LMFDB - Embedded newform 304.2.u.d.177.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [304,2,Mod(17,304)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("304.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(304, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.u (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,6,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			177.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	304.177
Dual form			304.2.u.d.225.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.76604 + 0.642788i) q^{3} +(0.0603074 + 0.342020i) q^{5} +(-2.37939 + 4.12122i) q^{7} +(0.407604 + 0.342020i) q^{9} +(2.37939 + 4.12122i) q^{11} +(1.76604 - 0.642788i) q^{13} +(-0.113341 + 0.642788i) q^{15} +(1.17365 - 0.984808i) q^{17} +(0.694593 - 4.30320i) q^{19} +(-6.85117 + 5.74881i) q^{21} +(1.06031 - 6.01330i) q^{23} +(4.58512 - 1.66885i) q^{25} +(-2.31908 - 4.01676i) q^{27} +(-1.52094 - 1.27622i) q^{29} +(-1.68479 + 2.91815i) q^{31} +(1.55303 + 8.80769i) q^{33} +(-1.55303 - 0.565258i) q^{35} -3.38919 q^{37} +3.53209 q^{39} +(4.21941 + 1.53574i) q^{41} +(-0.365715 - 2.07407i) q^{43} +(-0.0923963 + 0.160035i) q^{45} +(3.76991 + 3.16333i) q^{47} +(-7.82295 - 13.5497i) q^{49} +(2.70574 - 0.984808i) q^{51} +(-2.18092 + 12.3686i) q^{53} +(-1.26604 + 1.06234i) q^{55} +(3.99273 - 7.15317i) q^{57} +(-4.33615 + 3.63846i) q^{59} +(1.73530 - 9.84137i) q^{61} +(-2.37939 + 0.866025i) q^{63} +(0.326352 + 0.565258i) q^{65} +(-8.11721 - 6.81115i) q^{67} +(5.73783 - 9.93821i) q^{69} +(-1.99613 - 11.3206i) q^{71} +(13.7369 + 4.99984i) q^{73} +9.17024 q^{75} -22.6459 q^{77} +(2.21941 + 0.807798i) q^{79} +(-1.79086 - 10.1565i) q^{81} +(-5.76857 + 9.99146i) q^{83} +(0.407604 + 0.342020i) q^{85} +(-1.86571 - 3.23151i) q^{87} +(-5.29813 + 1.92836i) q^{89} +(-1.55303 + 8.80769i) q^{91} +(-4.85117 + 4.07061i) q^{93} +(1.51367 - 0.0219501i) q^{95} +(5.86824 - 4.92404i) q^{97} +(-0.439693 + 2.49362i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{3} + 6 q^{5} - 3 q^{7} + 6 q^{9} + 3 q^{11} + 6 q^{13} + 6 q^{15} + 6 q^{17} - 15 q^{21} + 12 q^{23} + 6 q^{25} + 3 q^{27} - 6 q^{29} - 3 q^{31} - 3 q^{33} + 3 q^{35} - 12 q^{37} + 12 q^{39}+ \cdots + 3 q^{99}+O(q^{100}) $ 6 * q + 6 * q^3 + 6 * q^5 - 3 * q^7 + 6 * q^9 + 3 * q^11 + 6 * q^13 + 6 * q^15 + 6 * q^17 - 15 * q^21 + 12 * q^23 + 6 * q^25 + 3 * q^27 - 6 * q^29 - 3 * q^31 - 3 * q^33 + 3 * q^35 - 12 * q^37 + 12 * q^39 - 6 * q^41 - 12 * q^43 + 3 * q^45 - 6 * q^47 - 6 * q^49 + 6 * q^51 - 30 * q^53 - 3 * q^55 + 6 * q^57 - 30 * q^59 + 6 * q^61 - 3 * q^63 + 3 * q^65 - 18 * q^67 + 15 * q^69 - 36 * q^71 + 6 * q^73 + 12 * q^75 - 54 * q^77 - 18 * q^79 + 21 * q^81 - 15 * q^83 + 6 * q^85 - 21 * q^87 - 18 * q^89 + 3 * q^91 - 3 * q^93 - 12 * q^95 + 30 * q^97 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$	$1$

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
$3$	1.76604	+	0.642788i	1.01963	+	0.371114i	0.797122	−	0.603818i	$-0.206355\pi$
$3$	1.76604	+	0.642788i	1.01963	+	0.371114i	0.222504	+	0.974932i	$0.428577\pi$
$4$		0			0
$5$	0.0603074	+	0.342020i	0.0269703	+	0.152956i	0.995319	−	0.0966457i	$-0.0308114\pi$
$5$	0.0603074	+	0.342020i	0.0269703	+	0.152956i	−0.968349	+	0.249602i	$0.919700\pi$
$6$		0			0
$7$	−2.37939	+	4.12122i	−0.899323	+	1.55767i	−0.0709618	+	0.997479i	$0.522607\pi$
$7$	−2.37939	+	4.12122i	−0.899323	+	1.55767i	−0.828361	+	0.560194i	$0.810726\pi$
$8$		0			0
$9$	0.407604	+	0.342020i	0.135868	+	0.114007i
$10$		0			0
$11$	2.37939	+	4.12122i	0.717412	+	1.24259i	0.962022	+	0.272972i	$0.0880066\pi$
$11$	2.37939	+	4.12122i	0.717412	+	1.24259i	−0.244610	+	0.969621i	$0.578660\pi$
$12$		0			0
$13$	1.76604	−	0.642788i	0.489813	−	0.178277i	−0.0852938	−	0.996356i	$-0.527183\pi$
$13$	1.76604	−	0.642788i	0.489813	−	0.178277i	0.575106	+	0.818079i	$0.304961\pi$
$14$		0			0
$15$	−0.113341	+	0.642788i	−0.0292645	+	0.165967i
$16$		0			0
$17$	1.17365	−	0.984808i	0.284651	−	0.238851i	−0.489270	−	0.872132i	$-0.662737\pi$
$17$	1.17365	−	0.984808i	0.284651	−	0.238851i	0.773922	+	0.633281i	$0.218292\pi$
$18$		0			0
$19$	0.694593	−	4.30320i	0.159350	−	0.987222i
$19$	0.694593	−	4.30320i	0.159350	−	0.987222i
$20$		0			0
$21$	−6.85117	+	5.74881i	−1.49505	+	1.25449i
$22$		0			0
$23$	1.06031	−	6.01330i	0.221089	−	1.25386i	−0.648932	−	0.760846i	$-0.724784\pi$
$23$	1.06031	−	6.01330i	0.221089	−	1.25386i	0.870021	−	0.493014i	$-0.164105\pi$
$24$		0			0
$25$	4.58512	−	1.66885i	0.917024	−	0.333770i
$26$		0			0
$27$	−2.31908	−	4.01676i	−0.446307	−	0.773026i
$28$		0			0
$29$	−1.52094	−	1.27622i	−0.282432	−	0.236989i	0.490555	−	0.871410i	$-0.336794\pi$
$29$	−1.52094	−	1.27622i	−0.282432	−	0.236989i	−0.772987	+	0.634421i	$0.781238\pi$
$30$		0			0
$31$	−1.68479	+	2.91815i	−0.302598	+	0.524115i	−0.976724	−	0.214502i	$-0.931187\pi$
$31$	−1.68479	+	2.91815i	−0.302598	+	0.524115i	0.674126	+	0.738616i	$0.264521\pi$
$32$		0			0
$33$	1.55303	+	8.80769i	0.270348	+	1.53322i
$34$		0			0
$35$	−1.55303	−	0.565258i	−0.262511	−	0.0955460i
$36$		0			0
$37$	−3.38919			−0.557179			−0.278589	−	0.960410i	$-0.589867\pi$
$37$	−3.38919			−0.557179			−0.278589	+	0.960410i	$0.589867\pi$
$38$		0			0
$39$	3.53209			0.565587
$40$		0			0
$41$	4.21941	+	1.53574i	0.658961	+	0.239842i	0.649788	−	0.760116i	$-0.274858\pi$
$41$	4.21941	+	1.53574i	0.658961	+	0.239842i	0.00917315	+	0.999958i	$0.497080\pi$
$42$		0			0
$43$	−0.365715	−	2.07407i	−0.0557710	−	0.316293i	0.944141	−	0.329541i	$-0.106894\pi$
$43$	−0.365715	−	2.07407i	−0.0557710	−	0.316293i	−0.999912	+	0.0132481i	$0.995783\pi$
$44$		0			0
$45$	−0.0923963	+	0.160035i	−0.0137736	+	0.0238566i
$46$		0			0
$47$	3.76991	+	3.16333i	0.549899	+	0.461420i	0.874907	−	0.484292i	$-0.160923\pi$
$47$	3.76991	+	3.16333i	0.549899	+	0.461420i	−0.325008	+	0.945711i	$0.605367\pi$
$48$		0			0
$49$	−7.82295	−	13.5497i	−1.11756	−	1.93568i
$50$		0			0
$51$	2.70574	−	0.984808i	0.378879	−	0.137901i
$52$		0			0
$53$	−2.18092	+	12.3686i	−0.299573	+	1.69896i	0.348440	+	0.937331i	$0.386712\pi$
$53$	−2.18092	+	12.3686i	−0.299573	+	1.69896i	−0.648012	+	0.761630i	$0.724399\pi$
$54$		0			0
$55$	−1.26604	+	1.06234i	−0.170713	+	0.143246i
$56$		0			0
$57$	3.99273	−	7.15317i	0.528849	−	0.947460i
$58$		0			0
$59$	−4.33615	+	3.63846i	−0.564519	+	0.473688i	−0.879822	−	0.475303i	$-0.842338\pi$
$59$	−4.33615	+	3.63846i	−0.564519	+	0.473688i	0.315303	+	0.948991i	$0.397894\pi$
$60$		0			0
$61$	1.73530	−	9.84137i	0.222182	−	1.26006i	−0.645817	−	0.763493i	$-0.723483\pi$
$61$	1.73530	−	9.84137i	0.222182	−	1.26006i	0.867999	−	0.496566i	$-0.165406\pi$
$62$		0			0
$63$	−2.37939	+	0.866025i	−0.299774	+	0.109109i
$64$		0			0
$65$	0.326352	+	0.565258i	0.0404790	+	0.0701116i
$66$		0			0
$67$	−8.11721	−	6.81115i	−0.991675	−	0.832114i	−0.00586579	−	0.999983i	$-0.501867\pi$
$67$	−8.11721	−	6.81115i	−0.991675	−	0.832114i	−0.985809	+	0.167869i	$0.946312\pi$
$68$		0			0
$69$	5.73783	−	9.93821i	0.690753	−	1.19642i
$70$		0			0
$71$	−1.99613	−	11.3206i	−0.236897	−	1.34351i	−0.838582	−	0.544776i	$-0.816615\pi$
$71$	−1.99613	−	11.3206i	−0.236897	−	1.34351i	0.601685	−	0.798734i	$-0.294496\pi$
$72$		0			0
$73$	13.7369	+	4.99984i	1.60779	+	0.585187i	0.981001	−	0.194003i	$-0.0621473\pi$
$73$	13.7369	+	4.99984i	1.60779	+	0.585187i	0.626787	+	0.779190i	$0.284369\pi$
$74$		0			0
$75$	9.17024			1.05889
$76$		0			0
$77$	−22.6459			−2.58074
$78$		0			0
$79$	2.21941	+	0.807798i	0.249703	+	0.0908844i	0.463839	−	0.885919i	$-0.346471\pi$
$79$	2.21941	+	0.807798i	0.249703	+	0.0908844i	−0.214136	+	0.976804i	$0.568694\pi$
$80$		0			0
$81$	−1.79086	−	10.1565i	−0.198984	−	1.12850i
$82$		0			0
$83$	−5.76857	+	9.99146i	−0.633183	+	1.09670i	0.353714	+	0.935354i	$0.384919\pi$
$83$	−5.76857	+	9.99146i	−0.633183	+	1.09670i	−0.986897	+	0.161351i	$0.948415\pi$
$84$		0			0
$85$	0.407604	+	0.342020i	0.0442108	+	0.0370973i
$86$		0			0
$87$	−1.86571	−	3.23151i	−0.200026	−	0.346455i
$88$		0			0
$89$	−5.29813	+	1.92836i	−0.561601	+	0.204406i	−0.607193	−	0.794554i	$-0.707705\pi$
$89$	−5.29813	+	1.92836i	−0.561601	+	0.204406i	0.0455924	+	0.998960i	$0.485482\pi$
$90$		0			0
$91$	−1.55303	+	8.80769i	−0.162802	+	0.923297i
$92$		0			0
$93$	−4.85117	+	4.07061i	−0.503043	+	0.422103i
$94$		0			0
$95$	1.51367	−	0.0219501i	0.155299	−	0.00225203i
$96$		0			0
$97$	5.86824	−	4.92404i	0.595830	−	0.499960i	−0.294273	−	0.955722i	$-0.595077\pi$
$97$	5.86824	−	4.92404i	0.595830	−	0.499960i	0.890102	+	0.455761i	$0.150633\pi$
$98$		0			0
$99$	−0.439693	+	2.49362i	−0.0441908	+	0.250618i
$100$		0			0
$101$	4.21941	−	1.53574i	0.419847	−	0.152812i	−0.123453	−	0.992350i	$-0.539397\pi$
$101$	4.21941	−	1.53574i	0.419847	−	0.152812i	0.543300	+	0.839539i	$0.317175\pi$
$102$		0			0
$103$	−7.50774	−	13.0038i	−0.739760	−	1.28130i	−0.952603	−	0.304215i	$-0.901606\pi$
$103$	−7.50774	−	13.0038i	−0.739760	−	1.28130i	0.212844	−	0.977086i	$-0.431727\pi$
$104$		0			0
$105$	−2.37939	−	1.99654i	−0.232204	−	0.194842i
$106$		0			0
$107$	−5.44356	+	9.42853i	−0.526249	+	0.911490i	0.473283	+	0.880910i	$0.343069\pi$
$107$	−5.44356	+	9.42853i	−0.526249	+	0.911490i	−0.999532	+	0.0305799i	$0.990265\pi$
$108$		0			0
$109$	−1.32888	−	7.53644i	−0.127283	−	0.721860i	−0.979925	−	0.199365i	$-0.936112\pi$
$109$	−1.32888	−	7.53644i	−0.127283	−	0.721860i	0.852642	−	0.522496i	$-0.174999\pi$
$110$		0			0
$111$	−5.98545	−	2.17853i	−0.568114	−	0.206777i
$112$		0			0
$113$	0.128356			0.0120747			0.00603734	−	0.999982i	$-0.498078\pi$
$113$	0.128356			0.0120747			0.00603734	+	0.999982i	$0.498078\pi$
$114$		0			0
$115$	2.12061			0.197748
$116$		0			0
$117$	0.939693	+	0.342020i	0.0868746	+	0.0316198i
$118$		0			0
$119$	1.26604	+	7.18009i	0.116058	+	0.658198i
$120$		0			0
$121$	−5.82295	+	10.0856i	−0.529359	+	0.916877i
$122$		0			0
$123$	6.46451	+	5.42437i	0.582885	+	0.489099i
$124$		0			0
$125$	1.71554	+	2.97140i	0.153442	+	0.265770i
$126$		0			0
$127$	18.1211	−	6.59553i	1.60799	−	0.585259i	0.626946	−	0.779063i	$-0.284305\pi$
$127$	18.1211	−	6.59553i	1.60799	−	0.585259i	0.981040	+	0.193804i	$0.0620826\pi$
$128$		0			0
$129$	0.687319	−	3.89798i	0.0605150	−	0.343198i
$130$		0			0
$131$	13.5064	−	11.3332i	1.18006	−	0.990187i	0.180081	−	0.983652i	$-0.442364\pi$
$131$	13.5064	−	11.3332i	1.18006	−	0.990187i	0.999979	−	0.00653553i	$-0.00208034\pi$
$132$		0			0
$133$	16.0817	+	13.1015i	1.39446	+	1.13605i
$134$		0			0
$135$	1.23396	−	1.03541i	0.106202	−	0.0891140i
$136$		0			0
$137$	−3.41266	+	19.3541i	−0.291563	+	1.65354i	0.389290	+	0.921115i	$0.372720\pi$
$137$	−3.41266	+	19.3541i	−0.291563	+	1.65354i	−0.680853	+	0.732420i	$0.738391\pi$
$138$		0			0
$139$	−9.73695	+	3.54396i	−0.825877	+	0.300595i	−0.720166	−	0.693802i	$-0.755934\pi$
$139$	−9.73695	+	3.54396i	−0.825877	+	0.300595i	−0.105712	+	0.994397i	$0.533712\pi$
$140$		0			0
$141$	4.62449	+	8.00984i	0.389452	+	0.674550i
$142$		0			0
$143$	6.85117	+	5.74881i	0.572923	+	0.480740i
$144$		0			0
$145$	0.344770	−	0.597159i	0.0286316	−	0.0495914i
$146$		0			0
$147$	−5.10607	−	28.9579i	−0.421141	−	2.38841i
$148$		0			0
$149$	0.00727396	+	0.00264750i	0.000595906	+	0.000216892i	0.342318	−	0.939584i	$-0.388788\pi$
$149$	0.00727396	+	0.00264750i	0.000595906	+	0.000216892i	−0.341722	+	0.939801i	$0.611010\pi$
$150$		0			0
$151$	16.0000			1.30206			0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000			1.30206			0.651031	+	0.759051i	$0.274337\pi$
$152$		0			0
$153$	0.815207			0.0659056
$154$		0			0
$155$	−1.09967	−	0.400247i	−0.0883276	−	0.0321486i
$156$		0			0
$157$	0.996130	+	5.64933i	0.0794998	+	0.450866i	0.998409	+	0.0563955i	$0.0179608\pi$
$157$	0.996130	+	5.64933i	0.0794998	+	0.450866i	−0.918909	+	0.394470i	$0.870928\pi$
$158$		0			0
$159$	−11.8020	+	20.4417i	−0.935960	+	1.62113i
$160$		0			0
$161$	22.2592	+	18.6777i	1.75427	+	1.47201i
$162$		0			0
$163$	−1.29561	−	2.24406i	−0.101480	−	0.175768i	0.810815	−	0.585303i	$-0.199024\pi$
$163$	−1.29561	−	2.24406i	−0.101480	−	0.175768i	−0.912295	+	0.409535i	$0.865691\pi$
$164$		0			0
$165$	−2.91875	+	1.06234i	−0.227224	+	0.0827029i
$166$		0			0
$167$	−3.15183	+	17.8749i	−0.243896	+	1.38320i	0.579148	+	0.815223i	$0.303385\pi$
$167$	−3.15183	+	17.8749i	−0.243896	+	1.38320i	−0.823043	+	0.567978i	$0.807726\pi$
$168$		0			0
$169$	−7.25284	+	6.08586i	−0.557911	+	0.468143i
$170$		0			0
$171$	1.75490	−	1.51644i	0.134201	−	0.115965i
$172$		0			0
$173$	−6.95471	+	5.83569i	−0.528757	+	0.443679i	−0.867672	−	0.497137i	$-0.834384\pi$
$173$	−6.95471	+	5.83569i	−0.528757	+	0.443679i	0.338915	+	0.940817i	$0.389940\pi$
$174$		0			0
$175$	−4.03209	+	22.8671i	−0.304797	+	1.72859i
$176$		0			0
$177$	−9.99660	+	3.63846i	−0.751390	+	0.273484i
$178$		0			0
$179$	3.31521	+	5.74211i	0.247790	+	0.429185i	0.962912	−	0.269814i	$-0.0869623\pi$
$179$	3.31521	+	5.74211i	0.247790	+	0.429185i	−0.715122	+	0.698999i	$0.753629\pi$
$180$		0			0
$181$	−3.89053	−	3.26454i	−0.289181	−	0.242651i	0.486643	−	0.873601i	$-0.338221\pi$
$181$	−3.89053	−	3.26454i	−0.289181	−	0.242651i	−0.775824	+	0.630949i	$0.782666\pi$
$182$		0			0
$183$	9.39053	−	16.2649i	0.694168	−	1.20233i
$184$		0			0
$185$	−0.204393	−	1.15917i	−0.0150273	−	0.0852239i
$186$		0			0
$187$	6.85117	+	2.49362i	0.501007	+	0.182352i
$188$		0			0
$189$	22.0719			1.60550
$190$		0			0
$191$	−8.90673			−0.644468			−0.322234	−	0.946660i	$-0.604434\pi$
$191$	−8.90673			−0.644468			−0.322234	+	0.946660i	$0.604434\pi$
$192$		0			0
$193$	−18.1211	−	6.59553i	−1.30438	−	0.474757i	−0.405962	−	0.913890i	$-0.633063\pi$
$193$	−18.1211	−	6.59553i	−1.30438	−	0.474757i	−0.898422	+	0.439133i	$0.855286\pi$
$194$		0			0
$195$	0.213011	+	1.20805i	0.0152540	+	0.0865099i
$196$		0			0
$197$	8.95336	−	15.5077i	0.637901	−	1.10488i	−0.347992	−	0.937498i	$-0.613136\pi$
$197$	8.95336	−	15.5077i	0.637901	−	1.10488i	0.985893	−	0.167379i	$-0.0535303\pi$
$198$		0			0
$199$	−6.68345	−	5.60808i	−0.473777	−	0.397546i	0.374393	−	0.927270i	$-0.377851\pi$
$199$	−6.68345	−	5.60808i	−0.473777	−	0.397546i	−0.848170	+	0.529724i	$0.822296\pi$
$200$		0			0
$201$	−9.95723	−	17.2464i	−0.702329	−	1.21647i
$202$		0			0
$203$	8.87851	−	3.23151i	0.623149	−	0.226808i
$204$		0			0
$205$	−0.270792	+	1.53574i	−0.0189129	+	0.107261i
$206$		0			0
$207$	2.48886	−	2.08840i	0.172987	−	0.145154i
$208$		0			0
$209$	19.3871	−	7.37641i	1.34104	−	0.510237i
$210$		0			0
$211$	−0.577382	+	0.484481i	−0.0397486	+	0.0333530i	−0.662446	−	0.749110i	$-0.730481\pi$
$211$	−0.577382	+	0.484481i	−0.0397486	+	0.0333530i	0.622697	+	0.782463i	$0.286037\pi$
$212$		0			0
$213$	3.75150	−	21.2758i	0.257048	−	1.45779i
$214$		0			0
$215$	0.687319	−	0.250164i	0.0468747	−	0.0170610i
$216$		0			0
$217$	−8.01754	−	13.8868i	−0.544266	−	0.942697i
$218$		0			0
$219$	21.0462	+	17.6599i	1.42217	+	1.19334i
$220$		0			0
$221$	1.43969	−	2.49362i	0.0968442	−	0.167739i
$222$		0			0
$223$	0.826819	+	4.68912i	0.0553679	+	0.314007i	0.999896	−	0.0144238i	$-0.00459140\pi$
$223$	0.826819	+	4.68912i	0.0553679	+	0.314007i	−0.944528	+	0.328431i	$0.893480\pi$
$224$		0			0
$225$	2.43969	+	0.887975i	0.162646	+	0.0591984i
$226$		0			0
$227$	−28.4243			−1.88658			−0.943292	−	0.331963i	$-0.892289\pi$
$227$	−28.4243			−1.88658			−0.943292	+	0.331963i	$0.892289\pi$
$228$		0			0
$229$	−15.6459			−1.03391			−0.516955	−	0.856013i	$-0.672935\pi$
$229$	−15.6459			−1.03391			−0.516955	+	0.856013i	$0.672935\pi$
$230$		0			0
$231$	−39.9937	−	14.5565i	−2.63139	−	0.957747i
$232$		0			0
$233$	0.0603074	+	0.342020i	0.00395087	+	0.0224065i	0.986719	−	0.162434i	$-0.0519344\pi$
$233$	0.0603074	+	0.342020i	0.00395087	+	0.0224065i	−0.982769	+	0.184840i	$0.940823\pi$
$234$		0			0
$235$	−0.854570	+	1.48016i	−0.0557460	+	0.0965549i
$236$		0			0
$237$	3.40033	+	2.85322i	0.220875	+	0.185336i
$238$		0			0
$239$	3.20233	+	5.54660i	0.207142	+	0.358780i	0.950813	−	0.309765i	$-0.100251\pi$
$239$	3.20233	+	5.54660i	0.207142	+	0.358780i	−0.743671	+	0.668545i	$0.766917\pi$
$240$		0			0
$241$	−15.4265	+	5.61478i	−0.993708	+	0.361680i	−0.787155	−	0.616756i	$-0.788447\pi$
$241$	−15.4265	+	5.61478i	−0.993708	+	0.361680i	−0.206553	+	0.978435i	$0.566224\pi$
$242$		0			0
$243$	0.949493	−	5.38484i	0.0609100	−	0.345438i
$244$		0			0
$245$	4.16250	−	3.49276i	0.265933	−	0.223144i
$246$		0			0
$247$	−1.53936	−	8.04612i	−0.0979473	−	0.511962i
$248$		0			0
$249$	−16.6099	+	13.9374i	−1.05261	+	0.883246i
$250$		0			0
$251$	−0.116744	+	0.662090i	−0.00736884	+	0.0417908i	−0.988270	−	0.152714i	$-0.951199\pi$
$251$	−0.116744	+	0.662090i	−0.00736884	+	0.0417908i	0.980902	+	0.194504i	$0.0623099\pi$
$252$		0			0
$253$	27.3050	−	9.93821i	1.71665	−	0.624810i
$254$		0			0
$255$	0.500000	+	0.866025i	0.0313112	+	0.0542326i
$256$		0			0
$257$	−7.15136	−	6.00070i	−0.446090	−	0.374314i	0.391893	−	0.920011i	$-0.371820\pi$
$257$	−7.15136	−	6.00070i	−0.446090	−	0.374314i	−0.837982	+	0.545697i	$0.816265\pi$
$258$		0			0
$259$	8.06418	−	13.9676i	0.501084	−	0.867902i
$260$		0			0
$261$	−0.183448	−	1.04039i	−0.0113552	−	0.0643984i
$262$		0			0
$263$	10.6728	+	3.88457i	0.658111	+	0.239533i	0.649421	−	0.760429i	$-0.275011\pi$
$263$	10.6728	+	3.88457i	0.658111	+	0.239533i	0.00869056	+	0.999962i	$0.497234\pi$
$264$		0			0
$265$	−4.36184			−0.267946
$266$		0			0
$267$	−10.5963			−0.648481
$268$		0			0
$269$	−17.4265	−	6.34272i	−1.06251	−	0.386723i	−0.249140	−	0.968467i	$-0.580148\pi$
$269$	−17.4265	−	6.34272i	−1.06251	−	0.386723i	−0.813371	+	0.581745i	$0.802370\pi$
$270$		0			0
$271$	−3.72580	−	21.1301i	−0.226326	−	1.28356i	−0.860133	−	0.510070i	$-0.829620\pi$
$271$	−3.72580	−	21.1301i	−0.226326	−	1.28356i	0.633807	−	0.773492i	$-0.281492\pi$
$272$		0			0
$273$	−8.40420	+	14.5565i	−0.508645	+	0.881000i
$274$		0			0
$275$	17.7875	+	14.9254i	1.07262	+	0.900038i
$276$		0			0
$277$	8.01754	+	13.8868i	0.481727	+	0.834376i	0.999780	−	0.0209725i	$-0.00667623\pi$
$277$	8.01754	+	13.8868i	0.481727	+	0.834376i	−0.518053	+	0.855349i	$0.673343\pi$
$278$		0			0
$279$	−1.68479	+	0.613214i	−0.100866	+	0.0367122i
$280$		0			0
$281$	3.25284	−	18.4478i	0.194048	−	1.10050i	−0.719719	−	0.694265i	$-0.755730\pi$
$281$	3.25284	−	18.4478i	0.194048	−	1.10050i	0.913768	−	0.406237i	$-0.133159\pi$
$282$		0			0
$283$	−5.40033	+	4.53141i	−0.321016	+	0.269365i	−0.789027	−	0.614358i	$-0.789415\pi$
$283$	−5.40033	+	4.53141i	−0.321016	+	0.269365i	0.468011	+	0.883723i	$0.344971\pi$
$284$		0			0
$285$	2.68732	+	0.934204i	0.159183	+	0.0553375i
$286$		0			0
$287$	−16.3687	+	13.7350i	−0.966214	+	0.810750i
$288$		0			0
$289$	−2.54442	+	14.4301i	−0.149671	+	0.848829i
$290$		0			0
$291$	13.5287	−	4.92404i	0.793066	−	0.288652i
$292$		0			0
$293$	4.13041	+	7.15409i	0.241301	+	0.417946i	0.961085	−	0.276252i	$-0.0890924\pi$
$293$	4.13041	+	7.15409i	0.241301	+	0.417946i	−0.719784	+	0.694198i	$0.755759\pi$
$294$		0			0
$295$	−1.50593	−	1.26363i	−0.0876786	−	0.0735711i
$296$		0			0
$297$	11.0360	−	19.1148i	0.640371	−	1.10916i
$298$		0			0
$299$	−1.99273	−	11.3013i	−0.115242	−	0.653572i
$300$		0			0
$301$	9.41787	+	3.42782i	0.542837	+	0.197577i
$302$		0			0
$303$	8.43882			0.484797
$304$		0			0
$305$	3.47060			0.198726
$306$		0			0
$307$	−4.44609	−	1.61824i	−0.253752	−	0.0923581i	0.212012	−	0.977267i	$-0.431998\pi$
$307$	−4.44609	−	1.61824i	−0.253752	−	0.0923581i	−0.465764	+	0.884909i	$0.654220\pi$
$308$		0			0
$309$	−4.90033	−	27.7912i	−0.278770	−	1.58098i
$310$		0			0
$311$	5.62061	−	9.73519i	0.318716	−	0.552032i	−0.661505	−	0.749941i	$-0.730082\pi$
$311$	5.62061	−	9.73519i	0.318716	−	0.552032i	0.980220	+	0.197909i	$0.0634151\pi$
$312$		0			0
$313$	5.30200	+	4.44891i	0.299687	+	0.251467i	0.780214	−	0.625513i	$-0.215110\pi$
$313$	5.30200	+	4.44891i	0.299687	+	0.251467i	−0.480527	+	0.876980i	$0.659555\pi$
$314$		0			0
$315$	−0.439693	−	0.761570i	−0.0247739	−	0.0429096i
$316$		0			0
$317$	13.7369	−	4.99984i	0.771544	−	0.280819i	0.0739019	−	0.997266i	$-0.476455\pi$
$317$	13.7369	−	4.99984i	0.771544	−	0.280819i	0.697642	+	0.716447i	$0.254233\pi$
$318$		0			0
$319$	1.64068	−	9.30477i	0.0918606	−	0.520967i
$320$		0			0
$321$	−15.6741	+	13.1521i	−0.874844	+	0.734081i
$322$		0			0
$323$	−3.42262	−	5.73448i	−0.190440	−	0.319075i
$324$		0			0
$325$	7.02481	−	5.89452i	0.389667	−	0.326969i
$326$		0			0
$327$	2.49747	−	14.1639i	0.138111	−	0.783264i
$328$		0			0
$329$	−22.0069	+	8.00984i	−1.21328	+	0.441597i
$330$		0			0
$331$	−1.83275	−	3.17441i	−0.100737	−	0.174482i	0.811252	−	0.584697i	$-0.198787\pi$
$331$	−1.83275	−	3.17441i	−0.100737	−	0.174482i	−0.911988	+	0.410216i	$0.865453\pi$
$332$		0			0
$333$	−1.38144	−	1.15917i	−0.0757027	−	0.0635221i
$334$		0			0
$335$	1.84002	−	3.18701i	0.100531	−	0.174125i
$336$		0			0
$337$	−0.579603	−	3.28709i	−0.0315730	−	0.179059i	0.964943	−	0.262459i	$-0.0845334\pi$
$337$	−0.579603	−	3.28709i	−0.0315730	−	0.179059i	−0.996516	+	0.0833994i	$0.973422\pi$
$338$		0			0
$339$	0.226682	+	0.0825054i	0.0123117	+	0.00448108i
$340$		0			0
$341$	−16.0351			−0.868348
$342$		0			0
$343$	41.1438			2.22156
$344$		0			0
$345$	3.74510	+	1.36310i	0.201629	+	0.0733871i
$346$		0			0
$347$	−1.55825	−	8.83726i	−0.0836511	−	0.474409i	−0.997640	−	0.0686688i	$-0.978125\pi$
$347$	−1.55825	−	8.83726i	−0.0836511	−	0.474409i	0.913988	−	0.405740i	$-0.132986\pi$
$348$		0			0
$349$	−5.50000	+	9.52628i	−0.294408	+	0.509930i	−0.974847	−	0.222875i	$-0.928456\pi$
$349$	−5.50000	+	9.52628i	−0.294408	+	0.509930i	0.680439	+	0.732805i	$0.261789\pi$
$350$		0			0
$351$	−6.67752	−	5.60310i	−0.356420	−	0.299072i
$352$		0			0
$353$	11.7763	+	20.3972i	0.626790	+	1.08563i	0.988192	+	0.153222i	$0.0489649\pi$
$353$	11.7763	+	20.3972i	0.626790	+	1.08563i	−0.361402	+	0.932410i	$0.617702\pi$
$354$		0			0
$355$	3.75150	−	1.36543i	0.199109	−	0.0724697i
$356$		0			0
$357$	−2.37939	+	13.4942i	−0.125930	+	0.714187i
$358$		0			0
$359$	−17.7854	+	14.9237i	−0.938677	+	0.787644i	−0.977355	−	0.211608i	$-0.932130\pi$
$359$	−17.7854	+	14.9237i	−0.938677	+	0.787644i	0.0386773	+	0.999252i	$0.487686\pi$
$360$		0			0
$361$	−18.0351	−	5.97794i	−0.949215	−	0.314629i
$362$		0			0
$363$	−16.7665	+	14.0688i	−0.880014	+	0.738419i
$364$		0			0
$365$	−0.881607	+	4.99984i	−0.0461454	+	0.261704i
$366$		0			0
$367$	8.44609	−	3.07413i	0.440882	−	0.160468i	−0.112035	−	0.993704i	$-0.535737\pi$
$367$	8.44609	−	3.07413i	0.440882	−	0.160468i	0.552917	+	0.833236i	$0.313515\pi$
$368$		0			0
$369$	1.19459	+	2.06910i	0.0621880	+	0.107713i
$370$		0			0
$371$	−45.7845	−	38.4178i	−2.37701	−	1.99455i
$372$		0			0
$373$	−10.3229	+	17.8799i	−0.534502	+	0.925785i	0.464685	+	0.885476i	$0.346167\pi$
$373$	−10.3229	+	17.8799i	−0.534502	+	0.925785i	−0.999187	+	0.0403087i	$0.987166\pi$
$374$		0			0
$375$	1.11974	+	6.35035i	0.0578230	+	0.327930i
$376$		0			0
$377$	−3.50640	−	1.27622i	−0.180589	−	0.0657289i
$378$		0			0
$379$	−0.650015			−0.0333890			−0.0166945	−	0.999861i	$-0.505314\pi$
$379$	−0.650015			−0.0333890			−0.0166945	+	0.999861i	$0.505314\pi$
$380$		0			0
$381$	36.2422			1.85674
$382$		0			0
$383$	17.4957	+	6.36792i	0.893989	+	0.325386i	0.747842	−	0.663877i	$-0.231090\pi$
$383$	17.4957	+	6.36792i	0.893989	+	0.325386i	0.146148	+	0.989263i	$0.453312\pi$
$384$		0			0
$385$	−1.36571	−	7.74535i	−0.0696033	−	0.394740i
$386$		0			0
$387$	0.560307	−	0.970481i	0.0284820	−	0.0493323i
$388$		0			0
$389$	0.479055	+	0.401975i	0.0242891	+	0.0203810i	0.654851	−	0.755758i	$-0.272731\pi$
$389$	0.479055	+	0.401975i	0.0242891	+	0.0203810i	−0.630562	+	0.776139i	$0.717176\pi$
$390$		0			0
$391$	−4.67752	−	8.10170i	−0.236552	−	0.409721i
$392$		0			0
$393$	31.1377	−	11.3332i	1.57069	−	0.571685i
$394$		0			0
$395$	−0.142437	+	0.807798i	−0.00716677	+	0.0406447i
$396$		0			0
$397$	−6.01889	+	5.05044i	−0.302079	+	0.253475i	−0.781209	−	0.624269i	$-0.785397\pi$
$397$	−6.01889	+	5.05044i	−0.302079	+	0.253475i	0.479130	+	0.877744i	$0.340952\pi$
$398$		0			0
$399$	19.9795	+	33.4750i	1.00023	+	1.67585i
$400$		0			0
$401$	−7.97431	+	6.69124i	−0.398218	+	0.334145i	−0.819804	−	0.572644i	$-0.805918\pi$
$401$	−7.97431	+	6.69124i	−0.398218	+	0.334145i	0.421586	+	0.906788i	$0.361473\pi$
$402$		0			0
$403$	−1.09967	+	6.23654i	−0.0547785	+	0.310664i
$404$		0			0
$405$	3.36571	−	1.22502i	0.167244	−	0.0608717i
$406$		0			0
$407$	−8.06418	−	13.9676i	−0.399726	−	0.692347i
$408$		0			0
$409$	11.2574	+	9.44610i	0.556644	+	0.467080i	0.877183	−	0.480155i	$-0.159420\pi$
$409$	11.2574	+	9.44610i	0.556644	+	0.467080i	−0.320540	+	0.947235i	$0.603864\pi$
$410$		0			0
$411$	−18.4675	+	31.9866i	−0.910935	+	1.57779i
$412$		0			0
$413$	−4.67752	−	26.5275i	−0.230166	−	1.30533i
$414$		0			0
$415$	−3.76517	−	1.37041i	−0.184825	−	0.0672707i
$416$		0			0
$417$	−19.4739			−0.953641
$418$		0			0
$419$	−7.03508			−0.343686			−0.171843	−	0.985124i	$-0.554972\pi$
$419$	−7.03508			−0.343686			−0.171843	+	0.985124i	$0.554972\pi$
$420$		0			0
$421$	−33.3974	−	12.1557i	−1.62769	−	0.592430i	−0.642864	−	0.765980i	$-0.722254\pi$
$421$	−33.3974	−	12.1557i	−1.62769	−	0.592430i	−0.984825	+	0.173550i	$0.944476\pi$
$422$		0			0
$423$	0.454707	+	2.57877i	0.0221086	+	0.125384i
$424$		0			0
$425$	3.73783	−	6.47410i	0.181311	−	0.314040i
$426$		0			0
$427$	36.4295	+	30.5680i	1.76295	+	1.47929i
$428$		0			0
$429$	8.40420	+	14.5565i	0.405759	+	0.702795i
$430$		0			0
$431$	19.2690	−	7.01336i	0.928157	−	0.337821i	0.166678	−	0.986011i	$-0.446696\pi$
$431$	19.2690	−	7.01336i	0.928157	−	0.337821i	0.761479	+	0.648190i	$0.224474\pi$
$432$		0			0
$433$	−3.50181	+	19.8598i	−0.168286	+	0.954399i	0.777325	+	0.629100i	$0.216576\pi$
$433$	−3.50181	+	19.8598i	−0.168286	+	0.954399i	−0.945611	+	0.325299i	$0.894535\pi$
$434$		0			0
$435$	0.992726	−	0.832996i	0.0475976	−	0.0399391i
$436$		0			0
$437$	−25.1400	−	8.73951i	−1.20261	−	0.418068i
$438$		0			0
$439$	−2.38073	+	1.99767i	−0.113626	+	0.0953435i	−0.697830	−	0.716263i	$-0.745851\pi$
$439$	−2.38073	+	1.99767i	−0.113626	+	0.0953435i	0.584204	+	0.811607i	$0.301407\pi$
$440$		0			0
$441$	1.44562	−	8.19853i	0.0688392	−	0.390406i
$442$		0			0
$443$	−8.21941	+	2.99162i	−0.390516	+	0.142136i	−0.529813	−	0.848114i	$-0.677738\pi$
$443$	−8.21941	+	2.99162i	−0.390516	+	0.142136i	0.139297	+	0.990251i	$0.455516\pi$
$444$		0			0
$445$	−0.979055	−	1.69577i	−0.0464117	−	0.0803874i
$446$		0			0
$447$	0.0111444	+	0.00935122i	0.000527110	+	0.000442298i
$448$		0			0
$449$	19.4067	−	33.6134i	0.915860	−	1.58632i	0.110223	−	0.993907i	$-0.464844\pi$
$449$	19.4067	−	33.6134i	0.915860	−	1.58632i	0.805637	−	0.592409i	$-0.201823\pi$
$450$		0			0
$451$	3.71048	+	21.0432i	0.174720	+	0.990886i
$452$		0			0
$453$	28.2567	+	10.2846i	1.32762	+	0.483213i
$454$		0			0
$455$	−3.10607			−0.145615
$456$		0			0
$457$	13.0933			0.612478			0.306239	−	0.951955i	$-0.400929\pi$
$457$	13.0933			0.612478			0.306239	+	0.951955i	$0.400929\pi$
$458$		0			0
$459$	−6.67752	−	2.43042i	−0.311680	−	0.113442i
$460$		0			0
$461$	−2.03895	−	11.5635i	−0.0949635	−	0.538565i	−0.994759	−	0.102252i	$-0.967395\pi$
$461$	−2.03895	−	11.5635i	−0.0949635	−	0.538565i	0.899795	−	0.436313i	$-0.143716\pi$
$462$		0			0
$463$	−7.57192	+	13.1149i	−0.351897	+	0.609503i	−0.986582	−	0.163268i	$-0.947797\pi$
$463$	−7.57192	+	13.1149i	−0.351897	+	0.609503i	0.634685	+	0.772771i	$0.281130\pi$
$464$		0			0
$465$	−1.68479	−	1.41371i	−0.0781304	−	0.0655592i
$466$		0			0
$467$	15.6848	+	27.1669i	0.725806	+	1.25713i	0.958642	+	0.284616i	$0.0918662\pi$
$467$	15.6848	+	27.1669i	0.725806	+	1.25713i	−0.232836	+	0.972516i	$0.574801\pi$
$468$		0			0
$469$	47.3842	−	17.2464i	2.18800	−	0.796366i
$470$		0			0
$471$	−1.87211	+	10.6173i	−0.0862623	+	0.489218i
$472$		0			0
$473$	7.67752	−	6.44220i	0.353013	−	0.296213i
$474$		0			0
$475$	−3.99660	−	20.8899i	−0.183376	−	0.958493i
$476$		0			0
$477$	−5.11927	+	4.29558i	−0.234395	+	0.196681i
$478$		0			0
$479$	2.65152	−	15.0375i	0.121151	−	0.687082i	−0.862369	−	0.506281i	$-0.831020\pi$
$479$	2.65152	−	15.0375i	0.121151	−	0.687082i	0.983520	−	0.180801i	$-0.0578690\pi$
$480$		0			0
$481$	−5.98545	+	2.17853i	−0.272913	+	0.0993323i
$482$		0			0
$483$	27.3050	+	47.2936i	1.24242	+	2.15194i
$484$		0			0
$485$	2.03802	+	1.71010i	0.0925417	+	0.0776517i
$486$		0			0
$487$	18.5428	−	32.1171i	0.840256	−	1.45537i	−0.0494231	−	0.998778i	$-0.515738\pi$
$487$	18.5428	−	32.1171i	0.840256	−	1.45537i	0.889679	−	0.456587i	$-0.150928\pi$
$488$		0			0
$489$	−0.845647	−	4.79591i	−0.0382415	−	0.216878i
$490$		0			0
$491$	26.4761	+	9.63652i	1.19485	+	0.434890i	0.861424	−	0.507886i	$-0.169573\pi$
$491$	26.4761	+	9.63652i	1.19485	+	0.434890i	0.333426	+	0.942776i	$0.391795\pi$
$492$		0			0
$493$	−3.04189			−0.137000
$494$		0			0
$495$	−0.879385			−0.0395254
$496$		0			0
$497$	51.4043	+	18.7096i	2.30580	+	0.839241i
$498$		0			0
$499$	−2.25284	−	12.7765i	−0.100851	−	0.571954i	−0.992797	−	0.119812i	$-0.961771\pi$
$499$	−2.25284	−	12.7765i	−0.100851	−	0.571954i	0.891946	−	0.452143i	$-0.149340\pi$
$500$		0			0
$501$	−17.0560	+	29.5419i	−0.762007	+	1.31983i
$502$		0			0
$503$	8.33615	+	6.99486i	0.371691	+	0.311885i	0.809430	−	0.587216i	$-0.199776\pi$
$503$	8.33615	+	6.99486i	0.371691	+	0.311885i	−0.437739	+	0.899102i	$0.644221\pi$
$504$		0			0
$505$	0.779715	+	1.35051i	0.0346969	+	0.0600967i
$506$		0			0
$507$	−16.7208	+	6.08586i	−0.742595	+	0.270282i
$508$		0			0
$509$	−1.99437	+	11.3107i	−0.0883991	+	0.501336i	0.908172	+	0.418597i	$0.137478\pi$
$509$	−1.99437	+	11.3107i	−0.0883991	+	0.501336i	−0.996571	+	0.0827393i	$0.973633\pi$
$510$		0			0
$511$	−53.2909	+	44.7164i	−2.35745	+	1.97814i
$512$		0			0
$513$	−18.8957	+	7.18945i	−0.834267	+	0.317422i
$514$		0			0
$515$	3.99479	−	3.35202i	0.176031	−	0.147708i
$516$		0			0
$517$	−4.06670	+	23.0634i	−0.178853	+	1.01433i
$518$		0			0
$519$	−16.0334	+	5.83569i	−0.703790	+	0.256158i
$520$		0			0
$521$	3.43582	+	5.95102i	0.150526	+	0.260719i	0.931421	−	0.363944i	$-0.118570\pi$
$521$	3.43582	+	5.95102i	0.150526	+	0.260719i	−0.780895	+	0.624662i	$0.785237\pi$
$522$		0			0
$523$	9.52869	+	7.99552i	0.416660	+	0.349620i	0.826891	−	0.562362i	$-0.190107\pi$
$523$	9.52869	+	7.99552i	0.416660	+	0.349620i	−0.410231	+	0.911982i	$0.634552\pi$
$524$		0			0
$525$	−21.8195	+	37.7926i	−0.952283	+	1.64940i
$526$		0			0
$527$	0.896459	+	5.08407i	0.0390504	+	0.221466i
$528$		0			0
$529$	−13.4226	−	4.88543i	−0.583592	−	0.212410i
$530$		0			0
$531$	−3.01186			−0.130704
$532$		0			0
$533$	8.43882			0.365526
$534$		0			0
$535$	−3.55303	−	1.29320i	−0.153611	−	0.0559098i
$536$		0			0
$537$	2.16385	+	12.2718i	0.0933769	+	0.529567i
$538$		0			0
$539$	37.2276	−	64.4801i	1.60351	−	2.77736i
$540$		0			0
$541$	−9.47637	−	7.95162i	−0.407421	−	0.341867i	0.415933	−	0.909395i	$-0.363455\pi$
$541$	−9.47637	−	7.95162i	−0.407421	−	0.341867i	−0.823354	+	0.567529i	$0.807900\pi$
$542$		0			0
$543$	−4.77244	−	8.26611i	−0.204805	−	0.354733i
$544$		0			0
$545$	2.49747	−	0.909006i	0.106980	−	0.0389375i
$546$		0			0
$547$	3.98252	−	22.5860i	0.170280	−	0.965706i	−0.773172	−	0.634197i	$-0.781331\pi$
$547$	3.98252	−	22.5860i	0.170280	−	0.965706i	0.943452	−	0.331510i	$-0.107558\pi$
$548$		0			0
$549$	4.07326	−	3.41787i	0.173843	−	0.145871i
$550$		0			0
$551$	−6.54829	+	5.65847i	−0.278966	+	0.241059i
$552$		0			0
$553$	−8.60994	+	7.22460i	−0.366132	+	0.307221i
$554$		0			0
$555$	0.384133	−	2.17853i	0.0163055	−	0.0924733i
$556$		0			0
$557$	−20.0373	+	7.29298i	−0.849008	+	0.309014i	−0.729636	−	0.683836i	$-0.760310\pi$
$557$	−20.0373	+	7.29298i	−0.849008	+	0.309014i	−0.119372	+	0.992850i	$0.538088\pi$
$558$		0			0
$559$	−1.97906	−	3.42782i	−0.0837051	−	0.144982i
$560$		0			0
$561$	10.4966	+	8.80769i	0.443167	+	0.371861i
$562$		0			0
$563$	9.37939	−	16.2456i	0.395294	−	0.684669i	−0.597845	−	0.801612i	$-0.703976\pi$
$563$	9.37939	−	16.2456i	0.395294	−	0.684669i	0.993139	+	0.116943i	$0.0373094\pi$
$564$		0			0
$565$	0.00774079	+	0.0439002i	0.000325657	+	0.00184689i
$566$		0			0
$567$	46.1181	+	16.7856i	1.93678	+	0.704930i
$568$		0			0
$569$	6.16756			0.258557			0.129279	−	0.991608i	$-0.458734\pi$
$569$	6.16756			0.258557			0.129279	+	0.991608i	$0.458734\pi$
$570$		0			0
$571$	−22.2175			−0.929774			−0.464887	−	0.885370i	$-0.653905\pi$
$571$	−22.2175			−0.929774			−0.464887	+	0.885370i	$0.653905\pi$
$572$		0			0
$573$	−15.7297	−	5.72513i	−0.657117	−	0.239171i
$574$		0			0
$575$	−5.17365	−	29.3412i	−0.215756	−	1.22361i
$576$		0			0
$577$	18.8851	−	32.7099i	0.786196	−	1.36173i	−0.142087	−	0.989854i	$-0.545381\pi$
$577$	18.8851	−	32.7099i	0.786196	−	1.36173i	0.928282	−	0.371877i	$-0.121286\pi$
$578$		0			0
$579$	−27.7631	−	23.2960i	−1.15380	−	0.968149i
$580$		0			0
$581$	−27.4513	−	47.5471i	−1.13887	−	1.97258i
$582$		0			0
$583$	−56.1630	+	20.4417i	−2.32603	+	0.846607i
$584$		0			0
$585$	−0.0603074	+	0.342020i	−0.00249340	+	0.0141408i
$586$		0			0
$587$	3.29426	−	2.76421i	0.135969	−	0.114091i	−0.572267	−	0.820067i	$-0.693936\pi$
$587$	3.29426	−	2.76421i	0.135969	−	0.114091i	0.708236	+	0.705976i	$0.249491\pi$
$588$		0			0
$589$	11.3871	+	9.27692i	0.469198	+	0.382249i
$590$		0			0
$591$	25.7802	−	21.6321i	1.06045	−	0.889827i
$592$		0			0
$593$	1.29204	−	7.32753i	0.0530578	−	0.300906i	−0.946718	−	0.322063i	$-0.895624\pi$
$593$	1.29204	−	7.32753i	0.0530578	−	0.300906i	0.999776	+	0.0211569i	$0.00673496\pi$
$594$		0			0
$595$	−2.37939	+	0.866025i	−0.0975453	+	0.0355036i
$596$		0			0
$597$	−8.19846	−	14.2002i	−0.335541	−	0.581174i
$598$		0			0
$599$	−0.486796	−	0.408471i	−0.0198900	−	0.0166897i	0.632788	−	0.774325i	$-0.281910\pi$
$599$	−0.486796	−	0.408471i	−0.0198900	−	0.0166897i	−0.652678	+	0.757635i	$0.726355\pi$
$600$		0			0
$601$	1.32295	−	2.29141i	0.0539642	−	0.0934687i	−0.837781	−	0.546006i	$-0.816148\pi$
$601$	1.32295	−	2.29141i	0.0539642	−	0.0934687i	0.891746	+	0.452537i	$0.149481\pi$
$602$		0			0
$603$	−0.979055	−	5.55250i	−0.0398702	−	0.226115i
$604$		0			0
$605$	−3.80066	−	1.38333i	−0.154519	−	0.0562402i
$606$		0			0
$607$	−18.3851			−0.746227			−0.373113	−	0.927786i	$-0.621710\pi$
$607$	−18.3851			−0.746227			−0.373113	+	0.927786i	$0.621710\pi$
$608$		0			0
$609$	17.7570			0.719551
$610$		0			0
$611$	8.69119	+	3.16333i	0.351608	+	0.127975i
$612$		0			0
$613$	3.13997	+	17.8076i	0.126822	+	0.719244i	0.980209	+	0.197966i	$0.0634334\pi$
$613$	3.13997	+	17.8076i	0.126822	+	0.719244i	−0.853387	+	0.521278i	$0.825455\pi$
$614$		0			0
$615$	−1.46538	+	2.53812i	−0.0590900	+	0.102347i
$616$		0			0
$617$	14.2533	+	11.9599i	0.573817	+	0.481489i	0.882910	−	0.469542i	$-0.155581\pi$
$617$	14.2533	+	11.9599i	0.573817	+	0.481489i	−0.309093	+	0.951032i	$0.600026\pi$
$618$		0			0
$619$	−5.42396	−	9.39458i	−0.218007	−	0.377600i	0.736191	−	0.676774i	$-0.236622\pi$
$619$	−5.42396	−	9.39458i	−0.218007	−	0.377600i	−0.954199	+	0.299174i	$0.903289\pi$
$620$		0			0
$621$	−26.6129	+	9.68631i	−1.06794	+	0.388698i
$622$		0			0
$623$	4.65910	−	26.4231i	0.186663	−	1.05862i
$624$		0			0
$625$	17.7763	−	14.9161i	0.711052	−	0.596644i
$626$		0			0
$627$	38.9800	−	0.565258i	1.55671	−	0.0225742i
$628$		0			0
$629$	−3.97771	+	3.33770i	−0.158602	+	0.133083i
$630$		0			0
$631$	2.62243	−	14.8725i	0.104397	−	0.592065i	−0.887062	−	0.461650i	$-0.847258\pi$
$631$	2.62243	−	14.8725i	0.104397	−	0.592065i	0.991459	−	0.130416i	$-0.0416312\pi$
$632$		0			0
$633$	−1.33110	+	0.484481i	−0.0529065	+	0.0192564i
$634$		0			0
$635$	3.34864	+	5.80002i	0.132887	+	0.230167i
$636$		0			0
$637$	−22.5253	−	18.9010i	−0.892484	−	0.748883i
$638$		0			0
$639$	3.05825	−	5.29704i	0.120982	−	0.209548i
$640$		0			0
$641$	−8.03895	−	45.5912i	−0.317520	−	1.80074i	−0.557731	−	0.830022i	$-0.688328\pi$
$641$	−8.03895	−	45.5912i	−0.317520	−	1.80074i	0.240211	−	0.970721i	$-0.422783\pi$
$642$		0			0
$643$	−12.7610	−	4.64462i	−0.503244	−	0.183166i	0.0779083	−	0.996961i	$-0.475176\pi$
$643$	−12.7610	−	4.64462i	−0.503244	−	0.183166i	−0.581153	+	0.813795i	$0.697398\pi$
$644$		0			0
$645$	1.37464			0.0541263
$646$		0			0
$647$	−33.8135			−1.32934			−0.664672	−	0.747135i	$-0.731429\pi$
$647$	−33.8135			−1.32934			−0.664672	+	0.747135i	$0.731429\pi$
$648$		0			0
$649$	−25.3123	−	9.21291i	−0.993594	−	0.361638i
$650$		0			0
$651$	−5.23308	−	29.6783i	−0.205101	−	1.16318i
$652$		0			0
$653$	−3.37164	+	5.83986i	−0.131943	+	0.228531i	−0.924425	−	0.381363i	$-0.875455\pi$
$653$	−3.37164	+	5.83986i	−0.131943	+	0.228531i	0.792483	+	0.609894i	$0.208788\pi$
$654$		0			0
$655$	4.69072	+	3.93598i	0.183282	+	0.153792i
$656$		0			0
$657$	3.88919	+	6.73627i	0.151732	+	0.262807i
$658$		0			0
$659$	0.446089	−	0.162363i	0.0173772	−	0.00632477i	−0.333317	−	0.942815i	$-0.608168\pi$
$659$	0.446089	−	0.162363i	0.0173772	−	0.00632477i	0.350694	+	0.936490i	$0.385946\pi$
$660$		0			0
$661$	0.671122	−	3.80612i	0.0261036	−	0.148041i	−0.968970	−	0.247177i	$-0.920497\pi$
$661$	0.671122	−	3.80612i	0.0261036	−	0.148041i	0.995074	+	0.0991365i	$0.0316080\pi$
$662$		0			0
$663$	4.14543	−	3.47843i	0.160995	−	0.135091i
$664$		0			0
$665$	−3.51114	+	6.29039i	−0.136156	+	0.243931i
$666$		0			0
$667$	−9.28699	+	7.79271i	−0.359594	+	0.301735i
$668$		0			0
$669$	−1.55391	+	8.81267i	−0.0600777	+	0.340717i
$670$		0			0
$671$	44.6874	−	16.2649i	1.72514	−	0.627899i
$672$		0			0
$673$	−2.11081	−	3.65604i	−0.0813659	−	0.140930i	0.822471	−	0.568807i	$-0.192595\pi$
$673$	−2.11081	−	3.65604i	−0.0813659	−	0.140930i	−0.903837	+	0.427877i	$0.859262\pi$
$674$		0			0
$675$	−17.3366	−	14.5472i	−0.667287	−	0.559920i
$676$		0			0
$677$	−9.06212	+	15.6960i	−0.348286	+	0.603248i	−0.985945	−	0.167070i	$-0.946569\pi$
$677$	−9.06212	+	15.6960i	−0.348286	+	0.603248i	0.637660	+	0.770318i	$0.279903\pi$
$678$		0			0
$679$	6.33022	+	35.9005i	0.242932	+	1.37773i
$680$		0			0
$681$	−50.1985	−	18.2708i	−1.92361	−	0.700137i
$682$		0			0
$683$	−27.2608			−1.04311			−0.521553	−	0.853219i	$-0.674647\pi$
$683$	−27.2608			−1.04311			−0.521553	+	0.853219i	$0.674647\pi$
$684$		0			0
$685$	−6.82531			−0.260782
$686$		0			0
$687$	−27.6313	−	10.0570i	−1.05420	−	0.383698i
$688$		0			0
$689$	4.09879	+	23.2454i	0.156152	+	0.885580i
$690$		0			0
$691$	−13.1186	+	22.7220i	−0.499053	+	0.864386i	−0.999999	−	0.00109273i	$-0.999652\pi$
$691$	−13.1186	+	22.7220i	−0.499053	+	0.864386i	0.500946	+	0.865479i	$0.332986\pi$
$692$		0			0
$693$	−9.23055	−	7.74535i	−0.350640	−	0.294222i
$694$		0			0
$695$	−1.79932	−	3.11651i	−0.0682519	−	0.118216i
$696$		0			0
$697$	6.46451	−	2.35289i	0.244861	−	0.0891220i
$698$		0			0
$699$	−0.113341	+	0.642788i	−0.00428694	+	0.0243125i
$700$		0			0
$701$	18.8195	−	15.7915i	0.710804	−	0.596436i	−0.214020	−	0.976829i	$-0.568656\pi$
$701$	18.8195	−	15.7915i	0.710804	−	0.596436i	0.924825	+	0.380394i	$0.124211\pi$
$702$		0			0
$703$	−2.35410	+	14.5843i	−0.0887867	+	0.550059i
$704$		0			0
$705$	−2.46064	+	2.06472i	−0.0926730	+	0.0777618i
$706$		0			0
$707$	−3.71048	+	21.0432i	−0.139547	+	0.791411i
$708$		0			0
$709$	10.2931	−	3.74638i	0.386565	−	0.140698i	−0.141425	−	0.989949i	$-0.545168\pi$
$709$	10.2931	−	3.74638i	0.386565	−	0.140698i	0.527989	+	0.849251i	$0.322946\pi$
$710$		0			0
$711$	0.628356	+	1.08834i	0.0235652	+	0.0408161i
$712$		0			0
$713$	15.7613	+	13.2253i	0.590265	+	0.495291i
$714$		0			0
$715$	−1.55303	+	2.68993i	−0.0580802	+	0.100598i
$716$		0			0
$717$	2.09017	+	11.8540i	0.0780590	+	0.442695i
$718$		0			0
$719$	−39.9791	−	14.5512i	−1.49097	−	0.542668i	−0.537265	−	0.843414i	$-0.680542\pi$
$719$	−39.9791	−	14.5512i	−1.49097	−	0.542668i	−0.953705	+	0.300745i	$0.902765\pi$
$720$		0			0
$721$	71.4552			2.66113
$722$		0			0
$723$	−30.8530			−1.14743
$724$		0			0
$725$	−9.10354	−	3.31342i	−0.338097	−	0.123057i
$726$		0			0
$727$	6.86602	+	38.9391i	0.254647	+	1.44417i	0.796978	+	0.604008i	$0.206430\pi$
$727$	6.86602	+	38.9391i	0.254647	+	1.44417i	−0.542332	+	0.840164i	$0.682458\pi$
$728$		0			0
$729$	−10.3316	+	17.8948i	−0.382651	+	0.662770i
$730$		0			0
$731$	−2.47178	−	2.07407i	−0.0914221	−	0.0767123i
$732$		0			0
$733$	22.1459	+	38.3578i	0.817977	+	1.41678i	0.907170	+	0.420764i	$0.138238\pi$
$733$	22.1459	+	38.3578i	0.817977	+	1.41678i	−0.0891928	+	0.996014i	$0.528429\pi$
$734$		0			0
$735$	9.59627	−	3.49276i	0.353964	−	0.128832i
$736$		0			0
$737$	8.75624	−	49.6591i	0.322540	−	1.82922i
$738$		0			0
$739$	41.2124	−	34.5813i	1.51602	−	1.27209i	0.665161	−	0.746700i	$-0.268363\pi$
$739$	41.2124	−	34.5813i	1.51602	−	1.27209i	0.850860	−	0.525392i	$-0.176081\pi$
$740$		0			0
$741$	2.45336	−	15.1993i	0.0901265	−	0.558360i
$742$		0			0
$743$	9.05303	−	7.59640i	0.332124	−	0.278685i	−0.461441	−	0.887171i	$-0.652667\pi$
$743$	9.05303	−	7.59640i	0.332124	−	0.278685i	0.793564	+	0.608486i	$0.208223\pi$
$744$		0			0
$745$	−0.000466827		0.00264750i	−1.71032e−5		9.69971e-5i
$746$		0			0
$747$	−5.76857	+	2.09959i	−0.211061	+	0.0768199i
$748$		0			0
$749$	−25.9047	−	44.8682i	−0.946536	−	1.63945i
$750$		0			0
$751$	28.8496	+	24.2077i	1.05274	+	0.883350i	0.993379	−	0.114886i	$-0.0366504\pi$
$751$	28.8496	+	24.2077i	1.05274	+	0.883350i	0.0593573	+	0.998237i	$0.481095\pi$
$752$		0			0
$753$	−0.631759	+	1.09424i	−0.0230226	+	0.0398763i
$754$		0			0
$755$	0.964918	+	5.47232i	0.0351170	+	0.199158i
$756$		0			0
$757$	−7.14068	−	2.59900i	−0.259532	−	0.0944621i	0.208977	−	0.977921i	$-0.432987\pi$
$757$	−7.14068	−	2.59900i	−0.259532	−	0.0944621i	−0.468510	+	0.883458i	$0.655209\pi$
$758$		0			0
$759$	54.6100			1.98222
$760$		0			0
$761$	−1.51754			−0.0550108			−0.0275054	−	0.999622i	$-0.508756\pi$
$761$	−1.51754			−0.0550108			−0.0275054	+	0.999622i	$0.508756\pi$
$762$		0			0
$763$	34.2212	+	12.4555i	1.23889	+	0.450920i
$764$		0			0
$765$	0.0491630	+	0.278817i	0.00177749	+	0.0100807i
$766$		0			0
$767$	−5.31908	+	9.21291i	−0.192061	+	0.332659i
$768$		0			0
$769$	−13.0831	−	10.9780i	−0.471787	−	0.395877i	0.375659	−	0.926758i	$-0.377416\pi$
$769$	−13.0831	−	10.9780i	−0.471787	−	0.395877i	−0.847446	+	0.530881i	$0.821861\pi$
$770$		0			0
$771$	−8.77244	−	15.1943i	−0.315932	−	0.547210i
$772$		0			0
$773$	−0.687319	+	0.250164i	−0.0247211	+	0.00899776i	−0.354351	−	0.935112i	$-0.615298\pi$
$773$	−0.687319	+	0.250164i	−0.0247211	+	0.00899776i	0.329630	+	0.944110i	$0.393076\pi$
$774$		0			0
$775$	−2.85504	+	16.1917i	−0.102556	+	0.581624i
$776$		0			0
$777$	23.2199	−	19.4838i	0.833008	−	0.698977i
$778$		0			0
$779$	9.53936	−	17.0902i	0.341783	−	0.612322i
$780$		0			0
$781$	41.9051	−	35.1626i	1.49948	−	1.25822i
$782$		0			0
$783$	−1.59910	+	9.06893i	−0.0571471	+	0.324097i
$784$		0			0
$785$	−1.87211	+	0.681393i	−0.0668185	+	0.0243200i
$786$		0			0
$787$	12.4786	+	21.6136i	0.444816	+	0.770443i	0.998039	−	0.0625894i	$-0.0199359\pi$
$787$	12.4786	+	21.6136i	0.444816	+	0.770443i	−0.553224	+	0.833033i	$0.686603\pi$
$788$		0			0
$789$	16.3516	+	13.7206i	0.582134	+	0.488468i
$790$		0			0
$791$	−0.305407	+	0.528981i	−0.0108590	+	0.0188084i
$792$		0			0
$793$	−3.26130	−	18.4957i	−0.115812	−	0.656803i
$794$		0			0
$795$	−7.70321	−	2.80374i	−0.273205	−	0.0994384i
$796$		0			0
$797$	−46.2877			−1.63959			−0.819797	−	0.572655i	$-0.805914\pi$
$797$	−46.2877			−1.63959			−0.819797	+	0.572655i	$0.805914\pi$
$798$		0			0
$799$	7.53983			0.266740
$800$		0			0
$801$	−2.81908	−	1.02606i	−0.0996072	−	0.0362541i
$802$		0			0
$803$	12.0801	+	68.5095i	0.426296	+	2.41765i
$804$		0			0
$805$	−5.04576	+	8.73951i	−0.177840	+	0.308027i
$806$		0			0
$807$	−26.6989	−	22.4031i	−0.939847	−	0.788625i
$808$		0			0
$809$	26.1905	+	45.3632i	0.920808	+	1.59489i	0.798168	+	0.602435i	$0.205803\pi$
$809$	26.1905	+	45.3632i	0.920808	+	1.59489i	0.122640	+	0.992451i	$0.460864\pi$
$810$		0			0
$811$	−44.9842	+	16.3729i	−1.57961	+	0.574930i	−0.975119	−	0.221683i	$-0.928845\pi$
$811$	−44.9842	+	16.3729i	−1.57961	+	0.574930i	−0.604489	+	0.796614i	$0.706623\pi$
$812$		0			0
$813$	7.00222	−	39.7116i	0.245579	−	1.39275i
$814$		0			0
$815$	0.689378	−	0.578457i	0.0241479	−	0.0202625i
$816$		0			0
$817$	−9.17917	+	0.133109i	−0.321138	+	0.00465690i
$818$		0			0
$819$	−3.64543	+	3.05888i	−0.127382	+	0.106886i
$820$		0			0
$821$	−5.87140	+	33.2983i	−0.204913	+	1.16212i	0.692663	+	0.721261i	$0.256437\pi$
$821$	−5.87140	+	33.2983i	−0.204913	+	1.16212i	−0.897576	+	0.440859i	$0.854674\pi$
$822$		0			0
$823$	5.67782	−	2.06656i	0.197916	−	0.0720357i	−0.241160	−	0.970485i	$-0.577528\pi$
$823$	5.67782	−	2.06656i	0.197916	−	0.0720357i	0.439077	+	0.898450i	$0.355306\pi$
$824$		0			0
$825$	21.8195	+	37.7926i	0.759659	+	1.31577i
$826$		0			0
$827$	18.6612	+	15.6586i	0.648912	+	0.544502i	0.906741	−	0.421689i	$-0.138563\pi$
$827$	18.6612	+	15.6586i	0.648912	+	0.544502i	−0.257829	+	0.966191i	$0.583007\pi$
$828$		0			0
$829$	−11.9534	+	20.7038i	−0.415157	+	0.719074i	−0.995445	−	0.0953379i	$-0.969607\pi$
$829$	−11.9534	+	20.7038i	−0.415157	+	0.719074i	0.580288	+	0.814412i	$0.302940\pi$
$830$		0			0
$831$	5.23308	+	29.6783i	0.181533	+	1.02953i
$832$		0			0
$833$	−22.5253	−	8.19853i	−0.780455	−	0.284062i
$834$		0			0
$835$	−6.30365			−0.218147
$836$		0			0
$837$	15.6287			0.540206
$838$		0			0
$839$	−14.8893	−	5.41928i	−0.514037	−	0.187094i	0.0719596	−	0.997408i	$-0.477075\pi$
$839$	−14.8893	−	5.41928i	−0.514037	−	0.187094i	−0.585997	+	0.810313i	$0.699297\pi$
$840$		0			0
$841$	−4.35127	−	24.6773i	−0.150044	−	0.850941i
$842$		0			0
$843$	17.6027	−	30.4887i	0.606268	−	1.05009i
$844$		0			0
$845$	−2.51889	−	2.11360i	−0.0866523	−	0.0727099i
$846$		0			0
$847$	−27.7101	−	47.9953i	−0.952129	−	1.64914i
$848$		0			0
$849$	−12.4500	+	4.53141i	−0.427282	+	0.155518i
$850$		0			0
$851$	−3.59358	+	20.3802i	−0.123186	+	0.698624i
$852$		0			0
$853$	0.932419	−	0.782392i	0.0319254	−	0.0267886i	−0.626685	−	0.779272i	$-0.715589\pi$
$853$	0.932419	−	0.782392i	0.0319254	−	0.0267886i	0.658611	+	0.752484i	$0.271144\pi$
$854$		0			0
$855$	0.624485	+	0.508759i	0.0213569	+	0.0173992i
$856$		0			0
$857$	35.5296	−	29.8129i	1.21367	−	1.01839i	0.214537	−	0.976716i	$-0.431176\pi$
$857$	35.5296	−	29.8129i	1.21367	−	1.01839i	0.999131	−	0.0416731i	$-0.0132688\pi$
$858$		0			0
$859$	−2.65926	+	15.0814i	−0.0907329	+	0.514572i	0.905239	+	0.424903i	$0.139692\pi$
$859$	−2.65926	+	15.0814i	−0.0907329	+	0.514572i	−0.995972	+	0.0896685i	$0.971419\pi$
$860$		0			0
$861$	−37.7365	+	13.7350i	−1.28606	+	0.468087i
$862$		0			0
$863$	−22.8678	−	39.6082i	−0.778430	−	1.34828i	−0.932846	−	0.360274i	$-0.882683\pi$
$863$	−22.8678	−	39.6082i	−0.778430	−	1.34828i	0.154416	−	0.988006i	$-0.450650\pi$
$864$		0			0
$865$	−2.41534	−	2.02671i	−0.0821242	−	0.0689104i
$866$		0			0
$867$	−13.7690	+	23.8487i	−0.467621	+	0.809943i
$868$		0			0
$869$	1.95171	+	11.0687i	0.0662074	+	0.375481i
$870$		0			0
$871$	−18.7135	−	6.81115i	−0.634082	−	0.230787i
$872$		0			0
$873$	4.07604			0.137953
$874$		0			0
$875$	−16.3277			−0.551977
$876$		0			0
$877$	31.1707	+	11.3452i	1.05256	+	0.383101i	0.809628	−	0.586943i	$-0.199669\pi$
$877$	31.1707	+	11.3452i	1.05256	+	0.383101i	0.242932	+	0.970043i	$0.421891\pi$
$878$		0			0
$879$	2.69594	+	15.2894i	0.0909317	+	0.515699i
$880$		0			0
$881$	−21.9243	+	37.9739i	−0.738647	+	1.27937i	0.214457	+	0.976733i	$0.431202\pi$
$881$	−21.9243	+	37.9739i	−0.738647	+	1.27937i	−0.953105	+	0.302641i	$0.902132\pi$
$882$		0			0
$883$	38.1942	+	32.0487i	1.28534	+	1.07853i	0.992485	+	0.122368i	$0.0390487\pi$
$883$	38.1942	+	32.0487i	1.28534	+	1.07853i	0.292852	+	0.956158i	$0.405396\pi$
$884$		0			0
$885$	−1.84730	−	3.19961i	−0.0620962	−	0.107554i
$886$		0			0
$887$	32.0373	−	11.6606i	1.07571	−	0.391525i	0.257399	−	0.966305i	$-0.417134\pi$
$887$	32.0373	−	11.6606i	1.07571	−	0.391525i	0.818308	+	0.574780i	$0.194912\pi$
$888$		0			0
$889$	−15.9354	+	90.3742i	−0.534457	+	3.03105i
$890$		0			0
$891$	37.5959	−	31.5467i	1.25951	−	1.05685i
$892$		0			0
$893$	16.2310	−	14.0255i	0.543150	−	0.469345i
$894$		0			0
$895$	−1.76399	+	1.48016i	−0.0589635	+	0.0494763i
$896$		0			0
$897$	3.74510	−	21.2395i	0.125045	−	0.709167i
$898$		0			0
$899$	6.28668	−	2.28817i	0.209673	−	0.0763146i
$900$		0			0
$901$	9.62108	+	16.6642i	0.320525	+	0.555165i
$902$		0			0
$903$	14.4290	+	12.1074i	0.480168	+	0.402908i
$904$		0			0
$905$	0.881911	−	1.52752i	0.0293157	−	0.0507763i
$906$		0			0
$907$	−8.06629	−	45.7462i	−0.267837	−	1.51898i	−0.760833	−	0.648947i	$-0.775210\pi$
$907$	−8.06629	−	45.7462i	−0.267837	−	1.51898i	0.492997	−	0.870031i	$-0.335902\pi$
$908$		0			0
$909$	2.24510	+	0.817150i	0.0744653	+	0.0271031i
$910$		0			0
$911$	19.8527			0.657748			0.328874	−	0.944374i	$-0.393331\pi$
$911$	19.8527			0.657748			0.328874	+	0.944374i	$0.393331\pi$
$912$		0			0
$913$	−54.9026			−1.81701
$914$		0			0
$915$	6.12923	+	2.23086i	0.202626	+	0.0737499i
$916$		0			0
$917$	14.5697	+	82.6289i	0.481134	+	2.72865i
$918$		0			0
$919$	12.5564	−	21.7484i	0.414199	−	0.717413i	−0.581145	−	0.813800i	$-0.697395\pi$
$919$	12.5564	−	21.7484i	0.414199	−	0.717413i	0.995344	+	0.0963867i	$0.0307286\pi$
$920$		0			0
$921$	−6.81180	−	5.71578i	−0.224457	−	0.188341i
$922$		0			0
$923$	−10.8020	−	18.7096i	−0.355552	−	0.615835i
$924$		0			0
$925$	−15.5398	+	5.65604i	−0.510946	+	0.185969i
$926$		0			0
$927$	1.38737	−	7.86819i	0.0455674	−	0.258425i
$928$		0			0
$929$	−41.3790	+	34.7211i	−1.35760	+	1.13916i	−0.380885	+	0.924623i	$0.624381\pi$
$929$	−41.3790	+	34.7211i	−1.35760	+	1.13916i	−0.976715	+	0.214539i	$0.931175\pi$
$930$		0			0
$931$	−63.7410	+	24.2522i	−2.08903	+	0.794833i
$932$		0			0
$933$	16.1839	−	13.5799i	0.529838	−	0.444587i
$934$		0			0
$935$	−0.439693	+	2.49362i	−0.0143795	+	0.0815501i
$936$		0			0
$937$	33.2991	−	12.1199i	1.08783	−	0.395939i	0.265015	−	0.964244i	$-0.414623\pi$
$937$	33.2991	−	12.1199i	1.08783	−	0.395939i	0.822818	+	0.568305i	$0.192401\pi$
$938$		0			0
$939$	6.50387	+	11.2650i	0.212246	+	0.367620i
$940$		0			0
$941$	21.7554	+	18.2549i	0.709205	+	0.595093i	0.924376	−	0.381483i	$-0.124587\pi$
$941$	21.7554	+	18.2549i	0.709205	+	0.595093i	−0.215171	+	0.976576i	$0.569031\pi$
$942$		0			0
$943$	13.7087	−	23.7442i	0.446418	−	0.773218i
$944$		0			0
$945$	1.33110	+	7.54904i	0.0433007	+	0.245570i
$946$		0			0
$947$	38.7429	+	14.1013i	1.25898	+	0.458230i	0.883425	−	0.468572i	$-0.155231\pi$
$947$	38.7429	+	14.1013i	1.25898	+	0.458230i	0.375551	+	0.926802i	$0.377454\pi$
$948$		0			0
$949$	27.4739			0.891840
$950$		0			0
$951$	27.4739			0.890902
$952$		0			0
$953$	23.8106	+	8.66636i	0.771302	+	0.280731i	0.697541	−	0.716545i	$-0.254278\pi$
$953$	23.8106	+	8.66636i	0.771302	+	0.280731i	0.0737609	+	0.997276i	$0.476500\pi$
$954$		0			0
$955$	−0.537141	−	3.04628i	−0.0173815	−	0.0985753i
$956$		0			0
$957$	8.87851	−	15.3780i	0.287001	−	0.497101i
$958$		0			0
$959$	−71.6425	−	60.1152i	−2.31346	−	1.94122i
$960$		0			0
$961$	9.82295	+	17.0138i	0.316869	+	0.548834i
$962$		0			0
$963$	−5.44356	+	1.98129i	−0.175416	+	0.0638463i
$964$		0			0
$965$	1.16297	−	6.59553i	0.0374373	−	0.212318i
$966$		0			0
$967$	2.90096	−	2.43419i	0.0932885	−	0.0782784i	−0.594951	−	0.803762i	$-0.702828\pi$
$967$	2.90096	−	2.43419i	0.0932885	−	0.0782784i	0.688239	+	0.725484i	$0.258384\pi$
$968$		0			0
$969$	−2.35844	−	12.3274i	−0.0757640	−	0.396012i
$970$		0			0
$971$	7.05303	−	5.91820i	0.226343	−	0.189924i	−0.522563	−	0.852601i	$-0.675024\pi$
$971$	7.05303	−	5.91820i	0.226343	−	0.189924i	0.748906	+	0.662677i	$0.230580\pi$
$972$		0			0
$973$	8.56253	−	48.5605i	0.274502	−	1.55678i
$974$		0			0
$975$	16.1951	−	5.89452i	0.518657	−	0.188776i
$976$		0			0
$977$	−25.2297	−	43.6991i	−0.807169	−	1.39806i	−0.914817	−	0.403868i	$-0.867665\pi$
$977$	−25.2297	−	43.6991i	−0.807169	−	1.39806i	0.107648	−	0.994189i	$-0.465668\pi$
$978$		0			0
$979$	−20.5535	−	17.2464i	−0.656893	−	0.551198i
$980$		0			0
$981$	2.03596	−	3.52638i	0.0650032	−	0.112589i
$982$		0			0
$983$	8.44175	+	47.8756i	0.269250	+	1.52699i	0.756653	+	0.653816i	$0.226833\pi$
$983$	8.44175	+	47.8756i	0.269250	+	1.52699i	−0.487403	+	0.873177i	$0.662056\pi$
$984$		0			0
$985$	5.84389	+	2.12700i	0.186202	+	0.0677720i
$986$		0			0
$987$	−44.0137			−1.40097
$988$		0			0
$989$	−12.8598			−0.408917
$990$		0			0
$991$	34.8748	+	12.6934i	1.10783	+	0.403219i	0.830199	−	0.557468i	$-0.188227\pi$
$991$	34.8748	+	12.6934i	1.10783	+	0.403219i	0.277636	+	0.960686i	$0.410449\pi$
$992$		0			0
$993$	−1.19624	−	6.78422i	−0.0379616	−	0.215291i
$994$		0			0
$995$	1.51501	−	2.62408i	0.0480292	−	0.0831890i
$996$		0			0
$997$	−31.6648	−	26.5699i	−1.00283	−	0.841477i	−0.0154592	−	0.999880i	$-0.504921\pi$
$997$	−31.6648	−	26.5699i	−1.00283	−	0.841477i	−0.987375	+	0.158403i	$0.949365\pi$
$998$		0			0
$999$	7.85978	+	13.6135i	0.248673	+	0.430714i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.u.d.177.1		6
4.3	odd	2		152.2.q.a.25.1	✓	6
19.4	even	9		5776.2.a.bl.1.1		3
19.15	odd	18		5776.2.a.bm.1.3		3
19.16	even	9	inner	304.2.u.d.225.1		6
76.15	even	18		2888.2.a.p.1.1		3
76.23	odd	18		2888.2.a.q.1.3		3
76.35	odd	18		152.2.q.a.73.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.q.a.25.1	✓	6	4.3	odd	2
152.2.q.a.73.1	yes	6	76.35	odd	18
304.2.u.d.177.1		6	1.1	even	1	trivial
304.2.u.d.225.1		6	19.16	even	9	inner
2888.2.a.p.1.1		3	76.15	even	18
2888.2.a.q.1.3		3	76.23	odd	18
5776.2.a.bl.1.1		3	19.4	even	9
5776.2.a.bm.1.3		3	19.15	odd	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.76604 + 0.642788i) q^{3} +(0.0603074 + 0.342020i) q^{5} +(-2.37939 + 4.12122i) q^{7} +(0.407604 + 0.342020i) q^{9} +(2.37939 + 4.12122i) q^{11} +(1.76604 - 0.642788i) q^{13} +(-0.113341 + 0.642788i) q^{15} +(1.17365 - 0.984808i) q^{17} +(0.694593 - 4.30320i) q^{19} +(-6.85117 + 5.74881i) q^{21} +(1.06031 - 6.01330i) q^{23} +(4.58512 - 1.66885i) q^{25} +(-2.31908 - 4.01676i) q^{27} +(-1.52094 - 1.27622i) q^{29} +(-1.68479 + 2.91815i) q^{31} +(1.55303 + 8.80769i) q^{33} +(-1.55303 - 0.565258i) q^{35} -3.38919 q^{37} +3.53209 q^{39} +(4.21941 + 1.53574i) q^{41} +(-0.365715 - 2.07407i) q^{43} +(-0.0923963 + 0.160035i) q^{45} +(3.76991 + 3.16333i) q^{47} +(-7.82295 - 13.5497i) q^{49} +(2.70574 - 0.984808i) q^{51} +(-2.18092 + 12.3686i) q^{53} +(-1.26604 + 1.06234i) q^{55} +(3.99273 - 7.15317i) q^{57} +(-4.33615 + 3.63846i) q^{59} +(1.73530 - 9.84137i) q^{61} +(-2.37939 + 0.866025i) q^{63} +(0.326352 + 0.565258i) q^{65} +(-8.11721 - 6.81115i) q^{67} +(5.73783 - 9.93821i) q^{69} +(-1.99613 - 11.3206i) q^{71} +(13.7369 + 4.99984i) q^{73} +9.17024 q^{75} -22.6459 q^{77} +(2.21941 + 0.807798i) q^{79} +(-1.79086 - 10.1565i) q^{81} +(-5.76857 + 9.99146i) q^{83} +(0.407604 + 0.342020i) q^{85} +(-1.86571 - 3.23151i) q^{87} +(-5.29813 + 1.92836i) q^{89} +(-1.55303 + 8.80769i) q^{91} +(-4.85117 + 4.07061i) q^{93} +(1.51367 - 0.0219501i) q^{95} +(5.86824 - 4.92404i) q^{97} +(-0.439693 + 2.49362i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{3} + 6 q^{5} - 3 q^{7} + 6 q^{9} + 3 q^{11} + 6 q^{13} + 6 q^{15} + 6 q^{17} - 15 q^{21} + 12 q^{23} + 6 q^{25} + 3 q^{27} - 6 q^{29} - 3 q^{31} - 3 q^{33} + 3 q^{35} - 12 q^{37} + 12 q^{39}+ \cdots + 3 q^{99}+O(q^{100}) \) 6 * q + 6 * q^3 + 6 * q^5 - 3 * q^7 + 6 * q^9 + 3 * q^11 + 6 * q^13 + 6 * q^15 + 6 * q^17 - 15 * q^21 + 12 * q^23 + 6 * q^25 + 3 * q^27 - 6 * q^29 - 3 * q^31 - 3 * q^33 + 3 * q^35 - 12 * q^37 + 12 * q^39 - 6 * q^41 - 12 * q^43 + 3 * q^45 - 6 * q^47 - 6 * q^49 + 6 * q^51 - 30 * q^53 - 3 * q^55 + 6 * q^57 - 30 * q^59 + 6 * q^61 - 3 * q^63 + 3 * q^65 - 18 * q^67 + 15 * q^69 - 36 * q^71 + 6 * q^73 + 12 * q^75 - 54 * q^77 - 18 * q^79 + 21 * q^81 - 15 * q^83 + 6 * q^85 - 21 * q^87 - 18 * q^89 + 3 * q^91 - 3 * q^93 - 12 * q^95 + 30 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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