LMFDB - Embedded newform 1350.2.q.e.143.1

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			143.1
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1350.143
Dual form			1350.2.q.e.557.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{8} +(1.50000 + 0.866025i) q^{11} +(1.79315 - 6.69213i) q^{13} +(0.500000 - 0.866025i) q^{16} +(-2.12132 - 2.12132i) q^{17} +4.00000i q^{19} +(-1.67303 - 0.448288i) q^{22} +(-5.79555 - 1.55291i) q^{23} +6.92820i q^{26} +(1.73205 - 3.00000i) q^{29} +(-2.00000 - 3.46410i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(2.59808 + 1.50000i) q^{34} +(-4.89898 + 4.89898i) q^{37} +(-1.03528 - 3.86370i) q^{38} +(6.00000 - 3.46410i) q^{41} +(8.36516 - 2.24144i) q^{43} +1.73205 q^{44} +6.00000 q^{46} +(-11.5911 + 3.10583i) q^{47} +(6.06218 - 3.50000i) q^{49} +(-1.79315 - 6.69213i) q^{52} +(8.48528 - 8.48528i) q^{53} +(-0.896575 + 3.34607i) q^{58} +(-4.33013 - 7.50000i) q^{59} +(-4.00000 + 6.92820i) q^{61} +(2.82843 + 2.82843i) q^{62} -1.00000i q^{64} +(3.34607 + 0.896575i) q^{67} +(-2.89778 - 0.776457i) q^{68} -3.46410i q^{71} +(-4.89898 - 4.89898i) q^{73} +(3.46410 - 6.00000i) q^{74} +(2.00000 + 3.46410i) q^{76} +(3.46410 + 2.00000i) q^{79} +(-4.89898 + 4.89898i) q^{82} +(-2.32937 - 8.69333i) q^{83} +(-7.50000 + 4.33013i) q^{86} +(-1.67303 + 0.448288i) q^{88} -1.73205 q^{89} +(-5.79555 + 1.55291i) q^{92} +(10.3923 - 6.00000i) q^{94} +(-4.03459 - 15.0573i) q^{97} +(-4.94975 + 4.94975i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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	$-0.0833333\pi$
$7$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$		0			0
$11$	1.50000	+	0.866025i	0.452267	+	0.261116i	0.708787	−	0.705422i	$-0.249243\pi$
$11$	1.50000	+	0.866025i	0.452267	+	0.261116i	−0.256520	+	0.966539i	$0.582576\pi$
$12$		0			0
$13$	1.79315	−	6.69213i	0.497331	−	1.85606i	−0.0192343	−	0.999815i	$-0.506123\pi$
$13$	1.79315	−	6.69213i	0.497331	−	1.85606i	0.516565	−	0.856248i	$-0.327210\pi$
$14$		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	$-0.368522\pi$
$17$	−2.12132	−	2.12132i	−0.514496	−	0.514496i	−0.915901	+	0.401405i	$0.868522\pi$
$18$		0			0
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$		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	$-0.631789\pi$
$23$	−5.79555	−	1.55291i	−1.20846	−	0.323805i	−0.806156	+	0.591703i	$0.798456\pi$
$24$		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	−0.659192	−	0.751975i	$-0.729101\pi$
$29$	1.73205	−	3.00000i	0.321634	−	0.557086i	0.980825	+	0.194889i	$0.0624347\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	−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	$-0.942861\pi$
$37$	−4.89898	+	4.89898i	−0.805387	+	0.805387i	0.178545	+	0.983932i	$0.442861\pi$
$38$	−1.03528	−	3.86370i	−0.167944	−	0.626775i
$39$		0			0
$40$		0			0
$41$	6.00000	−	3.46410i	0.937043	−	0.541002i	0.0480106	−	0.998847i	$-0.484712\pi$
$41$	6.00000	−	3.46410i	0.937043	−	0.541002i	0.889032	+	0.457845i	$0.151379\pi$
$42$		0			0
$43$	8.36516	−	2.24144i	1.27568	−	0.341816i	0.443473	−	0.896288i	$-0.353746\pi$
$43$	8.36516	−	2.24144i	1.27568	−	0.341816i	0.832203	+	0.554472i	$0.187080\pi$
$44$	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	$-0.922597\pi$
$47$	−11.5911	+	3.10583i	−1.69074	+	0.453032i	−0.720157	+	0.693811i	$0.755930\pi$
$48$		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	0.182300	−	0.983243i	$-0.441646\pi$
$53$	8.48528	−	8.48528i	1.16554	−	1.16554i	0.983243	−	0.182300i	$-0.0583542\pi$
$54$		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	−0.997166	−	0.0752304i	$-0.976031\pi$
$59$	−4.33013	−	7.50000i	−0.563735	−	0.976417i	0.433432	−	0.901186i	$-0.357303\pi$
$60$		0			0
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	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	$-0.348798\pi$
$67$	3.34607	+	0.896575i	0.408787	+	0.109534i	−0.0485648	+	0.998820i	$0.515465\pi$
$68$	−2.89778	−	0.776457i	−0.351407	−	0.0941593i
$69$		0			0
$70$		0			0
$71$		−	3.46410i		−	0.411113i	−0.978645	−	0.205557i	$-0.934100\pi$
$71$		−	3.46410i		−	0.411113i	0.978645	−	0.205557i	$-0.0659005\pi$
$72$		0			0
$73$	−4.89898	−	4.89898i	−0.573382	−	0.573382i	0.359690	−	0.933072i	$-0.382883\pi$
$73$	−4.89898	−	4.89898i	−0.573382	−	0.573382i	−0.933072	+	0.359690i	$0.882883\pi$
$74$	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	0.682048	−	0.731307i	$-0.261089\pi$
$79$	3.46410	+	2.00000i	0.389742	+	0.225018i	−0.292306	+	0.956325i	$0.594423\pi$
$80$		0			0
$81$		0			0
$82$	−4.89898	+	4.89898i	−0.541002	+	0.541002i
$83$	−2.32937	−	8.69333i	−0.255682	−	0.954217i	−0.967710	−	0.252066i	$-0.918890\pi$
$83$	−2.32937	−	8.69333i	−0.255682	−	0.954217i	0.712028	−	0.702151i	$-0.247777\pi$
$84$		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	−0.795314	−	0.606197i	$-0.792694\pi$
$97$	−4.03459	−	15.0573i	−0.409651	−	1.52884i	0.385664	−	0.922639i	$-0.373972\pi$
$98$	−4.94975	+	4.94975i	−0.500000	+	0.500000i
$99$		0			0
$100$		0			0
$101$	−12.0000	−	6.92820i	−1.19404	−	0.689382i	−0.234823	−	0.972038i	$-0.575451\pi$
$101$	−12.0000	−	6.92820i	−1.19404	−	0.689382i	−0.959221	+	0.282656i	$0.908784\pi$
$102$		0			0
$103$	1.79315	−	6.69213i	0.176684	−	0.659395i	−0.819574	−	0.572973i	$-0.805790\pi$
$103$	1.79315	−	6.69213i	0.176684	−	0.659395i	0.996259	−	0.0864221i	$-0.0275434\pi$
$104$	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	$-0.0530362\pi$
$107$	8.48528	+	8.48528i	0.820303	+	0.820303i	−0.165848	+	0.986151i	$0.553036\pi$
$108$		0			0
$109$			2.00000i			0.191565i	0.995402	+	0.0957826i	$0.0305354\pi$
$109$			2.00000i			0.191565i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.89778	+	0.776457i	0.272600	+	0.0730429i	0.392529	−	0.919739i	$-0.371600\pi$
$113$	2.89778	+	0.776457i	0.272600	+	0.0730429i	−0.119929	+	0.992782i	$0.538267\pi$
$114$		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	$-0.750000\pi$
$127$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$		0			0
$130$		0			0
$131$	15.0000	−	8.66025i	1.31056	−	0.756650i	0.328368	−	0.944550i	$-0.393501\pi$
$131$	15.0000	−	8.66025i	1.31056	−	0.756650i	0.982188	+	0.187900i	$0.0601681\pi$
$132$		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	$-0.304127\pi$
$137$	17.3867	−	4.65874i	1.48544	−	0.398023i	0.908196	+	0.418546i	$0.137460\pi$
$138$		0			0
$139$	11.2583	−	6.50000i	0.954919	−	0.551323i	0.0603135	−	0.998179i	$-0.480790\pi$
$139$	11.2583	−	6.50000i	0.954919	−	0.551323i	0.894606	+	0.446857i	$0.147457\pi$
$140$		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	0.570799	−	0.821090i	$-0.306634\pi$
$149$	−5.19615	−	9.00000i	−0.425685	−	0.737309i	−0.996484	+	0.0837813i	$0.973300\pi$
$150$		0			0
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	−0.822464	−	0.568818i	$-0.807401\pi$
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	0.903842	+	0.427865i	$0.140734\pi$
$152$	−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	$-0.327504\pi$
$157$	6.69213	+	1.79315i	0.534090	+	0.143109i	0.0183138	+	0.999832i	$0.494170\pi$
$158$	−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	$-0.271608\pi$
$163$	−1.22474	−	1.22474i	−0.0959294	−	0.0959294i	−0.753443	+	0.657513i	$0.771608\pi$
$164$	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	$-0.991242\pi$
$167$	−1.55291	+	5.79555i	−0.120168	+	0.448474i	0.879453	+	0.475985i	$0.157908\pi$
$168$		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	0.881491	+	0.472200i	$0.156540\pi$
$173$	4.65874	+	17.3867i	0.354198	+	1.32188i	−0.527294	+	0.849683i	$0.676793\pi$
$174$		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	0.387522	−	0.921861i	$-0.373331\pi$
$191$	−3.00000	−	1.73205i	−0.217072	−	0.125327i	−0.604594	+	0.796534i	$0.706665\pi$
$192$		0			0
$193$	−1.34486	+	5.01910i	−0.0968054	+	0.361283i	−0.997287	−	0.0736115i	$-0.976548\pi$
$193$	−1.34486	+	5.01910i	−0.0968054	+	0.361283i	0.900482	+	0.434894i	$0.143214\pi$
$194$	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	$-0.318565\pi$
$197$	−4.24264	−	4.24264i	−0.302276	−	0.302276i	−0.841904	+	0.539628i	$0.818565\pi$
$198$		0			0
$199$			26.0000i			1.84309i	0.388270	+	0.921546i	$0.373073\pi$
$199$			26.0000i			1.84309i	−0.388270	+	0.921546i	$0.626927\pi$
$200$		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	−0.924918	−	0.380166i	$-0.875867\pi$
$211$	−11.5000	−	19.9186i	−0.791693	−	1.37125i	0.133226	−	0.991086i	$-0.457467\pi$
$212$	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	$-0.620336\pi$
$223$	−3.34607	+	0.896575i	−0.224069	+	0.0600391i	0.145038	+	0.989426i	$0.453670\pi$
$224$		0			0
$225$		0			0
$226$	−3.00000			−0.199557
$227$	−2.89778	+	0.776457i	−0.192332	+	0.0515353i	−0.353699	−	0.935359i	$-0.615076\pi$
$227$	−2.89778	+	0.776457i	−0.192332	+	0.0515353i	0.161367	+	0.986894i	$0.448410\pi$
$228$		0			0
$229$	−17.3205	+	10.0000i	−1.14457	+	0.660819i	−0.947559	−	0.319582i	$-0.896457\pi$
$229$	−17.3205	+	10.0000i	−1.14457	+	0.660819i	−0.197013	+	0.980401i	$0.563124\pi$
$230$		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	$-0.845255\pi$
$233$	−6.36396	+	6.36396i	−0.416917	+	0.416917i	0.467223	+	0.884140i	$0.345255\pi$
$234$		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	0.983698	−	0.179830i	$-0.0575549\pi$
$239$	5.19615	+	9.00000i	0.336111	+	0.582162i	−0.647586	+	0.761992i	$0.724222\pi$
$240$		0			0
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$	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	$0.106367\pi$
$251$			10.3923i			0.655956i	−0.944685	+	0.327978i	$0.893633\pi$
$252$		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	$-0.886840\pi$
$257$	0.776457	−	2.89778i	0.0484341	−	0.180758i	0.985905	+	0.167304i	$0.0535063\pi$
$258$		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	0.841253	+	0.540641i	$0.181818\pi$
$263$	6.21166	+	23.1822i	0.383027	+	1.42948i	−0.458226	+	0.888836i	$0.651515\pi$
$264$		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	$-0.116520\pi$
$277$	−0.896575	−	3.34607i	−0.0538700	−	0.201046i	−0.987616	+	0.156891i	$0.949853\pi$
$278$	−9.19239	+	9.19239i	−0.551323	+	0.551323i
$279$		0			0
$280$		0			0
$281$	18.0000	+	10.3923i	1.07379	+	0.619953i	0.929214	−	0.369541i	$-0.120485\pi$
$281$	18.0000	+	10.3923i	1.07379	+	0.619953i	0.144575	+	0.989494i	$0.453818\pi$
$282$		0			0
$283$	−8.51747	+	31.7876i	−0.506311	+	1.88958i	−0.0521913	+	0.998637i	$0.516621\pi$
$283$	−8.51747	+	31.7876i	−0.506311	+	1.88958i	−0.454120	+	0.890941i	$0.650046\pi$
$284$	−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	$-0.302670\pi$
$293$	11.5911	+	3.10583i	0.677160	+	0.181444i	0.0961820	+	0.995364i	$0.469337\pi$
$294$		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	$-0.972122\pi$
$307$	−15.9217	+	15.9217i	−0.908698	+	0.908698i	0.0874688	+	0.996167i	$0.472122\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3.00000	−	1.73205i	0.170114	−	0.0982156i	−0.412525	−	0.910946i	$-0.635353\pi$
$311$	3.00000	−	1.73205i	0.170114	−	0.0982156i	0.582640	+	0.812731i	$0.302020\pi$
$312$		0			0
$313$	1.67303	−	0.448288i	0.0945654	−	0.0253387i	−0.211226	−	0.977437i	$-0.567746\pi$
$313$	1.67303	−	0.448288i	0.0945654	−	0.0253387i	0.305791	+	0.952099i	$0.401079\pi$
$314$	−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	$-0.264426\pi$
$317$	28.9778	−	7.76457i	1.62755	−	0.436102i	0.953208	+	0.302314i	$0.0977591\pi$
$318$		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	−0.851957	−	0.523612i	$-0.824584\pi$
$331$	0.500000	−	0.866025i	0.0274825	−	0.0476011i	0.879440	+	0.476011i	$0.157918\pi$
$332$	−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	$-0.492463\pi$
$337$	−8.36516	−	2.24144i	−0.455679	−	0.122099i	−0.479356	+	0.877621i	$0.659130\pi$
$338$	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	0.651967	+	0.758248i	$0.273944\pi$
$347$	−5.43520	+	20.2844i	−0.291777	+	1.08893i	−0.943744	+	0.330678i	$0.892722\pi$
$348$		0			0
$349$	−8.66025	−	5.00000i	−0.463573	−	0.267644i	0.249973	−	0.968253i	$-0.419578\pi$
$349$	−8.66025	−	5.00000i	−0.463573	−	0.267644i	−0.713545	+	0.700609i	$0.752912\pi$
$350$		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	$-0.00634627\pi$
$353$	2.32937	+	8.69333i	0.123980	+	0.462699i	−0.875821	+	0.482635i	$0.839680\pi$
$354$		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	0.911666	+	0.410932i	$0.134797\pi$
$367$	6.27603	+	23.4225i	0.327606	+	1.22264i	−0.584060	+	0.811710i	$0.698537\pi$
$368$	−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	$-0.916667\pi$
$373$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$374$	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	$0.162267\pi$
$379$			19.0000i			0.975964i	−0.872854	+	0.487982i	$0.837733\pi$
$380$		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	$-0.694652\pi$
$383$	−28.9778	−	7.76457i	−1.48070	−	0.396751i	−0.906584	+	0.422026i	$0.861319\pi$
$384$		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	−0.967158	−	0.254177i	$-0.918196\pi$
$389$	−5.19615	+	9.00000i	−0.263455	+	0.456318i	0.703702	+	0.710495i	$0.251529\pi$
$390$		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	$-0.777705\pi$
$397$	−2.44949	+	2.44949i	−0.122936	+	0.122936i	0.642962	+	0.765898i	$0.277705\pi$
$398$	−6.72930	−	25.1141i	−0.337309	−	1.25885i
$399$		0			0
$400$		0			0
$401$	−22.5000	+	12.9904i	−1.12360	+	0.648709i	−0.942317	−	0.334723i	$-0.891357\pi$
$401$	−22.5000	+	12.9904i	−1.12360	+	0.648709i	−0.181280	+	0.983432i	$0.558024\pi$
$402$		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	−0.542211	−	0.840243i	$-0.682412\pi$
$409$	−1.73205	+	1.00000i	−0.0856444	+	0.0494468i	0.456566	+	0.889689i	$0.349079\pi$
$410$		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	0.922484	−	0.386037i	$-0.126156\pi$
$419$	2.59808	+	4.50000i	0.126924	+	0.219839i	−0.795559	+	0.605876i	$0.792823\pi$
$420$		0			0
$421$	−14.0000	+	24.2487i	−0.682318	+	1.18181i	0.291953	+	0.956433i	$0.405695\pi$
$421$	−14.0000	+	24.2487i	−0.682318	+	1.18181i	−0.974272	+	0.225377i	$0.927639\pi$
$422$	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	$-0.801483\pi$
$431$		−	24.2487i		−	1.16802i	0.811747	−	0.584010i	$-0.198517\pi$
$432$		0			0
$433$	20.8207	+	20.8207i	1.00058	+	1.00058i	1.00000		0.000577367i	$0.000183782\pi$
$433$	20.8207	+	20.8207i	1.00058	+	1.00058i	0.000577367		1.00000i	$0.499816\pi$
$434$		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	0.692220	−	0.721686i	$-0.256633\pi$
$439$	8.66025	+	5.00000i	0.413331	+	0.238637i	−0.278889	+	0.960323i	$0.589966\pi$
$440$		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	$-0.0147488\pi$
$443$	2.32937	+	8.69333i	0.110672	+	0.413033i	−0.888255	+	0.459351i	$0.848082\pi$
$444$		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	$-0.0833333\pi$
$457$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$458$	14.1421	−	14.1421i	0.660819	−	0.660819i
$459$		0			0
$460$		0			0
$461$	−15.0000	−	8.66025i	−0.698620	−	0.403348i	0.108213	−	0.994128i	$-0.465487\pi$
$461$	−15.0000	−	8.66025i	−0.698620	−	0.403348i	−0.806833	+	0.590779i	$0.798820\pi$
$462$		0			0
$463$	0.896575	−	3.34607i	0.0416674	−	0.155505i	−0.941958	−	0.335732i	$-0.891016\pi$
$463$	0.896575	−	3.34607i	0.0416674	−	0.155505i	0.983625	+	0.180227i	$0.0576832\pi$
$464$	−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	$-0.362820\pi$
$467$	−10.6066	−	10.6066i	−0.490815	−	0.490815i	−0.908563	+	0.417748i	$0.862820\pi$
$468$		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	−0.775969	−	0.630771i	$-0.782739\pi$
$479$	3.46410	−	6.00000i	0.158279	−	0.274147i	0.934248	+	0.356624i	$0.116072\pi$
$480$		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	$-0.621633\pi$
$487$	12.2474	−	12.2474i	0.554985	−	0.554985i	0.927875	+	0.372890i	$0.121633\pi$
$488$	−2.07055	−	7.72741i	−0.0937295	−	0.349803i
$489$		0			0
$490$		0			0
$491$	19.5000	−	11.2583i	0.880023	−	0.508081i	0.00935679	−	0.999956i	$-0.497022\pi$
$491$	19.5000	−	11.2583i	0.880023	−	0.508081i	0.870666	+	0.491875i	$0.163688\pi$
$492$		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	−0.399937	−	0.916542i	$-0.630968\pi$
$499$	4.33013	−	2.50000i	0.193843	−	0.111915i	0.593780	+	0.804627i	$0.297635\pi$
$500$		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	$-0.929709\pi$
$503$	−16.9706	+	16.9706i	−0.756680	+	0.756680i	0.219037	+	0.975717i	$0.429709\pi$
$504$		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	−0.971528	−	0.236924i	$-0.923861\pi$
$509$	−15.5885	−	27.0000i	−0.690946	−	1.19675i	0.280582	−	0.959830i	$-0.409473\pi$
$510$		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	$-0.963690\pi$
$521$		−	5.19615i		−	0.227648i	0.993501	−	0.113824i	$-0.0363099\pi$
$522$		0			0
$523$	18.3712	+	18.3712i	0.803315	+	0.803315i	0.983612	−	0.180297i	$-0.0577059\pi$
$523$	18.3712	+	18.3712i	0.803315	+	0.803315i	−0.180297	+	0.983612i	$0.557706\pi$
$524$	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	0.993103	+	0.117247i	$0.0374069\pi$
$547$	4.48288	+	16.7303i	0.191674	+	0.715337i	−0.801429	+	0.598090i	$0.795926\pi$
$548$	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	$-0.290571\pi$
$557$	−4.24264	−	4.24264i	−0.179766	−	0.179766i	−0.791254	+	0.611488i	$0.790571\pi$
$558$		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	$-0.562583\pi$
$563$	−20.2844	−	5.43520i	−0.854887	−	0.229066i	−0.659542	+	0.751668i	$0.729250\pi$
$564$		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	−0.282092	−	0.959387i	$-0.591028\pi$
$569$	16.4545	−	28.5000i	0.689808	−	1.19478i	0.971900	−	0.235395i	$-0.0756383\pi$
$570$		0			0
$571$	−8.50000	−	14.7224i	−0.355714	−	0.616115i	0.631526	−	0.775355i	$-0.282429\pi$
$571$	−8.50000	−	14.7224i	−0.355714	−	0.616115i	−0.987240	+	0.159240i	$0.949096\pi$
$572$	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	$-0.607583\pi$
$577$	14.6969	−	14.6969i	0.611842	−	0.611842i	0.943426	+	0.331584i	$0.107583\pi$
$578$	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	$-0.395207\pi$
$587$	26.0800	−	6.98811i	1.07644	−	0.288430i	0.753135	+	0.657866i	$0.228541\pi$
$588$		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	$-0.891904\pi$
$593$	−14.8492	+	14.8492i	−0.609785	+	0.609785i	0.333105	+	0.942890i	$0.391904\pi$
$594$		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	0.799402	+	0.600796i	$0.205150\pi$
$599$	22.5167	+	39.0000i	0.920006	+	1.59350i	0.120603	+	0.992701i	$0.461517\pi$
$600$		0			0
$601$	−9.50000	+	16.4545i	−0.387513	+	0.671192i	−0.992114	−	0.125336i	$-0.959999\pi$
$601$	−9.50000	+	16.4545i	−0.387513	+	0.671192i	0.604601	+	0.796528i	$0.293332\pi$
$602$		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	$-0.371762\pi$
$607$	6.69213	+	1.79315i	0.271625	+	0.0727818i	−0.120435	+	0.992721i	$0.538429\pi$
$608$	−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	$-0.412893\pi$
$613$	−17.1464	−	17.1464i	−0.692538	−	0.692538i	−0.962790	+	0.270252i	$0.912893\pi$
$614$	11.2583	−	19.5000i	0.454349	−	0.786956i
$615$		0			0
$616$		0			0
$617$	−6.98811	+	26.0800i	−0.281331	+	1.04994i	0.670148	+	0.742227i	$0.266231\pi$
$617$	−6.98811	+	26.0800i	−0.281331	+	1.04994i	−0.951479	+	0.307714i	$0.900436\pi$
$618$		0			0
$619$	32.0429	+	18.5000i	1.28791	+	0.743578i	0.978282	−	0.207279i	$-0.0664606\pi$
$619$	32.0429	+	18.5000i	1.28791	+	0.743578i	0.309633	+	0.950856i	$0.399794\pi$
$620$		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	0.789111	−	0.614250i	$-0.210541\pi$
$641$	16.5000	+	9.52628i	0.651711	+	0.376265i	−0.137401	+	0.990516i	$0.543875\pi$
$642$		0			0
$643$	12.1038	−	45.1719i	0.477326	−	1.78141i	−0.135050	−	0.990839i	$-0.543120\pi$
$643$	12.1038	−	45.1719i	0.477326	−	1.78141i	0.612376	−	0.790566i	$-0.290214\pi$
$644$		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	$-0.325799\pi$
$647$	−8.48528	−	8.48528i	−0.333591	−	0.333591i	−0.853948	+	0.520358i	$0.825799\pi$
$648$		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	$-0.805091\pi$
$653$	−46.3644	−	12.4233i	−1.81438	−	0.486162i	−0.996066	+	0.0886092i	$0.971758\pi$
$654$		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	−0.673333	−	0.739339i	$-0.735138\pi$
$659$	7.79423	−	13.5000i	0.303620	−	0.525885i	0.976953	+	0.213454i	$0.0684713\pi$
$660$		0			0
$661$	−11.0000	−	19.0526i	−0.427850	−	0.741059i	0.568831	−	0.822454i	$-0.307396\pi$
$661$	−11.0000	−	19.0526i	−0.427850	−	0.741059i	−0.996682	+	0.0813955i	$0.974062\pi$
$662$	−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	$-0.198984\pi$
$673$	46.8449	−	12.5521i	1.80574	−	0.483846i	0.994850	+	0.101355i	$0.0323177\pi$
$674$	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	$-0.546551\pi$
$677$	5.79555	−	1.55291i	0.222741	−	0.0596833i	0.368464	+	0.929642i	$0.379884\pi$
$678$		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	$-0.676264\pi$
$683$	8.48528	−	8.48528i	0.324680	−	0.324680i	0.850559	+	0.525879i	$0.176264\pi$
$684$		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	−0.313355	−	0.949636i	$-0.601453\pi$
$691$	17.5000	−	30.3109i	0.665731	−	1.15308i	0.979086	−	0.203445i	$-0.0652137\pi$
$692$	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	$-0.824682\pi$
$701$		−	27.7128i		−	1.04670i	0.852118	−	0.523349i	$-0.175318\pi$
$702$		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	0.624423	−	0.781086i	$-0.285334\pi$
$709$	6.92820	+	4.00000i	0.260194	+	0.150223i	−0.364229	+	0.931309i	$0.618667\pi$
$710$		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	$-0.0628716\pi$
$727$	0.896575	+	3.34607i	0.0332521	+	0.124099i	−0.947305	+	0.320334i	$0.896205\pi$
$728$		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	0.792585	+	0.609762i	$0.208735\pi$
$733$	−5.37945	+	20.0764i	−0.198695	+	0.741538i	−0.991279	+	0.131777i	$0.957932\pi$
$734$	−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	$-0.728071\pi$
$739$		−	41.0000i		−	1.50821i	0.656754	−	0.754105i	$-0.271929\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	23.1822	+	6.21166i	0.850473	+	0.227884i	0.657625	−	0.753345i	$-0.271561\pi$
$743$	23.1822	+	6.21166i	0.850473	+	0.227884i	0.192848	+	0.981229i	$0.438228\pi$
$744$		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	0.970744	+	0.240118i	$0.0771860\pi$
$751$	19.0000	+	32.9090i	0.693320	+	1.20087i	−0.277424	+	0.960748i	$0.589481\pi$
$752$	−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	0.0708518	−	0.997487i	$-0.477428\pi$
$757$	29.3939	−	29.3939i	1.06834	−	1.06834i	0.997487	−	0.0708518i	$-0.0225717\pi$
$758$	−4.91756	−	18.3526i	−0.178614	−	0.666596i
$759$		0			0
$760$		0			0
$761$	−46.5000	+	26.8468i	−1.68562	+	0.973195i	−0.727822	+	0.685766i	$0.759467\pi$
$761$	−46.5000	+	26.8468i	−1.68562	+	0.973195i	−0.957802	+	0.287429i	$0.907200\pi$
$762$		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	−0.689063	−	0.724701i	$-0.741978\pi$
$769$	−11.2583	+	6.50000i	−0.405986	+	0.234396i	0.283078	+	0.959097i	$0.408645\pi$
$770$		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	$-0.784413\pi$
$773$	−4.24264	+	4.24264i	−0.152597	+	0.152597i	0.626680	+	0.779277i	$0.284413\pi$
$774$		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	$-0.793539\pi$
$787$	−50.1910	−	13.4486i	−1.78912	−	0.479392i	−0.992195	+	0.124693i	$0.960205\pi$
$788$	−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	0.764308	+	0.644852i	$0.223081\pi$
$797$	−6.21166	+	23.1822i	−0.220028	+	0.821156i	−0.984336	+	0.176304i	$0.943586\pi$
$798$		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	0.921810	−	0.387642i	$-0.126710\pi$
$821$	30.0000	+	17.3205i	1.04701	+	0.604490i	0.125197	+	0.992132i	$0.460044\pi$
$822$		0			0
$823$	−1.79315	+	6.69213i	−0.0625053	+	0.233273i	−0.990111	−	0.140289i	$-0.955197\pi$
$823$	−1.79315	+	6.69213i	−0.0625053	+	0.233273i	0.927605	+	0.373562i	$0.121864\pi$
$824$	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	$-0.0554837\pi$
$827$	23.3345	+	23.3345i	0.811421	+	0.811421i	−0.173426	+	0.984847i	$0.555484\pi$
$828$		0			0
$829$			16.0000i			0.555703i	0.960624	+	0.277851i	$0.0896223\pi$
$829$			16.0000i			0.555703i	−0.960624	+	0.277851i	$0.910378\pi$
$830$		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	−0.800013	−	0.599983i	$-0.795174\pi$
$839$	3.46410	−	6.00000i	0.119594	−	0.207143i	0.919607	+	0.392840i	$0.128507\pi$
$840$		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	$-0.679160\pi$
$853$	−16.7303	+	4.48288i	−0.572835	+	0.153491i	−0.0392388	+	0.999230i	$0.512493\pi$
$854$		0			0
$855$		0			0
$856$	−12.0000			−0.410152
$857$	−2.89778	+	0.776457i	−0.0989862	+	0.0265233i	−0.307972	−	0.951395i	$-0.599650\pi$
$857$	−2.89778	+	0.776457i	−0.0989862	+	0.0265233i	0.208986	+	0.977919i	$0.432984\pi$
$858$		0			0
$859$	27.7128	−	16.0000i	0.945549	−	0.545913i	0.0538535	−	0.998549i	$-0.482850\pi$
$859$	27.7128	−	16.0000i	0.945549	−	0.545913i	0.891695	+	0.452636i	$0.149516\pi$
$860$		0			0
$861$		0			0
$862$	6.27603	+	23.4225i	0.213762	+	0.797772i
$863$	33.9411	−	33.9411i	1.15537	−	1.15537i	0.169910	−	0.985460i	$-0.445652\pi$
$863$	33.9411	−	33.9411i	1.15537	−	1.15537i	0.985460	−	0.169910i	$-0.0543476\pi$
$864$		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	$-0.530799\pi$
$877$	−20.0764	−	5.37945i	−0.677932	−	0.181651i	−0.581325	+	0.813671i	$0.697466\pi$
$878$	−9.65926	−	2.58819i	−0.325984	−	0.0873472i
$879$		0			0
$880$		0			0
$881$			34.6410i			1.16709i	0.812082	+	0.583543i	$0.198334\pi$
$881$			34.6410i			1.16709i	−0.812082	+	0.583543i	$0.801666\pi$
$882$		0			0
$883$	−18.3712	−	18.3712i	−0.618239	−	0.618239i	0.326840	−	0.945080i	$-0.394016\pi$
$883$	−18.3712	−	18.3712i	−0.618239	−	0.618239i	−0.945080	+	0.326840i	$0.894016\pi$
$884$	−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	−0.502439	−	0.864613i	$-0.667564\pi$
$887$	10.8704	−	40.5689i	0.364992	−	1.36217i	0.867431	−	0.497557i	$-0.165770\pi$
$888$		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	$-0.0374077\pi$
$907$	2.24144	+	8.36516i	0.0744257	+	0.277761i	−0.918677	+	0.395010i	$0.870741\pi$
$908$	−2.12132	+	2.12132i	−0.0703985	+	0.0703985i
$909$		0			0
$910$		0			0
$911$	−33.0000	−	19.0526i	−1.09334	−	0.631239i	−0.158875	−	0.987299i	$-0.550787\pi$
$911$	−33.0000	−	19.0526i	−1.09334	−	0.631239i	−0.934463	+	0.356059i	$0.884120\pi$
$912$		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	$0.189498\pi$
$919$			34.0000i			1.12156i	−0.827966	+	0.560778i	$0.810502\pi$
$920$		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	−0.428470	−	0.903556i	$-0.640947\pi$
$929$	17.3205	−	30.0000i	0.568267	−	0.984268i	0.996737	−	0.0807121i	$-0.0257194\pi$
$930$		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	$-0.777049\pi$
$937$	−3.67423	+	3.67423i	−0.120032	+	0.120032i	0.644539	+	0.764571i	$0.277049\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	18.0000	−	10.3923i	0.586783	−	0.338779i	−0.177041	−	0.984203i	$-0.556653\pi$
$941$	18.0000	−	10.3923i	0.586783	−	0.338779i	0.763825	+	0.645424i	$0.223319\pi$
$942$		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	$-0.661700\pi$
$947$	−14.4889	+	3.88229i	−0.470826	+	0.126157i	0.0156019	+	0.999878i	$0.495034\pi$
$948$		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	$-0.639529\pi$
$953$	14.8492	−	14.8492i	0.481014	−	0.481014i	0.905455	+	0.424441i	$0.139529\pi$
$954$		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	$-0.488185\pi$
$967$	−13.3843	−	3.58630i	−0.430409	−	0.115328i	−0.467518	+	0.883984i	$0.654852\pi$
$968$	7.72741	+	2.07055i	0.248368	+	0.0665501i
$969$		0			0
$970$		0			0
$971$		−	12.1244i		−	0.389089i	−0.980894	−	0.194545i	$-0.937677\pi$
$971$		−	12.1244i		−	0.389089i	0.980894	−	0.194545i	$-0.0623229\pi$
$972$		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	$-0.886069\pi$
$977$	1.55291	−	5.79555i	0.0496821	−	0.185416i	0.986308	+	0.164916i	$0.0527353\pi$
$978$		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	0.890600	+	0.454788i	$0.150285\pi$
$983$	10.8704	+	40.5689i	0.346712	+	1.29395i	−0.543888	+	0.839158i	$0.683048\pi$
$984$		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	$-0.135955\pi$
$997$	−2.68973	−	10.0382i	−0.0851845	−	0.317913i	−0.995349	+	0.0963340i	$0.969288\pi$
$998$	−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.143.1		8
3.2	odd	2		450.2.p.b.443.2	yes	8
5.2	odd	4	inner	1350.2.q.e.1007.1		8
5.3	odd	4	inner	1350.2.q.e.1007.2		8
5.4	even	2	inner	1350.2.q.e.143.2		8
9.4	even	3		450.2.p.b.293.2	yes	8
9.5	odd	6	inner	1350.2.q.e.1043.1		8
15.2	even	4		450.2.p.b.407.2	yes	8
15.8	even	4		450.2.p.b.407.1	yes	8
15.14	odd	2		450.2.p.b.443.1	yes	8
45.4	even	6		450.2.p.b.293.1	yes	8
45.13	odd	12		450.2.p.b.257.1	✓	8
45.14	odd	6	inner	1350.2.q.e.1043.2		8
45.22	odd	12		450.2.p.b.257.2	yes	8
45.23	even	12	inner	1350.2.q.e.557.2		8
45.32	even	12	inner	1350.2.q.e.557.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.p.b.257.1	✓	8	45.13	odd	12
450.2.p.b.257.2	yes	8	45.22	odd	12
450.2.p.b.293.1	yes	8	45.4	even	6
450.2.p.b.293.2	yes	8	9.4	even	3
450.2.p.b.407.1	yes	8	15.8	even	4
450.2.p.b.407.2	yes	8	15.2	even	4
450.2.p.b.443.1	yes	8	15.14	odd	2
450.2.p.b.443.2	yes	8	3.2	odd	2
1350.2.q.e.143.1		8	1.1	even	1	trivial
1350.2.q.e.143.2		8	5.4	even	2	inner
1350.2.q.e.557.1		8	45.32	even	12	inner
1350.2.q.e.557.2		8	45.23	even	12	inner
1350.2.q.e.1007.1		8	5.2	odd	4	inner
1350.2.q.e.1007.2		8	5.3	odd	4	inner
1350.2.q.e.1043.1		8	9.5	odd	6	inner
1350.2.q.e.1043.2		8	45.14	odd	6	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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