LMFDB - Embedded newform 1134.2.f.q.757.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1134.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 1.50000i) q^{5} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 1.50000i) q^{5} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +1.73205 q^{10} +(-0.633975 - 1.09808i) q^{11} +(0.500000 - 0.866025i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} -0.464102 q^{17} +4.19615 q^{19} +(-0.866025 - 1.50000i) q^{20} +(-0.633975 + 1.09808i) q^{22} +(-2.36603 + 4.09808i) q^{23} +(1.00000 + 1.73205i) q^{25} -1.00000 q^{26} +1.00000 q^{28} +(0.232051 + 0.401924i) q^{29} +(3.09808 - 5.36603i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.232051 + 0.401924i) q^{34} +1.73205 q^{35} +7.19615 q^{37} +(-2.09808 - 3.63397i) q^{38} +(-0.866025 + 1.50000i) q^{40} +(-4.73205 + 8.19615i) q^{41} +(4.19615 + 7.26795i) q^{43} +1.26795 q^{44} +4.73205 q^{46} +(4.09808 + 7.09808i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(1.00000 - 1.73205i) q^{50} +(0.500000 + 0.866025i) q^{52} +2.53590 q^{53} +2.19615 q^{55} +(-0.500000 - 0.866025i) q^{56} +(0.232051 - 0.401924i) q^{58} +(-1.09808 + 1.90192i) q^{59} +(5.69615 + 9.86603i) q^{61} -6.19615 q^{62} +1.00000 q^{64} +(0.866025 + 1.50000i) q^{65} +(3.09808 - 5.36603i) q^{67} +(0.232051 - 0.401924i) q^{68} +(-0.866025 - 1.50000i) q^{70} +16.3923 q^{71} +1.19615 q^{73} +(-3.59808 - 6.23205i) q^{74} +(-2.09808 + 3.63397i) q^{76} +(-0.633975 + 1.09808i) q^{77} +(-2.09808 - 3.63397i) q^{79} +1.73205 q^{80} +9.46410 q^{82} +(-2.36603 - 4.09808i) q^{83} +(0.401924 - 0.696152i) q^{85} +(4.19615 - 7.26795i) q^{86} +(-0.633975 - 1.09808i) q^{88} -5.53590 q^{89} -1.00000 q^{91} +(-2.36603 - 4.09808i) q^{92} +(4.09808 - 7.09808i) q^{94} +(-3.63397 + 6.29423i) q^{95} +(8.00000 + 13.8564i) q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.866025	+	1.50000i	−0.387298	+	0.670820i	−0.992085	−	0.125567i	$-0.959925\pi$
$5$	−0.866025	+	1.50000i	−0.387298	+	0.670820i	0.604787	+	0.796387i	$0.293258\pi$
$6$		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
$11$	−0.633975	−	1.09808i	−0.191151	−	0.331082i	0.754481	−	0.656322i	$-0.227889\pi$
$11$	−0.633975	−	1.09808i	−0.191151	−	0.331082i	−0.945632	+	0.325239i	$0.894555\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	−0.788320	−	0.615265i	$-0.789049\pi$
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	0.926995	+	0.375073i	$0.122382\pi$
$14$	−0.500000	+	0.866025i	−0.133631	+	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.464102			−0.112561			−0.0562806	−	0.998415i	$-0.517924\pi$
$17$	−0.464102			−0.112561			−0.0562806	+	0.998415i	$0.517924\pi$
$18$		0			0
$19$	4.19615			0.962663			0.481332	−	0.876539i	$-0.340153\pi$
$19$	4.19615			0.962663			0.481332	+	0.876539i	$0.340153\pi$
$20$	−0.866025	−	1.50000i	−0.193649	−	0.335410i
$21$		0			0
$22$	−0.633975	+	1.09808i	−0.135164	+	0.234111i
$23$	−2.36603	+	4.09808i	−0.493350	+	0.854508i	−0.999971	−	0.00766135i	$-0.997561\pi$
$23$	−2.36603	+	4.09808i	−0.493350	+	0.854508i	0.506620	+	0.862169i	$0.330895\pi$
$24$		0			0
$25$	1.00000	+	1.73205i	0.200000	+	0.346410i
$26$	−1.00000			−0.196116
$27$		0			0
$28$	1.00000			0.188982
$29$	0.232051	+	0.401924i	0.0430908	+	0.0746354i	0.886766	−	0.462218i	$-0.152946\pi$
$29$	0.232051	+	0.401924i	0.0430908	+	0.0746354i	−0.843676	+	0.536853i	$0.819613\pi$
$30$		0			0
$31$	3.09808	−	5.36603i	0.556431	−	0.963767i	−0.441360	−	0.897330i	$-0.645504\pi$
$31$	3.09808	−	5.36603i	0.556431	−	0.963767i	0.997791	−	0.0664364i	$-0.0211629\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	0.232051	+	0.401924i	0.0397964	+	0.0689294i
$35$	1.73205			0.292770
$36$		0			0
$37$	7.19615			1.18304			0.591520	−	0.806290i	$-0.298528\pi$
$37$	7.19615			1.18304			0.591520	+	0.806290i	$0.298528\pi$
$38$	−2.09808	−	3.63397i	−0.340353	−	0.589509i
$39$		0			0
$40$	−0.866025	+	1.50000i	−0.136931	+	0.237171i
$41$	−4.73205	+	8.19615i	−0.739022	+	1.28002i	0.213914	+	0.976853i	$0.431379\pi$
$41$	−4.73205	+	8.19615i	−0.739022	+	1.28002i	−0.952936	+	0.303171i	$0.901955\pi$
$42$		0			0
$43$	4.19615	+	7.26795i	0.639907	+	1.10835i	0.985453	+	0.169950i	$0.0543606\pi$
$43$	4.19615	+	7.26795i	0.639907	+	1.10835i	−0.345545	+	0.938402i	$0.612306\pi$
$44$	1.26795			0.191151
$45$		0			0
$46$	4.73205			0.697703
$47$	4.09808	+	7.09808i	0.597766	+	1.03536i	0.993150	+	0.116845i	$0.0372781\pi$
$47$	4.09808	+	7.09808i	0.597766	+	1.03536i	−0.395384	+	0.918516i	$0.629389\pi$
$48$		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
$53$	2.53590			0.348332			0.174166	−	0.984716i	$-0.444277\pi$
$53$	2.53590			0.348332			0.174166	+	0.984716i	$0.444277\pi$
$54$		0			0
$55$	2.19615			0.296129
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$		0			0
$58$	0.232051	−	0.401924i	0.0304698	−	0.0527752i
$59$	−1.09808	+	1.90192i	−0.142957	+	0.247609i	−0.928609	−	0.371060i	$-0.878995\pi$
$59$	−1.09808	+	1.90192i	−0.142957	+	0.247609i	0.785652	+	0.618669i	$0.212328\pi$
$60$		0			0
$61$	5.69615	+	9.86603i	0.729318	+	1.26322i	0.957172	+	0.289520i	$0.0934956\pi$
$61$	5.69615	+	9.86603i	0.729318	+	1.26322i	−0.227854	+	0.973695i	$0.573171\pi$
$62$	−6.19615			−0.786912
$63$		0			0
$64$	1.00000			0.125000
$65$	0.866025	+	1.50000i	0.107417	+	0.186052i
$66$		0			0
$67$	3.09808	−	5.36603i	0.378490	−	0.655564i	−0.612353	−	0.790585i	$-0.709777\pi$
$67$	3.09808	−	5.36603i	0.378490	−	0.655564i	0.990843	+	0.135020i	$0.0431100\pi$
$68$	0.232051	−	0.401924i	0.0281403	−	0.0487404i
$69$		0			0
$70$	−0.866025	−	1.50000i	−0.103510	−	0.179284i
$71$	16.3923			1.94541			0.972704	−	0.232048i	$-0.0745426\pi$
$71$	16.3923			1.94541			0.972704	+	0.232048i	$0.0745426\pi$
$72$		0			0
$73$	1.19615			0.139999			0.0699995	−	0.997547i	$-0.477700\pi$
$73$	1.19615			0.139999			0.0699995	+	0.997547i	$0.477700\pi$
$74$	−3.59808	−	6.23205i	−0.418268	−	0.724461i
$75$		0			0
$76$	−2.09808	+	3.63397i	−0.240666	+	0.416845i
$77$	−0.633975	+	1.09808i	−0.0722481	+	0.125137i
$78$		0			0
$79$	−2.09808	−	3.63397i	−0.236052	−	0.408854i	0.723526	−	0.690297i	$-0.242520\pi$
$79$	−2.09808	−	3.63397i	−0.236052	−	0.408854i	−0.959578	+	0.281443i	$0.909187\pi$
$80$	1.73205			0.193649
$81$		0			0
$82$	9.46410			1.04514
$83$	−2.36603	−	4.09808i	−0.259705	−	0.449822i	0.706458	−	0.707755i	$-0.250292\pi$
$83$	−2.36603	−	4.09808i	−0.259705	−	0.449822i	−0.966163	+	0.257933i	$0.916959\pi$
$84$		0			0
$85$	0.401924	−	0.696152i	0.0435948	−	0.0755083i
$86$	4.19615	−	7.26795i	0.452483	−	0.783723i
$87$		0			0
$88$	−0.633975	−	1.09808i	−0.0675819	−	0.117055i
$89$	−5.53590			−0.586804			−0.293402	−	0.955989i	$-0.594787\pi$
$89$	−5.53590			−0.586804			−0.293402	+	0.955989i	$0.594787\pi$
$90$		0			0
$91$	−1.00000			−0.104828
$92$	−2.36603	−	4.09808i	−0.246675	−	0.427254i
$93$		0			0
$94$	4.09808	−	7.09808i	0.422684	−	0.732111i
$95$	−3.63397	+	6.29423i	−0.372838	+	0.645774i
$96$		0			0
$97$	8.00000	+	13.8564i	0.812277	+	1.40690i	0.911267	+	0.411816i	$0.135106\pi$
$97$	8.00000	+	13.8564i	0.812277	+	1.40690i	−0.0989899	+	0.995088i	$0.531561\pi$
$98$	1.00000			0.101015
$99$		0			0
$100$	−2.00000			−0.200000
$101$	0.464102	+	0.803848i	0.0461798	+	0.0799858i	0.888191	−	0.459474i	$-0.151962\pi$
$101$	0.464102	+	0.803848i	0.0461798	+	0.0799858i	−0.842012	+	0.539459i	$0.818629\pi$
$102$		0			0
$103$	−6.19615	+	10.7321i	−0.610525	+	1.05746i	0.380627	+	0.924729i	$0.375708\pi$
$103$	−6.19615	+	10.7321i	−0.610525	+	1.05746i	−0.991152	+	0.132732i	$0.957625\pi$
$104$	0.500000	−	0.866025i	0.0490290	−	0.0849208i
$105$		0			0
$106$	−1.26795	−	2.19615i	−0.123154	−	0.213309i
$107$	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
$109$	−15.1962			−1.45553			−0.727764	−	0.685828i	$-0.759440\pi$
$109$	−15.1962			−1.45553			−0.727764	+	0.685828i	$0.759440\pi$
$110$	−1.09808	−	1.90192i	−0.104697	−	0.181341i
$111$		0			0
$112$	−0.500000	+	0.866025i	−0.0472456	+	0.0818317i
$113$	6.86603	−	11.8923i	0.645901	−	1.11873i	−0.338191	−	0.941077i	$-0.609815\pi$
$113$	6.86603	−	11.8923i	0.645901	−	1.11873i	0.984093	−	0.177657i	$-0.0568516\pi$
$114$		0			0
$115$	−4.09808	−	7.09808i	−0.382148	−	0.661899i
$116$	−0.464102			−0.0430908
$117$		0			0
$118$	2.19615			0.202172
$119$	0.232051	+	0.401924i	0.0212721	+	0.0368443i
$120$		0			0
$121$	4.69615	−	8.13397i	0.426923	−	0.739452i
$122$	5.69615	−	9.86603i	0.515705	−	0.893228i
$123$		0			0
$124$	3.09808	+	5.36603i	0.278215	+	0.481883i
$125$	−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
$131$	4.73205	−	8.19615i	0.413441	−	0.716101i	−0.581822	−	0.813316i	$-0.697660\pi$
$131$	4.73205	−	8.19615i	0.413441	−	0.716101i	0.995263	+	0.0972148i	$0.0309934\pi$
$132$		0			0
$133$	−2.09808	−	3.63397i	−0.181926	−	0.315106i
$134$	−6.19615			−0.535266
$135$		0			0
$136$	−0.464102			−0.0397964
$137$	−7.33013	−	12.6962i	−0.626255	−	1.08471i	−0.988297	−	0.152544i	$-0.951254\pi$
$137$	−7.33013	−	12.6962i	−0.626255	−	1.08471i	0.362042	−	0.932162i	$-0.382080\pi$
$138$		0			0
$139$	3.90192	−	6.75833i	0.330957	−	0.573234i	−0.651743	−	0.758440i	$-0.725962\pi$
$139$	3.90192	−	6.75833i	0.330957	−	0.573234i	0.982700	+	0.185206i	$0.0592952\pi$
$140$	−0.866025	+	1.50000i	−0.0731925	+	0.126773i
$141$		0			0
$142$	−8.19615	−	14.1962i	−0.687806	−	1.19131i
$143$	−1.26795			−0.106031
$144$		0			0
$145$	−0.803848			−0.0667559
$146$	−0.598076	−	1.03590i	−0.0494971	−	0.0857316i
$147$		0			0
$148$	−3.59808	+	6.23205i	−0.295760	+	0.512271i
$149$	−4.96410	+	8.59808i	−0.406675	+	0.704382i	−0.994515	−	0.104596i	$-0.966645\pi$
$149$	−4.96410	+	8.59808i	−0.406675	+	0.704382i	0.587840	+	0.808977i	$0.299979\pi$
$150$		0			0
$151$	−4.29423	−	7.43782i	−0.349459	−	0.605281i	0.636694	−	0.771116i	$-0.280301\pi$
$151$	−4.29423	−	7.43782i	−0.349459	−	0.605281i	−0.986154	+	0.165835i	$0.946968\pi$
$152$	4.19615			0.340353
$153$		0			0
$154$	1.26795			0.102174
$155$	5.36603	+	9.29423i	0.431010	+	0.746530i
$156$		0			0
$157$	2.69615	−	4.66987i	0.215176	−	0.372696i	−0.738151	−	0.674636i	$-0.764301\pi$
$157$	2.69615	−	4.66987i	0.215176	−	0.372696i	0.953327	+	0.301939i	$0.0976340\pi$
$158$	−2.09808	+	3.63397i	−0.166914	+	0.289103i
$159$		0			0
$160$	−0.866025	−	1.50000i	−0.0684653	−	0.118585i
$161$	4.73205			0.372938
$162$		0			0
$163$	3.60770			0.282576			0.141288	−	0.989969i	$-0.454876\pi$
$163$	3.60770			0.282576			0.141288	+	0.989969i	$0.454876\pi$
$164$	−4.73205	−	8.19615i	−0.369511	−	0.640012i
$165$		0			0
$166$	−2.36603	+	4.09808i	−0.183639	+	0.318072i
$167$	5.36603	−	9.29423i	0.415236	−	0.719209i	−0.580218	−	0.814461i	$-0.697033\pi$
$167$	5.36603	−	9.29423i	0.415236	−	0.719209i	0.995453	+	0.0952525i	$0.0303658\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$	−0.803848			−0.0616523
$171$		0			0
$172$	−8.39230			−0.639907
$173$	11.5981	+	20.0885i	0.881785	+	1.52730i	0.849354	+	0.527823i	$0.176992\pi$
$173$	11.5981	+	20.0885i	0.881785	+	1.52730i	0.0324311	+	0.999474i	$0.489675\pi$
$174$		0			0
$175$	1.00000	−	1.73205i	0.0755929	−	0.130931i
$176$	−0.633975	+	1.09808i	−0.0477876	+	0.0827706i
$177$		0			0
$178$	2.76795	+	4.79423i	0.207467	+	0.359343i
$179$	10.7321			0.802151			0.401076	−	0.916045i	$-0.368636\pi$
$179$	10.7321			0.802151			0.401076	+	0.916045i	$0.368636\pi$
$180$		0			0
$181$	−20.3923			−1.51575			−0.757874	−	0.652401i	$-0.773762\pi$
$181$	−20.3923			−1.51575			−0.757874	+	0.652401i	$0.773762\pi$
$182$	0.500000	+	0.866025i	0.0370625	+	0.0641941i
$183$		0			0
$184$	−2.36603	+	4.09808i	−0.174426	+	0.302114i
$185$	−6.23205	+	10.7942i	−0.458189	+	0.793607i
$186$		0			0
$187$	0.294229	+	0.509619i	0.0215161	+	0.0372670i
$188$	−8.19615			−0.597766
$189$		0			0
$190$	7.26795			0.527272
$191$	3.29423	+	5.70577i	0.238362	+	0.412855i	0.960244	−	0.279161i	$-0.0900562\pi$
$191$	3.29423	+	5.70577i	0.238362	+	0.412855i	−0.721882	+	0.692016i	$0.756723\pi$
$192$		0			0
$193$	9.50000	−	16.4545i	0.683825	−	1.18442i	−0.289980	−	0.957033i	$-0.593649\pi$
$193$	9.50000	−	16.4545i	0.683825	−	1.18442i	0.973805	−	0.227387i	$-0.0730182\pi$
$194$	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
$199$	−10.5885			−0.750596			−0.375298	−	0.926904i	$-0.622460\pi$
$199$	−10.5885			−0.750596			−0.375298	+	0.926904i	$0.622460\pi$
$200$	1.00000	+	1.73205i	0.0707107	+	0.122474i
$201$		0			0
$202$	0.464102	−	0.803848i	0.0326541	−	0.0565585i
$203$	0.232051	−	0.401924i	0.0162868	−	0.0282095i
$204$		0			0
$205$	−8.19615	−	14.1962i	−0.572444	−	0.991502i
$206$	12.3923			0.863413
$207$		0			0
$208$	−1.00000			−0.0693375
$209$	−2.66025	−	4.60770i	−0.184014	−	0.318721i
$210$		0			0
$211$	−11.0981	+	19.2224i	−0.764023	+	1.32333i	0.176738	+	0.984258i	$0.443445\pi$
$211$	−11.0981	+	19.2224i	−0.764023	+	1.32333i	−0.940762	+	0.339069i	$0.889888\pi$
$212$	−1.26795	+	2.19615i	−0.0870831	+	0.150832i
$213$		0			0
$214$	−6.92820	−	12.0000i	−0.473602	−	0.820303i
$215$	−14.5359			−0.991340
$216$		0			0
$217$	−6.19615			−0.420622
$218$	7.59808	+	13.1603i	0.514607	+	0.891325i
$219$		0			0
$220$	−1.09808	+	1.90192i	−0.0740323	+	0.128228i
$221$	−0.232051	+	0.401924i	−0.0156094	+	0.0270363i
$222$		0			0
$223$	4.19615	+	7.26795i	0.280995	+	0.486698i	0.971630	−	0.236506i	$-0.0760022\pi$
$223$	4.19615	+	7.26795i	0.280995	+	0.486698i	−0.690635	+	0.723204i	$0.742669\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	−13.7321			−0.913442
$227$	9.46410	+	16.3923i	0.628154	+	1.08800i	0.987922	+	0.154953i	$0.0495227\pi$
$227$	9.46410	+	16.3923i	0.628154	+	1.08800i	−0.359767	+	0.933042i	$0.617144\pi$
$228$		0			0
$229$	−9.89230	+	17.1340i	−0.653702	+	1.13224i	0.328516	+	0.944499i	$0.393452\pi$
$229$	−9.89230	+	17.1340i	−0.653702	+	1.13224i	−0.982218	+	0.187746i	$0.939882\pi$
$230$	−4.09808	+	7.09808i	−0.270219	+	0.468033i
$231$		0			0
$232$	0.232051	+	0.401924i	0.0152349	+	0.0263876i
$233$	10.2679			0.672676			0.336338	−	0.941741i	$-0.390812\pi$
$233$	10.2679			0.672676			0.336338	+	0.941741i	$0.390812\pi$
$234$		0			0
$235$	−14.1962			−0.926055
$236$	−1.09808	−	1.90192i	−0.0714787	−	0.123805i
$237$		0			0
$238$	0.232051	−	0.401924i	0.0150416	−	0.0260528i
$239$	4.56218	−	7.90192i	0.295103	−	0.511133i	−0.679906	−	0.733299i	$-0.737979\pi$
$239$	4.56218	−	7.90192i	0.295103	−	0.511133i	0.975009	+	0.222166i	$0.0713128\pi$
$240$		0			0
$241$	−8.79423	−	15.2321i	−0.566486	−	0.981183i	−0.996910	−	0.0785557i	$-0.974969\pi$
$241$	−8.79423	−	15.2321i	−0.566486	−	0.981183i	0.430424	−	0.902627i	$-0.358364\pi$
$242$	−9.39230			−0.603760
$243$		0			0
$244$	−11.3923			−0.729318
$245$	−0.866025	−	1.50000i	−0.0553283	−	0.0958315i
$246$		0			0
$247$	2.09808	−	3.63397i	0.133497	−	0.231224i
$248$	3.09808	−	5.36603i	0.196728	−	0.340743i
$249$		0			0
$250$	6.06218	+	10.5000i	0.383406	+	0.664078i
$251$	−14.1962			−0.896053			−0.448027	−	0.894020i	$-0.647873\pi$
$251$	−14.1962			−0.896053			−0.448027	+	0.894020i	$0.647873\pi$
$252$		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
$257$	7.03590	−	12.1865i	0.438887	−	0.760175i	−0.558717	−	0.829359i	$-0.688706\pi$
$257$	7.03590	−	12.1865i	0.438887	−	0.760175i	0.997604	+	0.0691835i	$0.0220394\pi$
$258$		0			0
$259$	−3.59808	−	6.23205i	−0.223574	−	0.387241i
$260$	−1.73205			−0.107417
$261$		0			0
$262$	−9.46410			−0.584694
$263$	4.56218	+	7.90192i	0.281316	+	0.487253i	0.971709	−	0.236181i	$-0.0758958\pi$
$263$	4.56218	+	7.90192i	0.281316	+	0.487253i	−0.690393	+	0.723434i	$0.742562\pi$
$264$		0			0
$265$	−2.19615	+	3.80385i	−0.134909	+	0.233668i
$266$	−2.09808	+	3.63397i	−0.128641	+	0.222813i
$267$		0			0
$268$	3.09808	+	5.36603i	0.189245	+	0.327782i
$269$	−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
$271$	17.8038			1.08151			0.540753	−	0.841181i	$-0.318139\pi$
$271$	17.8038			1.08151			0.540753	+	0.841181i	$0.318139\pi$
$272$	0.232051	+	0.401924i	0.0140701	+	0.0243702i
$273$		0			0
$274$	−7.33013	+	12.6962i	−0.442829	+	0.767003i
$275$	1.26795	−	2.19615i	0.0764602	−	0.132433i
$276$		0			0
$277$	−11.3923	−	19.7321i	−0.684497	−	1.18558i	−0.973595	−	0.228284i	$-0.926688\pi$
$277$	−11.3923	−	19.7321i	−0.684497	−	1.18558i	0.289097	−	0.957300i	$-0.406645\pi$
$278$	−7.80385			−0.468044
$279$		0			0
$280$	1.73205			0.103510
$281$	5.13397	+	8.89230i	0.306267	+	0.530470i	0.977543	−	0.210738i	$-0.0675866\pi$
$281$	5.13397	+	8.89230i	0.306267	+	0.530470i	−0.671275	+	0.741208i	$0.734253\pi$
$282$		0			0
$283$	−12.1962	+	21.1244i	−0.724986	+	1.25571i	0.233994	+	0.972238i	$0.424820\pi$
$283$	−12.1962	+	21.1244i	−0.724986	+	1.25571i	−0.958980	+	0.283475i	$0.908513\pi$
$284$	−8.19615	+	14.1962i	−0.486352	+	0.842387i
$285$		0			0
$286$	0.633975	+	1.09808i	0.0374877	+	0.0649306i
$287$	9.46410			0.558648
$288$		0			0
$289$	−16.7846			−0.987330
$290$	0.401924	+	0.696152i	0.0236018	+	0.0408795i
$291$		0			0
$292$	−0.598076	+	1.03590i	−0.0349998	+	0.0606214i
$293$	4.66987	−	8.08846i	0.272817	−	0.472533i	−0.696765	−	0.717299i	$-0.745378\pi$
$293$	4.66987	−	8.08846i	0.272817	−	0.472533i	0.969582	+	0.244767i	$0.0787113\pi$
$294$		0			0
$295$	−1.90192	−	3.29423i	−0.110734	−	0.191797i
$296$	7.19615			0.418268
$297$		0			0
$298$	9.92820			0.575125
$299$	2.36603	+	4.09808i	0.136831	+	0.236998i
$300$		0			0
$301$	4.19615	−	7.26795i	0.241862	−	0.418918i
$302$	−4.29423	+	7.43782i	−0.247105	+	0.427999i
$303$		0			0
$304$	−2.09808	−	3.63397i	−0.120333	−	0.208423i
$305$	−19.7321			−1.12985
$306$		0			0
$307$	8.00000			0.456584			0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000			0.456584			0.228292	+	0.973593i	$0.426686\pi$
$308$	−0.633975	−	1.09808i	−0.0361241	−	0.0625687i
$309$		0			0
$310$	5.36603	−	9.29423i	0.304770	−	0.527877i
$311$	−14.4904	+	25.0981i	−0.821674	+	1.42318i	0.0827607	+	0.996569i	$0.473626\pi$
$311$	−14.4904	+	25.0981i	−0.821674	+	1.42318i	−0.904435	+	0.426612i	$0.859707\pi$
$312$		0			0
$313$	14.9904	+	25.9641i	0.847306	+	1.46758i	0.883603	+	0.468237i	$0.155111\pi$
$313$	14.9904	+	25.9641i	0.847306	+	1.46758i	−0.0362966	+	0.999341i	$0.511556\pi$
$314$	−5.39230			−0.304305
$315$		0			0
$316$	4.19615			0.236052
$317$	−9.69615	−	16.7942i	−0.544590	−	0.943258i	−0.998633	−	0.0522778i	$-0.983352\pi$
$317$	−9.69615	−	16.7942i	−0.544590	−	0.943258i	0.454042	−	0.890980i	$-0.349981\pi$
$318$		0			0
$319$	0.294229	−	0.509619i	0.0164736	−	0.0285332i
$320$	−0.866025	+	1.50000i	−0.0484123	+	0.0838525i
$321$		0			0
$322$	−2.36603	−	4.09808i	−0.131853	−	0.228377i
$323$	−1.94744			−0.108359
$324$		0			0
$325$	2.00000			0.110940
$326$	−1.80385	−	3.12436i	−0.0999059	−	0.173042i
$327$		0			0
$328$	−4.73205	+	8.19615i	−0.261284	+	0.452557i
$329$	4.09808	−	7.09808i	0.225934	−	0.391330i
$330$		0			0
$331$	−16.5885	−	28.7321i	−0.911784	−	1.57926i	−0.811543	−	0.584293i	$-0.801372\pi$
$331$	−16.5885	−	28.7321i	−0.911784	−	1.57926i	−0.100241	−	0.994963i	$-0.531962\pi$
$332$	4.73205			0.259705
$333$		0			0
$334$	−10.7321			−0.587232
$335$	5.36603	+	9.29423i	0.293177	+	0.507798i
$336$		0			0
$337$	5.80385	−	10.0526i	0.316156	−	0.547598i	−0.663527	−	0.748153i	$-0.730941\pi$
$337$	5.80385	−	10.0526i	0.316156	−	0.547598i	0.979682	+	0.200555i	$0.0642745\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$		0			0
$340$	0.401924	+	0.696152i	0.0217974	+	0.0377542i
$341$	−7.85641			−0.425448
$342$		0			0
$343$	1.00000			0.0539949
$344$	4.19615	+	7.26795i	0.226241	+	0.391862i
$345$		0			0
$346$	11.5981	−	20.0885i	0.623516	−	1.07996i
$347$	2.19615	−	3.80385i	0.117896	−	0.204201i	−0.801038	−	0.598614i	$-0.795719\pi$
$347$	2.19615	−	3.80385i	0.117896	−	0.204201i	0.918934	+	0.394412i	$0.129052\pi$
$348$		0			0
$349$	4.19615	+	7.26795i	0.224615	+	0.389044i	0.956204	−	0.292702i	$-0.0945543\pi$
$349$	4.19615	+	7.26795i	0.224615	+	0.389044i	−0.731589	+	0.681746i	$0.761221\pi$
$350$	−2.00000			−0.106904
$351$		0			0
$352$	1.26795			0.0675819
$353$	−15.9282	−	27.5885i	−0.847773	−	1.46839i	−0.883191	−	0.469013i	$-0.844610\pi$
$353$	−15.9282	−	27.5885i	−0.847773	−	1.46839i	0.0354186	−	0.999373i	$-0.488724\pi$
$354$		0			0
$355$	−14.1962	+	24.5885i	−0.753454	+	1.30502i
$356$	2.76795	−	4.79423i	0.146701	−	0.254094i
$357$		0			0
$358$	−5.36603	−	9.29423i	−0.283603	−	0.491215i
$359$	5.07180			0.267679			0.133840	−	0.991003i	$-0.457269\pi$
$359$	5.07180			0.267679			0.133840	+	0.991003i	$0.457269\pi$
$360$		0			0
$361$	−1.39230			−0.0732792
$362$	10.1962	+	17.6603i	0.535898	+	0.928202i
$363$		0			0
$364$	0.500000	−	0.866025i	0.0262071	−	0.0453921i
$365$	−1.03590	+	1.79423i	−0.0542214	+	0.0939142i
$366$		0			0
$367$	−13.2942	−	23.0263i	−0.693953	−	1.20196i	−0.970532	−	0.240971i	$-0.922534\pi$
$367$	−13.2942	−	23.0263i	−0.693953	−	1.20196i	0.276579	−	0.960991i	$-0.410799\pi$
$368$	4.73205			0.246675
$369$		0			0
$370$	12.4641			0.647978
$371$	−1.26795	−	2.19615i	−0.0658286	−	0.114019i
$372$		0			0
$373$	−10.0000	+	17.3205i	−0.517780	+	0.896822i	0.482006	+	0.876168i	$0.339908\pi$
$373$	−10.0000	+	17.3205i	−0.517780	+	0.896822i	−0.999787	+	0.0206542i	$0.993425\pi$
$374$	0.294229	−	0.509619i	0.0152142	−	0.0263518i
$375$		0			0
$376$	4.09808	+	7.09808i	0.211342	+	0.366055i
$377$	0.464102			0.0239024
$378$		0			0
$379$	14.5885			0.749359			0.374679	−	0.927154i	$-0.377753\pi$
$379$	14.5885			0.749359			0.374679	+	0.927154i	$0.377753\pi$
$380$	−3.63397	−	6.29423i	−0.186419	−	0.322887i
$381$		0			0
$382$	3.29423	−	5.70577i	0.168547	−	0.291933i
$383$	18.9282	−	32.7846i	0.967186	−	1.67522i	0.263562	−	0.964642i	$-0.415102\pi$
$383$	18.9282	−	32.7846i	0.967186	−	1.67522i	0.703624	−	0.710573i	$-0.251564\pi$
$384$		0			0
$385$	−1.09808	−	1.90192i	−0.0559631	−	0.0969310i
$386$	−19.0000			−0.967075
$387$		0			0
$388$	−16.0000			−0.812277
$389$	−9.12436	−	15.8038i	−0.462623	−	0.801287i	0.536468	−	0.843921i	$-0.319758\pi$
$389$	−9.12436	−	15.8038i	−0.462623	−	0.801287i	−0.999091	+	0.0426341i	$0.986425\pi$
$390$		0			0
$391$	1.09808	−	1.90192i	0.0555321	−	0.0961844i
$392$	−0.500000	+	0.866025i	−0.0252538	+	0.0437409i
$393$		0			0
$394$	7.50000	+	12.9904i	0.377845	+	0.654446i
$395$	7.26795			0.365690
$396$		0			0
$397$	−8.60770			−0.432008			−0.216004	−	0.976392i	$-0.569302\pi$
$397$	−8.60770			−0.432008			−0.216004	+	0.976392i	$0.569302\pi$
$398$	5.29423	+	9.16987i	0.265376	+	0.459644i
$399$		0			0
$400$	1.00000	−	1.73205i	0.0500000	−	0.0866025i
$401$	−12.8660	+	22.2846i	−0.642499	+	1.11284i	0.342375	+	0.939564i	$0.388769\pi$
$401$	−12.8660	+	22.2846i	−0.642499	+	1.11284i	−0.984873	+	0.173277i	$0.944564\pi$
$402$		0			0
$403$	−3.09808	−	5.36603i	−0.154326	−	0.267301i
$404$	−0.928203			−0.0461798
$405$		0			0
$406$	−0.464102			−0.0230330
$407$	−4.56218	−	7.90192i	−0.226139	−	0.391684i
$408$		0			0
$409$	5.40192	−	9.35641i	0.267108	−	0.462645i	−0.701006	−	0.713156i	$-0.747265\pi$
$409$	5.40192	−	9.35641i	0.267108	−	0.462645i	0.968114	+	0.250511i	$0.0805986\pi$
$410$	−8.19615	+	14.1962i	−0.404779	+	0.701098i
$411$		0			0
$412$	−6.19615	−	10.7321i	−0.305263	−	0.528730i
$413$	2.19615			0.108066
$414$		0			0
$415$	8.19615			0.402333
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$		0			0
$418$	−2.66025	+	4.60770i	−0.130117	+	0.225370i
$419$	5.66025	−	9.80385i	0.276522	−	0.478949i	−0.693996	−	0.719979i	$-0.744152\pi$
$419$	5.66025	−	9.80385i	0.276522	−	0.478949i	0.970518	+	0.241029i	$0.0774850\pi$
$420$		0			0
$421$	−1.40192	−	2.42820i	−0.0683256	−	0.118343i	0.829839	−	0.558003i	$-0.188432\pi$
$421$	−1.40192	−	2.42820i	−0.0683256	−	0.118343i	−0.898164	+	0.439660i	$0.855099\pi$
$422$	22.1962			1.08049
$423$		0			0
$424$	2.53590			0.123154
$425$	−0.464102	−	0.803848i	−0.0225122	−	0.0389923i
$426$		0			0
$427$	5.69615	−	9.86603i	0.275656	−	0.477450i
$428$	−6.92820	+	12.0000i	−0.334887	+	0.580042i
$429$		0			0
$430$	7.26795	+	12.5885i	0.350492	+	0.607069i
$431$	35.3205			1.70133			0.850665	−	0.525709i	$-0.176200\pi$
$431$	35.3205			1.70133			0.850665	+	0.525709i	$0.176200\pi$
$432$		0			0
$433$	−0.411543			−0.0197775			−0.00988874	−	0.999951i	$-0.503148\pi$
$433$	−0.411543			−0.0197775			−0.00988874	+	0.999951i	$0.503148\pi$
$434$	3.09808	+	5.36603i	0.148712	+	0.257577i
$435$		0			0
$436$	7.59808	−	13.1603i	0.363882	−	0.630262i
$437$	−9.92820	+	17.1962i	−0.474930	+	0.822604i
$438$		0			0
$439$	20.5885	+	35.6603i	0.982633	+	1.70197i	0.652014	+	0.758207i	$0.273924\pi$
$439$	20.5885	+	35.6603i	0.982633	+	1.70197i	0.330619	+	0.943764i	$0.392742\pi$
$440$	2.19615			0.104697
$441$		0			0
$442$	0.464102			0.0220751
$443$	4.09808	+	7.09808i	0.194705	+	0.337240i	0.946804	−	0.321811i	$-0.104292\pi$
$443$	4.09808	+	7.09808i	0.194705	+	0.337240i	−0.752098	+	0.659051i	$0.770958\pi$
$444$		0			0
$445$	4.79423	−	8.30385i	0.227268	−	0.393640i
$446$	4.19615	−	7.26795i	0.198694	−	0.344147i
$447$		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
$452$	6.86603	+	11.8923i	0.322951	+	0.559367i
$453$		0			0
$454$	9.46410	−	16.3923i	0.444172	−	0.769329i
$455$	0.866025	−	1.50000i	0.0405999	−	0.0703211i
$456$		0			0
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	0.877483	−	0.479608i	$-0.159221\pi$
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	−0.854094	+	0.520119i	$0.825888\pi$
$458$	19.7846			0.924474
$459$		0			0
$460$	8.19615			0.382148
$461$	−12.4641	−	21.5885i	−0.580511	−	1.00547i	−0.995419	−	0.0956112i	$-0.969519\pi$
$461$	−12.4641	−	21.5885i	−0.580511	−	1.00547i	0.414908	−	0.909864i	$-0.363814\pi$
$462$		0			0
$463$	−8.09808	+	14.0263i	−0.376350	+	0.651856i	−0.990528	−	0.137311i	$-0.956154\pi$
$463$	−8.09808	+	14.0263i	−0.376350	+	0.651856i	0.614179	+	0.789167i	$0.289487\pi$
$464$	0.232051	−	0.401924i	0.0107727	−	0.0186588i
$465$		0			0
$466$	−5.13397	−	8.89230i	−0.237827	−	0.411928i
$467$	−4.73205			−0.218973			−0.109487	−	0.993988i	$-0.534921\pi$
$467$	−4.73205			−0.218973			−0.109487	+	0.993988i	$0.534921\pi$
$468$		0			0
$469$	−6.19615			−0.286112
$470$	7.09808	+	12.2942i	0.327410	+	0.567090i
$471$		0			0
$472$	−1.09808	+	1.90192i	−0.0505431	+	0.0875431i
$473$	5.32051	−	9.21539i	0.244637	−	0.423724i
$474$		0			0
$475$	4.19615	+	7.26795i	0.192533	+	0.333476i
$476$	−0.464102			−0.0212721
$477$		0			0
$478$	−9.12436			−0.417338
$479$	−6.63397	−	11.4904i	−0.303114	−	0.525009i	0.673726	−	0.738982i	$-0.264693\pi$
$479$	−6.63397	−	11.4904i	−0.303114	−	0.525009i	−0.976840	+	0.213973i	$0.931360\pi$
$480$		0			0
$481$	3.59808	−	6.23205i	0.164058	−	0.284157i
$482$	−8.79423	+	15.2321i	−0.400566	+	0.693801i
$483$		0			0
$484$	4.69615	+	8.13397i	0.213461	+	0.369726i
$485$	−27.7128			−1.25837
$486$		0			0
$487$	4.19615			0.190146			0.0950729	−	0.995470i	$-0.469692\pi$
$487$	4.19615			0.190146			0.0950729	+	0.995470i	$0.469692\pi$
$488$	5.69615	+	9.86603i	0.257853	+	0.446614i
$489$		0			0
$490$	−0.866025	+	1.50000i	−0.0391230	+	0.0677631i
$491$	11.6603	−	20.1962i	0.526220	−	0.911440i	−0.473313	−	0.880894i	$-0.656942\pi$
$491$	11.6603	−	20.1962i	0.526220	−	0.911440i	0.999533	−	0.0305455i	$-0.00972446\pi$
$492$		0			0
$493$	−0.107695	−	0.186533i	−0.00485035	−	0.00840105i
$494$	−4.19615			−0.188794
$495$		0			0
$496$	−6.19615			−0.278215
$497$	−8.19615	−	14.1962i	−0.367648	−	0.636784i
$498$		0			0
$499$	5.29423	−	9.16987i	0.237002	−	0.410500i	−0.722850	−	0.691004i	$-0.757168\pi$
$499$	5.29423	−	9.16987i	0.237002	−	0.410500i	0.959853	+	0.280505i	$0.0905018\pi$
$500$	6.06218	−	10.5000i	0.271109	−	0.469574i
$501$		0			0
$502$	7.09808	+	12.2942i	0.316803	+	0.548718i
$503$	28.9808			1.29219			0.646094	−	0.763258i	$-0.276401\pi$
$503$	28.9808			1.29219			0.646094	+	0.763258i	$0.276401\pi$
$504$		0			0
$505$	−1.60770			−0.0715415
$506$	−3.00000	−	5.19615i	−0.133366	−	0.230997i
$507$		0			0
$508$	2.00000	−	3.46410i	0.0887357	−	0.153695i
$509$	−16.8564	+	29.1962i	−0.747147	+	1.29410i	0.202038	+	0.979378i	$0.435244\pi$
$509$	−16.8564	+	29.1962i	−0.747147	+	1.29410i	−0.949185	+	0.314719i	$0.898090\pi$
$510$		0			0
$511$	−0.598076	−	1.03590i	−0.0264573	−	0.0458254i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−14.0718			−0.620680
$515$	−10.7321	−	18.5885i	−0.472911	−	0.819105i
$516$		0			0
$517$	5.19615	−	9.00000i	0.228527	−	0.395820i
$518$	−3.59808	+	6.23205i	−0.158090	+	0.273821i
$519$		0			0
$520$	0.866025	+	1.50000i	0.0379777	+	0.0657794i
$521$	16.1436			0.707264			0.353632	−	0.935385i	$-0.384947\pi$
$521$	16.1436			0.707264			0.353632	+	0.935385i	$0.384947\pi$
$522$		0			0
$523$	36.3923			1.59132			0.795662	−	0.605741i	$-0.207123\pi$
$523$	36.3923			1.59132			0.795662	+	0.605741i	$0.207123\pi$
$524$	4.73205	+	8.19615i	0.206721	+	0.358051i
$525$		0			0
$526$	4.56218	−	7.90192i	0.198920	−	0.344540i
$527$	−1.43782	+	2.49038i	−0.0626325	+	0.108483i
$528$		0			0
$529$	0.303848	+	0.526279i	0.0132108	+	0.0228817i
$530$	4.39230			0.190790
$531$		0			0
$532$	4.19615			0.181926
$533$	4.73205	+	8.19615i	0.204968	+	0.355015i
$534$		0			0
$535$	−12.0000	+	20.7846i	−0.518805	+	0.898597i
$536$	3.09808	−	5.36603i	0.133817	−	0.231777i
$537$		0			0
$538$	14.7224	+	25.5000i	0.634729	+	1.09938i
$539$	1.26795			0.0546144
$540$		0			0
$541$	−0.411543			−0.0176936			−0.00884680	−	0.999961i	$-0.502816\pi$
$541$	−0.411543			−0.0176936			−0.00884680	+	0.999961i	$0.502816\pi$
$542$	−8.90192	−	15.4186i	−0.382370	−	0.662285i
$543$		0			0
$544$	0.232051	−	0.401924i	0.00994910	−	0.0172323i
$545$	13.1603	−	22.7942i	0.563723	−	0.976397i
$546$		0			0
$547$	15.0981	+	26.1506i	0.645547	+	1.11812i	0.984175	+	0.177200i	$0.0567039\pi$
$547$	15.0981	+	26.1506i	0.645547	+	1.11812i	−0.338628	+	0.940920i	$0.609963\pi$
$548$	14.6603			0.626255
$549$		0			0
$550$	−2.53590			−0.108131
$551$	0.973721	+	1.68653i	0.0414819	+	0.0718487i
$552$		0			0
$553$	−2.09808	+	3.63397i	−0.0892193	+	0.154532i
$554$	−11.3923	+	19.7321i	−0.484013	+	0.838335i
$555$		0			0
$556$	3.90192	+	6.75833i	0.165478	+	0.286617i
$557$	13.1436			0.556912			0.278456	−	0.960449i	$-0.410177\pi$
$557$	13.1436			0.556912			0.278456	+	0.960449i	$0.410177\pi$
$558$		0			0
$559$	8.39230			0.354957
$560$	−0.866025	−	1.50000i	−0.0365963	−	0.0633866i
$561$		0			0
$562$	5.13397	−	8.89230i	0.216564	−	0.375099i
$563$	−12.0000	+	20.7846i	−0.505740	+	0.875967i	0.494238	+	0.869326i	$0.335447\pi$
$563$	−12.0000	+	20.7846i	−0.505740	+	0.875967i	−0.999978	+	0.00664037i	$0.997886\pi$
$564$		0			0
$565$	11.8923	+	20.5981i	0.500313	+	0.866568i
$566$	24.3923			1.02529
$567$		0			0
$568$	16.3923			0.687806
$569$	−21.9904	−	38.0885i	−0.921885	−	1.59675i	−0.796496	−	0.604643i	$-0.793316\pi$
$569$	−21.9904	−	38.0885i	−0.921885	−	1.59675i	−0.125388	−	0.992108i	$-0.540018\pi$
$570$		0			0
$571$	15.0981	−	26.1506i	0.631835	−	1.09437i	−0.355342	−	0.934737i	$-0.615635\pi$
$571$	15.0981	−	26.1506i	0.631835	−	1.09437i	0.987176	−	0.159633i	$-0.0510312\pi$
$572$	0.633975	−	1.09808i	0.0265078	−	0.0459129i
$573$		0			0
$574$	−4.73205	−	8.19615i	−0.197512	−	0.342101i
$575$	−9.46410			−0.394680
$576$		0			0
$577$	20.8038			0.866076			0.433038	−	0.901376i	$-0.357442\pi$
$577$	20.8038			0.866076			0.433038	+	0.901376i	$0.357442\pi$
$578$	8.39230	+	14.5359i	0.349074	+	0.604614i
$579$		0			0
$580$	0.401924	−	0.696152i	0.0166890	−	0.0289062i
$581$	−2.36603	+	4.09808i	−0.0981593	+	0.170017i
$582$		0			0
$583$	−1.60770	−	2.78461i	−0.0665839	−	0.115327i
$584$	1.19615			0.0494971
$585$		0			0
$586$	−9.33975			−0.385821
$587$	3.63397	+	6.29423i	0.149990	+	0.259791i	0.931224	−	0.364448i	$-0.118742\pi$
$587$	3.63397	+	6.29423i	0.149990	+	0.259791i	−0.781233	+	0.624239i	$0.785409\pi$
$588$		0			0
$589$	13.0000	−	22.5167i	0.535656	−	0.927783i
$590$	−1.90192	+	3.29423i	−0.0783010	+	0.135621i
$591$		0			0
$592$	−3.59808	−	6.23205i	−0.147880	−	0.256136i
$593$	−13.1436			−0.539743			−0.269871	−	0.962896i	$-0.586981\pi$
$593$	−13.1436			−0.539743			−0.269871	+	0.962896i	$0.586981\pi$
$594$		0			0
$595$	−0.803848			−0.0329545
$596$	−4.96410	−	8.59808i	−0.203338	−	0.352191i
$597$		0			0
$598$	2.36603	−	4.09808i	0.0967540	−	0.167583i
$599$	7.09808	−	12.2942i	0.290020	−	0.502329i	−0.683794	−	0.729675i	$-0.739672\pi$
$599$	7.09808	−	12.2942i	0.290020	−	0.502329i	0.973814	+	0.227346i	$0.0730049\pi$
$600$		0			0
$601$	−0.598076	−	1.03590i	−0.0243960	−	0.0422552i	0.853570	−	0.520979i	$-0.174433\pi$
$601$	−0.598076	−	1.03590i	−0.0243960	−	0.0422552i	−0.877966	+	0.478724i	$0.841100\pi$
$602$	−8.39230			−0.342045
$603$		0			0
$604$	8.58846			0.349459
$605$	8.13397	+	14.0885i	0.330693	+	0.572777i
$606$		0			0
$607$	−1.29423	+	2.24167i	−0.0525311	+	0.0909866i	−0.891095	−	0.453816i	$-0.850062\pi$
$607$	−1.29423	+	2.24167i	−0.0525311	+	0.0909866i	0.838564	+	0.544803i	$0.183396\pi$
$608$	−2.09808	+	3.63397i	−0.0850882	+	0.147377i
$609$		0			0
$610$	9.86603	+	17.0885i	0.399464	+	0.691891i
$611$	8.19615			0.331581
$612$		0			0
$613$	34.7846			1.40494			0.702469	−	0.711715i	$-0.252081\pi$
$613$	34.7846			1.40494			0.702469	+	0.711715i	$0.252081\pi$
$614$	−4.00000	−	6.92820i	−0.161427	−	0.279600i
$615$		0			0
$616$	−0.633975	+	1.09808i	−0.0255436	+	0.0442428i
$617$	14.2583	−	24.6962i	0.574019	−	0.994230i	−0.422129	−	0.906536i	$-0.638717\pi$
$617$	14.2583	−	24.6962i	0.574019	−	0.994230i	0.996147	−	0.0876938i	$-0.0279497\pi$
$618$		0			0
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	0.903416	−	0.428765i	$-0.141051\pi$
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	−0.823029	+	0.567999i	$0.807718\pi$
$620$	−10.7321			−0.431010
$621$		0			0
$622$	28.9808			1.16202
$623$	2.76795	+	4.79423i	0.110896	+	0.192077i
$624$		0			0
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	14.9904	−	25.9641i	0.599136	−	1.03773i
$627$		0			0
$628$	2.69615	+	4.66987i	0.107588	+	0.186348i
$629$	−3.33975			−0.133164
$630$		0			0
$631$	8.58846			0.341901			0.170951	−	0.985280i	$-0.445316\pi$
$631$	8.58846			0.341901			0.170951	+	0.985280i	$0.445316\pi$
$632$	−2.09808	−	3.63397i	−0.0834570	−	0.144552i
$633$		0			0
$634$	−9.69615	+	16.7942i	−0.385083	+	0.666984i
$635$	3.46410	−	6.00000i	0.137469	−	0.238103i
$636$		0			0
$637$	0.500000	+	0.866025i	0.0198107	+	0.0343132i
$638$	−0.588457			−0.0232972
$639$		0			0
$640$	1.73205			0.0684653
$641$	−13.3301	−	23.0885i	−0.526508	−	0.911939i	−0.999523	−	0.0308846i	$-0.990168\pi$
$641$	−13.3301	−	23.0885i	−0.526508	−	0.911939i	0.473015	−	0.881055i	$-0.343166\pi$
$642$		0			0
$643$	−14.0981	+	24.4186i	−0.555974	+	0.962975i	0.441853	+	0.897087i	$0.354321\pi$
$643$	−14.0981	+	24.4186i	−0.555974	+	0.962975i	−0.997827	+	0.0658876i	$0.979012\pi$
$644$	−2.36603	+	4.09808i	−0.0932345	+	0.161487i
$645$		0			0
$646$	0.973721	+	1.68653i	0.0383105	+	0.0663558i
$647$	11.3205			0.445055			0.222528	−	0.974926i	$-0.428569\pi$
$647$	11.3205			0.445055			0.222528	+	0.974926i	$0.428569\pi$
$648$		0			0
$649$	2.78461			0.109305
$650$	−1.00000	−	1.73205i	−0.0392232	−	0.0679366i
$651$		0			0
$652$	−1.80385	+	3.12436i	−0.0706441	+	0.122359i
$653$	0.339746	−	0.588457i	0.0132953	−	0.0230281i	−0.859301	−	0.511470i	$-0.829101\pi$
$653$	0.339746	−	0.588457i	0.0132953	−	0.0230281i	0.872597	+	0.488442i	$0.162435\pi$
$654$		0			0
$655$	8.19615	+	14.1962i	0.320250	+	0.554690i
$656$	9.46410			0.369511
$657$		0			0
$658$	−8.19615			−0.319519
$659$	−17.6603	−	30.5885i	−0.687946	−	1.19156i	−0.972501	−	0.232898i	$-0.925179\pi$
$659$	−17.6603	−	30.5885i	−0.687946	−	1.19156i	0.284555	−	0.958660i	$-0.408154\pi$
$660$		0			0
$661$	−6.30385	+	10.9186i	−0.245191	+	0.424684i	−0.962185	−	0.272396i	$-0.912184\pi$
$661$	−6.30385	+	10.9186i	−0.245191	+	0.424684i	0.716994	+	0.697079i	$0.245517\pi$
$662$	−16.5885	+	28.7321i	−0.644729	+	1.11670i
$663$		0			0
$664$	−2.36603	−	4.09808i	−0.0918196	−	0.159036i
$665$	7.26795			0.281839
$666$		0			0
$667$	−2.19615			−0.0850354
$668$	5.36603	+	9.29423i	0.207618	+	0.359605i
$669$		0			0
$670$	5.36603	−	9.29423i	0.207308	−	0.359067i
$671$	7.22243	−	12.5096i	0.278819	−	0.482928i
$672$		0			0
$673$	22.0885	+	38.2583i	0.851447	+	1.47475i	0.879902	+	0.475155i	$0.157608\pi$
$673$	22.0885	+	38.2583i	0.851447	+	1.47475i	−0.0284546	+	0.999595i	$0.509059\pi$
$674$	−11.6077			−0.447112
$675$		0			0
$676$	−12.0000			−0.461538
$677$	−1.60770	−	2.78461i	−0.0617887	−	0.107021i	0.833476	−	0.552555i	$-0.186347\pi$
$677$	−1.60770	−	2.78461i	−0.0617887	−	0.107021i	−0.895265	+	0.445534i	$0.853014\pi$
$678$		0			0
$679$	8.00000	−	13.8564i	0.307012	−	0.531760i
$680$	0.401924	−	0.696152i	0.0154131	−	0.0266962i
$681$		0			0
$682$	3.92820	+	6.80385i	0.150419	+	0.260533i
$683$	15.7128			0.601234			0.300617	−	0.953745i	$-0.402807\pi$
$683$	15.7128			0.601234			0.300617	+	0.953745i	$0.402807\pi$
$684$		0			0
$685$	25.3923			0.970190
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$		0			0
$688$	4.19615	−	7.26795i	0.159977	−	0.277088i
$689$	1.26795	−	2.19615i	0.0483050	−	0.0836667i
$690$		0			0
$691$	−22.0000	−	38.1051i	−0.836919	−	1.44959i	−0.892458	−	0.451130i	$-0.851021\pi$
$691$	−22.0000	−	38.1051i	−0.836919	−	1.44959i	0.0555386	−	0.998457i	$-0.482312\pi$
$692$	−23.1962			−0.881785
$693$		0			0
$694$	−4.39230			−0.166730
$695$	6.75833	+	11.7058i	0.256358	+	0.444025i
$696$		0			0
$697$	2.19615	−	3.80385i	0.0831852	−	0.144081i
$698$	4.19615	−	7.26795i	0.158827	−	0.275096i
$699$		0			0
$700$	1.00000	+	1.73205i	0.0377964	+	0.0654654i
$701$	−16.1769			−0.610994			−0.305497	−	0.952193i	$-0.598823\pi$
$701$	−16.1769			−0.610994			−0.305497	+	0.952193i	$0.598823\pi$
$702$		0			0
$703$	30.1962			1.13887
$704$	−0.633975	−	1.09808i	−0.0238938	−	0.0413853i
$705$		0			0
$706$	−15.9282	+	27.5885i	−0.599466	+	1.03831i
$707$	0.464102	−	0.803848i	0.0174543	−	0.0302318i
$708$		0			0
$709$	−11.7942	−	20.4282i	−0.442942	−	0.767197i	0.554965	−	0.831874i	$-0.312732\pi$
$709$	−11.7942	−	20.4282i	−0.442942	−	0.767197i	−0.997906	+	0.0646766i	$0.979398\pi$
$710$	28.3923			1.06554
$711$		0			0
$712$	−5.53590			−0.207467
$713$	14.6603	+	25.3923i	0.549031	+	0.950949i
$714$		0			0
$715$	1.09808	−	1.90192i	0.0410657	−	0.0711279i
$716$	−5.36603	+	9.29423i	−0.200538	+	0.347342i
$717$		0			0
$718$	−2.53590	−	4.39230i	−0.0946389	−	0.163919i
$719$	−11.3205			−0.422184			−0.211092	−	0.977466i	$-0.567702\pi$
$719$	−11.3205			−0.422184			−0.211092	+	0.977466i	$0.567702\pi$
$720$		0			0
$721$	12.3923			0.461514
$722$	0.696152	+	1.20577i	0.0259081	+	0.0448742i
$723$		0			0
$724$	10.1962	−	17.6603i	0.378937	−	0.656338i
$725$	−0.464102	+	0.803848i	−0.0172363	+	0.0298541i
$726$		0			0
$727$	−18.1962	−	31.5167i	−0.674858	−	1.16889i	−0.976510	−	0.215470i	$-0.930872\pi$
$727$	−18.1962	−	31.5167i	−0.674858	−	1.16889i	0.301652	−	0.953418i	$-0.402462\pi$
$728$	−1.00000			−0.0370625
$729$		0			0
$730$	2.07180			0.0766806
$731$	−1.94744	−	3.37307i	−0.0720287	−	0.124757i
$732$		0			0
$733$	−16.5885	+	28.7321i	−0.612709	+	1.06124i	0.378073	+	0.925776i	$0.376587\pi$
$733$	−16.5885	+	28.7321i	−0.612709	+	1.06124i	−0.990782	+	0.135467i	$0.956747\pi$
$734$	−13.2942	+	23.0263i	−0.490699	+	0.849915i
$735$		0			0
$736$	−2.36603	−	4.09808i	−0.0872129	−	0.151057i
$737$	−7.85641			−0.289394
$738$		0			0
$739$	−13.8038			−0.507783			−0.253891	−	0.967233i	$-0.581711\pi$
$739$	−13.8038			−0.507783			−0.253891	+	0.967233i	$0.581711\pi$
$740$	−6.23205	−	10.7942i	−0.229095	−	0.396804i
$741$		0			0
$742$	−1.26795	+	2.19615i	−0.0465479	+	0.0806233i
$743$	7.26795	−	12.5885i	0.266635	−	0.461826i	−0.701356	−	0.712812i	$-0.747421\pi$
$743$	7.26795	−	12.5885i	0.266635	−	0.461826i	0.967991	+	0.250986i	$0.0807548\pi$
$744$		0			0
$745$	−8.59808	−	14.8923i	−0.315009	−	0.545612i
$746$	20.0000			0.732252
$747$		0			0
$748$	−0.588457			−0.0215161
$749$	−6.92820	−	12.0000i	−0.253151	−	0.438470i
$750$		0			0
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	−0.827225	−	0.561870i	$-0.810082\pi$
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	0.900207	+	0.435463i	$0.143415\pi$
$752$	4.09808	−	7.09808i	0.149441	−	0.258840i
$753$		0			0
$754$	−0.232051	−	0.401924i	−0.00845079	−	0.0146372i
$755$	14.8756			0.541380
$756$		0			0
$757$	−36.7846			−1.33696			−0.668480	−	0.743730i	$-0.733055\pi$
$757$	−36.7846			−1.33696			−0.668480	+	0.743730i	$0.733055\pi$
$758$	−7.29423	−	12.6340i	−0.264938	−	0.458887i
$759$		0			0
$760$	−3.63397	+	6.29423i	−0.131818	+	0.228316i
$761$	−13.1603	+	22.7942i	−0.477059	+	0.826290i	−0.999654	−	0.0262906i	$-0.991630\pi$
$761$	−13.1603	+	22.7942i	−0.477059	+	0.826290i	0.522596	+	0.852581i	$0.324964\pi$
$762$		0			0
$763$	7.59808	+	13.1603i	0.275069	+	0.476433i
$764$	−6.58846			−0.238362
$765$		0			0
$766$	−37.8564			−1.36781
$767$	1.09808	+	1.90192i	0.0396492	+	0.0686745i
$768$		0			0
$769$	1.59808	−	2.76795i	0.0576281	−	0.0998148i	−0.835772	−	0.549076i	$-0.814980\pi$
$769$	1.59808	−	2.76795i	0.0576281	−	0.0998148i	0.893400	+	0.449262i	$0.148313\pi$
$770$	−1.09808	+	1.90192i	−0.0395719	+	0.0685406i
$771$		0			0
$772$	9.50000	+	16.4545i	0.341912	+	0.592210i
$773$	−38.6603			−1.39051			−0.695256	−	0.718762i	$-0.744709\pi$
$773$	−38.6603			−1.39051			−0.695256	+	0.718762i	$0.744709\pi$
$774$		0			0
$775$	12.3923			0.445145
$776$	8.00000	+	13.8564i	0.287183	+	0.497416i
$777$		0			0
$778$	−9.12436	+	15.8038i	−0.327124	+	0.566595i
$779$	−19.8564	+	34.3923i	−0.711430	+	1.23223i
$780$		0			0
$781$	−10.3923	−	18.0000i	−0.371866	−	0.644091i
$782$	−2.19615			−0.0785343
$783$		0			0
$784$	1.00000			0.0357143
$785$	4.66987	+	8.08846i	0.166675	+	0.288689i
$786$		0			0
$787$	8.58846	−	14.8756i	0.306145	−	0.530259i	−0.671370	−	0.741122i	$-0.734294\pi$
$787$	8.58846	−	14.8756i	0.306145	−	0.530259i	0.977516	+	0.210863i	$0.0676273\pi$
$788$	7.50000	−	12.9904i	0.267176	−	0.462763i
$789$		0			0
$790$	−3.63397	−	6.29423i	−0.129291	−	0.223939i
$791$	−13.7321			−0.488256
$792$		0			0
$793$	11.3923			0.404553
$794$	4.30385	+	7.45448i	0.152738	+	0.264550i
$795$		0			0
$796$	5.29423	−	9.16987i	0.187649	−	0.325018i
$797$	−19.3301	+	33.4808i	−0.684708	+	1.18595i	0.288820	+	0.957383i	$0.406737\pi$
$797$	−19.3301	+	33.4808i	−0.684708	+	1.18595i	−0.973528	+	0.228566i	$0.926596\pi$
$798$		0			0
$799$	−1.90192	−	3.29423i	−0.0672852	−	0.116541i
$800$	−2.00000			−0.0707107
$801$		0			0
$802$	25.7321			0.908630
$803$	−0.758330	−	1.31347i	−0.0267609	−	0.0463512i
$804$		0			0
$805$	−4.09808	+	7.09808i	−0.144438	+	0.250174i
$806$	−3.09808	+	5.36603i	−0.109125	+	0.189010i
$807$		0			0
$808$	0.464102	+	0.803848i	0.0163270	+	0.0282793i
$809$	24.1244			0.848167			0.424084	−	0.905623i	$-0.360596\pi$
$809$	24.1244			0.848167			0.424084	+	0.905623i	$0.360596\pi$
$810$		0			0
$811$	3.01924			0.106020			0.0530099	−	0.998594i	$-0.483119\pi$
$811$	3.01924			0.106020			0.0530099	+	0.998594i	$0.483119\pi$
$812$	0.232051	+	0.401924i	0.00814339	+	0.0141048i
$813$		0			0
$814$	−4.56218	+	7.90192i	−0.159904	+	0.276962i
$815$	−3.12436	+	5.41154i	−0.109441	+	0.189558i
$816$		0			0
$817$	17.6077	+	30.4974i	0.616015	+	1.06697i
$818$	−10.8038			−0.377748
$819$		0			0
$820$	16.3923			0.572444
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	0.966708	−	0.255884i	$-0.0823665\pi$
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	−0.704956	+	0.709251i	$0.749033\pi$
$822$		0			0
$823$	−8.39230	+	14.5359i	−0.292537	+	0.506690i	−0.974409	−	0.224782i	$-0.927833\pi$
$823$	−8.39230	+	14.5359i	−0.292537	+	0.506690i	0.681872	+	0.731472i	$0.261166\pi$
$824$	−6.19615	+	10.7321i	−0.215853	+	0.373869i
$825$		0			0
$826$	−1.09808	−	1.90192i	−0.0382070	−	0.0661764i
$827$	40.3923			1.40458			0.702289	−	0.711892i	$-0.252161\pi$
$827$	40.3923			1.40458			0.702289	+	0.711892i	$0.252161\pi$
$828$		0			0
$829$	26.0000			0.903017			0.451509	−	0.892267i	$-0.350886\pi$
$829$	26.0000			0.903017			0.451509	+	0.892267i	$0.350886\pi$
$830$	−4.09808	−	7.09808i	−0.142246	−	0.246378i
$831$		0			0
$832$	0.500000	−	0.866025i	0.0173344	−	0.0300240i
$833$	0.232051	−	0.401924i	0.00804008	−	0.0139258i
$834$		0			0
$835$	9.29423	+	16.0981i	0.321640	+	0.557097i
$836$	5.32051			0.184014
$837$		0			0
$838$	−11.3205			−0.391060
$839$	3.12436	+	5.41154i	0.107865	+	0.186827i	0.914905	−	0.403669i	$-0.132265\pi$
$839$	3.12436	+	5.41154i	0.107865	+	0.186827i	−0.807040	+	0.590496i	$0.798932\pi$
$840$		0			0
$841$	14.3923	−	24.9282i	0.496286	−	0.859593i
$842$	−1.40192	+	2.42820i	−0.0483135	+	0.0836814i
$843$		0			0
$844$	−11.0981	−	19.2224i	−0.382012	−	0.661663i
$845$	−20.7846			−0.715012
$846$		0			0
$847$	−9.39230			−0.322723
$848$	−1.26795	−	2.19615i	−0.0435416	−	0.0754162i
$849$		0			0
$850$	−0.464102	+	0.803848i	−0.0159186	+	0.0275717i
$851$	−17.0263	+	29.4904i	−0.583653	+	1.01092i
$852$		0			0
$853$	−1.00000	−	1.73205i	−0.0342393	−	0.0593043i	0.848398	−	0.529359i	$-0.177568\pi$
$853$	−1.00000	−	1.73205i	−0.0342393	−	0.0593043i	−0.882637	+	0.470055i	$0.844234\pi$
$854$	−11.3923			−0.389837
$855$		0			0
$856$	13.8564			0.473602
$857$	5.76795	+	9.99038i	0.197029	+	0.341265i	0.947564	−	0.319566i	$-0.103537\pi$
$857$	5.76795	+	9.99038i	0.197029	+	0.341265i	−0.750535	+	0.660831i	$0.770204\pi$
$858$		0			0
$859$	10.1962	−	17.6603i	0.347888	−	0.602560i	−0.637986	−	0.770048i	$-0.720232\pi$
$859$	10.1962	−	17.6603i	0.347888	−	0.602560i	0.985874	+	0.167488i	$0.0535655\pi$
$860$	7.26795	−	12.5885i	0.247835	−	0.429263i
$861$		0			0
$862$	−17.6603	−	30.5885i	−0.601511	−	1.04185i
$863$	−41.9090			−1.42660			−0.713299	−	0.700860i	$-0.752800\pi$
$863$	−41.9090			−1.42660			−0.713299	+	0.700860i	$0.752800\pi$
$864$		0			0
$865$	−40.1769			−1.36606
$866$	0.205771	+	0.356406i	0.00699240	+	0.0121112i
$867$		0			0
$868$	3.09808	−	5.36603i	0.105156	−	0.182135i
$869$	−2.66025	+	4.60770i	−0.0902429	+	0.156305i
$870$		0			0
$871$	−3.09808	−	5.36603i	−0.104974	−	0.181821i
$872$	−15.1962			−0.514607
$873$		0			0
$874$	19.8564			0.671653
$875$	6.06218	+	10.5000i	0.204939	+	0.354965i
$876$		0			0
$877$	−10.4019	+	18.0167i	−0.351248	+	0.608379i	−0.986468	−	0.163952i	$-0.947576\pi$
$877$	−10.4019	+	18.0167i	−0.351248	+	0.608379i	0.635220	+	0.772331i	$0.280909\pi$
$878$	20.5885	−	35.6603i	0.694827	−	1.20348i
$879$		0			0
$880$	−1.09808	−	1.90192i	−0.0370161	−	0.0641138i
$881$	37.1769			1.25252			0.626261	−	0.779613i	$-0.284584\pi$
$881$	37.1769			1.25252			0.626261	+	0.779613i	$0.284584\pi$
$882$		0			0
$883$	−38.9808			−1.31181			−0.655904	−	0.754845i	$-0.727712\pi$
$883$	−38.9808			−1.31181			−0.655904	+	0.754845i	$0.727712\pi$
$884$	−0.232051	−	0.401924i	−0.00780471	−	0.0135182i
$885$		0			0
$886$	4.09808	−	7.09808i	0.137678	−	0.238465i
$887$	−9.16987	+	15.8827i	−0.307894	+	0.533288i	−0.977902	−	0.209066i	$-0.932958\pi$
$887$	−9.16987	+	15.8827i	−0.307894	+	0.533288i	0.670007	+	0.742355i	$0.266291\pi$
$888$		0			0
$889$	2.00000	+	3.46410i	0.0670778	+	0.116182i
$890$	−9.58846			−0.321406
$891$		0			0
$892$	−8.39230			−0.280995
$893$	17.1962	+	29.7846i	0.575447	+	0.996704i
$894$		0			0
$895$	−9.29423	+	16.0981i	−0.310672	+	0.538099i
$896$	−0.500000	+	0.866025i	−0.0167038	+	0.0289319i
$897$		0			0
$898$	−3.00000	−	5.19615i	−0.100111	−	0.173398i
$899$	2.87564			0.0959081
$900$		0			0
$901$	−1.17691			−0.0392087
$902$	−6.00000	−	10.3923i	−0.199778	−	0.346026i
$903$		0			0
$904$	6.86603	−	11.8923i	0.228361	−	0.395532i
$905$	17.6603	−	30.5885i	0.587047	−	1.01679i
$906$		0			0
$907$	−10.0000	−	17.3205i	−0.332045	−	0.575118i	0.650868	−	0.759191i	$-0.274405\pi$
$907$	−10.0000	−	17.3205i	−0.332045	−	0.575118i	−0.982913	+	0.184073i	$0.941072\pi$
$908$	−18.9282			−0.628154
$909$		0			0
$910$	−1.73205			−0.0574169
$911$	−22.0526	−	38.1962i	−0.730634	−	1.26549i	−0.956613	−	0.291363i	$-0.905891\pi$
$911$	−22.0526	−	38.1962i	−0.730634	−	1.26549i	0.225979	−	0.974132i	$-0.427442\pi$
$912$		0			0
$913$	−3.00000	+	5.19615i	−0.0992855	+	0.171968i
$914$	0.500000	−	0.866025i	0.0165385	−	0.0286456i
$915$		0			0
$916$	−9.89230	−	17.1340i	−0.326851	−	0.566122i
$917$	−9.46410			−0.312532
$918$		0			0
$919$	−48.1962			−1.58984			−0.794922	−	0.606711i	$-0.792488\pi$
$919$	−48.1962			−1.58984			−0.794922	+	0.606711i	$0.792488\pi$
$920$	−4.09808	−	7.09808i	−0.135110	−	0.234017i
$921$		0			0
$922$	−12.4641	+	21.5885i	−0.410483	+	0.710978i
$923$	8.19615	−	14.1962i	0.269780	−	0.467272i
$924$		0			0
$925$	7.19615	+	12.4641i	0.236608	+	0.409817i
$926$	16.1962			0.532239
$927$		0			0
$928$	−0.464102			−0.0152349
$929$	6.69615	+	11.5981i	0.219694	+	0.380521i	0.954714	−	0.297524i	$-0.0961609\pi$
$929$	6.69615	+	11.5981i	0.219694	+	0.380521i	−0.735021	+	0.678045i	$0.762828\pi$
$930$		0			0
$931$	−2.09808	+	3.63397i	−0.0687617	+	0.119099i
$932$	−5.13397	+	8.89230i	−0.168169	+	0.291277i
$933$		0			0
$934$	2.36603	+	4.09808i	0.0774187	+	0.134093i
$935$	−1.01924			−0.0333326
$936$		0			0
$937$	−33.1962			−1.08447			−0.542236	−	0.840227i	$-0.682422\pi$
$937$	−33.1962			−1.08447			−0.542236	+	0.840227i	$0.682422\pi$
$938$	3.09808	+	5.36603i	0.101156	+	0.175207i
$939$		0			0
$940$	7.09808	−	12.2942i	0.231514	−	0.400994i
$941$	−23.3827	+	40.5000i	−0.762254	+	1.32026i	0.179433	+	0.983770i	$0.442574\pi$
$941$	−23.3827	+	40.5000i	−0.762254	+	1.32026i	−0.941686	+	0.336492i	$0.890759\pi$
$942$		0			0
$943$	−22.3923	−	38.7846i	−0.729194	−	1.26300i
$944$	2.19615			0.0714787
$945$		0			0
$946$	−10.6410			−0.345969
$947$	14.1962	+	24.5885i	0.461313	+	0.799018i	0.999027	−	0.0441100i	$-0.0140452\pi$
$947$	14.1962	+	24.5885i	0.461313	+	0.799018i	−0.537714	+	0.843127i	$0.680712\pi$
$948$		0			0
$949$	0.598076	−	1.03590i	0.0194144	−	0.0336267i
$950$	4.19615	−	7.26795i	0.136141	−	0.235803i
$951$		0			0
$952$	0.232051	+	0.401924i	0.00752081	+	0.0130264i
$953$	−4.01924			−0.130196			−0.0650979	−	0.997879i	$-0.520736\pi$
$953$	−4.01924			−0.130196			−0.0650979	+	0.997879i	$0.520736\pi$
$954$		0			0
$955$	−11.4115			−0.369269
$956$	4.56218	+	7.90192i	0.147551	+	0.255566i
$957$		0			0
$958$	−6.63397	+	11.4904i	−0.214334	+	0.371237i
$959$	−7.33013	+	12.6962i	−0.236702	+	0.409980i
$960$		0			0
$961$	−3.69615	−	6.40192i	−0.119231	−	0.206514i
$962$	−7.19615			−0.232013
$963$		0			0
$964$	17.5885			0.566486
$965$	16.4545	+	28.5000i	0.529689	+	0.917447i
$966$		0			0
$967$	−4.29423	+	7.43782i	−0.138093	+	0.239184i	−0.926775	−	0.375618i	$-0.877431\pi$
$967$	−4.29423	+	7.43782i	−0.138093	+	0.239184i	0.788682	+	0.614802i	$0.210764\pi$
$968$	4.69615	−	8.13397i	0.150940	−	0.261436i
$969$		0			0
$970$	13.8564	+	24.0000i	0.444902	+	0.770594i
$971$	−21.1244			−0.677913			−0.338956	−	0.940802i	$-0.610074\pi$
$971$	−21.1244			−0.677913			−0.338956	+	0.940802i	$0.610074\pi$
$972$		0			0
$973$	−7.80385			−0.250180
$974$	−2.09808	−	3.63397i	−0.0672267	−	0.116440i
$975$		0			0
$976$	5.69615	−	9.86603i	0.182329	−	0.315804i
$977$	23.7846	−	41.1962i	0.760937	−	1.31798i	−0.181431	−	0.983404i	$-0.558073\pi$
$977$	23.7846	−	41.1962i	0.760937	−	1.31798i	0.942368	−	0.334578i	$-0.108594\pi$
$978$		0			0
$979$	3.50962	+	6.07884i	0.112168	+	0.194281i
$980$	1.73205			0.0553283
$981$		0			0
$982$	−23.3205			−0.744187
$983$	27.4641	+	47.5692i	0.875969	+	1.51722i	0.855727	+	0.517427i	$0.173110\pi$
$983$	27.4641	+	47.5692i	0.875969	+	1.51722i	0.0202417	+	0.999795i	$0.493556\pi$
$984$		0			0
$985$	12.9904	−	22.5000i	0.413908	−	0.716910i
$986$	−0.107695	+	0.186533i	−0.00342971	+	0.00594044i
$987$		0			0
$988$	2.09808	+	3.63397i	0.0667487	+	0.115612i
$989$	−39.7128			−1.26279
$990$		0			0
$991$	−8.98076			−0.285283			−0.142642	−	0.989774i	$-0.545560\pi$
$991$	−8.98076			−0.285283			−0.142642	+	0.989774i	$0.545560\pi$
$992$	3.09808	+	5.36603i	0.0983640	+	0.170371i
$993$		0			0
$994$	−8.19615	+	14.1962i	−0.259966	+	0.450275i
$995$	9.16987	−	15.8827i	0.290705	−	0.503515i
$996$		0			0
$997$	−9.89230	−	17.1340i	−0.313292	−	0.542638i	0.665781	−	0.746148i	$-0.268099\pi$
$997$	−9.89230	−	17.1340i	−0.313292	−	0.542638i	−0.979073	+	0.203509i	$0.934765\pi$
$998$	−10.5885			−0.335172
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.a.j.1.1	✓	2	9.5	odd	6
1134.2.a.o.1.2	yes	2	9.4	even	3
1134.2.f.q.379.1		4	9.7	even	3	inner
1134.2.f.q.757.1		4	1.1	even	1	trivial
1134.2.f.t.379.2		4	9.2	odd	6
1134.2.f.t.757.2		4	3.2	odd	2
7938.2.a.bi.1.2		2	63.41	even	6
7938.2.a.br.1.1		2	63.13	odd	6
9072.2.a.bf.1.2		2	36.31	odd	6
9072.2.a.bi.1.1		2	36.23	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 1.50000i) q^{5} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 1.50000i) q^{5} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +1.73205 q^{10} +(-0.633975 - 1.09808i) q^{11} +(0.500000 - 0.866025i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} -0.464102 q^{17} +4.19615 q^{19} +(-0.866025 - 1.50000i) q^{20} +(-0.633975 + 1.09808i) q^{22} +(-2.36603 + 4.09808i) q^{23} +(1.00000 + 1.73205i) q^{25} -1.00000 q^{26} +1.00000 q^{28} +(0.232051 + 0.401924i) q^{29} +(3.09808 - 5.36603i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.232051 + 0.401924i) q^{34} +1.73205 q^{35} +7.19615 q^{37} +(-2.09808 - 3.63397i) q^{38} +(-0.866025 + 1.50000i) q^{40} +(-4.73205 + 8.19615i) q^{41} +(4.19615 + 7.26795i) q^{43} +1.26795 q^{44} +4.73205 q^{46} +(4.09808 + 7.09808i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(1.00000 - 1.73205i) q^{50} +(0.500000 + 0.866025i) q^{52} +2.53590 q^{53} +2.19615 q^{55} +(-0.500000 - 0.866025i) q^{56} +(0.232051 - 0.401924i) q^{58} +(-1.09808 + 1.90192i) q^{59} +(5.69615 + 9.86603i) q^{61} -6.19615 q^{62} +1.00000 q^{64} +(0.866025 + 1.50000i) q^{65} +(3.09808 - 5.36603i) q^{67} +(0.232051 - 0.401924i) q^{68} +(-0.866025 - 1.50000i) q^{70} +16.3923 q^{71} +1.19615 q^{73} +(-3.59808 - 6.23205i) q^{74} +(-2.09808 + 3.63397i) q^{76} +(-0.633975 + 1.09808i) q^{77} +(-2.09808 - 3.63397i) q^{79} +1.73205 q^{80} +9.46410 q^{82} +(-2.36603 - 4.09808i) q^{83} +(0.401924 - 0.696152i) q^{85} +(4.19615 - 7.26795i) q^{86} +(-0.633975 - 1.09808i) q^{88} -5.53590 q^{89} -1.00000 q^{91} +(-2.36603 - 4.09808i) q^{92} +(4.09808 - 7.09808i) q^{94} +(-3.63397 + 6.29423i) q^{95} +(8.00000 + 13.8564i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{7} + 4 q^{8}+O(q^{10}) \) 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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