LMFDB - Embedded newform 2352.2.bl.t.31.2

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			31.2
Root			$1.60021 - 0.923880i$ of defining polynomial
Character	$\chi$	$=$	2352.31
Dual form			2352.2.bl.t.607.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(-1.45849 + 0.842061i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(-1.45849 + 0.842061i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-3.05870 - 1.76594i) q^{11} -2.93015i q^{13} +1.68412i q^{15} +(-1.74192 - 1.00570i) q^{17} +(0.848820 + 1.47020i) q^{19} +(-1.38435 + 0.799257i) q^{23} +(-1.08187 + 1.87385i) q^{25} -1.00000 q^{27} +7.94028 q^{29} +(-2.47683 + 4.29000i) q^{31} +(-3.05870 + 1.76594i) q^{33} +(5.23317 + 9.06412i) q^{37} +(-2.53759 - 1.46508i) q^{39} -2.86237i q^{41} +11.7518i q^{43} +(1.45849 + 0.842061i) q^{45} +(-3.35159 - 5.80513i) q^{47} +(-1.74192 + 1.00570i) q^{51} +(-1.46054 + 2.52974i) q^{53} +5.94812 q^{55} +1.69764 q^{57} +(-3.87766 + 6.71630i) q^{59} +(-10.9055 + 6.29627i) q^{61} +(2.46737 + 4.27361i) q^{65} +(-1.47393 - 0.850976i) q^{67} +1.59851i q^{69} -6.13052i q^{71} +(2.10588 + 1.21583i) q^{73} +(1.08187 + 1.87385i) q^{75} +(0.749517 - 0.432734i) q^{79} +(-0.500000 + 0.866025i) q^{81} -14.5319 q^{83} +3.38744 q^{85} +(3.97014 - 6.87648i) q^{87} +(-13.8033 + 7.96936i) q^{89} +(2.47683 + 4.29000i) q^{93} +(-2.47600 - 1.42952i) q^{95} +9.82270i q^{97} +3.53188i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.789321	−	0.613981i	$-0.789567\pi$
$5$	−1.45849	+	0.842061i	−0.652258	+	0.376581i	0.137063	+	0.990562i	$0.456234\pi$
$6$		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	$-0.866805\pi$
$13$		−	2.93015i		−	0.812678i	0.913722	−	0.406339i	$-0.133195\pi$
$14$		0			0
$15$			1.68412i			0.434839i
$16$		0			0
$17$	−1.74192	−	1.00570i	−0.422478	−	0.243918i	0.273659	−	0.961827i	$-0.411766\pi$
$17$	−1.74192	−	1.00570i	−0.422478	−	0.243918i	−0.696137	+	0.717909i	$0.745099\pi$
$18$		0			0
$19$	0.848820	+	1.47020i	0.194733	+	0.337287i	0.946813	−	0.321785i	$-0.104283\pi$
$19$	0.848820	+	1.47020i	0.194733	+	0.337287i	−0.752080	+	0.659072i	$0.770949\pi$
$20$		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	−0.998042	−	0.0625483i	$-0.980077\pi$
$31$	−2.47683	+	4.29000i	−0.444853	+	0.770507i	0.553189	+	0.833056i	$0.313411\pi$
$32$		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	$-0.928247\pi$
$41$		−	2.86237i		−	0.447027i	0.974701	−	0.223514i	$-0.0717527\pi$
$42$		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	0.511038	−	0.859558i	$-0.329261\pi$
$47$	−3.35159	−	5.80513i	−0.488880	−	0.846765i	−0.999918	+	0.0127930i	$0.995928\pi$
$48$		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	$0.335111\pi$
$59$	−3.87766	+	6.71630i	−0.504828	+	0.874388i	−0.999984	+	0.00558422i	$0.998222\pi$
$60$		0			0
$61$	−10.9055	+	6.29627i	−1.39630	+	0.806155i	−0.994003	−	0.109353i	$-0.965122\pi$
$61$	−10.9055	+	6.29627i	−1.39630	+	0.806155i	−0.402299	+	0.915508i	$0.631789\pi$
$62$		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	0.618149	−	0.786061i	$-0.287883\pi$
$73$	2.10588	+	1.21583i	0.246475	+	0.142302i	−0.371674	+	0.928363i	$0.621216\pi$
$74$		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	$-0.793866\pi$
$83$	−14.5319			−1.59508			−0.797540	+	0.603266i	$0.793866\pi$
$84$		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	−0.999156	−	0.0410870i	$-0.986918\pi$
$89$	−13.8033	+	7.96936i	−1.46315	+	0.844751i	−0.463995	+	0.885838i	$0.653585\pi$
$90$		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	$0.166179\pi$
$97$			9.82270i			0.997344i	−0.866791	+	0.498672i	$0.833821\pi$
$98$		0			0
$99$			3.53188i			0.354967i
$100$		0			0
$101$	8.16458	+	4.71382i	0.812406	+	0.469043i	0.847791	−	0.530331i	$-0.177932\pi$
$101$	8.16458	+	4.71382i	0.812406	+	0.469043i	−0.0353847	+	0.999374i	$0.511266\pi$
$102$		0			0
$103$	−7.83133	−	13.5643i	−0.771644	−	1.33653i	−0.936662	−	0.350236i	$-0.886102\pi$
$103$	−7.83133	−	13.5643i	−0.771644	−	1.33653i	0.165018	−	0.986291i	$-0.447232\pi$
$104$		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	$-0.933243\pi$
$131$	−7.66096	−	13.2692i	−0.669341	−	1.15933i	0.308748	−	0.951144i	$-0.400090\pi$
$132$		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	$-0.489955\pi$
$139$	0.743971			0.0631028			0.0315514	+	0.999502i	$0.489955\pi$
$140$		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	0.775283	−	0.631613i	$-0.217607\pi$
$157$	7.71761	+	4.45576i	0.615932	+	0.355608i	−0.159352	+	0.987222i	$0.550940\pi$
$158$		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	$-0.427599\pi$
$167$	5.82817			0.450997			0.225499	+	0.974243i	$0.427599\pi$
$168$		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	0.168008	−	0.985786i	$-0.446267\pi$
$173$	14.5436	−	8.39673i	1.10573	−	0.638392i	0.937719	+	0.347394i	$0.112933\pi$
$174$		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	$0.0325230\pi$
$181$			2.74444i			0.203993i	−0.994785	+	0.101996i	$0.967477\pi$
$182$		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	$-0.622360\pi$
$199$	8.68015	−	15.0345i	0.615319	−	1.06576i	0.990328	−	0.138743i	$-0.0443063\pi$
$200$		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	$-0.264785\pi$
$223$	20.1154			1.34702			0.673512	+	0.739176i	$0.264785\pi$
$224$		0			0
$225$	2.16373			0.144249
$226$		0			0
$227$	−8.79465	+	15.2328i	−0.583721	+	1.01103i	0.411312	+	0.911494i	$0.365071\pi$
$227$	−8.79465	+	15.2328i	−0.583721	+	1.01103i	−0.995034	+	0.0995403i	$0.968263\pi$
$228$		0			0
$229$	−3.45722	+	1.99602i	−0.228459	+	0.131901i	−0.609861	−	0.792508i	$-0.708775\pi$
$229$	−3.45722	+	1.99602i	−0.228459	+	0.131901i	0.381402	+	0.924409i	$0.375441\pi$
$230$		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	0.660714	−	0.750638i	$-0.270254\pi$
$241$	5.29374	+	3.05634i	0.341000	+	0.196876i	−0.319714	+	0.947514i	$0.603587\pi$
$242$		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	$-0.839594\pi$
$251$	−27.7471			−1.75138			−0.875691	+	0.482872i	$0.839594\pi$
$252$		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	−0.420689	−	0.907205i	$-0.638212\pi$
$257$	2.47889	−	1.43119i	0.154629	−	0.0892749i	0.575318	+	0.817930i	$0.304878\pi$
$258$		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	−0.00995197	−	0.999950i	$-0.503168\pi$
$269$	−14.4480	−	8.34156i	−0.880910	−	0.508594i	−0.870959	+	0.491357i	$0.836501\pi$
$270$		0			0
$271$	9.95283	+	17.2388i	0.604591	+	1.04718i	0.992116	+	0.125324i	$0.0399969\pi$
$271$	9.95283	+	17.2388i	0.604591	+	1.04718i	−0.387525	+	0.921859i	$0.626670\pi$
$272$		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	$-0.485795\pi$
$283$	14.9295	−	25.8587i	0.887469	−	1.53714i	0.842858	−	0.538137i	$-0.180872\pi$
$284$		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	$0.0598763\pi$
$293$			6.40183i			0.373999i	−0.982360	+	0.187000i	$0.940124\pi$
$294$		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	$-0.607886\pi$
$307$	−11.6511			−0.664961			−0.332480	+	0.943110i	$0.607886\pi$
$308$		0			0
$309$	−15.6627			−0.891017
$310$		0			0
$311$	−11.5386	+	19.9855i	−0.654295	+	1.13327i	0.327775	+	0.944756i	$0.393701\pi$
$311$	−11.5386	+	19.9855i	−0.654295	+	1.13327i	−0.982070	+	0.188516i	$0.939632\pi$
$312$		0			0
$313$	22.4738	−	12.9752i	1.27029	−	0.733404i	0.295249	−	0.955420i	$-0.404597\pi$
$313$	22.4738	−	12.9752i	1.27029	−	0.733404i	0.975043	+	0.222017i	$0.0712640\pi$
$314$		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	$-0.896350\pi$
$349$		−	11.9525i		−	0.639802i	0.947451	−	0.319901i	$-0.103650\pi$
$350$		0			0
$351$			2.93015i			0.156400i
$352$		0			0
$353$	−11.1916	−	6.46148i	−0.595669	−	0.343910i	0.171667	−	0.985155i	$-0.445085\pi$
$353$	−11.1916	−	6.46148i	−0.595669	−	0.343910i	−0.767336	+	0.641245i	$0.778418\pi$
$354$		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	−0.978426	−	0.206598i	$-0.933761\pi$
$367$	−5.94438	+	10.2960i	−0.310294	+	0.537445i	0.668132	+	0.744043i	$0.267094\pi$
$368$		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	0.834540	−	0.550947i	$-0.185734\pi$
$383$	−1.17157	−	2.02922i	−0.0598646	−	0.103688i	−0.894404	+	0.447259i	$0.852400\pi$
$384$		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	−0.559929	−	0.828541i	$-0.689172\pi$
$397$	−2.43793	+	1.40754i	−0.122356	+	0.0706425i	0.437573	+	0.899183i	$0.355838\pi$
$398$		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	0.669192	−	0.743090i	$-0.266641\pi$
$409$	7.28566	+	4.20638i	0.360253	+	0.207992i	−0.308939	+	0.951082i	$0.599974\pi$
$410$		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	$-0.650556\pi$
$419$	−18.6496			−0.911094			−0.455547	+	0.890212i	$0.650556\pi$
$420$		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	$0.112994\pi$
$433$			14.4650i			0.695146i	−0.937653	+	0.347573i	$0.887006\pi$
$434$		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	$0.00745195\pi$
$439$	10.8981	+	18.8760i	0.520136	+	0.900901i	−0.479590	+	0.877493i	$0.659215\pi$
$440$		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	$0.193509\pi$
$461$			24.5269i			1.14233i	−0.820834	+	0.571167i	$0.806491\pi$
$462$		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	0.964881	−	0.262689i	$-0.0846092\pi$
$467$	5.50941	+	9.54258i	0.254945	+	0.441578i	−0.709935	+	0.704267i	$0.751276\pi$
$468$		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	$0.476662\pi$
$479$	−18.1014	+	31.3525i	−0.827073	+	1.43253i	−0.900325	+	0.435218i	$0.856671\pi$
$480$		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	$-0.844129\pi$
$503$	−39.5840			−1.76496			−0.882482	+	0.470347i	$0.844129\pi$
$504$		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	0.361972	−	0.932189i	$-0.382104\pi$
$509$	30.4632	−	17.5879i	1.35026	−	0.779572i	0.988285	+	0.152617i	$0.0487702\pi$
$510$		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	0.0803894	−	0.996764i	$-0.474384\pi$
$521$	−16.9510	−	9.78669i	−0.742638	−	0.428762i	−0.823028	+	0.568001i	$0.807717\pi$
$522$		0			0
$523$	4.33120	+	7.50186i	0.189390	+	0.328033i	0.945047	−	0.326934i	$-0.106016\pi$
$523$	4.33120	+	7.50186i	0.189390	+	0.328033i	−0.755657	+	0.654968i	$0.772682\pi$
$524$		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	−0.732348	−	0.680931i	$-0.761575\pi$
$563$	5.30382	−	9.18648i	0.223529	−	0.387164i	0.955877	+	0.293767i	$0.0949088\pi$
$564$		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	0.483286	−	0.875463i	$-0.339443\pi$
$577$	−0.798556	−	0.461047i	−0.0332443	−	0.0191936i	−0.516530	+	0.856269i	$0.672777\pi$
$578$		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	$-0.560212\pi$
$587$	−9.11149			−0.376071			−0.188036	+	0.982162i	$0.560212\pi$
$588$		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	−0.266968	−	0.963705i	$-0.586022\pi$
$593$	10.5720	−	6.10377i	0.434142	−	0.250652i	0.701110	+	0.713054i	$0.252688\pi$
$594$		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	$0.214891\pi$
$601$			30.6430i			1.24995i	−0.780644	+	0.624976i	$0.785109\pi$
$602$		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	0.747014	−	0.664808i	$-0.231487\pi$
$607$	−4.98251	−	8.62996i	−0.202234	−	0.350279i	−0.949248	+	0.314529i	$0.898153\pi$
$608$		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	−0.783711	−	0.621126i	$-0.786676\pi$
$619$	3.63382	−	6.29396i	0.146055	−	0.252975i	0.929766	+	0.368150i	$0.120009\pi$
$620$		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	$-0.865591\pi$
$643$	−46.2604			−1.82433			−0.912166	+	0.409820i	$0.865591\pi$
$644$		0			0
$645$	−19.7915			−0.779290
$646$		0			0
$647$	17.3166	−	29.9932i	0.680786	−	1.17916i	−0.293955	−	0.955819i	$-0.594972\pi$
$647$	17.3166	−	29.9932i	0.680786	−	1.17916i	0.974741	−	0.223337i	$-0.0716950\pi$
$648$		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	0.0115171	−	0.999934i	$-0.496334\pi$
$661$	−21.8198	−	12.5977i	−0.848692	−	0.489993i	−0.860209	+	0.509941i	$0.829667\pi$
$662$		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	0.206485	−	0.978450i	$-0.433798\pi$
$677$	30.1066	−	17.3820i	1.15709	−	0.668046i	0.950605	+	0.310404i	$0.100464\pi$
$678$		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	0.953271	−	0.302116i	$-0.0976929\pi$
$691$	5.65157	+	9.78880i	0.214996	+	0.372383i	−0.738276	+	0.674499i	$0.764360\pi$
$692$		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	0.811208	−	0.584758i	$-0.198811\pi$
$719$	−2.70319	−	4.68205i	−0.100812	−	0.174611i	−0.912019	+	0.410147i	$0.865477\pi$
$720$		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	$-0.262974\pi$
$727$	36.5459			1.35541			0.677706	+	0.735333i	$0.262974\pi$
$728$		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	0.00535017	−	0.999986i	$-0.498297\pi$
$733$	23.6637	−	13.6622i	0.874038	−	0.504626i	0.868688	+	0.495359i	$0.164964\pi$
$734$		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	−0.756846	−	0.653593i	$-0.773261\pi$
$761$	−15.7032	+	9.06624i	−0.569240	+	0.328651i	0.187605	+	0.982244i	$0.439927\pi$
$762$		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	$-0.697757\pi$
$769$		−	45.0980i		−	1.62628i	0.582070	−	0.813139i	$-0.302243\pi$
$770$		0			0
$771$		−	2.86237i		−	0.103086i
$772$		0			0
$773$	31.2176	+	18.0235i	1.12282	+	0.648259i	0.942119	−	0.335279i	$-0.108831\pi$
$773$	31.2176	+	18.0235i	1.12282	+	0.648259i	0.180699	+	0.983538i	$0.442164\pi$
$774$		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	−0.999421	−	0.0340166i	$-0.989170\pi$
$787$	−13.1922	+	22.8496i	−0.470251	+	0.814499i	0.529170	+	0.848516i	$0.322503\pi$
$788$		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	$0.386065\pi$
$797$			52.8839i			1.87324i	−0.350344	+	0.936621i	$0.613935\pi$
$798$		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	$-0.476588\pi$
$811$	4.18532			0.146967			0.0734833	+	0.997296i	$0.476588\pi$
$812$		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	0.243016	−	0.970022i	$-0.421863\pi$
$829$	−13.6919	−	7.90504i	−0.475540	−	0.274553i	−0.718556	+	0.695469i	$0.755197\pi$
$830$		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	$-0.357167\pi$
$839$	25.1313			0.867629			0.433814	+	0.901002i	$0.357167\pi$
$840$		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	$0.181558\pi$
$853$			31.5399i			1.07991i	−0.841695	+	0.539953i	$0.818442\pi$
$854$		0			0
$855$			2.85903i			0.0977769i
$856$		0			0
$857$	−24.5514	−	14.1748i	−0.838660	−	0.484201i	0.0181483	−	0.999835i	$-0.494223\pi$
$857$	−24.5514	−	14.1748i	−0.838660	−	0.484201i	−0.856809	+	0.515635i	$0.827556\pi$
$858$		0			0
$859$	−17.3399	−	30.0336i	−0.591630	−	1.02473i	−0.994013	−	0.109262i	$-0.965151\pi$
$859$	−17.3399	−	30.0336i	−0.591630	−	1.02473i	0.402383	−	0.915471i	$-0.368182\pi$
$860$		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	$0.0242048\pi$
$881$			4.50973i			0.151937i	−0.997110	+	0.0759684i	$0.975795\pi$
$882$		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	0.823326	−	0.567569i	$-0.192116\pi$
$887$	−2.37863	−	4.11990i	−0.0798665	−	0.138333i	−0.903192	+	0.429236i	$0.858783\pi$
$888$		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	$0.670604\pi$
$929$	−46.0423	+	26.5825i	−1.51060	+	0.872144i	−0.999923	+	0.0123696i	$0.996063\pi$
$930$		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	$0.0898787\pi$
$937$			17.0577i			0.557250i	−0.960400	+	0.278625i	$0.910121\pi$
$938$		0			0
$939$		−	25.9505i		−	0.846861i
$940$		0			0
$941$	14.2306	+	8.21605i	0.463905	+	0.267836i	0.713685	−	0.700467i	$-0.247025\pi$
$941$	14.2306	+	8.21605i	0.463905	+	0.267836i	−0.249780	+	0.968303i	$0.580358\pi$
$942$		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	$0.0519667\pi$
$971$	19.7594	+	34.2243i	0.634110	+	1.09831i	−0.352593	+	0.935777i	$0.614700\pi$
$972$		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	$-0.571495\pi$
$983$	22.9788	−	39.8004i	0.732909	−	1.26944i	0.955635	−	0.294554i	$-0.0951712\pi$
$984$		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	0.639567	−	0.768735i	$-0.279114\pi$
$997$	9.27071	+	5.35244i	0.293606	+	0.169514i	−0.345961	+	0.938249i	$0.612447\pi$
$998$		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.t.31.2		8
4.3	odd	2		2352.2.bl.o.31.2		8
7.2	even	3		2352.2.bl.r.607.3		8
7.3	odd	6		2352.2.b.l.1567.6	yes	8
7.4	even	3		2352.2.b.k.1567.3	✓	8
7.5	odd	6		2352.2.bl.o.607.2		8
7.6	odd	2		2352.2.bl.q.31.3		8
21.11	odd	6		7056.2.b.x.1567.6		8
21.17	even	6		7056.2.b.w.1567.3		8
28.3	even	6		2352.2.b.k.1567.6	yes	8
28.11	odd	6		2352.2.b.l.1567.3	yes	8
28.19	even	6	inner	2352.2.bl.t.607.2		8
28.23	odd	6		2352.2.bl.q.607.3		8
28.27	even	2		2352.2.bl.r.31.3		8
84.11	even	6		7056.2.b.w.1567.6		8
84.59	odd	6		7056.2.b.x.1567.3		8

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

L-functions

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