LMFDB - Embedded newform 1350.2.q.e.557.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,2,Mod(143,1350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1350, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("1350.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1350.q (of order $12$, degree $4$, 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:	$10.7798042729$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 450)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.2
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1350.557
Dual form			1350.2.q.e.143.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{8} +(1.50000 - 0.866025i) q^{11} +(-1.79315 - 6.69213i) q^{13} +(0.500000 + 0.866025i) q^{16} +(2.12132 - 2.12132i) q^{17} -4.00000i q^{19} +(1.67303 - 0.448288i) q^{22} +(5.79555 - 1.55291i) q^{23} -6.92820i q^{26} +(1.73205 + 3.00000i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(0.258819 + 0.965926i) q^{32} +(2.59808 - 1.50000i) q^{34} +(4.89898 + 4.89898i) q^{37} +(1.03528 - 3.86370i) q^{38} +(6.00000 + 3.46410i) q^{41} +(-8.36516 - 2.24144i) q^{43} +1.73205 q^{44} +6.00000 q^{46} +(11.5911 + 3.10583i) q^{47} +(6.06218 + 3.50000i) q^{49} +(1.79315 - 6.69213i) q^{52} +(-8.48528 - 8.48528i) q^{53} +(0.896575 + 3.34607i) q^{58} +(-4.33013 + 7.50000i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(-2.82843 + 2.82843i) q^{62} +1.00000i q^{64} +(-3.34607 + 0.896575i) q^{67} +(2.89778 - 0.776457i) q^{68} +3.46410i q^{71} +(4.89898 - 4.89898i) q^{73} +(3.46410 + 6.00000i) q^{74} +(2.00000 - 3.46410i) q^{76} +(3.46410 - 2.00000i) q^{79} +(4.89898 + 4.89898i) q^{82} +(2.32937 - 8.69333i) q^{83} +(-7.50000 - 4.33013i) q^{86} +(1.67303 + 0.448288i) q^{88} -1.73205 q^{89} +(5.79555 + 1.55291i) q^{92} +(10.3923 + 6.00000i) q^{94} +(4.03459 - 15.0573i) q^{97} +(4.94975 + 4.94975i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 12 q^{11} + 4 q^{16} - 16 q^{31} + 48 q^{41} + 48 q^{46} - 32 q^{61} + 16 q^{76} - 60 q^{86}+O(q^{100}) $ 8 * q + 12 * q^11 + 4 * q^16 - 16 * q^31 + 48 * q^41 + 48 * q^46 - 32 * q^61 + 16 * q^76 - 60 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$7$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$		0			0
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	−0.256520	−	0.966539i	$-0.582576\pi$
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	0.708787	+	0.705422i	$0.249243\pi$
$12$		0			0
$13$	−1.79315	−	6.69213i	−0.497331	−	1.85606i	−0.516565	−	0.856248i	$-0.672790\pi$
$13$	−1.79315	−	6.69213i	−0.497331	−	1.85606i	0.0192343	−	0.999815i	$-0.493877\pi$
$14$		0			0
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.12132	−	2.12132i	0.514496	−	0.514496i	−0.401405	−	0.915901i	$-0.631478\pi$
$17$	2.12132	−	2.12132i	0.514496	−	0.514496i	0.915901	+	0.401405i	$0.131478\pi$
$18$		0			0
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$		0			0
$21$		0			0
$22$	1.67303	−	0.448288i	0.356692	−	0.0955753i
$23$	5.79555	−	1.55291i	1.20846	−	0.323805i	0.402300	−	0.915508i	$-0.368211\pi$
$23$	5.79555	−	1.55291i	1.20846	−	0.323805i	0.806156	+	0.591703i	$0.201544\pi$
$24$		0			0
$25$		0			0
$26$		−	6.92820i		−	1.35873i
$27$		0			0
$28$		0			0
$29$	1.73205	+	3.00000i	0.321634	+	0.557086i	0.980825	−	0.194889i	$-0.0624347\pi$
$29$	1.73205	+	3.00000i	0.321634	+	0.557086i	−0.659192	+	0.751975i	$0.729101\pi$
$30$		0			0
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$		0			0
$34$	2.59808	−	1.50000i	0.445566	−	0.257248i
$35$		0			0
$36$		0			0
$37$	4.89898	+	4.89898i	0.805387	+	0.805387i	0.983932	−	0.178545i	$-0.0571389\pi$
$37$	4.89898	+	4.89898i	0.805387	+	0.805387i	−0.178545	+	0.983932i	$0.557139\pi$
$38$	1.03528	−	3.86370i	0.167944	−	0.626775i
$39$		0			0
$40$		0			0
$41$	6.00000	+	3.46410i	0.937043	+	0.541002i	0.889032	−	0.457845i	$-0.151379\pi$
$41$	6.00000	+	3.46410i	0.937043	+	0.541002i	0.0480106	+	0.998847i	$0.484712\pi$
$42$		0			0
$43$	−8.36516	−	2.24144i	−1.27568	−	0.341816i	−0.443473	−	0.896288i	$-0.646254\pi$
$43$	−8.36516	−	2.24144i	−1.27568	−	0.341816i	−0.832203	+	0.554472i	$0.812920\pi$
$44$	1.73205			0.261116
$45$		0			0
$46$	6.00000			0.884652
$47$	11.5911	+	3.10583i	1.69074	+	0.453032i	0.970580	−	0.240779i	$-0.0774030\pi$
$47$	11.5911	+	3.10583i	1.69074	+	0.453032i	0.720157	+	0.693811i	$0.244070\pi$
$48$		0			0
$49$	6.06218	+	3.50000i	0.866025	+	0.500000i
$50$		0			0
$51$		0			0
$52$	1.79315	−	6.69213i	0.248665	−	0.928032i
$53$	−8.48528	−	8.48528i	−1.16554	−	1.16554i	−0.983243	−	0.182300i	$-0.941646\pi$
$53$	−8.48528	−	8.48528i	−1.16554	−	1.16554i	−0.182300	−	0.983243i	$-0.558354\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	0.896575	+	3.34607i	0.117726	+	0.439360i
$59$	−4.33013	+	7.50000i	−0.563735	+	0.976417i	0.433432	+	0.901186i	$0.357303\pi$
$59$	−4.33013	+	7.50000i	−0.563735	+	0.976417i	−0.997166	+	0.0752304i	$0.976031\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$	−2.82843	+	2.82843i	−0.359211	+	0.359211i
$63$		0			0
$64$			1.00000i			0.125000i
$65$		0			0
$66$		0			0
$67$	−3.34607	+	0.896575i	−0.408787	+	0.109534i	−0.457352	−	0.889286i	$-0.651202\pi$
$67$	−3.34607	+	0.896575i	−0.408787	+	0.109534i	0.0485648	+	0.998820i	$0.484535\pi$
$68$	2.89778	−	0.776457i	0.351407	−	0.0941593i
$69$		0			0
$70$		0			0
$71$			3.46410i			0.411113i	0.978645	+	0.205557i	$0.0659005\pi$
$71$			3.46410i			0.411113i	−0.978645	+	0.205557i	$0.934100\pi$
$72$		0			0
$73$	4.89898	−	4.89898i	0.573382	−	0.573382i	−0.359690	−	0.933072i	$-0.617117\pi$
$73$	4.89898	−	4.89898i	0.573382	−	0.573382i	0.933072	+	0.359690i	$0.117117\pi$
$74$	3.46410	+	6.00000i	0.402694	+	0.697486i
$75$		0			0
$76$	2.00000	−	3.46410i	0.229416	−	0.397360i
$77$		0			0
$78$		0			0
$79$	3.46410	−	2.00000i	0.389742	−	0.225018i	−0.292306	−	0.956325i	$-0.594423\pi$
$79$	3.46410	−	2.00000i	0.389742	−	0.225018i	0.682048	+	0.731307i	$0.261089\pi$
$80$		0			0
$81$		0			0
$82$	4.89898	+	4.89898i	0.541002	+	0.541002i
$83$	2.32937	−	8.69333i	0.255682	−	0.954217i	−0.712028	−	0.702151i	$-0.752223\pi$
$83$	2.32937	−	8.69333i	0.255682	−	0.954217i	0.967710	−	0.252066i	$-0.0811101\pi$
$84$		0			0
$85$		0			0
$86$	−7.50000	−	4.33013i	−0.808746	−	0.466930i
$87$		0			0
$88$	1.67303	+	0.448288i	0.178346	+	0.0477876i
$89$	−1.73205			−0.183597			−0.0917985	−	0.995778i	$-0.529262\pi$
$89$	−1.73205			−0.183597			−0.0917985	+	0.995778i	$0.529262\pi$
$90$		0			0
$91$		0			0
$92$	5.79555	+	1.55291i	0.604228	+	0.161903i
$93$		0			0
$94$	10.3923	+	6.00000i	1.07188	+	0.618853i
$95$		0			0
$96$		0			0
$97$	4.03459	−	15.0573i	0.409651	−	1.52884i	−0.385664	−	0.922639i	$-0.626028\pi$
$97$	4.03459	−	15.0573i	0.409651	−	1.52884i	0.795314	−	0.606197i	$-0.207306\pi$
$98$	4.94975	+	4.94975i	0.500000	+	0.500000i
$99$		0			0
$100$		0			0
$101$	−12.0000	+	6.92820i	−1.19404	+	0.689382i	−0.959221	−	0.282656i	$-0.908784\pi$
$101$	−12.0000	+	6.92820i	−1.19404	+	0.689382i	−0.234823	+	0.972038i	$0.575451\pi$
$102$		0			0
$103$	−1.79315	−	6.69213i	−0.176684	−	0.659395i	−0.996259	−	0.0864221i	$-0.972457\pi$
$103$	−1.79315	−	6.69213i	−0.176684	−	0.659395i	0.819574	−	0.572973i	$-0.194210\pi$
$104$	3.46410	−	6.00000i	0.339683	−	0.588348i
$105$		0			0
$106$	−6.00000	−	10.3923i	−0.582772	−	1.00939i
$107$	−8.48528	+	8.48528i	−0.820303	+	0.820303i	−0.986151	−	0.165848i	$-0.946964\pi$
$107$	−8.48528	+	8.48528i	−0.820303	+	0.820303i	0.165848	+	0.986151i	$0.446964\pi$
$108$		0			0
$109$		−	2.00000i		−	0.191565i	−0.995402	−	0.0957826i	$-0.969465\pi$
$109$		−	2.00000i		−	0.191565i	0.995402	−	0.0957826i	$-0.0305354\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.89778	+	0.776457i	−0.272600	+	0.0730429i	−0.392529	−	0.919739i	$-0.628400\pi$
$113$	−2.89778	+	0.776457i	−0.272600	+	0.0730429i	0.119929	+	0.992782i	$0.461733\pi$
$114$		0			0
$115$		0			0
$116$			3.46410i			0.321634i
$117$		0			0
$118$	−6.12372	+	6.12372i	−0.563735	+	0.563735i
$119$		0			0
$120$		0			0
$121$	−4.00000	+	6.92820i	−0.363636	+	0.629837i
$122$	−2.07055	−	7.72741i	−0.187459	−	0.699607i
$123$		0			0
$124$	−3.46410	+	2.00000i	−0.311086	+	0.179605i
$125$		0			0
$126$		0			0
$127$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$127$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$		0			0
$130$		0			0
$131$	15.0000	+	8.66025i	1.31056	+	0.756650i	0.982188	−	0.187900i	$-0.0601681\pi$
$131$	15.0000	+	8.66025i	1.31056	+	0.756650i	0.328368	+	0.944550i	$0.393501\pi$
$132$		0			0
$133$		0			0
$134$	−3.46410			−0.299253
$135$		0			0
$136$	3.00000			0.257248
$137$	−17.3867	−	4.65874i	−1.48544	−	0.398023i	−0.577247	−	0.816569i	$-0.695873\pi$
$137$	−17.3867	−	4.65874i	−1.48544	−	0.398023i	−0.908196	+	0.418546i	$0.862540\pi$
$138$		0			0
$139$	11.2583	+	6.50000i	0.954919	+	0.551323i	0.894606	−	0.446857i	$-0.147457\pi$
$139$	11.2583	+	6.50000i	0.954919	+	0.551323i	0.0603135	+	0.998179i	$0.480790\pi$
$140$		0			0
$141$		0			0
$142$	−0.896575	+	3.34607i	−0.0752389	+	0.280796i
$143$	−8.48528	−	8.48528i	−0.709575	−	0.709575i
$144$		0			0
$145$		0			0
$146$	6.00000	−	3.46410i	0.496564	−	0.286691i
$147$		0			0
$148$	1.79315	+	6.69213i	0.147396	+	0.550090i
$149$	−5.19615	+	9.00000i	−0.425685	+	0.737309i	−0.996484	−	0.0837813i	$-0.973300\pi$
$149$	−5.19615	+	9.00000i	−0.425685	+	0.737309i	0.570799	+	0.821090i	$0.306634\pi$
$150$		0			0
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	0.903842	−	0.427865i	$-0.140734\pi$
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	−0.822464	+	0.568818i	$0.807401\pi$
$152$	2.82843	−	2.82843i	0.229416	−	0.229416i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−6.69213	+	1.79315i	−0.534090	+	0.143109i	−0.515776	−	0.856723i	$-0.672496\pi$
$157$	−6.69213	+	1.79315i	−0.534090	+	0.143109i	−0.0183138	+	0.999832i	$0.505830\pi$
$158$	3.86370	−	1.03528i	0.307380	−	0.0823622i
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	1.22474	−	1.22474i	0.0959294	−	0.0959294i	−0.657513	−	0.753443i	$-0.728392\pi$
$163$	1.22474	−	1.22474i	0.0959294	−	0.0959294i	0.753443	+	0.657513i	$0.228392\pi$
$164$	3.46410	+	6.00000i	0.270501	+	0.468521i
$165$		0			0
$166$	4.50000	−	7.79423i	0.349268	−	0.604949i
$167$	1.55291	+	5.79555i	0.120168	+	0.448474i	0.999621	−	0.0275115i	$-0.00875830\pi$
$167$	1.55291	+	5.79555i	0.120168	+	0.448474i	−0.879453	+	0.475985i	$0.842092\pi$
$168$		0			0
$169$	−30.3109	+	17.5000i	−2.33161	+	1.34615i
$170$		0			0
$171$		0			0
$172$	−6.12372	−	6.12372i	−0.466930	−	0.466930i
$173$	−4.65874	+	17.3867i	−0.354198	+	1.32188i	0.527294	+	0.849683i	$0.323207\pi$
$173$	−4.65874	+	17.3867i	−0.354198	+	1.32188i	−0.881491	+	0.472200i	$0.843460\pi$
$174$		0			0
$175$		0			0
$176$	1.50000	+	0.866025i	0.113067	+	0.0652791i
$177$		0			0
$178$	−1.67303	−	0.448288i	−0.125399	−	0.0336006i
$179$	12.1244			0.906217			0.453108	−	0.891455i	$-0.350315\pi$
$179$	12.1244			0.906217			0.453108	+	0.891455i	$0.350315\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$		0			0
$184$	5.19615	+	3.00000i	0.383065	+	0.221163i
$185$		0			0
$186$		0			0
$187$	1.34486	−	5.01910i	0.0983461	−	0.367033i
$188$	8.48528	+	8.48528i	0.618853	+	0.618853i
$189$		0			0
$190$		0			0
$191$	−3.00000	+	1.73205i	−0.217072	+	0.125327i	−0.604594	−	0.796534i	$-0.706665\pi$
$191$	−3.00000	+	1.73205i	−0.217072	+	0.125327i	0.387522	+	0.921861i	$0.373331\pi$
$192$		0			0
$193$	1.34486	+	5.01910i	0.0968054	+	0.361283i	0.997287	−	0.0736115i	$-0.0234525\pi$
$193$	1.34486	+	5.01910i	0.0968054	+	0.361283i	−0.900482	+	0.434894i	$0.856786\pi$
$194$	7.79423	−	13.5000i	0.559593	−	0.969244i
$195$		0			0
$196$	3.50000	+	6.06218i	0.250000	+	0.433013i
$197$	4.24264	−	4.24264i	0.302276	−	0.302276i	−0.539628	−	0.841904i	$-0.681435\pi$
$197$	4.24264	−	4.24264i	0.302276	−	0.302276i	0.841904	+	0.539628i	$0.181435\pi$
$198$		0			0
$199$		−	26.0000i		−	1.84309i	−0.388270	−	0.921546i	$-0.626927\pi$
$199$		−	26.0000i		−	1.84309i	0.388270	−	0.921546i	$-0.373073\pi$
$200$		0			0
$201$		0			0
$202$	−13.3843	+	3.58630i	−0.941713	+	0.252331i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		−	6.92820i		−	0.482711i
$207$		0			0
$208$	4.89898	−	4.89898i	0.339683	−	0.339683i
$209$	−3.46410	−	6.00000i	−0.239617	−	0.415029i
$210$		0			0
$211$	−11.5000	+	19.9186i	−0.791693	+	1.37125i	0.133226	+	0.991086i	$0.457467\pi$
$211$	−11.5000	+	19.9186i	−0.791693	+	1.37125i	−0.924918	+	0.380166i	$0.875867\pi$
$212$	−3.10583	−	11.5911i	−0.213309	−	0.796081i
$213$		0			0
$214$	−10.3923	+	6.00000i	−0.710403	+	0.410152i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.517638	−	1.93185i	0.0350589	−	0.130842i
$219$		0			0
$220$		0			0
$221$	−18.0000	−	10.3923i	−1.21081	−	0.699062i
$222$		0			0
$223$	3.34607	+	0.896575i	0.224069	+	0.0600391i	0.369107	−	0.929387i	$-0.379664\pi$
$223$	3.34607	+	0.896575i	0.224069	+	0.0600391i	−0.145038	+	0.989426i	$0.546330\pi$
$224$		0			0
$225$		0			0
$226$	−3.00000			−0.199557
$227$	2.89778	+	0.776457i	0.192332	+	0.0515353i	0.353699	−	0.935359i	$-0.384924\pi$
$227$	2.89778	+	0.776457i	0.192332	+	0.0515353i	−0.161367	+	0.986894i	$0.551590\pi$
$228$		0			0
$229$	−17.3205	−	10.0000i	−1.14457	−	0.660819i	−0.197013	−	0.980401i	$-0.563124\pi$
$229$	−17.3205	−	10.0000i	−1.14457	−	0.660819i	−0.947559	+	0.319582i	$0.896457\pi$
$230$		0			0
$231$		0			0
$232$	−0.896575	+	3.34607i	−0.0588631	+	0.219680i
$233$	6.36396	+	6.36396i	0.416917	+	0.416917i	0.884140	−	0.467223i	$-0.154745\pi$
$233$	6.36396	+	6.36396i	0.416917	+	0.416917i	−0.467223	+	0.884140i	$0.654745\pi$
$234$		0			0
$235$		0			0
$236$	−7.50000	+	4.33013i	−0.488208	+	0.281867i
$237$		0			0
$238$		0			0
$239$	5.19615	−	9.00000i	0.336111	−	0.582162i	−0.647586	−	0.761992i	$-0.724222\pi$
$239$	5.19615	−	9.00000i	0.336111	−	0.582162i	0.983698	+	0.179830i	$0.0575549\pi$
$240$		0			0
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	0.980917	−	0.194429i	$-0.0622852\pi$
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	−0.658838	+	0.752285i	$0.728952\pi$
$242$	−5.65685	+	5.65685i	−0.363636	+	0.363636i
$243$		0			0
$244$		−	8.00000i		−	0.512148i
$245$		0			0
$246$		0			0
$247$	−26.7685	+	7.17260i	−1.70324	+	0.456382i
$248$	−3.86370	+	1.03528i	−0.245345	+	0.0657401i
$249$		0			0
$250$		0			0
$251$		−	10.3923i		−	0.655956i	−0.944685	−	0.327978i	$-0.893633\pi$
$251$		−	10.3923i		−	0.655956i	0.944685	−	0.327978i	$-0.106367\pi$
$252$		0			0
$253$	7.34847	−	7.34847i	0.461994	−	0.461994i
$254$		0			0
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.776457	−	2.89778i	−0.0484341	−	0.180758i	0.937471	−	0.348063i	$-0.113160\pi$
$257$	−0.776457	−	2.89778i	−0.0484341	−	0.180758i	−0.985905	+	0.167304i	$0.946494\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	12.2474	+	12.2474i	0.756650	+	0.756650i
$263$	−6.21166	+	23.1822i	−0.383027	+	1.42948i	0.458226	+	0.888836i	$0.348485\pi$
$263$	−6.21166	+	23.1822i	−0.383027	+	1.42948i	−0.841253	+	0.540641i	$0.818182\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−3.34607	−	0.896575i	−0.204393	−	0.0547671i
$269$	−6.92820			−0.422420			−0.211210	−	0.977441i	$-0.567740\pi$
$269$	−6.92820			−0.422420			−0.211210	+	0.977441i	$0.567740\pi$
$270$		0			0
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$	2.89778	+	0.776457i	0.175704	+	0.0470796i
$273$		0			0
$274$	−15.5885	−	9.00000i	−0.941733	−	0.543710i
$275$		0			0
$276$		0			0
$277$	0.896575	−	3.34607i	0.0538700	−	0.201046i	−0.933746	−	0.357936i	$-0.883480\pi$
$277$	0.896575	−	3.34607i	0.0538700	−	0.201046i	0.987616	+	0.156891i	$0.0501471\pi$
$278$	9.19239	+	9.19239i	0.551323	+	0.551323i
$279$		0			0
$280$		0			0
$281$	18.0000	−	10.3923i	1.07379	−	0.619953i	0.144575	−	0.989494i	$-0.453818\pi$
$281$	18.0000	−	10.3923i	1.07379	−	0.619953i	0.929214	+	0.369541i	$0.120485\pi$
$282$		0			0
$283$	8.51747	+	31.7876i	0.506311	+	1.88958i	0.454120	+	0.890941i	$0.349954\pi$
$283$	8.51747	+	31.7876i	0.506311	+	1.88958i	0.0521913	+	0.998637i	$0.483379\pi$
$284$	−1.73205	+	3.00000i	−0.102778	+	0.178017i
$285$		0			0
$286$	−6.00000	−	10.3923i	−0.354787	−	0.614510i
$287$		0			0
$288$		0			0
$289$			8.00000i			0.470588i
$290$		0			0
$291$		0			0
$292$	6.69213	−	1.79315i	0.391627	−	0.104936i
$293$	−11.5911	+	3.10583i	−0.677160	+	0.181444i	−0.580978	−	0.813919i	$-0.697330\pi$
$293$	−11.5911	+	3.10583i	−0.677160	+	0.181444i	−0.0961820	+	0.995364i	$0.530663\pi$
$294$		0			0
$295$		0			0
$296$			6.92820i			0.402694i
$297$		0			0
$298$	−7.34847	+	7.34847i	−0.425685	+	0.425685i
$299$	−20.7846	−	36.0000i	−1.20201	−	2.08193i
$300$		0			0
$301$		0			0
$302$	0.517638	+	1.93185i	0.0297867	+	0.111166i
$303$		0			0
$304$	3.46410	−	2.00000i	0.198680	−	0.114708i
$305$		0			0
$306$		0			0
$307$	15.9217	+	15.9217i	0.908698	+	0.908698i	0.996167	−	0.0874688i	$-0.0278778\pi$
$307$	15.9217	+	15.9217i	0.908698	+	0.908698i	−0.0874688	+	0.996167i	$0.527878\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3.00000	+	1.73205i	0.170114	+	0.0982156i	0.582640	−	0.812731i	$-0.302020\pi$
$311$	3.00000	+	1.73205i	0.170114	+	0.0982156i	−0.412525	+	0.910946i	$0.635353\pi$
$312$		0			0
$313$	−1.67303	−	0.448288i	−0.0945654	−	0.0253387i	0.211226	−	0.977437i	$-0.432254\pi$
$313$	−1.67303	−	0.448288i	−0.0945654	−	0.0253387i	−0.305791	+	0.952099i	$0.598921\pi$
$314$	−6.92820			−0.390981
$315$		0			0
$316$	4.00000			0.225018
$317$	−28.9778	−	7.76457i	−1.62755	−	0.436102i	−0.674346	−	0.738416i	$-0.735574\pi$
$317$	−28.9778	−	7.76457i	−1.62755	−	0.436102i	−0.953208	+	0.302314i	$0.902241\pi$
$318$		0			0
$319$	5.19615	+	3.00000i	0.290929	+	0.167968i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−8.48528	−	8.48528i	−0.472134	−	0.472134i
$324$		0			0
$325$		0			0
$326$	1.50000	−	0.866025i	0.0830773	−	0.0479647i
$327$		0			0
$328$	1.79315	+	6.69213i	0.0990102	+	0.369511i
$329$		0			0
$330$		0			0
$331$	0.500000	+	0.866025i	0.0274825	+	0.0476011i	0.879440	−	0.476011i	$-0.157918\pi$
$331$	0.500000	+	0.866025i	0.0274825	+	0.0476011i	−0.851957	+	0.523612i	$0.824584\pi$
$332$	6.36396	−	6.36396i	0.349268	−	0.349268i
$333$		0			0
$334$			6.00000i			0.328305i
$335$		0			0
$336$		0			0
$337$	8.36516	−	2.24144i	0.455679	−	0.122099i	−0.0236762	−	0.999720i	$-0.507537\pi$
$337$	8.36516	−	2.24144i	0.455679	−	0.122099i	0.479356	+	0.877621i	$0.340870\pi$
$338$	−33.8074	+	9.05867i	−1.83888	+	0.492727i
$339$		0			0
$340$		0			0
$341$			6.92820i			0.375183i
$342$		0			0
$343$		0			0
$344$	−4.33013	−	7.50000i	−0.233465	−	0.404373i
$345$		0			0
$346$	−9.00000	+	15.5885i	−0.483843	+	0.838041i
$347$	5.43520	+	20.2844i	0.291777	+	1.08893i	0.943744	+	0.330678i	$0.107278\pi$
$347$	5.43520	+	20.2844i	0.291777	+	1.08893i	−0.651967	+	0.758248i	$0.726056\pi$
$348$		0			0
$349$	−8.66025	+	5.00000i	−0.463573	+	0.267644i	−0.713545	−	0.700609i	$-0.752912\pi$
$349$	−8.66025	+	5.00000i	−0.463573	+	0.267644i	0.249973	+	0.968253i	$0.419578\pi$
$350$		0			0
$351$		0			0
$352$	1.22474	+	1.22474i	0.0652791	+	0.0652791i
$353$	−2.32937	+	8.69333i	−0.123980	+	0.462699i	−0.999801	−	0.0199361i	$-0.993654\pi$
$353$	−2.32937	+	8.69333i	−0.123980	+	0.462699i	0.875821	+	0.482635i	$0.160320\pi$
$354$		0			0
$355$		0			0
$356$	−1.50000	−	0.866025i	−0.0794998	−	0.0458993i
$357$		0			0
$358$	11.7112	+	3.13801i	0.618958	+	0.165849i
$359$	−13.8564			−0.731313			−0.365657	−	0.930750i	$-0.619156\pi$
$359$	−13.8564			−0.731313			−0.365657	+	0.930750i	$0.619156\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	−1.93185	−	0.517638i	−0.101536	−	0.0272065i
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−6.27603	+	23.4225i	−0.327606	+	1.22264i	0.584060	+	0.811710i	$0.301463\pi$
$367$	−6.27603	+	23.4225i	−0.327606	+	1.22264i	−0.911666	+	0.410932i	$0.865203\pi$
$368$	4.24264	+	4.24264i	0.221163	+	0.221163i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$373$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$374$	2.59808	−	4.50000i	0.134343	−	0.232689i
$375$		0			0
$376$	6.00000	+	10.3923i	0.309426	+	0.535942i
$377$	16.9706	−	16.9706i	0.874028	−	0.874028i
$378$		0			0
$379$		−	19.0000i		−	0.975964i	−0.872854	−	0.487982i	$-0.837733\pi$
$379$		−	19.0000i		−	0.975964i	0.872854	−	0.487982i	$-0.162267\pi$
$380$		0			0
$381$		0			0
$382$	−3.34607	+	0.896575i	−0.171200	+	0.0458728i
$383$	28.9778	−	7.76457i	1.48070	−	0.396751i	0.574111	−	0.818777i	$-0.305348\pi$
$383$	28.9778	−	7.76457i	1.48070	−	0.396751i	0.906584	+	0.422026i	$0.138681\pi$
$384$		0			0
$385$		0			0
$386$			5.19615i			0.264477i
$387$		0			0
$388$	11.0227	−	11.0227i	0.559593	−	0.559593i
$389$	−5.19615	−	9.00000i	−0.263455	−	0.456318i	0.703702	−	0.710495i	$-0.251529\pi$
$389$	−5.19615	−	9.00000i	−0.263455	−	0.456318i	−0.967158	+	0.254177i	$0.918196\pi$
$390$		0			0
$391$	9.00000	−	15.5885i	0.455150	−	0.788342i
$392$	1.81173	+	6.76148i	0.0915064	+	0.341506i
$393$		0			0
$394$	5.19615	−	3.00000i	0.261778	−	0.151138i
$395$		0			0
$396$		0			0
$397$	2.44949	+	2.44949i	0.122936	+	0.122936i	0.765898	−	0.642962i	$-0.222295\pi$
$397$	2.44949	+	2.44949i	0.122936	+	0.122936i	−0.642962	+	0.765898i	$0.722295\pi$
$398$	6.72930	−	25.1141i	0.337309	−	1.25885i
$399$		0			0
$400$		0			0
$401$	−22.5000	−	12.9904i	−1.12360	−	0.648709i	−0.181280	−	0.983432i	$-0.558024\pi$
$401$	−22.5000	−	12.9904i	−1.12360	−	0.648709i	−0.942317	+	0.334723i	$0.891357\pi$
$402$		0			0
$403$	26.7685	+	7.17260i	1.33344	+	0.357293i
$404$	−13.8564			−0.689382
$405$		0			0
$406$		0			0
$407$	11.5911	+	3.10583i	0.574550	+	0.153950i
$408$		0			0
$409$	−1.73205	−	1.00000i	−0.0856444	−	0.0494468i	0.456566	−	0.889689i	$-0.349079\pi$
$409$	−1.73205	−	1.00000i	−0.0856444	−	0.0494468i	−0.542211	+	0.840243i	$0.682412\pi$
$410$		0			0
$411$		0			0
$412$	1.79315	−	6.69213i	0.0883422	−	0.329698i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	6.00000	−	3.46410i	0.294174	−	0.169842i
$417$		0			0
$418$	−1.79315	−	6.69213i	−0.0877059	−	0.327323i
$419$	2.59808	−	4.50000i	0.126924	−	0.219839i	−0.795559	−	0.605876i	$-0.792823\pi$
$419$	2.59808	−	4.50000i	0.126924	−	0.219839i	0.922484	+	0.386037i	$0.126156\pi$
$420$		0			0
$421$	−14.0000	−	24.2487i	−0.682318	−	1.18181i	−0.974272	−	0.225377i	$-0.927639\pi$
$421$	−14.0000	−	24.2487i	−0.682318	−	1.18181i	0.291953	−	0.956433i	$-0.405695\pi$
$422$	−16.2635	+	16.2635i	−0.791693	+	0.791693i
$423$		0			0
$424$		−	12.0000i		−	0.582772i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−11.5911	+	3.10583i	−0.560277	+	0.150126i
$429$		0			0
$430$		0			0
$431$			24.2487i			1.16802i	0.811747	+	0.584010i	$0.198517\pi$
$431$			24.2487i			1.16802i	−0.811747	+	0.584010i	$0.801483\pi$
$432$		0			0
$433$	−20.8207	+	20.8207i	−1.00058	+	1.00058i	−0.000577367		1.00000i	$0.500184\pi$
$433$	−20.8207	+	20.8207i	−1.00058	+	1.00058i	−1.00000		0.000577367i	$0.999816\pi$
$434$		0			0
$435$		0			0
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$	−6.21166	−	23.1822i	−0.297144	−	1.10896i
$438$		0			0
$439$	8.66025	−	5.00000i	0.413331	−	0.238637i	−0.278889	−	0.960323i	$-0.589966\pi$
$439$	8.66025	−	5.00000i	0.413331	−	0.238637i	0.692220	+	0.721686i	$0.256633\pi$
$440$		0			0
$441$		0			0
$442$	−14.6969	−	14.6969i	−0.699062	−	0.699062i
$443$	−2.32937	+	8.69333i	−0.110672	+	0.413033i	−0.998927	−	0.0463181i	$-0.985251\pi$
$443$	−2.32937	+	8.69333i	−0.110672	+	0.413033i	0.888255	+	0.459351i	$0.151918\pi$
$444$		0			0
$445$		0			0
$446$	3.00000	+	1.73205i	0.142054	+	0.0820150i
$447$		0			0
$448$		0			0
$449$	34.6410			1.63481			0.817405	−	0.576063i	$-0.195412\pi$
$449$	34.6410			1.63481			0.817405	+	0.576063i	$0.195412\pi$
$450$		0			0
$451$	12.0000			0.565058
$452$	−2.89778	−	0.776457i	−0.136300	−	0.0365215i
$453$		0			0
$454$	2.59808	+	1.50000i	0.121934	+	0.0703985i
$455$		0			0
$456$		0			0
$457$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$457$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$458$	−14.1421	−	14.1421i	−0.660819	−	0.660819i
$459$		0			0
$460$		0			0
$461$	−15.0000	+	8.66025i	−0.698620	+	0.403348i	−0.806833	−	0.590779i	$-0.798820\pi$
$461$	−15.0000	+	8.66025i	−0.698620	+	0.403348i	0.108213	+	0.994128i	$0.465487\pi$
$462$		0			0
$463$	−0.896575	−	3.34607i	−0.0416674	−	0.155505i	0.941958	−	0.335732i	$-0.108984\pi$
$463$	−0.896575	−	3.34607i	−0.0416674	−	0.155505i	−0.983625	+	0.180227i	$0.942317\pi$
$464$	−1.73205	+	3.00000i	−0.0804084	+	0.139272i
$465$		0			0
$466$	4.50000	+	7.79423i	0.208458	+	0.361061i
$467$	10.6066	−	10.6066i	0.490815	−	0.490815i	−0.417748	−	0.908563i	$-0.637180\pi$
$467$	10.6066	−	10.6066i	0.490815	−	0.490815i	0.908563	+	0.417748i	$0.137180\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−8.36516	+	2.24144i	−0.385038	+	0.103171i
$473$	−14.4889	+	3.88229i	−0.666200	+	0.178508i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	7.34847	−	7.34847i	0.336111	−	0.336111i
$479$	3.46410	+	6.00000i	0.158279	+	0.274147i	0.934248	−	0.356624i	$-0.116072\pi$
$479$	3.46410	+	6.00000i	0.158279	+	0.274147i	−0.775969	+	0.630771i	$0.782739\pi$
$480$		0			0
$481$	24.0000	−	41.5692i	1.09431	−	1.89539i
$482$	2.58819	+	9.65926i	0.117889	+	0.439967i
$483$		0			0
$484$	−6.92820	+	4.00000i	−0.314918	+	0.181818i
$485$		0			0
$486$		0			0
$487$	−12.2474	−	12.2474i	−0.554985	−	0.554985i	0.372890	−	0.927875i	$-0.378367\pi$
$487$	−12.2474	−	12.2474i	−0.554985	−	0.554985i	−0.927875	+	0.372890i	$0.878367\pi$
$488$	2.07055	−	7.72741i	0.0937295	−	0.349803i
$489$		0			0
$490$		0			0
$491$	19.5000	+	11.2583i	0.880023	+	0.508081i	0.870666	−	0.491875i	$-0.163688\pi$
$491$	19.5000	+	11.2583i	0.880023	+	0.508081i	0.00935679	+	0.999956i	$0.497022\pi$
$492$		0			0
$493$	10.0382	+	2.68973i	0.452098	+	0.121139i
$494$	−27.7128			−1.24686
$495$		0			0
$496$	−4.00000			−0.179605
$497$		0			0
$498$		0			0
$499$	4.33013	+	2.50000i	0.193843	+	0.111915i	0.593780	−	0.804627i	$-0.297635\pi$
$499$	4.33013	+	2.50000i	0.193843	+	0.111915i	−0.399937	+	0.916542i	$0.630968\pi$
$500$		0			0
$501$		0			0
$502$	2.68973	−	10.0382i	0.120048	−	0.448027i
$503$	16.9706	+	16.9706i	0.756680	+	0.756680i	0.975717	−	0.219037i	$-0.0702914\pi$
$503$	16.9706	+	16.9706i	0.756680	+	0.756680i	−0.219037	+	0.975717i	$0.570291\pi$
$504$		0			0
$505$		0			0
$506$	9.00000	−	5.19615i	0.400099	−	0.230997i
$507$		0			0
$508$		0			0
$509$	−15.5885	+	27.0000i	−0.690946	+	1.19675i	0.280582	+	0.959830i	$0.409473\pi$
$509$	−15.5885	+	27.0000i	−0.690946	+	1.19675i	−0.971528	+	0.236924i	$0.923861\pi$
$510$		0			0
$511$		0			0
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	3.00000i		−	0.132324i
$515$		0			0
$516$		0			0
$517$	20.0764	−	5.37945i	0.882959	−	0.236588i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			5.19615i			0.227648i	0.993501	+	0.113824i	$0.0363099\pi$
$521$			5.19615i			0.227648i	−0.993501	+	0.113824i	$0.963690\pi$
$522$		0			0
$523$	−18.3712	+	18.3712i	−0.803315	+	0.803315i	−0.983612	−	0.180297i	$-0.942294\pi$
$523$	−18.3712	+	18.3712i	−0.803315	+	0.803315i	0.180297	+	0.983612i	$0.442294\pi$
$524$	8.66025	+	15.0000i	0.378325	+	0.655278i
$525$		0			0
$526$	−12.0000	+	20.7846i	−0.523225	+	0.906252i
$527$	3.10583	+	11.5911i	0.135292	+	0.504917i
$528$		0			0
$529$	11.2583	−	6.50000i	0.489493	−	0.282609i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	12.4233	−	46.3644i	0.538113	−	2.00827i
$534$		0			0
$535$		0			0
$536$	−3.00000	−	1.73205i	−0.129580	−	0.0748132i
$537$		0			0
$538$	−6.69213	−	1.79315i	−0.288518	−	0.0773082i
$539$	12.1244			0.522233
$540$		0			0
$541$	−4.00000			−0.171973			−0.0859867	−	0.996296i	$-0.527404\pi$
$541$	−4.00000			−0.171973			−0.0859867	+	0.996296i	$0.527404\pi$
$542$	7.72741	+	2.07055i	0.331921	+	0.0889378i
$543$		0			0
$544$	2.59808	+	1.50000i	0.111392	+	0.0643120i
$545$		0			0
$546$		0			0
$547$	−4.48288	+	16.7303i	−0.191674	+	0.715337i	0.801429	+	0.598090i	$0.204074\pi$
$547$	−4.48288	+	16.7303i	−0.191674	+	0.715337i	−0.993103	+	0.117247i	$0.962593\pi$
$548$	−12.7279	−	12.7279i	−0.543710	−	0.543710i
$549$		0			0
$550$		0			0
$551$	12.0000	−	6.92820i	0.511217	−	0.295151i
$552$		0			0
$553$		0			0
$554$	1.73205	−	3.00000i	0.0735878	−	0.127458i
$555$		0			0
$556$	6.50000	+	11.2583i	0.275661	+	0.477460i
$557$	4.24264	−	4.24264i	0.179766	−	0.179766i	−0.611488	−	0.791254i	$-0.709429\pi$
$557$	4.24264	−	4.24264i	0.179766	−	0.179766i	0.791254	+	0.611488i	$0.209429\pi$
$558$		0			0
$559$			60.0000i			2.53773i
$560$		0			0
$561$		0			0
$562$	20.0764	−	5.37945i	0.846871	−	0.226919i
$563$	20.2844	−	5.43520i	0.854887	−	0.229066i	0.195346	−	0.980734i	$-0.437417\pi$
$563$	20.2844	−	5.43520i	0.854887	−	0.229066i	0.659542	+	0.751668i	$0.270750\pi$
$564$		0			0
$565$		0			0
$566$			32.9090i			1.38327i
$567$		0			0
$568$	−2.44949	+	2.44949i	−0.102778	+	0.102778i
$569$	16.4545	+	28.5000i	0.689808	+	1.19478i	0.971900	+	0.235395i	$0.0756383\pi$
$569$	16.4545	+	28.5000i	0.689808	+	1.19478i	−0.282092	+	0.959387i	$0.591028\pi$
$570$		0			0
$571$	−8.50000	+	14.7224i	−0.355714	+	0.616115i	−0.987240	−	0.159240i	$-0.949096\pi$
$571$	−8.50000	+	14.7224i	−0.355714	+	0.616115i	0.631526	+	0.775355i	$0.282429\pi$
$572$	−3.10583	−	11.5911i	−0.129861	−	0.484649i
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−14.6969	−	14.6969i	−0.611842	−	0.611842i	0.331584	−	0.943426i	$-0.392417\pi$
$577$	−14.6969	−	14.6969i	−0.611842	−	0.611842i	−0.943426	+	0.331584i	$0.892417\pi$
$578$	−2.07055	+	7.72741i	−0.0861236	+	0.321418i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−20.0764	−	5.37945i	−0.831479	−	0.222794i
$584$	6.92820			0.286691
$585$		0			0
$586$	−12.0000			−0.495715
$587$	−26.0800	−	6.98811i	−1.07644	−	0.288430i	−0.323301	−	0.946296i	$-0.604793\pi$
$587$	−26.0800	−	6.98811i	−1.07644	−	0.288430i	−0.753135	+	0.657866i	$0.771459\pi$
$588$		0			0
$589$	13.8564	+	8.00000i	0.570943	+	0.329634i
$590$		0			0
$591$		0			0
$592$	−1.79315	+	6.69213i	−0.0736980	+	0.275045i
$593$	14.8492	+	14.8492i	0.609785	+	0.609785i	0.942890	−	0.333105i	$-0.108096\pi$
$593$	14.8492	+	14.8492i	0.609785	+	0.609785i	−0.333105	+	0.942890i	$0.608096\pi$
$594$		0			0
$595$		0			0
$596$	−9.00000	+	5.19615i	−0.368654	+	0.212843i
$597$		0			0
$598$	−10.7589	−	40.1528i	−0.439964	−	1.64197i
$599$	22.5167	−	39.0000i	0.920006	−	1.59350i	0.120603	−	0.992701i	$-0.461517\pi$
$599$	22.5167	−	39.0000i	0.920006	−	1.59350i	0.799402	−	0.600796i	$-0.205150\pi$
$600$		0			0
$601$	−9.50000	−	16.4545i	−0.387513	−	0.671192i	0.604601	−	0.796528i	$-0.293332\pi$
$601$	−9.50000	−	16.4545i	−0.387513	−	0.671192i	−0.992114	+	0.125336i	$0.959999\pi$
$602$		0			0
$603$		0			0
$604$			2.00000i			0.0813788i
$605$		0			0
$606$		0			0
$607$	−6.69213	+	1.79315i	−0.271625	+	0.0727818i	−0.392061	−	0.919939i	$-0.628238\pi$
$607$	−6.69213	+	1.79315i	−0.271625	+	0.0727818i	0.120435	+	0.992721i	$0.461571\pi$
$608$	3.86370	−	1.03528i	0.156694	−	0.0419860i
$609$		0			0
$610$		0			0
$611$		−	83.1384i		−	3.36342i
$612$		0			0
$613$	17.1464	−	17.1464i	0.692538	−	0.692538i	−0.270252	−	0.962790i	$-0.587107\pi$
$613$	17.1464	−	17.1464i	0.692538	−	0.692538i	0.962790	+	0.270252i	$0.0871070\pi$
$614$	11.2583	+	19.5000i	0.454349	+	0.786956i
$615$		0			0
$616$		0			0
$617$	6.98811	+	26.0800i	0.281331	+	1.04994i	0.951479	+	0.307714i	$0.0995639\pi$
$617$	6.98811	+	26.0800i	0.281331	+	1.04994i	−0.670148	+	0.742227i	$0.733769\pi$
$618$		0			0
$619$	32.0429	−	18.5000i	1.28791	−	0.743578i	0.309633	−	0.950856i	$-0.399794\pi$
$619$	32.0429	−	18.5000i	1.28791	−	0.743578i	0.978282	+	0.207279i	$0.0664606\pi$
$620$		0			0
$621$		0			0
$622$	2.44949	+	2.44949i	0.0982156	+	0.0982156i
$623$		0			0
$624$		0			0
$625$		0			0
$626$	−1.50000	−	0.866025i	−0.0599521	−	0.0346133i
$627$		0			0
$628$	−6.69213	−	1.79315i	−0.267045	−	0.0715545i
$629$	20.7846			0.828737
$630$		0			0
$631$	2.00000			0.0796187			0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000			0.0796187			0.0398094	+	0.999207i	$0.487325\pi$
$632$	3.86370	+	1.03528i	0.153690	+	0.0411811i
$633$		0			0
$634$	−25.9808	−	15.0000i	−1.03183	−	0.595726i
$635$		0			0
$636$		0			0
$637$	12.5521	−	46.8449i	0.497331	−	1.85606i
$638$	4.24264	+	4.24264i	0.167968	+	0.167968i
$639$		0			0
$640$		0			0
$641$	16.5000	−	9.52628i	0.651711	−	0.376265i	−0.137401	−	0.990516i	$-0.543875\pi$
$641$	16.5000	−	9.52628i	0.651711	−	0.376265i	0.789111	+	0.614250i	$0.210541\pi$
$642$		0			0
$643$	−12.1038	−	45.1719i	−0.477326	−	1.78141i	−0.612376	−	0.790566i	$-0.709786\pi$
$643$	−12.1038	−	45.1719i	−0.477326	−	1.78141i	0.135050	−	0.990839i	$-0.456880\pi$
$644$		0			0
$645$		0			0
$646$	−6.00000	−	10.3923i	−0.236067	−	0.408880i
$647$	8.48528	−	8.48528i	0.333591	−	0.333591i	−0.520358	−	0.853948i	$-0.674201\pi$
$647$	8.48528	−	8.48528i	0.333591	−	0.333591i	0.853948	+	0.520358i	$0.174201\pi$
$648$		0			0
$649$			15.0000i			0.588802i
$650$		0			0
$651$		0			0
$652$	1.67303	−	0.448288i	0.0655210	−	0.0175563i
$653$	46.3644	−	12.4233i	1.81438	−	0.486162i	0.818314	−	0.574771i	$-0.194909\pi$
$653$	46.3644	−	12.4233i	1.81438	−	0.486162i	0.996066	+	0.0886092i	$0.0282422\pi$
$654$		0			0
$655$		0			0
$656$			6.92820i			0.270501i
$657$		0			0
$658$		0			0
$659$	7.79423	+	13.5000i	0.303620	+	0.525885i	0.976953	−	0.213454i	$-0.0684713\pi$
$659$	7.79423	+	13.5000i	0.303620	+	0.525885i	−0.673333	+	0.739339i	$0.735138\pi$
$660$		0			0
$661$	−11.0000	+	19.0526i	−0.427850	+	0.741059i	−0.996682	−	0.0813955i	$-0.974062\pi$
$661$	−11.0000	+	19.0526i	−0.427850	+	0.741059i	0.568831	+	0.822454i	$0.307396\pi$
$662$	0.258819	+	0.965926i	0.0100593	+	0.0375418i
$663$		0			0
$664$	7.79423	−	4.50000i	0.302475	−	0.174634i
$665$		0			0
$666$		0			0
$667$	14.6969	+	14.6969i	0.569068	+	0.569068i
$668$	−1.55291	+	5.79555i	−0.0600841	+	0.224237i
$669$		0			0
$670$		0			0
$671$	−12.0000	−	6.92820i	−0.463255	−	0.267460i
$672$		0			0
$673$	−46.8449	−	12.5521i	−1.80574	−	0.483846i	−0.810888	−	0.585201i	$-0.801016\pi$
$673$	−46.8449	−	12.5521i	−1.80574	−	0.483846i	−0.994850	+	0.101355i	$0.967682\pi$
$674$	8.66025			0.333581
$675$		0			0
$676$	−35.0000			−1.34615
$677$	−5.79555	−	1.55291i	−0.222741	−	0.0596833i	0.145722	−	0.989326i	$-0.453449\pi$
$677$	−5.79555	−	1.55291i	−0.222741	−	0.0596833i	−0.368464	+	0.929642i	$0.620116\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	−1.79315	+	6.69213i	−0.0686633	+	0.256255i
$683$	−8.48528	−	8.48528i	−0.324680	−	0.324680i	0.525879	−	0.850559i	$-0.323736\pi$
$683$	−8.48528	−	8.48528i	−0.324680	−	0.324680i	−0.850559	+	0.525879i	$0.823736\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−2.24144	−	8.36516i	−0.0854540	−	0.318919i
$689$	−41.5692	+	72.0000i	−1.58366	+	2.74298i
$690$		0			0
$691$	17.5000	+	30.3109i	0.665731	+	1.15308i	0.979086	+	0.203445i	$0.0652137\pi$
$691$	17.5000	+	30.3109i	0.665731	+	1.15308i	−0.313355	+	0.949636i	$0.601453\pi$
$692$	−12.7279	+	12.7279i	−0.483843	+	0.483843i
$693$		0			0
$694$			21.0000i			0.797149i
$695$		0			0
$696$		0			0
$697$	20.0764	−	5.37945i	0.760448	−	0.203761i
$698$	−9.65926	+	2.58819i	−0.365608	+	0.0979645i
$699$		0			0
$700$		0			0
$701$			27.7128i			1.04670i	0.852118	+	0.523349i	$0.175318\pi$
$701$			27.7128i			1.04670i	−0.852118	+	0.523349i	$0.824682\pi$
$702$		0			0
$703$	19.5959	−	19.5959i	0.739074	−	0.739074i
$704$	0.866025	+	1.50000i	0.0326396	+	0.0565334i
$705$		0			0
$706$	−4.50000	+	7.79423i	−0.169360	+	0.293340i
$707$		0			0
$708$		0			0
$709$	6.92820	−	4.00000i	0.260194	−	0.150223i	−0.364229	−	0.931309i	$-0.618667\pi$
$709$	6.92820	−	4.00000i	0.260194	−	0.150223i	0.624423	+	0.781086i	$0.285334\pi$
$710$		0			0
$711$		0			0
$712$	−1.22474	−	1.22474i	−0.0458993	−	0.0458993i
$713$	−6.21166	+	23.1822i	−0.232628	+	0.868181i
$714$		0			0
$715$		0			0
$716$	10.5000	+	6.06218i	0.392403	+	0.226554i
$717$		0			0
$718$	−13.3843	−	3.58630i	−0.499496	−	0.133840i
$719$	34.6410			1.29189			0.645946	−	0.763383i	$-0.276463\pi$
$719$	34.6410			1.29189			0.645946	+	0.763383i	$0.276463\pi$
$720$		0			0
$721$		0			0
$722$	2.89778	+	0.776457i	0.107844	+	0.0288967i
$723$		0			0
$724$	−1.73205	−	1.00000i	−0.0643712	−	0.0371647i
$725$		0			0
$726$		0			0
$727$	−0.896575	+	3.34607i	−0.0332521	+	0.124099i	−0.980557	−	0.196235i	$-0.937128\pi$
$727$	−0.896575	+	3.34607i	−0.0332521	+	0.124099i	0.947305	+	0.320334i	$0.103795\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−22.5000	+	12.9904i	−0.832193	+	0.480467i
$732$		0			0
$733$	5.37945	+	20.0764i	0.198695	+	0.741538i	0.991279	+	0.131777i	$0.0420682\pi$
$733$	5.37945	+	20.0764i	0.198695	+	0.741538i	−0.792585	+	0.609762i	$0.791265\pi$
$734$	−12.1244	+	21.0000i	−0.447518	+	0.775124i
$735$		0			0
$736$	3.00000	+	5.19615i	0.110581	+	0.191533i
$737$	−4.24264	+	4.24264i	−0.156280	+	0.156280i
$738$		0			0
$739$			41.0000i			1.50821i	0.656754	+	0.754105i	$0.271929\pi$
$739$			41.0000i			1.50821i	−0.656754	+	0.754105i	$0.728071\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−23.1822	+	6.21166i	−0.850473	+	0.227884i	−0.657625	−	0.753345i	$-0.728439\pi$
$743$	−23.1822	+	6.21166i	−0.850473	+	0.227884i	−0.192848	+	0.981229i	$0.561772\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$	3.67423	−	3.67423i	0.134343	−	0.134343i
$749$		0			0
$750$		0			0
$751$	19.0000	−	32.9090i	0.693320	−	1.20087i	−0.277424	−	0.960748i	$-0.589481\pi$
$751$	19.0000	−	32.9090i	0.693320	−	1.20087i	0.970744	−	0.240118i	$-0.0771860\pi$
$752$	3.10583	+	11.5911i	0.113258	+	0.422684i
$753$		0			0
$754$	20.7846	−	12.0000i	0.756931	−	0.437014i
$755$		0			0
$756$		0			0
$757$	−29.3939	−	29.3939i	−1.06834	−	1.06834i	−0.997487	−	0.0708518i	$-0.977428\pi$
$757$	−29.3939	−	29.3939i	−1.06834	−	1.06834i	−0.0708518	−	0.997487i	$-0.522572\pi$
$758$	4.91756	−	18.3526i	0.178614	−	0.666596i
$759$		0			0
$760$		0			0
$761$	−46.5000	−	26.8468i	−1.68562	−	0.973195i	−0.957802	−	0.287429i	$-0.907200\pi$
$761$	−46.5000	−	26.8468i	−1.68562	−	0.973195i	−0.727822	−	0.685766i	$-0.759467\pi$
$762$		0			0
$763$		0			0
$764$	−3.46410			−0.125327
$765$		0			0
$766$	30.0000			1.08394
$767$	57.9555	+	15.5291i	2.09265	+	0.560725i
$768$		0			0
$769$	−11.2583	−	6.50000i	−0.405986	−	0.234396i	0.283078	−	0.959097i	$-0.408645\pi$
$769$	−11.2583	−	6.50000i	−0.405986	−	0.234396i	−0.689063	+	0.724701i	$0.741978\pi$
$770$		0			0
$771$		0			0
$772$	−1.34486	+	5.01910i	−0.0484027	+	0.180641i
$773$	4.24264	+	4.24264i	0.152597	+	0.152597i	0.779277	−	0.626680i	$-0.215587\pi$
$773$	4.24264	+	4.24264i	0.152597	+	0.152597i	−0.626680	+	0.779277i	$0.715587\pi$
$774$		0			0
$775$		0			0
$776$	13.5000	−	7.79423i	0.484622	−	0.279797i
$777$		0			0
$778$	−2.68973	−	10.0382i	−0.0964314	−	0.359887i
$779$	13.8564	−	24.0000i	0.496457	−	0.859889i
$780$		0			0
$781$	3.00000	+	5.19615i	0.107348	+	0.185933i
$782$	12.7279	−	12.7279i	0.455150	−	0.455150i
$783$		0			0
$784$			7.00000i			0.250000i
$785$		0			0
$786$		0			0
$787$	50.1910	−	13.4486i	1.78912	−	0.479392i	0.796920	−	0.604085i	$-0.206461\pi$
$787$	50.1910	−	13.4486i	1.78912	−	0.479392i	0.992195	+	0.124693i	$0.0397946\pi$
$788$	5.79555	−	1.55291i	0.206458	−	0.0553203i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−39.1918	+	39.1918i	−1.39174	+	1.39174i
$794$	1.73205	+	3.00000i	0.0614682	+	0.106466i
$795$		0			0
$796$	13.0000	−	22.5167i	0.460773	−	0.798082i
$797$	6.21166	+	23.1822i	0.220028	+	0.821156i	0.984336	+	0.176304i	$0.0564143\pi$
$797$	6.21166	+	23.1822i	0.220028	+	0.821156i	−0.764308	+	0.644852i	$0.776919\pi$
$798$		0			0
$799$	31.1769	−	18.0000i	1.10296	−	0.636794i
$800$		0			0
$801$		0			0
$802$	−18.3712	−	18.3712i	−0.648709	−	0.648709i
$803$	3.10583	−	11.5911i	0.109602	−	0.409041i
$804$		0			0
$805$		0			0
$806$	24.0000	+	13.8564i	0.845364	+	0.488071i
$807$		0			0
$808$	−13.3843	−	3.58630i	−0.470857	−	0.126166i
$809$	−8.66025			−0.304478			−0.152239	−	0.988344i	$-0.548648\pi$
$809$	−8.66025			−0.304478			−0.152239	+	0.988344i	$0.548648\pi$
$810$		0			0
$811$	−29.0000			−1.01833			−0.509164	−	0.860670i	$-0.670045\pi$
$811$	−29.0000			−1.01833			−0.509164	+	0.860670i	$0.670045\pi$
$812$		0			0
$813$		0			0
$814$	10.3923	+	6.00000i	0.364250	+	0.210300i
$815$		0			0
$816$		0			0
$817$	−8.96575	+	33.4607i	−0.313672	+	1.17064i
$818$	−1.41421	−	1.41421i	−0.0494468	−	0.0494468i
$819$		0			0
$820$		0			0
$821$	30.0000	−	17.3205i	1.04701	−	0.604490i	0.125197	−	0.992132i	$-0.460044\pi$
$821$	30.0000	−	17.3205i	1.04701	−	0.604490i	0.921810	+	0.387642i	$0.126710\pi$
$822$		0			0
$823$	1.79315	+	6.69213i	0.0625053	+	0.233273i	0.990111	−	0.140289i	$-0.0448031\pi$
$823$	1.79315	+	6.69213i	0.0625053	+	0.233273i	−0.927605	+	0.373562i	$0.878136\pi$
$824$	3.46410	−	6.00000i	0.120678	−	0.209020i
$825$		0			0
$826$		0			0
$827$	−23.3345	+	23.3345i	−0.811421	+	0.811421i	−0.984847	−	0.173426i	$-0.944516\pi$
$827$	−23.3345	+	23.3345i	−0.811421	+	0.811421i	0.173426	+	0.984847i	$0.444516\pi$
$828$		0			0
$829$		−	16.0000i		−	0.555703i	−0.960624	−	0.277851i	$-0.910378\pi$
$829$		−	16.0000i		−	0.555703i	0.960624	−	0.277851i	$-0.0896223\pi$
$830$		0			0
$831$		0			0
$832$	6.69213	−	1.79315i	0.232008	−	0.0621663i
$833$	20.2844	−	5.43520i	0.702814	−	0.188319i
$834$		0			0
$835$		0			0
$836$		−	6.92820i		−	0.239617i
$837$		0			0
$838$	3.67423	−	3.67423i	0.126924	−	0.126924i
$839$	3.46410	+	6.00000i	0.119594	+	0.207143i	0.919607	−	0.392840i	$-0.128507\pi$
$839$	3.46410	+	6.00000i	0.119594	+	0.207143i	−0.800013	+	0.599983i	$0.795174\pi$
$840$		0			0
$841$	8.50000	−	14.7224i	0.293103	−	0.507670i
$842$	−7.24693	−	27.0459i	−0.249746	−	0.932064i
$843$		0			0
$844$	−19.9186	+	11.5000i	−0.685626	+	0.395846i
$845$		0			0
$846$		0			0
$847$		0			0
$848$	3.10583	−	11.5911i	0.106655	−	0.398040i
$849$		0			0
$850$		0			0
$851$	36.0000	+	20.7846i	1.23406	+	0.712487i
$852$		0			0
$853$	16.7303	+	4.48288i	0.572835	+	0.153491i	0.533597	−	0.845739i	$-0.320840\pi$
$853$	16.7303	+	4.48288i	0.572835	+	0.153491i	0.0392388	+	0.999230i	$0.487507\pi$
$854$		0			0
$855$		0			0
$856$	−12.0000			−0.410152
$857$	2.89778	+	0.776457i	0.0989862	+	0.0265233i	0.307972	−	0.951395i	$-0.400350\pi$
$857$	2.89778	+	0.776457i	0.0989862	+	0.0265233i	−0.208986	+	0.977919i	$0.567016\pi$
$858$		0			0
$859$	27.7128	+	16.0000i	0.945549	+	0.545913i	0.891695	−	0.452636i	$-0.149516\pi$
$859$	27.7128	+	16.0000i	0.945549	+	0.545913i	0.0538535	+	0.998549i	$0.482850\pi$
$860$		0			0
$861$		0			0
$862$	−6.27603	+	23.4225i	−0.213762	+	0.797772i
$863$	−33.9411	−	33.9411i	−1.15537	−	1.15537i	−0.985460	−	0.169910i	$-0.945652\pi$
$863$	−33.9411	−	33.9411i	−1.15537	−	1.15537i	−0.169910	−	0.985460i	$-0.554348\pi$
$864$		0			0
$865$		0			0
$866$	−25.5000	+	14.7224i	−0.866525	+	0.500289i
$867$		0			0
$868$		0			0
$869$	3.46410	−	6.00000i	0.117512	−	0.203536i
$870$		0			0
$871$	12.0000	+	20.7846i	0.406604	+	0.704260i
$872$	1.41421	−	1.41421i	0.0478913	−	0.0478913i
$873$		0			0
$874$		−	24.0000i		−	0.811812i
$875$		0			0
$876$		0			0
$877$	20.0764	−	5.37945i	0.677932	−	0.181651i	0.0966065	−	0.995323i	$-0.469201\pi$
$877$	20.0764	−	5.37945i	0.677932	−	0.181651i	0.581325	+	0.813671i	$0.302534\pi$
$878$	9.65926	−	2.58819i	0.325984	−	0.0873472i
$879$		0			0
$880$		0			0
$881$		−	34.6410i		−	1.16709i	−0.812082	−	0.583543i	$-0.801666\pi$
$881$		−	34.6410i		−	1.16709i	0.812082	−	0.583543i	$-0.198334\pi$
$882$		0			0
$883$	18.3712	−	18.3712i	0.618239	−	0.618239i	−0.326840	−	0.945080i	$-0.605984\pi$
$883$	18.3712	−	18.3712i	0.618239	−	0.618239i	0.945080	+	0.326840i	$0.105984\pi$
$884$	−10.3923	−	18.0000i	−0.349531	−	0.605406i
$885$		0			0
$886$	−4.50000	+	7.79423i	−0.151180	+	0.261852i
$887$	−10.8704	−	40.5689i	−0.364992	−	1.36217i	−0.867431	−	0.497557i	$-0.834230\pi$
$887$	−10.8704	−	40.5689i	−0.364992	−	1.36217i	0.502439	−	0.864613i	$-0.332436\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	2.44949	+	2.44949i	0.0820150	+	0.0820150i
$893$	12.4233	−	46.3644i	0.415730	−	1.55153i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	33.4607	+	8.96575i	1.11660	+	0.299191i
$899$	−13.8564			−0.462137
$900$		0			0
$901$	−36.0000			−1.19933
$902$	11.5911	+	3.10583i	0.385942	+	0.103413i
$903$		0			0
$904$	−2.59808	−	1.50000i	−0.0864107	−	0.0498893i
$905$		0			0
$906$		0			0
$907$	−2.24144	+	8.36516i	−0.0744257	+	0.277761i	−0.993102	−	0.117250i	$-0.962592\pi$
$907$	−2.24144	+	8.36516i	−0.0744257	+	0.277761i	0.918677	+	0.395010i	$0.129259\pi$
$908$	2.12132	+	2.12132i	0.0703985	+	0.0703985i
$909$		0			0
$910$		0			0
$911$	−33.0000	+	19.0526i	−1.09334	+	0.631239i	−0.934463	−	0.356059i	$-0.884120\pi$
$911$	−33.0000	+	19.0526i	−1.09334	+	0.631239i	−0.158875	+	0.987299i	$0.550787\pi$
$912$		0			0
$913$	−4.03459	−	15.0573i	−0.133525	−	0.498324i
$914$		0			0
$915$		0			0
$916$	−10.0000	−	17.3205i	−0.330409	−	0.572286i
$917$		0			0
$918$		0			0
$919$		−	34.0000i		−	1.12156i	−0.827966	−	0.560778i	$-0.810502\pi$
$919$		−	34.0000i		−	1.12156i	0.827966	−	0.560778i	$-0.189498\pi$
$920$		0			0
$921$		0			0
$922$	−16.7303	+	4.48288i	−0.550984	+	0.147636i
$923$	23.1822	−	6.21166i	0.763052	−	0.204459i
$924$		0			0
$925$		0			0
$926$		−	3.46410i		−	0.113837i
$927$		0			0
$928$	−2.44949	+	2.44949i	−0.0804084	+	0.0804084i
$929$	17.3205	+	30.0000i	0.568267	+	0.984268i	0.996737	+	0.0807121i	$0.0257194\pi$
$929$	17.3205	+	30.0000i	0.568267	+	0.984268i	−0.428470	+	0.903556i	$0.640947\pi$
$930$		0			0
$931$	14.0000	−	24.2487i	0.458831	−	0.794719i
$932$	2.32937	+	8.69333i	0.0763011	+	0.284760i
$933$		0			0
$934$	12.9904	−	7.50000i	0.425058	−	0.245407i
$935$		0			0
$936$		0			0
$937$	3.67423	+	3.67423i	0.120032	+	0.120032i	0.764571	−	0.644539i	$-0.222951\pi$
$937$	3.67423	+	3.67423i	0.120032	+	0.120032i	−0.644539	+	0.764571i	$0.722951\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	18.0000	+	10.3923i	0.586783	+	0.338779i	0.763825	−	0.645424i	$-0.223319\pi$
$941$	18.0000	+	10.3923i	0.586783	+	0.338779i	−0.177041	+	0.984203i	$0.556653\pi$
$942$		0			0
$943$	40.1528	+	10.7589i	1.30755	+	0.350358i
$944$	−8.66025			−0.281867
$945$		0			0
$946$	−15.0000			−0.487692
$947$	14.4889	+	3.88229i	0.470826	+	0.126157i	0.486427	−	0.873721i	$-0.338300\pi$
$947$	14.4889	+	3.88229i	0.470826	+	0.126157i	−0.0156019	+	0.999878i	$0.504966\pi$
$948$		0			0
$949$	−41.5692	−	24.0000i	−1.34939	−	0.779073i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−14.8492	−	14.8492i	−0.481014	−	0.481014i	0.424441	−	0.905455i	$-0.360471\pi$
$953$	−14.8492	−	14.8492i	−0.481014	−	0.481014i	−0.905455	+	0.424441i	$0.860471\pi$
$954$		0			0
$955$		0			0
$956$	9.00000	−	5.19615i	0.291081	−	0.168056i
$957$		0			0
$958$	1.79315	+	6.69213i	0.0579341	+	0.216213i
$959$		0			0
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	33.9411	−	33.9411i	1.09431	−	1.09431i
$963$		0			0
$964$			10.0000i			0.322078i
$965$		0			0
$966$		0			0
$967$	13.3843	−	3.58630i	0.430409	−	0.115328i	−0.0371092	−	0.999311i	$-0.511815\pi$
$967$	13.3843	−	3.58630i	0.430409	−	0.115328i	0.467518	+	0.883984i	$0.345148\pi$
$968$	−7.72741	+	2.07055i	−0.248368	+	0.0665501i
$969$		0			0
$970$		0			0
$971$			12.1244i			0.389089i	0.980894	+	0.194545i	$0.0623229\pi$
$971$			12.1244i			0.389089i	−0.980894	+	0.194545i	$0.937677\pi$
$972$		0			0
$973$		0			0
$974$	−8.66025	−	15.0000i	−0.277492	−	0.480631i
$975$		0			0
$976$	4.00000	−	6.92820i	0.128037	−	0.221766i
$977$	−1.55291	−	5.79555i	−0.0496821	−	0.185416i	0.936625	−	0.350332i	$-0.113931\pi$
$977$	−1.55291	−	5.79555i	−0.0496821	−	0.185416i	−0.986308	+	0.164916i	$0.947265\pi$
$978$		0			0
$979$	−2.59808	+	1.50000i	−0.0830349	+	0.0479402i
$980$		0			0
$981$		0			0
$982$	15.9217	+	15.9217i	0.508081	+	0.508081i
$983$	−10.8704	+	40.5689i	−0.346712	+	1.29395i	0.543888	+	0.839158i	$0.316952\pi$
$983$	−10.8704	+	40.5689i	−0.346712	+	1.29395i	−0.890600	+	0.454788i	$0.849715\pi$
$984$		0			0
$985$		0			0
$986$	9.00000	+	5.19615i	0.286618	+	0.165479i
$987$		0			0
$988$	−26.7685	−	7.17260i	−0.851620	−	0.228191i
$989$	−51.9615			−1.65228
$990$		0			0
$991$	32.0000			1.01651			0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000			1.01651			0.508257	+	0.861206i	$0.330290\pi$
$992$	−3.86370	−	1.03528i	−0.122673	−	0.0328701i
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	2.68973	−	10.0382i	0.0851845	−	0.317913i	−0.910165	−	0.414247i	$-0.864045\pi$
$997$	2.68973	−	10.0382i	0.0851845	−	0.317913i	0.995349	+	0.0963340i	$0.0307117\pi$
$998$	3.53553	+	3.53553i	0.111915	+	0.111915i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.2.q.e.557.2		8
3.2	odd	2		450.2.p.b.257.1	✓	8
5.2	odd	4	inner	1350.2.q.e.1043.1		8
5.3	odd	4	inner	1350.2.q.e.1043.2		8
5.4	even	2	inner	1350.2.q.e.557.1		8
9.2	odd	6	inner	1350.2.q.e.1007.2		8
9.7	even	3		450.2.p.b.407.1	yes	8
15.2	even	4		450.2.p.b.293.2	yes	8
15.8	even	4		450.2.p.b.293.1	yes	8
15.14	odd	2		450.2.p.b.257.2	yes	8
45.2	even	12	inner	1350.2.q.e.143.1		8
45.7	odd	12		450.2.p.b.443.2	yes	8
45.29	odd	6	inner	1350.2.q.e.1007.1		8
45.34	even	6		450.2.p.b.407.2	yes	8
45.38	even	12	inner	1350.2.q.e.143.2		8
45.43	odd	12		450.2.p.b.443.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.p.b.257.1	✓	8	3.2	odd	2
450.2.p.b.257.2	yes	8	15.14	odd	2
450.2.p.b.293.1	yes	8	15.8	even	4
450.2.p.b.293.2	yes	8	15.2	even	4
450.2.p.b.407.1	yes	8	9.7	even	3
450.2.p.b.407.2	yes	8	45.34	even	6
450.2.p.b.443.1	yes	8	45.43	odd	12
450.2.p.b.443.2	yes	8	45.7	odd	12
1350.2.q.e.143.1		8	45.2	even	12	inner
1350.2.q.e.143.2		8	45.38	even	12	inner
1350.2.q.e.557.1		8	5.4	even	2	inner
1350.2.q.e.557.2		8	1.1	even	1	trivial
1350.2.q.e.1007.1		8	45.29	odd	6	inner
1350.2.q.e.1007.2		8	9.2	odd	6	inner
1350.2.q.e.1043.1		8	5.2	odd	4	inner
1350.2.q.e.1043.2		8	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1350.q (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{8} +(1.50000 - 0.866025i) q^{11} +(-1.79315 - 6.69213i) q^{13} +(0.500000 + 0.866025i) q^{16} +(2.12132 - 2.12132i) q^{17} -4.00000i q^{19} +(1.67303 - 0.448288i) q^{22} +(5.79555 - 1.55291i) q^{23} -6.92820i q^{26} +(1.73205 + 3.00000i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(0.258819 + 0.965926i) q^{32} +(2.59808 - 1.50000i) q^{34} +(4.89898 + 4.89898i) q^{37} +(1.03528 - 3.86370i) q^{38} +(6.00000 + 3.46410i) q^{41} +(-8.36516 - 2.24144i) q^{43} +1.73205 q^{44} +6.00000 q^{46} +(11.5911 + 3.10583i) q^{47} +(6.06218 + 3.50000i) q^{49} +(1.79315 - 6.69213i) q^{52} +(-8.48528 - 8.48528i) q^{53} +(0.896575 + 3.34607i) q^{58} +(-4.33013 + 7.50000i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(-2.82843 + 2.82843i) q^{62} +1.00000i q^{64} +(-3.34607 + 0.896575i) q^{67} +(2.89778 - 0.776457i) q^{68} +3.46410i q^{71} +(4.89898 - 4.89898i) q^{73} +(3.46410 + 6.00000i) q^{74} +(2.00000 - 3.46410i) q^{76} +(3.46410 - 2.00000i) q^{79} +(4.89898 + 4.89898i) q^{82} +(2.32937 - 8.69333i) q^{83} +(-7.50000 - 4.33013i) q^{86} +(1.67303 + 0.448288i) q^{88} -1.73205 q^{89} +(5.79555 + 1.55291i) q^{92} +(10.3923 + 6.00000i) q^{94} +(4.03459 - 15.0573i) q^{97} +(4.94975 + 4.94975i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 12 q^{11} + 4 q^{16} - 16 q^{31} + 48 q^{41} + 48 q^{46} - 32 q^{61} + 16 q^{76} - 60 q^{86}+O(q^{100}) \) 8 * q + 12 * q^11 + 4 * q^16 - 16 * q^31 + 48 * q^41 + 48 * q^46 - 32 * q^61 + 16 * q^76 - 60 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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