LMFDB - Embedded newform 1408.2.i.b.351.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1408,2,Mod(351,1408)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1408, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("1408.351");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1408 = 2^{7} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1408.i (of order $4$, 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:	$11.2429366046$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 176)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			351.2
Character	$\chi$	$=$	1408.351
Dual form			1408.2.i.b.1055.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.21950 + 2.21950i) q^{3} +(0.858137 - 0.858137i) q^{5} -1.49353i q^{7} -6.85234i q^{9} +O(q^{10})$	\(q+(-2.21950 + 2.21950i) q^{3} +(0.858137 - 0.858137i) q^{5} -1.49353i q^{7} -6.85234i q^{9} +(-1.33187 + 3.03745i) q^{11} +(2.98420 - 2.98420i) q^{13} +3.80927i q^{15} +2.42587i q^{17} +(-3.38116 - 3.38116i) q^{19} +(3.31490 + 3.31490i) q^{21} +0.410124 q^{23} +3.52720i q^{25} +(8.55026 + 8.55026i) q^{27} +(-6.31351 + 6.31351i) q^{29} +8.16683i q^{31} +(-3.78554 - 9.69770i) q^{33} +(-1.28166 - 1.28166i) q^{35} +(-1.37339 + 1.37339i) q^{37} +13.2469i q^{39} -4.70505 q^{41} +(2.16775 - 2.16775i) q^{43} +(-5.88024 - 5.88024i) q^{45} +0.963926i q^{47} +4.76936 q^{49} +(-5.38421 - 5.38421i) q^{51} +(-4.60851 + 4.60851i) q^{53} +(1.46363 + 3.74948i) q^{55} +15.0090 q^{57} +(-2.45022 - 2.45022i) q^{59} +(6.00102 - 6.00102i) q^{61} -10.2342 q^{63} -5.12171i q^{65} +(-5.95476 + 5.95476i) q^{67} +(-0.910270 + 0.910270i) q^{69} -12.2273 q^{71} -16.6606 q^{73} +(-7.82862 - 7.82862i) q^{75} +(4.53654 + 1.98919i) q^{77} +14.1682 q^{79} -17.3975 q^{81} +(1.12330 + 1.12330i) q^{83} +(2.08173 + 2.08173i) q^{85} -28.0256i q^{87} +5.40970i q^{89} +(-4.45701 - 4.45701i) q^{91} +(-18.1263 - 18.1263i) q^{93} -5.80300 q^{95} -5.47168 q^{97} +(20.8137 + 9.12641i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} + 4 q^{5}+O(q^{10}) $ 44 * q + 4 * q^3 + 4 * q^5	$ 44 q + 4 q^{3} + 4 q^{5} + 6 q^{11} - 24 q^{23} - 8 q^{27} - 4 q^{33} + 20 q^{37} - 28 q^{45} - 28 q^{49} - 12 q^{53} - 36 q^{55} + 20 q^{59} - 36 q^{67} + 16 q^{69} - 40 q^{71} - 60 q^{75} - 4 q^{77} - 20 q^{81} - 56 q^{91} - 8 q^{93} - 8 q^{97} + 42 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 + 4 * q^5 + 6 * q^11 - 24 * q^23 - 8 * q^27 - 4 * q^33 + 20 * q^37 - 28 * q^45 - 28 * q^49 - 12 * q^53 - 36 * q^55 + 20 * q^59 - 36 * q^67 + 16 * q^69 - 40 * q^71 - 60 * q^75 - 4 * q^77 - 20 * q^81 - 56 * q^91 - 8 * q^93 - 8 * q^97 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1408\mathbb{Z}\right)^\times$.

$n$	$133$	$639$	$1025$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

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
$3$	−2.21950	+	2.21950i	−1.28143	+	1.28143i	−0.341572	+	0.939856i	$0.610959\pi$
$3$	−2.21950	+	2.21950i	−1.28143	+	1.28143i	−0.939856	+	0.341572i	$0.889041\pi$
$4$		0			0
$5$	0.858137	−	0.858137i	0.383770	−	0.383770i	−0.488688	−	0.872459i	$-0.662524\pi$
$5$	0.858137	−	0.858137i	0.383770	−	0.383770i	0.872459	+	0.488688i	$0.162524\pi$
$6$		0			0
$7$		−	1.49353i		−	0.564503i	−0.959340	−	0.282251i	$-0.908919\pi$
$7$		−	1.49353i		−	0.564503i	0.959340	−	0.282251i	$-0.0910812\pi$
$8$		0			0
$9$		−	6.85234i		−	2.28411i
$10$		0			0
$11$	−1.33187	+	3.03745i	−0.401573	+	0.915827i
$11$	−1.33187	+	3.03745i	−0.401573	+	0.915827i
$12$		0			0
$13$	2.98420	−	2.98420i	0.827669	−	0.827669i	−0.159525	−	0.987194i	$-0.550996\pi$
$13$	2.98420	−	2.98420i	0.827669	−	0.827669i	0.987194	+	0.159525i	$0.0509962\pi$
$14$		0			0
$15$			3.80927i			0.983548i
$16$		0			0
$17$			2.42587i			0.588359i	0.955750	+	0.294180i	$0.0950464\pi$
$17$			2.42587i			0.588359i	−0.955750	+	0.294180i	$0.904954\pi$
$18$		0			0
$19$	−3.38116	−	3.38116i	−0.775691	−	0.775691i	0.203404	−	0.979095i	$-0.434800\pi$
$19$	−3.38116	−	3.38116i	−0.775691	−	0.775691i	−0.979095	+	0.203404i	$0.934800\pi$
$20$		0			0
$21$	3.31490	+	3.31490i	0.723370	+	0.723370i
$22$		0			0
$23$	0.410124			0.0855169			0.0427584	−	0.999085i	$-0.486385\pi$
$23$	0.410124			0.0855169			0.0427584	+	0.999085i	$0.486385\pi$
$24$		0			0
$25$			3.52720i			0.705440i
$26$		0			0
$27$	8.55026	+	8.55026i	1.64550	+	1.64550i
$28$		0			0
$29$	−6.31351	+	6.31351i	−1.17239	+	1.17239i	−0.190751	+	0.981638i	$0.561092\pi$
$29$	−6.31351	+	6.31351i	−1.17239	+	1.17239i	−0.981638	+	0.190751i	$0.938908\pi$
$30$		0			0
$31$			8.16683i			1.46681i	0.679794	+	0.733403i	$0.262069\pi$
$31$			8.16683i			1.46681i	−0.679794	+	0.733403i	$0.737931\pi$
$32$		0			0
$33$	−3.78554	−	9.69770i	−0.658978	−	1.68815i
$34$		0			0
$35$	−1.28166	−	1.28166i	−0.216640	−	0.216640i
$36$		0			0
$37$	−1.37339	+	1.37339i	−0.225784	+	0.225784i	−0.810929	−	0.585145i	$-0.801038\pi$
$37$	−1.37339	+	1.37339i	−0.225784	+	0.225784i	0.585145	+	0.810929i	$0.301038\pi$
$38$		0			0
$39$			13.2469i			2.12120i
$40$		0			0
$41$	−4.70505			−0.734806			−0.367403	−	0.930062i	$-0.619753\pi$
$41$	−4.70505			−0.734806			−0.367403	+	0.930062i	$0.619753\pi$
$42$		0			0
$43$	2.16775	−	2.16775i	0.330578	−	0.330578i	−0.522228	−	0.852806i	$-0.674899\pi$
$43$	2.16775	−	2.16775i	0.330578	−	0.330578i	0.852806	+	0.522228i	$0.174899\pi$
$44$		0			0
$45$	−5.88024	−	5.88024i	−0.876575	−	0.876575i
$46$		0			0
$47$			0.963926i			0.140603i	0.997526	+	0.0703016i	$0.0223962\pi$
$47$			0.963926i			0.140603i	−0.997526	+	0.0703016i	$0.977604\pi$
$48$		0			0
$49$	4.76936			0.681336
$50$		0			0
$51$	−5.38421	−	5.38421i	−0.753940	−	0.753940i
$52$		0			0
$53$	−4.60851	+	4.60851i	−0.633027	+	0.633027i	−0.948826	−	0.315799i	$-0.897727\pi$
$53$	−4.60851	+	4.60851i	−0.633027	+	0.633027i	0.315799	+	0.948826i	$0.397727\pi$
$54$		0			0
$55$	1.46363	+	3.74948i	0.197355	+	0.505579i
$56$		0			0
$57$	15.0090			1.98798
$58$		0			0
$59$	−2.45022	−	2.45022i	−0.318992	−	0.318992i	0.529388	−	0.848380i	$-0.322422\pi$
$59$	−2.45022	−	2.45022i	−0.318992	−	0.318992i	−0.848380	+	0.529388i	$0.822422\pi$
$60$		0			0
$61$	6.00102	−	6.00102i	0.768352	−	0.768352i	−0.209464	−	0.977816i	$-0.567172\pi$
$61$	6.00102	−	6.00102i	0.768352	−	0.768352i	0.977816	+	0.209464i	$0.0671719\pi$
$62$		0			0
$63$	−10.2342			−1.28939
$64$		0			0
$65$		−	5.12171i		−	0.635270i
$66$		0			0
$67$	−5.95476	+	5.95476i	−0.727490	+	0.727490i	−0.970119	−	0.242629i	$-0.921990\pi$
$67$	−5.95476	+	5.95476i	−0.727490	+	0.727490i	0.242629	+	0.970119i	$0.421990\pi$
$68$		0			0
$69$	−0.910270	+	0.910270i	−0.109584	+	0.109584i
$70$		0			0
$71$	−12.2273			−1.45112			−0.725559	−	0.688160i	$-0.758419\pi$
$71$	−12.2273			−1.45112			−0.725559	+	0.688160i	$0.758419\pi$
$72$		0			0
$73$	−16.6606			−1.94998			−0.974989	−	0.222255i	$-0.928658\pi$
$73$	−16.6606			−1.94998			−0.974989	+	0.222255i	$0.928658\pi$
$74$		0			0
$75$	−7.82862	−	7.82862i	−0.903971	−	0.903971i
$76$		0			0
$77$	4.53654	+	1.98919i	0.516987	+	0.226689i
$78$		0			0
$79$	14.1682			1.59404			0.797021	−	0.603952i	$-0.206408\pi$
$79$	14.1682			1.59404			0.797021	+	0.603952i	$0.206408\pi$
$80$		0			0
$81$	−17.3975			−1.93306
$82$		0			0
$83$	1.12330	+	1.12330i	0.123298	+	0.123298i	0.766063	−	0.642765i	$-0.222213\pi$
$83$	1.12330	+	1.12330i	0.123298	+	0.123298i	−0.642765	+	0.766063i	$0.722213\pi$
$84$		0			0
$85$	2.08173	+	2.08173i	0.225795	+	0.225795i
$86$		0			0
$87$		−	28.0256i		−	3.00466i
$88$		0			0
$89$			5.40970i			0.573427i	0.958016	+	0.286714i	$0.0925628\pi$
$89$			5.40970i			0.573427i	−0.958016	+	0.286714i	$0.907437\pi$
$90$		0			0
$91$	−4.45701	−	4.45701i	−0.467222	−	0.467222i
$92$		0			0
$93$	−18.1263	−	18.1263i	−1.87961	−	1.87961i
$94$		0			0
$95$	−5.80300			−0.595375
$96$		0			0
$97$	−5.47168			−0.555564			−0.277782	−	0.960644i	$-0.589599\pi$
$97$	−5.47168			−0.555564			−0.277782	+	0.960644i	$0.589599\pi$
$98$		0			0
$99$	20.8137	+	9.12641i	2.09185	+	0.917239i
$100$		0			0
$101$	1.92308	+	1.92308i	0.191353	+	0.191353i	0.796281	−	0.604927i	$-0.206798\pi$
$101$	1.92308	+	1.92308i	0.191353	+	0.191353i	−0.604927	+	0.796281i	$0.706798\pi$
$102$		0			0
$103$	−7.23916			−0.713296			−0.356648	−	0.934239i	$-0.616080\pi$
$103$	−7.23916			−0.713296			−0.356648	+	0.934239i	$0.616080\pi$
$104$		0			0
$105$	5.68927			0.555216
$106$		0			0
$107$	0.355487	−	0.355487i	0.0343663	−	0.0343663i	−0.689715	−	0.724081i	$-0.742264\pi$
$107$	0.355487	−	0.355487i	0.0343663	−	0.0343663i	0.724081	+	0.689715i	$0.242264\pi$
$108$		0			0
$109$	3.33902	−	3.33902i	0.319820	−	0.319820i	−0.528878	−	0.848698i	$-0.677387\pi$
$109$	3.33902	−	3.33902i	0.319820	−	0.319820i	0.848698	+	0.528878i	$0.177387\pi$
$110$		0			0
$111$		−	6.09647i		−	0.578652i
$112$		0			0
$113$	−13.5313			−1.27292			−0.636460	−	0.771310i	$-0.719602\pi$
$113$	−13.5313			−1.27292			−0.636460	+	0.771310i	$0.719602\pi$
$114$		0			0
$115$	0.351943	−	0.351943i	0.0328188	−	0.0328188i
$116$		0			0
$117$	−20.4488	−	20.4488i	−1.89049	−	1.89049i
$118$		0			0
$119$	3.62312			0.332131
$120$		0			0
$121$	−7.45225	−	8.09098i	−0.677478	−	0.735543i
$122$		0			0
$123$	10.4429	−	10.4429i	0.941600	−	0.941600i
$124$		0			0
$125$	7.31751	+	7.31751i	0.654498	+	0.654498i
$126$		0			0
$127$	−11.0003			−0.976116			−0.488058	−	0.872811i	$-0.662295\pi$
$127$	−11.0003			−0.976116			−0.488058	+	0.872811i	$0.662295\pi$
$128$		0			0
$129$			9.62262i			0.847224i
$130$		0			0
$131$	−5.18084	−	5.18084i	−0.452652	−	0.452652i	0.443582	−	0.896234i	$-0.353707\pi$
$131$	−5.18084	−	5.18084i	−0.452652	−	0.452652i	−0.896234	+	0.443582i	$0.853707\pi$
$132$		0			0
$133$	−5.04988	+	5.04988i	−0.437880	+	0.437880i
$134$		0			0
$135$	14.6746			1.26299
$136$		0			0
$137$			17.4691i			1.49249i	0.665673	+	0.746244i	$0.268145\pi$
$137$			17.4691i			1.49249i	−0.665673	+	0.746244i	$0.731855\pi$
$138$		0			0
$139$	−8.30153	+	8.30153i	−0.704127	+	0.704127i	−0.965294	−	0.261167i	$-0.915893\pi$
$139$	−8.30153	+	8.30153i	−0.704127	+	0.704127i	0.261167	+	0.965294i	$0.415893\pi$
$140$		0			0
$141$	−2.13943	−	2.13943i	−0.180173	−	0.180173i
$142$		0			0
$143$	5.08981	+	13.0389i	0.425632	+	1.09037i
$144$		0			0
$145$			10.8357i			0.899857i
$146$		0			0
$147$	−10.5856	+	10.5856i	−0.873083	+	0.873083i
$148$		0			0
$149$	−1.20078	−	1.20078i	−0.0983720	−	0.0983720i	0.656208	−	0.754580i	$-0.272159\pi$
$149$	−1.20078	−	1.20078i	−0.0983720	−	0.0983720i	−0.754580	+	0.656208i	$0.772159\pi$
$150$		0			0
$151$		−	13.1565i		−	1.07066i	−0.844642	−	0.535332i	$-0.820187\pi$
$151$		−	13.1565i		−	1.07066i	0.844642	−	0.535332i	$-0.179813\pi$
$152$		0			0
$153$	16.6229			1.34388
$154$		0			0
$155$	7.00826	+	7.00826i	0.562917	+	0.562917i
$156$		0			0
$157$	12.6073	+	12.6073i	1.00617	+	1.00617i	0.999981	+	0.00619243i	$0.00197112\pi$
$157$	12.6073	+	12.6073i	1.00617	+	1.00617i	0.00619243	+	0.999981i	$0.498029\pi$
$158$		0			0
$159$		−	20.4571i		−	1.62236i
$160$		0			0
$161$		−	0.612535i		−	0.0482745i
$162$		0			0
$163$	−7.27289	+	7.27289i	−0.569657	+	0.569657i	−0.932032	−	0.362375i	$-0.881966\pi$
$163$	−7.27289	+	7.27289i	−0.569657	+	0.569657i	0.362375	+	0.932032i	$0.381966\pi$
$164$		0			0
$165$	−11.5705	−	5.07344i	−0.900760	−	0.394967i
$166$		0			0
$167$			0.838210i			0.0648627i	0.999474	+	0.0324313i	$0.0103250\pi$
$167$			0.838210i			0.0648627i	−0.999474	+	0.0324313i	$0.989675\pi$
$168$		0			0
$169$		−	4.81094i		−	0.370073i
$170$		0			0
$171$	−23.1689	+	23.1689i	−1.77177	+	1.77177i
$172$		0			0
$173$	−4.71078	+	4.71078i	−0.358154	+	0.358154i	−0.863132	−	0.504978i	$-0.831501\pi$
$173$	−4.71078	+	4.71078i	−0.358154	+	0.358154i	0.504978	+	0.863132i	$0.331501\pi$
$174$		0			0
$175$	5.26800			0.398223
$176$		0			0
$177$	10.8765			0.817529
$178$		0			0
$179$	5.96080	−	5.96080i	0.445531	−	0.445531i	−0.448335	−	0.893866i	$-0.647983\pi$
$179$	5.96080	−	5.96080i	0.445531	−	0.445531i	0.893866	+	0.448335i	$0.147983\pi$
$180$		0			0
$181$	−4.89894	+	4.89894i	−0.364135	+	0.364135i	−0.865333	−	0.501198i	$-0.832893\pi$
$181$	−4.89894	+	4.89894i	−0.364135	+	0.364135i	0.501198	+	0.865333i	$0.332893\pi$
$182$		0			0
$183$			26.6385i			1.96918i
$184$		0			0
$185$			2.35711i			0.173298i
$186$		0			0
$187$	−7.36846	−	3.23094i	−0.538835	−	0.236269i
$188$		0			0
$189$	12.7701	−	12.7701i	0.928888	−	0.928888i
$190$		0			0
$191$		−	10.9855i		−	0.794880i	−0.917628	−	0.397440i	$-0.869899\pi$
$191$		−	10.9855i		−	0.794880i	0.917628	−	0.397440i	$-0.130101\pi$
$192$		0			0
$193$			1.35055i			0.0972150i	0.998818	+	0.0486075i	$0.0154783\pi$
$193$			1.35055i			0.0972150i	−0.998818	+	0.0486075i	$0.984522\pi$
$194$		0			0
$195$	11.3676	+	11.3676i	0.814052	+	0.814052i
$196$		0			0
$197$	11.6340	+	11.6340i	0.828889	+	0.828889i	0.987363	−	0.158474i	$-0.0506573\pi$
$197$	11.6340	+	11.6340i	0.828889	+	0.828889i	−0.158474	+	0.987363i	$0.550657\pi$
$198$		0			0
$199$	9.09752			0.644906			0.322453	−	0.946585i	$-0.395493\pi$
$199$	9.09752			0.644906			0.322453	+	0.946585i	$0.395493\pi$
$200$		0			0
$201$		−	26.4331i		−	1.86445i
$202$		0			0
$203$	9.42944	+	9.42944i	0.661817	+	0.661817i
$204$		0			0
$205$	−4.03758	+	4.03758i	−0.281997	+	0.281997i
$206$		0			0
$207$		−	2.81031i		−	0.195330i
$208$		0			0
$209$	14.7734	−	5.76686i	1.02190	−	0.398902i
$210$		0			0
$211$	−13.2222	−	13.2222i	−0.910252	−	0.910252i	0.0860401	−	0.996292i	$-0.472579\pi$
$211$	−13.2222	−	13.2222i	−0.910252	−	0.910252i	−0.996292	+	0.0860401i	$0.972579\pi$
$212$		0			0
$213$	27.1385	−	27.1385i	1.85950	−	1.85950i
$214$		0			0
$215$		−	3.72045i		−	0.253732i
$216$		0			0
$217$	12.1974			0.828017
$218$		0			0
$219$	36.9782	−	36.9782i	2.49875	−	2.49875i
$220$		0			0
$221$	7.23928	+	7.23928i	0.486967	+	0.486967i
$222$		0			0
$223$			13.7736i			0.922350i	0.887309	+	0.461175i	$0.152572\pi$
$223$			13.7736i			0.922350i	−0.887309	+	0.461175i	$0.847428\pi$
$224$		0			0
$225$	24.1696			1.61131
$226$		0			0
$227$	9.63854	+	9.63854i	0.639732	+	0.639732i	0.950489	−	0.310757i	$-0.100583\pi$
$227$	9.63854	+	9.63854i	0.639732	+	0.639732i	−0.310757	+	0.950489i	$0.600583\pi$
$228$		0			0
$229$	7.67274	−	7.67274i	0.507029	−	0.507029i	−0.406584	−	0.913613i	$-0.633280\pi$
$229$	7.67274	−	7.67274i	0.507029	−	0.507029i	0.913613	+	0.406584i	$0.133280\pi$
$230$		0			0
$231$	−14.4838	+	5.65384i	−0.952967	+	0.371995i
$232$		0			0
$233$	15.3491			1.00555			0.502775	−	0.864417i	$-0.332312\pi$
$233$	15.3491			1.00555			0.502775	+	0.864417i	$0.332312\pi$
$234$		0			0
$235$	0.827181	+	0.827181i	0.0539593	+	0.0539593i
$236$		0			0
$237$	−31.4462	+	31.4462i	−2.04265	+	2.04265i
$238$		0			0
$239$	−10.1198			−0.654593			−0.327296	−	0.944922i	$-0.606138\pi$
$239$	−10.1198			−0.654593			−0.327296	+	0.944922i	$0.606138\pi$
$240$		0			0
$241$			11.7286i			0.755506i	0.925906	+	0.377753i	$0.123303\pi$
$241$			11.7286i			0.755506i	−0.925906	+	0.377753i	$0.876697\pi$
$242$		0			0
$243$	12.9630	−	12.9630i	0.831578	−	0.831578i
$244$		0			0
$245$	4.09276	−	4.09276i	0.261477	−	0.261477i
$246$		0			0
$247$	−20.1801			−1.28403
$248$		0			0
$249$	−4.98631			−0.315995
$250$		0			0
$251$	14.6245	+	14.6245i	0.923089	+	0.923089i	0.997247	−	0.0741577i	$-0.0236268\pi$
$251$	14.6245	+	14.6245i	0.923089	+	0.923089i	−0.0741577	+	0.997247i	$0.523627\pi$
$252$		0			0
$253$	−0.546232	+	1.24573i	−0.0343413	+	0.0783186i
$254$		0			0
$255$	−9.24077			−0.578680
$256$		0			0
$257$	7.32370			0.456840			0.228420	−	0.973563i	$-0.426644\pi$
$257$	7.32370			0.456840			0.228420	+	0.973563i	$0.426644\pi$
$258$		0			0
$259$	2.05121	+	2.05121i	0.127456	+	0.127456i
$260$		0			0
$261$	43.2623	+	43.2623i	2.67787	+	2.67787i
$262$		0			0
$263$		−	5.97839i		−	0.368643i	−0.982866	−	0.184322i	$-0.940991\pi$
$263$		−	5.97839i		−	0.368643i	0.982866	−	0.184322i	$-0.0590088\pi$
$264$		0			0
$265$			7.90946i			0.485874i
$266$		0			0
$267$	−12.0068	−	12.0068i	−0.734805	−	0.734805i
$268$		0			0
$269$	9.23322	+	9.23322i	0.562959	+	0.562959i	0.930147	−	0.367187i	$-0.119679\pi$
$269$	9.23322	+	9.23322i	0.562959	+	0.562959i	−0.367187	+	0.930147i	$0.619679\pi$
$270$		0			0
$271$	21.2645			1.29172			0.645862	−	0.763454i	$-0.276498\pi$
$271$	21.2645			1.29172			0.645862	+	0.763454i	$0.276498\pi$
$272$		0			0
$273$	19.7846			1.19742
$274$		0			0
$275$	−10.7137	−	4.69777i	−0.646061	−	0.283286i
$276$		0			0
$277$	−3.80448	−	3.80448i	−0.228589	−	0.228589i	0.583514	−	0.812103i	$-0.301677\pi$
$277$	−3.80448	−	3.80448i	−0.228589	−	0.228589i	−0.812103	+	0.583514i	$0.801677\pi$
$278$		0			0
$279$	55.9619			3.35035
$280$		0			0
$281$	−22.3741			−1.33473			−0.667364	−	0.744732i	$-0.732577\pi$
$281$	−22.3741			−1.33473			−0.667364	+	0.744732i	$0.732577\pi$
$282$		0			0
$283$	−18.3167	+	18.3167i	−1.08882	+	1.08882i	−0.0931660	+	0.995651i	$0.529699\pi$
$283$	−18.3167	+	18.3167i	−1.08882	+	1.08882i	−0.995651	+	0.0931660i	$0.970301\pi$
$284$		0			0
$285$	12.8797	−	12.8797i	0.762930	−	0.762930i
$286$		0			0
$287$			7.02716i			0.414800i
$288$		0			0
$289$	11.1152			0.653833
$290$		0			0
$291$	12.1444	−	12.1444i	0.711916	−	0.711916i
$292$		0			0
$293$	−17.9765	−	17.9765i	−1.05020	−	1.05020i	−0.998672	−	0.0515240i	$-0.983592\pi$
$293$	−17.9765	−	17.9765i	−1.05020	−	1.05020i	−0.0515240	−	0.998672i	$-0.516408\pi$
$294$		0			0
$295$	−4.20525			−0.244839
$296$		0			0
$297$	−37.3588	+	14.5832i	−2.16778	+	0.846203i
$298$		0			0
$299$	1.22389	−	1.22389i	0.0707797	−	0.0707797i
$300$		0			0
$301$	−3.23761	−	3.23761i	−0.186612	−	0.186612i
$302$		0			0
$303$	−8.53653			−0.490411
$304$		0			0
$305$		−	10.2994i		−	0.589742i
$306$		0			0
$307$	−1.42901	−	1.42901i	−0.0815581	−	0.0815581i	0.665151	−	0.746709i	$-0.268367\pi$
$307$	−1.42901	−	1.42901i	−0.0815581	−	0.0815581i	−0.746709	+	0.665151i	$0.768367\pi$
$308$		0			0
$309$	16.0673	−	16.0673i	0.914037	−	0.914037i
$310$		0			0
$311$	12.6265			0.715981			0.357991	−	0.933725i	$-0.383462\pi$
$311$	12.6265			0.715981			0.357991	+	0.933725i	$0.383462\pi$
$312$		0			0
$313$		−	4.99088i		−	0.282101i	−0.990002	−	0.141050i	$-0.954952\pi$
$313$		−	4.99088i		−	0.282101i	0.990002	−	0.141050i	$-0.0450480\pi$
$314$		0			0
$315$	−8.78235	+	8.78235i	−0.494829	+	0.494829i
$316$		0			0
$317$	10.4127	+	10.4127i	0.584835	+	0.584835i	0.936228	−	0.351393i	$-0.114292\pi$
$317$	10.4127	+	10.4127i	0.584835	+	0.584835i	−0.351393	+	0.936228i	$0.614292\pi$
$318$		0			0
$319$	−10.7682	−	27.5858i	−0.602905	−	1.54451i
$320$		0			0
$321$			1.57801i			0.0880757i
$322$		0			0
$323$	8.20225	−	8.20225i	0.456385	−	0.456385i
$324$		0			0
$325$	10.5259	+	10.5259i	0.583871	+	0.583871i
$326$		0			0
$327$			14.8219i			0.819653i
$328$		0			0
$329$	1.43966			0.0793709
$330$		0			0
$331$	−13.8482	−	13.8482i	−0.761169	−	0.761169i	0.215365	−	0.976534i	$-0.430906\pi$
$331$	−13.8482	−	13.8482i	−0.761169	−	0.761169i	−0.976534	+	0.215365i	$0.930906\pi$
$332$		0			0
$333$	9.41094	+	9.41094i	0.515716	+	0.515716i
$334$		0			0
$335$			10.2200i			0.558378i
$336$		0			0
$337$		−	4.99025i		−	0.271836i	−0.990720	−	0.135918i	$-0.956602\pi$
$337$		−	4.99025i		−	0.271836i	0.990720	−	0.135918i	$-0.0433984\pi$
$338$		0			0
$339$	30.0327	−	30.0327i	1.63115	−	1.63115i
$340$		0			0
$341$	−24.8064	−	10.8771i	−1.34334	−	0.589031i
$342$		0			0
$343$		−	17.5779i		−	0.949119i
$344$		0			0
$345$			1.56227i			0.0841099i
$346$		0			0
$347$	−4.10880	+	4.10880i	−0.220572	+	0.220572i	−0.808739	−	0.588167i	$-0.799850\pi$
$347$	−4.10880	+	4.10880i	−0.220572	+	0.220572i	0.588167	+	0.808739i	$0.299850\pi$
$348$		0			0
$349$	4.14268	−	4.14268i	0.221753	−	0.221753i	−0.587484	−	0.809236i	$-0.699881\pi$
$349$	4.14268	−	4.14268i	0.221753	−	0.221753i	0.809236	+	0.587484i	$0.199881\pi$
$350$		0			0
$351$	51.0314			2.72386
$352$		0			0
$353$	−18.1771			−0.967469			−0.483735	−	0.875215i	$-0.660720\pi$
$353$	−18.1771			−0.967469			−0.483735	+	0.875215i	$0.660720\pi$
$354$		0			0
$355$	−10.4927	+	10.4927i	−0.556896	+	0.556896i
$356$		0			0
$357$	−8.04150	+	8.04150i	−0.425601	+	0.425601i
$358$		0			0
$359$			29.6636i			1.56559i	0.622282	+	0.782793i	$0.286206\pi$
$359$			29.6636i			1.56559i	−0.622282	+	0.782793i	$0.713794\pi$
$360$		0			0
$361$			3.86449i			0.203394i
$362$		0			0
$363$	34.4982	+	1.41765i	1.81068	+	0.0744072i
$364$		0			0
$365$	−14.2971	+	14.2971i	−0.748344	+	0.748344i
$366$		0			0
$367$			21.4620i			1.12031i	0.828389	+	0.560154i	$0.189258\pi$
$367$			21.4620i			1.12031i	−0.828389	+	0.560154i	$0.810742\pi$
$368$		0			0
$369$			32.2406i			1.67838i
$370$		0			0
$371$	6.88296	+	6.88296i	0.357346	+	0.357346i
$372$		0			0
$373$	−1.03844	−	1.03844i	−0.0537683	−	0.0537683i	0.679711	−	0.733480i	$-0.262105\pi$
$373$	−1.03844	−	1.03844i	−0.0537683	−	0.0537683i	−0.733480	+	0.679711i	$0.762105\pi$
$374$		0			0
$375$	−32.4824			−1.67738
$376$		0			0
$377$			37.6816i			1.94070i
$378$		0			0
$379$	−12.3476	−	12.3476i	−0.634256	−	0.634256i	0.314877	−	0.949133i	$-0.398037\pi$
$379$	−12.3476	−	12.3476i	−0.634256	−	0.634256i	−0.949133	+	0.314877i	$0.898037\pi$
$380$		0			0
$381$	24.4151	−	24.4151i	1.25082	−	1.25082i
$382$		0			0
$383$		−	17.7916i		−	0.909107i	−0.890720	−	0.454553i	$-0.849799\pi$
$383$		−	17.7916i		−	0.909107i	0.890720	−	0.454553i	$-0.150201\pi$
$384$		0			0
$385$	5.59997	−	2.18598i	0.285401	−	0.111408i
$386$		0			0
$387$	−14.8541	−	14.8541i	−0.755078	−	0.755078i
$388$		0			0
$389$	−25.7721	+	25.7721i	−1.30670	+	1.30670i	−0.382911	+	0.923785i	$0.625078\pi$
$389$	−25.7721	+	25.7721i	−1.30670	+	1.30670i	−0.923785	+	0.382911i	$0.874922\pi$
$390$		0			0
$391$			0.994908i			0.0503146i
$392$		0			0
$393$	22.9977			1.16008
$394$		0			0
$395$	12.1582	−	12.1582i	0.611746	−	0.611746i
$396$		0			0
$397$	−1.75280	−	1.75280i	−0.0879707	−	0.0879707i	0.661752	−	0.749723i	$-0.269813\pi$
$397$	−1.75280	−	1.75280i	−0.0879707	−	0.0879707i	−0.749723	+	0.661752i	$0.769813\pi$
$398$		0			0
$399$		−	22.4164i		−	1.12222i
$400$		0			0
$401$	−6.43741			−0.321469			−0.160734	−	0.986998i	$-0.551386\pi$
$401$	−6.43741			−0.321469			−0.160734	+	0.986998i	$0.551386\pi$
$402$		0			0
$403$	24.3715	+	24.3715i	1.21403	+	1.21403i
$404$		0			0
$405$	−14.9295	+	14.9295i	−0.741851	+	0.741851i
$406$		0			0
$407$	−2.34243	−	6.00078i	−0.116110	−	0.297448i
$408$		0			0
$409$	6.19702			0.306423			0.153212	−	0.988193i	$-0.451038\pi$
$409$	6.19702			0.306423			0.153212	+	0.988193i	$0.451038\pi$
$410$		0			0
$411$	−38.7727	−	38.7727i	−1.91252	−	1.91252i
$412$		0			0
$413$	−3.65949	+	3.65949i	−0.180072	+	0.180072i
$414$		0			0
$415$	1.92789			0.0946362
$416$		0			0
$417$		−	36.8505i		−	1.80458i
$418$		0			0
$419$	−7.57486	+	7.57486i	−0.370056	+	0.370056i	−0.867498	−	0.497441i	$-0.834273\pi$
$419$	−7.57486	+	7.57486i	−0.370056	+	0.370056i	0.497441	+	0.867498i	$0.334273\pi$
$420$		0			0
$421$	23.8701	−	23.8701i	1.16336	−	1.16336i	0.179621	−	0.983736i	$-0.442513\pi$
$421$	23.8701	−	23.8701i	1.16336	−	1.16336i	0.983736	−	0.179621i	$-0.0574873\pi$
$422$		0			0
$423$	6.60515			0.321153
$424$		0			0
$425$	−8.55653			−0.415052
$426$		0			0
$427$	−8.96273	−	8.96273i	−0.433737	−	0.433737i
$428$		0			0
$429$	−40.2367	−	17.6431i	−1.94265	−	0.851816i
$430$		0			0
$431$	9.14013			0.440264			0.220132	−	0.975470i	$-0.429351\pi$
$431$	9.14013			0.440264			0.220132	+	0.975470i	$0.429351\pi$
$432$		0			0
$433$	−3.48453			−0.167456			−0.0837280	−	0.996489i	$-0.526683\pi$
$433$	−3.48453			−0.167456			−0.0837280	+	0.996489i	$0.526683\pi$
$434$		0			0
$435$	−24.0498	−	24.0498i	−1.15310	−	1.15310i
$436$		0			0
$437$	−1.38670	−	1.38670i	−0.0663347	−	0.0663347i
$438$		0			0
$439$		−	16.6458i		−	0.794462i	−0.917719	−	0.397231i	$-0.869971\pi$
$439$		−	16.6458i		−	0.794462i	0.917719	−	0.397231i	$-0.130029\pi$
$440$		0			0
$441$		−	32.6812i		−	1.55625i
$442$		0			0
$443$	0.864881	+	0.864881i	0.0410917	+	0.0410917i	0.727354	−	0.686262i	$-0.240750\pi$
$443$	0.864881	+	0.864881i	0.0410917	+	0.0410917i	−0.686262	+	0.727354i	$0.740750\pi$
$444$		0			0
$445$	4.64226	+	4.64226i	0.220064	+	0.220064i
$446$		0			0
$447$	5.33027			0.252113
$448$		0			0
$449$	6.75878			0.318967			0.159483	−	0.987201i	$-0.449017\pi$
$449$	6.75878			0.318967			0.159483	+	0.987201i	$0.449017\pi$
$450$		0			0
$451$	6.26651	−	14.2914i	0.295078	−	0.672955i
$452$		0			0
$453$	29.2009	+	29.2009i	1.37198	+	1.37198i
$454$		0			0
$455$	−7.64945			−0.358612
$456$		0			0
$457$	−16.7380			−0.782972			−0.391486	−	0.920184i	$-0.628039\pi$
$457$	−16.7380			−0.782972			−0.391486	+	0.920184i	$0.628039\pi$
$458$		0			0
$459$	−20.7418	+	20.7418i	−0.968144	+	0.968144i
$460$		0			0
$461$	10.0097	−	10.0097i	0.466198	−	0.466198i	−0.434482	−	0.900680i	$-0.643069\pi$
$461$	10.0097	−	10.0097i	0.466198	−	0.466198i	0.900680	+	0.434482i	$0.143069\pi$
$462$		0			0
$463$		−	33.3827i		−	1.55142i	−0.631087	−	0.775712i	$-0.717391\pi$
$463$		−	33.3827i		−	1.55142i	0.631087	−	0.775712i	$-0.282609\pi$
$464$		0			0
$465$	−31.1096			−1.44267
$466$		0			0
$467$	−0.437902	+	0.437902i	−0.0202637	+	0.0202637i	−0.717166	−	0.696902i	$-0.754561\pi$
$467$	−0.437902	+	0.437902i	−0.0202637	+	0.0202637i	0.696902	+	0.717166i	$0.254561\pi$
$468$		0			0
$469$	8.89364	+	8.89364i	0.410670	+	0.410670i
$470$		0			0
$471$	−55.9638			−2.57868
$472$		0			0
$473$	3.69728	+	9.47159i	0.170001	+	0.435504i
$474$		0			0
$475$	11.9260	−	11.9260i	0.547204	−	0.547204i
$476$		0			0
$477$	31.5790	+	31.5790i	1.44591	+	1.44591i
$478$		0			0
$479$	−26.7292			−1.22129			−0.610644	−	0.791905i	$-0.709089\pi$
$479$	−26.7292			−1.22129			−0.610644	+	0.791905i	$0.709089\pi$
$480$		0			0
$481$			8.19695i			0.373749i
$482$		0			0
$483$	1.35952	+	1.35952i	0.0618603	+	0.0618603i
$484$		0			0
$485$	−4.69545	+	4.69545i	−0.213209	+	0.213209i
$486$		0			0
$487$	−6.35818			−0.288117			−0.144058	−	0.989569i	$-0.546015\pi$
$487$	−6.35818			−0.288117			−0.144058	+	0.989569i	$0.546015\pi$
$488$		0			0
$489$		−	32.2843i		−	1.45995i
$490$		0			0
$491$	17.1713	−	17.1713i	0.774930	−	0.774930i	−0.204034	−	0.978964i	$-0.565405\pi$
$491$	17.1713	−	17.1713i	0.774930	−	0.774930i	0.978964	+	0.204034i	$0.0654054\pi$
$492$		0			0
$493$	−15.3157	−	15.3157i	−0.689786	−	0.689786i
$494$		0			0
$495$	25.6927	−	10.0293i	1.15480	−	0.450782i
$496$		0			0
$497$			18.2619i			0.819160i
$498$		0			0
$499$	−3.59609	+	3.59609i	−0.160983	+	0.160983i	−0.783002	−	0.622019i	$-0.786313\pi$
$499$	−3.59609	+	3.59609i	−0.160983	+	0.160983i	0.622019	+	0.783002i	$0.286313\pi$
$500$		0			0
$501$	−1.86041	−	1.86041i	−0.0831168	−	0.0831168i
$502$		0			0
$503$			32.5489i			1.45128i	0.688073	+	0.725642i	$0.258457\pi$
$503$			32.5489i			1.45128i	−0.688073	+	0.725642i	$0.741543\pi$
$504$		0			0
$505$	3.30053			0.146871
$506$		0			0
$507$	10.6779	+	10.6779i	0.474221	+	0.474221i
$508$		0			0
$509$	−27.6307	−	27.6307i	−1.22471	−	1.22471i	−0.965938	−	0.258773i	$-0.916682\pi$
$509$	−27.6307	−	27.6307i	−1.22471	−	1.22471i	−0.258773	−	0.965938i	$-0.583318\pi$
$510$		0			0
$511$			24.8832i			1.10077i
$512$		0			0
$513$		−	57.8196i		−	2.55280i
$514$		0			0
$515$	−6.21219	+	6.21219i	−0.273742	+	0.273742i
$516$		0			0
$517$	−2.92788	−	1.28382i	−0.128768	−	0.0564625i
$518$		0			0
$519$		−	20.9111i		−	0.917897i
$520$		0			0
$521$		−	0.466613i		−	0.0204427i	−0.999948	−	0.0102213i	$-0.996746\pi$
$521$		−	0.466613i		−	0.0204427i	0.999948	−	0.0102213i	$-0.00325361\pi$
$522$		0			0
$523$	15.1381	−	15.1381i	0.661943	−	0.661943i	−0.293895	−	0.955838i	$-0.594952\pi$
$523$	15.1381	−	15.1381i	0.661943	−	0.661943i	0.955838	+	0.293895i	$0.0949516\pi$
$524$		0			0
$525$	−11.6923	+	11.6923i	−0.510294	+	0.510294i
$526$		0			0
$527$	−19.8117			−0.863009
$528$		0			0
$529$	−22.8318			−0.992687
$530$		0			0
$531$	−16.7897	+	16.7897i	−0.728613	+	0.728613i
$532$		0			0
$533$	−14.0408	+	14.0408i	−0.608176	+	0.608176i
$534$		0			0
$535$		−	0.610113i		−	0.0263775i
$536$		0			0
$537$			26.4600i			1.14183i
$538$		0			0
$539$	−6.35215	+	14.4867i	−0.273607	+	0.623986i
$540$		0			0
$541$	−18.1395	+	18.1395i	−0.779876	+	0.779876i	−0.979809	−	0.199934i	$-0.935927\pi$
$541$	−18.1395	+	18.1395i	−0.779876	+	0.779876i	0.199934	+	0.979809i	$0.435927\pi$
$542$		0			0
$543$		−	21.7464i		−	0.933226i
$544$		0			0
$545$		−	5.73068i		−	0.245475i
$546$		0			0
$547$	−21.2774	−	21.2774i	−0.909756	−	0.909756i	0.0864958	−	0.996252i	$-0.472433\pi$
$547$	−21.2774	−	21.2774i	−0.909756	−	0.909756i	−0.996252	+	0.0864958i	$0.972433\pi$
$548$		0			0
$549$	−41.1210	−	41.1210i	−1.75500	−	1.75500i
$550$		0			0
$551$	42.6940			1.81882
$552$		0			0
$553$		−	21.1606i		−	0.899841i
$554$		0			0
$555$	−5.23161	−	5.23161i	−0.222069	−	0.222069i
$556$		0			0
$557$	−11.4417	+	11.4417i	−0.484801	+	0.484801i	−0.906661	−	0.421860i	$-0.861377\pi$
$557$	−11.4417	+	11.4417i	−0.484801	+	0.484801i	0.421860	+	0.906661i	$0.361377\pi$
$558$		0			0
$559$		−	12.9380i		−	0.547219i
$560$		0			0
$561$	23.5253	−	9.18323i	0.993240	−	0.387716i
$562$		0			0
$563$	22.8161	+	22.8161i	0.961586	+	0.961586i	0.999289	−	0.0377035i	$-0.0120042\pi$
$563$	22.8161	+	22.8161i	0.961586	+	0.961586i	−0.0377035	+	0.999289i	$0.512004\pi$
$564$		0			0
$565$	−11.6117	+	11.6117i	−0.488509	+	0.488509i
$566$		0			0
$567$			25.9838i			1.09122i
$568$		0			0
$569$	13.6457			0.572059			0.286029	−	0.958221i	$-0.407665\pi$
$569$	13.6457			0.572059			0.286029	+	0.958221i	$0.407665\pi$
$570$		0			0
$571$	−3.01141	+	3.01141i	−0.126024	+	0.126024i	−0.767305	−	0.641282i	$-0.778403\pi$
$571$	−3.01141	+	3.01141i	−0.126024	+	0.126024i	0.641282	+	0.767305i	$0.278403\pi$
$572$		0			0
$573$	24.3822	+	24.3822i	1.01858	+	1.01858i
$574$		0			0
$575$			1.44659i			0.0603271i
$576$		0			0
$577$	32.1723			1.33935			0.669676	−	0.742654i	$-0.266433\pi$
$577$	32.1723			1.33935			0.669676	+	0.742654i	$0.266433\pi$
$578$		0			0
$579$	−2.99755	−	2.99755i	−0.124574	−	0.124574i
$580$		0			0
$581$	1.67768	−	1.67768i	0.0696021	−	0.0696021i
$582$		0			0
$583$	−7.86020	−	20.1360i	−0.325536	−	0.833950i
$584$		0			0
$585$	−35.0957			−1.45103
$586$		0			0
$587$	17.8690	+	17.8690i	0.737532	+	0.737532i	0.972100	−	0.234567i	$-0.0753674\pi$
$587$	17.8690	+	17.8690i	0.737532	+	0.737532i	−0.234567	+	0.972100i	$0.575367\pi$
$588$		0			0
$589$	27.6134	−	27.6134i	1.13779	−	1.13779i
$590$		0			0
$591$	−51.6434			−2.12432
$592$		0			0
$593$		−	8.25064i		−	0.338813i	−0.985546	−	0.169407i	$-0.945815\pi$
$593$		−	8.25064i		−	0.338813i	0.985546	−	0.169407i	$-0.0541851\pi$
$594$		0			0
$595$	3.10913	−	3.10913i	0.127462	−	0.127462i
$596$		0			0
$597$	−20.1919	+	20.1919i	−0.826400	+	0.826400i
$598$		0			0
$599$	45.8910			1.87505			0.937527	−	0.347911i	$-0.113109\pi$
$599$	45.8910			1.87505			0.937527	+	0.347911i	$0.113109\pi$
$600$		0			0
$601$	19.9475			0.813676			0.406838	−	0.913500i	$-0.366631\pi$
$601$	19.9475			0.813676			0.406838	+	0.913500i	$0.366631\pi$
$602$		0			0
$603$	40.8040	+	40.8040i	1.66167	+	1.66167i
$604$		0			0
$605$	−13.3382	−	0.548113i	−0.542276	−	0.0222840i
$606$		0			0
$607$	8.37457			0.339913			0.169957	−	0.985452i	$-0.445637\pi$
$607$	8.37457			0.339913			0.169957	+	0.985452i	$0.445637\pi$
$608$		0			0
$609$	−41.8573			−1.69614
$610$		0			0
$611$	2.87655	+	2.87655i	0.116373	+	0.116373i
$612$		0			0
$613$	−16.9366	−	16.9366i	−0.684065	−	0.684065i	0.276849	−	0.960913i	$-0.410710\pi$
$613$	−16.9366	−	16.9366i	−0.684065	−	0.684065i	−0.960913	+	0.276849i	$0.910710\pi$
$614$		0			0
$615$		−	17.9228i		−	0.722717i
$616$		0			0
$617$			13.7445i			0.553333i	0.960966	+	0.276666i	$0.0892297\pi$
$617$			13.7445i			0.553333i	−0.960966	+	0.276666i	$0.910770\pi$
$618$		0			0
$619$	18.9884	+	18.9884i	0.763209	+	0.763209i	0.976901	−	0.213692i	$-0.0685490\pi$
$619$	18.9884	+	18.9884i	0.763209	+	0.763209i	−0.213692	+	0.976901i	$0.568549\pi$
$620$		0			0
$621$	3.50667	+	3.50667i	0.140718	+	0.140718i
$622$		0			0
$623$	8.07957			0.323701
$624$		0			0
$625$	−5.07717			−0.203087
$626$		0			0
$627$	−19.9900	+	45.5890i	−0.798322	+	1.82065i
$628$		0			0
$629$	−3.33166	−	3.33166i	−0.132842	−	0.132842i
$630$		0			0
$631$	13.3143			0.530035			0.265018	−	0.964244i	$-0.414622\pi$
$631$	13.3143			0.530035			0.265018	+	0.964244i	$0.414622\pi$
$632$		0			0
$633$	58.6931			2.33284
$634$		0			0
$635$	−9.43974	+	9.43974i	−0.374605	+	0.374605i
$636$		0			0
$637$	14.2327	−	14.2327i	0.563921	−	0.563921i
$638$		0			0
$639$			83.7859i			3.31452i
$640$		0			0
$641$	2.01394			0.0795459			0.0397730	−	0.999209i	$-0.487337\pi$
$641$	2.01394			0.0795459			0.0397730	+	0.999209i	$0.487337\pi$
$642$		0			0
$643$	16.7740	−	16.7740i	0.661503	−	0.661503i	−0.294231	−	0.955734i	$-0.595064\pi$
$643$	16.7740	−	16.7740i	0.661503	−	0.661503i	0.955734	+	0.294231i	$0.0950637\pi$
$644$		0			0
$645$	8.25752	+	8.25752i	0.325140	+	0.325140i
$646$		0			0
$647$	38.2985			1.50567			0.752835	−	0.658210i	$-0.228686\pi$
$647$	38.2985			1.50567			0.752835	+	0.658210i	$0.228686\pi$
$648$		0			0
$649$	10.7058	−	4.17906i	0.420240	−	0.164043i
$650$		0			0
$651$	−27.0722	+	27.0722i	−1.06104	+	1.06104i
$652$		0			0
$653$	5.77359	+	5.77359i	0.225938	+	0.225938i	0.810993	−	0.585055i	$-0.198927\pi$
$653$	5.77359	+	5.77359i	0.225938	+	0.225938i	−0.585055	+	0.810993i	$0.698927\pi$
$654$		0			0
$655$	−8.89173			−0.347429
$656$		0			0
$657$			114.164i			4.45397i
$658$		0			0
$659$	25.9600	+	25.9600i	1.01126	+	1.01126i	0.999936	+	0.0113221i	$0.00360400\pi$
$659$	25.9600	+	25.9600i	1.01126	+	1.01126i	0.0113221	+	0.999936i	$0.496396\pi$
$660$		0			0
$661$	20.3491	−	20.3491i	0.791488	−	0.791488i	−0.190248	−	0.981736i	$-0.560929\pi$
$661$	20.3491	−	20.3491i	0.791488	−	0.791488i	0.981736	+	0.190248i	$0.0609291\pi$
$662$		0			0
$663$	−32.1351			−1.24803
$664$		0			0
$665$			8.66697i			0.336091i
$666$		0			0
$667$	−2.58932	+	2.58932i	−0.100259	+	0.100259i
$668$		0			0
$669$	−30.5705	−	30.5705i	−1.18192	−	1.18192i
$670$		0			0
$671$	10.2353	+	26.2204i	0.395128	+	1.01223i
$672$		0			0
$673$			16.9697i			0.654134i	0.945001	+	0.327067i	$0.106060\pi$
$673$			16.9697i			0.654134i	−0.945001	+	0.327067i	$0.893940\pi$
$674$		0			0
$675$	−30.1585	+	30.1585i	−1.16080	+	1.16080i
$676$		0			0
$677$	6.63631	+	6.63631i	0.255054	+	0.255054i	0.823039	−	0.567985i	$-0.192277\pi$
$677$	6.63631	+	6.63631i	0.255054	+	0.255054i	−0.567985	+	0.823039i	$0.692277\pi$
$678$		0			0
$679$			8.17213i			0.313618i
$680$		0			0
$681$	−42.7854			−1.63954
$682$		0			0
$683$	−25.4469	−	25.4469i	−0.973700	−	0.973700i	0.0259629	−	0.999663i	$-0.491735\pi$
$683$	−25.4469	−	25.4469i	−0.973700	−	0.973700i	−0.999663	+	0.0259629i	$0.991735\pi$
$684$		0			0
$685$	14.9909	+	14.9909i	0.572773	+	0.572773i
$686$		0			0
$687$			34.0592i			1.29944i
$688$		0			0
$689$			27.5054i			1.04787i
$690$		0			0
$691$	−8.16717	+	8.16717i	−0.310694	+	0.310694i	−0.845178	−	0.534484i	$-0.820506\pi$
$691$	−8.16717	+	8.16717i	−0.310694	+	0.310694i	0.534484	+	0.845178i	$0.320506\pi$
$692$		0			0
$693$	13.6306	−	31.0859i	0.517784	−	1.18086i
$694$		0			0
$695$			14.2477i			0.540446i
$696$		0			0
$697$		−	11.4138i		−	0.432330i
$698$		0			0
$699$	−34.0672	+	34.0672i	−1.28854	+	1.28854i
$700$		0			0
$701$	24.2824	−	24.2824i	0.917134	−	0.917134i	−0.0796864	−	0.996820i	$-0.525392\pi$
$701$	24.2824	−	24.2824i	0.917134	−	0.917134i	0.996820	+	0.0796864i	$0.0253919\pi$
$702$		0			0
$703$	9.28730			0.350277
$704$		0			0
$705$	−3.67185			−0.138290
$706$		0			0
$707$	2.87218	−	2.87218i	0.108019	−	0.108019i
$708$		0			0
$709$	15.9636	−	15.9636i	0.599524	−	0.599524i	−0.340662	−	0.940186i	$-0.610651\pi$
$709$	15.9636	−	15.9636i	0.599524	−	0.599524i	0.940186	+	0.340662i	$0.110651\pi$
$710$		0			0
$711$		−	97.0850i		−	3.64097i
$712$		0			0
$713$			3.34942i			0.125437i
$714$		0			0
$715$	15.5570	+	6.82144i	0.581797	+	0.255108i
$716$		0			0
$717$	22.4608	−	22.4608i	0.838813	−	0.838813i
$718$		0			0
$719$			32.7925i			1.22296i	0.791262	+	0.611478i	$0.209425\pi$
$719$			32.7925i			1.22296i	−0.791262	+	0.611478i	$0.790575\pi$
$720$		0			0
$721$			10.8119i			0.402658i
$722$		0			0
$723$	−26.0316	−	26.0316i	−0.968126	−	0.968126i
$724$		0			0
$725$	−22.2690	−	22.2690i	−0.827051	−	0.827051i
$726$		0			0
$727$	−15.5198			−0.575596			−0.287798	−	0.957691i	$-0.592923\pi$
$727$	−15.5198			−0.575596			−0.287798	+	0.957691i	$0.592923\pi$
$728$		0			0
$729$			5.35017i			0.198154i
$730$		0			0
$731$	5.25867	+	5.25867i	0.194499	+	0.194499i
$732$		0			0
$733$	−13.6498	+	13.6498i	−0.504168	+	0.504168i	−0.912730	−	0.408562i	$-0.866030\pi$
$733$	−13.6498	+	13.6498i	−0.504168	+	0.504168i	0.408562	+	0.912730i	$0.366030\pi$
$734$		0			0
$735$			18.1677i			0.670127i
$736$		0			0
$737$	−10.1564	−	26.0183i	−0.374114	−	0.958395i
$738$		0			0
$739$	4.21094	+	4.21094i	0.154902	+	0.154902i	0.780303	−	0.625401i	$-0.215065\pi$
$739$	4.21094	+	4.21094i	0.154902	+	0.154902i	−0.625401	+	0.780303i	$0.715065\pi$
$740$		0			0
$741$	44.7898	−	44.7898i	1.64539	−	1.64539i
$742$		0			0
$743$		−	2.55087i		−	0.0935823i	−0.998905	−	0.0467912i	$-0.985100\pi$
$743$		−	2.55087i		−	0.0935823i	0.998905	−	0.0467912i	$-0.0148995\pi$
$744$		0			0
$745$	−2.06087			−0.0755045
$746$		0			0
$747$	7.69722	−	7.69722i	0.281627	−	0.281627i
$748$		0			0
$749$	−0.530932	−	0.530932i	−0.0193998	−	0.0193998i
$750$		0			0
$751$		−	5.78624i		−	0.211143i	−0.994412	−	0.105571i	$-0.966333\pi$
$751$		−	5.78624i		−	0.211143i	0.994412	−	0.105571i	$-0.0336672\pi$
$752$		0			0
$753$	−64.9180			−2.36574
$754$		0			0
$755$	−11.2901	−	11.2901i	−0.410889	−	0.410889i
$756$		0			0
$757$	30.4106	−	30.4106i	1.10529	−	1.10529i	0.111530	−	0.993761i	$-0.464425\pi$
$757$	30.4106	−	30.4106i	1.10529	−	1.10529i	0.993761	−	0.111530i	$-0.0355752\pi$
$758$		0			0
$759$	−1.55254	−	3.97726i	−0.0563538	−	0.144366i
$760$		0			0
$761$	17.3401			0.628578			0.314289	−	0.949327i	$-0.398234\pi$
$761$	17.3401			0.628578			0.314289	+	0.949327i	$0.398234\pi$
$762$		0			0
$763$	−4.98694	−	4.98694i	−0.180539	−	0.180539i
$764$		0			0
$765$	14.2647	−	14.2647i	0.515741	−	0.515741i
$766$		0			0
$767$	−14.6239			−0.528039
$768$		0			0
$769$		−	47.2735i		−	1.70473i	−0.522950	−	0.852364i	$-0.675168\pi$
$769$		−	47.2735i		−	1.70473i	0.522950	−	0.852364i	$-0.324832\pi$
$770$		0			0
$771$	−16.2549	+	16.2549i	−0.585407	+	0.585407i
$772$		0			0
$773$	7.24469	−	7.24469i	0.260573	−	0.260573i	−0.564714	−	0.825287i	$-0.691013\pi$
$773$	7.24469	−	7.24469i	0.260573	−	0.260573i	0.825287	+	0.564714i	$0.191013\pi$
$774$		0			0
$775$	−28.8061			−1.03474
$776$		0			0
$777$	−9.10529			−0.326650
$778$		0			0
$779$	15.9085	+	15.9085i	0.569983	+	0.569983i
$780$		0			0
$781$	16.2852	−	37.1400i	0.582730	−	1.32897i
$782$		0			0
$783$	−107.964			−3.85833
$784$		0			0
$785$	21.6376			0.772279
$786$		0			0
$787$	34.4133	+	34.4133i	1.22670	+	1.22670i	0.965204	+	0.261499i	$0.0842168\pi$
$787$	34.4133	+	34.4133i	1.22670	+	1.22670i	0.261499	+	0.965204i	$0.415783\pi$
$788$		0			0
$789$	13.2690	+	13.2690i	0.472390	+	0.472390i
$790$		0			0
$791$			20.2095i			0.718566i
$792$		0			0
$793$		−	35.8165i		−	1.27188i
$794$		0			0
$795$	−17.5550	−	17.5550i	−0.622612	−	0.622612i
$796$		0			0
$797$	−25.6605	−	25.6605i	−0.908942	−	0.908942i	0.0872453	−	0.996187i	$-0.472194\pi$
$797$	−25.6605	−	25.6605i	−0.908942	−	0.908942i	−0.996187	+	0.0872453i	$0.972194\pi$
$798$		0			0
$799$	−2.33836			−0.0827251
$800$		0			0
$801$	37.0691			1.30977
$802$		0			0
$803$	22.1897	−	50.6058i	0.783059	−	1.78584i
$804$		0			0
$805$	−0.525639	−	0.525639i	−0.0185263	−	0.0185263i
$806$		0			0
$807$	−40.9862			−1.44278
$808$		0			0
$809$	24.4147			0.858376			0.429188	−	0.903215i	$-0.358800\pi$
$809$	24.4147			0.858376			0.429188	+	0.903215i	$0.358800\pi$
$810$		0			0
$811$	0.636876	−	0.636876i	0.0223637	−	0.0223637i	−0.695836	−	0.718200i	$-0.744966\pi$
$811$	0.636876	−	0.636876i	0.0223637	−	0.0223637i	0.718200	+	0.695836i	$0.244966\pi$
$812$		0			0
$813$	−47.1965	+	47.1965i	−1.65525	+	1.65525i
$814$		0			0
$815$			12.4823i			0.437235i
$816$		0			0
$817$	−14.6590			−0.512854
$818$		0			0
$819$	−30.5409	+	30.5409i	−1.06719	+	1.06719i
$820$		0			0
$821$	4.95802	+	4.95802i	0.173036	+	0.173036i	0.788312	−	0.615276i	$-0.210955\pi$
$821$	4.95802	+	4.95802i	0.173036	+	0.173036i	−0.615276	+	0.788312i	$0.710955\pi$
$822$		0			0
$823$	22.9952			0.801563			0.400781	−	0.916174i	$-0.368739\pi$
$823$	22.9952			0.801563			0.400781	+	0.916174i	$0.368739\pi$
$824$		0			0
$825$	34.2058	−	13.3524i	1.19089	−	0.464870i
$826$		0			0
$827$	−28.9808	+	28.9808i	−1.00776	+	1.00776i	−0.00779269	+	0.999970i	$0.502481\pi$
$827$	−28.9808	+	28.9808i	−1.00776	+	1.00776i	−0.999970	+	0.00779269i	$0.997519\pi$
$828$		0			0
$829$	−33.3896	−	33.3896i	−1.15967	−	1.15967i	−0.984547	−	0.175121i	$-0.943968\pi$
$829$	−33.3896	−	33.3896i	−1.15967	−	1.15967i	−0.175121	−	0.984547i	$-0.556032\pi$
$830$		0			0
$831$	16.8881			0.585840
$832$		0			0
$833$			11.5698i			0.400871i
$834$		0			0
$835$	0.719299	+	0.719299i	0.0248924	+	0.0248924i
$836$		0			0
$837$	−69.8285	+	69.8285i	−2.41363	+	2.41363i
$838$		0			0
$839$	16.7934			0.579773			0.289886	−	0.957061i	$-0.406382\pi$
$839$	16.7934			0.579773			0.289886	+	0.957061i	$0.406382\pi$
$840$		0			0
$841$		−	50.7208i		−	1.74899i
$842$		0			0
$843$	49.6593	−	49.6593i	1.71036	−	1.71036i
$844$		0			0
$845$	−4.12845	−	4.12845i	−0.142023	−	0.142023i
$846$		0			0
$847$	−12.0842	+	11.1302i	−0.415216	+	0.382438i
$848$		0			0
$849$		−	81.3079i		−	2.79048i
$850$		0			0
$851$	−0.563261	+	0.563261i	−0.0193083	+	0.0193083i
$852$		0			0
$853$	29.4591	+	29.4591i	1.00866	+	1.00866i	0.999962	+	0.00869892i	$0.00276899\pi$
$853$	29.4591	+	29.4591i	1.00866	+	1.00866i	0.00869892	+	0.999962i	$0.497231\pi$
$854$		0			0
$855$			39.7641i			1.35990i
$856$		0			0
$857$	−26.6180			−0.909252			−0.454626	−	0.890682i	$-0.650227\pi$
$857$	−26.6180			−0.909252			−0.454626	+	0.890682i	$0.650227\pi$
$858$		0			0
$859$	2.31300	+	2.31300i	0.0789186	+	0.0789186i	0.745464	−	0.666546i	$-0.232228\pi$
$859$	2.31300	+	2.31300i	0.0789186	+	0.0789186i	−0.666546	+	0.745464i	$0.732228\pi$
$860$		0			0
$861$	−15.5968	−	15.5968i	−0.531536	−	0.531536i
$862$		0			0
$863$		−	48.7535i		−	1.65959i	−0.558070	−	0.829794i	$-0.688458\pi$
$863$		−	48.7535i		−	1.65959i	0.558070	−	0.829794i	$-0.311542\pi$
$864$		0			0
$865$			8.08499i			0.274898i
$866$		0			0
$867$	−24.6701	+	24.6701i	−0.837840	+	0.837840i
$868$		0			0
$869$	−18.8701	+	43.0351i	−0.640125	+	1.45987i
$870$		0			0
$871$			35.5404i			1.20424i
$872$		0			0
$873$			37.4938i			1.26897i
$874$		0			0
$875$	10.9289	−	10.9289i	0.369466	−	0.369466i
$876$		0			0
$877$	−31.5218	+	31.5218i	−1.06441	+	1.06441i	−0.0666370	+	0.997777i	$0.521227\pi$
$877$	−31.5218	+	31.5218i	−1.06441	+	1.06441i	−0.997777	+	0.0666370i	$0.978773\pi$
$878$		0			0
$879$	79.7974			2.69150
$880$		0			0
$881$	16.2559			0.547675			0.273838	−	0.961776i	$-0.411707\pi$
$881$	16.2559			0.547675			0.273838	+	0.961776i	$0.411707\pi$
$882$		0			0
$883$	−0.694534	+	0.694534i	−0.0233729	+	0.0233729i	−0.718697	−	0.695324i	$-0.755261\pi$
$883$	−0.694534	+	0.694534i	−0.0233729	+	0.0233729i	0.695324	+	0.718697i	$0.255261\pi$
$884$		0			0
$885$	9.33354	−	9.33354i	0.313744	−	0.313744i
$886$		0			0
$887$		−	48.3198i		−	1.62242i	−0.584756	−	0.811209i	$-0.698810\pi$
$887$		−	48.3198i		−	1.62242i	0.584756	−	0.811209i	$-0.301190\pi$
$888$		0			0
$889$			16.4293i			0.551020i
$890$		0			0
$891$	23.1712	−	52.8442i	0.776265	−	1.77035i
$892$		0			0
$893$	3.25919	−	3.25919i	0.109065	−	0.109065i
$894$		0			0
$895$		−	10.2304i		−	0.341964i
$896$		0			0
$897$			5.43286i			0.181398i
$898$		0			0
$899$	−51.5614	−	51.5614i	−1.71967	−	1.71967i
$900$		0			0
$901$	−11.1796	−	11.1796i	−0.372447	−	0.372447i
$902$		0			0
$903$	14.3717			0.478261
$904$		0			0
$905$			8.40792i			0.279489i
$906$		0			0
$907$	6.57698	+	6.57698i	0.218385	+	0.218385i	0.807818	−	0.589433i	$-0.200649\pi$
$907$	6.57698	+	6.57698i	0.218385	+	0.218385i	−0.589433	+	0.807818i	$0.700649\pi$
$908$		0			0
$909$	13.1776	−	13.1776i	0.437072	−	0.437072i
$910$		0			0
$911$		−	25.3752i		−	0.840719i	−0.907358	−	0.420359i	$-0.861904\pi$
$911$		−	25.3752i		−	0.840719i	0.907358	−	0.420359i	$-0.138096\pi$
$912$		0			0
$913$	−4.90805	+	1.91588i	−0.162433	+	0.0634064i
$914$		0			0
$915$	22.8595	+	22.8595i	0.755711	+	0.755711i
$916$		0			0
$917$	−7.73776	+	7.73776i	−0.255523	+	0.255523i
$918$		0			0
$919$			43.8625i			1.44689i	0.690381	+	0.723446i	$0.257443\pi$
$919$			43.8625i			1.44689i	−0.690381	+	0.723446i	$0.742557\pi$
$920$		0			0
$921$	6.34338			0.209021
$922$		0			0
$923$	−36.4889	+	36.4889i	−1.20105	+	1.20105i
$924$		0			0
$925$	−4.84423	−	4.84423i	−0.159277	−	0.159277i
$926$		0			0
$927$			49.6052i			1.62925i
$928$		0			0
$929$	−6.35766			−0.208588			−0.104294	−	0.994547i	$-0.533258\pi$
$929$	−6.35766			−0.208588			−0.104294	+	0.994547i	$0.533258\pi$
$930$		0			0
$931$	−16.1260	−	16.1260i	−0.528507	−	0.528507i
$932$		0			0
$933$	−28.0244	+	28.0244i	−0.917478	+	0.917478i
$934$		0			0
$935$	−9.09573	+	3.55056i	−0.297462	+	0.116116i
$936$		0			0
$937$	−46.2991			−1.51253			−0.756264	−	0.654267i	$-0.772977\pi$
$937$	−46.2991			−1.51253			−0.756264	+	0.654267i	$0.772977\pi$
$938$		0			0
$939$	11.0772	+	11.0772i	0.361492	+	0.361492i
$940$		0			0
$941$	−8.22302	+	8.22302i	−0.268063	+	0.268063i	−0.828319	−	0.560256i	$-0.810703\pi$
$941$	−8.22302	+	8.22302i	−0.268063	+	0.268063i	0.560256	+	0.828319i	$0.310703\pi$
$942$		0			0
$943$	−1.92966			−0.0628383
$944$		0			0
$945$		−	21.9170i		−	0.712960i
$946$		0			0
$947$	18.5738	−	18.5738i	0.603567	−	0.603567i	−0.337690	−	0.941257i	$-0.609646\pi$
$947$	18.5738	−	18.5738i	0.603567	−	0.603567i	0.941257	+	0.337690i	$0.109646\pi$
$948$		0			0
$949$	−49.7187	+	49.7187i	−1.61394	+	1.61394i
$950$		0			0
$951$	−46.2219			−1.49885
$952$		0			0
$953$	−59.6764			−1.93311			−0.966555	−	0.256461i	$-0.917444\pi$
$953$	−59.6764			−1.93311			−0.966555	+	0.256461i	$0.917444\pi$
$954$		0			0
$955$	−9.42703	−	9.42703i	−0.305052	−	0.305052i
$956$		0			0
$957$	85.1266	+	37.3265i	2.75175	+	1.20659i
$958$		0			0
$959$	26.0907			0.842514
$960$		0			0
$961$	−35.6972			−1.15152
$962$		0			0
$963$	−2.43592	−	2.43592i	−0.0784964	−	0.0784964i
$964$		0			0
$965$	1.15896	+	1.15896i	0.0373082	+	0.0373082i
$966$		0			0
$967$			33.8014i			1.08698i	0.839416	+	0.543489i	$0.182897\pi$
$967$			33.8014i			1.08698i	−0.839416	+	0.543489i	$0.817103\pi$
$968$		0			0
$969$			36.4097i			1.16965i
$970$		0			0
$971$	12.9214	+	12.9214i	0.414666	+	0.414666i	0.883360	−	0.468694i	$-0.155275\pi$
$971$	12.9214	+	12.9214i	0.414666	+	0.414666i	−0.468694	+	0.883360i	$0.655275\pi$
$972$		0			0
$973$	12.3986	+	12.3986i	0.397482	+	0.397482i
$974$		0			0
$975$	−46.7244			−1.49638
$976$		0			0
$977$	−54.2061			−1.73421			−0.867104	−	0.498128i	$-0.834021\pi$
$977$	−54.2061			−1.73421			−0.867104	+	0.498128i	$0.834021\pi$
$978$		0			0
$979$	−16.4317	−	7.20501i	−0.525160	−	0.230273i
$980$		0			0
$981$	−22.8801	−	22.8801i	−0.730506	−	0.730506i
$982$		0			0
$983$	19.7172			0.628882			0.314441	−	0.949277i	$-0.398183\pi$
$983$	19.7172			0.628882			0.314441	+	0.949277i	$0.398183\pi$
$984$		0			0
$985$	19.9672			0.636207
$986$		0			0
$987$	−3.19532	+	3.19532i	−0.101708	+	0.101708i
$988$		0			0
$989$	0.889046	−	0.889046i	0.0282700	−	0.0282700i
$990$		0			0
$991$		−	32.4527i		−	1.03090i	−0.856921	−	0.515448i	$-0.827626\pi$
$991$		−	32.4527i		−	1.03090i	0.856921	−	0.515448i	$-0.172374\pi$
$992$		0			0
$993$	61.4723			1.95076
$994$		0			0
$995$	7.80692	−	7.80692i	0.247496	−	0.247496i
$996$		0			0
$997$	13.1500	+	13.1500i	0.416465	+	0.416465i	0.883983	−	0.467518i	$-0.154852\pi$
$997$	13.1500	+	13.1500i	0.416465	+	0.416465i	−0.467518	+	0.883983i	$0.654852\pi$
$998$		0			0
$999$	−23.4857			−0.743054

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1408.2.i.b.351.2		44
4.3	odd	2		1408.2.i.a.351.22		44
8.3	odd	2		704.2.i.a.175.2		44
8.5	even	2		176.2.i.a.131.7	yes	44
11.10	odd	2	inner	1408.2.i.b.351.1		44
16.3	odd	4		176.2.i.a.43.16	yes	44
16.5	even	4		1408.2.i.a.1055.21		44
16.11	odd	4	inner	1408.2.i.b.1055.1		44
16.13	even	4		704.2.i.a.527.2		44
44.43	even	2		1408.2.i.a.351.21		44
88.21	odd	2		176.2.i.a.131.16	yes	44
88.43	even	2		704.2.i.a.175.1		44
176.21	odd	4		1408.2.i.a.1055.22		44
176.43	even	4	inner	1408.2.i.b.1055.2		44
176.109	odd	4		704.2.i.a.527.1		44
176.131	even	4		176.2.i.a.43.7	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
176.2.i.a.43.7	✓	44	176.131	even	4
176.2.i.a.43.16	yes	44	16.3	odd	4
176.2.i.a.131.7	yes	44	8.5	even	2
176.2.i.a.131.16	yes	44	88.21	odd	2
704.2.i.a.175.1		44	88.43	even	2
704.2.i.a.175.2		44	8.3	odd	2
704.2.i.a.527.1		44	176.109	odd	4
704.2.i.a.527.2		44	16.13	even	4
1408.2.i.a.351.21		44	44.43	even	2
1408.2.i.a.351.22		44	4.3	odd	2
1408.2.i.a.1055.21		44	16.5	even	4
1408.2.i.a.1055.22		44	176.21	odd	4
1408.2.i.b.351.1		44	11.10	odd	2	inner
1408.2.i.b.351.2		44	1.1	even	1	trivial
1408.2.i.b.1055.1		44	16.11	odd	4	inner
1408.2.i.b.1055.2		44	176.43	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1408 = 2^{7} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1408.i (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.21950 + 2.21950i) q^{3} +(0.858137 - 0.858137i) q^{5} -1.49353i q^{7} -6.85234i q^{9} +O(q^{10})\)	\(q+(-2.21950 + 2.21950i) q^{3} +(0.858137 - 0.858137i) q^{5} -1.49353i q^{7} -6.85234i q^{9} +(-1.33187 + 3.03745i) q^{11} +(2.98420 - 2.98420i) q^{13} +3.80927i q^{15} +2.42587i q^{17} +(-3.38116 - 3.38116i) q^{19} +(3.31490 + 3.31490i) q^{21} +0.410124 q^{23} +3.52720i q^{25} +(8.55026 + 8.55026i) q^{27} +(-6.31351 + 6.31351i) q^{29} +8.16683i q^{31} +(-3.78554 - 9.69770i) q^{33} +(-1.28166 - 1.28166i) q^{35} +(-1.37339 + 1.37339i) q^{37} +13.2469i q^{39} -4.70505 q^{41} +(2.16775 - 2.16775i) q^{43} +(-5.88024 - 5.88024i) q^{45} +0.963926i q^{47} +4.76936 q^{49} +(-5.38421 - 5.38421i) q^{51} +(-4.60851 + 4.60851i) q^{53} +(1.46363 + 3.74948i) q^{55} +15.0090 q^{57} +(-2.45022 - 2.45022i) q^{59} +(6.00102 - 6.00102i) q^{61} -10.2342 q^{63} -5.12171i q^{65} +(-5.95476 + 5.95476i) q^{67} +(-0.910270 + 0.910270i) q^{69} -12.2273 q^{71} -16.6606 q^{73} +(-7.82862 - 7.82862i) q^{75} +(4.53654 + 1.98919i) q^{77} +14.1682 q^{79} -17.3975 q^{81} +(1.12330 + 1.12330i) q^{83} +(2.08173 + 2.08173i) q^{85} -28.0256i q^{87} +5.40970i q^{89} +(-4.45701 - 4.45701i) q^{91} +(-18.1263 - 18.1263i) q^{93} -5.80300 q^{95} -5.47168 q^{97} +(20.8137 + 9.12641i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} + 4 q^{5}+O(q^{10}) \) 44 * q + 4 * q^3 + 4 * q^5	\( 44 q + 4 q^{3} + 4 q^{5} + 6 q^{11} - 24 q^{23} - 8 q^{27} - 4 q^{33} + 20 q^{37} - 28 q^{45} - 28 q^{49} - 12 q^{53} - 36 q^{55} + 20 q^{59} - 36 q^{67} + 16 q^{69} - 40 q^{71} - 60 q^{75} - 4 q^{77} - 20 q^{81} - 56 q^{91} - 8 q^{93} - 8 q^{97} + 42 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 + 4 * q^5 + 6 * q^11 - 24 * q^23 - 8 * q^27 - 4 * q^33 + 20 * q^37 - 28 * q^45 - 28 * q^49 - 12 * q^53 - 36 * q^55 + 20 * q^59 - 36 * q^67 + 16 * q^69 - 40 * q^71 - 60 * q^75 - 4 * q^77 - 20 * q^81 - 56 * q^91 - 8 * q^93 - 8 * q^97 + 42 * q^99

Introduction

L-functions

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