LMFDB - Embedded newform 350.2.g.b.293.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(293,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("350.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.g (of order $4$, degree $2$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 22 x^{14} - 52 x^{13} + 72 x^{12} - 32 x^{11} + 148 x^{10} + 268 x^{9} - 461 x^{8} + \cdots + 81 $ x^16 - 4x^15 + 22x^14 - 52x^13 + 72x^12 - 32x^11 + 148x^10 + 268x^9 - 461x^8 - 1548x^7 - 840x^6 + 1800x^5 + 2772x^4 + 1296x^3 + 54x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			293.6
Root			$0.205100 + 0.267292i$ of defining polynomial
Character	$\chi$	$=$	350.293
Dual form			350.2.g.b.307.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.32964 + 1.32964i) q^{3} -1.00000i q^{4} +1.88040i q^{6} +(1.36804 + 2.26461i) q^{7} +(-0.707107 - 0.707107i) q^{8} -0.535898i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.32964 + 1.32964i) q^{3} -1.00000i q^{4} +1.88040i q^{6} +(1.36804 + 2.26461i) q^{7} +(-0.707107 - 0.707107i) q^{8} -0.535898i q^{9} +1.73205 q^{11} +(1.32964 + 1.32964i) q^{12} +(-3.63265 + 3.63265i) q^{13} +(2.56867 + 0.633975i) q^{14} -1.00000 q^{16} +(2.30301 + 2.30301i) q^{17} +(-0.378937 - 0.378937i) q^{18} +3.25695 q^{19} +(-4.83013 - 1.19212i) q^{21} +(1.22474 - 1.22474i) q^{22} +(5.79555 + 5.79555i) q^{23} +1.88040 q^{24} +5.13734i q^{26} +(-3.27637 - 3.27637i) q^{27} +(2.26461 - 1.36804i) q^{28} +4.73205i q^{29} -8.89814i q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.30301 + 2.30301i) q^{33} +3.25695 q^{34} -0.535898 q^{36} +(1.55291 - 1.55291i) q^{37} +(2.30301 - 2.30301i) q^{38} -9.66025i q^{39} +5.64120i q^{41} +(-4.25838 + 2.57246i) q^{42} +(-2.44949 - 2.44949i) q^{43} -1.73205i q^{44} +8.19615 q^{46} +(-6.29194 - 6.29194i) q^{47} +(1.32964 - 1.32964i) q^{48} +(-3.25695 + 6.19615i) q^{49} -6.12436 q^{51} +(3.63265 + 3.63265i) q^{52} +(-10.0382 - 10.0382i) q^{53} -4.63349 q^{54} +(0.633975 - 2.56867i) q^{56} +(-4.33057 + 4.33057i) q^{57} +(3.34607 + 3.34607i) q^{58} -6.51389i q^{61} +(-6.29194 - 6.29194i) q^{62} +(1.21360 - 0.733129i) q^{63} +1.00000i q^{64} +3.25695i q^{66} +(7.02030 - 7.02030i) q^{67} +(2.30301 - 2.30301i) q^{68} -15.4120 q^{69} +8.19615 q^{71} +(-0.378937 + 0.378937i) q^{72} +(7.62158 - 7.62158i) q^{73} -2.19615i q^{74} -3.25695i q^{76} +(2.36951 + 3.92243i) q^{77} +(-6.83083 - 6.83083i) q^{78} +2.00000i q^{79} +10.3205 q^{81} +(3.98893 + 3.98893i) q^{82} +(3.98893 - 3.98893i) q^{83} +(-1.19212 + 4.83013i) q^{84} -3.46410 q^{86} +(-6.29194 - 6.29194i) q^{87} +(-1.22474 - 1.22474i) q^{88} -5.64120 q^{89} +(-13.1962 - 3.25695i) q^{91} +(5.79555 - 5.79555i) q^{92} +(11.8313 + 11.8313i) q^{93} -8.89814 q^{94} -1.88040i q^{96} +(7.26530 + 7.26530i) q^{97} +(2.07833 + 6.68435i) q^{98} -0.928203i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 16 q^{16} - 8 q^{21} - 64 q^{36} + 48 q^{46} + 96 q^{51} + 24 q^{56} + 48 q^{71} - 112 q^{81} - 128 q^{91}+O(q^{100}) $ 16 * q - 16 * q^16 - 8 * q^21 - 64 * q^36 + 48 * q^46 + 96 * q^51 + 24 * q^56 + 48 * q^71 - 112 * q^81 - 128 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−1.32964	+	1.32964i	−0.767669	+	0.767669i	−0.977696	−	0.210026i	$-0.932645\pi$
$3$	−1.32964	+	1.32964i	−0.767669	+	0.767669i	0.210026	+	0.977696i	$0.432645\pi$
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$			1.88040i			0.767669i
$7$	1.36804	+	2.26461i	0.517070	+	0.855943i
$7$	1.36804	+	2.26461i	0.517070	+	0.855943i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		−	0.535898i		−	0.178633i
$10$		0			0
$11$	1.73205			0.522233			0.261116	−	0.965307i	$-0.415909\pi$
$11$	1.73205			0.522233			0.261116	+	0.965307i	$0.415909\pi$
$12$	1.32964	+	1.32964i	0.383835	+	0.383835i
$13$	−3.63265	+	3.63265i	−1.00752	+	1.00752i	−0.00754454	+	0.999972i	$0.502402\pi$
$13$	−3.63265	+	3.63265i	−1.00752	+	1.00752i	−0.999972	+	0.00754454i	$0.997598\pi$
$14$	2.56867	+	0.633975i	0.686506	+	0.169437i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	2.30301	+	2.30301i	0.558562	+	0.558562i	0.928898	−	0.370336i	$-0.120758\pi$
$17$	2.30301	+	2.30301i	0.558562	+	0.558562i	−0.370336	+	0.928898i	$0.620758\pi$
$18$	−0.378937	−	0.378937i	−0.0893164	−	0.0893164i
$19$	3.25695			0.747195			0.373597	−	0.927591i	$-0.378124\pi$
$19$	3.25695			0.747195			0.373597	+	0.927591i	$0.378124\pi$
$20$		0			0
$21$	−4.83013	−	1.19212i	−1.05402	−	0.260143i
$22$	1.22474	−	1.22474i	0.261116	−	0.261116i
$23$	5.79555	+	5.79555i	1.20846	+	1.20846i	0.971527	+	0.236930i	$0.0761412\pi$
$23$	5.79555	+	5.79555i	1.20846	+	1.20846i	0.236930	+	0.971527i	$0.423859\pi$
$24$	1.88040			0.383835
$25$		0			0
$26$			5.13734i			1.00752i
$27$	−3.27637	−	3.27637i	−0.630539	−	0.630539i
$28$	2.26461	−	1.36804i	0.427972	−	0.258535i
$29$			4.73205i			0.878720i	0.898311	+	0.439360i	$0.144795\pi$
$29$			4.73205i			0.878720i	−0.898311	+	0.439360i	$0.855205\pi$
$30$		0			0
$31$		−	8.89814i		−	1.59815i	−0.601229	−	0.799077i	$-0.705322\pi$
$31$		−	8.89814i		−	1.59815i	0.601229	−	0.799077i	$-0.294678\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−2.30301	+	2.30301i	−0.400902	+	0.400902i
$34$	3.25695			0.558562
$35$		0			0
$36$	−0.535898			−0.0893164
$37$	1.55291	−	1.55291i	0.255298	−	0.255298i	−0.567841	−	0.823138i	$-0.692221\pi$
$37$	1.55291	−	1.55291i	0.255298	−	0.255298i	0.823138	+	0.567841i	$0.192221\pi$
$38$	2.30301	−	2.30301i	0.373597	−	0.373597i
$39$		−	9.66025i		−	1.54688i
$40$		0			0
$41$			5.64120i			0.881007i	0.897751	+	0.440503i	$0.145200\pi$
$41$			5.64120i			0.881007i	−0.897751	+	0.440503i	$0.854800\pi$
$42$	−4.25838	+	2.57246i	−0.657082	+	0.396939i
$43$	−2.44949	−	2.44949i	−0.373544	−	0.373544i	0.495222	−	0.868766i	$-0.335087\pi$
$43$	−2.44949	−	2.44949i	−0.373544	−	0.373544i	−0.868766	+	0.495222i	$0.835087\pi$
$44$		−	1.73205i		−	0.261116i
$45$		0			0
$46$	8.19615			1.20846
$47$	−6.29194	−	6.29194i	−0.917773	−	0.917773i	0.0790940	−	0.996867i	$-0.474797\pi$
$47$	−6.29194	−	6.29194i	−0.917773	−	0.917773i	−0.996867	+	0.0790940i	$0.974797\pi$
$48$	1.32964	−	1.32964i	0.191917	−	0.191917i
$49$	−3.25695	+	6.19615i	−0.465278	+	0.885165i
$50$		0			0
$51$	−6.12436			−0.857581
$52$	3.63265	+	3.63265i	0.503758	+	0.503758i
$53$	−10.0382	−	10.0382i	−1.37885	−	1.37885i	−0.846562	−	0.532290i	$-0.821331\pi$
$53$	−10.0382	−	10.0382i	−1.37885	−	1.37885i	−0.532290	−	0.846562i	$-0.678669\pi$
$54$	−4.63349			−0.630539
$55$		0			0
$56$	0.633975	−	2.56867i	0.0847184	−	0.343253i
$57$	−4.33057	+	4.33057i	−0.573598	+	0.573598i
$58$	3.34607	+	3.34607i	0.439360	+	0.439360i
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$		−	6.51389i		−	0.834018i	−0.908902	−	0.417009i	$-0.863078\pi$
$61$		−	6.51389i		−	0.834018i	0.908902	−	0.417009i	$-0.136922\pi$
$62$	−6.29194	−	6.29194i	−0.799077	−	0.799077i
$63$	1.21360	−	0.733129i	0.152900	−	0.0923656i
$64$			1.00000i			0.125000i
$65$		0			0
$66$			3.25695i			0.400902i
$67$	7.02030	−	7.02030i	0.857666	−	0.857666i	−0.133397	−	0.991063i	$-0.542588\pi$
$67$	7.02030	−	7.02030i	0.857666	−	0.857666i	0.991063	+	0.133397i	$0.0425884\pi$
$68$	2.30301	−	2.30301i	0.279281	−	0.279281i
$69$	−15.4120			−1.85539
$70$		0			0
$71$	8.19615			0.972704			0.486352	−	0.873763i	$-0.338327\pi$
$71$	8.19615			0.972704			0.486352	+	0.873763i	$0.338327\pi$
$72$	−0.378937	+	0.378937i	−0.0446582	+	0.0446582i
$73$	7.62158	−	7.62158i	0.892038	−	0.892038i	−0.102677	−	0.994715i	$-0.532741\pi$
$73$	7.62158	−	7.62158i	0.892038	−	0.892038i	0.994715	+	0.102677i	$0.0327407\pi$
$74$		−	2.19615i		−	0.255298i
$75$		0			0
$76$		−	3.25695i		−	0.373597i
$77$	2.36951	+	3.92243i	0.270031	+	0.447002i
$78$	−6.83083	−	6.83083i	−0.773439	−	0.773439i
$79$			2.00000i			0.225018i	0.993651	+	0.112509i	$0.0358886\pi$
$79$			2.00000i			0.225018i	−0.993651	+	0.112509i	$0.964111\pi$
$80$		0			0
$81$	10.3205			1.14672
$82$	3.98893	+	3.98893i	0.440503	+	0.440503i
$83$	3.98893	−	3.98893i	0.437842	−	0.437842i	−0.453443	−	0.891285i	$-0.649805\pi$
$83$	3.98893	−	3.98893i	0.437842	−	0.437842i	0.891285	+	0.453443i	$0.149805\pi$
$84$	−1.19212	+	4.83013i	−0.130071	+	0.527010i
$85$		0			0
$86$	−3.46410			−0.373544
$87$	−6.29194	−	6.29194i	−0.674566	−	0.674566i
$88$	−1.22474	−	1.22474i	−0.130558	−	0.130558i
$89$	−5.64120			−0.597966			−0.298983	−	0.954259i	$-0.596647\pi$
$89$	−5.64120			−0.597966			−0.298983	+	0.954259i	$0.596647\pi$
$90$		0			0
$91$	−13.1962	−	3.25695i	−1.38333	−	0.341421i
$92$	5.79555	−	5.79555i	0.604228	−	0.604228i
$93$	11.8313	+	11.8313i	1.22685	+	1.22685i
$94$	−8.89814			−0.917773
$95$		0			0
$96$		−	1.88040i		−	0.191917i
$97$	7.26530	+	7.26530i	0.737680	+	0.737680i	0.972128	−	0.234449i	$-0.0753285\pi$
$97$	7.26530	+	7.26530i	0.737680	+	0.737680i	−0.234449	+	0.972128i	$0.575329\pi$
$98$	2.07833	+	6.68435i	0.209943	+	0.675221i
$99$		−	0.928203i		−	0.0932879i
$100$		0			0
$101$			15.4120i			1.53355i	0.641913	+	0.766777i	$0.278141\pi$
$101$			15.4120i			1.53355i	−0.641913	+	0.766777i	$0.721859\pi$
$102$	−4.33057	+	4.33057i	−0.428791	+	0.428791i
$103$	7.26530	−	7.26530i	0.715871	−	0.715871i	−0.251886	−	0.967757i	$-0.581051\pi$
$103$	7.26530	−	7.26530i	0.715871	−	0.715871i	0.967757	+	0.251886i	$0.0810507\pi$
$104$	5.13734			0.503758
$105$		0			0
$106$	−14.1962			−1.37885
$107$	−5.22715	+	5.22715i	−0.505328	+	0.505328i	−0.913089	−	0.407761i	$-0.866310\pi$
$107$	−5.22715	+	5.22715i	−0.505328	+	0.505328i	0.407761	+	0.913089i	$0.366310\pi$
$108$	−3.27637	+	3.27637i	−0.315269	+	0.315269i
$109$		−	2.00000i		−	0.191565i	−0.995402	−	0.0957826i	$-0.969465\pi$
$109$		−	2.00000i		−	0.191565i	0.995402	−	0.0957826i	$-0.0305354\pi$
$110$		0			0
$111$			4.12964i			0.391968i
$112$	−1.36804	−	2.26461i	−0.129267	−	0.213986i
$113$	−0.568406	−	0.568406i	−0.0534711	−	0.0534711i	0.679866	−	0.733337i	$-0.262038\pi$
$113$	−0.568406	−	0.568406i	−0.0534711	−	0.0534711i	−0.733337	+	0.679866i	$0.762038\pi$
$114$			6.12436i			0.573598i
$115$		0			0
$116$	4.73205			0.439360
$117$	1.94673	+	1.94673i	0.179975	+	0.179975i
$118$		0			0
$119$	−2.06482	+	8.36603i	−0.189282	+	0.766912i
$120$		0			0
$121$	−8.00000			−0.727273
$122$	−4.60602	−	4.60602i	−0.417009	−	0.417009i
$123$	−7.50077	−	7.50077i	−0.676322	−	0.676322i
$124$	−8.89814			−0.799077
$125$		0			0
$126$	0.339746	−	1.37655i	0.0302670	−	0.122633i
$127$	−12.7279	+	12.7279i	−1.12942	+	1.12942i	−0.139149	+	0.990271i	$0.544437\pi$
$127$	−12.7279	+	12.7279i	−1.12942	+	1.12942i	−0.990271	+	0.139149i	$0.955563\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	6.51389			0.573516
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$	2.30301	+	2.30301i	0.200451	+	0.200451i
$133$	4.45562	+	7.37572i	0.386352	+	0.639556i
$134$		−	9.92820i		−	0.857666i
$135$		0			0
$136$		−	3.25695i		−	0.279281i
$137$	7.91688	−	7.91688i	0.676384	−	0.676384i	−0.282796	−	0.959180i	$-0.591262\pi$
$137$	7.91688	−	7.91688i	0.676384	−	0.676384i	0.959180	+	0.282796i	$0.0912619\pi$
$138$	−10.8980	+	10.8980i	−0.927695	+	0.927695i
$139$	21.0532			1.78571			0.892856	−	0.450343i	$-0.148698\pi$
$139$	21.0532			1.78571			0.892856	+	0.450343i	$0.148698\pi$
$140$		0			0
$141$	16.7321			1.40909
$142$	5.79555	−	5.79555i	0.486352	−	0.486352i
$143$	−6.29194	+	6.29194i	−0.526158	+	0.526158i
$144$			0.535898i			0.0446582i
$145$		0			0
$146$		−	10.7785i		−	0.892038i
$147$	−3.90809	−	12.5692i	−0.322334	−	1.03669i
$148$	−1.55291	−	1.55291i	−0.127649	−	0.127649i
$149$			4.39230i			0.359832i	0.983682	+	0.179916i	$0.0575825\pi$
$149$			4.39230i			0.359832i	−0.983682	+	0.179916i	$0.942417\pi$
$150$		0			0
$151$	14.5885			1.18719			0.593596	−	0.804763i	$-0.297708\pi$
$151$	14.5885			1.18719			0.593596	+	0.804763i	$0.297708\pi$
$152$	−2.30301	−	2.30301i	−0.186799	−	0.186799i
$153$	1.23418	−	1.23418i	0.0997774	−	0.0997774i
$154$	4.44907	+	1.09808i	0.358516	+	0.0884855i
$155$		0			0
$156$	−9.66025			−0.773439
$157$	4.34520	+	4.34520i	0.346785	+	0.346785i	0.858911	−	0.512126i	$-0.171142\pi$
$157$	4.34520	+	4.34520i	0.346785	+	0.346785i	−0.512126	+	0.858911i	$0.671142\pi$
$158$	1.41421	+	1.41421i	0.112509	+	0.112509i
$159$	26.6944			2.11701
$160$		0			0
$161$	−5.19615	+	21.0532i	−0.409514	+	1.65923i
$162$	7.29770	−	7.29770i	0.573362	−	0.573362i
$163$	−7.02030	−	7.02030i	−0.549872	−	0.549872i	0.376531	−	0.926404i	$-0.377117\pi$
$163$	−7.02030	−	7.02030i	−0.549872	−	0.549872i	−0.926404	+	0.376531i	$0.877117\pi$
$164$	5.64120			0.440503
$165$		0			0
$166$		−	5.64120i		−	0.437842i
$167$	9.21203	+	9.21203i	0.712849	+	0.712849i	0.967130	−	0.254282i	$-0.0818390\pi$
$167$	9.21203	+	9.21203i	0.712849	+	0.712849i	−0.254282	+	0.967130i	$0.581839\pi$
$168$	2.57246	+	4.25838i	0.198469	+	0.328541i
$169$		−	13.3923i		−	1.03018i
$170$		0			0
$171$		−	1.74539i		−	0.133473i
$172$	−2.44949	+	2.44949i	−0.186772	+	0.186772i
$173$	−1.68592	+	1.68592i	−0.128178	+	0.128178i	−0.768285	−	0.640107i	$-0.778890\pi$
$173$	−1.68592	+	1.68592i	−0.128178	+	0.128178i	0.640107	+	0.768285i	$0.278890\pi$
$174$	−8.89814			−0.674566
$175$		0			0
$176$	−1.73205			−0.130558
$177$		0			0
$178$	−3.98893	+	3.98893i	−0.298983	+	0.298983i
$179$		−	17.1962i		−	1.28530i	−0.766160	−	0.642650i	$-0.777835\pi$
$179$		−	17.1962i		−	1.28530i	0.766160	−	0.642650i	$-0.222165\pi$
$180$		0			0
$181$		−	24.3102i		−	1.80696i	−0.428629	−	0.903480i	$-0.641003\pi$
$181$		−	24.3102i		−	1.80696i	0.428629	−	0.903480i	$-0.358997\pi$
$182$	−11.6341	+	7.02808i	−0.862377	+	0.520956i
$183$	8.66115	+	8.66115i	0.640250	+	0.640250i
$184$		−	8.19615i		−	0.604228i
$185$		0			0
$186$	16.7321			1.22685
$187$	3.98893	+	3.98893i	0.291699	+	0.291699i
$188$	−6.29194	+	6.29194i	−0.458887	+	0.458887i
$189$	2.93752	−	11.9019i	0.213673	−	0.865738i
$190$		0			0
$191$	−0.928203			−0.0671624			−0.0335812	−	0.999436i	$-0.510691\pi$
$191$	−0.928203			−0.0671624			−0.0335812	+	0.999436i	$0.510691\pi$
$192$	−1.32964	−	1.32964i	−0.0959587	−	0.0959587i
$193$	−12.8159	−	12.8159i	−0.922505	−	0.922505i	0.0747006	−	0.997206i	$-0.476200\pi$
$193$	−12.8159	−	12.8159i	−0.922505	−	0.922505i	−0.997206	+	0.0747006i	$0.976200\pi$
$194$	10.2747			0.737680
$195$		0			0
$196$	6.19615	+	3.25695i	0.442582	+	0.232639i
$197$	1.13681	−	1.13681i	0.0809945	−	0.0809945i	−0.665449	−	0.746443i	$-0.731760\pi$
$197$	1.13681	−	1.13681i	0.0809945	−	0.0809945i	0.746443	+	0.665449i	$0.231760\pi$
$198$	−0.656339	−	0.656339i	−0.0466440	−	0.0466440i
$199$	2.38425			0.169015			0.0845075	−	0.996423i	$-0.473068\pi$
$199$	2.38425			0.169015			0.0845075	+	0.996423i	$0.473068\pi$
$200$		0			0
$201$			18.6690i			1.31681i
$202$	10.8980	+	10.8980i	0.766777	+	0.766777i
$203$	−10.7163	+	6.47362i	−0.752134	+	0.454359i
$204$			6.12436i			0.428791i
$205$		0			0
$206$		−	10.2747i		−	0.715871i
$207$	3.10583	−	3.10583i	0.215870	−	0.215870i
$208$	3.63265	−	3.63265i	0.251879	−	0.251879i
$209$	5.64120			0.390210
$210$		0			0
$211$	−1.19615			−0.0823465			−0.0411733	−	0.999152i	$-0.513110\pi$
$211$	−1.19615			−0.0823465			−0.0411733	+	0.999152i	$0.513110\pi$
$212$	−10.0382	+	10.0382i	−0.689426	+	0.689426i
$213$	−10.8980	+	10.8980i	−0.746715	+	0.746715i
$214$			7.39230i			0.505328i
$215$		0			0
$216$			4.63349i			0.315269i
$217$	20.1508	−	12.1730i	1.36793	−	0.826357i
$218$	−1.41421	−	1.41421i	−0.0957826	−	0.0957826i
$219$			20.2679i			1.36958i
$220$		0			0
$221$	−16.7321			−1.12552
$222$	2.92010	+	2.92010i	0.195984	+	0.195984i
$223$	11.6105	−	11.6105i	0.777497	−	0.777497i	−0.201908	−	0.979405i	$-0.564714\pi$
$223$	11.6105	−	11.6105i	0.777497	−	0.777497i	0.979405	+	0.201908i	$0.0647141\pi$
$224$	−2.56867	−	0.633975i	−0.171627	−	0.0423592i
$225$		0			0
$226$	−0.803848			−0.0534711
$227$	−4.60602	−	4.60602i	−0.305712	−	0.305712i	0.537532	−	0.843244i	$-0.319357\pi$
$227$	−4.60602	−	4.60602i	−0.305712	−	0.305712i	−0.843244	+	0.537532i	$0.819357\pi$
$228$	4.33057	+	4.33057i	0.286799	+	0.286799i
$229$	−8.89814			−0.588006			−0.294003	−	0.955805i	$-0.594988\pi$
$229$	−8.89814			−0.588006			−0.294003	+	0.955805i	$0.594988\pi$
$230$		0			0
$231$	−8.36603	−	2.06482i	−0.550444	−	0.135855i
$232$	3.34607	−	3.34607i	0.219680	−	0.219680i
$233$	7.34847	+	7.34847i	0.481414	+	0.481414i	0.905583	−	0.424169i	$-0.139434\pi$
$233$	7.34847	+	7.34847i	0.481414	+	0.481414i	−0.424169	+	0.905583i	$0.639434\pi$
$234$	2.75309			0.179975
$235$		0			0
$236$		0			0
$237$	−2.65929	−	2.65929i	−0.172739	−	0.172739i
$238$	4.45562	+	7.37572i	0.288815	+	0.478097i
$239$			1.85641i			0.120081i	0.998196	+	0.0600405i	$0.0191230\pi$
$239$			1.85641i			0.120081i	−0.998196	+	0.0600405i	$0.980877\pi$
$240$		0			0
$241$			12.1551i			0.782978i	0.920183	+	0.391489i	$0.128040\pi$
$241$			12.1551i			0.782978i	−0.920183	+	0.391489i	$0.871960\pi$
$242$	−5.65685	+	5.65685i	−0.363636	+	0.363636i
$243$	−3.89346	+	3.89346i	−0.249766	+	0.249766i
$244$	−6.51389			−0.417009
$245$		0			0
$246$	−10.6077			−0.676322
$247$	−11.8313	+	11.8313i	−0.752811	+	0.752811i
$248$	−6.29194	+	6.29194i	−0.399538	+	0.399538i
$249$			10.6077i			0.672235i
$250$		0			0
$251$			9.77084i			0.616730i	0.951268	+	0.308365i	$0.0997818\pi$
$251$			9.77084i			0.616730i	−0.951268	+	0.308365i	$0.900218\pi$
$252$	−0.733129	−	1.21360i	−0.0461828	−	0.0764498i
$253$	10.0382	+	10.0382i	0.631096	+	0.631096i
$254$			18.0000i			1.12942i
$255$		0			0
$256$	1.00000			0.0625000
$257$	7.97786	+	7.97786i	0.497645	+	0.497645i	0.910704	−	0.413059i	$-0.135540\pi$
$257$	7.97786	+	7.97786i	0.497645	+	0.497645i	−0.413059	+	0.910704i	$0.635540\pi$
$258$	4.60602	−	4.60602i	0.286758	−	0.286758i
$259$	5.64120	+	1.39230i	0.350527	+	0.0865136i
$260$		0			0
$261$	2.53590			0.156968
$262$		0			0
$263$	1.13681	+	1.13681i	0.0700988	+	0.0700988i	0.741287	−	0.671188i	$-0.234216\pi$
$263$	1.13681	+	1.13681i	0.0700988	+	0.0700988i	−0.671188	+	0.741287i	$0.734216\pi$
$264$	3.25695			0.200451
$265$		0			0
$266$	8.36603	+	2.06482i	0.512954	+	0.126602i
$267$	7.50077	−	7.50077i	0.459040	−	0.459040i
$268$	−7.02030	−	7.02030i	−0.428833	−	0.428833i
$269$	−26.6944			−1.62759			−0.813794	−	0.581154i	$-0.802602\pi$
$269$	−26.6944			−1.62759			−0.813794	+	0.581154i	$0.802602\pi$
$270$		0			0
$271$		−	11.2824i		−	0.685356i	−0.939453	−	0.342678i	$-0.888666\pi$
$271$		−	11.2824i		−	0.685356i	0.939453	−	0.342678i	$-0.111334\pi$
$272$	−2.30301	−	2.30301i	−0.139640	−	0.139640i
$273$	21.8767	−	13.2156i	1.32404	−	0.799844i
$274$		−	11.1962i		−	0.676384i
$275$		0			0
$276$			15.4120i			0.927695i
$277$	−2.20925	+	2.20925i	−0.132741	+	0.132741i	−0.770356	−	0.637614i	$-0.779921\pi$
$277$	−2.20925	+	2.20925i	−0.132741	+	0.132741i	0.637614	+	0.770356i	$0.279921\pi$
$278$	14.8869	−	14.8869i	0.892856	−	0.892856i
$279$	−4.76850			−0.285483
$280$		0			0
$281$	13.8564			0.826604			0.413302	−	0.910594i	$-0.364375\pi$
$281$	13.8564			0.826604			0.413302	+	0.910594i	$0.364375\pi$
$282$	11.8313	−	11.8313i	0.704546	−	0.704546i
$283$	3.27637	−	3.27637i	0.194760	−	0.194760i	−0.602989	−	0.797749i	$-0.706024\pi$
$283$	3.27637	−	3.27637i	0.194760	−	0.194760i	0.797749	+	0.602989i	$0.206024\pi$
$284$		−	8.19615i		−	0.486352i
$285$		0			0
$286$			8.89814i			0.526158i
$287$	−12.7751	+	7.71737i	−0.754092	+	0.455542i
$288$	0.378937	+	0.378937i	0.0223291	+	0.0223291i
$289$		−	6.39230i		−	0.376018i
$290$		0			0
$291$	−19.3205			−1.13259
$292$	−7.62158	−	7.62158i	−0.446019	−	0.446019i
$293$	−17.1899	+	17.1899i	−1.00424	+	1.00424i	−0.00425306	+	0.999991i	$0.501354\pi$
$293$	−17.1899	+	17.1899i	−1.00424	+	1.00424i	−0.999991	+	0.00425306i	$0.998646\pi$
$294$	−11.6512	−	6.12436i	−0.679514	−	0.357180i
$295$		0			0
$296$	−2.19615			−0.127649
$297$	−5.67485	−	5.67485i	−0.329288	−	0.329288i
$298$	3.10583	+	3.10583i	0.179916	+	0.179916i
$299$	−42.1065			−2.43508
$300$		0			0
$301$	2.19615	−	8.89814i	0.126584	−	0.512880i
$302$	10.3156	−	10.3156i	0.593596	−	0.593596i
$303$	−20.4925	−	20.4925i	−1.17726	−	1.17726i
$304$	−3.25695			−0.186799
$305$		0			0
$306$		−	1.74539i		−	0.0997774i
$307$	−11.2542	−	11.2542i	−0.642313	−	0.642313i	0.308811	−	0.951124i	$-0.400069\pi$
$307$	−11.2542	−	11.2542i	−0.642313	−	0.642313i	−0.951124	+	0.308811i	$0.900069\pi$
$308$	3.92243	−	2.36951i	0.223501	−	0.135015i
$309$			19.3205i			1.09911i
$310$		0			0
$311$		−	11.2824i		−	0.639766i	−0.947457	−	0.319883i	$-0.896356\pi$
$311$		−	11.2824i		−	0.639766i	0.947457	−	0.319883i	$-0.103644\pi$
$312$	−6.83083	+	6.83083i	−0.386720	+	0.386720i
$313$	6.55275	−	6.55275i	0.370383	−	0.370383i	−0.497234	−	0.867617i	$-0.665651\pi$
$313$	6.55275	−	6.55275i	0.370383	−	0.370383i	0.867617	+	0.497234i	$0.165651\pi$
$314$	6.14505			0.346785
$315$		0			0
$316$	2.00000			0.112509
$317$	−3.10583	+	3.10583i	−0.174441	+	0.174441i	−0.788927	−	0.614487i	$-0.789363\pi$
$317$	−3.10583	+	3.10583i	−0.174441	+	0.174441i	0.614487	+	0.788927i	$0.289363\pi$
$318$	18.8758	−	18.8758i	1.05850	−	1.05850i
$319$			8.19615i			0.458896i
$320$		0			0
$321$		−	13.9005i		−	0.775849i
$322$	11.2126	+	18.5611i	0.624856	+	1.03437i
$323$	7.50077	+	7.50077i	0.417354	+	0.417354i
$324$		−	10.3205i		−	0.573362i
$325$		0			0
$326$	−9.92820			−0.549872
$327$	2.65929	+	2.65929i	0.147059	+	0.147059i
$328$	3.98893	−	3.98893i	0.220252	−	0.220252i
$329$	5.64120	−	22.8564i	0.311009	−	1.26011i
$330$		0			0
$331$	7.58846			0.417099			0.208550	−	0.978012i	$-0.433126\pi$
$331$	7.58846			0.417099			0.208550	+	0.978012i	$0.433126\pi$
$332$	−3.98893	−	3.98893i	−0.218921	−	0.218921i
$333$	−0.832204	−	0.832204i	−0.0456045	−	0.0456045i
$334$	13.0278			0.712849
$335$		0			0
$336$	4.83013	+	1.19212i	0.263505	+	0.0650357i
$337$	−15.7458	+	15.7458i	−0.857729	+	0.857729i	−0.991070	−	0.133341i	$-0.957429\pi$
$337$	−15.7458	+	15.7458i	−0.857729	+	0.857729i	0.133341	+	0.991070i	$0.457429\pi$
$338$	−9.46979	−	9.46979i	−0.515089	−	0.515089i
$339$	1.51155			0.0820963
$340$		0			0
$341$		−	15.4120i		−	0.834608i
$342$	−1.23418	−	1.23418i	−0.0667367	−	0.0667367i
$343$	−18.4875	+	1.10085i	−0.998232	+	0.0594402i
$344$			3.46410i			0.186772i
$345$		0			0
$346$			2.38425i			0.128178i
$347$	8.33298	−	8.33298i	0.447338	−	0.447338i	−0.447131	−	0.894469i	$-0.647554\pi$
$347$	8.33298	−	8.33298i	0.447338	−	0.447338i	0.894469	+	0.447131i	$0.147554\pi$
$348$	−6.29194	+	6.29194i	−0.337283	+	0.337283i
$349$	−15.4120			−0.824987			−0.412494	−	0.910961i	$-0.635342\pi$
$349$	−15.4120			−0.824987			−0.412494	+	0.910961i	$0.635342\pi$
$350$		0			0
$351$	23.8038			1.27056
$352$	−1.22474	+	1.22474i	−0.0652791	+	0.0652791i
$353$	20.5617	−	20.5617i	1.09439	−	1.09439i	0.0993364	−	0.995054i	$-0.468328\pi$
$353$	20.5617	−	20.5617i	1.09439	−	1.09439i	0.995054	−	0.0993364i	$-0.0316720\pi$
$354$		0			0
$355$		0			0
$356$			5.64120i			0.298983i
$357$	−8.37835	−	13.8693i	−0.443429	−	0.734041i
$358$	−12.1595	−	12.1595i	−0.642650	−	0.642650i
$359$			10.3923i			0.548485i	0.961661	+	0.274242i	$0.0884271\pi$
$359$			10.3923i			0.548485i	−0.961661	+	0.274242i	$0.911573\pi$
$360$		0			0
$361$	−8.39230			−0.441700
$362$	−17.1899	−	17.1899i	−0.903480	−	0.903480i
$363$	10.6371	−	10.6371i	0.558305	−	0.558305i
$364$	−3.25695	+	13.1962i	−0.170710	+	0.691666i
$365$		0			0
$366$	12.2487			0.640250
$367$	7.26530	+	7.26530i	0.379246	+	0.379246i	0.870830	−	0.491584i	$-0.163582\pi$
$367$	7.26530	+	7.26530i	0.379246	+	0.379246i	−0.491584	+	0.870830i	$0.663582\pi$
$368$	−5.79555	−	5.79555i	−0.302114	−	0.302114i
$369$	3.02311			0.157377
$370$		0			0
$371$	9.00000	−	36.4653i	0.467257	−	1.89318i
$372$	11.8313	−	11.8313i	0.613427	−	0.613427i
$373$	−11.8313	−	11.8313i	−0.612604	−	0.612604i	0.331020	−	0.943624i	$-0.392607\pi$
$373$	−11.8313	−	11.8313i	−0.612604	−	0.612604i	−0.943624	+	0.331020i	$0.892607\pi$
$374$	5.64120			0.291699
$375$		0			0
$376$			8.89814i			0.458887i
$377$	−17.1899	−	17.1899i	−0.885324	−	0.885324i
$378$	−6.33879	−	10.4931i	−0.326032	−	0.539705i
$379$		−	17.9808i		−	0.923610i	−0.886982	−	0.461805i	$-0.847202\pi$
$379$		−	17.9808i		−	0.923610i	0.886982	−	0.461805i	$-0.152798\pi$
$380$		0			0
$381$		−	33.8472i		−	1.73404i
$382$	−0.656339	+	0.656339i	−0.0335812	+	0.0335812i
$383$	−7.97786	+	7.97786i	−0.407649	+	0.407649i	−0.880918	−	0.473269i	$-0.843074\pi$
$383$	−7.97786	+	7.97786i	−0.407649	+	0.407649i	0.473269	+	0.880918i	$0.343074\pi$
$384$	−1.88040			−0.0959587
$385$		0			0
$386$	−18.1244			−0.922505
$387$	−1.31268	+	1.31268i	−0.0667272	+	0.0667272i
$388$	7.26530	−	7.26530i	0.368840	−	0.368840i
$389$			17.6603i			0.895410i	0.894181	+	0.447705i	$0.147759\pi$
$389$			17.6603i			0.895410i	−0.894181	+	0.447705i	$0.852241\pi$
$390$		0			0
$391$			26.6944i			1.35000i
$392$	6.68435	−	2.07833i	0.337611	−	0.104972i
$393$		0			0
$394$		−	1.60770i		−	0.0809945i
$395$		0			0
$396$	−0.928203			−0.0466440
$397$	−18.1633	−	18.1633i	−0.911588	−	0.911588i	0.0848096	−	0.996397i	$-0.472972\pi$
$397$	−18.1633	−	18.1633i	−0.911588	−	0.911588i	−0.996397	+	0.0848096i	$0.972972\pi$
$398$	1.68592	−	1.68592i	0.0845075	−	0.0845075i
$399$	−15.7315	−	3.88269i	−0.787558	−	0.194377i
$400$		0			0
$401$	27.9282			1.39467			0.697334	−	0.716746i	$-0.254369\pi$
$401$	27.9282			1.39467			0.697334	+	0.716746i	$0.254369\pi$
$402$	13.2010	+	13.2010i	0.658404	+	0.658404i
$403$	32.3238	+	32.3238i	1.61017	+	1.61017i
$404$	15.4120			0.766777
$405$		0			0
$406$	−3.00000	+	12.1551i	−0.148888	+	0.603247i
$407$	2.68973	−	2.68973i	0.133325	−	0.133325i
$408$	4.33057	+	4.33057i	0.214395	+	0.214395i
$409$	31.6968			1.56730			0.783652	−	0.621200i	$-0.213355\pi$
$409$	31.6968			1.56730			0.783652	+	0.621200i	$0.213355\pi$
$410$		0			0
$411$			21.0532i			1.03848i
$412$	−7.26530	−	7.26530i	−0.357936	−	0.357936i
$413$		0			0
$414$		−	4.39230i		−	0.215870i
$415$		0			0
$416$		−	5.13734i		−	0.251879i
$417$	−27.9933	+	27.9933i	−1.37084	+	1.37084i
$418$	3.98893	−	3.98893i	0.195105	−	0.195105i
$419$	−1.51155			−0.0738442			−0.0369221	−	0.999318i	$-0.511755\pi$
$419$	−1.51155			−0.0738442			−0.0369221	+	0.999318i	$0.511755\pi$
$420$		0			0
$421$	−33.1769			−1.61694			−0.808472	−	0.588535i	$-0.799705\pi$
$421$	−33.1769			−1.61694			−0.808472	+	0.588535i	$0.799705\pi$
$422$	−0.845807	+	0.845807i	−0.0411733	+	0.0411733i
$423$	−3.37184	+	3.37184i	−0.163944	+	0.163944i
$424$			14.1962i			0.689426i
$425$		0			0
$426$			15.4120i			0.746715i
$427$	14.7514	−	8.91125i	0.713872	−	0.431246i
$428$	5.22715	+	5.22715i	0.252664	+	0.252664i
$429$		−	16.7321i		−	0.807831i
$430$		0			0
$431$	−37.5167			−1.80711			−0.903557	−	0.428468i	$-0.859053\pi$
$431$	−37.5167			−1.80711			−0.903557	+	0.428468i	$0.859053\pi$
$432$	3.27637	+	3.27637i	0.157635	+	0.157635i
$433$	−14.1743	+	14.1743i	−0.681175	+	0.681175i	−0.960265	−	0.279090i	$-0.909967\pi$
$433$	−14.1743	+	14.1743i	−0.681175	+	0.681175i	0.279090	+	0.960265i	$0.409967\pi$
$434$	5.64120	−	22.8564i	0.270786	−	1.09714i
$435$		0			0
$436$	−2.00000			−0.0957826
$437$	18.8758	+	18.8758i	0.902952	+	0.902952i
$438$	14.3316	+	14.3316i	0.684791	+	0.684791i
$439$	−17.7963			−0.849370			−0.424685	−	0.905341i	$-0.639615\pi$
$439$	−17.7963			−0.849370			−0.424685	+	0.905341i	$0.639615\pi$
$440$		0			0
$441$	3.32051	+	1.74539i	0.158119	+	0.0831139i
$442$	−11.8313	+	11.8313i	−0.562760	+	0.562760i
$443$	10.6066	+	10.6066i	0.503935	+	0.503935i	0.912658	−	0.408723i	$-0.134026\pi$
$443$	10.6066	+	10.6066i	0.503935	+	0.503935i	−0.408723	+	0.912658i	$0.634026\pi$
$444$	4.12964			0.195984
$445$		0			0
$446$		−	16.4197i		−	0.777497i
$447$	−5.84020	−	5.84020i	−0.276232	−	0.276232i
$448$	−2.26461	+	1.36804i	−0.106993	+	0.0646337i
$449$			28.8564i			1.36182i	0.732368	+	0.680909i	$0.238415\pi$
$449$			28.8564i			1.36182i	−0.732368	+	0.680909i	$0.761585\pi$
$450$		0			0
$451$			9.77084i			0.460091i
$452$	−0.568406	+	0.568406i	−0.0267356	+	0.0267356i
$453$	−19.3974	+	19.3974i	−0.911371	+	0.911371i
$454$	−6.51389			−0.305712
$455$		0			0
$456$	6.12436			0.286799
$457$	16.4022	−	16.4022i	0.767261	−	0.767261i	−0.210363	−	0.977623i	$-0.567465\pi$
$457$	16.4022	−	16.4022i	0.767261	−	0.767261i	0.977623	+	0.210363i	$0.0674645\pi$
$458$	−6.29194	+	6.29194i	−0.294003	+	0.294003i
$459$		−	15.0910i		−	0.704389i
$460$		0			0
$461$		−	4.12964i		−	0.192337i	−0.995365	−	0.0961683i	$-0.969341\pi$
$461$		−	4.12964i		−	0.192337i	0.995365	−	0.0961683i	$-0.0306587\pi$
$462$	−7.37572	+	4.45562i	−0.343150	+	0.207294i
$463$	17.8028	+	17.8028i	0.827365	+	0.827365i	0.987152	−	0.159787i	$-0.0510807\pi$
$463$	17.8028	+	17.8028i	0.827365	+	0.827365i	−0.159787	+	0.987152i	$0.551081\pi$
$464$		−	4.73205i		−	0.219680i
$465$		0			0
$466$	10.3923			0.481414
$467$	12.5839	+	12.5839i	0.582312	+	0.582312i	0.935538	−	0.353226i	$-0.114915\pi$
$467$	12.5839	+	12.5839i	0.582312	+	0.582312i	−0.353226	+	0.935538i	$0.614915\pi$
$468$	1.94673	−	1.94673i	0.0899877	−	0.0899877i
$469$	25.5023	+	6.29423i	1.17759	+	0.290640i
$470$		0			0
$471$	−11.5551			−0.532433
$472$		0			0
$473$	−4.24264	−	4.24264i	−0.195077	−	0.195077i
$474$	−3.76080			−0.172739
$475$		0			0
$476$	8.36603	+	2.06482i	0.383456	+	0.0946409i
$477$	−5.37945	+	5.37945i	−0.246308	+	0.246308i
$478$	1.31268	+	1.31268i	0.0600405	+	0.0600405i
$479$	−11.2824			−0.515506			−0.257753	−	0.966211i	$-0.582982\pi$
$479$	−11.2824			−0.515506			−0.257753	+	0.966211i	$0.582982\pi$
$480$		0			0
$481$			11.2824i			0.514433i
$482$	8.59494	+	8.59494i	0.391489	+	0.391489i
$483$	−21.0842	−	34.9023i	−0.959366	−	1.58811i
$484$			8.00000i			0.363636i
$485$		0			0
$486$			5.50619i			0.249766i
$487$	19.4201	−	19.4201i	0.880007	−	0.880007i	−0.113528	−	0.993535i	$-0.536215\pi$
$487$	19.4201	−	19.4201i	0.880007	−	0.880007i	0.993535	+	0.113528i	$0.0362152\pi$
$488$	−4.60602	+	4.60602i	−0.208505	+	0.208505i
$489$	18.6690			0.844240
$490$		0			0
$491$	−5.07180			−0.228887			−0.114443	−	0.993430i	$-0.536508\pi$
$491$	−5.07180			−0.228887			−0.114443	+	0.993430i	$0.536508\pi$
$492$	−7.50077	+	7.50077i	−0.338161	+	0.338161i
$493$	−10.8980	+	10.8980i	−0.490819	+	0.490819i
$494$			16.7321i			0.752811i
$495$		0			0
$496$			8.89814i			0.399538i
$497$	11.2126	+	18.5611i	0.502956	+	0.832580i
$498$	7.50077	+	7.50077i	0.336118	+	0.336118i
$499$		−	16.7846i		−	0.751382i	−0.926745	−	0.375691i	$-0.877405\pi$
$499$		−	16.7846i		−	0.751382i	0.926745	−	0.375691i	$-0.122595\pi$
$500$		0			0
$501$	−24.4974			−1.09446
$502$	6.90903	+	6.90903i	0.308365	+	0.308365i
$503$	−15.5040	+	15.5040i	−0.691288	+	0.691288i	−0.962515	−	0.271227i	$-0.912570\pi$
$503$	−15.5040	+	15.5040i	−0.691288	+	0.691288i	0.271227	+	0.962515i	$0.412570\pi$
$504$	−1.37655	−	0.339746i	−0.0613163	−	0.0151335i
$505$		0			0
$506$	14.1962			0.631096
$507$	17.8070	+	17.8070i	0.790836	+	0.790836i
$508$	12.7279	+	12.7279i	0.564710	+	0.564710i
$509$	19.5417			0.866169			0.433085	−	0.901353i	$-0.357425\pi$
$509$	19.5417			0.866169			0.433085	+	0.901353i	$0.357425\pi$
$510$		0			0
$511$	27.6865	+	6.83332i	1.22478	+	0.302288i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−10.6710	−	10.6710i	−0.471135	−	0.471135i
$514$	11.2824			0.497645
$515$		0			0
$516$		−	6.51389i		−	0.286758i
$517$	−10.8980	−	10.8980i	−0.479291	−	0.479291i
$518$	4.97344	−	3.00442i	0.218520	−	0.132007i
$519$		−	4.48334i		−	0.196797i
$520$		0			0
$521$			16.9236i			0.741436i	0.928746	+	0.370718i	$0.120888\pi$
$521$			16.9236i			0.741436i	−0.928746	+	0.370718i	$0.879112\pi$
$522$	1.79315	−	1.79315i	0.0784841	−	0.0784841i
$523$	−4.70148	+	4.70148i	−0.205581	+	0.205581i	−0.802386	−	0.596805i	$-0.796437\pi$
$523$	−4.70148	+	4.70148i	−0.205581	+	0.205581i	0.596805	+	0.802386i	$0.296437\pi$
$524$		0			0
$525$		0			0
$526$	1.60770			0.0700988
$527$	20.4925	−	20.4925i	0.892667	−	0.892667i
$528$	2.30301	−	2.30301i	0.100226	−	0.100226i
$529$			44.1769i			1.92074i
$530$		0			0
$531$		0			0
$532$	7.37572	−	4.45562i	0.319778	−	0.193176i
$533$	−20.4925	−	20.4925i	−0.887628	−	0.887628i
$534$		−	10.6077i		−	0.459040i
$535$		0			0
$536$	−9.92820			−0.428833
$537$	22.8647	+	22.8647i	0.986686	+	0.986686i
$538$	−18.8758	+	18.8758i	−0.813794	+	0.813794i
$539$	−5.64120	+	10.7321i	−0.242983	+	0.462262i
$540$		0			0
$541$	13.4115			0.576607			0.288304	−	0.957539i	$-0.406909\pi$
$541$	13.4115			0.576607			0.288304	+	0.957539i	$0.406909\pi$
$542$	−7.97786	−	7.97786i	−0.342678	−	0.342678i
$543$	32.3238	+	32.3238i	1.38715	+	1.38715i
$544$	−3.25695			−0.139640
$545$		0			0
$546$	6.12436	−	24.8140i	0.262098	−	1.06194i
$547$	−9.46979	+	9.46979i	−0.404899	+	0.404899i	−0.879955	−	0.475056i	$-0.842428\pi$
$547$	−9.46979	+	9.46979i	−0.404899	+	0.404899i	0.475056	+	0.879955i	$0.342428\pi$
$548$	−7.91688	−	7.91688i	−0.338192	−	0.338192i
$549$	−3.49078			−0.148983
$550$		0			0
$551$			15.4120i			0.656575i
$552$	10.8980	+	10.8980i	0.463848	+	0.463848i
$553$	−4.52923	+	2.73608i	−0.192602	+	0.116350i
$554$			3.12436i			0.132741i
$555$		0			0
$556$		−	21.0532i		−	0.892856i
$557$	6.21166	−	6.21166i	0.263196	−	0.263196i	−0.563155	−	0.826351i	$-0.690413\pi$
$557$	6.21166	−	6.21166i	0.263196	−	0.263196i	0.826351	+	0.563155i	$0.190413\pi$
$558$	−3.37184	+	3.37184i	−0.142741	+	0.142741i
$559$	17.7963			0.752703
$560$		0			0
$561$	−10.6077			−0.447857
$562$	9.79796	−	9.79796i	0.413302	−	0.413302i
$563$	−7.97786	+	7.97786i	−0.336227	+	0.336227i	−0.854945	−	0.518719i	$-0.826409\pi$
$563$	−7.97786	+	7.97786i	−0.336227	+	0.336227i	0.518719	+	0.854945i	$0.326409\pi$
$564$		−	16.7321i		−	0.704546i
$565$		0			0
$566$		−	4.63349i		−	0.194760i
$567$	14.1188	+	23.3720i	0.592936	+	0.981530i
$568$	−5.79555	−	5.79555i	−0.243176	−	0.243176i
$569$		−	46.1769i		−	1.93584i	−0.251264	−	0.967918i	$-0.580846\pi$
$569$		−	46.1769i		−	1.93584i	0.251264	−	0.967918i	$-0.419154\pi$
$570$		0			0
$571$	30.3923			1.27188			0.635939	−	0.771739i	$-0.280613\pi$
$571$	30.3923			1.27188			0.635939	+	0.771739i	$0.280613\pi$
$572$	6.29194	+	6.29194i	0.263079	+	0.263079i
$573$	1.23418	−	1.23418i	0.0515585	−	0.0515585i
$574$	−3.57637	+	14.4904i	−0.149275	+	0.604817i
$575$		0			0
$576$	0.535898			0.0223291
$577$	−30.1300	−	30.1300i	−1.25433	−	1.25433i	−0.953760	−	0.300570i	$-0.902823\pi$
$577$	−30.1300	−	30.1300i	−1.25433	−	1.25433i	−0.300570	−	0.953760i	$-0.597177\pi$
$578$	−4.52004	−	4.52004i	−0.188009	−	0.188009i
$579$	34.0810			1.41636
$580$		0			0
$581$	14.4904	+	3.57637i	0.601162	+	0.148373i
$582$	−13.6617	+	13.6617i	−0.566294	+	0.566294i
$583$	−17.3867	−	17.3867i	−0.720082	−	0.720082i
$584$	−10.7785			−0.446019
$585$		0			0
$586$			24.3102i			1.00424i
$587$	25.7848	+	25.7848i	1.06425	+	1.06425i	0.997789	+	0.0664652i	$0.0211721\pi$
$587$	25.7848	+	25.7848i	1.06425	+	1.06425i	0.0664652	+	0.997789i	$0.478828\pi$
$588$	−12.5692	+	3.90809i	−0.518347	+	0.161167i
$589$		−	28.9808i		−	1.19413i
$590$		0			0
$591$			3.02311i			0.124354i
$592$	−1.55291	+	1.55291i	−0.0638244	+	0.0638244i
$593$	24.0989	−	24.0989i	0.989624	−	0.989624i	−0.0103229	−	0.999947i	$-0.503286\pi$
$593$	24.0989	−	24.0989i	0.989624	−	0.989624i	0.999947	+	0.0103229i	$0.00328595\pi$
$594$	−8.02545			−0.329288
$595$		0			0
$596$	4.39230			0.179916
$597$	−3.17020	+	3.17020i	−0.129748	+	0.129748i
$598$	−29.7738	+	29.7738i	−1.21754	+	1.21754i
$599$		−	19.2679i		−	0.787267i	−0.919267	−	0.393634i	$-0.871218\pi$
$599$		−	19.2679i		−	0.787267i	0.919267	−	0.393634i	$-0.128782\pi$
$600$		0			0
$601$			18.6690i			0.761524i	0.924673	+	0.380762i	$0.124338\pi$
$601$			18.6690i			0.761524i	−0.924673	+	0.380762i	$0.875662\pi$
$602$	−4.73902	−	7.84485i	−0.193148	−	0.319732i
$603$	−3.76217	−	3.76217i	−0.153207	−	0.153207i
$604$		−	14.5885i		−	0.593596i
$605$		0			0
$606$	−28.9808			−1.17726
$607$	−7.26530	−	7.26530i	−0.294890	−	0.294890i	0.544119	−	0.839008i	$-0.316864\pi$
$607$	−7.26530	−	7.26530i	−0.294890	−	0.294890i	−0.839008	+	0.544119i	$0.816864\pi$
$608$	−2.30301	+	2.30301i	−0.0933993	+	0.0933993i
$609$	5.64120	−	22.8564i	0.228593	−	0.926188i
$610$		0			0
$611$	45.7128			1.84934
$612$	−1.23418	−	1.23418i	−0.0498887	−	0.0498887i
$613$	4.24264	+	4.24264i	0.171359	+	0.171359i	0.787576	−	0.616217i	$-0.211336\pi$
$613$	4.24264	+	4.24264i	0.171359	+	0.171359i	−0.616217	+	0.787576i	$0.711336\pi$
$614$	−15.9159			−0.642313
$615$		0			0
$616$	1.09808	−	4.44907i	0.0442428	−	0.179258i
$617$	8.48528	−	8.48528i	0.341605	−	0.341605i	−0.515366	−	0.856970i	$-0.672344\pi$
$617$	8.48528	−	8.48528i	0.341605	−	0.341605i	0.856970	+	0.515366i	$0.172344\pi$
$618$	13.6617	+	13.6617i	0.549553	+	0.549553i
$619$	−40.3611			−1.62225			−0.811124	−	0.584874i	$-0.801144\pi$
$619$	−40.3611			−1.62225			−0.811124	+	0.584874i	$0.801144\pi$
$620$		0			0
$621$		−	37.9768i		−	1.52396i
$622$	−7.97786	−	7.97786i	−0.319883	−	0.319883i
$623$	−7.71737	−	12.7751i	−0.309190	−	0.511825i
$624$			9.66025i			0.386720i
$625$		0			0
$626$		−	9.26699i		−	0.370383i
$627$	−7.50077	+	7.50077i	−0.299552	+	0.299552i
$628$	4.34520	−	4.34520i	0.173393	−	0.173393i
$629$	7.15275			0.285199
$630$		0			0
$631$	−14.9808			−0.596375			−0.298187	−	0.954507i	$-0.596382\pi$
$631$	−14.9808			−0.596375			−0.298187	+	0.954507i	$0.596382\pi$
$632$	1.41421	−	1.41421i	0.0562544	−	0.0562544i
$633$	1.59046	−	1.59046i	0.0632149	−	0.0632149i
$634$			4.39230i			0.174441i
$635$		0			0
$636$		−	26.6944i		−	1.05850i
$637$	−10.6771	−	34.3398i	−0.423043	−	1.36059i
$638$	5.79555	+	5.79555i	0.229448	+	0.229448i
$639$		−	4.39230i		−	0.173757i
$640$		0			0
$641$	−36.0000			−1.42191			−0.710957	−	0.703235i	$-0.751738\pi$
$641$	−36.0000			−1.42191			−0.710957	+	0.703235i	$0.751738\pi$
$642$	−9.82912	−	9.82912i	−0.387925	−	0.387925i
$643$	6.55275	−	6.55275i	0.258415	−	0.258415i	−0.565994	−	0.824409i	$-0.691508\pi$
$643$	6.55275	−	6.55275i	0.258415	−	0.258415i	0.824409	+	0.565994i	$0.191508\pi$
$644$	21.0532	+	5.19615i	0.829613	+	0.204757i
$645$		0			0
$646$	10.6077			0.417354
$647$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$647$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$648$	−7.29770	−	7.29770i	−0.286681	−	0.286681i
$649$		0			0
$650$		0			0
$651$	−10.6077	+	42.9792i	−0.415748	+	1.68449i
$652$	−7.02030	+	7.02030i	−0.274936	+	0.274936i
$653$	30.9468	+	30.9468i	1.21104	+	1.21104i	0.970685	+	0.240357i	$0.0772645\pi$
$653$	30.9468	+	30.9468i	1.21104	+	1.21104i	0.240357	+	0.970685i	$0.422736\pi$
$654$	3.76080			0.147059
$655$		0			0
$656$		−	5.64120i		−	0.220252i
$657$	−4.08439	−	4.08439i	−0.159347	−	0.159347i
$658$	−12.1730	−	20.1508i	−0.474553	−	0.785562i
$659$			36.1244i			1.40721i	0.710594	+	0.703603i	$0.248426\pi$
$659$			36.1244i			1.40721i	−0.710594	+	0.703603i	$0.751574\pi$
$660$		0			0
$661$			4.12964i			0.160624i	0.996770	+	0.0803122i	$0.0255917\pi$
$661$			4.12964i			0.160624i	−0.996770	+	0.0803122i	$0.974408\pi$
$662$	5.36585	−	5.36585i	0.208550	−	0.208550i
$663$	22.2476	−	22.2476i	0.864027	−	0.864027i
$664$	−5.64120			−0.218921
$665$		0			0
$666$	−1.17691			−0.0456045
$667$	−27.4249	+	27.4249i	−1.06189	+	1.06189i
$668$	9.21203	−	9.21203i	0.356424	−	0.356424i
$669$			30.8756i			1.19372i
$670$		0			0
$671$		−	11.2824i		−	0.435552i
$672$	4.25838	−	2.57246i	0.164270	−	0.0992346i
$673$	−15.8338	−	15.8338i	−0.610346	−	0.610346i	0.332690	−	0.943036i	$-0.392044\pi$
$673$	−15.8338	−	15.8338i	−0.610346	−	0.610346i	−0.943036	+	0.332690i	$0.892044\pi$
$674$			22.2679i			0.857729i
$675$		0			0
$676$	−13.3923			−0.515089
$677$	−28.5396	−	28.5396i	−1.09687	−	1.09687i	−0.994775	−	0.102090i	$-0.967447\pi$
$677$	−28.5396	−	28.5396i	−1.09687	−	1.09687i	−0.102090	−	0.994775i	$-0.532553\pi$
$678$	1.06883	−	1.06883i	0.0410482	−	0.0410482i
$679$	−6.51389	+	26.3923i	−0.249980	+	1.01284i
$680$		0			0
$681$	12.2487			0.469372
$682$	−10.8980	−	10.8980i	−0.417304	−	0.417304i
$683$	29.5462	+	29.5462i	1.13055	+	1.13055i	0.990085	+	0.140468i	$0.0448607\pi$
$683$	29.5462	+	29.5462i	1.13055	+	1.13055i	0.140468	+	0.990085i	$0.455139\pi$
$684$	−1.74539			−0.0667367
$685$		0			0
$686$	−12.2942	+	13.8511i	−0.469396	+	0.528836i
$687$	11.8313	−	11.8313i	0.451394	−	0.451394i
$688$	2.44949	+	2.44949i	0.0933859	+	0.0933859i
$689$	72.9305			2.77843
$690$		0			0
$691$			9.77084i			0.371700i	0.982578	+	0.185850i	$0.0595039\pi$
$691$			9.77084i			0.371700i	−0.982578	+	0.185850i	$0.940496\pi$
$692$	1.68592	+	1.68592i	0.0640890	+	0.0640890i
$693$	2.10202	−	1.26982i	0.0798492	−	0.0482364i
$694$		−	11.7846i		−	0.447338i
$695$		0			0
$696$			8.89814i			0.337283i
$697$	−12.9917	+	12.9917i	−0.492096	+	0.492096i
$698$	−10.8980	+	10.8980i	−0.412494	+	0.412494i
$699$	−19.5417			−0.739134
$700$		0			0
$701$	−5.07180			−0.191559			−0.0957796	−	0.995403i	$-0.530534\pi$
$701$	−5.07180			−0.191559			−0.0957796	+	0.995403i	$0.530534\pi$
$702$	16.8319	−	16.8319i	0.635278	−	0.635278i
$703$	5.05776	−	5.05776i	0.190757	−	0.190757i
$704$			1.73205i			0.0652791i
$705$		0			0
$706$		−	29.0787i		−	1.09439i
$707$	−34.9023	+	21.0842i	−1.31264	+	0.792955i
$708$		0			0
$709$		−	20.3923i		−	0.765849i	−0.923780	−	0.382925i	$-0.874917\pi$
$709$		−	20.3923i		−	0.765849i	0.923780	−	0.382925i	$-0.125083\pi$
$710$		0			0
$711$	1.07180			0.0401955
$712$	3.98893	+	3.98893i	0.149491	+	0.149491i
$713$	51.5697	−	51.5697i	1.93130	−	1.93130i
$714$	−15.7315	−	3.88269i	−0.588735	−	0.145306i
$715$		0			0
$716$	−17.1962			−0.642650
$717$	−2.46836	−	2.46836i	−0.0921825	−	0.0921825i
$718$	7.34847	+	7.34847i	0.274242	+	0.274242i
$719$	−4.12964			−0.154010			−0.0770048	−	0.997031i	$-0.524536\pi$
$719$	−4.12964			−0.154010			−0.0770048	+	0.997031i	$0.524536\pi$
$720$		0			0
$721$	26.3923	+	6.51389i	0.982901	+	0.242590i
$722$	−5.93426	+	5.93426i	−0.220850	+	0.220850i
$723$	−16.1619	−	16.1619i	−0.601068	−	0.601068i
$724$	−24.3102			−0.903480
$725$		0			0
$726$		−	15.0432i		−	0.558305i
$727$	17.4507	+	17.4507i	0.647211	+	0.647211i	0.952318	−	0.305107i	$-0.0986923\pi$
$727$	17.4507	+	17.4507i	0.647211	+	0.647211i	−0.305107	+	0.952318i	$0.598692\pi$
$728$	7.02808	+	11.6341i	0.260478	+	0.431188i
$729$			20.6077i			0.763248i
$730$		0			0
$731$		−	11.2824i		−	0.417294i
$732$	8.66115	−	8.66115i	0.320125	−	0.320125i
$733$	−7.26530	+	7.26530i	−0.268350	+	0.268350i	−0.828435	−	0.560085i	$-0.810768\pi$
$733$	−7.26530	+	7.26530i	−0.268350	+	0.268350i	0.560085	+	0.828435i	$0.310768\pi$
$734$	10.2747			0.379246
$735$		0			0
$736$	−8.19615			−0.302114
$737$	12.1595	−	12.1595i	0.447902	−	0.447902i
$738$	2.13766	−	2.13766i	0.0786883	−	0.0786883i
$739$			24.7846i			0.911717i	0.890052	+	0.455858i	$0.150668\pi$
$739$			24.7846i			0.911717i	−0.890052	+	0.455858i	$0.849332\pi$
$740$		0			0
$741$		−	31.4629i		−	1.15582i
$742$	−19.4209	−	32.1488i	−0.712963	−	1.18022i
$743$	−17.3867	−	17.3867i	−0.637855	−	0.637855i	0.312171	−	0.950026i	$-0.398944\pi$
$743$	−17.3867	−	17.3867i	−0.637855	−	0.637855i	−0.950026	+	0.312171i	$0.898944\pi$
$744$		−	16.7321i		−	0.613427i
$745$		0			0
$746$	−16.7321			−0.612604
$747$	−2.13766	−	2.13766i	−0.0782129	−	0.0782129i
$748$	3.98893	−	3.98893i	0.145850	−	0.145850i
$749$	−18.9884	−	4.68653i	−0.693821	−	0.171242i
$750$		0			0
$751$	−24.1962			−0.882930			−0.441465	−	0.897278i	$-0.645541\pi$
$751$	−24.1962			−0.882930			−0.441465	+	0.897278i	$0.645541\pi$
$752$	6.29194	+	6.29194i	0.229443	+	0.229443i
$753$	−12.9917	−	12.9917i	−0.473445	−	0.473445i
$754$	−24.3102			−0.885324
$755$		0			0
$756$	−11.9019	−	2.93752i	−0.432869	−	0.106836i
$757$	−26.3524	+	26.3524i	−0.957795	+	0.957795i	−0.999145	−	0.0413498i	$-0.986834\pi$
$757$	−26.3524	+	26.3524i	−0.957795	+	0.957795i	0.0413498	+	0.999145i	$0.486834\pi$
$758$	−12.7143	−	12.7143i	−0.461805	−	0.461805i
$759$	−26.6944			−0.968946
$760$		0			0
$761$			16.9236i			0.613480i	0.951793	+	0.306740i	$0.0992381\pi$
$761$			16.9236i			0.613480i	−0.951793	+	0.306740i	$0.900762\pi$
$762$	−23.9336	−	23.9336i	−0.867022	−	0.867022i
$763$	4.52923	−	2.73608i	0.163969	−	0.0990526i
$764$			0.928203i			0.0335812i
$765$		0			0
$766$			11.2824i			0.407649i
$767$		0			0
$768$	−1.32964	+	1.32964i	−0.0479793	+	0.0479793i
$769$	−12.1551			−0.438324			−0.219162	−	0.975689i	$-0.570332\pi$
$769$	−12.1551			−0.438324			−0.219162	+	0.975689i	$0.570332\pi$
$770$		0			0
$771$	−21.2154			−0.764054
$772$	−12.8159	+	12.8159i	−0.461253	+	0.461253i
$773$	25.1677	−	25.1677i	0.905221	−	0.905221i	−0.0906610	−	0.995882i	$-0.528898\pi$
$773$	25.1677	−	25.1677i	0.905221	−	0.905221i	0.995882	+	0.0906610i	$0.0288980\pi$
$774$			1.85641i			0.0667272i
$775$		0			0
$776$		−	10.2747i		−	0.368840i
$777$	−9.35204	+	5.64951i	−0.335503	+	0.202675i
$778$	12.4877	+	12.4877i	0.447705	+	0.447705i
$779$			18.3731i			0.658283i
$780$		0			0
$781$	14.1962			0.507978
$782$	18.8758	+	18.8758i	0.674998	+	0.674998i
$783$	15.5040	−	15.5040i	0.554067	−	0.554067i
$784$	3.25695	−	6.19615i	0.116319	−	0.221291i
$785$		0			0
$786$		0			0
$787$	−15.2432	−	15.2432i	−0.543360	−	0.543360i	0.381152	−	0.924512i	$-0.375527\pi$
$787$	−15.2432	−	15.2432i	−0.543360	−	0.543360i	−0.924512	+	0.381152i	$0.875527\pi$
$788$	−1.13681	−	1.13681i	−0.0404973	−	0.0404973i
$789$	−3.02311			−0.107625
$790$		0			0
$791$	0.509619	−	2.06482i	0.0181200	−	0.0734166i
$792$	−0.656339	+	0.656339i	−0.0233220	+	0.0233220i
$793$	23.6627	+	23.6627i	0.840287	+	0.840287i
$794$	−25.6867			−0.911588
$795$		0			0
$796$		−	2.38425i		−	0.0845075i
$797$	33.1456	+	33.1456i	1.17408	+	1.17408i	0.981228	+	0.192849i	$0.0617727\pi$
$797$	33.1456	+	33.1456i	1.17408	+	1.17408i	0.192849	+	0.981228i	$0.438227\pi$
$798$	−13.8693	+	8.37835i	−0.490968	+	0.296590i
$799$		−	28.9808i		−	1.02527i
$800$		0			0
$801$			3.02311i			0.106816i
$802$	19.7482	−	19.7482i	0.697334	−	0.697334i
$803$	13.2010	−	13.2010i	0.465852	−	0.465852i
$804$	18.6690			0.658404
$805$		0			0
$806$	45.7128			1.61017
$807$	35.4940	−	35.4940i	1.24945	−	1.24945i
$808$	10.8980	−	10.8980i	0.383389	−	0.383389i
$809$		−	39.0333i		−	1.37234i	−0.727442	−	0.686169i	$-0.759291\pi$
$809$		−	39.0333i		−	1.37234i	0.727442	−	0.686169i	$-0.240709\pi$
$810$		0			0
$811$			1.74539i			0.0612890i	0.999530	+	0.0306445i	$0.00975597\pi$
$811$			1.74539i			0.0612890i	−0.999530	+	0.0306445i	$0.990244\pi$
$812$	6.47362	+	10.7163i	0.227180	+	0.376067i
$813$	15.0015	+	15.0015i	0.526127	+	0.526127i
$814$		−	3.80385i		−	0.133325i
$815$		0			0
$816$	6.12436			0.214395
$817$	−7.97786	−	7.97786i	−0.279110	−	0.279110i
$818$	22.4130	−	22.4130i	0.783652	−	0.783652i
$819$	−1.74539	+	7.07180i	−0.0609889	+	0.247109i
$820$		0			0
$821$	−8.87564			−0.309762			−0.154881	−	0.987933i	$-0.549499\pi$
$821$	−8.87564			−0.309762			−0.154881	+	0.987933i	$0.549499\pi$
$822$	14.8869	+	14.8869i	0.519240	+	0.519240i
$823$	−3.34607	−	3.34607i	−0.116637	−	0.116637i	0.646380	−	0.763016i	$-0.276282\pi$
$823$	−3.34607	−	3.34607i	−0.116637	−	0.116637i	−0.763016	+	0.646380i	$0.776282\pi$
$824$	−10.2747			−0.357936
$825$		0			0
$826$		0			0
$827$	24.1667	−	24.1667i	0.840359	−	0.840359i	−0.148546	−	0.988905i	$-0.547459\pi$
$827$	24.1667	−	24.1667i	0.840359	−	0.840359i	0.988905	+	0.148546i	$0.0474593\pi$
$828$	−3.10583	−	3.10583i	−0.107935	−	0.107935i
$829$	−30.8241			−1.07056			−0.535282	−	0.844673i	$-0.679795\pi$
$829$	−30.8241			−1.07056			−0.535282	+	0.844673i	$0.679795\pi$
$830$		0			0
$831$		−	5.87503i		−	0.203803i
$832$	−3.63265	−	3.63265i	−0.125940	−	0.125940i
$833$	−21.7706	+	6.76902i	−0.754305	+	0.234533i
$834$			39.5885i			1.37084i
$835$		0			0
$836$		−	5.64120i		−	0.195105i
$837$	−29.1536	+	29.1536i	−1.00770	+	1.00770i
$838$	−1.06883	+	1.06883i	−0.0369221	+	0.0369221i
$839$	−46.2361			−1.59625			−0.798124	−	0.602494i	$-0.794174\pi$
$839$	−46.2361			−1.59625			−0.798124	+	0.602494i	$0.794174\pi$
$840$		0			0
$841$	6.60770			0.227852
$842$	−23.4596	+	23.4596i	−0.808472	+	0.808472i
$843$	−18.4241	+	18.4241i	−0.634559	+	0.634559i
$844$			1.19615i			0.0411733i
$845$		0			0
$846$			4.76850i			0.163944i
$847$	−10.9443	−	18.1169i	−0.376051	−	0.622504i
$848$	10.0382	+	10.0382i	0.344713	+	0.344713i
$849$			8.71281i			0.299023i
$850$		0			0
$851$	18.0000			0.617032
$852$	10.8980	+	10.8980i	0.373358	+	0.373358i
$853$	−22.5085	+	22.5085i	−0.770675	+	0.770675i	−0.978225	−	0.207550i	$-0.933451\pi$
$853$	−22.5085	+	22.5085i	−0.770675	+	0.770675i	0.207550	+	0.978225i	$0.433451\pi$
$854$	4.12964	−	16.7321i	0.141313	−	0.572559i
$855$		0			0
$856$	7.39230			0.252664
$857$	−22.8647	−	22.8647i	−0.781044	−	0.781044i	0.198963	−	0.980007i	$-0.436243\pi$
$857$	−22.8647	−	22.8647i	−0.781044	−	0.781044i	−0.980007	+	0.198963i	$0.936243\pi$
$858$	−11.8313	−	11.8313i	−0.403916	−	0.403916i
$859$	1.51155			0.0515735			0.0257868	−	0.999667i	$-0.491791\pi$
$859$	1.51155			0.0515735			0.0257868	+	0.999667i	$0.491791\pi$
$860$		0			0
$861$	6.72501	−	27.2477i	0.229188	−	0.928599i
$862$	−26.5283	+	26.5283i	−0.903557	+	0.903557i
$863$	−37.0470	−	37.0470i	−1.26109	−	1.26109i	−0.950564	−	0.310529i	$-0.899494\pi$
$863$	−37.0470	−	37.0470i	−1.26109	−	1.26109i	−0.310529	−	0.950564i	$-0.600506\pi$
$864$	4.63349			0.157635
$865$		0			0
$866$			20.0455i			0.681175i
$867$	8.49948	+	8.49948i	0.288657	+	0.288657i
$868$	−12.1730	−	20.1508i	−0.413178	−	0.683964i
$869$			3.46410i			0.117512i
$870$		0			0
$871$			51.0046i			1.72822i
$872$	−1.41421	+	1.41421i	−0.0478913	+	0.0478913i
$873$	3.89346	−	3.89346i	0.131774	−	0.131774i
$874$	26.6944			0.902952
$875$		0			0
$876$	20.2679			0.684791
$877$	18.2832	−	18.2832i	0.617381	−	0.617381i	−0.327478	−	0.944859i	$-0.606199\pi$
$877$	18.2832	−	18.2832i	0.617381	−	0.617381i	0.944859	+	0.327478i	$0.106199\pi$
$878$	−12.5839	+	12.5839i	−0.424685	+	0.424685i
$879$		−	45.7128i		−	1.54185i
$880$		0			0
$881$			8.25928i			0.278262i	0.990274	+	0.139131i	$0.0444310\pi$
$881$			8.25928i			0.278262i	−0.990274	+	0.139131i	$0.955569\pi$
$882$	3.58213	−	1.11378i	0.120617	−	0.0375028i
$883$	−17.2987	−	17.2987i	−0.582149	−	0.582149i	0.353345	−	0.935493i	$-0.385044\pi$
$883$	−17.2987	−	17.2987i	−0.582149	−	0.582149i	−0.935493	+	0.353345i	$0.885044\pi$
$884$			16.7321i			0.562760i
$885$		0			0
$886$	15.0000			0.503935
$887$	18.8758	+	18.8758i	0.633788	+	0.633788i	0.949016	−	0.315228i	$-0.102081\pi$
$887$	18.8758	+	18.8758i	0.633788	+	0.633788i	−0.315228	+	0.949016i	$0.602081\pi$
$888$	2.92010	−	2.92010i	0.0979921	−	0.0979921i
$889$	−46.2361	−	11.4115i	−1.55071	−	0.382731i
$890$		0			0
$891$	17.8756			0.598857
$892$	−11.6105	−	11.6105i	−0.388748	−	0.388748i
$893$	−20.4925	−	20.4925i	−0.685755	−	0.685755i
$894$	−8.25928			−0.276232
$895$		0			0
$896$	−0.633975	+	2.56867i	−0.0211796	+	0.0858133i
$897$	55.9865	−	55.9865i	1.86934	−	1.86934i
$898$	20.4046	+	20.4046i	0.680909	+	0.680909i
$899$	42.1065			1.40433
$900$		0			0
$901$		−	46.2361i		−	1.54035i
$902$	6.90903	+	6.90903i	0.230045	+	0.230045i
$903$	8.91125	+	14.7514i	0.296548	+	0.490897i
$904$			0.803848i			0.0267356i
$905$		0			0
$906$			27.4321i			0.911371i
$907$	2.27362	−	2.27362i	0.0754945	−	0.0754945i	−0.668351	−	0.743846i	$-0.733000\pi$
$907$	2.27362	−	2.27362i	0.0754945	−	0.0754945i	0.743846	+	0.668351i	$0.233000\pi$
$908$	−4.60602	+	4.60602i	−0.152856	+	0.152856i
$909$	8.25928			0.273943
$910$		0			0
$911$	−24.0000			−0.795155			−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000			−0.795155			−0.397578	+	0.917568i	$0.630149\pi$
$912$	4.33057	−	4.33057i	0.143400	−	0.143400i
$913$	6.90903	−	6.90903i	0.228655	−	0.228655i
$914$		−	23.1962i		−	0.767261i
$915$		0			0
$916$			8.89814i			0.294003i
$917$		0			0
$918$	−10.6710	−	10.6710i	−0.352195	−	0.352195i
$919$			30.3923i			1.00255i	0.865288	+	0.501275i	$0.167135\pi$
$919$			30.3923i			1.00255i	−0.865288	+	0.501275i	$0.832865\pi$
$920$		0			0
$921$	29.9282			0.986168
$922$	−2.92010	−	2.92010i	−0.0961683	−	0.0961683i
$923$	−29.7738	+	29.7738i	−0.980015	+	0.980015i
$924$	−2.06482	+	8.36603i	−0.0679276	+	0.275222i
$925$		0			0
$926$	25.1769			0.827365
$927$	−3.89346	−	3.89346i	−0.127878	−	0.127878i
$928$	−3.34607	−	3.34607i	−0.109840	−	0.109840i
$929$	22.5648			0.740326			0.370163	−	0.928967i	$-0.379302\pi$
$929$	22.5648			0.740326			0.370163	+	0.928967i	$0.379302\pi$
$930$		0			0
$931$	−10.6077	+	20.1805i	−0.347653	+	0.661390i
$932$	7.34847	−	7.34847i	0.240707	−	0.240707i
$933$	15.0015	+	15.0015i	0.491129	+	0.491129i
$934$	17.7963			0.582312
$935$		0			0
$936$		−	2.75309i		−	0.0899877i
$937$	16.3120	+	16.3120i	0.532889	+	0.532889i	0.921431	−	0.388542i	$-0.127021\pi$
$937$	16.3120	+	16.3120i	0.532889	+	0.532889i	−0.388542	+	0.921431i	$0.627021\pi$
$938$	22.4835	−	13.5822i	0.734114	−	0.443473i
$939$			17.4256i			0.568664i
$940$		0			0
$941$			30.8241i			1.00484i	0.864625	+	0.502418i	$0.167556\pi$
$941$			30.8241i			1.00484i	−0.864625	+	0.502418i	$0.832444\pi$
$942$	−8.17072	+	8.17072i	−0.266216	+	0.266216i
$943$	−32.6939	+	32.6939i	−1.06466	+	1.06466i
$944$		0			0
$945$		0			0
$946$	−6.00000			−0.195077
$947$	−39.0160	+	39.0160i	−1.26785	+	1.26785i	−0.320651	+	0.947197i	$0.603902\pi$
$947$	−39.0160	+	39.0160i	−1.26785	+	1.26785i	−0.947197	+	0.320651i	$0.896098\pi$
$948$	−2.65929	+	2.65929i	−0.0863696	+	0.0863696i
$949$			55.3731i			1.79749i
$950$		0			0
$951$		−	8.25928i		−	0.267826i
$952$	7.37572	−	4.45562i	0.239049	−	0.144408i
$953$	3.67423	+	3.67423i	0.119020	+	0.119020i	0.764108	−	0.645088i	$-0.223179\pi$
$953$	3.67423	+	3.67423i	0.119020	+	0.119020i	−0.645088	+	0.764108i	$0.723179\pi$
$954$			7.60770i			0.246308i
$955$		0			0
$956$	1.85641			0.0600405
$957$	−10.8980	−	10.8980i	−0.352281	−	0.352281i
$958$	−7.97786	+	7.97786i	−0.257753	+	0.257753i
$959$	28.7592	+	7.09808i	0.928684	+	0.229209i
$960$		0			0
$961$	−48.1769			−1.55409
$962$	7.97786	+	7.97786i	0.257216	+	0.257216i
$963$	2.80122	+	2.80122i	0.0902681	+	0.0902681i
$964$	12.1551			0.391489
$965$		0			0
$966$	−39.5885	−	9.77084i	−1.27374	−	0.314372i
$967$	−6.93237	+	6.93237i	−0.222930	+	0.222930i	−0.809731	−	0.586801i	$-0.800387\pi$
$967$	−6.93237	+	6.93237i	−0.222930	+	0.222930i	0.586801	+	0.809731i	$0.300387\pi$
$968$	5.65685	+	5.65685i	0.181818	+	0.181818i
$969$	−19.9467			−0.640780
$970$		0			0
$971$		−	51.8773i		−	1.66482i	−0.554159	−	0.832411i	$-0.686960\pi$
$971$		−	51.8773i		−	1.66482i	0.554159	−	0.832411i	$-0.313040\pi$
$972$	3.89346	+	3.89346i	0.124883	+	0.124883i
$973$	28.8016	+	47.6774i	0.923337	+	1.52847i
$974$		−	27.4641i		−	0.880007i
$975$		0			0
$976$			6.51389i			0.208505i
$977$	−14.4331	+	14.4331i	−0.461757	+	0.461757i	−0.899231	−	0.437474i	$-0.855873\pi$
$977$	−14.4331	+	14.4331i	−0.461757	+	0.461757i	0.437474	+	0.899231i	$0.355873\pi$
$978$	13.2010	−	13.2010i	0.422120	−	0.422120i
$979$	−9.77084			−0.312277
$980$		0			0
$981$	−1.07180			−0.0342198
$982$	−3.58630	+	3.58630i	−0.114443	+	0.114443i
$983$	−7.52611	+	7.52611i	−0.240046	+	0.240046i	−0.816869	−	0.576823i	$-0.804292\pi$
$983$	−7.52611	+	7.52611i	−0.240046	+	0.240046i	0.576823	+	0.816869i	$0.304292\pi$
$984$			10.6077i			0.338161i
$985$		0			0
$986$			15.4120i			0.490819i
$987$	22.8901	+	37.8916i	0.728599	+	1.20610i
$988$	11.8313	+	11.8313i	0.376405	+	0.376405i
$989$		−	28.3923i		−	0.902823i
$990$		0			0
$991$	6.19615			0.196827			0.0984136	−	0.995146i	$-0.468623\pi$
$991$	6.19615			0.196827			0.0984136	+	0.995146i	$0.468623\pi$
$992$	6.29194	+	6.29194i	0.199769	+	0.199769i
$993$	−10.0899	+	10.0899i	−0.320194	+	0.320194i
$994$	21.0532	+	5.19615i	0.667768	+	0.164812i
$995$		0			0
$996$	10.6077			0.336118
$997$	18.1633	+	18.1633i	0.575236	+	0.575236i	0.933587	−	0.358351i	$-0.116661\pi$
$997$	18.1633	+	18.1633i	0.575236	+	0.575236i	−0.358351	+	0.933587i	$0.616661\pi$
$998$	−11.8685	−	11.8685i	−0.375691	−	0.375691i
$999$	−10.1759			−0.321950

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.g.b.293.6	yes	16
5.2	odd	4	inner	350.2.g.b.307.7	yes	16
5.3	odd	4	inner	350.2.g.b.307.2	yes	16
5.4	even	2	inner	350.2.g.b.293.3	yes	16
7.6	odd	2	inner	350.2.g.b.293.7	yes	16
35.13	even	4	inner	350.2.g.b.307.3	yes	16
35.27	even	4	inner	350.2.g.b.307.6	yes	16
35.34	odd	2	inner	350.2.g.b.293.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.g.b.293.2	✓	16	35.34	odd	2	inner
350.2.g.b.293.3	yes	16	5.4	even	2	inner
350.2.g.b.293.6	yes	16	1.1	even	1	trivial
350.2.g.b.293.7	yes	16	7.6	odd	2	inner
350.2.g.b.307.2	yes	16	5.3	odd	4	inner
350.2.g.b.307.3	yes	16	35.13	even	4	inner
350.2.g.b.307.6	yes	16	35.27	even	4	inner
350.2.g.b.307.7	yes	16	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.32964 + 1.32964i) q^{3} -1.00000i q^{4} +1.88040i q^{6} +(1.36804 + 2.26461i) q^{7} +(-0.707107 - 0.707107i) q^{8} -0.535898i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.32964 + 1.32964i) q^{3} -1.00000i q^{4} +1.88040i q^{6} +(1.36804 + 2.26461i) q^{7} +(-0.707107 - 0.707107i) q^{8} -0.535898i q^{9} +1.73205 q^{11} +(1.32964 + 1.32964i) q^{12} +(-3.63265 + 3.63265i) q^{13} +(2.56867 + 0.633975i) q^{14} -1.00000 q^{16} +(2.30301 + 2.30301i) q^{17} +(-0.378937 - 0.378937i) q^{18} +3.25695 q^{19} +(-4.83013 - 1.19212i) q^{21} +(1.22474 - 1.22474i) q^{22} +(5.79555 + 5.79555i) q^{23} +1.88040 q^{24} +5.13734i q^{26} +(-3.27637 - 3.27637i) q^{27} +(2.26461 - 1.36804i) q^{28} +4.73205i q^{29} -8.89814i q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.30301 + 2.30301i) q^{33} +3.25695 q^{34} -0.535898 q^{36} +(1.55291 - 1.55291i) q^{37} +(2.30301 - 2.30301i) q^{38} -9.66025i q^{39} +5.64120i q^{41} +(-4.25838 + 2.57246i) q^{42} +(-2.44949 - 2.44949i) q^{43} -1.73205i q^{44} +8.19615 q^{46} +(-6.29194 - 6.29194i) q^{47} +(1.32964 - 1.32964i) q^{48} +(-3.25695 + 6.19615i) q^{49} -6.12436 q^{51} +(3.63265 + 3.63265i) q^{52} +(-10.0382 - 10.0382i) q^{53} -4.63349 q^{54} +(0.633975 - 2.56867i) q^{56} +(-4.33057 + 4.33057i) q^{57} +(3.34607 + 3.34607i) q^{58} -6.51389i q^{61} +(-6.29194 - 6.29194i) q^{62} +(1.21360 - 0.733129i) q^{63} +1.00000i q^{64} +3.25695i q^{66} +(7.02030 - 7.02030i) q^{67} +(2.30301 - 2.30301i) q^{68} -15.4120 q^{69} +8.19615 q^{71} +(-0.378937 + 0.378937i) q^{72} +(7.62158 - 7.62158i) q^{73} -2.19615i q^{74} -3.25695i q^{76} +(2.36951 + 3.92243i) q^{77} +(-6.83083 - 6.83083i) q^{78} +2.00000i q^{79} +10.3205 q^{81} +(3.98893 + 3.98893i) q^{82} +(3.98893 - 3.98893i) q^{83} +(-1.19212 + 4.83013i) q^{84} -3.46410 q^{86} +(-6.29194 - 6.29194i) q^{87} +(-1.22474 - 1.22474i) q^{88} -5.64120 q^{89} +(-13.1962 - 3.25695i) q^{91} +(5.79555 - 5.79555i) q^{92} +(11.8313 + 11.8313i) q^{93} -8.89814 q^{94} -1.88040i q^{96} +(7.26530 + 7.26530i) q^{97} +(2.07833 + 6.68435i) q^{98} -0.928203i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 16 q^{16} - 8 q^{21} - 64 q^{36} + 48 q^{46} + 96 q^{51} + 24 q^{56} + 48 q^{71} - 112 q^{81} - 128 q^{91}+O(q^{100}) \) 16 * q - 16 * q^16 - 8 * q^21 - 64 * q^36 + 48 * q^46 + 96 * q^51 + 24 * q^56 + 48 * q^71 - 112 * q^81 - 128 * q^91

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