LMFDB - Embedded newform 1134.2.f.s.757.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(379,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("1134.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.f (of order $3$, degree $2$, not 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:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			757.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1134.757
Dual form			1134.2.f.s.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.86603 + 3.23205i) q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.86603 + 3.23205i) q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} -3.73205 q^{10} +(2.09808 + 3.63397i) q^{11} +(-0.232051 + 0.401924i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +7.00000 q^{17} -2.73205 q^{19} +(-1.86603 - 3.23205i) q^{20} +(-2.09808 + 3.63397i) q^{22} +(-3.09808 + 5.36603i) q^{23} +(-4.46410 - 7.73205i) q^{25} -0.464102 q^{26} -1.00000 q^{28} +(-4.23205 - 7.33013i) q^{29} +(1.09808 - 1.90192i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.50000 + 6.06218i) q^{34} -3.73205 q^{35} -6.66025 q^{37} +(-1.36603 - 2.36603i) q^{38} +(1.86603 - 3.23205i) q^{40} +(-4.73205 + 8.19615i) q^{41} +(-2.73205 - 4.73205i) q^{43} -4.19615 q^{44} -6.19615 q^{46} +(-0.633975 - 1.09808i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(4.46410 - 7.73205i) q^{50} +(-0.232051 - 0.401924i) q^{52} -2.53590 q^{53} -15.6603 q^{55} +(-0.500000 - 0.866025i) q^{56} +(4.23205 - 7.33013i) q^{58} +(3.09808 - 5.36603i) q^{59} +(4.96410 + 8.59808i) q^{61} +2.19615 q^{62} +1.00000 q^{64} +(-0.866025 - 1.50000i) q^{65} +(1.63397 - 2.83013i) q^{67} +(-3.50000 + 6.06218i) q^{68} +(-1.86603 - 3.23205i) q^{70} +13.4641 q^{71} +11.7321 q^{73} +(-3.33013 - 5.76795i) q^{74} +(1.36603 - 2.36603i) q^{76} +(-2.09808 + 3.63397i) q^{77} +(-7.56218 - 13.0981i) q^{79} +3.73205 q^{80} -9.46410 q^{82} +(7.29423 + 12.6340i) q^{83} +(-13.0622 + 22.6244i) q^{85} +(2.73205 - 4.73205i) q^{86} +(-2.09808 - 3.63397i) q^{88} -3.92820 q^{89} -0.464102 q^{91} +(-3.09808 - 5.36603i) q^{92} +(0.633975 - 1.09808i) q^{94} +(5.09808 - 8.83013i) q^{95} +(1.46410 + 2.53590i) q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} + 2 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 + 2 * q^7 - 4 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} + 2 q^{7} - 4 q^{8} - 8 q^{10} - 2 q^{11} + 6 q^{13} - 2 q^{14} - 2 q^{16} + 28 q^{17} - 4 q^{19} - 4 q^{20} + 2 q^{22} - 2 q^{23} - 4 q^{25} + 12 q^{26} - 4 q^{28} - 10 q^{29} - 6 q^{31} + 2 q^{32} + 14 q^{34} - 8 q^{35} + 8 q^{37} - 2 q^{38} + 4 q^{40} - 12 q^{41} - 4 q^{43} + 4 q^{44} - 4 q^{46} - 6 q^{47} - 2 q^{49} + 4 q^{50} + 6 q^{52} - 24 q^{53} - 28 q^{55} - 2 q^{56} + 10 q^{58} + 2 q^{59} + 6 q^{61} - 12 q^{62} + 4 q^{64} + 10 q^{67} - 14 q^{68} - 4 q^{70} + 40 q^{71} + 40 q^{73} + 4 q^{74} + 2 q^{76} + 2 q^{77} - 6 q^{79} + 8 q^{80} - 24 q^{82} - 2 q^{83} - 28 q^{85} + 4 q^{86} + 2 q^{88} + 12 q^{89} + 12 q^{91} - 2 q^{92} + 6 q^{94} + 10 q^{95} - 8 q^{97} - 4 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 + 2 * q^7 - 4 * q^8 - 8 * q^10 - 2 * q^11 + 6 * q^13 - 2 * q^14 - 2 * q^16 + 28 * q^17 - 4 * q^19 - 4 * q^20 + 2 * q^22 - 2 * q^23 - 4 * q^25 + 12 * q^26 - 4 * q^28 - 10 * q^29 - 6 * q^31 + 2 * q^32 + 14 * q^34 - 8 * q^35 + 8 * q^37 - 2 * q^38 + 4 * q^40 - 12 * q^41 - 4 * q^43 + 4 * q^44 - 4 * q^46 - 6 * q^47 - 2 * q^49 + 4 * q^50 + 6 * q^52 - 24 * q^53 - 28 * q^55 - 2 * q^56 + 10 * q^58 + 2 * q^59 + 6 * q^61 - 12 * q^62 + 4 * q^64 + 10 * q^67 - 14 * q^68 - 4 * q^70 + 40 * q^71 + 40 * q^73 + 4 * q^74 + 2 * q^76 + 2 * q^77 - 6 * q^79 + 8 * q^80 - 24 * q^82 - 2 * q^83 - 28 * q^85 + 4 * q^86 + 2 * q^88 + 12 * q^89 + 12 * q^91 - 2 * q^92 + 6 * q^94 + 10 * q^95 - 8 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.86603	+	3.23205i	−0.834512	+	1.44542i	0.0599153	+	0.998203i	$0.480917\pi$
$5$	−1.86603	+	3.23205i	−0.834512	+	1.44542i	−0.894427	+	0.447214i	$0.852416\pi$
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−3.73205			−1.18018
$11$	2.09808	+	3.63397i	0.632594	+	1.09568i	0.987020	+	0.160600i	$0.0513430\pi$
$11$	2.09808	+	3.63397i	0.632594	+	1.09568i	−0.354426	+	0.935084i	$0.615324\pi$
$12$		0			0
$13$	−0.232051	+	0.401924i	−0.0643593	+	0.111474i	−0.896410	−	0.443227i	$-0.853834\pi$
$13$	−0.232051	+	0.401924i	−0.0643593	+	0.111474i	0.832050	+	0.554700i	$0.187167\pi$
$14$	−0.500000	+	0.866025i	−0.133631	+	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	7.00000			1.69775			0.848875	−	0.528594i	$-0.177281\pi$
$17$	7.00000			1.69775			0.848875	+	0.528594i	$0.177281\pi$
$18$		0			0
$19$	−2.73205			−0.626775			−0.313388	−	0.949625i	$-0.601464\pi$
$19$	−2.73205			−0.626775			−0.313388	+	0.949625i	$0.601464\pi$
$20$	−1.86603	−	3.23205i	−0.417256	−	0.722709i
$21$		0			0
$22$	−2.09808	+	3.63397i	−0.447311	+	0.774766i
$23$	−3.09808	+	5.36603i	−0.645994	+	1.11889i	0.338078	+	0.941118i	$0.390223\pi$
$23$	−3.09808	+	5.36603i	−0.645994	+	1.11889i	−0.984071	+	0.177775i	$0.943110\pi$
$24$		0			0
$25$	−4.46410	−	7.73205i	−0.892820	−	1.54641i
$26$	−0.464102			−0.0910178
$27$		0			0
$28$	−1.00000			−0.188982
$29$	−4.23205	−	7.33013i	−0.785872	−	1.36117i	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−4.23205	−	7.33013i	−0.785872	−	1.36117i	0.142605	−	0.989780i	$-0.454452\pi$
$30$		0			0
$31$	1.09808	−	1.90192i	0.197220	−	0.341596i	−0.750406	−	0.660977i	$-0.770142\pi$
$31$	1.09808	−	1.90192i	0.197220	−	0.341596i	0.947626	+	0.319382i	$0.103475\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	3.50000	+	6.06218i	0.600245	+	1.03965i
$35$	−3.73205			−0.630832
$36$		0			0
$37$	−6.66025			−1.09494			−0.547470	−	0.836826i	$-0.684409\pi$
$37$	−6.66025			−1.09494			−0.547470	+	0.836826i	$0.684409\pi$
$38$	−1.36603	−	2.36603i	−0.221599	−	0.383820i
$39$		0			0
$40$	1.86603	−	3.23205i	0.295045	−	0.511032i
$41$	−4.73205	+	8.19615i	−0.739022	+	1.28002i	0.213914	+	0.976853i	$0.431379\pi$
$41$	−4.73205	+	8.19615i	−0.739022	+	1.28002i	−0.952936	+	0.303171i	$0.901955\pi$
$42$		0			0
$43$	−2.73205	−	4.73205i	−0.416634	−	0.721631i	0.578965	−	0.815353i	$-0.303457\pi$
$43$	−2.73205	−	4.73205i	−0.416634	−	0.721631i	−0.995598	+	0.0937217i	$0.970124\pi$
$44$	−4.19615			−0.632594
$45$		0			0
$46$	−6.19615			−0.913573
$47$	−0.633975	−	1.09808i	−0.0924747	−	0.160171i	0.816077	−	0.577943i	$-0.196144\pi$
$47$	−0.633975	−	1.09808i	−0.0924747	−	0.160171i	−0.908552	+	0.417772i	$0.862811\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	4.46410	−	7.73205i	0.631319	−	1.09348i
$51$		0			0
$52$	−0.232051	−	0.401924i	−0.0321797	−	0.0557368i
$53$	−2.53590			−0.348332			−0.174166	−	0.984716i	$-0.555723\pi$
$53$	−2.53590			−0.348332			−0.174166	+	0.984716i	$0.555723\pi$
$54$		0			0
$55$	−15.6603			−2.11163
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$		0			0
$58$	4.23205	−	7.33013i	0.555695	−	0.962493i
$59$	3.09808	−	5.36603i	0.403335	−	0.698597i	−0.590791	−	0.806825i	$-0.701184\pi$
$59$	3.09808	−	5.36603i	0.403335	−	0.698597i	0.994126	+	0.108228i	$0.0345175\pi$
$60$		0			0
$61$	4.96410	+	8.59808i	0.635588	+	1.10087i	0.986390	+	0.164421i	$0.0525756\pi$
$61$	4.96410	+	8.59808i	0.635588	+	1.10087i	−0.350802	+	0.936450i	$0.614091\pi$
$62$	2.19615			0.278912
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.866025	−	1.50000i	−0.107417	−	0.186052i
$66$		0			0
$67$	1.63397	−	2.83013i	0.199622	−	0.345755i	−0.748784	−	0.662814i	$-0.769362\pi$
$67$	1.63397	−	2.83013i	0.199622	−	0.345755i	0.948406	+	0.317059i	$0.102695\pi$
$68$	−3.50000	+	6.06218i	−0.424437	+	0.735147i
$69$		0			0
$70$	−1.86603	−	3.23205i	−0.223033	−	0.386304i
$71$	13.4641			1.59789			0.798947	−	0.601401i	$-0.205391\pi$
$71$	13.4641			1.59789			0.798947	+	0.601401i	$0.205391\pi$
$72$		0			0
$73$	11.7321			1.37313			0.686566	−	0.727067i	$-0.259117\pi$
$73$	11.7321			1.37313			0.686566	+	0.727067i	$0.259117\pi$
$74$	−3.33013	−	5.76795i	−0.387119	−	0.670510i
$75$		0			0
$76$	1.36603	−	2.36603i	0.156694	−	0.271402i
$77$	−2.09808	+	3.63397i	−0.239098	+	0.414130i
$78$		0			0
$79$	−7.56218	−	13.0981i	−0.850811	−	1.47365i	−0.880477	−	0.474089i	$-0.842778\pi$
$79$	−7.56218	−	13.0981i	−0.850811	−	1.47365i	0.0296655	−	0.999560i	$-0.490556\pi$
$80$	3.73205			0.417256
$81$		0			0
$82$	−9.46410			−1.04514
$83$	7.29423	+	12.6340i	0.800646	+	1.38676i	0.919192	+	0.393810i	$0.128843\pi$
$83$	7.29423	+	12.6340i	0.800646	+	1.38676i	−0.118546	+	0.992949i	$0.537823\pi$
$84$		0			0
$85$	−13.0622	+	22.6244i	−1.41679	+	2.45396i
$86$	2.73205	−	4.73205i	0.294605	−	0.510270i
$87$		0			0
$88$	−2.09808	−	3.63397i	−0.223656	−	0.387383i
$89$	−3.92820			−0.416389			−0.208194	−	0.978087i	$-0.566759\pi$
$89$	−3.92820			−0.416389			−0.208194	+	0.978087i	$0.566759\pi$
$90$		0			0
$91$	−0.464102			−0.0486511
$92$	−3.09808	−	5.36603i	−0.322997	−	0.559447i
$93$		0			0
$94$	0.633975	−	1.09808i	0.0653895	−	0.113258i
$95$	5.09808	−	8.83013i	0.523052	−	0.905952i
$96$		0			0
$97$	1.46410	+	2.53590i	0.148657	+	0.257481i	0.930731	−	0.365704i	$-0.119172\pi$
$97$	1.46410	+	2.53590i	0.148657	+	0.257481i	−0.782074	+	0.623185i	$0.785838\pi$
$98$	−1.00000			−0.101015
$99$		0			0
$100$	8.92820			0.892820
$101$	2.46410	+	4.26795i	0.245187	+	0.424677i	0.962184	−	0.272399i	$-0.0878172\pi$
$101$	2.46410	+	4.26795i	0.245187	+	0.424677i	−0.716997	+	0.697076i	$0.754484\pi$
$102$		0			0
$103$	−6.19615	+	10.7321i	−0.610525	+	1.05746i	0.380627	+	0.924729i	$0.375708\pi$
$103$	−6.19615	+	10.7321i	−0.610525	+	1.05746i	−0.991152	+	0.132732i	$0.957625\pi$
$104$	0.232051	−	0.401924i	0.0227545	−	0.0394119i
$105$		0			0
$106$	−1.26795	−	2.19615i	−0.123154	−	0.213309i
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$	−7.19615			−0.689266			−0.344633	−	0.938737i	$-0.611997\pi$
$109$	−7.19615			−0.689266			−0.344633	+	0.938737i	$0.611997\pi$
$110$	−7.83013	−	13.5622i	−0.746573	−	1.29310i
$111$		0			0
$112$	0.500000	−	0.866025i	0.0472456	−	0.0818317i
$113$	1.13397	−	1.96410i	0.106675	−	0.184767i	−0.807746	−	0.589531i	$-0.799313\pi$
$113$	1.13397	−	1.96410i	0.106675	−	0.184767i	0.914421	+	0.404763i	$0.132646\pi$
$114$		0			0
$115$	−11.5622	−	20.0263i	−1.07818	−	1.86746i
$116$	8.46410			0.785872
$117$		0			0
$118$	6.19615			0.570402
$119$	3.50000	+	6.06218i	0.320844	+	0.555719i
$120$		0			0
$121$	−3.30385	+	5.72243i	−0.300350	+	0.520221i
$122$	−4.96410	+	8.59808i	−0.449429	+	0.778433i
$123$		0			0
$124$	1.09808	+	1.90192i	0.0986102	+	0.170798i
$125$	14.6603			1.31125
$126$		0			0
$127$	12.0000			1.06483			0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000			1.06483			0.532414	+	0.846484i	$0.321285\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	0.866025	−	1.50000i	0.0759555	−	0.131559i
$131$	−8.73205	+	15.1244i	−0.762923	+	1.32142i	0.178415	+	0.983955i	$0.442903\pi$
$131$	−8.73205	+	15.1244i	−0.762923	+	1.32142i	−0.941338	+	0.337466i	$0.890430\pi$
$132$		0			0
$133$	−1.36603	−	2.36603i	−0.118449	−	0.205160i
$134$	3.26795			0.282308
$135$		0			0
$136$	−7.00000			−0.600245
$137$	5.86603	+	10.1603i	0.501168	+	0.868049i	0.999999	+	0.00134965i	$0.000429606\pi$
$137$	5.86603	+	10.1603i	0.501168	+	0.868049i	−0.498831	+	0.866699i	$0.666237\pi$
$138$		0			0
$139$	3.36603	−	5.83013i	0.285503	−	0.494505i	−0.687228	−	0.726441i	$-0.741173\pi$
$139$	3.36603	−	5.83013i	0.285503	−	0.494505i	0.972731	+	0.231937i	$0.0745062\pi$
$140$	1.86603	−	3.23205i	0.157708	−	0.273158i
$141$		0			0
$142$	6.73205	+	11.6603i	0.564941	+	0.978507i
$143$	−1.94744			−0.162853
$144$		0			0
$145$	31.5885			2.62328
$146$	5.86603	+	10.1603i	0.485476	+	0.840869i
$147$		0			0
$148$	3.33013	−	5.76795i	0.273735	−	0.474123i
$149$	−4.50000	+	7.79423i	−0.368654	+	0.638528i	−0.989355	−	0.145519i	$-0.953515\pi$
$149$	−4.50000	+	7.79423i	−0.368654	+	0.638528i	0.620701	+	0.784047i	$0.286848\pi$
$150$		0			0
$151$	8.09808	+	14.0263i	0.659012	+	1.14144i	0.980872	+	0.194655i	$0.0623587\pi$
$151$	8.09808	+	14.0263i	0.659012	+	1.14144i	−0.321860	+	0.946787i	$0.604308\pi$
$152$	2.73205			0.221599
$153$		0			0
$154$	−4.19615			−0.338136
$155$	4.09808	+	7.09808i	0.329165	+	0.570131i
$156$		0			0
$157$	0.500000	−	0.866025i	0.0399043	−	0.0691164i	−0.845383	−	0.534160i	$-0.820628\pi$
$157$	0.500000	−	0.866025i	0.0399043	−	0.0691164i	0.885288	+	0.465044i	$0.153961\pi$
$158$	7.56218	−	13.0981i	0.601615	−	1.04203i
$159$		0			0
$160$	1.86603	+	3.23205i	0.147522	+	0.255516i
$161$	−6.19615			−0.488325
$162$		0			0
$163$	−6.53590			−0.511931			−0.255966	−	0.966686i	$-0.582393\pi$
$163$	−6.53590			−0.511931			−0.255966	+	0.966686i	$0.582393\pi$
$164$	−4.73205	−	8.19615i	−0.369511	−	0.640012i
$165$		0			0
$166$	−7.29423	+	12.6340i	−0.566142	+	0.980587i
$167$	6.09808	−	10.5622i	0.471883	−	0.817326i	−0.527599	−	0.849493i	$-0.676908\pi$
$167$	6.09808	−	10.5622i	0.471883	−	0.817326i	0.999482	+	0.0321676i	$0.0102410\pi$
$168$		0			0
$169$	6.39230	+	11.0718i	0.491716	+	0.851677i
$170$	−26.1244			−2.00365
$171$		0			0
$172$	5.46410			0.416634
$173$	−4.86603	−	8.42820i	−0.369957	−	0.640784i	0.619601	−	0.784917i	$-0.287294\pi$
$173$	−4.86603	−	8.42820i	−0.369957	−	0.640784i	−0.989558	+	0.144132i	$0.953961\pi$
$174$		0			0
$175$	4.46410	−	7.73205i	0.337454	−	0.584488i
$176$	2.09808	−	3.63397i	0.158148	−	0.273921i
$177$		0			0
$178$	−1.96410	−	3.40192i	−0.147216	−	0.254985i
$179$	8.19615			0.612609			0.306305	−	0.951934i	$-0.400907\pi$
$179$	8.19615			0.612609			0.306305	+	0.951934i	$0.400907\pi$
$180$		0			0
$181$	4.39230			0.326477			0.163239	−	0.986587i	$-0.447806\pi$
$181$	4.39230			0.326477			0.163239	+	0.986587i	$0.447806\pi$
$182$	−0.232051	−	0.401924i	−0.0172008	−	0.0297926i
$183$		0			0
$184$	3.09808	−	5.36603i	0.228393	−	0.395589i
$185$	12.4282	−	21.5263i	0.913740	−	1.58264i
$186$		0			0
$187$	14.6865	+	25.4378i	1.07399	+	1.86020i
$188$	1.26795			0.0924747
$189$		0			0
$190$	10.1962			0.739707
$191$	−5.83013	−	10.0981i	−0.421853	−	0.730671i	0.574268	−	0.818668i	$-0.305287\pi$
$191$	−5.83013	−	10.0981i	−0.421853	−	0.730671i	−0.996121	+	0.0879965i	$0.971954\pi$
$192$		0			0
$193$	4.42820	−	7.66987i	0.318749	−	0.552090i	−0.661478	−	0.749964i	$-0.730071\pi$
$193$	4.42820	−	7.66987i	0.318749	−	0.552090i	0.980227	+	0.197875i	$0.0634039\pi$
$194$	−1.46410	+	2.53590i	−0.105116	+	0.182067i
$195$		0			0
$196$	−0.500000	−	0.866025i	−0.0357143	−	0.0618590i
$197$	−25.7846			−1.83708			−0.918539	−	0.395331i	$-0.870630\pi$
$197$	−25.7846			−1.83708			−0.918539	+	0.395331i	$0.870630\pi$
$198$		0			0
$199$	5.12436			0.363256			0.181628	−	0.983367i	$-0.441863\pi$
$199$	5.12436			0.363256			0.181628	+	0.983367i	$0.441863\pi$
$200$	4.46410	+	7.73205i	0.315660	+	0.546739i
$201$		0			0
$202$	−2.46410	+	4.26795i	−0.173374	+	0.300292i
$203$	4.23205	−	7.33013i	0.297032	−	0.514474i
$204$		0			0
$205$	−17.6603	−	30.5885i	−1.23345	−	2.13639i
$206$	−12.3923			−0.863413
$207$		0			0
$208$	0.464102			0.0321797
$209$	−5.73205	−	9.92820i	−0.396494	−	0.686748i
$210$		0			0
$211$	10.3660	−	17.9545i	0.713627	−	1.23604i	−0.249860	−	0.968282i	$-0.580385\pi$
$211$	10.3660	−	17.9545i	0.713627	−	1.23604i	0.963487	−	0.267756i	$-0.0862820\pi$
$212$	1.26795	−	2.19615i	0.0870831	−	0.150832i
$213$		0			0
$214$		0			0
$215$	20.3923			1.39074
$216$		0			0
$217$	2.19615			0.149085
$218$	−3.59808	−	6.23205i	−0.243692	−	0.422088i
$219$		0			0
$220$	7.83013	−	13.5622i	0.527907	−	0.914362i
$221$	−1.62436	+	2.81347i	−0.109266	+	0.189254i
$222$		0			0
$223$	9.26795	+	16.0526i	0.620628	+	1.07496i	0.989369	+	0.145427i	$0.0464555\pi$
$223$	9.26795	+	16.0526i	0.620628	+	1.07496i	−0.368741	+	0.929532i	$0.620211\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	2.26795			0.150862
$227$	2.53590	+	4.39230i	0.168313	+	0.291528i	0.937827	−	0.347103i	$-0.112835\pi$
$227$	2.53590	+	4.39230i	0.168313	+	0.291528i	−0.769514	+	0.638631i	$0.779501\pi$
$228$		0			0
$229$	−2.23205	+	3.86603i	−0.147498	+	0.255474i	−0.930302	−	0.366794i	$-0.880455\pi$
$229$	−2.23205	+	3.86603i	−0.147498	+	0.255474i	0.782804	+	0.622268i	$0.213789\pi$
$230$	11.5622	−	20.0263i	0.762387	−	1.32049i
$231$		0			0
$232$	4.23205	+	7.33013i	0.277848	+	0.481246i
$233$	−13.1962			−0.864509			−0.432254	−	0.901752i	$-0.642282\pi$
$233$	−13.1962			−0.864509			−0.432254	+	0.901752i	$0.642282\pi$
$234$		0			0
$235$	4.73205			0.308685
$236$	3.09808	+	5.36603i	0.201668	+	0.349299i
$237$		0			0
$238$	−3.50000	+	6.06218i	−0.226871	+	0.392953i
$239$	−14.0263	+	24.2942i	−0.907285	+	1.57146i	−0.0894638	+	0.995990i	$0.528515\pi$
$239$	−14.0263	+	24.2942i	−0.907285	+	1.57146i	−0.817821	+	0.575473i	$0.804818\pi$
$240$		0			0
$241$	8.86603	+	15.3564i	0.571111	+	0.989193i	0.996452	+	0.0841601i	$0.0268207\pi$
$241$	8.86603	+	15.3564i	0.571111	+	0.989193i	−0.425341	+	0.905033i	$0.639846\pi$
$242$	−6.60770			−0.424759
$243$		0			0
$244$	−9.92820			−0.635588
$245$	−1.86603	−	3.23205i	−0.119216	−	0.206488i
$246$		0			0
$247$	0.633975	−	1.09808i	0.0403388	−	0.0698689i
$248$	−1.09808	+	1.90192i	−0.0697279	+	0.120772i
$249$		0			0
$250$	7.33013	+	12.6962i	0.463598	+	0.802975i
$251$	16.0526			1.01323			0.506614	−	0.862173i	$-0.330897\pi$
$251$	16.0526			1.01323			0.506614	+	0.862173i	$0.330897\pi$
$252$		0			0
$253$	−26.0000			−1.63461
$254$	6.00000	+	10.3923i	0.376473	+	0.652071i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.232051	−	0.401924i	0.0144749	−	0.0250713i	−0.858697	−	0.512483i	$-0.828726\pi$
$257$	0.232051	−	0.401924i	0.0144749	−	0.0250713i	0.873172	+	0.487412i	$0.162059\pi$
$258$		0			0
$259$	−3.33013	−	5.76795i	−0.206924	−	0.358403i
$260$	1.73205			0.107417
$261$		0			0
$262$	−17.4641			−1.07894
$263$	11.8301	+	20.4904i	0.729477	+	1.26349i	0.957105	+	0.289743i	$0.0935698\pi$
$263$	11.8301	+	20.4904i	0.729477	+	1.26349i	−0.227628	+	0.973748i	$0.573097\pi$
$264$		0			0
$265$	4.73205	−	8.19615i	0.290688	−	0.503486i
$266$	1.36603	−	2.36603i	0.0837564	−	0.145070i
$267$		0			0
$268$	1.63397	+	2.83013i	0.0998109	+	0.172878i
$269$	−25.5885			−1.56016			−0.780078	−	0.625682i	$-0.784821\pi$
$269$	−25.5885			−1.56016			−0.780078	+	0.625682i	$0.784821\pi$
$270$		0			0
$271$	25.5167			1.55003			0.775013	−	0.631945i	$-0.217743\pi$
$271$	25.5167			1.55003			0.775013	+	0.631945i	$0.217743\pi$
$272$	−3.50000	−	6.06218i	−0.212219	−	0.367574i
$273$		0			0
$274$	−5.86603	+	10.1603i	−0.354380	+	0.613803i
$275$	18.7321	−	32.4449i	1.12959	−	1.95650i
$276$		0			0
$277$	−11.3923	−	19.7321i	−0.684497	−	1.18558i	−0.973595	−	0.228284i	$-0.926688\pi$
$277$	−11.3923	−	19.7321i	−0.684497	−	1.18558i	0.289097	−	0.957300i	$-0.406645\pi$
$278$	6.73205			0.403762
$279$		0			0
$280$	3.73205			0.223033
$281$	1.40192	+	2.42820i	0.0836318	+	0.144854i	0.904807	−	0.425821i	$-0.140015\pi$
$281$	1.40192	+	2.42820i	0.0836318	+	0.144854i	−0.821176	+	0.570676i	$0.806681\pi$
$282$		0			0
$283$	9.66025	−	16.7321i	0.574242	−	0.994617i	−0.421881	−	0.906651i	$-0.638630\pi$
$283$	9.66025	−	16.7321i	0.574242	−	0.994617i	0.996123	−	0.0879660i	$-0.0280367\pi$
$284$	−6.73205	+	11.6603i	−0.399474	+	0.691909i
$285$		0			0
$286$	−0.973721	−	1.68653i	−0.0575773	−	0.0997268i
$287$	−9.46410			−0.558648
$288$		0			0
$289$	32.0000			1.88235
$290$	15.7942	+	27.3564i	0.927469	+	1.60642i
$291$		0			0
$292$	−5.86603	+	10.1603i	−0.343283	+	0.594584i
$293$	−10.3301	+	17.8923i	−0.603492	+	1.04528i	0.388795	+	0.921324i	$0.372891\pi$
$293$	−10.3301	+	17.8923i	−0.603492	+	1.04528i	−0.992288	+	0.123955i	$0.960442\pi$
$294$		0			0
$295$	11.5622	+	20.0263i	0.673176	+	1.16598i
$296$	6.66025			0.387119
$297$		0			0
$298$	−9.00000			−0.521356
$299$	−1.43782	−	2.49038i	−0.0831514	−	0.144022i
$300$		0			0
$301$	2.73205	−	4.73205i	0.157473	−	0.272751i
$302$	−8.09808	+	14.0263i	−0.465992	+	0.807122i
$303$		0			0
$304$	1.36603	+	2.36603i	0.0783469	+	0.135701i
$305$	−37.0526			−2.12162
$306$		0			0
$307$	5.85641			0.334243			0.167121	−	0.985936i	$-0.446553\pi$
$307$	5.85641			0.334243			0.167121	+	0.985936i	$0.446553\pi$
$308$	−2.09808	−	3.63397i	−0.119549	−	0.207065i
$309$		0			0
$310$	−4.09808	+	7.09808i	−0.232755	+	0.403144i
$311$	0.0980762	−	0.169873i	0.00556139	−	0.00963261i	−0.863231	−	0.504809i	$-0.831563\pi$
$311$	0.0980762	−	0.169873i	0.00556139	−	0.00963261i	0.868793	+	0.495176i	$0.164896\pi$
$312$		0			0
$313$	2.79423	+	4.83975i	0.157939	+	0.273559i	0.934125	−	0.356945i	$-0.116182\pi$
$313$	2.79423	+	4.83975i	0.157939	+	0.273559i	−0.776186	+	0.630504i	$0.782848\pi$
$314$	1.00000			0.0564333
$315$		0			0
$316$	15.1244			0.850811
$317$	5.30385	+	9.18653i	0.297894	+	0.515967i	0.975654	−	0.219316i	$-0.0703825\pi$
$317$	5.30385	+	9.18653i	0.297894	+	0.515967i	−0.677760	+	0.735283i	$0.737049\pi$
$318$		0			0
$319$	17.7583	−	30.7583i	0.994276	−	1.72214i
$320$	−1.86603	+	3.23205i	−0.104314	+	0.180677i
$321$		0			0
$322$	−3.09808	−	5.36603i	−0.172649	−	0.299037i
$323$	−19.1244			−1.06411
$324$		0			0
$325$	4.14359			0.229845
$326$	−3.26795	−	5.66025i	−0.180995	−	0.313492i
$327$		0			0
$328$	4.73205	−	8.19615i	0.261284	−	0.452557i
$329$	0.633975	−	1.09808i	0.0349522	−	0.0605389i
$330$		0			0
$331$	4.19615	+	7.26795i	0.230641	+	0.399483i	0.957997	−	0.286778i	$-0.0925842\pi$
$331$	4.19615	+	7.26795i	0.230641	+	0.399483i	−0.727356	+	0.686261i	$0.759251\pi$
$332$	−14.5885			−0.800646
$333$		0			0
$334$	12.1962			0.667344
$335$	6.09808	+	10.5622i	0.333173	+	0.577073i
$336$		0			0
$337$	−2.19615	+	3.80385i	−0.119632	+	0.207209i	−0.919622	−	0.392805i	$-0.871505\pi$
$337$	−2.19615	+	3.80385i	−0.119632	+	0.207209i	0.799990	+	0.600014i	$0.204838\pi$
$338$	−6.39230	+	11.0718i	−0.347696	+	0.602226i
$339$		0			0
$340$	−13.0622	−	22.6244i	−0.708396	−	1.22698i
$341$	9.21539			0.499041
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	2.73205	+	4.73205i	0.147302	+	0.255135i
$345$		0			0
$346$	4.86603	−	8.42820i	0.261599	−	0.453103i
$347$	−7.26795	+	12.5885i	−0.390164	+	0.675784i	−0.992471	−	0.122481i	$-0.960915\pi$
$347$	−7.26795	+	12.5885i	−0.390164	+	0.675784i	0.602307	+	0.798265i	$0.294248\pi$
$348$		0			0
$349$	2.73205	+	4.73205i	0.146243	+	0.253301i	0.929836	−	0.367974i	$-0.119948\pi$
$349$	2.73205	+	4.73205i	0.146243	+	0.253301i	−0.783593	+	0.621275i	$0.786615\pi$
$350$	8.92820			0.477233
$351$		0			0
$352$	4.19615			0.223656
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	0.999711	−	0.0240566i	$-0.00765819\pi$
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	−0.520689	+	0.853746i	$0.674325\pi$
$354$		0			0
$355$	−25.1244	+	43.5167i	−1.33346	+	2.30962i
$356$	1.96410	−	3.40192i	0.104097	−	0.180302i
$357$		0			0
$358$	4.09808	+	7.09808i	0.216590	+	0.375145i
$359$	2.92820			0.154545			0.0772723	−	0.997010i	$-0.475379\pi$
$359$	2.92820			0.154545			0.0772723	+	0.997010i	$0.475379\pi$
$360$		0			0
$361$	−11.5359			−0.607153
$362$	2.19615	+	3.80385i	0.115427	+	0.199926i
$363$		0			0
$364$	0.232051	−	0.401924i	0.0121628	−	0.0210665i
$365$	−21.8923	+	37.9186i	−1.14590	+	1.98475i
$366$		0			0
$367$	6.56218	+	11.3660i	0.342543	+	0.593302i	0.984904	−	0.173100i	$-0.0553785\pi$
$367$	6.56218	+	11.3660i	0.342543	+	0.593302i	−0.642361	+	0.766402i	$0.722045\pi$
$368$	6.19615			0.322997
$369$		0			0
$370$	24.8564			1.29222
$371$	−1.26795	−	2.19615i	−0.0658286	−	0.114019i
$372$		0			0
$373$	16.9282	−	29.3205i	0.876509	−	1.51816i	0.0213627	−	0.999772i	$-0.493200\pi$
$373$	16.9282	−	29.3205i	0.876509	−	1.51816i	0.855146	−	0.518387i	$-0.173467\pi$
$374$	−14.6865	+	25.4378i	−0.759423	+	1.31536i
$375$		0			0
$376$	0.633975	+	1.09808i	0.0326947	+	0.0566290i
$377$	3.92820			0.202313
$378$		0			0
$379$	17.5167			0.899770			0.449885	−	0.893086i	$-0.351465\pi$
$379$	17.5167			0.899770			0.449885	+	0.893086i	$0.351465\pi$
$380$	5.09808	+	8.83013i	0.261526	+	0.452976i
$381$		0			0
$382$	5.83013	−	10.0981i	0.298295	−	0.516663i
$383$	17.8564	−	30.9282i	0.912420	−	1.58036i	0.101784	−	0.994807i	$-0.467545\pi$
$383$	17.8564	−	30.9282i	0.912420	−	1.58036i	0.810636	−	0.585551i	$-0.199122\pi$
$384$		0			0
$385$	−7.83013	−	13.5622i	−0.399060	−	0.691193i
$386$	8.85641			0.450779
$387$		0			0
$388$	−2.92820			−0.148657
$389$	3.26795	+	5.66025i	0.165692	+	0.286986i	0.936901	−	0.349596i	$-0.113681\pi$
$389$	3.26795	+	5.66025i	0.165692	+	0.286986i	−0.771209	+	0.636582i	$0.780348\pi$
$390$		0			0
$391$	−21.6865	+	37.5622i	−1.09674	+	1.89960i
$392$	0.500000	−	0.866025i	0.0252538	−	0.0437409i
$393$		0			0
$394$	−12.8923	−	22.3301i	−0.649505	−	1.12498i
$395$	56.4449			2.84005
$396$		0			0
$397$	−21.0000			−1.05396			−0.526980	−	0.849878i	$-0.676676\pi$
$397$	−21.0000			−1.05396			−0.526980	+	0.849878i	$0.676676\pi$
$398$	2.56218	+	4.43782i	0.128430	+	0.222448i
$399$		0			0
$400$	−4.46410	+	7.73205i	−0.223205	+	0.386603i
$401$	17.2583	−	29.8923i	0.861840	−	1.49275i	−0.00831121	−	0.999965i	$-0.502646\pi$
$401$	17.2583	−	29.8923i	0.861840	−	1.49275i	0.870151	−	0.492785i	$-0.164021\pi$
$402$		0			0
$403$	0.509619	+	0.882686i	0.0253859	+	0.0439697i
$404$	−4.92820			−0.245187
$405$		0			0
$406$	8.46410			0.420066
$407$	−13.9737	−	24.2032i	−0.692652	−	1.19971i
$408$		0			0
$409$	−17.3301	+	30.0167i	−0.856920	+	1.48423i	0.0179330	+	0.999839i	$0.494291\pi$
$409$	−17.3301	+	30.0167i	−0.856920	+	1.48423i	−0.874853	+	0.484389i	$0.839042\pi$
$410$	17.6603	−	30.5885i	0.872178	−	1.51066i
$411$		0			0
$412$	−6.19615	−	10.7321i	−0.305263	−	0.528730i
$413$	6.19615			0.304893
$414$		0			0
$415$	−54.4449			−2.67259
$416$	0.232051	+	0.401924i	0.0113772	+	0.0197059i
$417$		0			0
$418$	5.73205	−	9.92820i	0.280364	−	0.485604i
$419$	1.26795	−	2.19615i	0.0619434	−	0.107289i	−0.833391	−	0.552684i	$-0.813604\pi$
$419$	1.26795	−	2.19615i	0.0619434	−	0.107289i	0.895334	+	0.445395i	$0.146937\pi$
$420$		0			0
$421$	12.0622	+	20.8923i	0.587875	+	1.01823i	0.994510	+	0.104638i	$0.0333685\pi$
$421$	12.0622	+	20.8923i	0.587875	+	1.01823i	−0.406636	+	0.913590i	$0.633298\pi$
$422$	20.7321			1.00922
$423$		0			0
$424$	2.53590			0.123154
$425$	−31.2487	−	54.1244i	−1.51579	−	2.62542i
$426$		0			0
$427$	−4.96410	+	8.59808i	−0.240230	+	0.416090i
$428$		0			0
$429$		0			0
$430$	10.1962	+	17.6603i	0.491702	+	0.851653i
$431$	−21.4641			−1.03389			−0.516945	−	0.856019i	$-0.672931\pi$
$431$	−21.4641			−1.03389			−0.516945	+	0.856019i	$0.672931\pi$
$432$		0			0
$433$	12.2679			0.589560			0.294780	−	0.955565i	$-0.404754\pi$
$433$	12.2679			0.589560			0.294780	+	0.955565i	$0.404754\pi$
$434$	1.09808	+	1.90192i	0.0527093	+	0.0912953i
$435$		0			0
$436$	3.59808	−	6.23205i	0.172317	−	0.298461i
$437$	8.46410	−	14.6603i	0.404893	−	0.701295i
$438$		0			0
$439$	5.66025	+	9.80385i	0.270149	+	0.467912i	0.968900	−	0.247453i	$-0.0795936\pi$
$439$	5.66025	+	9.80385i	0.270149	+	0.467912i	−0.698751	+	0.715365i	$0.746260\pi$
$440$	15.6603			0.746573
$441$		0			0
$442$	−3.24871			−0.154525
$443$	9.36603	+	16.2224i	0.444993	+	0.770751i	0.998052	−	0.0623915i	$-0.0198727\pi$
$443$	9.36603	+	16.2224i	0.444993	+	0.770751i	−0.553058	+	0.833142i	$0.686539\pi$
$444$		0			0
$445$	7.33013	−	12.6962i	0.347481	−	0.601855i
$446$	−9.26795	+	16.0526i	−0.438850	+	0.760111i
$447$		0			0
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	−11.8564			−0.559538			−0.279769	−	0.960067i	$-0.590258\pi$
$449$	−11.8564			−0.559538			−0.279769	+	0.960067i	$0.590258\pi$
$450$		0			0
$451$	−39.7128			−1.87000
$452$	1.13397	+	1.96410i	0.0533377	+	0.0923836i
$453$		0			0
$454$	−2.53590	+	4.39230i	−0.119016	+	0.206141i
$455$	0.866025	−	1.50000i	0.0405999	−	0.0703211i
$456$		0			0
$457$	−10.4282	−	18.0622i	−0.487811	−	0.844913i	0.512091	−	0.858931i	$-0.328871\pi$
$457$	−10.4282	−	18.0622i	−0.487811	−	0.844913i	−0.999902	+	0.0140182i	$0.995538\pi$
$458$	−4.46410			−0.208594
$459$		0			0
$460$	23.1244			1.07818
$461$	−17.3923	−	30.1244i	−0.810040	−	1.40303i	−0.912835	−	0.408329i	$-0.866112\pi$
$461$	−17.3923	−	30.1244i	−0.810040	−	1.40303i	0.102795	−	0.994703i	$-0.467222\pi$
$462$		0			0
$463$	16.2942	−	28.2224i	0.757257	−	1.31161i	−0.186987	−	0.982362i	$-0.559872\pi$
$463$	16.2942	−	28.2224i	0.757257	−	1.31161i	0.944244	−	0.329245i	$-0.106794\pi$
$464$	−4.23205	+	7.33013i	−0.196468	+	0.340293i
$465$		0			0
$466$	−6.59808	−	11.4282i	−0.305650	−	0.529401i
$467$	14.5885			0.675073			0.337537	−	0.941312i	$-0.390406\pi$
$467$	14.5885			0.675073			0.337537	+	0.941312i	$0.390406\pi$
$468$		0			0
$469$	3.26795			0.150900
$470$	2.36603	+	4.09808i	0.109137	+	0.189030i
$471$		0			0
$472$	−3.09808	+	5.36603i	−0.142601	+	0.246991i
$473$	11.4641	−	19.8564i	0.527120	−	0.912999i
$474$		0			0
$475$	12.1962	+	21.1244i	0.559598	+	0.969252i
$476$	−7.00000			−0.320844
$477$		0			0
$478$	−28.0526			−1.28309
$479$	−11.7583	−	20.3660i	−0.537252	−	0.930547i	−0.999051	−	0.0435628i	$-0.986129\pi$
$479$	−11.7583	−	20.3660i	−0.537252	−	0.930547i	0.461799	−	0.886985i	$-0.347204\pi$
$480$		0			0
$481$	1.54552	−	2.67691i	0.0704695	−	0.122057i
$482$	−8.86603	+	15.3564i	−0.403836	+	0.699465i
$483$		0			0
$484$	−3.30385	−	5.72243i	−0.150175	−	0.260111i
$485$	−10.9282			−0.496224
$486$		0			0
$487$	−28.5885			−1.29547			−0.647733	−	0.761867i	$-0.724283\pi$
$487$	−28.5885			−1.29547			−0.647733	+	0.761867i	$0.724283\pi$
$488$	−4.96410	−	8.59808i	−0.224714	−	0.389217i
$489$		0			0
$490$	1.86603	−	3.23205i	0.0842984	−	0.146009i
$491$	−16.7321	+	28.9808i	−0.755107	+	1.30788i	0.190214	+	0.981743i	$0.439082\pi$
$491$	−16.7321	+	28.9808i	−0.755107	+	1.30788i	−0.945321	+	0.326141i	$0.894252\pi$
$492$		0			0
$493$	−29.6244	−	51.3109i	−1.33421	−	2.31093i
$494$	1.26795			0.0570477
$495$		0			0
$496$	−2.19615			−0.0986102
$497$	6.73205	+	11.6603i	0.301974	+	0.523034i
$498$		0			0
$499$	−15.0981	+	26.1506i	−0.675883	+	1.17066i	0.300327	+	0.953836i	$0.402904\pi$
$499$	−15.0981	+	26.1506i	−0.675883	+	1.17066i	−0.976210	+	0.216827i	$0.930429\pi$
$500$	−7.33013	+	12.6962i	−0.327813	+	0.567789i
$501$		0			0
$502$	8.02628	+	13.9019i	0.358230	+	0.620473i
$503$	1.94744			0.0868321			0.0434161	−	0.999057i	$-0.486176\pi$
$503$	1.94744			0.0868321			0.0434161	+	0.999057i	$0.486176\pi$
$504$		0			0
$505$	−18.3923			−0.818447
$506$	−13.0000	−	22.5167i	−0.577920	−	1.00099i
$507$		0			0
$508$	−6.00000	+	10.3923i	−0.266207	+	0.461084i
$509$	−2.07180	+	3.58846i	−0.0918308	+	0.159056i	−0.908282	−	0.418360i	$-0.862605\pi$
$509$	−2.07180	+	3.58846i	−0.0918308	+	0.159056i	0.816451	+	0.577415i	$0.195939\pi$
$510$		0			0
$511$	5.86603	+	10.1603i	0.259498	+	0.449463i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	0.464102			0.0204706
$515$	−23.1244	−	40.0526i	−1.01898	−	1.76493i
$516$		0			0
$517$	2.66025	−	4.60770i	0.116998	−	0.202646i
$518$	3.33013	−	5.76795i	0.146317	−	0.253429i
$519$		0			0
$520$	0.866025	+	1.50000i	0.0379777	+	0.0657794i
$521$	−30.0000			−1.31432			−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000			−1.31432			−0.657162	+	0.753749i	$0.728243\pi$
$522$		0			0
$523$	−29.1769			−1.27582			−0.637909	−	0.770112i	$-0.720200\pi$
$523$	−29.1769			−1.27582			−0.637909	+	0.770112i	$0.720200\pi$
$524$	−8.73205	−	15.1244i	−0.381461	−	0.660711i
$525$		0			0
$526$	−11.8301	+	20.4904i	−0.515818	+	0.893423i
$527$	7.68653	−	13.3135i	0.334831	−	0.579944i
$528$		0			0
$529$	−7.69615	−	13.3301i	−0.334615	−	0.579571i
$530$	9.46410			0.411094
$531$		0			0
$532$	2.73205			0.118449
$533$	−2.19615	−	3.80385i	−0.0951259	−	0.164763i
$534$		0			0
$535$		0			0
$536$	−1.63397	+	2.83013i	−0.0705770	+	0.122243i
$537$		0			0
$538$	−12.7942	−	22.1603i	−0.551598	−	0.955396i
$539$	−4.19615			−0.180741
$540$		0			0
$541$	20.6603			0.888254			0.444127	−	0.895964i	$-0.353514\pi$
$541$	20.6603			0.888254			0.444127	+	0.895964i	$0.353514\pi$
$542$	12.7583	+	22.0981i	0.548017	+	0.949194i
$543$		0			0
$544$	3.50000	−	6.06218i	0.150061	−	0.259914i
$545$	13.4282	−	23.2583i	0.575201	−	0.996277i
$546$		0			0
$547$	9.63397	+	16.6865i	0.411919	+	0.713465i	0.995100	−	0.0988779i	$-0.0315253\pi$
$547$	9.63397	+	16.6865i	0.411919	+	0.713465i	−0.583181	+	0.812343i	$0.698192\pi$
$548$	−11.7321			−0.501168
$549$		0			0
$550$	37.4641			1.59747
$551$	11.5622	+	20.0263i	0.492565	+	0.853148i
$552$		0			0
$553$	7.56218	−	13.0981i	0.321577	−	0.556987i
$554$	11.3923	−	19.7321i	0.484013	−	0.838335i
$555$		0			0
$556$	3.36603	+	5.83013i	0.142751	+	0.247252i
$557$	10.0718			0.426756			0.213378	−	0.976970i	$-0.431553\pi$
$557$	10.0718			0.426756			0.213378	+	0.976970i	$0.431553\pi$
$558$		0			0
$559$	2.53590			0.107257
$560$	1.86603	+	3.23205i	0.0788540	+	0.136579i
$561$		0			0
$562$	−1.40192	+	2.42820i	−0.0591366	+	0.102428i
$563$	17.8564	−	30.9282i	0.752558	−	1.30347i	−0.194022	−	0.980997i	$-0.562153\pi$
$563$	17.8564	−	30.9282i	0.752558	−	1.30347i	0.946579	−	0.322471i	$-0.104514\pi$
$564$		0			0
$565$	4.23205	+	7.33013i	0.178044	+	0.308381i
$566$	19.3205			0.812102
$567$		0			0
$568$	−13.4641			−0.564941
$569$	−6.40192	−	11.0885i	−0.268383	−	0.464852i	0.700062	−	0.714082i	$-0.253156\pi$
$569$	−6.40192	−	11.0885i	−0.268383	−	0.464852i	−0.968444	+	0.249230i	$0.919822\pi$
$570$		0			0
$571$	9.63397	−	16.6865i	0.403169	−	0.698310i	−0.590937	−	0.806718i	$-0.701242\pi$
$571$	9.63397	−	16.6865i	0.403169	−	0.698310i	0.994107	+	0.108408i	$0.0345752\pi$
$572$	0.973721	−	1.68653i	0.0407133	−	0.0705175i
$573$		0			0
$574$	−4.73205	−	8.19615i	−0.197512	−	0.342101i
$575$	55.3205			2.30702
$576$		0			0
$577$	7.33975			0.305558			0.152779	−	0.988260i	$-0.451178\pi$
$577$	7.33975			0.305558			0.152779	+	0.988260i	$0.451178\pi$
$578$	16.0000	+	27.7128i	0.665512	+	1.15270i
$579$		0			0
$580$	−15.7942	+	27.3564i	−0.655820	+	1.13591i
$581$	−7.29423	+	12.6340i	−0.302616	+	0.524146i
$582$		0			0
$583$	−5.32051	−	9.21539i	−0.220353	−	0.381662i
$584$	−11.7321			−0.485476
$585$		0			0
$586$	−20.6603			−0.853467
$587$	−5.63397	−	9.75833i	−0.232539	−	0.402769i	0.726016	−	0.687678i	$-0.241370\pi$
$587$	−5.63397	−	9.75833i	−0.232539	−	0.402769i	−0.958555	+	0.284909i	$0.908037\pi$
$588$		0			0
$589$	−3.00000	+	5.19615i	−0.123613	+	0.214104i
$590$	−11.5622	+	20.0263i	−0.476007	+	0.824469i
$591$		0			0
$592$	3.33013	+	5.76795i	0.136867	+	0.237061i
$593$	40.1769			1.64987			0.824934	−	0.565229i	$-0.191212\pi$
$593$	40.1769			1.64987			0.824934	+	0.565229i	$0.191212\pi$
$594$		0			0
$595$	−26.1244			−1.07099
$596$	−4.50000	−	7.79423i	−0.184327	−	0.319264i
$597$		0			0
$598$	1.43782	−	2.49038i	0.0587969	−	0.101839i
$599$	−4.56218	+	7.90192i	−0.186406	+	0.322864i	−0.944049	−	0.329805i	$-0.893017\pi$
$599$	−4.56218	+	7.90192i	−0.186406	+	0.322864i	0.757644	+	0.652668i	$0.226350\pi$
$600$		0			0
$601$	−4.40192	−	7.62436i	−0.179558	−	0.311004i	0.762171	−	0.647376i	$-0.224133\pi$
$601$	−4.40192	−	7.62436i	−0.179558	−	0.311004i	−0.941729	+	0.336372i	$0.890800\pi$
$602$	5.46410			0.222700
$603$		0			0
$604$	−16.1962			−0.659012
$605$	−12.3301	−	21.3564i	−0.501291	−	0.868261i
$606$		0			0
$607$	−3.29423	+	5.70577i	−0.133709	+	0.231590i	−0.925103	−	0.379715i	$-0.876022\pi$
$607$	−3.29423	+	5.70577i	−0.133709	+	0.231590i	0.791395	+	0.611305i	$0.209355\pi$
$608$	−1.36603	+	2.36603i	−0.0553996	+	0.0959550i
$609$		0			0
$610$	−18.5263	−	32.0885i	−0.750107	−	1.29922i
$611$	0.588457			0.0238064
$612$		0			0
$613$	−14.7846			−0.597145			−0.298572	−	0.954387i	$-0.596510\pi$
$613$	−14.7846			−0.597145			−0.298572	+	0.954387i	$0.596510\pi$
$614$	2.92820	+	5.07180i	0.118173	+	0.204681i
$615$		0			0
$616$	2.09808	−	3.63397i	0.0845339	−	0.146417i
$617$	19.9904	−	34.6244i	0.804782	−	1.39392i	−0.111655	−	0.993747i	$-0.535615\pi$
$617$	19.9904	−	34.6244i	0.804782	−	1.39392i	0.916438	−	0.400177i	$-0.131051\pi$
$618$		0			0
$619$	−15.8564	−	27.4641i	−0.637323	−	1.10388i	−0.986018	−	0.166639i	$-0.946708\pi$
$619$	−15.8564	−	27.4641i	−0.637323	−	1.10388i	0.348695	−	0.937236i	$-0.386625\pi$
$620$	−8.19615			−0.329165
$621$		0			0
$622$	0.196152			0.00786500
$623$	−1.96410	−	3.40192i	−0.0786901	−	0.136295i
$624$		0			0
$625$	−5.03590	+	8.72243i	−0.201436	+	0.348897i
$626$	−2.79423	+	4.83975i	−0.111680	+	0.193435i
$627$		0			0
$628$	0.500000	+	0.866025i	0.0199522	+	0.0345582i
$629$	−46.6218			−1.85893
$630$		0			0
$631$	13.6603			0.543806			0.271903	−	0.962325i	$-0.412347\pi$
$631$	13.6603			0.543806			0.271903	+	0.962325i	$0.412347\pi$
$632$	7.56218	+	13.0981i	0.300807	+	0.521013i
$633$		0			0
$634$	−5.30385	+	9.18653i	−0.210643	+	0.364844i
$635$	−22.3923	+	38.7846i	−0.888612	+	1.53912i
$636$		0			0
$637$	−0.232051	−	0.401924i	−0.00919419	−	0.0159248i
$638$	35.5167			1.40612
$639$		0			0
$640$	−3.73205			−0.147522
$641$	9.72243	+	16.8397i	0.384013	+	0.665130i	0.991632	−	0.129099i	$-0.0412085\pi$
$641$	9.72243	+	16.8397i	0.384013	+	0.665130i	−0.607619	+	0.794229i	$0.707875\pi$
$642$		0			0
$643$	20.2942	−	35.1506i	0.800326	−	1.38621i	−0.119075	−	0.992885i	$-0.537993\pi$
$643$	20.2942	−	35.1506i	0.800326	−	1.38621i	0.919401	−	0.393320i	$-0.128674\pi$
$644$	3.09808	−	5.36603i	0.122081	−	0.211451i
$645$		0			0
$646$	−9.56218	−	16.5622i	−0.376219	−	0.651630i
$647$	16.3923			0.644448			0.322224	−	0.946663i	$-0.395570\pi$
$647$	16.3923			0.644448			0.322224	+	0.946663i	$0.395570\pi$
$648$		0			0
$649$	26.0000			1.02059
$650$	2.07180	+	3.58846i	0.0812626	+	0.140751i
$651$		0			0
$652$	3.26795	−	5.66025i	0.127983	−	0.221673i
$653$	−9.12436	+	15.8038i	−0.357064	+	0.618452i	−0.987469	−	0.157814i	$-0.949555\pi$
$653$	−9.12436	+	15.8038i	−0.357064	+	0.618452i	0.630405	+	0.776266i	$0.282889\pi$
$654$		0			0
$655$	−32.5885	−	56.4449i	−1.27334	−	2.20548i
$656$	9.46410			0.369511
$657$		0			0
$658$	1.26795			0.0494298
$659$	7.80385	+	13.5167i	0.303995	+	0.526534i	0.977037	−	0.213070i	$-0.0683461\pi$
$659$	7.80385	+	13.5167i	0.303995	+	0.526534i	−0.673042	+	0.739604i	$0.735013\pi$
$660$		0			0
$661$	−7.42820	+	12.8660i	−0.288924	+	0.500430i	−0.973553	−	0.228461i	$-0.926631\pi$
$661$	−7.42820	+	12.8660i	−0.288924	+	0.500430i	0.684629	+	0.728891i	$0.259964\pi$
$662$	−4.19615	+	7.26795i	−0.163088	+	0.282477i
$663$		0			0
$664$	−7.29423	−	12.6340i	−0.283071	−	0.490293i
$665$	10.1962			0.395390
$666$		0			0
$667$	52.4449			2.03067
$668$	6.09808	+	10.5622i	0.235942	+	0.408663i
$669$		0			0
$670$	−6.09808	+	10.5622i	−0.235589	+	0.408053i
$671$	−20.8301	+	36.0788i	−0.804138	+	1.39281i
$672$		0			0
$673$	−8.16025	−	14.1340i	−0.314555	−	0.544825i	0.664788	−	0.747032i	$-0.268522\pi$
$673$	−8.16025	−	14.1340i	−0.314555	−	0.544825i	−0.979343	+	0.202207i	$0.935189\pi$
$674$	−4.39230			−0.169185
$675$		0			0
$676$	−12.7846			−0.491716
$677$	−18.0000	−	31.1769i	−0.691796	−	1.19823i	−0.971249	−	0.238067i	$-0.923486\pi$
$677$	−18.0000	−	31.1769i	−0.691796	−	1.19823i	0.279453	−	0.960159i	$-0.409847\pi$
$678$		0			0
$679$	−1.46410	+	2.53590i	−0.0561871	+	0.0973188i
$680$	13.0622	−	22.6244i	0.500912	−	0.867604i
$681$		0			0
$682$	4.60770	+	7.98076i	0.176438	+	0.305599i
$683$	25.8564			0.989368			0.494684	−	0.869073i	$-0.335284\pi$
$683$	25.8564			0.989368			0.494684	+	0.869073i	$0.335284\pi$
$684$		0			0
$685$	−43.7846			−1.67292
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$		0			0
$688$	−2.73205	+	4.73205i	−0.104158	+	0.180408i
$689$	0.588457	−	1.01924i	0.0224184	−	0.0388299i
$690$		0			0
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	0.999276	+	0.0380440i	$0.0121127\pi$
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	−0.466691	+	0.884420i	$0.654554\pi$
$692$	9.73205			0.369957
$693$		0			0
$694$	−14.5359			−0.551775
$695$	12.5622	+	21.7583i	0.476511	+	0.825341i
$696$		0			0
$697$	−33.1244	+	57.3731i	−1.25467	+	2.17316i
$698$	−2.73205	+	4.73205i	−0.103410	+	0.179111i
$699$		0			0
$700$	4.46410	+	7.73205i	0.168727	+	0.292244i
$701$	6.60770			0.249569			0.124785	−	0.992184i	$-0.460176\pi$
$701$	6.60770			0.249569			0.124785	+	0.992184i	$0.460176\pi$
$702$		0			0
$703$	18.1962			0.686281
$704$	2.09808	+	3.63397i	0.0790742	+	0.136961i
$705$		0			0
$706$	−9.00000	+	15.5885i	−0.338719	+	0.586679i
$707$	−2.46410	+	4.26795i	−0.0926721	+	0.160513i
$708$		0			0
$709$	14.0622	+	24.3564i	0.528116	+	0.914724i	0.999463	+	0.0327760i	$0.0104348\pi$
$709$	14.0622	+	24.3564i	0.528116	+	0.914724i	−0.471347	+	0.881948i	$0.656232\pi$
$710$	−50.2487			−1.88580
$711$		0			0
$712$	3.92820			0.147216
$713$	6.80385	+	11.7846i	0.254806	+	0.441337i
$714$		0			0
$715$	3.63397	−	6.29423i	0.135903	−	0.235391i
$716$	−4.09808	+	7.09808i	−0.153152	+	0.265268i
$717$		0			0
$718$	1.46410	+	2.53590i	0.0546398	+	0.0946389i
$719$	−2.53590			−0.0945731			−0.0472865	−	0.998881i	$-0.515057\pi$
$719$	−2.53590			−0.0945731			−0.0472865	+	0.998881i	$0.515057\pi$
$720$		0			0
$721$	−12.3923			−0.461514
$722$	−5.76795	−	9.99038i	−0.214661	−	0.371803i
$723$		0			0
$724$	−2.19615	+	3.80385i	−0.0816194	+	0.141369i
$725$	−37.7846	+	65.4449i	−1.40329	+	2.43056i
$726$		0			0
$727$	−8.33975	−	14.4449i	−0.309304	−	0.535730i	0.668906	−	0.743347i	$-0.266763\pi$
$727$	−8.33975	−	14.4449i	−0.309304	−	0.535730i	−0.978210	+	0.207616i	$0.933429\pi$
$728$	0.464102			0.0172008
$729$		0			0
$730$	−43.7846			−1.62054
$731$	−19.1244	−	33.1244i	−0.707340	−	1.22515i
$732$		0			0
$733$	−6.33975	+	10.9808i	−0.234164	+	0.405584i	−0.959029	−	0.283307i	$-0.908569\pi$
$733$	−6.33975	+	10.9808i	−0.234164	+	0.405584i	0.724865	+	0.688890i	$0.241902\pi$
$734$	−6.56218	+	11.3660i	−0.242214	+	0.419528i
$735$		0			0
$736$	3.09808	+	5.36603i	0.114197	+	0.197794i
$737$	13.7128			0.505118
$738$		0			0
$739$	−16.7321			−0.615498			−0.307749	−	0.951468i	$-0.599576\pi$
$739$	−16.7321			−0.615498			−0.307749	+	0.951468i	$0.599576\pi$
$740$	12.4282	+	21.5263i	0.456870	+	0.791322i
$741$		0			0
$742$	1.26795	−	2.19615i	0.0465479	−	0.0806233i
$743$	9.80385	−	16.9808i	0.359668	−	0.622964i	−0.628237	−	0.778022i	$-0.716223\pi$
$743$	9.80385	−	16.9808i	0.359668	−	0.622964i	0.987905	+	0.155058i	$0.0495565\pi$
$744$		0			0
$745$	−16.7942	−	29.0885i	−0.615293	−	1.06572i
$746$	33.8564			1.23957
$747$		0			0
$748$	−29.3731			−1.07399
$749$		0			0
$750$		0			0
$751$	24.9282	−	43.1769i	0.909643	−	1.57555i	0.0950825	−	0.995469i	$-0.469688\pi$
$751$	24.9282	−	43.1769i	0.909643	−	1.57555i	0.814561	−	0.580079i	$-0.196978\pi$
$752$	−0.633975	+	1.09808i	−0.0231187	+	0.0400427i
$753$		0			0
$754$	1.96410	+	3.40192i	0.0715284	+	0.123891i
$755$	−60.4449			−2.19981
$756$		0			0
$757$	−20.7846			−0.755429			−0.377715	−	0.925922i	$-0.623290\pi$
$757$	−20.7846			−0.755429			−0.377715	+	0.925922i	$0.623290\pi$
$758$	8.75833	+	15.1699i	0.318117	+	0.550995i
$759$		0			0
$760$	−5.09808	+	8.83013i	−0.184927	+	0.320302i
$761$	−18.5000	+	32.0429i	−0.670624	+	1.16156i	0.307103	+	0.951676i	$0.400640\pi$
$761$	−18.5000	+	32.0429i	−0.670624	+	1.16156i	−0.977727	+	0.209879i	$0.932693\pi$
$762$		0			0
$763$	−3.59808	−	6.23205i	−0.130259	−	0.225615i
$764$	11.6603			0.421853
$765$		0			0
$766$	35.7128			1.29036
$767$	1.43782	+	2.49038i	0.0519167	+	0.0899224i
$768$		0			0
$769$	17.7942	−	30.8205i	0.641676	−	1.11142i	−0.343382	−	0.939196i	$-0.611573\pi$
$769$	17.7942	−	30.8205i	0.641676	−	1.11142i	0.985058	−	0.172220i	$-0.0550941\pi$
$770$	7.83013	−	13.5622i	0.282178	−	0.488747i
$771$		0			0
$772$	4.42820	+	7.66987i	0.159375	+	0.276045i
$773$	20.1244			0.723823			0.361911	−	0.932213i	$-0.382124\pi$
$773$	20.1244			0.723823			0.361911	+	0.932213i	$0.382124\pi$
$774$		0			0
$775$	−19.6077			−0.704329
$776$	−1.46410	−	2.53590i	−0.0525582	−	0.0910334i
$777$		0			0
$778$	−3.26795	+	5.66025i	−0.117162	+	0.202930i
$779$	12.9282	−	22.3923i	0.463201	−	0.802288i
$780$		0			0
$781$	28.2487	+	48.9282i	1.01082	+	1.75079i
$782$	−43.3731			−1.55102
$783$		0			0
$784$	1.00000			0.0357143
$785$	1.86603	+	3.23205i	0.0666013	+	0.115357i
$786$		0			0
$787$	3.80385	−	6.58846i	0.135593	−	0.234853i	−0.790231	−	0.612809i	$-0.790040\pi$
$787$	3.80385	−	6.58846i	0.135593	−	0.234853i	0.925824	+	0.377956i	$0.123373\pi$
$788$	12.8923	−	22.3301i	0.459269	−	0.795478i
$789$		0			0
$790$	28.2224	+	48.8827i	1.00411	+	1.73917i
$791$	2.26795			0.0806390
$792$		0			0
$793$	−4.60770			−0.163624
$794$	−10.5000	−	18.1865i	−0.372631	−	0.645416i
$795$		0			0
$796$	−2.56218	+	4.43782i	−0.0908140	+	0.157294i
$797$	−14.7224	+	25.5000i	−0.521495	+	0.903256i	0.478192	+	0.878255i	$0.341292\pi$
$797$	−14.7224	+	25.5000i	−0.521495	+	0.903256i	−0.999687	+	0.0250011i	$0.992041\pi$
$798$		0			0
$799$	−4.43782	−	7.68653i	−0.156999	−	0.271930i
$800$	−8.92820			−0.315660
$801$		0			0
$802$	34.5167			1.21883
$803$	24.6147	+	42.6340i	0.868635	+	1.50452i
$804$		0			0
$805$	11.5622	−	20.0263i	0.407513	−	0.705834i
$806$	−0.509619	+	0.882686i	−0.0179506	+	0.0310913i
$807$		0			0
$808$	−2.46410	−	4.26795i	−0.0866868	−	0.150146i
$809$	7.87564			0.276893			0.138446	−	0.990370i	$-0.455789\pi$
$809$	7.87564			0.276893			0.138446	+	0.990370i	$0.455789\pi$
$810$		0			0
$811$	7.80385			0.274030			0.137015	−	0.990569i	$-0.456249\pi$
$811$	7.80385			0.274030			0.137015	+	0.990569i	$0.456249\pi$
$812$	4.23205	+	7.33013i	0.148516	+	0.257237i
$813$		0			0
$814$	13.9737	−	24.2032i	0.489779	−	0.848322i
$815$	12.1962	−	21.1244i	0.427213	−	0.739954i
$816$		0			0
$817$	7.46410	+	12.9282i	0.261136	+	0.452301i
$818$	−34.6603			−1.21187
$819$		0			0
$820$	35.3205			1.23345
$821$	−6.03590	−	10.4545i	−0.210654	−	0.364864i	0.741265	−	0.671212i	$-0.234226\pi$
$821$	−6.03590	−	10.4545i	−0.210654	−	0.364864i	−0.951919	+	0.306348i	$0.900893\pi$
$822$		0			0
$823$	20.3923	−	35.3205i	0.710831	−	1.23120i	−0.253715	−	0.967279i	$-0.581652\pi$
$823$	20.3923	−	35.3205i	0.710831	−	1.23120i	0.964546	−	0.263916i	$-0.0850143\pi$
$824$	6.19615	−	10.7321i	0.215853	−	0.373869i
$825$		0			0
$826$	3.09808	+	5.36603i	0.107796	+	0.186708i
$827$	11.3205			0.393653			0.196826	−	0.980438i	$-0.436936\pi$
$827$	11.3205			0.393653			0.196826	+	0.980438i	$0.436936\pi$
$828$		0			0
$829$	−14.0000			−0.486240			−0.243120	−	0.969996i	$-0.578171\pi$
$829$	−14.0000			−0.486240			−0.243120	+	0.969996i	$0.578171\pi$
$830$	−27.2224	−	47.1506i	−0.944904	−	1.63662i
$831$		0			0
$832$	−0.232051	+	0.401924i	−0.00804491	+	0.0139342i
$833$	−3.50000	+	6.06218i	−0.121268	+	0.210042i
$834$		0			0
$835$	22.7583	+	39.4186i	0.787584	+	1.36414i
$836$	11.4641			0.396494
$837$		0			0
$838$	2.53590			0.0876012
$839$	2.73205	+	4.73205i	0.0943209	+	0.163369i	0.909325	−	0.416087i	$-0.136599\pi$
$839$	2.73205	+	4.73205i	0.0943209	+	0.163369i	−0.815004	+	0.579455i	$0.803265\pi$
$840$		0			0
$841$	−21.3205	+	36.9282i	−0.735190	+	1.27339i
$842$	−12.0622	+	20.8923i	−0.415690	+	0.719996i
$843$		0			0
$844$	10.3660	+	17.9545i	0.356813	+	0.618019i
$845$	−47.7128			−1.64137
$846$		0			0
$847$	−6.60770			−0.227043
$848$	1.26795	+	2.19615i	0.0435416	+	0.0754162i
$849$		0			0
$850$	31.2487	−	54.1244i	1.07182	−	1.85645i
$851$	20.6340	−	35.7391i	0.707324	−	1.22512i
$852$		0			0
$853$	−2.85641	−	4.94744i	−0.0978015	−	0.169397i	0.812973	−	0.582302i	$-0.197848\pi$
$853$	−2.85641	−	4.94744i	−0.0978015	−	0.169397i	−0.910774	+	0.412904i	$0.864514\pi$
$854$	−9.92820			−0.339736
$855$		0			0
$856$		0			0
$857$	−5.42820	−	9.40192i	−0.185424	−	0.321164i	0.758295	−	0.651911i	$-0.226032\pi$
$857$	−5.42820	−	9.40192i	−0.185424	−	0.321164i	−0.943719	+	0.330748i	$0.892699\pi$
$858$		0			0
$859$	−1.80385	+	3.12436i	−0.0615465	+	0.106602i	−0.895157	−	0.445751i	$-0.852937\pi$
$859$	−1.80385	+	3.12436i	−0.0615465	+	0.106602i	0.833610	+	0.552353i	$0.186270\pi$
$860$	−10.1962	+	17.6603i	−0.347686	+	0.602210i
$861$		0			0
$862$	−10.7321	−	18.5885i	−0.365535	−	0.633125i
$863$	17.1244			0.582920			0.291460	−	0.956583i	$-0.405859\pi$
$863$	17.1244			0.582920			0.291460	+	0.956583i	$0.405859\pi$
$864$		0			0
$865$	36.3205			1.23493
$866$	6.13397	+	10.6244i	0.208441	+	0.361030i
$867$		0			0
$868$	−1.09808	+	1.90192i	−0.0372711	+	0.0645555i
$869$	31.7321	−	54.9615i	1.07644	−	1.86444i
$870$		0			0
$871$	0.758330	+	1.31347i	0.0256950	+	0.0445051i
$872$	7.19615			0.243692
$873$		0			0
$874$	16.9282			0.572605
$875$	7.33013	+	12.6962i	0.247804	+	0.429208i
$876$		0			0
$877$	−4.25833	+	7.37564i	−0.143794	+	0.249058i	−0.928922	−	0.370275i	$-0.879263\pi$
$877$	−4.25833	+	7.37564i	−0.143794	+	0.249058i	0.785129	+	0.619333i	$0.212597\pi$
$878$	−5.66025	+	9.80385i	−0.191024	+	0.330864i
$879$		0			0
$880$	7.83013	+	13.5622i	0.263954	+	0.457181i
$881$	−18.2487			−0.614815			−0.307407	−	0.951578i	$-0.599461\pi$
$881$	−18.2487			−0.614815			−0.307407	+	0.951578i	$0.599461\pi$
$882$		0			0
$883$	7.66025			0.257788			0.128894	−	0.991658i	$-0.458857\pi$
$883$	7.66025			0.257788			0.128894	+	0.991658i	$0.458857\pi$
$884$	−1.62436	−	2.81347i	−0.0546330	−	0.0946271i
$885$		0			0
$886$	−9.36603	+	16.2224i	−0.314658	+	0.545003i
$887$	−1.22243	+	2.11731i	−0.0410452	+	0.0710924i	−0.885818	−	0.464032i	$-0.846402\pi$
$887$	−1.22243	+	2.11731i	−0.0410452	+	0.0710924i	0.844773	+	0.535125i	$0.179735\pi$
$888$		0			0
$889$	6.00000	+	10.3923i	0.201234	+	0.348547i
$890$	14.6603			0.491413
$891$		0			0
$892$	−18.5359			−0.620628
$893$	1.73205	+	3.00000i	0.0579609	+	0.100391i
$894$		0			0
$895$	−15.2942	+	26.4904i	−0.511230	+	0.885476i
$896$	−0.500000	+	0.866025i	−0.0167038	+	0.0289319i
$897$		0			0
$898$	−5.92820	−	10.2679i	−0.197827	−	0.342646i
$899$	−18.5885			−0.619960
$900$		0			0
$901$	−17.7513			−0.591381
$902$	−19.8564	−	34.3923i	−0.661146	−	1.14514i
$903$		0			0
$904$	−1.13397	+	1.96410i	−0.0377154	+	0.0653250i
$905$	−8.19615	+	14.1962i	−0.272449	+	0.471896i
$906$		0			0
$907$	18.0000	+	31.1769i	0.597680	+	1.03521i	0.993163	+	0.116739i	$0.0372441\pi$
$907$	18.0000	+	31.1769i	0.597680	+	1.03521i	−0.395482	+	0.918474i	$0.629423\pi$
$908$	−5.07180			−0.168313
$909$		0			0
$910$	1.73205			0.0574169
$911$	3.12436	+	5.41154i	0.103515	+	0.179292i	0.913130	−	0.407668i	$-0.133658\pi$
$911$	3.12436	+	5.41154i	0.103515	+	0.179292i	−0.809616	+	0.586960i	$0.800325\pi$
$912$		0			0
$913$	−30.6077	+	53.0141i	−1.01297	+	1.75451i
$914$	10.4282	−	18.0622i	0.344934	−	0.597444i
$915$		0			0
$916$	−2.23205	−	3.86603i	−0.0737490	−	0.127737i
$917$	−17.4641			−0.576715
$918$		0			0
$919$	−24.9808			−0.824039			−0.412020	−	0.911175i	$-0.635176\pi$
$919$	−24.9808			−0.824039			−0.412020	+	0.911175i	$0.635176\pi$
$920$	11.5622	+	20.0263i	0.381194	+	0.660247i
$921$		0			0
$922$	17.3923	−	30.1244i	0.572785	−	0.992093i
$923$	−3.12436	+	5.41154i	−0.102839	+	0.178123i
$924$		0			0
$925$	29.7321	+	51.4974i	0.977584	+	1.69322i
$926$	32.5885			1.07092
$927$		0			0
$928$	−8.46410			−0.277848
$929$	−22.7487	−	39.4019i	−0.746361	−	1.29274i	−0.949556	−	0.313597i	$-0.898466\pi$
$929$	−22.7487	−	39.4019i	−0.746361	−	1.29274i	0.203195	−	0.979138i	$-0.434867\pi$
$930$		0			0
$931$	1.36603	−	2.36603i	0.0447697	−	0.0775434i
$932$	6.59808	−	11.4282i	0.216127	−	0.374343i
$933$		0			0
$934$	7.29423	+	12.6340i	0.238674	+	0.413396i
$935$	−109.622			−3.58502
$936$		0			0
$937$	53.8372			1.75878			0.879392	−	0.476099i	$-0.157950\pi$
$937$	53.8372			1.75878			0.879392	+	0.476099i	$0.157950\pi$
$938$	1.63397	+	2.83013i	0.0533512	+	0.0924069i
$939$		0			0
$940$	−2.36603	+	4.09808i	−0.0771712	+	0.133665i
$941$	4.93782	−	8.55256i	0.160968	−	0.278805i	−0.774248	−	0.632883i	$-0.781872\pi$
$941$	4.93782	−	8.55256i	0.160968	−	0.278805i	0.935216	+	0.354077i	$0.115205\pi$
$942$		0			0
$943$	−29.3205	−	50.7846i	−0.954807	−	1.65377i
$944$	−6.19615			−0.201668
$945$		0			0
$946$	22.9282			0.745460
$947$	−1.12436	−	1.94744i	−0.0365366	−	0.0632833i	0.847179	−	0.531308i	$-0.178299\pi$
$947$	−1.12436	−	1.94744i	−0.0365366	−	0.0632833i	−0.883715	+	0.468024i	$0.844966\pi$
$948$		0			0
$949$	−2.72243	+	4.71539i	−0.0883739	+	0.153068i
$950$	−12.1962	+	21.1244i	−0.395695	+	0.685365i
$951$		0			0
$952$	−3.50000	−	6.06218i	−0.113436	−	0.196476i
$953$	−10.4115			−0.337263			−0.168631	−	0.985679i	$-0.553935\pi$
$953$	−10.4115			−0.337263			−0.168631	+	0.985679i	$0.553935\pi$
$954$		0			0
$955$	43.5167			1.40817
$956$	−14.0263	−	24.2942i	−0.453642	−	0.785732i
$957$		0			0
$958$	11.7583	−	20.3660i	0.379894	−	0.657996i
$959$	−5.86603	+	10.1603i	−0.189424	+	0.328092i
$960$		0			0
$961$	13.0885	+	22.6699i	0.422208	+	0.731286i
$962$	3.09103			0.0996590
$963$		0			0
$964$	−17.7321			−0.571111
$965$	16.5263	+	28.6244i	0.532000	+	0.921451i
$966$		0			0
$967$	−6.83013	+	11.8301i	−0.219642	+	0.380431i	−0.954699	−	0.297575i	$-0.903822\pi$
$967$	−6.83013	+	11.8301i	−0.219642	+	0.380431i	0.735056	+	0.678006i	$0.237156\pi$
$968$	3.30385	−	5.72243i	0.106190	−	0.183926i
$969$		0			0
$970$	−5.46410	−	9.46410i	−0.175442	−	0.303874i
$971$	33.1244			1.06301			0.531506	−	0.847055i	$-0.321626\pi$
$971$	33.1244			1.06301			0.531506	+	0.847055i	$0.321626\pi$
$972$		0			0
$973$	6.73205			0.215820
$974$	−14.2942	−	24.7583i	−0.458017	−	0.793308i
$975$		0			0
$976$	4.96410	−	8.59808i	0.158897	−	0.275218i
$977$	−1.14359	+	1.98076i	−0.0365868	+	0.0633702i	−0.883739	−	0.467980i	$-0.844982\pi$
$977$	−1.14359	+	1.98076i	−0.0365868	+	0.0633702i	0.847152	+	0.531350i	$0.178315\pi$
$978$		0			0
$979$	−8.24167	−	14.2750i	−0.263405	−	0.456231i
$980$	3.73205			0.119216
$981$		0			0
$982$	−33.4641			−1.06788
$983$	5.32051	+	9.21539i	0.169698	+	0.293925i	0.938314	−	0.345785i	$-0.112387\pi$
$983$	5.32051	+	9.21539i	0.169698	+	0.293925i	−0.768616	+	0.639711i	$0.779054\pi$
$984$		0			0
$985$	48.1147	−	83.3372i	1.53306	−	2.65534i
$986$	29.6244	−	51.3109i	0.943432	−	1.63407i
$987$		0			0
$988$	0.633975	+	1.09808i	0.0201694	+	0.0349345i
$989$	33.8564			1.07657
$990$		0			0
$991$	−10.3397			−0.328453			−0.164226	−	0.986423i	$-0.552513\pi$
$991$	−10.3397			−0.328453			−0.164226	+	0.986423i	$0.552513\pi$
$992$	−1.09808	−	1.90192i	−0.0348640	−	0.0603861i
$993$		0			0
$994$	−6.73205	+	11.6603i	−0.213528	+	0.369841i
$995$	−9.56218	+	16.5622i	−0.303141	+	0.525056i
$996$		0			0
$997$	3.62436	+	6.27757i	0.114784	+	0.198813i	0.917694	−	0.397289i	$-0.130049\pi$
$997$	3.62436	+	6.27757i	0.114784	+	0.198813i	−0.802909	+	0.596101i	$0.796716\pi$
$998$	−30.1962			−0.955843
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.f.s.757.1		4
3.2	odd	2		1134.2.f.r.757.2		4
9.2	odd	6		1134.2.f.r.379.2		4
9.4	even	3		1134.2.a.l.1.2	✓	2
9.5	odd	6		1134.2.a.m.1.1	yes	2
9.7	even	3	inner	1134.2.f.s.379.1		4
36.23	even	6		9072.2.a.y.1.1		2
36.31	odd	6		9072.2.a.bp.1.2		2
63.13	odd	6		7938.2.a.bg.1.1		2
63.41	even	6		7938.2.a.bt.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.a.l.1.2	✓	2	9.4	even	3
1134.2.a.m.1.1	yes	2	9.5	odd	6
1134.2.f.r.379.2		4	9.2	odd	6
1134.2.f.r.757.2		4	3.2	odd	2
1134.2.f.s.379.1		4	9.7	even	3	inner
1134.2.f.s.757.1		4	1.1	even	1	trivial
7938.2.a.bg.1.1		2	63.13	odd	6
7938.2.a.bt.1.2		2	63.41	even	6
9072.2.a.y.1.1		2	36.23	even	6
9072.2.a.bp.1.2		2	36.31	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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.86603 + 3.23205i) q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.86603 + 3.23205i) q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} -3.73205 q^{10} +(2.09808 + 3.63397i) q^{11} +(-0.232051 + 0.401924i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +7.00000 q^{17} -2.73205 q^{19} +(-1.86603 - 3.23205i) q^{20} +(-2.09808 + 3.63397i) q^{22} +(-3.09808 + 5.36603i) q^{23} +(-4.46410 - 7.73205i) q^{25} -0.464102 q^{26} -1.00000 q^{28} +(-4.23205 - 7.33013i) q^{29} +(1.09808 - 1.90192i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.50000 + 6.06218i) q^{34} -3.73205 q^{35} -6.66025 q^{37} +(-1.36603 - 2.36603i) q^{38} +(1.86603 - 3.23205i) q^{40} +(-4.73205 + 8.19615i) q^{41} +(-2.73205 - 4.73205i) q^{43} -4.19615 q^{44} -6.19615 q^{46} +(-0.633975 - 1.09808i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(4.46410 - 7.73205i) q^{50} +(-0.232051 - 0.401924i) q^{52} -2.53590 q^{53} -15.6603 q^{55} +(-0.500000 - 0.866025i) q^{56} +(4.23205 - 7.33013i) q^{58} +(3.09808 - 5.36603i) q^{59} +(4.96410 + 8.59808i) q^{61} +2.19615 q^{62} +1.00000 q^{64} +(-0.866025 - 1.50000i) q^{65} +(1.63397 - 2.83013i) q^{67} +(-3.50000 + 6.06218i) q^{68} +(-1.86603 - 3.23205i) q^{70} +13.4641 q^{71} +11.7321 q^{73} +(-3.33013 - 5.76795i) q^{74} +(1.36603 - 2.36603i) q^{76} +(-2.09808 + 3.63397i) q^{77} +(-7.56218 - 13.0981i) q^{79} +3.73205 q^{80} -9.46410 q^{82} +(7.29423 + 12.6340i) q^{83} +(-13.0622 + 22.6244i) q^{85} +(2.73205 - 4.73205i) q^{86} +(-2.09808 - 3.63397i) q^{88} -3.92820 q^{89} -0.464102 q^{91} +(-3.09808 - 5.36603i) q^{92} +(0.633975 - 1.09808i) q^{94} +(5.09808 - 8.83013i) q^{95} +(1.46410 + 2.53590i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} + 2 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 + 2 * q^7 - 4 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} + 2 q^{7} - 4 q^{8} - 8 q^{10} - 2 q^{11} + 6 q^{13} - 2 q^{14} - 2 q^{16} + 28 q^{17} - 4 q^{19} - 4 q^{20} + 2 q^{22} - 2 q^{23} - 4 q^{25} + 12 q^{26} - 4 q^{28} - 10 q^{29} - 6 q^{31} + 2 q^{32} + 14 q^{34} - 8 q^{35} + 8 q^{37} - 2 q^{38} + 4 q^{40} - 12 q^{41} - 4 q^{43} + 4 q^{44} - 4 q^{46} - 6 q^{47} - 2 q^{49} + 4 q^{50} + 6 q^{52} - 24 q^{53} - 28 q^{55} - 2 q^{56} + 10 q^{58} + 2 q^{59} + 6 q^{61} - 12 q^{62} + 4 q^{64} + 10 q^{67} - 14 q^{68} - 4 q^{70} + 40 q^{71} + 40 q^{73} + 4 q^{74} + 2 q^{76} + 2 q^{77} - 6 q^{79} + 8 q^{80} - 24 q^{82} - 2 q^{83} - 28 q^{85} + 4 q^{86} + 2 q^{88} + 12 q^{89} + 12 q^{91} - 2 q^{92} + 6 q^{94} + 10 q^{95} - 8 q^{97} - 4 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 + 2 * q^7 - 4 * q^8 - 8 * q^10 - 2 * q^11 + 6 * q^13 - 2 * q^14 - 2 * q^16 + 28 * q^17 - 4 * q^19 - 4 * q^20 + 2 * q^22 - 2 * q^23 - 4 * q^25 + 12 * q^26 - 4 * q^28 - 10 * q^29 - 6 * q^31 + 2 * q^32 + 14 * q^34 - 8 * q^35 + 8 * q^37 - 2 * q^38 + 4 * q^40 - 12 * q^41 - 4 * q^43 + 4 * q^44 - 4 * q^46 - 6 * q^47 - 2 * q^49 + 4 * q^50 + 6 * q^52 - 24 * q^53 - 28 * q^55 - 2 * q^56 + 10 * q^58 + 2 * q^59 + 6 * q^61 - 12 * q^62 + 4 * q^64 + 10 * q^67 - 14 * q^68 - 4 * q^70 + 40 * q^71 + 40 * q^73 + 4 * q^74 + 2 * q^76 + 2 * q^77 - 6 * q^79 + 8 * q^80 - 24 * q^82 - 2 * q^83 - 28 * q^85 + 4 * q^86 + 2 * q^88 + 12 * q^89 + 12 * q^91 - 2 * q^92 + 6 * q^94 + 10 * q^95 - 8 * q^97 - 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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