LMFDB - Embedded newform 804.2.ba.b.353.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(41,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 33, 53]))

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

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

chi := DirichletCharacter("804.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.ba (of order $66$, degree $20$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			353.5
Character	$\chi$	$=$	804.353
Dual form			804.2.ba.b.41.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32247 + 1.11851i) q^{3} +(0.102406 + 0.712247i) q^{5} +(0.0729329 - 0.763788i) q^{7} +(0.497878 - 2.95840i) q^{9} +O(q^{10})$	\(q+(-1.32247 + 1.11851i) q^{3} +(0.102406 + 0.712247i) q^{5} +(0.0729329 - 0.763788i) q^{7} +(0.497878 - 2.95840i) q^{9} +(-0.457848 - 0.183294i) q^{11} +(3.42746 - 3.59462i) q^{13} +(-0.932083 - 0.827387i) q^{15} +(-6.00843 - 2.07954i) q^{17} +(1.10984 - 0.105977i) q^{19} +(0.757851 + 1.09167i) q^{21} +(7.01892 + 0.334352i) q^{23} +(4.30066 - 1.26279i) q^{25} +(2.65056 + 4.46929i) q^{27} +(-7.80897 - 4.50851i) q^{29} +(2.71627 + 2.84874i) q^{31} +(0.810508 - 0.269704i) q^{33} +(0.551474 - 0.0262700i) q^{35} +(0.597753 + 1.03534i) q^{37} +(-0.512121 + 8.58744i) q^{39} +(8.84237 - 1.70423i) q^{41} +(3.66095 - 3.17223i) q^{43} +(2.15810 + 0.0516556i) q^{45} +(2.65699 + 5.15385i) q^{47} +(6.29545 + 1.21335i) q^{49} +(10.2720 - 3.97034i) q^{51} +(1.01898 - 1.17596i) q^{53} +(0.0836648 - 0.344871i) q^{55} +(-1.34920 + 1.38152i) q^{57} +(1.87800 - 6.39587i) q^{59} +(-2.71070 - 6.77100i) q^{61} +(-2.22328 - 0.596038i) q^{63} +(2.91125 + 2.07309i) q^{65} +(-0.562265 + 8.16602i) q^{67} +(-9.65632 + 7.40855i) q^{69} +(-8.12417 + 2.81180i) q^{71} +(10.8460 - 4.34209i) q^{73} +(-4.27507 + 6.48032i) q^{75} +(-0.173390 + 0.336330i) q^{77} +(7.69406 + 1.86656i) q^{79} +(-8.50423 - 2.94584i) q^{81} +(-9.04632 - 11.5033i) q^{83} +(0.865847 - 4.49244i) q^{85} +(15.3700 - 2.77201i) q^{87} +(2.00976 + 3.12725i) q^{89} +(-2.49555 - 2.88002i) q^{91} +(-6.77854 - 0.729218i) q^{93} +(0.189136 + 0.779630i) q^{95} +(1.81643 - 1.04871i) q^{97} +(-0.770210 + 1.26324i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) $ 440 * q - 12 * q^7 + 4 * q^9	$ 440 q - 12 q^{7} + 4 q^{9} - 2 q^{15} - 10 q^{19} + 22 q^{21} - 68 q^{25} + 50 q^{31} + 11 q^{33} - 22 q^{37} - 45 q^{39} + 22 q^{43} + 22 q^{45} - 18 q^{49} - 6 q^{51} + 126 q^{55} - 183 q^{57} - 56 q^{61} - 141 q^{63} - 12 q^{67} + 33 q^{69} + 356 q^{73} + 165 q^{75} + 228 q^{79} + 24 q^{81} - 6 q^{85} + 75 q^{87} - 4 q^{91} - 75 q^{93} + 12 q^{97} + 88 q^{99}+O(q^{100}) $ 440 * q - 12 * q^7 + 4 * q^9 - 2 * q^15 - 10 * q^19 + 22 * q^21 - 68 * q^25 + 50 * q^31 + 11 * q^33 - 22 * q^37 - 45 * q^39 + 22 * q^43 + 22 * q^45 - 18 * q^49 - 6 * q^51 + 126 * q^55 - 183 * q^57 - 56 * q^61 - 141 * q^63 - 12 * q^67 + 33 * q^69 + 356 * q^73 + 165 * q^75 + 228 * q^79 + 24 * q^81 - 6 * q^85 + 75 * q^87 - 4 * q^91 - 75 * q^93 + 12 * q^97 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{13}{66}\right)$	$1$

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
$3$	−1.32247	+	1.11851i	−0.763531	+	0.645771i
$3$	−1.32247	+	1.11851i	−0.763531	+	0.645771i
$4$		0			0
$5$	0.102406	+	0.712247i	0.0457972	+	0.318527i	0.999823	+	0.0188027i	$0.00598544\pi$
$5$	0.102406	+	0.712247i	0.0457972	+	0.318527i	−0.954026	+	0.299724i	$0.903105\pi$
$6$		0			0
$7$	0.0729329	−	0.763788i	0.0275660	−	0.288685i	−0.971169	−	0.238394i	$-0.923379\pi$
$7$	0.0729329	−	0.763788i	0.0275660	−	0.288685i	0.998735	−	0.0502909i	$-0.0160148\pi$
$8$		0			0
$9$	0.497878	−	2.95840i	0.165959	−	0.986133i
$10$		0			0
$11$	−0.457848	−	0.183294i	−0.138046	−	0.0552654i	0.301611	−	0.953431i	$-0.402476\pi$
$11$	−0.457848	−	0.183294i	−0.138046	−	0.0552654i	−0.439657	+	0.898166i	$0.644900\pi$
$12$		0			0
$13$	3.42746	−	3.59462i	0.950607	−	0.996968i	−0.0493912	−	0.998780i	$-0.515728\pi$
$13$	3.42746	−	3.59462i	0.950607	−	0.996968i	0.999998	+	0.00181138i	$0.000576581\pi$
$14$		0			0
$15$	−0.932083	−	0.827387i	−0.240663	−	0.213630i
$16$		0			0
$17$	−6.00843	−	2.07954i	−1.45726	−	0.504362i	−0.520354	−	0.853951i	$-0.674200\pi$
$17$	−6.00843	−	2.07954i	−1.45726	−	0.504362i	−0.936903	+	0.349589i	$0.886321\pi$
$18$		0			0
$19$	1.10984	−	0.105977i	0.254616	−	0.0243128i	0.0330323	−	0.999454i	$-0.489484\pi$
$19$	1.10984	−	0.105977i	0.254616	−	0.0243128i	0.221583	+	0.975141i	$0.428878\pi$
$20$		0			0
$21$	0.757851	+	1.09167i	0.165377	+	0.238221i
$22$		0			0
$23$	7.01892	+	0.334352i	1.46355	+	0.0697173i	0.764160	−	0.645027i	$-0.223154\pi$
$23$	7.01892	+	0.334352i	1.46355	+	0.0697173i	0.699386	+	0.714744i	$0.253457\pi$
$24$		0			0
$25$	4.30066	−	1.26279i	0.860131	−	0.252557i
$26$		0			0
$27$	2.65056	+	4.46929i	0.510101	+	0.860115i
$28$		0			0
$29$	−7.80897	−	4.50851i	−1.45009	−	0.837210i	−0.451604	−	0.892219i	$-0.649148\pi$
$29$	−7.80897	−	4.50851i	−1.45009	−	0.837210i	−0.998486	+	0.0550091i	$0.982481\pi$
$30$		0			0
$31$	2.71627	+	2.84874i	0.487857	+	0.511649i	0.920940	−	0.389705i	$-0.127423\pi$
$31$	2.71627	+	2.84874i	0.487857	+	0.511649i	−0.433083	+	0.901354i	$0.642574\pi$
$32$		0			0
$33$	0.810508	−	0.269704i	0.141091	−	0.0469494i
$34$		0			0
$35$	0.551474	−	0.0262700i	0.0932162	−	0.00444043i
$36$		0			0
$37$	0.597753	+	1.03534i	0.0982700	+	0.170209i	0.910969	−	0.412476i	$-0.135336\pi$
$37$	0.597753	+	1.03534i	0.0982700	+	0.170209i	−0.812699	+	0.582684i	$0.802002\pi$
$38$		0			0
$39$	−0.512121	+	8.58744i	−0.0820049	+	1.37509i
$40$		0			0
$41$	8.84237	−	1.70423i	1.38095	−	0.266156i	0.555913	−	0.831240i	$-0.312369\pi$
$41$	8.84237	−	1.70423i	1.38095	−	0.266156i	0.825033	+	0.565085i	$0.191157\pi$
$42$		0			0
$43$	3.66095	−	3.17223i	0.558289	−	0.483761i	−0.329408	−	0.944188i	$-0.606849\pi$
$43$	3.66095	−	3.17223i	0.558289	−	0.483761i	0.887698	+	0.460427i	$0.152304\pi$
$44$		0			0
$45$	2.15810	+	0.0516556i	0.321710	+	0.00770036i
$46$		0			0
$47$	2.65699	+	5.15385i	0.387562	+	0.751766i	0.999225	−	0.0393523i	$-0.0125295\pi$
$47$	2.65699	+	5.15385i	0.387562	+	0.751766i	−0.611663	+	0.791118i	$0.709499\pi$
$48$		0			0
$49$	6.29545	+	1.21335i	0.899350	+	0.173335i
$50$		0			0
$51$	10.2720	−	3.97034i	1.43836	−	0.555959i
$52$		0			0
$53$	1.01898	−	1.17596i	0.139967	−	0.161531i	−0.681438	−	0.731876i	$-0.738645\pi$
$53$	1.01898	−	1.17596i	0.139967	−	0.161531i	0.821405	+	0.570345i	$0.193191\pi$
$54$		0			0
$55$	0.0836648	−	0.344871i	0.0112814	−	0.0465024i
$56$		0			0
$57$	−1.34920	+	1.38152i	−0.178706	+	0.182987i
$58$		0			0
$59$	1.87800	−	6.39587i	0.244495	−	0.832672i	−0.742213	−	0.670164i	$-0.766224\pi$
$59$	1.87800	−	6.39587i	0.244495	−	0.832672i	0.986707	−	0.162508i	$-0.0519582\pi$
$60$		0			0
$61$	−2.71070	−	6.77100i	−0.347070	−	0.866938i	−0.994493	−	0.104807i	$-0.966578\pi$
$61$	−2.71070	−	6.77100i	−0.347070	−	0.866938i	0.647423	−	0.762131i	$-0.275847\pi$
$62$		0			0
$63$	−2.22328	−	0.596038i	−0.280107	−	0.0750937i
$64$		0			0
$65$	2.91125	+	2.07309i	0.361096	+	0.257135i
$66$		0			0
$67$	−0.562265	+	8.16602i	−0.0686916	+	0.997638i
$67$	−0.562265	+	8.16602i	−0.0686916	+	0.997638i
$68$		0			0
$69$	−9.65632	+	7.40855i	−1.16248	+	0.891884i
$70$		0			0
$71$	−8.12417	+	2.81180i	−0.964162	+	0.333700i	−0.763390	−	0.645938i	$-0.776466\pi$
$71$	−8.12417	+	2.81180i	−0.964162	+	0.333700i	−0.200772	+	0.979638i	$0.564345\pi$
$72$		0			0
$73$	10.8460	−	4.34209i	1.26943	−	0.508203i	0.363486	−	0.931600i	$-0.381586\pi$
$73$	10.8460	−	4.34209i	1.26943	−	0.508203i	0.905945	+	0.423396i	$0.139162\pi$
$74$		0			0
$75$	−4.27507	+	6.48032i	−0.493643	+	0.748283i
$76$		0			0
$77$	−0.173390	+	0.336330i	−0.0197597	+	0.0383284i
$78$		0			0
$79$	7.69406	+	1.86656i	0.865649	+	0.210004i	0.643909	−	0.765102i	$-0.277311\pi$
$79$	7.69406	+	1.86656i	0.865649	+	0.210004i	0.221740	+	0.975106i	$0.428826\pi$
$80$		0			0
$81$	−8.50423	−	2.94584i	−0.944915	−	0.327316i
$82$		0			0
$83$	−9.04632	−	11.5033i	−0.992963	−	1.26265i	−0.964782	−	0.263052i	$-0.915271\pi$
$83$	−9.04632	−	11.5033i	−0.992963	−	1.26265i	−0.0281811	−	0.999603i	$-0.508972\pi$
$84$		0			0
$85$	0.865847	−	4.49244i	0.0939143	−	0.487273i
$86$		0			0
$87$	15.3700	−	2.77201i	1.64783	−	0.297190i
$88$		0			0
$89$	2.00976	+	3.12725i	0.213034	+	0.331487i	0.931282	−	0.364300i	$-0.118692\pi$
$89$	2.00976	+	3.12725i	0.213034	+	0.331487i	−0.718248	+	0.695788i	$0.755055\pi$
$90$		0			0
$91$	−2.49555	−	2.88002i	−0.261605	−	0.301908i
$92$		0			0
$93$	−6.77854	−	0.729218i	−0.702902	−	0.0756164i
$94$		0			0
$95$	0.189136	+	0.779630i	0.0194050	+	0.0799884i
$96$		0			0
$97$	1.81643	−	1.04871i	0.184430	−	0.106481i	−0.404942	−	0.914342i	$-0.632708\pi$
$97$	1.81643	−	1.04871i	0.184430	−	0.106481i	0.589372	+	0.807861i	$0.299375\pi$
$98$		0			0
$99$	−0.770210	+	1.26324i	−0.0774090	+	0.126960i
$100$		0			0
$101$	9.01742	+	12.6632i	0.897267	+	1.26004i	0.964978	+	0.262330i	$0.0844909\pi$
$101$	9.01742	+	12.6632i	0.897267	+	1.26004i	−0.0677112	+	0.997705i	$0.521570\pi$
$102$		0			0
$103$	0.855334	−	0.815559i	0.0842786	−	0.0803594i	−0.646769	−	0.762686i	$-0.723880\pi$
$103$	0.855334	−	0.815559i	0.0842786	−	0.0803594i	0.731048	+	0.682326i	$0.239032\pi$
$104$		0			0
$105$	−0.699928	+	0.651570i	−0.0683059	+	0.0635867i
$106$		0			0
$107$	14.7662	+	2.12306i	1.42750	+	0.205244i	0.812352	−	0.583168i	$-0.198187\pi$
$107$	14.7662	+	2.12306i	1.42750	+	0.205244i	0.615149	+	0.788411i	$0.289096\pi$
$108$		0			0
$109$	−5.42033	−	18.4599i	−0.519173	−	1.76814i	−0.632475	−	0.774581i	$-0.717961\pi$
$109$	−5.42033	−	18.4599i	−0.519173	−	1.76814i	0.113302	−	0.993561i	$-0.463857\pi$
$110$		0			0
$111$	−1.94855	−	0.700617i	−0.184948	−	0.0664997i
$112$		0			0
$113$	−13.0375	−	10.2528i	−1.22646	−	0.964499i	−0.226505	−	0.974010i	$-0.572730\pi$
$113$	−13.0375	−	10.2528i	−1.22646	−	0.964499i	−0.999955	+	0.00951088i	$0.996973\pi$
$114$		0			0
$115$	0.480636	+	5.03344i	0.0448195	+	0.469371i
$116$		0			0
$117$	−8.92786	−	11.9295i	−0.825381	−	1.10288i
$118$		0			0
$119$	−2.02654	+	4.43750i	−0.185772	+	0.406785i
$120$		0			0
$121$	−7.78505	−	7.42303i	−0.707732	−	0.674821i
$122$		0			0
$123$	−9.78762	+	12.1441i	−0.882520	+	1.09499i
$124$		0			0
$125$	2.83443	+	6.20654i	0.253519	+	0.555130i
$126$		0			0
$127$	−8.51309	−	0.812901i	−0.755414	−	0.0721333i	−0.289759	−	0.957100i	$-0.593575\pi$
$127$	−8.51309	−	0.812901i	−0.755414	−	0.0721333i	−0.465655	+	0.884966i	$0.654181\pi$
$128$		0			0
$129$	−1.29335	+	8.29000i	−0.113873	+	0.729893i
$130$		0			0
$131$	−10.2167	+	15.8976i	−0.892640	+	1.38898i	0.0284368	+	0.999596i	$0.490947\pi$
$131$	−10.2167	+	15.8976i	−0.892640	+	1.38898i	−0.921077	+	0.389380i	$0.872689\pi$
$132$		0			0
$133$		−	0.855415i		−	0.0741739i
$134$		0			0
$135$	−2.91180	+	2.34553i	−0.250608	+	0.201871i
$136$		0			0
$137$	−5.35826	−	3.44355i	−0.457787	−	0.294202i	0.291350	−	0.956616i	$-0.405895\pi$
$137$	−5.35826	−	3.44355i	−0.457787	−	0.294202i	−0.749138	+	0.662414i	$0.769532\pi$
$138$		0			0
$139$	−13.1584	+	1.89189i	−1.11608	+	0.160468i	−0.675581	−	0.737286i	$-0.736107\pi$
$139$	−13.1584	+	1.89189i	−1.11608	+	0.160468i	−0.440498	+	0.897754i	$0.645198\pi$
$140$		0			0
$141$	−9.27843	−	3.84396i	−0.781385	−	0.323720i
$142$		0			0
$143$	−2.22813	+	1.01755i	−0.186326	+	0.0850920i
$144$		0			0
$145$	2.41149	−	6.02361i	0.200263	−	0.500234i
$146$		0			0
$147$	−9.68271	+	5.43689i	−0.798616	+	0.448427i
$148$		0			0
$149$	−0.935127	−	0.427058i	−0.0766086	−	0.0349860i	0.376742	−	0.926318i	$-0.377044\pi$
$149$	−0.935127	−	0.427058i	−0.0766086	−	0.0349860i	−0.453351	+	0.891332i	$0.649772\pi$
$150$		0			0
$151$	2.20202	−	6.36232i	0.179198	−	0.517758i	−0.819251	−	0.573435i	$-0.805610\pi$
$151$	2.20202	−	6.36232i	0.179198	−	0.517758i	0.998449	+	0.0556768i	$0.0177316\pi$
$152$		0			0
$153$	−9.14356	+	16.7400i	−0.739213	+	1.35335i
$154$		0			0
$155$	−1.75085	+	2.22638i	−0.140631	+	0.178827i
$156$		0			0
$157$	0.123241	−	2.58715i	0.00983570	−	0.206477i	−0.988600	−	0.150565i	$-0.951891\pi$
$157$	0.123241	−	2.58715i	0.00983570	−	0.206477i	0.998436	−	0.0559113i	$-0.0178064\pi$
$158$		0			0
$159$	−0.0322477	+	2.69491i	−0.00255741	+	0.213720i
$160$		0			0
$161$	0.767285	−	5.33658i	0.0604705	−	0.420582i
$162$		0			0
$163$	−2.86411	+	4.96079i	−0.224335	+	0.388559i	−0.956120	−	0.292977i	$-0.905354\pi$
$163$	−2.86411	+	4.96079i	−0.224335	+	0.388559i	0.731785	+	0.681536i	$0.238688\pi$
$164$		0			0
$165$	0.275096	+	0.549663i	0.0214162	+	0.0427912i
$166$		0			0
$167$	13.2822	−	9.45824i	1.02781	−	0.731901i	0.0638540	−	0.997959i	$-0.479661\pi$
$167$	13.2822	−	9.45824i	1.02781	−	0.731901i	0.963957	+	0.266058i	$0.0857214\pi$
$168$		0			0
$169$	−0.555224	−	11.6556i	−0.0427095	−	0.896583i
$170$		0			0
$171$	0.239044	−	3.33612i	0.0182802	−	0.255120i
$172$		0			0
$173$	9.36076	−	2.27090i	0.711685	−	0.172653i	0.136457	−	0.990646i	$-0.456428\pi$
$173$	9.36076	−	2.27090i	0.711685	−	0.172653i	0.575228	+	0.817993i	$0.304913\pi$
$174$		0			0
$175$	−0.650842	−	3.37689i	−0.0491990	−	0.255269i
$176$		0			0
$177$	4.67023	+	10.5589i	0.351036	+	0.793658i
$178$		0			0
$179$	4.29867	−	2.76259i	0.321298	−	0.206486i	−0.370043	−	0.929015i	$-0.620657\pi$
$179$	4.29867	−	2.76259i	0.321298	−	0.206486i	0.691340	+	0.722529i	$0.257021\pi$
$180$		0			0
$181$	−22.5091	+	11.6043i	−1.67309	+	0.862537i	−0.681693	+	0.731638i	$0.738756\pi$
$181$	−22.5091	+	11.6043i	−1.67309	+	0.862537i	−0.991396	+	0.130899i	$0.958214\pi$
$182$		0			0
$183$	11.1583	+	5.92254i	0.824842	+	0.437806i
$184$		0			0
$185$	−0.676204	+	0.531772i	−0.0497155	+	0.0390967i
$186$		0			0
$187$	2.36978	+	2.05342i	0.173295	+	0.150161i
$188$		0			0
$189$	3.60690	−	1.69851i	0.262363	−	0.123548i
$190$		0			0
$191$	−12.7980	−	6.59782i	−0.926030	−	0.477402i	−0.0718711	−	0.997414i	$-0.522897\pi$
$191$	−12.7980	−	6.59782i	−0.926030	−	0.477402i	−0.854159	+	0.520012i	$0.825927\pi$
$192$		0			0
$193$	6.27247	+	1.84176i	0.451502	+	0.132573i	0.499575	−	0.866271i	$-0.333490\pi$
$193$	6.27247	+	1.84176i	0.451502	+	0.132573i	−0.0480724	+	0.998844i	$0.515308\pi$
$194$		0			0
$195$	−6.16882	+	0.514646i	−0.441758	+	0.0368546i
$196$		0			0
$197$	3.40216	+	9.82990i	0.242394	+	0.700351i	0.998923	+	0.0463916i	$0.0147722\pi$
$197$	3.40216	+	9.82990i	0.242394	+	0.700351i	−0.756529	+	0.653960i	$0.773107\pi$
$198$		0			0
$199$	−5.47924	+	7.69451i	−0.388413	+	0.545449i	−0.961771	−	0.273856i	$-0.911701\pi$
$199$	−5.47924	+	7.69451i	−0.388413	+	0.545449i	0.573358	+	0.819305i	$0.305640\pi$
$200$		0			0
$201$	−8.39018	−	11.4282i	−0.591798	−	0.806087i
$202$		0			0
$203$	−4.01308	+	5.63558i	−0.281663	+	0.395540i
$204$		0			0
$205$	2.11934	+	6.12343i	0.148021	+	0.427679i
$206$		0			0
$207$	4.48371	−	20.5983i	0.311640	−	1.43168i
$208$		0			0
$209$	−0.527564	−	0.154907i	−0.0364924	−	0.0107151i
$210$		0			0
$211$	−16.6300	−	8.57337i	−1.14486	−	0.590215i	−0.221882	−	0.975074i	$-0.571220\pi$
$211$	−16.6300	−	8.57337i	−1.14486	−	0.590215i	−0.922975	+	0.384859i	$0.874250\pi$
$212$		0			0
$213$	7.59899	−	12.8055i	0.520674	−	0.877418i
$214$		0			0
$215$	2.63431	+	2.28265i	0.179659	+	0.155675i
$216$		0			0
$217$	2.37394	−	1.86689i	0.161154	−	0.126733i
$218$		0			0
$219$	−9.48692	+	17.8737i	−0.641067	+	1.20779i
$220$		0			0
$221$	−28.0688	+	14.4705i	−1.88811	+	0.973389i
$222$		0			0
$223$	17.2618	−	11.0935i	1.15593	−	0.742873i	0.185121	−	0.982716i	$-0.440732\pi$
$223$	17.2618	−	11.0935i	1.15593	−	0.742873i	0.970812	+	0.239843i	$0.0770960\pi$
$224$		0			0
$225$	−1.59462	−	13.3518i	−0.106308	−	0.890118i
$226$		0			0
$227$	3.55785	+	18.4599i	0.236143	+	1.22522i	0.885463	+	0.464709i	$0.153841\pi$
$227$	3.55785	+	18.4599i	0.236143	+	1.22522i	−0.649321	+	0.760515i	$0.724947\pi$
$228$		0			0
$229$	−6.29360	+	1.52681i	−0.415892	+	0.100894i	−0.438245	−	0.898856i	$-0.644400\pi$
$229$	−6.29360	+	1.52681i	−0.415892	+	0.100894i	0.0223522	+	0.999750i	$0.492884\pi$
$230$		0			0
$231$	−0.146884	−	0.638727i	−0.00966425	−	0.0420251i
$232$		0			0
$233$	−0.455903	−	9.57058i	−0.0298672	−	0.626990i	−0.963331	−	0.268317i	$-0.913532\pi$
$233$	−0.455903	−	9.57058i	−0.0298672	−	0.626990i	0.933463	−	0.358673i	$-0.116771\pi$
$234$		0			0
$235$	−3.39872	+	2.42022i	−0.221708	+	0.157878i
$236$		0			0
$237$	−12.2630	+	6.13739i	−0.796565	+	0.398666i
$238$		0			0
$239$	6.97831	−	12.0868i	0.451389	−	0.781829i	−0.547083	−	0.837078i	$-0.684262\pi$
$239$	6.97831	−	12.0868i	0.451389	−	0.781829i	0.998473	+	0.0552490i	$0.0175953\pi$
$240$		0			0
$241$	−2.34857	+	16.3347i	−0.151285	+	1.05221i	0.762785	+	0.646652i	$0.223831\pi$
$241$	−2.34857	+	16.3347i	−0.151285	+	1.05221i	−0.914070	+	0.405557i	$0.867078\pi$
$242$		0			0
$243$	14.5416	−	5.61625i	0.932843	−	0.360283i
$244$		0			0
$245$	−0.219514	+	4.60817i	−0.0140242	+	0.294405i
$246$		0			0
$247$	3.42300	−	4.35270i	0.217800	−	0.276956i
$248$		0			0
$249$	24.8301	+	5.09448i	1.57354	+	0.322850i
$250$		0			0
$251$	−0.505431	+	1.46035i	−0.0319025	+	0.0921763i	−0.959828	−	0.280591i	$-0.909470\pi$
$251$	−0.505431	+	1.46035i	−0.0319025	+	0.0921763i	0.927925	+	0.372767i	$0.121591\pi$
$252$		0			0
$253$	−3.15231	−	1.43961i	−0.198184	−	0.0905076i
$254$		0			0
$255$	3.87977	+	6.90959i	0.242961	+	0.432696i
$256$		0			0
$257$	1.80024	−	4.49679i	0.112296	−	0.280502i	−0.861565	−	0.507648i	$-0.830515\pi$
$257$	1.80024	−	4.49679i	0.112296	−	0.280502i	0.973861	+	0.227146i	$0.0729393\pi$
$258$		0			0
$259$	0.834375	−	0.381046i	0.0518455	−	0.0236771i
$260$		0			0
$261$	−17.2259	+	20.8574i	−1.06626	+	1.29104i
$262$		0			0
$263$	15.9211	−	2.28910i	0.981735	−	0.141152i	0.367286	−	0.930108i	$-0.380287\pi$
$263$	15.9211	−	2.28910i	0.981735	−	0.141152i	0.614450	+	0.788956i	$0.289378\pi$
$264$		0			0
$265$	0.941924	+	0.605338i	0.0578619	+	0.0371856i
$266$		0			0
$267$	−6.15570	−	1.88777i	−0.376723	−	0.115530i
$268$		0			0
$269$		−	9.53004i		−	0.581057i	−0.956866	−	0.290528i	$-0.906169\pi$
$269$		−	9.53004i		−	0.581057i	0.956866	−	0.290528i	$-0.0938311\pi$
$270$		0			0
$271$	4.36800	−	6.79675i	0.265337	−	0.412873i	−0.682863	−	0.730547i	$-0.739265\pi$
$271$	4.36800	−	6.79675i	0.265337	−	0.412873i	0.948200	+	0.317674i	$0.102902\pi$
$272$		0			0
$273$	6.52163	+	1.01746i	0.394707	+	0.0615794i
$274$		0			0
$275$	−2.20051	−	0.210123i	−0.132696	−	0.0126709i
$276$		0			0
$277$	3.07594	+	6.73536i	0.184815	+	0.404689i	0.979249	−	0.202662i	$-0.0649594\pi$
$277$	3.07594	+	6.73536i	0.184815	+	0.404689i	−0.794434	+	0.607351i	$0.792232\pi$
$278$		0			0
$279$	9.78009	−	6.61748i	0.585518	−	0.396178i
$280$		0			0
$281$	11.3790	+	10.8499i	0.678817	+	0.647251i	0.948897	−	0.315587i	$-0.102202\pi$
$281$	11.3790	+	10.8499i	0.678817	+	0.647251i	−0.270080	+	0.962838i	$0.587050\pi$
$282$		0			0
$283$	−0.121689	+	0.266462i	−0.00723367	+	0.0158395i	−0.913214	−	0.407480i	$-0.866408\pi$
$283$	−0.121689	+	0.266462i	−0.00723367	+	0.0158395i	0.905981	+	0.423319i	$0.139135\pi$
$284$		0			0
$285$	−1.12215	−	0.819491i	−0.0664705	−	0.0485424i
$286$		0			0
$287$	−0.656768	−	6.87799i	−0.0387678	−	0.405995i
$288$		0			0
$289$	18.4138	+	14.4808i	1.08317	+	0.851810i
$290$		0			0
$291$	−1.22918	+	3.41858i	−0.0720559	+	0.200401i
$292$		0			0
$293$	1.94667	+	6.62975i	0.113726	+	0.387314i	0.996609	−	0.0822776i	$-0.0262194\pi$
$293$	1.94667	+	6.62975i	0.113726	+	0.387314i	−0.882884	+	0.469591i	$0.844401\pi$
$294$		0			0
$295$	4.74776	+	0.682625i	0.276425	+	0.0397439i
$296$		0			0
$297$	−0.394357	−	2.53209i	−0.0228829	−	0.146926i
$298$		0			0
$299$	25.2590	−	24.0844i	1.46076	−	1.39284i
$300$		0			0
$301$	−2.15591	−	3.02755i	−0.124264	−	0.174505i
$302$		0			0
$303$	−26.0892	−	6.66069i	−1.49879	−	0.382647i
$304$		0			0
$305$	4.54503	−	2.62408i	0.260248	−	0.150254i
$306$		0			0
$307$	5.52792	+	22.7864i	0.315495	+	1.30049i	0.879967	+	0.475035i	$0.157565\pi$
$307$	5.52792	+	22.7864i	0.315495	+	1.30049i	−0.564472	+	0.825452i	$0.690920\pi$
$308$		0			0
$309$	−0.218948	+	2.03525i	−0.0124555	+	0.115782i
$310$		0			0
$311$	−17.5008	−	20.1970i	−0.992382	−	1.14527i	−0.989391	−	0.145274i	$-0.953594\pi$
$311$	−17.5008	−	20.1970i	−0.992382	−	1.14527i	−0.00299002	−	0.999996i	$-0.500952\pi$
$312$		0			0
$313$	11.9394	+	18.5781i	0.674857	+	1.05010i	0.994719	+	0.102634i	$0.0327269\pi$
$313$	11.9394	+	18.5781i	0.674857	+	1.05010i	−0.319862	+	0.947464i	$0.603637\pi$
$314$		0			0
$315$	0.196850	−	1.64456i	0.0110912	−	0.0926604i
$316$		0			0
$317$	2.09975	−	10.8945i	0.117934	−	0.611897i	−0.874082	−	0.485779i	$-0.838536\pi$
$317$	2.09975	−	10.8945i	0.117934	−	0.611897i	0.992015	−	0.126118i	$-0.0402519\pi$
$318$		0			0
$319$	2.74893	+	3.49555i	0.153911	+	0.195713i
$320$		0			0
$321$	−21.9026	+	13.7084i	−1.22248	+	0.765129i
$322$		0			0
$323$	−6.88880	−	1.67120i	−0.383303	−	0.0929883i
$324$		0			0
$325$	10.2011	−	19.7874i	0.565855	−	1.09761i
$326$		0			0
$327$	27.8158	+	18.3501i	1.53822	+	1.01476i
$328$		0			0
$329$	4.13023	−	1.65349i	0.227707	−	0.0911601i
$330$		0			0
$331$	−21.2921	+	7.36927i	−1.17032	+	0.405052i	−0.841980	−	0.539508i	$-0.818610\pi$
$331$	−21.2921	+	7.36927i	−1.17032	+	0.405052i	−0.328340	+	0.944560i	$0.606489\pi$
$332$		0			0
$333$	3.36055	−	1.25292i	0.184157	−	0.0686595i
$334$		0			0
$335$	−5.87380	+	0.435775i	−0.320920	+	0.0238089i
$336$		0			0
$337$	−1.41006	−	1.00410i	−0.0768111	−	0.0546969i	0.541006	−	0.841019i	$-0.318044\pi$
$337$	−1.41006	−	1.00410i	−0.0768111	−	0.0546969i	−0.617817	+	0.786322i	$0.711983\pi$
$338$		0			0
$339$	28.7095	−	1.02348i	1.55929	−	0.0555876i
$340$		0			0
$341$	−0.721479	−	1.80217i	−0.0390703	−	0.0975928i
$342$		0			0
$343$	2.89903	−	9.87317i	0.156533	−	0.533101i
$344$		0			0
$345$	−6.26558	−	6.11901i	−0.337327	−	0.329436i
$346$		0			0
$347$	0.318692	−	1.31367i	0.0171083	−	0.0705213i	−0.962618	−	0.270864i	$-0.912691\pi$
$347$	0.318692	−	1.31367i	0.0171083	−	0.0705213i	0.979726	+	0.200343i	$0.0642057\pi$
$348$		0			0
$349$	16.6287	−	19.1905i	0.890112	−	1.02724i	−0.109335	−	0.994005i	$-0.534872\pi$
$349$	16.6287	−	19.1905i	0.890112	−	1.02724i	0.999447	−	0.0332396i	$-0.0105824\pi$
$350$		0			0
$351$	25.1501	+	5.79055i	1.34241	+	0.309077i
$352$		0			0
$353$	6.98868	+	1.34696i	0.371970	+	0.0716913i	0.371810	−	0.928309i	$-0.378737\pi$
$353$	6.98868	+	1.34696i	0.371970	+	0.0716913i	0.000159442		1.00000i	$0.499949\pi$
$354$		0			0
$355$	−2.83466	−	5.49847i	−0.150448	−	0.291829i
$356$		0			0
$357$	−2.28333	−	8.13517i	−0.120847	−	0.430559i
$358$		0			0
$359$	−25.8420	+	22.3923i	−1.36389	+	1.18182i	−0.399689	+	0.916651i	$0.630882\pi$
$359$	−25.8420	+	22.3923i	−1.36389	+	1.18182i	−0.964202	+	0.265167i	$0.914573\pi$
$360$		0			0
$361$	−17.4361	+	3.36054i	−0.917691	+	0.176870i
$362$		0			0
$363$	18.5982	+	1.10913i	0.976155	+	0.0582140i
$364$		0			0
$365$	4.20333	+	7.28039i	0.220013	+	0.381073i
$366$		0			0
$367$	10.0097	−	0.476822i	0.522504	−	0.0248899i	0.215326	−	0.976542i	$-0.430918\pi$
$367$	10.0097	−	0.476822i	0.522504	−	0.0248899i	0.307178	+	0.951652i	$0.400615\pi$
$368$		0			0
$369$	−0.639359	−	27.0077i	−0.0332837	−	1.40597i
$370$		0			0
$371$	−0.823868	−	0.864048i	−0.0427731	−	0.0448591i
$372$		0			0
$373$	0.674775	+	0.389582i	0.0349385	+	0.0201718i	0.517368	−	0.855763i	$-0.326912\pi$
$373$	0.674775	+	0.389582i	0.0349385	+	0.0201718i	−0.482429	+	0.875935i	$0.660245\pi$
$374$		0			0
$375$	−10.6905	−	5.03765i	−0.552056	−	0.260143i
$376$		0			0
$377$	−42.9713	+	12.6175i	−2.21314	+	0.649836i
$378$		0			0
$379$	−14.7383	−	0.702071i	−0.757055	−	0.0360630i	−0.334495	−	0.942398i	$-0.608566\pi$
$379$	−14.7383	−	0.702071i	−0.757055	−	0.0360630i	−0.422561	+	0.906335i	$0.638869\pi$
$380$		0			0
$381$	12.1676	−	8.44692i	0.623364	−	0.432749i
$382$		0			0
$383$	−12.4215	+	1.18611i	−0.634710	+	0.0606075i	−0.407451	−	0.913227i	$-0.633582\pi$
$383$	−12.4215	+	1.18611i	−0.634710	+	0.0606075i	−0.227259	+	0.973834i	$0.572976\pi$
$384$		0			0
$385$	−0.257306	−	0.0890546i	−0.0131135	−	0.00453864i
$386$		0			0
$387$	−7.56201	−	12.4099i	−0.384399	−	0.630832i
$388$		0			0
$389$	−6.30391	+	6.61135i	−0.319621	+	0.335209i	−0.863870	−	0.503715i	$-0.831966\pi$
$389$	−6.30391	+	6.61135i	−0.319621	+	0.335209i	0.544249	+	0.838924i	$0.316815\pi$
$390$		0			0
$391$	−41.4774	−	16.6050i	−2.09760	−	0.839753i
$392$		0			0
$393$	−4.27017	−	32.4516i	−0.215402	−	1.63697i
$394$		0			0
$395$	−0.541535	+	5.67122i	−0.0272476	+	0.285350i
$396$		0			0
$397$	3.68724	+	25.6453i	0.185057	+	1.28710i	0.844585	+	0.535422i	$0.179848\pi$
$397$	3.68724	+	25.6453i	0.185057	+	1.28710i	−0.659527	+	0.751681i	$0.729243\pi$
$398$		0			0
$399$	0.956788	+	1.13126i	0.0478993	+	0.0566340i
$400$		0			0
$401$	37.9003			1.89265			0.946325	−	0.323218i	$-0.104765\pi$
$401$	37.9003			1.89265			0.946325	+	0.323218i	$0.104765\pi$
$402$		0			0
$403$	19.5501			0.973858
$404$		0			0
$405$	1.22729	−	6.35879i	0.0609843	−	0.315971i
$406$		0			0
$407$	−0.0839079	−	0.583592i	−0.00415916	−	0.0289276i
$408$		0			0
$409$	−0.00694953	+	0.0727787i	−0.000343632	+	0.00359868i	−0.995642	−	0.0932565i	$-0.970272\pi$
$409$	−0.00694953	+	0.0727787i	−0.000343632	+	0.00359868i	0.995298	+	0.0968552i	$0.0308784\pi$
$410$		0			0
$411$	10.9378	−	1.43926i	0.539522	−	0.0709934i
$412$		0			0
$413$	−4.74812	−	1.90086i	−0.233640	−	0.0935353i
$414$		0			0
$415$	7.26682	−	7.62122i	0.356714	−	0.374111i
$416$		0			0
$417$	15.2855	−	17.2197i	0.748536	−	0.843254i
$418$		0			0
$419$	22.3142	+	7.72303i	1.09012	+	0.377295i	0.812242	−	0.583321i	$-0.198247\pi$
$419$	22.3142	+	7.72303i	1.09012	+	0.377295i	0.277880	+	0.960616i	$0.410368\pi$
$420$		0			0
$421$	1.13680	−	0.108551i	0.0554044	−	0.00529048i	−0.0673170	−	0.997732i	$-0.521444\pi$
$421$	1.13680	−	0.108551i	0.0554044	−	0.00529048i	0.122721	+	0.992441i	$0.460838\pi$
$422$		0			0
$423$	16.5700	−	5.29445i	0.805661	−	0.257425i
$424$		0			0
$425$	−28.4662	−	1.35601i	−1.38081	−	0.0657762i
$426$		0			0
$427$	−5.36931	+	1.57657i	−0.259839	+	0.0762956i
$428$		0			0
$429$	1.80850	−	3.83787i	0.0873154	−	0.185294i
$430$		0			0
$431$	21.1776	+	12.2269i	1.02009	+	0.588949i	0.914130	−	0.405422i	$-0.132875\pi$
$431$	21.1776	+	12.2269i	1.02009	+	0.588949i	0.105959	+	0.994370i	$0.466209\pi$
$432$		0			0
$433$	18.9387	+	19.8624i	0.910137	+	0.954525i	0.999138	−	0.0415069i	$-0.0132159\pi$
$433$	18.9387	+	19.8624i	0.910137	+	0.954525i	−0.0890008	+	0.996032i	$0.528367\pi$
$434$		0			0
$435$	3.54833	+	10.6633i	0.170129	+	0.511268i
$436$		0			0
$437$	7.82534	−	0.372767i	0.374337	−	0.0178319i
$438$		0			0
$439$	18.3953	+	31.8617i	0.877962	+	1.52067i	0.853574	+	0.520972i	$0.174431\pi$
$439$	18.3953	+	31.8617i	0.877962	+	1.52067i	0.0243886	+	0.999703i	$0.492236\pi$
$440$		0			0
$441$	6.72393	−	18.0203i	0.320187	−	0.858111i
$442$		0			0
$443$	7.27332	−	1.40182i	0.345566	−	0.0666024i	−0.0135154	−	0.999909i	$-0.504302\pi$
$443$	7.27332	−	1.40182i	0.345566	−	0.0666024i	0.359081	+	0.933306i	$0.383090\pi$
$444$		0			0
$445$	−2.02156	+	1.75169i	−0.0958312	+	0.0830382i
$446$		0			0
$447$	1.71435	−	0.481174i	0.0810860	−	0.0227587i
$448$		0			0
$449$	−1.84954	−	3.58761i	−0.0872852	−	0.169310i	0.841152	−	0.540798i	$-0.181878\pi$
$449$	−1.84954	−	3.58761i	−0.0872852	−	0.169310i	−0.928438	+	0.371489i	$0.878847\pi$
$450$		0			0
$451$	−4.36083	−	0.840482i	−0.205344	−	0.0395767i
$452$		0			0
$453$	4.20419	+	10.8770i	0.197530	+	0.511046i
$454$		0			0
$455$	1.79573	−	2.07238i	0.0841850	−	0.0971547i
$456$		0			0
$457$	0.138080	−	0.569175i	0.00645913	−	0.0266249i	−0.968491	−	0.249049i	$-0.919882\pi$
$457$	0.138080	−	0.569175i	0.00645913	−	0.0266249i	0.974950	+	0.222424i	$0.0713970\pi$
$458$		0			0
$459$	−6.63166	−	32.3653i	−0.309539	−	1.51068i
$460$		0			0
$461$	6.48390	−	22.0821i	0.301985	−	1.02847i	−0.659063	−	0.752087i	$-0.729047\pi$
$461$	6.48390	−	22.0821i	0.301985	−	1.02847i	0.961049	−	0.276380i	$-0.0891347\pi$
$462$		0			0
$463$	−12.1602	−	30.3748i	−0.565135	−	1.41164i	−0.885632	−	0.464389i	$-0.846274\pi$
$463$	−12.1602	−	30.3748i	−0.565135	−	1.41164i	0.320497	−	0.947250i	$-0.396150\pi$
$464$		0			0
$465$	−0.174777	−	4.90267i	−0.00810510	−	0.227356i
$466$		0			0
$467$	6.68274	+	4.75876i	0.309240	+	0.220209i	0.724131	−	0.689662i	$-0.242241\pi$
$467$	6.68274	+	4.75876i	0.309240	+	0.220209i	−0.414891	+	0.909871i	$0.636180\pi$
$468$		0			0
$469$	6.19610	+	1.02502i	0.286109	+	0.0473311i
$470$		0			0
$471$	2.73076	+	3.55928i	0.125827	+	0.164003i
$472$		0			0
$473$	−2.25761	+	0.781366i	−0.103805	+	0.0359272i
$474$		0			0
$475$	4.63923	−	1.85727i	0.212862	−	0.0852173i
$476$		0			0
$477$	−2.97163	−	3.60002i	−0.136062	−	0.164834i
$478$		0			0
$479$	−6.19309	+	12.0129i	−0.282970	+	0.548885i	−0.986890	−	0.161394i	$-0.948401\pi$
$479$	−6.19309	+	12.0129i	−0.282970	+	0.548885i	0.703920	+	0.710279i	$0.251431\pi$
$480$		0			0
$481$	5.77043	+	1.39989i	0.263109	+	0.0638295i
$482$		0			0
$483$	4.95430	+	7.91571i	0.225428	+	0.360177i
$484$		0			0
$485$	0.932955	+	1.18635i	0.0423633	+	0.0538693i
$486$		0			0
$487$	−0.665348	+	3.45215i	−0.0301498	+	0.156432i	−0.993883	−	0.110434i	$-0.964776\pi$
$487$	−0.665348	+	3.45215i	−0.0301498	+	0.156432i	0.963734	+	0.266866i	$0.0859881\pi$
$488$		0			0
$489$	−1.76097	−	9.76405i	−0.0796337	−	0.441546i
$490$		0			0
$491$	−12.7512	−	19.8412i	−0.575453	−	0.895422i	0.424497	−	0.905429i	$-0.360451\pi$
$491$	−12.7512	−	19.8412i	−0.575453	−	0.895422i	−0.999950	+	0.0100070i	$0.996815\pi$
$492$		0			0
$493$	37.5440	+	43.3281i	1.69090	+	1.95140i
$494$		0			0
$495$	−0.978610	−	0.419217i	−0.0439853	−	0.0188424i
$496$		0			0
$497$	1.55510	+	6.41022i	0.0697559	+	0.287538i
$498$		0			0
$499$	−33.2615	+	19.2035i	−1.48899	+	0.859668i	−0.999921	−	0.0125777i	$-0.995996\pi$
$499$	−33.2615	+	19.2035i	−1.48899	+	0.859668i	−0.489068	+	0.872246i	$0.662663\pi$
$500$		0			0
$501$	−6.98631	+	27.3646i	−0.312125	+	1.22256i
$502$		0			0
$503$	−8.66130	−	12.1631i	−0.386188	−	0.542325i	0.575024	−	0.818137i	$-0.304993\pi$
$503$	−8.66130	−	12.1631i	−0.386188	−	0.542325i	−0.961212	+	0.275811i	$0.911053\pi$
$504$		0			0
$505$	−8.09589	+	7.71941i	−0.360262	+	0.343509i
$506$		0			0
$507$	13.7711	+	14.7932i	0.611597	+	0.656988i
$508$		0			0
$509$	0.747224	+	0.107435i	0.0331201	+	0.00476196i	0.158855	−	0.987302i	$-0.449220\pi$
$509$	0.747224	+	0.107435i	0.0331201	+	0.00476196i	−0.125735	+	0.992064i	$0.540129\pi$
$510$		0			0
$511$	−2.52541	−	8.60074i	−0.111717	−	0.380474i
$512$		0			0
$513$	3.41535	+	4.67931i	0.150791	+	0.206597i
$514$		0			0
$515$	0.668471	+	0.525691i	0.0294563	+	0.0231647i
$516$		0			0
$517$	−0.271826	−	2.84669i	−0.0119549	−	0.125197i
$518$		0			0
$519$	−9.83935	+	13.4733i	−0.431899	+	0.591412i
$520$		0			0
$521$	−0.681593	+	1.49248i	−0.0298611	+	0.0653867i	−0.923975	−	0.382453i	$-0.875079\pi$
$521$	−0.681593	+	1.49248i	−0.0298611	+	0.0653867i	0.894114	+	0.447840i	$0.147807\pi$
$522$		0			0
$523$	−8.39247	−	8.00221i	−0.366977	−	0.349912i	0.484044	−	0.875044i	$-0.339168\pi$
$523$	−8.39247	−	8.00221i	−0.366977	−	0.349912i	−0.851021	+	0.525132i	$0.824016\pi$
$524$		0			0
$525$	4.63780	+	3.73788i	0.202410	+	0.163134i
$526$		0			0
$527$	−10.3964	−	22.7650i	−0.452876	−	0.991661i
$528$		0			0
$529$	26.2576	+	2.50730i	1.14163	+	0.109013i
$530$		0			0
$531$	−17.9865	−	8.74023i	−0.780549	−	0.379294i
$532$		0			0
$533$	24.1808	−	37.6261i	1.04739	−	1.62977i
$534$		0			0
$535$			10.7346i			0.464096i
$536$		0			0
$537$	−2.59491	+	8.46155i	−0.111978	+	0.365143i
$538$		0			0
$539$	−2.65996	−	1.70945i	−0.114572	−	0.0736312i
$540$		0			0
$541$	−0.802131	+	0.115329i	−0.0344863	+	0.00495839i	−0.159536	−	0.987192i	$-0.551000\pi$
$541$	−0.802131	+	0.115329i	−0.0344863	+	0.00495839i	0.125050	+	0.992150i	$0.460091\pi$
$542$		0			0
$543$	16.7883	−	40.5230i	0.720454	−	1.73901i
$544$		0			0
$545$	12.5930	−	5.75101i	0.539423	−	0.246346i
$546$		0			0
$547$	−0.289443	+	0.722993i	−0.0123757	+	0.0309129i	−0.934427	−	0.356154i	$-0.884088\pi$
$547$	−0.289443	+	0.722993i	−0.0123757	+	0.0309129i	0.922051	+	0.387067i	$0.126512\pi$
$548$		0			0
$549$	−21.3809	+	4.64819i	−0.912515	+	0.198380i
$550$		0			0
$551$	−9.14454	−	4.17617i	−0.389570	−	0.177911i
$552$		0			0
$553$	1.98680	−	5.74050i	0.0844875	−	0.244111i
$554$		0			0
$555$	0.299470	−	1.45959i	0.0127118	−	0.0619563i
$556$		0			0
$557$	25.5617	−	32.5044i	1.08309	−	1.37726i	0.162503	−	0.986708i	$-0.448043\pi$
$557$	25.5617	−	32.5044i	1.08309	−	1.37726i	0.920583	−	0.390547i	$-0.127714\pi$
$558$		0			0
$559$	1.14481	−	24.0324i	0.0484201	−	1.01646i
$560$		0			0
$561$	−5.43074	−	0.0649850i	−0.229286	−	0.00274367i
$562$		0			0
$563$	−2.56815	+	17.8618i	−0.108234	+	0.752787i	0.861347	+	0.508017i	$0.169621\pi$
$563$	−2.56815	+	17.8618i	−0.108234	+	0.752787i	−0.969581	+	0.244770i	$0.921288\pi$
$564$		0			0
$565$	5.96739	−	10.3358i	0.251050	−	0.434831i
$566$		0			0
$567$	−2.87024	+	6.28058i	−0.120539	+	0.263760i
$568$		0			0
$569$	−20.0817	+	14.3001i	−0.841868	+	0.599491i	−0.917541	−	0.397641i	$-0.869829\pi$
$569$	−20.0817	+	14.3001i	−0.841868	+	0.599491i	0.0756733	+	0.997133i	$0.475889\pi$
$570$		0			0
$571$	0.459882	+	9.65412i	0.0192455	+	0.404012i	0.987850	+	0.155407i	$0.0496690\pi$
$571$	0.459882	+	9.65412i	0.0192455	+	0.404012i	−0.968605	+	0.248605i	$0.920028\pi$
$572$		0			0
$573$	24.3047	−	5.58921i	1.01534	−	0.233492i
$574$		0			0
$575$	30.6082	−	7.42546i	1.27645	−	0.309663i
$576$		0			0
$577$	7.93038	+	41.1467i	0.330146	+	1.71296i	0.645308	+	0.763922i	$0.276729\pi$
$577$	7.93038	+	41.1467i	0.330146	+	1.71296i	−0.315162	+	0.949038i	$0.602059\pi$
$578$		0			0
$579$	−10.3552	+	4.58012i	−0.430348	+	0.190343i
$580$		0			0
$581$	−9.44588	+	6.07050i	−0.391881	+	0.251847i
$582$		0			0
$583$	−0.682083	+	0.351638i	−0.0282490	+	0.0145634i
$584$		0			0
$585$	7.58247	−	7.58048i	0.313497	−	0.313414i
$586$		0			0
$587$	−34.6085	+	27.2165i	−1.42845	+	1.12334i	−0.456066	+	0.889946i	$0.650742\pi$
$587$	−34.6085	+	27.2165i	−1.42845	+	1.12334i	−0.972382	+	0.233397i	$0.925016\pi$
$588$		0			0
$589$	3.31654	+	2.87380i	0.136656	+	0.118413i
$590$		0			0
$591$	−15.4941	−	9.19445i	−0.637342	−	0.378209i
$592$		0			0
$593$	−1.02148	−	0.526611i	−0.0419473	−	0.0216253i	0.437125	−	0.899401i	$-0.355997\pi$
$593$	−1.02148	−	0.526611i	−0.0419473	−	0.0216253i	−0.479073	+	0.877775i	$0.659027\pi$
$594$		0			0
$595$	−3.36812	−	0.988970i	−0.138080	−	0.0405438i
$596$		0			0
$597$	−1.36022	−	16.3044i	−0.0556702	−	0.667293i
$598$		0			0
$599$	7.05909	+	20.3959i	0.288427	+	0.833354i	0.992392	+	0.123120i	$0.0392899\pi$
$599$	7.05909	+	20.3959i	0.288427	+	0.833354i	−0.703965	+	0.710235i	$0.748589\pi$
$600$		0			0
$601$	−22.9755	+	32.2645i	−0.937189	+	1.31610i	0.0115161	+	0.999934i	$0.496334\pi$
$601$	−22.9755	+	32.2645i	−0.937189	+	1.31610i	−0.948705	+	0.316164i	$0.897605\pi$
$602$		0			0
$603$	23.8784	+	5.72909i	0.972403	+	0.233306i
$604$		0			0
$605$	4.48980	−	6.30504i	0.182536	−	0.256336i
$606$		0			0
$607$	7.86388	+	22.7212i	0.319185	+	0.922225i	0.984457	+	0.175624i	$0.0561943\pi$
$607$	7.86388	+	22.7212i	0.319185	+	0.922225i	−0.665272	+	0.746601i	$0.731684\pi$
$608$		0			0
$609$	−0.996249	−	11.9416i	−0.0403700	−	0.483897i
$610$		0			0
$611$	27.6329	+	8.11374i	1.11791	+	0.328247i
$612$		0			0
$613$	−11.3349	−	5.84355i	−0.457812	−	0.236019i	0.213864	−	0.976863i	$-0.431395\pi$
$613$	−11.3349	−	5.84355i	−0.457812	−	0.236019i	−0.671676	+	0.740845i	$0.734425\pi$
$614$		0			0
$615$	−9.65188	−	5.72758i	−0.389201	−	0.230958i
$616$		0			0
$617$	25.5107	+	22.1051i	1.02702	+	0.889919i	0.993983	−	0.109535i	$-0.0349362\pi$
$617$	25.5107	+	22.1051i	1.02702	+	0.889919i	0.0330383	+	0.999454i	$0.489482\pi$
$618$		0			0
$619$	−15.0547	+	11.8391i	−0.605099	+	0.475855i	−0.873085	−	0.487568i	$-0.837884\pi$
$619$	−15.0547	+	11.8391i	−0.605099	+	0.475855i	0.267986	+	0.963423i	$0.413642\pi$
$620$		0			0
$621$	17.1098	+	32.2558i	0.686591	+	1.29438i
$622$		0			0
$623$	2.53513	−	1.30695i	0.101568	−	0.0523619i
$624$		0			0
$625$	14.7231	−	9.46195i	0.588923	−	0.378478i
$626$		0			0
$627$	0.870955	−	0.385225i	0.0347826	−	0.0153844i
$628$		0			0
$629$	−1.43853	−	7.46380i	−0.0573580	−	0.297601i
$630$		0			0
$631$	−29.6306	+	7.18830i	−1.17958	+	0.286162i	−0.777165	−	0.629297i	$-0.783343\pi$
$631$	−29.6306	+	7.18830i	−1.17958	+	0.286162i	−0.402411	+	0.915459i	$0.631828\pi$
$632$		0			0
$633$	31.5821	−	7.26275i	1.25528	−	0.288668i
$634$		0			0
$635$	−0.292802	−	6.14667i	−0.0116195	−	0.243923i
$636$		0			0
$637$	25.9389	−	18.4710i	1.02774	−	0.731849i
$638$		0			0
$639$	4.27359	+	25.4345i	0.169060	+	1.00617i
$640$		0			0
$641$	−12.4842	+	21.6233i	−0.493098	+	0.854070i	−0.999968	−	0.00795173i	$-0.997469\pi$
$641$	−12.4842	+	21.6233i	−0.493098	+	0.854070i	0.506871	+	0.862022i	$0.330802\pi$
$642$		0			0
$643$	−4.85325	+	33.7551i	−0.191394	+	1.33117i	0.636930	+	0.770922i	$0.280204\pi$
$643$	−4.85325	+	33.7551i	−0.191394	+	1.33117i	−0.828323	+	0.560250i	$0.810705\pi$
$644$		0			0
$645$	−6.03697	−	0.0722392i	−0.237705	−	0.00284442i
$646$		0			0
$647$	1.46370	−	30.7268i	0.0575439	−	1.20800i	−0.766792	−	0.641895i	$-0.778148\pi$
$647$	1.46370	−	30.7268i	0.0575439	−	1.20800i	0.824336	−	0.566101i	$-0.191549\pi$
$648$		0			0
$649$	−2.03217	+	2.58411i	−0.0797695	+	0.101435i
$650$		0			0
$651$	−1.05135	+	5.12418i	−0.0412055	+	0.200833i
$652$		0			0
$653$	−11.9399	+	34.4979i	−0.467243	+	1.35001i	0.427738	+	0.903903i	$0.359311\pi$
$653$	−11.9399	+	34.4979i	−0.467243	+	1.35001i	−0.894980	+	0.446106i	$0.852811\pi$
$654$		0			0
$655$	−12.3692	−	5.64884i	−0.483306	−	0.220718i
$656$		0			0
$657$	−7.44564	−	34.2487i	−0.290482	−	1.33617i
$658$		0			0
$659$	−11.1980	+	27.9712i	−0.436211	+	1.08960i	0.533598	+	0.845738i	$0.320840\pi$
$659$	−11.1980	+	27.9712i	−0.436211	+	1.08960i	−0.969809	+	0.243865i	$0.921585\pi$
$660$		0			0
$661$	−14.5054	+	6.62441i	−0.564196	+	0.257660i	−0.677032	−	0.735954i	$-0.736734\pi$
$661$	−14.5054	+	6.62441i	−0.564196	+	0.257660i	0.112836	+	0.993614i	$0.464007\pi$
$662$		0			0
$663$	20.9349	−	50.5320i	0.813045	−	1.96250i
$664$		0			0
$665$	0.609266	−	0.0875993i	0.0236263	−	0.00339695i
$666$		0			0
$667$	−53.3031	−	34.2558i	−2.06390	−	1.32639i
$668$		0			0
$669$	−10.4201	+	33.9782i	−0.402865	+	1.31367i
$670$		0			0
$671$			3.59694i			0.138858i
$672$		0			0
$673$	−11.7725	+	18.3184i	−0.453797	+	0.706122i	−0.990479	−	0.137662i	$-0.956041\pi$
$673$	−11.7725	+	18.3184i	−0.453797	+	0.706122i	0.536682	+	0.843785i	$0.319677\pi$
$674$		0			0
$675$	17.0429	+	15.8738i	0.655982	+	0.610982i
$676$		0			0
$677$	−18.8041	−	1.79557i	−0.722701	−	0.0690095i	−0.272778	−	0.962077i	$-0.587942\pi$
$677$	−18.8041	−	1.79557i	−0.722701	−	0.0690095i	−0.449923	+	0.893068i	$0.648548\pi$
$678$		0			0
$679$	−0.668518	−	1.46385i	−0.0256554	−	0.0561774i
$680$		0			0
$681$	−25.3527	−	20.4332i	−0.971516	−	0.783002i
$682$		0			0
$683$	−3.78334	−	3.60741i	−0.144765	−	0.138034i	0.614236	−	0.789122i	$-0.289464\pi$
$683$	−3.78334	−	3.60741i	−0.144765	−	0.138034i	−0.759002	+	0.651089i	$0.774313\pi$
$684$		0			0
$685$	1.90394	−	4.16904i	0.0727457	−	0.159291i
$686$		0			0
$687$	6.61537	−	9.05861i	0.252392	−	0.345607i
$688$		0			0
$689$	−0.734630	−	7.69339i	−0.0279872	−	0.293095i
$690$		0			0
$691$	18.4389	+	14.5005i	0.701449	+	0.551625i	0.903940	−	0.427659i	$-0.140661\pi$
$691$	18.4389	+	14.5005i	0.701449	+	0.551625i	−0.202492	+	0.979284i	$0.564904\pi$
$692$		0			0
$693$	0.908671	+	0.680409i	0.0345176	+	0.0258466i
$694$		0			0
$695$	−2.69499	−	9.17828i	−0.102227	−	0.348152i
$696$		0			0
$697$	−56.6727	−	8.14831i	−2.14663	−	0.308639i
$698$		0			0
$699$	11.3077	+	12.1469i	0.427696	+	0.459439i
$700$		0			0
$701$	−3.03624	+	2.89505i	−0.114677	+	0.109345i	−0.745249	−	0.666787i	$-0.767669\pi$
$701$	−3.03624	+	2.89505i	−0.114677	+	0.109345i	0.630571	+	0.776131i	$0.282821\pi$
$702$		0			0
$703$	0.773135	+	1.08572i	0.0291593	+	0.0409486i
$704$		0			0
$705$	1.78769	−	7.00218i	0.0673282	−	0.263717i
$706$		0			0
$707$	10.3297	−	5.96383i	0.388487	−	0.224293i
$708$		0			0
$709$	−2.63551	−	10.8637i	−0.0989785	−	0.407995i	0.900670	−	0.434504i	$-0.143076\pi$
$709$	−2.63551	−	10.8637i	−0.0989785	−	0.407995i	−0.999649	+	0.0265087i	$0.991561\pi$
$710$		0			0
$711$	9.35273	−	21.8328i	0.350755	−	0.818793i
$712$		0			0
$713$	18.1128	+	20.9033i	0.678330	+	0.782834i
$714$		0			0
$715$	−0.952922	−	1.48278i	−0.0356373	−	0.0554526i
$716$		0			0
$717$	4.29053	+	23.7898i	0.160233	+	0.888445i
$718$		0			0
$719$	−4.48842	+	23.2881i	−0.167390	+	0.868501i	0.796993	+	0.603989i	$0.206423\pi$
$719$	−4.48842	+	23.2881i	−0.167390	+	0.868501i	−0.964382	+	0.264512i	$0.914789\pi$
$720$		0			0
$721$	−0.560532	−	0.712775i	−0.0208753	−	0.0265451i
$722$		0			0
$723$	−15.1645	−	24.2291i	−0.563975	−	0.901090i
$724$		0			0
$725$	−39.2770	−	9.52849i	−1.45871	−	0.353879i
$726$		0			0
$727$	14.2934	−	27.7254i	0.530113	−	1.02828i	−0.459988	−	0.887925i	$-0.652146\pi$
$727$	14.2934	−	27.7254i	0.530113	−	1.02828i	0.990102	−	0.140352i	$-0.0448233\pi$
$728$		0			0
$729$	−12.9490	+	23.6922i	−0.479594	+	0.877490i
$730$		0			0
$731$	−28.5933	+	11.4470i	−1.05756	+	0.423384i
$732$		0			0
$733$	12.0707	−	4.17770i	0.445841	−	0.154307i	−0.0949174	−	0.995485i	$-0.530259\pi$
$733$	12.0707	−	4.17770i	0.445841	−	0.154307i	0.540758	+	0.841178i	$0.318137\pi$
$734$		0			0
$735$	−4.86397	−	6.33971i	−0.179410	−	0.233844i
$736$		0			0
$737$	1.75422	−	3.63573i	0.0646174	−	0.133924i
$738$		0			0
$739$	−13.9275	−	9.91775i	−0.512332	−	0.364830i	0.294461	−	0.955663i	$-0.404860\pi$
$739$	−13.9275	−	9.91775i	−0.512332	−	0.364830i	−0.806794	+	0.590833i	$0.798799\pi$
$740$		0			0
$741$	0.341699	+	9.58499i	0.0125526	+	0.352113i
$742$		0			0
$743$	2.89884	+	7.24096i	0.106348	+	0.265645i	0.971991	−	0.235016i	$-0.0755144\pi$
$743$	2.89884	+	7.24096i	0.106348	+	0.265645i	−0.865643	+	0.500661i	$0.833090\pi$
$744$		0			0
$745$	0.208409	−	0.709775i	0.00763550	−	0.0260041i
$746$		0			0
$747$	−38.5354	+	21.0354i	−1.40994	+	0.769643i
$748$		0			0
$749$	2.69850	−	11.1234i	0.0986012	−	0.406440i
$750$		0			0
$751$	−21.2733	+	24.5507i	−0.776275	+	0.895869i	−0.996834	−	0.0795047i	$-0.974666\pi$
$751$	−21.2733	+	24.5507i	−0.776275	+	0.895869i	0.220560	+	0.975373i	$0.429212\pi$
$752$		0			0
$753$	−0.964991	−	2.49660i	−0.0351662	−	0.0909812i
$754$		0			0
$755$	4.75704	+	0.916845i	0.173127	+	0.0333674i
$756$		0			0
$757$	−12.8973	−	25.0173i	−0.468762	−	0.909271i	−0.998145	−	0.0608878i	$-0.980607\pi$
$757$	−12.8973	−	25.0173i	−0.468762	−	0.909271i	0.529383	−	0.848383i	$-0.322423\pi$
$758$		0			0
$759$	5.77907	−	1.62204i	0.209767	−	0.0588761i
$760$		0			0
$761$	35.4724	−	30.7370i	1.28587	−	1.11422i	0.298736	−	0.954336i	$-0.403435\pi$
$761$	35.4724	−	30.7370i	1.28587	−	1.11422i	0.987137	−	0.159879i	$-0.0511105\pi$
$762$		0			0
$763$	−14.4948	+	2.79364i	−0.524747	+	0.101137i
$764$		0			0
$765$	−12.8593	−	4.79821i	−0.464930	−	0.173480i
$766$		0			0
$767$	−16.5540	−	28.6723i	−0.597729	−	1.03530i
$768$		0			0
$769$	−53.7049	+	2.55828i	−1.93665	+	0.0922539i	−0.980000	−	0.198997i	$-0.936232\pi$
$769$	−53.7049	+	2.55828i	−1.93665	+	0.0922539i	−0.956647	+	0.291251i	$0.905929\pi$
$770$		0			0
$771$	2.64892	+	7.96048i	0.0953986	+	0.286690i
$772$		0			0
$773$	10.5107	+	11.0233i	0.378042	+	0.396479i	0.885076	−	0.465447i	$-0.154107\pi$
$773$	10.5107	+	11.0233i	0.378042	+	0.396479i	−0.507034	+	0.861926i	$0.669258\pi$
$774$		0			0
$775$	15.2791	+	8.82139i	0.548841	+	0.316874i
$776$		0			0
$777$	−0.677236	+	1.43718i	−0.0242957	+	0.0515585i
$778$		0			0
$779$	9.63304	−	2.82852i	0.345140	−	0.101342i
$780$		0			0
$781$	4.23502	+	0.201739i	0.151541	+	0.00721878i
$782$		0			0
$783$	−0.548326	−	46.8506i	−0.0195956	−	1.67430i
$784$		0			0
$785$	1.85531	−	0.177160i	0.0662188	−	0.00632312i
$786$		0			0
$787$	−50.0217	−	17.3127i	−1.78308	−	0.617130i	−0.783091	−	0.621907i	$-0.786358\pi$
$787$	−50.0217	−	17.3127i	−1.78308	−	0.617130i	−0.999989	+	0.00477672i	$0.998480\pi$
$788$		0			0
$789$	−18.4948	+	20.8351i	−0.658433	+	0.741750i
$790$		0			0
$791$	−8.78180	+	9.21008i	−0.312245	+	0.327473i
$792$		0			0
$793$	−33.6300	−	13.4634i	−1.19424	−	0.478100i
$794$		0			0
$795$	−1.92275	+	0.253006i	−0.0681927	+	0.00897319i
$796$		0			0
$797$	−0.407149	+	4.26386i	−0.0144220	+	0.151034i	−0.999814	−	0.0192654i	$-0.993867\pi$
$797$	−0.407149	+	4.26386i	−0.0144220	+	0.151034i	0.985392	+	0.170299i	$0.0544733\pi$
$798$		0			0
$799$	−5.24673	−	36.4918i	−0.185616	−	1.29099i
$800$		0			0
$801$	10.2523	−	4.38868i	0.362245	−	0.155066i
$802$		0			0
$803$	−5.76170			−0.203326
$804$		0			0
$805$	3.87954			0.136736
$806$		0			0
$807$	10.6594	+	12.6032i	0.375230	+	0.443655i
$808$		0			0
$809$	3.13245	+	21.7867i	0.110131	+	0.765979i	0.967790	+	0.251759i	$0.0810092\pi$
$809$	3.13245	+	21.7867i	0.110131	+	0.765979i	−0.857659	+	0.514219i	$0.828082\pi$
$810$		0			0
$811$	4.42591	−	46.3503i	0.155415	−	1.62758i	−0.495627	−	0.868536i	$-0.665062\pi$
$811$	4.42591	−	46.3503i	0.155415	−	1.62758i	0.651042	−	0.759042i	$-0.274332\pi$
$812$		0			0
$813$	1.82564	+	13.8742i	0.0640281	+	0.486589i
$814$		0			0
$815$	−3.82661	−	1.53194i	−0.134040	−	0.0536616i
$816$		0			0
$817$	3.72690	−	3.90866i	0.130388	−	0.136747i
$818$		0			0
$819$	−9.76273	+	5.94894i	−0.341137	+	0.207873i
$820$		0			0
$821$	−19.4033	−	6.71555i	−0.677180	−	0.234374i	−0.0332368	−	0.999448i	$-0.510582\pi$
$821$	−19.4033	−	6.71555i	−0.677180	−	0.234374i	−0.643943	+	0.765073i	$0.722703\pi$
$822$		0			0
$823$	18.5242	−	1.76885i	0.645714	−	0.0616582i	0.232939	−	0.972491i	$-0.425166\pi$
$823$	18.5242	−	1.76885i	0.645714	−	0.0616582i	0.412775	+	0.910833i	$0.364560\pi$
$824$		0			0
$825$	3.14514	−	2.18340i	0.109500	−	0.0760163i
$826$		0			0
$827$	−14.0703	−	0.670252i	−0.489273	−	0.0233069i	−0.198504	−	0.980100i	$-0.563608\pi$
$827$	−14.0703	−	0.670252i	−0.489273	−	0.0233069i	−0.290769	+	0.956793i	$0.593911\pi$
$828$		0			0
$829$	−15.1257	+	4.44131i	−0.525337	+	0.154253i	−0.533639	−	0.845713i	$-0.679176\pi$
$829$	−15.1257	+	4.44131i	−0.525337	+	0.154253i	0.00830134	+	0.999966i	$0.497358\pi$
$830$		0			0
$831$	−11.6014	−	5.46689i	−0.402448	−	0.189644i
$832$		0			0
$833$	−35.3025	−	20.3819i	−1.22316	−	0.706192i
$834$		0			0
$835$	8.09678	+	8.49166i	0.280201	+	0.293866i
$836$		0			0
$837$	−5.53221	+	19.6906i	−0.191221	+	0.680605i
$838$		0			0
$839$	21.3940	−	1.01912i	0.738601	−	0.0351839i	0.325090	−	0.945683i	$-0.394605\pi$
$839$	21.3940	−	1.01912i	0.738601	−	0.0351839i	0.413511	+	0.910499i	$0.364302\pi$
$840$		0			0
$841$	26.1534	+	45.2989i	0.901840	+	1.56203i
$842$		0			0
$843$	−27.1842	−	1.62116i	−0.936274	−	0.0558356i
$844$		0			0
$845$	8.24479	−	1.58905i	0.283629	−	0.0546651i
$846$		0			0
$847$	−6.23740	+	5.40474i	−0.214320	+	0.185709i
$848$		0			0
$849$	−0.137109	−	0.488500i	−0.00470558	−	0.0167653i
$850$		0			0
$851$	3.84941	+	7.46682i	0.131956	+	0.255959i
$852$		0			0
$853$	15.2116	+	2.93180i	0.520835	+	0.100383i	0.442892	−	0.896575i	$-0.353953\pi$
$853$	15.2116	+	2.93180i	0.520835	+	0.100383i	0.0779433	+	0.996958i	$0.475165\pi$
$854$		0			0
$855$	2.40062	−	0.171379i	0.0820996	−	0.00586105i
$856$		0			0
$857$	23.8020	−	27.4690i	0.813062	−	0.938324i	−0.185959	−	0.982558i	$-0.559539\pi$
$857$	23.8020	−	27.4690i	0.813062	−	0.938324i	0.999021	+	0.0442336i	$0.0140846\pi$
$858$		0			0
$859$	3.97902	−	16.4018i	0.135763	−	0.559621i	−0.862777	−	0.505585i	$-0.831277\pi$
$859$	3.97902	−	16.4018i	0.135763	−	0.559621i	0.998539	−	0.0540352i	$-0.0172083\pi$
$860$		0			0
$861$	8.56165	+	8.36137i	0.291780	+	0.284955i
$862$		0			0
$863$	0.721751	−	2.45806i	0.0245687	−	0.0836732i	−0.946296	−	0.323301i	$-0.895207\pi$
$863$	0.721751	−	2.45806i	0.0245687	−	0.0836732i	0.970865	+	0.239628i	$0.0770255\pi$
$864$		0			0
$865$	2.57603	+	6.43462i	0.0875877	+	0.218784i
$866$		0			0
$867$	−40.5487	+	1.44554i	−1.37710	+	0.0490930i
$868$		0			0
$869$	−3.18058	−	2.26488i	−0.107894	−	0.0768307i
$870$		0			0
$871$	27.4266	+	30.0099i	0.929315	+	1.01685i
$872$		0			0
$873$	−2.19815	−	5.89584i	−0.0743962	−	0.199544i
$874$		0			0
$875$	4.94720	−	1.71224i	0.167246	−	0.0578844i
$876$		0			0
$877$	−5.40740	+	2.16479i	−0.182595	+	0.0730999i	−0.461158	−	0.887318i	$-0.652566\pi$
$877$	−5.40740	+	2.16479i	−0.182595	+	0.0730999i	0.278564	+	0.960418i	$0.410142\pi$
$878$		0			0
$879$	−9.98985	−	6.59030i	−0.336949	−	0.222285i
$880$		0			0
$881$	−14.8928	+	28.8881i	−0.501752	+	0.973263i	0.492910	+	0.870080i	$0.335933\pi$
$881$	−14.8928	+	28.8881i	−0.501752	+	0.973263i	−0.994662	+	0.103183i	$0.967097\pi$
$882$		0			0
$883$	−5.20079	−	1.26170i	−0.175021	−	0.0424595i	0.147291	−	0.989093i	$-0.452945\pi$
$883$	−5.20079	−	1.26170i	−0.175021	−	0.0424595i	−0.322311	+	0.946634i	$0.604460\pi$
$884$		0			0
$885$	−7.04231	+	4.40765i	−0.236725	+	0.148162i
$886$		0			0
$887$	19.9515	+	25.3704i	0.669906	+	0.851854i	0.995608	−	0.0936179i	$-0.0298432\pi$
$887$	19.9515	+	25.3704i	0.669906	+	0.851854i	−0.325702	+	0.945472i	$0.605601\pi$
$888$		0			0
$889$	−1.24177	+	6.44291i	−0.0416476	+	0.216088i
$890$		0			0
$891$	3.35369	+	2.90753i	0.112353	+	0.0974058i
$892$		0			0
$893$	3.49504	+	5.43839i	0.116957	+	0.181989i
$894$		0			0
$895$	2.40785	+	2.77881i	0.0804857	+	0.0928854i
$896$		0			0
$897$	−6.46576	+	60.1033i	−0.215886	+	2.00679i
$898$		0			0
$899$	−8.36769	−	34.4921i	−0.279078	−	1.15038i
$900$		0			0
$901$	−8.56790	+	4.94668i	−0.285438	+	0.164798i
$902$		0			0
$903$	6.23747	+	1.59246i	0.207570	+	0.0529936i
$904$		0			0
$905$	−10.5702	−	14.8437i	−0.351364	−	0.493421i
$906$		0			0
$907$	−18.0987	+	17.2571i	−0.600958	+	0.573012i	−0.928271	−	0.371904i	$-0.878705\pi$
$907$	−18.0987	+	17.2571i	−0.600958	+	0.573012i	0.327314	+	0.944916i	$0.393857\pi$
$908$		0			0
$909$	41.9523	−	20.3724i	1.39147	−	0.675710i
$910$		0			0
$911$	−27.7046	−	3.98331i	−0.917893	−	0.131973i	−0.332854	−	0.942978i	$-0.608012\pi$
$911$	−27.7046	−	3.98331i	−0.917893	−	0.131973i	−0.585039	+	0.811005i	$0.698921\pi$
$912$		0			0
$913$	2.03334	+	6.92491i	0.0672937	+	0.229181i
$914$		0			0
$915$	−3.07564	+	8.55393i	−0.101678	+	0.282784i
$916$		0			0
$917$	11.3972	+	8.96287i	0.376369	+	0.295980i
$918$		0			0
$919$	−5.57336	−	58.3669i	−0.183848	−	1.92535i	−0.345350	−	0.938474i	$-0.612240\pi$
$919$	−5.57336	−	58.3669i	−0.183848	−	1.92535i	0.161502	−	0.986872i	$-0.448366\pi$
$920$		0			0
$921$	−32.7973	−	23.9514i	−1.08071	−	0.789225i
$922$		0			0
$923$	−17.7379	+	38.8407i	−0.583851	+	1.27846i
$924$		0			0
$925$	3.87814	+	3.69780i	0.127513	+	0.121583i
$926$		0			0
$927$	−1.98690	−	2.93647i	−0.0652583	−	0.0964462i
$928$		0			0
$929$	20.1531	+	44.1290i	0.661200	+	1.44783i	0.881399	+	0.472372i	$0.156602\pi$
$929$	20.1531	+	44.1290i	0.661200	+	1.44783i	−0.220199	+	0.975455i	$0.570671\pi$
$930$		0			0
$931$	7.11555	+	0.679453i	0.233203	+	0.0222682i
$932$		0			0
$933$	45.7350	+	7.13524i	1.49730	+	0.233597i
$934$		0			0
$935$	−1.21987	+	1.89815i	−0.0398939	+	0.0620760i
$936$		0			0
$937$			34.1192i			1.11463i	0.830303	+	0.557313i	$0.188168\pi$
$937$			34.1192i			1.11463i	−0.830303	+	0.557313i	$0.811832\pi$
$938$		0			0
$939$	−36.5694	−	11.2147i	−1.19340	−	0.365979i
$940$		0			0
$941$	37.3754	+	24.0197i	1.21840	+	0.783020i	0.982045	−	0.188647i	$-0.0604101\pi$
$941$	37.3754	+	24.0197i	1.21840	+	0.783020i	0.236357	+	0.971666i	$0.424046\pi$
$942$		0			0
$943$	62.6337	−	9.00537i	2.03963	−	0.293255i
$944$		0			0
$945$	1.57912	+	2.39507i	0.0513689	+	0.0779115i
$946$		0			0
$947$	15.8179	−	7.22381i	0.514014	−	0.234742i	−0.141482	−	0.989941i	$-0.545187\pi$
$947$	15.8179	−	7.22381i	0.514014	−	0.234742i	0.655496	+	0.755199i	$0.272460\pi$
$948$		0			0
$949$	21.5662	−	53.8697i	0.700067	−	1.74868i
$950$		0			0
$951$	9.40875	+	16.7563i	0.305100	+	0.543361i
$952$		0			0
$953$	−8.87013	−	4.05085i	−0.287332	−	0.131220i	0.266535	−	0.963825i	$-0.414121\pi$
$953$	−8.87013	−	4.05085i	−0.287332	−	0.131220i	−0.553867	+	0.832605i	$0.686848\pi$
$954$		0			0
$955$	3.38869	−	9.79098i	0.109655	−	0.316829i
$956$		0			0
$957$	−7.54520	−	1.54807i	−0.243902	−	0.0500422i
$958$		0			0
$959$	−3.02093	+	3.84143i	−0.0975510	+	0.124046i
$960$		0			0
$961$	0.737831	−	15.4890i	0.0238010	−	0.499644i
$962$		0			0
$963$	13.6326	−	42.6272i	0.439304	−	1.37364i
$964$		0			0
$965$	−0.669454	+	4.65615i	−0.0215505	+	0.149887i
$966$		0			0
$967$	2.99556	−	5.18846i	0.0963308	−	0.166850i	−0.813832	−	0.581100i	$-0.802623\pi$
$967$	2.99556	−	5.18846i	0.0963308	−	0.166850i	0.910163	+	0.414250i	$0.135956\pi$
$968$		0			0
$969$	10.9795	−	5.49505i	0.352713	−	0.176527i
$970$		0			0
$971$	24.5340	−	17.4706i	0.787332	−	0.560657i	−0.114155	−	0.993463i	$-0.536416\pi$
$971$	24.5340	−	17.4706i	0.787332	−	0.560657i	0.901487	+	0.432806i	$0.142477\pi$
$972$		0			0
$973$	0.485323	+	10.1882i	0.0155588	+	0.326618i
$974$		0			0
$975$	8.64165	+	37.5783i	0.276754	+	1.20347i
$976$		0			0
$977$	−41.2922	+	10.0174i	−1.32105	+	0.320484i	−0.833457	−	0.552584i	$-0.813642\pi$
$977$	−41.2922	+	10.0174i	−1.32105	+	0.320484i	−0.487598	+	0.873068i	$0.662127\pi$
$978$		0			0
$979$	−0.346956	−	1.80018i	−0.0110888	−	0.0575340i
$980$		0			0
$981$	−57.3105	+	6.84468i	−1.82978	+	0.218534i
$982$		0			0
$983$	50.1807	−	32.2492i	1.60052	−	1.02859i	0.633544	−	0.773707i	$-0.281600\pi$
$983$	50.1807	−	32.2492i	1.60052	−	1.02859i	0.966972	−	0.254883i	$-0.0820368\pi$
$984$		0			0
$985$	−6.65291	+	3.42982i	−0.211979	+	0.109283i
$986$		0			0
$987$	−3.61268	+	6.80640i	−0.114993	+	0.216650i
$988$		0			0
$989$	26.7565	−	21.0416i	0.850809	−	0.669083i
$990$		0			0
$991$	−16.1174	−	13.9658i	−0.511986	−	0.443638i	0.360156	−	0.932892i	$-0.382724\pi$
$991$	−16.1174	−	13.9658i	−0.511986	−	0.443638i	−0.872141	+	0.489254i	$0.837269\pi$
$992$		0			0
$993$	19.9157	−	33.5611i	0.632005	−	1.06503i
$994$		0			0
$995$	−6.04150	−	3.11461i	−0.191528	−	0.0987397i
$996$		0			0
$997$	33.9533	+	9.96958i	1.07531	+	0.315740i	0.771001	−	0.636834i	$-0.219756\pi$
$997$	33.9533	+	9.96958i	1.07531	+	0.315740i	0.304309	+	0.952573i	$0.401574\pi$
$998$		0			0
$999$	−3.04284	+	5.41576i	−0.0962713	+	0.171347i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.ba.b.353.5	yes	440
3.2	odd	2	inner	804.2.ba.b.353.10	yes	440
67.41	odd	66	inner	804.2.ba.b.41.10	yes	440
201.41	even	66	inner	804.2.ba.b.41.5	✓	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.ba.b.41.5	✓	440	201.41	even	66	inner
804.2.ba.b.41.10	yes	440	67.41	odd	66	inner
804.2.ba.b.353.5	yes	440	1.1	even	1	trivial
804.2.ba.b.353.10	yes	440	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.ba (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32247 + 1.11851i) q^{3} +(0.102406 + 0.712247i) q^{5} +(0.0729329 - 0.763788i) q^{7} +(0.497878 - 2.95840i) q^{9} +O(q^{10})\)	\(q+(-1.32247 + 1.11851i) q^{3} +(0.102406 + 0.712247i) q^{5} +(0.0729329 - 0.763788i) q^{7} +(0.497878 - 2.95840i) q^{9} +(-0.457848 - 0.183294i) q^{11} +(3.42746 - 3.59462i) q^{13} +(-0.932083 - 0.827387i) q^{15} +(-6.00843 - 2.07954i) q^{17} +(1.10984 - 0.105977i) q^{19} +(0.757851 + 1.09167i) q^{21} +(7.01892 + 0.334352i) q^{23} +(4.30066 - 1.26279i) q^{25} +(2.65056 + 4.46929i) q^{27} +(-7.80897 - 4.50851i) q^{29} +(2.71627 + 2.84874i) q^{31} +(0.810508 - 0.269704i) q^{33} +(0.551474 - 0.0262700i) q^{35} +(0.597753 + 1.03534i) q^{37} +(-0.512121 + 8.58744i) q^{39} +(8.84237 - 1.70423i) q^{41} +(3.66095 - 3.17223i) q^{43} +(2.15810 + 0.0516556i) q^{45} +(2.65699 + 5.15385i) q^{47} +(6.29545 + 1.21335i) q^{49} +(10.2720 - 3.97034i) q^{51} +(1.01898 - 1.17596i) q^{53} +(0.0836648 - 0.344871i) q^{55} +(-1.34920 + 1.38152i) q^{57} +(1.87800 - 6.39587i) q^{59} +(-2.71070 - 6.77100i) q^{61} +(-2.22328 - 0.596038i) q^{63} +(2.91125 + 2.07309i) q^{65} +(-0.562265 + 8.16602i) q^{67} +(-9.65632 + 7.40855i) q^{69} +(-8.12417 + 2.81180i) q^{71} +(10.8460 - 4.34209i) q^{73} +(-4.27507 + 6.48032i) q^{75} +(-0.173390 + 0.336330i) q^{77} +(7.69406 + 1.86656i) q^{79} +(-8.50423 - 2.94584i) q^{81} +(-9.04632 - 11.5033i) q^{83} +(0.865847 - 4.49244i) q^{85} +(15.3700 - 2.77201i) q^{87} +(2.00976 + 3.12725i) q^{89} +(-2.49555 - 2.88002i) q^{91} +(-6.77854 - 0.729218i) q^{93} +(0.189136 + 0.779630i) q^{95} +(1.81643 - 1.04871i) q^{97} +(-0.770210 + 1.26324i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) \) 440 * q - 12 * q^7 + 4 * q^9	\( 440 q - 12 q^{7} + 4 q^{9} - 2 q^{15} - 10 q^{19} + 22 q^{21} - 68 q^{25} + 50 q^{31} + 11 q^{33} - 22 q^{37} - 45 q^{39} + 22 q^{43} + 22 q^{45} - 18 q^{49} - 6 q^{51} + 126 q^{55} - 183 q^{57} - 56 q^{61} - 141 q^{63} - 12 q^{67} + 33 q^{69} + 356 q^{73} + 165 q^{75} + 228 q^{79} + 24 q^{81} - 6 q^{85} + 75 q^{87} - 4 q^{91} - 75 q^{93} + 12 q^{97} + 88 q^{99}+O(q^{100}) \) 440 * q - 12 * q^7 + 4 * q^9 - 2 * q^15 - 10 * q^19 + 22 * q^21 - 68 * q^25 + 50 * q^31 + 11 * q^33 - 22 * q^37 - 45 * q^39 + 22 * q^43 + 22 * q^45 - 18 * q^49 - 6 * q^51 + 126 * q^55 - 183 * q^57 - 56 * q^61 - 141 * q^63 - 12 * q^67 + 33 * q^69 + 356 * q^73 + 165 * q^75 + 228 * q^79 + 24 * q^81 - 6 * q^85 + 75 * q^87 - 4 * q^91 - 75 * q^93 + 12 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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