LMFDB - Embedded newform 352.2.bf.a.5.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [352,2,Mod(5,352)] 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("352.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(352, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([0, 5, 16])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 352 = 2^{5} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	352.bf (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$736$
Relative dimension:	$46$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			5.4
Character	$\chi$	$=$	352.5
Dual form			352.2.bf.a.141.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39808 + 0.212978i) q^{2} +(0.118797 - 0.494823i) q^{3} +(1.90928 - 0.595522i) q^{4} +(1.66537 - 1.94989i) q^{5} +(-0.0607012 + 0.717106i) q^{6} +(1.41232 + 0.223690i) q^{7} +(-2.54250 + 1.23922i) q^{8} +(2.44228 + 1.24440i) q^{9} +(-1.91304 + 3.08080i) q^{10} +(2.20307 + 2.47921i) q^{11} +(-0.0678622 - 1.01550i) q^{12} +(-2.54128 - 2.97546i) q^{13} +(-2.02219 - 0.0119440i) q^{14} +(-0.767013 - 1.05570i) q^{15} +(3.29071 - 2.27404i) q^{16} +(-6.12399 - 1.98980i) q^{17} +(-3.67955 - 1.21963i) q^{18} +(5.32151 + 1.27758i) q^{19} +(2.01845 - 4.71466i) q^{20} +(0.278466 - 0.672277i) q^{21} +(-3.60810 - 2.99693i) q^{22} +(0.346514 - 0.346514i) q^{23} +(0.311157 + 1.40531i) q^{24} +(-0.246467 - 1.55613i) q^{25} +(4.18664 + 3.61871i) q^{26} +(1.89738 - 2.22154i) q^{27} +(2.82974 - 0.413983i) q^{28} +(-0.644839 - 0.395158i) q^{29} +(1.29719 + 1.31260i) q^{30} +(0.309016 + 0.951052i) q^{31} +(-4.11637 + 3.88014i) q^{32} +(1.48849 - 0.795611i) q^{33} +(8.98563 + 1.47764i) q^{34} +(2.78821 - 2.38136i) q^{35} +(5.40407 + 0.921486i) q^{36} +(6.33746 - 1.52149i) q^{37} +(-7.71202 - 0.652804i) q^{38} +(-1.77422 + 0.904011i) q^{39} +(-1.81784 + 7.02137i) q^{40} +(-0.259738 + 0.0411385i) q^{41} +(-0.246139 + 0.999208i) q^{42} +(2.41232 - 5.82385i) q^{43} +(5.68271 + 3.42152i) q^{44} +(6.49375 - 2.68980i) q^{45} +(-0.410656 + 0.558256i) q^{46} +(3.53448 - 4.86479i) q^{47} +(-0.734322 - 1.89847i) q^{48} +(-4.71277 - 1.53127i) q^{49} +(0.676002 + 2.12311i) q^{50} +(-1.71211 + 2.79391i) q^{51} +(-6.62398 - 4.16760i) q^{52} +(-1.37926 - 0.108550i) q^{53} +(-2.17955 + 3.51000i) q^{54} +(8.50311 - 0.166974i) q^{55} +(-3.86804 + 1.18145i) q^{56} +(1.26435 - 2.48144i) q^{57} +(0.985699 + 0.415128i) q^{58} +(-7.07436 + 1.69840i) q^{59} +(-2.09314 - 1.55886i) q^{60} +(-4.80144 + 0.377882i) q^{61} +(-0.634583 - 1.26384i) q^{62} +(3.17093 + 2.30382i) q^{63} +(4.92864 - 6.30147i) q^{64} -10.0340 q^{65} +(-1.91158 + 1.42935i) q^{66} +(3.49617 + 8.44049i) q^{67} +(-12.8774 - 0.152125i) q^{68} +(-0.130299 - 0.212628i) q^{69} +(-3.39098 + 3.92316i) q^{70} +(-13.2194 + 6.73563i) q^{71} +(-7.75161 - 0.137367i) q^{72} +(-0.971783 + 6.13560i) q^{73} +(-8.53626 + 3.47691i) q^{74} +(-0.799288 - 0.0629053i) q^{75} +(10.9211 - 0.729815i) q^{76} +(2.55688 + 3.99425i) q^{77} +(2.28798 - 1.64175i) q^{78} +(5.07319 - 1.64838i) q^{79} +(1.04610 - 10.2036i) q^{80} +(3.95956 + 5.44986i) q^{81} +(0.354374 - 0.112834i) q^{82} +(0.837047 + 10.6357i) q^{83} +(0.131315 - 1.44940i) q^{84} +(-14.0786 + 8.62737i) q^{85} +(-2.13227 + 8.65600i) q^{86} +(-0.272138 + 0.272138i) q^{87} +(-8.67362 - 3.57328i) q^{88} +(-12.0282 - 12.0282i) q^{89} +(-8.50594 + 5.14359i) q^{90} +(-2.92354 - 4.77078i) q^{91} +(0.455236 - 0.867950i) q^{92} +(0.507313 - 0.0399264i) q^{93} +(-3.90540 + 7.55415i) q^{94} +(11.3534 - 8.24874i) q^{95} +(1.43098 + 2.49782i) q^{96} +(0.309803 + 0.953476i) q^{97} +(6.91498 + 1.13713i) q^{98} +(2.29539 + 8.79644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 736 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 12 q^{8} - 12 q^{9} - 32 q^{10} - 16 q^{11} - 64 q^{12} - 12 q^{13} - 28 q^{14} - 52 q^{16} + 48 q^{18} - 12 q^{19} - 28 q^{20}+ \cdots - 68 q^{99}+O(q^{100}) $ 736 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 12 * q^6 - 12 * q^7 - 12 * q^8 - 12 * q^9 - 32 * q^10 - 16 * q^11 - 64 * q^12 - 12 * q^13 - 28 * q^14 - 52 * q^16 + 48 * q^18 - 12 * q^19 - 28 * q^20 - 32 * q^21 - 28 * q^22 - 48 * q^23 - 12 * q^24 - 12 * q^25 - 72 * q^26 - 12 * q^27 - 12 * q^28 - 12 * q^29 - 28 * q^30 - 24 * q^31 + 8 * q^32 - 32 * q^33 - 8 * q^34 - 12 * q^35 - 12 * q^36 - 12 * q^37 - 12 * q^38 - 12 * q^39 + 28 * q^40 - 12 * q^41 - 52 * q^42 - 48 * q^43 - 56 * q^44 - 56 * q^45 - 76 * q^46 - 12 * q^48 - 12 * q^50 - 36 * q^51 - 28 * q^52 + 36 * q^53 - 120 * q^54 + 16 * q^55 + 184 * q^56 - 12 * q^57 - 12 * q^58 + 20 * q^59 + 4 * q^60 - 12 * q^61 + 4 * q^62 + 56 * q^63 - 156 * q^64 - 64 * q^65 + 8 * q^66 + 48 * q^67 - 100 * q^68 - 12 * q^69 + 36 * q^70 + 20 * q^71 + 168 * q^72 - 12 * q^73 - 44 * q^74 - 148 * q^75 - 32 * q^76 - 32 * q^77 + 16 * q^78 - 148 * q^80 - 52 * q^82 - 12 * q^83 + 100 * q^84 - 52 * q^85 + 92 * q^86 - 32 * q^87 - 20 * q^88 - 32 * q^89 - 180 * q^90 + 132 * q^91 + 132 * q^92 + 12 * q^93 + 8 * q^94 - 152 * q^95 - 76 * q^96 - 24 * q^97 - 48 * q^98 - 68 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$.

$n$	$133$	$287$	$321$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.39808	+	0.212978i	−0.988595	+	0.150598i
$2$	−1.39808	+	0.212978i	−0.988595	+	0.150598i
$3$	0.118797	−	0.494823i	0.0685872	−	0.285686i	−0.927527	−	0.373756i	$-0.878070\pi$
$3$	0.118797	−	0.494823i	0.0685872	−	0.285686i	0.996114	+	0.0880696i	$0.0280698\pi$
$4$	1.90928	−	0.595522i	0.954640	−	0.297761i
$5$	1.66537	−	1.94989i	0.744774	−	0.872019i	−0.250600	−	0.968091i	$-0.580628\pi$
$5$	1.66537	−	1.94989i	0.744774	−	0.872019i	0.995374	+	0.0960720i	$0.0306279\pi$
$6$	−0.0607012	+	0.717106i	−0.0247812	+	0.292757i
$7$	1.41232	+	0.223690i	0.533808	+	0.0845470i	0.417519	−	0.908668i	$-0.362900\pi$
$7$	1.41232	+	0.223690i	0.533808	+	0.0845470i	0.116290	+	0.993215i	$0.462900\pi$
$8$	−2.54250	+	1.23922i	−0.898911	+	0.438132i
$9$	2.44228	+	1.24440i	0.814094	+	0.414802i
$10$	−1.91304	+	3.08080i	−0.604956	+	0.974235i
$11$	2.20307	+	2.47921i	0.664252	+	0.747509i
$11$	2.20307	+	2.47921i	0.664252	+	0.747509i
$12$	−0.0678622	−	1.01550i	−0.0195901	−	0.293150i
$13$	−2.54128	−	2.97546i	−0.704825	−	0.825244i	0.286305	−	0.958139i	$-0.407573\pi$
$13$	−2.54128	−	2.97546i	−0.704825	−	0.825244i	−0.991130	+	0.132894i	$0.957573\pi$
$14$	−2.02219	−	0.0119440i	−0.540453	−	0.00319218i
$15$	−0.767013	−	1.05570i	−0.198042	−	0.272581i
$16$	3.29071	−	2.27404i	0.822677	−	0.568509i
$17$	−6.12399	−	1.98980i	−1.48528	−	0.482598i	−0.549598	−	0.835429i	$-0.685219\pi$
$17$	−6.12399	−	1.98980i	−1.48528	−	0.482598i	−0.935687	+	0.352831i	$0.885219\pi$
$18$	−3.67955	−	1.21963i	−0.867278	−	0.287470i
$19$	5.32151	+	1.27758i	1.22084	+	0.293097i	0.792134	−	0.610347i	$-0.208970\pi$
$19$	5.32151	+	1.27758i	1.22084	+	0.293097i	0.428705	+	0.903445i	$0.358970\pi$
$20$	2.01845	−	4.71466i	0.451338	−	1.05423i
$21$	0.278466	−	0.672277i	0.0607663	−	0.146703i
$22$	−3.60810	−	2.99693i	−0.769250	−	0.638948i
$23$	0.346514	−	0.346514i	0.0722532	−	0.0722532i	−0.670057	−	0.742310i	$-0.733730\pi$
$23$	0.346514	−	0.346514i	0.0722532	−	0.0722532i	0.742310	+	0.670057i	$0.233730\pi$
$24$	0.311157	+	1.40531i	0.0635146	+	0.286857i
$25$	−0.246467	−	1.55613i	−0.0492933	−	0.311226i
$26$	4.18664	+	3.61871i	0.821067	+	0.709687i
$27$	1.89738	−	2.22154i	0.365150	−	0.427536i
$28$	2.82974	−	0.413983i	0.534770	−	0.0782354i
$29$	−0.644839	−	0.395158i	−0.119744	−	0.0733790i	0.461337	−	0.887225i	$-0.347370\pi$
$29$	−0.644839	−	0.395158i	−0.119744	−	0.0733790i	−0.581081	+	0.813846i	$0.697370\pi$
$30$	1.29719	+	1.31260i	0.236833	+	0.239648i
$31$	0.309016	+	0.951052i	0.0555008	+	0.170814i	0.974964	−	0.222361i	$-0.0713765\pi$
$31$	0.309016	+	0.951052i	0.0555008	+	0.170814i	−0.919463	+	0.393175i	$0.871377\pi$
$32$	−4.11637	+	3.88014i	−0.727678	+	0.685919i
$33$	1.48849	−	0.795611i	0.259112	−	0.138498i
$34$	8.98563	+	1.47764i	1.54102	+	0.253413i
$35$	2.78821	−	2.38136i	0.471293	−	0.402523i
$36$	5.40407	+	0.921486i	0.900679	+	0.153581i
$37$	6.33746	−	1.52149i	1.04187	−	0.250131i	0.323819	−	0.946119i	$-0.395033\pi$
$37$	6.33746	−	1.52149i	1.04187	−	0.250131i	0.718054	+	0.695988i	$0.245033\pi$
$38$	−7.71202	−	0.652804i	−1.25105	−	0.105899i
$39$	−1.77422	+	0.904011i	−0.284103	+	0.144758i
$40$	−1.81784	+	7.02137i	−0.287426	+	1.11018i
$41$	−0.259738	+	0.0411385i	−0.0405643	+	0.00642475i	−0.176684	−	0.984268i	$-0.556537\pi$
$41$	−0.259738	+	0.0411385i	−0.0405643	+	0.00642475i	0.136119	+	0.990692i	$0.456537\pi$
$42$	−0.246139	+	0.999208i	−0.0379801	+	0.154181i
$43$	2.41232	−	5.82385i	0.367875	−	0.888129i	−0.626223	−	0.779644i	$-0.715400\pi$
$43$	2.41232	−	5.82385i	0.367875	−	0.888129i	0.994098	−	0.108485i	$-0.0345999\pi$
$44$	5.68271	+	3.42152i	0.856701	+	0.515814i
$45$	6.49375	−	2.68980i	0.968031	−	0.400972i
$46$	−0.410656	+	0.558256i	−0.0605480	+	0.0823103i
$47$	3.53448	−	4.86479i	0.515556	−	0.709602i	−0.469288	−	0.883045i	$-0.655489\pi$
$47$	3.53448	−	4.86479i	0.515556	−	0.709602i	0.984844	+	0.173443i	$0.0554892\pi$
$48$	−0.734322	−	1.89847i	−0.105990	−	0.274020i
$49$	−4.71277	−	1.53127i	−0.673253	−	0.218753i
$50$	0.676002	+	2.12311i	0.0956011	+	0.300253i
$51$	−1.71211	+	2.79391i	−0.239743	+	0.391225i
$52$	−6.62398	−	4.16760i	−0.918580	−	0.577942i
$53$	−1.37926	−	0.108550i	−0.189457	−	0.0149106i	−0.0166242	−	0.999862i	$-0.505292\pi$
$53$	−1.37926	−	0.108550i	−0.189457	−	0.0149106i	−0.172832	+	0.984951i	$0.555292\pi$
$54$	−2.17955	+	3.51000i	−0.296600	+	0.477651i
$55$	8.50311	−	0.166974i	1.14656	−	0.0225148i
$56$	−3.86804	+	1.18145i	−0.516889	+	0.157878i
$57$	1.26435	−	2.48144i	0.167468	−	0.328674i
$58$	0.985699	+	0.415128i	0.129429	+	0.0545089i
$59$	−7.07436	+	1.69840i	−0.921003	+	0.221113i	−0.666108	−	0.745856i	$-0.732041\pi$
$59$	−7.07436	+	1.69840i	−0.921003	+	0.221113i	−0.254895	+	0.966969i	$0.582041\pi$
$60$	−2.09314	−	1.55886i	−0.270223	−	0.201248i
$61$	−4.80144	+	0.377882i	−0.614762	+	0.0483828i	−0.382017	−	0.924155i	$-0.624771\pi$
$61$	−4.80144	+	0.377882i	−0.614762	+	0.0483828i	−0.232744	+	0.972538i	$0.574771\pi$
$62$	−0.634583	−	1.26384i	−0.0805921	−	0.160508i
$63$	3.17093	+	2.30382i	0.399500	+	0.290254i
$64$	4.92864	−	6.30147i	0.616081	−	0.787683i
$65$	−10.0340			−1.24456
$66$	−1.91158	+	1.42935i	−0.235299	+	0.175940i
$67$	3.49617	+	8.44049i	0.427125	+	1.03117i	0.980195	+	0.198036i	$0.0634562\pi$
$67$	3.49617	+	8.44049i	0.427125	+	1.03117i	−0.553070	+	0.833135i	$0.686544\pi$
$68$	−12.8774	−	0.152125i	−1.56161	−	0.0184479i
$69$	−0.130299	−	0.212628i	−0.0156861	−	0.0255974i
$70$	−3.39098	+	3.92316i	−0.405299	+	0.468908i
$71$	−13.2194	+	6.73563i	−1.56886	+	0.799372i	−0.999738	−	0.0228829i	$-0.992716\pi$
$71$	−13.2194	+	6.73563i	−1.56886	+	0.799372i	−0.569119	+	0.822255i	$0.692716\pi$
$72$	−7.75161	−	0.137367i	−0.913536	−	0.0161889i
$73$	−0.971783	+	6.13560i	−0.113739	+	0.718117i	0.863242	+	0.504790i	$0.168430\pi$
$73$	−0.971783	+	6.13560i	−0.113739	+	0.718117i	−0.976981	+	0.213327i	$0.931570\pi$
$74$	−8.53626	+	3.47691i	−0.992320	+	0.404183i
$75$	−0.799288	−	0.0629053i	−0.0922938	−	0.00726368i
$76$	10.9211	−	0.729815i	1.25273	−	0.0837155i
$77$	2.55688	+	3.99425i	0.291384	+	0.455187i
$78$	2.28798	−	1.64175i	0.259063	−	0.185892i
$79$	5.07319	−	1.64838i	0.570779	−	0.185457i	−0.00938674	−	0.999956i	$-0.502988\pi$
$79$	5.07319	−	1.64838i	0.570779	−	0.185457i	0.580165	+	0.814499i	$0.302988\pi$
$80$	1.04610	−	10.2036i	0.116958	−	1.14080i
$81$	3.95956	+	5.44986i	0.439951	+	0.605540i
$82$	0.354374	−	0.112834i	0.0391341	−	0.0124604i
$83$	0.837047	+	10.6357i	0.0918779	+	1.16742i	0.854102	+	0.520106i	$0.174108\pi$
$83$	0.837047	+	10.6357i	0.0918779	+	1.16742i	−0.762224	+	0.647313i	$0.775892\pi$
$84$	0.131315	−	1.44940i	0.0143276	−	0.158142i
$85$	−14.0786	+	8.62737i	−1.52704	+	0.935769i
$86$	−2.13227	+	8.65600i	−0.229929	+	0.933401i
$87$	−0.272138	+	0.272138i	−0.0291762	+	0.0291762i
$88$	−8.67362	−	3.57328i	−0.924611	−	0.380913i
$89$	−12.0282	−	12.0282i	−1.27499	−	1.27499i	−0.943437	−	0.331553i	$-0.892427\pi$
$89$	−12.0282	−	12.0282i	−1.27499	−	1.27499i	−0.331553	−	0.943437i	$-0.607573\pi$
$90$	−8.50594	+	5.14359i	−0.896605	+	0.542182i
$91$	−2.92354	−	4.77078i	−0.306470	−	0.500113i
$92$	0.455236	−	0.867950i	0.0474616	−	0.0904900i
$93$	0.507313	−	0.0399264i	0.0526059	−	0.00414017i
$94$	−3.90540	+	7.55415i	−0.402812	+	0.779151i
$95$	11.3534	−	8.24874i	1.16484	−	0.846303i
$96$	1.43098	+	2.49782i	0.146048	+	0.254933i
$97$	0.309803	+	0.953476i	0.0314558	+	0.0968109i	0.965552	−	0.260211i	$-0.0837921\pi$
$97$	0.309803	+	0.953476i	0.0314558	+	0.0968109i	−0.934096	+	0.357022i	$0.883792\pi$
$98$	6.91498	+	1.13713i	0.698519	+	0.114868i
$99$	2.29539	+	8.79644i	0.230696	+	0.884075i
$100$	−1.39728	−	2.82431i	−0.139728	−	0.282431i
$101$	1.00334	−	12.7486i	0.0998359	−	1.26854i	−0.719204	−	0.694799i	$-0.755493\pi$
$101$	1.00334	−	12.7486i	0.0998359	−	1.26854i	0.819040	−	0.573736i	$-0.194507\pi$
$102$	1.79863	−	4.27076i	0.178091	−	0.422868i
$103$	−3.58792	−	0.568270i	−0.353528	−	0.0559933i	−0.0228552	−	0.999739i	$-0.507276\pi$
$103$	−3.58792	−	0.568270i	−0.353528	−	0.0559933i	−0.330673	+	0.943745i	$0.607276\pi$
$104$	10.1485	+	4.41590i	0.995141	+	0.433014i
$105$	−0.847120	−	1.66257i	−0.0826705	−	0.162250i
$106$	1.95145	−	0.141990i	0.189541	−	0.0137913i
$107$	−10.9476	+	6.70869i	−1.05834	+	0.648553i	−0.938866	−	0.344284i	$-0.888122\pi$
$107$	−10.9476	+	6.70869i	−1.05834	+	0.648553i	−0.119477	+	0.992837i	$0.538122\pi$
$108$	2.29965	−	5.37148i	0.221284	−	0.516870i
$109$	6.71421	−	2.78112i	0.643105	−	0.266383i	−0.0372048	−	0.999308i	$-0.511845\pi$
$109$	6.71421	−	2.78112i	0.643105	−	0.266383i	0.680309	+	0.732925i	$0.261845\pi$
$110$	−11.8525	+	2.04442i	−1.13009	+	0.194928i
$111$		−	3.31667i		−	0.314804i
$112$	5.15623	−	2.47558i	0.487218	−	0.233920i
$113$	−7.88214	+	10.8488i	−0.741489	+	1.02057i	0.257043	+	0.966400i	$0.417252\pi$
$113$	−7.88214	+	10.8488i	−0.741489	+	1.02057i	−0.998532	+	0.0541719i	$0.982748\pi$
$114$	−1.23918	+	3.73854i	−0.116060	+	0.350146i
$115$	−0.0985927	−	1.25274i	−0.00919381	−	0.116818i
$116$	−1.46650	−	0.370451i	−0.136161	−	0.0343955i
$117$	−2.50385	−	10.4293i	−0.231481	−	0.964189i
$118$	9.52882	−	3.88119i	0.877199	−	0.357293i
$119$	−8.20396	−	4.18012i	−0.752055	−	0.383191i
$120$	3.25838	+	1.73363i	0.297448	+	0.158258i
$121$	−1.29293	+	10.9238i	−0.117539	+	0.993068i
$122$	6.63234	−	1.55091i	0.600464	−	0.140413i
$123$	−0.0104997	+	0.133412i	−0.000946728	+	0.0120293i
$124$	1.15637	+	1.63180i	0.103845	+	0.146540i
$125$	7.48729	+	4.58822i	0.669684	+	0.410383i
$126$	−4.92390	−	2.54559i	−0.438655	−	0.226780i
$127$	−1.90866	+	5.87424i	−0.169366	+	0.521254i	−0.999331	−	0.0365601i	$-0.988360\pi$
$127$	−1.90866	+	5.87424i	−0.169366	+	0.521254i	0.829966	+	0.557815i	$0.188360\pi$
$128$	−5.54859	+	9.85967i	−0.490431	+	0.871480i
$129$	−2.59520	−	1.88552i	−0.228495	−	0.166011i
$130$	14.0284	−	2.13702i	1.23037	−	0.187429i
$131$	4.21306	+	10.1712i	0.368097	+	0.888664i	0.994062	+	0.108813i	$0.0347051\pi$
$131$	4.21306	+	10.1712i	0.368097	+	0.888664i	−0.625966	+	0.779851i	$0.715295\pi$
$132$	2.36813	−	2.40547i	0.206120	−	0.209369i
$133$	7.22992	+	2.99473i	0.626913	+	0.259676i
$134$	−6.68558	−	11.0559i	−0.577546	−	0.955086i
$135$	−1.17194	−	7.39936i	−0.100865	−	0.636835i
$136$	18.0361	−	2.52991i	1.54658	−	0.216938i
$137$	−4.43438	−	8.70297i	−0.378855	−	0.743545i	0.620312	−	0.784355i	$-0.287006\pi$
$137$	−4.43438	−	8.70297i	−0.378855	−	0.743545i	−0.999167	+	0.0408104i	$0.987006\pi$
$138$	0.227453	+	0.269521i	0.0193621	+	0.0229432i
$139$	4.89000	+	20.3683i	0.414765	+	1.72762i	0.653853	+	0.756621i	$0.273151\pi$
$139$	4.89000	+	20.3683i	0.414765	+	1.72762i	−0.239089	+	0.970998i	$0.576849\pi$
$140$	3.90532	−	6.20712i	0.330060	−	0.524597i
$141$	−1.98733	−	2.32686i	−0.167363	−	0.195957i
$142$	17.0473	−	12.2324i	1.43058	−	1.02652i
$143$	1.77814	−	12.8555i	0.148696	−	1.07503i
$144$	10.8667	−	1.45887i	0.905555	−	0.121572i
$145$	−1.84441	+	0.599285i	−0.153170	+	0.0497679i
$146$	0.0518888	−	8.78505i	0.00429434	−	0.727056i
$147$	−1.31757	+	2.15008i	−0.108671	+	0.177336i
$148$	11.1939	−	6.67905i	0.920134	−	0.549014i
$149$	16.6517	+	14.2219i	1.36416	+	1.16510i	0.969164	+	0.246415i	$0.0792527\pi$
$149$	16.6517	+	14.2219i	1.36416	+	1.16510i	0.394992	+	0.918685i	$0.370747\pi$
$150$	1.13087	−	0.0822837i	0.0923351	−	0.00671843i
$151$	−17.0097	+	2.69407i	−1.38423	+	0.219240i	−0.803716	−	0.595013i	$-0.797147\pi$
$151$	−17.0097	+	2.69407i	−1.38423	+	0.219240i	−0.580510	+	0.814253i	$0.697147\pi$
$152$	−15.1132	+	3.34629i	−1.22584	+	0.271420i
$153$	−12.4804	−	12.4804i	−1.00898	−	1.00898i
$154$	−4.42542	−	5.03974i	−0.356611	−	0.406114i
$155$	2.36907	+	0.981302i	0.190289	+	0.0788201i
$156$	−2.84913	+	2.78260i	−0.228113	+	0.222786i
$157$	0.337573	−	1.40609i	0.0269413	−	0.112219i	−0.957279	−	0.289166i	$-0.906622\pi$
$157$	0.337573	−	1.40609i	0.0269413	−	0.112219i	0.984220	+	0.176947i	$0.0566222\pi$
$158$	−6.74168	+	3.38505i	−0.536339	+	0.269300i
$159$	−0.217565	+	0.669596i	−0.0172540	+	0.0531025i
$160$	0.710610	+	14.4883i	0.0561786	+	1.14540i
$161$	0.566902	−	0.411879i	0.0446782	−	0.0324606i
$162$	−6.69649	−	6.77607i	−0.526126	−	0.532378i
$163$	−5.12294	+	4.37541i	−0.401260	+	0.342708i	−0.827065	−	0.562107i	$-0.809991\pi$
$163$	−5.12294	+	4.37541i	−0.401260	+	0.342708i	0.425805	+	0.904815i	$0.359991\pi$
$164$	−0.471414	+	0.233225i	−0.0368113	+	0.0182118i
$165$	0.927517	−	4.22737i	0.0722071	−	0.329101i
$166$	−3.43543	−	14.6913i	−0.266641	−	1.14027i
$167$	7.89562	−	15.4960i	0.610982	−	1.19912i	−0.353615	−	0.935391i	$-0.615048\pi$
$167$	7.89562	−	15.4960i	0.610982	−	1.19912i	0.964597	−	0.263728i	$-0.0849522\pi$
$168$	0.125101	+	2.05435i	0.00965175	+	0.158496i
$169$	−0.361596	+	2.28303i	−0.0278151	+	0.175617i
$170$	17.8456	−	15.0602i	1.36870	−	1.15507i
$171$	11.4068	+	9.74233i	0.872300	+	0.745015i
$172$	1.13756	−	12.5560i	0.0867382	−	0.957382i
$173$	22.0105	+	5.28427i	1.67343	+	0.401755i	0.955648	−	0.294512i	$-0.0951569\pi$
$173$	22.0105	+	5.28427i	1.67343	+	0.401755i	0.717783	+	0.696267i	$0.245157\pi$
$174$	0.322512	−	0.438431i	0.0244496	−	0.0332374i
$175$		−	2.25289i		−	0.170303i
$176$	12.8875	+	3.14847i	0.971430	+	0.237325i
$177$			3.70232i			0.278283i
$178$	19.3782	+	14.2547i	1.45246	+	1.06844i
$179$	7.92753	+	1.90323i	0.592531	+	0.142254i	0.518611	−	0.855010i	$-0.326449\pi$
$179$	7.92753	+	1.90323i	0.592531	+	0.142254i	0.0739197	+	0.997264i	$0.476449\pi$
$180$	10.7966	−	9.00275i	0.804728	−	0.671026i
$181$	−17.3062	−	14.7809i	−1.28636	−	1.09866i	−0.989622	−	0.143698i	$-0.954101\pi$
$181$	−17.3062	−	14.7809i	−1.28636	−	1.09866i	−0.296740	−	0.954958i	$-0.595899\pi$
$182$	5.10342	+	6.04730i	0.378291	+	0.448256i
$183$	−0.383410	+	2.42076i	−0.0283425	+	0.178947i
$184$	−0.451604	+	1.31042i	−0.0332927	+	0.0966056i
$185$	7.58745	−	14.8912i	0.557840	−	1.09482i
$186$	−0.700762	+	0.163867i	−0.0513824	+	0.0120153i
$187$	−8.55846	−	19.5663i	−0.625857	−	1.43083i
$188$	3.85122	−	11.3931i	0.280879	−	0.830928i
$189$	3.17665	−	2.71311i	0.231067	−	0.197350i
$190$	−14.1162	+	13.9505i	−1.02410	+	1.01207i
$191$	−9.74954	+	7.08346i	−0.705452	+	0.512541i	−0.881703	−	0.471804i	$-0.843603\pi$
$191$	−9.74954	+	7.08346i	−0.705452	+	0.512541i	0.176251	+	0.984345i	$0.443603\pi$
$192$	−2.53261	−	3.18740i	−0.182775	−	0.230031i
$193$	−3.91537	+	12.0503i	−0.281835	+	0.867398i	0.705495	+	0.708715i	$0.250725\pi$
$193$	−3.91537	+	12.0503i	−0.281835	+	0.867398i	−0.987330	+	0.158683i	$0.949275\pi$
$194$	−0.636201	−	1.26706i	−0.0456765	−	0.0909696i
$195$	−1.19200	+	4.96505i	−0.0853612	+	0.355555i
$196$	−9.90991	−	0.117070i	−0.707851	−	0.00836211i
$197$	−8.36956	−	3.46679i	−0.596307	−	0.246998i	0.0640545	−	0.997946i	$-0.479597\pi$
$197$	−8.36956	−	3.46679i	−0.596307	−	0.246998i	−0.660361	+	0.750948i	$0.729597\pi$
$198$	−5.08260	−	11.8093i	−0.361205	−	0.839250i
$199$	14.2187	+	14.2187i	1.00794	+	1.00794i	0.999968	+	0.00797020i	$0.00253702\pi$
$199$	14.2187	+	14.2187i	1.00794	+	1.00794i	0.00797020	+	0.999968i	$0.497463\pi$
$200$	2.55504	+	3.65104i	0.180668	+	0.258167i
$201$	4.59188	−	0.727283i	0.323887	−	0.0512986i
$202$	1.31242	+	18.0373i	0.0923417	+	1.26910i
$203$	−0.822329	−	0.702335i	−0.0577162	−	0.0492943i
$204$	−1.60506	+	6.35395i	−0.112377	+	0.444866i
$205$	−0.352344	+	0.574972i	−0.0246087	+	0.0401578i
$206$	5.13724	+	0.0303430i	0.357929	+	0.00211410i
$207$	1.27749	−	0.415081i	0.0887916	−	0.0288502i
$208$	−15.1289	−	4.01239i	−1.04900	−	0.278209i
$209$	8.55630	+	16.0077i	0.591852	+	1.10728i
$210$	1.53844	+	2.14399i	0.106162	+	0.147949i
$211$	−3.39760	−	3.97808i	−0.233900	−	0.273862i	0.631025	−	0.775762i	$-0.282634\pi$
$211$	−3.39760	−	3.97808i	−0.233900	−	0.273862i	−0.864926	+	0.501900i	$0.832634\pi$
$212$	−2.69805	+	0.614129i	−0.185303	+	0.0421786i
$213$	1.76253	+	7.34145i	0.120766	+	0.503028i
$214$	13.8768	−	11.7109i	0.948601	−	0.800541i
$215$	−7.33849	−	14.4026i	−0.500481	−	0.982249i
$216$	−2.07109	+	7.99955i	−0.140920	+	0.544300i
$217$	0.223689	+	1.41232i	0.0151850	+	0.0958744i
$218$	−8.79472	+	5.31821i	−0.595653	+	0.360195i
$219$	2.92059	+	1.20975i	0.197355	+	0.0817472i
$220$	16.1354	−	5.38259i	1.08785	−	0.362894i
$221$	9.64220	+	23.2783i	0.648605	+	1.56587i
$222$	0.706377	+	4.63699i	0.0474089	+	0.311214i
$223$	2.89848	+	2.10587i	0.194096	+	0.141019i	0.680589	−	0.732665i	$-0.261724\pi$
$223$	2.89848	+	2.10587i	0.194096	+	0.141019i	−0.486493	+	0.873685i	$0.661724\pi$
$224$	−6.68160	+	4.55923i	−0.446433	+	0.304627i
$225$	1.33451	−	4.10721i	0.0889676	−	0.273814i
$226$	8.70933	−	16.8463i	0.579336	−	1.12060i
$227$	−10.6459	−	6.52382i	−0.706594	−	0.433001i	0.122237	−	0.992501i	$-0.460993\pi$
$227$	−10.6459	−	6.52382i	−0.706594	−	0.433001i	−0.828831	+	0.559500i	$0.810993\pi$
$228$	0.936258	−	5.49071i	0.0620052	−	0.363631i
$229$	−0.368997	+	4.68855i	−0.0243840	+	0.309828i	0.972615	+	0.232420i	$0.0746645\pi$
$229$	−0.368997	+	4.68855i	−0.0243840	+	0.309828i	−0.996999	+	0.0774082i	$0.975336\pi$
$230$	0.404646	+	1.73044i	0.0266816	+	0.114102i
$231$	2.28020	−	0.790701i	0.150026	−	0.0520243i
$232$	2.12919	+	0.205590i	0.139788	+	0.0134976i
$233$	10.7600	+	5.48251i	0.704913	+	0.359171i	0.769417	−	0.638746i	$-0.220547\pi$
$233$	10.7600	+	5.48251i	0.704913	+	0.359171i	−0.0645044	+	0.997917i	$0.520547\pi$
$234$	5.72181	+	14.0478i	0.374046	+	0.918332i
$235$	−3.59962	−	14.9935i	−0.234813	−	0.978068i
$236$	−12.4955	+	7.45566i	−0.813387	+	0.485322i
$237$	−0.212979	−	2.70615i	−0.0138345	−	0.175784i
$238$	12.3601	+	4.09691i	0.801186	+	0.265563i
$239$	−3.64001	+	5.01004i	−0.235452	+	0.324072i	−0.910350	−	0.413839i	$-0.864188\pi$
$239$	−3.64001	+	5.01004i	−0.235452	+	0.324072i	0.674898	+	0.737911i	$0.264188\pi$
$240$	−4.92472	−	1.72979i	−0.317889	−	0.111658i
$241$		−	17.1645i		−	1.10566i	−0.833294	−	0.552830i	$-0.813548\pi$
$241$		−	17.1645i		−	1.10566i	0.833294	−	0.552830i	$-0.186452\pi$
$242$	−0.518898	−	15.5477i	−0.0333560	−	0.999444i
$243$	11.2645	−	4.66591i	0.722618	−	0.299318i
$244$	−8.94226	+	3.58085i	−0.572470	+	0.229240i
$245$	−10.8343	+	6.63927i	−0.692179	+	0.424168i
$246$	−0.0137342	−	0.188757i	−0.000875662	−	0.0120347i
$247$	−9.72208	−	19.0806i	−0.618601	−	1.21407i
$248$	−1.96424	−	2.03511i	−0.124729	−	0.129230i
$249$	5.36223	+	0.849293i	0.339817	+	0.0538218i
$250$	−11.4451	−	4.82009i	−0.723849	−	0.304849i
$251$	1.24942	−	15.8754i	0.0788626	−	1.00204i	−0.822439	−	0.568853i	$-0.807387\pi$
$251$	1.24942	−	15.8754i	0.0788626	−	1.00204i	0.901302	−	0.433191i	$-0.142613\pi$
$252$	7.42618	+	2.51027i	0.467805	+	0.158132i
$253$	1.62248	+	0.0956835i	0.102004	+	0.00601557i
$254$	1.41738	−	8.61919i	0.0889343	−	0.540816i
$255$	2.59653	+	7.99131i	0.162601	+	0.500435i
$256$	5.65750	−	14.9664i	0.353594	−	0.935399i
$257$	−25.2415	+	18.3390i	−1.57452	+	1.14396i	−0.651860	+	0.758339i	$0.726011\pi$
$257$	−25.2415	+	18.3390i	−1.57452	+	1.14396i	−0.922659	+	0.385616i	$0.873989\pi$
$258$	4.02988	+	2.08340i	0.250890	+	0.129707i
$259$	9.29089	−	0.731209i	0.577308	−	0.0454351i
$260$	−19.1577	+	5.97547i	−1.18811	+	0.370583i
$261$	−1.08314	−	1.76753i	−0.0670448	−	0.109407i
$262$	−8.05646	−	13.3229i	−0.497730	−	0.823094i
$263$	7.99776	+	7.99776i	0.493163	+	0.493163i	0.909301	−	0.416138i	$-0.136617\pi$
$263$	7.99776	+	7.99776i	0.493163	+	0.493163i	−0.416138	+	0.909301i	$0.636617\pi$
$264$	−2.79854	+	3.86741i	−0.172238	+	0.238023i
$265$	−2.50864	+	2.50864i	−0.154105	+	0.154105i
$266$	−10.7458	−	2.64707i	−0.658870	−	0.162303i
$267$	−7.38076	+	4.52293i	−0.451695	+	0.276799i
$268$	11.7017	+	14.0332i	0.714793	+	0.857216i
$269$	1.12000	+	14.2310i	0.0682877	+	0.867677i	0.931712	+	0.363198i	$0.118315\pi$
$269$	1.12000	+	14.2310i	0.0682877	+	0.867677i	−0.863424	+	0.504479i	$0.831685\pi$
$270$	3.21438	+	10.0953i	0.195621	+	0.614382i
$271$	−15.5522	−	21.4058i	−0.944728	−	1.30031i	−0.953830	−	0.300348i	$-0.902897\pi$
$271$	−15.5522	−	21.4058i	−0.944728	−	1.30031i	0.00910137	−	0.999959i	$-0.497103\pi$
$272$	−24.6771	+	7.37831i	−1.49627	+	0.447376i
$273$	−2.70800	+	0.879881i	−0.163895	+	0.0532528i
$274$	8.05318	+	11.2231i	0.486511	+	0.678010i
$275$	3.31498	−	4.03931i	0.199901	−	0.243580i
$276$	−0.375401	−	0.328371i	−0.0225965	−	0.0197656i
$277$	−2.51193	−	0.197694i	−0.150928	−	0.0118783i	0.00277021	−	0.999996i	$-0.499118\pi$
$277$	−2.51193	−	0.197694i	−0.150928	−	0.0118783i	−0.153698	+	0.988118i	$0.549118\pi$
$278$	−11.1746	−	27.4352i	−0.670210	−	1.64545i
$279$	−0.428791	+	2.70728i	−0.0256710	+	0.162080i
$280$	−4.13800	+	9.50982i	−0.247293	+	0.568320i
$281$	22.1366	−	11.2792i	1.32056	−	0.672859i	0.355448	−	0.934696i	$-0.384328\pi$
$281$	22.1366	−	11.2792i	1.32056	−	0.672859i	0.965112	+	0.261837i	$0.0843282\pi$
$282$	3.27402	+	2.82989i	0.194965	+	0.168518i
$283$	−7.21918	−	11.7806i	−0.429136	−	0.700286i	0.562861	−	0.826552i	$-0.309701\pi$
$283$	−7.21918	−	11.7806i	−0.429136	−	0.700286i	−0.991996	+	0.126266i	$0.959701\pi$
$284$	−21.2284	+	20.7327i	−1.25967	+	1.23026i
$285$	−2.73292	−	6.59785i	−0.161884	−	0.390823i
$286$	0.251948	+	18.3518i	0.0148980	+	1.08517i
$287$	−0.376037			−0.0221968
$288$	−14.8818	+	4.35398i	−0.876919	+	0.256561i
$289$	19.7906	+	14.3787i	1.16415	+	0.845806i
$290$	2.45100	−	1.23067i	0.143928	−	0.0722673i
$291$	0.508606	−	0.0400281i	0.0298150	−	0.00234649i
$292$	1.79848	+	12.2933i	0.105248	+	0.719411i
$293$	−27.8772	+	6.69273i	−1.62861	+	0.390994i	−0.941887	−	0.335930i	$-0.890950\pi$
$293$	−27.8772	+	6.69273i	−1.62861	+	0.390994i	−0.686719	+	0.726923i	$0.740950\pi$
$294$	1.38416	−	3.28661i	0.0807256	−	0.191679i
$295$	−8.46969	+	16.6227i	−0.493124	+	0.967811i
$296$	−14.2275	+	11.7219i	−0.826959	+	0.681323i
$297$	9.68772	−	0.190236i	0.562138	−	0.0110386i
$298$	−26.3094	−	16.3369i	−1.52406	−	0.946372i
$299$	−1.91163	−	0.150449i	−0.110552	−	0.00870066i
$300$	−1.56353	+	0.355890i	−0.0902703	+	0.0205473i
$301$	4.70971	−	7.68555i	0.271463	−	0.442988i
$302$	23.2072	−	7.38921i	1.33542	−	0.425201i
$303$	−6.18912	−	2.01097i	−0.355556	−	0.115527i
$304$	20.4168	−	7.89717i	1.17098	−	0.452934i
$305$	−7.25933	+	9.99161i	−0.415668	+	0.572118i
$306$	20.1067	+	14.7906i	1.14942	+	0.845521i
$307$	−8.30901	+	3.44171i	−0.474220	+	0.196428i	−0.606976	−	0.794720i	$-0.707618\pi$
$307$	−8.30901	+	3.44171i	−0.474220	+	0.196428i	0.132755	+	0.991149i	$0.457618\pi$
$308$	7.26047	+	6.10346i	0.413704	+	0.347777i
$309$	−0.707425	+	1.70788i	−0.0402440	+	0.0971577i
$310$	−3.52116	−	0.867384i	−0.199989	−	0.0492641i
$311$	−9.99283	+	1.58271i	−0.566641	+	0.0897472i	−0.433181	−	0.901307i	$-0.642609\pi$
$311$	−9.99283	+	1.58271i	−0.566641	+	0.0897472i	−0.133460	+	0.991054i	$0.542609\pi$
$312$	3.39069	−	4.49711i	0.191960	−	0.254599i
$313$	−17.7963	+	9.06768i	−1.00591	+	0.512536i	−0.877699	−	0.479212i	$-0.840923\pi$
$313$	−17.7963	+	9.06768i	−1.00591	+	0.512536i	−0.128208	+	0.991747i	$0.540923\pi$
$314$	−0.172489	+	2.03773i	−0.00973413	+	0.114996i
$315$	9.77296	−	2.34628i	0.550644	−	0.132198i
$316$	8.70450	−	6.16842i	0.489666	−	0.347001i
$317$	12.2789	−	10.4872i	0.689654	−	0.589021i	−0.234005	−	0.972235i	$-0.575183\pi$
$317$	12.2789	−	10.4872i	0.689654	−	0.589021i	0.923659	+	0.383215i	$0.125183\pi$
$318$	0.161565	−	0.982489i	0.00906013	−	0.0550952i
$319$	−0.440951	−	2.46925i	−0.0246885	−	0.138251i
$320$	−4.07919	−	20.1046i	−0.228033	−	1.12388i
$321$	2.01908	+	6.21408i	0.112694	+	0.346836i
$322$	−0.704856	+	0.696579i	−0.0392801	+	0.0388188i
$323$	−30.0467	−	18.4127i	−1.67184	−	1.02451i
$324$	10.8054	+	8.04731i	0.600301	+	0.447073i
$325$	−4.00386	+	4.68792i	−0.222094	+	0.260039i
$326$	6.23044	−	7.20826i	0.345072	−	0.399229i
$327$	−0.578536	−	3.65273i	−0.0319931	−	0.201997i
$328$	0.609405	−	0.426469i	0.0336488	−	0.0235478i
$329$	6.08003	−	6.08003i	0.335203	−	0.335203i
$330$	−0.396411	+	6.10777i	−0.0218217	+	0.336221i
$331$	6.49407	−	15.6781i	0.356947	−	0.861745i	−0.638780	−	0.769390i	$-0.720560\pi$
$331$	6.49407	−	15.6781i	0.356947	−	0.861745i	0.995726	−	0.0923554i	$-0.0294396\pi$
$332$	7.93195	+	19.8081i	0.435322	+	1.08711i
$333$	17.3712	+	4.17046i	0.951937	+	0.228540i
$334$	−7.73844	+	23.3464i	−0.423428	+	1.27746i
$335$	22.2805	+	7.23936i	1.21731	+	0.395528i
$336$	−0.612433	−	2.84551i	−0.0334109	−	0.155235i
$337$	−6.07462	−	8.36100i	−0.330906	−	0.455453i	0.610852	−	0.791745i	$-0.290827\pi$
$337$	−6.07462	−	8.36100i	−0.330906	−	0.455453i	−0.941758	+	0.336292i	$0.890827\pi$
$338$	0.0193076	−	3.26888i	0.00105019	−	0.177803i
$339$	4.43188	+	5.18907i	0.240707	+	0.281831i
$340$	−21.7422	+	24.8562i	−1.17914	+	1.34802i
$341$	−1.67707	+	2.86135i	−0.0908184	+	0.154951i
$342$	−18.0226	−	11.1912i	−0.974549	−	0.605151i
$343$	−15.2320	−	7.76107i	−0.822449	−	0.419059i
$344$	1.08373	+	17.7966i	0.0584310	+	0.959526i
$345$	−0.631596	−	0.100035i	−0.0340040	−	0.00538571i
$346$	−31.8980	−	2.70009i	−1.71485	−	0.145158i
$347$	9.64348	−	11.2911i	0.517689	−	0.606136i	−0.438556	−	0.898704i	$-0.644510\pi$
$347$	9.64348	−	11.2911i	0.517689	−	0.606136i	0.956245	+	0.292568i	$0.0945098\pi$
$348$	−0.357523	+	0.681652i	−0.0191653	+	0.0365404i
$349$	4.71503	−	19.6395i	0.252390	−	1.05128i	−0.691856	−	0.722036i	$-0.743207\pi$
$349$	4.71503	−	19.6395i	0.252390	−	1.05128i	0.944245	−	0.329243i	$-0.106793\pi$
$350$	0.479816	+	3.14973i	0.0256472	+	0.168360i
$351$	−11.4319			−0.610188
$352$	−18.6883	−	1.65707i	−0.996092	−	0.0883223i
$353$	36.4049			1.93764			0.968818	−	0.247772i	$-0.0796984\pi$
$353$	36.4049			1.93764			0.968818	+	0.247772i	$0.0796984\pi$
$354$	−0.788512	−	5.17616i	−0.0419089	−	0.275110i
$355$	−8.88141	+	36.9938i	−0.471377	+	1.96342i
$356$	−30.1283	−	15.8022i	−1.59680	−	0.837514i
$357$	−3.04302	+	3.56292i	−0.161054	+	0.188570i
$358$	−11.4887	−	0.972490i	−0.607197	−	0.0513977i
$359$	−8.05601	−	1.27595i	−0.425180	−	0.0673419i	−0.0598222	−	0.998209i	$-0.519053\pi$
$359$	−8.05601	−	1.27595i	−0.425180	−	0.0673419i	−0.365358	+	0.930867i	$0.619053\pi$
$360$	−13.1771	+	14.8860i	−0.694495	+	0.784563i
$361$	9.75715	+	4.97152i	0.513534	+	0.261659i
$362$	27.3436	+	16.9791i	1.43715	+	0.892403i
$363$	5.25173	+	1.93747i	0.275644	+	0.101691i
$364$	−8.42295	−	7.36772i	−0.441483	−	0.386174i
$365$	10.3454	+	12.1129i	0.541502	+	0.634017i
$366$	0.0204723	−	3.46608i	0.00107011	−	0.181175i
$367$	−2.95070	−	4.06129i	−0.154025	−	0.211998i	0.725030	−	0.688717i	$-0.241826\pi$
$367$	−2.95070	−	4.06129i	−0.154025	−	0.211998i	−0.879055	+	0.476719i	$0.841826\pi$
$368$	0.352290	−	1.92826i	0.0183644	−	0.100518i
$369$	−0.685547	−	0.222748i	−0.0356882	−	0.0115958i
$370$	−7.43640	+	22.4351i	−0.386600	+	1.16635i
$371$	−1.92369	−	0.461836i	−0.0998728	−	0.0239773i
$372$	0.944825	−	0.378346i	0.0489869	−	0.0196164i
$373$	7.39715	−	17.8583i	0.383010	−	0.924668i	−0.608370	−	0.793653i	$-0.708176\pi$
$373$	7.39715	−	17.8583i	0.383010	−	0.924668i	0.991380	−	0.131015i	$-0.0418236\pi$
$374$	16.1326	+	25.5326i	0.834199	+	1.32026i
$375$	3.15982	−	3.15982i	0.163173	−	0.163173i
$376$	−2.95785	+	16.7488i	−0.152539	+	0.863751i
$377$	0.462942	+	2.92290i	0.0238427	+	0.150537i
$378$	−3.86339	+	4.46972i	−0.198711	+	0.229897i
$379$	−12.1311	+	14.2037i	−0.623132	+	0.729593i	−0.978754	−	0.205036i	$-0.934269\pi$
$379$	−12.1311	+	14.2037i	−0.623132	+	0.729593i	0.355623	+	0.934630i	$0.384269\pi$
$380$	16.7646	−	22.5104i	0.860003	−	1.15476i
$381$	2.67997	+	1.64229i	0.137299	+	0.0841369i
$382$	12.1221	−	11.9797i	0.620219	−	0.612935i
$383$	−2.27955	−	7.01573i	−0.116479	−	0.358487i	0.875773	−	0.482723i	$-0.160352\pi$
$383$	−2.27955	−	7.01573i	−0.116479	−	0.358487i	−0.992253	+	0.124236i	$0.960352\pi$
$384$	4.21964	+	3.91687i	0.215333	+	0.199882i
$385$	12.0465	+	1.66624i	0.613947	+	0.0849195i
$386$	2.90758	−	17.6812i	0.147992	−	0.899950i
$387$	13.1388	−	11.2216i	0.667882	−	0.570425i
$388$	1.15932	+	1.63596i	0.0588554	+	0.0830533i
$389$	28.8642	−	6.92967i	1.46347	−	0.351348i	0.577997	−	0.816039i	$-0.303834\pi$
$389$	28.8642	−	6.92967i	1.46347	−	0.351348i	0.885473	+	0.464690i	$0.153834\pi$
$390$	0.609076	−	7.19544i	0.0308418	−	0.364355i
$391$	−2.81154	+	1.43255i	−0.142186	+	0.0724473i
$392$	13.8798	−	1.94692i	0.701037	−	0.0983342i
$393$	5.53345	−	0.876413i	0.279126	−	0.0442092i
$394$	12.4397	+	3.06433i	0.626703	+	0.154379i
$395$	5.23456	−	12.6373i	0.263379	−	0.635853i
$396$	9.62102	+	15.4279i	0.483475	+	0.775282i
$397$	−9.58604	+	3.97067i	−0.481110	+	0.199282i	−0.610039	−	0.792372i	$-0.708846\pi$
$397$	−9.58604	+	3.97067i	−0.481110	+	0.199282i	0.128929	+	0.991654i	$0.458846\pi$
$398$	−22.9072	−	16.8507i	−1.14824	−	0.844649i
$399$	2.34075	−	3.22177i	0.117184	−	0.161290i
$400$	−4.34975	−	4.56029i	−0.217487	−	0.228014i
$401$	13.6012	+	4.41929i	0.679210	+	0.220689i	0.628249	−	0.778012i	$-0.283772\pi$
$401$	13.6012	+	4.41929i	0.679210	+	0.220689i	0.0509603	+	0.998701i	$0.483772\pi$
$402$	−6.26495	+	1.99477i	−0.312467	+	0.0994902i
$403$	2.04452	−	3.33636i	0.101845	−	0.166196i
$404$	−5.67643	−	24.9382i	−0.282413	−	1.24072i
$405$	17.2208	+	1.35530i	0.855706	+	0.0673455i
$406$	1.29927	+	0.806786i	0.0644815	+	0.0400401i
$407$	17.7340	+	12.3599i	0.879041	+	0.612658i
$408$	0.890763	−	9.22521i	0.0440993	−	0.456716i
$409$	2.43252	−	4.77408i	0.120280	−	0.236063i	−0.823014	−	0.568021i	$-0.807709\pi$
$409$	2.43252	−	4.77408i	0.120280	−	0.236063i	0.943294	+	0.331958i	$0.107709\pi$
$410$	0.370150	−	0.878901i	0.0182804	−	0.0434058i
$411$	−4.83322	+	1.16035i	−0.238405	+	0.0572360i
$412$	−7.18876	+	1.05170i	−0.354165	+	0.0518134i
$413$	−10.3712	+	0.816231i	−0.510333	+	0.0401641i
$414$	−1.69763	+	0.852396i	−0.0834342	+	0.0418930i
$415$	22.1325	+	16.0802i	1.08644	+	0.789345i
$416$	22.0061	+	2.38754i	1.07894	+	0.117059i
$417$	10.6596			0.522005
$418$	−15.3717	−	20.5579i	−0.751856	−	1.00552i
$419$	−3.22762	−	7.79216i	−0.157679	−	0.380672i	0.825221	−	0.564810i	$-0.191051\pi$
$419$	−3.22762	−	7.79216i	−0.157679	−	0.380672i	−0.982900	+	0.184138i	$0.941051\pi$
$420$	−2.60749	−	2.66983i	−0.127232	−	0.130274i
$421$	−20.7629	−	33.8820i	−1.01192	−	1.65131i	−0.718778	−	0.695240i	$-0.755298\pi$
$421$	−20.7629	−	33.8820i	−1.01192	−	1.65131i	−0.293145	−	0.956068i	$-0.594702\pi$
$422$	5.59737	+	4.83808i	0.272476	+	0.235514i
$423$	14.6860	−	7.48287i	0.714056	−	0.363829i
$424$	3.64130	−	1.43323i	0.176837	−	0.0696037i
$425$	−1.58703	+	10.0201i	−0.0769824	+	0.486048i
$426$	−4.02772	−	9.88858i	−0.195144	−	0.479103i
$427$	−6.86572	−	0.540344i	−0.332256	−	0.0261491i
$428$	−16.9068	+	19.3283i	−0.817223	+	0.934268i
$429$	−6.14997	−	2.40706i	−0.296924	−	0.116214i
$430$	13.3273	+	18.5731i	0.642698	+	0.895675i
$431$	34.2423	−	11.1260i	1.64940	−	0.535921i	0.670786	−	0.741651i	$-0.265957\pi$
$431$	34.2423	−	11.1260i	1.64940	−	0.535921i	0.978609	+	0.205730i	$0.0659567\pi$
$432$	1.19184	−	11.6251i	0.0573423	−	0.559315i
$433$	−6.45719	−	8.88756i	−0.310313	−	0.427109i	0.625166	−	0.780492i	$-0.285031\pi$
$433$	−6.45719	−	8.88756i	−0.310313	−	0.427109i	−0.935479	+	0.353383i	$0.885031\pi$
$434$	−0.613529	−	1.92690i	−0.0294503	−	0.0924941i
$435$	0.0774306	+	0.983849i	0.00371251	+	0.0471719i
$436$	11.1631	−	9.30839i	0.534615	−	0.445791i
$437$	2.28668	−	1.40128i	0.109387	−	0.0670323i
$438$	−4.34088	−	1.06931i	−0.207415	−	0.0510936i
$439$	−19.4539	+	19.4539i	−0.928482	+	0.928482i	−0.997608	−	0.0691260i	$-0.977979\pi$
$439$	−19.4539	+	19.4539i	−0.928482	+	0.928482i	0.0691260	+	0.997608i	$0.477979\pi$
$440$	−21.4123	+	10.9618i	−1.02079	+	0.522583i
$441$	−9.60440	−	9.60440i	−0.457352	−	0.457352i
$442$	−18.4384	−	30.4915i	−0.877024	−	1.45033i
$443$	10.5929	+	17.2861i	0.503285	+	0.821286i	0.998882	−	0.0472661i	$-0.0150509\pi$
$443$	10.5929	+	17.2861i	0.503285	+	0.821286i	−0.495598	+	0.868552i	$0.665051\pi$
$444$	−1.97515	−	6.33245i	−0.0937365	−	0.300525i
$445$	−43.4852	+	3.42236i	−2.06139	+	0.162235i
$446$	−4.50082	−	2.32687i	−0.213120	−	0.110180i
$447$	9.01546	−	6.55012i	0.426417	−	0.309810i
$448$	8.37042	−	7.79722i	0.395465	−	0.368384i
$449$	−4.37549	−	13.4664i	−0.206492	−	0.635517i	−0.999649	−	0.0264998i	$-0.991564\pi$
$449$	−4.37549	−	13.4664i	−0.206492	−	0.635517i	0.793157	−	0.609018i	$-0.208436\pi$
$450$	−0.991018	+	6.02645i	−0.0467170	+	0.284090i
$451$	−0.674213	−	0.553313i	−0.0317475	−	0.0260545i
$452$	−8.58849	+	25.4074i	−0.403969	+	1.19507i
$453$	−0.687602	+	8.73682i	−0.0323064	+	0.410492i
$454$	16.2733	+	6.85351i	0.763744	+	0.321651i
$455$	−14.1713	−	2.24451i	−0.664359	−	0.105224i
$456$	−0.139569	+	7.87588i	−0.00653593	+	0.368822i
$457$	−3.46252	−	6.79557i	−0.161970	−	0.317883i	0.795731	−	0.605651i	$-0.207087\pi$
$457$	−3.46252	−	6.79557i	−0.161970	−	0.317883i	−0.957700	+	0.287767i	$0.907087\pi$
$458$	−0.482669	−	6.63358i	−0.0225536	−	0.309967i
$459$	−16.0399	+	9.82928i	−0.748680	+	0.458792i
$460$	−0.934274	−	2.33312i	−0.0435608	−	0.108782i
$461$	6.92067	−	2.86663i	0.322328	−	0.133512i	−0.215652	−	0.976470i	$-0.569188\pi$
$461$	6.92067	−	2.86663i	0.322328	−	0.133512i	0.537980	+	0.842958i	$0.319188\pi$
$462$	−3.01950	+	1.59110i	−0.140480	+	0.0740246i
$463$			25.8614i			1.20188i	0.799294	+	0.600940i	$0.205207\pi$
$463$			25.8614i			1.20188i	−0.799294	+	0.600940i	$0.794793\pi$
$464$	−3.02058	+	0.166040i	−0.140227	+	0.00770819i
$465$	0.767009	−	1.05570i	0.0355692	−	0.0489568i
$466$	−16.2111	−	5.37336i	−0.750964	−	0.248916i
$467$	0.0505107	+	0.641799i	0.00233736	+	0.0296989i	0.997975	−	0.0636009i	$-0.0202585\pi$
$467$	0.0505107	+	0.641799i	0.00233736	+	0.0296989i	−0.995638	+	0.0932999i	$0.970258\pi$
$468$	−10.9914	−	18.4214i	−0.508079	−	0.851528i
$469$	3.04967	+	12.7028i	0.140821	+	0.586560i
$470$	8.22586	+	20.1955i	0.379431	+	0.931551i
$471$	−0.655666	−	0.334078i	−0.0302115	−	0.0153935i
$472$	15.8819	−	13.0849i	0.731022	−	0.602282i
$473$	19.7530	−	6.84974i	0.908246	−	0.314951i
$474$	0.874113	+	3.73807i	0.0401494	+	0.171695i
$475$	0.676507	−	8.59584i	0.0310403	−	0.394404i
$476$	−18.1530	−	3.09539i	−0.832042	−	0.141877i
$477$	−3.23347	−	1.98147i	−0.148051	−	0.0907255i
$478$	4.02201	−	7.77970i	0.183962	−	0.355835i
$479$	11.9008	−	36.6269i	0.543761	−	1.67352i	−0.180157	−	0.983638i	$-0.557661\pi$
$479$	11.9008	−	36.6269i	0.543761	−	1.67352i	0.723918	−	0.689886i	$-0.242339\pi$
$480$	7.25358	+	1.36954i	0.331079	+	0.0625106i
$481$	−20.6324	−	14.9903i	−0.940757	−	0.683500i
$482$	3.65565	+	23.9974i	0.166510	+	1.09305i
$483$	−0.136461	−	0.329446i	−0.00620919	−	0.0149903i
$484$	4.03678	+	21.6265i	0.183490	+	0.983022i
$485$	2.37511	+	0.983804i	0.107848	+	0.0446722i
$486$	−14.7550	+	8.92242i	−0.669300	+	0.404729i
$487$	4.70339	+	29.6960i	0.213131	+	1.34566i	0.829636	+	0.558305i	$0.188548\pi$
$487$	4.70339	+	29.6960i	0.213131	+	1.34566i	−0.616505	+	0.787351i	$0.711452\pi$
$488$	11.7394	−	6.91083i	0.531418	−	0.312839i
$489$	1.55646	+	3.05473i	0.0703858	+	0.138140i
$490$	13.7333	−	11.5897i	0.620406	−	0.523571i
$491$	−2.58269	−	10.7577i	−0.116555	−	0.485487i	−0.999861	−	0.0166895i	$-0.994687\pi$
$491$	−2.58269	−	10.7577i	−0.116555	−	0.485487i	0.883306	−	0.468798i	$-0.155313\pi$
$492$	0.0594026	+	0.260973i	0.00267808	+	0.0117656i
$493$	3.16270	+	3.70304i	0.142441	+	0.166777i
$494$	17.6560	+	24.6058i	0.794383	+	1.10707i
$495$	20.9748	+	10.1735i	0.942746	+	0.457266i
$496$	3.17961	+	2.42692i	0.142769	+	0.108972i
$497$	−20.1768	+	6.55584i	−0.905054	+	0.294070i
$498$	−7.67773	−	0.0453484i	−0.344047	−	0.00203211i
$499$	22.8298	−	37.2549i	1.02200	−	1.66776i	0.333119	−	0.942885i	$-0.391899\pi$
$499$	22.8298	−	37.2549i	1.02200	−	1.66776i	0.688884	−	0.724872i	$-0.258101\pi$
$500$	17.0277	+	4.30135i	0.761503	+	0.192362i
$501$	−6.72982	−	5.74781i	−0.300666	−	0.256793i
$502$	1.63431	+	22.4612i	0.0729428	+	1.00249i
$503$	5.41061	−	0.856956i	0.241247	−	0.0382098i	−0.0346399	−	0.999400i	$-0.511028\pi$
$503$	5.41061	−	0.856956i	0.241247	−	0.0382098i	0.275887	+	0.961190i	$0.411028\pi$
$504$	−10.9171	−	1.92797i	−0.486284	−	0.0858784i
$505$	−23.1875	−	23.1875i	−1.03183	−	1.03183i
$506$	−2.28874	+	0.211778i	−0.101747	+	0.00941468i
$507$	1.08674	+	0.450142i	0.0482637	+	0.0199915i
$508$	−0.145921	+	12.3522i	−0.00647422	+	0.548041i
$509$	1.25778	−	5.23902i	0.0557500	−	0.232215i	−0.937538	−	0.347883i	$-0.886901\pi$
$509$	1.25778	−	5.23902i	0.0557500	−	0.232215i	0.993288	+	0.115667i	$0.0369007\pi$
$510$	−5.33215	−	10.6195i	−0.236111	−	0.470240i
$511$	−2.74495	+	8.44807i	−0.121429	+	0.373721i
$512$	−4.72216	+	22.1292i	−0.208692	+	0.977981i
$513$	12.9351	−	9.39791i	0.571099	−	0.414928i
$514$	31.3839	−	31.0153i	1.38428	−	1.36803i
$515$	−7.08326	+	6.04968i	−0.312126	+	0.266581i
$516$	−6.07784	−	2.05449i	−0.267562	−	0.0904441i
$517$	19.8475	−	1.95480i	0.872893	−	0.0859719i
$518$	−12.8337	+	3.00105i	−0.563881	+	0.131858i
$519$	5.22955	−	10.2636i	0.229552	−	0.450521i
$520$	25.5115	−	12.4344i	1.11875	−	0.545283i
$521$	0.826526	−	5.21848i	0.0362108	−	0.228626i	−0.962945	−	0.269696i	$-0.913077\pi$
$521$	0.826526	−	5.21848i	0.0362108	−	0.228626i	0.999156	+	0.0410703i	$0.0130768\pi$
$522$	1.89077	+	2.24047i	0.0827567	+	0.0980626i
$523$	13.3354	+	11.3895i	0.583117	+	0.498029i	0.891371	−	0.453275i	$-0.149745\pi$
$523$	13.3354	+	11.3895i	0.583117	+	0.498029i	−0.308254	+	0.951304i	$0.599745\pi$
$524$	14.1011	+	16.9108i	0.616009	+	0.738750i
$525$	−1.11478	−	0.267636i	−0.0486531	−	0.0116806i
$526$	−12.8849	−	9.47820i	−0.561808	−	0.413269i
$527$		−	6.43911i		−	0.280492i
$528$	3.08892	−	6.00300i	0.134428	−	0.261247i
$529$			22.7599i			0.989559i
$530$	2.97301	−	4.04158i	0.129139	−	0.175555i
$531$	−19.3911	−	4.65538i	−0.841501	−	0.202026i
$532$	15.5874	+	1.41221i	0.675798	+	0.0612269i
$533$	0.782474	+	0.668296i	0.0338927	+	0.0289471i
$534$	9.35564	−	7.89538i	0.404858	−	0.341667i
$535$	−5.15051	+	32.5190i	−0.222676	+	1.40592i
$536$	−19.3487	−	17.1274i	−0.835736	−	0.739793i
$537$	1.88353	−	3.69663i	0.0812801	−	0.159521i
$538$	−4.59674	−	19.6576i	−0.198179	−	0.847497i
$539$	−6.58625	−	15.0574i	−0.283690	−	0.648570i
$540$	−6.64405	−	13.4295i	−0.285914	−	0.577915i
$541$	−8.83458	+	7.54544i	−0.379828	+	0.324404i	−0.818781	−	0.574106i	$-0.805350\pi$
$541$	−8.83458	+	7.54544i	−0.379828	+	0.324404i	0.438953	+	0.898510i	$0.355350\pi$
$542$	26.3022	+	26.6148i	1.12978	+	1.14320i
$543$	−9.36986	+	6.80760i	−0.402099	+	0.292142i
$544$	32.9293	−	15.5712i	1.41183	−	0.667609i
$545$	5.75874	−	17.7236i	0.246677	−	0.759194i
$546$	3.59861	−	1.80689i	0.154006	−	0.0773278i
$547$	−1.39112	+	5.79444i	−0.0594801	+	0.247752i	−0.994187	−	0.107667i	$-0.965662\pi$
$547$	−1.39112	+	5.79444i	−0.0594801	+	0.247752i	0.934707	+	0.355419i	$0.115662\pi$
$548$	−13.6493	−	13.9756i	−0.583069	−	0.597010i
$549$	−12.1967	−	5.05204i	−0.520543	−	0.215616i
$550$	−3.77434	+	6.35331i	−0.160938	+	0.270906i
$551$	−2.92667	−	2.92667i	−0.124680	−	0.124680i
$552$	0.594778	+	0.379138i	0.0253154	+	0.0161372i
$553$	7.53372	−	1.19322i	0.320366	−	0.0507410i
$554$	3.55400	−	0.258594i	0.150995	−	0.0109866i
$555$	−6.46715	−	5.52347i	−0.274515	−	0.234458i
$556$	21.4662	+	35.9768i	0.910369	+	1.52575i
$557$	−14.2523	+	23.2576i	−0.603889	+	0.985458i	0.393910	+	0.919149i	$0.371122\pi$
$557$	−14.2523	+	23.2576i	−0.603889	+	0.985458i	−0.997799	+	0.0663088i	$0.978878\pi$
$558$	0.0228955	−	3.87633i	0.000969242	−	0.164098i
$559$	−23.4590	+	7.62230i	−0.992211	+	0.322389i
$560$	3.75989	−	14.1768i	0.158884	−	0.599081i
$561$	−10.6986	+	1.91052i	−0.451694	+	0.0806621i
$562$	−28.5467	+	20.4839i	−1.20417	+	0.864059i
$563$	7.05062	+	8.25521i	0.297148	+	0.347916i	0.888814	−	0.458267i	$-0.151530\pi$
$563$	7.05062	+	8.25521i	0.297148	+	0.347916i	−0.591666	+	0.806183i	$0.701530\pi$
$564$	−5.18006	−	3.25913i	−0.218120	−	0.137234i
$565$	8.02741	+	33.4366i	0.337716	+	1.40669i
$566$	12.6020	+	14.9328i	0.529703	+	0.627672i
$567$	4.37310	+	8.58269i	0.183653	+	0.360439i
$568$	25.2635	−	33.5072i	1.06003	−	1.40593i
$569$	5.75088	+	36.3096i	0.241089	+	1.52218i	0.750045	+	0.661386i	$0.230032\pi$
$569$	5.75088	+	36.3096i	0.241089	+	1.52218i	−0.508956	+	0.860793i	$0.669968\pi$
$570$	5.22605	+	8.64231i	0.218895	+	0.361986i
$571$	−20.3613	−	8.43393i	−0.852094	−	0.352949i	−0.0864833	−	0.996253i	$-0.527563\pi$
$571$	−20.3613	−	8.43393i	−0.852094	−	0.352949i	−0.765610	+	0.643305i	$0.777563\pi$
$572$	−4.26077	−	25.6037i	−0.178152	−	1.07055i
$573$	2.34685	+	5.66579i	0.0980409	+	0.236692i
$574$	0.525731	−	0.0800875i	0.0219436	−	0.00334279i
$575$	−0.624625	−	0.453817i	−0.0260487	−	0.0189255i
$576$	19.8787	−	9.25673i	0.828280	−	0.385697i
$577$	3.57014	−	10.9878i	0.148627	−	0.457427i	−0.848833	−	0.528662i	$-0.822694\pi$
$577$	3.57014	−	10.9878i	0.148627	−	0.457427i	0.997460	+	0.0712350i	$0.0226940\pi$
$578$	−30.7313	−	15.8877i	−1.27825	−	0.660841i
$579$	5.49763	+	3.36895i	0.228474	+	0.140009i
$580$	−3.16461	+	2.24259i	−0.131403	+	0.0931184i
$581$	−1.19692	+	15.2083i	−0.0496565	+	0.630946i
$582$	−0.702549	+	0.164284i	−0.0291216	+	0.00680981i
$583$	−2.76950	−	3.65862i	−0.114701	−	0.151525i
$584$	−5.13262	−	16.8040i	−0.212389	−	0.695356i
$585$	−24.5058	−	12.4864i	−1.01319	−	0.516247i
$586$	37.5493	−	15.2942i	1.55115	−	0.631799i
$587$	−9.72379	−	40.5025i	−0.401344	−	1.67172i	−0.697506	−	0.716579i	$-0.745707\pi$
$587$	−9.72379	−	40.5025i	−0.401344	−	1.67172i	0.296162	−	0.955138i	$-0.404293\pi$
$588$	−1.23519	+	4.88975i	−0.0509385	+	0.201650i
$589$	0.429383	+	5.45583i	0.0176924	+	0.224803i
$590$	8.30107	−	25.0438i	0.341750	−	1.03104i
$591$	−2.70972	+	3.72961i	−0.111463	+	0.153416i
$592$	17.3948	−	19.4184i	0.714922	−	0.798091i
$593$		−	4.95156i		−	0.203336i	−0.994818	−	0.101668i	$-0.967582\pi$
$593$		−	4.95156i		−	0.203336i	0.994818	−	0.101668i	$-0.0324180\pi$
$594$	−13.5037	+	2.32924i	−0.554065	+	0.0955697i
$595$	−21.8134	+	9.03540i	−0.894261	+	0.370415i
$596$	40.2621	+	17.2371i	1.64920	+	0.706059i
$597$	8.72489	−	5.34662i	0.357086	−	0.218823i
$598$	2.70466	−	0.196795i	0.110602	−	0.00804755i
$599$	−7.41174	−	14.5463i	−0.302835	−	0.594348i	0.688571	−	0.725169i	$-0.258239\pi$
$599$	−7.41174	−	14.5463i	−0.302835	−	0.594348i	−0.991406	+	0.130822i	$0.958239\pi$
$600$	2.11015	−	0.830560i	0.0861464	−	0.0339075i
$601$	36.3566	+	5.75831i	1.48301	+	0.234886i	0.844846	−	0.535010i	$-0.179692\pi$
$601$	36.3566	+	5.75831i	1.48301	+	0.234886i	0.638169	+	0.769896i	$0.279692\pi$
$602$	−4.94772	+	11.7481i	−0.201654	+	0.478817i
$603$	−1.96477	+	24.9647i	−0.0800114	+	1.01664i
$604$	−30.8718	+	15.2734i	−1.25616	+	0.621464i
$605$	19.1470	+	20.7131i	0.778434	+	0.842108i
$606$	9.08121	+	1.49336i	0.368899	+	0.0606635i
$607$	−0.606006	−	1.86509i	−0.0245970	−	0.0757018i	0.938005	−	0.346623i	$-0.112672\pi$
$607$	−0.606006	−	1.86509i	−0.0245970	−	0.0757018i	−0.962602	+	0.270921i	$0.912672\pi$
$608$	−26.8625	+	15.3892i	−1.08942	+	0.624116i
$609$	−0.445221	+	0.323472i	−0.0180413	+	0.0131078i
$610$	8.02116	−	15.5152i	0.324767	−	0.628192i
$611$	−23.4571	+	1.84611i	−0.948972	+	0.0746857i
$612$	−31.2609	−	16.3962i	−1.26365	−	0.662777i
$613$	−15.6887	−	25.6016i	−0.633659	−	1.03404i	−0.994832	−	0.101539i	$-0.967623\pi$
$613$	−15.6887	−	25.6016i	−0.633659	−	1.03404i	0.361172	−	0.932499i	$-0.382377\pi$
$614$	10.8837	−	6.58143i	0.439230	−	0.265605i
$615$	0.242652	+	0.242652i	0.00978469	+	0.00978469i
$616$	−11.4507	−	6.98684i	−0.461360	−	0.281508i
$617$	−19.8283	+	19.8283i	−0.798259	+	0.798259i	−0.982821	−	0.184562i	$-0.940913\pi$
$617$	−19.8283	+	19.8283i	−0.798259	+	0.798259i	0.184562	+	0.982821i	$0.440913\pi$
$618$	0.625301	−	2.53842i	0.0251533	−	0.102110i
$619$	19.4488	−	11.9182i	0.781712	−	0.479034i	−0.0735104	−	0.997294i	$-0.523420\pi$
$619$	19.4488	−	11.9182i	0.781712	−	0.479034i	0.855223	+	0.518260i	$0.173420\pi$
$620$	5.10761	+	0.462746i	0.205127	+	0.0185843i
$621$	−0.112328	−	1.42726i	−0.00450757	−	0.0572741i
$622$	13.6337	−	4.34101i	0.546663	−	0.174059i
$623$	−14.2972	−	19.6784i	−0.572804	−	0.788397i
$624$	−3.78269	+	7.00949i	−0.151429	+	0.280604i
$625$	28.9077	−	9.39268i	1.15631	−	0.375707i
$626$	22.9495	−	16.4676i	0.917248	−	0.658178i
$627$	8.93746	−	2.33219i	0.356928	−	0.0931388i
$628$	−0.192838	−	2.88566i	−0.00769507	−	0.115150i
$629$	−41.8380	−	3.29272i	−1.66819	−	0.131289i
$630$	−13.1637	+	5.36172i	−0.524455	+	0.213616i
$631$	−6.33666	+	40.0081i	−0.252259	+	1.59270i	0.458128	+	0.888886i	$0.348520\pi$
$631$	−6.33666	+	40.0081i	−0.252259	+	1.59270i	−0.710387	+	0.703812i	$0.751480\pi$
$632$	−10.8559	+	10.4778i	−0.431824	+	0.416786i
$633$	−2.37207	+	1.20863i	−0.0942812	+	0.0480387i
$634$	−14.9335	+	17.2772i	−0.593084	+	0.686163i
$635$	8.27553	+	13.5044i	0.328404	+	0.535907i
$636$	−0.0166334	+	1.40801i	−0.000659557	+	0.0558313i
$637$	7.42025	+	17.9141i	0.294001	+	0.709781i
$638$	1.14238	+	3.35831i	0.0452273	+	0.132957i
$639$	−40.6674			−1.60878
$640$	9.98488	+	27.2391i	0.394687	+	1.07672i
$641$	−16.1129	−	11.7067i	−0.636420	−	0.462386i	0.222198	−	0.975001i	$-0.428677\pi$
$641$	−16.1129	−	11.7067i	−0.636420	−	0.462386i	−0.858618	+	0.512615i	$0.828677\pi$
$642$	−4.14630	−	8.25780i	−0.163642	−	0.325909i
$643$	40.3763	−	3.17768i	1.59228	−	0.125316i	0.748921	−	0.662659i	$-0.230572\pi$
$643$	40.3763	−	3.17768i	1.59228	−	0.125316i	0.843363	+	0.537344i	$0.180572\pi$
$644$	0.837093	−	1.12399i	0.0329861	−	0.0442916i
$645$	−7.99853	+	1.92028i	−0.314942	+	0.0756108i
$646$	45.9294	+	19.3432i	1.80707	+	0.761047i
$647$	1.38498	−	2.71817i	0.0544490	−	0.106862i	−0.862179	−	0.506605i	$-0.830900\pi$
$647$	1.38498	−	2.71817i	0.0544490	−	0.106862i	0.916628	+	0.399742i	$0.130900\pi$
$648$	−16.8208	−	8.94951i	−0.660783	−	0.351570i
$649$	−19.7960	−	13.7971i	−0.777062	−	0.541583i
$650$	4.59931	−	7.40684i	0.180400	−	0.290520i
$651$	0.725421	+	0.0570919i	0.0284315	+	0.00223761i
$652$	−7.17548	+	11.4047i	−0.281014	+	0.446643i
$653$	7.82463	−	12.7686i	0.306201	−	0.499675i	−0.662115	−	0.749402i	$-0.730341\pi$
$653$	7.82463	−	12.7686i	0.306201	−	0.499675i	0.968316	+	0.249727i	$0.0803409\pi$
$654$	1.58679	+	4.98362i	0.0620486	+	0.194875i
$655$	26.8491	+	8.72380i	1.04908	+	0.340867i
$656$	−0.761172	+	0.726029i	−0.0297188	+	0.0283467i
$657$	−10.0085	+	13.7756i	−0.390470	+	0.537436i
$658$	−7.20549	+	9.79531i	−0.280899	+	0.381861i
$659$	21.8554	−	9.05278i	0.851364	−	0.352646i	0.0860397	−	0.996292i	$-0.472579\pi$
$659$	21.8554	−	9.05278i	0.851364	−	0.352646i	0.765324	+	0.643645i	$0.222579\pi$
$660$	−0.746602	−	8.62360i	−0.0290615	−	0.335673i
$661$	5.32288	−	12.8506i	0.207036	−	0.499829i	−0.785918	−	0.618331i	$-0.787809\pi$
$661$	5.32288	−	12.8506i	0.207036	−	0.499829i	0.992954	+	0.118502i	$0.0378091\pi$
$662$	−5.74018	+	23.3024i	−0.223098	+	0.905672i
$663$	12.6641	−	2.00580i	0.491834	−	0.0778988i
$664$	−15.3082	−	26.0040i	−0.594074	−	1.00915i
$665$	17.8799	−	9.11025i	0.693351	−	0.353280i
$666$	−25.1746	−	2.13097i	−0.975498	−	0.0825735i
$667$	−0.360374	+	0.0865180i	−0.0139537	+	0.00334999i
$668$	5.84673	−	34.2883i	0.226217	−	1.32665i
$669$	1.38636	−	1.18406i	0.0535998	−	0.0457785i
$670$	−32.6918	−	5.37599i	−1.26299	−	0.207693i
$671$	−11.5148	−	11.0713i	−0.444523	−	0.427401i
$672$	1.46226	+	3.84783i	0.0564080	+	0.148433i
$673$	1.35806	+	4.17968i	0.0523494	+	0.161115i	0.973813	−	0.227349i	$-0.0730058\pi$
$673$	1.35806	+	4.17968i	0.0523494	+	0.161115i	−0.921464	+	0.388464i	$0.873006\pi$
$674$	10.2735	+	10.3956i	0.395722	+	0.400425i
$675$	−3.92464	−	2.40503i	−0.151060	−	0.0925695i
$676$	0.669205	+	4.57428i	0.0257386	+	0.175934i
$677$	2.68204	−	3.14026i	0.103079	−	0.120690i	−0.706468	−	0.707745i	$-0.749713\pi$
$677$	2.68204	−	3.14026i	0.103079	−	0.120690i	0.809547	+	0.587055i	$0.199713\pi$
$678$	−7.30130	−	6.31086i	−0.280405	−	0.242367i
$679$	0.224259	+	1.41592i	0.00860629	+	0.0543379i
$680$	25.1036	−	39.3816i	0.962679	−	1.51022i
$681$	−4.49284	+	4.49284i	−0.172166	+	0.172166i
$682$	1.73528	−	4.35759i	0.0664473	−	0.166861i
$683$	3.00066	−	7.24424i	0.114817	−	0.277193i	−0.856016	−	0.516949i	$-0.827068\pi$
$683$	3.00066	−	7.24424i	0.114817	−	0.277193i	0.970833	+	0.239756i	$0.0770675\pi$
$684$	27.5806	+	11.8078i	1.05457	+	0.451484i
$685$	−24.3547	−	5.84705i	−0.930547	−	0.223404i
$686$	22.9485	+	7.60657i	0.876178	+	0.290420i
$687$	2.27617	+	0.739572i	0.0868413	+	0.0282164i
$688$	−5.30542	−	24.6503i	−0.202267	−	0.939783i
$689$	3.18211	+	4.37980i	0.121229	+	0.166857i
$690$	0.904330	+	0.00534141i	0.0344273	+	0.000203344i
$691$	29.1765	+	34.1613i	1.10993	+	1.29956i	0.949938	+	0.312439i	$0.101146\pi$
$691$	29.1765	+	34.1613i	1.10993	+	1.29956i	0.159989	+	0.987119i	$0.448854\pi$
$692$	45.1712	−	3.01862i	1.71715	−	0.114751i
$693$	1.27416	+	12.9369i	0.0484015	+	0.491431i
$694$	−11.0776	+	17.8397i	−0.420502	+	0.677186i
$695$	47.8597	+	24.3857i	1.81542	+	0.925004i
$696$	0.354671	−	1.02915i	0.0134438	−	0.0390099i
$697$	1.67249	+	0.264897i	0.0633501	+	0.0100337i
$698$	−2.40923	+	28.4619i	−0.0911907	+	1.07730i
$699$	3.99113	−	4.67301i	0.150958	−	0.176749i
$700$	−1.34165	−	4.30140i	−0.0507095	−	0.162578i
$701$	9.49433	−	39.5467i	0.358596	−	1.49366i	−0.443396	−	0.896326i	$-0.646227\pi$
$701$	9.49433	−	39.5467i	0.358596	−	1.49366i	0.801992	−	0.597334i	$-0.203773\pi$
$702$	15.9827	−	2.43474i	0.603229	−	0.0918932i
$703$	35.6687			1.34527
$704$	26.4808	−	1.66347i	0.998033	−	0.0626945i
$705$	−7.84676			−0.295526
$706$	−50.8971	+	7.75343i	−1.91554	+	0.291804i
$707$	4.26878	−	17.7808i	0.160544	−	0.668714i
$708$	2.20481	+	7.06877i	0.0828619	+	0.265661i
$709$	−24.2883	+	28.4379i	−0.912165	+	1.06801i	0.0852646	+	0.996358i	$0.472826\pi$
$709$	−24.2883	+	28.4379i	−0.912165	+	1.06801i	−0.997430	+	0.0716499i	$0.977174\pi$
$710$	4.53812	−	53.6119i	0.170313	−	2.01202i
$711$	14.4414	+	2.28730i	0.541595	+	0.0857803i
$712$	45.4875	+	15.6761i	1.70472	+	0.587488i
$713$	0.436631	+	0.222475i	0.0163520	+	0.00833174i
$714$	3.49558	−	5.62936i	0.130819	−	0.210674i
$715$	−22.1056	−	24.8763i	−0.826704	−	0.930322i
$716$	16.2693	−	1.08721i	0.608012	−	0.0406311i
$717$	2.04666	+	2.39633i	0.0764340	+	0.0894928i
$718$	11.5347	+	0.0681297i	0.430472	+	0.00254258i
$719$	14.1033	+	19.4116i	0.525965	+	0.723929i	0.986509	−	0.163708i	$-0.0523456\pi$
$719$	14.1033	+	19.4116i	0.525965	+	0.723929i	−0.460544	+	0.887637i	$0.652346\pi$
$720$	15.2523	−	23.6184i	0.568421	−	0.880205i
$721$	−4.94019	−	1.60516i	−0.183982	−	0.0597794i
$722$	−14.7001	−	4.87254i	−0.547083	−	0.181337i
$723$	−8.49337	−	2.03908i	−0.315872	−	0.0758341i
$724$	−41.8448	−	17.9147i	−1.55515	−	0.665794i
$725$	−0.455985	+	1.10085i	−0.0169349	+	0.0408844i
$726$	−7.75500	−	1.59025i	−0.287815	−	0.0590197i
$727$	−6.93555	+	6.93555i	−0.257225	+	0.257225i	−0.823925	−	0.566699i	$-0.808220\pi$
$727$	−6.93555	+	6.93555i	−0.257225	+	0.257225i	0.566699	+	0.823925i	$0.308220\pi$
$728$	13.3452	+	8.50679i	0.494605	+	0.315283i
$729$	2.19080	+	13.8322i	0.0811407	+	0.512302i
$730$	−17.0435	−	14.7315i	−0.630808	−	0.545237i
$731$	−26.3613	+	30.8651i	−0.975008	+	1.14159i
$732$	0.709576	+	4.85023i	0.0262267	+	0.179270i
$733$	−7.26792	−	4.45379i	−0.268447	−	0.164504i	0.381761	−	0.924261i	$-0.375318\pi$
$733$	−7.26792	−	4.45379i	−0.268447	−	0.164504i	−0.650207	+	0.759757i	$0.725318\pi$
$734$	4.99029	+	5.04959i	0.184195	+	0.186384i
$735$	1.99819	+	6.14979i	0.0737043	+	0.226838i
$736$	−0.0818544	+	2.77090i	−0.00301719	+	0.102137i
$737$	−13.2234	+	27.2628i	−0.487090	+	1.00424i
$738$	1.00589	+	0.165414i	0.0370274	+	0.00608897i
$739$	35.3517	−	30.1932i	1.30044	−	1.11068i	0.313495	−	0.949590i	$-0.398500\pi$
$739$	35.3517	−	30.1932i	1.30044	−	1.11068i	0.986940	−	0.161087i	$-0.0514998\pi$
$740$	5.61853	−	32.9500i	0.206541	−	1.21127i
$741$	−10.5965	+	2.54399i	−0.389272	+	0.0934559i
$742$	2.78784	+	0.235984i	0.102345	+	0.00866323i
$743$	−5.78253	+	2.94634i	−0.212140	+	0.108091i	−0.556832	−	0.830625i	$-0.687983\pi$
$743$	−5.78253	+	2.94634i	−0.212140	+	0.108091i	0.344692	+	0.938716i	$0.387983\pi$
$744$	−1.24037	+	0.730187i	−0.0454740	+	0.0267700i
$745$	55.4622	−	8.78435i	2.03198	−	0.321834i
$746$	−6.53842	+	26.5429i	−0.239389	+	0.971803i
$747$	−11.1908	+	27.0170i	−0.409450	+	0.988500i
$748$	−27.9927	−	32.2608i	−1.02351	−	1.17957i
$749$	−16.9622	+	7.02597i	−0.619785	+	0.256724i
$750$	−3.74473	+	5.09067i	−0.136738	+	0.185885i
$751$	−8.95804	+	12.3297i	−0.326884	+	0.449917i	−0.940553	−	0.339646i	$-0.889693\pi$
$751$	−8.95804	+	12.3297i	−0.326884	+	0.449917i	0.613670	+	0.789563i	$0.289693\pi$
$752$	0.568211	−	24.0461i	0.0207205	−	0.876872i
$753$	−7.70707	−	2.50418i	−0.280861	−	0.0912574i
$754$	−1.26974	−	3.98787i	−0.0462414	−	0.145229i
$755$	−23.0742	+	37.6536i	−0.839755	+	1.37036i
$756$	4.44939	−	7.07186i	0.161823	−	0.257201i
$757$	−33.9600	−	2.67271i	−1.23430	−	0.0971414i	−0.555532	−	0.831495i	$-0.687485\pi$
$757$	−33.9600	−	2.67271i	−1.23430	−	0.0971414i	−0.678767	+	0.734354i	$0.737485\pi$
$758$	13.9352	−	22.4416i	0.506149	−	0.815115i
$759$	0.240091	−	0.791472i	0.00871475	−	0.0287286i
$760$	−18.6440	+	35.0419i	−0.676291	+	1.27110i
$761$	−14.4569	+	28.3733i	−0.524063	+	1.02853i	0.465583	+	0.885004i	$0.345845\pi$
$761$	−14.4569	+	28.3733i	−0.524063	+	1.02853i	−0.989646	+	0.143528i	$0.954155\pi$
$762$	−4.09659	−	1.72528i	−0.148404	−	0.0625004i
$763$	10.1048	−	2.42594i	0.365817	−	0.0878248i
$764$	−14.3963	+	19.3304i	−0.520838	+	0.699348i
$765$	−45.1198	+	3.55101i	−1.63131	+	0.128387i
$766$	4.68120	+	9.32309i	0.169139	+	0.336857i
$767$	23.0315	+	16.7333i	0.831618	+	0.604206i
$768$	−6.73362	−	4.57742i	−0.242979	−	0.165173i
$769$	4.47079			0.161221			0.0806105	−	0.996746i	$-0.474313\pi$
$769$	4.47079			0.161221			0.0806105	+	0.996746i	$0.474313\pi$
$770$	−17.1969	+	0.236092i	−0.619733	+	0.00850818i
$771$	6.07596	+	14.6687i	0.218820	+	0.528279i
$772$	−0.299340	+	25.3391i	−0.0107735	+	0.911973i
$773$	−5.75244	−	9.38713i	−0.206901	−	0.337632i	0.732310	−	0.680971i	$-0.238442\pi$
$773$	−5.75244	−	9.38713i	−0.206901	−	0.337632i	−0.939212	+	0.343339i	$0.888442\pi$
$774$	−15.9792	+	18.4870i	−0.574360	+	0.664501i
$775$	1.40380	−	0.715271i	0.0504259	−	0.0256933i
$776$	−1.96925	−	2.04030i	−0.0706919	−	0.0732425i
$777$	0.741907	−	4.68421i	0.0266158	−	0.168045i
$778$	−38.8787	+	15.8357i	−1.39387	+	0.567737i
$779$	−1.43476	−	0.112918i	−0.0514055	−	0.00404570i
$780$	0.680929	+	10.1895i	0.0243812	+	0.364844i
$781$	−45.8224	−	17.9346i	−1.63965	−	0.641749i
$782$	3.62567	−	2.60163i	0.129654	−	0.0930340i
$783$	−2.10136	+	0.682774i	−0.0750965	+	0.0244003i
$784$	−18.9905	+	5.67805i	−0.678233	+	0.202788i
$785$	−2.17955	−	2.99989i	−0.0777915	−	0.107071i
$786$	−7.54958	+	2.40380i	−0.269285	+	0.0857408i
$787$	0.792538	+	10.0701i	0.0282509	+	0.358962i	0.994753	+	0.102304i	$0.0326214\pi$
$787$	0.792538	+	10.0701i	0.0282509	+	0.358962i	−0.966502	+	0.256658i	$0.917379\pi$
$788$	−18.0444	−	1.63481i	−0.642805	−	0.0582377i
$789$	4.90758	−	3.00737i	0.174715	−	0.107065i
$790$	−4.62688	+	18.7829i	−0.164617	+	0.668266i
$791$	−13.5589	+	13.5589i	−0.482099	+	0.482099i
$792$	−16.7368	−	19.5205i	−0.594717	−	0.693629i
$793$	13.3262	+	13.3262i	0.473227	+	0.473227i
$794$	12.5564	−	7.59295i	0.445611	−	0.269464i
$795$	0.943316	+	1.53935i	0.0334560	+	0.0545952i
$796$	35.6151	+	18.6800i	1.26234	+	0.662094i
$797$	−25.7666	+	2.02787i	−0.912699	+	0.0718310i	−0.526106	−	0.850419i	$-0.676348\pi$
$797$	−25.7666	+	2.02787i	−0.912699	+	0.0718310i	−0.386593	+	0.922250i	$0.626348\pi$
$798$	−2.58640	+	5.00283i	−0.0915577	+	0.177098i
$799$	−31.3251	+	22.7590i	−1.10820	+	0.805155i
$800$	7.05255	+	5.44927i	0.249345	+	0.192661i
$801$	−14.4083	−	44.3443i	−0.509094	−	1.56683i
$802$	−19.9568	−	3.28179i	−0.704699	−	0.115884i
$803$	−17.3523	+	11.1079i	−0.612350	+	0.391990i
$804$	8.33408	−	4.12316i	0.293920	−	0.145413i
$805$	0.140981	−	1.79133i	0.00496891	−	0.0631360i
$806$	−2.14784	+	5.09995i	−0.0756546	+	0.179638i
$807$	7.17486	+	1.13639i	0.252567	+	0.0400027i
$808$	13.2474	+	33.6568i	0.466043	+	1.18404i
$809$	−5.60951	−	11.0093i	−0.197220	−	0.387066i	0.771124	−	0.636685i	$-0.219695\pi$
$809$	−5.60951	−	11.0093i	−0.197220	−	0.387066i	−0.968344	+	0.249619i	$0.919695\pi$
$810$	−24.3647	+	1.77281i	−0.856089	+	0.0622902i
$811$	−15.9833	+	9.79459i	−0.561250	+	0.343935i	−0.774013	−	0.633169i	$-0.781754\pi$
$811$	−15.9833	+	9.79459i	−0.561250	+	0.343935i	0.212763	+	0.977104i	$0.431754\pi$
$812$	−1.98831	−	0.851240i	−0.0697761	−	0.0298727i
$813$	−12.4396	+	5.15265i	−0.436276	+	0.180711i
$814$	−27.4260	−	13.5033i	−0.961281	−	0.473289i
$815$			17.2758i			0.605146i
$816$	0.719403	+	13.0873i	0.0251841	+	0.458148i
$817$	20.2776	−	27.9098i	0.709424	−	0.976439i
$818$	−2.38409	+	7.19264i	−0.0833577	+	0.251485i
$819$	−1.20332	−	15.2896i	−0.0420474	−	0.534263i
$820$	−0.330314	+	1.30761i	−0.0115351	+	0.0456638i
$821$	−6.42547	−	26.7640i	−0.224250	−	0.934070i	−0.964992	−	0.262280i	$-0.915526\pi$
$821$	−6.42547	−	26.7640i	−0.224250	−	0.934070i	0.740742	−	0.671790i	$-0.234474\pi$
$822$	6.51012	−	2.65164i	0.227067	−	0.0924866i
$823$	−19.5655	−	9.96913i	−0.682011	−	0.347502i	0.0784203	−	0.996920i	$-0.475012\pi$
$823$	−19.5655	−	9.96913i	−0.682011	−	0.347502i	−0.760431	+	0.649418i	$0.775012\pi$
$824$	9.82651	−	3.00141i	0.342323	−	0.104559i
$825$	−1.60494	−	2.12018i	−0.0558767	−	0.0738154i
$826$	14.3260	−	3.35000i	0.498464	−	0.116561i
$827$	2.54288	−	32.3103i	0.0884246	−	1.12354i	−0.779352	−	0.626586i	$-0.784452\pi$
$827$	2.54288	−	32.3103i	0.0884246	−	1.12354i	0.867777	−	0.496954i	$-0.165548\pi$
$828$	2.19190	−	1.55328i	0.0761736	−	0.0539802i
$829$	7.16925	+	4.39332i	0.248998	+	0.152586i	0.641398	−	0.767209i	$-0.278355\pi$
$829$	7.16925	+	4.39332i	0.248998	+	0.152586i	−0.392399	+	0.919795i	$0.628355\pi$
$830$	−34.3678	−	17.7677i	−1.19292	−	0.616726i
$831$	−0.396233	+	1.21948i	−0.0137452	+	0.0423032i
$832$	−31.2748	+	1.34882i	−1.08426	+	0.0467620i
$833$	25.8140	+	18.7550i	0.894403	+	0.649822i
$834$	−14.9031	+	2.27027i	−0.516051	+	0.0786129i
$835$	−17.0665	−	41.2022i	−0.590611	−	1.42586i
$836$	25.8693	+	25.4678i	0.894710	+	0.880822i
$837$	2.69912	+	1.11801i	0.0932952	+	0.0386442i
$838$	6.17204	+	10.2067i	0.213210	+	0.352584i
$839$	1.77262	+	11.1919i	0.0611975	+	0.386386i	0.999208	+	0.0397802i	$0.0126658\pi$
$839$	1.77262	+	11.1919i	0.0611975	+	0.386386i	−0.938011	+	0.346606i	$0.887334\pi$
$840$	4.21410	+	3.17731i	0.145400	+	0.109628i
$841$	−12.9061	−	25.3296i	−0.445036	−	0.873433i
$842$	36.2444	+	42.9479i	1.24907	+	1.48008i
$843$	−2.95144	−	12.2936i	−0.101653	−	0.423416i
$844$	−8.85600	−	5.57192i	−0.304836	−	0.191793i
$845$	3.84947	+	4.50715i	0.132426	+	0.155051i
$846$	−18.9385	+	13.5895i	−0.651120	+	0.467215i
$847$	−4.26957	+	15.1387i	−0.146704	+	0.520171i
$848$	−4.78560	+	2.77929i	−0.164338	+	0.0954413i
$849$	−6.68694	+	2.17272i	−0.229495	+	0.0745675i
$850$	0.0847403	−	14.3470i	0.00290657	−	0.492098i
$851$	1.66880	−	2.72324i	0.0572058	−	0.0933514i
$852$	7.73715	+	12.9673i	0.265070	+	0.444251i
$853$	−3.51473	−	3.00186i	−0.120342	−	0.102782i	0.587241	−	0.809412i	$-0.300214\pi$
$853$	−3.51473	−	3.00186i	−0.120342	−	0.102782i	−0.707583	+	0.706631i	$0.750214\pi$
$854$	9.71394	−	0.706800i	0.332404	−	0.0241862i
$855$	37.9930	−	6.01750i	1.29933	−	0.205794i
$856$	19.5207	−	30.6234i	0.667203	−	1.04669i
$857$	−7.33214	−	7.33214i	−0.250461	−	0.250461i	0.570699	−	0.821160i	$-0.306673\pi$
$857$	−7.33214	−	7.33214i	−0.250461	−	0.250461i	−0.821160	+	0.570699i	$0.806673\pi$
$858$	9.11083	+	2.05546i	0.311039	+	0.0701723i
$859$	−12.6584	−	5.24327i	−0.431898	−	0.178898i	0.156133	−	0.987736i	$-0.450097\pi$
$859$	−12.6584	−	5.24327i	−0.431898	−	0.178898i	−0.588032	+	0.808838i	$0.700097\pi$
$860$	−22.5883	−	23.1284i	−0.770255	−	0.788671i
$861$	−0.0446719	+	0.186072i	−0.00152241	+	0.00634131i
$862$	−45.5041	+	22.8480i	−1.54988	+	0.778205i
$863$	−13.8734	+	42.6979i	−0.472256	+	1.45345i	0.377367	+	0.926064i	$0.376830\pi$
$863$	−13.8734	+	42.6979i	−0.472256	+	1.45345i	−0.849623	+	0.527391i	$0.823170\pi$
$864$	0.809608	+	16.5068i	0.0275434	+	0.561572i
$865$	46.9594	−	34.1180i	1.59667	−	1.16005i
$866$	10.9205	+	11.0503i	0.371095	+	0.375505i
$867$	9.46597	−	8.08470i	0.321481	−	0.274571i
$868$	1.26815	+	2.56330i	0.0430439	+	0.0870041i
$869$	15.2633	+	8.94598i	0.517772	+	0.303472i
$870$	−0.317792	−	1.35901i	−0.0107742	−	0.0460748i
$871$	16.2296	−	31.8524i	0.549919	−	1.07928i
$872$	−13.6245	+	15.3914i	−0.461383	+	0.521219i
$873$	−0.429884	+	2.71418i	−0.0145494	+	0.0918611i
$874$	−2.89853	+	2.44612i	−0.0980442	+	0.0827412i
$875$	9.54815	+	8.15489i	0.322786	+	0.275686i
$876$	6.29666	+	0.570473i	0.212744	+	0.0192745i
$877$	−45.5972	−	10.9469i	−1.53971	−	0.369651i	−0.627249	−	0.778819i	$-0.715819\pi$
$877$	−45.5972	−	10.9469i	−1.53971	−	0.369651i	−0.912459	+	0.409167i	$0.865819\pi$
$878$	23.0549	−	31.3414i	0.778065	−	1.05772i
$879$			14.5894i			0.492087i
$880$	27.6015	−	19.8859i	0.930448	−	0.670352i
$881$		−	10.5367i		−	0.354992i	−0.984122	−	0.177496i	$-0.943200\pi$
$881$		−	10.5367i		−	0.354992i	0.984122	−	0.177496i	$-0.0567997\pi$
$882$	15.4733	+	11.3822i	0.521013	+	0.383260i
$883$	−18.5853	−	4.46194i	−0.625446	−	0.150156i	−0.0916798	−	0.995789i	$-0.529224\pi$
$883$	−18.5853	−	4.46194i	−0.625446	−	0.150156i	−0.533766	+	0.845632i	$0.679224\pi$
$884$	32.2724	+	38.7027i	1.08544	+	1.30171i
$885$	7.21913	+	6.16572i	0.242668	+	0.207258i
$886$	−18.4913	−	21.9113i	−0.621229	−	0.736126i
$887$	8.35405	−	52.7454i	0.280501	−	1.77102i	−0.297246	−	0.954801i	$-0.596068\pi$
$887$	8.35405	−	52.7454i	0.280501	−	1.77102i	0.577748	−	0.816215i	$-0.303932\pi$
$888$	4.11010	+	8.43264i	0.137926	+	0.282981i
$889$	−4.00965	+	7.86938i	−0.134479	+	0.263931i
$890$	60.0670	−	14.0461i	2.01345	−	0.470827i
$891$	−4.78813	+	21.8230i	−0.160408	+	0.731098i
$892$	6.78810	+	2.29458i	0.227282	+	0.0768283i
$893$	25.0239	−	21.3725i	0.837394	−	0.715202i
$894$	−11.2093	+	11.0777i	−0.374897	+	0.370494i
$895$	16.9133	−	12.2883i	0.565350	−	0.410751i
$896$	−10.0419	+	12.6839i	−0.335477	+	0.423739i
$897$	−0.301540	+	0.928046i	−0.0100681	+	0.0309866i
$898$	8.98534	+	17.8952i	0.299845	+	0.597172i
$899$	0.176550	−	0.735385i	0.00588828	−	0.0245265i
$900$	0.102027	−	8.63655i	0.00340089	−	0.287885i
$901$	8.23060	+	3.40923i	0.274201	+	0.113578i
$902$	1.06045	+	0.629986i	0.0353092	+	0.0209763i
$903$	−3.24349	−	3.24349i	−0.107937	−	0.107937i
$904$	6.59622	−	37.3509i	0.219387	−	1.24227i
$905$	−57.6424	+	9.12966i	−1.91610	+	0.303480i
$906$	−0.899422	−	12.3613i	−0.0298813	−	0.410675i
$907$	41.6011	+	35.5307i	1.38134	+	1.17978i	0.962359	+	0.271782i	$0.0876131\pi$
$907$	41.6011	+	35.5307i	1.38134	+	1.17978i	0.418982	+	0.907994i	$0.362387\pi$
$908$	−24.2111	−	6.11593i	−0.803474	−	0.202964i
$909$	18.3149	−	29.8872i	0.607466	−	0.991295i
$910$	20.2906	+	0.119846i	0.672628	+	0.00397287i
$911$	−55.4977	+	18.0323i	−1.83872	+	0.597437i	−0.840247	+	0.542203i	$0.817590\pi$
$911$	−55.4977	+	18.0323i	−1.83872	+	0.597437i	−0.998473	+	0.0552332i	$0.982410\pi$
$912$	−1.48226	−	11.0409i	−0.0490825	−	0.365600i
$913$	−24.5240	+	25.5064i	−0.811626	+	0.844140i
$914$	6.28819	+	8.76334i	0.207995	+	0.289866i
$915$	4.08170	+	4.77905i	0.134937	+	0.157991i
$916$	2.08762	+	9.17151i	0.0689769	+	0.303035i
$917$	3.67500	+	15.3075i	0.121359	+	0.505498i
$918$	20.3318	−	17.1583i	0.671048	−	0.566309i
$919$	8.96860	+	17.6019i	0.295847	+	0.580632i	0.990306	−	0.138899i	$-0.0443565\pi$
$919$	8.96860	+	17.6019i	0.295847	+	0.580632i	−0.694460	+	0.719532i	$0.744356\pi$
$920$	1.80310	+	3.06291i	0.0594463	+	0.100981i
$921$	0.715954	+	4.52035i	0.0235915	+	0.148951i
$922$	−9.06515	+	5.48174i	−0.298545	+	0.180532i
$923$	53.6359	+	22.2167i	1.76545	+	0.731272i
$924$	3.88265	−	2.86758i	0.127730	−	0.0943364i
$925$	−3.92961	−	9.48691i	−0.129205	−	0.311928i
$926$	−5.50790	−	36.1564i	−0.181001	−	1.18817i
$927$	−8.05555	−	5.85270i	−0.264579	−	0.192228i
$928$	4.18766	−	0.875454i	0.137467	−	0.0287382i
$929$	−9.23960	+	28.4366i	−0.303141	+	0.932973i	0.677223	+	0.735778i	$0.263183\pi$
$929$	−9.23960	+	28.4366i	−0.303141	+	0.932973i	−0.980364	+	0.197195i	$0.936817\pi$
$930$	−0.847503	+	1.63931i	−0.0277907	+	0.0537551i
$931$	−23.1228	−	14.1696i	−0.757818	−	0.464391i
$932$	23.8089	+	4.05982i	0.779886	+	0.132984i
$933$	−0.403952	+	5.13270i	−0.0132248	+	0.168037i
$934$	−0.207307	−	0.886532i	−0.00678330	−	0.0290082i
$935$	−52.4052	−	15.8970i	−1.71383	−	0.519887i
$936$	19.2903	+	23.4137i	0.630523	+	0.765300i
$937$	25.0676	+	12.7726i	0.818924	+	0.417262i	0.812674	−	0.582718i	$-0.198011\pi$
$937$	25.0676	+	12.7726i	0.818924	+	0.417262i	0.00624927	+	0.999980i	$0.498011\pi$
$938$	−6.96910	−	17.1100i	−0.227549	−	0.558663i
$939$	2.37276	+	9.88324i	0.0774320	+	0.322527i
$940$	−15.8017	−	26.4832i	−0.515393	−	0.863785i
$941$	−0.524488	−	6.66425i	−0.0170978	−	0.217248i	−0.999531	−	0.0306322i	$-0.990248\pi$
$941$	−0.524488	−	6.66425i	−0.0170978	−	0.217248i	0.982433	−	0.186616i	$-0.0597521\pi$
$942$	0.987827	+	0.327427i	0.0321851	+	0.0106682i
$943$	−0.0757479	+	0.104258i	−0.00246669	+	0.00339511i
$944$	−19.4174	+	21.6763i	−0.631983	+	0.705503i
$945$		−	10.7124i		−	0.348476i
$946$	−26.1576	+	13.7835i	−0.850456	+	0.448140i
$947$	−4.46481	+	1.84939i	−0.145087	+	0.0600970i	−0.454045	−	0.890979i	$-0.650020\pi$
$947$	−4.46481	+	1.84939i	−0.145087	+	0.0600970i	0.308958	+	0.951076i	$0.400020\pi$
$948$	−2.01821	−	5.03997i	−0.0655485	−	0.163691i
$949$	20.7258	−	12.7008i	0.672788	−	0.412285i
$950$	0.884909	+	12.1618i	0.0287102	+	0.394581i
$951$	−3.73062	−	7.32175i	−0.120974	−	0.237424i
$952$	26.0387	+	0.461434i	0.843919	+	0.0149552i
$953$	22.9798	+	3.63965i	0.744389	+	0.117900i	0.517097	−	0.855927i	$-0.327013\pi$
$953$	22.9798	+	3.63965i	0.744389	+	0.117900i	0.227292	+	0.973827i	$0.427013\pi$
$954$	4.94268	+	2.08161i	0.160025	+	0.0673946i
$955$	−2.42457	+	30.8071i	−0.0784573	+	0.996895i
$956$	−3.96621	+	11.7333i	−0.128276	+	0.379481i
$957$	−1.27423	−	0.0751458i	−0.0411899	−	0.00242912i
$958$	−8.83760	+	53.7420i	−0.285530	+	1.73633i
$959$	−4.31602	−	13.2833i	−0.139372	−	0.428942i
$960$	−10.4328	−	0.369878i	−0.336717	−	0.0119377i
$961$	24.2705	−	17.6336i	0.782920	−	0.568825i
$962$	32.0385	+	16.5635i	1.03296	+	0.534029i
$963$	−35.0854	+	2.76128i	−1.13061	+	0.0889810i
$964$	−10.2218	−	32.7718i	−0.329222	−	1.05551i
$965$	16.9762	+	27.7027i	0.546484	+	0.891781i
$966$	0.260949	+	0.431530i	0.00839589	+	0.0138843i
$967$	23.5216	+	23.5216i	0.756404	+	0.756404i	0.975666	−	0.219262i	$-0.0703649\pi$
$967$	23.5216	+	23.5216i	0.756404	+	0.756404i	−0.219262	+	0.975666i	$0.570365\pi$
$968$	−10.2497	−	29.3759i	−0.329438	−	0.944177i
$969$	−12.6805	+	12.6805i	−0.407355	+	0.407355i
$970$	−3.53014	−	0.869595i	−0.113346	−	0.0279210i
$971$	14.9553	−	9.16462i	0.479938	−	0.294107i	−0.261409	−	0.965228i	$-0.584187\pi$
$971$	14.9553	−	9.16462i	0.479938	−	0.294107i	0.741347	+	0.671122i	$0.234187\pi$
$972$	18.7284	−	15.6168i	0.600715	−	0.500909i
$973$	2.35007	+	29.8605i	0.0753399	+	0.957285i
$974$	−12.9003	−	40.5159i	−0.413353	−	1.29821i
$975$	1.84404	+	2.53811i	0.0590567	+	0.0812846i
$976$	−14.9408	+	12.1622i	−0.478244	+	0.389301i
$977$	50.0758	−	16.2706i	1.60207	−	0.520543i	0.634450	−	0.772964i	$-0.281227\pi$
$977$	50.0758	−	16.2706i	1.60207	−	0.520543i	0.967618	+	0.252420i	$0.0812265\pi$
$978$	−2.82666	−	3.93928i	−0.0903866	−	0.125964i
$979$	3.32137	−	56.3195i	0.106152	−	1.79998i
$980$	−16.7319	+	19.1283i	−0.534481	+	0.611031i
$981$	19.8588	+	1.56292i	0.634044	+	0.0499003i
$982$	5.90197	+	14.4901i	0.188339	+	0.462397i
$983$	5.58864	−	35.2853i	0.178250	−	1.12543i	−0.722590	−	0.691276i	$-0.757049\pi$
$983$	5.58864	−	35.2853i	0.178250	−	1.12543i	0.900840	−	0.434150i	$-0.142951\pi$
$984$	−0.138631	−	0.352211i	−0.00441941	−	0.0112281i
$985$	−20.6983	+	10.5463i	−0.659501	+	0.336033i
$986$	−5.21039	−	4.50358i	−0.165932	−	0.143423i
$987$	−2.28625	−	3.73083i	−0.0727723	−	0.118754i
$988$	−29.9251	−	30.6406i	−0.952045	−	0.974807i
$989$	−1.18214	−	2.85395i	−0.0375900	−	0.0907503i
$990$	−31.4913	−	9.75627i	−1.00086	−	0.310075i
$991$	10.1426			0.322191			0.161096	−	0.986939i	$-0.448497\pi$
$991$	10.1426			0.322191			0.161096	+	0.986939i	$0.448497\pi$
$992$	−4.96224	−	2.71585i	−0.157551	−	0.0862285i
$993$	−6.98640	−	5.07592i	−0.221707	−	0.161079i
$994$	26.8126	−	13.4628i	0.850445	−	0.427015i
$995$	51.4044	−	4.04561i	1.62963	−	0.128254i
$996$	10.7438	−	1.57178i	0.340429	−	0.0498039i
$997$	17.4464	−	4.18851i	0.552532	−	0.132651i	0.0524412	−	0.998624i	$-0.483300\pi$
$997$	17.4464	−	4.18851i	0.552532	−	0.132651i	0.500091	+	0.865973i	$0.333300\pi$
$998$	−23.9835	+	56.9477i	−0.759186	+	1.80265i
$999$	8.64449	−	16.9658i	0.273500	−	0.536773i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.bf.a.5.4	✓	736
11.9	even	5	inner	352.2.bf.a.229.40	yes	736
32.13	even	8	inner	352.2.bf.a.269.40	yes	736
352.141	even	40	inner	352.2.bf.a.141.4	yes	736

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.bf.a.5.4	✓	736	1.1	even	1	trivial
352.2.bf.a.141.4	yes	736	352.141	even	40	inner
352.2.bf.a.229.40	yes	736	11.9	even	5	inner
352.2.bf.a.269.40	yes	736	32.13	even	8	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:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.bf (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39808 + 0.212978i) q^{2} +(0.118797 - 0.494823i) q^{3} +(1.90928 - 0.595522i) q^{4} +(1.66537 - 1.94989i) q^{5} +(-0.0607012 + 0.717106i) q^{6} +(1.41232 + 0.223690i) q^{7} +(-2.54250 + 1.23922i) q^{8} +(2.44228 + 1.24440i) q^{9} +(-1.91304 + 3.08080i) q^{10} +(2.20307 + 2.47921i) q^{11} +(-0.0678622 - 1.01550i) q^{12} +(-2.54128 - 2.97546i) q^{13} +(-2.02219 - 0.0119440i) q^{14} +(-0.767013 - 1.05570i) q^{15} +(3.29071 - 2.27404i) q^{16} +(-6.12399 - 1.98980i) q^{17} +(-3.67955 - 1.21963i) q^{18} +(5.32151 + 1.27758i) q^{19} +(2.01845 - 4.71466i) q^{20} +(0.278466 - 0.672277i) q^{21} +(-3.60810 - 2.99693i) q^{22} +(0.346514 - 0.346514i) q^{23} +(0.311157 + 1.40531i) q^{24} +(-0.246467 - 1.55613i) q^{25} +(4.18664 + 3.61871i) q^{26} +(1.89738 - 2.22154i) q^{27} +(2.82974 - 0.413983i) q^{28} +(-0.644839 - 0.395158i) q^{29} +(1.29719 + 1.31260i) q^{30} +(0.309016 + 0.951052i) q^{31} +(-4.11637 + 3.88014i) q^{32} +(1.48849 - 0.795611i) q^{33} +(8.98563 + 1.47764i) q^{34} +(2.78821 - 2.38136i) q^{35} +(5.40407 + 0.921486i) q^{36} +(6.33746 - 1.52149i) q^{37} +(-7.71202 - 0.652804i) q^{38} +(-1.77422 + 0.904011i) q^{39} +(-1.81784 + 7.02137i) q^{40} +(-0.259738 + 0.0411385i) q^{41} +(-0.246139 + 0.999208i) q^{42} +(2.41232 - 5.82385i) q^{43} +(5.68271 + 3.42152i) q^{44} +(6.49375 - 2.68980i) q^{45} +(-0.410656 + 0.558256i) q^{46} +(3.53448 - 4.86479i) q^{47} +(-0.734322 - 1.89847i) q^{48} +(-4.71277 - 1.53127i) q^{49} +(0.676002 + 2.12311i) q^{50} +(-1.71211 + 2.79391i) q^{51} +(-6.62398 - 4.16760i) q^{52} +(-1.37926 - 0.108550i) q^{53} +(-2.17955 + 3.51000i) q^{54} +(8.50311 - 0.166974i) q^{55} +(-3.86804 + 1.18145i) q^{56} +(1.26435 - 2.48144i) q^{57} +(0.985699 + 0.415128i) q^{58} +(-7.07436 + 1.69840i) q^{59} +(-2.09314 - 1.55886i) q^{60} +(-4.80144 + 0.377882i) q^{61} +(-0.634583 - 1.26384i) q^{62} +(3.17093 + 2.30382i) q^{63} +(4.92864 - 6.30147i) q^{64} -10.0340 q^{65} +(-1.91158 + 1.42935i) q^{66} +(3.49617 + 8.44049i) q^{67} +(-12.8774 - 0.152125i) q^{68} +(-0.130299 - 0.212628i) q^{69} +(-3.39098 + 3.92316i) q^{70} +(-13.2194 + 6.73563i) q^{71} +(-7.75161 - 0.137367i) q^{72} +(-0.971783 + 6.13560i) q^{73} +(-8.53626 + 3.47691i) q^{74} +(-0.799288 - 0.0629053i) q^{75} +(10.9211 - 0.729815i) q^{76} +(2.55688 + 3.99425i) q^{77} +(2.28798 - 1.64175i) q^{78} +(5.07319 - 1.64838i) q^{79} +(1.04610 - 10.2036i) q^{80} +(3.95956 + 5.44986i) q^{81} +(0.354374 - 0.112834i) q^{82} +(0.837047 + 10.6357i) q^{83} +(0.131315 - 1.44940i) q^{84} +(-14.0786 + 8.62737i) q^{85} +(-2.13227 + 8.65600i) q^{86} +(-0.272138 + 0.272138i) q^{87} +(-8.67362 - 3.57328i) q^{88} +(-12.0282 - 12.0282i) q^{89} +(-8.50594 + 5.14359i) q^{90} +(-2.92354 - 4.77078i) q^{91} +(0.455236 - 0.867950i) q^{92} +(0.507313 - 0.0399264i) q^{93} +(-3.90540 + 7.55415i) q^{94} +(11.3534 - 8.24874i) q^{95} +(1.43098 + 2.49782i) q^{96} +(0.309803 + 0.953476i) q^{97} +(6.91498 + 1.13713i) q^{98} +(2.29539 + 8.79644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 736 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 12 q^{8} - 12 q^{9} - 32 q^{10} - 16 q^{11} - 64 q^{12} - 12 q^{13} - 28 q^{14} - 52 q^{16} + 48 q^{18} - 12 q^{19} - 28 q^{20}+ \cdots - 68 q^{99}+O(q^{100}) \) 736 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 12 * q^6 - 12 * q^7 - 12 * q^8 - 12 * q^9 - 32 * q^10 - 16 * q^11 - 64 * q^12 - 12 * q^13 - 28 * q^14 - 52 * q^16 + 48 * q^18 - 12 * q^19 - 28 * q^20 - 32 * q^21 - 28 * q^22 - 48 * q^23 - 12 * q^24 - 12 * q^25 - 72 * q^26 - 12 * q^27 - 12 * q^28 - 12 * q^29 - 28 * q^30 - 24 * q^31 + 8 * q^32 - 32 * q^33 - 8 * q^34 - 12 * q^35 - 12 * q^36 - 12 * q^37 - 12 * q^38 - 12 * q^39 + 28 * q^40 - 12 * q^41 - 52 * q^42 - 48 * q^43 - 56 * q^44 - 56 * q^45 - 76 * q^46 - 12 * q^48 - 12 * q^50 - 36 * q^51 - 28 * q^52 + 36 * q^53 - 120 * q^54 + 16 * q^55 + 184 * q^56 - 12 * q^57 - 12 * q^58 + 20 * q^59 + 4 * q^60 - 12 * q^61 + 4 * q^62 + 56 * q^63 - 156 * q^64 - 64 * q^65 + 8 * q^66 + 48 * q^67 - 100 * q^68 - 12 * q^69 + 36 * q^70 + 20 * q^71 + 168 * q^72 - 12 * q^73 - 44 * q^74 - 148 * q^75 - 32 * q^76 - 32 * q^77 + 16 * q^78 - 148 * q^80 - 52 * q^82 - 12 * q^83 + 100 * q^84 - 52 * q^85 + 92 * q^86 - 32 * q^87 - 20 * q^88 - 32 * q^89 - 180 * q^90 + 132 * q^91 + 132 * q^92 + 12 * q^93 + 8 * q^94 - 152 * q^95 - 76 * q^96 - 24 * q^97 - 48 * q^98 - 68 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more