LMFDB - Embedded newform 465.2.k.a.32.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [465,2,Mod(32,465)] 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("465.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(465, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,0,0,0,0,-4,0,0,0,-32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			32.9
Character	$\chi$	$=$	465.32
Dual form			465.2.k.a.218.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.04043 + 1.04043i) q^{2} +(0.828268 + 1.52117i) q^{3} -0.164984i q^{4} +(-0.204789 - 2.22667i) q^{5} +(-2.44443 - 0.720921i) q^{6} +(-1.82623 - 1.82623i) q^{7} +(-1.90920 - 1.90920i) q^{8} +(-1.62795 + 2.51988i) q^{9} +(2.52976 + 2.10362i) q^{10} -5.69997i q^{11} +(0.250969 - 0.136651i) q^{12} +(4.14610 - 4.14610i) q^{13} +3.80013 q^{14} +(3.21754 - 2.15580i) q^{15} +4.30275 q^{16} +(0.349849 - 0.349849i) q^{17} +(-0.927994 - 4.31552i) q^{18} +4.02199i q^{19} +(-0.367365 + 0.0337869i) q^{20} +(1.26541 - 4.29062i) q^{21} +(5.93041 + 5.93041i) q^{22} +(-3.77007 - 3.77007i) q^{23} +(1.32290 - 4.48556i) q^{24} +(-4.91612 + 0.911995i) q^{25} +8.62745i q^{26} +(-5.18155 - 0.389255i) q^{27} +(-0.301299 + 0.301299i) q^{28} -4.44138 q^{29} +(-1.10466 + 5.59057i) q^{30} +1.00000 q^{31} +(-0.658296 + 0.658296i) q^{32} +(8.67065 - 4.72110i) q^{33} +0.727986i q^{34} +(-3.69242 + 4.44041i) q^{35} +(0.415740 + 0.268585i) q^{36} +(-2.31485 - 2.31485i) q^{37} +(-4.18460 - 4.18460i) q^{38} +(9.74103 + 2.87286i) q^{39} +(-3.86018 + 4.64215i) q^{40} +7.89322i q^{41} +(3.14752 + 5.78066i) q^{42} +(-3.86457 + 3.86457i) q^{43} -0.940404 q^{44} +(5.94433 + 3.10885i) q^{45} +7.84498 q^{46} +(7.41618 - 7.41618i) q^{47} +(3.56383 + 6.54523i) q^{48} -0.329760i q^{49} +(4.16601 - 6.06374i) q^{50} +(0.821950 + 0.242413i) q^{51} +(-0.684040 - 0.684040i) q^{52} +(-2.50032 - 2.50032i) q^{53} +(5.79603 - 4.98604i) q^{54} +(-12.6920 + 1.16729i) q^{55} +6.97329i q^{56} +(-6.11815 + 3.33129i) q^{57} +(4.62094 - 4.62094i) q^{58} +6.80022 q^{59} +(-0.355672 - 0.530842i) q^{60} +11.1169 q^{61} +(-1.04043 + 1.04043i) q^{62} +(7.57489 - 1.62888i) q^{63} +7.23568i q^{64} +(-10.0811 - 8.38293i) q^{65} +(-4.10923 + 13.9332i) q^{66} +(-5.48050 - 5.48050i) q^{67} +(-0.0577195 - 0.0577195i) q^{68} +(2.61231 - 8.85756i) q^{69} +(-0.778224 - 8.46163i) q^{70} +1.37150i q^{71} +(7.91904 - 1.70288i) q^{72} +(4.49182 - 4.49182i) q^{73} +4.81688 q^{74} +(-5.45917 - 6.72291i) q^{75} +0.663564 q^{76} +(-10.4095 + 10.4095i) q^{77} +(-13.1239 + 7.14583i) q^{78} -0.679232i q^{79} +(-0.881155 - 9.58080i) q^{80} +(-3.69959 - 8.20445i) q^{81} +(-8.21233 - 8.21233i) q^{82} +(-6.41272 - 6.41272i) q^{83} +(-0.707884 - 0.208772i) q^{84} +(-0.850644 - 0.707353i) q^{85} -8.04162i q^{86} +(-3.67865 - 6.75612i) q^{87} +(-10.8824 + 10.8824i) q^{88} +8.86891 q^{89} +(-9.41919 + 2.95011i) q^{90} -15.1435 q^{91} +(-0.622001 + 0.622001i) q^{92} +(0.828268 + 1.52117i) q^{93} +15.4320i q^{94} +(8.95565 - 0.823659i) q^{95} +(-1.54663 - 0.456138i) q^{96} +(7.46117 + 7.46117i) q^{97} +(0.343092 + 0.343092i) q^{98} +(14.3632 + 9.27924i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 4 q^{6} - 32 q^{10} + 4 q^{13} + 20 q^{15} - 60 q^{16} - 46 q^{18} - 4 q^{21} + 8 q^{22} - 8 q^{25} - 6 q^{27} + 112 q^{28} + 54 q^{30} + 60 q^{31} - 30 q^{33} - 4 q^{36} - 36 q^{37} - 36 q^{40}+ \cdots - 8 q^{97}+O(q^{100}) $ 60 * q - 4 * q^6 - 32 * q^10 + 4 * q^13 + 20 * q^15 - 60 * q^16 - 46 * q^18 - 4 * q^21 + 8 * q^22 - 8 * q^25 - 6 * q^27 + 112 * q^28 + 54 * q^30 + 60 * q^31 - 30 * q^33 - 4 * q^36 - 36 * q^37 - 36 * q^40 + 44 * q^42 + 16 * q^43 + 14 * q^45 + 40 * q^46 - 104 * q^48 - 48 * q^51 - 12 * q^52 - 48 * q^55 + 42 * q^57 + 80 * q^58 + 60 * q^60 - 8 * q^61 - 10 * q^63 - 24 * q^66 - 88 * q^67 - 84 * q^70 + 84 * q^72 + 60 * q^73 + 14 * q^75 + 72 * q^76 - 152 * q^78 - 132 * q^81 - 60 * q^82 - 16 * q^85 + 34 * q^87 + 124 * q^88 + 190 * q^90 + 64 * q^91 - 88 * q^96 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−1.04043	+	1.04043i	−0.735694	+	0.735694i	−0.971742	−	0.236047i	$-0.924148\pi$
$2$	−1.04043	+	1.04043i	−0.735694	+	0.735694i	0.236047	+	0.971742i	$0.424148\pi$
$3$	0.828268	+	1.52117i	0.478201	+	0.878251i
$3$	0.828268	+	1.52117i	0.478201	+	0.878251i
$4$		−	0.164984i		−	0.0824920i
$5$	−0.204789	−	2.22667i	−0.0915844	−	0.995797i
$5$	−0.204789	−	2.22667i	−0.0915844	−	0.995797i
$6$	−2.44443	−	0.720921i	−0.997933	−	0.294315i
$7$	−1.82623	−	1.82623i	−0.690250	−	0.690250i	0.272036	−	0.962287i	$-0.412303\pi$
$7$	−1.82623	−	1.82623i	−0.690250	−	0.690250i	−0.962287	+	0.272036i	$0.912303\pi$
$8$	−1.90920	−	1.90920i	−0.675005	−	0.675005i
$9$	−1.62795	+	2.51988i	−0.542648	+	0.839960i
$10$	2.52976	+	2.10362i	0.799980	+	0.665224i
$11$		−	5.69997i		−	1.71861i	−0.511467	−	0.859303i	$-0.670898\pi$
$11$		−	5.69997i		−	1.71861i	0.511467	−	0.859303i	$-0.329102\pi$
$12$	0.250969	−	0.136651i	0.0724486	−	0.0394477i
$13$	4.14610	−	4.14610i	1.14992	−	1.14992i	0.163354	−	0.986568i	$-0.447769\pi$
$13$	4.14610	−	4.14610i	1.14992	−	1.14992i	0.986568	−	0.163354i	$-0.0522313\pi$
$14$	3.80013			1.01563
$15$	3.21754	−	2.15580i	0.830764	−	0.556625i
$16$	4.30275			1.07569
$17$	0.349849	−	0.349849i	0.0848509	−	0.0848509i	−0.663407	−	0.748258i	$-0.730890\pi$
$17$	0.349849	−	0.349849i	0.0848509	−	0.0848509i	0.748258	+	0.663407i	$0.230890\pi$
$18$	−0.927994	−	4.31552i	−0.218730	−	1.01718i
$19$			4.02199i			0.922708i	0.887216	+	0.461354i	$0.152636\pi$
$19$			4.02199i			0.922708i	−0.887216	+	0.461354i	$0.847364\pi$
$20$	−0.367365	+	0.0337869i	−0.0821453	+	0.00755498i
$21$	1.26541	−	4.29062i	0.276135	−	0.936291i
$22$	5.93041	+	5.93041i	1.26437	+	1.26437i
$23$	−3.77007	−	3.77007i	−0.786114	−	0.786114i	0.194741	−	0.980855i	$-0.437613\pi$
$23$	−3.77007	−	3.77007i	−0.786114	−	0.786114i	−0.980855	+	0.194741i	$0.937613\pi$
$24$	1.32290	−	4.48556i	0.270036	−	0.915612i
$25$	−4.91612	+	0.911995i	−0.983225	+	0.182399i
$26$			8.62745i			1.69198i
$27$	−5.18155	−	0.389255i	−0.997190	−	0.0749121i
$28$	−0.301299	+	0.301299i	−0.0569401	+	0.0569401i
$29$	−4.44138			−0.824744			−0.412372	−	0.911016i	$-0.635300\pi$
$29$	−4.44138			−0.824744			−0.412372	+	0.911016i	$0.635300\pi$
$30$	−1.10466	+	5.59057i	−0.201683	+	1.02069i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−0.658296	+	0.658296i	−0.116371	+	0.116371i
$33$	8.67065	−	4.72110i	1.50937	−	0.821838i
$34$			0.727986i			0.124849i
$35$	−3.69242	+	4.44041i	−0.624133	+	0.750566i
$36$	0.415740	+	0.268585i	0.0692900	+	0.0447642i
$37$	−2.31485	−	2.31485i	−0.380559	−	0.380559i	0.490744	−	0.871304i	$-0.336725\pi$
$37$	−2.31485	−	2.31485i	−0.380559	−	0.380559i	−0.871304	+	0.490744i	$0.836725\pi$
$38$	−4.18460	−	4.18460i	−0.678831	−	0.678831i
$39$	9.74103	+	2.87286i	1.55981	+	0.460026i
$40$	−3.86018	+	4.64215i	−0.610349	+	0.733988i
$41$			7.89322i			1.23271i	0.787467	+	0.616357i	$0.211392\pi$
$41$			7.89322i			1.23271i	−0.787467	+	0.616357i	$0.788608\pi$
$42$	3.14752	+	5.78066i	0.485673	+	0.891975i
$43$	−3.86457	+	3.86457i	−0.589342	+	0.589342i	−0.937453	−	0.348111i	$-0.886823\pi$
$43$	−3.86457	+	3.86457i	−0.589342	+	0.589342i	0.348111	+	0.937453i	$0.386823\pi$
$44$	−0.940404			−0.141771
$45$	5.94433	+	3.10885i	0.886128	+	0.463441i
$46$	7.84498			1.15668
$47$	7.41618	−	7.41618i	1.08176	−	1.08176i	0.0854163	−	0.996345i	$-0.472778\pi$
$47$	7.41618	−	7.41618i	1.08176	−	1.08176i	0.996345	−	0.0854163i	$-0.0272220\pi$
$48$	3.56383	+	6.54523i	0.514394	+	0.944723i
$49$		−	0.329760i		−	0.0471086i
$50$	4.16601	−	6.06374i	0.589163	−	0.857543i
$51$	0.821950	+	0.242413i	0.115096	+	0.0339446i
$52$	−0.684040	−	0.684040i	−0.0948593	−	0.0948593i
$53$	−2.50032	−	2.50032i	−0.343445	−	0.343445i	0.514216	−	0.857661i	$-0.328083\pi$
$53$	−2.50032	−	2.50032i	−0.343445	−	0.343445i	−0.857661	+	0.514216i	$0.828083\pi$
$54$	5.79603	−	4.98604i	0.788739	−	0.678515i
$55$	−12.6920	+	1.16729i	−1.71138	+	0.157397i
$56$			6.97329i			0.931845i
$57$	−6.11815	+	3.33129i	−0.810369	+	0.441240i
$58$	4.62094	−	4.62094i	0.606759	−	0.606759i
$59$	6.80022			0.885313			0.442656	−	0.896691i	$-0.354036\pi$
$59$	6.80022			0.885313			0.442656	+	0.896691i	$0.354036\pi$
$60$	−0.355672	−	0.530842i	−0.0459171	−	0.0685314i
$61$	11.1169			1.42337			0.711686	−	0.702498i	$-0.247932\pi$
$61$	11.1169			1.42337			0.711686	+	0.702498i	$0.247932\pi$
$62$	−1.04043	+	1.04043i	−0.132135	+	0.132135i
$63$	7.57489	−	1.62888i	0.954346	−	0.205219i
$64$			7.23568i			0.904460i
$65$	−10.0811	−	8.38293i	−1.25040	−	1.03977i
$66$	−4.10923	+	13.9332i	−0.505811	+	1.71505i
$67$	−5.48050	−	5.48050i	−0.669550	−	0.669550i	0.288062	−	0.957612i	$-0.406989\pi$
$67$	−5.48050	−	5.48050i	−0.669550	−	0.669550i	−0.957612	+	0.288062i	$0.906989\pi$
$68$	−0.0577195	−	0.0577195i	−0.00699952	−	0.00699952i
$69$	2.61231	−	8.85756i	0.314485	−	1.06633i
$70$	−0.778224	−	8.46163i	−0.0930155	−	1.01136i
$71$			1.37150i			0.162767i	0.996683	+	0.0813833i	$0.0259338\pi$
$71$			1.37150i			0.162767i	−0.996683	+	0.0813833i	$0.974066\pi$
$72$	7.91904	−	1.70288i	0.933268	−	0.200687i
$73$	4.49182	−	4.49182i	0.525728	−	0.525728i	−0.393568	−	0.919296i	$-0.628759\pi$
$73$	4.49182	−	4.49182i	0.525728	−	0.525728i	0.919296	+	0.393568i	$0.128759\pi$
$74$	4.81688			0.559951
$75$	−5.45917	−	6.72291i	−0.630371	−	0.776294i
$76$	0.663564			0.0761160
$77$	−10.4095	+	10.4095i	−1.18627	+	1.18627i
$78$	−13.1239	+	7.14583i	−1.48598	+	0.809106i
$79$		−	0.679232i		−	0.0764196i	−0.999270	−	0.0382098i	$-0.987834\pi$
$79$		−	0.679232i		−	0.0764196i	0.999270	−	0.0382098i	$-0.0121655\pi$
$80$	−0.881155	−	9.58080i	−0.0985161	−	1.07117i
$81$	−3.69959	−	8.20445i	−0.411065	−	0.911606i
$82$	−8.21233	−	8.21233i	−0.906900	−	0.906900i
$83$	−6.41272	−	6.41272i	−0.703887	−	0.703887i	0.261355	−	0.965243i	$-0.415831\pi$
$83$	−6.41272	−	6.41272i	−0.703887	−	0.703887i	−0.965243	+	0.261355i	$0.915831\pi$
$84$	−0.707884	−	0.208772i	−0.0772365	−	0.0227789i
$85$	−0.850644	−	0.707353i	−0.0922653	−	0.0767233i
$86$		−	8.04162i		−	0.867150i
$87$	−3.67865	−	6.75612i	−0.394393	−	0.724332i
$88$	−10.8824	+	10.8824i	−1.16007	+	1.16007i
$89$	8.86891			0.940102			0.470051	−	0.882639i	$-0.344235\pi$
$89$	8.86891			0.940102			0.470051	+	0.882639i	$0.344235\pi$
$90$	−9.41919	+	2.95011i	−0.992870	+	0.310969i
$91$	−15.1435			−1.58747
$92$	−0.622001	+	0.622001i	−0.0648481	+	0.0648481i
$93$	0.828268	+	1.52117i	0.0858874	+	0.157738i
$94$			15.4320i			1.59169i
$95$	8.95565	−	0.823659i	0.918830	−	0.0845056i
$96$	−1.54663	−	0.456138i	−0.157852	−	0.0465544i
$97$	7.46117	+	7.46117i	0.757567	+	0.757567i	0.975879	−	0.218312i	$-0.0700551\pi$
$97$	7.46117	+	7.46117i	0.757567	+	0.757567i	−0.218312	+	0.975879i	$0.570055\pi$
$98$	0.343092	+	0.343092i	0.0346575	+	0.0346575i
$99$	14.3632	+	9.27924i	1.44356	+	0.932599i
$100$	0.150465	+	0.811082i	0.0150465	+	0.0811082i
$101$			2.26929i			0.225802i	0.993606	+	0.112901i	$0.0360143\pi$
$101$			2.26929i			0.225802i	−0.993606	+	0.112901i	$0.963986\pi$
$102$	−1.10739	+	0.602967i	−0.109648	+	0.0597027i
$103$	8.37230	−	8.37230i	0.824947	−	0.824947i	−0.161866	−	0.986813i	$-0.551751\pi$
$103$	8.37230	−	8.37230i	0.824947	−	0.824947i	0.986813	+	0.161866i	$0.0517512\pi$
$104$	−15.8315			−1.55241
$105$	−9.81295	−	1.93898i	−0.957646	−	0.189225i
$106$	5.20281			0.505342
$107$	−10.6567	+	10.6567i	−1.03022	+	1.03022i	−0.0306958	+	0.999529i	$0.509772\pi$
$107$	−10.6567	+	10.6567i	−1.03022	+	1.03022i	−0.999529	+	0.0306958i	$0.990228\pi$
$108$	−0.0642208	+	0.854873i	−0.00617965	+	0.0822602i
$109$		−	3.33299i		−	0.319242i	−0.987178	−	0.159621i	$-0.948973\pi$
$109$		−	3.33299i		−	0.319242i	0.987178	−	0.159621i	$-0.0510273\pi$
$110$	11.9906	−	14.4196i	1.14326	−	1.37485i
$111$	1.60398	−	5.43861i	0.152243	−	0.516210i
$112$	−7.85781	−	7.85781i	−0.742493	−	0.742493i
$113$	11.2546	+	11.2546i	1.05874	+	1.05874i	0.998163	+	0.0605812i	$0.0192954\pi$
$113$	11.2546	+	11.2546i	1.05874	+	1.05874i	0.0605812	+	0.998163i	$0.480705\pi$
$114$	2.89954	−	9.83147i	0.271566	−	0.920801i
$115$	−7.62264	+	9.16677i	−0.710814	+	0.854806i
$116$			0.732757i			0.0680348i
$117$	3.69805	+	17.1973i	0.341885	+	1.58989i
$118$	−7.07514	+	7.07514i	−0.651319	+	0.651319i
$119$	−1.27781			−0.117137
$120$	−10.2588	−	2.02707i	−0.936495	−	0.185045i
$121$	−21.4897			−1.95361
$122$	−11.5663	+	11.5663i	−1.04717	+	1.04717i
$123$	−12.0070	+	6.53770i	−1.08263	+	0.589484i
$124$		−	0.164984i		−	0.0148160i
$125$	3.03748	+	10.7598i	0.271680	+	0.962388i
$126$	−6.18640	+	9.57586i	−0.551128	+	0.853086i
$127$	−8.75060	−	8.75060i	−0.776491	−	0.776491i	0.202742	−	0.979232i	$-0.435015\pi$
$127$	−8.75060	−	8.75060i	−0.776491	−	0.776491i	−0.979232	+	0.202742i	$0.935015\pi$
$128$	−8.84480	−	8.84480i	−0.781777	−	0.781777i
$129$	−9.07959	−	2.67779i	−0.799413	−	0.235766i
$130$	19.2105	−	1.76680i	1.68487	−	0.154959i
$131$		−	0.153224i		−	0.0133872i	−0.999978	−	0.00669361i	$-0.997869\pi$
$131$		−	0.153224i		−	0.0133872i	0.999978	−	0.00669361i	$-0.00213066\pi$
$132$	−0.778906	−	1.43052i	−0.0677951	−	0.124511i
$133$	7.34509	−	7.34509i	0.636900	−	0.636900i
$134$	11.4041			0.985168
$135$	0.194382	+	11.6173i	0.0167297	+	0.999860i
$136$	−1.33587			−0.114550
$137$	6.14227	−	6.14227i	0.524770	−	0.524770i	−0.394238	−	0.919008i	$-0.628992\pi$
$137$	6.14227	−	6.14227i	0.524770	−	0.524770i	0.919008	+	0.394238i	$0.128992\pi$
$138$	6.49774	+	11.9336i	0.553125	+	1.01585i
$139$		−	13.7149i		−	1.16329i	−0.813444	−	0.581643i	$-0.802410\pi$
$139$		−	13.7149i		−	1.16329i	0.813444	−	0.581643i	$-0.197590\pi$
$140$	0.732596	+	0.609191i	0.0619157	+	0.0514860i
$141$	17.4239	+	5.13873i	1.46736	+	0.432759i
$142$	−1.42694	−	1.42694i	−0.119746	−	0.119746i
$143$	−23.6327	−	23.6327i	−1.97626	−	1.97626i
$144$	−7.00464	+	10.8424i	−0.583720	+	0.903534i
$145$	0.909546	+	9.88949i	0.0755336	+	0.821278i
$146$			9.34684i			0.773550i
$147$	0.501623	−	0.273130i	0.0413732	−	0.0225274i
$148$	−0.381914	+	0.381914i	−0.0313931	+	0.0313931i
$149$	−7.21546			−0.591114			−0.295557	−	0.955325i	$-0.595505\pi$
$149$	−7.21546			−0.591114			−0.295557	+	0.955325i	$0.595505\pi$
$150$	12.6746	+	1.31483i	1.03488	+	0.107355i
$151$	5.03037			0.409366			0.204683	−	0.978828i	$-0.434384\pi$
$151$	5.03037			0.409366			0.204683	+	0.978828i	$0.434384\pi$
$152$	7.67880	−	7.67880i	0.622833	−	0.622833i
$153$	0.312042	+	1.45111i	0.0252271	+	0.117316i
$154$		−	21.6606i		−	1.74546i
$155$	−0.204789	−	2.22667i	−0.0164490	−	0.178850i
$156$	0.473976	−	1.60711i	0.0379485	−	0.128672i
$157$	−0.117792	−	0.117792i	−0.00940082	−	0.00940082i	0.702391	−	0.711792i	$-0.252116\pi$
$157$	−0.117792	−	0.117792i	−0.00940082	−	0.00940082i	−0.711792	+	0.702391i	$0.752116\pi$
$158$	0.706693	+	0.706693i	0.0562215	+	0.0562215i
$159$	1.73249	−	5.87436i	0.137395	−	0.465867i
$160$	1.60062	+	1.33100i	0.126540	+	0.105225i
$161$			13.7700i			1.08523i
$162$	12.3853	+	4.68699i	0.973082	+	0.368245i
$163$	0.0734366	−	0.0734366i	0.00575200	−	0.00575200i	−0.704225	−	0.709977i	$-0.748705\pi$
$163$	0.0734366	−	0.0734366i	0.00575200	−	0.00575200i	0.709977	+	0.704225i	$0.248705\pi$
$164$	1.30225			0.101689
$165$	−12.2880	−	18.3399i	−0.956619	−	1.42776i
$166$	13.3440			1.03569
$167$	−13.3273	+	13.3273i	−1.03130	+	1.03130i	−0.0318041	+	0.999494i	$0.510125\pi$
$167$	−13.3273	+	13.3273i	−1.03130	+	1.03130i	−0.999494	+	0.0318041i	$0.989875\pi$
$168$	−10.6076	+	5.77575i	−0.818394	+	0.445609i
$169$		−	21.3803i		−	1.64464i
$170$	1.62099	−	0.149083i	0.124324	−	0.0114342i
$171$	−10.1349	−	6.54758i	−0.775038	−	0.500706i
$172$	0.637592	+	0.637592i	0.0486160	+	0.0486160i
$173$	17.1936	+	17.1936i	1.30721	+	1.30721i	0.923422	+	0.383787i	$0.125380\pi$
$173$	17.1936	+	17.1936i	1.30721	+	1.30721i	0.383787	+	0.923422i	$0.374620\pi$
$174$	10.8566	+	3.20188i	0.823039	+	0.242734i
$175$	10.6435	+	7.31246i	0.804572	+	0.552770i
$176$		−	24.5255i		−	1.84868i
$177$	5.63240	+	10.3443i	0.423357	+	0.777527i
$178$	−9.22747	+	9.22747i	−0.691628	+	0.691628i
$179$	−5.15771			−0.385505			−0.192753	−	0.981247i	$-0.561741\pi$
$179$	−5.15771			−0.385505			−0.192753	+	0.981247i	$0.561741\pi$
$180$	0.512911	−	0.980719i	0.0382301	−	0.0730985i
$181$	5.24583			0.389919			0.194960	−	0.980811i	$-0.437542\pi$
$181$	5.24583			0.389919			0.194960	+	0.980811i	$0.437542\pi$
$182$	15.7557	−	15.7557i	1.16789	−	1.16789i
$183$	9.20775	+	16.9107i	0.680657	+	1.25008i
$184$			14.3957i			1.06126i
$185$	−4.68036	+	5.62847i	−0.344107	+	0.413813i
$186$	−2.44443	−	0.720921i	−0.179234	−	0.0528605i
$187$	−1.99413	−	1.99413i	−0.145825	−	0.145825i
$188$	−1.22355	−	1.22355i	−0.0892367	−	0.0892367i
$189$	8.75184	+	10.1736i	0.636603	+	0.740019i
$190$	−8.46076	+	10.1747i	−0.613808	+	0.738148i
$191$		−	13.0264i		−	0.942556i	−0.881985	−	0.471278i	$-0.843793\pi$
$191$		−	13.0264i		−	0.942556i	0.881985	−	0.471278i	$-0.156207\pi$
$192$	−11.0067	+	5.99308i	−0.794342	+	0.432513i
$193$	−2.48322	+	2.48322i	−0.178746	+	0.178746i	−0.790809	−	0.612063i	$-0.790340\pi$
$193$	−2.48322	+	2.48322i	−0.178746	+	0.178746i	0.612063	+	0.790809i	$0.290340\pi$
$194$	−15.5256			−1.11468
$195$	4.40207	−	22.2784i	0.315239	−	1.59539i
$196$	−0.0544052			−0.00388608
$197$	−9.14100	+	9.14100i	−0.651269	+	0.651269i	−0.953299	−	0.302030i	$-0.902336\pi$
$197$	−9.14100	+	9.14100i	−0.651269	+	0.651269i	0.302030	+	0.953299i	$0.402336\pi$
$198$	−24.5983	+	5.28954i	−1.74813	+	0.375911i
$199$		−	3.96835i		−	0.281309i	−0.990059	−	0.140655i	$-0.955079\pi$
$199$		−	3.96835i		−	0.281309i	0.990059	−	0.140655i	$-0.0449207\pi$
$200$	11.1271	+	7.64470i	0.786802	+	0.540562i
$201$	3.79748	−	12.8761i	0.267854	−	0.908212i
$202$	−2.36103	−	2.36103i	−0.166121	−	0.166121i
$203$	8.11099	+	8.11099i	0.569280	+	0.569280i
$204$	0.0399943	−	0.135609i	0.00280016	−	0.00949450i
$205$	17.5756	−	1.61644i	1.22753	−	0.112897i
$206$			17.4216i			1.21382i
$207$	15.6376	−	3.36265i	1.08689	−	0.233721i
$208$	17.8396	−	17.8396i	1.23696	−	1.23696i
$209$	22.9252			1.58577
$210$	12.2270	−	8.19231i	0.843746	−	0.565323i
$211$	9.27403			0.638451			0.319225	−	0.947679i	$-0.396577\pi$
$211$	9.27403			0.638451			0.319225	+	0.947679i	$0.396577\pi$
$212$	−0.412513	+	0.412513i	−0.0283315	+	0.0283315i
$213$	−2.08628	+	1.13597i	−0.142950	+	0.0778351i
$214$		−	22.1751i		−	1.51586i
$215$	9.39655	+	7.81371i	0.640839	+	0.532890i
$216$	9.14947	+	10.6358i	0.622543	+	0.723675i
$217$	−1.82623	−	1.82623i	−0.123973	−	0.123973i
$218$	3.46774	+	3.46774i	0.234865	+	0.234865i
$219$	10.5533	+	3.11242i	0.713124	+	0.210318i
$220$	0.192584	+	2.09397i	0.0129840	+	0.141175i
$221$		−	2.90102i		−	0.195144i
$222$	3.98966	+	7.32731i	0.267769	+	0.491777i
$223$	13.0559	−	13.0559i	0.874287	−	0.874287i	−0.118650	−	0.992936i	$-0.537857\pi$
$223$	13.0559	−	13.0559i	0.874287	−	0.874287i	0.992936	+	0.118650i	$0.0378565\pi$
$224$	2.40440			0.160651
$225$	5.70506	−	13.8727i	0.380338	−	0.924848i
$226$	−23.4192			−1.55782
$227$	−8.43652	+	8.43652i	−0.559952	+	0.559952i	−0.929294	−	0.369342i	$-0.879583\pi$
$227$	−8.43652	+	8.43652i	−0.559952	+	0.559952i	0.369342	+	0.929294i	$0.379583\pi$
$228$	0.549609	+	1.00940i	0.0363987	+	0.0668490i
$229$			10.2675i			0.678496i	0.940697	+	0.339248i	$0.110173\pi$
$229$			10.2675i			0.678496i	−0.940697	+	0.339248i	$0.889827\pi$
$230$	−1.60656	−	17.4682i	−0.105934	−	1.15182i
$231$	−24.4564	−	7.21279i	−1.60912	−	0.474567i
$232$	8.47950	+	8.47950i	0.556707	+	0.556707i
$233$	−4.12263	−	4.12263i	−0.270082	−	0.270082i	0.559051	−	0.829133i	$-0.311166\pi$
$233$	−4.12263	−	4.12263i	−0.270082	−	0.270082i	−0.829133	+	0.559051i	$0.811166\pi$
$234$	−21.7401	−	14.0450i	−1.42120	−	0.918151i
$235$	−18.0322	−	14.9946i	−1.17629	−	0.978143i
$236$		−	1.12193i		−	0.0730312i
$237$	1.03323	−	0.562586i	0.0671156	−	0.0365439i
$238$	1.32947	−	1.32947i	0.0861768	−	0.0861768i
$239$	−8.29796			−0.536750			−0.268375	−	0.963314i	$-0.586487\pi$
$239$	−8.29796			−0.536750			−0.268375	+	0.963314i	$0.586487\pi$
$240$	13.8442	−	9.27586i	0.893642	−	0.598754i
$241$	26.0155			1.67581			0.837903	−	0.545819i	$-0.183781\pi$
$241$	26.0155			1.67581			0.837903	+	0.545819i	$0.183781\pi$
$242$	22.3585	−	22.3585i	1.43726	−	1.43726i
$243$	9.41616	−	12.4232i	0.604047	−	0.796949i
$244$		−	1.83411i		−	0.117417i
$245$	−0.734268	+	0.0675313i	−0.0469107	+	0.00431441i
$246$	5.69038	−	19.2944i	0.362806	−	1.23017i
$247$	16.6756	+	16.6756i	1.06104	+	1.06104i
$248$	−1.90920	−	1.90920i	−0.121235	−	0.121235i
$249$	4.44342	−	15.0663i	0.281590	−	0.954789i
$250$	−14.3551	−	8.03455i	−0.907897	−	0.508149i
$251$			22.9451i			1.44828i	0.689651	+	0.724142i	$0.257764\pi$
$251$			22.9451i			1.44828i	−0.689651	+	0.724142i	$0.742236\pi$
$252$	−0.268739	−	1.24973i	−0.0169290	−	0.0787259i
$253$	−21.4893	+	21.4893i	−1.35102	+	1.35102i
$254$	18.2088			1.14252
$255$	0.371447	−	1.87986i	0.0232609	−	0.117721i
$256$	3.93341			0.245838
$257$	21.2929	−	21.2929i	1.32822	−	1.32822i	0.421292	−	0.906925i	$-0.361577\pi$
$257$	21.2929	−	21.2929i	1.32822	−	1.32822i	0.906925	−	0.421292i	$-0.138423\pi$
$258$	12.2327	−	6.66062i	0.761575	−	0.414672i
$259$			8.45491i			0.525363i
$260$	−1.38305	+	1.66322i	−0.0857730	+	0.103148i
$261$	7.23033	−	11.1917i	0.447546	−	0.692752i
$262$	0.159418	+	0.159418i	0.00984890	+	0.00984890i
$263$	4.55744	+	4.55744i	0.281024	+	0.281024i	0.833517	−	0.552493i	$-0.186324\pi$
$263$	4.55744	+	4.55744i	0.281024	+	0.281024i	−0.552493	+	0.833517i	$0.686324\pi$
$264$	−25.5676	−	7.54049i	−1.57358	−	0.464085i
$265$	−5.05535	+	6.07943i	−0.310548	+	0.373456i
$266$			15.2841i			0.937127i
$267$	7.34583	+	13.4912i	0.449557	+	0.825645i
$268$	−0.904195	+	0.904195i	−0.0552325	+	0.0552325i
$269$	−8.84874			−0.539517			−0.269759	−	0.962928i	$-0.586944\pi$
$269$	−8.84874			−0.539517			−0.269759	+	0.962928i	$0.586944\pi$
$270$	−12.2892	−	11.8848i	−0.747899	−	0.723283i
$271$	−19.2008			−1.16637			−0.583184	−	0.812340i	$-0.698193\pi$
$271$	−19.2008			−1.16637			−0.583184	+	0.812340i	$0.698193\pi$
$272$	1.50531	−	1.50531i	0.0912730	−	0.0912730i
$273$	−12.5429	−	23.0359i	−0.759128	−	1.39419i
$274$			12.7812i			0.772140i
$275$	5.19834	+	28.0218i	0.313472	+	1.68978i
$276$	−1.46136	−	0.430989i	−0.0879633	−	0.0259425i
$277$	−3.81947	−	3.81947i	−0.229490	−	0.229490i	0.582990	−	0.812480i	$-0.301883\pi$
$277$	−3.81947	−	3.81947i	−0.229490	−	0.229490i	−0.812480	+	0.582990i	$0.801883\pi$
$278$	14.2694	+	14.2694i	0.855822	+	0.855822i
$279$	−1.62795	+	2.51988i	−0.0974625	+	0.150861i
$280$	15.5272	−	1.42805i	0.927929	−	0.0853425i
$281$			6.55765i			0.391196i	0.980684	+	0.195598i	$0.0626648\pi$
$281$			6.55765i			0.391196i	−0.980684	+	0.195598i	$0.937335\pi$
$282$	−23.4748	+	12.7818i	−1.39790	+	0.761148i
$283$	3.40697	−	3.40697i	0.202523	−	0.202523i	−0.598557	−	0.801080i	$-0.704259\pi$
$283$	3.40697	−	3.40697i	0.202523	−	0.202523i	0.801080	+	0.598557i	$0.204259\pi$
$284$	0.226275			0.0134269
$285$	8.67060	+	12.9409i	0.513602	+	0.766553i
$286$	49.1762			2.90785
$287$	14.4148	−	14.4148i	0.850881	−	0.850881i
$288$	−0.587157	−	2.73050i	−0.0345986	−	0.160896i
$289$			16.7552i			0.985601i
$290$	−11.2356	−	9.34300i	−0.659779	−	0.548640i
$291$	−5.16990	+	17.5296i	−0.303065	+	1.02760i
$292$	−0.741079	−	0.741079i	−0.0433683	−	0.0433683i
$293$	−2.62772	−	2.62772i	−0.153513	−	0.153513i	0.626172	−	0.779685i	$-0.284621\pi$
$293$	−2.62772	−	2.62772i	−0.153513	−	0.153513i	−0.779685	+	0.626172i	$0.784621\pi$
$294$	−0.237731	+	0.806075i	−0.0138648	+	0.0470113i
$295$	−1.39261	−	15.1418i	−0.0810808	−	0.881592i
$296$			8.83905i			0.513759i
$297$	−2.21874	+	29.5347i	−0.128744	+	1.71378i
$298$	7.50718	−	7.50718i	0.434879	−	0.434879i
$299$	−31.2622			−1.80794
$300$	−1.10917	+	0.900675i	−0.0640381	+	0.0520005i
$301$	14.1152			0.813587
$302$	−5.23375	+	5.23375i	−0.301168	+	0.301168i
$303$	−3.45198	+	1.87958i	−0.198311	+	0.107979i
$304$			17.3056i			0.992545i
$305$	−2.27661	−	24.7536i	−0.130359	−	1.41739i
$306$	−1.83444	−	1.18512i	−0.104868	−	0.0677489i
$307$	1.25958	+	1.25958i	0.0718881	+	0.0718881i	0.742137	−	0.670249i	$-0.233813\pi$
$307$	1.25958	+	1.25958i	0.0718881	+	0.0718881i	−0.670249	+	0.742137i	$0.733813\pi$
$308$	1.71739	+	1.71739i	0.0978576	+	0.0978576i
$309$	19.6702	+	5.80122i	1.11900	+	0.330020i
$310$	2.52976	+	2.10362i	0.143681	+	0.119478i
$311$			4.39924i			0.249458i	0.992191	+	0.124729i	$0.0398061\pi$
$311$			4.39924i			0.249458i	−0.992191	+	0.124729i	$0.960194\pi$
$312$	−13.1127	−	24.0825i	−0.742362	−	1.36340i
$313$	−8.99252	+	8.99252i	−0.508287	+	0.508287i	−0.914000	−	0.405713i	$-0.867023\pi$
$313$	−8.99252	+	8.99252i	−0.508287	+	0.508287i	0.405713	+	0.914000i	$0.367023\pi$
$314$	0.245108			0.0138323
$315$	−5.17823	−	16.5332i	−0.291760	−	0.931540i
$316$	−0.112062			−0.00630401
$317$	19.8703	−	19.8703i	1.11603	−	1.11603i	0.123709	−	0.992319i	$-0.460521\pi$
$317$	19.8703	−	19.8703i	1.11603	−	1.11603i	0.992319	−	0.123709i	$-0.0394789\pi$
$318$	4.30932	+	7.91438i	0.241655	+	0.443817i
$319$			25.3157i			1.41741i
$320$	16.1115	−	1.48179i	0.900658	−	0.0828343i
$321$	−25.0374	−	7.38412i	−1.39745	−	0.412141i
$322$	−14.3267	−	14.3267i	−0.798398	−	0.798398i
$323$	1.40709	+	1.40709i	0.0782926	+	0.0782926i
$324$	−1.35360	+	0.610373i	−0.0752002	+	0.0339096i
$325$	−16.6015	+	24.1640i	−0.920887	+	1.34038i
$326$			0.152811i			0.00846342i
$327$	5.07006	−	2.76061i	0.280375	−	0.152662i
$328$	15.0698	−	15.0698i	0.832088	−	0.832088i
$329$	−27.0873			−1.49337
$330$	31.8661	+	6.29653i	1.75417	+	0.346613i
$331$	−22.1597			−1.21801			−0.609005	−	0.793167i	$-0.708431\pi$
$331$	−22.1597			−1.21801			−0.609005	+	0.793167i	$0.708431\pi$
$332$	−1.05800	+	1.05800i	−0.0580651	+	0.0580651i
$333$	9.60160	−	2.06470i	0.526165	−	0.113145i
$334$		−	27.7322i		−	1.51744i
$335$	−11.0809	+	13.3256i	−0.605416	+	0.728056i
$336$	5.44473	−	18.4615i	0.297035	−	1.00716i
$337$	10.4927	+	10.4927i	0.571574	+	0.571574i	0.932568	−	0.360994i	$-0.117563\pi$
$337$	10.4927	+	10.4927i	0.571574	+	0.571574i	−0.360994	+	0.932568i	$0.617563\pi$
$338$	22.2447	+	22.2447i	1.20995	+	1.20995i
$339$	−7.79840	+	26.4421i	−0.423551	+	1.43614i
$340$	−0.116702	+	0.140343i	−0.00632905	+	0.00761115i
$341$		−	5.69997i		−	0.308671i
$342$	17.3570	−	3.73238i	0.938557	−	0.201824i
$343$	−13.3858	+	13.3858i	−0.722767	+	0.722767i
$344$	14.7565			0.795618
$345$	−20.2578	−	4.00282i	−1.09065	−	0.215505i
$346$	−35.7775			−1.92341
$347$	8.19072	−	8.19072i	0.439701	−	0.439701i	−0.452210	−	0.891911i	$-0.649364\pi$
$347$	8.19072	−	8.19072i	0.439701	−	0.439701i	0.891911	+	0.452210i	$0.149364\pi$
$348$	−1.11465	+	0.606919i	−0.0597516	+	0.0325343i
$349$			20.7840i			1.11254i	0.831000	+	0.556272i	$0.187769\pi$
$349$			20.7840i			1.11254i	−0.831000	+	0.556272i	$0.812231\pi$
$350$	−18.6819	+	3.46570i	−0.998589	+	0.185249i
$351$	−23.0971	+	19.8694i	−1.23283	+	1.06055i
$352$	3.75227	+	3.75227i	0.199997	+	0.199997i
$353$	−13.4202	−	13.4202i	−0.714287	−	0.714287i	0.253142	−	0.967429i	$-0.418536\pi$
$353$	−13.4202	−	13.4202i	−0.714287	−	0.714287i	−0.967429	+	0.253142i	$0.918536\pi$
$354$	−16.6226	−	4.90242i	−0.883483	−	0.260560i
$355$	3.05387	−	0.280867i	0.162083	−	0.0149069i
$356$		−	1.46323i		−	0.0775509i
$357$	−1.05837	−	1.94377i	−0.0560148	−	0.102875i
$358$	5.36623	−	5.36623i	0.283614	−	0.283614i
$359$	26.5470			1.40110			0.700549	−	0.713604i	$-0.252939\pi$
$359$	26.5470			1.40110			0.700549	+	0.713604i	$0.252939\pi$
$360$	−5.41349	−	17.2844i	−0.285316	−	0.910966i
$361$	2.82359			0.148610
$362$	−5.45791	+	5.45791i	−0.286861	+	0.286861i
$363$	−17.7992	−	32.6895i	−0.934215	−	1.71576i
$364$			2.49843i			0.130953i
$365$	−10.9217	−	9.08193i	−0.571667	−	0.475370i
$366$	−27.1744	−	8.01439i	−1.42043	−	0.418919i
$367$	15.2873	+	15.2873i	0.797992	+	0.797992i	0.982779	−	0.184786i	$-0.0591593\pi$
$367$	15.2873	+	15.2873i	0.797992	+	0.797992i	−0.184786	+	0.982779i	$0.559159\pi$
$368$	−16.2217	−	16.2217i	−0.845613	−	0.845613i
$369$	−19.8900	−	12.8497i	−1.03543	−	0.668930i
$370$	−0.986443	−	10.7256i	−0.0512827	−	0.557597i
$371$			9.13233i			0.474127i
$372$	0.250969	−	0.136651i	0.0130122	−	0.00708502i
$373$	19.0095	−	19.0095i	0.984274	−	0.984274i	−0.0156039	−	0.999878i	$-0.504967\pi$
$373$	19.0095	−	19.0095i	0.984274	−	0.984274i	0.999878	+	0.0156039i	$0.00496707\pi$
$374$	4.14950			0.214566
$375$	−13.8517	+	13.5325i	−0.715300	+	0.698818i
$376$	−28.3180			−1.46039
$377$	−18.4144	+	18.4144i	−0.948391	+	0.948391i
$378$	−19.6906	−	1.47922i	−1.01277	−	0.0760827i
$379$			6.18378i			0.317639i	0.987308	+	0.158820i	$0.0507688\pi$
$379$			6.18378i			0.317639i	−0.987308	+	0.158820i	$0.949231\pi$
$380$	−0.135891	−	1.47754i	−0.00697104	−	0.0757961i
$381$	6.06336	−	20.5590i	0.310635	−	1.05327i
$382$	13.5530	+	13.5530i	0.693433	+	0.693433i
$383$	5.89078	+	5.89078i	0.301005	+	0.301005i	0.841407	−	0.540402i	$-0.181728\pi$
$383$	5.89078	+	5.89078i	0.301005	+	0.301005i	−0.540402	+	0.841407i	$0.681728\pi$
$384$	6.12862	−	20.7803i	0.312750	−	1.06044i
$385$	25.3102	+	21.0467i	1.28993	+	1.07264i
$386$		−	5.16724i		−	0.263005i
$387$	−3.44694	−	16.0296i	−0.175218	−	0.814829i
$388$	1.23097	−	1.23097i	0.0624932	−	0.0624932i
$389$	21.8636			1.10853			0.554265	−	0.832340i	$-0.312999\pi$
$389$	21.8636			1.10853			0.554265	+	0.832340i	$0.312999\pi$
$390$	18.5990	+	27.7591i	0.941799	+	1.40564i
$391$	−2.63791			−0.133405
$392$	−0.629580	+	0.629580i	−0.0317986	+	0.0317986i
$393$	0.233080	−	0.126910i	0.0117573	−	0.00640177i
$394$		−	19.0211i		−	0.958270i
$395$	−1.51243	+	0.139099i	−0.0760985	+	0.00699884i
$396$	1.53093	−	2.36970i	0.0769319	−	0.119082i
$397$	−25.0456	−	25.0456i	−1.25700	−	1.25700i	−0.952518	−	0.304483i	$-0.901516\pi$
$397$	−25.0456	−	25.0456i	−1.25700	−	1.25700i	−0.304483	−	0.952518i	$-0.598484\pi$
$398$	4.12879	+	4.12879i	0.206957	+	0.206957i
$399$	17.2569	+	5.08946i	0.863923	+	0.254792i
$400$	−21.1528	+	3.92408i	−1.05764	+	0.196204i
$401$		−	12.5489i		−	0.626665i	−0.949644	−	0.313332i	$-0.898555\pi$
$401$		−	12.5489i		−	0.626665i	0.949644	−	0.313332i	$-0.101445\pi$
$402$	9.44568	+	17.3477i	0.471108	+	0.865224i
$403$	4.14610	−	4.14610i	0.206532	−	0.206532i
$404$	0.374396			0.0186269
$405$	−17.5110	+	9.91794i	−0.870128	+	0.492827i
$406$	−16.8778			−0.837632
$407$	−13.1946	+	13.1946i	−0.654032	+	0.654032i
$408$	−1.10645	−	2.03209i	−0.0547777	−	0.100603i
$409$		−	32.3354i		−	1.59888i	−0.600744	−	0.799441i	$-0.705129\pi$
$409$		−	32.3354i		−	1.59888i	0.600744	−	0.799441i	$-0.294871\pi$
$410$	−16.6044	+	19.9680i	−0.820031	+	0.986147i
$411$	14.4309	+	4.25603i	0.711825	+	0.209934i
$412$	−1.38129	−	1.38129i	−0.0680515	−	0.0680515i
$413$	−12.4188	−	12.4188i	−0.611088	−	0.611088i
$414$	−12.7712	+	19.7684i	−0.627670	+	0.971564i
$415$	−12.9658	+	15.5923i	−0.636464	+	0.765394i
$416$			5.45872i			0.267636i
$417$	20.8628	−	11.3596i	1.02166	−	0.556284i
$418$	−23.8521	+	23.8521i	−1.16664	+	1.16664i
$419$	−18.4637			−0.902010			−0.451005	−	0.892521i	$-0.648934\pi$
$419$	−18.4637			−0.902010			−0.451005	+	0.892521i	$0.648934\pi$
$420$	−0.319900	+	1.61898i	−0.0156095	+	0.0789981i
$421$	23.2173			1.13154			0.565770	−	0.824563i	$-0.308579\pi$
$421$	23.2173			1.13154			0.565770	+	0.824563i	$0.308579\pi$
$422$	−9.64897	+	9.64897i	−0.469705	+	0.469705i
$423$	6.61475	+	30.7610i	0.321620	+	1.49565i
$424$			9.54724i			0.463655i
$425$	−1.40084	+	2.03896i	−0.0679508	+	0.0989042i
$426$	0.988739	−	3.35252i	0.0479046	−	0.162430i
$427$	−20.3020	−	20.3020i	−0.982482	−	0.982482i
$428$	1.75819	+	1.75819i	0.0849853	+	0.0849853i
$429$	16.3752	−	55.5236i	0.790604	−	2.68070i
$430$	−17.9060	+	1.64683i	−0.863506	+	0.0794174i
$431$		−	11.5554i		−	0.556602i	−0.960494	−	0.278301i	$-0.910229\pi$
$431$		−	11.5554i		−	0.556602i	0.960494	−	0.278301i	$-0.0897713\pi$
$432$	−22.2949	−	1.67487i	−1.07266	−	0.0805820i
$433$	−16.7397	+	16.7397i	−0.804458	+	0.804458i	−0.983789	−	0.179331i	$-0.942607\pi$
$433$	−16.7397	+	16.7397i	−0.804458	+	0.804458i	0.179331	+	0.983789i	$0.442607\pi$
$434$	3.80013			0.182412
$435$	−14.2903	+	9.57473i	−0.685168	+	0.459073i
$436$	−0.549890			−0.0263349
$437$	15.1632	−	15.1632i	0.725354	−	0.725354i
$438$	−14.2182	+	7.74169i	−0.679371	+	0.369912i
$439$			28.2802i			1.34974i	0.737936	+	0.674870i	$0.235800\pi$
$439$			28.2802i			1.34974i	−0.737936	+	0.674870i	$0.764200\pi$
$440$	26.4601	+	22.0029i	1.26144	+	1.04895i
$441$	0.830957	+	0.536832i	0.0395694	+	0.0255634i
$442$	3.01830	+	3.01830i	0.143566	+	0.143566i
$443$	19.1703	+	19.1703i	0.910809	+	0.910809i	0.996336	−	0.0855269i	$-0.0272574\pi$
$443$	19.1703	+	19.1703i	0.910809	+	0.910809i	−0.0855269	+	0.996336i	$0.527257\pi$
$444$	−0.897284	−	0.264631i	−0.0425832	−	0.0125588i
$445$	−1.81625	−	19.7481i	−0.0860987	−	0.936151i
$446$			27.1674i			1.28642i
$447$	−5.97633	−	10.9760i	−0.282671	−	0.519146i
$448$	13.2140	−	13.2140i	0.624304	−	0.624304i
$449$	−1.34571			−0.0635078			−0.0317539	−	0.999496i	$-0.510109\pi$
$449$	−1.34571			−0.0635078			−0.0317539	+	0.999496i	$0.510109\pi$
$450$	8.49786	+	20.3693i	0.400593	+	0.960217i
$451$	44.9911			2.11855
$452$	1.85683	−	1.85683i	0.0873379	−	0.0873379i
$453$	4.16650	+	7.65208i	0.195759	+	0.359526i
$454$		−	17.5552i		−	0.823907i
$455$	3.10122	+	33.7195i	0.145387	+	1.58080i
$456$	18.0409	+	5.32070i	0.844842	+	0.249164i
$457$	3.32534	+	3.32534i	0.155553	+	0.155553i	0.780593	−	0.625040i	$-0.214917\pi$
$457$	3.32534	+	3.32534i	0.155553	+	0.155553i	−0.625040	+	0.780593i	$0.714917\pi$
$458$	−10.6826	−	10.6826i	−0.499166	−	0.499166i
$459$	−1.94894	+	1.67658i	−0.0909688	+	0.0782561i
$460$	1.51237	+	1.25761i	0.0705146	+	0.0586365i
$461$		−	23.9555i		−	1.11572i	−0.829936	−	0.557858i	$-0.811623\pi$
$461$		−	23.9555i		−	1.11572i	0.829936	−	0.557858i	$-0.188377\pi$
$462$	32.9496	−	17.9408i	1.53295	−	0.834681i
$463$	−2.39286	+	2.39286i	−0.111206	+	0.111206i	−0.760520	−	0.649314i	$-0.775056\pi$
$463$	−2.39286	+	2.39286i	−0.111206	+	0.111206i	0.649314	+	0.760520i	$0.275056\pi$
$464$	−19.1101			−0.887166
$465$	3.21754	−	2.15580i	0.149210	−	0.0999728i
$466$	8.57860			0.397396
$467$	−4.57676	+	4.57676i	−0.211787	+	0.211787i	−0.805026	−	0.593239i	$-0.797849\pi$
$467$	−4.57676	+	4.57676i	−0.211787	+	0.211787i	0.593239	+	0.805026i	$0.297849\pi$
$468$	2.83728	−	0.610119i	0.131153	−	0.0282028i
$469$			20.0173i			0.924314i
$470$	34.3620	−	3.16031i	1.58500	−	0.145774i
$471$	0.0816188	−	0.276745i	0.00376080	−	0.0127517i
$472$	−12.9830	−	12.9830i	−0.597591	−	0.597591i
$473$	22.0279	+	22.0279i	1.01285	+	1.01285i
$474$	−0.489673	+	1.66033i	−0.0224914	+	0.0762617i
$475$	−3.66803	−	19.7726i	−0.168301	−	0.907229i
$476$			0.210818i			0.00966284i
$477$	10.3709	−	2.23012i	0.474851	−	0.102110i
$478$	8.63344	−	8.63344i	0.394884	−	0.394884i
$479$	23.5366			1.07541			0.537707	−	0.843132i	$-0.319291\pi$
$479$	23.5366			1.07541			0.537707	+	0.843132i	$0.319291\pi$
$480$	−0.698937	+	3.53724i	−0.0319020	+	0.161452i
$481$	−19.1952			−0.875227
$482$	−27.0673	+	27.0673i	−1.23288	+	1.23288i
$483$	−20.9466	+	11.4053i	−0.953105	+	0.518958i
$484$			3.54545i			0.161157i
$485$	15.0856	−	18.1415i	0.685002	−	0.823764i
$486$	3.12861	+	22.7223i	0.141917	+	1.03070i
$487$	28.9214	+	28.9214i	1.31056	+	1.31056i	0.921005	+	0.389551i	$0.127370\pi$
$487$	28.9214	+	28.9214i	1.31056	+	1.31056i	0.389551	+	0.921005i	$0.372630\pi$
$488$	−21.2244	−	21.2244i	−0.960783	−	0.960783i
$489$	0.172535	+	0.0508847i	0.00780230	+	0.00230109i
$490$	0.693692	−	0.834215i	0.0313378	−	0.0376860i
$491$		−	24.9974i		−	1.12812i	−0.825734	−	0.564059i	$-0.809239\pi$
$491$		−	24.9974i		−	1.12812i	0.825734	−	0.564059i	$-0.190761\pi$
$492$	1.07862	+	1.98096i	0.0486277	+	0.0893084i
$493$	−1.55381	+	1.55381i	−0.0699802	+	0.0699802i
$494$	−34.6995			−1.56120
$495$	17.7204	−	33.8825i	0.796472	−	1.52290i
$496$	4.30275			0.193199
$497$	2.50467	−	2.50467i	0.112350	−	0.112350i
$498$	11.0524	+	20.2985i	0.495268	+	0.909597i
$499$		−	16.5062i		−	0.738918i	−0.929247	−	0.369459i	$-0.879543\pi$
$499$		−	16.5062i		−	0.738918i	0.929247	−	0.369459i	$-0.120457\pi$
$500$	1.77520	−	0.501135i	0.0793893	−	0.0224115i
$501$	−31.3117	−	9.23459i	−1.39891	−	0.412571i
$502$	−23.8728	−	23.8728i	−1.06549	−	1.06549i
$503$	11.6138	+	11.6138i	0.517835	+	0.517835i	0.916916	−	0.399081i	$-0.130671\pi$
$503$	11.6138	+	11.6138i	0.517835	+	0.517835i	−0.399081	+	0.916916i	$0.630671\pi$
$504$	−17.5719	−	11.3521i	−0.782713	−	0.505665i
$505$	5.05295	−	0.464724i	0.224853	−	0.0206800i
$506$		−	44.7161i		−	1.98788i
$507$	32.5232	−	17.7086i	1.44441	−	0.786467i
$508$	−1.44371	+	1.44371i	−0.0640543	+	0.0640543i
$509$	33.0579			1.46527			0.732634	−	0.680623i	$-0.238291\pi$
$509$	33.0579			1.46527			0.732634	+	0.680623i	$0.238291\pi$
$510$	1.56939	+	2.34232i	0.0694938	+	0.103720i
$511$	−16.4062			−0.725768
$512$	13.5972	−	13.5972i	0.600915	−	0.600915i
$513$	1.56558	−	20.8402i	0.0691220	−	0.920115i
$514$			44.3076i			1.95432i
$515$	−20.3569	−	16.9278i	−0.897032	−	0.745928i
$516$	−0.441792	+	1.49799i	−0.0194488	+	0.0659452i
$517$	−42.2720	−	42.2720i	−1.85912	−	1.85912i
$518$	−8.79673	−	8.79673i	−0.386506	−	0.386506i
$519$	−11.9136	+	40.3955i	−0.522949	+	1.77316i
$520$	3.24212	+	35.2515i	0.142176	+	1.54588i
$521$		−	5.67303i		−	0.248540i	−0.992248	−	0.124270i	$-0.960341\pi$
$521$		−	5.67303i		−	0.248540i	0.992248	−	0.124270i	$-0.0396589\pi$
$522$	4.12158	+	19.1669i	0.180396	+	0.838911i
$523$	12.1577	−	12.1577i	0.531621	−	0.531621i	−0.389434	−	0.921055i	$-0.627329\pi$
$523$	12.1577	−	12.1577i	0.531621	−	0.531621i	0.921055	+	0.389434i	$0.127329\pi$
$524$	−0.0252795			−0.00110434
$525$	−2.30788	+	22.2473i	−0.100724	+	0.970951i
$526$	−9.48339			−0.413495
$527$	0.349849	−	0.349849i	0.0152397	−	0.0152397i
$528$	37.3076	−	20.3137i	1.62361	−	0.884041i
$529$			5.42686i			0.235950i
$530$	−1.06548	−	11.5849i	−0.0462814	−	0.503218i
$531$	−11.0704	+	17.1357i	−0.480414	+	0.743627i
$532$	−1.21182	−	1.21182i	−0.0525391	−	0.0525391i
$533$	32.7261	+	32.7261i	1.41752	+	1.41752i
$534$	−21.6794	−	6.39378i	−0.938159	−	0.276686i
$535$	25.9114	+	21.5466i	1.12025	+	0.931542i
$536$			20.9268i			0.903899i
$537$	−4.27196	−	7.84578i	−0.184349	−	0.338570i
$538$	9.20648	−	9.20648i	0.396920	−	0.396920i
$539$	−1.87962			−0.0809612
$540$	1.91667	−	0.0320699i	0.0824804	−	0.00138007i
$541$	10.9567			0.471064			0.235532	−	0.971867i	$-0.424317\pi$
$541$	10.9567			0.471064			0.235532	+	0.971867i	$0.424317\pi$
$542$	19.9771	−	19.9771i	0.858090	−	0.858090i
$543$	4.34495	+	7.97982i	0.186460	+	0.342447i
$544$			0.460609i			0.0197484i
$545$	−7.42147	+	0.682559i	−0.317901	+	0.0292376i
$546$	37.0171	+	10.9172i	1.58419	+	0.467215i
$547$	−30.1252	−	30.1252i	−1.28806	−	1.28806i	−0.935963	−	0.352099i	$-0.885468\pi$
$547$	−30.1252	−	30.1252i	−1.28806	−	1.28806i	−0.352099	−	0.935963i	$-0.614532\pi$
$548$	−1.01338	−	1.01338i	−0.0432893	−	0.0432893i
$549$	−18.0977	+	28.0132i	−0.772390	+	1.19557i
$550$	−34.5631	−	23.7461i	−1.47378	−	1.01254i
$551$		−	17.8632i		−	0.760998i
$552$	−21.8983	+	11.9235i	−0.932054	+	0.507496i
$553$	−1.24044	+	1.24044i	−0.0527487	+	0.0527487i
$554$	7.94778			0.337669
$555$	−12.4385	−	2.45776i	−0.527984	−	0.104326i
$556$	−2.26274			−0.0959617
$557$	−0.552934	+	0.552934i	−0.0234286	+	0.0234286i	−0.718724	−	0.695295i	$-0.755274\pi$
$557$	−0.552934	+	0.552934i	−0.0234286	+	0.0234286i	0.695295	+	0.718724i	$0.255274\pi$
$558$	−0.927994	−	4.31552i	−0.0392851	−	0.182690i
$559$			32.0458i			1.35539i
$560$	−15.8876	+	19.1060i	−0.671372	+	0.807374i
$561$	1.38175	−	4.68509i	0.0583374	−	0.197805i
$562$	−6.82276	−	6.82276i	−0.287801	−	0.287801i
$563$	13.6902	+	13.6902i	0.576972	+	0.576972i	0.934068	−	0.357096i	$-0.116233\pi$
$563$	13.6902	+	13.6902i	0.576972	+	0.576972i	−0.357096	+	0.934068i	$0.616233\pi$
$564$	0.847808	−	2.87466i	0.0356991	−	0.121045i
$565$	22.7555	−	27.3651i	0.957330	−	1.15126i
$566$			7.08941i			0.297990i
$567$	−8.22693	+	21.7395i	−0.345498	+	0.912974i
$568$	2.61846	−	2.61846i	0.109868	−	0.109868i
$569$	−21.0505			−0.882485			−0.441242	−	0.897388i	$-0.645462\pi$
$569$	−21.0505			−0.882485			−0.441242	+	0.897388i	$0.645462\pi$
$570$	−22.4852	−	4.44294i	−0.941803	−	0.186094i
$571$	−9.07240			−0.379668			−0.189834	−	0.981816i	$-0.560795\pi$
$571$	−9.07240			−0.379668			−0.189834	+	0.981816i	$0.560795\pi$
$572$	−3.89901	+	3.89901i	−0.163026	+	0.163026i
$573$	19.8154	−	10.7893i	0.827800	−	0.450731i
$574$			29.9952i			1.25198i
$575$	21.9724	+	15.0958i	0.916313	+	0.629540i
$576$	−18.2330	−	11.7793i	−0.759710	−	0.490804i
$577$	24.4714	+	24.4714i	1.01876	+	1.01876i	0.999821	+	0.0189390i	$0.00602883\pi$
$577$	24.4714	+	24.4714i	1.01876	+	1.01876i	0.0189390	+	0.999821i	$0.493971\pi$
$578$	−17.4326	−	17.4326i	−0.725101	−	0.725101i
$579$	−5.83419	−	1.72064i	−0.242461	−	0.0715075i
$580$	1.63161	−	0.150060i	0.0677488	−	0.00623092i
$581$			23.4222i			0.971717i
$582$	−12.8594	−	23.6172i	−0.533038	−	0.978964i
$583$	−14.2518	+	14.2518i	−0.590247	+	0.590247i
$584$	−17.1516			−0.709738
$585$	37.5354	−	11.7562i	1.55190	−	0.486057i
$586$	5.46791			0.225877
$587$	23.4513	−	23.4513i	0.967939	−	0.967939i	−0.0315627	−	0.999502i	$-0.510048\pi$
$587$	23.4513	−	23.4513i	0.967939	−	0.967939i	0.999502	+	0.0315627i	$0.0100484\pi$
$588$	−0.0450621	−	0.0827598i	−0.00185833	−	0.00341296i
$589$			4.02199i			0.165723i
$590$	17.2029	+	14.3051i	0.708233	+	0.588932i
$591$	−21.4762	−	6.33386i	−0.883415	−	0.260540i
$592$	−9.96023	−	9.96023i	−0.409363	−	0.409363i
$593$	12.5239	+	12.5239i	0.514295	+	0.514295i	0.915840	−	0.401544i	$-0.131526\pi$
$593$	12.5239	+	12.5239i	0.514295	+	0.514295i	−0.401544	+	0.915840i	$0.631526\pi$
$594$	−28.4203	−	33.0372i	−1.16610	−	1.35553i
$595$	0.261681	+	2.84526i	0.0107279	+	0.116644i
$596$			1.19044i			0.0487622i
$597$	6.03656	−	3.28686i	0.247060	−	0.134522i
$598$	32.5261	−	32.5261i	1.33009	−	1.33009i
$599$	−13.4427			−0.549254			−0.274627	−	0.961551i	$-0.588554\pi$
$599$	−13.4427			−0.549254			−0.274627	+	0.961551i	$0.588554\pi$
$600$	−2.41273	+	23.2581i	−0.0984994	+	0.949506i
$601$	5.32649			0.217272			0.108636	−	0.994082i	$-0.465352\pi$
$601$	5.32649			0.217272			0.108636	+	0.994082i	$0.465352\pi$
$602$	−14.6859	+	14.6859i	−0.598551	+	0.598551i
$603$	22.7322	−	4.88825i	0.925725	−	0.199065i
$604$		−	0.829931i		−	0.0337694i
$605$	4.40084	+	47.8504i	0.178920	+	1.94540i
$606$	1.63597	−	5.54710i	0.0664569	−	0.225336i
$607$	−28.5624	−	28.5624i	−1.15931	−	1.15931i	−0.984624	−	0.174687i	$-0.944109\pi$
$607$	−28.5624	−	28.5624i	−1.15931	−	1.15931i	−0.174687	−	0.984624i	$-0.555891\pi$
$608$	−2.64766	−	2.64766i	−0.107377	−	0.107377i
$609$	−5.62016	+	19.0563i	−0.227740	+	0.772200i
$610$	28.1230	+	23.3857i	1.13867	+	0.946861i
$611$		−	61.4965i		−	2.48788i
$612$	0.239410	−	0.0514820i	0.00967759	−	0.00208104i
$613$	−7.86404	+	7.86404i	−0.317625	+	0.317625i	−0.847854	−	0.530229i	$-0.822106\pi$
$613$	−7.86404	+	7.86404i	−0.317625	+	0.317625i	0.530229	+	0.847854i	$0.322106\pi$
$614$	−2.62101			−0.105775
$615$	17.0162	+	25.3967i	0.686159	+	1.02409i
$616$	39.7476			1.60147
$617$	−19.4262	+	19.4262i	−0.782069	+	0.782069i	−0.980180	−	0.198111i	$-0.936519\pi$
$617$	−19.4262	+	19.4262i	−0.782069	+	0.782069i	0.198111	+	0.980180i	$0.436519\pi$
$618$	−26.5012	+	14.4297i	−1.06604	+	0.580448i
$619$		−	37.5107i		−	1.50768i	−0.657058	−	0.753840i	$-0.728199\pi$
$619$		−	37.5107i		−	1.50768i	0.657058	−	0.753840i	$-0.271801\pi$
$620$	−0.367365	+	0.0337869i	−0.0147537	+	0.00135691i
$621$	18.0673	+	21.0023i	0.725016	+	0.842795i
$622$	−4.57709	−	4.57709i	−0.183525	−	0.183525i
$623$	−16.1967	−	16.1967i	−0.648906	−	0.648906i
$624$	41.9132	+	12.3612i	1.67787	+	0.494844i
$625$	23.3365	−	8.96696i	0.933461	−	0.358678i
$626$		−	18.7121i		−	0.747888i
$627$	18.9882	+	34.8733i	0.758317	+	1.39270i
$628$	−0.0194338	+	0.0194338i	−0.000775492	+	0.000775492i
$629$	−1.61970			−0.0645816
$630$	22.5892	+	11.8140i	0.899975	+	0.470683i
$631$	19.5170			0.776959			0.388480	−	0.921457i	$-0.373000\pi$
$631$	19.5170			0.776959			0.388480	+	0.921457i	$0.373000\pi$
$632$	−1.29679	+	1.29679i	−0.0515837	+	0.0515837i
$633$	7.68138	+	14.1074i	0.305307	+	0.560720i
$634$			41.3473i			1.64211i
$635$	−17.6927	+	21.2767i	−0.702113	+	0.844342i
$636$	−0.969175	−	0.285833i	−0.0384303	−	0.0113340i
$637$	−1.36722	−	1.36722i	−0.0541712	−	0.0541712i
$638$	−26.3392	−	26.3392i	−1.04278	−	1.04278i
$639$	−3.45600	−	2.23272i	−0.136717	−	0.0883250i
$640$	−17.8831	+	21.5058i	−0.706893	+	0.850090i
$641$		−	31.4906i		−	1.24380i	−0.783096	−	0.621901i	$-0.786361\pi$
$641$		−	31.4906i		−	1.24380i	0.783096	−	0.621901i	$-0.213639\pi$
$642$	33.7322	−	18.3669i	1.33131	−	0.724885i
$643$	13.3230	−	13.3230i	0.525409	−	0.525409i	−0.393791	−	0.919200i	$-0.628837\pi$
$643$	13.3230	−	13.3230i	0.525409	−	0.525409i	0.919200	+	0.393791i	$0.128837\pi$
$644$	2.27184			0.0895229
$645$	−4.10316	+	20.7656i	−0.161562	+	0.817646i
$646$	−2.92795			−0.115199
$647$	−22.3622	+	22.3622i	−0.879148	+	0.879148i	−0.993446	−	0.114298i	$-0.963538\pi$
$647$	−22.3622	+	22.3622i	−0.879148	+	0.879148i	0.114298	+	0.993446i	$0.463538\pi$
$648$	−8.60071	+	22.7272i	−0.337868	+	0.892810i
$649$		−	38.7610i		−	1.52150i
$650$	−7.86818	−	42.4136i	−0.308616	−	1.66360i
$651$	1.26541	−	4.29062i	0.0495953	−	0.168163i
$652$	−0.0121159	−	0.0121159i	−0.000474494	−	0.000474494i
$653$	0.0987075	+	0.0987075i	0.00386272	+	0.00386272i	0.709036	−	0.705173i	$-0.249131\pi$
$653$	0.0987075	+	0.0987075i	0.00386272	+	0.00386272i	−0.705173	+	0.709036i	$0.749131\pi$
$654$	−2.40282	+	8.14725i	−0.0939577	+	0.318583i
$655$	−0.341179	+	0.0313785i	−0.0133310	+	0.00122606i
$656$			33.9625i			1.32601i
$657$	4.00641	+	18.6313i	0.156305	+	0.726876i
$658$	28.1824	−	28.1824i	1.09867	−	1.09867i
$659$	−31.5045			−1.22724			−0.613620	−	0.789601i	$-0.710287\pi$
$659$	−31.5045			−1.22724			−0.613620	+	0.789601i	$0.710287\pi$
$660$	−3.02578	+	2.02732i	−0.117778	+	0.0789134i
$661$	42.9995			1.67249			0.836243	−	0.548359i	$-0.184747\pi$
$661$	42.9995			1.67249			0.836243	+	0.548359i	$0.184747\pi$
$662$	23.0556	−	23.0556i	0.896082	−	0.896082i
$663$	4.41296	−	2.40282i	0.171385	−	0.0933178i
$664$			24.4864i			0.950255i
$665$	−17.8593	−	14.8509i	−0.692553	−	0.575893i
$666$	−7.84162	+	12.1380i	−0.303856	+	0.470336i
$667$	16.7443	+	16.7443i	0.648343	+	0.648343i
$668$	2.19879	+	2.19879i	0.0850738	+	0.0850738i
$669$	30.6740	+	9.04651i	1.18593	+	0.349758i
$670$	−2.33544	−	25.3933i	−0.0902260	−	0.981028i
$671$		−	63.3659i		−	2.44621i
$672$	1.99149	+	3.65752i	0.0768233	+	0.141092i
$673$	14.0766	−	14.0766i	0.542613	−	0.542613i	−0.381681	−	0.924294i	$-0.624655\pi$
$673$	14.0766	−	14.0766i	0.542613	−	0.542613i	0.924294	+	0.381681i	$0.124655\pi$
$674$	−21.8338			−0.841008
$675$	25.8281	−	2.81192i	0.994126	−	0.108231i
$676$	−3.52741			−0.135670
$677$	−6.97865	+	6.97865i	−0.268211	+	0.268211i	−0.828379	−	0.560168i	$-0.810737\pi$
$677$	−6.97865	+	6.97865i	−0.268211	+	0.268211i	0.560168	+	0.828379i	$0.310737\pi$
$678$	−19.3974	−	35.6248i	−0.744952	−	1.36816i
$679$		−	27.2516i		−	1.04582i
$680$	0.273571	+	2.97453i	0.0104910	+	0.114068i
$681$	−19.8211	−	5.84573i	−0.759547	−	0.224009i
$682$	5.93041	+	5.93041i	0.227087	+	0.227087i
$683$	−5.03584	−	5.03584i	−0.192691	−	0.192691i	0.604167	−	0.796858i	$-0.293506\pi$
$683$	−5.03584	−	5.03584i	−0.192691	−	0.192691i	−0.796858	+	0.604167i	$0.793506\pi$
$684$	−1.08025	+	1.67210i	−0.0413042	+	0.0639344i
$685$	−14.9347	−	12.4190i	−0.570625	−	0.474504i
$686$		−	27.8540i		−	1.06347i
$687$	−15.6187	+	8.50425i	−0.595890	+	0.324457i
$688$	−16.6283	+	16.6283i	−0.633947	+	0.633947i
$689$	−20.7332			−0.789871
$690$	25.2415	−	16.9122i	0.960927	−	0.643836i
$691$	−10.0644			−0.382870			−0.191435	−	0.981505i	$-0.561314\pi$
$691$	−10.0644			−0.382870			−0.191435	+	0.981505i	$0.561314\pi$
$692$	2.83668	−	2.83668i	0.107834	−	0.107834i
$693$	−9.28456	−	43.1766i	−0.352691	−	1.64014i
$694$			17.0437i			0.646971i
$695$	−30.5386	+	2.80867i	−1.15840	+	0.106539i
$696$	−5.87551	+	19.9221i	−0.222711	+	0.755145i
$697$	2.76144	+	2.76144i	0.104597	+	0.104597i
$698$	−21.6243	−	21.6243i	−0.818493	−	0.818493i
$699$	2.85660	−	9.68588i	0.108046	−	0.366354i
$700$	1.20644	−	1.75601i	0.0455991	−	0.0663708i
$701$			23.2458i			0.877983i	0.898491	+	0.438991i	$0.144664\pi$
$701$			23.2458i			0.877983i	−0.898491	+	0.438991i	$0.855336\pi$
$702$	3.35827	−	44.7036i	0.126750	−	1.68723i
$703$	9.31032	−	9.31032i	0.351145	−	0.351145i
$704$	41.2431			1.55441
$705$	7.87403	−	39.8496i	0.296553	−	1.50082i
$706$	27.9256			1.05099
$707$	4.14424	−	4.14424i	0.155860	−	0.155860i
$708$	1.70665	−	0.929256i	0.0641397	−	0.0349236i
$709$		−	32.7196i		−	1.22881i	−0.788991	−	0.614405i	$-0.789396\pi$
$709$		−	32.7196i		−	1.22881i	0.788991	−	0.614405i	$-0.210604\pi$
$710$	−2.88511	+	3.46956i	−0.108276	+	0.130210i
$711$	1.71158	+	1.10575i	0.0641894	+	0.0414690i
$712$	−16.9325	−	16.9325i	−0.634574	−	0.634574i
$713$	−3.77007	−	3.77007i	−0.141190	−	0.141190i
$714$	3.12352	+	0.921200i	0.116895	+	0.0344750i
$715$	−47.7824	+	57.4618i	−1.78696	+	2.14895i
$716$			0.850939i			0.0318011i
$717$	−6.87293	−	12.6226i	−0.256674	−	0.471401i
$718$	−27.6203	+	27.6203i	−1.03078	+	1.03078i
$719$	−33.7766			−1.25965			−0.629826	−	0.776736i	$-0.716874\pi$
$719$	−33.7766			−1.25965			−0.629826	+	0.776736i	$0.716874\pi$
$720$	25.5769	+	13.3766i	0.953196	+	0.498517i
$721$	−30.5795			−1.13884
$722$	−2.93774	+	2.93774i	−0.109331	+	0.109331i
$723$	21.5478	+	39.5741i	0.801372	+	1.47178i
$724$		−	0.865478i		−	0.0321652i
$725$	21.8344	−	4.05052i	0.810909	−	0.150432i
$726$	52.5299	+	15.4923i	1.94957	+	0.574975i
$727$	−5.96182	−	5.96182i	−0.221112	−	0.221112i	0.587855	−	0.808967i	$-0.299973\pi$
$727$	−5.96182	−	5.96182i	−0.221112	−	0.221112i	−0.808967	+	0.587855i	$0.799973\pi$
$728$	28.9120	+	28.9120i	1.07155	+	1.07155i
$729$	26.6970	+	4.03389i	0.988776	+	0.149403i
$730$	20.8123	−	1.91413i	0.770299	−	0.0708451i
$731$			2.70403i			0.100012i
$732$	2.79000	−	1.51913i	0.103121	−	0.0561487i
$733$	−13.0530	+	13.0530i	−0.482122	+	0.482122i	−0.905809	−	0.423687i	$-0.860736\pi$
$733$	−13.0530	+	13.0530i	−0.482122	+	0.482122i	0.423687	+	0.905809i	$0.360736\pi$
$734$	−31.8108			−1.17416
$735$	−0.710897	−	1.06102i	−0.0262218	−	0.0391362i
$736$	4.96365			0.182962
$737$	−31.2387	+	31.2387i	−1.15069	+	1.15069i
$738$	34.0633	−	7.32486i	1.25389	−	0.269632i
$739$		−	21.1712i		−	0.778793i	−0.921070	−	0.389397i	$-0.872684\pi$
$739$		−	21.1712i		−	0.778793i	0.921070	−	0.389397i	$-0.127316\pi$
$740$	0.928607	+	0.772184i	0.0341363	+	0.0283861i
$741$	−11.5546	+	39.1783i	−0.424470	+	1.43925i
$742$	−9.50153	−	9.50153i	−0.348812	−	0.348812i
$743$	−2.65585	−	2.65585i	−0.0974336	−	0.0974336i	0.656710	−	0.754143i	$-0.271948\pi$
$743$	−2.65585	−	2.65585i	−0.0974336	−	0.0974336i	−0.754143	+	0.656710i	$0.771948\pi$
$744$	1.32290	−	4.48556i	0.0484999	−	0.164449i
$745$	1.47765	+	16.0665i	0.0541368	+	0.588630i
$746$			39.5561i			1.44825i
$747$	26.5988	−	5.71972i	0.973200	−	0.209274i
$748$	−0.328999	+	0.328999i	−0.0120294	+	0.0120294i
$749$	38.9233			1.42223
$750$	0.332078	−	28.4914i	0.0121258	−	1.04036i
$751$	11.8492			0.432385			0.216193	−	0.976351i	$-0.430636\pi$
$751$	11.8492			0.432385			0.216193	+	0.976351i	$0.430636\pi$
$752$	31.9100	−	31.9100i	1.16364	−	1.16364i
$753$	−34.9035	+	19.0047i	−1.27196	+	0.692570i
$754$		−	38.3178i		−	1.39545i
$755$	−1.03016	−	11.2010i	−0.0374915	−	0.407646i
$756$	1.67848	−	1.44391i	0.0610456	−	0.0525146i
$757$	10.5885	+	10.5885i	0.384845	+	0.384845i	0.872844	−	0.487999i	$-0.162273\pi$
$757$	10.5885	+	10.5885i	0.384845	+	0.384845i	−0.487999	+	0.872844i	$0.662273\pi$
$758$	−6.43378	−	6.43378i	−0.233685	−	0.233685i
$759$	−50.4878	−	14.8901i	−1.83259	−	0.540476i
$760$	−18.6707	−	15.5256i	−0.677257	−	0.563174i
$761$		−	6.62645i		−	0.240209i	−0.992761	−	0.120104i	$-0.961677\pi$
$761$		−	6.62645i		−	0.240209i	0.992761	−	0.120104i	$-0.0383229\pi$
$762$	15.0817	+	27.6987i	0.546353	+	1.00342i
$763$	−6.08681	+	6.08681i	−0.220357	+	0.220357i
$764$	−2.14914			−0.0777533
$765$	3.16725	−	0.991987i	0.114512	−	0.0358654i
$766$	−12.2579			−0.442895
$767$	28.1944	−	28.1944i	1.01804	−	1.01804i
$768$	3.25792	+	5.98341i	0.117560	+	0.215908i
$769$			31.7137i			1.14362i	0.820385	+	0.571812i	$0.193759\pi$
$769$			31.7137i			1.14362i	−0.820385	+	0.571812i	$0.806241\pi$
$770$	−48.2310	+	4.43585i	−1.73813	+	0.159857i
$771$	50.0265	+	14.7540i	1.80166	+	0.531353i
$772$	0.409692	+	0.409692i	0.0147451	+	0.0147451i
$773$	11.7114	+	11.7114i	0.421231	+	0.421231i	0.885627	−	0.464396i	$-0.153729\pi$
$773$	11.7114	+	11.7114i	0.421231	+	0.421231i	−0.464396	+	0.885627i	$0.653729\pi$
$774$	20.2639	+	13.0913i	0.728372	+	0.470558i
$775$	−4.91612	+	0.911995i	−0.176592	+	0.0327598i
$776$		−	28.4898i		−	1.02272i
$777$	−12.8614	+	7.00293i	−0.461400	+	0.251229i
$778$	−22.7475	+	22.7475i	−0.815539	+	0.815539i
$779$	−31.7465			−1.13743
$780$	−3.67558	−	0.726270i	−0.131607	−	0.0260047i
$781$	7.81748			0.279732
$782$	2.74456	−	2.74456i	0.0981452	−	0.0981452i
$783$	23.0133	+	1.72883i	0.822426	+	0.0617833i
$784$		−	1.41888i		−	0.0506741i
$785$	−0.238161	+	0.286406i	−0.00850034	+	0.0102223i
$786$	−0.110462	+	0.374544i	−0.00394005	+	0.0133595i
$787$	−28.0355	−	28.0355i	−0.999357	−	0.999357i	0.000642610	−	1.00000i	$-0.499795\pi$
$787$	−28.0355	−	28.0355i	−0.999357	−	0.999357i	−1.00000		0.000642610i	$0.999795\pi$
$788$	1.50812	+	1.50812i	0.0537245	+	0.0537245i
$789$	−3.15788	+	10.7074i	−0.112424	+	0.381195i
$790$	1.42885	−	1.71830i	0.0508362	−	0.0611342i
$791$		−	41.1070i		−	1.46160i
$792$	−9.70639	−	45.1383i	−0.344901	−	1.60392i
$793$	46.0917	−	46.0917i	1.63677	−	1.63677i
$794$	52.1162			1.84954
$795$	−13.4351	−	2.65468i	−0.476492	−	0.0941518i
$796$	−0.654715			−0.0232057
$797$	−3.44795	+	3.44795i	−0.122133	+	0.122133i	−0.765531	−	0.643399i	$-0.777524\pi$
$797$	−3.44795	+	3.44795i	−0.122133	+	0.122133i	0.643399	+	0.765531i	$0.277524\pi$
$798$	−23.2498	+	12.6593i	−0.823032	+	0.448135i
$799$		−	5.18909i		−	0.183577i
$800$	2.63590	−	3.83663i	0.0931932	−	0.135645i
$801$	−14.4381	+	22.3486i	−0.510145	+	0.789648i
$802$	13.0563	+	13.0563i	0.461033	+	0.461033i
$803$	−25.6032	−	25.6032i	−0.903519	−	0.903519i
$804$	−2.12435	−	0.626523i	−0.0749202	−	0.0220958i
$805$	30.6613	−	2.81995i	1.08067	−	0.0993902i
$806$			8.62745i			0.303889i
$807$	−7.32912	−	13.4605i	−0.257997	−	0.473831i
$808$	4.33253	−	4.33253i	0.152418	−	0.152418i
$809$	−11.8818			−0.417742			−0.208871	−	0.977943i	$-0.566979\pi$
$809$	−11.8818			−0.417742			−0.208871	+	0.977943i	$0.566979\pi$
$810$	7.90001	−	28.5378i	0.277578	−	1.00272i
$811$	12.6223			0.443229			0.221614	−	0.975134i	$-0.428867\pi$
$811$	12.6223			0.443229			0.221614	+	0.975134i	$0.428867\pi$
$812$	1.33818	−	1.33818i	0.0469610	−	0.0469610i
$813$	−15.9034	−	29.2078i	−0.557758	−	1.02436i
$814$		−	27.4561i		−	0.962335i
$815$	−0.178558	−	0.148480i	−0.00625462	−	0.00520103i
$816$	3.53665	+	1.04304i	0.123807	+	0.0365138i
$817$	−15.5433	−	15.5433i	−0.543790	−	0.543790i
$818$	33.6427	+	33.6427i	1.17629	+	1.17629i
$819$	24.6528	−	38.1597i	0.861437	−	1.33341i
$820$	−0.266687	−	2.89969i	−0.00931312	−	0.101262i
$821$		−	41.4475i		−	1.44653i	−0.690571	−	0.723264i	$-0.742641\pi$
$821$		−	41.4475i		−	1.44653i	0.690571	−	0.723264i	$-0.257359\pi$
$822$	−19.4424	+	10.5863i	−0.678133	+	0.369238i
$823$	−20.1208	+	20.1208i	−0.701368	+	0.701368i	−0.964704	−	0.263336i	$-0.915177\pi$
$823$	−20.1208	+	20.1208i	−0.701368	+	0.701368i	0.263336	+	0.964704i	$0.415177\pi$
$824$	−31.9688			−1.11369
$825$	−38.3204	+	31.1171i	−1.33414	+	1.08336i
$826$	25.8417			0.899147
$827$	−15.3731	+	15.3731i	−0.534576	+	0.534576i	−0.921931	−	0.387355i	$-0.873389\pi$
$827$	−15.3731	+	15.3731i	−0.534576	+	0.534576i	0.387355	+	0.921931i	$0.373389\pi$
$828$	−0.554784	−	2.57995i	−0.0192801	−	0.0896595i
$829$		−	44.8017i		−	1.55603i	−0.628247	−	0.778014i	$-0.716227\pi$
$829$		−	44.8017i		−	1.55603i	0.628247	−	0.778014i	$-0.283773\pi$
$830$	−2.73269	−	29.7126i	−0.0948532	−	1.03134i
$831$	2.64654	−	8.97363i	0.0918075	−	0.311292i
$832$	29.9998	+	29.9998i	1.04006	+	1.04006i
$833$	−0.115366	−	0.115366i	−0.00399721	−	0.00399721i
$834$	−9.88738	+	33.5252i	−0.342372	+	1.16088i
$835$	32.4048	+	26.9462i	1.12141	+	0.932513i
$836$		−	3.78230i		−	0.130813i
$837$	−5.18155	−	0.389255i	−0.179101	−	0.0134546i
$838$	19.2102	−	19.2102i	0.663604	−	0.663604i
$839$	51.2933			1.77084			0.885420	−	0.464791i	$-0.153871\pi$
$839$	51.2933			1.77084			0.885420	+	0.464791i	$0.153871\pi$
$840$	15.0330	+	22.4368i	0.518688	+	0.774144i
$841$	−9.27413			−0.319797
$842$	−24.1559	+	24.1559i	−0.832467	+	0.832467i
$843$	−9.97532	+	5.43149i	−0.343568	+	0.187070i
$844$		−	1.53007i		−	0.0526671i
$845$	−47.6069	+	4.37845i	−1.63773	+	0.150623i
$846$	−38.8868	−	25.1225i	−1.33696	−	0.863729i
$847$	39.2451	+	39.2451i	1.34848	+	1.34848i
$848$	−10.7583	−	10.7583i	−0.369440	−	0.369440i
$849$	8.00447	+	2.36071i	0.274713	+	0.0810194i
$850$	−0.663919	−	3.57887i	−0.0227722	−	0.122754i
$851$			17.4543i			0.598326i
$852$	0.187416	+	0.344204i	0.00642077	+	0.0117922i
$853$	−24.0420	+	24.0420i	−0.823184	+	0.823184i	−0.986563	−	0.163379i	$-0.947761\pi$
$853$	−24.0420	+	24.0420i	−0.823184	+	0.823184i	0.163379	+	0.986563i	$0.447761\pi$
$854$	42.2456			1.44561
$855$	−12.5038	+	23.9080i	−0.427620	+	0.817637i
$856$	40.6917			1.39081
$857$	16.2662	−	16.2662i	0.555643	−	0.555643i	−0.372421	−	0.928064i	$-0.621472\pi$
$857$	16.2662	−	16.2662i	0.555643	−	0.555643i	0.928064	+	0.372421i	$0.121472\pi$
$858$	40.7310	+	74.8056i	1.39053	+	2.55382i
$859$		−	21.1629i		−	0.722070i	−0.932552	−	0.361035i	$-0.882423\pi$
$859$		−	21.1629i		−	0.722070i	0.932552	−	0.361035i	$-0.117577\pi$
$860$	1.28914	−	1.55028i	0.0439592	−	0.0528641i
$861$	33.8668	+	9.98815i	1.15418	+	0.340395i
$862$	12.0225	+	12.0225i	0.409489	+	0.409489i
$863$	16.1278	+	16.1278i	0.548998	+	0.548998i	0.926151	−	0.377153i	$-0.123097\pi$
$863$	16.1278	+	16.1278i	0.548998	+	0.548998i	−0.377153	+	0.926151i	$0.623097\pi$
$864$	3.66724	−	3.15475i	0.124762	−	0.107327i
$865$	34.7635	−	41.8056i	1.18199	−	1.42143i
$866$		−	34.8329i		−	1.18367i
$867$	−25.4876	+	13.8778i	−0.865604	+	0.471315i
$868$	−0.301299	+	0.301299i	−0.0102267	+	0.0102267i
$869$	−3.87160			−0.131335
$870$	4.90622	−	24.8299i	0.166336	−	0.841811i
$871$	−45.4454			−1.53986
$872$	−6.36335	+	6.36335i	−0.215490	+	0.215490i
$873$	−30.9476	+	6.65487i	−1.04742	+	0.225233i
$874$			31.5524i			1.06728i
$875$	14.1028	−	25.1971i	0.476761	−	0.851816i
$876$	0.513499	−	1.74112i	0.0173495	−	0.0588270i
$877$	−2.86308	−	2.86308i	−0.0966792	−	0.0966792i	0.657113	−	0.753792i	$-0.271777\pi$
$877$	−2.86308	−	2.86308i	−0.0966792	−	0.0966792i	−0.753792	+	0.657113i	$0.771777\pi$
$878$	−29.4235	−	29.4235i	−0.992996	−	0.992996i
$879$	1.82077	−	6.17368i	0.0614129	−	0.208233i
$880$	−54.6103	+	5.02256i	−1.84091	+	0.169310i
$881$			36.9673i			1.24546i	0.782436	+	0.622730i	$0.213977\pi$
$881$			36.9673i			1.24546i	−0.782436	+	0.622730i	$0.786023\pi$
$882$	−1.42309	+	0.306016i	−0.0479178	+	0.0103041i
$883$	9.83858	−	9.83858i	0.331094	−	0.331094i	−0.521908	−	0.853002i	$-0.674779\pi$
$883$	9.83858	−	9.83858i	0.331094	−	0.331094i	0.853002	+	0.521908i	$0.174779\pi$
$884$	−0.478622			−0.0160978
$885$	21.8799	−	14.6599i	0.735486	−	0.492787i
$886$	−39.8907			−1.34015
$887$	10.0492	−	10.0492i	0.337420	−	0.337420i	−0.517976	−	0.855395i	$-0.673314\pi$
$887$	10.0492	−	10.0492i	0.337420	−	0.337420i	0.855395	+	0.517976i	$0.173314\pi$
$888$	−13.4457	+	7.32110i	−0.451209	+	0.245680i
$889$			31.9613i			1.07195i
$890$	22.4362	+	18.6568i	0.752063	+	0.625379i
$891$	−46.7651	+	21.0875i	−1.56669	+	0.706459i
$892$	−2.15401	−	2.15401i	−0.0721216	−	0.0721216i
$893$	29.8278	+	29.8278i	0.998150	+	0.998150i
$894$	17.6377	+	5.20178i	0.589892	+	0.173973i
$895$	1.05624	+	11.4845i	0.0353063	+	0.383885i
$896$			32.3053i			1.07924i
$897$	−25.8935	−	47.5552i	−0.864557	−	1.58782i
$898$	1.40011	−	1.40011i	0.0467223	−	0.0467223i
$899$	−4.44138			−0.148128
$900$	−2.28878	−	0.941244i	−0.0762925	−	0.0313748i
$901$	−1.74947			−0.0582833
$902$	−46.8100	+	46.8100i	−1.55860	+	1.55860i
$903$	11.6912	+	21.4717i	0.389058	+	0.714533i
$904$		−	42.9747i		−	1.42932i
$905$	−1.07429	−	11.6807i	−0.0357105	−	0.388281i
$906$	−12.2964	−	3.62650i	−0.408520	−	0.120482i
$907$	31.4767	+	31.4767i	1.04517	+	1.04517i	0.998931	+	0.0462346i	$0.0147222\pi$
$907$	31.4767	+	31.4767i	1.04517	+	1.04517i	0.0462346	+	0.998931i	$0.485278\pi$
$908$	1.39189	+	1.39189i	0.0461915	+	0.0461915i
$909$	−5.71833	−	3.69427i	−0.189665	−	0.122531i
$910$	−38.3094	−	31.8562i	−1.26994	−	1.05602i
$911$		−	2.08358i		−	0.0690320i	−0.999404	−	0.0345160i	$-0.989011\pi$
$911$		−	2.08358i		−	0.0690320i	0.999404	−	0.0345160i	$-0.0109890\pi$
$912$	−26.3249	+	14.3337i	−0.871703	+	0.474636i
$913$	−36.5523	+	36.5523i	−1.20970	+	1.20970i
$914$	−6.91955			−0.228878
$915$	35.7690	−	23.9658i	1.18249	−	0.792284i
$916$	1.69397			0.0559705
$917$	−0.279822	+	0.279822i	−0.00924053	+	0.00924053i
$918$	0.283372	−	3.77210i	0.00935267	−	0.124498i
$919$		−	15.9391i		−	0.525782i	−0.964826	−	0.262891i	$-0.915324\pi$
$919$		−	15.9391i		−	0.525782i	0.964826	−	0.262891i	$-0.0846760\pi$
$920$	32.0544	−	2.94807i	1.05680	−	0.0971950i
$921$	−0.872773	+	2.95932i	−0.0287589	+	0.0975128i
$922$	24.9239	+	24.9239i	0.820826	+	0.820826i
$923$	5.68636	+	5.68636i	0.187169	+	0.187169i
$924$	−1.18999	+	4.03492i	−0.0391480	+	0.132739i
$925$	13.4912	+	9.26897i	0.443589	+	0.304762i
$926$		−	4.97920i		−	0.163627i
$927$	7.46754	+	34.7268i	0.245266	+	1.14058i
$928$	2.92374	−	2.92374i	0.0959766	−	0.0959766i
$929$	27.9730			0.917764			0.458882	−	0.888497i	$-0.348250\pi$
$929$	27.9730			0.917764			0.458882	+	0.888497i	$0.348250\pi$
$930$	−1.10466	+	5.59057i	−0.0362233	+	0.183322i
$931$	1.32629			0.0434675
$932$	−0.680168	+	0.680168i	−0.0222796	+	0.0222796i
$933$	−6.69201	+	3.64374i	−0.219086	+	0.119291i
$934$		−	9.52359i		−	0.311622i
$935$	−4.03189	+	4.84865i	−0.131857	+	0.158568i
$936$	25.7728	−	39.8935i	0.842411	−	1.30396i
$937$	13.5270	+	13.5270i	0.441909	+	0.441909i	0.892653	−	0.450744i	$-0.148841\pi$
$937$	13.5270	+	13.5270i	0.441909	+	0.441909i	−0.450744	+	0.892653i	$0.648841\pi$
$938$	−20.8266	−	20.8266i	−0.680013	−	0.680013i
$939$	−21.1274	−	6.23098i	−0.689467	−	0.203340i
$940$	−2.47388	+	2.97502i	−0.0806890	+	0.0970343i
$941$			28.3915i			0.925537i	0.886479	+	0.462769i	$0.153144\pi$
$941$			28.3915i			0.925537i	−0.886479	+	0.462769i	$0.846856\pi$
$942$	0.203015	+	0.372852i	0.00661459	+	0.0121482i
$943$	29.7580	−	29.7580i	0.969053	−	0.969053i
$944$	29.2596			0.952319
$945$	20.8609	−	21.5709i	0.678606	−	0.701702i
$946$	−45.8370			−1.49029
$947$	−26.7170	+	26.7170i	−0.868187	+	0.868187i	−0.992272	−	0.124084i	$-0.960401\pi$
$947$	−26.7170	+	26.7170i	−0.868187	+	0.868187i	0.124084	+	0.992272i	$0.460401\pi$
$948$	−0.0928177	−	0.170467i	−0.00301458	−	0.00553650i
$949$		−	37.2471i		−	1.20909i
$950$	24.3883	+	16.7557i	0.791261	+	0.543625i
$951$	46.6841	+	13.7683i	1.51384	+	0.446467i
$952$	2.43960	+	2.43960i	0.0790679	+	0.0790679i
$953$	6.49815	+	6.49815i	0.210496	+	0.210496i	0.804478	−	0.593982i	$-0.202445\pi$
$953$	6.49815	+	6.49815i	0.210496	+	0.210496i	−0.593982	+	0.804478i	$0.702445\pi$
$954$	−8.46989	+	13.1105i	−0.274223	+	0.424467i
$955$	−29.0055	+	2.66766i	−0.938595	+	0.0863234i
$956$			1.36903i			0.0442776i
$957$	−38.5097	+	20.9682i	−1.24484	+	0.677806i
$958$	−24.4881	+	24.4881i	−0.791176	+	0.791176i
$959$	−22.4344			−0.724445
$960$	15.5987	+	23.2810i	0.503445	+	0.751392i
$961$	1.00000			0.0322581
$962$	19.9713	−	19.9713i	0.643900	−	0.643900i
$963$	−9.50510	−	44.2022i	−0.306298	−	1.42440i
$964$		−	4.29214i		−	0.138241i
$965$	6.03786	+	5.02079i	0.194366	+	0.161625i
$966$	9.92710	−	33.6599i	0.319399	−	1.08299i
$967$	9.39335	+	9.39335i	0.302070	+	0.302070i	0.841823	−	0.539753i	$-0.181483\pi$
$967$	9.39335	+	9.39335i	0.302070	+	0.302070i	−0.539753	+	0.841823i	$0.681483\pi$
$968$	41.0281	+	41.0281i	1.31869	+	1.31869i
$969$	−0.974983	+	3.30588i	−0.0313210	+	0.106200i
$970$	3.17948	+	34.5705i	0.102087	+	1.10999i
$971$			32.6750i			1.04859i	0.851537	+	0.524295i	$0.175671\pi$
$971$			32.6750i			1.04859i	−0.851537	+	0.524295i	$0.824329\pi$
$972$	−2.04963	−	1.55352i	−0.0657419	−	0.0498290i
$973$	−25.0466	+	25.0466i	−0.802958	+	0.802958i
$974$	−60.1814			−1.92834
$975$	−50.5081	−	5.23959i	−1.61755	−	0.167801i
$976$	47.8331			1.53110
$977$	−21.1843	+	21.1843i	−0.677747	+	0.677747i	−0.959490	−	0.281743i	$-0.909087\pi$
$977$	−21.1843	+	21.1843i	−0.677747	+	0.677747i	0.281743	+	0.959490i	$0.409087\pi$
$978$	−0.232452	+	0.126568i	−0.00743301	+	0.00404721i
$979$		−	50.5525i		−	1.61567i
$980$	0.0111416	+	0.121142i	0.000355905	+	0.00386975i
$981$	8.39873	+	5.42592i	0.268151	+	0.173236i
$982$	26.0081	+	26.0081i	0.829951	+	0.829951i
$983$	15.9122	+	15.9122i	0.507521	+	0.507521i	0.913765	−	0.406244i	$-0.133162\pi$
$983$	15.9122	+	15.9122i	0.507521	+	0.507521i	−0.406244	+	0.913765i	$0.633162\pi$
$984$	35.4055	+	10.4419i	1.12869	+	0.332877i
$985$	22.2260	+	18.4820i	0.708178	+	0.588886i
$986$		−	3.23326i		−	0.102968i
$987$	−22.4356	−	41.2046i	−0.714132	−	1.31156i
$988$	2.75120	−	2.75120i	0.0875275	−	0.0875275i
$989$	29.1394			0.926579
$990$	16.8155	+	53.6891i	0.534432	+	1.70635i
$991$	−36.1800			−1.14930			−0.574649	−	0.818400i	$-0.694861\pi$
$991$	−36.1800			−1.14930			−0.574649	+	0.818400i	$0.694861\pi$
$992$	−0.658296	+	0.658296i	−0.0209009	+	0.0209009i
$993$	−18.3542	−	33.7088i	−0.582453	−	1.06972i
$994$			5.21186i			0.165310i
$995$	−8.83621	+	0.812674i	−0.280127	+	0.0257635i
$996$	−2.48570	−	0.733093i	−0.0787624	−	0.0232289i
$997$	15.5342	+	15.5342i	0.491972	+	0.491972i	0.908927	−	0.416955i	$-0.136903\pi$
$997$	15.5342	+	15.5342i	0.491972	+	0.491972i	−0.416955	+	0.908927i	$0.636903\pi$
$998$	17.1735	+	17.1735i	0.543618	+	0.543618i
$999$	11.0935	+	12.8956i	0.350982	+	0.407999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.k.a.32.9	✓	60
3.2	odd	2	inner	465.2.k.a.32.22	yes	60
5.3	odd	4	inner	465.2.k.a.218.22	yes	60
15.8	even	4	inner	465.2.k.a.218.9	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.k.a.32.9	✓	60	1.1	even	1	trivial
465.2.k.a.32.22	yes	60	3.2	odd	2	inner
465.2.k.a.218.9	yes	60	15.8	even	4	inner
465.2.k.a.218.22	yes	60	5.3	odd	4	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:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04043 + 1.04043i) q^{2} +(0.828268 + 1.52117i) q^{3} -0.164984i q^{4} +(-0.204789 - 2.22667i) q^{5} +(-2.44443 - 0.720921i) q^{6} +(-1.82623 - 1.82623i) q^{7} +(-1.90920 - 1.90920i) q^{8} +(-1.62795 + 2.51988i) q^{9} +(2.52976 + 2.10362i) q^{10} -5.69997i q^{11} +(0.250969 - 0.136651i) q^{12} +(4.14610 - 4.14610i) q^{13} +3.80013 q^{14} +(3.21754 - 2.15580i) q^{15} +4.30275 q^{16} +(0.349849 - 0.349849i) q^{17} +(-0.927994 - 4.31552i) q^{18} +4.02199i q^{19} +(-0.367365 + 0.0337869i) q^{20} +(1.26541 - 4.29062i) q^{21} +(5.93041 + 5.93041i) q^{22} +(-3.77007 - 3.77007i) q^{23} +(1.32290 - 4.48556i) q^{24} +(-4.91612 + 0.911995i) q^{25} +8.62745i q^{26} +(-5.18155 - 0.389255i) q^{27} +(-0.301299 + 0.301299i) q^{28} -4.44138 q^{29} +(-1.10466 + 5.59057i) q^{30} +1.00000 q^{31} +(-0.658296 + 0.658296i) q^{32} +(8.67065 - 4.72110i) q^{33} +0.727986i q^{34} +(-3.69242 + 4.44041i) q^{35} +(0.415740 + 0.268585i) q^{36} +(-2.31485 - 2.31485i) q^{37} +(-4.18460 - 4.18460i) q^{38} +(9.74103 + 2.87286i) q^{39} +(-3.86018 + 4.64215i) q^{40} +7.89322i q^{41} +(3.14752 + 5.78066i) q^{42} +(-3.86457 + 3.86457i) q^{43} -0.940404 q^{44} +(5.94433 + 3.10885i) q^{45} +7.84498 q^{46} +(7.41618 - 7.41618i) q^{47} +(3.56383 + 6.54523i) q^{48} -0.329760i q^{49} +(4.16601 - 6.06374i) q^{50} +(0.821950 + 0.242413i) q^{51} +(-0.684040 - 0.684040i) q^{52} +(-2.50032 - 2.50032i) q^{53} +(5.79603 - 4.98604i) q^{54} +(-12.6920 + 1.16729i) q^{55} +6.97329i q^{56} +(-6.11815 + 3.33129i) q^{57} +(4.62094 - 4.62094i) q^{58} +6.80022 q^{59} +(-0.355672 - 0.530842i) q^{60} +11.1169 q^{61} +(-1.04043 + 1.04043i) q^{62} +(7.57489 - 1.62888i) q^{63} +7.23568i q^{64} +(-10.0811 - 8.38293i) q^{65} +(-4.10923 + 13.9332i) q^{66} +(-5.48050 - 5.48050i) q^{67} +(-0.0577195 - 0.0577195i) q^{68} +(2.61231 - 8.85756i) q^{69} +(-0.778224 - 8.46163i) q^{70} +1.37150i q^{71} +(7.91904 - 1.70288i) q^{72} +(4.49182 - 4.49182i) q^{73} +4.81688 q^{74} +(-5.45917 - 6.72291i) q^{75} +0.663564 q^{76} +(-10.4095 + 10.4095i) q^{77} +(-13.1239 + 7.14583i) q^{78} -0.679232i q^{79} +(-0.881155 - 9.58080i) q^{80} +(-3.69959 - 8.20445i) q^{81} +(-8.21233 - 8.21233i) q^{82} +(-6.41272 - 6.41272i) q^{83} +(-0.707884 - 0.208772i) q^{84} +(-0.850644 - 0.707353i) q^{85} -8.04162i q^{86} +(-3.67865 - 6.75612i) q^{87} +(-10.8824 + 10.8824i) q^{88} +8.86891 q^{89} +(-9.41919 + 2.95011i) q^{90} -15.1435 q^{91} +(-0.622001 + 0.622001i) q^{92} +(0.828268 + 1.52117i) q^{93} +15.4320i q^{94} +(8.95565 - 0.823659i) q^{95} +(-1.54663 - 0.456138i) q^{96} +(7.46117 + 7.46117i) q^{97} +(0.343092 + 0.343092i) q^{98} +(14.3632 + 9.27924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{6} - 32 q^{10} + 4 q^{13} + 20 q^{15} - 60 q^{16} - 46 q^{18} - 4 q^{21} + 8 q^{22} - 8 q^{25} - 6 q^{27} + 112 q^{28} + 54 q^{30} + 60 q^{31} - 30 q^{33} - 4 q^{36} - 36 q^{37} - 36 q^{40}+ \cdots - 8 q^{97}+O(q^{100}) \) 60 * q - 4 * q^6 - 32 * q^10 + 4 * q^13 + 20 * q^15 - 60 * q^16 - 46 * q^18 - 4 * q^21 + 8 * q^22 - 8 * q^25 - 6 * q^27 + 112 * q^28 + 54 * q^30 + 60 * q^31 - 30 * q^33 - 4 * q^36 - 36 * q^37 - 36 * q^40 + 44 * q^42 + 16 * q^43 + 14 * q^45 + 40 * q^46 - 104 * q^48 - 48 * q^51 - 12 * q^52 - 48 * q^55 + 42 * q^57 + 80 * q^58 + 60 * q^60 - 8 * q^61 - 10 * q^63 - 24 * q^66 - 88 * q^67 - 84 * q^70 + 84 * q^72 + 60 * q^73 + 14 * q^75 + 72 * q^76 - 152 * q^78 - 132 * q^81 - 60 * q^82 - 16 * q^85 + 34 * q^87 + 124 * q^88 + 190 * q^90 + 64 * q^91 - 88 * q^96 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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