LMFDB - Embedded newform 804.2.q.b.193.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(25,804)]

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, 0, 10]))

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

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

chi := DirichletCharacter("804.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.q (of order $11$, 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:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			193.4
Character	$\chi$	$=$	804.193
Dual form			804.2.q.b.25.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 + 0.755750i) q^{3} +(1.12656 + 0.723994i) q^{5} +(-0.202268 + 1.40680i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.654861 + 0.755750i) q^{3} +(1.12656 + 0.723994i) q^{5} +(-0.202268 + 1.40680i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-2.52874 - 1.62512i) q^{11} +(1.08620 + 2.37844i) q^{13} +(0.190580 + 1.32551i) q^{15} +(2.15851 - 0.633795i) q^{17} +(1.08664 + 7.55774i) q^{19} +(-1.19565 + 0.768395i) q^{21} +(5.68168 + 6.55701i) q^{23} +(-1.33211 - 2.91692i) q^{25} +(-0.841254 + 0.540641i) q^{27} -3.39419 q^{29} +(1.49181 - 3.26660i) q^{31} +(-0.427787 - 2.97532i) q^{33} +(-1.24638 + 1.43840i) q^{35} -6.63386 q^{37} +(-1.08620 + 2.37844i) q^{39} +(1.86302 - 0.547031i) q^{41} +(-8.87900 + 2.60711i) q^{43} +(-0.876951 + 1.01206i) q^{45} +(-0.660772 - 0.762571i) q^{47} +(4.77827 + 1.40303i) q^{49} +(1.89251 + 1.21624i) q^{51} +(11.0069 + 3.23191i) q^{53} +(-1.67219 - 3.66158i) q^{55} +(-5.00016 + 5.77049i) q^{57} +(3.66918 - 8.03438i) q^{59} +(8.80650 - 5.65959i) q^{61} +(-1.36370 - 0.400417i) q^{63} +(-0.498313 + 3.46584i) q^{65} +(0.105510 + 8.18467i) q^{67} +(-1.23475 + 8.58786i) q^{69} +(-3.96022 - 1.16283i) q^{71} +(-6.59618 + 4.23911i) q^{73} +(1.33211 - 2.91692i) q^{75} +(2.79770 - 3.22872i) q^{77} +(3.97765 + 8.70984i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(-7.38873 - 4.74845i) q^{83} +(2.89055 + 0.848742i) q^{85} +(-2.22272 - 2.56516i) q^{87} +(7.60486 - 8.77648i) q^{89} +(-3.56569 + 1.04698i) q^{91} +(3.44566 - 1.01174i) q^{93} +(-4.24760 + 9.30095i) q^{95} -5.54010 q^{97} +(1.96846 - 2.27172i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) $ 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9	$ 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9} - 11 q^{11} - 2 q^{13} + 9 q^{15} + 21 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 36 q^{25} + 6 q^{27} + 4 q^{29} - 24 q^{31} - 32 q^{35} + 2 q^{37} + 2 q^{39} + 10 q^{41} + 23 q^{43} + 2 q^{45} + 66 q^{47} + 34 q^{49} + 23 q^{51} - 13 q^{53} + 27 q^{55} + q^{57} + 35 q^{59} + 56 q^{61} - 9 q^{63} + 48 q^{65} + 13 q^{67} + 10 q^{69} + 76 q^{71} - q^{73} + 36 q^{75} - 38 q^{77} - 46 q^{79} - 6 q^{81} - 26 q^{83} + 42 q^{85} + 7 q^{87} + 58 q^{89} - 40 q^{91} - 9 q^{93} - 29 q^{95} - 46 q^{97}+O(q^{100}) $ 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 11 * q^11 - 2 * q^13 + 9 * q^15 + 21 * q^17 + 10 * q^19 - 2 * q^21 - 10 * q^23 - 36 * q^25 + 6 * q^27 + 4 * q^29 - 24 * q^31 - 32 * q^35 + 2 * q^37 + 2 * q^39 + 10 * q^41 + 23 * q^43 + 2 * q^45 + 66 * q^47 + 34 * q^49 + 23 * q^51 - 13 * q^53 + 27 * q^55 + q^57 + 35 * q^59 + 56 * q^61 - 9 * q^63 + 48 * q^65 + 13 * q^67 + 10 * q^69 + 76 * q^71 - q^73 + 36 * q^75 - 38 * q^77 - 46 * q^79 - 6 * q^81 - 26 * q^83 + 42 * q^85 + 7 * q^87 + 58 * q^89 - 40 * q^91 - 9 * q^93 - 29 * q^95 - 46 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{6}{11}\right)$	$1$

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
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$		0			0
$5$	1.12656	+	0.723994i	0.503812	+	0.323780i	0.767739	−	0.640762i	$-0.221382\pi$
$5$	1.12656	+	0.723994i	0.503812	+	0.323780i	−0.263928	+	0.964543i	$0.585018\pi$
$6$		0			0
$7$	−0.202268	+	1.40680i	−0.0764499	+	0.531721i	0.915224	+	0.402946i	$0.132014\pi$
$7$	−0.202268	+	1.40680i	−0.0764499	+	0.531721i	−0.991674	+	0.128775i	$0.958895\pi$
$8$		0			0
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$		0			0
$11$	−2.52874	−	1.62512i	−0.762443	−	0.489992i	0.100722	−	0.994915i	$-0.467885\pi$
$11$	−2.52874	−	1.62512i	−0.762443	−	0.489992i	−0.863165	+	0.504922i	$0.831521\pi$
$12$		0			0
$13$	1.08620	+	2.37844i	0.301256	+	0.659660i	0.998356	−	0.0573146i	$-0.0182538\pi$
$13$	1.08620	+	2.37844i	0.301256	+	0.659660i	−0.697100	+	0.716974i	$0.745527\pi$
$14$		0			0
$15$	0.190580	+	1.32551i	0.0492075	+	0.342245i
$16$		0			0
$17$	2.15851	−	0.633795i	0.523515	−	0.153718i	−0.00928835	−	0.999957i	$-0.502957\pi$
$17$	2.15851	−	0.633795i	0.523515	−	0.153718i	0.532804	+	0.846239i	$0.321138\pi$
$18$		0			0
$19$	1.08664	+	7.55774i	0.249292	+	1.73386i	0.602323	+	0.798253i	$0.294242\pi$
$19$	1.08664	+	7.55774i	0.249292	+	1.73386i	−0.353030	+	0.935612i	$0.614849\pi$
$20$		0			0
$21$	−1.19565	+	0.768395i	−0.260911	+	0.167678i
$22$		0			0
$23$	5.68168	+	6.55701i	1.18471	+	1.36723i	0.914578	+	0.404409i	$0.132523\pi$
$23$	5.68168	+	6.55701i	1.18471	+	1.36723i	0.270135	+	0.962823i	$0.412932\pi$
$24$		0			0
$25$	−1.33211	−	2.91692i	−0.266422	−	0.583384i
$26$		0			0
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$		0			0
$29$	−3.39419			−0.630286			−0.315143	−	0.949044i	$-0.602052\pi$
$29$	−3.39419			−0.630286			−0.315143	+	0.949044i	$0.602052\pi$
$30$		0			0
$31$	1.49181	−	3.26660i	0.267936	−	0.586699i	−0.727064	−	0.686570i	$-0.759116\pi$
$31$	1.49181	−	3.26660i	0.267936	−	0.586699i	0.995000	+	0.0998707i	$0.0318429\pi$
$32$		0			0
$33$	−0.427787	−	2.97532i	−0.0744681	−	0.517937i
$34$		0			0
$35$	−1.24638	+	1.43840i	−0.210677	+	0.243134i
$36$		0			0
$37$	−6.63386			−1.09060			−0.545300	−	0.838241i	$-0.683584\pi$
$37$	−6.63386			−1.09060			−0.545300	+	0.838241i	$0.683584\pi$
$38$		0			0
$39$	−1.08620	+	2.37844i	−0.173930	+	0.380855i
$40$		0			0
$41$	1.86302	−	0.547031i	0.290954	−	0.0854319i	−0.132998	−	0.991116i	$-0.542461\pi$
$41$	1.86302	−	0.547031i	0.290954	−	0.0854319i	0.423953	+	0.905684i	$0.360642\pi$
$42$		0			0
$43$	−8.87900	+	2.60711i	−1.35403	+	0.397581i	−0.876656	−	0.481117i	$-0.840231\pi$
$43$	−8.87900	+	2.60711i	−1.35403	+	0.397581i	−0.477379	+	0.878698i	$0.658413\pi$
$44$		0			0
$45$	−0.876951	+	1.01206i	−0.130728	+	0.150868i
$46$		0			0
$47$	−0.660772	−	0.762571i	−0.0963835	−	0.111232i	0.705509	−	0.708701i	$-0.250719\pi$
$47$	−0.660772	−	0.762571i	−0.0963835	−	0.111232i	−0.801892	+	0.597469i	$0.796173\pi$
$48$		0			0
$49$	4.77827	+	1.40303i	0.682610	+	0.200432i
$50$		0			0
$51$	1.89251	+	1.21624i	0.265005	+	0.170308i
$52$		0			0
$53$	11.0069	+	3.23191i	1.51191	+	0.443937i	0.929458	−	0.368927i	$-0.120275\pi$
$53$	11.0069	+	3.23191i	1.51191	+	0.443937i	0.582453	+	0.812864i	$0.302093\pi$
$54$		0			0
$55$	−1.67219	−	3.66158i	−0.225478	−	0.493728i
$56$		0			0
$57$	−5.00016	+	5.77049i	−0.662288	+	0.764321i
$58$		0			0
$59$	3.66918	−	8.03438i	0.477687	−	1.04599i	−0.505407	−	0.862881i	$-0.668657\pi$
$59$	3.66918	−	8.03438i	0.477687	−	1.04599i	0.983093	−	0.183106i	$-0.0586152\pi$
$60$		0			0
$61$	8.80650	−	5.65959i	1.12756	−	0.724637i	0.162508	−	0.986707i	$-0.448042\pi$
$61$	8.80650	−	5.65959i	1.12756	−	0.724637i	0.965049	+	0.262071i	$0.0844053\pi$
$62$		0			0
$63$	−1.36370	−	0.400417i	−0.171810	−	0.0504479i
$64$		0			0
$65$	−0.498313	+	3.46584i	−0.0618081	+	0.429885i
$66$		0			0
$67$	0.105510	+	8.18467i	0.0128902	+	0.999917i
$67$	0.105510	+	8.18467i	0.0128902	+	0.999917i
$68$		0			0
$69$	−1.23475	+	8.58786i	−0.148646	+	1.03386i
$70$		0			0
$71$	−3.96022	−	1.16283i	−0.469992	−	0.138002i	0.0381560	−	0.999272i	$-0.487852\pi$
$71$	−3.96022	−	1.16283i	−0.469992	−	0.138002i	−0.508148	+	0.861270i	$0.669670\pi$
$72$		0			0
$73$	−6.59618	+	4.23911i	−0.772024	+	0.496150i	−0.866378	−	0.499389i	$-0.833558\pi$
$73$	−6.59618	+	4.23911i	−0.772024	+	0.496150i	0.0943538	+	0.995539i	$0.469922\pi$
$74$		0			0
$75$	1.33211	−	2.91692i	0.153819	−	0.336817i
$76$		0			0
$77$	2.79770	−	3.22872i	0.318828	−	0.367947i
$78$		0			0
$79$	3.97765	+	8.70984i	0.447521	+	0.979934i	0.990156	+	0.139966i	$0.0446992\pi$
$79$	3.97765	+	8.70984i	0.447521	+	0.979934i	−0.542635	+	0.839968i	$0.682573\pi$
$80$		0			0
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$		0			0
$83$	−7.38873	−	4.74845i	−0.811018	−	0.521210i	0.0681759	−	0.997673i	$-0.478282\pi$
$83$	−7.38873	−	4.74845i	−0.811018	−	0.521210i	−0.879194	+	0.476463i	$0.841918\pi$
$84$		0			0
$85$	2.89055	+	0.848742i	0.313524	+	0.0920589i
$86$		0			0
$87$	−2.22272	−	2.56516i	−0.238301	−	0.275014i
$88$		0			0
$89$	7.60486	−	8.77648i	0.806113	−	0.930305i	−0.192586	−	0.981280i	$-0.561688\pi$
$89$	7.60486	−	8.77648i	0.806113	−	0.930305i	0.998700	+	0.0509754i	$0.0162330\pi$
$90$		0			0
$91$	−3.56569	+	1.04698i	−0.373786	+	0.109753i
$92$		0			0
$93$	3.44566	−	1.01174i	0.357298	−	0.104912i
$94$		0			0
$95$	−4.24760	+	9.30095i	−0.435795	+	0.954257i
$96$		0			0
$97$	−5.54010			−0.562512			−0.281256	−	0.959633i	$-0.590751\pi$
$97$	−5.54010			−0.562512			−0.281256	+	0.959633i	$0.590751\pi$
$98$		0			0
$99$	1.96846	−	2.27172i	0.197837	−	0.228316i
$100$		0			0
$101$	−1.94942	−	13.5585i	−0.193974	−	1.34912i	−0.821360	−	0.570411i	$-0.806784\pi$
$101$	−1.94942	−	13.5585i	−0.193974	−	1.34912i	0.627385	−	0.778709i	$-0.284125\pi$
$102$		0			0
$103$	−5.86913	+	12.8516i	−0.578303	+	1.26631i	0.363955	+	0.931417i	$0.381426\pi$
$103$	−5.86913	+	12.8516i	−0.578303	+	1.26631i	−0.942257	+	0.334890i	$0.891301\pi$
$104$		0			0
$105$	−1.90328			−0.185741
$106$		0			0
$107$	11.6790	−	7.50566i	1.12905	−	0.725600i	0.163692	−	0.986511i	$-0.447660\pi$
$107$	11.6790	−	7.50566i	1.12905	−	0.725600i	0.965363	+	0.260912i	$0.0840232\pi$
$108$		0			0
$109$	−0.953650	−	2.08820i	−0.0913431	−	0.200013i	0.858446	−	0.512904i	$-0.171430\pi$
$109$	−0.953650	−	2.08820i	−0.0913431	−	0.200013i	−0.949789	+	0.312890i	$0.898703\pi$
$110$		0			0
$111$	−4.34426	−	5.01354i	−0.412339	−	0.475864i
$112$		0			0
$113$	11.3583	−	7.29951i	1.06849	−	0.686680i	0.116623	−	0.993176i	$-0.462793\pi$
$113$	11.3583	−	7.29951i	1.06849	−	0.686680i	0.951872	+	0.306497i	$0.0991568\pi$
$114$		0			0
$115$	1.65350	+	11.5004i	0.154190	+	1.07241i
$116$		0			0
$117$	−2.50881	+	0.736653i	−0.231940	+	0.0681036i
$118$		0			0
$119$	0.455028	+	3.16479i	0.0417124	+	0.290116i
$120$		0			0
$121$	−0.816068	−	1.78694i	−0.0741880	−	0.162449i
$122$		0			0
$123$	1.63343	+	1.04974i	0.147282	+	0.0946523i
$124$		0			0
$125$	1.56403	−	10.8781i	0.139891	−	0.972964i
$126$		0			0
$127$	1.92871	−	13.4145i	0.171146	−	1.19034i	−0.705323	−	0.708886i	$-0.749198\pi$
$127$	1.92871	−	13.4145i	0.171146	−	1.19034i	0.876469	−	0.481459i	$-0.159893\pi$
$128$		0			0
$129$	−7.78483	−	5.00301i	−0.685416	−	0.440490i
$130$		0			0
$131$	9.57774	+	11.0533i	0.836811	+	0.965731i	0.999782	−	0.0208995i	$-0.00665300\pi$
$131$	9.57774	+	11.0533i	0.836811	+	0.965731i	−0.162971	+	0.986631i	$0.552108\pi$
$132$		0			0
$133$	−10.8520			−0.940991
$134$		0			0
$135$	−1.33914			−0.115255
$136$		0			0
$137$	3.72372	+	4.29740i	0.318139	+	0.367152i	0.892184	−	0.451672i	$-0.149172\pi$
$137$	3.72372	+	4.29740i	0.318139	+	0.367152i	−0.574045	+	0.818823i	$0.694627\pi$
$138$		0			0
$139$	−11.7701	−	7.56419i	−0.998328	−	0.641587i	−0.0639811	−	0.997951i	$-0.520380\pi$
$139$	−11.7701	−	7.56419i	−0.998328	−	0.641587i	−0.934347	+	0.356365i	$0.884016\pi$
$140$		0			0
$141$	0.143599	−	0.998756i	0.0120933	−	0.0841104i
$142$		0			0
$143$	1.11854	−	7.77964i	0.0935373	−	0.650566i
$144$		0			0
$145$	−3.82375	−	2.45738i	−0.317545	−	0.204074i
$146$		0			0
$147$	2.06877	+	4.52997i	0.170629	+	0.373625i
$148$		0			0
$149$	−3.09970	−	21.5589i	−0.253938	−	1.76617i	−0.574074	−	0.818803i	$-0.694638\pi$
$149$	−3.09970	−	21.5589i	−0.253938	−	1.76617i	0.320137	−	0.947371i	$-0.396271\pi$
$150$		0			0
$151$	9.93981	−	2.91859i	0.808890	−	0.237512i	0.148965	−	0.988843i	$-0.452406\pi$
$151$	9.93981	−	2.91859i	0.808890	−	0.237512i	0.659926	+	0.751331i	$0.270588\pi$
$152$		0			0
$153$	0.320156	+	2.22674i	0.0258831	+	0.180021i
$154$		0			0
$155$	4.04561	−	2.59995i	0.324951	−	0.208833i
$156$		0			0
$157$	1.48075	+	1.70888i	0.118177	+	0.136383i	0.811755	−	0.583998i	$-0.198512\pi$
$157$	1.48075	+	1.70888i	0.118177	+	0.136383i	−0.693578	+	0.720381i	$0.743967\pi$
$158$		0			0
$159$	4.76546	+	10.4349i	0.377925	+	0.827541i
$160$		0			0
$161$	−10.3736	+	6.66673i	−0.817557	+	0.525412i
$162$		0			0
$163$	16.1499			1.26496			0.632479	−	0.774577i	$-0.282037\pi$
$163$	16.1499			1.26496			0.632479	+	0.774577i	$0.282037\pi$
$164$		0			0
$165$	1.67219	−	3.66158i	0.130180	−	0.285054i
$166$		0			0
$167$	−0.874032	−	6.07902i	−0.0676346	−	0.470409i	−0.995288	−	0.0969660i	$-0.969086\pi$
$167$	−0.874032	−	6.07902i	−0.0676346	−	0.470409i	0.927653	−	0.373443i	$-0.121823\pi$
$168$		0			0
$169$	4.03605	−	4.65785i	0.310465	−	0.358296i
$170$		0			0
$171$	−7.63546			−0.583898
$172$		0			0
$173$	2.01439	−	4.41090i	0.153151	−	0.335355i	−0.817468	−	0.575974i	$-0.804623\pi$
$173$	2.01439	−	4.41090i	0.153151	−	0.335355i	0.970620	+	0.240619i	$0.0773504\pi$
$174$		0			0
$175$	4.37297	−	1.28402i	0.330565	−	0.0970627i
$176$		0			0
$177$	8.47478	−	2.48842i	0.637004	−	0.187041i
$178$		0			0
$179$	−14.9942	+	17.3042i	−1.12072	+	1.29338i	−0.169267	+	0.985570i	$0.554140\pi$
$179$	−14.9942	+	17.3042i	−1.12072	+	1.29338i	−0.951449	+	0.307806i	$0.900405\pi$
$180$		0			0
$181$	−7.12283	−	8.22018i	−0.529435	−	0.611001i	0.426532	−	0.904472i	$-0.359735\pi$
$181$	−7.12283	−	8.22018i	−0.529435	−	0.611001i	−0.955968	+	0.293471i	$0.905190\pi$
$182$		0			0
$183$	10.0443	+	2.94926i	0.742493	+	0.218016i
$184$		0			0
$185$	−7.47343	−	4.80288i	−0.549457	−	0.353115i
$186$		0			0
$187$	−6.48830	−	1.90514i	−0.474471	−	0.139317i
$188$		0			0
$189$	−0.590416	−	1.29283i	−0.0429464	−	0.0940396i
$190$		0			0
$191$	10.8396	−	12.5095i	0.784323	−	0.905157i	−0.213091	−	0.977032i	$-0.568353\pi$
$191$	10.8396	−	12.5095i	0.784323	−	0.905157i	0.997414	+	0.0718758i	$0.0228985\pi$
$192$		0			0
$193$	4.01603	−	8.79387i	0.289080	−	0.632997i	−0.708255	−	0.705957i	$-0.750517\pi$
$193$	4.01603	−	8.79387i	0.289080	−	0.632997i	0.997335	+	0.0729601i	$0.0232446\pi$
$194$		0			0
$195$	−2.94564	+	1.89305i	−0.210941	+	0.135564i
$196$		0			0
$197$	4.17889	+	1.22703i	0.297734	+	0.0874226i	0.427188	−	0.904163i	$-0.359504\pi$
$197$	4.17889	+	1.22703i	0.297734	+	0.0874226i	−0.129454	+	0.991585i	$0.541322\pi$
$198$		0			0
$199$	2.24247	−	15.5967i	0.158964	−	1.10562i	−0.741582	−	0.670862i	$-0.765924\pi$
$199$	2.24247	−	15.5967i	0.158964	−	1.10562i	0.900547	−	0.434759i	$-0.143166\pi$
$200$		0			0
$201$	−6.11647	+	5.43956i	−0.431422	+	0.383677i
$202$		0			0
$203$	0.686535	−	4.77495i	0.0481853	−	0.335136i
$204$		0			0
$205$	2.49484	+	0.732551i	0.174247	+	0.0511636i
$206$		0			0
$207$	−7.29886	+	4.69069i	−0.507306	+	0.326026i
$208$		0			0
$209$	9.53442	−	20.8775i	0.659510	−	1.44412i
$210$		0			0
$211$	−9.34056	+	10.7796i	−0.643031	+	0.742097i	−0.979908	−	0.199451i	$-0.936084\pi$
$211$	−9.34056	+	10.7796i	−0.643031	+	0.742097i	0.336877	+	0.941549i	$0.390629\pi$
$212$		0			0
$213$	−1.71459	−	3.75443i	−0.117482	−	0.257249i
$214$		0			0
$215$	−11.8902	−	3.49129i	−0.810907	−	0.238104i
$216$		0			0
$217$	4.29372	+	2.75940i	0.291476	+	0.187321i
$218$		0			0
$219$	−7.52328	−	2.20903i	−0.508376	−	0.149273i
$220$		0			0
$221$	3.85201	+	4.44545i	0.259114	+	0.299033i
$222$		0			0
$223$	14.7457	−	17.0174i	0.987444	−	1.13957i	−0.00276766	−	0.999996i	$-0.500881\pi$
$223$	14.7457	−	17.0174i	0.987444	−	1.13957i	0.990212	−	0.139575i	$-0.0445736\pi$
$224$		0			0
$225$	3.07681	−	0.903432i	0.205120	−	0.0602288i
$226$		0			0
$227$	−9.14491	+	2.68519i	−0.606969	+	0.178222i	−0.570753	−	0.821122i	$-0.693349\pi$
$227$	−9.14491	+	2.68519i	−0.606969	+	0.178222i	−0.0362160	+	0.999344i	$0.511530\pi$
$228$		0			0
$229$	−2.91562	+	6.38432i	−0.192670	+	0.421888i	−0.981170	−	0.193147i	$-0.938131\pi$
$229$	−2.91562	+	6.38432i	−0.192670	+	0.421888i	0.788500	+	0.615034i	$0.210858\pi$
$230$		0			0
$231$	4.27221			0.281091
$232$		0			0
$233$	6.11516	−	7.05727i	0.400617	−	0.462337i	−0.519218	−	0.854642i	$-0.673777\pi$
$233$	6.11516	−	7.05727i	0.400617	−	0.462337i	0.919835	+	0.392305i	$0.128322\pi$
$234$		0			0
$235$	−0.192300	−	1.33748i	−0.0125443	−	0.0872473i
$236$		0			0
$237$	−3.97765	+	8.70984i	−0.258376	+	0.565765i
$238$		0			0
$239$	−26.4821			−1.71299			−0.856493	−	0.516158i	$-0.827362\pi$
$239$	−26.4821			−1.71299			−0.856493	+	0.516158i	$0.827362\pi$
$240$		0			0
$241$	−18.3896	+	11.8182i	−1.18458	+	0.761280i	−0.976222	−	0.216773i	$-0.930447\pi$
$241$	−18.3896	+	11.8182i	−1.18458	+	0.761280i	−0.208353	+	0.978054i	$0.566810\pi$
$242$		0			0
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$		0			0
$245$	4.36721	+	5.04003i	0.279011	+	0.321996i
$246$		0			0
$247$	−16.7953	+	10.7937i	−1.06866	+	0.686786i
$248$		0			0
$249$	−1.24995	−	8.69360i	−0.0792124	−	0.550935i
$250$		0			0
$251$	−8.16027	+	2.39607i	−0.515072	+	0.151239i	−0.528930	−	0.848665i	$-0.677407\pi$
$251$	−8.16027	+	2.39607i	−0.515072	+	0.151239i	0.0138586	+	0.999904i	$0.495589\pi$
$252$		0			0
$253$	−3.71155	−	25.8144i	−0.233343	−	1.62294i
$254$		0			0
$255$	1.25147	+	2.74034i	0.0783701	+	0.171607i
$256$		0			0
$257$	10.2447	+	6.58389i	0.639049	+	0.410692i	0.819650	−	0.572865i	$-0.194168\pi$
$257$	10.2447	+	6.58389i	0.639049	+	0.410692i	−0.180601	+	0.983556i	$0.557804\pi$
$258$		0			0
$259$	1.34182	−	9.33253i	0.0833763	−	0.579895i
$260$		0			0
$261$	0.483044	−	3.35964i	0.0298997	−	0.207957i
$262$		0			0
$263$	8.47112	+	5.44406i	0.522352	+	0.335695i	0.775102	−	0.631837i	$-0.217699\pi$
$263$	8.47112	+	5.44406i	0.522352	+	0.335695i	−0.252750	+	0.967532i	$0.581335\pi$
$264$		0			0
$265$	10.0600	+	11.6099i	0.617981	+	0.713188i
$266$		0			0
$267$	11.6129			0.710700
$268$		0			0
$269$	14.3381			0.874208			0.437104	−	0.899411i	$-0.356004\pi$
$269$	14.3381			0.874208			0.437104	+	0.899411i	$0.356004\pi$
$270$		0			0
$271$	1.12115	+	1.29388i	0.0681050	+	0.0785974i	0.788780	−	0.614676i	$-0.210713\pi$
$271$	1.12115	+	1.29388i	0.0681050	+	0.0785974i	−0.720675	+	0.693273i	$0.756168\pi$
$272$		0			0
$273$	−3.12629	−	2.00914i	−0.189211	−	0.121599i
$274$		0			0
$275$	−1.37178	+	9.54096i	−0.0827217	+	0.575342i
$276$		0			0
$277$	0.214899	−	1.49466i	0.0129120	−	0.0898052i	−0.982346	−	0.187071i	$-0.940101\pi$
$277$	0.214899	−	1.49466i	0.0129120	−	0.0898052i	0.995258	+	0.0972657i	$0.0310097\pi$
$278$		0			0
$279$	3.02105	+	1.94151i	0.180865	+	0.116235i
$280$		0			0
$281$	2.61728	+	5.73104i	0.156134	+	0.341885i	0.971492	−	0.237071i	$-0.0761875\pi$
$281$	2.61728	+	5.73104i	0.156134	+	0.341885i	−0.815359	+	0.578956i	$0.803460\pi$
$282$		0			0
$283$	2.63994	+	18.3612i	0.156928	+	1.09146i	0.904252	+	0.426999i	$0.140429\pi$
$283$	2.63994	+	18.3612i	0.156928	+	1.09146i	−0.747324	+	0.664460i	$0.768662\pi$
$284$		0			0
$285$	−9.81077	+	2.88070i	−0.581140	+	0.170638i
$286$		0			0
$287$	0.392736	+	2.73154i	0.0231825	+	0.161238i
$288$		0			0
$289$	−10.0438	+	6.45479i	−0.590814	+	0.379693i
$290$		0			0
$291$	−3.62799	−	4.18693i	−0.212677	−	0.245442i
$292$		0			0
$293$	−2.59390	−	5.67986i	−0.151537	−	0.331821i	0.818605	−	0.574357i	$-0.194748\pi$
$293$	−2.59390	−	5.67986i	−0.151537	−	0.331821i	−0.970142	+	0.242536i	$0.922021\pi$
$294$		0			0
$295$	9.95039	−	6.39473i	0.579334	−	0.372315i
$296$		0			0
$297$	3.00592			0.174421
$298$		0			0
$299$	−9.42402	+	20.6357i	−0.545005	+	1.19339i
$300$		0			0
$301$	−1.87175	−	13.0183i	−0.107886	−	0.750364i
$302$		0			0
$303$	8.97022	−	10.3522i	0.515326	−	0.594718i
$304$		0			0
$305$	14.0185			0.802699
$306$		0			0
$307$	8.79483	−	19.2580i	0.501948	−	1.09911i	−0.473884	−	0.880587i	$-0.657148\pi$
$307$	8.79483	−	19.2580i	0.501948	−	1.09911i	0.975831	−	0.218524i	$-0.0701243\pi$
$308$		0			0
$309$	−13.5561	+	3.98042i	−0.771177	+	0.226438i
$310$		0			0
$311$	11.5887	−	3.40276i	0.657137	−	0.192953i	0.0638697	−	0.997958i	$-0.479656\pi$
$311$	11.5887	−	3.40276i	0.657137	−	0.192953i	0.593268	+	0.805005i	$0.297838\pi$
$312$		0			0
$313$	9.62902	−	11.1125i	0.544265	−	0.628115i	−0.415273	−	0.909697i	$-0.636314\pi$
$313$	9.62902	−	11.1125i	0.544265	−	0.628115i	0.959537	+	0.281582i	$0.0908592\pi$
$314$		0			0
$315$	−1.24638	−	1.43840i	−0.0702257	−	0.0810448i
$316$		0			0
$317$	−27.7406	−	8.14537i	−1.55807	−	0.457490i	−0.614567	−	0.788865i	$-0.710669\pi$
$317$	−27.7406	−	8.14537i	−1.55807	−	0.457490i	−0.943499	+	0.331375i	$0.892487\pi$
$318$		0			0
$319$	8.58302	+	5.51597i	0.480557	+	0.308835i
$320$		0			0
$321$	13.3205	+	3.91126i	0.743480	+	0.218305i
$322$		0			0
$323$	7.13558	+	15.6247i	0.397034	+	0.869384i
$324$		0			0
$325$	5.49077	−	6.33669i	0.304573	−	0.351496i
$326$		0			0
$327$	0.953650	−	2.08820i	0.0527370	−	0.115478i
$328$		0			0
$329$	1.20644	−	0.775331i	0.0665132	−	0.0427454i
$330$		0			0
$331$	−15.3580	−	4.50953i	−0.844154	−	0.247866i	−0.169068	−	0.985604i	$-0.554076\pi$
$331$	−15.3580	−	4.50953i	−0.844154	−	0.247866i	−0.675087	+	0.737738i	$0.735894\pi$
$332$		0			0
$333$	0.944097	−	6.56634i	0.0517362	−	0.359833i
$334$		0			0
$335$	−5.80679	+	9.29689i	−0.317259	+	0.507943i
$336$		0			0
$337$	−2.75983	+	19.1950i	−0.150337	+	1.04562i	0.765317	+	0.643654i	$0.222582\pi$
$337$	−2.75983	+	19.1950i	−0.150337	+	1.04562i	−0.915654	+	0.401966i	$0.868327\pi$
$338$		0			0
$339$	12.9547	+	3.80384i	0.703601	+	0.206596i
$340$		0			0
$341$	−9.08101	+	5.83601i	−0.491764	+	0.316038i
$342$		0			0
$343$	−7.07318	+	15.4881i	−0.381916	+	0.836279i
$344$		0			0
$345$	−7.60858	+	8.78076i	−0.409632	+	0.472740i
$346$		0			0
$347$	7.53963	+	16.5095i	0.404749	+	0.886276i	0.996767	+	0.0803511i	$0.0256041\pi$
$347$	7.53963	+	16.5095i	0.404749	+	0.886276i	−0.592018	+	0.805925i	$0.701669\pi$
$348$		0			0
$349$	18.6250	+	5.46879i	0.996973	+	0.292738i	0.739213	−	0.673471i	$-0.235198\pi$
$349$	18.6250	+	5.46879i	0.996973	+	0.292738i	0.257760	+	0.966209i	$0.417016\pi$
$350$		0			0
$351$	−2.19965	−	1.41363i	−0.117408	−	0.0754538i
$352$		0			0
$353$	4.25790	+	1.25023i	0.226625	+	0.0665432i	0.393074	−	0.919507i	$-0.371412\pi$
$353$	4.25790	+	1.25023i	0.226625	+	0.0665432i	−0.166448	+	0.986050i	$0.553230\pi$
$354$		0			0
$355$	−3.61954	−	4.17717i	−0.192105	−	0.221701i
$356$		0			0
$357$	−2.09381	+	2.41638i	−0.110816	+	0.127889i
$358$		0			0
$359$	−5.39866	+	1.58519i	−0.284930	+	0.0836631i	−0.421075	−	0.907026i	$-0.638347\pi$
$359$	−5.39866	+	1.58519i	−0.284930	+	0.0836631i	0.136144	+	0.990689i	$0.456529\pi$
$360$		0			0
$361$	−37.7083	+	11.0722i	−1.98465	+	0.582745i
$362$		0			0
$363$	0.816068	−	1.78694i	0.0428325	−	0.0937900i
$364$		0			0
$365$	−10.5001			−0.549598
$366$		0			0
$367$	−10.2868	+	11.8716i	−0.536966	+	0.619692i	−0.957796	−	0.287447i	$-0.907193\pi$
$367$	−10.2868	+	11.8716i	−0.536966	+	0.619692i	0.420830	+	0.907139i	$0.361739\pi$
$368$		0			0
$369$	0.276328	+	1.92190i	0.0143851	+	0.100050i
$370$		0			0
$371$	−6.77299	+	14.8308i	−0.351636	+	0.769976i
$372$		0			0
$373$	13.5332			0.700723			0.350361	−	0.936615i	$-0.386059\pi$
$373$	13.5332			0.700723			0.350361	+	0.936615i	$0.386059\pi$
$374$		0			0
$375$	9.24532	−	5.94161i	0.477426	−	0.306823i
$376$		0			0
$377$	−3.68676	−	8.07287i	−0.189878	−	0.415774i
$378$		0			0
$379$	12.5546	+	14.4888i	0.644886	+	0.744238i	0.980231	−	0.197857i	$-0.0633982\pi$
$379$	12.5546	+	14.4888i	0.644886	+	0.744238i	−0.335345	+	0.942096i	$0.608853\pi$
$380$		0			0
$381$	11.4010	−	7.32701i	0.584093	−	0.375374i
$382$		0			0
$383$	−4.66462	−	32.4431i	−0.238351	−	1.65777i	−0.660191	−	0.751097i	$-0.729525\pi$
$383$	−4.66462	−	32.4431i	−0.238351	−	1.65777i	0.421840	−	0.906670i	$-0.361384\pi$
$384$		0			0
$385$	5.48935	−	1.61182i	0.279763	−	0.0821459i
$386$		0			0
$387$	−1.31696	−	9.15966i	−0.0669448	−	0.465611i
$388$		0			0
$389$	−2.93841	−	6.43422i	−0.148983	−	0.326228i	0.820396	−	0.571795i	$-0.193753\pi$
$389$	−2.93841	−	6.43422i	−0.148983	−	0.326228i	−0.969379	+	0.245568i	$0.921026\pi$
$390$		0			0
$391$	16.4198	+	10.5523i	0.830383	+	0.533655i
$392$		0			0
$393$	−2.08144	+	14.4767i	−0.104995	+	0.730255i
$394$		0			0
$395$	−1.82482	+	12.6919i	−0.0918169	+	0.638601i
$396$		0			0
$397$	−0.325544	−	0.209214i	−0.0163386	−	0.0105002i	0.532446	−	0.846464i	$-0.321273\pi$
$397$	−0.325544	−	0.209214i	−0.0163386	−	0.0105002i	−0.548785	+	0.835964i	$0.684909\pi$
$398$		0			0
$399$	−7.10657	−	8.20142i	−0.355774	−	0.410585i
$400$		0			0
$401$	9.41238			0.470032			0.235016	−	0.971992i	$-0.424486\pi$
$401$	9.41238			0.470032			0.235016	+	0.971992i	$0.424486\pi$
$402$		0			0
$403$	9.38980			0.467739
$404$		0			0
$405$	−0.876951	−	1.01206i	−0.0435760	−	0.0502894i
$406$		0			0
$407$	16.7753	+	10.7808i	0.831521	+	0.534386i
$408$		0			0
$409$	0.104187	−	0.724633i	0.00515169	−	0.0358308i	−0.987083	−	0.160207i	$-0.948784\pi$
$409$	0.104187	−	0.724633i	0.00515169	−	0.0358308i	0.992235	+	0.124376i	$0.0396929\pi$
$410$		0			0
$411$	−0.809241	+	5.62840i	−0.0399169	+	0.277628i
$412$		0			0
$413$	10.5606	+	6.78690i	0.519654	+	0.333962i
$414$		0			0
$415$	−4.88598	−	10.6988i	−0.239843	−	0.525183i
$416$		0			0
$417$	−1.99115	−	13.8488i	−0.0975070	−	0.678176i
$418$		0			0
$419$	−20.3895	+	5.98689i	−0.996091	+	0.292479i	−0.738851	−	0.673869i	$-0.764631\pi$
$419$	−20.3895	+	5.98689i	−0.996091	+	0.292479i	−0.257240	+	0.966348i	$0.582813\pi$
$420$		0			0
$421$	4.74139	+	32.9771i	0.231081	+	1.60721i	0.693441	+	0.720514i	$0.256094\pi$
$421$	4.74139	+	32.9771i	0.231081	+	1.60721i	−0.462359	+	0.886693i	$0.652997\pi$
$422$		0			0
$423$	0.848847	−	0.545521i	0.0412724	−	0.0265241i
$424$		0			0
$425$	−4.72410	−	5.45191i	−0.229153	−	0.264456i
$426$		0			0
$427$	6.18066	+	13.5337i	0.299103	+	0.654944i
$428$		0			0
$429$	6.61195	−	4.24924i	0.319228	−	0.205155i
$430$		0			0
$431$	18.1531			0.874402			0.437201	−	0.899364i	$-0.355970\pi$
$431$	18.1531			0.874402			0.437201	+	0.899364i	$0.355970\pi$
$432$		0			0
$433$	−4.44435	+	9.73177i	−0.213582	+	0.467679i	−0.985853	−	0.167614i	$-0.946394\pi$
$433$	−4.44435	+	9.73177i	−0.213582	+	0.467679i	0.772271	+	0.635294i	$0.219121\pi$
$434$		0			0
$435$	−0.646864	−	4.49904i	−0.0310148	−	0.215712i
$436$		0			0
$437$	−43.3823	+	50.0658i	−2.07525	+	2.39497i
$438$		0			0
$439$	13.5190			0.645229			0.322614	−	0.946531i	$-0.395438\pi$
$439$	13.5190			0.645229			0.322614	+	0.946531i	$0.395438\pi$
$440$		0			0
$441$	−2.06877	+	4.52997i	−0.0985127	+	0.215713i
$442$		0			0
$443$	−3.50537	+	1.02927i	−0.166545	+	0.0489020i	−0.363942	−	0.931422i	$-0.618569\pi$
$443$	−3.50537	+	1.02927i	−0.166545	+	0.0489020i	0.197397	+	0.980324i	$0.436751\pi$
$444$		0			0
$445$	14.9214	−	4.38133i	0.707344	−	0.207695i
$446$		0			0
$447$	14.2633	−	16.4607i	0.674629	−	0.778564i
$448$		0			0
$449$	22.3267	+	25.7664i	1.05366	+	1.21599i	0.975717	+	0.219035i	$0.0702908\pi$
$449$	22.3267	+	25.7664i	1.05366	+	1.21599i	0.0779464	+	0.996958i	$0.475164\pi$
$450$		0			0
$451$	−5.60007	−	1.64433i	−0.263697	−	0.0774284i
$452$		0			0
$453$	8.71492	+	5.60074i	0.409462	+	0.263146i
$454$		0			0
$455$	−4.77496	−	1.40206i	−0.223854	−	0.0657294i
$456$		0			0
$457$	9.00452	+	19.7172i	0.421214	+	0.922330i	0.994672	+	0.103094i	$0.0328744\pi$
$457$	9.00452	+	19.7172i	0.421214	+	0.922330i	−0.573458	+	0.819235i	$0.694398\pi$
$458$		0			0
$459$	−1.47320	+	1.70016i	−0.0687630	+	0.0793567i
$460$		0			0
$461$	−7.24083	+	15.8552i	−0.337239	+	0.738450i	−0.999946	−	0.0104288i	$-0.996680\pi$
$461$	−7.24083	+	15.8552i	−0.337239	+	0.738450i	0.662707	+	0.748879i	$0.269408\pi$
$462$		0			0
$463$	32.5779	−	20.9366i	1.51402	−	0.973004i	0.521198	−	0.853436i	$-0.325485\pi$
$463$	32.5779	−	20.9366i	1.51402	−	0.973004i	0.992826	−	0.119569i	$-0.0381512\pi$
$464$		0			0
$465$	4.61422	+	1.35486i	0.213980	+	0.0628301i
$466$		0			0
$467$	−4.81787	+	33.5091i	−0.222945	+	1.55061i	0.503869	+	0.863780i	$0.331909\pi$
$467$	−4.81787	+	33.5091i	−0.222945	+	1.55061i	−0.726814	+	0.686834i	$0.759000\pi$
$468$		0			0
$469$	−11.5356	−	1.50706i	−0.532662	−	0.0695896i
$470$		0			0
$471$	−0.321798	+	2.23815i	−0.0148277	+	0.103129i
$472$		0			0
$473$	26.6895	+	7.83675i	1.22719	+	0.360334i
$474$		0			0
$475$	20.5978	−	13.2374i	0.945091	−	0.607373i
$476$		0			0
$477$	−4.76546	+	10.4349i	−0.218195	+	0.477781i
$478$		0			0
$479$	−6.59804	+	7.61455i	−0.301472	+	0.347918i	−0.886192	−	0.463318i	$-0.846659\pi$
$479$	−6.59804	+	7.61455i	−0.301472	+	0.347918i	0.584720	+	0.811235i	$0.301204\pi$
$480$		0			0
$481$	−7.20567	−	15.7782i	−0.328550	−	0.719425i
$482$		0			0
$483$	−11.8317	−	3.47409i	−0.538359	−	0.158077i
$484$		0			0
$485$	−6.24124	−	4.01100i	−0.283400	−	0.182130i
$486$		0			0
$487$	−27.1679	−	7.97722i	−1.23110	−	0.361482i	−0.399433	−	0.916763i	$-0.630793\pi$
$487$	−27.1679	−	7.97722i	−1.23110	−	0.361482i	−0.831663	+	0.555280i	$0.812611\pi$
$488$		0			0
$489$	10.5759	+	12.2053i	0.478260	+	0.551942i
$490$		0			0
$491$	−22.6326	+	26.1194i	−1.02139	+	1.17875i	−0.0376286	+	0.999292i	$0.511980\pi$
$491$	−22.6326	+	26.1194i	−1.02139	+	1.17875i	−0.983765	+	0.179460i	$0.942565\pi$
$492$		0			0
$493$	−7.32639	+	2.15122i	−0.329964	+	0.0968862i
$494$		0			0
$495$	3.86229	−	1.13407i	0.173597	−	0.0509727i
$496$		0			0
$497$	2.43689	−	5.33605i	0.109310	−	0.239354i
$498$		0			0
$499$	1.49914			0.0671108			0.0335554	−	0.999437i	$-0.489317\pi$
$499$	1.49914			0.0671108			0.0335554	+	0.999437i	$0.489317\pi$
$500$		0			0
$501$	4.02185	−	4.64146i	0.179683	−	0.207365i
$502$		0			0
$503$	1.10404	+	7.67875i	0.0492266	+	0.342379i	0.999519	+	0.0310191i	$0.00987526\pi$
$503$	1.10404	+	7.67875i	0.0492266	+	0.342379i	−0.950292	+	0.311360i	$0.899216\pi$
$504$		0			0
$505$	7.62014	−	16.6858i	0.339092	−	0.742507i
$506$		0			0
$507$	6.16322			0.273718
$508$		0			0
$509$	7.04353	−	4.52660i	0.312199	−	0.200638i	−0.375152	−	0.926963i	$-0.622410\pi$
$509$	7.04353	−	4.52660i	0.312199	−	0.200638i	0.687351	+	0.726325i	$0.258773\pi$
$510$		0			0
$511$	−4.62939	−	10.1369i	−0.204792	−	0.448432i
$512$		0			0
$513$	−5.00016	−	5.77049i	−0.220763	−	0.254774i
$514$		0			0
$515$	−15.9164	+	10.2289i	−0.701360	+	0.450737i
$516$		0			0
$517$	0.431648	+	3.00218i	0.0189839	+	0.132036i
$518$		0			0
$519$	4.65268	−	1.36615i	0.204230	−	0.0599674i
$520$		0			0
$521$	−4.66783	−	32.4655i	−0.204502	−	1.42234i	−0.790716	−	0.612183i	$-0.790291\pi$
$521$	−4.66783	−	32.4655i	−0.204502	−	1.42234i	0.586214	−	0.810156i	$-0.300618\pi$
$522$		0			0
$523$	−2.29293	−	5.02082i	−0.100263	−	0.219545i	0.852853	−	0.522152i	$-0.174870\pi$
$523$	−2.29293	−	5.02082i	−0.100263	−	0.219545i	−0.953116	+	0.302606i	$0.902143\pi$
$524$		0			0
$525$	3.83408	+	2.46401i	0.167333	+	0.107538i
$526$		0			0
$527$	1.14972	−	7.99649i	0.0500827	−	0.348333i
$528$		0			0
$529$	−7.43964	+	51.7438i	−0.323463	+	2.24973i
$530$		0			0
$531$	7.43043	+	4.77524i	0.322453	+	0.207228i
$532$		0			0
$533$	3.32468	+	3.83688i	0.144008	+	0.166194i
$534$		0			0
$535$	18.5912			0.803766
$536$		0			0
$537$	−22.8967			−0.988067
$538$		0			0
$539$	−9.80291	−	11.3132i	−0.422241	−	0.487292i
$540$		0			0
$541$	−25.5915	−	16.4466i	−1.10026	−	0.707096i	−0.141112	−	0.989994i	$-0.545068\pi$
$541$	−25.5915	−	16.4466i	−1.10026	−	0.707096i	−0.959150	+	0.282898i	$0.908704\pi$
$542$		0			0
$543$	1.54794	−	10.7661i	0.0664284	−	0.462020i
$544$		0			0
$545$	0.437505	−	3.04292i	0.0187407	−	0.130344i
$546$		0			0
$547$	−18.3111	−	11.7678i	−0.782924	−	0.503155i	0.0870789	−	0.996201i	$-0.472247\pi$
$547$	−18.3111	−	11.7678i	−0.782924	−	0.503155i	−0.870003	+	0.493047i	$0.835883\pi$
$548$		0			0
$549$	4.34869	+	9.52231i	0.185598	+	0.406402i
$550$		0			0
$551$	−3.68826	−	25.6524i	−0.157125	−	1.09283i
$552$		0			0
$553$	−13.0576	+	3.83405i	−0.555264	+	0.163040i
$554$		0			0
$555$	−1.26428	−	8.79326i	−0.0536657	−	0.373253i
$556$		0			0
$557$	−22.9401	+	14.7427i	−0.972004	+	0.624669i	−0.927295	−	0.374331i	$-0.877872\pi$
$557$	−22.9401	+	14.7427i	−0.972004	+	0.624669i	−0.0447088	+	0.999000i	$0.514236\pi$
$558$		0			0
$559$	−15.8452	−	18.2863i	−0.670180	−	0.773428i
$560$		0			0
$561$	−2.80913	−	6.15113i	−0.118601	−	0.259701i
$562$		0			0
$563$	−11.7296	+	7.53816i	−0.494344	+	0.317695i	−0.763950	−	0.645275i	$-0.776743\pi$
$563$	−11.7296	+	7.53816i	−0.494344	+	0.317695i	0.269607	+	0.962971i	$0.413106\pi$
$564$		0			0
$565$	18.0805			0.760653
$566$		0			0
$567$	0.590416	−	1.29283i	0.0247951	−	0.0542938i
$568$		0			0
$569$	0.736629	+	5.12337i	0.0308811	+	0.214783i	0.999419	−	0.0340833i	$-0.0108512\pi$
$569$	0.736629	+	5.12337i	0.0308811	+	0.214783i	−0.968538	+	0.248866i	$0.919942\pi$
$570$		0			0
$571$	4.73028	−	5.45904i	0.197956	−	0.228454i	−0.648089	−	0.761564i	$-0.724432\pi$
$571$	4.73028	−	5.45904i	0.197956	−	0.228454i	0.846045	+	0.533111i	$0.178977\pi$
$572$		0			0
$573$	16.5525			0.691489
$574$		0			0
$575$	11.5576	−	25.3077i	0.481986	−	1.05540i
$576$		0			0
$577$	21.1778	−	6.21837i	0.881645	−	0.258874i	0.190584	−	0.981671i	$-0.438962\pi$
$577$	21.1778	−	6.21837i	0.881645	−	0.258874i	0.691061	+	0.722797i	$0.257144\pi$
$578$		0			0
$579$	9.27590	−	2.72365i	0.385493	−	0.113191i
$580$		0			0
$581$	8.17462	−	9.43402i	0.339140	−	0.391389i
$582$		0			0
$583$	−22.5813	−	26.0602i	−0.935221	−	1.07930i
$584$		0			0
$585$	−3.35965	−	0.986482i	−0.138904	−	0.0407860i
$586$		0			0
$587$	−8.22817	−	5.28793i	−0.339613	−	0.218256i	0.359706	−	0.933066i	$-0.382877\pi$
$587$	−8.22817	−	5.28793i	−0.339613	−	0.218256i	−0.699319	+	0.714810i	$0.746513\pi$
$588$		0			0
$589$	26.3092	+	7.72507i	1.08405	+	0.318306i
$590$		0			0
$591$	1.80926	+	3.96173i	0.0744231	+	0.162964i
$592$		0			0
$593$	−14.3954	+	16.6132i	−0.591148	+	0.682221i	−0.969963	−	0.243252i	$-0.921786\pi$
$593$	−14.3954	+	16.6132i	−0.591148	+	0.682221i	0.378816	+	0.925472i	$0.376331\pi$
$594$		0			0
$595$	−1.77867	+	3.89475i	−0.0729186	+	0.159669i
$596$		0			0
$597$	13.2557	−	8.51892i	0.542520	−	0.348656i
$598$		0			0
$599$	−41.6630	−	12.2334i	−1.70230	−	0.499841i	−0.721102	−	0.692829i	$-0.756364\pi$
$599$	−41.6630	−	12.2334i	−1.70230	−	0.499841i	−0.981201	+	0.192988i	$0.938182\pi$
$600$		0			0
$601$	−0.313733	+	2.18206i	−0.0127974	+	0.0890080i	−0.995219	−	0.0976669i	$-0.968862\pi$
$601$	−0.313733	+	2.18206i	−0.0127974	+	0.0890080i	0.982422	+	0.186675i	$0.0597711\pi$
$602$		0			0
$603$	−8.11638	−	1.06036i	−0.330525	−	0.0431814i
$604$		0			0
$605$	0.374387	−	2.60392i	0.0152210	−	0.105864i
$606$		0			0
$607$	34.4626	+	10.1191i	1.39879	+	0.410723i	0.892270	−	0.451502i	$-0.149112\pi$
$607$	34.4626	+	10.1191i	1.39879	+	0.410723i	0.506525	+	0.862226i	$0.330930\pi$
$608$		0			0
$609$	4.05825	−	2.60808i	0.164449	−	0.105685i
$610$		0			0
$611$	1.09600	−	2.39991i	0.0443394	−	0.0970898i
$612$		0			0
$613$	−1.28231	+	1.47986i	−0.0517918	+	0.0597710i	−0.781054	−	0.624463i	$-0.785318\pi$
$613$	−1.28231	+	1.47986i	−0.0517918	+	0.0597710i	0.729263	+	0.684234i	$0.239863\pi$
$614$		0			0
$615$	1.08015	+	2.36519i	0.0435558	+	0.0953738i
$616$		0			0
$617$	8.62792	+	2.53339i	0.347347	+	0.101990i	0.450752	−	0.892649i	$-0.351156\pi$
$617$	8.62792	+	2.53339i	0.347347	+	0.101990i	−0.103405	+	0.994639i	$0.532974\pi$
$618$		0			0
$619$	7.30225	+	4.69287i	0.293502	+	0.188622i	0.679102	−	0.734044i	$-0.262369\pi$
$619$	7.30225	+	4.69287i	0.293502	+	0.188622i	−0.385600	+	0.922666i	$0.626006\pi$
$620$		0			0
$621$	−8.32472	−	2.44436i	−0.334060	−	0.0980888i
$622$		0			0
$623$	10.8085	+	12.4737i	0.433035	+	0.499749i
$624$		0			0
$625$	−0.862081	+	0.994895i	−0.0344833	+	0.0397958i
$626$		0			0
$627$	22.0219	−	6.46620i	0.879468	−	0.258235i
$628$		0			0
$629$	−14.3193	+	4.20451i	−0.570946	+	0.167645i
$630$		0			0
$631$	6.08155	−	13.3167i	0.242103	−	0.530131i	−0.749104	−	0.662452i	$-0.769516\pi$
$631$	6.08155	−	13.3167i	0.242103	−	0.530131i	0.991207	+	0.132321i	$0.0422431\pi$
$632$		0			0
$633$	−14.2634			−0.566921
$634$		0			0
$635$	11.8848	−	13.7158i	0.471635	−	0.544296i
$636$		0			0
$637$	1.85313	+	12.8888i	0.0734236	+	0.510672i
$638$		0			0
$639$	1.71459	−	3.75443i	0.0678281	−	0.148523i
$640$		0			0
$641$	11.8875			0.469526			0.234763	−	0.972053i	$-0.424569\pi$
$641$	11.8875			0.469526			0.234763	+	0.972053i	$0.424569\pi$
$642$		0			0
$643$	29.4878	−	18.9507i	1.16288	−	0.747341i	0.190721	−	0.981644i	$-0.438917\pi$
$643$	29.4878	−	18.9507i	1.16288	−	0.747341i	0.972164	+	0.234303i	$0.0752809\pi$
$644$		0			0
$645$	−5.14791	−	11.2723i	−0.202699	−	0.443848i
$646$		0			0
$647$	−29.7892	−	34.3785i	−1.17113	−	1.35156i	−0.923914	−	0.382600i	$-0.875029\pi$
$647$	−29.7892	−	34.3785i	−1.17113	−	1.35156i	−0.247219	−	0.968960i	$-0.579517\pi$
$648$		0			0
$649$	−22.3352	+	14.3540i	−0.876735	+	0.563443i
$650$		0			0
$651$	0.726368	+	5.05200i	0.0284686	+	0.198003i
$652$		0			0
$653$	42.0184	−	12.3377i	1.64431	−	0.482812i	0.676908	−	0.736068i	$-0.263320\pi$
$653$	42.0184	−	12.3377i	1.64431	−	0.482812i	0.967399	+	0.253256i	$0.0815013\pi$
$654$		0			0
$655$	2.78734	+	19.3864i	0.108911	+	0.757490i
$656$		0			0
$657$	−3.25722	−	7.13232i	−0.127076	−	0.278258i
$658$		0			0
$659$	−11.3357	−	7.28503i	−0.441577	−	0.283785i	0.300900	−	0.953656i	$-0.402713\pi$
$659$	−11.3357	−	7.28503i	−0.441577	−	0.283785i	−0.742477	+	0.669871i	$0.766349\pi$
$660$		0			0
$661$	−4.48663	+	31.2052i	−0.174510	+	1.21374i	0.694700	+	0.719299i	$0.255537\pi$
$661$	−4.48663	+	31.2052i	−0.174510	+	1.21374i	−0.869210	+	0.494443i	$0.835372\pi$
$662$		0			0
$663$	−0.837121	+	5.82230i	−0.0325111	+	0.226119i
$664$		0			0
$665$	−12.2254	−	7.85681i	−0.474082	−	0.304674i
$666$		0			0
$667$	−19.2847	−	22.2558i	−0.746707	−	0.861746i
$668$		0			0
$669$	22.5173			0.870568
$670$		0			0
$671$	−31.4669			−1.21476
$672$		0			0
$673$	−27.0163	−	31.1784i	−1.04140	−	1.20184i	−0.979015	−	0.203789i	$-0.934674\pi$
$673$	−27.0163	−	31.1784i	−1.04140	−	1.20184i	−0.0623859	−	0.998052i	$-0.519871\pi$
$674$		0			0
$675$	2.69765	+	1.73367i	0.103833	+	0.0667291i
$676$		0			0
$677$	−7.19945	+	50.0733i	−0.276697	+	1.92447i	0.0937016	+	0.995600i	$0.470130\pi$
$677$	−7.19945	+	50.0733i	−0.276697	+	1.92447i	−0.370399	+	0.928873i	$0.620779\pi$
$678$		0			0
$679$	1.12058	−	7.79382i	0.0430040	−	0.299099i
$680$		0			0
$681$	−8.01797	−	5.15284i	−0.307249	−	0.197457i
$682$		0			0
$683$	−13.2896	−	29.1002i	−0.508512	−	1.11349i	−0.973608	−	0.228226i	$-0.926707\pi$
$683$	−13.2896	−	29.1002i	−0.508512	−	1.11349i	0.465096	−	0.885260i	$-0.346020\pi$
$684$		0			0
$685$	1.08369	+	7.53722i	0.0414056	+	0.287982i
$686$		0			0
$687$	−6.73427	+	1.97736i	−0.256928	+	0.0754410i
$688$		0			0
$689$	4.26873	+	29.6897i	0.162626	+	1.13109i
$690$		0			0
$691$	−29.2522	+	18.7993i	−1.11281	+	0.715158i	−0.961903	−	0.273390i	$-0.911855\pi$
$691$	−29.2522	+	18.7993i	−1.11281	+	0.715158i	−0.150904	+	0.988548i	$0.548219\pi$
$692$		0			0
$693$	2.79770	+	3.22872i	0.106276	+	0.122649i
$694$		0			0
$695$	−7.78327	−	17.0430i	−0.295236	−	0.646478i
$696$		0			0
$697$	3.67463	−	2.36154i	0.139187	−	0.0894498i
$698$		0			0
$699$	9.33811			0.353200
$700$		0			0
$701$	−4.30651	+	9.42994i	−0.162655	+	0.356164i	−0.973357	−	0.229294i	$-0.926358\pi$
$701$	−4.30651	+	9.42994i	−0.162655	+	0.356164i	0.810702	+	0.585458i	$0.199085\pi$
$702$		0			0
$703$	−7.20862	−	50.1370i	−0.271878	−	1.89095i
$704$		0			0
$705$	0.884867	−	1.02119i	0.0333260	−	0.0384603i
$706$		0			0
$707$	19.4684			0.732185
$708$		0			0
$709$	7.78656	−	17.0502i	0.292431	−	0.640334i	−0.705209	−	0.708999i	$-0.749147\pi$
$709$	7.78656	−	17.0502i	0.292431	−	0.640334i	0.997640	+	0.0686658i	$0.0218742\pi$
$710$		0			0
$711$	−9.18727	+	2.69763i	−0.344550	+	0.101169i
$712$		0			0
$713$	29.8951	−	8.77800i	1.11958	−	0.328739i
$714$		0			0
$715$	6.89252	−	7.95439i	0.257766	−	0.297477i
$716$		0			0
$717$	−17.3421	−	20.0139i	−0.647653	−	0.747431i
$718$		0			0
$719$	2.89873	+	0.851145i	0.108104	+	0.0317423i	0.335337	−	0.942098i	$-0.391150\pi$
$719$	2.89873	+	0.851145i	0.108104	+	0.0317423i	−0.227233	+	0.973840i	$0.572968\pi$
$720$		0			0
$721$	−16.8925	−	10.8562i	−0.629110	−	0.404305i
$722$		0			0
$723$	−20.9742	−	6.15859i	−0.780040	−	0.229040i
$724$		0			0
$725$	4.52144	+	9.90058i	0.167922	+	0.367698i
$726$		0			0
$727$	19.9419	−	23.0141i	0.739603	−	0.853547i	−0.253915	−	0.967227i	$-0.581718\pi$
$727$	19.9419	−	23.0141i	0.739603	−	0.853547i	0.993517	+	0.113680i	$0.0362638\pi$
$728$		0			0
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$		0			0
$731$	−17.5130	+	11.2549i	−0.647743	+	0.416279i
$732$		0			0
$733$	4.42962	+	1.30065i	0.163612	+	0.0480408i	0.362513	−	0.931979i	$-0.381919\pi$
$733$	4.42962	+	1.30065i	0.163612	+	0.0480408i	−0.198901	+	0.980020i	$0.563737\pi$
$734$		0			0
$735$	−0.949086	+	6.60104i	−0.0350076	+	0.243483i
$736$		0			0
$737$	13.0343	−	20.8684i	0.480124	−	0.768696i
$738$		0			0
$739$	4.41634	−	30.7163i	0.162458	−	1.12992i	−0.731524	−	0.681815i	$-0.761191\pi$
$739$	4.41634	−	30.7163i	0.162458	−	1.12992i	0.893982	−	0.448103i	$-0.147900\pi$
$740$		0			0
$741$	−19.1559	−	5.62468i	−0.703710	−	0.206628i
$742$		0			0
$743$	4.00743	−	2.57542i	0.147018	−	0.0944830i	−0.465064	−	0.885277i	$-0.653969\pi$
$743$	4.00743	−	2.57542i	0.147018	−	0.0944830i	0.612082	+	0.790794i	$0.290332\pi$
$744$		0			0
$745$	12.1165	−	26.5315i	0.443916	−	0.972039i
$746$		0			0
$747$	5.75164	−	6.63775i	0.210442	−	0.242862i
$748$		0			0
$749$	8.19668	+	17.9482i	0.299500	+	0.655814i
$750$		0			0
$751$	18.2482	+	5.35816i	0.665886	+	0.195522i	0.597170	−	0.802114i	$-0.296292\pi$
$751$	18.2482	+	5.35816i	0.665886	+	0.195522i	0.0687160	+	0.997636i	$0.478110\pi$
$752$		0			0
$753$	−7.15467	−	4.59803i	−0.260731	−	0.167561i
$754$		0			0
$755$	13.3108	+	3.90841i	0.484430	+	0.142241i
$756$		0			0
$757$	−3.76964	−	4.35040i	−0.137010	−	0.158118i	0.683098	−	0.730327i	$-0.260632\pi$
$757$	−3.76964	−	4.35040i	−0.137010	−	0.158118i	−0.820108	+	0.572209i	$0.806087\pi$
$758$		0			0
$759$	17.0787	−	19.7098i	0.619916	−	0.715422i
$760$		0			0
$761$	−25.5030	+	7.48836i	−0.924483	+	0.271453i	−0.709125	−	0.705083i	$-0.750910\pi$
$761$	−25.5030	+	7.48836i	−0.924483	+	0.271453i	−0.215358	+	0.976535i	$0.569092\pi$
$762$		0			0
$763$	3.13058	−	0.919221i	0.113335	−	0.0332780i
$764$		0			0
$765$	−1.25147	+	2.74034i	−0.0452470	+	0.0990771i
$766$		0			0
$767$	23.0947			0.833902
$768$		0			0
$769$	10.0105	−	11.5528i	0.360989	−	0.416604i	−0.545982	−	0.837797i	$-0.683843\pi$
$769$	10.0105	−	11.5528i	0.360989	−	0.416604i	0.906971	+	0.421193i	$0.138389\pi$
$770$		0			0
$771$	1.73310	+	12.0540i	0.0624161	+	0.434113i
$772$		0			0
$773$	−12.4743	+	27.3149i	−0.448669	+	0.982447i	0.541257	+	0.840857i	$0.317949\pi$
$773$	−12.4743	+	27.3149i	−0.448669	+	0.982447i	−0.989925	+	0.141590i	$0.954779\pi$
$774$		0			0
$775$	−11.5157			−0.413655
$776$		0			0
$777$	7.93176	−	5.09743i	0.284550	−	0.182869i
$778$		0			0
$779$	6.15874	+	13.4858i	0.220660	+	0.483178i
$780$		0			0
$781$	8.12464	+	9.37633i	0.290722	+	0.335511i
$782$		0			0
$783$	2.85538	−	1.83504i	0.102043	−	0.0655789i
$784$		0			0
$785$	0.430932	+	2.99720i	0.0153806	+	0.106975i
$786$		0			0
$787$	−4.18330	+	1.22833i	−0.149119	+	0.0437852i	−0.355440	−	0.934699i	$-0.615669\pi$
$787$	−4.18330	+	1.22833i	−0.149119	+	0.0437852i	0.206321	+	0.978484i	$0.433851\pi$
$788$		0			0
$789$	1.43306	+	9.96715i	0.0510183	+	0.354840i
$790$		0			0
$791$	7.97155	+	17.4553i	0.283436	+	0.620638i
$792$		0			0
$793$	23.0266	+	14.7983i	0.817697	+	0.525502i
$794$		0			0
$795$	−2.18625	+	15.2057i	−0.0775382	+	0.539290i
$796$		0			0
$797$	0.648156	−	4.50803i	0.0229589	−	0.159682i	−0.975117	−	0.221692i	$-0.928842\pi$
$797$	0.648156	−	4.50803i	0.0229589	−	0.159682i	0.998076	+	0.0620099i	$0.0197510\pi$
$798$		0			0
$799$	−1.90960	−	1.22722i	−0.0675567	−	0.0434160i
$800$		0			0
$801$	7.60486	+	8.77648i	0.268704	+	0.310102i
$802$		0			0
$803$	23.5691			0.831734
$804$		0			0
$805$	−16.5132			−0.582013
$806$		0			0
$807$	9.38945	+	10.8360i	0.330524	+	0.381445i
$808$		0			0
$809$	2.60377	+	1.67334i	0.0915438	+	0.0588316i	0.585612	−	0.810592i	$-0.300854\pi$
$809$	2.60377	+	1.67334i	0.0915438	+	0.0588316i	−0.494068	+	0.869423i	$0.664491\pi$
$810$		0			0
$811$	−0.717384	+	4.98952i	−0.0251908	+	0.175206i	−0.998533	−	0.0541536i	$-0.982754\pi$
$811$	−0.717384	+	4.98952i	−0.0251908	+	0.175206i	0.973342	+	0.229359i	$0.0736630\pi$
$812$		0			0
$813$	−0.243649	+	1.69462i	−0.00854515	+	0.0594328i
$814$		0			0
$815$	18.1938	+	11.6924i	0.637301	+	0.409568i
$816$		0			0
$817$	−29.3521	−	64.2722i	−1.02690	−	2.24860i
$818$		0			0
$819$	−0.528874	−	3.67840i	−0.0184803	−	0.128534i
$820$		0			0
$821$	15.7214	−	4.61623i	0.548681	−	0.161107i	0.00436976	−	0.999990i	$-0.498609\pi$
$821$	15.7214	−	4.61623i	0.548681	−	0.161107i	0.544312	+	0.838883i	$0.316791\pi$
$822$		0			0
$823$	−2.42735	−	16.8826i	−0.0846123	−	0.588491i	−0.987381	−	0.158364i	$-0.949378\pi$
$823$	−2.42735	−	16.8826i	−0.0846123	−	0.588491i	0.902768	−	0.430127i	$-0.141531\pi$
$824$		0			0
$825$	−8.10891	+	5.21128i	−0.282316	+	0.181433i
$826$		0			0
$827$	−3.50963	−	4.05033i	−0.122042	−	0.140844i	0.691441	−	0.722433i	$-0.256976\pi$
$827$	−3.50963	−	4.05033i	−0.122042	−	0.140844i	−0.813482	+	0.581590i	$0.802431\pi$
$828$		0			0
$829$	−12.3315	−	27.0022i	−0.428291	−	0.937826i	−0.993601	−	0.112948i	$-0.963971\pi$
$829$	−12.3315	−	27.0022i	−0.428291	−	0.937826i	0.565310	−	0.824878i	$-0.308757\pi$
$830$		0			0
$831$	1.27031	−	0.816382i	0.0440667	−	0.0283200i
$832$		0			0
$833$	11.2032			0.388167
$834$		0			0
$835$	3.41653	−	7.48116i	0.118234	−	0.258896i
$836$		0			0
$837$	0.511070	+	3.55457i	0.0176652	+	0.122864i
$838$		0			0
$839$	2.40070	−	2.77056i	0.0828815	−	0.0956503i	−0.712794	−	0.701373i	$-0.752571\pi$
$839$	2.40070	−	2.77056i	0.0828815	−	0.0956503i	0.795676	+	0.605723i	$0.207116\pi$
$840$		0			0
$841$	−17.4795			−0.602740
$842$		0			0
$843$	−2.61728	+	5.73104i	−0.0901438	+	0.197387i
$844$		0			0
$845$	7.91910	−	2.32526i	0.272425	−	0.0799913i
$846$		0			0
$847$	2.67893	−	0.786606i	0.0920493	−	0.0270281i
$848$		0			0
$849$	−12.1477	+	14.0192i	−0.416907	+	0.481136i
$850$		0			0
$851$	−37.6915	−	43.4983i	−1.29205	−	1.49110i
$852$		0			0
$853$	19.7102	+	5.78744i	0.674865	+	0.198158i	0.601168	−	0.799123i	$-0.294702\pi$
$853$	19.7102	+	5.78744i	0.674865	+	0.198158i	0.0736966	+	0.997281i	$0.476520\pi$
$854$		0			0
$855$	−8.60178	−	5.52803i	−0.294175	−	0.189055i
$856$		0			0
$857$	−31.1486	−	9.14607i	−1.06402	−	0.312424i	−0.297550	−	0.954706i	$-0.596169\pi$
$857$	−31.1486	−	9.14607i	−1.06402	−	0.312424i	−0.766468	+	0.642283i	$0.777988\pi$
$858$		0			0
$859$	23.4346	+	51.3146i	0.799578	+	1.75083i	0.646927	+	0.762552i	$0.276054\pi$
$859$	23.4346	+	51.3146i	0.799578	+	1.75083i	0.152652	+	0.988280i	$0.451219\pi$
$860$		0			0
$861$	−1.80717	+	2.08559i	−0.0615883	+	0.0710767i
$862$		0			0
$863$	10.0703	−	22.0509i	0.342798	−	0.750623i	−0.657197	−	0.753719i	$-0.728258\pi$
$863$	10.0703	−	22.0509i	0.342798	−	0.750623i	0.999995	+	0.00309591i	$0.000985460\pi$
$864$		0			0
$865$	5.46280	−	3.51073i	0.185741	−	0.119368i
$866$		0			0
$867$	−11.4555	−	3.36365i	−0.389050	−	0.114235i
$868$		0			0
$869$	4.09611	−	28.4891i	0.138951	−	0.966426i
$870$		0			0
$871$	−19.3521	+	9.14111i	−0.655722	+	0.309735i
$872$		0			0
$873$	0.788438	−	5.48371i	0.0266846	−	0.185595i
$874$		0			0
$875$	14.9869	+	4.40056i	0.506651	+	0.148766i
$876$		0			0
$877$	−10.3942	+	6.67996i	−0.350988	+	0.225566i	−0.704240	−	0.709962i	$-0.748712\pi$
$877$	−10.3942	+	6.67996i	−0.350988	+	0.225566i	0.353252	+	0.935528i	$0.385076\pi$
$878$		0			0
$879$	2.59390	−	5.67986i	0.0874902	−	0.191577i
$880$		0			0
$881$	2.16964	−	2.50390i	0.0730970	−	0.0843584i	−0.718023	−	0.696019i	$-0.754953\pi$
$881$	2.16964	−	2.50390i	0.0730970	−	0.0843584i	0.791120	+	0.611661i	$0.209498\pi$
$882$		0			0
$883$	13.5583	+	29.6886i	0.456274	+	0.999101i	0.988321	+	0.152386i	$0.0486957\pi$
$883$	13.5583	+	29.6886i	0.456274	+	0.999101i	−0.532047	+	0.846715i	$0.678577\pi$
$884$		0			0
$885$	11.3489	+	3.33235i	0.381490	+	0.112016i
$886$		0			0
$887$	11.8355	+	7.60619i	0.397396	+	0.255391i	0.724042	−	0.689756i	$-0.242282\pi$
$887$	11.8355	+	7.60619i	0.397396	+	0.255391i	−0.326646	+	0.945147i	$0.605919\pi$
$888$		0			0
$889$	18.4814	+	5.42664i	0.619847	+	0.182004i
$890$		0			0
$891$	1.96846	+	2.27172i	0.0659458	+	0.0761055i
$892$		0			0
$893$	5.04530	−	5.82258i	0.168834	−	0.194845i
$894$		0			0
$895$	−29.4199	+	8.63847i	−0.983400	+	0.288752i
$896$		0			0
$897$	−21.7669	+	6.39133i	−0.726774	+	0.213400i
$898$		0			0
$899$	−5.06348	+	11.0875i	−0.168877	+	0.369788i
$900$		0			0
$901$	25.8068			0.859750
$902$		0			0
$903$	8.61286	−	9.93977i	0.286618	−	0.330775i
$904$		0			0
$905$	−2.07291	−	14.4174i	−0.0689058	−	0.479250i
$906$		0			0
$907$	−13.9008	+	30.4385i	−0.461569	+	1.01070i	0.525558	+	0.850758i	$0.323857\pi$
$907$	−13.9008	+	30.4385i	−0.461569	+	1.01070i	−0.987127	+	0.159938i	$0.948871\pi$
$908$		0			0
$909$	13.6979			0.454331
$910$		0			0
$911$	15.7747	−	10.1378i	0.522640	−	0.335880i	−0.252576	−	0.967577i	$-0.581278\pi$
$911$	15.7747	−	10.1378i	0.522640	−	0.335880i	0.775215	+	0.631697i	$0.217641\pi$
$912$		0			0
$913$	10.9674	+	24.0152i	0.362967	+	0.794786i
$914$		0			0
$915$	9.18019	+	10.5945i	0.303488	+	0.350244i
$916$		0			0
$917$	−17.4871	+	11.2383i	−0.577474	+	0.371120i
$918$		0			0
$919$	−4.92642	−	34.2640i	−0.162508	−	1.13027i	−0.893886	−	0.448294i	$-0.852032\pi$
$919$	−4.92642	−	34.2640i	−0.162508	−	1.13027i	0.731378	−	0.681972i	$-0.238877\pi$
$920$		0			0
$921$	20.3136	−	5.96461i	0.669356	−	0.196541i
$922$		0			0
$923$	−1.53587	−	10.6822i	−0.0505537	−	0.351609i
$924$		0			0
$925$	8.83705	+	19.3504i	0.290560	+	0.636238i
$926$		0			0
$927$	−11.8855	−	7.63837i	−0.390372	−	0.250877i
$928$		0			0
$929$	4.79276	−	33.3344i	0.157245	−	1.09367i	−0.746435	−	0.665458i	$-0.768236\pi$
$929$	4.79276	−	33.3344i	0.157245	−	1.09367i	0.903681	−	0.428207i	$-0.140855\pi$
$930$		0			0
$931$	−5.41146	+	37.6375i	−0.177353	+	1.23352i
$932$		0			0
$933$	10.1606	+	6.52985i	0.332645	+	0.213778i
$934$		0			0
$935$	−5.93013	−	6.84374i	−0.193936	−	0.223814i
$936$		0			0
$937$	−6.12445			−0.200077			−0.100039	−	0.994984i	$-0.531897\pi$
$937$	−6.12445			−0.200077			−0.100039	+	0.994984i	$0.531897\pi$
$938$		0			0
$939$	14.7039			0.479844
$940$		0			0
$941$	−7.78831	−	8.98819i	−0.253892	−	0.293007i	0.614468	−	0.788942i	$-0.289371\pi$
$941$	−7.78831	−	8.98819i	−0.253892	−	0.293007i	−0.868359	+	0.495935i	$0.834825\pi$
$942$		0			0
$943$	14.1720	+	9.10776i	0.461502	+	0.296590i
$944$		0			0
$945$	0.270865	−	1.88391i	0.00881123	−	0.0612835i
$946$		0			0
$947$	6.64143	−	46.1922i	0.215817	−	1.50104i	−0.537431	−	0.843308i	$-0.680605\pi$
$947$	6.64143	−	46.1922i	0.215817	−	1.50104i	0.753249	−	0.657736i	$-0.228486\pi$
$948$		0			0
$949$	−17.2472	−	11.0841i	−0.559867	−	0.359805i
$950$		0			0
$951$	−12.0104	−	26.2990i	−0.389463	−	0.852804i
$952$		0			0
$953$	−1.72852	−	12.0221i	−0.0559924	−	0.389436i	−0.998476	−	0.0551838i	$-0.982426\pi$
$953$	−1.72852	−	12.0221i	−0.0559924	−	0.389436i	0.942484	−	0.334252i	$-0.108484\pi$
$954$		0			0
$955$	21.2682	−	6.24491i	0.688223	−	0.202080i
$956$		0			0
$957$	1.45199	+	10.0988i	0.0469362	+	0.326448i
$958$		0			0
$959$	−6.79878	+	4.36931i	−0.219544	+	0.141092i
$960$		0			0
$961$	11.8555	+	13.6820i	0.382435	+	0.441353i
$962$		0			0
$963$	5.76716	+	12.6283i	0.185844	+	0.406942i
$964$		0			0
$965$	10.8910	−	6.99922i	0.350594	−	0.225313i
$966$		0			0
$967$	39.4714			1.26932			0.634658	−	0.772793i	$-0.281141\pi$
$967$	39.4714			1.26932			0.634658	+	0.772793i	$0.281141\pi$
$968$		0			0
$969$	−7.13558	+	15.6247i	−0.229228	+	0.501939i
$970$		0			0
$971$	−0.361402	−	2.51361i	−0.0115980	−	0.0806655i	0.983200	−	0.182529i	$-0.0584285\pi$
$971$	−0.361402	−	2.51361i	−0.0115980	−	0.0806655i	−0.994798	+	0.101864i	$0.967519\pi$
$972$		0			0
$973$	13.0220	−	15.0282i	0.417467	−	0.481783i
$974$		0			0
$975$	8.38464			0.268523
$976$		0			0
$977$	1.64239	−	3.59632i	0.0525446	−	0.115057i	−0.881539	−	0.472112i	$-0.843492\pi$
$977$	1.64239	−	3.59632i	0.0525446	−	0.115057i	0.934083	+	0.357055i	$0.116219\pi$
$978$		0			0
$979$	−33.4935	+	9.83459i	−1.07046	+	0.314315i
$980$		0			0
$981$	2.20267	−	0.646761i	0.0703257	−	0.0206495i
$982$		0			0
$983$	4.05025	−	4.67424i	0.129183	−	0.149085i	−0.687473	−	0.726210i	$-0.741280\pi$
$983$	4.05025	−	4.67424i	0.129183	−	0.149085i	0.816656	+	0.577125i	$0.195825\pi$
$984$		0			0
$985$	3.81940	+	4.40782i	0.121696	+	0.140445i
$986$		0			0
$987$	1.37601	+	0.404032i	0.0437988	+	0.0128605i
$988$		0			0
$989$	−67.5425	−	43.4069i	−2.14773	−	1.38026i
$990$		0			0
$991$	−16.8314	−	4.94214i	−0.534666	−	0.156992i	0.00324337	−	0.999995i	$-0.498968\pi$
$991$	−16.8314	−	4.94214i	−0.534666	−	0.156992i	−0.537909	+	0.843003i	$0.680786\pi$
$992$		0			0
$993$	−6.64931	−	14.5599i	−0.211009	−	0.462046i
$994$		0			0
$995$	13.8182	−	15.9470i	0.438066	−	0.505555i
$996$		0			0
$997$	−12.1638	+	26.6350i	−0.385231	+	0.843539i	0.613325	+	0.789830i	$0.289831\pi$
$997$	−12.1638	+	26.6350i	−0.385231	+	0.843539i	−0.998557	+	0.0537087i	$0.982896\pi$
$998$		0			0
$999$	5.58076	−	3.58654i	0.176567	−	0.113473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.q.b.193.4	yes	60
67.25	even	11	inner	804.2.q.b.25.4	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.q.b.25.4	✓	60	67.25	even	11	inner
804.2.q.b.193.4	yes	60	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.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 + 0.755750i) q^{3} +(1.12656 + 0.723994i) q^{5} +(-0.202268 + 1.40680i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.654861 + 0.755750i) q^{3} +(1.12656 + 0.723994i) q^{5} +(-0.202268 + 1.40680i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-2.52874 - 1.62512i) q^{11} +(1.08620 + 2.37844i) q^{13} +(0.190580 + 1.32551i) q^{15} +(2.15851 - 0.633795i) q^{17} +(1.08664 + 7.55774i) q^{19} +(-1.19565 + 0.768395i) q^{21} +(5.68168 + 6.55701i) q^{23} +(-1.33211 - 2.91692i) q^{25} +(-0.841254 + 0.540641i) q^{27} -3.39419 q^{29} +(1.49181 - 3.26660i) q^{31} +(-0.427787 - 2.97532i) q^{33} +(-1.24638 + 1.43840i) q^{35} -6.63386 q^{37} +(-1.08620 + 2.37844i) q^{39} +(1.86302 - 0.547031i) q^{41} +(-8.87900 + 2.60711i) q^{43} +(-0.876951 + 1.01206i) q^{45} +(-0.660772 - 0.762571i) q^{47} +(4.77827 + 1.40303i) q^{49} +(1.89251 + 1.21624i) q^{51} +(11.0069 + 3.23191i) q^{53} +(-1.67219 - 3.66158i) q^{55} +(-5.00016 + 5.77049i) q^{57} +(3.66918 - 8.03438i) q^{59} +(8.80650 - 5.65959i) q^{61} +(-1.36370 - 0.400417i) q^{63} +(-0.498313 + 3.46584i) q^{65} +(0.105510 + 8.18467i) q^{67} +(-1.23475 + 8.58786i) q^{69} +(-3.96022 - 1.16283i) q^{71} +(-6.59618 + 4.23911i) q^{73} +(1.33211 - 2.91692i) q^{75} +(2.79770 - 3.22872i) q^{77} +(3.97765 + 8.70984i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(-7.38873 - 4.74845i) q^{83} +(2.89055 + 0.848742i) q^{85} +(-2.22272 - 2.56516i) q^{87} +(7.60486 - 8.77648i) q^{89} +(-3.56569 + 1.04698i) q^{91} +(3.44566 - 1.01174i) q^{93} +(-4.24760 + 9.30095i) q^{95} -5.54010 q^{97} +(1.96846 - 2.27172i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9	\( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9} - 11 q^{11} - 2 q^{13} + 9 q^{15} + 21 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 36 q^{25} + 6 q^{27} + 4 q^{29} - 24 q^{31} - 32 q^{35} + 2 q^{37} + 2 q^{39} + 10 q^{41} + 23 q^{43} + 2 q^{45} + 66 q^{47} + 34 q^{49} + 23 q^{51} - 13 q^{53} + 27 q^{55} + q^{57} + 35 q^{59} + 56 q^{61} - 9 q^{63} + 48 q^{65} + 13 q^{67} + 10 q^{69} + 76 q^{71} - q^{73} + 36 q^{75} - 38 q^{77} - 46 q^{79} - 6 q^{81} - 26 q^{83} + 42 q^{85} + 7 q^{87} + 58 q^{89} - 40 q^{91} - 9 q^{93} - 29 q^{95} - 46 q^{97}+O(q^{100}) \) 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 11 * q^11 - 2 * q^13 + 9 * q^15 + 21 * q^17 + 10 * q^19 - 2 * q^21 - 10 * q^23 - 36 * q^25 + 6 * q^27 + 4 * q^29 - 24 * q^31 - 32 * q^35 + 2 * q^37 + 2 * q^39 + 10 * q^41 + 23 * q^43 + 2 * q^45 + 66 * q^47 + 34 * q^49 + 23 * q^51 - 13 * q^53 + 27 * q^55 + q^57 + 35 * q^59 + 56 * q^61 - 9 * q^63 + 48 * q^65 + 13 * q^67 + 10 * q^69 + 76 * q^71 - q^73 + 36 * q^75 - 38 * q^77 - 46 * q^79 - 6 * q^81 - 26 * q^83 + 42 * q^85 + 7 * q^87 + 58 * q^89 - 40 * q^91 - 9 * q^93 - 29 * q^95 - 46 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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