LMFDB - Embedded newform 975.2.k.d.343.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(307,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("975.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.k (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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			343.3
Character	$\chi$	$=$	975.343
Dual form			975.2.k.d.307.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.94332i q^{2} +(0.707107 + 0.707107i) q^{3} -1.77647 q^{4} +(1.37413 - 1.37413i) q^{6} -2.33552 q^{7} -0.434380i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q-1.94332i q^{2} +(0.707107 + 0.707107i) q^{3} -1.77647 q^{4} +(1.37413 - 1.37413i) q^{6} -2.33552 q^{7} -0.434380i q^{8} +1.00000i q^{9} +(-0.233447 - 0.233447i) q^{11} +(-1.25616 - 1.25616i) q^{12} +(3.58770 + 0.358340i) q^{13} +4.53865i q^{14} -4.39709 q^{16} +(-5.71657 - 5.71657i) q^{17} +1.94332 q^{18} +(-3.63852 - 3.63852i) q^{19} +(-1.65146 - 1.65146i) q^{21} +(-0.453661 + 0.453661i) q^{22} +(0.974048 - 0.974048i) q^{23} +(0.307153 - 0.307153i) q^{24} +(0.696369 - 6.97203i) q^{26} +(-0.707107 + 0.707107i) q^{27} +4.14899 q^{28} -9.59085i q^{29} +(3.43455 - 3.43455i) q^{31} +7.67617i q^{32} -0.330144i q^{33} +(-11.1091 + 11.1091i) q^{34} -1.77647i q^{36} +1.32880 q^{37} +(-7.07079 + 7.07079i) q^{38} +(2.28350 + 2.79027i) q^{39} +(-1.14586 + 1.14586i) q^{41} +(-3.20931 + 3.20931i) q^{42} +(-3.06448 + 3.06448i) q^{43} +(0.414712 + 0.414712i) q^{44} +(-1.89288 - 1.89288i) q^{46} +6.39859 q^{47} +(-3.10921 - 3.10921i) q^{48} -1.54535 q^{49} -8.08444i q^{51} +(-6.37346 - 0.636583i) q^{52} +(-2.64422 - 2.64422i) q^{53} +(1.37413 + 1.37413i) q^{54} +1.01450i q^{56} -5.14564i q^{57} -18.6380 q^{58} +(5.84154 - 5.84154i) q^{59} -6.24856 q^{61} +(-6.67441 - 6.67441i) q^{62} -2.33552i q^{63} +6.12304 q^{64} -0.641573 q^{66} +12.6687i q^{67} +(10.1553 + 10.1553i) q^{68} +1.37751 q^{69} +(-0.562923 + 0.562923i) q^{71} +0.434380 q^{72} +3.65149i q^{73} -2.58228i q^{74} +(6.46373 + 6.46373i) q^{76} +(0.545220 + 0.545220i) q^{77} +(5.42238 - 4.43756i) q^{78} -7.38140i q^{79} -1.00000 q^{81} +(2.22677 + 2.22677i) q^{82} +11.3338 q^{83} +(2.93378 + 2.93378i) q^{84} +(5.95524 + 5.95524i) q^{86} +(6.78175 - 6.78175i) q^{87} +(-0.101405 + 0.101405i) q^{88} +(-7.56761 + 7.56761i) q^{89} +(-8.37914 - 0.836911i) q^{91} +(-1.73037 + 1.73037i) q^{92} +4.85718 q^{93} -12.4345i q^{94} +(-5.42787 + 5.42787i) q^{96} -9.27392i q^{97} +3.00310i q^{98} +(0.233447 - 0.233447i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4}+O(q^{10}) $ 28 * q - 28 * q^4	$ 28 q - 28 q^{4} - 8 q^{11} - 8 q^{12} + 12 q^{13} + 28 q^{16} + 28 q^{17} + 4 q^{18} + 8 q^{21} + 32 q^{22} - 8 q^{23} - 16 q^{31} + 28 q^{34} - 32 q^{37} + 8 q^{39} + 4 q^{41} + 40 q^{44} - 16 q^{46} + 24 q^{47} + 16 q^{48} - 28 q^{49} - 52 q^{52} - 20 q^{53} + 8 q^{58} + 32 q^{59} + 8 q^{61} - 72 q^{62} - 28 q^{64} + 16 q^{66} - 60 q^{68} + 8 q^{69} + 40 q^{71} - 12 q^{72} - 40 q^{76} + 48 q^{77} - 8 q^{78} - 28 q^{81} - 4 q^{82} + 104 q^{83} - 32 q^{84} + 16 q^{86} + 24 q^{87} - 72 q^{88} - 36 q^{89} - 56 q^{91} + 32 q^{92} + 8 q^{99}+O(q^{100}) $ 28 * q - 28 * q^4 - 8 * q^11 - 8 * q^12 + 12 * q^13 + 28 * q^16 + 28 * q^17 + 4 * q^18 + 8 * q^21 + 32 * q^22 - 8 * q^23 - 16 * q^31 + 28 * q^34 - 32 * q^37 + 8 * q^39 + 4 * q^41 + 40 * q^44 - 16 * q^46 + 24 * q^47 + 16 * q^48 - 28 * q^49 - 52 * q^52 - 20 * q^53 + 8 * q^58 + 32 * q^59 + 8 * q^61 - 72 * q^62 - 28 * q^64 + 16 * q^66 - 60 * q^68 + 8 * q^69 + 40 * q^71 - 12 * q^72 - 40 * q^76 + 48 * q^77 - 8 * q^78 - 28 * q^81 - 4 * q^82 + 104 * q^83 - 32 * q^84 + 16 * q^86 + 24 * q^87 - 72 * q^88 - 36 * q^89 - 56 * q^91 + 32 * q^92 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	1.94332i		−	1.37413i	−0.726595	−	0.687066i	$-0.758898\pi$
$2$		−	1.94332i		−	1.37413i	0.726595	−	0.687066i	$-0.241102\pi$
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−1.77647			−0.888237
$5$		0			0
$5$		0			0
$6$	1.37413	−	1.37413i	0.560987	−	0.560987i
$7$	−2.33552			−0.882743			−0.441372	−	0.897324i	$-0.645508\pi$
$7$	−2.33552			−0.882743			−0.441372	+	0.897324i	$0.645508\pi$
$8$		−	0.434380i		−	0.153577i
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−0.233447	−	0.233447i	−0.0703869	−	0.0703869i	0.671037	−	0.741424i	$-0.265849\pi$
$11$	−0.233447	−	0.233447i	−0.0703869	−	0.0703869i	−0.741424	+	0.671037i	$0.765849\pi$
$12$	−1.25616	−	1.25616i	−0.362621	−	0.362621i
$13$	3.58770	+	0.358340i	0.995049	+	0.0993858i
$13$	3.58770	+	0.358340i	0.995049	+	0.0993858i
$14$			4.53865i			1.21301i
$15$		0			0
$16$	−4.39709			−1.09927
$17$	−5.71657	−	5.71657i	−1.38647	−	1.38647i	−0.832608	−	0.553863i	$-0.813153\pi$
$17$	−5.71657	−	5.71657i	−1.38647	−	1.38647i	−0.553863	−	0.832608i	$-0.686847\pi$
$18$	1.94332			0.458044
$19$	−3.63852	−	3.63852i	−0.834733	−	0.834733i	0.153427	−	0.988160i	$-0.450969\pi$
$19$	−3.63852	−	3.63852i	−0.834733	−	0.834733i	−0.988160	+	0.153427i	$0.950969\pi$
$20$		0			0
$21$	−1.65146	−	1.65146i	−0.360378	−	0.360378i
$22$	−0.453661	+	0.453661i	−0.0967208	+	0.0967208i
$23$	0.974048	−	0.974048i	0.203103	−	0.203103i	−0.598225	−	0.801328i	$-0.704127\pi$
$23$	0.974048	−	0.974048i	0.203103	−	0.203103i	0.801328	+	0.598225i	$0.204127\pi$
$24$	0.307153	−	0.307153i	0.0626974	−	0.0626974i
$25$		0			0
$26$	0.696369	−	6.97203i	0.136569	−	1.36733i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	4.14899			0.784086
$29$		−	9.59085i		−	1.78098i	−0.455007	−	0.890488i	$-0.650363\pi$
$29$		−	9.59085i		−	1.78098i	0.455007	−	0.890488i	$-0.349637\pi$
$30$		0			0
$31$	3.43455	−	3.43455i	0.616863	−	0.616863i	−0.327862	−	0.944725i	$-0.606328\pi$
$31$	3.43455	−	3.43455i	0.616863	−	0.616863i	0.944725	+	0.327862i	$0.106328\pi$
$32$			7.67617i			1.35697i
$33$		−	0.330144i		−	0.0574706i
$34$	−11.1091	+	11.1091i	−1.90519	+	1.90519i
$35$		0			0
$36$		−	1.77647i		−	0.296079i
$37$	1.32880			0.218454			0.109227	−	0.994017i	$-0.465163\pi$
$37$	1.32880			0.218454			0.109227	+	0.994017i	$0.465163\pi$
$38$	−7.07079	+	7.07079i	−1.14703	+	1.14703i
$39$	2.28350	+	2.79027i	0.365653	+	0.446801i
$40$		0			0
$41$	−1.14586	+	1.14586i	−0.178953	+	0.178953i	−0.790899	−	0.611946i	$-0.790387\pi$
$41$	−1.14586	+	1.14586i	−0.178953	+	0.178953i	0.611946	+	0.790899i	$0.290387\pi$
$42$	−3.20931	+	3.20931i	−0.495207	+	0.495207i
$43$	−3.06448	+	3.06448i	−0.467328	+	0.467328i	−0.901048	−	0.433720i	$-0.857201\pi$
$43$	−3.06448	+	3.06448i	−0.467328	+	0.467328i	0.433720	+	0.901048i	$0.357201\pi$
$44$	0.414712	+	0.414712i	0.0625202	+	0.0625202i
$45$		0			0
$46$	−1.89288	−	1.89288i	−0.279090	−	0.279090i
$47$	6.39859			0.933330			0.466665	−	0.884434i	$-0.345455\pi$
$47$	6.39859			0.933330			0.466665	+	0.884434i	$0.345455\pi$
$48$	−3.10921	−	3.10921i	−0.448776	−	0.448776i
$49$	−1.54535			−0.220764
$50$		0			0
$51$		−	8.08444i		−	1.13205i
$52$	−6.37346	−	0.636583i	−0.883840	−	0.0882781i
$53$	−2.64422	−	2.64422i	−0.363211	−	0.363211i	0.501783	−	0.864994i	$-0.332678\pi$
$53$	−2.64422	−	2.64422i	−0.363211	−	0.363211i	−0.864994	+	0.501783i	$0.832678\pi$
$54$	1.37413	+	1.37413i	0.186996	+	0.186996i
$55$		0			0
$56$			1.01450i			0.135569i
$57$		−	5.14564i		−	0.681557i
$58$	−18.6380			−2.44729
$59$	5.84154	−	5.84154i	0.760503	−	0.760503i	−0.215910	−	0.976413i	$-0.569272\pi$
$59$	5.84154	−	5.84154i	0.760503	−	0.760503i	0.976413	+	0.215910i	$0.0692718\pi$
$60$		0			0
$61$	−6.24856			−0.800047			−0.400023	−	0.916505i	$-0.630998\pi$
$61$	−6.24856			−0.800047			−0.400023	+	0.916505i	$0.630998\pi$
$62$	−6.67441	−	6.67441i	−0.847651	−	0.847651i
$63$		−	2.33552i		−	0.294248i
$64$	6.12304			0.765380
$65$		0			0
$66$	−0.641573			−0.0789722
$67$			12.6687i			1.54773i	0.633349	+	0.773867i	$0.281680\pi$
$67$			12.6687i			1.54773i	−0.633349	+	0.773867i	$0.718320\pi$
$68$	10.1553	+	10.1553i	1.23152	+	1.23152i
$69$	1.37751			0.165833
$70$		0			0
$71$	−0.562923	+	0.562923i	−0.0668066	+	0.0668066i	−0.739721	−	0.672914i	$-0.765042\pi$
$71$	−0.562923	+	0.562923i	−0.0668066	+	0.0668066i	0.672914	+	0.739721i	$0.265042\pi$
$72$	0.434380			0.0511922
$73$			3.65149i			0.427375i	0.976902	+	0.213688i	$0.0685474\pi$
$73$			3.65149i			0.427375i	−0.976902	+	0.213688i	$0.931453\pi$
$74$		−	2.58228i		−	0.300184i
$75$		0			0
$76$	6.46373	+	6.46373i	0.741441	+	0.741441i
$77$	0.545220	+	0.545220i	0.0621335	+	0.0621335i
$78$	5.42238	−	4.43756i	0.613963	−	0.502455i
$79$		−	7.38140i		−	0.830472i	−0.909714	−	0.415236i	$-0.863699\pi$
$79$		−	7.38140i		−	0.830472i	0.909714	−	0.415236i	$-0.136301\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	2.22677	+	2.22677i	0.245905	+	0.245905i
$83$	11.3338			1.24405			0.622025	−	0.782997i	$-0.286310\pi$
$83$	11.3338			1.24405			0.622025	+	0.782997i	$0.286310\pi$
$84$	2.93378	+	2.93378i	0.320102	+	0.320102i
$85$		0			0
$86$	5.95524	+	5.95524i	0.642171	+	0.642171i
$87$	6.78175	−	6.78175i	0.727080	−	0.727080i
$88$	−0.101405	+	0.101405i	−0.0108098	+	0.0108098i
$89$	−7.56761	+	7.56761i	−0.802165	+	0.802165i	−0.983434	−	0.181269i	$-0.941980\pi$
$89$	−7.56761	+	7.56761i	−0.802165	+	0.802165i	0.181269	+	0.983434i	$0.441980\pi$
$90$		0			0
$91$	−8.37914	−	0.836911i	−0.878373	−	0.0877321i
$92$	−1.73037	+	1.73037i	−0.180404	+	0.180404i
$93$	4.85718			0.503667
$94$		−	12.4345i		−	1.28252i
$95$		0			0
$96$	−5.42787	+	5.42787i	−0.553980	+	0.553980i
$97$		−	9.27392i		−	0.941624i	−0.882234	−	0.470812i	$-0.843961\pi$
$97$		−	9.27392i		−	0.941624i	0.882234	−	0.470812i	$-0.156039\pi$
$98$			3.00310i			0.303359i
$99$	0.233447	−	0.233447i	0.0234623	−	0.0234623i
$100$		0			0
$101$			12.3141i			1.22530i	0.790354	+	0.612651i	$0.209897\pi$
$101$			12.3141i			1.22530i	−0.790354	+	0.612651i	$0.790103\pi$
$102$	−15.7106			−1.55558
$103$	−6.85102	+	6.85102i	−0.675051	+	0.675051i	−0.958876	−	0.283825i	$-0.908397\pi$
$103$	−6.85102	+	6.85102i	−0.675051	+	0.675051i	0.283825	+	0.958876i	$0.408397\pi$
$104$	0.155656	−	1.55843i	0.0152633	−	0.152816i
$105$		0			0
$106$	−5.13854	+	5.13854i	−0.499100	+	0.499100i
$107$	7.44452	−	7.44452i	0.719689	−	0.719689i	−0.248853	−	0.968541i	$-0.580053\pi$
$107$	7.44452	−	7.44452i	0.719689	−	0.719689i	0.968541	+	0.248853i	$0.0800535\pi$
$108$	1.25616	−	1.25616i	0.120874	−	0.120874i
$109$	7.05924	+	7.05924i	0.676152	+	0.676152i	0.959127	−	0.282975i	$-0.0913213\pi$
$109$	7.05924	+	7.05924i	0.676152	+	0.676152i	−0.282975	+	0.959127i	$0.591321\pi$
$110$		0			0
$111$	0.939604	+	0.939604i	0.0891833	+	0.0891833i
$112$	10.2695			0.970375
$113$	−2.50383	−	2.50383i	−0.235541	−	0.235541i	0.579460	−	0.815001i	$-0.303264\pi$
$113$	−2.50383	−	2.50383i	−0.235541	−	0.235541i	−0.815001	+	0.579460i	$0.803264\pi$
$114$	−9.99960			−0.936548
$115$		0			0
$116$			17.0379i			1.58193i
$117$	−0.358340	+	3.58770i	−0.0331286	+	0.331683i
$118$	−11.3519	−	11.3519i	−1.04503	−	1.04503i
$119$	13.3511	+	13.3511i	1.22390	+	1.22390i
$120$		0			0
$121$		−	10.8910i		−	0.990091i
$122$			12.1429i			1.09937i
$123$	−1.62049			−0.146115
$124$	−6.10139	+	6.10139i	−0.547921	+	0.547921i
$125$		0			0
$126$	−4.53865			−0.404335
$127$	−3.70439	−	3.70439i	−0.328712	−	0.328712i	0.523385	−	0.852096i	$-0.324669\pi$
$127$	−3.70439	−	3.70439i	−0.328712	−	0.328712i	−0.852096	+	0.523385i	$0.824669\pi$
$128$			3.45334i			0.305235i
$129$	−4.33382			−0.381572
$130$		0			0
$131$	8.33540			0.728267			0.364134	−	0.931347i	$-0.381365\pi$
$131$	8.33540			0.728267			0.364134	+	0.931347i	$0.381365\pi$
$132$			0.586492i			0.0510476i
$133$	8.49783	+	8.49783i	0.736855	+	0.736855i
$134$	24.6194			2.12679
$135$		0			0
$136$	−2.48316	+	2.48316i	−0.212929	+	0.212929i
$137$	6.36241			0.543577			0.271789	−	0.962357i	$-0.412385\pi$
$137$	6.36241			0.543577			0.271789	+	0.962357i	$0.412385\pi$
$138$		−	2.67694i		−	0.227876i
$139$			9.32196i			0.790679i	0.918535	+	0.395339i	$0.129373\pi$
$139$			9.32196i			0.790679i	−0.918535	+	0.395339i	$0.870627\pi$
$140$		0			0
$141$	4.52448	+	4.52448i	0.381030	+	0.381030i
$142$	1.09394	+	1.09394i	0.0918011	+	0.0918011i
$143$	−0.753884	−	0.921191i	−0.0630429	−	0.0770338i
$144$		−	4.39709i		−	0.366424i
$145$		0			0
$146$	7.09600			0.587270
$147$	−1.09273	−	1.09273i	−0.0901266	−	0.0901266i
$148$	−2.36058			−0.194039
$149$	1.23267	+	1.23267i	0.100984	+	0.100984i	0.755794	−	0.654810i	$-0.227251\pi$
$149$	1.23267	+	1.23267i	0.100984	+	0.100984i	−0.654810	+	0.755794i	$0.727251\pi$
$150$		0			0
$151$	8.97344	+	8.97344i	0.730248	+	0.730248i	0.970669	−	0.240421i	$-0.0772854\pi$
$151$	8.97344	+	8.97344i	0.730248	+	0.730248i	−0.240421	+	0.970669i	$0.577285\pi$
$152$	−1.58050	+	1.58050i	−0.128195	+	0.128195i
$153$	5.71657	−	5.71657i	0.462157	−	0.462157i
$154$	1.05953	−	1.05953i	0.0853796	−	0.0853796i
$155$		0			0
$156$	−4.05658	−	4.95685i	−0.324787	−	0.396865i
$157$	−9.19439	+	9.19439i	−0.733792	+	0.733792i	−0.971369	−	0.237576i	$-0.923647\pi$
$157$	−9.19439	+	9.19439i	−0.733792	+	0.733792i	0.237576	+	0.971369i	$0.423647\pi$
$158$	−14.3444			−1.14118
$159$		−	3.73949i		−	0.296560i
$160$		0			0
$161$	−2.27491	+	2.27491i	−0.179288	+	0.179288i
$162$			1.94332i			0.152681i
$163$		−	12.4311i		−	0.973682i	−0.873491	−	0.486841i	$-0.838149\pi$
$163$		−	12.4311i		−	0.973682i	0.873491	−	0.486841i	$-0.161851\pi$
$164$	2.03559	−	2.03559i	0.158953	−	0.158953i
$165$		0			0
$166$		−	22.0252i		−	1.70949i
$167$	23.9518			1.85345			0.926724	−	0.375744i	$-0.122613\pi$
$167$	23.9518			1.85345			0.926724	+	0.375744i	$0.122613\pi$
$168$	−0.717362	+	0.717362i	−0.0553457	+	0.0553457i
$169$	12.7432	+	2.57124i	0.980245	+	0.197787i
$170$		0			0
$171$	3.63852	−	3.63852i	0.278244	−	0.278244i
$172$	5.44397	−	5.44397i	0.415098	−	0.415098i
$173$	9.25151	−	9.25151i	0.703380	−	0.703380i	−0.261755	−	0.965134i	$-0.584301\pi$
$173$	9.25151	−	9.25151i	0.703380	−	0.703380i	0.965134	+	0.261755i	$0.0843012\pi$
$174$	−13.1791	−	13.1791i	−0.999104	−	0.999104i
$175$		0			0
$176$	1.02649	+	1.02649i	0.0773743	+	0.0773743i
$177$	8.26118			0.620948
$178$	14.7063	+	14.7063i	1.10228	+	1.10228i
$179$	5.00257			0.373910			0.186955	−	0.982368i	$-0.440138\pi$
$179$	5.00257			0.373910			0.186955	+	0.982368i	$0.440138\pi$
$180$		0			0
$181$			5.69556i			0.423348i	0.977340	+	0.211674i	$0.0678914\pi$
$181$			5.69556i			0.423348i	−0.977340	+	0.211674i	$0.932109\pi$
$182$	−1.62638	+	16.2833i	−0.120555	+	1.20700i
$183$	−4.41840	−	4.41840i	−0.326618	−	0.326618i
$184$	−0.423107	−	0.423107i	−0.0311919	−	0.0311919i
$185$		0			0
$186$		−	9.43904i		−	0.692104i
$187$			2.66903i			0.195179i
$188$	−11.3669			−0.829018
$189$	1.65146	−	1.65146i	0.120126	−	0.120126i
$190$		0			0
$191$	16.2034			1.17244			0.586218	−	0.810153i	$-0.300616\pi$
$191$	16.2034			1.17244			0.586218	+	0.810153i	$0.300616\pi$
$192$	4.32964	+	4.32964i	0.312465	+	0.312465i
$193$		−	6.54564i		−	0.471165i	−0.971854	−	0.235583i	$-0.924300\pi$
$193$		−	6.54564i		−	0.471165i	0.971854	−	0.235583i	$-0.0756998\pi$
$194$	−18.0221			−1.29391
$195$		0			0
$196$	2.74527			0.196091
$197$		−	15.5862i		−	1.11047i	−0.831694	−	0.555234i	$-0.812629\pi$
$197$		−	15.5862i		−	1.11047i	0.831694	−	0.555234i	$-0.187371\pi$
$198$	−0.453661	−	0.453661i	−0.0322403	−	0.0322403i
$199$	−19.6618			−1.39379			−0.696893	−	0.717175i	$-0.745435\pi$
$199$	−19.6618			−1.39379			−0.696893	+	0.717175i	$0.745435\pi$
$200$		0			0
$201$	−8.95815	+	8.95815i	−0.631859	+	0.631859i
$202$	23.9302			1.68372
$203$			22.3996i			1.57214i
$204$			14.3618i			1.00553i
$205$		0			0
$206$	13.3137	+	13.3137i	0.927609	+	0.927609i
$207$	0.974048	+	0.974048i	0.0677010	+	0.0677010i
$208$	−15.7754	−	1.57565i	−1.09383	−	0.109252i
$209$			1.69880i			0.117508i
$210$		0			0
$211$	8.07359			0.555809			0.277904	−	0.960609i	$-0.410360\pi$
$211$	8.07359			0.555809			0.277904	+	0.960609i	$0.410360\pi$
$212$	4.69738	+	4.69738i	0.322618	+	0.322618i
$213$	−0.796093			−0.0545474
$214$	−14.4670	−	14.4670i	−0.988947	−	0.988947i
$215$		0			0
$216$	0.307153	+	0.307153i	0.0208991	+	0.0208991i
$217$	−8.02145	+	8.02145i	−0.544532	+	0.544532i
$218$	13.7183	−	13.7183i	0.929122	−	0.929122i
$219$	−2.58200	+	2.58200i	−0.174475	+	0.174475i
$220$		0			0
$221$	−18.4608	−	22.5578i	−1.24181	−	1.51740i
$222$	1.82595	−	1.82595i	0.122550	−	0.122550i
$223$	14.8348			0.993413			0.496706	−	0.867919i	$-0.334543\pi$
$223$	14.8348			0.993413			0.496706	+	0.867919i	$0.334543\pi$
$224$		−	17.9278i		−	1.19785i
$225$		0			0
$226$	−4.86574	+	4.86574i	−0.323664	+	0.323664i
$227$			0.417274i			0.0276954i	0.999904	+	0.0138477i	$0.00440800\pi$
$227$			0.417274i			0.0276954i	−0.999904	+	0.0138477i	$0.995592\pi$
$228$			9.14110i			0.605384i
$229$	12.8346	−	12.8346i	0.848135	−	0.848135i	−0.141765	−	0.989900i	$-0.545278\pi$
$229$	12.8346	−	12.8346i	0.848135	−	0.848135i	0.989900	+	0.141765i	$0.0452778\pi$
$230$		0			0
$231$			0.771057i			0.0507318i
$232$	−4.16607			−0.273516
$233$	−8.13574	+	8.13574i	−0.532990	+	0.532990i	−0.921461	−	0.388471i	$-0.873003\pi$
$233$	−8.13574	+	8.13574i	−0.532990	+	0.532990i	0.388471	+	0.921461i	$0.373003\pi$
$234$	6.97203	+	0.696369i	0.455776	+	0.0455230i
$235$		0			0
$236$	−10.3773	+	10.3773i	−0.675507	+	0.675507i
$237$	5.21944	−	5.21944i	0.339039	−	0.339039i
$238$	25.9455	−	25.9455i	1.68180	−	1.68180i
$239$	−14.5707	−	14.5707i	−0.942501	−	0.942501i	0.0559333	−	0.998435i	$-0.482187\pi$
$239$	−14.5707	−	14.5707i	−0.942501	−	0.942501i	−0.998435	+	0.0559333i	$0.982187\pi$
$240$		0			0
$241$	−9.02552	−	9.02552i	−0.581385	−	0.581385i	0.353899	−	0.935284i	$-0.384856\pi$
$241$	−9.02552	−	9.02552i	−0.581385	−	0.581385i	−0.935284	+	0.353899i	$0.884856\pi$
$242$	−21.1647			−1.36052
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	11.1004			0.710631
$245$		0			0
$246$			3.14912i			0.200781i
$247$	−11.7501	−	14.3577i	−0.747640	−	0.913561i
$248$	−1.49190	−	1.49190i	−0.0947357	−	0.0947357i
$249$	8.01423	+	8.01423i	0.507881	+	0.507881i
$250$		0			0
$251$		−	6.58691i		−	0.415762i	−0.978154	−	0.207881i	$-0.933343\pi$
$251$		−	6.58691i		−	0.415762i	0.978154	−	0.207881i	$-0.0666567\pi$
$252$			4.14899i			0.261362i
$253$	−0.454777			−0.0285916
$254$	−7.19881	+	7.19881i	−0.451693	+	0.451693i
$255$		0			0
$256$	18.9570			1.18481
$257$	−12.4943	−	12.4943i	−0.779371	−	0.779371i	0.200353	−	0.979724i	$-0.435791\pi$
$257$	−12.4943	−	12.4943i	−0.779371	−	0.779371i	−0.979724	+	0.200353i	$0.935791\pi$
$258$			8.42199i			0.524330i
$259$	−3.10344			−0.192838
$260$		0			0
$261$	9.59085			0.593659
$262$		−	16.1983i		−	1.00073i
$263$	−17.8119	−	17.8119i	−1.09833	−	1.09833i	−0.994607	−	0.103720i	$-0.966925\pi$
$263$	−17.8119	−	17.8119i	−1.09833	−	1.09833i	−0.103720	−	0.994607i	$-0.533075\pi$
$264$	−0.143408			−0.00882614
$265$		0			0
$266$	16.5140	−	16.5140i	1.01254	−	1.01254i
$267$	−10.7022			−0.654965
$268$		−	22.5057i		−	1.37475i
$269$		−	24.0742i		−	1.46783i	−0.679241	−	0.733916i	$-0.737691\pi$
$269$		−	24.0742i		−	1.46783i	0.679241	−	0.733916i	$-0.262309\pi$
$270$		0			0
$271$	−4.18975	−	4.18975i	−0.254509	−	0.254509i	0.568307	−	0.822816i	$-0.307599\pi$
$271$	−4.18975	−	4.18975i	−0.254509	−	0.254509i	−0.822816	+	0.568307i	$0.807599\pi$
$272$	25.1362	+	25.1362i	1.52411	+	1.52411i
$273$	−5.33316	−	6.51673i	−0.322778	−	0.394411i
$274$		−	12.3642i		−	0.746947i
$275$		0			0
$276$	−2.44711			−0.147299
$277$	−10.8816	−	10.8816i	−0.653810	−	0.653810i	0.300098	−	0.953908i	$-0.402980\pi$
$277$	−10.8816	−	10.8816i	−0.653810	−	0.653810i	−0.953908	+	0.300098i	$0.902980\pi$
$278$	18.1155			1.08650
$279$	3.43455	+	3.43455i	0.205621	+	0.205621i
$280$		0			0
$281$	−0.342678	−	0.342678i	−0.0204424	−	0.0204424i	0.696812	−	0.717254i	$-0.254601\pi$
$281$	−0.342678	−	0.342678i	−0.0204424	−	0.0204424i	−0.717254	+	0.696812i	$0.754601\pi$
$282$	8.79250	−	8.79250i	0.523586	−	0.523586i
$283$	18.2779	−	18.2779i	1.08651	−	1.08651i	0.0906253	−	0.995885i	$-0.471113\pi$
$283$	18.2779	−	18.2779i	1.08651	−	1.08651i	0.995885	−	0.0906253i	$-0.0288866\pi$
$284$	1.00002	−	1.00002i	0.0593402	−	0.0593402i
$285$		0			0
$286$	−1.79016	+	1.46503i	−0.105855	+	0.0866293i
$287$	2.67618	−	2.67618i	0.157970	−	0.157970i
$288$	−7.67617			−0.452322
$289$			48.3582i			2.84460i
$290$		0			0
$291$	6.55765	−	6.55765i	0.384416	−	0.384416i
$292$		−	6.48679i		−	0.379610i
$293$		−	13.8013i		−	0.806282i	−0.915138	−	0.403141i	$-0.867918\pi$
$293$		−	13.8013i		−	0.806282i	0.915138	−	0.403141i	$-0.132082\pi$
$294$	−2.12351	+	2.12351i	−0.123846	+	0.123846i
$295$		0			0
$296$		−	0.577205i		−	0.0335493i
$297$	0.330144			0.0191569
$298$	2.39547	−	2.39547i	0.138766	−	0.138766i
$299$	3.84363	−	3.14555i	0.222283	−	0.181912i
$300$		0			0
$301$	7.15714	−	7.15714i	0.412531	−	0.412531i
$302$	17.4382	−	17.4382i	1.00346	−	1.00346i
$303$	−8.70740	+	8.70740i	−0.500227	+	0.500227i
$304$	15.9989	+	15.9989i	0.917598	+	0.917598i
$305$		0			0
$306$	−11.1091	−	11.1091i	−0.635064	−	0.635064i
$307$	23.3385			1.33200			0.666000	−	0.745952i	$-0.268005\pi$
$307$	23.3385			1.33200			0.666000	+	0.745952i	$0.268005\pi$
$308$	−0.968569	−	0.968569i	−0.0551893	−	0.0551893i
$309$	−9.68881			−0.551177
$310$		0			0
$311$			27.6379i			1.56720i	0.621265	+	0.783601i	$0.286619\pi$
$311$			27.6379i			1.56720i	−0.621265	+	0.783601i	$0.713381\pi$
$312$	1.21204	−	0.991908i	0.0686182	−	0.0561557i
$313$	−2.26616	−	2.26616i	−0.128091	−	0.128091i	0.640155	−	0.768246i	$-0.278870\pi$
$313$	−2.26616	−	2.26616i	−0.128091	−	0.128091i	−0.768246	+	0.640155i	$0.778870\pi$
$314$	17.8676	+	17.8676i	1.00833	+	1.00833i
$315$		0			0
$316$			13.1129i			0.737656i
$317$			33.4912i			1.88105i	0.339722	+	0.940526i	$0.389667\pi$
$317$			33.4912i			1.88105i	−0.339722	+	0.940526i	$0.610333\pi$
$318$	−7.26700			−0.407513
$319$	−2.23895	+	2.23895i	−0.125357	+	0.125357i
$320$		0			0
$321$	10.5281			0.587623
$322$	4.42086	+	4.42086i	0.246365	+	0.246365i
$323$			41.5996i			2.31467i
$324$	1.77647			0.0986930
$325$		0			0
$326$	−24.1576			−1.33797
$327$			9.98327i			0.552076i
$328$	0.497738	+	0.497738i	0.0274830	+	0.0274830i
$329$	−14.9440			−0.823891
$330$		0			0
$331$	−12.7870	+	12.7870i	−0.702838	+	0.702838i	−0.965019	−	0.262181i	$-0.915558\pi$
$331$	−12.7870	+	12.7870i	−0.702838	+	0.702838i	0.262181	+	0.965019i	$0.415558\pi$
$332$	−20.1343			−1.10501
$333$			1.32880i			0.0728178i
$334$		−	46.5459i		−	2.54688i
$335$		0			0
$336$	7.26162	+	7.26162i	0.396154	+	0.396154i
$337$	0.301897	+	0.301897i	0.0164454	+	0.0164454i	0.715282	−	0.698836i	$-0.246298\pi$
$337$	0.301897	+	0.301897i	0.0164454	+	0.0164454i	−0.698836	+	0.715282i	$0.746298\pi$
$338$	4.99672	−	24.7640i	0.271786	−	1.34699i
$339$		−	3.54096i		−	0.192318i
$340$		0			0
$341$	−1.60357			−0.0868381
$342$	−7.07079	−	7.07079i	−0.382344	−	0.382344i
$343$	19.9578			1.07762
$344$	1.33115	+	1.33115i	0.0717707	+	0.0717707i
$345$		0			0
$346$	−17.9786	−	17.9786i	−0.966536	−	0.966536i
$347$	−0.152124	+	0.152124i	−0.00816647	+	0.00816647i	−0.711178	−	0.703012i	$-0.751838\pi$
$347$	−0.152124	+	0.152124i	−0.00816647	+	0.00816647i	0.703012	+	0.711178i	$0.251838\pi$
$348$	−12.0476	+	12.0476i	−0.645820	+	0.645820i
$349$	3.10267	−	3.10267i	0.166082	−	0.166082i	−0.619173	−	0.785255i	$-0.712532\pi$
$349$	3.10267	−	3.10267i	0.166082	−	0.166082i	0.785255	+	0.619173i	$0.212532\pi$
$350$		0			0
$351$	−2.79027	+	2.28350i	−0.148934	+	0.121884i
$352$	1.79198	−	1.79198i	0.0955127	−	0.0955127i
$353$	16.5017			0.878297			0.439149	−	0.898414i	$-0.355280\pi$
$353$	16.5017			0.878297			0.439149	+	0.898414i	$0.355280\pi$
$354$		−	16.0541i		−	0.853265i
$355$		0			0
$356$	13.4437	−	13.4437i	0.712513	−	0.712513i
$357$			18.8814i			0.999308i
$358$		−	9.72158i		−	0.513801i
$359$	−19.9727	+	19.9727i	−1.05412	+	1.05412i	−0.0556708	+	0.998449i	$0.517730\pi$
$359$	−19.9727	+	19.9727i	−1.05412	+	1.05412i	−0.998449	+	0.0556708i	$0.982270\pi$
$360$		0			0
$361$			7.47761i			0.393558i
$362$	11.0683			0.581735
$363$	7.70110	−	7.70110i	0.404203	−	0.404203i
$364$	14.8853	+	1.48675i	0.780204	+	0.0779269i
$365$		0			0
$366$	−8.58635	+	8.58635i	−0.448816	+	0.448816i
$367$	−26.1777	+	26.1777i	−1.36646	+	1.36646i	−0.501040	+	0.865424i	$0.667049\pi$
$367$	−26.1777	+	26.1777i	−1.36646	+	1.36646i	−0.865424	+	0.501040i	$0.832951\pi$
$368$	−4.28297	+	4.28297i	−0.223265	+	0.223265i
$369$	−1.14586	−	1.14586i	−0.0596510	−	0.0596510i
$370$		0			0
$371$	6.17562	+	6.17562i	0.320622	+	0.320622i
$372$	−8.62866			−0.447375
$373$	22.7942	+	22.7942i	1.18024	+	1.18024i	0.979682	+	0.200556i	$0.0642748\pi$
$373$	22.7942	+	22.7942i	1.18024	+	1.18024i	0.200556	+	0.979682i	$0.435725\pi$
$374$	5.18676			0.268201
$375$		0			0
$376$		−	2.77942i		−	0.143338i
$377$	3.43679	−	34.4091i	0.177004	−	1.77216i
$378$	−3.20931	−	3.20931i	−0.165069	−	0.165069i
$379$	23.1221	+	23.1221i	1.18770	+	1.18770i	0.977700	+	0.210004i	$0.0673477\pi$
$379$	23.1221	+	23.1221i	1.18770	+	1.18770i	0.210004	+	0.977700i	$0.432652\pi$
$380$		0			0
$381$		−	5.23880i		−	0.268392i
$382$		−	31.4883i		−	1.61108i
$383$	−16.7647			−0.856636			−0.428318	−	0.903628i	$-0.640894\pi$
$383$	−16.7647			−0.856636			−0.428318	+	0.903628i	$0.640894\pi$
$384$	−2.44188	+	2.44188i	−0.124612	+	0.124612i
$385$		0			0
$386$	−12.7202			−0.647443
$387$	−3.06448	−	3.06448i	−0.155776	−	0.155776i
$388$			16.4749i			0.836385i
$389$	0.398160			0.0201875			0.0100938	−	0.999949i	$-0.496787\pi$
$389$	0.398160			0.0201875			0.0100938	+	0.999949i	$0.496787\pi$
$390$		0			0
$391$	−11.1364			−0.563193
$392$			0.671269i			0.0339042i
$393$	5.89402	+	5.89402i	0.297314	+	0.297314i
$394$	−30.2888			−1.52593
$395$		0			0
$396$	−0.414712	+	0.414712i	−0.0208401	+	0.0208401i
$397$	−6.56895			−0.329686			−0.164843	−	0.986320i	$-0.552712\pi$
$397$	−6.56895			−0.329686			−0.164843	+	0.986320i	$0.552712\pi$
$398$			38.2090i			1.91525i
$399$			12.0177i			0.601640i
$400$		0			0
$401$	−9.58776	−	9.58776i	−0.478790	−	0.478790i	0.425954	−	0.904745i	$-0.359938\pi$
$401$	−9.58776	−	9.58776i	−0.478790	−	0.478790i	−0.904745	+	0.425954i	$0.859938\pi$
$402$	17.4085	+	17.4085i	0.868258	+	0.868258i
$403$	13.5529	−	11.0914i	0.675116	−	0.552502i
$404$		−	21.8757i		−	1.08836i
$405$		0			0
$406$	43.5295			2.16033
$407$	−0.310204	−	0.310204i	−0.0153763	−	0.0153763i
$408$	−3.51172			−0.173856
$409$	0.394438	+	0.394438i	0.0195037	+	0.0195037i	0.716791	−	0.697288i	$-0.245610\pi$
$409$	0.394438	+	0.394438i	0.0195037	+	0.0195037i	−0.697288	+	0.716791i	$0.745610\pi$
$410$		0			0
$411$	4.49890	+	4.49890i	0.221915	+	0.221915i
$412$	12.1707	−	12.1707i	0.599606	−	0.599606i
$413$	−13.6430	+	13.6430i	−0.671329	+	0.671329i
$414$	1.89288	−	1.89288i	0.0930301	−	0.0930301i
$415$		0			0
$416$	−2.75068	+	27.5398i	−0.134863	+	1.35025i
$417$	−6.59162	+	6.59162i	−0.322793	+	0.322793i
$418$	3.30130			0.161472
$419$		−	19.5115i		−	0.953198i	−0.879121	−	0.476599i	$-0.841869\pi$
$419$		−	19.5115i		−	0.953198i	0.879121	−	0.476599i	$-0.158131\pi$
$420$		0			0
$421$	17.5178	−	17.5178i	0.853764	−	0.853764i	−0.136830	−	0.990594i	$-0.543692\pi$
$421$	17.5178	−	17.5178i	0.853764	−	0.853764i	0.990594	+	0.136830i	$0.0436916\pi$
$422$		−	15.6895i		−	0.763754i
$423$			6.39859i			0.311110i
$424$	−1.14859	+	1.14859i	−0.0557807	+	0.0557807i
$425$		0			0
$426$			1.54706i			0.0749553i
$427$	14.5936			0.706236
$428$	−13.2250	+	13.2250i	−0.639254	+	0.639254i
$429$	0.118304	−	1.18446i	0.00571176	−	0.0571861i
$430$		0			0
$431$	1.07458	−	1.07458i	0.0517608	−	0.0517608i	−0.680753	−	0.732513i	$-0.738347\pi$
$431$	1.07458	−	1.07458i	0.0517608	−	0.0517608i	0.732513	+	0.680753i	$0.238347\pi$
$432$	3.10921	−	3.10921i	0.149592	−	0.149592i
$433$	−1.79696	+	1.79696i	−0.0863564	+	0.0863564i	−0.748965	−	0.662609i	$-0.769449\pi$
$433$	−1.79696	+	1.79696i	−0.0863564	+	0.0863564i	0.662609	+	0.748965i	$0.269449\pi$
$434$	15.5882	+	15.5882i	0.748258	+	0.748258i
$435$		0			0
$436$	−12.5406	−	12.5406i	−0.600584	−	0.600584i
$437$	−7.08818			−0.339074
$438$	5.01763	+	5.01763i	0.239752	+	0.239752i
$439$	22.7567			1.08612			0.543058	−	0.839695i	$-0.317266\pi$
$439$	22.7567			1.08612			0.543058	+	0.839695i	$0.317266\pi$
$440$		0			0
$441$		−	1.54535i		−	0.0735881i
$442$	−43.8369	+	35.8752i	−2.08511	+	1.70641i
$443$	−24.0285	−	24.0285i	−1.14163	−	1.14163i	−0.988152	−	0.153476i	$-0.950953\pi$
$443$	−24.0285	−	24.0285i	−1.14163	−	1.14163i	−0.153476	−	0.988152i	$-0.549047\pi$
$444$	−1.66918	−	1.66918i	−0.0792159	−	0.0792159i
$445$		0			0
$446$		−	28.8287i		−	1.36508i
$447$			1.74326i			0.0824533i
$448$	−14.3005			−0.675634
$449$	−9.30869	+	9.30869i	−0.439304	+	0.439304i	−0.891778	−	0.452473i	$-0.850542\pi$
$449$	−9.30869	+	9.30869i	−0.439304	+	0.439304i	0.452473	+	0.891778i	$0.350542\pi$
$450$		0			0
$451$	0.534994			0.0251919
$452$	4.44800	+	4.44800i	0.209216	+	0.209216i
$453$			12.6904i			0.596245i
$454$	0.810894			0.0380571
$455$		0			0
$456$	−2.23516			−0.104671
$457$			15.2997i			0.715689i	0.933781	+	0.357845i	$0.116488\pi$
$457$			15.2997i			0.715689i	−0.933781	+	0.357845i	$0.883512\pi$
$458$	−24.9417	−	24.9417i	−1.16545	−	1.16545i
$459$	8.08444			0.377350
$460$		0			0
$461$	−3.62065	+	3.62065i	−0.168631	+	0.168631i	−0.786377	−	0.617747i	$-0.788046\pi$
$461$	−3.62065	+	3.62065i	−0.168631	+	0.168631i	0.617747	+	0.786377i	$0.288046\pi$
$462$	1.49841			0.0697122
$463$		−	9.60651i		−	0.446452i	−0.974767	−	0.223226i	$-0.928341\pi$
$463$		−	9.60651i		−	0.446452i	0.974767	−	0.223226i	$-0.0716588\pi$
$464$			42.1718i			1.95778i
$465$		0			0
$466$	15.8103	+	15.8103i	0.732399	+	0.732399i
$467$	−0.654055	−	0.654055i	−0.0302661	−	0.0302661i	0.691812	−	0.722078i	$-0.256813\pi$
$467$	−0.654055	−	0.654055i	−0.0302661	−	0.0302661i	−0.722078	+	0.691812i	$0.756813\pi$
$468$	0.636583	−	6.37346i	0.0294260	−	0.294613i
$469$		−	29.5881i		−	1.36625i
$470$		0			0
$471$	−13.0028			−0.599139
$472$	−2.53745	−	2.53745i	−0.116796	−	0.116796i
$473$	1.43078			0.0657876
$474$	−10.1430	−	10.1430i	−0.465884	−	0.465884i
$475$		0			0
$476$	−23.7180	−	23.7180i	−1.08711	−	1.08711i
$477$	2.64422	−	2.64422i	0.121070	−	0.121070i
$478$	−28.3155	+	28.3155i	−1.29512	+	1.29512i
$479$	5.52526	−	5.52526i	0.252455	−	0.252455i	−0.569521	−	0.821977i	$-0.692871\pi$
$479$	5.52526	−	5.52526i	0.252455	−	0.252455i	0.821977	+	0.569521i	$0.192871\pi$
$480$		0			0
$481$	4.76734	+	0.476163i	0.217372	+	0.0217112i
$482$	−17.5394	+	17.5394i	−0.798899	+	0.798899i
$483$	−3.21721			−0.146388
$484$			19.3476i			0.879436i
$485$		0			0
$486$	−1.37413	+	1.37413i	−0.0623319	+	0.0623319i
$487$			22.6360i			1.02574i	0.858468	+	0.512868i	$0.171417\pi$
$487$			22.6360i			1.02574i	−0.858468	+	0.512868i	$0.828583\pi$
$488$			2.71425i			0.122868i
$489$	8.79014	−	8.79014i	0.397504	−	0.397504i
$490$		0			0
$491$		−	4.26897i		−	0.192656i	−0.995350	−	0.0963280i	$-0.969290\pi$
$491$		−	4.26897i		−	0.192656i	0.995350	−	0.0963280i	$-0.0307098\pi$
$492$	2.87876			0.129784
$493$	−54.8267	+	54.8267i	−2.46927	+	2.46927i
$494$	−27.9016	+	22.8341i	−1.25535	+	1.02736i
$495$		0			0
$496$	−15.1020	+	15.1020i	−0.678100	+	0.678100i
$497$	1.31472	−	1.31472i	0.0589731	−	0.0589731i
$498$	15.5742	−	15.5742i	0.697896	−	0.697896i
$499$	−0.792199	−	0.792199i	−0.0354637	−	0.0354637i	0.689153	−	0.724616i	$-0.257983\pi$
$499$	−0.792199	−	0.792199i	−0.0354637	−	0.0354637i	−0.724616	+	0.689153i	$0.757983\pi$
$500$		0			0
$501$	16.9365	+	16.9365i	0.756667	+	0.756667i
$502$	−12.8004			−0.571312
$503$	3.33985	+	3.33985i	0.148916	+	0.148916i	0.777634	−	0.628717i	$-0.216420\pi$
$503$	3.33985	+	3.33985i	0.148916	+	0.148916i	−0.628717	+	0.777634i	$0.716420\pi$
$504$	−1.01450			−0.0451896
$505$		0			0
$506$			0.883775i			0.0392886i
$507$	7.19265	+	10.8289i	0.319437	+	0.480930i
$508$	6.58076	+	6.58076i	0.291974	+	0.291974i
$509$	−7.90970	−	7.90970i	−0.350591	−	0.350591i	0.509738	−	0.860330i	$-0.329742\pi$
$509$	−7.90970	−	7.90970i	−0.350591	−	0.350591i	−0.860330	+	0.509738i	$0.829742\pi$
$510$		0			0
$511$		−	8.52813i		−	0.377262i
$512$		−	29.9328i		−	1.32285i
$513$	5.14564			0.227186
$514$	−24.2803	+	24.2803i	−1.07096	+	1.07096i
$515$		0			0
$516$	7.69893			0.338926
$517$	−1.49373	−	1.49373i	−0.0656942	−	0.0656942i
$518$			6.03096i			0.264985i
$519$	13.0836			0.574307
$520$		0			0
$521$	30.1540			1.32107			0.660535	−	0.750796i	$-0.270330\pi$
$521$	30.1540			1.32107			0.660535	+	0.750796i	$0.270330\pi$
$522$		−	18.6380i		−	0.815765i
$523$	−1.32078	−	1.32078i	−0.0577535	−	0.0577535i	0.677640	−	0.735394i	$-0.263003\pi$
$523$	−1.32078	−	1.32078i	−0.0577535	−	0.0577535i	−0.735394	+	0.677640i	$0.763003\pi$
$524$	−14.8076			−0.646874
$525$		0			0
$526$	−34.6141	+	34.6141i	−1.50925	+	1.50925i
$527$	−39.2676			−1.71053
$528$			1.45167i			0.0631758i
$529$			21.1025i			0.917498i
$530$		0			0
$531$	5.84154	+	5.84154i	0.253501	+	0.253501i
$532$	−15.0962	−	15.0962i	−0.654502	−	0.654502i
$533$	−4.52161	+	3.70039i	−0.195853	+	0.160282i
$534$			20.7978i			0.900008i
$535$		0			0
$536$	5.50305			0.237696
$537$	3.53735	+	3.53735i	0.152648	+	0.152648i
$538$	−46.7838			−2.01699
$539$	0.360757	+	0.360757i	0.0155389	+	0.0155389i
$540$		0			0
$541$	−11.4734	−	11.4734i	−0.493281	−	0.493281i	0.416058	−	0.909338i	$-0.363411\pi$
$541$	−11.4734	−	11.4734i	−0.493281	−	0.493281i	−0.909338	+	0.416058i	$0.863411\pi$
$542$	−8.14201	+	8.14201i	−0.349729	+	0.349729i
$543$	−4.02737	+	4.02737i	−0.172831	+	0.172831i
$544$	43.8813	−	43.8813i	1.88140	−	1.88140i
$545$		0			0
$546$	−12.6641	+	10.3640i	−0.541972	+	0.443539i
$547$	13.9025	−	13.9025i	0.594427	−	0.594427i	−0.344397	−	0.938824i	$-0.611917\pi$
$547$	13.9025	−	13.9025i	0.594427	−	0.594427i	0.938824	+	0.344397i	$0.111917\pi$
$548$	−11.3027			−0.482826
$549$		−	6.24856i		−	0.266682i
$550$		0			0
$551$	−34.8965	+	34.8965i	−1.48664	+	1.48664i
$552$		−	0.598364i		−	0.0254681i
$553$			17.2394i			0.733094i
$554$	−21.1463	+	21.1463i	−0.898421	+	0.898421i
$555$		0			0
$556$		−	16.5602i		−	0.702310i
$557$	−43.3035			−1.83483			−0.917414	−	0.397934i	$-0.869727\pi$
$557$	−43.3035			−1.83483			−0.917414	+	0.397934i	$0.869727\pi$
$558$	6.67441	−	6.67441i	0.282550	−	0.282550i
$559$	−12.0925	+	9.89630i	−0.511460	+	0.418569i
$560$		0			0
$561$	−1.88729	+	1.88729i	−0.0796814	+	0.0796814i
$562$	−0.665931	+	0.665931i	−0.0280906	+	0.0280906i
$563$	14.1035	−	14.1035i	0.594390	−	0.594390i	−0.344424	−	0.938814i	$-0.611926\pi$
$563$	14.1035	−	14.1035i	0.594390	−	0.594390i	0.938814	+	0.344424i	$0.111926\pi$
$564$	−8.03763	−	8.03763i	−0.338445	−	0.338445i
$565$		0			0
$566$	−35.5198	−	35.5198i	−1.49301	−	1.49301i
$567$	2.33552			0.0980826
$568$	0.244522	+	0.244522i	0.0102599	+	0.0102599i
$569$	6.15514			0.258037			0.129019	−	0.991642i	$-0.458817\pi$
$569$	6.15514			0.258037			0.129019	+	0.991642i	$0.458817\pi$
$570$		0			0
$571$			29.0825i			1.21706i	0.793530	+	0.608532i	$0.208241\pi$
$571$			29.0825i			1.21706i	−0.793530	+	0.608532i	$0.791759\pi$
$572$	1.33926	+	1.63647i	0.0559971	+	0.0684243i
$573$	11.4575	+	11.4575i	0.478645	+	0.478645i
$574$	−5.20065	−	5.20065i	−0.217071	−	0.217071i
$575$		0			0
$576$			6.12304i			0.255127i
$577$			1.10695i			0.0460829i	0.999735	+	0.0230415i	$0.00733498\pi$
$577$			1.10695i			0.0460829i	−0.999735	+	0.0230415i	$0.992665\pi$
$578$	93.9753			3.90886
$579$	4.62846	−	4.62846i	0.192352	−	0.192352i
$580$		0			0
$581$	−26.4704			−1.09818
$582$	−12.7436	−	12.7436i	−0.528238	−	0.528238i
$583$			1.23457i			0.0511306i
$584$	1.58614			0.0656348
$585$		0			0
$586$	−26.8203			−1.10794
$587$			7.65633i			0.316010i	0.987438	+	0.158005i	$0.0505063\pi$
$587$			7.65633i			0.316010i	−0.987438	+	0.158005i	$0.949494\pi$
$588$	1.94120	+	1.94120i	0.0800538	+	0.0800538i
$589$	−24.9933			−1.02983
$590$		0			0
$591$	11.0211	−	11.0211i	0.453347	−	0.453347i
$592$	−5.84285			−0.240140
$593$		−	46.8058i		−	1.92209i	−0.276400	−	0.961043i	$-0.589141\pi$
$593$		−	46.8058i		−	1.92209i	0.276400	−	0.961043i	$-0.410859\pi$
$594$		−	0.641573i		−	0.0263241i
$595$		0			0
$596$	−2.18981	−	2.18981i	−0.0896979	−	0.0896979i
$597$	−13.9030	−	13.9030i	−0.569011	−	0.569011i
$598$	−6.11280	−	7.46939i	−0.249971	−	0.305446i
$599$		−	20.0674i		−	0.819933i	−0.912101	−	0.409967i	$-0.865540\pi$
$599$		−	20.0674i		−	0.819933i	0.912101	−	0.409967i	$-0.134460\pi$
$600$		0			0
$601$	23.8311			0.972092			0.486046	−	0.873933i	$-0.338439\pi$
$601$	23.8311			0.972092			0.486046	+	0.873933i	$0.338439\pi$
$602$	−13.9086	−	13.9086i	−0.566872	−	0.566872i
$603$	−12.6687			−0.515911
$604$	−15.9411	−	15.9411i	−0.648633	−	0.648633i
$605$		0			0
$606$	16.9212	+	16.9212i	0.687378	+	0.687378i
$607$	20.3443	−	20.3443i	0.825748	−	0.825748i	−0.161177	−	0.986925i	$-0.551529\pi$
$607$	20.3443	−	20.3443i	0.825748	−	0.825748i	0.986925	+	0.161177i	$0.0515290\pi$
$608$	27.9299	−	27.9299i	1.13271	−	1.13271i
$609$	−15.8389	+	15.8389i	−0.641825	+	0.641825i
$610$		0			0
$611$	22.9562	+	2.29287i	0.928709	+	0.0927597i
$612$	−10.1553	+	10.1553i	−0.410505	+	0.410505i
$613$	−7.88256			−0.318374			−0.159187	−	0.987248i	$-0.550887\pi$
$613$	−7.88256			−0.318374			−0.159187	+	0.987248i	$0.550887\pi$
$614$		−	45.3541i		−	1.83034i
$615$		0			0
$616$	0.236833	−	0.236833i	0.00954226	−	0.00954226i
$617$			6.36174i			0.256114i	0.991767	+	0.128057i	$0.0408740\pi$
$617$			6.36174i			0.256114i	−0.991767	+	0.128057i	$0.959126\pi$
$618$			18.8284i			0.757390i
$619$	−8.80252	+	8.80252i	−0.353803	+	0.353803i	−0.861523	−	0.507719i	$-0.830489\pi$
$619$	−8.80252	+	8.80252i	−0.353803	+	0.353803i	0.507719	+	0.861523i	$0.330489\pi$
$620$		0			0
$621$			1.37751i			0.0552776i
$622$	53.7091			2.15354
$623$	17.6743	−	17.6743i	0.708106	−	0.708106i
$624$	−10.0408	−	12.2691i	−0.401952	−	0.491156i
$625$		0			0
$626$	−4.40387	+	4.40387i	−0.176014	+	0.176014i
$627$	−1.20123	+	1.20123i	−0.0479726	+	0.0479726i
$628$	16.3336	−	16.3336i	0.651782	−	0.651782i
$629$	−7.59618	−	7.59618i	−0.302879	−	0.302879i
$630$		0			0
$631$	−1.64324	−	1.64324i	−0.0654164	−	0.0654164i	0.673642	−	0.739058i	$-0.264729\pi$
$631$	−1.64324	−	1.64324i	−0.0654164	−	0.0654164i	−0.739058	+	0.673642i	$0.764729\pi$
$632$	−3.20633			−0.127541
$633$	5.70889	+	5.70889i	0.226908	+	0.226908i
$634$	65.0839			2.58481
$635$		0			0
$636$			6.64310i			0.263416i
$637$	−5.54425	−	0.553761i	−0.219671	−	0.0219408i
$638$	4.35099	+	4.35099i	0.172257	+	0.172257i
$639$	−0.562923	−	0.562923i	−0.0222689	−	0.0222689i
$640$		0			0
$641$		−	29.5982i		−	1.16906i	−0.811373	−	0.584529i	$-0.801279\pi$
$641$		−	29.5982i		−	1.16906i	0.811373	−	0.584529i	$-0.198721\pi$
$642$		−	20.4595i		−	0.807472i
$643$	30.1991			1.19094			0.595468	−	0.803379i	$-0.296967\pi$
$643$	30.1991			1.19094			0.595468	+	0.803379i	$0.296967\pi$
$644$	4.04132	−	4.04132i	0.159250	−	0.159250i
$645$		0			0
$646$	80.8412			3.18066
$647$	19.9747	+	19.9747i	0.785285	+	0.785285i	0.980717	−	0.195432i	$-0.0626110\pi$
$647$	19.9747	+	19.9747i	0.785285	+	0.785285i	−0.195432	+	0.980717i	$0.562611\pi$
$648$			0.434380i			0.0170641i
$649$	−2.72738			−0.107059
$650$		0			0
$651$	−11.3440			−0.444608
$652$			22.0836i			0.864861i
$653$	15.7632	+	15.7632i	0.616863	+	0.616863i	0.944726	−	0.327862i	$-0.106328\pi$
$653$	15.7632	+	15.7632i	0.616863	+	0.616863i	−0.327862	+	0.944726i	$0.606328\pi$
$654$	19.4006			0.758625
$655$		0			0
$656$	5.03844	−	5.03844i	0.196718	−	0.196718i
$657$	−3.65149			−0.142458
$658$			29.0409i			1.13213i
$659$			18.4911i			0.720311i	0.932892	+	0.360156i	$0.117276\pi$
$659$			18.4911i			0.720311i	−0.932892	+	0.360156i	$0.882724\pi$
$660$		0			0
$661$	−24.3251	−	24.3251i	−0.946138	−	0.946138i	0.0524836	−	0.998622i	$-0.483286\pi$
$661$	−24.3251	−	24.3251i	−0.946138	−	0.946138i	−0.998622	+	0.0524836i	$0.983286\pi$
$662$	24.8492	+	24.8492i	0.965792	+	0.965792i
$663$	2.89698	−	29.0046i	0.112510	−	1.12644i
$664$		−	4.92320i		−	0.191057i
$665$		0			0
$666$	2.58228			0.100061
$667$	−9.34195	−	9.34195i	−0.361722	−	0.361722i
$668$	−42.5498			−1.64630
$669$	10.4898	+	10.4898i	0.405559	+	0.405559i
$670$		0			0
$671$	1.45871	+	1.45871i	0.0563128	+	0.0563128i
$672$	12.6769	−	12.6769i	0.489022	−	0.489022i
$673$	−12.4572	+	12.4572i	−0.480190	+	0.480190i	−0.905192	−	0.425002i	$-0.860273\pi$
$673$	−12.4572	+	12.4572i	−0.480190	+	0.480190i	0.425002	+	0.905192i	$0.360273\pi$
$674$	0.586681	−	0.586681i	0.0225981	−	0.0225981i
$675$		0			0
$676$	−22.6379	−	4.56774i	−0.870690	−	0.175682i
$677$	−11.5255	+	11.5255i	−0.442960	+	0.442960i	−0.893006	−	0.450045i	$-0.851408\pi$
$677$	−11.5255	+	11.5255i	−0.442960	+	0.442960i	0.450045	+	0.893006i	$0.351408\pi$
$678$	−6.88120			−0.264271
$679$			21.6594i			0.831212i
$680$		0			0
$681$	−0.295057	+	0.295057i	−0.0113066	+	0.0113066i
$682$			3.11624i			0.119327i
$683$		−	4.24801i		−	0.162546i	−0.996692	−	0.0812729i	$-0.974101\pi$
$683$		−	4.24801i		−	0.162546i	0.996692	−	0.0812729i	$-0.0258985\pi$
$684$	−6.46373	+	6.46373i	−0.247147	+	0.247147i
$685$		0			0
$686$		−	38.7844i		−	1.48079i
$687$	18.1509			0.692499
$688$	13.4748	−	13.4748i	0.513721	−	0.513721i
$689$	−8.53912	−	10.4342i	−0.325315	−	0.397511i
$690$		0			0
$691$	−4.57211	+	4.57211i	−0.173931	+	0.173931i	−0.788704	−	0.614773i	$-0.789248\pi$
$691$	−4.57211	+	4.57211i	−0.173931	+	0.173931i	0.614773	+	0.788704i	$0.289248\pi$
$692$	−16.4351	+	16.4351i	−0.624768	+	0.624768i
$693$	−0.545220	+	0.545220i	−0.0207112	+	0.0207112i
$694$	0.295626	+	0.295626i	0.0112218	+	0.0112218i
$695$		0			0
$696$	−2.94586	−	2.94586i	−0.111663	−	0.111663i
$697$	13.1008			0.496227
$698$	−6.02946	−	6.02946i	−0.228218	−	0.228218i
$699$	−11.5057			−0.435185
$700$		0			0
$701$		−	9.67189i		−	0.365302i	−0.983178	−	0.182651i	$-0.941532\pi$
$701$		−	9.67189i		−	0.365302i	0.983178	−	0.182651i	$-0.0584679\pi$
$702$	4.43756	+	5.42238i	0.167485	+	0.204654i
$703$	−4.83486	−	4.83486i	−0.182350	−	0.182350i
$704$	−1.42940	−	1.42940i	−0.0538727	−	0.0538727i
$705$		0			0
$706$		−	32.0680i		−	1.20690i
$707$		−	28.7599i		−	1.08163i
$708$	−14.6758			−0.551550
$709$	1.02427	−	1.02427i	0.0384674	−	0.0384674i	−0.687611	−	0.726079i	$-0.741341\pi$
$709$	1.02427	−	1.02427i	0.0384674	−	0.0384674i	0.726079	+	0.687611i	$0.241341\pi$
$710$		0			0
$711$	7.38140			0.276824
$712$	3.28722	+	3.28722i	0.123194	+	0.123194i
$713$		−	6.69083i		−	0.250574i
$714$	36.6925			1.37318
$715$		0			0
$716$	−8.88695			−0.332121
$717$		−	20.6061i		−	0.769549i
$718$	38.8133	+	38.8133i	1.44850	+	1.44850i
$719$	14.1969			0.529457			0.264728	−	0.964323i	$-0.414718\pi$
$719$	14.1969			0.529457			0.264728	+	0.964323i	$0.414718\pi$
$720$		0			0
$721$	16.0007	−	16.0007i	0.595897	−	0.595897i
$722$	14.5314			0.540801
$723$		−	12.7640i		−	0.474699i
$724$		−	10.1180i		−	0.376033i
$725$		0			0
$726$	−14.9657	−	14.9657i	−0.555428	−	0.555428i
$727$	−27.1036	−	27.1036i	−1.00522	−	1.00522i	−0.999986	−	0.00523224i	$-0.998335\pi$
$727$	−27.1036	−	27.1036i	−1.00522	−	1.00522i	−0.00523224	−	0.999986i	$-0.501665\pi$
$728$	−0.363538	+	3.63973i	−0.0134736	+	0.134898i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	35.0366			1.29587
$732$	7.84918	+	7.84918i	0.290114	+	0.290114i
$733$	−33.8532			−1.25040			−0.625198	−	0.780467i	$-0.714982\pi$
$733$	−33.8532			−1.25040			−0.625198	+	0.780467i	$0.714982\pi$
$734$	50.8715	+	50.8715i	1.87770	+	1.87770i
$735$		0			0
$736$	7.47695	+	7.47695i	0.275604	+	0.275604i
$737$	2.95748	−	2.95748i	0.108940	−	0.108940i
$738$	−2.22677	+	2.22677i	−0.0819684	+	0.0819684i
$739$	−1.91247	+	1.91247i	−0.0703512	+	0.0703512i	−0.741407	−	0.671056i	$-0.765841\pi$
$739$	−1.91247	+	1.91247i	−0.0703512	+	0.0703512i	0.671056	+	0.741407i	$0.265841\pi$
$740$		0			0
$741$	1.84389	−	18.4610i	0.0677370	−	0.678182i
$742$	12.0012	−	12.0012i	0.440577	−	0.440577i
$743$	−26.9709			−0.989467			−0.494734	−	0.869045i	$-0.664734\pi$
$743$	−26.9709			−0.989467			−0.494734	+	0.869045i	$0.664734\pi$
$744$		−	2.10986i		−	0.0773514i
$745$		0			0
$746$	44.2963	−	44.2963i	1.62180	−	1.62180i
$747$			11.3338i			0.414683i
$748$		−	4.74146i		−	0.173365i
$749$	−17.3868	+	17.3868i	−0.635300	+	0.635300i
$750$		0			0
$751$			16.2375i			0.592516i	0.955108	+	0.296258i	$0.0957389\pi$
$751$			16.2375i			0.592516i	−0.955108	+	0.296258i	$0.904261\pi$
$752$	−28.1351			−1.02598
$753$	4.65765	−	4.65765i	0.169734	−	0.169734i
$754$	−66.8677	−	6.67876i	−2.43518	−	0.243226i
$755$		0			0
$756$	−2.93378	+	2.93378i	−0.106701	+	0.106701i
$757$	−11.0138	+	11.0138i	−0.400304	+	0.400304i	−0.878340	−	0.478036i	$-0.841349\pi$
$757$	−11.0138	+	11.0138i	−0.400304	+	0.400304i	0.478036	+	0.878340i	$0.341349\pi$
$758$	44.9336	−	44.9336i	1.63206	−	1.63206i
$759$	−0.321576	−	0.321576i	−0.0116725	−	0.0116725i
$760$		0			0
$761$	−12.2514	−	12.2514i	−0.444114	−	0.444114i	0.449278	−	0.893392i	$-0.351681\pi$
$761$	−12.2514	−	12.2514i	−0.444114	−	0.444114i	−0.893392	+	0.449278i	$0.851681\pi$
$762$	−10.1806			−0.368806
$763$	−16.4870	−	16.4870i	−0.596869	−	0.596869i
$764$	−28.7849			−1.04140
$765$		0			0
$766$			32.5791i			1.17713i
$767$	23.0509	−	18.8644i	0.832321	−	0.681155i
$768$	13.4046	+	13.4046i	0.483698	+	0.483698i
$769$	−15.7236	−	15.7236i	−0.567007	−	0.567007i	0.364282	−	0.931289i	$-0.381315\pi$
$769$	−15.7236	−	15.7236i	−0.567007	−	0.567007i	−0.931289	+	0.364282i	$0.881315\pi$
$770$		0			0
$771$		−	17.6696i		−	0.636354i
$772$			11.6282i			0.418507i
$773$	12.3241			0.443266			0.221633	−	0.975130i	$-0.428861\pi$
$773$	12.3241			0.443266			0.221633	+	0.975130i	$0.428861\pi$
$774$	−5.95524	+	5.95524i	−0.214057	+	0.214057i
$775$		0			0
$776$	−4.02841			−0.144611
$777$	−2.19446	−	2.19446i	−0.0787259	−	0.0787259i
$778$		−	0.773751i		−	0.0277403i
$779$	8.33845			0.298756
$780$		0			0
$781$	0.262825			0.00940462
$782$			21.6416i			0.773901i
$783$	6.78175	+	6.78175i	0.242360	+	0.242360i
$784$	6.79504			0.242680
$785$		0			0
$786$	11.4539	−	11.4539i	0.408548	−	0.408548i
$787$	39.5841			1.41102			0.705511	−	0.708699i	$-0.250717\pi$
$787$	39.5841			1.41102			0.705511	+	0.708699i	$0.250717\pi$
$788$			27.6884i			0.986359i
$789$		−	25.1898i		−	0.896780i
$790$		0			0
$791$	5.84775	+	5.84775i	0.207922	+	0.207922i
$792$	−0.101405	−	0.101405i	−0.00360326	−	0.00360326i
$793$	−22.4180	−	2.23911i	−0.796086	−	0.0795133i
$794$			12.7655i			0.453032i
$795$		0			0
$796$	34.9287			1.23801
$797$	5.60381	+	5.60381i	0.198497	+	0.198497i	0.799355	−	0.600858i	$-0.205174\pi$
$797$	5.60381	+	5.60381i	0.198497	+	0.198497i	−0.600858	+	0.799355i	$0.705174\pi$
$798$	23.3543			0.826732
$799$	−36.5779	−	36.5779i	−1.29403	−	1.29403i
$800$		0			0
$801$	−7.56761	−	7.56761i	−0.267388	−	0.267388i
$802$	−18.6321	+	18.6321i	−0.657921	+	0.657921i
$803$	0.852430	−	0.852430i	0.0300816	−	0.0300816i
$804$	15.9139	−	15.9139i	0.561241	−	0.561241i
$805$		0			0
$806$	−21.5541	−	26.3375i	−0.759210	−	0.927699i
$807$	17.0230	−	17.0230i	0.599240	−	0.599240i
$808$	5.34901			0.188178
$809$			29.3142i			1.03063i	0.857000	+	0.515316i	$0.172325\pi$
$809$			29.3142i			1.03063i	−0.857000	+	0.515316i	$0.827675\pi$
$810$		0			0
$811$	15.3791	−	15.3791i	0.540032	−	0.540032i	−0.383506	−	0.923538i	$-0.625284\pi$
$811$	15.3791	−	15.3791i	0.540032	−	0.540032i	0.923538	+	0.383506i	$0.125284\pi$
$812$		−	39.7923i		−	1.39644i
$813$		−	5.92521i		−	0.207806i
$814$	−0.602825	+	0.602825i	−0.0211290	+	0.0211290i
$815$		0			0
$816$			35.5480i			1.24443i
$817$	22.3003			0.780189
$818$	0.766517	−	0.766517i	0.0268006	−	0.0268006i
$819$	0.836911	−	8.37914i	0.0292440	−	0.292791i
$820$		0			0
$821$	−2.40447	+	2.40447i	−0.0839167	+	0.0839167i	−0.747819	−	0.663902i	$-0.768899\pi$
$821$	−2.40447	+	2.40447i	−0.0839167	+	0.0839167i	0.663902	+	0.747819i	$0.268899\pi$
$822$	8.74279	−	8.74279i	0.304940	−	0.304940i
$823$	−21.3112	+	21.3112i	−0.742861	+	0.742861i	−0.973128	−	0.230267i	$-0.926040\pi$
$823$	−21.3112	+	21.3112i	−0.742861	+	0.742861i	0.230267	+	0.973128i	$0.426040\pi$
$824$	2.97595	+	2.97595i	0.103672	+	0.103672i
$825$		0			0
$826$	26.5127	+	26.5127i	0.922495	+	0.922495i
$827$	30.9701			1.07694			0.538468	−	0.842646i	$-0.319003\pi$
$827$	30.9701			1.07694			0.538468	+	0.842646i	$0.319003\pi$
$828$	−1.73037	−	1.73037i	−0.0601346	−	0.0601346i
$829$	−18.1038			−0.628771			−0.314386	−	0.949295i	$-0.601799\pi$
$829$	−18.1038			−0.628771			−0.314386	+	0.949295i	$0.601799\pi$
$830$		0			0
$831$		−	15.3889i		−	0.533833i
$832$	21.9676	+	2.19413i	0.761590	+	0.0760679i
$833$	8.83409	+	8.83409i	0.306083	+	0.306083i
$834$	12.8096	+	12.8096i	0.443560	+	0.443560i
$835$		0			0
$836$		−	3.01788i		−	0.104375i
$837$			4.85718i			0.167889i
$838$	−37.9170			−1.30982
$839$	24.5646	−	24.5646i	0.848063	−	0.848063i	−0.141828	−	0.989891i	$-0.545298\pi$
$839$	24.5646	−	24.5646i	0.848063	−	0.848063i	0.989891	+	0.141828i	$0.0452981\pi$
$840$		0			0
$841$	−62.9844			−2.17187
$842$	−34.0426	−	34.0426i	−1.17318	−	1.17318i
$843$		−	0.484619i		−	0.0166912i
$844$	−14.3425			−0.493690
$845$		0			0
$846$	12.4345			0.427506
$847$			25.4362i			0.873997i
$848$	11.6268	+	11.6268i	0.399268	+	0.399268i
$849$	25.8489			0.887132
$850$		0			0
$851$	1.29432	−	1.29432i	0.0443686	−	0.0443686i
$852$	1.41424			0.0484510
$853$		−	41.9606i		−	1.43670i	−0.695680	−	0.718352i	$-0.744897\pi$
$853$		−	41.9606i		−	1.43670i	0.695680	−	0.718352i	$-0.255103\pi$
$854$		−	28.3601i		−	0.970461i
$855$		0			0
$856$	−3.23375	−	3.23375i	−0.110527	−	0.110527i
$857$	−2.33764	−	2.33764i	−0.0798523	−	0.0798523i	0.666053	−	0.745905i	$-0.267983\pi$
$857$	−2.33764	−	2.33764i	−0.0798523	−	0.0798523i	−0.745905	+	0.666053i	$0.767983\pi$
$858$	−2.30177	−	0.229902i	−0.0785812	−	0.00784871i
$859$		−	28.8875i		−	0.985627i	−0.870135	−	0.492814i	$-0.835968\pi$
$859$		−	28.8875i		−	0.985627i	0.870135	−	0.492814i	$-0.164032\pi$
$860$		0			0
$861$	3.78468			0.128982
$862$	−2.08825	−	2.08825i	−0.0711262	−	0.0711262i
$863$	11.3214			0.385386			0.192693	−	0.981259i	$-0.438278\pi$
$863$	11.3214			0.385386			0.192693	+	0.981259i	$0.438278\pi$
$864$	−5.42787	−	5.42787i	−0.184660	−	0.184660i
$865$		0			0
$866$	3.49206	+	3.49206i	0.118665	+	0.118665i
$867$	−34.1944	+	34.1944i	−1.16130	+	1.16130i
$868$	14.2499	−	14.2499i	0.483673	−	0.483673i
$869$	−1.72316	+	1.72316i	−0.0584543	+	0.0584543i
$870$		0			0
$871$	−4.53972	+	45.4516i	−0.153823	+	1.54007i
$872$	3.06639	−	3.06639i	0.103841	−	0.103841i
$873$	9.27392			0.313875
$874$			13.7746i			0.465932i
$875$		0			0
$876$	4.58685	−	4.58685i	0.154975	−	0.154975i
$877$			44.6698i			1.50839i	0.656649	+	0.754196i	$0.271973\pi$
$877$			44.6698i			1.50839i	−0.656649	+	0.754196i	$0.728027\pi$
$878$		−	44.2234i		−	1.49247i
$879$	9.75901	−	9.75901i	0.329163	−	0.329163i
$880$		0			0
$881$		−	19.0340i		−	0.641271i	−0.947203	−	0.320635i	$-0.896104\pi$
$881$		−	19.0340i		−	0.641271i	0.947203	−	0.320635i	$-0.103896\pi$
$882$	−3.00310			−0.101120
$883$	32.7369	−	32.7369i	1.10169	−	1.10169i	0.107478	−	0.994208i	$-0.465723\pi$
$883$	32.7369	−	32.7369i	1.10169	−	1.10169i	0.994208	−	0.107478i	$-0.0342774\pi$
$884$	32.7952	+	40.0734i	1.10302	+	1.34781i
$885$		0			0
$886$	−46.6949	+	46.6949i	−1.56875	+	1.56875i
$887$	31.0236	−	31.0236i	1.04167	−	1.04167i	0.0425761	−	0.999093i	$-0.486444\pi$
$887$	31.0236	−	31.0236i	1.04167	−	1.04167i	0.999093	−	0.0425761i	$-0.0135565\pi$
$888$	0.408145	−	0.408145i	0.0136965	−	0.0136965i
$889$	8.65168	+	8.65168i	0.290168	+	0.290168i
$890$		0			0
$891$	0.233447	+	0.233447i	0.00782076	+	0.00782076i
$892$	−26.3537			−0.882386
$893$	−23.2814	−	23.2814i	−0.779081	−	0.779081i
$894$	3.38770			0.113302
$895$		0			0
$896$		−	8.06534i		−	0.269444i
$897$	4.94210	+	0.493618i	0.165012	+	0.0164814i
$898$	18.0897	+	18.0897i	0.603662	+	0.603662i
$899$	−32.9402	−	32.9402i	−1.09862	−	1.09862i
$900$		0			0
$901$			30.2317i			1.00716i
$902$		−	1.03966i		−	0.0346170i
$903$	10.1217			0.336830
$904$	−1.08762	+	1.08762i	−0.0361736	+	0.0361736i
$905$		0			0
$906$	24.6614			0.819319
$907$	28.8160	+	28.8160i	0.956820	+	0.956820i	0.999106	−	0.0422855i	$-0.0134639\pi$
$907$	28.8160	+	28.8160i	0.956820	+	0.956820i	−0.0422855	+	0.999106i	$0.513464\pi$
$908$		−	0.741276i		−	0.0246001i
$909$	−12.3141			−0.408434
$910$		0			0
$911$	−27.9461			−0.925895			−0.462948	−	0.886386i	$-0.653208\pi$
$911$	−27.9461			−0.925895			−0.462948	+	0.886386i	$0.653208\pi$
$912$			22.6258i			0.749216i
$913$	−2.64585	−	2.64585i	−0.0875648	−	0.0875648i
$914$	29.7321			0.983451
$915$		0			0
$916$	−22.8004	+	22.8004i	−0.753345	+	0.753345i
$917$	−19.4675			−0.642873
$918$		−	15.7106i		−	0.518528i
$919$		−	28.3713i		−	0.935884i	−0.883759	−	0.467942i	$-0.844996\pi$
$919$		−	28.3713i		−	0.935884i	0.883759	−	0.467942i	$-0.155004\pi$
$920$		0			0
$921$	16.5028	+	16.5028i	0.543786	+	0.543786i
$922$	7.03607	+	7.03607i	0.231721	+	0.231721i
$923$	−2.22132	+	1.81788i	−0.0731155	+	0.0598362i
$924$		−	1.36976i		−	0.0450619i
$925$		0			0
$926$	−18.6685			−0.613484
$927$	−6.85102	−	6.85102i	−0.225017	−	0.225017i
$928$	73.6209			2.41673
$929$	16.2725	+	16.2725i	0.533885	+	0.533885i	0.921726	−	0.387841i	$-0.126779\pi$
$929$	16.2725	+	16.2725i	0.533885	+	0.533885i	−0.387841	+	0.921726i	$0.626779\pi$
$930$		0			0
$931$	5.62278	+	5.62278i	0.184279	+	0.184279i
$932$	14.4529	−	14.4529i	0.473422	−	0.473422i
$933$	−19.5429	+	19.5429i	−0.639807	+	0.639807i
$934$	−1.27104	+	1.27104i	−0.0415896	+	0.0415896i
$935$		0			0
$936$	1.55843	+	0.155656i	0.0509387	+	0.00508778i
$937$	39.2274	−	39.2274i	1.28150	−	1.28150i	0.341693	−	0.939812i	$-0.389000\pi$
$937$	39.2274	−	39.2274i	1.28150	−	1.28150i	0.939812	−	0.341693i	$-0.111000\pi$
$938$	−57.4990			−1.87741
$939$		−	3.20484i		−	0.104586i
$940$		0			0
$941$	−28.9473	+	28.9473i	−0.943655	+	0.943655i	−0.998495	−	0.0548404i	$-0.982535\pi$
$941$	−28.9473	+	28.9473i	−0.943655	+	0.943655i	0.0548404	+	0.998495i	$0.482535\pi$
$942$			25.2686i			0.823296i
$943$			2.23224i			0.0726918i
$944$	−25.6857	+	25.6857i	−0.836000	+	0.836000i
$945$		0			0
$946$		−	2.78047i		−	0.0904007i
$947$	−10.0893			−0.327859			−0.163929	−	0.986472i	$-0.552417\pi$
$947$	−10.0893			−0.327859			−0.163929	+	0.986472i	$0.552417\pi$
$948$	−9.27220	+	9.27220i	−0.301147	+	0.301147i
$949$	−1.30848	+	13.1005i	−0.0424750	+	0.425259i
$950$		0			0
$951$	−23.6818	+	23.6818i	−0.767936	+	0.767936i
$952$	5.79947	−	5.79947i	0.187962	−	0.187962i
$953$	−18.3680	+	18.3680i	−0.594996	+	0.594996i	−0.938977	−	0.343980i	$-0.888225\pi$
$953$	−18.3680	+	18.3680i	−0.594996	+	0.594996i	0.343980	+	0.938977i	$0.388225\pi$
$954$	−5.13854	−	5.13854i	−0.166367	−	0.166367i
$955$		0			0
$956$	25.8845	+	25.8845i	0.837165	+	0.837165i
$957$	−3.16636			−0.102354
$958$	−10.7373	−	10.7373i	−0.346907	−	0.346907i
$959$	−14.8595			−0.479839
$960$		0			0
$961$			7.40776i			0.238960i
$962$	0.925335	−	9.26444i	0.0298340	−	0.298698i
$963$	7.44452	+	7.44452i	0.239896	+	0.239896i
$964$	16.0336	+	16.0336i	0.516408	+	0.516408i
$965$		0			0
$966$			6.25204i			0.201156i
$967$			30.3379i			0.975600i	0.872955	+	0.487800i	$0.162200\pi$
$967$			30.3379i			0.975600i	−0.872955	+	0.487800i	$0.837800\pi$
$968$	−4.73084			−0.152055
$969$	−29.4154	+	29.4154i	−0.944958	+	0.944958i
$970$		0			0
$971$	−22.4552			−0.720622			−0.360311	−	0.932832i	$-0.617329\pi$
$971$	−22.4552			−0.720622			−0.360311	+	0.932832i	$0.617329\pi$
$972$	1.25616	+	1.25616i	0.0402913	+	0.0402913i
$973$		−	21.7716i		−	0.697966i
$974$	43.9889			1.40950
$975$		0			0
$976$	27.4755			0.879469
$977$			15.8680i			0.507664i	0.967248	+	0.253832i	$0.0816910\pi$
$977$			15.8680i			0.507664i	−0.967248	+	0.253832i	$0.918309\pi$
$978$	−17.0820	−	17.0820i	−0.546223	−	0.546223i
$979$	3.53327			0.112924
$980$		0			0
$981$	−7.05924	+	7.05924i	−0.225384	+	0.225384i
$982$	−8.29596			−0.264735
$983$		−	6.22199i		−	0.198451i	−0.995065	−	0.0992253i	$-0.968364\pi$
$983$		−	6.22199i		−	0.198451i	0.995065	−	0.0992253i	$-0.0316365\pi$
$984$			0.703909i			0.0224398i
$985$		0			0
$986$	106.546	+	106.546i	3.39310	+	3.39310i
$987$	−10.5670	−	10.5670i	−0.336352	−	0.336352i
$988$	20.8737	+	25.5062i	0.664081	+	0.811459i
$989$			5.96989i			0.189832i
$990$		0			0
$991$	28.0780			0.891928			0.445964	−	0.895051i	$-0.352861\pi$
$991$	28.0780			0.891928			0.445964	+	0.895051i	$0.352861\pi$
$992$	26.3642	+	26.3642i	0.837063	+	0.837063i
$993$	−18.0836			−0.573865
$994$	−2.55491	−	2.55491i	−0.0810368	−	0.0810368i
$995$		0			0
$996$	−14.2371	−	14.2371i	−0.451119	−	0.451119i
$997$	−25.9092	+	25.9092i	−0.820554	+	0.820554i	−0.986187	−	0.165634i	$-0.947033\pi$
$997$	−25.9092	+	25.9092i	−0.820554	+	0.820554i	0.165634	+	0.986187i	$0.447033\pi$
$998$	−1.53949	+	1.53949i	−0.0487318	+	0.0487318i
$999$	−0.939604	+	0.939604i	−0.0297278	+	0.0297278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.k.d.343.3		28
5.2	odd	4		975.2.t.d.382.12		28
5.3	odd	4		195.2.t.a.187.3	yes	28
5.4	even	2		195.2.k.a.148.12	yes	28
13.8	odd	4		975.2.t.d.268.12		28
15.8	even	4		585.2.w.g.577.12		28
15.14	odd	2		585.2.n.g.343.3		28
65.8	even	4		195.2.k.a.112.3	✓	28
65.34	odd	4		195.2.t.a.73.3	yes	28
65.47	even	4	inner	975.2.k.d.307.12		28
195.8	odd	4		585.2.n.g.307.12		28
195.164	even	4		585.2.w.g.73.12		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.k.a.112.3	✓	28	65.8	even	4
195.2.k.a.148.12	yes	28	5.4	even	2
195.2.t.a.73.3	yes	28	65.34	odd	4
195.2.t.a.187.3	yes	28	5.3	odd	4
585.2.n.g.307.12		28	195.8	odd	4
585.2.n.g.343.3		28	15.14	odd	2
585.2.w.g.73.12		28	195.164	even	4
585.2.w.g.577.12		28	15.8	even	4
975.2.k.d.307.12		28	65.47	even	4	inner
975.2.k.d.343.3		28	1.1	even	1	trivial
975.2.t.d.268.12		28	13.8	odd	4
975.2.t.d.382.12		28	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.94332i q^{2} +(0.707107 + 0.707107i) q^{3} -1.77647 q^{4} +(1.37413 - 1.37413i) q^{6} -2.33552 q^{7} -0.434380i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q-1.94332i q^{2} +(0.707107 + 0.707107i) q^{3} -1.77647 q^{4} +(1.37413 - 1.37413i) q^{6} -2.33552 q^{7} -0.434380i q^{8} +1.00000i q^{9} +(-0.233447 - 0.233447i) q^{11} +(-1.25616 - 1.25616i) q^{12} +(3.58770 + 0.358340i) q^{13} +4.53865i q^{14} -4.39709 q^{16} +(-5.71657 - 5.71657i) q^{17} +1.94332 q^{18} +(-3.63852 - 3.63852i) q^{19} +(-1.65146 - 1.65146i) q^{21} +(-0.453661 + 0.453661i) q^{22} +(0.974048 - 0.974048i) q^{23} +(0.307153 - 0.307153i) q^{24} +(0.696369 - 6.97203i) q^{26} +(-0.707107 + 0.707107i) q^{27} +4.14899 q^{28} -9.59085i q^{29} +(3.43455 - 3.43455i) q^{31} +7.67617i q^{32} -0.330144i q^{33} +(-11.1091 + 11.1091i) q^{34} -1.77647i q^{36} +1.32880 q^{37} +(-7.07079 + 7.07079i) q^{38} +(2.28350 + 2.79027i) q^{39} +(-1.14586 + 1.14586i) q^{41} +(-3.20931 + 3.20931i) q^{42} +(-3.06448 + 3.06448i) q^{43} +(0.414712 + 0.414712i) q^{44} +(-1.89288 - 1.89288i) q^{46} +6.39859 q^{47} +(-3.10921 - 3.10921i) q^{48} -1.54535 q^{49} -8.08444i q^{51} +(-6.37346 - 0.636583i) q^{52} +(-2.64422 - 2.64422i) q^{53} +(1.37413 + 1.37413i) q^{54} +1.01450i q^{56} -5.14564i q^{57} -18.6380 q^{58} +(5.84154 - 5.84154i) q^{59} -6.24856 q^{61} +(-6.67441 - 6.67441i) q^{62} -2.33552i q^{63} +6.12304 q^{64} -0.641573 q^{66} +12.6687i q^{67} +(10.1553 + 10.1553i) q^{68} +1.37751 q^{69} +(-0.562923 + 0.562923i) q^{71} +0.434380 q^{72} +3.65149i q^{73} -2.58228i q^{74} +(6.46373 + 6.46373i) q^{76} +(0.545220 + 0.545220i) q^{77} +(5.42238 - 4.43756i) q^{78} -7.38140i q^{79} -1.00000 q^{81} +(2.22677 + 2.22677i) q^{82} +11.3338 q^{83} +(2.93378 + 2.93378i) q^{84} +(5.95524 + 5.95524i) q^{86} +(6.78175 - 6.78175i) q^{87} +(-0.101405 + 0.101405i) q^{88} +(-7.56761 + 7.56761i) q^{89} +(-8.37914 - 0.836911i) q^{91} +(-1.73037 + 1.73037i) q^{92} +4.85718 q^{93} -12.4345i q^{94} +(-5.42787 + 5.42787i) q^{96} -9.27392i q^{97} +3.00310i q^{98} +(0.233447 - 0.233447i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4}+O(q^{10}) \) 28 * q - 28 * q^4	\( 28 q - 28 q^{4} - 8 q^{11} - 8 q^{12} + 12 q^{13} + 28 q^{16} + 28 q^{17} + 4 q^{18} + 8 q^{21} + 32 q^{22} - 8 q^{23} - 16 q^{31} + 28 q^{34} - 32 q^{37} + 8 q^{39} + 4 q^{41} + 40 q^{44} - 16 q^{46} + 24 q^{47} + 16 q^{48} - 28 q^{49} - 52 q^{52} - 20 q^{53} + 8 q^{58} + 32 q^{59} + 8 q^{61} - 72 q^{62} - 28 q^{64} + 16 q^{66} - 60 q^{68} + 8 q^{69} + 40 q^{71} - 12 q^{72} - 40 q^{76} + 48 q^{77} - 8 q^{78} - 28 q^{81} - 4 q^{82} + 104 q^{83} - 32 q^{84} + 16 q^{86} + 24 q^{87} - 72 q^{88} - 36 q^{89} - 56 q^{91} + 32 q^{92} + 8 q^{99}+O(q^{100}) \) 28 * q - 28 * q^4 - 8 * q^11 - 8 * q^12 + 12 * q^13 + 28 * q^16 + 28 * q^17 + 4 * q^18 + 8 * q^21 + 32 * q^22 - 8 * q^23 - 16 * q^31 + 28 * q^34 - 32 * q^37 + 8 * q^39 + 4 * q^41 + 40 * q^44 - 16 * q^46 + 24 * q^47 + 16 * q^48 - 28 * q^49 - 52 * q^52 - 20 * q^53 + 8 * q^58 + 32 * q^59 + 8 * q^61 - 72 * q^62 - 28 * q^64 + 16 * q^66 - 60 * q^68 + 8 * q^69 + 40 * q^71 - 12 * q^72 - 40 * q^76 + 48 * q^77 - 8 * q^78 - 28 * q^81 - 4 * q^82 + 104 * q^83 - 32 * q^84 + 16 * q^86 + 24 * q^87 - 72 * q^88 - 36 * q^89 - 56 * q^91 + 32 * q^92 + 8 * q^99

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