LMFDB - Embedded newform 720.2.cq.a.173.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(173,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2, 9]))

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

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

chi := DirichletCharacter("720.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cq (of order $12$, degree $4$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$560$
Relative dimension:	$140$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			173.11
Character	$\chi$	$=$	720.173
Dual form			720.2.cq.a.437.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36843 - 0.356938i) q^{2} +(0.114404 + 1.72827i) q^{3} +(1.74519 + 0.976889i) q^{4} +(0.267661 + 2.21999i) q^{5} +(0.460331 - 2.40585i) q^{6} +(3.21344 - 0.861040i) q^{7} +(-2.03948 - 1.95973i) q^{8} +(-2.97382 + 0.395443i) q^{9} +O(q^{10})$	\(q+(-1.36843 - 0.356938i) q^{2} +(0.114404 + 1.72827i) q^{3} +(1.74519 + 0.976889i) q^{4} +(0.267661 + 2.21999i) q^{5} +(0.460331 - 2.40585i) q^{6} +(3.21344 - 0.861040i) q^{7} +(-2.03948 - 1.95973i) q^{8} +(-2.97382 + 0.395443i) q^{9} +(0.426125 - 3.13344i) q^{10} +(-4.91782 + 1.31773i) q^{11} +(-1.48867 + 3.12792i) q^{12} +(-4.66401 + 2.69277i) q^{13} +(-4.70470 + 0.0312693i) q^{14} +(-3.80612 + 0.716566i) q^{15} +(2.09138 + 3.40971i) q^{16} +(-3.16799 - 3.16799i) q^{17} +(4.21061 + 0.520337i) q^{18} +(2.14171 - 2.14171i) q^{19} +(-1.70157 + 4.13578i) q^{20} +(1.85574 + 5.45519i) q^{21} +(7.20004 - 0.0478542i) q^{22} +(-1.50843 + 5.62954i) q^{23} +(3.15361 - 3.74897i) q^{24} +(-4.85672 + 1.18841i) q^{25} +(7.34352 - 2.02010i) q^{26} +(-1.02365 - 5.09432i) q^{27} +(6.44921 + 1.63650i) q^{28} +(7.68718 - 2.05977i) q^{29} +(5.46417 + 0.377980i) q^{30} +(-1.12501 - 1.94858i) q^{31} +(-1.64484 - 5.41244i) q^{32} +(-2.84001 - 8.34857i) q^{33} +(3.20439 + 5.46595i) q^{34} +(2.77161 + 6.90335i) q^{35} +(-5.57619 - 2.21497i) q^{36} -0.728034i q^{37} +(-3.69523 + 2.16631i) q^{38} +(-5.18741 - 7.75260i) q^{39} +(3.80469 - 5.05216i) q^{40} +(0.944086 + 1.63520i) q^{41} +(-0.592280 - 8.12741i) q^{42} +(-4.56126 + 7.90033i) q^{43} +(-9.86981 - 2.50448i) q^{44} +(-1.67385 - 6.49601i) q^{45} +(4.07358 - 7.16520i) q^{46} +(-9.01103 + 2.41450i) q^{47} +(-5.65364 + 4.00455i) q^{48} +(3.52265 - 2.03380i) q^{49} +(7.07025 + 0.107296i) q^{50} +(5.11271 - 5.83757i) q^{51} +(-10.7701 + 0.143171i) q^{52} +3.03024i q^{53} +(-0.417570 + 7.33660i) q^{54} +(-4.24165 - 10.5648i) q^{55} +(-8.24115 - 4.54140i) q^{56} +(3.94646 + 3.45642i) q^{57} +(-11.2546 + 0.0748022i) q^{58} +(5.37197 + 1.43942i) q^{59} +(-7.34240 - 2.46761i) q^{60} +(6.75394 - 1.80971i) q^{61} +(0.843977 + 3.06805i) q^{62} +(-9.21572 + 3.83131i) q^{63} +(0.318937 + 7.99364i) q^{64} +(-7.22630 - 9.63332i) q^{65} +(0.906420 + 12.4381i) q^{66} +(5.26269 + 9.11524i) q^{67} +(-2.43397 - 8.62352i) q^{68} +(-9.90193 - 1.96293i) q^{69} +(-1.32868 - 10.4360i) q^{70} -2.44549 q^{71} +(6.84001 + 5.02139i) q^{72} +(7.23007 - 7.23007i) q^{73} +(-0.259863 + 0.996262i) q^{74} +(-2.60952 - 8.25775i) q^{75} +(5.82989 - 1.64547i) q^{76} +(-14.6685 + 8.46888i) q^{77} +(4.33140 + 12.4605i) q^{78} +(-5.56508 - 3.21300i) q^{79} +(-7.00975 + 5.55548i) q^{80} +(8.68725 - 2.35195i) q^{81} +(-0.708246 - 2.57464i) q^{82} +(-4.32919 + 7.49838i) q^{83} +(-2.09049 + 11.3332i) q^{84} +(6.18496 - 7.88086i) q^{85} +(9.06168 - 9.18294i) q^{86} +(4.43929 + 13.0499i) q^{87} +(12.6122 + 6.95012i) q^{88} +2.70240i q^{89} +(-0.0281272 + 9.48679i) q^{90} +(-12.6690 + 12.6690i) q^{91} +(-8.13193 + 8.35105i) q^{92} +(3.23896 - 2.16725i) q^{93} +(13.1928 - 0.0876843i) q^{94} +(5.32782 + 4.18131i) q^{95} +(9.16597 - 3.46193i) q^{96} +(0.414347 + 1.54636i) q^{97} +(-5.54644 + 1.52574i) q^{98} +(14.1037 - 5.86341i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 560 q - 6 q^{2} - 6 q^{5} - 8 q^{6}+O(q^{10}) $ 560 * q - 6 * q^2 - 6 * q^5 - 8 * q^6	$ 560 q - 6 q^{2} - 6 q^{5} - 8 q^{6} - 12 q^{11} - 10 q^{12} - 8 q^{15} - 4 q^{16} + 20 q^{18} - 6 q^{20} - 8 q^{21} + 6 q^{22} - 24 q^{24} + 8 q^{28} + 28 q^{30} - 8 q^{31} + 54 q^{32} - 8 q^{33} - 12 q^{34} + 8 q^{36} - 18 q^{38} - 24 q^{39} + 8 q^{40} - 46 q^{42} - 4 q^{43} - 14 q^{45} - 40 q^{46} - 12 q^{47} - 22 q^{48} - 6 q^{50} - 8 q^{51} - 18 q^{52} + 24 q^{54} - 12 q^{56} + 24 q^{57} - 10 q^{58} - 88 q^{60} - 4 q^{61} + 20 q^{63} - 24 q^{64} - 12 q^{65} + 24 q^{66} - 4 q^{67} - 30 q^{68} + 12 q^{69} + 2 q^{70} - 22 q^{72} + 24 q^{74} - 66 q^{75} + 8 q^{76} - 12 q^{77} - 122 q^{78} - 16 q^{81} - 12 q^{84} - 12 q^{85} - 12 q^{86} + 12 q^{87} - 10 q^{88} - 94 q^{90} - 16 q^{91} - 120 q^{92} - 12 q^{95} + 48 q^{96} - 4 q^{97} + 32 q^{99}+O(q^{100}) $ 560 * q - 6 * q^2 - 6 * q^5 - 8 * q^6 - 12 * q^11 - 10 * q^12 - 8 * q^15 - 4 * q^16 + 20 * q^18 - 6 * q^20 - 8 * q^21 + 6 * q^22 - 24 * q^24 + 8 * q^28 + 28 * q^30 - 8 * q^31 + 54 * q^32 - 8 * q^33 - 12 * q^34 + 8 * q^36 - 18 * q^38 - 24 * q^39 + 8 * q^40 - 46 * q^42 - 4 * q^43 - 14 * q^45 - 40 * q^46 - 12 * q^47 - 22 * q^48 - 6 * q^50 - 8 * q^51 - 18 * q^52 + 24 * q^54 - 12 * q^56 + 24 * q^57 - 10 * q^58 - 88 * q^60 - 4 * q^61 + 20 * q^63 - 24 * q^64 - 12 * q^65 + 24 * q^66 - 4 * q^67 - 30 * q^68 + 12 * q^69 + 2 * q^70 - 22 * q^72 + 24 * q^74 - 66 * q^75 + 8 * q^76 - 12 * q^77 - 122 * q^78 - 16 * q^81 - 12 * q^84 - 12 * q^85 - 12 * q^86 + 12 * q^87 - 10 * q^88 - 94 * q^90 - 16 * q^91 - 120 * q^92 - 12 * q^95 + 48 * q^96 - 4 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.36843	−	0.356938i	−0.967625	−	0.252394i
$2$	−1.36843	−	0.356938i	−0.967625	−	0.252394i
$3$	0.114404	+	1.72827i	0.0660513	+	0.997816i
$3$	0.114404	+	1.72827i	0.0660513	+	0.997816i
$4$	1.74519	+	0.976889i	0.872595	+	0.488444i
$5$	0.267661	+	2.21999i	0.119702	+	0.992810i
$5$	0.267661	+	2.21999i	0.119702	+	0.992810i
$6$	0.460331	−	2.40585i	0.187929	−	0.982183i
$7$	3.21344	−	0.861040i	1.21457	−	0.325442i	0.406015	−	0.913866i	$-0.366918\pi$
$7$	3.21344	−	0.861040i	1.21457	−	0.325442i	0.808552	+	0.588424i	$0.200251\pi$
$8$	−2.03948	−	1.95973i	−0.721064	−	0.692868i
$9$	−2.97382	+	0.395443i	−0.991274	+	0.131814i
$10$	0.426125	−	3.13344i	0.134753	−	0.990879i
$11$	−4.91782	+	1.31773i	−1.48278	+	0.397310i	−0.907292	−	0.420501i	$-0.861854\pi$
$11$	−4.91782	+	1.31773i	−1.48278	+	0.397310i	−0.575488	+	0.817810i	$0.695188\pi$
$12$	−1.48867	+	3.12792i	−0.429742	+	0.902952i
$13$	−4.66401	+	2.69277i	−1.29356	+	0.746840i	−0.979284	−	0.202490i	$-0.935097\pi$
$13$	−4.66401	+	2.69277i	−1.29356	+	0.746840i	−0.314280	+	0.949330i	$0.601763\pi$
$14$	−4.70470	+	0.0312693i	−1.25738	+	0.00835706i
$15$	−3.80612	+	0.716566i	−0.982735	+	0.185017i
$16$	2.09138	+	3.40971i	0.522844	+	0.852428i
$17$	−3.16799	−	3.16799i	−0.768351	−	0.768351i	0.209465	−	0.977816i	$-0.432828\pi$
$17$	−3.16799	−	3.16799i	−0.768351	−	0.768351i	−0.977816	+	0.209465i	$0.932828\pi$
$18$	4.21061	+	0.520337i	0.992451	+	0.122645i
$19$	2.14171	−	2.14171i	0.491341	−	0.491341i	−0.417388	−	0.908729i	$-0.637054\pi$
$19$	2.14171	−	2.14171i	0.491341	−	0.491341i	0.908729	+	0.417388i	$0.137054\pi$
$20$	−1.70157	+	4.13578i	−0.380482	+	0.924789i
$21$	1.85574	+	5.45519i	0.404955	+	1.19042i
$22$	7.20004	−	0.0478542i	1.53505	−	0.0102026i
$23$	−1.50843	+	5.62954i	−0.314529	+	1.17384i	0.609897	+	0.792480i	$0.291211\pi$
$23$	−1.50843	+	5.62954i	−0.314529	+	1.17384i	−0.924427	+	0.381360i	$0.875456\pi$
$24$	3.15361	−	3.74897i	0.643728	−	0.765254i
$25$	−4.85672	+	1.18841i	−0.971343	+	0.237682i
$26$	7.34352	−	2.02010i	1.44018	−	0.396173i
$27$	−1.02365	−	5.09432i	−0.197001	−	0.980403i
$28$	6.44921	+	1.63650i	1.21879	+	0.309269i
$29$	7.68718	−	2.05977i	1.42747	−	0.382490i	0.539345	−	0.842085i	$-0.318672\pi$
$29$	7.68718	−	2.05977i	1.42747	−	0.382490i	0.888129	+	0.459594i	$0.152005\pi$
$30$	5.46417	+	0.377980i	0.997616	+	0.0690095i
$31$	−1.12501	−	1.94858i	−0.202058	−	0.349975i	0.747133	−	0.664674i	$-0.231430\pi$
$31$	−1.12501	−	1.94858i	−0.202058	−	0.349975i	−0.949192	+	0.314699i	$0.898096\pi$
$32$	−1.64484	−	5.41244i	−0.290769	−	0.956793i
$33$	−2.84001	−	8.34857i	−0.494382	−	1.45330i
$34$	3.20439	+	5.46595i	0.549549	+	0.937402i
$35$	2.77161	+	6.90335i	0.468488	+	1.16688i
$36$	−5.57619	−	2.21497i	−0.929365	−	0.369162i
$37$		−	0.728034i		−	0.119688i	−0.998208	−	0.0598440i	$-0.980940\pi$
$37$		−	0.728034i		−	0.119688i	0.998208	−	0.0598440i	$-0.0190603\pi$
$38$	−3.69523	+	2.16631i	−0.599445	+	0.351422i
$39$	−5.18741	−	7.75260i	−0.830651	−	1.24141i
$40$	3.80469	−	5.05216i	0.601574	−	0.798817i
$41$	0.944086	+	1.63520i	0.147441	+	0.255376i	0.930281	−	0.366847i	$-0.119563\pi$
$41$	0.944086	+	1.63520i	0.147441	+	0.255376i	−0.782840	+	0.622223i	$0.786230\pi$
$42$	−0.592280	−	8.12741i	−0.0913908	−	1.25409i
$43$	−4.56126	+	7.90033i	−0.695585	+	1.20479i	0.274398	+	0.961616i	$0.411521\pi$
$43$	−4.56126	+	7.90033i	−0.695585	+	1.20479i	−0.969983	+	0.243172i	$0.921812\pi$
$44$	−9.86981	−	2.50448i	−1.48793	−	0.377565i
$45$	−1.67385	−	6.49601i	−0.249524	−	0.968369i
$46$	4.07358	−	7.16520i	0.600616	−	1.05645i
$47$	−9.01103	+	2.41450i	−1.31439	+	0.352191i	−0.846875	−	0.531792i	$-0.821519\pi$
$47$	−9.01103	+	2.41450i	−1.31439	+	0.352191i	−0.467519	+	0.883983i	$0.654852\pi$
$48$	−5.65364	+	4.00455i	−0.816032	+	0.578006i
$49$	3.52265	−	2.03380i	0.503236	−	0.290543i
$50$	7.07025	+	0.107296i	0.999885	+	0.0151739i
$51$	5.11271	−	5.83757i	0.715922	−	0.817424i
$52$	−10.7701	+	0.143171i	−1.49355	+	0.0198543i
$53$			3.03024i			0.416235i	0.978104	+	0.208118i	$0.0667337\pi$
$53$			3.03024i			0.416235i	−0.978104	+	0.208118i	$0.933266\pi$
$54$	−0.417570	+	7.33660i	−0.0568241	+	0.998384i
$55$	−4.24165	−	10.5648i	−0.571944	−	1.42456i
$56$	−8.24115	−	4.54140i	−1.10127	−	0.606870i
$57$	3.94646	+	3.45642i	0.522722	+	0.457814i
$58$	−11.2546	+	0.0748022i	−1.47780	+	0.00982201i
$59$	5.37197	+	1.43942i	0.699371	+	0.187396i	0.590949	−	0.806709i	$-0.298753\pi$
$59$	5.37197	+	1.43942i	0.699371	+	0.187396i	0.108422	+	0.994105i	$0.465420\pi$
$60$	−7.34240	−	2.46761i	−0.947900	−	0.318567i
$61$	6.75394	−	1.80971i	0.864754	−	0.231710i	0.200936	−	0.979604i	$-0.435602\pi$
$61$	6.75394	−	1.80971i	0.864754	−	0.231710i	0.663818	+	0.747894i	$0.268935\pi$
$62$	0.843977	+	3.06805i	0.107185	+	0.389643i
$63$	−9.21572	+	3.83131i	−1.16107	+	0.482700i
$64$	0.318937	+	7.99364i	0.0398672	+	0.999205i
$65$	−7.22630	−	9.63332i	−0.896312	−	1.19487i
$66$	0.906420	+	12.4381i	0.111573	+	1.53103i
$67$	5.26269	+	9.11524i	0.642939	+	1.11360i	0.984773	+	0.173843i	$0.0556187\pi$
$67$	5.26269	+	9.11524i	0.642939	+	1.11360i	−0.341834	+	0.939760i	$0.611048\pi$
$68$	−2.43397	−	8.62352i	−0.295162	−	1.04576i
$69$	−9.90193	−	1.96293i	−1.19205	−	0.236309i
$70$	−1.32868	−	10.4360i	−0.158808	−	1.24734i
$71$	−2.44549			−0.290227			−0.145113	−	0.989415i	$-0.546355\pi$
$71$	−2.44549			−0.290227			−0.145113	+	0.989415i	$0.546355\pi$
$72$	6.84001	+	5.02139i	0.806102	+	0.591776i
$73$	7.23007	−	7.23007i	0.846215	−	0.846215i	−0.143443	−	0.989659i	$-0.545817\pi$
$73$	7.23007	−	7.23007i	0.846215	−	0.846215i	0.989659	+	0.143443i	$0.0458175\pi$
$74$	−0.259863	+	0.996262i	−0.0302085	+	0.115813i
$75$	−2.60952	−	8.25775i	−0.301321	−	0.953523i
$76$	5.82989	−	1.64547i	0.668734	−	0.188749i
$77$	−14.6685	+	8.46888i	−1.67163	+	0.965119i
$78$	4.33140	+	12.4605i	0.490434	+	1.41087i
$79$	−5.56508	−	3.21300i	−0.626120	−	0.361491i	0.153128	−	0.988206i	$-0.451065\pi$
$79$	−5.56508	−	3.21300i	−0.626120	−	0.361491i	−0.779248	+	0.626716i	$0.784399\pi$
$80$	−7.00975	+	5.55548i	−0.783714	+	0.621122i
$81$	8.68725	−	2.35195i	0.965250	−	0.261328i
$82$	−0.708246	−	2.57464i	−0.0782127	−	0.284321i
$83$	−4.32919	+	7.49838i	−0.475191	+	0.823054i	−0.999596	−	0.0284143i	$-0.990954\pi$
$83$	−4.32919	+	7.49838i	−0.475191	+	0.823054i	0.524406	+	0.851469i	$0.324288\pi$
$84$	−2.09049	+	11.3332i	−0.228092	+	1.23655i
$85$	6.18496	−	7.88086i	0.670854	−	0.854799i
$86$	9.06168	−	9.18294i	0.977146	−	0.990222i
$87$	4.43929	+	13.0499i	0.475942	+	1.39909i
$88$	12.6122	+	6.95012i	1.34446	+	0.740885i
$89$			2.70240i			0.286454i	0.989690	+	0.143227i	$0.0457478\pi$
$89$			2.70240i			0.286454i	−0.989690	+	0.143227i	$0.954252\pi$
$90$	−0.0281272	+	9.48679i	−0.00296487	+	0.999996i
$91$	−12.6690	+	12.6690i	−1.32807	+	1.32807i
$92$	−8.13193	+	8.35105i	−0.847813	+	0.870657i
$93$	3.23896	−	2.16725i	0.335865	−	0.224734i
$94$	13.1928	−	0.0876843i	1.36073	−	0.00904394i
$95$	5.32782	+	4.18131i	0.546622	+	0.428994i
$96$	9.16597	−	3.46193i	0.935498	−	0.353332i
$97$	0.414347	+	1.54636i	0.0420705	+	0.157009i	0.983766	−	0.179458i	$-0.0574344\pi$
$97$	0.414347	+	1.54636i	0.0420705	+	0.157009i	−0.941695	+	0.336468i	$0.890768\pi$
$98$	−5.54644	+	1.52574i	−0.560275	+	0.154123i
$99$	14.1037	−	5.86341i	1.41747	−	0.589294i
$100$	−9.63683	−	2.67047i	−0.963683	−	0.267047i
$101$	13.8692	−	3.71625i	1.38004	−	0.369781i	0.508906	−	0.860822i	$-0.330050\pi$
$101$	13.8692	−	3.71625i	1.38004	−	0.369781i	0.871136	+	0.491041i	$0.163384\pi$
$102$	−9.08003	+	6.16338i	−0.899057	+	0.610265i
$103$	−16.3014	−	4.36794i	−1.60622	−	0.430386i	−0.659309	−	0.751872i	$-0.729151\pi$
$103$	−16.3014	−	4.36794i	−1.60622	−	0.430386i	−0.946914	+	0.321486i	$0.895818\pi$
$104$	14.7892	+	3.64835i	1.45020	+	0.357750i
$105$	−11.6138	+	5.57986i	−1.13339	+	0.544539i
$106$	1.08161	−	4.14666i	0.105055	−	0.402760i
$107$	−10.6459			−1.02918			−0.514589	−	0.857437i	$-0.672056\pi$
$107$	−10.6459			−1.02918			−0.514589	+	0.857437i	$0.672056\pi$
$108$	3.19013	−	9.89056i	0.306970	−	0.951719i
$109$	−11.4790	+	11.4790i	−1.09949	+	1.09949i	−0.105017	+	0.994470i	$0.533490\pi$
$109$	−11.4790	+	11.4790i	−1.09949	+	1.09949i	−0.994470	+	0.105017i	$0.966510\pi$
$110$	2.03340	+	15.9712i	0.193877	+	1.52279i
$111$	1.25824	−	0.0832902i	0.119427	−	0.00790556i
$112$	9.65642	+	9.15616i	0.912446	+	0.865176i
$113$	1.74078	+	0.466442i	0.163759	+	0.0438791i	0.339767	−	0.940510i	$-0.389652\pi$
$113$	1.74078	+	0.466442i	0.163759	+	0.0438791i	−0.176008	+	0.984389i	$0.556318\pi$
$114$	−4.16672	−	6.13851i	−0.390249	−	0.574924i
$115$	−12.9013	−	1.84189i	−1.20305	−	0.171758i
$116$	15.4278	+	3.91483i	1.43243	+	0.363482i
$117$	12.8051	−	9.85217i	1.18383	−	0.910834i
$118$	−6.83738	−	3.88720i	−0.629431	−	0.357846i
$119$	−12.9079	−	7.45240i	−1.18327	−	0.683160i
$120$	9.16677	+	5.99753i	0.836807	+	0.547497i
$121$	12.9223	−	7.46070i	1.17476	−	0.678246i
$122$	−9.88824	+	0.0657210i	−0.895239	+	0.00595010i
$123$	−2.71807	+	1.81871i	−0.245080	+	0.163987i
$124$	−0.0598156	−	4.49966i	−0.00537160	−	0.404081i
$125$	−3.93821	−	10.4638i	−0.352244	−	0.935908i
$126$	13.9786	−	1.95343i	1.24531	−	0.174025i
$127$	1.05008	−	1.05008i	0.0931794	−	0.0931794i	−0.658981	−	0.752160i	$-0.729012\pi$
$127$	1.05008	−	1.05008i	0.0931794	−	0.0931794i	0.752160	+	0.658981i	$0.229012\pi$
$128$	2.41679	−	11.0526i	0.213616	−	0.976918i
$129$	−14.1757	−	6.97924i	−1.24810	−	0.614488i
$130$	6.45017	+	15.7618i	0.565717	+	1.38241i
$131$	−5.40820	−	1.44912i	−0.472516	−	0.126610i	0.0146995	−	0.999892i	$-0.495321\pi$
$131$	−5.40820	−	1.44912i	−0.472516	−	0.126610i	−0.487216	+	0.873282i	$0.661988\pi$
$132$	3.19927	−	17.3442i	0.278461	−	1.50962i
$133$	5.03816	−	8.72634i	0.436864	−	0.756670i
$134$	−3.94803	−	14.3520i	−0.341058	−	1.23982i
$135$	11.0354	−	3.63604i	0.949773	−	0.312941i
$136$	0.252648	+	12.6694i	0.0216644	+	1.08640i
$137$	−0.770981	−	2.87734i	−0.0658693	−	0.245828i	0.925139	−	0.379629i	$-0.123948\pi$
$137$	−0.770981	−	2.87734i	−0.0658693	−	0.245828i	−0.991008	+	0.133801i	$0.957282\pi$
$138$	12.8494	+	6.22050i	1.09382	+	0.529525i
$139$	−1.86735	+	6.96905i	−0.158387	+	0.591107i	0.840405	+	0.541959i	$0.182317\pi$
$139$	−1.86735	+	6.96905i	−0.158387	+	0.591107i	−0.998792	+	0.0491479i	$0.984349\pi$
$140$	−1.90681	+	14.7552i	−0.161155	+	1.24704i
$141$	−5.20380	−	15.2973i	−0.438239	−	1.28826i
$142$	3.34648	+	0.872890i	0.280830	+	0.0732513i
$143$	19.3885	−	19.3885i	1.62135	−	1.62135i
$144$	−7.56773	−	9.31287i	−0.630644	−	0.776072i
$145$	6.63024	+	16.5141i	0.550611	+	1.37143i
$146$	−12.4745	+	7.31314i	−1.03240	+	0.605239i
$147$	3.91797	+	5.85541i	0.323148	+	0.482946i
$148$	0.711208	−	1.27056i	0.0584610	−	0.104439i
$149$	0.958684	+	0.256879i	0.0785385	+	0.0210443i	0.297874	−	0.954605i	$-0.403722\pi$
$149$	0.958684	+	0.256879i	0.0785385	+	0.0210443i	−0.219336	+	0.975649i	$0.570389\pi$
$150$	0.623431	+	12.2316i	0.0509029	+	0.998704i
$151$	14.2695	+	8.23852i	1.16124	+	0.670441i	0.951600	−	0.307338i	$-0.0994383\pi$
$151$	14.2695	+	8.23852i	1.16124	+	0.670441i	0.209638	+	0.977779i	$0.432772\pi$
$152$	−8.56512	+	0.170801i	−0.694723	+	0.0138538i
$153$	10.6738	+	8.16829i	0.862926	+	0.660367i
$154$	23.0957	−	6.35329i	1.86110	−	0.511963i
$155$	4.02471	−	3.01908i	0.323272	−	0.242498i
$156$	−1.47959	−	18.5973i	−0.118462	−	1.48897i
$157$	−1.04827	−	1.81566i	−0.0836612	−	0.144906i	0.821159	−	0.570700i	$-0.193328\pi$
$157$	−1.04827	−	1.81566i	−0.0836612	−	0.144906i	−0.904820	+	0.425794i	$0.859995\pi$
$158$	6.46856	+	6.38315i	0.514611	+	0.507816i
$159$	−5.23707	+	0.346672i	−0.415326	+	0.0274929i
$160$	11.5753	−	5.10023i	0.915108	−	0.403208i
$161$			19.3890i			1.52807i
$162$	−12.7274	+	0.117665i	−0.999957	+	0.00924465i
$163$			14.6410i			1.14677i	0.819285	+	0.573387i	$0.194371\pi$
$163$			14.6410i			1.14677i	−0.819285	+	0.573387i	$0.805629\pi$
$164$	0.0501959	+	3.77601i	0.00391964	+	0.294857i
$165$	17.7736	−	8.53937i	1.38367	−	0.664789i
$166$	8.60065	−	8.71574i	0.667540	−	0.676473i
$167$	18.0108	+	4.82599i	1.39372	+	0.373446i	0.876085	−	0.482156i	$-0.160146\pi$
$167$	18.0108	+	4.82599i	1.39372	+	0.373446i	0.517634	+	0.855602i	$0.326813\pi$
$168$	6.90594	−	14.7625i	0.532805	−	1.13895i
$169$	8.00202	−	13.8599i	0.615540	−	1.06615i
$170$	−11.2767	+	8.57674i	−0.864880	+	0.657806i
$171$	−5.52213	+	7.21597i	−0.422288	+	0.551819i
$172$	−15.6780	+	9.33173i	−1.19544	+	0.711538i
$173$	−0.348833	+	0.604196i	−0.0265213	+	0.0459362i	−0.878981	−	0.476856i	$-0.841776\pi$
$173$	−0.348833	+	0.604196i	−0.0265213	+	0.0459362i	0.852460	+	0.522792i	$0.175110\pi$
$174$	−1.41685	−	19.4424i	−0.107411	−	1.47392i
$175$	−14.5835	+	8.00071i	−1.10241	+	0.604797i
$176$	−14.7781	−	14.0125i	−1.11394	−	1.05623i
$177$	−1.87312	+	9.44889i	−0.140792	+	0.710222i
$178$	0.964590	−	3.69804i	0.0722990	−	0.277180i
$179$	14.6359	+	14.6359i	1.09394	+	1.09394i	0.995104	+	0.0988379i	$0.0315125\pi$
$179$	14.6359	+	14.6359i	1.09394	+	1.09394i	0.0988379	+	0.995104i	$0.468487\pi$
$180$	3.42469	−	12.9720i	0.255261	−	0.966872i
$181$	−3.47267	+	3.47267i	−0.258122	+	0.258122i	−0.824290	−	0.566168i	$-0.808425\pi$
$181$	−3.47267	+	3.47267i	−0.258122	+	0.258122i	0.566168	+	0.824290i	$0.308425\pi$
$182$	21.8586	−	12.8145i	1.62027	−	0.949876i
$183$	3.90035	+	11.4656i	0.288322	+	0.847560i
$184$	14.1088	−	8.52521i	1.04011	−	0.628487i
$185$	1.61623	−	0.194866i	0.118827	−	0.0143268i
$186$	−5.20586	+	1.80962i	−0.381713	+	0.132688i
$187$	19.7542	+	11.4051i	1.44457	+	0.834022i
$188$	−18.0847	−	4.58902i	−1.31896	−	0.334689i
$189$	−7.67585	−	15.4889i	−0.558336	−	1.12665i
$190$	−5.79826	−	7.62353i	−0.420650	−	0.553069i
$191$	−13.1691	−	7.60316i	−0.952879	−	0.550145i	−0.0589051	−	0.998264i	$-0.518761\pi$
$191$	−13.1691	−	7.60316i	−0.952879	−	0.550145i	−0.893974	+	0.448118i	$0.852094\pi$
$192$	−13.7787	+	1.46572i	−0.994390	+	0.105779i
$193$	−1.21365	+	4.52941i	−0.0873607	+	0.326034i	−0.995751	−	0.0920893i	$-0.970645\pi$
$193$	−1.21365	+	4.52941i	−0.0873607	+	0.326034i	0.908390	+	0.418124i	$0.137312\pi$
$194$	−0.0150473	−	2.26398i	−0.00108033	−	0.162545i
$195$	15.8222	−	13.5911i	1.13305	−	0.973277i
$196$	8.13450	−	0.108135i	0.581035	−	0.00772391i
$197$	6.95556			0.495563			0.247782	−	0.968816i	$-0.420298\pi$
$197$	6.95556			0.495563			0.247782	+	0.968816i	$0.420298\pi$
$198$	−21.3927	+	2.98951i	−1.52031	+	0.212455i
$199$	2.25215			0.159651			0.0798254	−	0.996809i	$-0.474564\pi$
$199$	2.25215			0.159651			0.0798254	+	0.996809i	$0.474564\pi$
$200$	12.2341	+	7.09410i	0.865083	+	0.501629i
$201$	−15.1515	+	10.1382i	−1.06870	+	0.715090i
$202$	−20.3055	+	0.134958i	−1.42869	+	0.00949564i
$203$	22.9288	−	13.2379i	1.60928	−	0.929121i
$204$	14.6253	−	5.19312i	1.02398	−	0.363591i
$205$	−3.37744	+	2.53354i	−0.235891	+	0.176950i
$206$	20.7482	+	11.7958i	1.44559	+	0.821853i
$207$	2.25965	−	17.3378i	0.157056	−	1.20506i
$208$	−18.9358	−	10.2714i	−1.31296	−	0.712190i
$209$	−7.71035	+	13.3547i	−0.533336	+	0.923765i
$210$	17.8843	−	3.49025i	1.23413	−	0.240850i
$211$	−4.51679	+	16.8569i	−0.310949	+	1.16048i	0.616754	+	0.787156i	$0.288447\pi$
$211$	−4.51679	+	16.8569i	−0.310949	+	1.16048i	−0.927703	+	0.373320i	$0.878219\pi$
$212$	−2.96021	+	5.28834i	−0.203308	+	0.363205i
$213$	−0.279775	−	4.22647i	−0.0191699	−	0.289593i
$214$	14.5682	+	3.79993i	0.995858	+	0.259758i
$215$	−18.7595	−	8.01134i	−1.27939	−	0.546369i
$216$	−7.89578	+	12.3958i	−0.537240	+	0.843430i
$217$	−5.29297	−	5.29297i	−0.359310	−	0.359310i
$218$	19.8055	−	11.6109i	1.34139	−	0.786388i
$219$	13.3226	+	11.6683i	0.900261	+	0.788474i
$220$	2.91817	−	22.5812i	0.196743	−	1.52243i
$221$	23.3062	+	6.24489i	1.56775	+	0.420076i
$222$	−1.75154	−	0.335137i	−0.117556	−	0.0224929i
$223$	17.4935	−	4.68737i	1.17145	−	0.313890i	0.379922	−	0.925019i	$-0.375951\pi$
$223$	17.4935	−	4.68737i	1.17145	−	0.313890i	0.791531	+	0.611129i	$0.209284\pi$
$224$	−9.94592	−	15.9763i	−0.664540	−	1.06746i
$225$	13.9731	−	5.45467i	0.931538	−	0.363645i
$226$	−2.21565	−	1.25964i	−0.147383	−	0.0837903i
$227$	10.0613	+	5.80889i	0.667792	+	0.385550i	0.795239	−	0.606295i	$-0.207345\pi$
$227$	10.0613	+	5.80889i	0.667792	+	0.385550i	−0.127447	+	0.991845i	$0.540678\pi$
$228$	3.51079	+	9.88737i	0.232507	+	0.654807i
$229$	−2.37587	+	8.86686i	−0.157002	+	0.585938i	0.841924	+	0.539596i	$0.181423\pi$
$229$	−2.37587	+	8.86686i	−0.157002	+	0.585938i	−0.998926	+	0.0463421i	$0.985244\pi$
$230$	16.9970	+	7.12546i	1.12075	+	0.469839i
$231$	−16.3146	−	24.3823i	−1.07342	−	1.60424i
$232$	−19.7144	−	10.8639i	−1.29432	−	0.713251i
$233$	8.53060	+	8.53060i	0.558858	+	0.558858i	0.928982	−	0.370124i	$-0.120685\pi$
$233$	8.53060	+	8.53060i	0.558858	+	0.558858i	−0.370124	+	0.928982i	$0.620685\pi$
$234$	−21.0395	+	8.91135i	−1.37540	+	0.582553i
$235$	−7.77206	−	19.3581i	−0.506994	−	1.26279i
$236$	7.96897	+	7.75988i	0.518735	+	0.505125i
$237$	4.91626	−	9.98553i	0.319345	−	0.648630i
$238$	15.0035	+	14.8054i	0.972534	+	0.959692i
$239$	−3.26618	−	5.65720i	−0.211272	−	0.365934i	0.740841	−	0.671680i	$-0.234427\pi$
$239$	−3.26618	−	5.65720i	−0.211272	−	0.365934i	−0.952113	+	0.305747i	$0.901094\pi$
$240$	−10.4033	−	11.4792i	−0.671531	−	0.740977i
$241$	4.04160	−	7.00026i	0.260342	−	0.450926i	−0.705991	−	0.708221i	$-0.749498\pi$
$241$	4.04160	−	7.00026i	0.260342	−	0.450926i	0.966333	+	0.257295i	$0.0828312\pi$
$242$	−20.3463	+	5.59696i	−1.30791	+	0.359786i
$243$	5.05866	+	14.7448i	0.324514	+	0.945881i
$244$	13.5548	+	3.43956i	0.867757	+	0.220195i
$245$	5.45790	+	7.27588i	0.348692	+	0.464839i
$246$	4.36864	−	1.51859i	0.278535	−	0.0968217i
$247$	−4.22182	+	15.7561i	−0.268628	+	1.00253i
$248$	−1.52425	+	6.17881i	−0.0967898	+	0.392355i
$249$	−13.4545	−	6.62416i	−0.852644	−	0.419789i
$250$	1.65423	+	15.7246i	0.104623	+	0.994512i
$251$	8.80747	+	8.80747i	0.555923	+	0.555923i	0.928144	−	0.372221i	$-0.121404\pi$
$251$	8.80747	+	8.80747i	0.555923	+	0.555923i	−0.372221	+	0.928144i	$0.621404\pi$
$252$	−19.8260	−	2.31637i	−1.24892	−	0.145917i
$253$		−	29.6728i		−	1.86551i
$254$	−1.81177	+	1.06214i	−0.113681	+	0.0666448i
$255$	14.3278	+	9.78768i	0.897243	+	0.612928i
$256$	−7.25229	+	14.2620i	−0.453268	+	0.891374i
$257$	−3.66330	+	13.6716i	−0.228511	+	0.852813i	0.752457	+	0.658642i	$0.228869\pi$
$257$	−3.66330	+	13.6716i	−0.228511	+	0.852813i	−0.980968	+	0.194172i	$0.937798\pi$
$258$	16.9073	+	14.6104i	1.05260	+	0.909607i
$259$	−0.626866	−	2.33950i	−0.0389516	−	0.145369i
$260$	−3.20058	−	23.8713i	−0.198492	−	1.48043i
$261$	−22.0458	+	9.16524i	−1.36460	+	0.567314i
$262$	6.88348	+	3.91341i	0.425263	+	0.241771i
$263$	15.1114	−	4.04910i	0.931811	−	0.249678i	0.239184	−	0.970974i	$-0.423120\pi$
$263$	15.1114	−	4.04910i	0.931811	−	0.249678i	0.692627	+	0.721296i	$0.256453\pi$
$264$	−10.5688	+	22.5924i	−0.650464	+	1.39046i
$265$	−6.72710	+	0.811076i	−0.413243	+	0.0498240i
$266$	−10.0091	+	10.1431i	−0.613698	+	0.621911i
$267$	−4.67047	+	0.309166i	−0.285828	+	0.0189206i
$268$	0.279810	+	21.0489i	0.0170921	+	1.28577i
$269$	4.34881	+	4.34881i	0.265151	+	0.265151i	0.827143	−	0.561992i	$-0.189965\pi$
$269$	4.34881	+	4.34881i	0.265151	+	0.265151i	−0.561992	+	0.827143i	$0.689965\pi$
$270$	−16.3989	+	1.03672i	−0.998008	+	0.0630927i
$271$	−21.3250			−1.29540			−0.647701	−	0.761895i	$-0.724269\pi$
$271$	−21.3250			−1.29540			−0.647701	+	0.761895i	$0.724269\pi$
$272$	4.17648	−	17.4274i	0.253236	−	1.05669i
$273$	−23.3448	−	20.4460i	−1.41289	−	1.23745i
$274$	0.0279987	+	4.21262i	0.00169146	+	0.254494i
$275$	22.3185	−	12.2442i	1.34585	−	0.738354i
$276$	−15.3632	−	13.0988i	−0.924755	−	0.788453i
$277$	−9.75770	−	5.63361i	−0.586283	−	0.338491i	0.177343	−	0.984149i	$-0.443250\pi$
$277$	−9.75770	−	5.63361i	−0.586283	−	0.338491i	−0.763626	+	0.645658i	$0.776583\pi$
$278$	5.04286	−	8.87011i	0.302450	−	0.531994i
$279$	4.11614	+	5.34986i	0.246427	+	0.320288i
$280$	7.87604	−	19.5108i	0.470683	−	1.16599i
$281$	13.9174	−	24.1057i	0.830243	−	1.43802i	−0.0676027	−	0.997712i	$-0.521535\pi$
$281$	13.9174	−	24.1057i	0.830243	−	1.43802i	0.897846	−	0.440310i	$-0.145132\pi$
$282$	1.66085	+	22.7906i	0.0989023	+	1.35716i
$283$	5.91431	+	10.2439i	0.351569	+	0.608936i	0.986525	−	0.163613i	$-0.0523148\pi$
$283$	5.91431	+	10.2439i	0.351569	+	0.608936i	−0.634955	+	0.772549i	$0.718981\pi$
$284$	−4.26785	−	2.38897i	−0.253250	−	0.141760i
$285$	−6.61691	+	9.68626i	−0.391952	+	0.573764i
$286$	−33.4522	+	19.6112i	−1.97807	+	1.15964i
$287$	4.44174	+	4.44174i	0.262188	+	0.262188i
$288$	7.03177	+	15.4452i	0.414351	+	0.910117i
$289$			3.07235i			0.180726i
$290$	−3.17847	−	24.9650i	−0.186646	−	1.46600i
$291$	−2.62513	+	0.893013i	−0.153888	+	0.0523494i
$292$	19.6808	−	5.55487i	1.15173	−	0.325074i
$293$	−0.506253	+	0.292285i	−0.0295756	+	0.0170755i	−0.514715	−	0.857361i	$-0.672102\pi$
$293$	−0.506253	+	0.292285i	−0.0295756	+	0.0170755i	0.485139	+	0.874437i	$0.338769\pi$
$294$	−3.27143	−	9.41118i	−0.190794	−	0.548871i
$295$	−1.75762	+	12.3110i	−0.102333	+	0.716774i
$296$	−1.42675	+	1.48481i	−0.0829280	+	0.0863028i
$297$	11.7471	+	23.7041i	0.681633	+	1.37545i
$298$	−1.22020	−	0.693711i	−0.0706843	−	0.0401856i
$299$	−8.12371	−	30.3181i	−0.469806	−	1.75334i
$300$	3.51280	−	16.9606i	0.202811	−	0.979218i
$301$	−7.85484	+	29.3147i	−0.452746	+	1.68967i
$302$	−16.5862	−	16.3672i	−0.954427	−	0.941824i
$303$	8.00939	+	23.5446i	0.460127	+	1.35260i
$304$	11.7817	+	2.82349i	0.675728	+	0.161938i
$305$	5.82531	+	14.5093i	0.333556	+	0.830800i
$306$	−11.6908	−	14.9876i	−0.668316	−	0.856784i
$307$	−7.20507			−0.411215			−0.205607	−	0.978635i	$-0.565917\pi$
$307$	−7.20507			−0.411215			−0.205607	+	0.978635i	$0.565917\pi$
$308$	−33.8725	+	0.450280i	−1.93007	+	0.0256571i
$309$	5.68403	−	28.6729i	0.323353	−	1.63114i
$310$	−6.58515	+	2.69482i	−0.374011	+	0.153055i
$311$	10.1182	+	17.5252i	0.573748	+	0.993761i	0.996176	+	0.0873648i	$0.0278446\pi$
$311$	10.1182	+	17.5252i	0.573748	+	0.993761i	−0.422428	+	0.906396i	$0.638822\pi$
$312$	−4.61338	+	25.9772i	−0.261181	+	1.47067i
$313$	2.36730	+	8.83488i	0.133808	+	0.499377i	1.00000		0.000333938i	$-0.000106296\pi$
$313$	2.36730	+	8.83488i	0.133808	+	0.499377i	−0.866192	+	0.499711i	$0.833440\pi$
$314$	0.786406	+	2.85877i	0.0443795	+	0.161330i
$315$	−10.9722	−	19.4333i	−0.618211	−	1.09494i
$316$	−6.57337	−	11.0438i	−0.369781	−	0.621260i
$317$	−8.91820	−	5.14893i	−0.500896	−	0.289193i	0.228187	−	0.973617i	$-0.426720\pi$
$317$	−8.91820	−	5.14893i	−0.500896	−	0.289193i	−0.729084	+	0.684425i	$0.760053\pi$
$318$	7.29029	+	1.39491i	0.408819	+	0.0782229i
$319$	−35.0900	+	20.2592i	−1.96466	+	1.13430i
$320$	−17.6604	+	2.84762i	−0.987248	+	0.159187i
$321$	−1.21794	−	18.3990i	−0.0679786	−	1.02693i
$322$	6.92069	−	26.5325i	0.385675	−	1.47860i
$323$	−13.5698			−0.755045
$324$	17.4585	+	4.38187i	0.969917	+	0.243437i
$325$	19.4517	−	18.6208i	1.07898	−	1.03289i
$326$	5.22595	−	20.0352i	0.289438	−	1.10965i
$327$	−21.1520	−	18.5255i	−1.16971	−	1.02446i
$328$	1.27911	−	5.18511i	0.0706272	−	0.286300i
$329$	−26.8775	+	15.5177i	−1.48180	+	0.855519i
$330$	−27.3699	+	5.34144i	−1.50666	+	0.294037i
$331$	−0.313289	−	1.16921i	−0.0172199	−	0.0642657i	0.956781	−	0.290809i	$-0.0939243\pi$
$331$	−0.313289	−	1.16921i	−0.0172199	−	0.0642657i	−0.974001	+	0.226543i	$0.927258\pi$
$332$	−14.8803	+	8.85696i	−0.816665	+	0.486089i
$333$	0.287896	+	2.16504i	0.0157766	+	0.118644i
$334$	−22.9239	−	13.0328i	−1.25434	−	0.713121i
$335$	−18.8271	+	14.1229i	−1.02864	+	0.771617i
$336$	−14.7196	+	17.7364i	−0.803019	+	0.967599i
$337$	−25.1804	−	6.74707i	−1.37167	−	0.367537i	−0.503579	−	0.863949i	$-0.667984\pi$
$337$	−25.1804	−	6.74707i	−1.37167	−	0.367537i	−0.868087	+	0.496413i	$0.834650\pi$
$338$	−15.8973	+	16.1100i	−0.864700	+	0.876271i
$339$	−0.606983	+	3.06191i	−0.0329668	+	0.166300i
$340$	18.4927	−	7.71157i	1.00291	−	0.418219i
$341$	8.10032	+	8.10032i	0.438657	+	0.438657i
$342$	10.1323	−	7.90348i	0.547892	−	0.427371i
$343$	−6.89817	+	6.89817i	−0.372466	+	0.372466i
$344$	24.7851	−	7.17372i	1.33632	−	0.386781i
$345$	1.70733	−	22.5076i	0.0919194	−	1.21177i
$346$	0.693013	−	0.702287i	0.0372566	−	0.0377552i
$347$	−3.15091	−	5.45754i	−0.169150	−	0.292976i	0.768971	−	0.639283i	$-0.220769\pi$
$347$	−3.15091	−	5.45754i	−0.169150	−	0.292976i	−0.938121	+	0.346307i	$0.887435\pi$
$348$	−5.00087	+	27.1112i	−0.268075	+	1.45331i
$349$	2.15842	+	8.05534i	0.115538	+	0.431192i	0.999327	−	0.0366935i	$-0.0116825\pi$
$349$	2.15842	+	8.05534i	0.115538	+	0.431192i	−0.883789	+	0.467886i	$0.845016\pi$
$350$	22.8122	−	5.74298i	1.21937	−	0.306975i
$351$	18.4922	+	21.0035i	0.987038	+	1.12109i
$352$	15.2212	+	24.4500i	0.811290	+	1.30319i
$353$	4.99132	+	18.6278i	0.265661	+	0.991460i	0.961845	+	0.273596i	$0.0882132\pi$
$353$	4.99132	+	18.6278i	0.265661	+	0.991460i	−0.696184	+	0.717864i	$0.745120\pi$
$354$	5.93590	−	12.2615i	0.315490	−	0.651693i
$355$	−0.654563	−	5.42897i	−0.0347406	−	0.288140i
$356$	−2.63994	+	4.71620i	−0.139917	+	0.249958i
$357$	11.4030	−	23.1610i	0.603512	−	1.22581i
$358$	−14.8041	−	25.2524i	−0.782421	−	1.33463i
$359$			15.0594i			0.794803i	0.917645	+	0.397401i	$0.130088\pi$
$359$			15.0594i			0.794803i	−0.917645	+	0.397401i	$0.869912\pi$
$360$	−9.31663	+	16.5288i	−0.491029	+	0.871143i
$361$			9.82620i			0.517168i
$362$	5.99163	−	3.51257i	0.314913	−	0.184617i
$363$	14.3725	+	21.4797i	0.754359	+	1.12739i
$364$	−34.4859	+	9.73358i	−1.80755	+	0.510178i
$365$	17.9859	+	14.1155i	0.941424	+	0.738838i
$366$	−1.24484	−	17.0820i	−0.0650689	−	0.892891i
$367$	−2.79703	−	10.4387i	−0.146004	−	0.544894i	−0.999709	−	0.0241369i	$-0.992316\pi$
$367$	−2.79703	−	10.4387i	−0.146004	−	0.544894i	0.853705	−	0.520757i	$-0.174350\pi$
$368$	−22.3498	+	6.63017i	−1.16506	+	0.345621i
$369$	−3.45417	−	4.48948i	−0.179817	−	0.233713i
$370$	−2.28125	−	0.310234i	−0.118596	−	0.0161283i
$371$	2.60916	+	9.73750i	0.135461	+	0.505546i
$372$	7.76977	−	0.618157i	0.402844	−	0.0320500i
$373$	−11.2574	−	19.4984i	−0.582887	−	1.00959i	−0.995135	−	0.0985189i	$-0.968590\pi$
$373$	−11.2574	−	19.4984i	−0.582887	−	1.00959i	0.412248	−	0.911072i	$-0.364744\pi$
$374$	−22.9613	−	22.6581i	−1.18730	−	1.17162i
$375$	17.6337	−	8.00338i	0.910598	−	0.413293i
$376$	23.1096	+	12.7348i	1.19178	+	0.656750i
$377$	−30.3066	+	30.3066i	−1.56087	+	1.56087i
$378$	4.97526	+	23.9353i	0.255900	+	1.23110i
$379$	−9.05026	−	9.05026i	−0.464880	−	0.464880i	0.435371	−	0.900251i	$-0.356617\pi$
$379$	−9.05026	−	9.05026i	−0.464880	−	0.464880i	−0.900251	+	0.435371i	$0.856617\pi$
$380$	5.21337	+	12.5019i	0.267440	+	0.641333i
$381$	1.93495	+	1.69468i	0.0991305	+	0.0868213i
$382$	15.3070	+	15.1049i	0.783176	+	0.772835i
$383$	−15.8674	−	4.25165i	−0.810784	−	0.217249i	−0.170471	−	0.985363i	$-0.554529\pi$
$383$	−15.8674	−	4.25165i	−0.810784	−	0.217249i	−0.640313	+	0.768114i	$0.721196\pi$
$384$	19.3783	+	2.91241i	0.988894	+	0.148623i
$385$	−22.7270	−	30.2972i	−1.15828	−	1.54409i
$386$	3.27752	−	5.76498i	0.166821	−	0.293430i
$387$	10.4402	−	25.2979i	0.530707	−	1.28596i
$388$	−0.787511	+	3.10347i	−0.0399798	+	0.157555i
$389$	−7.33803	−	27.3859i	−0.372053	−	1.38852i	−0.857603	−	0.514312i	$-0.828047\pi$
$389$	−7.33803	−	27.3859i	−0.372053	−	1.38852i	0.485550	−	0.874209i	$-0.338619\pi$
$390$	−26.5028	+	12.9508i	−1.34202	+	0.655791i
$391$	22.6130	−	13.0556i	1.14359	−	0.660252i
$392$	−11.1701	−	2.75554i	−0.564174	−	0.139176i
$393$	1.88575	−	9.51260i	0.0951236	−	0.479847i
$394$	−9.51819	−	2.48271i	−0.479519	−	0.125077i
$395$	5.64327	−	13.2144i	0.283944	−	0.664889i
$396$	30.3415	+	3.54495i	1.52472	+	0.178140i
$397$	−12.4026			−0.622466			−0.311233	−	0.950334i	$-0.600742\pi$
$397$	−12.4026			−0.622466			−0.311233	+	0.950334i	$0.600742\pi$
$398$	−3.08191	−	0.803879i	−0.154482	−	0.0402948i
$399$	15.6578	+	7.70895i	0.783873	+	0.385930i
$400$	−14.2094	−	14.0746i	−0.710468	−	0.703730i
$401$	28.0338	−	16.1853i	1.39994	−	0.808256i	0.405554	−	0.914071i	$-0.367079\pi$
$401$	28.0338	−	16.1853i	1.39994	−	0.808256i	0.994386	+	0.105816i	$0.0337453\pi$
$402$	24.3524	−	8.46518i	1.21459	−	0.422205i
$403$	10.4942	+	6.05881i	0.522751	+	0.301811i
$404$	27.8348	+	7.06315i	1.38484	+	0.351405i
$405$	7.54655	+	18.6561i	0.374991	+	0.927028i
$406$	−36.1015	+	9.93100i	−1.79169	+	0.492867i
$407$	0.959350	+	3.58034i	0.0475532	+	0.177471i
$408$	−21.8673	+	1.88608i	−1.08259	+	0.0933750i
$409$	18.1005	+	31.3509i	0.895010	+	1.55020i	0.833792	+	0.552078i	$0.186165\pi$
$409$	18.1005	+	31.3509i	0.895010	+	1.55020i	0.0612177	+	0.998124i	$0.480502\pi$
$410$	5.52611	−	2.26143i	0.272915	−	0.111684i
$411$	4.88461	−	1.66164i	0.240940	−	0.0819627i
$412$	−24.1820	−	23.5475i	−1.19136	−	1.16010i
$413$	18.5019			0.910420
$414$	−9.28067	+	22.9189i	−0.456120	+	1.12640i
$415$	−17.8051	−	7.60374i	−0.874018	−	0.373253i
$416$	22.2460	+	20.8145i	1.09070	+	1.02052i
$417$	−12.2580	−	2.42999i	−0.600278	−	0.118997i
$418$	15.3179	−	15.5228i	0.749221	−	0.759247i
$419$	−1.61933	+	6.04343i	−0.0791095	+	0.295241i	−0.994134	−	0.108158i	$-0.965505\pi$
$419$	−1.61933	+	6.04343i	−0.0791095	+	0.295241i	0.915024	+	0.403399i	$0.132171\pi$
$420$	−25.7191	−	1.60742i	−1.25496	−	0.0784343i
$421$	−7.00812	−	26.1547i	−0.341555	−	1.27470i	−0.896585	−	0.442871i	$-0.853960\pi$
$421$	−7.00812	−	26.1547i	−0.341555	−	1.27470i	0.555030	−	0.831830i	$-0.312707\pi$
$422$	12.1978	−	21.4552i	0.593778	−	1.04442i
$423$	25.8424	−	10.7436i	1.25650	−	0.522374i
$424$	5.93844	−	6.18010i	0.288396	−	0.300132i
$425$	19.1509	+	11.6212i	0.928955	+	0.563709i
$426$	−1.12574	+	5.88348i	−0.0545421	+	0.285055i
$427$	20.1452	−	11.6308i	0.974893	−	0.562855i
$428$	−18.5791	−	10.3999i	−0.898056	−	0.502697i
$429$	35.7266	+	31.2904i	1.72490	+	1.51071i
$430$	22.8115	+	17.6589i	1.10007	+	0.851589i
$431$			11.7892i			0.567868i	0.958844	+	0.283934i	$0.0916396\pi$
$431$			11.7892i			0.567868i	−0.958844	+	0.283934i	$0.908360\pi$
$432$	15.2294	−	14.1445i	0.732723	−	0.680528i
$433$	27.9641	+	27.9641i	1.34387	+	1.34387i	0.892171	+	0.451697i	$0.149181\pi$
$433$	27.9641	+	27.9641i	1.34387	+	1.34387i	0.451697	+	0.892171i	$0.350819\pi$
$434$	5.35379	+	9.13232i	0.256990	+	0.438365i
$435$	−27.7824	+	13.3481i	−1.33206	+	0.639993i
$436$	−31.2467	+	8.81932i	−1.49645	+	0.422369i
$437$	8.82620	+	15.2874i	0.422214	+	0.731297i
$438$	−14.0662	−	20.7227i	−0.672109	−	0.990167i
$439$	−1.84454	+	3.19485i	−0.0880353	+	0.152482i	−0.906681	−	0.421818i	$-0.861392\pi$
$439$	−1.84454	+	3.19485i	−0.0880353	+	0.152482i	0.818645	+	0.574299i	$0.194726\pi$
$440$	−12.0534	+	29.8592i	−0.574624	+	1.42348i
$441$	−9.67149	+	7.44118i	−0.460547	+	0.354342i
$442$	−29.6639	−	16.8646i	−1.41097	−	0.802166i
$443$	−20.5828	−	11.8835i	−0.977917	−	0.564601i	−0.0762765	−	0.997087i	$-0.524303\pi$
$443$	−20.5828	−	11.8835i	−0.977917	−	0.564601i	−0.901641	+	0.432486i	$0.857637\pi$
$444$	2.27723	+	1.08380i	0.108073	+	0.0514349i
$445$	−5.99930	+	0.723326i	−0.284394	+	0.0342889i
$446$	−25.6117	+	0.170225i	−1.21275	+	0.00806041i
$447$	−0.334278	+	1.68625i	−0.0158108	+	0.0797570i
$448$	7.90773	+	25.4125i	0.373605	+	1.20063i
$449$	5.95485			0.281027			0.140513	−	0.990079i	$-0.455125\pi$
$449$	5.95485			0.281027			0.140513	+	0.990079i	$0.455125\pi$
$450$	−21.0681	+	2.47680i	−0.993160	+	0.116757i
$451$	−6.79760	−	6.79760i	−0.320087	−	0.320087i
$452$	2.58234	+	2.51458i	0.121463	+	0.118276i
$453$	−12.6059	+	25.6041i	−0.592276	+	1.20299i
$454$	−11.6947	−	11.5403i	−0.548862	−	0.541614i
$455$	−31.5160	−	24.7340i	−1.47749	−	1.15955i
$456$	−1.27508	−	14.7833i	−0.0597109	−	0.692291i
$457$	28.0033	−	7.50347i	1.30994	−	0.350998i	0.464740	−	0.885447i	$-0.346148\pi$
$457$	28.0033	−	7.50347i	1.30994	−	0.350998i	0.845200	+	0.534450i	$0.179481\pi$
$458$	6.41612	−	11.2856i	0.299806	−	0.527342i
$459$	−12.8959	+	19.3817i	−0.601928	+	0.904660i
$460$	−20.7158	−	15.8176i	−0.965881	−	0.737498i
$461$	9.31393	+	34.7601i	0.433793	+	1.61894i	0.743938	+	0.668249i	$0.232956\pi$
$461$	9.31393	+	34.7601i	0.433793	+	1.61894i	−0.310145	+	0.950689i	$0.600378\pi$
$462$	13.6224	+	39.1887i	0.633773	+	1.82322i
$463$	4.42686	−	16.5213i	0.205734	−	0.767809i	−0.783491	−	0.621403i	$-0.786563\pi$
$463$	4.42686	−	16.5213i	0.205734	−	0.767809i	0.989225	−	0.146406i	$-0.0467705\pi$
$464$	23.1000	+	21.9033i	1.07239	+	1.01684i
$465$	5.67822	+	6.61038i	0.263321	+	0.306549i
$466$	−8.62861	−	14.7184i	−0.399713	−	0.681817i
$467$			15.6305i			0.723293i	0.932315	+	0.361646i	$0.117785\pi$
$467$			15.6305i			0.723293i	−0.932315	+	0.361646i	$0.882215\pi$
$468$	31.9718	−	4.68473i	1.47790	−	0.216552i
$469$	24.7599	+	24.7599i	1.14331	+	1.14331i
$470$	3.72585	+	29.2644i	0.171861	+	1.34986i
$471$	3.01802	−	2.01942i	0.139063	−	0.0930497i
$472$	−8.13516	−	13.4633i	−0.374451	−	0.619697i
$473$	12.0210	−	44.8629i	0.552725	−	2.06280i
$474$	−10.2918	+	11.9097i	−0.472716	+	0.547029i
$475$	−7.85643	+	12.9469i	−0.360478	+	0.594043i
$476$	−15.2466	−	25.6155i	−0.698828	−	1.17408i
$477$	−1.19829	−	9.01139i	−0.0548657	−	0.412603i
$478$	2.45027	+	8.90729i	0.112073	+	0.407410i
$479$	7.72604	−	13.3819i	0.353012	−	0.611434i	−0.633764	−	0.773527i	$-0.718491\pi$
$479$	7.72604	−	13.3819i	0.353012	−	0.611434i	0.986776	+	0.162092i	$0.0518242\pi$
$480$	10.1388	+	19.4217i	0.462772	+	0.886477i
$481$	1.96043	+	3.39556i	0.0893878	+	0.154824i
$482$	−8.02930	+	8.13675i	−0.365725	+	0.370619i
$483$	−33.5094	+	2.21819i	−1.52473	+	0.100931i
$484$	29.8402	−	0.396676i	1.35637	−	0.0180307i
$485$	−3.32201	+	1.33375i	−0.150845	+	0.0605623i
$486$	−1.65942	−	21.9829i	−0.0752730	−	0.997163i
$487$	1.44599	+	1.44599i	0.0655239	+	0.0655239i	0.739109	−	0.673585i	$-0.235247\pi$
$487$	1.44599	+	1.44599i	0.0655239	+	0.0655239i	−0.673585	+	0.739109i	$0.735247\pi$
$488$	−17.3211	−	9.54501i	−0.784087	−	0.432083i
$489$	−25.3036	+	1.67500i	−1.14427	+	0.0757460i
$490$	−4.87170	−	11.9047i	−0.220081	−	0.537798i
$491$	9.46170	−	35.3116i	0.427001	−	1.59359i	−0.332514	−	0.943098i	$-0.607897\pi$
$491$	9.46170	−	35.3116i	0.427001	−	1.59359i	0.759515	−	0.650490i	$-0.225436\pi$
$492$	−6.52022	+	0.518744i	−0.293954	+	0.0233868i
$493$	−30.8783	−	17.8276i	−1.39069	−	0.802914i
$494$	11.4012	−	20.0541i	0.512964	−	0.902277i
$495$	16.7917	+	29.7406i	0.754731	+	1.33674i
$496$	4.29128	−	7.91119i	0.192684	−	0.355223i
$497$	−7.85845	+	2.10567i	−0.352500	+	0.0944520i
$498$	16.0471	+	13.8671i	0.719087	+	0.621400i
$499$	−6.64149	−	1.77958i	−0.297314	−	0.0796650i	0.107079	−	0.994251i	$-0.465850\pi$
$499$	−6.64149	−	1.77958i	−0.297314	−	0.0796650i	−0.404392	+	0.914586i	$0.632517\pi$
$500$	3.34902	−	22.1085i	0.149773	−	0.988720i
$501$	−6.28008	+	31.6797i	−0.280573	+	1.41534i
$502$	−8.90866	−	15.1961i	−0.397613	−	0.678236i
$503$	−20.0090	−	20.0090i	−0.892156	−	0.892156i	0.102570	−	0.994726i	$-0.467294\pi$
$503$	−20.0090	−	20.0090i	−0.892156	−	0.892156i	−0.994726	+	0.102570i	$0.967294\pi$
$504$	26.3036	+	10.2464i	1.17165	+	0.456412i
$505$	11.9623	+	29.7949i	0.532316	+	1.32586i
$506$	−10.5914	+	40.6051i	−0.470843	+	1.80512i
$507$	24.8691	+	12.2440i	1.10448	+	0.543775i
$508$	2.85840	−	0.806776i	0.126821	−	0.0357949i
$509$	7.16232	−	26.7301i	0.317464	−	1.18479i	−0.604209	−	0.796826i	$-0.706511\pi$
$509$	7.16232	−	26.7301i	0.317464	−	1.18479i	0.921673	−	0.387967i	$-0.126822\pi$
$510$	−16.1130	−	18.5079i	−0.713496	−	0.819543i
$511$	17.0080	−	29.4588i	0.752391	−	1.30318i
$512$	15.0149	−	16.9279i	0.663571	−	0.748114i
$513$	−13.1029	−	8.71819i	−0.578507	−	0.384917i
$514$	9.89290	−	17.4011i	0.436357	−	0.767529i
$515$	5.33355	−	37.3581i	0.235024	−	1.64619i
$516$	−17.9214	−	26.0282i	−0.788944	−	1.14583i
$517$	41.1330	−	23.7482i	1.80903	−	1.04444i
$518$	0.0227651	+	3.42518i	0.00100024	+	0.150494i
$519$	−1.08412	−	0.533754i	−0.0475876	−	0.0234292i
$520$	−4.14081	+	33.8085i	−0.181586	+	1.48260i
$521$	7.29370			0.319543			0.159771	−	0.987154i	$-0.448924\pi$
$521$	7.29370			0.319543			0.159771	+	0.987154i	$0.448924\pi$
$522$	33.4395	−	4.67298i	1.46361	−	0.204531i
$523$	25.4354			1.11221			0.556105	−	0.831112i	$-0.312295\pi$
$523$	25.4354			1.11221			0.556105	+	0.831112i	$0.312295\pi$
$524$	−8.02270	−	7.81220i	−0.350473	−	0.341278i
$525$	−15.4958	−	24.2889i	−0.676292	−	1.06005i
$526$	−22.1242	+	0.147046i	−0.964661	+	0.00641151i
$527$	−2.60905	+	9.73712i	−0.113652	+	0.424156i
$528$	22.5267	−	27.1436i	0.980349	−	1.18127i
$529$	−9.49776	−	5.48354i	−0.412946	−	0.238415i
$530$	9.49506	+	1.29126i	0.412439	+	0.0560888i
$531$	−16.5445	−	2.15626i	−0.717970	−	0.0935738i
$532$	17.3172	−	10.3074i	0.750796	−	0.446883i
$533$	−8.80646	−	5.08441i	−0.381450	−	0.220230i
$534$	6.50155	+	1.24400i	0.281350	+	0.0538331i
$535$	−2.84949	−	23.6338i	−0.123194	−	1.02178i
$536$	7.13025	−	28.9038i	0.307980	−	1.24845i
$537$	−23.6204	+	26.9692i	−1.01930	+	1.16381i
$538$	−4.39877	−	7.50328i	−0.189644	−	0.323489i
$539$	−14.6438	+	14.6438i	−0.630752	+	0.630752i
$540$	22.8108	+	4.43474i	0.981621	+	0.190841i
$541$	4.74796	+	4.74796i	0.204131	+	0.204131i	0.801767	−	0.597637i	$-0.203893\pi$
$541$	4.74796	+	4.74796i	0.204131	+	0.204131i	−0.597637	+	0.801767i	$0.703893\pi$
$542$	29.1817	+	7.61171i	1.25346	+	0.326951i
$543$	−6.39900	−	5.60442i	−0.274607	−	0.240509i
$544$	−11.9357	+	22.3574i	−0.511740	+	0.958566i
$545$	−28.5557	−	22.4108i	−1.22319	−	0.959972i
$546$	24.6477	+	36.3115i	1.05482	+	1.55399i
$547$	−5.33334	+	9.23761i	−0.228037	+	0.394972i	−0.957226	−	0.289340i	$-0.906564\pi$
$547$	−5.33334	+	9.23761i	−0.228037	+	0.394972i	0.729189	+	0.684312i	$0.239897\pi$
$548$	1.46533	−	5.77466i	0.0625959	−	0.246681i
$549$	−19.3694	+	8.05256i	−0.826665	+	0.343675i
$550$	−34.9117	+	8.78900i	−1.48864	+	0.374764i
$551$	12.0522	−	20.8751i	0.513443	−	0.889310i
$552$	16.3479	+	23.4084i	0.695815	+	0.996329i
$553$	−20.6496	−	5.53304i	−0.878109	−	0.235289i
$554$	11.3419	+	11.1921i	0.481869	+	0.475506i
$555$	0.521685	+	2.77098i	0.0221443	+	0.117622i
$556$	−10.0669	+	10.3381i	−0.426930	+	0.438434i
$557$			3.33790i			0.141431i	0.997497	+	0.0707157i	$0.0225283\pi$
$557$			3.33790i			0.141431i	−0.997497	+	0.0707157i	$0.977472\pi$
$558$	−3.72308	−	8.79010i	−0.157610	−	0.372115i
$559$		−	49.1296i		−	2.07796i
$560$	−17.7420	+	23.8879i	−0.749734	+	1.00945i
$561$	−17.4511	+	35.4453i	−0.736785	+	1.49650i
$562$	−27.6492	+	28.0192i	−1.16631	+	1.18192i
$563$	9.42212	+	16.3196i	0.397095	+	0.687789i	0.993366	−	0.114994i	$-0.0366850\pi$
$563$	9.42212	+	16.3196i	0.397095	+	0.687789i	−0.596271	+	0.802783i	$0.703352\pi$
$564$	5.86209	−	31.7801i	0.246839	−	1.33819i
$565$	−0.569556	+	3.98937i	−0.0239614	+	0.167834i
$566$	−4.43687	−	16.1291i	−0.186496	−	0.677956i
$567$	25.8909	−	15.0379i	1.08731	−	0.631534i
$568$	4.98753	+	4.79250i	0.209272	+	0.201089i
$569$	−22.9235	−	13.2349i	−0.961004	−	0.554836i	−0.0645221	−	0.997916i	$-0.520552\pi$
$569$	−22.9235	−	13.2349i	−0.961004	−	0.554836i	−0.896482	+	0.443080i	$0.853886\pi$
$570$	12.5122	−	10.8931i	0.524077	−	0.456262i
$571$	−29.2251	−	7.83083i	−1.22303	−	0.327710i	−0.411169	−	0.911559i	$-0.634879\pi$
$571$	−29.2251	−	7.83083i	−1.22303	−	0.327710i	−0.811862	+	0.583849i	$0.801546\pi$
$572$	52.7769	−	14.8962i	2.20671	−	0.622841i
$573$	11.6337	−	23.6295i	0.486005	−	0.987136i
$574$	−4.49278	−	7.66363i	−0.187525	−	0.319874i
$575$	0.635822	−	29.1337i	0.0265156	−	1.21496i
$576$	−4.10949	−	23.6456i	−0.171229	−	0.985231i
$577$	4.50725	−	4.50725i	0.187639	−	0.187639i	−0.607035	−	0.794675i	$-0.707641\pi$
$577$	4.50725	−	4.50725i	0.187639	−	0.187639i	0.794675	+	0.607035i	$0.207641\pi$
$578$	1.09664	−	4.20429i	0.0456142	−	0.174875i
$579$	−7.96689	−	1.57933i	−0.331093	−	0.0656349i
$580$	−4.56147	+	35.2973i	−0.189405	+	1.46564i
$581$	−7.45521	+	27.8232i	−0.309294	+	1.15430i
$582$	3.91105	−	0.285015i	0.162118	−	0.0118143i
$583$	−3.99303	−	14.9022i	−0.165374	−	0.617185i
$584$	−28.9145	+	0.576599i	−1.19649	+	0.0238598i
$585$	25.2992	+	25.7902i	1.04599	+	1.06629i
$586$	0.797099	−	0.219270i	0.0329279	−	0.00905798i
$587$	2.57255	−	4.45578i	0.106180	−	0.183910i	−0.808039	−	0.589128i	$-0.799471\pi$
$587$	2.57255	−	4.45578i	0.106180	−	0.183910i	0.914220	+	0.405219i	$0.132805\pi$
$588$	1.11751	+	14.0462i	0.0460852	+	0.579256i
$589$	−6.58273	−	1.76384i	−0.271237	−	0.0726777i
$590$	6.79945	−	16.2194i	0.279929	−	0.667741i
$591$	0.795746	+	12.0211i	0.0327326	+	0.494481i
$592$	2.48239	−	1.52259i	0.102025	−	0.0625782i
$593$	−4.84275	+	4.84275i	−0.198868	+	0.198868i	−0.799515	−	0.600647i	$-0.794910\pi$
$593$	−4.84275	+	4.84275i	−0.198868	+	0.198868i	0.600647	+	0.799515i	$0.294910\pi$
$594$	−7.61410	−	36.6303i	−0.312410	−	1.50296i
$595$	13.0893	−	30.6502i	0.536609	−	1.25654i
$596$	1.42214	+	1.38483i	0.0582533	+	0.0567249i
$597$	0.257656	+	3.89232i	0.0105451	+	0.159302i
$598$	0.295018	+	44.3878i	0.0120642	+	1.81515i
$599$	−2.21970	+	1.28155i	−0.0906947	+	0.0523626i	−0.544661	−	0.838656i	$-0.683342\pi$
$599$	−2.21970	+	1.28155i	−0.0906947	+	0.0523626i	0.453967	+	0.891019i	$0.350008\pi$
$600$	−10.8609	+	21.9554i	−0.443394	+	0.896327i
$601$	10.7506	+	6.20686i	0.438526	+	0.253183i	0.702972	−	0.711217i	$-0.251856\pi$
$601$	10.7506	+	6.20686i	0.438526	+	0.253183i	−0.264446	+	0.964400i	$0.585189\pi$
$602$	21.2123	−	37.3113i	0.864550	−	1.52070i
$603$	−19.2549	−	25.0260i	−0.784118	−	1.01914i
$604$	16.8549	+	28.3175i	0.685817	+	1.15222i
$605$	20.0215	+	26.6905i	0.813989	+	1.08512i
$606$	−2.55629	−	35.0780i	−0.103842	−	1.42495i
$607$	13.3404	+	3.57455i	0.541471	+	0.145087i	0.519180	−	0.854665i	$-0.326237\pi$
$607$	13.3404	+	3.57455i	0.541471	+	0.145087i	0.0222908	+	0.999752i	$0.492904\pi$
$608$	−15.1146	−	8.06909i	−0.612979	−	0.327245i
$609$	25.5019	+	38.1126i	1.03339	+	1.54440i
$610$	−2.79259	−	21.9342i	−0.113069	−	0.888090i
$611$	35.5259	−	35.5259i	1.43722	−	1.43722i
$612$	10.6483	+	24.6823i	0.430432	+	0.997725i
$613$	25.3920			1.02557			0.512787	−	0.858516i	$-0.328613\pi$
$613$	25.3920			1.02557			0.512787	+	0.858516i	$0.328613\pi$
$614$	9.85961	+	2.57176i	0.397902	+	0.103788i
$615$	−4.76504	−	5.54728i	−0.192145	−	0.223688i
$616$	46.5129	+	11.4742i	1.87406	+	0.462310i
$617$	28.6427	+	7.67478i	1.15311	+	0.308975i	0.784211	−	0.620494i	$-0.213068\pi$
$617$	28.6427	+	7.67478i	1.15311	+	0.308975i	0.368900	+	0.929469i	$0.379735\pi$
$618$	−18.0126	+	37.2079i	−0.724575	+	1.49672i
$619$	3.13679	−	0.840501i	0.126078	−	0.0337826i	−0.195228	−	0.980758i	$-0.562545\pi$
$619$	3.13679	−	0.840501i	0.126078	−	0.0337826i	0.321306	+	0.946975i	$0.395878\pi$
$620$	9.97319	−	1.33717i	0.400533	−	0.0537021i
$621$	30.2228	+	1.92176i	1.21280	+	0.0771176i
$622$	−7.59057	−	27.5935i	−0.304354	−	1.10640i
$623$	2.32687	+	8.68400i	0.0932241	+	0.347917i
$624$	15.5853	−	33.9012i	0.623912	−	1.35713i
$625$	22.1754	−	11.5435i	0.887015	−	0.461741i
$626$	−0.0859702	−	12.9349i	−0.00343606	−	0.516982i
$627$	−23.9626	−	11.7977i	−0.956975	−	0.471155i
$628$	−0.0557353	−	4.19272i	−0.00222408	−	0.167308i
$629$	−2.30641	+	2.30641i	−0.0919624	+	0.0919624i
$630$	8.07812	+	30.5095i	0.321840	+	1.21553i
$631$			9.73037i			0.387360i	0.981065	+	0.193680i	$0.0620424\pi$
$631$			9.73037i			0.387360i	−0.981065	+	0.193680i	$0.937958\pi$
$632$	5.05325	+	17.4589i	0.201007	+	0.694477i
$633$	−29.6500	−	5.87772i	−1.17848	−	0.233618i
$634$	10.3661	+	10.2292i	0.411689	+	0.406253i
$635$	2.61223	+	2.05010i	0.103663	+	0.0813557i
$636$	−9.47834	−	4.51102i	−0.375840	−	0.178874i
$637$	−10.9531	+	18.9714i	−0.433979	+	0.751673i
$638$	55.2494	−	15.1983i	2.18735	−	0.601707i
$639$	7.27246	−	0.967052i	0.287694	−	0.0382560i
$640$	25.1835	+	2.40692i	0.995464	+	0.0951420i
$641$	−10.4332	−	6.02359i	−0.412085	−	0.237917i	0.279600	−	0.960117i	$-0.409798\pi$
$641$	−10.4332	−	6.02359i	−0.412085	−	0.237917i	−0.691685	+	0.722199i	$0.743131\pi$
$642$	−4.90064	+	25.6124i	−0.193413	+	1.01084i
$643$	−3.91401	+	2.25975i	−0.154353	+	0.0891160i	−0.575187	−	0.818022i	$-0.695071\pi$
$643$	−3.91401	+	2.25975i	−0.154353	+	0.0891160i	0.420834	+	0.907138i	$0.361738\pi$
$644$	−18.9409	+	33.8375i	−0.746377	+	1.33339i
$645$	11.6996	−	33.3380i	0.460670	−	1.31268i
$646$	18.5693	+	4.84359i	0.730600	+	0.190568i
$647$	19.6466	−	19.6466i	0.772388	−	0.772388i	−0.206136	−	0.978523i	$-0.566089\pi$
$647$	19.6466	−	19.6466i	0.772388	−	0.772388i	0.978523	+	0.206136i	$0.0660888\pi$
$648$	−22.3266	−	12.2279i	−0.877073	−	0.480357i
$649$	−28.3152			−1.11147
$650$	−33.2647	+	18.5381i	−1.30475	+	0.727125i
$651$	8.54214	−	9.75322i	0.334793	−	0.382259i
$652$	−14.3027	+	25.5514i	−0.560136	+	1.00067i
$653$	−19.7885	−	34.2747i	−0.774385	−	1.34127i	−0.935140	−	0.354279i	$-0.884726\pi$
$653$	−19.7885	−	34.2747i	−0.774385	−	1.34127i	0.160755	−	0.986994i	$-0.448607\pi$
$654$	22.3325	+	32.9008i	0.873271	+	1.28652i
$655$	1.76947	−	12.3940i	0.0691391	−	0.484274i
$656$	−3.60114	+	6.63889i	−0.140601	+	0.259205i
$657$	−18.6419	+	24.3600i	−0.727288	+	0.950375i
$658$	42.3187	−	11.6413i	1.64976	−	0.453824i
$659$	−1.70471	+	0.456775i	−0.0664060	+	0.0177934i	−0.291869	−	0.956458i	$-0.594277\pi$
$659$	−1.70471	+	0.456775i	−0.0664060	+	0.0177934i	0.225463	+	0.974252i	$0.427610\pi$
$660$	39.3603	+	2.45999i	1.53210	+	0.0957549i
$661$	−37.8897	−	10.1525i	−1.47374	−	0.394887i	−0.569526	−	0.821973i	$-0.692873\pi$
$661$	−37.8897	−	10.1525i	−1.47374	−	0.394887i	−0.904211	+	0.427086i	$0.859540\pi$
$662$	0.0113773	+	1.71181i	0.000442193	+	0.0665313i
$663$	−8.12651	+	40.9939i	−0.315607	+	1.59207i
$664$	23.5241	−	6.80874i	0.912911	−	0.264230i
$665$	20.7209	+	8.84896i	0.803523	+	0.343148i
$666$	0.378823	−	3.06547i	0.0146791	−	0.118784i
$667$			46.3823i			1.79593i
$668$	26.7179	+	26.0168i	1.03375	+	1.00662i
$669$	10.1024	+	29.6972i	0.390580	+	1.14816i
$670$	30.8046	−	12.6061i	1.19008	−	0.487014i
$671$	−30.8300	+	17.7997i	−1.19018	+	0.687150i
$672$	26.4735	−	19.0170i	1.02124	−	0.733596i
$673$	21.4312	−	5.74247i	0.826111	−	0.221356i	0.179095	−	0.983832i	$-0.442683\pi$
$673$	21.4312	−	5.74247i	0.826111	−	0.221356i	0.647016	+	0.762476i	$0.276016\pi$
$674$	32.0493	+	18.2207i	1.23449	+	0.701837i
$675$	11.0257	+	23.5252i	0.424380	+	0.905484i
$676$	27.5046	−	16.3711i	1.05787	−	0.629657i
$677$	−14.8978	+	25.8038i	−0.572569	+	0.991719i	0.423732	+	0.905788i	$0.360720\pi$
$677$	−14.8978	+	25.8038i	−0.572569	+	0.991719i	−0.996301	+	0.0859313i	$0.972613\pi$
$678$	1.92352	−	3.97334i	0.0738725	−	0.152595i
$679$	2.66296	+	4.61238i	0.102195	+	0.177007i
$680$	−28.0584	+	3.95199i	−1.07599	+	0.151552i
$681$	−8.88827	+	18.0532i	−0.340599	+	0.691800i
$682$	−8.19339	−	13.9760i	−0.313741	−	0.535169i
$683$		−	36.0666i		−	1.38005i	−0.723785	−	0.690025i	$-0.757599\pi$
$683$		−	36.0666i		−	1.38005i	0.723785	−	0.690025i	$-0.242401\pi$
$684$	−16.6864	+	7.19874i	−0.638019	+	0.275251i
$685$	6.18130	−	2.48172i	0.236175	−	0.0948217i
$686$	11.9019	−	6.97743i	0.454416	−	0.266399i
$687$	−15.5961	−	3.09173i	−0.595029	−	0.117957i
$688$	−36.4772	+	0.969979i	−1.39068	+	0.0369801i
$689$	−8.15974	−	14.1331i	−0.310861	−	0.538427i
$690$	−10.3702	+	30.1906i	−0.394786	+	1.14934i
$691$	−26.6463	+	7.13985i	−1.01367	+	0.271613i	−0.727163	−	0.686465i	$-0.759162\pi$
$691$	−26.6463	+	7.13985i	−1.01367	+	0.271613i	−0.286509	+	0.958077i	$0.592495\pi$
$692$	−1.19901	+	0.713666i	−0.0455796	+	0.0271295i
$693$	40.2727	−	30.9855i	1.52983	−	1.17704i
$694$	2.36379	+	8.59293i	0.0897282	+	0.326183i
$695$	−15.9710	−	2.28016i	−0.605816	−	0.0864914i
$696$	16.5204	−	35.3147i	0.626202	−	1.33860i
$697$	2.18946	−	8.17117i	0.0829317	−	0.309505i
$698$	−0.0783846	−	11.7936i	−0.00296690	−	0.446393i
$699$	−13.7672	+	15.7191i	−0.520725	+	0.594551i
$700$	−33.2668	−	0.283714i	−1.25737	−	0.0107234i
$701$	−35.5618	+	35.5618i	−1.34315	+	1.34315i	−0.450246	+	0.892905i	$0.648664\pi$
$701$	−35.5618	+	35.5618i	−1.34315	+	1.34315i	−0.892905	+	0.450246i	$0.851336\pi$
$702$	−17.8082	−	35.3424i	−0.672128	−	1.33391i
$703$	−1.55923	−	1.55923i	−0.0588076	−	0.0588076i
$704$	−12.1019	−	38.8910i	−0.456108	−	1.46576i
$705$	32.5669	−	15.6469i	1.22654	−	0.589295i
$706$	−0.181263	−	27.2725i	−0.00682193	−	1.02641i
$707$	41.3682	−	23.8839i	1.55581	−	0.898248i
$708$	−12.4995	+	14.6603i	−0.469759	+	0.550967i
$709$	−27.2683	+	7.30651i	−1.02408	+	0.274402i	−0.731502	−	0.681839i	$-0.761180\pi$
$709$	−27.2683	+	7.30651i	−1.02408	+	0.274402i	−0.292580	+	0.956241i	$0.594514\pi$
$710$	−1.04209	+	7.66279i	−0.0391088	+	0.287579i
$711$	17.8201	+	7.35422i	0.668306	+	0.275805i
$712$	5.29596	−	5.51148i	0.198475	−	0.206551i
$713$	12.6666	−	3.39401i	0.474369	−	0.127107i
$714$	−23.8712	+	27.6239i	−0.893359	+	1.03380i
$715$	48.2317	+	37.8527i	1.80377	+	1.41561i
$716$	11.2448	+	39.8402i	0.420238	+	1.48890i
$717$	9.40349	−	6.29205i	0.351180	−	0.234981i
$718$	5.37527	−	20.6077i	0.200603	−	0.769071i
$719$	10.1740			0.379425			0.189713	−	0.981840i	$-0.439244\pi$
$719$	10.1740			0.379425			0.189713	+	0.981840i	$0.439244\pi$
$720$	18.6489	−	19.2930i	0.695003	−	0.719007i
$721$	−56.1446			−2.09093
$722$	3.50735	−	13.4464i	0.130530	−	0.500425i
$723$	12.5607	+	6.18411i	0.467137	+	0.229990i
$724$	−9.45289	+	2.66806i	−0.351314	+	0.0991576i
$725$	−34.8866	+	19.1393i	−1.29566	+	0.710814i
$726$	−12.0008	−	34.5235i	−0.445390	−	1.28129i
$727$	−12.8799	+	3.45116i	−0.477689	+	0.127996i	−0.489626	−	0.871932i	$-0.662867\pi$
$727$	−12.8799	+	3.45116i	−0.477689	+	0.127996i	0.0119375	+	0.999929i	$0.496200\pi$
$728$	50.6658	−	1.01035i	1.87780	−	0.0374461i
$729$	−24.9043	+	10.4296i	−0.922381	+	0.386282i
$730$	−19.5740	−	25.7359i	−0.724467	−	0.952527i
$731$	39.4782	−	10.5782i	1.46015	−	0.391247i
$732$	−4.39375	+	23.8198i	−0.162398	+	0.880406i
$733$	45.9717	−	26.5418i	1.69801	−	0.980344i	0.750354	−	0.661036i	$-0.229883\pi$
$733$	45.9717	−	26.5418i	1.69801	−	0.980344i	0.947651	−	0.319307i	$-0.103450\pi$
$734$	0.101576	+	15.2829i	0.00374925	+	0.564104i
$735$	−11.9503	+	10.2651i	−0.440792	+	0.378634i
$736$	32.9507	−	1.09540i	1.21458	−	0.0403770i
$737$	−37.8924	−	37.8924i	−1.39578	−	1.39578i
$738$	3.12432	+	7.37646i	0.115008	+	0.271531i
$739$	−10.5841	+	10.5841i	−0.389342	+	0.389342i	−0.874453	−	0.485111i	$-0.838779\pi$
$739$	−10.5841	+	10.5841i	−0.389342	+	0.389342i	0.485111	+	0.874453i	$0.338779\pi$
$740$	3.01099	+	1.23880i	0.110686	+	0.0455391i
$741$	−27.7137	−	5.49388i	−1.01809	−	0.201823i
$742$	−0.0947534	−	14.2564i	−0.00347851	−	0.523368i
$743$	−4.66974	+	17.4277i	−0.171316	+	0.639361i	0.825834	+	0.563914i	$0.190705\pi$
$743$	−4.66974	+	17.4277i	−0.171316	+	0.639361i	−0.997150	+	0.0754471i	$0.975962\pi$
$744$	−10.8530	−	1.92743i	−0.397891	−	0.0706629i
$745$	−0.313666	+	2.19703i	−0.0114918	+	0.0804928i
$746$	8.44524	+	30.7004i	0.309202	+	1.12402i
$747$	9.90907	−	24.0108i	0.362554	−	0.878510i
$748$	23.3333	+	39.2017i	0.853150	+	1.43336i
$749$	−34.2100	+	9.16655i	−1.25001	+	0.334938i
$750$	−26.9871	+	4.65792i	−0.985430	+	0.170083i
$751$	−0.286762	−	0.496686i	−0.0104641	−	0.0181243i	0.860746	−	0.509035i	$-0.169998\pi$
$751$	−0.286762	−	0.496686i	−0.0104641	−	0.0181243i	−0.871210	+	0.490910i	$0.836664\pi$
$752$	−27.0782	−	25.6754i	−0.987440	−	0.936286i
$753$	−14.2141	+	16.2293i	−0.517989	+	0.591428i
$754$	52.2900	−	30.6548i	1.90429	−	1.11638i
$755$	−14.4700	+	33.8833i	−0.526618	+	1.23314i
$756$	1.73513	−	34.5296i	0.0631062	−	1.25583i
$757$		−	19.5783i		−	0.711587i	−0.934565	−	0.355793i	$-0.884211\pi$
$757$		−	19.5783i		−	0.711587i	0.934565	−	0.355793i	$-0.115789\pi$
$758$	9.15424	+	15.6150i	0.332497	+	0.567163i
$759$	51.2825	−	3.39469i	1.86144	−	0.123220i
$760$	−2.67172	−	18.9688i	−0.0969136	−	0.688069i
$761$	−6.57474	−	11.3878i	−0.238334	−	0.412807i	0.721902	−	0.691995i	$-0.243268\pi$
$761$	−6.57474	−	11.3878i	−0.238334	−	0.412807i	−0.960236	+	0.279188i	$0.909935\pi$
$762$	−2.04294	−	3.00971i	−0.0740080	−	0.109030i
$763$	−27.0032	+	46.7709i	−0.977582	+	1.69322i
$764$	−15.5551	−	26.1337i	−0.562762	−	0.945483i
$765$	−15.2766	+	25.8821i	−0.552325	+	0.935769i
$766$	20.1958	+	11.4817i	0.729703	+	0.414852i
$767$	−28.9310	+	7.75203i	−1.04464	+	0.279910i
$768$	−25.4782	−	10.9023i	−0.919367	−	0.393402i
$769$	33.5562	−	19.3737i	1.21007	−	0.698632i	0.247293	−	0.968941i	$-0.420459\pi$
$769$	33.5562	−	19.3737i	1.21007	−	0.698632i	0.962774	+	0.270309i	$0.0871258\pi$
$770$	20.2861	+	49.5717i	0.731059	+	1.78644i
$771$	−24.0474	−	4.76708i	−0.866044	−	0.171682i
$772$	−6.54279	+	6.71909i	−0.235480	+	0.241825i
$773$			33.6424i			1.21003i	0.796213	+	0.605017i	$0.206834\pi$
$773$			33.6424i			1.21003i	−0.796213	+	0.605017i	$0.793166\pi$
$774$	−23.3165	+	30.8918i	−0.838095	+	1.11038i
$775$	7.77958	+	8.12673i	0.279451	+	0.291921i
$776$	2.18540	−	3.96578i	0.0784513	−	0.142363i
$777$	3.97156	−	1.35104i	0.142479	−	0.0484683i
$778$	0.266486	+	40.0949i	0.00955399	+	1.43747i
$779$	5.52408	+	1.48017i	0.197921	+	0.0530327i
$780$	40.8898	−	8.26244i	1.46409	−	0.295843i
$781$	12.0265	−	3.22249i	0.430342	−	0.115310i
$782$	−35.6044	+	9.79424i	−1.27321	+	0.350241i
$783$	−18.3621	−	37.0525i	−0.656209	−	1.32415i
$784$	14.3019	+	7.75778i	0.510781	+	0.277064i
$785$	3.75017	−	2.81314i	0.133849	−	0.100405i
$786$	−5.97593	+	12.3442i	−0.213154	+	0.440304i
$787$	1.67071	+	2.89375i	0.0595543	+	0.103151i	0.894265	−	0.447537i	$-0.147699\pi$
$787$	1.67071	+	2.89375i	0.0595543	+	0.103151i	−0.834711	+	0.550688i	$0.814365\pi$
$788$	12.1388	+	6.79481i	0.432426	+	0.242055i
$789$	8.72674	+	25.6534i	0.310680	+	0.913285i
$790$	−12.4391	+	16.0687i	−0.442565	+	0.571698i
$791$	5.99554			0.213177
$792$	−40.2548	−	15.6810i	−1.43039	−	0.557201i
$793$	−26.6273	+	26.6273i	−0.945564	+	0.945564i
$794$	16.9720	+	4.42695i	0.602314	+	0.157106i
$795$	−2.17137	−	11.5334i	−0.0770104	−	0.409049i
$796$	3.93043	+	2.20010i	0.139310	+	0.0779805i
$797$	26.9073	−	15.5349i	0.953106	−	0.550276i	0.0590613	−	0.998254i	$-0.481189\pi$
$797$	26.9073	−	15.5349i	0.953106	−	0.550276i	0.894044	+	0.447979i	$0.147856\pi$
$798$	−18.6750	−	16.1380i	−0.661088	−	0.571280i
$799$	36.1960	+	20.8978i	1.28052	+	0.739310i
$800$	14.4207	+	24.3319i	0.509849	+	0.860264i
$801$	−1.06864	−	8.03645i	−0.0377587	−	0.283954i
$802$	−44.1393	+	12.1421i	−1.55861	+	0.428752i
$803$	−26.0289	+	45.0835i	−0.918541	+	1.59096i
$804$	−36.3461	+	2.89167i	−1.28183	+	0.101981i
$805$	−43.0434	+	5.18968i	−1.51708	+	0.182912i
$806$	−12.1979	−	12.0368i	−0.429652	−	0.423978i
$807$	−7.01838	+	8.01342i	−0.247059	+	0.282086i
$808$	−35.5689	−	19.6007i	−1.25131	−	0.689551i
$809$		−	38.7307i		−	1.36170i	−0.732424	−	0.680849i	$-0.761611\pi$
$809$		−	38.7307i		−	1.36170i	0.732424	−	0.680849i	$-0.238389\pi$
$810$	−3.66784	−	28.2232i	−0.128875	−	0.991661i
$811$	−32.1202	+	32.1202i	−1.12789	+	1.12789i	−0.137375	+	0.990519i	$0.543867\pi$
$811$	−32.1202	+	32.1202i	−1.12789	+	1.12789i	−0.990519	+	0.137375i	$0.956133\pi$
$812$	52.9471	−	0.703844i	1.85808	−	0.0247001i
$813$	−2.43967	−	36.8553i	−0.0855630	−	1.29257i
$814$	−0.0348395	−	5.24187i	−0.00122112	−	0.183727i
$815$	−32.5030	+	3.91883i	−1.13853	+	0.137271i
$816$	30.5970	+	5.22431i	1.07111	+	0.182888i
$817$	7.15131	+	26.6890i	0.250193	+	0.933731i
$818$	−13.5788	−	49.3622i	−0.474773	−	1.72591i
$819$	32.6654	−	42.6851i	1.14142	−	1.49154i
$820$	−8.36927	+	1.12212i	−0.292268	+	0.0391863i
$821$	−32.6378	+	8.74527i	−1.13907	+	0.305212i	−0.778576	−	0.627551i	$-0.784058\pi$
$821$	−32.6378	+	8.74527i	−1.13907	+	0.305212i	−0.360491	+	0.932763i	$0.617391\pi$
$822$	−7.27734	+	0.530331i	−0.253826	+	0.0184974i
$823$	35.5660	+	9.52988i	1.23975	+	0.332191i	0.818370	−	0.574692i	$-0.194878\pi$
$823$	35.5660	+	9.52988i	1.23975	+	0.332191i	0.421383	+	0.906883i	$0.361545\pi$
$824$	24.6863	+	40.8546i	0.859989	+	1.42324i
$825$	23.7146	+	37.1715i	0.825637	+	1.29415i
$826$	−25.3186	−	6.60405i	−0.880945	−	0.229784i
$827$	−28.9777			−1.00765			−0.503826	−	0.863805i	$-0.668075\pi$
$827$	−28.9777			−1.00765			−0.503826	+	0.863805i	$0.668075\pi$
$828$	20.8806	−	28.0502i	0.725650	−	0.974814i
$829$	−5.11175	+	5.11175i	−0.177538	+	0.177538i	−0.790282	−	0.612743i	$-0.790066\pi$
$829$	−5.11175	+	5.11175i	−0.177538	+	0.177538i	0.612743	+	0.790282i	$0.290066\pi$
$830$	21.6509	+	16.7605i	0.751514	+	0.581765i
$831$	8.62007	−	17.5084i	0.299027	−	0.607361i
$832$	−23.0126	−	36.4236i	−0.797817	−	1.26276i
$833$	−17.6028	−	4.71666i	−0.609901	−	0.163422i
$834$	15.9069	+	7.70063i	0.550809	+	0.266651i
$835$	−5.89285	+	41.2756i	−0.203931	+	1.42840i
$836$	−26.5021	+	15.7744i	−0.916594	+	0.545568i
$837$	−8.77508	+	7.72585i	−0.303311	+	0.267044i
$838$	4.37307	−	7.69199i	0.151065	−	0.265715i
$839$	7.82624	+	4.51848i	0.270192	+	0.155995i	0.628975	−	0.777426i	$-0.283475\pi$
$839$	7.82624	+	4.51848i	0.270192	+	0.155995i	−0.358783	+	0.933421i	$0.616808\pi$
$840$	34.6210	+	11.3798i	1.19454	+	0.392640i
$841$	29.7354	−	17.1677i	1.02536	−	0.591990i
$842$	0.254505	+	38.2923i	0.00877082	+	1.31964i
$843$	43.2533	+	21.2952i	1.48972	+	0.733446i
$844$	−24.3500	+	25.0061i	−0.838160	+	0.860744i
$845$	32.9107	+	14.0546i	1.13216	+	0.483495i
$846$	−39.1983	+	5.47774i	−1.34767	+	0.188329i
$847$	35.1012	−	35.1012i	1.20609	−	1.20609i
$848$	−10.3322	+	6.33737i	−0.354811	+	0.217626i
$849$	−17.0276	+	11.3935i	−0.584385	+	0.391023i
$850$	−22.0586	−	22.7384i	−0.756604	−	0.779921i
$851$	4.09850	+	1.09819i	0.140495	+	0.0376454i
$852$	3.64053	−	7.64930i	0.124722	−	0.262061i
$853$	14.3898	−	24.9239i	0.492698	−	0.853378i	−0.507267	−	0.861789i	$-0.669344\pi$
$853$	14.3898	−	24.9239i	0.492698	−	0.853378i	0.999965	+	0.00841115i	$0.00267738\pi$
$854$	−31.7187	+	8.72536i	−1.08539	+	0.298576i
$855$	−17.4975	−	10.3276i	−0.598400	−	0.353198i
$856$	21.7121	+	20.8631i	0.742104	+	0.713085i
$857$	−9.57024	−	35.7166i	−0.326913	−	1.22006i	−0.912375	−	0.409356i	$-0.865753\pi$
$857$	−9.57024	−	35.7166i	−0.326913	−	1.22006i	0.585461	−	0.810700i	$-0.300913\pi$
$858$	−37.7205	−	55.5708i	−1.28776	−	1.89716i
$859$	12.3511	−	46.0950i	0.421415	−	1.57274i	−0.350215	−	0.936669i	$-0.613891\pi$
$859$	12.3511	−	46.0950i	0.421415	−	1.57274i	0.771630	−	0.636072i	$-0.219442\pi$
$860$	−24.9127	−	32.3073i	−0.849517	−	1.10167i
$861$	−7.16837	+	8.18468i	−0.244297	+	0.278933i
$862$	4.20803	−	16.1327i	0.143326	−	0.549483i
$863$	−20.1770	+	20.1770i	−0.686833	+	0.686833i	−0.961531	−	0.274698i	$-0.911422\pi$
$863$	−20.1770	+	20.1770i	−0.686833	+	0.686833i	0.274698	+	0.961531i	$0.411422\pi$
$864$	−25.8890	+	13.9198i	−0.880761	+	0.473561i
$865$	−1.43468	−	0.612686i	−0.0487805	−	0.0208319i
$866$	−28.2854	−	48.2483i	−0.961177	−	1.63954i
$867$	−5.30984	+	0.351490i	−0.180332	+	0.0119372i
$868$	−4.06660	−	14.4079i	−0.138029	−	0.489036i
$869$	31.6019	+	8.46771i	1.07202	+	0.287247i
$870$	42.7826	−	8.34935i	1.45047	−	0.283069i
$871$	−49.0905	−	28.3424i	−1.66337	−	0.960346i
$872$	45.9068	−	0.915451i	1.55460	−	0.0310011i
$873$	−1.84369	−	4.43476i	−0.0623995	−	0.150094i
$874$	−6.62135	−	24.0702i	−0.223970	−	0.814185i
$875$	−21.6649	−	30.2338i	−0.732408	−	1.02209i
$876$	11.8519	+	33.3782i	0.400438	+	1.12775i
$877$	17.1691	+	29.7377i	0.579758	+	1.00417i	0.995507	+	0.0946912i	$0.0301864\pi$
$877$	17.1691	+	29.7377i	0.579758	+	1.00417i	−0.415748	+	0.909480i	$0.636480\pi$
$878$	3.66449	−	3.71353i	0.123671	−	0.125325i
$879$	−0.563065	−	0.841503i	−0.0189917	−	0.0283832i
$880$	27.1521	−	36.5578i	0.915298	−	1.23236i
$881$			11.6848i			0.393671i	0.980437	+	0.196836i	$0.0630665\pi$
$881$			11.6848i			0.393671i	−0.980437	+	0.196836i	$0.936933\pi$
$882$	15.8908	−	6.73059i	0.535070	−	0.226631i
$883$		−	57.3121i		−	1.92870i	−0.264622	−	0.964352i	$-0.585247\pi$
$883$		−	57.3121i		−	1.92870i	0.264622	−	0.964352i	$-0.414753\pi$
$884$	34.5732	+	33.6661i	1.16282	+	1.13231i
$885$	−21.4778	−	1.62921i	−0.721968	−	0.0547654i
$886$	23.9244	+	23.6085i	0.803755	+	0.793142i
$887$	36.7450	+	9.84580i	1.23378	+	0.330590i	0.816049	−	0.577982i	$-0.196160\pi$
$887$	36.7450	+	9.84580i	1.23378	+	0.330590i	0.417728	+	0.908572i	$0.362826\pi$
$888$	−2.72937	−	2.29594i	−0.0915918	−	0.0770465i
$889$	2.47021	−	4.27853i	0.0828481	−	0.143497i
$890$	8.46779	+	1.15156i	0.283841	+	0.0386004i
$891$	−39.6231	+	23.0139i	−1.32743	+	0.770995i
$892$	35.1086	+	8.90887i	1.17552	+	0.298291i
$893$	−14.1278	+	24.4701i	−0.472770	+	0.818861i
$894$	1.05932	−	2.18820i	0.0354291	−	0.0731843i
$895$	−28.5742	+	36.4091i	−0.955129	+	1.21702i
$896$	−1.75046	−	37.5977i	−0.0584788	−	1.25605i
$897$	51.4684	−	17.5085i	1.71848	−	0.584591i
$898$	−8.14878	−	2.12551i	−0.271928	−	0.0709293i
$899$	−12.6618	−	12.6618i	−0.422295	−	0.422295i
$900$	29.7143	+	4.13070i	0.990475	+	0.137690i
$901$	9.59977	−	9.59977i	0.319815	−	0.319815i
$902$	6.87570	+	11.7284i	0.228936	+	0.390512i
$903$	−51.5623	−	10.2216i	−1.71588	−	0.340152i
$904$	−2.63619	−	4.36276i	−0.0876784	−	0.145103i
$905$	−8.63880	−	6.77980i	−0.287163	−	0.225368i
$906$	26.3893	−	30.5378i	0.876726	−	1.01455i
$907$	−5.69078	−	3.28557i	−0.188959	−	0.109096i	0.402536	−	0.915404i	$-0.368129\pi$
$907$	−5.69078	−	3.28557i	−0.188959	−	0.109096i	−0.591495	+	0.806309i	$0.701462\pi$
$908$	11.8842	+	19.9664i	0.394392	+	0.662608i
$909$	−39.7751	+	16.5360i	−1.31926	+	0.548464i
$910$	34.2988	+	45.0959i	1.13699	+	1.49492i
$911$	30.8230	+	17.7957i	1.02121	+	0.589597i	0.914455	−	0.404688i	$-0.132620\pi$
$911$	30.8230	+	17.7957i	1.02121	+	0.589597i	0.106757	+	0.994285i	$0.465953\pi$
$912$	−3.53187	+	20.6850i	−0.116952	+	0.684948i
$913$	11.4094	−	42.5804i	0.377596	−	1.40921i
$914$	−40.9988	+	0.272494i	−1.35612	+	0.00901330i
$915$	−24.4095	+	11.7276i	−0.806954	+	0.387703i
$916$	−12.8083	+	13.1534i	−0.423197	+	0.434600i
$917$	−18.6267			−0.615107
$918$	24.5651	−	21.9194i	0.810770	−	0.723449i
$919$	−18.0954			−0.596912			−0.298456	−	0.954423i	$-0.596472\pi$
$919$	−18.0954			−0.596912			−0.298456	+	0.954423i	$0.596472\pi$
$920$	22.7022	+	29.0395i	0.748471	+	0.957403i
$921$	−0.824290	−	12.4523i	−0.0271613	−	0.410317i
$922$	−0.338242	−	50.8912i	−0.0111394	−	1.67601i
$923$	11.4058	−	6.58515i	0.375427	−	0.216753i
$924$	−4.65337	−	58.4893i	−0.153085	−	1.92416i
$925$	0.865202	+	3.53585i	0.0284477	+	0.116258i
$926$	−11.9549	+	21.0281i	−0.392863	+	0.691025i
$927$	50.2047	+	6.54323i	1.64894	+	0.214908i
$928$	−23.7926	−	38.2184i	−0.781030	−	1.25458i
$929$	15.5615	−	26.9534i	0.510557	−	0.884311i	−0.489368	−	0.872077i	$-0.662772\pi$
$929$	15.5615	−	26.9534i	0.510557	−	0.884311i	0.999925	−	0.0122336i	$-0.00389417\pi$
$930$	−5.41074	−	11.0726i	−0.177425	−	0.363085i
$931$	3.18867	−	11.9003i	0.104505	−	0.390016i
$932$	6.55407	+	23.2210i	0.214686	+	0.760628i
$933$	−29.1306	+	19.4919i	−0.953694	+	0.638135i
$934$	5.57912	−	21.3892i	0.182554	−	0.699876i
$935$	−20.0318	+	46.9068i	−0.655108	+	1.53402i
$936$	−45.4233	−	5.00126i	−1.48471	−	0.163471i
$937$	20.2822	+	20.2822i	0.662591	+	0.662591i	0.955990	−	0.293399i	$-0.0947865\pi$
$937$	20.2822	+	20.2822i	0.662591	+	0.662591i	−0.293399	+	0.955990i	$0.594786\pi$
$938$	−25.0444	−	42.7199i	−0.817729	−	1.39486i
$939$	−14.9982	+	5.10208i	−0.489448	+	0.166500i
$940$	5.34702	−	41.3761i	0.174401	−	1.34954i
$941$	−5.20858	−	1.39563i	−0.169795	−	0.0454964i	0.172920	−	0.984936i	$-0.444680\pi$
$941$	−5.20858	−	1.39563i	−0.169795	−	0.0454964i	−0.342715	+	0.939439i	$0.611346\pi$
$942$	−4.85075	+	1.68618i	−0.158046	+	0.0549386i
$943$	−10.6295	+	2.84818i	−0.346145	+	0.0927494i
$944$	6.32682	+	21.3273i	0.205920	+	0.694143i
$945$	32.3307	−	21.1861i	1.05172	−	0.689184i
$946$	−32.4631	+	57.1009i	−1.05547	+	1.85651i
$947$	−23.3664	−	13.4906i	−0.759308	−	0.438386i	0.0697395	−	0.997565i	$-0.477783\pi$
$947$	−23.3664	−	13.4906i	−0.759308	−	0.438386i	−0.829047	+	0.559179i	$0.811117\pi$
$948$	18.3345	−	12.6240i	0.595478	−	0.410009i
$949$	−14.2522	+	53.1900i	−0.462647	+	1.72662i
$950$	15.3722	−	14.9126i	0.498740	−	0.483829i
$951$	7.87845	−	16.0021i	0.255476	−	0.518904i
$952$	11.7208	+	40.4950i	0.379872	+	1.31245i
$953$	−26.3588	−	26.3588i	−0.853847	−	0.853847i	0.136758	−	0.990604i	$-0.456332\pi$
$953$	−26.3588	−	26.3588i	−0.853847	−	0.853847i	−0.990604	+	0.136758i	$0.956332\pi$
$954$	−1.57675	+	12.7592i	−0.0510490	+	0.413093i
$955$	13.3541	−	31.2702i	0.432128	−	1.01188i
$956$	−0.173659	−	13.0636i	−0.00561653	−	0.422506i
$957$	−39.0278	−	58.3272i	−1.26159	−	1.88545i
$958$	−15.3490	+	15.5544i	−0.495905	+	0.502541i
$959$	−4.95500	−	8.58232i	−0.160005	−	0.277138i
$960$	−6.94189	−	30.1962i	−0.224048	−	0.974578i
$961$	12.9687	−	22.4624i	0.418345	−	0.724594i
$962$	−1.47070	−	5.34633i	−0.0474172	−	0.172373i
$963$	31.6590	−	4.20984i	1.02020	−	0.135660i
$964$	13.8918	−	8.26858i	0.447426	−	0.266313i
$965$	−10.3801	−	1.48195i	−0.334147	−	0.0477057i
$966$	46.6470	+	8.92537i	1.50084	+	0.287169i
$967$	2.23215	−	8.33050i	0.0717812	−	0.267891i	−0.920703	−	0.390264i	$-0.872384\pi$
$967$	2.23215	−	8.33050i	0.0717812	−	0.267891i	0.992484	+	0.122373i	$0.0390504\pi$
$968$	−40.9757	−	10.1083i	−1.31701	−	0.324892i
$969$	−1.55244	−	23.4523i	−0.0498717	−	0.753396i
$970$	5.02199	−	0.639385i	0.161246	−	0.0205294i
$971$	11.8887	+	11.8887i	0.381527	+	0.381527i	0.871652	−	0.490125i	$-0.163049\pi$
$971$	11.8887	+	11.8887i	0.381527	+	0.381527i	−0.490125	+	0.871652i	$0.663049\pi$
$972$	−5.57573	+	30.6743i	−0.178842	+	0.983878i
$973$			24.0025i			0.769485i
$974$	−1.46260	−	2.49486i	−0.0468648	−	0.0799404i
$975$	34.4070	+	31.4874i	1.10191	+	1.00840i
$976$	20.2956	+	19.2442i	0.649647	+	0.615992i
$977$	−14.2362	+	53.1304i	−0.455458	+	1.69979i	0.231281	+	0.972887i	$0.425708\pi$
$977$	−14.2362	+	53.1304i	−0.455458	+	1.69979i	−0.686739	+	0.726904i	$0.740958\pi$
$978$	35.2241	+	6.73973i	1.12634	+	0.215513i
$979$	−3.56102	−	13.2899i	−0.113811	−	0.424748i
$980$	2.41734	+	18.0296i	0.0772192	+	0.575933i
$981$	29.5972	−	38.6758i	0.944966	−	1.23482i
$982$	−25.5517	+	44.9441i	−0.815388	+	1.43422i
$983$	9.22940	−	2.47301i	0.294372	−	0.0788768i	−0.108611	−	0.994084i	$-0.534640\pi$
$983$	9.22940	−	2.47301i	0.294372	−	0.0788768i	0.402983	+	0.915208i	$0.367973\pi$
$984$	9.10761	+	1.61745i	0.290340	+	0.0515625i
$985$	1.86173	+	15.4413i	0.0593197	+	0.492000i
$986$	35.8914	+	35.4174i	1.14301	+	1.12792i
$987$	−29.8937	−	44.6762i	−0.951526	−	1.42206i
$988$	−22.7598	+	23.3731i	−0.724086	+	0.743596i
$989$	−37.5949	−	37.5949i	−1.19545	−	1.19545i
$990$	−12.3627	−	46.6914i	−0.392912	−	1.48395i
$991$	41.6360			1.32261			0.661306	−	0.750116i	$-0.270003\pi$
$991$	41.6360			1.32261			0.661306	+	0.750116i	$0.270003\pi$
$992$	−8.69611	+	9.29417i	−0.276102	+	0.295090i
$993$	1.98487	−	0.675211i	0.0629880	−	0.0214272i
$994$	11.5053	−	0.0764688i	0.364926	−	0.00242544i
$995$	0.602813	+	4.99975i	0.0191104	+	0.158503i
$996$	−17.0096	−	24.7040i	−0.538969	−	0.782775i
$997$	−2.54488	−	1.46929i	−0.0805971	−	0.0465327i	0.459160	−	0.888354i	$-0.348151\pi$
$997$	−2.54488	−	1.46929i	−0.0805971	−	0.0465327i	−0.539757	+	0.841821i	$0.681484\pi$
$998$	8.45320	+	4.80583i	0.267581	+	0.152126i
$999$	−3.70884	+	0.745251i	−0.117343	+	0.0235787i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cq.a.173.11	yes	560
5.2	odd	4		720.2.cm.a.317.83	yes	560
9.5	odd	6	inner	720.2.cq.a.653.36	yes	560
16.5	even	4		720.2.cm.a.533.36	yes	560
45.32	even	12		720.2.cm.a.77.36	✓	560
80.37	odd	4	inner	720.2.cq.a.677.36	yes	560
144.5	odd	12		720.2.cm.a.293.83	yes	560
720.437	even	12	inner	720.2.cq.a.437.11	yes	560

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.cm.a.77.36	✓	560	45.32	even	12
720.2.cm.a.293.83	yes	560	144.5	odd	12
720.2.cm.a.317.83	yes	560	5.2	odd	4
720.2.cm.a.533.36	yes	560	16.5	even	4
720.2.cq.a.173.11	yes	560	1.1	even	1	trivial
720.2.cq.a.437.11	yes	560	720.437	even	12	inner
720.2.cq.a.653.36	yes	560	9.5	odd	6	inner
720.2.cq.a.677.36	yes	560	80.37	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cq (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36843 - 0.356938i) q^{2} +(0.114404 + 1.72827i) q^{3} +(1.74519 + 0.976889i) q^{4} +(0.267661 + 2.21999i) q^{5} +(0.460331 - 2.40585i) q^{6} +(3.21344 - 0.861040i) q^{7} +(-2.03948 - 1.95973i) q^{8} +(-2.97382 + 0.395443i) q^{9} +O(q^{10})\)	\(q+(-1.36843 - 0.356938i) q^{2} +(0.114404 + 1.72827i) q^{3} +(1.74519 + 0.976889i) q^{4} +(0.267661 + 2.21999i) q^{5} +(0.460331 - 2.40585i) q^{6} +(3.21344 - 0.861040i) q^{7} +(-2.03948 - 1.95973i) q^{8} +(-2.97382 + 0.395443i) q^{9} +(0.426125 - 3.13344i) q^{10} +(-4.91782 + 1.31773i) q^{11} +(-1.48867 + 3.12792i) q^{12} +(-4.66401 + 2.69277i) q^{13} +(-4.70470 + 0.0312693i) q^{14} +(-3.80612 + 0.716566i) q^{15} +(2.09138 + 3.40971i) q^{16} +(-3.16799 - 3.16799i) q^{17} +(4.21061 + 0.520337i) q^{18} +(2.14171 - 2.14171i) q^{19} +(-1.70157 + 4.13578i) q^{20} +(1.85574 + 5.45519i) q^{21} +(7.20004 - 0.0478542i) q^{22} +(-1.50843 + 5.62954i) q^{23} +(3.15361 - 3.74897i) q^{24} +(-4.85672 + 1.18841i) q^{25} +(7.34352 - 2.02010i) q^{26} +(-1.02365 - 5.09432i) q^{27} +(6.44921 + 1.63650i) q^{28} +(7.68718 - 2.05977i) q^{29} +(5.46417 + 0.377980i) q^{30} +(-1.12501 - 1.94858i) q^{31} +(-1.64484 - 5.41244i) q^{32} +(-2.84001 - 8.34857i) q^{33} +(3.20439 + 5.46595i) q^{34} +(2.77161 + 6.90335i) q^{35} +(-5.57619 - 2.21497i) q^{36} -0.728034i q^{37} +(-3.69523 + 2.16631i) q^{38} +(-5.18741 - 7.75260i) q^{39} +(3.80469 - 5.05216i) q^{40} +(0.944086 + 1.63520i) q^{41} +(-0.592280 - 8.12741i) q^{42} +(-4.56126 + 7.90033i) q^{43} +(-9.86981 - 2.50448i) q^{44} +(-1.67385 - 6.49601i) q^{45} +(4.07358 - 7.16520i) q^{46} +(-9.01103 + 2.41450i) q^{47} +(-5.65364 + 4.00455i) q^{48} +(3.52265 - 2.03380i) q^{49} +(7.07025 + 0.107296i) q^{50} +(5.11271 - 5.83757i) q^{51} +(-10.7701 + 0.143171i) q^{52} +3.03024i q^{53} +(-0.417570 + 7.33660i) q^{54} +(-4.24165 - 10.5648i) q^{55} +(-8.24115 - 4.54140i) q^{56} +(3.94646 + 3.45642i) q^{57} +(-11.2546 + 0.0748022i) q^{58} +(5.37197 + 1.43942i) q^{59} +(-7.34240 - 2.46761i) q^{60} +(6.75394 - 1.80971i) q^{61} +(0.843977 + 3.06805i) q^{62} +(-9.21572 + 3.83131i) q^{63} +(0.318937 + 7.99364i) q^{64} +(-7.22630 - 9.63332i) q^{65} +(0.906420 + 12.4381i) q^{66} +(5.26269 + 9.11524i) q^{67} +(-2.43397 - 8.62352i) q^{68} +(-9.90193 - 1.96293i) q^{69} +(-1.32868 - 10.4360i) q^{70} -2.44549 q^{71} +(6.84001 + 5.02139i) q^{72} +(7.23007 - 7.23007i) q^{73} +(-0.259863 + 0.996262i) q^{74} +(-2.60952 - 8.25775i) q^{75} +(5.82989 - 1.64547i) q^{76} +(-14.6685 + 8.46888i) q^{77} +(4.33140 + 12.4605i) q^{78} +(-5.56508 - 3.21300i) q^{79} +(-7.00975 + 5.55548i) q^{80} +(8.68725 - 2.35195i) q^{81} +(-0.708246 - 2.57464i) q^{82} +(-4.32919 + 7.49838i) q^{83} +(-2.09049 + 11.3332i) q^{84} +(6.18496 - 7.88086i) q^{85} +(9.06168 - 9.18294i) q^{86} +(4.43929 + 13.0499i) q^{87} +(12.6122 + 6.95012i) q^{88} +2.70240i q^{89} +(-0.0281272 + 9.48679i) q^{90} +(-12.6690 + 12.6690i) q^{91} +(-8.13193 + 8.35105i) q^{92} +(3.23896 - 2.16725i) q^{93} +(13.1928 - 0.0876843i) q^{94} +(5.32782 + 4.18131i) q^{95} +(9.16597 - 3.46193i) q^{96} +(0.414347 + 1.54636i) q^{97} +(-5.54644 + 1.52574i) q^{98} +(14.1037 - 5.86341i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 560 q - 6 q^{2} - 6 q^{5} - 8 q^{6}+O(q^{10}) \) 560 * q - 6 * q^2 - 6 * q^5 - 8 * q^6	\( 560 q - 6 q^{2} - 6 q^{5} - 8 q^{6} - 12 q^{11} - 10 q^{12} - 8 q^{15} - 4 q^{16} + 20 q^{18} - 6 q^{20} - 8 q^{21} + 6 q^{22} - 24 q^{24} + 8 q^{28} + 28 q^{30} - 8 q^{31} + 54 q^{32} - 8 q^{33} - 12 q^{34} + 8 q^{36} - 18 q^{38} - 24 q^{39} + 8 q^{40} - 46 q^{42} - 4 q^{43} - 14 q^{45} - 40 q^{46} - 12 q^{47} - 22 q^{48} - 6 q^{50} - 8 q^{51} - 18 q^{52} + 24 q^{54} - 12 q^{56} + 24 q^{57} - 10 q^{58} - 88 q^{60} - 4 q^{61} + 20 q^{63} - 24 q^{64} - 12 q^{65} + 24 q^{66} - 4 q^{67} - 30 q^{68} + 12 q^{69} + 2 q^{70} - 22 q^{72} + 24 q^{74} - 66 q^{75} + 8 q^{76} - 12 q^{77} - 122 q^{78} - 16 q^{81} - 12 q^{84} - 12 q^{85} - 12 q^{86} + 12 q^{87} - 10 q^{88} - 94 q^{90} - 16 q^{91} - 120 q^{92} - 12 q^{95} + 48 q^{96} - 4 q^{97} + 32 q^{99}+O(q^{100}) \) 560 * q - 6 * q^2 - 6 * q^5 - 8 * q^6 - 12 * q^11 - 10 * q^12 - 8 * q^15 - 4 * q^16 + 20 * q^18 - 6 * q^20 - 8 * q^21 + 6 * q^22 - 24 * q^24 + 8 * q^28 + 28 * q^30 - 8 * q^31 + 54 * q^32 - 8 * q^33 - 12 * q^34 + 8 * q^36 - 18 * q^38 - 24 * q^39 + 8 * q^40 - 46 * q^42 - 4 * q^43 - 14 * q^45 - 40 * q^46 - 12 * q^47 - 22 * q^48 - 6 * q^50 - 8 * q^51 - 18 * q^52 + 24 * q^54 - 12 * q^56 + 24 * q^57 - 10 * q^58 - 88 * q^60 - 4 * q^61 + 20 * q^63 - 24 * q^64 - 12 * q^65 + 24 * q^66 - 4 * q^67 - 30 * q^68 + 12 * q^69 + 2 * q^70 - 22 * q^72 + 24 * q^74 - 66 * q^75 + 8 * q^76 - 12 * q^77 - 122 * q^78 - 16 * q^81 - 12 * q^84 - 12 * q^85 - 12 * q^86 + 12 * q^87 - 10 * q^88 - 94 * q^90 - 16 * q^91 - 120 * q^92 - 12 * q^95 + 48 * q^96 - 4 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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