LMFDB - Embedded newform 804.2.ba.b.353.10

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			353.10
Character	$\chi$	$=$	804.353
Dual form			804.2.ba.b.41.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.468055 + 1.66761i) q^{3} +(-0.102406 - 0.712247i) q^{5} +(0.0729329 - 0.763788i) q^{7} +(-2.56185 - 1.56107i) q^{9} +O(q^{10})$	\(q+(-0.468055 + 1.66761i) q^{3} +(-0.102406 - 0.712247i) q^{5} +(0.0729329 - 0.763788i) q^{7} +(-2.56185 - 1.56107i) q^{9} +(0.457848 + 0.183294i) q^{11} +(3.42746 - 3.59462i) q^{13} +(1.23568 + 0.162598i) q^{15} +(6.00843 + 2.07954i) q^{17} +(1.10984 - 0.105977i) q^{19} +(1.23956 + 0.479119i) q^{21} +(-7.01892 - 0.334352i) q^{23} +(4.30066 - 1.26279i) q^{25} +(3.80234 - 3.54150i) q^{27} +(7.80897 + 4.50851i) q^{29} +(2.71627 + 2.84874i) q^{31} +(-0.519962 + 0.677719i) q^{33} +(-0.551474 + 0.0262700i) q^{35} +(0.597753 + 1.03534i) q^{37} +(4.39018 + 7.39815i) q^{39} +(-8.84237 + 1.70423i) q^{41} +(3.66095 - 3.17223i) q^{43} +(-0.849518 + 1.98453i) q^{45} +(-2.65699 - 5.15385i) q^{47} +(6.29545 + 1.21335i) q^{49} +(-6.28013 + 9.04638i) q^{51} +(-1.01898 + 1.17596i) q^{53} +(0.0836648 - 0.344871i) q^{55} +(-0.342739 + 1.90039i) q^{57} +(-1.87800 + 6.39587i) q^{59} +(-2.71070 - 6.77100i) q^{61} +(-1.37917 + 1.84286i) q^{63} +(-2.91125 - 2.07309i) q^{65} +(-0.562265 + 8.16602i) q^{67} +(3.84281 - 11.5483i) q^{69} +(8.12417 - 2.81180i) q^{71} +(10.8460 - 4.34209i) q^{73} +(0.0928916 + 7.76287i) q^{75} +(0.173390 - 0.336330i) q^{77} +(7.69406 + 1.86656i) q^{79} +(4.12614 + 7.99844i) q^{81} +(9.04632 + 11.5033i) q^{83} +(0.865847 - 4.49244i) q^{85} +(-11.1735 + 10.9121i) q^{87} +(-2.00976 - 3.12725i) q^{89} +(-2.49555 - 2.88002i) q^{91} +(-6.02196 + 3.19631i) q^{93} +(-0.189136 - 0.779630i) q^{95} +(1.81643 - 1.04871i) q^{97} +(-0.886801 - 1.18430i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.468055	+	1.66761i	−0.270232	+	0.962795i
$3$	−0.468055	+	1.66761i	−0.270232	+	0.962795i
$4$		0			0
$5$	−0.102406	−	0.712247i	−0.0457972	−	0.318527i	−0.999823	−	0.0188027i	$-0.994015\pi$
$5$	−0.102406	−	0.712247i	−0.0457972	−	0.318527i	0.954026	−	0.299724i	$-0.0968945\pi$
$6$		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
$9$	−2.56185	−	1.56107i	−0.853950	−	0.520356i
$10$		0			0
$11$	0.457848	+	0.183294i	0.138046	+	0.0552654i	0.439657	−	0.898166i	$-0.355100\pi$
$11$	0.457848	+	0.183294i	0.138046	+	0.0552654i	−0.301611	+	0.953431i	$0.597524\pi$
$12$		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
$15$	1.23568	+	0.162598i	0.319052	+	0.0419827i
$16$		0			0
$17$	6.00843	+	2.07954i	1.45726	+	0.504362i	0.936903	−	0.349589i	$-0.113679\pi$
$17$	6.00843	+	2.07954i	1.45726	+	0.504362i	0.520354	+	0.853951i	$0.325800\pi$
$18$		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
$21$	1.23956	+	0.479119i	0.270495	+	0.104552i
$22$		0			0
$23$	−7.01892	−	0.334352i	−1.46355	−	0.0697173i	−0.699386	−	0.714744i	$-0.746543\pi$
$23$	−7.01892	−	0.334352i	−1.46355	−	0.0697173i	−0.764160	+	0.645027i	$0.776846\pi$
$24$		0			0
$25$	4.30066	−	1.26279i	0.860131	−	0.252557i
$26$		0			0
$27$	3.80234	−	3.54150i	0.731760	−	0.681562i
$28$		0			0
$29$	7.80897	+	4.50851i	1.45009	+	0.837210i	0.998486	−	0.0550091i	$-0.0175188\pi$
$29$	7.80897	+	4.50851i	1.45009	+	0.837210i	0.451604	+	0.892219i	$0.350852\pi$
$30$		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
$33$	−0.519962	+	0.677719i	−0.0905137	+	0.117976i
$34$		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
$39$	4.39018	+	7.39815i	0.702992	+	1.18465i
$40$		0			0
$41$	−8.84237	+	1.70423i	−1.38095	+	0.266156i	−0.825033	−	0.565085i	$-0.808843\pi$
$41$	−8.84237	+	1.70423i	−1.38095	+	0.266156i	−0.555913	+	0.831240i	$0.687631\pi$
$42$		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
$45$	−0.849518	+	1.98453i	−0.126639	+	0.295836i
$46$		0			0
$47$	−2.65699	−	5.15385i	−0.387562	−	0.751766i	0.611663	−	0.791118i	$-0.290501\pi$
$47$	−2.65699	−	5.15385i	−0.387562	−	0.751766i	−0.999225	+	0.0393523i	$0.987471\pi$
$48$		0			0
$49$	6.29545	+	1.21335i	0.899350	+	0.173335i
$50$		0			0
$51$	−6.28013	+	9.04638i	−0.879394	+	1.26675i
$52$		0			0
$53$	−1.01898	+	1.17596i	−0.139967	+	0.161531i	−0.821405	−	0.570345i	$-0.806809\pi$
$53$	−1.01898	+	1.17596i	−0.139967	+	0.161531i	0.681438	+	0.731876i	$0.261355\pi$
$54$		0			0
$55$	0.0836648	−	0.344871i	0.0112814	−	0.0465024i
$56$		0			0
$57$	−0.342739	+	1.90039i	−0.0453969	+	0.251713i
$58$		0			0
$59$	−1.87800	+	6.39587i	−0.244495	+	0.832672i	0.742213	+	0.670164i	$0.233776\pi$
$59$	−1.87800	+	6.39587i	−0.244495	+	0.832672i	−0.986707	+	0.162508i	$0.948042\pi$
$60$		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
$63$	−1.37917	+	1.84286i	−0.173759	+	0.232178i
$64$		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
$69$	3.84281	−	11.5483i	0.462620	−	1.39026i
$70$		0			0
$71$	8.12417	−	2.81180i	0.964162	−	0.333700i	0.200772	−	0.979638i	$-0.435655\pi$
$71$	8.12417	−	2.81180i	0.964162	−	0.333700i	0.763390	+	0.645938i	$0.223534\pi$
$72$		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
$75$	0.0928916	+	7.76287i	0.0107262	+	0.896379i
$76$		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
$81$	4.12614	+	7.99844i	0.458460	+	0.888715i
$82$		0			0
$83$	9.04632	+	11.5033i	0.992963	+	1.26265i	0.964782	+	0.263052i	$0.0847291\pi$
$83$	9.04632	+	11.5033i	0.992963	+	1.26265i	0.0281811	+	0.999603i	$0.491028\pi$
$84$		0			0
$85$	0.865847	−	4.49244i	0.0939143	−	0.487273i
$86$		0			0
$87$	−11.1735	+	10.9121i	−1.19792	+	1.16990i
$88$		0			0
$89$	−2.00976	−	3.12725i	−0.213034	−	0.331487i	0.718248	−	0.695788i	$-0.244945\pi$
$89$	−2.00976	−	3.12725i	−0.213034	−	0.331487i	−0.931282	+	0.364300i	$0.881308\pi$
$90$		0			0
$91$	−2.49555	−	2.88002i	−0.261605	−	0.301908i
$92$		0			0
$93$	−6.02196	+	3.19631i	−0.624448	+	0.331442i
$94$		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
$99$	−0.886801	−	1.18430i	−0.0891269	−	0.119027i
$100$		0			0
$101$	−9.01742	−	12.6632i	−0.897267	−	1.26004i	−0.964978	−	0.262330i	$-0.915509\pi$
$101$	−9.01742	−	12.6632i	−0.897267	−	1.26004i	0.0677112	−	0.997705i	$-0.478430\pi$
$102$		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
$105$	0.214312	−	0.931940i	0.0209147	−	0.0909480i
$106$		0			0
$107$	−14.7662	−	2.12306i	−1.42750	−	0.205244i	−0.615149	−	0.788411i	$-0.710904\pi$
$107$	−14.7662	−	2.12306i	−1.42750	−	0.205244i	−0.812352	+	0.583168i	$0.801813\pi$
$108$		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
$111$	−2.00632	+	0.512224i	−0.190432	+	0.0486181i
$112$		0			0
$113$	13.0375	+	10.2528i	1.22646	+	0.964499i	0.999955	−	0.00951088i	$-0.00302745\pi$
$113$	13.0375	+	10.2528i	1.22646	+	0.964499i	0.226505	+	0.974010i	$0.427270\pi$
$114$		0			0
$115$	0.480636	+	5.03344i	0.0448195	+	0.469371i
$116$		0			0
$117$	−14.3921	+	3.85837i	−1.33055	+	0.356707i
$118$		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
$123$	1.29673	−	15.5433i	0.116922	−	1.40149i
$124$		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
$129$	3.57652	+	7.58981i	0.314895	+	0.668246i
$130$		0			0
$131$	10.2167	−	15.8976i	0.892640	−	1.38898i	−0.0284368	−	0.999596i	$-0.509053\pi$
$131$	10.2167	−	15.8976i	0.892640	−	1.38898i	0.921077	−	0.389380i	$-0.127311\pi$
$132$		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	0.749138	−	0.662414i	$-0.230468\pi$
$137$	5.35826	+	3.44355i	0.457787	+	0.294202i	−0.291350	+	0.956616i	$0.594105\pi$
$138$		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
$141$	9.83823	−	2.01854i	0.828528	−	0.169992i
$142$		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
$147$	−4.97001	+	9.93044i	−0.409919	+	0.819049i
$148$		0			0
$149$	0.935127	+	0.427058i	0.0766086	+	0.0349860i	0.453351	−	0.891332i	$-0.350228\pi$
$149$	0.935127	+	0.427058i	0.0766086	+	0.0349860i	−0.376742	+	0.926318i	$0.622956\pi$
$150$		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
$153$	−12.1464	−	14.7070i	−0.981977	−	1.18899i
$154$		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
$159$	−1.48411	−	2.24967i	−0.117697	−	0.178410i
$160$		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
$165$	0.535951	+	0.300939i	0.0417237	+	0.0234281i
$166$		0			0
$167$	−13.2822	+	9.45824i	−1.02781	+	0.731901i	−0.963957	−	0.266058i	$-0.914279\pi$
$167$	−13.2822	+	9.45824i	−1.02781	+	0.731901i	−0.0638540	+	0.997959i	$0.520339\pi$
$168$		0			0
$169$	−0.555224	−	11.6556i	−0.0427095	−	0.896583i
$170$		0			0
$171$	−3.00869	−	1.46104i	−0.230080	−	0.111729i
$172$		0			0
$173$	−9.36076	+	2.27090i	−0.711685	+	0.172653i	−0.575228	−	0.817993i	$-0.695087\pi$
$173$	−9.36076	+	2.27090i	−0.711685	+	0.172653i	−0.136457	+	0.990646i	$0.543572\pi$
$174$		0			0
$175$	−0.650842	−	3.37689i	−0.0491990	−	0.255269i
$176$		0			0
$177$	−9.78682	−	6.12539i	−0.735622	−	0.460413i
$178$		0			0
$179$	−4.29867	+	2.76259i	−0.321298	+	0.206486i	−0.691340	−	0.722529i	$-0.742979\pi$
$179$	−4.29867	+	2.76259i	−0.321298	+	0.206486i	0.370043	+	0.929015i	$0.379343\pi$
$180$		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
$183$	12.5601	−	1.35119i	0.928473	−	0.0998828i
$184$		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
$189$	−2.42764	−	3.16247i	−0.176585	−	0.230036i
$190$		0			0
$191$	12.7980	+	6.59782i	0.926030	+	0.477402i	0.854159	−	0.520012i	$-0.174073\pi$
$191$	12.7980	+	6.59782i	0.926030	+	0.477402i	0.0718711	+	0.997414i	$0.477103\pi$
$192$		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
$195$	4.81973	−	3.88451i	0.345148	−	0.278175i
$196$		0			0
$197$	−3.40216	−	9.82990i	−0.242394	−	0.700351i	−0.998923	−	0.0463916i	$-0.985228\pi$
$197$	−3.40216	−	9.82990i	−0.242394	−	0.700351i	0.756529	−	0.653960i	$-0.226893\pi$
$198$		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
$201$	−13.3546	−	4.75979i	−0.941958	−	0.335729i
$202$		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
$207$	17.4595	+	11.8136i	1.21352	+	0.821100i
$208$		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
$213$	0.886432	+	14.8640i	0.0607373	+	1.01847i
$214$		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
$219$	2.16438	+	20.1193i	0.146255	+	1.35953i
$220$		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
$225$	−12.9889	−	3.47855i	−0.865928	−	0.231903i
$226$		0			0
$227$	−3.55785	−	18.4599i	−0.236143	−	1.22522i	−0.885463	−	0.464709i	$-0.846159\pi$
$227$	−3.55785	−	18.4599i	−0.236143	−	1.22522i	0.649321	−	0.760515i	$-0.275053\pi$
$228$		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
$231$	0.479712	+	0.446569i	0.0315627	+	0.0293821i
$232$		0			0
$233$	0.455903	+	9.57058i	0.0298672	+	0.626990i	0.963331	+	0.268317i	$0.0864675\pi$
$233$	0.455903	+	9.57058i	0.0298672	+	0.626990i	−0.933463	+	0.358673i	$0.883229\pi$
$234$		0			0
$235$	−3.39872	+	2.42022i	−0.221708	+	0.157878i
$236$		0			0
$237$	−6.71394	+	11.9570i	−0.436117	+	0.776693i
$238$		0			0
$239$	−6.97831	+	12.0868i	−0.451389	+	0.781829i	−0.998473	−	0.0552490i	$-0.982405\pi$
$239$	−6.97831	+	12.0868i	−0.451389	+	0.781829i	0.547083	+	0.837078i	$0.315738\pi$
$240$		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
$243$	−15.2695	+	3.13708i	−0.979541	+	0.201244i
$244$		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
$249$	−23.4173	+	9.70154i	−1.48401	+	0.614810i
$250$		0			0
$251$	0.505431	−	1.46035i	0.0319025	−	0.0921763i	−0.927925	−	0.372767i	$-0.878409\pi$
$251$	0.505431	−	1.46035i	0.0319025	−	0.0921763i	0.959828	+	0.280591i	$0.0905303\pi$
$252$		0			0
$253$	−3.15231	−	1.43961i	−0.198184	−	0.0905076i
$254$		0			0
$255$	7.08637	+	3.54660i	0.443766	+	0.222097i
$256$		0			0
$257$	−1.80024	+	4.49679i	−0.112296	+	0.280502i	−0.973861	−	0.227146i	$-0.927061\pi$
$257$	−1.80024	+	4.49679i	−0.112296	+	0.280502i	0.861565	+	0.507648i	$0.169485\pi$
$258$		0			0
$259$	0.834375	−	0.381046i	0.0518455	−	0.0236771i
$260$		0			0
$261$	−12.9673	−	23.7405i	−0.802656	−	1.46950i
$262$		0			0
$263$	−15.9211	+	2.28910i	−0.981735	+	0.141152i	−0.614450	−	0.788956i	$-0.710622\pi$
$263$	−15.9211	+	2.28910i	−0.981735	+	0.141152i	−0.367286	+	0.930108i	$0.619713\pi$
$264$		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	$0.0938311\pi$
$269$			9.53004i			0.581057i	−0.956866	+	0.290528i	$0.906169\pi$
$270$		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
$273$	5.97081	−	2.81360i	0.361370	−	0.170287i
$274$		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
$279$	−2.51160	−	11.5383i	−0.150365	−	0.690782i
$280$		0			0
$281$	−11.3790	−	10.8499i	−0.678817	−	0.647251i	0.270080	−	0.962838i	$-0.412950\pi$
$281$	−11.3790	−	10.8499i	−0.678817	−	0.647251i	−0.948897	+	0.315587i	$0.897798\pi$
$282$		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
$285$	1.38865	+	0.0495044i	0.0822563	+	0.00293239i
$286$		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
$291$	0.898659	+	3.51995i	0.0526803	+	0.206343i
$292$		0			0
$293$	−1.94667	−	6.62975i	−0.113726	−	0.387314i	0.882884	−	0.469591i	$-0.155599\pi$
$293$	−1.94667	−	6.62975i	−0.113726	−	0.387314i	−0.996609	+	0.0822776i	$0.973781\pi$
$294$		0			0
$295$	4.74776	+	0.682625i	0.276425	+	0.0397439i
$296$		0			0
$297$	2.39003	−	0.924519i	0.138684	−	0.0536460i
$298$		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
$303$	25.3379	−	9.11047i	1.45563	−	0.523383i
$304$		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
$309$	0.959692	+	1.80809i	0.0545950	+	0.102859i
$310$		0			0
$311$	17.5008	+	20.1970i	0.992382	+	1.14527i	0.989391	+	0.145274i	$0.0464063\pi$
$311$	17.5008	+	20.1970i	0.992382	+	1.14527i	0.00299002	+	0.999996i	$0.499048\pi$
$312$		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
$315$	1.45380	+	0.793589i	0.0819125	+	0.0447137i
$316$		0			0
$317$	−2.09975	+	10.8945i	−0.117934	+	0.611897i	0.874082	+	0.485779i	$0.161464\pi$
$317$	−2.09975	+	10.8945i	−0.117934	+	0.611897i	−0.992015	+	0.126118i	$0.959748\pi$
$318$		0			0
$319$	2.74893	+	3.49555i	0.153911	+	0.195713i
$320$		0			0
$321$	10.4518	−	23.6305i	0.583364	−	1.31893i
$322$		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
$327$	33.3210	−	0.398724i	1.84266	−	0.0220495i
$328$		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
$333$	0.0848805	−	3.58551i	0.00465142	−	0.196485i
$334$		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
$339$	−23.1999	+	16.9425i	−1.26004	+	0.920192i
$340$		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
$345$	−8.61879	−	1.55442i	−0.464020	−	0.0836870i
$346$		0			0
$347$	−0.318692	+	1.31367i	−0.0171083	+	0.0705213i	−0.979726	−	0.200343i	$-0.935794\pi$
$347$	−0.318692	+	1.31367i	−0.0171083	+	0.0705213i	0.962618	+	0.270864i	$0.0873095\pi$
$348$		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
$351$	0.302030	−	25.8063i	0.0161211	−	1.37744i
$352$		0			0
$353$	−6.98868	−	1.34696i	−0.371970	−	0.0716913i	−0.000159442	−	1.00000i	$-0.500051\pi$
$353$	−6.98868	−	1.34696i	−0.371970	−	0.0716913i	−0.371810	+	0.928309i	$0.621263\pi$
$354$		0			0
$355$	−2.83466	−	5.49847i	−0.150448	−	0.291829i
$356$		0			0
$357$	6.45148	+	5.45647i	0.341449	+	0.288787i
$358$		0			0
$359$	25.8420	−	22.3923i	1.36389	−	1.18182i	0.399689	−	0.916651i	$-0.369118\pi$
$359$	25.8420	−	22.3923i	1.36389	−	1.18182i	0.964202	−	0.265167i	$-0.0854272\pi$
$360$		0			0
$361$	−17.4361	+	3.36054i	−0.917691	+	0.176870i
$362$		0			0
$363$	16.0225	−	9.50804i	0.840966	−	0.499043i
$364$		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
$369$	25.3132	+	9.43756i	1.31775	+	0.491300i
$370$		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
$375$	11.6768	−	1.82172i	0.602985	−	0.0940734i
$376$		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
$381$	5.34020	−	13.8160i	0.273587	−	0.707817i
$382$		0			0
$383$	12.4215	−	1.18611i	0.634710	−	0.0606075i	0.227259	−	0.973834i	$-0.427024\pi$
$383$	12.4215	−	1.18611i	0.634710	−	0.0606075i	0.407451	+	0.913227i	$0.366418\pi$
$384$		0			0
$385$	−0.257306	−	0.0890546i	−0.0131135	−	0.00453864i
$386$		0			0
$387$	−14.3309	+	2.41179i	−0.728479	+	0.122598i
$388$		0			0
$389$	6.30391	−	6.61135i	0.319621	−	0.335209i	−0.544249	−	0.838924i	$-0.683185\pi$
$389$	6.30391	−	6.61135i	0.319621	−	0.335209i	0.863870	+	0.503715i	$0.168034\pi$
$390$		0			0
$391$	−41.4774	−	16.6050i	−2.09760	−	0.839753i
$392$		0			0
$393$	21.7289	+	24.4785i	1.09608	+	1.23478i
$394$		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
$399$	1.42650	+	0.400381i	0.0714142	+	0.0200441i
$400$		0			0
$401$	−37.9003			−1.89265			−0.946325	−	0.323218i	$-0.895235\pi$
$401$	−37.9003			−1.89265			−0.946325	+	0.323218i	$0.895235\pi$
$402$		0			0
$403$	19.5501			0.973858
$404$		0			0
$405$	5.27432	−	3.75791i	0.262083	−	0.186732i
$406$		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
$411$	−8.25045	+	7.32372i	−0.406965	+	0.361253i
$412$		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
$417$	3.00391	−	22.8286i	0.147102	−	1.11792i
$418$		0			0
$419$	−22.3142	−	7.72303i	−1.09012	−	0.377295i	−0.277880	−	0.960616i	$-0.589632\pi$
$419$	−22.3142	−	7.72303i	−1.09012	−	0.377295i	−0.812242	+	0.583321i	$0.801753\pi$
$420$		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
$423$	−1.23869	+	17.3511i	−0.0602271	+	0.843641i
$424$		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
$429$	0.653994	+	4.19192i	0.0315751	+	0.202388i
$430$		0			0
$431$	−21.1776	−	12.2269i	−1.02009	−	0.588949i	−0.105959	−	0.994370i	$-0.533791\pi$
$431$	−21.1776	−	12.2269i	−1.02009	−	0.588949i	−0.914130	+	0.405422i	$0.867125\pi$
$432$		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
$435$	8.91633	+	6.84081i	0.427505	+	0.327992i
$436$		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
$441$	−14.2339	−	12.9360i	−0.677803	−	0.616002i
$442$		0			0
$443$	−7.27332	+	1.40182i	−0.345566	+	0.0666024i	−0.359081	−	0.933306i	$-0.616910\pi$
$443$	−7.27332	+	1.40182i	−0.345566	+	0.0666024i	0.0135154	+	0.999909i	$0.495698\pi$
$444$		0			0
$445$	−2.02156	+	1.75169i	−0.0958312	+	0.0830382i
$446$		0			0
$447$	−1.14986	+	1.35954i	−0.0543864	+	0.0643041i
$448$		0			0
$449$	1.84954	+	3.58761i	0.0872852	+	0.169310i	0.928438	−	0.371489i	$-0.121153\pi$
$449$	1.84954	+	3.58761i	0.0872852	+	0.169310i	−0.841152	+	0.540798i	$0.818122\pi$
$450$		0			0
$451$	−4.36083	−	0.840482i	−0.205344	−	0.0395767i
$452$		0			0
$453$	9.57921	+	6.65003i	0.450070	+	0.312446i
$454$		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
$459$	30.2107	−	13.3717i	1.41012	−	0.624139i
$460$		0			0
$461$	−6.48390	+	22.0821i	−0.301985	+	1.02847i	0.659063	+	0.752087i	$0.270953\pi$
$461$	−6.48390	+	22.0821i	−0.301985	+	1.02847i	−0.961049	+	0.276380i	$0.910865\pi$
$462$		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
$465$	2.89325	+	3.96180i	0.134171	+	0.183724i
$466$		0			0
$467$	−6.68274	−	4.75876i	−0.309240	−	0.220209i	0.414891	−	0.909871i	$-0.363820\pi$
$467$	−6.68274	−	4.75876i	−0.309240	−	0.220209i	−0.724131	+	0.689662i	$0.757759\pi$
$468$		0			0
$469$	6.19610	+	1.02502i	0.286109	+	0.0473311i
$470$		0			0
$471$	4.25667	+	1.41644i	0.196137	+	0.0652663i
$472$		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
$477$	4.44622	−	1.42194i	0.203578	−	0.0651064i
$478$		0			0
$479$	6.19309	−	12.0129i	0.282970	−	0.548885i	−0.703920	−	0.710279i	$-0.748569\pi$
$479$	6.19309	−	12.0129i	0.282970	−	0.548885i	0.986890	+	0.161394i	$0.0515991\pi$
$480$		0			0
$481$	5.77043	+	1.39989i	0.263109	+	0.0638295i
$482$		0			0
$483$	−8.54021	−	3.77735i	−0.388593	−	0.171875i
$484$		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
$489$	−6.93210	−	7.09815i	−0.313480	−	0.320989i
$490$		0			0
$491$	12.7512	+	19.8412i	0.575453	+	0.895422i	0.999950	−	0.0100070i	$-0.00318537\pi$
$491$	12.7512	+	19.8412i	0.575453	+	0.895422i	−0.424497	+	0.905429i	$0.639549\pi$
$492$		0			0
$493$	37.5440	+	43.3281i	1.69090	+	1.95140i
$494$		0			0
$495$	−0.752703	+	0.752901i	−0.0338315	+	0.0338404i
$496$		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
$501$	−9.55584	−	26.5766i	−0.426924	−	1.18735i
$502$		0			0
$503$	8.66130	+	12.1631i	0.386188	+	0.542325i	0.961212	−	0.275811i	$-0.0889465\pi$
$503$	8.66130	+	12.1631i	0.386188	+	0.542325i	−0.575024	+	0.818137i	$0.695007\pi$
$504$		0			0
$505$	−8.09589	+	7.71941i	−0.360262	+	0.343509i
$506$		0			0
$507$	19.6968	+	4.52956i	0.874767	+	0.201165i
$508$		0			0
$509$	−0.747224	−	0.107435i	−0.0331201	−	0.00476196i	0.125735	−	0.992064i	$-0.459871\pi$
$509$	−0.747224	−	0.107435i	−0.0331201	−	0.00476196i	−0.158855	+	0.987302i	$0.550780\pi$
$510$		0			0
$511$	−2.52541	−	8.60074i	−0.111717	−	0.380474i
$512$		0			0
$513$	3.84468	−	4.33347i	0.169747	−	0.191328i
$514$		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
$519$	0.594383	−	16.6730i	0.0260905	−	0.731863i
$520$		0			0
$521$	0.681593	−	1.49248i	0.0298611	−	0.0653867i	−0.894114	−	0.447840i	$-0.852193\pi$
$521$	0.681593	−	1.49248i	0.0298611	−	0.0653867i	0.923975	+	0.382453i	$0.124921\pi$
$522$		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
$525$	5.93596	+	0.495219i	0.259067	+	0.0216131i
$526$		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
$531$	14.7955	−	13.4536i	0.642072	−	0.583836i
$532$		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
$543$	−8.81587	−	42.9679i	−0.378325	−	1.84393i
$544$		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
$549$	−3.62558	+	21.5779i	−0.154736	+	0.920921i
$550$		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
$555$	0.570288	+	1.37654i	0.0242074	+	0.0584310i
$556$		0			0
$557$	−25.5617	+	32.5044i	−1.08309	+	1.37726i	−0.162503	+	0.986708i	$0.551957\pi$
$557$	−25.5617	+	32.5044i	−1.08309	+	1.37726i	−0.920583	+	0.390547i	$0.872286\pi$
$558$		0			0
$559$	1.14481	−	24.0324i	0.0484201	−	1.01646i
$560$		0			0
$561$	−4.53349	+	2.99075i	−0.191404	+	0.126269i
$562$		0			0
$563$	2.56815	−	17.8618i	0.108234	−	0.752787i	−0.861347	−	0.508017i	$-0.830379\pi$
$563$	2.56815	−	17.8618i	0.108234	−	0.752787i	0.969581	−	0.244770i	$-0.0787123\pi$
$564$		0			0
$565$	5.96739	−	10.3358i	0.251050	−	0.434831i
$566$		0			0
$567$	6.41004	−	2.56814i	0.269196	−	0.107852i
$568$		0			0
$569$	20.0817	−	14.3001i	0.841868	−	0.599491i	−0.0756733	−	0.997133i	$-0.524111\pi$
$569$	20.0817	−	14.3001i	0.841868	−	0.599491i	0.917541	+	0.397641i	$0.130171\pi$
$570$		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
$573$	−16.9928	+	18.2539i	−0.709883	+	0.762568i
$574$		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
$579$	−6.00721	+	9.59799i	−0.249651	+	0.398879i
$580$		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
$585$	4.22194	+	9.85560i	0.174556	+	0.407479i
$586$		0			0
$587$	34.6085	−	27.2165i	1.42845	−	1.12334i	0.456066	−	0.889946i	$-0.349258\pi$
$587$	34.6085	−	27.2165i	1.42845	−	1.12334i	0.972382	−	0.233397i	$-0.0749842\pi$
$588$		0			0
$589$	3.31654	+	2.87380i	0.136656	+	0.118413i
$590$		0			0
$591$	17.9848	−	1.07254i	0.739797	−	0.0441186i
$592$		0			0
$593$	1.02148	+	0.526611i	0.0419473	+	0.0216253i	0.479073	−	0.877775i	$-0.340973\pi$
$593$	1.02148	+	0.526611i	0.0419473	+	0.0216253i	−0.437125	+	0.899401i	$0.644003\pi$
$594$		0			0
$595$	−3.36812	−	0.988970i	−0.138080	−	0.0405438i
$596$		0			0
$597$	−10.2669	−	12.7387i	−0.420195	−	0.521360i
$598$		0			0
$599$	−7.05909	−	20.3959i	−0.288427	−	0.833354i	−0.992392	−	0.123120i	$-0.960710\pi$
$599$	−7.05909	−	20.3959i	−0.288427	−	0.833354i	0.703965	−	0.710235i	$-0.251411\pi$
$600$		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
$603$	14.1881	−	20.0424i	0.577786	−	0.816188i
$604$		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
$609$	7.51961	+	9.33001i	0.304710	+	0.378071i
$610$		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
$615$	−11.2035	+	0.668130i	−0.451767	+	0.0269416i
$616$		0			0
$617$	−25.5107	−	22.1051i	−1.02702	−	0.889919i	−0.0330383	−	0.999454i	$-0.510518\pi$
$617$	−25.5107	−	22.1051i	−1.02702	−	0.889919i	−0.993983	+	0.109535i	$0.965064\pi$
$618$		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
$621$	−27.8724	+	23.5862i	−1.11848	+	0.946481i
$622$		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
$627$	−0.505253	+	0.807267i	−0.0201779	+	0.0322391i
$628$		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
$633$	22.0808	−	23.7196i	0.877633	−	0.942768i
$634$		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
$639$	−25.2023	−	5.47897i	−0.996988	−	0.216745i
$640$		0			0
$641$	12.4842	−	21.6233i	0.493098	−	0.854070i	−0.506871	−	0.862022i	$-0.669198\pi$
$641$	12.4842	−	21.6233i	0.493098	−	0.854070i	0.999968	+	0.00795173i	$0.00253114\pi$
$642$		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
$645$	5.03957	−	3.32460i	0.198433	−	0.130906i
$646$		0			0
$647$	−1.46370	+	30.7268i	−0.0575439	+	1.20800i	0.766792	+	0.641895i	$0.221852\pi$
$647$	−1.46370	+	30.7268i	−0.0575439	+	1.20800i	−0.824336	+	0.566101i	$0.808451\pi$
$648$		0			0
$649$	−2.03217	+	2.58411i	−0.0797695	+	0.101435i
$650$		0			0
$651$	2.00211	+	4.83261i	0.0784687	+	0.189405i
$652$		0			0
$653$	11.9399	−	34.4979i	0.467243	−	1.35001i	−0.427738	−	0.903903i	$-0.640689\pi$
$653$	11.9399	−	34.4979i	0.467243	−	1.35001i	0.894980	−	0.446106i	$-0.147189\pi$
$654$		0			0
$655$	−12.3692	−	5.64884i	−0.483306	−	0.220718i
$656$		0			0
$657$	−34.5642	−	5.80759i	−1.34848	−	0.226575i
$658$		0			0
$659$	11.1980	−	27.9712i	0.436211	−	1.08960i	−0.533598	−	0.845738i	$-0.679160\pi$
$659$	11.1980	−	27.9712i	0.436211	−	1.08960i	0.969809	−	0.243865i	$-0.0784154\pi$
$660$		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
$663$	10.9934	+	53.5808i	0.426947	+	2.08091i
$664$		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
$675$	11.8804	−	20.0323i	0.457277	−	0.771044i
$676$		0			0
$677$	18.8041	+	1.79557i	0.722701	+	0.0690095i	0.449923	−	0.893068i	$-0.351452\pi$
$677$	18.8041	+	1.79557i	0.722701	+	0.0690095i	0.272778	+	0.962077i	$0.412058\pi$
$678$		0			0
$679$	−0.668518	−	1.46385i	−0.0256554	−	0.0561774i
$680$		0			0
$681$	32.4491	+	2.70713i	1.24345	+	0.103737i
$682$		0			0
$683$	3.78334	+	3.60741i	0.144765	+	0.138034i	0.759002	−	0.651089i	$-0.225687\pi$
$683$	3.78334	+	3.60741i	0.144765	+	0.138034i	−0.614236	+	0.789122i	$0.710536\pi$
$684$		0			0
$685$	1.90394	−	4.16904i	0.0727457	−	0.159291i
$686$		0			0
$687$	0.399626	−	11.2099i	0.0152467	−	0.427684i
$688$		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
$693$	−0.969234	+	0.590953i	−0.0368181	+	0.0224485i
$694$		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
$699$	−16.1734	−	3.71929i	−0.611734	−	0.140677i
$700$		0			0
$701$	3.03624	−	2.89505i	0.114677	−	0.109345i	−0.630571	−	0.776131i	$-0.717179\pi$
$701$	3.03624	−	2.89505i	0.114677	−	0.109345i	0.745249	+	0.666787i	$0.232331\pi$
$702$		0			0
$703$	0.773135	+	1.08572i	0.0291593	+	0.0409486i
$704$		0			0
$705$	−2.44519	−	6.80054i	−0.0920913	−	0.256123i
$706$		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
$711$	−16.7972	−	16.7928i	−0.629944	−	0.629779i
$712$		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
$717$	−16.8898	−	17.2944i	−0.630762	−	0.645871i
$718$		0			0
$719$	4.48842	−	23.2881i	0.167390	−	0.868501i	−0.796993	−	0.603989i	$-0.793577\pi$
$719$	4.48842	−	23.2881i	0.167390	−	0.868501i	0.964382	−	0.264512i	$-0.0852108\pi$
$720$		0			0
$721$	−0.560532	−	0.712775i	−0.0208753	−	0.0265451i
$722$		0			0
$723$	−26.1406	−	11.5620i	−0.972180	−	0.429997i
$724$		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
$729$	1.91556	−	26.9320i	0.0709466	−	0.997480i
$730$		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
$735$	7.58188	+	2.52294i	0.279662	+	0.0930601i
$736$		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
$741$	5.65645	+	7.74554i	0.207795	+	0.284539i
$742$		0			0
$743$	−2.89884	−	7.24096i	−0.106348	−	0.265645i	0.865643	−	0.500661i	$-0.166910\pi$
$743$	−2.89884	−	7.24096i	−0.106348	−	0.265645i	−0.971991	+	0.235016i	$0.924486\pi$
$744$		0			0
$745$	0.208409	−	0.709775i	0.00763550	−	0.0260041i
$746$		0			0
$747$	−5.21783	−	43.5917i	−0.190910	−	1.59494i
$748$		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
$753$	2.19872	+	1.52639i	0.0801259	+	0.0556246i
$754$		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
$759$	3.87617	−	4.58301i	0.140696	−	0.166353i
$760$		0			0
$761$	−35.4724	+	30.7370i	−1.28587	+	1.11422i	−0.298736	+	0.954336i	$0.596565\pi$
$761$	−35.4724	+	30.7370i	−1.28587	+	1.11422i	−0.987137	+	0.159879i	$0.948889\pi$
$762$		0			0
$763$	−14.4948	+	2.79364i	−0.524747	+	0.101137i
$764$		0			0
$765$	−9.23117	+	10.1573i	−0.333754	+	0.367238i
$766$		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
$771$	−6.65629	−	5.10685i	−0.239720	−	0.183919i
$772$		0			0
$773$	−10.5107	−	11.0233i	−0.378042	−	0.396479i	0.507034	−	0.861926i	$-0.330742\pi$
$773$	−10.5107	−	11.0233i	−0.378042	−	0.396479i	−0.885076	+	0.465447i	$0.845893\pi$
$774$		0			0
$775$	15.2791	+	8.82139i	0.548841	+	0.316874i
$776$		0			0
$777$	0.244903	+	1.56976i	0.00878585	+	0.0563149i
$778$		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
$783$	45.6592	−	10.5126i	1.63173	−	0.375689i
$784$		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
$789$	3.63461	−	27.6216i	0.129395	−	0.983354i
$790$		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
$795$	−1.45034	+	1.28743i	−0.0514382	+	0.0456604i
$796$		0			0
$797$	0.407149	−	4.26386i	0.0144220	−	0.151034i	−0.985392	−	0.170299i	$-0.945527\pi$
$797$	0.407149	−	4.26386i	0.0144220	−	0.151034i	0.999814	+	0.0192654i	$0.00613274\pi$
$798$		0			0
$799$	−5.24673	−	36.4918i	−0.185616	−	1.29099i
$800$		0			0
$801$	0.266857	+	11.1489i	0.00942892	+	0.393927i
$802$		0			0
$803$	5.76170			0.203326
$804$		0			0
$805$	3.87954			0.136736
$806$		0			0
$807$	−15.8924	−	4.46058i	−0.559439	−	0.157020i
$808$		0			0
$809$	−3.13245	−	21.7867i	−0.110131	−	0.765979i	−0.967790	−	0.251759i	$-0.918991\pi$
$809$	−3.13245	−	21.7867i	−0.110131	−	0.765979i	0.857659	−	0.514219i	$-0.171918\pi$
$810$		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
$813$	9.28986	+	10.4654i	0.325810	+	0.367037i
$814$		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
$819$	1.89732	+	11.2739i	0.0662978	+	0.393942i
$820$		0			0
$821$	19.4033	+	6.71555i	0.677180	+	0.234374i	0.643943	−	0.765073i	$-0.277297\pi$
$821$	19.4033	+	6.71555i	0.677180	+	0.234374i	0.0332368	+	0.999448i	$0.489418\pi$
$822$		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
$825$	−1.38036	+	3.57124i	−0.0480580	+	0.124335i
$826$		0			0
$827$	14.0703	+	0.670252i	0.489273	+	0.0233069i	0.290769	−	0.956793i	$-0.406089\pi$
$827$	14.0703	+	0.670252i	0.489273	+	0.0233069i	0.198504	+	0.980100i	$0.436392\pi$
$828$		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
$831$	−12.6717	+	1.97694i	−0.439575	+	0.0685794i
$832$		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
$837$	20.4170	+	1.21221i	0.705715	+	0.0419002i
$838$		0			0
$839$	−21.3940	+	1.01912i	−0.738601	+	0.0351839i	−0.413511	−	0.910499i	$-0.635698\pi$
$839$	−21.3940	+	1.01912i	−0.738601	+	0.0351839i	−0.325090	+	0.945683i	$0.605395\pi$
$840$		0			0
$841$	26.1534	+	45.2989i	0.901840	+	1.56203i
$842$		0			0
$843$	23.4194	−	13.8975i	0.806608	−	0.478654i
$844$		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
$849$	−0.387398	−	0.327649i	−0.0132955	−	0.0112449i
$850$		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
$855$	−0.732517	+	2.29255i	−0.0250515	+	0.0784035i
$856$		0			0
$857$	−23.8020	+	27.4690i	−0.813062	+	0.938324i	−0.999021	−	0.0442336i	$-0.985915\pi$
$857$	−23.8020	+	27.4690i	−0.813062	+	0.938324i	0.185959	+	0.982558i	$0.440461\pi$
$858$		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
$861$	−11.7772	−	2.12404i	−0.401366	−	0.0723873i
$862$		0			0
$863$	−0.721751	+	2.45806i	−0.0245687	+	0.0836732i	−0.970865	−	0.239628i	$-0.922975\pi$
$863$	−0.721751	+	2.45806i	−0.0245687	+	0.0836732i	0.946296	+	0.323301i	$0.104793\pi$
$864$		0			0
$865$	2.57603	+	6.43462i	0.0875877	+	0.218784i
$866$		0			0
$867$	−32.7670	+	23.9293i	−1.11282	+	0.812680i
$868$		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
$873$	−6.29052	−	0.148917i	−0.212902	−	0.00504006i
$874$		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
$879$	11.9670	−	0.143199i	0.403636	−	0.00482997i
$880$		0			0
$881$	14.8928	−	28.8881i	0.501752	−	0.973263i	−0.492910	−	0.870080i	$-0.664067\pi$
$881$	14.8928	−	28.8881i	0.501752	−	0.973263i	0.994662	−	0.103183i	$-0.0329028\pi$
$882$		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
$885$	−3.36057	+	7.59791i	−0.112964	+	0.255401i
$886$		0			0
$887$	−19.9515	−	25.3704i	−0.669906	−	0.851854i	0.325702	−	0.945472i	$-0.394399\pi$
$887$	−19.9515	−	25.3704i	−0.669906	−	0.851854i	−0.995608	+	0.0936179i	$0.970157\pi$
$888$		0			0
$889$	−1.24177	+	6.44291i	−0.0416476	+	0.216088i
$890$		0			0
$891$	0.423072	+	4.41836i	0.0141735	+	0.148021i
$892$		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
$897$	−28.3408	−	53.3949i	−0.946270	−	1.78280i
$898$		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
$903$	6.05785	−	2.17815i	0.201593	−	0.0724844i
$904$		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
$909$	3.33317	+	46.5180i	0.110554	+	1.54290i
$910$		0			0
$911$	27.7046	+	3.98331i	0.917893	+	0.131973i	0.585039	−	0.811005i	$-0.301079\pi$
$911$	27.7046	+	3.98331i	0.917893	+	0.131973i	0.332854	+	0.942978i	$0.391988\pi$
$912$		0			0
$913$	2.03334	+	6.92491i	0.0672937	+	0.229181i
$914$		0			0
$915$	−2.24861	−	8.80756i	−0.0743368	−	0.291169i
$916$		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
$921$	−40.5862	−	1.44687i	−1.33736	−	0.0476761i
$922$		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
$927$	−3.46438	+	0.754106i	−0.113785	+	0.0247681i
$928$		0			0
$929$	−20.1531	−	44.1290i	−0.661200	−	1.44783i	−0.881399	−	0.472372i	$-0.843398\pi$
$929$	−20.1531	−	44.1290i	−0.661200	−	1.44783i	0.220199	−	0.975455i	$-0.429329\pi$
$930$		0			0
$931$	7.11555	+	0.679453i	0.233203	+	0.0222682i
$932$		0			0
$933$	−41.8722	+	19.7312i	−1.37083	+	0.645972i
$934$		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	−0.236357	−	0.971666i	$-0.575954\pi$
$941$	−37.3754	−	24.0197i	−1.21840	−	0.783020i	−0.982045	+	0.188647i	$0.939590\pi$
$942$		0			0
$943$	62.6337	−	9.00537i	2.03963	−	0.293255i
$944$		0			0
$945$	−2.00386	+	2.05293i	−0.0651855	+	0.0667819i
$946$		0			0
$947$	−15.8179	+	7.22381i	−0.514014	+	0.234742i	−0.655496	−	0.755199i	$-0.727540\pi$
$947$	−15.8179	+	7.22381i	−0.514014	+	0.234742i	0.141482	+	0.989941i	$0.454813\pi$
$948$		0			0
$949$	21.5662	−	53.8697i	0.700067	−	1.74868i
$950$		0			0
$951$	−17.1850	−	8.60080i	−0.557263	−	0.278900i
$952$		0			0
$953$	8.87013	+	4.05085i	0.287332	+	0.131220i	0.553867	−	0.832605i	$-0.313152\pi$
$953$	8.87013	+	4.05085i	0.287332	+	0.131220i	−0.266535	+	0.963825i	$0.585879\pi$
$954$		0			0
$955$	3.38869	−	9.79098i	0.109655	−	0.316829i
$956$		0			0
$957$	−7.11587	+	2.94804i	−0.230023	+	0.0952965i
$958$		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
$963$	34.5145	+	28.4899i	1.11221	+	0.918076i
$964$		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
$969$	−6.01126	+	10.7056i	−0.193109	+	0.343914i
$970$		0			0
$971$	−24.5340	+	17.4706i	−0.787332	+	0.560657i	−0.901487	−	0.432806i	$-0.857523\pi$
$971$	−24.5340	+	17.4706i	−0.787332	+	0.560657i	0.114155	+	0.993463i	$0.463584\pi$
$972$		0			0
$973$	0.485323	+	10.1882i	0.0155588	+	0.326618i
$974$		0			0
$975$	28.2230	+	26.2730i	0.903858	+	0.841411i
$976$		0			0
$977$	41.2922	−	10.0174i	1.32105	−	0.320484i	0.487598	−	0.873068i	$-0.337873\pi$
$977$	41.2922	−	10.0174i	1.32105	−	0.320484i	0.833457	+	0.552584i	$0.186358\pi$
$978$		0			0
$979$	−0.346956	−	1.80018i	−0.0110888	−	0.0575340i
$980$		0			0
$981$	−14.9312	+	55.7531i	−0.476715	+	1.78006i
$982$		0			0
$983$	−50.1807	+	32.2492i	−1.60052	+	1.02859i	−0.633544	+	0.773707i	$0.718400\pi$
$983$	−50.1807	+	32.2492i	−1.60052	+	1.02859i	−0.966972	+	0.254883i	$0.917963\pi$
$984$		0			0
$985$	−6.65291	+	3.42982i	−0.211979	+	0.109283i
$986$		0			0
$987$	−0.824209	−	7.66154i	−0.0262349	−	0.243870i
$988$		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
$993$	−2.32319	−	38.9562i	−0.0737242	−	1.23624i
$994$		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
$999$	5.93951	+	1.81977i	0.187918	+	0.0575748i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(-0.468055 + 1.66761i) q^{3} +(-0.102406 - 0.712247i) q^{5} +(0.0729329 - 0.763788i) q^{7} +(-2.56185 - 1.56107i) q^{9} +O(q^{10})\)	\(q+(-0.468055 + 1.66761i) q^{3} +(-0.102406 - 0.712247i) q^{5} +(0.0729329 - 0.763788i) q^{7} +(-2.56185 - 1.56107i) q^{9} +(0.457848 + 0.183294i) q^{11} +(3.42746 - 3.59462i) q^{13} +(1.23568 + 0.162598i) q^{15} +(6.00843 + 2.07954i) q^{17} +(1.10984 - 0.105977i) q^{19} +(1.23956 + 0.479119i) q^{21} +(-7.01892 - 0.334352i) q^{23} +(4.30066 - 1.26279i) q^{25} +(3.80234 - 3.54150i) q^{27} +(7.80897 + 4.50851i) q^{29} +(2.71627 + 2.84874i) q^{31} +(-0.519962 + 0.677719i) q^{33} +(-0.551474 + 0.0262700i) q^{35} +(0.597753 + 1.03534i) q^{37} +(4.39018 + 7.39815i) q^{39} +(-8.84237 + 1.70423i) q^{41} +(3.66095 - 3.17223i) q^{43} +(-0.849518 + 1.98453i) q^{45} +(-2.65699 - 5.15385i) q^{47} +(6.29545 + 1.21335i) q^{49} +(-6.28013 + 9.04638i) q^{51} +(-1.01898 + 1.17596i) q^{53} +(0.0836648 - 0.344871i) q^{55} +(-0.342739 + 1.90039i) q^{57} +(-1.87800 + 6.39587i) q^{59} +(-2.71070 - 6.77100i) q^{61} +(-1.37917 + 1.84286i) q^{63} +(-2.91125 - 2.07309i) q^{65} +(-0.562265 + 8.16602i) q^{67} +(3.84281 - 11.5483i) q^{69} +(8.12417 - 2.81180i) q^{71} +(10.8460 - 4.34209i) q^{73} +(0.0928916 + 7.76287i) q^{75} +(0.173390 - 0.336330i) q^{77} +(7.69406 + 1.86656i) q^{79} +(4.12614 + 7.99844i) q^{81} +(9.04632 + 11.5033i) q^{83} +(0.865847 - 4.49244i) q^{85} +(-11.1735 + 10.9121i) q^{87} +(-2.00976 - 3.12725i) q^{89} +(-2.49555 - 2.88002i) q^{91} +(-6.02196 + 3.19631i) q^{93} +(-0.189136 - 0.779630i) q^{95} +(1.81643 - 1.04871i) q^{97} +(-0.886801 - 1.18430i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) \) 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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