LMFDB - Embedded newform 465.2.k.a.32.22

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)

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")

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);

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			32.22
Character	$\chi$	$=$	465.32
Dual form			465.2.k.a.218.22

$q$-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} +(-1.52117 - 0.828268i) 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} +(-0.136651 + 0.250969i) q^{12} +(4.14610 - 4.14610i) q^{13} -3.80013 q^{14} +(1.53276 - 3.55678i) q^{15} +4.30275 q^{16} +(-0.349849 + 0.349849i) q^{17} +(4.31552 + 0.927994i) 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} +(-0.389255 - 5.18155i) q^{27} +(-0.301299 + 0.301299i) q^{28} +4.44138 q^{29} +(-2.10584 - 5.29530i) q^{30} +1.00000 q^{31} +(0.658296 - 0.658296i) q^{32} +(4.72110 - 8.67065i) 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} +(5.78066 + 3.14752i) q^{42} +(-3.86457 + 3.86457i) q^{43} +0.940404 q^{44} +(-5.27756 + 4.14094i) q^{45} +7.84498 q^{46} +(-7.41618 + 7.41618i) q^{47} +(-6.54523 - 3.56383i) 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} +(3.33129 - 6.11815i) q^{57} +(4.62094 - 4.62094i) q^{58} -6.80022 q^{59} +(-0.586811 - 0.252881i) q^{60} +11.1169 q^{61} +(1.04043 - 1.04043i) q^{62} +(1.62888 - 7.57489i) 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} +(-1.70288 + 7.91904i) q^{72} +(4.49182 - 4.49182i) q^{73} -4.81688 q^{74} +(8.23366 + 2.68456i) q^{75} +0.663564 q^{76} +(10.4095 - 10.4095i) q^{77} +(-7.14583 + 13.1239i) 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} +(-6.75612 - 3.67865i) q^{87} +(-10.8824 + 10.8824i) q^{88} -8.86891 q^{89} +(-1.18257 + 9.79928i) q^{90} -15.1435 q^{91} +(0.622001 - 0.622001i) q^{92} +(-1.52117 - 0.828268i) 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	−0.236047	−	0.971742i	$-0.575852\pi$
$2$	1.04043	−	1.04043i	0.735694	−	0.735694i	0.971742	+	0.236047i	$0.0758520\pi$
$3$	−1.52117	−	0.828268i	−0.878251	−	0.478201i
$3$	−1.52117	−	0.828268i	−0.878251	−	0.478201i
$4$		−	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	$0.329102\pi$
$11$			5.69997i			1.71861i	−0.511467	+	0.859303i	$0.670898\pi$
$12$	−0.136651	+	0.250969i	−0.0394477	+	0.0724486i
$13$	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
$15$	1.53276	−	3.55678i	0.395757	−	0.918355i
$16$	4.30275			1.07569
$17$	−0.349849	+	0.349849i	−0.0848509	+	0.0848509i	−0.748258	−	0.663407i	$-0.769110\pi$
$17$	−0.349849	+	0.349849i	−0.0848509	+	0.0848509i	0.663407	+	0.748258i	$0.269110\pi$
$18$	4.31552	+	0.927994i	1.01718	+	0.218730i
$19$			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	0.980855	−	0.194741i	$-0.0623866\pi$
$23$	3.77007	+	3.77007i	0.786114	+	0.786114i	−0.194741	+	0.980855i	$0.562387\pi$
$24$	−1.32290	−	4.48556i	−0.270036	−	0.915612i
$25$	−4.91612	+	0.911995i	−0.983225	+	0.182399i
$26$		−	8.62745i		−	1.69198i
$27$	−0.389255	−	5.18155i	−0.0749121	−	0.997190i
$28$	−0.301299	+	0.301299i	−0.0569401	+	0.0569401i
$29$	4.44138			0.824744			0.412372	−	0.911016i	$-0.364700\pi$
$29$	4.44138			0.824744			0.412372	+	0.911016i	$0.364700\pi$
$30$	−2.10584	−	5.29530i	−0.384473	−	0.966785i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	0.658296	−	0.658296i	0.116371	−	0.116371i
$33$	4.72110	−	8.67065i	0.821838	−	1.50937i
$34$			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	$-0.788608\pi$
$41$		−	7.89322i		−	1.23271i	0.787467	−	0.616357i	$-0.211392\pi$
$42$	5.78066	+	3.14752i	0.891975	+	0.485673i
$43$	−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
$45$	−5.27756	+	4.14094i	−0.786732	+	0.617295i
$46$	7.84498			1.15668
$47$	−7.41618	+	7.41618i	−1.08176	+	1.08176i	−0.0854163	+	0.996345i	$0.527222\pi$
$47$	−7.41618	+	7.41618i	−1.08176	+	1.08176i	−0.996345	+	0.0854163i	$0.972778\pi$
$48$	−6.54523	−	3.56383i	−0.944723	−	0.514394i
$49$		−	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	0.857661	−	0.514216i	$-0.171917\pi$
$53$	2.50032	+	2.50032i	0.343445	+	0.343445i	−0.514216	+	0.857661i	$0.671917\pi$
$54$	−5.79603	−	4.98604i	−0.788739	−	0.678515i
$55$	−12.6920	+	1.16729i	−1.71138	+	0.157397i
$56$		−	6.97329i		−	0.931845i
$57$	3.33129	−	6.11815i	0.441240	−	0.810369i
$58$	4.62094	−	4.62094i	0.606759	−	0.606759i
$59$	−6.80022			−0.885313			−0.442656	−	0.896691i	$-0.645964\pi$
$59$	−6.80022			−0.885313			−0.442656	+	0.896691i	$0.645964\pi$
$60$	−0.586811	−	0.252881i	−0.0757570	−	0.0326468i
$61$	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
$63$	1.62888	−	7.57489i	0.205219	−	0.954346i
$64$			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	$-0.974066\pi$
$71$		−	1.37150i		−	0.162767i	0.996683	−	0.0813833i	$-0.0259338\pi$
$72$	−1.70288	+	7.91904i	−0.200687	+	0.933268i
$73$	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
$75$	8.23366	+	2.68456i	0.950741	+	0.309987i
$76$	0.663564			0.0761160
$77$	10.4095	−	10.4095i	1.18627	−	1.18627i
$78$	−7.14583	+	13.1239i	−0.809106	+	1.48598i
$79$		−	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	0.965243	−	0.261355i	$-0.0841695\pi$
$83$	6.41272	+	6.41272i	0.703887	+	0.703887i	−0.261355	+	0.965243i	$0.584169\pi$
$84$	0.707884	−	0.208772i	0.0772365	−	0.0227789i
$85$	−0.850644	−	0.707353i	−0.0922653	−	0.0767233i
$86$			8.04162i			0.867150i
$87$	−6.75612	−	3.67865i	−0.724332	−	0.394393i
$88$	−10.8824	+	10.8824i	−1.16007	+	1.16007i
$89$	−8.86891			−0.940102			−0.470051	−	0.882639i	$-0.655765\pi$
$89$	−8.86891			−0.940102			−0.470051	+	0.882639i	$0.655765\pi$
$90$	−1.18257	+	9.79928i	−0.124654	+	1.03293i
$91$	−15.1435			−1.58747
$92$	0.622001	−	0.622001i	0.0648481	−	0.0648481i
$93$	−1.52117	−	0.828268i	−0.157738	−	0.0858874i
$94$			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	$-0.963986\pi$
$101$		−	2.26929i		−	0.225802i	0.993606	−	0.112901i	$-0.0360143\pi$
$102$	0.602967	−	1.10739i	0.0597027	−	0.109648i
$103$	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
$105$	−9.29467	+	3.69632i	−0.907067	+	0.360724i
$106$	5.20281			0.505342
$107$	10.6567	−	10.6567i	1.03022	−	1.03022i	0.0306958	−	0.999529i	$-0.490228\pi$
$107$	10.6567	−	10.6567i	1.03022	−	1.03022i	0.999529	−	0.0306958i	$-0.00977231\pi$
$108$	−0.854873	+	0.0642208i	−0.0822602	+	0.00617965i
$109$		−	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	$-0.980705\pi$
$113$	−11.2546	−	11.2546i	−1.05874	−	1.05874i	−0.0605812	−	0.998163i	$-0.519295\pi$
$114$	−2.89954	−	9.83147i	−0.271566	−	0.920801i
$115$	−7.62264	+	9.16677i	−0.710814	+	0.854806i
$116$		−	0.732757i		−	0.0680348i
$117$	17.1973	+	3.69805i	1.58989	+	0.341885i
$118$	−7.07514	+	7.07514i	−0.651319	+	0.651319i
$119$	1.27781			0.117137
$120$	9.71696	−	3.86426i	0.887033	−	0.352757i
$121$	−21.4897			−1.95361
$122$	11.5663	−	11.5663i	1.04717	−	1.04717i
$123$	−6.53770	+	12.0070i	−0.589484	+	1.08263i
$124$		−	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	$0.00213066\pi$
$131$			0.153224i			0.0133872i	−0.999978	+	0.00669361i	$0.997869\pi$
$132$	−1.43052	−	0.778906i	−0.124511	−	0.0677951i
$133$	7.34509	−	7.34509i	0.636900	−	0.636900i
$134$	−11.4041			−0.985168
$135$	11.4579	−	1.92787i	0.986138	−	0.165924i
$136$	−1.33587			−0.114550
$137$	−6.14227	+	6.14227i	−0.524770	+	0.524770i	−0.919008	−	0.394238i	$-0.871008\pi$
$137$	−6.14227	+	6.14227i	−0.524770	+	0.524770i	0.394238	+	0.919008i	$0.371008\pi$
$138$	−11.9336	−	6.49774i	−1.01585	−	0.553125i
$139$		−	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
$147$	−0.273130	+	0.501623i	−0.0225274	+	0.0413732i
$148$	−0.381914	+	0.381914i	−0.0313931	+	0.0313931i
$149$	7.21546			0.591114			0.295557	−	0.955325i	$-0.404495\pi$
$149$	7.21546			0.591114			0.295557	+	0.955325i	$0.404495\pi$
$150$	11.3596	−	5.77344i	0.927510	−	0.471399i
$151$	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
$153$	−1.45111	−	0.312042i	−0.117316	−	0.0252271i
$154$		−	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
$162$	4.68699	+	12.3853i	0.368245	+	0.973082i
$163$	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
$165$	20.2735	+	8.73668i	1.57829	+	0.680150i
$166$	13.3440			1.03569
$167$	13.3273	−	13.3273i	1.03130	−	1.03130i	0.0318041	−	0.999494i	$-0.489875\pi$
$167$	13.3273	−	13.3273i	1.03130	−	1.03130i	0.999494	−	0.0318041i	$-0.0101253\pi$
$168$	−5.77575	+	10.6076i	−0.445609	+	0.818394i
$169$		−	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	$-0.874620\pi$
$173$	−17.1936	−	17.1936i	−1.30721	−	1.30721i	−0.383787	−	0.923422i	$-0.625380\pi$
$174$	−10.8566	+	3.20188i	−0.823039	+	0.242734i
$175$	10.6435	+	7.31246i	0.804572	+	0.552770i
$176$			24.5255i			1.84868i
$177$	10.3443	+	5.63240i	0.777527	+	0.423357i
$178$	−9.22747	+	9.22747i	−0.691628	+	0.691628i
$179$	5.15771			0.385505			0.192753	−	0.981247i	$-0.438259\pi$
$179$	5.15771			0.385505			0.192753	+	0.981247i	$0.438259\pi$
$180$	0.683189	+	0.870712i	0.0509219	+	0.0648991i
$181$	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
$183$	−16.9107	−	9.20775i	−1.25008	−	0.680657i
$184$			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	$0.156207\pi$
$191$			13.0264i			0.942556i	−0.881985	+	0.471278i	$0.843793\pi$
$192$	5.99308	−	11.0067i	0.432513	−	0.794342i
$193$	−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
$195$	−8.39177	−	21.1017i	−0.600947	−	1.51113i
$196$	−0.0544052			−0.00388608
$197$	9.14100	−	9.14100i	0.651269	−	0.651269i	−0.302030	−	0.953299i	$-0.597664\pi$
$197$	9.14100	−	9.14100i	0.651269	−	0.651269i	0.953299	+	0.302030i	$0.0976641\pi$
$198$	−5.28954	+	24.5983i	−0.375911	+	1.74813i
$199$		−	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
$207$	−3.36265	+	15.6376i	−0.233721	+	1.08689i
$208$	17.8396	−	17.8396i	1.23696	−	1.23696i
$209$	−22.9252			−1.58577
$210$	−5.82468	+	13.5162i	−0.401941	+	0.932706i
$211$	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
$213$	−1.13597	+	2.08628i	−0.0778351	+	0.142950i
$214$		−	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
$222$	7.32731	+	3.98966i	0.491777	+	0.267769i
$223$	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
$225$	−10.3013	−	10.9034i	−0.686753	−	0.726891i
$226$	−23.4192			−1.55782
$227$	8.43652	−	8.43652i	0.559952	−	0.559952i	−0.369342	−	0.929294i	$-0.620417\pi$
$227$	8.43652	−	8.43652i	0.559952	−	0.559952i	0.929294	+	0.369342i	$0.120417\pi$
$228$	−1.00940	−	0.549609i	−0.0668490	−	0.0363987i
$229$			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	0.829133	−	0.559051i	$-0.188834\pi$
$233$	4.12263	+	4.12263i	0.270082	+	0.270082i	−0.559051	+	0.829133i	$0.688834\pi$
$234$	21.7401	−	14.0450i	1.42120	−	0.918151i
$235$	−18.0322	−	14.9946i	−1.17629	−	0.978143i
$236$			1.12193i			0.0730312i
$237$	−0.562586	+	1.03323i	−0.0365439	+	0.0671156i
$238$	1.32947	−	1.32947i	0.0861768	−	0.0861768i
$239$	8.29796			0.536750			0.268375	−	0.963314i	$-0.413513\pi$
$239$	8.29796			0.536750			0.268375	+	0.963314i	$0.413513\pi$
$240$	6.59508	−	15.3039i	0.425710	−	0.987863i
$241$	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
$243$	12.4232	−	9.41616i	0.796949	−	0.604047i
$244$		−	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	$-0.742236\pi$
$251$		−	22.9451i		−	1.44828i	0.689651	−	0.724142i	$-0.257764\pi$
$252$	−1.24973	−	0.268739i	−0.0787259	−	0.0169290i
$253$	−21.4893	+	21.4893i	−1.35102	+	1.35102i
$254$	−18.2088			−1.14252
$255$	0.708100	+	1.78057i	0.0443429	+	0.111504i
$256$	3.93341			0.245838
$257$	−21.2929	+	21.2929i	−1.32822	+	1.32822i	−0.421292	+	0.906925i	$0.638423\pi$
$257$	−21.2929	+	21.2929i	−1.32822	+	1.32822i	−0.906925	+	0.421292i	$0.861577\pi$
$258$	6.66062	−	12.2327i	0.414672	−	0.761575i
$259$			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	0.552493	−	0.833517i	$-0.313676\pi$
$263$	−4.55744	−	4.55744i	−0.281024	−	0.281024i	−0.833517	+	0.552493i	$0.813676\pi$
$264$	25.5676	−	7.54049i	1.57358	−	0.464085i
$265$	−5.05535	+	6.07943i	−0.310548	+	0.373456i
$266$		−	15.2841i		−	0.937127i
$267$	13.4912	+	7.34583i	0.825645	+	0.449557i
$268$	−0.904195	+	0.904195i	−0.0552325	+	0.0552325i
$269$	8.84874			0.539517			0.269759	−	0.962928i	$-0.413056\pi$
$269$	8.84874			0.539517			0.269759	+	0.962928i	$0.413056\pi$
$270$	9.91531	−	13.9269i	0.603427	−	0.847566i
$271$	−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
$273$	23.0359	+	12.5429i	1.39419	+	0.759128i
$274$			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	$-0.937335\pi$
$281$		−	6.55765i		−	0.391196i	0.980684	−	0.195598i	$-0.0626648\pi$
$282$	12.7818	−	23.4748i	0.761148	−	1.39790i
$283$	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
$285$	14.3053	+	6.16475i	0.847374	+	0.365168i
$286$	49.1762			2.90785
$287$	−14.4148	+	14.4148i	−0.850881	+	0.850881i
$288$	2.73050	+	0.587157i	0.160896	+	0.0345986i
$289$			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	0.779685	−	0.626172i	$-0.215379\pi$
$293$	2.62772	+	2.62772i	0.153513	+	0.153513i	−0.626172	+	0.779685i	$0.715379\pi$
$294$	0.237731	+	0.806075i	0.0138648	+	0.0470113i
$295$	−1.39261	−	15.1418i	−0.0810808	−	0.881592i
$296$		−	8.83905i		−	0.513759i
$297$	29.5347	−	2.21874i	1.71378	−	0.128744i
$298$	7.50718	−	7.50718i	0.434879	−	0.434879i
$299$	31.2622			1.80794
$300$	0.442910	−	1.35842i	0.0255714	−	0.0784285i
$301$	14.1152			0.813587
$302$	5.23375	−	5.23375i	0.301168	−	0.301168i
$303$	−1.87958	+	3.45198i	−0.107979	+	0.198311i
$304$			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	$-0.960194\pi$
$311$		−	4.39924i		−	0.249458i	0.992191	−	0.124729i	$-0.0398061\pi$
$312$	−24.0825	−	13.1127i	−1.36340	−	0.742362i
$313$	−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
$315$	17.2004	+	2.07572i	0.969130	+	0.116954i
$316$	−0.112062			−0.00630401
$317$	−19.8703	+	19.8703i	−1.11603	+	1.11603i	−0.123709	+	0.992319i	$0.539479\pi$
$317$	−19.8703	+	19.8703i	−1.11603	+	1.11603i	−0.992319	+	0.123709i	$0.960521\pi$
$318$	−7.91438	−	4.30932i	−0.443817	−	0.241655i
$319$			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
$327$	−2.76061	+	5.07006i	−0.152662	+	0.280375i
$328$	15.0698	−	15.0698i	0.832088	−	0.832088i
$329$	27.0873			1.49337
$330$	30.1830	−	12.0032i	1.66152	−	0.660757i
$331$	−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
$333$	2.06470	−	9.60160i	0.113145	−	0.526165i
$334$		−	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
$342$	−3.73238	+	17.3570i	−0.201824	+	0.938557i
$343$	−13.3858	+	13.3858i	−0.722767	+	0.722767i
$344$	−14.7565			−0.795618
$345$	19.1879	−	7.63068i	1.03304	−	0.410822i
$346$	−35.7775			−1.92341
$347$	−8.19072	+	8.19072i	−0.439701	+	0.439701i	−0.891911	−	0.452210i	$-0.850636\pi$
$347$	−8.19072	+	8.19072i	−0.439701	+	0.439701i	0.452210	+	0.891911i	$0.350636\pi$
$348$	−0.606919	+	1.11465i	−0.0325343	+	0.0597516i
$349$			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	0.967429	−	0.253142i	$-0.0814639\pi$
$353$	13.4202	+	13.4202i	0.714287	+	0.714287i	−0.253142	+	0.967429i	$0.581464\pi$
$354$	16.6226	−	4.90242i	0.883483	−	0.260560i
$355$	3.05387	−	0.280867i	0.162083	−	0.0149069i
$356$			1.46323i			0.0775509i
$357$	−1.94377	−	1.05837i	−0.102875	−	0.0560148i
$358$	5.36623	−	5.36623i	0.283614	−	0.283614i
$359$	−26.5470			−1.40110			−0.700549	−	0.713604i	$-0.747061\pi$
$359$	−26.5470			−1.40110			−0.700549	+	0.713604i	$0.747061\pi$
$360$	−17.9818	−	2.17003i	−0.947726	−	0.114371i
$361$	2.82359			0.148610
$362$	5.45791	−	5.45791i	0.286861	−	0.286861i
$363$	32.6895	+	17.7992i	1.71576	+	0.934215i
$364$			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
$372$	−0.136651	+	0.250969i	−0.00708502	+	0.0130122i
$373$	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
$375$	−4.29147	+	18.8834i	−0.221611	+	0.975135i
$376$	−28.3180			−1.46039
$377$	18.4144	−	18.4144i	0.948391	−	0.948391i
$378$	1.47922	+	19.6906i	0.0760827	+	1.01277i
$379$			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	0.540402	−	0.841407i	$-0.318272\pi$
$383$	−5.89078	−	5.89078i	−0.301005	−	0.301005i	−0.841407	+	0.540402i	$0.818272\pi$
$384$	−6.12862	−	20.7803i	−0.312750	−	1.06044i
$385$	25.3102	+	21.0467i	1.28993	+	1.07264i
$386$			5.16724i			0.263005i
$387$	−16.0296	−	3.44694i	−0.814829	−	0.175218i
$388$	1.23097	−	1.23097i	0.0624932	−	0.0624932i
$389$	−21.8636			−1.10853			−0.554265	−	0.832340i	$-0.687001\pi$
$389$	−21.8636			−1.10853			−0.554265	+	0.832340i	$0.687001\pi$
$390$	−30.6859	−	13.2238i	−1.55384	−	0.669613i
$391$	−2.63791			−0.133405
$392$	0.629580	−	0.629580i	0.0317986	−	0.0317986i
$393$	0.126910	−	0.233080i	0.00640177	−	0.0117573i
$394$		−	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	$0.101445\pi$
$401$			12.5489i			0.626665i	−0.949644	+	0.313332i	$0.898555\pi$
$402$	17.3477	+	9.44568i	0.865224	+	0.471108i
$403$	4.14610	−	4.14610i	0.206532	−	0.206532i
$404$	−0.374396			−0.0186269
$405$	−19.0262	−	6.55758i	−0.945422	−	0.325849i
$406$	−16.8778			−0.837632
$407$	13.1946	−	13.1946i	0.654032	−	0.654032i
$408$	2.03209	+	1.10645i	0.100603	+	0.0547777i
$409$		−	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
$417$	−11.3596	+	20.8628i	−0.556284	+	1.02166i
$418$	−23.8521	+	23.8521i	−1.16664	+	1.16664i
$419$	18.4637			0.902010			0.451005	−	0.892521i	$-0.351066\pi$
$419$	18.4637			0.902010			0.451005	+	0.892521i	$0.351066\pi$
$420$	0.609834	+	1.53347i	0.0297568	+	0.0748257i
$421$	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
$423$	−30.7610	−	6.61475i	−1.49565	−	0.321620i
$424$			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	$0.0897713\pi$
$431$			11.5554i			0.556602i	−0.960494	+	0.278301i	$0.910229\pi$
$432$	−1.67487	−	22.2949i	−0.0805820	−	1.07266i
$433$	−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
$435$	6.80757	−	15.7970i	0.326398	−	0.757408i
$436$	−0.549890			−0.0263349
$437$	−15.1632	+	15.1632i	−0.725354	+	0.725354i
$438$	−7.74169	+	14.2182i	−0.369912	+	0.679371i
$439$			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	0.0855269	−	0.996336i	$-0.472743\pi$
$443$	−19.1703	−	19.1703i	−0.910809	−	0.910809i	−0.996336	+	0.0855269i	$0.972743\pi$
$444$	0.897284	−	0.264631i	0.0425832	−	0.0125588i
$445$	−1.81625	−	19.7481i	−0.0860987	−	0.936151i
$446$		−	27.1674i		−	1.28642i
$447$	−10.9760	−	5.97633i	−0.519146	−	0.282671i
$448$	13.2140	−	13.2140i	0.624304	−	0.624304i
$449$	1.34571			0.0635078			0.0317539	−	0.999496i	$-0.489891\pi$
$449$	1.34571			0.0635078			0.0317539	+	0.999496i	$0.489891\pi$
$450$	−22.0619	−	0.626405i	−1.04001	−	0.0295290i
$451$	44.9911			2.11855
$452$	−1.85683	+	1.85683i	−0.0873379	+	0.0873379i
$453$	−7.65208	−	4.16650i	−0.359526	−	0.195759i
$454$		−	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	$0.188377\pi$
$461$			23.9555i			1.11572i	−0.829936	+	0.557858i	$0.811623\pi$
$462$	−17.9408	+	32.9496i	−0.834681	+	1.53295i
$463$	−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
$465$	1.53276	−	3.55678i	0.0710800	−	0.164941i
$466$	8.57860			0.397396
$467$	4.57676	−	4.57676i	0.211787	−	0.211787i	−0.593239	−	0.805026i	$-0.702151\pi$
$467$	4.57676	−	4.57676i	0.211787	−	0.211787i	0.805026	+	0.593239i	$0.202151\pi$
$468$	0.610119	−	2.83728i	0.0282028	−	0.131153i
$469$			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
$477$	−2.23012	+	10.3709i	−0.102110	+	0.474851i
$478$	8.63344	−	8.63344i	0.394884	−	0.394884i
$479$	−23.5366			−1.07541			−0.537707	−	0.843132i	$-0.680709\pi$
$479$	−23.5366			−1.07541			−0.537707	+	0.843132i	$0.680709\pi$
$480$	−1.33240	−	3.35042i	−0.0608155	−	0.152925i
$481$	−19.1952			−0.875227
$482$	27.0673	−	27.0673i	1.23288	−	1.23288i
$483$	−11.4053	+	20.9466i	−0.518958	+	0.953105i
$484$			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	$0.190761\pi$
$491$			24.9974i			1.12812i	−0.825734	+	0.564059i	$0.809239\pi$
$492$	1.98096	+	1.07862i	0.0893084	+	0.0486277i
$493$	−1.55381	+	1.55381i	−0.0699802	+	0.0699802i
$494$	34.6995			1.56120
$495$	−23.6032	−	30.0819i	−1.06089	−	1.35208i
$496$	4.30275			0.193199
$497$	−2.50467	+	2.50467i	−0.112350	+	0.112350i
$498$	−20.2985	−	11.0524i	−0.909597	−	0.495268i
$499$		−	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	0.399081	−	0.916916i	$-0.369329\pi$
$503$	−11.6138	−	11.6138i	−0.517835	−	0.517835i	−0.916916	+	0.399081i	$0.869329\pi$
$504$	17.5719	−	11.3521i	0.782713	−	0.505665i
$505$	5.05295	−	0.464724i	0.224853	−	0.0206800i
$506$			44.7161i			1.98788i
$507$	−17.7086	+	32.5232i	−0.786467	+	1.44441i
$508$	−1.44371	+	1.44371i	−0.0640543	+	0.0640543i
$509$	−33.0579			−1.46527			−0.732634	−	0.680623i	$-0.761709\pi$
$509$	−33.0579			−1.46527			−0.732634	+	0.680623i	$0.761709\pi$
$510$	2.58928	+	1.11583i	0.114655	+	0.0494097i
$511$	−16.4062			−0.725768
$512$	−13.5972	+	13.5972i	−0.600915	+	0.600915i
$513$	20.8402	−	1.56558i	0.920115	−	0.0691220i
$514$			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	$0.0396589\pi$
$521$			5.67303i			0.248540i	−0.992248	+	0.124270i	$0.960341\pi$
$522$	19.1669	+	4.12158i	0.838911	+	0.180396i
$523$	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
$525$	−10.1339	−	19.9392i	−0.442281	−	0.870218i
$526$	−9.48339			−0.413495
$527$	−0.349849	+	0.349849i	−0.0152397	+	0.0152397i
$528$	20.3137	−	37.3076i	0.884041	−	1.62361i
$529$			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
$537$	−7.84578	−	4.27196i	−0.338570	−	0.184349i
$538$	9.20648	−	9.20648i	0.396920	−	0.396920i
$539$	1.87962			0.0809612
$540$	−0.318067	−	1.89037i	−0.0136874	−	0.0813485i
$541$	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
$543$	−7.97982	−	4.34495i	−0.342447	−	0.186460i
$544$			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
$552$	11.9235	−	21.8983i	0.507496	−	0.932054i
$553$	−1.24044	+	1.24044i	−0.0527487	+	0.0527487i
$554$	−7.94778			−0.337669
$555$	−11.7815	+	4.68530i	−0.500098	+	0.198880i
$556$	−2.26274			−0.0959617
$557$	0.552934	−	0.552934i	0.0234286	−	0.0234286i	−0.695295	−	0.718724i	$-0.744726\pi$
$557$	0.552934	−	0.552934i	0.0234286	−	0.0234286i	0.718724	+	0.695295i	$0.244726\pi$
$558$	4.31552	+	0.927994i	0.182690	+	0.0392851i
$559$			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	0.357096	−	0.934068i	$-0.383767\pi$
$563$	−13.6902	−	13.6902i	−0.576972	−	0.576972i	−0.934068	+	0.357096i	$0.883767\pi$
$564$	−0.847808	−	2.87466i	−0.0356991	−	0.121045i
$565$	22.7555	−	27.3651i	0.957330	−	1.15126i
$566$		−	7.08941i		−	0.297990i
$567$	21.7395	−	8.22693i	0.912974	−	0.345498i
$568$	2.61846	−	2.61846i	0.109868	−	0.109868i
$569$	21.0505			0.882485			0.441242	−	0.897388i	$-0.354538\pi$
$569$	21.0505			0.882485			0.441242	+	0.897388i	$0.354538\pi$
$570$	21.2976	−	8.46969i	0.892060	−	0.354756i
$571$	−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
$573$	10.7893	−	19.8154i	0.450731	−	0.827800i
$574$			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
$582$	−23.6172	−	12.8594i	−0.978964	−	0.533038i
$583$	−14.2518	+	14.2518i	−0.590247	+	0.590247i
$584$	17.1516			0.709738
$585$	−4.71252	+	39.0500i	−0.194839	+	1.61452i
$586$	5.46791			0.225877
$587$	−23.4513	+	23.4513i	−0.967939	+	0.967939i	−0.999502	−	0.0315627i	$-0.989952\pi$
$587$	−23.4513	+	23.4513i	−0.967939	+	0.967939i	0.0315627	+	0.999502i	$0.489952\pi$
$588$	0.0827598	+	0.0450621i	0.00341296	+	0.00185833i
$589$			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	0.401544	−	0.915840i	$-0.368474\pi$
$593$	−12.5239	−	12.5239i	−0.514295	−	0.514295i	−0.915840	+	0.401544i	$0.868474\pi$
$594$	28.4203	−	33.0372i	1.16610	−	1.35553i
$595$	0.261681	+	2.84526i	0.0107279	+	0.116644i
$596$		−	1.19044i		−	0.0487622i
$597$	−3.28686	+	6.03656i	−0.134522	+	0.247060i
$598$	32.5261	−	32.5261i	1.33009	−	1.33009i
$599$	13.4427			0.549254			0.274627	−	0.961551i	$-0.411446\pi$
$599$	13.4427			0.549254			0.274627	+	0.961551i	$0.411446\pi$
$600$	10.5944	+	20.8451i	0.432513	+	0.850998i
$601$	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
$603$	4.88825	−	22.7322i	0.199065	−	0.925725i
$604$		−	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
$612$	−0.0514820	+	0.239410i	−0.00208104	+	0.00967759i
$613$	−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
$615$	−28.0744	−	12.0984i	−1.13207	−	0.487855i
$616$	39.7476			1.60147
$617$	19.4262	−	19.4262i	0.782069	−	0.782069i	−0.198111	−	0.980180i	$-0.563481\pi$
$617$	19.4262	−	19.4262i	0.782069	−	0.782069i	0.980180	+	0.198111i	$0.0634806\pi$
$618$	−14.4297	+	26.5012i	−0.580448	+	1.06604i
$619$		−	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
$627$	34.8733	+	18.9882i	1.39270	+	0.758317i
$628$	−0.0194338	+	0.0194338i	−0.000775492	+	0.000775492i
$629$	1.61970			0.0645816
$630$	20.0554	−	15.7361i	0.799026	−	0.626941i
$631$	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
$633$	−14.1074	−	7.68138i	−0.560720	−	0.305307i
$634$			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	$0.213639\pi$
$641$			31.4906i			1.24380i	−0.783096	+	0.621901i	$0.786361\pi$
$642$	−18.3669	+	33.7322i	−0.724885	+	1.33131i
$643$	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
$645$	7.82195	+	19.6689i	0.307989	+	0.774461i
$646$	−2.92795			−0.115199
$647$	22.3622	−	22.3622i	0.879148	−	0.879148i	−0.114298	−	0.993446i	$-0.536462\pi$
$647$	22.3622	−	22.3622i	0.879148	−	0.879148i	0.993446	+	0.114298i	$0.0364619\pi$
$648$	−22.7272	+	8.60071i	−0.892810	+	0.337868i
$649$		−	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	0.705173	−	0.709036i	$-0.250869\pi$
$653$	−0.0987075	−	0.0987075i	−0.00386272	−	0.00386272i	−0.709036	+	0.705173i	$0.750869\pi$
$654$	2.40282	+	8.14725i	0.0939577	+	0.318583i
$655$	−0.341179	+	0.0313785i	−0.0133310	+	0.00122606i
$656$		−	33.9625i		−	1.32601i
$657$	18.6313	+	4.00641i	0.726876	+	0.156305i
$658$	28.1824	−	28.1824i	1.09867	−	1.09867i
$659$	31.5045			1.22724			0.613620	−	0.789601i	$-0.289713\pi$
$659$	31.5045			1.22724			0.613620	+	0.789601i	$0.289713\pi$
$660$	1.44141	−	3.34480i	0.0561069	−	0.130196i
$661$	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
$663$	2.40282	−	4.41296i	0.0933178	−	0.171385i
$664$			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
$672$	3.65752	+	1.99149i	0.141092	+	0.0768233i
$673$	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
$675$	6.63917	+	25.1181i	0.255542	+	0.966798i
$676$	−3.52741			−0.135670
$677$	6.97865	−	6.97865i	0.268211	−	0.268211i	−0.560168	−	0.828379i	$-0.689263\pi$
$677$	6.97865	−	6.97865i	0.268211	−	0.268211i	0.828379	+	0.560168i	$0.189263\pi$
$678$	35.6248	+	19.3974i	1.36816	+	0.744952i
$679$		−	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	0.796858	−	0.604167i	$-0.206494\pi$
$683$	5.03584	+	5.03584i	0.192691	+	0.192691i	−0.604167	+	0.796858i	$0.706494\pi$
$684$	1.08025	+	1.67210i	0.0413042	+	0.0639344i
$685$	−14.9347	−	12.4190i	−0.570625	−	0.474504i
$686$			27.8540i			1.06347i
$687$	8.50425	−	15.6187i	0.324457	−	0.595890i
$688$	−16.6283	+	16.6283i	−0.633947	+	0.633947i
$689$	20.7332			0.789871
$690$	12.0245	−	27.9028i	0.457764	−	1.06224i
$691$	−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
$693$	43.1766	+	9.28456i	1.64014	+	0.352691i
$694$			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	$-0.855336\pi$
$701$		−	23.2458i		−	0.877983i	0.898491	−	0.438991i	$-0.144664\pi$
$702$	−44.7036	+	3.35827i	−1.68723	+	0.126750i
$703$	9.31032	−	9.31032i	0.351145	−	0.351145i
$704$	−41.2431			−1.55441
$705$	15.0105	+	37.7449i	0.565327	+	1.42156i
$706$	27.9256			1.05099
$707$	−4.14424	+	4.14424i	−0.155860	+	0.155860i
$708$	0.929256	−	1.70665i	0.0349236	−	0.0641397i
$709$		−	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
$717$	−12.6226	−	6.87293i	−0.471401	−	0.256674i
$718$	−27.6203	+	27.6203i	−1.03078	+	1.03078i
$719$	33.7766			1.25965			0.629826	−	0.776736i	$-0.283126\pi$
$719$	33.7766			1.25965			0.629826	+	0.776736i	$0.283126\pi$
$720$	−22.7080	+	17.8174i	−0.846277	+	0.664016i
$721$	−30.5795			−1.13884
$722$	2.93774	−	2.93774i	0.109331	−	0.109331i
$723$	−39.5741	−	21.5478i	−1.47178	−	0.801372i
$724$		−	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
$732$	−1.51913	+	2.79000i	−0.0561487	+	0.103121i
$733$	−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
$735$	−1.17288	−	0.505443i	−0.0432625	−	0.0186436i
$736$	4.96365			0.182962
$737$	31.2387	−	31.2387i	1.15069	−	1.15069i
$738$	7.32486	−	34.0633i	0.269632	−	1.25389i
$739$		−	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	0.754143	−	0.656710i	$-0.228052\pi$
$743$	2.65585	+	2.65585i	0.0974336	+	0.0974336i	−0.656710	+	0.754143i	$0.728052\pi$
$744$	−1.32290	−	4.48556i	−0.0484999	−	0.164449i
$745$	1.47765	+	16.0665i	0.0541368	+	0.588630i
$746$		−	39.5561i		−	1.44825i
$747$	−5.71972	+	26.5988i	−0.209274	+	0.973200i
$748$	−0.328999	+	0.328999i	−0.0120294	+	0.0120294i
$749$	−38.9233			−1.42223
$750$	15.1819	+	24.1118i	0.554364	+	0.880439i
$751$	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
$753$	−19.0047	+	34.9035i	−0.692570	+	1.27196i
$754$		−	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	$0.0383229\pi$
$761$			6.62645i			0.240209i	−0.992761	+	0.120104i	$0.961677\pi$
$762$	27.6987	+	15.0817i	1.00342	+	0.546353i
$763$	−6.08681	+	6.08681i	−0.220357	+	0.220357i
$764$	2.14914			0.0777533
$765$	0.397644	−	3.29505i	0.0143768	−	0.119133i
$766$	−12.2579			−0.442895
$767$	−28.1944	+	28.1944i	−1.01804	+	1.01804i
$768$	−5.98341	−	3.25792i	−0.215908	−	0.117560i
$769$			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	0.464396	−	0.885627i	$-0.346271\pi$
$773$	−11.7114	−	11.7114i	−0.421231	−	0.421231i	−0.885627	+	0.464396i	$0.846271\pi$
$774$	−20.2639	+	13.0913i	−0.728372	+	0.470558i
$775$	−4.91612	+	0.911995i	−0.176592	+	0.0327598i
$776$			28.4898i			1.02272i
$777$	7.00293	−	12.8614i	0.251229	−	0.461400i
$778$	−22.7475	+	22.7475i	−0.815539	+	0.815539i
$779$	31.7465			1.13743
$780$	−3.48145	+	1.38451i	−0.124656	+	0.0495733i
$781$	7.81748			0.279732
$782$	−2.74456	+	2.74456i	−0.0981452	+	0.0981452i
$783$	−1.72883	−	23.0133i	−0.0617833	−	0.822426i
$784$		−	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
$792$	−45.1383	−	9.70639i	−1.60392	−	0.344901i
$793$	46.0917	−	46.0917i	1.63677	−	1.63677i
$794$	−52.1162			−1.84954
$795$	12.7255	−	5.06069i	0.451326	−	0.179484i
$796$	−0.654715			−0.0232057
$797$	3.44795	−	3.44795i	0.122133	−	0.122133i	−0.643399	−	0.765531i	$-0.722476\pi$
$797$	3.44795	−	3.44795i	0.122133	−	0.122133i	0.765531	+	0.643399i	$0.222476\pi$
$798$	−12.6593	+	23.2498i	−0.448135	+	0.823032i
$799$		−	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
$807$	−13.4605	−	7.32912i	−0.473831	−	0.257997i
$808$	4.33253	−	4.33253i	0.152418	−	0.152418i
$809$	11.8818			0.417742			0.208871	−	0.977943i	$-0.433021\pi$
$809$	11.8818			0.417742			0.208871	+	0.977943i	$0.433021\pi$
$810$	−26.6182	+	12.9728i	−0.935267	+	0.455816i
$811$	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
$813$	29.2078	+	15.9034i	1.02436	+	0.557758i
$814$		−	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	$0.257359\pi$
$821$			41.4475i			1.44653i	−0.690571	+	0.723264i	$0.742641\pi$
$822$	10.5863	−	19.4424i	0.369238	−	0.678133i
$823$	−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
$825$	−15.3019	+	46.9316i	−0.532745	+	1.63395i
$826$	25.8417			0.899147
$827$	15.3731	−	15.3731i	0.534576	−	0.534576i	−0.387355	−	0.921931i	$-0.626611\pi$
$827$	15.3731	−	15.3731i	0.534576	−	0.534576i	0.921931	+	0.387355i	$0.126611\pi$
$828$	2.57995	+	0.554784i	0.0896595	+	0.0192801i
$829$		−	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
$837$	−0.389255	−	5.18155i	−0.0134546	−	0.179101i
$838$	19.2102	−	19.2102i	0.663604	−	0.663604i
$839$	−51.2933			−1.77084			−0.885420	−	0.464791i	$-0.846129\pi$
$839$	−51.2933			−1.77084			−0.885420	+	0.464791i	$0.846129\pi$
$840$	−24.8024	−	10.6884i	−0.855765	−	0.368784i
$841$	−9.27413			−0.319797
$842$	24.1559	−	24.1559i	0.832467	−	0.832467i
$843$	−5.43149	+	9.97532i	−0.187070	+	0.343568i
$844$		−	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
$852$	0.344204	+	0.187416i	0.0117922	+	0.00642077i
$853$	−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
$855$	−16.6548	−	21.2263i	−0.569583	−	0.725924i
$856$	40.6917			1.39081
$857$	−16.2662	+	16.2662i	−0.555643	+	0.555643i	−0.928064	−	0.372421i	$-0.878528\pi$
$857$	−16.2662	+	16.2662i	−0.555643	+	0.555643i	0.372421	+	0.928064i	$0.378528\pi$
$858$	−74.8056	−	40.7310i	−2.55382	−	1.39053i
$859$		−	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	0.377153	−	0.926151i	$-0.376903\pi$
$863$	−16.1278	−	16.1278i	−0.548998	−	0.548998i	−0.926151	+	0.377153i	$0.876903\pi$
$864$	−3.66724	−	3.15475i	−0.124762	−	0.107327i
$865$	34.7635	−	41.8056i	1.18199	−	1.42143i
$866$			34.8329i			1.18367i
$867$	13.8778	−	25.4876i	0.471315	−	0.865604i
$868$	−0.301299	+	0.301299i	−0.0102267	+	0.0102267i
$869$	3.87160			0.131335
$870$	−9.35286	−	23.5184i	−0.317092	−	0.797350i
$871$	−45.4454			−1.53986
$872$	6.36335	−	6.36335i	0.215490	−	0.215490i
$873$	−6.65487	+	30.9476i	−0.225233	+	1.04742i
$874$			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	$-0.786023\pi$
$881$		−	36.9673i		−	1.24546i	0.782436	−	0.622730i	$-0.213977\pi$
$882$	0.306016	−	1.42309i	0.0103041	−	0.0479178i
$883$	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
$885$	−10.4231	+	24.1868i	−0.350369	+	0.813032i
$886$	−39.8907			−1.34015
$887$	−10.0492	+	10.0492i	−0.337420	+	0.337420i	−0.855395	−	0.517976i	$-0.826686\pi$
$887$	−10.0492	+	10.0492i	−0.337420	+	0.337420i	0.517976	+	0.855395i	$0.326686\pi$
$888$	−7.32110	+	13.4457i	−0.245680	+	0.451209i
$889$			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
$897$	−47.5552	−	25.8935i	−1.58782	−	0.864557i
$898$	1.40011	−	1.40011i	0.0467223	−	0.0467223i
$899$	4.44138			0.148128
$900$	−1.79888	+	1.69955i	−0.0599627	+	0.0566516i
$901$	−1.74947			−0.0582833
$902$	46.8100	−	46.8100i	1.55860	−	1.55860i
$903$	−21.4717	−	11.6912i	−0.714533	−	0.389058i
$904$		−	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	$0.0109890\pi$
$911$			2.08358i			0.0690320i	−0.999404	+	0.0345160i	$0.989011\pi$
$912$	14.3337	−	26.3249i	0.474636	−	0.871703i
$913$	−36.5523	+	36.5523i	−1.20970	+	1.20970i
$914$	6.91955			0.228878
$915$	17.0395	−	39.5403i	0.563309	−	1.30716i
$916$	1.69397			0.0559705
$917$	0.279822	−	0.279822i	0.00924053	−	0.00924053i
$918$	3.77210	−	0.283372i	0.124498	−	0.00935267i
$919$		−	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
$927$	34.7268	+	7.46754i	1.14058	+	0.245266i
$928$	2.92374	−	2.92374i	0.0959766	−	0.0959766i
$929$	−27.9730			−0.917764			−0.458882	−	0.888497i	$-0.651750\pi$
$929$	−27.9730			−0.917764			−0.458882	+	0.888497i	$0.651750\pi$
$930$	−2.10584	−	5.29530i	−0.0690533	−	0.173640i
$931$	1.32629			0.0434675
$932$	0.680168	−	0.680168i	0.0222796	−	0.0222796i
$933$	−3.64374	+	6.69201i	−0.119291	+	0.219086i
$934$		−	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	$-0.846856\pi$
$941$		−	28.3915i		−	0.925537i	0.886479	−	0.462769i	$-0.153144\pi$
$942$	0.372852	+	0.203015i	0.0121482	+	0.00661459i
$943$	29.7580	−	29.7580i	0.969053	−	0.969053i
$944$	−29.2596			−0.952319
$945$	−24.4455	−	17.4040i	−0.795212	−	0.566153i
$946$	−45.8370			−1.49029
$947$	26.7170	−	26.7170i	0.868187	−	0.868187i	−0.124084	−	0.992272i	$-0.539599\pi$
$947$	26.7170	−	26.7170i	0.868187	−	0.868187i	0.992272	+	0.124084i	$0.0395993\pi$
$948$	0.170467	+	0.0928177i	0.00553650	+	0.00301458i
$949$		−	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	0.593982	−	0.804478i	$-0.297555\pi$
$953$	−6.49815	−	6.49815i	−0.210496	−	0.210496i	−0.804478	+	0.593982i	$0.797555\pi$
$954$	8.46989	+	13.1105i	0.274223	+	0.424467i
$955$	−29.0055	+	2.66766i	−0.938595	+	0.0863234i
$956$		−	1.36903i		−	0.0442776i
$957$	20.9682	−	38.5097i	0.677806	−	1.24484i
$958$	−24.4881	+	24.4881i	−0.791176	+	0.791176i
$959$	22.4344			0.724445
$960$	25.7357	+	11.0906i	0.830615	+	0.357946i
$961$	1.00000			0.0322581
$962$	−19.9713	+	19.9713i	−0.643900	+	0.643900i
$963$	44.2022	+	9.50510i	1.42440	+	0.306298i
$964$		−	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	$-0.824329\pi$
$971$		−	32.6750i		−	1.04859i	0.851537	−	0.524295i	$-0.175671\pi$
$972$	−1.55352	−	2.04963i	−0.0498290	−	0.0657419i
$973$	−25.0466	+	25.0466i	−0.802958	+	0.802958i
$974$	60.1814			1.92834
$975$	45.2680	−	23.0071i	1.44974	−	0.736817i
$976$	47.8331			1.53110
$977$	21.1843	−	21.1843i	0.677747	−	0.677747i	−0.281743	−	0.959490i	$-0.590913\pi$
$977$	21.1843	−	21.1843i	0.677747	−	0.677747i	0.959490	+	0.281743i	$0.0909125\pi$
$978$	−0.126568	+	0.232452i	−0.00404721	+	0.00743301i
$979$		−	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	0.406244	−	0.913765i	$-0.366838\pi$
$983$	−15.9122	−	15.9122i	−0.507521	−	0.507521i	−0.913765	+	0.406244i	$0.866838\pi$
$984$	−35.4055	+	10.4419i	−1.12869	+	0.332877i
$985$	22.2260	+	18.4820i	0.708178	+	0.588886i
$986$			3.23326i			0.102968i
$987$	−41.2046	−	22.4356i	−1.31156	−	0.714132i
$988$	2.75120	−	2.75120i	0.0875275	−	0.0875275i
$989$	−29.1394			−0.926579
$990$	−55.8556	−	6.74060i	−1.77521	−	0.214230i
$991$	−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
$993$	33.7088	+	18.3542i	1.06972	+	0.582453i
$994$			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.32.22	yes	60
3.2	odd	2	inner	465.2.k.a.32.9	✓	60
5.3	odd	4	inner	465.2.k.a.218.9	yes	60
15.8	even	4	inner	465.2.k.a.218.22	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.k.a.32.9	✓	60	3.2	odd	2	inner
465.2.k.a.32.22	yes	60	1.1	even	1	trivial
465.2.k.a.218.9	yes	60	5.3	odd	4	inner
465.2.k.a.218.22	yes	60	15.8	even	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} +(-1.52117 - 0.828268i) 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} +(-0.136651 + 0.250969i) q^{12} +(4.14610 - 4.14610i) q^{13} -3.80013 q^{14} +(1.53276 - 3.55678i) q^{15} +4.30275 q^{16} +(-0.349849 + 0.349849i) q^{17} +(4.31552 + 0.927994i) 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} +(-0.389255 - 5.18155i) q^{27} +(-0.301299 + 0.301299i) q^{28} +4.44138 q^{29} +(-2.10584 - 5.29530i) q^{30} +1.00000 q^{31} +(0.658296 - 0.658296i) q^{32} +(4.72110 - 8.67065i) 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} +(5.78066 + 3.14752i) q^{42} +(-3.86457 + 3.86457i) q^{43} +0.940404 q^{44} +(-5.27756 + 4.14094i) q^{45} +7.84498 q^{46} +(-7.41618 + 7.41618i) q^{47} +(-6.54523 - 3.56383i) 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} +(3.33129 - 6.11815i) q^{57} +(4.62094 - 4.62094i) q^{58} -6.80022 q^{59} +(-0.586811 - 0.252881i) q^{60} +11.1169 q^{61} +(1.04043 - 1.04043i) q^{62} +(1.62888 - 7.57489i) 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} +(-1.70288 + 7.91904i) q^{72} +(4.49182 - 4.49182i) q^{73} -4.81688 q^{74} +(8.23366 + 2.68456i) q^{75} +0.663564 q^{76} +(10.4095 - 10.4095i) q^{77} +(-7.14583 + 13.1239i) 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} +(-6.75612 - 3.67865i) q^{87} +(-10.8824 + 10.8824i) q^{88} -8.86891 q^{89} +(-1.18257 + 9.79928i) q^{90} -15.1435 q^{91} +(0.622001 - 0.622001i) q^{92} +(-1.52117 - 0.828268i) 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

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Representations

Groups

Database

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