LMFDB - Embedded newform 756.2.ck.a.5.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(5,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5, 15]))

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

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

chi := DirichletCharacter("756.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ck (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.11
Character	$\chi$	$=$	756.5
Dual form			756.2.ck.a.605.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.230632 - 1.71663i) q^{3} +(0.315692 - 1.79038i) q^{5} +(0.645961 + 2.56568i) q^{7} +(-2.89362 + 0.791819i) q^{9} +O(q^{10})$	\(q+(-0.230632 - 1.71663i) q^{3} +(0.315692 - 1.79038i) q^{5} +(0.645961 + 2.56568i) q^{7} +(-2.89362 + 0.791819i) q^{9} +(-5.18280 + 0.913868i) q^{11} +(-4.33786 + 5.16966i) q^{13} +(-3.14622 - 0.129007i) q^{15} -5.78942 q^{17} +1.82961i q^{19} +(4.25534 - 1.70060i) q^{21} +(3.09892 - 3.69315i) q^{23} +(1.59267 + 0.579685i) q^{25} +(2.02662 + 4.78464i) q^{27} +(0.0973787 + 0.116051i) q^{29} +(-2.86208 - 7.86351i) q^{31} +(2.76409 + 8.68617i) q^{33} +(4.79747 - 0.346549i) q^{35} +(-2.28287 - 3.95404i) q^{37} +(9.87483 + 6.25420i) q^{39} +(4.02366 + 3.37625i) q^{41} +(-0.904658 - 0.329269i) q^{43} +(0.504163 + 5.43064i) q^{45} +(-10.7114 - 3.89862i) q^{47} +(-6.16547 + 3.31466i) q^{49} +(1.33523 + 9.93828i) q^{51} +(1.23298 - 0.711859i) q^{53} +9.56767i q^{55} +(3.14076 - 0.421968i) q^{57} +(-5.70576 - 4.78770i) q^{59} +(-5.09450 + 13.9970i) q^{61} +(-3.90072 - 6.91262i) q^{63} +(7.88622 + 9.39843i) q^{65} +(1.25272 - 7.10453i) q^{67} +(-7.05447 - 4.46793i) q^{69} +(5.35129 + 3.08957i) q^{71} +(6.14864 + 3.54992i) q^{73} +(0.627782 - 2.86772i) q^{75} +(-5.69258 - 12.7071i) q^{77} +(-0.525918 - 2.98263i) q^{79} +(7.74605 - 4.58244i) q^{81} +(3.88765 - 3.26213i) q^{83} +(-1.82767 + 10.3652i) q^{85} +(0.176758 - 0.193928i) q^{87} +8.80084 q^{89} +(-16.0658 - 7.79018i) q^{91} +(-12.8386 + 6.72671i) q^{93} +(3.27570 + 0.577594i) q^{95} +(-0.860050 + 2.36297i) q^{97} +(14.2734 - 6.74822i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−0.230632	−	1.71663i	−0.133156	−	0.991095i
$3$	−0.230632	−	1.71663i	−0.133156	−	0.991095i
$4$		0			0
$5$	0.315692	−	1.79038i	0.141182	−	0.800681i	−0.829172	−	0.558993i	$-0.811188\pi$
$5$	0.315692	−	1.79038i	0.141182	−	0.800681i	0.970354	−	0.241688i	$-0.0777011\pi$
$6$		0			0
$7$	0.645961	+	2.56568i	0.244150	+	0.969737i
$7$	0.645961	+	2.56568i	0.244150	+	0.969737i
$8$		0			0
$9$	−2.89362	+	0.791819i	−0.964539	+	0.263940i
$10$		0			0
$11$	−5.18280	+	0.913868i	−1.56267	+	0.275541i	−0.887039	−	0.461695i	$-0.847241\pi$
$11$	−5.18280	+	0.913868i	−1.56267	+	0.275541i	−0.675635	+	0.737237i	$0.736130\pi$
$12$		0			0
$13$	−4.33786	+	5.16966i	−1.20311	+	1.43381i	−0.331601	+	0.943420i	$0.607589\pi$
$13$	−4.33786	+	5.16966i	−1.20311	+	1.43381i	−0.871505	+	0.490387i	$0.836856\pi$
$14$		0			0
$15$	−3.14622	−	0.129007i	−0.812350	−	0.0333094i
$16$		0			0
$17$	−5.78942			−1.40414			−0.702070	−	0.712108i	$-0.747741\pi$
$17$	−5.78942			−1.40414			−0.702070	+	0.712108i	$0.747741\pi$
$18$		0			0
$19$			1.82961i			0.419742i	0.977729	+	0.209871i	$0.0673044\pi$
$19$			1.82961i			0.419742i	−0.977729	+	0.209871i	$0.932696\pi$
$20$		0			0
$21$	4.25534	−	1.70060i	0.928592	−	0.371102i
$22$		0			0
$23$	3.09892	−	3.69315i	0.646170	−	0.770075i	−0.339161	−	0.940728i	$-0.610143\pi$
$23$	3.09892	−	3.69315i	0.646170	−	0.770075i	0.985331	+	0.170653i	$0.0545878\pi$
$24$		0			0
$25$	1.59267	+	0.579685i	0.318534	+	0.115937i
$26$		0			0
$27$	2.02662	+	4.78464i	0.390023	+	0.920805i
$28$		0			0
$29$	0.0973787	+	0.116051i	0.0180828	+	0.0215502i	0.775010	−	0.631949i	$-0.217745\pi$
$29$	0.0973787	+	0.116051i	0.0180828	+	0.0215502i	−0.756927	+	0.653499i	$0.773300\pi$
$30$		0			0
$31$	−2.86208	−	7.86351i	−0.514045	−	1.41233i	−0.876986	−	0.480515i	$-0.840450\pi$
$31$	−2.86208	−	7.86351i	−0.514045	−	1.41233i	0.362941	−	0.931812i	$-0.381773\pi$
$32$		0			0
$33$	2.76409	+	8.68617i	0.481166	+	1.51207i
$34$		0			0
$35$	4.79747	−	0.346549i	0.810920	−	0.0585774i
$36$		0			0
$37$	−2.28287	−	3.95404i	−0.375301	−	0.650041i	0.615071	−	0.788472i	$-0.289127\pi$
$37$	−2.28287	−	3.95404i	−0.375301	−	0.650041i	−0.990372	+	0.138431i	$0.955794\pi$
$38$		0			0
$39$	9.87483	+	6.25420i	1.58124	+	1.00147i
$40$		0			0
$41$	4.02366	+	3.37625i	0.628390	+	0.527282i	0.900428	−	0.435005i	$-0.143253\pi$
$41$	4.02366	+	3.37625i	0.628390	+	0.527282i	−0.272038	+	0.962286i	$0.587698\pi$
$42$		0			0
$43$	−0.904658	−	0.329269i	−0.137959	−	0.0502130i	0.272118	−	0.962264i	$-0.412276\pi$
$43$	−0.904658	−	0.329269i	−0.137959	−	0.0502130i	−0.410077	+	0.912051i	$0.634498\pi$
$44$		0			0
$45$	0.504163	+	5.43064i	0.0751562	+	0.809552i
$46$		0			0
$47$	−10.7114	−	3.89862i	−1.56242	−	0.568673i	−0.591127	−	0.806578i	$-0.701317\pi$
$47$	−10.7114	−	3.89862i	−1.56242	−	0.568673i	−0.971288	+	0.237906i	$0.923539\pi$
$48$		0			0
$49$	−6.16547	+	3.31466i	−0.880781	+	0.473523i
$50$		0			0
$51$	1.33523	+	9.93828i	0.186969	+	1.39164i
$52$		0			0
$53$	1.23298	−	0.711859i	0.169362	−	0.0977814i	−0.412923	−	0.910766i	$-0.635492\pi$
$53$	1.23298	−	0.711859i	0.169362	−	0.0977814i	0.582285	+	0.812985i	$0.302159\pi$
$54$		0			0
$55$			9.56767i			1.29010i
$56$		0			0
$57$	3.14076	−	0.421968i	0.416004	−	0.0558910i
$58$		0			0
$59$	−5.70576	−	4.78770i	−0.742826	−	0.623305i	0.190769	−	0.981635i	$-0.438902\pi$
$59$	−5.70576	−	4.78770i	−0.742826	−	0.623305i	−0.933595	+	0.358330i	$0.883346\pi$
$60$		0			0
$61$	−5.09450	+	13.9970i	−0.652284	+	1.79214i	−0.0431508	+	0.999069i	$0.513740\pi$
$61$	−5.09450	+	13.9970i	−0.652284	+	1.79214i	−0.609133	+	0.793068i	$0.708483\pi$
$62$		0			0
$63$	−3.90072	−	6.91262i	−0.491445	−	0.870909i
$64$		0			0
$65$	7.88622	+	9.39843i	0.978165	+	1.16573i
$66$		0			0
$67$	1.25272	−	7.10453i	0.153044	−	0.867957i	−0.807508	−	0.589857i	$-0.799184\pi$
$67$	1.25272	−	7.10453i	0.153044	−	0.867957i	0.960552	−	0.278100i	$-0.0897047\pi$
$68$		0			0
$69$	−7.05447	−	4.46793i	−0.849259	−	0.537876i
$70$		0			0
$71$	5.35129	+	3.08957i	0.635082	+	0.366665i	0.782717	−	0.622377i	$-0.213833\pi$
$71$	5.35129	+	3.08957i	0.635082	+	0.366665i	−0.147636	+	0.989042i	$0.547166\pi$
$72$		0			0
$73$	6.14864	+	3.54992i	0.719643	+	0.415486i	0.814621	−	0.579993i	$-0.196945\pi$
$73$	6.14864	+	3.54992i	0.719643	+	0.415486i	−0.0949780	+	0.995479i	$0.530278\pi$
$74$		0			0
$75$	0.627782	−	2.86772i	0.0724900	−	0.331136i
$76$		0			0
$77$	−5.69258	−	12.7071i	−0.648730	−	1.44811i
$78$		0			0
$79$	−0.525918	−	2.98263i	−0.0591704	−	0.335572i	0.940824	−	0.338895i	$-0.110053\pi$
$79$	−0.525918	−	2.98263i	−0.0591704	−	0.335572i	−0.999994	+	0.00332345i	$0.998942\pi$
$80$		0			0
$81$	7.74605	−	4.58244i	0.860672	−	0.509160i
$82$		0			0
$83$	3.88765	−	3.26213i	0.426725	−	0.358065i	−0.403989	−	0.914764i	$-0.632377\pi$
$83$	3.88765	−	3.26213i	0.426725	−	0.358065i	0.830714	+	0.556699i	$0.187932\pi$
$84$		0			0
$85$	−1.82767	+	10.3652i	−0.198239	+	1.12427i
$86$		0			0
$87$	0.176758	−	0.193928i	0.0189505	−	0.0207913i
$88$		0			0
$89$	8.80084			0.932887			0.466443	−	0.884551i	$-0.345535\pi$
$89$	8.80084			0.932887			0.466443	+	0.884551i	$0.345535\pi$
$90$		0			0
$91$	−16.0658	−	7.79018i	−1.68415	−	0.816633i
$92$		0			0
$93$	−12.8386	+	6.72671i	−1.33130	+	0.697527i
$94$		0			0
$95$	3.27570	+	0.577594i	0.336080	+	0.0592599i
$96$		0			0
$97$	−0.860050	+	2.36297i	−0.0873249	+	0.239923i	−0.975666	−	0.219260i	$-0.929636\pi$
$97$	−0.860050	+	2.36297i	−0.0873249	+	0.239923i	0.888342	+	0.459183i	$0.151858\pi$
$98$		0			0
$99$	14.2734	−	6.74822i	1.43453	−	0.678222i
$100$		0			0
$101$	−1.40806	+	1.18150i	−0.140107	+	0.117564i	−0.710148	−	0.704053i	$-0.751372\pi$
$101$	−1.40806	+	1.18150i	−0.140107	+	0.117564i	0.570041	+	0.821617i	$0.306927\pi$
$102$		0			0
$103$	−11.5504	−	2.03665i	−1.13809	−	0.200677i	−0.427322	−	0.904100i	$-0.640543\pi$
$103$	−11.5504	−	2.03665i	−1.13809	−	0.200677i	−0.710772	+	0.703423i	$0.751654\pi$
$104$		0			0
$105$	−1.70135	−	8.15554i	−0.166034	−	0.795899i
$106$		0			0
$107$	−0.729358	−	0.421095i	−0.0705097	−	0.0407088i	0.464331	−	0.885662i	$-0.346295\pi$
$107$	−0.729358	−	0.421095i	−0.0705097	−	0.0407088i	−0.534840	+	0.844953i	$0.679628\pi$
$108$		0			0
$109$	−1.56999	−	2.71930i	−0.150378	−	0.260462i	0.780989	−	0.624545i	$-0.214716\pi$
$109$	−1.56999	−	2.71930i	−0.150378	−	0.260462i	−0.931366	+	0.364084i	$0.881382\pi$
$110$		0			0
$111$	−6.26111	+	4.83076i	−0.594279	+	0.458516i
$112$		0			0
$113$	1.91026	+	5.24839i	0.179702	+	0.493727i	0.996538	−	0.0831437i	$-0.0264960\pi$
$113$	1.91026	+	5.24839i	0.179702	+	0.493727i	−0.816836	+	0.576870i	$0.804274\pi$
$114$		0			0
$115$	−5.63383	−	6.71414i	−0.525357	−	0.626096i
$116$		0			0
$117$	8.45868	−	18.3938i	0.782005	−	1.70051i
$118$		0			0
$119$	−3.73974	−	14.8538i	−0.342821	−	1.36165i
$120$		0			0
$121$	15.6897	−	5.71057i	1.42633	−	0.519142i
$122$		0			0
$123$	4.86778	−	7.68580i	0.438913	−	0.693005i
$124$		0			0
$125$	6.08564	−	10.5406i	0.544316	−	0.942784i
$126$		0			0
$127$	7.84663	+	13.5908i	0.696276	+	1.20598i	0.969749	+	0.244105i	$0.0784943\pi$
$127$	7.84663	+	13.5908i	0.696276	+	1.20598i	−0.273473	+	0.961880i	$0.588172\pi$
$128$		0			0
$129$	−0.356588	+	1.62890i	−0.0313958	+	0.143417i
$130$		0			0
$131$	−13.7132	−	11.5067i	−1.19813	−	1.00535i	−0.999682	−	0.0252344i	$-0.991967\pi$
$131$	−13.7132	−	11.5067i	−1.19813	−	1.00535i	−0.198444	−	0.980112i	$-0.563589\pi$
$132$		0			0
$133$	−4.69421	+	1.18186i	−0.407040	+	0.102480i
$134$		0			0
$135$	9.20611	−	2.11794i	0.792335	−	0.182283i
$136$		0			0
$137$	−4.00541	+	11.0048i	−0.342205	+	0.940202i	0.642548	+	0.766245i	$0.277877\pi$
$137$	−4.00541	+	11.0048i	−0.342205	+	0.940202i	−0.984753	+	0.173956i	$0.944345\pi$
$138$		0			0
$139$	−8.72732	−	1.53886i	−0.740241	−	0.130525i	−0.209203	−	0.977872i	$-0.567087\pi$
$139$	−8.72732	−	1.53886i	−0.740241	−	0.130525i	−0.531038	+	0.847348i	$0.678198\pi$
$140$		0			0
$141$	−4.22209	+	19.2866i	−0.355565	+	1.62422i
$142$		0			0
$143$	17.7579	−	30.7576i	1.48499	−	2.57208i
$144$		0			0
$145$	0.238517	−	0.137708i	0.0198078	−	0.0114360i
$146$		0			0
$147$	7.11200	+	9.81934i	0.586588	+	0.809886i
$148$		0			0
$149$	0.302146	+	0.830140i	0.0247528	+	0.0680077i	0.951454	−	0.307792i	$-0.0995902\pi$
$149$	0.302146	+	0.830140i	0.0247528	+	0.0680077i	−0.926701	+	0.375800i	$0.877368\pi$
$150$		0			0
$151$	1.39213	+	7.89518i	0.113290	+	0.642501i	0.987583	+	0.157101i	$0.0502148\pi$
$151$	1.39213	+	7.89518i	0.113290	+	0.642501i	−0.874292	+	0.485400i	$0.838674\pi$
$152$		0			0
$153$	16.7524	−	4.58417i	1.35435	−	0.370608i
$154$		0			0
$155$	−14.9822	+	2.64176i	−1.20340	+	0.212192i
$156$		0			0
$157$	−1.89950	+	2.26374i	−0.151597	+	0.180666i	−0.836498	−	0.547970i	$-0.815401\pi$
$157$	−1.89950	+	2.26374i	−0.151597	+	0.180666i	0.684901	+	0.728636i	$0.259845\pi$
$158$		0			0
$159$	−1.50636	−	1.95238i	−0.119462	−	0.154834i
$160$		0			0
$161$	11.4772	+	5.56522i	0.904533	+	0.438601i
$162$		0			0
$163$	−4.81113	+	8.33312i	−0.376837	+	0.652700i	−0.990600	−	0.136790i	$-0.956321\pi$
$163$	−4.81113	+	8.33312i	−0.376837	+	0.652700i	0.613764	+	0.789490i	$0.289655\pi$
$164$		0			0
$165$	16.4241	−	2.20661i	1.27862	−	0.171785i
$166$		0			0
$167$	−1.38609	+	0.504495i	−0.107259	+	0.0390390i	−0.395092	−	0.918642i	$-0.629287\pi$
$167$	−1.38609	+	0.504495i	−0.107259	+	0.0390390i	0.287833	+	0.957681i	$0.407065\pi$
$168$		0			0
$169$	−5.65094	−	32.0480i	−0.434687	−	2.46523i
$170$		0			0
$171$	−1.44872	−	5.29420i	−0.110787	−	0.404858i
$172$		0			0
$173$	−9.17580	+	7.69941i	−0.697623	+	0.585375i	−0.921096	−	0.389335i	$-0.872705\pi$
$173$	−9.17580	+	7.69941i	−0.697623	+	0.585375i	0.223473	+	0.974710i	$0.428260\pi$
$174$		0			0
$175$	−0.458485	+	4.46075i	−0.0346582	+	0.337201i
$176$		0			0
$177$	−6.90276	+	10.8989i	−0.518844	+	0.819208i
$178$		0			0
$179$		−	19.8615i		−	1.48452i	−0.670115	−	0.742258i	$-0.733755\pi$
$179$		−	19.8615i		−	1.48452i	0.670115	−	0.742258i	$-0.266245\pi$
$180$		0			0
$181$	−10.5009	+	6.06267i	−0.780523	+	0.450635i	−0.836616	−	0.547791i	$-0.815469\pi$
$181$	−10.5009	+	6.06267i	−0.780523	+	0.450635i	0.0560928	+	0.998426i	$0.482136\pi$
$182$		0			0
$183$	25.2026	+	5.51720i	1.86303	+	0.407843i
$184$		0			0
$185$	−7.79991	+	2.83894i	−0.573461	+	0.208723i
$186$		0			0
$187$	30.0054	−	5.29076i	2.19421	−	0.386899i
$188$		0			0
$189$	−10.9668	+	8.29036i	−0.797715	+	0.603035i
$190$		0			0
$191$	21.1412	−	3.72777i	1.52972	−	0.269732i	0.655478	−	0.755214i	$-0.272467\pi$
$191$	21.1412	−	3.72777i	1.52972	−	0.269732i	0.874246	+	0.485483i	$0.161356\pi$
$192$		0			0
$193$	−1.19954	+	0.436597i	−0.0863449	+	0.0314270i	−0.384831	−	0.922987i	$-0.625740\pi$
$193$	−1.19954	+	0.436597i	−0.0863449	+	0.0314270i	0.298487	+	0.954414i	$0.403518\pi$
$194$		0			0
$195$	14.3148	−	15.7053i	1.02510	−	1.12468i
$196$		0			0
$197$	−21.5364	+	12.4340i	−1.53440	+	0.885889i	−0.535253	+	0.844692i	$0.679784\pi$
$197$	−21.5364	+	12.4340i	−1.53440	+	0.885889i	−0.999151	+	0.0411970i	$0.986883\pi$
$198$		0			0
$199$			12.5210i			0.887593i	0.896127	+	0.443797i	$0.146369\pi$
$199$			12.5210i			0.887593i	−0.896127	+	0.443797i	$0.853631\pi$
$200$		0			0
$201$	−12.4847	−	0.511921i	−0.880606	−	0.0361081i
$202$		0			0
$203$	−0.234848	+	0.324808i	−0.0164831	+	0.0227970i
$204$		0			0
$205$	7.31500	−	6.13802i	0.510902	−	0.428698i
$206$		0			0
$207$	−6.04279	+	13.1403i	−0.420003	+	0.913317i
$208$		0			0
$209$	−1.67202	−	9.48252i	−0.115656	−	0.655920i
$210$		0			0
$211$	−17.7817	+	6.47201i	−1.22414	+	0.445552i	−0.871588	−	0.490239i	$-0.836909\pi$
$211$	−17.7817	+	6.47201i	−1.22414	+	0.445552i	−0.352555	+	0.935791i	$0.614687\pi$
$212$		0			0
$213$	4.06946	−	9.89873i	0.278835	−	0.678250i
$214$		0			0
$215$	−0.875108	+	1.51573i	−0.0596819	+	0.103372i
$216$		0			0
$217$	18.3265	−	12.4227i	1.24408	−	0.843309i
$218$		0			0
$219$	4.67581	−	11.3736i	0.315962	−	0.768559i
$220$		0			0
$221$	25.1137	−	29.9293i	1.68933	−	2.01327i
$222$		0			0
$223$	27.2213	−	4.79986i	1.82288	−	0.321422i	0.845669	−	0.533708i	$-0.179202\pi$
$223$	27.2213	−	4.79986i	1.82288	−	0.321422i	0.977208	+	0.212286i	$0.0680909\pi$
$224$		0			0
$225$	−5.06759	−	0.416280i	−0.337839	−	0.0277520i
$226$		0			0
$227$	−1.81605	−	10.2993i	−0.120535	−	0.683590i	−0.983860	−	0.178941i	$-0.942733\pi$
$227$	−1.81605	−	10.2993i	−0.120535	−	0.683590i	0.863325	−	0.504649i	$-0.168378\pi$
$228$		0			0
$229$	−6.09555	−	16.7474i	−0.402805	−	1.10670i	−0.960894	−	0.276917i	$-0.910687\pi$
$229$	−6.09555	−	16.7474i	−0.402805	−	1.10670i	0.558089	−	0.829781i	$-0.311535\pi$
$230$		0			0
$231$	−20.5005	+	12.7027i	−1.34883	+	0.835777i
$232$		0			0
$233$	−17.9372	+	10.3560i	−1.17510	+	0.678446i	−0.954877	−	0.297002i	$-0.904013\pi$
$233$	−17.9372	+	10.3560i	−1.17510	+	0.678446i	−0.220227	+	0.975449i	$0.570680\pi$
$234$		0			0
$235$	−10.3615	+	17.9467i	−0.675910	+	1.17071i
$236$		0			0
$237$	−4.99877	+	1.59069i	−0.324705	+	0.103327i
$238$		0			0
$239$	4.70161	+	0.829021i	0.304122	+	0.0536249i	0.323627	−	0.946185i	$-0.395098\pi$
$239$	4.70161	+	0.829021i	0.304122	+	0.0536249i	−0.0195046	+	0.999810i	$0.506209\pi$
$240$		0			0
$241$	2.94531	−	8.09217i	0.189724	−	0.521263i	−0.807963	−	0.589233i	$-0.799430\pi$
$241$	2.94531	−	8.09217i	0.189724	−	0.521263i	0.997687	+	0.0679702i	$0.0216523\pi$
$242$		0			0
$243$	−9.65283	−	12.2402i	−0.619229	−	0.785210i
$244$		0			0
$245$	3.98811	+	12.0849i	0.254791	+	0.772078i
$246$		0			0
$247$	−9.45849	−	7.93661i	−0.601829	−	0.504994i
$248$		0			0
$249$	−6.49647	−	5.92129i	−0.411697	−	0.375247i
$250$		0			0
$251$	10.1667	+	17.6092i	0.641715	+	1.11148i	0.985050	+	0.172270i	$0.0551101\pi$
$251$	10.1667	+	17.6092i	0.641715	+	1.11148i	−0.343335	+	0.939213i	$0.611557\pi$
$252$		0			0
$253$	−12.6860	+	21.9729i	−0.797564	+	1.38142i
$254$		0			0
$255$	18.2148	+	0.746874i	1.14065	+	0.0467710i
$256$		0			0
$257$	−24.5648	+	8.94086i	−1.53231	+	0.557715i	−0.964186	−	0.265227i	$-0.914553\pi$
$257$	−24.5648	+	8.94086i	−1.53231	+	0.557715i	−0.568124	+	0.822943i	$0.692331\pi$
$258$		0			0
$259$	8.67018	−	8.41127i	0.538739	−	0.522651i
$260$		0			0
$261$	−0.373668	−	0.258702i	−0.0231295	−	0.0160133i
$262$		0			0
$263$	1.08151	+	1.28890i	0.0666890	+	0.0794768i	0.798358	−	0.602184i	$-0.205703\pi$
$263$	1.08151	+	1.28890i	0.0666890	+	0.0794768i	−0.731669	+	0.681661i	$0.761258\pi$
$264$		0			0
$265$	−0.885256	−	2.43222i	−0.0543809	−	0.149410i
$266$		0			0
$267$	−2.02976	−	15.1078i	−0.124219	−	0.924580i
$268$		0			0
$269$	−0.872457	−	1.51114i	−0.0531946	−	0.0921358i	0.838202	−	0.545360i	$-0.183607\pi$
$269$	−0.872457	−	1.51114i	−0.0531946	−	0.0921358i	−0.891397	+	0.453224i	$0.850274\pi$
$270$		0			0
$271$	12.3127	+	7.10874i	0.747943	+	0.431825i	0.824950	−	0.565206i	$-0.191203\pi$
$271$	12.3127	+	7.10874i	0.747943	+	0.431825i	−0.0770073	+	0.997031i	$0.524536\pi$
$272$		0			0
$273$	−9.66754	+	29.3757i	−0.585106	+	1.77790i
$274$		0			0
$275$	−8.78426	−	1.54890i	−0.529711	−	0.0934023i
$276$		0			0
$277$	13.1335	−	11.0203i	0.789114	−	0.662145i	−0.156412	−	0.987692i	$-0.549993\pi$
$277$	13.1335	−	11.0203i	0.789114	−	0.662145i	0.945526	+	0.325547i	$0.105548\pi$
$278$		0			0
$279$	14.5082	+	20.4877i	0.868586	+	1.22657i
$280$		0			0
$281$	2.63156	−	7.23016i	0.156986	−	0.431315i	−0.836118	−	0.548549i	$-0.815180\pi$
$281$	2.63156	−	7.23016i	0.156986	−	0.431315i	0.993104	+	0.117234i	$0.0374027\pi$
$282$		0			0
$283$	10.3777	+	1.82987i	0.616890	+	0.108774i	0.473356	−	0.880871i	$-0.343042\pi$
$283$	10.3777	+	1.82987i	0.616890	+	0.108774i	0.143533	+	0.989645i	$0.454154\pi$
$284$		0			0
$285$	0.236032	−	5.75637i	0.0139813	−	0.340978i
$286$		0			0
$287$	−6.06327	+	12.5044i	−0.357903	+	0.738109i
$288$		0			0
$289$	16.5174			0.971611
$290$		0			0
$291$	4.25469	+	0.931409i	0.249414	+	0.0546002i
$292$		0			0
$293$	−1.28836	+	7.30665i	−0.0752668	+	0.426859i	0.923769	+	0.382951i	$0.125092\pi$
$293$	−1.28836	+	7.30665i	−0.0752668	+	0.426859i	−0.999036	+	0.0439083i	$0.986019\pi$
$294$		0			0
$295$	−10.3731	+	8.70402i	−0.603942	+	0.506768i
$296$		0			0
$297$	−14.8761	−	22.9458i	−0.863198	−	1.33145i
$298$		0			0
$299$	5.64965	+	32.0407i	0.326728	+	1.85296i
$300$		0			0
$301$	0.260425	−	2.53376i	0.0150107	−	0.146044i
$302$		0			0
$303$	2.35295	+	2.14462i	0.135173	+	0.123205i
$304$		0			0
$305$	23.4517	+	13.5398i	1.34284	+	0.775289i
$306$		0			0
$307$	9.63531	+	5.56295i	0.549916	+	0.317494i	0.749088	−	0.662470i	$-0.230492\pi$
$307$	9.63531	+	5.56295i	0.549916	+	0.317494i	−0.199172	+	0.979965i	$0.563825\pi$
$308$		0			0
$309$	−0.832269	+	20.2974i	−0.0473462	+	1.15468i
$310$		0			0
$311$	4.05426	−	22.9929i	0.229896	−	1.30381i	−0.623205	−	0.782059i	$-0.714170\pi$
$311$	4.05426	−	22.9929i	0.229896	−	1.30381i	0.853101	−	0.521746i	$-0.174719\pi$
$312$		0			0
$313$	10.7008	+	12.7528i	0.604847	+	0.720828i	0.978386	−	0.206786i	$-0.0663003\pi$
$313$	10.7008	+	12.7528i	0.604847	+	0.720828i	−0.373539	+	0.927614i	$0.621856\pi$
$314$		0			0
$315$	−13.6076	+	4.80151i	−0.766703	+	0.270534i
$316$		0			0
$317$	−4.90817	+	13.4851i	−0.275670	+	0.757398i	0.722170	+	0.691715i	$0.243145\pi$
$317$	−4.90817	+	13.4851i	−0.275670	+	0.757398i	−0.997841	+	0.0656825i	$0.979078\pi$
$318$		0			0
$319$	−0.610750	−	0.512480i	−0.0341954	−	0.0286934i
$320$		0			0
$321$	−0.554650	+	1.34915i	−0.0309576	+	0.0753025i
$322$		0			0
$323$		−	10.5924i		−	0.589377i
$324$		0			0
$325$	−9.90557	+	5.71898i	−0.549462	+	0.317232i
$326$		0			0
$327$	−4.30593	+	3.32224i	−0.238119	+	0.183720i
$328$		0			0
$329$	3.08350	−	30.0004i	0.169999	−	1.65397i
$330$		0			0
$331$	1.26284	+	0.459636i	0.0694120	+	0.0252639i	0.376493	−	0.926420i	$-0.377130\pi$
$331$	1.26284	+	0.459636i	0.0694120	+	0.0252639i	−0.307081	+	0.951683i	$0.599352\pi$
$332$		0			0
$333$	9.73663	+	9.63387i	0.533564	+	0.527933i
$334$		0			0
$335$	−12.3243	−	4.48569i	−0.673350	−	0.245079i
$336$		0			0
$337$	−18.4097	−	15.4476i	−1.00284	−	0.841483i	−0.0154653	−	0.999880i	$-0.504923\pi$
$337$	−18.4097	−	15.4476i	−1.00284	−	0.841483i	−0.987375	+	0.158397i	$0.949367\pi$
$338$		0			0
$339$	8.56895	−	4.48964i	0.465402	−	0.243844i
$340$		0			0
$341$	22.0198	+	38.1394i	1.19244	+	2.06537i
$342$		0			0
$343$	−12.4870	−	13.6775i	−0.674236	−	0.738516i
$344$		0			0
$345$	−10.2263	+	11.2197i	−0.550567	+	0.604047i
$346$		0			0
$347$	2.11988	+	5.82432i	0.113801	+	0.312666i	0.983498	−	0.180921i	$-0.0579078\pi$
$347$	2.11988	+	5.82432i	0.113801	+	0.312666i	−0.869697	+	0.493587i	$0.835686\pi$
$348$		0			0
$349$	−14.8710	−	17.7226i	−0.796028	−	0.948669i	0.203510	−	0.979073i	$-0.434765\pi$
$349$	−14.8710	−	17.7226i	−0.796028	−	0.948669i	−0.999538	+	0.0304036i	$0.990321\pi$
$350$		0			0
$351$	−33.5262	−	10.2782i	−1.78950	−	0.548609i
$352$		0			0
$353$	12.0988	+	4.40361i	0.643955	+	0.234380i	0.643294	−	0.765619i	$-0.277567\pi$
$353$	12.0988	+	4.40361i	0.643955	+	0.234380i	0.000661077		1.00000i	$0.499790\pi$
$354$		0			0
$355$	7.22086	−	8.60548i	0.383243	−	0.456732i
$356$		0			0
$357$	−24.6360	+	9.84551i	−1.30387	+	0.521080i
$358$		0			0
$359$			10.8382i			0.572021i	0.958227	+	0.286010i	$0.0923292\pi$
$359$			10.8382i			0.572021i	−0.958227	+	0.286010i	$0.907671\pi$
$360$		0			0
$361$	15.6525			0.823816
$362$		0			0
$363$	−13.4215	−	25.6162i	−0.704444	−	1.34450i
$364$		0			0
$365$	8.29677	−	9.88770i	0.434273	−	0.517546i
$366$		0			0
$367$	−36.3151	+	6.40333i	−1.89563	+	0.334251i	−0.994962	−	0.100253i	$-0.968035\pi$
$367$	−36.3151	+	6.40333i	−1.89563	+	0.334251i	−0.900670	+	0.434504i	$0.856924\pi$
$368$		0			0
$369$	−14.3163	−	6.58357i	−0.745277	−	0.342727i
$370$		0			0
$371$	2.62286	+	2.70359i	0.136172	+	0.140364i
$372$		0			0
$373$	0.0371083	−	0.210452i	0.00192140	−	0.0108968i	−0.983832	−	0.179094i	$-0.942683\pi$
$373$	0.0371083	−	0.210452i	0.00192140	−	0.0108968i	0.985753	+	0.168197i	$0.0537945\pi$
$374$		0			0
$375$	−19.4979	−	8.01577i	−1.00687	−	0.413932i
$376$		0			0
$377$	−1.02236			−0.0526543
$378$		0			0
$379$	5.01195			0.257447			0.128723	−	0.991681i	$-0.458912\pi$
$379$	5.01195			0.257447			0.128723	+	0.991681i	$0.458912\pi$
$380$		0			0
$381$	21.5206	−	16.6042i	1.10253	−	0.850659i
$382$		0			0
$383$	−2.18975	+	12.4187i	−0.111891	+	0.634564i	0.876352	+	0.481671i	$0.159970\pi$
$383$	−2.18975	+	12.4187i	−0.111891	+	0.634564i	−0.988243	+	0.152893i	$0.951141\pi$
$384$		0			0
$385$	−24.5476	+	6.18034i	−1.25106	+	0.314980i
$386$		0			0
$387$	2.87846	+	0.236452i	0.146320	+	0.0120195i
$388$		0			0
$389$	3.73108	−	0.657890i	0.189173	−	0.0333564i	−0.0782587	−	0.996933i	$-0.524936\pi$
$389$	3.73108	−	0.657890i	0.189173	−	0.0333564i	0.267432	+	0.963577i	$0.413825\pi$
$390$		0			0
$391$	−17.9410	+	21.3812i	−0.907313	+	1.08129i
$392$		0			0
$393$	−16.5900	+	26.1942i	−0.836857	+	1.32132i
$394$		0			0
$395$	−5.50606			−0.277040
$396$		0			0
$397$			27.7630i			1.39338i	0.717370	+	0.696692i	$0.245346\pi$
$397$			27.7630i			1.39338i	−0.717370	+	0.696692i	$0.754654\pi$
$398$		0			0
$399$	3.11145	+	7.78564i	0.155767	+	0.389769i
$400$		0			0
$401$	−9.88822	+	11.7843i	−0.493794	+	0.588481i	−0.954178	−	0.299239i	$-0.903267\pi$
$401$	−9.88822	+	11.7843i	−0.493794	+	0.588481i	0.460384	+	0.887720i	$0.347712\pi$
$402$		0			0
$403$	53.0670	+	19.3148i	2.64345	+	0.962139i
$404$		0			0
$405$	−5.75894	−	15.3150i	−0.286164	−	0.761008i
$406$		0			0
$407$	15.4451	+	18.4068i	0.765586	+	0.912390i
$408$		0			0
$409$	−1.53558	−	4.21896i	−0.0759293	−	0.208614i	0.895921	−	0.444214i	$-0.146517\pi$
$409$	−1.53558	−	4.21896i	−0.0759293	−	0.208614i	−0.971850	+	0.235600i	$0.924295\pi$
$410$		0			0
$411$	19.8149	+	4.33774i	0.977396	+	0.213965i
$412$		0			0
$413$	8.59803	−	17.7318i	0.423081	−	0.872527i
$414$		0			0
$415$	−4.61314	−	7.99019i	−0.226450	−	0.392223i
$416$		0			0
$417$	−0.628851	+	15.3365i	−0.0307950	+	0.751030i
$418$		0			0
$419$	−27.2205	−	22.8408i	−1.32981	−	1.11584i	−0.984122	−	0.177495i	$-0.943201\pi$
$419$	−27.2205	−	22.8408i	−1.32981	−	1.11584i	−0.345689	−	0.938349i	$-0.612355\pi$
$420$		0			0
$421$	13.9948	+	5.09367i	0.682063	+	0.248250i	0.659733	−	0.751500i	$-0.270669\pi$
$421$	13.9948	+	5.09367i	0.682063	+	0.248250i	0.0223297	+	0.999751i	$0.492892\pi$
$422$		0			0
$423$	34.0816	+	2.79965i	1.65711	+	0.136124i
$424$		0			0
$425$	−9.22065	−	3.35604i	−0.447267	−	0.162792i
$426$		0			0
$427$	−39.2028	−	4.02935i	−1.89716	−	0.194994i
$428$		0			0
$429$	−56.8948	−	23.3900i	−2.74691	−	1.12928i
$430$		0			0
$431$	−30.2447	+	17.4618i	−1.45684	+	0.841105i	−0.998854	−	0.0478566i	$-0.984761\pi$
$431$	−30.2447	+	17.4618i	−1.45684	+	0.841105i	−0.457982	+	0.888961i	$0.651428\pi$
$432$		0			0
$433$		−	31.8455i		−	1.53040i	−0.643795	−	0.765198i	$-0.722641\pi$
$433$		−	31.8455i		−	1.53040i	0.643795	−	0.765198i	$-0.277359\pi$
$434$		0			0
$435$	−0.291403	−	0.377686i	−0.0139717	−	0.0181086i
$436$		0			0
$437$	6.75704	+	5.66983i	0.323233	+	0.271225i
$438$		0			0
$439$	8.72292	−	23.9660i	0.416322	−	1.14384i	−0.537448	−	0.843297i	$-0.680611\pi$
$439$	8.72292	−	23.9660i	0.416322	−	1.14384i	0.953770	−	0.300538i	$-0.0971664\pi$
$440$		0			0
$441$	15.2159	−	14.4733i	0.724566	−	0.689205i
$442$		0			0
$443$	1.72020	+	2.05006i	0.0817294	+	0.0974013i	0.805360	−	0.592787i	$-0.201972\pi$
$443$	1.72020	+	2.05006i	0.0817294	+	0.0974013i	−0.723630	+	0.690188i	$0.757528\pi$
$444$		0			0
$445$	2.77835	−	15.7568i	0.131707	−	0.746945i
$446$		0			0
$447$	1.35536	−	0.710129i	0.0641062	−	0.0335880i
$448$		0			0
$449$	26.1501	+	15.0977i	1.23410	+	0.712507i	0.967882	−	0.251407i	$-0.0808932\pi$
$449$	26.1501	+	15.0977i	1.23410	+	0.712507i	0.266216	+	0.963913i	$0.414226\pi$
$450$		0			0
$451$	−23.9393	−	13.8213i	−1.12726	−	0.650822i
$452$		0			0
$453$	13.2320	−	4.21066i	0.621694	−	0.197834i
$454$		0			0
$455$	−19.0192	+	26.3046i	−0.891634	+	1.23318i
$456$		0			0
$457$	−0.604538	−	3.42851i	−0.0282791	−	0.160379i	0.967398	−	0.253261i	$-0.0815031\pi$
$457$	−0.604538	−	3.42851i	−0.0282791	−	0.160379i	−0.995677	+	0.0928822i	$0.970392\pi$
$458$		0			0
$459$	−11.7329	−	27.7003i	−0.547647	−	1.29294i
$460$		0			0
$461$	−30.1613	+	25.3083i	−1.40475	+	1.17873i	−0.445807	+	0.895129i	$0.647083\pi$
$461$	−30.1613	+	25.3083i	−1.40475	+	1.17873i	−0.958944	+	0.283596i	$0.908472\pi$
$462$		0			0
$463$	−2.07957	+	11.7939i	−0.0966460	+	0.548107i	0.897585	+	0.440842i	$0.145320\pi$
$463$	−2.07957	+	11.7939i	−0.0966460	+	0.548107i	−0.994231	+	0.107264i	$0.965791\pi$
$464$		0			0
$465$	7.99029	+	25.1095i	0.370541	+	1.16443i
$466$		0			0
$467$	−10.4635			−0.484192			−0.242096	−	0.970252i	$-0.577835\pi$
$467$	−10.4635			−0.484192			−0.242096	+	0.970252i	$0.577835\pi$
$468$		0			0
$469$	19.0372	−	1.37517i	0.879056	−	0.0634993i
$470$		0			0
$471$	4.32408	+	2.73865i	0.199243	+	0.126190i
$472$		0			0
$473$	4.98957	+	0.879796i	0.229421	+	0.0404531i
$474$		0			0
$475$	−1.06060	+	2.91398i	−0.0486637	+	0.133702i
$476$		0			0
$477$	−3.00410	+	3.03614i	−0.137548	+	0.139015i
$478$		0			0
$479$	−22.7994	+	19.1310i	−1.04173	+	0.874117i	−0.992200	−	0.124656i	$-0.960217\pi$
$479$	−22.7994	+	19.1310i	−1.04173	+	0.874117i	−0.0495316	+	0.998773i	$0.515773\pi$
$480$		0			0
$481$	30.3438	+	5.35044i	1.38356	+	0.243959i
$482$		0			0
$483$	6.90639	−	20.9857i	0.314252	−	0.954881i
$484$		0			0
$485$	3.95910	+	2.28579i	0.179773	+	0.103792i
$486$		0			0
$487$	2.80442	+	4.85739i	0.127080	+	0.220109i	0.922544	−	0.385892i	$-0.126106\pi$
$487$	2.80442	+	4.85739i	0.127080	+	0.220109i	−0.795464	+	0.606001i	$0.792773\pi$
$488$		0			0
$489$	15.4145	+	6.33703i	0.697066	+	0.286570i
$490$		0			0
$491$	−7.88767	−	21.6712i	−0.355965	−	0.978007i	−0.980415	−	0.196942i	$-0.936899\pi$
$491$	−7.88767	−	21.6712i	−0.355965	−	0.978007i	0.624450	−	0.781065i	$-0.285323\pi$
$492$		0			0
$493$	−0.563766	−	0.671870i	−0.0253907	−	0.0302595i
$494$		0			0
$495$	−7.57586	−	27.6852i	−0.340510	−	1.24436i
$496$		0			0
$497$	−4.47013	+	15.7255i	−0.200513	+	0.705384i
$498$		0			0
$499$	34.5616	−	12.5794i	1.54719	−	0.563132i	0.579435	−	0.815018i	$-0.303273\pi$
$499$	34.5616	−	12.5794i	1.54719	−	0.563132i	0.967757	+	0.251887i	$0.0810510\pi$
$500$		0			0
$501$	1.18571	+	2.26304i	0.0529735	+	0.101105i
$502$		0			0
$503$	−8.09397	+	14.0192i	−0.360892	+	0.625083i	−0.988108	−	0.153762i	$-0.950861\pi$
$503$	−8.09397	+	14.0192i	−0.360892	+	0.625083i	0.627216	+	0.778846i	$0.284194\pi$
$504$		0			0
$505$	1.67082	+	2.89395i	0.0743507	+	0.128779i
$506$		0			0
$507$	−53.7113	+	17.0919i	−2.38540	+	0.759076i
$508$		0			0
$509$	2.79910	+	2.34872i	0.124068	+	0.104105i	0.702710	−	0.711476i	$-0.251973\pi$
$509$	2.79910	+	2.34872i	0.124068	+	0.104105i	−0.578643	+	0.815581i	$0.696417\pi$
$510$		0			0
$511$	−5.13618	+	18.0686i	−0.227211	+	0.799306i
$512$		0			0
$513$	−8.75405	+	3.70793i	−0.386501	+	0.163709i
$514$		0			0
$515$	−7.29273	+	20.0366i	−0.321356	+	0.882918i
$516$		0			0
$517$	59.0778	+	10.4170i	2.59824	+	0.458139i
$518$		0			0
$519$	15.3332	+	13.9757i	0.673055	+	0.613465i
$520$		0			0
$521$	15.6036	−	27.0262i	0.683605	−	1.18404i	−0.290268	−	0.956945i	$-0.593744\pi$
$521$	15.6036	−	27.0262i	0.683605	−	1.18404i	0.973873	−	0.227093i	$-0.0729222\pi$
$522$		0			0
$523$	−10.0499	+	5.80229i	−0.439450	+	0.253717i	−0.703364	−	0.710830i	$-0.748320\pi$
$523$	−10.0499	+	5.80229i	−0.439450	+	0.253717i	0.263914	+	0.964546i	$0.414986\pi$
$524$		0			0
$525$	7.76318	−	0.241744i	0.338813	−	0.0105506i
$526$		0			0
$527$	16.5698	+	45.5251i	0.721792	+	1.98311i
$528$		0			0
$529$	−0.0421389	−	0.238982i	−0.00183213	−	0.0103905i
$530$		0			0
$531$	20.3013	+	9.33585i	0.881000	+	0.405141i
$532$		0			0
$533$	−34.9082	+	6.15525i	−1.51204	+	0.266613i
$534$		0			0
$535$	−0.984172	+	1.17289i	−0.0425495	+	0.0507085i
$536$		0			0
$537$	−34.0947	+	4.58069i	−1.47130	+	0.197671i
$538$		0			0
$539$	28.9252	−	22.8137i	1.24590	−	0.982654i
$540$		0			0
$541$	8.29085	−	14.3602i	0.356451	−	0.617392i	−0.630914	−	0.775853i	$-0.717320\pi$
$541$	8.29085	−	14.3602i	0.356451	−	0.617392i	0.987365	+	0.158461i	$0.0506532\pi$
$542$		0			0
$543$	12.8292	+	16.6278i	0.550553	+	0.713568i
$544$		0			0
$545$	−5.36420	+	1.95241i	−0.229777	+	0.0836321i
$546$		0			0
$547$	0.477153	+	2.70607i	0.0204016	+	0.115703i	0.993308	−	0.115497i	$-0.0368460\pi$
$547$	0.477153	+	2.70607i	0.0204016	+	0.115703i	−0.972906	+	0.231200i	$0.925735\pi$
$548$		0			0
$549$	3.65843	−	44.5360i	0.156138	−	1.90075i
$550$		0			0
$551$	−0.212329	+	0.178165i	−0.00904553	+	0.00759010i
$552$		0			0
$553$	7.31276	−	3.27600i	0.310970	−	0.139310i
$554$		0			0
$555$	6.67231	+	12.7348i	0.283224	+	0.540562i
$556$		0			0
$557$			31.1083i			1.31810i	0.752098	+	0.659051i	$0.229042\pi$
$557$			31.1083i			1.31810i	−0.752098	+	0.659051i	$0.770958\pi$
$558$		0			0
$559$	5.62649	−	3.24845i	0.237975	−	0.137395i
$560$		0			0
$561$	−16.0025	−	50.2879i	−0.675625	−	2.12316i
$562$		0			0
$563$	−3.26144	+	1.18707i	−0.137453	+	0.0500289i	−0.409831	−	0.912162i	$-0.634412\pi$
$563$	−3.26144	+	1.18707i	−0.137453	+	0.0500289i	0.272378	+	0.962190i	$0.412190\pi$
$564$		0			0
$565$	9.99964	−	1.76321i	0.420688	−	0.0741787i
$566$		0			0
$567$	16.7607	+	16.9138i	0.703885	+	0.710314i
$568$		0			0
$569$	36.9880	−	6.52198i	1.55062	−	0.273416i	0.668236	−	0.743949i	$-0.267050\pi$
$569$	36.9880	−	6.52198i	1.55062	−	0.273416i	0.882382	+	0.470534i	$0.155939\pi$
$570$		0			0
$571$	8.86644	−	3.22712i	0.371049	−	0.135051i	−0.149764	−	0.988722i	$-0.547851\pi$
$571$	8.86644	−	3.22712i	0.371049	−	0.135051i	0.520813	+	0.853671i	$0.325629\pi$
$572$		0			0
$573$	−11.2750	−	35.4318i	−0.471021	−	1.48019i
$574$		0			0
$575$	7.07643	−	4.08558i	0.295108	−	0.170380i
$576$		0			0
$577$			16.6185i			0.691838i	0.938264	+	0.345919i	$0.112433\pi$
$577$			16.6185i			0.691838i	−0.938264	+	0.345919i	$0.887567\pi$
$578$		0			0
$579$	1.02613	+	1.95847i	0.0426444	+	0.0813913i
$580$		0			0
$581$	10.8809	+	7.86727i	0.451414	+	0.326390i
$582$		0			0
$583$	−5.73973	+	4.81620i	−0.237715	+	0.199467i
$584$		0			0
$585$	−30.2616	−	20.9510i	−1.25116	−	0.866218i
$586$		0			0
$587$	1.04950	+	5.95201i	0.0433175	+	0.245666i	0.998776	−	0.0494593i	$-0.0157498\pi$
$587$	1.04950	+	5.95201i	0.0433175	+	0.245666i	−0.955459	+	0.295125i	$0.904639\pi$
$588$		0			0
$589$	14.3872	−	5.23651i	0.592813	−	0.215766i
$590$		0			0
$591$	26.3116	+	34.1023i	1.08231	+	1.40278i
$592$		0			0
$593$	2.00470	−	3.47223i	0.0823230	−	0.142588i	−0.821924	−	0.569597i	$-0.807099\pi$
$593$	2.00470	−	3.47223i	0.0823230	−	0.142588i	0.904247	+	0.427009i	$0.140433\pi$
$594$		0			0
$595$	−27.7746	+	2.00632i	−1.13865	+	0.0822510i
$596$		0			0
$597$	21.4940	−	2.88776i	0.879690	−	0.118188i
$598$		0			0
$599$	−23.8029	+	28.3671i	−0.972559	+	1.15905i	0.0146946	+	0.999892i	$0.495322\pi$
$599$	−23.8029	+	28.3671i	−0.972559	+	1.15905i	−0.987253	+	0.159158i	$0.949122\pi$
$600$		0			0
$601$	12.1383	−	2.14031i	0.495132	−	0.0873050i	0.0794939	−	0.996835i	$-0.474670\pi$
$601$	12.1383	−	2.14031i	0.495132	−	0.0873050i	0.415638	+	0.909530i	$0.363558\pi$
$602$		0			0
$603$	2.00061	+	21.5497i	0.0814710	+	0.877573i
$604$		0			0
$605$	−5.27097	−	29.8932i	−0.214296	−	1.21533i
$606$		0			0
$607$	7.20692	+	19.8008i	0.292520	+	0.803691i	0.995696	+	0.0926761i	$0.0295421\pi$
$607$	7.20692	+	19.8008i	0.292520	+	0.803691i	−0.703177	+	0.711015i	$0.748236\pi$
$608$		0			0
$609$	0.611737	+	0.328236i	0.0247888	+	0.0133008i
$610$		0			0
$611$	66.6190	−	38.4625i	2.69512	−	1.55603i
$612$		0			0
$613$	8.07169	−	13.9806i	0.326012	−	0.564670i	−0.655704	−	0.755018i	$-0.727628\pi$
$613$	8.07169	−	13.9806i	0.326012	−	0.564670i	0.981717	+	0.190348i	$0.0609615\pi$
$614$		0			0
$615$	−12.2238	−	11.1415i	−0.492910	−	0.449269i
$616$		0			0
$617$	5.70078	+	1.00520i	0.229505	+	0.0404679i	0.287218	−	0.957865i	$-0.407270\pi$
$617$	5.70078	+	1.00520i	0.229505	+	0.0404679i	−0.0577128	+	0.998333i	$0.518381\pi$
$618$		0			0
$619$	3.07725	−	8.45468i	0.123685	−	0.339822i	−0.862361	−	0.506294i	$-0.831015\pi$
$619$	3.07725	−	8.45468i	0.123685	−	0.339822i	0.986046	+	0.166472i	$0.0532374\pi$
$620$		0			0
$621$	23.9507	+	7.34262i	0.961110	+	0.294649i
$622$		0			0
$623$	5.68500	+	22.5802i	0.227765	+	0.904655i
$624$		0			0
$625$	−10.4587	−	8.77593i	−0.418350	−	0.351037i
$626$		0			0
$627$	−15.8923	+	5.05722i	−0.634679	+	0.201966i
$628$		0			0
$629$	13.2165	+	22.8916i	0.526976	+	0.912748i
$630$		0			0
$631$	−0.233768	+	0.404898i	−0.00930616	+	0.0161187i	−0.870641	−	0.491919i	$-0.836296\pi$
$631$	−0.233768	+	0.404898i	−0.00930616	+	0.0161187i	0.861335	+	0.508038i	$0.169629\pi$
$632$		0			0
$633$	15.2111	+	29.0319i	0.604586	+	1.15391i
$634$		0			0
$635$	26.8097	−	9.75794i	1.06391	−	0.387232i
$636$		0			0
$637$	9.60925	−	46.2519i	0.380732	−	1.83257i
$638$		0			0
$639$	−17.9310	−	4.70278i	−0.709338	−	0.186039i
$640$		0			0
$641$	−16.9589	−	20.2108i	−0.669835	−	0.798279i	0.318926	−	0.947780i	$-0.396678\pi$
$641$	−16.9589	−	20.2108i	−0.669835	−	0.798279i	−0.988762	+	0.149501i	$0.952233\pi$
$642$		0			0
$643$	10.7678	+	29.5842i	0.424639	+	1.16669i	0.949024	+	0.315205i	$0.102073\pi$
$643$	10.7678	+	29.5842i	0.424639	+	1.16669i	−0.524385	+	0.851481i	$0.675705\pi$
$644$		0			0
$645$	2.80377	+	1.15266i	0.110399	+	0.0453859i
$646$		0			0
$647$	−12.0438	−	20.8605i	−0.473491	−	0.820110i	0.526049	−	0.850455i	$-0.323673\pi$
$647$	−12.0438	−	20.8605i	−0.473491	−	0.820110i	−0.999540	+	0.0303442i	$0.990340\pi$
$648$		0			0
$649$	33.9471	+	19.5994i	1.33254	+	0.769343i
$650$		0			0
$651$	−25.5518	−	28.5947i	−1.00146	−	1.12071i
$652$		0			0
$653$	22.7631	+	4.01375i	0.890790	+	0.157070i	0.600269	−	0.799798i	$-0.295060\pi$
$653$	22.7631	+	4.01375i	0.890790	+	0.157070i	0.290521	+	0.956869i	$0.406171\pi$
$654$		0			0
$655$	−24.9305	+	20.9192i	−0.974116	+	0.817380i
$656$		0			0
$657$	−20.6027	−	5.40350i	−0.803788	−	0.210810i
$658$		0			0
$659$	10.3121	−	28.3323i	0.401703	−	1.10367i	−0.559740	−	0.828668i	$-0.689099\pi$
$659$	10.3121	−	28.3323i	0.401703	−	1.10367i	0.961443	−	0.275003i	$-0.0886788\pi$
$660$		0			0
$661$	−21.6681	−	3.82067i	−0.842792	−	0.148607i	−0.264448	−	0.964400i	$-0.585190\pi$
$661$	−21.6681	−	3.82067i	−0.842792	−	0.148607i	−0.578344	+	0.815793i	$0.696301\pi$
$662$		0			0
$663$	−57.1696	−	36.2082i	−2.22028	−	1.40621i
$664$		0			0
$665$	0.634051	+	8.77751i	0.0245874	+	0.340377i
$666$		0			0
$667$	0.730364			0.0282798
$668$		0			0
$669$	−14.5177	−	45.6219i	−0.561286	−	1.76384i
$670$		0			0
$671$	13.6124	−	77.1995i	0.525499	−	2.98025i
$672$		0			0
$673$	27.5418	−	23.1103i	1.06166	−	0.890836i	0.0673860	−	0.997727i	$-0.478534\pi$
$673$	27.5418	−	23.1103i	1.06166	−	0.890836i	0.994271	+	0.106891i	$0.0340896\pi$
$674$		0			0
$675$	0.454152	+	8.79517i	0.0174803	+	0.338526i
$676$		0			0
$677$	−3.13527	−	17.7810i	−0.120498	−	0.683379i	−0.983880	−	0.178828i	$-0.942769\pi$
$677$	−3.13527	−	17.7810i	−0.120498	−	0.683379i	0.863382	−	0.504550i	$-0.168342\pi$
$678$		0			0
$679$	−6.61819	−	0.680231i	−0.253983	−	0.0261049i
$680$		0			0
$681$	−17.2612	+	5.49283i	−0.661452	+	0.210486i
$682$		0			0
$683$	−15.3970	−	8.88943i	−0.589148	−	0.340145i	0.175613	−	0.984459i	$-0.443809\pi$
$683$	−15.3970	−	8.88943i	−0.589148	−	0.340145i	−0.764761	+	0.644315i	$0.777143\pi$
$684$		0			0
$685$	18.4382	+	10.6453i	0.704489	+	0.406737i
$686$		0			0
$687$	−27.3432	+	14.3263i	−1.04321	+	0.546581i
$688$		0			0
$689$	−1.66841	+	9.46202i	−0.0635613	+	0.360474i
$690$		0			0
$691$	−31.7257	−	37.8092i	−1.20690	−	1.43833i	−0.867320	−	0.497752i	$-0.834159\pi$
$691$	−31.7257	−	37.8092i	−1.20690	−	1.43833i	−0.339581	−	0.940577i	$-0.610285\pi$
$692$		0			0
$693$	26.5339	+	32.2620i	1.00794	+	1.22553i
$694$		0			0
$695$	−5.51029	+	15.1394i	−0.209017	+	0.574270i
$696$		0			0
$697$	−23.2947	−	19.5465i	−0.882348	−	0.740378i
$698$		0			0
$699$	21.9143	+	28.4030i	0.828877	+	1.07430i
$700$		0			0
$701$		−	33.0791i		−	1.24938i	−0.780873	−	0.624690i	$-0.785226\pi$
$701$		−	33.0791i		−	1.24938i	0.780873	−	0.624690i	$-0.214774\pi$
$702$		0			0
$703$	7.23437	−	4.17677i	0.272849	−	0.157530i
$704$		0			0
$705$	33.1974	+	13.6478i	1.25029	+	0.514005i
$706$		0			0
$707$	−3.94092	−	2.84943i	−0.148213	−	0.107164i
$708$		0			0
$709$	28.2248	+	10.2730i	1.06000	+	0.385810i	0.812430	−	0.583059i	$-0.198144\pi$
$709$	28.2248	+	10.2730i	1.06000	+	0.385810i	0.247575	+	0.968869i	$0.420366\pi$
$710$		0			0
$711$	3.88350	+	8.21415i	0.145643	+	0.308055i
$712$		0			0
$713$	−37.9105	−	13.7983i	−1.41976	−	0.516750i
$714$		0			0
$715$	−49.4616	−	41.5032i	−1.84976	−	1.55213i
$716$		0			0
$717$	0.338777	−	8.26212i	0.0126519	−	0.308554i
$718$		0			0
$719$	−9.32614	−	16.1534i	−0.347806	−	0.602418i	0.638053	−	0.769992i	$-0.279740\pi$
$719$	−9.32614	−	16.1534i	−0.347806	−	0.602418i	−0.985860	+	0.167574i	$0.946407\pi$
$720$		0			0
$721$	−2.23571	−	30.9502i	−0.0832624	−	1.15265i
$722$		0			0
$723$	−14.5705	−	3.18968i	−0.541884	−	0.118626i
$724$		0			0
$725$	0.0878190	+	0.241281i	0.00326152	+	0.00896094i
$726$		0			0
$727$	−1.99281	−	2.37494i	−0.0739093	−	0.0880817i	0.727823	−	0.685765i	$-0.240532\pi$
$727$	−1.99281	−	2.37494i	−0.0739093	−	0.0880817i	−0.801732	+	0.597684i	$0.796088\pi$
$728$		0			0
$729$	−18.7856	+	19.3933i	−0.695764	+	0.718270i
$730$		0			0
$731$	5.23744	+	1.90627i	0.193714	+	0.0705061i
$732$		0			0
$733$	−10.8974	+	12.9870i	−0.402503	+	0.479685i	−0.928782	−	0.370628i	$-0.879143\pi$
$733$	−10.8974	+	12.9870i	−0.402503	+	0.479685i	0.526278	+	0.850312i	$0.323587\pi$
$734$		0			0
$735$	19.8255	−	9.63328i	0.731276	−	0.355329i
$736$		0			0
$737$			37.9662i			1.39850i
$738$		0			0
$739$	18.2858			0.672654			0.336327	−	0.941745i	$-0.390815\pi$
$739$	18.2858			0.672654			0.336327	+	0.941745i	$0.390815\pi$
$740$		0			0
$741$	−11.4428	+	18.0671i	−0.420361	+	0.663713i
$742$		0			0
$743$	5.10611	−	6.08522i	0.187325	−	0.223245i	−0.664206	−	0.747550i	$-0.731230\pi$
$743$	5.10611	−	6.08522i	0.187325	−	0.223245i	0.851531	+	0.524304i	$0.175675\pi$
$744$		0			0
$745$	1.58165	−	0.278887i	0.0579471	−	0.0102176i
$746$		0			0
$747$	−8.66636	+	12.5177i	−0.317086	+	0.457997i
$748$		0			0
$749$	0.609260	−	2.14331i	0.0222619	−	0.0783150i
$750$		0			0
$751$	8.65479	−	49.0838i	0.315818	−	1.79109i	−0.251778	−	0.967785i	$-0.581015\pi$
$751$	8.65479	−	49.0838i	0.315818	−	1.79109i	0.567596	−	0.823307i	$-0.307874\pi$
$752$		0			0
$753$	27.8837	−	21.5136i	1.01614	−	0.784001i
$754$		0			0
$755$	14.5748			0.530433
$756$		0			0
$757$	−22.2840			−0.809927			−0.404963	−	0.914333i	$-0.632716\pi$
$757$	−22.2840			−0.809927			−0.404963	+	0.914333i	$0.632716\pi$
$758$		0			0
$759$	40.6450	+	16.7096i	1.47532	+	0.606518i
$760$		0			0
$761$	−4.94389	+	28.0382i	−0.179216	+	1.01638i	0.753949	+	0.656933i	$0.228147\pi$
$761$	−4.94389	+	28.0382i	−0.179216	+	1.01638i	−0.933164	+	0.359450i	$0.882964\pi$
$762$		0			0
$763$	5.96271	−	5.78465i	0.215865	−	0.209418i
$764$		0			0
$765$	−2.91881	−	31.4403i	−0.105530	−	1.13672i
$766$		0			0
$767$	49.5016	−	8.72846i	1.78740	−	0.315167i
$768$		0			0
$769$	−4.26169	+	5.07888i	−0.153680	+	0.183149i	−0.837391	−	0.546604i	$-0.815920\pi$
$769$	−4.26169	+	5.07888i	−0.153680	+	0.183149i	0.683711	+	0.729753i	$0.260365\pi$
$770$		0			0
$771$	21.0135	+	40.1066i	0.756784	+	1.44440i
$772$		0			0
$773$	−38.5225			−1.38556			−0.692778	−	0.721151i	$-0.743614\pi$
$773$	−38.5225			−1.38556			−0.692778	+	0.721151i	$0.743614\pi$
$774$		0			0
$775$		−	14.1831i		−	0.509472i
$776$		0			0
$777$	−16.4386	−	12.9436i	−0.589733	−	0.464347i
$778$		0			0
$779$	−6.17724	+	7.36174i	−0.221322	+	0.263762i
$780$		0			0
$781$	−30.5581	−	11.1223i	−1.09346	−	0.397986i
$782$		0			0
$783$	−0.357915	+	0.701114i	−0.0127908	+	0.0250558i
$784$		0			0
$785$	3.45329	+	4.11547i	0.123253	+	0.146887i
$786$		0			0
$787$	10.7890	+	29.6426i	0.384588	+	1.05665i	0.969402	+	0.245479i	$0.0789452\pi$
$787$	10.7890	+	29.6426i	0.384588	+	1.05665i	−0.584814	+	0.811167i	$0.698833\pi$
$788$		0			0
$789$	1.96312	−	2.15382i	0.0698891	−	0.0766779i
$790$		0			0
$791$	−12.2317	+	8.29137i	−0.434911	+	0.294807i
$792$		0			0
$793$	−50.2607	−	87.0540i	−1.78481	−	3.09138i
$794$		0			0
$795$	−3.97105	+	2.08060i	−0.140839	+	0.0737914i
$796$		0			0
$797$	11.7938	+	9.89620i	0.417759	+	0.350542i	0.827310	−	0.561746i	$-0.189870\pi$
$797$	11.7938	+	9.89620i	0.417759	+	0.350542i	−0.409551	+	0.912287i	$0.634315\pi$
$798$		0			0
$799$	62.0127	+	22.5708i	2.19385	+	0.798496i
$800$		0			0
$801$	−25.4663	+	6.96867i	−0.899806	+	0.246226i
$802$		0			0
$803$	−35.1113	−	12.7795i	−1.23905	−	0.450978i
$804$		0			0
$805$	13.5871	−	18.7917i	0.478883	−	0.662320i
$806$		0			0
$807$	−2.39285	+	1.84620i	−0.0842322	+	0.0649893i
$808$		0			0
$809$	−32.2256	+	18.6055i	−1.13299	+	0.654133i	−0.944686	−	0.327977i	$-0.893633\pi$
$809$	−32.2256	+	18.6055i	−1.13299	+	0.654133i	−0.188306	+	0.982110i	$0.560300\pi$
$810$		0			0
$811$			19.0501i			0.668940i	0.942406	+	0.334470i	$0.108557\pi$
$811$			19.0501i			0.668940i	−0.942406	+	0.334470i	$0.891443\pi$
$812$		0			0
$813$	9.36335	−	22.7758i	0.328387	−	0.798782i
$814$		0			0
$815$	13.4006	+	11.2444i	0.469402	+	0.393875i
$816$		0			0
$817$	0.602434	−	1.65517i	0.0210765	−	0.0579072i
$818$		0			0
$819$	52.6567	+	9.82059i	1.83997	+	0.343159i
$820$		0			0
$821$	−9.02401	−	10.7544i	−0.314940	−	0.375331i	0.585232	−	0.810866i	$-0.301004\pi$
$821$	−9.02401	−	10.7544i	−0.314940	−	0.375331i	−0.900172	+	0.435535i	$0.856559\pi$
$822$		0			0
$823$	4.59111	−	26.0375i	0.160036	−	0.907610i	−0.794000	−	0.607918i	$-0.792005\pi$
$823$	4.59111	−	26.0375i	0.160036	−	0.907610i	0.954036	−	0.299692i	$-0.0968840\pi$
$824$		0			0
$825$	−0.632955	+	15.4365i	−0.0220366	+	0.537431i
$826$		0			0
$827$	−1.07723	−	0.621942i	−0.0374591	−	0.0216270i	0.481153	−	0.876636i	$-0.340218\pi$
$827$	−1.07723	−	0.621942i	−0.0374591	−	0.0216270i	−0.518613	+	0.855009i	$0.673551\pi$
$828$		0			0
$829$	31.0264	+	17.9131i	1.07759	+	0.622147i	0.930246	−	0.366938i	$-0.119594\pi$
$829$	31.0264	+	17.9131i	1.07759	+	0.622147i	0.147345	+	0.989085i	$0.452927\pi$
$830$		0			0
$831$	−21.9467	−	20.0036i	−0.761324	−	0.693918i
$832$		0			0
$833$	35.6945	−	19.1900i	1.23674	−	0.664894i
$834$		0			0
$835$	0.465660	+	2.64089i	0.0161148	+	0.0913917i
$836$		0			0
$837$	31.8237	−	29.6304i	1.09999	−	1.02418i
$838$		0			0
$839$	1.26662	−	1.06282i	0.0437286	−	0.0366926i	−0.620661	−	0.784079i	$-0.713136\pi$
$839$	1.26662	−	1.06282i	0.0437286	−	0.0366926i	0.664390	+	0.747386i	$0.268691\pi$
$840$		0			0
$841$	5.03181	−	28.5368i	0.173511	−	0.984028i
$842$		0			0
$843$	−13.0184	−	2.84991i	−0.448378	−	0.0981559i
$844$		0			0
$845$	−59.1621			−2.03524
$846$		0			0
$847$	24.7864	+	36.5659i	0.851671	+	1.25642i
$848$		0			0
$849$	0.747770	−	18.2366i	0.0256634	−	0.625880i
$850$		0			0
$851$	−21.6773	−	3.82229i	−0.743088	−	0.131027i
$852$		0			0
$853$	−10.9655	+	30.1274i	−0.375451	+	1.03154i	0.597769	+	0.801669i	$0.296054\pi$
$853$	−10.9655	+	30.1274i	−0.375451	+	1.03154i	−0.973220	+	0.229875i	$0.926168\pi$
$854$		0			0
$855$	−9.93597	+	0.922424i	−0.339803	+	0.0315462i
$856$		0			0
$857$	−5.23483	+	4.39255i	−0.178818	+	0.150046i	−0.727804	−	0.685786i	$-0.759459\pi$
$857$	−5.23483	+	4.39255i	−0.178818	+	0.150046i	0.548985	+	0.835832i	$0.315014\pi$
$858$		0			0
$859$	18.1930	+	3.20792i	0.620738	+	0.109453i	0.475168	−	0.879895i	$-0.342387\pi$
$859$	18.1930	+	3.20792i	0.620738	+	0.109453i	0.145570	+	0.989348i	$0.453498\pi$
$860$		0			0
$861$	22.8637	+	7.52446i	0.779193	+	0.256433i
$862$		0			0
$863$	3.68919	+	2.12996i	0.125582	+	0.0725046i	0.561475	−	0.827494i	$-0.310234\pi$
$863$	3.68919	+	2.12996i	0.125582	+	0.0725046i	−0.435893	+	0.899998i	$0.643567\pi$
$864$		0			0
$865$	10.8881	+	18.8588i	0.370207	+	0.641218i
$866$		0			0
$867$	−3.80944	−	28.3542i	−0.129375	−	0.962959i
$868$		0			0
$869$	5.45145	+	14.9777i	0.184928	+	0.508085i
$870$		0			0
$871$	31.2939	+	37.2946i	1.06035	+	1.26368i
$872$		0			0
$873$	0.617614	−	7.51853i	0.0209031	−	0.254464i
$874$		0			0
$875$	30.9750	+	8.80499i	1.04715	+	0.297663i
$876$		0			0
$877$	−40.5605	+	14.7628i	−1.36963	+	0.498505i	−0.919019	−	0.394214i	$-0.871017\pi$
$877$	−40.5605	+	14.7628i	−1.36963	+	0.498505i	−0.450614	+	0.892719i	$0.648795\pi$
$878$		0			0
$879$	12.8399	+	0.526485i	0.433080	+	0.0177579i
$880$		0			0
$881$	−17.6461	+	30.5639i	−0.594511	+	1.02972i	0.399105	+	0.916905i	$0.369321\pi$
$881$	−17.6461	+	30.5639i	−0.594511	+	1.02972i	−0.993616	+	0.112818i	$0.964012\pi$
$882$		0			0
$883$	27.7816	+	48.1192i	0.934926	+	1.61934i	0.774766	+	0.632248i	$0.217868\pi$
$883$	27.7816	+	48.1192i	0.934926	+	1.61934i	0.160160	+	0.987091i	$0.448799\pi$
$884$		0			0
$885$	17.3339	+	15.7992i	0.582674	+	0.531086i
$886$		0			0
$887$	3.77547	+	3.16800i	0.126768	+	0.106371i	0.703968	−	0.710232i	$-0.251410\pi$
$887$	3.77547	+	3.16800i	0.126768	+	0.106371i	−0.577199	+	0.816603i	$0.695854\pi$
$888$		0			0
$889$	−29.8010	+	28.9111i	−0.999493	+	0.969646i
$890$		0			0
$891$	−35.9585	+	30.8287i	−1.20465	+	1.03280i
$892$		0			0
$893$	7.13298	−	19.5977i	0.238696	−	0.655812i
$894$		0			0
$895$	−35.5595	−	6.27010i	−1.18862	−	0.209586i
$896$		0			0
$897$	53.6990	−	17.0880i	1.79296	−	0.570551i
$898$		0			0
$899$	0.633865	−	1.09789i	0.0211406	−	0.0366166i
$900$		0			0
$901$	−7.13822	+	4.12125i	−0.237809	+	0.137299i
$902$		0			0
$903$	−4.40959	+	0.137314i	−0.146742	+	0.00456952i
$904$		0			0
$905$	7.53944	+	20.7144i	0.250619	+	0.688571i
$906$		0			0
$907$	−2.24899	−	12.7547i	−0.0746765	−	0.423511i	−0.999110	−	0.0421692i	$-0.986573\pi$
$907$	−2.24899	−	12.7547i	−0.0746765	−	0.423511i	0.924434	−	0.381342i	$-0.124538\pi$
$908$		0			0
$909$	3.13885	−	4.53375i	0.104109	−	0.150375i
$910$		0			0
$911$	−4.56975	+	0.805770i	−0.151403	+	0.0266963i	−0.248836	−	0.968546i	$-0.580048\pi$
$911$	−4.56975	+	0.805770i	−0.151403	+	0.0266963i	0.0974331	+	0.995242i	$0.468937\pi$
$912$		0			0
$913$	−17.1678	+	20.4597i	−0.568170	+	0.677119i
$914$		0			0
$915$	17.8341	−	43.3805i	0.589578	−	1.43412i
$916$		0			0
$917$	20.6644	−	42.6166i	0.682399	−	1.40732i
$918$		0			0
$919$	−6.21698	+	10.7681i	−0.205079	+	0.355208i	−0.950158	−	0.311769i	$-0.899079\pi$
$919$	−6.21698	+	10.7681i	−0.205079	+	0.355208i	0.745079	+	0.666977i	$0.232412\pi$
$920$		0			0
$921$	7.32730	−	17.8232i	0.241443	−	0.587296i
$922$		0			0
$923$	−39.1852	+	14.2622i	−1.28980	+	0.469448i
$924$		0			0
$925$	−1.34376	−	7.62084i	−0.0441825	−	0.250572i
$926$		0			0
$927$	35.0351	−	3.25254i	1.15070	−	0.106828i
$928$		0			0
$929$	25.5981	−	21.4793i	0.839845	−	0.704714i	−0.117684	−	0.993051i	$-0.537547\pi$
$929$	25.5981	−	21.4793i	0.839845	−	0.704714i	0.957529	+	0.288338i	$0.0931025\pi$
$930$		0			0
$931$	−6.06456	−	11.2804i	−0.198758	−	0.369701i
$932$		0			0
$933$	−40.4052	−	1.65676i	−1.32281	−	0.0542400i
$934$		0			0
$935$		−	55.3913i		−	1.81149i
$936$		0			0
$937$	41.0487	−	23.6995i	1.34100	−	0.774229i	0.354049	−	0.935227i	$-0.384805\pi$
$937$	41.0487	−	23.6995i	1.34100	−	0.774229i	0.986955	+	0.160998i	$0.0514714\pi$
$938$		0			0
$939$	19.4238	−	21.3105i	0.633871	−	0.695443i
$940$		0			0
$941$	1.98826	−	0.723667i	0.0648154	−	0.0235909i	−0.309409	−	0.950929i	$-0.600131\pi$
$941$	1.98826	−	0.723667i	0.0648154	−	0.0235909i	0.374224	+	0.927338i	$0.377909\pi$
$942$		0			0
$943$	24.9380	−	4.39724i	0.812093	−	0.143194i
$944$		0			0
$945$	11.3808	+	22.2519i	0.370216	+	0.723853i
$946$		0			0
$947$	−3.10977	+	0.548336i	−0.101054	+	0.0178185i	−0.223946	−	0.974601i	$-0.571894\pi$
$947$	−3.10977	+	0.548336i	−0.101054	+	0.0178185i	0.122892	+	0.992420i	$0.460783\pi$
$948$		0			0
$949$	−45.0238	+	16.3873i	−1.46153	+	0.531955i
$950$		0			0
$951$	24.2808	+	5.31540i	0.787360	+	0.172364i
$952$		0			0
$953$	5.48543	−	3.16701i	0.177690	−	0.102590i	−0.408517	−	0.912751i	$-0.633954\pi$
$953$	5.48543	−	3.16701i	0.177690	−	0.102590i	0.586207	+	0.810161i	$0.300620\pi$
$954$		0			0
$955$		−	39.0276i		−	1.26290i
$956$		0			0
$957$	−0.738879	+	1.16662i	−0.0238846	+	0.0377116i
$958$		0			0
$959$	−30.8221	−	3.16796i	−0.995298	−	0.102299i
$960$		0			0
$961$	−29.8958	+	25.0856i	−0.964382	+	0.809212i
$962$		0			0
$963$	2.44392	+	0.640969i	0.0787541	+	0.0206549i
$964$		0			0
$965$	0.402989	+	2.28546i	0.0129727	+	0.0735716i
$966$		0			0
$967$	−16.0907	+	5.85655i	−0.517443	+	0.188334i	−0.587523	−	0.809208i	$-0.699897\pi$
$967$	−16.0907	+	5.85655i	−0.517443	+	0.188334i	0.0700799	+	0.997541i	$0.477675\pi$
$968$		0			0
$969$	−18.1832	+	2.44295i	−0.584129	+	0.0784788i
$970$		0			0
$971$	−20.6911	+	35.8380i	−0.664008	+	1.15009i	0.315546	+	0.948910i	$0.397812\pi$
$971$	−20.6911	+	35.8380i	−0.664008	+	1.15009i	−0.979553	+	0.201185i	$0.935521\pi$
$972$		0			0
$973$	−1.68928	−	23.3856i	−0.0541557	−	0.749707i
$974$		0			0
$975$	12.1019	+	15.6852i	0.387571	+	0.502328i
$976$		0			0
$977$	14.5268	−	17.3124i	0.464753	−	0.553871i	−0.481858	−	0.876249i	$-0.660038\pi$
$977$	14.5268	−	17.3124i	0.464753	−	0.553871i	0.946611	+	0.322378i	$0.104482\pi$
$978$		0			0
$979$	−45.6130	+	8.04280i	−1.45780	+	0.257049i
$980$		0			0
$981$	6.69613	+	6.62546i	0.213791	+	0.211535i
$982$		0			0
$983$	−1.65881	−	9.40761i	−0.0529080	−	0.300056i	0.946859	−	0.321649i	$-0.104237\pi$
$983$	−1.65881	−	9.40761i	−0.0529080	−	0.300056i	−0.999767	+	0.0215933i	$0.993126\pi$
$984$		0			0
$985$	15.4628	+	42.4836i	0.492685	+	1.35364i
$986$		0			0
$987$	−52.2106	+	1.62583i	−1.66188	+	0.0517508i
$988$		0			0
$989$	−4.01950	+	2.32066i	−0.127813	+	0.0737927i
$990$		0			0
$991$	−27.5103	+	47.6493i	−0.873895	+	1.51363i	−0.0159588	+	0.999873i	$0.505080\pi$
$991$	−27.5103	+	47.6493i	−0.873895	+	1.51363i	−0.857936	+	0.513757i	$0.828253\pi$
$992$		0			0
$993$	0.497773	−	2.27383i	0.0157963	−	0.0721579i
$994$		0			0
$995$	22.4174	+	3.95279i	0.710679	+	0.125312i
$996$		0			0
$997$	−19.7121	+	54.1585i	−0.624288	+	1.71522i	0.0719505	+	0.997408i	$0.477078\pi$
$997$	−19.7121	+	54.1585i	−0.624288	+	1.71522i	−0.696239	+	0.717810i	$0.745145\pi$
$998$		0			0
$999$	14.2922	−	18.9360i	0.452185	−	0.599110i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ck.a.5.11	yes	144
7.3	odd	6		756.2.ca.a.437.19	yes	144
27.11	odd	18		756.2.ca.a.173.19	✓	144
189.38	even	18	inner	756.2.ck.a.605.11	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.19	✓	144	27.11	odd	18
756.2.ca.a.437.19	yes	144	7.3	odd	6
756.2.ck.a.5.11	yes	144	1.1	even	1	trivial
756.2.ck.a.605.11	yes	144	189.38	even	18	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ck (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.230632 - 1.71663i) q^{3} +(0.315692 - 1.79038i) q^{5} +(0.645961 + 2.56568i) q^{7} +(-2.89362 + 0.791819i) q^{9} +O(q^{10})\)	\(q+(-0.230632 - 1.71663i) q^{3} +(0.315692 - 1.79038i) q^{5} +(0.645961 + 2.56568i) q^{7} +(-2.89362 + 0.791819i) q^{9} +(-5.18280 + 0.913868i) q^{11} +(-4.33786 + 5.16966i) q^{13} +(-3.14622 - 0.129007i) q^{15} -5.78942 q^{17} +1.82961i q^{19} +(4.25534 - 1.70060i) q^{21} +(3.09892 - 3.69315i) q^{23} +(1.59267 + 0.579685i) q^{25} +(2.02662 + 4.78464i) q^{27} +(0.0973787 + 0.116051i) q^{29} +(-2.86208 - 7.86351i) q^{31} +(2.76409 + 8.68617i) q^{33} +(4.79747 - 0.346549i) q^{35} +(-2.28287 - 3.95404i) q^{37} +(9.87483 + 6.25420i) q^{39} +(4.02366 + 3.37625i) q^{41} +(-0.904658 - 0.329269i) q^{43} +(0.504163 + 5.43064i) q^{45} +(-10.7114 - 3.89862i) q^{47} +(-6.16547 + 3.31466i) q^{49} +(1.33523 + 9.93828i) q^{51} +(1.23298 - 0.711859i) q^{53} +9.56767i q^{55} +(3.14076 - 0.421968i) q^{57} +(-5.70576 - 4.78770i) q^{59} +(-5.09450 + 13.9970i) q^{61} +(-3.90072 - 6.91262i) q^{63} +(7.88622 + 9.39843i) q^{65} +(1.25272 - 7.10453i) q^{67} +(-7.05447 - 4.46793i) q^{69} +(5.35129 + 3.08957i) q^{71} +(6.14864 + 3.54992i) q^{73} +(0.627782 - 2.86772i) q^{75} +(-5.69258 - 12.7071i) q^{77} +(-0.525918 - 2.98263i) q^{79} +(7.74605 - 4.58244i) q^{81} +(3.88765 - 3.26213i) q^{83} +(-1.82767 + 10.3652i) q^{85} +(0.176758 - 0.193928i) q^{87} +8.80084 q^{89} +(-16.0658 - 7.79018i) q^{91} +(-12.8386 + 6.72671i) q^{93} +(3.27570 + 0.577594i) q^{95} +(-0.860050 + 2.36297i) q^{97} +(14.2734 - 6.74822i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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