655i	0.492130	+	0.917100i
$815$	−18.6214	+	39.8423i	−0.652280	+	1.39561i
$816$	16.8385	+	3.57913i	0.589465	+	0.125295i
$817$	−17.6331	+	14.2790i	−0.616905	+	0.499560i
$818$	1.65553	−	10.4526i	0.0578842	−	0.365466i
$819$	−3.48492	−	5.37683i	−0.121773	−	0.187882i
$820$	5.37580	+	8.61994i	0.187731	+	0.301022i
$821$	−26.8720	−	11.9642i	−0.937840	−	0.417553i	−0.119854	−	0.992792i	$-0.538243\pi$
$821$	−26.8720	−	11.9642i	−0.937840	−	0.417553i	−0.817986	+	0.575238i	$0.804909\pi$
$822$	29.9601	+	11.5006i	1.04498	+	0.401129i
$823$	4.23915	+	6.52772i	0.147767	+	0.227542i	0.904802	−	0.425833i	$-0.140019\pi$
$823$	4.23915	+	6.52772i	0.147767	+	0.227542i	−0.757034	+	0.653375i	$0.773352\pi$
$824$	1.33834	+	2.31808i	0.0466234	+	0.0807541i
$825$	−35.3248	+	10.8794i	−1.22985	+	0.378772i
$826$	−13.8761	+	5.31229i	−0.482811	+	0.184838i
$827$	−35.9205	−	18.3024i	−1.24908	−	0.636437i	−0.300742	−	0.953706i	$-0.597234\pi$
$827$	−35.9205	−	18.3024i	−1.24908	−	0.636437i	−0.948336	+	0.317269i	$0.897234\pi$
$828$	12.5938	−	10.1983i	0.437665	−	0.354414i
$829$	−4.51901	−	42.9955i	−0.156952	−	1.49330i	−0.735432	−	0.677599i	$-0.763021\pi$
$829$	−4.51901	−	42.9955i	−0.156952	−	1.49330i	0.578480	−	0.815696i	$-0.303646\pi$
$830$	0.223507	+	6.56599i	0.00775804	+	0.227909i
$831$	−12.5988	−	59.2725i	−0.437046	−	2.05614i
$832$	1.21542	+	0.192504i	0.0421371	+	0.00667386i
$833$	−19.2843	−	50.5073i	−0.668163	−	1.74998i
$834$	6.56543	−	2.13324i	0.227342	−	0.0738679i
$835$	6.37212	+	9.11739i	0.220516	+	0.315520i
$836$	1.61412	+	21.8825i	0.0558254	+	0.756822i
$837$	4.20291	+	15.6855i	0.145274	+	0.542170i
$838$	1.65433	+	31.5666i	0.0571480	+	1.09045i
$839$	−20.6796	−	15.0246i	−0.713939	−	0.518707i	0.170503	−	0.985357i	$-0.445461\pi$
$839$	−20.6796	−	15.0246i	−0.713939	−	0.518707i	−0.884442	+	0.466650i	$0.845461\pi$
$840$	−6.21127	+	11.6319i	−0.214309	+	0.401338i
$841$	8.95920	−	27.5736i	0.308938	−	0.950813i
$842$	−0.179338	+	0.276156i	−0.00618039	+	0.00951697i
$843$	−0.917655	−	0.743102i	−0.0316057	−	0.0255938i
$844$	−0.927538	−	2.08328i	−0.0319272	−	0.0717096i
$845$	−25.4360	+	3.55198i	−0.875025	+	0.122192i
$846$			9.96682i			0.342666i
$847$	−27.2804	+	10.1380i	−0.937367	+	0.348344i
$848$	−2.79084	−	2.79084i	−0.0958378	−	0.0958378i
$849$	21.9170	+	19.7342i	0.752190	+	0.677275i
$850$	−21.5379	−	32.0528i	−0.738745	−	1.09940i
$851$	7.70627	+	73.3203i	0.264168	+	2.51339i
$852$	20.7321	+	13.4636i	0.710270	+	0.461254i
$853$	−11.5053	−	22.5805i	−0.393935	−	0.773141i	0.605812	−	0.795608i	$-0.292848\pi$
$853$	−11.5053	−	22.5805i	−0.393935	−	0.773141i	−0.999748	+	0.0224662i	$0.992848\pi$
$854$	25.0781	−	12.7497i	0.858154	−	0.436285i
$855$	−7.01829	−	28.2547i	−0.240020	−	0.966289i
$856$	−6.94492	+	7.71311i	−0.237372	+	0.263629i
$857$	−14.1430	+	3.78960i	−0.483114	+	0.129450i	−0.492152	−	0.870509i	$-0.663790\pi$
$857$	−14.1430	+	3.78960i	−0.483114	+	0.129450i	0.00903803	+	0.999959i	$0.497123\pi$
$858$	−6.88825	−	5.94187i	−0.235161	−	0.202852i
$859$	8.83924	+	15.3100i	0.301591	+	0.522371i	0.976496	−	0.215533i	$-0.0691490\pi$
$859$	8.83924	+	15.3100i	0.301591	+	0.522371i	−0.674906	+	0.737904i	$0.735816\pi$
$860$	−7.06190	+	2.99027i	−0.240809	+	0.101967i
$861$	−18.9277	−	18.9616i	−0.645053	−	0.646208i
$862$	0.977210	−	6.16986i	0.0332839	−	0.210146i
$863$	12.6689	+	8.22730i	0.431255	+	0.280060i	0.741958	−	0.670447i	$-0.233898\pi$
$863$	12.6689	+	8.22730i	0.431255	+	0.280060i	−0.310702	+	0.950507i	$0.600564\pi$
$864$	−1.53914	−	1.70939i	−0.0523626	−	0.0581545i
$865$	13.5250	−	2.61666i	0.459865	−	0.0889690i
$866$	16.2962	+	1.71280i	0.553768	+	0.0582034i
$867$	43.1581	−	84.7026i	1.46573	−	2.87665i
$868$	−1.93579	−	18.5777i	−0.0657050	−	0.630567i
$869$	−4.13796	−	3.20758i	−0.140371	−	0.108810i
$870$	−0.423021	−	0.0749737i	−0.0143417	−	0.00254185i
$871$	−3.18526	+	14.9855i	−0.107929	+	0.507764i
$872$	−2.74984	+	7.16359i	−0.0931215	+	0.242590i
$873$	15.7097	−	6.03038i	0.531692	−	0.204098i
$874$	−16.8340	+	51.8098i	−0.569419	+	1.75249i
$875$	28.1648	−	9.04139i	0.952142	−	0.305655i
$876$	1.87098	−	1.35935i	0.0632146	−	0.0459281i
$877$	15.5719	+	19.2297i	0.525826	+	0.649341i	0.968990	−	0.247100i	$-0.0794776\pi$
$877$	15.5719	+	19.2297i	0.525826	+	0.649341i	−0.443164	+	0.896440i	$0.646144\pi$
$878$	−31.6718	+	20.5679i	−1.06887	+	0.694133i
$879$	−43.3169	−	25.0090i	−1.46104	−	0.843532i
$880$	−1.52060	+	7.25863i	−0.0512595	+	0.244688i
$881$		−	18.4982i		−	0.623220i	−0.950210	−	0.311610i	$-0.899132\pi$
$881$		−	18.4982i		−	0.623220i	0.950210	−	0.311610i	$-0.100868\pi$
$882$	3.58931	−	13.3003i	0.120858	−	0.447843i
$883$	2.18093	+	13.7699i	0.0733942	+	0.463392i	0.996825	+	0.0796270i	$0.0253729\pi$
$883$	2.18093	+	13.7699i	0.0733942	+	0.463392i	−0.923431	+	0.383766i	$0.874627\pi$
$884$	3.86569	−	8.68248i	0.130017	−	0.292023i
$885$	19.1067	−	20.4534i	0.642266	−	0.687532i
$886$	10.4669	+	11.6246i	0.351642	+	0.390537i
$887$	−12.5697	−	32.7451i	−0.422048	−	1.09947i	−0.965585	−	0.260088i	$-0.916248\pi$
$887$	−12.5697	−	32.7451i	−0.422048	−	1.09947i	0.543537	−	0.839385i	$-0.317085\pi$
$888$	−19.7103	+	3.12181i	−0.661436	+	0.104761i
$889$	23.9310	+	29.6065i	0.802621	+	0.992970i
$890$	−1.59567	−	18.4253i	−0.0534871	−	0.617617i
$891$	6.49048	+	36.0053i	0.217439	+	1.20622i
$892$	−3.15949	+	0.846582i	−0.105787	+	0.0283457i
$893$	−18.2481	−	28.0996i	−0.610648	−	0.940316i
$894$	−2.68455	+	25.5418i	−0.0897848	+	0.854246i
$895$	−33.6823	−	2.38507i	−1.12588	−	0.0797241i
$896$	1.43899	+	2.22020i	0.0480734	+	0.0741717i
$897$	−10.2535	−	20.1236i	−0.342354	−	0.671907i
$898$	−0.576429	−	1.50165i	−0.0192357	−	0.0501107i
$899$	0.555928	−	0.247515i	0.0185413	−	0.00825510i
$900$	0.360712	−	9.83343i	0.0120237	−	0.327781i
$901$	−26.3990	+	15.2415i	−0.879479	+	0.507767i
$902$	−13.2066	−	7.25478i	−0.439731	−	0.241558i
$903$	16.3730	−	11.8733i	0.544859	−	0.395119i
$904$	−5.74375	+	1.86626i	−0.191034	+	0.0620708i
$905$	15.2442	−	14.6952i	0.506734	−	0.488486i
$906$	12.6248	−	1.32692i	0.419431	−	0.0440839i
$907$	53.2196	+	2.78912i	1.76713	+	0.0926113i	0.907954	−	0.419070i	$-0.137644\pi$
$907$	53.2196	+	2.78912i	1.76713	+	0.0926113i	0.859175	+	0.511682i	$0.170977\pi$
$908$	−6.90881	+	10.6386i	−0.229277	+	0.353056i
$909$	20.7458	−	15.0727i	0.688095	−	0.499930i
$910$	5.56861	+	4.68948i	0.184598	+	0.155455i
$911$	1.34092	+	4.12693i	0.0444267	+	0.136731i	0.970809	−	0.239852i	$-0.0770989\pi$
$911$	1.34092	+	4.12693i	0.0444267	+	0.136731i	−0.926383	+	0.376583i	$0.877099\pi$
$912$	−14.2434	−	3.81651i	−0.471646	−	0.126377i
$913$	−5.05067	−	8.33352i	−0.167153	−	0.275799i
$914$	16.1315	+	9.31354i	0.533584	+	0.308065i
$915$	−31.9310	+	42.2964i	−1.05561	+	1.39828i
$916$	−12.9790	+	17.8640i	−0.428837	+	0.590244i
$917$	15.2541	−	13.7102i	0.503735	−	0.452750i
$918$	−15.8291	+	8.06530i	−0.522437	+	0.266195i
$919$	−2.06712	−	9.72503i	−0.0681879	−	0.320799i	0.930813	−	0.365497i	$-0.119101\pi$
$919$	−2.06712	−	9.72503i	−0.0681879	−	0.320799i	−0.999001	+	0.0446977i	$0.985768\pi$
$920$	−10.3095	+	15.2556i	−0.339895	+	0.502961i
$921$	−15.1300	+	6.73632i	−0.498551	+	0.221969i
$922$	7.90136	−	0.414093i	0.260217	−	0.0136374i
$923$	9.65055	−	9.65055i	0.317652	−	0.317652i
$924$	−0.398480	−	19.5545i	−0.0131090	−	0.643295i
$925$	36.6253	+	25.7415i	1.20423	+	0.846375i
$926$	−21.4208	+	23.7903i	−0.703933	+	0.781796i
$927$	4.91786	+	1.88779i	0.161524	+	0.0620032i
$928$	−0.0542467	+	0.0669891i	−0.00178073	+	0.00219902i
$929$	−19.7280	+	4.19331i	−0.647254	+	0.137578i	−0.519829	−	0.854270i	$-0.674004\pi$
$929$	−19.7280	+	4.19331i	−0.647254	+	0.137578i	−0.127425	+	0.991848i	$0.540671\pi$
$930$	18.6192	+	29.8554i	0.610548	+	0.978996i
$931$	14.2318	+	44.0692i	0.466429	+	1.44431i
$932$	−28.2417	+	4.47305i	−0.925088	+	0.146519i
$933$	−21.4734	+	1.12537i	−0.703008	+	0.0368431i
$934$	10.1828	−	17.6372i	0.333192	−	0.577105i
$935$	51.1113	+	25.8537i	1.67152	+	0.845507i
$936$	2.09732	−	1.21089i	0.0685530	−	0.0395791i
$937$	25.5859	−	50.2152i	0.835856	−	1.64046i	0.0699100	−	0.997553i	$-0.477729\pi$
$937$	25.5859	−	50.2152i	0.835856	−	1.64046i	0.765946	−	0.642906i	$-0.222271\pi$
$938$	−28.5406	+	16.4439i	−0.931885	+	0.536913i
$939$	−15.0121	−	20.6624i	−0.489901	−	0.674291i
$940$	−3.30140	−	10.8325i	−0.107680	−	0.353316i
$941$	−2.92196	+	2.63094i	−0.0952531	+	0.0857663i	−0.715382	−	0.698734i	$-0.753747\pi$
$941$	−2.92196	+	2.63094i	−0.0952531	+	0.0857663i	0.620128	+	0.784500i	$0.287080\pi$
$942$	−4.32306	−	3.50074i	−0.140853	−	0.114060i
$943$	−23.5429	−	29.0730i	−0.766661	−	0.946747i
$944$	−1.73540	−	5.34101i	−0.0564825	−	0.173835i
$945$	−2.57286	−	13.3628i	−0.0836953	−	0.434691i
$946$	6.96878	−	8.99014i	0.226575	−	0.292295i
$947$	10.3693	+	2.77846i	0.336958	+	0.0902877i	0.423331	−	0.905975i	$-0.360861\pi$
$947$	10.3693	+	2.77846i	0.336958	+	0.0902877i	−0.0863724	+	0.996263i	$0.527527\pi$
$948$	2.95088	−	1.91632i	0.0958400	−	0.0622392i
$949$	−0.519327	−	1.16643i	−0.0168581	−	0.0378638i
$950$	16.9869	+	28.3839i	0.551128	+	0.920896i
$951$	−44.7243	−	14.5318i	−1.45029	−	0.471226i
$952$	19.4397	−	6.29711i	0.630043	−	0.204090i
$953$	−10.7944	−	1.70967i	−0.349665	−	0.0553815i	−0.0208684	−	0.999782i	$-0.506643\pi$
$953$	−10.7944	−	1.70967i	−0.349665	−	0.0553815i	−0.328797	+	0.944401i	$0.606643\pi$
$954$	−7.72487	−	0.811917i	−0.250102	−	0.0262868i
$955$	21.5183	−	16.7815i	0.696315	−	0.543035i
$956$	4.40009	−	7.62117i	0.142309	−	0.246486i
$957$	0.601707	−	0.209756i	0.0194504	−	0.00678046i
$958$	4.26192	−	4.26192i	0.137696	−	0.137696i
$959$	37.6296	−	5.92545i	1.21512	−	0.191343i
$960$	−4.26984	−	2.57070i	−0.137809	−	0.0829689i
$961$	−17.2108	−	7.66276i	−0.555188	−	0.247186i
$962$	−0.576620	+	11.0026i	−0.0185910	+	0.354737i
$963$	−1.06901	+	20.3980i	−0.0344485	+	0.657317i
$964$	−3.23440	−	1.44005i	−0.104173	−	0.0463809i
$965$	−8.23109	−	4.95560i	−0.264968	−	0.159526i
$966$	17.4424	−	45.3179i	0.561201	−	1.45808i
$967$	−3.03736	+	3.03736i	−0.0976748	+	0.0976748i	−0.754256	−	0.656581i	$-0.772002\pi$
$967$	−3.03736	+	3.03736i	−0.0976748	+	0.0976748i	0.656581	+	0.754256i	$0.272002\pi$
$968$	−3.29629	−	10.4945i	−0.105947	−	0.337306i
$969$	−56.9439	+	98.6297i	−1.82930	+	3.16844i
$970$	−15.0766	+	11.7578i	−0.484081	+	0.377520i
$971$	−18.4674	−	1.94101i	−0.592649	−	0.0622899i	−0.196544	−	0.980495i	$-0.562972\pi$
$971$	−18.4674	−	1.94101i	−0.592649	−	0.0622899i	−0.396105	+	0.918205i	$0.629638\pi$
$972$	−17.4686	−	2.76675i	−0.560305	−	0.0887436i
$973$	5.48853	−	6.08468i	0.175954	−	0.195066i
$974$	26.2703	+	8.53573i	0.841754	+	0.273502i
$975$	−13.3009	−	3.34115i	−0.425969	−	0.107002i
$976$	4.32494	+	9.71397i	0.138438	+	0.310937i
$977$	17.0278	−	11.0580i	0.544769	−	0.353777i	−0.242729	−	0.970094i	$-0.578043\pi$
$977$	17.0278	−	11.0580i	0.544769	−	0.353777i	0.787498	+	0.616317i	$0.211376\pi$
$978$	42.3445	+	11.3462i	1.35403	+	0.362810i
$979$	15.4261	+	22.6830i	0.493021	+	0.724951i
$980$	0.504514	+	15.6443i	0.0161161	+	0.499740i
$981$	4.66647	+	14.3619i	0.148989	+	0.458541i
$982$	12.1166	+	14.9627i	0.386656	+	0.477480i
$983$	22.5243	+	18.2398i	0.718413	+	0.581759i	0.917268	−	0.398270i	$-0.130389\pi$
$983$	22.5243	+	18.2398i	0.718413	+	0.581759i	−0.198856	+	0.980029i	$0.563722\pi$
$984$	7.52532	−	6.77583i	0.239899	−	0.216006i
$985$	−5.86686	−	19.2502i	−0.186934	−	0.613362i
$986$	0.391316	+	0.538600i	0.0124620	+	0.0171525i
$987$	14.9096	+	25.8776i	0.474578	+	0.823694i
$988$	−3.69600	+	7.25381i	−0.117585	+	0.230774i
$989$	24.4571	−	14.1203i	0.777692	−	0.449001i
$990$	6.66422	+	12.9849i	0.211803	+	0.412686i
$991$	−23.4967	+	40.6974i	−0.746396	+	1.29280i	0.203144	+	0.979149i	$0.434884\pi$
$991$	−23.4967	+	40.6974i	−0.746396	+	1.29280i	−0.949540	+	0.313647i	$0.898449\pi$
$992$	7.05004	−	0.369477i	0.223839	−	0.0117309i
$993$	64.9282	−	10.2836i	2.06044	−	0.326341i
$994$	29.3017	+	1.56192i	0.929394	+	0.0495412i
$995$	29.7990	+	47.7819i	0.944692	+	1.51479i
$996$	6.40564	−	1.36156i	0.202970	−	0.0431427i
$997$	5.82587	−	7.19435i	0.184507	−	0.227847i	−0.676497	−	0.736445i	$-0.736503\pi$
$997$	5.82587	−	7.19435i	0.184507	−	0.227847i	0.861004	+	0.508598i	$0.169836\pi$
$998$	18.1337	+	6.96086i	0.574011	+	0.220342i
$999$	13.7804	−	15.3047i	0.435992	−	0.484218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.423.29	yes	768
5.2	odd	4	inner	770.2.bv.a.577.20	yes	768
7.5	odd	6	inner	770.2.bv.a.313.44	✓	768
11.9	even	5	inner	770.2.bv.a.493.44	yes	768
35.12	even	12	inner	770.2.bv.a.467.44	yes	768
55.42	odd	20	inner	770.2.bv.a.647.44	yes	768
77.75	odd	30	inner	770.2.bv.a.383.20	yes	768
385.152	even	60	inner	770.2.bv.a.537.29	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.313.44	✓	768	7.5	odd	6	inner
770.2.bv.a.383.20	yes	768	77.75	odd	30	inner
770.2.bv.a.423.29	yes	768	1.1	even	1	trivial
770.2.bv.a.467.44	yes	768	35.12	even	12	inner
770.2.bv.a.493.44	yes	768	11.9	even	5	inner
770.2.bv.a.537.29	yes	768	385.152	even	60	inner
770.2.bv.a.577.20	yes	768	5.2	odd	4	inner
770.2.bv.a.647.44	yes	768	55.42	odd	20	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0523360 + 0.998630i) q^{2} +(-0.798767 + 2.08086i) q^{3} +(-0.994522 + 0.104528i) q^{4} +(1.05151 - 1.97341i) q^{5} +(-2.11981 - 0.688769i) q^{6} +(-2.58843 + 0.547767i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-1.46252 - 1.31686i) q^{9} +O(q^{10})\)	\(q+(0.0523360 + 0.998630i) q^{2} +(-0.798767 + 2.08086i) q^{3} +(-0.994522 + 0.104528i) q^{4} +(1.05151 - 1.97341i) q^{5} +(-2.11981 - 0.688769i) q^{6} +(-2.58843 + 0.547767i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-1.46252 - 1.31686i) q^{9} +(2.02573 + 0.946785i) q^{10} +(-3.30764 + 0.243981i) q^{11} +(0.576883 - 2.15296i) q^{12} +(-1.09645 - 0.558667i) q^{13} +(-0.682484 - 2.55621i) q^{14} +(3.26647 + 3.76433i) q^{15} +(0.978148 - 0.207912i) q^{16} +(0.404210 - 7.71279i) q^{17} +(1.23851 - 1.52943i) q^{18} +(-0.691534 + 6.57950i) q^{19} +(-0.839469 + 2.07251i) q^{20} +(0.927724 - 5.82369i) q^{21} +(-0.416755 - 3.29034i) q^{22} +(2.13119 - 7.95372i) q^{23} +(2.18020 + 0.463415i) q^{24} +(-2.78867 - 4.15010i) q^{25} +(0.500518 - 1.12418i) q^{26} +(-2.04950 + 1.04427i) q^{27} +(2.51699 - 0.815331i) q^{28} +(0.0506664 + 0.0697363i) q^{29} +(-3.58822 + 3.45901i) q^{30} +(1.46780 - 6.90545i) q^{31} +(0.258819 + 0.965926i) q^{32} +(2.13434 - 7.07762i) q^{33} +7.72338 q^{34} +(-1.64078 + 5.68400i) q^{35} +(1.59215 + 1.15677i) q^{36} +(-8.35863 + 3.20858i) q^{37} +(-6.60668 - 0.346241i) q^{38} +(2.03831 - 1.83531i) q^{39} +(-2.11360 - 0.729852i) q^{40} +(2.67042 - 3.67551i) q^{41} +(5.86426 + 0.621664i) q^{42} +(2.42512 + 2.42512i) q^{43} +(3.26402 - 0.588387i) q^{44} +(-4.13654 + 1.50146i) q^{45} +(8.05436 + 1.71201i) q^{46} +(-3.93579 + 3.18714i) q^{47} +(-0.348677 + 2.20146i) q^{48} +(6.39990 - 2.83571i) q^{49} +(3.99846 - 3.00205i) q^{50} +(15.7264 + 7.00183i) q^{51} +(1.14884 + 0.440997i) q^{52} +(-2.14960 - 3.31010i) q^{53} +(-1.15010 - 1.99204i) q^{54} +(-2.99653 + 6.78386i) q^{55} +(0.945942 + 2.47087i) q^{56} +(-13.1387 - 6.69448i) q^{57} +(-0.0669891 + 0.0542467i) q^{58} +(-0.587019 - 5.58511i) q^{59} +(-3.64206 - 3.40227i) q^{60} +(2.21078 + 10.4009i) q^{61} +(6.97280 + 1.10438i) q^{62} +(4.50695 + 2.60746i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-2.25540 + 1.57629i) q^{65} +(7.17962 + 1.76100i) q^{66} +(-3.22223 - 12.0255i) q^{67} +(0.404210 + 7.71279i) q^{68} +(14.8483 + 10.7879i) q^{69} +(-5.76208 - 1.34105i) q^{70} +(-3.42723 + 10.5479i) q^{71} +(-1.07185 + 1.65051i) q^{72} +(0.806350 + 0.652969i) q^{73} +(-3.64164 - 8.17925i) q^{74} +(10.8633 - 2.48786i) q^{75} -6.61574i q^{76} +(8.42793 - 2.44334i) q^{77} +(1.93947 + 1.93947i) q^{78} +(1.17312 + 1.05628i) q^{79} +(0.618234 - 2.14890i) q^{80} +(-1.15305 - 10.9705i) q^{81} +(3.81024 + 2.47440i) q^{82} +(1.33387 + 2.61787i) q^{83} +(-0.313900 + 5.88876i) q^{84} +(-14.7954 - 8.90772i) q^{85} +(-2.29488 + 2.54872i) q^{86} +(-0.185582 + 0.0497266i) q^{87} +(0.758406 + 3.22875i) q^{88} +(-4.13544 - 7.16280i) q^{89} +(-1.71589 - 4.05229i) q^{90} +(3.14409 + 0.845472i) q^{91} +(-1.28813 + 8.13292i) q^{92} +(13.1968 + 8.57013i) q^{93} +(-3.38876 - 3.76359i) q^{94} +(12.2569 + 8.28307i) q^{95} +(-2.21669 - 0.232984i) q^{96} +(-3.88182 + 7.61850i) q^{97} +(3.16677 + 6.24272i) q^{98} +(5.15876 + 3.99886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) \) 768 * q + 24 * q^5 + 4 * q^7	\( 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) \) 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

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