LMFDB - Embedded newform 1344.2.s.d.239.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(239,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))

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

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

chi := DirichletCharacter("1344.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.s (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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.15
Character	$\chi$	$=$	1344.239
Dual form			1344.2.s.d.911.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.505560 - 1.65663i) q^{3} +(-2.00763 - 2.00763i) q^{5} -1.00000 q^{7} +(-2.48882 - 1.67505i) q^{9} +O(q^{10})$	\(q+(0.505560 - 1.65663i) q^{3} +(-2.00763 - 2.00763i) q^{5} -1.00000 q^{7} +(-2.48882 - 1.67505i) q^{9} +(-2.67559 + 2.67559i) q^{11} +(4.14527 + 4.14527i) q^{13} +(-4.34086 + 2.31091i) q^{15} +3.45751i q^{17} +(-5.27680 + 5.27680i) q^{19} +(-0.505560 + 1.65663i) q^{21} -2.11865i q^{23} +3.06114i q^{25} +(-4.03317 + 3.27620i) q^{27} +(0.808582 - 0.808582i) q^{29} -7.56529i q^{31} +(3.07978 + 5.78512i) q^{33} +(2.00763 + 2.00763i) q^{35} +(-1.06877 + 1.06877i) q^{37} +(8.96285 - 4.77148i) q^{39} +11.1364 q^{41} +(5.32616 + 5.32616i) q^{43} +(1.63375 + 8.35949i) q^{45} -6.19416 q^{47} +1.00000 q^{49} +(5.72779 + 1.74798i) q^{51} +(-0.414682 - 0.414682i) q^{53} +10.7432 q^{55} +(6.07394 + 11.4094i) q^{57} +(-7.26431 + 7.26431i) q^{59} +(-1.06878 - 1.06878i) q^{61} +(2.48882 + 1.67505i) q^{63} -16.6443i q^{65} +(-4.81554 + 4.81554i) q^{67} +(-3.50981 - 1.07110i) q^{69} -1.83771i q^{71} -0.150117i q^{73} +(5.07116 + 1.54759i) q^{75} +(2.67559 - 2.67559i) q^{77} +4.73116i q^{79} +(3.38843 + 8.33778i) q^{81} +(1.94899 + 1.94899i) q^{83} +(6.94138 - 6.94138i) q^{85} +(-0.930731 - 1.74830i) q^{87} -11.7352 q^{89} +(-4.14527 - 4.14527i) q^{91} +(-12.5328 - 3.82471i) q^{93} +21.1877 q^{95} -15.6205 q^{97} +(11.1408 - 2.17731i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{7}+O(q^{10}) $ 48 * q - 48 * q^7	$ 48 q - 48 q^{7} - 8 q^{19} + 12 q^{27} + 16 q^{37} + 24 q^{39} + 48 q^{43} + 20 q^{45} + 48 q^{49} + 32 q^{55} + 8 q^{61} + 16 q^{67} - 28 q^{69} + 12 q^{75} - 48 q^{85} - 56 q^{87} - 64 q^{93} - 32 q^{99}+O(q^{100}) $ 48 * q - 48 * q^7 - 8 * q^19 + 12 * q^27 + 16 * q^37 + 24 * q^39 + 48 * q^43 + 20 * q^45 + 48 * q^49 + 32 * q^55 + 8 * q^61 + 16 * q^67 - 28 * q^69 + 12 * q^75 - 48 * q^85 - 56 * q^87 - 64 * q^93 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.505560	−	1.65663i	0.291885	−	0.956453i
$3$	0.505560	−	1.65663i	0.291885	−	0.956453i
$4$		0			0
$5$	−2.00763	−	2.00763i	−0.897838	−	0.897838i	0.0974064	−	0.995245i	$-0.468945\pi$
$5$	−2.00763	−	2.00763i	−0.897838	−	0.897838i	−0.995245	+	0.0974064i	$0.968945\pi$
$6$		0			0
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$		0			0
$9$	−2.48882	−	1.67505i	−0.829606	−	0.558349i
$10$		0			0
$11$	−2.67559	+	2.67559i	−0.806720	+	0.806720i	−0.984136	−	0.177416i	$-0.943226\pi$
$11$	−2.67559	+	2.67559i	−0.806720	+	0.806720i	0.177416	+	0.984136i	$0.443226\pi$
$12$		0			0
$13$	4.14527	+	4.14527i	1.14969	+	1.14969i	0.986613	+	0.163079i	$0.0521424\pi$
$13$	4.14527	+	4.14527i	1.14969	+	1.14969i	0.163079	+	0.986613i	$0.447858\pi$
$14$		0			0
$15$	−4.34086	+	2.31091i	−1.12081	+	0.596675i
$16$		0			0
$17$			3.45751i			0.838568i	0.907855	+	0.419284i	$0.137719\pi$
$17$			3.45751i			0.838568i	−0.907855	+	0.419284i	$0.862281\pi$
$18$		0			0
$19$	−5.27680	+	5.27680i	−1.21058	+	1.21058i	−0.239744	+	0.970836i	$0.577063\pi$
$19$	−5.27680	+	5.27680i	−1.21058	+	1.21058i	−0.970836	+	0.239744i	$0.922937\pi$
$20$		0			0
$21$	−0.505560	+	1.65663i	−0.110322	+	0.361505i
$22$		0			0
$23$		−	2.11865i		−	0.441768i	−0.975300	−	0.220884i	$-0.929106\pi$
$23$		−	2.11865i		−	0.441768i	0.975300	−	0.220884i	$-0.0708943\pi$
$24$		0			0
$25$			3.06114i			0.612227i
$26$		0			0
$27$	−4.03317	+	3.27620i	−0.776185	+	0.630506i
$28$		0			0
$29$	0.808582	−	0.808582i	0.150150	−	0.150150i	−0.628035	−	0.778185i	$-0.716141\pi$
$29$	0.808582	−	0.808582i	0.150150	−	0.150150i	0.778185	+	0.628035i	$0.216141\pi$
$30$		0			0
$31$		−	7.56529i		−	1.35877i	−0.733784	−	0.679383i	$-0.762248\pi$
$31$		−	7.56529i		−	1.35877i	0.733784	−	0.679383i	$-0.237752\pi$
$32$		0			0
$33$	3.07978	+	5.78512i	0.536120	+	1.00706i
$34$		0			0
$35$	2.00763	+	2.00763i	0.339351	+	0.339351i
$36$		0			0
$37$	−1.06877	+	1.06877i	−0.175705	+	0.175705i	−0.789480	−	0.613776i	$-0.789650\pi$
$37$	−1.06877	+	1.06877i	−0.175705	+	0.175705i	0.613776	+	0.789480i	$0.289650\pi$
$38$		0			0
$39$	8.96285	−	4.77148i	1.43520	−	0.764048i
$40$		0			0
$41$	11.1364			1.73922			0.869609	−	0.493741i	$-0.164371\pi$
$41$	11.1364			1.73922			0.869609	+	0.493741i	$0.164371\pi$
$42$		0			0
$43$	5.32616	+	5.32616i	0.812232	+	0.812232i	0.984968	−	0.172736i	$-0.0552608\pi$
$43$	5.32616	+	5.32616i	0.812232	+	0.812232i	−0.172736	+	0.984968i	$0.555261\pi$
$44$		0			0
$45$	1.63375	+	8.35949i	0.243545	+	1.24616i
$46$		0			0
$47$	−6.19416			−0.903512			−0.451756	−	0.892142i	$-0.649202\pi$
$47$	−6.19416			−0.903512			−0.451756	+	0.892142i	$0.649202\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$		0			0
$51$	5.72779	+	1.74798i	0.802051	+	0.244766i
$52$		0			0
$53$	−0.414682	−	0.414682i	−0.0569609	−	0.0569609i	0.678053	−	0.735013i	$-0.262824\pi$
$53$	−0.414682	−	0.414682i	−0.0569609	−	0.0569609i	−0.735013	+	0.678053i	$0.762824\pi$
$54$		0			0
$55$	10.7432			1.44861
$56$		0			0
$57$	6.07394	+	11.4094i	0.804513	+	1.51121i
$58$		0			0
$59$	−7.26431	+	7.26431i	−0.945733	+	0.945733i	−0.998601	−	0.0528685i	$-0.983164\pi$
$59$	−7.26431	+	7.26431i	−0.945733	+	0.945733i	0.0528685	+	0.998601i	$0.483164\pi$
$60$		0			0
$61$	−1.06878	−	1.06878i	−0.136844	−	0.136844i	0.635367	−	0.772211i	$-0.280849\pi$
$61$	−1.06878	−	1.06878i	−0.136844	−	0.136844i	−0.772211	+	0.635367i	$0.780849\pi$
$62$		0			0
$63$	2.48882	+	1.67505i	0.313562	+	0.211036i
$64$		0			0
$65$		−	16.6443i		−	2.06447i
$66$		0			0
$67$	−4.81554	+	4.81554i	−0.588312	+	0.588312i	−0.937174	−	0.348862i	$-0.886568\pi$
$67$	−4.81554	+	4.81554i	−0.588312	+	0.588312i	0.348862	+	0.937174i	$0.386568\pi$
$68$		0			0
$69$	−3.50981	−	1.07110i	−0.422531	−	0.128946i
$70$		0			0
$71$		−	1.83771i		−	0.218096i	−0.994037	−	0.109048i	$-0.965220\pi$
$71$		−	1.83771i		−	0.218096i	0.994037	−	0.109048i	$-0.0347802\pi$
$72$		0			0
$73$		−	0.150117i		−	0.0175698i	−0.999961	−	0.00878491i	$-0.997204\pi$
$73$		−	0.150117i		−	0.0175698i	0.999961	−	0.00878491i	$-0.00279636\pi$
$74$		0			0
$75$	5.07116	+	1.54759i	0.585567	+	0.178700i
$76$		0			0
$77$	2.67559	−	2.67559i	0.304911	−	0.304911i
$78$		0			0
$79$			4.73116i			0.532297i	0.963932	+	0.266149i	$0.0857512\pi$
$79$			4.73116i			0.532297i	−0.963932	+	0.266149i	$0.914249\pi$
$80$		0			0
$81$	3.38843	+	8.33778i	0.376492	+	0.926420i
$82$		0			0
$83$	1.94899	+	1.94899i	0.213930	+	0.213930i	0.805934	−	0.592005i	$-0.201663\pi$
$83$	1.94899	+	1.94899i	0.213930	+	0.213930i	−0.592005	+	0.805934i	$0.701663\pi$
$84$		0			0
$85$	6.94138	−	6.94138i	0.752899	−	0.752899i
$86$		0			0
$87$	−0.930731	−	1.74830i	−0.0997848	−	0.187438i
$88$		0			0
$89$	−11.7352			−1.24393			−0.621965	−	0.783045i	$-0.713665\pi$
$89$	−11.7352			−1.24393			−0.621965	+	0.783045i	$0.713665\pi$
$90$		0			0
$91$	−4.14527	−	4.14527i	−0.434543	−	0.434543i
$92$		0			0
$93$	−12.5328	−	3.82471i	−1.29960	−	0.396604i
$94$		0			0
$95$	21.1877			2.17381
$96$		0			0
$97$	−15.6205			−1.58602			−0.793009	−	0.609210i	$-0.791486\pi$
$97$	−15.6205			−1.58602			−0.793009	+	0.609210i	$0.791486\pi$
$98$		0			0
$99$	11.1408	−	2.17731i	1.11969	−	0.218828i
$100$		0			0
$101$	2.48366	+	2.48366i	0.247134	+	0.247134i	0.819793	−	0.572660i	$-0.194088\pi$
$101$	2.48366	+	2.48366i	0.247134	+	0.247134i	−0.572660	+	0.819793i	$0.694088\pi$
$102$		0			0
$103$	−4.06008			−0.400051			−0.200026	−	0.979791i	$-0.564103\pi$
$103$	−4.06008			−0.400051			−0.200026	+	0.979791i	$0.564103\pi$
$104$		0			0
$105$	4.34086	−	2.31091i	0.423625	−	0.225522i
$106$		0			0
$107$	−4.05064	+	4.05064i	−0.391590	+	0.391590i	−0.875254	−	0.483664i	$-0.839306\pi$
$107$	−4.05064	+	4.05064i	−0.391590	+	0.391590i	0.483664	+	0.875254i	$0.339306\pi$
$108$		0			0
$109$	−0.171210	−	0.171210i	−0.0163989	−	0.0163989i	0.698860	−	0.715259i	$-0.253691\pi$
$109$	−0.171210	−	0.171210i	−0.0163989	−	0.0163989i	−0.715259	+	0.698860i	$0.753691\pi$
$110$		0			0
$111$	1.23022	+	2.31088i	0.116768	+	0.219339i
$112$		0			0
$113$			11.0745i			1.04180i	0.853618	+	0.520899i	$0.174403\pi$
$113$			11.0745i			1.04180i	−0.853618	+	0.520899i	$0.825597\pi$
$114$		0			0
$115$	−4.25345	+	4.25345i	−0.396637	+	0.396637i
$116$		0			0
$117$	−3.37330	−	17.2604i	−0.311862	−	1.59572i
$118$		0			0
$119$		−	3.45751i		−	0.316949i
$120$		0			0
$121$		−	3.31753i		−	0.301594i
$122$		0			0
$123$	5.63014	−	18.4489i	0.507652	−	1.66348i
$124$		0			0
$125$	−3.89252	+	3.89252i	−0.348157	+	0.348157i
$126$		0			0
$127$			20.3588i			1.80655i	0.429060	+	0.903276i	$0.358845\pi$
$127$			20.3588i			1.80655i	−0.429060	+	0.903276i	$0.641155\pi$
$128$		0			0
$129$	11.5162	−	6.13076i	1.01394	−	0.539783i
$130$		0			0
$131$	1.47580	+	1.47580i	0.128941	+	0.128941i	0.768632	−	0.639691i	$-0.220938\pi$
$131$	1.47580	+	1.47580i	0.128941	+	0.128941i	−0.639691	+	0.768632i	$0.720938\pi$
$132$		0			0
$133$	5.27680	−	5.27680i	0.457556	−	0.457556i
$134$		0			0
$135$	14.6745	+	1.51972i	1.26298	+	0.130796i
$136$		0			0
$137$	1.99767			0.170672			0.0853360	−	0.996352i	$-0.472804\pi$
$137$	1.99767			0.170672			0.0853360	+	0.996352i	$0.472804\pi$
$138$		0			0
$139$	−13.2241	−	13.2241i	−1.12166	−	1.12166i	−0.991493	−	0.130163i	$-0.958450\pi$
$139$	−13.2241	−	13.2241i	−1.12166	−	1.12166i	−0.130163	−	0.991493i	$-0.541550\pi$
$140$		0			0
$141$	−3.13152	+	10.2614i	−0.263722	+	0.864167i
$142$		0			0
$143$	−22.1821			−1.85496
$144$		0			0
$145$	−3.24666			−0.269621
$146$		0			0
$147$	0.505560	−	1.65663i	0.0416979	−	0.136636i
$148$		0			0
$149$	5.49854	+	5.49854i	0.450458	+	0.450458i	0.895507	−	0.445048i	$-0.146814\pi$
$149$	5.49854	+	5.49854i	0.450458	+	0.450458i	−0.445048	+	0.895507i	$0.646814\pi$
$150$		0			0
$151$	0.422728			0.0344011			0.0172005	−	0.999852i	$-0.494525\pi$
$151$	0.422728			0.0344011			0.0172005	+	0.999852i	$0.494525\pi$
$152$		0			0
$153$	5.79149	−	8.60510i	0.468214	−	0.695681i
$154$		0			0
$155$	−15.1883	+	15.1883i	−1.21995	+	1.21995i
$156$		0			0
$157$	−2.60688	−	2.60688i	−0.208051	−	0.208051i	0.595387	−	0.803439i	$-0.296999\pi$
$157$	−2.60688	−	2.60688i	−0.208051	−	0.208051i	−0.803439	+	0.595387i	$0.796999\pi$
$158$		0			0
$159$	−0.896619	+	0.477326i	−0.0711065	+	0.0378544i
$160$		0			0
$161$			2.11865i			0.166973i
$162$		0			0
$163$	6.94163	−	6.94163i	0.543710	−	0.543710i	−0.380904	−	0.924614i	$-0.624387\pi$
$163$	6.94163	−	6.94163i	0.543710	−	0.543710i	0.924614	+	0.380904i	$0.124387\pi$
$164$		0			0
$165$	5.43131	−	17.7974i	0.422827	−	1.38553i
$166$		0			0
$167$		−	6.67600i		−	0.516604i	−0.966064	−	0.258302i	$-0.916837\pi$
$167$		−	6.67600i		−	0.516604i	0.966064	−	0.258302i	$-0.0831630\pi$
$168$		0			0
$169$			21.3666i			1.64358i
$170$		0			0
$171$	21.9719	−	4.29410i	1.68023	−	0.328378i
$172$		0			0
$173$	−13.4463	+	13.4463i	−1.02231	+	1.02231i	−0.0225608	+	0.999745i	$0.507182\pi$
$173$	−13.4463	+	13.4463i	−1.02231	+	1.02231i	−0.999745	+	0.0225608i	$0.992818\pi$
$174$		0			0
$175$		−	3.06114i		−	0.231400i
$176$		0			0
$177$	8.36170	+	15.7068i	0.628504	+	1.18060i
$178$		0			0
$179$	6.72788	+	6.72788i	0.502865	+	0.502865i	0.912327	−	0.409462i	$-0.134284\pi$
$179$	6.72788	+	6.72788i	0.502865	+	0.502865i	−0.409462	+	0.912327i	$0.634284\pi$
$180$		0			0
$181$	−7.21372	+	7.21372i	−0.536192	+	0.536192i	−0.922408	−	0.386216i	$-0.873782\pi$
$181$	−7.21372	+	7.21372i	−0.536192	+	0.536192i	0.386216	+	0.922408i	$0.373782\pi$
$182$		0			0
$183$	−2.31091	+	1.23024i	−0.170827	+	0.0909421i
$184$		0			0
$185$	4.29139			0.315509
$186$		0			0
$187$	−9.25086	−	9.25086i	−0.676490	−	0.676490i
$188$		0			0
$189$	4.03317	−	3.27620i	0.293370	−	0.238309i
$190$		0			0
$191$	21.6813			1.56881			0.784403	−	0.620252i	$-0.212970\pi$
$191$	21.6813			1.56881			0.784403	+	0.620252i	$0.212970\pi$
$192$		0			0
$193$	−15.6933			−1.12963			−0.564814	−	0.825218i	$-0.691052\pi$
$193$	−15.6933			−1.12963			−0.564814	+	0.825218i	$0.691052\pi$
$194$		0			0
$195$	−27.5734	−	8.41471i	−1.97457	−	0.602590i
$196$		0			0
$197$	−10.9491	−	10.9491i	−0.780091	−	0.780091i	0.199755	−	0.979846i	$-0.435985\pi$
$197$	−10.9491	−	10.9491i	−0.780091	−	0.780091i	−0.979846	+	0.199755i	$0.935985\pi$
$198$		0			0
$199$	−7.64114			−0.541666			−0.270833	−	0.962626i	$-0.587299\pi$
$199$	−7.64114			−0.541666			−0.270833	+	0.962626i	$0.587299\pi$
$200$		0			0
$201$	5.54301	+	10.4121i	0.390973	+	0.734413i
$202$		0			0
$203$	−0.808582	+	0.808582i	−0.0567513	+	0.0567513i
$204$		0			0
$205$	−22.3578	−	22.3578i	−1.56154	−	1.56154i
$206$		0			0
$207$	−3.54883	+	5.27293i	−0.246661	+	0.366494i
$208$		0			0
$209$		−	28.2371i		−	1.95320i
$210$		0			0
$211$	1.74847	−	1.74847i	0.120369	−	0.120369i	−0.644356	−	0.764726i	$-0.722875\pi$
$211$	1.74847	−	1.74847i	0.120369	−	0.120369i	0.764726	+	0.644356i	$0.222875\pi$
$212$		0			0
$213$	−3.04439	−	0.929071i	−0.208598	−	0.0636589i
$214$		0			0
$215$		−	21.3859i		−	1.45851i
$216$		0			0
$217$			7.56529i			0.513565i
$218$		0			0
$219$	−0.248687	−	0.0758930i	−0.0168047	−	0.00512837i
$220$		0			0
$221$	−14.3323	+	14.3323i	−0.964095	+	0.964095i
$222$		0			0
$223$		−	18.6969i		−	1.25203i	−0.779809	−	0.626017i	$-0.784684\pi$
$223$		−	18.6969i		−	1.25203i	0.779809	−	0.626017i	$-0.215316\pi$
$224$		0			0
$225$	5.12755	−	7.61861i	0.341837	−	0.507907i
$226$		0			0
$227$	3.39283	+	3.39283i	0.225190	+	0.225190i	0.810680	−	0.585490i	$-0.199098\pi$
$227$	3.39283	+	3.39283i	0.225190	+	0.225190i	−0.585490	+	0.810680i	$0.699098\pi$
$228$		0			0
$229$	−16.0898	+	16.0898i	−1.06324	+	1.06324i	−0.0653832	+	0.997860i	$0.520827\pi$
$229$	−16.0898	+	16.0898i	−1.06324	+	1.06324i	−0.997860	+	0.0653832i	$0.979173\pi$
$230$		0			0
$231$	−3.07978	−	5.78512i	−0.202634	−	0.380633i
$232$		0			0
$233$	13.9468			0.913682			0.456841	−	0.889548i	$-0.348981\pi$
$233$	13.9468			0.913682			0.456841	+	0.889548i	$0.348981\pi$
$234$		0			0
$235$	12.4356	+	12.4356i	0.811207	+	0.811207i
$236$		0			0
$237$	7.83776	+	2.39189i	0.509117	+	0.155370i
$238$		0			0
$239$	18.6801			1.20832			0.604158	−	0.796865i	$-0.293510\pi$
$239$	18.6801			1.20832			0.604158	+	0.796865i	$0.293510\pi$
$240$		0			0
$241$	2.73195			0.175980			0.0879902	−	0.996121i	$-0.471956\pi$
$241$	2.73195			0.175980			0.0879902	+	0.996121i	$0.471956\pi$
$242$		0			0
$243$	15.5256	−	1.39811i	0.995970	−	0.0896890i
$244$		0			0
$245$	−2.00763	−	2.00763i	−0.128263	−	0.128263i
$246$		0			0
$247$	−43.7475			−2.78359
$248$		0			0
$249$	4.21409	−	2.24342i	0.267057	−	0.142171i
$250$		0			0
$251$	−6.66001	+	6.66001i	−0.420376	+	0.420376i	−0.885333	−	0.464957i	$-0.846070\pi$
$251$	−6.66001	+	6.66001i	−0.420376	+	0.420376i	0.464957	+	0.885333i	$0.346070\pi$
$252$		0			0
$253$	5.66862	+	5.66862i	0.356383	+	0.356383i
$254$		0			0
$255$	−7.98999	−	15.0086i	−0.500352	−	0.939873i
$256$		0			0
$257$			4.55034i			0.283842i	0.989878	+	0.141921i	$0.0453279\pi$
$257$			4.55034i			0.283842i	−0.989878	+	0.141921i	$0.954672\pi$
$258$		0			0
$259$	1.06877	−	1.06877i	0.0664102	−	0.0664102i
$260$		0			0
$261$	−3.36683	+	0.658000i	−0.208401	+	0.0407292i
$262$		0			0
$263$		−	4.64087i		−	0.286168i	−0.989711	−	0.143084i	$-0.954298\pi$
$263$		−	4.64087i		−	0.286168i	0.989711	−	0.143084i	$-0.0457020\pi$
$264$		0			0
$265$			1.66505i			0.102283i
$266$		0			0
$267$	−5.93285	+	19.4408i	−0.363085	+	1.18976i
$268$		0			0
$269$	10.6868	−	10.6868i	0.651587	−	0.651587i	−0.301788	−	0.953375i	$-0.597583\pi$
$269$	10.6868	−	10.6868i	0.651587	−	0.651587i	0.953375	+	0.301788i	$0.0975834\pi$
$270$		0			0
$271$		−	4.31029i		−	0.261832i	−0.991393	−	0.130916i	$-0.958208\pi$
$271$		−	4.31029i		−	0.261832i	0.991393	−	0.130916i	$-0.0417918\pi$
$272$		0			0
$273$	−8.96285	+	4.77148i	−0.542456	+	0.288783i
$274$		0			0
$275$	−8.19033	−	8.19033i	−0.493896	−	0.493896i
$276$		0			0
$277$	7.23390	−	7.23390i	0.434643	−	0.434643i	−0.455562	−	0.890204i	$-0.650562\pi$
$277$	7.23390	−	7.23390i	0.434643	−	0.434643i	0.890204	+	0.455562i	$0.150562\pi$
$278$		0			0
$279$	−12.6722	+	18.8286i	−0.758666	+	1.12724i
$280$		0			0
$281$	−17.1958			−1.02581			−0.512907	−	0.858444i	$-0.671431\pi$
$281$	−17.1958			−1.02581			−0.512907	+	0.858444i	$0.671431\pi$
$282$		0			0
$283$	5.45037	+	5.45037i	0.323991	+	0.323991i	0.850296	−	0.526305i	$-0.176423\pi$
$283$	5.45037	+	5.45037i	0.323991	+	0.323991i	−0.526305	+	0.850296i	$0.676423\pi$
$284$		0			0
$285$	10.7116	−	35.1001i	0.634503	−	2.07915i
$286$		0			0
$287$	−11.1364			−0.657363
$288$		0			0
$289$	5.04565			0.296803
$290$		0			0
$291$	−7.89708	+	25.8773i	−0.462935	+	1.51695i
$292$		0			0
$293$	9.85020	+	9.85020i	0.575455	+	0.575455i	0.933648	−	0.358193i	$-0.116607\pi$
$293$	9.85020	+	9.85020i	0.575455	+	0.575455i	−0.358193	+	0.933648i	$0.616607\pi$
$294$		0			0
$295$	29.1681			1.69823
$296$		0			0
$297$	2.02534	−	19.5569i	0.117522	−	1.13480i
$298$		0			0
$299$	8.78237	−	8.78237i	0.507898	−	0.507898i
$300$		0			0
$301$	−5.32616	−	5.32616i	−0.306995	−	0.306995i
$302$		0			0
$303$	5.37014	−	2.85886i	0.308507	−	0.164237i
$304$		0			0
$305$			4.29144i			0.245727i
$306$		0			0
$307$	−3.30903	+	3.30903i	−0.188856	+	0.188856i	−0.795202	−	0.606345i	$-0.792635\pi$
$307$	−3.30903	+	3.30903i	−0.188856	+	0.188856i	0.606345	+	0.795202i	$0.292635\pi$
$308$		0			0
$309$	−2.05261	+	6.72603i	−0.116769	+	0.382630i
$310$		0			0
$311$			17.1152i			0.970516i	0.874371	+	0.485258i	$0.161274\pi$
$311$			17.1152i			0.970516i	−0.874371	+	0.485258i	$0.838726\pi$
$312$		0			0
$313$		−	24.7605i		−	1.39954i	−0.714367	−	0.699772i	$-0.753285\pi$
$313$		−	24.7605i		−	1.39954i	0.714367	−	0.699772i	$-0.246715\pi$
$314$		0			0
$315$	−1.63375	−	8.35949i	−0.0920512	−	0.471004i
$316$		0			0
$317$	13.2530	−	13.2530i	0.744362	−	0.744362i	−0.229052	−	0.973414i	$-0.573563\pi$
$317$	13.2530	−	13.2530i	0.744362	−	0.744362i	0.973414	+	0.229052i	$0.0735626\pi$
$318$		0			0
$319$			4.32686i			0.242258i
$320$		0			0
$321$	4.66255	+	8.75824i	0.260238	+	0.488837i
$322$		0			0
$323$	−18.2446	−	18.2446i	−1.01515	−	1.01515i
$324$		0			0
$325$	−12.6892	+	12.6892i	−0.703872	+	0.703872i
$326$		0			0
$327$	−0.370188	+	0.197074i	−0.0204714	+	0.0108982i
$328$		0			0
$329$	6.19416			0.341495
$330$		0			0
$331$	−7.58184	−	7.58184i	−0.416736	−	0.416736i	0.467341	−	0.884077i	$-0.345212\pi$
$331$	−7.58184	−	7.58184i	−0.416736	−	0.416736i	−0.884077	+	0.467341i	$0.845212\pi$
$332$		0			0
$333$	4.45022	−	0.869733i	0.243870	−	0.0476611i
$334$		0			0
$335$	19.3356			1.05642
$336$		0			0
$337$	22.4627			1.22362			0.611811	−	0.791004i	$-0.290441\pi$
$337$	22.4627			1.22362			0.611811	+	0.791004i	$0.290441\pi$
$338$		0			0
$339$	18.3463	+	5.59881i	0.996432	+	0.304086i
$340$		0			0
$341$	20.2416	+	20.2416i	1.09614	+	1.09614i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	4.89600	+	9.19676i	0.263592	+	0.495137i
$346$		0			0
$347$	−1.00753	+	1.00753i	−0.0540872	+	0.0540872i	−0.733633	−	0.679546i	$-0.762177\pi$
$347$	−1.00753	+	1.00753i	−0.0540872	+	0.0540872i	0.679546	+	0.733633i	$0.262177\pi$
$348$		0			0
$349$	−21.6491	−	21.6491i	−1.15885	−	1.15885i	−0.984724	−	0.174123i	$-0.944291\pi$
$349$	−21.6491	−	21.6491i	−1.15885	−	1.15885i	−0.174123	−	0.984724i	$-0.555709\pi$
$350$		0			0
$351$	−30.2994	−	3.13785i	−1.61726	−	0.167486i
$352$		0			0
$353$		−	1.39430i		−	0.0742112i	−0.999311	−	0.0371056i	$-0.988186\pi$
$353$		−	1.39430i		−	0.0742112i	0.999311	−	0.0371056i	$-0.0118138\pi$
$354$		0			0
$355$	−3.68943	+	3.68943i	−0.195815	+	0.195815i
$356$		0			0
$357$	−5.72779	−	1.74798i	−0.303147	−	0.0925128i
$358$		0			0
$359$		−	9.30045i		−	0.490859i	−0.969414	−	0.245429i	$-0.921071\pi$
$359$		−	9.30045i		−	0.490859i	0.969414	−	0.245429i	$-0.0789290\pi$
$360$		0			0
$361$		−	36.6892i		−	1.93101i
$362$		0			0
$363$	−5.49590	−	1.67721i	−0.288460	−	0.0880307i
$364$		0			0
$365$	−0.301378	+	0.301378i	−0.0157749	+	0.0157749i
$366$		0			0
$367$		−	3.12450i		−	0.163097i	−0.996669	−	0.0815487i	$-0.974013\pi$
$367$		−	3.12450i		−	0.163097i	0.996669	−	0.0815487i	$-0.0259866\pi$
$368$		0			0
$369$	−27.7166	−	18.6541i	−1.44287	−	0.971091i
$370$		0			0
$371$	0.414682	+	0.414682i	0.0215292	+	0.0215292i
$372$		0			0
$373$	−16.5105	+	16.5105i	−0.854881	+	0.854881i	−0.990730	−	0.135849i	$-0.956624\pi$
$373$	−16.5105	+	16.5105i	−0.854881	+	0.854881i	0.135849	+	0.990730i	$0.456624\pi$
$374$		0			0
$375$	4.48054	+	8.41635i	0.231374	+	0.434618i
$376$		0			0
$377$	6.70358			0.345252
$378$		0			0
$379$	−21.0013	−	21.0013i	−1.07876	−	1.07876i	−0.996621	−	0.0821428i	$-0.973824\pi$
$379$	−21.0013	−	21.0013i	−1.07876	−	1.07876i	−0.0821428	−	0.996621i	$-0.526176\pi$
$380$		0			0
$381$	33.7269	+	10.2926i	1.72788	+	0.527306i
$382$		0			0
$383$	13.2705			0.678093			0.339047	−	0.940770i	$-0.389896\pi$
$383$	13.2705			0.678093			0.339047	+	0.940770i	$0.389896\pi$
$384$		0			0
$385$	−10.7432			−0.547522
$386$		0			0
$387$	−4.33427	−	22.1774i	−0.220323	−	1.12734i
$388$		0			0
$389$	−14.9931	−	14.9931i	−0.760180	−	0.760180i	0.216174	−	0.976355i	$-0.430642\pi$
$389$	−14.9931	−	14.9931i	−0.760180	−	0.760180i	−0.976355	+	0.216174i	$0.930642\pi$
$390$		0			0
$391$	7.32523			0.370453
$392$		0			0
$393$	3.19095	−	1.69874i	0.160962	−	0.0856902i
$394$		0			0
$395$	9.49841	−	9.49841i	0.477917	−	0.477917i
$396$		0			0
$397$	−3.95817	−	3.95817i	−0.198655	−	0.198655i	0.600768	−	0.799423i	$-0.294861\pi$
$397$	−3.95817	−	3.95817i	−0.198655	−	0.198655i	−0.799423	+	0.600768i	$0.794861\pi$
$398$		0			0
$399$	−6.07394	−	11.4094i	−0.304077	−	0.571185i
$400$		0			0
$401$		−	33.5372i		−	1.67477i	−0.546617	−	0.837383i	$-0.684084\pi$
$401$		−	33.5372i		−	1.67477i	0.546617	−	0.837383i	$-0.315916\pi$
$402$		0			0
$403$	31.3602	−	31.3602i	1.56216	−	1.56216i
$404$		0			0
$405$	9.93645	−	23.5419i	0.493746	−	1.16980i
$406$		0			0
$407$		−	5.71918i		−	0.283489i
$408$		0			0
$409$			28.4656i			1.40754i	0.710430	+	0.703768i	$0.248500\pi$
$409$			28.4656i			1.40754i	−0.710430	+	0.703768i	$0.751500\pi$
$410$		0			0
$411$	1.00994	−	3.30938i	0.0498167	−	0.163240i
$412$		0			0
$413$	7.26431	−	7.26431i	0.357453	−	0.357453i
$414$		0			0
$415$		−	7.82570i		−	0.384149i
$416$		0			0
$417$	−28.5930	+	15.2218i	−1.40021	+	0.745416i
$418$		0			0
$419$	−10.5259	−	10.5259i	−0.514223	−	0.514223i	0.401594	−	0.915818i	$-0.368456\pi$
$419$	−10.5259	−	10.5259i	−0.514223	−	0.514223i	−0.915818	+	0.401594i	$0.868456\pi$
$420$		0			0
$421$	4.65055	−	4.65055i	0.226654	−	0.226654i	−0.584639	−	0.811293i	$-0.698764\pi$
$421$	4.65055	−	4.65055i	0.226654	−	0.226654i	0.811293	+	0.584639i	$0.198764\pi$
$422$		0			0
$423$	15.4161	+	10.3755i	0.749559	+	0.504475i
$424$		0			0
$425$	−10.5839			−0.513394
$426$		0			0
$427$	1.06878	+	1.06878i	0.0517221	+	0.0517221i
$428$		0			0
$429$	−11.2144	+	36.7474i	−0.541435	+	1.77418i
$430$		0			0
$431$	−34.5433			−1.66389			−0.831947	−	0.554856i	$-0.812774\pi$
$431$	−34.5433			−1.66389			−0.831947	+	0.554856i	$0.812774\pi$
$432$		0			0
$433$	5.75271			0.276458			0.138229	−	0.990400i	$-0.455859\pi$
$433$	5.75271			0.276458			0.138229	+	0.990400i	$0.455859\pi$
$434$		0			0
$435$	−1.64138	+	5.37850i	−0.0786983	+	0.257880i
$436$		0			0
$437$	11.1797	+	11.1797i	0.534796	+	0.534796i
$438$		0			0
$439$	−36.8774			−1.76006			−0.880032	−	0.474915i	$-0.842479\pi$
$439$	−36.8774			−1.76006			−0.880032	+	0.474915i	$0.842479\pi$
$440$		0			0
$441$	−2.48882	−	1.67505i	−0.118515	−	0.0797642i
$442$		0			0
$443$	16.6096	−	16.6096i	0.789148	−	0.789148i	−0.192207	−	0.981354i	$-0.561564\pi$
$443$	16.6096	−	16.6096i	0.789148	−	0.789148i	0.981354	+	0.192207i	$0.0615644\pi$
$444$		0			0
$445$	23.5599	+	23.5599i	1.11685	+	1.11685i
$446$		0			0
$447$	11.8889	−	6.32918i	0.562324	−	0.299360i
$448$		0			0
$449$			2.85703i			0.134831i	0.997725	+	0.0674157i	$0.0214754\pi$
$449$			2.85703i			0.134831i	−0.997725	+	0.0674157i	$0.978525\pi$
$450$		0			0
$451$	−29.7965	+	29.7965i	−1.40306	+	1.40306i
$452$		0			0
$453$	0.213714	−	0.700302i	0.0100412	−	0.0329030i
$454$		0			0
$455$			16.6443i			0.780298i
$456$		0			0
$457$		−	8.32925i		−	0.389626i	−0.980840	−	0.194813i	$-0.937590\pi$
$457$		−	8.32925i		−	0.389626i	0.980840	−	0.194813i	$-0.0624100\pi$
$458$		0			0
$459$	−11.3275	−	13.9447i	−0.528722	−	0.650884i
$460$		0			0
$461$	−6.23607	+	6.23607i	−0.290443	+	0.290443i	−0.837255	−	0.546812i	$-0.815841\pi$
$461$	−6.23607	+	6.23607i	−0.290443	+	0.290443i	0.546812	+	0.837255i	$0.315841\pi$
$462$		0			0
$463$			12.8147i			0.595548i	0.954636	+	0.297774i	$0.0962442\pi$
$463$			12.8147i			0.595548i	−0.954636	+	0.297774i	$0.903756\pi$
$464$		0			0
$465$	17.4827	+	32.8399i	0.810741	+	1.52291i
$466$		0			0
$467$	5.58235	+	5.58235i	0.258320	+	0.258320i	0.824371	−	0.566050i	$-0.191529\pi$
$467$	5.58235	+	5.58235i	0.258320	+	0.258320i	−0.566050	+	0.824371i	$0.691529\pi$
$468$		0			0
$469$	4.81554	−	4.81554i	0.222361	−	0.222361i
$470$		0			0
$471$	−5.63655	+	3.00069i	−0.259719	+	0.138264i
$472$		0			0
$473$	−28.5012			−1.31049
$474$		0			0
$475$	−16.1530	−	16.1530i	−0.741150	−	0.741150i
$476$		0			0
$477$	0.337456	+	1.72668i	0.0154510	+	0.0790592i
$478$		0			0
$479$	1.70870			0.0780725			0.0390363	−	0.999238i	$-0.487571\pi$
$479$	1.70870			0.0780725			0.0390363	+	0.999238i	$0.487571\pi$
$480$		0			0
$481$	−8.86069			−0.404013
$482$		0			0
$483$	3.50981	+	1.07110i	0.159702	+	0.0487369i
$484$		0			0
$485$	31.3601	+	31.3601i	1.42399	+	1.42399i
$486$		0			0
$487$	3.00954			0.136375			0.0681876	−	0.997673i	$-0.478278\pi$
$487$	3.00954			0.136375			0.0681876	+	0.997673i	$0.478278\pi$
$488$		0			0
$489$	−7.99027	−	15.0091i	−0.361332	−	0.678734i
$490$		0			0
$491$	−7.27511	+	7.27511i	−0.328321	+	0.328321i	−0.851948	−	0.523627i	$-0.824579\pi$
$491$	−7.27511	+	7.27511i	−0.328321	+	0.328321i	0.523627	+	0.851948i	$0.324579\pi$
$492$		0			0
$493$	2.79568	+	2.79568i	0.125911	+	0.125911i
$494$		0			0
$495$	−26.7378	−	17.9953i	−1.20177	−	0.808829i
$496$		0			0
$497$			1.83771i			0.0824324i
$498$		0			0
$499$	−5.03619	+	5.03619i	−0.225451	+	0.225451i	−0.810789	−	0.585338i	$-0.800962\pi$
$499$	−5.03619	+	5.03619i	−0.225451	+	0.225451i	0.585338	+	0.810789i	$0.300962\pi$
$500$		0			0
$501$	−11.0596	−	3.37512i	−0.494108	−	0.150789i
$502$		0			0
$503$		−	37.1849i		−	1.65799i	−0.559255	−	0.828996i	$-0.688913\pi$
$503$		−	37.1849i		−	1.65799i	0.559255	−	0.828996i	$-0.311087\pi$
$504$		0			0
$505$		−	9.97254i		−	0.443772i
$506$		0			0
$507$	35.3964	+	10.8021i	1.57201	+	0.479737i
$508$		0			0
$509$	19.5596	−	19.5596i	0.866964	−	0.866964i	−0.125171	−	0.992135i	$-0.539948\pi$
$509$	19.5596	−	19.5596i	0.866964	−	0.866964i	0.992135	+	0.125171i	$0.0399479\pi$
$510$		0			0
$511$			0.150117i			0.00664077i
$512$		0			0
$513$	3.99438	−	38.5701i	0.176356	−	1.70291i
$514$		0			0
$515$	8.15112	+	8.15112i	0.359181	+	0.359181i
$516$		0			0
$517$	16.5730	−	16.5730i	0.728881	−	0.728881i
$518$		0			0
$519$	15.4776	+	29.0735i	0.679392	+	1.27618i
$520$		0			0
$521$	−25.4362			−1.11438			−0.557191	−	0.830385i	$-0.688121\pi$
$521$	−25.4362			−1.11438			−0.557191	+	0.830385i	$0.688121\pi$
$522$		0			0
$523$	14.8379	+	14.8379i	0.648818	+	0.648818i	0.952707	−	0.303890i	$-0.0982854\pi$
$523$	14.8379	+	14.8379i	0.648818	+	0.648818i	−0.303890	+	0.952707i	$0.598285\pi$
$524$		0			0
$525$	−5.07116	−	1.54759i	−0.221323	−	0.0675423i
$526$		0			0
$527$	26.1570			1.13942
$528$		0			0
$529$	18.5113			0.804841
$530$		0			0
$531$	30.2476	−	5.91148i	1.31264	−	0.256536i
$532$		0			0
$533$	46.1635	+	46.1635i	1.99957	+	1.99957i
$534$		0			0
$535$	16.2644			0.703169
$536$		0			0
$537$	14.5469	−	7.74423i	0.627746	−	0.334188i
$538$		0			0
$539$	−2.67559	+	2.67559i	−0.115246	+	0.115246i
$540$		0			0
$541$	12.7481	+	12.7481i	0.548084	+	0.548084i	0.925886	−	0.377802i	$-0.123320\pi$
$541$	12.7481	+	12.7481i	0.548084	+	0.548084i	−0.377802	+	0.925886i	$0.623320\pi$
$542$		0			0
$543$	8.30347	+	15.5974i	0.356336	+	0.669349i
$544$		0			0
$545$			0.687452i			0.0294472i
$546$		0			0
$547$	−2.64668	+	2.64668i	−0.113164	+	0.113164i	−0.761421	−	0.648257i	$-0.775498\pi$
$547$	−2.64668	+	2.64668i	−0.113164	+	0.113164i	0.648257	+	0.761421i	$0.275498\pi$
$548$		0			0
$549$	0.869745	+	4.45028i	0.0371198	+	0.189933i
$550$		0			0
$551$			8.53344i			0.363537i
$552$		0			0
$553$		−	4.73116i		−	0.201189i
$554$		0			0
$555$	2.16955	−	7.10922i	0.0920924	−	0.301770i
$556$		0			0
$557$	23.4164	−	23.4164i	0.992185	−	0.992185i	−0.00778475	−	0.999970i	$-0.502478\pi$
$557$	23.4164	−	23.4164i	0.992185	−	0.992185i	0.999970	+	0.00778475i	$0.00247799\pi$
$558$		0			0
$559$			44.1568i			1.86763i
$560$		0			0
$561$	−20.0021	+	10.6483i	−0.844488	+	0.449573i
$562$		0			0
$563$	17.1877	+	17.1877i	0.724377	+	0.724377i	0.969494	−	0.245117i	$-0.0788264\pi$
$563$	17.1877	+	17.1877i	0.724377	+	0.724377i	−0.245117	+	0.969494i	$0.578826\pi$
$564$		0			0
$565$	22.2334	−	22.2334i	0.935367	−	0.935367i
$566$		0			0
$567$	−3.38843	−	8.33778i	−0.142301	−	0.350154i
$568$		0			0
$569$	−41.2360			−1.72870			−0.864352	−	0.502887i	$-0.832271\pi$
$569$	−41.2360			−1.72870			−0.864352	+	0.502887i	$0.832271\pi$
$570$		0			0
$571$	18.2966	+	18.2966i	0.765689	+	0.765689i	0.977344	−	0.211655i	$-0.0678854\pi$
$571$	18.2966	+	18.2966i	0.765689	+	0.765689i	−0.211655	+	0.977344i	$0.567885\pi$
$572$		0			0
$573$	10.9612	−	35.9178i	0.457911	−	1.50049i
$574$		0			0
$575$	6.48547			0.270463
$576$		0			0
$577$	−38.7981			−1.61519			−0.807594	−	0.589739i	$-0.799230\pi$
$577$	−38.7981			−1.61519			−0.807594	+	0.589739i	$0.799230\pi$
$578$		0			0
$579$	−7.93390	+	25.9979i	−0.329722	+	1.08044i
$580$		0			0
$581$	−1.94899	−	1.94899i	−0.0808579	−	0.0808579i
$582$		0			0
$583$	2.21903			0.0919030
$584$		0			0
$585$	−27.8800	+	41.4247i	−1.15270	+	1.71270i
$586$		0			0
$587$	1.20968	−	1.20968i	0.0499288	−	0.0499288i	−0.681702	−	0.731630i	$-0.738760\pi$
$587$	1.20968	−	1.20968i	0.0499288	−	0.0499288i	0.731630	+	0.681702i	$0.238760\pi$
$588$		0			0
$589$	39.9205	+	39.9205i	1.64489	+	1.64489i
$590$		0			0
$591$	−23.6740	+	12.6031i	−0.973817	+	0.518423i
$592$		0			0
$593$			36.1610i			1.48496i	0.669870	+	0.742478i	$0.266350\pi$
$593$			36.1610i			1.48496i	−0.669870	+	0.742478i	$0.733650\pi$
$594$		0			0
$595$	−6.94138	+	6.94138i	−0.284569	+	0.284569i
$596$		0			0
$597$	−3.86306	+	12.6585i	−0.158104	+	0.518079i
$598$		0			0
$599$		−	0.305811i		−	0.0124951i	−0.999980	−	0.00624754i	$-0.998011\pi$
$599$		−	0.305811i		−	0.0124951i	0.999980	−	0.00624754i	$-0.00198867\pi$
$600$		0			0
$601$			24.1870i			0.986608i	0.869857	+	0.493304i	$0.164211\pi$
$601$			24.1870i			0.986608i	−0.869857	+	0.493304i	$0.835789\pi$
$602$		0			0
$603$	20.0513	−	3.91875i	0.816551	−	0.159584i
$604$		0			0
$605$	−6.66036	+	6.66036i	−0.270782	+	0.270782i
$606$		0			0
$607$		−	28.4958i		−	1.15661i	−0.815821	−	0.578304i	$-0.803715\pi$
$607$		−	28.4958i		−	1.15661i	0.815821	−	0.578304i	$-0.196285\pi$
$608$		0			0
$609$	0.930731	+	1.74830i	0.0377151	+	0.0708449i
$610$		0			0
$611$	−25.6765	−	25.6765i	−1.03876	−	1.03876i
$612$		0			0
$613$	−16.5522	+	16.5522i	−0.668539	+	0.668539i	−0.957378	−	0.288839i	$-0.906731\pi$
$613$	−16.5522	+	16.5522i	−0.668539	+	0.668539i	0.288839	+	0.957378i	$0.406731\pi$
$614$		0			0
$615$	−48.3417	+	25.7353i	−1.94933	+	1.03775i
$616$		0			0
$617$	−13.3264			−0.536502			−0.268251	−	0.963349i	$-0.586446\pi$
$617$	−13.3264			−0.536502			−0.268251	+	0.963349i	$0.586446\pi$
$618$		0			0
$619$	21.1744	+	21.1744i	0.851072	+	0.851072i	0.990265	−	0.139193i	$-0.0444509\pi$
$619$	21.1744	+	21.1744i	0.851072	+	0.851072i	−0.139193	+	0.990265i	$0.544451\pi$
$620$		0			0
$621$	6.94112	+	8.54487i	0.278537	+	0.342894i
$622$		0			0
$623$	11.7352			0.470161
$624$		0			0
$625$	30.9351			1.23741
$626$		0			0
$627$	−46.7782	−	14.2755i	−1.86814	−	0.570110i
$628$		0			0
$629$	−3.69528	−	3.69528i	−0.147340	−	0.147340i
$630$		0			0
$631$	24.6361			0.980750			0.490375	−	0.871512i	$-0.336860\pi$
$631$	24.6361			0.980750			0.490375	+	0.871512i	$0.336860\pi$
$632$		0			0
$633$	−2.01260	−	3.78051i	−0.0799937	−	0.150262i
$634$		0			0
$635$	40.8729	−	40.8729i	1.62199	−	1.62199i
$636$		0			0
$637$	4.14527	+	4.14527i	0.164242	+	0.164242i
$638$		0			0
$639$	−3.07825	+	4.57372i	−0.121774	+	0.180933i
$640$		0			0
$641$			4.61434i			0.182255i	0.995839	+	0.0911277i	$0.0290471\pi$
$641$			4.61434i			0.182255i	−0.995839	+	0.0911277i	$0.970953\pi$
$642$		0			0
$643$	20.0646	−	20.0646i	0.791270	−	0.791270i	−0.190430	−	0.981701i	$-0.560988\pi$
$643$	20.0646	−	20.0646i	0.791270	−	0.791270i	0.981701	+	0.190430i	$0.0609883\pi$
$644$		0			0
$645$	−35.4284	−	10.8119i	−1.39499	−	0.425716i
$646$		0			0
$647$			0.937803i			0.0368689i	0.999830	+	0.0184344i	$0.00586819\pi$
$647$			0.937803i			0.0368689i	−0.999830	+	0.0184344i	$0.994132\pi$
$648$		0			0
$649$		−	38.8726i		−	1.52588i
$650$		0			0
$651$	12.5328	+	3.82471i	0.491201	+	0.149902i
$652$		0			0
$653$	−35.8179	+	35.8179i	−1.40166	+	1.40166i	−0.606830	+	0.794832i	$0.707559\pi$
$653$	−35.8179	+	35.8179i	−1.40166	+	1.40166i	−0.794832	+	0.606830i	$0.792441\pi$
$654$		0			0
$655$		−	5.92571i		−	0.231537i
$656$		0			0
$657$	−0.251453	+	0.373613i	−0.00981010	+	0.0145760i
$658$		0			0
$659$	−6.40546	−	6.40546i	−0.249521	−	0.249521i	0.571253	−	0.820774i	$-0.306458\pi$
$659$	−6.40546	−	6.40546i	−0.249521	−	0.249521i	−0.820774	+	0.571253i	$0.806458\pi$
$660$		0			0
$661$	−14.4512	+	14.4512i	−0.562087	+	0.562087i	−0.929900	−	0.367813i	$-0.880107\pi$
$661$	−14.4512	+	14.4512i	−0.562087	+	0.562087i	0.367813	+	0.929900i	$0.380107\pi$
$662$		0			0
$663$	16.4974	+	30.9891i	0.640707	+	1.20352i
$664$		0			0
$665$	−21.1877			−0.821623
$666$		0			0
$667$	−1.71310	−	1.71310i	−0.0663315	−	0.0663315i
$668$		0			0
$669$	−30.9737	−	9.45238i	−1.19751	−	0.365450i
$670$		0			0
$671$	5.71925			0.220789
$672$		0			0
$673$	43.3652			1.67161			0.835803	−	0.549030i	$-0.185003\pi$
$673$	43.3652			1.67161			0.835803	+	0.549030i	$0.185003\pi$
$674$		0			0
$675$	−10.0289	−	12.3461i	−0.386013	−	0.475201i
$676$		0			0
$677$	−30.9808	−	30.9808i	−1.19069	−	1.19069i	−0.976874	−	0.213814i	$-0.931411\pi$
$677$	−30.9808	−	30.9808i	−1.19069	−	1.19069i	−0.213814	−	0.976874i	$-0.568589\pi$
$678$		0			0
$679$	15.6205			0.599458
$680$		0			0
$681$	7.33592	−	3.90537i	0.281113	−	0.149654i
$682$		0			0
$683$	−26.9852	+	26.9852i	−1.03256	+	1.03256i	−0.0331099	+	0.999452i	$0.510541\pi$
$683$	−26.9852	+	26.9852i	−1.03256	+	1.03256i	−0.999452	+	0.0331099i	$0.989459\pi$
$684$		0			0
$685$	−4.01057	−	4.01057i	−0.153236	−	0.153236i
$686$		0			0
$687$	18.5204	+	34.7891i	0.706598	+	1.32729i
$688$		0			0
$689$		−	3.43794i		−	0.130975i
$690$		0			0
$691$	11.3245	−	11.3245i	0.430804	−	0.430804i	−0.458098	−	0.888902i	$-0.651469\pi$
$691$	11.3245	−	11.3245i	0.430804	−	0.430804i	0.888902	+	0.458098i	$0.151469\pi$
$692$		0			0
$693$	−11.1408	+	2.17731i	−0.423203	+	0.0827093i
$694$		0			0
$695$			53.0982i			2.01413i
$696$		0			0
$697$			38.5043i			1.45845i
$698$		0			0
$699$	7.05092	−	23.1045i	0.266690	−	0.873894i
$700$		0			0
$701$	−32.4006	+	32.4006i	−1.22376	+	1.22376i	−0.257468	+	0.966287i	$0.582888\pi$
$701$	−32.4006	+	32.4006i	−1.22376	+	1.22376i	−0.966287	+	0.257468i	$0.917112\pi$
$702$		0			0
$703$		−	11.2794i		−	0.425409i
$704$		0			0
$705$	26.8880	−	14.3142i	1.01266	−	0.539103i
$706$		0			0
$707$	−2.48366	−	2.48366i	−0.0934078	−	0.0934078i
$708$		0			0
$709$	17.3817	−	17.3817i	0.652782	−	0.652782i	−0.300880	−	0.953662i	$-0.597280\pi$
$709$	17.3817	−	17.3817i	0.652782	−	0.652782i	0.953662	+	0.300880i	$0.0972804\pi$
$710$		0			0
$711$	7.92492	−	11.7750i	0.297208	−	0.441597i
$712$		0			0
$713$	−16.0282			−0.600260
$714$		0			0
$715$	44.5333	+	44.5333i	1.66545	+	1.66545i
$716$		0			0
$717$	9.44391	−	30.9459i	0.352689	−	1.15570i
$718$		0			0
$719$	7.89298			0.294359			0.147179	−	0.989110i	$-0.452981\pi$
$719$	7.89298			0.294359			0.147179	+	0.989110i	$0.452981\pi$
$720$		0			0
$721$	4.06008			0.151205
$722$		0			0
$723$	1.38117	−	4.52582i	0.0513661	−	0.168317i
$724$		0			0
$725$	2.47518	+	2.47518i	0.0919258	+	0.0919258i
$726$		0			0
$727$	−19.4072			−0.719772			−0.359886	−	0.932996i	$-0.617184\pi$
$727$	−19.4072			−0.719772			−0.359886	+	0.932996i	$0.617184\pi$
$728$		0			0
$729$	5.53299	−	26.4270i	0.204926	−	0.978778i
$730$		0			0
$731$	−18.4152	+	18.4152i	−0.681112	+	0.681112i
$732$		0			0
$733$	−0.611163	−	0.611163i	−0.0225738	−	0.0225738i	0.695730	−	0.718304i	$-0.255081\pi$
$733$	−0.611163	−	0.611163i	−0.0225738	−	0.0225738i	−0.718304	+	0.695730i	$0.755081\pi$
$734$		0			0
$735$	−4.34086	+	2.31091i	−0.160115	+	0.0852392i
$736$		0			0
$737$		−	25.7688i		−	0.949206i
$738$		0			0
$739$	1.88492	−	1.88492i	0.0693379	−	0.0693379i	−0.671587	−	0.740925i	$-0.734387\pi$
$739$	1.88492	−	1.88492i	0.0693379	−	0.0693379i	0.740925	+	0.671587i	$0.234387\pi$
$740$		0			0
$741$	−22.1170	+	72.4733i	−0.812488	+	2.66237i
$742$		0			0
$743$			33.5550i			1.23101i	0.788132	+	0.615506i	$0.211048\pi$
$743$			33.5550i			1.23101i	−0.788132	+	0.615506i	$0.788952\pi$
$744$		0			0
$745$		−	22.0780i		−	0.808877i
$746$		0			0
$747$	−1.58603	−	8.11534i	−0.0580299	−	0.296925i
$748$		0			0
$749$	4.05064	−	4.05064i	0.148007	−	0.148007i
$750$		0			0
$751$			48.8813i			1.78370i	0.452327	+	0.891852i	$0.350594\pi$
$751$			48.8813i			1.78370i	−0.452327	+	0.891852i	$0.649406\pi$
$752$		0			0
$753$	7.66611	+	14.4002i	0.279369	+	0.524772i
$754$		0			0
$755$	−0.848680	−	0.848680i	−0.0308866	−	0.0308866i
$756$		0			0
$757$	0.316040	−	0.316040i	0.0114867	−	0.0114867i	−0.701340	−	0.712827i	$-0.747415\pi$
$757$	0.316040	−	0.316040i	0.0114867	−	0.0114867i	0.712827	+	0.701340i	$0.247415\pi$
$758$		0			0
$759$	12.2566	−	6.52496i	0.444887	−	0.236841i
$760$		0			0
$761$	5.43529			0.197029			0.0985146	−	0.995136i	$-0.468591\pi$
$761$	5.43529			0.197029			0.0985146	+	0.995136i	$0.468591\pi$
$762$		0			0
$763$	0.171210	+	0.171210i	0.00619822	+	0.00619822i
$764$		0			0
$765$	−28.9030	+	5.64869i	−1.04499	+	0.204229i
$766$		0			0
$767$	−60.2251			−2.17460
$768$		0			0
$769$	17.0188			0.613715			0.306858	−	0.951755i	$-0.400722\pi$
$769$	17.0188			0.613715			0.306858	+	0.951755i	$0.400722\pi$
$770$		0			0
$771$	7.53821	+	2.30047i	0.271482	+	0.0828494i
$772$		0			0
$773$	−18.9777	−	18.9777i	−0.682581	−	0.682581i	0.278000	−	0.960581i	$-0.410329\pi$
$773$	−18.9777	−	18.9777i	−0.682581	−	0.682581i	−0.960581	+	0.278000i	$0.910329\pi$
$774$		0			0
$775$	23.1584			0.831873
$776$		0			0
$777$	−1.23022	−	2.31088i	−0.0441341	−	0.0829024i
$778$		0			0
$779$	−58.7647	+	58.7647i	−2.10546	+	2.10546i
$780$		0			0
$781$	4.91694	+	4.91694i	0.175942	+	0.175942i
$782$		0			0
$783$	−0.612073	+	5.91023i	−0.0218737	+	0.211214i
$784$		0			0
$785$			10.4673i			0.373593i
$786$		0			0
$787$	27.6585	−	27.6585i	0.985920	−	0.985920i	−0.0139824	−	0.999902i	$-0.504451\pi$
$787$	27.6585	−	27.6585i	0.985920	−	0.985920i	0.999902	+	0.0139824i	$0.00445090\pi$
$788$		0			0
$789$	−7.68818	−	2.34624i	−0.273707	−	0.0835283i
$790$		0			0
$791$		−	11.0745i		−	0.393763i
$792$		0			0
$793$		−	8.86081i		−	0.314656i
$794$		0			0
$795$	2.75837	+	0.841785i	0.0978293	+	0.0298550i
$796$		0			0
$797$	−39.0228	+	39.0228i	−1.38226	+	1.38226i	−0.541658	+	0.840599i	$0.682203\pi$
$797$	−39.0228	+	39.0228i	−1.38226	+	1.38226i	−0.840599	+	0.541658i	$0.817797\pi$
$798$		0			0
$799$		−	21.4164i		−	0.757656i
$800$		0			0
$801$	29.2068	+	19.6570i	1.03197	+	0.694547i
$802$		0			0
$803$	0.401650	+	0.401650i	0.0141739	+	0.0141739i
$804$		0			0
$805$	4.25345	−	4.25345i	0.149915	−	0.149915i
$806$		0			0
$807$	−12.3012	−	23.1069i	−0.433024	−	0.813402i
$808$		0			0
$809$	29.8574			1.04973			0.524864	−	0.851186i	$-0.324116\pi$
$809$	29.8574			1.04973			0.524864	+	0.851186i	$0.324116\pi$
$810$		0			0
$811$	26.0869	+	26.0869i	0.916033	+	0.916033i	0.996738	−	0.0807047i	$-0.0257171\pi$
$811$	26.0869	+	26.0869i	0.916033	+	0.916033i	−0.0807047	+	0.996738i	$0.525717\pi$
$812$		0			0
$813$	−7.14054	−	2.17911i	−0.250430	−	0.0764248i
$814$		0			0
$815$	−27.8724			−0.976327
$816$		0			0
$817$	−56.2101			−1.96654
$818$		0			0
$819$	3.37330	+	17.2604i	0.117873	+	0.603126i
$820$		0			0
$821$	1.05370	+	1.05370i	0.0367745	+	0.0367745i	0.725255	−	0.688480i	$-0.241722\pi$
$821$	1.05370	+	1.05370i	0.0367745	+	0.0367745i	−0.688480	+	0.725255i	$0.741722\pi$
$822$		0			0
$823$	−3.65490			−0.127402			−0.0637009	−	0.997969i	$-0.520290\pi$
$823$	−3.65490			−0.127402			−0.0637009	+	0.997969i	$0.520290\pi$
$824$		0			0
$825$	−17.7090	+	9.42761i	−0.616549	+	0.328227i
$826$		0			0
$827$	30.2097	−	30.2097i	1.05049	−	1.05049i	0.0518372	−	0.998656i	$-0.483492\pi$
$827$	30.2097	−	30.2097i	1.05049	−	1.05049i	0.998656	−	0.0518372i	$-0.0165077\pi$
$828$		0			0
$829$	12.1139	+	12.1139i	0.420733	+	0.420733i	0.885456	−	0.464723i	$-0.153846\pi$
$829$	12.1139	+	12.1139i	0.420733	+	0.420733i	−0.464723	+	0.885456i	$0.653846\pi$
$830$		0			0
$831$	−8.32669	−	15.6410i	−0.288850	−	0.542581i
$832$		0			0
$833$			3.45751i			0.119795i
$834$		0			0
$835$	−13.4029	+	13.4029i	−0.463827	+	0.463827i
$836$		0			0
$837$	24.7854	+	30.5121i	0.856709	+	1.05465i
$838$		0			0
$839$			7.94474i			0.274283i	0.990551	+	0.137142i	$0.0437915\pi$
$839$			7.94474i			0.274283i	−0.990551	+	0.137142i	$0.956208\pi$
$840$		0			0
$841$			27.6924i			0.954910i
$842$		0			0
$843$	−8.69349	+	28.4869i	−0.299420	+	0.981142i
$844$		0			0
$845$	42.8961	−	42.8961i	1.47567	−	1.47567i
$846$		0			0
$847$			3.31753i			0.113992i
$848$		0			0
$849$	11.7847	−	6.27374i	0.404450	−	0.215314i
$850$		0			0
$851$	2.26435	+	2.26435i	0.0776208	+	0.0776208i
$852$		0			0
$853$	1.88989	−	1.88989i	0.0647086	−	0.0647086i	−0.674012	−	0.738720i	$-0.735430\pi$
$853$	1.88989	−	1.88989i	0.0647086	−	0.0647086i	0.738720	+	0.674012i	$0.235430\pi$
$854$		0			0
$855$	−52.7323	−	35.4904i	−1.80341	−	1.21375i
$856$		0			0
$857$	−23.8277			−0.813940			−0.406970	−	0.913441i	$-0.633415\pi$
$857$	−23.8277			−0.813940			−0.406970	+	0.913441i	$0.633415\pi$
$858$		0			0
$859$	6.88165	+	6.88165i	0.234799	+	0.234799i	0.814692	−	0.579893i	$-0.196906\pi$
$859$	6.88165	+	6.88165i	0.234799	+	0.234799i	−0.579893	+	0.814692i	$0.696906\pi$
$860$		0			0
$861$	−5.63014	+	18.4489i	−0.191874	+	0.628737i
$862$		0			0
$863$	45.2371			1.53989			0.769944	−	0.638111i	$-0.220284\pi$
$863$	45.2371			1.53989			0.769944	+	0.638111i	$0.220284\pi$
$864$		0			0
$865$	53.9905			1.83573
$866$		0			0
$867$	2.55088	−	8.35876i	0.0866325	−	0.283878i
$868$		0			0
$869$	−12.6586	−	12.6586i	−0.429415	−	0.429415i
$870$		0			0
$871$	−39.9235			−1.35276
$872$		0			0
$873$	38.8765	+	26.1650i	1.31577	+	0.885551i
$874$		0			0
$875$	3.89252	−	3.89252i	0.131591	−	0.131591i
$876$		0			0
$877$	−6.65724	−	6.65724i	−0.224799	−	0.224799i	0.585717	−	0.810516i	$-0.300813\pi$
$877$	−6.65724	−	6.65724i	−0.224799	−	0.224799i	−0.810516	+	0.585717i	$0.800813\pi$
$878$		0			0
$879$	21.2980	−	11.3382i	0.718363	−	0.382429i
$880$		0			0
$881$		−	48.4915i		−	1.63372i	−0.576836	−	0.816860i	$-0.695713\pi$
$881$		−	48.4915i		−	1.63372i	0.576836	−	0.816860i	$-0.304287\pi$
$882$		0			0
$883$	19.5308	−	19.5308i	0.657265	−	0.657265i	−0.297467	−	0.954732i	$-0.596142\pi$
$883$	19.5308	−	19.5308i	0.657265	−	0.657265i	0.954732	+	0.297467i	$0.0961419\pi$
$884$		0			0
$885$	14.7462	−	48.3206i	0.495688	−	1.62428i
$886$		0			0
$887$			0.143214i			0.00480867i	0.999997	+	0.00240433i	$0.000765324\pi$
$887$			0.143214i			0.00480867i	−0.999997	+	0.00240433i	$0.999235\pi$
$888$		0			0
$889$		−	20.3588i		−	0.682812i
$890$		0			0
$891$	−31.3745	−	13.2424i	−1.05108	−	0.443637i
$892$		0			0
$893$	32.6853	−	32.6853i	1.09377	−	1.09377i
$894$		0			0
$895$		−	27.0141i		−	0.902983i
$896$		0			0
$897$	−10.1091	−	18.9891i	−0.337532	−	0.634028i
$898$		0			0
$899$	−6.11715	−	6.11715i	−0.204018	−	0.204018i
$900$		0			0
$901$	1.43377	−	1.43377i	0.0477656	−	0.0477656i
$902$		0			0
$903$	−11.5162	+	6.13076i	−0.383234	+	0.204019i
$904$		0			0
$905$	28.9649			0.962827
$906$		0			0
$907$	17.7033	+	17.7033i	0.587828	+	0.587828i	0.937043	−	0.349215i	$-0.113552\pi$
$907$	17.7033	+	17.7033i	0.587828	+	0.587828i	−0.349215	+	0.937043i	$0.613552\pi$
$908$		0			0
$909$	−2.02113	−	10.3416i	−0.0670367	−	0.343011i
$910$		0			0
$911$	3.93986			0.130534			0.0652668	−	0.997868i	$-0.479210\pi$
$911$	3.93986			0.130534			0.0652668	+	0.997868i	$0.479210\pi$
$912$		0			0
$913$	−10.4294			−0.345163
$914$		0			0
$915$	7.10931	+	2.16958i	0.235027	+	0.0717242i
$916$		0			0
$917$	−1.47580	−	1.47580i	−0.0487352	−	0.0487352i
$918$		0			0
$919$	30.7916			1.01572			0.507861	−	0.861439i	$-0.330436\pi$
$919$	30.7916			1.01572			0.507861	+	0.861439i	$0.330436\pi$
$920$		0			0
$921$	3.80891	+	7.15474i	0.125508	+	0.235757i
$922$		0			0
$923$	7.61779	−	7.61779i	0.250743	−	0.250743i
$924$		0			0
$925$	−3.27165	−	3.27165i	−0.107571	−	0.107571i
$926$		0			0
$927$	10.1048	+	6.80082i	0.331885	+	0.223368i
$928$		0			0
$929$			47.2601i			1.55055i	0.631623	+	0.775276i	$0.282389\pi$
$929$			47.2601i			1.55055i	−0.631623	+	0.775276i	$0.717611\pi$
$930$		0			0
$931$	−5.27680	+	5.27680i	−0.172940	+	0.172940i
$932$		0			0
$933$	28.3535	+	8.65278i	0.928253	+	0.283279i
$934$		0			0
$935$			37.1445i			1.21476i
$936$		0			0
$937$			8.56087i			0.279672i	0.990175	+	0.139836i	$0.0446575\pi$
$937$			8.56087i			0.279672i	−0.990175	+	0.139836i	$0.955343\pi$
$938$		0			0
$939$	−41.0188	−	12.5179i	−1.33860	−	0.408506i
$940$		0			0
$941$	−6.46572	+	6.46572i	−0.210777	+	0.210777i	−0.804597	−	0.593821i	$-0.797619\pi$
$941$	−6.46572	+	6.46572i	−0.210777	+	0.210777i	0.593821	+	0.804597i	$0.297619\pi$
$942$		0			0
$943$		−	23.5942i		−	0.768332i
$944$		0			0
$945$	−14.6745	−	1.51972i	−0.477362	−	0.0494364i
$946$		0			0
$947$	−38.7816	−	38.7816i	−1.26023	−	1.26023i	−0.950980	−	0.309251i	$-0.899922\pi$
$947$	−38.7816	−	38.7816i	−1.26023	−	1.26023i	−0.309251	−	0.950980i	$-0.600078\pi$
$948$		0			0
$949$	0.622275	−	0.622275i	0.0201999	−	0.0201999i
$950$		0			0
$951$	−15.2551	−	28.6554i	−0.494679	−	0.929216i
$952$		0			0
$953$	30.9603			1.00290			0.501451	−	0.865186i	$-0.332800\pi$
$953$	30.9603			1.00290			0.501451	+	0.865186i	$0.332800\pi$
$954$		0			0
$955$	−43.5280	−	43.5280i	−1.40853	−	1.40853i
$956$		0			0
$957$	7.16799	+	2.18749i	0.231708	+	0.0707115i
$958$		0			0
$959$	−1.99767			−0.0645080
$960$		0			0
$961$	−26.2335			−0.846244
$962$		0			0
$963$	16.8663	−	3.29629i	0.543510	−	0.106221i
$964$		0			0
$965$	31.5063	+	31.5063i	1.01422	+	1.01422i
$966$		0			0
$967$	8.53720			0.274538			0.137269	−	0.990534i	$-0.456168\pi$
$967$	8.53720			0.274538			0.137269	+	0.990534i	$0.456168\pi$
$968$		0			0
$969$	−39.4481	+	21.0007i	−1.26726	+	0.674639i
$970$		0			0
$971$	−5.49472	+	5.49472i	−0.176334	+	0.176334i	−0.789756	−	0.613422i	$-0.789793\pi$
$971$	−5.49472	+	5.49472i	−0.176334	+	0.176334i	0.613422	+	0.789756i	$0.289793\pi$
$972$		0			0
$973$	13.2241	+	13.2241i	0.423946	+	0.423946i
$974$		0			0
$975$	14.6062	+	27.4365i	0.467771	+	0.878671i
$976$		0			0
$977$		−	30.5696i		−	0.978007i	−0.872282	−	0.489003i	$-0.837361\pi$
$977$		−	30.5696i		−	0.978007i	0.872282	−	0.489003i	$-0.162639\pi$
$978$		0			0
$979$	31.3986	−	31.3986i	1.00350	−	1.00350i
$980$		0			0
$981$	0.139326	+	0.712895i	0.00444832	+	0.0227610i
$982$		0			0
$983$		−	41.1178i		−	1.31146i	−0.754998	−	0.655728i	$-0.772362\pi$
$983$		−	41.1178i		−	1.31146i	0.754998	−	0.655728i	$-0.227638\pi$
$984$		0			0
$985$			43.9634i			1.40079i
$986$		0			0
$987$	3.13152	−	10.2614i	0.0996775	−	0.326624i
$988$		0			0
$989$	11.2843	−	11.2843i	0.358818	−	0.358818i
$990$		0			0
$991$		−	28.3786i		−	0.901477i	−0.892656	−	0.450739i	$-0.851161\pi$
$991$		−	28.3786i		−	0.901477i	0.892656	−	0.450739i	$-0.148839\pi$
$992$		0			0
$993$	−16.3933	+	8.72719i	−0.520227	+	0.276949i
$994$		0			0
$995$	15.3406	+	15.3406i	0.486329	+	0.486329i
$996$		0			0
$997$	34.4849	−	34.4849i	1.09215	−	1.09215i	0.0968479	−	0.995299i	$-0.469124\pi$
$997$	34.4849	−	34.4849i	1.09215	−	1.09215i	0.995299	−	0.0968479i	$-0.0308761\pi$
$998$		0			0
$999$	0.809029	−	7.81205i	0.0255965	−	0.247162i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.s.d.239.15		48
3.2	odd	2	inner	1344.2.s.d.239.21		48
4.3	odd	2		336.2.s.d.323.5	yes	48
12.11	even	2		336.2.s.d.323.20	yes	48
16.5	even	4		336.2.s.d.155.20	yes	48
16.11	odd	4	inner	1344.2.s.d.911.21		48
48.5	odd	4		336.2.s.d.155.5	✓	48
48.11	even	4	inner	1344.2.s.d.911.15		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.d.155.5	✓	48	48.5	odd	4
336.2.s.d.155.20	yes	48	16.5	even	4
336.2.s.d.323.5	yes	48	4.3	odd	2
336.2.s.d.323.20	yes	48	12.11	even	2
1344.2.s.d.239.15		48	1.1	even	1	trivial
1344.2.s.d.239.21		48	3.2	odd	2	inner
1344.2.s.d.911.15		48	48.11	even	4	inner
1344.2.s.d.911.21		48	16.11	odd	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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.505560 - 1.65663i) q^{3} +(-2.00763 - 2.00763i) q^{5} -1.00000 q^{7} +(-2.48882 - 1.67505i) q^{9} +O(q^{10})\)	\(q+(0.505560 - 1.65663i) q^{3} +(-2.00763 - 2.00763i) q^{5} -1.00000 q^{7} +(-2.48882 - 1.67505i) q^{9} +(-2.67559 + 2.67559i) q^{11} +(4.14527 + 4.14527i) q^{13} +(-4.34086 + 2.31091i) q^{15} +3.45751i q^{17} +(-5.27680 + 5.27680i) q^{19} +(-0.505560 + 1.65663i) q^{21} -2.11865i q^{23} +3.06114i q^{25} +(-4.03317 + 3.27620i) q^{27} +(0.808582 - 0.808582i) q^{29} -7.56529i q^{31} +(3.07978 + 5.78512i) q^{33} +(2.00763 + 2.00763i) q^{35} +(-1.06877 + 1.06877i) q^{37} +(8.96285 - 4.77148i) q^{39} +11.1364 q^{41} +(5.32616 + 5.32616i) q^{43} +(1.63375 + 8.35949i) q^{45} -6.19416 q^{47} +1.00000 q^{49} +(5.72779 + 1.74798i) q^{51} +(-0.414682 - 0.414682i) q^{53} +10.7432 q^{55} +(6.07394 + 11.4094i) q^{57} +(-7.26431 + 7.26431i) q^{59} +(-1.06878 - 1.06878i) q^{61} +(2.48882 + 1.67505i) q^{63} -16.6443i q^{65} +(-4.81554 + 4.81554i) q^{67} +(-3.50981 - 1.07110i) q^{69} -1.83771i q^{71} -0.150117i q^{73} +(5.07116 + 1.54759i) q^{75} +(2.67559 - 2.67559i) q^{77} +4.73116i q^{79} +(3.38843 + 8.33778i) q^{81} +(1.94899 + 1.94899i) q^{83} +(6.94138 - 6.94138i) q^{85} +(-0.930731 - 1.74830i) q^{87} -11.7352 q^{89} +(-4.14527 - 4.14527i) q^{91} +(-12.5328 - 3.82471i) q^{93} +21.1877 q^{95} -15.6205 q^{97} +(11.1408 - 2.17731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{7}+O(q^{10}) \) 48 * q - 48 * q^7	\( 48 q - 48 q^{7} - 8 q^{19} + 12 q^{27} + 16 q^{37} + 24 q^{39} + 48 q^{43} + 20 q^{45} + 48 q^{49} + 32 q^{55} + 8 q^{61} + 16 q^{67} - 28 q^{69} + 12 q^{75} - 48 q^{85} - 56 q^{87} - 64 q^{93} - 32 q^{99}+O(q^{100}) \) 48 * q - 48 * q^7 - 8 * q^19 + 12 * q^27 + 16 * q^37 + 24 * q^39 + 48 * q^43 + 20 * q^45 + 48 * q^49 + 32 * q^55 + 8 * q^61 + 16 * q^67 - 28 * q^69 + 12 * q^75 - 48 * q^85 - 56 * q^87 - 64 * q^93 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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