LMFDB - Embedded newform 804.2.y.b.169.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(49,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 46]))

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

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

chi := DirichletCharacter("804.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.y (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			169.2
Character	$\chi$	$=$	804.169
Dual form			804.2.y.b.157.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{3} +(-1.19502 + 2.61673i) q^{5} +(-1.34977 - 1.28701i) q^{7} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{3} +(-1.19502 + 2.61673i) q^{5} +(-1.34977 - 1.28701i) q^{7} +(-0.959493 + 0.281733i) q^{9} +(-4.03738 + 0.385523i) q^{11} +(4.55479 - 0.877865i) q^{13} +(-2.76016 - 0.810456i) q^{15} +(-4.03473 + 2.08005i) q^{17} +(0.436555 - 0.416254i) q^{19} +(1.08181 - 1.51919i) q^{21} +(-4.41195 - 1.76628i) q^{23} +(-2.14488 - 2.47533i) q^{25} +(-0.415415 - 0.909632i) q^{27} +(-0.934423 - 1.61847i) q^{29} +(-8.97739 - 1.73025i) q^{31} +(-0.956177 - 3.94142i) q^{33} +(4.98075 - 1.99399i) q^{35} +(-2.34904 + 4.06866i) q^{37} +(1.51714 + 4.38350i) q^{39} +(0.430155 - 9.03006i) q^{41} +(3.06430 + 1.96930i) q^{43} +(0.409395 - 2.84741i) q^{45} +(6.26934 - 4.93026i) q^{47} +(-0.167571 - 3.51774i) q^{49} +(-2.63308 - 3.69764i) q^{51} +(-8.74113 + 5.61758i) q^{53} +(3.81593 - 11.0254i) q^{55} +(0.474145 + 0.372872i) q^{57} +(-7.56473 + 8.73016i) q^{59} +(7.89708 + 0.754080i) q^{61} +(1.65769 + 0.854598i) q^{63} +(-3.14593 + 12.9677i) q^{65} +(-4.96592 - 6.50689i) q^{67} +(1.12041 - 4.61841i) q^{69} +(1.67654 + 0.864316i) q^{71} +(-1.31904 - 0.125953i) q^{73} +(2.14488 - 2.47533i) q^{75} +(5.94571 + 4.67576i) q^{77} +(-3.04218 + 8.78980i) q^{79} +(0.841254 - 0.540641i) q^{81} +(2.64677 + 3.71687i) q^{83} +(-0.621337 - 13.0435i) q^{85} +(1.46901 - 1.15524i) q^{87} +(-1.52653 + 10.6173i) q^{89} +(-7.27776 - 4.67713i) q^{91} +(0.435023 - 9.13225i) q^{93} +(0.567532 + 1.63978i) q^{95} +(-6.97677 + 12.0841i) q^{97} +(3.76522 - 1.50737i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{19}{33}\right)$	$1$

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
$3$	0.142315	+	0.989821i	0.0821655	+	0.571474i
$3$	0.142315	+	0.989821i	0.0821655	+	0.571474i
$4$		0			0
$5$	−1.19502	+	2.61673i	−0.534429	+	1.17024i	0.429254	+	0.903184i	$0.358777\pi$
$5$	−1.19502	+	2.61673i	−0.534429	+	1.17024i	−0.963682	+	0.267052i	$0.913951\pi$
$6$		0			0
$7$	−1.34977	−	1.28701i	−0.510166	−	0.486443i	0.390713	−	0.920513i	$-0.372229\pi$
$7$	−1.34977	−	1.28701i	−0.510166	−	0.486443i	−0.900879	+	0.434070i	$0.857077\pi$
$8$		0			0
$9$	−0.959493	+	0.281733i	−0.319831	+	0.0939109i
$10$		0			0
$11$	−4.03738	+	0.385523i	−1.21731	+	0.116239i	−0.683875	−	0.729599i	$-0.739707\pi$
$11$	−4.03738	+	0.385523i	−1.21731	+	0.116239i	−0.533439	+	0.845838i	$0.679101\pi$
$12$		0			0
$13$	4.55479	−	0.877865i	1.26327	−	0.243476i	0.486737	−	0.873549i	$-0.338187\pi$
$13$	4.55479	−	0.877865i	1.26327	−	0.243476i	0.776536	+	0.630073i	$0.216975\pi$
$14$		0			0
$15$	−2.76016	−	0.810456i	−0.712670	−	0.209259i
$16$		0			0
$17$	−4.03473	+	2.08005i	−0.978565	+	0.504486i	−0.871834	−	0.489802i	$-0.837069\pi$
$17$	−4.03473	+	2.08005i	−0.978565	+	0.504486i	−0.106732	+	0.994288i	$0.534039\pi$
$18$		0			0
$19$	0.436555	−	0.416254i	0.100152	−	0.0954952i	−0.638349	−	0.769747i	$-0.720382\pi$
$19$	0.436555	−	0.416254i	0.100152	−	0.0954952i	0.738501	+	0.674252i	$0.235534\pi$
$20$		0			0
$21$	1.08181	−	1.51919i	0.236071	−	0.331515i
$22$		0			0
$23$	−4.41195	−	1.76628i	−0.919956	−	0.368295i	−0.137142	−	0.990551i	$-0.543792\pi$
$23$	−4.41195	−	1.76628i	−0.919956	−	0.368295i	−0.782813	+	0.622257i	$0.786216\pi$
$24$		0			0
$25$	−2.14488	−	2.47533i	−0.428977	−	0.495065i
$26$		0			0
$27$	−0.415415	−	0.909632i	−0.0799467	−	0.175059i
$28$		0			0
$29$	−0.934423	−	1.61847i	−0.173518	−	0.300542i	0.766129	−	0.642686i	$-0.222180\pi$
$29$	−0.934423	−	1.61847i	−0.173518	−	0.300542i	−0.939647	+	0.342144i	$0.888847\pi$
$30$		0			0
$31$	−8.97739	−	1.73025i	−1.61239	−	0.310762i	−0.698152	−	0.715949i	$-0.745994\pi$
$31$	−8.97739	−	1.73025i	−1.61239	−	0.310762i	−0.914234	+	0.405187i	$0.867206\pi$
$32$		0			0
$33$	−0.956177	−	3.94142i	−0.166449	−	0.686113i
$34$		0			0
$35$	4.98075	−	1.99399i	0.841900	−	0.337046i
$36$		0			0
$37$	−2.34904	+	4.06866i	−0.386180	+	0.668883i	−0.991932	−	0.126770i	$-0.959539\pi$
$37$	−2.34904	+	4.06866i	−0.386180	+	0.668883i	0.605752	+	0.795653i	$0.292872\pi$
$38$		0			0
$39$	1.51714	+	4.38350i	0.242937	+	0.701922i
$40$		0			0
$41$	0.430155	−	9.03006i	0.0671789	−	1.41026i	−0.673891	−	0.738831i	$-0.735378\pi$
$41$	0.430155	−	9.03006i	0.0671789	−	1.41026i	0.741070	−	0.671428i	$-0.234319\pi$
$42$		0			0
$43$	3.06430	+	1.96930i	0.467301	+	0.300316i	0.753020	−	0.657997i	$-0.228596\pi$
$43$	3.06430	+	1.96930i	0.467301	+	0.300316i	−0.285720	+	0.958313i	$0.592233\pi$
$44$		0			0
$45$	0.409395	−	2.84741i	0.0610290	−	0.424466i
$46$		0			0
$47$	6.26934	−	4.93026i	0.914478	−	0.719153i	−0.0455786	−	0.998961i	$-0.514513\pi$
$47$	6.26934	−	4.93026i	0.914478	−	0.719153i	0.960056	+	0.279808i	$0.0902707\pi$
$48$		0			0
$49$	−0.167571	−	3.51774i	−0.0239386	−	0.502534i
$50$		0			0
$51$	−2.63308	−	3.69764i	−0.368705	−	0.517773i
$52$		0			0
$53$	−8.74113	+	5.61758i	−1.20069	+	0.771635i	−0.979075	−	0.203500i	$-0.934768\pi$
$53$	−8.74113	+	5.61758i	−1.20069	+	0.771635i	−0.221612	+	0.975135i	$0.571132\pi$
$54$		0			0
$55$	3.81593	−	11.0254i	0.514540	−	1.48667i
$56$		0			0
$57$	0.474145	+	0.372872i	0.0628021	+	0.0493881i
$58$		0			0
$59$	−7.56473	+	8.73016i	−0.984843	+	1.13657i	0.00578483	+	0.999983i	$0.498159\pi$
$59$	−7.56473	+	8.73016i	−0.984843	+	1.13657i	−0.990628	+	0.136587i	$0.956387\pi$
$60$		0			0
$61$	7.89708	+	0.754080i	1.01112	+	0.0965500i	0.587444	−	0.809265i	$-0.300134\pi$
$61$	7.89708	+	0.754080i	1.01112	+	0.0965500i	0.423674	+	0.905815i	$0.360740\pi$
$62$		0			0
$63$	1.65769	+	0.854598i	0.208849	+	0.107669i
$64$		0			0
$65$	−3.14593	+	12.9677i	−0.390205	+	1.60845i
$66$		0			0
$67$	−4.96592	−	6.50689i	−0.606683	−	0.794944i
$67$	−4.96592	−	6.50689i	−0.606683	−	0.794944i
$68$		0			0
$69$	1.12041	−	4.61841i	0.134882	−	0.555992i
$70$		0			0
$71$	1.67654	+	0.864316i	0.198969	+	0.102575i	0.554832	−	0.831963i	$-0.312783\pi$
$71$	1.67654	+	0.864316i	0.198969	+	0.102575i	−0.355863	+	0.934538i	$0.615813\pi$
$72$		0			0
$73$	−1.31904	−	0.125953i	−0.154382	−	0.0147417i	0.0175788	−	0.999845i	$-0.494404\pi$
$73$	−1.31904	−	0.125953i	−0.154382	−	0.0147417i	−0.171961	+	0.985104i	$0.555010\pi$
$74$		0			0
$75$	2.14488	−	2.47533i	0.247670	−	0.285826i
$76$		0			0
$77$	5.94571	+	4.67576i	0.677577	+	0.532852i
$78$		0			0
$79$	−3.04218	+	8.78980i	−0.342272	+	0.988929i	0.634179	+	0.773187i	$0.281338\pi$
$79$	−3.04218	+	8.78980i	−0.342272	+	0.988929i	−0.976450	+	0.215743i	$0.930783\pi$
$80$		0			0
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$		0			0
$83$	2.64677	+	3.71687i	0.290521	+	0.407980i	0.933881	−	0.357584i	$-0.116399\pi$
$83$	2.64677	+	3.71687i	0.290521	+	0.407980i	−0.643360	+	0.765564i	$0.722460\pi$
$84$		0			0
$85$	−0.621337	−	13.0435i	−0.0673935	−	1.41476i
$86$		0			0
$87$	1.46901	−	1.15524i	0.157495	−	0.123855i
$88$		0			0
$89$	−1.52653	+	10.6173i	−0.161812	+	1.12543i	0.733403	+	0.679794i	$0.237931\pi$
$89$	−1.52653	+	10.6173i	−0.161812	+	1.12543i	−0.895215	+	0.445635i	$0.852978\pi$
$90$		0			0
$91$	−7.27776	−	4.67713i	−0.762916	−	0.490296i
$92$		0			0
$93$	0.435023	−	9.13225i	0.0451097	−	0.946970i
$94$		0			0
$95$	0.567532	+	1.63978i	0.0582275	+	0.168237i
$96$		0			0
$97$	−6.97677	+	12.0841i	−0.708383	+	1.22696i	0.257073	+	0.966392i	$0.417242\pi$
$97$	−6.97677	+	12.0841i	−0.708383	+	1.22696i	−0.965457	+	0.260564i	$0.916092\pi$
$98$		0			0
$99$	3.76522	−	1.50737i	0.378419	−	0.151496i
$100$		0			0
$101$	2.21161	+	9.11638i	0.220063	+	0.907114i	0.969511	+	0.245050i	$0.0788042\pi$
$101$	2.21161	+	9.11638i	0.220063	+	0.907114i	−0.749447	+	0.662064i	$0.769681\pi$
$102$		0			0
$103$	−9.31730	−	1.79576i	−0.918061	−	0.176942i	−0.291732	−	0.956500i	$-0.594231\pi$
$103$	−9.31730	−	1.79576i	−0.918061	−	0.176942i	−0.626329	+	0.779558i	$0.715444\pi$
$104$		0			0
$105$	2.68253	+	4.64628i	0.261788	+	0.453430i
$106$		0			0
$107$	−0.578222	−	1.26613i	−0.0558989	−	0.122401i	0.879621	−	0.475674i	$-0.157796\pi$
$107$	−0.578222	−	1.26613i	−0.0558989	−	0.122401i	−0.935520	+	0.353273i	$0.885069\pi$
$108$		0			0
$109$	4.92924	+	5.68865i	0.472136	+	0.544874i	0.941005	−	0.338394i	$-0.109884\pi$
$109$	4.92924	+	5.68865i	0.472136	+	0.544874i	−0.468869	+	0.883268i	$0.655338\pi$
$110$		0			0
$111$	−4.36155	−	1.74610i	−0.413980	−	0.165732i
$112$		0			0
$113$	−3.30446	+	4.64046i	−0.310857	+	0.436538i	−0.940217	−	0.340576i	$-0.889378\pi$
$113$	−3.30446	+	4.64046i	−0.310857	+	0.436538i	0.629360	+	0.777114i	$0.283317\pi$
$114$		0			0
$115$	9.89424	−	9.43414i	0.922642	−	0.879738i
$116$		0			0
$117$	−4.12297	+	2.12554i	−0.381169	+	0.196506i
$118$		0			0
$119$	8.12300	+	2.38513i	0.744634	+	0.218644i
$120$		0			0
$121$	5.35057	−	1.03124i	0.486415	−	0.0937489i
$122$		0			0
$123$	8.99937	−	0.859335i	0.811445	−	0.0774836i
$124$		0			0
$125$	−4.76037	+	1.39777i	−0.425781	+	0.125021i
$126$		0			0
$127$	9.12722	+	8.70278i	0.809909	+	0.772247i	0.976897	−	0.213712i	$-0.0685554\pi$
$127$	9.12722	+	8.70278i	0.809909	+	0.772247i	−0.166987	+	0.985959i	$0.553404\pi$
$128$		0			0
$129$	−1.51316	+	3.31337i	−0.133227	+	0.291726i
$130$		0			0
$131$	−1.66634	−	11.5897i	−0.145589	−	1.01259i	−0.923330	−	0.384008i	$-0.874543\pi$
$131$	−1.66634	−	11.5897i	−0.145589	−	1.01259i	0.777741	−	0.628585i	$-0.216366\pi$
$132$		0			0
$133$	−1.12497			−0.0975474
$134$		0			0
$135$	2.87669			0.247586
$136$		0			0
$137$	2.41103	+	16.7691i	0.205989	+	1.43268i	0.786077	+	0.618128i	$0.212109\pi$
$137$	2.41103	+	16.7691i	0.205989	+	1.43268i	−0.580089	+	0.814553i	$0.696982\pi$
$138$		0			0
$139$	4.50079	−	9.85536i	0.381752	−	0.835921i	−0.617047	−	0.786926i	$-0.711671\pi$
$139$	4.50079	−	9.85536i	0.381752	−	0.835921i	0.998799	−	0.0489942i	$-0.0156016\pi$
$140$		0			0
$141$	5.77230	+	5.50388i	0.486116	+	0.463510i
$142$		0			0
$143$	−18.0510	+	5.30025i	−1.50950	+	0.443229i
$144$		0			0
$145$	5.35174	−	0.511029i	0.444438	−	0.0424387i
$146$		0			0
$147$	3.45809	−	0.666491i	0.285218	−	0.0549713i
$148$		0			0
$149$	18.2670	+	5.36368i	1.49649	+	0.439410i	0.924607	−	0.380923i	$-0.124394\pi$
$149$	18.2670	+	5.36368i	1.49649	+	0.439410i	0.571886	+	0.820333i	$0.306212\pi$
$150$		0			0
$151$	−21.0271	+	10.8402i	−1.71116	+	0.882164i	−0.731408	+	0.681940i	$0.761137\pi$
$151$	−21.0271	+	10.8402i	−1.71116	+	0.882164i	−0.979750	+	0.200224i	$0.935833\pi$
$152$		0			0
$153$	3.28528	−	3.13251i	0.265599	−	0.253248i
$154$		0			0
$155$	15.2557	−	21.4237i	1.22537	−	1.72079i
$156$		0			0
$157$	15.1716	+	6.07380i	1.21083	+	0.484742i	0.887174	−	0.461434i	$-0.152665\pi$
$157$	15.1716	+	6.07380i	1.21083	+	0.484742i	0.323652	+	0.946176i	$0.395089\pi$
$158$		0			0
$159$	−6.80440	−	7.85269i	−0.539624	−	0.622759i
$160$		0			0
$161$	3.68192	+	8.06229i	0.290176	+	0.635397i
$162$		0			0
$163$	−9.70461	−	16.8089i	−0.760124	−	1.31657i	−0.942786	−	0.333397i	$-0.891805\pi$
$163$	−9.70461	−	16.8089i	−0.760124	−	1.31657i	0.182663	−	0.983176i	$-0.441528\pi$
$164$		0			0
$165$	11.4563	+	2.20801i	0.891869	+	0.171894i
$166$		0			0
$167$	0.931492	+	3.83966i	0.0720810	+	0.297122i	0.996430	−	0.0844269i	$-0.0269060\pi$
$167$	0.931492	+	3.83966i	0.0720810	+	0.297122i	−0.924349	+	0.381549i	$0.875391\pi$
$168$		0			0
$169$	7.90672	−	3.16537i	0.608209	−	0.243490i
$170$		0			0
$171$	−0.301599	+	0.522384i	−0.0230638	+	0.0399477i
$172$		0			0
$173$	−1.67945	−	4.85245i	−0.127686	−	0.368925i	0.862979	−	0.505239i	$-0.168596\pi$
$173$	−1.67945	−	4.85245i	−0.127686	−	0.368925i	−0.990666	+	0.136314i	$0.956474\pi$
$174$		0			0
$175$	−0.290655	+	6.10161i	−0.0219715	+	0.461238i
$176$		0			0
$177$	−9.71787	−	6.24530i	−0.730440	−	0.469425i
$178$		0			0
$179$	1.42366	−	9.90179i	0.106410	−	0.740094i	−0.864843	−	0.502042i	$-0.832582\pi$
$179$	1.42366	−	9.90179i	0.106410	−	0.740094i	0.971252	−	0.238052i	$-0.0765088\pi$
$180$		0			0
$181$	−13.6389	+	10.7257i	−1.01377	+	0.797238i	−0.979350	−	0.202170i	$-0.935201\pi$
$181$	−13.6389	+	10.7257i	−1.01377	+	0.797238i	−0.0344197	+	0.999407i	$0.510958\pi$
$182$		0			0
$183$	0.377467	+	7.92402i	0.0279032	+	0.585760i
$184$		0			0
$185$	−7.83941	−	11.0089i	−0.576365	−	0.809392i
$186$		0			0
$187$	15.4878	−	9.95341i	1.13258	−	0.727866i
$188$		0			0
$189$	−0.609986	+	1.76244i	−0.0443699	+	0.128199i
$190$		0			0
$191$	14.5778	+	11.4641i	1.05481	+	0.829512i	0.985770	−	0.168102i	$-0.0537637\pi$
$191$	14.5778	+	11.4641i	1.05481	+	0.829512i	0.0690409	+	0.997614i	$0.478006\pi$
$192$		0			0
$193$	5.94841	−	6.86483i	0.428176	−	0.494141i	−0.500135	−	0.865948i	$-0.666716\pi$
$193$	5.94841	−	6.86483i	0.428176	−	0.494141i	0.928310	+	0.371807i	$0.121262\pi$
$194$		0			0
$195$	−13.2834	−	1.26841i	−0.951246	−	0.0908330i
$196$		0			0
$197$	−3.04557	−	1.57010i	−0.216988	−	0.111865i	0.346306	−	0.938122i	$-0.387436\pi$
$197$	−3.04557	−	1.57010i	−0.216988	−	0.111865i	−0.563294	+	0.826257i	$0.690466\pi$
$198$		0			0
$199$	1.56994	−	6.47140i	0.111290	−	0.458745i	−0.888710	−	0.458471i	$-0.848397\pi$
$199$	1.56994	−	6.47140i	0.111290	−	0.458745i	1.00000		0.000274706i	$-8.74415e-5\pi$
$200$		0			0
$201$	5.73394	−	5.84140i	0.404441	−	0.412021i
$202$		0			0
$203$	−0.821719	+	3.38717i	−0.0576734	+	0.237733i
$204$		0			0
$205$	23.1152	+	11.9167i	1.61443	+	0.832298i
$206$		0			0
$207$	4.73086	+	0.451742i	0.328817	+	0.0313982i
$208$		0			0
$209$	−1.60206	+	1.84888i	−0.110817	+	0.127889i
$210$		0			0
$211$	5.85986	+	4.60825i	0.403410	+	0.317245i	0.799166	−	0.601111i	$-0.205275\pi$
$211$	5.85986	+	4.60825i	0.403410	+	0.317245i	−0.395756	+	0.918356i	$0.629517\pi$
$212$		0			0
$213$	−0.616922	+	1.78248i	−0.0422708	+	0.122133i
$214$		0			0
$215$	−8.81502	+	5.66507i	−0.601179	+	0.386354i
$216$		0			0
$217$	9.89059	+	13.8894i	0.671417	+	0.942874i
$218$		0			0
$219$	−0.0630480	−	1.32354i	−0.00426039	−	0.0894365i
$220$		0			0
$221$	−16.5514	+	13.0161i	−1.11336	+	0.875560i
$222$		0			0
$223$	−2.09690	+	14.5842i	−0.140418	+	0.976632i	0.790775	+	0.612107i	$0.209678\pi$
$223$	−2.09690	+	14.5842i	−0.140418	+	0.976632i	−0.931194	+	0.364525i	$0.881231\pi$
$224$		0			0
$225$	2.75538	+	1.77078i	0.183692	+	0.118052i
$226$		0			0
$227$	0.248861	−	5.22424i	0.0165175	−	0.346745i	−0.975447	−	0.220232i	$-0.929318\pi$
$227$	0.248861	−	5.22424i	0.0165175	−	0.346745i	0.991965	−	0.126513i	$-0.0403785\pi$
$228$		0			0
$229$	1.70756	+	4.93367i	0.112839	+	0.326026i	0.987254	−	0.159152i	$-0.0508760\pi$
$229$	1.70756	+	4.93367i	0.112839	+	0.326026i	−0.874415	+	0.485178i	$0.838755\pi$
$230$		0			0
$231$	−3.78200	+	6.55062i	−0.248838	+	0.430999i
$232$		0			0
$233$	18.8674	−	7.55336i	1.23604	−	0.494837i	0.340682	−	0.940179i	$-0.389342\pi$
$233$	18.8674	−	7.55336i	1.23604	−	0.494837i	0.895361	+	0.445342i	$0.146918\pi$
$234$		0			0
$235$	5.40917	+	22.2969i	0.352856	+	1.45449i
$236$		0			0
$237$	−9.13327	−	1.76029i	−0.593270	−	0.114343i
$238$		0			0
$239$	3.93905	+	6.82263i	0.254796	+	0.441319i	0.964840	−	0.262838i	$-0.0846585\pi$
$239$	3.93905	+	6.82263i	0.254796	+	0.441319i	−0.710044	+	0.704157i	$0.751325\pi$
$240$		0			0
$241$	−7.78131	−	17.0387i	−0.501238	−	1.09756i	−0.976065	−	0.217479i	$-0.930217\pi$
$241$	−7.78131	−	17.0387i	−0.501238	−	1.09756i	0.474827	−	0.880079i	$-0.342511\pi$
$242$		0			0
$243$	0.654861	+	0.755750i	0.0420093	+	0.0484814i
$244$		0			0
$245$	9.40521	+	3.76528i	0.600877	+	0.240555i
$246$		0			0
$247$	1.62300	−	2.27919i	0.103269	−	0.145021i
$248$		0			0
$249$	−3.30236	+	3.14880i	−0.209279	+	0.199547i
$250$		0			0
$251$	−11.4912	+	5.92415i	−0.725321	+	0.373929i	−0.781009	−	0.624519i	$-0.785295\pi$
$251$	−11.4912	+	5.92415i	−0.725321	+	0.373929i	0.0556884	+	0.998448i	$0.482265\pi$
$252$		0			0
$253$	18.4937	+	5.43023i	1.16269	+	0.341395i
$254$		0			0
$255$	12.8223	−	2.47129i	0.802963	−	0.154758i
$256$		0			0
$257$	6.35637	−	0.606960i	0.396500	−	0.0378611i	0.105098	−	0.994462i	$-0.466484\pi$
$257$	6.35637	−	0.606960i	0.396500	−	0.0378611i	0.291402	+	0.956601i	$0.405878\pi$
$258$		0			0
$259$	8.40706	−	2.46853i	0.522389	−	0.153387i
$260$		0			0
$261$	1.35255	+	1.28965i	0.0837206	+	0.0798274i
$262$		0			0
$263$	4.17725	−	9.14690i	0.257580	−	0.564022i	−0.736022	−	0.676958i	$-0.763298\pi$
$263$	4.17725	−	9.14690i	0.257580	−	0.564022i	0.993602	+	0.112935i	$0.0360253\pi$
$264$		0			0
$265$	−4.25386	−	29.5863i	−0.261313	−	1.81747i
$266$		0			0
$267$	−10.7265			−0.656448
$268$		0			0
$269$	−7.24161			−0.441529			−0.220764	−	0.975327i	$-0.570855\pi$
$269$	−7.24161			−0.441529			−0.220764	+	0.975327i	$0.570855\pi$
$270$		0			0
$271$	4.34254	+	30.2030i	0.263791	+	1.83470i	0.503663	+	0.863900i	$0.331985\pi$
$271$	4.34254	+	30.2030i	0.263791	+	1.83470i	−0.239873	+	0.970804i	$0.577106\pi$
$272$		0			0
$273$	3.59379	−	7.86930i	0.217506	−	0.476272i
$274$		0			0
$275$	9.61400	+	9.16693i	0.579746	+	0.552787i
$276$		0			0
$277$	4.54685	−	1.33508i	0.273194	−	0.0802169i	−0.142266	−	0.989828i	$-0.545439\pi$
$277$	4.54685	−	1.33508i	0.273194	−	0.0802169i	0.415460	+	0.909612i	$0.363621\pi$
$278$		0			0
$279$	9.10121	−	0.869060i	0.544875	−	0.0520292i
$280$		0			0
$281$	−5.18852	+	1.00000i	−0.309521	+	0.0596553i	−0.341646	−	0.939829i	$-0.610985\pi$
$281$	−5.18852	+	1.00000i	−0.309521	+	0.0596553i	0.0321254	+	0.999484i	$0.489772\pi$
$282$		0			0
$283$	−20.4236	−	5.99690i	−1.21406	−	0.356479i	−0.388844	−	0.921304i	$-0.627126\pi$
$283$	−20.4236	−	5.99690i	−1.21406	−	0.356479i	−0.825211	+	0.564825i	$0.808944\pi$
$284$		0			0
$285$	−1.54232	+	0.795119i	−0.0913590	+	0.0470988i
$286$		0			0
$287$	−12.2024	+	11.6349i	−0.720282	+	0.686788i
$288$		0			0
$289$	2.09147	−	2.93706i	0.123028	−	0.172768i
$290$		0			0
$291$	−12.9540	−	5.18600i	−0.759378	−	0.304009i
$292$		0			0
$293$	−7.67437	−	8.85670i	−0.448342	−	0.517414i	0.485919	−	0.874004i	$-0.338485\pi$
$293$	−7.67437	−	8.85670i	−0.448342	−	0.517414i	−0.934261	+	0.356590i	$0.883939\pi$
$294$		0			0
$295$	−13.8044	−	30.2275i	−0.803726	−	1.75991i
$296$		0			0
$297$	2.02787	+	3.51238i	0.117669	+	0.203809i
$298$		0			0
$299$	−21.6461	−	4.17194i	−1.25183	−	0.241270i
$300$		0			0
$301$	−1.60160	−	6.60188i	−0.0923146	−	0.380526i
$302$		0			0
$303$	−8.70884	+	3.48650i	−0.500310	+	0.200294i
$304$		0			0
$305$	−11.4104	+	19.7634i	−0.653357	+	1.13165i
$306$		0			0
$307$	−6.21136	−	17.9465i	−0.354501	−	1.02426i	−0.971447	−	0.237258i	$-0.923751\pi$
$307$	−6.21136	−	17.9465i	−0.354501	−	1.02426i	0.616946	−	0.787006i	$-0.288370\pi$
$308$		0			0
$309$	0.451494	−	9.47803i	0.0256846	−	0.539186i
$310$		0			0
$311$	0.870718	+	0.559577i	0.0493739	+	0.0317307i	0.565095	−	0.825026i	$-0.308840\pi$
$311$	0.870718	+	0.559577i	0.0493739	+	0.0317307i	−0.515721	+	0.856757i	$0.672476\pi$
$312$		0			0
$313$	3.81862	−	26.5591i	0.215841	−	1.50121i	−0.537324	−	0.843376i	$-0.680565\pi$
$313$	3.81862	−	26.5591i	0.215841	−	1.50121i	0.753165	−	0.657832i	$-0.228526\pi$
$314$		0			0
$315$	−4.21722	+	3.31646i	−0.237613	+	0.186861i
$316$		0			0
$317$	−1.50358	−	31.5640i	−0.0844494	−	1.77281i	−0.502683	−	0.864471i	$-0.667654\pi$
$317$	−1.50358	−	31.5640i	−0.0844494	−	1.77281i	0.418234	−	0.908340i	$-0.362649\pi$
$318$		0			0
$319$	4.39657	+	6.17412i	0.246161	+	0.345684i
$320$		0			0
$321$	1.17095	−	0.752526i	0.0653562	−	0.0420019i
$322$		0			0
$323$	−0.895552	+	2.58753i	−0.0498298	+	0.143974i
$324$		0			0
$325$	−11.9425	−	9.39169i	−0.662451	−	0.520957i
$326$		0			0
$327$	−4.92924	+	5.68865i	−0.272588	+	0.314583i
$328$		0			0
$329$	−14.8075	−	1.41394i	−0.816362	−	0.0779531i
$330$		0			0
$331$	−2.09251	−	1.07876i	−0.115015	−	0.0592941i	0.399759	−	0.916620i	$-0.369094\pi$
$331$	−2.09251	−	1.07876i	−0.115015	−	0.0592941i	−0.514774	+	0.857326i	$0.672124\pi$
$332$		0			0
$333$	1.10761	−	4.56565i	0.0606969	−	0.250196i
$334$		0			0
$335$	22.9611	−	5.21859i	1.25450	−	0.285122i
$336$		0			0
$337$	−4.41376	+	18.1938i	−0.240433	+	0.991077i	0.715762	+	0.698345i	$0.246080\pi$
$337$	−4.41376	+	18.1938i	−0.240433	+	0.991077i	−0.956194	+	0.292732i	$0.905435\pi$
$338$		0			0
$339$	−5.06350	−	2.61042i	−0.275012	−	0.141778i
$340$		0			0
$341$	36.9121	+	3.52468i	1.99890	+	0.190872i
$342$		0			0
$343$	−12.8504	+	14.8302i	−0.693858	+	0.800755i
$344$		0			0
$345$	10.7462	+	8.45091i	0.578556	+	0.454982i
$346$		0			0
$347$	7.46155	−	21.5587i	0.400557	−	1.15733i	−0.546830	−	0.837244i	$-0.684166\pi$
$347$	7.46155	−	21.5587i	0.400557	−	1.15733i	0.947387	−	0.320090i	$-0.103713\pi$
$348$		0			0
$349$	16.3819	−	10.5280i	0.876903	−	0.563551i	−0.0229542	−	0.999737i	$-0.507307\pi$
$349$	16.3819	−	10.5280i	0.876903	−	0.563551i	0.899857	+	0.436185i	$0.143671\pi$
$350$		0			0
$351$	−2.69066	−	3.77851i	−0.143617	−	0.201682i
$352$		0			0
$353$	−0.155515	−	3.26467i	−0.00827725	−	0.173761i	−0.999220	−	0.0394788i	$-0.987430\pi$
$353$	−0.155515	−	3.26467i	−0.00827725	−	0.173761i	0.990943	−	0.134282i	$-0.0428728\pi$
$354$		0			0
$355$	−4.26517	+	3.35417i	−0.226372	+	0.178021i
$356$		0			0
$357$	−1.20483	+	8.37976i	−0.0637662	+	0.443504i
$358$		0			0
$359$	−12.8182	−	8.23776i	−0.676519	−	0.434773i	0.156751	−	0.987638i	$-0.449898\pi$
$359$	−12.8182	−	8.23776i	−0.676519	−	0.434773i	−0.833270	+	0.552866i	$0.813534\pi$
$360$		0			0
$361$	−0.886744	+	18.6150i	−0.0466707	+	0.979739i
$362$		0			0
$363$	1.78221	+	5.14935i	0.0935416	+	0.270271i
$364$		0			0
$365$	1.90586	−	3.30105i	0.0997575	−	0.172785i
$366$		0			0
$367$	0.484492	−	0.193962i	0.0252903	−	0.0101247i	−0.358983	−	0.933344i	$-0.616876\pi$
$367$	0.484492	−	0.193962i	0.0252903	−	0.0101247i	0.384273	+	0.923219i	$0.374452\pi$
$368$		0			0
$369$	2.13133	+	8.78547i	0.110953	+	0.457353i
$370$		0			0
$371$	19.0284	+	3.66743i	0.987906	+	0.190403i
$372$		0			0
$373$	−6.71847	−	11.6367i	−0.347869	−	0.602527i	0.638002	−	0.770035i	$-0.279761\pi$
$373$	−6.71847	−	11.6367i	−0.347869	−	0.602527i	−0.985871	+	0.167508i	$0.946428\pi$
$374$		0			0
$375$	−2.06102	−	4.51300i	−0.106430	−	0.233050i
$376$		0			0
$377$	−5.67690	−	6.55149i	−0.292375	−	0.337419i
$378$		0			0
$379$	26.1231	+	10.4581i	1.34186	+	0.537198i	0.927808	−	0.373057i	$-0.121690\pi$
$379$	26.1231	+	10.4581i	1.34186	+	0.537198i	0.414048	+	0.910255i	$0.364115\pi$
$380$		0			0
$381$	−7.31526	+	10.2728i	−0.374772	+	0.526294i
$382$		0			0
$383$	14.2059	−	13.5453i	0.725889	−	0.692134i	−0.234087	−	0.972216i	$-0.575210\pi$
$383$	14.2059	−	13.5453i	0.725889	−	0.692134i	0.959976	+	0.280082i	$0.0903617\pi$
$384$		0			0
$385$	−19.3404	+	9.97068i	−0.985679	+	0.508153i
$386$		0			0
$387$	−3.49499	−	1.02622i	−0.177660	−	0.0521657i
$388$		0			0
$389$	−28.8371	+	5.55789i	−1.46210	+	0.281796i	−0.857396	−	0.514657i	$-0.827919\pi$
$389$	−28.8371	+	5.55789i	−1.46210	+	0.281796i	−0.604701	+	0.796453i	$0.706707\pi$
$390$		0			0
$391$	21.4750	−	2.05061i	1.08604	−	0.103704i
$392$		0			0
$393$	11.2346	−	3.29876i	0.566708	−	0.166401i
$394$		0			0
$395$	−19.3650	−	18.4645i	−0.974360	−	0.929051i
$396$		0			0
$397$	−9.97163	+	21.8348i	−0.500462	+	1.09586i	0.475857	+	0.879523i	$0.342138\pi$
$397$	−9.97163	+	21.8348i	−0.500462	+	1.09586i	−0.976319	+	0.216336i	$0.930589\pi$
$398$		0			0
$399$	−0.160100	−	1.11352i	−0.00801503	−	0.0557458i
$400$		0			0
$401$	−20.3950			−1.01848			−0.509239	−	0.860625i	$-0.670073\pi$
$401$	−20.3950			−1.01848			−0.509239	+	0.860625i	$0.670073\pi$
$402$		0			0
$403$	−42.4091			−2.11255
$404$		0			0
$405$	0.409395	+	2.84741i	0.0203430	+	0.141489i
$406$		0			0
$407$	7.91540	−	17.3323i	0.392352	−	0.859131i
$408$		0			0
$409$	−17.2059	−	16.4058i	−0.850778	−	0.811215i	0.132904	−	0.991129i	$-0.457570\pi$
$409$	−17.2059	−	16.4058i	−0.850778	−	0.811215i	−0.983682	+	0.179914i	$0.942418\pi$
$410$		0			0
$411$	−16.2553	+	4.77299i	−0.801815	+	0.235434i
$412$		0			0
$413$	21.4464	−	2.04789i	1.05531	−	0.100770i
$414$		0			0
$415$	−12.8890	+	2.48415i	−0.632695	+	0.121942i
$416$		0			0
$417$	10.3956	+	3.05242i	0.509073	+	0.149477i
$418$		0			0
$419$	−6.15672	+	3.17401i	−0.300776	+	0.155061i	−0.602008	−	0.798490i	$-0.705632\pi$
$419$	−6.15672	+	3.17401i	−0.300776	+	0.155061i	0.301232	+	0.953551i	$0.402602\pi$
$420$		0			0
$421$	−7.71084	+	7.35227i	−0.375803	+	0.358328i	−0.854317	−	0.519752i	$-0.826024\pi$
$421$	−7.71084	+	7.35227i	−0.375803	+	0.358328i	0.478514	+	0.878080i	$0.341176\pi$
$422$		0			0
$423$	−4.62637	+	6.49683i	−0.224942	+	0.315887i
$424$		0			0
$425$	13.8028	+	5.52582i	0.669535	+	0.268041i
$426$		0			0
$427$	−9.68876	−	11.1814i	−0.468872	−	0.541107i
$428$		0			0
$429$	−7.81522	−	17.1129i	−0.377322	−	0.826221i
$430$		0			0
$431$	−6.62300	−	11.4714i	−0.319018	−	0.552556i	0.661265	−	0.750152i	$-0.270020\pi$
$431$	−6.62300	−	11.4714i	−0.319018	−	0.552556i	−0.980284	+	0.197596i	$0.936687\pi$
$432$		0			0
$433$	−29.5366	−	5.69271i	−1.41944	−	0.273574i	−0.578932	−	0.815376i	$-0.696530\pi$
$433$	−29.5366	−	5.69271i	−1.41944	−	0.273574i	−0.840507	+	0.541801i	$0.817742\pi$
$434$		0			0
$435$	1.26746	+	5.22454i	0.0607700	+	0.250497i
$436$		0			0
$437$	−2.66128	+	1.06542i	−0.127306	+	0.0509657i
$438$		0			0
$439$	−10.0159	+	17.3480i	−0.478031	+	0.827975i	−0.999683	−	0.0251839i	$-0.991983\pi$
$439$	−10.0159	+	17.3480i	−0.478031	+	0.827975i	0.521651	+	0.853159i	$0.325316\pi$
$440$		0			0
$441$	1.15184	+	3.32804i	0.0548497	+	0.158478i
$442$		0			0
$443$	1.80741	−	37.9423i	0.0858729	−	1.80269i	−0.387540	−	0.921853i	$-0.626675\pi$
$443$	1.80741	−	37.9423i	0.0858729	−	1.80269i	0.473413	−	0.880841i	$-0.343022\pi$
$444$		0			0
$445$	−25.9583	−	16.6824i	−1.23054	−	0.790820i
$446$		0			0
$447$	−2.70942	+	18.8444i	−0.128151	+	0.891311i
$448$		0			0
$449$	−9.58226	+	7.53558i	−0.452215	+	0.355626i	−0.818141	−	0.575018i	$-0.804995\pi$
$449$	−9.58226	+	7.53558i	−0.452215	+	0.355626i	0.365926	+	0.930644i	$0.380752\pi$
$450$		0			0
$451$	1.74460	+	36.6236i	0.0821499	+	1.72454i
$452$		0			0
$453$	−13.7223	−	19.2703i	−0.644731	−	0.905399i
$454$		0			0
$455$	20.9358	−	13.4546i	0.981487	−	0.630763i
$456$		0			0
$457$	7.58828	−	21.9249i	0.354965	−	1.02560i	−0.616281	−	0.787526i	$-0.711362\pi$
$457$	7.58828	−	21.9249i	0.354965	−	1.02560i	0.971246	−	0.238077i	$-0.0765172\pi$
$458$		0			0
$459$	3.56816	+	2.80604i	0.166548	+	0.130975i
$460$		0			0
$461$	−19.5037	+	22.5084i	−0.908377	+	1.04832i	0.0902492	+	0.995919i	$0.471234\pi$
$461$	−19.5037	+	22.5084i	−0.908377	+	1.04832i	−0.998626	+	0.0524034i	$0.983312\pi$
$462$		0			0
$463$	10.3390	+	0.987253i	0.480493	+	0.0458815i	0.332493	−	0.943106i	$-0.392110\pi$
$463$	10.3390	+	0.987253i	0.480493	+	0.0458815i	0.148000	+	0.988987i	$0.452716\pi$
$464$		0			0
$465$	23.3767	+	12.0515i	1.08407	+	0.558877i
$466$		0			0
$467$	−3.50959	+	14.4667i	−0.162405	+	0.669441i	0.831146	+	0.556054i	$0.187685\pi$
$467$	−3.50959	+	14.4667i	−0.162405	+	0.669441i	−0.993551	+	0.113387i	$0.963830\pi$
$468$		0			0
$469$	−1.67155	+	15.1740i	−0.0771850	+	0.700670i
$470$		0			0
$471$	−3.85283	+	15.8816i	−0.177529	+	0.731785i
$472$		0			0
$473$	−13.1309	−	6.76946i	−0.603761	−	0.311260i
$474$		0			0
$475$	−1.96672	−	0.187799i	−0.0902395	−	0.00861682i
$476$		0			0
$477$	6.80440	−	7.85269i	0.311552	−	0.359550i
$478$		0			0
$479$	−7.80563	−	6.13841i	−0.356648	−	0.280471i	0.423718	−	0.905794i	$-0.360725\pi$
$479$	−7.80563	−	6.13841i	−0.356648	−	0.280471i	−0.780366	+	0.625323i	$0.784967\pi$
$480$		0			0
$481$	−7.12766	+	20.5940i	−0.324993	+	0.939007i
$482$		0			0
$483$	−7.45623	+	4.79183i	−0.339270	+	0.218036i
$484$		0			0
$485$	−23.2834	−	32.6970i	−1.05725	−	1.48470i
$486$		0			0
$487$	1.69173	+	35.5139i	0.0766598	+	1.60929i	0.630179	+	0.776450i	$0.282981\pi$
$487$	1.69173	+	35.5139i	0.0766598	+	1.60929i	−0.553519	+	0.832836i	$0.686715\pi$
$488$		0			0
$489$	15.2567	−	11.9980i	0.689931	−	0.542568i
$490$		0			0
$491$	−3.11346	+	21.6546i	−0.140508	+	0.977258i	0.790552	+	0.612394i	$0.209794\pi$
$491$	−3.11346	+	21.6546i	−0.140508	+	0.977258i	−0.931061	+	0.364864i	$0.881116\pi$
$492$		0			0
$493$	7.13663	+	4.58643i	0.321418	+	0.206563i
$494$		0			0
$495$	−0.555143	+	11.6539i	−0.0249518	+	0.523803i
$496$		0			0
$497$	−1.15057	−	3.32435i	−0.0516100	−	0.149117i
$498$		0			0
$499$	5.71634	−	9.90100i	0.255899	−	0.443230i	−0.709241	−	0.704967i	$-0.750962\pi$
$499$	5.71634	−	9.90100i	0.255899	−	0.443230i	0.965139	+	0.261737i	$0.0842953\pi$
$500$		0			0
$501$	−3.66801	+	1.46845i	−0.163875	+	0.0656056i
$502$		0			0
$503$	−4.12016	−	16.9835i	−0.183709	−	0.757257i	−0.986873	−	0.161500i	$-0.948367\pi$
$503$	−4.12016	−	16.9835i	−0.183709	−	0.757257i	0.803164	−	0.595758i	$-0.203148\pi$
$504$		0			0
$505$	−26.4980	−	5.10707i	−1.17915	−	0.227262i
$506$		0			0
$507$	4.25840	+	7.37576i	0.189122	+	0.327569i
$508$		0			0
$509$	6.25360	+	13.6935i	0.277186	+	0.606953i	0.996108	−	0.0881376i	$-0.0280915\pi$
$509$	6.25360	+	13.6935i	0.277186	+	0.606953i	−0.718922	+	0.695091i	$0.755364\pi$
$510$		0			0
$511$	1.61830	+	1.86762i	0.0715895	+	0.0826187i
$512$		0			0
$513$	−0.559989	−	0.224186i	−0.0247241	−	0.00989805i
$514$		0			0
$515$	15.8334	−	22.2349i	0.697702	−	0.979785i
$516$		0			0
$517$	−23.4110	+	22.3223i	−1.02961	+	0.981734i
$518$		0			0
$519$	4.56405	−	2.35293i	0.200340	−	0.103282i
$520$		0			0
$521$	41.2715	+	12.1184i	1.80814	+	0.530917i	0.998435	−	0.0559264i	$-0.0178112\pi$
$521$	41.2715	+	12.1184i	1.80814	+	0.530917i	0.809701	+	0.586843i	$0.199629\pi$
$522$		0			0
$523$	5.24917	−	1.01170i	0.229530	−	0.0442383i	−0.0731890	−	0.997318i	$-0.523318\pi$
$523$	5.24917	−	1.01170i	0.229530	−	0.0442383i	0.302719	+	0.953080i	$0.402106\pi$
$524$		0			0
$525$	−6.08087	+	0.580652i	−0.265391	+	0.0253418i
$526$		0			0
$527$	39.8203	−	11.6923i	1.73460	−	0.509325i
$528$		0			0
$529$	−0.300302	−	0.286337i	−0.0130566	−	0.0124495i
$530$		0			0
$531$	4.79873	−	10.5078i	0.208247	−	0.455998i
$532$		0			0
$533$	−5.96790	−	41.5077i	−0.258499	−	1.79790i
$534$		0			0
$535$	4.00410			0.173112
$536$		0			0
$537$	10.0036			0.431688
$538$		0			0
$539$	2.03271	+	14.1378i	0.0875552	+	0.608960i
$540$		0			0
$541$	−8.40727	+	18.4094i	−0.361457	+	0.791480i	0.638308	+	0.769781i	$0.279635\pi$
$541$	−8.40727	+	18.4094i	−0.361457	+	0.791480i	−0.999765	+	0.0216989i	$0.993092\pi$
$542$		0			0
$543$	−12.5576	−	11.9736i	−0.538897	−	0.513838i
$544$		0			0
$545$	−20.7762	+	6.10044i	−0.889954	+	0.261314i
$546$		0			0
$547$	12.9980	−	1.24116i	0.555753	−	0.0530680i	0.186599	−	0.982436i	$-0.440254\pi$
$547$	12.9980	−	1.24116i	0.555753	−	0.0530680i	0.369154	+	0.929368i	$0.379647\pi$
$548$		0			0
$549$	−7.78964	+	1.50133i	−0.332454	+	0.0640752i
$550$		0			0
$551$	−1.08162	−	0.317592i	−0.0460786	−	0.0135299i
$552$		0			0
$553$	15.4188	−	7.94893i	0.655673	−	0.338023i
$554$		0			0
$555$	9.78120	−	9.32635i	0.415189	−	0.395882i
$556$		0			0
$557$	20.4899	−	28.7740i	0.868184	−	1.21919i	−0.106210	−	0.994344i	$-0.533871\pi$
$557$	20.4899	−	28.7740i	0.868184	−	1.21919i	0.974393	−	0.224850i	$-0.0721891\pi$
$558$		0			0
$559$	15.6860	+	6.27973i	0.663448	+	0.265604i
$560$		0			0
$561$	12.0562	+	13.9137i	0.509015	+	0.587435i
$562$		0			0
$563$	1.82599	+	3.99836i	0.0769564	+	0.168511i	0.944200	−	0.329374i	$-0.106838\pi$
$563$	1.82599	+	3.99836i	0.0769564	+	0.168511i	−0.867243	+	0.497885i	$0.834110\pi$
$564$		0			0
$565$	−8.19393	−	14.1923i	−0.344721	−	0.597075i
$566$		0			0
$567$	−1.83131	−	0.352956i	−0.0769078	−	0.0148228i
$568$		0			0
$569$	−0.331472	−	1.36635i	−0.0138960	−	0.0572802i	0.964441	−	0.264297i	$-0.0851398\pi$
$569$	−0.331472	−	1.36635i	−0.0138960	−	0.0572802i	−0.978337	+	0.207016i	$0.933625\pi$
$570$		0			0
$571$	22.9306	−	9.18004i	0.959617	−	0.384173i	0.161633	−	0.986851i	$-0.448324\pi$
$571$	22.9306	−	9.18004i	0.959617	−	0.384173i	0.797984	+	0.602678i	$0.205900\pi$
$572$		0			0
$573$	−9.27277	+	16.0609i	−0.387375	+	0.670954i
$574$		0			0
$575$	5.09100	+	14.7095i	0.212310	+	0.613428i
$576$		0			0
$577$	0.878402	−	18.4399i	0.0365684	−	0.767664i	−0.903892	−	0.427761i	$-0.859303\pi$
$577$	0.878402	−	18.4399i	0.0365684	−	0.767664i	0.940460	−	0.339904i	$-0.110394\pi$
$578$		0			0
$579$	7.64150	+	4.91089i	0.317570	+	0.204090i
$580$		0			0
$581$	1.21109	−	8.42335i	0.0502447	−	0.349459i
$582$		0			0
$583$	33.1255	−	26.0502i	1.37192	−	1.07889i
$584$		0			0
$585$	−0.634926	−	13.3287i	−0.0262510	−	0.551076i
$586$		0			0
$587$	4.96805	+	6.97664i	0.205053	+	0.287957i	0.904277	−	0.426946i	$-0.140410\pi$
$587$	4.96805	+	6.97664i	0.205053	+	0.287957i	−0.699224	+	0.714903i	$0.746471\pi$
$588$		0			0
$589$	−4.63934	+	2.98152i	−0.191161	+	0.122852i
$590$		0			0
$591$	1.12069	−	3.23801i	0.0460989	−	0.133194i
$592$		0			0
$593$	−29.1476	−	22.9219i	−1.19695	−	0.941291i	−0.197709	−	0.980261i	$-0.563350\pi$
$593$	−29.1476	−	22.9219i	−1.19695	−	0.941291i	−0.999240	+	0.0389697i	$0.987592\pi$
$594$		0			0
$595$	−15.9484	+	18.4054i	−0.653819	+	0.754548i
$596$		0			0
$597$	6.62896	+	0.632989i	0.271305	+	0.0259065i
$598$		0			0
$599$	28.7615	+	14.8276i	1.17516	+	0.605839i	0.931400	−	0.363996i	$-0.118588\pi$
$599$	28.7615	+	14.8276i	1.17516	+	0.605839i	0.243762	+	0.969835i	$0.421618\pi$
$600$		0			0
$601$	−2.69009	+	11.0887i	−0.109731	+	0.452317i	−0.999995	−	0.00312724i	$-0.999005\pi$
$601$	−2.69009	+	11.0887i	−0.109731	+	0.452317i	0.890264	+	0.455445i	$0.150520\pi$
$602$		0			0
$603$	6.59797	+	4.84426i	0.268690	+	0.197273i
$604$		0			0
$605$	−3.69556	+	15.2333i	−0.150246	+	0.619323i
$606$		0			0
$607$	0.675098	+	0.348037i	0.0274014	+	0.0141264i	0.471873	−	0.881667i	$-0.343578\pi$
$607$	0.675098	+	0.348037i	0.0274014	+	0.0141264i	−0.444471	+	0.895793i	$0.646608\pi$
$608$		0			0
$609$	−3.46964	−	0.331310i	−0.140597	−	0.0134254i
$610$		0			0
$611$	24.2275	−	27.9600i	0.980138	−	1.13114i
$612$		0			0
$613$	8.26184	+	6.49719i	0.333693	+	0.262419i	0.770920	−	0.636932i	$-0.219797\pi$
$613$	8.26184	+	6.49719i	0.333693	+	0.262419i	−0.437227	+	0.899351i	$0.644039\pi$
$614$		0			0
$615$	−8.50577	+	24.5758i	−0.342986	+	0.990992i
$616$		0			0
$617$	−17.2571	+	11.0904i	−0.694743	+	0.446485i	−0.839769	−	0.542943i	$-0.817310\pi$
$617$	−17.2571	+	11.0904i	−0.694743	+	0.446485i	0.145026	+	0.989428i	$0.453673\pi$
$618$		0			0
$619$	−11.5943	−	16.2819i	−0.466012	−	0.654423i	0.512961	−	0.858412i	$-0.328549\pi$
$619$	−11.5943	−	16.2819i	−0.466012	−	0.654423i	−0.978973	+	0.203989i	$0.934609\pi$
$620$		0			0
$621$	0.226127	+	4.74699i	0.00907417	+	0.190490i
$622$		0			0
$623$	15.7250	−	12.3663i	0.630008	−	0.495444i
$624$		0			0
$625$	4.36179	−	30.3369i	0.174472	−	1.21348i
$626$		0			0
$627$	−2.05805	−	1.32263i	−0.0821908	−	0.0528208i
$628$		0			0
$629$	1.01474	−	21.3020i	0.0404604	−	0.849368i
$630$		0			0
$631$	−0.311254	−	0.899309i	−0.0123908	−	0.0358009i	0.938636	−	0.344910i	$-0.112090\pi$
$631$	−0.311254	−	0.899309i	−0.0123908	−	0.0358009i	−0.951027	+	0.309109i	$0.899969\pi$
$632$		0			0
$633$	−3.72740	+	6.45604i	−0.148151	+	0.256605i
$634$		0			0
$635$	−33.6800	+	13.4834i	−1.33655	+	0.535074i
$636$		0			0
$637$	−3.85135	−	15.8755i	−0.152596	−	0.629009i
$638$		0			0
$639$	−1.85213	−	0.356969i	−0.0732693	−	0.0141215i
$640$		0			0
$641$	−18.8450	−	32.6405i	−0.744333	−	1.28922i	−0.950506	−	0.310707i	$-0.899434\pi$
$641$	−18.8450	−	32.6405i	−0.744333	−	1.28922i	0.206173	−	0.978516i	$-0.433899\pi$
$642$		0			0
$643$	−2.86236	−	6.26770i	−0.112881	−	0.247174i	0.844757	−	0.535150i	$-0.179745\pi$
$643$	−2.86236	−	6.26770i	−0.112881	−	0.247174i	−0.957638	+	0.287976i	$0.907018\pi$
$644$		0			0
$645$	−6.86191	−	7.91907i	−0.270188	−	0.311813i
$646$		0			0
$647$	−8.81273	−	3.52808i	−0.346464	−	0.138703i	0.191903	−	0.981414i	$-0.438534\pi$
$647$	−8.81273	−	3.52808i	−0.346464	−	0.138703i	−0.538367	+	0.842711i	$0.680958\pi$
$648$		0			0
$649$	27.1760	−	38.1633i	1.06675	−	1.49804i
$650$		0			0
$651$	−12.3404	+	11.7666i	−0.483660	+	0.461169i
$652$		0			0
$653$	25.2957	−	13.0408i	0.989896	−	0.510327i	0.114339	−	0.993442i	$-0.463525\pi$
$653$	25.2957	−	13.0408i	0.989896	−	0.510327i	0.875557	+	0.483115i	$0.160495\pi$
$654$		0			0
$655$	32.3183	+	9.48951i	1.26278	+	0.370786i
$656$		0			0
$657$	1.30110	−	0.250766i	0.0507606	−	0.00978330i
$658$		0			0
$659$	−31.6100	+	3.01839i	−1.23135	+	0.117580i	−0.690371	−	0.723455i	$-0.742553\pi$
$659$	−31.6100	+	3.01839i	−1.23135	+	0.117580i	−0.540981	+	0.841035i	$0.681947\pi$
$660$		0			0
$661$	27.5854	−	8.09981i	1.07295	−	0.315046i	0.302894	−	0.953024i	$-0.402047\pi$
$661$	27.5854	−	8.09981i	1.07295	−	0.315046i	0.770054	+	0.637978i	$0.220229\pi$
$662$		0			0
$663$	−15.2392	−	14.5305i	−0.591840	−	0.564318i
$664$		0			0
$665$	1.34436	−	2.94374i	0.0521321	−	0.114153i
$666$		0			0
$667$	1.26396	+	8.79105i	0.0489408	+	0.340391i
$668$		0			0
$669$	−14.7342			−0.569657
$670$		0			0
$671$	−32.1742			−1.24207
$672$		0			0
$673$	5.98465	+	41.6242i	0.230691	+	1.60449i	0.695127	+	0.718886i	$0.255348\pi$
$673$	5.98465	+	41.6242i	0.230691	+	1.60449i	−0.464436	+	0.885607i	$0.653743\pi$
$674$		0			0
$675$	−1.36062	+	2.97934i	−0.0523703	+	0.114675i
$676$		0			0
$677$	6.85195	+	6.53332i	0.263342	+	0.251096i	0.810233	−	0.586108i	$-0.199340\pi$
$677$	6.85195	+	6.53332i	0.263342	+	0.251096i	−0.546891	+	0.837204i	$0.684189\pi$
$678$		0			0
$679$	24.9694	−	7.33167i	0.958237	−	0.281364i
$680$		0			0
$681$	5.20648	−	0.497159i	0.199513	−	0.0190512i
$682$		0			0
$683$	47.1977	−	9.09661i	1.80597	−	0.348072i	0.828637	−	0.559786i	$-0.189117\pi$
$683$	47.1977	−	9.09661i	1.80597	−	0.348072i	0.977332	+	0.211714i	$0.0679044\pi$
$684$		0			0
$685$	−46.7614	−	13.7304i	−1.78666	−	0.524611i
$686$		0			0
$687$	−4.64044	+	2.39231i	−0.177044	+	0.0912725i
$688$		0			0
$689$	−34.8826	+	33.2605i	−1.32892	+	1.26712i
$690$		0			0
$691$	−22.3417	+	31.3745i	−0.849919	+	1.19354i	0.129475	+	0.991583i	$0.458671\pi$
$691$	−22.3417	+	31.3745i	−0.849919	+	1.19354i	−0.979394	+	0.201961i	$0.935269\pi$
$692$		0			0
$693$	−7.02218	−	2.81126i	−0.266751	−	0.106791i
$694$		0			0
$695$	20.4102	+	23.5547i	0.774205	+	0.893480i
$696$		0			0
$697$	17.0474	+	37.3286i	0.645716	+	1.41392i
$698$		0			0
$699$	10.1616	+	17.6004i	0.384346	+	0.665707i
$700$		0			0
$701$	49.7297	+	9.58461i	1.87826	+	0.362006i	0.994395	−	0.105728i	$-0.0337173\pi$
$701$	49.7297	+	9.58461i	1.87826	+	0.362006i	0.883869	+	0.467734i	$0.154929\pi$
$702$		0			0
$703$	0.668110	+	2.75399i	0.0251983	+	0.103869i
$704$		0			0
$705$	−21.3002	+	8.52730i	−0.802210	+	0.321157i
$706$		0			0
$707$	8.74767	−	15.1514i	0.328990	−	0.569827i
$708$		0			0
$709$	1.10334	+	3.18790i	0.0414369	+	0.119724i	0.963821	−	0.266549i	$-0.0858834\pi$
$709$	1.10334	+	3.18790i	0.0414369	+	0.119724i	−0.922384	+	0.386273i	$0.873762\pi$
$710$		0			0
$711$	0.442577	−	9.29083i	0.0165979	−	0.348433i
$712$		0			0
$713$	36.5517	+	23.4903i	1.36887	+	0.879720i
$714$		0			0
$715$	7.70197	−	53.5684i	0.288037	−	2.00334i
$716$		0			0
$717$	−6.19260	+	4.86991i	−0.231267	+	0.181870i
$718$		0			0
$719$	0.875249	+	18.3737i	0.0326413	+	0.685225i	0.954592	+	0.297917i	$0.0962919\pi$
$719$	0.875249	+	18.3737i	0.0326413	+	0.685225i	−0.921951	+	0.387308i	$0.873405\pi$
$720$		0			0
$721$	10.2651	+	14.4153i	0.382292	+	0.536854i
$722$		0			0
$723$	15.7579	−	10.1270i	0.586041	−	0.376626i
$724$		0			0
$725$	−2.00201	+	5.78443i	−0.0743528	+	0.214828i
$726$		0			0
$727$	18.1795	+	14.2965i	0.674241	+	0.530229i	0.895542	−	0.444976i	$-0.146788\pi$
$727$	18.1795	+	14.2965i	0.674241	+	0.530229i	−0.221301	+	0.975206i	$0.571030\pi$
$728$		0			0
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$		0			0
$731$	−16.4598	−	1.57172i	−0.608789	−	0.0581323i
$732$		0			0
$733$	30.4339	+	15.6898i	1.12410	+	0.579514i	0.917033	−	0.398812i	$-0.130577\pi$
$733$	30.4339	+	15.6898i	1.12410	+	0.579514i	0.207068	+	0.978326i	$0.433608\pi$
$734$		0			0
$735$	−2.38845	+	9.84533i	−0.0880994	+	0.363151i
$736$		0			0
$737$	22.5578	+	24.3563i	0.830929	+	0.897176i
$738$		0			0
$739$	−5.96983	+	24.6080i	−0.219604	+	0.905220i	0.750176	+	0.661238i	$0.229969\pi$
$739$	−5.96983	+	24.6080i	−0.219604	+	0.905220i	−0.969780	+	0.243981i	$0.921546\pi$
$740$		0			0
$741$	2.48697	+	1.28212i	0.0913610	+	0.0470998i
$742$		0			0
$743$	1.88517	+	0.180012i	0.0691602	+	0.00660400i	0.129579	−	0.991569i	$-0.458637\pi$
$743$	1.88517	+	0.180012i	0.0691602	+	0.00660400i	−0.0604186	+	0.998173i	$0.519244\pi$
$744$		0			0
$745$	−35.8647	+	41.3901i	−1.31398	+	1.51642i
$746$		0			0
$747$	−3.58672	−	2.82063i	−0.131231	−	0.103201i
$748$		0			0
$749$	−0.849049	+	2.45316i	−0.0310236	+	0.0896367i
$750$		0			0
$751$	36.7557	−	23.6214i	1.34123	−	0.861959i	0.344198	−	0.938897i	$-0.388151\pi$
$751$	36.7557	−	23.6214i	1.34123	−	0.861959i	0.997036	+	0.0769387i	$0.0245146\pi$
$752$		0			0
$753$	−7.49922	−	10.5312i	−0.273287	−	0.383778i
$754$		0			0
$755$	−3.23811	−	67.9763i	−0.117847	−	2.47391i
$756$		0			0
$757$	26.4453	−	20.7968i	0.961171	−	0.755873i	−0.00858144	−	0.999963i	$-0.502732\pi$
$757$	26.4453	−	20.7968i	0.961171	−	0.755873i	0.969753	+	0.244090i	$0.0784892\pi$
$758$		0			0
$759$	−2.74303	+	19.0782i	−0.0995658	+	0.692495i
$760$		0			0
$761$	−5.89441	−	3.78811i	−0.213672	−	0.137319i	0.429427	−	0.903101i	$-0.358715\pi$
$761$	−5.89441	−	3.78811i	−0.213672	−	0.137319i	−0.643099	+	0.765783i	$0.722352\pi$
$762$		0			0
$763$	0.667967	−	14.0224i	0.0241820	−	0.507643i
$764$		0			0
$765$	4.27094	+	12.3401i	0.154416	+	0.446156i
$766$		0			0
$767$	−26.7919	+	46.4049i	−0.967398	+	1.67558i
$768$		0			0
$769$	47.0324	−	18.8289i	1.69603	−	0.678989i	0.696766	−	0.717299i	$-0.254622\pi$
$769$	47.0324	−	18.8289i	1.69603	−	0.678989i	0.999266	+	0.0383102i	$0.0121975\pi$
$770$		0			0
$771$	1.50539	+	6.20530i	0.0542152	+	0.223478i
$772$		0			0
$773$	−14.9147	−	2.87457i	−0.536445	−	0.103391i	−0.0861686	−	0.996281i	$-0.527462\pi$
$773$	−14.9147	−	2.87457i	−0.536445	−	0.103391i	−0.450276	+	0.892889i	$0.648674\pi$
$774$		0			0
$775$	14.9725	+	25.9331i	0.537828	+	0.931546i
$776$		0			0
$777$	3.63986	+	7.97018i	0.130579	+	0.285928i
$778$		0			0
$779$	−3.57101	−	4.12117i	−0.127945	−	0.147656i
$780$		0			0
$781$	−7.10203	−	2.84323i	−0.254131	−	0.101739i
$782$		0			0
$783$	−1.08404	+	1.52232i	−0.0387403	+	0.0544031i
$784$		0			0
$785$	−34.0238	+	32.4417i	−1.21436	+	1.15789i
$786$		0			0
$787$	−41.7055	+	21.5007i	−1.48664	+	0.766417i	−0.994563	−	0.104133i	$-0.966793\pi$
$787$	−41.7055	+	21.5007i	−1.48664	+	0.766417i	−0.492079	+	0.870551i	$0.663763\pi$
$788$		0			0
$789$	9.64829	+	2.83299i	0.343488	+	0.100857i
$790$		0			0
$791$	10.4326	−	2.01071i	0.370940	−	0.0714928i
$792$		0			0
$793$	36.6316	−	3.49789i	1.30082	−	0.124214i
$794$		0			0
$795$	28.6797	−	8.42113i	1.01717	−	0.298667i
$796$		0			0
$797$	30.3151	+	28.9054i	1.07382	+	1.02388i	0.999645	+	0.0266357i	$0.00847941\pi$
$797$	30.3151	+	28.9054i	1.07382	+	1.02388i	0.0741706	+	0.997246i	$0.476369\pi$
$798$		0			0
$799$	−15.0399	+	32.9328i	−0.532074	+	1.16508i
$800$		0			0
$801$	−1.52653	−	10.6173i	−0.0539374	−	0.375143i
$802$		0			0
$803$	5.37402			0.189645
$804$		0			0
$805$	−25.4968			−0.898643
$806$		0			0
$807$	−1.03059	−	7.16790i	−0.0362784	−	0.252322i
$808$		0			0
$809$	12.7108	−	27.8328i	0.446889	−	0.978550i	−0.543393	−	0.839478i	$-0.682861\pi$
$809$	12.7108	−	27.8328i	0.446889	−	0.978550i	0.990282	−	0.139072i	$-0.0444120\pi$
$810$		0			0
$811$	6.92436	+	6.60237i	0.243147	+	0.231840i	0.801847	−	0.597530i	$-0.203851\pi$
$811$	6.92436	+	6.60237i	0.243147	+	0.231840i	−0.558700	+	0.829370i	$0.688699\pi$
$812$		0			0
$813$	−29.2776	+	8.59668i	−1.02681	+	0.301499i
$814$		0			0
$815$	55.5814	−	5.30738i	1.94693	−	0.185910i
$816$		0			0
$817$	2.15746	−	0.415817i	0.0754801	−	0.0145476i
$818$		0			0
$819$	8.30066	+	2.43729i	0.290048	+	0.0851659i
$820$		0			0
$821$	−26.3100	+	13.5638i	−0.918226	+	0.473378i	−0.851477	−	0.524392i	$-0.824293\pi$
$821$	−26.3100	+	13.5638i	−0.918226	+	0.473378i	−0.0667485	+	0.997770i	$0.521263\pi$
$822$		0			0
$823$	−25.6659	+	24.4724i	−0.894659	+	0.853055i	−0.989808	−	0.142408i	$-0.954516\pi$
$823$	−25.6659	+	24.4724i	−0.894659	+	0.853055i	0.0951494	+	0.995463i	$0.469667\pi$
$824$		0			0
$825$	−7.70541	+	10.8207i	−0.268268	+	0.376729i
$826$		0			0
$827$	46.5166	+	18.6224i	1.61754	+	0.647566i	0.991247	−	0.132020i	$-0.0421464\pi$
$827$	46.5166	+	18.6224i	1.61754	+	0.647566i	0.626295	+	0.779586i	$0.284571\pi$
$828$		0			0
$829$	28.4639	+	32.8491i	0.988592	+	1.14090i	0.990024	+	0.140896i	$0.0449985\pi$
$829$	28.4639	+	32.8491i	0.988592	+	1.14090i	−0.00143278	+	0.999999i	$0.500456\pi$
$830$		0			0
$831$	1.96857	+	4.31057i	0.0682890	+	0.149532i
$832$		0			0
$833$	7.99316	+	13.8446i	0.276947	+	0.479686i
$834$		0			0
$835$	−11.1605	−	2.15101i	−0.386225	−	0.0744387i
$836$		0			0
$837$	2.15545	+	8.88489i	0.0745033	+	0.307107i
$838$		0			0
$839$	−39.1082	+	15.6566i	−1.35017	+	0.540525i	−0.930213	−	0.367020i	$-0.880378\pi$
$839$	−39.1082	+	15.6566i	−1.35017	+	0.540525i	−0.419954	+	0.907546i	$0.637954\pi$
$840$		0			0
$841$	12.7537	−	22.0901i	0.439783	−	0.761727i
$842$		0			0
$843$	−1.72823	−	4.99339i	−0.0595234	−	0.171982i
$844$		0			0
$845$	−1.16576	+	24.4724i	−0.0401035	+	0.841876i
$846$		0			0
$847$	−8.54926	−	5.49428i	−0.293756	−	0.188786i
$848$		0			0
$849$	3.02928	−	21.0691i	0.103965	−	0.723091i
$850$		0			0
$851$	17.5502	−	13.8017i	0.601614	−	0.473115i
$852$		0			0
$853$	−1.75145	−	36.7674i	−0.0599684	−	1.25889i	−0.805570	−	0.592500i	$-0.798141\pi$
$853$	−1.75145	−	36.7674i	−0.0599684	−	1.25889i	0.745602	−	0.666392i	$-0.232162\pi$
$854$		0			0
$855$	−1.00652	−	1.41346i	−0.0344223	−	0.0483393i
$856$		0			0
$857$	−24.4549	+	15.7162i	−0.835365	+	0.536856i	−0.886979	−	0.461811i	$-0.847200\pi$
$857$	−24.4549	+	15.7162i	−0.835365	+	0.536856i	0.0516136	+	0.998667i	$0.483564\pi$
$858$		0			0
$859$	−17.3694	+	50.1856i	−0.592636	+	1.71231i	0.103715	+	0.994607i	$0.466927\pi$
$859$	−17.3694	+	50.1856i	−0.592636	+	1.71231i	−0.696350	+	0.717702i	$0.745194\pi$
$860$		0			0
$861$	−13.2531	−	10.4223i	−0.451663	−	0.355192i
$862$		0			0
$863$	−9.09474	+	10.4959i	−0.309589	+	0.357284i	−0.889127	−	0.457661i	$-0.848687\pi$
$863$	−9.09474	+	10.4959i	−0.309589	+	0.357284i	0.579538	+	0.814945i	$0.303233\pi$
$864$		0			0
$865$	14.7045	+	1.40411i	0.499968	+	0.0477412i
$866$		0			0
$867$	3.20481	+	1.65220i	0.108841	+	0.0561115i
$868$		0			0
$869$	8.89375	−	36.6605i	0.301700	−	1.24362i
$870$		0			0
$871$	−28.3309	−	25.2782i	−0.959956	−	0.856518i
$872$		0			0
$873$	3.28967	−	13.5602i	0.111338	−	0.458943i
$874$		0			0
$875$	8.22437	+	4.23996i	0.278034	+	0.143337i
$876$		0			0
$877$	−55.0324	−	5.25495i	−1.85831	−	0.177447i	−0.895041	−	0.445984i	$-0.852854\pi$
$877$	−55.0324	−	5.25495i	−1.85831	−	0.177447i	−0.963270	+	0.268536i	$0.913460\pi$
$878$		0			0
$879$	7.67437	−	8.85670i	0.258850	−	0.298729i
$880$		0			0
$881$	−14.8100	−	11.6467i	−0.498961	−	0.392387i	0.336718	−	0.941606i	$-0.390683\pi$
$881$	−14.8100	−	11.6467i	−0.498961	−	0.392387i	−0.835679	+	0.549218i	$0.814926\pi$
$882$		0			0
$883$	−0.268715	+	0.776402i	−0.00904299	+	0.0261280i	−0.949432	−	0.313973i	$-0.898340\pi$
$883$	−0.268715	+	0.776402i	−0.00904299	+	0.0261280i	0.940389	+	0.340101i	$0.110461\pi$
$884$		0			0
$885$	27.9553	−	17.9658i	0.939706	−	0.603912i
$886$		0			0
$887$	−6.59824	−	9.26593i	−0.221547	−	0.311120i	0.688811	−	0.724941i	$-0.258133\pi$
$887$	−6.59824	−	9.26593i	−0.221547	−	0.311120i	−0.910358	+	0.413822i	$0.864194\pi$
$888$		0			0
$889$	−1.11914	−	23.4936i	−0.0375346	−	0.787949i
$890$		0			0
$891$	−3.18803	+	2.50709i	−0.106803	+	0.0839908i
$892$		0			0
$893$	0.684668	−	4.76197i	0.0229115	−	0.159353i
$894$		0			0
$895$	24.2090	+	15.5582i	0.809216	+	0.520052i
$896$		0			0
$897$	1.04892	−	22.0195i	0.0350223	−	0.735209i
$898$		0			0
$899$	5.58832	+	16.1464i	0.186381	+	0.538512i
$900$		0			0
$901$	23.5833	−	40.8474i	0.785672	−	1.36082i
$902$		0			0
$903$	6.30675	−	2.52484i	0.209876	−	0.0840215i
$904$		0			0
$905$	−11.7676	−	48.5067i	−0.391168	−	1.61242i
$906$		0			0
$907$	25.2037	+	4.85762i	0.836876	+	0.161295i	0.589646	−	0.807662i	$-0.299267\pi$
$907$	25.2037	+	4.85762i	0.836876	+	0.161295i	0.247231	+	0.968957i	$0.420480\pi$
$908$		0			0
$909$	−4.69041	−	8.12402i	−0.155571	−	0.269457i
$910$		0			0
$911$	−2.37424	−	5.19887i	−0.0786622	−	0.172246i	0.866215	−	0.499672i	$-0.166546\pi$
$911$	−2.37424	−	5.19887i	−0.0786622	−	0.172246i	−0.944877	+	0.327426i	$0.893819\pi$
$912$		0			0
$913$	−12.1190	−	13.9860i	−0.401079	−	0.462870i
$914$		0			0
$915$	−21.1861	−	8.48162i	−0.700390	−	0.280394i
$916$		0			0
$917$	−12.6668	+	17.7880i	−0.418294	+	0.587412i
$918$		0			0
$919$	−42.3262	+	40.3580i	−1.39621	+	1.33129i	−0.516095	+	0.856532i	$0.672615\pi$
$919$	−42.3262	+	40.3580i	−1.39621	+	1.33129i	−0.880118	+	0.474755i	$0.842537\pi$
$920$		0			0
$921$	16.8799	−	8.70220i	0.556212	−	0.286747i
$922$		0			0
$923$	8.39504	+	2.46501i	0.276326	+	0.0811367i
$924$		0			0
$925$	15.1097	−	2.91215i	0.496803	−	0.0957509i
$926$		0			0
$927$	9.44581	−	0.901966i	0.310241	−	0.0296244i
$928$		0			0
$929$	17.6206	−	5.17386i	0.578112	−	0.169749i	0.0204120	−	0.999792i	$-0.493502\pi$
$929$	17.6206	−	5.17386i	0.578112	−	0.169749i	0.557700	+	0.830043i	$0.311684\pi$
$930$		0			0
$931$	−1.53743	−	1.46593i	−0.0503871	−	0.0480440i
$932$		0			0
$933$	−0.429965	+	0.941492i	−0.0140764	+	0.0308231i
$934$		0			0
$935$	7.53713	+	52.4219i	0.246491	+	1.71438i
$936$		0			0
$937$	25.9109			0.846472			0.423236	−	0.906019i	$-0.360894\pi$
$937$	25.9109			0.846472			0.423236	+	0.906019i	$0.360894\pi$
$938$		0			0
$939$	26.8322			0.875636
$940$		0			0
$941$	1.31053	+	9.11496i	0.0427222	+	0.297139i	0.999969	+	0.00786704i	$0.00250418\pi$
$941$	1.31053	+	9.11496i	0.0427222	+	0.297139i	−0.957247	+	0.289272i	$0.906587\pi$
$942$		0			0
$943$	−17.8474	+	39.0804i	−0.581192	+	1.27263i
$944$		0			0
$945$	−3.88287	−	3.70231i	−0.126310	−	0.120436i
$946$		0			0
$947$	−4.21816	+	1.23856i	−0.137072	+	0.0402479i	−0.349549	−	0.936918i	$-0.613665\pi$
$947$	−4.21816	+	1.23856i	−0.137072	+	0.0402479i	0.212477	+	0.977166i	$0.431847\pi$
$948$		0			0
$949$	−6.11853	+	0.584249i	−0.198616	+	0.0189655i
$950$		0			0
$951$	31.0287	−	5.98030i	1.00618	−	0.193924i
$952$		0			0
$953$	−42.4203	−	12.4557i	−1.37413	−	0.403480i	−0.490406	−	0.871494i	$-0.663151\pi$
$953$	−42.4203	−	12.4557i	−1.37413	−	0.403480i	−0.883721	+	0.468014i	$0.844970\pi$
$954$		0			0
$955$	−47.4191	+	24.4462i	−1.53445	+	0.791062i
$956$		0			0
$957$	−5.48558	+	5.23049i	−0.177324	+	0.169078i
$958$		0			0
$959$	18.3276	−	25.7375i	0.591829	−	0.831108i
$960$		0			0
$961$	48.8203	+	19.5447i	1.57485	+	0.630474i
$962$		0			0
$963$	0.911510	+	1.05194i	0.0293730	+	0.0338983i
$964$		0			0
$965$	10.8549	+	23.7690i	0.349432	+	0.765150i
$966$		0			0
$967$	−16.1956	−	28.0516i	−0.520816	−	0.902079i	−0.999707	−	0.0242051i	$-0.992295\pi$
$967$	−16.1956	−	28.0516i	−0.520816	−	0.902079i	0.478891	−	0.877874i	$-0.341039\pi$
$968$		0			0
$969$	−2.68864	−	0.518193i	−0.0863715	−	0.0166467i
$970$		0			0
$971$	3.91497	+	16.1377i	0.125637	+	0.517884i	0.999497	+	0.0317063i	$0.0100941\pi$
$971$	3.91497	+	16.1377i	0.125637	+	0.517884i	−0.873860	+	0.486178i	$0.838391\pi$
$972$		0			0
$973$	−18.7590	+	7.50995i	−0.601384	+	0.240758i
$974$		0			0
$975$	7.59650	−	13.1575i	0.243283	−	0.421378i
$976$		0			0
$977$	−18.2225	−	52.6506i	−0.582991	−	1.68444i	−0.720087	−	0.693883i	$-0.755898\pi$
$977$	−18.2225	−	52.6506i	−0.582991	−	1.68444i	0.137097	−	0.990558i	$-0.456223\pi$
$978$		0			0
$979$	2.06999	−	43.4545i	0.0661572	−	1.38881i
$980$		0			0
$981$	−6.33225	−	4.06949i	−0.202173	−	0.129929i
$982$		0			0
$983$	−2.47036	+	17.1817i	−0.0787922	+	0.548012i	0.911744	+	0.410759i	$0.134736\pi$
$983$	−2.47036	+	17.1817i	−0.0787922	+	0.548012i	−0.990536	+	0.137253i	$0.956173\pi$
$984$		0			0
$985$	7.74803	−	6.09312i	0.246873	−	0.194143i
$986$		0			0
$987$	−0.707773	−	14.8580i	−0.0225287	−	0.472935i
$988$		0			0
$989$	−10.0412	−	14.1009i	−0.319291	−	0.448382i
$990$		0			0
$991$	48.8113	−	31.3691i	1.55054	−	0.996472i	0.565382	−	0.824829i	$-0.308729\pi$
$991$	48.8113	−	31.3691i	1.55054	−	0.996472i	0.985159	−	0.171643i	$-0.0549076\pi$
$992$		0			0
$993$	0.769987	−	2.22473i	0.0244348	−	0.0705997i
$994$		0			0
$995$	15.0578	+	11.8416i	0.477363	+	0.375403i
$996$		0			0
$997$	22.2257	−	25.6498i	0.703895	−	0.812338i	−0.285378	−	0.958415i	$-0.592119\pi$
$997$	22.2257	−	25.6498i	0.703895	−	0.812338i	0.989273	+	0.146077i	$0.0466647\pi$
$998$		0			0
$999$	4.67681	+	0.446581i	0.147968	+	0.0141292i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.b.169.2	yes	120
67.23	even	33	inner	804.2.y.b.157.2	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.b.157.2	✓	120	67.23	even	33	inner
804.2.y.b.169.2	yes	120	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.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{3} +(-1.19502 + 2.61673i) q^{5} +(-1.34977 - 1.28701i) q^{7} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{3} +(-1.19502 + 2.61673i) q^{5} +(-1.34977 - 1.28701i) q^{7} +(-0.959493 + 0.281733i) q^{9} +(-4.03738 + 0.385523i) q^{11} +(4.55479 - 0.877865i) q^{13} +(-2.76016 - 0.810456i) q^{15} +(-4.03473 + 2.08005i) q^{17} +(0.436555 - 0.416254i) q^{19} +(1.08181 - 1.51919i) q^{21} +(-4.41195 - 1.76628i) q^{23} +(-2.14488 - 2.47533i) q^{25} +(-0.415415 - 0.909632i) q^{27} +(-0.934423 - 1.61847i) q^{29} +(-8.97739 - 1.73025i) q^{31} +(-0.956177 - 3.94142i) q^{33} +(4.98075 - 1.99399i) q^{35} +(-2.34904 + 4.06866i) q^{37} +(1.51714 + 4.38350i) q^{39} +(0.430155 - 9.03006i) q^{41} +(3.06430 + 1.96930i) q^{43} +(0.409395 - 2.84741i) q^{45} +(6.26934 - 4.93026i) q^{47} +(-0.167571 - 3.51774i) q^{49} +(-2.63308 - 3.69764i) q^{51} +(-8.74113 + 5.61758i) q^{53} +(3.81593 - 11.0254i) q^{55} +(0.474145 + 0.372872i) q^{57} +(-7.56473 + 8.73016i) q^{59} +(7.89708 + 0.754080i) q^{61} +(1.65769 + 0.854598i) q^{63} +(-3.14593 + 12.9677i) q^{65} +(-4.96592 - 6.50689i) q^{67} +(1.12041 - 4.61841i) q^{69} +(1.67654 + 0.864316i) q^{71} +(-1.31904 - 0.125953i) q^{73} +(2.14488 - 2.47533i) q^{75} +(5.94571 + 4.67576i) q^{77} +(-3.04218 + 8.78980i) q^{79} +(0.841254 - 0.540641i) q^{81} +(2.64677 + 3.71687i) q^{83} +(-0.621337 - 13.0435i) q^{85} +(1.46901 - 1.15524i) q^{87} +(-1.52653 + 10.6173i) q^{89} +(-7.27776 - 4.67713i) q^{91} +(0.435023 - 9.13225i) q^{93} +(0.567532 + 1.63978i) q^{95} +(-6.97677 + 12.0841i) q^{97} +(3.76522 - 1.50737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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