LMFDB - Embedded newform 1120.2.q.h.961.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1120,2,Mod(641,1120)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1120.641"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1120, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,4,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.94324502638$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1445900625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 9x^{6} + 77x^{4} + 36x^{2} + 16 $ x^8 + 9x^6 + 77x^4 + 36*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.3
Root			$-1.46040 + 2.52950i$ of defining polynomial
Character	$\chi$	$=$	1120.961
Dual form			1120.2.q.h.641.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.342371 + 0.593004i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.57844 - 0.593004i) q^{7} +(1.26556 - 2.19202i) q^{9} +(1.46040 + 2.52950i) q^{11} -2.53113 q^{13} +0.684742 q^{15} +(1.00000 + 1.73205i) q^{17} +(0.775663 - 1.34349i) q^{19} +(1.23444 + 1.32600i) q^{21} +(3.35410 - 5.80948i) q^{23} +(-0.500000 - 0.866025i) q^{25} +3.78739 q^{27} -1.53113 q^{29} +(0.684742 + 1.18601i) q^{31} +(-1.00000 + 1.73205i) q^{33} +(0.775663 - 2.52950i) q^{35} +(0.265564 - 0.459971i) q^{37} +(-0.866585 - 1.50097i) q^{39} -8.06226 q^{41} +2.05422 q^{43} +(-1.26556 - 2.19202i) q^{45} +(2.14515 - 3.71550i) q^{47} +(6.29669 - 3.05805i) q^{49} +(-0.684742 + 1.18601i) q^{51} +(-1.73444 - 3.00413i) q^{53} +2.92081 q^{55} +1.06226 q^{57} +(4.47214 + 7.74597i) q^{59} +(0.234436 - 0.406054i) q^{61} +(1.96330 - 6.40248i) q^{63} +(-1.26556 + 2.19202i) q^{65} +(3.26318 + 5.65199i) q^{67} +4.59339 q^{69} +8.94427 q^{71} +(5.53113 + 9.58020i) q^{73} +(0.342371 - 0.593004i) q^{75} +(5.26556 + 5.65612i) q^{77} +(2.92081 - 5.05899i) q^{79} +(-2.50000 - 4.33013i) q^{81} +3.78739 q^{83} +2.00000 q^{85} +(-0.524214 - 0.907965i) q^{87} +(-4.76556 + 8.25420i) q^{89} +(-6.52636 + 1.50097i) q^{91} +(-0.468871 + 0.812109i) q^{93} +(-0.775663 - 1.34349i) q^{95} -2.00000 q^{97} +7.39295 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{5} - 6 q^{9} + 12 q^{13} + 8 q^{17} + 26 q^{21} - 4 q^{25} + 20 q^{29} - 8 q^{33} - 14 q^{37} + 6 q^{45} + 2 q^{49} - 30 q^{53} - 56 q^{57} + 18 q^{61} + 6 q^{65} - 60 q^{69} + 12 q^{73} + 26 q^{77}+ \cdots - 16 q^{97}+O(q^{100}) $ 8 * q + 4 * q^5 - 6 * q^9 + 12 * q^13 + 8 * q^17 + 26 * q^21 - 4 * q^25 + 20 * q^29 - 8 * q^33 - 14 * q^37 + 6 * q^45 + 2 * q^49 - 30 * q^53 - 56 * q^57 + 18 * q^61 + 6 * q^65 - 60 * q^69 + 12 * q^73 + 26 * q^77 - 20 * q^81 + 16 * q^85 - 22 * q^89 - 36 * q^93 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	0.342371	+	0.593004i	0.197668	+	0.342371i	0.947772	−	0.318949i	$-0.103330\pi$
$3$	0.342371	+	0.593004i	0.197668	+	0.342371i	−0.750104	+	0.661320i	$0.769997\pi$
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	2.57844	−	0.593004i	0.974558	−	0.224134i
$7$	2.57844	−	0.593004i	0.974558	−	0.224134i
$8$		0			0
$9$	1.26556	−	2.19202i	0.421855	−	0.730674i
$10$		0			0
$11$	1.46040	+	2.52950i	0.440329	+	0.762672i	0.997714	−	0.0675826i	$-0.0215286\pi$
$11$	1.46040	+	2.52950i	0.440329	+	0.762672i	−0.557385	+	0.830254i	$0.688195\pi$
$12$		0			0
$13$	−2.53113			−0.702009			−0.351004	−	0.936374i	$-0.614160\pi$
$13$	−2.53113			−0.702009			−0.351004	+	0.936374i	$0.614160\pi$
$14$		0			0
$15$	0.684742			0.176800
$16$		0			0
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$		0			0
$19$	0.775663	−	1.34349i	0.177949	−	0.308217i	−0.763229	−	0.646128i	$-0.776387\pi$
$19$	0.775663	−	1.34349i	0.177949	−	0.308217i	0.941178	+	0.337911i	$0.109720\pi$
$20$		0			0
$21$	1.23444	+	1.32600i	0.269376	+	0.289356i
$22$		0			0
$23$	3.35410	−	5.80948i	0.699379	−	1.21136i	−0.269304	−	0.963055i	$-0.586793\pi$
$23$	3.35410	−	5.80948i	0.699379	−	1.21136i	0.968682	−	0.248304i	$-0.0798732\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	3.78739			0.728884
$28$		0			0
$29$	−1.53113			−0.284323			−0.142162	−	0.989843i	$-0.545405\pi$
$29$	−1.53113			−0.284323			−0.142162	+	0.989843i	$0.545405\pi$
$30$		0			0
$31$	0.684742	+	1.18601i	0.122983	+	0.213013i	0.920943	−	0.389698i	$-0.127421\pi$
$31$	0.684742	+	1.18601i	0.122983	+	0.213013i	−0.797960	+	0.602711i	$0.794087\pi$
$32$		0			0
$33$	−1.00000	+	1.73205i	−0.174078	+	0.301511i
$34$		0			0
$35$	0.775663	−	2.52950i	0.131111	−	0.427563i
$36$		0			0
$37$	0.265564	−	0.459971i	0.0436585	−	0.0756188i	−0.843370	−	0.537333i	$-0.819432\pi$
$37$	0.265564	−	0.459971i	0.0436585	−	0.0756188i	0.887029	+	0.461714i	$0.152765\pi$
$38$		0			0
$39$	−0.866585	−	1.50097i	−0.138765	−	0.240347i
$40$		0			0
$41$	−8.06226			−1.25911			−0.629557	−	0.776955i	$-0.716763\pi$
$41$	−8.06226			−1.25911			−0.629557	+	0.776955i	$0.716763\pi$
$42$		0			0
$43$	2.05422			0.313266			0.156633	−	0.987657i	$-0.449936\pi$
$43$	2.05422			0.313266			0.156633	+	0.987657i	$0.449936\pi$
$44$		0			0
$45$	−1.26556	−	2.19202i	−0.188659	−	0.326767i
$46$		0			0
$47$	2.14515	−	3.71550i	0.312902	−	0.541962i	−0.666087	−	0.745874i	$-0.732032\pi$
$47$	2.14515	−	3.71550i	0.312902	−	0.541962i	0.978989	+	0.203912i	$0.0653656\pi$
$48$		0			0
$49$	6.29669	−	3.05805i	0.899528	−	0.436864i
$50$		0			0
$51$	−0.684742	+	1.18601i	−0.0958830	+	0.166074i
$52$		0			0
$53$	−1.73444	−	3.00413i	−0.238243	−	0.412649i	0.721967	−	0.691927i	$-0.243238\pi$
$53$	−1.73444	−	3.00413i	−0.238243	−	0.412649i	−0.960210	+	0.279278i	$0.909905\pi$
$54$		0			0
$55$	2.92081			0.393842
$56$		0			0
$57$	1.06226			0.140699
$58$		0			0
$59$	4.47214	+	7.74597i	0.582223	+	1.00844i	0.995215	+	0.0977047i	$0.0311501\pi$
$59$	4.47214	+	7.74597i	0.582223	+	1.00844i	−0.412993	+	0.910734i	$0.635517\pi$
$60$		0			0
$61$	0.234436	−	0.406054i	0.0300164	−	0.0519899i	−0.850627	−	0.525770i	$-0.823777\pi$
$61$	0.234436	−	0.406054i	0.0300164	−	0.0519899i	0.880643	+	0.473780i	$0.157111\pi$
$62$		0			0
$63$	1.96330	−	6.40248i	0.247353	−	0.806636i
$64$		0			0
$65$	−1.26556	+	2.19202i	−0.156974	+	0.271887i
$66$		0			0
$67$	3.26318	+	5.65199i	0.398661	+	0.690501i	0.993561	−	0.113299i	$-0.0361417\pi$
$67$	3.26318	+	5.65199i	0.398661	+	0.690501i	−0.594900	+	0.803800i	$0.702808\pi$
$68$		0			0
$69$	4.59339			0.552979
$70$		0			0
$71$	8.94427			1.06149			0.530745	−	0.847532i	$-0.321912\pi$
$71$	8.94427			1.06149			0.530745	+	0.847532i	$0.321912\pi$
$72$		0			0
$73$	5.53113	+	9.58020i	0.647370	+	1.12128i	0.983749	+	0.179550i	$0.0574643\pi$
$73$	5.53113	+	9.58020i	0.647370	+	1.12128i	−0.336379	+	0.941727i	$0.609202\pi$
$74$		0			0
$75$	0.342371	−	0.593004i	0.0395336	−	0.0684742i
$76$		0			0
$77$	5.26556	+	5.65612i	0.600067	+	0.644575i
$78$		0			0
$79$	2.92081	−	5.05899i	0.328617	−	0.569181i	−0.653621	−	0.756822i	$-0.726751\pi$
$79$	2.92081	−	5.05899i	0.328617	−	0.569181i	0.982238	+	0.187641i	$0.0600842\pi$
$80$		0			0
$81$	−2.50000	−	4.33013i	−0.277778	−	0.481125i
$82$		0			0
$83$	3.78739			0.415721			0.207860	−	0.978159i	$-0.433350\pi$
$83$	3.78739			0.415721			0.207860	+	0.978159i	$0.433350\pi$
$84$		0			0
$85$	2.00000			0.216930
$86$		0			0
$87$	−0.524214	−	0.907965i	−0.0562016	−	0.0973441i
$88$		0			0
$89$	−4.76556	+	8.25420i	−0.505149	+	0.874943i	0.494833	+	0.868988i	$0.335229\pi$
$89$	−4.76556	+	8.25420i	−0.505149	+	0.874943i	−0.999982	+	0.00595558i	$0.998104\pi$
$90$		0			0
$91$	−6.52636	+	1.50097i	−0.684149	+	0.157344i
$92$		0			0
$93$	−0.468871	+	0.812109i	−0.0486197	+	0.0842117i
$94$		0			0
$95$	−0.775663	−	1.34349i	−0.0795814	−	0.137839i
$96$		0			0
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$	7.39295			0.743019
$100$		0			0
$101$	−0.234436	−	0.406054i	−0.0233272	−	0.0404039i	0.854126	−	0.520066i	$-0.174093\pi$
$101$	−0.234436	−	0.406054i	−0.0233272	−	0.0404039i	−0.877453	+	0.479662i	$0.840759\pi$
$102$		0			0
$103$	9.10480	−	15.7700i	0.897123	−	1.55386i	0.0659671	−	0.997822i	$-0.478987\pi$
$103$	9.10480	−	15.7700i	0.897123	−	1.55386i	0.831155	−	0.556040i	$-0.187680\pi$
$104$		0			0
$105$	1.76556	−	0.406054i	0.172301	−	0.0396268i
$106$		0			0
$107$	−9.78954	+	16.9560i	−0.946391	+	1.63920i	−0.193448	+	0.981111i	$0.561967\pi$
$107$	−9.78954	+	16.9560i	−0.946391	+	1.63920i	−0.752943	+	0.658086i	$0.771366\pi$
$108$		0			0
$109$	−4.23444	−	7.33426i	−0.405585	−	0.702494i	0.588804	−	0.808276i	$-0.299599\pi$
$109$	−4.23444	−	7.33426i	−0.405585	−	0.702494i	−0.994389	+	0.105781i	$0.966266\pi$
$110$		0			0
$111$	0.363686			0.0345196
$112$		0			0
$113$	4.00000			0.376288			0.188144	−	0.982141i	$-0.439753\pi$
$113$	4.00000			0.376288			0.188144	+	0.982141i	$0.439753\pi$
$114$		0			0
$115$	−3.35410	−	5.80948i	−0.312772	−	0.541736i
$116$		0			0
$117$	−3.20331	+	5.54829i	−0.296146	+	0.512940i
$118$		0			0
$119$	3.60555	+	3.87298i	0.330520	+	0.355036i
$120$		0			0
$121$	1.23444	−	2.13811i	0.112221	−	0.194373i
$122$		0			0
$123$	−2.76028	−	4.78095i	−0.248886	−	0.431084i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−7.39295			−0.656018			−0.328009	−	0.944675i	$-0.606378\pi$
$127$	−7.39295			−0.656018			−0.328009	+	0.944675i	$0.606378\pi$
$128$		0			0
$129$	0.703307	+	1.21816i	0.0619227	+	0.107253i
$130$		0			0
$131$	−9.53809	+	16.5205i	−0.833347	+	1.44340i	0.0620223	+	0.998075i	$0.480245\pi$
$131$	−9.53809	+	16.5205i	−0.833347	+	1.44340i	−0.895369	+	0.445325i	$0.853088\pi$
$132$		0			0
$133$	1.20331	−	3.92407i	0.104340	−	0.340260i
$134$		0			0
$135$	1.89370	−	3.27998i	0.162984	−	0.282296i
$136$		0			0
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	−0.999893	−	0.0146279i	$-0.995344\pi$
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	0.487278	−	0.873247i	$-0.337990\pi$
$138$		0			0
$139$	−15.7917			−1.33943			−0.669717	−	0.742617i	$-0.733584\pi$
$139$	−15.7917			−1.33943			−0.669717	+	0.742617i	$0.733584\pi$
$140$		0			0
$141$	2.93774			0.247403
$142$		0			0
$143$	−3.69647	−	6.40248i	−0.309115	−	0.535402i
$144$		0			0
$145$	−0.765564	+	1.32600i	−0.0635767	+	0.110118i
$146$		0			0
$147$	3.96924	+	2.68698i	0.327377	+	0.221618i
$148$		0			0
$149$	−9.82782	+	17.0223i	−0.805127	+	1.39452i	0.111079	+	0.993812i	$0.464569\pi$
$149$	−9.82782	+	17.0223i	−0.805127	+	1.39452i	−0.916206	+	0.400709i	$0.868764\pi$
$150$		0			0
$151$	8.07769	+	13.9910i	0.657353	+	1.13857i	0.981298	+	0.192493i	$0.0616572\pi$
$151$	8.07769	+	13.9910i	0.657353	+	1.13857i	−0.323946	+	0.946076i	$0.605009\pi$
$152$		0			0
$153$	5.06226			0.409259
$154$		0			0
$155$	1.36948			0.110000
$156$		0			0
$157$	−3.79669	−	6.57607i	−0.303009	−	0.524827i	0.673807	−	0.738907i	$-0.264658\pi$
$157$	−3.79669	−	6.57607i	−0.303009	−	0.524827i	−0.976816	+	0.214080i	$0.931325\pi$
$158$		0			0
$159$	1.18764	−	2.05705i	0.0941860	−	0.163135i
$160$		0			0
$161$	5.20331	−	16.9684i	0.410078	−	1.33729i
$162$		0			0
$163$	7.21110	−	12.4900i	0.564817	−	0.978292i	−0.432250	−	0.901754i	$-0.642280\pi$
$163$	7.21110	−	12.4900i	0.564817	−	0.978292i	0.997067	−	0.0765379i	$-0.0243866\pi$
$164$		0			0
$165$	1.00000	+	1.73205i	0.0778499	+	0.134840i
$166$		0			0
$167$	−12.5498			−0.971134			−0.485567	−	0.874199i	$-0.661387\pi$
$167$	−12.5498			−0.971134			−0.485567	+	0.874199i	$0.661387\pi$
$168$		0			0
$169$	−6.59339			−0.507184
$170$		0			0
$171$	−1.96330	−	3.40054i	−0.150138	−	0.260046i
$172$		0			0
$173$	0.265564	−	0.459971i	0.0201905	−	0.0349710i	−0.855754	−	0.517384i	$-0.826906\pi$
$173$	0.265564	−	0.459971i	0.0201905	−	0.0349710i	0.875944	+	0.482413i	$0.160239\pi$
$174$		0			0
$175$	−1.80278	−	1.93649i	−0.136277	−	0.146385i
$176$		0			0
$177$	−3.06226	+	5.30399i	−0.230173	+	0.398672i
$178$		0			0
$179$	4.38121	+	7.58849i	0.327467	+	0.567190i	0.982009	−	0.188836i	$-0.0604715\pi$
$179$	4.38121	+	7.58849i	0.327467	+	0.567190i	−0.654541	+	0.756026i	$0.727138\pi$
$180$		0			0
$181$	−10.4689			−0.778145			−0.389073	−	0.921207i	$-0.627204\pi$
$181$	−10.4689			−0.778145			−0.389073	+	0.921207i	$0.627204\pi$
$182$		0			0
$183$	0.321056			0.0237331
$184$		0			0
$185$	−0.265564	−	0.459971i	−0.0195247	−	0.0338177i
$186$		0			0
$187$	−2.92081	+	5.05899i	−0.213591	+	0.369950i
$188$		0			0
$189$	9.76556	−	2.24594i	0.710340	−	0.163368i
$190$		0			0
$191$	−10.9985	+	19.0500i	−0.795823	+	1.37841i	0.126492	+	0.991968i	$0.459628\pi$
$191$	−10.9985	+	19.0500i	−0.795823	+	1.37841i	−0.922315	+	0.386439i	$0.873705\pi$
$192$		0			0
$193$	−12.5934	−	21.8124i	−0.906492	−	1.57009i	−0.818902	−	0.573933i	$-0.805417\pi$
$193$	−12.5934	−	21.8124i	−0.906492	−	1.57009i	−0.0875897	−	0.996157i	$-0.527916\pi$
$194$		0			0
$195$	−1.73317			−0.124115
$196$		0			0
$197$	27.5934			1.96595			0.982974	−	0.183746i	$-0.0588225\pi$
$197$	27.5934			1.96595			0.982974	+	0.183746i	$0.0588225\pi$
$198$		0			0
$199$	−5.84162	−	10.1180i	−0.414101	−	0.717245i	0.581232	−	0.813738i	$-0.302571\pi$
$199$	−5.84162	−	10.1180i	−0.414101	−	0.717245i	−0.995334	+	0.0964930i	$0.969237\pi$
$200$		0			0
$201$	−2.23444	+	3.87016i	−0.157605	+	0.272980i
$202$		0			0
$203$	−3.94792	+	0.907965i	−0.277090	+	0.0637267i
$204$		0			0
$205$	−4.03113	+	6.98212i	−0.281546	+	0.487652i
$206$		0			0
$207$	−8.48966	−	14.7045i	−0.590072	−	1.02204i
$208$		0			0
$209$	4.53113			0.313425
$210$		0			0
$211$	−10.4956			−0.722547			−0.361273	−	0.932460i	$-0.617658\pi$
$211$	−10.4956			−0.722547			−0.361273	+	0.932460i	$0.617658\pi$
$212$		0			0
$213$	3.06226	+	5.30399i	0.209822	+	0.363423i
$214$		0			0
$215$	1.02711	−	1.77901i	0.0700485	−	0.121328i
$216$		0			0
$217$	2.46887	+	2.65199i	0.167598	+	0.180029i
$218$		0			0
$219$	−3.78739	+	6.55996i	−0.255928	+	0.443281i
$220$		0			0
$221$	−2.53113	−	4.38404i	−0.170262	−	0.294903i
$222$		0			0
$223$	−8.94427			−0.598953			−0.299476	−	0.954104i	$-0.596812\pi$
$223$	−8.94427			−0.598953			−0.299476	+	0.954104i	$0.596812\pi$
$224$		0			0
$225$	−2.53113			−0.168742
$226$		0			0
$227$	8.94427	+	15.4919i	0.593652	+	1.02824i	0.993736	+	0.111757i	$0.0356478\pi$
$227$	8.94427	+	15.4919i	0.593652	+	1.02824i	−0.400083	+	0.916479i	$0.631019\pi$
$228$		0			0
$229$	−5.53113	+	9.58020i	−0.365507	+	0.633077i	−0.988857	−	0.148866i	$-0.952438\pi$
$229$	−5.53113	+	9.58020i	−0.365507	+	0.633077i	0.623350	+	0.781943i	$0.285771\pi$
$230$		0			0
$231$	−1.55133	+	5.05899i	−0.102070	+	0.332857i
$232$		0			0
$233$	6.06226	−	10.5001i	0.397152	−	0.687887i	−0.596222	−	0.802820i	$-0.703332\pi$
$233$	6.06226	−	10.5001i	0.397152	−	0.687887i	0.993373	+	0.114933i	$0.0366653\pi$
$234$		0			0
$235$	−2.14515	−	3.71550i	−0.139934	−	0.242373i
$236$		0			0
$237$	4.00000			0.259828
$238$		0			0
$239$	−21.6333			−1.39934			−0.699671	−	0.714465i	$-0.746670\pi$
$239$	−21.6333			−1.39934			−0.699671	+	0.714465i	$0.746670\pi$
$240$		0			0
$241$	13.7967	+	23.8966i	0.888723	+	1.53931i	0.841386	+	0.540435i	$0.181740\pi$
$241$	13.7967	+	23.8966i	0.888723	+	1.53931i	0.0473372	+	0.998879i	$0.484926\pi$
$242$		0			0
$243$	7.39295	−	12.8050i	0.474258	−	0.821438i
$244$		0			0
$245$	0.500000	−	6.98212i	0.0319438	−	0.446071i
$246$		0			0
$247$	−1.96330	+	3.40054i	−0.124922	+	0.216371i
$248$		0			0
$249$	1.29669	+	2.24594i	0.0821746	+	0.142331i
$250$		0			0
$251$	−23.1846			−1.46340			−0.731701	−	0.681626i	$-0.761273\pi$
$251$	−23.1846			−1.46340			−0.731701	+	0.681626i	$0.761273\pi$
$252$		0			0
$253$	19.5934			1.23183
$254$		0			0
$255$	0.684742	+	1.18601i	0.0428802	+	0.0742707i
$256$		0			0
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	−0.990217	−	0.139533i	$-0.955440\pi$
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	0.615948	+	0.787787i	$0.288773\pi$
$258$		0			0
$259$	0.411977	−	1.34349i	0.0255990	−	0.0834803i
$260$		0			0
$261$	−1.93774	+	3.35627i	−0.119943	+	0.207748i
$262$		0			0
$263$	−7.05057	−	12.2120i	−0.434757	−	0.753021i	0.562519	−	0.826785i	$-0.309832\pi$
$263$	−7.05057	−	12.2120i	−0.434757	−	0.753021i	−0.997276	+	0.0737632i	$0.976499\pi$
$264$		0			0
$265$	−3.46887			−0.213091
$266$		0			0
$267$	−6.52636			−0.399407
$268$		0			0
$269$	−4.23444	−	7.33426i	−0.258178	−	0.447178i	0.707576	−	0.706637i	$-0.249789\pi$
$269$	−4.23444	−	7.33426i	−0.258178	−	0.447178i	−0.965754	+	0.259460i	$0.916455\pi$
$270$		0			0
$271$	−13.0527	+	22.6080i	−0.792896	+	1.37334i	0.131270	+	0.991347i	$0.458095\pi$
$271$	−13.0527	+	22.6080i	−0.792896	+	1.37334i	−0.924166	+	0.381990i	$0.875239\pi$
$272$		0			0
$273$	−3.12452	−	3.35627i	−0.189104	−	0.203131i
$274$		0			0
$275$	1.46040	−	2.52950i	0.0880657	−	0.152534i
$276$		0			0
$277$	−16.0623	−	27.8206i	−0.965088	−	1.67158i	−0.709380	−	0.704827i	$-0.751025\pi$
$277$	−16.0623	−	27.8206i	−0.965088	−	1.67158i	−0.255708	−	0.966754i	$-0.582309\pi$
$278$		0			0
$279$	3.46634			0.207524
$280$		0			0
$281$	15.5934			0.930223			0.465112	−	0.885252i	$-0.346014\pi$
$281$	15.5934			0.930223			0.465112	+	0.885252i	$0.346014\pi$
$282$		0			0
$283$	−13.2346	−	22.9229i	−0.786713	−	1.36263i	−0.927970	−	0.372654i	$-0.878448\pi$
$283$	−13.2346	−	22.9229i	−0.786713	−	1.36263i	0.141257	−	0.989973i	$-0.454886\pi$
$284$		0			0
$285$	0.531129	−	0.919942i	0.0314614	−	0.0544927i
$286$		0			0
$287$	−20.7880	+	4.78095i	−1.22708	+	0.282210i
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$	−0.684742	−	1.18601i	−0.0401403	−	0.0695250i
$292$		0			0
$293$	−27.7179			−1.61930			−0.809649	−	0.586915i	$-0.800342\pi$
$293$	−27.7179			−1.61930			−0.809649	+	0.586915i	$0.800342\pi$
$294$		0			0
$295$	8.94427			0.520756
$296$		0			0
$297$	5.53113	+	9.58020i	0.320949	+	0.555899i
$298$		0			0
$299$	−8.48966	+	14.7045i	−0.490970	+	0.850385i
$300$		0			0
$301$	5.29669	−	1.21816i	0.305296	−	0.0702137i
$302$		0			0
$303$	0.160528	−	0.278042i	0.00922208	−	0.0159731i
$304$		0			0
$305$	−0.234436	−	0.406054i	−0.0134237	−	0.0232506i
$306$		0			0
$307$	16.4764			0.940360			0.470180	−	0.882571i	$-0.344189\pi$
$307$	16.4764			0.940360			0.470180	+	0.882571i	$0.344189\pi$
$308$		0			0
$309$	12.4689			0.709329
$310$		0			0
$311$	14.7859	+	25.6099i	0.838431	+	1.45221i	0.891206	+	0.453599i	$0.149860\pi$
$311$	14.7859	+	25.6099i	0.838431	+	1.45221i	−0.0527751	+	0.998606i	$0.516807\pi$
$312$		0			0
$313$	−12.0000	+	20.7846i	−0.678280	+	1.17482i	0.297218	+	0.954810i	$0.403941\pi$
$313$	−12.0000	+	20.7846i	−0.678280	+	1.17482i	−0.975499	+	0.220006i	$0.929392\pi$
$314$		0			0
$315$	−4.56306	−	4.90151i	−0.257099	−	0.276169i
$316$		0			0
$317$	−1.00000	+	1.73205i	−0.0561656	+	0.0972817i	−0.892741	−	0.450570i	$-0.851221\pi$
$317$	−1.00000	+	1.73205i	−0.0561656	+	0.0972817i	0.836576	+	0.547852i	$0.184554\pi$
$318$		0			0
$319$	−2.23607	−	3.87298i	−0.125196	−	0.216845i
$320$		0			0
$321$	−13.4066			−0.748284
$322$		0			0
$323$	3.10265			0.172636
$324$		0			0
$325$	1.26556	+	2.19202i	0.0702009	+	0.121591i
$326$		0			0
$327$	2.89949	−	5.02207i	0.160342	−	0.277721i
$328$		0			0
$329$	3.32782	−	10.8523i	0.183469	−	0.598305i
$330$		0			0
$331$	2.64805	−	4.58655i	0.145550	−	0.252100i	−0.784028	−	0.620725i	$-0.786838\pi$
$331$	2.64805	−	4.58655i	0.145550	−	0.252100i	0.929578	+	0.368626i	$0.120172\pi$
$332$		0			0
$333$	−0.672178	−	1.16425i	−0.0368351	−	0.0638003i
$334$		0			0
$335$	6.52636			0.356573
$336$		0			0
$337$	−17.0623			−0.929440			−0.464720	−	0.885458i	$-0.653845\pi$
$337$	−17.0623			−0.929440			−0.464720	+	0.885458i	$0.653845\pi$
$338$		0			0
$339$	1.36948	+	2.37201i	0.0743801	+	0.128830i
$340$		0			0
$341$	−2.00000	+	3.46410i	−0.108306	+	0.187592i
$342$		0			0
$343$	14.4222	−	11.6190i	0.778726	−	0.627364i
$344$		0			0
$345$	2.29669	−	3.97799i	0.123650	−	0.214168i
$346$		0			0
$347$	4.99635	+	8.65393i	0.268218	+	0.464567i	0.968402	−	0.249395i	$-0.0802319\pi$
$347$	4.99635	+	8.65393i	0.268218	+	0.464567i	−0.700184	+	0.713963i	$0.746899\pi$
$348$		0			0
$349$	−5.53113			−0.296075			−0.148037	−	0.988982i	$-0.547296\pi$
$349$	−5.53113			−0.296075			−0.148037	+	0.988982i	$0.547296\pi$
$350$		0			0
$351$	−9.58638			−0.511683
$352$		0			0
$353$	2.00000	+	3.46410i	0.106449	+	0.184376i	0.914329	−	0.404971i	$-0.132718\pi$
$353$	2.00000	+	3.46410i	0.106449	+	0.184376i	−0.807880	+	0.589347i	$0.799385\pi$
$354$		0			0
$355$	4.47214	−	7.74597i	0.237356	−	0.411113i
$356$		0			0
$357$	−1.06226	+	3.46410i	−0.0562206	+	0.183340i
$358$		0			0
$359$	−9.81086	+	16.9929i	−0.517797	+	0.896851i	0.481989	+	0.876177i	$0.339914\pi$
$359$	−9.81086	+	16.9929i	−0.517797	+	0.896851i	−0.999786	+	0.0206738i	$0.993419\pi$
$360$		0			0
$361$	8.29669	+	14.3703i	0.436668	+	0.756331i
$362$		0			0
$363$	1.69054			0.0887303
$364$		0			0
$365$	11.0623			0.579025
$366$		0			0
$367$	12.9831	+	22.4874i	0.677713	+	1.17383i	0.975668	+	0.219254i	$0.0703622\pi$
$367$	12.9831	+	22.4874i	0.677713	+	1.17383i	−0.297955	+	0.954580i	$0.596304\pi$
$368$		0			0
$369$	−10.2033	+	17.6726i	−0.531163	+	0.920001i
$370$		0			0
$371$	−6.25360	−	6.71744i	−0.324671	−	0.348752i
$372$		0			0
$373$	−2.53113	+	4.38404i	−0.131057	+	0.226997i	−0.924084	−	0.382189i	$-0.875170\pi$
$373$	−2.53113	+	4.38404i	−0.131057	+	0.226997i	0.793027	+	0.609186i	$0.208504\pi$
$374$		0			0
$375$	−0.342371	−	0.593004i	−0.0176800	−	0.0306226i
$376$		0			0
$377$	3.87548			0.199598
$378$		0			0
$379$	−5.01767			−0.257740			−0.128870	−	0.991661i	$-0.541135\pi$
$379$	−5.01767			−0.257740			−0.128870	+	0.991661i	$0.541135\pi$
$380$		0			0
$381$	−2.53113	−	4.38404i	−0.129674	−	0.224601i
$382$		0			0
$383$	−8.32914	+	14.4265i	−0.425599	+	0.737159i	−0.996476	−	0.0838764i	$-0.973270\pi$
$383$	−8.32914	+	14.4265i	−0.425599	+	0.737159i	0.570877	+	0.821035i	$0.306603\pi$
$384$		0			0
$385$	7.53113	−	1.73205i	0.383822	−	0.0882735i
$386$		0			0
$387$	2.59975	−	4.50291i	0.132153	−	0.228896i
$388$		0			0
$389$	−15.5311	−	26.9007i	−0.787459	−	1.36392i	−0.927519	−	0.373777i	$-0.878063\pi$
$389$	−15.5311	−	26.9007i	−0.787459	−	1.36392i	0.140059	−	0.990143i	$-0.455271\pi$
$390$		0			0
$391$	13.4164			0.678497
$392$		0			0
$393$	−13.0623			−0.658904
$394$		0			0
$395$	−2.92081	−	5.05899i	−0.146962	−	0.254545i
$396$		0			0
$397$	−15.1245	+	26.1964i	−0.759078	+	1.31476i	0.184244	+	0.982881i	$0.441016\pi$
$397$	−15.1245	+	26.1964i	−0.759078	+	1.31476i	−0.943321	+	0.331881i	$0.892317\pi$
$398$		0			0
$399$	2.73897	−	0.629923i	0.137120	−	0.0315356i
$400$		0			0
$401$	−8.96887	+	15.5345i	−0.447884	+	0.775758i	−0.998248	−	0.0591669i	$-0.981156\pi$
$401$	−8.96887	+	15.5345i	−0.447884	+	0.775758i	0.550364	+	0.834925i	$0.314489\pi$
$402$		0			0
$403$	−1.73317	−	3.00194i	−0.0863353	−	0.149537i
$404$		0			0
$405$	−5.00000			−0.248452
$406$		0			0
$407$	1.55133			0.0768964
$408$		0			0
$409$	−2.29669	−	3.97799i	−0.113564	−	0.196699i	0.803641	−	0.595115i	$-0.202893\pi$
$409$	−2.29669	−	3.97799i	−0.113564	−	0.196699i	−0.917205	+	0.398416i	$0.869560\pi$
$410$		0			0
$411$	4.10845	−	7.11604i	0.202655	−	0.351009i
$412$		0			0
$413$	16.1245	+	17.3205i	0.793436	+	0.852286i
$414$		0			0
$415$	1.89370	−	3.27998i	0.0929579	−	0.161008i
$416$		0			0
$417$	−5.40661	−	9.36453i	−0.264763	−	0.458583i
$418$		0			0
$419$	16.3372			0.798125			0.399063	−	0.916924i	$-0.369336\pi$
$419$	16.3372			0.798125			0.399063	+	0.916924i	$0.369336\pi$
$420$		0			0
$421$	32.5934			1.58850			0.794252	−	0.607588i	$-0.207863\pi$
$421$	32.5934			1.58850			0.794252	+	0.607588i	$0.207863\pi$
$422$		0			0
$423$	−5.42964	−	9.40442i	−0.263998	−	0.457258i
$424$		0			0
$425$	1.00000	−	1.73205i	0.0485071	−	0.0840168i
$426$		0			0
$427$	0.363686	−	1.18601i	0.0176000	−	0.0573949i
$428$		0			0
$429$	2.53113	−	4.38404i	0.122204	−	0.211664i
$430$		0			0
$431$	12.7317	+	22.0519i	0.613263	+	1.06220i	0.990687	+	0.136162i	$0.0434767\pi$
$431$	12.7317	+	22.0519i	0.613263	+	1.06220i	−0.377424	+	0.926041i	$0.623190\pi$
$432$		0			0
$433$	14.1245			0.678781			0.339390	−	0.940646i	$-0.389779\pi$
$433$	14.1245			0.678781			0.339390	+	0.940646i	$0.389779\pi$
$434$		0			0
$435$	−1.04843			−0.0502683
$436$		0			0
$437$	−5.20331	−	9.01239i	−0.248908	−	0.431121i
$438$		0			0
$439$	0.181843	−	0.314961i	0.00867889	−	0.0150323i	−0.861653	−	0.507497i	$-0.830571\pi$
$439$	0.181843	−	0.314961i	0.00867889	−	0.0150323i	0.870332	+	0.492465i	$0.163904\pi$
$440$		0			0
$441$	1.26556	−	17.6726i	0.0602650	−	0.841555i
$442$		0			0
$443$	10.4743	−	18.1420i	0.497648	−	0.861952i	−0.502348	−	0.864665i	$-0.667530\pi$
$443$	10.4743	−	18.1420i	0.497648	−	0.861952i	0.999996	+	0.00271350i	$0.000863733\pi$
$444$		0			0
$445$	4.76556	+	8.25420i	0.225909	+	0.391287i
$446$		0			0
$447$	−13.4590			−0.636591
$448$		0			0
$449$	12.0623			0.569253			0.284627	−	0.958638i	$-0.408130\pi$
$449$	12.0623			0.569253			0.284627	+	0.958638i	$0.408130\pi$
$450$		0			0
$451$	−11.7742	−	20.3934i	−0.554424	−	0.960290i
$452$		0			0
$453$	−5.53113	+	9.58020i	−0.259875	+	0.450117i
$454$		0			0
$455$	−1.96330	+	6.40248i	−0.0920411	+	0.300153i
$456$		0			0
$457$	17.5934	−	30.4726i	0.822984	−	1.42545i	−0.0804665	−	0.996757i	$-0.525641\pi$
$457$	17.5934	−	30.4726i	0.822984	−	1.42545i	0.903450	−	0.428693i	$-0.141026\pi$
$458$		0			0
$459$	3.78739	+	6.55996i	0.176780	+	0.306193i
$460$		0			0
$461$	−26.0000			−1.21094			−0.605470	−	0.795868i	$-0.707015\pi$
$461$	−26.0000			−1.21094			−0.605470	+	0.795868i	$0.707015\pi$
$462$		0			0
$463$	3.96924			0.184466			0.0922331	−	0.995737i	$-0.470600\pi$
$463$	3.96924			0.184466			0.0922331	+	0.995737i	$0.470600\pi$
$464$		0			0
$465$	0.468871	+	0.812109i	0.0217434	+	0.0376606i
$466$		0			0
$467$	−3.76608	+	6.52304i	−0.174273	+	0.301850i	−0.939910	−	0.341424i	$-0.889091\pi$
$467$	−3.76608	+	6.52304i	−0.174273	+	0.301850i	0.765636	+	0.643274i	$0.222424\pi$
$468$		0			0
$469$	11.7656	+	12.6382i	0.543283	+	0.583580i
$470$		0			0
$471$	2.59975	−	4.50291i	0.119790	−	0.207483i
$472$		0			0
$473$	3.00000	+	5.19615i	0.137940	+	0.238919i
$474$		0			0
$475$	−1.55133			−0.0711797
$476$		0			0
$477$	−8.78016			−0.402016
$478$		0			0
$479$	−9.26533	−	16.0480i	−0.423344	−	0.733253i	0.572921	−	0.819611i	$-0.305810\pi$
$479$	−9.26533	−	16.0480i	−0.423344	−	0.733253i	−0.996264	+	0.0863583i	$0.972477\pi$
$480$		0			0
$481$	−0.672178	+	1.16425i	−0.0306487	+	0.0530851i
$482$		0			0
$483$	11.8438	−	2.72390i	0.538910	−	0.123942i
$484$		0			0
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$		0			0
$487$	−4.47214	−	7.74597i	−0.202652	−	0.351003i	0.746730	−	0.665127i	$-0.231623\pi$
$487$	−4.47214	−	7.74597i	−0.202652	−	0.351003i	−0.949382	+	0.314124i	$0.898289\pi$
$488$		0			0
$489$	9.87548			0.446585
$490$		0			0
$491$	−10.3138			−0.465453			−0.232727	−	0.972542i	$-0.574765\pi$
$491$	−10.3138			−0.465453			−0.232727	+	0.972542i	$0.574765\pi$
$492$		0			0
$493$	−1.53113	−	2.65199i	−0.0689586	−	0.119440i
$494$		0			0
$495$	3.69647	−	6.40248i	0.166144	−	0.287770i
$496$		0			0
$497$	23.0623	−	5.30399i	1.03448	−	0.237916i
$498$		0			0
$499$	20.9486	−	36.2840i	0.937787	−	1.62429i	0.168199	−	0.985753i	$-0.446205\pi$
$499$	20.9486	−	36.2840i	0.937787	−	1.62429i	0.769588	−	0.638541i	$-0.220462\pi$
$500$		0			0
$501$	−4.29669	−	7.44209i	−0.191962	−	0.332488i
$502$		0			0
$503$	21.6759			0.966482			0.483241	−	0.875487i	$-0.339459\pi$
$503$	21.6759			0.966482			0.483241	+	0.875487i	$0.339459\pi$
$504$		0			0
$505$	−0.468871			−0.0208645
$506$		0			0
$507$	−2.25738	−	3.90990i	−0.100254	−	0.173645i
$508$		0			0
$509$	6.76556	−	11.7183i	0.299878	−	0.519405i	−0.676230	−	0.736691i	$-0.736387\pi$
$509$	6.76556	−	11.7183i	0.299878	−	0.519405i	0.976108	+	0.217286i	$0.0697206\pi$
$510$		0			0
$511$	19.9428	+	21.4220i	0.882216	+	0.947652i
$512$		0			0
$513$	2.93774	−	5.08832i	0.129704	−	0.224655i
$514$		0			0
$515$	−9.10480	−	15.7700i	−0.401205	−	0.694908i
$516$		0			0
$517$	12.5311			0.551118
$518$		0			0
$519$	0.363686			0.0159640
$520$		0			0
$521$	−1.79669	−	3.11196i	−0.0787146	−	0.136338i	0.823981	−	0.566617i	$-0.191748\pi$
$521$	−1.79669	−	3.11196i	−0.0787146	−	0.136338i	−0.902696	+	0.430280i	$0.858415\pi$
$522$		0			0
$523$	8.58059	−	14.8620i	0.375203	−	0.649870i	−0.615155	−	0.788407i	$-0.710906\pi$
$523$	8.58059	−	14.8620i	0.375203	−	0.649870i	0.990357	+	0.138536i	$0.0442397\pi$
$524$		0			0
$525$	0.531129	−	1.73205i	0.0231804	−	0.0755929i
$526$		0			0
$527$	−1.36948	+	2.37201i	−0.0596556	+	0.103327i
$528$		0			0
$529$	−11.0000	−	19.0526i	−0.478261	−	0.828372i
$530$		0			0
$531$	22.6391			0.982453
$532$		0			0
$533$	20.4066			0.883909
$534$		0			0
$535$	9.78954	+	16.9560i	0.423239	+	0.733071i
$536$		0			0
$537$	−3.00000	+	5.19615i	−0.129460	+	0.224231i
$538$		0			0
$539$	16.9310	+	11.4615i	0.729271	+	0.493680i
$540$		0			0
$541$	−10.2344	+	17.7266i	−0.440013	+	0.762124i	−0.997690	−	0.0679335i	$-0.978359\pi$
$541$	−10.2344	+	17.7266i	−0.440013	+	0.762124i	0.557677	+	0.830058i	$0.311693\pi$
$542$		0			0
$543$	−3.58424	−	6.20808i	−0.153814	−	0.266414i
$544$		0			0
$545$	−8.46887			−0.362767
$546$		0			0
$547$	37.4676			1.60200			0.801000	−	0.598664i	$-0.204302\pi$
$547$	37.4676			1.60200			0.801000	+	0.598664i	$0.204302\pi$
$548$		0			0
$549$	−0.593387	−	1.02778i	−0.0253251	−	0.0438644i
$550$		0			0
$551$	−1.18764	+	2.05705i	−0.0505952	+	0.0876334i
$552$		0			0
$553$	4.53113	−	14.7763i	0.192683	−	0.628354i
$554$		0			0
$555$	0.181843	−	0.314961i	0.00771881	−	0.0133694i
$556$		0			0
$557$	−8.73444	−	15.1285i	−0.370090	−	0.641015i	0.619489	−	0.785005i	$-0.287340\pi$
$557$	−8.73444	−	15.1285i	−0.370090	−	0.641015i	−0.989579	+	0.143991i	$0.954006\pi$
$558$		0			0
$559$	−5.19951			−0.219916
$560$		0			0
$561$	−4.00000			−0.168880
$562$		0			0
$563$	13.0740	+	22.6449i	0.551005	+	0.954369i	0.998202	+	0.0599333i	$0.0190888\pi$
$563$	13.0740	+	22.6449i	0.551005	+	0.954369i	−0.447197	+	0.894435i	$0.647578\pi$
$564$		0			0
$565$	2.00000	−	3.46410i	0.0841406	−	0.145736i
$566$		0			0
$567$	−9.01388	−	9.68246i	−0.378547	−	0.406625i
$568$		0			0
$569$	−1.79669	+	3.11196i	−0.0753213	+	0.130460i	−0.901226	−	0.433349i	$-0.857332\pi$
$569$	−1.79669	+	3.11196i	−0.0753213	+	0.130460i	0.825905	+	0.563810i	$0.190665\pi$
$570$		0			0
$571$	−17.8885	−	30.9839i	−0.748612	−	1.29663i	−0.948488	−	0.316813i	$-0.897387\pi$
$571$	−17.8885	−	30.9839i	−0.748612	−	1.29663i	0.199876	−	0.979821i	$-0.435946\pi$
$572$		0			0
$573$	−15.0623			−0.629235
$574$		0			0
$575$	−6.70820			−0.279751
$576$		0			0
$577$	10.4689	+	18.1326i	0.435825	+	0.754871i	0.997363	−	0.0725804i	$-0.0231234\pi$
$577$	10.4689	+	18.1326i	0.435825	+	0.754871i	−0.561538	+	0.827451i	$0.689790\pi$
$578$		0			0
$579$	8.62322	−	14.9358i	0.358369	−	0.620713i
$580$		0			0
$581$	9.76556	−	2.24594i	0.405144	−	0.0931772i
$582$		0			0
$583$	5.06596	−	8.77449i	0.209810	−	0.363402i
$584$		0			0
$585$	3.20331	+	5.54829i	0.132440	+	0.229394i
$586$		0			0
$587$	17.1612			0.708317			0.354159	−	0.935185i	$-0.384767\pi$
$587$	17.1612			0.708317			0.354159	+	0.935185i	$0.384767\pi$
$588$		0			0
$589$	2.12452			0.0875391
$590$		0			0
$591$	9.44717	+	16.3630i	0.388605	+	0.673083i
$592$		0			0
$593$	−9.06226	+	15.6963i	−0.372142	+	0.644569i	−0.989895	−	0.141803i	$-0.954710\pi$
$593$	−9.06226	+	15.6963i	−0.372142	+	0.644569i	0.617753	+	0.786373i	$0.288043\pi$
$594$		0			0
$595$	5.15688	−	1.18601i	0.211411	−	0.0486216i
$596$		0			0
$597$	4.00000	−	6.92820i	0.163709	−	0.283552i
$598$		0			0
$599$	21.8152	+	37.7849i	0.891343	+	1.54385i	0.838267	+	0.545261i	$0.183569\pi$
$599$	21.8152	+	37.7849i	0.891343	+	1.54385i	0.0530764	+	0.998590i	$0.483097\pi$
$600$		0			0
$601$	−26.2490			−1.07072			−0.535360	−	0.844624i	$-0.679824\pi$
$601$	−26.2490			−1.07072			−0.535360	+	0.844624i	$0.679824\pi$
$602$		0			0
$603$	16.5191			0.672708
$604$		0			0
$605$	−1.23444	−	2.13811i	−0.0501869	−	0.0869263i
$606$		0			0
$607$	−2.99042	+	5.17955i	−0.121377	+	0.210232i	−0.920311	−	0.391187i	$-0.872064\pi$
$607$	−2.99042	+	5.17955i	−0.121377	+	0.210232i	0.798934	+	0.601419i	$0.205398\pi$
$608$		0			0
$609$	−1.89008	−	2.03027i	−0.0765899	−	0.0822708i
$610$		0			0
$611$	−5.42964	+	9.40442i	−0.219660	+	0.380462i
$612$		0			0
$613$	−7.26556	−	12.5843i	−0.293453	−	0.508276i	0.681171	−	0.732125i	$-0.261471\pi$
$613$	−7.26556	−	12.5843i	−0.293453	−	0.508276i	−0.974624	+	0.223849i	$0.928138\pi$
$614$		0			0
$615$	−5.52056			−0.222611
$616$		0			0
$617$	−35.1868			−1.41657			−0.708283	−	0.705929i	$-0.750530\pi$
$617$	−35.1868			−1.41657			−0.708283	+	0.705929i	$0.750530\pi$
$618$		0			0
$619$	−1.27856	−	2.21453i	−0.0513897	−	0.0890096i	0.839186	−	0.543844i	$-0.183032\pi$
$619$	−1.27856	−	2.21453i	−0.0513897	−	0.0890096i	−0.890576	+	0.454835i	$0.849698\pi$
$620$		0			0
$621$	12.7033	−	22.0028i	0.509766	−	0.882941i
$622$		0			0
$623$	−7.39295	+	24.1089i	−0.296192	+	0.965905i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	1.55133	+	2.68698i	0.0619540	+	0.107307i
$628$		0			0
$629$	1.06226			0.0423550
$630$		0			0
$631$	33.6802			1.34079			0.670394	−	0.742005i	$-0.266125\pi$
$631$	33.6802			1.34079			0.670394	+	0.742005i	$0.266125\pi$
$632$		0			0
$633$	−3.59339	−	6.22393i	−0.142824	−	0.247379i
$634$		0			0
$635$	−3.69647	+	6.40248i	−0.146690	+	0.254075i
$636$		0			0
$637$	−15.9377	+	7.74031i	−0.631476	+	0.306682i
$638$		0			0
$639$	11.3196	−	19.6060i	0.447795	−	0.775603i
$640$		0			0
$641$	10.0311	+	17.3744i	0.396206	+	0.686249i	0.993254	−	0.115957i	$-0.0369934\pi$
$641$	10.0311	+	17.3744i	0.396206	+	0.686249i	−0.597049	+	0.802205i	$0.703660\pi$
$642$		0			0
$643$	2.37528			0.0936719			0.0468360	−	0.998903i	$-0.485086\pi$
$643$	2.37528			0.0936719			0.0468360	+	0.998903i	$0.485086\pi$
$644$		0			0
$645$	1.40661			0.0553853
$646$		0			0
$647$	−16.5887	−	28.7324i	−0.652168	−	1.12959i	−0.982596	−	0.185757i	$-0.940526\pi$
$647$	−16.5887	−	28.7324i	−0.652168	−	1.12959i	0.330428	−	0.943831i	$-0.392807\pi$
$648$		0			0
$649$	−13.0623	+	22.6245i	−0.512738	+	0.888089i
$650$		0			0
$651$	−0.727372	+	2.37201i	−0.0285080	+	0.0929666i
$652$		0			0
$653$	−6.73444	+	11.6644i	−0.263539	+	0.456463i	−0.967180	−	0.254093i	$-0.918223\pi$
$653$	−6.73444	+	11.6644i	−0.263539	+	0.456463i	0.703641	+	0.710556i	$0.251556\pi$
$654$		0			0
$655$	9.53809	+	16.5205i	0.372684	+	0.645508i
$656$		0			0
$657$	28.0000			1.09238
$658$		0			0
$659$	32.3107			1.25865			0.629324	−	0.777143i	$-0.283332\pi$
$659$	32.3107			1.25865			0.629324	+	0.777143i	$0.283332\pi$
$660$		0			0
$661$	4.23444	+	7.33426i	0.164700	+	0.285270i	0.936549	−	0.350537i	$-0.114001\pi$
$661$	4.23444	+	7.33426i	0.164700	+	0.285270i	−0.771848	+	0.635807i	$0.780668\pi$
$662$		0			0
$663$	1.73317	−	3.00194i	0.0673107	−	0.116586i
$664$		0			0
$665$	−2.79669	−	3.00413i	−0.108451	−	0.116495i
$666$		0			0
$667$	−5.13556	+	8.89505i	−0.198850	+	0.344418i
$668$		0			0
$669$	−3.06226	−	5.30399i	−0.118394	−	0.205064i
$670$		0			0
$671$	1.36948			0.0528683
$672$		0			0
$673$	−2.93774			−0.113242			−0.0566208	−	0.998396i	$-0.518033\pi$
$673$	−2.93774			−0.113242			−0.0566208	+	0.998396i	$0.518033\pi$
$674$		0			0
$675$	−1.89370	−	3.27998i	−0.0728884	−	0.126246i
$676$		0			0
$677$	−14.7344	+	25.5208i	−0.566290	+	0.980844i	0.430638	+	0.902525i	$0.358289\pi$
$677$	−14.7344	+	25.5208i	−0.566290	+	0.980844i	−0.996928	+	0.0783189i	$0.975045\pi$
$678$		0			0
$679$	−5.15688	+	1.18601i	−0.197903	+	0.0455148i
$680$		0			0
$681$	−6.12452	+	10.6080i	−0.234692	+	0.406498i
$682$		0			0
$683$	7.37163	+	12.7680i	0.282068	+	0.488555i	0.971894	−	0.235420i	$-0.0756464\pi$
$683$	7.37163	+	12.7680i	0.282068	+	0.488555i	−0.689826	+	0.723975i	$0.742313\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$		0			0
$687$	−7.57479			−0.288996
$688$		0			0
$689$	4.39008	+	7.60384i	0.167249	+	0.289683i
$690$		0			0
$691$	19.9428	−	34.5419i	0.758659	−	1.31404i	−0.184876	−	0.982762i	$-0.559188\pi$
$691$	19.9428	−	34.5419i	0.758659	−	1.31404i	0.943535	−	0.331274i	$-0.107478\pi$
$692$		0			0
$693$	19.0623	−	4.38404i	0.724115	−	0.166536i
$694$		0			0
$695$	−7.89584	+	13.6760i	−0.299506	+	0.518760i
$696$		0			0
$697$	−8.06226	−	13.9642i	−0.305380	−	0.528933i
$698$		0			0
$699$	8.30216			0.314017
$700$		0			0
$701$	28.5934			1.07996			0.539979	−	0.841679i	$-0.318432\pi$
$701$	28.5934			1.07996			0.539979	+	0.841679i	$0.318432\pi$
$702$		0			0
$703$	−0.411977	−	0.713565i	−0.0155380	−	0.0269126i
$704$		0			0
$705$	1.46887	−	2.54416i	0.0553209	−	0.0958186i
$706$		0			0
$707$	−0.845269	−	0.907965i	−0.0317896	−	0.0341475i
$708$		0			0
$709$	−5.23444	+	9.06631i	−0.196583	+	0.340492i	−0.947418	−	0.319997i	$-0.896318\pi$
$709$	−5.23444	+	9.06631i	−0.196583	+	0.340492i	0.750835	+	0.660490i	$0.229651\pi$
$710$		0			0
$711$	−7.39295	−	12.8050i	−0.277257	−	0.480223i
$712$		0			0
$713$	9.18677			0.344047
$714$		0			0
$715$	−7.39295			−0.276480
$716$		0			0
$717$	−7.40661	−	12.8286i	−0.276605	−	0.479094i
$718$		0			0
$719$	−0.684742	+	1.18601i	−0.0255366	+	0.0442306i	−0.878511	−	0.477722i	$-0.841463\pi$
$719$	−0.684742	+	1.18601i	−0.0255366	+	0.0442306i	0.852975	+	0.521952i	$0.174796\pi$
$720$		0			0
$721$	14.1245	−	46.0611i	0.526024	−	1.71540i
$722$		0			0
$723$	−9.44717	+	16.3630i	−0.351344	+	0.608546i
$724$		0			0
$725$	0.765564	+	1.32600i	0.0284323	+	0.0492463i
$726$		0			0
$727$	37.6495			1.39634			0.698171	−	0.715931i	$-0.253998\pi$
$727$	37.6495			1.39634			0.698171	+	0.715931i	$0.253998\pi$
$728$		0			0
$729$	−4.87548			−0.180574
$730$		0			0
$731$	2.05422	+	3.55802i	0.0759783	+	0.131598i
$732$		0			0
$733$	19.9212	−	34.5045i	0.735807	−	1.27445i	−0.218562	−	0.975823i	$-0.570137\pi$
$733$	19.9212	−	34.5045i	0.735807	−	1.27445i	0.954369	−	0.298631i	$-0.0965301\pi$
$734$		0			0
$735$	4.31161	−	2.09397i	0.159036	−	0.0772373i
$736$		0			0
$737$	−9.53113	+	16.5084i	−0.351084	+	0.608095i
$738$		0			0
$739$	−21.9061	−	37.9424i	−0.805828	−	1.39573i	−0.915731	−	0.401793i	$-0.868387\pi$
$739$	−21.9061	−	37.9424i	−0.805828	−	1.39573i	0.109903	−	0.993942i	$-0.464946\pi$
$740$		0			0
$741$	−2.68871			−0.0987723
$742$		0			0
$743$	−5.70241			−0.209201			−0.104601	−	0.994514i	$-0.533356\pi$
$743$	−5.70241			−0.209201			−0.104601	+	0.994514i	$0.533356\pi$
$744$		0			0
$745$	9.82782	+	17.0223i	0.360064	+	0.623648i
$746$		0			0
$747$	4.79319	−	8.30205i	0.175374	−	0.303756i
$748$		0			0
$749$	−15.1868	+	49.5252i	−0.554913	+	1.80961i
$750$		0			0
$751$	−1.55133	+	2.68698i	−0.0566087	+	0.0980491i	−0.892941	−	0.450174i	$-0.851362\pi$
$751$	−1.55133	+	2.68698i	−0.0566087	+	0.0980491i	0.836332	+	0.548223i	$0.184695\pi$
$752$		0			0
$753$	−7.93774	−	13.7486i	−0.289267	−	0.501026i
$754$		0			0
$755$	16.1554			0.587954
$756$		0			0
$757$	24.1245			0.876820			0.438410	−	0.898775i	$-0.355542\pi$
$757$	24.1245			0.876820			0.438410	+	0.898775i	$0.355542\pi$
$758$		0			0
$759$	6.70820	+	11.6190i	0.243492	+	0.421741i
$760$		0			0
$761$	19.2656	−	33.3689i	0.698376	−	1.20962i	−0.270653	−	0.962677i	$-0.587240\pi$
$761$	19.2656	−	33.3689i	0.698376	−	1.20962i	0.969029	−	0.246946i	$-0.0794270\pi$
$762$		0			0
$763$	−15.2675	−	16.3999i	−0.552720	−	0.593716i
$764$		0			0
$765$	2.53113	−	4.38404i	0.0915132	−	0.158505i
$766$		0			0
$767$	−11.3196	−	19.6060i	−0.408725	−	0.707933i
$768$		0			0
$769$	−15.5934			−0.562312			−0.281156	−	0.959662i	$-0.590718\pi$
$769$	−15.5934			−0.562312			−0.281156	+	0.959662i	$0.590718\pi$
$770$		0			0
$771$	−8.21690			−0.295924
$772$		0			0
$773$	−17.3901	−	30.1205i	−0.625478	−	1.08336i	−0.988448	−	0.151559i	$-0.951571\pi$
$773$	−17.3901	−	30.1205i	−0.625478	−	1.08336i	0.362971	−	0.931801i	$-0.381763\pi$
$774$		0			0
$775$	0.684742	−	1.18601i	0.0245966	−	0.0426026i
$776$		0			0
$777$	0.937742	−	0.215667i	0.0336413	−	0.00773702i
$778$		0			0
$779$	−6.25360	+	10.8315i	−0.224058	+	0.388080i
$780$		0			0
$781$	13.0623	+	22.6245i	0.467404	+	0.809568i
$782$		0			0
$783$	−5.79899			−0.207239
$784$		0			0
$785$	−7.59339			−0.271020
$786$		0			0
$787$	1.71185	+	2.96502i	0.0610210	+	0.105691i	0.894922	−	0.446222i	$-0.147231\pi$
$787$	1.71185	+	2.96502i	0.0610210	+	0.105691i	−0.833901	+	0.551914i	$0.813898\pi$
$788$		0			0
$789$	4.82782	−	8.36203i	0.171875	−	0.297696i
$790$		0			0
$791$	10.3138	−	2.37201i	0.366715	−	0.0843391i
$792$		0			0
$793$	−0.593387	+	1.02778i	−0.0210718	+	0.0364974i
$794$		0			0
$795$	−1.18764	−	2.05705i	−0.0421213	−	0.0729562i
$796$		0			0
$797$	37.3113			1.32163			0.660817	−	0.750547i	$-0.270210\pi$
$797$	37.3113			1.32163			0.660817	+	0.750547i	$0.270210\pi$
$798$		0			0
$799$	8.58059			0.303559
$800$		0			0
$801$	12.0623	+	20.8924i	0.426199	+	0.738198i
$802$		0			0
$803$	−16.1554	+	27.9819i	−0.570111	+	0.987461i
$804$		0			0
$805$	−12.0934	−	12.9904i	−0.426236	−	0.457851i
$806$		0			0
$807$	2.89949	−	5.02207i	0.102067	−	0.176785i
$808$		0			0
$809$	0.968871	+	1.67813i	0.0340637	+	0.0590001i	0.882555	−	0.470210i	$-0.155822\pi$
$809$	0.968871	+	1.67813i	0.0340637	+	0.0590001i	−0.848491	+	0.529210i	$0.822488\pi$
$810$		0			0
$811$	−29.7536			−1.04479			−0.522396	−	0.852703i	$-0.674962\pi$
$811$	−29.7536			−1.04479			−0.522396	+	0.852703i	$0.674962\pi$
$812$		0			0
$813$	−17.8755			−0.626921
$814$		0			0
$815$	−7.21110	−	12.4900i	−0.252594	−	0.437505i
$816$		0			0
$817$	1.59339	−	2.75983i	0.0557455	−	0.0965541i
$818$		0			0
$819$	−4.96937	+	16.2055i	−0.173644	+	0.566266i
$820$		0			0
$821$	−14.0623	+	24.3565i	−0.490776	+	0.850049i	−0.999944	−	0.0106182i	$-0.996620\pi$
$821$	−14.0623	+	24.3565i	−0.490776	+	0.850049i	0.509167	+	0.860667i	$0.329953\pi$
$822$		0			0
$823$	3.94792	+	6.83800i	0.137616	+	0.238358i	0.926594	−	0.376064i	$-0.122723\pi$
$823$	3.94792	+	6.83800i	0.137616	+	0.238358i	−0.788978	+	0.614422i	$0.789389\pi$
$824$		0			0
$825$	2.00000			0.0696311
$826$		0			0
$827$	3.42371			0.119054			0.0595270	−	0.998227i	$-0.481041\pi$
$827$	3.42371			0.119054			0.0595270	+	0.998227i	$0.481041\pi$
$828$		0			0
$829$	19.1245	+	33.1246i	0.664222	+	1.15047i	0.979496	+	0.201465i	$0.0645703\pi$
$829$	19.1245	+	33.1246i	0.664222	+	1.15047i	−0.315274	+	0.949001i	$0.602096\pi$
$830$		0			0
$831$	10.9985	−	19.0500i	0.381534	−	0.660836i
$832$		0			0
$833$	11.5934	+	7.84815i	0.401687	+	0.271922i
$834$		0			0
$835$	−6.27491	+	10.8685i	−0.217152	+	0.376119i
$836$		0			0
$837$	2.59339	+	4.49188i	0.0896406	+	0.155262i
$838$		0			0
$839$	−30.5776			−1.05566			−0.527828	−	0.849352i	$-0.676993\pi$
$839$	−30.5776			−1.05566			−0.527828	+	0.849352i	$0.676993\pi$
$840$		0			0
$841$	−26.6556			−0.919160
$842$		0			0
$843$	5.33872	+	9.24694i	0.183875	+	0.318481i
$844$		0			0
$845$	−3.29669	+	5.71004i	−0.113410	+	0.196431i
$846$		0			0
$847$	1.91501	−	6.24500i	0.0658006	−	0.214581i
$848$		0			0
$849$	9.06226	−	15.6963i	0.311016	−	0.538695i
$850$		0			0
$851$	−1.78146	−	3.08558i	−0.0610677	−	0.105772i
$852$		0			0
$853$	19.7179			0.675128			0.337564	−	0.941303i	$-0.390397\pi$
$853$	19.7179			0.675128			0.337564	+	0.941303i	$0.390397\pi$
$854$		0			0
$855$	−3.92661			−0.134287
$856$		0			0
$857$	12.0623	+	20.8924i	0.412039	+	0.713672i	0.995113	−	0.0987470i	$-0.0314835\pi$
$857$	12.0623	+	20.8924i	0.412039	+	0.713672i	−0.583074	+	0.812419i	$0.698150\pi$
$858$		0			0
$859$	−20.9912	+	36.3578i	−0.716210	+	1.24051i	0.246280	+	0.969199i	$0.420792\pi$
$859$	−20.9912	+	36.3578i	−0.716210	+	1.24051i	−0.962491	+	0.271314i	$0.912542\pi$
$860$		0			0
$861$	−9.95234	−	10.6905i	−0.339175	−	0.364332i
$862$		0			0
$863$	−1.80278	+	3.12250i	−0.0613672	+	0.106291i	−0.895077	−	0.445912i	$-0.852879\pi$
$863$	−1.80278	+	3.12250i	−0.0613672	+	0.106291i	0.833710	+	0.552203i	$0.186213\pi$
$864$		0			0
$865$	−0.265564	−	0.459971i	−0.00902946	−	0.0156395i
$866$		0			0
$867$	8.90164			0.302316
$868$		0			0
$869$	17.0623			0.578797
$870$		0			0
$871$	−8.25953	−	14.3059i	−0.279864	−	0.484738i
$872$		0			0
$873$	−2.53113	+	4.38404i	−0.0856657	+	0.148377i
$874$		0			0
$875$	−2.57844	+	0.593004i	−0.0871671	+	0.0200472i
$876$		0			0
$877$	5.73444	−	9.93233i	0.193638	−	0.335391i	−0.752815	−	0.658232i	$-0.771305\pi$
$877$	5.73444	−	9.93233i	0.193638	−	0.335391i	0.946453	+	0.322841i	$0.104638\pi$
$878$		0			0
$879$	−9.48980	−	16.4368i	−0.320083	−	0.554400i
$880$		0			0
$881$	−27.0000			−0.909653			−0.454827	−	0.890580i	$-0.650299\pi$
$881$	−27.0000			−0.909653			−0.454827	+	0.890580i	$0.650299\pi$
$882$		0			0
$883$	−46.7330			−1.57269			−0.786345	−	0.617788i	$-0.788029\pi$
$883$	−46.7330			−1.57269			−0.786345	+	0.617788i	$0.788029\pi$
$884$		0			0
$885$	3.06226	+	5.30399i	0.102937	+	0.178292i
$886$		0			0
$887$	−7.05057	+	12.2120i	−0.236735	+	0.410037i	−0.959776	−	0.280768i	$-0.909411\pi$
$887$	−7.05057	+	12.2120i	−0.236735	+	0.410037i	0.723040	+	0.690806i	$0.242744\pi$
$888$		0			0
$889$	−19.0623	+	4.38404i	−0.639328	+	0.147036i
$890$		0			0
$891$	7.30202	−	12.6475i	0.244627	−	0.423706i
$892$		0			0
$893$	−3.32782	−	5.76396i	−0.111361	−	0.192883i
$894$		0			0
$895$	8.76243			0.292896
$896$		0			0
$897$	−11.6265			−0.388196
$898$		0			0
$899$	−1.04843	−	1.81593i	−0.0349670	−	0.0605647i
$900$		0			0
$901$	3.46887	−	6.00826i	0.115565	−	0.200164i
$902$		0			0
$903$	2.53581	+	2.72390i	0.0843864	+	0.0906456i
$904$		0			0
$905$	−5.23444	+	9.06631i	−0.173999	+	0.301374i
$906$		0			0
$907$	11.7046	+	20.2729i	0.388643	+	0.673150i	0.992267	−	0.124119i	$-0.0396105\pi$
$907$	11.7046	+	20.2729i	0.388643	+	0.673150i	−0.603624	+	0.797269i	$0.706277\pi$
$908$		0			0
$909$	−1.18677			−0.0393628
$910$		0			0
$911$	−14.1438			−0.468604			−0.234302	−	0.972164i	$-0.575281\pi$
$911$	−14.1438			−0.468604			−0.234302	+	0.972164i	$0.575281\pi$
$912$		0			0
$913$	5.53113	+	9.58020i	0.183054	+	0.317058i
$914$		0			0
$915$	0.160528	−	0.278042i	0.00530689	−	0.00919179i
$916$		0			0
$917$	−14.7967	+	48.2531i	−0.488630	+	1.59346i
$918$		0			0
$919$	5.65978	−	9.80302i	0.186699	−	0.323372i	−0.757449	−	0.652894i	$-0.773554\pi$
$919$	5.65978	−	9.80302i	0.186699	−	0.323372i	0.944148	+	0.329523i	$0.106888\pi$
$920$		0			0
$921$	5.64105	+	9.77058i	0.185879	+	0.321952i
$922$		0			0
$923$	−22.6391			−0.745175
$924$		0			0
$925$	−0.531129			−0.0174634
$926$		0			0
$927$	−23.0454	−	39.9158i	−0.756911	−	1.31101i
$928$		0			0
$929$	−12.0311	+	20.8385i	−0.394729	+	0.683690i	−0.993066	−	0.117554i	$-0.962495\pi$
$929$	−12.0311	+	20.8385i	−0.394729	+	0.683690i	0.598338	+	0.801244i	$0.295828\pi$
$930$		0			0
$931$	0.775663	−	10.8315i	0.0254213	−	0.354990i
$932$		0			0
$933$	−10.1245	+	17.5362i	−0.331462	+	0.574109i
$934$		0			0
$935$	2.92081	+	5.05899i	0.0955207	+	0.165447i
$936$		0			0
$937$	39.1868			1.28018			0.640088	−	0.768302i	$-0.278898\pi$
$937$	39.1868			1.28018			0.640088	+	0.768302i	$0.278898\pi$
$938$		0			0
$939$	−16.4338			−0.536297
$940$		0			0
$941$	−7.53113	−	13.0443i	−0.245508	−	0.425232i	0.716766	−	0.697313i	$-0.245621\pi$
$941$	−7.53113	−	13.0443i	−0.245508	−	0.425232i	−0.962274	+	0.272081i	$0.912288\pi$
$942$		0			0
$943$	−27.0416	+	46.8375i	−0.880597	+	1.52524i
$944$		0			0
$945$	2.93774	−	9.58020i	0.0955648	−	0.311644i
$946$		0			0
$947$	−7.23242	+	12.5269i	−0.235022	+	0.407070i	−0.959279	−	0.282460i	$-0.908850\pi$
$947$	−7.23242	+	12.5269i	−0.235022	+	0.407070i	0.724257	+	0.689530i	$0.242183\pi$
$948$		0			0
$949$	−14.0000	−	24.2487i	−0.454459	−	0.787146i
$950$		0			0
$951$	−1.36948			−0.0444085
$952$		0			0
$953$	2.12452			0.0688198			0.0344099	−	0.999408i	$-0.489045\pi$
$953$	2.12452			0.0688198			0.0344099	+	0.999408i	$0.489045\pi$
$954$		0			0
$955$	10.9985	+	19.0500i	0.355903	+	0.616442i
$956$		0			0
$957$	1.53113	−	2.65199i	0.0494944	−	0.0857268i
$958$		0			0
$959$	−21.6333	−	23.2379i	−0.698576	−	0.750391i
$960$		0			0
$961$	14.5623	−	25.2226i	0.469750	−	0.813631i
$962$		0			0
$963$	24.7786	+	42.9178i	0.798479	+	1.38301i
$964$		0			0
$965$	−25.1868			−0.810791
$966$		0			0
$967$	7.16847			0.230523			0.115261	−	0.993335i	$-0.463229\pi$
$967$	7.16847			0.230523			0.115261	+	0.993335i	$0.463229\pi$
$968$		0			0
$969$	1.06226	+	1.83988i	0.0341246	+	0.0591056i
$970$		0			0
$971$	18.3005	−	31.6974i	0.587292	−	1.01722i	−0.407294	−	0.913297i	$-0.633527\pi$
$971$	18.3005	−	31.6974i	0.587292	−	1.01722i	0.994585	−	0.103922i	$-0.0331392\pi$
$972$		0			0
$973$	−40.7179	+	9.36453i	−1.30536	+	0.300213i
$974$		0			0
$975$	−0.866585	+	1.50097i	−0.0277529	+	0.0480695i
$976$		0			0
$977$	−30.1868	−	52.2850i	−0.965760	−	1.67275i	−0.707558	−	0.706655i	$-0.750203\pi$
$977$	−30.1868	−	52.2850i	−0.965760	−	1.67275i	−0.258202	−	0.966091i	$-0.583130\pi$
$978$		0			0
$979$	−27.8386			−0.889726
$980$		0			0
$981$	−21.4358			−0.684393
$982$		0			0
$983$	14.5344	+	25.1744i	0.463577	+	0.802938i	0.999136	−	0.0415592i	$-0.0132325\pi$
$983$	14.5344	+	25.1744i	0.463577	+	0.802938i	−0.535559	+	0.844498i	$0.679899\pi$
$984$		0			0
$985$	13.7967	−	23.8966i	0.439599	−	0.761408i
$986$		0			0
$987$	7.57479	−	1.74209i	0.241108	−	0.0554514i
$988$		0			0
$989$	6.89008	−	11.9340i	0.219092	−	0.379478i
$990$		0			0
$991$	−10.9985	−	19.0500i	−0.349379	−	0.605142i	0.636760	−	0.771062i	$-0.280274\pi$
$991$	−10.9985	−	19.0500i	−0.349379	−	0.605142i	−0.986139	+	0.165920i	$0.946941\pi$
$992$		0			0
$993$	3.62645			0.115082
$994$		0			0
$995$	−11.6832			−0.370384
$996$		0			0
$997$	−10.5311	−	18.2405i	−0.333524	−	0.577681i	0.649676	−	0.760211i	$-0.274905\pi$
$997$	−10.5311	−	18.2405i	−0.333524	−	0.577681i	−0.983200	+	0.182530i	$0.941571\pi$
$998$		0			0
$999$	1.00580	−	1.74209i	0.0318220	−	0.0551173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.q.h.961.3	yes	8
4.3	odd	2	inner	1120.2.q.h.961.2	yes	8
7.2	even	3		7840.2.a.bs.1.2		4
7.4	even	3	inner	1120.2.q.h.641.3	yes	8
7.5	odd	6		7840.2.a.bv.1.3		4
28.11	odd	6	inner	1120.2.q.h.641.2	✓	8
28.19	even	6		7840.2.a.bv.1.2		4
28.23	odd	6		7840.2.a.bs.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1120.2.q.h.641.2	✓	8	28.11	odd	6	inner
1120.2.q.h.641.3	yes	8	7.4	even	3	inner
1120.2.q.h.961.2	yes	8	4.3	odd	2	inner
1120.2.q.h.961.3	yes	8	1.1	even	1	trivial
7840.2.a.bs.1.2		4	7.2	even	3
7840.2.a.bs.1.3		4	28.23	odd	6
7840.2.a.bv.1.2		4	28.19	even	6
7840.2.a.bv.1.3		4	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.342371 + 0.593004i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.57844 - 0.593004i) q^{7} +(1.26556 - 2.19202i) q^{9} +(1.46040 + 2.52950i) q^{11} -2.53113 q^{13} +0.684742 q^{15} +(1.00000 + 1.73205i) q^{17} +(0.775663 - 1.34349i) q^{19} +(1.23444 + 1.32600i) q^{21} +(3.35410 - 5.80948i) q^{23} +(-0.500000 - 0.866025i) q^{25} +3.78739 q^{27} -1.53113 q^{29} +(0.684742 + 1.18601i) q^{31} +(-1.00000 + 1.73205i) q^{33} +(0.775663 - 2.52950i) q^{35} +(0.265564 - 0.459971i) q^{37} +(-0.866585 - 1.50097i) q^{39} -8.06226 q^{41} +2.05422 q^{43} +(-1.26556 - 2.19202i) q^{45} +(2.14515 - 3.71550i) q^{47} +(6.29669 - 3.05805i) q^{49} +(-0.684742 + 1.18601i) q^{51} +(-1.73444 - 3.00413i) q^{53} +2.92081 q^{55} +1.06226 q^{57} +(4.47214 + 7.74597i) q^{59} +(0.234436 - 0.406054i) q^{61} +(1.96330 - 6.40248i) q^{63} +(-1.26556 + 2.19202i) q^{65} +(3.26318 + 5.65199i) q^{67} +4.59339 q^{69} +8.94427 q^{71} +(5.53113 + 9.58020i) q^{73} +(0.342371 - 0.593004i) q^{75} +(5.26556 + 5.65612i) q^{77} +(2.92081 - 5.05899i) q^{79} +(-2.50000 - 4.33013i) q^{81} +3.78739 q^{83} +2.00000 q^{85} +(-0.524214 - 0.907965i) q^{87} +(-4.76556 + 8.25420i) q^{89} +(-6.52636 + 1.50097i) q^{91} +(-0.468871 + 0.812109i) q^{93} +(-0.775663 - 1.34349i) q^{95} -2.00000 q^{97} +7.39295 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{5} - 6 q^{9} + 12 q^{13} + 8 q^{17} + 26 q^{21} - 4 q^{25} + 20 q^{29} - 8 q^{33} - 14 q^{37} + 6 q^{45} + 2 q^{49} - 30 q^{53} - 56 q^{57} + 18 q^{61} + 6 q^{65} - 60 q^{69} + 12 q^{73} + 26 q^{77}+ \cdots - 16 q^{97}+O(q^{100}) \) 8 * q + 4 * q^5 - 6 * q^9 + 12 * q^13 + 8 * q^17 + 26 * q^21 - 4 * q^25 + 20 * q^29 - 8 * q^33 - 14 * q^37 + 6 * q^45 + 2 * q^49 - 30 * q^53 - 56 * q^57 + 18 * q^61 + 6 * q^65 - 60 * q^69 + 12 * q^73 + 26 * q^77 - 20 * q^81 + 16 * q^85 - 22 * q^89 - 36 * q^93 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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