LMFDB - Embedded newform 1134.2.f.t.379.1

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			379.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1134.379
Dual form			1134.2.f.t.757.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} -1.73205 q^{10} +(2.36603 - 4.09808i) q^{11} +(0.500000 + 0.866025i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} -6.46410 q^{17} -6.19615 q^{19} +(-0.866025 + 1.50000i) q^{20} +(-2.36603 - 4.09808i) q^{22} +(0.633975 + 1.09808i) q^{23} +(1.00000 - 1.73205i) q^{25} +1.00000 q^{26} +1.00000 q^{28} +(3.23205 - 5.59808i) q^{29} +(-2.09808 - 3.63397i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.23205 + 5.59808i) q^{34} +1.73205 q^{35} -3.19615 q^{37} +(-3.09808 + 5.36603i) q^{38} +(0.866025 + 1.50000i) q^{40} +(1.26795 + 2.19615i) q^{41} +(-6.19615 + 10.7321i) q^{43} -4.73205 q^{44} +1.26795 q^{46} +(1.09808 - 1.90192i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-1.00000 - 1.73205i) q^{50} +(0.500000 - 0.866025i) q^{52} -9.46410 q^{53} -8.19615 q^{55} +(0.500000 - 0.866025i) q^{56} +(-3.23205 - 5.59808i) q^{58} +(-4.09808 - 7.09808i) q^{59} +(-4.69615 + 8.13397i) q^{61} -4.19615 q^{62} +1.00000 q^{64} +(0.866025 - 1.50000i) q^{65} +(-2.09808 - 3.63397i) q^{67} +(3.23205 + 5.59808i) q^{68} +(0.866025 - 1.50000i) q^{70} +4.39230 q^{71} -9.19615 q^{73} +(-1.59808 + 2.76795i) q^{74} +(3.09808 + 5.36603i) q^{76} +(2.36603 + 4.09808i) q^{77} +(3.09808 - 5.36603i) q^{79} +1.73205 q^{80} +2.53590 q^{82} +(0.633975 - 1.09808i) q^{83} +(5.59808 + 9.69615i) q^{85} +(6.19615 + 10.7321i) q^{86} +(-2.36603 + 4.09808i) q^{88} +12.4641 q^{89} -1.00000 q^{91} +(0.633975 - 1.09808i) q^{92} +(-1.09808 - 1.90192i) q^{94} +(5.36603 + 9.29423i) q^{95} +(8.00000 - 13.8564i) q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 2 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^7 - 4 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} - 2 q^{7} - 4 q^{8} + 6 q^{11} + 2 q^{13} + 2 q^{14} - 2 q^{16} - 12 q^{17} - 4 q^{19} - 6 q^{22} + 6 q^{23} + 4 q^{25} + 4 q^{26} + 4 q^{28} + 6 q^{29} + 2 q^{31} + 2 q^{32} - 6 q^{34} + 8 q^{37} - 2 q^{38} + 12 q^{41} - 4 q^{43} - 12 q^{44} + 12 q^{46} - 6 q^{47} - 2 q^{49} - 4 q^{50} + 2 q^{52} - 24 q^{53} - 12 q^{55} + 2 q^{56} - 6 q^{58} - 6 q^{59} + 2 q^{61} + 4 q^{62} + 4 q^{64} + 2 q^{67} + 6 q^{68} - 24 q^{71} - 16 q^{73} + 4 q^{74} + 2 q^{76} + 6 q^{77} + 2 q^{79} + 24 q^{82} + 6 q^{83} + 12 q^{85} + 4 q^{86} - 6 q^{88} + 36 q^{89} - 4 q^{91} + 6 q^{92} + 6 q^{94} + 18 q^{95} + 32 q^{97} - 4 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^7 - 4 * q^8 + 6 * q^11 + 2 * q^13 + 2 * q^14 - 2 * q^16 - 12 * q^17 - 4 * q^19 - 6 * q^22 + 6 * q^23 + 4 * q^25 + 4 * q^26 + 4 * q^28 + 6 * q^29 + 2 * q^31 + 2 * q^32 - 6 * q^34 + 8 * q^37 - 2 * q^38 + 12 * q^41 - 4 * q^43 - 12 * q^44 + 12 * q^46 - 6 * q^47 - 2 * q^49 - 4 * q^50 + 2 * q^52 - 24 * q^53 - 12 * q^55 + 2 * q^56 - 6 * q^58 - 6 * q^59 + 2 * q^61 + 4 * q^62 + 4 * q^64 + 2 * q^67 + 6 * q^68 - 24 * q^71 - 16 * q^73 + 4 * q^74 + 2 * q^76 + 6 * q^77 + 2 * q^79 + 24 * q^82 + 6 * q^83 + 12 * q^85 + 4 * q^86 - 6 * q^88 + 36 * q^89 - 4 * q^91 + 6 * q^92 + 6 * q^94 + 18 * q^95 + 32 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	−0.866025	−	1.50000i	−0.387298	−	0.670820i	0.604787	−	0.796387i	$-0.293258\pi$
$5$	−0.866025	−	1.50000i	−0.387298	−	0.670820i	−0.992085	+	0.125567i	$0.959925\pi$
$6$		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
$10$	−1.73205			−0.547723
$11$	2.36603	−	4.09808i	0.713384	−	1.23562i	−0.250196	−	0.968195i	$-0.580495\pi$
$11$	2.36603	−	4.09808i	0.713384	−	1.23562i	0.963580	−	0.267421i	$-0.0861715\pi$
$12$		0			0
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	0.926995	−	0.375073i	$-0.122382\pi$
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	−0.788320	+	0.615265i	$0.789049\pi$
$14$	0.500000	+	0.866025i	0.133631	+	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−6.46410			−1.56777			−0.783887	−	0.620903i	$-0.786766\pi$
$17$	−6.46410			−1.56777			−0.783887	+	0.620903i	$0.786766\pi$
$18$		0			0
$19$	−6.19615			−1.42149			−0.710747	−	0.703447i	$-0.751643\pi$
$19$	−6.19615			−1.42149			−0.710747	+	0.703447i	$0.751643\pi$
$20$	−0.866025	+	1.50000i	−0.193649	+	0.335410i
$21$		0			0
$22$	−2.36603	−	4.09808i	−0.504438	−	0.873713i
$23$	0.633975	+	1.09808i	0.132193	+	0.228965i	0.924522	−	0.381130i	$-0.124465\pi$
$23$	0.633975	+	1.09808i	0.132193	+	0.228965i	−0.792329	+	0.610094i	$0.791132\pi$
$24$		0			0
$25$	1.00000	−	1.73205i	0.200000	−	0.346410i
$26$	1.00000			0.196116
$27$		0			0
$28$	1.00000			0.188982
$29$	3.23205	−	5.59808i	0.600177	−	1.03954i	−0.392617	−	0.919702i	$-0.628430\pi$
$29$	3.23205	−	5.59808i	0.600177	−	1.03954i	0.992794	−	0.119835i	$-0.0382364\pi$
$30$		0			0
$31$	−2.09808	−	3.63397i	−0.376826	−	0.652681i	0.613773	−	0.789483i	$-0.289651\pi$
$31$	−2.09808	−	3.63397i	−0.376826	−	0.652681i	−0.990598	+	0.136802i	$0.956318\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−3.23205	+	5.59808i	−0.554292	+	0.960062i
$35$	1.73205			0.292770
$36$		0			0
$37$	−3.19615			−0.525444			−0.262722	−	0.964872i	$-0.584620\pi$
$37$	−3.19615			−0.525444			−0.262722	+	0.964872i	$0.584620\pi$
$38$	−3.09808	+	5.36603i	−0.502574	+	0.870484i
$39$		0			0
$40$	0.866025	+	1.50000i	0.136931	+	0.237171i
$41$	1.26795	+	2.19615i	0.198020	+	0.342981i	0.947886	−	0.318608i	$-0.103215\pi$
$41$	1.26795	+	2.19615i	0.198020	+	0.342981i	−0.749866	+	0.661590i	$0.769882\pi$
$42$		0			0
$43$	−6.19615	+	10.7321i	−0.944904	+	1.63662i	−0.188962	+	0.981984i	$0.560512\pi$
$43$	−6.19615	+	10.7321i	−0.944904	+	1.63662i	−0.755943	+	0.654638i	$0.772821\pi$
$44$	−4.73205			−0.713384
$45$		0			0
$46$	1.26795			0.186949
$47$	1.09808	−	1.90192i	0.160171	−	0.277424i	−0.774759	−	0.632257i	$-0.782129\pi$
$47$	1.09808	−	1.90192i	0.160171	−	0.277424i	0.934930	+	0.354833i	$0.115462\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−1.00000	−	1.73205i	−0.141421	−	0.244949i
$51$		0			0
$52$	0.500000	−	0.866025i	0.0693375	−	0.120096i
$53$	−9.46410			−1.29999			−0.649997	−	0.759937i	$-0.725230\pi$
$53$	−9.46410			−1.29999			−0.649997	+	0.759937i	$0.725230\pi$
$54$		0			0
$55$	−8.19615			−1.10517
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$		0			0
$58$	−3.23205	−	5.59808i	−0.424389	−	0.735063i
$59$	−4.09808	−	7.09808i	−0.533524	−	0.924091i	−0.999233	−	0.0391530i	$-0.987534\pi$
$59$	−4.09808	−	7.09808i	−0.533524	−	0.924091i	0.465709	−	0.884938i	$-0.345799\pi$
$60$		0			0
$61$	−4.69615	+	8.13397i	−0.601281	+	1.04145i	0.391347	+	0.920243i	$0.372009\pi$
$61$	−4.69615	+	8.13397i	−0.601281	+	1.04145i	−0.992627	+	0.121205i	$0.961324\pi$
$62$	−4.19615			−0.532912
$63$		0			0
$64$	1.00000			0.125000
$65$	0.866025	−	1.50000i	0.107417	−	0.186052i
$66$		0			0
$67$	−2.09808	−	3.63397i	−0.256321	−	0.443961i	0.708933	−	0.705276i	$-0.249177\pi$
$67$	−2.09808	−	3.63397i	−0.256321	−	0.443961i	−0.965253	+	0.261316i	$0.915844\pi$
$68$	3.23205	+	5.59808i	0.391944	+	0.678866i
$69$		0			0
$70$	0.866025	−	1.50000i	0.103510	−	0.179284i
$71$	4.39230			0.521271			0.260635	−	0.965437i	$-0.416068\pi$
$71$	4.39230			0.521271			0.260635	+	0.965437i	$0.416068\pi$
$72$		0			0
$73$	−9.19615			−1.07633			−0.538164	−	0.842840i	$-0.680882\pi$
$73$	−9.19615			−1.07633			−0.538164	+	0.842840i	$0.680882\pi$
$74$	−1.59808	+	2.76795i	−0.185773	+	0.321768i
$75$		0			0
$76$	3.09808	+	5.36603i	0.355374	+	0.615525i
$77$	2.36603	+	4.09808i	0.269634	+	0.467019i
$78$		0			0
$79$	3.09808	−	5.36603i	0.348561	−	0.603725i	−0.637433	−	0.770506i	$-0.720004\pi$
$79$	3.09808	−	5.36603i	0.348561	−	0.603725i	0.985994	+	0.166781i	$0.0533372\pi$
$80$	1.73205			0.193649
$81$		0			0
$82$	2.53590			0.280043
$83$	0.633975	−	1.09808i	0.0695878	−	0.120530i	−0.829132	−	0.559053i	$-0.811165\pi$
$83$	0.633975	−	1.09808i	0.0695878	−	0.120530i	0.898720	+	0.438523i	$0.144498\pi$
$84$		0			0
$85$	5.59808	+	9.69615i	0.607197	+	1.05170i
$86$	6.19615	+	10.7321i	0.668148	+	1.15727i
$87$		0			0
$88$	−2.36603	+	4.09808i	−0.252219	+	0.436856i
$89$	12.4641			1.32119			0.660596	−	0.750742i	$-0.270304\pi$
$89$	12.4641			1.32119			0.660596	+	0.750742i	$0.270304\pi$
$90$		0			0
$91$	−1.00000			−0.104828
$92$	0.633975	−	1.09808i	0.0660964	−	0.114482i
$93$		0			0
$94$	−1.09808	−	1.90192i	−0.113258	−	0.196168i
$95$	5.36603	+	9.29423i	0.550543	+	0.953568i
$96$		0			0
$97$	8.00000	−	13.8564i	0.812277	−	1.40690i	−0.0989899	−	0.995088i	$-0.531561\pi$
$97$	8.00000	−	13.8564i	0.812277	−	1.40690i	0.911267	−	0.411816i	$-0.135106\pi$
$98$	−1.00000			−0.101015
$99$		0			0
$100$	−2.00000			−0.200000
$101$	6.46410	−	11.1962i	0.643202	−	1.11406i	−0.341511	−	0.939878i	$-0.610939\pi$
$101$	6.46410	−	11.1962i	0.643202	−	1.11406i	0.984714	−	0.174181i	$-0.0557278\pi$
$102$		0			0
$103$	4.19615	+	7.26795i	0.413459	+	0.716132i	0.995265	−	0.0971952i	$-0.0309871\pi$
$103$	4.19615	+	7.26795i	0.413459	+	0.716132i	−0.581806	+	0.813327i	$0.697654\pi$
$104$	−0.500000	−	0.866025i	−0.0490290	−	0.0849208i
$105$		0			0
$106$	−4.73205	+	8.19615i	−0.459617	+	0.796081i
$107$	13.8564			1.33955			0.669775	−	0.742564i	$-0.266391\pi$
$107$	13.8564			1.33955			0.669775	+	0.742564i	$0.266391\pi$
$108$		0			0
$109$	−4.80385			−0.460125			−0.230063	−	0.973176i	$-0.573893\pi$
$109$	−4.80385			−0.460125			−0.230063	+	0.973176i	$0.573893\pi$
$110$	−4.09808	+	7.09808i	−0.390736	+	0.676775i
$111$		0			0
$112$	−0.500000	−	0.866025i	−0.0472456	−	0.0818317i
$113$	−5.13397	−	8.89230i	−0.482964	−	0.836518i	0.516845	−	0.856079i	$-0.327106\pi$
$113$	−5.13397	−	8.89230i	−0.482964	−	0.836518i	−0.999809	+	0.0195613i	$0.993773\pi$
$114$		0			0
$115$	1.09808	−	1.90192i	0.102396	−	0.177355i
$116$	−6.46410			−0.600177
$117$		0			0
$118$	−8.19615			−0.754517
$119$	3.23205	−	5.59808i	0.296282	−	0.513175i
$120$		0			0
$121$	−5.69615	−	9.86603i	−0.517832	−	0.896911i
$122$	4.69615	+	8.13397i	0.425170	+	0.736415i
$123$		0			0
$124$	−2.09808	+	3.63397i	−0.188413	+	0.326341i
$125$	−12.1244			−1.08444
$126$		0			0
$127$	−4.00000			−0.354943			−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000			−0.354943			−0.177471	+	0.984126i	$0.556792\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−0.866025	−	1.50000i	−0.0759555	−	0.131559i
$131$	−1.26795	−	2.19615i	−0.110781	−	0.191879i	0.805304	−	0.592862i	$-0.202002\pi$
$131$	−1.26795	−	2.19615i	−0.110781	−	0.191879i	−0.916085	+	0.400983i	$0.868669\pi$
$132$		0			0
$133$	3.09808	−	5.36603i	0.268637	−	0.465293i
$134$	−4.19615			−0.362492
$135$		0			0
$136$	6.46410			0.554292
$137$	−1.33013	+	2.30385i	−0.113640	+	0.196831i	−0.917235	−	0.398345i	$-0.869585\pi$
$137$	−1.33013	+	2.30385i	−0.113640	+	0.196831i	0.803595	+	0.595176i	$0.202918\pi$
$138$		0			0
$139$	9.09808	+	15.7583i	0.771689	+	1.33660i	0.936637	+	0.350302i	$0.113921\pi$
$139$	9.09808	+	15.7583i	0.771689	+	1.33660i	−0.164948	+	0.986302i	$0.552746\pi$
$140$	−0.866025	−	1.50000i	−0.0731925	−	0.126773i
$141$		0			0
$142$	2.19615	−	3.80385i	0.184297	−	0.319212i
$143$	4.73205			0.395714
$144$		0			0
$145$	−11.1962			−0.929790
$146$	−4.59808	+	7.96410i	−0.380539	+	0.659114i
$147$		0			0
$148$	1.59808	+	2.76795i	0.131361	+	0.227524i
$149$	−1.96410	−	3.40192i	−0.160905	−	0.278696i	0.774288	−	0.632833i	$-0.218108\pi$
$149$	−1.96410	−	3.40192i	−0.160905	−	0.278696i	−0.935194	+	0.354137i	$0.884775\pi$
$150$		0			0
$151$	11.2942	−	19.5622i	0.919111	−	1.59195i	0.118343	−	0.992973i	$-0.462242\pi$
$151$	11.2942	−	19.5622i	0.919111	−	1.59195i	0.800768	−	0.598975i	$-0.204425\pi$
$152$	6.19615			0.502574
$153$		0			0
$154$	4.73205			0.381320
$155$	−3.63397	+	6.29423i	−0.291888	+	0.505565i
$156$		0			0
$157$	−7.69615	−	13.3301i	−0.614220	−	1.06386i	−0.990521	−	0.137362i	$-0.956137\pi$
$157$	−7.69615	−	13.3301i	−0.614220	−	1.06386i	0.376301	−	0.926497i	$-0.377196\pi$
$158$	−3.09808	−	5.36603i	−0.246470	−	0.426898i
$159$		0			0
$160$	0.866025	−	1.50000i	0.0684653	−	0.118585i
$161$	−1.26795			−0.0999284
$162$		0			0
$163$	24.3923			1.91055			0.955276	−	0.295714i	$-0.0955577\pi$
$163$	24.3923			1.91055			0.955276	+	0.295714i	$0.0955577\pi$
$164$	1.26795	−	2.19615i	0.0990102	−	0.171491i
$165$		0			0
$166$	−0.633975	−	1.09808i	−0.0492060	−	0.0852272i
$167$	−3.63397	−	6.29423i	−0.281205	−	0.487062i	0.690477	−	0.723355i	$-0.257401\pi$
$167$	−3.63397	−	6.29423i	−0.281205	−	0.487062i	−0.971682	+	0.236293i	$0.924068\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$	11.1962			0.858706
$171$		0			0
$172$	12.3923			0.944904
$173$	−6.40192	+	11.0885i	−0.486729	+	0.843040i	−0.999884	−	0.0152565i	$-0.995144\pi$
$173$	−6.40192	+	11.0885i	−0.486729	+	0.843040i	0.513154	+	0.858296i	$0.328477\pi$
$174$		0			0
$175$	1.00000	+	1.73205i	0.0755929	+	0.130931i
$176$	2.36603	+	4.09808i	0.178346	+	0.308904i
$177$		0			0
$178$	6.23205	−	10.7942i	0.467112	−	0.809062i
$179$	−7.26795			−0.543232			−0.271616	−	0.962406i	$-0.587558\pi$
$179$	−7.26795			−0.543232			−0.271616	+	0.962406i	$0.587558\pi$
$180$		0			0
$181$	0.392305			0.0291598			0.0145799	−	0.999894i	$-0.495359\pi$
$181$	0.392305			0.0291598			0.0145799	+	0.999894i	$0.495359\pi$
$182$	−0.500000	+	0.866025i	−0.0370625	+	0.0641941i
$183$		0			0
$184$	−0.633975	−	1.09808i	−0.0467372	−	0.0809513i
$185$	2.76795	+	4.79423i	0.203504	+	0.352479i
$186$		0			0
$187$	−15.2942	+	26.4904i	−1.11842	+	1.93717i
$188$	−2.19615			−0.160171
$189$		0			0
$190$	10.7321			0.778585
$191$	12.2942	−	21.2942i	0.889579	−	1.54080i	0.0492056	−	0.998789i	$-0.484331\pi$
$191$	12.2942	−	21.2942i	0.889579	−	1.54080i	0.840374	−	0.542008i	$-0.182336\pi$
$192$		0			0
$193$	9.50000	+	16.4545i	0.683825	+	1.18442i	0.973805	+	0.227387i	$0.0730182\pi$
$193$	9.50000	+	16.4545i	0.683825	+	1.18442i	−0.289980	+	0.957033i	$0.593649\pi$
$194$	−8.00000	−	13.8564i	−0.574367	−	0.994832i
$195$		0			0
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	15.0000			1.06871			0.534353	−	0.845262i	$-0.320555\pi$
$197$	15.0000			1.06871			0.534353	+	0.845262i	$0.320555\pi$
$198$		0			0
$199$	20.5885			1.45948			0.729739	−	0.683726i	$-0.239642\pi$
$199$	20.5885			1.45948			0.729739	+	0.683726i	$0.239642\pi$
$200$	−1.00000	+	1.73205i	−0.0707107	+	0.122474i
$201$		0			0
$202$	−6.46410	−	11.1962i	−0.454813	−	0.787759i
$203$	3.23205	+	5.59808i	0.226845	+	0.392908i
$204$		0			0
$205$	2.19615	−	3.80385i	0.153386	−	0.265672i
$206$	8.39230			0.584720
$207$		0			0
$208$	−1.00000			−0.0693375
$209$	−14.6603	+	25.3923i	−1.01407	+	1.75642i
$210$		0			0
$211$	−5.90192	−	10.2224i	−0.406305	−	0.703741i	0.588167	−	0.808739i	$-0.299850\pi$
$211$	−5.90192	−	10.2224i	−0.406305	−	0.703741i	−0.994472	+	0.104998i	$0.966516\pi$
$212$	4.73205	+	8.19615i	0.324999	+	0.562914i
$213$		0			0
$214$	6.92820	−	12.0000i	0.473602	−	0.820303i
$215$	21.4641			1.46384
$216$		0			0
$217$	4.19615			0.284853
$218$	−2.40192	+	4.16025i	−0.162679	+	0.281768i
$219$		0			0
$220$	4.09808	+	7.09808i	0.276292	+	0.478552i
$221$	−3.23205	−	5.59808i	−0.217411	−	0.376567i
$222$		0			0
$223$	−6.19615	+	10.7321i	−0.414925	+	0.718671i	−0.995421	−	0.0955922i	$-0.969526\pi$
$223$	−6.19615	+	10.7321i	−0.414925	+	0.718671i	0.580496	+	0.814263i	$0.302859\pi$
$224$	−1.00000			−0.0668153
$225$		0			0
$226$	−10.2679			−0.683014
$227$	−2.53590	+	4.39230i	−0.168313	+	0.291528i	−0.937827	−	0.347103i	$-0.887165\pi$
$227$	−2.53590	+	4.39230i	−0.168313	+	0.291528i	0.769514	+	0.638631i	$0.220499\pi$
$228$		0			0
$229$	10.8923	+	18.8660i	0.719784	+	1.24670i	0.961085	+	0.276252i	$0.0890924\pi$
$229$	10.8923	+	18.8660i	0.719784	+	1.24670i	−0.241302	+	0.970450i	$0.577574\pi$
$230$	−1.09808	−	1.90192i	−0.0724050	−	0.125409i
$231$		0			0
$232$	−3.23205	+	5.59808i	−0.212195	+	0.367532i
$233$	−13.7321			−0.899617			−0.449808	−	0.893125i	$-0.648508\pi$
$233$	−13.7321			−0.899617			−0.449808	+	0.893125i	$0.648508\pi$
$234$		0			0
$235$	−3.80385			−0.248136
$236$	−4.09808	+	7.09808i	−0.266762	+	0.462045i
$237$		0			0
$238$	−3.23205	−	5.59808i	−0.209503	−	0.362869i
$239$	7.56218	+	13.0981i	0.489157	+	0.847244i	0.999922	−	0.0124759i	$-0.00397131\pi$
$239$	7.56218	+	13.0981i	0.489157	+	0.847244i	−0.510766	+	0.859720i	$0.670638\pi$
$240$		0			0
$241$	6.79423	−	11.7679i	0.437655	−	0.758040i	−0.559853	−	0.828592i	$-0.689143\pi$
$241$	6.79423	−	11.7679i	0.437655	−	0.758040i	0.997508	+	0.0705514i	$0.0224759\pi$
$242$	−11.3923			−0.732325
$243$		0			0
$244$	9.39230			0.601281
$245$	−0.866025	+	1.50000i	−0.0553283	+	0.0958315i
$246$		0			0
$247$	−3.09808	−	5.36603i	−0.197126	−	0.341432i
$248$	2.09808	+	3.63397i	0.133228	+	0.230758i
$249$		0			0
$250$	−6.06218	+	10.5000i	−0.383406	+	0.664078i
$251$	3.80385			0.240097			0.120048	−	0.992768i	$-0.461695\pi$
$251$	3.80385			0.240097			0.120048	+	0.992768i	$0.461695\pi$
$252$		0			0
$253$	6.00000			0.377217
$254$	−2.00000	+	3.46410i	−0.125491	+	0.217357i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−13.9641	−	24.1865i	−0.871057	−	1.50871i	−0.860905	−	0.508766i	$-0.830102\pi$
$257$	−13.9641	−	24.1865i	−0.871057	−	1.50871i	−0.0101519	−	0.999948i	$-0.503232\pi$
$258$		0			0
$259$	1.59808	−	2.76795i	0.0992996	−	0.171992i
$260$	−1.73205			−0.107417
$261$		0			0
$262$	−2.53590			−0.156668
$263$	7.56218	−	13.0981i	0.466304	−	0.807662i	−0.532955	−	0.846143i	$-0.678919\pi$
$263$	7.56218	−	13.0981i	0.466304	−	0.807662i	0.999259	+	0.0384813i	$0.0122520\pi$
$264$		0			0
$265$	8.19615	+	14.1962i	0.503486	+	0.872063i
$266$	−3.09808	−	5.36603i	−0.189955	−	0.329012i
$267$		0			0
$268$	−2.09808	+	3.63397i	−0.128160	+	0.221980i
$269$	−29.4449			−1.79529			−0.897643	−	0.440724i	$-0.854722\pi$
$269$	−29.4449			−1.79529			−0.897643	+	0.440724i	$0.854722\pi$
$270$		0			0
$271$	28.1962			1.71279			0.856397	−	0.516318i	$-0.172698\pi$
$271$	28.1962			1.71279			0.856397	+	0.516318i	$0.172698\pi$
$272$	3.23205	−	5.59808i	0.195972	−	0.339433i
$273$		0			0
$274$	1.33013	+	2.30385i	0.0803559	+	0.139181i
$275$	−4.73205	−	8.19615i	−0.285353	−	0.494247i
$276$		0			0
$277$	9.39230	−	16.2679i	0.564329	−	0.977446i	−0.432783	−	0.901498i	$-0.642468\pi$
$277$	9.39230	−	16.2679i	0.564329	−	0.977446i	0.997112	−	0.0759481i	$-0.0241983\pi$
$278$	18.1962			1.09133
$279$		0			0
$280$	−1.73205			−0.103510
$281$	−6.86603	+	11.8923i	−0.409593	+	0.709435i	−0.994844	−	0.101417i	$-0.967663\pi$
$281$	−6.86603	+	11.8923i	−0.409593	+	0.709435i	0.585251	+	0.810852i	$0.300996\pi$
$282$		0			0
$283$	−1.80385	−	3.12436i	−0.107228	−	0.185724i	0.807419	−	0.589979i	$-0.200864\pi$
$283$	−1.80385	−	3.12436i	−0.107228	−	0.185724i	−0.914646	+	0.404255i	$0.867531\pi$
$284$	−2.19615	−	3.80385i	−0.130318	−	0.225717i
$285$		0			0
$286$	2.36603	−	4.09808i	0.139906	−	0.242324i
$287$	−2.53590			−0.149689
$288$		0			0
$289$	24.7846			1.45792
$290$	−5.59808	+	9.69615i	−0.328730	+	0.569378i
$291$		0			0
$292$	4.59808	+	7.96410i	0.269082	+	0.466064i
$293$	−13.3301	−	23.0885i	−0.778754	−	1.34884i	−0.932660	−	0.360757i	$-0.882519\pi$
$293$	−13.3301	−	23.0885i	−0.778754	−	1.34884i	0.153906	−	0.988086i	$-0.450815\pi$
$294$		0			0
$295$	−7.09808	+	12.2942i	−0.413266	+	0.715798i
$296$	3.19615			0.185773
$297$		0			0
$298$	−3.92820			−0.227555
$299$	−0.633975	+	1.09808i	−0.0366637	+	0.0635034i
$300$		0			0
$301$	−6.19615	−	10.7321i	−0.357140	−	0.618585i
$302$	−11.2942	−	19.5622i	−0.649910	−	1.12568i
$303$		0			0
$304$	3.09808	−	5.36603i	0.177687	−	0.307763i
$305$	16.2679			0.931500
$306$		0			0
$307$	8.00000			0.456584			0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000			0.456584			0.228292	+	0.973593i	$0.426686\pi$
$308$	2.36603	−	4.09808i	0.134817	−	0.233510i
$309$		0			0
$310$	3.63397	+	6.29423i	0.206396	+	0.357488i
$311$	−11.4904	−	19.9019i	−0.651560	−	1.12853i	−0.982744	−	0.184969i	$-0.940782\pi$
$311$	−11.4904	−	19.9019i	−0.651560	−	1.12853i	0.331185	−	0.943566i	$-0.392552\pi$
$312$		0			0
$313$	−10.9904	+	19.0359i	−0.621213	+	1.07597i	0.368047	+	0.929807i	$0.380027\pi$
$313$	−10.9904	+	19.0359i	−0.621213	+	1.07597i	−0.989260	+	0.146165i	$0.953307\pi$
$314$	−15.3923			−0.868638
$315$		0			0
$316$	−6.19615			−0.348561
$317$	−0.696152	+	1.20577i	−0.0390998	+	0.0677229i	−0.884913	−	0.465756i	$-0.845782\pi$
$317$	−0.696152	+	1.20577i	−0.0390998	+	0.0677229i	0.845813	+	0.533479i	$0.179116\pi$
$318$		0			0
$319$	−15.2942	−	26.4904i	−0.856312	−	1.48318i
$320$	−0.866025	−	1.50000i	−0.0484123	−	0.0838525i
$321$		0			0
$322$	−0.633975	+	1.09808i	−0.0353300	+	0.0611934i
$323$	40.0526			2.22858
$324$		0			0
$325$	2.00000			0.110940
$326$	12.1962	−	21.1244i	0.675482	−	1.16997i
$327$		0			0
$328$	−1.26795	−	2.19615i	−0.0700108	−	0.121262i
$329$	1.09808	+	1.90192i	0.0605389	+	0.104856i
$330$		0			0
$331$	14.5885	−	25.2679i	0.801854	−	1.38885i	−0.116540	−	0.993186i	$-0.537180\pi$
$331$	14.5885	−	25.2679i	0.801854	−	1.38885i	0.918394	−	0.395666i	$-0.129486\pi$
$332$	−1.26795			−0.0695878
$333$		0			0
$334$	−7.26795			−0.397684
$335$	−3.63397	+	6.29423i	−0.198545	+	0.343890i
$336$		0			0
$337$	16.1962	+	28.0526i	0.882261	+	1.52812i	0.848822	+	0.528679i	$0.177313\pi$
$337$	16.1962	+	28.0526i	0.882261	+	1.52812i	0.0334391	+	0.999441i	$0.489354\pi$
$338$	−6.00000	−	10.3923i	−0.326357	−	0.565267i
$339$		0			0
$340$	5.59808	−	9.69615i	0.303598	−	0.525848i
$341$	−19.8564			−1.07528
$342$		0			0
$343$	1.00000			0.0539949
$344$	6.19615	−	10.7321i	0.334074	−	0.578633i
$345$		0			0
$346$	6.40192	+	11.0885i	0.344170	+	0.596119i
$347$	8.19615	+	14.1962i	0.439993	+	0.762089i	0.997688	−	0.0679560i	$-0.0216478\pi$
$347$	8.19615	+	14.1962i	0.439993	+	0.762089i	−0.557696	+	0.830045i	$0.688314\pi$
$348$		0			0
$349$	−6.19615	+	10.7321i	−0.331672	+	0.574474i	−0.982840	−	0.184461i	$-0.940946\pi$
$349$	−6.19615	+	10.7321i	−0.331672	+	0.574474i	0.651167	+	0.758934i	$0.274280\pi$
$350$	2.00000			0.106904
$351$		0			0
$352$	4.73205			0.252219
$353$	2.07180	−	3.58846i	0.110271	−	0.190994i	−0.805609	−	0.592448i	$-0.798162\pi$
$353$	2.07180	−	3.58846i	0.110271	−	0.190994i	0.915879	+	0.401454i	$0.131495\pi$
$354$		0			0
$355$	−3.80385	−	6.58846i	−0.201887	−	0.349679i
$356$	−6.23205	−	10.7942i	−0.330298	−	0.572093i
$357$		0			0
$358$	−3.63397	+	6.29423i	−0.192062	+	0.332660i
$359$	−18.9282			−0.998992			−0.499496	−	0.866316i	$-0.666482\pi$
$359$	−18.9282			−0.998992			−0.499496	+	0.866316i	$0.666482\pi$
$360$		0			0
$361$	19.3923			1.02065
$362$	0.196152	−	0.339746i	0.0103095	−	0.0178567i
$363$		0			0
$364$	0.500000	+	0.866025i	0.0262071	+	0.0453921i
$365$	7.96410	+	13.7942i	0.416860	+	0.722023i
$366$		0			0
$367$	2.29423	−	3.97372i	0.119758	−	0.207427i	−0.799914	−	0.600115i	$-0.795122\pi$
$367$	2.29423	−	3.97372i	0.119758	−	0.207427i	0.919672	+	0.392688i	$0.128455\pi$
$368$	−1.26795			−0.0660964
$369$		0			0
$370$	5.53590			0.287798
$371$	4.73205	−	8.19615i	0.245676	−	0.425523i
$372$		0			0
$373$	−10.0000	−	17.3205i	−0.517780	−	0.896822i	−0.999787	−	0.0206542i	$-0.993425\pi$
$373$	−10.0000	−	17.3205i	−0.517780	−	0.896822i	0.482006	−	0.876168i	$-0.339908\pi$
$374$	15.2942	+	26.4904i	0.790846	+	1.36978i
$375$		0			0
$376$	−1.09808	+	1.90192i	−0.0566290	+	0.0980842i
$377$	6.46410			0.332918
$378$		0			0
$379$	−16.5885			−0.852092			−0.426046	−	0.904702i	$-0.640094\pi$
$379$	−16.5885			−0.852092			−0.426046	+	0.904702i	$0.640094\pi$
$380$	5.36603	−	9.29423i	0.275271	−	0.476784i
$381$		0			0
$382$	−12.2942	−	21.2942i	−0.629027	−	1.08951i
$383$	−5.07180	−	8.78461i	−0.259157	−	0.448873i	0.706860	−	0.707354i	$-0.250111\pi$
$383$	−5.07180	−	8.78461i	−0.259157	−	0.448873i	−0.966016	+	0.258481i	$0.916778\pi$
$384$		0			0
$385$	4.09808	−	7.09808i	0.208857	−	0.361751i
$386$	19.0000			0.967075
$387$		0			0
$388$	−16.0000			−0.812277
$389$	−15.1244	+	26.1962i	−0.766835	+	1.32820i	0.172436	+	0.985021i	$0.444836\pi$
$389$	−15.1244	+	26.1962i	−0.766835	+	1.32820i	−0.939271	+	0.343177i	$0.888497\pi$
$390$		0			0
$391$	−4.09808	−	7.09808i	−0.207249	−	0.358965i
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$		0			0
$394$	7.50000	−	12.9904i	0.377845	−	0.654446i
$395$	−10.7321			−0.539988
$396$		0			0
$397$	−29.3923			−1.47516			−0.737579	−	0.675261i	$-0.764031\pi$
$397$	−29.3923			−1.47516			−0.737579	+	0.675261i	$0.764031\pi$
$398$	10.2942	−	17.8301i	0.516003	−	0.893744i
$399$		0			0
$400$	1.00000	+	1.73205i	0.0500000	+	0.0866025i
$401$	11.1340	+	19.2846i	0.556004	+	0.963027i	0.997825	+	0.0659240i	$0.0209995\pi$
$401$	11.1340	+	19.2846i	0.556004	+	0.963027i	−0.441820	+	0.897103i	$0.645667\pi$
$402$		0			0
$403$	2.09808	−	3.63397i	0.104513	−	0.181021i
$404$	−12.9282			−0.643202
$405$		0			0
$406$	6.46410			0.320808
$407$	−7.56218	+	13.0981i	−0.374843	+	0.649248i
$408$		0			0
$409$	10.5981	+	18.3564i	0.524041	+	0.907666i	0.999608	+	0.0279865i	$0.00890953\pi$
$409$	10.5981	+	18.3564i	0.524041	+	0.907666i	−0.475567	+	0.879679i	$0.657757\pi$
$410$	−2.19615	−	3.80385i	−0.108460	−	0.187859i
$411$		0			0
$412$	4.19615	−	7.26795i	0.206730	−	0.358066i
$413$	8.19615			0.403306
$414$		0			0
$415$	−2.19615			−0.107805
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$		0			0
$418$	14.6603	+	25.3923i	0.717056	+	1.24198i
$419$	11.6603	+	20.1962i	0.569641	+	0.986647i	0.996601	+	0.0823764i	$0.0262510\pi$
$419$	11.6603	+	20.1962i	0.569641	+	0.986647i	−0.426961	+	0.904270i	$0.640416\pi$
$420$		0			0
$421$	−6.59808	+	11.4282i	−0.321571	+	0.556977i	−0.980812	−	0.194955i	$-0.937544\pi$
$421$	−6.59808	+	11.4282i	−0.321571	+	0.556977i	0.659242	+	0.751931i	$0.270877\pi$
$422$	−11.8038			−0.574602
$423$		0			0
$424$	9.46410			0.459617
$425$	−6.46410	+	11.1962i	−0.313555	+	0.543093i
$426$		0			0
$427$	−4.69615	−	8.13397i	−0.227263	−	0.393631i
$428$	−6.92820	−	12.0000i	−0.334887	−	0.580042i
$429$		0			0
$430$	10.7321	−	18.5885i	0.517545	−	0.896415i
$431$	−0.679492			−0.0327300			−0.0163650	−	0.999866i	$-0.505209\pi$
$431$	−0.679492			−0.0327300			−0.0163650	+	0.999866i	$0.505209\pi$
$432$		0			0
$433$	−31.5885			−1.51804			−0.759022	−	0.651065i	$-0.774323\pi$
$433$	−31.5885			−1.51804			−0.759022	+	0.651065i	$0.774323\pi$
$434$	2.09808	−	3.63397i	0.100711	−	0.174436i
$435$		0			0
$436$	2.40192	+	4.16025i	0.115031	+	0.199240i
$437$	−3.92820	−	6.80385i	−0.187911	−	0.325472i
$438$		0			0
$439$	−10.5885	+	18.3397i	−0.505359	+	0.875308i	0.494621	+	0.869109i	$0.335307\pi$
$439$	−10.5885	+	18.3397i	−0.505359	+	0.875308i	−0.999981	+	0.00619971i	$0.998027\pi$
$440$	8.19615			0.390736
$441$		0			0
$442$	−6.46410			−0.307466
$443$	1.09808	−	1.90192i	0.0521712	−	0.0903631i	−0.838760	−	0.544501i	$-0.816719\pi$
$443$	1.09808	−	1.90192i	0.0521712	−	0.0903631i	0.890932	+	0.454138i	$0.150053\pi$
$444$		0			0
$445$	−10.7942	−	18.6962i	−0.511696	−	0.886283i
$446$	6.19615	+	10.7321i	0.293396	+	0.508177i
$447$		0			0
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$		0			0
$451$	12.0000			0.565058
$452$	−5.13397	+	8.89230i	−0.241482	+	0.418259i
$453$		0			0
$454$	2.53590	+	4.39230i	0.119016	+	0.206141i
$455$	0.866025	+	1.50000i	0.0405999	+	0.0703211i
$456$		0			0
$457$	0.500000	−	0.866025i	0.0233890	−	0.0405110i	−0.854094	−	0.520119i	$-0.825888\pi$
$457$	0.500000	−	0.866025i	0.0233890	−	0.0405110i	0.877483	+	0.479608i	$0.159221\pi$
$458$	21.7846			1.01793
$459$		0			0
$460$	−2.19615			−0.102396
$461$	5.53590	−	9.58846i	0.257832	−	0.446579i	−0.707829	−	0.706384i	$-0.750325\pi$
$461$	5.53590	−	9.58846i	0.257832	−	0.446579i	0.965661	+	0.259805i	$0.0836584\pi$
$462$		0			0
$463$	−2.90192	−	5.02628i	−0.134864	−	0.233591i	0.790682	−	0.612228i	$-0.209726\pi$
$463$	−2.90192	−	5.02628i	−0.134864	−	0.233591i	−0.925545	+	0.378637i	$0.876393\pi$
$464$	3.23205	+	5.59808i	0.150044	+	0.259884i
$465$		0			0
$466$	−6.86603	+	11.8923i	−0.318062	+	0.550900i
$467$	1.26795			0.0586737			0.0293368	−	0.999570i	$-0.490660\pi$
$467$	1.26795			0.0586737			0.0293368	+	0.999570i	$0.490660\pi$
$468$		0			0
$469$	4.19615			0.193760
$470$	−1.90192	+	3.29423i	−0.0877292	+	0.151951i
$471$		0			0
$472$	4.09808	+	7.09808i	0.188629	+	0.326715i
$473$	29.3205	+	50.7846i	1.34816	+	2.33508i
$474$		0			0
$475$	−6.19615	+	10.7321i	−0.284299	+	0.492420i
$476$	−6.46410			−0.296282
$477$		0			0
$478$	15.1244			0.691772
$479$	8.36603	−	14.4904i	0.382253	−	0.662082i	−0.609131	−	0.793070i	$-0.708481\pi$
$479$	8.36603	−	14.4904i	0.382253	−	0.662082i	0.991384	+	0.130988i	$0.0418148\pi$
$480$		0			0
$481$	−1.59808	−	2.76795i	−0.0728660	−	0.126208i
$482$	−6.79423	−	11.7679i	−0.309469	−	0.536015i
$483$		0			0
$484$	−5.69615	+	9.86603i	−0.258916	+	0.448456i
$485$	−27.7128			−1.25837
$486$		0			0
$487$	−6.19615			−0.280774			−0.140387	−	0.990097i	$-0.544835\pi$
$487$	−6.19615			−0.280774			−0.140387	+	0.990097i	$0.544835\pi$
$488$	4.69615	−	8.13397i	0.212585	−	0.368208i
$489$		0			0
$490$	0.866025	+	1.50000i	0.0391230	+	0.0677631i
$491$	5.66025	+	9.80385i	0.255444	+	0.442441i	0.965016	−	0.262191i	$-0.0844451\pi$
$491$	5.66025	+	9.80385i	0.255444	+	0.442441i	−0.709572	+	0.704633i	$0.751112\pi$
$492$		0			0
$493$	−20.8923	+	36.1865i	−0.940942	+	1.62976i
$494$	−6.19615			−0.278778
$495$		0			0
$496$	4.19615			0.188413
$497$	−2.19615	+	3.80385i	−0.0985109	+	0.170626i
$498$		0			0
$499$	−10.2942	−	17.8301i	−0.460833	−	0.798186i	0.538170	−	0.842836i	$-0.319116\pi$
$499$	−10.2942	−	17.8301i	−0.460833	−	0.798186i	−0.999003	+	0.0446504i	$0.985783\pi$
$500$	6.06218	+	10.5000i	0.271109	+	0.469574i
$501$		0			0
$502$	1.90192	−	3.29423i	0.0848870	−	0.147029i
$503$	22.9808			1.02466			0.512331	−	0.858788i	$-0.328782\pi$
$503$	22.9808			1.02466			0.512331	+	0.858788i	$0.328782\pi$
$504$		0			0
$505$	−22.3923			−0.996444
$506$	3.00000	−	5.19615i	0.133366	−	0.230997i
$507$		0			0
$508$	2.00000	+	3.46410i	0.0887357	+	0.153695i
$509$	−10.8564	−	18.8038i	−0.481202	−	0.833466i	0.518566	−	0.855038i	$-0.326466\pi$
$509$	−10.8564	−	18.8038i	−0.481202	−	0.833466i	−0.999767	+	0.0215720i	$0.993133\pi$
$510$		0			0
$511$	4.59808	−	7.96410i	0.203407	−	0.352311i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−27.9282			−1.23186
$515$	7.26795	−	12.5885i	0.320264	−	0.554714i
$516$		0			0
$517$	−5.19615	−	9.00000i	−0.228527	−	0.395820i
$518$	−1.59808	−	2.76795i	−0.0702154	−	0.121617i
$519$		0			0
$520$	−0.866025	+	1.50000i	−0.0379777	+	0.0657794i
$521$	−43.8564			−1.92138			−0.960692	−	0.277616i	$-0.910456\pi$
$521$	−43.8564			−1.92138			−0.960692	+	0.277616i	$0.910456\pi$
$522$		0			0
$523$	15.6077			0.682477			0.341238	−	0.939977i	$-0.389154\pi$
$523$	15.6077			0.682477			0.341238	+	0.939977i	$0.389154\pi$
$524$	−1.26795	+	2.19615i	−0.0553906	+	0.0959394i
$525$		0			0
$526$	−7.56218	−	13.0981i	−0.329727	−	0.571103i
$527$	13.5622	+	23.4904i	0.590778	+	1.02326i
$528$		0			0
$529$	10.6962	−	18.5263i	0.465050	−	0.805490i
$530$	16.3923			0.712036
$531$		0			0
$532$	−6.19615			−0.268637
$533$	−1.26795	+	2.19615i	−0.0549210	+	0.0951259i
$534$		0			0
$535$	−12.0000	−	20.7846i	−0.518805	−	0.898597i
$536$	2.09808	+	3.63397i	0.0906231	+	0.156964i
$537$		0			0
$538$	−14.7224	+	25.5000i	−0.634729	+	1.09938i
$539$	−4.73205			−0.203824
$540$		0			0
$541$	−31.5885			−1.35809			−0.679047	−	0.734095i	$-0.737607\pi$
$541$	−31.5885			−1.35809			−0.679047	+	0.734095i	$0.737607\pi$
$542$	14.0981	−	24.4186i	0.605564	−	1.04887i
$543$		0			0
$544$	−3.23205	−	5.59808i	−0.138573	−	0.240016i
$545$	4.16025	+	7.20577i	0.178206	+	0.308661i
$546$		0			0
$547$	9.90192	−	17.1506i	0.423376	−	0.733308i	−0.572892	−	0.819631i	$-0.694178\pi$
$547$	9.90192	−	17.1506i	0.423376	−	0.733308i	0.996267	+	0.0863230i	$0.0275117\pi$
$548$	2.66025			0.113640
$549$		0			0
$550$	−9.46410			−0.403551
$551$	−20.0263	+	34.6865i	−0.853148	+	1.47770i
$552$		0			0
$553$	3.09808	+	5.36603i	0.131744	+	0.228187i
$554$	−9.39230	−	16.2679i	−0.399041	−	0.691159i
$555$		0			0
$556$	9.09808	−	15.7583i	0.385844	−	0.668302i
$557$	−40.8564			−1.73114			−0.865571	−	0.500787i	$-0.833044\pi$
$557$	−40.8564			−1.73114			−0.865571	+	0.500787i	$0.833044\pi$
$558$		0			0
$559$	−12.3923			−0.524139
$560$	−0.866025	+	1.50000i	−0.0365963	+	0.0633866i
$561$		0			0
$562$	6.86603	+	11.8923i	0.289626	+	0.501647i
$563$	12.0000	+	20.7846i	0.505740	+	0.875967i	0.999978	+	0.00664037i	$0.00211371\pi$
$563$	12.0000	+	20.7846i	0.505740	+	0.875967i	−0.494238	+	0.869326i	$0.664553\pi$
$564$		0			0
$565$	−8.89230	+	15.4019i	−0.374102	+	0.647964i
$566$	−3.60770			−0.151643
$567$		0			0
$568$	−4.39230			−0.184297
$569$	−3.99038	+	6.91154i	−0.167285	+	0.289747i	−0.937465	−	0.348081i	$-0.886833\pi$
$569$	−3.99038	+	6.91154i	−0.167285	+	0.289747i	0.770179	+	0.637828i	$0.220167\pi$
$570$		0			0
$571$	9.90192	+	17.1506i	0.414383	+	0.717732i	0.995363	−	0.0961855i	$-0.0306642\pi$
$571$	9.90192	+	17.1506i	0.414383	+	0.717732i	−0.580981	+	0.813917i	$0.697331\pi$
$572$	−2.36603	−	4.09808i	−0.0989285	−	0.171349i
$573$		0			0
$574$	−1.26795	+	2.19615i	−0.0529232	+	0.0916656i
$575$	2.53590			0.105754
$576$		0			0
$577$	31.1962			1.29871			0.649356	−	0.760484i	$-0.275038\pi$
$577$	31.1962			1.29871			0.649356	+	0.760484i	$0.275038\pi$
$578$	12.3923	−	21.4641i	0.515452	−	0.892789i
$579$		0			0
$580$	5.59808	+	9.69615i	0.232447	+	0.402611i
$581$	0.633975	+	1.09808i	0.0263017	+	0.0455559i
$582$		0			0
$583$	−22.3923	+	38.7846i	−0.927395	+	1.60629i
$584$	9.19615			0.380539
$585$		0			0
$586$	−26.6603			−1.10132
$587$	−5.36603	+	9.29423i	−0.221480	+	0.383614i	−0.955257	−	0.295776i	$-0.904422\pi$
$587$	−5.36603	+	9.29423i	−0.221480	+	0.383614i	0.733778	+	0.679389i	$0.237755\pi$
$588$		0			0
$589$	13.0000	+	22.5167i	0.535656	+	0.927783i
$590$	7.09808	+	12.2942i	0.292223	+	0.506145i
$591$		0			0
$592$	1.59808	−	2.76795i	0.0656805	−	0.113762i
$593$	40.8564			1.67777			0.838886	−	0.544308i	$-0.183208\pi$
$593$	40.8564			1.67777			0.838886	+	0.544308i	$0.183208\pi$
$594$		0			0
$595$	−11.1962			−0.458997
$596$	−1.96410	+	3.40192i	−0.0804527	+	0.139348i
$597$		0			0
$598$	0.633975	+	1.09808i	0.0259251	+	0.0449037i
$599$	−1.90192	−	3.29423i	−0.0777105	−	0.134599i	0.824551	−	0.565787i	$-0.191428\pi$
$599$	−1.90192	−	3.29423i	−0.0777105	−	0.134599i	−0.902262	+	0.431189i	$0.858094\pi$
$600$		0			0
$601$	4.59808	−	7.96410i	0.187559	−	0.324862i	−0.756877	−	0.653558i	$-0.773276\pi$
$601$	4.59808	−	7.96410i	0.187559	−	0.324862i	0.944436	+	0.328695i	$0.106609\pi$
$602$	−12.3923			−0.505073
$603$		0			0
$604$	−22.5885			−0.919111
$605$	−9.86603	+	17.0885i	−0.401111	+	0.694745i
$606$		0			0
$607$	14.2942	+	24.7583i	0.580185	+	1.00491i	0.995457	+	0.0952124i	$0.0303530\pi$
$607$	14.2942	+	24.7583i	0.580185	+	1.00491i	−0.415272	+	0.909697i	$0.636314\pi$
$608$	−3.09808	−	5.36603i	−0.125644	−	0.217621i
$609$		0			0
$610$	8.13397	−	14.0885i	0.329335	−	0.570425i
$611$	2.19615			0.0888468
$612$		0			0
$613$	−6.78461			−0.274028			−0.137014	−	0.990569i	$-0.543751\pi$
$613$	−6.78461			−0.274028			−0.137014	+	0.990569i	$0.543751\pi$
$614$	4.00000	−	6.92820i	0.161427	−	0.279600i
$615$		0			0
$616$	−2.36603	−	4.09808i	−0.0953299	−	0.165116i
$617$	8.25833	+	14.3038i	0.332468	+	0.575851i	0.982995	−	0.183632i	$-0.0587854\pi$
$617$	8.25833	+	14.3038i	0.332468	+	0.575851i	−0.650527	+	0.759483i	$0.725452\pi$
$618$		0			0
$619$	2.00000	−	3.46410i	0.0803868	−	0.139234i	−0.823029	−	0.567999i	$-0.807718\pi$
$619$	2.00000	−	3.46410i	0.0803868	−	0.139234i	0.903416	+	0.428765i	$0.141051\pi$
$620$	7.26795			0.291888
$621$		0			0
$622$	−22.9808			−0.921445
$623$	−6.23205	+	10.7942i	−0.249682	+	0.432462i
$624$		0			0
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	10.9904	+	19.0359i	0.439264	+	0.760828i
$627$		0			0
$628$	−7.69615	+	13.3301i	−0.307110	+	0.531930i
$629$	20.6603			0.823778
$630$		0			0
$631$	−22.5885			−0.899232			−0.449616	−	0.893222i	$-0.648439\pi$
$631$	−22.5885			−0.899232			−0.449616	+	0.893222i	$0.648439\pi$
$632$	−3.09808	+	5.36603i	−0.123235	+	0.213449i
$633$		0			0
$634$	0.696152	+	1.20577i	0.0276477	+	0.0478873i
$635$	3.46410	+	6.00000i	0.137469	+	0.238103i
$636$		0			0
$637$	0.500000	−	0.866025i	0.0198107	−	0.0343132i
$638$	−30.5885			−1.21101
$639$		0			0
$640$	−1.73205			−0.0684653
$641$	4.66987	−	8.08846i	0.184449	−	0.319475i	−0.758942	−	0.651158i	$-0.774283\pi$
$641$	4.66987	−	8.08846i	0.184449	−	0.319475i	0.943391	+	0.331684i	$0.107617\pi$
$642$		0			0
$643$	−8.90192	−	15.4186i	−0.351058	−	0.608050i	0.635377	−	0.772202i	$-0.280845\pi$
$643$	−8.90192	−	15.4186i	−0.351058	−	0.608050i	−0.986435	+	0.164152i	$0.947511\pi$
$644$	0.633975	+	1.09808i	0.0249821	+	0.0432703i
$645$		0			0
$646$	20.0263	−	34.6865i	0.787923	−	1.36472i
$647$	23.3205			0.916824			0.458412	−	0.888740i	$-0.348418\pi$
$647$	23.3205			0.916824			0.458412	+	0.888740i	$0.348418\pi$
$648$		0			0
$649$	−38.7846			−1.52243
$650$	1.00000	−	1.73205i	0.0392232	−	0.0679366i
$651$		0			0
$652$	−12.1962	−	21.1244i	−0.477638	−	0.827294i
$653$	−17.6603	−	30.5885i	−0.691099	−	1.19702i	−0.971478	−	0.237129i	$-0.923793\pi$
$653$	−17.6603	−	30.5885i	−0.691099	−	1.19702i	0.280379	−	0.959889i	$-0.409540\pi$
$654$		0			0
$655$	−2.19615	+	3.80385i	−0.0858108	+	0.148629i
$656$	−2.53590			−0.0990102
$657$		0			0
$658$	2.19615			0.0856149
$659$	0.339746	−	0.588457i	0.0132346	−	0.0229230i	−0.859332	−	0.511418i	$-0.829120\pi$
$659$	0.339746	−	0.588457i	0.0132346	−	0.0229230i	0.872567	+	0.488495i	$0.162454\pi$
$660$		0			0
$661$	−16.6962	−	28.9186i	−0.649405	−	1.12480i	−0.983265	−	0.182180i	$-0.941685\pi$
$661$	−16.6962	−	28.9186i	−0.649405	−	1.12480i	0.333860	−	0.942623i	$-0.391649\pi$
$662$	−14.5885	−	25.2679i	−0.566996	−	0.982067i
$663$		0			0
$664$	−0.633975	+	1.09808i	−0.0246030	+	0.0426136i
$665$	−10.7321			−0.416171
$666$		0			0
$667$	8.19615			0.317356
$668$	−3.63397	+	6.29423i	−0.140603	+	0.243531i
$669$		0			0
$670$	3.63397	+	6.29423i	0.140393	+	0.243167i
$671$	22.2224	+	38.4904i	0.857887	+	1.48590i
$672$		0			0
$673$	−9.08846	+	15.7417i	−0.350334	+	0.606797i	−0.986308	−	0.164914i	$-0.947265\pi$
$673$	−9.08846	+	15.7417i	−0.350334	+	0.606797i	0.635974	+	0.771711i	$0.280599\pi$
$674$	32.3923			1.24770
$675$		0			0
$676$	−12.0000			−0.461538
$677$	22.3923	−	38.7846i	0.860606	−	1.49061i	−0.0107386	−	0.999942i	$-0.503418\pi$
$677$	22.3923	−	38.7846i	0.860606	−	1.49061i	0.871345	−	0.490671i	$-0.163248\pi$
$678$		0			0
$679$	8.00000	+	13.8564i	0.307012	+	0.531760i
$680$	−5.59808	−	9.69615i	−0.214676	−	0.371830i
$681$		0			0
$682$	−9.92820	+	17.1962i	−0.380171	+	0.658475i
$683$	39.7128			1.51957			0.759784	−	0.650175i	$-0.225305\pi$
$683$	39.7128			1.51957			0.759784	+	0.650175i	$0.225305\pi$
$684$		0			0
$685$	4.60770			0.176051
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$		0			0
$688$	−6.19615	−	10.7321i	−0.236226	−	0.409156i
$689$	−4.73205	−	8.19615i	−0.180277	−	0.312249i
$690$		0			0
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	0.0555386	+	0.998457i	$0.482312\pi$
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	−0.892458	+	0.451130i	$0.851021\pi$
$692$	12.8038			0.486729
$693$		0			0
$694$	16.3923			0.622243
$695$	15.7583	−	27.2942i	0.597748	−	1.03533i
$696$		0			0
$697$	−8.19615	−	14.1962i	−0.310451	−	0.537718i
$698$	6.19615	+	10.7321i	0.234528	+	0.406214i
$699$		0			0
$700$	1.00000	−	1.73205i	0.0377964	−	0.0654654i
$701$	−46.1769			−1.74408			−0.872039	−	0.489436i	$-0.837203\pi$
$701$	−46.1769			−1.74408			−0.872039	+	0.489436i	$0.837203\pi$
$702$		0			0
$703$	19.8038			0.746916
$704$	2.36603	−	4.09808i	0.0891729	−	0.154452i
$705$		0			0
$706$	−2.07180	−	3.58846i	−0.0779731	−	0.135053i
$707$	6.46410	+	11.1962i	0.243108	+	0.421075i
$708$		0			0
$709$	3.79423	−	6.57180i	0.142495	−	0.246809i	−0.785940	−	0.618302i	$-0.787821\pi$
$709$	3.79423	−	6.57180i	0.142495	−	0.246809i	0.928436	+	0.371493i	$0.121154\pi$
$710$	−7.60770			−0.285512
$711$		0			0
$712$	−12.4641			−0.467112
$713$	2.66025	−	4.60770i	0.0996273	−	0.172560i
$714$		0			0
$715$	−4.09808	−	7.09808i	−0.153259	−	0.265453i
$716$	3.63397	+	6.29423i	0.135808	+	0.235226i
$717$		0			0
$718$	−9.46410	+	16.3923i	−0.353197	+	0.611755i
$719$	−23.3205			−0.869708			−0.434854	−	0.900501i	$-0.643200\pi$
$719$	−23.3205			−0.869708			−0.434854	+	0.900501i	$0.643200\pi$
$720$		0			0
$721$	−8.39230			−0.312546
$722$	9.69615	−	16.7942i	0.360853	−	0.625016i
$723$		0			0
$724$	−0.196152	−	0.339746i	−0.00728995	−	0.0126266i
$725$	−6.46410	−	11.1962i	−0.240071	−	0.415815i
$726$		0			0
$727$	−7.80385	+	13.5167i	−0.289429	+	0.501305i	−0.973673	−	0.227947i	$-0.926799\pi$
$727$	−7.80385	+	13.5167i	−0.289429	+	0.501305i	0.684245	+	0.729252i	$0.260132\pi$
$728$	1.00000			0.0370625
$729$		0			0
$730$	15.9282			0.589529
$731$	40.0526	−	69.3731i	1.48140	−	2.56586i
$732$		0			0
$733$	14.5885	+	25.2679i	0.538837	+	0.933293i	0.998967	+	0.0454415i	$0.0144694\pi$
$733$	14.5885	+	25.2679i	0.538837	+	0.933293i	−0.460130	+	0.887852i	$0.652197\pi$
$734$	−2.29423	−	3.97372i	−0.0846815	−	0.146673i
$735$		0			0
$736$	−0.633975	+	1.09808i	−0.0233686	+	0.0404756i
$737$	−19.8564			−0.731420
$738$		0			0
$739$	−24.1962			−0.890070			−0.445035	−	0.895513i	$-0.646809\pi$
$739$	−24.1962			−0.890070			−0.445035	+	0.895513i	$0.646809\pi$
$740$	2.76795	−	4.79423i	0.101752	−	0.176239i
$741$		0			0
$742$	−4.73205	−	8.19615i	−0.173719	−	0.300890i
$743$	−10.7321	−	18.5885i	−0.393721	−	0.681944i	0.599216	−	0.800587i	$-0.295479\pi$
$743$	−10.7321	−	18.5885i	−0.393721	−	0.681944i	−0.992937	+	0.118643i	$0.962146\pi$
$744$		0			0
$745$	−3.40192	+	5.89230i	−0.124637	+	0.215877i
$746$	−20.0000			−0.732252
$747$		0			0
$748$	30.5885			1.11842
$749$	−6.92820	+	12.0000i	−0.253151	+	0.438470i
$750$		0			0
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	0.900207	−	0.435463i	$-0.143415\pi$
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	−0.827225	+	0.561870i	$0.810082\pi$
$752$	1.09808	+	1.90192i	0.0400427	+	0.0693560i
$753$		0			0
$754$	3.23205	−	5.59808i	0.117704	−	0.203870i
$755$	−39.1244			−1.42388
$756$		0			0
$757$	4.78461			0.173900			0.0869498	−	0.996213i	$-0.472288\pi$
$757$	4.78461			0.173900			0.0869498	+	0.996213i	$0.472288\pi$
$758$	−8.29423	+	14.3660i	−0.301260	+	0.521798i
$759$		0			0
$760$	−5.36603	−	9.29423i	−0.194646	−	0.337137i
$761$	−4.16025	−	7.20577i	−0.150809	−	0.261209i	0.780716	−	0.624886i	$-0.214855\pi$
$761$	−4.16025	−	7.20577i	−0.150809	−	0.261209i	−0.931525	+	0.363677i	$0.881521\pi$
$762$		0			0
$763$	2.40192	−	4.16025i	0.0869555	−	0.150611i
$764$	−24.5885			−0.889579
$765$		0			0
$766$	−10.1436			−0.366503
$767$	4.09808	−	7.09808i	0.147973	−	0.256297i
$768$		0			0
$769$	−3.59808	−	6.23205i	−0.129750	−	0.224733i	0.793830	−	0.608140i	$-0.208084\pi$
$769$	−3.59808	−	6.23205i	−0.129750	−	0.224733i	−0.923580	+	0.383407i	$0.874751\pi$
$770$	−4.09808	−	7.09808i	−0.147684	−	0.255797i
$771$		0			0
$772$	9.50000	−	16.4545i	0.341912	−	0.592210i
$773$	21.3397			0.767537			0.383769	−	0.923429i	$-0.374626\pi$
$773$	21.3397			0.767537			0.383769	+	0.923429i	$0.374626\pi$
$774$		0			0
$775$	−8.39230			−0.301460
$776$	−8.00000	+	13.8564i	−0.287183	+	0.497416i
$777$		0			0
$778$	15.1244	+	26.1962i	0.542234	+	0.939178i
$779$	−7.85641	−	13.6077i	−0.281485	−	0.487546i
$780$		0			0
$781$	10.3923	−	18.0000i	0.371866	−	0.644091i
$782$	−8.19615			−0.293094
$783$		0			0
$784$	1.00000			0.0357143
$785$	−13.3301	+	23.0885i	−0.475773	+	0.824062i
$786$		0			0
$787$	−22.5885	−	39.1244i	−0.805192	−	1.39463i	−0.916162	−	0.400809i	$-0.868729\pi$
$787$	−22.5885	−	39.1244i	−0.805192	−	1.39463i	0.110970	−	0.993824i	$-0.464604\pi$
$788$	−7.50000	−	12.9904i	−0.267176	−	0.462763i
$789$		0			0
$790$	−5.36603	+	9.29423i	−0.190915	+	0.330674i
$791$	10.2679			0.365086
$792$		0			0
$793$	−9.39230			−0.333531
$794$	−14.6962	+	25.4545i	−0.521547	+	0.903346i
$795$		0			0
$796$	−10.2942	−	17.8301i	−0.364869	−	0.631972i
$797$	10.6699	+	18.4808i	0.377946	+	0.654622i	0.990763	−	0.135603i	$-0.0432971\pi$
$797$	10.6699	+	18.4808i	0.377946	+	0.654622i	−0.612817	+	0.790225i	$0.709964\pi$
$798$		0			0
$799$	−7.09808	+	12.2942i	−0.251112	+	0.434939i
$800$	2.00000			0.0707107
$801$		0			0
$802$	22.2679			0.786309
$803$	−21.7583	+	37.6865i	−0.767835	+	1.32993i
$804$		0			0
$805$	1.09808	+	1.90192i	0.0387021	+	0.0670340i
$806$	−2.09808	−	3.63397i	−0.0739016	−	0.128001i
$807$		0			0
$808$	−6.46410	+	11.1962i	−0.227406	+	0.393879i
$809$	0.124356			0.00437211			0.00218606	−	0.999998i	$-0.499304\pi$
$809$	0.124356			0.00437211			0.00218606	+	0.999998i	$0.499304\pi$
$810$		0			0
$811$	54.9808			1.93064			0.965318	−	0.261078i	$-0.0840778\pi$
$811$	54.9808			1.93064			0.965318	+	0.261078i	$0.0840778\pi$
$812$	3.23205	−	5.59808i	0.113423	−	0.196454i
$813$		0			0
$814$	7.56218	+	13.0981i	0.265054	+	0.459087i
$815$	−21.1244	−	36.5885i	−0.739954	−	1.28164i
$816$		0			0
$817$	38.3923	−	66.4974i	1.34318	−	2.32645i
$818$	21.1962			0.741106
$819$		0			0
$820$	−4.39230			−0.153386
$821$	−7.50000	+	12.9904i	−0.261752	+	0.453367i	−0.966708	−	0.255884i	$-0.917634\pi$
$821$	−7.50000	+	12.9904i	−0.261752	+	0.453367i	0.704956	+	0.709251i	$0.250967\pi$
$822$		0			0
$823$	12.3923	+	21.4641i	0.431969	+	0.748192i	0.997043	−	0.0768486i	$-0.0244858\pi$
$823$	12.3923	+	21.4641i	0.431969	+	0.748192i	−0.565074	+	0.825040i	$0.691152\pi$
$824$	−4.19615	−	7.26795i	−0.146180	−	0.253191i
$825$		0			0
$826$	4.09808	−	7.09808i	0.142590	−	0.246974i
$827$	−19.6077			−0.681826			−0.340913	−	0.940095i	$-0.610736\pi$
$827$	−19.6077			−0.681826			−0.340913	+	0.940095i	$0.610736\pi$
$828$		0			0
$829$	26.0000			0.903017			0.451509	−	0.892267i	$-0.350886\pi$
$829$	26.0000			0.903017			0.451509	+	0.892267i	$0.350886\pi$
$830$	−1.09808	+	1.90192i	−0.0381148	+	0.0660167i
$831$		0			0
$832$	0.500000	+	0.866025i	0.0173344	+	0.0300240i
$833$	3.23205	+	5.59808i	0.111984	+	0.193962i
$834$		0			0
$835$	−6.29423	+	10.9019i	−0.217821	+	0.377277i
$836$	29.3205			1.01407
$837$		0			0
$838$	23.3205			0.805594
$839$	21.1244	−	36.5885i	0.729294	−	1.26317i	−0.227888	−	0.973687i	$-0.573182\pi$
$839$	21.1244	−	36.5885i	0.729294	−	1.26317i	0.957182	−	0.289487i	$-0.0934846\pi$
$840$		0			0
$841$	−6.39230	−	11.0718i	−0.220424	−	0.381786i
$842$	6.59808	+	11.4282i	0.227385	+	0.393842i
$843$		0			0
$844$	−5.90192	+	10.2224i	−0.203153	+	0.351871i
$845$	−20.7846			−0.715012
$846$		0			0
$847$	11.3923			0.391444
$848$	4.73205	−	8.19615i	0.162499	−	0.281457i
$849$		0			0
$850$	6.46410	+	11.1962i	0.221717	+	0.384025i
$851$	−2.02628	−	3.50962i	−0.0694600	−	0.120308i
$852$		0			0
$853$	−1.00000	+	1.73205i	−0.0342393	+	0.0593043i	−0.882637	−	0.470055i	$-0.844234\pi$
$853$	−1.00000	+	1.73205i	−0.0342393	+	0.0593043i	0.848398	+	0.529359i	$0.177568\pi$
$854$	−9.39230			−0.321398
$855$		0			0
$856$	−13.8564			−0.473602
$857$	−9.23205	+	15.9904i	−0.315361	+	0.546221i	−0.979514	−	0.201375i	$-0.935459\pi$
$857$	−9.23205	+	15.9904i	−0.315361	+	0.546221i	0.664153	+	0.747596i	$0.268792\pi$
$858$		0			0
$859$	−0.196152	−	0.339746i	−0.00669263	−	0.0115920i	0.862660	−	0.505785i	$-0.168797\pi$
$859$	−0.196152	−	0.339746i	−0.00669263	−	0.0115920i	−0.869352	+	0.494193i	$0.835464\pi$
$860$	−10.7321	−	18.5885i	−0.365960	−	0.633861i
$861$		0			0
$862$	−0.339746	+	0.588457i	−0.0115718	+	0.0200429i
$863$	−23.9090			−0.813871			−0.406935	−	0.913457i	$-0.633403\pi$
$863$	−23.9090			−0.813871			−0.406935	+	0.913457i	$0.633403\pi$
$864$		0			0
$865$	22.1769			0.754038
$866$	−15.7942	+	27.3564i	−0.536710	+	0.929609i
$867$		0			0
$868$	−2.09808	−	3.63397i	−0.0712133	−	0.123345i
$869$	−14.6603	−	25.3923i	−0.497315	−	0.861375i
$870$		0			0
$871$	2.09808	−	3.63397i	0.0710906	−	0.123133i
$872$	4.80385			0.162679
$873$		0			0
$874$	−7.85641			−0.265747
$875$	6.06218	−	10.5000i	0.204939	−	0.354965i
$876$		0			0
$877$	−15.5981	−	27.0167i	−0.526710	−	0.912288i	−0.999516	−	0.0311213i	$-0.990092\pi$
$877$	−15.5981	−	27.0167i	−0.526710	−	0.912288i	0.472806	−	0.881167i	$-0.343241\pi$
$878$	10.5885	+	18.3397i	0.357343	+	0.618936i
$879$		0			0
$880$	4.09808	−	7.09808i	0.138146	−	0.239276i
$881$	25.1769			0.848232			0.424116	−	0.905608i	$-0.360585\pi$
$881$	25.1769			0.848232			0.424116	+	0.905608i	$0.360585\pi$
$882$		0			0
$883$	12.9808			0.436837			0.218419	−	0.975855i	$-0.429910\pi$
$883$	12.9808			0.436837			0.218419	+	0.975855i	$0.429910\pi$
$884$	−3.23205	+	5.59808i	−0.108706	+	0.188284i
$885$		0			0
$886$	−1.09808	−	1.90192i	−0.0368906	−	0.0638964i
$887$	17.8301	+	30.8827i	0.598677	+	1.03694i	0.993017	+	0.117974i	$0.0376400\pi$
$887$	17.8301	+	30.8827i	0.598677	+	1.03694i	−0.394340	+	0.918965i	$0.629027\pi$
$888$		0			0
$889$	2.00000	−	3.46410i	0.0670778	−	0.116182i
$890$	−21.5885			−0.723647
$891$		0			0
$892$	12.3923			0.414925
$893$	−6.80385	+	11.7846i	−0.227682	+	0.394357i
$894$		0			0
$895$	6.29423	+	10.9019i	0.210393	+	0.364411i
$896$	0.500000	+	0.866025i	0.0167038	+	0.0289319i
$897$		0			0
$898$	−3.00000	+	5.19615i	−0.100111	+	0.173398i
$899$	−27.1244			−0.904648
$900$		0			0
$901$	61.1769			2.03810
$902$	6.00000	−	10.3923i	0.199778	−	0.346026i
$903$		0			0
$904$	5.13397	+	8.89230i	0.170753	+	0.295754i
$905$	−0.339746	−	0.588457i	−0.0112935	−	0.0195610i
$906$		0			0
$907$	−10.0000	+	17.3205i	−0.332045	+	0.575118i	−0.982913	−	0.184073i	$-0.941072\pi$
$907$	−10.0000	+	17.3205i	−0.332045	+	0.575118i	0.650868	+	0.759191i	$0.274405\pi$
$908$	5.07180			0.168313
$909$		0			0
$910$	1.73205			0.0574169
$911$	−16.0526	+	27.8038i	−0.531845	+	0.921183i	0.467464	+	0.884012i	$0.345168\pi$
$911$	−16.0526	+	27.8038i	−0.531845	+	0.921183i	−0.999309	+	0.0371704i	$0.988166\pi$
$912$		0			0
$913$	−3.00000	−	5.19615i	−0.0992855	−	0.171968i
$914$	−0.500000	−	0.866025i	−0.0165385	−	0.0286456i
$915$		0			0
$916$	10.8923	−	18.8660i	0.359892	−	0.623351i
$917$	2.53590			0.0837427
$918$		0			0
$919$	−37.8038			−1.24703			−0.623517	−	0.781810i	$-0.714297\pi$
$919$	−37.8038			−1.24703			−0.623517	+	0.781810i	$0.714297\pi$
$920$	−1.09808	+	1.90192i	−0.0362025	+	0.0627046i
$921$		0			0
$922$	−5.53590	−	9.58846i	−0.182315	−	0.315779i
$923$	2.19615	+	3.80385i	0.0722872	+	0.125205i
$924$		0			0
$925$	−3.19615	+	5.53590i	−0.105089	+	0.182019i
$926$	−5.80385			−0.190726
$927$		0			0
$928$	6.46410			0.212195
$929$	3.69615	−	6.40192i	0.121267	−	0.210040i	−0.799001	−	0.601330i	$-0.794638\pi$
$929$	3.69615	−	6.40192i	0.121267	−	0.210040i	0.920268	+	0.391290i	$0.127971\pi$
$930$		0			0
$931$	3.09808	+	5.36603i	0.101535	+	0.175864i
$932$	6.86603	+	11.8923i	0.224904	+	0.389545i
$933$		0			0
$934$	0.633975	−	1.09808i	0.0207443	−	0.0359302i
$935$	52.9808			1.73266
$936$		0			0
$937$	−22.8038			−0.744969			−0.372485	−	0.928038i	$-0.621494\pi$
$937$	−22.8038			−0.744969			−0.372485	+	0.928038i	$0.621494\pi$
$938$	2.09808	−	3.63397i	0.0685046	−	0.118653i
$939$		0			0
$940$	1.90192	+	3.29423i	0.0620339	+	0.107446i
$941$	−23.3827	−	40.5000i	−0.762254	−	1.32026i	−0.941686	−	0.336492i	$-0.890759\pi$
$941$	−23.3827	−	40.5000i	−0.762254	−	1.32026i	0.179433	−	0.983770i	$-0.442574\pi$
$942$		0			0
$943$	−1.60770	+	2.78461i	−0.0523538	+	0.0906794i
$944$	8.19615			0.266762
$945$		0			0
$946$	58.6410			1.90658
$947$	−3.80385	+	6.58846i	−0.123608	+	0.214096i	−0.921188	−	0.389117i	$-0.872780\pi$
$947$	−3.80385	+	6.58846i	−0.123608	+	0.214096i	0.797580	+	0.603214i	$0.206113\pi$
$948$		0			0
$949$	−4.59808	−	7.96410i	−0.149260	−	0.258526i
$950$	6.19615	+	10.7321i	0.201030	+	0.348194i
$951$		0			0
$952$	−3.23205	+	5.59808i	−0.104751	+	0.181435i
$953$	55.9808			1.81339			0.906697	−	0.421782i	$-0.138595\pi$
$953$	55.9808			1.81339			0.906697	+	0.421782i	$0.138595\pi$
$954$		0			0
$955$	−42.5885			−1.37813
$956$	7.56218	−	13.0981i	0.244578	−	0.423622i
$957$		0			0
$958$	−8.36603	−	14.4904i	−0.270294	−	0.468163i
$959$	−1.33013	−	2.30385i	−0.0429520	−	0.0743951i
$960$		0			0
$961$	6.69615	−	11.5981i	0.216005	−	0.374131i
$962$	−3.19615			−0.103048
$963$		0			0
$964$	−13.5885			−0.437655
$965$	16.4545	−	28.5000i	0.529689	−	0.917447i
$966$		0			0
$967$	11.2942	+	19.5622i	0.363198	+	0.629077i	0.988485	−	0.151317i	$-0.0483516\pi$
$967$	11.2942	+	19.5622i	0.363198	+	0.629077i	−0.625287	+	0.780395i	$0.715018\pi$
$968$	5.69615	+	9.86603i	0.183081	+	0.317106i
$969$		0			0
$970$	−13.8564	+	24.0000i	−0.444902	+	0.770594i
$971$	−3.12436			−0.100265			−0.0501327	−	0.998743i	$-0.515964\pi$
$971$	−3.12436			−0.100265			−0.0501327	+	0.998743i	$0.515964\pi$
$972$		0			0
$973$	−18.1962			−0.583342
$974$	−3.09808	+	5.36603i	−0.0992688	+	0.171939i
$975$		0			0
$976$	−4.69615	−	8.13397i	−0.150320	−	0.260362i
$977$	17.7846	+	30.8038i	0.568980	+	0.985502i	0.996667	+	0.0815755i	$0.0259952\pi$
$977$	17.7846	+	30.8038i	0.568980	+	0.985502i	−0.427687	+	0.903927i	$0.640671\pi$
$978$		0			0
$979$	29.4904	−	51.0788i	0.942517	−	1.63249i
$980$	1.73205			0.0553283
$981$		0			0
$982$	11.3205			0.361252
$983$	−20.5359	+	35.5692i	−0.654993	+	1.13448i	0.326902	+	0.945058i	$0.393995\pi$
$983$	−20.5359	+	35.5692i	−0.654993	+	1.13448i	−0.981895	+	0.189424i	$0.939338\pi$
$984$		0			0
$985$	−12.9904	−	22.5000i	−0.413908	−	0.716910i
$986$	20.8923	+	36.1865i	0.665347	+	1.15241i
$987$		0			0
$988$	−3.09808	+	5.36603i	−0.0985629	+	0.170716i
$989$	−15.7128			−0.499638
$990$		0			0
$991$	42.9808			1.36533			0.682664	−	0.730732i	$-0.260821\pi$
$991$	42.9808			1.36533			0.682664	+	0.730732i	$0.260821\pi$
$992$	2.09808	−	3.63397i	0.0666140	−	0.115379i
$993$		0			0
$994$	2.19615	+	3.80385i	0.0696577	+	0.120651i
$995$	−17.8301	−	30.8827i	−0.565253	−	0.979047i
$996$		0			0
$997$	10.8923	−	18.8660i	0.344963	−	0.597493i	−0.640384	−	0.768055i	$-0.721225\pi$
$997$	10.8923	−	18.8660i	0.344963	−	0.597493i	0.985347	+	0.170562i	$0.0545582\pi$
$998$	−20.5885			−0.651716
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.f.t.379.1		4
3.2	odd	2		1134.2.f.q.379.2		4
9.2	odd	6		1134.2.a.o.1.1	yes	2
9.4	even	3	inner	1134.2.f.t.757.1		4
9.5	odd	6		1134.2.f.q.757.2		4
9.7	even	3		1134.2.a.j.1.2	✓	2
36.7	odd	6		9072.2.a.bi.1.2		2
36.11	even	6		9072.2.a.bf.1.1		2
63.20	even	6		7938.2.a.br.1.2		2
63.34	odd	6		7938.2.a.bi.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.a.j.1.2	✓	2	9.7	even	3
1134.2.a.o.1.1	yes	2	9.2	odd	6
1134.2.f.q.379.2		4	3.2	odd	2
1134.2.f.q.757.2		4	9.5	odd	6
1134.2.f.t.379.1		4	1.1	even	1	trivial
1134.2.f.t.757.1		4	9.4	even	3	inner
7938.2.a.bi.1.1		2	63.34	odd	6
7938.2.a.br.1.2		2	63.20	even	6
9072.2.a.bf.1.1		2	36.11	even	6
9072.2.a.bi.1.2		2	36.7	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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} -1.73205 q^{10} +(2.36603 - 4.09808i) q^{11} +(0.500000 + 0.866025i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} -6.46410 q^{17} -6.19615 q^{19} +(-0.866025 + 1.50000i) q^{20} +(-2.36603 - 4.09808i) q^{22} +(0.633975 + 1.09808i) q^{23} +(1.00000 - 1.73205i) q^{25} +1.00000 q^{26} +1.00000 q^{28} +(3.23205 - 5.59808i) q^{29} +(-2.09808 - 3.63397i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.23205 + 5.59808i) q^{34} +1.73205 q^{35} -3.19615 q^{37} +(-3.09808 + 5.36603i) q^{38} +(0.866025 + 1.50000i) q^{40} +(1.26795 + 2.19615i) q^{41} +(-6.19615 + 10.7321i) q^{43} -4.73205 q^{44} +1.26795 q^{46} +(1.09808 - 1.90192i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-1.00000 - 1.73205i) q^{50} +(0.500000 - 0.866025i) q^{52} -9.46410 q^{53} -8.19615 q^{55} +(0.500000 - 0.866025i) q^{56} +(-3.23205 - 5.59808i) q^{58} +(-4.09808 - 7.09808i) q^{59} +(-4.69615 + 8.13397i) q^{61} -4.19615 q^{62} +1.00000 q^{64} +(0.866025 - 1.50000i) q^{65} +(-2.09808 - 3.63397i) q^{67} +(3.23205 + 5.59808i) q^{68} +(0.866025 - 1.50000i) q^{70} +4.39230 q^{71} -9.19615 q^{73} +(-1.59808 + 2.76795i) q^{74} +(3.09808 + 5.36603i) q^{76} +(2.36603 + 4.09808i) q^{77} +(3.09808 - 5.36603i) q^{79} +1.73205 q^{80} +2.53590 q^{82} +(0.633975 - 1.09808i) q^{83} +(5.59808 + 9.69615i) q^{85} +(6.19615 + 10.7321i) q^{86} +(-2.36603 + 4.09808i) q^{88} +12.4641 q^{89} -1.00000 q^{91} +(0.633975 - 1.09808i) q^{92} +(-1.09808 - 1.90192i) q^{94} +(5.36603 + 9.29423i) q^{95} +(8.00000 - 13.8564i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^7 - 4 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{7} - 4 q^{8} + 6 q^{11} + 2 q^{13} + 2 q^{14} - 2 q^{16} - 12 q^{17} - 4 q^{19} - 6 q^{22} + 6 q^{23} + 4 q^{25} + 4 q^{26} + 4 q^{28} + 6 q^{29} + 2 q^{31} + 2 q^{32} - 6 q^{34} + 8 q^{37} - 2 q^{38} + 12 q^{41} - 4 q^{43} - 12 q^{44} + 12 q^{46} - 6 q^{47} - 2 q^{49} - 4 q^{50} + 2 q^{52} - 24 q^{53} - 12 q^{55} + 2 q^{56} - 6 q^{58} - 6 q^{59} + 2 q^{61} + 4 q^{62} + 4 q^{64} + 2 q^{67} + 6 q^{68} - 24 q^{71} - 16 q^{73} + 4 q^{74} + 2 q^{76} + 6 q^{77} + 2 q^{79} + 24 q^{82} + 6 q^{83} + 12 q^{85} + 4 q^{86} - 6 q^{88} + 36 q^{89} - 4 q^{91} + 6 q^{92} + 6 q^{94} + 18 q^{95} + 32 q^{97} - 4 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^7 - 4 * q^8 + 6 * q^11 + 2 * q^13 + 2 * q^14 - 2 * q^16 - 12 * q^17 - 4 * q^19 - 6 * q^22 + 6 * q^23 + 4 * q^25 + 4 * q^26 + 4 * q^28 + 6 * q^29 + 2 * q^31 + 2 * q^32 - 6 * q^34 + 8 * q^37 - 2 * q^38 + 12 * q^41 - 4 * q^43 - 12 * q^44 + 12 * q^46 - 6 * q^47 - 2 * q^49 - 4 * q^50 + 2 * q^52 - 24 * q^53 - 12 * q^55 + 2 * q^56 - 6 * q^58 - 6 * q^59 + 2 * q^61 + 4 * q^62 + 4 * q^64 + 2 * q^67 + 6 * q^68 - 24 * q^71 - 16 * q^73 + 4 * q^74 + 2 * q^76 + 6 * q^77 + 2 * q^79 + 24 * q^82 + 6 * q^83 + 12 * q^85 + 4 * q^86 - 6 * q^88 + 36 * q^89 - 4 * q^91 + 6 * q^92 + 6 * q^94 + 18 * q^95 + 32 * q^97 - 4 * q^98

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