LMFDB - Embedded newform 1344.2.u.a.1231.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(559,1344)]

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, 0, 2]))

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

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

chi := DirichletCharacter("1344.559");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.u (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:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1231.4
Character	$\chi$	$=$	1344.1231
Dual form			1344.2.u.a.559.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(-1.80101 + 1.80101i) q^{5} +(1.67026 + 2.05189i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(-1.80101 + 1.80101i) q^{5} +(1.67026 + 2.05189i) q^{7} -1.00000i q^{9} +(4.52322 - 4.52322i) q^{11} +(-2.59667 - 2.59667i) q^{13} -2.54701i q^{15} -6.20372i q^{17} +(1.43485 - 1.43485i) q^{19} +(-2.63195 - 0.269853i) q^{21} +3.79802 q^{23} -1.48727i q^{25} +(0.707107 + 0.707107i) q^{27} +(-1.50697 + 1.50697i) q^{29} +4.03614 q^{31} +6.39680i q^{33} +(-6.70362 - 0.687319i) q^{35} +(-1.57956 - 1.57956i) q^{37} +3.67224 q^{39} +9.26889 q^{41} +(-4.81028 + 4.81028i) q^{43} +(1.80101 + 1.80101i) q^{45} +4.48761 q^{47} +(-1.42048 + 6.85436i) q^{49} +(4.38669 + 4.38669i) q^{51} +(6.91789 + 6.91789i) q^{53} +16.2927i q^{55} +2.02919i q^{57} +(-0.516751 - 0.516751i) q^{59} +(-6.02748 - 6.02748i) q^{61} +(2.05189 - 1.67026i) q^{63} +9.35325 q^{65} +(-6.19917 - 6.19917i) q^{67} +(-2.68560 + 2.68560i) q^{69} +10.5595 q^{71} +3.85786 q^{73} +(1.05166 + 1.05166i) q^{75} +(16.8361 + 1.72620i) q^{77} -5.09974i q^{79} -1.00000 q^{81} +(10.0631 - 10.0631i) q^{83} +(11.1730 + 11.1730i) q^{85} -2.13118i q^{87} +0.264516 q^{89} +(0.990965 - 9.66517i) q^{91} +(-2.85398 + 2.85398i) q^{93} +5.16836i q^{95} +7.14810i q^{97} +(-4.52322 - 4.52322i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 8 q^{11} + 16 q^{23} + 16 q^{29} - 24 q^{35} + 16 q^{37} + 8 q^{43} + 16 q^{53} - 56 q^{67} + 128 q^{71} - 64 q^{81} - 8 q^{91} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^11 + 16 * q^23 + 16 * q^29 - 24 * q^35 + 16 * q^37 + 8 * q^43 + 16 * q^53 - 56 * q^67 + 128 * q^71 - 64 * q^81 - 8 * q^91 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	−1.80101	+	1.80101i	−0.805436	+	0.805436i	−0.983939	−	0.178503i	$-0.942875\pi$
$5$	−1.80101	+	1.80101i	−0.805436	+	0.805436i	0.178503	+	0.983939i	$0.442875\pi$
$6$		0			0
$7$	1.67026	+	2.05189i	0.631298	+	0.775540i
$7$	1.67026	+	2.05189i	0.631298	+	0.775540i
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	4.52322	−	4.52322i	1.36380	−	1.36380i	0.494789	−	0.869013i	$-0.335245\pi$
$11$	4.52322	−	4.52322i	1.36380	−	1.36380i	0.869013	−	0.494789i	$-0.164755\pi$
$12$		0			0
$13$	−2.59667	−	2.59667i	−0.720186	−	0.720186i	0.248457	−	0.968643i	$-0.420077\pi$
$13$	−2.59667	−	2.59667i	−0.720186	−	0.720186i	−0.968643	+	0.248457i	$0.920077\pi$
$14$		0			0
$15$		−	2.54701i		−	0.657636i
$16$		0			0
$17$		−	6.20372i		−	1.50462i	−0.658808	−	0.752311i	$-0.728939\pi$
$17$		−	6.20372i		−	1.50462i	0.658808	−	0.752311i	$-0.271061\pi$
$18$		0			0
$19$	1.43485	−	1.43485i	0.329178	−	0.329178i	−0.523096	−	0.852274i	$-0.675223\pi$
$19$	1.43485	−	1.43485i	0.329178	−	0.329178i	0.852274	+	0.523096i	$0.175223\pi$
$20$		0			0
$21$	−2.63195	−	0.269853i	−0.574339	−	0.0588867i
$22$		0			0
$23$	3.79802			0.791942			0.395971	−	0.918263i	$-0.370408\pi$
$23$	3.79802			0.791942			0.395971	+	0.918263i	$0.370408\pi$
$24$		0			0
$25$		−	1.48727i		−	0.297455i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$	−1.50697	+	1.50697i	−0.279837	+	0.279837i	−0.833044	−	0.553207i	$-0.813404\pi$
$29$	−1.50697	+	1.50697i	−0.279837	+	0.279837i	0.553207	+	0.833044i	$0.313404\pi$
$30$		0			0
$31$	4.03614			0.724912			0.362456	−	0.932001i	$-0.381938\pi$
$31$	4.03614			0.724912			0.362456	+	0.932001i	$0.381938\pi$
$32$		0			0
$33$			6.39680i			1.11354i
$34$		0			0
$35$	−6.70362	−	0.687319i	−1.13312	−	0.116178i
$36$		0			0
$37$	−1.57956	−	1.57956i	−0.259678	−	0.259678i	0.565245	−	0.824923i	$-0.308782\pi$
$37$	−1.57956	−	1.57956i	−0.259678	−	0.259678i	−0.824923	+	0.565245i	$0.808782\pi$
$38$		0			0
$39$	3.67224			0.588029
$40$		0			0
$41$	9.26889			1.44756			0.723779	−	0.690032i	$-0.242404\pi$
$41$	9.26889			1.44756			0.723779	+	0.690032i	$0.242404\pi$
$42$		0			0
$43$	−4.81028	+	4.81028i	−0.733561	+	0.733561i	−0.971323	−	0.237762i	$-0.923586\pi$
$43$	−4.81028	+	4.81028i	−0.733561	+	0.733561i	0.237762	+	0.971323i	$0.423586\pi$
$44$		0			0
$45$	1.80101	+	1.80101i	0.268479	+	0.268479i
$46$		0			0
$47$	4.48761			0.654585			0.327292	−	0.944923i	$-0.393864\pi$
$47$	4.48761			0.654585			0.327292	+	0.944923i	$0.393864\pi$
$48$		0			0
$49$	−1.42048	+	6.85436i	−0.202926	+	0.979194i
$50$		0			0
$51$	4.38669	+	4.38669i	0.614260	+	0.614260i
$52$		0			0
$53$	6.91789	+	6.91789i	0.950245	+	0.950245i	0.998820	−	0.0485746i	$-0.0154679\pi$
$53$	6.91789	+	6.91789i	0.950245	+	0.950245i	−0.0485746	+	0.998820i	$0.515468\pi$
$54$		0			0
$55$			16.2927i			2.19691i
$56$		0			0
$57$			2.02919i			0.268772i
$58$		0			0
$59$	−0.516751	−	0.516751i	−0.0672753	−	0.0672753i	0.672669	−	0.739944i	$-0.265148\pi$
$59$	−0.516751	−	0.516751i	−0.0672753	−	0.0672753i	−0.739944	+	0.672669i	$0.765148\pi$
$60$		0			0
$61$	−6.02748	−	6.02748i	−0.771739	−	0.771739i	0.206671	−	0.978410i	$-0.433737\pi$
$61$	−6.02748	−	6.02748i	−0.771739	−	0.771739i	−0.978410	+	0.206671i	$0.933737\pi$
$62$		0			0
$63$	2.05189	−	1.67026i	0.258513	−	0.210433i
$64$		0			0
$65$	9.35325			1.16013
$66$		0			0
$67$	−6.19917	−	6.19917i	−0.757349	−	0.757349i	0.218490	−	0.975839i	$-0.429887\pi$
$67$	−6.19917	−	6.19917i	−0.757349	−	0.757349i	−0.975839	+	0.218490i	$0.929887\pi$
$68$		0			0
$69$	−2.68560	+	2.68560i	−0.323309	+	0.323309i
$70$		0			0
$71$	10.5595			1.25318			0.626590	−	0.779349i	$-0.284450\pi$
$71$	10.5595			1.25318			0.626590	+	0.779349i	$0.284450\pi$
$72$		0			0
$73$	3.85786			0.451529			0.225764	−	0.974182i	$-0.427512\pi$
$73$	3.85786			0.451529			0.225764	+	0.974182i	$0.427512\pi$
$74$		0			0
$75$	1.05166	+	1.05166i	0.121435	+	0.121435i
$76$		0			0
$77$	16.8361	+	1.72620i	1.91865	+	0.196718i
$78$		0			0
$79$		−	5.09974i		−	0.573765i	−0.957966	−	0.286883i	$-0.907381\pi$
$79$		−	5.09974i		−	0.573765i	0.957966	−	0.286883i	$-0.0926190\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	10.0631	−	10.0631i	1.10457	−	1.10457i	0.110721	−	0.993851i	$-0.464684\pi$
$83$	10.0631	−	10.0631i	1.10457	−	1.10457i	0.993851	−	0.110721i	$-0.0353161\pi$
$84$		0			0
$85$	11.1730	+	11.1730i	1.21188	+	1.21188i
$86$		0			0
$87$		−	2.13118i		−	0.228486i
$88$		0			0
$89$	0.264516			0.0280386			0.0140193	−	0.999902i	$-0.495537\pi$
$89$	0.264516			0.0280386			0.0140193	+	0.999902i	$0.495537\pi$
$90$		0			0
$91$	0.990965	−	9.66517i	0.103881	−	1.01319i
$92$		0			0
$93$	−2.85398	+	2.85398i	−0.295944	+	0.295944i
$94$		0			0
$95$			5.16836i			0.530263i
$96$		0			0
$97$			7.14810i			0.725780i	0.931832	+	0.362890i	$0.118210\pi$
$97$			7.14810i			0.725780i	−0.931832	+	0.362890i	$0.881790\pi$
$98$		0			0
$99$	−4.52322	−	4.52322i	−0.454601	−	0.454601i
$100$		0			0
$101$	−0.548004	+	0.548004i	−0.0545285	+	0.0545285i	−0.733845	−	0.679317i	$-0.762276\pi$
$101$	−0.548004	+	0.548004i	−0.0545285	+	0.0545285i	0.679317	+	0.733845i	$0.262276\pi$
$102$		0			0
$103$		−	2.18981i		−	0.215768i	−0.994163	−	0.107884i	$-0.965592\pi$
$103$		−	2.18981i		−	0.215768i	0.994163	−	0.107884i	$-0.0344075\pi$
$104$		0			0
$105$	5.22618	−	4.25417i	0.510023	−	0.415164i
$106$		0			0
$107$	−5.39210	+	5.39210i	−0.521274	+	0.521274i	−0.917956	−	0.396682i	$-0.870162\pi$
$107$	−5.39210	+	5.39210i	−0.521274	+	0.521274i	0.396682	+	0.917956i	$0.370162\pi$
$108$		0			0
$109$	0.576562	−	0.576562i	0.0552247	−	0.0552247i	−0.678955	−	0.734180i	$-0.737567\pi$
$109$	0.576562	−	0.576562i	0.0552247	−	0.0552247i	0.734180	+	0.678955i	$0.237567\pi$
$110$		0			0
$111$	2.23384			0.212026
$112$		0			0
$113$	−11.7404			−1.10444			−0.552221	−	0.833698i	$-0.686220\pi$
$113$	−11.7404			−1.10444			−0.552221	+	0.833698i	$0.686220\pi$
$114$		0			0
$115$	−6.84027	+	6.84027i	−0.637858	+	0.637858i
$116$		0			0
$117$	−2.59667	+	2.59667i	−0.240062	+	0.240062i
$118$		0			0
$119$	12.7293	−	10.3618i	1.16690	−	0.949865i
$120$		0			0
$121$		−	29.9191i		−	2.71991i
$122$		0			0
$123$	−6.55410	+	6.55410i	−0.590963	+	0.590963i
$124$		0			0
$125$	−6.32646	−	6.32646i	−0.565855	−	0.565855i
$126$		0			0
$127$			12.6059i			1.11859i	0.828969	+	0.559295i	$0.188928\pi$
$127$			12.6059i			1.11859i	−0.828969	+	0.559295i	$0.811072\pi$
$128$		0			0
$129$		−	6.80277i		−	0.598950i
$130$		0			0
$131$	5.45251	−	5.45251i	0.476388	−	0.476388i	−0.427586	−	0.903975i	$-0.640636\pi$
$131$	5.45251	−	5.45251i	0.476388	−	0.476388i	0.903975	+	0.427586i	$0.140636\pi$
$132$		0			0
$133$	5.34073	+	0.547582i	0.463100	+	0.0474814i
$134$		0			0
$135$	−2.54701			−0.219212
$136$		0			0
$137$		−	13.0524i		−	1.11515i	−0.830128	−	0.557573i	$-0.811733\pi$
$137$		−	13.0524i		−	1.11515i	0.830128	−	0.557573i	$-0.188267\pi$
$138$		0			0
$139$	13.9478	+	13.9478i	1.18304	+	1.18304i	0.978953	+	0.204085i	$0.0654218\pi$
$139$	13.9478	+	13.9478i	1.18304	+	1.18304i	0.204085	+	0.978953i	$0.434578\pi$
$140$		0			0
$141$	−3.17322	+	3.17322i	−0.267233	+	0.267233i
$142$		0			0
$143$	−23.4906			−1.96438
$144$		0			0
$145$		−	5.42813i		−	0.450782i
$146$		0			0
$147$	−3.84233	−	5.85120i	−0.316910	−	0.482598i
$148$		0			0
$149$	6.12637	+	6.12637i	0.501892	+	0.501892i	0.912025	−	0.410134i	$-0.134518\pi$
$149$	6.12637	+	6.12637i	0.501892	+	0.501892i	−0.410134	+	0.912025i	$0.634518\pi$
$150$		0			0
$151$	−7.95142			−0.647077			−0.323539	−	0.946215i	$-0.604873\pi$
$151$	−7.95142			−0.647077			−0.323539	+	0.946215i	$0.604873\pi$
$152$		0			0
$153$	−6.20372			−0.501541
$154$		0			0
$155$	−7.26912	+	7.26912i	−0.583870	+	0.583870i
$156$		0			0
$157$	11.9223	+	11.9223i	0.951506	+	0.951506i	0.998877	−	0.0473717i	$-0.0150845\pi$
$157$	11.9223	+	11.9223i	0.951506	+	0.951506i	−0.0473717	+	0.998877i	$0.515085\pi$
$158$		0			0
$159$	−9.78337			−0.775872
$160$		0			0
$161$	6.34367	+	7.79311i	0.499951	+	0.614183i
$162$		0			0
$163$	1.04533	+	1.04533i	0.0818768	+	0.0818768i	0.746859	−	0.664982i	$-0.231561\pi$
$163$	1.04533	+	1.04533i	0.0818768	+	0.0818768i	−0.664982	+	0.746859i	$0.731561\pi$
$164$		0			0
$165$	−11.5207	−	11.5207i	−0.896885	−	0.896885i
$166$		0			0
$167$			15.4439i			1.19508i	0.801839	+	0.597541i	$0.203855\pi$
$167$			15.4439i			1.19508i	−0.801839	+	0.597541i	$0.796145\pi$
$168$		0			0
$169$			0.485362i			0.0373356i
$170$		0			0
$171$	−1.43485	−	1.43485i	−0.109726	−	0.109726i
$172$		0			0
$173$	−14.6842	−	14.6842i	−1.11642	−	1.11642i	−0.992263	−	0.124152i	$-0.960379\pi$
$173$	−14.6842	−	14.6842i	−1.11642	−	1.11642i	−0.124152	−	0.992263i	$-0.539621\pi$
$174$		0			0
$175$	3.05172	−	2.48413i	0.230688	−	0.187783i
$176$		0			0
$177$	0.730797			0.0549300
$178$		0			0
$179$	16.9529	+	16.9529i	1.26712	+	1.26712i	0.947569	+	0.319552i	$0.103532\pi$
$179$	16.9529	+	16.9529i	1.26712	+	1.26712i	0.319552	+	0.947569i	$0.396468\pi$
$180$		0			0
$181$	0.938465	−	0.938465i	0.0697555	−	0.0697555i	−0.671368	−	0.741124i	$-0.734293\pi$
$181$	0.938465	−	0.938465i	0.0697555	−	0.0697555i	0.741124	+	0.671368i	$0.234293\pi$
$182$		0			0
$183$	8.52414			0.630122
$184$		0			0
$185$	5.68961			0.418308
$186$		0			0
$187$	−28.0608	−	28.0608i	−2.05201	−	2.05201i
$188$		0			0
$189$	−0.269853	+	2.63195i	−0.0196289	+	0.191446i
$190$		0			0
$191$		−	17.1005i		−	1.23735i	−0.785646	−	0.618676i	$-0.787670\pi$
$191$		−	17.1005i		−	1.23735i	0.785646	−	0.618676i	$-0.212330\pi$
$192$		0			0
$193$	5.76603			0.415048			0.207524	−	0.978230i	$-0.433460\pi$
$193$	5.76603			0.415048			0.207524	+	0.978230i	$0.433460\pi$
$194$		0			0
$195$	−6.61374	+	6.61374i	−0.473620	+	0.473620i
$196$		0			0
$197$	−1.62195	−	1.62195i	−0.115559	−	0.115559i	0.646963	−	0.762522i	$-0.276039\pi$
$197$	−1.62195	−	1.62195i	−0.115559	−	0.115559i	−0.762522	+	0.646963i	$0.776039\pi$
$198$		0			0
$199$			22.0946i			1.56624i	0.621868	+	0.783122i	$0.286374\pi$
$199$			22.0946i			1.56624i	−0.621868	+	0.783122i	$0.713626\pi$
$200$		0			0
$201$	8.76695			0.618373
$202$		0			0
$203$	−5.60915	−	0.575104i	−0.393685	−	0.0403644i
$204$		0			0
$205$	−16.6934	+	16.6934i	−1.16592	+	1.16592i
$206$		0			0
$207$		−	3.79802i		−	0.263981i
$208$		0			0
$209$		−	12.9803i		−	0.897866i
$210$		0			0
$211$	−3.04584	−	3.04584i	−0.209684	−	0.209684i	0.594449	−	0.804133i	$-0.297370\pi$
$211$	−3.04584	−	3.04584i	−0.209684	−	0.209684i	−0.804133	+	0.594449i	$0.797370\pi$
$212$		0			0
$213$	−7.46668	+	7.46668i	−0.511608	+	0.511608i
$214$		0			0
$215$		−	17.3267i		−	1.18167i
$216$		0			0
$217$	6.74139	+	8.28170i	0.457635	+	0.562198i
$218$		0			0
$219$	−2.72792	+	2.72792i	−0.184336	+	0.184336i
$220$		0			0
$221$	−16.1090	+	16.1090i	−1.08361	+	1.08361i
$222$		0			0
$223$	8.93656			0.598436			0.299218	−	0.954185i	$-0.403274\pi$
$223$	8.93656			0.598436			0.299218	+	0.954185i	$0.403274\pi$
$224$		0			0
$225$	−1.48727			−0.0991516
$226$		0			0
$227$	17.3870	−	17.3870i	1.15402	−	1.15402i	0.168277	−	0.985740i	$-0.446180\pi$
$227$	17.3870	−	17.3870i	1.15402	−	1.15402i	0.985740	−	0.168277i	$-0.0538204\pi$
$228$		0			0
$229$	7.54281	−	7.54281i	0.498443	−	0.498443i	−0.412510	−	0.910953i	$-0.635348\pi$
$229$	7.54281	−	7.54281i	0.498443	−	0.498443i	0.910953	+	0.412510i	$0.135348\pi$
$230$		0			0
$231$	−13.1255	+	10.6843i	−0.863595	+	0.702975i
$232$		0			0
$233$			21.1778i			1.38741i	0.720262	+	0.693703i	$0.244022\pi$
$233$			21.1778i			1.38741i	−0.720262	+	0.693703i	$0.755978\pi$
$234$		0			0
$235$	−8.08222	+	8.08222i	−0.527226	+	0.527226i
$236$		0			0
$237$	3.60606	+	3.60606i	0.234239	+	0.234239i
$238$		0			0
$239$		−	1.99595i		−	0.129108i	−0.997914	−	0.0645538i	$-0.979438\pi$
$239$		−	1.99595i		−	0.129108i	0.997914	−	0.0645538i	$-0.0205624\pi$
$240$		0			0
$241$		−	1.36012i		−	0.0876132i	−0.999040	−	0.0438066i	$-0.986051\pi$
$241$		−	1.36012i		−	0.0876132i	0.999040	−	0.0438066i	$-0.0139485\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	−9.78647	−	14.9031i	−0.625235	−	0.952122i
$246$		0			0
$247$	−7.45167			−0.474138
$248$		0			0
$249$			14.2314i			0.901880i
$250$		0			0
$251$	0.580793	+	0.580793i	0.0366593	+	0.0366593i	0.725199	−	0.688540i	$-0.241748\pi$
$251$	0.580793	+	0.580793i	0.0366593	+	0.0366593i	−0.688540	+	0.725199i	$0.741748\pi$
$252$		0			0
$253$	17.1793	−	17.1793i	1.08005	−	1.08005i
$254$		0			0
$255$	−15.8009			−0.989494
$256$		0			0
$257$		−	18.3155i		−	1.14249i	−0.820779	−	0.571246i	$-0.806460\pi$
$257$		−	18.3155i		−	1.14249i	0.820779	−	0.571246i	$-0.193540\pi$
$258$		0			0
$259$	0.602807	−	5.87935i	0.0374566	−	0.365325i
$260$		0			0
$261$	1.50697	+	1.50697i	0.0932790	+	0.0932790i
$262$		0			0
$263$	−2.28033			−0.140611			−0.0703055	−	0.997526i	$-0.522397\pi$
$263$	−2.28033			−0.140611			−0.0703055	+	0.997526i	$0.522397\pi$
$264$		0			0
$265$	−24.9184			−1.53072
$266$		0			0
$267$	−0.187041	+	0.187041i	−0.0114467	+	0.0114467i
$268$		0			0
$269$	−5.53677	−	5.53677i	−0.337583	−	0.337583i	0.517874	−	0.855457i	$-0.326724\pi$
$269$	−5.53677	−	5.53677i	−0.337583	−	0.337583i	−0.855457	+	0.517874i	$0.826724\pi$
$270$		0			0
$271$	17.1905			1.04425			0.522124	−	0.852869i	$-0.325140\pi$
$271$	17.1905			1.04425			0.522124	+	0.852869i	$0.325140\pi$
$272$		0			0
$273$	6.13359	+	7.53503i	0.371222	+	0.456041i
$274$		0			0
$275$	−6.72727	−	6.72727i	−0.405669	−	0.405669i
$276$		0			0
$277$	−1.37433	−	1.37433i	−0.0825758	−	0.0825758i	0.664612	−	0.747188i	$-0.268597\pi$
$277$	−1.37433	−	1.37433i	−0.0825758	−	0.0825758i	−0.747188	+	0.664612i	$0.768597\pi$
$278$		0			0
$279$		−	4.03614i		−	0.241637i
$280$		0			0
$281$		−	14.2452i		−	0.849798i	−0.905241	−	0.424899i	$-0.860310\pi$
$281$		−	14.2452i		−	0.849798i	0.905241	−	0.424899i	$-0.139690\pi$
$282$		0			0
$283$	−4.98832	−	4.98832i	−0.296525	−	0.296525i	0.543126	−	0.839651i	$-0.317240\pi$
$283$	−4.98832	−	4.98832i	−0.296525	−	0.296525i	−0.839651	+	0.543126i	$0.817240\pi$
$284$		0			0
$285$	−3.65459	−	3.65459i	−0.216479	−	0.216479i
$286$		0			0
$287$	15.4814	+	19.0187i	0.913840	+	1.12264i
$288$		0			0
$289$	−21.4861			−1.26389
$290$		0			0
$291$	−5.05447	−	5.05447i	−0.296298	−	0.296298i
$292$		0			0
$293$	−19.4035	+	19.4035i	−1.13356	+	1.13356i	−0.143982	+	0.989580i	$0.545991\pi$
$293$	−19.4035	+	19.4035i	−1.13356	+	1.13356i	−0.989580	+	0.143982i	$0.954009\pi$
$294$		0			0
$295$	1.86135			0.108372
$296$		0			0
$297$	6.39680			0.371180
$298$		0			0
$299$	−9.86219	−	9.86219i	−0.570345	−	0.570345i
$300$		0			0
$301$	−17.9046	−	1.83575i	−1.03200	−	0.105811i
$302$		0			0
$303$		−	0.774995i		−	0.0445223i
$304$		0			0
$305$	21.7111			1.24317
$306$		0			0
$307$	−1.13227	+	1.13227i	−0.0646220	+	0.0646220i	−0.738679	−	0.674057i	$-0.764550\pi$
$307$	−1.13227	+	1.13227i	−0.0646220	+	0.0646220i	0.674057	+	0.738679i	$0.264550\pi$
$308$		0			0
$309$	1.54843	+	1.54843i	0.0880869	+	0.0880869i
$310$		0			0
$311$		−	31.9613i		−	1.81236i	−0.422894	−	0.906179i	$-0.638986\pi$
$311$		−	31.9613i		−	1.81236i	0.422894	−	0.906179i	$-0.361014\pi$
$312$		0			0
$313$	−28.5000			−1.61092			−0.805459	−	0.592652i	$-0.798081\pi$
$313$	−28.5000			−1.61092			−0.805459	+	0.592652i	$0.798081\pi$
$314$		0			0
$315$	−0.687319	+	6.70362i	−0.0387260	+	0.377706i
$316$		0			0
$317$	3.11011	−	3.11011i	0.174681	−	0.174681i	−0.614351	−	0.789033i	$-0.710582\pi$
$317$	3.11011	−	3.11011i	0.174681	−	0.174681i	0.789033	+	0.614351i	$0.210582\pi$
$318$		0			0
$319$			13.6327i			0.763285i
$320$		0			0
$321$		−	7.62559i		−	0.425619i
$322$		0			0
$323$	−8.90142	−	8.90142i	−0.495288	−	0.495288i
$324$		0			0
$325$	−3.86195	+	3.86195i	−0.214223	+	0.214223i
$326$		0			0
$327$			0.815382i			0.0450907i
$328$		0			0
$329$	7.49546	+	9.20806i	0.413238	+	0.507657i
$330$		0			0
$331$	22.4914	−	22.4914i	1.23624	−	1.23624i	0.274714	−	0.961526i	$-0.411417\pi$
$331$	22.4914	−	22.4914i	1.23624	−	1.23624i	0.961526	−	0.274714i	$-0.0885832\pi$
$332$		0			0
$333$	−1.57956	+	1.57956i	−0.0865594	+	0.0865594i
$334$		0			0
$335$	22.3295			1.21999
$336$		0			0
$337$	−24.8695			−1.35473			−0.677364	−	0.735648i	$-0.736878\pi$
$337$	−24.8695			−1.35473			−0.677364	+	0.735648i	$0.736878\pi$
$338$		0			0
$339$	8.30171	−	8.30171i	0.450887	−	0.450887i
$340$		0			0
$341$	18.2563	−	18.2563i	0.988636	−	0.988636i
$342$		0			0
$343$	−16.4369	+	8.53388i	−0.887511	+	0.460786i
$344$		0			0
$345$		−	9.67360i		−	0.520809i
$346$		0			0
$347$	5.93378	−	5.93378i	0.318542	−	0.318542i	−0.529665	−	0.848207i	$-0.677682\pi$
$347$	5.93378	−	5.93378i	0.318542	−	0.318542i	0.848207	+	0.529665i	$0.177682\pi$
$348$		0			0
$349$	17.9498	+	17.9498i	0.960829	+	0.960829i	0.999261	−	0.0384320i	$-0.0122363\pi$
$349$	17.9498	+	17.9498i	0.960829	+	0.960829i	−0.0384320	+	0.999261i	$0.512236\pi$
$350$		0			0
$351$		−	3.67224i		−	0.196010i
$352$		0			0
$353$		−	19.0051i		−	1.01154i	−0.862668	−	0.505770i	$-0.831209\pi$
$353$		−	19.0051i		−	1.01154i	0.862668	−	0.505770i	$-0.168791\pi$
$354$		0			0
$355$	−19.0177	+	19.0177i	−1.00936	+	1.00936i
$356$		0			0
$357$	−1.67409	+	16.3279i	−0.0886023	+	0.864164i
$358$		0			0
$359$	−8.22606			−0.434155			−0.217077	−	0.976154i	$-0.569652\pi$
$359$	−8.22606			−0.434155			−0.217077	+	0.976154i	$0.569652\pi$
$360$		0			0
$361$			14.8824i			0.783284i
$362$		0			0
$363$	21.1560	+	21.1560i	1.11040	+	1.11040i
$364$		0			0
$365$	−6.94805	+	6.94805i	−0.363677	+	0.363677i
$366$		0			0
$367$	−27.2942			−1.42474			−0.712372	−	0.701802i	$-0.752379\pi$
$367$	−27.2942			−1.42474			−0.712372	+	0.701802i	$0.752379\pi$
$368$		0			0
$369$		−	9.26889i		−	0.482519i
$370$		0			0
$371$	−2.64007	+	25.7494i	−0.137066	+	1.33684i
$372$		0			0
$373$	12.3883	+	12.3883i	0.641440	+	0.641440i	0.950909	−	0.309469i	$-0.100151\pi$
$373$	12.3883	+	12.3883i	0.641440	+	0.641440i	−0.309469	+	0.950909i	$0.600151\pi$
$374$		0			0
$375$	8.94696			0.462019
$376$		0			0
$377$	7.82619			0.403069
$378$		0			0
$379$	2.83357	−	2.83357i	0.145551	−	0.145551i	−0.630576	−	0.776127i	$-0.717181\pi$
$379$	2.83357	−	2.83357i	0.145551	−	0.145551i	0.776127	+	0.630576i	$0.217181\pi$
$380$		0			0
$381$	−8.91370	−	8.91370i	−0.456663	−	0.456663i
$382$		0			0
$383$	−3.10041			−0.158424			−0.0792118	−	0.996858i	$-0.525240\pi$
$383$	−3.10041			−0.158424			−0.0792118	+	0.996858i	$0.525240\pi$
$384$		0			0
$385$	−33.4308	+	27.2131i	−1.70379	+	1.38691i
$386$		0			0
$387$	4.81028	+	4.81028i	0.244520	+	0.244520i
$388$		0			0
$389$	−1.89523	−	1.89523i	−0.0960920	−	0.0960920i	0.657427	−	0.753519i	$-0.271645\pi$
$389$	−1.89523	−	1.89523i	−0.0960920	−	0.0960920i	−0.753519	+	0.657427i	$0.771645\pi$
$390$		0			0
$391$		−	23.5618i		−	1.19157i
$392$		0			0
$393$			7.71102i			0.388969i
$394$		0			0
$395$	9.18468	+	9.18468i	0.462131	+	0.462131i
$396$		0			0
$397$	−16.4165	−	16.4165i	−0.823923	−	0.823923i	0.162745	−	0.986668i	$-0.447965\pi$
$397$	−16.4165	−	16.4165i	−0.823923	−	0.823923i	−0.986668	+	0.162745i	$0.947965\pi$
$398$		0			0
$399$	−4.16366	+	3.38926i	−0.208444	+	0.169675i
$400$		0			0
$401$	11.6333			0.580938			0.290469	−	0.956884i	$-0.406189\pi$
$401$	11.6333			0.580938			0.290469	+	0.956884i	$0.406189\pi$
$402$		0			0
$403$	−10.4805	−	10.4805i	−0.522071	−	0.522071i
$404$		0			0
$405$	1.80101	−	1.80101i	0.0894929	−	0.0894929i
$406$		0			0
$407$	−14.2894			−0.708300
$408$		0			0
$409$	0.396994			0.0196301			0.00981504	−	0.999952i	$-0.496876\pi$
$409$	0.396994			0.0196301			0.00981504	+	0.999952i	$0.496876\pi$
$410$		0			0
$411$	9.22947	+	9.22947i	0.455256	+	0.455256i
$412$		0			0
$413$	0.197208	−	1.92342i	0.00970395	−	0.0946455i
$414$		0			0
$415$			36.2476i			1.77933i
$416$		0			0
$417$	−19.7252			−0.965946
$418$		0			0
$419$	−11.8396	+	11.8396i	−0.578402	+	0.578402i	−0.934463	−	0.356061i	$-0.884120\pi$
$419$	−11.8396	+	11.8396i	−0.578402	+	0.578402i	0.356061	+	0.934463i	$0.384120\pi$
$420$		0			0
$421$	−1.04319	−	1.04319i	−0.0508420	−	0.0508420i	0.681229	−	0.732071i	$-0.261446\pi$
$421$	−1.04319	−	1.04319i	−0.0508420	−	0.0508420i	−0.732071	+	0.681229i	$0.761446\pi$
$422$		0			0
$423$		−	4.48761i		−	0.218195i
$424$		0			0
$425$	−9.22662			−0.447557
$426$		0			0
$427$	2.30026	−	22.4351i	0.111318	−	1.08571i
$428$		0			0
$429$	16.6104	−	16.6104i	0.801956	−	0.801956i
$430$		0			0
$431$		−	12.9393i		−	0.623266i	−0.950202	−	0.311633i	$-0.899124\pi$
$431$		−	12.9393i		−	0.623266i	0.950202	−	0.311633i	$-0.100876\pi$
$432$		0			0
$433$			8.67090i			0.416697i	0.978055	+	0.208348i	$0.0668088\pi$
$433$			8.67090i			0.416697i	−0.978055	+	0.208348i	$0.933191\pi$
$434$		0			0
$435$	3.83827	+	3.83827i	0.184031	+	0.184031i
$436$		0			0
$437$	5.44959	−	5.44959i	0.260689	−	0.260689i
$438$		0			0
$439$		−	19.6051i		−	0.935700i	−0.883808	−	0.467850i	$-0.845029\pi$
$439$		−	19.6051i		−	0.935700i	0.883808	−	0.467850i	$-0.154971\pi$
$440$		0			0
$441$	6.85436	+	1.42048i	0.326398	+	0.0676419i
$442$		0			0
$443$	−11.6535	+	11.6535i	−0.553673	+	0.553673i	−0.927499	−	0.373826i	$-0.878046\pi$
$443$	−11.6535	+	11.6535i	−0.553673	+	0.553673i	0.373826	+	0.927499i	$0.378046\pi$
$444$		0			0
$445$	−0.476395	+	0.476395i	−0.0225833	+	0.0225833i
$446$		0			0
$447$	−8.66400			−0.409793
$448$		0			0
$449$	−1.15967			−0.0547280			−0.0273640	−	0.999626i	$-0.508711\pi$
$449$	−1.15967			−0.0547280			−0.0273640	+	0.999626i	$0.508711\pi$
$450$		0			0
$451$	41.9252	−	41.9252i	1.97418	−	1.97418i
$452$		0			0
$453$	5.62250	−	5.62250i	0.264168	−	0.264168i
$454$		0			0
$455$	15.6223	+	19.1918i	0.732386	+	0.899726i
$456$		0			0
$457$			12.4379i			0.581820i	0.956750	+	0.290910i	$0.0939580\pi$
$457$			12.4379i			0.581820i	−0.956750	+	0.290910i	$0.906042\pi$
$458$		0			0
$459$	4.38669	−	4.38669i	0.204753	−	0.204753i
$460$		0			0
$461$	5.93297	+	5.93297i	0.276326	+	0.276326i	0.831641	−	0.555314i	$-0.187402\pi$
$461$	5.93297	+	5.93297i	0.276326	+	0.276326i	−0.555314	+	0.831641i	$0.687402\pi$
$462$		0			0
$463$		−	34.3424i		−	1.59603i	−0.602640	−	0.798013i	$-0.705884\pi$
$463$		−	34.3424i		−	1.59603i	0.602640	−	0.798013i	$-0.294116\pi$
$464$		0			0
$465$		−	10.2801i		−	0.476728i
$466$		0			0
$467$	−19.0809	+	19.0809i	−0.882959	+	0.882959i	−0.993834	−	0.110875i	$-0.964635\pi$
$467$	−19.0809	+	19.0809i	−0.882959	+	0.882959i	0.110875	+	0.993834i	$0.464635\pi$
$468$		0			0
$469$	2.36579	−	23.0742i	0.109242	−	1.06547i
$470$		0			0
$471$	−16.8607			−0.776901
$472$		0			0
$473$			43.5159i			2.00087i
$474$		0			0
$475$	−2.13402	−	2.13402i	−0.0979154	−	0.0979154i
$476$		0			0
$477$	6.91789	−	6.91789i	0.316748	−	0.316748i
$478$		0			0
$479$	−15.0304			−0.686758			−0.343379	−	0.939197i	$-0.611571\pi$
$479$	−15.0304			−0.686758			−0.343379	+	0.939197i	$0.611571\pi$
$480$		0			0
$481$			8.20319i			0.374033i
$482$		0			0
$483$	−9.99621	−	1.02491i	−0.454843	−	0.0466349i
$484$		0			0
$485$	−12.8738	−	12.8738i	−0.584569	−	0.584569i
$486$		0			0
$487$	−23.2550			−1.05379			−0.526893	−	0.849932i	$-0.676643\pi$
$487$	−23.2550			−1.05379			−0.526893	+	0.849932i	$0.676643\pi$
$488$		0			0
$489$	−1.47832			−0.0668521
$490$		0			0
$491$	−2.45372	+	2.45372i	−0.110735	+	0.110735i	−0.760303	−	0.649568i	$-0.774950\pi$
$491$	−2.45372	+	2.45372i	−0.110735	+	0.110735i	0.649568	+	0.760303i	$0.274950\pi$
$492$		0			0
$493$	9.34881	+	9.34881i	0.421049	+	0.421049i
$494$		0			0
$495$	16.2927			0.732304
$496$		0			0
$497$	17.6370	+	21.6669i	0.791130	+	0.971891i
$498$		0			0
$499$	14.0960	+	14.0960i	0.631025	+	0.631025i	0.948325	−	0.317300i	$-0.102776\pi$
$499$	14.0960	+	14.0960i	0.631025	+	0.631025i	−0.317300	+	0.948325i	$0.602776\pi$
$500$		0			0
$501$	−10.9205	−	10.9205i	−0.487890	−	0.487890i
$502$		0			0
$503$			13.4597i			0.600140i	0.953917	+	0.300070i	$0.0970100\pi$
$503$			13.4597i			0.600140i	−0.953917	+	0.300070i	$0.902990\pi$
$504$		0			0
$505$		−	1.97392i		−	0.0878384i
$506$		0			0
$507$	−0.343203	−	0.343203i	−0.0152422	−	0.0152422i
$508$		0			0
$509$	−14.4875	−	14.4875i	−0.642145	−	0.642145i	0.308937	−	0.951082i	$-0.400027\pi$
$509$	−14.4875	−	14.4875i	−0.642145	−	0.642145i	−0.951082	+	0.308937i	$0.900027\pi$
$510$		0			0
$511$	6.44362	+	7.91590i	0.285049	+	0.350179i
$512$		0			0
$513$	2.02919			0.0895908
$514$		0			0
$515$	3.94386	+	3.94386i	0.173787	+	0.173787i
$516$		0			0
$517$	20.2984	−	20.2984i	0.892724	−	0.892724i
$518$		0			0
$519$	20.7665			0.911549
$520$		0			0
$521$	−26.0056			−1.13932			−0.569662	−	0.821879i	$-0.692926\pi$
$521$	−26.0056			−1.13932			−0.569662	+	0.821879i	$0.692926\pi$
$522$		0			0
$523$	0.601049	+	0.601049i	0.0262820	+	0.0262820i	0.720126	−	0.693844i	$-0.244084\pi$
$523$	0.601049	+	0.601049i	0.0262820	+	0.0262820i	−0.693844	+	0.720126i	$0.744084\pi$
$524$		0			0
$525$	−0.401345	+	3.91443i	−0.0175161	+	0.170840i
$526$		0			0
$527$		−	25.0391i		−	1.09072i
$528$		0			0
$529$	−8.57505			−0.372828
$530$		0			0
$531$	−0.516751	+	0.516751i	−0.0224251	+	0.0224251i
$532$		0			0
$533$	−24.0682	−	24.0682i	−1.04251	−	1.04251i
$534$		0			0
$535$		−	19.4225i		−	0.839706i
$536$		0			0
$537$	−23.9750			−1.03460
$538$		0			0
$539$	24.5786	+	37.4289i	1.05868	+	1.61218i
$540$		0			0
$541$	−8.43386	+	8.43386i	−0.362600	+	0.362600i	−0.864769	−	0.502169i	$-0.832535\pi$
$541$	−8.43386	+	8.43386i	−0.362600	+	0.362600i	0.502169	+	0.864769i	$0.332535\pi$
$542$		0			0
$543$			1.32719i			0.0569551i
$544$		0			0
$545$			2.07679i			0.0889599i
$546$		0			0
$547$	17.1165	+	17.1165i	0.731848	+	0.731848i	0.970986	−	0.239137i	$-0.0768646\pi$
$547$	17.1165	+	17.1165i	0.731848	+	0.731848i	−0.239137	+	0.970986i	$0.576865\pi$
$548$		0			0
$549$	−6.02748	+	6.02748i	−0.257246	+	0.257246i
$550$		0			0
$551$			4.32455i			0.184232i
$552$		0			0
$553$	10.4641	−	8.51787i	0.444978	−	0.362217i
$554$		0			0
$555$	−4.02316	+	4.02316i	−0.170774	+	0.170774i
$556$		0			0
$557$	26.9281	−	26.9281i	1.14098	−	1.14098i	0.152707	−	0.988271i	$-0.451201\pi$
$557$	26.9281	−	26.9281i	1.14098	−	1.14098i	0.988271	−	0.152707i	$-0.0487991\pi$
$558$		0			0
$559$	24.9814			1.05660
$560$		0			0
$561$	39.6839			1.67546
$562$		0			0
$563$	−16.0469	+	16.0469i	−0.676295	+	0.676295i	−0.959160	−	0.282865i	$-0.908715\pi$
$563$	−16.0469	+	16.0469i	−0.676295	+	0.676295i	0.282865	+	0.959160i	$0.408715\pi$
$564$		0			0
$565$	21.1445	−	21.1445i	0.889558	−	0.889558i
$566$		0			0
$567$	−1.67026	−	2.05189i	−0.0701442	−	0.0861712i
$568$		0			0
$569$			3.81256i			0.159831i	0.996802	+	0.0799154i	$0.0254650\pi$
$569$			3.81256i			0.159831i	−0.996802	+	0.0799154i	$0.974535\pi$
$570$		0			0
$571$	6.20325	−	6.20325i	0.259598	−	0.259598i	−0.565293	−	0.824891i	$-0.691237\pi$
$571$	6.20325	−	6.20325i	0.259598	−	0.259598i	0.824891	+	0.565293i	$0.191237\pi$
$572$		0			0
$573$	12.0919	+	12.0919i	0.505147	+	0.505147i
$574$		0			0
$575$		−	5.64869i		−	0.235567i
$576$		0			0
$577$			10.7648i			0.448144i	0.974573	+	0.224072i	$0.0719351\pi$
$577$			10.7648i			0.448144i	−0.974573	+	0.224072i	$0.928065\pi$
$578$		0			0
$579$	−4.07720	+	4.07720i	−0.169443	+	0.169443i
$580$		0			0
$581$	37.4565	+	3.84039i	1.55396	+	0.159326i
$582$		0			0
$583$	62.5823			2.59189
$584$		0			0
$585$		−	9.35325i		−	0.386709i
$586$		0			0
$587$	26.2489	+	26.2489i	1.08341	+	1.08341i	0.996189	+	0.0872210i	$0.0277986\pi$
$587$	26.2489	+	26.2489i	1.08341	+	1.08341i	0.0872210	+	0.996189i	$0.472201\pi$
$588$		0			0
$589$	5.79126	−	5.79126i	0.238625	−	0.238625i
$590$		0			0
$591$	2.29378			0.0943536
$592$		0			0
$593$			36.5539i			1.50109i	0.660820	+	0.750545i	$0.270209\pi$
$593$			36.5539i			1.50109i	−0.660820	+	0.750545i	$0.729791\pi$
$594$		0			0
$595$	−4.26393	+	41.5874i	−0.174804	+	1.70492i
$596$		0			0
$597$	−15.6232	−	15.6232i	−0.639417	−	0.639417i
$598$		0			0
$599$	0.0689795			0.00281842			0.00140921	−	0.999999i	$-0.499551\pi$
$599$	0.0689795			0.00281842			0.00140921	+	0.999999i	$0.499551\pi$
$600$		0			0
$601$	14.1634			0.577738			0.288869	−	0.957369i	$-0.406721\pi$
$601$	14.1634			0.577738			0.288869	+	0.957369i	$0.406721\pi$
$602$		0			0
$603$	−6.19917	+	6.19917i	−0.252450	+	0.252450i
$604$		0			0
$605$	53.8845	+	53.8845i	2.19072	+	2.19072i
$606$		0			0
$607$	−0.622926			−0.0252838			−0.0126419	−	0.999920i	$-0.504024\pi$
$607$	−0.622926			−0.0252838			−0.0126419	+	0.999920i	$0.504024\pi$
$608$		0			0
$609$	4.37293	−	3.55961i	0.177200	−	0.144243i
$610$		0			0
$611$	−11.6528	−	11.6528i	−0.471423	−	0.471423i
$612$		0			0
$613$	13.5765	+	13.5765i	0.548349	+	0.548349i	0.925963	−	0.377614i	$-0.123255\pi$
$613$	13.5765	+	13.5765i	0.548349	+	0.548349i	−0.377614	+	0.925963i	$0.623255\pi$
$614$		0			0
$615$		−	23.6080i		−	0.951966i
$616$		0			0
$617$		−	23.0955i		−	0.929790i	−0.885366	−	0.464895i	$-0.846092\pi$
$617$		−	23.0955i		−	0.929790i	0.885366	−	0.464895i	$-0.153908\pi$
$618$		0			0
$619$	2.92078	+	2.92078i	0.117396	+	0.117396i	0.763364	−	0.645968i	$-0.223546\pi$
$619$	2.92078	+	2.92078i	0.117396	+	0.117396i	−0.645968	+	0.763364i	$0.723546\pi$
$620$		0			0
$621$	2.68560	+	2.68560i	0.107770	+	0.107770i
$622$		0			0
$623$	0.441809	+	0.542756i	0.0177007	+	0.0217451i
$624$		0			0
$625$	30.2244			1.20898
$626$		0			0
$627$	9.17846	+	9.17846i	0.366552	+	0.366552i
$628$		0			0
$629$	−9.79915	+	9.79915i	−0.390718	+	0.390718i
$630$		0			0
$631$	−29.4643			−1.17296			−0.586478	−	0.809965i	$-0.699486\pi$
$631$	−29.4643			−1.17296			−0.586478	+	0.809965i	$0.699486\pi$
$632$		0			0
$633$	4.30747			0.171206
$634$		0			0
$635$	−22.7033	−	22.7033i	−0.900953	−	0.900953i
$636$		0			0
$637$	21.4870	−	14.1100i	0.851346	−	0.559058i
$638$		0			0
$639$		−	10.5595i		−	0.417727i
$640$		0			0
$641$	−5.40014			−0.213293			−0.106646	−	0.994297i	$-0.534011\pi$
$641$	−5.40014			−0.213293			−0.106646	+	0.994297i	$0.534011\pi$
$642$		0			0
$643$	−9.28303	+	9.28303i	−0.366087	+	0.366087i	−0.866048	−	0.499961i	$-0.833348\pi$
$643$	−9.28303	+	9.28303i	−0.366087	+	0.366087i	0.499961	+	0.866048i	$0.333348\pi$
$644$		0			0
$645$	12.2519	+	12.2519i	0.482416	+	0.482416i
$646$		0			0
$647$		−	21.5623i		−	0.847703i	−0.905732	−	0.423852i	$-0.860678\pi$
$647$		−	21.5623i		−	0.847703i	0.905732	−	0.423852i	$-0.139322\pi$
$648$		0			0
$649$	−4.67476			−0.183500
$650$		0			0
$651$	−10.6229	−	1.08916i	−0.416345	−	0.0426877i
$652$		0			0
$653$	31.1997	−	31.1997i	1.22094	−	1.22094i	0.253638	−	0.967299i	$-0.418373\pi$
$653$	31.1997	−	31.1997i	1.22094	−	1.22094i	0.967299	−	0.253638i	$-0.0816273\pi$
$654$		0			0
$655$			19.6401i			0.767401i
$656$		0			0
$657$		−	3.85786i		−	0.150510i
$658$		0			0
$659$	8.41759	+	8.41759i	0.327903	+	0.327903i	0.851789	−	0.523886i	$-0.175518\pi$
$659$	8.41759	+	8.41759i	0.327903	+	0.327903i	−0.523886	+	0.851789i	$0.675518\pi$
$660$		0			0
$661$	−30.4079	+	30.4079i	−1.18273	+	1.18273i	−0.203695	+	0.979034i	$0.565295\pi$
$661$	−30.4079	+	30.4079i	−1.18273	+	1.18273i	−0.979034	+	0.203695i	$0.934705\pi$
$662$		0			0
$663$		−	22.7816i		−	0.884762i
$664$		0			0
$665$	−10.6049	+	8.63250i	−0.411240	+	0.334754i
$666$		0			0
$667$	−5.72350	+	5.72350i	−0.221615	+	0.221615i
$668$		0			0
$669$	−6.31910	+	6.31910i	−0.244310	+	0.244310i
$670$		0			0
$671$	−54.5272			−2.10500
$672$		0			0
$673$	51.5164			1.98581			0.992906	−	0.118898i	$-0.0379361\pi$
$673$	51.5164			1.98581			0.992906	+	0.118898i	$0.0379361\pi$
$674$		0			0
$675$	1.05166	−	1.05166i	0.0404785	−	0.0404785i
$676$		0			0
$677$	−12.8377	+	12.8377i	−0.493393	+	0.493393i	−0.909373	−	0.415981i	$-0.863438\pi$
$677$	−12.8377	+	12.8377i	−0.493393	+	0.493393i	0.415981	+	0.909373i	$0.363438\pi$
$678$		0			0
$679$	−14.6671	+	11.9392i	−0.562872	+	0.458183i
$680$		0			0
$681$			24.5890i			0.942251i
$682$		0			0
$683$	27.6581	−	27.6581i	1.05831	−	1.05831i	0.0601146	−	0.998191i	$-0.480853\pi$
$683$	27.6581	−	27.6581i	1.05831	−	1.05831i	0.998191	−	0.0601146i	$-0.0191466\pi$
$684$		0			0
$685$	23.5076	+	23.5076i	0.898178	+	0.898178i
$686$		0			0
$687$			10.6671i			0.406977i
$688$		0			0
$689$		−	35.9269i		−	1.36871i
$690$		0			0
$691$	15.0732	−	15.0732i	0.573413	−	0.573413i	−0.359668	−	0.933081i	$-0.617110\pi$
$691$	15.0732	−	15.0732i	0.573413	−	0.573413i	0.933081	+	0.359668i	$0.117110\pi$
$692$		0			0
$693$	1.72620	−	16.8361i	0.0655727	−	0.639550i
$694$		0			0
$695$	−50.2403			−1.90572
$696$		0			0
$697$		−	57.5016i		−	2.17803i
$698$		0			0
$699$	−14.9750	−	14.9750i	−0.566406	−	0.566406i
$700$		0			0
$701$	−7.57647	+	7.57647i	−0.286159	+	0.286159i	−0.835559	−	0.549400i	$-0.814856\pi$
$701$	−7.57647	+	7.57647i	−0.286159	+	0.286159i	0.549400	+	0.835559i	$0.314856\pi$
$702$		0			0
$703$	−4.53287			−0.170961
$704$		0			0
$705$		−	11.4300i		−	0.430478i
$706$		0			0
$707$	−2.03975	−	0.209135i	−0.0767127	−	0.00786532i
$708$		0			0
$709$	−19.7005	−	19.7005i	−0.739866	−	0.739866i	0.232686	−	0.972552i	$-0.425249\pi$
$709$	−19.7005	−	19.7005i	−0.739866	−	0.739866i	−0.972552	+	0.232686i	$0.925249\pi$
$710$		0			0
$711$	−5.09974			−0.191255
$712$		0			0
$713$	15.3293			0.574088
$714$		0			0
$715$	42.3068	−	42.3068i	1.58218	−	1.58218i
$716$		0			0
$717$	1.41135	+	1.41135i	0.0527079	+	0.0527079i
$718$		0			0
$719$	0.0891935			0.00332636			0.00166318	−	0.999999i	$-0.499471\pi$
$719$	0.0891935			0.00332636			0.00166318	+	0.999999i	$0.499471\pi$
$720$		0			0
$721$	4.49323	−	3.65754i	0.167337	−	0.136214i
$722$		0			0
$723$	0.961751	+	0.961751i	0.0357679	+	0.0357679i
$724$		0			0
$725$	2.24127	+	2.24127i	0.0832388	+	0.0832388i
$726$		0			0
$727$			31.1159i			1.15403i	0.816735	+	0.577013i	$0.195782\pi$
$727$			31.1159i			1.15403i	−0.816735	+	0.577013i	$0.804218\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	29.8416	+	29.8416i	1.10373	+	1.10373i
$732$		0			0
$733$	−19.9681	−	19.9681i	−0.737539	−	0.737539i	0.234562	−	0.972101i	$-0.424634\pi$
$733$	−19.9681	−	19.9681i	−0.737539	−	0.737539i	−0.972101	+	0.234562i	$0.924634\pi$
$734$		0			0
$735$	17.4581	+	3.61798i	0.643953	+	0.133451i
$736$		0			0
$737$	−56.0804			−2.06575
$738$		0			0
$739$	−9.59456	−	9.59456i	−0.352942	−	0.352942i	0.508261	−	0.861203i	$-0.330288\pi$
$739$	−9.59456	−	9.59456i	−0.352942	−	0.352942i	−0.861203	+	0.508261i	$0.830288\pi$
$740$		0			0
$741$	5.26912	−	5.26912i	0.193566	−	0.193566i
$742$		0			0
$743$	−20.5150			−0.752621			−0.376310	−	0.926494i	$-0.622807\pi$
$743$	−20.5150			−0.752621			−0.376310	+	0.926494i	$0.622807\pi$
$744$		0			0
$745$	−22.0673			−0.808484
$746$		0			0
$747$	−10.0631	−	10.0631i	−0.368191	−	0.368191i
$748$		0			0
$749$	−20.0702	−	2.05779i	−0.733349	−	0.0751899i
$750$		0			0
$751$			29.9255i			1.09200i	0.837787	+	0.545998i	$0.183849\pi$
$751$			29.9255i			1.09200i	−0.837787	+	0.545998i	$0.816151\pi$
$752$		0			0
$753$	−0.821365			−0.0299322
$754$		0			0
$755$	14.3206	−	14.3206i	0.521179	−	0.521179i
$756$		0			0
$757$	18.3461	+	18.3461i	0.666799	+	0.666799i	0.956974	−	0.290175i	$-0.0937135\pi$
$757$	18.3461	+	18.3461i	0.666799	+	0.666799i	−0.290175	+	0.956974i	$0.593714\pi$
$758$		0			0
$759$			24.2952i			0.881859i
$760$		0			0
$761$	29.7121			1.07706			0.538531	−	0.842605i	$-0.318979\pi$
$761$	29.7121			1.07706			0.538531	+	0.842605i	$0.318979\pi$
$762$		0			0
$763$	2.14605	+	0.220033i	0.0776922	+	0.00796574i
$764$		0			0
$765$	11.1730	−	11.1730i	0.403959	−	0.403959i
$766$		0			0
$767$			2.68366i			0.0969014i
$768$		0			0
$769$			26.1826i			0.944168i	0.881554	+	0.472084i	$0.156498\pi$
$769$			26.1826i			0.944168i	−0.881554	+	0.472084i	$0.843502\pi$
$770$		0			0
$771$	12.9510	+	12.9510i	0.466420	+	0.466420i
$772$		0			0
$773$	−29.9716	+	29.9716i	−1.07800	+	1.07800i	−0.0813162	+	0.996688i	$0.525912\pi$
$773$	−29.9716	+	29.9716i	−1.07800	+	1.07800i	−0.996688	+	0.0813162i	$0.974088\pi$
$774$		0			0
$775$		−	6.00284i		−	0.215628i
$776$		0			0
$777$	3.73108	+	4.58358i	0.133852	+	0.164435i
$778$		0			0
$779$	13.2995	−	13.2995i	0.476504	−	0.476504i
$780$		0			0
$781$	47.7629	−	47.7629i	1.70909	−	1.70909i
$782$		0			0
$783$	−2.13118			−0.0761620
$784$		0			0
$785$	−42.9445			−1.53275
$786$		0			0
$787$	−10.6861	+	10.6861i	−0.380920	+	0.380920i	−0.871433	−	0.490514i	$-0.836809\pi$
$787$	−10.6861	+	10.6861i	−0.380920	+	0.380920i	0.490514	+	0.871433i	$0.336809\pi$
$788$		0			0
$789$	1.61243	−	1.61243i	0.0574042	−	0.0574042i
$790$		0			0
$791$	−19.6095	−	24.0899i	−0.697232	−	0.856540i
$792$		0			0
$793$			31.3027i			1.11159i
$794$		0			0
$795$	17.6199	−	17.6199i	0.624915	−	0.624915i
$796$		0			0
$797$	14.9215	+	14.9215i	0.528547	+	0.528547i	0.920139	−	0.391592i	$-0.128076\pi$
$797$	14.9215	+	14.9215i	0.528547	+	0.528547i	−0.391592	+	0.920139i	$0.628076\pi$
$798$		0			0
$799$		−	27.8398i		−	0.984903i
$800$		0			0
$801$		−	0.264516i		−	0.00934620i
$802$		0			0
$803$	17.4500	−	17.4500i	0.615796	−	0.615796i
$804$		0			0
$805$	−25.4605	−	2.61045i	−0.897364	−	0.0920063i
$806$		0			0
$807$	7.83017			0.275635
$808$		0			0
$809$		−	19.2298i		−	0.676082i	−0.941131	−	0.338041i	$-0.890236\pi$
$809$		−	19.2298i		−	0.676082i	0.941131	−	0.338041i	$-0.109764\pi$
$810$		0			0
$811$	−0.502502	−	0.502502i	−0.0176452	−	0.0176452i	0.698229	−	0.715874i	$-0.253972\pi$
$811$	−0.502502	−	0.502502i	−0.0176452	−	0.0176452i	−0.715874	+	0.698229i	$0.753972\pi$
$812$		0			0
$813$	−12.1555	+	12.1555i	−0.426313	+	0.426313i
$814$		0			0
$815$	−3.76531			−0.131893
$816$		0			0
$817$			13.8041i			0.482944i
$818$		0			0
$819$	−9.66517	−	0.990965i	−0.337728	−	0.0346271i
$820$		0			0
$821$	3.57175	+	3.57175i	0.124655	+	0.124655i	0.766682	−	0.642027i	$-0.221906\pi$
$821$	3.57175	+	3.57175i	0.124655	+	0.124655i	−0.642027	+	0.766682i	$0.721906\pi$
$822$		0			0
$823$	−30.5512			−1.06495			−0.532474	−	0.846446i	$-0.678738\pi$
$823$	−30.5512			−1.06495			−0.532474	+	0.846446i	$0.678738\pi$
$824$		0			0
$825$	9.51379			0.331228
$826$		0			0
$827$	−9.21840	+	9.21840i	−0.320555	+	0.320555i	−0.848980	−	0.528425i	$-0.822783\pi$
$827$	−9.21840	+	9.21840i	−0.320555	+	0.320555i	0.528425	+	0.848980i	$0.322783\pi$
$828$		0			0
$829$	−3.61659	−	3.61659i	−0.125609	−	0.125609i	0.641507	−	0.767117i	$-0.278309\pi$
$829$	−3.61659	−	3.61659i	−0.125609	−	0.125609i	−0.767117	+	0.641507i	$0.778309\pi$
$830$		0			0
$831$	1.94360			0.0674228
$832$		0			0
$833$	42.5225	+	8.81226i	1.47332	+	0.305327i
$834$		0			0
$835$	−27.8145	−	27.8145i	−0.962561	−	0.962561i
$836$		0			0
$837$	2.85398	+	2.85398i	0.0986480	+	0.0986480i
$838$		0			0
$839$			25.3066i			0.873681i	0.899539	+	0.436841i	$0.143903\pi$
$839$			25.3066i			0.873681i	−0.899539	+	0.436841i	$0.856097\pi$
$840$		0			0
$841$			24.4581i			0.843382i
$842$		0			0
$843$	10.0729	+	10.0729i	0.346928	+	0.346928i
$844$		0			0
$845$	−0.874142	−	0.874142i	−0.0300714	−	0.0300714i
$846$		0			0
$847$	61.3905	−	49.9725i	2.10940	−	1.71708i
$848$		0			0
$849$	7.05455			0.242111
$850$		0			0
$851$	−5.99920	−	5.99920i	−0.205650	−	0.205650i
$852$		0			0
$853$	−12.8593	+	12.8593i	−0.440296	+	0.440296i	−0.892111	−	0.451816i	$-0.850776\pi$
$853$	−12.8593	+	12.8593i	−0.440296	+	0.440296i	0.451816	+	0.892111i	$0.350776\pi$
$854$		0			0
$855$	5.16836			0.176754
$856$		0			0
$857$	−41.8529			−1.42967			−0.714834	−	0.699295i	$-0.753498\pi$
$857$	−41.8529			−1.42967			−0.714834	+	0.699295i	$0.753498\pi$
$858$		0			0
$859$	−9.11357	−	9.11357i	−0.310951	−	0.310951i	0.534327	−	0.845278i	$-0.320565\pi$
$859$	−9.11357	−	9.11357i	−0.310951	−	0.310951i	−0.845278	+	0.534327i	$0.820565\pi$
$860$		0			0
$861$	−24.3953	−	2.50124i	−0.831389	−	0.0852420i
$862$		0			0
$863$			50.1906i			1.70851i	0.519856	+	0.854254i	$0.325986\pi$
$863$			50.1906i			1.70851i	−0.519856	+	0.854254i	$0.674014\pi$
$864$		0			0
$865$	52.8926			1.79840
$866$		0			0
$867$	15.1930	−	15.1930i	0.515981	−	0.515981i
$868$		0			0
$869$	−23.0672	−	23.0672i	−0.782502	−	0.782502i
$870$		0			0
$871$			32.1944i			1.09086i
$872$		0			0
$873$	7.14810			0.241927
$874$		0			0
$875$	2.41436	−	23.5480i	0.0816204	−	0.796067i
$876$		0			0
$877$	−6.62177	+	6.62177i	−0.223601	+	0.223601i	−0.810013	−	0.586412i	$-0.800540\pi$
$877$	−6.62177	+	6.62177i	−0.223601	+	0.223601i	0.586412	+	0.810013i	$0.300540\pi$
$878$		0			0
$879$		−	27.4406i		−	0.925550i
$880$		0			0
$881$			40.4323i			1.36220i	0.732191	+	0.681099i	$0.238498\pi$
$881$			40.4323i			1.36220i	−0.732191	+	0.681099i	$0.761502\pi$
$882$		0			0
$883$	24.8546	+	24.8546i	0.836423	+	0.836423i	0.988386	−	0.151963i	$-0.0485596\pi$
$883$	24.8546	+	24.8546i	0.836423	+	0.836423i	−0.151963	+	0.988386i	$0.548560\pi$
$884$		0			0
$885$	−1.31617	+	1.31617i	−0.0442426	+	0.0442426i
$886$		0			0
$887$			15.9559i			0.535748i	0.963454	+	0.267874i	$0.0863211\pi$
$887$			15.9559i			0.535748i	−0.963454	+	0.267874i	$0.913679\pi$
$888$		0			0
$889$	−25.8658	+	21.0551i	−0.867512	+	0.706164i
$890$		0			0
$891$	−4.52322	+	4.52322i	−0.151534	+	0.151534i
$892$		0			0
$893$	6.43905	−	6.43905i	0.215475	−	0.215475i
$894$		0			0
$895$	−61.0647			−2.04117
$896$		0			0
$897$	13.9472			0.465685
$898$		0			0
$899$	−6.08233	+	6.08233i	−0.202857	+	0.202857i
$900$		0			0
$901$	42.9166	−	42.9166i	1.42976	−	1.42976i
$902$		0			0
$903$	13.9585	−	11.3624i	0.464510	−	0.378116i
$904$		0			0
$905$			3.38037i			0.112367i
$906$		0			0
$907$	−5.32214	+	5.32214i	−0.176719	+	0.176719i	−0.789924	−	0.613205i	$-0.789880\pi$
$907$	−5.32214	+	5.32214i	−0.176719	+	0.176719i	0.613205	+	0.789924i	$0.289880\pi$
$908$		0			0
$909$	0.548004	+	0.548004i	0.0181762	+	0.0181762i
$910$		0			0
$911$			19.2821i			0.638843i	0.947613	+	0.319422i	$0.103489\pi$
$911$			19.2821i			0.638843i	−0.947613	+	0.319422i	$0.896511\pi$
$912$		0			0
$913$		−	91.0356i		−	3.01284i
$914$		0			0
$915$	−15.3521	+	15.3521i	−0.507523	+	0.507523i
$916$		0			0
$917$	20.2950	+	2.08084i	0.670201	+	0.0687154i
$918$		0			0
$919$	44.6669			1.47342			0.736712	−	0.676207i	$-0.236377\pi$
$919$	44.6669			1.47342			0.736712	+	0.676207i	$0.236377\pi$
$920$		0			0
$921$		−	1.60127i		−	0.0527637i
$922$		0			0
$923$	−27.4195	−	27.4195i	−0.902522	−	0.902522i
$924$		0			0
$925$	−2.34924	+	2.34924i	−0.0772425	+	0.0772425i
$926$		0			0
$927$	−2.18981			−0.0719227
$928$		0			0
$929$		−	6.37514i		−	0.209162i	−0.994516	−	0.104581i	$-0.966650\pi$
$929$		−	6.37514i		−	0.209162i	0.994516	−	0.104581i	$-0.0333501\pi$
$930$		0			0
$931$	7.79681	+	11.8732i	0.255530	+	0.389127i
$932$		0			0
$933$	22.6000	+	22.6000i	0.739892	+	0.739892i
$934$		0			0
$935$	101.076			3.30552
$936$		0			0
$937$	19.8223			0.647568			0.323784	−	0.946131i	$-0.395045\pi$
$937$	19.8223			0.647568			0.323784	+	0.946131i	$0.395045\pi$
$938$		0			0
$939$	20.1526	−	20.1526i	0.657654	−	0.657654i
$940$		0			0
$941$	16.6010	+	16.6010i	0.541178	+	0.541178i	0.923874	−	0.382696i	$-0.125004\pi$
$941$	16.6010	+	16.6010i	0.541178	+	0.541178i	−0.382696	+	0.923874i	$0.625004\pi$
$942$		0			0
$943$	35.2034			1.14638
$944$		0			0
$945$	−4.25417	−	5.22618i	−0.138388	−	0.170008i
$946$		0			0
$947$	10.3480	+	10.3480i	0.336265	+	0.336265i	0.854960	−	0.518695i	$-0.173582\pi$
$947$	10.3480	+	10.3480i	0.336265	+	0.336265i	−0.518695	+	0.854960i	$0.673582\pi$
$948$		0			0
$949$	−10.0176	−	10.0176i	−0.325185	−	0.325185i
$950$		0			0
$951$			4.39836i			0.142627i
$952$		0			0
$953$			29.2556i			0.947682i	0.880610	+	0.473841i	$0.157133\pi$
$953$			29.2556i			0.947682i	−0.880610	+	0.473841i	$0.842867\pi$
$954$		0			0
$955$	30.7982	+	30.7982i	0.996607	+	0.996607i
$956$		0			0
$957$	−9.63978	−	9.63978i	−0.311610	−	0.311610i
$958$		0			0
$959$	26.7821	−	21.8009i	0.864840	−	0.703989i
$960$		0			0
$961$	−14.7096			−0.474503
$962$		0			0
$963$	5.39210	+	5.39210i	0.173758	+	0.173758i
$964$		0			0
$965$	−10.3847	+	10.3847i	−0.334294	+	0.334294i
$966$		0			0
$967$	6.89322			0.221671			0.110835	−	0.993839i	$-0.464647\pi$
$967$	6.89322			0.221671			0.110835	+	0.993839i	$0.464647\pi$
$968$		0			0
$969$	12.5885			0.404401
$970$		0			0
$971$	1.36810	+	1.36810i	0.0439045	+	0.0439045i	0.728718	−	0.684814i	$-0.240116\pi$
$971$	1.36810	+	1.36810i	0.0439045	+	0.0439045i	−0.684814	+	0.728718i	$0.740116\pi$
$972$		0			0
$973$	−5.32290	+	51.9158i	−0.170644	+	1.66434i
$974$		0			0
$975$		−	5.46163i		−	0.174912i
$976$		0			0
$977$	−29.6235			−0.947740			−0.473870	−	0.880595i	$-0.657143\pi$
$977$	−29.6235			−0.947740			−0.473870	+	0.880595i	$0.657143\pi$
$978$		0			0
$979$	1.19646	−	1.19646i	0.0382391	−	0.0382391i
$980$		0			0
$981$	−0.576562	−	0.576562i	−0.0184082	−	0.0184082i
$982$		0			0
$983$			37.6263i			1.20009i	0.799965	+	0.600046i	$0.204851\pi$
$983$			37.6263i			1.20009i	−0.799965	+	0.600046i	$0.795149\pi$
$984$		0			0
$985$	5.84229			0.186151
$986$		0			0
$987$	−11.8112	−	1.21099i	−0.375954	−	0.0385464i
$988$		0			0
$989$	−18.2695	+	18.2695i	−0.580938	+	0.580938i
$990$		0			0
$991$		−	6.15019i		−	0.195367i	−0.995218	−	0.0976836i	$-0.968857\pi$
$991$		−	6.15019i		−	0.195367i	0.995218	−	0.0976836i	$-0.0311433\pi$
$992$		0			0
$993$			31.8077i			1.00939i
$994$		0			0
$995$	−39.7926	−	39.7926i	−1.26151	−	1.26151i
$996$		0			0
$997$	38.9462	−	38.9462i	1.23344	−	1.23344i	0.270805	−	0.962634i	$-0.412710\pi$
$997$	38.9462	−	38.9462i	1.23344	−	1.23344i	0.962634	−	0.270805i	$-0.0872898\pi$
$998$		0			0
$999$		−	2.23384i		−	0.0706755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.u.a.1231.4		64
4.3	odd	2		336.2.u.a.139.12	yes	64
7.6	odd	2	inner	1344.2.u.a.1231.29		64
16.3	odd	4	inner	1344.2.u.a.559.29		64
16.13	even	4		336.2.u.a.307.11	yes	64
28.27	even	2		336.2.u.a.139.11	✓	64
112.13	odd	4		336.2.u.a.307.12	yes	64
112.83	even	4	inner	1344.2.u.a.559.4		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.u.a.139.11	✓	64	28.27	even	2
336.2.u.a.139.12	yes	64	4.3	odd	2
336.2.u.a.307.11	yes	64	16.13	even	4
336.2.u.a.307.12	yes	64	112.13	odd	4
1344.2.u.a.559.4		64	112.83	even	4	inner
1344.2.u.a.559.29		64	16.3	odd	4	inner
1344.2.u.a.1231.4		64	1.1	even	1	trivial
1344.2.u.a.1231.29		64	7.6	odd	2	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.u (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-1.80101 + 1.80101i) q^{5} +(1.67026 + 2.05189i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-1.80101 + 1.80101i) q^{5} +(1.67026 + 2.05189i) q^{7} -1.00000i q^{9} +(4.52322 - 4.52322i) q^{11} +(-2.59667 - 2.59667i) q^{13} -2.54701i q^{15} -6.20372i q^{17} +(1.43485 - 1.43485i) q^{19} +(-2.63195 - 0.269853i) q^{21} +3.79802 q^{23} -1.48727i q^{25} +(0.707107 + 0.707107i) q^{27} +(-1.50697 + 1.50697i) q^{29} +4.03614 q^{31} +6.39680i q^{33} +(-6.70362 - 0.687319i) q^{35} +(-1.57956 - 1.57956i) q^{37} +3.67224 q^{39} +9.26889 q^{41} +(-4.81028 + 4.81028i) q^{43} +(1.80101 + 1.80101i) q^{45} +4.48761 q^{47} +(-1.42048 + 6.85436i) q^{49} +(4.38669 + 4.38669i) q^{51} +(6.91789 + 6.91789i) q^{53} +16.2927i q^{55} +2.02919i q^{57} +(-0.516751 - 0.516751i) q^{59} +(-6.02748 - 6.02748i) q^{61} +(2.05189 - 1.67026i) q^{63} +9.35325 q^{65} +(-6.19917 - 6.19917i) q^{67} +(-2.68560 + 2.68560i) q^{69} +10.5595 q^{71} +3.85786 q^{73} +(1.05166 + 1.05166i) q^{75} +(16.8361 + 1.72620i) q^{77} -5.09974i q^{79} -1.00000 q^{81} +(10.0631 - 10.0631i) q^{83} +(11.1730 + 11.1730i) q^{85} -2.13118i q^{87} +0.264516 q^{89} +(0.990965 - 9.66517i) q^{91} +(-2.85398 + 2.85398i) q^{93} +5.16836i q^{95} +7.14810i q^{97} +(-4.52322 - 4.52322i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 8 q^{11} + 16 q^{23} + 16 q^{29} - 24 q^{35} + 16 q^{37} + 8 q^{43} + 16 q^{53} - 56 q^{67} + 128 q^{71} - 64 q^{81} - 8 q^{91} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^11 + 16 * q^23 + 16 * q^29 - 24 * q^35 + 16 * q^37 + 8 * q^43 + 16 * q^53 - 56 * q^67 + 128 * q^71 - 64 * q^81 - 8 * q^91 + 8 * q^99

Introduction

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