LMFDB - Embedded newform 2352.2.bl.q.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2352,2,Mod(31,2352)]

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([3, 0, 0, 1]))

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

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

chi := DirichletCharacter("2352.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2352 = 2^{4} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2352.bl (of order $6$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.339738624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 $ x^8 - 4x^6 + 14x^4 - 8*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.3
Root			$1.60021 - 0.923880i$ of defining polynomial
Character	$\chi$	$=$	2352.31
Dual form			2352.2.bl.q.607.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(1.45849 - 0.842061i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} +(1.45849 - 0.842061i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-3.05870 - 1.76594i) q^{11} +2.93015i q^{13} +1.68412i q^{15} +(1.74192 + 1.00570i) q^{17} +(-0.848820 - 1.47020i) q^{19} +(-1.38435 + 0.799257i) q^{23} +(-1.08187 + 1.87385i) q^{25} +1.00000 q^{27} +7.94028 q^{29} +(2.47683 - 4.29000i) q^{31} +(3.05870 - 1.76594i) q^{33} +(5.23317 + 9.06412i) q^{37} +(-2.53759 - 1.46508i) q^{39} +2.86237i q^{41} +11.7518i q^{43} +(-1.45849 - 0.842061i) q^{45} +(3.35159 + 5.80513i) q^{47} +(-1.74192 + 1.00570i) q^{51} +(-1.46054 + 2.52974i) q^{53} -5.94812 q^{55} +1.69764 q^{57} +(3.87766 - 6.71630i) q^{59} +(10.9055 - 6.29627i) q^{61} +(2.46737 + 4.27361i) q^{65} +(-1.47393 - 0.850976i) q^{67} -1.59851i q^{69} -6.13052i q^{71} +(-2.10588 - 1.21583i) q^{73} +(-1.08187 - 1.87385i) q^{75} +(0.749517 - 0.432734i) q^{79} +(-0.500000 + 0.866025i) q^{81} +14.5319 q^{83} +3.38744 q^{85} +(-3.97014 + 6.87648i) q^{87} +(13.8033 - 7.96936i) q^{89} +(2.47683 + 4.29000i) q^{93} +(-2.47600 - 1.42952i) q^{95} -9.82270i q^{97} +3.53188i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 - 4 * q^9	$ 8 q - 4 q^{3} - 4 q^{9} + 24 q^{23} + 12 q^{25} + 8 q^{27} + 16 q^{29} + 16 q^{31} + 8 q^{47} - 8 q^{53} - 64 q^{55} - 24 q^{59} + 48 q^{61} + 8 q^{65} - 48 q^{67} + 48 q^{73} + 12 q^{75} - 24 q^{79} - 4 q^{81} - 64 q^{85} - 8 q^{87} + 48 q^{89} + 16 q^{93} + 72 q^{95}+O(q^{100}) $ 8 * q - 4 * q^3 - 4 * q^9 + 24 * q^23 + 12 * q^25 + 8 * q^27 + 16 * q^29 + 16 * q^31 + 8 * q^47 - 8 * q^53 - 64 * q^55 - 24 * q^59 + 48 * q^61 + 8 * q^65 - 48 * q^67 + 48 * q^73 + 12 * q^75 - 24 * q^79 - 4 * q^81 - 64 * q^85 - 8 * q^87 + 48 * q^89 + 16 * q^93 + 72 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1471$	$1765$	$2257$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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
$5$	1.45849	−	0.842061i	0.652258	−	0.376581i	−0.137063	−	0.990562i	$-0.543766\pi$
$5$	1.45849	−	0.842061i	0.652258	−	0.376581i	0.789321	+	0.613981i	$0.210433\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−3.05870	−	1.76594i	−0.922233	−	0.532451i	−0.0378860	−	0.999282i	$-0.512062\pi$
$11$	−3.05870	−	1.76594i	−0.922233	−	0.532451i	−0.884347	+	0.466831i	$0.845396\pi$
$12$		0			0
$13$			2.93015i			0.812678i	0.913722	+	0.406339i	$0.133195\pi$
$13$			2.93015i			0.812678i	−0.913722	+	0.406339i	$0.866805\pi$
$14$		0			0
$15$			1.68412i			0.434839i
$16$		0			0
$17$	1.74192	+	1.00570i	0.422478	+	0.243918i	0.696137	−	0.717909i	$-0.254901\pi$
$17$	1.74192	+	1.00570i	0.422478	+	0.243918i	−0.273659	+	0.961827i	$0.588234\pi$
$18$		0			0
$19$	−0.848820	−	1.47020i	−0.194733	−	0.337287i	0.752080	−	0.659072i	$-0.229051\pi$
$19$	−0.848820	−	1.47020i	−0.194733	−	0.337287i	−0.946813	+	0.321785i	$0.895717\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.38435	+	0.799257i	−0.288658	+	0.166657i	−0.637336	−	0.770586i	$-0.719964\pi$
$23$	−1.38435	+	0.799257i	−0.288658	+	0.166657i	0.348679	+	0.937242i	$0.386630\pi$
$24$		0			0
$25$	−1.08187	+	1.87385i	−0.216373	+	0.374769i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	7.94028			1.47447			0.737237	−	0.675635i	$-0.236130\pi$
$29$	7.94028			1.47447			0.737237	+	0.675635i	$0.236130\pi$
$30$		0			0
$31$	2.47683	−	4.29000i	0.444853	−	0.770507i	−0.553189	−	0.833056i	$-0.686589\pi$
$31$	2.47683	−	4.29000i	0.444853	−	0.770507i	0.998042	+	0.0625483i	$0.0199227\pi$
$32$		0			0
$33$	3.05870	−	1.76594i	0.532451	−	0.307411i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	5.23317	+	9.06412i	0.860328	+	1.49013i	0.871612	+	0.490196i	$0.163075\pi$
$37$	5.23317	+	9.06412i	0.860328	+	1.49013i	−0.0112836	+	0.999936i	$0.503592\pi$
$38$		0			0
$39$	−2.53759	−	1.46508i	−0.406339	−	0.234600i
$40$		0			0
$41$			2.86237i			0.447027i	0.974701	+	0.223514i	$0.0717527\pi$
$41$			2.86237i			0.447027i	−0.974701	+	0.223514i	$0.928247\pi$
$42$		0			0
$43$			11.7518i			1.79214i	0.443917	+	0.896068i	$0.353589\pi$
$43$			11.7518i			1.79214i	−0.443917	+	0.896068i	$0.646411\pi$
$44$		0			0
$45$	−1.45849	−	0.842061i	−0.217419	−	0.125527i
$46$		0			0
$47$	3.35159	+	5.80513i	0.488880	+	0.846765i	0.999918	−	0.0127930i	$-0.00407224\pi$
$47$	3.35159	+	5.80513i	0.488880	+	0.846765i	−0.511038	+	0.859558i	$0.670739\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−1.74192	+	1.00570i	−0.243918	+	0.140826i
$52$		0			0
$53$	−1.46054	+	2.52974i	−0.200621	+	0.347486i	−0.948729	−	0.316091i	$-0.897629\pi$
$53$	−1.46054	+	2.52974i	−0.200621	+	0.347486i	0.748108	+	0.663578i	$0.230963\pi$
$54$		0			0
$55$	−5.94812			−0.802045
$56$		0			0
$57$	1.69764			0.224858
$58$		0			0
$59$	3.87766	−	6.71630i	0.504828	−	0.874388i	−0.495156	−	0.868804i	$-0.664889\pi$
$59$	3.87766	−	6.71630i	0.504828	−	0.874388i	0.999984	−	0.00558422i	$-0.00177752\pi$
$60$		0			0
$61$	10.9055	−	6.29627i	1.39630	−	0.806155i	0.402299	−	0.915508i	$-0.368211\pi$
$61$	10.9055	−	6.29627i	1.39630	−	0.806155i	0.994003	+	0.109353i	$0.0348779\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.46737	+	4.27361i	0.306039	+	0.530076i
$66$		0			0
$67$	−1.47393	−	0.850976i	−0.180070	−	0.103963i	0.407256	−	0.913314i	$-0.366486\pi$
$67$	−1.47393	−	0.850976i	−0.180070	−	0.103963i	−0.587325	+	0.809351i	$0.699819\pi$
$68$		0			0
$69$		−	1.59851i		−	0.192438i
$70$		0			0
$71$		−	6.13052i		−	0.727558i	−0.931485	−	0.363779i	$-0.881486\pi$
$71$		−	6.13052i		−	0.727558i	0.931485	−	0.363779i	$-0.118514\pi$
$72$		0			0
$73$	−2.10588	−	1.21583i	−0.246475	−	0.142302i	0.371674	−	0.928363i	$-0.378784\pi$
$73$	−2.10588	−	1.21583i	−0.246475	−	0.142302i	−0.618149	+	0.786061i	$0.712117\pi$
$74$		0			0
$75$	−1.08187	−	1.87385i	−0.124923	−	0.216373i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	0.749517	−	0.432734i	0.0843272	−	0.0486863i	−0.457243	−	0.889342i	$-0.651163\pi$
$79$	0.749517	−	0.432734i	0.0843272	−	0.0486863i	0.541571	+	0.840655i	$0.317830\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	14.5319			1.59508			0.797540	−	0.603266i	$-0.206134\pi$
$83$	14.5319			1.59508			0.797540	+	0.603266i	$0.206134\pi$
$84$		0			0
$85$	3.38744			0.367419
$86$		0			0
$87$	−3.97014	+	6.87648i	−0.425644	+	0.737237i
$88$		0			0
$89$	13.8033	−	7.96936i	1.46315	−	0.844751i	0.463995	−	0.885838i	$-0.346415\pi$
$89$	13.8033	−	7.96936i	1.46315	−	0.844751i	0.999156	+	0.0410870i	$0.0130821\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	2.47683	+	4.29000i	0.256836	+	0.444853i
$94$		0			0
$95$	−2.47600	−	1.42952i	−0.254032	−	0.146665i
$96$		0			0
$97$		−	9.82270i		−	0.997344i	−0.866791	−	0.498672i	$-0.833821\pi$
$97$		−	9.82270i		−	0.997344i	0.866791	−	0.498672i	$-0.166179\pi$
$98$		0			0
$99$			3.53188i			0.354967i
$100$		0			0
$101$	−8.16458	−	4.71382i	−0.812406	−	0.469043i	0.0353847	−	0.999374i	$-0.488734\pi$
$101$	−8.16458	−	4.71382i	−0.812406	−	0.469043i	−0.847791	+	0.530331i	$0.822068\pi$
$102$		0			0
$103$	7.83133	+	13.5643i	0.771644	+	1.33653i	0.936662	+	0.350236i	$0.113898\pi$
$103$	7.83133	+	13.5643i	0.771644	+	1.33653i	−0.165018	+	0.986291i	$0.552768\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−16.4365	+	9.48961i	−1.58898	+	0.917395i	−0.595499	+	0.803356i	$0.703046\pi$
$107$	−16.4365	+	9.48961i	−1.58898	+	0.917395i	−0.993476	+	0.114039i	$0.963621\pi$
$108$		0			0
$109$	−5.27950	+	9.14437i	−0.505685	+	0.875872i	0.494294	+	0.869295i	$0.335427\pi$
$109$	−5.27950	+	9.14437i	−0.505685	+	0.875872i	−0.999978	+	0.00657678i	$0.997907\pi$
$110$		0			0
$111$	−10.4663			−0.993422
$112$		0			0
$113$	15.4530			1.45369			0.726846	−	0.686800i	$-0.240985\pi$
$113$	15.4530			1.45369			0.726846	+	0.686800i	$0.240985\pi$
$114$		0			0
$115$	−1.34605	+	2.33142i	−0.125520	+	0.217406i
$116$		0			0
$117$	2.53759	−	1.46508i	0.234600	−	0.135446i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.737095	+	1.27669i	0.0670086	+	0.116062i
$122$		0			0
$123$	−2.47889	−	1.43119i	−0.223514	−	0.129046i
$124$		0			0
$125$			12.0646i			1.07909i
$126$		0			0
$127$			2.16478i			0.192094i	0.995377	+	0.0960468i	$0.0306198\pi$
$127$			2.16478i			0.192094i	−0.995377	+	0.0960468i	$0.969380\pi$
$128$		0			0
$129$	−10.1774	−	5.87591i	−0.896068	−	0.517345i
$130$		0			0
$131$	7.66096	+	13.2692i	0.669341	+	1.15933i	0.978089	+	0.208189i	$0.0667568\pi$
$131$	7.66096	+	13.2692i	0.669341	+	1.15933i	−0.308748	+	0.951144i	$0.599910\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	1.45849	−	0.842061i	0.125527	−	0.0724731i
$136$		0			0
$137$	−6.43068	+	11.1383i	−0.549410	+	0.951607i	0.448905	+	0.893580i	$0.351814\pi$
$137$	−6.43068	+	11.1383i	−0.549410	+	0.951607i	−0.998315	+	0.0580272i	$0.981519\pi$
$138$		0			0
$139$	−0.743971			−0.0631028			−0.0315514	−	0.999502i	$-0.510045\pi$
$139$	−0.743971			−0.0631028			−0.0315514	+	0.999502i	$0.510045\pi$
$140$		0			0
$141$	−6.70319			−0.564510
$142$		0			0
$143$	5.17447	−	8.96245i	0.432711	−	0.749478i
$144$		0			0
$145$	11.5808	−	6.68620i	0.961737	−	0.555259i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.65131	+	6.32425i	0.299127	+	0.518103i	0.975936	−	0.218055i	$-0.0699713\pi$
$149$	3.65131	+	6.32425i	0.299127	+	0.518103i	−0.676810	+	0.736158i	$0.736638\pi$
$150$		0			0
$151$	−5.44161	−	3.14172i	−0.442832	−	0.255669i	0.261966	−	0.965077i	$-0.415629\pi$
$151$	−5.44161	−	3.14172i	−0.442832	−	0.255669i	−0.704798	+	0.709408i	$0.748962\pi$
$152$		0			0
$153$		−	2.01140i		−	0.162612i
$154$		0			0
$155$		−	8.34259i		−	0.670093i
$156$		0			0
$157$	−7.71761	−	4.45576i	−0.615932	−	0.355608i	0.159352	−	0.987222i	$-0.449060\pi$
$157$	−7.71761	−	4.45576i	−0.615932	−	0.355608i	−0.775283	+	0.631613i	$0.782393\pi$
$158$		0			0
$159$	−1.46054	−	2.52974i	−0.115829	−	0.200621i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	0.209698	−	0.121069i	0.0164248	−	0.00948287i	−0.491765	−	0.870728i	$-0.663648\pi$
$163$	0.209698	−	0.121069i	0.0164248	−	0.00948287i	0.508190	+	0.861245i	$0.330315\pi$
$164$		0			0
$165$	2.97406	−	5.15123i	0.231530	−	0.401022i
$166$		0			0
$167$	−5.82817			−0.450997			−0.225499	−	0.974243i	$-0.572401\pi$
$167$	−5.82817			−0.450997			−0.225499	+	0.974243i	$0.572401\pi$
$168$		0			0
$169$	4.41421			0.339555
$170$		0			0
$171$	−0.848820	+	1.47020i	−0.0649109	+	0.112429i
$172$		0			0
$173$	−14.5436	+	8.39673i	−1.10573	+	0.638392i	−0.937719	−	0.347394i	$-0.887067\pi$
$173$	−14.5436	+	8.39673i	−1.10573	+	0.638392i	−0.168008	+	0.985786i	$0.553733\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3.87766	+	6.71630i	0.291463	+	0.504828i
$178$		0			0
$179$	18.3943	+	10.6199i	1.37485	+	0.793771i	0.991534	−	0.129846i	$-0.0414482\pi$
$179$	18.3943	+	10.6199i	1.37485	+	0.793771i	0.383317	+	0.923617i	$0.374782\pi$
$180$		0			0
$181$		−	2.74444i		−	0.203993i	−0.994785	−	0.101996i	$-0.967477\pi$
$181$		−	2.74444i		−	0.203993i	0.994785	−	0.101996i	$-0.0325230\pi$
$182$		0			0
$183$			12.5925i			0.930868i
$184$		0			0
$185$	15.2651	+	8.81331i	1.12231	+	0.647967i
$186$		0			0
$187$	−3.55201	−	6.15225i	−0.259748	−	0.449897i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.39364	+	0.804618i	−0.100840	+	0.0582201i	−0.549572	−	0.835446i	$-0.685209\pi$
$191$	−1.39364	+	0.804618i	−0.100840	+	0.0582201i	0.448732	+	0.893666i	$0.351876\pi$
$192$		0			0
$193$	−2.00555	+	3.47371i	−0.144362	+	0.250043i	−0.929135	−	0.369741i	$-0.879446\pi$
$193$	−2.00555	+	3.47371i	−0.144362	+	0.250043i	0.784773	+	0.619784i	$0.212780\pi$
$194$		0			0
$195$	−4.93473			−0.353384
$196$		0			0
$197$	11.7413			0.836534			0.418267	−	0.908324i	$-0.362638\pi$
$197$	11.7413			0.836534			0.418267	+	0.908324i	$0.362638\pi$
$198$		0			0
$199$	−8.68015	+	15.0345i	−0.615319	+	1.06576i	0.375009	+	0.927021i	$0.377640\pi$
$199$	−8.68015	+	15.0345i	−0.615319	+	1.06576i	−0.990328	+	0.138743i	$0.955694\pi$
$200$		0			0
$201$	1.47393	−	0.850976i	0.103963	−	0.0600232i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	2.41029	+	4.17475i	0.168342	+	0.291577i
$206$		0			0
$207$	1.38435	+	0.799257i	0.0962192	+	0.0555522i
$208$		0			0
$209$			5.99586i			0.414743i
$210$		0			0
$211$			24.1172i			1.66030i	0.557543	+	0.830148i	$0.311744\pi$
$211$			24.1172i			1.66030i	−0.557543	+	0.830148i	$0.688256\pi$
$212$		0			0
$213$	5.30918	+	3.06526i	0.363779	+	0.210028i
$214$		0			0
$215$	9.89576	+	17.1400i	0.674885	+	1.16893i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	2.10588	−	1.21583i	0.142302	−	0.0821582i
$220$		0			0
$221$	−2.94685	+	5.10409i	−0.198226	+	0.343338i
$222$		0			0
$223$	−20.1154			−1.34702			−0.673512	−	0.739176i	$-0.735215\pi$
$223$	−20.1154			−1.34702			−0.673512	+	0.739176i	$0.735215\pi$
$224$		0			0
$225$	2.16373			0.144249
$226$		0			0
$227$	8.79465	−	15.2328i	0.583721	−	1.01103i	−0.411312	−	0.911494i	$-0.634929\pi$
$227$	8.79465	−	15.2328i	0.583721	−	1.01103i	0.995034	−	0.0995403i	$-0.0317372\pi$
$228$		0			0
$229$	3.45722	−	1.99602i	0.228459	−	0.131901i	−0.381402	−	0.924409i	$-0.624559\pi$
$229$	3.45722	−	1.99602i	0.228459	−	0.131901i	0.609861	+	0.792508i	$0.291225\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.63484	−	2.83162i	−0.107102	−	0.185506i	0.807493	−	0.589877i	$-0.200824\pi$
$233$	−1.63484	−	2.83162i	−0.107102	−	0.185506i	−0.914595	+	0.404371i	$0.867490\pi$
$234$		0			0
$235$	9.77655	+	5.64449i	0.637752	+	0.368206i
$236$		0			0
$237$			0.865467i			0.0562181i
$238$		0			0
$239$		−	28.9127i		−	1.87021i	−0.354371	−	0.935105i	$-0.615305\pi$
$239$		−	28.9127i		−	1.87021i	0.354371	−	0.935105i	$-0.384695\pi$
$240$		0			0
$241$	−5.29374	−	3.05634i	−0.341000	−	0.196876i	0.319714	−	0.947514i	$-0.396413\pi$
$241$	−5.29374	−	3.05634i	−0.341000	−	0.196876i	−0.660714	+	0.750638i	$0.729746\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	4.30791	−	2.48717i	0.274105	−	0.158255i
$248$		0			0
$249$	−7.26593	+	12.5850i	−0.460460	+	0.797540i
$250$		0			0
$251$	27.7471			1.75138			0.875691	−	0.482872i	$-0.160406\pi$
$251$	27.7471			1.75138			0.875691	+	0.482872i	$0.160406\pi$
$252$		0			0
$253$	5.64576			0.354946
$254$		0			0
$255$	−1.69372	+	2.93361i	−0.106065	+	0.183710i
$256$		0			0
$257$	−2.47889	+	1.43119i	−0.154629	+	0.0892749i	−0.575318	−	0.817930i	$-0.695122\pi$
$257$	−2.47889	+	1.43119i	−0.154629	+	0.0892749i	0.420689	+	0.907205i	$0.361788\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3.97014	−	6.87648i	−0.245746	−	0.425644i
$262$		0			0
$263$	−16.8466	−	9.72639i	−1.03881	−	0.599755i	−0.119311	−	0.992857i	$-0.538069\pi$
$263$	−16.8466	−	9.72639i	−1.03881	−	0.599755i	−0.919495	+	0.393102i	$0.871402\pi$
$264$		0			0
$265$			4.91947i			0.302201i
$266$		0			0
$267$			15.9387i			0.975434i
$268$		0			0
$269$	14.4480	+	8.34156i	0.880910	+	0.508594i	0.870959	−	0.491357i	$-0.163499\pi$
$269$	14.4480	+	8.34156i	0.880910	+	0.508594i	0.00995197	+	0.999950i	$0.496832\pi$
$270$		0			0
$271$	−9.95283	−	17.2388i	−0.604591	−	1.04718i	−0.992116	−	0.125324i	$-0.960003\pi$
$271$	−9.95283	−	17.2388i	−0.604591	−	1.04718i	0.387525	−	0.921859i	$-0.373330\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.61820	−	3.82102i	0.399092	−	0.230416i
$276$		0			0
$277$	7.16373	−	12.4079i	0.430427	−	0.745521i	−0.566483	−	0.824073i	$-0.691696\pi$
$277$	7.16373	−	12.4079i	0.430427	−	0.745521i	0.996910	+	0.0785522i	$0.0250297\pi$
$278$		0			0
$279$	−4.95367			−0.296568
$280$		0			0
$281$	16.5450			0.986992			0.493496	−	0.869748i	$-0.335719\pi$
$281$	16.5450			0.986992			0.493496	+	0.869748i	$0.335719\pi$
$282$		0			0
$283$	−14.9295	+	25.8587i	−0.887469	+	1.53714i	−0.0446112	+	0.999004i	$0.514205\pi$
$283$	−14.9295	+	25.8587i	−0.887469	+	1.53714i	−0.842858	+	0.538137i	$0.819128\pi$
$284$		0			0
$285$	2.47600	−	1.42952i	0.146665	−	0.0846773i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−6.47714	−	11.2187i	−0.381009	−	0.659926i
$290$		0			0
$291$	8.50671	+	4.91135i	0.498672	+	0.287908i
$292$		0			0
$293$		−	6.40183i		−	0.373999i	−0.982360	−	0.187000i	$-0.940124\pi$
$293$		−	6.40183i		−	0.373999i	0.982360	−	0.187000i	$-0.0598763\pi$
$294$		0			0
$295$		−	13.0609i		−	0.760436i
$296$		0			0
$297$	−3.05870	−	1.76594i	−0.177484	−	0.102470i
$298$		0			0
$299$	−2.34194	−	4.05637i	−0.135438	−	0.234586i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	8.16458	−	4.71382i	0.469043	−	0.270802i
$304$		0			0
$305$	10.6037	−	18.3661i	0.607166	−	1.05164i
$306$		0			0
$307$	11.6511			0.664961			0.332480	−	0.943110i	$-0.392114\pi$
$307$	11.6511			0.664961			0.332480	+	0.943110i	$0.392114\pi$
$308$		0			0
$309$	−15.6627			−0.891017
$310$		0			0
$311$	11.5386	−	19.9855i	0.654295	−	1.13327i	−0.327775	−	0.944756i	$-0.606299\pi$
$311$	11.5386	−	19.9855i	0.654295	−	1.13327i	0.982070	−	0.188516i	$-0.0603678\pi$
$312$		0			0
$313$	−22.4738	+	12.9752i	−1.27029	+	0.733404i	−0.975043	−	0.222017i	$-0.928736\pi$
$313$	−22.4738	+	12.9752i	−1.27029	+	0.733404i	−0.295249	+	0.955420i	$0.595403\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.2715	−	17.7907i	−0.576904	−	0.999227i	−0.995832	−	0.0912073i	$-0.970927\pi$
$317$	−10.2715	−	17.7907i	−0.576904	−	0.999227i	0.418928	−	0.908019i	$-0.362406\pi$
$318$		0			0
$319$	−24.2869	−	14.0221i	−1.35981	−	0.785085i
$320$		0			0
$321$		−	18.9792i		−	1.05932i
$322$		0			0
$323$		−	3.41462i		−	0.189995i
$324$		0			0
$325$	−5.49065	−	3.17003i	−0.304566	−	0.175842i
$326$		0			0
$327$	−5.27950	−	9.14437i	−0.291957	−	0.505685i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−28.3851	+	16.3882i	−1.56019	+	0.900775i	−0.562951	+	0.826490i	$0.690334\pi$
$331$	−28.3851	+	16.3882i	−1.56019	+	0.900775i	−0.997237	+	0.0742851i	$0.976333\pi$
$332$		0			0
$333$	5.23317	−	9.06412i	0.286776	−	0.496711i
$334$		0			0
$335$	−2.86630			−0.156602
$336$		0			0
$337$	−33.2791			−1.81283			−0.906414	−	0.422391i	$-0.861191\pi$
$337$	−33.2791			−1.81283			−0.906414	+	0.422391i	$0.861191\pi$
$338$		0			0
$339$	−7.72648	+	13.3827i	−0.419645	+	0.726846i
$340$		0			0
$341$	−15.1518	+	8.74789i	−0.820515	+	0.473725i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−1.34605	−	2.33142i	−0.0724687	−	0.125520i
$346$		0			0
$347$	8.36516	+	4.82963i	0.449065	+	0.259268i	0.707435	−	0.706778i	$-0.249852\pi$
$347$	8.36516	+	4.82963i	0.449065	+	0.259268i	−0.258370	+	0.966046i	$0.583185\pi$
$348$		0			0
$349$			11.9525i			0.639802i	0.947451	+	0.319901i	$0.103650\pi$
$349$			11.9525i			0.639802i	−0.947451	+	0.319901i	$0.896350\pi$
$350$		0			0
$351$			2.93015i			0.156400i
$352$		0			0
$353$	11.1916	+	6.46148i	0.595669	+	0.343910i	0.767336	−	0.641245i	$-0.221582\pi$
$353$	11.1916	+	6.46148i	0.595669	+	0.343910i	−0.171667	+	0.985155i	$0.554915\pi$
$354$		0			0
$355$	−5.16227	−	8.94132i	−0.273985	−	0.474556i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	9.58077	−	5.53146i	0.505654	−	0.291939i	−0.225392	−	0.974268i	$-0.572366\pi$
$359$	9.58077	−	5.53146i	0.505654	−	0.291939i	0.731045	+	0.682329i	$0.239033\pi$
$360$		0			0
$361$	8.05901	−	13.9586i	0.424158	−	0.734664i
$362$		0			0
$363$	−1.47419			−0.0773749
$364$		0			0
$365$	−4.09522			−0.214353
$366$		0			0
$367$	5.94438	−	10.2960i	0.310294	−	0.537445i	−0.668132	−	0.744043i	$-0.732906\pi$
$367$	5.94438	−	10.2960i	0.310294	−	0.537445i	0.978426	+	0.206598i	$0.0662391\pi$
$368$		0			0
$369$	2.47889	−	1.43119i	0.129046	−	0.0745045i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	4.76290	+	8.24959i	0.246614	+	0.427148i	0.962584	−	0.270983i	$-0.0873487\pi$
$373$	4.76290	+	8.24959i	0.246614	+	0.427148i	−0.715970	+	0.698131i	$0.754015\pi$
$374$		0			0
$375$	−10.4483	−	6.03230i	−0.539545	−	0.311507i
$376$		0			0
$377$			23.2662i			1.19827i
$378$		0			0
$379$		−	4.52128i		−	0.232243i	−0.993235	−	0.116121i	$-0.962954\pi$
$379$		−	4.52128i		−	0.232243i	0.993235	−	0.116121i	$-0.0370461\pi$
$380$		0			0
$381$	−1.87476	−	1.08239i	−0.0960468	−	0.0554526i
$382$		0			0
$383$	1.17157	+	2.02922i	0.0598646	+	0.103688i	0.894404	−	0.447259i	$-0.147600\pi$
$383$	1.17157	+	2.02922i	0.0598646	+	0.103688i	−0.834540	+	0.550947i	$0.814266\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	10.1774	−	5.87591i	0.517345	−	0.298689i
$388$		0			0
$389$	−9.04905	+	15.6734i	−0.458805	+	0.794674i	−0.998898	−	0.0469316i	$-0.985056\pi$
$389$	−9.04905	+	15.6734i	−0.458805	+	0.794674i	0.540093	+	0.841605i	$0.318389\pi$
$390$		0			0
$391$	−3.21524			−0.162602
$392$		0			0
$393$	−15.3219			−0.772888
$394$		0			0
$395$	0.728777	−	1.26228i	0.0366687	−	0.0635121i
$396$		0			0
$397$	2.43793	−	1.40754i	0.122356	−	0.0706425i	−0.437573	−	0.899183i	$-0.644162\pi$
$397$	2.43793	−	1.40754i	0.122356	−	0.0706425i	0.559929	+	0.828541i	$0.310828\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.04121	−	5.26753i	−0.151871	−	0.263048i	0.780044	−	0.625724i	$-0.215196\pi$
$401$	−3.04121	−	5.26753i	−0.151871	−	0.263048i	−0.931915	+	0.362676i	$0.881863\pi$
$402$		0			0
$403$	12.5704	+	7.25750i	0.626174	+	0.361522i
$404$		0			0
$405$			1.68412i			0.0836847i
$406$		0			0
$407$		−	36.9659i		−	1.83233i
$408$		0			0
$409$	−7.28566	−	4.20638i	−0.360253	−	0.207992i	0.308939	−	0.951082i	$-0.400026\pi$
$409$	−7.28566	−	4.20638i	−0.360253	−	0.207992i	−0.669192	+	0.743090i	$0.733359\pi$
$410$		0			0
$411$	−6.43068	−	11.1383i	−0.317202	−	0.549410i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	21.1946	−	12.2367i	1.04040	−	0.600677i
$416$		0			0
$417$	0.371985	−	0.644298i	0.0182162	−	0.0315514i
$418$		0			0
$419$	18.6496			0.911094			0.455547	−	0.890212i	$-0.349444\pi$
$419$	18.6496			0.911094			0.455547	+	0.890212i	$0.349444\pi$
$420$		0			0
$421$	−22.6274			−1.10279			−0.551396	−	0.834243i	$-0.685905\pi$
$421$	−22.6274			−1.10279			−0.551396	+	0.834243i	$0.685905\pi$
$422$		0			0
$423$	3.35159	−	5.80513i	0.162960	−	0.282255i
$424$		0			0
$425$	−3.76904	+	2.17606i	−0.182825	+	0.105554i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	5.17447	+	8.96245i	0.249826	+	0.432711i
$430$		0			0
$431$	13.7759	+	7.95352i	0.663561	+	0.383107i	0.793633	−	0.608397i	$-0.208187\pi$
$431$	13.7759	+	7.95352i	0.663561	+	0.383107i	−0.130071	+	0.991505i	$0.541521\pi$
$432$		0			0
$433$		−	14.4650i		−	0.695146i	−0.937653	−	0.347573i	$-0.887006\pi$
$433$		−	14.4650i		−	0.695146i	0.937653	−	0.347573i	$-0.112994\pi$
$434$		0			0
$435$			13.3724i			0.641158i
$436$		0			0
$437$	2.35013	+	1.35685i	0.112422	+	0.0649070i
$438$		0			0
$439$	−10.8981	−	18.8760i	−0.520136	−	0.900901i	−0.999726	−	0.0234089i	$-0.992548\pi$
$439$	−10.8981	−	18.8760i	−0.520136	−	0.900901i	0.479590	−	0.877493i	$-0.340785\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.2743	+	5.93187i	−0.488147	+	0.281832i	−0.723805	−	0.690004i	$-0.757609\pi$
$443$	−10.2743	+	5.93187i	−0.488147	+	0.281832i	0.235658	+	0.971836i	$0.424275\pi$
$444$		0			0
$445$	13.4214	−	23.2465i	0.636235	−	1.10199i
$446$		0			0
$447$	−7.30262			−0.345402
$448$		0			0
$449$	−38.6472			−1.82388			−0.911938	−	0.410329i	$-0.865414\pi$
$449$	−38.6472			−1.82388			−0.911938	+	0.410329i	$0.865414\pi$
$450$		0			0
$451$	5.05478	−	8.75513i	0.238020	−	0.412263i
$452$		0			0
$453$	5.44161	−	3.14172i	0.255669	−	0.147611i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−9.47189	−	16.4058i	−0.443076	−	0.767431i	0.554840	−	0.831957i	$-0.312780\pi$
$457$	−9.47189	−	16.4058i	−0.443076	−	0.767431i	−0.997916	+	0.0645264i	$0.979446\pi$
$458$		0			0
$459$	1.74192	+	1.00570i	0.0813058	+	0.0469419i
$460$		0			0
$461$		−	24.5269i		−	1.14233i	−0.820834	−	0.571167i	$-0.806491\pi$
$461$		−	24.5269i		−	1.14233i	0.820834	−	0.571167i	$-0.193509\pi$
$462$		0			0
$463$			7.59791i			0.353105i	0.984291	+	0.176552i	$0.0564945\pi$
$463$			7.59791i			0.353105i	−0.984291	+	0.176552i	$0.943505\pi$
$464$		0			0
$465$	7.22489	+	4.17129i	0.335046	+	0.193439i
$466$		0			0
$467$	−5.50941	−	9.54258i	−0.254945	−	0.441578i	0.709935	−	0.704267i	$-0.248724\pi$
$467$	−5.50941	−	9.54258i	−0.254945	−	0.441578i	−0.964881	+	0.262689i	$0.915391\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	7.71761	−	4.45576i	0.355608	−	0.205311i
$472$		0			0
$473$	20.7530	−	35.9453i	0.954225	−	1.65277i
$474$		0			0
$475$	3.67323			0.168540
$476$		0			0
$477$	2.92109			0.133747
$478$		0			0
$479$	18.1014	−	31.3525i	0.827073	−	1.43253i	−0.0732525	−	0.997313i	$-0.523338\pi$
$479$	18.1014	−	31.3525i	0.827073	−	1.43253i	0.900325	−	0.435218i	$-0.143329\pi$
$480$		0			0
$481$	−26.5593	+	15.3340i	−1.21100	+	0.699170i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−8.27131	−	14.3263i	−0.375581	−	0.650525i
$486$		0			0
$487$	−15.0792	−	8.70596i	−0.683302	−	0.394505i	0.117796	−	0.993038i	$-0.462417\pi$
$487$	−15.0792	−	8.70596i	−0.683302	−	0.394505i	−0.801098	+	0.598533i	$0.795751\pi$
$488$		0			0
$489$			0.242138i			0.0109499i
$490$		0			0
$491$		−	21.5154i		−	0.970977i	−0.874243	−	0.485489i	$-0.838642\pi$
$491$		−	21.5154i		−	0.970977i	0.874243	−	0.485489i	$-0.161358\pi$
$492$		0			0
$493$	13.8313	+	7.98552i	0.622932	+	0.359650i
$494$		0			0
$495$	2.97406	+	5.15123i	0.133674	+	0.231530i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	31.5566	−	18.2192i	1.41267	−	0.815604i	0.417029	−	0.908893i	$-0.363071\pi$
$499$	31.5566	−	18.2192i	1.41267	−	0.815604i	0.995639	+	0.0932893i	$0.0297381\pi$
$500$		0			0
$501$	2.91409	−	5.04734i	0.130192	−	0.225499i
$502$		0			0
$503$	39.5840			1.76496			0.882482	−	0.470347i	$-0.155871\pi$
$503$	39.5840			1.76496			0.882482	+	0.470347i	$0.155871\pi$
$504$		0			0
$505$	−15.8773			−0.706531
$506$		0			0
$507$	−2.20711	+	3.82282i	−0.0980211	+	0.169777i
$508$		0			0
$509$	−30.4632	+	17.5879i	−1.35026	+	0.779572i	−0.988285	−	0.152617i	$-0.951230\pi$
$509$	−30.4632	+	17.5879i	−1.35026	+	0.779572i	−0.361972	+	0.932189i	$0.617896\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−0.848820	−	1.47020i	−0.0374763	−	0.0649109i
$514$		0			0
$515$	22.8439	+	13.1889i	1.00662	+	0.581173i
$516$		0			0
$517$		−	23.6749i		−	1.04122i
$518$		0			0
$519$		−	16.7935i		−	0.737151i
$520$		0			0
$521$	16.9510	+	9.78669i	0.742638	+	0.428762i	0.823028	−	0.568001i	$-0.192283\pi$
$521$	16.9510	+	9.78669i	0.742638	+	0.428762i	−0.0803894	+	0.996764i	$0.525616\pi$
$522$		0			0
$523$	−4.33120	−	7.50186i	−0.189390	−	0.328033i	0.755657	−	0.654968i	$-0.227318\pi$
$523$	−4.33120	−	7.50186i	−0.189390	−	0.328033i	−0.945047	+	0.326934i	$0.893984\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	8.62889	−	4.98189i	0.375880	−	0.217015i
$528$		0			0
$529$	−10.2224	+	17.7057i	−0.444451	+	0.769812i
$530$		0			0
$531$	−7.75532			−0.336552
$532$		0			0
$533$	−8.38718			−0.363289
$534$		0			0
$535$	−15.9817	+	27.6811i	−0.690948	+	1.19676i
$536$		0			0
$537$	−18.3943	+	10.6199i	−0.793771	+	0.458284i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−12.5453	−	21.7290i	−0.539363	−	0.934204i	−0.998938	−	0.0460651i	$-0.985332\pi$
$541$	−12.5453	−	21.7290i	−0.539363	−	0.934204i	0.459576	−	0.888139i	$-0.348001\pi$
$542$		0			0
$543$	2.37676	+	1.37222i	0.101996	+	0.0588876i
$544$		0			0
$545$			17.7827i			0.761726i
$546$		0			0
$547$			0.523032i			0.0223632i	0.999937	+	0.0111816i	$0.00355929\pi$
$547$			0.523032i			0.0223632i	−0.999937	+	0.0111816i	$0.996441\pi$
$548$		0			0
$549$	−10.9055	−	6.29627i	−0.465434	−	0.268718i
$550$		0			0
$551$	−6.73987	−	11.6738i	−0.287128	−	0.497320i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−15.2651	+	8.81331i	−0.647967	+	0.374104i
$556$		0			0
$557$	−11.0670	+	19.1685i	−0.468922	+	0.812197i	−0.999369	−	0.0355210i	$-0.988691\pi$
$557$	−11.0670	+	19.1685i	−0.468922	+	0.812197i	0.530447	+	0.847718i	$0.322024\pi$
$558$		0			0
$559$	−34.4346			−1.45643
$560$		0			0
$561$	7.10401			0.299932
$562$		0			0
$563$	−5.30382	+	9.18648i	−0.223529	+	0.387164i	−0.955877	−	0.293767i	$-0.905091\pi$
$563$	−5.30382	+	9.18648i	−0.223529	+	0.387164i	0.732348	+	0.680931i	$0.238425\pi$
$564$		0			0
$565$	22.5380	−	13.0123i	0.948182	−	0.547433i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.19939	−	9.00561i	−0.217970	−	0.377535i	0.736217	−	0.676745i	$-0.236610\pi$
$569$	−5.19939	−	9.00561i	−0.217970	−	0.377535i	−0.954187	+	0.299210i	$0.903277\pi$
$570$		0			0
$571$	18.4912	+	10.6759i	0.773832	+	0.446772i	0.834240	−	0.551402i	$-0.185907\pi$
$571$	18.4912	+	10.6759i	0.773832	+	0.446772i	−0.0604077	+	0.998174i	$0.519240\pi$
$572$		0			0
$573$		−	1.60924i		−	0.0672268i
$574$		0			0
$575$		−	3.45875i		−	0.144240i
$576$		0			0
$577$	0.798556	+	0.461047i	0.0332443	+	0.0191936i	0.516530	−	0.856269i	$-0.327223\pi$
$577$	0.798556	+	0.461047i	0.0332443	+	0.0191936i	−0.483286	+	0.875463i	$0.660557\pi$
$578$		0			0
$579$	−2.00555	−	3.47371i	−0.0833476	−	0.144362i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	8.93473	−	5.15847i	0.370039	−	0.213642i
$584$		0			0
$585$	2.46737	−	4.27361i	0.102013	−	0.176692i
$586$		0			0
$587$	9.11149			0.376071			0.188036	−	0.982162i	$-0.439788\pi$
$587$	9.11149			0.376071			0.188036	+	0.982162i	$0.439788\pi$
$588$		0			0
$589$	−8.40955			−0.346509
$590$		0			0
$591$	−5.87066	+	10.1683i	−0.241486	+	0.418267i
$592$		0			0
$593$	−10.5720	+	6.10377i	−0.434142	+	0.250652i	−0.701110	−	0.713054i	$-0.747312\pi$
$593$	−10.5720	+	6.10377i	−0.434142	+	0.250652i	0.266968	+	0.963705i	$0.413978\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−8.68015	−	15.0345i	−0.355255	−	0.615319i
$598$		0			0
$599$	−30.4985	−	17.6083i	−1.24614	−	0.719457i	−0.275800	−	0.961215i	$-0.588943\pi$
$599$	−30.4985	−	17.6083i	−1.24614	−	0.719457i	−0.970337	+	0.241758i	$0.922276\pi$
$600$		0			0
$601$		−	30.6430i		−	1.24995i	−0.780644	−	0.624976i	$-0.785109\pi$
$601$		−	30.6430i		−	1.24995i	0.780644	−	0.624976i	$-0.214891\pi$
$602$		0			0
$603$			1.70195i			0.0693088i
$604$		0			0
$605$	2.15010	+	1.24136i	0.0874138	+	0.0504684i
$606$		0			0
$607$	4.98251	+	8.62996i	0.202234	+	0.350279i	0.949248	−	0.314529i	$-0.101847\pi$
$607$	4.98251	+	8.62996i	0.202234	+	0.350279i	−0.747014	+	0.664808i	$0.768513\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−17.0099	+	9.82067i	−0.688147	+	0.397302i
$612$		0			0
$613$	7.56293	−	13.0994i	0.305464	−	0.529079i	−0.671901	−	0.740641i	$-0.734522\pi$
$613$	7.56293	−	13.0994i	0.305464	−	0.529079i	0.977365	+	0.211562i	$0.0678551\pi$
$614$		0			0
$615$	−4.82058			−0.194385
$616$		0			0
$617$	11.7055			0.471245			0.235622	−	0.971845i	$-0.424287\pi$
$617$	11.7055			0.471245			0.235622	+	0.971845i	$0.424287\pi$
$618$		0			0
$619$	−3.63382	+	6.29396i	−0.146055	+	0.252975i	−0.929766	−	0.368150i	$-0.879991\pi$
$619$	−3.63382	+	6.29396i	−0.146055	+	0.252975i	0.783711	+	0.621126i	$0.213324\pi$
$620$		0			0
$621$	−1.38435	+	0.799257i	−0.0555522	+	0.0320731i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	4.74981	+	8.22691i	0.189992	+	0.329077i
$626$		0			0
$627$	−5.19257	−	2.99793i	−0.207371	−	0.119726i
$628$		0			0
$629$			21.0520i			0.839397i
$630$		0			0
$631$		−	1.40366i		−	0.0558789i	−0.999610	−	0.0279395i	$-0.991105\pi$
$631$		−	1.40366i		−	0.0558789i	0.999610	−	0.0279395i	$-0.00889456\pi$
$632$		0			0
$633$	−20.8861	−	12.0586i	−0.830148	−	0.479286i
$634$		0			0
$635$	1.82288	+	3.15732i	0.0723388	+	0.125295i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−5.30918	+	3.06526i	−0.210028	+	0.121260i
$640$		0			0
$641$	16.6136	−	28.7756i	0.656198	−	1.13657i	−0.325394	−	0.945579i	$-0.605497\pi$
$641$	16.6136	−	28.7756i	0.656198	−	1.13657i	0.981592	−	0.190990i	$-0.0611697\pi$
$642$		0			0
$643$	46.2604			1.82433			0.912166	−	0.409820i	$-0.134409\pi$
$643$	46.2604			1.82433			0.912166	+	0.409820i	$0.134409\pi$
$644$		0			0
$645$	−19.7915			−0.779290
$646$		0			0
$647$	−17.3166	+	29.9932i	−0.680786	+	1.17916i	0.293955	+	0.955819i	$0.405028\pi$
$647$	−17.3166	+	29.9932i	−0.680786	+	1.17916i	−0.974741	+	0.223337i	$0.928305\pi$
$648$		0			0
$649$	−23.7212	+	13.6954i	−0.931138	+	0.537593i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.11432	−	7.12620i	−0.161006	−	0.278870i	0.774224	−	0.632912i	$-0.218140\pi$
$653$	−4.11432	−	7.12620i	−0.161006	−	0.278870i	−0.935230	+	0.354042i	$0.884807\pi$
$654$		0			0
$655$	22.3469	+	12.9020i	0.873166	+	0.504123i
$656$		0			0
$657$			2.43166i			0.0948681i
$658$		0			0
$659$			10.9381i			0.426087i	0.977043	+	0.213044i	$0.0683376\pi$
$659$			10.9381i			0.426087i	−0.977043	+	0.213044i	$0.931662\pi$
$660$		0			0
$661$	21.8198	+	12.5977i	0.848692	+	0.489993i	0.860209	−	0.509941i	$-0.170333\pi$
$661$	21.8198	+	12.5977i	0.848692	+	0.489993i	−0.0115171	+	0.999934i	$0.503666\pi$
$662$		0			0
$663$	−2.94685	−	5.10409i	−0.114446	−	0.198226i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−10.9922	+	6.34632i	−0.425618	+	0.245731i
$668$		0			0
$669$	10.0577	−	17.4204i	0.388852	−	0.673512i
$670$		0			0
$671$	−44.4754			−1.71695
$672$		0			0
$673$	11.5831			0.446497			0.223248	−	0.974762i	$-0.428334\pi$
$673$	11.5831			0.446497			0.223248	+	0.974762i	$0.428334\pi$
$674$		0			0
$675$	−1.08187	+	1.87385i	−0.0416410	+	0.0721243i
$676$		0			0
$677$	−30.1066	+	17.3820i	−1.15709	+	0.668046i	−0.950605	−	0.310404i	$-0.899536\pi$
$677$	−30.1066	+	17.3820i	−1.15709	+	0.668046i	−0.206485	+	0.978450i	$0.566202\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	8.79465	+	15.2328i	0.337012	+	0.583721i
$682$		0			0
$683$	10.1924	+	5.88459i	0.390002	+	0.225167i	0.682161	−	0.731202i	$-0.261040\pi$
$683$	10.1924	+	5.88459i	0.390002	+	0.225167i	−0.292159	+	0.956370i	$0.594374\pi$
$684$		0			0
$685$			21.6601i			0.827591i
$686$		0			0
$687$			3.99205i			0.152306i
$688$		0			0
$689$	−7.41251	−	4.27962i	−0.282394	−	0.163040i
$690$		0			0
$691$	−5.65157	−	9.78880i	−0.214996	−	0.372383i	0.738276	−	0.674499i	$-0.235640\pi$
$691$	−5.65157	−	9.78880i	−0.214996	−	0.372383i	−0.953271	+	0.302116i	$0.902307\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.08508	+	0.626469i	−0.0411593	+	0.0237633i
$696$		0			0
$697$	−2.87868	+	4.98602i	−0.109038	+	0.188859i
$698$		0			0
$699$	3.26967			0.123670
$700$		0			0
$701$	24.9265			0.941462			0.470731	−	0.882277i	$-0.343990\pi$
$701$	24.9265			0.941462			0.470731	+	0.882277i	$0.343990\pi$
$702$		0			0
$703$	8.88404	−	15.3876i	0.335068	−	0.580355i
$704$		0			0
$705$	−9.77655	+	5.64449i	−0.368206	+	0.212584i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−22.1190	−	38.3113i	−0.830697	−	1.43881i	−0.897486	−	0.441043i	$-0.854609\pi$
$709$	−22.1190	−	38.3113i	−0.830697	−	1.43881i	0.0667887	−	0.997767i	$-0.478725\pi$
$710$		0			0
$711$	−0.749517	−	0.432734i	−0.0281091	−	0.0162288i
$712$		0			0
$713$			7.91851i			0.296551i
$714$		0			0
$715$		−	17.4289i		−	0.651804i
$716$		0			0
$717$	25.0392	+	14.4564i	0.935105	+	0.539883i
$718$		0			0
$719$	2.70319	+	4.68205i	0.100812	+	0.174611i	0.912019	−	0.410147i	$-0.134523\pi$
$719$	2.70319	+	4.68205i	0.100812	+	0.174611i	−0.811208	+	0.584758i	$0.801189\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	5.29374	−	3.05634i	0.196876	−	0.113667i
$724$		0			0
$725$	−8.59031	+	14.8789i	−0.319036	+	0.552587i
$726$		0			0
$727$	−36.5459			−1.35541			−0.677706	−	0.735333i	$-0.737026\pi$
$727$	−36.5459			−1.35541			−0.677706	+	0.735333i	$0.737026\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−11.8188	+	20.4707i	−0.437133	+	0.757137i
$732$		0			0
$733$	−23.6637	+	13.6622i	−0.874038	+	0.504626i	−0.868688	−	0.495359i	$-0.835036\pi$
$733$	−23.6637	+	13.6622i	−0.874038	+	0.504626i	−0.00535017	+	0.999986i	$0.501703\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.00555	+	5.20576i	0.110711	+	0.191757i
$738$		0			0
$739$	15.4043	+	8.89369i	0.566657	+	0.327160i	0.755813	−	0.654787i	$-0.227242\pi$
$739$	15.4043	+	8.89369i	0.566657	+	0.327160i	−0.189156	+	0.981947i	$0.560575\pi$
$740$		0			0
$741$			4.97434i			0.182737i
$742$		0			0
$743$		−	30.1701i		−	1.10683i	−0.832904	−	0.553417i	$-0.813324\pi$
$743$		−	30.1701i		−	1.10683i	0.832904	−	0.553417i	$-0.186676\pi$
$744$		0			0
$745$	10.6508	+	6.14925i	0.390216	+	0.225291i
$746$		0			0
$747$	−7.26593	−	12.5850i	−0.265847	−	0.460460i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	37.2330	−	21.4965i	1.35865	−	0.784418i	0.369210	−	0.929346i	$-0.379628\pi$
$751$	37.2330	−	21.4965i	1.35865	−	0.784418i	0.989442	+	0.144928i	$0.0462950\pi$
$752$		0			0
$753$	−13.8736	+	24.0297i	−0.505581	+	0.875691i
$754$		0			0
$755$	−10.5821			−0.385121
$756$		0			0
$757$	−13.2021			−0.479839			−0.239919	−	0.970793i	$-0.577121\pi$
$757$	−13.2021			−0.479839			−0.239919	+	0.970793i	$0.577121\pi$
$758$		0			0
$759$	−2.82288	+	4.88937i	−0.102464	+	0.177473i
$760$		0			0
$761$	15.7032	−	9.06624i	0.569240	−	0.328651i	−0.187605	−	0.982244i	$-0.560073\pi$
$761$	15.7032	−	9.06624i	0.569240	−	0.328651i	0.756846	+	0.653593i	$0.226739\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.69372	−	2.93361i	−0.0612365	−	0.106065i
$766$		0			0
$767$	19.6798	+	11.3621i	0.710596	+	0.410263i
$768$		0			0
$769$			45.0980i			1.62628i	0.582070	+	0.813139i	$0.302243\pi$
$769$			45.0980i			1.62628i	−0.582070	+	0.813139i	$0.697757\pi$
$770$		0			0
$771$		−	2.86237i		−	0.103086i
$772$		0			0
$773$	−31.2176	−	18.0235i	−1.12282	−	0.648259i	−0.180699	−	0.983538i	$-0.557836\pi$
$773$	−31.2176	−	18.0235i	−1.12282	−	0.648259i	−0.942119	+	0.335279i	$0.891169\pi$
$774$		0			0
$775$	5.35920	+	9.28241i	0.192508	+	0.333434i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4.20826	−	2.42964i	0.150776	−	0.0870508i
$780$		0			0
$781$	−10.8261	+	18.7514i	−0.387389	+	0.670978i
$782$		0			0
$783$	7.94028			0.283762
$784$		0			0
$785$	−15.0081			−0.535662
$786$		0			0
$787$	13.1922	−	22.8496i	0.470251	−	0.814499i	−0.529170	−	0.848516i	$-0.677497\pi$
$787$	13.1922	−	22.8496i	0.470251	−	0.814499i	0.999421	+	0.0340166i	$0.0108299\pi$
$788$		0			0
$789$	16.8466	−	9.72639i	0.599755	−	0.346269i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	18.4490	+	31.9547i	0.655145	+	1.13474i
$794$		0			0
$795$	−4.26039	−	2.45974i	−0.151100	−	0.0872379i
$796$		0			0
$797$		−	52.8839i		−	1.87324i	−0.350344	−	0.936621i	$-0.613935\pi$
$797$		−	52.8839i		−	1.87324i	0.350344	−	0.936621i	$-0.386065\pi$
$798$		0			0
$799$			13.4828i			0.476986i
$800$		0			0
$801$	−13.8033	−	7.96936i	−0.487717	−	0.281584i
$802$		0			0
$803$	4.29417	+	7.43772i	0.151538	+	0.262471i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−14.4480	+	8.34156i	−0.508594	+	0.293637i
$808$		0			0
$809$	−8.08508	+	14.0038i	−0.284256	+	0.492346i	−0.972429	−	0.233201i	$-0.925080\pi$
$809$	−8.08508	+	14.0038i	−0.284256	+	0.492346i	0.688172	+	0.725547i	$0.258413\pi$
$810$		0			0
$811$	−4.18532			−0.146967			−0.0734833	−	0.997296i	$-0.523412\pi$
$811$	−4.18532			−0.146967			−0.0734833	+	0.997296i	$0.523412\pi$
$812$		0			0
$813$	19.9057			0.698122
$814$		0			0
$815$	0.203895	−	0.353157i	0.00714214	−	0.0123706i
$816$		0			0
$817$	17.2775	−	9.97518i	0.604464	−	0.348987i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	2.44860	+	4.24110i	0.0854567	+	0.148015i	0.905586	−	0.424163i	$-0.139432\pi$
$821$	2.44860	+	4.24110i	0.0854567	+	0.148015i	−0.820129	+	0.572179i	$0.806098\pi$
$822$		0			0
$823$	5.62077	+	3.24515i	0.195928	+	0.113119i	0.594755	−	0.803907i	$-0.297249\pi$
$823$	5.62077	+	3.24515i	0.195928	+	0.113119i	−0.398827	+	0.917026i	$0.630583\pi$
$824$		0			0
$825$			7.64204i			0.266062i
$826$		0			0
$827$			18.8437i			0.655258i	0.944806	+	0.327629i	$0.106250\pi$
$827$			18.8437i			0.655258i	−0.944806	+	0.327629i	$0.893750\pi$
$828$		0			0
$829$	13.6919	+	7.90504i	0.475540	+	0.274553i	0.718556	−	0.695469i	$-0.244803\pi$
$829$	13.6919	+	7.90504i	0.475540	+	0.274553i	−0.243016	+	0.970022i	$0.578137\pi$
$830$		0			0
$831$	7.16373	+	12.4079i	0.248507	+	0.430427i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−8.50035	+	4.90768i	−0.294167	+	0.169837i
$836$		0			0
$837$	2.47683	−	4.29000i	0.0856119	−	0.148284i
$838$		0			0
$839$	−25.1313			−0.867629			−0.433814	−	0.901002i	$-0.642833\pi$
$839$	−25.1313			−0.867629			−0.433814	+	0.901002i	$0.642833\pi$
$840$		0			0
$841$	34.0481			1.17407
$842$		0			0
$843$	−8.27250	+	14.3284i	−0.284920	+	0.493496i
$844$		0			0
$845$	6.43810	−	3.71704i	0.221477	−	0.127870i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−14.9295	−	25.8587i	−0.512380	−	0.887469i
$850$		0			0
$851$	−14.4891	−	8.36530i	−0.496681	−	0.286759i
$852$		0			0
$853$		−	31.5399i		−	1.07991i	−0.841695	−	0.539953i	$-0.818442\pi$
$853$		−	31.5399i		−	1.07991i	0.841695	−	0.539953i	$-0.181558\pi$
$854$		0			0
$855$			2.85903i			0.0977769i
$856$		0			0
$857$	24.5514	+	14.1748i	0.838660	+	0.484201i	0.856809	−	0.515635i	$-0.172444\pi$
$857$	24.5514	+	14.1748i	0.838660	+	0.484201i	−0.0181483	+	0.999835i	$0.505777\pi$
$858$		0			0
$859$	17.3399	+	30.0336i	0.591630	+	1.02473i	0.994013	+	0.109262i	$0.0348486\pi$
$859$	17.3399	+	30.0336i	0.591630	+	1.02473i	−0.402383	+	0.915471i	$0.631818\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	16.0002	−	9.23770i	0.544652	−	0.314455i	−0.202310	−	0.979321i	$-0.564845\pi$
$863$	16.0002	−	9.23770i	0.544652	−	0.314455i	0.746962	+	0.664867i	$0.231512\pi$
$864$		0			0
$865$	−14.1411	+	24.4932i	−0.480813	+	0.832792i
$866$		0			0
$867$	12.9543			0.439951
$868$		0			0
$869$	−3.05673			−0.103692
$870$		0			0
$871$	2.49349	−	4.31885i	0.0844886	−	0.146339i
$872$		0			0
$873$	−8.50671	+	4.91135i	−0.287908	+	0.166224i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	21.4892	+	37.2204i	0.725639	+	1.25684i	0.958711	+	0.284384i	$0.0917890\pi$
$877$	21.4892	+	37.2204i	0.725639	+	1.25684i	−0.233072	+	0.972460i	$0.574878\pi$
$878$		0			0
$879$	5.54415	+	3.20092i	0.187000	+	0.107964i
$880$		0			0
$881$		−	4.50973i		−	0.151937i	−0.997110	−	0.0759684i	$-0.975795\pi$
$881$		−	4.50973i		−	0.151937i	0.997110	−	0.0759684i	$-0.0242048\pi$
$882$		0			0
$883$			42.8824i			1.44311i	0.692359	+	0.721553i	$0.256571\pi$
$883$			42.8824i			1.44311i	−0.692359	+	0.721553i	$0.743429\pi$
$884$		0			0
$885$	11.3111	+	6.53046i	0.380218	+	0.219519i
$886$		0			0
$887$	2.37863	+	4.11990i	0.0798665	+	0.138333i	0.903192	−	0.429236i	$-0.141217\pi$
$887$	2.37863	+	4.11990i	0.0798665	+	0.138333i	−0.823326	+	0.567569i	$0.807884\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	3.05870	−	1.76594i	0.102470	−	0.0591612i
$892$		0			0
$893$	5.68980	−	9.85502i	0.190402	−	0.329786i
$894$		0			0
$895$	35.7705			1.19568
$896$		0			0
$897$	4.68389			0.156390
$898$		0			0
$899$	19.6668	−	34.0638i	0.655923	−	1.13609i
$900$		0			0
$901$	−5.08830	+	2.93773i	−0.169516	+	0.0978701i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.31099	−	4.00275i	−0.0768199	−	0.133056i
$906$		0			0
$907$	−13.6921	−	7.90513i	−0.454639	−	0.262486i	0.255149	−	0.966902i	$-0.417876\pi$
$907$	−13.6921	−	7.90513i	−0.454639	−	0.262486i	−0.709787	+	0.704416i	$0.751209\pi$
$908$		0			0
$909$			9.42764i			0.312695i
$910$		0			0
$911$			15.5236i			0.514320i	0.966369	+	0.257160i	$0.0827868\pi$
$911$			15.5236i			0.514320i	−0.966369	+	0.257160i	$0.917213\pi$
$912$		0			0
$913$	−44.4486	−	25.6624i	−1.47103	−	0.849302i
$914$		0			0
$915$	10.6037	+	18.3661i	0.350548	+	0.607166i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−50.6854	+	29.2632i	−1.67196	+	0.965304i	−0.705413	+	0.708796i	$0.749239\pi$
$919$	−50.6854	+	29.2632i	−1.67196	+	0.965304i	−0.966542	+	0.256508i	$0.917428\pi$
$920$		0			0
$921$	−5.82553	+	10.0901i	−0.191958	+	0.332480i
$922$		0			0
$923$	17.9633			0.591271
$924$		0			0
$925$	−22.6464			−0.744607
$926$		0			0
$927$	7.83133	−	13.5643i	0.257215	−	0.445509i
$928$		0			0
$929$	46.0423	−	26.5825i	1.51060	−	0.872144i	0.510674	−	0.859774i	$-0.329396\pi$
$929$	46.0423	−	26.5825i	1.51060	−	0.872144i	0.999923	−	0.0123696i	$-0.00393746\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	11.5386	+	19.9855i	0.377757	+	0.654295i
$934$		0			0
$935$	−10.3612	−	5.98201i	−0.338846	−	0.195633i
$936$		0			0
$937$		−	17.0577i		−	0.557250i	−0.960400	−	0.278625i	$-0.910121\pi$
$937$		−	17.0577i		−	0.557250i	0.960400	−	0.278625i	$-0.0898787\pi$
$938$		0			0
$939$		−	25.9505i		−	0.846861i
$940$		0			0
$941$	−14.2306	−	8.21605i	−0.463905	−	0.267836i	0.249780	−	0.968303i	$-0.419642\pi$
$941$	−14.2306	−	8.21605i	−0.463905	−	0.267836i	−0.713685	+	0.700467i	$0.752975\pi$
$942$		0			0
$943$	−2.28777	−	3.96253i	−0.0745000	−	0.129038i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	22.3879	−	12.9256i	0.727508	−	0.420027i	−0.0900020	−	0.995942i	$-0.528687\pi$
$947$	22.3879	−	12.9256i	0.727508	−	0.420027i	0.817510	+	0.575915i	$0.195354\pi$
$948$		0			0
$949$	3.56257	−	6.17055i	0.115646	−	0.200304i
$950$		0			0
$951$	20.5430			0.666151
$952$		0			0
$953$	−3.79848			−0.123045			−0.0615224	−	0.998106i	$-0.519596\pi$
$953$	−3.79848			−0.123045			−0.0615224	+	0.998106i	$0.519596\pi$
$954$		0			0
$955$	−1.35508	+	2.34706i	−0.0438492	+	0.0759491i
$956$		0			0
$957$	24.2869	−	14.0221i	0.785085	−	0.453269i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	3.23058	+	5.59553i	0.104212	+	0.180501i
$962$		0			0
$963$	16.4365	+	9.48961i	0.529658	+	0.305798i
$964$		0			0
$965$			6.75517i			0.217457i
$966$		0			0
$967$		−	20.7285i		−	0.666582i	−0.942824	−	0.333291i	$-0.891841\pi$
$967$		−	20.7285i		−	0.666582i	0.942824	−	0.333291i	$-0.108159\pi$
$968$		0			0
$969$	2.95715	+	1.70731i	0.0949974	+	0.0548468i
$970$		0			0
$971$	−19.7594	−	34.2243i	−0.634110	−	1.09831i	−0.986703	−	0.162534i	$-0.948033\pi$
$971$	−19.7594	−	34.2243i	−0.634110	−	1.09831i	0.352593	−	0.935777i	$-0.385300\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	5.49065	−	3.17003i	0.175842	−	0.101522i
$976$		0			0
$977$	10.5617	−	18.2935i	0.337900	−	0.585259i	−0.646138	−	0.763221i	$-0.723617\pi$
$977$	10.5617	−	18.2935i	0.337900	−	0.585259i	0.984037	+	0.177961i	$0.0569502\pi$
$978$		0			0
$979$	−56.2937			−1.79915
$980$		0			0
$981$	10.5590			0.337123
$982$		0			0
$983$	−22.9788	+	39.8004i	−0.732909	+	1.26944i	0.222726	+	0.974881i	$0.428505\pi$
$983$	−22.9788	+	39.8004i	−0.732909	+	1.26944i	−0.955635	+	0.294554i	$0.904829\pi$
$984$		0			0
$985$	17.1246	−	9.88690i	0.545636	−	0.315023i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−9.39273	−	16.2687i	−0.298671	−	0.517314i
$990$		0			0
$991$	3.40626	+	1.96661i	0.108204	+	0.0624714i	0.553125	−	0.833098i	$-0.313435\pi$
$991$	3.40626	+	1.96661i	0.108204	+	0.0624714i	−0.444922	+	0.895570i	$0.646768\pi$
$992$		0			0
$993$		−	32.7763i		−	1.04013i
$994$		0			0
$995$			29.2369i			0.926871i
$996$		0			0
$997$	−9.27071	−	5.35244i	−0.293606	−	0.169514i	0.345961	−	0.938249i	$-0.387553\pi$
$997$	−9.27071	−	5.35244i	−0.293606	−	0.169514i	−0.639567	+	0.768735i	$0.720886\pi$
$998$		0			0
$999$	5.23317	+	9.06412i	0.165570	+	0.286776i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2352.2.bl.q.31.3		8
4.3	odd	2		2352.2.bl.r.31.3		8
7.2	even	3		2352.2.bl.o.607.2		8
7.3	odd	6		2352.2.b.k.1567.3	✓	8
7.4	even	3		2352.2.b.l.1567.6	yes	8
7.5	odd	6		2352.2.bl.r.607.3		8
7.6	odd	2		2352.2.bl.t.31.2		8
21.11	odd	6		7056.2.b.w.1567.3		8
21.17	even	6		7056.2.b.x.1567.6		8
28.3	even	6		2352.2.b.l.1567.3	yes	8
28.11	odd	6		2352.2.b.k.1567.6	yes	8
28.19	even	6	inner	2352.2.bl.q.607.3		8
28.23	odd	6		2352.2.bl.t.607.2		8
28.27	even	2		2352.2.bl.o.31.2		8
84.11	even	6		7056.2.b.x.1567.3		8
84.59	odd	6		7056.2.b.w.1567.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2352.2.b.k.1567.3	✓	8	7.3	odd	6
2352.2.b.k.1567.6	yes	8	28.11	odd	6
2352.2.b.l.1567.3	yes	8	28.3	even	6
2352.2.b.l.1567.6	yes	8	7.4	even	3
2352.2.bl.o.31.2		8	28.27	even	2
2352.2.bl.o.607.2		8	7.2	even	3
2352.2.bl.q.31.3		8	1.1	even	1	trivial
2352.2.bl.q.607.3		8	28.19	even	6	inner
2352.2.bl.r.31.3		8	4.3	odd	2
2352.2.bl.r.607.3		8	7.5	odd	6
2352.2.bl.t.31.2		8	7.6	odd	2
2352.2.bl.t.607.2		8	28.23	odd	6
7056.2.b.w.1567.3		8	21.11	odd	6
7056.2.b.w.1567.6		8	84.59	odd	6
7056.2.b.x.1567.3		8	84.11	even	6
7056.2.b.x.1567.6		8	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2352.bl (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(1.45849 - 0.842061i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(1.45849 - 0.842061i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-3.05870 - 1.76594i) q^{11} +2.93015i q^{13} +1.68412i q^{15} +(1.74192 + 1.00570i) q^{17} +(-0.848820 - 1.47020i) q^{19} +(-1.38435 + 0.799257i) q^{23} +(-1.08187 + 1.87385i) q^{25} +1.00000 q^{27} +7.94028 q^{29} +(2.47683 - 4.29000i) q^{31} +(3.05870 - 1.76594i) q^{33} +(5.23317 + 9.06412i) q^{37} +(-2.53759 - 1.46508i) q^{39} +2.86237i q^{41} +11.7518i q^{43} +(-1.45849 - 0.842061i) q^{45} +(3.35159 + 5.80513i) q^{47} +(-1.74192 + 1.00570i) q^{51} +(-1.46054 + 2.52974i) q^{53} -5.94812 q^{55} +1.69764 q^{57} +(3.87766 - 6.71630i) q^{59} +(10.9055 - 6.29627i) q^{61} +(2.46737 + 4.27361i) q^{65} +(-1.47393 - 0.850976i) q^{67} -1.59851i q^{69} -6.13052i q^{71} +(-2.10588 - 1.21583i) q^{73} +(-1.08187 - 1.87385i) q^{75} +(0.749517 - 0.432734i) q^{79} +(-0.500000 + 0.866025i) q^{81} +14.5319 q^{83} +3.38744 q^{85} +(-3.97014 + 6.87648i) q^{87} +(13.8033 - 7.96936i) q^{89} +(2.47683 + 4.29000i) q^{93} +(-2.47600 - 1.42952i) q^{95} -9.82270i q^{97} +3.53188i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 - 4 * q^9	\( 8 q - 4 q^{3} - 4 q^{9} + 24 q^{23} + 12 q^{25} + 8 q^{27} + 16 q^{29} + 16 q^{31} + 8 q^{47} - 8 q^{53} - 64 q^{55} - 24 q^{59} + 48 q^{61} + 8 q^{65} - 48 q^{67} + 48 q^{73} + 12 q^{75} - 24 q^{79} - 4 q^{81} - 64 q^{85} - 8 q^{87} + 48 q^{89} + 16 q^{93} + 72 q^{95}+O(q^{100}) \) 8 * q - 4 * q^3 - 4 * q^9 + 24 * q^23 + 12 * q^25 + 8 * q^27 + 16 * q^29 + 16 * q^31 + 8 * q^47 - 8 * q^53 - 64 * q^55 - 24 * q^59 + 48 * q^61 + 8 * q^65 - 48 * q^67 + 48 * q^73 + 12 * q^75 - 24 * q^79 - 4 * q^81 - 64 * q^85 - 8 * q^87 + 48 * q^89 + 16 * q^93 + 72 * q^95

Introduction

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