LMFDB - Embedded newform 804.2.q.a.25.5

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			25.5
Character	$\chi$	$=$	804.25
Dual form			804.2.q.a.193.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 + 0.755750i) q^{3} +(1.20911 - 0.777049i) q^{5} +(-0.250069 - 1.73927i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.654861 + 0.755750i) q^{3} +(1.20911 - 0.777049i) q^{5} +(-0.250069 - 1.73927i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(1.56789 - 1.00762i) q^{11} +(0.0764634 - 0.167432i) q^{13} +(-0.204546 + 1.42265i) q^{15} +(-5.54950 - 1.62948i) q^{17} +(0.468082 - 3.25558i) q^{19} +(1.47821 + 0.949989i) q^{21} +(4.51470 - 5.21024i) q^{23} +(-1.21893 + 2.66908i) q^{25} +(0.841254 + 0.540641i) q^{27} -1.72534 q^{29} +(-2.97782 - 6.52052i) q^{31} +(-0.265240 + 1.84479i) q^{33} +(-1.65386 - 1.90865i) q^{35} +1.42345 q^{37} +(0.0764634 + 0.167432i) q^{39} +(0.495048 + 0.145359i) q^{41} +(5.66408 + 1.66312i) q^{43} +(-0.941215 - 1.08622i) q^{45} +(7.39028 - 8.52884i) q^{47} +(3.75393 - 1.10225i) q^{49} +(4.86563 - 3.12695i) q^{51} +(-0.625578 + 0.183686i) q^{53} +(1.11278 - 2.43666i) q^{55} +(2.15388 + 2.48571i) q^{57} +(-3.56051 - 7.79643i) q^{59} +(3.36567 + 2.16298i) q^{61} +(-1.68598 + 0.495047i) q^{63} +(-0.0376497 - 0.261859i) q^{65} +(2.71268 + 7.72278i) q^{67} +(0.981139 + 6.82397i) q^{69} +(-4.81930 + 1.41507i) q^{71} +(8.78593 + 5.64637i) q^{73} +(-1.21893 - 2.66908i) q^{75} +(-2.14461 - 2.47501i) q^{77} +(1.37975 - 3.02123i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(3.71907 - 2.39010i) q^{83} +(-7.97616 + 2.34201i) q^{85} +(1.12986 - 1.30393i) q^{87} +(-7.30415 - 8.42944i) q^{89} +(-0.310329 - 0.0911209i) q^{91} +(6.87793 + 2.01954i) q^{93} +(-1.96379 - 4.30009i) q^{95} -9.00963 q^{97} +(-1.22050 - 1.40853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 7 q^{11} - 2 q^{13} + 9 q^{15} - 19 q^{17} + 2 q^{19} - 2 q^{21} + 4 q^{23} + 16 q^{25} - 6 q^{27} + 16 q^{29} - 28 q^{31} - 4 q^{33} + 28 q^{35} + 2 q^{37} - 2 q^{39} + 32 q^{41} + 19 q^{43} - 2 q^{45} + 2 q^{47} - 70 q^{49} - 19 q^{51} + 31 q^{53} - 5 q^{55} + 13 q^{57} + 59 q^{59} + 32 q^{61} + 9 q^{63} + 28 q^{65} + 7 q^{67} + 4 q^{69} + 16 q^{71} + 19 q^{73} + 16 q^{75} - 46 q^{77} + 48 q^{79} - 6 q^{81} + 60 q^{83} - 66 q^{85} + 5 q^{87} - 22 q^{89} + 24 q^{91} + 5 q^{93} + 103 q^{95} - 46 q^{97} - 4 q^{99}+O(q^{100}) $ 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9 + 7 * q^11 - 2 * q^13 + 9 * q^15 - 19 * q^17 + 2 * q^19 - 2 * q^21 + 4 * q^23 + 16 * q^25 - 6 * q^27 + 16 * q^29 - 28 * q^31 - 4 * q^33 + 28 * q^35 + 2 * q^37 - 2 * q^39 + 32 * q^41 + 19 * q^43 - 2 * q^45 + 2 * q^47 - 70 * q^49 - 19 * q^51 + 31 * q^53 - 5 * q^55 + 13 * q^57 + 59 * q^59 + 32 * q^61 + 9 * q^63 + 28 * q^65 + 7 * q^67 + 4 * q^69 + 16 * q^71 + 19 * q^73 + 16 * q^75 - 46 * q^77 + 48 * q^79 - 6 * q^81 + 60 * q^83 - 66 * q^85 + 5 * q^87 - 22 * q^89 + 24 * q^91 + 5 * q^93 + 103 * q^95 - 46 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{5}{11}\right)$	$1$

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
$5$	1.20911	−	0.777049i	0.540732	−	0.347507i	−0.241593	−	0.970378i	$-0.577670\pi$
$5$	1.20911	−	0.777049i	0.540732	−	0.347507i	0.782325	+	0.622871i	$0.214034\pi$
$6$		0			0
$7$	−0.250069	−	1.73927i	−0.0945172	−	0.657381i	−0.980912	−	0.194452i	$-0.937707\pi$
$7$	−0.250069	−	1.73927i	−0.0945172	−	0.657381i	0.886395	−	0.462930i	$-0.153202\pi$
$8$		0			0
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$		0			0
$11$	1.56789	−	1.00762i	0.472737	−	0.303810i	−0.282493	−	0.959269i	$-0.591161\pi$
$11$	1.56789	−	1.00762i	0.472737	−	0.303810i	0.755230	+	0.655460i	$0.227525\pi$
$12$		0			0
$13$	0.0764634	−	0.167432i	0.0212071	−	0.0464372i	−0.898732	−	0.438498i	$-0.855511\pi$
$13$	0.0764634	−	0.167432i	0.0212071	−	0.0464372i	0.919939	+	0.392061i	$0.128238\pi$
$14$		0			0
$15$	−0.204546	+	1.42265i	−0.0528134	+	0.367325i
$16$		0			0
$17$	−5.54950	−	1.62948i	−1.34595	−	0.395207i	−0.472163	−	0.881511i	$-0.656527\pi$
$17$	−5.54950	−	1.62948i	−1.34595	−	0.395207i	−0.873790	+	0.486304i	$0.838345\pi$
$18$		0			0
$19$	0.468082	−	3.25558i	0.107385	−	0.746882i	−0.862980	−	0.505239i	$-0.831404\pi$
$19$	0.468082	−	3.25558i	0.107385	−	0.746882i	0.970365	−	0.241643i	$-0.0776864\pi$
$20$		0			0
$21$	1.47821	+	0.949989i	0.322572	+	0.207305i
$22$		0			0
$23$	4.51470	−	5.21024i	0.941381	−	1.08641i	−0.0547478	−	0.998500i	$-0.517435\pi$
$23$	4.51470	−	5.21024i	0.941381	−	1.08641i	0.996128	−	0.0879108i	$-0.0280191\pi$
$24$		0			0
$25$	−1.21893	+	2.66908i	−0.243786	+	0.533816i
$26$		0			0
$27$	0.841254	+	0.540641i	0.161899	+	0.104046i
$28$		0			0
$29$	−1.72534			−0.320388			−0.160194	−	0.987086i	$-0.551212\pi$
$29$	−1.72534			−0.320388			−0.160194	+	0.987086i	$0.551212\pi$
$30$		0			0
$31$	−2.97782	−	6.52052i	−0.534832	−	1.17112i	−0.963513	−	0.267663i	$-0.913749\pi$
$31$	−2.97782	−	6.52052i	−0.534832	−	1.17112i	0.428680	−	0.903456i	$-0.358979\pi$
$32$		0			0
$33$	−0.265240	+	1.84479i	−0.0461724	+	0.321136i
$34$		0			0
$35$	−1.65386	−	1.90865i	−0.279553	−	0.322622i
$36$		0			0
$37$	1.42345			0.234013			0.117007	−	0.993131i	$-0.462670\pi$
$37$	1.42345			0.234013			0.117007	+	0.993131i	$0.462670\pi$
$38$		0			0
$39$	0.0764634	+	0.167432i	0.0122439	+	0.0268105i
$40$		0			0
$41$	0.495048	+	0.145359i	0.0773135	+	0.0227013i	0.320161	−	0.947363i	$-0.396263\pi$
$41$	0.495048	+	0.145359i	0.0773135	+	0.0227013i	−0.242847	+	0.970065i	$0.578081\pi$
$42$		0			0
$43$	5.66408	+	1.66312i	0.863763	+	0.253624i	0.683461	−	0.729987i	$-0.260474\pi$
$43$	5.66408	+	1.66312i	0.863763	+	0.253624i	0.180303	+	0.983611i	$0.442292\pi$
$44$		0			0
$45$	−0.941215	−	1.08622i	−0.140308	−	0.161924i
$46$		0			0
$47$	7.39028	−	8.52884i	1.07798	−	1.24406i	0.109764	−	0.993958i	$-0.464991\pi$
$47$	7.39028	−	8.52884i	1.07798	−	1.24406i	0.968220	−	0.250101i	$-0.0804639\pi$
$48$		0			0
$49$	3.75393	−	1.10225i	0.536276	−	0.157465i
$50$		0			0
$51$	4.86563	−	3.12695i	0.681325	−	0.437861i
$52$		0			0
$53$	−0.625578	+	0.183686i	−0.0859297	+	0.0252312i	−0.324415	−	0.945915i	$-0.605167\pi$
$53$	−0.625578	+	0.183686i	−0.0859297	+	0.0252312i	0.238485	+	0.971146i	$0.423349\pi$
$54$		0			0
$55$	1.11278	−	2.43666i	0.150048	−	0.328559i
$56$		0			0
$57$	2.15388	+	2.48571i	0.285288	+	0.329240i
$58$		0			0
$59$	−3.56051	−	7.79643i	−0.463539	−	1.01501i	−0.986667	−	0.162755i	$-0.947962\pi$
$59$	−3.56051	−	7.79643i	−0.463539	−	1.01501i	0.523127	−	0.852255i	$-0.324765\pi$
$60$		0			0
$61$	3.36567	+	2.16298i	0.430930	+	0.276942i	0.738072	−	0.674722i	$-0.235736\pi$
$61$	3.36567	+	2.16298i	0.430930	+	0.276942i	−0.307142	+	0.951664i	$0.599373\pi$
$62$		0			0
$63$	−1.68598	+	0.495047i	−0.212413	+	0.0623701i
$64$		0			0
$65$	−0.0376497	−	0.261859i	−0.00466987	−	0.0324797i
$66$		0			0
$67$	2.71268	+	7.72278i	0.331406	+	0.943488i
$67$	2.71268	+	7.72278i	0.331406	+	0.943488i
$68$		0			0
$69$	0.981139	+	6.82397i	0.118115	+	0.821509i
$70$		0			0
$71$	−4.81930	+	1.41507i	−0.571946	+	0.167938i	−0.554901	−	0.831916i	$-0.687244\pi$
$71$	−4.81930	+	1.41507i	−0.571946	+	0.167938i	−0.0170447	+	0.999855i	$0.505426\pi$
$72$		0			0
$73$	8.78593	+	5.64637i	1.02832	+	0.660858i	0.942070	−	0.335416i	$-0.108877\pi$
$73$	8.78593	+	5.64637i	1.02832	+	0.660858i	0.0862451	+	0.996274i	$0.472513\pi$
$74$		0			0
$75$	−1.21893	−	2.66908i	−0.140750	−	0.308199i
$76$		0			0
$77$	−2.14461	−	2.47501i	−0.244401	−	0.282053i
$78$		0			0
$79$	1.37975	−	3.02123i	0.155234	−	0.339915i	−0.815996	−	0.578057i	$-0.803811\pi$
$79$	1.37975	−	3.02123i	0.155234	−	0.339915i	0.971230	+	0.238142i	$0.0765384\pi$
$80$		0			0
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$		0			0
$83$	3.71907	−	2.39010i	0.408221	−	0.262348i	−0.320376	−	0.947291i	$-0.603809\pi$
$83$	3.71907	−	2.39010i	0.408221	−	0.262348i	0.728597	+	0.684943i	$0.240173\pi$
$84$		0			0
$85$	−7.97616	+	2.34201i	−0.865136	+	0.254027i
$86$		0			0
$87$	1.12986	−	1.30393i	0.121134	−	0.139796i
$88$		0			0
$89$	−7.30415	−	8.42944i	−0.774238	−	0.893518i	0.222441	−	0.974946i	$-0.428597\pi$
$89$	−7.30415	−	8.42944i	−0.774238	−	0.893518i	−0.996679	+	0.0814277i	$0.974052\pi$
$90$		0			0
$91$	−0.310329	−	0.0911209i	−0.0325314	−	0.00955207i
$92$		0			0
$93$	6.87793	+	2.01954i	0.713209	+	0.209417i
$94$		0			0
$95$	−1.96379	−	4.30009i	−0.201480	−	0.441180i
$96$		0			0
$97$	−9.00963			−0.914789			−0.457395	−	0.889264i	$-0.651217\pi$
$97$	−9.00963			−0.914789			−0.457395	+	0.889264i	$0.651217\pi$
$98$		0			0
$99$	−1.22050	−	1.40853i	−0.122665	−	0.141563i
$100$		0			0
$101$	1.88655	−	13.1212i	0.187719	−	1.30561i	−0.650178	−	0.759782i	$-0.725306\pi$
$101$	1.88655	−	13.1212i	0.187719	−	1.30561i	0.837896	−	0.545829i	$-0.183785\pi$
$102$		0			0
$103$	6.74939	+	14.7791i	0.665038	+	1.45623i	0.877752	+	0.479115i	$0.159042\pi$
$103$	6.74939	+	14.7791i	0.665038	+	1.45623i	−0.212715	+	0.977114i	$0.568231\pi$
$104$		0			0
$105$	2.52551			0.246465
$106$		0			0
$107$	−3.89540	−	2.50342i	−0.376583	−	0.242015i	0.338633	−	0.940918i	$-0.390035\pi$
$107$	−3.89540	−	2.50342i	−0.376583	−	0.242015i	−0.715216	+	0.698903i	$0.753672\pi$
$108$		0			0
$109$	−0.186444	+	0.408254i	−0.0178581	+	0.0391037i	−0.918351	−	0.395767i	$-0.870479\pi$
$109$	−0.186444	+	0.408254i	−0.0178581	+	0.0391037i	0.900493	+	0.434871i	$0.143206\pi$
$110$		0			0
$111$	−0.932159	+	1.07577i	−0.0884766	+	0.102107i
$112$		0			0
$113$	−1.18593	−	0.762152i	−0.111563	−	0.0716973i	0.483669	−	0.875251i	$-0.339304\pi$
$113$	−1.18593	−	0.762152i	−0.111563	−	0.0716973i	−0.595233	+	0.803553i	$0.702940\pi$
$114$		0			0
$115$	1.41017	−	9.80792i	0.131499	−	0.914593i
$116$		0			0
$117$	−0.176609	−	0.0518571i	−0.0163275	−	0.00479419i
$118$		0			0
$119$	−1.44635	+	10.0596i	−0.132586	+	0.922158i
$120$		0			0
$121$	−3.12658	+	6.84627i	−0.284235	+	0.622388i
$122$		0			0
$123$	−0.434043	+	0.278942i	−0.0391363	+	0.0251514i
$124$		0			0
$125$	1.62291	+	11.2876i	0.145158	+	1.00959i
$126$		0			0
$127$	1.16483	+	8.10156i	0.103362	+	0.718897i	0.973930	+	0.226849i	$0.0728425\pi$
$127$	1.16483	+	8.10156i	0.103362	+	0.718897i	−0.870568	+	0.492048i	$0.836248\pi$
$128$		0			0
$129$	−4.96608	+	3.19151i	−0.437239	+	0.280997i
$130$		0			0
$131$	3.79396	−	4.37846i	0.331480	−	0.382548i	−0.565404	−	0.824814i	$-0.691280\pi$
$131$	3.79396	−	4.37846i	0.331480	−	0.382548i	0.896884	+	0.442266i	$0.145825\pi$
$132$		0			0
$133$	−5.77938			−0.501136
$134$		0			0
$135$	1.43727			0.123701
$136$		0			0
$137$	−12.6768	+	14.6298i	−1.08305	+	1.24991i	−0.116567	+	0.993183i	$0.537189\pi$
$137$	−12.6768	+	14.6298i	−1.08305	+	1.24991i	−0.966485	+	0.256725i	$0.917357\pi$
$138$		0			0
$139$	−8.57069	+	5.50804i	−0.726956	+	0.467186i	−0.851050	−	0.525084i	$-0.824034\pi$
$139$	−8.57069	+	5.50804i	−0.726956	+	0.467186i	0.124094	+	0.992270i	$0.460397\pi$
$140$		0			0
$141$	1.60606	+	11.1704i	0.135255	+	0.940718i
$142$		0			0
$143$	−0.0488215	−	0.339561i	−0.00408266	−	0.0283955i
$144$		0			0
$145$	−2.08614	+	1.34068i	−0.173244	+	0.111337i
$146$		0			0
$147$	−1.62528	+	3.55886i	−0.134050	+	0.293529i
$148$		0			0
$149$	−1.23744	+	8.60655i	−0.101375	+	0.705076i	0.874225	+	0.485521i	$0.161370\pi$
$149$	−1.23744	+	8.60655i	−0.101375	+	0.705076i	−0.975600	+	0.219556i	$0.929539\pi$
$150$		0			0
$151$	−11.0864	−	3.25525i	−0.902196	−	0.264909i	−0.202444	−	0.979294i	$-0.564888\pi$
$151$	−11.0864	−	3.25525i	−0.902196	−	0.264909i	−0.699753	+	0.714385i	$0.746706\pi$
$152$		0			0
$153$	−0.823119	+	5.72492i	−0.0665452	+	0.462832i
$154$		0			0
$155$	−8.66728	−	5.57012i	−0.696173	−	0.447403i
$156$		0			0
$157$	−4.54901	+	5.24983i	−0.363050	+	0.418982i	−0.907659	−	0.419708i	$-0.862133\pi$
$157$	−4.54901	+	5.24983i	−0.363050	+	0.418982i	0.544609	+	0.838690i	$0.316678\pi$
$158$		0			0
$159$	0.270845	−	0.593069i	0.0214794	−	0.0470334i
$160$		0			0
$161$	−10.1910	−	6.54936i	−0.803163	−	0.516162i
$162$		0			0
$163$	−2.30631			−0.180644			−0.0903220	−	0.995913i	$-0.528790\pi$
$163$	−2.30631			−0.180644			−0.0903220	+	0.995913i	$0.528790\pi$
$164$		0			0
$165$	1.11278	+	2.43666i	0.0866302	+	0.189694i
$166$		0			0
$167$	−0.743070	+	5.16817i	−0.0575005	+	0.399925i	0.940663	+	0.339343i	$0.110205\pi$
$167$	−0.743070	+	5.16817i	−0.0575005	+	0.399925i	−0.998163	+	0.0605819i	$0.980704\pi$
$168$		0			0
$169$	8.49100	+	9.79914i	0.653154	+	0.753780i
$170$		0			0
$171$	−3.28906			−0.251521
$172$		0			0
$173$	−1.83071	−	4.00869i	−0.139186	−	0.304775i	0.827184	−	0.561932i	$-0.189942\pi$
$173$	−1.83071	−	4.00869i	−0.139186	−	0.304775i	−0.966370	+	0.257157i	$0.917214\pi$
$174$		0			0
$175$	4.94706	+	1.45259i	0.373963	+	0.109805i
$176$		0			0
$177$	8.22379	+	2.41472i	0.618138	+	0.181502i
$178$		0			0
$179$	0.0339598	+	0.0391917i	0.00253828	+	0.00292933i	0.757017	−	0.653395i	$-0.226656\pi$
$179$	0.0339598	+	0.0391917i	0.00253828	+	0.00292933i	−0.754479	+	0.656324i	$0.772110\pi$
$180$		0			0
$181$	10.2400	−	11.8176i	0.761136	−	0.878398i	−0.234461	−	0.972125i	$-0.575333\pi$
$181$	10.2400	−	11.8176i	0.761136	−	0.878398i	0.995598	+	0.0937271i	$0.0298781\pi$
$182$		0			0
$183$	−3.83872	+	1.12715i	−0.283766	+	0.0833212i
$184$		0			0
$185$	1.72111	−	1.10609i	0.126538	−	0.0813212i
$186$		0			0
$187$	−10.3429	+	3.03696i	−0.756349	+	0.222084i
$188$		0			0
$189$	0.729948	−	1.59836i	0.0530959	−	0.116264i
$190$		0			0
$191$	−0.123919	−	0.143011i	−0.00896649	−	0.0103479i	0.751249	−	0.660019i	$-0.229452\pi$
$191$	−0.123919	−	0.143011i	−0.00896649	−	0.0103479i	−0.760215	+	0.649671i	$0.774906\pi$
$192$		0			0
$193$	8.36038	+	18.3067i	0.601793	+	1.31774i	0.928048	+	0.372461i	$0.121486\pi$
$193$	8.36038	+	18.3067i	0.601793	+	1.31774i	−0.326255	+	0.945282i	$0.605787\pi$
$194$		0			0
$195$	0.222555	+	0.143028i	0.0159375	+	0.0102424i
$196$		0			0
$197$	15.4816	−	4.54582i	1.10302	−	0.323876i	0.320969	−	0.947090i	$-0.395991\pi$
$197$	15.4816	−	4.54582i	1.10302	−	0.323876i	0.782052	+	0.623213i	$0.214173\pi$
$198$		0			0
$199$	2.76290	+	19.2164i	0.195856	+	1.36221i	0.816149	+	0.577841i	$0.196105\pi$
$199$	2.76290	+	19.2164i	0.195856	+	1.36221i	−0.620293	+	0.784370i	$0.712986\pi$
$200$		0			0
$201$	−7.61292	−	3.00724i	−0.536974	−	0.212115i
$202$		0			0
$203$	0.431455	+	3.00084i	0.0302822	+	0.210617i
$204$		0			0
$205$	0.711520	−	0.208921i	0.0496947	−	0.0145917i
$206$		0			0
$207$	−5.79972	−	3.72725i	−0.403108	−	0.259062i
$208$		0			0
$209$	−2.54650	−	5.57605i	−0.176145	−	0.385704i
$210$		0			0
$211$	−15.2378	−	17.5853i	−1.04901	−	1.21062i	−0.977005	−	0.213219i	$-0.931605\pi$
$211$	−15.2378	−	17.5853i	−1.04901	−	1.21062i	−0.0720062	−	0.997404i	$-0.522940\pi$
$212$		0			0
$213$	2.08653	−	4.56886i	0.142967	−	0.313053i
$214$		0			0
$215$	8.14083	−	2.39036i	0.555200	−	0.163021i
$216$		0			0
$217$	−10.5963	+	6.80980i	−0.719321	+	0.462280i
$218$		0			0
$219$	−10.0208	+	2.94237i	−0.677143	+	0.198827i
$220$		0			0
$221$	−0.697161	+	0.804566i	−0.0468961	+	0.0541210i
$222$		0			0
$223$	7.15375	+	8.25586i	0.479050	+	0.552854i	0.942907	−	0.333057i	$-0.108080\pi$
$223$	7.15375	+	8.25586i	0.479050	+	0.552854i	−0.463856	+	0.885910i	$0.653535\pi$
$224$		0			0
$225$	2.81538	+	0.826671i	0.187692	+	0.0551114i
$226$		0			0
$227$	18.1991	+	5.34375i	1.20792	+	0.354677i	0.822876	−	0.568222i	$-0.192368\pi$
$227$	18.1991	+	5.34375i	1.20792	+	0.354677i	0.385043	+	0.922899i	$0.374187\pi$
$228$		0			0
$229$	10.4084	+	22.7913i	0.687808	+	1.50609i	0.854153	+	0.520022i	$0.174076\pi$
$229$	10.4084	+	22.7913i	0.687808	+	1.50609i	−0.166344	+	0.986068i	$0.553196\pi$
$230$		0			0
$231$	3.27491			0.215473
$232$		0			0
$233$	−3.97725	−	4.58999i	−0.260558	−	0.300700i	0.610364	−	0.792121i	$-0.291023\pi$
$233$	−3.97725	−	4.58999i	−0.260558	−	0.300700i	−0.870922	+	0.491421i	$0.836478\pi$
$234$		0			0
$235$	2.30835	−	16.0549i	0.150580	−	1.04731i
$236$		0			0
$237$	1.37975	+	3.02123i	0.0896243	+	0.196250i
$238$		0			0
$239$	−2.03163			−0.131415			−0.0657076	−	0.997839i	$-0.520930\pi$
$239$	−2.03163			−0.131415			−0.0657076	+	0.997839i	$0.520930\pi$
$240$		0			0
$241$	−0.515764	−	0.331461i	−0.0332233	−	0.0213513i	0.523924	−	0.851765i	$-0.324468\pi$
$241$	−0.515764	−	0.331461i	−0.0332233	−	0.0213513i	−0.557147	+	0.830414i	$0.688104\pi$
$242$		0			0
$243$	0.415415	−	0.909632i	0.0266489	−	0.0583529i
$244$		0			0
$245$	3.68242	−	4.24974i	0.235261	−	0.271506i
$246$		0			0
$247$	−0.509296	−	0.327305i	−0.0324057	−	0.0208259i
$248$		0			0
$249$	−0.629155	+	4.37587i	−0.0398711	+	0.277309i
$250$		0			0
$251$	−4.51145	−	1.32468i	−0.284760	−	0.0836131i	0.136233	−	0.990677i	$-0.456500\pi$
$251$	−4.51145	−	1.32468i	−0.284760	−	0.0836131i	−0.420994	+	0.907064i	$0.638318\pi$
$252$		0			0
$253$	1.82860	−	12.7182i	0.114963	−	0.799587i
$254$		0			0
$255$	3.45330	−	7.56167i	0.216254	−	0.473530i
$256$		0			0
$257$	−9.74818	+	6.26478i	−0.608075	+	0.390786i	−0.808135	−	0.588998i	$-0.799523\pi$
$257$	−9.74818	+	6.26478i	−0.608075	+	0.390786i	0.200060	+	0.979784i	$0.435886\pi$
$258$		0			0
$259$	−0.355960	−	2.47575i	−0.0221183	−	0.153836i
$260$		0			0
$261$	0.245542	+	1.70778i	0.0151987	+	0.105709i
$262$		0			0
$263$	−17.4251	+	11.1985i	−1.07448	+	0.690527i	−0.953276	−	0.302101i	$-0.902312\pi$
$263$	−17.4251	+	11.1985i	−1.07448	+	0.690527i	−0.121205	+	0.992628i	$0.538676\pi$
$264$		0			0
$265$	−0.613660	+	0.708202i	−0.0376969	+	0.0435045i
$266$		0			0
$267$	11.1537			0.682598
$268$		0			0
$269$	9.23329			0.562963			0.281482	−	0.959567i	$-0.409174\pi$
$269$	9.23329			0.562963			0.281482	+	0.959567i	$0.409174\pi$
$270$		0			0
$271$	12.0716	−	13.9313i	0.733296	−	0.846269i	−0.259543	−	0.965732i	$-0.583572\pi$
$271$	12.0716	−	13.9313i	0.733296	−	0.846269i	0.992839	+	0.119463i	$0.0381173\pi$
$272$		0			0
$273$	0.272087	−	0.174860i	0.0164675	−	0.0105830i
$274$		0			0
$275$	0.778279	+	5.41305i	0.0469320	+	0.326419i
$276$		0			0
$277$	−1.94287	−	13.5130i	−0.116736	−	0.811917i	−0.961111	−	0.276164i	$-0.910937\pi$
$277$	−1.94287	−	13.5130i	−0.116736	−	0.811917i	0.844375	−	0.535753i	$-0.179972\pi$
$278$		0			0
$279$	−6.03036	+	3.87548i	−0.361028	+	0.232019i
$280$		0			0
$281$	0.978022	−	2.14157i	0.0583439	−	0.127755i	−0.878214	−	0.478267i	$-0.841265\pi$
$281$	0.978022	−	2.14157i	0.0583439	−	0.127755i	0.936558	+	0.350512i	$0.113992\pi$
$282$		0			0
$283$	2.21267	−	15.3894i	0.131529	−	0.914807i	−0.812033	−	0.583612i	$-0.801639\pi$
$283$	2.21267	−	15.3894i	0.131529	−	0.914807i	0.943562	−	0.331195i	$-0.107452\pi$
$284$		0			0
$285$	4.53580	+	1.33183i	0.268677	+	0.0788908i
$286$		0			0
$287$	0.129023	−	0.897371i	0.00761596	−	0.0529702i
$288$		0			0
$289$	13.8405	+	8.89474i	0.814146	+	0.523220i
$290$		0			0
$291$	5.90005	−	6.80903i	0.345867	−	0.399152i
$292$		0			0
$293$	−5.25835	+	11.5142i	−0.307196	+	0.672666i	−0.998767	−	0.0496428i	$-0.984192\pi$
$293$	−5.25835	+	11.5142i	−0.307196	+	0.672666i	0.691571	+	0.722309i	$0.256919\pi$
$294$		0			0
$295$	−10.3633	−	6.66007i	−0.603373	−	0.387764i
$296$		0			0
$297$	1.86376			0.108146
$298$		0			0
$299$	−0.527150	−	1.15430i	−0.0304859	−	0.0667547i
$300$		0			0
$301$	1.47621	−	10.2672i	0.0850871	−	0.591794i
$302$		0			0
$303$	8.68094	+	10.0183i	0.498707	+	0.575539i
$304$		0			0
$305$	5.75022			0.329256
$306$		0			0
$307$	−10.3577	−	22.6802i	−0.591145	−	1.29443i	−0.934748	−	0.355312i	$-0.884375\pi$
$307$	−10.3577	−	22.6802i	−0.591145	−	1.29443i	0.343602	−	0.939115i	$-0.388353\pi$
$308$		0			0
$309$	−15.5892	−	4.57741i	−0.886840	−	0.260400i
$310$		0			0
$311$	12.5853	+	3.69537i	0.713646	+	0.209545i	0.618349	−	0.785903i	$-0.287802\pi$
$311$	12.5853	+	3.69537i	0.713646	+	0.209545i	0.0952970	+	0.995449i	$0.469620\pi$
$312$		0			0
$313$	6.71109	+	7.74501i	0.379333	+	0.437774i	0.913024	−	0.407906i	$-0.133741\pi$
$313$	6.71109	+	7.74501i	0.379333	+	0.437774i	−0.533691	+	0.845680i	$0.679195\pi$
$314$		0			0
$315$	−1.65386	+	1.90865i	−0.0931844	+	0.107541i
$316$		0			0
$317$	−8.01339	+	2.35294i	−0.450077	+	0.132154i	−0.498913	−	0.866652i	$-0.666267\pi$
$317$	−8.01339	+	2.35294i	−0.450077	+	0.132154i	0.0488357	+	0.998807i	$0.484449\pi$
$318$		0			0
$319$	−2.70515	+	1.73850i	−0.151460	+	0.0973371i
$320$		0			0
$321$	4.44290	−	1.30455i	0.247979	−	0.0728131i
$322$		0			0
$323$	−7.90254	+	17.3041i	−0.439709	+	0.962828i
$324$		0			0
$325$	0.353685	+	0.408174i	0.0196189	+	0.0226414i
$326$		0			0
$327$	−0.186444	−	0.408254i	−0.0103104	−	0.0225765i
$328$		0			0
$329$	−16.6820	−	10.7209i	−0.919709	−	0.591061i
$330$		0			0
$331$	19.9054	−	5.84474i	1.09410	−	0.321256i	0.315593	−	0.948895i	$-0.397797\pi$
$331$	19.9054	−	5.84474i	1.09410	−	0.321256i	0.778505	+	0.627639i	$0.215978\pi$
$332$		0			0
$333$	−0.202578	−	1.40896i	−0.0111012	−	0.0772104i
$334$		0			0
$335$	9.28092	+	7.22983i	0.507071	+	0.395008i
$336$		0			0
$337$	−0.380523	−	2.64660i	−0.0207284	−	0.144169i	0.976829	−	0.214022i	$-0.0686563\pi$
$337$	−0.380523	−	2.64660i	−0.0207284	−	0.144169i	−0.997557	+	0.0698523i	$0.977747\pi$
$338$		0			0
$339$	1.35262	−	0.397164i	0.0734640	−	0.0215710i
$340$		0			0
$341$	−11.2391	−	7.22294i	−0.608632	−	0.391144i
$342$		0			0
$343$	−7.96549	−	17.4420i	−0.430096	−	0.941779i
$344$		0			0
$345$	6.48887	+	7.48855i	0.349349	+	0.403170i
$346$		0			0
$347$	−6.53328	+	14.3059i	−0.350725	+	0.767980i	0.649248	+	0.760577i	$0.275084\pi$
$347$	−6.53328	+	14.3059i	−0.350725	+	0.767980i	−0.999973	+	0.00740308i	$0.997644\pi$
$348$		0			0
$349$	−16.4966	+	4.84384i	−0.883043	+	0.259285i	−0.691654	−	0.722229i	$-0.743118\pi$
$349$	−16.4966	+	4.84384i	−0.883043	+	0.259285i	−0.191389	+	0.981514i	$0.561299\pi$
$350$		0			0
$351$	0.154845	−	0.0995131i	0.00826504	−	0.00531162i
$352$		0			0
$353$	20.4327	−	5.99958i	1.08752	−	0.319325i	0.311638	−	0.950201i	$-0.399122\pi$
$353$	20.4327	−	5.99958i	1.08752	−	0.319325i	0.775884	+	0.630876i	$0.217304\pi$
$354$		0			0
$355$	−4.72750	+	5.45582i	−0.250909	+	0.289565i
$356$		0			0
$357$	−6.65535	−	7.68068i	−0.352239	−	0.406505i
$358$		0			0
$359$	27.2736	+	8.00826i	1.43945	+	0.422660i	0.906037	−	0.423198i	$-0.139092\pi$
$359$	27.2736	+	8.00826i	1.43945	+	0.422660i	0.533409	+	0.845857i	$0.320911\pi$
$360$		0			0
$361$	7.85064	+	2.30516i	0.413192	+	0.121324i
$362$		0			0
$363$	−3.12658	−	6.84627i	−0.164103	−	0.359336i
$364$		0			0
$365$	15.0107			0.785695
$366$		0			0
$367$	10.8178	+	12.4844i	0.564686	+	0.651683i	0.964241	−	0.265027i	$-0.0853808\pi$
$367$	10.8178	+	12.4844i	0.564686	+	0.651683i	−0.399555	+	0.916709i	$0.630835\pi$
$368$		0			0
$369$	0.0734270	−	0.510696i	0.00382246	−	0.0265858i
$370$		0			0
$371$	0.475917	+	1.04211i	0.0247084	+	0.0541038i
$372$		0			0
$373$	−17.1346			−0.887195			−0.443598	−	0.896226i	$-0.646298\pi$
$373$	−17.1346			−0.887195			−0.443598	+	0.896226i	$0.646298\pi$
$374$		0			0
$375$	−9.59339	−	6.16530i	−0.495401	−	0.318375i
$376$		0			0
$377$	−0.131926	+	0.288877i	−0.00679452	+	0.0148779i
$378$		0			0
$379$	17.4771	−	20.1697i	0.897739	−	1.03605i	−0.101412	−	0.994845i	$-0.532336\pi$
$379$	17.4771	−	20.1697i	0.897739	−	1.03605i	0.999151	−	0.0412013i	$-0.0131185\pi$
$380$		0			0
$381$	−6.88555	−	4.42508i	−0.352758	−	0.226704i
$382$		0			0
$383$	1.63400	−	11.3647i	0.0834936	−	0.580711i	−0.904530	−	0.426410i	$-0.859778\pi$
$383$	1.63400	−	11.3647i	0.0834936	−	0.580711i	0.988024	−	0.154301i	$-0.0493127\pi$
$384$		0			0
$385$	−4.51627	−	1.32610i	−0.230171	−	0.0675842i
$386$		0			0
$387$	0.840112	−	5.84311i	0.0427053	−	0.297022i
$388$		0			0
$389$	8.98069	−	19.6650i	0.455339	−	0.997054i	−0.533186	−	0.845998i	$-0.679005\pi$
$389$	8.98069	−	19.6650i	0.455339	−	0.997054i	0.988525	−	0.151056i	$-0.0482673\pi$
$390$		0			0
$391$	−33.5444	+	21.5576i	−1.69641	+	1.09022i
$392$		0			0
$393$	0.824506	+	5.73457i	0.0415908	+	0.289271i
$394$		0			0
$395$	−0.679372	−	4.72514i	−0.0341829	−	0.237748i
$396$		0			0
$397$	21.7905	−	14.0039i	1.09363	−	0.702835i	0.135965	−	0.990714i	$-0.456586\pi$
$397$	21.7905	−	14.0039i	1.09363	−	0.702835i	0.957667	+	0.287879i	$0.0929501\pi$
$398$		0			0
$399$	3.78469	−	4.36777i	0.189472	−	0.218662i
$400$		0			0
$401$	−24.5531			−1.22612			−0.613062	−	0.790035i	$-0.710062\pi$
$401$	−24.5531			−1.22612			−0.613062	+	0.790035i	$0.710062\pi$
$402$		0			0
$403$	−1.31943			−0.0657257
$404$		0			0
$405$	−0.941215	+	1.08622i	−0.0467693	+	0.0539747i
$406$		0			0
$407$	2.23181	−	1.43430i	0.110627	−	0.0710954i
$408$		0			0
$409$	−3.01392	−	20.9622i	−0.149029	−	1.03652i	−0.917814	−	0.397010i	$-0.870048\pi$
$409$	−3.01392	−	20.9622i	−0.149029	−	1.03652i	0.768786	−	0.639506i	$-0.220861\pi$
$410$		0			0
$411$	−2.75493	−	19.1610i	−0.135891	−	0.945140i
$412$		0			0
$413$	−12.6697	+	8.14233i	−0.623436	+	0.400658i
$414$		0			0
$415$	2.63955	−	5.77980i	0.129570	−	0.283719i
$416$		0			0
$417$	1.44990	−	10.0843i	0.0710020	−	0.493830i
$418$		0			0
$419$	10.2522	+	3.01031i	0.500851	+	0.147063i	0.522393	−	0.852705i	$-0.325039\pi$
$419$	10.2522	+	3.01031i	0.500851	+	0.147063i	−0.0215422	+	0.999768i	$0.506858\pi$
$420$		0			0
$421$	−1.43939	+	10.0112i	−0.0701516	+	0.487915i	0.924211	+	0.381882i	$0.124724\pi$
$421$	−1.43939	+	10.0112i	−0.0701516	+	0.487915i	−0.994363	+	0.106033i	$0.966185\pi$
$422$		0			0
$423$	−9.49377	−	6.10128i	−0.461603	−	0.296654i
$424$		0			0
$425$	11.1137	−	12.8258i	0.539092	−	0.622145i
$426$		0			0
$427$	2.92036	−	6.39469i	0.141326	−	0.309461i
$428$		0			0
$429$	0.288594	+	0.185468i	0.0139335	+	0.00895449i
$430$		0			0
$431$	−5.19985			−0.250468			−0.125234	−	0.992127i	$-0.539968\pi$
$431$	−5.19985			−0.250468			−0.125234	+	0.992127i	$0.539968\pi$
$432$		0			0
$433$	9.88155	+	21.6376i	0.474877	+	1.03984i	0.983840	+	0.179048i	$0.0573016\pi$
$433$	9.88155	+	21.6376i	0.474877	+	1.03984i	−0.508963	+	0.860788i	$0.669971\pi$
$434$		0			0
$435$	0.352912	−	2.45455i	0.0169208	−	0.117687i
$436$		0			0
$437$	−14.8491	−	17.1368i	−0.710330	−	0.819765i
$438$		0			0
$439$	−19.7528			−0.942750			−0.471375	−	0.881933i	$-0.656242\pi$
$439$	−19.7528			−0.942750			−0.471375	+	0.881933i	$0.656242\pi$
$440$		0			0
$441$	−1.62528	−	3.55886i	−0.0773940	−	0.169469i
$442$		0			0
$443$	16.1792	+	4.75064i	0.768696	+	0.225710i	0.642490	−	0.766294i	$-0.277902\pi$
$443$	16.1792	+	4.75064i	0.768696	+	0.225710i	0.126207	+	0.992004i	$0.459720\pi$
$444$		0			0
$445$	−15.3816	−	4.51645i	−0.729159	−	0.214100i
$446$		0			0
$447$	−5.69405	−	6.57129i	−0.269319	−	0.310811i
$448$		0			0
$449$	13.7556	−	15.8748i	0.649165	−	0.749177i	−0.331802	−	0.943349i	$-0.607657\pi$
$449$	13.7556	−	15.8748i	0.649165	−	0.749177i	0.980967	+	0.194172i	$0.0622021\pi$
$450$		0			0
$451$	0.922649	−	0.270914i	0.0434459	−	0.0127569i
$452$		0			0
$453$	9.72019	−	6.24678i	0.456694	−	0.293499i
$454$		0			0
$455$	−0.446029	+	0.130966i	−0.0209101	+	0.00613977i
$456$		0			0
$457$	−2.39358	+	5.24121i	−0.111967	+	0.245173i	−0.957317	−	0.289039i	$-0.906664\pi$
$457$	−2.39358	+	5.24121i	−0.111967	+	0.245173i	0.845350	+	0.534212i	$0.179392\pi$
$458$		0			0
$459$	−3.78758	−	4.37110i	−0.176789	−	0.204025i
$460$		0			0
$461$	12.6927	+	27.7931i	0.591157	+	1.29445i	0.934740	+	0.355332i	$0.115632\pi$
$461$	12.6927	+	27.7931i	0.591157	+	1.29445i	−0.343583	+	0.939122i	$0.611641\pi$
$462$		0			0
$463$	18.5951	+	11.9503i	0.864187	+	0.555379i	0.895969	−	0.444116i	$-0.146482\pi$
$463$	18.5951	+	11.9503i	0.864187	+	0.555379i	−0.0317828	+	0.999495i	$0.510118\pi$
$464$		0			0
$465$	9.88548	−	2.90264i	0.458428	−	0.134607i
$466$		0			0
$467$	−1.32080	−	9.18637i	−0.0611194	−	0.425095i	−0.997291	−	0.0735523i	$-0.976566\pi$
$467$	−1.32080	−	9.18637i	−0.0611194	−	0.425095i	0.936172	−	0.351542i	$-0.114343\pi$
$468$		0			0
$469$	12.7536	−	6.64930i	0.588908	−	0.307036i
$470$		0			0
$471$	−0.988593	−	6.87582i	−0.0455520	−	0.316821i
$472$		0			0
$473$	10.5565	−	3.09966i	0.485386	−	0.142522i
$474$		0			0
$475$	8.11885	+	5.21767i	0.372519	+	0.239403i
$476$		0			0
$477$	0.270845	+	0.593069i	0.0124012	+	0.0271548i
$478$		0			0
$479$	18.4223	+	21.2604i	0.841736	+	0.971415i	0.999872	−	0.0160027i	$-0.00509404\pi$
$479$	18.4223	+	21.2604i	0.841736	+	0.971415i	−0.158136	+	0.987417i	$0.550549\pi$
$480$		0			0
$481$	0.108842	−	0.238330i	0.00496275	−	0.0108669i
$482$		0			0
$483$	11.6234	−	3.41293i	0.528881	−	0.155293i
$484$		0			0
$485$	−10.8937	+	7.00093i	−0.494656	+	0.317896i
$486$		0			0
$487$	9.50453	−	2.79078i	0.430691	−	0.126462i	−0.0591994	−	0.998246i	$-0.518855\pi$
$487$	9.50453	−	2.79078i	0.430691	−	0.126462i	0.489891	+	0.871784i	$0.337037\pi$
$488$		0			0
$489$	1.51031	−	1.74299i	0.0682986	−	0.0788208i
$490$		0			0
$491$	−17.7494	−	20.4839i	−0.801019	−	0.924425i	0.197418	−	0.980319i	$-0.436744\pi$
$491$	−17.7494	−	20.4839i	−0.801019	−	0.924425i	−0.998437	+	0.0558946i	$0.982199\pi$
$492$		0			0
$493$	9.57481	+	2.81142i	0.431228	+	0.126620i
$494$		0			0
$495$	−2.57022	−	0.754685i	−0.115523	−	0.0339206i
$496$		0			0
$497$	3.66635	+	8.02819i	0.164458	+	0.360114i
$498$		0			0
$499$	−23.0891			−1.03361			−0.516805	−	0.856103i	$-0.672879\pi$
$499$	−23.0891			−1.03361			−0.516805	+	0.856103i	$0.672879\pi$
$500$		0			0
$501$	−3.41923	−	3.94601i	−0.152760	−	0.176295i
$502$		0			0
$503$	−4.91782	+	34.2042i	−0.219275	+	1.52509i	0.521451	+	0.853281i	$0.325391\pi$
$503$	−4.91782	+	34.2042i	−0.219275	+	1.52509i	−0.740726	+	0.671808i	$0.765518\pi$
$504$		0			0
$505$	−7.91480	−	17.3310i	−0.352204	−	0.771219i
$506$		0			0
$507$	−12.9661			−0.575846
$508$		0			0
$509$	3.75751	+	2.41480i	0.166549	+	0.107034i	0.621260	−	0.783605i	$-0.286621\pi$
$509$	3.75751	+	2.41480i	0.166549	+	0.107034i	−0.454711	+	0.890639i	$0.650258\pi$
$510$		0			0
$511$	7.62347	−	16.6931i	0.337242	−	0.738458i
$512$		0			0
$513$	2.15388	−	2.48571i	0.0950960	−	0.109747i
$514$		0			0
$515$	19.6449	+	12.6250i	0.865657	+	0.556324i
$516$		0			0
$517$	2.99331	−	20.8189i	0.131646	−	0.915615i
$518$		0			0
$519$	4.22842	+	1.24158i	0.185607	+	0.0544992i
$520$		0			0
$521$	6.11147	−	42.5062i	0.267748	−	1.86223i	−0.201939	−	0.979398i	$-0.564724\pi$
$521$	6.11147	−	42.5062i	0.267748	−	1.86223i	0.469687	−	0.882833i	$-0.344367\pi$
$522$		0			0
$523$	14.6860	−	32.1578i	0.642172	−	1.40616i	−0.256069	−	0.966658i	$-0.582428\pi$
$523$	14.6860	−	32.1578i	0.642172	−	1.40616i	0.898241	−	0.439502i	$-0.144845\pi$
$524$		0			0
$525$	−4.33743	+	2.78750i	−0.189301	+	0.121656i
$526$		0			0
$527$	5.90036	+	41.0379i	0.257024	+	1.78764i
$528$		0			0
$529$	−3.49087	−	24.2795i	−0.151777	−	1.05563i
$530$		0			0
$531$	−7.21036	+	4.63382i	−0.312903	+	0.201091i
$532$		0			0
$533$	0.0621908	−	0.0717720i	0.00269378	−	0.00310879i
$534$		0			0
$535$	−6.65526			−0.287732
$536$		0			0
$537$	−0.0518581			−0.00223784
$538$		0			0
$539$	4.77510	−	5.51076i	0.205678	−	0.237365i
$540$		0			0
$541$	−15.2157	+	9.77851i	−0.654172	+	0.420411i	−0.825189	−	0.564857i	$-0.808931\pi$
$541$	−15.2157	+	9.77851i	−0.654172	+	0.420411i	0.171016	+	0.985268i	$0.445295\pi$
$542$		0			0
$543$	2.22537	+	15.4778i	0.0954999	+	0.664217i
$544$		0			0
$545$	0.0918026	+	0.638501i	0.00393239	+	0.0273504i
$546$		0			0
$547$	0.525402	−	0.337655i	0.0224646	−	0.0144371i	−0.529360	−	0.848397i	$-0.677568\pi$
$547$	0.525402	−	0.337655i	0.0224646	−	0.0144371i	0.551825	+	0.833960i	$0.313932\pi$
$548$		0			0
$549$	1.66198	−	3.63923i	0.0709317	−	0.155319i
$550$		0			0
$551$	−0.807603	+	5.61700i	−0.0344051	+	0.239292i
$552$		0			0
$553$	−5.59976	−	1.64424i	−0.238126	−	0.0699201i
$554$		0			0
$555$	−0.291160	+	2.02506i	−0.0123590	+	0.0859590i
$556$		0			0
$557$	−3.60844	−	2.31901i	−0.152895	−	0.0982594i	0.461957	−	0.886903i	$-0.347148\pi$
$557$	−3.60844	−	2.31901i	−0.152895	−	0.0982594i	−0.614851	+	0.788643i	$0.710784\pi$
$558$		0			0
$559$	0.711554	−	0.821177i	0.0300955	−	0.0347321i
$560$		0			0
$561$	4.47800	−	9.80544i	0.189061	−	0.413986i
$562$		0			0
$563$	19.0279	+	12.2285i	0.801929	+	0.515369i	0.876245	−	0.481866i	$-0.160041\pi$
$563$	19.0279	+	12.2285i	0.801929	+	0.515369i	−0.0743155	+	0.997235i	$0.523677\pi$
$564$		0			0
$565$	−2.02616			−0.0852410
$566$		0			0
$567$	0.729948	+	1.59836i	0.0306549	+	0.0671249i
$568$		0			0
$569$	1.22282	−	8.50493i	0.0512635	−	0.356545i	−0.948003	−	0.318260i	$-0.896901\pi$
$569$	1.22282	−	8.50493i	0.0512635	−	0.356545i	0.999267	−	0.0382851i	$-0.0121895\pi$
$570$		0			0
$571$	−5.51022	−	6.35914i	−0.230596	−	0.266122i	0.628646	−	0.777692i	$-0.283610\pi$
$571$	−5.51022	−	6.35914i	−0.230596	−	0.266122i	−0.859242	+	0.511570i	$0.829064\pi$
$572$		0			0
$573$	0.189230			0.00790520
$574$		0			0
$575$	8.40346	+	18.4010i	0.350449	+	0.767375i
$576$		0			0
$577$	22.1509	+	6.50410i	0.922156	+	0.270769i	0.708149	−	0.706063i	$-0.249530\pi$
$577$	22.1509	+	6.50410i	0.922156	+	0.270769i	0.214007	+	0.976832i	$0.431349\pi$
$578$		0			0
$579$	−19.3101	−	5.66997i	−0.802502	−	0.235636i
$580$		0			0
$581$	−5.08705	−	5.87077i	−0.211046	−	0.243561i
$582$		0			0
$583$	−0.795751	+	0.918346i	−0.0329567	+	0.0380340i
$584$		0			0
$585$	−0.253836	+	0.0745330i	−0.0104948	+	0.00308156i
$586$		0			0
$587$	18.7552	−	12.0532i	0.774108	−	0.497489i	−0.0929652	−	0.995669i	$-0.529635\pi$
$587$	18.7552	−	12.0532i	0.774108	−	0.497489i	0.867074	+	0.498180i	$0.165998\pi$
$588$		0			0
$589$	−22.6219	+	6.64240i	−0.932121	+	0.273695i
$590$		0			0
$591$	−6.70282	+	14.6771i	−0.275717	+	0.603736i
$592$		0			0
$593$	19.2790	+	22.2492i	0.791695	+	0.913665i	0.997895	−	0.0648446i	$-0.0206552\pi$
$593$	19.2790	+	22.2492i	0.791695	+	0.913665i	−0.206200	+	0.978510i	$0.566110\pi$
$594$		0			0
$595$	6.06798	+	13.2870i	0.248763	+	0.544715i
$596$		0			0
$597$	−16.3321	−	10.4960i	−0.668427	−	0.429572i
$598$		0			0
$599$	39.1357	−	11.4913i	1.59904	−	0.469521i	0.643763	−	0.765225i	$-0.277372\pi$
$599$	39.1357	−	11.4913i	1.59904	−	0.469521i	0.955280	+	0.295703i	$0.0955539\pi$
$600$		0			0
$601$	−1.26905	−	8.82642i	−0.0517656	−	0.360037i	−0.999197	−	0.0400773i	$-0.987240\pi$
$601$	−1.26905	−	8.82642i	−0.0517656	−	0.360037i	0.947431	−	0.319960i	$-0.103670\pi$
$602$		0			0
$603$	7.25812	−	3.78413i	0.295574	−	0.154102i
$604$		0			0
$605$	1.53949	+	10.7074i	0.0625893	+	0.435318i
$606$		0			0
$607$	−29.2701	+	8.59448i	−1.18804	+	0.348839i	−0.815268	−	0.579084i	$-0.803410\pi$
$607$	−29.2701	+	8.59448i	−1.18804	+	0.348839i	−0.372770	+	0.927924i	$0.621592\pi$
$608$		0			0
$609$	−2.55042	−	1.63906i	−0.103348	−	0.0664180i
$610$		0			0
$611$	−0.862911	−	1.88951i	−0.0349096	−	0.0764414i
$612$		0			0
$613$	18.9497	+	21.8691i	0.765371	+	0.883285i	0.995963	−	0.0897654i	$-0.0286117\pi$
$613$	18.9497	+	21.8691i	0.765371	+	0.883285i	−0.230592	+	0.973051i	$0.574066\pi$
$614$		0			0
$615$	−0.308055	+	0.674545i	−0.0124220	+	0.0272003i
$616$		0			0
$617$	−17.7102	+	5.20020i	−0.712988	+	0.209352i	−0.618059	−	0.786132i	$-0.712081\pi$
$617$	−17.7102	+	5.20020i	−0.712988	+	0.209352i	−0.0949289	+	0.995484i	$0.530262\pi$
$618$		0			0
$619$	−6.70629	+	4.30987i	−0.269548	+	0.173228i	−0.668432	−	0.743773i	$-0.733034\pi$
$619$	−6.70629	+	4.30987i	−0.269548	+	0.173228i	0.398883	+	0.917002i	$0.369398\pi$
$620$		0			0
$621$	6.61488	−	1.94230i	0.265446	−	0.0779420i
$622$		0			0
$623$	−12.8345	+	14.8118i	−0.514204	+	0.593423i
$624$		0			0
$625$	1.12572	+	1.29915i	0.0450288	+	0.0519660i
$626$		0			0
$627$	5.88170	+	1.72702i	0.234892	+	0.0689707i
$628$		0			0
$629$	−7.89942	−	2.31948i	−0.314971	−	0.0924837i
$630$		0			0
$631$	13.7047	+	30.0091i	0.545575	+	1.19464i	0.958818	+	0.284021i	$0.0916686\pi$
$631$	13.7047	+	30.0091i	0.545575	+	1.19464i	−0.413243	+	0.910621i	$0.635604\pi$
$632$		0			0
$633$	23.2687			0.924848
$634$		0			0
$635$	7.70372	+	8.89057i	0.305713	+	0.352812i
$636$		0			0
$637$	0.102486	−	0.712809i	0.00406066	−	0.0282425i
$638$		0			0
$639$	2.08653	+	4.56886i	0.0825418	+	0.180741i
$640$		0			0
$641$	−30.9416			−1.22212			−0.611060	−	0.791585i	$-0.709256\pi$
$641$	−30.9416			−1.22212			−0.611060	+	0.791585i	$0.709256\pi$
$642$		0			0
$643$	−15.0314	−	9.66008i	−0.592780	−	0.380956i	0.209585	−	0.977790i	$-0.432789\pi$
$643$	−15.0314	−	9.66008i	−0.592780	−	0.380956i	−0.802365	+	0.596834i	$0.796425\pi$
$644$		0			0
$645$	−3.52460	+	7.71779i	−0.138781	+	0.303888i
$646$		0			0
$647$	−21.8943	+	25.2674i	−0.860756	+	0.993365i	0.139240	+	0.990259i	$0.455534\pi$
$647$	−21.8943	+	25.2674i	−0.860756	+	0.993365i	−0.999995	+	0.00310620i	$0.999011\pi$
$648$		0			0
$649$	−13.4384	−	8.63631i	−0.527502	−	0.339005i
$650$		0			0
$651$	1.79257	−	12.4676i	0.0702563	−	0.488644i
$652$		0			0
$653$	38.1356	+	11.1976i	1.49236	+	0.438197i	0.923294	−	0.384093i	$-0.125486\pi$
$653$	38.1356	+	11.1976i	1.49236	+	0.438197i	0.569068	+	0.822290i	$0.307304\pi$
$654$		0			0
$655$	1.18504	−	8.24215i	0.0463034	−	0.322047i
$656$		0			0
$657$	4.33853	−	9.50006i	0.169262	−	0.370633i
$658$		0			0
$659$	−23.1914	+	14.9042i	−0.903407	+	0.580585i	−0.907799	−	0.419406i	$-0.862238\pi$
$659$	−23.1914	+	14.9042i	−0.903407	+	0.580585i	0.00439157	+	0.999990i	$0.498602\pi$
$660$		0			0
$661$	−4.80686	−	33.4325i	−0.186965	−	1.30037i	−0.839810	−	0.542880i	$-0.817334\pi$
$661$	−4.80686	−	33.4325i	−0.186965	−	1.30037i	0.652845	−	0.757492i	$-0.273575\pi$
$662$		0			0
$663$	−0.151508	−	1.05376i	−0.00588406	−	0.0409246i
$664$		0			0
$665$	−6.98793	+	4.49087i	−0.270980	+	0.174148i
$666$		0			0
$667$	−7.78942	+	8.98947i	−0.301607	+	0.348074i
$668$		0			0
$669$	−10.9241			−0.422349
$670$		0			0
$671$	7.45647			0.287854
$672$		0			0
$673$	−10.5420	+	12.1662i	−0.406366	+	0.468971i	−0.921635	−	0.388057i	$-0.873146\pi$
$673$	−10.5420	+	12.1662i	−0.406366	+	0.468971i	0.515269	+	0.857028i	$0.327692\pi$
$674$		0			0
$675$	−2.46844	+	1.58637i	−0.0950103	+	0.0610594i
$676$		0			0
$677$	−2.20850	−	15.3604i	−0.0848794	−	0.590349i	−0.987225	−	0.159335i	$-0.949065\pi$
$677$	−2.20850	−	15.3604i	−0.0848794	−	0.590349i	0.902345	−	0.431014i	$-0.141844\pi$
$678$		0			0
$679$	2.25303	+	15.6702i	0.0864633	+	0.601366i
$680$		0			0
$681$	−15.9564	+	10.2546i	−0.611452	+	0.392956i
$682$		0			0
$683$	−9.96933	+	21.8298i	−0.381466	+	0.835294i	0.617352	+	0.786687i	$0.288205\pi$
$683$	−9.96933	+	21.8298i	−0.381466	+	0.835294i	−0.998818	+	0.0486068i	$0.984522\pi$
$684$		0			0
$685$	−3.95959	+	27.5396i	−0.151288	+	1.05223i
$686$		0			0
$687$	−24.0406	−	7.05895i	−0.917205	−	0.269316i
$688$		0			0
$689$	−0.0170789	+	0.118787i	−0.000650656	+	0.00452541i
$690$		0			0
$691$	11.0801	+	7.12076i	0.421508	+	0.270886i	0.734154	−	0.678983i	$-0.237579\pi$
$691$	11.0801	+	7.12076i	0.421508	+	0.270886i	−0.312646	+	0.949870i	$0.601215\pi$
$692$		0			0
$693$	−2.14461	+	2.47501i	−0.0814669	+	0.0940178i
$694$		0			0
$695$	−6.08290	+	13.3197i	−0.230738	+	0.505245i
$696$		0			0
$697$	−2.51041	−	1.61334i	−0.0950886	−	0.0611098i
$698$		0			0
$699$	6.07343			0.229718
$700$		0			0
$701$	11.6084	+	25.4189i	0.438444	+	0.960057i	0.991881	+	0.127167i	$0.0405884\pi$
$701$	11.6084	+	25.4189i	0.438444	+	0.960057i	−0.553438	+	0.832890i	$0.686684\pi$
$702$		0			0
$703$	0.666290	−	4.63415i	0.0251296	−	0.174780i
$704$		0			0
$705$	10.6219	+	12.2583i	0.400043	+	0.461674i
$706$		0			0
$707$	−23.2931			−0.876028
$708$		0			0
$709$	−3.72768	−	8.16247i	−0.139996	−	0.306548i	0.826628	−	0.562749i	$-0.190256\pi$
$709$	−3.72768	−	8.16247i	−0.139996	−	0.306548i	−0.966624	+	0.256201i	$0.917529\pi$
$710$		0			0
$711$	−3.18684	−	0.935740i	−0.119516	−	0.0350930i
$712$		0			0
$713$	−47.4174	−	13.9230i	−1.77580	−	0.521421i
$714$		0			0
$715$	−0.322886	−	0.372630i	−0.0120753	−	0.0139356i
$716$		0			0
$717$	1.33043	−	1.53540i	0.0496860	−	0.0573407i
$718$		0			0
$719$	−25.8275	+	7.58365i	−0.963204	+	0.282822i	−0.725274	−	0.688460i	$-0.758287\pi$
$719$	−25.8275	+	7.58365i	−0.963204	+	0.282822i	−0.237930	+	0.971282i	$0.576469\pi$
$720$		0			0
$721$	24.0170	−	15.4348i	0.894441	−	0.574822i
$722$		0			0
$723$	0.588255	−	0.172727i	0.0218774	−	0.00642380i
$724$		0			0
$725$	2.10307	−	4.60508i	0.0781061	−	0.171028i
$726$		0			0
$727$	7.86237	+	9.07366i	0.291599	+	0.336523i	0.882580	−	0.470162i	$-0.155805\pi$
$727$	7.86237	+	9.07366i	0.291599	+	0.336523i	−0.590981	+	0.806686i	$0.701259\pi$
$728$		0			0
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$		0			0
$731$	−28.7228	−	18.4590i	−1.06235	−	0.682731i
$732$		0			0
$733$	22.4757	−	6.59946i	0.830159	−	0.243757i	0.161074	−	0.986942i	$-0.448504\pi$
$733$	22.4757	−	6.59946i	0.830159	−	0.243757i	0.669085	+	0.743186i	$0.266686\pi$
$734$		0			0
$735$	0.800267	+	5.56598i	0.0295183	+	0.205304i
$736$		0			0
$737$	12.0348	+	9.37513i	0.443309	+	0.345337i
$738$		0			0
$739$	−5.71490	−	39.7480i	−0.210226	−	1.46216i	−0.772400	−	0.635136i	$-0.780944\pi$
$739$	−5.71490	−	39.7480i	−0.210226	−	1.46216i	0.562174	−	0.827019i	$-0.309965\pi$
$740$		0			0
$741$	0.580879	−	0.170561i	0.0213391	−	0.00626573i
$742$		0			0
$743$	14.8863	+	9.56685i	0.546126	+	0.350974i	0.784431	−	0.620217i	$-0.212955\pi$
$743$	14.8863	+	9.56685i	0.546126	+	0.350974i	−0.238305	+	0.971190i	$0.576592\pi$
$744$		0			0
$745$	5.19152	+	11.3678i	0.190203	+	0.416485i
$746$		0			0
$747$	−2.89505	−	3.34107i	−0.105924	−	0.122243i
$748$		0			0
$749$	−3.38000	+	7.40117i	−0.123503	+	0.270433i
$750$		0			0
$751$	−21.9252	+	6.43781i	−0.800061	+	0.234919i	−0.656110	−	0.754666i	$-0.727799\pi$
$751$	−21.9252	+	6.43781i	−0.800061	+	0.234919i	−0.143951	+	0.989585i	$0.545981\pi$
$752$		0			0
$753$	3.95550	−	2.54204i	0.144146	−	0.0926372i
$754$		0			0
$755$	−15.9342	+	4.67869i	−0.579904	+	0.170275i
$756$		0			0
$757$	19.3073	−	22.2818i	0.701735	−	0.809846i	−0.287251	−	0.957855i	$-0.592741\pi$
$757$	19.3073	−	22.2818i	0.701735	−	0.809846i	0.988986	+	0.148010i	$0.0472867\pi$
$758$		0			0
$759$	8.41430	+	9.71062i	0.305420	+	0.352473i
$760$		0			0
$761$	−7.94129	−	2.33177i	−0.287872	−	0.0845267i	0.134609	−	0.990899i	$-0.457022\pi$
$761$	−7.94129	−	2.33177i	−0.287872	−	0.0845267i	−0.422480	+	0.906372i	$0.638840\pi$
$762$		0			0
$763$	0.756687	+	0.222183i	0.0273939	+	0.00804358i
$764$		0			0
$765$	3.45330	+	7.56167i	0.124854	+	0.273393i
$766$		0			0
$767$	−1.57762			−0.0569645
$768$		0			0
$769$	13.6241	+	15.7230i	0.491297	+	0.566987i	0.946212	−	0.323548i	$-0.104876\pi$
$769$	13.6241	+	15.7230i	0.491297	+	0.566987i	−0.454915	+	0.890535i	$0.650330\pi$
$770$		0			0
$771$	1.64910	−	11.4697i	0.0593909	−	0.413073i
$772$		0			0
$773$	10.8058	+	23.6615i	0.388659	+	0.851044i	0.998295	+	0.0583628i	$0.0185880\pi$
$773$	10.8058	+	23.6615i	0.388659	+	0.851044i	−0.609637	+	0.792681i	$0.708685\pi$
$774$		0			0
$775$	21.0335			0.755546
$776$		0			0
$777$	2.10415	+	1.35226i	0.0754861	+	0.0485120i
$778$		0			0
$779$	0.704953	−	1.54363i	0.0252575	−	0.0553063i
$780$		0			0
$781$	−6.13028	+	7.07472i	−0.219359	+	0.253153i
$782$		0			0
$783$	−1.45145	−	0.932792i	−0.0518707	−	0.0333353i
$784$		0			0
$785$	−1.42088	+	9.88244i	−0.0507134	+	0.352719i
$786$		0			0
$787$	−3.43598	−	1.00889i	−0.122479	−	0.0359632i	0.219918	−	0.975518i	$-0.429421\pi$
$787$	−3.43598	−	1.00889i	−0.122479	−	0.0359632i	−0.342398	+	0.939555i	$0.611239\pi$
$788$		0			0
$789$	2.94781	−	20.5025i	0.104945	−	0.729908i
$790$		0			0
$791$	−1.02902	+	2.25324i	−0.0365878	+	0.0801161i
$792$		0			0
$793$	0.619502	−	0.398130i	0.0219992	−	0.0141380i
$794$		0			0
$795$	−0.133361	−	0.927547i	−0.00472983	−	0.0328967i
$796$		0			0
$797$	3.11826	+	21.6880i	0.110454	+	0.768228i	0.967479	+	0.252952i	$0.0814014\pi$
$797$	3.11826	+	21.6880i	0.110454	+	0.768228i	−0.857024	+	0.515276i	$0.827690\pi$
$798$		0			0
$799$	−54.9100	+	35.2885i	−1.94258	+	1.24842i
$800$		0			0
$801$	−7.30415	+	8.42944i	−0.258079	+	0.297839i
$802$		0			0
$803$	19.4648			0.686898
$804$		0			0
$805$	−17.4112			−0.613665
$806$		0			0
$807$	−6.04652	+	6.97805i	−0.212847	+	0.245639i
$808$		0			0
$809$	20.6919	−	13.2979i	0.727488	−	0.467528i	−0.123746	−	0.992314i	$-0.539491\pi$
$809$	20.6919	−	13.2979i	0.727488	−	0.467528i	0.851234	+	0.524786i	$0.175855\pi$
$810$		0			0
$811$	−3.91974	−	27.2624i	−0.137641	−	0.957313i	−0.935212	−	0.354088i	$-0.884791\pi$
$811$	−3.91974	−	27.2624i	−0.137641	−	0.957313i	0.797571	−	0.603225i	$-0.206118\pi$
$812$		0			0
$813$	2.62340	+	18.2462i	0.0920068	+	0.639921i
$814$		0			0
$815$	−2.78859	+	1.79212i	−0.0976799	+	0.0627751i
$816$		0			0
$817$	8.06569	−	17.6614i	0.282183	−	0.617894i
$818$		0			0
$819$	−0.0460290	+	0.320139i	−0.00160838	+	0.0111865i
$820$		0			0
$821$	−11.5426	−	3.38921i	−0.402839	−	0.118284i	0.0740353	−	0.997256i	$-0.476412\pi$
$821$	−11.5426	−	3.38921i	−0.402839	−	0.118284i	−0.476875	+	0.878971i	$0.658230\pi$
$822$		0			0
$823$	−5.37161	+	37.3604i	−0.187243	+	1.30230i	0.651865	+	0.758335i	$0.273987\pi$
$823$	−5.37161	+	37.3604i	−0.187243	+	1.30230i	−0.839107	+	0.543966i	$0.816922\pi$
$824$		0			0
$825$	−4.60057	−	2.95661i	−0.160171	−	0.102936i
$826$		0			0
$827$	15.4905	−	17.8770i	0.538656	−	0.621643i	−0.419546	−	0.907734i	$-0.637811\pi$
$827$	15.4905	−	17.8770i	0.538656	−	0.621643i	0.958202	+	0.286091i	$0.0923561\pi$
$828$		0			0
$829$	12.3858	−	27.1211i	0.430177	−	0.941956i	−0.563121	−	0.826374i	$-0.690400\pi$
$829$	12.3858	−	27.1211i	0.430177	−	0.941956i	0.993298	−	0.115582i	$-0.0368732\pi$
$830$		0			0
$831$	11.4847	+	7.38080i	0.398401	+	0.256037i
$832$		0			0
$833$	−22.6286			−0.784033
$834$		0			0
$835$	3.11747	+	6.82630i	0.107884	+	0.236234i
$836$		0			0
$837$	1.02016	−	7.09534i	0.0352617	−	0.245251i
$838$		0			0
$839$	22.9785	+	26.5187i	0.793308	+	0.915526i	0.997994	−	0.0633017i	$-0.0201630\pi$
$839$	22.9785	+	26.5187i	0.793308	+	0.915526i	−0.204687	+	0.978828i	$0.565618\pi$
$840$		0			0
$841$	−26.0232			−0.897351
$842$		0			0
$843$	0.978022	+	2.14157i	0.0336849	+	0.0737596i
$844$		0			0
$845$	17.8810	+	5.25033i	0.615125	+	0.180617i
$846$		0			0
$847$	12.6894	+	3.72593i	0.436011	+	0.128024i
$848$		0			0
$849$	10.1816	+	11.7502i	0.349431	+	0.403264i
$850$		0			0
$851$	6.42644	−	7.41650i	0.220295	−	0.254234i
$852$		0			0
$853$	−29.5493	+	8.67646i	−1.01175	+	0.297076i	−0.745269	−	0.666764i	$-0.767679\pi$
$853$	−29.5493	+	8.67646i	−1.01175	+	0.297076i	−0.266480	+	0.963840i	$0.585861\pi$
$854$		0			0
$855$	−3.97685	+	2.55576i	−0.136005	+	0.0874053i
$856$		0			0
$857$	−52.8280	+	15.5117i	−1.80457	+	0.529869i	−0.998112	−	0.0614240i	$-0.980436\pi$
$857$	−52.8280	+	15.5117i	−1.80457	+	0.529869i	−0.806457	+	0.591293i	$0.798618\pi$
$858$		0			0
$859$	−21.3405	+	46.7292i	−0.728128	+	1.59438i	0.0740226	+	0.997257i	$0.476416\pi$
$859$	−21.3405	+	46.7292i	−0.728128	+	1.59438i	−0.802151	+	0.597122i	$0.796311\pi$
$860$		0			0
$861$	0.593696	+	0.685162i	0.0202331	+	0.0233503i
$862$		0			0
$863$	4.05883	+	8.88759i	0.138164	+	0.302537i	0.966048	−	0.258362i	$-0.0831828\pi$
$863$	4.05883	+	8.88759i	0.138164	+	0.302537i	−0.827884	+	0.560899i	$0.810455\pi$
$864$		0			0
$865$	−5.32848	−	3.42441i	−0.181174	−	0.116433i
$866$		0			0
$867$	−15.7858	+	4.63512i	−0.536113	+	0.157417i
$868$		0			0
$869$	−0.880962	−	6.12723i	−0.0298846	−	0.207852i
$870$		0			0
$871$	1.50046	+	0.136323i	0.0508411	+	0.00461912i
$872$		0			0
$873$	1.28220	+	8.91793i	0.0433960	+	0.301826i
$874$		0			0
$875$	19.2263	−	5.64536i	0.649969	−	0.190848i
$876$		0			0
$877$	17.0844	+	10.9795i	0.576900	+	0.370751i	0.796317	−	0.604880i	$-0.206779\pi$
$877$	17.0844	+	10.9795i	0.576900	+	0.370751i	−0.219416	+	0.975631i	$0.570415\pi$
$878$		0			0
$879$	−5.25835	−	11.5142i	−0.177360	−	0.388364i
$880$		0			0
$881$	−3.38993	−	3.91219i	−0.114210	−	0.131805i	0.695766	−	0.718269i	$-0.255065\pi$
$881$	−3.38993	−	3.91219i	−0.114210	−	0.131805i	−0.809975	+	0.586464i	$0.800520\pi$
$882$		0			0
$883$	−17.8352	+	39.0536i	−0.600202	+	1.31426i	0.328876	+	0.944373i	$0.393330\pi$
$883$	−17.8352	+	39.0536i	−0.600202	+	1.31426i	−0.929077	+	0.369885i	$0.879397\pi$
$884$		0			0
$885$	11.8198	−	3.47062i	0.397320	−	0.116664i
$886$		0			0
$887$	1.22899	−	0.789823i	0.0412654	−	0.0265197i	−0.519845	−	0.854260i	$-0.674010\pi$
$887$	1.22899	−	0.789823i	0.0412654	−	0.0265197i	0.561111	+	0.827741i	$0.310374\pi$
$888$		0			0
$889$	13.7995	−	4.05190i	0.462820	−	0.135896i
$890$		0			0
$891$	−1.22050	+	1.40853i	−0.0408883	+	0.0471876i
$892$		0			0
$893$	−24.3071	−	28.0519i	−0.813406	−	0.938720i
$894$		0			0
$895$	0.0715151	+	0.0209987i	0.00239049	+	0.000701911i
$896$		0			0
$897$	1.21757	+	0.357510i	0.0406534	+	0.0119369i
$898$		0			0
$899$	5.13777	+	11.2501i	0.171354	+	0.375213i
$900$		0			0
$901$	3.77096			0.125629
$902$		0			0
$903$	6.79275	+	7.83925i	0.226049	+	0.260874i
$904$		0			0
$905$	3.19847	−	22.2459i	0.106321	−	0.739478i
$906$		0			0
$907$	11.3089	+	24.7630i	0.375506	+	0.822243i	0.999177	+	0.0405563i	$0.0129130\pi$
$907$	11.3089	+	24.7630i	0.375506	+	0.822243i	−0.623672	+	0.781686i	$0.714360\pi$
$908$		0			0
$909$	−13.2562			−0.439679
$910$		0			0
$911$	−13.6824	−	8.79317i	−0.453319	−	0.291331i	0.293988	−	0.955809i	$-0.405017\pi$
$911$	−13.6824	−	8.79317i	−0.453319	−	0.291331i	−0.747307	+	0.664478i	$0.768654\pi$
$912$		0			0
$913$	3.42278	−	7.49484i	0.113277	−	0.248043i
$914$		0			0
$915$	−3.76559	+	4.34572i	−0.124487	+	0.143665i
$916$		0			0
$917$	−8.56407	−	5.50379i	−0.282811	−	0.181751i
$918$		0			0
$919$	2.31850	−	16.1255i	0.0764802	−	0.531931i	−0.915179	−	0.403047i	$-0.867951\pi$
$919$	2.31850	−	16.1255i	0.0764802	−	0.531931i	0.991660	−	0.128885i	$-0.0411397\pi$
$920$		0			0
$921$	23.9234	+	7.02455i	0.788303	+	0.231467i
$922$		0			0
$923$	−0.131572	+	0.915105i	−0.00433075	+	0.0301210i
$924$		0			0
$925$	−1.73508	+	3.79929i	−0.0570490	+	0.124920i
$926$		0			0
$927$	13.6681	−	8.78398i	0.448921	−	0.288504i
$928$		0			0
$929$	−0.0237808	−	0.165399i	−0.000780223	−	0.00542657i	0.989428	−	0.145028i	$-0.0463271\pi$
$929$	−0.0237808	−	0.165399i	−0.000780223	−	0.00542657i	−0.990208	+	0.139601i	$0.955418\pi$
$930$		0			0
$931$	−1.83133	−	12.7372i	−0.0600194	−	0.417444i
$932$		0			0
$933$	−11.0344	+	7.09137i	−0.361250	+	0.232161i
$934$		0			0
$935$	−10.1459	+	11.7090i	−0.331806	+	0.382925i
$936$		0			0
$937$	23.1949			0.757745			0.378872	−	0.925449i	$-0.376312\pi$
$937$	23.1949			0.757745			0.378872	+	0.925449i	$0.376312\pi$
$938$		0			0
$939$	−10.2481			−0.334435
$940$		0			0
$941$	13.4691	−	15.5441i	0.439079	−	0.506724i	−0.492475	−	0.870326i	$-0.663908\pi$
$941$	13.4691	−	15.5441i	0.439079	−	0.506724i	0.931554	+	0.363602i	$0.118453\pi$
$942$		0			0
$943$	2.99235	−	1.92307i	0.0974444	−	0.0626237i
$944$		0			0
$945$	−0.359418	−	2.49981i	−0.0116919	−	0.0813187i
$946$		0			0
$947$	−1.07324	−	7.46457i	−0.0348757	−	0.242566i	0.964925	−	0.262525i	$-0.0845554\pi$
$947$	−1.07324	−	7.46457i	−0.0348757	−	0.242566i	−0.999801	+	0.0199594i	$0.993646\pi$
$948$		0			0
$949$	1.61718	−	1.03930i	0.0524960	−	0.0337371i
$950$		0			0
$951$	3.46942	−	7.59697i	0.112504	−	0.246348i
$952$		0			0
$953$	1.15067	−	8.00307i	0.0372738	−	0.259245i	−0.962660	−	0.270712i	$-0.912741\pi$
$953$	1.15067	−	8.00307i	0.0372738	−	0.259245i	0.999934	+	0.0114668i	$0.00365008\pi$
$954$		0			0
$955$	−0.260959	−	0.0766244i	−0.00844442	−	0.00247951i
$956$		0			0
$957$	0.457631	−	3.18289i	0.0147931	−	0.102888i
$958$		0			0
$959$	28.6152	+	18.3899i	0.924033	+	0.593840i
$960$		0			0
$961$	−13.3490	+	15.4056i	−0.430614	+	0.496955i
$962$		0			0
$963$	−1.92357	+	4.21202i	−0.0619861	+	0.135731i
$964$		0			0
$965$	24.3338	+	15.6384i	0.783333	+	0.503418i
$966$		0			0
$967$	−17.8601			−0.574343			−0.287171	−	0.957879i	$-0.592715\pi$
$967$	−17.8601			−0.574343			−0.287171	+	0.957879i	$0.592715\pi$
$968$		0			0
$969$	−7.90254	−	17.3041i	−0.253866	−	0.555889i
$970$		0			0
$971$	7.69606	−	53.5273i	0.246978	−	1.71777i	−0.368508	−	0.929625i	$-0.620131\pi$
$971$	7.69606	−	53.5273i	0.246978	−	1.71777i	0.615486	−	0.788148i	$-0.288960\pi$
$972$		0			0
$973$	11.7232	+	13.5293i	0.375829	+	0.433730i
$974$		0			0
$975$	−0.540092			−0.0172968
$976$		0			0
$977$	−11.6137	−	25.4305i	−0.371556	−	0.813593i	−0.999379	−	0.0352373i	$-0.988781\pi$
$977$	−11.6137	−	25.4305i	−0.371556	−	0.813593i	0.627823	−	0.778356i	$-0.283946\pi$
$978$		0			0
$979$	−19.9458	−	5.85662i	−0.637471	−	0.187178i
$980$		0			0
$981$	0.430633	+	0.126445i	0.0137490	+	0.00403708i
$982$		0			0
$983$	−30.6478	−	35.3694i	−0.977512	−	1.12811i	−0.991747	−	0.128211i	$-0.959077\pi$
$983$	−30.6478	−	35.3694i	−0.977512	−	1.12811i	0.0142345	−	0.999899i	$-0.495469\pi$
$984$		0			0
$985$	15.1867	−	17.5264i	0.483889	−	0.558438i
$986$		0			0
$987$	19.0267	−	5.58674i	0.605626	−	0.177828i
$988$		0			0
$989$	34.2369	−	22.0027i	1.08867	−	0.699646i
$990$		0			0
$991$	23.4526	−	6.88631i	0.744997	−	0.218751i	0.112864	−	0.993610i	$-0.463998\pi$
$991$	23.4526	−	6.88631i	0.744997	−	0.218751i	0.632133	+	0.774860i	$0.282180\pi$
$992$		0			0
$993$	−8.61808	+	18.8710i	−0.273486	+	0.598852i
$994$		0			0
$995$	18.2727	+	21.0878i	0.579284	+	0.668529i
$996$		0			0
$997$	−16.6815	−	36.5275i	−0.528310	−	1.15684i	−0.966196	−	0.257807i	$-0.917000\pi$
$997$	−16.6815	−	36.5275i	−0.528310	−	1.15684i	0.437887	−	0.899030i	$-0.355727\pi$
$998$		0			0
$999$	1.19748	+	0.769573i	0.0378866	+	0.0243482i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.q.a.25.5	✓	60
67.59	even	11	inner	804.2.q.a.193.5	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.q.a.25.5	✓	60	1.1	even	1	trivial
804.2.q.a.193.5	yes	60	67.59	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654861 + 0.755750i) q^{3} +(1.20911 - 0.777049i) q^{5} +(-0.250069 - 1.73927i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.654861 + 0.755750i) q^{3} +(1.20911 - 0.777049i) q^{5} +(-0.250069 - 1.73927i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(1.56789 - 1.00762i) q^{11} +(0.0764634 - 0.167432i) q^{13} +(-0.204546 + 1.42265i) q^{15} +(-5.54950 - 1.62948i) q^{17} +(0.468082 - 3.25558i) q^{19} +(1.47821 + 0.949989i) q^{21} +(4.51470 - 5.21024i) q^{23} +(-1.21893 + 2.66908i) q^{25} +(0.841254 + 0.540641i) q^{27} -1.72534 q^{29} +(-2.97782 - 6.52052i) q^{31} +(-0.265240 + 1.84479i) q^{33} +(-1.65386 - 1.90865i) q^{35} +1.42345 q^{37} +(0.0764634 + 0.167432i) q^{39} +(0.495048 + 0.145359i) q^{41} +(5.66408 + 1.66312i) q^{43} +(-0.941215 - 1.08622i) q^{45} +(7.39028 - 8.52884i) q^{47} +(3.75393 - 1.10225i) q^{49} +(4.86563 - 3.12695i) q^{51} +(-0.625578 + 0.183686i) q^{53} +(1.11278 - 2.43666i) q^{55} +(2.15388 + 2.48571i) q^{57} +(-3.56051 - 7.79643i) q^{59} +(3.36567 + 2.16298i) q^{61} +(-1.68598 + 0.495047i) q^{63} +(-0.0376497 - 0.261859i) q^{65} +(2.71268 + 7.72278i) q^{67} +(0.981139 + 6.82397i) q^{69} +(-4.81930 + 1.41507i) q^{71} +(8.78593 + 5.64637i) q^{73} +(-1.21893 - 2.66908i) q^{75} +(-2.14461 - 2.47501i) q^{77} +(1.37975 - 3.02123i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(3.71907 - 2.39010i) q^{83} +(-7.97616 + 2.34201i) q^{85} +(1.12986 - 1.30393i) q^{87} +(-7.30415 - 8.42944i) q^{89} +(-0.310329 - 0.0911209i) q^{91} +(6.87793 + 2.01954i) q^{93} +(-1.96379 - 4.30009i) q^{95} -9.00963 q^{97} +(-1.22050 - 1.40853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9}+O(q^{10}) \) 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9	\( 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9} + 7 q^{11} - 2 q^{13} + 9 q^{15} - 19 q^{17} + 2 q^{19} - 2 q^{21} + 4 q^{23} + 16 q^{25} - 6 q^{27} + 16 q^{29} - 28 q^{31} - 4 q^{33} + 28 q^{35} + 2 q^{37} - 2 q^{39} + 32 q^{41} + 19 q^{43} - 2 q^{45} + 2 q^{47} - 70 q^{49} - 19 q^{51} + 31 q^{53} - 5 q^{55} + 13 q^{57} + 59 q^{59} + 32 q^{61} + 9 q^{63} + 28 q^{65} + 7 q^{67} + 4 q^{69} + 16 q^{71} + 19 q^{73} + 16 q^{75} - 46 q^{77} + 48 q^{79} - 6 q^{81} + 60 q^{83} - 66 q^{85} + 5 q^{87} - 22 q^{89} + 24 q^{91} + 5 q^{93} + 103 q^{95} - 46 q^{97} - 4 q^{99}+O(q^{100}) \) 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9 + 7 * q^11 - 2 * q^13 + 9 * q^15 - 19 * q^17 + 2 * q^19 - 2 * q^21 + 4 * q^23 + 16 * q^25 - 6 * q^27 + 16 * q^29 - 28 * q^31 - 4 * q^33 + 28 * q^35 + 2 * q^37 - 2 * q^39 + 32 * q^41 + 19 * q^43 - 2 * q^45 + 2 * q^47 - 70 * q^49 - 19 * q^51 + 31 * q^53 - 5 * q^55 + 13 * q^57 + 59 * q^59 + 32 * q^61 + 9 * q^63 + 28 * q^65 + 7 * q^67 + 4 * q^69 + 16 * q^71 + 19 * q^73 + 16 * q^75 - 46 * q^77 + 48 * q^79 - 6 * q^81 + 60 * q^83 - 66 * q^85 + 5 * q^87 - 22 * q^89 + 24 * q^91 + 5 * q^93 + 103 * q^95 - 46 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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