LMFDB - Embedded newform 325.2.s.c.132.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,2,Mod(32,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.32"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.s (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			132.3
Character	$\chi$	$=$	325.132
Dual form			325.2.s.c.293.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.880562 - 1.52518i) q^{2} +(3.15371 + 0.845033i) q^{3} +(-0.550780 + 0.953979i) q^{4} +(-1.48821 - 5.55407i) q^{6} +(1.20362 + 0.694909i) q^{7} -1.58226 q^{8} +(6.63370 + 3.82997i) q^{9} +(0.949498 - 3.54358i) q^{11} +(-2.54314 + 2.54314i) q^{12} +(-3.27006 + 1.51879i) q^{13} -2.44764i q^{14} +(2.49484 + 4.32119i) q^{16} +(-1.05282 - 3.92917i) q^{17} -13.4901i q^{18} +(2.25062 - 0.603051i) q^{19} +(3.20863 + 3.20863i) q^{21} +(-6.24068 + 1.67219i) q^{22} +(-1.47867 + 5.51848i) q^{23} +(-4.99000 - 1.33707i) q^{24} +(5.19592 + 3.65003i) q^{26} +(10.7583 + 10.7583i) q^{27} +(-1.32586 + 0.765484i) q^{28} +(2.47021 - 1.42618i) q^{29} +(0.220086 - 0.220086i) q^{31} +(2.81146 - 4.86960i) q^{32} +(5.98888 - 10.3730i) q^{33} +(-5.06561 + 5.06561i) q^{34} +(-7.30742 + 4.21894i) q^{36} +(-5.26488 + 3.03968i) q^{37} +(-2.90157 - 2.90157i) q^{38} +(-11.5962 + 2.02651i) q^{39} +(-10.9769 - 2.94124i) q^{41} +(2.06834 - 7.71914i) q^{42} +(-5.35430 + 1.43468i) q^{43} +(2.85753 + 2.85753i) q^{44} +(9.71874 - 2.60413i) q^{46} -5.06887i q^{47} +(4.21645 + 15.7360i) q^{48} +(-2.53420 - 4.38937i) q^{49} -13.2811i q^{51} +(0.352188 - 3.95609i) q^{52} +(-0.586010 + 0.586010i) q^{53} +(6.93496 - 25.8816i) q^{54} +(-1.90444 - 1.09953i) q^{56} +7.60737 q^{57} +(-4.35035 - 2.51168i) q^{58} +(0.878129 + 3.27722i) q^{59} +(-3.03437 + 5.25569i) q^{61} +(-0.529470 - 0.141871i) q^{62} +(5.32296 + 9.21963i) q^{63} +0.0766898 q^{64} -21.0943 q^{66} +(0.660446 + 1.14393i) q^{67} +(4.32821 + 1.15974i) q^{68} +(-9.32660 + 16.1541i) q^{69} +(1.41960 + 5.29800i) q^{71} +(-10.4963 - 6.06002i) q^{72} +2.15999 q^{73} +(9.27212 + 5.35326i) q^{74} +(-0.664297 + 2.47919i) q^{76} +(3.60529 - 3.60529i) q^{77} +(13.3020 + 15.9018i) q^{78} +3.44072i q^{79} +(13.3474 + 23.1184i) q^{81} +(5.17990 + 19.3316i) q^{82} -1.38257i q^{83} +(-4.82822 + 1.29372i) q^{84} +(6.90294 + 6.90294i) q^{86} +(8.99549 - 2.41033i) q^{87} +(-1.50236 + 5.60687i) q^{88} +(1.09501 + 0.293408i) q^{89} +(-4.99132 - 0.444348i) q^{91} +(-4.45010 - 4.45010i) q^{92} +(0.880067 - 0.508107i) q^{93} +(-7.73094 + 4.46346i) q^{94} +(12.9815 - 12.9815i) q^{96} +(-7.92101 + 13.7196i) q^{97} +(-4.46305 + 7.73023i) q^{98} +(19.8705 - 19.8705i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 24 q^{4} - 12 q^{6} + 24 q^{9} + 8 q^{11} - 32 q^{16} - 24 q^{19} + 32 q^{21} + 56 q^{24} + 76 q^{26} - 36 q^{29} + 8 q^{31} + 44 q^{34} - 60 q^{36} + 44 q^{39} - 52 q^{41} - 80 q^{44} - 60 q^{46}+ \cdots + 208 q^{99}+O(q^{100}) $ 40 * q - 24 * q^4 - 12 * q^6 + 24 * q^9 + 8 * q^11 - 32 * q^16 - 24 * q^19 + 32 * q^21 + 56 * q^24 + 76 * q^26 - 36 * q^29 + 8 * q^31 + 44 * q^34 - 60 * q^36 + 44 * q^39 - 52 * q^41 - 80 * q^44 - 60 * q^46 + 28 * q^49 - 68 * q^54 + 72 * q^56 - 72 * q^59 + 144 * q^64 + 24 * q^66 - 80 * q^69 - 52 * q^71 + 168 * q^74 + 8 * q^76 - 20 * q^81 - 248 * q^84 - 168 * q^86 + 60 * q^89 - 100 * q^91 - 156 * q^94 - 36 * q^96 + 208 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−0.880562	−	1.52518i	−0.622652	−	1.07846i	−0.988990	−	0.147983i	$-0.952722\pi$
$2$	−0.880562	−	1.52518i	−0.622652	−	1.07846i	0.366338	−	0.930482i	$-0.380611\pi$
$3$	3.15371	+	0.845033i	1.82079	+	0.487880i	0.996887	−	0.0788467i	$-0.0251238\pi$
$3$	3.15371	+	0.845033i	1.82079	+	0.487880i	0.823906	+	0.566727i	$0.191790\pi$
$4$	−0.550780	+	0.953979i	−0.275390	+	0.476990i
$5$		0			0
$5$		0			0
$6$	−1.48821	−	5.55407i	−0.607558	−	2.26744i
$7$	1.20362	+	0.694909i	0.454925	+	0.262651i	0.709908	−	0.704295i	$-0.248737\pi$
$7$	1.20362	+	0.694909i	0.454925	+	0.262651i	−0.254983	+	0.966945i	$0.582070\pi$
$8$	−1.58226			−0.559415
$9$	6.63370	+	3.82997i	2.21123	+	1.27666i
$10$		0			0
$11$	0.949498	−	3.54358i	0.286285	−	1.06843i	−0.661611	−	0.749847i	$-0.730127\pi$
$11$	0.949498	−	3.54358i	0.286285	−	1.06843i	0.947896	−	0.318581i	$-0.103206\pi$
$12$	−2.54314	+	2.54314i	−0.734142	+	0.734142i
$13$	−3.27006	+	1.51879i	−0.906951	+	0.421237i
$13$	−3.27006	+	1.51879i	−0.906951	+	0.421237i
$14$		−	2.44764i		−	0.654160i
$15$		0			0
$16$	2.49484	+	4.32119i	0.623711	+	1.08030i
$17$	−1.05282	−	3.92917i	−0.255346	−	0.952963i	−0.967898	−	0.251344i	$-0.919128\pi$
$17$	−1.05282	−	3.92917i	−0.255346	−	0.952963i	0.712552	−	0.701619i	$-0.247539\pi$
$18$		−	13.4901i		−	3.17965i
$19$	2.25062	−	0.603051i	0.516327	−	0.138349i	0.00875965	−	0.999962i	$-0.497212\pi$
$19$	2.25062	−	0.603051i	0.516327	−	0.138349i	0.507567	+	0.861612i	$0.330545\pi$
$20$		0			0
$21$	3.20863	+	3.20863i	0.700181	+	0.700181i
$22$	−6.24068	+	1.67219i	−1.33052	+	0.356511i
$23$	−1.47867	+	5.51848i	−0.308325	+	1.15068i	0.621721	+	0.783239i	$0.286434\pi$
$23$	−1.47867	+	5.51848i	−0.308325	+	1.15068i	−0.930045	+	0.367444i	$0.880233\pi$
$24$	−4.99000	−	1.33707i	−1.01858	−	0.272927i
$25$		0			0
$26$	5.19592	+	3.65003i	1.01900	+	0.715830i
$27$	10.7583	+	10.7583i	2.07043	+	2.07043i
$28$	−1.32586	+	0.765484i	−0.250563	+	0.144663i
$29$	2.47021	−	1.42618i	0.458707	−	0.264835i	−0.252793	−	0.967520i	$-0.581349\pi$
$29$	2.47021	−	1.42618i	0.458707	−	0.264835i	0.711500	+	0.702686i	$0.248016\pi$
$30$		0			0
$31$	0.220086	−	0.220086i	0.0395287	−	0.0395287i	−0.687066	−	0.726595i	$-0.741102\pi$
$31$	0.220086	−	0.220086i	0.0395287	−	0.0395287i	0.726595	+	0.687066i	$0.241102\pi$
$32$	2.81146	−	4.86960i	0.497001	−	0.860832i
$33$	5.98888	−	10.3730i	1.04253	−	1.80571i
$34$	−5.06561	+	5.06561i	−0.868745	+	0.868745i
$35$		0			0
$36$	−7.30742	+	4.21894i	−1.21790	+	0.703157i
$37$	−5.26488	+	3.03968i	−0.865542	+	0.499721i	−0.865864	−	0.500279i	$-0.833231\pi$
$37$	−5.26488	+	3.03968i	−0.865542	+	0.499721i	0.000322437		1.00000i	$0.499897\pi$
$38$	−2.90157	−	2.90157i	−0.470696	−	0.470696i
$39$	−11.5962	+	2.02651i	−1.85688	+	0.324502i
$40$		0			0
$41$	−10.9769	−	2.94124i	−1.71430	−	0.459345i	−0.737827	−	0.674990i	$-0.764148\pi$
$41$	−10.9769	−	2.94124i	−1.71430	−	0.459345i	−0.976472	+	0.215645i	$0.930815\pi$
$42$	2.06834	−	7.71914i	0.319151	−	1.19109i
$43$	−5.35430	+	1.43468i	−0.816524	+	0.218787i	−0.642826	−	0.766012i	$-0.722238\pi$
$43$	−5.35430	+	1.43468i	−0.816524	+	0.218787i	−0.173698	+	0.984799i	$0.555572\pi$
$44$	2.85753	+	2.85753i	0.430789	+	0.430789i
$45$		0			0
$46$	9.71874	−	2.60413i	1.43295	−	0.383958i
$47$		−	5.06887i		−	0.739371i	−0.929157	−	0.369686i	$-0.879465\pi$
$47$		−	5.06887i		−	0.739371i	0.929157	−	0.369686i	$-0.120535\pi$
$48$	4.21645	+	15.7360i	0.608592	+	2.27130i
$49$	−2.53420	−	4.38937i	−0.362029	−	0.627053i
$50$		0			0
$51$		−	13.2811i		−	1.85973i
$52$	0.352188	−	3.95609i	0.0488397	−	0.548611i
$53$	−0.586010	+	0.586010i	−0.0804946	+	0.0804946i	−0.746208	−	0.665713i	$-0.768127\pi$
$53$	−0.586010	+	0.586010i	−0.0804946	+	0.0804946i	0.665713	+	0.746208i	$0.268127\pi$
$54$	6.93496	−	25.8816i	0.943728	−	3.52204i
$55$		0			0
$56$	−1.90444	−	1.09953i	−0.254492	−	0.146931i
$57$	7.60737			1.00762
$58$	−4.35035	−	2.51168i	−0.571229	−	0.329799i
$59$	0.878129	+	3.27722i	0.114323	+	0.426658i	0.999235	−	0.0390991i	$-0.0124488\pi$
$59$	0.878129	+	3.27722i	0.114323	+	0.426658i	−0.884913	+	0.465757i	$0.845782\pi$
$60$		0			0
$61$	−3.03437	+	5.25569i	−0.388512	+	0.672922i	−0.992250	−	0.124261i	$-0.960344\pi$
$61$	−3.03437	+	5.25569i	−0.388512	+	0.672922i	0.603738	+	0.797183i	$0.293677\pi$
$62$	−0.529470	−	0.141871i	−0.0672428	−	0.0180177i
$63$	5.32296	+	9.21963i	0.670630	+	1.16156i
$64$	0.0766898			0.00958623
$65$		0			0
$66$	−21.0943			−2.59653
$67$	0.660446	+	1.14393i	0.0806864	+	0.139753i	0.903545	−	0.428493i	$-0.140955\pi$
$67$	0.660446	+	1.14393i	0.0806864	+	0.139753i	−0.822859	+	0.568246i	$0.807622\pi$
$68$	4.32821	+	1.15974i	0.524873	+	0.140639i
$69$	−9.32660	+	16.1541i	−1.12279	+	1.94473i
$70$		0			0
$71$	1.41960	+	5.29800i	0.168475	+	0.628758i	0.997571	+	0.0696517i	$0.0221888\pi$
$71$	1.41960	+	5.29800i	0.168475	+	0.628758i	−0.829096	+	0.559106i	$0.811145\pi$
$72$	−10.4963	−	6.06002i	−1.23700	−	0.714181i
$73$	2.15999			0.252808			0.126404	−	0.991979i	$-0.459656\pi$
$73$	2.15999			0.252808			0.126404	+	0.991979i	$0.459656\pi$
$74$	9.27212	+	5.35326i	1.07786	+	0.622304i
$75$		0			0
$76$	−0.664297	+	2.47919i	−0.0762000	+	0.284382i
$77$	3.60529	−	3.60529i	0.410861	−	0.410861i
$78$	13.3020	+	15.9018i	1.50615	+	1.80053i
$79$			3.44072i			0.387111i	0.981089	+	0.193555i	$0.0620020\pi$
$79$			3.44072i			0.387111i	−0.981089	+	0.193555i	$0.937998\pi$
$80$		0			0
$81$	13.3474	+	23.1184i	1.48305	+	2.56871i
$82$	5.17990	+	19.3316i	0.572024	+	2.13482i
$83$		−	1.38257i		−	0.151757i	−0.997117	−	0.0758783i	$-0.975824\pi$
$83$		−	1.38257i		−	0.151757i	0.997117	−	0.0758783i	$-0.0241760\pi$
$84$	−4.82822	+	1.29372i	−0.526802	+	0.141156i
$85$		0			0
$86$	6.90294	+	6.90294i	0.744364	+	0.744364i
$87$	8.99549	−	2.41033i	0.964418	−	0.258415i
$88$	−1.50236	+	5.60687i	−0.160152	+	0.597695i
$89$	1.09501	+	0.293408i	0.116071	+	0.0311012i	0.316387	−	0.948630i	$-0.397530\pi$
$89$	1.09501	+	0.293408i	0.116071	+	0.0311012i	−0.200316	+	0.979731i	$0.564197\pi$
$90$		0			0
$91$	−4.99132	−	0.444348i	−0.523232	−	0.0465804i
$92$	−4.45010	−	4.45010i	−0.463955	−	0.463955i
$93$	0.880067	−	0.508107i	0.0912587	−	0.0526882i
$94$	−7.73094	+	4.46346i	−0.797385	+	0.460371i
$95$		0			0
$96$	12.9815	−	12.9815i	1.32492	−	1.32492i
$97$	−7.92101	+	13.7196i	−0.804256	+	1.39301i	0.112536	+	0.993648i	$0.464103\pi$
$97$	−7.92101	+	13.7196i	−0.804256	+	1.39301i	−0.916792	+	0.399365i	$0.869231\pi$
$98$	−4.46305	+	7.73023i	−0.450836	+	0.780871i
$99$	19.8705	−	19.8705i	1.99706	−	1.99706i
$100$		0			0
$101$	−2.26191	+	1.30591i	−0.225068	+	0.129943i	−0.608295	−	0.793711i	$-0.708146\pi$
$101$	−2.26191	+	1.30591i	−0.225068	+	0.129943i	0.383227	+	0.923654i	$0.374813\pi$
$102$	−20.2560	+	11.6948i	−2.00565	+	1.15796i
$103$	0.960893	+	0.960893i	0.0946796	+	0.0946796i	0.752860	−	0.658181i	$-0.228674\pi$
$103$	0.960893	+	0.960893i	0.0946796	+	0.0946796i	−0.658181	+	0.752860i	$0.728674\pi$
$104$	5.17409	−	2.40313i	0.507362	−	0.235646i
$105$		0			0
$106$	1.40979	+	0.377751i	0.136931	+	0.0366905i
$107$	4.03770	−	15.0689i	0.390339	−	1.45677i	−0.439236	−	0.898372i	$-0.644751\pi$
$107$	4.03770	−	15.0689i	0.390339	−	1.45677i	0.829576	−	0.558394i	$-0.188582\pi$
$108$	−16.1886	+	4.33773i	−1.55775	+	0.417398i
$109$	9.51962	+	9.51962i	0.911814	+	0.911814i	0.996415	−	0.0846007i	$-0.0269615\pi$
$109$	9.51962	+	9.51962i	0.911814	+	0.911814i	−0.0846007	+	0.996415i	$0.526961\pi$
$110$		0			0
$111$	−19.1725	+	5.13726i	−1.81978	+	0.487607i
$112$			6.93475i			0.655272i
$113$	−2.96358	−	11.0602i	−0.278790	−	1.04046i	−0.953259	−	0.302154i	$-0.902294\pi$
$113$	−2.96358	−	11.0602i	−0.278790	−	1.04046i	0.674469	−	0.738303i	$-0.264373\pi$
$114$	−6.69877	−	11.6026i	−0.627397	−	1.08668i
$115$		0			0
$116$			3.14204i			0.291731i
$117$	−27.5095	−	2.44901i	−2.54325	−	0.226411i
$118$	4.22510	−	4.22510i	0.388952	−	0.388952i
$119$	1.46322	−	5.46082i	0.134133	−	0.500593i
$120$		0			0
$121$	−2.12911	−	1.22924i	−0.193555	−	0.111749i
$122$	10.6878			0.967630
$123$	−32.1324	−	18.5516i	−2.89728	−	1.67274i
$124$	0.0887386	+	0.331177i	0.00796896	+	0.0297406i
$125$		0			0
$126$	9.37439	−	16.2369i	0.835137	−	1.44650i
$127$	18.7572	+	5.02598i	1.66443	+	0.445983i	0.963601	−	0.267343i	$-0.0861458\pi$
$127$	18.7572	+	5.02598i	1.66443	+	0.445983i	0.700832	+	0.713327i	$0.252812\pi$
$128$	−5.69046	−	9.85617i	−0.502970	−	0.871170i
$129$	−18.0983			−1.59346
$130$		0			0
$131$	4.21678			0.368422			0.184211	−	0.982887i	$-0.441027\pi$
$131$	4.21678			0.368422			0.184211	+	0.982887i	$0.441027\pi$
$132$	6.59711	+	11.4265i	0.574205	+	0.994552i
$133$	3.12794	+	0.838130i	0.271227	+	0.0726751i
$134$	1.16313	−	2.01460i	0.100479	−	0.174035i
$135$		0			0
$136$	1.66583	+	6.21698i	0.142844	+	0.533101i
$137$	9.71890	+	5.61121i	0.830342	+	0.479398i	0.853970	−	0.520323i	$-0.174188\pi$
$137$	9.71890	+	5.61121i	0.830342	+	0.479398i	−0.0236280	+	0.999721i	$0.507522\pi$
$138$	32.8506			2.79643
$139$	−1.44435	−	0.833895i	−0.122508	−	0.0707301i	0.437494	−	0.899221i	$-0.355866\pi$
$139$	−1.44435	−	0.833895i	−0.122508	−	0.0707301i	−0.560002	+	0.828491i	$0.689200\pi$
$140$		0			0
$141$	4.28336	−	15.9857i	0.360724	−	1.34624i
$142$	6.83036	−	6.83036i	0.573191	−	0.573191i
$143$	2.27704	+	13.0298i	0.190415	+	1.08961i
$144$			38.2207i			3.18506i
$145$		0			0
$146$	−1.90201	−	3.29437i	−0.157411	−	0.272644i
$147$	−4.28297	−	15.9843i	−0.353253	−	1.31836i
$148$		−	6.69679i		−	0.550473i
$149$	−11.6304	+	3.11636i	−0.952802	+	0.255302i	−0.701551	−	0.712620i	$-0.747509\pi$
$149$	−11.6304	+	3.11636i	−0.952802	+	0.255302i	−0.251251	+	0.967922i	$0.580842\pi$
$150$		0			0
$151$	−6.13780	−	6.13780i	−0.499487	−	0.499487i	0.411791	−	0.911278i	$-0.364903\pi$
$151$	−6.13780	−	6.13780i	−0.499487	−	0.499487i	−0.911278	+	0.411791i	$0.864903\pi$
$152$	−3.56107	+	0.954185i	−0.288841	+	0.0773946i
$153$	8.06451	−	30.0972i	0.651977	−	2.43321i
$154$	−8.67341	−	2.32403i	−0.698923	−	0.187276i
$155$		0			0
$156$	4.45372	−	12.1787i	0.356583	−	0.975078i
$157$	−9.72344	−	9.72344i	−0.776015	−	0.776015i	0.203135	−	0.979151i	$-0.434887\pi$
$157$	−9.72344	−	9.72344i	−0.776015	−	0.776015i	−0.979151	+	0.203135i	$0.934887\pi$
$158$	5.24771	−	3.02977i	0.417485	−	0.241035i
$159$	−2.34330	+	1.35290i	−0.185836	+	0.107292i
$160$		0			0
$161$	−5.61460	+	5.61460i	−0.442492	+	0.442492i
$162$	23.5065	−	40.7144i	1.84684	−	3.19883i
$163$	1.99232	−	3.45081i	0.156051	−	0.270288i	−0.777390	−	0.629019i	$-0.783457\pi$
$163$	1.99232	−	3.45081i	0.156051	−	0.270288i	0.933441	+	0.358730i	$0.116790\pi$
$164$	8.85173	−	8.85173i	0.691204	−	0.691204i
$165$		0			0
$166$	−2.10866	+	1.21744i	−0.163664	+	0.0944915i
$167$	4.72436	−	2.72761i	0.365582	−	0.211069i	−0.305945	−	0.952049i	$-0.598972\pi$
$167$	4.72436	−	2.72761i	0.365582	−	0.211069i	0.671527	+	0.740980i	$0.265639\pi$
$168$	−5.07691	−	5.07691i	−0.391692	−	0.391692i
$169$	8.38655	−	9.93307i	0.645119	−	0.764082i
$170$		0			0
$171$	17.2396	+	4.61933i	1.31834	+	0.353249i
$172$	1.58039	−	5.89809i	0.120503	−	0.449725i
$173$	19.6062	−	5.25347i	1.49063	−	0.399414i	0.580682	−	0.814131i	$-0.302786\pi$
$173$	19.6062	−	5.25347i	1.49063	−	0.399414i	0.909951	+	0.414717i	$0.136119\pi$
$174$	−11.5973	−	11.5973i	−0.879188	−	0.879188i
$175$		0			0
$176$	17.6813	−	4.73770i	1.33278	−	0.357117i
$177$			11.0774i			0.832631i
$178$	−0.516728	−	1.92845i	−0.0387304	−	0.144544i
$179$	0.485197	+	0.840386i	0.0362654	+	0.0628134i	0.883588	−	0.468264i	$-0.155121\pi$
$179$	0.485197	+	0.840386i	0.0362654	+	0.0628134i	−0.847323	+	0.531078i	$0.821787\pi$
$180$		0			0
$181$		−	18.2170i		−	1.35406i	−0.735956	−	0.677029i	$-0.763267\pi$
$181$		−	18.2170i		−	1.35406i	0.735956	−	0.677029i	$-0.236733\pi$
$182$	3.71746	+	8.00393i	0.275556	+	0.593291i
$183$	−14.0107	+	14.0107i	−1.03570	+	1.03570i
$184$	2.33965	−	8.73170i	0.172481	−	0.643709i
$185$		0			0
$186$	−1.54991	−	0.894840i	−0.113645	−	0.0656128i
$187$	−14.9229			−1.09127
$188$	4.83560	+	2.79183i	0.352672	+	0.203615i
$189$	5.47282	+	20.4249i	0.398089	+	1.48569i
$190$		0			0
$191$	−8.18780	+	14.1817i	−0.592449	+	1.02615i	0.401453	+	0.915880i	$0.368505\pi$
$191$	−8.18780	+	14.1817i	−0.592449	+	1.02615i	−0.993901	+	0.110272i	$0.964828\pi$
$192$	0.241857	+	0.0648054i	0.0174545	+	0.00467693i
$193$	5.14757	+	8.91585i	0.370530	+	0.641777i	0.989647	−	0.143522i	$-0.0458426\pi$
$193$	5.14757	+	8.91585i	0.370530	+	0.641777i	−0.619117	+	0.785299i	$0.712509\pi$
$194$	27.8998			2.00309
$195$		0			0
$196$	5.58316			0.398797
$197$	−6.19621	−	10.7321i	−0.441461	−	0.764633i	0.556337	−	0.830957i	$-0.312206\pi$
$197$	−6.19621	−	10.7321i	−0.441461	−	0.764633i	−0.997798	+	0.0663234i	$0.978873\pi$
$198$	−47.8032	−	12.8088i	−3.39723	−	0.910284i
$199$	−2.14630	+	3.71750i	−0.152147	+	0.263527i	−0.932017	−	0.362416i	$-0.881952\pi$
$199$	−2.14630	+	3.71750i	−0.152147	+	0.263527i	0.779869	+	0.625942i	$0.215285\pi$
$200$		0			0
$201$	1.11620	+	4.16571i	0.0787305	+	0.293826i
$202$	3.98350	+	2.29988i	0.280278	+	0.161819i
$203$	3.96425			0.278236
$204$	12.6699	+	7.31496i	0.887070	+	0.512150i
$205$		0			0
$206$	0.619407	−	2.31166i	0.0431561	−	0.161061i
$207$	−30.9447	+	30.9447i	−2.15081	+	2.15081i
$208$	−14.7213	−	10.3414i	−1.02074	−	0.717048i
$209$		−	8.54782i		−	0.591265i
$210$		0			0
$211$	−13.4327	−	23.2662i	−0.924747	−	1.60171i	−0.791968	−	0.610562i	$-0.790943\pi$
$211$	−13.4327	−	23.2662i	−0.924747	−	1.60171i	−0.132778	−	0.991146i	$-0.542390\pi$
$212$	−0.236279	−	0.881803i	−0.0162277	−	0.0605625i
$213$			17.9080i			1.22703i
$214$	−26.5382	+	7.11089i	−1.81412	+	0.486091i
$215$		0			0
$216$	−17.0224	−	17.0224i	−1.15823	−	1.15823i
$217$	0.417839	−	0.111960i	0.0283648	−	0.00760032i
$218$	6.13650	−	22.9017i	0.415616	−	1.55110i
$219$	6.81198	+	1.82526i	0.460311	+	0.123340i
$220$		0			0
$221$	9.41035	+	11.2496i	0.633009	+	0.756729i
$222$	24.7179	+	24.7179i	1.65895	+	1.65895i
$223$	17.2143	−	9.93870i	1.15276	−	0.665545i	0.203199	−	0.979137i	$-0.434866\pi$
$223$	17.2143	−	9.93870i	1.15276	−	0.665545i	0.949558	+	0.313593i	$0.101533\pi$
$224$	6.76785	−	3.90742i	0.452196	−	0.261076i
$225$		0			0
$226$	−14.2592	+	14.2592i	−0.948507	+	0.948507i
$227$	−5.58741	+	9.67768i	−0.370849	+	0.642330i	−0.989696	−	0.143181i	$-0.954267\pi$
$227$	−5.58741	+	9.67768i	−0.370849	+	0.642330i	0.618847	+	0.785512i	$0.287600\pi$
$228$	−4.18999	+	7.25728i	−0.277489	+	0.480625i
$229$	12.7032	−	12.7032i	0.839450	−	0.839450i	−0.149336	−	0.988786i	$-0.547714\pi$
$229$	12.7032	−	12.7032i	0.839450	−	0.839450i	0.988786	+	0.149336i	$0.0477136\pi$
$230$		0			0
$231$	14.4166	−	8.32344i	0.948545	−	0.547642i
$232$	−3.90853	+	2.25659i	−0.256608	+	0.148152i
$233$	0.0102716	+	0.0102716i	0.000672916	+	0.000672916i	0.707443	−	0.706770i	$-0.249849\pi$
$233$	0.0102716	+	0.0102716i	0.000672916	+	0.000672916i	−0.706770	+	0.707443i	$0.749849\pi$
$234$	20.4887	+	44.1134i	1.33938	+	2.88378i
$235$		0			0
$236$	−3.61006	−	0.967312i	−0.234995	−	0.0629666i
$237$	−2.90752	+	10.8510i	−0.188864	+	0.704849i
$238$	−9.61719	+	2.57692i	−0.623390	+	0.167037i
$239$	−8.78399	−	8.78399i	−0.568189	−	0.568189i	0.363432	−	0.931621i	$-0.381605\pi$
$239$	−8.78399	−	8.78399i	−0.568189	−	0.568189i	−0.931621	+	0.363432i	$0.881605\pi$
$240$		0			0
$241$	21.5510	−	5.77458i	1.38822	−	0.371973i	0.514122	−	0.857717i	$-0.328118\pi$
$241$	21.5510	−	5.77458i	1.38822	−	0.371973i	0.874101	+	0.485743i	$0.161451\pi$
$242$			4.32969i			0.278323i
$243$	10.7446	+	40.0994i	0.689267	+	2.57238i
$244$	−3.34254	−	5.78946i	−0.213985	−	0.370632i
$245$		0			0
$246$			65.3435i			4.16615i
$247$	−6.44373	+	5.39022i	−0.410005	+	0.342972i
$248$	−0.348235	+	0.348235i	−0.0221129	+	0.0221129i
$249$	1.16832	−	4.36021i	0.0740390	−	0.276317i
$250$		0			0
$251$	1.04874	+	0.605490i	0.0661959	+	0.0382182i	0.532733	−	0.846284i	$-0.321165\pi$
$251$	1.04874	+	0.605490i	0.0661959	+	0.0382182i	−0.466537	+	0.884502i	$0.654498\pi$
$252$	−11.7271			−0.738739
$253$	18.1512	+	10.4796i	1.14115	+	0.658846i
$254$	−8.85137	−	33.0338i	−0.555385	−	2.07272i
$255$		0			0
$256$	−9.94492	+	17.2251i	−0.621558	+	1.07657i
$257$	−12.3205	−	3.30128i	−0.768535	−	0.205928i	−0.146811	−	0.989165i	$-0.546901\pi$
$257$	−12.3205	−	3.30128i	−0.768535	−	0.205928i	−0.621724	+	0.783236i	$0.713567\pi$
$258$	15.9366	+	27.6031i	0.992172	+	1.71849i
$259$	−8.44921			−0.525008
$260$		0			0
$261$	21.8489			1.35241
$262$	−3.71314	−	6.43135i	−0.229399	−	0.397330i
$263$	−11.4213	−	3.06032i	−0.704266	−	0.188707i	−0.111125	−	0.993806i	$-0.535445\pi$
$263$	−11.4213	−	3.06032i	−0.704266	−	0.188707i	−0.593140	+	0.805099i	$0.702112\pi$
$264$	−9.47599	+	16.4129i	−0.583207	+	1.01014i
$265$		0			0
$266$	−1.47605	−	5.50870i	−0.0905025	−	0.337760i
$267$	3.20541	+	1.85064i	0.196168	+	0.113258i
$268$	−1.45504			−0.0888809
$269$	14.0608	+	8.11799i	0.857300	+	0.494963i	0.863107	−	0.505021i	$-0.168515\pi$
$269$	14.0608	+	8.11799i	0.857300	+	0.494963i	−0.00580692	+	0.999983i	$0.501848\pi$
$270$		0			0
$271$	0.567117	−	2.11651i	0.0344499	−	0.128569i	−0.946559	−	0.322530i	$-0.895467\pi$
$271$	0.567117	−	2.11651i	0.0344499	−	0.128569i	0.981009	+	0.193961i	$0.0621335\pi$
$272$	14.3521	−	14.3521i	0.870222	−	0.870222i
$273$	−15.3657	−	5.61917i	−0.929972	−	0.340088i
$274$		−	19.7641i		−	1.19399i
$275$		0			0
$276$	−10.2738	−	17.7948i	−0.618411	−	1.07112i
$277$	−4.83197	−	18.0331i	−0.290325	−	1.08351i	−0.944860	−	0.327475i	$-0.893802\pi$
$277$	−4.83197	−	18.0331i	−0.290325	−	1.08351i	0.654535	−	0.756031i	$-0.272864\pi$
$278$			2.93719i			0.176161i
$279$	2.30291	−	0.617063i	0.137872	−	0.0369426i
$280$		0			0
$281$	7.76642	+	7.76642i	0.463306	+	0.463306i	0.899737	−	0.436432i	$-0.143758\pi$
$281$	7.76642	+	7.76642i	0.463306	+	0.463306i	−0.436432	+	0.899737i	$0.643758\pi$
$282$	−28.1529	+	7.54354i	−1.67648	+	0.449211i
$283$	−2.52759	+	9.43309i	−0.150250	+	0.560739i	0.849216	+	0.528046i	$0.177075\pi$
$283$	−2.52759	+	9.43309i	−0.150250	+	0.560739i	−0.999465	+	0.0326932i	$0.989592\pi$
$284$	−5.83607	−	1.56377i	−0.346307	−	0.0927927i
$285$		0			0
$286$	17.8677	−	14.9464i	1.05654	−	0.883801i
$287$	−11.1681	−	11.1681i	−0.659229	−	0.659229i
$288$	37.3008	−	21.5356i	2.19797	−	1.26900i
$289$	0.392513	−	0.226617i	0.0230890	−	0.0133304i
$290$		0			0
$291$	−36.5740	+	36.5740i	−2.14401	+	2.14401i
$292$	−1.18968	+	2.06059i	−0.0696208	+	0.120587i
$293$	−16.8881	+	29.2511i	−0.986615	+	1.70887i	−0.352086	+	0.935968i	$0.614527\pi$
$293$	−16.8881	+	29.2511i	−0.986615	+	1.70887i	−0.634529	+	0.772899i	$0.718806\pi$
$294$	−20.6074	+	20.6074i	−1.20185	+	1.20185i
$295$		0			0
$296$	8.33044	−	4.80958i	0.484197	−	0.279551i
$297$	48.3377	−	27.9078i	2.80484	−	1.61937i
$298$	14.9943	+	14.9943i	0.868598	+	0.868598i
$299$	−3.54608	−	20.2916i	−0.205075	−	1.17349i
$300$		0			0
$301$	−7.44150	−	1.99395i	−0.428921	−	0.114929i
$302$	−3.95652	+	14.7660i	−0.227672	+	0.849685i
$303$	−8.23693	+	2.20708i	−0.473199	+	0.126793i
$304$	8.22083	+	8.22083i	0.471497	+	0.471497i
$305$		0			0
$306$	−53.0049	+	14.2026i	−3.03009	+	0.811909i
$307$		−	16.4317i		−	0.937804i	−0.883250	−	0.468902i	$-0.844650\pi$
$307$		−	16.4317i		−	0.937804i	0.883250	−	0.468902i	$-0.155350\pi$
$308$	1.45365	+	5.42510i	0.0828295	+	0.309124i
$309$	2.21839	+	3.84236i	0.126200	+	0.218584i
$310$		0			0
$311$		−	1.31200i		−	0.0743968i	−0.999308	−	0.0371984i	$-0.988157\pi$
$311$		−	1.31200i		−	0.0743968i	0.999308	−	0.0371984i	$-0.0118434\pi$
$312$	18.3483	−	3.20648i	1.03877	−	0.181531i
$313$	19.5519	−	19.5519i	1.10514	−	1.10514i	0.111361	−	0.993780i	$-0.464479\pi$
$313$	19.5519	−	19.5519i	1.10514	−	1.10514i	0.993780	−	0.111361i	$-0.0355211\pi$
$314$	−6.26789	+	23.3921i	−0.353718	+	1.32009i
$315$		0			0
$316$	−3.28237	−	1.89508i	−0.184648	−	0.106607i
$317$	34.9576			1.96342			0.981708	−	0.190394i	$-0.0609767\pi$
$317$	34.9576			1.96342			0.981708	+	0.190394i	$0.0609767\pi$
$318$	4.12684	+	2.38263i	0.231422	+	0.133611i
$319$	−2.70831	−	10.1075i	−0.151636	−	0.565914i
$320$		0			0
$321$	25.4674	−	44.1109i	1.42145	−	2.46203i
$322$	13.5073	+	3.61926i	0.752731	+	0.201694i
$323$	−4.73897	−	8.20814i	−0.263683	−	0.456713i
$324$	−29.4060			−1.63367
$325$		0			0
$326$	−7.01746			−0.388661
$327$	21.9777	+	38.0665i	1.21537	+	2.10508i
$328$	17.3683	+	4.65382i	0.959004	+	0.256964i
$329$	3.52240	−	6.10098i	0.194196	−	0.336358i
$330$		0			0
$331$	−0.658550	−	2.45774i	−0.0361972	−	0.135090i	0.945463	−	0.325730i	$-0.105610\pi$
$331$	−0.658550	−	2.45774i	−0.0361972	−	0.135090i	−0.981660	+	0.190641i	$0.938943\pi$
$332$	1.31894	+	0.761491i	0.0723863	+	0.0417923i
$333$	−46.5676			−2.55189
$334$	−8.32019	−	4.80366i	−0.455260	−	0.262845i
$335$		0			0
$336$	−5.86009	+	21.8702i	−0.319694	+	1.19312i
$337$	8.33325	−	8.33325i	0.453941	−	0.453941i	−0.442719	−	0.896660i	$-0.645986\pi$
$337$	8.33325	−	8.33325i	0.453941	−	0.453941i	0.896660	+	0.442719i	$0.145986\pi$
$338$	−22.5346	−	4.04430i	−1.22572	−	0.219981i
$339$		−	37.3850i		−	2.03047i
$340$		0			0
$341$	−0.570921	−	0.988864i	−0.0309171	−	0.0535500i
$342$	−8.13522	−	30.3610i	−0.439902	−	1.64174i
$343$		−	16.7729i		−	0.905651i
$344$	8.47192	−	2.27005i	0.456776	−	0.122393i
$345$		0			0
$346$	−25.2770	−	25.2770i	−1.35890	−	1.35890i
$347$	−10.3655	+	2.77743i	−0.556449	+	0.149100i	−0.526075	−	0.850438i	$-0.676337\pi$
$347$	−10.3655	+	2.77743i	−0.556449	+	0.149100i	−0.0303747	+	0.999539i	$0.509670\pi$
$348$	−2.65513	+	9.90908i	−0.142330	+	0.531182i
$349$	23.0049	+	6.16415i	1.23143	+	0.329960i	0.815135	−	0.579272i	$-0.196663\pi$
$349$	23.0049	+	6.16415i	1.23143	+	0.329960i	0.416291	+	0.909231i	$0.363330\pi$
$350$		0			0
$351$	−51.5197	−	18.8406i	−2.74992	−	1.00564i
$352$	−14.5863	−	14.5863i	−0.777453	−	0.777453i
$353$	22.4026	−	12.9342i	1.19237	−	0.688416i	0.233527	−	0.972350i	$-0.424973\pi$
$353$	22.4026	−	12.9342i	1.19237	−	0.688416i	0.958844	+	0.283935i	$0.0916398\pi$
$354$	16.8951	−	9.75437i	0.897963	−	0.518439i
$355$		0			0
$356$	−0.883016	+	0.883016i	−0.0467998	+	0.0467998i
$357$	9.22915	−	15.9854i	0.488458	−	0.846035i
$358$	0.854493	−	1.48003i	0.0451614	−	0.0782218i
$359$	−19.3811	+	19.3811i	−1.02289	+	1.02289i	−0.0231615	+	0.999732i	$0.507373\pi$
$359$	−19.3811	+	19.3811i	−1.02289	+	1.02289i	−0.999732	+	0.0231615i	$0.992627\pi$
$360$		0			0
$361$	−11.7529	+	6.78553i	−0.618573	+	0.357133i
$362$	−27.7842	+	16.0412i	−1.46030	+	0.843107i
$363$	−5.67583	−	5.67583i	−0.297904	−	0.297904i
$364$	3.17302	−	4.51688i	0.166311	−	0.236749i
$365$		0			0
$366$	33.7062	+	9.03156i	1.76185	+	0.472087i
$367$	6.23046	−	23.2524i	0.325227	−	1.21376i	−0.588856	−	0.808238i	$-0.700421\pi$
$367$	6.23046	−	23.2524i	0.325227	−	1.21376i	0.914083	−	0.405527i	$-0.132912\pi$
$368$	−27.5355	+	7.37811i	−1.43539	+	0.384611i
$369$	−61.5524	−	61.5524i	−3.20429	−	3.20429i
$370$		0			0
$371$	−1.11255	+	0.298108i	−0.0577609	+	0.0154770i
$372$			1.11942i			0.0580393i
$373$	6.01280	+	22.4401i	0.311331	+	1.16190i	0.927357	+	0.374177i	$0.122075\pi$
$373$	6.01280	+	22.4401i	0.311331	+	1.16190i	−0.616027	+	0.787725i	$0.711259\pi$
$374$	13.1406	+	22.7602i	0.679483	+	1.17690i
$375$		0			0
$376$			8.02030i			0.413615i
$377$	−5.91167	+	8.41542i	−0.304467	+	0.433416i
$378$	26.3324	−	26.3324i	1.35439	−	1.35439i
$379$	−7.19748	+	26.8614i	−0.369710	+	1.37978i	0.491212	+	0.871040i	$0.336554\pi$
$379$	−7.19748	+	26.8614i	−0.369710	+	1.37978i	−0.860922	+	0.508736i	$0.830113\pi$
$380$		0			0
$381$	54.9076	+	31.7009i	2.81300	+	1.62409i
$382$	28.8395			1.47556
$383$	−14.6107	−	8.43549i	−0.746572	−	0.431034i	0.0778820	−	0.996963i	$-0.475184\pi$
$383$	−14.6107	−	8.43549i	−0.746572	−	0.431034i	−0.824454	+	0.565929i	$0.808518\pi$
$384$	−9.61725	−	35.8921i	−0.490778	−	1.83161i
$385$		0			0
$386$	9.06551	−	15.7019i	0.461423	−	0.799207i
$387$	−41.0136	−	10.9896i	−2.08484	−	0.558631i
$388$	−8.72547	−	15.1129i	−0.442968	−	0.767244i
$389$	−15.9554			−0.808973			−0.404487	−	0.914544i	$-0.632550\pi$
$389$	−15.9554			−0.808973			−0.404487	+	0.914544i	$0.632550\pi$
$390$		0			0
$391$	23.2398			1.17529
$392$	4.00978	+	6.94514i	0.202524	+	0.350783i
$393$	13.2985	+	3.56332i	0.670820	+	0.179746i
$394$	−10.9123	+	18.9006i	−0.549753	+	0.952201i
$395$		0			0
$396$	8.01176	+	29.9003i	0.402606	+	1.50255i
$397$	14.3828	+	8.30391i	0.721852	+	0.416761i	0.815434	−	0.578850i	$-0.196498\pi$
$397$	14.3828	+	8.30391i	0.721852	+	0.416761i	−0.0935822	+	0.995612i	$0.529832\pi$
$398$	7.55981			0.378939
$399$	9.15637	+	5.28643i	0.458392	+	0.264653i
$400$		0			0
$401$	−4.73738	+	17.6802i	−0.236574	+	0.882905i	0.740859	+	0.671660i	$0.234418\pi$
$401$	−4.73738	+	17.6802i	−0.236574	+	0.882905i	−0.977433	+	0.211245i	$0.932248\pi$
$402$	5.37057	−	5.37057i	0.267859	−	0.267859i
$403$	−0.385430	+	1.05396i	−0.0191996	+	0.0525015i
$404$		−	2.87708i		−	0.143140i
$405$		0			0
$406$	−3.49077	−	6.04620i	−0.173244	−	0.300068i
$407$	5.77235	+	21.5427i	0.286125	+	1.06783i
$408$			21.0142i			1.04036i
$409$	−11.9171	+	3.19317i	−0.589261	+	0.157892i	−0.541116	−	0.840948i	$-0.681998\pi$
$409$	−11.9171	+	3.19317i	−0.589261	+	0.157892i	−0.0481458	+	0.998840i	$0.515331\pi$
$410$		0			0
$411$	25.9089	+	25.9089i	1.27799	+	1.27799i
$412$	−1.44591	+	0.387431i	−0.0712350	+	0.0190874i
$413$	−1.22044	+	4.55474i	−0.0600538	+	0.224124i
$414$	74.4449	+	19.9475i	3.65877	+	0.980364i
$415$		0			0
$416$	−1.79775	+	20.1939i	−0.0881418	+	0.990087i
$417$	−3.85038	−	3.85038i	−0.188554	−	0.188554i
$418$	−13.0370	+	7.52689i	−0.637658	+	0.368152i
$419$	−15.6063	+	9.01028i	−0.762416	+	0.440181i	−0.830163	−	0.557521i	$-0.811752\pi$
$419$	−15.6063	+	9.01028i	−0.762416	+	0.440181i	0.0677464	+	0.997703i	$0.478419\pi$
$420$		0			0
$421$	12.6982	−	12.6982i	0.618871	−	0.618871i	−0.326371	−	0.945242i	$-0.605826\pi$
$421$	12.6982	−	12.6982i	0.618871	−	0.618871i	0.945242	+	0.326371i	$0.105826\pi$
$422$	−23.6567	+	40.9746i	−1.15159	+	1.99461i
$423$	19.4136	−	33.6254i	0.943923	−	1.63492i
$424$	0.927222	−	0.927222i	0.0450299	−	0.0450299i
$425$		0			0
$426$	27.3128	−	15.7691i	1.32331	−	0.764014i
$427$	−7.30445	+	4.21722i	−0.353487	+	0.204086i
$428$	12.1515	+	12.1515i	0.587367	+	0.587367i
$429$	−3.82949	+	43.0163i	−0.184890	+	2.07685i
$430$		0			0
$431$	−7.07051	−	1.89454i	−0.340574	−	0.0912566i	0.0844781	−	0.996425i	$-0.473078\pi$
$431$	−7.07051	−	1.89454i	−0.340574	−	0.0912566i	−0.425052	+	0.905169i	$0.639744\pi$
$432$	−19.6484	+	73.3288i	−0.945334	+	3.52803i
$433$	8.56975	−	2.29626i	0.411836	−	0.110351i	−0.0469516	−	0.998897i	$-0.514951\pi$
$433$	8.56975	−	2.29626i	0.411836	−	0.110351i	0.458787	+	0.888546i	$0.348284\pi$
$434$	−0.538692	−	0.538692i	−0.0258581	−	0.0258581i
$435$		0			0
$436$	−14.3247	+	3.83830i	−0.686031	+	0.183821i
$437$			13.3117i			0.636785i
$438$	−3.21452	−	11.9967i	−0.153596	−	0.573226i
$439$	11.8892	+	20.5927i	0.567440	+	0.982835i	0.996818	+	0.0797100i	$0.0253994\pi$
$439$	11.8892	+	20.5927i	0.567440	+	0.982835i	−0.429378	+	0.903125i	$0.641267\pi$
$440$		0			0
$441$		−	38.8237i		−	1.84875i
$442$	8.87123	−	24.2584i	0.421961	−	1.15386i
$443$	5.18634	−	5.18634i	0.246410	−	0.246410i	−0.573085	−	0.819496i	$-0.694254\pi$
$443$	5.18634	−	5.18634i	0.246410	−	0.246410i	0.819496	+	0.573085i	$0.194254\pi$
$444$	5.65901	−	21.1197i	0.268565	−	1.00230i
$445$		0			0
$446$	−30.3166	−	17.5033i	−1.43553	−	0.828805i
$447$	−39.3124			−1.85941
$448$	0.0923052	+	0.0532924i	0.00436101	+	0.00251783i
$449$	8.47234	+	31.6192i	0.399834	+	1.49220i	0.813388	+	0.581722i	$0.197621\pi$
$449$	8.47234	+	31.6192i	0.399834	+	1.49220i	−0.413553	+	0.910480i	$0.635712\pi$
$450$		0			0
$451$	−20.8450	+	36.1047i	−0.981555	+	1.70010i
$452$	12.1835	+	3.26456i	0.573063	+	0.153552i
$453$	−14.1702	−	24.5434i	−0.665772	−	1.15315i
$454$	19.6803			0.923640
$455$		0			0
$456$	−12.0369			−0.563678
$457$	9.01757	+	15.6189i	0.421824	+	0.730621i	0.996118	−	0.0880283i	$-0.0280566\pi$
$457$	9.01757	+	15.6189i	0.421824	+	0.730621i	−0.574294	+	0.818649i	$0.694723\pi$
$458$	−30.5606	−	8.18868i	−1.42800	−	0.382632i
$459$	30.9445	−	53.5975i	1.44437	−	2.50172i
$460$		0			0
$461$	0.541259	+	2.02001i	0.0252090	+	0.0940811i	0.977384	−	0.211471i	$-0.0678255\pi$
$461$	0.541259	+	2.02001i	0.0252090	+	0.0940811i	−0.952175	+	0.305553i	$0.901159\pi$
$462$	−25.3895	−	14.6586i	−1.18123	−	0.681981i
$463$	−36.2345			−1.68396			−0.841980	−	0.539509i	$-0.818610\pi$
$463$	−36.2345			−1.68396			−0.841980	+	0.539509i	$0.818610\pi$
$464$	12.3256	+	7.11618i	0.572201	+	0.330360i
$465$		0			0
$466$	0.00662125	−	0.0247108i	0.000306723	−	0.00114471i
$467$	28.6381	−	28.6381i	1.32521	−	1.32521i	0.415719	−	0.909493i	$-0.363530\pi$
$467$	28.6381	−	28.6381i	1.32521	−	1.32521i	0.909493	−	0.415719i	$-0.136470\pi$
$468$	17.4880	−	24.8946i	0.808383	−	1.15075i
$469$			1.83580i			0.0847694i
$470$		0			0
$471$	−22.4482	−	38.8815i	−1.03436	−	1.79157i
$472$	−1.38943	−	5.18543i	−0.0639538	−	0.238679i
$473$			20.3356i			0.935032i
$474$	19.1100	−	5.12050i	0.877751	−	0.235193i
$475$		0			0
$476$	4.40360	+	4.40360i	0.201839	+	0.201839i
$477$	−6.13181	+	1.64301i	−0.280756	+	0.0752284i
$478$	−5.66230	+	21.1320i	−0.258988	+	0.966555i
$479$	−32.0790	−	8.59555i	−1.46573	−	0.392741i	−0.564264	−	0.825594i	$-0.690840\pi$
$479$	−32.0790	−	8.59555i	−1.46573	−	0.392741i	−0.901464	+	0.432854i	$0.857507\pi$
$480$		0			0
$481$	12.5998	−	17.9362i	0.574503	−	0.817820i
$482$	−27.7843	−	27.7843i	−1.26554	−	1.26554i
$483$	−22.4513	+	12.9623i	−1.02157	+	0.589804i
$484$	2.34534	−	1.35408i	0.106606	−	0.0615492i
$485$		0			0
$486$	51.6975	−	51.6975i	2.34505	−	2.34505i
$487$	−10.4790	+	18.1501i	−0.474847	+	0.822460i	−0.999585	−	0.0288042i	$-0.990830\pi$
$487$	−10.4790	+	18.1501i	−0.474847	+	0.822460i	0.524738	+	0.851264i	$0.324163\pi$
$488$	4.80118	−	8.31589i	0.217339	−	0.376443i
$489$	9.19925	−	9.19925i	0.416004	−	0.416004i
$490$		0			0
$491$	20.3975	−	11.7765i	0.920527	−	0.531466i	0.0367236	−	0.999325i	$-0.488308\pi$
$491$	20.3975	−	11.7765i	0.920527	−	0.531466i	0.883803	+	0.467859i	$0.154975\pi$
$492$	35.3957	−	20.4357i	1.59576	−	0.921314i
$493$	−8.20437	−	8.20437i	−0.369506	−	0.369506i
$494$	13.8952	+	5.08142i	0.625173	+	0.228624i
$495$		0			0
$496$	1.50012	+	0.401955i	0.0673572	+	0.0180483i
$497$	−1.97298	+	7.36326i	−0.0885002	+	0.330287i
$498$	−7.67888	+	2.05755i	−0.344099	+	0.0922010i
$499$	18.2233	+	18.2233i	0.815789	+	0.815789i	0.985495	−	0.169706i	$-0.0542818\pi$
$499$	18.2233	+	18.2233i	0.815789	+	0.815789i	−0.169706	+	0.985495i	$0.554282\pi$
$500$		0			0
$501$	17.2042	−	4.60984i	0.768625	−	0.205952i
$502$		−	2.13269i		−	0.0951865i
$503$	2.61801	+	9.77054i	0.116731	+	0.435647i	0.999411	−	0.0343287i	$-0.0109293\pi$
$503$	2.61801	+	9.77054i	0.116731	+	0.435647i	−0.882679	+	0.469976i	$0.844263\pi$
$504$	−8.42233	−	14.5879i	−0.375160	−	0.649797i
$505$		0			0
$506$		−	36.9117i		−	1.64093i
$507$	34.8425	−	24.2391i	1.54741	−	1.07649i
$508$	−15.1258	+	15.1258i	−0.671098	+	0.671098i
$509$	−0.411564	+	1.53598i	−0.0182422	+	0.0680810i	−0.974447	−	0.224618i	$-0.927887\pi$
$509$	−0.411564	+	1.53598i	−0.0182422	+	0.0680810i	0.956205	+	0.292699i	$0.0945533\pi$
$510$		0			0
$511$	2.59980	+	1.50100i	0.115008	+	0.0664002i
$512$	12.2666			0.542114
$513$	30.7005	+	17.7249i	1.35546	+	0.782576i
$514$	5.81397	+	21.6980i	0.256443	+	0.957059i
$515$		0			0
$516$	9.96816	−	17.2654i	0.438824	−	0.760065i
$517$	−17.9619	−	4.81289i	−0.789965	−	0.211671i
$518$	7.44005	+	12.8866i	0.326897	+	0.566203i
$519$	66.2716			2.90900
$520$		0			0
$521$	−27.2541			−1.19402			−0.597012	−	0.802232i	$-0.703646\pi$
$521$	−27.2541			−1.19402			−0.597012	+	0.802232i	$0.703646\pi$
$522$	−19.2393	−	33.3234i	−0.842081	−	1.45853i
$523$	19.9043	+	5.33334i	0.870354	+	0.233211i	0.666241	−	0.745737i	$-0.267902\pi$
$523$	19.9043	+	5.33334i	0.870354	+	0.233211i	0.204113	+	0.978947i	$0.434569\pi$
$524$	−2.32252	+	4.02272i	−0.101460	+	0.175733i
$525$		0			0
$526$	5.38960	+	20.1143i	0.234998	+	0.877024i
$527$	−1.09647	−	0.633045i	−0.0477628	−	0.0275759i
$528$	59.7652			2.60095
$529$	−8.34861	−	4.82007i	−0.362983	−	0.209568i
$530$		0			0
$531$	−6.72641	+	25.1033i	−0.291901	+	1.08939i
$532$	−2.52237	+	2.52237i	−0.109359	+	0.109359i
$533$	40.3621	−	7.05353i	1.74828	−	0.305523i
$534$		−	6.51843i		−	0.282080i
$535$		0			0
$536$	−1.04500	−	1.80999i	−0.0451372	−	0.0781799i
$537$	0.820015	+	3.06034i	0.0353863	+	0.132063i
$538$		−	28.5936i		−	1.23276i
$539$	−17.9603	+	4.81245i	−0.773604	+	0.207287i
$540$		0			0
$541$	−26.3998	−	26.3998i	−1.13502	−	1.13502i	−0.989331	−	0.145684i	$-0.953462\pi$
$541$	−26.3998	−	26.3998i	−1.13502	−	1.13502i	−0.145684	−	0.989331i	$-0.546538\pi$
$542$	−3.72744	+	0.998764i	−0.160107	+	0.0429006i
$543$	15.3940	−	57.4510i	0.660618	−	2.46546i
$544$	−22.0934	−	5.91991i	−0.947248	−	0.253814i
$545$		0			0
$546$	4.96018	+	28.3834i	0.212276	+	1.21470i
$547$	−8.78649	−	8.78649i	−0.375683	−	0.375683i	0.493859	−	0.869542i	$-0.335586\pi$
$547$	−8.78649	−	8.78649i	−0.375683	−	0.375683i	−0.869542	+	0.493859i	$0.835586\pi$
$548$	−10.7060	+	6.18109i	−0.457336	+	0.264043i
$549$	−40.2582	+	23.2431i	−1.71818	+	0.991992i
$550$		0			0
$551$	4.69944	−	4.69944i	0.200203	−	0.200203i
$552$	14.7571	−	25.5601i	0.628106	−	1.08791i
$553$	−2.39098	+	4.14131i	−0.101675	+	0.176106i
$554$	−23.2489	+	23.2489i	−0.987752	+	0.987752i
$555$		0			0
$556$	1.59104	−	0.918586i	0.0674750	−	0.0389567i
$557$	−14.1343	+	8.16044i	−0.598889	+	0.345769i	−0.768604	−	0.639724i	$-0.779049\pi$
$557$	−14.1343	+	8.16044i	−0.598889	+	0.345769i	0.169715	+	0.985493i	$0.445715\pi$
$558$	−2.96899	−	2.96899i	−0.125687	−	0.125687i
$559$	15.3299	−	12.8236i	0.648386	−	0.542379i
$560$		0			0
$561$	−47.0626	−	12.6104i	−1.98698	−	0.532411i
$562$	5.00636	−	18.6840i	0.211181	−	0.788137i
$563$	11.2729	−	3.02058i	0.475098	−	0.127302i	−0.0133211	−	0.999911i	$-0.504240\pi$
$563$	11.2729	−	3.02058i	0.475098	−	0.127302i	0.488419	+	0.872609i	$0.337574\pi$
$564$	12.8909	+	12.8909i	0.542803	+	0.542803i
$565$		0			0
$566$	16.6128	−	4.45140i	0.698290	−	0.187106i
$567$			37.1010i			1.55809i
$568$	−2.24618	−	8.38284i	−0.0942475	−	0.351736i
$569$	1.62041	+	2.80663i	0.0679311	+	0.117660i	0.897990	−	0.440015i	$-0.145027\pi$
$569$	1.62041	+	2.80663i	0.0679311	+	0.117660i	−0.830059	+	0.557675i	$0.811694\pi$
$570$		0			0
$571$			35.5421i			1.48739i	0.668520	+	0.743694i	$0.266928\pi$
$571$			35.5421i			1.48739i	−0.668520	+	0.743694i	$0.733072\pi$
$572$	−13.6843	−	5.00430i	−0.572169	−	0.209240i
$573$	−37.8059	+	37.8059i	−1.57936	+	1.57936i
$574$	−7.19911	+	26.8674i	−0.300485	+	1.12143i
$575$		0			0
$576$	0.508738	+	0.293720i	0.0211974	+	0.0122383i
$577$	−16.1725			−0.673272			−0.336636	−	0.941635i	$-0.609289\pi$
$577$	−16.1725			−0.673272			−0.336636	+	0.941635i	$0.609289\pi$
$578$	−0.691264	−	0.399102i	−0.0287528	−	0.0166004i
$579$	8.69973	+	32.4678i	0.361549	+	1.34932i
$580$		0			0
$581$	0.960759	−	1.66408i	0.0398590	−	0.0690378i
$582$	87.9876	+	23.5762i	3.64720	+	0.977265i
$583$	1.52015	+	2.63298i	0.0629584	+	0.109047i
$584$	−3.41768			−0.141424
$585$		0			0
$586$	59.4842			2.45727
$587$	7.95555	+	13.7794i	0.328361	+	0.568737i	0.982187	−	0.187908i	$-0.0601706\pi$
$587$	7.95555	+	13.7794i	0.328361	+	0.568737i	−0.653826	+	0.756645i	$0.726837\pi$
$588$	17.6076	+	4.71795i	0.726127	+	0.194565i
$589$	0.362606	−	0.628053i	0.0149409	−	0.0258785i
$590$		0			0
$591$	−10.4720	−	39.0820i	−0.430760	−	1.60762i
$592$	−26.2701	−	15.1671i	−1.07970	−	0.623362i
$593$	−6.24369			−0.256397			−0.128199	−	0.991748i	$-0.540920\pi$
$593$	−6.24369			−0.256397			−0.128199	+	0.991748i	$0.540920\pi$
$594$	−85.1288	−	49.1491i	−3.49288	−	2.01661i
$595$		0			0
$596$	3.43286	−	12.8116i	0.140616	−	0.524784i
$597$	−9.91021	+	9.91021i	−0.405598	+	0.405598i
$598$	−27.8257	+	23.2764i	−1.13788	+	0.951842i
$599$		−	18.0428i		−	0.737210i	−0.929586	−	0.368605i	$-0.879835\pi$
$599$		−	18.0428i		−	0.737210i	0.929586	−	0.368605i	$-0.120165\pi$
$600$		0			0
$601$	17.1374	+	29.6828i	0.699048	+	1.21079i	0.968797	+	0.247856i	$0.0797259\pi$
$601$	17.1374	+	29.6828i	0.699048	+	1.21079i	−0.269749	+	0.962931i	$0.586941\pi$
$602$	3.51159	+	13.1054i	0.143122	+	0.534137i
$603$			10.1180i			0.412035i
$604$	9.23591	−	2.47475i	0.375804	−	0.100696i
$605$		0			0
$606$	10.6193	+	10.6193i	0.431380	+	0.431380i
$607$	18.3613	−	4.91988i	0.745260	−	0.199692i	0.133846	−	0.991002i	$-0.457267\pi$
$607$	18.3613	−	4.91988i	0.745260	−	0.199692i	0.611415	+	0.791310i	$0.290601\pi$
$608$	3.39091	−	12.6551i	0.137520	−	0.513230i
$609$	12.5021	+	3.34992i	0.506610	+	0.135746i
$610$		0			0
$611$	7.69856	+	16.5755i	0.311450	+	0.670573i
$612$	24.2703	+	24.2703i	0.981069	+	0.981069i
$613$	−15.5555	+	8.98095i	−0.628279	+	0.362737i	−0.780085	−	0.625673i	$-0.784824\pi$
$613$	−15.5555	+	8.98095i	−0.628279	+	0.362737i	0.151806	+	0.988410i	$0.451491\pi$
$614$	−25.0612	+	14.4691i	−1.01139	+	0.583925i
$615$		0			0
$616$	−5.70453	+	5.70453i	−0.229842	+	0.229842i
$617$	9.44966	−	16.3673i	0.380429	−	0.658922i	−0.610695	−	0.791866i	$-0.709110\pi$
$617$	9.44966	−	16.3673i	0.380429	−	0.658922i	0.991124	+	0.132944i	$0.0424431\pi$
$618$	3.90686	−	6.76687i	0.157157	−	0.272204i
$619$	26.9541	−	26.9541i	1.08338	−	1.08338i	0.0871850	−	0.996192i	$-0.472213\pi$
$619$	26.9541	−	26.9541i	1.08338	−	1.08338i	0.996192	−	0.0871850i	$-0.0277871\pi$
$620$		0			0
$621$	−75.2773	+	43.4614i	−3.02077	+	1.74405i
$622$	−2.00104	+	1.15530i	−0.0802343	+	0.0463233i
$623$	1.11408	+	1.11408i	0.0446349	+	0.0446349i
$624$	−37.6877	−	45.0537i	−1.50872	−	1.80359i
$625$		0			0
$626$	−47.0369	−	12.6035i	−1.87997	−	0.503737i
$627$	7.22319	−	26.9573i	0.288466	−	1.07657i
$628$	14.6314	−	3.92048i	0.583858	−	0.156444i
$629$	17.4864	+	17.4864i	0.697227	+	0.697227i
$630$		0			0
$631$	10.7162	−	2.87140i	0.426606	−	0.114309i	−0.0391265	−	0.999234i	$-0.512458\pi$
$631$	10.7162	−	2.87140i	0.426606	−	0.114309i	0.465733	+	0.884926i	$0.345791\pi$
$632$		−	5.44412i		−	0.216556i
$633$	−22.7022	−	84.7257i	−0.902331	−	3.36754i
$634$	−30.7824	−	53.3166i	−1.22252	−	2.11747i
$635$		0			0
$636$		−	2.98061i		−	0.118189i
$637$	14.9535	+	10.5046i	0.592480	+	0.416206i
$638$	−13.0310	+	13.0310i	−0.515901	+	0.515901i
$639$	−10.8740	+	40.5824i	−0.430170	+	1.60541i
$640$		0			0
$641$	19.7159	+	11.3830i	0.778731	+	0.449600i	0.835980	−	0.548760i	$-0.184900\pi$
$641$	19.7159	+	11.3830i	0.778731	+	0.449600i	−0.0572496	+	0.998360i	$0.518233\pi$
$642$	−89.7027			−3.54028
$643$	−29.9622	−	17.2987i	−1.18160	−	0.682195i	−0.225212	−	0.974310i	$-0.572308\pi$
$643$	−29.9622	−	17.2987i	−1.18160	−	0.682195i	−0.956383	+	0.292115i	$0.905641\pi$
$644$	−2.26380	−	8.44862i	−0.0892063	−	0.332922i
$645$		0			0
$646$	−8.34592	+	14.4556i	−0.328366	+	0.568746i
$647$	−37.9832	−	10.1776i	−1.49328	−	0.400122i	−0.582434	−	0.812878i	$-0.697900\pi$
$647$	−37.9832	−	10.1776i	−1.49328	−	0.400122i	−0.910842	+	0.412756i	$0.864566\pi$
$648$	−21.1191	−	36.5794i	−0.829638	−	1.43698i
$649$	12.4469			0.488582
$650$		0			0
$651$	1.41235			0.0553544
$652$	2.19467	+	3.80127i	0.0859497	+	0.148869i
$653$	9.21671	+	2.46961i	0.360678	+	0.0966433i	0.434607	−	0.900620i	$-0.356887\pi$
$653$	9.21671	+	2.46961i	0.360678	+	0.0966433i	−0.0739293	+	0.997263i	$0.523554\pi$
$654$	38.7054	−	67.0398i	1.51350	−	2.62146i
$655$		0			0
$656$	−14.6759	−	54.7711i	−0.572997	−	2.13845i
$657$	14.3287	+	8.27270i	0.559017	+	0.322749i
$658$	−12.4068			−0.483667
$659$	−15.6774	−	9.05138i	−0.610707	−	0.352592i	0.162535	−	0.986703i	$-0.448033\pi$
$659$	−15.6774	−	9.05138i	−0.610707	−	0.352592i	−0.773242	+	0.634111i	$0.781366\pi$
$660$		0			0
$661$	4.48311	−	16.7312i	0.174373	−	0.650768i	−0.822285	−	0.569076i	$-0.807301\pi$
$661$	4.48311	−	16.7312i	0.174373	−	0.650768i	0.996658	−	0.0816920i	$-0.0260324\pi$
$662$	−3.16860	+	3.16860i	−0.123151	+	0.123151i
$663$	20.1712	+	43.4299i	0.783385	+	1.68668i
$664$			2.18759i			0.0848949i
$665$		0			0
$666$	41.0056	+	71.0239i	1.58894	+	2.75212i
$667$	4.21770	+	15.7407i	0.163310	+	0.609482i
$668$			6.00925i			0.232505i
$669$	62.6875	−	16.7971i	2.42364	−	0.649412i
$670$		0			0
$671$	15.7428	+	15.7428i	0.607744	+	0.607744i
$672$	24.6457	−	6.60380i	0.950729	−	0.254747i
$673$	−2.75296	+	10.2742i	−0.106119	+	0.396040i	−0.998470	−	0.0553019i	$-0.982388\pi$
$673$	−2.75296	+	10.2742i	−0.106119	+	0.396040i	0.892351	+	0.451342i	$0.149055\pi$
$674$	−20.0476	−	5.37175i	−0.772207	−	0.206912i
$675$		0			0
$676$	4.85679	+	13.4715i	0.186800	+	0.518136i
$677$	−4.88408	−	4.88408i	−0.187710	−	0.187710i	0.606995	−	0.794706i	$-0.292375\pi$
$677$	−4.88408	−	4.88408i	−0.187710	−	0.187710i	−0.794706	+	0.606995i	$0.792375\pi$
$678$	−57.0188	+	32.9198i	−2.18979	+	1.26428i
$679$	−19.0677	+	11.0088i	−0.731752	+	0.422477i
$680$		0			0
$681$	−25.7990	+	25.7990i	−0.988620	+	0.988620i
$682$	−1.00546	+	1.74151i	−0.0385012	+	0.0666860i
$683$	−23.4080	+	40.5438i	−0.895681	+	1.55137i	−0.0627219	+	0.998031i	$0.519978\pi$
$683$	−23.4080	+	40.5438i	−0.895681	+	1.55137i	−0.832959	+	0.553334i	$0.813355\pi$
$684$	−13.9020	+	13.9020i	−0.531555	+	0.531555i
$685$		0			0
$686$	−25.5816	+	14.7696i	−0.976712	+	0.563905i
$687$	50.7967	−	29.3275i	1.93802	−	1.11891i
$688$	−19.5577	−	19.5577i	−0.745630	−	0.745630i
$689$	1.02626	−	2.80631i	0.0390973	−	0.106912i
$690$		0			0
$691$	30.4266	+	8.15279i	1.15748	+	0.310147i	0.785960	−	0.618277i	$-0.212169\pi$
$691$	30.4266	+	8.15279i	1.15748	+	0.310147i	0.371523	+	0.928424i	$0.378836\pi$
$692$	−5.78701	+	21.5974i	−0.219989	+	0.821011i
$693$	37.7246	−	10.1083i	1.43304	−	0.383982i
$694$	13.3635	+	13.3635i	0.507273	+	0.507273i
$695$		0			0
$696$	−14.2332	+	3.81379i	−0.539510	+	0.144561i
$697$			46.2265i			1.75095i
$698$	−10.8558	−	40.5146i	−0.410900	−	1.53350i
$699$	0.0237138	+	0.0410735i	0.000896938	+	0.00155354i
$700$		0			0
$701$			5.09953i			0.192607i	0.995352	+	0.0963034i	$0.0307019\pi$
$701$			5.09953i			0.192607i	−0.995352	+	0.0963034i	$0.969298\pi$
$702$	16.6311	+	95.1671i	0.627699	+	3.59185i
$703$	−10.0161	+	10.0161i	−0.377766	+	0.377766i
$704$	0.0728169	−	0.271756i	0.00274439	−	0.0102422i
$705$		0			0
$706$	−39.4538	−	22.7787i	−1.48486	−	0.857286i
$707$	−3.62996			−0.136519
$708$	−10.5676	−	6.10123i	−0.397156	−	0.229298i
$709$	−11.1632	−	41.6615i	−0.419241	−	1.56463i	−0.776186	−	0.630504i	$-0.782848\pi$
$709$	−11.1632	−	41.6615i	−0.419241	−	1.56463i	0.356945	−	0.934125i	$-0.383818\pi$
$710$		0			0
$711$	−13.1778	+	22.8247i	−0.494208	+	0.855993i
$712$	−1.73260	−	0.464249i	−0.0649319	−	0.0173985i
$713$	0.889107	+	1.53998i	0.0332973	+	0.0576726i
$714$	−32.5074			−1.21656
$715$		0			0
$716$	−1.06895			−0.0399485
$717$	−20.2793	−	35.1249i	−0.757346	−	1.31176i
$718$	46.6258	+	12.4933i	1.74006	+	0.466248i
$719$	−26.2618	+	45.4868i	−0.979400	+	1.69637i	−0.314824	+	0.949150i	$0.601946\pi$
$719$	−26.2618	+	45.4868i	−0.979400	+	1.69637i	−0.664576	+	0.747221i	$0.731388\pi$
$720$		0			0
$721$	0.488814	+	1.82428i	0.0182044	+	0.0679397i
$722$	20.6983	+	11.9502i	0.770311	+	0.444739i
$723$	72.8453			2.70915
$724$	17.3786	+	10.0336i	0.645872	+	0.372894i
$725$		0			0
$726$	−3.65873	+	13.6546i	−0.135788	+	0.506769i
$727$	−3.04083	+	3.04083i	−0.112778	+	0.112778i	−0.761244	−	0.648466i	$-0.775411\pi$
$727$	−3.04083	+	3.04083i	−0.112778	+	0.112778i	0.648466	+	0.761244i	$0.275411\pi$
$728$	7.89758	+	0.703077i	0.292704	+	0.0260578i
$729$			55.4569i			2.05396i
$730$		0			0
$731$	11.2742	+	19.5275i	0.416991	+	0.722250i
$732$	−5.64912	−	21.0828i	−0.208797	−	0.779243i
$733$		−	25.6949i		−	0.949061i	−0.880239	−	0.474531i	$-0.842618\pi$
$733$		−	25.6949i		−	0.949061i	0.880239	−	0.474531i	$-0.157382\pi$
$734$	−40.9504	+	10.9726i	−1.51151	+	0.405007i
$735$		0			0
$736$	22.7156	+	22.7156i	0.837307	+	0.837307i
$737$	4.68068	−	1.25419i	0.172415	−	0.0461985i
$738$	−39.6777	+	148.079i	−1.46056	+	5.45087i
$739$	16.5169	+	4.42570i	0.607586	+	0.162802i	0.549478	−	0.835508i	$-0.314827\pi$
$739$	16.5169	+	4.42570i	0.607586	+	0.162802i	0.0581076	+	0.998310i	$0.481493\pi$
$740$		0			0
$741$	−24.8766	+	11.5540i	−0.913863	+	0.424447i
$742$	1.43434	+	1.43434i	0.0526563	+	0.0526563i
$743$	15.9085	−	9.18480i	0.583628	−	0.336958i	−0.178946	−	0.983859i	$-0.557269\pi$
$743$	15.9085	−	9.18480i	0.583628	−	0.336958i	0.762574	+	0.646901i	$0.223935\pi$
$744$	−1.39250	+	0.803960i	−0.0510515	+	0.0294746i
$745$		0			0
$746$	28.9305	−	28.9305i	1.05922	−	1.05922i
$747$	5.29519	−	9.17154i	0.193741	−	0.335569i
$748$	8.21926	−	14.2362i	0.300526	−	0.520526i
$749$	15.3314	−	15.3314i	0.560196	−	0.560196i
$750$		0			0
$751$	−28.0217	+	16.1783i	−1.02252	+	0.590355i	−0.914834	−	0.403830i	$-0.867679\pi$
$751$	−28.0217	+	16.1783i	−1.02252	+	0.590355i	−0.107690	+	0.994184i	$0.534346\pi$
$752$	21.9036	−	12.6460i	0.798742	−	0.461154i
$753$	2.79576	+	2.79576i	0.101883	+	0.101883i
$754$	18.0406	+	1.60605i	0.657000	+	0.0584890i
$755$		0			0
$756$	−22.4992	−	6.02865i	−0.818288	−	0.219260i
$757$	−0.157864	+	0.589155i	−0.00573766	+	0.0214132i	−0.968735	−	0.248097i	$-0.920195\pi$
$757$	−0.157864	+	0.589155i	−0.00573766	+	0.0214132i	0.962998	+	0.269510i	$0.0868616\pi$
$758$	47.3062	−	12.6757i	1.71824	−	0.460401i
$759$	48.3879	+	48.3879i	1.75637	+	1.75637i
$760$		0			0
$761$	11.9275	−	3.19596i	0.432371	−	0.115854i	−0.0360677	−	0.999349i	$-0.511483\pi$
$761$	11.9275	−	3.19596i	0.432371	−	0.115854i	0.468439	+	0.883496i	$0.344817\pi$
$762$		−	111.659i		−	4.04496i
$763$	4.84271	+	18.0732i	0.175318	+	0.654295i
$764$	−9.01936	−	15.6220i	−0.326309	−	0.565184i
$765$		0			0
$766$			29.7119i			1.07353i
$767$	−7.84894	−	9.38300i	−0.283409	−	0.338801i
$768$	−45.9191	+	45.9191i	−1.65696	+	1.65696i
$769$	12.1625	−	45.3911i	0.438591	−	1.63684i	−0.293733	−	0.955888i	$-0.594898\pi$
$769$	12.1625	−	45.3911i	0.438591	−	1.63684i	0.732324	−	0.680956i	$-0.238436\pi$
$770$		0			0
$771$	−36.0657	−	20.8225i	−1.29887	−	0.749905i
$772$	−11.3407			−0.408161
$773$	29.5748	+	17.0750i	1.06373	+	0.614145i	0.926462	−	0.376389i	$-0.122834\pi$
$773$	29.5748	+	17.0750i	1.06373	+	0.614145i	0.137269	+	0.990534i	$0.456168\pi$
$774$	19.3540	+	72.2301i	0.695665	+	2.59626i
$775$		0			0
$776$	12.5331	−	21.7080i	0.449913	−	0.779272i
$777$	−26.6463	−	7.13986i	−0.955931	−	0.256141i
$778$	14.0498	+	24.3349i	0.503709	+	0.872449i
$779$	−26.4784			−0.948688
$780$		0			0
$781$	20.1218			0.720014
$782$	−20.4641	−	35.4449i	−0.731795	−	1.26751i
$783$	41.9184	+	11.2320i	1.49804	+	0.401399i
$784$	12.6449	−	21.9016i	0.451603	−	0.782199i
$785$		0			0
$786$	−6.27545	−	23.4203i	−0.223838	−	0.835374i
$787$	−7.53904	−	4.35267i	−0.268738	−	0.155156i	0.359576	−	0.933116i	$-0.382921\pi$
$787$	−7.53904	−	4.35267i	−0.268738	−	0.155156i	−0.628314	+	0.777960i	$0.716255\pi$
$788$	13.6510			0.486296
$789$	−33.4332	−	19.3027i	−1.19026	−	0.687194i
$790$		0			0
$791$	4.11883	−	15.3717i	0.146449	−	0.546554i
$792$	−31.4403	+	31.4403i	−1.11718	+	1.11718i
$793$	1.94028	−	21.7950i	0.0689014	−	0.773962i
$794$		−	29.2484i		−	1.03799i
$795$		0			0
$796$	−2.36428	−	4.09505i	−0.0837997	−	0.145145i
$797$	7.57637	+	28.2754i	0.268369	+	1.00157i	0.960156	+	0.279464i	$0.0901568\pi$
$797$	7.57637	+	28.2754i	0.268369	+	1.00157i	−0.691787	+	0.722101i	$0.743176\pi$
$798$		−	18.6201i		−	0.659145i
$799$	−19.9164	+	5.33659i	−0.704593	+	0.188795i
$800$		0			0
$801$	6.14025	+	6.14025i	0.216955	+	0.216955i
$802$	31.1370	−	8.34312i	1.09948	−	0.294606i
$803$	2.05091	−	7.65409i	0.0723750	−	0.270107i
$804$	−4.58878	−	1.22956i	−0.161834	−	0.0433632i
$805$		0			0
$806$	1.94687	−	0.340228i	0.0685756	−	0.0119840i
$807$	37.4836	+	37.4836i	1.31948	+	1.31948i
$808$	3.57894	−	2.06630i	0.125907	−	0.0726922i
$809$	29.2507	−	16.8879i	1.02840	−	0.593748i	0.111875	−	0.993722i	$-0.464314\pi$
$809$	29.2507	−	16.8879i	1.02840	−	0.593748i	0.916526	+	0.399975i	$0.130981\pi$
$810$		0			0
$811$	34.8970	−	34.8970i	1.22540	−	1.22540i	0.259712	−	0.965686i	$-0.416372\pi$
$811$	34.8970	−	34.8970i	1.22540	−	1.22540i	0.965686	−	0.259712i	$-0.0836277\pi$
$812$	−2.18343	+	3.78182i	−0.0766235	+	0.132716i
$813$	3.57704	−	6.19561i	0.125452	−	0.217290i
$814$	27.7735	−	27.7735i	0.973462	−	0.973462i
$815$		0			0
$816$	57.3902	−	33.1342i	2.00906	−	1.15993i
$817$	−11.1853	+	6.45783i	−0.391324	+	0.225931i
$818$	15.3639	+	15.3639i	0.537186	+	0.537186i
$819$	−31.4091	−	22.0643i	−1.09752	−	0.770988i
$820$		0			0
$821$	−20.4287	−	5.47385i	−0.712966	−	0.191039i	−0.115935	−	0.993257i	$-0.536986\pi$
$821$	−20.4287	−	5.47385i	−0.712966	−	0.191039i	−0.597031	+	0.802218i	$0.703653\pi$
$822$	16.7013	−	62.3301i	0.582525	−	2.17401i
$823$	−49.8251	+	13.3506i	−1.73679	+	0.465373i	−0.981730	−	0.190278i	$-0.939061\pi$
$823$	−49.8251	+	13.3506i	−1.73679	+	0.465373i	−0.755064	+	0.655651i	$0.772394\pi$
$824$	−1.52039	−	1.52039i	−0.0529652	−	0.0529652i
$825$		0			0
$826$	8.02146	−	2.14934i	0.279102	−	0.0747852i
$827$			2.11823i			0.0736582i	0.999322	+	0.0368291i	$0.0117257\pi$
$827$			2.11823i			0.0736582i	−0.999322	+	0.0368291i	$0.988274\pi$
$828$	−12.4769	−	46.5643i	−0.433601	−	1.61822i
$829$	6.39435	+	11.0753i	0.222085	+	0.384662i	0.955441	−	0.295183i	$-0.0953805\pi$
$829$	6.39435	+	11.0753i	0.222085	+	0.384662i	−0.733356	+	0.679845i	$0.762047\pi$
$830$		0			0
$831$		−	60.9544i		−	2.11448i
$832$	−0.250780	+	0.116476i	−0.00869424	+	0.00403807i
$833$	−14.5785	+	14.5785i	−0.505115	+	0.505115i
$834$	−2.48202	+	9.26302i	−0.0859453	+	0.320752i
$835$		0			0
$836$	8.15445	+	4.70797i	0.282027	+	0.162829i
$837$	4.73549			0.163683
$838$	27.4846	+	15.8682i	0.949439	+	0.548159i
$839$	−8.24394	−	30.7668i	−0.284612	−	1.06219i	−0.949122	−	0.314908i	$-0.898026\pi$
$839$	−8.24394	−	30.7668i	−0.284612	−	1.06219i	0.664510	−	0.747280i	$-0.268640\pi$
$840$		0			0
$841$	−10.4320	+	18.0688i	−0.359725	+	0.623062i
$842$	−30.5485	−	8.18545i	−1.05277	−	0.282089i
$843$	17.9301	+	31.0559i	0.617546	+	1.06962i
$844$	29.5939			1.01866
$845$		0			0
$846$	−68.3796			−2.35094
$847$	−1.70842	−	2.95907i	−0.0587020	−	0.101675i
$848$	−3.99426	−	1.07026i	−0.137164	−	0.0367529i
$849$	−15.9425	+	27.6133i	−0.547147	+	0.947686i
$850$		0			0
$851$	−8.98940	−	33.5489i	−0.308152	−	1.15004i
$852$	−17.0838	−	9.86335i	−0.585282	−	0.337913i
$853$	−37.3304			−1.27817			−0.639083	−	0.769137i	$-0.720686\pi$
$853$	−37.3304			−1.27817			−0.639083	+	0.769137i	$0.720686\pi$
$854$	12.8640	+	7.42706i	0.440198	+	0.254149i
$855$		0			0
$856$	−6.38871	+	23.8430i	−0.218362	+	0.814937i
$857$	−8.71215	+	8.71215i	−0.297601	+	0.297601i	−0.840074	−	0.542472i	$-0.817488\pi$
$857$	−8.71215	+	8.71215i	−0.297601	+	0.297601i	0.542472	+	0.840074i	$0.317488\pi$
$858$	68.9796	−	32.0379i	2.35493	−	1.09375i
$859$			3.04501i			0.103895i	0.998650	+	0.0519473i	$0.0165428\pi$
$859$			3.04501i			0.103895i	−0.998650	+	0.0519473i	$0.983457\pi$
$860$		0			0
$861$	−25.7834	−	44.6581i	−0.878695	−	1.52194i
$862$	3.33652	+	12.4520i	0.113642	+	0.424118i
$863$			23.2413i			0.791142i	0.918435	+	0.395571i	$0.129453\pi$
$863$			23.2413i			0.791142i	−0.918435	+	0.395571i	$0.870547\pi$
$864$	82.6350	−	22.1420i	2.81130	−	0.753285i
$865$		0			0
$866$	−11.0484	−	11.0484i	−0.375440	−	0.375440i
$867$	1.42937	−	0.382998i	0.0485439	−	0.0130073i
$868$	−0.123330	+	0.460275i	−0.00418611	+	0.0156228i
$869$	12.1924	+	3.26696i	0.413600	+	0.110824i
$870$		0			0
$871$	−3.89708	−	2.73763i	−0.132048	−	0.0927609i
$872$	−15.0626	−	15.0626i	−0.510082	−	0.510082i
$873$	−105.091	+	60.6744i	−3.55680	+	2.05352i
$874$	20.3027	−	11.7218i	0.686750	−	0.396495i
$875$		0			0
$876$	−5.49316	+	5.49316i	−0.185597	+	0.185597i
$877$	−12.4978	+	21.6468i	−0.422021	+	0.730961i	−0.996137	−	0.0878124i	$-0.972012\pi$
$877$	−12.4978	+	21.6468i	−0.422021	+	0.730961i	0.574116	+	0.818774i	$0.305346\pi$
$878$	20.9383	−	36.2663i	0.706635	−	1.22393i
$879$	−77.9783	+	77.9783i	−2.63014	+	2.63014i
$880$		0			0
$881$	−26.3994	+	15.2417i	−0.889417	+	0.513505i	−0.873752	−	0.486372i	$-0.838320\pi$
$881$	−26.3994	+	15.2417i	−0.889417	+	0.513505i	−0.0156653	+	0.999877i	$0.504987\pi$
$882$	−59.2131	+	34.1867i	−1.99381	+	1.15113i
$883$	−40.0008	−	40.0008i	−1.34613	−	1.34613i	−0.889818	−	0.456315i	$-0.849169\pi$
$883$	−40.0008	−	40.0008i	−1.34613	−	1.34613i	−0.456315	−	0.889818i	$-0.650831\pi$
$884$	−15.9149	+	2.78123i	−0.535276	+	0.0935429i
$885$		0			0
$886$	−12.4770	−	3.34320i	−0.419173	−	0.112317i
$887$	−11.7241	+	43.7550i	−0.393657	+	1.46915i	0.430398	+	0.902639i	$0.358373\pi$
$887$	−11.7241	+	43.7550i	−0.393657	+	1.46915i	−0.824055	+	0.566509i	$0.808294\pi$
$888$	30.3360	−	8.12851i	1.01801	−	0.272775i
$889$	19.0839	+	19.0839i	0.640053	+	0.640053i
$890$		0			0
$891$	94.5952	−	25.3467i	3.16906	−	0.849147i
$892$			21.8962i			0.733138i
$893$	−3.05679	−	11.4081i	−0.102291	−	0.381757i
$894$	34.6170	+	59.9584i	1.15777	+	2.00531i
$895$		0			0
$896$		−	15.8174i		−	0.528422i
$897$	5.96375	−	66.9901i	0.199124	−	2.23674i
$898$	40.7645	−	40.7645i	1.36033	−	1.36033i
$899$	0.229778	−	0.857542i	0.00766351	−	0.0286006i
$900$		0			0
$901$	2.91949	+	1.68557i	0.0972623	+	0.0561544i
$902$	73.4214			2.44467
$903$	−21.7834	−	12.5766i	−0.724905	−	0.418524i
$904$	4.68916	+	17.5002i	0.155959	+	0.582047i
$905$		0			0
$906$	−24.9554	+	43.2241i	−0.829089	+	1.43602i
$907$	49.2541	+	13.1976i	1.63545	+	0.438219i	0.955489	−	0.295026i	$-0.0953283\pi$
$907$	49.2541	+	13.1976i	1.63545	+	0.438219i	0.679965	+	0.733245i	$0.261995\pi$
$908$	−6.15487	−	10.6605i	−0.204257	−	0.353783i
$909$	−20.0064			−0.663571
$910$		0			0
$911$	−42.2460			−1.39967			−0.699836	−	0.714304i	$-0.746743\pi$
$911$	−42.2460			−1.39967			−0.699836	+	0.714304i	$0.746743\pi$
$912$	18.9792	+	32.8729i	0.628464	+	1.08853i
$913$	−4.89924	−	1.31275i	−0.162141	−	0.0434456i
$914$	15.8811	−	27.5068i	0.525299	−	0.909845i
$915$		0			0
$916$	5.12191	+	19.1152i	0.169233	+	0.631585i
$917$	5.07539	+	2.93028i	0.167604	+	0.0967663i
$918$	−108.994			−3.59735
$919$	−51.0057	−	29.4481i	−1.68252	−	0.971405i	−0.959976	−	0.280082i	$-0.909638\pi$
$919$	−51.0057	−	29.4481i	−1.68252	−	0.971405i	−0.722546	−	0.691323i	$-0.757028\pi$
$920$		0			0
$921$	13.8853	−	51.8206i	0.457536	−	1.70755i
$922$	2.60426	−	2.60426i	0.0857667	−	0.0857667i
$923$	−12.6887	−	15.1687i	−0.417654	−	0.499284i
$924$			18.3376i			0.603261i
$925$		0			0
$926$	31.9067	+	55.2641i	1.04852	+	1.81609i
$927$	2.69409	+	10.0545i	0.0884854	+	0.330232i
$928$		−	16.0386i		−	0.526493i
$929$	13.3277	−	3.57114i	0.437267	−	0.117165i	−0.0334683	−	0.999440i	$-0.510655\pi$
$929$	13.3277	−	3.57114i	0.437267	−	0.117165i	0.470736	+	0.882274i	$0.343989\pi$
$930$		0			0
$931$	−8.35053	−	8.35053i	−0.273678	−	0.273678i
$932$	−0.0154563	+	0.00414150i	−0.000506288	+	0.000135659i
$933$	1.10869	−	4.13767i	0.0362967	−	0.135461i
$934$	−68.8958	−	18.4606i	−2.25434	−	0.604048i
$935$		0			0
$936$	43.5273	+	3.87499i	1.42273	+	0.126658i
$937$	8.81699	+	8.81699i	0.288038	+	0.288038i	0.836304	−	0.548266i	$-0.184712\pi$
$937$	8.81699	+	8.81699i	0.288038	+	0.288038i	−0.548266	+	0.836304i	$0.684712\pi$
$938$	2.79992	−	1.61654i	0.0914207	−	0.0527818i
$939$	78.1831	−	45.1390i	2.55141	−	1.47306i
$940$		0			0
$941$	−22.1697	+	22.1697i	−0.722711	+	0.722711i	−0.969157	−	0.246446i	$-0.920737\pi$
$941$	−22.1697	+	22.1697i	−0.722711	+	0.722711i	0.246446	+	0.969157i	$0.420737\pi$
$942$	−39.5342	+	68.4752i	−1.28809	+	2.23104i
$943$	32.4624	−	56.2265i	1.05712	−	1.83099i
$944$	−11.9707	+	11.9707i	−0.389614	+	0.389614i
$945$		0			0
$946$	31.0154	−	17.9068i	1.00840	−	0.582199i
$947$	−9.06381	+	5.23299i	−0.294534	+	0.170049i	−0.639985	−	0.768388i	$-0.721059\pi$
$947$	−9.06381	+	5.23299i	−0.294534	+	0.170049i	0.345451	+	0.938437i	$0.387726\pi$
$948$	−8.75023	−	8.75023i	−0.284194	−	0.284194i
$949$	−7.06329	+	3.28057i	−0.229284	+	0.106492i
$950$		0			0
$951$	110.246	+	29.5403i	3.57497	+	0.957911i
$952$	−2.31521	+	8.64046i	−0.0750362	+	0.280039i
$953$	10.9837	−	2.94307i	0.355796	−	0.0953353i	−0.0764935	−	0.997070i	$-0.524372\pi$
$953$	10.9837	−	2.94307i	0.355796	−	0.0953353i	0.432290	+	0.901735i	$0.357706\pi$
$954$	7.90533	+	7.90533i	0.255945	+	0.255945i
$955$		0			0
$956$	13.2178	−	3.54169i	0.427494	−	0.114547i
$957$		−	34.1648i		−	1.10439i
$958$	15.1378	+	56.4952i	0.489081	+	1.82528i
$959$	7.79856	+	13.5075i	0.251828	+	0.436180i
$960$		0			0
$961$			30.9031i			0.996875i
$962$	−38.4508	−	3.42306i	−1.23970	−	0.110364i
$963$	84.4983	−	84.4983i	2.72292	−	2.72292i
$964$	−6.36105	+	23.7398i	−0.204876	+	0.764606i
$965$		0			0
$966$	39.5396	+	22.8282i	1.27216	+	0.734485i
$967$	21.5436			0.692795			0.346398	−	0.938088i	$-0.387405\pi$
$967$	21.5436			0.692795			0.346398	+	0.938088i	$0.387405\pi$
$968$	3.36881	+	1.94498i	0.108278	+	0.0625141i
$969$	−8.00917	−	29.8906i	−0.257292	−	0.960226i
$970$		0			0
$971$	11.5450	−	19.9965i	0.370497	−	0.641719i	−0.619145	−	0.785276i	$-0.712521\pi$
$971$	11.5450	−	19.9965i	0.370497	−	0.641719i	0.989642	+	0.143557i	$0.0458541\pi$
$972$	−44.1720	−	11.8358i	−1.41682	−	0.379635i
$973$	−1.15896	−	2.00738i	−0.0371546	−	0.0643537i
$974$	36.9095			1.18266
$975$		0			0
$976$	−30.2811			−0.969275
$977$	3.36817	+	5.83384i	0.107757	+	0.186641i	0.914861	−	0.403768i	$-0.132300\pi$
$977$	3.36817	+	5.83384i	0.107757	+	0.186641i	−0.807104	+	0.590409i	$0.798966\pi$
$978$	−22.1310	−	5.92999i	−0.707672	−	0.189620i
$979$	2.07943	−	3.60167i	0.0664587	−	0.115110i
$980$		0			0
$981$	26.6905	+	99.6102i	0.852161	+	3.18031i
$982$	−35.9226	−	20.7399i	−1.14633	−	0.661837i
$983$	−12.0774			−0.385209			−0.192604	−	0.981276i	$-0.561693\pi$
$983$	−12.0774			−0.385209			−0.192604	+	0.981276i	$0.561693\pi$
$984$	50.8419	+	29.3536i	1.62078	+	0.935758i
$985$		0			0
$986$	−5.28867	+	19.7376i	−0.168426	+	0.628573i
$987$	16.2642	−	16.2642i	0.517694	−	0.517694i
$988$	−1.59308	−	9.11602i	−0.0506827	−	0.290019i
$989$		−	31.6691i		−	1.00702i
$990$		0			0
$991$	5.00080	+	8.66164i	0.158856	+	0.275146i	0.934456	−	0.356078i	$-0.115886\pi$
$991$	5.00080	+	8.66164i	0.158856	+	0.275146i	−0.775601	+	0.631224i	$0.782553\pi$
$992$	−0.452967	−	1.69050i	−0.0143817	−	0.0536733i
$993$		−	8.30749i		−	0.263630i
$994$	12.9676	−	3.47466i	0.411308	−	0.110210i
$995$		0			0
$996$	3.51607	+	3.51607i	0.111411	+	0.111411i
$997$	14.2508	−	3.81848i	0.451326	−	0.120932i	−0.0259937	−	0.999662i	$-0.508275\pi$
$997$	14.2508	−	3.81848i	0.451326	−	0.120932i	0.477320	+	0.878730i	$0.341608\pi$
$998$	11.7471	−	43.8406i	0.371847	−	1.38775i
$999$	−89.3428	−	23.9393i	−2.82668	−	0.757407i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.s.c.132.3	✓	40
5.2	odd	4		325.2.x.c.93.8	yes	40
5.3	odd	4		325.2.x.c.93.3	yes	40
5.4	even	2	inner	325.2.s.c.132.8	yes	40
13.7	odd	12		325.2.x.c.7.3	yes	40
65.7	even	12	inner	325.2.s.c.293.8	yes	40
65.33	even	12	inner	325.2.s.c.293.3	yes	40
65.59	odd	12		325.2.x.c.7.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.s.c.132.3	✓	40	1.1	even	1	trivial
325.2.s.c.132.8	yes	40	5.4	even	2	inner
325.2.s.c.293.3	yes	40	65.33	even	12	inner
325.2.s.c.293.8	yes	40	65.7	even	12	inner
325.2.x.c.7.3	yes	40	13.7	odd	12
325.2.x.c.7.8	yes	40	65.59	odd	12
325.2.x.c.93.3	yes	40	5.3	odd	4
325.2.x.c.93.8	yes	40	5.2	odd	4

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.s (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.880562 - 1.52518i) q^{2} +(3.15371 + 0.845033i) q^{3} +(-0.550780 + 0.953979i) q^{4} +(-1.48821 - 5.55407i) q^{6} +(1.20362 + 0.694909i) q^{7} -1.58226 q^{8} +(6.63370 + 3.82997i) q^{9} +(0.949498 - 3.54358i) q^{11} +(-2.54314 + 2.54314i) q^{12} +(-3.27006 + 1.51879i) q^{13} -2.44764i q^{14} +(2.49484 + 4.32119i) q^{16} +(-1.05282 - 3.92917i) q^{17} -13.4901i q^{18} +(2.25062 - 0.603051i) q^{19} +(3.20863 + 3.20863i) q^{21} +(-6.24068 + 1.67219i) q^{22} +(-1.47867 + 5.51848i) q^{23} +(-4.99000 - 1.33707i) q^{24} +(5.19592 + 3.65003i) q^{26} +(10.7583 + 10.7583i) q^{27} +(-1.32586 + 0.765484i) q^{28} +(2.47021 - 1.42618i) q^{29} +(0.220086 - 0.220086i) q^{31} +(2.81146 - 4.86960i) q^{32} +(5.98888 - 10.3730i) q^{33} +(-5.06561 + 5.06561i) q^{34} +(-7.30742 + 4.21894i) q^{36} +(-5.26488 + 3.03968i) q^{37} +(-2.90157 - 2.90157i) q^{38} +(-11.5962 + 2.02651i) q^{39} +(-10.9769 - 2.94124i) q^{41} +(2.06834 - 7.71914i) q^{42} +(-5.35430 + 1.43468i) q^{43} +(2.85753 + 2.85753i) q^{44} +(9.71874 - 2.60413i) q^{46} -5.06887i q^{47} +(4.21645 + 15.7360i) q^{48} +(-2.53420 - 4.38937i) q^{49} -13.2811i q^{51} +(0.352188 - 3.95609i) q^{52} +(-0.586010 + 0.586010i) q^{53} +(6.93496 - 25.8816i) q^{54} +(-1.90444 - 1.09953i) q^{56} +7.60737 q^{57} +(-4.35035 - 2.51168i) q^{58} +(0.878129 + 3.27722i) q^{59} +(-3.03437 + 5.25569i) q^{61} +(-0.529470 - 0.141871i) q^{62} +(5.32296 + 9.21963i) q^{63} +0.0766898 q^{64} -21.0943 q^{66} +(0.660446 + 1.14393i) q^{67} +(4.32821 + 1.15974i) q^{68} +(-9.32660 + 16.1541i) q^{69} +(1.41960 + 5.29800i) q^{71} +(-10.4963 - 6.06002i) q^{72} +2.15999 q^{73} +(9.27212 + 5.35326i) q^{74} +(-0.664297 + 2.47919i) q^{76} +(3.60529 - 3.60529i) q^{77} +(13.3020 + 15.9018i) q^{78} +3.44072i q^{79} +(13.3474 + 23.1184i) q^{81} +(5.17990 + 19.3316i) q^{82} -1.38257i q^{83} +(-4.82822 + 1.29372i) q^{84} +(6.90294 + 6.90294i) q^{86} +(8.99549 - 2.41033i) q^{87} +(-1.50236 + 5.60687i) q^{88} +(1.09501 + 0.293408i) q^{89} +(-4.99132 - 0.444348i) q^{91} +(-4.45010 - 4.45010i) q^{92} +(0.880067 - 0.508107i) q^{93} +(-7.73094 + 4.46346i) q^{94} +(12.9815 - 12.9815i) q^{96} +(-7.92101 + 13.7196i) q^{97} +(-4.46305 + 7.73023i) q^{98} +(19.8705 - 19.8705i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 24 q^{4} - 12 q^{6} + 24 q^{9} + 8 q^{11} - 32 q^{16} - 24 q^{19} + 32 q^{21} + 56 q^{24} + 76 q^{26} - 36 q^{29} + 8 q^{31} + 44 q^{34} - 60 q^{36} + 44 q^{39} - 52 q^{41} - 80 q^{44} - 60 q^{46}+ \cdots + 208 q^{99}+O(q^{100}) \) 40 * q - 24 * q^4 - 12 * q^6 + 24 * q^9 + 8 * q^11 - 32 * q^16 - 24 * q^19 + 32 * q^21 + 56 * q^24 + 76 * q^26 - 36 * q^29 + 8 * q^31 + 44 * q^34 - 60 * q^36 + 44 * q^39 - 52 * q^41 - 80 * q^44 - 60 * q^46 + 28 * q^49 - 68 * q^54 + 72 * q^56 - 72 * q^59 + 144 * q^64 + 24 * q^66 - 80 * q^69 - 52 * q^71 + 168 * q^74 + 8 * q^76 - 20 * q^81 - 248 * q^84 - 168 * q^86 + 60 * q^89 - 100 * q^91 - 156 * q^94 - 36 * q^96 + 208 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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