LMFDB - Embedded newform 804.2.s.b.161.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(5,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 5]))

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

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

chi := DirichletCharacter("804.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.s (of order $22$, degree $10$, 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:	$200$
Relative dimension:	$20$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			161.15
Character	$\chi$	$=$	804.161
Dual form			804.2.s.b.5.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.650892 - 1.60510i) q^{3} +(-0.966140 - 0.283684i) q^{5} +(1.54930 - 1.34247i) q^{7} +(-2.15268 - 2.08949i) q^{9} +O(q^{10})$	\(q+(0.650892 - 1.60510i) q^{3} +(-0.966140 - 0.283684i) q^{5} +(1.54930 - 1.34247i) q^{7} +(-2.15268 - 2.08949i) q^{9} +(-2.68695 - 0.788959i) q^{11} +(0.303154 - 0.471717i) q^{13} +(-1.08419 + 1.36610i) q^{15} +(-2.99315 + 0.430350i) q^{17} +(3.48728 - 4.02453i) q^{19} +(-1.14638 - 3.36058i) q^{21} +(-1.38260 - 0.631411i) q^{23} +(-3.35332 - 2.15505i) q^{25} +(-4.75500 + 2.09523i) q^{27} -1.01679i q^{29} +(1.77218 + 2.75757i) q^{31} +(-3.01527 + 3.79929i) q^{33} +(-1.87767 + 0.857505i) q^{35} +0.414150 q^{37} +(-0.559831 - 0.793629i) q^{39} +(-0.649850 - 4.51980i) q^{41} +(0.863281 - 0.124121i) q^{43} +(1.48703 + 2.62942i) q^{45} +(-1.67750 - 0.766089i) q^{47} +(-0.398118 + 2.76897i) q^{49} +(-1.25746 + 5.08441i) q^{51} +(1.21708 - 8.46498i) q^{53} +(2.37215 + 1.52449i) q^{55} +(-4.18993 - 8.21696i) q^{57} +(-1.75024 - 2.72343i) q^{59} +(-0.230536 - 0.785133i) q^{61} +(-6.14022 - 0.347328i) q^{63} +(-0.426708 + 0.369744i) q^{65} +(8.16532 + 0.572263i) q^{67} +(-1.91340 + 1.80822i) q^{69} +(-2.98320 - 0.428919i) q^{71} +(-3.06133 + 0.898887i) q^{73} +(-5.64171 + 3.97970i) q^{75} +(-5.22203 + 2.38482i) q^{77} +(0.0461512 - 0.0718126i) q^{79} +(0.268052 + 8.99601i) q^{81} +(-3.01301 + 10.2614i) q^{83} +(3.01389 + 0.433331i) q^{85} +(-1.63205 - 0.661823i) q^{87} +(8.74397 - 3.99324i) q^{89} +(-0.163592 - 1.13781i) q^{91} +(5.57967 - 1.04965i) q^{93} +(-4.51089 + 2.89897i) q^{95} -3.47150i q^{97} +(4.13561 + 7.31273i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 10 q^{9}+O(q^{10}) $ 200 * q - 10 * q^9	$ 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) $ 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{17}{22}\right)$	$1$

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
$3$	0.650892	−	1.60510i	0.375793	−	0.926704i
$3$	0.650892	−	1.60510i	0.375793	−	0.926704i
$4$		0			0
$5$	−0.966140	−	0.283684i	−0.432071	−	0.126867i	0.0584631	−	0.998290i	$-0.481380\pi$
$5$	−0.966140	−	0.283684i	−0.432071	−	0.126867i	−0.490534	+	0.871422i	$0.663198\pi$
$6$		0			0
$7$	1.54930	−	1.34247i	0.585579	−	0.507407i	−0.310930	−	0.950433i	$-0.600640\pi$
$7$	1.54930	−	1.34247i	0.585579	−	0.507407i	0.896509	+	0.443026i	$0.146095\pi$
$8$		0			0
$9$	−2.15268	−	2.08949i	−0.717560	−	0.696497i
$10$		0			0
$11$	−2.68695	−	0.788959i	−0.810145	−	0.237880i	−0.149678	−	0.988735i	$-0.547824\pi$
$11$	−2.68695	−	0.788959i	−0.810145	−	0.237880i	−0.660467	+	0.750855i	$0.729642\pi$
$12$		0			0
$13$	0.303154	−	0.471717i	0.0840798	−	0.130831i	−0.796666	−	0.604419i	$-0.793405\pi$
$13$	0.303154	−	0.471717i	0.0840798	−	0.130831i	0.880746	+	0.473588i	$0.157042\pi$
$14$		0			0
$15$	−1.08419	+	1.36610i	−0.279938	+	0.352726i
$16$		0			0
$17$	−2.99315	+	0.430350i	−0.725946	+	0.104375i	−0.495374	−	0.868680i	$-0.664969\pi$
$17$	−2.99315	+	0.430350i	−0.725946	+	0.104375i	−0.230572	+	0.973055i	$0.574060\pi$
$18$		0			0
$19$	3.48728	−	4.02453i	0.800036	−	0.923291i	−0.198347	−	0.980132i	$-0.563557\pi$
$19$	3.48728	−	4.02453i	0.800036	−	0.923291i	0.998383	+	0.0568410i	$0.0181028\pi$
$20$		0			0
$21$	−1.14638	−	3.36058i	−0.250160	−	0.733338i
$22$		0			0
$23$	−1.38260	−	0.631411i	−0.288292	−	0.131658i	0.266020	−	0.963967i	$-0.414291\pi$
$23$	−1.38260	−	0.631411i	−0.288292	−	0.131658i	−0.554312	+	0.832309i	$0.687018\pi$
$24$		0			0
$25$	−3.35332	−	2.15505i	−0.670664	−	0.431009i
$26$		0			0
$27$	−4.75500	+	2.09523i	−0.915100	+	0.403227i
$28$		0			0
$29$		−	1.01679i		−	0.188814i	−0.995534	−	0.0944069i	$-0.969905\pi$
$29$		−	1.01679i		−	0.188814i	0.995534	−	0.0944069i	$-0.0300955\pi$
$30$		0			0
$31$	1.77218	+	2.75757i	0.318293	+	0.495274i	0.963126	−	0.269049i	$-0.0867095\pi$
$31$	1.77218	+	2.75757i	0.318293	+	0.495274i	−0.644833	+	0.764323i	$0.723073\pi$
$32$		0			0
$33$	−3.01527	+	3.79929i	−0.524891	+	0.661371i
$34$		0			0
$35$	−1.87767	+	0.857505i	−0.317385	+	0.144945i
$36$		0			0
$37$	0.414150			0.0680858			0.0340429	−	0.999420i	$-0.489162\pi$
$37$	0.414150			0.0680858			0.0340429	+	0.999420i	$0.489162\pi$
$38$		0			0
$39$	−0.559831	−	0.793629i	−0.0896448	−	0.127082i
$40$		0			0
$41$	−0.649850	−	4.51980i	−0.101489	−	0.705875i	−0.975505	−	0.219977i	$-0.929402\pi$
$41$	−0.649850	−	4.51980i	−0.101489	−	0.705875i	0.874016	−	0.485898i	$-0.161507\pi$
$42$		0			0
$43$	0.863281	−	0.124121i	0.131649	−	0.0189283i	−0.0761752	−	0.997094i	$-0.524271\pi$
$43$	0.863281	−	0.124121i	0.131649	−	0.0189283i	0.207824	+	0.978166i	$0.433362\pi$
$44$		0			0
$45$	1.48703	+	2.62942i	0.221674	+	0.391971i
$46$		0			0
$47$	−1.67750	−	0.766089i	−0.244689	−	0.111746i	0.289296	−	0.957240i	$-0.406579\pi$
$47$	−1.67750	−	0.766089i	−0.244689	−	0.111746i	−0.533985	+	0.845494i	$0.679306\pi$
$48$		0			0
$49$	−0.398118	+	2.76897i	−0.0568740	+	0.395568i
$50$		0			0
$51$	−1.25746	+	5.08441i	−0.176080	+	0.711960i
$52$		0			0
$53$	1.21708	−	8.46498i	0.167179	−	1.16275i	−0.717502	−	0.696557i	$-0.754715\pi$
$53$	1.21708	−	8.46498i	0.167179	−	1.16275i	0.884681	−	0.466197i	$-0.154376\pi$
$54$		0			0
$55$	2.37215	+	1.52449i	0.319861	+	0.205562i
$56$		0			0
$57$	−4.18993	−	8.21696i	−0.554969	−	1.08836i
$58$		0			0
$59$	−1.75024	−	2.72343i	−0.227862	−	0.354560i	0.708431	−	0.705780i	$-0.249403\pi$
$59$	−1.75024	−	2.72343i	−0.227862	−	0.354560i	−0.936293	+	0.351220i	$0.885767\pi$
$60$		0			0
$61$	−0.230536	−	0.785133i	−0.0295171	−	0.100526i	0.943417	−	0.331609i	$-0.107591\pi$
$61$	−0.230536	−	0.785133i	−0.0295171	−	0.100526i	−0.972934	+	0.231083i	$0.925773\pi$
$62$		0			0
$63$	−6.14022	−	0.347328i	−0.773595	−	0.0437593i
$64$		0			0
$65$	−0.426708	+	0.369744i	−0.0529266	+	0.0458612i
$66$		0			0
$67$	8.16532	+	0.572263i	0.997553	+	0.0699131i
$67$	8.16532	+	0.572263i	0.997553	+	0.0699131i
$68$		0			0
$69$	−1.91340	+	1.80822i	−0.230346	+	0.217685i
$70$		0			0
$71$	−2.98320	−	0.428919i	−0.354040	−	0.0509033i	−0.0369996	−	0.999315i	$-0.511780\pi$
$71$	−2.98320	−	0.428919i	−0.354040	−	0.0509033i	−0.317041	+	0.948412i	$0.602689\pi$
$72$		0			0
$73$	−3.06133	+	0.898887i	−0.358301	+	0.105207i	−0.455929	−	0.890016i	$-0.650693\pi$
$73$	−3.06133	+	0.898887i	−0.358301	+	0.105207i	0.0976275	+	0.995223i	$0.468875\pi$
$74$		0			0
$75$	−5.64171	+	3.97970i	−0.651449	+	0.459536i
$76$		0			0
$77$	−5.22203	+	2.38482i	−0.595106	+	0.271776i
$78$		0			0
$79$	0.0461512	−	0.0718126i	0.00519241	−	0.00807955i	−0.838648	−	0.544674i	$-0.816653\pi$
$79$	0.0461512	−	0.0718126i	0.00519241	−	0.00807955i	0.843840	+	0.536595i	$0.180290\pi$
$80$		0			0
$81$	0.268052	+	8.99601i	0.0297835	+	0.999556i
$82$		0			0
$83$	−3.01301	+	10.2614i	−0.330720	+	1.12633i	0.611474	+	0.791264i	$0.290577\pi$
$83$	−3.01301	+	10.2614i	−0.330720	+	1.12633i	−0.942195	+	0.335066i	$0.891241\pi$
$84$		0			0
$85$	3.01389	+	0.433331i	0.326902	+	0.0470014i
$86$		0			0
$87$	−1.63205	−	0.661823i	−0.174975	−	0.0709549i
$88$		0			0
$89$	8.74397	−	3.99324i	0.926859	−	0.423282i	0.105970	−	0.994369i	$-0.466205\pi$
$89$	8.74397	−	3.99324i	0.926859	−	0.423282i	0.820890	+	0.571087i	$0.193478\pi$
$90$		0			0
$91$	−0.163592	−	1.13781i	−0.0171491	−	0.119274i
$92$		0			0
$93$	5.57967	−	1.04965i	0.578585	−	0.108843i
$94$		0			0
$95$	−4.51089	+	2.89897i	−0.462808	+	0.297428i
$96$		0			0
$97$		−	3.47150i		−	0.352477i	−0.984347	−	0.176239i	$-0.943607\pi$
$97$		−	3.47150i		−	0.352477i	0.984347	−	0.176239i	$-0.0563930\pi$
$98$		0			0
$99$	4.13561	+	7.31273i	0.415645	+	0.734957i
$100$		0			0
$101$	2.21410	−	2.55520i	0.220311	−	0.254252i	−0.634825	−	0.772656i	$-0.718928\pi$
$101$	2.21410	−	2.55520i	0.220311	−	0.254252i	0.855136	+	0.518403i	$0.173473\pi$
$102$		0			0
$103$	8.21404	−	5.27884i	0.809354	−	0.520140i	−0.0693021	−	0.997596i	$-0.522077\pi$
$103$	8.21404	−	5.27884i	0.809354	−	0.520140i	0.878656	+	0.477456i	$0.158441\pi$
$104$		0			0
$105$	0.154216	+	3.57200i	0.0150500	+	0.348591i
$106$		0			0
$107$	1.90540	+	6.48919i	0.184202	+	0.627334i	0.998875	+	0.0474140i	$0.0150980\pi$
$107$	1.90540	+	6.48919i	0.184202	+	0.627334i	−0.814673	+	0.579920i	$0.803084\pi$
$108$		0			0
$109$	7.92724	−	12.3350i	0.759292	−	1.18148i	−0.219297	−	0.975658i	$-0.570376\pi$
$109$	7.92724	−	12.3350i	0.759292	−	1.18148i	0.978589	−	0.205824i	$-0.0659873\pi$
$110$		0			0
$111$	0.269567	−	0.664751i	0.0255861	−	0.0630953i
$112$		0			0
$113$	12.4656	−	3.66022i	1.17266	−	0.344324i	0.363321	−	0.931664i	$-0.381643\pi$
$113$	12.4656	−	3.66022i	1.17266	−	0.344324i	0.809340	+	0.587340i	$0.199825\pi$
$114$		0			0
$115$	1.15666	+	1.00225i	0.107859	+	0.0934606i
$116$		0			0
$117$	−1.63824	+	0.382017i	−0.151456	+	0.0353175i
$118$		0			0
$119$	−4.05954	+	4.68496i	−0.372138	+	0.429470i
$120$		0			0
$121$	−2.65656	−	1.70727i	−0.241505	−	0.155206i
$122$		0			0
$123$	−7.67771	−	1.89883i	−0.692276	−	0.171212i
$124$		0			0
$125$	5.92541	+	6.83828i	0.529985	+	0.611635i
$126$		0			0
$127$	−1.39668	−	1.61186i	−0.123936	−	0.143029i	0.690391	−	0.723437i	$-0.257439\pi$
$127$	−1.39668	−	1.61186i	−0.123936	−	0.143029i	−0.814326	+	0.580408i	$0.802893\pi$
$128$		0			0
$129$	0.362676	−	1.46644i	0.0319319	−	0.129113i
$130$		0			0
$131$	7.30624	+	3.33665i	0.638349	+	0.291524i	0.708177	−	0.706035i	$-0.249518\pi$
$131$	7.30624	+	3.33665i	0.638349	+	0.291524i	−0.0698282	+	0.997559i	$0.522245\pi$
$132$		0			0
$133$		−	10.9168i		−	0.946604i
$134$		0			0
$135$	5.18838	−	0.675363i	0.446544	−	0.0581260i
$136$		0			0
$137$	6.97149	−	15.2654i	0.595615	−	1.30421i	−0.336375	−	0.941728i	$-0.609201\pi$
$137$	6.97149	−	15.2654i	0.595615	−	1.30421i	0.931989	−	0.362486i	$-0.118072\pi$
$138$		0			0
$139$	−2.28442	+	7.78001i	−0.193762	+	0.659892i	0.804098	+	0.594497i	$0.202649\pi$
$139$	−2.28442	+	7.78001i	−0.193762	+	0.659892i	−0.997859	+	0.0653948i	$0.979169\pi$
$140$		0			0
$141$	−2.32152	+	2.19391i	−0.195507	+	0.184761i
$142$		0			0
$143$	−1.18672	+	1.02830i	−0.0992389	+	0.0859910i
$144$		0			0
$145$	−0.288448	+	0.982365i	−0.0239543	+	0.0815809i
$146$		0			0
$147$	4.18534	+	2.44132i	0.345201	+	0.201357i
$148$		0			0
$149$	16.1494	+	13.9935i	1.32301	+	1.14640i	0.978187	+	0.207729i	$0.0666071\pi$
$149$	16.1494	+	13.9935i	1.32301	+	1.14640i	0.344825	+	0.938667i	$0.387938\pi$
$150$		0			0
$151$	0.189990	+	1.32141i	0.0154611	+	0.107535i	0.996091	−	0.0883374i	$-0.0281554\pi$
$151$	0.189990	+	1.32141i	0.0154611	+	0.107535i	−0.980629	+	0.195872i	$0.937246\pi$
$152$		0			0
$153$	7.34251	+	5.32776i	0.593606	+	0.430724i
$154$		0			0
$155$	−0.929896	−	3.16694i	−0.0746911	−	0.254374i
$156$		0			0
$157$	8.86174	−	19.4045i	0.707244	−	1.54865i	−0.123718	−	0.992317i	$-0.539482\pi$
$157$	8.86174	−	19.4045i	0.707244	−	1.54865i	0.830961	−	0.556330i	$-0.187791\pi$
$158$		0			0
$159$	−12.7949	−	7.46332i	−1.01470	−	0.591880i
$160$		0			0
$161$	−2.98971	+	0.877857i	−0.235622	+	0.0691848i
$162$		0			0
$163$	−1.47744			−0.115722			−0.0578608	−	0.998325i	$-0.518428\pi$
$163$	−1.47744			−0.115722			−0.0578608	+	0.998325i	$0.518428\pi$
$164$		0			0
$165$	3.99097	−	2.81526i	0.310697	−	0.219167i
$166$		0			0
$167$	−1.89688	−	1.64366i	−0.146785	−	0.127190i	0.578373	−	0.815773i	$-0.303688\pi$
$167$	−1.89688	−	1.64366i	−0.146785	−	0.127190i	−0.725158	+	0.688582i	$0.758233\pi$
$168$		0			0
$169$	5.26978	+	11.5392i	0.405368	+	0.887632i
$170$		0			0
$171$	−15.9162	+	1.37689i	−1.21714	+	0.105293i
$172$		0			0
$173$	6.75608	+	10.5127i	0.513655	+	0.799263i	0.997099	−	0.0761122i	$-0.0242507\pi$
$173$	6.75608	+	10.5127i	0.513655	+	0.799263i	−0.483444	+	0.875375i	$0.660614\pi$
$174$		0			0
$175$	−8.08838	+	1.16293i	−0.611424	+	0.0879095i
$176$		0			0
$177$	−5.51059	+	1.03665i	−0.414201	+	0.0779194i
$178$		0			0
$179$	4.58992	+	10.0505i	0.343067	+	0.751212i	0.999996	−	0.00274020i	$-0.000872234\pi$
$179$	4.58992	+	10.0505i	0.343067	+	0.751212i	−0.656929	+	0.753952i	$0.728145\pi$
$180$		0			0
$181$	0.387326	−	0.848125i	0.0287897	−	0.0630406i	−0.894691	−	0.446686i	$-0.852604\pi$
$181$	0.387326	−	0.848125i	0.0287897	−	0.0630406i	0.923481	+	0.383645i	$0.125331\pi$
$182$		0			0
$183$	−1.41027	−	0.141004i	−0.104250	−	0.0104233i
$184$		0			0
$185$	−0.400126	−	0.117488i	−0.0294179	−	0.00863787i
$186$		0			0
$187$	8.38197	+	1.20515i	0.612950	+	0.0881289i
$188$		0			0
$189$	−4.55412	+	9.62959i	−0.331263	+	0.700449i
$190$		0			0
$191$	−3.97243	−	8.69841i	−0.287435	−	0.629395i	0.709744	−	0.704460i	$-0.248811\pi$
$191$	−3.97243	−	8.69841i	−0.287435	−	0.629395i	−0.997179	+	0.0750653i	$0.976083\pi$
$192$		0			0
$193$	20.1470	−	12.9477i	1.45021	−	0.931994i	0.450990	−	0.892529i	$-0.351071\pi$
$193$	20.1470	−	12.9477i	1.45021	−	0.931994i	0.999221	−	0.0394647i	$-0.0125653\pi$
$194$		0			0
$195$	0.315735	+	0.925572i	0.0226103	+	0.0662816i
$196$		0			0
$197$	1.49850	−	10.4223i	0.106764	−	0.742560i	−0.864168	−	0.503204i	$-0.832155\pi$
$197$	1.49850	−	10.4223i	0.106764	−	0.742560i	0.970932	−	0.239356i	$-0.0769363\pi$
$198$		0			0
$199$	−7.29446	−	8.41826i	−0.517091	−	0.596755i	0.435809	−	0.900039i	$-0.356462\pi$
$199$	−7.29446	−	8.41826i	−0.517091	−	0.596755i	−0.952900	+	0.303284i	$0.901917\pi$
$200$		0			0
$201$	6.23328	−	12.7337i	0.439662	−	0.898163i
$202$		0			0
$203$	−1.36502	−	1.57531i	−0.0958055	−	0.110565i
$204$		0			0
$205$	−0.654351	+	4.55111i	−0.0457019	+	0.317864i
$206$		0			0
$207$	1.65696	+	4.24815i	0.115167	+	0.295267i
$208$		0			0
$209$	−12.5453	+	8.06239i	−0.867778	+	0.557687i
$210$		0			0
$211$	5.67188	+	12.4197i	0.390468	+	0.855006i	0.998148	+	0.0608245i	$0.0193730\pi$
$211$	5.67188	+	12.4197i	0.390468	+	0.855006i	−0.607680	+	0.794182i	$0.707900\pi$
$212$		0			0
$213$	−2.63020	+	4.50914i	−0.180218	+	0.308961i
$214$		0			0
$215$	−0.869261	−	0.124981i	−0.0592831	−	0.00852362i
$216$		0			0
$217$	6.44760	+	1.89319i	0.437691	+	0.128518i
$218$		0			0
$219$	−0.549793	+	5.49881i	−0.0371515	+	0.371575i
$220$		0			0
$221$	−0.704383	+	1.54238i	−0.0473819	+	0.103752i
$222$		0			0
$223$	2.86676	+	6.27733i	0.191973	+	0.420361i	0.981003	−	0.193993i	$-0.0621439\pi$
$223$	2.86676	+	6.27733i	0.191973	+	0.420361i	−0.789030	+	0.614354i	$0.789417\pi$
$224$		0			0
$225$	2.71567	+	11.6459i	0.181044	+	0.776390i
$226$		0			0
$227$	21.5035	−	3.09174i	1.42724	−	0.205206i	0.614997	−	0.788529i	$-0.289157\pi$
$227$	21.5035	−	3.09174i	1.42724	−	0.205206i	0.812240	+	0.583324i	$0.198248\pi$
$228$		0			0
$229$	9.34315	+	14.5382i	0.617413	+	0.960713i	0.999333	+	0.0365175i	$0.0116265\pi$
$229$	9.34315	+	14.5382i	0.617413	+	0.960713i	−0.381920	+	0.924195i	$0.624737\pi$
$230$		0			0
$231$	0.428893	+	9.93414i	0.0282191	+	0.653618i
$232$		0			0
$233$	5.77365	+	12.6425i	0.378245	+	0.828240i	0.999020	+	0.0442520i	$0.0140905\pi$
$233$	5.77365	+	12.6425i	0.378245	+	0.828240i	−0.620776	+	0.783988i	$0.713182\pi$
$234$		0			0
$235$	1.40337	+	1.21603i	0.0915460	+	0.0793250i
$236$		0			0
$237$	−0.0852269	−	0.120819i	−0.00553608	−	0.00784807i
$238$		0			0
$239$	3.28691			0.212613			0.106306	−	0.994333i	$-0.466098\pi$
$239$	3.28691			0.212613			0.106306	+	0.994333i	$0.466098\pi$
$240$		0			0
$241$	−24.1310	+	7.08551i	−1.55442	+	0.456418i	−0.942417	−	0.334441i	$-0.891453\pi$
$241$	−24.1310	+	7.08551i	−1.55442	+	0.456418i	−0.611999	+	0.790859i	$0.709634\pi$
$242$		0			0
$243$	14.6139	+	5.42518i	0.937485	+	0.348026i
$244$		0			0
$245$	1.17015	−	2.56227i	0.0747583	−	0.163698i
$246$		0			0
$247$	−0.841258	−	2.86506i	−0.0535279	−	0.182299i
$248$		0			0
$249$	14.5093	+	11.5152i	0.919492	+	0.729747i
$250$		0			0
$251$	1.44108	+	10.0229i	0.0909599	+	0.632640i	0.983397	+	0.181468i	$0.0580848\pi$
$251$	1.44108	+	10.0229i	0.0909599	+	0.632640i	−0.892437	+	0.451172i	$0.851006\pi$
$252$		0			0
$253$	3.21681	+	2.78738i	0.202239	+	0.175241i
$254$		0			0
$255$	2.65725	−	4.55553i	0.166404	−	0.285278i
$256$		0			0
$257$	−3.00280	+	10.2266i	−0.187310	+	0.637919i	0.811271	+	0.584670i	$0.198776\pi$
$257$	−3.00280	+	10.2266i	−0.187310	+	0.637919i	−0.998581	+	0.0532489i	$0.983042\pi$
$258$		0			0
$259$	0.641641	−	0.555985i	0.0398696	−	0.0345472i
$260$		0			0
$261$	−2.12458	+	2.18883i	−0.131508	+	0.135485i
$262$		0			0
$263$	−5.74612	+	19.5695i	−0.354321	+	1.20671i	0.568891	+	0.822413i	$0.307373\pi$
$263$	−5.74612	+	19.5695i	−0.354321	+	1.20671i	−0.923211	+	0.384292i	$0.874445\pi$
$264$		0			0
$265$	−3.57725	+	7.83308i	−0.219749	+	0.481182i
$266$		0			0
$267$	−0.718155	−	16.6341i	−0.0439504	−	1.01799i
$268$		0			0
$269$		−	18.7758i		−	1.14478i	−0.819980	−	0.572392i	$-0.806016\pi$
$269$		−	18.7758i		−	1.14478i	0.819980	−	0.572392i	$-0.193984\pi$
$270$		0			0
$271$	−10.3459	−	4.72482i	−0.628470	−	0.287013i	0.0756055	−	0.997138i	$-0.475911\pi$
$271$	−10.3459	−	4.72482i	−0.628470	−	0.287013i	−0.704075	+	0.710125i	$0.748638\pi$
$272$		0			0
$273$	−1.93277	−	0.478008i	−0.116977	−	0.0289304i
$274$		0			0
$275$	7.30995	+	8.43613i	0.440806	+	0.508718i
$276$		0			0
$277$	−7.83597	−	9.04319i	−0.470818	−	0.543353i	0.469821	−	0.882762i	$-0.344318\pi$
$277$	−7.83597	−	9.04319i	−0.470818	−	0.543353i	−0.940639	+	0.339409i	$0.889773\pi$
$278$		0			0
$279$	1.94698	−	9.63912i	0.116563	−	0.577079i
$280$		0			0
$281$	−3.01821	−	1.93968i	−0.180051	−	0.115712i	0.447511	−	0.894279i	$-0.352311\pi$
$281$	−3.01821	−	1.93968i	−0.180051	−	0.115712i	−0.627562	+	0.778567i	$0.715947\pi$
$282$		0			0
$283$	−7.46491	+	8.61497i	−0.443743	+	0.512107i	−0.932923	−	0.360076i	$-0.882751\pi$
$283$	−7.46491	+	8.61497i	−0.443743	+	0.512107i	0.489180	+	0.872183i	$0.337296\pi$
$284$		0			0
$285$	1.71703	+	9.12734i	0.101708	+	0.540657i
$286$		0			0
$287$	−7.07452	−	6.13011i	−0.417596	−	0.361849i
$288$		0			0
$289$	−7.53763	+	2.21325i	−0.443390	+	0.130191i
$290$		0			0
$291$	−5.57209	−	2.25957i	−0.326642	−	0.132458i
$292$		0			0
$293$	5.35113	−	8.32652i	0.312616	−	0.486441i	−0.649019	−	0.760772i	$-0.724820\pi$
$293$	5.35113	−	8.32652i	0.312616	−	0.486441i	0.961635	+	0.274332i	$0.0884567\pi$
$294$		0			0
$295$	0.918384	+	3.12773i	0.0534704	+	0.182103i
$296$		0			0
$297$	14.4295	−	1.87826i	0.837284	−	0.108988i
$298$		0			0
$299$	−0.716988	+	0.460780i	−0.0414645	+	0.0266476i
$300$		0			0
$301$	1.17085	−	1.35123i	0.0674866	−	0.0778837i
$302$		0			0
$303$	−2.66022	−	5.21701i	−0.152825	−	0.299709i
$304$		0			0
$305$			0.823948i			0.0471791i
$306$		0			0
$307$	5.18062	−	3.32938i	0.295674	−	0.190018i	−0.384390	−	0.923171i	$-0.625588\pi$
$307$	5.18062	−	3.32938i	0.295674	−	0.190018i	0.680064	+	0.733153i	$0.261952\pi$
$308$		0			0
$309$	−3.12661	−	16.6203i	−0.177866	−	0.945496i
$310$		0			0
$311$	−4.81843	−	33.5129i	−0.273228	−	1.90034i	−0.413957	−	0.910297i	$-0.635853\pi$
$311$	−4.81843	−	33.5129i	−0.273228	−	1.90034i	0.140728	−	0.990048i	$-0.455056\pi$
$312$		0			0
$313$	−21.8275	+	9.96830i	−1.23377	+	0.563442i	−0.922174	−	0.386775i	$-0.873589\pi$
$313$	−21.8275	+	9.96830i	−1.23377	+	0.563442i	−0.311591	+	0.950216i	$0.600862\pi$
$314$		0			0
$315$	5.83378	+	2.07745i	0.328696	+	0.117051i
$316$		0			0
$317$	−19.5268	−	2.80753i	−1.09673	−	0.157687i	−0.429888	−	0.902882i	$-0.641447\pi$
$317$	−19.5268	−	2.80753i	−1.09673	−	0.157687i	−0.666846	+	0.745195i	$0.732356\pi$
$318$		0			0
$319$	−0.802209	+	2.73207i	−0.0449151	+	0.152967i
$320$		0			0
$321$	11.6560	+	1.16541i	0.650574	+	0.0650470i
$322$		0			0
$323$	−8.70599	+	13.5468i	−0.484414	+	0.753763i
$324$		0			0
$325$	−2.03314	+	0.928506i	−0.112779	+	0.0515042i
$326$		0			0
$327$	−14.6392	−	20.7528i	−0.809547	−	1.14763i
$328$		0			0
$329$	−3.62740	+	1.06510i	−0.199985	+	0.0587209i
$330$		0			0
$331$	−8.36891	−	1.20327i	−0.459997	−	0.0661375i	−0.0915788	−	0.995798i	$-0.529191\pi$
$331$	−8.36891	−	1.20327i	−0.459997	−	0.0661375i	−0.368418	+	0.929660i	$0.620100\pi$
$332$		0			0
$333$	−0.891531	−	0.865362i	−0.0488556	−	0.0474216i
$334$		0			0
$335$	−7.72650	−	2.86926i	−0.422144	−	0.156764i
$336$		0			0
$337$	−2.94419	+	2.55116i	−0.160380	+	0.138970i	−0.731354	−	0.681998i	$-0.761111\pi$
$337$	−2.94419	+	2.55116i	−0.160380	+	0.138970i	0.570974	+	0.820968i	$0.306566\pi$
$338$		0			0
$339$	2.23873	−	22.3908i	0.121591	−	1.21610i
$340$		0			0
$341$	−2.58615	−	8.80762i	−0.140048	−	0.476959i
$342$		0			0
$343$	10.8587	+	16.8965i	0.586315	+	0.912325i
$344$		0			0
$345$	2.36158	−	1.20420i	0.127143	−	0.0648318i
$346$		0			0
$347$	9.66034	+	6.20832i	0.518594	+	0.333280i	0.773616	−	0.633655i	$-0.218446\pi$
$347$	9.66034	+	6.20832i	0.518594	+	0.333280i	−0.255022	+	0.966935i	$0.582083\pi$
$348$		0			0
$349$	4.77161	−	33.1873i	0.255418	−	1.77647i	−0.309076	−	0.951037i	$-0.600020\pi$
$349$	4.77161	−	33.1873i	0.255418	−	1.77647i	0.564494	−	0.825437i	$-0.309071\pi$
$350$		0			0
$351$	−0.453144	+	2.87819i	−0.0241870	+	0.153626i
$352$		0			0
$353$	0.418454	−	2.91041i	0.0222721	−	0.154906i	−0.975650	−	0.219331i	$-0.929612\pi$
$353$	0.418454	−	2.91041i	0.0222721	−	0.154906i	0.997923	+	0.0644256i	$0.0205215\pi$
$354$		0			0
$355$	2.76051	+	1.26068i	0.146512	+	0.0669100i
$356$		0			0
$357$	4.87750	+	9.56537i	0.258145	+	0.506253i
$358$		0			0
$359$	−36.2740	+	5.21541i	−1.91447	+	0.275259i	−0.993450	−	0.114265i	$-0.963549\pi$
$359$	−36.2740	+	5.21541i	−1.91447	+	0.275259i	−0.921016	+	0.389524i	$0.872640\pi$
$360$		0			0
$361$	−1.33177	−	9.26270i	−0.0700934	−	0.487510i
$362$		0			0
$363$	−4.46946	+	3.15279i	−0.234586	+	0.165478i
$364$		0			0
$365$	3.21267			0.168159
$366$		0			0
$367$	−15.0174	+	6.85821i	−0.783901	+	0.357995i	−0.766823	−	0.641859i	$-0.778164\pi$
$367$	−15.0174	+	6.85821i	−0.783901	+	0.357995i	−0.0170778	+	0.999854i	$0.505436\pi$
$368$		0			0
$369$	−8.04517	+	11.0875i	−0.418815	+	0.577194i
$370$		0			0
$371$	−9.47838	−	14.7487i	−0.492093	−	0.765712i
$372$		0			0
$373$		−	24.2146i		−	1.25378i	−0.779106	−	0.626892i	$-0.784327\pi$
$373$		−	24.2146i		−	1.25378i	0.779106	−	0.626892i	$-0.215673\pi$
$374$		0			0
$375$	14.8329	−	5.05987i	0.765969	−	0.261291i
$376$		0			0
$377$	−0.479639	−	0.308245i	−0.0247027	−	0.0158754i
$378$		0			0
$379$	3.71132	+	1.69490i	0.190638	+	0.0870612i	0.508447	−	0.861093i	$-0.330220\pi$
$379$	3.71132	+	1.69490i	0.190638	+	0.0870612i	−0.317809	+	0.948155i	$0.602947\pi$
$380$		0			0
$381$	−3.49628	+	1.19267i	−0.179120	+	0.0611022i
$382$		0			0
$383$	−4.71606	+	5.44262i	−0.240979	+	0.278105i	−0.863337	−	0.504628i	$-0.831630\pi$
$383$	−4.71606	+	5.44262i	−0.240979	+	0.278105i	0.622357	+	0.782733i	$0.286175\pi$
$384$		0			0
$385$	5.72175	−	0.822664i	0.291607	−	0.0419268i
$386$		0			0
$387$	−2.11772	−	1.53663i	−0.107650	−	0.0781111i
$388$		0			0
$389$	8.77788	−	13.6586i	0.445056	−	0.692521i	−0.544160	−	0.838981i	$-0.683152\pi$
$389$	8.77788	−	13.6586i	0.445056	−	0.692521i	0.989217	+	0.146460i	$0.0467881\pi$
$390$		0			0
$391$	4.41005	+	1.29491i	0.223026	+	0.0654863i
$392$		0			0
$393$	10.1112	−	9.55543i	0.510043	−	0.482008i
$394$		0			0
$395$	−0.0649606	+	0.0562887i	−0.00326852	+	0.00283219i
$396$		0			0
$397$	−5.99947	−	1.76160i	−0.301105	−	0.0884123i	0.127690	−	0.991814i	$-0.459244\pi$
$397$	−5.99947	−	1.76160i	−0.301105	−	0.0884123i	−0.428795	+	0.903402i	$0.641062\pi$
$398$		0			0
$399$	−17.5225	−	7.10564i	−0.877221	−	0.355727i
$400$		0			0
$401$	−20.2313			−1.01030			−0.505152	−	0.863030i	$-0.668564\pi$
$401$	−20.2313			−1.01030			−0.505152	+	0.863030i	$0.668564\pi$
$402$		0			0
$403$	1.83804			0.0915591
$404$		0			0
$405$	2.29305	−	8.76744i	0.113943	−	0.435658i
$406$		0			0
$407$	−1.11280	−	0.326747i	−0.0551594	−	0.0161963i
$408$		0			0
$409$	0.00324140	−	0.00280869i	0.000160277	−	0.000138881i	−0.654781	−	0.755819i	$-0.727239\pi$
$409$	0.00324140	−	0.00280869i	0.000160277	−	0.000138881i	0.654941	+	0.755680i	$0.272694\pi$
$410$		0			0
$411$	−19.9648	−	21.1261i	−0.984792	−	1.04207i
$412$		0			0
$413$	−6.36777	−	1.86975i	−0.313338	−	0.0920042i
$414$		0			0
$415$	5.82197	−	9.05916i	0.285789	−	0.444697i
$416$		0			0
$417$	11.0008	+	8.73066i	0.538710	+	0.427542i
$418$		0			0
$419$	22.8438	−	3.28445i	1.11600	−	0.160456i	0.440452	−	0.897776i	$-0.354818\pi$
$419$	22.8438	−	3.28445i	1.11600	−	0.160456i	0.675543	+	0.737320i	$0.263909\pi$
$420$		0			0
$421$	−3.60373	+	4.15892i	−0.175635	+	0.202693i	−0.836741	−	0.547599i	$-0.815542\pi$
$421$	−3.60373	+	4.15892i	−0.175635	+	0.202693i	0.661106	+	0.750293i	$0.270087\pi$
$422$		0			0
$423$	2.01038	+	5.15427i	0.0977482	+	0.250609i
$424$		0			0
$425$	10.9644	+	5.00728i	0.531852	+	0.242889i
$426$		0			0
$427$	−1.41119	−	0.906916i	−0.0682922	−	0.0438887i
$428$		0			0
$429$	0.878097	+	2.57412i	0.0423949	+	0.124280i
$430$		0			0
$431$		−	33.0153i		−	1.59029i	−0.606418	−	0.795146i	$-0.707394\pi$
$431$		−	33.0153i		−	1.59029i	0.606418	−	0.795146i	$-0.292606\pi$
$432$		0			0
$433$	5.71980	+	8.90018i	0.274876	+	0.427716i	0.951055	−	0.309022i	$-0.100002\pi$
$433$	5.71980	+	8.90018i	0.274876	+	0.427716i	−0.676179	+	0.736738i	$0.736365\pi$
$434$		0			0
$435$	1.38904	+	1.10240i	0.0665995	+	0.0528561i
$436$		0			0
$437$	−7.36264	+	3.36240i	−0.352203	+	0.160846i
$438$		0			0
$439$	−28.9237			−1.38045			−0.690226	−	0.723593i	$-0.742489\pi$
$439$	−28.9237			−1.38045			−0.690226	+	0.723593i	$0.742489\pi$
$440$		0			0
$441$	6.64277	−	5.12885i	0.316322	−	0.244231i
$442$		0			0
$443$	2.62916	+	18.2862i	0.124915	+	0.868803i	0.951863	+	0.306524i	$0.0991661\pi$
$443$	2.62916	+	18.2862i	0.124915	+	0.868803i	−0.826948	+	0.562279i	$0.809925\pi$
$444$		0			0
$445$	−9.58071	+	1.37750i	−0.454169	+	0.0652997i
$446$		0			0
$447$	32.9725	−	16.8131i	1.55955	−	0.795232i
$448$		0			0
$449$	−16.1989	−	7.39779i	−0.764473	−	0.349123i	−0.00527804	−	0.999986i	$-0.501680\pi$
$449$	−16.1989	−	7.39779i	−0.764473	−	0.349123i	−0.759195	+	0.650863i	$0.774407\pi$
$450$		0			0
$451$	−1.81983	+	12.6572i	−0.0856924	+	0.596003i
$452$		0			0
$453$	2.24465	+	0.555142i	0.105463	+	0.0260828i
$454$		0			0
$455$	−0.164725	+	1.14569i	−0.00772243	+	0.0537107i
$456$		0			0
$457$	−28.4659	−	18.2939i	−1.33158	−	0.855754i	−0.335315	−	0.942106i	$-0.608843\pi$
$457$	−28.4659	−	18.2939i	−1.33158	−	0.855754i	−0.996265	+	0.0863520i	$0.972479\pi$
$458$		0			0
$459$	13.3308	−	8.31764i	0.622226	−	0.388234i
$460$		0			0
$461$	−2.94920	−	4.58905i	−0.137358	−	0.213733i	0.765759	−	0.643128i	$-0.222364\pi$
$461$	−2.94920	−	4.58905i	−0.137358	−	0.213733i	−0.903117	+	0.429394i	$0.858727\pi$
$462$		0			0
$463$	5.34889	+	18.2166i	0.248584	+	0.846599i	0.985364	+	0.170466i	$0.0545274\pi$
$463$	5.34889	+	18.2166i	0.248584	+	0.846599i	−0.736780	+	0.676133i	$0.763654\pi$
$464$		0			0
$465$	−5.68851	−	0.568759i	−0.263798	−	0.0263756i
$466$		0			0
$467$	14.0193	−	12.1478i	0.648736	−	0.562133i	−0.267108	−	0.963667i	$-0.586068\pi$
$467$	14.0193	−	12.1478i	0.648736	−	0.562133i	0.915844	+	0.401534i	$0.131523\pi$
$468$		0			0
$469$	13.4188	−	10.0751i	0.619621	−	0.465226i
$470$		0			0
$471$	−25.3781	−	26.8542i	−1.16936	−	1.23738i
$472$		0			0
$473$	−2.41752	−	0.347586i	−0.111158	−	0.0159820i
$474$		0			0
$475$	−20.3670	+	5.98029i	−0.934502	+	0.274395i
$476$		0			0
$477$	−20.3075	+	15.6793i	−0.929816	+	0.717906i
$478$		0			0
$479$	24.8352	−	11.3419i	1.13475	−	0.518222i	0.242673	−	0.970108i	$-0.421976\pi$
$479$	24.8352	−	11.3419i	1.13475	−	0.518222i	0.892076	+	0.451886i	$0.149249\pi$
$480$		0			0
$481$	0.125551	−	0.195361i	0.00572464	−	0.00890771i
$482$		0			0
$483$	−0.536930	+	5.37016i	−0.0244312	+	0.244351i
$484$		0			0
$485$	−0.984809	+	3.35395i	−0.0447179	+	0.152295i
$486$		0			0
$487$	27.5010	+	3.95405i	1.24619	+	0.179175i	0.733673	−	0.679503i	$-0.237804\pi$
$487$	27.5010	+	3.95405i	1.24619	+	0.179175i	0.512516	+	0.858678i	$0.328714\pi$
$488$		0			0
$489$	−0.961651	+	2.37143i	−0.0434874	+	0.107240i
$490$		0			0
$491$	−2.78595	+	1.27230i	−0.125728	+	0.0574182i	−0.477286	−	0.878748i	$-0.658379\pi$
$491$	−2.78595	+	1.27230i	−0.125728	+	0.0574182i	0.351558	+	0.936166i	$0.385652\pi$
$492$		0			0
$493$	0.437577	+	3.04342i	0.0197075	+	0.137069i
$494$		0			0
$495$	−1.92107	−	8.23833i	−0.0863458	−	0.370285i
$496$		0			0
$497$	−5.19767	+	3.34034i	−0.233147	+	0.149835i
$498$		0			0
$499$			33.7775i			1.51209i	0.654521	+	0.756044i	$0.272870\pi$
$499$			33.7775i			1.51209i	−0.654521	+	0.756044i	$0.727130\pi$
$500$		0			0
$501$	−3.87290	+	1.97484i	−0.173028	+	0.0882293i
$502$		0			0
$503$	−8.18125	+	9.44167i	−0.364784	+	0.420983i	−0.908237	−	0.418456i	$-0.862571\pi$
$503$	−8.18125	+	9.44167i	−0.364784	+	0.420983i	0.543453	+	0.839440i	$0.317117\pi$
$504$		0			0
$505$	−2.86400	+	1.84058i	−0.127446	+	0.0819047i
$506$		0			0
$507$	21.9516	−	0.947733i	0.974906	−	0.0420903i
$508$		0			0
$509$	−7.15954	−	24.3831i	−0.317341	−	1.08076i	−0.951522	−	0.307580i	$-0.900481\pi$
$509$	−7.15954	−	24.3831i	−0.317341	−	1.08076i	0.634181	−	0.773184i	$-0.281337\pi$
$510$		0			0
$511$	−3.53617	+	5.50239i	−0.156431	+	0.243411i
$512$		0			0
$513$	−8.14969	+	26.4433i	−0.359818	+	1.16750i
$514$		0			0
$515$	−9.43344	+	2.76991i	−0.415687	+	0.122057i
$516$		0			0
$517$	3.90295	+	3.38192i	0.171651	+	0.148737i
$518$		0			0
$519$	21.2713	−	4.00156i	0.933708	−	0.175649i
$520$		0			0
$521$	−8.55265	+	9.87029i	−0.374699	+	0.432425i	−0.911511	−	0.411277i	$-0.865083\pi$
$521$	−8.55265	+	9.87029i	−0.374699	+	0.432425i	0.536812	+	0.843702i	$0.319628\pi$
$522$		0			0
$523$	19.5661	+	12.5744i	0.855567	+	0.549840i	0.893306	−	0.449448i	$-0.148379\pi$
$523$	19.5661	+	12.5744i	0.855567	+	0.549840i	−0.0377395	+	0.999288i	$0.512016\pi$
$524$		0			0
$525$	−3.39804	+	13.7396i	−0.148303	+	0.599644i
$526$		0			0
$527$	−6.49113	−	7.49116i	−0.282758	−	0.326320i
$528$		0			0
$529$	−13.5489	−	15.6363i	−0.589083	−	0.679838i
$530$		0			0
$531$	−1.92287	+	9.51978i	−0.0834456	+	0.413123i
$532$		0			0
$533$	−2.32907	−	1.06365i	−0.100883	−	0.0460719i
$534$		0			0
$535$		−	6.81000i		−	0.294422i
$536$		0			0
$537$	19.1196	−	0.825465i	0.825073	−	0.0356215i
$538$		0			0
$539$	3.25433	−	7.12599i	0.140174	−	0.306938i
$540$		0			0
$541$	−10.6811	+	36.3766i	−0.459218	+	1.56395i	0.326393	+	0.945234i	$0.394167\pi$
$541$	−10.6811	+	36.3766i	−0.459218	+	1.56395i	−0.785612	+	0.618720i	$0.787652\pi$
$542$		0			0
$543$	−1.10922	−	1.17373i	−0.0476010	−	0.0503697i
$544$		0			0
$545$	−11.1581	+	9.66853i	−0.477960	+	0.414154i
$546$		0			0
$547$	6.93535	−	23.6196i	0.296534	−	1.00990i	−0.667607	−	0.744514i	$-0.732681\pi$
$547$	6.93535	−	23.6196i	0.296534	−	1.00990i	0.964141	−	0.265389i	$-0.0855005\pi$
$548$		0			0
$549$	−1.14426	+	2.17184i	−0.0488358	+	0.0926920i
$550$		0			0
$551$	−4.09212	−	3.54584i	−0.174330	−	0.151058i
$552$		0			0
$553$	−0.0249047	−	0.173216i	−0.00105905	−	0.00736588i
$554$		0			0
$555$	−0.449018	+	0.565770i	−0.0190598	+	0.0240156i
$556$		0			0
$557$	−0.197657	−	0.673158i	−0.00837500	−	0.0285226i	0.955199	−	0.295963i	$-0.0956404\pi$
$557$	−0.197657	−	0.673158i	−0.00837500	−	0.0285226i	−0.963574	+	0.267440i	$0.913822\pi$
$558$		0			0
$559$	0.203157	−	0.444852i	0.00859263	−	0.0188152i
$560$		0			0
$561$	7.39013	−	12.6695i	0.312012	−	0.534905i
$562$		0			0
$563$	3.72548	−	1.09390i	0.157010	−	0.0461024i	−0.202283	−	0.979327i	$-0.564836\pi$
$563$	3.72548	−	1.09390i	0.157010	−	0.0461024i	0.359293	+	0.933225i	$0.383018\pi$
$564$		0			0
$565$	−13.0818			−0.550356
$566$		0			0
$567$	12.4922	+	13.5776i	0.524623	+	0.570207i
$568$		0			0
$569$	−10.8384	−	9.39154i	−0.454370	−	0.393714i	0.397387	−	0.917651i	$-0.369917\pi$
$569$	−10.8384	−	9.39154i	−0.454370	−	0.393714i	−0.851757	+	0.523937i	$0.824463\pi$
$570$		0			0
$571$	10.9314	+	23.9364i	0.457464	+	1.00171i	0.988058	+	0.154081i	$0.0492416\pi$
$571$	10.9314	+	23.9364i	0.457464	+	1.00171i	−0.530594	+	0.847626i	$0.678031\pi$
$572$		0			0
$573$	−16.5474	+	0.714413i	−0.691278	+	0.0298450i
$574$		0			0
$575$	3.27557	+	5.09689i	0.136601	+	0.212555i
$576$		0			0
$577$	−38.1561	+	5.48602i	−1.58846	+	0.228386i	−0.879162	−	0.476523i	$-0.841897\pi$
$577$	−38.1561	+	5.48602i	−1.58846	+	0.228386i	−0.709297	+	0.704909i	$0.750988\pi$
$578$		0			0
$579$	−7.66878	−	40.7654i	−0.318703	−	1.69415i
$580$		0			0
$581$	9.10755	+	19.9428i	0.377845	+	0.827365i
$582$		0			0
$583$	−9.94875	+	21.7847i	−0.412035	+	0.902231i
$584$		0			0
$585$	1.69114	+	0.0956613i	0.0699202	+	0.00395511i
$586$		0			0
$587$	23.3634	+	6.86013i	0.964313	+	0.283148i	0.725734	−	0.687975i	$-0.241500\pi$
$587$	23.3634	+	6.86013i	0.964313	+	0.283148i	0.238579	+	0.971123i	$0.423318\pi$
$588$		0			0
$589$	17.2780	+	2.48420i	0.711928	+	0.102360i
$590$		0			0
$591$	−15.7535	−	9.18905i	−0.648012	−	0.377987i
$592$		0			0
$593$	5.35922	+	11.7351i	0.220077	+	0.481901i	0.987178	−	0.159626i	$-0.0510287\pi$
$593$	5.35922	+	11.7351i	0.220077	+	0.481901i	−0.767101	+	0.641526i	$0.778301\pi$
$594$		0			0
$595$	5.25114	−	3.37470i	0.215276	−	0.138349i
$596$		0			0
$597$	−18.2600	+	6.22895i	−0.747334	+	0.254934i
$598$		0			0
$599$	4.00325	−	27.8432i	0.163568	−	1.13764i	−0.728271	−	0.685290i	$-0.759676\pi$
$599$	4.00325	−	27.8432i	0.163568	−	1.13764i	0.891839	−	0.452353i	$-0.149415\pi$
$600$		0			0
$601$	−16.3336	−	18.8499i	−0.666260	−	0.768905i	0.317526	−	0.948249i	$-0.397148\pi$
$601$	−16.3336	−	18.8499i	−0.666260	−	0.768905i	−0.983786	+	0.179345i	$0.942602\pi$
$602$		0			0
$603$	−16.3816	−	18.2933i	−0.667110	−	0.744960i
$604$		0			0
$605$	2.08228	+	2.40308i	0.0846567	+	0.0976991i
$606$		0			0
$607$	0.952491	−	6.62472i	0.0386604	−	0.268889i	−0.961318	−	0.275440i	$-0.911176\pi$
$607$	0.952491	−	6.62472i	0.0386604	−	0.268889i	0.999979	+	0.00655145i	$0.00208541\pi$
$608$		0			0
$609$	−3.41701	+	1.16563i	−0.138464	+	0.0472336i
$610$		0			0
$611$	−0.869919	+	0.559063i	−0.0351931	+	0.0226173i
$612$		0			0
$613$	5.13198	+	11.2375i	0.207279	+	0.453877i	0.984508	−	0.175340i	$-0.0561026\pi$
$613$	5.13198	+	11.2375i	0.207279	+	0.453877i	−0.777229	+	0.629218i	$0.783375\pi$
$614$		0			0
$615$	6.87907	+	4.01258i	0.277391	+	0.161803i
$616$		0			0
$617$	−5.84688	−	0.840654i	−0.235386	−	0.0338435i	0.0236120	−	0.999721i	$-0.492483\pi$
$617$	−5.84688	−	0.840654i	−0.235386	−	0.0338435i	−0.258998	+	0.965878i	$0.583392\pi$
$618$		0			0
$619$	−39.7054	−	11.6586i	−1.59590	−	0.468597i	−0.641496	−	0.767127i	$-0.721686\pi$
$619$	−39.7054	−	11.6586i	−1.59590	−	0.468597i	−0.954401	+	0.298529i	$0.903504\pi$
$620$		0			0
$621$	7.89720	+	0.105505i	0.316904	+	0.00423376i
$622$		0			0
$623$	8.18619	−	17.9253i	0.327973	−	0.718160i
$624$		0			0
$625$	4.49457	+	9.84173i	0.179783	+	0.393669i
$626$		0			0
$627$	4.77527	+	25.3842i	0.190706	+	1.01375i
$628$		0			0
$629$	−1.23961	+	0.178229i	−0.0494266	+	0.00710647i
$630$		0			0
$631$	21.6056	+	33.6190i	0.860105	+	1.33835i	0.939869	+	0.341536i	$0.110947\pi$
$631$	21.6056	+	33.6190i	0.860105	+	1.33835i	−0.0797638	+	0.996814i	$0.525417\pi$
$632$		0			0
$633$	23.6266	−	1.02005i	0.939073	−	0.0405432i
$634$		0			0
$635$	0.892132	+	1.95350i	0.0354032	+	0.0775222i
$636$		0			0
$637$	1.18548	+	1.02722i	0.0469705	+	0.0407001i
$638$		0			0
$639$	5.52564	+	7.15669i	0.218591	+	0.283114i
$640$		0			0
$641$	21.3864			0.844712			0.422356	−	0.906430i	$-0.361203\pi$
$641$	21.3864			0.844712			0.422356	+	0.906430i	$0.361203\pi$
$642$		0			0
$643$	16.2695	−	4.77715i	0.641606	−	0.188393i	0.0552841	−	0.998471i	$-0.482394\pi$
$643$	16.2695	−	4.77715i	0.641606	−	0.188393i	0.586322	+	0.810078i	$0.300575\pi$
$644$		0			0
$645$	−0.766402	+	1.31390i	−0.0301770	+	0.0517348i
$646$		0			0
$647$	4.74123	−	10.3819i	0.186397	−	0.408153i	−0.793246	−	0.608902i	$-0.791610\pi$
$647$	4.74123	−	10.3819i	0.186397	−	0.408153i	0.979643	+	0.200749i	$0.0643376\pi$
$648$		0			0
$649$	2.55413	+	8.69858i	0.100259	+	0.341449i
$650$		0			0
$651$	7.23544	−	9.11676i	0.283579	−	0.357314i
$652$		0			0
$653$	6.71761	+	46.7220i	0.262880	+	1.82837i	0.510925	+	0.859625i	$0.329303\pi$
$653$	6.71761	+	46.7220i	0.262880	+	1.82837i	−0.248045	+	0.968749i	$0.579788\pi$
$654$		0			0
$655$	−6.11229	−	5.29633i	−0.238827	−	0.206945i
$656$		0			0
$657$	8.46827	+	4.46160i	0.330379	+	0.174064i
$658$		0			0
$659$	−11.1587	+	38.0030i	−0.434681	+	1.48039i	0.393185	+	0.919459i	$0.371373\pi$
$659$	−11.1587	+	38.0030i	−0.434681	+	1.48039i	−0.827865	+	0.560927i	$0.810445\pi$
$660$		0			0
$661$	1.78336	−	1.54529i	0.0693648	−	0.0601049i	−0.619488	−	0.785006i	$-0.712660\pi$
$661$	1.78336	−	1.54529i	0.0693648	−	0.0601049i	0.688853	+	0.724901i	$0.258114\pi$
$662$		0			0
$663$	2.01720	+	2.13453i	0.0783415	+	0.0828982i
$664$		0			0
$665$	−3.09691	+	10.5471i	−0.120093	+	0.409000i
$666$		0			0
$667$	−0.642015	+	1.40582i	−0.0248589	+	0.0544335i
$668$		0			0
$669$	11.9417	−	0.515567i	0.461692	−	0.0199330i
$670$		0			0
$671$			2.29149i			0.0884622i
$672$		0			0
$673$	−36.5482	−	16.6910i	−1.40883	−	0.643391i	−0.441581	−	0.897221i	$-0.645582\pi$
$673$	−36.5482	−	16.6910i	−1.40883	−	0.643391i	−0.967249	+	0.253830i	$0.918309\pi$
$674$		0			0
$675$	20.4603	+	3.22129i	0.787519	+	0.123987i
$676$		0			0
$677$	9.77120	+	11.2766i	0.375538	+	0.433393i	0.911785	−	0.410667i	$-0.134704\pi$
$677$	9.77120	+	11.2766i	0.375538	+	0.433393i	−0.536248	+	0.844061i	$0.680159\pi$
$678$		0			0
$679$	−4.66039	−	5.37838i	−0.178849	−	0.206403i
$680$		0			0
$681$	9.03392	−	36.5276i	0.346180	−	1.39974i
$682$		0			0
$683$	29.6644	+	19.0642i	1.13508	+	0.729471i	0.966614	−	0.256237i	$-0.0824828\pi$
$683$	29.6644	+	19.0642i	1.13508	+	0.729471i	0.168465	+	0.985708i	$0.446119\pi$
$684$		0			0
$685$	−11.0660	+	12.7708i	−0.422810	+	0.487949i
$686$		0			0
$687$	29.4166	−	5.53385i	1.12232	−	0.211130i
$688$		0			0
$689$	−3.62411	−	3.14031i	−0.138068	−	0.119636i
$690$		0			0
$691$	−1.16029	+	0.340691i	−0.0441395	+	0.0129605i	−0.303728	−	0.952759i	$-0.598231\pi$
$691$	−1.16029	+	0.340691i	−0.0441395	+	0.0129605i	0.259588	+	0.965719i	$0.416413\pi$
$692$		0			0
$693$	16.2244	+	5.77764i	0.616315	+	0.219474i
$694$		0			0
$695$	4.41413	−	6.86852i	0.167438	−	0.260538i
$696$		0			0
$697$	3.89020	+	13.2488i	0.147352	+	0.501834i
$698$		0			0
$699$	24.0505	−	1.03835i	0.909675	−	0.0392740i
$700$		0			0
$701$	−22.7655	+	14.6305i	−0.859840	+	0.552585i	−0.894629	−	0.446809i	$-0.852560\pi$
$701$	−22.7655	+	14.6305i	−0.859840	+	0.552585i	0.0347895	+	0.999395i	$0.488924\pi$
$702$		0			0
$703$	1.44425	−	1.66676i	0.0544711	−	0.0628630i
$704$		0			0
$705$	2.86529	−	1.46105i	0.107913	−	0.0550262i
$706$		0			0
$707$		−	6.93114i		−	0.260672i
$708$		0			0
$709$	−21.0873	+	13.5520i	−0.791950	+	0.508956i	−0.872980	−	0.487756i	$-0.837816\pi$
$709$	−21.0873	+	13.5520i	−0.791950	+	0.508956i	0.0810296	+	0.996712i	$0.474179\pi$
$710$		0			0
$711$	−0.249401	+	0.0581570i	−0.00935325	+	0.00218106i
$712$		0			0
$713$	−0.709055	−	4.93159i	−0.0265543	−	0.184689i
$714$		0			0
$715$	1.43826	−	0.656829i	0.0537877	−	0.0245640i
$716$		0			0
$717$	2.13943	−	5.27582i	0.0798984	−	0.197029i
$718$		0			0
$719$	36.2245	+	5.20830i	1.35095	+	0.194237i	0.779500	−	0.626402i	$-0.215473\pi$
$719$	36.2245	+	5.20830i	1.35095	+	0.194237i	0.571447	+	0.820639i	$0.306382\pi$
$720$		0			0
$721$	5.63928	−	19.2056i	0.210018	−	0.715255i
$722$		0			0
$723$	−4.33376	+	43.3446i	−0.161174	+	1.61200i
$724$		0			0
$725$	−2.19124	+	3.40963i	−0.0813805	+	0.126631i
$726$		0			0
$727$	2.87291	−	1.31201i	0.106550	−	0.0486599i	−0.361427	−	0.932401i	$-0.617710\pi$
$727$	2.87291	−	1.31201i	0.106550	−	0.0486599i	0.467977	+	0.883741i	$0.344983\pi$
$728$		0			0
$729$	18.2201	−	19.9256i	0.674817	−	0.737985i
$730$		0			0
$731$	−2.53051	+	0.743026i	−0.0935945	+	0.0274818i
$732$		0			0
$733$	1.93442	+	0.278128i	0.0714494	+	0.0102729i	0.177947	−	0.984040i	$-0.443054\pi$
$733$	1.93442	+	0.278128i	0.0714494	+	0.0102729i	−0.106497	+	0.994313i	$0.533964\pi$
$734$		0			0
$735$	−3.35106	−	3.54597i	−0.123606	−	0.130795i
$736$		0			0
$737$	−21.4883	−	7.97975i	−0.791532	−	0.293938i
$738$		0			0
$739$	−15.9300	+	13.8034i	−0.585995	+	0.507768i	−0.896641	−	0.442758i	$-0.854000\pi$
$739$	−15.9300	+	13.8034i	−0.585995	+	0.507768i	0.310646	+	0.950526i	$0.399455\pi$
$740$		0			0
$741$	−5.14627	−	0.514545i	−0.189053	−	0.0189023i
$742$		0			0
$743$	6.85255	+	23.3376i	0.251396	+	0.856175i	0.984399	+	0.175950i	$0.0562998\pi$
$743$	6.85255	+	23.3376i	0.251396	+	0.856175i	−0.733003	+	0.680225i	$0.761882\pi$
$744$		0			0
$745$	−11.6328	−	18.1010i	−0.426194	−	0.663171i
$746$		0			0
$747$	27.9270	−	15.7938i	1.02180	−	0.577863i
$748$		0			0
$749$	11.6636	+	7.49574i	0.426178	+	0.273888i
$750$		0			0
$751$	2.12290	−	14.7651i	0.0774656	−	0.538785i	−0.913724	−	0.406335i	$-0.866807\pi$
$751$	2.12290	−	14.7651i	0.0774656	−	0.538785i	0.991190	−	0.132450i	$-0.0422844\pi$
$752$		0			0
$753$	17.0257	+	4.21076i	0.620452	+	0.153449i
$754$		0			0
$755$	0.191306	−	1.33056i	0.00696233	−	0.0484241i
$756$		0			0
$757$	1.05419	+	0.481431i	0.0383150	+	0.0174979i	0.434480	−	0.900681i	$-0.356932\pi$
$757$	1.05419	+	0.481431i	0.0383150	+	0.0174979i	−0.396165	+	0.918179i	$0.629659\pi$
$758$		0			0
$759$	6.56782	−	3.34901i	0.238397	−	0.121561i
$760$		0			0
$761$	23.9508	−	3.44360i	0.868215	−	0.124830i	0.306209	−	0.951964i	$-0.400939\pi$
$761$	23.9508	−	3.44360i	0.868215	−	0.124830i	0.562005	+	0.827134i	$0.310030\pi$
$762$		0			0
$763$	−4.27780	−	29.7527i	−0.154867	−	1.07712i
$764$		0			0
$765$	−5.58248	−	7.23031i	−0.201835	−	0.261412i
$766$		0			0
$767$	−1.81528			−0.0655460
$768$		0			0
$769$	15.4927	−	7.07527i	0.558680	−	0.255141i	−0.116002	−	0.993249i	$-0.537008\pi$
$769$	15.4927	−	7.07527i	0.558680	−	0.255141i	0.674682	+	0.738108i	$0.264281\pi$
$770$		0			0
$771$	14.4602	+	11.4762i	0.520772	+	0.413306i
$772$		0			0
$773$	14.4824	+	22.5351i	0.520897	+	0.810531i	0.997651	−	0.0685055i	$-0.0218231\pi$
$773$	14.4824	+	22.5351i	0.520897	+	0.810531i	−0.476754	+	0.879037i	$0.658187\pi$
$774$		0			0
$775$		−	13.0661i		−	0.469350i
$776$		0			0
$777$	−0.474771	−	1.39178i	−0.0170323	−	0.0499299i
$778$		0			0
$779$	−20.4563	−	13.1465i	−0.732923	−	0.471021i
$780$		0			0
$781$	7.67729	+	3.50610i	0.274715	+	0.125458i
$782$		0			0
$783$	2.13041	+	4.83485i	0.0761348	+	0.172784i
$784$		0			0
$785$	−14.0664	+	16.2335i	−0.502052	+	0.579399i
$786$		0			0
$787$	−2.61100	+	0.375406i	−0.0930723	+	0.0133818i	−0.188694	−	0.982036i	$-0.560425\pi$
$787$	−2.61100	+	0.375406i	−0.0930723	+	0.0133818i	0.0956213	+	0.995418i	$0.469516\pi$
$788$		0			0
$789$	27.6708	+	21.9607i	0.985107	+	0.781822i
$790$		0			0
$791$	14.3991	−	22.4054i	0.511973	−	0.796646i
$792$		0			0
$793$	−0.440249	−	0.129269i	−0.0156337	−	0.00459046i
$794$		0			0
$795$	10.2445	+	10.8403i	0.363334	+	0.384467i
$796$		0			0
$797$	−27.9982	+	24.2605i	−0.991746	+	0.859352i	−0.990060	−	0.140646i	$-0.955082\pi$
$797$	−27.9982	+	24.2605i	−0.991746	+	0.859352i	−0.00168569	+	0.999999i	$0.500537\pi$
$798$		0			0
$799$	5.35070	+	1.57111i	0.189294	+	0.0555818i
$800$		0			0
$801$	−27.1668	−	9.67429i	−0.959891	−	0.341824i
$802$		0			0
$803$	8.93481			0.315303
$804$		0			0
$805$	3.13751			0.110583
$806$		0			0
$807$	−30.1371	−	12.2210i	−1.06087	−	0.430201i
$808$		0			0
$809$	16.0045	+	4.69934i	0.562688	+	0.165220i	0.550693	−	0.834708i	$-0.314364\pi$
$809$	16.0045	+	4.69934i	0.562688	+	0.165220i	0.0119949	+	0.999928i	$0.496182\pi$
$810$		0			0
$811$	20.7879	−	18.0128i	0.729963	−	0.632517i	−0.208450	−	0.978033i	$-0.566842\pi$
$811$	20.7879	−	18.0128i	0.729963	−	0.632517i	0.938413	+	0.345516i	$0.112296\pi$
$812$		0			0
$813$	−14.3179	+	13.5309i	−0.502150	+	0.474548i
$814$		0			0
$815$	1.42741	+	0.419125i	0.0499999	+	0.0146813i
$816$		0			0
$817$	2.51097	−	3.90715i	0.0878477	−	0.136694i
$818$		0			0
$819$	−2.02527	+	2.79115i	−0.0707688	+	0.0975308i
$820$		0			0
$821$	14.8405	−	2.13374i	0.517936	−	0.0744679i	0.121610	−	0.992578i	$-0.461194\pi$
$821$	14.8405	−	2.13374i	0.517936	−	0.0744679i	0.396326	+	0.918110i	$0.370285\pi$
$822$		0			0
$823$	−8.65464	+	9.98799i	−0.301682	+	0.348159i	−0.886268	−	0.463172i	$-0.846711\pi$
$823$	−8.65464	+	9.98799i	−0.301682	+	0.348159i	0.584587	+	0.811331i	$0.301257\pi$
$824$		0			0
$825$	18.2988	−	6.24217i	0.637083	−	0.217325i
$826$		0			0
$827$	17.8256	+	8.14067i	0.619856	+	0.283079i	0.700487	−	0.713665i	$-0.252966\pi$
$827$	17.8256	+	8.14067i	0.619856	+	0.283079i	−0.0806307	+	0.996744i	$0.525693\pi$
$828$		0			0
$829$	−6.02006	−	3.86886i	−0.209085	−	0.134371i	0.431907	−	0.901918i	$-0.357841\pi$
$829$	−6.02006	−	3.86886i	−0.209085	−	0.134371i	−0.640993	+	0.767547i	$0.721477\pi$
$830$		0			0
$831$	−19.6156	+	6.69135i	−0.680457	+	0.232121i
$832$		0			0
$833$		−	8.45928i		−	0.293097i
$834$		0			0
$835$	1.36637	+	2.12612i	0.0472853	+	0.0735774i
$836$		0			0
$837$	−14.2045	−	9.39912i	−0.490978	−	0.324881i
$838$		0			0
$839$	7.63535	−	3.48695i	0.263601	−	0.120383i	−0.279230	−	0.960224i	$-0.590079\pi$
$839$	7.63535	−	3.48695i	0.263601	−	0.120383i	0.542832	+	0.839841i	$0.317352\pi$
$840$		0			0
$841$	27.9661			0.964349
$842$		0			0
$843$	−5.07791	+	3.58199i	−0.174893	+	0.123370i
$844$		0			0
$845$	−1.81785	−	12.6434i	−0.0625360	−	0.434948i
$846$		0			0
$847$	−6.40775	+	0.921296i	−0.220173	+	0.0316561i
$848$		0			0
$849$	8.96902	+	17.5893i	0.307816	+	0.603664i
$850$		0			0
$851$	−0.572603	−	0.261499i	−0.0196286	−	0.00896406i
$852$		0			0
$853$	1.63189	−	11.3501i	0.0558749	−	0.388619i	−0.942624	−	0.333855i	$-0.891650\pi$
$853$	1.63189	−	11.3501i	0.0558749	−	0.388619i	0.998499	−	0.0547635i	$-0.0174405\pi$
$854$		0			0
$855$	15.7679	+	3.18491i	0.539250	+	0.108922i
$856$		0			0
$857$	1.83260	−	12.7460i	0.0626003	−	0.435395i	−0.934285	−	0.356527i	$-0.883961\pi$
$857$	1.83260	−	12.7460i	0.0626003	−	0.435395i	0.996885	−	0.0788672i	$-0.0251303\pi$
$858$		0			0
$859$	−11.8921	−	7.64260i	−0.405754	−	0.260762i	0.321807	−	0.946805i	$-0.395710\pi$
$859$	−11.8921	−	7.64260i	−0.405754	−	0.260762i	−0.727561	+	0.686043i	$0.759346\pi$
$860$		0			0
$861$	−14.4442	+	7.36526i	−0.492256	+	0.251008i
$862$		0			0
$863$	11.0327	+	17.1672i	0.375557	+	0.584378i	0.976659	−	0.214794i	$-0.0689079\pi$
$863$	11.0327	+	17.1672i	0.375557	+	0.584378i	−0.601102	+	0.799172i	$0.705272\pi$
$864$		0			0
$865$	−3.54504	−	12.0733i	−0.120535	−	0.410504i
$866$		0			0
$867$	−1.35370	+	13.5392i	−0.0459742	+	0.459816i
$868$		0			0
$869$	−0.180663	+	0.156545i	−0.00612857	+	0.00531044i
$870$		0			0
$871$	2.74530	−	3.67824i	0.0930209	−	0.124632i
$872$		0			0
$873$	−7.25366	+	7.47302i	−0.245499	+	0.252923i
$874$		0			0
$875$	18.3604	+	2.63983i	0.620696	+	0.0892426i
$876$		0			0
$877$	10.6670	−	3.13210i	0.360197	−	0.105763i	−0.0966264	−	0.995321i	$-0.530805\pi$
$877$	10.6670	−	3.13210i	0.360197	−	0.105763i	0.456824	+	0.889557i	$0.348987\pi$
$878$		0			0
$879$	−9.88187	−	14.0088i	−0.333307	−	0.472504i
$880$		0			0
$881$	14.6371	−	6.68455i	0.493137	−	0.225208i	−0.153294	−	0.988181i	$-0.548988\pi$
$881$	14.6371	−	6.68455i	0.493137	−	0.225208i	0.646431	+	0.762973i	$0.276261\pi$
$882$		0			0
$883$	12.8188	−	19.9464i	0.431385	−	0.671249i	−0.555711	−	0.831375i	$-0.687554\pi$
$883$	12.8188	−	19.9464i	0.431385	−	0.671249i	0.987096	+	0.160127i	$0.0511903\pi$
$884$		0			0
$885$	5.61808	+	0.561718i	0.188850	+	0.0188819i
$886$		0			0
$887$	11.8144	−	40.2361i	0.396688	−	1.35100i	−0.483073	−	0.875580i	$-0.660479\pi$
$887$	11.8144	−	40.2361i	0.396688	−	1.35100i	0.879761	−	0.475416i	$-0.157703\pi$
$888$		0			0
$889$	−4.32775	−	0.622237i	−0.145148	−	0.0208691i
$890$		0			0
$891$	6.37724	−	24.3833i	0.213646	−	0.816871i
$892$		0			0
$893$	−8.93306	+	4.07959i	−0.298933	+	0.136518i
$894$		0			0
$895$	−1.58333	−	11.0123i	−0.0529249	−	0.368101i
$896$		0			0
$897$	0.272915	+	1.45075i	0.00911238	+	0.0484393i
$898$		0			0
$899$	2.80388	−	1.80194i	0.0935146	−	0.0600982i
$900$		0			0
$901$			25.8607i			0.861546i
$902$		0			0
$903$	−1.40676	−	2.75883i	−0.0468141	−	0.0918082i
$904$		0			0
$905$	−0.614810	+	0.709529i	−0.0204370	+	0.0235855i
$906$		0			0
$907$	−32.9158	+	21.1537i	−1.09295	+	0.702396i	−0.957513	−	0.288390i	$-0.906880\pi$
$907$	−32.9158	+	21.1537i	−1.09295	+	0.702396i	−0.135437	+	0.990786i	$0.543244\pi$
$908$		0			0
$909$	−10.1053	+	0.874197i	−0.335172	+	0.0289953i
$910$		0			0
$911$	−9.40813	−	32.0411i	−0.311705	−	1.06157i	−0.955161	−	0.296087i	$-0.904318\pi$
$911$	−9.40813	−	32.0411i	−0.311705	−	1.06157i	0.643456	−	0.765483i	$-0.277500\pi$
$912$		0			0
$913$	16.1916	−	25.1946i	0.535863	−	0.833819i
$914$		0			0
$915$	1.32252	+	0.536301i	0.0437210	+	0.0177296i
$916$		0			0
$917$	15.7989	−	4.63897i	0.521725	−	0.153192i
$918$		0			0
$919$	13.5490	+	11.7403i	0.446940	+	0.387276i	0.849047	−	0.528317i	$-0.177177\pi$
$919$	13.5490	+	11.7403i	0.446940	+	0.387276i	−0.402107	+	0.915593i	$0.631722\pi$
$920$		0			0
$921$	−1.97196	−	10.4825i	−0.0649783	−	0.345409i
$922$		0			0
$923$	−1.10670	+	1.27720i	−0.0364274	+	0.0420394i
$924$		0			0
$925$	−1.38878	−	0.892512i	−0.0456627	−	0.0293456i
$926$		0			0
$927$	−28.7123	−	5.79951i	−0.943036	−	0.190481i
$928$		0			0
$929$	26.2500	+	30.2941i	0.861235	+	0.993918i	0.999994	+	0.00359196i	$0.00114336\pi$
$929$	26.2500	+	30.2941i	0.861235	+	0.993918i	−0.138759	+	0.990326i	$0.544311\pi$
$930$		0			0
$931$	9.75547	+	11.2584i	0.319723	+	0.368980i
$932$		0			0
$933$	−56.9278	−	14.0793i	−1.86373	−	0.460934i
$934$		0			0
$935$	−7.75627	−	3.54217i	−0.253657	−	0.115841i
$936$		0			0
$937$			16.6410i			0.543638i	0.962348	+	0.271819i	$0.0876253\pi$
$937$			16.6410i			0.543638i	−0.962348	+	0.271819i	$0.912375\pi$
$938$		0			0
$939$	1.79273	+	41.5236i	0.0585035	+	1.35507i
$940$		0			0
$941$	10.6549	−	23.3310i	0.347340	−	0.760568i	−0.652656	−	0.757654i	$-0.726345\pi$
$941$	10.6549	−	23.3310i	0.347340	−	0.760568i	0.999996	−	0.00291342i	$-0.000927371\pi$
$942$		0			0
$943$	−1.95537	+	6.65940i	−0.0636758	+	0.216860i
$944$		0			0
$945$	7.13168	−	8.01159i	0.231993	−	0.260617i
$946$		0			0
$947$	−25.8510	+	22.4001i	−0.840046	+	0.727904i	−0.964432	−	0.264330i	$-0.914849\pi$
$947$	−25.8510	+	22.4001i	−0.840046	+	0.727904i	0.124386	+	0.992234i	$0.460304\pi$
$948$		0			0
$949$	−0.504034	+	1.71658i	−0.0163616	+	0.0557226i
$950$		0			0
$951$	−17.2162	+	29.5150i	−0.558274	+	0.957091i
$952$		0			0
$953$	32.3020	+	27.9898i	1.04636	+	0.906680i	0.995755	−	0.0920385i	$-0.0293383\pi$
$953$	32.3020	+	27.9898i	1.04636	+	0.906680i	0.0506091	+	0.998719i	$0.483884\pi$
$954$		0			0
$955$	1.37032	+	9.53079i	0.0443425	+	0.308409i
$956$		0			0
$957$	3.86309	+	3.06591i	0.124876	+	0.0991067i
$958$		0			0
$959$	−9.69253	−	33.0097i	−0.312988	−	1.06594i
$960$		0			0
$961$	8.41431	−	18.4248i	0.271429	−	0.594347i
$962$		0			0
$963$	9.45740	−	17.9505i	0.304760	−	0.578445i
$964$		0			0
$965$	−23.1378	+	6.79388i	−0.744833	+	0.218703i
$966$		0			0
$967$	25.9422			0.834244			0.417122	−	0.908850i	$-0.363039\pi$
$967$	25.9422			0.834244			0.417122	+	0.908850i	$0.363039\pi$
$968$		0			0
$969$	16.0772	+	22.7915i	0.516476	+	0.732167i
$970$		0			0
$971$	−30.7269	−	26.6250i	−0.986072	−	0.854436i	0.00327763	−	0.999995i	$-0.498957\pi$
$971$	−30.7269	−	26.6250i	−0.986072	−	0.854436i	−0.989350	+	0.145558i	$0.953502\pi$
$972$		0			0
$973$	6.90521	+	15.1203i	0.221371	+	0.484735i
$974$		0			0
$975$	0.166985	+	3.86775i	0.00534781	+	0.123867i
$976$		0			0
$977$	−11.2919	−	17.5706i	−0.361261	−	0.562133i	0.612281	−	0.790640i	$-0.290252\pi$
$977$	−11.2919	−	17.5706i	−0.361261	−	0.562133i	−0.973542	+	0.228507i	$0.926616\pi$
$978$		0			0
$979$	−26.6451	+	3.83099i	−0.851581	+	0.122439i
$980$		0			0
$981$	−42.8388	+	9.98945i	−1.36774	+	0.318939i
$982$		0			0
$983$	19.2208	+	42.0876i	0.613047	+	1.34239i	0.920470	+	0.390813i	$0.127806\pi$
$983$	19.2208	+	42.0876i	0.613047	+	1.34239i	−0.307423	+	0.951573i	$0.599467\pi$
$984$		0			0
$985$	−4.40441	+	9.64431i	−0.140336	+	0.307293i
$986$		0			0
$987$	−0.651455	+	6.51560i	−0.0207361	+	0.207394i
$988$		0			0
$989$	−1.27194	−	0.373476i	−0.0404454	−	0.0118758i
$990$		0			0
$991$	34.8046	+	5.00415i	1.10560	+	0.158962i	0.670854	−	0.741589i	$-0.265928\pi$
$991$	34.8046	+	5.00415i	1.10560	+	0.158962i	0.434750	+	0.900551i	$0.356837\pi$
$992$		0			0
$993$	−7.37862	+	12.6497i	−0.234153	+	0.401427i
$994$		0			0
$995$	4.65934	+	10.2025i	0.147711	+	0.323442i
$996$		0			0
$997$	38.6314	−	24.8269i	1.22347	−	0.786275i	0.240606	−	0.970623i	$-0.422654\pi$
$997$	38.6314	−	24.8269i	1.22347	−	0.786275i	0.982861	+	0.184348i	$0.0590173\pi$
$998$		0			0
$999$	−1.96928	+	0.867737i	−0.0623053	+	0.0274540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.s.b.161.15	yes	200
3.2	odd	2	inner	804.2.s.b.161.8	yes	200
67.5	odd	22	inner	804.2.s.b.5.8	✓	200
201.5	even	22	inner	804.2.s.b.5.15	yes	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.s.b.5.8	✓	200	67.5	odd	22	inner
804.2.s.b.5.15	yes	200	201.5	even	22	inner
804.2.s.b.161.8	yes	200	3.2	odd	2	inner
804.2.s.b.161.15	yes	200	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.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.650892 - 1.60510i) q^{3} +(-0.966140 - 0.283684i) q^{5} +(1.54930 - 1.34247i) q^{7} +(-2.15268 - 2.08949i) q^{9} +O(q^{10})\)	\(q+(0.650892 - 1.60510i) q^{3} +(-0.966140 - 0.283684i) q^{5} +(1.54930 - 1.34247i) q^{7} +(-2.15268 - 2.08949i) q^{9} +(-2.68695 - 0.788959i) q^{11} +(0.303154 - 0.471717i) q^{13} +(-1.08419 + 1.36610i) q^{15} +(-2.99315 + 0.430350i) q^{17} +(3.48728 - 4.02453i) q^{19} +(-1.14638 - 3.36058i) q^{21} +(-1.38260 - 0.631411i) q^{23} +(-3.35332 - 2.15505i) q^{25} +(-4.75500 + 2.09523i) q^{27} -1.01679i q^{29} +(1.77218 + 2.75757i) q^{31} +(-3.01527 + 3.79929i) q^{33} +(-1.87767 + 0.857505i) q^{35} +0.414150 q^{37} +(-0.559831 - 0.793629i) q^{39} +(-0.649850 - 4.51980i) q^{41} +(0.863281 - 0.124121i) q^{43} +(1.48703 + 2.62942i) q^{45} +(-1.67750 - 0.766089i) q^{47} +(-0.398118 + 2.76897i) q^{49} +(-1.25746 + 5.08441i) q^{51} +(1.21708 - 8.46498i) q^{53} +(2.37215 + 1.52449i) q^{55} +(-4.18993 - 8.21696i) q^{57} +(-1.75024 - 2.72343i) q^{59} +(-0.230536 - 0.785133i) q^{61} +(-6.14022 - 0.347328i) q^{63} +(-0.426708 + 0.369744i) q^{65} +(8.16532 + 0.572263i) q^{67} +(-1.91340 + 1.80822i) q^{69} +(-2.98320 - 0.428919i) q^{71} +(-3.06133 + 0.898887i) q^{73} +(-5.64171 + 3.97970i) q^{75} +(-5.22203 + 2.38482i) q^{77} +(0.0461512 - 0.0718126i) q^{79} +(0.268052 + 8.99601i) q^{81} +(-3.01301 + 10.2614i) q^{83} +(3.01389 + 0.433331i) q^{85} +(-1.63205 - 0.661823i) q^{87} +(8.74397 - 3.99324i) q^{89} +(-0.163592 - 1.13781i) q^{91} +(5.57967 - 1.04965i) q^{93} +(-4.51089 + 2.89897i) q^{95} -3.47150i q^{97} +(4.13561 + 7.31273i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 10 q^{9}+O(q^{10}) \) 200 * q - 10 * q^9	\( 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) \) 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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