LMFDB - Embedded newform 2352.2.q.bb.1537.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2352,2,Mod(961,2352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2352, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("2352.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2352 = 2^{4} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2352.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.7808145554$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1537.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	2352.1537
Dual form			2352.2.q.bb.961.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(1.70711 + 2.95680i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} +(1.70711 + 2.95680i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{11} -2.58579 q^{13} -3.41421 q^{15} +(-1.12132 + 1.94218i) q^{17} +(1.41421 + 2.44949i) q^{19} +(-3.82843 - 6.63103i) q^{23} +(-3.32843 + 5.76500i) q^{25} +1.00000 q^{27} -6.82843 q^{29} +(0.585786 - 1.01461i) q^{31} +(-1.00000 - 1.73205i) q^{33} +(2.00000 + 3.46410i) q^{37} +(1.29289 - 2.23936i) q^{39} -6.24264 q^{41} -5.65685 q^{43} +(1.70711 - 2.95680i) q^{45} +(1.41421 + 2.44949i) q^{47} +(-1.12132 - 1.94218i) q^{51} +(1.00000 - 1.73205i) q^{53} -6.82843 q^{55} -2.82843 q^{57} +(0.585786 - 1.01461i) q^{59} +(6.12132 + 10.6024i) q^{61} +(-4.41421 - 7.64564i) q^{65} +(-2.82843 + 4.89898i) q^{67} +7.65685 q^{69} -9.31371 q^{71} +(6.94975 - 12.0373i) q^{73} +(-3.32843 - 5.76500i) q^{75} +(6.82843 + 11.8272i) q^{79} +(-0.500000 + 0.866025i) q^{81} +7.31371 q^{83} -7.65685 q^{85} +(3.41421 - 5.91359i) q^{87} +(-7.12132 - 12.3345i) q^{89} +(0.585786 + 1.01461i) q^{93} +(-4.82843 + 8.36308i) q^{95} -2.58579 q^{97} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 4 q^{5} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 4 * q^5 - 2 * q^9	$ 4 q - 2 q^{3} + 4 q^{5} - 2 q^{9} - 4 q^{11} - 16 q^{13} - 8 q^{15} + 4 q^{17} - 4 q^{23} - 2 q^{25} + 4 q^{27} - 16 q^{29} + 8 q^{31} - 4 q^{33} + 8 q^{37} + 8 q^{39} - 8 q^{41} + 4 q^{45} + 4 q^{51} + 4 q^{53} - 16 q^{55} + 8 q^{59} + 16 q^{61} - 12 q^{65} + 8 q^{69} + 8 q^{71} + 8 q^{73} - 2 q^{75} + 16 q^{79} - 2 q^{81} - 16 q^{83} - 8 q^{85} + 8 q^{87} - 20 q^{89} + 8 q^{93} - 8 q^{95} - 16 q^{97} + 8 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 + 4 * q^5 - 2 * q^9 - 4 * q^11 - 16 * q^13 - 8 * q^15 + 4 * q^17 - 4 * q^23 - 2 * q^25 + 4 * q^27 - 16 * q^29 + 8 * q^31 - 4 * q^33 + 8 * q^37 + 8 * q^39 - 8 * q^41 + 4 * q^45 + 4 * q^51 + 4 * q^53 - 16 * q^55 + 8 * q^59 + 16 * q^61 - 12 * q^65 + 8 * q^69 + 8 * q^71 + 8 * q^73 - 2 * q^75 + 16 * q^79 - 2 * q^81 - 16 * q^83 - 8 * q^85 + 8 * q^87 - 20 * q^89 + 8 * q^93 - 8 * q^95 - 16 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times$.

$n$	$785$	$1471$	$1765$	$2257$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$	1.70711	+	2.95680i	0.763441	+	1.32232i	0.941067	+	0.338221i	$0.109825\pi$
$5$	1.70711	+	2.95680i	0.763441	+	1.32232i	−0.177625	+	0.984098i	$0.556842\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$		0			0
$13$	−2.58579			−0.717168			−0.358584	−	0.933497i	$-0.616740\pi$
$13$	−2.58579			−0.717168			−0.358584	+	0.933497i	$0.616740\pi$
$14$		0			0
$15$	−3.41421			−0.881546
$16$		0			0
$17$	−1.12132	+	1.94218i	−0.271960	+	0.471049i	−0.969364	−	0.245630i	$-0.921005\pi$
$17$	−1.12132	+	1.94218i	−0.271960	+	0.471049i	0.697404	+	0.716679i	$0.254339\pi$
$18$		0			0
$19$	1.41421	+	2.44949i	0.324443	+	0.561951i	0.981399	−	0.191977i	$-0.0614899\pi$
$19$	1.41421	+	2.44949i	0.324443	+	0.561951i	−0.656957	+	0.753928i	$0.728157\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.82843	−	6.63103i	−0.798282	−	1.38267i	−0.920734	−	0.390191i	$-0.872409\pi$
$23$	−3.82843	−	6.63103i	−0.798282	−	1.38267i	0.122452	−	0.992474i	$-0.460924\pi$
$24$		0			0
$25$	−3.32843	+	5.76500i	−0.665685	+	1.15300i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−6.82843			−1.26801			−0.634004	−	0.773330i	$-0.718590\pi$
$29$	−6.82843			−1.26801			−0.634004	+	0.773330i	$0.718590\pi$
$30$		0			0
$31$	0.585786	−	1.01461i	0.105210	−	0.182230i	−0.808614	−	0.588340i	$-0.799782\pi$
$31$	0.585786	−	1.01461i	0.105210	−	0.182230i	0.913824	+	0.406110i	$0.133115\pi$
$32$		0			0
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	0.982274	−	0.187453i	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$		0			0
$39$	1.29289	−	2.23936i	0.207029	−	0.358584i
$40$		0			0
$41$	−6.24264			−0.974937			−0.487468	−	0.873141i	$-0.662080\pi$
$41$	−6.24264			−0.974937			−0.487468	+	0.873141i	$0.662080\pi$
$42$		0			0
$43$	−5.65685			−0.862662			−0.431331	−	0.902194i	$-0.641956\pi$
$43$	−5.65685			−0.862662			−0.431331	+	0.902194i	$0.641956\pi$
$44$		0			0
$45$	1.70711	−	2.95680i	0.254480	−	0.440773i
$46$		0			0
$47$	1.41421	+	2.44949i	0.206284	+	0.357295i	0.950541	−	0.310599i	$-0.100530\pi$
$47$	1.41421	+	2.44949i	0.206284	+	0.357295i	−0.744257	+	0.667893i	$0.767196\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−1.12132	−	1.94218i	−0.157016	−	0.271960i
$52$		0			0
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	−0.789136	−	0.614218i	$-0.789471\pi$
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	0.926497	+	0.376303i	$0.122805\pi$
$54$		0			0
$55$	−6.82843			−0.920745
$56$		0			0
$57$	−2.82843			−0.374634
$58$		0			0
$59$	0.585786	−	1.01461i	0.0762629	−	0.132091i	−0.825372	−	0.564589i	$-0.809035\pi$
$59$	0.585786	−	1.01461i	0.0762629	−	0.132091i	0.901635	+	0.432498i	$0.142368\pi$
$60$		0			0
$61$	6.12132	+	10.6024i	0.783755	+	1.35750i	0.929740	+	0.368216i	$0.120031\pi$
$61$	6.12132	+	10.6024i	0.783755	+	1.35750i	−0.145985	+	0.989287i	$0.546635\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.41421	−	7.64564i	−0.547516	−	0.948325i
$66$		0			0
$67$	−2.82843	+	4.89898i	−0.345547	+	0.598506i	−0.985453	−	0.169948i	$-0.945640\pi$
$67$	−2.82843	+	4.89898i	−0.345547	+	0.598506i	0.639906	+	0.768453i	$0.278973\pi$
$68$		0			0
$69$	7.65685			0.921777
$70$		0			0
$71$	−9.31371			−1.10533			−0.552667	−	0.833402i	$-0.686390\pi$
$71$	−9.31371			−1.10533			−0.552667	+	0.833402i	$0.686390\pi$
$72$		0			0
$73$	6.94975	−	12.0373i	0.813406	−	1.40886i	−0.0970601	−	0.995279i	$-0.530944\pi$
$73$	6.94975	−	12.0373i	0.813406	−	1.40886i	0.910467	−	0.413583i	$-0.135723\pi$
$74$		0			0
$75$	−3.32843	−	5.76500i	−0.384334	−	0.665685i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	6.82843	+	11.8272i	0.768258	+	1.33066i	0.938507	+	0.345261i	$0.112210\pi$
$79$	6.82843	+	11.8272i	0.768258	+	1.33066i	−0.170249	+	0.985401i	$0.554457\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	7.31371			0.802784			0.401392	−	0.915906i	$-0.368527\pi$
$83$	7.31371			0.802784			0.401392	+	0.915906i	$0.368527\pi$
$84$		0			0
$85$	−7.65685			−0.830502
$86$		0			0
$87$	3.41421	−	5.91359i	0.366042	−	0.634004i
$88$		0			0
$89$	−7.12132	−	12.3345i	−0.754858	−	1.30745i	−0.945445	−	0.325783i	$-0.894372\pi$
$89$	−7.12132	−	12.3345i	−0.754858	−	1.30745i	0.190586	−	0.981670i	$-0.438961\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	0.585786	+	1.01461i	0.0607432	+	0.105210i
$94$		0			0
$95$	−4.82843	+	8.36308i	−0.495386	+	0.858034i
$96$		0			0
$97$	−2.58579			−0.262547			−0.131273	−	0.991346i	$-0.541907\pi$
$97$	−2.58579			−0.262547			−0.131273	+	0.991346i	$0.541907\pi$
$98$		0			0
$99$	2.00000			0.201008
$100$		0			0
$101$	1.46447	−	2.53653i	0.145720	−	0.252394i	−0.783921	−	0.620860i	$-0.786784\pi$
$101$	1.46447	−	2.53653i	0.145720	−	0.252394i	0.929641	+	0.368466i	$0.120117\pi$
$102$		0			0
$103$	−2.24264	−	3.88437i	−0.220974	−	0.382738i	0.734130	−	0.679009i	$-0.237590\pi$
$103$	−2.24264	−	3.88437i	−0.220974	−	0.382738i	−0.955104	+	0.296271i	$0.904257\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.171573	−	0.297173i	−0.0165866	−	0.0287288i	0.857613	−	0.514296i	$-0.171947\pi$
$107$	−0.171573	−	0.297173i	−0.0165866	−	0.0287288i	−0.874200	+	0.485567i	$0.838613\pi$
$108$		0			0
$109$	2.82843	−	4.89898i	0.270914	−	0.469237i	−0.698182	−	0.715920i	$-0.746007\pi$
$109$	2.82843	−	4.89898i	0.270914	−	0.469237i	0.969096	+	0.246683i	$0.0793407\pi$
$110$		0			0
$111$	−4.00000			−0.379663
$112$		0			0
$113$	−5.31371			−0.499872			−0.249936	−	0.968262i	$-0.580410\pi$
$113$	−5.31371			−0.499872			−0.249936	+	0.968262i	$0.580410\pi$
$114$		0			0
$115$	13.0711	−	22.6398i	1.21888	−	2.11117i
$116$		0			0
$117$	1.29289	+	2.23936i	0.119528	+	0.207029i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$	3.12132	−	5.40629i	0.281440	−	0.487468i
$124$		0			0
$125$	−5.65685			−0.505964
$126$		0			0
$127$	1.65685			0.147022			0.0735110	−	0.997294i	$-0.476580\pi$
$127$	1.65685			0.147022			0.0735110	+	0.997294i	$0.476580\pi$
$128$		0			0
$129$	2.82843	−	4.89898i	0.249029	−	0.431331i
$130$		0			0
$131$	7.65685	+	13.2621i	0.668982	+	1.15871i	0.978189	+	0.207717i	$0.0666032\pi$
$131$	7.65685	+	13.2621i	0.668982	+	1.15871i	−0.309207	+	0.950995i	$0.600063\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	1.70711	+	2.95680i	0.146924	+	0.254480i
$136$		0			0
$137$	−7.07107	+	12.2474i	−0.604122	+	1.04637i	0.388067	+	0.921631i	$0.373143\pi$
$137$	−7.07107	+	12.2474i	−0.604122	+	1.04637i	−0.992190	+	0.124739i	$0.960191\pi$
$138$		0			0
$139$	−17.6569			−1.49763			−0.748817	−	0.662776i	$-0.769378\pi$
$139$	−17.6569			−1.49763			−0.748817	+	0.662776i	$0.769378\pi$
$140$		0			0
$141$	−2.82843			−0.238197
$142$		0			0
$143$	2.58579	−	4.47871i	0.216234	−	0.374529i
$144$		0			0
$145$	−11.6569	−	20.1903i	−0.968049	−	1.67671i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−8.65685	−	14.9941i	−0.709197	−	1.22837i	−0.965155	−	0.261678i	$-0.915724\pi$
$149$	−8.65685	−	14.9941i	−0.709197	−	1.22837i	0.255958	−	0.966688i	$-0.417609\pi$
$150$		0			0
$151$	6.00000	−	10.3923i	0.488273	−	0.845714i	−0.511636	−	0.859202i	$-0.670960\pi$
$151$	6.00000	−	10.3923i	0.488273	−	0.845714i	0.999909	+	0.0134886i	$0.00429367\pi$
$152$		0			0
$153$	2.24264			0.181307
$154$		0			0
$155$	4.00000			0.321288
$156$		0			0
$157$	5.87868	−	10.1822i	0.469170	−	0.812626i	−0.530209	−	0.847867i	$-0.677887\pi$
$157$	5.87868	−	10.1822i	0.469170	−	0.812626i	0.999379	+	0.0352411i	$0.0112199\pi$
$158$		0			0
$159$	1.00000	+	1.73205i	0.0793052	+	0.137361i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−5.65685	−	9.79796i	−0.443079	−	0.767435i	0.554837	−	0.831959i	$-0.312781\pi$
$163$	−5.65685	−	9.79796i	−0.443079	−	0.767435i	−0.997916	+	0.0645236i	$0.979447\pi$
$164$		0			0
$165$	3.41421	−	5.91359i	0.265796	−	0.460372i
$166$		0			0
$167$	−19.7990			−1.53209			−0.766046	−	0.642786i	$-0.777779\pi$
$167$	−19.7990			−1.53209			−0.766046	+	0.642786i	$0.777779\pi$
$168$		0			0
$169$	−6.31371			−0.485670
$170$		0			0
$171$	1.41421	−	2.44949i	0.108148	−	0.187317i
$172$		0			0
$173$	10.5355	+	18.2481i	0.801002	+	1.38738i	0.918957	+	0.394357i	$0.129033\pi$
$173$	10.5355	+	18.2481i	0.801002	+	1.38738i	−0.117956	+	0.993019i	$0.537634\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.585786	+	1.01461i	0.0440304	+	0.0762629i
$178$		0			0
$179$	−9.82843	+	17.0233i	−0.734611	+	1.27238i	0.220283	+	0.975436i	$0.429302\pi$
$179$	−9.82843	+	17.0233i	−0.734611	+	1.27238i	−0.954894	+	0.296948i	$0.904031\pi$
$180$		0			0
$181$	2.58579			0.192200			0.0961000	−	0.995372i	$-0.469363\pi$
$181$	2.58579			0.192200			0.0961000	+	0.995372i	$0.469363\pi$
$182$		0			0
$183$	−12.2426			−0.905002
$184$		0			0
$185$	−6.82843	+	11.8272i	−0.502036	+	0.869552i
$186$		0			0
$187$	−2.24264	−	3.88437i	−0.163998	−	0.284053i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	−0.982828	−	0.184525i	$-0.940925\pi$
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	0.331611	−	0.943416i	$-0.392408\pi$
$192$		0			0
$193$	−2.65685	+	4.60181i	−0.191245	+	0.331245i	−0.945663	−	0.325149i	$-0.894586\pi$
$193$	−2.65685	+	4.60181i	−0.191245	+	0.331245i	0.754418	+	0.656394i	$0.227919\pi$
$194$		0			0
$195$	8.82843			0.632217
$196$		0			0
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$		0			0
$199$	−10.8284	+	18.7554i	−0.767607	+	1.32953i	0.171250	+	0.985228i	$0.445219\pi$
$199$	−10.8284	+	18.7554i	−0.767607	+	1.32953i	−0.938857	+	0.344307i	$0.888114\pi$
$200$		0			0
$201$	−2.82843	−	4.89898i	−0.199502	−	0.345547i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−10.6569	−	18.4582i	−0.744307	−	1.28918i
$206$		0			0
$207$	−3.82843	+	6.63103i	−0.266094	+	0.460888i
$208$		0			0
$209$	−5.65685			−0.391293
$210$		0			0
$211$	−12.9706			−0.892930			−0.446465	−	0.894801i	$-0.647317\pi$
$211$	−12.9706			−0.892930			−0.446465	+	0.894801i	$0.647317\pi$
$212$		0			0
$213$	4.65685	−	8.06591i	0.319082	−	0.552667i
$214$		0			0
$215$	−9.65685	−	16.7262i	−0.658592	−	1.14071i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	6.94975	+	12.0373i	0.469620	+	0.813406i
$220$		0			0
$221$	2.89949	−	5.02207i	0.195041	−	0.337821i
$222$		0			0
$223$	24.9706			1.67215			0.836076	−	0.548613i	$-0.184844\pi$
$223$	24.9706			1.67215			0.836076	+	0.548613i	$0.184844\pi$
$224$		0			0
$225$	6.65685			0.443790
$226$		0			0
$227$	−11.8995	+	20.6105i	−0.789797	+	1.36797i	0.136294	+	0.990668i	$0.456481\pi$
$227$	−11.8995	+	20.6105i	−0.789797	+	1.36797i	−0.926091	+	0.377300i	$0.876852\pi$
$228$		0			0
$229$	−0.121320	−	0.210133i	−0.00801707	−	0.0138860i	0.861989	−	0.506927i	$-0.169219\pi$
$229$	−0.121320	−	0.210133i	−0.00801707	−	0.0138860i	−0.870006	+	0.493041i	$0.835885\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.07107	+	5.31925i	0.201192	+	0.348475i	0.948913	−	0.315538i	$-0.102185\pi$
$233$	3.07107	+	5.31925i	0.201192	+	0.348475i	−0.747721	+	0.664014i	$0.768852\pi$
$234$		0			0
$235$	−4.82843	+	8.36308i	−0.314972	+	0.545547i
$236$		0			0
$237$	−13.6569			−0.887108
$238$		0			0
$239$	15.6569			1.01276			0.506379	−	0.862311i	$-0.330984\pi$
$239$	15.6569			1.01276			0.506379	+	0.862311i	$0.330984\pi$
$240$		0			0
$241$	−8.12132	+	14.0665i	−0.523140	+	0.906105i	0.476497	+	0.879176i	$0.341906\pi$
$241$	−8.12132	+	14.0665i	−0.523140	+	0.906105i	−0.999637	+	0.0269294i	$0.991427\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3.65685	−	6.33386i	−0.232680	−	0.403014i
$248$		0			0
$249$	−3.65685	+	6.33386i	−0.231744	+	0.401392i
$250$		0			0
$251$	−12.4853			−0.788064			−0.394032	−	0.919097i	$-0.628920\pi$
$251$	−12.4853			−0.788064			−0.394032	+	0.919097i	$0.628920\pi$
$252$		0			0
$253$	15.3137			0.962765
$254$		0			0
$255$	3.82843	−	6.63103i	0.239745	−	0.415251i
$256$		0			0
$257$	11.6066	+	20.1032i	0.724000	+	1.25400i	0.959384	+	0.282102i	$0.0910318\pi$
$257$	11.6066	+	20.1032i	0.724000	+	1.25400i	−0.235384	+	0.971902i	$0.575635\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	3.41421	+	5.91359i	0.211335	+	0.366042i
$262$		0			0
$263$	2.65685	−	4.60181i	0.163829	−	0.283760i	−0.772410	−	0.635124i	$-0.780949\pi$
$263$	2.65685	−	4.60181i	0.163829	−	0.283760i	0.936239	+	0.351365i	$0.114282\pi$
$264$		0			0
$265$	6.82843			0.419467
$266$		0			0
$267$	14.2426			0.871635
$268$		0			0
$269$	−7.36396	+	12.7548i	−0.448989	+	0.777671i	−0.998320	−	0.0579332i	$-0.981549\pi$
$269$	−7.36396	+	12.7548i	−0.448989	+	0.777671i	0.549332	+	0.835604i	$0.314882\pi$
$270$		0			0
$271$	5.07107	+	8.78335i	0.308045	+	0.533550i	0.977935	−	0.208911i	$-0.0669918\pi$
$271$	5.07107	+	8.78335i	0.308045	+	0.533550i	−0.669889	+	0.742461i	$0.733658\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−6.65685	−	11.5300i	−0.401423	−	0.695286i
$276$		0			0
$277$	4.65685	−	8.06591i	0.279803	−	0.484633i	−0.691532	−	0.722345i	$-0.743064\pi$
$277$	4.65685	−	8.06591i	0.279803	−	0.484633i	0.971336	+	0.237712i	$0.0763974\pi$
$278$		0			0
$279$	−1.17157			−0.0701402
$280$		0			0
$281$	0.485281			0.0289495			0.0144747	−	0.999895i	$-0.495392\pi$
$281$	0.485281			0.0289495			0.0144747	+	0.999895i	$0.495392\pi$
$282$		0			0
$283$	4.24264	−	7.34847i	0.252199	−	0.436821i	−0.711932	−	0.702248i	$-0.752180\pi$
$283$	4.24264	−	7.34847i	0.252199	−	0.436821i	0.964131	+	0.265427i	$0.0855130\pi$
$284$		0			0
$285$	−4.82843	−	8.36308i	−0.286011	−	0.495386i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	5.98528	+	10.3668i	0.352075	+	0.609812i
$290$		0			0
$291$	1.29289	−	2.23936i	0.0757907	−	0.131273i
$292$		0			0
$293$	−16.5858			−0.968952			−0.484476	−	0.874805i	$-0.660990\pi$
$293$	−16.5858			−0.968952			−0.484476	+	0.874805i	$0.660990\pi$
$294$		0			0
$295$	4.00000			0.232889
$296$		0			0
$297$	−1.00000	+	1.73205i	−0.0580259	+	0.100504i
$298$		0			0
$299$	9.89949	+	17.1464i	0.572503	+	0.991604i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	1.46447	+	2.53653i	0.0841314	+	0.145720i
$304$		0			0
$305$	−20.8995	+	36.1990i	−1.19670	+	2.07275i
$306$		0			0
$307$	30.1421			1.72030			0.860151	−	0.510039i	$-0.170369\pi$
$307$	30.1421			1.72030			0.860151	+	0.510039i	$0.170369\pi$
$308$		0			0
$309$	4.48528			0.255159
$310$		0			0
$311$	−3.07107	+	5.31925i	−0.174144	+	0.301627i	−0.939865	−	0.341547i	$-0.889049\pi$
$311$	−3.07107	+	5.31925i	−0.174144	+	0.301627i	0.765721	+	0.643173i	$0.222383\pi$
$312$		0			0
$313$	0.949747	+	1.64501i	0.0536829	+	0.0929815i	0.891618	−	0.452788i	$-0.149571\pi$
$313$	0.949747	+	1.64501i	0.0536829	+	0.0929815i	−0.837935	+	0.545770i	$0.816237\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.00000	−	8.66025i	−0.280828	−	0.486408i	0.690761	−	0.723083i	$-0.257276\pi$
$317$	−5.00000	−	8.66025i	−0.280828	−	0.486408i	−0.971589	+	0.236675i	$0.923942\pi$
$318$		0			0
$319$	6.82843	−	11.8272i	0.382319	−	0.662195i
$320$		0			0
$321$	0.343146			0.0191525
$322$		0			0
$323$	−6.34315			−0.352942
$324$		0			0
$325$	8.60660	−	14.9071i	0.477408	−	0.826896i
$326$		0			0
$327$	2.82843	+	4.89898i	0.156412	+	0.270914i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	0.805812	−	0.592172i	$-0.201729\pi$
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	−0.915742	+	0.401768i	$0.868396\pi$
$332$		0			0
$333$	2.00000	−	3.46410i	0.109599	−	0.189832i
$334$		0			0
$335$	−19.3137			−1.05522
$336$		0			0
$337$	−29.6569			−1.61551			−0.807756	−	0.589517i	$-0.799318\pi$
$337$	−29.6569			−1.61551			−0.807756	+	0.589517i	$0.799318\pi$
$338$		0			0
$339$	2.65685	−	4.60181i	0.144301	−	0.249936i
$340$		0			0
$341$	1.17157	+	2.02922i	0.0634442	+	0.109889i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	13.0711	+	22.6398i	0.703723	+	1.21888i
$346$		0			0
$347$	16.6569	−	28.8505i	0.894187	−	1.54878i	0.0593789	−	0.998236i	$-0.481088\pi$
$347$	16.6569	−	28.8505i	0.894187	−	1.54878i	0.834808	−	0.550541i	$-0.185579\pi$
$348$		0			0
$349$	9.89949			0.529908			0.264954	−	0.964261i	$-0.414643\pi$
$349$	9.89949			0.529908			0.264954	+	0.964261i	$0.414643\pi$
$350$		0			0
$351$	−2.58579			−0.138019
$352$		0			0
$353$	−7.36396	+	12.7548i	−0.391944	+	0.678867i	−0.992706	−	0.120561i	$-0.961531\pi$
$353$	−7.36396	+	12.7548i	−0.391944	+	0.678867i	0.600762	+	0.799428i	$0.294864\pi$
$354$		0			0
$355$	−15.8995	−	27.5387i	−0.843858	−	1.46160i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.171573	−	0.297173i	−0.00905527	−	0.0156842i	0.861462	−	0.507822i	$-0.169549\pi$
$359$	−0.171573	−	0.297173i	−0.00905527	−	0.0156842i	−0.870518	+	0.492137i	$0.836216\pi$
$360$		0			0
$361$	5.50000	−	9.52628i	0.289474	−	0.501383i
$362$		0			0
$363$	−7.00000			−0.367405
$364$		0			0
$365$	47.4558			2.48395
$366$		0			0
$367$	1.65685	−	2.86976i	0.0864871	−	0.149800i	−0.819537	−	0.573027i	$-0.805769\pi$
$367$	1.65685	−	2.86976i	0.0864871	−	0.149800i	0.906024	+	0.423226i	$0.139103\pi$
$368$		0			0
$369$	3.12132	+	5.40629i	0.162489	+	0.281440i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	5.34315	+	9.25460i	0.276658	+	0.479185i	0.970552	−	0.240892i	$-0.0774399\pi$
$373$	5.34315	+	9.25460i	0.276658	+	0.479185i	−0.693894	+	0.720077i	$0.744107\pi$
$374$		0			0
$375$	2.82843	−	4.89898i	0.146059	−	0.252982i
$376$		0			0
$377$	17.6569			0.909374
$378$		0			0
$379$	−8.68629			−0.446185			−0.223092	−	0.974797i	$-0.571615\pi$
$379$	−8.68629			−0.446185			−0.223092	+	0.974797i	$0.571615\pi$
$380$		0			0
$381$	−0.828427	+	1.43488i	−0.0424416	+	0.0735110i
$382$		0			0
$383$	9.17157	+	15.8856i	0.468645	+	0.811718i	0.999358	−	0.0358343i	$-0.0114088\pi$
$383$	9.17157	+	15.8856i	0.468645	+	0.811718i	−0.530712	+	0.847552i	$0.678076\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.82843	+	4.89898i	0.143777	+	0.249029i
$388$		0			0
$389$	9.07107	−	15.7116i	0.459921	−	0.796607i	−0.539035	−	0.842283i	$-0.681211\pi$
$389$	9.07107	−	15.7116i	0.459921	−	0.796607i	0.998956	+	0.0456762i	$0.0145442\pi$
$390$		0			0
$391$	17.1716			0.868404
$392$		0			0
$393$	−15.3137			−0.772474
$394$		0			0
$395$	−23.3137	+	40.3805i	−1.17304	+	2.03176i
$396$		0			0
$397$	−1.19239	−	2.06528i	−0.0598442	−	0.103653i	0.834551	−	0.550931i	$-0.185727\pi$
$397$	−1.19239	−	2.06528i	−0.0598442	−	0.103653i	−0.894395	+	0.447277i	$0.852394\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.07107	+	5.31925i	0.153362	+	0.265630i	0.932461	−	0.361270i	$-0.117657\pi$
$401$	3.07107	+	5.31925i	0.153362	+	0.265630i	−0.779100	+	0.626900i	$0.784323\pi$
$402$		0			0
$403$	−1.51472	+	2.62357i	−0.0754535	+	0.130689i
$404$		0			0
$405$	−3.41421			−0.169654
$406$		0			0
$407$	−8.00000			−0.396545
$408$		0			0
$409$	−10.7071	+	18.5453i	−0.529432	+	0.917004i	0.469978	+	0.882678i	$0.344262\pi$
$409$	−10.7071	+	18.5453i	−0.529432	+	0.917004i	−0.999411	+	0.0343258i	$0.989072\pi$
$410$		0			0
$411$	−7.07107	−	12.2474i	−0.348790	−	0.604122i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	12.4853	+	21.6251i	0.612878	+	1.06154i
$416$		0			0
$417$	8.82843	−	15.2913i	0.432330	−	0.748817i
$418$		0			0
$419$	33.1716			1.62054			0.810269	−	0.586059i	$-0.199321\pi$
$419$	33.1716			1.62054			0.810269	+	0.586059i	$0.199321\pi$
$420$		0			0
$421$	16.6274			0.810371			0.405185	−	0.914235i	$-0.367207\pi$
$421$	16.6274			0.810371			0.405185	+	0.914235i	$0.367207\pi$
$422$		0			0
$423$	1.41421	−	2.44949i	0.0687614	−	0.119098i
$424$		0			0
$425$	−7.46447	−	12.9288i	−0.362080	−	0.627141i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	2.58579	+	4.47871i	0.124843	+	0.216234i
$430$		0			0
$431$	−13.4853	+	23.3572i	−0.649563	+	1.12508i	0.333664	+	0.942692i	$0.391715\pi$
$431$	−13.4853	+	23.3572i	−0.649563	+	1.12508i	−0.983227	+	0.182384i	$0.941618\pi$
$432$		0			0
$433$	20.2426			0.972799			0.486400	−	0.873736i	$-0.338310\pi$
$433$	20.2426			0.972799			0.486400	+	0.873736i	$0.338310\pi$
$434$		0			0
$435$	23.3137			1.11781
$436$		0			0
$437$	10.8284	−	18.7554i	0.517994	−	0.897192i
$438$		0			0
$439$	−6.34315	−	10.9867i	−0.302742	−	0.524364i	0.674014	−	0.738718i	$-0.264569\pi$
$439$	−6.34315	−	10.9867i	−0.302742	−	0.524364i	−0.976756	+	0.214354i	$0.931235\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	17.4853	+	30.2854i	0.830751	+	1.43890i	0.897444	+	0.441129i	$0.145422\pi$
$443$	17.4853	+	30.2854i	0.830751	+	1.43890i	−0.0666929	+	0.997774i	$0.521245\pi$
$444$		0			0
$445$	24.3137	−	42.1126i	1.15258	−	1.99633i
$446$		0			0
$447$	17.3137			0.818910
$448$		0			0
$449$	−5.31371			−0.250769			−0.125385	−	0.992108i	$-0.540017\pi$
$449$	−5.31371			−0.250769			−0.125385	+	0.992108i	$0.540017\pi$
$450$		0			0
$451$	6.24264	−	10.8126i	0.293954	−	0.509144i
$452$		0			0
$453$	6.00000	+	10.3923i	0.281905	+	0.488273i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	0.996038	−	0.0889312i	$-0.0283451\pi$
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	−0.575036	+	0.818128i	$0.695012\pi$
$458$		0			0
$459$	−1.12132	+	1.94218i	−0.0523388	+	0.0906534i
$460$		0			0
$461$	16.5858			0.772477			0.386239	−	0.922399i	$-0.373774\pi$
$461$	16.5858			0.772477			0.386239	+	0.922399i	$0.373774\pi$
$462$		0			0
$463$	26.6274			1.23748			0.618741	−	0.785595i	$-0.287643\pi$
$463$	26.6274			1.23748			0.618741	+	0.785595i	$0.287643\pi$
$464$		0			0
$465$	−2.00000	+	3.46410i	−0.0927478	+	0.160644i
$466$		0			0
$467$	−0.100505	−	0.174080i	−0.00465082	−	0.00805546i	0.863691	−	0.504022i	$-0.168147\pi$
$467$	−0.100505	−	0.174080i	−0.00465082	−	0.00805546i	−0.868341	+	0.495967i	$0.834814\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	5.87868	+	10.1822i	0.270875	+	0.469170i
$472$		0			0
$473$	5.65685	−	9.79796i	0.260102	−	0.450511i
$474$		0			0
$475$	−18.8284			−0.863907
$476$		0			0
$477$	−2.00000			−0.0915737
$478$		0			0
$479$	−0.928932	+	1.60896i	−0.0424440	+	0.0735152i	−0.886467	−	0.462792i	$-0.846848\pi$
$479$	−0.928932	+	1.60896i	−0.0424440	+	0.0735152i	0.844023	+	0.536307i	$0.180181\pi$
$480$		0			0
$481$	−5.17157	−	8.95743i	−0.235803	−	0.408424i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.41421	−	7.64564i	−0.200439	−	0.347171i
$486$		0			0
$487$	13.3137	−	23.0600i	0.603302	−	1.04495i	−0.389016	−	0.921231i	$-0.627185\pi$
$487$	13.3137	−	23.0600i	0.603302	−	1.04495i	0.992317	−	0.123718i	$-0.0394819\pi$
$488$		0			0
$489$	11.3137			0.511624
$490$		0			0
$491$	−5.02944			−0.226975			−0.113488	−	0.993539i	$-0.536202\pi$
$491$	−5.02944			−0.226975			−0.113488	+	0.993539i	$0.536202\pi$
$492$		0			0
$493$	7.65685	−	13.2621i	0.344847	−	0.597293i
$494$		0			0
$495$	3.41421	+	5.91359i	0.153457	+	0.265796i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	1.65685	+	2.86976i	0.0741710	+	0.128468i	0.900725	−	0.434389i	$-0.143036\pi$
$499$	1.65685	+	2.86976i	0.0741710	+	0.128468i	−0.826554	+	0.562857i	$0.809702\pi$
$500$		0			0
$501$	9.89949	−	17.1464i	0.442277	−	0.766046i
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	10.0000			0.444994
$506$		0			0
$507$	3.15685	−	5.46783i	0.140201	−	0.242835i
$508$		0			0
$509$	2.77817	+	4.81194i	0.123140	+	0.213285i	0.921005	−	0.389552i	$-0.127370\pi$
$509$	2.77817	+	4.81194i	0.123140	+	0.213285i	−0.797864	+	0.602837i	$0.794037\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	1.41421	+	2.44949i	0.0624391	+	0.108148i
$514$		0			0
$515$	7.65685	−	13.2621i	0.337401	−	0.584396i
$516$		0			0
$517$	−5.65685			−0.248788
$518$		0			0
$519$	−21.0711			−0.924917
$520$		0			0
$521$	−17.7071	+	30.6696i	−0.775762	+	1.34366i	0.158603	+	0.987343i	$0.449301\pi$
$521$	−17.7071	+	30.6696i	−0.775762	+	1.34366i	−0.934365	+	0.356317i	$0.884032\pi$
$522$		0			0
$523$	12.8284	+	22.2195i	0.560948	+	0.971590i	0.997414	+	0.0718696i	$0.0228966\pi$
$523$	12.8284	+	22.2195i	0.560948	+	0.971590i	−0.436466	+	0.899721i	$0.643770\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.31371	+	2.27541i	0.0572260	+	0.0991184i
$528$		0			0
$529$	−17.8137	+	30.8542i	−0.774509	+	1.34149i
$530$		0			0
$531$	−1.17157			−0.0508419
$532$		0			0
$533$	16.1421			0.699194
$534$		0			0
$535$	0.585786	−	1.01461i	0.0253258	−	0.0438655i
$536$		0			0
$537$	−9.82843	−	17.0233i	−0.424128	−	0.734611i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−8.65685	−	14.9941i	−0.372187	−	0.644647i	0.617715	−	0.786402i	$-0.288059\pi$
$541$	−8.65685	−	14.9941i	−0.372187	−	0.644647i	−0.989902	+	0.141755i	$0.954725\pi$
$542$		0			0
$543$	−1.29289	+	2.23936i	−0.0554834	+	0.0961000i
$544$		0			0
$545$	19.3137			0.827308
$546$		0			0
$547$	36.9706			1.58075			0.790374	−	0.612625i	$-0.209886\pi$
$547$	36.9706			1.58075			0.790374	+	0.612625i	$0.209886\pi$
$548$		0			0
$549$	6.12132	−	10.6024i	0.261252	−	0.452501i
$550$		0			0
$551$	−9.65685	−	16.7262i	−0.411396	−	0.712558i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−6.82843	−	11.8272i	−0.289851	−	0.502036i
$556$		0			0
$557$	−13.0000	+	22.5167i	−0.550828	+	0.954062i	0.447387	+	0.894340i	$0.352355\pi$
$557$	−13.0000	+	22.5167i	−0.550828	+	0.954062i	−0.998215	+	0.0597213i	$0.980979\pi$
$558$		0			0
$559$	14.6274			0.618674
$560$		0			0
$561$	4.48528			0.189369
$562$		0			0
$563$	0.585786	−	1.01461i	0.0246880	−	0.0427608i	−0.853417	−	0.521228i	$-0.825474\pi$
$563$	0.585786	−	1.01461i	0.0246880	−	0.0427608i	0.878105	+	0.478467i	$0.158807\pi$
$564$		0			0
$565$	−9.07107	−	15.7116i	−0.381623	−	0.660990i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8.24264	+	14.2767i	0.345549	+	0.598509i	0.985453	−	0.169946i	$-0.0543592\pi$
$569$	8.24264	+	14.2767i	0.345549	+	0.598509i	−0.639904	+	0.768455i	$0.721026\pi$
$570$		0			0
$571$	11.1716	−	19.3497i	0.467516	−	0.809761i	−0.531795	−	0.846873i	$-0.678482\pi$
$571$	11.1716	−	19.3497i	0.467516	−	0.809761i	0.999311	+	0.0371118i	$0.0118158\pi$
$572$		0			0
$573$	18.0000			0.751961
$574$		0			0
$575$	50.9706			2.12562
$576$		0			0
$577$	−16.9497	+	29.3578i	−0.705627	+	1.22218i	0.260837	+	0.965383i	$0.416001\pi$
$577$	−16.9497	+	29.3578i	−0.705627	+	1.22218i	−0.966465	+	0.256799i	$0.917332\pi$
$578$		0			0
$579$	−2.65685	−	4.60181i	−0.110415	−	0.191245i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	2.00000	+	3.46410i	0.0828315	+	0.143468i
$584$		0			0
$585$	−4.41421	+	7.64564i	−0.182505	+	0.316108i
$586$		0			0
$587$	−22.8284			−0.942230			−0.471115	−	0.882072i	$-0.656148\pi$
$587$	−22.8284			−0.942230			−0.471115	+	0.882072i	$0.656148\pi$
$588$		0			0
$589$	3.31371			0.136539
$590$		0			0
$591$	−1.00000	+	1.73205i	−0.0411345	+	0.0712470i
$592$		0			0
$593$	−3.46447	−	6.00063i	−0.142269	−	0.246416i	0.786082	−	0.618122i	$-0.212106\pi$
$593$	−3.46447	−	6.00063i	−0.142269	−	0.246416i	−0.928351	+	0.371706i	$0.878773\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−10.8284	−	18.7554i	−0.443178	−	0.767607i
$598$		0			0
$599$	−1.00000	+	1.73205i	−0.0408589	+	0.0707697i	−0.885732	−	0.464198i	$-0.846343\pi$
$599$	−1.00000	+	1.73205i	−0.0408589	+	0.0707697i	0.844873	+	0.534967i	$0.179676\pi$
$600$		0			0
$601$	15.0711			0.614762			0.307381	−	0.951587i	$-0.400547\pi$
$601$	15.0711			0.614762			0.307381	+	0.951587i	$0.400547\pi$
$602$		0			0
$603$	5.65685			0.230365
$604$		0			0
$605$	−11.9497	+	20.6976i	−0.485826	+	0.841476i
$606$		0			0
$607$	9.17157	+	15.8856i	0.372263	+	0.644778i	0.989913	−	0.141675i	$-0.0452487\pi$
$607$	9.17157	+	15.8856i	0.372263	+	0.644778i	−0.617651	+	0.786453i	$0.711915\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−3.65685	−	6.33386i	−0.147940	−	0.256240i
$612$		0			0
$613$	−2.34315	+	4.05845i	−0.0946388	+	0.163919i	−0.909458	−	0.415796i	$-0.863503\pi$
$613$	−2.34315	+	4.05845i	−0.0946388	+	0.163919i	0.814819	+	0.579715i	$0.196836\pi$
$614$		0			0
$615$	21.3137			0.859452
$616$		0			0
$617$	−24.4853			−0.985740			−0.492870	−	0.870103i	$-0.664052\pi$
$617$	−24.4853			−0.985740			−0.492870	+	0.870103i	$0.664052\pi$
$618$		0			0
$619$	−14.4853	+	25.0892i	−0.582213	+	1.00842i	0.413004	+	0.910729i	$0.364480\pi$
$619$	−14.4853	+	25.0892i	−0.582213	+	1.00842i	−0.995217	+	0.0976926i	$0.968854\pi$
$620$		0			0
$621$	−3.82843	−	6.63103i	−0.153629	−	0.266094i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	6.98528	+	12.0989i	0.279411	+	0.483954i
$626$		0			0
$627$	2.82843	−	4.89898i	0.112956	−	0.195646i
$628$		0			0
$629$	−8.97056			−0.357680
$630$		0			0
$631$	−23.3137			−0.928104			−0.464052	−	0.885808i	$-0.653605\pi$
$631$	−23.3137			−0.928104			−0.464052	+	0.885808i	$0.653605\pi$
$632$		0			0
$633$	6.48528	−	11.2328i	0.257767	−	0.446465i
$634$		0			0
$635$	2.82843	+	4.89898i	0.112243	+	0.194410i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	4.65685	+	8.06591i	0.184222	+	0.319082i
$640$		0			0
$641$	5.41421	−	9.37769i	0.213849	−	0.370397i	−0.739067	−	0.673632i	$-0.764733\pi$
$641$	5.41421	−	9.37769i	0.213849	−	0.370397i	0.952916	+	0.303235i	$0.0980668\pi$
$642$		0			0
$643$	−34.4264			−1.35764			−0.678822	−	0.734302i	$-0.737509\pi$
$643$	−34.4264			−1.35764			−0.678822	+	0.734302i	$0.737509\pi$
$644$		0			0
$645$	19.3137			0.760477
$646$		0			0
$647$	−13.4142	+	23.2341i	−0.527367	+	0.913427i	0.472124	+	0.881532i	$0.343487\pi$
$647$	−13.4142	+	23.2341i	−0.527367	+	0.913427i	−0.999491	+	0.0318946i	$0.989846\pi$
$648$		0			0
$649$	1.17157	+	2.02922i	0.0459883	+	0.0796540i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−18.2426	−	31.5972i	−0.713890	−	1.23649i	−0.963386	−	0.268118i	$-0.913598\pi$
$653$	−18.2426	−	31.5972i	−0.713890	−	1.23649i	0.249497	−	0.968376i	$-0.419735\pi$
$654$		0			0
$655$	−26.1421	+	45.2795i	−1.02146	+	1.76922i
$656$		0			0
$657$	−13.8995			−0.542271
$658$		0			0
$659$	−9.31371			−0.362811			−0.181405	−	0.983408i	$-0.558065\pi$
$659$	−9.31371			−0.362811			−0.181405	+	0.983408i	$0.558065\pi$
$660$		0			0
$661$	−11.7782	+	20.4004i	−0.458118	+	0.793483i	−0.998862	−	0.0477040i	$-0.984810\pi$
$661$	−11.7782	+	20.4004i	−0.458118	+	0.793483i	0.540744	+	0.841187i	$0.318143\pi$
$662$		0			0
$663$	2.89949	+	5.02207i	0.112607	+	0.195041i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	26.1421	+	45.2795i	1.01223	+	1.75323i
$668$		0			0
$669$	−12.4853	+	21.6251i	−0.482709	+	0.836076i
$670$		0			0
$671$	−24.4853			−0.945244
$672$		0			0
$673$	23.3137			0.898677			0.449339	−	0.893361i	$-0.351660\pi$
$673$	23.3137			0.898677			0.449339	+	0.893361i	$0.351660\pi$
$674$		0			0
$675$	−3.32843	+	5.76500i	−0.128111	+	0.221895i
$676$		0			0
$677$	15.7071	+	27.2055i	0.603673	+	1.04559i	0.992260	+	0.124180i	$0.0396301\pi$
$677$	15.7071	+	27.2055i	0.603673	+	1.04559i	−0.388587	+	0.921412i	$0.627037\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−11.8995	−	20.6105i	−0.455990	−	0.789797i
$682$		0			0
$683$	−9.82843	+	17.0233i	−0.376074	+	0.651380i	−0.990487	−	0.137605i	$-0.956060\pi$
$683$	−9.82843	+	17.0233i	−0.376074	+	0.651380i	0.614413	+	0.788985i	$0.289393\pi$
$684$		0			0
$685$	−48.2843			−1.84485
$686$		0			0
$687$	0.242641			0.00925732
$688$		0			0
$689$	−2.58579	+	4.47871i	−0.0985106	+	0.170625i
$690$		0			0
$691$	0.343146	+	0.594346i	0.0130539	+	0.0226100i	0.872479	−	0.488652i	$-0.162511\pi$
$691$	0.343146	+	0.594346i	0.0130539	+	0.0226100i	−0.859425	+	0.511262i	$0.829178\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−30.1421	−	52.2077i	−1.14336	−	1.98035i
$696$		0			0
$697$	7.00000	−	12.1244i	0.265144	−	0.459243i
$698$		0			0
$699$	−6.14214			−0.232317
$700$		0			0
$701$	−17.1716			−0.648561			−0.324281	−	0.945961i	$-0.605122\pi$
$701$	−17.1716			−0.648561			−0.324281	+	0.945961i	$0.605122\pi$
$702$		0			0
$703$	−5.65685	+	9.79796i	−0.213352	+	0.369537i
$704$		0			0
$705$	−4.82843	−	8.36308i	−0.181849	−	0.314972i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	18.1421	+	31.4231i	0.681342	+	1.18012i	0.974571	+	0.224077i	$0.0719368\pi$
$709$	18.1421	+	31.4231i	0.681342	+	1.18012i	−0.293229	+	0.956042i	$0.594730\pi$
$710$		0			0
$711$	6.82843	−	11.8272i	0.256086	−	0.443554i
$712$		0			0
$713$	−8.97056			−0.335950
$714$		0			0
$715$	17.6569			0.660329
$716$		0			0
$717$	−7.82843	+	13.5592i	−0.292358	+	0.506379i
$718$		0			0
$719$	−20.9706	−	36.3221i	−0.782070	−	1.35459i	−0.930734	−	0.365697i	$-0.880831\pi$
$719$	−20.9706	−	36.3221i	−0.782070	−	1.35459i	0.148664	−	0.988888i	$-0.452503\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−8.12132	−	14.0665i	−0.302035	−	0.523140i
$724$		0			0
$725$	22.7279	−	39.3659i	0.844094	−	1.46201i
$726$		0			0
$727$	12.4853			0.463053			0.231527	−	0.972829i	$-0.425628\pi$
$727$	12.4853			0.463053			0.231527	+	0.972829i	$0.425628\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	6.34315	−	10.9867i	0.234610	−	0.406356i
$732$		0			0
$733$	24.8492	+	43.0402i	0.917828	+	1.58972i	0.802708	+	0.596373i	$0.203392\pi$
$733$	24.8492	+	43.0402i	0.917828	+	1.58972i	0.115120	+	0.993352i	$0.463275\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.65685	−	9.79796i	−0.208373	−	0.360912i
$738$		0			0
$739$	2.34315	−	4.05845i	0.0861940	−	0.149292i	−0.819705	−	0.572785i	$-0.805863\pi$
$739$	2.34315	−	4.05845i	0.0861940	−	0.149292i	0.905899	+	0.423493i	$0.139196\pi$
$740$		0			0
$741$	7.31371			0.268676
$742$		0			0
$743$	50.9706			1.86993			0.934964	−	0.354742i	$-0.115431\pi$
$743$	50.9706			1.86993			0.934964	+	0.354742i	$0.115431\pi$
$744$		0			0
$745$	29.5563	−	51.1931i	1.08286	−	1.87557i
$746$		0			0
$747$	−3.65685	−	6.33386i	−0.133797	−	0.231744i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	6.82843	+	11.8272i	0.249173	+	0.431580i	0.963297	−	0.268440i	$-0.0865079\pi$
$751$	6.82843	+	11.8272i	0.249173	+	0.431580i	−0.714124	+	0.700020i	$0.753175\pi$
$752$		0			0
$753$	6.24264	−	10.8126i	0.227494	−	0.394032i
$754$		0			0
$755$	40.9706			1.49107
$756$		0			0
$757$	26.3431			0.957458			0.478729	−	0.877963i	$-0.341098\pi$
$757$	26.3431			0.957458			0.478729	+	0.877963i	$0.341098\pi$
$758$		0			0
$759$	−7.65685	+	13.2621i	−0.277926	+	0.481382i
$760$		0			0
$761$	−9.26346	−	16.0448i	−0.335800	−	0.581623i	0.647838	−	0.761778i	$-0.275673\pi$
$761$	−9.26346	−	16.0448i	−0.335800	−	0.581623i	−0.983638	+	0.180155i	$0.942340\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	3.82843	+	6.63103i	0.138417	+	0.239745i
$766$		0			0
$767$	−1.51472	+	2.62357i	−0.0546933	+	0.0947316i
$768$		0			0
$769$	−29.6985			−1.07095			−0.535477	−	0.844550i	$-0.679868\pi$
$769$	−29.6985			−1.07095			−0.535477	+	0.844550i	$0.679868\pi$
$770$		0			0
$771$	−23.2132			−0.836003
$772$		0			0
$773$	−4.77817	+	8.27604i	−0.171859	+	0.297669i	−0.939070	−	0.343727i	$-0.888311\pi$
$773$	−4.77817	+	8.27604i	−0.171859	+	0.297669i	0.767211	+	0.641395i	$0.221644\pi$
$774$		0			0
$775$	3.89949	+	6.75412i	0.140074	+	0.242615i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−8.82843	−	15.2913i	−0.316311	−	0.547867i
$780$		0			0
$781$	9.31371	−	16.1318i	0.333271	−	0.577242i
$782$		0			0
$783$	−6.82843			−0.244028
$784$		0			0
$785$	40.1421			1.43273
$786$		0			0
$787$	−12.3431	+	21.3790i	−0.439986	+	0.762077i	−0.997688	−	0.0679637i	$-0.978350\pi$
$787$	−12.3431	+	21.3790i	−0.439986	+	0.762077i	0.557702	+	0.830041i	$0.311683\pi$
$788$		0			0
$789$	2.65685	+	4.60181i	0.0945865	+	0.163829i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−15.8284	−	27.4156i	−0.562084	−	0.973558i
$794$		0			0
$795$	−3.41421	+	5.91359i	−0.121090	+	0.209733i
$796$		0			0
$797$	8.38478			0.297004			0.148502	−	0.988912i	$-0.452555\pi$
$797$	8.38478			0.297004			0.148502	+	0.988912i	$0.452555\pi$
$798$		0			0
$799$	−6.34315			−0.224404
$800$		0			0
$801$	−7.12132	+	12.3345i	−0.251619	+	0.435818i
$802$		0			0
$803$	13.8995	+	24.0746i	0.490503	+	0.849575i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−7.36396	−	12.7548i	−0.259224	−	0.448989i
$808$		0			0
$809$	−9.97056	+	17.2695i	−0.350546	+	0.607164i	−0.986345	−	0.164691i	$-0.947337\pi$
$809$	−9.97056	+	17.2695i	−0.350546	+	0.607164i	0.635799	+	0.771855i	$0.280671\pi$
$810$		0			0
$811$	−17.6569			−0.620016			−0.310008	−	0.950734i	$-0.600332\pi$
$811$	−17.6569			−0.620016			−0.310008	+	0.950734i	$0.600332\pi$
$812$		0			0
$813$	−10.1421			−0.355700
$814$		0			0
$815$	19.3137	−	33.4523i	0.676530	−	1.17178i
$816$		0			0
$817$	−8.00000	−	13.8564i	−0.279885	−	0.484774i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	5.34315	+	9.25460i	0.186477	+	0.322988i	0.944073	−	0.329736i	$-0.106960\pi$
$821$	5.34315	+	9.25460i	0.186477	+	0.322988i	−0.757596	+	0.652724i	$0.773626\pi$
$822$		0			0
$823$	4.48528	−	7.76874i	0.156347	−	0.270801i	−0.777202	−	0.629252i	$-0.783361\pi$
$823$	4.48528	−	7.76874i	0.156347	−	0.270801i	0.933549	+	0.358451i	$0.116695\pi$
$824$		0			0
$825$	13.3137			0.463524
$826$		0			0
$827$	−47.6569			−1.65719			−0.828596	−	0.559848i	$-0.810860\pi$
$827$	−47.6569			−1.65719			−0.828596	+	0.559848i	$0.810860\pi$
$828$		0			0
$829$	−0.363961	+	0.630399i	−0.0126409	+	0.0218947i	−0.872277	−	0.489013i	$-0.837357\pi$
$829$	−0.363961	+	0.630399i	−0.0126409	+	0.0218947i	0.859636	+	0.510907i	$0.170690\pi$
$830$		0			0
$831$	4.65685	+	8.06591i	0.161544	+	0.279803i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−33.7990	−	58.5416i	−1.16966	−	2.02591i
$836$		0			0
$837$	0.585786	−	1.01461i	0.0202477	−	0.0350701i
$838$		0			0
$839$	50.8284			1.75479			0.877396	−	0.479767i	$-0.159279\pi$
$839$	50.8284			1.75479			0.877396	+	0.479767i	$0.159279\pi$
$840$		0			0
$841$	17.6274			0.607842
$842$		0			0
$843$	−0.242641	+	0.420266i	−0.00835699	+	0.0144747i
$844$		0			0
$845$	−10.7782	−	18.6683i	−0.370780	−	0.642211i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	4.24264	+	7.34847i	0.145607	+	0.252199i
$850$		0			0
$851$	15.3137	−	26.5241i	0.524947	−	0.909235i
$852$		0			0
$853$	49.4975			1.69476			0.847381	−	0.530986i	$-0.178178\pi$
$853$	49.4975			1.69476			0.847381	+	0.530986i	$0.178178\pi$
$854$		0			0
$855$	9.65685			0.330257
$856$		0			0
$857$	7.70711	−	13.3491i	0.263270	−	0.455997i	−0.703839	−	0.710359i	$-0.748532\pi$
$857$	7.70711	−	13.3491i	0.263270	−	0.455997i	0.967109	+	0.254363i	$0.0818657\pi$
$858$		0			0
$859$	−28.7279	−	49.7582i	−0.980184	−	1.69773i	−0.661642	−	0.749820i	$-0.730140\pi$
$859$	−28.7279	−	49.7582i	−0.980184	−	1.69773i	−0.318542	−	0.947909i	$-0.603193\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	8.65685	+	14.9941i	0.294683	+	0.510405i	0.974911	−	0.222595i	$-0.0714527\pi$
$863$	8.65685	+	14.9941i	0.294683	+	0.510405i	−0.680228	+	0.733000i	$0.738119\pi$
$864$		0			0
$865$	−35.9706	+	62.3028i	−1.22304	+	2.11836i
$866$		0			0
$867$	−11.9706			−0.406542
$868$		0			0
$869$	−27.3137			−0.926554
$870$		0			0
$871$	7.31371	−	12.6677i	0.247816	−	0.429229i
$872$		0			0
$873$	1.29289	+	2.23936i	0.0437578	+	0.0757907i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	5.65685	+	9.79796i	0.191018	+	0.330854i	0.945588	−	0.325366i	$-0.105488\pi$
$877$	5.65685	+	9.79796i	0.191018	+	0.330854i	−0.754570	+	0.656220i	$0.772154\pi$
$878$		0			0
$879$	8.29289	−	14.3637i	0.279712	−	0.484476i
$880$		0			0
$881$	−21.7574			−0.733024			−0.366512	−	0.930413i	$-0.619448\pi$
$881$	−21.7574			−0.733024			−0.366512	+	0.930413i	$0.619448\pi$
$882$		0			0
$883$	4.68629			0.157706			0.0788531	−	0.996886i	$-0.474874\pi$
$883$	4.68629			0.157706			0.0788531	+	0.996886i	$0.474874\pi$
$884$		0			0
$885$	−2.00000	+	3.46410i	−0.0672293	+	0.116445i
$886$		0			0
$887$	1.41421	+	2.44949i	0.0474846	+	0.0822458i	0.888791	−	0.458313i	$-0.151546\pi$
$887$	1.41421	+	2.44949i	0.0474846	+	0.0822458i	−0.841306	+	0.540559i	$0.818213\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1.00000	−	1.73205i	−0.0335013	−	0.0580259i
$892$		0			0
$893$	−4.00000	+	6.92820i	−0.133855	+	0.231843i
$894$		0			0
$895$	−67.1127			−2.24333
$896$		0			0
$897$	−19.7990			−0.661069
$898$		0			0
$899$	−4.00000	+	6.92820i	−0.133407	+	0.231069i
$900$		0			0
$901$	2.24264	+	3.88437i	0.0747132	+	0.129407i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4.41421	+	7.64564i	0.146733	+	0.254150i
$906$		0			0
$907$	−8.00000	+	13.8564i	−0.265636	+	0.460094i	−0.967730	−	0.251990i	$-0.918915\pi$
$907$	−8.00000	+	13.8564i	−0.265636	+	0.460094i	0.702094	+	0.712084i	$0.252248\pi$
$908$		0			0
$909$	−2.92893			−0.0971465
$910$		0			0
$911$	1.02944			0.0341068			0.0170534	−	0.999855i	$-0.494571\pi$
$911$	1.02944			0.0341068			0.0170534	+	0.999855i	$0.494571\pi$
$912$		0			0
$913$	−7.31371	+	12.6677i	−0.242048	+	0.419240i
$914$		0			0
$915$	−20.8995	−	36.1990i	−0.690916	−	1.19670i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−4.14214	−	7.17439i	−0.136636	−	0.236661i	0.789585	−	0.613641i	$-0.210296\pi$
$919$	−4.14214	−	7.17439i	−0.136636	−	0.236661i	−0.926221	+	0.376980i	$0.876963\pi$
$920$		0			0
$921$	−15.0711	+	26.1039i	−0.496609	+	0.860151i
$922$		0			0
$923$	24.0833			0.792710
$924$		0			0
$925$	−26.6274			−0.875504
$926$		0			0
$927$	−2.24264	+	3.88437i	−0.0736580	+	0.127579i
$928$		0			0
$929$	−19.6066	−	33.9596i	−0.643272	−	1.11418i	−0.984698	−	0.174271i	$-0.944243\pi$
$929$	−19.6066	−	33.9596i	−0.643272	−	1.11418i	0.341426	−	0.939909i	$-0.389090\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−3.07107	−	5.31925i	−0.100542	−	0.174144i
$934$		0			0
$935$	7.65685	−	13.2621i	0.250406	−	0.433716i
$936$		0			0
$937$	−30.5858			−0.999194			−0.499597	−	0.866258i	$-0.666519\pi$
$937$	−30.5858			−0.999194			−0.499597	+	0.866258i	$0.666519\pi$
$938$		0			0
$939$	−1.89949			−0.0619877
$940$		0			0
$941$	17.6066	−	30.4955i	0.573959	−	0.994126i	−0.422195	−	0.906505i	$-0.638740\pi$
$941$	17.6066	−	30.4955i	0.573959	−	0.994126i	0.996154	−	0.0876208i	$-0.0279264\pi$
$942$		0			0
$943$	23.8995	+	41.3951i	0.778275	+	1.34801i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	15.3431	+	26.5751i	0.498585	+	0.863575i	0.999999	−	0.00163285i	$-0.000519752\pi$
$947$	15.3431	+	26.5751i	0.498585	+	0.863575i	−0.501413	+	0.865208i	$0.667186\pi$
$948$		0			0
$949$	−17.9706	+	31.1259i	−0.583349	+	1.01039i
$950$		0			0
$951$	10.0000			0.324272
$952$		0			0
$953$	2.00000			0.0647864			0.0323932	−	0.999475i	$-0.489687\pi$
$953$	2.00000			0.0647864			0.0323932	+	0.999475i	$0.489687\pi$
$954$		0			0
$955$	30.7279	−	53.2223i	0.994332	−	1.72223i
$956$		0			0
$957$	6.82843	+	11.8272i	0.220732	+	0.382319i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	14.8137	+	25.6581i	0.477862	+	0.827681i
$962$		0			0
$963$	−0.171573	+	0.297173i	−0.00552886	+	0.00957626i
$964$		0			0
$965$	−18.1421			−0.584016
$966$		0			0
$967$	−33.6569			−1.08233			−0.541166	−	0.840916i	$-0.682017\pi$
$967$	−33.6569			−1.08233			−0.541166	+	0.840916i	$0.682017\pi$
$968$		0			0
$969$	3.17157	−	5.49333i	0.101886	−	0.176471i
$970$		0			0
$971$	25.3137	+	43.8446i	0.812356	+	1.40704i	0.911211	+	0.411939i	$0.135148\pi$
$971$	25.3137	+	43.8446i	0.812356	+	1.40704i	−0.0988557	+	0.995102i	$0.531518\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	8.60660	+	14.9071i	0.275632	+	0.477408i
$976$		0			0
$977$	10.5858	−	18.3351i	0.338669	−	0.586592i	−0.645513	−	0.763749i	$-0.723357\pi$
$977$	10.5858	−	18.3351i	0.338669	−	0.586592i	0.984183	+	0.177157i	$0.0566899\pi$
$978$		0			0
$979$	28.4853			0.910394
$980$		0			0
$981$	−5.65685			−0.180609
$982$		0			0
$983$	26.6274	−	46.1200i	0.849283	−	1.47100i	−0.0325667	−	0.999470i	$-0.510368\pi$
$983$	26.6274	−	46.1200i	0.849283	−	1.47100i	0.881849	−	0.471531i	$-0.156299\pi$
$984$		0			0
$985$	3.41421	+	5.91359i	0.108786	+	0.188423i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	21.6569	+	37.5108i	0.688648	+	1.19277i
$990$		0			0
$991$	−6.48528	+	11.2328i	−0.206012	+	0.356823i	−0.950455	−	0.310863i	$-0.899382\pi$
$991$	−6.48528	+	11.2328i	−0.206012	+	0.356823i	0.744443	+	0.667686i	$0.232715\pi$
$992$		0			0
$993$	4.00000			0.126936
$994$		0			0
$995$	−73.9411			−2.34409
$996$		0			0
$997$	13.1924	−	22.8499i	0.417807	−	0.723663i	−0.577911	−	0.816099i	$-0.696132\pi$
$997$	13.1924	−	22.8499i	0.417807	−	0.723663i	0.995719	+	0.0924363i	$0.0294654\pi$
$998$		0			0
$999$	2.00000	+	3.46410i	0.0632772	+	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2352.2.q.bb.1537.2		4
4.3	odd	2		147.2.e.e.67.1		4
7.2	even	3	inner	2352.2.q.bb.961.2		4
7.3	odd	6		2352.2.a.bc.1.2		2
7.4	even	3		2352.2.a.be.1.1		2
7.5	odd	6		2352.2.q.bd.961.1		4
7.6	odd	2		2352.2.q.bd.1537.1		4
12.11	even	2		441.2.e.f.361.2		4
21.11	odd	6		7056.2.a.cv.1.2		2
21.17	even	6		7056.2.a.cf.1.1		2
28.3	even	6		147.2.a.e.1.2	yes	2
28.11	odd	6		147.2.a.d.1.2	✓	2
28.19	even	6		147.2.e.d.79.1		4
28.23	odd	6		147.2.e.e.79.1		4
28.27	even	2		147.2.e.d.67.1		4
56.3	even	6		9408.2.a.di.1.1		2
56.11	odd	6		9408.2.a.ef.1.2		2
56.45	odd	6		9408.2.a.dt.1.1		2
56.53	even	6		9408.2.a.dq.1.2		2
84.11	even	6		441.2.a.j.1.1		2
84.23	even	6		441.2.e.f.226.2		4
84.47	odd	6		441.2.e.g.226.2		4
84.59	odd	6		441.2.a.i.1.1		2
84.83	odd	2		441.2.e.g.361.2		4
140.39	odd	6		3675.2.a.bf.1.1		2
140.59	even	6		3675.2.a.bd.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.a.d.1.2	✓	2	28.11	odd	6
147.2.a.e.1.2	yes	2	28.3	even	6
147.2.e.d.67.1		4	28.27	even	2
147.2.e.d.79.1		4	28.19	even	6
147.2.e.e.67.1		4	4.3	odd	2
147.2.e.e.79.1		4	28.23	odd	6
441.2.a.i.1.1		2	84.59	odd	6
441.2.a.j.1.1		2	84.11	even	6
441.2.e.f.226.2		4	84.23	even	6
441.2.e.f.361.2		4	12.11	even	2
441.2.e.g.226.2		4	84.47	odd	6
441.2.e.g.361.2		4	84.83	odd	2
2352.2.a.bc.1.2		2	7.3	odd	6
2352.2.a.be.1.1		2	7.4	even	3
2352.2.q.bb.961.2		4	7.2	even	3	inner
2352.2.q.bb.1537.2		4	1.1	even	1	trivial
2352.2.q.bd.961.1		4	7.5	odd	6
2352.2.q.bd.1537.1		4	7.6	odd	2
3675.2.a.bd.1.1		2	140.59	even	6
3675.2.a.bf.1.1		2	140.39	odd	6
7056.2.a.cf.1.1		2	21.17	even	6
7056.2.a.cv.1.2		2	21.11	odd	6
9408.2.a.di.1.1		2	56.3	even	6
9408.2.a.dq.1.2		2	56.53	even	6
9408.2.a.dt.1.1		2	56.45	odd	6
9408.2.a.ef.1.2		2	56.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2352.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(1.70711 + 2.95680i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(1.70711 + 2.95680i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{11} -2.58579 q^{13} -3.41421 q^{15} +(-1.12132 + 1.94218i) q^{17} +(1.41421 + 2.44949i) q^{19} +(-3.82843 - 6.63103i) q^{23} +(-3.32843 + 5.76500i) q^{25} +1.00000 q^{27} -6.82843 q^{29} +(0.585786 - 1.01461i) q^{31} +(-1.00000 - 1.73205i) q^{33} +(2.00000 + 3.46410i) q^{37} +(1.29289 - 2.23936i) q^{39} -6.24264 q^{41} -5.65685 q^{43} +(1.70711 - 2.95680i) q^{45} +(1.41421 + 2.44949i) q^{47} +(-1.12132 - 1.94218i) q^{51} +(1.00000 - 1.73205i) q^{53} -6.82843 q^{55} -2.82843 q^{57} +(0.585786 - 1.01461i) q^{59} +(6.12132 + 10.6024i) q^{61} +(-4.41421 - 7.64564i) q^{65} +(-2.82843 + 4.89898i) q^{67} +7.65685 q^{69} -9.31371 q^{71} +(6.94975 - 12.0373i) q^{73} +(-3.32843 - 5.76500i) q^{75} +(6.82843 + 11.8272i) q^{79} +(-0.500000 + 0.866025i) q^{81} +7.31371 q^{83} -7.65685 q^{85} +(3.41421 - 5.91359i) q^{87} +(-7.12132 - 12.3345i) q^{89} +(0.585786 + 1.01461i) q^{93} +(-4.82843 + 8.36308i) q^{95} -2.58579 q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 4 q^{5} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 4 * q^5 - 2 * q^9	\( 4 q - 2 q^{3} + 4 q^{5} - 2 q^{9} - 4 q^{11} - 16 q^{13} - 8 q^{15} + 4 q^{17} - 4 q^{23} - 2 q^{25} + 4 q^{27} - 16 q^{29} + 8 q^{31} - 4 q^{33} + 8 q^{37} + 8 q^{39} - 8 q^{41} + 4 q^{45} + 4 q^{51} + 4 q^{53} - 16 q^{55} + 8 q^{59} + 16 q^{61} - 12 q^{65} + 8 q^{69} + 8 q^{71} + 8 q^{73} - 2 q^{75} + 16 q^{79} - 2 q^{81} - 16 q^{83} - 8 q^{85} + 8 q^{87} - 20 q^{89} + 8 q^{93} - 8 q^{95} - 16 q^{97} + 8 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 + 4 * q^5 - 2 * q^9 - 4 * q^11 - 16 * q^13 - 8 * q^15 + 4 * q^17 - 4 * q^23 - 2 * q^25 + 4 * q^27 - 16 * q^29 + 8 * q^31 - 4 * q^33 + 8 * q^37 + 8 * q^39 - 8 * q^41 + 4 * q^45 + 4 * q^51 + 4 * q^53 - 16 * q^55 + 8 * q^59 + 16 * q^61 - 12 * q^65 + 8 * q^69 + 8 * q^71 + 8 * q^73 - 2 * q^75 + 16 * q^79 - 2 * q^81 - 16 * q^83 - 8 * q^85 + 8 * q^87 - 20 * q^89 + 8 * q^93 - 8 * q^95 - 16 * q^97 + 8 * q^99

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