LMFDB - Embedded newform 768.2.n.b.673.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(97,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("768.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.n (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			673.8
Character	$\chi$	$=$	768.673
Dual form			768.2.n.b.97.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.923880 + 0.382683i) q^{3} +(1.35803 + 3.27858i) q^{5} +(-2.48546 + 2.48546i) q^{7} +(0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(0.923880 + 0.382683i) q^{3} +(1.35803 + 3.27858i) q^{5} +(-2.48546 + 2.48546i) q^{7} +(0.707107 + 0.707107i) q^{9} +(0.420646 - 0.174237i) q^{11} +(1.98881 - 4.80141i) q^{13} +3.54871i q^{15} +4.75470i q^{17} +(-0.402518 + 0.971765i) q^{19} +(-3.24741 + 1.34512i) q^{21} +(-0.739125 - 0.739125i) q^{23} +(-5.36930 + 5.36930i) q^{25} +(0.382683 + 0.923880i) q^{27} +(0.153117 + 0.0634229i) q^{29} -8.57458 q^{31} +0.455304 q^{33} +(-11.5241 - 4.77344i) q^{35} +(2.67583 + 6.46002i) q^{37} +(3.67484 - 3.67484i) q^{39} +(-1.39247 - 1.39247i) q^{41} +(2.84883 - 1.18002i) q^{43} +(-1.35803 + 3.27858i) q^{45} -0.715661i q^{47} -5.35501i q^{49} +(-1.81955 + 4.39277i) q^{51} +(10.4455 - 4.32668i) q^{53} +(1.14250 + 1.14250i) q^{55} +(-0.743756 + 0.743756i) q^{57} +(2.09568 + 5.05941i) q^{59} +(2.81202 + 1.16478i) q^{61} -3.51497 q^{63} +18.4427 q^{65} +(-5.39384 - 2.23420i) q^{67} +(-0.400012 - 0.965714i) q^{69} +(8.26068 - 8.26068i) q^{71} +(4.37354 + 4.37354i) q^{73} +(-7.01532 + 2.90584i) q^{75} +(-0.612439 + 1.47856i) q^{77} +9.46948i q^{79} +1.00000i q^{81} +(2.85195 - 6.88522i) q^{83} +(-15.5887 + 6.45704i) q^{85} +(0.117190 + 0.117190i) q^{87} +(8.60493 - 8.60493i) q^{89} +(6.99060 + 16.8768i) q^{91} +(-7.92188 - 3.28135i) q^{93} -3.73264 q^{95} -10.2117 q^{97} +(0.420646 + 0.174237i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 16 q^{23} + 48 q^{31} - 48 q^{35} - 16 q^{43} + 16 q^{51} + 32 q^{53} - 32 q^{55} + 64 q^{59} + 32 q^{61} - 16 q^{63} + 16 q^{67} + 32 q^{69} - 64 q^{71} + 32 q^{75} + 32 q^{77} - 48 q^{91}+O(q^{100}) $ 32 * q + 16 * q^23 + 48 * q^31 - 48 * q^35 - 16 * q^43 + 16 * q^51 + 32 * q^53 - 32 * q^55 + 64 * q^59 + 32 * q^61 - 16 * q^63 + 16 * q^67 + 32 * q^69 - 64 * q^71 + 32 * q^75 + 32 * q^77 - 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.923880	+	0.382683i	0.533402	+	0.220942i
$3$	0.923880	+	0.382683i	0.533402	+	0.220942i
$4$		0			0
$5$	1.35803	+	3.27858i	0.607330	+	1.46623i	0.865892	+	0.500230i	$0.166751\pi$
$5$	1.35803	+	3.27858i	0.607330	+	1.46623i	−0.258562	+	0.965995i	$0.583249\pi$
$6$		0			0
$7$	−2.48546	+	2.48546i	−0.939415	+	0.939415i	−0.998267	−	0.0588516i	$-0.981256\pi$
$7$	−2.48546	+	2.48546i	−0.939415	+	0.939415i	0.0588516	+	0.998267i	$0.481256\pi$
$8$		0			0
$9$	0.707107	+	0.707107i	0.235702	+	0.235702i
$10$		0			0
$11$	0.420646	−	0.174237i	0.126829	−	0.0525345i	−0.318366	−	0.947968i	$-0.603134\pi$
$11$	0.420646	−	0.174237i	0.126829	−	0.0525345i	0.445196	+	0.895433i	$0.353134\pi$
$12$		0			0
$13$	1.98881	−	4.80141i	0.551596	−	1.33167i	−0.364684	−	0.931131i	$-0.618823\pi$
$13$	1.98881	−	4.80141i	0.551596	−	1.33167i	0.916280	−	0.400539i	$-0.131177\pi$
$14$		0			0
$15$			3.54871i			0.916273i
$16$		0			0
$17$			4.75470i			1.15318i	0.817032	+	0.576592i	$0.195618\pi$
$17$			4.75470i			1.15318i	−0.817032	+	0.576592i	$0.804382\pi$
$18$		0			0
$19$	−0.402518	+	0.971765i	−0.0923440	+	0.222938i	−0.963302	−	0.268419i	$-0.913499\pi$
$19$	−0.402518	+	0.971765i	−0.0923440	+	0.222938i	0.870958	+	0.491357i	$0.163499\pi$
$20$		0			0
$21$	−3.24741	+	1.34512i	−0.708643	+	0.293529i
$22$		0			0
$23$	−0.739125	−	0.739125i	−0.154118	−	0.154118i	0.625836	−	0.779955i	$-0.284758\pi$
$23$	−0.739125	−	0.739125i	−0.154118	−	0.154118i	−0.779955	+	0.625836i	$0.784758\pi$
$24$		0			0
$25$	−5.36930	+	5.36930i	−1.07386	+	1.07386i
$26$		0			0
$27$	0.382683	+	0.923880i	0.0736475	+	0.177801i
$28$		0			0
$29$	0.153117	+	0.0634229i	0.0284330	+	0.0117773i	0.396855	−	0.917881i	$-0.370102\pi$
$29$	0.153117	+	0.0634229i	0.0284330	+	0.0117773i	−0.368422	+	0.929659i	$0.620102\pi$
$30$		0			0
$31$	−8.57458			−1.54004			−0.770020	−	0.638020i	$-0.779754\pi$
$31$	−8.57458			−1.54004			−0.770020	+	0.638020i	$0.779754\pi$
$32$		0			0
$33$	0.455304			0.0792582
$34$		0			0
$35$	−11.5241	−	4.77344i	−1.94793	−	0.806859i
$36$		0			0
$37$	2.67583	+	6.46002i	0.439903	+	1.06202i	0.975982	+	0.217852i	$0.0699051\pi$
$37$	2.67583	+	6.46002i	0.439903	+	1.06202i	−0.536079	+	0.844168i	$0.680095\pi$
$38$		0			0
$39$	3.67484	−	3.67484i	0.588445	−	0.588445i
$40$		0			0
$41$	−1.39247	−	1.39247i	−0.217467	−	0.217467i	0.589963	−	0.807430i	$-0.299142\pi$
$41$	−1.39247	−	1.39247i	−0.217467	−	0.217467i	−0.807430	+	0.589963i	$0.799142\pi$
$42$		0			0
$43$	2.84883	−	1.18002i	0.434443	−	0.179952i	−0.154734	−	0.987956i	$-0.549452\pi$
$43$	2.84883	−	1.18002i	0.434443	−	0.179952i	0.589177	+	0.808004i	$0.299452\pi$
$44$		0			0
$45$	−1.35803	+	3.27858i	−0.202443	+	0.488742i
$46$		0			0
$47$		−	0.715661i		−	0.104390i	−0.998637	−	0.0521949i	$-0.983378\pi$
$47$		−	0.715661i		−	0.104390i	0.998637	−	0.0521949i	$-0.0166217\pi$
$48$		0			0
$49$		−	5.35501i		−	0.765002i
$50$		0			0
$51$	−1.81955	+	4.39277i	−0.254787	+	0.615111i
$52$		0			0
$53$	10.4455	−	4.32668i	1.43480	−	0.594316i	0.476272	−	0.879298i	$-0.341988\pi$
$53$	10.4455	−	4.32668i	1.43480	−	0.594316i	0.958533	+	0.284982i	$0.0919877\pi$
$54$		0			0
$55$	1.14250	+	1.14250i	0.154055	+	0.154055i
$56$		0			0
$57$	−0.743756	+	0.743756i	−0.0985130	+	0.0985130i
$58$		0			0
$59$	2.09568	+	5.05941i	0.272834	+	0.658679i	0.999602	−	0.0282033i	$-0.00897857\pi$
$59$	2.09568	+	5.05941i	0.272834	+	0.658679i	−0.726768	+	0.686883i	$0.758979\pi$
$60$		0			0
$61$	2.81202	+	1.16478i	0.360042	+	0.149134i	0.555369	−	0.831604i	$-0.312577\pi$
$61$	2.81202	+	1.16478i	0.360042	+	0.149134i	−0.195327	+	0.980738i	$0.562577\pi$
$62$		0			0
$63$	−3.51497			−0.442845
$64$		0			0
$65$	18.4427			2.28753
$66$		0			0
$67$	−5.39384	−	2.23420i	−0.658962	−	0.272951i	0.0280395	−	0.999607i	$-0.491074\pi$
$67$	−5.39384	−	2.23420i	−0.658962	−	0.272951i	−0.687002	+	0.726656i	$0.741074\pi$
$68$		0			0
$69$	−0.400012	−	0.965714i	−0.0481558	−	0.116258i
$70$		0			0
$71$	8.26068	−	8.26068i	0.980363	−	0.980363i	−0.0194483	−	0.999811i	$-0.506191\pi$
$71$	8.26068	−	8.26068i	0.980363	−	0.980363i	0.999811	+	0.0194483i	$0.00619097\pi$
$72$		0			0
$73$	4.37354	+	4.37354i	0.511884	+	0.511884i	0.915103	−	0.403219i	$-0.132109\pi$
$73$	4.37354	+	4.37354i	0.511884	+	0.511884i	−0.403219	+	0.915103i	$0.632109\pi$
$74$		0			0
$75$	−7.01532	+	2.90584i	−0.810060	+	0.335538i
$76$		0			0
$77$	−0.612439	+	1.47856i	−0.0697938	+	0.168497i
$78$		0			0
$79$			9.46948i			1.06540i	0.846304	+	0.532700i	$0.178823\pi$
$79$			9.46948i			1.06540i	−0.846304	+	0.532700i	$0.821177\pi$
$80$		0			0
$81$			1.00000i			0.111111i
$82$		0			0
$83$	2.85195	−	6.88522i	0.313042	−	0.755751i	−0.686547	−	0.727086i	$-0.740874\pi$
$83$	2.85195	−	6.88522i	0.313042	−	0.755751i	0.999589	−	0.0286653i	$-0.00912568\pi$
$84$		0			0
$85$	−15.5887	+	6.45704i	−1.69083	+	0.700364i
$86$		0			0
$87$	0.117190	+	0.117190i	0.0125641	+	0.0125641i
$88$		0			0
$89$	8.60493	−	8.60493i	0.912120	−	0.912120i	−0.0843186	−	0.996439i	$-0.526871\pi$
$89$	8.60493	−	8.60493i	0.912120	−	0.912120i	0.996439	+	0.0843186i	$0.0268713\pi$
$90$		0			0
$91$	6.99060	+	16.8768i	0.732814	+	1.76917i
$92$		0			0
$93$	−7.92188	−	3.28135i	−0.821460	−	0.340260i
$94$		0			0
$95$	−3.73264			−0.382961
$96$		0			0
$97$	−10.2117			−1.03684			−0.518420	−	0.855126i	$-0.673480\pi$
$97$	−10.2117			−1.03684			−0.518420	+	0.855126i	$0.673480\pi$
$98$		0			0
$99$	0.420646	+	0.174237i	0.0422765	+	0.0175115i
$100$		0			0
$101$	1.92210	+	4.64035i	0.191256	+	0.461732i	0.990197	−	0.139677i	$-0.0446063\pi$
$101$	1.92210	+	4.64035i	0.191256	+	0.461732i	−0.798941	+	0.601409i	$0.794606\pi$
$102$		0			0
$103$	2.99647	−	2.99647i	0.295251	−	0.295251i	−0.543900	−	0.839150i	$-0.683053\pi$
$103$	2.99647	−	2.99647i	0.295251	−	0.295251i	0.839150	+	0.543900i	$0.183053\pi$
$104$		0			0
$105$	−8.82017	−	8.82017i	−0.860760	−	0.860760i
$106$		0			0
$107$	−0.420364	+	0.174120i	−0.0406381	+	0.0168328i	−0.402910	−	0.915240i	$-0.632001\pi$
$107$	−0.420364	+	0.174120i	−0.0406381	+	0.0168328i	0.362272	+	0.932072i	$0.382001\pi$
$108$		0			0
$109$	1.97979	−	4.77963i	0.189629	−	0.457806i	−0.800259	−	0.599655i	$-0.795305\pi$
$109$	1.97979	−	4.77963i	0.189629	−	0.457806i	0.989888	+	0.141849i	$0.0453046\pi$
$110$		0			0
$111$			6.99227i			0.663677i
$112$		0			0
$113$		−	6.63496i		−	0.624164i	−0.950055	−	0.312082i	$-0.898974\pi$
$113$		−	6.63496i		−	0.624164i	0.950055	−	0.312082i	$-0.101026\pi$
$114$		0			0
$115$	1.41953	−	3.42704i	0.132371	−	0.319573i
$116$		0			0
$117$	4.80141	−	1.98881i	0.443890	−	0.183865i
$118$		0			0
$119$	−11.8176	−	11.8176i	−1.08332	−	1.08332i
$120$		0			0
$121$	−7.63159	+	7.63159i	−0.693781	+	0.693781i
$122$		0			0
$123$	−0.753600	−	1.81935i	−0.0679498	−	0.164045i
$124$		0			0
$125$	−8.50244	−	3.52183i	−0.760481	−	0.315002i
$126$		0			0
$127$	19.1639			1.70052			0.850262	−	0.526360i	$-0.176443\pi$
$127$	19.1639			1.70052			0.850262	+	0.526360i	$0.176443\pi$
$128$		0			0
$129$	3.08355			0.271492
$130$		0			0
$131$	16.6367	+	6.89115i	1.45356	+	0.602083i	0.963042	−	0.269350i	$-0.0868089\pi$
$131$	16.6367	+	6.89115i	1.45356	+	0.602083i	0.490514	+	0.871433i	$0.336809\pi$
$132$		0			0
$133$	−1.41484	−	3.41572i	−0.122682	−	0.296181i
$134$		0			0
$135$	−2.50932	+	2.50932i	−0.215968	+	0.215968i
$136$		0			0
$137$	−4.17579	−	4.17579i	−0.356762	−	0.356762i	0.505856	−	0.862618i	$-0.331177\pi$
$137$	−4.17579	−	4.17579i	−0.356762	−	0.356762i	−0.862618	+	0.505856i	$0.831177\pi$
$138$		0			0
$139$	17.1703	−	7.11217i	1.45636	−	0.603246i	0.492661	−	0.870221i	$-0.336024\pi$
$139$	17.1703	−	7.11217i	1.45636	−	0.603246i	0.963703	+	0.266975i	$0.0860242\pi$
$140$		0			0
$141$	0.273872	−	0.661185i	0.0230642	−	0.0556818i
$142$		0			0
$143$		−	2.36622i		−	0.197873i
$144$		0			0
$145$			0.588135i			0.0488420i
$146$		0			0
$147$	2.04927	−	4.94739i	0.169021	−	0.408054i
$148$		0			0
$149$	−7.65604	+	3.17123i	−0.627207	+	0.259798i	−0.673566	−	0.739127i	$-0.735238\pi$
$149$	−7.65604	+	3.17123i	−0.627207	+	0.259798i	0.0463589	+	0.998925i	$0.485238\pi$
$150$		0			0
$151$	8.34642	+	8.34642i	0.679222	+	0.679222i	0.959824	−	0.280602i	$-0.0905341\pi$
$151$	8.34642	+	8.34642i	0.679222	+	0.679222i	−0.280602	+	0.959824i	$0.590534\pi$
$152$		0			0
$153$	−3.36208	+	3.36208i	−0.271808	+	0.271808i
$154$		0			0
$155$	−11.6445	−	28.1124i	−0.935313	−	2.25804i
$156$		0			0
$157$	−1.13210	−	0.468931i	−0.0903514	−	0.0374248i	0.337050	−	0.941487i	$-0.390571\pi$
$157$	−1.13210	−	0.468931i	−0.0903514	−	0.0374248i	−0.427401	+	0.904062i	$0.640571\pi$
$158$		0			0
$159$	11.3062			0.896637
$160$		0			0
$161$	3.67413			0.289562
$162$		0			0
$163$	−12.5235	−	5.18742i	−0.980920	−	0.406310i	−0.166154	−	0.986100i	$-0.553135\pi$
$163$	−12.5235	−	5.18742i	−0.980920	−	0.406310i	−0.814766	+	0.579790i	$0.803135\pi$
$164$		0			0
$165$	0.618317	+	1.49275i	0.0481359	+	0.116210i
$166$		0			0
$167$	6.60580	−	6.60580i	0.511172	−	0.511172i	−0.403713	−	0.914886i	$-0.632281\pi$
$167$	6.60580	−	6.60580i	0.511172	−	0.511172i	0.914886	+	0.403713i	$0.132281\pi$
$168$		0			0
$169$	−9.90575	−	9.90575i	−0.761981	−	0.761981i
$170$		0			0
$171$	−0.971765	+	0.402518i	−0.0743127	+	0.0307813i
$172$		0			0
$173$	7.14385	−	17.2468i	0.543137	−	1.31125i	−0.379361	−	0.925249i	$-0.623856\pi$
$173$	7.14385	−	17.2468i	0.543137	−	1.31125i	0.922499	−	0.386000i	$-0.126144\pi$
$174$		0			0
$175$		−	26.6903i		−	2.01760i
$176$		0			0
$177$			5.47627i			0.411622i
$178$		0			0
$179$	3.80659	−	9.18993i	0.284518	−	0.686887i	−0.715412	−	0.698703i	$-0.753761\pi$
$179$	3.80659	−	9.18993i	0.284518	−	0.686887i	0.999930	+	0.0118153i	$0.00376101\pi$
$180$		0			0
$181$	5.55971	−	2.30291i	0.413250	−	0.171174i	−0.166365	−	0.986064i	$-0.553203\pi$
$181$	5.55971	−	2.30291i	0.413250	−	0.171174i	0.579615	+	0.814890i	$0.303203\pi$
$182$		0			0
$183$	2.15222	+	2.15222i	0.159097	+	0.159097i
$184$		0			0
$185$	−17.5458	+	17.5458i	−1.28999	+	1.28999i
$186$		0			0
$187$	0.828446	+	2.00005i	0.0605820	+	0.146258i
$188$		0			0
$189$	−3.24741	−	1.34512i	−0.236214	−	0.0978431i
$190$		0			0
$191$	−5.75185			−0.416190			−0.208095	−	0.978109i	$-0.566726\pi$
$191$	−5.75185			−0.416190			−0.208095	+	0.978109i	$0.566726\pi$
$192$		0			0
$193$	−2.02898			−0.146049			−0.0730246	−	0.997330i	$-0.523265\pi$
$193$	−2.02898			−0.146049			−0.0730246	+	0.997330i	$0.523265\pi$
$194$		0			0
$195$	17.0388	+	7.05770i	1.22017	+	0.505412i
$196$		0			0
$197$	−3.54890	−	8.56781i	−0.252849	−	0.610431i	0.745583	−	0.666413i	$-0.232171\pi$
$197$	−3.54890	−	8.56781i	−0.252849	−	0.610431i	−0.998432	+	0.0559816i	$0.982171\pi$
$198$		0			0
$199$	−12.7457	+	12.7457i	−0.903520	+	0.903520i	−0.995739	−	0.0922191i	$-0.970604\pi$
$199$	−12.7457	+	12.7457i	−0.903520	+	0.903520i	0.0922191	+	0.995739i	$0.470604\pi$
$200$		0			0
$201$	−4.12827	−	4.12827i	−0.291185	−	0.291185i
$202$		0			0
$203$	−0.538200	+	0.222930i	−0.0377742	+	0.0156466i
$204$		0			0
$205$	2.67431	−	6.45635i	0.186782	−	0.450931i
$206$		0			0
$207$		−	1.04528i		−	0.0726521i
$208$		0			0
$209$			0.478902i			0.0331264i
$210$		0			0
$211$	−8.49277	+	20.5034i	−0.584666	+	1.41151i	0.303874	+	0.952712i	$0.401720\pi$
$211$	−8.49277	+	20.5034i	−0.584666	+	1.41151i	−0.888541	+	0.458798i	$0.848280\pi$
$212$		0			0
$213$	10.7931	−	4.47065i	0.739531	−	0.306324i
$214$		0			0
$215$	7.73761	+	7.73761i	0.527700	+	0.527700i
$216$		0			0
$217$	21.3118	−	21.3118i	1.44674	−	1.44674i
$218$		0			0
$219$	2.36694	+	5.71430i	0.159943	+	0.386137i
$220$		0			0
$221$	22.8293	+	9.45619i	1.53566	+	0.636092i
$222$		0			0
$223$	−1.93870			−0.129825			−0.0649123	−	0.997891i	$-0.520677\pi$
$223$	−1.93870			−0.129825			−0.0649123	+	0.997891i	$0.520677\pi$
$224$		0			0
$225$	−7.59333			−0.506222
$226$		0			0
$227$	19.8529	+	8.22334i	1.31768	+	0.545802i	0.927117	−	0.374773i	$-0.122279\pi$
$227$	19.8529	+	8.22334i	1.31768	+	0.545802i	0.390566	+	0.920575i	$0.372279\pi$
$228$		0			0
$229$	−9.21270	−	22.2414i	−0.608792	−	1.46975i	−0.864315	−	0.502951i	$-0.832247\pi$
$229$	−9.21270	−	22.2414i	−0.608792	−	1.46975i	0.255522	−	0.966803i	$-0.417753\pi$
$230$		0			0
$231$	−1.13164	+	1.13164i	−0.0744564	+	0.0744564i
$232$		0			0
$233$	7.56463	+	7.56463i	0.495575	+	0.495575i	0.910057	−	0.414482i	$-0.136037\pi$
$233$	7.56463	+	7.56463i	0.495575	+	0.495575i	−0.414482	+	0.910057i	$0.636037\pi$
$234$		0			0
$235$	2.34635	−	0.971890i	0.153059	−	0.0633991i
$236$		0			0
$237$	−3.62381	+	8.74866i	−0.235392	+	0.568287i
$238$		0			0
$239$			21.0655i			1.36261i	0.731997	+	0.681307i	$0.238588\pi$
$239$			21.0655i			1.36261i	−0.731997	+	0.681307i	$0.761412\pi$
$240$		0			0
$241$		−	24.1957i		−	1.55858i	−0.626664	−	0.779289i	$-0.715580\pi$
$241$		−	24.1957i		−	1.55858i	0.626664	−	0.779289i	$-0.284420\pi$
$242$		0			0
$243$	−0.382683	+	0.923880i	−0.0245492	+	0.0592669i
$244$		0			0
$245$	17.5568	−	7.27228i	1.12166	−	0.464609i
$246$		0			0
$247$	3.86531	+	3.86531i	0.245943	+	0.245943i
$248$		0			0
$249$	5.26972	−	5.26972i	0.333955	−	0.333955i
$250$		0			0
$251$	0.0707278	+	0.170752i	0.00446430	+	0.0107778i	0.926096	−	0.377288i	$-0.123143\pi$
$251$	0.0707278	+	0.170752i	0.00446430	+	0.0107778i	−0.921632	+	0.388066i	$0.873143\pi$
$252$		0			0
$253$	−0.439693	−	0.182127i	−0.0276433	−	0.0114502i
$254$		0			0
$255$	−16.8731			−1.05663
$256$		0			0
$257$	−29.7460			−1.85550			−0.927751	−	0.373199i	$-0.878261\pi$
$257$	−29.7460			−1.85550			−0.927751	+	0.373199i	$0.878261\pi$
$258$		0			0
$259$	−22.7068	−	9.40545i	−1.41093	−	0.584426i
$260$		0			0
$261$	0.0634229	+	0.153117i	0.00392578	+	0.00947768i
$262$		0			0
$263$	−0.211270	+	0.211270i	−0.0130275	+	0.0130275i	−0.713591	−	0.700563i	$-0.752932\pi$
$263$	−0.211270	+	0.211270i	−0.0130275	+	0.0130275i	0.700563	+	0.713591i	$0.252932\pi$
$264$		0			0
$265$	28.3707	+	28.3707i	1.74280	+	1.74280i
$266$		0			0
$267$	11.2429	−	4.65695i	0.688053	−	0.285001i
$268$		0			0
$269$	−9.18492	+	22.1744i	−0.560014	+	1.35199i	0.349740	+	0.936847i	$0.386270\pi$
$269$	−9.18492	+	22.1744i	−0.560014	+	1.35199i	−0.909754	+	0.415148i	$0.863730\pi$
$270$		0			0
$271$		−	15.5563i		−	0.944979i	−0.881336	−	0.472489i	$-0.843356\pi$
$271$		−	15.5563i		−	0.944979i	0.881336	−	0.472489i	$-0.156644\pi$
$272$		0			0
$273$			18.2673i			1.10559i
$274$		0			0
$275$	−1.32304	+	3.19410i	−0.0797824	+	0.192612i
$276$		0			0
$277$	−24.1714	+	10.0121i	−1.45232	+	0.601570i	−0.962750	−	0.270394i	$-0.912846\pi$
$277$	−24.1714	+	10.0121i	−1.45232	+	0.601570i	−0.489570	+	0.871964i	$0.662846\pi$
$278$		0			0
$279$	−6.06314	−	6.06314i	−0.362991	−	0.362991i
$280$		0			0
$281$	18.5324	−	18.5324i	1.10555	−	1.10555i	0.111820	−	0.993729i	$-0.464332\pi$
$281$	18.5324	−	18.5324i	1.10555	−	1.10555i	0.993729	−	0.111820i	$-0.0356679\pi$
$282$		0			0
$283$	−3.60189	−	8.69574i	−0.214110	−	0.516908i	0.779937	−	0.625858i	$-0.215251\pi$
$283$	−3.60189	−	8.69574i	−0.214110	−	0.516908i	−0.994047	+	0.108950i	$0.965251\pi$
$284$		0			0
$285$	−3.44851	−	1.42842i	−0.204272	−	0.0846123i
$286$		0			0
$287$	6.92186			0.408584
$288$		0			0
$289$	−5.60720			−0.329836
$290$		0			0
$291$	−9.43437	−	3.90784i	−0.553052	−	0.229082i
$292$		0			0
$293$	−8.32183	−	20.0907i	−0.486167	−	1.17371i	−0.956634	−	0.291293i	$-0.905915\pi$
$293$	−8.32183	−	20.0907i	−0.486167	−	1.17371i	0.470467	−	0.882417i	$-0.344085\pi$
$294$		0			0
$295$	−13.7417	+	13.7417i	−0.800072	+	0.800072i
$296$		0			0
$297$	0.321948	+	0.321948i	0.0186813	+	0.0186813i
$298$		0			0
$299$	−5.01882	+	2.07886i	−0.290246	+	0.120224i
$300$		0			0
$301$	−4.14775	+	10.0136i	−0.239072	+	0.577172i
$302$		0			0
$303$			5.02268i			0.288545i
$304$		0			0
$305$			10.8012i			0.618476i
$306$		0			0
$307$	11.7750	−	28.4274i	0.672036	−	1.62244i	−0.106111	−	0.994354i	$-0.533840\pi$
$307$	11.7750	−	28.4274i	0.672036	−	1.62244i	0.778146	−	0.628083i	$-0.216160\pi$
$308$		0			0
$309$	3.91507	−	1.62168i	0.222721	−	0.0922539i
$310$		0			0
$311$	1.08506	+	1.08506i	0.0615284	+	0.0615284i	0.737201	−	0.675673i	$-0.236147\pi$
$311$	1.08506	+	1.08506i	0.0615284	+	0.0615284i	−0.675673	+	0.737201i	$0.736147\pi$
$312$		0			0
$313$	3.44537	−	3.44537i	0.194744	−	0.194744i	−0.602998	−	0.797742i	$-0.706027\pi$
$313$	3.44537	−	3.44537i	0.194744	−	0.194744i	0.797742	+	0.602998i	$0.206027\pi$
$314$		0			0
$315$	−4.77344	−	11.5241i	−0.268953	−	0.649310i
$316$		0			0
$317$	−1.87234	−	0.775548i	−0.105161	−	0.0435591i	0.329483	−	0.944162i	$-0.393126\pi$
$317$	−1.87234	−	0.775548i	−0.105161	−	0.0435591i	−0.434644	+	0.900603i	$0.643126\pi$
$318$		0			0
$319$	0.0754585			0.00422486
$320$		0			0
$321$	−0.454998			−0.0253955
$322$		0			0
$323$	−4.62045	−	1.91385i	−0.257089	−	0.106490i
$324$		0			0
$325$	15.1017	+	36.4587i	0.837690	+	2.02236i
$326$		0			0
$327$	3.65817	−	3.65817i	0.202297	−	0.202297i
$328$		0			0
$329$	1.77875	+	1.77875i	0.0980654	+	0.0980654i
$330$		0			0
$331$	−27.3713	+	11.3376i	−1.50446	+	0.623168i	−0.974406	−	0.224795i	$-0.927829\pi$
$331$	−27.3713	+	11.3376i	−1.50446	+	0.623168i	−0.530055	+	0.847963i	$0.677829\pi$
$332$		0			0
$333$	−2.67583	+	6.46002i	−0.146634	+	0.354007i
$334$		0			0
$335$		−	20.7182i		−	1.13196i
$336$		0			0
$337$		−	8.28014i		−	0.451048i	−0.974238	−	0.225524i	$-0.927591\pi$
$337$		−	8.28014i		−	0.451048i	0.974238	−	0.225524i	$-0.0724094\pi$
$338$		0			0
$339$	2.53909	−	6.12990i	0.137904	−	0.332930i
$340$		0			0
$341$	−3.60686	+	1.49401i	−0.195322	+	0.0809052i
$342$		0			0
$343$	−4.08855	−	4.08855i	−0.220761	−	0.220761i
$344$		0			0
$345$	2.62294	−	2.62294i	0.141214	−	0.141214i
$346$		0			0
$347$	7.72315	+	18.6453i	0.414601	+	1.00093i	0.983886	+	0.178795i	$0.0572198\pi$
$347$	7.72315	+	18.6453i	0.414601	+	1.00093i	−0.569286	+	0.822140i	$0.692780\pi$
$348$		0			0
$349$	1.13179	+	0.468804i	0.0605835	+	0.0250945i	0.412769	−	0.910836i	$-0.364562\pi$
$349$	1.13179	+	0.468804i	0.0605835	+	0.0250945i	−0.352186	+	0.935930i	$0.614562\pi$
$350$		0			0
$351$	5.19700			0.277396
$352$		0			0
$353$	−11.9551			−0.636306			−0.318153	−	0.948039i	$-0.603063\pi$
$353$	−11.9551			−0.636306			−0.318153	+	0.948039i	$0.603063\pi$
$354$		0			0
$355$	38.3016	+	15.8650i	2.03284	+	0.842028i
$356$		0			0
$357$	−6.39565	−	15.4405i	−0.338494	−	0.817196i
$358$		0			0
$359$	−5.02082	+	5.02082i	−0.264989	+	0.264989i	−0.827077	−	0.562088i	$-0.809998\pi$
$359$	−5.02082	+	5.02082i	−0.264989	+	0.264989i	0.562088	+	0.827077i	$0.309998\pi$
$360$		0			0
$361$	12.6527	+	12.6527i	0.665933	+	0.665933i
$362$		0			0
$363$	−9.97115	+	4.13019i	−0.523350	+	0.216779i
$364$		0			0
$365$	−8.39959	+	20.2784i	−0.439655	+	1.06142i
$366$		0			0
$367$		−	23.7760i		−	1.24109i	−0.784169	−	0.620547i	$-0.786910\pi$
$367$		−	23.7760i		−	1.24109i	0.784169	−	0.620547i	$-0.213090\pi$
$368$		0			0
$369$		−	1.96925i		−	0.102515i
$370$		0			0
$371$	−15.2082	+	36.7157i	−0.789568	+	1.90619i
$372$		0			0
$373$	−3.85917	+	1.59852i	−0.199820	+	0.0827683i	−0.480349	−	0.877077i	$-0.659490\pi$
$373$	−3.85917	+	1.59852i	−0.199820	+	0.0827683i	0.280529	+	0.959846i	$0.409490\pi$
$374$		0			0
$375$	−6.50749	−	6.50749i	−0.336045	−	0.336045i
$376$		0			0
$377$	0.609039	−	0.609039i	0.0313671	−	0.0313671i
$378$		0			0
$379$	−3.43755	−	8.29899i	−0.176575	−	0.426290i	0.810669	−	0.585505i	$-0.199104\pi$
$379$	−3.43755	−	8.29899i	−0.176575	−	0.426290i	−0.987244	+	0.159215i	$0.949104\pi$
$380$		0			0
$381$	17.7052	+	7.33372i	0.907063	+	0.375718i
$382$		0			0
$383$	9.61765			0.491439			0.245720	−	0.969341i	$-0.420976\pi$
$383$	9.61765			0.491439			0.245720	+	0.969341i	$0.420976\pi$
$384$		0			0
$385$	−5.67928			−0.289443
$386$		0			0
$387$	2.84883	+	1.18002i	0.144814	+	0.0599840i
$388$		0			0
$389$	11.3406	+	27.3786i	0.574991	+	1.38815i	0.897260	+	0.441503i	$0.145555\pi$
$389$	11.3406	+	27.3786i	0.574991	+	1.38815i	−0.322269	+	0.946648i	$0.604445\pi$
$390$		0			0
$391$	3.51432	−	3.51432i	0.177727	−	0.177727i
$392$		0			0
$393$	12.7332	+	12.7332i	0.642305	+	0.642305i
$394$		0			0
$395$	−31.0465	+	12.8599i	−1.56212	+	0.647050i
$396$		0			0
$397$	−0.283457	+	0.684326i	−0.0142263	+	0.0343453i	−0.930833	−	0.365445i	$-0.880917\pi$
$397$	−0.283457	+	0.684326i	−0.0142263	+	0.0343453i	0.916607	+	0.399790i	$0.130917\pi$
$398$		0			0
$399$		−	3.69715i		−	0.185089i
$400$		0			0
$401$			4.48635i			0.224038i	0.993706	+	0.112019i	$0.0357317\pi$
$401$			4.48635i			0.224038i	−0.993706	+	0.112019i	$0.964268\pi$
$402$		0			0
$403$	−17.0532	+	41.1700i	−0.849480	+	2.05083i
$404$		0			0
$405$	−3.27858	+	1.35803i	−0.162914	+	0.0674811i
$406$		0			0
$407$	2.25115	+	2.25115i	0.111585	+	0.111585i
$408$		0			0
$409$	−15.2251	+	15.2251i	−0.752833	+	0.752833i	−0.975007	−	0.222174i	$-0.928685\pi$
$409$	−15.2251	+	15.2251i	−0.752833	+	0.752833i	0.222174	+	0.975007i	$0.428685\pi$
$410$		0			0
$411$	−2.25992	−	5.45593i	−0.111474	−	0.269121i
$412$		0			0
$413$	−17.7837	−	7.36624i	−0.875078	−	0.362469i
$414$		0			0
$415$	26.4468			1.29822
$416$		0			0
$417$	18.5850			0.910111
$418$		0			0
$419$	−13.2128	−	5.47292i	−0.645487	−	0.267369i	0.0358301	−	0.999358i	$-0.488592\pi$
$419$	−13.2128	−	5.47292i	−0.645487	−	0.267369i	−0.681317	+	0.731988i	$0.738592\pi$
$420$		0			0
$421$	−5.77775	−	13.9487i	−0.281590	−	0.679819i	0.718283	−	0.695751i	$-0.244928\pi$
$421$	−5.77775	−	13.9487i	−0.281590	−	0.679819i	−0.999873	+	0.0159320i	$0.994928\pi$
$422$		0			0
$423$	0.506049	−	0.506049i	0.0246049	−	0.0246049i
$424$		0			0
$425$	−25.5294	−	25.5294i	−1.23836	−	1.23836i
$426$		0			0
$427$	−9.88415	+	4.09415i	−0.478328	+	0.198130i
$428$		0			0
$429$	0.905512	−	2.18610i	0.0437185	−	0.105546i
$430$		0			0
$431$			30.9700i			1.49177i	0.666073	+	0.745886i	$0.267974\pi$
$431$			30.9700i			1.49177i	−0.666073	+	0.745886i	$0.732026\pi$
$432$		0			0
$433$			38.8143i			1.86529i	0.360790	+	0.932647i	$0.382507\pi$
$433$			38.8143i			1.86529i	−0.360790	+	0.932647i	$0.617493\pi$
$434$		0			0
$435$	−0.225070	+	0.543366i	−0.0107913	+	0.0260524i
$436$		0			0
$437$	1.01577	−	0.420745i	0.0485907	−	0.0201269i
$438$		0			0
$439$	4.15330	+	4.15330i	0.198226	+	0.198226i	0.799239	−	0.601013i	$-0.205236\pi$
$439$	4.15330	+	4.15330i	0.198226	+	0.198226i	−0.601013	+	0.799239i	$0.705236\pi$
$440$		0			0
$441$	3.78657	−	3.78657i	0.180313	−	0.180313i
$442$		0			0
$443$	−2.26978	−	5.47973i	−0.107840	−	0.260350i	0.860742	−	0.509041i	$-0.170000\pi$
$443$	−2.26978	−	5.47973i	−0.107840	−	0.260350i	−0.968583	+	0.248691i	$0.920000\pi$
$444$		0			0
$445$	39.8977	+	16.5262i	1.89133	+	0.783415i
$446$		0			0
$447$	−8.28683			−0.391954
$448$		0			0
$449$	7.31556			0.345243			0.172621	−	0.984988i	$-0.444776\pi$
$449$	7.31556			0.345243			0.172621	+	0.984988i	$0.444776\pi$
$450$		0			0
$451$	−0.828358	−	0.343117i	−0.0390058	−	0.0161567i
$452$		0			0
$453$	4.51705	+	10.9051i	0.212230	+	0.512367i
$454$		0			0
$455$	−45.8385	+	45.8385i	−2.14894	+	2.14894i
$456$		0			0
$457$	1.80714	+	1.80714i	0.0845343	+	0.0845343i	0.748110	−	0.663575i	$-0.230962\pi$
$457$	1.80714	+	1.80714i	0.0845343	+	0.0845343i	−0.663575	+	0.748110i	$0.730962\pi$
$458$		0			0
$459$	−4.39277	+	1.81955i	−0.205037	+	0.0849291i
$460$		0			0
$461$	−5.44672	+	13.1495i	−0.253679	+	0.612436i	−0.998495	−	0.0548340i	$-0.982537\pi$
$461$	−5.44672	+	13.1495i	−0.253679	+	0.612436i	0.744816	+	0.667269i	$0.232537\pi$
$462$		0			0
$463$			28.6674i			1.33229i	0.745824	+	0.666143i	$0.232056\pi$
$463$			28.6674i			1.33229i	−0.745824	+	0.666143i	$0.767944\pi$
$464$		0			0
$465$		−	30.4287i		−	1.41110i
$466$		0			0
$467$	−0.0184119	+	0.0444502i	−0.000852000	+	0.00205691i	−0.924305	−	0.381655i	$-0.875354\pi$
$467$	−0.0184119	+	0.0444502i	−0.000852000	+	0.00205691i	0.923453	+	0.383712i	$0.125354\pi$
$468$		0			0
$469$	18.9592	−	7.85315i	0.875454	−	0.362625i
$470$		0			0
$471$	−0.866471	−	0.866471i	−0.0399249	−	0.0399249i
$472$		0			0
$473$	0.992745	−	0.992745i	0.0456465	−	0.0456465i
$474$		0			0
$475$	−3.05645	−	7.37893i	−0.140240	−	0.338569i
$476$		0			0
$477$	10.4455	+	4.32668i	0.478268	+	0.198105i
$478$		0			0
$479$	−8.64155			−0.394843			−0.197421	−	0.980319i	$-0.563257\pi$
$479$	−8.64155			−0.394843			−0.197421	+	0.980319i	$0.563257\pi$
$480$		0			0
$481$	36.3389			1.65691
$482$		0			0
$483$	3.39446	+	1.40603i	0.154453	+	0.0639766i
$484$		0			0
$485$	−13.8678	−	33.4798i	−0.629704	−	1.52024i
$486$		0			0
$487$	−2.15820	+	2.15820i	−0.0977973	+	0.0977973i	−0.754313	−	0.656515i	$-0.772030\pi$
$487$	−2.15820	+	2.15820i	−0.0977973	+	0.0977973i	0.656515	+	0.754313i	$0.272030\pi$
$488$		0			0
$489$	−9.58511	−	9.58511i	−0.433454	−	0.433454i
$490$		0			0
$491$	24.4583	−	10.1310i	1.10379	−	0.457204i	0.244994	−	0.969525i	$-0.421214\pi$
$491$	24.4583	−	10.1310i	1.10379	−	0.457204i	0.858794	+	0.512321i	$0.171214\pi$
$492$		0			0
$493$	−0.301557	+	0.728024i	−0.0135815	+	0.0327885i
$494$		0			0
$495$			1.61574i			0.0726221i
$496$		0			0
$497$			41.0632i			1.84193i
$498$		0			0
$499$	4.98970	−	12.0462i	0.223370	−	0.539263i	−0.771974	−	0.635655i	$-0.780730\pi$
$499$	4.98970	−	12.0462i	0.223370	−	0.539263i	0.995343	+	0.0963921i	$0.0307303\pi$
$500$		0			0
$501$	8.63089	−	3.57503i	0.385600	−	0.159721i
$502$		0			0
$503$	7.59295	+	7.59295i	0.338553	+	0.338553i	0.855823	−	0.517270i	$-0.173052\pi$
$503$	7.59295	+	7.59295i	0.338553	+	0.338553i	−0.517270	+	0.855823i	$0.673052\pi$
$504$		0			0
$505$	−12.6035	+	12.6035i	−0.560848	+	0.560848i
$506$		0			0
$507$	−5.36096	−	12.9425i	−0.238088	−	0.574796i
$508$		0			0
$509$	−12.9910	−	5.38103i	−0.575814	−	0.238510i	0.0757202	−	0.997129i	$-0.475874\pi$
$509$	−12.9910	−	5.38103i	−0.575814	−	0.238510i	−0.651534	+	0.758619i	$0.725874\pi$
$510$		0			0
$511$	−21.7405			−0.961743
$512$		0			0
$513$	−1.05183			−0.0464395
$514$		0			0
$515$	13.8934	+	5.75485i	0.612218	+	0.253589i
$516$		0			0
$517$	−0.124695	−	0.301040i	−0.00548407	−	0.0132397i
$518$		0			0
$519$	13.2001	−	13.2001i	0.579421	−	0.579421i
$520$		0			0
$521$	17.0333	+	17.0333i	0.746242	+	0.746242i	0.973771	−	0.227529i	$-0.0730647\pi$
$521$	17.0333	+	17.0333i	0.746242	+	0.746242i	−0.227529	+	0.973771i	$0.573065\pi$
$522$		0			0
$523$	38.4247	−	15.9160i	1.68020	−	0.695960i	0.680860	−	0.732414i	$-0.261606\pi$
$523$	38.4247	−	15.9160i	1.68020	−	0.695960i	0.999335	+	0.0364542i	$0.0116063\pi$
$524$		0			0
$525$	10.2139	−	24.6586i	0.445773	−	1.07619i
$526$		0			0
$527$		−	40.7696i		−	1.77595i
$528$		0			0
$529$		−	21.9074i		−	0.952495i
$530$		0			0
$531$	−2.09568	+	5.05941i	−0.0909447	+	0.219560i
$532$		0			0
$533$	−9.45518	+	3.91646i	−0.409549	+	0.169641i
$534$		0			0
$535$	−1.14173	−	1.14173i	−0.0493615	−	0.0493615i
$536$		0			0
$537$	7.03367	−	7.03367i	0.303525	−	0.303525i
$538$		0			0
$539$	−0.933042	−	2.25256i	−0.0401890	−	0.0970248i
$540$		0			0
$541$	8.78427	+	3.63857i	0.377665	+	0.156434i	0.563437	−	0.826159i	$-0.309479\pi$
$541$	8.78427	+	3.63857i	0.377665	+	0.156434i	−0.185772	+	0.982593i	$0.559479\pi$
$542$		0			0
$543$	6.01779			0.258248
$544$		0			0
$545$	18.3590			0.786414
$546$		0			0
$547$	3.07217	+	1.27253i	0.131357	+	0.0544097i	0.447393	−	0.894337i	$-0.352352\pi$
$547$	3.07217	+	1.27253i	0.131357	+	0.0544097i	−0.316037	+	0.948747i	$0.602352\pi$
$548$		0			0
$549$	1.16478	+	2.81202i	0.0497114	+	0.120014i
$550$		0			0
$551$	−0.123264	+	0.123264i	−0.00525124	+	0.00525124i
$552$		0			0
$553$	−23.5360	−	23.5360i	−1.00085	−	1.00085i
$554$		0			0
$555$	−22.9247	+	9.49573i	−0.973100	+	0.403071i
$556$		0			0
$557$	−0.215669	+	0.520670i	−0.00913817	+	0.0220615i	−0.928383	−	0.371625i	$-0.878801\pi$
$557$	−0.215669	+	0.520670i	−0.00913817	+	0.0220615i	0.919245	+	0.393687i	$0.128801\pi$
$558$		0			0
$559$		−	16.0252i		−	0.677795i
$560$		0			0
$561$			2.16483i			0.0913994i
$562$		0			0
$563$	11.9538	−	28.8591i	0.503793	−	1.21626i	−0.443610	−	0.896220i	$-0.646302\pi$
$563$	11.9538	−	28.8591i	0.503793	−	1.21626i	0.947403	−	0.320044i	$-0.103698\pi$
$564$		0			0
$565$	21.7532	−	9.01048i	0.915165	−	0.379074i
$566$		0			0
$567$	−2.48546	−	2.48546i	−0.104379	−	0.104379i
$568$		0			0
$569$	−22.2286	+	22.2286i	−0.931873	+	0.931873i	−0.997823	−	0.0659498i	$-0.978992\pi$
$569$	−22.2286	+	22.2286i	−0.931873	+	0.931873i	0.0659498	+	0.997823i	$0.478992\pi$
$570$		0			0
$571$	−2.84886	−	6.87776i	−0.119221	−	0.287825i	0.852991	−	0.521925i	$-0.174786\pi$
$571$	−2.84886	−	6.87776i	−0.119221	−	0.287825i	−0.972213	+	0.234099i	$0.924786\pi$
$572$		0			0
$573$	−5.31402	−	2.20114i	−0.221996	−	0.0919539i
$574$		0			0
$575$	7.93717			0.331003
$576$		0			0
$577$	−31.1728			−1.29774			−0.648871	−	0.760899i	$-0.724758\pi$
$577$	−31.1728			−1.29774			−0.648871	+	0.760899i	$0.724758\pi$
$578$		0			0
$579$	−1.87453	−	0.776457i	−0.0779029	−	0.0322685i
$580$		0			0
$581$	10.0245	+	24.2013i	0.415887	+	1.00404i
$582$		0			0
$583$	3.64000	−	3.64000i	0.150754	−	0.150754i
$584$		0			0
$585$	13.0409	+	13.0409i	0.539176	+	0.539176i
$586$		0			0
$587$	−13.5567	+	5.61536i	−0.559544	+	0.231771i	−0.644487	−	0.764615i	$-0.722929\pi$
$587$	−13.5567	+	5.61536i	−0.559544	+	0.231771i	0.0849433	+	0.996386i	$0.472929\pi$
$588$		0			0
$589$	3.45142	−	8.33247i	0.142213	−	0.343334i
$590$		0			0
$591$		−	9.27373i		−	0.381470i
$592$		0			0
$593$		−	20.0872i		−	0.824883i	−0.910984	−	0.412442i	$-0.864676\pi$
$593$		−	20.0872i		−	0.824883i	0.910984	−	0.412442i	$-0.135324\pi$
$594$		0			0
$595$	22.6963	−	54.7937i	0.930457	−	2.24632i
$596$		0			0
$597$	−16.6531	+	6.89793i	−0.681565	+	0.282313i
$598$		0			0
$599$	−22.9392	−	22.9392i	−0.937271	−	0.937271i	0.0608749	−	0.998145i	$-0.480611\pi$
$599$	−22.9392	−	22.9392i	−0.937271	−	0.937271i	−0.998145	+	0.0608749i	$0.980611\pi$
$600$		0			0
$601$	19.0481	−	19.0481i	0.776990	−	0.776990i	−0.202328	−	0.979318i	$-0.564851\pi$
$601$	19.0481	−	19.0481i	0.776990	−	0.776990i	0.979318	+	0.202328i	$0.0648507\pi$
$602$		0			0
$603$	−2.23420	−	5.39384i	−0.0909837	−	0.219654i
$604$		0			0
$605$	−35.3847	−	14.6568i	−1.43859	−	0.595885i
$606$		0			0
$607$	−39.8682			−1.61820			−0.809100	−	0.587672i	$-0.800045\pi$
$607$	−39.8682			−1.61820			−0.809100	+	0.587672i	$0.800045\pi$
$608$		0			0
$609$	−0.582543			−0.0236059
$610$		0			0
$611$	−3.43618	−	1.42331i	−0.139013	−	0.0575810i
$612$		0			0
$613$	−7.28252	−	17.5816i	−0.294138	−	0.710113i	−0.999998	−	0.00176143i	$-0.999439\pi$
$613$	−7.28252	−	17.5816i	−0.294138	−	0.710113i	0.705860	−	0.708351i	$-0.250561\pi$
$614$		0			0
$615$	4.94147	−	4.94147i	0.199259	−	0.199259i
$616$		0			0
$617$	−17.7361	−	17.7361i	−0.714027	−	0.714027i	0.253348	−	0.967375i	$-0.418468\pi$
$617$	−17.7361	−	17.7361i	−0.714027	−	0.714027i	−0.967375	+	0.253348i	$0.918468\pi$
$618$		0			0
$619$	7.84831	−	3.25088i	0.315450	−	0.130664i	−0.219340	−	0.975648i	$-0.570391\pi$
$619$	7.84831	−	3.25088i	0.315450	−	0.130664i	0.534790	+	0.844985i	$0.320391\pi$
$620$		0			0
$621$	0.400012	−	0.965714i	0.0160519	−	0.0387528i
$622$		0			0
$623$			42.7744i			1.71372i
$624$		0			0
$625$			5.30798i			0.212319i
$626$		0			0
$627$	−0.183268	+	0.442448i	−0.00731902	+	0.0176697i
$628$		0			0
$629$	−30.7155	+	12.7228i	−1.22471	+	0.507290i
$630$		0			0
$631$	−29.7910	−	29.7910i	−1.18596	−	1.18596i	−0.978174	−	0.207785i	$-0.933374\pi$
$631$	−29.7910	−	29.7910i	−1.18596	−	1.18596i	−0.207785	−	0.978174i	$-0.566626\pi$
$632$		0			0
$633$	−15.6926	+	15.6926i	−0.623725	+	0.623725i
$634$		0			0
$635$	26.0252	+	62.8305i	1.03278	+	2.49335i
$636$		0			0
$637$	−25.7116	−	10.6501i	−1.01873	−	0.421972i
$638$		0			0
$639$	11.6824			0.462147
$640$		0			0
$641$	−25.6481			−1.01304			−0.506520	−	0.862228i	$-0.669068\pi$
$641$	−25.6481			−1.01304			−0.506520	+	0.862228i	$0.669068\pi$
$642$		0			0
$643$	−24.6616	−	10.2152i	−0.972559	−	0.402847i	−0.160895	−	0.986972i	$-0.551438\pi$
$643$	−24.6616	−	10.2152i	−0.972559	−	0.402847i	−0.811664	+	0.584125i	$0.801438\pi$
$644$		0			0
$645$	4.18756	+	10.1097i	0.164885	+	0.398068i
$646$		0			0
$647$	33.8051	−	33.8051i	1.32902	−	1.32902i	0.422786	−	0.906230i	$-0.361052\pi$
$647$	33.8051	−	33.8051i	1.32902	−	1.32902i	0.906230	−	0.422786i	$-0.138948\pi$
$648$		0			0
$649$	1.76308	+	1.76308i	0.0692068	+	0.0692068i
$650$		0			0
$651$	27.8452	−	11.5338i	1.09134	−	0.452047i
$652$		0			0
$653$	12.1078	−	29.2307i	0.473813	−	1.14389i	−0.488652	−	0.872479i	$-0.662511\pi$
$653$	12.1078	−	29.2307i	0.473813	−	1.14389i	0.962465	−	0.271407i	$-0.0874889\pi$
$654$		0			0
$655$			63.9032i			2.49690i
$656$		0			0
$657$			6.18512i			0.241304i
$658$		0			0
$659$	−0.896470	+	2.16427i	−0.0349215	+	0.0843080i	−0.940378	−	0.340131i	$-0.889529\pi$
$659$	−0.896470	+	2.16427i	−0.0349215	+	0.0843080i	0.905457	+	0.424439i	$0.139529\pi$
$660$		0			0
$661$	24.9607	−	10.3391i	0.970859	−	0.402143i	0.159827	−	0.987145i	$-0.448906\pi$
$661$	24.9607	−	10.3391i	0.970859	−	0.402143i	0.811032	+	0.585002i	$0.198906\pi$
$662$		0			0
$663$	17.4728	+	17.4728i	0.678586	+	0.678586i
$664$		0			0
$665$	9.27732	−	9.27732i	0.359759	−	0.359759i
$666$		0			0
$667$	−0.0662948	−	0.160050i	−0.00256695	−	0.00619715i
$668$		0			0
$669$	−1.79112	−	0.741907i	−0.0692487	−	0.0286838i
$670$		0			0
$671$	1.38581			0.0534986
$672$		0			0
$673$	−29.0320			−1.11910			−0.559550	−	0.828797i	$-0.689026\pi$
$673$	−29.0320			−1.11910			−0.559550	+	0.828797i	$0.689026\pi$
$674$		0			0
$675$	−7.01532	−	2.90584i	−0.270020	−	0.111846i
$676$		0			0
$677$	−4.97128	−	12.0017i	−0.191062	−	0.461264i	0.799099	−	0.601200i	$-0.205310\pi$
$677$	−4.97128	−	12.0017i	−0.191062	−	0.461264i	−0.990161	+	0.139936i	$0.955310\pi$
$678$		0			0
$679$	25.3807	−	25.3807i	0.974023	−	0.974023i
$680$		0			0
$681$	15.1947	+	15.1947i	0.582264	+	0.582264i
$682$		0			0
$683$	31.6243	−	13.0992i	1.21007	−	0.501227i	0.315830	−	0.948816i	$-0.397717\pi$
$683$	31.6243	−	13.0992i	1.21007	−	0.501227i	0.894239	+	0.447589i	$0.147717\pi$
$684$		0			0
$685$	8.01980	−	19.3615i	0.306421	−	0.739765i
$686$		0			0
$687$		−	24.0739i		−	0.918478i
$688$		0			0
$689$		−	58.7582i		−	2.23851i
$690$		0			0
$691$	−4.38682	+	10.5907i	−0.166883	+	0.402890i	−0.985092	−	0.172031i	$-0.944967\pi$
$691$	−4.38682	+	10.5907i	−0.166883	+	0.402890i	0.818209	+	0.574921i	$0.194967\pi$
$692$		0			0
$693$	−1.47856	+	0.612439i	−0.0561658	+	0.0232646i
$694$		0			0
$695$	46.6356	+	46.6356i	1.76899	+	1.76899i
$696$		0			0
$697$	6.62079	−	6.62079i	0.250780	−	0.250780i
$698$		0			0
$699$	4.09395	+	9.88366i	0.154847	+	0.373834i
$700$		0			0
$701$	−1.31276	−	0.543761i	−0.0495821	−	0.0205376i	0.357755	−	0.933816i	$-0.383542\pi$
$701$	−1.31276	−	0.543761i	−0.0495821	−	0.0205376i	−0.407337	+	0.913278i	$0.633542\pi$
$702$		0			0
$703$	−7.35469			−0.277387
$704$		0			0
$705$	2.53967			0.0956496
$706$		0			0
$707$	−16.3107	−	6.75611i	−0.613427	−	0.254090i
$708$		0			0
$709$	−2.19698	−	5.30398i	−0.0825094	−	0.199195i	0.877241	−	0.480051i	$-0.159382\pi$
$709$	−2.19698	−	5.30398i	−0.0825094	−	0.199195i	−0.959750	+	0.280856i	$0.909382\pi$
$710$		0			0
$711$	−6.69594	+	6.69594i	−0.251117	+	0.251117i
$712$		0			0
$713$	6.33769	+	6.33769i	0.237348	+	0.237348i
$714$		0			0
$715$	7.75782	−	3.21340i	0.290126	−	0.120174i
$716$		0			0
$717$	−8.06142	+	19.4620i	−0.301059	+	0.726822i
$718$		0			0
$719$			7.05462i			0.263093i	0.991310	+	0.131547i	$0.0419943\pi$
$719$			7.05462i			0.263093i	−0.991310	+	0.131547i	$0.958006\pi$
$720$		0			0
$721$			14.8952i			0.554726i
$722$		0			0
$723$	9.25928	−	22.3539i	0.344356	−	0.831349i
$724$		0			0
$725$	−1.16266	+	0.481591i	−0.0431803	+	0.0178859i
$726$		0			0
$727$	−6.68778	−	6.68778i	−0.248036	−	0.248036i	0.572128	−	0.820164i	$-0.306118\pi$
$727$	−6.68778	−	6.68778i	−0.248036	−	0.248036i	−0.820164	+	0.572128i	$0.806118\pi$
$728$		0			0
$729$	−0.707107	+	0.707107i	−0.0261891	+	0.0261891i
$730$		0			0
$731$	5.61067	+	13.5453i	0.207518	+	0.500993i
$732$		0			0
$733$	1.39035	+	0.575901i	0.0513537	+	0.0212714i	0.408212	−	0.912887i	$-0.366152\pi$
$733$	1.39035	+	0.575901i	0.0513537	+	0.0212714i	−0.356859	+	0.934158i	$0.616152\pi$
$734$		0			0
$735$	19.0034			0.700950
$736$		0			0
$737$	−2.65818			−0.0979152
$738$		0			0
$739$	−4.78590	−	1.98239i	−0.176052	−	0.0729233i	0.292916	−	0.956138i	$-0.405374\pi$
$739$	−4.78590	−	1.98239i	−0.176052	−	0.0729233i	−0.468969	+	0.883215i	$0.655374\pi$
$740$		0			0
$741$	2.09189	+	5.05026i	0.0768474	+	0.185526i
$742$		0			0
$743$	5.78338	−	5.78338i	0.212172	−	0.212172i	−0.593018	−	0.805189i	$-0.702064\pi$
$743$	5.78338	−	5.78338i	0.212172	−	0.212172i	0.805189	+	0.593018i	$0.202064\pi$
$744$		0			0
$745$	−20.7943	−	20.7943i	−0.761844	−	0.761844i
$746$		0			0
$747$	6.88522	−	2.85195i	0.251917	−	0.104347i
$748$		0			0
$749$	0.612028	−	1.47757i	0.0223630	−	0.0539891i
$750$		0			0
$751$			16.4504i			0.600283i	0.953895	+	0.300141i	$0.0970338\pi$
$751$			16.4504i			0.600283i	−0.953895	+	0.300141i	$0.902966\pi$
$752$		0			0
$753$			0.184821i			0.00673524i
$754$		0			0
$755$	−16.0297	+	38.6991i	−0.583380	+	1.40840i
$756$		0			0
$757$	6.29845	−	2.60890i	0.228921	−	0.0948222i	−0.265275	−	0.964173i	$-0.585463\pi$
$757$	6.29845	−	2.60890i	0.228921	−	0.0948222i	0.494196	+	0.869351i	$0.335463\pi$
$758$		0			0
$759$	−0.336527	−	0.336527i	−0.0122151	−	0.0122151i
$760$		0			0
$761$	−8.75540	+	8.75540i	−0.317383	+	0.317383i	−0.847761	−	0.530378i	$-0.822050\pi$
$761$	−8.75540	+	8.75540i	−0.317383	+	0.317383i	0.530378	+	0.847761i	$0.322050\pi$
$762$		0			0
$763$	6.95890	+	16.8003i	0.251929	+	0.608211i
$764$		0			0
$765$	−15.5887	−	6.45704i	−0.563610	−	0.233455i
$766$		0			0
$767$	28.4602			1.02764
$768$		0			0
$769$	31.9426			1.15188			0.575940	−	0.817492i	$-0.304636\pi$
$769$	31.9426			1.15188			0.575940	+	0.817492i	$0.304636\pi$
$770$		0			0
$771$	−27.4817	−	11.3833i	−0.989729	−	0.409959i
$772$		0			0
$773$	11.4245	+	27.5812i	0.410911	+	0.992027i	0.984894	+	0.173159i	$0.0553976\pi$
$773$	11.4245	+	27.5812i	0.410911	+	0.992027i	−0.573983	+	0.818867i	$0.694602\pi$
$774$		0			0
$775$	46.0394	−	46.0394i	1.65379	−	1.65379i
$776$		0			0
$777$	−17.3790	−	17.3790i	−0.623468	−	0.623468i
$778$		0			0
$779$	1.91365	−	0.792659i	0.0685636	−	0.0284000i
$780$		0			0
$781$	2.03550	−	4.91414i	0.0728360	−	0.175842i
$782$		0			0
$783$			0.165732i			0.00592278i
$784$		0			0
$785$		−	4.34850i		−	0.155205i
$786$		0			0
$787$	4.33415	−	10.4636i	0.154496	−	0.372986i	−0.827613	−	0.561299i	$-0.810302\pi$
$787$	4.33415	−	10.4636i	0.154496	−	0.372986i	0.982109	+	0.188313i	$0.0603019\pi$
$788$		0			0
$789$	−0.276038	+	0.114338i	−0.00982720	+	0.00407056i
$790$		0			0
$791$	16.4909	+	16.4909i	0.586349	+	0.586349i
$792$		0			0
$793$	11.1851	−	11.1851i	0.397195	−	0.397195i
$794$		0			0
$795$	15.3541	+	37.0682i	0.544555	+	1.31467i
$796$		0			0
$797$	46.7451	+	19.3624i	1.65580	+	0.685853i	0.997745	−	0.0671211i	$-0.0213814\pi$
$797$	46.7451	+	19.3624i	1.65580	+	0.685853i	0.658050	+	0.752974i	$0.271381\pi$
$798$		0			0
$799$	3.40276			0.120381
$800$		0			0
$801$	12.1692			0.429978
$802$		0			0
$803$	2.60174	+	1.07768i	0.0918136	+	0.0380304i
$804$		0			0
$805$	4.98959	+	12.0459i	0.175860	+	0.424563i
$806$		0			0
$807$	−16.9715	+	16.9715i	−0.597426	+	0.597426i
$808$		0			0
$809$	−1.47101	−	1.47101i	−0.0517179	−	0.0517179i	0.680775	−	0.732493i	$-0.261643\pi$
$809$	−1.47101	−	1.47101i	−0.0517179	−	0.0517179i	−0.732493	+	0.680775i	$0.761643\pi$
$810$		0			0
$811$	−27.3097	+	11.3120i	−0.958972	+	0.397219i	−0.806596	−	0.591103i	$-0.798693\pi$
$811$	−27.3097	+	11.3120i	−0.958972	+	0.397219i	−0.152376	+	0.988323i	$0.548693\pi$
$812$		0			0
$813$	5.95314	−	14.3722i	0.208786	−	0.504054i
$814$		0			0
$815$		−	48.1041i		−	1.68501i
$816$		0			0
$817$			3.24337i			0.113471i
$818$		0			0
$819$	−6.99060	+	16.8768i	−0.244271	+	0.589723i
$820$		0			0
$821$	2.95519	−	1.22408i	0.103137	−	0.0427207i	−0.330518	−	0.943800i	$-0.607224\pi$
$821$	2.95519	−	1.22408i	0.103137	−	0.0427207i	0.433655	+	0.901079i	$0.357224\pi$
$822$		0			0
$823$	11.2350	+	11.2350i	0.391626	+	0.391626i	0.875267	−	0.483640i	$-0.160686\pi$
$823$	11.2350	+	11.2350i	0.391626	+	0.391626i	−0.483640	+	0.875267i	$0.660686\pi$
$824$		0			0
$825$	−2.44466	+	2.44466i	−0.0851122	+	0.0851122i
$826$		0			0
$827$	−16.2758	−	39.2934i	−0.565967	−	1.36636i	−0.904928	−	0.425564i	$-0.860076\pi$
$827$	−16.2758	−	39.2934i	−0.565967	−	1.36636i	0.338962	−	0.940800i	$-0.389924\pi$
$828$		0			0
$829$	−41.9981	−	17.3962i	−1.45866	−	0.604195i	−0.494416	−	0.869226i	$-0.664618\pi$
$829$	−41.9981	−	17.3962i	−1.45866	−	0.604195i	−0.964240	+	0.265031i	$0.914618\pi$
$830$		0			0
$831$	−26.1629			−0.907583
$832$		0			0
$833$	25.4615			0.882188
$834$		0			0
$835$	30.6285	+	12.6867i	1.05994	+	0.439043i
$836$		0			0
$837$	−3.28135	−	7.92188i	−0.113420	−	0.273820i
$838$		0			0
$839$	36.5559	−	36.5559i	1.26205	−	1.26205i	0.311954	−	0.950097i	$-0.399017\pi$
$839$	36.5559	−	36.5559i	1.26205	−	1.26205i	0.950097	−	0.311954i	$-0.100983\pi$
$840$		0			0
$841$	−20.4867	−	20.4867i	−0.706437	−	0.706437i
$842$		0			0
$843$	24.2137	−	10.0296i	0.833964	−	0.345439i
$844$		0			0
$845$	19.0245	−	45.9291i	0.654462	−	1.58001i
$846$		0			0
$847$		−	37.9360i		−	1.30350i
$848$		0			0
$849$		−	9.41220i		−	0.323026i
$850$		0			0
$851$	2.79699	−	6.75254i	0.0958796	−	0.231474i
$852$		0			0
$853$	−37.5279	+	15.5446i	−1.28493	+	0.532236i	−0.917471	−	0.397802i	$-0.869773\pi$
$853$	−37.5279	+	15.5446i	−1.28493	+	0.532236i	−0.367461	+	0.930039i	$0.619773\pi$
$854$		0			0
$855$	−2.63937	−	2.63937i	−0.0902647	−	0.0902647i
$856$		0			0
$857$	−14.0544	+	14.0544i	−0.480088	+	0.480088i	−0.905160	−	0.425072i	$-0.860249\pi$
$857$	−14.0544	+	14.0544i	−0.480088	+	0.480088i	0.425072	+	0.905160i	$0.360249\pi$
$858$		0			0
$859$	2.44981	+	5.91435i	0.0835863	+	0.201795i	0.960147	−	0.279497i	$-0.0901677\pi$
$859$	2.44981	+	5.91435i	0.0835863	+	0.201795i	−0.876560	+	0.481292i	$0.840168\pi$
$860$		0			0
$861$	6.39496	+	2.64888i	0.217940	+	0.0902736i
$862$		0			0
$863$	−49.2474			−1.67640			−0.838201	−	0.545361i	$-0.816392\pi$
$863$	−49.2474			−1.67640			−0.838201	+	0.545361i	$0.816392\pi$
$864$		0			0
$865$	66.2465			2.25245
$866$		0			0
$867$	−5.18038	−	2.14578i	−0.175935	−	0.0728746i
$868$		0			0
$869$	1.64994	+	3.98330i	0.0559703	+	0.135124i
$870$		0			0
$871$	−21.4546	+	21.4546i	−0.726962	+	0.726962i
$872$		0			0
$873$	−7.22075	−	7.22075i	−0.244385	−	0.244385i
$874$		0			0
$875$	29.8858	−	12.3791i	1.01033	−	0.418490i
$876$		0			0
$877$	−3.14641	+	7.59609i	−0.106247	+	0.256502i	−0.968058	−	0.250727i	$-0.919330\pi$
$877$	−3.14641	+	7.59609i	−0.106247	+	0.256502i	0.861811	+	0.507229i	$0.169330\pi$
$878$		0			0
$879$		−	21.7460i		−	0.733474i
$880$		0			0
$881$			0.591830i			0.0199392i	0.999950	+	0.00996962i	$0.00317348\pi$
$881$			0.591830i			0.0199392i	−0.999950	+	0.00996962i	$0.996827\pi$
$882$		0			0
$883$	−12.2234	+	29.5100i	−0.411352	+	0.993091i	0.573424	+	0.819259i	$0.305615\pi$
$883$	−12.2234	+	29.5100i	−0.411352	+	0.993091i	−0.984775	+	0.173832i	$0.944385\pi$
$884$		0			0
$885$	−17.9544	+	7.43695i	−0.603530	+	0.249990i
$886$		0			0
$887$	−19.3889	−	19.3889i	−0.651017	−	0.651017i	0.302221	−	0.953238i	$-0.402272\pi$
$887$	−19.3889	−	19.3889i	−0.651017	−	0.651017i	−0.953238	+	0.302221i	$0.902272\pi$
$888$		0			0
$889$	−47.6312	+	47.6312i	−1.59750	+	1.59750i
$890$		0			0
$891$	0.174237	+	0.420646i	0.00583717	+	0.0140922i
$892$		0			0
$893$	0.695454	+	0.288067i	0.0232725	+	0.00963978i
$894$		0			0
$895$	35.2994			1.17993
$896$		0			0
$897$	−5.43233			−0.181380
$898$		0			0
$899$	−1.31291	−	0.543825i	−0.0437880	−	0.0181376i
$900$		0			0
$901$	20.5721	+	49.6654i	0.685356	+	1.65460i
$902$		0			0
$903$	−7.66404	+	7.66404i	−0.255043	+	0.255043i
$904$		0			0
$905$	15.1005	+	15.1005i	0.501959	+	0.501959i
$906$		0			0
$907$	−7.79114	+	3.22719i	−0.258700	+	0.107157i	−0.508264	−	0.861201i	$-0.669713\pi$
$907$	−7.79114	+	3.22719i	−0.258700	+	0.107157i	0.249564	+	0.968358i	$0.419713\pi$
$908$		0			0
$909$	−1.92210	+	4.64035i	−0.0637519	+	0.153911i
$910$		0			0
$911$			32.8156i			1.08723i	0.839335	+	0.543615i	$0.182945\pi$
$911$			32.8156i			1.08723i	−0.839335	+	0.543615i	$0.817055\pi$
$912$		0			0
$913$		−	3.39315i		−	0.112297i
$914$		0			0
$915$	−4.13345	+	9.97903i	−0.136648	+	0.329896i
$916$		0			0
$917$	−58.4776	+	24.2222i	−1.93110	+	0.799887i
$918$		0			0
$919$	3.20080	+	3.20080i	0.105584	+	0.105584i	0.757926	−	0.652341i	$-0.226213\pi$
$919$	3.20080	+	3.20080i	0.105584	+	0.105584i	−0.652341	+	0.757926i	$0.726213\pi$
$920$		0			0
$921$	21.7574	−	21.7574i	0.716930	−	0.716930i
$922$		0			0
$923$	−23.2340	−	56.0918i	−0.764756	−	1.84628i
$924$		0			0
$925$	−49.0531	−	20.3184i	−1.61285	−	0.668066i
$926$		0			0
$927$	4.23764			0.139182
$928$		0			0
$929$	−5.46430			−0.179278			−0.0896389	−	0.995974i	$-0.528571\pi$
$929$	−5.46430			−0.179278			−0.0896389	+	0.995974i	$0.528571\pi$
$930$		0			0
$931$	5.20381	+	2.15549i	0.170548	+	0.0706433i
$932$		0			0
$933$	0.587233	+	1.41771i	0.0192251	+	0.0464136i
$934$		0			0
$935$	−5.43225	+	5.43225i	−0.177654	+	0.177654i
$936$		0			0
$937$	−20.1655	−	20.1655i	−0.658779	−	0.658779i	0.296312	−	0.955091i	$-0.404243\pi$
$937$	−20.1655	−	20.1655i	−0.658779	−	0.658779i	−0.955091	+	0.296312i	$0.904243\pi$
$938$		0			0
$939$	4.50160	−	1.86462i	0.146904	−	0.0608497i
$940$		0			0
$941$	10.4612	−	25.2557i	0.341027	−	0.823311i	−0.656586	−	0.754251i	$-0.728000\pi$
$941$	10.4612	−	25.2557i	0.341027	−	0.823311i	0.997613	−	0.0690598i	$-0.0219999\pi$
$942$		0			0
$943$			2.05842i			0.0670314i
$944$		0			0
$945$		−	12.4736i		−	0.405766i
$946$		0			0
$947$	7.10795	−	17.1601i	0.230977	−	0.557628i	−0.765316	−	0.643655i	$-0.777417\pi$
$947$	7.10795	−	17.1601i	0.230977	−	0.557628i	0.996293	+	0.0860269i	$0.0274171\pi$
$948$		0			0
$949$	29.6973	−	12.3010i	0.964014	−	0.399308i
$950$		0			0
$951$	−1.43303	−	1.43303i	−0.0464690	−	0.0464690i
$952$		0			0
$953$	−8.36834	+	8.36834i	−0.271077	+	0.271077i	−0.829534	−	0.558457i	$-0.811394\pi$
$953$	−8.36834	+	8.36834i	−0.271077	+	0.271077i	0.558457	+	0.829534i	$0.311394\pi$
$954$		0			0
$955$	−7.81120	−	18.8579i	−0.252765	−	0.610228i
$956$		0			0
$957$	0.0697145	+	0.0288767i	0.00225355	+	0.000933451i
$958$		0			0
$959$	20.7575			0.670294
$960$		0			0
$961$	42.5234			1.37172
$962$		0			0
$963$	−0.420364	−	0.174120i	−0.0135460	−	0.00561095i
$964$		0			0
$965$	−2.75542	−	6.65217i	−0.0887001	−	0.214141i
$966$		0			0
$967$	−15.9921	+	15.9921i	−0.514273	+	0.514273i	−0.915833	−	0.401560i	$-0.868468\pi$
$967$	−15.9921	+	15.9921i	−0.514273	+	0.514273i	0.401560	+	0.915833i	$0.368468\pi$
$968$		0			0
$969$	−3.53634	−	3.53634i	−0.113604	−	0.113604i
$970$		0			0
$971$	−30.0555	+	12.4494i	−0.964528	+	0.399521i	−0.808673	−	0.588259i	$-0.799814\pi$
$971$	−30.0555	+	12.4494i	−0.964528	+	0.399521i	−0.155856	+	0.987780i	$0.549814\pi$
$972$		0			0
$973$	−24.9990	+	60.3530i	−0.801433	+	1.93483i
$974$		0			0
$975$			39.4626i			1.26381i
$976$		0			0
$977$		−	25.2550i		−	0.807979i	−0.914764	−	0.403989i	$-0.867623\pi$
$977$		−	25.2550i		−	0.807979i	0.914764	−	0.403989i	$-0.132377\pi$
$978$		0			0
$979$	2.12033	−	5.11892i	0.0677660	−	0.163602i
$980$		0			0
$981$	4.77963	−	1.97979i	0.152602	−	0.0632098i
$982$		0			0
$983$	−37.2730	−	37.2730i	−1.18882	−	1.18882i	−0.977393	−	0.211432i	$-0.932187\pi$
$983$	−37.2730	−	37.2730i	−1.18882	−	1.18882i	−0.211432	−	0.977393i	$-0.567813\pi$
$984$		0			0
$985$	23.2707	−	23.2707i	0.741467	−	0.741467i
$986$		0			0
$987$	0.962650	+	2.32404i	0.0306415	+	0.0739751i
$988$		0			0
$989$	−2.97783	−	1.23346i	−0.0946895	−	0.0392217i
$990$		0			0
$991$	21.7711			0.691581			0.345791	−	0.938312i	$-0.387611\pi$
$991$	21.7711			0.691581			0.345791	+	0.938312i	$0.387611\pi$
$992$		0			0
$993$	−29.6265			−0.940167
$994$		0			0
$995$	−59.0969	−	24.4787i	−1.87350	−	0.776028i
$996$		0			0
$997$	−7.63502	−	18.4326i	−0.241803	−	0.583765i	0.755659	−	0.654966i	$-0.227317\pi$
$997$	−7.63502	−	18.4326i	−0.241803	−	0.583765i	−0.997462	+	0.0712005i	$0.977317\pi$
$998$		0			0
$999$	−4.94428	+	4.94428i	−0.156430	+	0.156430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.n.b.673.8		32
4.3	odd	2		768.2.n.a.673.4		32
8.3	odd	2		96.2.n.a.61.4	✓	32
8.5	even	2		384.2.n.a.337.1		32
24.5	odd	2		1152.2.v.c.721.7		32
24.11	even	2		288.2.v.d.253.5		32
32.5	even	8		384.2.n.a.49.1		32
32.11	odd	8		768.2.n.a.97.4		32
32.21	even	8	inner	768.2.n.b.97.8		32
32.27	odd	8		96.2.n.a.85.4	yes	32
96.5	odd	8		1152.2.v.c.433.7		32
96.59	even	8		288.2.v.d.181.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.61.4	✓	32	8.3	odd	2
96.2.n.a.85.4	yes	32	32.27	odd	8
288.2.v.d.181.5		32	96.59	even	8
288.2.v.d.253.5		32	24.11	even	2
384.2.n.a.49.1		32	32.5	even	8
384.2.n.a.337.1		32	8.5	even	2
768.2.n.a.97.4		32	32.11	odd	8
768.2.n.a.673.4		32	4.3	odd	2
768.2.n.b.97.8		32	32.21	even	8	inner
768.2.n.b.673.8		32	1.1	even	1	trivial
1152.2.v.c.433.7		32	96.5	odd	8
1152.2.v.c.721.7		32	24.5	odd	2

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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.923880 + 0.382683i) q^{3} +(1.35803 + 3.27858i) q^{5} +(-2.48546 + 2.48546i) q^{7} +(0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(0.923880 + 0.382683i) q^{3} +(1.35803 + 3.27858i) q^{5} +(-2.48546 + 2.48546i) q^{7} +(0.707107 + 0.707107i) q^{9} +(0.420646 - 0.174237i) q^{11} +(1.98881 - 4.80141i) q^{13} +3.54871i q^{15} +4.75470i q^{17} +(-0.402518 + 0.971765i) q^{19} +(-3.24741 + 1.34512i) q^{21} +(-0.739125 - 0.739125i) q^{23} +(-5.36930 + 5.36930i) q^{25} +(0.382683 + 0.923880i) q^{27} +(0.153117 + 0.0634229i) q^{29} -8.57458 q^{31} +0.455304 q^{33} +(-11.5241 - 4.77344i) q^{35} +(2.67583 + 6.46002i) q^{37} +(3.67484 - 3.67484i) q^{39} +(-1.39247 - 1.39247i) q^{41} +(2.84883 - 1.18002i) q^{43} +(-1.35803 + 3.27858i) q^{45} -0.715661i q^{47} -5.35501i q^{49} +(-1.81955 + 4.39277i) q^{51} +(10.4455 - 4.32668i) q^{53} +(1.14250 + 1.14250i) q^{55} +(-0.743756 + 0.743756i) q^{57} +(2.09568 + 5.05941i) q^{59} +(2.81202 + 1.16478i) q^{61} -3.51497 q^{63} +18.4427 q^{65} +(-5.39384 - 2.23420i) q^{67} +(-0.400012 - 0.965714i) q^{69} +(8.26068 - 8.26068i) q^{71} +(4.37354 + 4.37354i) q^{73} +(-7.01532 + 2.90584i) q^{75} +(-0.612439 + 1.47856i) q^{77} +9.46948i q^{79} +1.00000i q^{81} +(2.85195 - 6.88522i) q^{83} +(-15.5887 + 6.45704i) q^{85} +(0.117190 + 0.117190i) q^{87} +(8.60493 - 8.60493i) q^{89} +(6.99060 + 16.8768i) q^{91} +(-7.92188 - 3.28135i) q^{93} -3.73264 q^{95} -10.2117 q^{97} +(0.420646 + 0.174237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 16 q^{23} + 48 q^{31} - 48 q^{35} - 16 q^{43} + 16 q^{51} + 32 q^{53} - 32 q^{55} + 64 q^{59} + 32 q^{61} - 16 q^{63} + 16 q^{67} + 32 q^{69} - 64 q^{71} + 32 q^{75} + 32 q^{77} - 48 q^{91}+O(q^{100}) \) 32 * q + 16 * q^23 + 48 * q^31 - 48 * q^35 - 16 * q^43 + 16 * q^51 + 32 * q^53 - 32 * q^55 + 64 * q^59 + 32 * q^61 - 16 * q^63 + 16 * q^67 + 32 * q^69 - 64 * q^71 + 32 * q^75 + 32 * q^77 - 48 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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