LMFDB - Embedded newform 1134.2.f.q.379.2

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			379.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1134.379
Dual form			1134.2.f.q.757.2

$q$-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	0.992085	−	0.125567i	$-0.0400750\pi$
$5$	0.866025	+	1.50000i	0.387298	+	0.670820i	−0.604787	+	0.796387i	$0.706742\pi$
$6$		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	$0.419505\pi$
$11$	−2.36603	+	4.09808i	−0.713384	+	1.23562i	−0.963580	+	0.267421i	$0.913828\pi$
$12$		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	$-0.213234\pi$
$17$	6.46410			1.56777			0.783887	+	0.620903i	$0.213234\pi$
$18$		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	0.792329	−	0.610094i	$-0.208868\pi$
$23$	−0.633975	−	1.09808i	−0.132193	−	0.228965i	−0.924522	+	0.381130i	$0.875535\pi$
$24$		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	$0.371570\pi$
$29$	−3.23205	+	5.59808i	−0.600177	+	1.03954i	−0.992794	+	0.119835i	$0.961764\pi$
$30$		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	0.749866	−	0.661590i	$-0.230118\pi$
$41$	−1.26795	−	2.19615i	−0.198020	−	0.342981i	−0.947886	+	0.318608i	$0.896785\pi$
$42$		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	−0.934930	−	0.354833i	$-0.884538\pi$
$47$	−1.09808	+	1.90192i	−0.160171	+	0.277424i	0.774759	+	0.632257i	$0.217871\pi$
$48$		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	$-0.274770\pi$
$53$	9.46410			1.29999			0.649997	+	0.759937i	$0.274770\pi$
$54$		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	$0.0124660\pi$
$59$	4.09808	+	7.09808i	0.533524	+	0.924091i	−0.465709	+	0.884938i	$0.654201\pi$
$60$		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	$-0.583932\pi$
$71$	−4.39230			−0.521271			−0.260635	+	0.965437i	$0.583932\pi$
$72$		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	−0.898720	−	0.438523i	$-0.855502\pi$
$83$	−0.633975	+	1.09808i	−0.0695878	+	0.120530i	0.829132	+	0.559053i	$0.188835\pi$
$84$		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	$-0.729696\pi$
$89$	−12.4641			−1.32119			−0.660596	+	0.750742i	$0.729696\pi$
$90$		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	$0.389061\pi$
$101$	−6.46410	+	11.1962i	−0.643202	+	1.11406i	−0.984714	+	0.174181i	$0.944272\pi$
$102$		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	$-0.733609\pi$
$107$	−13.8564			−1.33955			−0.669775	+	0.742564i	$0.733609\pi$
$108$		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	0.999809	−	0.0195613i	$-0.00622697\pi$
$113$	5.13397	+	8.89230i	0.482964	+	0.836518i	−0.516845	+	0.856079i	$0.672894\pi$
$114$		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	0.916085	−	0.400983i	$-0.131331\pi$
$131$	1.26795	+	2.19615i	0.110781	+	0.191879i	−0.805304	+	0.592862i	$0.797998\pi$
$132$		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	−0.803595	−	0.595176i	$-0.797082\pi$
$137$	1.33013	−	2.30385i	0.113640	−	0.196831i	0.917235	+	0.398345i	$0.130415\pi$
$138$		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	0.935194	−	0.354137i	$-0.115225\pi$
$149$	1.96410	+	3.40192i	0.160905	+	0.278696i	−0.774288	+	0.632833i	$0.781892\pi$
$150$		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	0.971682	−	0.236293i	$-0.0759324\pi$
$167$	3.63397	+	6.29423i	0.281205	+	0.487062i	−0.690477	+	0.723355i	$0.742599\pi$
$168$		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	−0.513154	−	0.858296i	$-0.671523\pi$
$173$	6.40192	−	11.0885i	0.486729	−	0.843040i	0.999884	+	0.0152565i	$0.00485650\pi$
$174$		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	$-0.412442\pi$
$179$	7.26795			0.543232			0.271616	+	0.962406i	$0.412442\pi$
$180$		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	$0.515669\pi$
$191$	−12.2942	+	21.2942i	−0.889579	+	1.54080i	−0.840374	+	0.542008i	$0.817664\pi$
$192$		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	$-0.679445\pi$
$197$	−15.0000			−1.06871			−0.534353	+	0.845262i	$0.679445\pi$
$198$		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	−0.769514	−	0.638631i	$-0.779501\pi$
$227$	2.53590	−	4.39230i	0.168313	−	0.291528i	0.937827	+	0.347103i	$0.112835\pi$
$228$		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	$-0.351492\pi$
$233$	13.7321			0.899617			0.449808	+	0.893125i	$0.351492\pi$
$234$		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	0.510766	−	0.859720i	$-0.329362\pi$
$239$	−7.56218	−	13.0981i	−0.489157	−	0.847244i	−0.999922	+	0.0124759i	$0.996029\pi$
$240$		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	$-0.538305\pi$
$251$	−3.80385			−0.240097			−0.120048	+	0.992768i	$0.538305\pi$
$252$		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	$0.169898\pi$
$257$	13.9641	+	24.1865i	0.871057	+	1.50871i	0.0101519	+	0.999948i	$0.496768\pi$
$258$		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	−0.999259	−	0.0384813i	$-0.987748\pi$
$263$	−7.56218	+	13.0981i	−0.466304	+	0.807662i	0.532955	+	0.846143i	$0.321081\pi$
$264$		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	$-0.145278\pi$
$269$	29.4449			1.79529			0.897643	+	0.440724i	$0.145278\pi$
$270$		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	−0.585251	−	0.810852i	$-0.699004\pi$
$281$	6.86603	−	11.8923i	0.409593	−	0.709435i	0.994844	+	0.101417i	$0.0323375\pi$
$282$		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	$0.117481\pi$
$293$	13.3301	+	23.0885i	0.778754	+	1.34884i	−0.153906	+	0.988086i	$0.549185\pi$
$294$		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	$0.0592183\pi$
$311$	11.4904	+	19.9019i	0.651560	+	1.12853i	−0.331185	+	0.943566i	$0.607448\pi$
$312$		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	−0.845813	−	0.533479i	$-0.820884\pi$
$317$	0.696152	−	1.20577i	0.0390998	−	0.0677229i	0.884913	+	0.465756i	$0.154218\pi$
$318$		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	0.557696	−	0.830045i	$-0.311686\pi$
$347$	−8.19615	−	14.1962i	−0.439993	−	0.762089i	−0.997688	+	0.0679560i	$0.978352\pi$
$348$		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	−0.915879	−	0.401454i	$-0.868505\pi$
$353$	−2.07180	+	3.58846i	−0.110271	+	0.190994i	0.805609	+	0.592448i	$0.201838\pi$
$354$		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	$-0.333518\pi$
$359$	18.9282			0.998992			0.499496	+	0.866316i	$0.333518\pi$
$360$		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	0.966016	−	0.258481i	$-0.0832221\pi$
$383$	5.07180	+	8.78461i	0.259157	+	0.448873i	−0.706860	+	0.707354i	$0.749889\pi$
$384$		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	$-0.555164\pi$
$389$	15.1244	−	26.1962i	0.766835	−	1.32820i	0.939271	−	0.343177i	$-0.111503\pi$
$390$		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	$-0.979001\pi$
$401$	−11.1340	−	19.2846i	−0.556004	−	0.963027i	0.441820	−	0.897103i	$-0.354333\pi$
$402$		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	$-0.973749\pi$
$419$	−11.6603	−	20.1962i	−0.569641	−	0.986647i	0.426961	−	0.904270i	$-0.359584\pi$
$420$		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	$-0.494791\pi$
$431$	0.679492			0.0327300			0.0163650	+	0.999866i	$0.494791\pi$
$432$		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	−0.890932	−	0.454138i	$-0.849947\pi$
$443$	−1.09808	+	1.90192i	−0.0521712	+	0.0903631i	0.838760	+	0.544501i	$0.183281\pi$
$444$		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	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$		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	−0.965661	−	0.259805i	$-0.916342\pi$
$461$	−5.53590	+	9.58846i	−0.257832	+	0.446579i	0.707829	+	0.706384i	$0.249675\pi$
$462$		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	$-0.509340\pi$
$467$	−1.26795			−0.0586737			−0.0293368	+	0.999570i	$0.509340\pi$
$468$		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	−0.991384	−	0.130988i	$-0.958185\pi$
$479$	−8.36603	+	14.4904i	−0.382253	+	0.662082i	0.609131	+	0.793070i	$0.291519\pi$
$480$		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	0.709572	−	0.704633i	$-0.248888\pi$
$491$	−5.66025	−	9.80385i	−0.255444	−	0.442441i	−0.965016	+	0.262191i	$0.915555\pi$
$492$		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	$-0.671218\pi$
$503$	−22.9808			−1.02466			−0.512331	+	0.858788i	$0.671218\pi$
$504$		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	0.999767	−	0.0215720i	$-0.00686711\pi$
$509$	10.8564	+	18.8038i	0.481202	+	0.833466i	−0.518566	+	0.855038i	$0.673534\pi$
$510$		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	$-0.0895444\pi$
$521$	43.8564			1.92138			0.960692	+	0.277616i	$0.0895444\pi$
$522$		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	$-0.166956\pi$
$557$	40.8564			1.73114			0.865571	+	0.500787i	$0.166956\pi$
$558$		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	$-0.997886\pi$
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	0.494238	−	0.869326i	$-0.335447\pi$
$564$		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	−0.770179	−	0.637828i	$-0.779833\pi$
$569$	3.99038	−	6.91154i	0.167285	−	0.289747i	0.937465	+	0.348081i	$0.113167\pi$
$570$		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	−0.733778	−	0.679389i	$-0.762245\pi$
$587$	5.36603	−	9.29423i	0.221480	−	0.383614i	0.955257	+	0.295776i	$0.0955781\pi$
$588$		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	$-0.816792\pi$
$593$	−40.8564			−1.67777			−0.838886	+	0.544308i	$0.816792\pi$
$594$		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	0.902262	−	0.431189i	$-0.141906\pi$
$599$	1.90192	+	3.29423i	0.0777105	+	0.134599i	−0.824551	+	0.565787i	$0.808572\pi$
$600$		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	0.650527	−	0.759483i	$-0.274548\pi$
$617$	−8.25833	−	14.3038i	−0.332468	−	0.575851i	−0.982995	+	0.183632i	$0.941215\pi$
$618$		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	−0.943391	−	0.331684i	$-0.892383\pi$
$641$	−4.66987	+	8.08846i	−0.184449	+	0.319475i	0.758942	+	0.651158i	$0.225717\pi$
$642$		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	$-0.651582\pi$
$647$	−23.3205			−0.916824			−0.458412	+	0.888740i	$0.651582\pi$
$648$		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	$0.0762065\pi$
$653$	17.6603	+	30.5885i	0.691099	+	1.19702i	−0.280379	+	0.959889i	$0.590460\pi$
$654$		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	−0.872567	−	0.488495i	$-0.837546\pi$
$659$	−0.339746	+	0.588457i	−0.0132346	+	0.0229230i	0.859332	+	0.511418i	$0.170880\pi$
$660$		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	$0.496582\pi$
$677$	−22.3923	+	38.7846i	−0.860606	+	1.49061i	−0.871345	+	0.490671i	$0.836752\pi$
$678$		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	$-0.774695\pi$
$683$	−39.7128			−1.51957			−0.759784	+	0.650175i	$0.774695\pi$
$684$		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	$-0.162797\pi$
$701$	46.1769			1.74408			0.872039	+	0.489436i	$0.162797\pi$
$702$		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	$-0.356800\pi$
$719$	23.3205			0.869708			0.434854	+	0.900501i	$0.356800\pi$
$720$		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	0.992937	−	0.118643i	$-0.0378544\pi$
$743$	10.7321	+	18.5885i	0.393721	+	0.681944i	−0.599216	+	0.800587i	$0.704521\pi$
$744$		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	0.931525	−	0.363677i	$-0.118479\pi$
$761$	4.16025	+	7.20577i	0.150809	+	0.261209i	−0.780716	+	0.624886i	$0.785145\pi$
$762$		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	$-0.625374\pi$
$773$	−21.3397			−0.767537			−0.383769	+	0.923429i	$0.625374\pi$
$774$		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	0.612817	−	0.790225i	$-0.290036\pi$
$797$	−10.6699	−	18.4808i	−0.377946	−	0.654622i	−0.990763	+	0.135603i	$0.956703\pi$
$798$		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	$-0.500696\pi$
$809$	−0.124356			−0.00437211			−0.00218606	+	0.999998i	$0.500696\pi$
$810$		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	−0.704956	−	0.709251i	$-0.749033\pi$
$821$	7.50000	−	12.9904i	0.261752	−	0.453367i	0.966708	+	0.255884i	$0.0823665\pi$
$822$		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	$-0.389264\pi$
$827$	19.6077			0.681826			0.340913	+	0.940095i	$0.389264\pi$
$828$		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	$0.426818\pi$
$839$	−21.1244	+	36.5885i	−0.729294	+	1.26317i	−0.957182	+	0.289487i	$0.906515\pi$
$840$		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	−0.664153	−	0.747596i	$-0.731208\pi$
$857$	9.23205	−	15.9904i	0.315361	−	0.546221i	0.979514	+	0.201375i	$0.0645411\pi$
$858$		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	$-0.366597\pi$
$863$	23.9090			0.813871			0.406935	+	0.913457i	$0.366597\pi$
$864$		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	$-0.639415\pi$
$881$	−25.1769			−0.848232			−0.424116	+	0.905608i	$0.639415\pi$
$882$		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	$-0.962360\pi$
$887$	−17.8301	−	30.8827i	−0.598677	−	1.03694i	0.394340	−	0.918965i	$-0.370973\pi$
$888$		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	$-0.654832\pi$
$911$	16.0526	−	27.8038i	0.531845	−	0.921183i	0.999309	−	0.0371704i	$-0.0118344\pi$
$912$		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	−0.920268	−	0.391290i	$-0.872029\pi$
$929$	−3.69615	+	6.40192i	−0.121267	+	0.210040i	0.799001	+	0.601330i	$0.205362\pi$
$930$		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	$0.109241\pi$
$941$	23.3827	+	40.5000i	0.762254	+	1.32026i	−0.179433	+	0.983770i	$0.557426\pi$
$942$		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	−0.797580	−	0.603214i	$-0.793887\pi$
$947$	3.80385	−	6.58846i	0.123608	−	0.214096i	0.921188	+	0.389117i	$0.127220\pi$
$948$		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	$-0.861405\pi$
$953$	−55.9808			−1.81339			−0.906697	+	0.421782i	$0.861405\pi$
$954$		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	$-0.484036\pi$
$971$	3.12436			0.100265			0.0501327	+	0.998743i	$0.484036\pi$
$972$		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	$-0.974005\pi$
$977$	−17.7846	−	30.8038i	−0.568980	−	0.985502i	0.427687	−	0.903927i	$-0.359329\pi$
$978$		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	$-0.606005\pi$
$983$	20.5359	−	35.5692i	0.654993	−	1.13448i	0.981895	−	0.189424i	$-0.0606620\pi$
$984$		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.q.379.2		4
3.2	odd	2		1134.2.f.t.379.1		4
9.2	odd	6		1134.2.a.j.1.2	✓	2
9.4	even	3	inner	1134.2.f.q.757.2		4
9.5	odd	6		1134.2.f.t.757.1		4
9.7	even	3		1134.2.a.o.1.1	yes	2
36.7	odd	6		9072.2.a.bf.1.1		2
36.11	even	6		9072.2.a.bi.1.2		2
63.20	even	6		7938.2.a.bi.1.1		2
63.34	odd	6		7938.2.a.br.1.2		2

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

Introduction

L-functions

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