LMFDB - Embedded newform 546.2.by.b.397.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(19,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.by (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			397.3
Character	$\chi$	$=$	546.397
Dual form			546.2.by.b.535.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.263036 - 0.981662i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(2.62182 - 0.355062i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.263036 - 0.981662i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(2.62182 - 0.355062i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +1.01629 q^{10} +(2.99497 - 2.99497i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-0.709237 - 3.53511i) q^{13} +(-0.335613 + 2.62438i) q^{14} +(0.981662 - 0.263036i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.447736 + 0.775501i) q^{17} +(0.258819 - 0.965926i) q^{18} +(2.03633 - 2.03633i) q^{19} +(-0.263036 + 0.981662i) q^{20} +(0.355062 + 2.62182i) q^{21} +(2.11776 + 3.66807i) q^{22} +(0.963738 - 0.556414i) q^{23} +(0.707107 + 0.707107i) q^{24} +(3.43565 - 1.98358i) q^{25} +(3.59822 + 0.229883i) q^{26} -1.00000i q^{27} +(-2.44809 - 1.00342i) q^{28} +(-4.64609 + 8.04727i) q^{29} +1.01629i q^{30} +(3.90146 + 1.04539i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(2.99497 + 2.99497i) q^{33} +(-0.633194 - 0.633194i) q^{34} +(-1.03818 - 2.48035i) q^{35} +(0.866025 + 0.500000i) q^{36} +(9.34028 + 2.50272i) q^{37} +(1.43990 + 2.49399i) q^{38} +(3.53511 - 0.709237i) q^{39} +(-0.880134 - 0.508146i) q^{40} +(-0.375020 - 1.39959i) q^{41} +(-2.62438 - 0.335613i) q^{42} +(-4.62926 + 2.67270i) q^{43} +(-4.09120 + 1.09623i) q^{44} +(0.263036 + 0.981662i) q^{45} +(0.288021 + 1.07491i) q^{46} +(-3.06581 + 0.821480i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(6.74786 - 1.86181i) q^{49} +(1.02677 + 3.83197i) q^{50} +(-0.775501 - 0.447736i) q^{51} +(-1.15334 + 3.41611i) q^{52} +(-1.89754 - 3.28664i) q^{53} +(0.965926 + 0.258819i) q^{54} +(-3.72783 - 2.15226i) q^{55} +(1.60284 - 2.10497i) q^{56} +(2.03633 + 2.03633i) q^{57} +(-6.57057 - 6.57057i) q^{58} +(-7.47136 + 2.00194i) q^{59} +(-0.981662 - 0.263036i) q^{60} +2.35876i q^{61} +(-2.01954 + 3.49795i) q^{62} +(-2.62182 + 0.355062i) q^{63} -1.00000i q^{64} +(-3.28373 + 1.62609i) q^{65} +(-3.66807 + 2.11776i) q^{66} +(3.05928 + 3.05928i) q^{67} +(0.775501 - 0.447736i) q^{68} +(0.556414 + 0.963738i) q^{69} +(2.66453 - 0.360846i) q^{70} +(0.229950 - 0.858187i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(0.120528 - 0.449816i) q^{73} +(-4.83488 + 8.37426i) q^{74} +(1.98358 + 3.43565i) q^{75} +(-2.78168 + 0.745350i) q^{76} +(6.78886 - 8.91566i) q^{77} +(-0.229883 + 3.59822i) q^{78} +(3.14658 - 5.45004i) q^{79} +(0.718627 - 0.718627i) q^{80} +1.00000 q^{81} +1.44897 q^{82} +(-7.53308 + 7.53308i) q^{83} +(1.00342 - 2.44809i) q^{84} +(0.879051 + 0.235541i) q^{85} +(-1.38349 - 5.16327i) q^{86} +(-8.04727 - 4.64609i) q^{87} -4.23552i q^{88} +(3.39783 - 12.6809i) q^{89} -1.01629 q^{90} +(-3.11467 - 9.01659i) q^{91} -1.11283 q^{92} +(-1.04539 + 3.90146i) q^{93} -3.17396i q^{94} +(-2.53462 - 1.46336i) q^{95} +(-0.258819 - 0.965926i) q^{96} +(-8.06565 - 2.16118i) q^{97} +(0.0518991 + 6.99981i) q^{98} +(-2.99497 + 2.99497i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 4 * q^7 - 40 * q^9	$ 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−0.263036	−	0.981662i	−0.117633	−	0.439013i	0.881837	−	0.471554i	$-0.156307\pi$
$5$	−0.263036	−	0.981662i	−0.117633	−	0.439013i	−0.999470	+	0.0325411i	$0.989640\pi$
$6$	−0.965926	−	0.258819i	−0.394338	−	0.105662i
$7$	2.62182	−	0.355062i	0.990954	−	0.134201i
$7$	2.62182	−	0.355062i	0.990954	−	0.134201i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.00000			−0.333333
$10$	1.01629			0.321380
$11$	2.99497	−	2.99497i	0.903016	−	0.903016i	−0.0926796	−	0.995696i	$-0.529543\pi$
$11$	2.99497	−	2.99497i	0.903016	−	0.903016i	0.995696	+	0.0926796i	$0.0295432\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−0.709237	−	3.53511i	−0.196707	−	0.980462i
$13$	−0.709237	−	3.53511i	−0.196707	−	0.980462i
$14$	−0.335613	+	2.62438i	−0.0896964	+	0.701395i
$15$	0.981662	−	0.263036i	0.253464	−	0.0679155i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.447736	+	0.775501i	−0.108592	+	0.188087i	−0.915200	−	0.403000i	$-0.867968\pi$
$17$	−0.447736	+	0.775501i	−0.108592	+	0.188087i	0.806608	+	0.591087i	$0.201301\pi$
$18$	0.258819	−	0.965926i	0.0610042	−	0.227671i
$19$	2.03633	−	2.03633i	0.467167	−	0.467167i	−0.433829	−	0.900995i	$-0.642838\pi$
$19$	2.03633	−	2.03633i	0.467167	−	0.467167i	0.900995	+	0.433829i	$0.142838\pi$
$20$	−0.263036	+	0.981662i	−0.0588166	+	0.219506i
$21$	0.355062	+	2.62182i	0.0774808	+	0.572128i
$22$	2.11776	+	3.66807i	0.451508	+	0.782035i
$23$	0.963738	−	0.556414i	0.200953	−	0.116020i	−0.396147	−	0.918187i	$-0.629653\pi$
$23$	0.963738	−	0.556414i	0.200953	−	0.116020i	0.597100	+	0.802167i	$0.296320\pi$
$24$	0.707107	+	0.707107i	0.144338	+	0.144338i
$25$	3.43565	−	1.98358i	0.687131	−	0.396715i
$26$	3.59822	+	0.229883i	0.705668	+	0.0450838i
$27$		−	1.00000i		−	0.192450i
$28$	−2.44809	−	1.00342i	−0.462646	−	0.189628i
$29$	−4.64609	+	8.04727i	−0.862758	+	1.49434i	0.00649921	+	0.999979i	$0.497931\pi$
$29$	−4.64609	+	8.04727i	−0.862758	+	1.49434i	−0.869257	+	0.494361i	$0.835402\pi$
$30$			1.01629i			0.185549i
$31$	3.90146	+	1.04539i	0.700723	+	0.187758i	0.591554	−	0.806265i	$-0.298515\pi$
$31$	3.90146	+	1.04539i	0.700723	+	0.187758i	0.109169	+	0.994023i	$0.465181\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	2.99497	+	2.99497i	0.521357	+	0.521357i
$34$	−0.633194	−	0.633194i	−0.108592	−	0.108592i
$35$	−1.03818	−	2.48035i	−0.175485	−	0.419255i
$36$	0.866025	+	0.500000i	0.144338	+	0.0833333i
$37$	9.34028	+	2.50272i	1.53553	+	0.411444i	0.924819	−	0.380408i	$-0.124216\pi$
$37$	9.34028	+	2.50272i	1.53553	+	0.411444i	0.610713	+	0.791852i	$0.290883\pi$
$38$	1.43990	+	2.49399i	0.233583	+	0.404578i
$39$	3.53511	−	0.709237i	0.566070	−	0.113569i
$40$	−0.880134	−	0.508146i	−0.139161	−	0.0803449i
$41$	−0.375020	−	1.39959i	−0.0585683	−	0.218580i	0.930439	−	0.366447i	$-0.119426\pi$
$41$	−0.375020	−	1.39959i	−0.0585683	−	0.218580i	−0.989007	+	0.147867i	$0.952759\pi$
$42$	−2.62438	−	0.335613i	−0.404950	−	0.0517863i
$43$	−4.62926	+	2.67270i	−0.705955	+	0.407583i	−0.809562	−	0.587035i	$-0.800295\pi$
$43$	−4.62926	+	2.67270i	−0.705955	+	0.407583i	0.103606	+	0.994618i	$0.466962\pi$
$44$	−4.09120	+	1.09623i	−0.616772	+	0.165263i
$45$	0.263036	+	0.981662i	0.0392110	+	0.146338i
$46$	0.288021	+	1.07491i	0.0424664	+	0.158487i
$47$	−3.06581	+	0.821480i	−0.447194	+	0.119825i	−0.475386	−	0.879777i	$-0.657692\pi$
$47$	−3.06581	+	0.821480i	−0.447194	+	0.119825i	0.0281923	+	0.999603i	$0.491025\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	6.74786	−	1.86181i	0.963980	−	0.265973i
$50$	1.02677	+	3.83197i	0.145208	+	0.541923i
$51$	−0.775501	−	0.447736i	−0.108592	−	0.0626956i
$52$	−1.15334	+	3.41611i	−0.159939	+	0.473729i
$53$	−1.89754	−	3.28664i	−0.260647	−	0.451454i	0.705767	−	0.708444i	$-0.250603\pi$
$53$	−1.89754	−	3.28664i	−0.260647	−	0.451454i	−0.966414	+	0.256990i	$0.917269\pi$
$54$	0.965926	+	0.258819i	0.131446	+	0.0352208i
$55$	−3.72783	−	2.15226i	−0.502660	−	0.290211i
$56$	1.60284	−	2.10497i	0.214188	−	0.281289i
$57$	2.03633	+	2.03633i	0.269719	+	0.269719i
$58$	−6.57057	−	6.57057i	−0.862758	−	0.862758i
$59$	−7.47136	+	2.00194i	−0.972688	+	0.260631i	−0.709962	−	0.704240i	$-0.751288\pi$
$59$	−7.47136	+	2.00194i	−0.972688	+	0.260631i	−0.262725	+	0.964871i	$0.584621\pi$
$60$	−0.981662	−	0.263036i	−0.126732	−	0.0339578i
$61$			2.35876i			0.302009i	0.988533	+	0.151004i	$0.0482507\pi$
$61$			2.35876i			0.302009i	−0.988533	+	0.151004i	$0.951749\pi$
$62$	−2.01954	+	3.49795i	−0.256482	+	0.444240i
$63$	−2.62182	+	0.355062i	−0.330318	+	0.0447336i
$64$		−	1.00000i		−	0.125000i
$65$	−3.28373	+	1.62609i	−0.407296	+	0.201692i
$66$	−3.66807	+	2.11776i	−0.451508	+	0.260678i
$67$	3.05928	+	3.05928i	0.373751	+	0.373751i	0.868841	−	0.495091i	$-0.164865\pi$
$67$	3.05928	+	3.05928i	0.373751	+	0.373751i	−0.495091	+	0.868841i	$0.664865\pi$
$68$	0.775501	−	0.447736i	0.0940434	−	0.0542960i
$69$	0.556414	+	0.963738i	0.0669844	+	0.116020i
$70$	2.66453	−	0.360846i	0.318473	−	0.0431294i
$71$	0.229950	−	0.858187i	0.0272901	−	0.101848i	−0.950937	−	0.309383i	$-0.899877\pi$
$71$	0.229950	−	0.858187i	0.0272901	−	0.101848i	0.978228	+	0.207535i	$0.0665441\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	0.120528	−	0.449816i	0.0141067	−	0.0526470i	−0.958514	−	0.285046i	$-0.907991\pi$
$73$	0.120528	−	0.449816i	0.0141067	−	0.0526470i	0.972620	+	0.232399i	$0.0746576\pi$
$74$	−4.83488	+	8.37426i	−0.562044	+	0.973488i
$75$	1.98358	+	3.43565i	0.229044	+	0.396715i
$76$	−2.78168	+	0.745350i	−0.319081	+	0.0854975i
$77$	6.78886	−	8.91566i	0.773662	−	1.01603i
$78$	−0.229883	+	3.59822i	−0.0260291	+	0.407418i
$79$	3.14658	−	5.45004i	0.354018	−	0.613177i	−0.632931	−	0.774208i	$-0.718148\pi$
$79$	3.14658	−	5.45004i	0.354018	−	0.613177i	0.986949	+	0.161031i	$0.0514818\pi$
$80$	0.718627	−	0.718627i	0.0803449	−	0.0803449i
$81$	1.00000			0.111111
$82$	1.44897			0.160011
$83$	−7.53308	+	7.53308i	−0.826863	+	0.826863i	−0.987082	−	0.160219i	$-0.948780\pi$
$83$	−7.53308	+	7.53308i	−0.826863	+	0.826863i	0.160219	+	0.987082i	$0.448780\pi$
$84$	1.00342	−	2.44809i	0.109482	−	0.267109i
$85$	0.879051	+	0.235541i	0.0953465	+	0.0255480i
$86$	−1.38349	−	5.16327i	−0.149186	−	0.556769i
$87$	−8.04727	−	4.64609i	−0.862758	−	0.498113i
$88$		−	4.23552i		−	0.451508i
$89$	3.39783	−	12.6809i	0.360169	−	1.34417i	−0.513684	−	0.857979i	$-0.671720\pi$
$89$	3.39783	−	12.6809i	0.360169	−	1.34417i	0.873853	−	0.486190i	$-0.161614\pi$
$90$	−1.01629			−0.107127
$91$	−3.11467	−	9.01659i	−0.326506	−	0.945195i
$92$	−1.11283			−0.116020
$93$	−1.04539	+	3.90146i	−0.108402	+	0.404563i
$94$		−	3.17396i		−	0.327369i
$95$	−2.53462	−	1.46336i	−0.260046	−	0.150138i
$96$	−0.258819	−	0.965926i	−0.0264156	−	0.0985844i
$97$	−8.06565	−	2.16118i	−0.818943	−	0.219435i	−0.175058	−	0.984558i	$-0.556011\pi$
$97$	−8.06565	−	2.16118i	−0.818943	−	0.219435i	−0.643884	+	0.765123i	$0.722678\pi$
$98$	0.0518991	+	6.99981i	0.00524260	+	0.707087i
$99$	−2.99497	+	2.99497i	−0.301005	+	0.301005i
$100$	−3.96715			−0.396715
$101$	8.20488			0.816416			0.408208	−	0.912889i	$-0.366154\pi$
$101$	8.20488			0.816416			0.408208	+	0.912889i	$0.366154\pi$
$102$	0.633194	−	0.633194i	0.0626956	−	0.0626956i
$103$	5.96169	−	10.3259i	0.587423	−	1.01745i	−0.407146	−	0.913363i	$-0.633476\pi$
$103$	5.96169	−	10.3259i	0.587423	−	1.01745i	0.994569	−	0.104083i	$-0.0331907\pi$
$104$	−3.00120	−	1.99819i	−0.294292	−	0.195939i
$105$	2.48035	−	1.03818i	0.242057	−	0.101316i
$106$	3.66577	−	0.982239i	0.356051	−	0.0954035i
$107$	−0.607288	−	1.05185i	−0.0587088	−	0.101687i	0.835177	−	0.549981i	$-0.185365\pi$
$107$	−0.607288	−	1.05185i	−0.0587088	−	0.101687i	−0.893886	+	0.448294i	$0.852032\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	2.80174	−	10.4562i	0.268358	−	1.00152i	−0.691805	−	0.722084i	$-0.743184\pi$
$109$	2.80174	−	10.4562i	0.268358	−	1.00152i	0.960163	−	0.279440i	$-0.0901489\pi$
$110$	3.04376	−	3.04376i	0.290211	−	0.290211i
$111$	−2.50272	+	9.34028i	−0.237548	+	0.886540i
$112$	1.61840	+	2.09303i	0.152925	+	0.197773i
$113$	6.77909	+	11.7417i	0.637723	+	1.10457i	0.985931	+	0.167152i	$0.0534570\pi$
$113$	6.77909	+	11.7417i	0.637723	+	1.10457i	−0.348208	+	0.937417i	$0.613210\pi$
$114$	−2.49399	+	1.43990i	−0.233583	+	0.134859i
$115$	−0.799709	−	0.799709i	−0.0745732	−	0.0745732i
$116$	8.04727	−	4.64609i	0.747170	−	0.431379i
$117$	0.709237	+	3.53511i	0.0655690	+	0.326821i
$118$		−	7.73492i		−	0.712057i
$119$	−0.898532	+	2.19220i	−0.0823683	+	0.200958i
$120$	0.508146	−	0.880134i	0.0463872	−	0.0803449i
$121$		−	6.93965i		−	0.630877i
$122$	−2.27839	−	0.610493i	−0.206276	−	0.0552714i
$123$	1.39959	−	0.375020i	0.126197	−	0.0338144i
$124$	−2.85607	−	2.85607i	−0.256482	−	0.256482i
$125$	−6.44403	−	6.44403i	−0.576372	−	0.576372i
$126$	0.335613	−	2.62438i	0.0298988	−	0.233798i
$127$	−7.87288	−	4.54541i	−0.698605	−	0.403340i	0.108223	−	0.994127i	$-0.465484\pi$
$127$	−7.87288	−	4.54541i	−0.698605	−	0.403340i	−0.806828	+	0.590787i	$0.798817\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−2.67270	−	4.62926i	−0.235318	−	0.407583i
$130$	−0.720791	−	3.59270i	−0.0632176	−	0.315101i
$131$	−5.46001	−	3.15234i	−0.477043	−	0.275421i	0.242140	−	0.970241i	$-0.422151\pi$
$131$	−5.46001	−	3.15234i	−0.477043	−	0.275421i	−0.719183	+	0.694820i	$0.755484\pi$
$132$	−1.09623	−	4.09120i	−0.0954149	−	0.356093i
$133$	4.61587	−	6.06192i	0.400247	−	0.525635i
$134$	−3.74684	+	2.16324i	−0.323678	+	0.186875i
$135$	−0.981662	+	0.263036i	−0.0844880	+	0.0226385i
$136$	0.231765	+	0.864960i	0.0198737	+	0.0741697i
$137$	5.88086	+	21.9477i	0.502436	+	1.87512i	0.483589	+	0.875295i	$0.339333\pi$
$137$	5.88086	+	21.9477i	0.502436	+	1.87512i	0.0188467	+	0.999822i	$0.494001\pi$
$138$	−1.07491	+	0.288021i	−0.0915024	+	0.0245180i
$139$	−13.7959	+	7.96507i	−1.17015	+	0.675588i	−0.953716	−	0.300708i	$-0.902777\pi$
$139$	−13.7959	+	7.96507i	−1.17015	+	0.675588i	−0.216437	+	0.976297i	$0.569444\pi$
$140$	−0.341081	+	2.66713i	−0.0288266	+	0.225414i
$141$	−0.821480	−	3.06581i	−0.0691811	−	0.258187i
$142$	0.769429	+	0.444230i	0.0645691	+	0.0372790i
$143$	−12.7117	−	8.46339i	−1.06300	−	0.707744i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	9.12179	+	2.44418i	0.757523	+	0.202978i
$146$	0.403294	+	0.232842i	0.0333769	+	0.0192701i
$147$	1.86181	+	6.74786i	0.153560	+	0.556554i
$148$	−6.83756	−	6.83756i	−0.562044	−	0.562044i
$149$	2.51772	+	2.51772i	0.206260	+	0.206260i	0.802676	−	0.596416i	$-0.203409\pi$
$149$	2.51772	+	2.51772i	0.206260	+	0.206260i	−0.596416	+	0.802676i	$0.703409\pi$
$150$	−3.83197	+	1.02677i	−0.312879	+	0.0838358i
$151$	4.76017	+	1.27548i	0.387377	+	0.103797i	0.447251	−	0.894409i	$-0.352403\pi$
$151$	4.76017	+	1.27548i	0.387377	+	0.103797i	−0.0598738	+	0.998206i	$0.519070\pi$
$152$		−	2.87981i		−	0.233583i
$153$	0.447736	−	0.775501i	0.0361973	−	0.0626956i
$154$	6.85478	+	8.86508i	0.552374	+	0.714368i
$155$		−	4.10489i		−	0.329713i
$156$	−3.41611	−	1.15334i	−0.273508	−	0.0923408i
$157$	9.25317	−	5.34232i	0.738483	−	0.426363i	−0.0830344	−	0.996547i	$-0.526461\pi$
$157$	9.25317	−	5.34232i	0.738483	−	0.426363i	0.821518	+	0.570183i	$0.193128\pi$
$158$	4.44994	+	4.44994i	0.354018	+	0.354018i
$159$	3.28664	−	1.89754i	0.260647	−	0.150485i
$160$	0.508146	+	0.880134i	0.0401725	+	0.0695807i
$161$	2.32918	−	1.80100i	0.183565	−	0.141939i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	−16.5804	+	16.5804i	−1.29868	+	1.29868i	−0.369410	+	0.929267i	$0.620440\pi$
$163$	−16.5804	+	16.5804i	−1.29868	+	1.29868i	−0.929267	+	0.369410i	$0.879560\pi$
$164$	−0.375020	+	1.39959i	−0.0292841	+	0.109290i
$165$	2.15226	−	3.72783i	0.167553	−	0.290211i
$166$	−5.32669	−	9.22610i	−0.413431	−	0.716084i
$167$	−15.7780	+	4.22772i	−1.22094	+	0.327150i	−0.811046	−	0.584982i	$-0.801102\pi$
$167$	−15.7780	+	4.22772i	−1.22094	+	0.327150i	−0.409896	+	0.912132i	$0.634435\pi$
$168$	2.10497	+	1.60284i	0.162402	+	0.123662i
$169$	−11.9940	+	5.01446i	−0.922613	+	0.385727i
$170$	−0.455030	+	0.788136i	−0.0348992	+	0.0604473i
$171$	−2.03633	+	2.03633i	−0.155722	+	0.155722i
$172$	5.34541			0.407583
$173$	−18.5214			−1.40815			−0.704077	−	0.710124i	$-0.748639\pi$
$173$	−18.5214			−1.40815			−0.704077	+	0.710124i	$0.748639\pi$
$174$	6.57057	−	6.57057i	0.498113	−	0.498113i
$175$	8.30337	−	6.42044i	0.627676	−	0.485340i
$176$	4.09120	+	1.09623i	0.308386	+	0.0826317i
$177$	−2.00194	−	7.47136i	−0.150475	−	0.561581i
$178$	11.3694	+	6.56410i	0.852169	+	0.492000i
$179$		−	22.1207i		−	1.65338i	−0.562657	−	0.826691i	$-0.690221\pi$
$179$		−	22.1207i		−	1.65338i	0.562657	−	0.826691i	$-0.309779\pi$
$180$	0.263036	−	0.981662i	0.0196055	−	0.0731688i
$181$	−12.9441			−0.962126			−0.481063	−	0.876686i	$-0.659749\pi$
$181$	−12.9441			−0.962126			−0.481063	+	0.876686i	$0.659749\pi$
$182$	9.51549	−	0.674877i	0.705335	−	0.0500252i
$183$	−2.35876			−0.174365
$184$	0.288021	−	1.07491i	0.0212332	−	0.0792434i
$185$		−	9.82730i		−	0.722518i
$186$	−3.49795	−	2.01954i	−0.256482	−	0.148080i
$187$	0.981647	+	3.66356i	0.0717851	+	0.267906i
$188$	3.06581	+	0.821480i	0.223597	+	0.0599126i
$189$	−0.355062	−	2.62182i	−0.0258269	−	0.190709i
$190$	2.06951	−	2.06951i	0.150138	−	0.150138i
$191$	7.30247			0.528388			0.264194	−	0.964470i	$-0.414894\pi$
$191$	7.30247			0.528388			0.264194	+	0.964470i	$0.414894\pi$
$192$	1.00000			0.0721688
$193$	−14.5932	+	14.5932i	−1.05044	+	1.05044i	−0.0517794	+	0.998659i	$0.516489\pi$
$193$	−14.5932	+	14.5932i	−1.05044	+	1.05044i	−0.998659	+	0.0517794i	$0.983511\pi$
$194$	4.17509	−	7.23146i	0.299754	−	0.519189i
$195$	−1.62609	−	3.28373i	−0.116447	−	0.235153i
$196$	−6.77473	−	1.76155i	−0.483909	−	0.125825i
$197$	16.2233	−	4.34702i	1.15586	−	0.309712i	0.370550	−	0.928812i	$-0.379169\pi$
$197$	16.2233	−	4.34702i	1.15586	−	0.309712i	0.785312	+	0.619100i	$0.212503\pi$
$198$	−2.11776	−	3.66807i	−0.150503	−	0.260678i
$199$	2.13133	−	3.69158i	0.151086	−	0.261689i	−0.780541	−	0.625105i	$-0.785056\pi$
$199$	2.13133	−	3.69158i	0.151086	−	0.261689i	0.931627	+	0.363416i	$0.118390\pi$
$200$	1.02677	−	3.83197i	0.0726039	−	0.270961i
$201$	−3.05928	+	3.05928i	−0.215785	+	0.215785i
$202$	−2.12358	+	7.92531i	−0.149415	+	0.557623i
$203$	−9.32393	+	22.7481i	−0.654412	+	1.59660i
$204$	0.447736	+	0.775501i	0.0313478	+	0.0542960i
$205$	−1.27528	+	0.736286i	−0.0890697	+	0.0514244i
$206$	8.43110	+	8.43110i	0.587423	+	0.587423i
$207$	−0.963738	+	0.556414i	−0.0669844	+	0.0386735i
$208$	2.70687	−	2.38177i	0.187688	−	0.165146i
$209$		−	12.1975i		−	0.843718i
$210$	0.360846	+	2.66453i	0.0249008	+	0.183870i
$211$	−7.88634	+	13.6595i	−0.542918	+	0.940362i	0.455816	+	0.890074i	$0.349347\pi$
$211$	−7.88634	+	13.6595i	−0.542918	+	0.940362i	−0.998735	+	0.0502883i	$0.983986\pi$
$212$			3.79508i			0.260647i
$213$	0.858187	+	0.229950i	0.0588020	+	0.0157559i
$214$	1.17319	−	0.314355i	0.0801976	−	0.0214889i
$215$	3.84135	+	3.84135i	0.261978	+	0.261978i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	10.6001	+	1.35557i	0.719582	+	0.0920222i
$218$	9.37479	+	5.41254i	0.634941	+	0.366583i
$219$	0.449816	+	0.120528i	0.0303958	+	0.00814452i
$220$	2.15226	+	3.72783i	0.145106	+	0.251330i
$221$	3.05903	+	1.03278i	0.205773	+	0.0694723i
$222$	−8.37426	−	4.83488i	−0.562044	−	0.324496i
$223$	7.04837	+	26.3049i	0.471994	+	1.76151i	0.632592	+	0.774486i	$0.281991\pi$
$223$	7.04837	+	26.3049i	0.471994	+	1.76151i	−0.160598	+	0.987020i	$0.551342\pi$
$224$	−2.44059	+	1.02154i	−0.163068	+	0.0682545i
$225$	−3.43565	+	1.98358i	−0.229044	+	0.132238i
$226$	−13.0962	+	3.50912i	−0.871146	+	0.233423i
$227$	−2.64057	−	9.85473i	−0.175261	−	0.654082i	−0.996507	−	0.0835081i	$-0.973388\pi$
$227$	−2.64057	−	9.85473i	−0.175261	−	0.654082i	0.821246	−	0.570574i	$-0.193279\pi$
$228$	−0.745350	−	2.78168i	−0.0493620	−	0.184221i
$229$	−25.6314	+	6.86791i	−1.69377	+	0.453844i	−0.971359	−	0.237618i	$-0.923633\pi$
$229$	−25.6314	+	6.86791i	−1.69377	+	0.453844i	−0.722412	+	0.691463i	$0.756967\pi$
$230$	0.979439	−	0.565479i	0.0645823	−	0.0372866i
$231$	8.91566	+	6.78886i	0.586607	+	0.446674i
$232$	2.40499	+	8.97556i	0.157896	+	0.589274i
$233$	23.6788	+	13.6710i	1.55125	+	0.895614i	0.998041	+	0.0625709i	$0.0199300\pi$
$233$	23.6788	+	13.6710i	1.55125	+	0.895614i	0.553208	+	0.833043i	$0.313403\pi$
$234$	−3.59822	−	0.229883i	−0.235223	−	0.0150279i
$235$	1.61283	+	2.79351i	0.105210	+	0.182228i
$236$	7.47136	+	2.00194i	0.486344	+	0.130315i
$237$	5.45004	+	3.14658i	0.354018	+	0.204392i
$238$	−1.88494	−	1.43530i	−0.122183	−	0.0930365i
$239$	19.5943	+	19.5943i	1.26745	+	1.26745i	0.947402	+	0.320045i	$0.103698\pi$
$239$	19.5943	+	19.5943i	1.26745	+	1.26745i	0.320045	+	0.947402i	$0.396302\pi$
$240$	0.718627	+	0.718627i	0.0463872	+	0.0463872i
$241$	24.2575	−	6.49978i	1.56256	−	0.418688i	0.629089	−	0.777333i	$-0.283428\pi$
$241$	24.2575	−	6.49978i	1.56256	−	0.418688i	0.933474	+	0.358645i	$0.116761\pi$
$242$	6.70318	+	1.79611i	0.430897	+	0.115459i
$243$			1.00000i			0.0641500i
$244$	1.17938	−	2.04275i	0.0755021	−	0.130774i
$245$	−3.60260	−	6.13440i	−0.230162	−	0.391912i
$246$			1.44897i			0.0923827i
$247$	−8.64290	−	5.75441i	−0.549934	−	0.366145i
$248$	3.49795	−	2.01954i	0.222120	−	0.128241i
$249$	−7.53308	−	7.53308i	−0.477389	−	0.477389i
$250$	7.89230	−	4.55662i	0.499153	−	0.288186i
$251$	−7.23404	−	12.5297i	−0.456609	−	0.790869i	0.542171	−	0.840268i	$-0.317603\pi$
$251$	−7.23404	−	12.5297i	−0.456609	−	0.790869i	−0.998779	+	0.0493992i	$0.984269\pi$
$252$	2.44809	+	1.00342i	0.154215	+	0.0632093i
$253$	1.21992	−	4.55281i	0.0766958	−	0.286232i
$254$	6.42818	−	6.42818i	0.403340	−	0.403340i
$255$	−0.235541	+	0.879051i	−0.0147502	+	0.0550483i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.42437	+	11.1273i	0.400741	+	0.694104i	0.993816	−	0.111044i	$-0.0354194\pi$
$257$	6.42437	+	11.1273i	0.400741	+	0.694104i	−0.593075	+	0.805148i	$0.702086\pi$
$258$	5.16327	−	1.38349i	0.321451	−	0.0861325i
$259$	25.3771	+	3.24530i	1.57686	+	0.201653i
$260$	3.65684	+	0.233628i	0.226787	+	0.0144890i
$261$	4.64609	−	8.04727i	0.287586	−	0.498113i
$262$	4.45808	−	4.45808i	0.275421	−	0.275421i
$263$	−10.6596			−0.657301			−0.328651	−	0.944452i	$-0.606594\pi$
$263$	−10.6596			−0.657301			−0.328651	+	0.944452i	$0.606594\pi$
$264$	4.23552			0.260678
$265$	−2.72725	+	2.72725i	−0.167533	+	0.167533i
$266$	4.66069	+	6.02753i	0.285765	+	0.369571i
$267$	12.6809	+	3.39783i	0.776056	+	0.207944i
$268$	−1.11978	−	4.17906i	−0.0684012	−	0.255277i
$269$	−8.31736	−	4.80203i	−0.507119	−	0.292785i	0.224530	−	0.974467i	$-0.427915\pi$
$269$	−8.31736	−	4.80203i	−0.507119	−	0.292785i	−0.731648	+	0.681682i	$0.761249\pi$
$270$		−	1.01629i		−	0.0618495i
$271$	−3.40472	+	12.7066i	−0.206822	+	0.771870i	0.782065	+	0.623197i	$0.214167\pi$
$271$	−3.40472	+	12.7066i	−0.206822	+	0.771870i	−0.988887	+	0.148672i	$0.952500\pi$
$272$	−0.895472			−0.0542960
$273$	9.01659	−	3.11467i	0.545709	−	0.188508i
$274$	−22.7219			−1.37268
$275$	4.34893	−	16.2304i	0.262250	−	0.978731i
$276$		−	1.11283i		−	0.0669844i
$277$	17.0682	+	9.85432i	1.02553	+	0.592089i	0.915700	−	0.401862i	$-0.131637\pi$
$277$	17.0682	+	9.85432i	1.02553	+	0.592089i	0.109827	+	0.993951i	$0.464970\pi$
$278$	−4.12302	−	15.3873i	−0.247283	−	0.922871i
$279$	−3.90146	−	1.04539i	−0.233574	−	0.0625860i
$280$	−2.48798	−	1.01976i	−0.148685	−	0.0609426i
$281$	−12.8366	+	12.8366i	−0.765767	+	0.765767i	−0.977358	−	0.211591i	$-0.932135\pi$
$281$	−12.8366	+	12.8366i	−0.765767	+	0.765767i	0.211591	+	0.977358i	$0.432135\pi$
$282$	3.17396			0.189006
$283$	−19.3480			−1.15012			−0.575058	−	0.818112i	$-0.695021\pi$
$283$	−19.3480			−1.15012			−0.575058	+	0.818112i	$0.695021\pi$
$284$	−0.628236	+	0.628236i	−0.0372790	+	0.0372790i
$285$	1.46336	−	2.53462i	0.0866822	−	0.150138i
$286$	11.4650	−	10.0880i	0.677941	−	0.596518i
$287$	−1.48018	−	3.53632i	−0.0873720	−	0.208743i
$288$	0.965926	−	0.258819i	0.0569177	−	0.0152511i
$289$	8.09906	+	14.0280i	0.476416	+	0.825176i
$290$	−4.72178	+	8.17837i	−0.277273	+	0.480250i
$291$	2.16118	−	8.06565i	0.126691	−	0.472817i
$292$	−0.329288	+	0.329288i	−0.0192701	+	0.0192701i
$293$	2.77511	−	10.3569i	0.162124	−	0.605054i	−0.836266	−	0.548324i	$-0.815266\pi$
$293$	2.77511	−	10.3569i	0.162124	−	0.605054i	0.998390	−	0.0567298i	$-0.0180674\pi$
$294$	−6.99981	+	0.0518991i	−0.408237	+	0.00302682i
$295$	3.93047	+	6.80777i	0.228841	+	0.396363i
$296$	8.37426	−	4.83488i	0.486744	−	0.281022i
$297$	−2.99497	−	2.99497i	−0.173786	−	0.173786i
$298$	−3.08357	+	1.78030i	−0.178626	+	0.103130i
$299$	−2.65050	−	3.01229i	−0.153283	−	0.174205i
$300$		−	3.96715i		−	0.229044i
$301$	−11.1881	+	8.65102i	−0.644871	+	0.498636i
$302$	−2.46404	+	4.26785i	−0.141790	+	0.245587i
$303$			8.20488i			0.471358i
$304$	2.78168	+	0.745350i	0.159540	+	0.0427487i
$305$	2.31551	−	0.620438i	0.132586	−	0.0355262i
$306$	0.633194	+	0.633194i	0.0361973	+	0.0361973i
$307$	4.30658	+	4.30658i	0.245789	+	0.245789i	0.819240	−	0.573451i	$-0.194396\pi$
$307$	4.30658	+	4.30658i	0.245789	+	0.245789i	−0.573451	+	0.819240i	$0.694396\pi$
$308$	−10.3372	+	4.32675i	−0.589014	+	0.246540i
$309$	10.3259	+	5.96169i	0.587423	+	0.339149i
$310$	3.96502	+	1.06242i	0.225198	+	0.0603416i
$311$	−0.316677	−	0.548501i	−0.0179571	−	0.0311027i	0.856907	−	0.515471i	$-0.172383\pi$
$311$	−0.316677	−	0.548501i	−0.0179571	−	0.0311027i	−0.874864	+	0.484368i	$0.839050\pi$
$312$	1.99819	−	3.00120i	0.113125	−	0.169910i
$313$	6.23316	+	3.59872i	0.352319	+	0.203411i	0.665706	−	0.746214i	$-0.268130\pi$
$313$	6.23316	+	3.59872i	0.352319	+	0.203411i	−0.313387	+	0.949625i	$0.601464\pi$
$314$	2.76539	+	10.3206i	0.156060	+	0.582423i
$315$	1.03818	+	2.48035i	0.0584949	+	0.139752i
$316$	−5.45004	+	3.14658i	−0.306589	+	0.177009i
$317$	8.44978	−	2.26411i	0.474587	−	0.127165i	−0.0135942	−	0.999908i	$-0.504327\pi$
$317$	8.44978	−	2.26411i	0.474587	−	0.127165i	0.488181	+	0.872742i	$0.337661\pi$
$318$	0.982239	+	3.66577i	0.0550812	+	0.205566i
$319$	10.1864	+	38.0162i	0.570329	+	2.12850i
$320$	−0.981662	+	0.263036i	−0.0548766	+	0.0147041i
$321$	1.05185	−	0.607288i	0.0587088	−	0.0338955i
$322$	1.13680	+	2.71595i	0.0633513	+	0.151354i
$323$	0.667440	+	2.49092i	0.0371373	+	0.138598i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$	−9.44884	−	10.7386i	−0.524128	−	0.595669i
$326$	−11.7241	−	20.3067i	−0.649338	−	1.12469i
$327$	10.4562	+	2.80174i	0.578230	+	0.154936i
$328$	−1.25484	−	0.724483i	−0.0692870	−	0.0400029i
$329$	−7.74631	+	3.24232i	−0.427068	+	0.178755i
$330$	3.04376	+	3.04376i	0.167553	+	0.167553i
$331$	−8.99033	−	8.99033i	−0.494153	−	0.494153i	0.415459	−	0.909612i	$-0.363621\pi$
$331$	−8.99033	−	8.99033i	−0.494153	−	0.494153i	−0.909612	+	0.415459i	$0.863621\pi$
$332$	10.2904	−	2.75730i	0.564758	−	0.151326i
$333$	−9.34028	−	2.50272i	−0.511844	−	0.137148i
$334$		−	16.3346i		−	0.893792i
$335$	2.19848	−	3.80788i	0.120116	−	0.208047i
$336$	−2.09303	+	1.61840i	−0.114184	+	0.0882910i
$337$		−	19.1949i		−	1.04561i	−0.852451	−	0.522807i	$-0.824885\pi$
$337$		−	19.1949i		−	1.04561i	0.852451	−	0.522807i	$-0.175115\pi$
$338$	−1.73933	−	12.8831i	−0.0946069	−	0.700749i
$339$	−11.7417	+	6.77909i	−0.637723	+	0.368190i
$340$	−0.643510	−	0.643510i	−0.0348992	−	0.0348992i
$341$	14.8157	−	8.55382i	0.802313	−	0.463216i
$342$	−1.43990	−	2.49399i	−0.0778611	−	0.134859i
$343$	17.0306	−	7.27725i	0.919567	−	0.392934i
$344$	−1.38349	+	5.16327i	−0.0745930	+	0.278385i
$345$	0.799709	−	0.799709i	0.0430549	−	0.0430549i
$346$	4.79368	−	17.8903i	0.257710	−	0.961787i
$347$	−7.73415	+	13.3959i	−0.415191	+	0.719132i	−0.995449	−	0.0953010i	$-0.969619\pi$
$347$	−7.73415	+	13.3959i	−0.415191	+	0.719132i	0.580257	+	0.814433i	$0.302952\pi$
$348$	4.64609	+	8.04727i	0.249057	+	0.431379i
$349$	−5.37886	+	1.44126i	−0.287924	+	0.0771489i	−0.399890	−	0.916563i	$-0.630952\pi$
$349$	−5.37886	+	1.44126i	−0.287924	+	0.0771489i	0.111966	+	0.993712i	$0.464285\pi$
$350$	4.05260	+	9.68217i	0.216621	+	0.517534i
$351$	−3.53511	+	0.709237i	−0.188690	+	0.0378563i
$352$	−2.11776	+	3.66807i	−0.112877	+	0.195509i
$353$	−20.3875	+	20.3875i	−1.08512	+	1.08512i	−0.0890954	+	0.996023i	$0.528398\pi$
$353$	−20.3875	+	20.3875i	−1.08512	+	1.08512i	−0.996023	+	0.0890954i	$0.971602\pi$
$354$	7.73492			0.411106
$355$	−0.902935			−0.0479228
$356$	−9.28304	+	9.28304i	−0.492000	+	0.492000i
$357$	−2.19220	−	0.898532i	−0.116023	−	0.0475553i
$358$	21.3670	+	5.72527i	1.12928	+	0.302590i
$359$	0.766652	+	2.86118i	0.0404623	+	0.151007i	0.983202	−	0.182523i	$-0.0584265\pi$
$359$	0.766652	+	2.86118i	0.0404623	+	0.151007i	−0.942739	+	0.333531i	$0.891760\pi$
$360$	0.880134	+	0.508146i	0.0463872	+	0.0267816i
$361$			10.7067i			0.563510i
$362$	3.35018	−	12.5030i	0.176081	−	0.657145i
$363$	6.93965			0.364237
$364$	−1.81091	+	9.36593i	−0.0949174	+	0.490908i
$365$	−0.473271			−0.0247721
$366$	0.610493	−	2.27839i	0.0319110	−	0.119093i
$367$			12.7468i			0.665379i	0.943036	+	0.332689i	$0.107956\pi$
$367$			12.7468i			0.665379i	−0.943036	+	0.332689i	$0.892044\pi$
$368$	0.963738	+	0.556414i	0.0502383	+	0.0290051i
$369$	0.375020	+	1.39959i	0.0195228	+	0.0728599i
$370$	9.49244	+	2.54349i	0.493489	+	0.132230i
$371$	−6.14196	−	7.94322i	−0.318875	−	0.412391i
$372$	2.85607	−	2.85607i	0.148080	−	0.148080i
$373$	15.2757			0.790944			0.395472	−	0.918478i	$-0.370581\pi$
$373$	15.2757			0.790944			0.395472	+	0.918478i	$0.370581\pi$
$374$	−3.79279			−0.196121
$375$	6.44403	−	6.44403i	0.332769	−	0.332769i
$376$	−1.58698	+	2.74873i	−0.0818421	+	0.141755i
$377$	31.7431	+	10.7170i	1.63485	+	0.551954i
$378$	2.62438	+	0.335613i	0.134983	+	0.0172621i
$379$	−14.6944	+	3.93734i	−0.754799	+	0.202248i	−0.615646	−	0.788023i	$-0.711105\pi$
$379$	−14.6944	+	3.93734i	−0.754799	+	0.202248i	−0.139153	+	0.990271i	$0.544438\pi$
$380$	1.46336	+	2.53462i	0.0750689	+	0.130023i
$381$	4.54541	−	7.87288i	0.232868	−	0.403340i
$382$	−1.89002	+	7.05364i	−0.0967017	+	0.360896i
$383$	−10.1147	+	10.1147i	−0.516838	+	0.516838i	−0.916613	−	0.399775i	$-0.869088\pi$
$383$	−10.1147	+	10.1147i	−0.516838	+	0.516838i	0.399775	+	0.916613i	$0.369088\pi$
$384$	−0.258819	+	0.965926i	−0.0132078	+	0.0492922i
$385$	−10.5379	−	4.31923i	−0.537060	−	0.220129i
$386$	−10.3189	−	17.8729i	−0.525219	−	0.909706i
$387$	4.62926	−	2.67270i	0.235318	−	0.135861i
$388$	5.90446	+	5.90446i	0.299754	+	0.299754i
$389$	6.99902	−	4.04089i	0.354864	−	0.204881i	−0.311961	−	0.950095i	$-0.600986\pi$
$389$	6.99902	−	4.04089i	0.354864	−	0.204881i	0.666826	+	0.745214i	$0.267653\pi$
$390$	3.59270	−	0.720791i	0.181923	−	0.0364987i
$391$			0.996507i			0.0503955i
$392$	3.45496	−	6.08796i	0.174502	−	0.307488i
$393$	3.15234	−	5.46001i	0.159014	−	0.275421i
$394$			16.7956i			0.846150i
$395$	−6.17776	−	1.65533i	−0.310837	−	0.0832885i
$396$	4.09120	−	1.09623i	0.205591	−	0.0550878i
$397$	21.1162	+	21.1162i	1.05979	+	1.05979i	0.998095	+	0.0616994i	$0.0196520\pi$
$397$	21.1162	+	21.1162i	1.05979	+	1.05979i	0.0616994	+	0.998095i	$0.480348\pi$
$398$	3.01416	+	3.01416i	0.151086	+	0.151086i
$399$	6.06192	+	4.61587i	0.303475	+	0.231083i
$400$	3.43565	+	1.98358i	0.171783	+	0.0991788i
$401$	−7.63476	−	2.04573i	−0.381262	−	0.102159i	0.0630976	−	0.998007i	$-0.479902\pi$
$401$	−7.63476	−	2.04573i	−0.381262	−	0.102159i	−0.444360	+	0.895849i	$0.646569\pi$
$402$	−2.16324	−	3.74684i	−0.107893	−	0.186875i
$403$	0.928518	−	14.5335i	0.0462528	−	0.723966i
$404$	−7.10564	−	4.10244i	−0.353519	−	0.204104i
$405$	−0.263036	−	0.981662i	−0.0130703	−	0.0487792i
$406$	−19.5598	−	14.8939i	−0.970736	−	0.739171i
$407$	35.4694	−	20.4783i	1.75815	−	1.01507i
$408$	−0.864960	+	0.231765i	−0.0428219	+	0.0114741i
$409$	−1.77430	−	6.62177i	−0.0877334	−	0.327426i	0.908084	−	0.418787i	$-0.137545\pi$
$409$	−1.77430	−	6.62177i	−0.0877334	−	0.327426i	−0.995818	+	0.0913617i	$0.970878\pi$
$410$	−0.381130	−	1.42239i	−0.0188226	−	0.0702471i
$411$	−21.9477	+	5.88086i	−1.08260	+	0.290082i
$412$	−10.3259	+	5.96169i	−0.508723	+	0.293711i
$413$	−18.8777	+	7.90152i	−0.928912	+	0.388809i
$414$	−0.288021	−	1.07491i	−0.0141555	−	0.0528290i
$415$	9.37641	+	5.41347i	0.460270	+	0.265737i
$416$	1.60002	+	3.23109i	0.0784476	+	0.158417i
$417$	−7.96507	−	13.7959i	−0.390051	−	0.675588i
$418$	11.7819	+	3.15694i	0.576270	+	0.154411i
$419$	−24.6906	−	14.2551i	−1.20622	−	0.696409i	−0.244285	−	0.969704i	$-0.578553\pi$
$419$	−24.6906	−	14.2551i	−1.20622	−	0.696409i	−0.961930	+	0.273295i	$0.911887\pi$
$420$	−2.66713	−	0.341081i	−0.130143	−	0.0166430i
$421$	−26.7911	−	26.7911i	−1.30572	−	1.30572i	−0.924475	−	0.381243i	$-0.875496\pi$
$421$	−26.7911	−	26.7911i	−1.30572	−	1.30572i	−0.381243	−	0.924475i	$-0.624504\pi$
$422$	−11.1530	−	11.1530i	−0.542918	−	0.542918i
$423$	3.06581	−	0.821480i	0.149065	−	0.0399417i
$424$	−3.66577	−	0.982239i	−0.178025	−	0.0477017i
$425$			3.55247i			0.172320i
$426$	−0.444230	+	0.769429i	−0.0215230	+	0.0372790i
$427$	0.837506	+	6.18425i	0.0405298	+	0.299277i
$428$			1.21458i			0.0587088i
$429$	8.46339	−	12.7117i	0.408616	−	0.613725i
$430$	−4.70468	+	2.71625i	−0.226880	+	0.130989i
$431$	−5.81069	−	5.81069i	−0.279891	−	0.279891i	0.553174	−	0.833066i	$-0.313416\pi$
$431$	−5.81069	−	5.81069i	−0.279891	−	0.279891i	−0.833066	+	0.553174i	$0.813416\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	−8.27418	−	14.3313i	−0.397632	−	0.688719i	0.595801	−	0.803132i	$-0.296835\pi$
$433$	−8.27418	−	14.3313i	−0.397632	−	0.688719i	−0.993433	+	0.114413i	$0.963501\pi$
$434$	−4.05289	+	9.88806i	−0.194545	+	0.474642i
$435$	−2.44418	+	9.12179i	−0.117189	+	0.437356i
$436$	−7.65449	+	7.65449i	−0.366583	+	0.366583i
$437$	0.829447	−	3.09554i	0.0396778	−	0.148080i
$438$	−0.232842	+	0.403294i	−0.0111256	+	0.0192701i
$439$	−18.0705	−	31.2991i	−0.862460	−	1.49382i	−0.869547	−	0.493850i	$-0.835589\pi$
$439$	−18.0705	−	31.2991i	−0.862460	−	1.49382i	0.00708718	−	0.999975i	$-0.497744\pi$
$440$	−4.15785	+	1.11409i	−0.198218	+	0.0531123i
$441$	−6.74786	+	1.86181i	−0.321327	+	0.0886578i
$442$	−1.78933	+	2.68749i	−0.0851095	+	0.127831i
$443$	9.04555	−	15.6673i	0.429767	−	0.744378i	−0.567085	−	0.823659i	$-0.691929\pi$
$443$	9.04555	−	15.6673i	0.429767	−	0.744378i	0.996852	+	0.0792809i	$0.0252624\pi$
$444$	6.83756	−	6.83756i	0.324496	−	0.324496i
$445$	−13.3421			−0.632475
$446$	−27.2328			−1.28951
$447$	−2.51772	+	2.51772i	−0.119084	+	0.119084i
$448$	−0.355062	−	2.62182i	−0.0167751	−	0.123869i
$449$	−11.6055	−	3.10969i	−0.547699	−	0.146755i	−0.0256499	−	0.999671i	$-0.508166\pi$
$449$	−11.6055	−	3.10969i	−0.547699	−	0.146755i	−0.522049	+	0.852916i	$0.674832\pi$
$450$	−1.02677	−	3.83197i	−0.0484026	−	0.180641i
$451$	−5.31491	−	3.06856i	−0.250269	−	0.144493i
$452$		−	13.5582i		−	0.637723i
$453$	−1.27548	+	4.76017i	−0.0599274	+	0.223652i
$454$	10.2024			0.478821
$455$	−8.03197	+	5.42924i	−0.376545	+	0.254527i
$456$	2.87981			0.134859
$457$	−3.85704	+	14.3947i	−0.180425	+	0.673354i	0.815139	+	0.579265i	$0.196661\pi$
$457$	−3.85704	+	14.3947i	−0.180425	+	0.673354i	−0.995564	+	0.0940890i	$0.970006\pi$
$458$		−	26.5356i		−	1.23993i
$459$	0.775501	+	0.447736i	0.0361973	+	0.0208985i
$460$	0.292714	+	1.09242i	0.0136478	+	0.0509345i
$461$	32.6783	+	8.75614i	1.52198	+	0.407814i	0.920394	−	0.390992i	$-0.127868\pi$
$461$	32.6783	+	8.75614i	1.52198	+	0.407814i	0.601588	+	0.798806i	$0.294535\pi$
$462$	−8.86508	+	6.85478i	−0.412441	+	0.318913i
$463$	20.8393	−	20.8393i	0.968486	−	0.968486i	−0.0310326	−	0.999518i	$-0.509880\pi$
$463$	20.8393	−	20.8393i	0.968486	−	0.968486i	0.999518	+	0.0310326i	$0.00987956\pi$
$464$	−9.29218			−0.431379
$465$	4.10489			0.190360
$466$	−19.3336	+	19.3336i	−0.895614	+	0.895614i
$467$	19.7862	−	34.2707i	0.915597	−	1.58586i	0.109572	−	0.993979i	$-0.465052\pi$
$467$	19.7862	−	34.2707i	0.915597	−	1.58586i	0.806025	−	0.591882i	$-0.201615\pi$
$468$	1.15334	−	3.41611i	0.0533130	−	0.157910i
$469$	9.10712	+	6.93465i	0.420528	+	0.320212i
$470$	−3.11575	+	0.834863i	−0.143719	+	0.0385094i
$471$	5.34232	+	9.25317i	0.246161	+	0.426363i
$472$	−3.86746	+	6.69863i	−0.178014	+	0.308330i
$473$	−5.85982	+	21.8691i	−0.269435	+	1.00554i
$474$	−4.44994	+	4.44994i	−0.204392	+	0.204392i
$475$	2.95691	−	11.0354i	0.135673	−	0.506337i
$476$	1.87425	−	1.44923i	0.0859061	−	0.0664255i
$477$	1.89754	+	3.28664i	0.0868824	+	0.150485i
$478$	−23.9980	+	13.8552i	−1.09764	+	0.633724i
$479$	−13.5586	−	13.5586i	−0.619507	−	0.619507i	0.325898	−	0.945405i	$-0.394333\pi$
$479$	−13.5586	−	13.5586i	−0.619507	−	0.619507i	−0.945405	+	0.325898i	$0.894333\pi$
$480$	−0.880134	+	0.508146i	−0.0401725	+	0.0231936i
$481$	2.22291	−	34.7939i	0.101356	−	1.58647i
$482$			25.1132i			1.14388i
$483$	1.80100	+	2.32918i	0.0819485	+	0.105982i
$484$	−3.46982	+	6.00991i	−0.157719	+	0.273178i
$485$			8.48621i			0.385339i
$486$	−0.965926	−	0.258819i	−0.0438153	−	0.0117403i
$487$	3.59718	−	0.963862i	0.163004	−	0.0436767i	−0.176394	−	0.984320i	$-0.556443\pi$
$487$	3.59718	−	0.963862i	0.163004	−	0.0436767i	0.339398	+	0.940643i	$0.389777\pi$
$488$	1.66790	+	1.66790i	0.0755021	+	0.0755021i
$489$	−16.5804	−	16.5804i	−0.749791	−	0.749791i
$490$	6.85780	−	1.89215i	0.309804	−	0.0854785i
$491$	−3.19473	−	1.84448i	−0.144176	−	0.0832401i	0.426177	−	0.904640i	$-0.359860\pi$
$491$	−3.19473	−	1.84448i	−0.144176	−	0.0832401i	−0.570353	+	0.821400i	$0.693194\pi$
$492$	−1.39959	−	0.375020i	−0.0630985	−	0.0169072i
$493$	−4.16044	−	7.20610i	−0.187377	−	0.324546i
$494$	7.79528	−	6.85905i	0.350726	−	0.308603i
$495$	3.72783	+	2.15226i	0.167553	+	0.0967370i
$496$	1.04539	+	3.90146i	0.0469395	+	0.175181i
$497$	0.298179	−	2.33166i	0.0133752	−	0.104589i
$498$	9.22610	−	5.32669i	0.413431	−	0.238695i
$499$	−26.9472	+	7.22047i	−1.20632	+	0.323233i	−0.805318	−	0.592844i	$-0.798005\pi$
$499$	−26.9472	+	7.22047i	−1.20632	+	0.323233i	−0.401004	+	0.916076i	$0.631339\pi$
$500$	2.35868	+	8.80272i	0.105483	+	0.393669i
$501$	−4.22772	−	15.7780i	−0.188880	−	0.704911i
$502$	13.9751	−	3.74461i	0.623739	−	0.167130i
$503$	12.6397	−	7.29753i	0.563576	−	0.325381i	−0.191003	−	0.981589i	$-0.561174\pi$
$503$	12.6397	−	7.29753i	0.563576	−	0.325381i	0.754580	+	0.656208i	$0.227841\pi$
$504$	−1.60284	+	2.10497i	−0.0713961	+	0.0937629i
$505$	−2.15818	−	8.05443i	−0.0960376	−	0.358417i
$506$	4.08193	+	2.35671i	0.181464	+	0.104768i
$507$	−5.01446	−	11.9940i	−0.222700	−	0.532671i
$508$	4.54541	+	7.87288i	0.201670	+	0.349303i
$509$	23.1174	+	6.19428i	1.02466	+	0.274556i	0.731742	−	0.681581i	$-0.238708\pi$
$509$	23.1174	+	6.19428i	1.02466	+	0.274556i	0.292917	+	0.956138i	$0.405374\pi$
$510$	−0.788136	−	0.455030i	−0.0348992	−	0.0201491i
$511$	0.156290	−	1.22213i	0.00691385	−	0.0540639i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−2.03633	−	2.03633i	−0.0899063	−	0.0899063i
$514$	−12.4109	+	3.32550i	−0.547422	+	0.146681i
$515$	−11.7047	−	3.13627i	−0.515772	−	0.138201i
$516$			5.34541i			0.235318i
$517$	−6.72168	+	11.6423i	−0.295619	+	0.512027i
$518$	−9.70280	+	23.6725i	−0.426317	+	1.04011i
$519$		−	18.5214i		−	0.812998i
$520$	−1.17213	+	3.47177i	−0.0514011	+	0.152247i
$521$	−6.38446	+	3.68607i	−0.279708	+	0.161490i	−0.633291	−	0.773913i	$-0.718297\pi$
$521$	−6.38446	+	3.68607i	−0.279708	+	0.161490i	0.353583	+	0.935403i	$0.384963\pi$
$522$	6.57057	+	6.57057i	0.287586	+	0.287586i
$523$	−29.1550	+	16.8327i	−1.27486	+	0.736041i	−0.975899	−	0.218224i	$-0.929974\pi$
$523$	−29.1550	+	16.8327i	−1.27486	+	0.736041i	−0.298962	+	0.954265i	$0.596640\pi$
$524$	3.15234	+	5.46001i	0.137711	+	0.238522i
$525$	6.42044	+	8.30337i	0.280211	+	0.362389i
$526$	2.75892	−	10.2964i	0.120294	−	0.448945i
$527$	−2.55753	+	2.55753i	−0.111408	+	0.111408i
$528$	−1.09623	+	4.09120i	−0.0477075	+	0.178047i
$529$	−10.8808	+	18.8461i	−0.473079	+	0.819396i
$530$	−1.92845	−	3.34018i	−0.0837667	−	0.145088i
$531$	7.47136	−	2.00194i	0.324229	−	0.0868770i
$532$	−7.02842	+	2.94184i	−0.304721	+	0.127545i
$533$	−4.68173	+	2.31838i	−0.202788	+	0.100420i
$534$	−6.56410	+	11.3694i	−0.284056	+	0.492000i
$535$	−0.872827	+	0.872827i	−0.0377356	+	0.0377356i
$536$	4.32648			0.186875
$537$	22.1207			0.954580
$538$	6.79110	−	6.79110i	0.292785	−	0.292785i
$539$	14.6336	−	25.7857i	0.630312	−	1.11067i
$540$	0.981662	+	0.263036i	0.0422440	+	0.0113193i
$541$	−2.49477	−	9.31061i	−0.107259	−	0.400294i	0.891333	−	0.453349i	$-0.149771\pi$
$541$	−2.49477	−	9.31061i	−0.107259	−	0.400294i	−0.998592	+	0.0530547i	$0.983104\pi$
$542$	−11.3924	−	6.57741i	−0.489346	−	0.282524i
$543$		−	12.9441i		−	0.555484i
$544$	0.231765	−	0.864960i	0.00993685	−	0.0370848i
$545$	−11.0014			−0.471250
$546$	0.674877	+	9.51549i	0.0288821	+	0.407225i
$547$	−7.74134			−0.330996			−0.165498	−	0.986210i	$-0.552923\pi$
$547$	−7.74134			−0.330996			−0.165498	+	0.986210i	$0.552923\pi$
$548$	5.88086	−	21.9477i	0.251218	−	0.937559i
$549$		−	2.35876i		−	0.100670i
$550$	14.5518	+	8.40148i	0.620490	+	0.358240i
$551$	6.92592	+	25.8479i	0.295054	+	1.10116i
$552$	1.07491	+	0.288021i	0.0457512	+	0.0122590i
$553$	6.31466	−	15.4062i	0.268527	−	0.655140i
$554$	−13.9361	+	13.9361i	−0.592089	+	0.592089i
$555$	9.82730			0.417146
$556$	15.9301			0.675588
$557$	9.83492	−	9.83492i	0.416719	−	0.416719i	−0.467352	−	0.884071i	$-0.654792\pi$
$557$	9.83492	−	9.83492i	0.416719	−	0.416719i	0.884071	+	0.467352i	$0.154792\pi$
$558$	2.01954	−	3.49795i	0.0854941	−	0.148080i
$559$	12.7315	+	14.4693i	0.538487	+	0.611988i
$560$	1.62895	−	2.13927i	0.0688358	−	0.0904005i
$561$	−3.66356	+	0.981647i	−0.154675	+	0.0414452i
$562$	−9.07684	−	15.7215i	−0.382883	−	0.663174i
$563$	0.745107	−	1.29056i	0.0314025	−	0.0543907i	−0.849897	−	0.526949i	$-0.823336\pi$
$563$	0.745107	−	1.29056i	0.0314025	−	0.0543907i	0.881300	+	0.472558i	$0.156669\pi$
$564$	−0.821480	+	3.06581i	−0.0345906	+	0.129094i
$565$	9.74327	−	9.74327i	0.409903	−	0.409903i
$566$	5.00762	−	18.6887i	0.210486	−	0.785544i
$567$	2.62182	−	0.355062i	0.110106	−	0.0149112i
$568$	−0.444230	−	0.769429i	−0.0186395	−	0.0322845i
$569$	1.30002	−	0.750567i	0.0544997	−	0.0314654i	−0.472503	−	0.881329i	$-0.656649\pi$
$569$	1.30002	−	0.750567i	0.0544997	−	0.0314654i	0.527002	+	0.849864i	$0.323316\pi$
$570$	2.06951	+	2.06951i	0.0866822	+	0.0866822i
$571$	−27.0036	+	15.5905i	−1.13006	+	0.652443i	−0.943951	−	0.330085i	$-0.892922\pi$
$571$	−27.0036	+	15.5905i	−1.13006	+	0.652443i	−0.186113	+	0.982528i	$0.559589\pi$
$572$	6.77693	+	13.6853i	0.283358	+	0.572213i
$573$			7.30247i			0.305065i
$574$	3.79892	−	0.514472i	0.158564	−	0.0214736i
$575$	2.20738	−	3.82329i	0.0920541	−	0.159442i
$576$			1.00000i			0.0416667i
$577$	40.9897	+	10.9832i	1.70643	+	0.457235i	0.974544	−	0.224197i	$-0.0719759\pi$
$577$	40.9897	+	10.9832i	1.70643	+	0.457235i	0.731881	+	0.681432i	$0.238643\pi$
$578$	−15.6462	+	4.19238i	−0.650796	+	0.174380i
$579$	−14.5932	−	14.5932i	−0.606471	−	0.606471i
$580$	−6.67761	−	6.67761i	−0.277273	−	0.277273i
$581$	−17.0757	+	22.4251i	−0.708418	+	0.930349i
$582$	7.23146	+	4.17509i	0.299754	+	0.173063i
$583$	−15.5264	−	4.16030i	−0.643039	−	0.172302i
$584$	−0.232842	−	0.403294i	−0.00963507	−	0.0166884i
$585$	3.28373	−	1.62609i	0.135765	−	0.0672306i
$586$	9.28570	+	5.36110i	0.383589	+	0.221465i
$587$	2.49601	+	9.31524i	0.103021	+	0.384481i	0.998113	−	0.0614008i	$-0.0195568\pi$
$587$	2.49601	+	9.31524i	0.103021	+	0.384481i	−0.895092	+	0.445882i	$0.852890\pi$
$588$	1.76155	−	6.77473i	0.0726452	−	0.279385i
$589$	10.0734	−	5.81590i	0.415069	−	0.239640i
$590$	−7.59308	+	2.03456i	−0.312602	+	0.0837615i
$591$	4.34702	+	16.2233i	0.178812	+	0.667337i
$592$	2.50272	+	9.34028i	0.102861	+	0.383883i
$593$	−22.7705	+	6.10134i	−0.935073	+	0.250552i	−0.694016	−	0.719959i	$-0.744161\pi$
$593$	−22.7705	+	6.10134i	−0.935073	+	0.250552i	−0.241056	+	0.970511i	$0.577494\pi$
$594$	3.66807	−	2.11776i	0.150503	−	0.0868928i
$595$	2.38834	+	0.305428i	0.0979126	+	0.0125213i
$596$	−0.921550	−	3.43927i	−0.0377482	−	0.140878i
$597$	3.69158	+	2.13133i	0.151086	+	0.0872297i
$598$	3.59565	−	1.78055i	0.147037	−	0.0728122i
$599$	−14.5945	−	25.2784i	−0.596314	−	1.03285i	−0.993360	−	0.115048i	$-0.963298\pi$
$599$	−14.5945	−	25.2784i	−0.596314	−	1.03285i	0.397046	−	0.917799i	$-0.370035\pi$
$600$	3.83197	+	1.02677i	0.156440	+	0.0419179i
$601$	22.5127	+	12.9977i	0.918311	+	0.530187i	0.883096	−	0.469192i	$-0.155455\pi$
$601$	22.5127	+	12.9977i	0.918311	+	0.530187i	0.0352154	+	0.999380i	$0.488788\pi$
$602$	−5.46055	−	13.0459i	−0.222555	−	0.531712i
$603$	−3.05928	−	3.05928i	−0.124584	−	0.124584i
$604$	−3.48468	−	3.48468i	−0.141790	−	0.141790i
$605$	−6.81239	+	1.82537i	−0.276963	+	0.0742120i
$606$	−7.92531	−	2.12358i	−0.321944	−	0.0862645i
$607$			23.0604i			0.935993i	0.883730	+	0.467997i	$0.155024\pi$
$607$			23.0604i			0.935993i	−0.883730	+	0.467997i	$0.844976\pi$
$608$	−1.43990	+	2.49399i	−0.0583958	+	0.101145i
$609$	−22.7481	−	9.32393i	−0.921800	−	0.377825i
$610$			2.39719i			0.0970594i
$611$	5.07840	+	10.2553i	0.205450	+	0.414886i
$612$	−0.775501	+	0.447736i	−0.0313478	+	0.0180987i
$613$	−19.4589	−	19.4589i	−0.785939	−	0.785939i	0.194887	−	0.980826i	$-0.437566\pi$
$613$	−19.4589	−	19.4589i	−0.785939	−	0.785939i	−0.980826	+	0.194887i	$0.937566\pi$
$614$	−5.27446	+	3.04521i	−0.212860	+	0.122895i
$615$	−0.736286	−	1.27528i	−0.0296899	−	0.0514244i
$616$	−1.50387	−	11.1048i	−0.0605927	−	0.447424i
$617$	−3.65190	+	13.6291i	−0.147020	+	0.548687i	0.852637	+	0.522504i	$0.175002\pi$
$617$	−3.65190	+	13.6291i	−0.147020	+	0.548687i	−0.999657	+	0.0261829i	$0.991665\pi$
$618$	−8.43110	+	8.43110i	−0.339149	+	0.339149i
$619$	2.02195	−	7.54604i	0.0812692	−	0.303301i	−0.913312	−	0.407260i	$-0.866484\pi$
$619$	2.02195	−	7.54604i	0.0812692	−	0.303301i	0.994582	+	0.103959i	$0.0331510\pi$
$620$	−2.05245	+	3.55494i	−0.0824282	+	0.142770i
$621$	−0.556414	−	0.963738i	−0.0223281	−	0.0386735i
$622$	0.611774	−	0.163924i	0.0245299	−	0.00657276i
$623$	4.40600	−	34.4534i	0.176523	−	1.38034i
$624$	2.38177	+	2.70687i	0.0953471	+	0.108362i
$625$	5.28702	−	9.15739i	0.211481	−	0.366296i
$626$	−5.08935	+	5.08935i	−0.203411	+	0.203411i
$627$	12.1975			0.487121
$628$	−10.6846			−0.426363
$629$	−6.12284	+	6.12284i	−0.244134	+	0.244134i
$630$	−2.66453	+	0.360846i	−0.106158	+	0.0143765i
$631$	5.31050	+	1.42295i	0.211408	+	0.0566466i	0.362969	−	0.931801i	$-0.381763\pi$
$631$	5.31050	+	1.42295i	0.211408	+	0.0566466i	−0.151561	+	0.988448i	$0.548430\pi$
$632$	−1.62879	−	6.07873i	−0.0647898	−	0.241799i
$633$	−13.6595	−	7.88634i	−0.542918	−	0.313454i
$634$			8.74785i			0.347422i
$635$	−2.39121	+	8.92411i	−0.0948922	+	0.354143i
$636$	−3.79508			−0.150485
$637$	−11.3675	−	22.5340i	−0.450399	−	0.892828i
$638$	−39.3572			−1.55817
$639$	−0.229950	+	0.858187i	−0.00909670	+	0.0339493i
$640$		−	1.01629i		−	0.0401725i
$641$	−17.4317	−	10.0642i	−0.688512	−	0.397513i	0.114542	−	0.993418i	$-0.463460\pi$
$641$	−17.4317	−	10.0642i	−0.688512	−	0.397513i	−0.803055	+	0.595906i	$0.796793\pi$
$642$	0.314355	+	1.17319i	0.0124066	+	0.0463021i
$643$	35.9273	+	9.62668i	1.41683	+	0.379639i	0.884359	−	0.466807i	$-0.154596\pi$
$643$	35.9273	+	9.62668i	1.41683	+	0.379639i	0.532474	+	0.846446i	$0.321262\pi$
$644$	−2.91764	+	0.395123i	−0.114971	+	0.0155700i
$645$	−3.84135	+	3.84135i	−0.151253	+	0.151253i
$646$	−2.57879			−0.101461
$647$	18.6485			0.733147			0.366574	−	0.930389i	$-0.380531\pi$
$647$	18.6485			0.733147			0.366574	+	0.930389i	$0.380531\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	−16.3807	+	28.3722i	−0.642999	+	1.11371i
$650$	12.8182	−	6.34753i	0.502772	−	0.248971i
$651$	−1.35557	+	10.6001i	−0.0531290	+	0.415451i
$652$	22.6492	−	6.06884i	0.887012	−	0.237674i
$653$	−1.92830	−	3.33991i	−0.0754602	−	0.130701i	0.825826	−	0.563925i	$-0.190709\pi$
$653$	−1.92830	−	3.33991i	−0.0754602	−	0.130701i	−0.901286	+	0.433224i	$0.857376\pi$
$654$	−5.41254	+	9.37479i	−0.211647	+	0.366583i
$655$	−1.65835	+	6.18906i	−0.0647973	+	0.241827i
$656$	1.02457	−	1.02457i	0.0400029	−	0.0400029i
$657$	−0.120528	+	0.449816i	−0.00470224	+	0.0175490i
$658$	−1.12695	−	8.32153i	−0.0439331	−	0.324407i
$659$	13.9329	+	24.1325i	0.542748	+	0.940067i	0.998745	+	0.0500858i	$0.0159495\pi$
$659$	13.9329	+	24.1325i	0.542748	+	0.940067i	−0.455997	+	0.889981i	$0.650717\pi$
$660$	−3.72783	+	2.15226i	−0.145106	+	0.0837767i
$661$	23.2802	+	23.2802i	0.905495	+	0.905495i	0.995905	−	0.0904098i	$-0.0288177\pi$
$661$	23.2802	+	23.2802i	0.905495	+	0.905495i	−0.0904098	+	0.995905i	$0.528818\pi$
$662$	11.0109	−	6.35712i	0.427949	−	0.247077i
$663$	−1.03278	+	3.05903i	−0.0401099	+	0.118803i
$664$			10.6534i			0.413431i
$665$	−7.16490	−	2.93673i	−0.277843	−	0.113881i
$666$	4.83488	−	8.37426i	0.187348	−	0.324496i
$667$			10.3406i			0.400390i
$668$	15.7780	+	4.22772i	0.610471	+	0.163575i
$669$	−26.3049	+	7.04837i	−1.01701	+	0.272506i
$670$	3.10912	+	3.10912i	0.120116	+	0.120116i
$671$	7.06441	+	7.06441i	0.272719	+	0.272719i
$672$	−1.02154	−	2.44059i	−0.0394068	−	0.0941476i
$673$	−41.7627	−	24.1117i	−1.60983	−	0.929438i	−0.989406	−	0.145174i	$-0.953626\pi$
$673$	−41.7627	−	24.1117i	−1.60983	−	0.929438i	−0.620427	−	0.784264i	$-0.713041\pi$
$674$	18.5409	+	4.96801i	0.714168	+	0.191361i
$675$	−1.98358	−	3.43565i	−0.0763479	−	0.132238i
$676$	12.8943	+	1.65434i	0.495935	+	0.0636283i
$677$	38.4502	+	22.1992i	1.47776	+	0.853185i	0.999684	−	0.0251328i	$-0.00800086\pi$
$677$	38.4502	+	22.1992i	1.47776	+	0.853185i	0.478076	+	0.878318i	$0.341334\pi$
$678$	−3.50912	−	13.0962i	−0.134767	−	0.502956i
$679$	−21.9140	−	2.80243i	−0.840983	−	0.107547i
$680$	0.788136	−	0.455030i	0.0302236	−	0.0174496i
$681$	9.85473	−	2.64057i	0.377634	−	0.101187i
$682$	4.42779	+	16.5247i	0.169549	+	0.632764i
$683$	−3.59911	−	13.4320i	−0.137716	−	0.513963i	−0.999972	−	0.00749023i	$-0.997616\pi$
$683$	−3.59911	−	13.4320i	−0.137716	−	0.513963i	0.862256	−	0.506473i	$-0.169051\pi$
$684$	2.78168	−	0.745350i	0.106360	−	0.0284992i
$685$	19.9983	−	11.5460i	0.764097	−	0.441152i
$686$	2.62143	+	18.3338i	0.100087	+	0.699988i
$687$	−6.86791	−	25.6314i	−0.262027	−	0.977899i
$688$	−4.62926	−	2.67270i	−0.176489	−	0.101896i
$689$	−10.2728	+	9.03901i	−0.391363	+	0.344359i
$690$	0.565479	+	0.979439i	0.0215274	+	0.0372866i
$691$	−8.71695	−	2.33570i	−0.331608	−	0.0888542i	0.0891733	−	0.996016i	$-0.471578\pi$
$691$	−8.71695	−	2.33570i	−0.331608	−	0.0888542i	−0.420782	+	0.907162i	$0.638244\pi$
$692$	16.0400	+	9.26068i	0.609748	+	0.352038i
$693$	−6.78886	+	8.91566i	−0.257887	+	0.338678i
$694$	−10.9377	−	10.9377i	−0.415191	−	0.415191i
$695$	11.4478	+	11.4478i	0.434241	+	0.434241i
$696$	−8.97556	+	2.40499i	−0.340218	+	0.0911611i
$697$	1.25330	+	0.335820i	0.0474720	+	0.0127201i
$698$		−	5.56860i		−	0.210775i
$699$	−13.6710	+	23.6788i	−0.517083	+	0.895614i
$700$	−10.4011	+	1.40858i	−0.393127	+	0.0532394i
$701$		−	41.6879i		−	1.57453i	−0.616615	−	0.787265i	$-0.711497\pi$
$701$		−	41.6879i		−	1.57453i	0.616615	−	0.787265i	$-0.288503\pi$
$702$	0.229883	−	3.59822i	0.00867637	−	0.135806i
$703$	24.1163	−	13.9235i	0.909563	−	0.525136i
$704$	−2.99497	−	2.99497i	−0.112877	−	0.112877i
$705$	−2.79351	+	1.61283i	−0.105210	+	0.0607428i
$706$	−14.4162	−	24.9695i	−0.542559	−	0.939740i
$707$	21.5117	−	2.91324i	0.809031	−	0.109564i
$708$	−2.00194	+	7.47136i	−0.0752377	+	0.280791i
$709$	2.26047	−	2.26047i	0.0848936	−	0.0848936i	−0.663385	−	0.748278i	$-0.730881\pi$
$709$	2.26047	−	2.26047i	0.0848936	−	0.0848936i	0.748278	+	0.663385i	$0.230881\pi$
$710$	0.233697	−	0.872168i	0.00877048	−	0.0327319i
$711$	−3.14658	+	5.45004i	−0.118006	+	0.204392i
$712$	−6.56410	−	11.3694i	−0.246000	−	0.426085i
$713$	4.34166	−	1.16334i	0.162596	−	0.0435676i
$714$	1.43530	−	1.88494i	0.0537147	−	0.0705422i
$715$	−4.96457	+	14.7047i	−0.185664	+	0.549926i
$716$	−11.0604	+	19.1571i	−0.413345	+	0.715935i
$717$	−19.5943	+	19.5943i	−0.731761	+	0.731761i
$718$	−2.96211			−0.110545
$719$	−5.03910			−0.187927			−0.0939634	−	0.995576i	$-0.529954\pi$
$719$	−5.03910			−0.187927			−0.0939634	+	0.995576i	$0.529954\pi$
$720$	−0.718627	+	0.718627i	−0.0267816	+	0.0267816i
$721$	11.9641	−	29.1895i	0.445567	−	1.08707i
$722$	−10.3419	−	2.77110i	−0.384885	−	0.103130i
$723$	6.49978	+	24.2575i	0.241729	+	0.902146i
$724$	11.2099	+	6.47204i	0.416613	+	0.240532i
$725$			36.8635i			1.36908i
$726$	−1.79611	+	6.70318i	−0.0666600	+	0.248779i
$727$	−4.03230			−0.149550			−0.0747748	−	0.997200i	$-0.523824\pi$
$727$	−4.03230			−0.149550			−0.0747748	+	0.997200i	$0.523824\pi$
$728$	−8.57809	−	4.17328i	−0.317925	−	0.154672i
$729$	−1.00000			−0.0370370
$730$	0.122491	−	0.457144i	0.00453361	−	0.0169197i
$731$		−	4.78666i		−	0.177041i
$732$	2.04275	+	1.17938i	0.0755021	+	0.0435912i
$733$	−5.02527	−	18.7546i	−0.185613	−	0.692716i	−0.994499	−	0.104750i	$-0.966596\pi$
$733$	−5.02527	−	18.7546i	−0.185613	−	0.692716i	0.808886	−	0.587966i	$-0.200071\pi$
$734$	−12.3125	−	3.29912i	−0.454462	−	0.121773i
$735$	6.13440	−	3.60260i	0.226271	−	0.132884i
$736$	−0.786889	+	0.786889i	−0.0290051	+	0.0290051i
$737$	18.3249			0.675006
$738$	−1.44897			−0.0533372
$739$	16.5052	−	16.5052i	0.607153	−	0.607153i	−0.335048	−	0.942201i	$-0.608752\pi$
$739$	16.5052	−	16.5052i	0.607153	−	0.607153i	0.942201	+	0.335048i	$0.108752\pi$
$740$	−4.91365	+	8.51069i	−0.180629	+	0.312859i
$741$	5.75441	−	8.64290i	0.211394	−	0.317505i
$742$	9.26222	−	3.87683i	0.340027	−	0.142323i
$743$	33.0260	−	8.84929i	1.21161	−	0.324649i	0.404214	−	0.914664i	$-0.367545\pi$
$743$	33.0260	−	8.84929i	1.21161	−	0.324649i	0.807392	+	0.590016i	$0.200878\pi$
$744$	2.01954	+	3.49795i	0.0740401	+	0.128241i
$745$	1.80930	−	3.13380i	0.0662877	−	0.114814i
$746$	−3.95363	+	14.7552i	−0.144753	+	0.540225i
$747$	7.53308	−	7.53308i	0.275621	−	0.275621i
$748$	0.981647	−	3.66356i	0.0358926	−	0.133953i
$749$	−1.96567	−	2.54214i	−0.0718241	−	0.0928879i
$750$	4.55662	+	7.89230i	0.166384	+	0.288186i
$751$	32.0740	−	18.5180i	1.17040	−	0.675730i	0.216624	−	0.976255i	$-0.430495\pi$
$751$	32.0740	−	18.5180i	1.17040	−	0.675730i	0.953774	+	0.300525i	$0.0971620\pi$
$752$	−2.24433	−	2.24433i	−0.0818421	−	0.0818421i
$753$	12.5297	−	7.23404i	0.456609	−	0.263623i
$754$	−18.5676	+	27.8877i	−0.676191	+	1.01561i
$755$		−	5.00838i		−	0.182273i
$756$	−1.00342	+	2.44809i	−0.0364939	+	0.0890362i
$757$	−21.9087	+	37.9470i	−0.796286	+	1.37921i	0.125733	+	0.992064i	$0.459872\pi$
$757$	−21.9087	+	37.9470i	−0.796286	+	1.37921i	−0.922019	+	0.387144i	$0.873461\pi$
$758$		−	15.2127i		−	0.552551i
$759$	4.55281	+	1.21992i	0.165256	+	0.0442803i
$760$	−2.82700	+	0.757493i	−0.102546	+	0.0274771i
$761$	16.5369	+	16.5369i	0.599463	+	0.599463i	0.940170	−	0.340707i	$-0.110666\pi$
$761$	16.5369	+	16.5369i	0.599463	+	0.599463i	−0.340707	+	0.940170i	$0.610666\pi$
$762$	6.42818	+	6.42818i	0.232868	+	0.232868i
$763$	3.63304	−	28.4091i	0.131525	−	1.02848i
$764$	−6.32412	−	3.65123i	−0.228799	−	0.132097i
$765$	−0.879051	−	0.235541i	−0.0317822	−	0.00851600i
$766$	−7.15218	−	12.3879i	−0.258419	−	0.447595i
$767$	12.3760	+	24.9922i	0.446873	+	0.902416i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−11.6639	−	43.5304i	−0.420613	−	1.56975i	−0.773321	−	0.634014i	$-0.781406\pi$
$769$	−11.6639	−	43.5304i	−0.420613	−	1.56975i	0.352709	−	0.935733i	$-0.385261\pi$
$770$	6.89946	−	9.06091i	0.248639	−	0.326532i
$771$	−11.1273	+	6.42437i	−0.400741	+	0.231368i
$772$	19.9346	−	5.34146i	0.717462	−	0.192243i
$773$	12.0859	+	45.1051i	0.434698	+	1.62232i	0.741787	+	0.670636i	$0.233979\pi$
$773$	12.0859	+	45.1051i	0.434698	+	1.62232i	−0.307089	+	0.951681i	$0.599355\pi$
$774$	1.38349	+	5.16327i	0.0497286	+	0.185590i
$775$	15.4777	−	4.14723i	0.555975	−	0.148973i
$776$	−7.23146	+	4.17509i	−0.259594	+	0.149877i
$777$	−3.24530	+	25.3771i	−0.116425	+	0.910399i
$778$	2.09172	+	7.80639i	0.0749917	+	0.279873i
$779$	−3.61370	−	2.08637i	−0.129474	−	0.0747520i
$780$	−0.233628	+	3.65684i	−0.00836523	+	0.130936i
$781$	−1.88155	−	3.25893i	−0.0673270	−	0.116614i
$782$	−0.962552	−	0.257915i	−0.0344208	−	0.00922302i
$783$	8.04727	+	4.64609i	0.287586	+	0.166038i
$784$	4.98631	+	4.91291i	0.178082	+	0.175461i
$785$	−7.67827	−	7.67827i	−0.274049	−	0.274049i
$786$	4.45808	+	4.45808i	0.159014	+	0.159014i
$787$	21.6957	−	5.81335i	0.773368	−	0.207223i	0.149509	−	0.988760i	$-0.452231\pi$
$787$	21.6957	−	5.81335i	0.773368	−	0.207223i	0.623859	+	0.781537i	$0.285564\pi$
$788$	−16.2233	−	4.34702i	−0.577931	−	0.154856i
$789$		−	10.6596i		−	0.379493i
$790$	3.19784	−	5.53883i	0.113774	−	0.197063i
$791$	21.9426	+	28.3777i	0.780188	+	1.00899i
$792$			4.23552i			0.150503i
$793$	8.33848	−	1.67292i	0.296108	−	0.0594072i
$794$	−25.8620	+	14.9314i	−0.917809	+	0.529897i
$795$	−2.72725	−	2.72725i	−0.0967255	−	0.0967255i
$796$	−3.69158	+	2.13133i	−0.130845	+	0.0755431i
$797$	1.10641	+	1.91635i	0.0391909	+	0.0678807i	0.884956	−	0.465676i	$-0.154189\pi$
$797$	1.10641	+	1.91635i	0.0391909	+	0.0678807i	−0.845765	+	0.533556i	$0.820855\pi$
$798$	−6.02753	+	4.66069i	−0.213372	+	0.164987i
$799$	0.735612	−	2.74534i	0.0260241	−	0.0971233i
$800$	−2.80520	+	2.80520i	−0.0991788	+	0.0991788i
$801$	−3.39783	+	12.6809i	−0.120056	+	0.448056i
$802$	3.95204	−	6.84514i	0.139552	−	0.241710i
$803$	−0.986207	−	1.70816i	−0.0348025	−	0.0602797i
$804$	4.17906	−	1.11978i	0.147384	−	0.0394914i
$805$	−2.38064	−	1.81274i	−0.0839064	−	0.0638909i
$806$	13.7980	+	4.65843i	0.486013	+	0.164086i
$807$	4.80203	−	8.31736i	0.169040	−	0.292785i
$808$	5.80173	−	5.80173i	0.204104	−	0.204104i
$809$	43.3374			1.52366			0.761831	−	0.647776i	$-0.224301\pi$
$809$	43.3374			1.52366			0.761831	+	0.647776i	$0.224301\pi$
$810$	1.01629			0.0357089
$811$	6.31443	−	6.31443i	0.221729	−	0.221729i	−0.587497	−	0.809226i	$-0.699887\pi$
$811$	6.31443	−	6.31443i	0.221729	−	0.221729i	0.809226	+	0.587497i	$0.199887\pi$
$812$	19.4488	−	15.0385i	0.682520	−	0.527747i
$813$	−12.7066	−	3.40472i	−0.445639	−	0.119409i
$814$	10.6003	+	39.5609i	0.371541	+	1.38661i
$815$	20.6376	+	11.9151i	0.722903	+	0.417368i
$816$		−	0.895472i		−	0.0313478i
$817$	−3.98420	+	14.8692i	−0.139389	+	0.520208i
$818$	6.85536			0.239692
$819$	3.11467	+	9.01659i	0.108835	+	0.315065i
$820$	1.47257			0.0514244
$821$	−7.22125	+	26.9501i	−0.252023	+	0.940564i	0.717699	+	0.696354i	$0.245195\pi$
$821$	−7.22125	+	26.9501i	−0.252023	+	0.940564i	−0.969722	+	0.244210i	$0.921471\pi$
$822$		−	22.7219i		−	0.792518i
$823$	2.61901	+	1.51209i	0.0912930	+	0.0527080i	0.544951	−	0.838468i	$-0.316548\pi$
$823$	2.61901	+	1.51209i	0.0912930	+	0.0527080i	−0.453658	+	0.891176i	$0.649881\pi$
$824$	−3.08600	−	11.5171i	−0.107506	−	0.401217i
$825$	16.2304	+	4.34893i	0.565070	+	0.151410i
$826$	−2.74637	−	20.2795i	−0.0955585	−	0.705616i
$827$	17.9726	−	17.9726i	0.624969	−	0.624969i	−0.321829	−	0.946798i	$-0.604297\pi$
$827$	17.9726	−	17.9726i	0.624969	−	0.624969i	0.946798	+	0.321829i	$0.104297\pi$
$828$	1.11283			0.0386735
$829$	15.3002			0.531397			0.265699	−	0.964056i	$-0.414397\pi$
$829$	15.3002			0.531397			0.265699	+	0.964056i	$0.414397\pi$
$830$	−7.65581	+	7.65581i	−0.265737	+	0.265737i
$831$	−9.85432	+	17.0682i	−0.341843	+	0.592089i
$832$	−3.53511	+	0.709237i	−0.122558	+	0.0245884i
$833$	−1.57742	+	6.06658i	−0.0546544	+	0.210194i
$834$	15.3873	−	4.12302i	0.532820	−	0.142769i
$835$	8.30038	+	14.3767i	0.287246	+	0.497525i
$836$	−6.09875	+	10.5633i	−0.210930	+	0.365341i
$837$	1.04539	−	3.90146i	0.0361341	−	0.134854i
$838$	20.1598	−	20.1598i	0.696409	−	0.696409i
$839$	11.4181	−	42.6129i	0.394196	−	1.47116i	−0.428949	−	0.903329i	$-0.641116\pi$
$839$	11.4181	−	42.6129i	0.394196	−	1.47116i	0.823145	−	0.567831i	$-0.192217\pi$
$840$	1.01976	−	2.48798i	0.0351852	−	0.0858433i
$841$	−28.6723	−	49.6619i	−0.988701	−	1.71248i
$842$	32.8123	−	18.9442i	1.13078	−	0.652859i
$843$	−12.8366	−	12.8366i	−0.442116	−	0.442116i
$844$	13.6595	−	7.88634i	0.470181	−	0.271459i
$845$	8.07734	+	10.4550i	0.277869	+	0.359664i
$846$			3.17396i			0.109123i
$847$	−2.46400	−	18.1945i	−0.0846641	−	0.625170i
$848$	1.89754	−	3.28664i	0.0651618	−	0.112864i
$849$		−	19.3480i		−	0.664020i
$850$	−3.43143	−	0.919448i	−0.117697	−	0.0315368i
$851$	10.3941	−	2.78510i	0.356306	−	0.0954719i
$852$	−0.628236	−	0.628236i	−0.0215230	−	0.0215230i
$853$	22.1233	+	22.1233i	0.757488	+	0.757488i	0.975865	−	0.218376i	$-0.0700760\pi$
$853$	22.1233	+	22.1233i	0.757488	+	0.757488i	−0.218376	+	0.975865i	$0.570076\pi$
$854$	−6.19028	−	0.791632i	−0.211827	−	0.0270891i
$855$	2.53462	+	1.46336i	0.0866822	+	0.0500460i
$856$	−1.17319	−	0.314355i	−0.0400988	−	0.0107444i
$857$	2.72862	+	4.72611i	0.0932078	+	0.161441i	0.908859	−	0.417103i	$-0.136955\pi$
$857$	2.72862	+	4.72611i	0.0932078	+	0.161441i	−0.815651	+	0.578544i	$0.803621\pi$
$858$	10.0880	+	11.4650i	0.344400	+	0.391410i
$859$	1.26573	+	0.730767i	0.0431860	+	0.0249335i	0.521438	−	0.853289i	$-0.325396\pi$
$859$	1.26573	+	0.730767i	0.0431860	+	0.0249335i	−0.478252	+	0.878223i	$0.658729\pi$
$860$	−1.40603	−	5.24739i	−0.0479453	−	0.178934i
$861$	3.53632	−	1.48018i	0.120518	−	0.0504443i
$862$	7.11662	−	4.10878i	0.242393	−	0.139946i
$863$	−24.2938	+	6.50952i	−0.826972	+	0.221587i	−0.647392	−	0.762157i	$-0.724140\pi$
$863$	−24.2938	+	6.50952i	−0.826972	+	0.221587i	−0.179580	+	0.983743i	$0.557474\pi$
$864$	0.258819	+	0.965926i	0.00880520	+	0.0328615i
$865$	4.87178	+	18.1817i	0.165646	+	0.618197i
$866$	15.9845	−	4.28303i	0.543175	−	0.145543i
$867$	−14.0280	+	8.09906i	−0.476416	+	0.275059i
$868$	−8.50217	−	6.47401i	−0.288582	−	0.219742i
$869$	−6.89878	−	25.7466i	−0.234025	−	0.873393i
$870$	−8.17837	−	4.72178i	−0.277273	−	0.160083i
$871$	8.64514	−	12.9846i	0.292929	−	0.439968i
$872$	−5.41254	−	9.37479i	−0.183292	−	0.317471i
$873$	8.06565	+	2.16118i	0.272981	+	0.0731450i
$874$	2.77538	+	1.60237i	0.0938787	+	0.0542009i
$875$	−19.1831	−	14.6071i	−0.648508	−	0.493809i
$876$	−0.329288	−	0.329288i	−0.0111256	−	0.0111256i
$877$	5.26283	+	5.26283i	0.177713	+	0.177713i	0.790358	−	0.612645i	$-0.209894\pi$
$877$	5.26283	+	5.26283i	0.177713	+	0.177713i	−0.612645	+	0.790358i	$0.709894\pi$
$878$	34.9096	−	9.35400i	1.17814	−	0.315682i
$879$	10.3569	+	2.77511i	0.349328	+	0.0936022i
$880$		−	4.30453i		−	0.145106i
$881$	−10.8357	+	18.7680i	−0.365064	+	0.632309i	−0.988786	−	0.149337i	$-0.952286\pi$
$881$	−10.8357	+	18.7680i	−0.365064	+	0.632309i	0.623723	+	0.781646i	$0.285619\pi$
$882$	−0.0518991	−	6.99981i	−0.00174753	−	0.235696i
$883$			18.1254i			0.609968i	0.952357	+	0.304984i	$0.0986512\pi$
$883$			18.1254i			0.609968i	−0.952357	+	0.304984i	$0.901349\pi$
$884$	−2.13281	−	2.42393i	−0.0717341	−	0.0815256i
$885$	−6.80777	+	3.93047i	−0.228841	+	0.132121i
$886$	12.7923	+	12.7923i	0.429767	+	0.429767i
$887$	−35.7122	+	20.6185i	−1.19910	+	0.692300i	−0.960354	−	0.278782i	$-0.910069\pi$
$887$	−35.7122	+	20.6185i	−1.19910	+	0.692300i	−0.238745	+	0.971082i	$0.576736\pi$
$888$	4.83488	+	8.37426i	0.162248	+	0.281022i
$889$	−22.2552	−	9.12188i	−0.746414	−	0.305938i
$890$	3.45318	−	12.8875i	0.115751	−	0.431989i
$891$	2.99497	−	2.99497i	0.100335	−	0.100335i
$892$	7.04837	−	26.3049i	0.235997	−	0.880753i
$893$	−4.57019	+	7.91581i	−0.152936	+	0.264892i
$894$	−1.78030	−	3.08357i	−0.0595421	−	0.103130i
$895$	−21.7151	+	5.81854i	−0.725855	+	0.194492i
$896$	2.62438	+	0.335613i	0.0876743	+	0.0112121i
$897$	3.01229	−	2.65050i	0.100577	−	0.0884977i
$898$	6.00746	−	10.4052i	0.200472	−	0.347227i
$899$	−26.5391	+	26.5391i	−0.885128	+	0.885128i
$900$	3.96715			0.132238
$901$	3.39839			0.113217
$902$	4.33960	−	4.33960i	0.144493	−	0.144493i
$903$	−8.65102	−	11.1881i	−0.287888	−	0.372317i
$904$	13.0962	+	3.50912i	0.435573	+	0.116711i
$905$	3.40476	+	12.7067i	0.113178	+	0.422386i
$906$	−4.26785	−	2.46404i	−0.141790	−	0.0818624i
$907$		−	44.0072i		−	1.46123i	−0.682788	−	0.730617i	$-0.739233\pi$
$907$		−	44.0072i		−	1.46123i	0.682788	−	0.730617i	$-0.260767\pi$
$908$	−2.64057	+	9.85473i	−0.0876303	+	0.327041i
$909$	−8.20488			−0.272139
$910$	−3.16541	−	9.16348i	−0.104932	−	0.303766i
$911$	27.0222			0.895287			0.447643	−	0.894212i	$-0.352263\pi$
$911$	27.0222			0.895287			0.447643	+	0.894212i	$0.352263\pi$
$912$	−0.745350	+	2.78168i	−0.0246810	+	0.0921107i
$913$			45.1226i			1.49334i
$914$	−12.9059	−	7.45123i	−0.426890	−	0.246465i
$915$	0.620438	+	2.31551i	0.0205111	+	0.0765483i
$916$	25.6314	+	6.86791i	0.846885	+	0.226922i
$917$	−15.4344	−	6.32622i	−0.509690	−	0.208910i
$918$	−0.633194	+	0.633194i	−0.0208985	+	0.0208985i
$919$	31.9945			1.05540			0.527701	−	0.849430i	$-0.323054\pi$
$919$	31.9945			1.05540			0.527701	+	0.849430i	$0.323054\pi$
$920$	−1.13096			−0.0372866
$921$	−4.30658	+	4.30658i	−0.141907	+	0.141907i
$922$	−16.9156	+	29.2986i	−0.557084	+	0.964898i
$923$	−3.19687	−	0.204242i	−0.105226	−	0.00672270i
$924$	−4.32675	−	10.3372i	−0.142340	−	0.340067i
$925$	37.0543	−	9.92867i	1.21834	−	0.326453i
$926$	14.7356	+	25.5229i	0.484243	+	0.838733i
$927$	−5.96169	+	10.3259i	−0.195808	+	0.339149i
$928$	2.40499	−	8.97556i	0.0789478	−	0.294637i
$929$	−30.6879	+	30.6879i	−1.00684	+	1.00684i	−0.00685933	+	0.999976i	$0.502183\pi$
$929$	−30.6879	+	30.6879i	−1.00684	+	1.00684i	−0.999976	+	0.00685933i	$0.997817\pi$
$930$	−1.06242	+	3.96502i	−0.0348383	+	0.130018i
$931$	9.94962	−	17.5322i	0.326086	−	0.574594i
$932$	−13.6710	−	23.6788i	−0.447807	−	0.775624i
$933$	0.548501	−	0.316677i	0.0179571	−	0.0103676i
$934$	27.9819	+	27.9819i	0.915597	+	0.915597i
$935$	3.33817	−	1.92729i	0.109170	−	0.0630292i
$936$	3.00120	+	1.99819i	0.0980974	+	0.0653130i
$937$			14.3005i			0.467178i	0.972335	+	0.233589i	$0.0750471\pi$
$937$			14.3005i			0.467178i	−0.972335	+	0.233589i	$0.924953\pi$
$938$	−9.05545	+	7.00198i	−0.295671	+	0.228623i
$939$	−3.59872	+	6.23316i	−0.117440	+	0.203411i
$940$		−	3.22566i		−	0.105210i
$941$	−4.84640	−	1.29859i	−0.157988	−	0.0423328i	0.178958	−	0.983857i	$-0.442727\pi$
$941$	−4.84640	−	1.29859i	−0.157988	−	0.0423328i	−0.336946	+	0.941524i	$0.609394\pi$
$942$	−10.3206	+	2.76539i	−0.336262	+	0.0901012i
$943$	−1.14017	−	1.14017i	−0.0371292	−	0.0371292i
$944$	−5.46941	−	5.46941i	−0.178014	−	0.178014i
$945$	−2.48035	+	1.03818i	−0.0806857	+	0.0337721i
$946$	−19.6073	−	11.3203i	−0.637489	−	0.368055i
$947$	−43.8499	−	11.7496i	−1.42493	−	0.381809i	−0.537701	−	0.843136i	$-0.680707\pi$
$947$	−43.8499	−	11.7496i	−1.42493	−	0.381809i	−0.887230	+	0.461327i	$0.847374\pi$
$948$	−3.14658	−	5.45004i	−0.102196	−	0.177009i
$949$	−1.67563	−	0.107053i	−0.0543933	−	0.00347508i
$950$	9.89403	+	5.71232i	0.321005	+	0.185332i
$951$	2.26411	+	8.44978i	0.0734188	+	0.274003i
$952$	0.914760	+	2.18548i	0.0296475	+	0.0708317i
$953$	40.9867	−	23.6637i	1.32769	−	0.766542i	0.342748	−	0.939427i	$-0.388642\pi$
$953$	40.9867	−	23.6637i	1.32769	−	0.766542i	0.984942	+	0.172885i	$0.0553091\pi$
$954$	−3.66577	+	0.982239i	−0.118684	+	0.0318012i
$955$	−1.92081	−	7.16856i	−0.0621559	−	0.231969i
$956$	−7.17200	−	26.7663i	−0.231959	−	0.865683i
$957$	−38.0162	+	10.1864i	−1.22889	+	0.329280i
$958$	16.6058	−	9.58736i	0.536509	−	0.309753i
$959$	23.2113	+	55.4548i	0.749533	+	1.79073i
$960$	−0.263036	−	0.981662i	−0.00848944	−	0.0316830i
$961$	−12.7182	−	7.34288i	−0.410266	−	0.236867i
$962$	33.0330	+	11.1525i	1.06503	+	0.359571i
$963$	0.607288	+	1.05185i	0.0195696	+	0.0338955i
$964$	−24.2575	−	6.49978i	−0.781282	−	0.209344i
$965$	18.1641	+	10.4870i	0.584722	+	0.337589i
$966$	−2.71595	+	1.13680i	−0.0873844	+	0.0365759i
$967$	5.00087	+	5.00087i	0.160817	+	0.160817i	0.782929	−	0.622111i	$-0.213725\pi$
$967$	5.00087	+	5.00087i	0.160817	+	0.160817i	−0.622111	+	0.782929i	$0.713725\pi$
$968$	−4.90707	−	4.90707i	−0.157719	−	0.157719i
$969$	−2.49092	+	0.667440i	−0.0800198	+	0.0214412i
$970$	−8.19705	−	2.19639i	−0.263191	−	0.0705219i
$971$		−	11.1442i		−	0.357634i	−0.983882	−	0.178817i	$-0.942773\pi$
$971$		−	11.1442i		−	0.357634i	0.983882	−	0.178817i	$-0.0572270\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−33.3423	+	25.7814i	−1.06890	+	0.826513i
$974$			3.72408i			0.119327i
$975$	10.7386	−	9.44884i	0.343910	−	0.302605i
$976$	−2.04275	+	1.17938i	−0.0653868	+	0.0377511i
$977$	−4.58077	−	4.58077i	−0.146552	−	0.146552i	0.630024	−	0.776576i	$-0.283045\pi$
$977$	−4.58077	−	4.58077i	−0.146552	−	0.146552i	−0.776576	+	0.630024i	$0.783045\pi$
$978$	20.3067	−	11.7241i	0.649338	−	0.374896i
$979$	−27.8024	−	48.1551i	−0.888568	−	1.53905i
$980$	0.0527446	+	7.11385i	0.00168487	+	0.227243i
$981$	−2.80174	+	10.4562i	−0.0894526	+	0.333841i
$982$	2.60849	−	2.60849i	0.0832401	−	0.0832401i
$983$	2.48852	−	9.28727i	0.0793713	−	0.296218i	−0.914818	−	0.403867i	$-0.867666\pi$
$983$	2.48852	−	9.28727i	0.0793713	−	0.296218i	0.994189	+	0.107649i	$0.0343324\pi$
$984$	0.724483	−	1.25484i	0.0230957	−	0.0400029i
$985$	−8.53461	−	14.7824i	−0.271935	−	0.471006i
$986$	8.03736	−	2.15360i	0.255962	−	0.0685847i
$987$	−3.24232	−	7.74631i	−0.103204	−	0.246568i
$988$	4.60776	+	9.30492i	0.146592	+	0.296029i
$989$	−2.97426	+	5.15157i	−0.0945760	+	0.163810i
$990$	−3.04376	+	3.04376i	−0.0967370	+	0.0967370i
$991$	15.9233			0.505820			0.252910	−	0.967490i	$-0.418612\pi$
$991$	15.9233			0.505820			0.252910	+	0.967490i	$0.418612\pi$
$992$	−4.03909			−0.128241
$993$	8.99033	−	8.99033i	0.285299	−	0.285299i
$994$	2.17503	+	0.891496i	0.0689878	+	0.0282765i
$995$	−4.18450	−	1.12123i	−0.132658	−	0.0355455i
$996$	2.75730	+	10.2904i	0.0873683	+	0.326063i
$997$	−24.9154	−	14.3849i	−0.789080	−	0.455576i	0.0505585	−	0.998721i	$-0.483900\pi$
$997$	−24.9154	−	14.3849i	−0.789080	−	0.455576i	−0.839639	+	0.543145i	$0.817233\pi$
$998$		−	27.8978i		−	0.883088i
$999$	2.50272	−	9.34028i	0.0791825	−	0.295513i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.b.397.3	✓	40
7.3	odd	6		546.2.cg.b.241.3	yes	40
13.2	odd	12		546.2.cg.b.145.3	yes	40
91.80	even	12	inner	546.2.by.b.535.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.3	✓	40	1.1	even	1	trivial
546.2.by.b.535.3	yes	40	91.80	even	12	inner
546.2.cg.b.145.3	yes	40	13.2	odd	12
546.2.cg.b.241.3	yes	40	7.3	odd	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.263036 - 0.981662i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(2.62182 - 0.355062i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.263036 - 0.981662i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(2.62182 - 0.355062i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +1.01629 q^{10} +(2.99497 - 2.99497i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-0.709237 - 3.53511i) q^{13} +(-0.335613 + 2.62438i) q^{14} +(0.981662 - 0.263036i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.447736 + 0.775501i) q^{17} +(0.258819 - 0.965926i) q^{18} +(2.03633 - 2.03633i) q^{19} +(-0.263036 + 0.981662i) q^{20} +(0.355062 + 2.62182i) q^{21} +(2.11776 + 3.66807i) q^{22} +(0.963738 - 0.556414i) q^{23} +(0.707107 + 0.707107i) q^{24} +(3.43565 - 1.98358i) q^{25} +(3.59822 + 0.229883i) q^{26} -1.00000i q^{27} +(-2.44809 - 1.00342i) q^{28} +(-4.64609 + 8.04727i) q^{29} +1.01629i q^{30} +(3.90146 + 1.04539i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(2.99497 + 2.99497i) q^{33} +(-0.633194 - 0.633194i) q^{34} +(-1.03818 - 2.48035i) q^{35} +(0.866025 + 0.500000i) q^{36} +(9.34028 + 2.50272i) q^{37} +(1.43990 + 2.49399i) q^{38} +(3.53511 - 0.709237i) q^{39} +(-0.880134 - 0.508146i) q^{40} +(-0.375020 - 1.39959i) q^{41} +(-2.62438 - 0.335613i) q^{42} +(-4.62926 + 2.67270i) q^{43} +(-4.09120 + 1.09623i) q^{44} +(0.263036 + 0.981662i) q^{45} +(0.288021 + 1.07491i) q^{46} +(-3.06581 + 0.821480i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(6.74786 - 1.86181i) q^{49} +(1.02677 + 3.83197i) q^{50} +(-0.775501 - 0.447736i) q^{51} +(-1.15334 + 3.41611i) q^{52} +(-1.89754 - 3.28664i) q^{53} +(0.965926 + 0.258819i) q^{54} +(-3.72783 - 2.15226i) q^{55} +(1.60284 - 2.10497i) q^{56} +(2.03633 + 2.03633i) q^{57} +(-6.57057 - 6.57057i) q^{58} +(-7.47136 + 2.00194i) q^{59} +(-0.981662 - 0.263036i) q^{60} +2.35876i q^{61} +(-2.01954 + 3.49795i) q^{62} +(-2.62182 + 0.355062i) q^{63} -1.00000i q^{64} +(-3.28373 + 1.62609i) q^{65} +(-3.66807 + 2.11776i) q^{66} +(3.05928 + 3.05928i) q^{67} +(0.775501 - 0.447736i) q^{68} +(0.556414 + 0.963738i) q^{69} +(2.66453 - 0.360846i) q^{70} +(0.229950 - 0.858187i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(0.120528 - 0.449816i) q^{73} +(-4.83488 + 8.37426i) q^{74} +(1.98358 + 3.43565i) q^{75} +(-2.78168 + 0.745350i) q^{76} +(6.78886 - 8.91566i) q^{77} +(-0.229883 + 3.59822i) q^{78} +(3.14658 - 5.45004i) q^{79} +(0.718627 - 0.718627i) q^{80} +1.00000 q^{81} +1.44897 q^{82} +(-7.53308 + 7.53308i) q^{83} +(1.00342 - 2.44809i) q^{84} +(0.879051 + 0.235541i) q^{85} +(-1.38349 - 5.16327i) q^{86} +(-8.04727 - 4.64609i) q^{87} -4.23552i q^{88} +(3.39783 - 12.6809i) q^{89} -1.01629 q^{90} +(-3.11467 - 9.01659i) q^{91} -1.11283 q^{92} +(-1.04539 + 3.90146i) q^{93} -3.17396i q^{94} +(-2.53462 - 1.46336i) q^{95} +(-0.258819 - 0.965926i) q^{96} +(-8.06565 - 2.16118i) q^{97} +(0.0518991 + 6.99981i) q^{98} +(-2.99497 + 2.99497i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 4 * q^7 - 40 * q^9	\( 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

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