LMFDB - Embedded newform 1456.2.cc.c.673.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(225,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1456.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.cc (of order $6$, degree $2$, not 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:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.4
Root			$-1.12906 - 0.851598i$ of defining polynomial
Character	$\chi$	$=$	1456.673
Dual form			1456.2.cc.c.225.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.172975 - 0.299601i) q^{3} -3.25812i q^{5} +(-0.866025 - 0.500000i) q^{7} +(1.44016 - 2.49443i) q^{9} +O(q^{10})$	\(q+(-0.172975 - 0.299601i) q^{3} -3.25812i q^{5} +(-0.866025 - 0.500000i) q^{7} +(1.44016 - 2.49443i) q^{9} +(1.59871 - 0.923014i) q^{11} +(3.60550 + 0.0186461i) q^{13} +(-0.976136 + 0.563573i) q^{15} +(1.07657 - 1.86467i) q^{17} +(2.07929 + 1.20048i) q^{19} +0.345949i q^{21} +(-0.906314 - 1.56978i) q^{23} -5.61537 q^{25} -2.03429 q^{27} +(1.36703 + 2.36777i) q^{29} +1.74236i q^{31} +(-0.553071 - 0.319316i) q^{33} +(-1.62906 + 2.82162i) q^{35} +(-5.14042 + 2.96783i) q^{37} +(-0.618074 - 1.08344i) q^{39} +(3.65577 - 2.11066i) q^{41} +(4.34111 - 7.51903i) q^{43} +(-8.12716 - 4.69222i) q^{45} -5.87774i q^{47} +(0.500000 + 0.866025i) q^{49} -0.744877 q^{51} -9.30628 q^{53} +(-3.00729 - 5.20878i) q^{55} -0.830609i q^{57} +(-9.31173 - 5.37613i) q^{59} +(-5.05504 + 8.75558i) q^{61} +(-2.49443 + 1.44016i) q^{63} +(0.0607514 - 11.7472i) q^{65} +(-0.716130 + 0.413458i) q^{67} +(-0.313538 + 0.543065i) q^{69} +(2.03884 + 1.17712i) q^{71} +3.19482i q^{73} +(0.971316 + 1.68237i) q^{75} -1.84603 q^{77} -0.801911 q^{79} +(-3.96860 - 6.87381i) q^{81} +9.97031i q^{83} +(-6.07534 - 3.50760i) q^{85} +(0.472923 - 0.819127i) q^{87} +(13.0886 - 7.55674i) q^{89} +(-3.11313 - 1.81890i) q^{91} +(0.522012 - 0.301384i) q^{93} +(3.91130 - 6.77458i) q^{95} +(7.99489 + 4.61585i) q^{97} -5.31715i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{9}+O(q^{10}) $ 12 * q - 4 * q^9	$ 12 q - 4 q^{9} - 6 q^{11} + 4 q^{13} - 6 q^{15} - 4 q^{17} + 12 q^{23} - 20 q^{25} - 12 q^{27} + 8 q^{29} - 30 q^{33} - 6 q^{35} - 42 q^{37} + 4 q^{39} + 30 q^{41} - 2 q^{43} + 6 q^{49} - 52 q^{51} - 44 q^{53} + 6 q^{55} - 18 q^{59} + 14 q^{61} - 12 q^{63} + 60 q^{65} + 24 q^{67} + 4 q^{69} + 24 q^{71} - 46 q^{75} + 8 q^{77} + 56 q^{79} + 2 q^{81} - 48 q^{85} + 2 q^{87} - 12 q^{89} - 14 q^{91} - 18 q^{93} + 22 q^{95} + 6 q^{97}+O(q^{100}) $ 12 * q - 4 * q^9 - 6 * q^11 + 4 * q^13 - 6 * q^15 - 4 * q^17 + 12 * q^23 - 20 * q^25 - 12 * q^27 + 8 * q^29 - 30 * q^33 - 6 * q^35 - 42 * q^37 + 4 * q^39 + 30 * q^41 - 2 * q^43 + 6 * q^49 - 52 * q^51 - 44 * q^53 + 6 * q^55 - 18 * q^59 + 14 * q^61 - 12 * q^63 + 60 * q^65 + 24 * q^67 + 4 * q^69 + 24 * q^71 - 46 * q^75 + 8 * q^77 + 56 * q^79 + 2 * q^81 - 48 * q^85 + 2 * q^87 - 12 * q^89 - 14 * q^91 - 18 * q^93 + 22 * q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.172975	−	0.299601i	−0.0998669	−	0.172975i	0.811763	−	0.583988i	$-0.198508\pi$
$3$	−0.172975	−	0.299601i	−0.0998669	−	0.172975i	−0.911629	+	0.411013i	$0.865175\pi$
$4$		0			0
$5$		−	3.25812i		−	1.45708i	−0.685005	−	0.728539i	$-0.740200\pi$
$5$		−	3.25812i		−	1.45708i	0.685005	−	0.728539i	$-0.259800\pi$
$6$		0			0
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$		0			0
$9$	1.44016	−	2.49443i	0.480053	−	0.831477i
$10$		0			0
$11$	1.59871	−	0.923014i	0.482028	−	0.278299i	−0.239233	−	0.970962i	$-0.576896\pi$
$11$	1.59871	−	0.923014i	0.482028	−	0.278299i	0.721261	+	0.692663i	$0.243563\pi$
$12$		0			0
$13$	3.60550	+	0.0186461i	0.999987	+	0.00517151i
$13$	3.60550	+	0.0186461i	0.999987	+	0.00517151i
$14$		0			0
$15$	−0.976136	+	0.563573i	−0.252037	+	0.145514i
$16$		0			0
$17$	1.07657	−	1.86467i	0.261107	−	0.452250i	−0.705430	−	0.708780i	$-0.749246\pi$
$17$	1.07657	−	1.86467i	0.261107	−	0.452250i	0.966536	+	0.256530i	$0.0825793\pi$
$18$		0			0
$19$	2.07929	+	1.20048i	0.477021	+	0.275408i	0.719174	−	0.694830i	$-0.244520\pi$
$19$	2.07929	+	1.20048i	0.477021	+	0.275408i	−0.242153	+	0.970238i	$0.577854\pi$
$20$		0			0
$21$			0.345949i			0.0754923i
$22$		0			0
$23$	−0.906314	−	1.56978i	−0.188979	−	0.327322i	0.755931	−	0.654652i	$-0.227185\pi$
$23$	−0.906314	−	1.56978i	−0.188979	−	0.327322i	−0.944910	+	0.327329i	$0.893851\pi$
$24$		0			0
$25$	−5.61537			−1.12307
$26$		0			0
$27$	−2.03429			−0.391500
$28$		0			0
$29$	1.36703	+	2.36777i	0.253851	+	0.439683i	0.964583	−	0.263780i	$-0.0849693\pi$
$29$	1.36703	+	2.36777i	0.253851	+	0.439683i	−0.710732	+	0.703463i	$0.751636\pi$
$30$		0			0
$31$			1.74236i			0.312937i	0.987683	+	0.156468i	$0.0500110\pi$
$31$			1.74236i			0.312937i	−0.987683	+	0.156468i	$0.949989\pi$
$32$		0			0
$33$	−0.553071	−	0.319316i	−0.0962774	−	0.0555858i
$34$		0			0
$35$	−1.62906	+	2.82162i	−0.275362	+	0.476940i
$36$		0			0
$37$	−5.14042	+	2.96783i	−0.845081	+	0.487908i	−0.858988	−	0.511996i	$-0.828906\pi$
$37$	−5.14042	+	2.96783i	−0.845081	+	0.487908i	0.0139073	+	0.999903i	$0.495573\pi$
$38$		0			0
$39$	−0.618074	−	1.08344i	−0.0989710	−	0.173489i
$40$		0			0
$41$	3.65577	−	2.11066i	0.570935	−	0.329629i	−0.186588	−	0.982438i	$-0.559743\pi$
$41$	3.65577	−	2.11066i	0.570935	−	0.329629i	0.757523	+	0.652809i	$0.226410\pi$
$42$		0			0
$43$	4.34111	−	7.51903i	0.662014	−	1.14664i	−0.318072	−	0.948067i	$-0.603035\pi$
$43$	4.34111	−	7.51903i	0.662014	−	1.14664i	0.980086	−	0.198575i	$-0.0636313\pi$
$44$		0			0
$45$	−8.12716	−	4.69222i	−1.21153	−	0.699475i
$46$		0			0
$47$		−	5.87774i		−	0.857357i	−0.903457	−	0.428678i	$-0.858979\pi$
$47$		−	5.87774i		−	0.857357i	0.903457	−	0.428678i	$-0.141021\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$		0			0
$51$	−0.744877			−0.104304
$52$		0			0
$53$	−9.30628			−1.27832			−0.639158	−	0.769076i	$-0.720717\pi$
$53$	−9.30628			−1.27832			−0.639158	+	0.769076i	$0.720717\pi$
$54$		0			0
$55$	−3.00729	−	5.20878i	−0.405503	−	0.702352i
$56$		0			0
$57$		−	0.830609i		−	0.110017i
$58$		0			0
$59$	−9.31173	−	5.37613i	−1.21228	−	0.699912i	−0.249028	−	0.968496i	$-0.580111\pi$
$59$	−9.31173	−	5.37613i	−1.21228	−	0.699912i	−0.963256	+	0.268584i	$0.913444\pi$
$60$		0			0
$61$	−5.05504	+	8.75558i	−0.647231	+	1.12104i	0.336550	+	0.941665i	$0.390740\pi$
$61$	−5.05504	+	8.75558i	−0.647231	+	1.12104i	−0.983781	+	0.179371i	$0.942594\pi$
$62$		0			0
$63$	−2.49443	+	1.44016i	−0.314269	+	0.181443i
$64$		0			0
$65$	0.0607514	−	11.7472i	0.00753529	−	1.45706i
$66$		0			0
$67$	−0.716130	+	0.413458i	−0.0874892	+	0.0505119i	−0.543106	−	0.839664i	$-0.682752\pi$
$67$	−0.716130	+	0.413458i	−0.0874892	+	0.0505119i	0.455617	+	0.890176i	$0.349419\pi$
$68$		0			0
$69$	−0.313538	+	0.543065i	−0.0377456	+	0.0653773i
$70$		0			0
$71$	2.03884	+	1.17712i	0.241965	+	0.139699i	0.616080	−	0.787684i	$-0.288720\pi$
$71$	2.03884	+	1.17712i	0.241965	+	0.139699i	−0.374114	+	0.927383i	$0.622053\pi$
$72$		0			0
$73$			3.19482i			0.373925i	0.982367	+	0.186963i	$0.0598644\pi$
$73$			3.19482i			0.373925i	−0.982367	+	0.186963i	$0.940136\pi$
$74$		0			0
$75$	0.971316	+	1.68237i	0.112158	+	0.194263i
$76$		0			0
$77$	−1.84603			−0.210374
$78$		0			0
$79$	−0.801911			−0.0902220			−0.0451110	−	0.998982i	$-0.514364\pi$
$79$	−0.801911			−0.0902220			−0.0451110	+	0.998982i	$0.514364\pi$
$80$		0			0
$81$	−3.96860	−	6.87381i	−0.440955	−	0.763757i
$82$		0			0
$83$			9.97031i			1.09438i	0.837007	+	0.547192i	$0.184303\pi$
$83$			9.97031i			1.09438i	−0.837007	+	0.547192i	$0.815697\pi$
$84$		0			0
$85$	−6.07534	−	3.50760i	−0.658963	−	0.380452i
$86$		0			0
$87$	0.472923	−	0.819127i	0.0507027	−	0.0878196i
$88$		0			0
$89$	13.0886	−	7.55674i	1.38739	−	0.801012i	0.394373	−	0.918950i	$-0.370962\pi$
$89$	13.0886	−	7.55674i	1.38739	−	0.801012i	0.993021	+	0.117938i	$0.0376284\pi$
$90$		0			0
$91$	−3.11313	−	1.81890i	−0.326345	−	0.190672i
$92$		0			0
$93$	0.522012	−	0.301384i	0.0541301	−	0.0312520i
$94$		0			0
$95$	3.91130	−	6.77458i	0.401291	−	0.695057i
$96$		0			0
$97$	7.99489	+	4.61585i	0.811758	+	0.468669i	0.847566	−	0.530690i	$-0.178067\pi$
$97$	7.99489	+	4.61585i	0.811758	+	0.468669i	−0.0358079	+	0.999359i	$0.511400\pi$
$98$		0			0
$99$		−	5.31715i		−	0.534394i
$100$		0			0
$101$	7.41169	+	12.8374i	0.737491	+	1.27737i	0.953622	+	0.301007i	$0.0973228\pi$
$101$	7.41169	+	12.8374i	0.737491	+	1.27737i	−0.216131	+	0.976364i	$0.569344\pi$
$102$		0			0
$103$	−4.28286			−0.422003			−0.211001	−	0.977486i	$-0.567672\pi$
$103$	−4.28286			−0.422003			−0.211001	+	0.977486i	$0.567672\pi$
$104$		0			0
$105$	1.12715			0.109998
$106$		0			0
$107$	−9.56289	−	16.5634i	−0.924479	−	1.60124i	−0.792397	−	0.610006i	$-0.791167\pi$
$107$	−9.56289	−	16.5634i	−0.924479	−	1.60124i	−0.132082	−	0.991239i	$-0.542166\pi$
$108$		0			0
$109$		−	4.27153i		−	0.409139i	−0.978852	−	0.204569i	$-0.934421\pi$
$109$		−	4.27153i		−	0.409139i	0.978852	−	0.204569i	$-0.0655794\pi$
$110$		0			0
$111$	1.77833	+	1.02672i	0.168791	+	0.0974516i
$112$		0			0
$113$	−1.37488	+	2.38137i	−0.129338	+	0.224020i	−0.923420	−	0.383790i	$-0.874619\pi$
$113$	−1.37488	+	2.38137i	−0.129338	+	0.224020i	0.794082	+	0.607810i	$0.207952\pi$
$114$		0			0
$115$	−5.11454	+	2.95288i	−0.476934	+	0.275358i
$116$		0			0
$117$	5.23901	−	8.96682i	0.484347	−	0.828983i
$118$		0			0
$119$	−1.86467	+	1.07657i	−0.170934	+	0.0986890i
$120$		0			0
$121$	−3.79609	+	6.57502i	−0.345099	+	0.597729i
$122$		0			0
$123$	−1.26471	−	0.730180i	−0.114035	−	0.0658381i
$124$		0			0
$125$			2.00495i			0.179329i
$126$		0			0
$127$	4.86719	+	8.43022i	0.431893	+	0.748061i	0.997036	−	0.0769320i	$-0.0245124\pi$
$127$	4.86719	+	8.43022i	0.431893	+	0.748061i	−0.565143	+	0.824993i	$0.691179\pi$
$128$		0			0
$129$	−3.00361			−0.264453
$130$		0			0
$131$	18.6615			1.63046			0.815230	−	0.579138i	$-0.196611\pi$
$131$	18.6615			1.63046			0.815230	+	0.579138i	$0.196611\pi$
$132$		0			0
$133$	−1.20048	−	2.07929i	−0.104095	−	0.180297i
$134$		0			0
$135$			6.62797i			0.570445i
$136$		0			0
$137$	−7.29328	−	4.21078i	−0.623107	−	0.359751i	0.154971	−	0.987919i	$-0.450472\pi$
$137$	−7.29328	−	4.21078i	−0.623107	−	0.359751i	−0.778078	+	0.628168i	$0.783805\pi$
$138$		0			0
$139$	−8.81809	+	15.2734i	−0.747941	+	1.29547i	0.200867	+	0.979619i	$0.435624\pi$
$139$	−8.81809	+	15.2734i	−0.747941	+	1.29547i	−0.948808	+	0.315853i	$0.897709\pi$
$140$		0			0
$141$	−1.76098	+	1.01670i	−0.148301	+	0.0856216i
$142$		0			0
$143$	5.78135	−	3.29812i	0.483461	−	0.275803i
$144$		0			0
$145$	7.71448	−	4.45396i	0.640653	−	0.369881i
$146$		0			0
$147$	0.172975	−	0.299601i	0.0142667	−	0.0247107i
$148$		0			0
$149$	−3.48232	−	2.01052i	−0.285283	−	0.164708i	0.350530	−	0.936552i	$-0.386002\pi$
$149$	−3.48232	−	2.01052i	−0.285283	−	0.164708i	−0.635813	+	0.771843i	$0.719335\pi$
$150$		0			0
$151$		−	18.9010i		−	1.53814i	−0.639165	−	0.769069i	$-0.720720\pi$
$151$		−	18.9010i		−	1.53814i	0.639165	−	0.769069i	$-0.279280\pi$
$152$		0			0
$153$	−3.10086	−	5.37086i	−0.250690	−	0.434208i
$154$		0			0
$155$	5.67682			0.455973
$156$		0			0
$157$	−11.5735			−0.923670			−0.461835	−	0.886966i	$-0.652809\pi$
$157$	−11.5735			−0.923670			−0.461835	+	0.886966i	$0.652809\pi$
$158$		0			0
$159$	1.60975	+	2.78817i	0.127661	+	0.221116i
$160$		0			0
$161$			1.81263i			0.142855i
$162$		0			0
$163$	3.81520	+	2.20271i	0.298830	+	0.172529i	0.641917	−	0.766774i	$-0.278139\pi$
$163$	3.81520	+	2.20271i	0.298830	+	0.172529i	−0.343087	+	0.939304i	$0.611473\pi$
$164$		0			0
$165$	−1.04037	+	1.80197i	−0.0809927	+	0.140284i
$166$		0			0
$167$	7.81076	−	4.50954i	0.604415	−	0.348959i	−0.166362	−	0.986065i	$-0.553202\pi$
$167$	7.81076	−	4.50954i	0.604415	−	0.348959i	0.770776	+	0.637106i	$0.219869\pi$
$168$		0			0
$169$	12.9993	+	0.134457i	0.999947	+	0.0103429i
$170$		0			0
$171$	5.98901	−	3.45776i	0.457991	−	0.264421i
$172$		0			0
$173$	3.04600	−	5.27583i	0.231583	−	0.401114i	−0.726691	−	0.686964i	$-0.758943\pi$
$173$	3.04600	−	5.27583i	0.231583	−	0.401114i	0.958274	+	0.285851i	$0.0922761\pi$
$174$		0			0
$175$	4.86305	+	2.80769i	0.367612	+	0.212241i
$176$		0			0
$177$			3.71974i			0.279592i
$178$		0			0
$179$	−1.93982	−	3.35987i	−0.144989	−	0.251128i	0.784380	−	0.620281i	$-0.212981\pi$
$179$	−1.93982	−	3.35987i	−0.144989	−	0.251128i	−0.929369	+	0.369152i	$0.879648\pi$
$180$		0			0
$181$	−6.58392			−0.489379			−0.244690	−	0.969601i	$-0.578686\pi$
$181$	−6.58392			−0.489379			−0.244690	+	0.969601i	$0.578686\pi$
$182$		0			0
$183$	3.49757			0.258548
$184$		0			0
$185$	9.66954	+	16.7481i	0.710919	+	1.23135i
$186$		0			0
$187$		−	3.97476i		−	0.290663i
$188$		0			0
$189$	1.76175	+	1.01715i	0.128148	+	0.0739865i
$190$		0			0
$191$	−6.87168	+	11.9021i	−0.497218	+	0.861206i	−0.999995	−	0.00320983i	$-0.998978\pi$
$191$	−6.87168	+	11.9021i	−0.497218	+	0.861206i	0.502777	+	0.864416i	$0.332312\pi$
$192$		0			0
$193$	19.7047	−	11.3765i	1.41838	−	0.818899i	0.422219	−	0.906494i	$-0.361251\pi$
$193$	19.7047	−	11.3765i	1.41838	−	0.818899i	0.996156	+	0.0875946i	$0.0279180\pi$
$194$		0			0
$195$	−3.52997	+	2.01376i	−0.252786	+	0.144208i
$196$		0			0
$197$	−12.5809	+	7.26358i	−0.896352	+	0.517509i	−0.876015	−	0.482284i	$-0.839807\pi$
$197$	−12.5809	+	7.26358i	−0.896352	+	0.517509i	−0.0203371	+	0.999793i	$0.506474\pi$
$198$		0			0
$199$	−11.9202	+	20.6464i	−0.845001	+	1.46358i	0.0406192	+	0.999175i	$0.487067\pi$
$199$	−11.9202	+	20.6464i	−0.845001	+	1.46358i	−0.885620	+	0.464410i	$0.846266\pi$
$200$		0			0
$201$	0.247745	+	0.143035i	0.0174746	+	0.0100889i
$202$		0			0
$203$		−	2.73406i		−	0.191894i
$204$		0			0
$205$	−6.87678	−	11.9109i	−0.480295	−	0.831896i
$206$		0			0
$207$	−5.22095			−0.362881
$208$		0			0
$209$	4.43223			0.306584
$210$		0			0
$211$	2.15764	+	3.73714i	0.148538	+	0.257275i	0.930687	−	0.365816i	$-0.119210\pi$
$211$	2.15764	+	3.73714i	0.148538	+	0.257275i	−0.782149	+	0.623091i	$0.785877\pi$
$212$		0			0
$213$		−	0.814450i		−	0.0558052i
$214$		0			0
$215$	−24.4979	−	14.1439i	−1.67075	−	0.964605i
$216$		0			0
$217$	0.871180	−	1.50893i	0.0591395	−	0.102433i
$218$		0			0
$219$	0.957171	−	0.552623i	0.0646796	−	0.0373428i
$220$		0			0
$221$	3.91635	−	6.70301i	0.263442	−	0.450893i
$222$		0			0
$223$	20.2604	−	11.6973i	1.35674	−	0.783312i	0.367553	−	0.930003i	$-0.380196\pi$
$223$	20.2604	−	11.6973i	1.35674	−	0.783312i	0.989182	+	0.146691i	$0.0468623\pi$
$224$		0			0
$225$	−8.08703	+	14.0071i	−0.539135	+	0.933810i
$226$		0			0
$227$	23.1427	+	13.3614i	1.53603	+	0.886829i	0.999065	+	0.0432270i	$0.0137639\pi$
$227$	23.1427	+	13.3614i	1.53603	+	0.886829i	0.536968	+	0.843602i	$0.319569\pi$
$228$		0			0
$229$		−	3.00670i		−	0.198688i	−0.995053	−	0.0993442i	$-0.968326\pi$
$229$		−	3.00670i		−	0.198688i	0.995053	−	0.0993442i	$-0.0316745\pi$
$230$		0			0
$231$	0.319316	+	0.553071i	0.0210094	+	0.0363894i
$232$		0			0
$233$	11.7148			0.767462			0.383731	−	0.923445i	$-0.374639\pi$
$233$	11.7148			0.767462			0.383731	+	0.923445i	$0.374639\pi$
$234$		0			0
$235$	−19.1504			−1.24924
$236$		0			0
$237$	0.138710	+	0.240253i	0.00901019	+	0.0156061i
$238$		0			0
$239$		−	1.42797i		−	0.0923677i	−0.998933	−	0.0461838i	$-0.985294\pi$
$239$		−	1.42797i		−	0.0923677i	0.998933	−	0.0461838i	$-0.0147060\pi$
$240$		0			0
$241$	−2.32068	−	1.33984i	−0.149488	−	0.0863069i	0.423390	−	0.905947i	$-0.360840\pi$
$241$	−2.32068	−	1.33984i	−0.149488	−	0.0863069i	−0.572878	+	0.819640i	$0.694173\pi$
$242$		0			0
$243$	−4.42437	+	7.66323i	−0.283824	+	0.491597i
$244$		0			0
$245$	2.82162	−	1.62906i	0.180267	−	0.104077i
$246$		0			0
$247$	7.47450	+	4.36710i	0.475591	+	0.277872i
$248$		0			0
$249$	2.98711	−	1.72461i	0.189301	−	0.109293i
$250$		0			0
$251$	−5.46696	+	9.46906i	−0.345072	+	0.597681i	−0.985367	−	0.170447i	$-0.945479\pi$
$251$	−5.46696	+	9.46906i	−0.345072	+	0.597681i	0.640295	+	0.768129i	$0.278812\pi$
$252$		0			0
$253$	−2.89786	−	1.67308i	−0.182187	−	0.105186i
$254$		0			0
$255$			2.42690i			0.151978i
$256$		0			0
$257$	2.07569	+	3.59520i	0.129478	+	0.224262i	0.923474	−	0.383660i	$-0.125337\pi$
$257$	2.07569	+	3.59520i	0.129478	+	0.224262i	−0.793996	+	0.607922i	$0.792003\pi$
$258$		0			0
$259$	5.93565			0.368823
$260$		0			0
$261$	7.87497			0.487448
$262$		0			0
$263$	2.02680	+	3.51052i	0.124978	+	0.216468i	0.921724	−	0.387846i	$-0.126781\pi$
$263$	2.02680	+	3.51052i	0.124978	+	0.216468i	−0.796747	+	0.604314i	$0.793447\pi$
$264$		0			0
$265$			30.3210i			1.86260i
$266$		0			0
$267$	−4.52801	−	2.61425i	−0.277110	−	0.159989i
$268$		0			0
$269$	−2.00011	+	3.46430i	−0.121949	+	0.211222i	−0.920536	−	0.390657i	$-0.872248\pi$
$269$	−2.00011	+	3.46430i	−0.121949	+	0.211222i	0.798587	+	0.601879i	$0.205581\pi$
$270$		0			0
$271$	2.41189	−	1.39251i	0.146512	−	0.0845888i	−0.424952	−	0.905216i	$-0.639709\pi$
$271$	2.41189	−	1.39251i	0.146512	−	0.0845888i	0.571464	+	0.820627i	$0.306376\pi$
$272$		0			0
$273$	−0.00645062	+	1.24732i	−0.000390409	+	0.0754913i
$274$		0			0
$275$	−8.97733	+	5.18306i	−0.541353	+	0.312551i
$276$		0			0
$277$	8.34618	−	14.4560i	0.501474	−	0.868578i	−0.498525	−	0.866875i	$-0.666125\pi$
$277$	8.34618	−	14.4560i	0.501474	−	0.868578i	0.999999	−	0.00170243i	$-0.000541901\pi$
$278$		0			0
$279$	4.34619	+	2.50928i	0.260200	+	0.150226i
$280$		0			0
$281$			13.3731i			0.797774i	0.917000	+	0.398887i	$0.130603\pi$
$281$			13.3731i			0.797774i	−0.917000	+	0.398887i	$0.869397\pi$
$282$		0			0
$283$	9.44312	+	16.3560i	0.561335	+	0.972261i	0.997380	+	0.0723362i	$0.0230455\pi$
$283$	9.44312	+	16.3560i	0.561335	+	0.972261i	−0.436045	+	0.899925i	$0.643621\pi$
$284$		0			0
$285$	−2.70623			−0.160303
$286$		0			0
$287$	−4.22131			−0.249176
$288$		0			0
$289$	6.18199	+	10.7075i	0.363647	+	0.629855i
$290$		0			0
$291$		−	3.19370i		−	0.187218i
$292$		0			0
$293$	−2.95999	−	1.70895i	−0.172925	−	0.0998380i	0.411040	−	0.911617i	$-0.365166\pi$
$293$	−2.95999	−	1.70895i	−0.172925	−	0.0998380i	−0.583964	+	0.811779i	$0.698499\pi$
$294$		0			0
$295$	−17.5161	+	30.3388i	−1.01983	+	1.76639i
$296$		0			0
$297$	−3.25224	+	1.87768i	−0.188714	+	0.108954i
$298$		0			0
$299$	−3.23845	−	5.67675i	−0.187284	−	0.328295i
$300$		0			0
$301$	−7.51903	+	4.34111i	−0.433390	+	0.250218i
$302$		0			0
$303$	2.56407	−	4.44110i	0.147302	−	0.255134i
$304$		0			0
$305$	28.5268	+	16.4699i	1.63344	+	0.943066i
$306$		0			0
$307$			16.3679i			0.934165i	0.884214	+	0.467083i	$0.154695\pi$
$307$			16.3679i			0.934165i	−0.884214	+	0.467083i	$0.845305\pi$
$308$		0			0
$309$	0.740826	+	1.28315i	0.0421441	+	0.0729958i
$310$		0			0
$311$	23.6979			1.34378			0.671891	−	0.740650i	$-0.265482\pi$
$311$	23.6979			1.34378			0.671891	+	0.740650i	$0.265482\pi$
$312$		0			0
$313$	−5.18025			−0.292805			−0.146403	−	0.989225i	$-0.546769\pi$
$313$	−5.18025			−0.292805			−0.146403	+	0.989225i	$0.546769\pi$
$314$		0			0
$315$	4.69222	+	8.12716i	0.264377	+	0.457914i
$316$		0			0
$317$		−	6.06537i		−	0.340665i	−0.985387	−	0.170332i	$-0.945516\pi$
$317$		−	6.06537i		−	0.340665i	0.985387	−	0.170332i	$-0.0544842\pi$
$318$		0			0
$319$	4.37096	+	2.52358i	0.244727	+	0.141293i
$320$		0			0
$321$	−3.30827	+	5.73010i	−0.184650	+	0.319823i
$322$		0			0
$323$	4.47700	−	2.58480i	0.249107	−	0.143822i
$324$		0			0
$325$	−20.2462	−	0.104705i	−1.12306	−	0.00580799i
$326$		0			0
$327$	−1.27975	+	0.738866i	−0.0707706	+	0.0408594i
$328$		0			0
$329$	−2.93887	+	5.09027i	−0.162025	+	0.280636i
$330$		0			0
$331$	−14.9605	−	8.63743i	−0.822301	−	0.474756i	0.0289082	−	0.999582i	$-0.490797\pi$
$331$	−14.9605	−	8.63743i	−0.822301	−	0.474756i	−0.851209	+	0.524826i	$0.824130\pi$
$332$		0			0
$333$			17.0966i			0.936886i
$334$		0			0
$335$	1.34710	+	2.33324i	0.0735998	+	0.127479i
$336$		0			0
$337$	−8.35464			−0.455106			−0.227553	−	0.973766i	$-0.573073\pi$
$337$	−8.35464			−0.455106			−0.227553	+	0.973766i	$0.573073\pi$
$338$		0			0
$339$	0.951279			0.0516664
$340$		0			0
$341$	1.60822	+	2.78552i	0.0870901	+	0.150844i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$	1.76937	+	1.02155i	0.0952598	+	0.0549983i
$346$		0			0
$347$	14.4110	−	24.9606i	0.773623	−	1.33995i	−0.161942	−	0.986800i	$-0.551776\pi$
$347$	14.4110	−	24.9606i	0.773623	−	1.33995i	0.935565	−	0.353154i	$-0.114891\pi$
$348$		0			0
$349$	−10.1516	+	5.86103i	−0.543403	+	0.313734i	−0.746457	−	0.665434i	$-0.768247\pi$
$349$	−10.1516	+	5.86103i	−0.543403	+	0.313734i	0.203054	+	0.979167i	$0.434913\pi$
$350$		0			0
$351$	−7.33464	−	0.0379317i	−0.391494	−	0.00202464i
$352$		0			0
$353$	15.4466	−	8.91811i	0.822141	−	0.474663i	−0.0290134	−	0.999579i	$-0.509237\pi$
$353$	15.4466	−	8.91811i	0.822141	−	0.474663i	0.851154	+	0.524916i	$0.175903\pi$
$354$		0			0
$355$	3.83521	−	6.64278i	0.203552	−	0.352562i
$356$		0			0
$357$	0.645082	+	0.372438i	0.0341414	+	0.0197115i
$358$		0			0
$359$			5.68162i			0.299864i	0.988696	+	0.149932i	$0.0479055\pi$
$359$			5.68162i			0.299864i	−0.988696	+	0.149932i	$0.952094\pi$
$360$		0			0
$361$	−6.61771	−	11.4622i	−0.348300	−	0.603274i
$362$		0			0
$363$	2.62651			0.137856
$364$		0			0
$365$	10.4091			0.544838
$366$		0			0
$367$	−9.81580	−	17.0015i	−0.512381	−	0.887469i	−0.999897	−	0.0143554i	$-0.995430\pi$
$367$	−9.81580	−	17.0015i	−0.512381	−	0.887469i	0.487516	−	0.873114i	$-0.337903\pi$
$368$		0			0
$369$		−	12.1587i		−	0.632958i
$370$		0			0
$371$	8.05947	+	4.65314i	0.418427	+	0.241579i
$372$		0			0
$373$	−16.0323	+	27.7687i	−0.830119	+	1.43781i	0.0678240	+	0.997697i	$0.478394\pi$
$373$	−16.0323	+	27.7687i	−0.830119	+	1.43781i	−0.897943	+	0.440111i	$0.854939\pi$
$374$		0			0
$375$	0.600686	−	0.346806i	0.0310193	−	0.0179090i
$376$		0			0
$377$	4.88468	+	8.56248i	0.251574	+	0.440990i
$378$		0			0
$379$	16.4745	−	9.51154i	0.846237	−	0.488575i	−0.0131425	−	0.999914i	$-0.504184\pi$
$379$	16.4745	−	9.51154i	0.846237	−	0.488575i	0.859379	+	0.511339i	$0.170850\pi$
$380$		0			0
$381$	1.68380	−	2.91643i	0.0862637	−	0.149413i
$382$		0			0
$383$	−0.606070	−	0.349915i	−0.0309687	−	0.0178798i	0.484436	−	0.874827i	$-0.339025\pi$
$383$	−0.606070	−	0.349915i	−0.0309687	−	0.0178798i	−0.515404	+	0.856947i	$0.672358\pi$
$384$		0			0
$385$			6.01459i			0.306532i
$386$		0			0
$387$	−12.5038	−	21.6572i	−0.635604	−	1.10090i
$388$		0			0
$389$	20.0547			1.01681			0.508407	−	0.861117i	$-0.330235\pi$
$389$	20.0547			1.01681			0.508407	+	0.861117i	$0.330235\pi$
$390$		0			0
$391$	−3.90284			−0.197375
$392$		0			0
$393$	−3.22796	−	5.59099i	−0.162829	−	0.282028i
$394$		0			0
$395$			2.61272i			0.131460i
$396$		0			0
$397$	−19.2953	−	11.1401i	−0.968403	−	0.559108i	−0.0696541	−	0.997571i	$-0.522190\pi$
$397$	−19.2953	−	11.1401i	−0.968403	−	0.559108i	−0.898749	+	0.438463i	$0.855523\pi$
$398$		0			0
$399$	−0.415304	+	0.719328i	−0.0207912	+	0.0360114i
$400$		0			0
$401$	−4.16341	+	2.40374i	−0.207911	+	0.120037i	−0.600340	−	0.799745i	$-0.704968\pi$
$401$	−4.16341	+	2.40374i	−0.207911	+	0.120037i	0.392429	+	0.919782i	$0.371635\pi$
$402$		0			0
$403$	−0.0324883	+	6.28208i	−0.00161836	+	0.312933i
$404$		0			0
$405$	−22.3957	+	12.9302i	−1.11285	+	0.642506i
$406$		0			0
$407$	−5.47869	+	9.48937i	−0.271568	+	0.470370i
$408$		0			0
$409$	31.8727	+	18.4017i	1.57601	+	0.909907i	0.995409	+	0.0957164i	$0.0305142\pi$
$409$	31.8727	+	18.4017i	1.57601	+	0.909907i	0.580597	+	0.814191i	$0.302819\pi$
$410$		0			0
$411$			2.91343i			0.143709i
$412$		0			0
$413$	5.37613	+	9.31173i	0.264542	+	0.458200i
$414$		0			0
$415$	32.4845			1.59460
$416$		0			0
$417$	6.10122			0.298778
$418$		0			0
$419$	14.6334	+	25.3457i	0.714887	+	1.23822i	0.963003	+	0.269490i	$0.0868552\pi$
$419$	14.6334	+	25.3457i	0.714887	+	1.23822i	−0.248116	+	0.968730i	$0.579812\pi$
$420$		0			0
$421$		−	7.53862i		−	0.367410i	−0.982981	−	0.183705i	$-0.941191\pi$
$421$		−	7.53862i		−	0.367410i	0.982981	−	0.183705i	$-0.0588091\pi$
$422$		0			0
$423$	−14.6616	−	8.46489i	−0.712872	−	0.411577i
$424$		0			0
$425$	−6.04534	+	10.4708i	−0.293242	+	0.507910i
$426$		0			0
$427$	8.75558	−	5.05504i	0.423712	−	0.244630i
$428$		0			0
$429$	−1.98815	−	1.16161i	−0.0959886	−	0.0560829i
$430$		0			0
$431$	27.0426	−	15.6131i	1.30260	−	0.752055i	0.321748	−	0.946825i	$-0.395730\pi$
$431$	27.0426	−	15.6131i	1.30260	−	0.752055i	0.980849	+	0.194771i	$0.0623963\pi$
$432$		0			0
$433$	2.94202	−	5.09573i	0.141384	−	0.244885i	−0.786634	−	0.617420i	$-0.788178\pi$
$433$	2.94202	−	5.09573i	0.141384	−	0.244885i	0.928018	+	0.372535i	$0.121511\pi$
$434$		0			0
$435$	−2.66882	−	1.54084i	−0.127960	−	0.0738777i
$436$		0			0
$437$		−	4.35204i		−	0.208186i
$438$		0			0
$439$	4.97821	+	8.62251i	0.237597	+	0.411530i	0.960024	−	0.279917i	$-0.0903069\pi$
$439$	4.97821	+	8.62251i	0.237597	+	0.411530i	−0.722427	+	0.691447i	$0.756974\pi$
$440$		0			0
$441$	2.88032			0.137158
$442$		0			0
$443$	35.8813			1.70477			0.852385	−	0.522915i	$-0.175155\pi$
$443$	35.8813			1.70477			0.852385	+	0.522915i	$0.175155\pi$
$444$		0			0
$445$	−24.6208	−	42.6444i	−1.16714	−	2.02154i
$446$		0			0
$447$			1.39108i			0.0657956i
$448$		0			0
$449$	3.46001	+	1.99764i	0.163288	+	0.0942744i	0.579417	−	0.815031i	$-0.303280\pi$
$449$	3.46001	+	1.99764i	0.163288	+	0.0942744i	−0.416129	+	0.909306i	$0.636614\pi$
$450$		0			0
$451$	3.89633	−	6.74864i	0.183471	−	0.317781i
$452$		0			0
$453$	−5.66274	+	3.26939i	−0.266059	+	0.153609i
$454$		0			0
$455$	−5.92620	+	10.1430i	−0.277825	+	0.475510i
$456$		0			0
$457$	35.6995	−	20.6111i	1.66995	−	0.964147i	0.702291	−	0.711890i	$-0.252160\pi$
$457$	35.6995	−	20.6111i	1.66995	−	0.964147i	0.967660	−	0.252257i	$-0.0811729\pi$
$458$		0			0
$459$	−2.19006	+	3.79329i	−0.102223	+	0.177056i
$460$		0			0
$461$	21.4139	+	12.3633i	0.997343	+	0.575816i	0.907461	−	0.420136i	$-0.138018\pi$
$461$	21.4139	+	12.3633i	0.997343	+	0.575816i	0.0898818	+	0.995952i	$0.471351\pi$
$462$		0			0
$463$			24.4057i			1.13423i	0.823639	+	0.567115i	$0.191940\pi$
$463$			24.4057i			1.13423i	−0.823639	+	0.567115i	$0.808060\pi$
$464$		0			0
$465$	−0.981946	−	1.70078i	−0.0455366	−	0.0788718i
$466$		0			0
$467$	−4.44860			−0.205857			−0.102928	−	0.994689i	$-0.532821\pi$
$467$	−4.44860			−0.205857			−0.102928	+	0.994689i	$0.532821\pi$
$468$		0			0
$469$	0.826916			0.0381834
$470$		0			0
$471$	2.00193	+	3.46744i	0.0922441	+	0.159771i
$472$		0			0
$473$		−	16.0276i		−	0.736951i
$474$		0			0
$475$	−11.6760	−	6.74113i	−0.535730	−	0.309304i
$476$		0			0
$477$	−13.4025	+	23.2139i	−0.613660	+	1.06289i
$478$		0			0
$479$	27.4328	−	15.8383i	1.25343	−	0.723671i	0.281645	−	0.959519i	$-0.409120\pi$
$479$	27.4328	−	15.8383i	1.25343	−	0.723671i	0.971790	+	0.235848i	$0.0757868\pi$
$480$		0			0
$481$	−18.5892	+	10.6047i	−0.847593	+	0.483531i
$482$		0			0
$483$	0.543065	−	0.313538i	0.0247103	−	0.0142665i
$484$		0			0
$485$	15.0390	−	26.0483i	0.682887	−	1.18279i
$486$		0			0
$487$	−23.3096	−	13.4578i	−1.05626	−	0.609832i	−0.131864	−	0.991268i	$-0.542096\pi$
$487$	−23.3096	−	13.4578i	−1.05626	−	0.609832i	−0.924395	+	0.381436i	$0.875430\pi$
$488$		0			0
$489$		−	1.52405i		−	0.0689200i
$490$		0			0
$491$	−4.86358	−	8.42396i	−0.219490	−	0.380168i	0.735162	−	0.677891i	$-0.237106\pi$
$491$	−4.86358	−	8.42396i	−0.219490	−	0.380168i	−0.954652	+	0.297723i	$0.903773\pi$
$492$		0			0
$493$	5.88682			0.265129
$494$		0			0
$495$	−17.3239			−0.778653
$496$		0			0
$497$	−1.17712	−	2.03884i	−0.0528012	−	0.0914543i
$498$		0			0
$499$		−	7.87525i		−	0.352545i	−0.984341	−	0.176272i	$-0.943596\pi$
$499$		−	7.87525i		−	0.352545i	0.984341	−	0.176272i	$-0.0564039\pi$
$500$		0			0
$501$	−2.70213	−	1.56007i	−0.120722	−	0.0696989i
$502$		0			0
$503$	−4.87603	+	8.44553i	−0.217411	+	0.376568i	−0.954016	−	0.299756i	$-0.903095\pi$
$503$	−4.87603	+	8.44553i	−0.217411	+	0.376568i	0.736604	+	0.676324i	$0.236428\pi$
$504$		0			0
$505$	41.8259	−	24.1482i	1.86123	−	1.07458i
$506$		0			0
$507$	−2.20827	−	3.91786i	−0.0980725	−	0.173998i
$508$		0			0
$509$	−19.9407	+	11.5128i	−0.883857	+	0.510295i	−0.871928	−	0.489634i	$-0.837130\pi$
$509$	−19.9407	+	11.5128i	−0.883857	+	0.510295i	−0.0119288	+	0.999929i	$0.503797\pi$
$510$		0			0
$511$	1.59741	−	2.76680i	0.0706653	−	0.122396i
$512$		0			0
$513$	−4.22988	−	2.44212i	−0.186754	−	0.107822i
$514$		0			0
$515$			13.9541i			0.614891i
$516$		0			0
$517$	−5.42524	−	9.39679i	−0.238602	−	0.413270i
$518$		0			0
$519$	−2.10752			−0.0925100
$520$		0			0
$521$	0.486481			0.0213131			0.0106566	−	0.999943i	$-0.496608\pi$
$521$	0.486481			0.0213131			0.0106566	+	0.999943i	$0.496608\pi$
$522$		0			0
$523$	−17.3135	−	29.9878i	−0.757065	−	1.31128i	−0.944341	−	0.328968i	$-0.893299\pi$
$523$	−17.3135	−	29.9878i	−0.757065	−	1.31128i	0.187275	−	0.982307i	$-0.440034\pi$
$524$		0			0
$525$		−	1.94263i		−	0.0847834i
$526$		0			0
$527$	3.24893	+	1.87577i	0.141526	+	0.0817099i
$528$		0			0
$529$	9.85719	−	17.0732i	0.428574	−	0.742311i
$530$		0			0
$531$	−26.8208	+	15.4850i	−1.16392	+	0.671990i
$532$		0			0
$533$	13.2202	−	7.54182i	0.572632	−	0.326672i
$534$		0			0
$535$	−53.9656	+	31.1571i	−2.33314	+	1.34704i
$536$		0			0
$537$	−0.671080	+	1.16234i	−0.0289592	+	0.0501589i
$538$		0			0
$539$	1.59871	+	0.923014i	0.0688612	+	0.0397570i
$540$		0			0
$541$			22.5384i			0.969002i	0.874791	+	0.484501i	$0.160999\pi$
$541$			22.5384i			0.969002i	−0.874791	+	0.484501i	$0.839001\pi$
$542$		0			0
$543$	1.13885	+	1.97255i	0.0488728	+	0.0846502i
$544$		0			0
$545$	−13.9172			−0.596146
$546$		0			0
$547$	−39.3716			−1.68341			−0.841704	−	0.539940i	$-0.818447\pi$
$547$	−39.3716			−1.68341			−0.841704	+	0.539940i	$0.818447\pi$
$548$		0			0
$549$	14.5601	+	25.2189i	0.621411	+	1.07631i
$550$		0			0
$551$			6.56436i			0.279651i
$552$		0			0
$553$	0.694475	+	0.400955i	0.0295321	+	0.0170504i
$554$		0			0
$555$	3.34517	−	5.79401i	0.141995	−	0.245942i
$556$		0			0
$557$	0.629579	−	0.363487i	0.0266761	−	0.0154015i	−0.486603	−	0.873623i	$-0.661764\pi$
$557$	0.629579	−	0.363487i	0.0266761	−	0.0154015i	0.513279	+	0.858222i	$0.328431\pi$
$558$		0			0
$559$	15.7921	−	27.0289i	0.667935	−	1.14320i
$560$		0			0
$561$	−1.19084	+	0.687532i	−0.0502773	+	0.0290276i
$562$		0			0
$563$	−20.8038	+	36.0333i	−0.876777	+	1.51862i	−0.0219200	+	0.999760i	$0.506978\pi$
$563$	−20.8038	+	36.0333i	−0.876777	+	1.51862i	−0.854857	+	0.518863i	$0.826355\pi$
$564$		0			0
$565$	7.75879	+	4.47954i	0.326415	+	0.188456i
$566$		0			0
$567$			7.93720i			0.333331i
$568$		0			0
$569$	−12.6944	−	21.9873i	−0.532177	−	0.921757i	−0.999294	−	0.0375618i	$-0.988041\pi$
$569$	−12.6944	−	21.9873i	−0.532177	−	0.921757i	0.467118	−	0.884195i	$-0.345292\pi$
$570$		0			0
$571$	16.9992			0.711393			0.355697	−	0.934602i	$-0.384244\pi$
$571$	16.9992			0.711393			0.355697	+	0.934602i	$0.384244\pi$
$572$		0			0
$573$	4.75451			0.198622
$574$		0			0
$575$	5.08929	+	8.81490i	0.212238	+	0.367607i
$576$		0			0
$577$		−	15.9759i		−	0.665084i	−0.943088	−	0.332542i	$-0.892094\pi$
$577$		−	15.9759i		−	0.665084i	0.943088	−	0.332542i	$-0.107906\pi$
$578$		0			0
$579$	−6.81682	−	3.93570i	−0.283298	−	0.163562i
$580$		0			0
$581$	4.98516	−	8.63454i	0.206819	−	0.358221i
$582$		0			0
$583$	−14.8780	+	8.58982i	−0.616184	+	0.355754i
$584$		0			0
$585$	−29.2150	−	17.0693i	−1.20789	−	0.705731i
$586$		0			0
$587$	13.8404	−	7.99075i	0.571254	−	0.329814i	−0.186396	−	0.982475i	$-0.559681\pi$
$587$	13.8404	−	7.99075i	0.571254	−	0.329814i	0.757650	+	0.652661i	$0.226347\pi$
$588$		0			0
$589$	−2.09166	+	3.62287i	−0.0861855	+	0.149278i
$590$		0			0
$591$	4.35235	+	2.51283i	0.179032	+	0.103364i
$592$		0			0
$593$		−	29.0532i		−	1.19307i	−0.802586	−	0.596536i	$-0.796543\pi$
$593$		−	29.0532i		−	1.19307i	0.802586	−	0.596536i	$-0.203457\pi$
$594$		0			0
$595$	3.50760	+	6.07534i	0.143797	+	0.249065i
$596$		0			0
$597$	8.24757			0.337551
$598$		0			0
$599$	−3.45554			−0.141190			−0.0705948	−	0.997505i	$-0.522490\pi$
$599$	−3.45554			−0.141190			−0.0705948	+	0.997505i	$0.522490\pi$
$600$		0			0
$601$	−7.76518	−	13.4497i	−0.316748	−	0.548624i	0.663059	−	0.748567i	$-0.269258\pi$
$601$	−7.76518	−	13.4497i	−0.316748	−	0.548624i	−0.979808	+	0.199943i	$0.935924\pi$
$602$		0			0
$603$			2.38178i			0.0969936i
$604$		0			0
$605$	21.4222	+	12.3681i	0.870938	+	0.502836i
$606$		0			0
$607$	7.73922	−	13.4047i	0.314125	−	0.544081i	−0.665126	−	0.746731i	$-0.731622\pi$
$607$	7.73922	−	13.4047i	0.314125	−	0.544081i	0.979251	+	0.202650i	$0.0649555\pi$
$608$		0			0
$609$	−0.819127	+	0.472923i	−0.0331927	+	0.0191638i
$610$		0			0
$611$	0.109597	−	21.1922i	0.00443383	−	0.857345i
$612$		0			0
$613$	−6.17669	+	3.56611i	−0.249474	+	0.144034i	−0.619523	−	0.784978i	$-0.712674\pi$
$613$	−6.17669	+	3.56611i	−0.249474	+	0.144034i	0.370049	+	0.929012i	$0.379341\pi$
$614$		0			0
$615$	−2.37902	+	4.12058i	−0.0959312	+	0.166158i
$616$		0			0
$617$	−4.30142	−	2.48342i	−0.173168	−	0.0999789i	0.410911	−	0.911676i	$-0.365211\pi$
$617$	−4.30142	−	2.48342i	−0.173168	−	0.0999789i	−0.584079	+	0.811697i	$0.698544\pi$
$618$		0			0
$619$			42.3570i			1.70247i	0.524784	+	0.851235i	$0.324146\pi$
$619$			42.3570i			1.70247i	−0.524784	+	0.851235i	$0.675854\pi$
$620$		0			0
$621$	1.84371	+	3.19339i	0.0739854	+	0.128146i
$622$		0			0
$623$	−15.1135			−0.605508
$624$		0			0
$625$	−21.5445			−0.861779
$626$		0			0
$627$	−0.766663	−	1.32790i	−0.0306176	−	0.0530312i
$628$		0			0
$629$			12.7803i			0.509583i
$630$		0			0
$631$	5.42803	+	3.13387i	0.216086	+	0.124758i	0.604137	−	0.796881i	$-0.293518\pi$
$631$	5.42803	+	3.13387i	0.216086	+	0.124758i	−0.388050	+	0.921638i	$0.626851\pi$
$632$		0			0
$633$	0.746432	−	1.29286i	0.0296680	−	0.0513865i
$634$		0			0
$635$	27.4667	−	15.8579i	1.08998	−	0.629302i
$636$		0			0
$637$	1.78660	+	3.13178i	0.0707878	+	0.124086i
$638$		0			0
$639$	5.87250	−	3.39049i	0.232313	−	0.134126i
$640$		0			0
$641$	−15.7818	+	27.3350i	−0.623345	+	1.07967i	0.365513	+	0.930806i	$0.380894\pi$
$641$	−15.7818	+	27.3350i	−0.623345	+	1.07967i	−0.988858	+	0.148860i	$0.952440\pi$
$642$		0			0
$643$	−15.8053	−	9.12520i	−0.623300	−	0.359863i	0.154852	−	0.987938i	$-0.450510\pi$
$643$	−15.8053	−	9.12520i	−0.623300	−	0.359863i	−0.778153	+	0.628075i	$0.783843\pi$
$644$		0			0
$645$			9.78613i			0.385329i
$646$		0			0
$647$	−11.5137	−	19.9423i	−0.452649	−	0.784011i	0.545901	−	0.837850i	$-0.316188\pi$
$647$	−11.5137	−	19.9423i	−0.452649	−	0.784011i	−0.998550	+	0.0538387i	$0.982854\pi$
$648$		0			0
$649$	−19.8490			−0.779140
$650$		0			0
$651$	−0.602768			−0.0236243
$652$		0			0
$653$	−14.4062	−	24.9523i	−0.563759	−	0.976459i	−0.997164	−	0.0752597i	$-0.976021\pi$
$653$	−14.4062	−	24.9523i	−0.563759	−	0.976459i	0.433405	−	0.901199i	$-0.357312\pi$
$654$		0			0
$655$		−	60.8014i		−	2.37571i
$656$		0			0
$657$	7.96926	+	4.60105i	0.310910	+	0.179504i
$658$		0			0
$659$	−15.6114	+	27.0397i	−0.608134	+	1.05332i	0.383414	+	0.923577i	$0.374748\pi$
$659$	−15.6114	+	27.0397i	−0.608134	+	1.05332i	−0.991548	+	0.129742i	$0.958585\pi$
$660$		0			0
$661$	−23.0000	+	13.2791i	−0.894598	+	0.516496i	−0.875444	−	0.483320i	$-0.839431\pi$
$661$	−23.0000	+	13.2791i	−0.894598	+	0.516496i	−0.0191541	+	0.999817i	$0.506097\pi$
$662$		0			0
$663$	−2.68566	−	0.0138891i	−0.104302	−	0.000539407i
$664$		0			0
$665$	−6.77458	+	3.91130i	−0.262707	+	0.151674i
$666$		0			0
$667$	2.47792	−	4.29188i	0.0959454	−	0.166182i
$668$		0			0
$669$	−7.00906	−	4.04668i	−0.270986	−	0.156454i
$670$		0			0
$671$			18.6635i			0.720495i
$672$		0			0
$673$	−9.86930	−	17.0941i	−0.380434	−	0.658930i	0.610691	−	0.791869i	$-0.290892\pi$
$673$	−9.86930	−	17.0941i	−0.380434	−	0.658930i	−0.991124	+	0.132939i	$0.957559\pi$
$674$		0			0
$675$	11.4233			0.439683
$676$		0			0
$677$	−13.1440			−0.505163			−0.252582	−	0.967576i	$-0.581280\pi$
$677$	−13.1440			−0.505163			−0.252582	+	0.967576i	$0.581280\pi$
$678$		0			0
$679$	−4.61585	−	7.99489i	−0.177140	−	0.306816i
$680$		0			0
$681$		−	9.24475i		−	0.354260i
$682$		0			0
$683$	5.85654	+	3.38128i	0.224094	+	0.129381i	0.607845	−	0.794056i	$-0.292034\pi$
$683$	5.85654	+	3.38128i	0.224094	+	0.129381i	−0.383750	+	0.923437i	$0.625368\pi$
$684$		0			0
$685$	−13.7192	+	23.7624i	−0.524185	+	0.907915i
$686$		0			0
$687$	−0.900810	+	0.520083i	−0.0343681	+	0.0198424i
$688$		0			0
$689$	−33.5538	−	0.173526i	−1.27830	−	0.00661082i
$690$		0			0
$691$	−7.94223	+	4.58545i	−0.302137	+	0.174439i	−0.643402	−	0.765528i	$-0.722478\pi$
$691$	−7.94223	+	4.58545i	−0.302137	+	0.174439i	0.341266	+	0.939967i	$0.389144\pi$
$692$		0			0
$693$	−2.65857	+	4.60479i	−0.100991	+	0.174921i
$694$		0			0
$695$	49.7626	+	28.7304i	1.88760	+	1.08981i
$696$		0			0
$697$		−	9.08908i		−	0.344273i
$698$		0			0
$699$	−2.02636	−	3.50976i	−0.0766440	−	0.132751i
$700$		0			0
$701$	47.4700			1.79292			0.896459	−	0.443127i	$-0.146131\pi$
$701$	47.4700			1.79292			0.896459	+	0.443127i	$0.146131\pi$
$702$		0			0
$703$	−14.2512			−0.537495
$704$		0			0
$705$	3.31253	+	5.73748i	0.124757	+	0.216086i
$706$		0			0
$707$		−	14.8234i		−	0.557491i
$708$		0			0
$709$	30.2866	+	17.4860i	1.13744	+	0.656699i	0.945795	−	0.324766i	$-0.105285\pi$
$709$	30.2866	+	17.4860i	1.13744	+	0.656699i	0.191642	+	0.981465i	$0.438619\pi$
$710$		0			0
$711$	−1.15488	+	2.00031i	−0.0433114	+	0.0750175i
$712$		0			0
$713$	2.73512	−	1.57912i	0.102431	−	0.0591387i
$714$		0			0
$715$	−10.7457	−	18.8364i	−0.401866	−	0.704440i
$716$		0			0
$717$	−0.427821	+	0.247002i	−0.0159773	+	0.00922448i
$718$		0			0
$719$	4.18051	−	7.24085i	0.155907	−	0.270038i	−0.777482	−	0.628905i	$-0.783503\pi$
$719$	4.18051	−	7.24085i	0.155907	−	0.270038i	0.933389	+	0.358867i	$0.116837\pi$
$720$		0			0
$721$	3.70907	+	2.14143i	0.138133	+	0.0797511i
$722$		0			0
$723$			0.927035i			0.0344768i
$724$		0			0
$725$	−7.67639	−	13.2959i	−0.285094	−	0.493797i
$726$		0			0
$727$	27.4014			1.01626			0.508131	−	0.861280i	$-0.330337\pi$
$727$	27.4014			1.01626			0.508131	+	0.861280i	$0.330337\pi$
$728$		0			0
$729$	−20.7504			−0.768532
$730$		0			0
$731$	−9.34703	−	16.1895i	−0.345712	−	0.598791i
$732$		0			0
$733$		−	12.1569i		−	0.449026i	−0.974471	−	0.224513i	$-0.927921\pi$
$733$		−	12.1569i		−	0.449026i	0.974471	−	0.224513i	$-0.0720792\pi$
$734$		0			0
$735$	−0.976136	−	0.563573i	−0.0360053	−	0.0207877i
$736$		0			0
$737$	−0.763255	+	1.32200i	−0.0281148	+	0.0486963i
$738$		0			0
$739$	41.9537	−	24.2220i	1.54329	−	0.891019i	0.544662	−	0.838656i	$-0.316658\pi$
$739$	41.9537	−	24.2220i	1.54329	−	0.891019i	0.998628	−	0.0523634i	$-0.0166754\pi$
$740$		0			0
$741$	0.0154876	−	2.99476i	0.000568953	−	0.110015i
$742$		0			0
$743$	14.7143	−	8.49532i	0.539816	−	0.311663i	−0.205188	−	0.978722i	$-0.565781\pi$
$743$	14.7143	−	8.49532i	0.539816	−	0.311663i	0.745004	+	0.667060i	$0.232447\pi$
$744$		0			0
$745$	−6.55052	+	11.3458i	−0.239993	+	0.415679i
$746$		0			0
$747$	24.8702	+	14.3588i	0.909955	+	0.525363i
$748$		0			0
$749$			19.1258i			0.698841i
$750$		0			0
$751$	−21.5162	−	37.2671i	−0.785136	−	1.35990i	−0.928918	−	0.370287i	$-0.879259\pi$
$751$	−21.5162	−	37.2671i	−0.785136	−	1.35990i	0.143781	−	0.989610i	$-0.454074\pi$
$752$		0			0
$753$	3.78258			0.137845
$754$		0			0
$755$	−61.5817			−2.24119
$756$		0			0
$757$	−14.5892	−	25.2693i	−0.530255	−	0.918428i	−0.999377	−	0.0352949i	$-0.988763\pi$
$757$	−14.5892	−	25.2693i	−0.530255	−	0.918428i	0.469122	−	0.883133i	$-0.344570\pi$
$758$		0			0
$759$			1.15760i			0.0420183i
$760$		0			0
$761$	−25.4829	−	14.7126i	−0.923754	−	0.533330i	−0.0389234	−	0.999242i	$-0.512393\pi$
$761$	−25.4829	−	14.7126i	−0.923754	−	0.533330i	−0.884831	+	0.465912i	$0.845726\pi$
$762$		0			0
$763$	−2.13577	+	3.69925i	−0.0773199	+	0.133922i
$764$		0			0
$765$	−17.4989	+	10.1030i	−0.632675	+	0.365275i
$766$		0			0
$767$	−33.4732	−	19.5573i	−1.20865	−	0.706172i
$768$		0			0
$769$	14.8839	−	8.59322i	0.536727	−	0.309879i	−0.207024	−	0.978336i	$-0.566378\pi$
$769$	14.8839	−	8.59322i	0.536727	−	0.309879i	0.743751	+	0.668456i	$0.233045\pi$
$770$		0			0
$771$	0.718083	−	1.24376i	0.0258611	−	0.0447928i
$772$		0			0
$773$	19.0180	+	10.9801i	0.684031	+	0.394926i	0.801372	−	0.598166i	$-0.204104\pi$
$773$	19.0180	+	10.9801i	0.684031	+	0.394926i	−0.117341	+	0.993092i	$0.537437\pi$
$774$		0			0
$775$		−	9.78399i		−	0.351451i
$776$		0			0
$777$	−1.02672	−	1.77833i	−0.0368333	−	0.0637971i
$778$		0			0
$779$	10.1352			0.363131
$780$		0			0
$781$	4.34600			0.155512
$782$		0			0
$783$	−2.78094	−	4.81673i	−0.0993827	−	0.172136i
$784$		0			0
$785$			37.7081i			1.34586i
$786$		0			0
$787$	2.02275	+	1.16784i	0.0721033	+	0.0416289i	0.535618	−	0.844460i	$-0.320079\pi$
$787$	2.02275	+	1.16784i	0.0721033	+	0.0416289i	−0.463515	+	0.886089i	$0.653412\pi$
$788$		0			0
$789$	0.701169	−	1.21446i	0.0249623	−	0.0432359i
$790$		0			0
$791$	2.38137	−	1.37488i	0.0846716	−	0.0488852i
$792$		0			0
$793$	−18.3892	+	31.4740i	−0.653020	+	1.11767i
$794$		0			0
$795$	9.08420	−	5.24476i	0.322183	−	0.186013i
$796$		0			0
$797$	13.9020	−	24.0790i	0.492434	−	0.852921i	−0.507528	−	0.861635i	$-0.669440\pi$
$797$	13.9020	−	24.0790i	0.492434	−	0.852921i	0.999962	+	0.00871411i	$0.00277382\pi$
$798$		0			0
$799$	−10.9601	−	6.32780i	−0.387739	−	0.223861i
$800$		0			0
$801$		−	43.5316i		−	1.53811i
$802$		0			0
$803$	2.94886	+	5.10758i	0.104063	+	0.180243i
$804$		0			0
$805$	5.90576			0.208151
$806$		0			0
$807$	1.38387			0.0487147
$808$		0			0
$809$	−7.51017	−	13.0080i	−0.264043	−	0.457337i	0.703269	−	0.710924i	$-0.251723\pi$
$809$	−7.51017	−	13.0080i	−0.264043	−	0.457337i	−0.967313	+	0.253587i	$0.918390\pi$
$810$		0			0
$811$		−	43.6933i		−	1.53428i	−0.641481	−	0.767139i	$-0.721680\pi$
$811$		−	43.6933i		−	1.53428i	0.641481	−	0.767139i	$-0.278320\pi$
$812$		0			0
$813$	−0.834393	−	0.481737i	−0.0292634	−	0.0168953i
$814$		0			0
$815$	7.17670	−	12.4304i	0.251389	−	0.435418i
$816$		0			0
$817$	18.0529	−	10.4228i	0.631590	−	0.364648i
$818$		0			0
$819$	−9.02053	+	5.14599i	−0.315203	+	0.179815i
$820$		0			0
$821$	15.6492	−	9.03506i	0.546160	−	0.315326i	−0.201412	−	0.979507i	$-0.564553\pi$
$821$	15.6492	−	9.03506i	0.546160	−	0.315326i	0.747572	+	0.664181i	$0.231220\pi$
$822$		0			0
$823$	−2.22775	+	3.85857i	−0.0776544	+	0.134501i	−0.902238	−	0.431239i	$-0.858076\pi$
$823$	−2.22775	+	3.85857i	−0.0776544	+	0.134501i	0.824583	+	0.565741i	$0.191410\pi$
$824$		0			0
$825$	3.10570	+	1.79308i	0.108127	+	0.0624269i
$826$		0			0
$827$		−	11.8352i		−	0.411549i	−0.978599	−	0.205774i	$-0.934029\pi$
$827$		−	11.8352i		−	0.411549i	0.978599	−	0.205774i	$-0.0659713\pi$
$828$		0			0
$829$	−1.76947	−	3.06482i	−0.0614563	−	0.106445i	0.833660	−	0.552278i	$-0.186241\pi$
$829$	−1.76947	−	3.06482i	−0.0614563	−	0.106445i	−0.895117	+	0.445832i	$0.852908\pi$
$830$		0			0
$831$	−5.77471			−0.200323
$832$		0			0
$833$	2.15314			0.0746019
$834$		0			0
$835$	−14.6927	−	25.4484i	−0.508460	−	0.880679i
$836$		0			0
$837$		−	3.54447i		−	0.122515i
$838$		0			0
$839$	28.9991	+	16.7426i	1.00116	+	0.578020i	0.908591	−	0.417686i	$-0.137159\pi$
$839$	28.9991	+	16.7426i	1.00116	+	0.578020i	0.0925687	+	0.995706i	$0.470492\pi$
$840$		0			0
$841$	10.7625	−	18.6411i	0.371119	−	0.642797i
$842$		0			0
$843$	4.00660	−	2.31321i	0.137995	−	0.0796713i
$844$		0			0
$845$	0.438079	−	42.3533i	0.0150704	−	1.45700i
$846$		0			0
$847$	6.57502	−	3.79609i	0.225920	−	0.130435i
$848$		0			0
$849$	3.26684	−	5.65833i	0.112118	−	0.194193i
$850$		0			0
$851$	9.31768	+	5.37956i	0.319406	+	0.184409i
$852$		0			0
$853$			22.0871i			0.756248i	0.925755	+	0.378124i	$0.123431\pi$
$853$			22.0871i			0.756248i	−0.925755	+	0.378124i	$0.876569\pi$
$854$		0			0
$855$	−11.2658	−	19.5129i	−0.385282	−	0.667329i
$856$		0			0
$857$	6.89363			0.235482			0.117741	−	0.993044i	$-0.462435\pi$
$857$	6.89363			0.235482			0.117741	+	0.993044i	$0.462435\pi$
$858$		0			0
$859$	37.4834			1.27892			0.639459	−	0.768825i	$-0.279158\pi$
$859$	37.4834			1.27892			0.639459	+	0.768825i	$0.279158\pi$
$860$		0			0
$861$	0.730180	+	1.26471i	0.0248845	+	0.0431012i
$862$		0			0
$863$			17.5248i			0.596552i	0.954480	+	0.298276i	$0.0964115\pi$
$863$			17.5248i			0.596552i	−0.954480	+	0.298276i	$0.903588\pi$
$864$		0			0
$865$	−17.1893	−	9.92425i	−0.584454	−	0.337435i
$866$		0			0
$867$	2.13866	−	3.70426i	0.0726326	−	0.125803i
$868$		0			0
$869$	−1.28202	+	0.740175i	−0.0434896	+	0.0251087i
$870$		0			0
$871$	−2.58972	+	1.47737i	−0.0877493	+	0.0500588i
$872$		0			0
$873$	23.0278	−	13.2951i	0.779374	−	0.449972i
$874$		0			0
$875$	1.00248	−	1.73634i	0.0338899	−	0.0586990i
$876$		0			0
$877$	−40.4859	−	23.3745i	−1.36711	−	0.789302i	−0.376553	−	0.926395i	$-0.622891\pi$
$877$	−40.4859	−	23.3745i	−1.36711	−	0.789302i	−0.990558	+	0.137093i	$0.956224\pi$
$878$		0			0
$879$			1.18242i			0.0398821i
$880$		0			0
$881$	−1.45937	−	2.52771i	−0.0491675	−	0.0851606i	0.840394	−	0.541976i	$-0.182323\pi$
$881$	−1.45937	−	2.52771i	−0.0491675	−	0.0851606i	−0.889562	+	0.456815i	$0.848990\pi$
$882$		0			0
$883$	−28.5505			−0.960801			−0.480400	−	0.877049i	$-0.659509\pi$
$883$	−28.5505			−0.960801			−0.480400	+	0.877049i	$0.659509\pi$
$884$		0			0
$885$	12.1194			0.407388
$886$		0			0
$887$	0.211457	+	0.366254i	0.00710004	+	0.0122976i	0.869554	−	0.493839i	$-0.164407\pi$
$887$	0.211457	+	0.366254i	0.00710004	+	0.0122976i	−0.862454	+	0.506136i	$0.831073\pi$
$888$		0			0
$889$		−	9.73438i		−	0.326480i
$890$		0			0
$891$	−12.6892	−	7.32614i	−0.425106	−	0.245435i
$892$		0			0
$893$	7.05610	−	12.2215i	0.236123	−	0.408978i
$894$		0			0
$895$	−10.9469	+	6.32018i	−0.365914	+	0.211260i
$896$		0			0
$897$	−1.14059	+	1.95217i	−0.0380832	+	0.0651812i
$898$		0			0
$899$	−4.12550	+	2.38186i	−0.137593	+	0.0794394i
$900$		0			0
$901$	−10.0189	+	17.3532i	−0.333777	+	0.578118i
$902$		0			0
$903$	2.60120	+	1.50181i	0.0865626	+	0.0499769i
$904$		0			0
$905$			21.4512i			0.713063i
$906$		0			0
$907$	11.2142	+	19.4236i	0.372361	+	0.644949i	0.989928	−	0.141570i	$-0.0452149\pi$
$907$	11.2142	+	19.4236i	0.372361	+	0.644949i	−0.617567	+	0.786518i	$0.711882\pi$
$908$		0			0
$909$	42.6961			1.41614
$910$		0			0
$911$	32.5788			1.07938			0.539692	−	0.841863i	$-0.318541\pi$
$911$	32.5788			1.07938			0.539692	+	0.841863i	$0.318541\pi$
$912$		0			0
$913$	9.20274	+	15.9396i	0.304566	+	0.527524i
$914$		0			0
$915$		−	11.3955i		−	0.376724i
$916$		0			0
$917$	−16.1613	−	9.33073i	−0.533693	−	0.308128i
$918$		0			0
$919$	−4.93957	+	8.55558i	−0.162941	+	0.282223i	−0.935922	−	0.352207i	$-0.885431\pi$
$919$	−4.93957	+	8.55558i	−0.162941	+	0.282223i	0.772981	+	0.634429i	$0.218765\pi$
$920$		0			0
$921$	4.90383	−	2.83123i	0.161587	−	0.0932922i
$922$		0			0
$923$	7.32908	+	4.28214i	0.241240	+	0.140948i
$924$		0			0
$925$	28.8654	−	16.6654i	0.949088	−	0.547956i
$926$		0			0
$927$	−6.16800	+	10.6833i	−0.202584	+	0.350886i
$928$		0			0
$929$	25.9060	+	14.9568i	0.849947	+	0.490717i	0.860633	−	0.509226i	$-0.170068\pi$
$929$	25.9060	+	14.9568i	0.849947	+	0.490717i	−0.0106859	+	0.999943i	$0.503401\pi$
$930$		0			0
$931$			2.40096i			0.0786881i
$932$		0			0
$933$	−4.09913	−	7.09990i	−0.134199	−	0.232440i
$934$		0			0
$935$	−12.9502			−0.423518
$936$		0			0
$937$	−31.8296			−1.03983			−0.519914	−	0.854219i	$-0.674036\pi$
$937$	−31.8296			−1.03983			−0.519914	+	0.854219i	$0.674036\pi$
$938$		0			0
$939$	0.896052	+	1.55201i	0.0292416	+	0.0506479i
$940$		0			0
$941$		−	42.0885i		−	1.37205i	−0.727580	−	0.686023i	$-0.759355\pi$
$941$		−	42.0885i		−	1.37205i	0.727580	−	0.686023i	$-0.240645\pi$
$942$		0			0
$943$	−6.62654	−	3.82584i	−0.215790	−	0.124586i
$944$		0			0
$945$	3.31399	−	5.73999i	0.107804	−	0.186722i
$946$		0			0
$947$	−52.2540	+	30.1689i	−1.69803	+	0.980357i	−0.750397	+	0.660988i	$0.770138\pi$
$947$	−52.2540	+	30.1689i	−1.69803	+	0.980357i	−0.947630	+	0.319369i	$0.896529\pi$
$948$		0			0
$949$	−0.0595711	+	11.5189i	−0.00193376	+	0.373920i
$950$		0			0
$951$	−1.81719	+	1.04915i	−0.0589264	+	0.0340212i
$952$		0			0
$953$	−8.68770	+	15.0475i	−0.281422	+	0.487438i	−0.971735	−	0.236073i	$-0.924139\pi$
$953$	−8.68770	+	15.0475i	−0.281422	+	0.487438i	0.690313	+	0.723511i	$0.257473\pi$
$954$		0			0
$955$	38.7785	+	22.3888i	1.25484	+	0.724484i
$956$		0			0
$957$		−	1.74606i		−	0.0564421i
$958$		0			0
$959$	4.21078	+	7.29328i	0.135973	+	0.235512i
$960$		0			0
$961$	27.9642			0.902070
$962$		0			0
$963$	−55.0883			−1.77520
$964$		0			0
$965$	−37.0661	−	64.2003i	−1.19320	−	2.06668i
$966$		0			0
$967$		−	18.8630i		−	0.606594i	−0.952896	−	0.303297i	$-0.901913\pi$
$967$		−	18.8630i		−	0.606594i	0.952896	−	0.303297i	$-0.0980874\pi$
$968$		0			0
$969$	−1.54881	−	0.894208i	−0.0497551	−	0.0287261i
$970$		0			0
$971$	−0.782231	+	1.35486i	−0.0251030	+	0.0434797i	−0.878304	−	0.478103i	$-0.841325\pi$
$971$	−0.782231	+	1.35486i	−0.0251030	+	0.0434797i	0.853201	+	0.521582i	$0.174658\pi$
$972$		0			0
$973$	15.2734	−	8.81809i	0.489642	−	0.282695i
$974$		0			0
$975$	3.47071	+	6.08390i	0.111152	+	0.194841i
$976$		0			0
$977$	−24.1409	+	13.9378i	−0.772336	+	0.445909i	−0.833707	−	0.552206i	$-0.813786\pi$
$977$	−24.1409	+	13.9378i	−0.772336	+	0.445909i	0.0613710	+	0.998115i	$0.480453\pi$
$978$		0			0
$979$	13.9499	−	24.1620i	0.445842	−	0.772221i
$980$		0			0
$981$	−10.6550	−	6.15169i	−0.340189	−	0.196408i
$982$		0			0
$983$		−	33.4239i		−	1.06606i	−0.846097	−	0.533029i	$-0.821054\pi$
$983$		−	33.4239i		−	1.06606i	0.846097	−	0.533029i	$-0.178946\pi$
$984$		0			0
$985$	23.6657	+	40.9901i	0.754051	+	1.30605i
$986$		0			0
$987$	2.03340			0.0647238
$988$		0			0
$989$	−15.7376			−0.500428
$990$		0			0
$991$	−9.45548	−	16.3774i	−0.300363	−	0.520244i	0.675855	−	0.737035i	$-0.263775\pi$
$991$	−9.45548	−	16.3774i	−0.300363	−	0.520244i	−0.976218	+	0.216790i	$0.930441\pi$
$992$		0			0
$993$			5.97622i			0.189650i
$994$		0			0
$995$	67.2685	+	38.8375i	2.13256	+	1.23123i
$996$		0			0
$997$	−21.7888	+	37.7393i	−0.690057	+	1.19521i	0.281762	+	0.959484i	$0.409081\pi$
$997$	−21.7888	+	37.7393i	−0.690057	+	1.19521i	−0.971819	+	0.235730i	$0.924252\pi$
$998$		0			0
$999$	10.4571	−	6.03742i	0.330849	−	0.191016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.c.673.4		12
4.3	odd	2		91.2.q.a.36.1	✓	12
12.11	even	2		819.2.ct.a.127.6		12
13.4	even	6	inner	1456.2.cc.c.225.4		12
28.3	even	6		637.2.k.g.569.1		12
28.11	odd	6		637.2.k.h.569.1		12
28.19	even	6		637.2.u.i.361.6		12
28.23	odd	6		637.2.u.h.361.6		12
28.27	even	2		637.2.q.h.491.1		12
52.3	odd	6		1183.2.c.i.337.1		12
52.11	even	12		1183.2.a.p.1.6		6
52.15	even	12		1183.2.a.m.1.1		6
52.23	odd	6		1183.2.c.i.337.12		12
52.43	odd	6		91.2.q.a.43.1	yes	12
156.95	even	6		819.2.ct.a.316.6		12
364.95	odd	6		637.2.u.h.30.6		12
364.167	odd	12		8281.2.a.ch.1.6		6
364.199	even	6		637.2.u.i.30.6		12
364.223	odd	12		8281.2.a.by.1.1		6
364.251	even	6		637.2.q.h.589.1		12
364.303	odd	6		637.2.k.h.459.6		12
364.355	even	6		637.2.k.g.459.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.1	✓	12	4.3	odd	2
91.2.q.a.43.1	yes	12	52.43	odd	6
637.2.k.g.459.6		12	364.355	even	6
637.2.k.g.569.1		12	28.3	even	6
637.2.k.h.459.6		12	364.303	odd	6
637.2.k.h.569.1		12	28.11	odd	6
637.2.q.h.491.1		12	28.27	even	2
637.2.q.h.589.1		12	364.251	even	6
637.2.u.h.30.6		12	364.95	odd	6
637.2.u.h.361.6		12	28.23	odd	6
637.2.u.i.30.6		12	364.199	even	6
637.2.u.i.361.6		12	28.19	even	6
819.2.ct.a.127.6		12	12.11	even	2
819.2.ct.a.316.6		12	156.95	even	6
1183.2.a.m.1.1		6	52.15	even	12
1183.2.a.p.1.6		6	52.11	even	12
1183.2.c.i.337.1		12	52.3	odd	6
1183.2.c.i.337.12		12	52.23	odd	6
1456.2.cc.c.225.4		12	13.4	even	6	inner
1456.2.cc.c.673.4		12	1.1	even	1	trivial
8281.2.a.by.1.1		6	364.223	odd	12
8281.2.a.ch.1.6		6	364.167	odd	12

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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.172975 - 0.299601i) q^{3} -3.25812i q^{5} +(-0.866025 - 0.500000i) q^{7} +(1.44016 - 2.49443i) q^{9} +O(q^{10})\)	\(q+(-0.172975 - 0.299601i) q^{3} -3.25812i q^{5} +(-0.866025 - 0.500000i) q^{7} +(1.44016 - 2.49443i) q^{9} +(1.59871 - 0.923014i) q^{11} +(3.60550 + 0.0186461i) q^{13} +(-0.976136 + 0.563573i) q^{15} +(1.07657 - 1.86467i) q^{17} +(2.07929 + 1.20048i) q^{19} +0.345949i q^{21} +(-0.906314 - 1.56978i) q^{23} -5.61537 q^{25} -2.03429 q^{27} +(1.36703 + 2.36777i) q^{29} +1.74236i q^{31} +(-0.553071 - 0.319316i) q^{33} +(-1.62906 + 2.82162i) q^{35} +(-5.14042 + 2.96783i) q^{37} +(-0.618074 - 1.08344i) q^{39} +(3.65577 - 2.11066i) q^{41} +(4.34111 - 7.51903i) q^{43} +(-8.12716 - 4.69222i) q^{45} -5.87774i q^{47} +(0.500000 + 0.866025i) q^{49} -0.744877 q^{51} -9.30628 q^{53} +(-3.00729 - 5.20878i) q^{55} -0.830609i q^{57} +(-9.31173 - 5.37613i) q^{59} +(-5.05504 + 8.75558i) q^{61} +(-2.49443 + 1.44016i) q^{63} +(0.0607514 - 11.7472i) q^{65} +(-0.716130 + 0.413458i) q^{67} +(-0.313538 + 0.543065i) q^{69} +(2.03884 + 1.17712i) q^{71} +3.19482i q^{73} +(0.971316 + 1.68237i) q^{75} -1.84603 q^{77} -0.801911 q^{79} +(-3.96860 - 6.87381i) q^{81} +9.97031i q^{83} +(-6.07534 - 3.50760i) q^{85} +(0.472923 - 0.819127i) q^{87} +(13.0886 - 7.55674i) q^{89} +(-3.11313 - 1.81890i) q^{91} +(0.522012 - 0.301384i) q^{93} +(3.91130 - 6.77458i) q^{95} +(7.99489 + 4.61585i) q^{97} -5.31715i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{9}+O(q^{10}) \) 12 * q - 4 * q^9	\( 12 q - 4 q^{9} - 6 q^{11} + 4 q^{13} - 6 q^{15} - 4 q^{17} + 12 q^{23} - 20 q^{25} - 12 q^{27} + 8 q^{29} - 30 q^{33} - 6 q^{35} - 42 q^{37} + 4 q^{39} + 30 q^{41} - 2 q^{43} + 6 q^{49} - 52 q^{51} - 44 q^{53} + 6 q^{55} - 18 q^{59} + 14 q^{61} - 12 q^{63} + 60 q^{65} + 24 q^{67} + 4 q^{69} + 24 q^{71} - 46 q^{75} + 8 q^{77} + 56 q^{79} + 2 q^{81} - 48 q^{85} + 2 q^{87} - 12 q^{89} - 14 q^{91} - 18 q^{93} + 22 q^{95} + 6 q^{97}+O(q^{100}) \) 12 * q - 4 * q^9 - 6 * q^11 + 4 * q^13 - 6 * q^15 - 4 * q^17 + 12 * q^23 - 20 * q^25 - 12 * q^27 + 8 * q^29 - 30 * q^33 - 6 * q^35 - 42 * q^37 + 4 * q^39 + 30 * q^41 - 2 * q^43 + 6 * q^49 - 52 * q^51 - 44 * q^53 + 6 * q^55 - 18 * q^59 + 14 * q^61 - 12 * q^63 + 60 * q^65 + 24 * q^67 + 4 * q^69 + 24 * q^71 - 46 * q^75 + 8 * q^77 + 56 * q^79 + 2 * q^81 - 48 * q^85 + 2 * q^87 - 12 * q^89 - 14 * q^91 - 18 * q^93 + 22 * q^95 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more