LMFDB - Embedded newform 840.2.bg.i.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [840,2,Mod(121,840)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(840, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2]))

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

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

chi := DirichletCharacter("840.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.bg (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.38363328.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 3x^{4} - 2x^{3} - 21x^{2} - 49x + 343 $ x^6 - x^5 - 3x^4 - 2x^3 - 21x^2 - 49x + 343
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$2.59174 + 0.531877i$ of defining polynomial
Character	$\chi$	$=$	840.361
Dual form			840.2.bg.i.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.835250 - 2.51045i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.835250 - 2.51045i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-0.335250 + 0.580670i) q^{11} -3.51298 q^{13} +1.00000 q^{15} +(-3.25649 + 5.64040i) q^{17} +(4.01298 + 6.95068i) q^{19} +(2.59174 + 0.531877i) q^{21} +(2.84823 + 4.93327i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{27} -5.85398 q^{29} +(-3.09174 + 5.35505i) q^{31} +(-0.335250 - 0.580670i) q^{33} +(-1.75649 + 1.97857i) q^{35} +(-5.42699 - 9.39982i) q^{37} +(1.75649 - 3.04233i) q^{39} +8.35545 q^{41} -1.67050 q^{43} +(-0.500000 + 0.866025i) q^{45} +(-0.591738 - 1.02492i) q^{47} +(-5.60471 + 4.19371i) q^{49} +(-3.25649 - 5.64040i) q^{51} +(-6.10471 + 10.5737i) q^{53} +0.670500 q^{55} -8.02595 q^{57} +(-4.92699 + 8.53379i) q^{59} +(-4.51298 - 7.81670i) q^{61} +(-1.75649 + 1.97857i) q^{63} +(1.75649 + 3.04233i) q^{65} +(-1.67773 + 2.90591i) q^{67} -5.69645 q^{69} +12.8799 q^{71} +(4.34823 - 7.53135i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(1.73776 + 0.356624i) q^{77} +(-4.42124 - 7.65781i) q^{79} +(-0.500000 + 0.866025i) q^{81} +3.17198 q^{83} +6.51298 q^{85} +(2.92699 - 5.06969i) q^{87} +(-1.74351 - 3.01985i) q^{89} +(2.93421 + 8.81915i) q^{91} +(-3.09174 - 5.35505i) q^{93} +(4.01298 - 6.95068i) q^{95} -5.02595 q^{97} +0.670500 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} - 3 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 - 3 * q^5 - 2 * q^7 - 3 * q^9	$ 6 q - 3 q^{3} - 3 q^{5} - 2 q^{7} - 3 q^{9} + q^{11} + 2 q^{13} + 6 q^{15} - 8 q^{17} + q^{19} + q^{21} - 9 q^{23} - 3 q^{25} + 6 q^{27} - 4 q^{31} + q^{33} + q^{35} - 15 q^{37} - q^{39} + 10 q^{41} - 4 q^{43} - 3 q^{45} + 11 q^{47} + 4 q^{49} - 8 q^{51} + q^{53} - 2 q^{55} - 2 q^{57} - 12 q^{59} - 4 q^{61} + q^{63} - q^{65} + 10 q^{67} + 18 q^{69} - 4 q^{71} - 3 q^{75} + 31 q^{77} - 18 q^{79} - 3 q^{81} + 8 q^{83} + 16 q^{85} - 22 q^{89} - 14 q^{91} - 4 q^{93} + q^{95} + 16 q^{97} - 2 q^{99}+O(q^{100}) $ 6 * q - 3 * q^3 - 3 * q^5 - 2 * q^7 - 3 * q^9 + q^11 + 2 * q^13 + 6 * q^15 - 8 * q^17 + q^19 + q^21 - 9 * q^23 - 3 * q^25 + 6 * q^27 - 4 * q^31 + q^33 + q^35 - 15 * q^37 - q^39 + 10 * q^41 - 4 * q^43 - 3 * q^45 + 11 * q^47 + 4 * q^49 - 8 * q^51 + q^53 - 2 * q^55 - 2 * q^57 - 12 * q^59 - 4 * q^61 + q^63 - q^65 + 10 * q^67 + 18 * q^69 - 4 * q^71 - 3 * q^75 + 31 * q^77 - 18 * q^79 - 3 * q^81 + 8 * q^83 + 16 * q^85 - 22 * q^89 - 14 * q^91 - 4 * q^93 + q^95 + 16 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$	$1$

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
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−0.835250	−	2.51045i	−0.315695	−	0.948861i
$7$	−0.835250	−	2.51045i	−0.315695	−	0.948861i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−0.335250	+	0.580670i	−0.101082	+	0.175079i	−0.912131	−	0.409900i	$-0.865564\pi$
$11$	−0.335250	+	0.580670i	−0.101082	+	0.175079i	0.811049	+	0.584978i	$0.198897\pi$
$12$		0			0
$13$	−3.51298			−0.974324			−0.487162	−	0.873312i	$-0.661968\pi$
$13$	−3.51298			−0.974324			−0.487162	+	0.873312i	$0.661968\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	−3.25649	+	5.64040i	−0.789814	+	1.36800i	0.136266	+	0.990672i	$0.456490\pi$
$17$	−3.25649	+	5.64040i	−0.789814	+	1.36800i	−0.926080	+	0.377326i	$0.876844\pi$
$18$		0			0
$19$	4.01298	+	6.95068i	0.920640	+	1.59459i	0.798427	+	0.602091i	$0.205666\pi$
$19$	4.01298	+	6.95068i	0.920640	+	1.59459i	0.122212	+	0.992504i	$0.461001\pi$
$20$		0			0
$21$	2.59174	+	0.531877i	0.565564	+	0.116065i
$22$		0			0
$23$	2.84823	+	4.93327i	0.593896	+	1.02866i	0.993702	+	0.112058i	$0.0357444\pi$
$23$	2.84823	+	4.93327i	0.593896	+	1.02866i	−0.399805	+	0.916600i	$0.630922\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−5.85398			−1.08706			−0.543528	−	0.839391i	$-0.682912\pi$
$29$	−5.85398			−1.08706			−0.543528	+	0.839391i	$0.682912\pi$
$30$		0			0
$31$	−3.09174	+	5.35505i	−0.555293	+	0.961795i	0.442588	+	0.896725i	$0.354060\pi$
$31$	−3.09174	+	5.35505i	−0.555293	+	0.961795i	−0.997881	+	0.0650699i	$0.979273\pi$
$32$		0			0
$33$	−0.335250	−	0.580670i	−0.0583596	−	0.101082i
$34$		0			0
$35$	−1.75649	+	1.97857i	−0.296901	+	0.334440i
$36$		0			0
$37$	−5.42699	−	9.39982i	−0.892191	−	1.54532i	−0.837243	−	0.546832i	$-0.815834\pi$
$37$	−5.42699	−	9.39982i	−0.892191	−	1.54532i	−0.0549488	−	0.998489i	$-0.517500\pi$
$38$		0			0
$39$	1.75649	−	3.04233i	0.281263	−	0.487162i
$40$		0			0
$41$	8.35545			1.30490			0.652451	−	0.757831i	$-0.273741\pi$
$41$	8.35545			1.30490			0.652451	+	0.757831i	$0.273741\pi$
$42$		0			0
$43$	−1.67050			−0.254749			−0.127374	−	0.991855i	$-0.540655\pi$
$43$	−1.67050			−0.254749			−0.127374	+	0.991855i	$0.540655\pi$
$44$		0			0
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$		0			0
$47$	−0.591738	−	1.02492i	−0.0863139	−	0.149500i	0.819636	−	0.572884i	$-0.194175\pi$
$47$	−0.591738	−	1.02492i	−0.0863139	−	0.149500i	−0.905950	+	0.423384i	$0.860842\pi$
$48$		0			0
$49$	−5.60471	+	4.19371i	−0.800673	+	0.599101i
$50$		0			0
$51$	−3.25649	−	5.64040i	−0.456000	−	0.789814i
$52$		0			0
$53$	−6.10471	+	10.5737i	−0.838547	+	1.45241i	0.0525625	+	0.998618i	$0.483261\pi$
$53$	−6.10471	+	10.5737i	−0.838547	+	1.45241i	−0.891109	+	0.453788i	$0.850072\pi$
$54$		0			0
$55$	0.670500			0.0904103
$56$		0			0
$57$	−8.02595			−1.06306
$58$		0			0
$59$	−4.92699	+	8.53379i	−0.641439	+	1.11101i	0.343672	+	0.939090i	$0.388329\pi$
$59$	−4.92699	+	8.53379i	−0.641439	+	1.11101i	−0.985112	+	0.171916i	$0.945004\pi$
$60$		0			0
$61$	−4.51298	−	7.81670i	−0.577827	−	1.00083i	−0.995728	−	0.0923337i	$-0.970567\pi$
$61$	−4.51298	−	7.81670i	−0.577827	−	1.00083i	0.417901	−	0.908493i	$-0.362766\pi$
$62$		0			0
$63$	−1.75649	+	1.97857i	−0.221297	+	0.249277i
$64$		0			0
$65$	1.75649	+	3.04233i	0.217866	+	0.377354i
$66$		0			0
$67$	−1.67773	+	2.90591i	−0.204967	+	0.355013i	−0.950122	−	0.311878i	$-0.899042\pi$
$67$	−1.67773	+	2.90591i	−0.204967	+	0.355013i	0.745155	+	0.666891i	$0.232375\pi$
$68$		0			0
$69$	−5.69645			−0.685772
$70$		0			0
$71$	12.8799			1.52857			0.764283	−	0.644881i	$-0.223093\pi$
$71$	12.8799			1.52857			0.764283	+	0.644881i	$0.223093\pi$
$72$		0			0
$73$	4.34823	−	7.53135i	0.508921	−	0.881478i	−0.491025	−	0.871145i	$-0.663378\pi$
$73$	4.34823	−	7.53135i	0.508921	−	0.881478i	0.999947	−	0.0103323i	$-0.00328895\pi$
$74$		0			0
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$		0			0
$77$	1.73776	+	0.356624i	0.198036	+	0.0406410i
$78$		0			0
$79$	−4.42124	−	7.65781i	−0.497428	−	0.861571i	0.502567	−	0.864538i	$-0.332389\pi$
$79$	−4.42124	−	7.65781i	−0.497428	−	0.861571i	−0.999996	+	0.00296721i	$0.999056\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	3.17198			0.348170			0.174085	−	0.984731i	$-0.444303\pi$
$83$	3.17198			0.348170			0.174085	+	0.984731i	$0.444303\pi$
$84$		0			0
$85$	6.51298			0.706431
$86$		0			0
$87$	2.92699	−	5.06969i	0.313806	−	0.543528i
$88$		0			0
$89$	−1.74351	−	3.01985i	−0.184812	−	0.320104i	0.758701	−	0.651439i	$-0.225834\pi$
$89$	−1.74351	−	3.01985i	−0.184812	−	0.320104i	−0.943513	+	0.331335i	$0.892501\pi$
$90$		0			0
$91$	2.93421	+	8.81915i	0.307589	+	0.924498i
$92$		0			0
$93$	−3.09174	−	5.35505i	−0.320598	−	0.555293i
$94$		0			0
$95$	4.01298	−	6.95068i	0.411723	−	0.713125i
$96$		0			0
$97$	−5.02595			−0.510308			−0.255154	−	0.966900i	$-0.582126\pi$
$97$	−5.02595			−0.510308			−0.255154	+	0.966900i	$0.582126\pi$
$98$		0			0
$99$	0.670500			0.0673878
$100$		0			0
$101$	−9.25649	+	16.0327i	−0.921055	+	1.59531i	−0.123269	+	0.992373i	$0.539338\pi$
$101$	−9.25649	+	16.0327i	−0.921055	+	1.59531i	−0.797786	+	0.602941i	$0.793996\pi$
$102$		0			0
$103$	0.322274	+	0.558195i	0.0317546	+	0.0550006i	0.881466	−	0.472248i	$-0.156557\pi$
$103$	0.322274	+	0.558195i	0.0317546	+	0.0550006i	−0.849711	+	0.527248i	$0.823224\pi$
$104$		0			0
$105$	−0.835250	−	2.51045i	−0.0815121	−	0.244995i
$106$		0			0
$107$	−5.92699	−	10.2658i	−0.572984	−	0.992437i	−0.996257	−	0.0864349i	$-0.972453\pi$
$107$	−5.92699	−	10.2658i	−0.572984	−	0.992437i	0.423274	−	0.906002i	$-0.360881\pi$
$108$		0			0
$109$	2.76224	−	4.78434i	0.264574	−	0.458256i	−0.702878	−	0.711311i	$-0.748102\pi$
$109$	2.76224	−	4.78434i	0.264574	−	0.458256i	0.967452	+	0.253054i	$0.0814352\pi$
$110$		0			0
$111$	10.8540			1.03021
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$	2.84823	−	4.93327i	0.265598	−	0.460030i
$116$		0			0
$117$	1.75649	+	3.04233i	0.162387	+	0.281263i
$118$		0			0
$119$	16.8799	+	3.46410i	1.54738	+	0.317554i
$120$		0			0
$121$	5.27521	+	9.13694i	0.479565	+	0.830631i
$122$		0			0
$123$	−4.17773	+	7.23603i	−0.376693	+	0.652451i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−6.53893			−0.580236			−0.290118	−	0.956991i	$-0.593695\pi$
$127$	−6.53893			−0.580236			−0.290118	+	0.956991i	$0.593695\pi$
$128$		0			0
$129$	0.835250	−	1.44670i	0.0735397	−	0.127374i
$130$		0			0
$131$	10.4457	+	18.0925i	0.912646	+	1.58075i	0.810311	+	0.586000i	$0.199298\pi$
$131$	10.4457	+	18.0925i	0.912646	+	1.58075i	0.102335	+	0.994750i	$0.467369\pi$
$132$		0			0
$133$	14.0975	−	15.8799i	1.22241	−	1.37696i
$134$		0			0
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$		0			0
$137$	0.585988	−	1.01496i	0.0500643	−	0.0867139i	−0.839907	−	0.542730i	$-0.817391\pi$
$137$	0.585988	−	1.01496i	0.0500643	−	0.0867139i	0.889972	+	0.456016i	$0.150724\pi$
$138$		0			0
$139$	5.50147			0.466629			0.233315	−	0.972401i	$-0.425043\pi$
$139$	5.50147			0.466629			0.233315	+	0.972401i	$0.425043\pi$
$140$		0			0
$141$	1.18348			0.0996667
$142$		0			0
$143$	1.17773	−	2.03988i	0.0984864	−	0.170583i
$144$		0			0
$145$	2.92699	+	5.06969i	0.243073	+	0.421015i
$146$		0			0
$147$	−0.829500	−	6.95068i	−0.0684160	−	0.573282i
$148$		0			0
$149$	2.00000	+	3.46410i	0.163846	+	0.283790i	0.936245	−	0.351348i	$-0.114277\pi$
$149$	2.00000	+	3.46410i	0.163846	+	0.283790i	−0.772399	+	0.635138i	$0.780943\pi$
$150$		0			0
$151$	7.51298	−	13.0129i	0.611397	−	1.05897i	−0.379608	−	0.925147i	$-0.623941\pi$
$151$	7.51298	−	13.0129i	0.611397	−	1.05897i	0.991005	−	0.133824i	$-0.0427256\pi$
$152$		0			0
$153$	6.51298			0.526543
$154$		0			0
$155$	6.18348			0.496669
$156$		0			0
$157$	−9.92124	+	17.1841i	−0.791801	+	1.37144i	0.133050	+	0.991109i	$0.457523\pi$
$157$	−9.92124	+	17.1841i	−0.791801	+	1.37144i	−0.924851	+	0.380330i	$0.875810\pi$
$158$		0			0
$159$	−6.10471	−	10.5737i	−0.484135	−	0.838547i
$160$		0			0
$161$	10.0058	−	11.2708i	0.788564	−	0.888267i
$162$		0			0
$163$	−8.00000	−	13.8564i	−0.626608	−	1.08532i	−0.988227	−	0.152992i	$-0.951109\pi$
$163$	−8.00000	−	13.8564i	−0.626608	−	1.08532i	0.361619	−	0.932326i	$-0.382224\pi$
$164$		0			0
$165$	−0.335250	+	0.580670i	−0.0260992	+	0.0452051i
$166$		0			0
$167$	−13.0145			−1.00709			−0.503544	−	0.863969i	$-0.667971\pi$
$167$	−13.0145			−1.00709			−0.503544	+	0.863969i	$0.667971\pi$
$168$		0			0
$169$	−0.658999			−0.0506923
$170$		0			0
$171$	4.01298	−	6.95068i	0.306880	−	0.531532i
$172$		0			0
$173$	−3.07876	−	5.33257i	−0.234074	−	0.405428i	0.724929	−	0.688823i	$-0.241872\pi$
$173$	−3.07876	−	5.33257i	−0.234074	−	0.405428i	−0.959003	+	0.283395i	$0.908539\pi$
$174$		0			0
$175$	2.59174	+	0.531877i	0.195917	+	0.0402061i
$176$		0			0
$177$	−4.92699	−	8.53379i	−0.370335	−	0.641439i
$178$		0			0
$179$	3.40826	−	5.90328i	0.254745	−	0.441232i	−0.710081	−	0.704120i	$-0.751342\pi$
$179$	3.40826	−	5.90328i	0.254745	−	0.441232i	0.964826	+	0.262888i	$0.0846750\pi$
$180$		0			0
$181$	20.5504			1.52750			0.763751	−	0.645511i	$-0.223356\pi$
$181$	20.5504			1.52750			0.763751	+	0.645511i	$0.223356\pi$
$182$		0			0
$183$	9.02595			0.667218
$184$		0			0
$185$	−5.42699	+	9.39982i	−0.399000	+	0.691088i
$186$		0			0
$187$	−2.18348	−	3.78189i	−0.159672	−	0.276559i
$188$		0			0
$189$	−0.835250	−	2.51045i	−0.0607555	−	0.182608i
$190$		0			0
$191$	0.341001	+	0.590631i	0.0246739	+	0.0427365i	0.878099	−	0.478480i	$-0.158812\pi$
$191$	0.341001	+	0.590631i	0.0246739	+	0.0427365i	−0.853425	+	0.521216i	$0.825479\pi$
$192$		0			0
$193$	11.0447	−	19.1299i	0.795013	−	1.37700i	−0.127817	−	0.991798i	$-0.540797\pi$
$193$	11.0447	−	19.1299i	0.795013	−	1.37700i	0.922831	−	0.385206i	$-0.125870\pi$
$194$		0			0
$195$	−3.51298			−0.251569
$196$		0			0
$197$	4.35545			0.310313			0.155157	−	0.987890i	$-0.450412\pi$
$197$	4.35545			0.310313			0.155157	+	0.987890i	$0.450412\pi$
$198$		0			0
$199$	−4.32950	+	7.49891i	−0.306910	+	0.531584i	−0.977685	−	0.210077i	$-0.932628\pi$
$199$	−4.32950	+	7.49891i	−0.306910	+	0.531584i	0.670775	+	0.741661i	$0.265962\pi$
$200$		0			0
$201$	−1.67773	−	2.90591i	−0.118338	−	0.204967i
$202$		0			0
$203$	4.88954	+	14.6961i	0.343178	+	1.03146i
$204$		0			0
$205$	−4.17773	−	7.23603i	−0.291785	−	0.505386i
$206$		0			0
$207$	2.84823	−	4.93327i	0.197965	−	0.342886i
$208$		0			0
$209$	−5.38140			−0.372239
$210$		0			0
$211$	−14.5245			−0.999906			−0.499953	−	0.866052i	$-0.666649\pi$
$211$	−14.5245			−0.999906			−0.499953	+	0.866052i	$0.666649\pi$
$212$		0			0
$213$	−6.43996	+	11.1543i	−0.441259	+	0.764283i
$214$		0			0
$215$	0.835250	+	1.44670i	0.0569636	+	0.0986638i
$216$		0			0
$217$	16.0260	+	3.28885i	1.08791	+	0.223262i
$218$		0			0
$219$	4.34823	+	7.53135i	0.293826	+	0.508921i
$220$		0			0
$221$	11.4400	−	19.8146i	0.769535	−	1.33287i
$222$		0			0
$223$	15.7080			1.05188			0.525941	−	0.850521i	$-0.323713\pi$
$223$	15.7080			1.05188			0.525941	+	0.850521i	$0.323713\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−5.58599	+	9.67521i	−0.370755	+	0.642167i	−0.989682	−	0.143282i	$-0.954234\pi$
$227$	−5.58599	+	9.67521i	−0.370755	+	0.642167i	0.618927	+	0.785449i	$0.287568\pi$
$228$		0			0
$229$	−13.2752	−	22.9933i	−0.877251	−	1.51944i	−0.854346	−	0.519705i	$-0.826042\pi$
$229$	−13.2752	−	22.9933i	−0.877251	−	1.51944i	−0.0229054	−	0.999738i	$-0.507292\pi$
$230$		0			0
$231$	−1.17773	+	1.32663i	−0.0774887	+	0.0872861i
$232$		0			0
$233$	4.48702	+	7.77175i	0.293955	+	0.509144i	0.974741	−	0.223337i	$-0.0716952\pi$
$233$	4.48702	+	7.77175i	0.293955	+	0.509144i	−0.680786	+	0.732482i	$0.738362\pi$
$234$		0			0
$235$	−0.591738	+	1.02492i	−0.0386007	+	0.0668585i
$236$		0			0
$237$	8.84248			0.574381
$238$		0			0
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	5.43421	−	9.41233i	0.350048	−	0.606302i	−0.636209	−	0.771517i	$-0.719498\pi$
$241$	5.43421	−	9.41233i	0.350048	−	0.606302i	0.986258	+	0.165215i	$0.0528318\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	6.43421	+	2.75697i	0.411067	+	0.176136i
$246$		0			0
$247$	−14.0975	−	24.4176i	−0.897002	−	1.55365i
$248$		0			0
$249$	−1.58599	+	2.74701i	−0.100508	+	0.174085i
$250$		0			0
$251$	3.69645			0.233318			0.116659	−	0.993172i	$-0.462782\pi$
$251$	3.69645			0.233318			0.116659	+	0.993172i	$0.462782\pi$
$252$		0			0
$253$	−3.81947			−0.240128
$254$		0			0
$255$	−3.25649	+	5.64040i	−0.203929	+	0.353216i
$256$		0			0
$257$	−0.414012	−	0.717090i	−0.0258254	−	0.0447309i	0.852824	−	0.522199i	$-0.174888\pi$
$257$	−0.414012	−	0.717090i	−0.0258254	−	0.0447309i	−0.878649	+	0.477468i	$0.841555\pi$
$258$		0			0
$259$	−19.0649	+	21.4754i	−1.18463	+	1.33442i
$260$		0			0
$261$	2.92699	+	5.06969i	0.181176	+	0.313806i
$262$		0			0
$263$	6.51298	−	11.2808i	0.401607	−	0.695604i	−0.592313	−	0.805708i	$-0.701785\pi$
$263$	6.51298	−	11.2808i	0.401607	−	0.695604i	0.993920	+	0.110104i	$0.0351183\pi$
$264$		0			0
$265$	12.2094			0.750019
$266$		0			0
$267$	3.48702			0.213402
$268$		0			0
$269$	2.69645	−	4.67039i	0.164406	−	0.284759i	−0.772038	−	0.635576i	$-0.780763\pi$
$269$	2.69645	−	4.67039i	0.164406	−	0.284759i	0.936444	+	0.350817i	$0.114096\pi$
$270$		0			0
$271$	11.3555	+	19.6682i	0.689795	+	1.19476i	0.971904	+	0.235377i	$0.0756325\pi$
$271$	11.3555	+	19.6682i	0.689795	+	1.19476i	−0.282110	+	0.959382i	$0.591034\pi$
$272$		0			0
$273$	−9.10471	−	1.86847i	−0.551042	−	0.113085i
$274$		0			0
$275$	−0.335250	−	0.580670i	−0.0202163	−	0.0350157i
$276$		0			0
$277$	−8.53170	+	14.7773i	−0.512620	+	0.887884i	0.487273	+	0.873250i	$0.337992\pi$
$277$	−8.53170	+	14.7773i	−0.512620	+	0.887884i	−0.999893	+	0.0146345i	$0.995342\pi$
$278$		0			0
$279$	6.18348			0.370195
$280$		0			0
$281$	−4.81652			−0.287330			−0.143665	−	0.989626i	$-0.545889\pi$
$281$	−4.81652			−0.287330			−0.143665	+	0.989626i	$0.545889\pi$
$282$		0			0
$283$	−15.8872	+	27.5174i	−0.944393	+	1.63574i	−0.187432	+	0.982278i	$0.560016\pi$
$283$	−15.8872	+	27.5174i	−0.944393	+	1.63574i	−0.756961	+	0.653460i	$0.773317\pi$
$284$		0			0
$285$	4.01298	+	6.95068i	0.237708	+	0.411723i
$286$		0			0
$287$	−6.97889	−	20.9759i	−0.411951	−	1.23817i
$288$		0			0
$289$	−12.7094	−	22.0134i	−0.747613	−	1.29490i
$290$		0			0
$291$	2.51298	−	4.35260i	0.147313	−	0.255154i
$292$		0			0
$293$	−7.18348			−0.419663			−0.209832	−	0.977738i	$-0.567292\pi$
$293$	−7.18348			−0.419663			−0.209832	+	0.977738i	$0.567292\pi$
$294$		0			0
$295$	9.85398			0.573721
$296$		0			0
$297$	−0.335250	+	0.580670i	−0.0194532	+	0.0336939i
$298$		0			0
$299$	−10.0058	−	17.3305i	−0.578647	−	1.00225i
$300$		0			0
$301$	1.39529	+	4.19371i	0.0804229	+	0.241721i
$302$		0			0
$303$	−9.25649	−	16.0327i	−0.531771	−	0.921055i
$304$		0			0
$305$	−4.51298	+	7.81670i	−0.258412	+	0.447583i
$306$		0			0
$307$	−14.4044			−0.822103			−0.411051	−	0.911612i	$-0.634838\pi$
$307$	−14.4044			−0.822103			−0.411051	+	0.911612i	$0.634838\pi$
$308$		0			0
$309$	−0.644548			−0.0366671
$310$		0			0
$311$	12.7954	−	22.1623i	0.725561	−	1.25671i	−0.233181	−	0.972433i	$-0.574913\pi$
$311$	12.7954	−	22.1623i	0.725561	−	1.25671i	0.958742	−	0.284276i	$-0.0917532\pi$
$312$		0			0
$313$	−1.16475	−	2.01741i	−0.0658356	−	0.114031i	0.831229	−	0.555931i	$-0.187638\pi$
$313$	−1.16475	−	2.01741i	−0.0658356	−	0.114031i	−0.897064	+	0.441900i	$0.854305\pi$
$314$		0			0
$315$	2.59174	+	0.531877i	0.146028	+	0.0299679i
$316$		0			0
$317$	14.2939	+	24.7578i	0.802828	+	1.39054i	0.917748	+	0.397164i	$0.130005\pi$
$317$	14.2939	+	24.7578i	0.802828	+	1.39054i	−0.114920	+	0.993375i	$0.536661\pi$
$318$		0			0
$319$	1.96255	−	3.39923i	0.109882	−	0.190320i
$320$		0			0
$321$	11.8540			0.661624
$322$		0			0
$323$	−52.2728			−2.90854
$324$		0			0
$325$	1.75649	−	3.04233i	0.0974324	−	0.168758i
$326$		0			0
$327$	2.76224	+	4.78434i	0.152752	+	0.264574i
$328$		0			0
$329$	−2.07876	+	2.34159i	−0.114606	+	0.129096i
$330$		0			0
$331$	5.85545	+	10.1419i	0.321845	+	0.557451i	0.980869	−	0.194671i	$-0.0623638\pi$
$331$	5.85545	+	10.1419i	0.321845	+	0.557451i	−0.659024	+	0.752122i	$0.729030\pi$
$332$		0			0
$333$	−5.42699	+	9.39982i	−0.297397	+	0.515107i
$334$		0			0
$335$	3.35545			0.183328
$336$		0			0
$337$	0.673450			0.0366852			0.0183426	−	0.999832i	$-0.494161\pi$
$337$	0.673450			0.0366852			0.0183426	+	0.999832i	$0.494161\pi$
$338$		0			0
$339$	3.00000	−	5.19615i	0.162938	−	0.282216i
$340$		0			0
$341$	−2.07301	−	3.59056i	−0.112260	−	0.194440i
$342$		0			0
$343$	15.2094	+	10.5676i	0.821232	+	0.570595i
$344$		0			0
$345$	2.84823	+	4.93327i	0.153343	+	0.265598i
$346$		0			0
$347$	4.15752	−	7.20104i	0.223188	−	0.386572i	−0.732587	−	0.680674i	$-0.761687\pi$
$347$	4.15752	−	7.20104i	0.223188	−	0.386572i	0.955774	+	0.294102i	$0.0950204\pi$
$348$		0			0
$349$	36.3670			1.94668			0.973339	−	0.229371i	$-0.0736668\pi$
$349$	36.3670			1.94668			0.973339	+	0.229371i	$0.0736668\pi$
$350$		0			0
$351$	−3.51298			−0.187509
$352$		0			0
$353$	0.414012	−	0.717090i	0.0220357	−	0.0381669i	−0.854797	−	0.518962i	$-0.826319\pi$
$353$	0.414012	−	0.717090i	0.0220357	−	0.0381669i	0.876833	+	0.480795i	$0.159652\pi$
$354$		0			0
$355$	−6.43996	−	11.1543i	−0.341798	−	0.592011i
$356$		0			0
$357$	−11.4400	+	12.8864i	−0.605467	+	0.682020i
$358$		0			0
$359$	7.07301	+	12.2508i	0.373299	+	0.646573i	0.990071	−	0.140569i	$-0.0448931\pi$
$359$	7.07301	+	12.2508i	0.373299	+	0.646573i	−0.616772	+	0.787142i	$0.711560\pi$
$360$		0			0
$361$	−22.7080	+	39.3313i	−1.19516	+	2.07007i
$362$		0			0
$363$	−10.5504			−0.553754
$364$		0			0
$365$	−8.69645			−0.455193
$366$		0			0
$367$	−6.24351	+	10.8141i	−0.325909	+	0.564490i	−0.981696	−	0.190455i	$-0.939004\pi$
$367$	−6.24351	+	10.8141i	−0.325909	+	0.564490i	0.655787	+	0.754946i	$0.272337\pi$
$368$		0			0
$369$	−4.17773	−	7.23603i	−0.217484	−	0.376693i
$370$		0			0
$371$	31.6436	+	6.49391i	1.64286	+	0.337147i
$372$		0			0
$373$	1.83525	+	3.17875i	0.0950257	+	0.164589i	0.909619	−	0.415443i	$-0.136373\pi$
$373$	1.83525	+	3.17875i	0.0950257	+	0.164589i	−0.814594	+	0.580032i	$0.803040\pi$
$374$		0			0
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$		0			0
$377$	20.5649			1.05915
$378$		0			0
$379$	−17.6820			−0.908263			−0.454132	−	0.890935i	$-0.650050\pi$
$379$	−17.6820			−0.908263			−0.454132	+	0.890935i	$0.650050\pi$
$380$		0			0
$381$	3.26946	−	5.66288i	0.167500	−	0.290118i
$382$		0			0
$383$	6.10471	+	10.5737i	0.311936	+	0.540290i	0.978782	−	0.204907i	$-0.0656891\pi$
$383$	6.10471	+	10.5737i	0.311936	+	0.540290i	−0.666845	+	0.745196i	$0.732356\pi$
$384$		0			0
$385$	−0.560036	−	1.68326i	−0.0285421	−	0.0857867i
$386$		0			0
$387$	0.835250	+	1.44670i	0.0424582	+	0.0735397i
$388$		0			0
$389$	7.41401	−	12.8414i	0.375905	−	0.651087i	−0.614557	−	0.788873i	$-0.710665\pi$
$389$	7.41401	−	12.8414i	0.375905	−	0.651087i	0.990462	+	0.137785i	$0.0439984\pi$
$390$		0			0
$391$	−37.1009			−1.87627
$392$		0			0
$393$	−20.8914			−1.05383
$394$		0			0
$395$	−4.42124	+	7.65781i	−0.222457	+	0.385306i
$396$		0			0
$397$	−4.49425	−	7.78427i	−0.225560	−	0.390681i	0.730927	−	0.682455i	$-0.239088\pi$
$397$	−4.49425	−	7.78427i	−0.225560	−	0.390681i	−0.956487	+	0.291774i	$0.905754\pi$
$398$		0			0
$399$	6.70368	+	20.1487i	0.335604	+	1.00870i
$400$		0			0
$401$	−5.44571	−	9.43226i	−0.271946	−	0.471024i	0.697414	−	0.716668i	$-0.254334\pi$
$401$	−5.44571	−	9.43226i	−0.271946	−	0.471024i	−0.969360	+	0.245644i	$0.921001\pi$
$402$		0			0
$403$	10.8612	−	18.8122i	0.541035	−	0.937100i
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	7.27760			0.360737
$408$		0			0
$409$	−1.27521	+	2.20874i	−0.0630553	+	0.109215i	−0.895830	−	0.444398i	$-0.853418\pi$
$409$	−1.27521	+	2.20874i	−0.0630553	+	0.109215i	0.832774	+	0.553613i	$0.186751\pi$
$410$		0			0
$411$	0.585988	+	1.01496i	0.0289046	+	0.0500643i
$412$		0			0
$413$	25.5389	+	5.24110i	1.25669	+	0.257898i
$414$		0			0
$415$	−1.58599	−	2.74701i	−0.0778531	−	0.134845i
$416$		0			0
$417$	−2.75074	+	4.76442i	−0.134704	+	0.233315i
$418$		0			0
$419$	−30.2094			−1.47583			−0.737914	−	0.674895i	$-0.764189\pi$
$419$	−30.2094			−1.47583			−0.737914	+	0.674895i	$0.764189\pi$
$420$		0			0
$421$	−0.790571			−0.0385301			−0.0192650	−	0.999814i	$-0.506133\pi$
$421$	−0.790571			−0.0385301			−0.0192650	+	0.999814i	$0.506133\pi$
$422$		0			0
$423$	−0.591738	+	1.02492i	−0.0287713	+	0.0498333i
$424$		0			0
$425$	−3.25649	−	5.64040i	−0.157963	−	0.273600i
$426$		0			0
$427$	−15.8540	+	17.8585i	−0.767228	+	0.864233i
$428$		0			0
$429$	1.17773	+	2.03988i	0.0568611	+	0.0984864i
$430$		0			0
$431$	−6.01445	+	10.4173i	−0.289706	+	0.501785i	−0.973739	−	0.227665i	$-0.926891\pi$
$431$	−6.01445	+	10.4173i	−0.289706	+	0.501785i	0.684034	+	0.729451i	$0.260224\pi$
$432$		0			0
$433$	13.6705			0.656962			0.328481	−	0.944511i	$-0.393463\pi$
$433$	13.6705			0.656962			0.328481	+	0.944511i	$0.393463\pi$
$434$		0			0
$435$	−5.85398			−0.280677
$436$		0			0
$437$	−22.8597	+	39.5942i	−1.09353	+	1.89405i
$438$		0			0
$439$	0.183476	+	0.317790i	0.00875685	+	0.0151673i	0.870371	−	0.492397i	$-0.163879\pi$
$439$	0.183476	+	0.317790i	0.00875685	+	0.0151673i	−0.861614	+	0.507564i	$0.830546\pi$
$440$		0			0
$441$	6.43421	+	2.75697i	0.306391	+	0.131284i
$442$		0			0
$443$	−7.85398	−	13.6035i	−0.373154	−	0.646321i	0.616895	−	0.787045i	$-0.288390\pi$
$443$	−7.85398	−	13.6035i	−0.373154	−	0.646321i	−0.990049	+	0.140724i	$0.955057\pi$
$444$		0			0
$445$	−1.74351	+	3.01985i	−0.0826504	+	0.143155i
$446$		0			0
$447$	−4.00000			−0.189194
$448$		0			0
$449$	−10.5015			−0.495595			−0.247798	−	0.968812i	$-0.579707\pi$
$449$	−10.5015			−0.495595			−0.247798	+	0.968812i	$0.579707\pi$
$450$		0			0
$451$	−2.80117	+	4.85176i	−0.131902	+	0.228461i
$452$		0			0
$453$	7.51298	+	13.0129i	0.352990	+	0.611397i
$454$		0			0
$455$	6.17050	−	6.95068i	0.289278	−	0.325853i
$456$		0			0
$457$	9.55765	+	16.5543i	0.447088	+	0.774380i	0.998195	−	0.0600552i	$-0.0191277\pi$
$457$	9.55765	+	16.5543i	0.447088	+	0.774380i	−0.551107	+	0.834435i	$0.685794\pi$
$458$		0			0
$459$	−3.25649	+	5.64040i	−0.152000	+	0.263271i
$460$		0			0
$461$	−16.9318			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$461$	−16.9318			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$462$		0			0
$463$	17.9318			0.833363			0.416681	−	0.909053i	$-0.363193\pi$
$463$	17.9318			0.833363			0.416681	+	0.909053i	$0.363193\pi$
$464$		0			0
$465$	−3.09174	+	5.35505i	−0.143376	+	0.248334i
$466$		0			0
$467$	−10.5504	−	18.2739i	−0.488216	−	0.845614i	0.511692	−	0.859169i	$-0.329019\pi$
$467$	−10.5504	−	18.2739i	−0.488216	−	0.845614i	−0.999908	+	0.0135544i	$0.995685\pi$
$468$		0			0
$469$	8.69645	+	1.78469i	0.401565	+	0.0824092i
$470$		0			0
$471$	−9.92124	−	17.1841i	−0.457147	−	0.791801i
$472$		0			0
$473$	0.560036	−	0.970010i	0.0257505	−	0.0446011i
$474$		0			0
$475$	−8.02595			−0.368256
$476$		0			0
$477$	12.2094			0.559031
$478$		0			0
$479$	−10.8684	+	18.8247i	−0.496591	+	0.860121i	−0.999992	−	0.00393175i	$-0.998748\pi$
$479$	−10.8684	+	18.8247i	−0.496591	+	0.860121i	0.503401	+	0.864053i	$0.332082\pi$
$480$		0			0
$481$	19.0649	+	33.0213i	0.869284	+	1.50564i
$482$		0			0
$483$	4.75796	+	14.3007i	0.216495	+	0.650702i
$484$		0			0
$485$	2.51298	+	4.35260i	0.114108	+	0.197641i
$486$		0			0
$487$	2.17625	−	3.76938i	0.0986153	−	0.170807i	−0.812496	−	0.582966i	$-0.801892\pi$
$487$	2.17625	−	3.76938i	0.0986153	−	0.170807i	0.911112	+	0.412159i	$0.135225\pi$
$488$		0			0
$489$	16.0000			0.723545
$490$		0			0
$491$	7.70795			0.347855			0.173928	−	0.984758i	$-0.444354\pi$
$491$	7.70795			0.347855			0.173928	+	0.984758i	$0.444354\pi$
$492$		0			0
$493$	19.0634	−	33.0188i	0.858573	−	1.48709i
$494$		0			0
$495$	−0.335250	−	0.580670i	−0.0150684	−	0.0260992i
$496$		0			0
$497$	−10.7580	−	32.3344i	−0.482561	−	1.45040i
$498$		0			0
$499$	18.8026	+	32.5671i	0.841722	+	1.45790i	0.888438	+	0.458997i	$0.151791\pi$
$499$	18.8026	+	32.5671i	0.841722	+	1.45790i	−0.0467161	+	0.998908i	$0.514876\pi$
$500$		0			0
$501$	6.50723	−	11.2708i	0.290721	−	0.503544i
$502$		0			0
$503$	−0.658999			−0.0293833			−0.0146917	−	0.999892i	$-0.504677\pi$
$503$	−0.658999			−0.0293833			−0.0146917	+	0.999892i	$0.504677\pi$
$504$		0			0
$505$	18.5130			0.823817
$506$		0			0
$507$	0.329500	−	0.570710i	0.0146336	−	0.0253461i
$508$		0			0
$509$	−15.1979	−	26.3236i	−0.673636	−	1.16677i	−0.976865	−	0.213855i	$-0.931398\pi$
$509$	−15.1979	−	26.3236i	−0.673636	−	1.16677i	0.303229	−	0.952918i	$-0.401935\pi$
$510$		0			0
$511$	−22.5389	−	4.62544i	−0.997063	−	0.204618i
$512$		0			0
$513$	4.01298	+	6.95068i	0.177177	+	0.306880i
$514$		0			0
$515$	0.322274	−	0.558195i	0.0142011	−	0.0245970i
$516$		0			0
$517$	0.793521			0.0348990
$518$		0			0
$519$	6.15752			0.270285
$520$		0			0
$521$	−8.76371	+	15.1792i	−0.383945	+	0.665013i	−0.991622	−	0.129172i	$-0.958768\pi$
$521$	−8.76371	+	15.1792i	−0.383945	+	0.665013i	0.607677	+	0.794184i	$0.292102\pi$
$522$		0			0
$523$	4.16475	+	7.21356i	0.182112	+	0.315427i	0.942599	−	0.333925i	$-0.108373\pi$
$523$	4.16475	+	7.21356i	0.182112	+	0.315427i	−0.760488	+	0.649352i	$0.775040\pi$
$524$		0			0
$525$	−1.75649	+	1.97857i	−0.0766594	+	0.0863520i
$526$		0			0
$527$	−20.1364	−	34.8773i	−0.877156	−	1.51928i
$528$		0			0
$529$	−4.72479	+	8.18357i	−0.205425	+	0.355807i
$530$		0			0
$531$	9.85398			0.427626
$532$		0			0
$533$	−29.3525			−1.27140
$534$		0			0
$535$	−5.92699	+	10.2658i	−0.256246	+	0.443831i
$536$		0			0
$537$	3.40826	+	5.90328i	0.147077	+	0.254745i
$538$		0			0
$539$	−0.556180	−	4.66043i	−0.0239564	−	0.200739i
$540$		0			0
$541$	−9.27521	−	16.0651i	−0.398773	−	0.690694i	0.594802	−	0.803872i	$-0.297230\pi$
$541$	−9.27521	−	16.0651i	−0.398773	−	0.690694i	−0.993575	+	0.113178i	$0.963897\pi$
$542$		0			0
$543$	−10.2752	+	17.7972i	−0.440952	+	0.763751i
$544$		0			0
$545$	−5.52448			−0.236643
$546$		0			0
$547$	33.7599			1.44347			0.721734	−	0.692171i	$-0.243346\pi$
$547$	33.7599			1.44347			0.721734	+	0.692171i	$0.243346\pi$
$548$		0			0
$549$	−4.51298	+	7.81670i	−0.192609	+	0.333609i
$550$		0			0
$551$	−23.4919	−	40.6891i	−1.00079	−	1.73341i
$552$		0			0
$553$	−15.5317	+	17.4955i	−0.660475	+	0.743984i
$554$		0			0
$555$	−5.42699	−	9.39982i	−0.230363	−	0.399000i
$556$		0			0
$557$	11.4602	−	19.8496i	0.485583	−	0.841054i	−0.514280	−	0.857622i	$-0.671941\pi$
$557$	11.4602	−	19.8496i	0.485583	−	0.841054i	0.999863	+	0.0165683i	$0.00527409\pi$
$558$		0			0
$559$	5.86843			0.248208
$560$		0			0
$561$	4.36695			0.184373
$562$		0			0
$563$	−0.0259521	+	0.0449504i	−0.00109375	+	0.00189443i	−0.866572	−	0.499052i	$-0.833681\pi$
$563$	−0.0259521	+	0.0449504i	−0.00109375	+	0.00189443i	0.865478	+	0.500947i	$0.167015\pi$
$564$		0			0
$565$	3.00000	+	5.19615i	0.126211	+	0.218604i
$566$		0			0
$567$	2.59174	+	0.531877i	0.108843	+	0.0223367i
$568$		0			0
$569$	10.1777	+	17.6283i	0.426672	+	0.739018i	0.996575	−	0.0826939i	$-0.0263524\pi$
$569$	10.1777	+	17.6283i	0.426672	+	0.739018i	−0.569903	+	0.821712i	$0.693019\pi$
$570$		0			0
$571$	−14.9717	+	25.9317i	−0.626545	+	1.08521i	0.361695	+	0.932296i	$0.382198\pi$
$571$	−14.9717	+	25.9317i	−0.626545	+	1.08521i	−0.988240	+	0.152911i	$0.951135\pi$
$572$		0			0
$573$	−0.682001			−0.0284910
$574$		0			0
$575$	−5.69645			−0.237558
$576$		0			0
$577$	−10.5317	+	18.2414i	−0.438441	+	0.759401i	−0.997569	−	0.0696795i	$-0.977802\pi$
$577$	−10.5317	+	18.2414i	−0.438441	+	0.759401i	0.559129	+	0.829081i	$0.311136\pi$
$578$		0			0
$579$	11.0447	+	19.1299i	0.459001	+	0.795013i
$580$		0			0
$581$	−2.64939	−	7.96308i	−0.109915	−	0.330364i
$582$		0			0
$583$	−4.09321	−	7.08965i	−0.169524	−	0.293623i
$584$		0			0
$585$	1.75649	−	3.04233i	0.0726218	−	0.125785i
$586$		0			0
$587$	−37.1720			−1.53425			−0.767126	−	0.641497i	$-0.778314\pi$
$587$	−37.1720			−1.53425			−0.767126	+	0.641497i	$0.778314\pi$
$588$		0			0
$589$	−49.6283			−2.04490
$590$		0			0
$591$	−2.17773	+	3.77193i	−0.0895797	+	0.155157i
$592$		0			0
$593$	−12.4659	−	21.5916i	−0.511914	−	0.886661i	−0.999905	−	0.0138120i	$-0.995603\pi$
$593$	−12.4659	−	21.5916i	−0.511914	−	0.886661i	0.487991	−	0.872849i	$-0.337730\pi$
$594$		0			0
$595$	−5.43996	−	16.3505i	−0.223017	−	0.670305i
$596$		0			0
$597$	−4.32950	−	7.49891i	−0.177195	−	0.306910i
$598$		0			0
$599$	3.32950	−	5.76686i	0.136040	−	0.235628i	−0.789954	−	0.613166i	$-0.789896\pi$
$599$	3.32950	−	5.76686i	0.136040	−	0.235628i	0.925994	+	0.377538i	$0.123229\pi$
$600$		0			0
$601$	−13.8914			−0.566643			−0.283322	−	0.959025i	$-0.591436\pi$
$601$	−13.8914			−0.566643			−0.283322	+	0.959025i	$0.591436\pi$
$602$		0			0
$603$	3.35545			0.136645
$604$		0			0
$605$	5.27521	−	9.13694i	0.214468	−	0.371469i
$606$		0			0
$607$	19.5990	+	33.9464i	0.795497	+	1.37784i	0.922523	+	0.385942i	$0.126124\pi$
$607$	19.5990	+	33.9464i	0.795497	+	1.37784i	−0.127025	+	0.991899i	$0.540543\pi$
$608$		0			0
$609$	−15.1720	−	3.11360i	−0.614799	−	0.126169i
$610$		0			0
$611$	2.07876	+	3.60052i	0.0840977	+	0.145662i
$612$		0			0
$613$	−1.89529	+	3.28273i	−0.0765499	+	0.132588i	−0.901759	−	0.432239i	$-0.857724\pi$
$613$	−1.89529	+	3.28273i	−0.0765499	+	0.132588i	0.825209	+	0.564827i	$0.191057\pi$
$614$		0			0
$615$	8.35545			0.336924
$616$		0			0
$617$	18.0230			0.725579			0.362789	−	0.931871i	$-0.381824\pi$
$617$	18.0230			0.725579			0.362789	+	0.931871i	$0.381824\pi$
$618$		0			0
$619$	13.6979	−	23.7255i	0.550566	−	0.953609i	−0.447668	−	0.894200i	$-0.647745\pi$
$619$	13.6979	−	23.7255i	0.550566	−	0.953609i	0.998234	−	0.0594085i	$-0.0189215\pi$
$620$		0			0
$621$	2.84823	+	4.93327i	0.114295	+	0.197965i
$622$		0			0
$623$	−6.12492	+	6.89933i	−0.245390	+	0.276416i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	2.69070	−	4.66043i	0.107456	−	0.186120i
$628$		0			0
$629$	70.6917			2.81866
$630$		0			0
$631$	−37.1528			−1.47903			−0.739514	−	0.673141i	$-0.764945\pi$
$631$	−37.1528			−1.47903			−0.739514	+	0.673141i	$0.764945\pi$
$632$		0			0
$633$	7.26224	−	12.5786i	0.288648	−	0.499953i
$634$		0			0
$635$	3.26946	+	5.66288i	0.129745	+	0.224724i
$636$		0			0
$637$	19.6892	−	14.7324i	0.780116	−	0.583719i
$638$		0			0
$639$	−6.43996	−	11.1543i	−0.254761	−	0.441259i
$640$		0			0
$641$	13.8597	−	24.0058i	0.547426	−	0.948170i	−0.451024	−	0.892512i	$-0.648941\pi$
$641$	13.8597	−	24.0058i	0.547426	−	0.948170i	0.998450	−	0.0556582i	$-0.0177257\pi$
$642$		0			0
$643$	27.0115			1.06523			0.532615	−	0.846358i	$-0.321209\pi$
$643$	27.0115			1.06523			0.532615	+	0.846358i	$0.321209\pi$
$644$		0			0
$645$	−1.67050			−0.0657759
$646$		0			0
$647$	7.85973	−	13.6134i	0.308998	−	0.535200i	−0.669146	−	0.743131i	$-0.733340\pi$
$647$	7.85973	−	13.6134i	0.308998	−	0.535200i	0.978143	+	0.207931i	$0.0666731\pi$
$648$		0			0
$649$	−3.30355	−	5.72191i	−0.129676	−	0.224605i
$650$		0			0
$651$	−10.8612	+	12.2345i	−0.425684	+	0.479506i
$652$		0			0
$653$	4.81077	+	8.33250i	0.188260	+	0.326076i	0.944670	−	0.328022i	$-0.106382\pi$
$653$	4.81077	+	8.33250i	0.188260	+	0.326076i	−0.756410	+	0.654098i	$0.773049\pi$
$654$		0			0
$655$	10.4457	−	18.0925i	0.408148	−	0.706933i
$656$		0			0
$657$	−8.69645			−0.339281
$658$		0			0
$659$	6.05190			0.235749			0.117874	−	0.993029i	$-0.462392\pi$
$659$	6.05190			0.235749			0.117874	+	0.993029i	$0.462392\pi$
$660$		0			0
$661$	−5.11769	+	8.86410i	−0.199055	+	0.344774i	−0.948222	−	0.317607i	$-0.897121\pi$
$661$	−5.11769	+	8.86410i	−0.199055	+	0.344774i	0.749167	+	0.662381i	$0.230454\pi$
$662$		0			0
$663$	11.4400	+	19.8146i	0.444291	+	0.769535i
$664$		0			0
$665$	−20.8012	−	4.26882i	−0.806635	−	0.165538i
$666$		0			0
$667$	−16.6735	−	28.8793i	−0.645599	−	1.11821i
$668$		0			0
$669$	−7.85398	+	13.6035i	−0.303652	+	0.525941i
$670$		0			0
$671$	6.05190			0.233631
$672$		0			0
$673$	6.69645			0.258129			0.129065	−	0.991636i	$-0.458803\pi$
$673$	6.69645			0.258129			0.129065	+	0.991636i	$0.458803\pi$
$674$		0			0
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$		0			0
$677$	22.2411	+	38.5228i	0.854796	+	1.48055i	0.876834	+	0.480793i	$0.159651\pi$
$677$	22.2411	+	38.5228i	0.854796	+	1.48055i	−0.0220379	+	0.999757i	$0.507015\pi$
$678$		0			0
$679$	4.19793	+	12.6174i	0.161102	+	0.484211i
$680$		0			0
$681$	−5.58599	−	9.67521i	−0.214056	−	0.370755i
$682$		0			0
$683$	0.743512	−	1.28780i	0.0284497	−	0.0492763i	−0.851450	−	0.524436i	$-0.824276\pi$
$683$	0.743512	−	1.28780i	0.0284497	−	0.0492763i	0.879900	+	0.475159i	$0.157610\pi$
$684$		0			0
$685$	−1.17198			−0.0447789
$686$		0			0
$687$	26.5504			1.01296
$688$		0			0
$689$	21.4457	−	37.1451i	0.817017	−	1.41511i
$690$		0			0
$691$	2.73629	+	4.73939i	0.104093	+	0.180295i	0.913367	−	0.407136i	$-0.133473\pi$
$691$	2.73629	+	4.73939i	0.104093	+	0.180295i	−0.809274	+	0.587431i	$0.800139\pi$
$692$		0			0
$693$	−0.560036	−	1.68326i	−0.0212740	−	0.0639417i
$694$		0			0
$695$	−2.75074	−	4.76442i	−0.104341	−	0.180725i
$696$		0			0
$697$	−27.2094	+	47.1281i	−1.03063	+	1.78510i
$698$		0			0
$699$	−8.97405			−0.339430
$700$		0			0
$701$	−38.5649			−1.45658			−0.728288	−	0.685271i	$-0.759684\pi$
$701$	−38.5649			−1.45658			−0.728288	+	0.685271i	$0.759684\pi$
$702$		0			0
$703$	43.5567	−	75.4425i	1.64277	−	2.84537i
$704$		0			0
$705$	−0.591738	−	1.02492i	−0.0222862	−	0.0386007i
$706$		0			0
$707$	47.9808	+	9.84662i	1.80450	+	0.370320i
$708$		0			0
$709$	−3.48702	−	6.03970i	−0.130958	−	0.226826i	0.793088	−	0.609107i	$-0.208472\pi$
$709$	−3.48702	−	6.03970i	−0.130958	−	0.226826i	−0.924046	+	0.382281i	$0.875139\pi$
$710$		0			0
$711$	−4.42124	+	7.65781i	−0.165809	+	0.287190i
$712$		0			0
$713$	−35.2239			−1.31914
$714$		0			0
$715$	−2.35545			−0.0880889
$716$		0			0
$717$	3.00000	−	5.19615i	0.112037	−	0.194054i
$718$		0			0
$719$	−2.48702	−	4.30765i	−0.0927503	−	0.160648i	0.815917	−	0.578169i	$-0.196233\pi$
$719$	−2.48702	−	4.30765i	−0.0927503	−	0.160648i	−0.908667	+	0.417521i	$0.862899\pi$
$720$		0			0
$721$	1.13214	−	1.27529i	0.0421631	−	0.0474941i
$722$		0			0
$723$	5.43421	+	9.41233i	0.202101	+	0.350048i
$724$		0			0
$725$	2.92699	−	5.06969i	0.108706	−	0.188284i
$726$		0			0
$727$	35.9548			1.33349			0.666746	−	0.745285i	$-0.267687\pi$
$727$	35.9548			1.33349			0.666746	+	0.745285i	$0.267687\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	5.43996	−	9.42229i	0.201204	−	0.348496i
$732$		0			0
$733$	−11.9400	−	20.6806i	−0.441013	−	0.763856i	0.556752	−	0.830679i	$-0.312047\pi$
$733$	−11.9400	−	20.6806i	−0.441013	−	0.763856i	−0.997765	+	0.0668223i	$0.978714\pi$
$734$		0			0
$735$	−5.60471	+	4.19371i	−0.206733	+	0.154687i
$736$		0			0
$737$	−1.12492	−	1.94841i	−0.0414368	−	0.0717707i
$738$		0			0
$739$	10.5260	−	18.2315i	0.387203	−	0.670656i	−0.604869	−	0.796325i	$-0.706774\pi$
$739$	10.5260	−	18.2315i	0.387203	−	0.670656i	0.992072	+	0.125669i	$0.0401078\pi$
$740$		0			0
$741$	28.1950			1.03577
$742$		0			0
$743$	38.7973			1.42334			0.711668	−	0.702516i	$-0.247940\pi$
$743$	38.7973			1.42334			0.711668	+	0.702516i	$0.247940\pi$
$744$		0			0
$745$	2.00000	−	3.46410i	0.0732743	−	0.126915i
$746$		0			0
$747$	−1.58599	−	2.74701i	−0.0580283	−	0.100508i
$748$		0			0
$749$	−20.8214	+	23.4540i	−0.760796	+	0.856989i
$750$		0			0
$751$	4.08024	+	7.06718i	0.148890	+	0.257885i	0.930817	−	0.365484i	$-0.119097\pi$
$751$	4.08024	+	7.06718i	0.148890	+	0.257885i	−0.781928	+	0.623369i	$0.785763\pi$
$752$		0			0
$753$	−1.84823	+	3.20122i	−0.0673531	+	0.116659i
$754$		0			0
$755$	−15.0260			−0.546850
$756$		0			0
$757$	13.2661			0.482164			0.241082	−	0.970505i	$-0.422498\pi$
$757$	13.2661			0.482164			0.241082	+	0.970505i	$0.422498\pi$
$758$		0			0
$759$	1.90974	−	3.30776i	0.0693191	−	0.120064i
$760$		0			0
$761$	−12.3727	−	21.4302i	−0.448510	−	0.776842i	0.549779	−	0.835310i	$-0.314712\pi$
$761$	−12.3727	−	21.4302i	−0.448510	−	0.776842i	−0.998289	+	0.0584677i	$0.981379\pi$
$762$		0			0
$763$	−14.3180	−	2.93834i	−0.518346	−	0.106375i
$764$		0			0
$765$	−3.25649	−	5.64040i	−0.117739	−	0.203929i
$766$		0			0
$767$	17.3084	−	29.9790i	0.624970	−	1.08248i
$768$		0			0
$769$	17.3150			0.624397			0.312198	−	0.950017i	$-0.398935\pi$
$769$	17.3150			0.624397			0.312198	+	0.950017i	$0.398935\pi$
$770$		0			0
$771$	0.828025			0.0298206
$772$		0			0
$773$	−7.85973	+	13.6134i	−0.282695	+	0.489642i	−0.972048	−	0.234784i	$-0.924562\pi$
$773$	−7.85973	+	13.6134i	−0.282695	+	0.489642i	0.689353	+	0.724426i	$0.257895\pi$
$774$		0			0
$775$	−3.09174	−	5.35505i	−0.111059	−	0.192359i
$776$		0			0
$777$	−9.06579	−	27.2484i	−0.325233	−	0.977530i
$778$		0			0
$779$	33.5302	+	58.0761i	1.20135	+	2.08079i
$780$		0			0
$781$	−4.31800	+	7.47899i	−0.154510	+	0.267619i
$782$		0			0
$783$	−5.85398			−0.209204
$784$		0			0
$785$	19.8425			0.708208
$786$		0			0
$787$	−5.64455	+	9.77664i	−0.201206	+	0.348500i	−0.948917	−	0.315525i	$-0.897820\pi$
$787$	−5.64455	+	9.77664i	−0.201206	+	0.348500i	0.747711	+	0.664024i	$0.231153\pi$
$788$		0			0
$789$	6.51298	+	11.2808i	0.231868	+	0.401607i
$790$		0			0
$791$	5.01150	+	15.0627i	0.178188	+	0.535568i
$792$		0			0
$793$	15.8540	+	27.4599i	0.562991	+	0.975129i
$794$		0			0
$795$	−6.10471	+	10.5737i	−0.216512	+	0.375010i
$796$		0			0
$797$	1.51003			0.0534879			0.0267439	−	0.999642i	$-0.491486\pi$
$797$	1.51003			0.0534879			0.0267439	+	0.999642i	$0.491486\pi$
$798$		0			0
$799$	7.70795			0.272688
$800$		0			0
$801$	−1.74351	+	3.01985i	−0.0616040	+	0.106701i
$802$		0			0
$803$	2.91549	+	5.04977i	0.102885	+	0.178203i
$804$		0			0
$805$	−14.7637	−	3.02981i	−0.520353	−	0.106787i
$806$		0			0
$807$	2.69645	+	4.67039i	0.0949196	+	0.164406i
$808$		0			0
$809$	8.11917	−	14.0628i	0.285455	−	0.494422i	−0.687265	−	0.726407i	$-0.741189\pi$
$809$	8.11917	−	14.0628i	0.285455	−	0.494422i	0.972719	+	0.231985i	$0.0745221\pi$
$810$		0			0
$811$	9.91738			0.348246			0.174123	−	0.984724i	$-0.444291\pi$
$811$	9.91738			0.348246			0.174123	+	0.984724i	$0.444291\pi$
$812$		0			0
$813$	−22.7109			−0.796506
$814$		0			0
$815$	−8.00000	+	13.8564i	−0.280228	+	0.485369i
$816$		0			0
$817$	−6.70368	−	11.6111i	−0.234532	−	0.406221i
$818$		0			0
$819$	6.17050	−	6.95068i	0.215615	−	0.242876i
$820$		0			0
$821$	−4.29394	−	7.43732i	−0.149860	−	0.259564i	0.781316	−	0.624136i	$-0.214549\pi$
$821$	−4.29394	−	7.43732i	−0.149860	−	0.259564i	−0.931175	+	0.364571i	$0.881215\pi$
$822$		0			0
$823$	3.81652	−	6.61041i	0.133036	−	0.230425i	−0.791810	−	0.610768i	$-0.790861\pi$
$823$	3.81652	−	6.61041i	0.133036	−	0.230425i	0.924845	+	0.380343i	$0.124194\pi$
$824$		0			0
$825$	0.670500			0.0233438
$826$		0			0
$827$	22.2920			0.775170			0.387585	−	0.921834i	$-0.373309\pi$
$827$	22.2920			0.775170			0.387585	+	0.921834i	$0.373309\pi$
$828$		0			0
$829$	−8.61917	+	14.9288i	−0.299356	+	0.518500i	−0.975989	−	0.217821i	$-0.930105\pi$
$829$	−8.61917	+	14.9288i	−0.299356	+	0.518500i	0.676633	+	0.736321i	$0.263438\pi$
$830$		0			0
$831$	−8.53170	−	14.7773i	−0.295961	−	0.512620i
$832$		0			0
$833$	−5.40251	−	45.2696i	−0.187186	−	1.56850i
$834$		0			0
$835$	6.50723	+	11.2708i	0.225192	+	0.390044i
$836$		0			0
$837$	−3.09174	+	5.35505i	−0.106866	+	0.185098i
$838$		0			0
$839$	−22.1460			−0.764566			−0.382283	−	0.924045i	$-0.624862\pi$
$839$	−22.1460			−0.764566			−0.382283	+	0.924045i	$0.624862\pi$
$840$		0			0
$841$	5.26904			0.181691
$842$		0			0
$843$	2.40826	−	4.17123i	0.0829449	−	0.143665i
$844$		0			0
$845$	0.329500	+	0.570710i	0.0113351	+	0.0196330i
$846$		0			0
$847$	18.5317	−	20.8748i	0.636757	−	0.717266i
$848$		0			0
$849$	−15.8872	−	27.5174i	−0.545246	−	0.944393i
$850$		0			0
$851$	30.9146	−	53.5456i	1.05974	−	1.83552i
$852$		0			0
$853$	30.2699			1.03642			0.518211	−	0.855253i	$-0.326598\pi$
$853$	30.2699			1.03642			0.518211	+	0.855253i	$0.326598\pi$
$854$		0			0
$855$	−8.02595			−0.274482
$856$		0			0
$857$	25.0048	−	43.3097i	0.854149	−	1.47943i	−0.0232828	−	0.999729i	$-0.507412\pi$
$857$	25.0048	−	43.3097i	0.854149	−	1.47943i	0.877432	−	0.479701i	$-0.159255\pi$
$858$		0			0
$859$	12.8655	+	22.2837i	0.438964	+	0.760309i	0.997610	−	0.0690979i	$-0.0220121\pi$
$859$	12.8655	+	22.2837i	0.438964	+	0.760309i	−0.558645	+	0.829407i	$0.688679\pi$
$860$		0			0
$861$	21.6551	+	4.44407i	0.738005	+	0.151454i
$862$		0			0
$863$	24.3401	+	42.1583i	0.828546	+	1.43508i	0.899178	+	0.437582i	$0.144165\pi$
$863$	24.3401	+	42.1583i	0.828546	+	1.43508i	−0.0706320	+	0.997502i	$0.522502\pi$
$864$		0			0
$865$	−3.07876	+	5.33257i	−0.104681	+	0.181313i
$866$		0			0
$867$	25.4189			0.863270
$868$		0			0
$869$	5.92888			0.201124
$870$		0			0
$871$	5.89381	−	10.2084i	0.199704	−	0.345898i
$872$		0			0
$873$	2.51298	+	4.35260i	0.0850514	+	0.147313i
$874$		0			0
$875$	−0.835250	−	2.51045i	−0.0282366	−	0.0848687i
$876$		0			0
$877$	−27.7752	−	48.1081i	−0.937902	−	1.62449i	−0.769375	−	0.638798i	$-0.779432\pi$
$877$	−27.7752	−	48.1081i	−0.937902	−	1.62449i	−0.168528	−	0.985697i	$-0.553901\pi$
$878$		0			0
$879$	3.59174	−	6.22107i	0.121146	−	0.209832i
$880$		0			0
$881$	−44.9203			−1.51340			−0.756702	−	0.653760i	$-0.773191\pi$
$881$	−44.9203			−1.51340			−0.756702	+	0.653760i	$0.773191\pi$
$882$		0			0
$883$	−15.3324			−0.515978			−0.257989	−	0.966148i	$-0.583060\pi$
$883$	−15.3324			−0.515978			−0.257989	+	0.966148i	$0.583060\pi$
$884$		0			0
$885$	−4.92699	+	8.53379i	−0.165619	+	0.286860i
$886$		0			0
$887$	8.26799	+	14.3206i	0.277612	+	0.480838i	0.970791	−	0.239928i	$-0.0771237\pi$
$887$	8.26799	+	14.3206i	0.277612	+	0.480838i	−0.693179	+	0.720766i	$0.743790\pi$
$888$		0			0
$889$	5.46164	+	16.4156i	0.183178	+	0.550563i
$890$		0			0
$891$	−0.335250	−	0.580670i	−0.0112313	−	0.0194532i
$892$		0			0
$893$	4.74926	−	8.22596i	0.158928	−	0.275271i
$894$		0			0
$895$	−6.81652			−0.227851
$896$		0			0
$897$	20.0115			0.668165
$898$		0			0
$899$	18.0990	−	31.3483i	0.603634	−	1.04553i
$900$		0			0
$901$	−39.7599	−	68.8661i	−1.32459	−	2.29426i
$902$		0			0
$903$	−4.32950	−	0.888501i	−0.144077	−	0.0295674i
$904$		0			0
$905$	−10.2752	−	17.7972i	−0.341560	−	0.591599i
$906$		0			0
$907$	12.0332	−	20.8421i	0.399555	−	0.692050i	−0.594116	−	0.804379i	$-0.702498\pi$
$907$	12.0332	−	20.8421i	0.399555	−	0.692050i	0.993671	+	0.112330i	$0.0358313\pi$
$908$		0			0
$909$	18.5130			0.614037
$910$		0			0
$911$	17.8310			0.590767			0.295383	−	0.955379i	$-0.404553\pi$
$911$	17.8310			0.590767			0.295383	+	0.955379i	$0.404553\pi$
$912$		0			0
$913$	−1.06341	+	1.84187i	−0.0351936	+	0.0609571i
$914$		0			0
$915$	−4.51298	−	7.81670i	−0.149194	−	0.258412i
$916$		0			0
$917$	36.6955	−	41.3352i	1.21179	−	1.36501i
$918$		0			0
$919$	19.7622	+	34.2292i	0.651896	+	1.12912i	0.982662	+	0.185404i	$0.0593595\pi$
$919$	19.7622	+	34.2292i	0.651896	+	1.12912i	−0.330766	+	0.943713i	$0.607307\pi$
$920$		0			0
$921$	7.20220	−	12.4746i	0.237321	−	0.411051i
$922$		0			0
$923$	−45.2469			−1.48932
$924$		0			0
$925$	10.8540			0.356877
$926$		0			0
$927$	0.322274	−	0.558195i	0.0105849	−	0.0183335i
$928$		0			0
$929$	−6.70220	−	11.6086i	−0.219892	−	0.380864i	0.734883	−	0.678194i	$-0.237237\pi$
$929$	−6.70220	−	11.6086i	−0.219892	−	0.380864i	−0.954775	+	0.297330i	$0.903904\pi$
$930$		0			0
$931$	−51.6407	−	22.1273i	−1.69246	−	0.725194i
$932$		0			0
$933$	12.7954	+	22.1623i	0.418903	+	0.725561i
$934$		0			0
$935$	−2.18348	+	3.78189i	−0.0714073	+	0.123681i
$936$		0			0
$937$	1.40736			0.0459763			0.0229882	−	0.999736i	$-0.492682\pi$
$937$	1.40736			0.0459763			0.0229882	+	0.999736i	$0.492682\pi$
$938$		0			0
$939$	2.32950			0.0760203
$940$		0			0
$941$	−11.9414	+	20.6832i	−0.389280	+	0.674252i	−0.992353	−	0.123434i	$-0.960609\pi$
$941$	−11.9414	+	20.6832i	−0.389280	+	0.674252i	0.603073	+	0.797686i	$0.293943\pi$
$942$		0			0
$943$	23.7982	+	41.2197i	0.774977	+	1.34230i
$944$		0			0
$945$	−1.75649	+	1.97857i	−0.0571386	+	0.0643630i
$946$		0			0
$947$	25.9644	+	44.9717i	0.843731	+	1.46138i	0.886719	+	0.462309i	$0.152979\pi$
$947$	25.9644	+	44.9717i	0.843731	+	1.46138i	−0.0429877	+	0.999076i	$0.513688\pi$
$948$		0			0
$949$	−15.2752	+	26.4574i	−0.495854	+	0.858845i
$950$		0			0
$951$	−28.5879			−0.927026
$952$		0			0
$953$	51.8118			1.67835			0.839174	−	0.543863i	$-0.183039\pi$
$953$	51.8118			1.67835			0.839174	+	0.543863i	$0.183039\pi$
$954$		0			0
$955$	0.341001	−	0.590631i	0.0110345	−	0.0191124i
$956$		0			0
$957$	1.96255	+	3.39923i	0.0634401	+	0.109882i
$958$		0			0
$959$	−3.03745	−	0.623347i	−0.0980845	−	0.0201289i
$960$		0			0
$961$	−3.61769	−	6.26602i	−0.116700	−	0.202130i
$962$		0			0
$963$	−5.92699	+	10.2658i	−0.190995	+	0.330812i
$964$		0			0
$965$	−22.0894			−0.711082
$966$		0			0
$967$	1.67050			0.0537197			0.0268598	−	0.999639i	$-0.491449\pi$
$967$	1.67050			0.0537197			0.0268598	+	0.999639i	$0.491449\pi$
$968$		0			0
$969$	26.1364	−	45.2696i	0.839623	−	1.45427i
$970$		0			0
$971$	4.77521	+	8.27091i	0.153244	+	0.265426i	0.932418	−	0.361381i	$-0.117695\pi$
$971$	4.77521	+	8.27091i	0.153244	+	0.265426i	−0.779174	+	0.626807i	$0.784361\pi$
$972$		0			0
$973$	−4.59511	−	13.8112i	−0.147312	−	0.442766i
$974$		0			0
$975$	1.75649	+	3.04233i	0.0562526	+	0.0974324i
$976$		0			0
$977$	−29.3343	+	50.8086i	−0.938489	+	1.62551i	−0.170198	+	0.985410i	$0.554441\pi$
$977$	−29.3343	+	50.8086i	−0.938489	+	1.62551i	−0.768291	+	0.640100i	$0.778893\pi$
$978$		0			0
$979$	2.33805			0.0747244
$980$		0			0
$981$	−5.52448			−0.176383
$982$		0			0
$983$	−23.2152	+	40.2099i	−0.740449	+	1.28250i	0.211842	+	0.977304i	$0.432054\pi$
$983$	−23.2152	+	40.2099i	−0.740449	+	1.28250i	−0.952291	+	0.305192i	$0.901279\pi$
$984$		0			0
$985$	−2.17773	−	3.77193i	−0.0693881	−	0.120184i
$986$		0			0
$987$	−0.988499	−	2.97106i	−0.0314643	−	0.0945698i
$988$		0			0
$989$	−4.75796	−	8.24103i	−0.151294	−	0.262050i
$990$		0			0
$991$	−4.08024	+	7.06718i	−0.129613	+	0.224496i	−0.923527	−	0.383534i	$-0.874707\pi$
$991$	−4.08024	+	7.06718i	−0.129613	+	0.224496i	0.793914	+	0.608030i	$0.208040\pi$
$992$		0			0
$993$	−11.7109			−0.371634
$994$		0			0
$995$	8.65900			0.274509
$996$		0			0
$997$	−11.4683	+	19.8637i	−0.363205	+	0.629089i	−0.988486	−	0.151310i	$-0.951651\pi$
$997$	−11.4683	+	19.8637i	−0.363205	+	0.629089i	0.625282	+	0.780399i	$0.284984\pi$
$998$		0			0
$999$	−5.42699	−	9.39982i	−0.171702	−	0.297397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.bg.i.361.2	yes	6
3.2	odd	2		2520.2.bi.o.361.2		6
4.3	odd	2		1680.2.bg.u.1201.2		6
7.2	even	3	inner	840.2.bg.i.121.2	✓	6
7.3	odd	6		5880.2.a.bt.1.2		3
7.4	even	3		5880.2.a.bw.1.2		3
21.2	odd	6		2520.2.bi.o.1801.2		6
28.23	odd	6		1680.2.bg.u.961.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bg.i.121.2	✓	6	7.2	even	3	inner
840.2.bg.i.361.2	yes	6	1.1	even	1	trivial
1680.2.bg.u.961.2		6	28.23	odd	6
1680.2.bg.u.1201.2		6	4.3	odd	2
2520.2.bi.o.361.2		6	3.2	odd	2
2520.2.bi.o.1801.2		6	21.2	odd	6
5880.2.a.bt.1.2		3	7.3	odd	6
5880.2.a.bw.1.2		3	7.4	even	3

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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.bg (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.835250 - 2.51045i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.835250 - 2.51045i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-0.335250 + 0.580670i) q^{11} -3.51298 q^{13} +1.00000 q^{15} +(-3.25649 + 5.64040i) q^{17} +(4.01298 + 6.95068i) q^{19} +(2.59174 + 0.531877i) q^{21} +(2.84823 + 4.93327i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{27} -5.85398 q^{29} +(-3.09174 + 5.35505i) q^{31} +(-0.335250 - 0.580670i) q^{33} +(-1.75649 + 1.97857i) q^{35} +(-5.42699 - 9.39982i) q^{37} +(1.75649 - 3.04233i) q^{39} +8.35545 q^{41} -1.67050 q^{43} +(-0.500000 + 0.866025i) q^{45} +(-0.591738 - 1.02492i) q^{47} +(-5.60471 + 4.19371i) q^{49} +(-3.25649 - 5.64040i) q^{51} +(-6.10471 + 10.5737i) q^{53} +0.670500 q^{55} -8.02595 q^{57} +(-4.92699 + 8.53379i) q^{59} +(-4.51298 - 7.81670i) q^{61} +(-1.75649 + 1.97857i) q^{63} +(1.75649 + 3.04233i) q^{65} +(-1.67773 + 2.90591i) q^{67} -5.69645 q^{69} +12.8799 q^{71} +(4.34823 - 7.53135i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(1.73776 + 0.356624i) q^{77} +(-4.42124 - 7.65781i) q^{79} +(-0.500000 + 0.866025i) q^{81} +3.17198 q^{83} +6.51298 q^{85} +(2.92699 - 5.06969i) q^{87} +(-1.74351 - 3.01985i) q^{89} +(2.93421 + 8.81915i) q^{91} +(-3.09174 - 5.35505i) q^{93} +(4.01298 - 6.95068i) q^{95} -5.02595 q^{97} +0.670500 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} - 3 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 - 3 * q^5 - 2 * q^7 - 3 * q^9	\( 6 q - 3 q^{3} - 3 q^{5} - 2 q^{7} - 3 q^{9} + q^{11} + 2 q^{13} + 6 q^{15} - 8 q^{17} + q^{19} + q^{21} - 9 q^{23} - 3 q^{25} + 6 q^{27} - 4 q^{31} + q^{33} + q^{35} - 15 q^{37} - q^{39} + 10 q^{41} - 4 q^{43} - 3 q^{45} + 11 q^{47} + 4 q^{49} - 8 q^{51} + q^{53} - 2 q^{55} - 2 q^{57} - 12 q^{59} - 4 q^{61} + q^{63} - q^{65} + 10 q^{67} + 18 q^{69} - 4 q^{71} - 3 q^{75} + 31 q^{77} - 18 q^{79} - 3 q^{81} + 8 q^{83} + 16 q^{85} - 22 q^{89} - 14 q^{91} - 4 q^{93} + q^{95} + 16 q^{97} - 2 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 - 3 * q^5 - 2 * q^7 - 3 * q^9 + q^11 + 2 * q^13 + 6 * q^15 - 8 * q^17 + q^19 + q^21 - 9 * q^23 - 3 * q^25 + 6 * q^27 - 4 * q^31 + q^33 + q^35 - 15 * q^37 - q^39 + 10 * q^41 - 4 * q^43 - 3 * q^45 + 11 * q^47 + 4 * q^49 - 8 * q^51 + q^53 - 2 * q^55 - 2 * q^57 - 12 * q^59 - 4 * q^61 + q^63 - q^65 + 10 * q^67 + 18 * q^69 - 4 * q^71 - 3 * q^75 + 31 * q^77 - 18 * q^79 - 3 * q^81 + 8 * q^83 + 16 * q^85 - 22 * q^89 - 14 * q^91 - 4 * q^93 + q^95 + 16 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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