LMFDB - Embedded newform 690.2.n.b.89.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(89,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 5]))

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

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

chi := DirichletCharacter("690.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.n (of order $22$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			89.15
Character	$\chi$	$=$	690.89
Dual form			690.2.n.b.659.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{2} +(0.479764 - 1.66428i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(0.0269160 - 2.23591i) q^{5} +(1.71562 + 0.238029i) q^{6} +(-2.74772 + 1.76585i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-2.53965 - 1.59692i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{2} +(0.479764 - 1.66428i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(0.0269160 - 2.23591i) q^{5} +(1.71562 + 0.238029i) q^{6} +(-2.74772 + 1.76585i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-2.53965 - 1.59692i) q^{9} +(2.21698 - 0.291561i) q^{10} +(0.103499 - 0.719848i) q^{11} +(0.00855129 + 1.73203i) q^{12} +(-0.797957 + 1.24165i) q^{13} +(-2.13892 - 2.46844i) q^{14} +(-3.70826 - 1.11750i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-0.487896 + 1.66162i) q^{17} +(1.21924 - 2.74107i) q^{18} +(-1.66137 - 5.65810i) q^{19} +(0.604102 + 2.15292i) q^{20} +(1.62061 + 5.42016i) q^{21} +0.727250 q^{22} +(-1.82495 - 4.43504i) q^{23} +(-1.71318 + 0.254958i) q^{24} +(-4.99855 - 0.120363i) q^{25} +(-1.34257 - 0.613130i) q^{26} +(-3.87616 + 3.46054i) q^{27} +(2.13892 - 2.46844i) q^{28} +(-1.91557 + 6.52384i) q^{29} +(0.578389 - 3.82955i) q^{30} +(-1.61915 - 3.54544i) q^{31} +(0.654861 + 0.755750i) q^{32} +(-1.14837 - 0.517608i) q^{33} +(-1.71414 - 0.246456i) q^{34} +(3.87432 + 6.19116i) q^{35} +(2.88668 + 0.816734i) q^{36} +(-7.28503 - 8.40738i) q^{37} +(5.36407 - 2.44969i) q^{38} +(1.68361 + 1.92372i) q^{39} +(-2.04503 + 0.904345i) q^{40} +(-0.240142 - 0.208084i) q^{41} +(-5.13435 + 2.37549i) q^{42} +(-3.85328 + 8.43752i) q^{43} +(0.103499 + 0.719848i) q^{44} +(-3.63893 + 5.63544i) q^{45} +(4.13018 - 2.43755i) q^{46} -0.296017 q^{47} +(-0.496174 - 1.65946i) q^{48} +(1.52381 - 3.33668i) q^{49} +(-0.592230 - 4.96480i) q^{50} +(2.53133 + 1.60918i) q^{51} +(0.415822 - 1.41616i) q^{52} +(1.32976 + 2.06915i) q^{53} +(-3.97696 - 3.34422i) q^{54} +(-1.60673 - 0.250788i) q^{55} +(2.74772 + 1.76585i) q^{56} +(-10.2137 + 0.0504267i) q^{57} +(-6.73005 - 0.967635i) q^{58} +(4.64023 - 7.22033i) q^{59} +(3.87289 + 0.0274993i) q^{60} +(4.22497 - 1.92948i) q^{61} +(3.27893 - 2.10724i) q^{62} +(9.79817 - 0.0967525i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(2.75472 + 1.81758i) q^{65} +(0.348909 - 1.21035i) q^{66} +(-0.0578385 - 0.402276i) q^{67} -1.73177i q^{68} +(-8.25669 + 0.909463i) q^{69} +(-5.57677 + 4.71598i) q^{70} +(7.98308 - 1.14779i) q^{71} +(-0.397603 + 2.97354i) q^{72} +(-0.808166 - 2.75236i) q^{73} +(7.28503 - 8.40738i) q^{74} +(-2.59844 + 8.26124i) q^{75} +(3.18814 + 4.96084i) q^{76} +(0.986759 + 2.16070i) q^{77} +(-1.66454 + 1.94025i) q^{78} +(-1.78670 + 2.78017i) q^{79} +(-1.18618 - 1.89552i) q^{80} +(3.89967 + 8.11126i) q^{81} +(0.171790 - 0.267311i) q^{82} +(11.9849 - 10.3850i) q^{83} +(-3.08200 - 4.74403i) q^{84} +(3.70209 + 1.13561i) q^{85} +(-8.90001 - 2.61328i) q^{86} +(9.93847 + 6.31795i) q^{87} +(-0.697792 + 0.204890i) q^{88} +(3.56233 - 7.80041i) q^{89} +(-6.09595 - 2.79988i) q^{90} -4.82076i q^{91} +(3.00053 + 3.74124i) q^{92} +(-6.67742 + 0.993741i) q^{93} +(-0.0421276 - 0.293004i) q^{94} +(-12.6957 + 3.56237i) q^{95} +(1.57196 - 0.727290i) q^{96} +(8.74637 - 10.0938i) q^{97} +(3.51958 + 1.03344i) q^{98} +(-1.41239 + 1.66288i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} + 24 q^{8} - 6 q^{9}+O(q^{10}) $ 240 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 + 24 * q^8 - 6 * q^9	$ 240 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} + 24 q^{8} - 6 q^{9} + 9 q^{12} + 11 q^{15} - 24 q^{16} + 6 q^{18} + 4 q^{23} + 2 q^{24} - 12 q^{25} - 2 q^{27} + 22 q^{30} + 28 q^{31} + 24 q^{32} + 36 q^{35} - 6 q^{36} - 4 q^{46} - 104 q^{47} + 9 q^{48} + 70 q^{49} - 54 q^{50} - 9 q^{54} - 26 q^{55} + 44 q^{57} - 11 q^{60} + 44 q^{61} - 28 q^{62} + 121 q^{63} - 24 q^{64} - 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} - 16 q^{72} - 102 q^{75} - 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} + 93 q^{87} + 4 q^{92} - 172 q^{93} + 16 q^{94} - 26 q^{95} + 2 q^{96} - 4 q^{98}+O(q^{100}) $ 240 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 + 24 * q^8 - 6 * q^9 + 9 * q^12 + 11 * q^15 - 24 * q^16 + 6 * q^18 + 4 * q^23 + 2 * q^24 - 12 * q^25 - 2 * q^27 + 22 * q^30 + 28 * q^31 + 24 * q^32 + 36 * q^35 - 6 * q^36 - 4 * q^46 - 104 * q^47 + 9 * q^48 + 70 * q^49 - 54 * q^50 - 9 * q^54 - 26 * q^55 + 44 * q^57 - 11 * q^60 + 44 * q^61 - 28 * q^62 + 121 * q^63 - 24 * q^64 - 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 - 16 * q^72 - 102 * q^75 - 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 + 93 * q^87 + 4 * q^92 - 172 * q^93 + 16 * q^94 - 26 * q^95 + 2 * q^96 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{22}\right)$

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 $

$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$3$	0.479764	−	1.66428i	0.276992	−	0.960872i
$3$	0.479764	−	1.66428i	0.276992	−	0.960872i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	0.0269160	−	2.23591i	0.0120372	−	0.999928i
$5$	0.0269160	−	2.23591i	0.0120372	−	0.999928i
$6$	1.71562	+	0.238029i	0.700398	+	0.0971750i
$7$	−2.74772	+	1.76585i	−1.03854	+	0.667429i	−0.944625	−	0.328152i	$-0.893574\pi$
$7$	−2.74772	+	1.76585i	−1.03854	+	0.667429i	−0.0939141	+	0.995580i	$0.529938\pi$
$8$	−0.415415	−	0.909632i	−0.146871	−	0.321603i
$9$	−2.53965	−	1.59692i	−0.846551	−	0.532308i
$10$	2.21698	−	0.291561i	0.701070	−	0.0921996i
$11$	0.103499	−	0.719848i	0.0312060	−	0.217042i	−0.968251	−	0.249978i	$-0.919577\pi$
$11$	0.103499	−	0.719848i	0.0312060	−	0.217042i	0.999457	+	0.0329357i	$0.0104857\pi$
$12$	0.00855129	+	1.73203i	0.00246855	+	0.499994i
$13$	−0.797957	+	1.24165i	−0.221313	+	0.344370i	−0.934101	−	0.357010i	$-0.883796\pi$
$13$	−0.797957	+	1.24165i	−0.221313	+	0.344370i	0.712787	+	0.701380i	$0.247433\pi$
$14$	−2.13892	−	2.46844i	−0.571650	−	0.659719i
$15$	−3.70826	−	1.11750i	−0.957468	−	0.288538i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−0.487896	+	1.66162i	−0.118332	+	0.403002i	−0.997262	−	0.0739488i	$-0.976440\pi$
$17$	−0.487896	+	1.66162i	−0.118332	+	0.403002i	0.878930	+	0.476951i	$0.158258\pi$
$18$	1.21924	−	2.74107i	0.287377	−	0.646076i
$19$	−1.66137	−	5.65810i	−0.381144	−	1.29806i	−0.897247	−	0.441530i	$-0.854436\pi$
$19$	−1.66137	−	5.65810i	−0.381144	−	1.29806i	0.516103	−	0.856527i	$-0.327382\pi$
$20$	0.604102	+	2.15292i	0.135081	+	0.481407i
$21$	1.62061	+	5.42016i	0.353647	+	1.18278i
$22$	0.727250			0.155050
$23$	−1.82495	−	4.43504i	−0.380529	−	0.924769i
$23$	−1.82495	−	4.43504i	−0.380529	−	0.924769i
$24$	−1.71318	+	0.254958i	−0.349702	+	0.0520430i
$25$	−4.99855	−	0.120363i	−0.999710	−	0.0240726i
$26$	−1.34257	−	0.613130i	−0.263299	−	0.120245i
$27$	−3.87616	+	3.46054i	−0.745968	+	0.665982i
$28$	2.13892	−	2.46844i	0.404217	−	0.466492i
$29$	−1.91557	+	6.52384i	−0.355713	+	1.21145i	0.566271	+	0.824219i	$0.308385\pi$
$29$	−1.91557	+	6.52384i	−0.355713	+	1.21145i	−0.921984	+	0.387228i	$0.873433\pi$
$30$	0.578389	−	3.82955i	0.105599	−	0.699177i
$31$	−1.61915	−	3.54544i	−0.290808	−	0.636780i	0.706687	−	0.707527i	$-0.250189\pi$
$31$	−1.61915	−	3.54544i	−0.290808	−	0.636780i	−0.997494	+	0.0707465i	$0.977462\pi$
$32$	0.654861	+	0.755750i	0.115764	+	0.133599i
$33$	−1.14837	−	0.517608i	−0.199906	−	0.0901040i
$34$	−1.71414	−	0.246456i	−0.293973	−	0.0422669i
$35$	3.87432	+	6.19116i	0.654879	+	1.04650i
$36$	2.88668	+	0.816734i	0.481114	+	0.136122i
$37$	−7.28503	−	8.40738i	−1.19765	−	1.38216i	−0.904707	−	0.426035i	$-0.859910\pi$
$37$	−7.28503	−	8.40738i	−1.19765	−	1.38216i	−0.292945	−	0.956129i	$-0.594635\pi$
$38$	5.36407	−	2.44969i	0.870167	−	0.397392i
$39$	1.68361	+	1.92372i	0.269594	+	0.308042i
$40$	−2.04503	+	0.904345i	−0.323348	+	0.142990i
$41$	−0.240142	−	0.208084i	−0.0375038	−	0.0324973i	0.635907	−	0.771766i	$-0.280626\pi$
$41$	−0.240142	−	0.208084i	−0.0375038	−	0.0324973i	−0.673411	+	0.739268i	$0.735172\pi$
$42$	−5.13435	+	2.37549i	−0.792248	+	0.366545i
$43$	−3.85328	+	8.43752i	−0.587620	+	1.28671i	0.349249	+	0.937030i	$0.386437\pi$
$43$	−3.85328	+	8.43752i	−0.587620	+	1.28671i	−0.936870	+	0.349679i	$0.886291\pi$
$44$	0.103499	+	0.719848i	0.0156030	+	0.108521i
$45$	−3.63893	+	5.63544i	−0.542459	+	0.840082i
$46$	4.13018	−	2.43755i	0.608961	−	0.359397i
$47$	−0.296017			−0.0431785			−0.0215892	−	0.999767i	$-0.506873\pi$
$47$	−0.296017			−0.0431785			−0.0215892	+	0.999767i	$0.506873\pi$
$48$	−0.496174	−	1.65946i	−0.0716166	−	0.239523i
$49$	1.52381	−	3.33668i	0.217688	−	0.476669i
$50$	−0.592230	−	4.96480i	−0.0837540	−	0.702129i
$51$	2.53133	+	1.60918i	0.354456	+	0.225330i
$52$	0.415822	−	1.41616i	0.0576642	−	0.196386i
$53$	1.32976	+	2.06915i	0.182656	+	0.284219i	0.920492	−	0.390762i	$-0.127788\pi$
$53$	1.32976	+	2.06915i	0.182656	+	0.284219i	−0.737835	+	0.674981i	$0.764152\pi$
$54$	−3.97696	−	3.34422i	−0.541195	−	0.455091i
$55$	−1.60673	−	0.250788i	−0.216651	−	0.0338163i
$56$	2.74772	+	1.76585i	0.367179	+	0.235972i
$57$	−10.2137	+	0.0504267i	−1.35284	+	0.00667918i
$58$	−6.73005	−	0.967635i	−0.883699	−	0.127057i
$59$	4.64023	−	7.22033i	0.604106	−	0.940008i	−0.395660	−	0.918397i	$-0.629484\pi$
$59$	4.64023	−	7.22033i	0.604106	−	0.940008i	0.999766	−	0.0216106i	$-0.00687940\pi$
$60$	3.87289	+	0.0274993i	0.499987	+	0.00355015i
$61$	4.22497	−	1.92948i	0.540953	−	0.247045i	−0.126149	−	0.992011i	$-0.540262\pi$
$61$	4.22497	−	1.92948i	0.540953	−	0.247045i	0.667102	+	0.744966i	$0.267535\pi$
$62$	3.27893	−	2.10724i	0.416424	−	0.267619i
$63$	9.79817	−	0.0967525i	1.23445	−	0.0121897i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	2.75472	+	1.81758i	0.341682	+	0.225443i
$66$	0.348909	−	1.21035i	0.0429477	−	0.148984i
$67$	−0.0578385	−	0.402276i	−0.00706610	−	0.0491458i	0.985983	−	0.166844i	$-0.0533576\pi$
$67$	−0.0578385	−	0.402276i	−0.00706610	−	0.0491458i	−0.993049	+	0.117698i	$0.962449\pi$
$68$		−	1.73177i		−	0.210008i
$69$	−8.25669	+	0.909463i	−0.993988	+	0.109486i
$70$	−5.57677	+	4.71598i	−0.666552	+	0.563667i
$71$	7.98308	−	1.14779i	0.947417	−	0.136218i	0.348750	−	0.937216i	$-0.386606\pi$
$71$	7.98308	−	1.14779i	0.947417	−	0.136218i	0.598667	+	0.800998i	$0.295697\pi$
$72$	−0.397603	+	2.97354i	−0.0468580	+	0.350434i
$73$	−0.808166	−	2.75236i	−0.0945887	−	0.322140i	0.898583	−	0.438804i	$-0.144598\pi$
$73$	−0.808166	−	2.75236i	−0.0945887	−	0.322140i	−0.993171	+	0.116665i	$0.962780\pi$
$74$	7.28503	−	8.40738i	0.846868	−	0.977337i
$75$	−2.59844	+	8.26124i	−0.300042	+	0.953926i
$76$	3.18814	+	4.96084i	0.365705	+	0.569048i
$77$	0.986759	+	2.16070i	0.112452	+	0.246235i
$78$	−1.66454	+	1.94025i	−0.188472	+	0.219690i
$79$	−1.78670	+	2.78017i	−0.201020	+	0.312793i	−0.927098	−	0.374819i	$-0.877705\pi$
$79$	−1.78670	+	2.78017i	−0.201020	+	0.312793i	0.726078	+	0.687612i	$0.241341\pi$
$80$	−1.18618	−	1.89552i	−0.132619	−	0.211925i
$81$	3.89967	+	8.11126i	0.433297	+	0.901251i
$82$	0.171790	−	0.267311i	0.0189711	−	0.0295196i
$83$	11.9849	−	10.3850i	1.31552	−	1.13990i	0.335272	−	0.942122i	$-0.391172\pi$
$83$	11.9849	−	10.3850i	1.31552	−	1.13990i	0.980246	−	0.197781i	$-0.0633735\pi$
$84$	−3.08200	−	4.74403i	−0.336274	−	0.517616i
$85$	3.70209	+	1.13561i	0.401548	+	0.123175i
$86$	−8.90001	−	2.61328i	−0.959713	−	0.281797i
$87$	9.93847	+	6.31795i	1.06552	+	0.677356i
$88$	−0.697792	+	0.204890i	−0.0743848	+	0.0218414i
$89$	3.56233	−	7.80041i	0.377606	−	0.826841i	−0.621452	−	0.783452i	$-0.713457\pi$
$89$	3.56233	−	7.80041i	0.377606	−	0.826841i	0.999058	−	0.0433895i	$-0.0138156\pi$
$90$	−6.09595	−	2.79988i	−0.642570	−	0.295134i
$91$		−	4.82076i		−	0.505353i
$92$	3.00053	+	3.74124i	0.312826	+	0.390051i
$93$	−6.67742	+	0.993741i	−0.692416	+	0.103046i
$94$	−0.0421276	−	0.293004i	−0.00434513	−	0.0302210i
$95$	−12.6957	+	3.56237i	−1.30255	+	0.365491i
$96$	1.57196	−	0.727290i	0.160437	−	0.0742287i
$97$	8.74637	−	10.0938i	0.888059	−	1.02487i	−0.111457	−	0.993769i	$-0.535552\pi$
$97$	8.74637	−	10.0938i	0.888059	−	1.02487i	0.999516	−	0.0311057i	$-0.00990284\pi$
$98$	3.51958	+	1.03344i	0.355532	+	0.104394i
$99$	−1.41239	+	1.66288i	−0.141951	+	0.167126i
$100$	4.82998	−	1.29277i	0.482998	−	0.129277i
$101$	−4.21978	+	3.65646i	−0.419884	+	0.363831i	−0.839028	−	0.544088i	$-0.816876\pi$
$101$	−4.21978	+	3.65646i	−0.419884	+	0.363831i	0.419144	+	0.907920i	$0.362330\pi$
$102$	−1.23256	+	2.73457i	−0.122041	+	0.270763i
$103$	2.60682	−	18.1308i	0.256857	−	1.78648i	−0.298030	−	0.954557i	$-0.596329\pi$
$103$	2.60682	−	18.1308i	0.256857	−	1.78648i	0.554887	−	0.831926i	$-0.312761\pi$
$104$	1.46092	+	0.210049i	0.143255	+	0.0205970i
$105$	12.1626	−	3.47765i	1.18695	−	0.339384i
$106$	−1.85884	+	1.61069i	−0.180547	+	0.156444i
$107$	9.34180	−	4.26626i	0.903106	−	0.412435i	0.0909369	−	0.995857i	$-0.471014\pi$
$107$	9.34180	−	4.26626i	0.903106	−	0.412435i	0.812169	+	0.583422i	$0.198287\pi$
$108$	2.74420	−	4.41241i	0.264061	−	0.424584i
$109$	−3.44409	+	11.7295i	−0.329884	+	1.12348i	0.612922	+	0.790143i	$0.289994\pi$
$109$	−3.44409	+	11.7295i	−0.329884	+	1.12348i	−0.942807	+	0.333340i	$0.891824\pi$
$110$	0.0195746	−	1.62606i	0.00186637	−	0.155039i
$111$	−17.4873	+	8.09077i	−1.65982	+	0.767942i
$112$	−1.35684	+	2.97106i	−0.128209	+	0.280738i
$113$	9.35371	−	1.34486i	0.879923	−	0.126514i	0.312478	−	0.949925i	$-0.398841\pi$
$113$	9.35371	−	1.34486i	0.879923	−	0.126514i	0.567445	+	0.823411i	$0.307932\pi$
$114$	−1.50348	−	10.1026i	−0.140814	−	0.946194i
$115$	−9.96544	+	3.96105i	−0.929282	+	0.369370i
$116$		−	6.79926i		−	0.631295i
$117$	4.00935	−	1.87907i	0.370664	−	0.173720i
$118$	7.80722	+	3.56544i	0.718712	+	0.328225i
$119$	−1.59357	−	5.42721i	−0.146083	−	0.497512i
$120$	0.523950	+	3.83738i	0.0478298	+	0.350303i
$121$	10.0470	+	2.95005i	0.913359	+	0.268187i
$122$	2.51112	+	3.90738i	0.227346	+	0.353757i
$123$	−0.461521	+	0.299832i	−0.0416140	+	0.0270349i
$124$	2.55243	+	2.94566i	0.229215	+	0.264528i
$125$	−0.403661	+	11.1731i	−0.0361046	+	0.999348i
$126$	1.49019	+	9.68467i	0.132757	+	0.862779i
$127$	11.0052	+	1.58231i	0.976553	+	0.140407i	0.612070	−	0.790803i	$-0.290337\pi$
$127$	11.0052	+	1.58231i	0.976553	+	0.140407i	0.364482	+	0.931210i	$0.381246\pi$
$128$	−0.841254	−	0.540641i	−0.0743570	−	0.0477863i
$129$	12.1937	+	10.4610i	1.07360	+	0.921036i
$130$	−1.40704	+	2.98535i	−0.123405	+	0.261833i
$131$	−7.01612	−	10.9173i	−0.613001	−	0.953848i	−0.999502	−	0.0315591i	$-0.989953\pi$
$131$	−7.01612	−	10.9173i	−0.613001	−	0.953848i	0.386501	−	0.922289i	$-0.373684\pi$
$132$	1.24768	+	0.173107i	0.108597	+	0.0150670i
$133$	14.5563	+	12.6131i	1.26219	+	1.09370i
$134$	0.389950	−	0.114500i	0.0336866	−	0.00989126i
$135$	7.63312	+	8.75988i	0.656955	+	0.753930i
$136$	1.71414	−	0.246456i	0.146986	−	0.0211335i
$137$		−	2.34987i		−	0.200763i	−0.994949	−	0.100382i	$-0.967994\pi$
$137$		−	2.34987i		−	0.200763i	0.994949	−	0.100382i	$-0.0320064\pi$
$138$	−2.07526	−	8.04322i	−0.176657	−	0.684684i
$139$	0.917075			0.0777853			0.0388926	−	0.999243i	$-0.487617\pi$
$139$	0.917075			0.0777853			0.0388926	+	0.999243i	$0.487617\pi$
$140$	−5.46163	−	4.84886i	−0.461592	−	0.409803i
$141$	−0.142018	+	0.492655i	−0.0119601	+	0.0414890i
$142$	2.27222	+	7.73848i	0.190681	+	0.649398i
$143$	0.811209	+	0.702916i	0.0678367	+	0.0587808i
$144$	−2.99985	+	0.0296222i	−0.249988	+	0.00246852i
$145$	14.5351	+	4.45864i	1.20708	+	0.370269i
$146$	2.60933	−	1.19164i	0.215950	−	0.0986210i
$147$	−4.82211	−	4.13687i	−0.397721	−	0.341204i
$148$	9.35857	+	6.01439i	0.769270	+	0.494380i
$149$	−1.45041	+	10.0879i	−0.118823	+	0.826429i	0.840033	+	0.542535i	$0.182535\pi$
$149$	−1.45041	+	10.0879i	−0.118823	+	0.826429i	−0.958856	+	0.283894i	$0.908374\pi$
$150$	−8.54695	−	1.39630i	−0.697856	−	0.114007i
$151$	−17.7643	−	11.4164i	−1.44564	−	0.929054i	−0.999417	−	0.0341294i	$-0.989134\pi$
$151$	−17.7643	−	11.4164i	−1.44564	−	0.929054i	−0.446218	−	0.894924i	$-0.647229\pi$
$152$	−4.45663	+	3.86169i	−0.361480	+	0.313225i
$153$	3.89257	−	3.44081i	0.314695	−	0.278173i
$154$	−1.99828	+	1.28422i	−0.161026	+	0.103485i
$155$	−7.97086	+	3.52484i	−0.640235	+	0.283122i
$156$	−2.15739	−	1.37147i	−0.172729	−	0.109805i
$157$	−15.3988	+	4.52150i	−1.22896	+	0.360855i	−0.830857	−	0.556485i	$-0.812149\pi$
$157$	−15.3988	+	4.52150i	−1.22896	+	0.360855i	−0.398103	+	0.917341i	$0.630331\pi$
$158$	−3.00614	−	1.37286i	−0.239156	−	0.109219i
$159$	4.08161	−	1.22039i	0.323692	−	0.0967831i
$160$	1.70741	−	1.44387i	0.134983	−	0.114148i
$161$	12.8461	+	8.96362i	1.01241	+	0.706432i
$162$	−7.47372	+	5.01433i	−0.587191	+	0.393963i
$163$	−14.5365	+	2.09003i	−1.13859	+	0.163704i	−0.685714	−	0.727871i	$-0.740510\pi$
$163$	−14.5365	+	2.09003i	−1.13859	+	0.163704i	−0.452872	+	0.891575i	$0.649601\pi$
$164$	0.289038	+	0.131999i	0.0225701	+	0.0103074i
$165$	−1.18823	+	2.55372i	−0.0925037	+	0.198807i
$166$	11.9849	+	10.3850i	0.930212	+	0.806033i
$167$	−4.12542	−	1.21133i	−0.319234	−	0.0937357i	0.118190	−	0.992991i	$-0.462291\pi$
$167$	−4.12542	−	1.21133i	−0.319234	−	0.0937357i	−0.437424	+	0.899255i	$0.644109\pi$
$168$	4.25712	−	3.72578i	0.328444	−	0.287450i
$169$	4.49545	+	9.84366i	0.345804	+	0.757204i
$170$	−0.597191	+	3.82603i	−0.0458025	+	0.293443i
$171$	−4.81625	+	17.0227i	−0.368308	+	1.30176i
$172$	1.32008	−	9.18133i	0.100655	−	0.700070i
$173$	−2.27457	+	15.8200i	−0.172932	+	1.20277i	0.699716	+	0.714421i	$0.253310\pi$
$173$	−2.27457	+	15.8200i	−0.172932	+	1.20277i	−0.872648	+	0.488349i	$0.837599\pi$
$174$	−4.83925	+	10.7364i	−0.366863	+	0.813928i
$175$	13.9471	−	8.49597i	1.05430	−	0.642235i
$176$	−0.302111	−	0.661530i	−0.0227725	−	0.0498647i
$177$	−9.79044	−	11.1867i	−0.735895	−	0.840843i
$178$	8.22798	+	2.41595i	0.616713	+	0.181083i
$179$	−13.3592	−	11.5758i	−0.998511	−	0.865215i	−0.00763206	−	0.999971i	$-0.502429\pi$
$179$	−13.3592	−	11.5758i	−0.998511	−	0.865215i	−0.990879	+	0.134756i	$0.956975\pi$
$180$	1.90384	−	6.43237i	0.141904	−	0.479441i
$181$	−18.4414	−	8.42192i	−1.37074	−	0.625997i	−0.412238	−	0.911076i	$-0.635253\pi$
$181$	−18.4414	−	8.42192i	−1.37074	−	0.625997i	−0.958504	+	0.285080i	$0.907980\pi$
$182$	4.77169	−	0.686066i	0.353701	−	0.0508546i
$183$	−1.18420	−	7.95724i	−0.0875389	−	0.588216i
$184$	−3.27614	+	3.50242i	−0.241520	+	0.258202i
$185$	−18.9942	+	16.0624i	−1.39648	+	1.18093i
$186$	−1.93392	−	6.46803i	−0.141802	−	0.474259i
$187$	1.14562	+	0.523186i	0.0837758	+	0.0382591i
$188$	0.284026	−	0.0833976i	0.0207147	−	0.00608239i
$189$	4.53979	−	16.3533i	0.330221	−	1.18953i
$190$	−5.33289	−	12.0595i	−0.386889	−	0.874887i
$191$	−0.401041	+	0.257733i	−0.0290183	+	0.0186489i	−0.555070	−	0.831804i	$-0.687308\pi$
$191$	−0.401041	+	0.257733i	−0.0290183	+	0.0186489i	0.526051	+	0.850453i	$0.323672\pi$
$192$	0.943600	+	1.45245i	0.0680984	+	0.104822i
$193$	2.50162	−	2.16767i	0.180070	−	0.156032i	−0.560162	−	0.828383i	$-0.689261\pi$
$193$	2.50162	−	2.16767i	0.180070	−	0.156032i	0.740232	+	0.672351i	$0.234716\pi$
$194$	11.2358	+	7.22084i	0.806687	+	0.518426i
$195$	4.34657	−	3.71262i	0.311265	−	0.265866i
$196$	−0.522035	+	3.63083i	−0.0372882	+	0.259345i
$197$	−2.16157	−	1.38916i	−0.154006	−	0.0989735i	0.461368	−	0.887209i	$-0.347359\pi$
$197$	−2.16157	−	1.38916i	−0.154006	−	0.0989735i	−0.615374	+	0.788235i	$0.710995\pi$
$198$	−1.84696	−	1.16136i	−0.131258	−	0.0825345i
$199$	8.19677	−	3.74334i	0.581053	−	0.265358i	−0.103130	−	0.994668i	$-0.532886\pi$
$199$	8.19677	−	3.74334i	0.581053	−	0.265358i	0.684184	+	0.729310i	$0.260159\pi$
$200$	1.96699	+	4.59684i	0.139087	+	0.325046i
$201$	−0.697248	−	0.0967381i	−0.0491801	−	0.00682338i
$202$	−4.21978	−	3.65646i	−0.296903	−	0.257268i
$203$	−6.25667	−	21.3083i	−0.439132	−	1.49555i
$204$	−2.88215	−	0.830841i	−0.201791	−	0.0581705i
$205$	−0.471720	+	0.531334i	−0.0329464	+	0.0371100i
$206$	18.3173			1.27622
$207$	−2.44766	+	14.1778i	−0.170124	+	0.985423i
$208$			1.47595i			0.102338i
$209$	−4.24492	+	0.610327i	−0.293627	+	0.0422172i
$210$	5.17317	+	11.5439i	0.356982	+	0.796603i
$211$	−15.4355	+	4.53227i	−1.06262	+	0.312014i	−0.765907	−	0.642951i	$-0.777710\pi$
$211$	−15.4355	+	4.53227i	−1.06262	+	0.312014i	−0.296716	+	0.954966i	$0.595892\pi$
$212$	−1.85884	−	1.61069i	−0.127666	−	0.110623i
$213$	1.91975	−	13.8367i	0.131539	−	0.948078i
$214$	5.55231	+	8.63957i	0.379548	+	0.590589i
$215$	18.7618	+	8.84268i	1.27954	+	0.603066i
$216$	4.75804	+	2.08832i	0.323743	+	0.142092i
$217$	10.7097	+	6.88270i	0.727021	+	0.467228i
$218$	−12.1003	−	1.73975i	−0.819533	−	0.117831i
$219$	−4.96843	+	0.0245299i	−0.335735	+	0.00165758i
$220$	1.61230	−	0.212038i	0.108701	−	0.0142956i
$221$	−1.67382	−	1.93169i	−0.112594	−	0.129940i
$222$	−10.4971	−	16.1579i	−0.704521	−	1.08445i
$223$	1.88085	+	2.92665i	0.125951	+	0.195983i	0.898502	−	0.438969i	$-0.144656\pi$
$223$	1.88085	+	2.92665i	0.125951	+	0.195983i	−0.772551	+	0.634952i	$0.781020\pi$
$224$	−3.13391	−	0.920200i	−0.209393	−	0.0614834i
$225$	12.5024	+	8.28798i	0.833491	+	0.552532i
$226$	2.66234	+	9.06711i	0.177097	+	0.603135i
$227$	18.4257	+	8.41476i	1.22296	+	0.558507i	0.919030	−	0.394188i	$-0.128974\pi$
$227$	18.4257	+	8.41476i	1.22296	+	0.558507i	0.303930	+	0.952695i	$0.401701\pi$
$228$	9.78579	−	2.92592i	0.648080	−	0.193774i
$229$			9.44144i			0.623908i	0.950097	+	0.311954i	$0.100983\pi$
$229$			9.44144i			0.623908i	−0.950097	+	0.311954i	$0.899017\pi$
$230$	−5.33897	−	9.30029i	−0.352041	−	0.613243i
$231$	4.06942	−	0.605616i	0.267748	−	0.0398466i
$232$	6.73005	−	0.967635i	0.441850	−	0.0635284i
$233$	4.97061	−	10.8841i	0.325636	−	0.713042i	−0.674035	−	0.738699i	$-0.735440\pi$
$233$	4.97061	−	10.8841i	0.325636	−	0.713042i	0.999671	+	0.0256568i	$0.00816769\pi$
$234$	2.43053	+	3.70112i	0.158889	+	0.241950i
$235$	−0.00796757	+	0.661866i	−0.000519747	+	0.0431754i
$236$	−2.41806	+	8.23516i	−0.157402	+	0.536063i
$237$	3.76978	+	4.30740i	0.244873	+	0.279796i
$238$	5.14518	−	2.34973i	0.333513	−	0.152310i
$239$	−15.5939	+	13.5122i	−1.00869	+	0.874034i	−0.992052	−	0.125828i	$-0.959841\pi$
$239$	−15.5939	+	13.5122i	−1.00869	+	0.874034i	−0.0166366	+	0.999862i	$0.505296\pi$
$240$	−3.72375	+	1.06473i	−0.240367	+	0.0687282i
$241$	−9.29277	−	1.33610i	−0.598600	−	0.0860657i	−0.163647	−	0.986519i	$-0.552326\pi$
$241$	−9.29277	−	1.33610i	−0.598600	−	0.0860657i	−0.434953	+	0.900453i	$0.643235\pi$
$242$	−1.49019	+	10.3645i	−0.0957933	+	0.666257i
$243$	15.3703	−	2.59865i	0.986007	−	0.166703i
$244$	−3.51024	+	3.04164i	−0.224720	+	0.194721i
$245$	−7.41950	−	3.49691i	−0.474014	−	0.223410i
$246$	−0.362461	−	0.414153i	−0.0231097	−	0.0264054i
$247$	8.35105	+	2.45209i	0.531365	+	0.156023i
$248$	−2.55243	+	2.94566i	−0.162079	+	0.187050i
$249$	−11.5336	−	24.9286i	−0.730913	−	1.57979i
$250$	−11.1168	+	1.19054i	−0.703086	+	0.0752962i
$251$	−3.51524	−	24.4491i	−0.221880	−	1.54321i	−0.730917	−	0.682466i	$-0.760908\pi$
$251$	−3.51524	−	24.4491i	−0.221880	−	1.54321i	0.509037	−	0.860745i	$-0.330002\pi$
$252$	−9.37402	+	2.85330i	−0.590508	+	0.179741i
$253$	−3.38143	+	0.854670i	−0.212589	+	0.0537327i
$254$			11.1184i			0.697628i
$255$	3.66611	−	5.61649i	0.229581	−	0.351718i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−1.94338	+	0.570628i	−0.121225	+	0.0355948i	−0.341782	−	0.939779i	$-0.611031\pi$
$257$	−1.94338	+	0.570628i	−0.121225	+	0.0355948i	0.220557	+	0.975374i	$0.429212\pi$
$258$	−8.61914	+	13.5584i	−0.536604	+	0.844106i
$259$	34.8634	+	10.2368i	2.16630	+	0.636084i
$260$	−3.15521	−	0.967857i	−0.195678	−	0.0600239i
$261$	15.2830	−	13.5093i	0.945992	−	0.836203i
$262$	9.80767	−	8.49840i	0.605920	−	0.525033i
$263$	10.8582	−	16.8957i	0.669547	−	1.04184i	−0.325796	−	0.945440i	$-0.605632\pi$
$263$	10.8582	−	16.8957i	0.669547	−	1.04184i	0.995343	−	0.0963952i	$-0.0307312\pi$
$264$	0.00621893	+	1.25962i	0.000382749	+	0.0775242i
$265$	4.66221	−	2.91752i	0.286397	−	0.179222i
$266$	−10.4132	+	16.2032i	−0.638472	+	0.993481i
$267$	−11.2730	−	9.67106i	−0.689895	−	0.591859i
$268$	0.168830	+	0.369686i	0.0103129	+	0.0225822i
$269$	7.98286	+	12.4216i	0.486723	+	0.757356i	0.994568	−	0.104093i	$-0.0331938\pi$
$269$	7.98286	+	12.4216i	0.486723	+	0.757356i	−0.507844	+	0.861449i	$0.669557\pi$
$270$	−7.58441	+	8.80209i	−0.461572	+	0.535678i
$271$	−5.87144	+	6.77600i	−0.356664	+	0.411613i	−0.905519	−	0.424305i	$-0.860518\pi$
$271$	−5.87144	+	6.77600i	−0.356664	+	0.411613i	0.548855	+	0.835918i	$0.315064\pi$
$272$	0.487896	+	1.66162i	0.0295830	+	0.100751i
$273$	−8.02310	−	2.31283i	−0.485580	−	0.139979i
$274$	2.32595	−	0.334422i	0.140516	−	0.0202032i
$275$	−0.603986	+	3.58574i	−0.0364217	+	0.216228i
$276$	7.66601	−	3.19880i	0.461439	−	0.192545i
$277$			32.6649i			1.96264i	0.192377	+	0.981321i	$0.438380\pi$
$277$			32.6649i			1.96264i	−0.192377	+	0.981321i	$0.561620\pi$
$278$	0.130513	+	0.907741i	0.00782767	+	0.0544427i
$279$	−1.54972	+	11.5899i	−0.0927796	+	0.693866i
$280$	4.02223	−	6.09611i	0.240374	−	0.364312i
$281$	−3.24036	+	3.73957i	−0.193304	+	0.223084i	−0.844125	−	0.536147i	$-0.819879\pi$
$281$	−3.24036	+	3.73957i	−0.193304	+	0.223084i	0.650821	+	0.759231i	$0.274425\pi$
$282$	−0.507851	−	0.0704607i	−0.0302421	−	0.00419587i
$283$	−7.79627	+	5.01036i	−0.463440	+	0.297835i	−0.751447	−	0.659793i	$-0.770644\pi$
$283$	−7.79627	+	5.01036i	−0.463440	+	0.297835i	0.288007	+	0.957628i	$0.407007\pi$
$284$	−7.33634	+	3.35039i	−0.435332	+	0.198809i
$285$	−0.162163	+	22.8383i	−0.00960569	+	1.35282i
$286$	−0.580315	+	0.902987i	−0.0343147	+	0.0533948i
$287$	1.02729	+	0.147702i	0.0606388	+	0.00871854i
$288$	−0.456244	−	2.96510i	−0.0268845	−	0.174720i
$289$	11.7784	+	7.56950i	0.692845	+	0.445265i
$290$	−2.34469	+	15.0217i	−0.137685	+	0.882106i
$291$	−12.6028	−	19.3991i	−0.738789	−	1.13719i
$292$	1.55086	+	2.41319i	0.0907572	+	0.141221i
$293$	6.42750	−	21.8900i	0.375498	−	1.27883i	−0.527636	−	0.849471i	$-0.676921\pi$
$293$	6.42750	−	21.8900i	0.375498	−	1.27883i	0.903134	−	0.429359i	$-0.141260\pi$
$294$	3.40851	−	5.36176i	0.198788	−	0.312704i
$295$	−16.0191	−	10.5695i	−0.932668	−	0.615377i
$296$	−4.62131	+	10.1192i	−0.268608	+	0.588169i
$297$	2.08989	+	3.14841i	0.121268	+	0.182689i
$298$	−10.1916			−0.590383
$299$	6.96298	+	1.27302i	0.402679	+	0.0736207i
$300$	0.165728	−	8.65867i	0.00956833	−	0.499908i
$301$	−4.31165	−	29.9882i	−0.248520	−	1.72849i
$302$	8.77208	−	19.2082i	0.504776	−	1.10531i
$303$	4.06087	+	8.77713i	0.233291	+	0.504233i
$304$	−4.45663	−	3.86169i	−0.255605	−	0.221483i
$305$	−4.20042	−	9.49858i	−0.240515	−	0.543887i
$306$	3.95975	+	3.36327i	0.226364	+	0.192265i
$307$	−16.0568	+	7.33288i	−0.916408	+	0.418509i	−0.817066	−	0.576544i	$-0.804401\pi$
$307$	−16.0568	+	7.33288i	−0.916408	+	0.418509i	−0.0993417	+	0.995053i	$0.531674\pi$
$308$	−1.55553	−	1.79518i	−0.0886344	−	0.102290i
$309$	−28.9241	−	13.0370i	−1.64543	−	0.741648i
$310$	−4.62333	−	7.38809i	−0.262588	−	0.419615i
$311$	22.4582	+	3.22901i	1.27349	+	0.183100i	0.745704	−	0.666277i	$-0.232113\pi$
$311$	22.4582	+	3.22901i	1.27349	+	0.183100i	0.527786	+	0.849377i	$0.323022\pi$
$312$	1.05048	−	2.33061i	0.0594717	−	0.131945i
$313$	−6.80241	−	7.85039i	−0.384495	−	0.443731i	0.530202	−	0.847871i	$-0.322116\pi$
$313$	−6.80241	−	7.85039i	−0.384495	−	0.443731i	−0.914697	+	0.404141i	$0.867571\pi$
$314$	−6.66696	−	14.5986i	−0.376238	−	0.823847i
$315$	0.0473977	−	21.9104i	0.00267056	−	1.23451i
$316$	0.931067	−	3.17092i	0.0523766	−	0.178378i
$317$	1.99686	−	2.30450i	0.112155	−	0.129434i	−0.696896	−	0.717172i	$-0.745436\pi$
$317$	1.99686	−	2.30450i	0.112155	−	0.129434i	0.809051	+	0.587738i	$0.199982\pi$
$318$	1.78884	+	3.86638i	0.100313	+	0.216816i
$319$	4.49791	+	2.05413i	0.251835	+	0.115009i
$320$	1.67216	+	1.48455i	0.0934765	+	0.0829888i
$321$	−2.61838	−	17.5942i	−0.146144	−	0.982011i
$322$	−7.04420	+	13.9910i	−0.392558	+	0.779686i
$323$	10.2122			0.568221
$324$	−6.02691	−	6.68404i	−0.334828	−	0.371335i
$325$	4.13808	−	6.11038i	0.229539	−	0.338943i
$326$	−4.13752	−	14.0911i	−0.229156	−	0.780433i
$327$	17.8688	+	11.3593i	0.988148	+	0.628172i
$328$	−0.0895214	+	0.304882i	−0.00494299	+	0.0168343i
$329$	0.813370	−	0.522721i	0.0448425	−	0.0288186i
$330$	−2.69683	−	0.812705i	−0.148456	−	0.0447379i
$331$	−20.2113	−	23.3251i	−1.11091	−	1.28206i	−0.955753	−	0.294172i	$-0.904956\pi$
$331$	−20.2113	−	23.3251i	−1.11091	−	1.28206i	−0.155160	−	0.987889i	$-0.549589\pi$
$332$	−8.57367	+	13.3409i	−0.470541	+	0.732176i
$333$	5.07551	+	32.9855i	0.278136	+	1.80759i
$334$	0.611894	−	4.25582i	0.0334814	−	0.232868i
$335$	−0.901008	+	0.118494i	−0.0492273	+	0.00647401i
$336$	4.29370	+	3.68356i	0.234241	+	0.200955i
$337$	−6.43537	−	14.0915i	−0.350557	−	0.767613i	−0.999974	−	0.00718065i	$-0.997714\pi$
$337$	−6.43537	−	14.0915i	−0.350557	−	0.767613i	0.649417	−	0.760432i	$-0.275013\pi$
$338$	−9.10369	+	5.85059i	−0.495176	+	0.318230i
$339$	2.24935	−	16.2124i	0.122168	−	0.880537i
$340$	−3.87207	−	0.0466122i	−0.209993	−	0.00252790i
$341$	−2.71976	+	0.798593i	−0.147283	+	0.0432463i
$342$	−17.5348	−	2.34465i	−0.948175	−	0.126784i
$343$	−1.54874	−	10.7717i	−0.0836240	−	0.581618i
$344$	9.27575			0.500115
$345$	1.81124	+	18.4857i	0.0975137	+	0.995234i
$346$	−15.9827			−0.859233
$347$	−3.43226	−	23.8719i	−0.184254	−	1.28151i	−0.846566	−	0.532284i	$-0.821334\pi$
$347$	−3.43226	−	23.8719i	−0.184254	−	1.28151i	0.662312	−	0.749228i	$-0.269575\pi$
$348$	−11.3159	−	3.26204i	−0.606594	−	0.174864i
$349$	−4.83714	+	1.42031i	−0.258926	+	0.0760276i	−0.408619	−	0.912705i	$-0.633990\pi$
$349$	−4.83714	+	1.42031i	−0.258926	+	0.0760276i	0.149693	+	0.988733i	$0.452171\pi$
$350$	10.3944	+	12.5961i	0.555603	+	0.673289i
$351$	−1.20376	−	7.57419i	−0.0642519	−	0.404280i
$352$	0.611802	−	0.393181i	0.0326092	−	0.0209566i
$353$	6.56143	+	14.3675i	0.349230	+	0.764707i	0.999985	+	0.00541925i	$0.00172501\pi$
$353$	6.56143	+	14.3675i	0.349230	+	0.764707i	−0.650756	+	0.759287i	$0.725548\pi$
$354$	9.67950	−	11.2828i	0.514460	−	0.599675i
$355$	−2.35149	−	17.8803i	−0.124804	−	0.948988i
$356$	−1.22040	+	8.48806i	−0.0646810	+	0.449866i
$357$	−9.79693	+	0.0483690i	−0.518509	+	0.00255996i
$358$	9.55675	−	14.8706i	0.505090	−	0.785935i
$359$	−1.03639	−	1.19605i	−0.0546984	−	0.0631254i	0.727741	−	0.685852i	$-0.240570\pi$
$359$	−1.03639	−	1.19605i	−0.0546984	−	0.0631254i	−0.782439	+	0.622727i	$0.786025\pi$
$360$	6.63784	+	0.969039i	0.349845	+	0.0510728i
$361$	−13.2701	+	8.52818i	−0.698427	+	0.448852i
$362$	5.71171	−	19.4523i	0.300201	−	1.02239i
$363$	9.72988	−	15.3056i	0.510686	−	0.803336i
$364$	1.35817	+	4.62549i	0.0711872	+	0.242441i
$365$	−6.17577	+	1.73290i	−0.323255	+	0.0907042i
$366$	7.70771	−	2.30458i	0.402889	−	0.120463i
$367$	−34.0866			−1.77931			−0.889653	−	0.456637i	$-0.849054\pi$
$367$	−34.0866			−1.77931			−0.889653	+	0.456637i	$0.849054\pi$
$368$	−3.93301	−	2.74434i	−0.205022	−	0.143059i
$369$	0.277582	+	0.911949i	0.0144504	+	0.0474742i
$370$	−18.6020	−	16.5149i	−0.967073	−	0.858571i
$371$	−7.30760	−	3.33727i	−0.379392	−	0.173262i
$372$	6.12697	−	2.83473i	0.317668	−	0.146974i
$373$	7.49073	−	8.64477i	0.387855	−	0.447609i	−0.527923	−	0.849292i	$-0.677029\pi$
$373$	7.49073	−	8.64477i	0.387855	−	0.447609i	0.915779	+	0.401683i	$0.131575\pi$
$374$	−0.354822	+	1.20841i	−0.0183474	+	0.0624856i
$375$	18.4014	+	6.03224i	0.950245	+	0.311503i
$376$	0.122970	+	0.269266i	0.00634168	+	0.0138863i
$377$	−6.57175	−	7.58421i	−0.338462	−	0.390607i
$378$	16.8329	+	2.16626i	0.865793	+	0.111420i
$379$	26.4513	+	3.80312i	1.35871	+	0.195353i	0.782858	−	0.622200i	$-0.213761\pi$
$379$	26.4513	+	3.80312i	1.35871	+	0.195353i	0.575853	+	0.817553i	$0.304670\pi$
$380$	11.1778	−	6.99486i	0.573409	−	0.358829i
$381$	7.91330	−	17.5566i	0.405410	−	0.899451i
$382$	−0.312184	−	0.360280i	−0.0159727	−	0.0184335i
$383$	11.7553	−	5.36847i	0.600668	−	0.274316i	−0.0917849	−	0.995779i	$-0.529257\pi$
$383$	11.7553	−	5.36847i	0.600668	−	0.274316i	0.692453	+	0.721463i	$0.256530\pi$
$384$	−1.30338	+	1.14070i	−0.0665129	+	0.0582111i
$385$	4.85768	−	2.14814i	0.247570	−	0.109480i
$386$	2.50162	+	2.16767i	0.127329	+	0.110331i
$387$	23.2601	−	15.2750i	1.18238	−	0.776470i
$388$	−5.54831	+	12.1491i	−0.281673	+	0.616778i
$389$	−3.82143	−	26.5786i	−0.193754	−	1.34759i	−0.821962	−	0.569543i	$-0.807120\pi$
$389$	−3.82143	−	26.5786i	−0.193754	−	1.34759i	0.628208	−	0.778046i	$-0.283789\pi$
$390$	4.29342	+	3.77397i	0.217406	+	0.191102i
$391$	8.25973	−	0.868547i	0.417713	−	0.0439243i
$392$	−3.66817			−0.185271
$393$	−21.5355	+	6.43905i	−1.08632	+	0.324807i
$394$	1.06740	−	2.33727i	0.0537746	−	0.117750i
$395$	6.16810	+	4.06973i	0.310351	+	0.204770i
$396$	0.886692	−	1.99344i	0.0445580	−	0.100174i
$397$	6.70727	−	22.8429i	0.336628	−	1.14645i	−0.601127	−	0.799154i	$-0.705281\pi$
$397$	6.70727	−	22.8429i	0.336628	−	1.14645i	0.937755	−	0.347297i	$-0.112901\pi$
$398$	4.87176	+	7.58060i	0.244199	+	0.379981i
$399$	27.9754	−	18.1745i	1.40052	−	0.909861i
$400$	−4.27012	+	2.60116i	−0.213506	+	0.130058i
$401$	−27.8844	−	17.9202i	−1.39248	−	0.894893i	−0.392787	−	0.919629i	$-0.628489\pi$
$401$	−27.8844	−	17.9202i	−1.39248	−	0.894893i	−0.999694	+	0.0247360i	$0.992125\pi$
$402$	−0.00347535	−	0.703919i	−0.000173335	−	0.0351083i
$403$	5.69419	+	0.818702i	0.283648	+	0.0407824i
$404$	3.01870	−	4.69720i	0.150186	−	0.233694i
$405$	18.2410	−	8.50097i	0.906402	−	0.422417i
$406$	20.2010	−	9.22547i	1.00256	−	0.457853i
$407$	−6.80602	+	4.37397i	−0.337362	+	0.216809i
$408$	0.412212	−	2.97105i	0.0204075	−	0.147089i
$409$	−0.427761	+	0.493663i	−0.0211514	+	0.0244101i	−0.766227	−	0.642570i	$-0.777868\pi$
$409$	−0.427761	+	0.493663i	−0.0211514	+	0.0244101i	0.745075	+	0.666980i	$0.232414\pi$
$410$	−0.593058	−	0.391302i	−0.0292891	−	0.0193250i
$411$	−3.91085	−	1.12739i	−0.192908	−	0.0556098i
$412$	2.60682	+	18.1308i	0.128429	+	0.893241i
$413$			28.0334i			1.37943i
$414$	−14.3818	−	0.405043i	−0.706827	−	0.0199068i
$415$	−22.8973	−	27.0767i	−1.12398	−	1.32914i
$416$	−1.46092	+	0.210049i	−0.0716277	+	0.0102985i
$417$	0.439980	−	1.52627i	0.0215459	−	0.0747417i
$418$	−1.20823	−	4.11485i	−0.0590965	−	0.201264i
$419$	−17.0320	+	19.6560i	−0.832069	+	0.960259i	−0.999672	−	0.0255957i	$-0.991852\pi$
$419$	−17.0320	+	19.6560i	−0.832069	+	0.960259i	0.167603	+	0.985855i	$0.446397\pi$
$420$	−10.6902	+	6.76337i	−0.521626	+	0.330019i
$421$	−1.48052	−	2.30373i	−0.0721561	−	0.112277i	0.803300	−	0.595574i	$-0.203075\pi$
$421$	−1.48052	−	2.30373i	−0.0721561	−	0.112277i	−0.875456	+	0.483297i	$0.839439\pi$
$422$	−6.68284	−	14.6334i	−0.325315	−	0.712342i
$423$	0.751780	+	0.472716i	0.0365528	+	0.0229842i
$424$	1.32976	−	2.06915i	0.0645788	−	0.100487i
$425$	2.63877	−	8.24697i	0.127999	−	0.400037i
$426$	13.9691	−	0.0689676i	0.676806	−	0.00334149i
$427$	−8.20186	+	12.7623i	−0.396916	+	0.617613i
$428$	−7.76145	+	6.72534i	−0.375164	+	0.325081i
$429$	1.55904	−	1.01284i	0.0752711	−	0.0489006i
$430$	−6.08260	+	19.8293i	−0.293329	+	0.956251i
$431$	−3.54845	−	1.04192i	−0.170923	−	0.0501875i	0.195151	−	0.980773i	$-0.437480\pi$
$431$	−3.54845	−	1.04192i	−0.170923	−	0.0501875i	−0.366074	+	0.930586i	$0.619298\pi$
$432$	−1.38992	+	5.00681i	−0.0668727	+	0.240890i
$433$	−26.7068	+	7.84183i	−1.28345	+	0.376854i	−0.851172	−	0.524887i	$-0.824107\pi$
$433$	−26.7068	+	7.84183i	−1.28345	+	0.376854i	−0.432276	+	0.901742i	$0.642289\pi$
$434$	−5.28849	+	11.5802i	−0.253856	+	0.555867i
$435$	14.3939	−	22.0514i	0.690132	−	1.05729i
$436$		−	12.2247i		−	0.585456i
$437$	−22.0619	+	17.6940i	−1.05537	+	0.846419i
$438$	−0.731361	−	4.91437i	−0.0349458	−	0.234818i
$439$	4.14197	+	28.8080i	0.197686	+	1.37493i	0.810978	+	0.585077i	$0.198936\pi$
$439$	4.14197	+	28.8080i	0.197686	+	1.37493i	−0.613292	+	0.789856i	$0.710155\pi$
$440$	0.439333	+	1.56571i	0.0209444	+	0.0746424i
$441$	−9.19839	+	6.04061i	−0.438018	+	0.287648i
$442$	1.67382	−	1.93169i	0.0796156	−	0.0918814i
$443$	−32.1145	−	9.42968i	−1.52581	−	0.448017i	−0.592043	−	0.805906i	$-0.701679\pi$
$443$	−32.1145	−	9.42968i	−1.52581	−	0.448017i	−0.933764	+	0.357889i	$0.883497\pi$
$444$	14.4995	−	12.6898i	0.688117	−	0.602231i
$445$	−17.3451	−	8.17498i	−0.822236	−	0.387531i
$446$	−2.62919	+	2.27821i	−0.124496	+	0.107876i
$447$	16.0932	+	7.25369i	0.761180	+	0.343088i
$448$	0.464831	−	3.23297i	0.0219612	−	0.152744i
$449$	38.0510	+	5.47090i	1.79574	+	0.258188i	0.957770	−	0.287534i	$-0.0928354\pi$
$449$	38.0510	+	5.47090i	1.79574	+	0.258188i	0.837966	+	0.545722i	$0.183745\pi$
$450$	−6.42435	+	13.5546i	−0.302847	+	0.638971i
$451$	−0.174643	+	0.151329i	−0.00822363	+	0.00712581i
$452$	−8.59593	+	3.92563i	−0.404319	+	0.184646i
$453$	−27.5227	+	24.0875i	−1.29313	+	1.13173i
$454$	−5.70685	+	19.4357i	−0.267836	+	0.912164i
$455$	−10.7788	−	0.129755i	−0.505317	−	0.00608303i
$456$	4.28880	+	9.26978i	0.200842	+	0.434097i
$457$	3.10118	−	6.79064i	0.145067	−	0.317653i	−0.823125	−	0.567860i	$-0.807771\pi$
$457$	3.10118	−	6.79064i	0.145067	−	0.317653i	0.968192	+	0.250207i	$0.0804988\pi$
$458$	−9.34534	+	1.34366i	−0.436679	+	0.0627850i
$459$	−3.85895	−	8.12909i	−0.180120	−	0.379434i
$460$	8.44581	−	6.60819i	0.393788	−	0.308109i
$461$			23.1040i			1.07606i	0.842925	+	0.538030i	$0.180831\pi$
$461$			23.1040i			1.07606i	−0.842925	+	0.538030i	$0.819169\pi$
$462$	1.17859	+	3.94181i	0.0548330	+	0.183390i
$463$	9.46248	+	4.32137i	0.439759	+	0.200831i	0.622975	−	0.782242i	$-0.285924\pi$
$463$	9.46248	+	4.32137i	0.439759	+	0.200831i	−0.183217	+	0.983073i	$0.558651\pi$
$464$	1.91557	+	6.52384i	0.0889282	+	0.302862i
$465$	2.04218	+	14.9568i	0.0947039	+	0.693606i
$466$	11.4807	+	3.37105i	0.531834	+	0.156161i
$467$	16.4551	+	25.6047i	0.761453	+	1.18484i	0.978007	+	0.208573i	$0.0668819\pi$
$467$	16.4551	+	25.6047i	0.761453	+	1.18484i	−0.216554	+	0.976271i	$0.569482\pi$
$468$	−3.31754	+	2.93252i	−0.153354	+	0.135556i
$469$	0.869283	+	1.00321i	0.0401397	+	0.0463237i
$470$	−0.656263	+	0.0863068i	−0.0302711	+	0.00398104i
$471$	0.137239	+	27.7972i	0.00632364	+	1.28083i
$472$	−8.49547	−	1.22146i	−0.391036	−	0.0562224i
$473$	5.67492	+	3.64705i	0.260933	+	0.167692i
$474$	−3.72706	+	4.34441i	−0.171190	+	0.199545i
$475$	7.62340	+	28.4823i	0.349786	+	1.30686i
$476$	3.05804	+	4.75841i	0.140165	+	0.218101i
$477$	−0.0728587	−	7.37843i	−0.00333597	−	0.337835i
$478$	−15.5939	−	13.5122i	−0.713251	−	0.618035i
$479$	11.3558	−	3.33437i	0.518861	−	0.152351i	−0.0118082	−	0.999930i	$-0.503759\pi$
$479$	11.3558	−	3.33437i	0.518861	−	0.152351i	0.530669	+	0.847579i	$0.321941\pi$
$480$	−1.58384	−	3.53432i	−0.0722921	−	0.161319i
$481$	16.2521	−	2.33670i	0.741033	−	0.106544i
$482$		−	9.38833i		−	0.427627i
$483$	21.0811	−	17.0790i	0.959221	−	0.777122i
$484$	−10.4711			−0.475959
$485$	−22.3335	−	19.8277i	−1.01411	−	0.900331i
$486$	4.75962	+	14.8441i	0.215901	+	0.673340i
$487$	−0.399122	−	1.35928i	−0.0180859	−	0.0615951i	0.949956	−	0.312385i	$-0.101128\pi$
$487$	−0.399122	−	1.35928i	−0.0180859	−	0.0615951i	−0.968042	+	0.250790i	$0.919310\pi$
$488$	−3.51024	−	3.04164i	−0.158901	−	0.137688i
$489$	−3.49569	+	25.1955i	−0.158081	+	1.13938i
$490$	2.40541	−	7.84164i	0.108666	−	0.354249i
$491$	−12.9167	+	5.89886i	−0.582922	+	0.266212i	−0.684974	−	0.728567i	$-0.740187\pi$
$491$	−12.9167	+	5.89886i	−0.582922	+	0.266212i	0.102052	+	0.994779i	$0.467459\pi$
$492$	0.358354	−	0.417712i	0.0161559	−	0.0188319i
$493$	−9.90554	−	6.36591i	−0.446123	−	0.286706i
$494$	−1.23865	+	8.61502i	−0.0557296	+	0.387608i
$495$	3.68004	+	3.20274i	0.165405	+	0.143952i
$496$	−3.27893	−	2.10724i	−0.147228	−	0.0946178i
$497$	−19.9084	+	17.2507i	−0.893014	+	0.773801i
$498$	23.0335	−	14.9639i	1.03216	−	0.670550i
$499$	27.0882	−	17.4085i	1.21263	−	0.779312i	0.231536	−	0.972826i	$-0.425625\pi$
$499$	27.0882	−	17.4085i	1.21263	−	0.779312i	0.981098	+	0.193514i	$0.0619885\pi$
$500$	−2.76050	−	10.8342i	−0.123453	−	0.484520i
$501$	−3.99522	+	6.28470i	−0.178493	+	0.280779i
$502$	23.6999	−	6.95893i	1.05778	−	0.310592i
$503$	−36.7413	−	16.7792i	−1.63821	−	0.748146i	−0.638444	−	0.769669i	$-0.720421\pi$
$503$	−36.7413	−	16.7792i	−1.63821	−	0.748146i	−0.999768	+	0.0215221i	$0.993149\pi$
$504$	−4.15832	−	8.87254i	−0.185226	−	0.395214i
$505$	8.06192	+	9.53345i	0.358751	+	0.424233i
$506$	−1.32720	−	3.22538i	−0.0590012	−	0.143386i
$507$	18.5394	−	2.75905i	0.823361	−	0.122534i
$508$	−11.0052	+	1.58231i	−0.488276	+	0.0702035i
$509$	17.8004	+	8.12919i	0.788991	+	0.360320i	0.768811	−	0.639476i	$-0.220849\pi$
$509$	17.8004	+	8.12919i	0.788991	+	0.360320i	0.0201799	+	0.999796i	$0.493576\pi$
$510$	6.08107	+	2.82948i	0.269274	+	0.125292i
$511$	7.08087	+	6.13561i	0.313239	+	0.271423i
$512$	0.959493	+	0.281733i	0.0424040	+	0.0124509i
$513$	26.0198	+	16.1825i	1.14880	+	0.714473i
$514$	−0.841392	−	1.84239i	−0.0371122	−	0.0812644i
$515$	−40.4686	−	6.31661i	−1.78326	−	0.278343i
$516$	−14.6470	−	6.60185i	−0.644797	−	0.290630i
$517$	−0.0306373	+	0.213087i	−0.00134743	+	0.00937156i
$518$	−5.17104	+	35.9654i	−0.227202	+	1.58023i
$519$	25.2376	+	11.3754i	1.10781	+	0.499324i
$520$	0.508972	−	3.26083i	0.0223199	−	0.142997i
$521$	13.6630	+	29.9179i	0.598588	+	1.31073i	0.930111	+	0.367279i	$0.119710\pi$
$521$	13.6630	+	29.9179i	0.598588	+	1.31073i	−0.331522	+	0.943447i	$0.607562\pi$
$522$	15.5468	+	13.2048i	0.680463	+	0.577960i
$523$	25.0573	+	7.35747i	1.09568	+	0.321720i	0.779134	−	0.626858i	$-0.215659\pi$
$523$	25.0573	+	7.35747i	1.09568	+	0.321720i	0.316544	+	0.948578i	$0.397478\pi$
$524$	9.80767	+	8.49840i	0.428450	+	0.371254i
$525$	−7.44832	−	27.2880i	−0.325072	−	1.19095i
$526$	18.2690	+	8.34319i	0.796568	+	0.363780i
$527$	6.68115	−	0.960605i	0.291036	−	0.0418446i
$528$	−1.24591	+	0.185418i	−0.0542214	+	0.00806929i
$529$	−16.3391	+	16.1875i	−0.710395	+	0.703803i
$530$	3.55133	+	4.19954i	0.154260	+	0.182417i
$531$	−23.3149	+	10.9271i	−1.01178	+	0.474194i
$532$	−17.5202	−	8.00121i	−0.759597	−	0.346897i
$533$	0.449989	−	0.132129i	0.0194912	−	0.00572313i
$534$	7.96831	−	12.5346i	0.344823	−	0.542424i
$535$	−9.28751	−	21.0022i	−0.401534	−	0.908005i
$536$	−0.341896	+	0.219723i	−0.0147677	+	0.00949060i
$537$	−25.6746	+	16.6797i	−1.10794	+	0.719784i
$538$	−11.1591	+	9.66937i	−0.481101	+	0.416876i
$539$	−2.24419	−	1.44226i	−0.0966643	−	0.0621224i
$540$	−9.79187	−	6.25454i	−0.421375	−	0.269153i
$541$	−2.56904	+	17.8681i	−0.110452	+	0.768209i	0.857030	+	0.515267i	$0.172307\pi$
$541$	−2.56904	+	17.8681i	−0.110452	+	0.768209i	−0.967481	+	0.252942i	$0.918602\pi$
$542$	−7.54262	−	4.84735i	−0.323983	−	0.208212i
$543$	−22.8640	+	26.6512i	−0.981187	+	1.14371i
$544$	−1.57527	+	0.719403i	−0.0675392	+	0.0308441i
$545$	26.1334	+	8.01638i	1.11943	+	0.343384i
$546$	1.14748	−	8.27058i	0.0491077	−	0.353948i
$547$	−8.62440	−	7.47309i	−0.368753	−	0.319526i	0.450697	−	0.892677i	$-0.351175\pi$
$547$	−8.62440	−	7.47309i	−0.368753	−	0.319526i	−0.819450	+	0.573151i	$0.805721\pi$
$548$	0.662036	+	2.25469i	0.0282808	+	0.0963154i
$549$	−13.8112	−	1.84675i	−0.589448	−	0.0788174i
$550$	−3.63520	−	0.0875341i	−0.155005	−	0.00373247i
$551$	40.0950			1.70810
$552$	4.25723	+	7.13274i	0.181200	+	0.303590i
$553$		−	10.7942i		−	0.459014i
$554$	−32.3324	+	4.64870i	−1.37367	+	0.197504i
$555$	17.6195	+	39.3178i	0.747907	+	1.66895i
$556$	−0.879927	+	0.258370i	−0.0373172	+	0.0109573i
$557$	15.3807	+	13.3275i	0.651703	+	0.564704i	0.916715	−	0.399541i	$-0.130831\pi$
$557$	15.3807	+	13.3275i	0.651703	+	0.564704i	−0.265012	+	0.964245i	$0.585376\pi$
$558$	−11.6924	+	0.115457i	−0.494980	+	0.00488770i
$559$	−7.40165	−	11.5172i	−0.313056	−	0.487125i
$560$	6.60648	+	3.11373i	0.279175	+	0.131579i
$561$	1.42035	−	1.65562i	0.0599674	−	0.0699004i
$562$	−4.16266	−	2.67518i	−0.175591	−	0.112846i
$563$	10.7639	+	1.54761i	0.453643	+	0.0652241i	0.365350	−	0.930870i	$-0.380949\pi$
$563$	10.7639	+	1.54761i	0.453643	+	0.0652241i	0.0882938	+	0.996094i	$0.471859\pi$
$564$	−0.00253133	−	0.512710i	−0.000106588	−	0.0215890i
$565$	−2.75522	−	20.9502i	−0.115913	−	0.881382i
$566$	−6.06889	−	7.00387i	−0.255094	−	0.294395i
$567$	−25.0385	−	15.4012i	−1.05152	−	0.646790i
$568$	−4.36036	−	6.78485i	−0.182957	−	0.284686i
$569$	−25.0014	−	7.34108i	−1.04811	−	0.307754i	−0.288059	−	0.957613i	$-0.593010\pi$
$569$	−25.0014	−	7.34108i	−1.04811	−	0.307754i	−0.760055	+	0.649859i	$0.774828\pi$
$570$	−22.6289	+	3.08971i	−0.947820	+	0.129414i
$571$	−0.973707	−	3.31614i	−0.0407484	−	0.138776i	0.936607	−	0.350383i	$-0.113949\pi$
$571$	−0.973707	−	3.31614i	−0.0407484	−	0.138776i	−0.977355	+	0.211607i	$0.932130\pi$
$572$	−0.976383	−	0.445899i	−0.0408246	−	0.0186440i
$573$	0.236535	+	0.791095i	0.00988140	+	0.0330485i
$574$			1.03785i			0.0433190i
$575$	8.58831	+	22.3884i	0.358157	+	0.933661i
$576$	2.86999	−	0.873579i	0.119583	−	0.0363991i
$577$	28.9240	−	4.15865i	1.20412	−	0.173127i	0.489100	−	0.872227i	$-0.337325\pi$
$577$	28.9240	−	4.15865i	1.20412	−	0.173127i	0.715023	+	0.699101i	$0.246416\pi$
$578$	−5.81622	+	12.7357i	−0.241923	+	0.529737i
$579$	−2.40741	−	5.20336i	−0.100049	−	0.216244i
$580$	−15.2025	−	0.183009i	−0.631250	−	0.00759902i
$581$	−14.5928	+	49.6987i	−0.605413	+	2.06185i
$582$	17.4081	−	15.2353i	0.721587	−	0.631523i
$583$	1.62710	−	0.743071i	0.0673875	−	0.0307749i
$584$	−2.16791	+	1.87851i	−0.0897088	+	0.0777331i
$585$	−4.09351	−	9.01510i	−0.169246	−	0.372728i
$586$	22.5820	+	3.24680i	0.932852	+	0.134124i
$587$	−0.787458	+	5.47689i	−0.0325019	+	0.226056i	−0.999598	−	0.0283562i	$-0.990973\pi$
$587$	−0.787458	+	5.47689i	−0.0325019	+	0.226056i	0.967096	+	0.254412i	$0.0818818\pi$
$588$	5.79227	+	2.61076i	0.238869	+	0.107666i
$589$	−17.3705	+	15.0516i	−0.715737	+	0.620190i
$590$	8.18212	−	17.3602i	0.336852	−	0.714709i
$591$	−3.34900	+	2.93100i	−0.137759	+	0.120565i
$592$	−10.6739	−	3.13415i	−0.438696	−	0.128813i
$593$	−21.7749	+	25.1296i	−0.894189	+	1.03195i	0.105108	+	0.994461i	$0.466481\pi$
$593$	−21.7749	+	25.1296i	−0.894189	+	1.03195i	−0.999297	+	0.0374879i	$0.988064\pi$
$594$	−2.81894	+	2.51668i	−0.115663	+	0.103261i
$595$	−12.1776	+	3.41700i	−0.499234	+	0.140083i
$596$	−1.45041	−	10.0879i	−0.0594113	−	0.413215i
$597$	−2.29745	−	15.4376i	−0.0940282	−	0.631820i
$598$	−0.269129	+	7.07327i	−0.0110055	+	0.289248i
$599$			17.0942i			0.698449i	0.937039	+	0.349224i	$0.113555\pi$
$599$			17.0942i			0.698449i	−0.937039	+	0.349224i	$0.886445\pi$
$600$	8.59412	−	1.06822i	0.350854	−	0.0436097i
$601$	4.53694	−	9.93452i	0.185066	−	0.405237i	−0.794246	−	0.607597i	$-0.792134\pi$
$601$	4.53694	−	9.93452i	0.185066	−	0.405237i	0.979311	+	0.202359i	$0.0648609\pi$
$602$	29.0694	−	8.53554i	1.18478	−	0.347883i
$603$	−0.495514	+	1.11400i	−0.0201789	+	0.0453658i
$604$	20.2611	+	5.94918i	0.824411	+	0.242069i
$605$	6.86646	−	22.3846i	0.279161	−	0.910065i
$606$	−8.10987	+	5.26865i	−0.329441	+	0.214024i
$607$	13.4570	−	11.6605i	0.546202	−	0.473287i	−0.337507	−	0.941323i	$-0.609584\pi$
$607$	13.4570	−	11.6605i	0.546202	−	0.473287i	0.883709	+	0.468036i	$0.155038\pi$
$608$	3.18814	−	4.96084i	0.129296	−	0.201189i
$609$	−38.4647	+	0.189906i	−1.55867	+	0.00769537i
$610$	8.80412	−	5.50945i	0.356468	−	0.223071i
$611$	0.236209	−	0.367548i	0.00955598	−	0.0148694i
$612$	−2.76550	+	4.39809i	−0.111789	+	0.177782i
$613$	16.4861	+	36.0995i	0.665867	+	1.45805i	0.876952	+	0.480577i	$0.159573\pi$
$613$	16.4861	+	36.0995i	0.665867	+	1.45805i	−0.211085	+	0.977468i	$0.567700\pi$
$614$	−9.54336	−	14.8498i	−0.385138	−	0.599287i
$615$	0.657973	+	1.03999i	0.0265320	+	0.0419364i
$616$	1.55553	−	1.79518i	0.0626740	−	0.0723297i
$617$	−7.78003	−	26.4963i	−0.313212	−	1.06670i	−0.954205	−	0.299155i	$-0.903295\pi$
$617$	−7.78003	−	26.4963i	−0.313212	−	1.06670i	0.640992	−	0.767547i	$-0.278523\pi$
$618$	8.78797	−	30.4850i	0.353504	−	1.22629i
$619$	12.4756	−	1.79372i	0.501437	−	0.0720958i	0.113045	−	0.993590i	$-0.463940\pi$
$619$	12.4756	−	1.79372i	0.501437	−	0.0720958i	0.388392	+	0.921494i	$0.373030\pi$
$620$	6.65492	−	5.62771i	0.267268	−	0.226014i
$621$	22.4215	+	10.8756i	0.899742	+	0.436422i
$622$			22.6892i			0.909754i
$623$	3.98609	+	27.7238i	0.159699	+	1.11073i
$624$	2.45639	+	0.708107i	0.0983342	+	0.0283469i
$625$	24.9710	+	1.20328i	0.998841	+	0.0481313i
$626$	6.80241	−	7.85039i	0.271879	−	0.313765i
$627$	−1.02081	+	7.35755i	−0.0407670	+	0.293832i
$628$	13.5012	−	8.67670i	0.538757	−	0.346238i
$629$	17.5242	−	8.00303i	0.698736	−	0.319102i
$630$	21.6941	−	3.07126i	0.864315	−	0.122362i
$631$	24.5281	−	38.1665i	0.976449	−	1.51938i	0.126872	−	0.991919i	$-0.459506\pi$
$631$	24.5281	−	38.1665i	0.976449	−	1.51938i	0.849577	−	0.527465i	$-0.176857\pi$
$632$	3.27115	+	0.470321i	0.130119	+	0.0187083i
$633$	0.137566	+	27.8634i	0.00546775	+	1.10747i
$634$	2.56523	+	1.64857i	0.101878	+	0.0654731i
$635$	3.83411	−	24.5640i	0.152152	−	0.974792i
$636$	−3.57245	+	2.32088i	−0.141657	+	0.0920287i
$637$	2.92704	+	4.55457i	0.115974	+	0.180459i
$638$	−1.39310	+	4.74447i	−0.0551534	+	0.187835i
$639$	−22.1072	−	9.83337i	−0.874547	−	0.389002i
$640$	−1.23147	+	1.86641i	−0.0486779	+	0.0737764i
$641$	15.0340	−	32.9199i	0.593808	−	1.30026i	−0.339305	−	0.940676i	$-0.610192\pi$
$641$	15.0340	−	32.9199i	0.593808	−	1.30026i	0.933113	−	0.359582i	$-0.117081\pi$
$642$	17.0425	−	5.09564i	0.672612	−	0.201109i
$643$	21.0704			0.830935			0.415468	−	0.909608i	$-0.363618\pi$
$643$	21.0704			0.830935			0.415468	+	0.909608i	$0.363618\pi$
$644$	−14.8511	−	4.98138i	−0.585213	−	0.196294i
$645$	23.7179	−	26.9824i	0.933893	−	1.06243i
$646$	1.45335	+	10.1082i	0.0571811	+	0.397703i
$647$	−11.0528	+	24.2022i	−0.434530	+	0.951487i	0.558040	+	0.829814i	$0.311553\pi$
$647$	−11.0528	+	24.2022i	−0.434530	+	0.951487i	−0.992570	+	0.121674i	$0.961174\pi$
$648$	5.75828	−	6.91680i	0.226207	−	0.271718i
$649$	−4.71729	−	4.08755i	−0.185170	−	0.160450i
$650$	6.63710	+	3.22636i	0.260328	+	0.126548i
$651$	16.5929	−	14.5218i	0.650325	−	0.569156i
$652$	13.3588	−	6.10077i	0.523172	−	0.238925i
$653$	−24.4803	−	28.2518i	−0.957989	−	1.10558i	−0.994341	−	0.106239i	$-0.966119\pi$
$653$	−24.4803	−	28.2518i	−0.957989	−	1.10558i	0.0363521	−	0.999339i	$-0.488426\pi$
$654$	−8.70071	+	19.3035i	−0.340225	+	0.754828i
$655$	−24.5989	+	15.3935i	−0.961158	+	0.601475i
$656$	−0.314519	−	0.0452210i	−0.0122799	−	0.00176558i
$657$	−2.34285	+	8.28062i	−0.0914033	+	0.323058i
$658$	0.633155	+	0.730700i	0.0246830	+	0.0284857i
$659$	−3.52585	−	7.72053i	−0.137347	−	0.300749i	0.828443	−	0.560074i	$-0.189227\pi$
$659$	−3.52585	−	7.72053i	−0.137347	−	0.300749i	−0.965790	+	0.259325i	$0.916500\pi$
$660$	0.420633	−	2.78504i	0.0163731	−	0.108408i
$661$	−14.1762	+	48.2796i	−0.551389	+	1.87786i	−0.0781093	+	0.996945i	$0.524888\pi$
$661$	−14.1762	+	48.2796i	−0.551389	+	1.87786i	−0.473279	+	0.880912i	$0.656930\pi$
$662$	20.2113	−	23.3251i	0.785534	−	0.906554i
$663$	−4.01792	+	1.85895i	−0.156043	+	0.0721957i
$664$	−14.4253	−	6.58779i	−0.559809	−	0.255656i
$665$	28.5935	−	32.2071i	1.10881	−	1.24894i
$666$	−31.9274	+	9.71817i	−1.23716	+	0.376572i
$667$	32.4293	−	3.41008i	1.25567	−	0.132039i
$668$	4.29958			0.166356
$669$	5.77313	−	1.72615i	0.223202	−	0.0667368i
$670$	−0.245515	−	0.874973i	−0.00948506	−	0.0338032i
$671$	−0.951655	−	3.24104i	−0.0367382	−	0.125119i
$672$	−3.03501	+	4.77423i	−0.117078	+	0.184170i
$673$	10.3983	−	35.4134i	0.400825	−	1.36509i	−0.473948	−	0.880553i	$-0.657172\pi$
$673$	10.3983	−	35.4134i	0.400825	−	1.36509i	0.874773	−	0.484532i	$-0.161010\pi$
$674$	13.0322	−	8.37530i	0.501982	−	0.322605i
$675$	19.7917	−	16.8312i	0.761783	−	0.647832i
$676$	−7.08663	−	8.17841i	−0.272563	−	0.314554i
$677$	8.84282	−	13.7597i	0.339857	−	0.528828i	−0.628691	−	0.777656i	$-0.716409\pi$
$677$	8.84282	−	13.7597i	0.339857	−	0.528828i	0.968548	+	0.248827i	$0.0800452\pi$
$678$	16.3675	−	0.0808089i	0.628590	−	0.00310345i
$679$	−6.20832	+	43.1798i	−0.238253	+	1.65709i
$680$	−0.504916	−	3.83929i	−0.0193626	−	0.147230i
$681$	22.8445	−	26.6285i	0.875404	−	1.02041i
$682$	−1.17753	−	2.57842i	−0.0450898	−	0.0987330i
$683$	11.3707	−	7.30751i	0.435088	−	0.279614i	−0.304707	−	0.952446i	$-0.598559\pi$
$683$	11.3707	−	7.30751i	0.435088	−	0.279614i	0.739795	+	0.672832i	$0.234922\pi$
$684$	−0.174681	−	17.6900i	−0.00667910	−	0.676395i
$685$	−5.25409	−	0.0632491i	−0.200749	−	0.00241662i
$686$	10.4417	−	3.06595i	0.398664	−	0.117058i
$687$	15.7132	+	4.52967i	0.599496	+	0.172818i
$688$	1.32008	+	9.18133i	0.0503274	+	0.350035i
$689$	−3.63024			−0.138301
$690$	−18.0397	+	4.42358i	−0.686761	+	0.168403i
$691$	22.9769			0.874082			0.437041	−	0.899442i	$-0.356027\pi$
$691$	22.9769			0.874082			0.437041	+	0.899442i	$0.356027\pi$
$692$	−2.27457	−	15.8200i	−0.0864661	−	0.601385i
$693$	0.944449	−	7.06321i	0.0358767	−	0.268309i
$694$	23.1405	−	6.79466i	0.878401	−	0.257922i
$695$	0.0246840	−	2.05049i	0.000936316	−	0.0777797i
$696$	1.61842	−	11.6649i	0.0613461	−	0.442158i
$697$	0.462921	−	0.297501i	0.0175344	−	0.0112687i
$698$	−2.09425	−	4.58577i	−0.0792686	−	0.173574i
$699$	−15.7295	−	13.4943i	−0.594944	−	0.510401i
$700$	−10.9886	+	12.0812i	−0.415330	+	0.456626i
$701$	2.66198	−	18.5145i	0.100542	−	0.699283i	−0.875741	−	0.482782i	$-0.839626\pi$
$701$	2.66198	−	18.5145i	0.100542	−	0.699283i	0.976282	−	0.216501i	$-0.0694645\pi$
$702$	7.32578	−	2.26943i	0.276494	−	0.0856539i
$703$	−35.4666	+	55.1872i	−1.33765	+	2.08142i
$704$	0.476248	+	0.549619i	0.0179493	+	0.0207146i
$705$	1.09771	+	0.330800i	0.0413420	+	0.0124586i
$706$	−13.2875	+	8.53936i	−0.500082	+	0.321383i
$707$	5.13800	−	17.4984i	0.193234	−	0.658095i
$708$	12.5455	+	7.97527i	0.471489	+	0.299729i
$709$	−7.26287	−	24.7351i	−0.272763	−	0.928945i	−0.975960	−	0.217950i	$-0.930063\pi$
$709$	−7.26287	−	24.7351i	−0.272763	−	0.928945i	0.703197	−	0.710995i	$-0.251755\pi$
$710$	17.3637	−	4.87218i	0.651647	−	0.182850i
$711$	8.97732	−	4.20742i	0.336676	−	0.157791i
$712$	−8.57534			−0.321375
$713$	−12.7693	+	13.6513i	−0.478214	+	0.511244i
$714$	−1.44213	−	9.69033i	−0.0539702	−	0.362652i
$715$	1.59349	−	1.79487i	0.0595931	−	0.0671242i
$716$	16.0793	+	7.34317i	0.600912	+	0.274427i
$717$	15.0067	+	32.4354i	0.560436	+	1.21132i
$718$	1.03639	−	1.19605i	0.0386776	−	0.0446364i
$719$	−9.22894	+	31.4309i	−0.344181	+	1.17217i	0.587599	+	0.809152i	$0.300073\pi$
$719$	−9.22894	+	31.4309i	−0.344181	+	1.17217i	−0.931781	+	0.363022i	$0.881745\pi$
$720$	−0.0145115	+	6.70819i	−0.000540812	+	0.249999i
$721$	24.8535	+	54.4216i	0.925593	+	2.02677i
$722$	−10.3299	−	11.9214i	−0.384439	−	0.443667i
$723$	−6.68198	+	14.8248i	−0.248506	+	0.551339i
$724$	20.0672	+	2.88522i	0.745790	+	0.107228i
$725$	10.3603	−	32.3792i	0.384772	−	1.20253i
$726$	16.5345	+	7.45263i	0.613654	+	0.276593i
$727$	−7.08273	−	8.17391i	−0.262684	−	0.303154i	0.609051	−	0.793131i	$-0.291550\pi$
$727$	−7.08273	−	8.17391i	−0.262684	−	0.303154i	−0.871735	+	0.489977i	$0.837005\pi$
$728$	−4.38512	+	2.00262i	−0.162523	+	0.0742219i
$729$	3.04926	−	26.8273i	0.112936	−	0.993602i
$730$	−2.59417	−	5.86630i	−0.0960144	−	0.217121i
$731$	−12.1399	−	10.5193i	−0.449012	−	0.389071i
$732$	3.37805	+	7.30128i	0.124856	+	0.269863i
$733$	1.90844	−	4.17890i	0.0704898	−	0.154351i	−0.871107	−	0.491093i	$-0.836598\pi$
$733$	1.90844	−	4.17890i	0.0704898	−	0.154351i	0.941597	+	0.336742i	$0.109325\pi$
$734$	−4.85103	−	33.7397i	−0.179055	−	1.24535i
$735$	−9.37945	+	10.6704i	−0.345966	+	0.393585i
$736$	2.15669	−	4.28354i	0.0794965	−	0.157893i
$737$	−0.295564			−0.0108872
$738$	−0.863163	+	0.404541i	−0.0317735	+	0.0148914i
$739$	−6.55482	+	14.3531i	−0.241123	+	0.527986i	−0.991043	−	0.133543i	$-0.957365\pi$
$739$	−6.55482	+	14.3531i	−0.241123	+	0.527986i	0.749920	+	0.661529i	$0.230092\pi$
$740$	13.6995	−	20.7630i	0.503604	−	0.763263i
$741$	8.08750	−	12.7221i	0.297102	−	0.467356i
$742$	2.26332	−	7.70816i	0.0830891	−	0.282976i
$743$	11.1301	+	17.3188i	0.408324	+	0.635364i	0.983126	−	0.182928i	$-0.0585575\pi$
$743$	11.1301	+	17.3188i	0.408324	+	0.635364i	−0.574802	+	0.818292i	$0.694921\pi$
$744$	3.67784	+	5.66118i	0.134836	+	0.207549i
$745$	22.5165	+	3.51451i	0.824939	+	0.128762i
$746$	9.62282	+	6.18421i	0.352316	+	0.226420i
$747$	−47.0216	+	7.23528i	−1.72043	+	0.264725i
$748$	−1.24661	−	0.179236i	−0.0455806	−	0.00655350i
$749$	−18.1351	+	28.2187i	−0.662640	+	1.03109i
$750$	−3.35204	+	19.0726i	−0.122399	+	0.696433i
$751$	−3.21312	+	1.46738i	−0.117249	+	0.0535456i	−0.473176	−	0.880968i	$-0.656892\pi$
$751$	−3.21312	+	1.46738i	−0.117249	+	0.0535456i	0.355927	+	0.934514i	$0.384165\pi$
$752$	−0.249025	+	0.160039i	−0.00908101	+	0.00583601i
$753$	−42.3765	−	5.87943i	−1.54429	−	0.214258i
$754$	6.57175	−	7.58421i	0.239329	−	0.276201i
$755$	−26.0041	+	39.4119i	−0.946388	+	1.43435i
$756$	0.251365	+	16.9699i	0.00914206	+	0.617189i
$757$	3.07665	+	21.3986i	0.111823	+	0.777745i	0.966145	+	0.258000i	$0.0830636\pi$
$757$	3.07665	+	21.3986i	0.111823	+	0.777745i	−0.854322	+	0.519744i	$0.826027\pi$
$758$			26.7233i			0.970633i
$759$	−0.199880	+	6.03769i	−0.00725517	+	0.219154i
$760$	8.51442	+	10.0685i	0.308851	+	0.365225i
$761$	−20.1120	+	2.89166i	−0.729058	+	0.104823i	−0.496841	−	0.867841i	$-0.665507\pi$
$761$	−20.1120	+	2.89166i	−0.729058	+	0.104823i	−0.232217	+	0.972664i	$0.574598\pi$
$762$	18.5041	+	5.33419i	0.670331	+	0.193237i
$763$	−11.2492	−	38.3111i	−0.407247	−	1.38695i
$764$	0.312184	−	0.360280i	0.0112944	−	0.0130345i
$765$	−7.58855	−	8.79602i	−0.274364	−	0.318021i
$766$	6.98678	+	10.8716i	0.252443	+	0.392808i
$767$	5.26239	+	11.5230i	0.190014	+	0.416073i
$768$	−1.31458	−	1.12778i	−0.0474358	−	0.0406951i
$769$	0.712759	−	1.10907i	0.0257027	−	0.0399942i	−0.828164	−	0.560485i	$-0.810615\pi$
$769$	0.712759	−	1.10907i	0.0257027	−	0.0399942i	0.853867	+	0.520491i	$0.174251\pi$
$770$	2.81760	+	4.50253i	0.101539	+	0.162260i
$771$	0.0173200	+	3.50810i	0.000623765	+	0.126341i
$772$	−1.78958	+	2.78465i	−0.0644085	+	0.100222i
$773$	3.24542	−	2.81217i	0.116729	−	0.101147i	−0.594540	−	0.804066i	$-0.702666\pi$
$773$	3.24542	−	2.81217i	0.116729	−	0.101147i	0.711270	+	0.702919i	$0.248120\pi$
$774$	18.4297	+	20.8495i	0.662443	+	0.749418i
$775$	7.66666	+	17.9170i	0.275395	+	0.643596i
$776$	−12.8151	−	3.76284i	−0.460034	−	0.135078i
$777$	33.7631	−	53.1111i	1.21124	−	1.90535i
$778$	25.7642	−	7.56506i	0.923692	−	0.271220i
$779$	−0.778396	+	1.70445i	−0.0278889	+	0.0610682i
$780$	−3.12454	+	4.78681i	−0.111877	+	0.171395i
$781$		−	5.86540i		−	0.209880i
$782$	2.03519	+	8.05205i	0.0727782	+	0.287941i
$783$	−15.1510	−	31.9164i	−0.541452	−	1.14060i
$784$	−0.522035	−	3.63083i	−0.0186441	−	0.129673i
$785$	9.69518	+	34.5520i	0.346036	+	1.23321i
$786$	−9.43834	−	20.3999i	−0.336654	−	0.727641i
$787$	−2.36241	+	2.72636i	−0.0842107	+	0.0971843i	−0.796291	−	0.604914i	$-0.793208\pi$
$787$	−2.36241	+	2.72636i	−0.0842107	+	0.0971843i	0.712080	+	0.702098i	$0.247753\pi$
$788$	2.46539	+	0.723903i	0.0878258	+	0.0257880i
$789$	−22.9098	−	26.1771i	−0.815611	−	0.931929i
$790$	−3.15050	+	6.68450i	−0.112090	+	0.237824i
$791$	−23.3265	+	20.2126i	−0.829396	+	0.718676i
$792$	2.09934	+	0.593970i	0.0745969	+	0.0211058i
$793$	−0.975617	+	6.78556i	−0.0346452	+	0.240962i
$794$	23.5649	+	3.38812i	0.836288	+	0.120240i
$795$	−2.61881	−	9.15894i	−0.0928798	−	0.324834i
$796$	−6.81012	+	5.90100i	−0.241378	+	0.209156i
$797$	−16.0810	+	7.34397i	−0.569620	+	0.260137i	−0.679337	−	0.733826i	$-0.737733\pi$
$797$	−16.0810	+	7.34397i	−0.569620	+	0.260137i	0.109717	+	0.993963i	$0.465005\pi$
$798$	21.9708	+	25.1041i	0.777757	+	0.888676i
$799$	0.144425	−	0.491867i	0.00510940	−	0.0174010i
$800$	−3.18239	−	3.85647i	−0.112514	−	0.136347i
$801$	−21.5037	+	14.1216i	−0.759797	+	0.498961i
$802$	13.7695	−	30.1509i	0.486216	−	1.06467i
$803$	−2.06493	+	0.296892i	−0.0728697	+	0.0104771i
$804$	0.696259	−	0.103618i	0.0245552	−	0.00365433i
$805$	20.3876	−	28.4813i	0.718568	−	1.00383i
$806$			5.75275i			0.202632i
$807$	24.5028	−	7.32628i	0.862541	−	0.257897i
$808$	5.07899	+	2.31950i	0.178678	+	0.0815997i
$809$	−9.54583	−	32.5101i	−0.335613	−	1.14299i	−0.938532	−	0.345192i	$-0.887814\pi$
$809$	−9.54583	−	32.5101i	−0.335613	−	1.14299i	0.602919	−	0.797803i	$-0.294004\pi$
$810$	11.0104	+	16.8455i	0.386866	+	0.591891i
$811$	−33.3775	−	9.80052i	−1.17204	−	0.344143i	−0.362942	−	0.931812i	$-0.618228\pi$
$811$	−33.3775	−	9.80052i	−1.17204	−	0.344143i	−0.809101	+	0.587669i	$0.800046\pi$
$812$	12.0065	+	18.6824i	0.421344	+	0.655625i
$813$	8.46025	+	13.0226i	0.296714	+	0.456722i
$814$	−5.29804	−	6.11427i	−0.185696	−	0.214305i
$815$	4.28185	+	32.5585i	0.149987	+	1.14047i
$816$	2.99948	−	0.0148089i	0.105003	−	0.000518414i
$817$	54.1420	+	7.78445i	1.89419	+	0.272343i
$818$	−0.549515	−	0.353152i	−0.0192133	−	0.0123477i
$819$	−7.69839	+	12.2431i	−0.269003	+	0.427807i
$820$	0.302918	−	0.642710i	0.0105784	−	0.0224444i
$821$	−8.99520	−	13.9968i	−0.313935	−	0.488492i	0.648049	−	0.761599i	$-0.275585\pi$
$821$	−8.99520	−	13.9968i	−0.313935	−	0.488492i	−0.961984	+	0.273107i	$0.911949\pi$
$822$	0.559339	−	4.03148i	0.0195092	−	0.140614i
$823$	−15.7420	−	13.6405i	−0.548732	−	0.475479i	0.335817	−	0.941927i	$-0.390988\pi$
$823$	−15.7420	−	13.6405i	−0.548732	−	0.475479i	−0.884548	+	0.466449i	$0.845533\pi$
$824$	−17.5753	+	5.16057i	−0.612264	+	0.179777i
$825$	5.67790	+	2.72551i	0.197679	+	0.0948901i
$826$	−27.7480	+	3.98957i	−0.965478	+	0.138815i
$827$		−	28.5676i		−	0.993394i	−0.867924	−	0.496697i	$-0.834546\pi$
$827$		−	28.5676i		−	0.993394i	0.867924	−	0.496697i	$-0.165454\pi$
$828$	−1.64582	−	14.2930i	−0.0571963	−	0.496718i
$829$	−13.7720			−0.478322			−0.239161	−	0.970980i	$-0.576872\pi$
$829$	−13.7720			−0.478322			−0.239161	+	0.970980i	$0.576872\pi$
$830$	23.5425	−	26.5177i	0.817172	−	0.920442i
$831$	54.3635	+	15.6714i	1.88585	+	0.543636i
$832$	−0.415822	−	1.41616i	−0.0144160	−	0.0490965i
$833$	4.80084	+	4.15995i	0.166339	+	0.144134i
$834$	1.57335	+	0.218291i	0.0544806	+	0.00755879i
$835$	−2.81946	+	9.19144i	−0.0975716	+	0.318083i
$836$	3.90102	−	1.78154i	0.134920	−	0.0616157i
$837$	18.5452	+	8.13957i	0.641018	+	0.281345i
$838$	−21.8798	−	14.0613i	−0.755827	−	0.485740i
$839$	2.77281	−	19.2853i	0.0957281	−	0.665804i	−0.884296	−	0.466926i	$-0.845361\pi$
$839$	2.77281	−	19.2853i	0.0957281	−	0.665804i	0.980024	−	0.198877i	$-0.0637295\pi$
$840$	−8.21590	−	9.61881i	−0.283475	−	0.331881i
$841$	−14.4947	−	9.31519i	−0.499818	−	0.321214i
$842$	2.06958	−	1.79331i	0.0713226	−	0.0618014i
$843$	4.66909	+	7.18698i	0.160812	+	0.247533i
$844$	13.5334	−	8.69736i	0.465837	−	0.299376i
$845$	22.1305	−	9.78645i	0.761312	−	0.336664i
$846$	−0.360915	+	0.811402i	−0.0124085	+	0.0278966i
$847$	−32.8155	+	9.63551i	−1.12755	+	0.331080i
$848$	2.23733	+	1.02175i	0.0768302	+	0.0350872i
$849$	4.59827	+	15.3790i	0.157812	+	0.527805i
$850$	8.53856	+	1.43824i	0.292870	+	0.0493314i
$851$	−23.9922	+	47.6525i	−0.822440	+	1.63351i
$852$	2.05628	+	13.8171i	0.0704469	+	0.473367i
$853$	37.9732	−	5.45972i	1.30018	−	0.186937i	0.542771	−	0.839881i	$-0.317375\pi$
$853$	37.9732	−	5.45972i	1.30018	−	0.186937i	0.757407	+	0.652944i	$0.226466\pi$
$854$	−13.7997	−	6.30210i	−0.472215	−	0.215654i
$855$	37.9315	+	11.2269i	1.29723	+	0.383951i
$856$	−7.76145	−	6.72534i	−0.265281	−	0.229867i
$857$	−1.10896	−	0.325621i	−0.0378815	−	0.0111230i	0.262737	−	0.964868i	$-0.415375\pi$
$857$	−1.10896	−	0.325621i	−0.0378815	−	0.0111230i	−0.300618	+	0.953745i	$0.597193\pi$
$858$	1.22441	+	1.39903i	0.0418006	+	0.0477620i
$859$	1.84217	+	4.03379i	0.0628541	+	0.137631i	0.938452	−	0.345409i	$-0.112260\pi$
$859$	1.84217	+	4.03379i	0.0628541	+	0.137631i	−0.875598	+	0.483040i	$0.839533\pi$
$860$	−20.4931	−	3.19869i	−0.698808	−	0.109074i
$861$	0.738672	−	1.63883i	0.0251739	−	0.0558512i
$862$	0.526317	−	3.66062i	0.0179264	−	0.124681i
$863$	−8.00726	+	55.6917i	−0.272570	+	1.89577i	0.148782	+	0.988870i	$0.452465\pi$
$863$	−8.00726	+	55.6917i	−0.272570	+	1.89577i	−0.421352	+	0.906897i	$0.638444\pi$
$864$	−5.15365	−	0.663233i	−0.175331	−	0.0225636i
$865$	35.3108	+	5.51153i	1.20060	+	0.187398i
$866$	−11.5628	−	25.3190i	−0.392919	−	0.860373i
$867$	18.2486	−	15.9709i	0.619755	−	0.542401i
$868$	−12.2149	−	3.58663i	−0.414602	−	0.121738i
$869$	1.81638	+	1.57390i	0.0616163	+	0.0533908i
$870$	23.8754	+	11.1091i	0.809453	+	0.376634i
$871$	0.545637	+	0.249184i	0.0184882	+	0.00844328i
$872$	12.1003	−	1.73975i	0.409767	−	0.0589155i
$873$	−38.3318	+	11.6676i	−1.29734	+	0.394888i
$874$	−20.6536	−	19.3193i	−0.698620	−	0.653484i
$875$	−18.6208	−	31.4132i	−0.629497	−	1.06196i
$876$	4.76026	−	1.42330i	0.160834	−	0.0480890i
$877$	−36.2487	−	16.5542i	−1.22403	−	0.558996i	−0.304687	−	0.952452i	$-0.598552\pi$
$877$	−36.2487	−	16.5542i	−1.22403	−	0.558996i	−0.919343	+	0.393456i	$0.871279\pi$
$878$	−27.9254	+	8.19962i	−0.942435	+	0.276724i
$879$	−33.3475	−	21.1992i	−1.12478	−	0.715032i
$880$	−1.48725	+	0.657685i	−0.0501352	+	0.0221706i
$881$	34.2315	−	21.9993i	1.15329	−	0.741174i	0.182997	−	0.983113i	$-0.441420\pi$
$881$	34.2315	−	21.9993i	1.15329	−	0.741174i	0.970291	+	0.241940i	$0.0777836\pi$
$882$	−7.28819	−	8.24509i	−0.245406	−	0.277627i
$883$	−5.05124	+	4.37693i	−0.169988	+	0.147295i	−0.735700	−	0.677307i	$-0.763147\pi$
$883$	−5.05124	+	4.37693i	−0.169988	+	0.147295i	0.565712	+	0.824603i	$0.308601\pi$
$884$	2.15024	+	1.38188i	0.0723205	+	0.0464776i
$885$	−25.2759	+	21.5894i	−0.849641	+	0.725720i
$886$	4.76332	−	33.1296i	0.160027	−	1.11301i
$887$	−43.5714	−	28.0016i	−1.46298	−	0.940203i	−0.998507	−	0.0546172i	$-0.982606\pi$
$887$	−43.5714	−	28.0016i	−1.46298	−	0.940203i	−0.464476	−	0.885585i	$-0.653757\pi$
$888$	14.6241	+	12.5460i	0.490753	+	0.421016i
$889$	−33.0332	+	15.0858i	−1.10790	+	0.505961i
$890$	5.62331	−	18.3320i	0.188494	−	0.614489i
$891$	6.24249	−	1.96767i	0.209131	−	0.0659193i
$892$	−2.62919	−	2.27821i	−0.0880319	−	0.0762801i
$893$	0.491793	+	1.67489i	0.0164572	+	0.0560481i
$894$	−4.88956	+	16.9617i	−0.163531	+	0.567283i
$895$	−26.2419	+	29.5583i	−0.877171	+	0.988024i
$896$	3.26622			0.109117
$897$	5.45925	−	10.9776i	0.182279	−	0.366531i
$898$			38.4423i			1.28284i
$899$	26.2315	−	3.77152i	0.874869	−	0.125787i
$900$	−14.3309	−	4.42994i	−0.477698	−	0.147665i
$901$	−4.08692	+	1.20003i	−0.136155	+	0.0399787i
$902$	−0.174643	−	0.151329i	−0.00581498	−	0.00503871i
$903$	−51.9774	−	7.21148i	−1.72970	−	0.239983i
$904$	−5.10900	−	7.94976i	−0.169923	−	0.264405i
$905$	−19.3270	+	41.0066i	−0.642451	+	1.36311i
$906$	−27.7592	−	23.8146i	−0.922239	−	0.791187i
$907$	−39.9731	−	25.6892i	−1.32729	−	0.852994i	−0.331389	−	0.943494i	$-0.607517\pi$
$907$	−39.9731	−	25.6892i	−1.32729	−	0.852994i	−0.995896	+	0.0905000i	$0.971153\pi$
$908$	−20.0501	−	2.88277i	−0.665385	−	0.0956680i
$909$	16.5559	−	2.54747i	0.549123	−	0.0844943i
$910$	−1.40554	−	10.6875i	−0.0465933	−	0.354288i
$911$	27.2784	+	31.4810i	0.903774	+	1.04301i	0.998869	+	0.0475426i	$0.0151390\pi$
$911$	27.2784	+	31.4810i	0.903774	+	1.04301i	−0.0950953	+	0.995468i	$0.530316\pi$
$912$	−8.56507	+	5.56438i	−0.283618	+	0.184255i
$913$	−6.23520	−	9.70217i	−0.206355	−	0.321095i
$914$	7.16287	+	2.10321i	0.236927	+	0.0695679i
$915$	−17.8235	+	2.43359i	−0.589227	+	0.0804521i
$916$	−2.65996	−	9.05900i	−0.0878876	−	0.299318i
$917$	38.5566	+	17.6082i	1.27325	+	0.581474i
$918$	7.49716	−	4.97656i	0.247443	−	0.164251i
$919$			1.30308i			0.0429847i	0.999769	+	0.0214923i	$0.00684175\pi$
$919$			1.30308i			0.0429847i	−0.999769	+	0.0214923i	$0.993158\pi$
$920$	7.74290	+	7.41940i	0.255276	+	0.244611i
$921$	4.50050	+	30.2410i	0.148296	+	0.996475i
$922$	−22.8688	+	3.28804i	−0.753145	+	0.108286i
$923$	−4.94500	+	10.8280i	−0.162767	+	0.356409i
$924$	−3.73396	+	1.72757i	−0.122838	+	0.0568330i
$925$	35.4027	+	42.9015i	1.16403	+	1.41059i
$926$	−2.93073	+	9.98116i	−0.0963098	+	0.328001i
$927$	−35.5739	+	41.8831i	−1.16840	+	1.37562i
$928$	−6.18482	+	2.82451i	−0.203027	+	0.0927192i
$929$	−8.19025	+	7.09689i	−0.268713	+	0.232841i	−0.778786	−	0.627290i	$-0.784164\pi$
$929$	−8.19025	+	7.09689i	−0.268713	+	0.232841i	0.510072	+	0.860131i	$0.329619\pi$
$930$	−14.5140	+	4.14997i	−0.475931	+	0.136083i
$931$	−21.4109	−	3.07842i	−0.701714	−	0.100891i
$932$	−1.70286	+	11.8436i	−0.0557789	+	0.387951i
$933$	16.1486	−	35.8276i	0.528683	−	1.17294i
$934$	−23.0023	+	19.9316i	−0.752657	+	0.652181i
$935$	1.20063	−	2.54741i	0.0392648	−	0.0833092i
$936$	−3.37481	−	2.86644i	−0.110309	−	0.0936924i
$937$	19.7668	+	5.80405i	0.645752	+	0.189610i	0.588178	−	0.808731i	$-0.299845\pi$
$937$	19.7668	+	5.80405i	0.645752	+	0.189610i	0.0575740	+	0.998341i	$0.481663\pi$
$938$	−0.869283	+	1.00321i	−0.0283831	+	0.0327558i
$939$	−16.3288	+	7.55477i	−0.532870	+	0.246540i
$940$	−0.178824	−	0.637300i	−0.00583260	−	0.0207864i
$941$	−5.45299	−	37.9264i	−0.177762	−	1.23636i	−0.861925	−	0.507035i	$-0.830741\pi$
$941$	−5.45299	−	37.9264i	−0.177762	−	1.23636i	0.684163	−	0.729329i	$-0.260168\pi$
$942$	−27.4947	+	4.09180i	−0.895827	+	0.133318i
$943$	−0.484612	+	1.44478i	−0.0157811	+	0.0470485i
$944$		−	8.58283i		−	0.279347i
$945$	−36.4423	−	10.5907i	−1.18547	−	0.344516i
$946$	−2.80230	+	6.13619i	−0.0911107	+	0.199505i
$947$	14.1055	−	4.14174i	0.458366	−	0.134588i	−0.0443948	−	0.999014i	$-0.514136\pi$
$947$	14.1055	−	4.14174i	0.458366	−	0.134588i	0.502760	+	0.864426i	$0.332318\pi$
$948$	−4.83061	−	3.07085i	−0.156891	−	0.0997366i
$949$	4.06234	+	1.19281i	0.131869	+	0.0387203i
$950$	−27.1074	+	11.5993i	−0.879481	+	0.376330i
$951$	−2.87731	−	4.42895i	−0.0933031	−	0.143619i
$952$	−4.27477	+	3.70411i	−0.138546	+	0.120051i
$953$	22.3031	−	34.7043i	0.722467	−	1.12418i	−0.264675	−	0.964338i	$-0.585265\pi$
$953$	22.3031	−	34.7043i	0.722467	−	1.12418i	0.987142	−	0.159843i	$-0.0510989\pi$
$954$	7.29296	−	1.12218i	0.236118	−	0.0363318i
$955$	0.565473	+	0.903627i	0.0182983	+	0.0292407i
$956$	11.1554	−	17.3582i	0.360793	−	0.561405i
$957$	5.57658	−	6.50029i	0.180265	−	0.210125i
$958$	4.91654	+	10.7657i	0.158846	+	0.347824i
$959$	4.14952	+	6.45678i	0.133995	+	0.208500i
$960$	3.27295	−	2.07071i	0.105634	−	0.0668318i
$961$	10.3522	−	11.9470i	0.333941	−	0.385388i
$962$	4.62584	+	15.7542i	0.149143	+	0.507934i
$963$	−30.5378	−	4.08333i	−0.984068	−	0.131584i
$964$	9.29277	−	1.33610i	0.299300	−	0.0430329i
$965$	−4.77936	−	5.65173i	−0.153853	−	0.181936i
$966$	19.9053	+	18.4359i	0.640443	+	0.593165i
$967$		−	36.3789i		−	1.16987i	−0.811082	−	0.584933i	$-0.801121\pi$
$967$		−	36.3789i		−	1.16987i	0.811082	−	0.584933i	$-0.198879\pi$
$968$	−1.49019	−	10.3645i	−0.0478966	−	0.333128i
$969$	4.89944	−	16.9959i	0.157393	−	0.545988i
$970$	16.4475	−	24.9279i	0.528099	−	0.800388i
$971$	16.7981	−	19.3861i	0.539078	−	0.622130i	−0.419225	−	0.907882i	$-0.637698\pi$
$971$	16.7981	−	19.3861i	0.539078	−	0.622130i	0.958303	+	0.285753i	$0.0922436\pi$
$972$	−14.0156	+	6.82371i	−0.449551	+	0.218870i
$973$	−2.51986	+	1.61942i	−0.0807831	+	0.0519161i
$974$	1.28865	−	0.588506i	0.0412909	−	0.0188569i
$975$	−8.18408	−	9.81846i	−0.262100	−	0.314442i
$976$	2.51112	−	3.90738i	0.0803789	−	0.125072i
$977$	−22.1530	−	3.18512i	−0.708738	−	0.101901i	−0.221487	−	0.975163i	$-0.571091\pi$
$977$	−22.1530	−	3.18512i	−0.708738	−	0.101901i	−0.487251	+	0.873262i	$0.662000\pi$
$978$	−25.4365	+	0.125584i	−0.813371	+	0.00401574i
$979$	−5.24641	−	3.37166i	−0.167676	−	0.107759i
$980$	8.10415	+	1.26495i	0.258878	+	0.0404073i
$981$	27.4779	−	24.2889i	0.877303	−	0.775485i
$982$	−7.67705	−	11.9457i	−0.244985	−	0.381204i
$983$	−1.72652	+	5.88000i	−0.0550676	+	0.187543i	−0.982434	−	0.186612i	$-0.940249\pi$
$983$	−1.72652	+	5.88000i	−0.0550676	+	0.187543i	0.927366	+	0.374155i	$0.122067\pi$
$984$	0.464459	+	0.295260i	0.0148064	+	0.00941255i
$985$	−3.16421	+	4.79569i	−0.100820	+	0.152803i
$986$	4.89141	−	10.7107i	0.155774	−	0.341098i
$987$	−0.479728	−	1.60446i	−0.0152699	−	0.0510705i
$988$	−8.70361			−0.276899
$989$	44.4527	+	1.69137i	1.41352	+	0.0537824i
$990$	−2.64641	+	4.09838i	−0.0841085	+	0.130255i
$991$	2.14252	+	14.9016i	0.0680595	+	0.473364i	0.995137	+	0.0984958i	$0.0314031\pi$
$991$	2.14252	+	14.9016i	0.0680595	+	0.473364i	−0.927078	+	0.374869i	$0.877688\pi$
$992$	1.61915	−	3.54544i	0.0514080	−	0.112568i
$993$	−48.5161	+	22.4467i	−1.53961	+	0.712324i
$994$	−19.9084	−	17.2507i	−0.631456	−	0.547160i
$995$	−8.14913	−	18.4280i	−0.258345	−	0.584206i
$996$	18.0896	+	20.6695i	0.573192	+	0.654937i
$997$	20.8895	−	9.53992i	0.661577	−	0.302132i	−0.0561851	−	0.998420i	$-0.517894\pi$
$997$	20.8895	−	9.53992i	0.661577	−	0.302132i	0.717762	+	0.696288i	$0.245166\pi$
$998$	21.0864	+	24.3350i	0.667478	+	0.770310i
$999$	57.3321	+	7.37817i	1.81391	+	0.233435i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.n.b.89.15	yes	240
3.2	odd	2		690.2.n.a.89.8	✓	240
5.4	even	2		690.2.n.a.89.10	yes	240
15.14	odd	2	inner	690.2.n.b.89.17	yes	240
23.15	odd	22	inner	690.2.n.b.659.17	yes	240
69.38	even	22		690.2.n.a.659.10	yes	240
115.84	odd	22		690.2.n.a.659.8	yes	240
345.314	even	22	inner	690.2.n.b.659.15	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.n.a.89.8	✓	240	3.2	odd	2
690.2.n.a.89.10	yes	240	5.4	even	2
690.2.n.a.659.8	yes	240	115.84	odd	22
690.2.n.a.659.10	yes	240	69.38	even	22
690.2.n.b.89.15	yes	240	1.1	even	1	trivial
690.2.n.b.89.17	yes	240	15.14	odd	2	inner
690.2.n.b.659.15	yes	240	345.314	even	22	inner
690.2.n.b.659.17	yes	240	23.15	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.n (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{2} +(0.479764 - 1.66428i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(0.0269160 - 2.23591i) q^{5} +(1.71562 + 0.238029i) q^{6} +(-2.74772 + 1.76585i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-2.53965 - 1.59692i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{2} +(0.479764 - 1.66428i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(0.0269160 - 2.23591i) q^{5} +(1.71562 + 0.238029i) q^{6} +(-2.74772 + 1.76585i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-2.53965 - 1.59692i) q^{9} +(2.21698 - 0.291561i) q^{10} +(0.103499 - 0.719848i) q^{11} +(0.00855129 + 1.73203i) q^{12} +(-0.797957 + 1.24165i) q^{13} +(-2.13892 - 2.46844i) q^{14} +(-3.70826 - 1.11750i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-0.487896 + 1.66162i) q^{17} +(1.21924 - 2.74107i) q^{18} +(-1.66137 - 5.65810i) q^{19} +(0.604102 + 2.15292i) q^{20} +(1.62061 + 5.42016i) q^{21} +0.727250 q^{22} +(-1.82495 - 4.43504i) q^{23} +(-1.71318 + 0.254958i) q^{24} +(-4.99855 - 0.120363i) q^{25} +(-1.34257 - 0.613130i) q^{26} +(-3.87616 + 3.46054i) q^{27} +(2.13892 - 2.46844i) q^{28} +(-1.91557 + 6.52384i) q^{29} +(0.578389 - 3.82955i) q^{30} +(-1.61915 - 3.54544i) q^{31} +(0.654861 + 0.755750i) q^{32} +(-1.14837 - 0.517608i) q^{33} +(-1.71414 - 0.246456i) q^{34} +(3.87432 + 6.19116i) q^{35} +(2.88668 + 0.816734i) q^{36} +(-7.28503 - 8.40738i) q^{37} +(5.36407 - 2.44969i) q^{38} +(1.68361 + 1.92372i) q^{39} +(-2.04503 + 0.904345i) q^{40} +(-0.240142 - 0.208084i) q^{41} +(-5.13435 + 2.37549i) q^{42} +(-3.85328 + 8.43752i) q^{43} +(0.103499 + 0.719848i) q^{44} +(-3.63893 + 5.63544i) q^{45} +(4.13018 - 2.43755i) q^{46} -0.296017 q^{47} +(-0.496174 - 1.65946i) q^{48} +(1.52381 - 3.33668i) q^{49} +(-0.592230 - 4.96480i) q^{50} +(2.53133 + 1.60918i) q^{51} +(0.415822 - 1.41616i) q^{52} +(1.32976 + 2.06915i) q^{53} +(-3.97696 - 3.34422i) q^{54} +(-1.60673 - 0.250788i) q^{55} +(2.74772 + 1.76585i) q^{56} +(-10.2137 + 0.0504267i) q^{57} +(-6.73005 - 0.967635i) q^{58} +(4.64023 - 7.22033i) q^{59} +(3.87289 + 0.0274993i) q^{60} +(4.22497 - 1.92948i) q^{61} +(3.27893 - 2.10724i) q^{62} +(9.79817 - 0.0967525i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(2.75472 + 1.81758i) q^{65} +(0.348909 - 1.21035i) q^{66} +(-0.0578385 - 0.402276i) q^{67} -1.73177i q^{68} +(-8.25669 + 0.909463i) q^{69} +(-5.57677 + 4.71598i) q^{70} +(7.98308 - 1.14779i) q^{71} +(-0.397603 + 2.97354i) q^{72} +(-0.808166 - 2.75236i) q^{73} +(7.28503 - 8.40738i) q^{74} +(-2.59844 + 8.26124i) q^{75} +(3.18814 + 4.96084i) q^{76} +(0.986759 + 2.16070i) q^{77} +(-1.66454 + 1.94025i) q^{78} +(-1.78670 + 2.78017i) q^{79} +(-1.18618 - 1.89552i) q^{80} +(3.89967 + 8.11126i) q^{81} +(0.171790 - 0.267311i) q^{82} +(11.9849 - 10.3850i) q^{83} +(-3.08200 - 4.74403i) q^{84} +(3.70209 + 1.13561i) q^{85} +(-8.90001 - 2.61328i) q^{86} +(9.93847 + 6.31795i) q^{87} +(-0.697792 + 0.204890i) q^{88} +(3.56233 - 7.80041i) q^{89} +(-6.09595 - 2.79988i) q^{90} -4.82076i q^{91} +(3.00053 + 3.74124i) q^{92} +(-6.67742 + 0.993741i) q^{93} +(-0.0421276 - 0.293004i) q^{94} +(-12.6957 + 3.56237i) q^{95} +(1.57196 - 0.727290i) q^{96} +(8.74637 - 10.0938i) q^{97} +(3.51958 + 1.03344i) q^{98} +(-1.41239 + 1.66288i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} + 24 q^{8} - 6 q^{9}+O(q^{10}) \) 240 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 + 24 * q^8 - 6 * q^9	\( 240 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} + 24 q^{8} - 6 q^{9} + 9 q^{12} + 11 q^{15} - 24 q^{16} + 6 q^{18} + 4 q^{23} + 2 q^{24} - 12 q^{25} - 2 q^{27} + 22 q^{30} + 28 q^{31} + 24 q^{32} + 36 q^{35} - 6 q^{36} - 4 q^{46} - 104 q^{47} + 9 q^{48} + 70 q^{49} - 54 q^{50} - 9 q^{54} - 26 q^{55} + 44 q^{57} - 11 q^{60} + 44 q^{61} - 28 q^{62} + 121 q^{63} - 24 q^{64} - 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} - 16 q^{72} - 102 q^{75} - 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} + 93 q^{87} + 4 q^{92} - 172 q^{93} + 16 q^{94} - 26 q^{95} + 2 q^{96} - 4 q^{98}+O(q^{100}) \) 240 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 + 24 * q^8 - 6 * q^9 + 9 * q^12 + 11 * q^15 - 24 * q^16 + 6 * q^18 + 4 * q^23 + 2 * q^24 - 12 * q^25 - 2 * q^27 + 22 * q^30 + 28 * q^31 + 24 * q^32 + 36 * q^35 - 6 * q^36 - 4 * q^46 - 104 * q^47 + 9 * q^48 + 70 * q^49 - 54 * q^50 - 9 * q^54 - 26 * q^55 + 44 * q^57 - 11 * q^60 + 44 * q^61 - 28 * q^62 + 121 * q^63 - 24 * q^64 - 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 - 16 * q^72 - 102 * q^75 - 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 + 93 * q^87 + 4 * q^92 - 172 * q^93 + 16 * q^94 - 26 * q^95 + 2 * q^96 - 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more