LMFDB - Embedded newform 840.2.bt.b.97.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(97,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.97"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.bt (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.11
Character	$\chi$	$=$	840.97
Dual form			840.2.bt.b.433.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{3} +(1.35806 - 1.77642i) q^{5} +(2.59845 - 0.498068i) q^{7} +1.00000i q^{9} -1.97065 q^{11} +(4.59535 + 4.59535i) q^{13} +(2.21641 - 0.295823i) q^{15} +(-4.07417 + 4.07417i) q^{17} +0.683247 q^{19} +(2.18957 + 1.48519i) q^{21} +(5.64986 - 5.64986i) q^{23} +(-1.31133 - 4.82498i) q^{25} +(-0.707107 + 0.707107i) q^{27} -5.55225i q^{29} -6.08883i q^{31} +(-1.39346 - 1.39346i) q^{33} +(2.64408 - 5.29234i) q^{35} +(2.16069 + 2.16069i) q^{37} +6.49881i q^{39} +9.16323i q^{41} +(0.140863 - 0.140863i) q^{43} +(1.77642 + 1.35806i) q^{45} +(-1.75970 + 1.75970i) q^{47} +(6.50386 - 2.58841i) q^{49} -5.76175 q^{51} +(-0.681330 + 0.681330i) q^{53} +(-2.67627 + 3.50070i) q^{55} +(0.483129 + 0.483129i) q^{57} +9.12135 q^{59} +2.91963i q^{61} +(0.498068 + 2.59845i) q^{63} +(14.4040 - 1.92249i) q^{65} +(-7.72475 - 7.72475i) q^{67} +7.99011 q^{69} -13.9714 q^{71} +(7.15260 + 7.15260i) q^{73} +(2.48452 - 4.33903i) q^{75} +(-5.12063 + 0.981518i) q^{77} +12.3497i q^{79} -1.00000 q^{81} +(-7.79039 - 7.79039i) q^{83} +(1.70446 + 12.7704i) q^{85} +(3.92604 - 3.92604i) q^{87} -9.74211 q^{89} +(14.2296 + 9.65198i) q^{91} +(4.30545 - 4.30545i) q^{93} +(0.927893 - 1.21373i) q^{95} +(-0.937590 + 0.937590i) q^{97} -1.97065i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{11} - 16 q^{13} + 4 q^{15} - 20 q^{17} - 8 q^{19} + 24 q^{23} - 4 q^{25} + 4 q^{37} - 16 q^{43} + 4 q^{45} + 24 q^{47} - 36 q^{49} + 16 q^{53} - 28 q^{55} + 4 q^{57} - 8 q^{59} + 4 q^{63} + 24 q^{65}+ \cdots + 28 q^{97}+O(q^{100}) $ 24 * q - 8 * q^11 - 16 * q^13 + 4 * q^15 - 20 * q^17 - 8 * q^19 + 24 * q^23 - 4 * q^25 + 4 * q^37 - 16 * q^43 + 4 * q^45 + 24 * q^47 - 36 * q^49 + 16 * q^53 - 28 * q^55 + 4 * q^57 - 8 * q^59 + 4 * q^63 + 24 * q^65 + 16 * q^67 + 8 * q^69 + 8 * q^71 + 28 * q^73 + 28 * q^77 - 24 * q^81 - 64 * q^83 - 20 * q^85 - 20 * q^87 - 16 * q^89 + 24 * q^91 - 12 * q^93 + 24 * q^95 + 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		0			0
$5$	1.35806	−	1.77642i	0.607344	−	0.794439i
$5$	1.35806	−	1.77642i	0.607344	−	0.794439i
$6$		0			0
$7$	2.59845	−	0.498068i	0.982121	−	0.188252i
$7$	2.59845	−	0.498068i	0.982121	−	0.188252i
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−1.97065			−0.594173			−0.297087	−	0.954851i	$-0.596015\pi$
$11$	−1.97065			−0.594173			−0.297087	+	0.954851i	$0.596015\pi$
$12$		0			0
$13$	4.59535	+	4.59535i	1.27452	+	1.27452i	0.943690	+	0.330831i	$0.107329\pi$
$13$	4.59535	+	4.59535i	1.27452	+	1.27452i	0.330831	+	0.943690i	$0.392671\pi$
$14$		0			0
$15$	2.21641	−	0.295823i	0.572276	−	0.0763811i
$16$		0			0
$17$	−4.07417	+	4.07417i	−0.988132	+	0.988132i	−0.999930	−	0.0117982i	$-0.996244\pi$
$17$	−4.07417	+	4.07417i	−0.988132	+	0.988132i	0.0117982	+	0.999930i	$0.496244\pi$
$18$		0			0
$19$	0.683247			0.156748			0.0783738	−	0.996924i	$-0.475027\pi$
$19$	0.683247			0.156748			0.0783738	+	0.996924i	$0.475027\pi$
$20$		0			0
$21$	2.18957	+	1.48519i	0.477803	+	0.324095i
$22$		0			0
$23$	5.64986	−	5.64986i	1.17808	−	1.17808i	0.197844	−	0.980233i	$-0.436606\pi$
$23$	5.64986	−	5.64986i	1.17808	−	1.17808i	0.980233	−	0.197844i	$-0.0633941\pi$
$24$		0			0
$25$	−1.31133	−	4.82498i	−0.262266	−	0.964996i
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$		−	5.55225i		−	1.03103i	−0.856881	−	0.515514i	$-0.827601\pi$
$29$		−	5.55225i		−	1.03103i	0.856881	−	0.515514i	$-0.172399\pi$
$30$		0			0
$31$		−	6.08883i		−	1.09359i	−0.837268	−	0.546793i	$-0.815848\pi$
$31$		−	6.08883i		−	1.09359i	0.837268	−	0.546793i	$-0.184152\pi$
$32$		0			0
$33$	−1.39346	−	1.39346i	−0.242570	−	0.242570i
$34$		0			0
$35$	2.64408	−	5.29234i	0.446930	−	0.894569i
$36$		0			0
$37$	2.16069	+	2.16069i	0.355215	+	0.355215i	0.862046	−	0.506831i	$-0.169183\pi$
$37$	2.16069	+	2.16069i	0.355215	+	0.355215i	−0.506831	+	0.862046i	$0.669183\pi$
$38$		0			0
$39$			6.49881i			1.04064i
$40$		0			0
$41$			9.16323i			1.43106i	0.698584	+	0.715528i	$0.253814\pi$
$41$			9.16323i			1.43106i	−0.698584	+	0.715528i	$0.746186\pi$
$42$		0			0
$43$	0.140863	−	0.140863i	0.0214814	−	0.0214814i	−0.696284	−	0.717766i	$-0.745165\pi$
$43$	0.140863	−	0.140863i	0.0214814	−	0.0214814i	0.717766	+	0.696284i	$0.245165\pi$
$44$		0			0
$45$	1.77642	+	1.35806i	0.264813	+	0.202448i
$46$		0			0
$47$	−1.75970	+	1.75970i	−0.256678	+	0.256678i	−0.823702	−	0.567023i	$-0.808095\pi$
$47$	−1.75970	+	1.75970i	−0.256678	+	0.256678i	0.567023	+	0.823702i	$0.308095\pi$
$48$		0			0
$49$	6.50386	−	2.58841i	0.929122	−	0.369773i
$50$		0			0
$51$	−5.76175			−0.806807
$52$		0			0
$53$	−0.681330	+	0.681330i	−0.0935878	+	0.0935878i	−0.752351	−	0.658763i	$-0.771080\pi$
$53$	−0.681330	+	0.681330i	−0.0935878	+	0.0935878i	0.658763	+	0.752351i	$0.271080\pi$
$54$		0			0
$55$	−2.67627	+	3.50070i	−0.360868	+	0.472034i
$56$		0			0
$57$	0.483129	+	0.483129i	0.0639920	+	0.0639920i
$58$		0			0
$59$	9.12135			1.18750			0.593749	−	0.804650i	$-0.297647\pi$
$59$	9.12135			1.18750			0.593749	+	0.804650i	$0.297647\pi$
$60$		0			0
$61$			2.91963i			0.373820i	0.982377	+	0.186910i	$0.0598473\pi$
$61$			2.91963i			0.373820i	−0.982377	+	0.186910i	$0.940153\pi$
$62$		0			0
$63$	0.498068	+	2.59845i	0.0627507	+	0.327374i
$64$		0			0
$65$	14.4040	−	1.92249i	1.78660	−	0.238456i
$66$		0			0
$67$	−7.72475	−	7.72475i	−0.943729	−	0.943729i	0.0547703	−	0.998499i	$-0.482557\pi$
$67$	−7.72475	−	7.72475i	−0.943729	−	0.943729i	−0.998499	+	0.0547703i	$0.982557\pi$
$68$		0			0
$69$	7.99011			0.961897
$70$		0			0
$71$	−13.9714			−1.65810			−0.829048	−	0.559177i	$-0.811117\pi$
$71$	−13.9714			−1.65810			−0.829048	+	0.559177i	$0.811117\pi$
$72$		0			0
$73$	7.15260	+	7.15260i	0.837148	+	0.837148i	0.988483	−	0.151335i	$-0.0483571\pi$
$73$	7.15260	+	7.15260i	0.837148	+	0.837148i	−0.151335	+	0.988483i	$0.548357\pi$
$74$		0			0
$75$	2.48452	−	4.33903i	0.286888	−	0.501028i
$76$		0			0
$77$	−5.12063	+	0.981518i	−0.583550	+	0.111854i
$78$		0			0
$79$			12.3497i			1.38945i	0.719278	+	0.694723i	$0.244473\pi$
$79$			12.3497i			1.38945i	−0.719278	+	0.694723i	$0.755527\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−7.79039	−	7.79039i	−0.855107	−	0.855107i	0.135650	−	0.990757i	$-0.456688\pi$
$83$	−7.79039	−	7.79039i	−0.855107	−	0.855107i	−0.990757	+	0.135650i	$0.956688\pi$
$84$		0			0
$85$	1.70446	+	12.7704i	0.184874	+	1.38515i
$86$		0			0
$87$	3.92604	−	3.92604i	0.420915	−	0.420915i
$88$		0			0
$89$	−9.74211			−1.03266			−0.516331	−	0.856389i	$-0.672702\pi$
$89$	−9.74211			−1.03266			−0.516331	+	0.856389i	$0.672702\pi$
$90$		0			0
$91$	14.2296	+	9.65198i	1.49166	+	1.01180i
$92$		0			0
$93$	4.30545	−	4.30545i	0.446455	−	0.446455i
$94$		0			0
$95$	0.927893	−	1.21373i	0.0951998	−	0.124526i
$96$		0			0
$97$	−0.937590	+	0.937590i	−0.0951979	+	0.0951979i	−0.753102	−	0.657904i	$-0.771443\pi$
$97$	−0.937590	+	0.937590i	−0.0951979	+	0.0951979i	0.657904	+	0.753102i	$0.271443\pi$
$98$		0			0
$99$		−	1.97065i		−	0.198058i
$100$		0			0
$101$		−	6.31532i		−	0.628398i	−0.949357	−	0.314199i	$-0.898264\pi$
$101$		−	6.31532i		−	0.628398i	0.949357	−	0.314199i	$-0.101736\pi$
$102$		0			0
$103$	−2.56589	−	2.56589i	−0.252824	−	0.252824i	0.569303	−	0.822128i	$-0.307213\pi$
$103$	−2.56589	−	2.56589i	−0.252824	−	0.252824i	−0.822128	+	0.569303i	$0.807213\pi$
$104$		0			0
$105$	5.61189	−	1.87261i	0.547665	−	0.182748i
$106$		0			0
$107$	−6.52588	−	6.52588i	−0.630880	−	0.630880i	0.317408	−	0.948289i	$-0.397187\pi$
$107$	−6.52588	−	6.52588i	−0.630880	−	0.630880i	−0.948289	+	0.317408i	$0.897187\pi$
$108$		0			0
$109$			12.1055i			1.15950i	0.814795	+	0.579749i	$0.196849\pi$
$109$			12.1055i			1.15950i	−0.814795	+	0.579749i	$0.803151\pi$
$110$		0			0
$111$			3.05567i			0.290032i
$112$		0			0
$113$	9.03766	−	9.03766i	0.850192	−	0.850192i	−0.139965	−	0.990156i	$-0.544699\pi$
$113$	9.03766	−	9.03766i	0.850192	−	0.850192i	0.990156	+	0.139965i	$0.0446989\pi$
$114$		0			0
$115$	−2.36366	−	17.7094i	−0.220412	−	1.65141i
$116$		0			0
$117$	−4.59535	+	4.59535i	−0.424840	+	0.424840i
$118$		0			0
$119$	−8.55731	+	12.6157i	−0.784447	+	1.15648i
$120$		0			0
$121$	−7.11654			−0.646958
$122$		0			0
$123$	−6.47938	+	6.47938i	−0.584226	+	0.584226i
$124$		0			0
$125$	−10.3521	−	4.22315i	−0.925916	−	0.377730i
$126$		0			0
$127$	−1.88536	−	1.88536i	−0.167298	−	0.167298i	0.618492	−	0.785791i	$-0.287744\pi$
$127$	−1.88536	−	1.88536i	−0.167298	−	0.167298i	−0.785791	+	0.618492i	$0.787744\pi$
$128$		0			0
$129$	0.199211			0.0175395
$130$		0			0
$131$			6.91889i			0.604506i	0.953228	+	0.302253i	$0.0977387\pi$
$131$			6.91889i			0.604506i	−0.953228	+	0.302253i	$0.902261\pi$
$132$		0			0
$133$	1.77538	−	0.340304i	0.153945	−	0.0295081i
$134$		0			0
$135$	0.295823	+	2.21641i	0.0254604	+	0.190759i
$136$		0			0
$137$	−13.3157	−	13.3157i	−1.13764	−	1.13764i	−0.988872	−	0.148768i	$-0.952469\pi$
$137$	−13.3157	−	13.3157i	−1.13764	−	1.13764i	−0.148768	−	0.988872i	$-0.547531\pi$
$138$		0			0
$139$	4.45662			0.378005			0.189003	−	0.981977i	$-0.439474\pi$
$139$	4.45662			0.378005			0.189003	+	0.981977i	$0.439474\pi$
$140$		0			0
$141$	−2.48859			−0.209577
$142$		0			0
$143$	−9.05583	−	9.05583i	−0.757286	−	0.757286i
$144$		0			0
$145$	−9.86313	−	7.54031i	−0.819088	−	0.626189i
$146$		0			0
$147$	6.42920	+	2.76864i	0.530272	+	0.228354i
$148$		0			0
$149$		−	8.00416i		−	0.655726i	−0.944725	−	0.327863i	$-0.893672\pi$
$149$		−	8.00416i		−	0.655726i	0.944725	−	0.327863i	$-0.106328\pi$
$150$		0			0
$151$	−10.8999			−0.887019			−0.443510	−	0.896270i	$-0.646267\pi$
$151$	−10.8999			−0.887019			−0.443510	+	0.896270i	$0.646267\pi$
$152$		0			0
$153$	−4.07417	−	4.07417i	−0.329377	−	0.329377i
$154$		0			0
$155$	−10.8163	−	8.26902i	−0.868788	−	0.664183i
$156$		0			0
$157$	−6.30526	+	6.30526i	−0.503214	+	0.503214i	−0.912435	−	0.409221i	$-0.865800\pi$
$157$	−6.30526	+	6.30526i	−0.503214	+	0.503214i	0.409221	+	0.912435i	$0.365800\pi$
$158$		0			0
$159$	−0.963546			−0.0764142
$160$		0			0
$161$	11.8669	−	17.4949i	0.935239	−	1.37879i
$162$		0			0
$163$	17.7122	−	17.7122i	1.38732	−	1.38732i	0.556426	−	0.830897i	$-0.312172\pi$
$163$	17.7122	−	17.7122i	1.38732	−	1.38732i	0.830897	−	0.556426i	$-0.187828\pi$
$164$		0			0
$165$	−4.36778	+	0.582963i	−0.340031	+	0.0453836i
$166$		0			0
$167$	−3.68257	+	3.68257i	−0.284966	+	0.284966i	−0.835086	−	0.550120i	$-0.814582\pi$
$167$	−3.68257	+	3.68257i	−0.284966	+	0.284966i	0.550120	+	0.835086i	$0.314582\pi$
$168$		0			0
$169$			29.2345i			2.24881i
$170$		0			0
$171$			0.683247i			0.0522492i
$172$		0			0
$173$	11.7646	+	11.7646i	0.894449	+	0.894449i	0.994938	−	0.100489i	$-0.0320409\pi$
$173$	11.7646	+	11.7646i	0.894449	+	0.894449i	−0.100489	+	0.994938i	$0.532041\pi$
$174$		0			0
$175$	−5.81059	−	11.8843i	−0.439240	−	0.898370i
$176$		0			0
$177$	6.44977	+	6.44977i	0.484794	+	0.484794i
$178$		0			0
$179$			5.16770i			0.386252i	0.981174	+	0.193126i	$0.0618626\pi$
$179$			5.16770i			0.386252i	−0.981174	+	0.193126i	$0.938137\pi$
$180$		0			0
$181$		−	1.59465i		−	0.118529i	−0.998242	−	0.0592646i	$-0.981124\pi$
$181$		−	1.59465i		−	0.118529i	0.998242	−	0.0592646i	$-0.0188756\pi$
$182$		0			0
$183$	−2.06449	+	2.06449i	−0.152612	+	0.152612i
$184$		0			0
$185$	6.77264	−	0.903938i	0.497934	−	0.0664588i
$186$		0			0
$187$	8.02877	−	8.02877i	0.587122	−	0.587122i
$188$		0			0
$189$	−1.48519	+	2.18957i	−0.108032	+	0.159268i
$190$		0			0
$191$	8.88021			0.642549			0.321275	−	0.946986i	$-0.395889\pi$
$191$	8.88021			0.642549			0.321275	+	0.946986i	$0.395889\pi$
$192$		0			0
$193$	−9.68963	+	9.68963i	−0.697475	+	0.697475i	−0.963865	−	0.266391i	$-0.914169\pi$
$193$	−9.68963	+	9.68963i	−0.697475	+	0.697475i	0.266391	+	0.963865i	$0.414169\pi$
$194$		0			0
$195$	11.5446	+	8.82579i	0.826726	+	0.632028i
$196$		0			0
$197$	−0.207918	−	0.207918i	−0.0148135	−	0.0148135i	0.699661	−	0.714475i	$-0.253334\pi$
$197$	−0.207918	−	0.207918i	−0.0148135	−	0.0148135i	−0.714475	+	0.699661i	$0.753334\pi$
$198$		0			0
$199$	−12.1051			−0.858105			−0.429052	−	0.903280i	$-0.641152\pi$
$199$	−12.1051			−0.858105			−0.429052	+	0.903280i	$0.641152\pi$
$200$		0			0
$201$		−	10.9244i		−	0.770551i
$202$		0			0
$203$	−2.76540	−	14.4272i	−0.194093	−	1.01259i
$204$		0			0
$205$	16.2777	+	12.4442i	1.13689	+	0.869144i
$206$		0			0
$207$	5.64986	+	5.64986i	0.392693	+	0.392693i
$208$		0			0
$209$	−1.34644			−0.0931353
$210$		0			0
$211$	−16.6097			−1.14346			−0.571729	−	0.820442i	$-0.693727\pi$
$211$	−16.6097			−1.14346			−0.571729	+	0.820442i	$0.693727\pi$
$212$		0			0
$213$	−9.87925	−	9.87925i	−0.676915	−	0.676915i
$214$		0			0
$215$	−0.0589311	−	0.441533i	−0.00401906	−	0.0301123i
$216$		0			0
$217$	−3.03265	−	15.8215i	−0.205870	−	1.07403i
$218$		0			0
$219$			10.1153i			0.683529i
$220$		0			0
$221$	−37.4445			−2.51879
$222$		0			0
$223$	−16.5656	−	16.5656i	−1.10932	−	1.10932i	−0.993240	−	0.116075i	$-0.962969\pi$
$223$	−16.5656	−	16.5656i	−1.10932	−	1.10932i	−0.116075	−	0.993240i	$-0.537031\pi$
$224$		0			0
$225$	4.82498	−	1.31133i	0.321665	−	0.0874221i
$226$		0			0
$227$	−10.3172	+	10.3172i	−0.684776	+	0.684776i	−0.961072	−	0.276297i	$-0.910893\pi$
$227$	−10.3172	+	10.3172i	−0.684776	+	0.684776i	0.276297	+	0.961072i	$0.410893\pi$
$228$		0			0
$229$	12.2436			0.809083			0.404541	−	0.914520i	$-0.367431\pi$
$229$	12.2436			0.809083			0.404541	+	0.914520i	$0.367431\pi$
$230$		0			0
$231$	−4.31487	−	2.92679i	−0.283898	−	0.192569i
$232$		0			0
$233$	−12.5193	+	12.5193i	−0.820169	+	0.820169i	−0.986132	−	0.165963i	$-0.946927\pi$
$233$	−12.5193	+	12.5193i	−0.820169	+	0.820169i	0.165963	+	0.986132i	$0.446927\pi$
$234$		0			0
$235$	0.736181	+	5.51574i	0.0480232	+	0.359807i
$236$		0			0
$237$	−8.73253	+	8.73253i	−0.567239	+	0.567239i
$238$		0			0
$239$			0.767767i			0.0496627i	0.999692	+	0.0248314i	$0.00790488\pi$
$239$			0.767767i			0.0496627i	−0.999692	+	0.0248314i	$0.992095\pi$
$240$		0			0
$241$			20.1582i			1.29850i	0.760573	+	0.649252i	$0.224918\pi$
$241$			20.1582i			1.29850i	−0.760573	+	0.649252i	$0.775082\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	4.23455	−	15.0688i	0.270535	−	0.962710i
$246$		0			0
$247$	3.13976	+	3.13976i	0.199778	+	0.199778i
$248$		0			0
$249$		−	11.0173i		−	0.698192i
$250$		0			0
$251$		−	6.15272i		−	0.388356i	−0.980966	−	0.194178i	$-0.937796\pi$
$251$		−	6.15272i		−	0.388356i	0.980966	−	0.194178i	$-0.0622040\pi$
$252$		0			0
$253$	−11.1339	+	11.1339i	−0.699982	+	0.699982i
$254$		0			0
$255$	−7.82482	+	10.2353i	−0.490009	+	0.640958i
$256$		0			0
$257$	−4.35819	+	4.35819i	−0.271856	+	0.271856i	−0.829847	−	0.557991i	$-0.811572\pi$
$257$	−4.35819	+	4.35819i	−0.271856	+	0.271856i	0.557991	+	0.829847i	$0.311572\pi$
$258$		0			0
$259$	6.69060	+	4.53826i	0.415734	+	0.281994i
$260$		0			0
$261$	5.55225			0.343676
$262$		0			0
$263$	−13.4490	+	13.4490i	−0.829301	+	0.829301i	−0.987420	−	0.158119i	$-0.949457\pi$
$263$	−13.4490	+	13.4490i	−0.829301	+	0.829301i	0.158119	+	0.987420i	$0.449457\pi$
$264$		0			0
$265$	0.285039	+	2.13562i	0.0175098	+	0.131190i
$266$		0			0
$267$	−6.88871	−	6.88871i	−0.421582	−	0.421582i
$268$		0			0
$269$	−4.88078			−0.297587			−0.148793	−	0.988868i	$-0.547539\pi$
$269$	−4.88078			−0.297587			−0.148793	+	0.988868i	$0.547539\pi$
$270$		0			0
$271$			8.71993i			0.529698i	0.964290	+	0.264849i	$0.0853222\pi$
$271$			8.71993i			0.529698i	−0.964290	+	0.264849i	$0.914678\pi$
$272$		0			0
$273$	3.23685	+	16.8868i	0.195903	+	1.02204i
$274$		0			0
$275$	2.58417	+	9.50834i	0.155832	+	0.573375i
$276$		0			0
$277$	−23.0209	−	23.0209i	−1.38319	−	1.38319i	−0.838887	−	0.544306i	$-0.816793\pi$
$277$	−23.0209	−	23.0209i	−1.38319	−	1.38319i	−0.544306	−	0.838887i	$-0.683207\pi$
$278$		0			0
$279$	6.08883			0.364529
$280$		0			0
$281$	15.6786			0.935304			0.467652	−	0.883913i	$-0.345100\pi$
$281$	15.6786			0.935304			0.467652	+	0.883913i	$0.345100\pi$
$282$		0			0
$283$	17.0637	+	17.0637i	1.01433	+	1.01433i	0.999896	+	0.0144337i	$0.00459453\pi$
$283$	17.0637	+	17.0637i	1.01433	+	1.01433i	0.0144337	+	0.999896i	$0.495405\pi$
$284$		0			0
$285$	1.51436	−	0.202120i	0.0897029	−	0.0119726i
$286$		0			0
$287$	4.56392	+	23.8102i	0.269399	+	1.40547i
$288$		0			0
$289$		−	16.1978i		−	0.952810i
$290$		0			0
$291$	−1.32595			−0.0777287
$292$		0			0
$293$	−22.0794	−	22.0794i	−1.28989	−	1.28989i	−0.934851	−	0.355040i	$-0.884467\pi$
$293$	−22.0794	−	22.0794i	−1.28989	−	1.28989i	−0.355040	−	0.934851i	$-0.615533\pi$
$294$		0			0
$295$	12.3874	−	16.2033i	0.721220	−	0.943395i
$296$		0			0
$297$	1.39346	−	1.39346i	0.0808567	−	0.0808567i
$298$		0			0
$299$	51.9262			3.00297
$300$		0			0
$301$	0.295866	−	0.436185i	0.0170534	−	0.0251413i
$302$		0			0
$303$	4.46561	−	4.46561i	0.256543	−	0.256543i
$304$		0			0
$305$	5.18649	+	3.96504i	0.296977	+	0.227038i
$306$		0			0
$307$	15.4182	−	15.4182i	0.879961	−	0.879961i	−0.113569	−	0.993530i	$-0.536228\pi$
$307$	15.4182	−	15.4182i	0.879961	−	0.879961i	0.993530	+	0.113569i	$0.0362284\pi$
$308$		0			0
$309$		−	3.62871i		−	0.206430i
$310$		0			0
$311$			20.0281i			1.13569i	0.823136	+	0.567844i	$0.192222\pi$
$311$			20.0281i			1.13569i	−0.823136	+	0.567844i	$0.807778\pi$
$312$		0			0
$313$	−18.6499	−	18.6499i	−1.05415	−	1.05415i	−0.998447	−	0.0557054i	$-0.982259\pi$
$313$	−18.6499	−	18.6499i	−1.05415	−	1.05415i	−0.0557054	−	0.998447i	$-0.517741\pi$
$314$		0			0
$315$	5.29234	+	2.64408i	0.298190	+	0.148977i
$316$		0			0
$317$	7.14162	+	7.14162i	0.401113	+	0.401113i	0.878625	−	0.477512i	$-0.158461\pi$
$317$	7.14162	+	7.14162i	0.401113	+	0.401113i	−0.477512	+	0.878625i	$0.658461\pi$
$318$		0			0
$319$			10.9415i			0.612609i
$320$		0			0
$321$		−	9.22899i		−	0.515112i
$322$		0			0
$323$	−2.78367	+	2.78367i	−0.154887	+	0.154887i
$324$		0			0
$325$	16.1464	−	28.1985i	0.895643	−	1.56417i
$326$		0			0
$327$	−8.55989	+	8.55989i	−0.473363	+	0.473363i
$328$		0			0
$329$	−3.69603	+	5.44893i	−0.203769	+	0.300409i
$330$		0			0
$331$	18.9660			1.04247			0.521233	−	0.853414i	$-0.325472\pi$
$331$	18.9660			1.04247			0.521233	+	0.853414i	$0.325472\pi$
$332$		0			0
$333$	−2.16069	+	2.16069i	−0.118405	+	0.118405i
$334$		0			0
$335$	−24.2131	+	3.23170i	−1.32290	+	0.176567i
$336$		0			0
$337$	−16.0050	−	16.0050i	−0.871850	−	0.871850i	0.120824	−	0.992674i	$-0.461446\pi$
$337$	−16.0050	−	16.0050i	−0.871850	−	0.871850i	−0.992674	+	0.120824i	$0.961446\pi$
$338$		0			0
$339$	12.7812			0.694179
$340$		0			0
$341$			11.9990i			0.649780i
$342$		0			0
$343$	15.6107	−	9.96521i	0.842900	−	0.538071i
$344$		0			0
$345$	10.8511	−	14.1938i	0.584202	−	0.764168i
$346$		0			0
$347$	6.34709	+	6.34709i	0.340730	+	0.340730i	0.856642	−	0.515912i	$-0.172547\pi$
$347$	6.34709	+	6.34709i	0.340730	+	0.340730i	−0.515912	+	0.856642i	$0.672547\pi$
$348$		0			0
$349$	20.6689			1.10638			0.553192	−	0.833054i	$-0.313410\pi$
$349$	20.6689			1.10638			0.553192	+	0.833054i	$0.313410\pi$
$350$		0			0
$351$	−6.49881			−0.346881
$352$		0			0
$353$	1.82560	+	1.82560i	0.0971667	+	0.0971667i	0.754019	−	0.656852i	$-0.228113\pi$
$353$	1.82560	+	1.82560i	0.0971667	+	0.0971667i	−0.656852	+	0.754019i	$0.728113\pi$
$354$		0			0
$355$	−18.9740	+	24.8190i	−1.00704	+	1.31726i
$356$		0			0
$357$	−14.9716	+	2.86975i	−0.792381	+	0.151883i
$358$		0			0
$359$		−	13.5919i		−	0.717351i	−0.933462	−	0.358675i	$-0.883228\pi$
$359$		−	13.5919i		−	0.717351i	0.933462	−	0.358675i	$-0.116772\pi$
$360$		0			0
$361$	−18.5332			−0.975430
$362$		0			0
$363$	−5.03215	−	5.03215i	−0.264120	−	0.264120i
$364$		0			0
$365$	22.4197	−	2.99233i	1.17350	−	0.156626i
$366$		0			0
$367$	4.58532	−	4.58532i	0.239352	−	0.239352i	−0.577230	−	0.816582i	$-0.695866\pi$
$367$	4.58532	−	4.58532i	0.239352	−	0.239352i	0.816582	+	0.577230i	$0.195866\pi$
$368$		0			0
$369$	−9.16323			−0.477019
$370$		0			0
$371$	−1.43105	+	2.10975i	−0.0742965	+	0.109533i
$372$		0			0
$373$	4.52482	−	4.52482i	0.234286	−	0.234286i	−0.580193	−	0.814479i	$-0.697023\pi$
$373$	4.52482	−	4.52482i	0.234286	−	0.234286i	0.814479	+	0.580193i	$0.197023\pi$
$374$		0			0
$375$	−4.33379	−	10.3062i	−0.223796	−	0.532211i
$376$		0			0
$377$	25.5146	−	25.5146i	1.31407	−	1.31407i
$378$		0			0
$379$			0.424878i			0.0218245i	0.999940	+	0.0109123i	$0.00347355\pi$
$379$			0.424878i			0.0218245i	−0.999940	+	0.0109123i	$0.996526\pi$
$380$		0			0
$381$		−	2.66630i		−	0.136599i
$382$		0			0
$383$	13.5933	+	13.5933i	0.694587	+	0.694587i	0.963238	−	0.268650i	$-0.0865776\pi$
$383$	13.5933	+	13.5933i	0.694587	+	0.694587i	−0.268650	+	0.963238i	$0.586578\pi$
$384$		0			0
$385$	−5.21055	+	10.4293i	−0.265554	+	0.531529i
$386$		0			0
$387$	0.140863	+	0.140863i	0.00716048	+	0.00716048i
$388$		0			0
$389$			0.439801i			0.0222988i	0.999938	+	0.0111494i	$0.00354903\pi$
$389$			0.439801i			0.0222988i	−0.999938	+	0.0111494i	$0.996451\pi$
$390$		0			0
$391$			46.0370i			2.32819i
$392$		0			0
$393$	−4.89239	+	4.89239i	−0.246788	+	0.246788i
$394$		0			0
$395$	21.9382	+	16.7716i	1.10383	+	0.843872i
$396$		0			0
$397$	10.5788	−	10.5788i	0.530934	−	0.530934i	−0.389916	−	0.920850i	$-0.627496\pi$
$397$	10.5788	−	10.5788i	0.530934	−	0.530934i	0.920850	+	0.389916i	$0.127496\pi$
$398$		0			0
$399$	1.49602	+	1.01475i	0.0748945	+	0.0508012i
$400$		0			0
$401$	−11.6054			−0.579545			−0.289772	−	0.957096i	$-0.593580\pi$
$401$	−11.6054			−0.579545			−0.289772	+	0.957096i	$0.593580\pi$
$402$		0			0
$403$	27.9803	−	27.9803i	1.39380	−	1.39380i
$404$		0			0
$405$	−1.35806	+	1.77642i	−0.0674827	+	0.0882710i
$406$		0			0
$407$	−4.25796	−	4.25796i	−0.211059	−	0.211059i
$408$		0			0
$409$	−30.7361			−1.51980			−0.759901	−	0.650039i	$-0.774752\pi$
$409$	−30.7361			−1.51980			−0.759901	+	0.650039i	$0.774752\pi$
$410$		0			0
$411$		−	18.8313i		−	0.928879i
$412$		0			0
$413$	23.7013	−	4.54306i	1.16627	−	0.223549i
$414$		0			0
$415$	−24.4188	+	3.25916i	−1.19867	+	0.159986i
$416$		0			0
$417$	3.15131	+	3.15131i	0.154320	+	0.154320i
$418$		0			0
$419$	15.1533			0.740289			0.370144	−	0.928974i	$-0.379308\pi$
$419$	15.1533			0.740289			0.370144	+	0.928974i	$0.379308\pi$
$420$		0			0
$421$	32.9975			1.60820			0.804099	−	0.594495i	$-0.202648\pi$
$421$	32.9975			1.60820			0.804099	+	0.594495i	$0.202648\pi$
$422$		0			0
$423$	−1.75970	−	1.75970i	−0.0855594	−	0.0855594i
$424$		0			0
$425$	25.0004	+	14.3152i	1.21270	+	0.694390i
$426$		0			0
$427$	1.45418	+	7.58650i	0.0703725	+	0.367137i
$428$		0			0
$429$		−	12.8069i		−	0.618322i
$430$		0			0
$431$	−6.72817			−0.324084			−0.162042	−	0.986784i	$-0.551808\pi$
$431$	−6.72817			−0.324084			−0.162042	+	0.986784i	$0.551808\pi$
$432$		0			0
$433$	19.1760	+	19.1760i	0.921539	+	0.921539i	0.997138	−	0.0755993i	$-0.0240870\pi$
$433$	19.1760	+	19.1760i	0.921539	+	0.921539i	−0.0755993	+	0.997138i	$0.524087\pi$
$434$		0			0
$435$	−1.64248	−	12.3061i	−0.0787510	−	0.590032i
$436$		0			0
$437$	3.86025	−	3.86025i	0.184661	−	0.184661i
$438$		0			0
$439$	−24.4669			−1.16774			−0.583870	−	0.811847i	$-0.698462\pi$
$439$	−24.4669			−1.16774			−0.583870	+	0.811847i	$0.698462\pi$
$440$		0			0
$441$	2.58841	+	6.50386i	0.123258	+	0.309707i
$442$		0			0
$443$	17.7405	−	17.7405i	0.842874	−	0.842874i	−0.146357	−	0.989232i	$-0.546755\pi$
$443$	17.7405	−	17.7405i	0.842874	−	0.842874i	0.989232	+	0.146357i	$0.0467549\pi$
$444$		0			0
$445$	−13.2304	+	17.3061i	−0.627181	+	0.820386i
$446$		0			0
$447$	5.65979	−	5.65979i	0.267699	−	0.267699i
$448$		0			0
$449$			23.5455i			1.11118i	0.831456	+	0.555590i	$0.187508\pi$
$449$			23.5455i			1.11118i	−0.831456	+	0.555590i	$0.812492\pi$
$450$		0			0
$451$		−	18.0575i		−	0.850296i
$452$		0			0
$453$	−7.70737	−	7.70737i	−0.362124	−	0.362124i
$454$		0			0
$455$	36.4706	−	12.1697i	1.70977	−	0.570524i
$456$		0			0
$457$	13.1762	+	13.1762i	0.616358	+	0.616358i	0.944595	−	0.328237i	$-0.106455\pi$
$457$	13.1762	+	13.1762i	0.616358	+	0.616358i	−0.328237	+	0.944595i	$0.606455\pi$
$458$		0			0
$459$		−	5.76175i		−	0.268936i
$460$		0			0
$461$		−	12.4128i		−	0.578124i	−0.957310	−	0.289062i	$-0.906657\pi$
$461$		−	12.4128i		−	0.578124i	0.957310	−	0.289062i	$-0.0933433\pi$
$462$		0			0
$463$	1.78817	−	1.78817i	0.0831035	−	0.0831035i	−0.664333	−	0.747437i	$-0.731284\pi$
$463$	1.78817	−	1.78817i	0.0831035	−	0.0831035i	0.747437	+	0.664333i	$0.231284\pi$
$464$		0			0
$465$	−1.80121	−	13.4954i	−0.0835293	−	0.625833i
$466$		0			0
$467$	−3.33894	+	3.33894i	−0.154508	+	0.154508i	−0.780128	−	0.625620i	$-0.784846\pi$
$467$	−3.33894	+	3.33894i	−0.154508	+	0.154508i	0.625620	+	0.780128i	$0.284846\pi$
$468$		0			0
$469$	−23.9198	−	16.2249i	−1.10451	−	0.749197i
$470$		0			0
$471$	−8.91698			−0.410873
$472$		0			0
$473$	−0.277592	+	0.277592i	−0.0127637	+	0.0127637i
$474$		0			0
$475$	−0.895963	−	3.29665i	−0.0411096	−	0.151261i
$476$		0			0
$477$	−0.681330	−	0.681330i	−0.0311959	−	0.0311959i
$478$		0			0
$479$	22.0895			1.00930			0.504648	−	0.863325i	$-0.331622\pi$
$479$	22.0895			1.00930			0.504648	+	0.863325i	$0.331622\pi$
$480$		0			0
$481$			19.8582i			0.905457i
$482$		0			0
$483$	20.7619	−	3.97962i	0.944699	−	0.181079i
$484$		0			0
$485$	0.392247	+	2.93886i	0.0178110	+	0.133447i
$486$		0			0
$487$	17.5844	+	17.5844i	0.796826	+	0.796826i	0.982594	−	0.185768i	$-0.0594773\pi$
$487$	17.5844	+	17.5844i	0.796826	+	0.796826i	−0.185768	+	0.982594i	$0.559477\pi$
$488$		0			0
$489$	25.0488			1.13274
$490$		0			0
$491$	11.9520			0.539384			0.269692	−	0.962947i	$-0.413078\pi$
$491$	11.9520			0.539384			0.269692	+	0.962947i	$0.413078\pi$
$492$		0			0
$493$	22.6208	+	22.6208i	1.01879	+	1.01879i
$494$		0			0
$495$	−3.50070	−	2.67627i	−0.157345	−	0.120289i
$496$		0			0
$497$	−36.3039	+	6.95870i	−1.62845	+	0.312140i
$498$		0			0
$499$		−	12.3288i		−	0.551914i	−0.961170	−	0.275957i	$-0.911005\pi$
$499$		−	12.3288i		−	0.551914i	0.961170	−	0.275957i	$-0.0889948\pi$
$500$		0			0
$501$	−5.20794			−0.232674
$502$		0			0
$503$	2.91554	+	2.91554i	0.129997	+	0.129997i	0.769112	−	0.639114i	$-0.220699\pi$
$503$	2.91554	+	2.91554i	0.129997	+	0.129997i	−0.639114	+	0.769112i	$0.720699\pi$
$504$		0			0
$505$	−11.2187	−	8.57661i	−0.499224	−	0.381654i
$506$		0			0
$507$	−20.6719	+	20.6719i	−0.918071	+	0.918071i
$508$		0			0
$509$	17.3375			0.768472			0.384236	−	0.923235i	$-0.374465\pi$
$509$	17.3375			0.768472			0.384236	+	0.923235i	$0.374465\pi$
$510$		0			0
$511$	22.1481	+	15.0232i	0.979775	+	0.664586i
$512$		0			0
$513$	−0.483129	+	0.483129i	−0.0213307	+	0.0213307i
$514$		0			0
$515$	−8.04273	+	1.07346i	−0.354405	+	0.0473021i
$516$		0			0
$517$	3.46775	−	3.46775i	0.152511	−	0.152511i
$518$		0			0
$519$			16.6377i			0.730314i
$520$		0			0
$521$		−	40.4613i		−	1.77264i	−0.463073	−	0.886320i	$-0.653253\pi$
$521$		−	40.4613i		−	1.77264i	0.463073	−	0.886320i	$-0.346747\pi$
$522$		0			0
$523$	−10.9217	−	10.9217i	−0.477574	−	0.477574i	0.426781	−	0.904355i	$-0.359648\pi$
$523$	−10.9217	−	10.9217i	−0.477574	−	0.477574i	−0.904355	+	0.426781i	$0.859648\pi$
$524$		0			0
$525$	4.29477	−	12.5122i	0.187439	−	0.546077i
$526$		0			0
$527$	24.8070	+	24.8070i	1.08061	+	1.08061i
$528$		0			0
$529$		−	40.8419i		−	1.77573i
$530$		0			0
$531$			9.12135i			0.395833i
$532$		0			0
$533$	−42.1083	+	42.1083i	−1.82391	+	1.82391i
$534$		0			0
$535$	−20.4552	+	2.73014i	−0.884357	+	0.118034i
$536$		0			0
$537$	−3.65411	+	3.65411i	−0.157687	+	0.157687i
$538$		0			0
$539$	−12.8168	+	5.10085i	−0.552060	+	0.219709i
$540$		0			0
$541$	38.3587			1.64917			0.824585	−	0.565738i	$-0.191409\pi$
$541$	38.3587			1.64917			0.824585	+	0.565738i	$0.191409\pi$
$542$		0			0
$543$	1.12759	−	1.12759i	0.0483894	−	0.0483894i
$544$		0			0
$545$	21.5045	+	16.4400i	0.921150	+	0.704214i
$546$		0			0
$547$	−32.8559	−	32.8559i	−1.40482	−	1.40482i	−0.783786	−	0.621031i	$-0.786714\pi$
$547$	−32.8559	−	32.8559i	−1.40482	−	1.40482i	−0.621031	−	0.783786i	$-0.713286\pi$
$548$		0			0
$549$	−2.91963			−0.124607
$550$		0			0
$551$		−	3.79356i		−	0.161611i
$552$		0			0
$553$	6.15098	+	32.0899i	0.261566	+	1.36460i
$554$		0			0
$555$	5.42816	+	4.14980i	0.230412	+	0.176149i
$556$		0			0
$557$	4.40050	+	4.40050i	0.186455	+	0.186455i	0.794162	−	0.607706i	$-0.207910\pi$
$557$	4.40050	+	4.40050i	0.186455	+	0.186455i	−0.607706	+	0.794162i	$0.707910\pi$
$558$		0			0
$559$	1.29463			0.0547571
$560$		0			0
$561$	11.3544			0.479383
$562$		0			0
$563$	14.3199	+	14.3199i	0.603512	+	0.603512i	0.941243	−	0.337731i	$-0.109659\pi$
$563$	14.3199	+	14.3199i	0.603512	+	0.603512i	−0.337731	+	0.941243i	$0.609659\pi$
$564$		0			0
$565$	−3.78096	−	28.3284i	−0.159066	−	1.19178i
$566$		0			0
$567$	−2.59845	+	0.498068i	−0.109125	+	0.0209169i
$568$		0			0
$569$			30.2602i			1.26857i	0.773099	+	0.634286i	$0.218706\pi$
$569$			30.2602i			1.26857i	−0.773099	+	0.634286i	$0.781294\pi$
$570$		0			0
$571$	−18.9669			−0.793742			−0.396871	−	0.917874i	$-0.629904\pi$
$571$	−18.9669			−0.793742			−0.396871	+	0.917874i	$0.629904\pi$
$572$		0			0
$573$	6.27926	+	6.27926i	0.262320	+	0.262320i
$574$		0			0
$575$	−34.6693	−	19.8516i	−1.44581	−	0.827870i
$576$		0			0
$577$	−4.89591	+	4.89591i	−0.203820	+	0.203820i	−0.801634	−	0.597815i	$-0.796036\pi$
$577$	−4.89591	+	4.89591i	−0.203820	+	0.203820i	0.597815	+	0.801634i	$0.296036\pi$
$578$		0			0
$579$	−13.7032			−0.569486
$580$		0			0
$581$	−24.1231	−	16.3628i	−1.00079	−	0.678842i
$582$		0			0
$583$	1.34266	−	1.34266i	0.0556074	−	0.0556074i
$584$		0			0
$585$	1.92249	+	14.4040i	0.0794854	+	0.595534i
$586$		0			0
$587$	11.7091	−	11.7091i	0.483285	−	0.483285i	−0.422894	−	0.906179i	$-0.638986\pi$
$587$	11.7091	−	11.7091i	0.483285	−	0.483285i	0.906179	+	0.422894i	$0.138986\pi$
$588$		0			0
$589$		−	4.16018i		−	0.171417i
$590$		0			0
$591$		−	0.294040i		−	0.0120952i
$592$		0			0
$593$	12.5801	+	12.5801i	0.516603	+	0.516603i	0.916542	−	0.399939i	$-0.130969\pi$
$593$	12.5801	+	12.5801i	0.516603	+	0.516603i	−0.399939	+	0.916542i	$0.630969\pi$
$594$		0			0
$595$	10.7895	+	32.3343i	0.442326	+	1.32558i
$596$		0			0
$597$	−8.55957	−	8.55957i	−0.350320	−	0.350320i
$598$		0			0
$599$		−	2.61211i		−	0.106728i	−0.998575	−	0.0533640i	$-0.983006\pi$
$599$		−	2.61211i		−	0.106728i	0.998575	−	0.0533640i	$-0.0169944\pi$
$600$		0			0
$601$			1.90438i			0.0776814i	0.999245	+	0.0388407i	$0.0123665\pi$
$601$			1.90438i			0.0776814i	−0.999245	+	0.0388407i	$0.987634\pi$
$602$		0			0
$603$	7.72475	−	7.72475i	0.314576	−	0.314576i
$604$		0			0
$605$	−9.66471	+	12.6420i	−0.392926	+	0.513969i
$606$		0			0
$607$	27.7279	−	27.7279i	1.12544	−	1.12544i	0.134530	−	0.990909i	$-0.457047\pi$
$607$	27.7279	−	27.7279i	1.12544	−	1.12544i	0.990909	−	0.134530i	$-0.0429526\pi$
$608$		0			0
$609$	8.24616	−	12.1570i	0.334151	−	0.492628i
$610$		0			0
$611$	−16.1729			−0.654284
$612$		0			0
$613$	−9.91105	+	9.91105i	−0.400304	+	0.400304i	−0.878340	−	0.478036i	$-0.841349\pi$
$613$	−9.91105	+	9.91105i	−0.400304	+	0.400304i	0.478036	+	0.878340i	$0.341349\pi$
$614$		0			0
$615$	2.71069	+	20.3095i	0.109306	+	0.818959i
$616$		0			0
$617$	12.8082	+	12.8082i	0.515637	+	0.515637i	0.916248	−	0.400611i	$-0.131202\pi$
$617$	12.8082	+	12.8082i	0.515637	+	0.515637i	−0.400611	+	0.916248i	$0.631202\pi$
$618$		0			0
$619$	−31.8325			−1.27946			−0.639728	−	0.768601i	$-0.720953\pi$
$619$	−31.8325			−1.27946			−0.639728	+	0.768601i	$0.720953\pi$
$620$		0			0
$621$			7.99011i			0.320632i
$622$		0			0
$623$	−25.3143	+	4.85223i	−1.01420	+	0.194401i
$624$		0			0
$625$	−21.5608	+	12.6543i	−0.862433	+	0.506171i
$626$		0			0
$627$	−0.952078	−	0.952078i	−0.0380223	−	0.0380223i
$628$		0			0
$629$	−17.6060			−0.701998
$630$		0			0
$631$	9.75354			0.388282			0.194141	−	0.980974i	$-0.437808\pi$
$631$	9.75354			0.388282			0.194141	+	0.980974i	$0.437808\pi$
$632$		0			0
$633$	−11.7448	−	11.7448i	−0.466815	−	0.466815i
$634$		0			0
$635$	−5.90962	+	0.788751i	−0.234516	+	0.0313006i
$636$		0			0
$637$	41.7821	+	17.9929i	1.65547	+	0.712903i
$638$		0			0
$639$		−	13.9714i		−	0.552699i
$640$		0			0
$641$	31.4887			1.24373			0.621864	−	0.783125i	$-0.286376\pi$
$641$	31.4887			1.24373			0.621864	+	0.783125i	$0.286376\pi$
$642$		0			0
$643$	3.16301	+	3.16301i	0.124737	+	0.124737i	0.766719	−	0.641982i	$-0.221888\pi$
$643$	3.16301	+	3.16301i	0.124737	+	0.124737i	−0.641982	+	0.766719i	$0.721888\pi$
$644$		0			0
$645$	0.270541	−	0.353882i	0.0106525	−	0.0139341i
$646$		0			0
$647$	−12.7949	+	12.7949i	−0.503018	+	0.503018i	−0.912375	−	0.409356i	$-0.865753\pi$
$647$	−12.7949	+	12.7949i	−0.503018	+	0.503018i	0.409356	+	0.912375i	$0.365753\pi$
$648$		0			0
$649$	−17.9750			−0.705580
$650$		0			0
$651$	9.04309	−	13.3319i	0.354426	−	0.522519i
$652$		0			0
$653$	15.0684	−	15.0684i	0.589671	−	0.589671i	−0.347871	−	0.937542i	$-0.613095\pi$
$653$	15.0684	−	15.0684i	0.589671	−	0.589671i	0.937542	+	0.347871i	$0.113095\pi$
$654$		0			0
$655$	12.2908	+	9.39628i	0.480243	+	0.367143i
$656$		0			0
$657$	−7.15260	+	7.15260i	−0.279049	+	0.279049i
$658$		0			0
$659$			1.22588i			0.0477537i	0.999715	+	0.0238768i	$0.00760095\pi$
$659$			1.22588i			0.0477537i	−0.999715	+	0.0238768i	$0.992399\pi$
$660$		0			0
$661$			19.0300i			0.740180i	0.928996	+	0.370090i	$0.120673\pi$
$661$			19.0300i			0.740180i	−0.928996	+	0.370090i	$0.879327\pi$
$662$		0			0
$663$	−26.4773	−	26.4773i	−1.02829	−	1.02829i
$664$		0			0
$665$	1.80656	−	3.61598i	0.0700553	−	0.140222i
$666$		0			0
$667$	−31.3695	−	31.3695i	−1.21463	−	1.21463i
$668$		0			0
$669$		−	23.4273i		−	0.905752i
$670$		0			0
$671$		−	5.75357i		−	0.222114i
$672$		0			0
$673$	33.5536	−	33.5536i	1.29340	−	1.29340i	0.360724	−	0.932673i	$-0.382530\pi$
$673$	33.5536	−	33.5536i	1.29340	−	1.29340i	0.932673	−	0.360724i	$-0.117470\pi$
$674$		0			0
$675$	4.33903	+	2.48452i	0.167009	+	0.0956294i
$676$		0			0
$677$	12.4780	−	12.4780i	0.479569	−	0.479569i	−0.425425	−	0.904994i	$-0.639875\pi$
$677$	12.4780	−	12.4780i	0.479569	−	0.479569i	0.904994	+	0.425425i	$0.139875\pi$
$678$		0			0
$679$	−1.96929	+	2.90326i	−0.0755746	+	0.111417i
$680$		0			0
$681$	−14.5907			−0.559117
$682$		0			0
$683$	−2.96088	+	2.96088i	−0.113295	+	0.113295i	−0.761481	−	0.648187i	$-0.775528\pi$
$683$	−2.96088	+	2.96088i	−0.113295	+	0.113295i	0.648187	+	0.761481i	$0.275528\pi$
$684$		0			0
$685$	−41.7379	+	5.57073i	−1.59472	+	0.212846i
$686$		0			0
$687$	8.65757	+	8.65757i	0.330307	+	0.330307i
$688$		0			0
$689$	−6.26190			−0.238559
$690$		0			0
$691$		−	27.7109i		−	1.05417i	−0.849812	−	0.527085i	$-0.823285\pi$
$691$		−	27.7109i		−	1.05417i	0.849812	−	0.527085i	$-0.176715\pi$
$692$		0			0
$693$	−0.981518	−	5.12063i	−0.0372848	−	0.194517i
$694$		0			0
$695$	6.05237	−	7.91682i	0.229579	−	0.300302i
$696$		0			0
$697$	−37.3326	−	37.3326i	−1.41407	−	1.41407i
$698$		0			0
$699$	−17.7050			−0.669665
$700$		0			0
$701$	28.5208			1.07722			0.538608	−	0.842556i	$-0.318950\pi$
$701$	28.5208			1.07722			0.538608	+	0.842556i	$0.318950\pi$
$702$		0			0
$703$	1.47628	+	1.47628i	0.0556791	+	0.0556791i
$704$		0			0
$705$	−3.37966	+	4.42078i	−0.127285	+	0.166496i
$706$		0			0
$707$	−3.14546	−	16.4100i	−0.118297	−	0.617163i
$708$		0			0
$709$		−	15.9132i		−	0.597633i	−0.954311	−	0.298816i	$-0.903408\pi$
$709$		−	15.9132i		−	0.597633i	0.954311	−	0.298816i	$-0.0965918\pi$
$710$		0			0
$711$	−12.3497			−0.463149
$712$		0			0
$713$	−34.4011	−	34.4011i	−1.28833	−	1.28833i
$714$		0			0
$715$	−28.3853	+	3.78856i	−1.06155	+	0.141684i
$716$		0			0
$717$	−0.542894	+	0.542894i	−0.0202747	+	0.0202747i
$718$		0			0
$719$	4.32645			0.161349			0.0806746	−	0.996740i	$-0.474293\pi$
$719$	4.32645			0.161349			0.0806746	+	0.996740i	$0.474293\pi$
$720$		0			0
$721$	−7.94531	−	5.38934i	−0.295899	−	0.200709i
$722$		0			0
$723$	−14.2540	+	14.2540i	−0.530112	+	0.530112i
$724$		0			0
$725$	−26.7895	+	7.28084i	−0.994937	+	0.270404i
$726$		0			0
$727$	24.9770	−	24.9770i	0.926347	−	0.926347i	−0.0711208	−	0.997468i	$-0.522658\pi$
$727$	24.9770	−	24.9770i	0.926347	−	0.926347i	0.997468	+	0.0711208i	$0.0226576\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$			1.14780i			0.0424530i
$732$		0			0
$733$	−31.3036	−	31.3036i	−1.15623	−	1.15623i	−0.985280	−	0.170946i	$-0.945318\pi$
$733$	−31.3036	−	31.3036i	−1.15623	−	1.15623i	−0.170946	−	0.985280i	$-0.554682\pi$
$734$		0			0
$735$	13.6495	−	7.66097i	0.503470	−	0.282579i
$736$		0			0
$737$	15.2228	+	15.2228i	0.560738	+	0.560738i
$738$		0			0
$739$			48.2374i			1.77444i	0.461345	+	0.887221i	$0.347367\pi$
$739$			48.2374i			1.77444i	−0.461345	+	0.887221i	$0.652633\pi$
$740$		0			0
$741$			4.44029i			0.163118i
$742$		0			0
$743$	−23.2968	+	23.2968i	−0.854678	+	0.854678i	−0.990705	−	0.136027i	$-0.956567\pi$
$743$	−23.2968	+	23.2968i	−0.854678	+	0.854678i	0.136027	+	0.990705i	$0.456567\pi$
$744$		0			0
$745$	−14.2187	−	10.8702i	−0.520934	−	0.398251i
$746$		0			0
$747$	7.79039	−	7.79039i	0.285036	−	0.285036i
$748$		0			0
$749$	−20.2075	−	13.7068i	−0.738365	−	0.500836i
$750$		0			0
$751$	−33.1438			−1.20943			−0.604717	−	0.796440i	$-0.706714\pi$
$751$	−33.1438			−1.20943			−0.604717	+	0.796440i	$0.706714\pi$
$752$		0			0
$753$	4.35063	−	4.35063i	0.158546	−	0.158546i
$754$		0			0
$755$	−14.8027	+	19.3627i	−0.538726	+	0.704682i
$756$		0			0
$757$	30.8579	+	30.8579i	1.12155	+	1.12155i	0.991509	+	0.130040i	$0.0415106\pi$
$757$	30.8579	+	30.8579i	1.12155	+	1.12155i	0.130040	+	0.991509i	$0.458489\pi$
$758$		0			0
$759$	−15.7457			−0.571533
$760$		0			0
$761$			23.1590i			0.839512i	0.907637	+	0.419756i	$0.137884\pi$
$761$			23.1590i			0.839512i	−0.907637	+	0.419756i	$0.862116\pi$
$762$		0			0
$763$	6.02937	+	31.4555i	0.218278	+	1.13877i
$764$		0			0
$765$	−12.7704	+	1.70446i	−0.461716	+	0.0616248i
$766$		0			0
$767$	41.9158	+	41.9158i	1.51349	+	1.51349i
$768$		0			0
$769$	2.05749			0.0741949			0.0370975	−	0.999312i	$-0.488189\pi$
$769$	2.05749			0.0741949			0.0370975	+	0.999312i	$0.488189\pi$
$770$		0			0
$771$	−6.16341			−0.221970
$772$		0			0
$773$	36.8161	+	36.8161i	1.32418	+	1.32418i	0.910356	+	0.413825i	$0.135808\pi$
$773$	36.8161	+	36.8161i	1.32418	+	1.32418i	0.413825	+	0.910356i	$0.364192\pi$
$774$		0			0
$775$	−29.3785	+	7.98447i	−1.05531	+	0.286811i
$776$		0			0
$777$	1.52193	+	7.94001i	0.0545991	+	0.284846i
$778$		0			0
$779$			6.26075i			0.224315i
$780$		0			0
$781$	27.5327			0.985197
$782$		0			0
$783$	3.92604	+	3.92604i	0.140305	+	0.140305i
$784$		0			0
$785$	2.63784	+	19.7637i	0.0941487	+	0.705397i
$786$		0			0
$787$	4.12436	−	4.12436i	0.147018	−	0.147018i	−0.629767	−	0.776784i	$-0.716850\pi$
$787$	4.12436	−	4.12436i	0.147018	−	0.147018i	0.776784	+	0.629767i	$0.216850\pi$
$788$		0			0
$789$	−19.0198			−0.677122
$790$		0			0
$791$	18.9825	−	27.9853i	0.674941	−	0.995041i
$792$		0			0
$793$	−13.4167	+	13.4167i	−0.476442	+	0.476442i
$794$		0			0
$795$	−1.30856	+	1.71166i	−0.0464097	+	0.0607064i
$796$		0			0
$797$	−33.5761	+	33.5761i	−1.18933	+	1.18933i	−0.212073	+	0.977254i	$0.568021\pi$
$797$	−33.5761	+	33.5761i	−1.18933	+	1.18933i	−0.977254	+	0.212073i	$0.931979\pi$
$798$		0			0
$799$		−	14.3386i		−	0.507264i
$800$		0			0
$801$		−	9.74211i		−	0.344220i
$802$		0			0
$803$	−14.0953	−	14.0953i	−0.497411	−	0.497411i
$804$		0			0
$805$	−14.9623	−	44.8397i	−0.527353	−	1.58039i
$806$		0			0
$807$	−3.45123	−	3.45123i	−0.121489	−	0.121489i
$808$		0			0
$809$		−	15.9367i		−	0.560306i	−0.959955	−	0.280153i	$-0.909615\pi$
$809$		−	15.9367i		−	0.560306i	0.959955	−	0.280153i	$-0.0903852\pi$
$810$		0			0
$811$		−	12.0920i		−	0.424608i	−0.977204	−	0.212304i	$-0.931903\pi$
$811$		−	12.0920i		−	0.424608i	0.977204	−	0.212304i	$-0.0680967\pi$
$812$		0			0
$813$	−6.16592	+	6.16592i	−0.216248	+	0.216248i
$814$		0			0
$815$	−7.41000	−	55.5184i	−0.259561	−	1.94473i
$816$		0			0
$817$	0.0962444	−	0.0962444i	0.00336717	−	0.00336717i
$818$		0			0
$819$	−9.65198	+	14.2296i	−0.337267	+	0.497222i
$820$		0			0
$821$	−1.45068			−0.0506291			−0.0253146	−	0.999680i	$-0.508059\pi$
$821$	−1.45068			−0.0506291			−0.0253146	+	0.999680i	$0.508059\pi$
$822$		0			0
$823$	−5.18910	+	5.18910i	−0.180881	+	0.180881i	−0.791740	−	0.610859i	$-0.790824\pi$
$823$	−5.18910	+	5.18910i	−0.180881	+	0.180881i	0.610859	+	0.791740i	$0.290824\pi$
$824$		0			0
$825$	−4.89613	+	8.55070i	−0.170461	+	0.297697i
$826$		0			0
$827$	24.6960	+	24.6960i	0.858763	+	0.858763i	0.991192	−	0.132430i	$-0.0422778\pi$
$827$	24.6960	+	24.6960i	0.858763	+	0.858763i	−0.132430	+	0.991192i	$0.542278\pi$
$828$		0			0
$829$	−12.4758			−0.433303			−0.216652	−	0.976249i	$-0.569514\pi$
$829$	−12.4758			−0.433303			−0.216652	+	0.976249i	$0.569514\pi$
$830$		0			0
$831$		−	32.5565i		−	1.12937i
$832$		0			0
$833$	−15.9522	+	37.0435i	−0.552711	+	1.28348i
$834$		0			0
$835$	1.54063	+	11.5430i	0.0533156	+	0.399460i
$836$		0			0
$837$	4.30545	+	4.30545i	0.148818	+	0.148818i
$838$		0			0
$839$	22.8955			0.790439			0.395219	−	0.918587i	$-0.370669\pi$
$839$	22.8955			0.790439			0.395219	+	0.918587i	$0.370669\pi$
$840$		0			0
$841$	−1.82753			−0.0630182
$842$		0			0
$843$	11.0864	+	11.0864i	0.381836	+	0.381836i
$844$		0			0
$845$	51.9327	+	39.7023i	1.78654	+	1.36580i
$846$		0			0
$847$	−18.4920	+	3.54452i	−0.635391	+	0.121791i
$848$		0			0
$849$			24.1317i			0.828197i
$850$		0			0
$851$	24.4152			0.836942
$852$		0			0
$853$	−15.1444	−	15.1444i	−0.518534	−	0.518534i	0.398594	−	0.917128i	$-0.369498\pi$
$853$	−15.1444	−	15.1444i	−0.518534	−	0.518534i	−0.917128	+	0.398594i	$0.869498\pi$
$854$		0			0
$855$	1.21373	+	0.927893i	0.0415088	+	0.0317333i
$856$		0			0
$857$	11.6937	−	11.6937i	0.399451	−	0.399451i	−0.478588	−	0.878039i	$-0.658851\pi$
$857$	11.6937	−	11.6937i	0.399451	−	0.399451i	0.878039	+	0.478588i	$0.158851\pi$
$858$		0			0
$859$	−3.79617			−0.129524			−0.0647618	−	0.997901i	$-0.520629\pi$
$859$	−3.79617			−0.129524			−0.0647618	+	0.997901i	$0.520629\pi$
$860$		0			0
$861$	−13.6092	+	20.0635i	−0.463799	+	0.683763i
$862$		0			0
$863$	−9.47926	+	9.47926i	−0.322678	+	0.322678i	−0.849793	−	0.527116i	$-0.823273\pi$
$863$	−9.47926	+	9.47926i	−0.322678	+	0.322678i	0.527116	+	0.849793i	$0.323273\pi$
$864$		0			0
$865$	36.8760	−	4.92181i	1.25382	−	0.167347i
$866$		0			0
$867$	11.4536	−	11.4536i	0.388983	−	0.388983i
$868$		0			0
$869$		−	24.3369i		−	0.825572i
$870$		0			0
$871$		−	70.9959i		−	2.40560i
$872$		0			0
$873$	−0.937590	−	0.937590i	−0.0317326	−	0.0317326i
$874$		0			0
$875$	−29.0027	−	5.81760i	−0.980470	−	0.196671i
$876$		0			0
$877$	−14.6600	−	14.6600i	−0.495032	−	0.495032i	0.414855	−	0.909887i	$-0.363832\pi$
$877$	−14.6600	−	14.6600i	−0.495032	−	0.495032i	−0.909887	+	0.414855i	$0.863832\pi$
$878$		0			0
$879$		−	31.2250i		−	1.05319i
$880$		0			0
$881$		−	22.7855i		−	0.767661i	−0.923403	−	0.383831i	$-0.874605\pi$
$881$		−	22.7855i		−	0.767661i	0.923403	−	0.383831i	$-0.125395\pi$
$882$		0			0
$883$	11.6399	−	11.6399i	0.391713	−	0.391713i	−0.483585	−	0.875298i	$-0.660666\pi$
$883$	11.6399	−	11.6399i	0.391713	−	0.391713i	0.875298	+	0.483585i	$0.160666\pi$
$884$		0			0
$885$	20.2167	−	2.69830i	0.679576	−	0.0907024i
$886$		0			0
$887$	−4.73444	+	4.73444i	−0.158967	+	0.158967i	−0.782109	−	0.623142i	$-0.785856\pi$
$887$	−4.73444	+	4.73444i	−0.158967	+	0.158967i	0.623142	+	0.782109i	$0.285856\pi$
$888$		0			0
$889$	−5.83804	−	3.95996i	−0.195801	−	0.132813i
$890$		0			0
$891$	1.97065			0.0660193
$892$		0			0
$893$	−1.20231	+	1.20231i	−0.0402337	+	0.0402337i
$894$		0			0
$895$	9.17999	+	7.01805i	0.306853	+	0.234588i
$896$		0			0
$897$	36.7174	+	36.7174i	1.22596	+	1.22596i
$898$		0			0
$899$	−33.8067			−1.12752
$900$		0			0
$901$		−	5.55171i		−	0.184954i
$902$		0			0
$903$	0.517639	−	0.0992206i	0.0172259	−	0.00330185i
$904$		0			0
$905$	−2.83276	−	2.16563i	−0.0941642	−	0.0719880i
$906$		0			0
$907$	26.6203	+	26.6203i	0.883912	+	0.883912i	0.993930	−	0.110018i	$-0.0350907\pi$
$907$	26.6203	+	26.6203i	0.883912	+	0.883912i	−0.110018	+	0.993930i	$0.535091\pi$
$908$		0			0
$909$	6.31532			0.209466
$910$		0			0
$911$	−28.4116			−0.941318			−0.470659	−	0.882315i	$-0.655984\pi$
$911$	−28.4116			−0.941318			−0.470659	+	0.882315i	$0.655984\pi$
$912$		0			0
$913$	15.3521	+	15.3521i	0.508081	+	0.508081i
$914$		0			0
$915$	0.863693	+	6.47111i	0.0285528	+	0.213928i
$916$		0			0
$917$	3.44608	+	17.9784i	0.113800	+	0.593698i
$918$		0			0
$919$		−	8.04720i		−	0.265453i	−0.991153	−	0.132726i	$-0.957627\pi$
$919$		−	8.04720i		−	0.265453i	0.991153	−	0.132726i	$-0.0423731\pi$
$920$		0			0
$921$	21.8046			0.718485
$922$		0			0
$923$	−64.2033	−	64.2033i	−2.11328	−	2.11328i
$924$		0			0
$925$	7.59189	−	13.2586i	0.249620	−	0.435942i
$926$		0			0
$927$	2.56589	−	2.56589i	0.0842748	−	0.0842748i
$928$		0			0
$929$	−13.0181			−0.427109			−0.213555	−	0.976931i	$-0.568504\pi$
$929$	−13.0181			−0.427109			−0.213555	+	0.976931i	$0.568504\pi$
$930$		0			0
$931$	4.44374	−	1.76852i	0.145638	−	0.0579610i
$932$		0			0
$933$	−14.1620	+	14.1620i	−0.463643	+	0.463643i
$934$		0			0
$935$	−3.35889	−	25.1660i	−0.109847	−	0.823017i
$936$		0			0
$937$	9.43451	−	9.43451i	0.308212	−	0.308212i	−0.536004	−	0.844216i	$-0.680067\pi$
$937$	9.43451	−	9.43451i	0.308212	−	0.308212i	0.844216	+	0.536004i	$0.180067\pi$
$938$		0			0
$939$		−	26.3749i		−	0.860712i
$940$		0			0
$941$		−	11.7663i		−	0.383570i	−0.981437	−	0.191785i	$-0.938572\pi$
$941$		−	11.7663i		−	0.383570i	0.981437	−	0.191785i	$-0.0614277\pi$
$942$		0			0
$943$	51.7710	+	51.7710i	1.68590	+	1.68590i
$944$		0			0
$945$	1.87261	+	5.61189i	0.0609158	+	0.182555i
$946$		0			0
$947$	5.73808	+	5.73808i	0.186462	+	0.186462i	0.794165	−	0.607702i	$-0.207909\pi$
$947$	5.73808	+	5.73808i	0.186462	+	0.186462i	−0.607702	+	0.794165i	$0.707909\pi$
$948$		0			0
$949$			65.7374i			2.13393i
$950$		0			0
$951$			10.0998i			0.327508i
$952$		0			0
$953$	7.48123	−	7.48123i	0.242341	−	0.242341i	−0.575477	−	0.817818i	$-0.695184\pi$
$953$	7.48123	−	7.48123i	0.242341	−	0.242341i	0.817818	+	0.575477i	$0.195184\pi$
$954$		0			0
$955$	12.0599	−	15.7750i	0.390249	−	0.510466i
$956$		0			0
$957$	−7.73684	+	7.73684i	−0.250097	+	0.250097i
$958$		0			0
$959$	−41.2324	−	27.9681i	−1.33146	−	0.903137i
$960$		0			0
$961$	−6.07387			−0.195931
$962$		0			0
$963$	6.52588	−	6.52588i	0.210293	−	0.210293i
$964$		0			0
$965$	4.05372	+	30.3720i	0.130494	+	0.977708i
$966$		0			0
$967$	−9.63598	−	9.63598i	−0.309872	−	0.309872i	0.534988	−	0.844860i	$-0.320316\pi$
$967$	−9.63598	−	9.63598i	−0.309872	−	0.309872i	−0.844860	+	0.534988i	$0.820316\pi$
$968$		0			0
$969$	−3.93670			−0.126465
$970$		0			0
$971$			6.59374i			0.211603i	0.994387	+	0.105802i	$0.0337409\pi$
$971$			6.59374i			0.211603i	−0.994387	+	0.105802i	$0.966259\pi$
$972$		0			0
$973$	11.5803	−	2.21970i	0.371247	−	0.0711603i
$974$		0			0
$975$	31.3566	−	8.52208i	1.00421	−	0.272925i
$976$		0			0
$977$	−9.55056	−	9.55056i	−0.305550	−	0.305550i	0.537631	−	0.843180i	$-0.319319\pi$
$977$	−9.55056	−	9.55056i	−0.305550	−	0.305550i	−0.843180	+	0.537631i	$0.819319\pi$
$978$		0			0
$979$	19.1983			0.613580
$980$		0			0
$981$	−12.1055			−0.386499
$982$		0			0
$983$	18.8461	+	18.8461i	0.601098	+	0.601098i	0.940604	−	0.339506i	$-0.110260\pi$
$983$	18.8461	+	18.8461i	0.601098	+	0.601098i	−0.339506	+	0.940604i	$0.610260\pi$
$984$		0			0
$985$	−0.651714	+	0.0869836i	−0.0207653	+	0.00277153i
$986$		0			0
$987$	−6.46647	+	1.23949i	−0.205830	+	0.0394533i
$988$		0			0
$989$		−	1.59172i		−	0.0506136i
$990$		0			0
$991$	−0.336364			−0.0106850			−0.00534248	−	0.999986i	$-0.501701\pi$
$991$	−0.336364			−0.0106850			−0.00534248	+	0.999986i	$0.501701\pi$
$992$		0			0
$993$	13.4110	+	13.4110i	0.425585	+	0.425585i
$994$		0			0
$995$	−16.4394	+	21.5037i	−0.521165	+	0.681712i
$996$		0			0
$997$	1.35096	−	1.35096i	0.0427854	−	0.0427854i	−0.685390	−	0.728176i	$-0.740368\pi$
$997$	1.35096	−	1.35096i	0.0427854	−	0.0427854i	0.728176	+	0.685390i	$0.240368\pi$
$998$		0			0
$999$	−3.05567			−0.0966772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.bt.b.97.11	yes	24
4.3	odd	2		1680.2.cz.e.97.1		24
5.3	odd	4		840.2.bt.a.433.2	yes	24
7.6	odd	2		840.2.bt.a.97.2	✓	24
20.3	even	4		1680.2.cz.f.433.12		24
28.27	even	2		1680.2.cz.f.97.12		24
35.13	even	4	inner	840.2.bt.b.433.11	yes	24
140.83	odd	4		1680.2.cz.e.433.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bt.a.97.2	✓	24	7.6	odd	2
840.2.bt.a.433.2	yes	24	5.3	odd	4
840.2.bt.b.97.11	yes	24	1.1	even	1	trivial
840.2.bt.b.433.11	yes	24	35.13	even	4	inner
1680.2.cz.e.97.1		24	4.3	odd	2
1680.2.cz.e.433.1		24	140.83	odd	4
1680.2.cz.f.97.12		24	28.27	even	2
1680.2.cz.f.433.12		24	20.3	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.bt (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(1.35806 - 1.77642i) q^{5} +(2.59845 - 0.498068i) q^{7} +1.00000i q^{9} -1.97065 q^{11} +(4.59535 + 4.59535i) q^{13} +(2.21641 - 0.295823i) q^{15} +(-4.07417 + 4.07417i) q^{17} +0.683247 q^{19} +(2.18957 + 1.48519i) q^{21} +(5.64986 - 5.64986i) q^{23} +(-1.31133 - 4.82498i) q^{25} +(-0.707107 + 0.707107i) q^{27} -5.55225i q^{29} -6.08883i q^{31} +(-1.39346 - 1.39346i) q^{33} +(2.64408 - 5.29234i) q^{35} +(2.16069 + 2.16069i) q^{37} +6.49881i q^{39} +9.16323i q^{41} +(0.140863 - 0.140863i) q^{43} +(1.77642 + 1.35806i) q^{45} +(-1.75970 + 1.75970i) q^{47} +(6.50386 - 2.58841i) q^{49} -5.76175 q^{51} +(-0.681330 + 0.681330i) q^{53} +(-2.67627 + 3.50070i) q^{55} +(0.483129 + 0.483129i) q^{57} +9.12135 q^{59} +2.91963i q^{61} +(0.498068 + 2.59845i) q^{63} +(14.4040 - 1.92249i) q^{65} +(-7.72475 - 7.72475i) q^{67} +7.99011 q^{69} -13.9714 q^{71} +(7.15260 + 7.15260i) q^{73} +(2.48452 - 4.33903i) q^{75} +(-5.12063 + 0.981518i) q^{77} +12.3497i q^{79} -1.00000 q^{81} +(-7.79039 - 7.79039i) q^{83} +(1.70446 + 12.7704i) q^{85} +(3.92604 - 3.92604i) q^{87} -9.74211 q^{89} +(14.2296 + 9.65198i) q^{91} +(4.30545 - 4.30545i) q^{93} +(0.927893 - 1.21373i) q^{95} +(-0.937590 + 0.937590i) q^{97} -1.97065i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{11} - 16 q^{13} + 4 q^{15} - 20 q^{17} - 8 q^{19} + 24 q^{23} - 4 q^{25} + 4 q^{37} - 16 q^{43} + 4 q^{45} + 24 q^{47} - 36 q^{49} + 16 q^{53} - 28 q^{55} + 4 q^{57} - 8 q^{59} + 4 q^{63} + 24 q^{65}+ \cdots + 28 q^{97}+O(q^{100}) \) 24 * q - 8 * q^11 - 16 * q^13 + 4 * q^15 - 20 * q^17 - 8 * q^19 + 24 * q^23 - 4 * q^25 + 4 * q^37 - 16 * q^43 + 4 * q^45 + 24 * q^47 - 36 * q^49 + 16 * q^53 - 28 * q^55 + 4 * q^57 - 8 * q^59 + 4 * q^63 + 24 * q^65 + 16 * q^67 + 8 * q^69 + 8 * q^71 + 28 * q^73 + 28 * q^77 - 24 * q^81 - 64 * q^83 - 20 * q^85 - 20 * q^87 - 16 * q^89 + 24 * q^91 - 12 * q^93 + 24 * q^95 + 28 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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