LMFDB - Embedded newform 261.2.x.a.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(2,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(84))

chi = DirichletCharacter(H, H._module([14, 3]))

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

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

chi := DirichletCharacter("261.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.x (of order $84$, degree $24$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			101.3
Character	$\chi$	$=$	261.101
Dual form			261.2.x.a.230.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.942454 + 2.16013i) q^{2} +(-1.73131 + 0.0507054i) q^{3} +(-2.41758 - 2.60553i) q^{4} +(3.53430 + 0.532711i) q^{5} +(1.52215 - 3.78763i) q^{6} +(2.36493 + 2.19434i) q^{7} +(3.45771 - 1.20991i) q^{8} +(2.99486 - 0.175573i) q^{9} +(-4.48164 + 7.13249i) q^{10} +(4.16848 - 3.58727i) q^{11} +(4.31770 + 4.38840i) q^{12} +(-3.02441 + 4.43599i) q^{13} +(-6.96888 + 3.04049i) q^{14} +(-6.14598 - 0.743078i) q^{15} +(-0.113947 + 1.52052i) q^{16} +(0.320183 + 0.320183i) q^{17} +(-2.44325 + 6.63474i) q^{18} +(-1.53180 - 0.962495i) q^{19} +(-7.15648 - 10.4966i) q^{20} +(-4.20569 - 3.67916i) q^{21} +(3.82035 + 12.3853i) q^{22} +(-2.14938 - 0.843569i) q^{23} +(-5.92502 + 2.27004i) q^{24} +(7.42966 + 2.29175i) q^{25} +(-6.73194 - 10.7138i) q^{26} +(-5.17612 + 0.455827i) q^{27} -11.4669i q^{28} +(3.80595 + 3.80983i) q^{29} +(7.39745 - 12.5758i) q^{30} +(-3.49443 + 2.57900i) q^{31} +(3.30040 + 1.74431i) q^{32} +(-7.03503 + 6.42203i) q^{33} +(-0.993395 + 0.389879i) q^{34} +(7.18944 + 9.01528i) q^{35} +(-7.69778 - 7.37874i) q^{36} +(-1.06614 - 3.04685i) q^{37} +(3.52276 - 2.40178i) q^{38} +(5.01126 - 7.83343i) q^{39} +(12.8651 - 2.43421i) q^{40} +(0.766126 + 0.205283i) q^{41} +(11.9111 - 5.61739i) q^{42} +(-3.30862 + 4.48302i) q^{43} +(-19.4244 - 2.18860i) q^{44} +(10.6783 + 0.974863i) q^{45} +(3.84791 - 3.84791i) q^{46} +(-6.95668 - 8.08380i) q^{47} +(0.120179 - 2.63827i) q^{48} +(0.254681 + 3.39849i) q^{49} +(-11.9526 + 13.8891i) q^{50} +(-0.570571 - 0.538101i) q^{51} +(18.8699 - 2.84418i) q^{52} +(5.65175 + 4.50712i) q^{53} +(3.89361 - 11.6107i) q^{54} +(16.6436 - 10.4579i) q^{55} +(10.8322 + 4.72604i) q^{56} +(2.70082 + 1.58870i) q^{57} +(-11.8166 + 4.63074i) q^{58} +(-2.18960 + 1.26417i) q^{59} +(12.9223 + 17.8100i) q^{60} +(3.14446 - 0.117657i) q^{61} +(-2.27764 - 9.97900i) q^{62} +(7.46790 + 6.15651i) q^{63} +(-9.26266 + 7.38673i) q^{64} +(-13.0523 + 14.0670i) q^{65} +(-7.24221 - 21.2490i) q^{66} +(-3.09824 + 0.232181i) q^{67} +(0.0601790 - 1.60832i) q^{68} +(3.76401 + 1.35149i) q^{69} +(-26.2499 + 7.03363i) q^{70} +(6.93040 - 3.33751i) q^{71} +(10.1429 - 4.23058i) q^{72} +(-0.346814 + 3.07806i) q^{73} +(7.58637 + 0.568520i) q^{74} +(-12.9792 - 3.59100i) q^{75} +(1.19544 + 6.31807i) q^{76} +(17.7298 + 0.663404i) q^{77} +(12.1983 + 18.2076i) q^{78} +(1.51220 - 7.99218i) q^{79} +(-1.21272 + 5.31328i) q^{80} +(8.93835 - 1.05163i) q^{81} +(-1.16547 + 1.46146i) q^{82} +(4.05257 - 13.1381i) q^{83} +(0.581434 + 19.8527i) q^{84} +(0.961060 + 1.30219i) q^{85} +(-6.56567 - 11.3721i) q^{86} +(-6.78245 - 6.40300i) q^{87} +(10.0731 - 17.4472i) q^{88} +(-6.94131 + 0.782098i) q^{89} +(-12.1696 + 22.1476i) q^{90} +(-16.8866 + 3.85425i) q^{91} +(2.99835 + 7.63968i) q^{92} +(5.91916 - 4.64224i) q^{93} +(24.0184 - 7.40869i) q^{94} +(-4.90112 - 4.21776i) q^{95} +(-5.80246 - 2.85260i) q^{96} +(-3.86112 - 7.30559i) q^{97} +(-7.58119 - 2.65277i) q^{98} +(11.8542 - 11.4752i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20}+ \cdots - 16 q^{99}+O(q^{100}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.942454	+	2.16013i	−0.666415	+	1.52744i	0.173565	+	0.984823i	$0.444471\pi$
$2$	−0.942454	+	2.16013i	−0.666415	+	1.52744i	−0.839980	+	0.542618i	$0.817433\pi$
$3$	−1.73131	+	0.0507054i	−0.999571	+	0.0292748i
$3$	−1.73131	+	0.0507054i	−0.999571	+	0.0292748i
$4$	−2.41758	−	2.60553i	−1.20879	−	1.30277i
$5$	3.53430	+	0.532711i	1.58059	+	0.238235i	0.879874	−	0.475206i	$-0.157627\pi$
$5$	3.53430	+	0.532711i	1.58059	+	0.238235i	0.700714	+	0.713442i	$0.252865\pi$
$6$	1.52215	−	3.78763i	0.621414	−	1.54629i
$7$	2.36493	+	2.19434i	0.893860	+	0.829381i	0.986065	−	0.166359i	$-0.0532010\pi$
$7$	2.36493	+	2.19434i	0.893860	+	0.829381i	−0.0922049	+	0.995740i	$0.529391\pi$
$8$	3.45771	−	1.20991i	1.22249	−	0.427766i
$9$	2.99486	−	0.175573i	0.998286	−	0.0585244i
$10$	−4.48164	+	7.13249i	−1.41722	+	2.25549i
$11$	4.16848	−	3.58727i	1.25684	−	1.08160i	0.263712	−	0.964601i	$-0.415053\pi$
$11$	4.16848	−	3.58727i	1.25684	−	1.08160i	0.993132	−	0.117000i	$-0.0373278\pi$
$12$	4.31770	+	4.38840i	1.24641	+	1.26682i
$13$	−3.02441	+	4.43599i	−0.838820	+	1.23032i	0.132176	+	0.991226i	$0.457804\pi$
$13$	−3.02441	+	4.43599i	−0.838820	+	1.23032i	−0.970996	+	0.239097i	$0.923149\pi$
$14$	−6.96888	+	3.04049i	−1.86251	+	0.812606i
$15$	−6.14598	−	0.743078i	−1.58689	−	0.191862i
$16$	−0.113947	+	1.52052i	−0.0284868	+	0.380130i
$17$	0.320183	+	0.320183i	0.0776559	+	0.0776559i	0.744868	−	0.667212i	$-0.232512\pi$
$17$	0.320183	+	0.320183i	0.0776559	+	0.0776559i	−0.667212	+	0.744868i	$0.732512\pi$
$18$	−2.44325	+	6.63474i	−0.575880	+	1.56382i
$19$	−1.53180	−	0.962495i	−0.351419	−	0.220811i	0.344741	−	0.938698i	$-0.387967\pi$
$19$	−1.53180	−	0.962495i	−0.351419	−	0.220811i	−0.696160	+	0.717886i	$0.745110\pi$
$20$	−7.15648	−	10.4966i	−1.60024	−	2.34712i
$21$	−4.20569	−	3.67916i	−0.917757	−	0.802858i
$22$	3.82035	+	12.3853i	0.814502	+	2.64055i
$23$	−2.14938	−	0.843569i	−0.448177	−	0.175896i	0.130509	−	0.991447i	$-0.458339\pi$
$23$	−2.14938	−	0.843569i	−0.448177	−	0.175896i	−0.578685	+	0.815551i	$0.696434\pi$
$24$	−5.92502	+	2.27004i	−1.20944	+	0.463371i
$25$	7.42966	+	2.29175i	1.48593	+	0.458349i
$26$	−6.73194	−	10.7138i	−1.32024	−	2.10115i
$27$	−5.17612	+	0.455827i	−0.996145	+	0.0877240i
$28$		−	11.4669i		−	2.16704i
$29$	3.80595	+	3.80983i	0.706747	+	0.707467i
$29$	3.80595	+	3.80983i	0.706747	+	0.707467i
$30$	7.39745	−	12.5758i	1.35058	−	2.29601i
$31$	−3.49443	+	2.57900i	−0.627618	+	0.463203i	−0.860602	−	0.509278i	$-0.829913\pi$
$31$	−3.49443	+	2.57900i	−0.627618	+	0.463203i	0.232985	+	0.972480i	$0.425151\pi$
$32$	3.30040	+	1.74431i	0.583435	+	0.308354i
$33$	−7.03503	+	6.42203i	−1.22464	+	1.11793i
$34$	−0.993395	+	0.389879i	−0.170366	+	0.0668636i
$35$	7.18944	+	9.01528i	1.21524	+	1.52386i
$36$	−7.69778	−	7.37874i	−1.28296	−	1.22979i
$37$	−1.06614	−	3.04685i	−0.175272	−	0.500899i	0.822414	−	0.568890i	$-0.192627\pi$
$37$	−1.06614	−	3.04685i	−0.175272	−	0.500899i	−0.997686	+	0.0679905i	$0.978341\pi$
$38$	3.52276	−	2.40178i	0.571468	−	0.389620i
$39$	5.01126	−	7.83343i	0.802443	−	1.25435i
$40$	12.8651	−	2.43421i	2.03416	−	0.384883i
$41$	0.766126	+	0.205283i	0.119649	+	0.0320598i	0.318147	−	0.948042i	$-0.396940\pi$
$41$	0.766126	+	0.205283i	0.119649	+	0.0320598i	−0.198498	+	0.980101i	$0.563606\pi$
$42$	11.9111	−	5.61739i	1.83793	−	0.866782i
$43$	−3.30862	+	4.48302i	−0.504560	+	0.683654i	−0.980656	−	0.195739i	$-0.937289\pi$
$43$	−3.30862	+	4.48302i	−0.504560	+	0.683654i	0.476096	+	0.879393i	$0.342051\pi$
$44$	−19.4244	−	2.18860i	−2.92834	−	0.329944i
$45$	10.6783	+	0.974863i	1.59182	+	0.145324i
$46$	3.84791	−	3.84791i	0.567343	−	0.567343i
$47$	−6.95668	−	8.08380i	−1.01474	−	1.17914i	−0.983735	−	0.179624i	$-0.942512\pi$
$47$	−6.95668	−	8.08380i	−1.01474	−	1.17914i	−0.0310001	−	0.999519i	$-0.509869\pi$
$48$	0.120179	−	2.63827i	0.0173464	−	0.380801i
$49$	0.254681	+	3.39849i	0.0363831	+	0.485498i
$50$	−11.9526	+	13.8891i	−1.69035	+	1.96422i
$51$	−0.570571	−	0.538101i	−0.0798960	−	0.0753492i
$52$	18.8699	−	2.84418i	2.61678	−	0.394417i
$53$	5.65175	+	4.50712i	0.776327	+	0.619100i	0.929383	−	0.369117i	$-0.120340\pi$
$53$	5.65175	+	4.50712i	0.776327	+	0.619100i	−0.153055	+	0.988218i	$0.548911\pi$
$54$	3.89361	−	11.6107i	0.529853	−	1.58001i
$55$	16.6436	−	10.4579i	2.24423	−	1.41014i
$56$	10.8322	+	4.72604i	1.44751	+	0.631543i
$57$	2.70082	+	1.58870i	0.357733	+	0.210429i
$58$	−11.8166	+	4.63074i	−1.55160	+	0.608046i
$59$	−2.18960	+	1.26417i	−0.285062	+	0.164580i	−0.635713	−	0.771926i	$-0.719294\pi$
$59$	−2.18960	+	1.26417i	−0.285062	+	0.164580i	0.350651	+	0.936506i	$0.385960\pi$
$60$	12.9223	+	17.8100i	1.66826	+	2.29926i
$61$	3.14446	−	0.117657i	0.402607	−	0.0150645i	0.164679	−	0.986347i	$-0.447341\pi$
$61$	3.14446	−	0.117657i	0.402607	−	0.0150645i	0.237928	+	0.971283i	$0.423532\pi$
$62$	−2.27764	−	9.97900i	−0.289261	−	1.26733i
$63$	7.46790	+	6.15651i	0.940867	+	0.775647i
$64$	−9.26266	+	7.38673i	−1.15783	+	0.923341i
$65$	−13.0523	+	14.0670i	−1.61894	+	1.74480i
$66$	−7.24221	−	21.2490i	−0.891454	−	2.61557i
$67$	−3.09824	+	0.232181i	−0.378511	+	0.0283654i	−0.262627	−	0.964897i	$-0.584589\pi$
$67$	−3.09824	+	0.232181i	−0.378511	+	0.0283654i	−0.115883	+	0.993263i	$0.536970\pi$
$68$	0.0601790	−	1.60832i	0.00729778	−	0.195037i
$69$	3.76401	+	1.35149i	0.453134	+	0.162701i
$70$	−26.2499	+	7.03363i	−3.13746	+	0.840679i
$71$	6.93040	−	3.33751i	0.822488	−	0.396089i	0.0251953	−	0.999683i	$-0.491979\pi$
$71$	6.93040	−	3.33751i	0.822488	−	0.396089i	0.797292	+	0.603593i	$0.206265\pi$
$72$	10.1429	−	4.23058i	1.19536	−	0.498578i
$73$	−0.346814	+	3.07806i	−0.0405915	+	0.360259i	0.956954	+	0.290239i	$0.0937349\pi$
$73$	−0.346814	+	3.07806i	−0.0405915	+	0.360259i	−0.997546	+	0.0700200i	$0.977694\pi$
$74$	7.58637	+	0.568520i	0.881898	+	0.0660891i
$75$	−12.9792	−	3.59100i	−1.49871	−	0.414653i
$76$	1.19544	+	6.31807i	0.137127	+	0.724733i
$77$	17.7298	+	0.663404i	2.02050	+	0.0756019i
$78$	12.1983	+	18.2076i	1.38119	+	2.06160i
$79$	1.51220	−	7.99218i	0.170136	−	0.899191i	−0.788603	−	0.614903i	$-0.789195\pi$
$79$	1.51220	−	7.99218i	0.170136	−	0.899191i	0.958739	−	0.284288i	$-0.0917572\pi$
$80$	−1.21272	+	5.31328i	−0.135586	+	0.594042i
$81$	8.93835	−	1.05163i	0.993150	−	0.116848i
$82$	−1.16547	+	1.46146i	−0.128705	+	0.161391i
$83$	4.05257	−	13.1381i	0.444828	−	1.44210i	−0.404650	−	0.914472i	$-0.632607\pi$
$83$	4.05257	−	13.1381i	0.444828	−	1.44210i	0.849478	−	0.527625i	$-0.176917\pi$
$84$	0.581434	+	19.8527i	0.0634396	+	2.16611i
$85$	0.961060	+	1.30219i	0.104242	+	0.141242i
$86$	−6.56567	−	11.3721i	−0.707995	−	1.22628i
$87$	−6.78245	−	6.40300i	−0.727155	−	0.686474i
$88$	10.0731	−	17.4472i	1.07380	−	1.85988i
$89$	−6.94131	+	0.782098i	−0.735777	+	0.0829022i	−0.471898	−	0.881653i	$-0.656431\pi$
$89$	−6.94131	+	0.782098i	−0.735777	+	0.0829022i	−0.263880	+	0.964556i	$0.585002\pi$
$90$	−12.1696	+	22.1476i	−1.28279	+	2.33457i
$91$	−16.8866	+	3.85425i	−1.77019	+	0.404035i
$92$	2.99835	+	7.63968i	0.312600	+	0.796492i
$93$	5.91916	−	4.64224i	0.613788	−	0.481378i
$94$	24.0184	−	7.40869i	2.47731	−	0.764148i
$95$	−4.90112	−	4.21776i	−0.502844	−	0.432733i
$96$	−5.80246	−	2.85260i	−0.592212	−	0.291142i
$97$	−3.86112	−	7.30559i	−0.392037	−	0.741771i	0.606542	−	0.795051i	$-0.292556\pi$
$97$	−3.86112	−	7.30559i	−0.392037	−	0.741771i	−0.998580	+	0.0532804i	$0.983032\pi$
$98$	−7.58119	−	2.65277i	−0.765816	−	0.267970i
$99$	11.8542	−	11.4752i	1.19139	−	1.15330i
$100$	−11.9906	−	24.8987i	−1.19906	−	2.48987i
$101$	3.44209	+	2.54038i	0.342500	+	0.252777i	0.751464	−	0.659774i	$-0.229348\pi$
$101$	3.44209	+	2.54038i	0.342500	+	0.252777i	−0.408964	+	0.912551i	$0.634110\pi$
$102$	1.70010	−	0.725371i	0.168335	−	0.0718224i
$103$	−7.52951	−	5.13353i	−0.741904	−	0.505822i	0.132402	−	0.991196i	$-0.457731\pi$
$103$	−7.52951	−	5.13353i	−0.741904	−	0.505822i	−0.874306	+	0.485374i	$0.838683\pi$
$104$	−5.09040	+	18.9976i	−0.499155	+	1.86287i
$105$	−12.9043	−	15.2437i	−1.25933	−	1.48763i
$106$	−15.0625	+	7.96074i	−1.46300	+	0.773216i
$107$	6.62628	−	13.7596i	0.640587	−	1.33019i	−0.287483	−	0.957786i	$-0.592818\pi$
$107$	6.62628	−	13.7596i	0.640587	−	1.33019i	0.928070	−	0.372407i	$-0.121467\pi$
$108$	13.7014	+	12.3846i	1.31842	+	1.19170i
$109$	−1.68836	−	0.385357i	−0.161716	−	0.0369106i	0.140896	−	0.990024i	$-0.455002\pi$
$109$	−1.68836	−	0.385357i	−0.161716	−	0.0369106i	−0.302612	+	0.953114i	$0.597859\pi$
$110$	6.90452	+	45.8085i	0.658320	+	4.36767i
$111$	2.00031	+	5.22098i	0.189861	+	0.495554i
$112$	−3.60601	+	3.34589i	−0.340736	+	0.316157i
$113$	0.480961	−	0.910023i	0.0452450	−	0.0856078i	−0.860456	−	0.509525i	$-0.829821\pi$
$113$	0.480961	−	0.910023i	0.0452450	−	0.0856078i	0.905701	+	0.423917i	$0.139345\pi$
$114$	−5.97721	+	4.33684i	−0.559817	+	0.406183i
$115$	−7.14718	−	4.12643i	−0.666478	−	0.384791i
$116$	0.725442	−	19.1271i	0.0673556	−	1.77591i
$117$	−8.27883	+	13.8162i	−0.765378	+	1.27731i
$118$	−0.667162	−	5.92123i	−0.0614173	−	0.545093i
$119$	0.0546219	+	1.45980i	0.00500719	+	0.133820i
$120$	−22.1501	+	4.86671i	−2.02202	+	0.444267i
$121$	2.86827	−	19.0298i	0.260752	−	1.72998i
$122$	−2.70935	+	6.90332i	−0.245293	+	0.624997i
$123$	−1.33681	−	0.316561i	−0.120536	−	0.0285434i
$124$	15.1677	+	2.86989i	1.36210	+	0.257724i
$125$	8.93651	+	4.30360i	0.799306	+	0.384925i
$126$	−20.3370	+	10.3294i	−1.81176	+	0.920215i
$127$	−2.19137	+	6.26259i	−0.194453	+	0.555715i	−0.999286	−	0.0377868i	$-0.987969\pi$
$127$	−2.19137	+	6.26259i	−0.194453	+	0.555715i	0.804833	+	0.593502i	$0.202255\pi$
$128$	−5.29429	−	19.7586i	−0.467954	−	1.74643i
$129$	5.50093	−	7.92926i	0.484330	−	0.698132i
$130$	−18.0854	−	41.4521i	−1.58619	−	3.63559i
$131$	−1.04444	−	2.39388i	−0.0912530	−	0.209154i	0.864950	−	0.501858i	$-0.167350\pi$
$131$	−1.04444	−	2.39388i	−0.0912530	−	0.209154i	−0.956203	+	0.292703i	$0.905445\pi$
$132$	33.7406	+	2.80423i	2.93674	+	0.244077i
$133$	−1.51057	−	5.63752i	−0.130983	−	0.488835i
$134$	2.41841	−	6.91142i	0.208919	−	0.597055i
$135$	−18.5368	−	1.14634i	−1.59539	−	0.0986615i
$136$	1.49449	+	0.719710i	0.128152	+	0.0617146i
$137$	6.75317	+	1.27777i	0.576962	+	0.109167i	0.466199	−	0.884680i	$-0.345623\pi$
$137$	6.75317	+	1.27777i	0.576962	+	0.109167i	0.110763	+	0.993847i	$0.464671\pi$
$138$	−6.46680	+	6.85702i	−0.550491	+	0.583709i
$139$	−4.26444	+	10.8656i	−0.361705	+	0.921609i	0.627965	+	0.778242i	$0.283888\pi$
$139$	−4.26444	+	10.8656i	−0.361705	+	0.921609i	−0.989670	+	0.143367i	$0.954207\pi$
$140$	6.10854	−	40.5275i	0.516266	−	3.42520i
$141$	12.4540	+	13.6428i	1.04882	+	1.14893i
$142$	0.677853	+	18.1160i	0.0568841	+	1.52026i
$143$	3.30590	+	29.3407i	0.276454	+	2.45359i
$144$	−0.0742929	+	4.57374i	−0.00619108	+	0.381145i
$145$	11.4218	+	15.4925i	0.948532	+	1.28659i
$146$	−6.32213	−	3.65009i	−0.523224	−	0.302083i
$147$	−0.613254	−	5.87092i	−0.0505803	−	0.484225i
$148$	−5.36120	+	10.1439i	−0.440688	+	0.833822i
$149$	−15.3477	+	14.2406i	−1.25734	+	1.16664i	−0.278847	+	0.960336i	$0.589952\pi$
$149$	−15.3477	+	14.2406i	−1.25734	+	1.16664i	−0.978489	+	0.206301i	$0.933857\pi$
$150$	19.9893	−	24.6524i	1.63212	−	2.01286i
$151$	−0.894466	−	5.93440i	−0.0727906	−	0.482934i	−0.995291	−	0.0969369i	$-0.969095\pi$
$151$	−0.894466	−	5.93440i	−0.0727906	−	0.482934i	0.922500	−	0.385997i	$-0.126143\pi$
$152$	−6.46105	−	1.47469i	−0.524061	−	0.119613i
$153$	1.01512	+	0.902688i	0.0820675	+	0.0729780i
$154$	−18.1426	+	37.6735i	−1.46197	+	3.03581i
$155$	−13.7242	+	7.25347i	−1.10236	+	0.582612i
$156$	−32.5254	+	5.88095i	−2.60411	+	0.470853i
$157$	−2.79570	+	10.4337i	−0.223121	+	0.832700i	0.760027	+	0.649891i	$0.225186\pi$
$157$	−2.79570	+	10.4337i	−0.223121	+	0.832700i	−0.983148	+	0.182809i	$0.941481\pi$
$158$	15.8389	+	10.7988i	1.26008	+	0.859107i
$159$	−10.0135	−	7.51664i	−0.794119	−	0.596108i
$160$	10.7354	+	7.92310i	0.848709	+	0.626376i
$161$	−3.23206	−	6.71145i	−0.254722	−	0.528936i
$162$	−6.15231	+	20.2991i	−0.483371	+	1.59485i
$163$	13.8854	+	4.85870i	1.08759	+	0.380563i	0.813751	−	0.581214i	$-0.197422\pi$
$163$	13.8854	+	4.85870i	1.08759	+	0.380563i	0.273835	+	0.961777i	$0.411708\pi$
$164$	−1.31730	−	2.49246i	−0.102864	−	0.194628i
$165$	−28.2850	+	18.9498i	−2.20199	+	1.47524i
$166$	24.5606	+	21.1361i	1.90628	+	1.64048i
$167$	7.95277	−	2.45311i	0.615404	−	0.189827i	0.0286464	−	0.999590i	$-0.490880\pi$
$167$	7.95277	−	2.45311i	0.615404	−	0.189827i	0.586758	+	0.809763i	$0.300404\pi$
$168$	−18.9935	−	7.63298i	−1.46538	−	0.588897i
$169$	−5.78155	−	14.7311i	−0.444735	−	1.13317i
$170$	−3.71865	+	0.848758i	−0.285208	+	0.0650968i
$171$	−4.75652	−	2.61359i	−0.363740	−	0.199866i
$172$	19.6795	−	2.21735i	1.50055	−	0.169071i
$173$	3.50229	−	6.06614i	0.266274	−	0.461200i	−0.701623	−	0.712549i	$-0.747541\pi$
$173$	3.50229	−	6.06614i	0.266274	−	0.461200i	0.967897	+	0.251349i	$0.0808741\pi$
$174$	20.2234	−	8.61641i	1.53313	−	0.653208i
$175$	12.5418	+	21.7230i	0.948069	+	1.64210i
$176$	4.97952	+	6.74701i	0.375345	+	0.508575i
$177$	3.72677	−	2.29968i	0.280121	−	0.172855i
$178$	4.85243	−	15.7312i	0.363705	−	1.17910i
$179$	−11.3960	+	14.2901i	−0.851776	+	1.06809i	0.145123	+	0.989414i	$0.453642\pi$
$179$	−11.3960	+	14.2901i	−0.851776	+	1.06809i	−0.996900	+	0.0786804i	$0.974929\pi$
$180$	−23.2756	−	30.1794i	−1.73486	−	2.24944i
$181$	4.89992	−	21.4679i	0.364208	−	1.59570i	−0.378182	−	0.925731i	$-0.623450\pi$
$181$	4.89992	−	21.4679i	0.364208	−	1.59570i	0.742390	−	0.669968i	$-0.233692\pi$
$182$	7.58915	−	40.1096i	0.562545	−	2.97312i
$183$	−5.43807	+	0.363142i	−0.401993	+	0.0268443i
$184$	−8.45257	−	0.316273i	−0.623132	−	0.0233159i
$185$	−2.14497	−	11.3364i	−0.157701	−	0.833472i
$186$	4.44929	+	17.1612i	0.326238	+	1.25832i
$187$	2.48326	+	0.186095i	0.181594	+	0.0136086i
$188$	−4.24429	+	37.6691i	−0.309547	+	2.74730i
$189$	−13.2414	−	10.2801i	−0.963171	−	0.747771i
$190$	13.7300	−	6.61200i	0.996076	−	0.479685i
$191$	10.7405	−	2.87790i	0.777153	−	0.208237i	0.151624	−	0.988438i	$-0.451550\pi$
$191$	10.7405	−	2.87790i	0.777153	−	0.208237i	0.625529	+	0.780201i	$0.284883\pi$
$192$	15.6620	−	13.2584i	1.13031	−	0.956841i
$193$	0.516878	−	13.8139i	0.0372057	−	0.994343i	−0.848243	−	0.529606i	$-0.822340\pi$
$193$	0.516878	−	13.8139i	0.0372057	−	0.994343i	0.885449	−	0.464736i	$-0.153851\pi$
$194$	19.4199	−	1.45532i	1.39427	−	0.104486i
$195$	21.8842	−	25.0162i	1.56716	−	1.79144i
$196$	8.23916	−	8.87970i	0.588511	−	0.634264i
$197$	11.8845	−	9.47755i	0.846733	−	0.675247i	−0.100799	−	0.994907i	$-0.532140\pi$
$197$	11.8845	−	9.47755i	0.846733	−	0.675247i	0.947533	+	0.319659i	$0.103568\pi$
$198$	13.6159	+	36.4214i	0.967642	+	2.58836i
$199$	4.35430	+	19.0774i	0.308668	+	1.35236i	0.856660	+	0.515881i	$0.172535\pi$
$199$	4.35430	+	19.0774i	0.308668	+	1.35236i	−0.547992	+	0.836484i	$0.684608\pi$
$200$	28.4624	−	1.06499i	2.01260	−	0.0753060i
$201$	5.35224	−	0.559075i	0.377518	−	0.0394341i
$202$	−8.73154	+	5.04116i	−0.614349	+	0.354695i
$203$	0.640766	+	17.3615i	0.0449730	+	1.21854i
$204$	−0.0226381	+	2.78755i	−0.00158498	+	0.195167i
$205$	2.59837	+	1.13366i	0.181478	+	0.0791779i
$206$	18.1853	−	11.4266i	1.26703	−	0.796127i
$207$	−6.58519	−	2.14900i	−0.457703	−	0.149366i
$208$	−6.40039	−	5.10414i	−0.443787	−	0.353908i
$209$	−9.83801	+	1.48284i	−0.680509	+	0.102570i
$210$	45.0899	−	13.5084i	3.11150	−	0.932167i
$211$	1.73335	−	2.01419i	0.119329	−	0.138663i	−0.695130	−	0.718884i	$-0.744653\pi$
$211$	1.73335	−	2.01419i	0.119329	−	0.138663i	0.814459	+	0.580222i	$0.197034\pi$
$212$	−1.92012	−	25.6222i	−0.131874	−	1.75974i
$213$	−11.8294	+	6.12966i	−0.810540	+	0.419998i
$214$	23.4775	+	27.2814i	1.60489	+	1.86492i
$215$	−14.0818	+	14.0818i	−0.960372	+	0.960372i
$216$	−17.3460	+	7.83873i	−1.18025	+	0.533358i
$217$	−13.9233	−	1.56878i	−0.945174	−	0.106496i
$218$	2.42362	−	3.28389i	0.164148	−	0.222413i
$219$	0.444367	−	5.34665i	0.0300276	−	0.361293i
$220$	−67.4858	−	18.0828i	−4.54989	−	1.21914i
$221$	−2.38870	+	0.451966i	−0.160681	+	0.0304025i
$222$	−13.1632	−	0.599614i	−0.883455	−	0.0402434i
$223$	20.1547	−	13.7412i	1.34966	−	0.920180i	0.349794	−	0.936826i	$-0.386251\pi$
$223$	20.1547	−	13.7412i	1.34966	−	0.920180i	0.999861	+	0.0166467i	$0.00529905\pi$
$224$	3.97762	+	11.3674i	0.265766	+	0.759515i
$225$	22.6531	+	5.55900i	1.51021	+	0.370600i
$226$	1.51248	+	1.89659i	0.100609	+	0.126159i
$227$	−13.5946	+	5.33548i	−0.902304	+	0.354128i	−0.770718	−	0.637176i	$-0.780102\pi$
$227$	−13.5946	+	5.33548i	−0.902304	+	0.354128i	−0.131586	+	0.991305i	$0.542007\pi$
$228$	−2.39004	−	10.8779i	−0.158284	−	0.720408i
$229$	−16.3351	−	8.63337i	−1.07946	−	0.570509i	−0.169634	−	0.985507i	$-0.554259\pi$
$229$	−16.3351	−	8.63337i	−1.07946	−	0.570509i	−0.909822	+	0.414998i	$0.863782\pi$
$230$	15.6495	−	11.5499i	1.03190	−	0.761575i
$231$	−30.7295	−	0.249558i	−2.02185	−	0.0164197i
$232$	17.7694	+	8.56844i	1.16662	+	0.562546i
$233$		−	12.3880i		−	0.811565i	−0.913970	−	0.405782i	$-0.866999\pi$
$233$		−	12.3880i		−	0.811565i	0.913970	−	0.405782i	$-0.133001\pi$
$234$	−22.0423	−	30.9044i	−1.44095	−	2.02029i
$235$	−20.2807	−	32.2765i	−1.32297	−	2.10549i
$236$	8.58736	+	2.64885i	0.558990	+	0.172425i
$237$	−2.21284	+	13.9136i	−0.143740	+	0.903786i
$238$	−3.20484	−	1.25781i	−0.207739	−	0.0815314i
$239$	−2.54231	−	8.24197i	−0.164448	−	0.533129i	0.835416	−	0.549619i	$-0.185227\pi$
$239$	−2.54231	−	8.24197i	−0.164448	−	0.533129i	−0.999864	+	0.0164899i	$0.994751\pi$
$240$	1.83018	−	9.26041i	0.118138	−	0.597757i
$241$	10.1102	+	14.8289i	0.651255	+	0.955215i	0.999839	+	0.0179377i	$0.00571007\pi$
$241$	10.1102	+	14.8289i	0.651255	+	0.955215i	−0.348584	+	0.937277i	$0.613338\pi$
$242$	38.4035	+	24.1305i	2.46867	+	1.55117i
$243$	−15.4217	+	2.27393i	−0.989303	+	0.145872i
$244$	−7.90855	−	7.90855i	−0.506293	−	0.506293i
$245$	−0.910289	+	12.1470i	−0.0581562	+	0.776041i
$246$	1.94369	−	2.58933i	0.123925	−	0.165090i
$247$	8.90241	−	3.88408i	0.566447	−	0.247138i
$248$	−8.96237	+	13.1454i	−0.569111	+	0.834732i
$249$	−6.35008	+	22.9516i	−0.402420	+	1.45450i
$250$	−17.7186	+	15.2481i	−1.12062	+	0.964372i
$251$	−11.1519	+	17.7482i	−0.703904	+	1.12026i	0.283027	+	0.959112i	$0.408661\pi$
$251$	−11.1519	+	17.7482i	−0.703904	+	1.12026i	−0.986931	+	0.161145i	$0.948481\pi$
$252$	−2.01328	−	34.3417i	−0.126825	−	2.16333i
$253$	−11.9858	+	4.19400i	−0.753538	+	0.263674i
$254$	−11.4627	−	10.6358i	−0.719235	−	0.667352i
$255$	−1.72992	−	2.20576i	−0.108332	−	0.138130i
$256$	24.2405	+	3.65367i	1.51503	+	0.228354i
$257$	−19.9753	−	21.5283i	−1.24603	−	1.34290i	−0.917159	−	0.398521i	$-0.869524\pi$
$257$	−19.9753	−	21.5283i	−1.24603	−	1.34290i	−0.328867	−	0.944376i	$-0.606667\pi$
$258$	11.9438	+	19.3557i	0.743590	+	1.20503i
$259$	4.16447	−	9.54507i	0.258768	−	0.593102i
$260$	68.2070			4.23002
$261$	12.0672	+	10.7417i	0.746939	+	0.664892i
$262$	6.15542			0.380283
$263$	−3.69118	+	8.46027i	−0.227608	+	0.521683i	−0.992467	−	0.122515i	$-0.960904\pi$
$263$	−3.69118	+	8.46027i	−0.227608	+	0.521683i	0.764859	+	0.644198i	$0.222809\pi$
$264$	−16.5551	+	30.7172i	−1.01889	+	1.89052i
$265$	17.5740	+	18.9403i	1.07956	+	1.16349i
$266$	13.6014	+	2.05008i	0.833956	+	0.125699i
$267$	11.9779	−	1.70601i	0.733035	−	0.104406i
$268$	8.09521	+	7.51126i	0.494494	+	0.458823i
$269$	9.55569	−	3.34368i	0.582621	−	0.203868i	−0.0228452	−	0.999739i	$-0.507272\pi$
$269$	9.55569	−	3.34368i	0.582621	−	0.203868i	0.605466	+	0.795871i	$0.292987\pi$
$270$	19.9463	−	38.9615i	1.21389	−	2.37112i
$271$	−1.82205	+	2.89977i	−0.110681	+	0.176148i	−0.897472	−	0.441072i	$-0.854598\pi$
$271$	−1.82205	+	2.89977i	−0.110681	+	0.176148i	0.786790	+	0.617220i	$0.211741\pi$
$272$	−0.523329	+	0.450361i	−0.0317315	+	0.0273071i
$273$	29.0404	−	7.52914i	1.75761	−	0.455684i
$274$	−9.12469	+	13.3835i	−0.551243	+	0.808525i
$275$	39.1915	−	17.0991i	2.36334	−	1.03111i
$276$	−5.57845	−	13.0746i	−0.335783	−	0.786999i
$277$	0.240136	−	3.20439i	0.0144284	−	0.192533i	−0.985332	−	0.170648i	$-0.945414\pi$
$277$	0.240136	−	3.20439i	0.0144284	−	0.192533i	0.999760	−	0.0218856i	$-0.00696695\pi$
$278$	−19.4521	−	19.4521i	−1.16666	−	1.16666i
$279$	−10.0125	+	8.33728i	−0.599433	+	0.499140i
$280$	35.7666	+	22.4737i	2.13747	+	1.34306i
$281$	−0.503285	−	0.738184i	−0.0300235	−	0.0440363i	0.810934	−	0.585138i	$-0.198960\pi$
$281$	−0.503285	−	0.738184i	−0.0300235	−	0.0440363i	−0.840957	+	0.541102i	$0.818007\pi$
$282$	−41.2076	+	14.0446i	−2.45387	+	0.836343i
$283$	1.33305	+	4.32165i	0.0792417	+	0.256895i	0.986521	−	0.163632i	$-0.0523211\pi$
$283$	1.33305	+	4.32165i	0.0792417	+	0.256895i	−0.907280	+	0.420528i	$0.861845\pi$
$284$	−25.4508	−	9.98871i	−1.51023	−	0.592721i
$285$	8.69922	+	7.05372i	0.515297	+	0.417827i
$286$	−66.4953	−	20.5111i	−3.93195	−	1.21285i
$287$	1.36138	+	2.16662i	0.0803595	+	0.127891i
$288$	10.1905	+	4.64451i	0.600481	+	0.273680i
$289$		−	16.7950i		−	0.987939i
$290$	−44.2304	+	10.0716i	−2.59730	+	0.591425i
$291$	7.05522	+	12.4525i	0.413584	+	0.729976i
$292$	8.85843	−	6.53782i	0.518400	−	0.382597i
$293$	−8.03833	−	4.24838i	−0.469604	−	0.248193i	0.215686	−	0.976463i	$-0.430801\pi$
$293$	−8.03833	−	4.24838i	−0.469604	−	0.248193i	−0.685291	+	0.728270i	$0.740325\pi$
$294$	13.2599	+	4.20836i	0.773332	+	0.245437i
$295$	−8.41214	+	3.30152i	−0.489774	+	0.192222i
$296$	−7.37281	−	9.24521i	−0.428536	−	0.537367i
$297$	−19.9414	+	20.4682i	−1.15712	+	1.18769i
$298$	−16.2970	−	46.5742i	−0.944060	−	2.69797i
$299$	10.2427	−	6.98333i	0.592349	−	0.403857i
$300$	22.0219	+	42.4994i	1.27144	+	2.45370i
$301$	−17.6619	+	3.34182i	−1.01802	+	0.192619i
$302$	13.6620	+	3.66073i	0.786162	+	0.210651i
$303$	−6.08812	−	4.22364i	−0.349754	−	0.242642i
$304$	1.63804	−	2.21946i	0.0939478	−	0.127295i
$305$	11.1762	+	1.25925i	0.639945	+	0.0721045i
$306$	−2.90662	+	1.34204i	−0.166161	+	0.0767196i
$307$	8.49534	−	8.49534i	0.484855	−	0.484855i	−0.421823	−	0.906678i	$-0.638610\pi$
$307$	8.49534	−	8.49534i	0.484855	−	0.484855i	0.906678	+	0.421823i	$0.138610\pi$
$308$	−41.1348	−	47.7995i	−2.34387	−	2.72363i
$309$	13.2962	+	8.50594i	0.756394	+	0.483886i
$310$	−2.73396	−	36.4821i	−0.155278	−	2.07205i
$311$	19.3011	−	22.4282i	1.09446	−	1.27179i	0.134728	−	0.990883i	$-0.456984\pi$
$311$	19.3011	−	22.4282i	1.09446	−	1.27179i	0.959735	−	0.280907i	$-0.0906351\pi$
$312$	7.84977	−	33.1489i	0.444406	−	1.87668i
$313$	−11.7595	+	1.77246i	−0.664686	+	0.100185i	−0.472715	−	0.881215i	$-0.656726\pi$
$313$	−11.7595	+	1.77246i	−0.664686	+	0.100185i	−0.191971	+	0.981401i	$0.561488\pi$
$314$	−19.9033	−	15.8724i	−1.12321	−	0.895729i
$315$	23.1142	+	25.7372i	1.30234	+	1.45013i
$316$	−24.4798	+	15.3817i	−1.37710	+	0.865286i
$317$	6.48219	+	2.82815i	0.364076	+	0.158845i	0.573964	−	0.818881i	$-0.305405\pi$
$317$	6.48219	+	2.82815i	0.364076	+	0.158845i	−0.209888	+	0.977726i	$0.567310\pi$
$318$	25.6741	−	14.5462i	1.43973	−	0.815713i
$319$	29.5319	+	2.22823i	1.65347	+	0.124757i
$320$	−36.6721	+	21.1726i	−2.05003	+	1.18359i
$321$	−10.7745	+	24.1581i	−0.601371	+	1.34838i
$322$	17.5436	−	0.656437i	0.977669	−	0.0365818i
$323$	−0.182283	−	0.798632i	−0.0101425	−	0.0444371i
$324$	−24.3493	−	20.7468i	−1.35274	−	1.15260i
$325$	−32.6365	+	26.0267i	−1.81035	+	1.44370i
$326$	−23.5817	+	25.4151i	−1.30607	+	1.40761i
$327$	2.94261	+	0.581564i	0.162727	+	0.0321605i
$328$	2.89741	−	0.217131i	0.159983	−	0.0119891i
$329$	1.28652	−	34.3829i	0.0709281	−	1.89559i
$330$	−14.2766	−	78.9585i	−0.785900	−	4.34652i
$331$	−9.66389	+	2.58943i	−0.531175	+	0.142328i	−0.514431	−	0.857532i	$-0.671997\pi$
$331$	−9.66389	+	2.58943i	−0.531175	+	0.142328i	−0.0167444	+	0.999860i	$0.505330\pi$
$332$	−44.0293	+	21.2034i	−2.41642	+	1.16369i
$333$	−3.72788	−	8.93770i	−0.204287	−	0.489783i
$334$	−2.19610	+	19.4909i	−0.120165	+	1.06650i
$335$	−11.0738	−	0.829868i	−0.605027	−	0.0453405i
$336$	6.07346	−	5.97560i	0.331334	−	0.325996i
$337$	−2.52143	−	13.3261i	−0.137351	−	0.725919i	−0.981746	−	0.190197i	$-0.939087\pi$
$337$	−2.52143	−	13.3261i	−0.137351	−	0.725919i	0.844395	−	0.535722i	$-0.179960\pi$
$338$	37.2700	+	1.39454i	2.02722	+	0.0758532i
$339$	−0.786549	+	1.59992i	−0.0427195	+	0.0868957i
$340$	1.06946	−	5.65223i	0.0579996	−	0.306535i
$341$	−5.31487	+	23.2860i	−0.287816	+	1.26101i
$342$	10.1285	−	7.81149i	0.547686	−	0.422397i
$343$	7.22516	−	9.06007i	0.390122	−	0.489198i
$344$	−6.01622	+	19.5041i	−0.324373	+	1.05159i
$345$	12.5832	+	6.78172i	0.677457	+	0.365115i
$346$	9.80288	+	13.2824i	0.527006	+	0.714068i
$347$	4.57695	+	7.92751i	0.245704	+	0.425571i	0.962329	−	0.271887i	$-0.0876477\pi$
$347$	4.57695	+	7.92751i	0.245704	+	0.425571i	−0.716626	+	0.697458i	$0.754314\pi$
$348$	−0.286116	+	33.1517i	−0.0153374	+	1.77712i
$349$	−8.60261	+	14.9002i	−0.460487	+	0.797587i	−0.998985	−	0.0450398i	$-0.985659\pi$
$349$	−8.60261	+	14.9002i	−0.460487	+	0.797587i	0.538498	+	0.842627i	$0.318992\pi$
$350$	−58.7445	+	6.61891i	−3.14002	+	0.353796i
$351$	13.6327	−	24.3398i	0.727657	−	1.29916i
$352$	20.0150	−	4.56829i	1.06680	−	0.243491i
$353$	−11.4561	−	29.1897i	−0.609748	−	1.55361i	−0.817804	−	0.575497i	$-0.804809\pi$
$353$	−11.4561	−	29.1897i	−0.609748	−	1.55361i	0.208056	−	0.978117i	$-0.433286\pi$
$354$	1.45530	+	10.2176i	0.0773484	+	0.543062i
$355$	26.2721	−	8.10386i	1.39438	−	0.430108i
$356$	18.8190	+	16.1950i	0.997403	+	0.858335i
$357$	−0.168587	−	2.52460i	−0.00892258	−	0.133616i
$358$	−20.1283	−	38.0846i	−1.06381	−	2.01283i
$359$	−1.99775	−	0.699041i	−0.105437	−	0.0368940i	0.277045	−	0.960857i	$-0.410645\pi$
$359$	−1.99775	−	0.699041i	−0.105437	−	0.0368940i	−0.382482	+	0.923963i	$0.624931\pi$
$360$	38.1019	−	9.54890i	2.00814	−	0.503271i
$361$	−6.82377	−	14.1697i	−0.359146	−	0.745774i
$362$	41.7555	+	30.8170i	2.19462	+	1.61970i
$363$	−4.00096	+	33.0918i	−0.209996	+	1.73687i
$364$	50.8671	+	34.6806i	2.66616	+	1.81776i
$365$	−2.86546	+	10.6940i	−0.149985	+	0.559751i
$366$	4.34069	−	12.0892i	0.226892	−	0.631910i
$367$	−9.43696	+	4.98758i	−0.492605	+	0.260350i	−0.695073	−	0.718939i	$-0.744628\pi$
$367$	−9.43696	+	4.98758i	−0.492605	+	0.260350i	0.202467	+	0.979289i	$0.435104\pi$
$368$	1.52758	−	3.17205i	0.0796305	−	0.165355i
$369$	2.33048	+	0.480282i	0.121320	+	0.0250025i
$370$	26.5097	+	6.05066i	1.37817	+	0.314559i
$371$	3.47587	+	23.0609i	0.180458	+	1.19726i
$372$	−26.4056	−	4.19958i	−1.36906	−	0.217738i
$373$	1.42506	−	1.32226i	0.0737869	−	0.0684642i	−0.642417	−	0.766355i	$-0.722068\pi$
$373$	1.42506	−	1.32226i	0.0737869	−	0.0684642i	0.716204	+	0.697891i	$0.245878\pi$
$374$	−2.74235	+	5.18877i	−0.141803	+	0.268305i
$375$	−15.6901	−	6.99772i	−0.810232	−	0.361361i
$376$	−33.8348	−	19.5345i	−1.74490	−	1.00742i
$377$	−28.4111	+	5.36068i	−1.46325	+	0.276089i
$378$	34.6858	−	18.9146i	1.78405	−	0.972860i
$379$	1.85518	+	16.4652i	0.0952941	+	0.845759i	0.946890	+	0.321559i	$0.104207\pi$
$379$	1.85518	+	16.4652i	0.0952941	+	0.845759i	−0.851595	+	0.524200i	$0.824365\pi$
$380$	0.859358	+	22.9668i	0.0440841	+	1.17817i
$381$	3.47640	−	10.9536i	0.178101	−	0.561169i
$382$	−3.90576	+	25.9131i	−0.199836	+	1.32583i
$383$	−9.91355	+	25.2593i	−0.506559	+	1.29069i	0.417582	+	0.908639i	$0.362877\pi$
$383$	−9.91355	+	25.2593i	−0.506559	+	1.29069i	−0.924141	+	0.382051i	$0.875218\pi$
$384$	10.1679	+	33.9397i	0.518879	+	1.73198i
$385$	62.3092	+	11.7895i	3.17557	+	0.600851i
$386$	29.3525	+	14.1354i	1.49400	+	0.719475i
$387$	−9.12175	+	14.0069i	−0.463685	+	0.712012i
$388$	−9.70040	+	27.7222i	−0.492463	+	1.40738i
$389$	1.85937	+	6.93927i	0.0942738	+	0.351835i	0.996908	−	0.0785731i	$-0.0250364\pi$
$389$	1.85937	+	6.93927i	0.0942738	+	0.351835i	−0.902635	+	0.430408i	$0.858370\pi$
$390$	33.4132	+	70.8493i	1.69194	+	3.58759i
$391$	−0.418099	−	0.958292i	−0.0211442	−	0.0484629i
$392$	4.99246	+	11.4428i	0.252157	+	0.577951i
$393$	1.92963	+	4.09158i	0.0973369	+	0.206393i
$394$	9.27214	+	34.6041i	0.467124	+	1.74333i
$395$	9.60210	−	27.4412i	0.483134	−	1.38072i
$396$	−58.5575	−	3.14415i	−2.94263	−	0.157999i
$397$	32.9873	+	15.8858i	1.65558	+	0.797287i	0.999077	+	0.0429663i	$0.0136808\pi$
$397$	32.9873	+	15.8858i	1.65558	+	0.797287i	0.656506	+	0.754320i	$0.272033\pi$
$398$	−45.3134	−	8.57376i	−2.27136	−	0.429764i
$399$	2.90112	+	9.68370i	0.145237	+	0.484791i
$400$	−4.33123	+	11.0358i	−0.216562	+	0.551790i
$401$	0.531357	−	3.52533i	0.0265347	−	0.176046i	−0.971638	−	0.236474i	$-0.924008\pi$
$401$	0.531357	−	3.52533i	0.0265347	−	0.176046i	0.998173	+	0.0604274i	$0.0192464\pi$
$402$	−3.83657	+	12.0884i	−0.191351	+	0.602916i
$403$	−0.871870	−	23.3012i	−0.0434309	−	1.16072i
$404$	−1.70249	−	15.1100i	−0.0847022	−	0.751753i
$405$	32.1511	+	1.04476i	1.59760	+	0.0519144i
$406$	−38.1069	−	14.9783i	−1.89122	−	0.743359i
$407$	−15.3741	−	8.87621i	−0.762064	−	0.439978i
$408$	−2.62392	−	1.17026i	−0.129903	−	0.0579366i
$409$	−5.07645	+	9.60511i	−0.251014	+	0.474942i	−0.977134	−	0.212627i	$-0.931798\pi$
$409$	−5.07645	+	9.60511i	−0.251014	+	0.474942i	0.726119	+	0.687569i	$0.241322\pi$
$410$	−4.89768	+	4.54438i	−0.241879	+	0.224431i
$411$	−11.7566	−	1.86979i	−0.579911	−	0.0922299i
$412$	4.82761	+	32.0291i	0.237839	+	1.57796i
$413$	−7.95226	−	1.81505i	−0.391305	−	0.0893128i
$414$	10.8483	−	12.1995i	0.533167	−	0.599574i
$415$	21.3218	−	44.2753i	1.04665	−	2.17339i
$416$	−17.7195	+	9.36505i	−0.868772	+	0.459159i
$417$	6.83211	−	19.0279i	0.334570	−	0.931803i
$418$	6.06874	−	22.6489i	0.296832	−	1.10779i
$419$	−23.4112	−	15.9615i	−1.14371	−	0.779770i	−0.165262	−	0.986250i	$-0.552847\pi$
$419$	−23.4112	−	15.9615i	−1.14371	−	0.779770i	−0.978451	+	0.206479i	$0.933799\pi$
$420$	−8.52080	+	70.4754i	−0.415773	+	3.43885i
$421$	24.8686	+	18.3539i	1.21202	+	0.894512i	0.996631	−	0.0820156i	$-0.0261357\pi$
$421$	24.8686	+	18.3539i	1.21202	+	0.894512i	0.215390	+	0.976528i	$0.430898\pi$
$422$	2.71731	+	5.64255i	0.132276	+	0.274675i
$423$	−22.2536	−	22.9884i	−1.08200	−	1.11774i
$424$	24.9953	+	8.74623i	1.21388	+	0.424755i
$425$	1.64507	+	3.11263i	0.0797978	+	0.150985i
$426$	−2.09215	−	31.3300i	−0.101365	−	1.51794i
$427$	7.69462	+	6.62175i	0.372369	+	0.320449i
$428$	−51.8707	+	16.0000i	−2.50727	+	0.773389i
$429$	−7.21127	−	50.6302i	−0.348163	−	2.44445i
$430$	−17.1471	−	43.6900i	−0.826904	−	2.10692i
$431$	8.59567	−	1.96191i	0.414039	−	0.0945017i	−0.0104269	−	0.999946i	$-0.503319\pi$
$431$	8.59567	−	1.96191i	0.414039	−	0.0945017i	0.424466	+	0.905444i	$0.360462\pi$
$432$	−0.103290	−	7.92233i	−0.00496952	−	0.381163i
$433$	−8.08849	+	0.911354i	−0.388708	+	0.0437969i	−0.304156	−	0.952622i	$-0.598374\pi$
$433$	−8.08849	+	0.911354i	−0.388708	+	0.0437969i	−0.0845520	+	0.996419i	$0.526946\pi$
$434$	16.5108	−	28.5976i	0.792544	−	1.37273i
$435$	−20.5603	−	26.2432i	−0.985790	−	1.25827i
$436$	3.07769	+	5.33072i	0.147395	+	0.255295i
$437$	2.48049	+	3.36095i	0.118658	+	0.160776i
$438$	11.1306	+	5.99886i	0.531843	+	0.286637i
$439$	0.616706	−	1.99931i	0.0294338	−	0.0954220i	−0.939664	−	0.342099i	$-0.888862\pi$
$439$	0.616706	−	1.99931i	0.0294338	−	0.0954220i	0.969098	+	0.246677i	$0.0793385\pi$
$440$	44.8959	−	56.2976i	2.14033	−	2.68388i
$441$	1.35942	+	10.1333i	0.0647342	+	0.482537i
$442$	1.27493	−	5.58584i	0.0606423	−	0.265691i
$443$	−5.23546	+	27.6701i	−0.248744	+	1.31464i	0.605946	+	0.795506i	$0.292795\pi$
$443$	−5.23546	+	27.6701i	−0.248744	+	1.31464i	−0.854690	+	0.519139i	$0.826253\pi$
$444$	8.76754	−	17.8340i	0.416089	−	0.846366i
$445$	−24.9493	−	0.933538i	−1.18271	−	0.0442539i
$446$	10.6879	+	56.4871i	0.506088	+	2.67474i
$447$	25.8496	−	25.4331i	1.22264	−	1.20294i
$448$	−38.1145	−	2.85629i	−1.80074	−	0.134947i
$449$	3.60772	−	32.0194i	0.170259	−	1.51109i	−0.560328	−	0.828271i	$-0.689325\pi$
$449$	3.60772	−	32.0194i	0.170259	−	1.51109i	0.730587	−	0.682820i	$-0.239247\pi$
$450$	−33.3577	+	43.6946i	−1.57250	+	2.05978i
$451$	3.92998	−	1.89258i	0.185056	−	0.0891181i
$452$	−3.53386	+	0.946895i	−0.166219	+	0.0445382i
$453$	1.84950	+	10.2289i	0.0868972	+	0.480596i
$454$	1.28695	−	34.3945i	0.0603996	−	1.61421i
$455$	−61.7355	+	4.62644i	−2.89421	+	0.216891i
$456$	11.2609	+	2.22554i	0.527338	+	0.104220i
$457$	−18.8729	+	20.3402i	−0.882839	+	0.951474i	−0.999128	−	0.0417413i	$-0.986709\pi$
$457$	−18.8729	+	20.3402i	−0.882839	+	0.951474i	0.116290	+	0.993215i	$0.462900\pi$
$458$	34.0443	−	27.1494i	1.59079	−	1.26861i
$459$	−1.80326	−	1.51136i	−0.0841688	−	0.0705442i
$460$	6.52735	+	28.5982i	0.304339	+	1.33340i
$461$	21.4636	−	0.803113i	0.999661	−	0.0374047i	0.467453	−	0.884018i	$-0.345172\pi$
$461$	21.4636	−	0.803113i	0.999661	−	0.0374047i	0.532209	+	0.846613i	$0.321362\pi$
$462$	29.5002	−	66.1443i	1.37247	−	3.07731i
$463$	−32.3329	+	18.6674i	−1.50264	+	0.867547i	−0.502640	+	0.864496i	$0.667638\pi$
$463$	−32.3329	+	18.6674i	−1.50264	+	0.867547i	−0.999995	+	0.00305157i	$0.999029\pi$
$464$	−6.22659	+	5.35290i	−0.289062	+	0.248502i
$465$	23.3931	−	13.2539i	1.08483	−	0.614634i
$466$	26.7596	+	11.6751i	1.23962	+	0.540839i
$467$	−26.8496	+	16.8707i	−1.24245	+	0.780683i	−0.982738	−	0.185003i	$-0.940770\pi$
$467$	−26.8496	+	16.8707i	−1.24245	+	0.780683i	−0.259712	+	0.965686i	$0.583628\pi$
$468$	56.0133	−	11.8310i	2.58921	−	0.546886i
$469$	−7.83662	−	6.24949i	−0.361861	−	0.288575i
$470$	88.8349	−	13.3897i	4.09765	−	0.617621i
$471$	4.31118	−	18.2057i	0.198649	−	0.838875i
$472$	−6.04148	+	7.02033i	−0.278082	+	0.323137i
$473$	2.28988	+	30.5563i	0.105289	+	1.40498i
$474$	−27.9697	−	17.8930i	−1.28469	−	0.821850i
$475$	−9.17497	−	10.6615i	−0.420977	−	0.489184i
$476$	3.67151	−	3.67151i	0.168283	−	0.168283i
$477$	17.7175	+	12.5059i	0.811229	+	0.572605i
$478$	20.1997	+	2.27596i	0.923913	+	0.104100i
$479$	3.61257	−	4.89486i	0.165063	−	0.223652i	−0.714258	−	0.699883i	$-0.753236\pi$
$479$	3.61257	−	4.89486i	0.165063	−	0.223652i	0.879320	+	0.476231i	$0.157997\pi$
$480$	−18.9881	−	13.1730i	−0.866683	−	0.601262i
$481$	16.7403	+	4.48554i	0.763290	+	0.204523i
$482$	−41.5607	+	7.86372i	−1.89304	+	0.358182i
$483$	5.93600	+	11.4557i	0.270097	+	0.521252i
$484$	−56.5170	+	38.5326i	−2.56895	+	1.75148i
$485$	−9.75460	−	27.8771i	−0.442934	−	1.26583i
$486$	9.62228	−	35.4559i	0.436476	−	1.60831i
$487$	−7.02594	−	8.81025i	−0.318376	−	0.399231i	0.596731	−	0.802441i	$-0.296466\pi$
$487$	−7.02594	−	8.81025i	−0.318376	−	0.399231i	−0.915107	+	0.403210i	$0.867894\pi$
$488$	10.7303	−	4.21133i	0.485737	−	0.190638i
$489$	−24.2862	−	7.70785i	−1.09826	−	0.348561i
$490$	−25.3811	−	13.4143i	−1.14660	−	0.605995i
$491$	−30.7853	+	22.7206i	−1.38932	+	1.02537i	−0.395032	+	0.918668i	$0.629266\pi$
$491$	−30.7853	+	22.7206i	−1.38932	+	1.02537i	−0.994291	+	0.106699i	$0.965972\pi$
$492$	2.40704	+	4.24841i	0.108518	+	0.191533i
$493$	−0.00124203	+	2.43844i	−5.59380e−5	+	0.109822i
$494$			22.8909i			1.02991i
$495$	48.0092	−	34.2421i	2.15785	−	1.53907i
$496$	−3.52324	−	5.60721i	−0.158198	−	0.251771i
$497$	23.7135	+	7.31466i	1.06370	+	0.328107i
$498$	−43.5938	−	35.3478i	−1.95348	−	1.58397i
$499$	−1.02915	−	0.403910i	−0.0460709	−	0.0180815i	0.342194	−	0.939629i	$-0.388830\pi$
$499$	−1.02915	−	0.403910i	−0.0460709	−	0.0180815i	−0.388265	+	0.921548i	$0.626925\pi$
$500$	−10.3916	−	33.6887i	−0.464726	−	1.50660i
$501$	−13.6443	+	4.65033i	−0.609583	+	0.207761i
$502$	−27.8282	−	40.8165i	−1.24203	−	1.82173i
$503$	16.9150	+	10.6284i	0.754201	+	0.473896i	0.853455	−	0.521166i	$-0.174503\pi$
$503$	16.9150	+	10.6284i	0.754201	+	0.473896i	−0.0992539	+	0.995062i	$0.531646\pi$
$504$	33.2706	+	12.2520i	1.48199	+	0.545746i
$505$	10.8121	+	10.8121i	0.481132	+	0.481132i
$506$	2.23645	−	29.8434i	0.0994224	−	1.32670i
$507$	10.7566	+	25.2110i	0.477717	+	1.11966i
$508$	21.6152	−	9.43062i	0.959020	−	0.418416i
$509$	13.8475	−	20.3106i	0.613780	−	0.900250i	−0.385972	−	0.922511i	$-0.626134\pi$
$509$	13.8475	−	20.3106i	0.613780	−	0.900250i	0.999752	+	0.0222601i	$0.00708621\pi$
$510$	6.39510	−	1.65802i	0.283180	−	0.0734182i
$511$	−7.57448	+	6.51837i	−0.335075	+	0.288356i
$512$	−8.97189	+	14.2787i	−0.396505	+	0.631034i
$513$	8.36752	+	4.28375i	0.369435	+	0.189132i
$514$	65.3296	−	22.8598i	2.88157	−	1.00830i
$515$	−23.8769	−	22.1545i	−1.05214	−	0.976244i
$516$	−33.9589	+	4.83678i	−1.49496	+	0.212927i
$517$	−57.9975	−	8.74172i	−2.55073	−	0.384460i
$518$	16.6937	+	17.9916i	0.733481	+	0.790504i
$519$	−5.75595	+	10.6799i	−0.252658	+	0.468797i
$520$	−28.1113	+	64.4317i	−1.23276	+	2.82552i
$521$	9.44830			0.413938			0.206969	−	0.978348i	$-0.433640\pi$
$521$	9.44830			0.413938			0.206969	+	0.978348i	$0.433640\pi$
$522$	−34.5761	+	15.9431i	−1.51335	+	0.697811i
$523$	−34.2714			−1.49859			−0.749293	−	0.662239i	$-0.769606\pi$
$523$	−34.2714			−1.49859			−0.749293	+	0.662239i	$0.769606\pi$
$524$	−3.71232	+	8.50872i	−0.162173	+	0.371705i
$525$	−22.8152	−	36.9733i	−0.995735	−	1.61365i
$526$	−14.7965	−	15.9468i	−0.645158	−	0.695315i
$527$	−1.94461	−	0.293103i	−0.0847086	−	0.0127678i
$528$	−8.96320	−	11.4287i	−0.390073	−	0.497369i
$529$	−12.9520	−	12.0177i	−0.563129	−	0.522508i
$530$	−57.4761	+	20.1118i	−2.49660	+	0.873599i
$531$	−6.33558	+	4.17043i	−0.274941	+	0.180981i
$532$	−11.0368	+	17.5650i	−0.478507	+	0.761540i
$533$	−3.22771	+	2.77767i	−0.139808	+	0.120314i
$534$	−7.60340	+	27.4816i	−0.329031	+	1.18925i
$535$	30.7492	−	45.1008i	1.32940	−	1.94988i
$536$	−10.4319	+	4.55140i	−0.450590	+	0.196590i
$537$	19.0054	−	25.3184i	0.820143	−	1.09257i
$538$	−1.78302	+	23.7928i	−0.0768715	+	1.02578i
$539$	13.2529	+	13.2529i	0.570843	+	0.570843i
$540$	41.8274	+	51.0697i	1.79997	+	2.19769i
$541$	12.8823	+	8.09451i	0.553855	+	0.348010i	0.779700	−	0.626153i	$-0.215371\pi$
$541$	12.8823	+	8.09451i	0.553855	+	0.348010i	−0.225845	+	0.974163i	$0.572514\pi$
$542$	−4.54667	−	6.66875i	−0.195296	−	0.286447i
$543$	−7.39473	+	37.4161i	−0.317338	+	1.60568i
$544$	0.498234	+	1.61524i	0.0213616	+	0.0692526i
$545$	−5.76190	−	2.26138i	−0.246813	−	0.0968668i
$546$	−11.1054	+	69.8269i	−0.475266	+	2.98832i
$547$	42.6216	+	13.1470i	1.82237	+	0.562126i	0.999977	−	0.00679875i	$-0.00216413\pi$
$547$	42.6216	+	13.1470i	1.82237	+	0.562126i	0.822390	+	0.568924i	$0.192640\pi$
$548$	−12.9971	−	20.6847i	−0.555208	−	0.883608i
$549$	9.39656	−	0.904451i	0.401035	−	0.0386010i
$550$			100.774i			4.29700i
$551$	−2.16302	−	9.49910i	−0.0921477	−	0.404675i
$552$	14.6500	+	0.118975i	0.623547	+	0.00506391i
$553$	21.1138	−	15.5827i	0.897850	−	0.662643i
$554$	6.69558	+	3.53871i	0.284468	+	0.150346i
$555$	4.28843	+	19.5181i	0.182034	+	0.828498i
$556$	38.6203	−	15.1574i	1.63787	−	0.642815i
$557$	−18.6580	−	23.3963i	−0.790563	−	0.991335i	−0.999909	−	0.0134933i	$-0.995705\pi$
$557$	−18.6580	−	23.3963i	−0.790563	−	0.991335i	0.209346	−	0.977842i	$-0.432867\pi$
$558$	−8.57326	−	29.4858i	−0.362935	−	1.24823i
$559$	−9.88003	−	28.2355i	−0.417881	−	1.19423i
$560$	−14.5271	+	9.90442i	−0.613883	+	0.418538i
$561$	−4.30873	−	0.196273i	−0.181915	−	0.00828664i
$562$	2.06889	−	0.391456i	0.0872710	−	0.0165126i
$563$	24.3248	+	6.51780i	1.02517	+	0.274692i	0.731953	−	0.681355i	$-0.238609\pi$
$563$	24.3248	+	6.51780i	1.02517	+	0.274692i	0.293213	+	0.956047i	$0.405276\pi$
$564$	5.43815	−	65.4321i	0.228987	−	2.75519i
$565$	2.18464	−	2.96009i	0.0919086	−	0.124532i
$566$	−10.5916	−	1.19339i	−0.445200	−	0.0501620i
$567$	23.4462	+	17.1267i	0.984649	+	0.719254i
$568$	19.9253	−	19.9253i	0.836046	−	0.836046i
$569$	7.29214	+	8.47362i	0.305702	+	0.355233i	0.889719	−	0.456509i	$-0.150901\pi$
$569$	7.29214	+	8.47362i	0.305702	+	0.355233i	−0.584016	+	0.811742i	$0.698520\pi$
$570$	−23.4355	+	12.1436i	−0.981607	+	0.508639i
$571$	0.691698	+	9.23007i	0.0289467	+	0.386267i	0.992796	+	0.119818i	$0.0382312\pi$
$571$	0.691698	+	9.23007i	0.0289467	+	0.386267i	−0.963849	+	0.266448i	$0.914150\pi$
$572$	68.4559	−	79.5472i	2.86229	−	3.32604i
$573$	−18.4491	+	5.52713i	−0.770724	+	0.230899i
$574$	−5.96320	+	0.898808i	−0.248899	+	0.0375155i
$575$	−14.0359	−	11.1933i	−0.585338	−	0.466791i
$576$	−26.4435	+	23.7485i	−1.10181	+	0.989520i
$577$	−13.7996	+	8.67088i	−0.574486	+	0.360973i	−0.787725	−	0.616027i	$-0.788741\pi$
$577$	−13.7996	+	8.67088i	−0.574486	+	0.360973i	0.213239	+	0.977000i	$0.431599\pi$
$578$	36.2793	+	15.8285i	1.50902	+	0.658378i
$579$	−0.194438	+	23.9422i	−0.00808058	+	0.995006i
$580$	12.7531	−	67.2145i	0.529545	−	2.79093i
$581$	38.4135	−	22.1781i	1.59366	−	0.920101i
$582$	−33.5481	+	3.50431i	−1.39061	+	0.145258i
$583$	39.7274	−	1.48650i	1.64534	−	0.0615644i
$584$	2.52498	+	11.0626i	0.104484	+	0.457775i
$585$	−36.6199	+	44.4203i	−1.51405	+	1.83655i
$586$	16.7528	−	13.3599i	0.692052	−	0.551893i
$587$	−18.5196	+	19.9594i	−0.764386	+	0.823813i	−0.988574	−	0.150733i	$-0.951837\pi$
$587$	−18.5196	+	19.9594i	−0.764386	+	0.823813i	0.224188	+	0.974546i	$0.428027\pi$
$588$	−13.8143	+	15.7913i	−0.569691	+	0.651221i
$589$	7.83505	−	0.587156i	0.322837	−	0.0241933i
$590$	0.796347	−	21.2828i	0.0327851	−	0.876200i
$591$	−20.0951	+	17.0112i	−0.826603	+	0.699746i
$592$	4.75428	−	1.27391i	0.195400	−	0.0523572i
$593$	9.67498	−	4.65923i	0.397304	−	0.191331i	−0.224554	−	0.974462i	$-0.572092\pi$
$593$	9.67498	−	4.65923i	0.397304	−	0.191331i	0.621858	+	0.783130i	$0.286378\pi$
$594$	−25.4201	−	62.3663i	−1.04300	−	2.55892i
$595$	−0.584602	+	5.18848i	−0.0239663	+	0.212707i
$596$	74.2088	+	5.56118i	3.03971	+	0.227795i
$597$	−8.50597	−	32.8082i	−0.348126	−	1.34275i
$598$	5.43164	+	28.7069i	0.222116	+	1.17391i
$599$	11.0967	+	0.415208i	0.453398	+	0.0169649i	0.263115	−	0.964764i	$-0.415250\pi$
$599$	11.0967	+	0.415208i	0.453398	+	0.0169649i	0.190282	+	0.981729i	$0.439060\pi$
$600$	−49.2232	+	3.28702i	−2.00953	+	0.134192i
$601$	−7.49934	+	39.6350i	−0.305904	+	1.61674i	0.405592	+	0.914054i	$0.367065\pi$
$601$	−7.49934	+	39.6350i	−0.305904	+	1.61674i	−0.711497	+	0.702689i	$0.751982\pi$
$602$	9.42679	−	41.3015i	0.384207	−	1.68332i
$603$	−9.23803	+	1.23932i	−0.376202	+	0.0504689i
$604$	−13.2998	+	16.6775i	−0.541162	+	0.678596i
$605$	20.2747	−	65.7290i	0.824284	−	2.67226i
$606$	14.8614	−	9.17053i	0.603702	−	0.372527i
$607$	4.87217	+	6.60156i	0.197755	+	0.267949i	0.892243	−	0.451556i	$-0.149131\pi$
$607$	4.87217	+	6.60156i	0.197755	+	0.267949i	−0.694488	+	0.719505i	$0.744369\pi$
$608$	−3.37667	−	5.84857i	−0.136942	−	0.237191i
$609$	−1.98969	−	30.0256i	−0.0806262	−	1.21670i
$610$	−13.2531	+	22.9551i	−0.536604	+	0.929426i
$611$	56.8995	−	6.41104i	2.30191	−	0.259363i
$612$	−0.102150	−	4.82725i	−0.00412918	−	0.195130i
$613$	−38.0411	+	8.68264i	−1.53647	+	0.350689i	−0.905237	−	0.424907i	$-0.860307\pi$
$613$	−38.0411	+	8.68264i	−1.53647	+	0.350689i	−0.631230	+	0.775596i	$0.717450\pi$
$614$	10.3445	+	26.3575i	0.417472	+	1.06370i
$615$	−4.55605	−	1.83096i	−0.183718	−	0.0738313i
$616$	62.1073	−	19.1576i	2.50238	−	0.771880i
$617$	29.4774	+	25.3673i	1.18671	+	1.02125i	0.999240	+	0.0389801i	$0.0124109\pi$
$617$	29.4774	+	25.3673i	1.18671	+	1.02125i	0.187474	+	0.982270i	$0.439970\pi$
$618$	−30.9050	+	20.7050i	−1.24318	+	0.832878i
$619$	−9.98491	−	18.8924i	−0.401327	−	0.759349i	0.597777	−	0.801662i	$-0.296051\pi$
$619$	−9.98491	−	18.8924i	−0.401327	−	0.759349i	−0.999104	+	0.0423139i	$0.986527\pi$
$620$	52.0786	+	18.2231i	2.09153	+	0.731857i
$621$	11.5100	+	3.38667i	0.461879	+	0.135902i
$622$	30.2575	+	62.8303i	1.21321	+	2.51927i
$623$	−18.1319	−	13.3820i	−0.726440	−	0.536137i
$624$	11.3399	+	8.51231i	0.453957	+	0.340765i
$625$	−2.82861	−	1.92852i	−0.113144	−	0.0771406i
$626$	7.25405	−	27.0725i	0.289930	−	1.08203i
$627$	16.9574	−	3.06610i	0.677215	−	0.122448i
$628$	33.9442	−	17.9400i	1.35452	−	0.715886i
$629$	0.634191	−	1.31691i	0.0252869	−	0.0525087i
$630$	−77.3797	+	25.6735i	−3.08288	+	1.02286i
$631$	−1.89374	−	0.432234i	−0.0753886	−	0.0172070i	0.184660	−	0.982802i	$-0.440882\pi$
$631$	−1.89374	−	0.432234i	−0.0753886	−	0.0172070i	−0.260049	+	0.965595i	$0.583739\pi$
$632$	−4.44103	−	29.4643i	−0.176654	−	1.17203i
$633$	−2.89884	+	3.57508i	−0.115218	+	0.142097i
$634$	−12.2183	+	11.3369i	−0.485252	+	0.450248i
$635$	−11.0811	+	20.9665i	−0.439741	+	0.832031i
$636$	4.62349	+	44.2625i	0.183333	+	1.75512i
$637$	−15.8459	−	9.14865i	−0.627838	−	0.362483i
$638$	−32.6457	+	61.6926i	−1.29246	+	2.44243i
$639$	20.1696	−	11.2122i	0.797897	−	0.443546i
$640$	−8.18604	−	72.6531i	−0.323582	−	2.87187i
$641$	0.605745	+	16.1889i	0.0239255	+	0.639422i	0.958740	+	0.284285i	$0.0917563\pi$
$641$	0.605745	+	16.1889i	0.0239255	+	0.639422i	−0.934814	+	0.355137i	$0.884434\pi$
$642$	−42.0302	−	46.0421i	−1.65880	−	1.81714i
$643$	−2.13167	+	14.1427i	−0.0840648	+	0.557734i	0.906661	+	0.421859i	$0.138622\pi$
$643$	−2.13167	+	14.1427i	−0.0840648	+	0.557734i	−0.990726	+	0.135874i	$0.956616\pi$
$644$	−9.67312	+	24.6467i	−0.381174	+	0.971217i
$645$	23.6660	−	25.0940i	0.931846	−	0.988075i
$646$	1.89694	+	0.358920i	0.0746341	+	0.0141215i
$647$	12.2459	+	5.89730i	0.481435	+	0.231847i	0.658828	−	0.752293i	$-0.271052\pi$
$647$	12.2459	+	5.89730i	0.481435	+	0.231847i	−0.177394	+	0.984140i	$0.556767\pi$
$648$	29.6338	−	14.4508i	1.16413	−	0.567681i
$649$	−4.59240	+	13.1243i	−0.180267	+	0.515175i
$650$	−25.4627	−	95.0280i	−0.998728	−	3.72730i
$651$	24.1850	+	2.01005i	0.947887	+	0.0787801i
$652$	−20.9095	−	47.9251i	−0.818880	−	1.87689i
$653$	1.95262	+	4.47545i	0.0764120	+	0.175138i	0.950575	−	0.310494i	$-0.100494\pi$
$653$	1.95262	+	4.47545i	0.0764120	+	0.175138i	−0.874163	+	0.485632i	$0.838590\pi$
$654$	−4.02953	+	5.80832i	−0.157567	+	0.227123i
$655$	−2.41612	−	9.01708i	−0.0944056	−	0.352326i
$656$	−0.399434	+	1.14152i	−0.0155953	+	0.0445688i
$657$	−0.498233	+	9.27923i	−0.0194379	+	0.362017i
$658$	73.0590	+	35.1834i	2.84814	+	1.37159i
$659$	23.5476	+	4.45545i	0.917284	+	0.173560i	0.623058	−	0.782176i	$-0.285890\pi$
$659$	23.5476	+	4.45545i	0.917284	+	0.173560i	0.294227	+	0.955736i	$0.404938\pi$
$660$	117.756	+	27.8850i	4.58363	+	1.08542i
$661$	−5.84618	+	14.8958i	−0.227390	+	0.579380i	−0.998345	−	0.0575096i	$-0.981684\pi$
$661$	−5.84618	+	14.8958i	−0.227390	+	0.579380i	0.770955	+	0.636890i	$0.219779\pi$
$662$	3.51427	−	23.3156i	0.136586	−	0.906188i
$663$	4.11265	−	0.903612i	0.159722	−	0.0350934i
$664$	−1.88326	−	50.3311i	−0.0730845	−	1.95322i
$665$	−2.33564	−	20.7294i	−0.0905724	−	0.803852i
$666$	22.8199	+	0.370672i	0.884254	+	0.0143632i
$667$	−4.96657	−	11.3993i	−0.192306	−	0.441384i
$668$	−25.6181	−	14.7906i	−0.991195	−	0.572267i
$669$	−34.1972	+	24.8122i	−1.32214	+	0.959296i
$670$	12.2292	−	23.1387i	0.472454	−	0.893927i
$671$	12.6856	−	11.7705i	0.489720	−	0.454394i
$672$	−7.46287	−	19.4788i	−0.287887	−	0.751409i
$673$	0.251203	+	1.66662i	0.00968316	+	0.0642436i	0.993151	−	0.116842i	$-0.0372771\pi$
$673$	0.251203	+	1.66662i	0.00968316	+	0.0642436i	−0.983467	+	0.181085i	$0.942039\pi$
$674$	31.1624	+	7.11261i	1.20033	+	0.273968i
$675$	−39.5015	−	8.47572i	−1.52041	−	0.326230i
$676$	−24.4051	+	50.6778i	−0.938659	+	1.94915i
$677$	16.4166	−	8.67644i	0.630942	−	0.333463i	−0.121038	−	0.992648i	$-0.538622\pi$
$677$	16.4166	−	8.67644i	0.630942	−	0.333463i	0.751981	+	0.659185i	$0.229099\pi$
$678$	−2.71474	−	3.20690i	−0.104259	−	0.123160i
$679$	6.89965	−	25.7498i	0.264784	−	0.988188i
$680$	4.89860	+	3.33981i	0.187853	+	0.128076i
$681$	23.2659	−	9.92668i	0.891551	−	0.380391i
$682$	−45.2916	−	33.4267i	−1.73431	−	1.27998i
$683$	−18.5321	−	38.4823i	−0.709111	−	1.47248i	−0.873875	−	0.486150i	$-0.838401\pi$
$683$	−18.5321	−	38.4823i	−0.709111	−	1.47248i	0.164765	−	0.986333i	$-0.447314\pi$
$684$	4.68947	+	18.7118i	0.179306	+	0.715465i
$685$	23.1871	+	8.11351i	0.885933	+	0.310001i
$686$	12.7615	+	24.1460i	0.487237	+	0.921897i
$687$	28.7189	+	14.1188i	1.09570	+	0.538664i
$688$	−6.43951	−	5.54165i	−0.245504	−	0.211273i
$689$	−37.0867	+	11.4397i	−1.41289	+	0.435820i
$690$	−26.5085	+	20.7899i	−1.00916	+	0.791457i
$691$	3.23819	+	8.25077i	0.123186	+	0.313874i	0.979143	−	0.203175i	$-0.0651259\pi$
$691$	3.23819	+	8.25077i	0.123186	+	0.313874i	−0.855956	+	0.517049i	$0.827031\pi$
$692$	−24.2726	+	5.54006i	−0.922705	+	0.210601i
$693$	53.2148	−	1.12609i	2.02146	−	0.0427765i
$694$	−21.4380	+	2.41548i	−0.813775	+	0.0916904i
$695$	−20.8600	+	36.1306i	−0.791266	+	1.37051i
$696$	−31.1988	−	13.9336i	−1.18259	−	0.528152i
$697$	0.179573	+	0.311029i	0.00680180	+	0.0117811i
$698$	−24.0787	−	32.6254i	−0.911391	−	1.23489i
$699$	0.628138	+	21.4474i	0.0237584	+	0.811217i
$700$	26.2792	−	85.1952i	0.993262	−	3.22007i
$701$	−0.619060	+	0.776277i	−0.0233816	+	0.0293196i	−0.793385	−	0.608720i	$-0.791683\pi$
$701$	−0.619060	+	0.776277i	−0.0233816	+	0.0293196i	0.770003	+	0.638040i	$0.220255\pi$
$702$	39.7290	+	52.3874i	1.49947	+	1.97724i
$703$	−1.29946	+	5.69333i	−0.0490102	+	0.214728i
$704$	−12.1131	+	64.0191i	−0.456528	+	2.41281i
$705$	36.7487	+	54.8523i	1.38404	+	2.06586i
$706$	73.8504	+	2.76329i	2.77940	+	0.103998i
$707$	2.56586	+	13.5609i	0.0964992	+	0.510011i
$708$	−15.0017	−	4.15055i	−0.563798	−	0.155987i
$709$	−34.1623	−	2.56011i	−1.28299	−	0.0961471i	−0.584282	−	0.811551i	$-0.698624\pi$
$709$	−34.1623	−	2.56011i	−1.28299	−	0.0961471i	−0.698711	+	0.715404i	$0.746243\pi$
$710$	−7.25484	+	64.3885i	−0.272269	+	2.41646i
$711$	3.12562	−	24.2010i	0.117220	−	0.907607i
$712$	−23.0548	+	11.1026i	−0.864014	+	0.416087i
$713$	9.68642	−	2.59547i	0.362759	−	0.0972010i
$714$	5.61234	+	2.01515i	0.210036	+	0.0754150i
$715$	−3.94604	+	105.460i	−0.147573	+	3.94398i
$716$	64.7842	−	4.85490i	2.42110	−	0.181436i
$717$	4.81944	+	14.1405i	0.179985	+	0.528086i
$718$	3.39280	−	3.65657i	0.126618	−	0.136462i
$719$	34.3429	−	27.3875i	1.28077	−	1.02138i	0.282708	−	0.959206i	$-0.408767\pi$
$719$	34.3429	−	27.3875i	1.28077	−	1.02138i	0.998065	−	0.0621768i	$-0.0198043\pi$
$720$	−2.69906	+	16.1254i	−0.100588	+	0.600959i
$721$	−6.54208	−	28.6627i	−0.243640	−	1.06746i
$722$	37.0394	−	1.38592i	1.37847	−	0.0515785i
$723$	−18.2558	−	25.1608i	−0.678939	−	0.935740i
$724$	−67.7814	+	39.1336i	−2.51908	+	1.45439i
$725$	19.5457	+	37.0280i	0.725910	+	1.37518i
$726$	−67.7118	−	39.8301i	−2.51302	−	1.47823i
$727$	12.0312	+	5.24915i	0.446212	+	0.194680i	0.610970	−	0.791654i	$-0.290780\pi$
$727$	12.0312	+	5.24915i	0.446212	+	0.194680i	−0.164758	+	0.986334i	$0.552684\pi$
$728$	−53.7256	+	33.7581i	−1.99120	+	1.25116i
$729$	26.5844	−	4.71883i	0.984609	−	0.174772i
$730$	−20.3999	−	16.2684i	−0.755034	−	0.602120i
$731$	−2.49475	+	0.376024i	−0.0922718	+	0.0139077i
$732$	14.0932	+	13.2911i	0.520898	+	0.491255i
$733$	−22.0338	+	25.6037i	−0.813836	+	0.945694i	−0.999317	−	0.0369536i	$-0.988235\pi$
$733$	−22.0338	+	25.6037i	−0.813836	+	0.945694i	0.185481	+	0.982648i	$0.440616\pi$
$734$	−1.87991	−	25.0856i	−0.0693886	−	0.925926i
$735$	0.960074	−	21.0763i	0.0354129	−	0.777410i
$736$	−5.62237	−	6.53331i	−0.207243	−	0.240821i
$737$	−12.0821	+	12.0821i	−0.445049	+	0.445049i
$738$	−3.23384	+	4.58149i	−0.119039	+	0.168647i
$739$	−7.09425	−	0.799330i	−0.260966	−	0.0294038i	−0.0194880	−	0.999810i	$-0.506204\pi$
$739$	−7.09425	−	0.799330i	−0.260966	−	0.0294038i	−0.241478	+	0.970406i	$0.577632\pi$
$740$	−24.3519	+	32.9956i	−0.895192	+	1.21294i
$741$	−15.2159	+	7.17595i	−0.558969	+	0.263615i
$742$	−53.0902	−	14.2255i	−1.94900	−	0.522234i
$743$	−13.8552	+	2.62155i	−0.508299	+	0.0961754i	−0.433734	−	0.901041i	$-0.642804\pi$
$743$	−13.8552	+	2.62155i	−0.508299	+	0.0961754i	−0.0745647	+	0.997216i	$0.523757\pi$
$744$	14.8501	−	23.2131i	0.544430	−	0.851035i
$745$	−61.8297	+	42.1548i	−2.26526	+	1.54443i
$746$	1.51320	+	4.32448i	0.0554023	+	0.158331i
$747$	9.83018	−	40.0583i	0.359668	−	1.46566i
$748$	−5.51861	−	6.92012i	−0.201780	−	0.253025i
$749$	45.8639	−	18.0003i	1.67583	−	0.657715i
$750$	29.9031	−	27.2975i	1.09191	−	0.996764i
$751$	−24.8912	−	13.1554i	−0.908292	−	0.480047i	−0.0532362	−	0.998582i	$-0.516954\pi$
$751$	−24.8912	−	13.1554i	−0.908292	−	0.480047i	−0.855056	+	0.518535i	$0.826477\pi$
$752$	13.0843	−	9.65663i	0.477134	−	0.352141i
$753$	18.4075	−	31.2931i	0.670807	−	1.14038i
$754$	15.1964	−	66.4238i	0.553420	−	2.41901i
$755$		−	21.4504i		−	0.780662i
$756$	5.22692	+	59.3541i	0.190101	+	2.15869i
$757$	13.6560	+	21.7333i	0.496335	+	0.789912i	0.997134	−	0.0756513i	$-0.0241036\pi$
$757$	13.6560	+	21.7333i	0.496335	+	0.789912i	−0.500800	+	0.865563i	$0.666961\pi$
$758$	−37.3153	−	11.5102i	−1.35535	−	0.418070i
$759$	20.5384	−	7.86884i	0.745496	−	0.285621i
$760$	−22.0497	−	8.65389i	−0.799828	−	0.313910i
$761$	−0.0610922	−	0.198056i	−0.00221459	−	0.00717953i	0.954459	−	0.298343i	$-0.0964339\pi$
$761$	−0.0610922	−	0.198056i	−0.00221459	−	0.00717953i	−0.956673	+	0.291163i	$0.905958\pi$
$762$	20.3848	+	17.8327i	0.738463	+	0.646011i
$763$	−3.14726	−	4.61618i	−0.113938	−	0.167117i
$764$	−33.4644	−	21.0271i	−1.21070	−	0.760733i
$765$	3.10687	+	3.73114i	0.112329	+	0.134900i
$766$	−45.2202	−	45.2202i	−1.63387	−	1.63387i
$767$	1.01441	−	13.5364i	0.0366283	−	0.488771i
$768$	−42.1530	−	5.09650i	−1.52107	−	0.183904i
$769$	30.2361	−	13.1919i	1.09034	−	0.475711i	0.223708	−	0.974656i	$-0.428184\pi$
$769$	30.2361	−	13.1919i	1.09034	−	0.475711i	0.866634	+	0.498945i	$0.166279\pi$
$770$	−84.1905	+	123.485i	−3.03401	+	4.45008i
$771$	35.6750	+	36.2592i	1.28481	+	1.30584i
$772$	−37.2421	+	32.0494i	−1.34037	+	1.15348i
$773$	−24.6365	+	39.2087i	−0.886112	+	1.41024i	0.0257176	+	0.999669i	$0.491813\pi$
$773$	−24.6365	+	39.2087i	−0.886112	+	1.41024i	−0.911829	+	0.410569i	$0.865330\pi$
$774$	−21.6599	−	32.9050i	−0.778549	−	1.18275i
$775$	−31.8728	+	11.1528i	−1.14491	+	0.400620i
$776$	−22.1897	−	20.5890i	−0.796564	−	0.739104i
$777$	−6.72600	+	16.7366i	−0.241294	+	0.600423i
$778$	−16.7421	−	2.52346i	−0.600232	−	0.0904704i
$779$	−0.975969	−	1.05184i	−0.0349677	−	0.0376863i
$780$	−118.087	+	3.45846i	−4.22821	+	0.123833i
$781$	16.9167	−	38.7735i	0.605328	−	1.38743i
$782$	2.46407			0.0881150
$783$	−21.4367	−	17.9853i	−0.766084	−	0.642741i
$784$	−5.19648			−0.185589
$785$	−15.4390	+	35.3866i	−0.551042	+	1.26300i
$786$	−10.6569	+	0.312113i	−0.380120	+	0.0111327i
$787$	23.7650	+	25.6126i	0.847130	+	0.912989i	0.997131	−	0.0756965i	$-0.0241180\pi$
$787$	23.7650	+	25.6126i	0.847130	+	0.912989i	−0.150001	+	0.988686i	$0.547928\pi$
$788$	−53.4258	−	8.05264i	−1.90321	−	0.286863i
$789$	5.96159	−	14.8345i	0.212238	−	0.528122i
$790$	50.2270	+	46.6038i	1.78700	+	1.65809i
$791$	3.13434	−	1.09675i	0.111444	−	0.0389960i
$792$	27.1044	−	54.0204i	0.963112	−	1.91953i
$793$	−8.98821	+	14.3046i	−0.319181	+	0.507973i
$794$	−65.4044	+	56.2850i	−2.32111	+	1.99748i
$795$	−31.3864	−	31.9004i	−1.11316	−	1.13139i
$796$	39.1801	−	57.4666i	1.38870	−	2.03685i
$797$	−22.4419	+	9.79128i	−0.794931	+	0.346825i	−0.757801	−	0.652485i	$-0.773726\pi$
$797$	−22.4419	+	9.79128i	−0.794931	+	0.346825i	−0.0371301	+	0.999310i	$0.511822\pi$
$798$	−23.6522	−	2.85966i	−0.837278	−	0.101231i
$799$	0.360888	−	4.81571i	0.0127673	−	0.170368i
$800$	20.5234	+	20.5234i	0.725610	+	0.725610i
$801$	−20.6509	+	3.56098i	−0.729664	+	0.125821i
$802$	7.11437	+	4.47026i	0.251217	+	0.157850i
$803$	9.59612	+	14.0749i	0.338640	+	0.496693i
$804$	−14.3962	−	12.5938i	−0.507714	−	0.444150i
$805$	−7.84783	−	25.4420i	−0.276600	−	0.896714i
$806$	51.1553	+	20.0770i	1.80187	+	0.707181i
$807$	−16.3743	+	6.27347i	−0.576403	+	0.220837i
$808$	14.9754	+	4.61928i	0.526831	+	0.162506i
$809$	12.2838	+	19.5495i	0.431875	+	0.687325i	0.989784	−	0.142578i	$-0.0455390\pi$
$809$	12.2838	+	19.5495i	0.431875	+	0.687325i	−0.557909	+	0.829902i	$0.688396\pi$
$810$	−32.5577	+	68.4657i	−1.14396	+	2.40564i
$811$			42.9446i			1.50799i	0.656880	+	0.753995i	$0.271876\pi$
$811$			42.9446i			1.50799i	−0.656880	+	0.753995i	$0.728124\pi$
$812$	43.6869	−	43.6424i	1.53311	−	1.53155i
$813$	3.00749	−	5.11278i	0.105477	−	0.179313i
$814$	33.6631	−	24.8445i	1.17989	−	0.870799i
$815$	46.4869	+	24.5690i	1.62836	+	0.860615i
$816$	0.883208	−	0.806249i	0.0309185	−	0.0282244i
$817$	9.38303	−	3.68257i	0.328271	−	0.128837i
$818$	−15.9639	−	20.0182i	−0.558166	−	0.699918i
$819$	−49.8962	+	14.5078i	−1.74351	+	0.506943i
$820$	−3.32799	−	9.51084i	−0.116218	−	0.332133i
$821$	26.5171	−	18.0790i	0.925452	−	0.630963i	−0.00396537	−	0.999992i	$-0.501262\pi$
$821$	26.5171	−	18.0790i	0.925452	−	0.630963i	0.929418	+	0.369029i	$0.120310\pi$
$822$	15.1190	−	23.6336i	0.527337	−	0.824316i
$823$	26.1670	−	4.95107i	0.912126	−	0.172584i	0.291391	−	0.956604i	$-0.405882\pi$
$823$	26.1670	−	4.95107i	0.912126	−	0.172584i	0.620735	+	0.784021i	$0.286834\pi$
$824$	−32.2459	−	8.64027i	−1.12334	−	0.300998i
$825$	−66.9855	+	31.5910i	−2.33214	+	1.09986i
$826$	11.4154	−	15.4673i	0.397192	−	0.538176i
$827$	−30.4112	−	3.42652i	−1.05750	−	0.119152i	−0.433952	−	0.900936i	$-0.642881\pi$
$827$	−30.4112	−	3.42652i	−1.05750	−	0.119152i	−0.623549	+	0.781784i	$0.714310\pi$
$828$	10.3210	+	22.3533i	0.358678	+	0.776832i
$829$	−2.80717	+	2.80717i	−0.0974971	+	0.0974971i	−0.754173	−	0.656676i	$-0.771962\pi$
$829$	−2.80717	+	2.80717i	−0.0974971	+	0.0974971i	0.656676	+	0.754173i	$0.271962\pi$
$830$	75.5453	+	87.7853i	2.62222	+	3.04707i
$831$	−0.253270	+	5.55997i	−0.00878582	+	0.192873i
$832$	−4.75339	−	63.4296i	−0.164794	−	2.19903i
$833$	−1.00659	+	1.16968i	−0.0348764	+	0.0405271i
$834$	34.6638	+	32.6912i	1.20031	+	1.13200i
$835$	29.4143	−	4.43349i	1.01792	−	0.153427i
$836$	27.6478	+	22.0484i	0.956219	+	0.762559i
$837$	16.9120	−	14.9421i	0.584564	−	0.516474i
$838$	56.5429	−	35.5282i	1.95324	−	1.22730i
$839$	−12.3844	−	5.40328i	−0.427558	−	0.186542i	0.175083	−	0.984554i	$-0.443980\pi$
$839$	−12.3844	−	5.40328i	−0.427558	−	0.186542i	−0.602642	+	0.798012i	$0.705885\pi$
$840$	−63.0626	−	37.0953i	−2.17587	−	1.27991i
$841$	−0.0295424	+	29.0000i	−0.00101870	+	0.999999i
$842$	−63.0842	+	36.4217i	−2.17402	+	1.25517i
$843$	0.908772	+	1.25250i	0.0312998	+	0.0431385i
$844$	−9.43857	+	0.353166i	−0.324889	+	0.0121565i
$845$	−12.5863	−	55.1443i	−0.432982	−	1.89702i
$846$	70.6309	−	26.4050i	2.42834	−	0.907821i
$847$	48.5410	−	38.7101i	1.66789	−	1.33010i
$848$	−7.49716	+	8.08002i	−0.257454	+	0.277469i
$849$	−2.52706	−	7.41451i	−0.0867283	−	0.254465i
$850$	−8.27409	+	0.620057i	−0.283799	+	0.0212678i
$851$	−0.278692	+	7.44820i	−0.00955344	+	0.255321i
$852$	44.5697	+	16.0030i	1.52693	+	0.548255i
$853$	−6.84863	+	1.83508i	−0.234492	+	0.0628321i	−0.374152	−	0.927368i	$-0.622066\pi$
$853$	−6.84863	+	1.83508i	−0.234492	+	0.0628321i	0.139659	+	0.990200i	$0.455399\pi$
$854$	−21.5556	+	10.3807i	−0.737619	+	0.355219i
$855$	−15.4187	−	11.7711i	−0.527308	−	0.402562i
$856$	6.26393	−	55.5939i	0.214097	−	1.90016i
$857$	−43.2320	−	3.23979i	−1.47678	−	0.110669i	−0.688163	−	0.725557i	$-0.741582\pi$
$857$	−43.2320	−	3.23979i	−1.47678	−	0.110669i	−0.788615	+	0.614887i	$0.789201\pi$
$858$	116.164	+	32.1393i	3.96577	+	1.09722i
$859$	1.08139	+	5.71529i	0.0368966	+	0.195003i	0.996165	−	0.0874925i	$-0.0278854\pi$
$859$	1.08139	+	5.71529i	0.0368966	+	0.195003i	−0.959269	+	0.282496i	$0.908838\pi$
$860$	70.7346	+	2.64670i	2.41203	+	0.0902518i
$861$	−2.46682	−	3.68205i	−0.0840691	−	0.125484i
$862$	−3.86306	+	20.4167i	−0.131576	+	0.695397i
$863$	−10.6021	+	46.4506i	−0.360898	+	1.58120i	0.390022	+	0.920805i	$0.372467\pi$
$863$	−10.6021	+	46.4506i	−0.360898	+	1.58120i	−0.750920	+	0.660393i	$0.770390\pi$
$864$	−17.8784	−	7.52437i	−0.608235	−	0.255984i
$865$	15.6096	−	19.5739i	0.530744	−	0.665531i
$866$	5.65439	−	18.3311i	0.192144	−	0.622915i
$867$	0.851595	+	29.0773i	0.0289217	+	0.987516i
$868$	29.5732	+	40.0702i	1.00378	+	1.36007i
$869$	−22.3665	−	38.7399i	−0.758732	−	1.31416i
$870$	76.0658	−	19.6798i	2.57887	−	0.667207i
$871$	8.34040	−	14.4460i	0.282604	−	0.489484i
$872$	−6.30411	+	0.710303i	−0.213484	+	0.0240539i
$873$	−12.8462	−	21.2013i	−0.434777	−	0.717556i
$874$	−9.59782	+	2.19064i	−0.324651	+	0.0740995i
$875$	11.6907	+	29.7874i	0.395218	+	1.00700i
$876$	−15.0052	+	11.7682i	−0.506978	+	0.397609i
$877$	−47.8811	+	14.7694i	−1.61683	+	0.498726i	−0.965573	−	0.260133i	$-0.916234\pi$
$877$	−47.8811	+	14.7694i	−1.61683	+	0.498726i	−0.651256	+	0.758858i	$0.725758\pi$
$878$	3.73755	+	3.21642i	0.126136	+	0.108549i
$879$	14.1322	+	6.94767i	0.476669	+	0.234339i
$880$	14.0049	+	26.4986i	0.472106	+	0.893269i
$881$	−41.1094	−	14.3848i	−1.38501	−	0.484636i	−0.468081	−	0.883685i	$-0.655055\pi$
$881$	−41.1094	−	14.3848i	−1.38501	−	0.484636i	−0.916930	+	0.399049i	$0.869340\pi$
$882$	−23.1703	−	6.61362i	−0.780186	−	0.222692i
$883$	16.7178	+	34.7148i	0.562598	+	1.16825i	0.967262	+	0.253781i	$0.0816741\pi$
$883$	16.7178	+	34.7148i	0.562598	+	1.16825i	−0.404664	+	0.914465i	$0.632612\pi$
$884$	6.95248	+	5.13117i	0.233837	+	0.172580i
$885$	14.3966	−	6.14250i	0.483937	−	0.206478i
$886$	−54.8367	−	37.3870i	−1.84227	−	1.25604i
$887$	10.2441	−	38.2316i	0.343964	−	1.28369i	−0.549854	−	0.835261i	$-0.685317\pi$
$887$	10.2441	−	38.2316i	0.343964	−	1.28369i	0.893818	−	0.448430i	$-0.148017\pi$
$888$	13.2334	+	15.6325i	0.444083	+	0.524591i
$889$	−18.9247	+	10.0020i	−0.634713	+	0.335456i
$890$	25.5301	−	53.0139i	0.855772	−	1.77703i
$891$	33.4868	−	36.4480i	1.12185	−	1.22105i
$892$	−84.5288	−	19.2931i	−2.83023	−	0.645982i
$893$	2.87563	+	19.0785i	0.0962292	+	0.638439i
$894$	30.5767	+	79.8079i	1.02264	+	2.66918i
$895$	−47.8894	+	44.4349i	−1.60077	+	1.48529i
$896$	30.8363	−	58.3451i	1.03017	−	1.94917i
$897$	−17.3791	+	12.6097i	−0.580272	+	0.421024i
$898$	65.7659	+	37.9700i	2.19464	+	1.26707i
$899$	−23.1252	−	3.49760i	−0.771267	−	0.116652i
$900$	−40.2817	−	72.4629i	−1.34272	−	2.41543i
$901$	0.366491	+	3.25270i	0.0122096	+	0.108363i
$902$	0.384386	+	10.2729i	0.0127987	+	0.342051i
$903$	30.4088	−	6.68127i	1.01194	−	0.222339i
$904$	0.561983	−	3.72852i	0.0186913	−	0.124009i
$905$	28.7540	−	73.2640i	0.955815	−	2.43538i
$906$	−23.8388	−	5.64512i	−0.791992	−	0.187546i
$907$	19.2664	+	3.64539i	0.639729	+	0.121043i	0.495649	−	0.868523i	$-0.334930\pi$
$907$	19.2664	+	3.64539i	0.639729	+	0.121043i	0.144080	+	0.989566i	$0.453978\pi$
$908$	46.7678	+	22.5222i	1.55204	+	0.747425i
$909$	10.7546	+	7.00373i	0.356707	+	0.232299i
$910$	48.1892	−	137.717i	1.59746	−	4.56526i
$911$	−12.3634	−	46.1407i	−0.409617	−	1.52871i	−0.795379	−	0.606112i	$-0.792728\pi$
$911$	−12.3634	−	46.1407i	−0.409617	−	1.52871i	0.385762	−	0.922598i	$-0.373939\pi$
$912$	−2.72341	+	3.92563i	−0.0901810	+	0.129991i
$913$	−30.2369	−	69.3037i	−1.00069	−	2.29362i
$914$	−26.1505	−	59.9376i	−0.864982	−	1.98256i
$915$	−19.4132	−	1.61346i	−0.641781	−	0.0533393i
$916$	16.9970	+	63.4337i	0.561597	+	2.09591i
$917$	2.78295	−	7.95321i	0.0919011	−	0.262638i
$918$	4.96421	−	2.47088i	0.163843	−	0.0815510i
$919$	−39.8479	−	19.1897i	−1.31446	−	0.633011i	−0.360449	−	0.932779i	$-0.617376\pi$
$919$	−39.8479	−	19.1897i	−1.31446	−	0.633011i	−0.954012	+	0.299768i	$0.903091\pi$
$920$	−29.7055	−	5.62058i	−0.979360	−	0.185305i
$921$	−14.2773	+	15.1388i	−0.470453	+	0.498841i
$922$	−18.4937	+	47.1211i	−0.609056	+	1.55185i
$923$	−6.15522	+	40.8372i	−0.202601	+	1.34417i
$924$	73.6408	+	80.6700i	2.42260	+	2.65385i
$925$	−0.938442	−	25.0804i	−0.0308558	−	0.824638i
$926$	−9.85170	−	87.4362i	−0.323747	−	2.87333i
$927$	−23.4511	−	14.0522i	−0.770236	−	0.461535i
$928$	5.91563	+	19.2127i	0.194190	+	0.630689i
$929$	9.34459	+	5.39510i	0.306586	+	0.177008i	0.645398	−	0.763847i	$-0.276692\pi$
$929$	9.34459	+	5.39510i	0.306586	+	0.177008i	−0.338812	+	0.940854i	$0.610025\pi$
$930$	6.58316	+	63.0232i	0.215870	+	2.06661i
$931$	2.88090	−	5.45094i	0.0944178	−	0.178647i
$932$	−32.2774	+	29.9490i	−1.05728	+	0.981012i
$933$	−32.2789	+	39.8089i	−1.05676	+	1.30328i
$934$	−11.1384	−	73.8983i	−0.364459	−	2.41803i
$935$	8.67746	+	1.98057i	0.283783	+	0.0647717i
$936$	−11.9095	+	57.7889i	−0.389276	+	1.88889i
$937$	3.94832	−	8.19877i	0.128986	−	0.267842i	−0.826467	−	0.562985i	$-0.809653\pi$
$937$	3.94832	−	8.19877i	0.128986	−	0.267842i	0.955453	+	0.295143i	$0.0953672\pi$
$938$	20.8853	−	11.0382i	0.681931	−	0.360411i
$939$	20.2694	−	3.66494i	0.661468	−	0.119601i
$940$	−35.0673	+	130.873i	−1.14377	+	4.26861i
$941$	41.8531	+	28.5350i	1.36437	+	0.930213i	0.999999	−	0.00103975i	$-0.000330964\pi$
$941$	41.8531	+	28.5350i	1.36437	+	0.930213i	0.364373	+	0.931253i	$0.381283\pi$
$942$	35.2636	+	26.4707i	1.14895	+	0.862463i
$943$	−1.47352	−	1.08751i	−0.0479846	−	0.0354142i
$944$	−1.67269	−	3.47337i	−0.0544414	−	0.113049i
$945$	−41.3228	−	43.3870i	−1.34423	−	1.41138i
$946$	−68.1635	−	23.8515i	−2.21619	−	0.775478i
$947$	−22.2974	−	42.1888i	−0.724569	−	1.37095i	−0.920660	−	0.390366i	$-0.872348\pi$
$947$	−22.2974	−	42.1888i	−0.724569	−	1.37095i	0.196090	−	0.980586i	$-0.437175\pi$
$948$	41.6021	−	27.8717i	1.35117	−	0.905230i
$949$	−12.6053	−	10.8478i	−0.409186	−	0.352133i
$950$	31.6772	−	9.77112i	1.02774	−	0.317017i
$951$	−11.3661	−	4.56772i	−0.368570	−	0.148118i
$952$	1.95509	+	4.98149i	0.0633648	+	0.161451i
$953$	9.65880	−	2.20456i	0.312879	−	0.0714127i	−0.0631978	−	0.998001i	$-0.520130\pi$
$953$	9.65880	−	2.20456i	0.312879	−	0.0714127i	0.376077	+	0.926588i	$0.377273\pi$
$954$	−43.7122	+	26.4859i	−1.41524	+	0.857511i
$955$	39.4932	−	4.44981i	1.27797	−	0.143992i
$956$	−15.3285	+	26.5497i	−0.495759	+	0.858680i
$957$	−51.2418	−	2.36034i	−1.65641	−	0.0762989i
$958$	7.16883	+	12.4168i	0.231615	+	0.401168i
$959$	13.1669	+	17.8406i	0.425183	+	0.576102i
$960$	62.4171	−	38.5158i	2.01450	−	1.24309i
$961$	−3.57766	+	11.5985i	−0.115408	+	0.374144i
$962$	−25.4662	+	31.9337i	−0.821065	+	1.02958i
$963$	17.4290	−	42.3715i	0.561640	−	1.36540i
$964$	14.1951	−	62.1926i	0.457192	−	2.00309i
$965$	9.18559	−	48.5470i	0.295695	−	1.56278i
$966$	−30.3402	+	2.02605i	−0.976179	+	0.0651871i
$967$	9.69506	+	0.362763i	0.311772	+	0.0116657i	0.192819	−	0.981234i	$-0.438237\pi$
$967$	9.69506	+	0.362763i	0.311772	+	0.0116657i	0.118953	+	0.992900i	$0.462046\pi$
$968$	−13.1065	−	69.2697i	−0.421260	−	2.22641i
$969$	0.356082	+	1.37344i	0.0114390	+	0.0441211i
$970$	69.4112	+	5.20165i	2.22866	+	0.167015i
$971$	−4.25744	+	37.7859i	−0.136628	+	1.21261i	0.718998	+	0.695012i	$0.244601\pi$
$971$	−4.25744	+	37.7859i	−0.136628	+	1.21261i	−0.855626	+	0.517594i	$0.826828\pi$
$972$	43.2081	+	34.6844i	1.38590	+	1.11250i
$973$	−33.9279	+	16.3388i	−1.08768	+	0.523798i
$974$	25.6529	−	6.87367i	0.821972	−	0.220247i
$975$	55.1841	−	46.7152i	1.76731	−	1.49608i
$976$	−0.179402	+	4.79462i	−0.00574252	+	0.153472i
$977$	−16.5152	+	1.23764i	−0.528368	+	0.0395957i	−0.336244	−	0.941775i	$-0.609157\pi$
$977$	−16.5152	+	1.23764i	−0.528368	+	0.0395957i	−0.192124	+	0.981371i	$0.561538\pi$
$978$	39.5386	−	45.1970i	1.26430	−	1.44524i
$979$	−26.1291	+	28.1605i	−0.835090	+	0.900013i
$980$	33.8500	−	26.9945i	1.08130	−	0.862307i
$981$	−5.12406	−	0.857660i	−0.163599	−	0.0273830i
$982$	−20.0656	−	87.9134i	−0.640321	−	2.80543i
$983$	18.2531	−	0.682983i	0.582183	−	0.0217838i	0.255322	−	0.966856i	$-0.417818\pi$
$983$	18.2531	−	0.682983i	0.582183	−	0.0217838i	0.326861	+	0.945072i	$0.394009\pi$
$984$	−5.00531	+	0.522836i	−0.159563	+	0.0166674i
$985$	47.0521	−	27.1656i	1.49921	−	0.865567i
$986$	−5.26618	−	2.30080i	−0.167709	−	0.0732725i
$987$	−0.483960	+	59.5927i	−0.0154046	+	1.89686i
$988$	−31.6424	−	13.8055i	−1.00668	−	0.439210i
$989$	10.8932	−	6.84466i	0.346384	−	0.217648i
$990$	28.7208	+	135.978i	0.912807	+	4.32165i
$991$	31.1949	+	24.8771i	0.990939	+	0.790247i	0.977773	−	0.209666i	$-0.0672377\pi$
$991$	31.1949	+	24.8771i	0.990939	+	0.790247i	0.0131656	+	0.999913i	$0.495809\pi$
$992$	−16.0316	+	2.41638i	−0.509004	+	0.0767201i
$993$	16.5999	−	4.97312i	0.526781	−	0.157817i
$994$	−38.1495	+	44.3305i	−1.21003	+	1.40608i
$995$	5.22667	+	69.7451i	0.165697	+	2.21107i
$996$	75.1531	−	38.9421i	2.38132	−	1.23393i
$997$	0.397626	+	0.462050i	0.0125930	+	0.0146333i	0.764233	−	0.644940i	$-0.223118\pi$
$997$	0.397626	+	0.462050i	0.0125930	+	0.0146333i	−0.751640	+	0.659574i	$0.770737\pi$
$998$	1.84242	−	1.84242i	0.0583208	−	0.0583208i
$999$	6.90731	+	15.2849i	0.218537	+	0.483593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.x.a.101.3	yes	672
3.2	odd	2		783.2.be.a.710.26		672
9.4	even	3		783.2.be.a.449.3		672
9.5	odd	6	inner	261.2.x.a.14.26	✓	672
29.27	odd	28	inner	261.2.x.a.56.26	yes	672
87.56	even	28		783.2.be.a.143.3		672
261.85	odd	84		783.2.be.a.665.26		672
261.230	even	84	inner	261.2.x.a.230.3	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.14.26	✓	672	9.5	odd	6	inner
261.2.x.a.56.26	yes	672	29.27	odd	28	inner
261.2.x.a.101.3	yes	672	1.1	even	1	trivial
261.2.x.a.230.3	yes	672	261.230	even	84	inner
783.2.be.a.143.3		672	87.56	even	28
783.2.be.a.449.3		672	9.4	even	3
783.2.be.a.665.26		672	261.85	odd	84
783.2.be.a.710.26		672	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.942454 + 2.16013i) q^{2} +(-1.73131 + 0.0507054i) q^{3} +(-2.41758 - 2.60553i) q^{4} +(3.53430 + 0.532711i) q^{5} +(1.52215 - 3.78763i) q^{6} +(2.36493 + 2.19434i) q^{7} +(3.45771 - 1.20991i) q^{8} +(2.99486 - 0.175573i) q^{9} +(-4.48164 + 7.13249i) q^{10} +(4.16848 - 3.58727i) q^{11} +(4.31770 + 4.38840i) q^{12} +(-3.02441 + 4.43599i) q^{13} +(-6.96888 + 3.04049i) q^{14} +(-6.14598 - 0.743078i) q^{15} +(-0.113947 + 1.52052i) q^{16} +(0.320183 + 0.320183i) q^{17} +(-2.44325 + 6.63474i) q^{18} +(-1.53180 - 0.962495i) q^{19} +(-7.15648 - 10.4966i) q^{20} +(-4.20569 - 3.67916i) q^{21} +(3.82035 + 12.3853i) q^{22} +(-2.14938 - 0.843569i) q^{23} +(-5.92502 + 2.27004i) q^{24} +(7.42966 + 2.29175i) q^{25} +(-6.73194 - 10.7138i) q^{26} +(-5.17612 + 0.455827i) q^{27} -11.4669i q^{28} +(3.80595 + 3.80983i) q^{29} +(7.39745 - 12.5758i) q^{30} +(-3.49443 + 2.57900i) q^{31} +(3.30040 + 1.74431i) q^{32} +(-7.03503 + 6.42203i) q^{33} +(-0.993395 + 0.389879i) q^{34} +(7.18944 + 9.01528i) q^{35} +(-7.69778 - 7.37874i) q^{36} +(-1.06614 - 3.04685i) q^{37} +(3.52276 - 2.40178i) q^{38} +(5.01126 - 7.83343i) q^{39} +(12.8651 - 2.43421i) q^{40} +(0.766126 + 0.205283i) q^{41} +(11.9111 - 5.61739i) q^{42} +(-3.30862 + 4.48302i) q^{43} +(-19.4244 - 2.18860i) q^{44} +(10.6783 + 0.974863i) q^{45} +(3.84791 - 3.84791i) q^{46} +(-6.95668 - 8.08380i) q^{47} +(0.120179 - 2.63827i) q^{48} +(0.254681 + 3.39849i) q^{49} +(-11.9526 + 13.8891i) q^{50} +(-0.570571 - 0.538101i) q^{51} +(18.8699 - 2.84418i) q^{52} +(5.65175 + 4.50712i) q^{53} +(3.89361 - 11.6107i) q^{54} +(16.6436 - 10.4579i) q^{55} +(10.8322 + 4.72604i) q^{56} +(2.70082 + 1.58870i) q^{57} +(-11.8166 + 4.63074i) q^{58} +(-2.18960 + 1.26417i) q^{59} +(12.9223 + 17.8100i) q^{60} +(3.14446 - 0.117657i) q^{61} +(-2.27764 - 9.97900i) q^{62} +(7.46790 + 6.15651i) q^{63} +(-9.26266 + 7.38673i) q^{64} +(-13.0523 + 14.0670i) q^{65} +(-7.24221 - 21.2490i) q^{66} +(-3.09824 + 0.232181i) q^{67} +(0.0601790 - 1.60832i) q^{68} +(3.76401 + 1.35149i) q^{69} +(-26.2499 + 7.03363i) q^{70} +(6.93040 - 3.33751i) q^{71} +(10.1429 - 4.23058i) q^{72} +(-0.346814 + 3.07806i) q^{73} +(7.58637 + 0.568520i) q^{74} +(-12.9792 - 3.59100i) q^{75} +(1.19544 + 6.31807i) q^{76} +(17.7298 + 0.663404i) q^{77} +(12.1983 + 18.2076i) q^{78} +(1.51220 - 7.99218i) q^{79} +(-1.21272 + 5.31328i) q^{80} +(8.93835 - 1.05163i) q^{81} +(-1.16547 + 1.46146i) q^{82} +(4.05257 - 13.1381i) q^{83} +(0.581434 + 19.8527i) q^{84} +(0.961060 + 1.30219i) q^{85} +(-6.56567 - 11.3721i) q^{86} +(-6.78245 - 6.40300i) q^{87} +(10.0731 - 17.4472i) q^{88} +(-6.94131 + 0.782098i) q^{89} +(-12.1696 + 22.1476i) q^{90} +(-16.8866 + 3.85425i) q^{91} +(2.99835 + 7.63968i) q^{92} +(5.91916 - 4.64224i) q^{93} +(24.0184 - 7.40869i) q^{94} +(-4.90112 - 4.21776i) q^{95} +(-5.80246 - 2.85260i) q^{96} +(-3.86112 - 7.30559i) q^{97} +(-7.58119 - 2.65277i) q^{98} +(11.8542 - 11.4752i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20}+ \cdots - 16 q^{99}+O(q^{100}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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