LMFDB - Embedded newform 1638.2.m.k.1621.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(289,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1638.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.m (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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 15x^{8} + 14x^{7} + 110x^{6} + 36x^{5} + 233x^{4} + 164x^{3} + 345x^{2} + 76x + 16 $ x^10 - 2x^9 + 15x^8 + 14x^7 + 110x^6 + 36x^5 + 233x^4 + 164x^3 + 345x^2 + 76*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1621.2
Root			$-0.623307 + 1.07960i$ of defining polynomial
Character	$\chi$	$=$	1638.1621
Dual form			1638.2.m.k.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(-0.623307 - 1.07960i) q^{5} +(2.30301 - 1.30235i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.623307 - 1.07960i) q^{5} +(2.30301 - 1.30235i) q^{7} +1.00000 q^{8} +(-0.623307 - 1.07960i) q^{10} +(-1.24766 - 2.16101i) q^{11} +(-0.785103 + 3.51904i) q^{13} +(2.30301 - 1.30235i) q^{14} +1.00000 q^{16} -0.495324 q^{17} +(3.83578 - 6.64376i) q^{19} +(-0.623307 - 1.07960i) q^{20} +(-1.24766 - 2.16101i) q^{22} -0.448052 q^{23} +(1.72298 - 2.98428i) q^{25} +(-0.785103 + 3.51904i) q^{26} +(2.30301 - 1.30235i) q^{28} +(3.71142 - 6.42837i) q^{29} +(-4.06448 + 7.03989i) q^{31} +1.00000 q^{32} -0.495324 q^{34} +(-2.84150 - 1.67457i) q^{35} +2.74194 q^{37} +(3.83578 - 6.64376i) q^{38} +(-0.623307 - 1.07960i) q^{40} +(1.87097 - 3.24061i) q^{41} +(1.47532 + 2.55532i) q^{43} +(-1.24766 - 2.16101i) q^{44} -0.448052 q^{46} +(-3.29729 - 5.71107i) q^{47} +(3.60775 - 5.99868i) q^{49} +(1.72298 - 2.98428i) q^{50} +(-0.785103 + 3.51904i) q^{52} +(-3.86750 + 6.69870i) q^{53} +(-1.55535 + 2.69395i) q^{55} +(2.30301 - 1.30235i) q^{56} +(3.71142 - 6.42837i) q^{58} +1.45531 q^{59} +(2.09967 - 3.63674i) q^{61} +(-4.06448 + 7.03989i) q^{62} +1.00000 q^{64} +(4.28851 - 1.34584i) q^{65} +(-0.0138047 - 0.0239105i) q^{67} -0.495324 q^{68} +(-2.84150 - 1.67457i) q^{70} +(-4.68884 - 8.12130i) q^{71} +(-5.07151 + 8.78412i) q^{73} +2.74194 q^{74} +(3.83578 - 6.64376i) q^{76} +(-5.68779 - 3.35195i) q^{77} +(-4.93545 - 8.54845i) q^{79} +(-0.623307 - 1.07960i) q^{80} +(1.87097 - 3.24061i) q^{82} -7.42285 q^{83} +(0.308739 + 0.534751i) q^{85} +(1.47532 + 2.55532i) q^{86} +(-1.24766 - 2.16101i) q^{88} +11.4811 q^{89} +(2.77493 + 9.12687i) q^{91} -0.448052 q^{92} +(-3.29729 - 5.71107i) q^{94} -9.56347 q^{95} +(-0.509831 - 0.883054i) q^{97} +(3.60775 - 5.99868i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 10 q^{4} + 2 q^{5} - 2 q^{7} + 10 q^{8}+O(q^{10}) $ 10 * q + 10 * q^2 + 10 * q^4 + 2 * q^5 - 2 * q^7 + 10 * q^8	$ 10 q + 10 q^{2} + 10 q^{4} + 2 q^{5} - 2 q^{7} + 10 q^{8} + 2 q^{10} - 6 q^{11} - 4 q^{13} - 2 q^{14} + 10 q^{16} + 8 q^{17} + 3 q^{19} + 2 q^{20} - 6 q^{22} + 12 q^{23} - q^{25} - 4 q^{26} - 2 q^{28} - 10 q^{31} + 10 q^{32} + 8 q^{34} - 16 q^{35} - 2 q^{37} + 3 q^{38} + 2 q^{40} + 4 q^{41} + 3 q^{43} - 6 q^{44} + 12 q^{46} + 15 q^{47} + 4 q^{49} - q^{50} - 4 q^{52} + 17 q^{53} + 3 q^{55} - 2 q^{56} + 4 q^{59} + 11 q^{61} - 10 q^{62} + 10 q^{64} + 4 q^{65} - q^{67} + 8 q^{68} - 16 q^{70} - 18 q^{71} + 12 q^{73} - 2 q^{74} + 3 q^{76} - 18 q^{77} - 4 q^{79} + 2 q^{80} + 4 q^{82} + q^{85} + 3 q^{86} - 6 q^{88} + 14 q^{89} + 26 q^{91} + 12 q^{92} + 15 q^{94} + 48 q^{95} - 6 q^{97} + 4 q^{98}+O(q^{100}) $ 10 * q + 10 * q^2 + 10 * q^4 + 2 * q^5 - 2 * q^7 + 10 * q^8 + 2 * q^10 - 6 * q^11 - 4 * q^13 - 2 * q^14 + 10 * q^16 + 8 * q^17 + 3 * q^19 + 2 * q^20 - 6 * q^22 + 12 * q^23 - q^25 - 4 * q^26 - 2 * q^28 - 10 * q^31 + 10 * q^32 + 8 * q^34 - 16 * q^35 - 2 * q^37 + 3 * q^38 + 2 * q^40 + 4 * q^41 + 3 * q^43 - 6 * q^44 + 12 * q^46 + 15 * q^47 + 4 * q^49 - q^50 - 4 * q^52 + 17 * q^53 + 3 * q^55 - 2 * q^56 + 4 * q^59 + 11 * q^61 - 10 * q^62 + 10 * q^64 + 4 * q^65 - q^67 + 8 * q^68 - 16 * q^70 - 18 * q^71 + 12 * q^73 - 2 * q^74 + 3 * q^76 - 18 * q^77 - 4 * q^79 + 2 * q^80 + 4 * q^82 + q^85 + 3 * q^86 - 6 * q^88 + 14 * q^89 + 26 * q^91 + 12 * q^92 + 15 * q^94 + 48 * q^95 - 6 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−0.623307	−	1.07960i	−0.278751	−	0.482811i	0.692323	−	0.721587i	$-0.256587\pi$
$5$	−0.623307	−	1.07960i	−0.278751	−	0.482811i	−0.971075	+	0.238776i	$0.923254\pi$
$6$		0			0
$7$	2.30301	−	1.30235i	0.870458	−	0.492243i
$7$	2.30301	−	1.30235i	0.870458	−	0.492243i
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.623307	−	1.07960i	−0.197107	−	0.341399i
$11$	−1.24766	−	2.16101i	−0.376184	−	0.651570i	0.614319	−	0.789058i	$-0.289431\pi$
$11$	−1.24766	−	2.16101i	−0.376184	−	0.651570i	−0.990504	+	0.137487i	$0.956097\pi$
$12$		0			0
$13$	−0.785103	+	3.51904i	−0.217748	+	0.976005i
$13$	−0.785103	+	3.51904i	−0.217748	+	0.976005i
$14$	2.30301	−	1.30235i	0.615506	−	0.348069i
$15$		0			0
$16$	1.00000			0.250000
$17$	−0.495324			−0.120134			−0.0600669	−	0.998194i	$-0.519131\pi$
$17$	−0.495324			−0.120134			−0.0600669	+	0.998194i	$0.519131\pi$
$18$		0			0
$19$	3.83578	−	6.64376i	0.879988	−	1.52418i	0.0286358	−	0.999590i	$-0.490884\pi$
$19$	3.83578	−	6.64376i	0.879988	−	1.52418i	0.851352	−	0.524594i	$-0.175783\pi$
$20$	−0.623307	−	1.07960i	−0.139376	−	0.241406i
$21$		0			0
$22$	−1.24766	−	2.16101i	−0.266002	−	0.460730i
$23$	−0.448052			−0.0934253			−0.0467127	−	0.998908i	$-0.514875\pi$
$23$	−0.448052			−0.0934253			−0.0467127	+	0.998908i	$0.514875\pi$
$24$		0			0
$25$	1.72298	−	2.98428i	0.344595	−	0.596857i
$26$	−0.785103	+	3.51904i	−0.153971	+	0.690140i
$27$		0			0
$28$	2.30301	−	1.30235i	0.435229	−	0.246122i
$29$	3.71142	−	6.42837i	0.689194	−	1.19372i	−0.282905	−	0.959148i	$-0.591298\pi$
$29$	3.71142	−	6.42837i	0.689194	−	1.19372i	0.972099	−	0.234571i	$-0.0753686\pi$
$30$		0			0
$31$	−4.06448	+	7.03989i	−0.730002	+	1.26440i	0.226879	+	0.973923i	$0.427148\pi$
$31$	−4.06448	+	7.03989i	−0.730002	+	1.26440i	−0.956882	+	0.290478i	$0.906186\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−0.495324			−0.0849474
$35$	−2.84150	−	1.67457i	−0.480302	−	0.283053i
$36$		0			0
$37$	2.74194			0.450772			0.225386	−	0.974270i	$-0.427636\pi$
$37$	2.74194			0.450772			0.225386	+	0.974270i	$0.427636\pi$
$38$	3.83578	−	6.64376i	0.622246	−	1.07776i
$39$		0			0
$40$	−0.623307	−	1.07960i	−0.0985534	−	0.170700i
$41$	1.87097	−	3.24061i	0.292196	−	0.506099i	−0.682133	−	0.731229i	$-0.738947\pi$
$41$	1.87097	−	3.24061i	0.292196	−	0.506099i	0.974329	+	0.225130i	$0.0722806\pi$
$42$		0			0
$43$	1.47532	+	2.55532i	0.224983	+	0.389683i	0.956314	−	0.292340i	$-0.0944339\pi$
$43$	1.47532	+	2.55532i	0.224983	+	0.389683i	−0.731331	+	0.682023i	$0.761101\pi$
$44$	−1.24766	−	2.16101i	−0.188092	−	0.325785i
$45$		0			0
$46$	−0.448052			−0.0660617
$47$	−3.29729	−	5.71107i	−0.480959	−	0.833046i	0.518802	−	0.854894i	$-0.326378\pi$
$47$	−3.29729	−	5.71107i	−0.480959	−	0.833046i	−0.999761	+	0.0218486i	$0.993045\pi$
$48$		0			0
$49$	3.60775	−	5.99868i	0.515393	−	0.856954i
$50$	1.72298	−	2.98428i	0.243666	−	0.422042i
$51$		0			0
$52$	−0.785103	+	3.51904i	−0.108874	+	0.488002i
$53$	−3.86750	+	6.69870i	−0.531241	+	0.920137i	0.468094	+	0.883679i	$0.344941\pi$
$53$	−3.86750	+	6.69870i	−0.531241	+	0.920137i	−0.999335	+	0.0364583i	$0.988392\pi$
$54$		0			0
$55$	−1.55535	+	2.69395i	−0.209724	+	0.363252i
$56$	2.30301	−	1.30235i	0.307753	−	0.174034i
$57$		0			0
$58$	3.71142	−	6.42837i	0.487334	−	0.844087i
$59$	1.45531			0.189465			0.0947324	−	0.995503i	$-0.469800\pi$
$59$	1.45531			0.189465			0.0947324	+	0.995503i	$0.469800\pi$
$60$		0			0
$61$	2.09967	−	3.63674i	0.268835	−	0.465636i	−0.699726	−	0.714411i	$-0.746695\pi$
$61$	2.09967	−	3.63674i	0.268835	−	0.465636i	0.968561	+	0.248775i	$0.0800279\pi$
$62$	−4.06448	+	7.03989i	−0.516190	+	0.894067i
$63$		0			0
$64$	1.00000			0.125000
$65$	4.28851	−	1.34584i	0.531924	−	0.166931i
$66$		0			0
$67$	−0.0138047	−	0.0239105i	−0.00168652	−	0.00292113i	0.865181	−	0.501460i	$-0.167204\pi$
$67$	−0.0138047	−	0.0239105i	−0.00168652	−	0.00292113i	−0.866867	+	0.498539i	$0.833870\pi$
$68$	−0.495324			−0.0600669
$69$		0			0
$70$	−2.84150	−	1.67457i	−0.339625	−	0.200149i
$71$	−4.68884	−	8.12130i	−0.556463	−	0.963821i	−0.997788	−	0.0664743i	$-0.978825\pi$
$71$	−4.68884	−	8.12130i	−0.556463	−	0.963821i	0.441326	−	0.897347i	$-0.354508\pi$
$72$		0			0
$73$	−5.07151	+	8.78412i	−0.593576	+	1.02810i	0.400170	+	0.916441i	$0.368951\pi$
$73$	−5.07151	+	8.78412i	−0.593576	+	1.02810i	−0.993746	+	0.111663i	$0.964382\pi$
$74$	2.74194			0.318744
$75$		0			0
$76$	3.83578	−	6.64376i	0.439994	−	0.762092i
$77$	−5.68779	−	3.35195i	−0.648184	−	0.381990i
$78$		0			0
$79$	−4.93545	−	8.54845i	−0.555282	−	0.961776i	−0.997882	−	0.0650567i	$-0.979277\pi$
$79$	−4.93545	−	8.54845i	−0.555282	−	0.961776i	0.442600	−	0.896719i	$-0.354056\pi$
$80$	−0.623307	−	1.07960i	−0.0696878	−	0.120703i
$81$		0			0
$82$	1.87097	−	3.24061i	0.206614	−	0.357866i
$83$	−7.42285			−0.814763			−0.407382	−	0.913258i	$-0.633558\pi$
$83$	−7.42285			−0.814763			−0.407382	+	0.913258i	$0.633558\pi$
$84$		0			0
$85$	0.308739	+	0.534751i	0.0334874	+	0.0580019i
$86$	1.47532	+	2.55532i	0.159087	+	0.275547i
$87$		0			0
$88$	−1.24766	−	2.16101i	−0.133001	−	0.230365i
$89$	11.4811			1.21700			0.608498	−	0.793555i	$-0.291772\pi$
$89$	11.4811			1.21700			0.608498	+	0.793555i	$0.291772\pi$
$90$		0			0
$91$	2.77493	+	9.12687i	0.290891	+	0.956756i
$92$	−0.448052			−0.0467127
$93$		0			0
$94$	−3.29729	−	5.71107i	−0.340089	−	0.589052i
$95$	−9.56347			−0.981191
$96$		0			0
$97$	−0.509831	−	0.883054i	−0.0517655	−	0.0896605i	0.838982	−	0.544160i	$-0.183152\pi$
$97$	−0.509831	−	0.883054i	−0.0517655	−	0.0896605i	−0.890747	+	0.454499i	$0.849818\pi$
$98$	3.60775	−	5.99868i	0.364438	−	0.605958i
$99$		0			0
$100$	1.72298	−	2.98428i	0.172298	−	0.298428i
$101$	8.97127	+	15.5387i	0.892675	+	1.54616i	0.836656	+	0.547729i	$0.184507\pi$
$101$	8.97127	+	15.5387i	0.892675	+	1.54616i	0.0560191	+	0.998430i	$0.482159\pi$
$102$		0			0
$103$	0.524685	+	0.908780i	0.0516987	+	0.0895448i	0.890717	−	0.454559i	$-0.150203\pi$
$103$	0.524685	+	0.908780i	0.0516987	+	0.0895448i	−0.839018	+	0.544104i	$0.816870\pi$
$104$	−0.785103	+	3.51904i	−0.0769857	+	0.345070i
$105$		0			0
$106$	−3.86750	+	6.69870i	−0.375644	+	0.650635i
$107$	10.1830			0.984432			0.492216	−	0.870473i	$-0.336187\pi$
$107$	10.1830			0.984432			0.492216	+	0.870473i	$0.336187\pi$
$108$		0			0
$109$	9.92285	−	17.1869i	0.950436	−	1.64620i	0.205955	−	0.978562i	$-0.433970\pi$
$109$	9.92285	−	17.1869i	0.950436	−	1.64620i	0.744482	−	0.667643i	$-0.232697\pi$
$110$	−1.55535	+	2.69395i	−0.148297	+	0.256858i
$111$		0			0
$112$	2.30301	−	1.30235i	0.217614	−	0.123061i
$113$	7.93440	+	13.7428i	0.746406	+	1.29281i	0.949535	+	0.313661i	$0.101555\pi$
$113$	7.93440	+	13.7428i	0.746406	+	1.29281i	−0.203129	+	0.979152i	$0.565111\pi$
$114$		0			0
$115$	0.279274	+	0.483717i	0.0260424	+	0.0451068i
$116$	3.71142	−	6.42837i	0.344597	−	0.596860i
$117$		0			0
$118$	1.45531			0.133972
$119$	−1.14074	+	0.645087i	−0.104571	+	0.0591350i
$120$		0			0
$121$	2.38668	−	4.13385i	0.216971	−	0.375804i
$122$	2.09967	−	3.63674i	0.190095	−	0.329255i
$123$		0			0
$124$	−4.06448	+	7.03989i	−0.365001	+	0.632201i
$125$	−10.5288			−0.941728
$126$		0			0
$127$	4.23846	−	7.34124i	0.376103	−	0.651429i	−0.614389	−	0.789004i	$-0.710597\pi$
$127$	4.23846	−	7.34124i	0.376103	−	0.651429i	0.990491	+	0.137574i	$0.0439306\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	4.28851	−	1.34584i	0.376127	−	0.118038i
$131$	8.26678	+	14.3185i	0.722272	+	1.25101i	0.960087	+	0.279701i	$0.0902353\pi$
$131$	8.26678	+	14.3185i	0.722272	+	1.25101i	−0.237816	+	0.971310i	$0.576431\pi$
$132$		0			0
$133$	0.181325	−	20.2962i	0.0157229	−	1.75991i
$134$	−0.0138047	−	0.0239105i	−0.00119255	−	0.00206555i
$135$		0			0
$136$	−0.495324			−0.0424737
$137$	0.856837			0.0732045			0.0366023	−	0.999330i	$-0.488347\pi$
$137$	0.856837			0.0732045			0.0366023	+	0.999330i	$0.488347\pi$
$138$		0			0
$139$	4.74886	+	8.22528i	0.402793	+	0.697659i	0.994062	−	0.108816i	$-0.0347060\pi$
$139$	4.74886	+	8.22528i	0.402793	+	0.697659i	−0.591268	+	0.806475i	$0.701373\pi$
$140$	−2.84150	−	1.67457i	−0.240151	−	0.141527i
$141$		0			0
$142$	−4.68884	−	8.12130i	−0.393478	−	0.681525i
$143$	8.58423	−	2.69395i	0.717849	−	0.225279i
$144$		0			0
$145$	−9.25342			−0.768455
$146$	−5.07151	+	8.78412i	−0.419721	+	0.726979i
$147$		0			0
$148$	2.74194			0.225386
$149$	−2.36872	+	4.10274i	−0.194053	+	0.336109i	−0.946590	−	0.322441i	$-0.895497\pi$
$149$	−2.36872	+	4.10274i	−0.194053	+	0.336109i	0.752537	+	0.658550i	$0.228830\pi$
$150$		0			0
$151$	−3.56085	+	6.16758i	−0.289778	+	0.501911i	−0.973757	−	0.227592i	$-0.926915\pi$
$151$	−3.56085	+	6.16758i	−0.289778	+	0.501911i	0.683978	+	0.729502i	$0.260248\pi$
$152$	3.83578	−	6.64376i	0.311123	−	0.538880i
$153$		0			0
$154$	−5.68779	−	3.35195i	−0.458335	−	0.270108i
$155$	10.1337			0.813956
$156$		0			0
$157$	−7.52147	+	13.0276i	−0.600279	+	1.03971i	0.392500	+	0.919752i	$0.371610\pi$
$157$	−7.52147	+	13.0276i	−0.600279	+	1.03971i	−0.992779	+	0.119961i	$0.961723\pi$
$158$	−4.93545	−	8.54845i	−0.392643	−	0.680078i
$159$		0			0
$160$	−0.623307	−	1.07960i	−0.0492767	−	0.0853498i
$161$	−1.03187	+	0.583522i	−0.0813228	+	0.0459880i
$162$		0			0
$163$	4.51485	−	7.81996i	0.353631	−	0.612506i	−0.633252	−	0.773946i	$-0.718280\pi$
$163$	4.51485	−	7.81996i	0.353631	−	0.612506i	0.986883	+	0.161439i	$0.0516137\pi$
$164$	1.87097	−	3.24061i	0.146098	−	0.253049i
$165$		0			0
$166$	−7.42285			−0.576125
$167$	−1.42442	+	2.46716i	−0.110225	+	0.190915i	−0.915861	−	0.401496i	$-0.868490\pi$
$167$	−1.42442	+	2.46716i	−0.110225	+	0.190915i	0.805636	+	0.592411i	$0.201824\pi$
$168$		0			0
$169$	−11.7672	−	5.52561i	−0.905171	−	0.425047i
$170$	0.308739	+	0.534751i	0.0236792	+	0.0410136i
$171$		0			0
$172$	1.47532	+	2.55532i	0.112492	+	0.194841i
$173$	−12.7438	+	22.0729i	−0.968891	+	1.67817i	−0.270116	+	0.962828i	$0.587062\pi$
$173$	−12.7438	+	22.0729i	−0.968891	+	1.67817i	−0.698776	+	0.715341i	$0.746271\pi$
$174$		0			0
$175$	0.0814487	−	9.11678i	0.00615695	−	0.689163i
$176$	−1.24766	−	2.16101i	−0.0940461	−	0.162893i
$177$		0			0
$178$	11.4811			0.860547
$179$	9.10030	+	15.7622i	0.680189	+	1.17812i	0.974923	+	0.222542i	$0.0714355\pi$
$179$	9.10030	+	15.7622i	0.680189	+	1.17812i	−0.294734	+	0.955579i	$0.595231\pi$
$180$		0			0
$181$	−13.7305			−1.02058			−0.510290	−	0.860003i	$-0.670462\pi$
$181$	−13.7305			−1.02058			−0.510290	+	0.860003i	$0.670462\pi$
$182$	2.77493	+	9.12687i	0.205691	+	0.676529i
$183$		0			0
$184$	−0.448052			−0.0330308
$185$	−1.70907	−	2.96019i	−0.125653	−	0.217638i
$186$		0			0
$187$	0.617997	+	1.07040i	0.0451924	+	0.0782756i
$188$	−3.29729	−	5.71107i	−0.240480	−	0.416523i
$189$		0			0
$190$	−9.56347			−0.693807
$191$	2.64294	−	4.57771i	0.191236	−	0.331231i	−0.754424	−	0.656388i	$-0.772084\pi$
$191$	2.64294	−	4.57771i	0.191236	−	0.331231i	0.945660	+	0.325156i	$0.105417\pi$
$192$		0			0
$193$	−2.40599	−	4.16729i	−0.173187	−	0.299968i	0.766346	−	0.642429i	$-0.222073\pi$
$193$	−2.40599	−	4.16729i	−0.173187	−	0.299968i	−0.939532	+	0.342461i	$0.888740\pi$
$194$	−0.509831	−	0.883054i	−0.0366038	−	0.0633996i
$195$		0			0
$196$	3.60775	−	5.99868i	0.257696	−	0.428477i
$197$	−11.7743	+	20.3937i	−0.838883	+	1.45299i	0.0519458	+	0.998650i	$0.483458\pi$
$197$	−11.7743	+	20.3937i	−0.838883	+	1.45299i	−0.890829	+	0.454339i	$0.849876\pi$
$198$		0			0
$199$	11.2797			0.799596			0.399798	−	0.916603i	$-0.369080\pi$
$199$	11.2797			0.799596			0.399798	+	0.916603i	$0.369080\pi$
$200$	1.72298	−	2.98428i	0.121833	−	0.211021i
$201$		0			0
$202$	8.97127	+	15.5387i	0.631217	+	1.09330i
$203$	0.175447	−	19.6382i	0.0123139	−	1.37833i
$204$		0			0
$205$	−4.66475			−0.325800
$206$	0.524685	+	0.908780i	0.0365565	+	0.0633177i
$207$		0			0
$208$	−0.785103	+	3.51904i	−0.0544371	+	0.244001i
$209$	−19.1430			−1.32415
$210$		0			0
$211$	−6.22021	+	10.7737i	−0.428217	+	0.741693i	−0.996715	−	0.0809915i	$-0.974191\pi$
$211$	−6.22021	+	10.7737i	−0.428217	+	0.741693i	0.568498	+	0.822685i	$0.307525\pi$
$212$	−3.86750	+	6.69870i	−0.265621	+	0.460069i
$213$		0			0
$214$	10.1830			0.696099
$215$	1.83915	−	3.18550i	0.125429	−	0.217249i
$216$		0			0
$217$	−0.192136	+	21.5064i	−0.0130431	+	1.45995i
$218$	9.92285	−	17.1869i	0.672060	−	1.16404i
$219$		0			0
$220$	−1.55535	+	2.69395i	−0.104862	+	0.181626i
$221$	0.388880	−	1.74306i	0.0261589	−	0.117251i
$222$		0			0
$223$	−10.4651	+	18.1260i	−0.700793	+	1.21381i	0.267396	+	0.963587i	$0.413837\pi$
$223$	−10.4651	+	18.1260i	−0.700793	+	1.21381i	−0.968188	+	0.250222i	$0.919496\pi$
$224$	2.30301	−	1.30235i	0.153877	−	0.0870172i
$225$		0			0
$226$	7.93440	+	13.7428i	0.527789	+	0.914157i
$227$	−17.5810			−1.16689			−0.583447	−	0.812151i	$-0.698296\pi$
$227$	−17.5810			−1.16689			−0.583447	+	0.812151i	$0.698296\pi$
$228$		0			0
$229$	7.24620	+	12.5508i	0.478842	+	0.829379i	0.999706	−	0.0242609i	$-0.00772324\pi$
$229$	7.24620	+	12.5508i	0.478842	+	0.829379i	−0.520863	+	0.853640i	$0.674390\pi$
$230$	0.279274	+	0.483717i	0.0184148	+	0.0318953i
$231$		0			0
$232$	3.71142	−	6.42837i	0.243667	−	0.422043i
$233$	7.24897	+	12.5556i	0.474896	+	0.822544i	0.999587	−	0.0287492i	$-0.00915242\pi$
$233$	7.24897	+	12.5556i	0.474896	+	0.822544i	−0.524691	+	0.851293i	$0.675819\pi$
$234$		0			0
$235$	−4.11045	+	7.11950i	−0.268136	+	0.464425i
$236$	1.45531			0.0947324
$237$		0			0
$238$	−1.14074	+	0.645087i	−0.0739431	+	0.0418148i
$239$	−3.15093			−0.203817			−0.101908	−	0.994794i	$-0.532495\pi$
$239$	−3.15093			−0.203817			−0.101908	+	0.994794i	$0.532495\pi$
$240$		0			0
$241$	−24.8446			−1.60038			−0.800189	−	0.599747i	$-0.795268\pi$
$241$	−24.8446			−1.60038			−0.800189	+	0.599747i	$0.795268\pi$
$242$	2.38668	−	4.13385i	0.153422	−	0.265734i
$243$		0			0
$244$	2.09967	−	3.63674i	0.134418	−	0.232818i
$245$	−8.72490	−	0.155908i	−0.557414	−	0.00996059i
$246$		0			0
$247$	20.3682	+	18.7143i	1.29600	+	1.19076i
$248$	−4.06448	+	7.03989i	−0.258095	+	0.447033i
$249$		0			0
$250$	−10.5288			−0.665902
$251$	3.69421	+	6.39857i	0.233177	+	0.403874i	0.958741	−	0.284280i	$-0.0917546\pi$
$251$	3.69421	+	6.39857i	0.233177	+	0.403874i	−0.725564	+	0.688154i	$0.758421\pi$
$252$		0			0
$253$	0.559018	+	0.968247i	0.0351451	+	0.0608732i
$254$	4.23846	−	7.34124i	0.265945	−	0.460630i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−26.8892			−1.67730			−0.838650	−	0.544671i	$-0.816655\pi$
$257$	−26.8892			−1.67730			−0.838650	+	0.544671i	$0.816655\pi$
$258$		0			0
$259$	6.31472	−	3.57097i	0.392378	−	0.221889i
$260$	4.28851	−	1.34584i	0.265962	−	0.0834656i
$261$		0			0
$262$	8.26678	+	14.3185i	0.510723	+	0.884598i
$263$	−1.46562	−	2.53852i	−0.0903738	−	0.156532i	0.817295	−	0.576220i	$-0.195473\pi$
$263$	−1.46562	−	2.53852i	−0.0903738	−	0.156532i	−0.907668	+	0.419688i	$0.862140\pi$
$264$		0			0
$265$	9.64254			0.592337
$266$	0.181325	−	20.2962i	0.0111178	−	1.24444i
$267$		0			0
$268$	−0.0138047	−	0.0239105i	−0.000843258	−	0.00146056i
$269$	−2.14443			−0.130748			−0.0653741	−	0.997861i	$-0.520824\pi$
$269$	−2.14443			−0.130748			−0.0653741	+	0.997861i	$0.520824\pi$
$270$		0			0
$271$	17.2844			1.04995			0.524976	−	0.851117i	$-0.324074\pi$
$271$	17.2844			1.04995			0.524976	+	0.851117i	$0.324074\pi$
$272$	−0.495324			−0.0300334
$273$		0			0
$274$	0.856837			0.0517634
$275$	−8.59877			−0.518526
$276$		0			0
$277$	−2.83381			−0.170267			−0.0851336	−	0.996370i	$-0.527132\pi$
$277$	−2.83381			−0.170267			−0.0851336	+	0.996370i	$0.527132\pi$
$278$	4.74886	+	8.22528i	0.284818	+	0.493319i
$279$		0			0
$280$	−2.84150	−	1.67457i	−0.169812	−	0.100074i
$281$	28.5254			1.70168			0.850842	−	0.525422i	$-0.176093\pi$
$281$	28.5254			1.70168			0.850842	+	0.525422i	$0.176093\pi$
$282$		0			0
$283$	2.29901	+	3.98201i	0.136662	+	0.236706i	0.926231	−	0.376956i	$-0.123029\pi$
$283$	2.29901	+	3.98201i	0.136662	+	0.236706i	−0.789569	+	0.613662i	$0.789696\pi$
$284$	−4.68884	−	8.12130i	−0.278231	−	0.481911i
$285$		0			0
$286$	8.58423	−	2.69395i	0.507596	−	0.159297i
$287$	0.0884446	−	9.89984i	0.00522072	−	0.584369i
$288$		0			0
$289$	−16.7547			−0.985568
$290$	−9.25342			−0.543380
$291$		0			0
$292$	−5.07151	+	8.78412i	−0.296788	+	0.514052i
$293$	−3.19384	−	5.53189i	−0.186586	−	0.323177i	0.757524	−	0.652808i	$-0.226409\pi$
$293$	−3.19384	−	5.53189i	−0.186586	−	0.323177i	−0.944110	+	0.329631i	$0.893076\pi$
$294$		0			0
$295$	−0.907102	−	1.57115i	−0.0528135	−	0.0914757i
$296$	2.74194			0.159372
$297$		0			0
$298$	−2.36872	+	4.10274i	−0.137216	+	0.237665i
$299$	0.351767	−	1.57671i	0.0203432	−	0.0911836i
$300$		0			0
$301$	6.72560	+	3.96356i	0.387657	+	0.228456i
$302$	−3.56085	+	6.16758i	−0.204904	+	0.354904i
$303$		0			0
$304$	3.83578	−	6.64376i	0.219997	−	0.381046i
$305$	−5.23496			−0.299753
$306$		0			0
$307$	−1.39899			−0.0798446			−0.0399223	−	0.999203i	$-0.512711\pi$
$307$	−1.39899			−0.0798446			−0.0399223	+	0.999203i	$0.512711\pi$
$308$	−5.68779	−	3.35195i	−0.324092	−	0.190995i
$309$		0			0
$310$	10.1337			0.575554
$311$	8.55183	−	14.8122i	0.484930	−	0.839923i	−0.514920	−	0.857238i	$-0.672178\pi$
$311$	8.55183	−	14.8122i	0.484930	−	0.839923i	0.999850	+	0.0173150i	$0.00551183\pi$
$312$		0			0
$313$	−5.81247	−	10.0675i	−0.328540	−	0.569048i	0.653682	−	0.756769i	$-0.273223\pi$
$313$	−5.81247	−	10.0675i	−0.328540	−	0.569048i	−0.982222	+	0.187721i	$0.939890\pi$
$314$	−7.52147	+	13.0276i	−0.424461	+	0.735188i
$315$		0			0
$316$	−4.93545	−	8.54845i	−0.277641	−	0.480888i
$317$	3.29277	+	5.70324i	0.184940	+	0.320326i	0.943556	−	0.331212i	$-0.107457\pi$
$317$	3.29277	+	5.70324i	0.184940	+	0.320326i	−0.758616	+	0.651538i	$0.774124\pi$
$318$		0			0
$319$	−18.5224			−1.03706
$320$	−0.623307	−	1.07960i	−0.0348439	−	0.0603514i
$321$		0			0
$322$	−1.03187	+	0.583522i	−0.0575039	+	0.0325184i
$323$	−1.89995	+	3.29082i	−0.105716	+	0.183106i
$324$		0			0
$325$	9.14909	+	8.40619i	0.507500	+	0.466292i
$326$	4.51485	−	7.81996i	0.250055	−	0.433107i
$327$		0			0
$328$	1.87097	−	3.24061i	0.103307	−	0.178933i
$329$	−15.0315	−	8.85845i	−0.828716	−	0.488382i
$330$		0			0
$331$	11.6343	−	20.1512i	0.639477	−	1.10761i	−0.346070	−	0.938209i	$-0.612484\pi$
$331$	11.6343	−	20.1512i	0.639477	−	1.10761i	0.985548	−	0.169399i	$-0.0541826\pi$
$332$	−7.42285			−0.407382
$333$		0			0
$334$	−1.42442	+	2.46716i	−0.0779406	+	0.134997i
$335$	−0.0172092	+	0.0298071i	−0.000940236	+	0.00162854i
$336$		0			0
$337$	19.4320			1.05853			0.529263	−	0.848458i	$-0.322468\pi$
$337$	19.4320			1.05853			0.529263	+	0.848458i	$0.322468\pi$
$338$	−11.7672	−	5.52561i	−0.640053	−	0.300554i
$339$		0			0
$340$	0.308739	+	0.534751i	0.0167437	+	0.0290010i
$341$	20.2844			1.09846
$342$		0			0
$343$	0.496304	−	18.5136i	0.0267979	−	0.999641i
$344$	1.47532	+	2.55532i	0.0795437	+	0.137774i
$345$		0			0
$346$	−12.7438	+	22.0729i	−0.685110	+	1.18664i
$347$	−29.6707			−1.59281			−0.796404	−	0.604765i	$-0.793267\pi$
$347$	−29.6707			−1.59281			−0.796404	+	0.604765i	$0.793267\pi$
$348$		0			0
$349$	−13.3023	+	23.0403i	−0.712058	+	1.23332i	0.252025	+	0.967721i	$0.418904\pi$
$349$	−13.3023	+	23.0403i	−0.712058	+	1.23332i	−0.964083	+	0.265600i	$0.914430\pi$
$350$	0.0814487	−	9.11678i	0.00435362	−	0.487312i
$351$		0			0
$352$	−1.24766	−	2.16101i	−0.0665006	−	0.115182i
$353$	−6.90939	−	11.9674i	−0.367750	−	0.636961i	0.621464	−	0.783443i	$-0.286538\pi$
$353$	−6.90939	−	11.9674i	−0.367750	−	0.636961i	−0.989213	+	0.146482i	$0.953205\pi$
$354$		0			0
$355$	−5.84517	+	10.1241i	−0.310229	+	0.537333i
$356$	11.4811			0.608498
$357$		0			0
$358$	9.10030	+	15.7622i	0.480966	+	0.833058i
$359$	−1.38095	−	2.39188i	−0.0728840	−	0.126239i	0.827280	−	0.561790i	$-0.189887\pi$
$359$	−1.38095	−	2.39188i	−0.0728840	−	0.126239i	−0.900164	+	0.435551i	$0.856554\pi$
$360$		0			0
$361$	−19.9264	−	34.5135i	−1.04876	−	1.81650i
$362$	−13.7305			−0.721658
$363$		0			0
$364$	2.77493	+	9.12687i	0.145446	+	0.478378i
$365$	12.6444			0.661840
$366$		0			0
$367$	5.46151	+	9.45961i	0.285089	+	0.493788i	0.972631	−	0.232357i	$-0.0746437\pi$
$367$	5.46151	+	9.45961i	0.285089	+	0.493788i	−0.687542	+	0.726145i	$0.741310\pi$
$368$	−0.448052			−0.0233563
$369$		0			0
$370$	−1.70907	−	2.96019i	−0.0888502	−	0.153893i
$371$	−0.182825	+	20.4640i	−0.00949178	+	1.06244i
$372$		0			0
$373$	−9.84303	+	17.0486i	−0.509653	+	0.882745i	0.490285	+	0.871562i	$0.336893\pi$
$373$	−9.84303	+	17.0486i	−0.509653	+	0.882745i	−0.999937	+	0.0111823i	$0.996440\pi$
$374$	0.617997	+	1.07040i	0.0319559	+	0.0553492i
$375$		0			0
$376$	−3.29729	−	5.71107i	−0.170045	−	0.294526i
$377$	19.7078	+	18.1076i	1.01501	+	0.932587i
$378$		0			0
$379$	−8.31713	+	14.4057i	−0.427222	+	0.739970i	−0.996625	−	0.0820882i	$-0.973841\pi$
$379$	−8.31713	+	14.4057i	−0.427222	+	0.739970i	0.569403	+	0.822059i	$0.307174\pi$
$380$	−9.56347			−0.490596
$381$		0			0
$382$	2.64294	−	4.57771i	0.135225	−	0.234216i
$383$	18.1834	−	31.4945i	0.929127	−	1.60929i	0.144341	−	0.989528i	$-0.453894\pi$
$383$	18.1834	−	31.4945i	0.929127	−	1.60929i	0.784786	−	0.619767i	$-0.212773\pi$
$384$		0			0
$385$	−0.0735247	+	8.22982i	−0.00374717	+	0.419431i
$386$	−2.40599	−	4.16729i	−0.122461	−	0.212109i
$387$		0			0
$388$	−0.509831	−	0.883054i	−0.0258828	−	0.0448303i
$389$	−8.89008	+	15.3981i	−0.450745	+	0.780713i	−0.998432	−	0.0559696i	$-0.982175\pi$
$389$	−8.89008	+	15.3981i	−0.450745	+	0.780713i	0.547687	+	0.836683i	$0.315508\pi$
$390$		0			0
$391$	0.221931			0.0112235
$392$	3.60775	−	5.99868i	0.182219	−	0.302979i
$393$		0			0
$394$	−11.7743	+	20.3937i	−0.593180	+	1.02742i
$395$	−6.15260	+	10.6566i	−0.309571	+	0.536192i
$396$		0			0
$397$	−4.43952	+	7.68948i	−0.222813	+	0.385924i	−0.955661	−	0.294469i	$-0.904857\pi$
$397$	−4.43952	+	7.68948i	−0.222813	+	0.385924i	0.732848	+	0.680392i	$0.238191\pi$
$398$	11.2797			0.565400
$399$		0			0
$400$	1.72298	−	2.98428i	0.0861489	−	0.149214i
$401$	30.1630			1.50627			0.753134	−	0.657867i	$-0.228541\pi$
$401$	30.1630			1.50627			0.753134	+	0.657867i	$0.228541\pi$
$402$		0			0
$403$	−21.5826	−	19.8301i	−1.07511	−	0.987807i
$404$	8.97127	+	15.5387i	0.446338	+	0.773079i
$405$		0			0
$406$	0.175447	−	19.6382i	0.00870728	−	0.974629i
$407$	−3.42101	−	5.92537i	−0.169573	−	0.293709i
$408$		0			0
$409$	16.7720			0.829323			0.414662	−	0.909976i	$-0.363900\pi$
$409$	16.7720			0.829323			0.414662	+	0.909976i	$0.363900\pi$
$410$	−4.66475			−0.230376
$411$		0			0
$412$	0.524685	+	0.908780i	0.0258494	+	0.0447724i
$413$	3.35159	−	1.89532i	0.164921	−	0.0932628i
$414$		0			0
$415$	4.62671	+	8.01370i	0.227116	+	0.393377i
$416$	−0.785103	+	3.51904i	−0.0384928	+	0.172535i
$417$		0			0
$418$	−19.1430			−0.936316
$419$	19.8098	−	34.3115i	0.967770	−	1.67623i	0.265788	−	0.964031i	$-0.414368\pi$
$419$	19.8098	−	34.3115i	0.967770	−	1.67623i	0.701982	−	0.712195i	$-0.252299\pi$
$420$		0			0
$421$	−32.2271			−1.57065			−0.785326	−	0.619083i	$-0.787505\pi$
$421$	−32.2271			−1.57065			−0.785326	+	0.619083i	$0.787505\pi$
$422$	−6.22021	+	10.7737i	−0.302795	+	0.524456i
$423$		0			0
$424$	−3.86750	+	6.69870i	−0.187822	+	0.325318i
$425$	−0.853432	+	1.47819i	−0.0413975	+	0.0717027i
$426$		0			0
$427$	0.0992558	−	11.1100i	0.00480333	−	0.537649i
$428$	10.1830			0.492216
$429$		0			0
$430$	1.83915	−	3.18550i	0.0886916	−	0.153618i
$431$	5.50063	+	9.52738i	0.264956	+	0.458918i	0.967552	−	0.252671i	$-0.0813092\pi$
$431$	5.50063	+	9.52738i	0.264956	+	0.458918i	−0.702596	+	0.711589i	$0.747976\pi$
$432$		0			0
$433$	15.9643	+	27.6509i	0.767193	+	1.32882i	0.939079	+	0.343701i	$0.111681\pi$
$433$	15.9643	+	27.6509i	0.767193	+	1.32882i	−0.171886	+	0.985117i	$0.554986\pi$
$434$	−0.192136	+	21.5064i	−0.00922285	+	1.03234i
$435$		0			0
$436$	9.92285	−	17.1869i	0.475218	−	0.823102i
$437$	−1.71863	+	2.97675i	−0.0822132	+	0.142397i
$438$		0			0
$439$	−1.43526			−0.0685010			−0.0342505	−	0.999413i	$-0.510904\pi$
$439$	−1.43526			−0.0685010			−0.0342505	+	0.999413i	$0.510904\pi$
$440$	−1.55535	+	2.69395i	−0.0741485	+	0.128429i
$441$		0			0
$442$	0.388880	−	1.74306i	0.0184972	−	0.0829091i
$443$	−5.72758	−	9.92047i	−0.272126	−	0.471336i	0.697280	−	0.716799i	$-0.254393\pi$
$443$	−5.72758	−	9.92047i	−0.272126	−	0.471336i	−0.969406	+	0.245463i	$0.921060\pi$
$444$		0			0
$445$	−7.15626	−	12.3950i	−0.339239	−	0.587580i
$446$	−10.4651	+	18.1260i	−0.495535	+	0.858292i
$447$		0			0
$448$	2.30301	−	1.30235i	0.108807	−	0.0615304i
$449$	17.3713	+	30.0880i	0.819803	+	1.41994i	0.905827	+	0.423647i	$0.139250\pi$
$449$	17.3713	+	30.0880i	0.819803	+	1.41994i	−0.0860243	+	0.996293i	$0.527416\pi$
$450$		0			0
$451$	−9.33735			−0.439679
$452$	7.93440	+	13.7428i	0.373203	+	0.646406i
$453$		0			0
$454$	−17.5810			−0.825119
$455$	8.12373	−	8.68465i	0.380846	−	0.407143i
$456$		0			0
$457$	36.8048			1.72166			0.860829	−	0.508894i	$-0.169946\pi$
$457$	36.8048			1.72166			0.860829	+	0.508894i	$0.169946\pi$
$458$	7.24620	+	12.5508i	0.338593	+	0.586460i
$459$		0			0
$460$	0.279274	+	0.483717i	0.0130212	+	0.0225534i
$461$	3.99129	+	6.91311i	0.185893	+	0.321976i	0.943877	−	0.330297i	$-0.107149\pi$
$461$	3.99129	+	6.91311i	0.185893	+	0.321976i	−0.757984	+	0.652273i	$0.773816\pi$
$462$		0			0
$463$	26.4799			1.23063			0.615314	−	0.788282i	$-0.289029\pi$
$463$	26.4799			1.23063			0.615314	+	0.788282i	$0.289029\pi$
$464$	3.71142	−	6.42837i	0.172299	−	0.298430i
$465$		0			0
$466$	7.24897	+	12.5556i	0.335802	+	0.581626i
$467$	3.12210	+	5.40764i	0.144474	+	0.250236i	0.929176	−	0.369636i	$-0.120518\pi$
$467$	3.12210	+	5.40764i	0.144474	+	0.250236i	−0.784703	+	0.619872i	$0.787184\pi$
$468$		0			0
$469$	−0.0629324	−	0.0370876i	−0.00290595	−	0.00171254i
$470$	−4.11045	+	7.11950i	−0.189601	+	0.328398i
$471$		0			0
$472$	1.45531			0.0669859
$473$	3.68139	−	6.37635i	0.169270	−	0.293185i
$474$		0			0
$475$	−13.2179	−	22.8941i	−0.606480	−	1.05045i
$476$	−1.14074	+	0.645087i	−0.0522857	+	0.0295675i
$477$		0			0
$478$	−3.15093			−0.144120
$479$	10.7862	+	18.6823i	0.492836	+	0.853617i	0.999966	−	0.00825291i	$-0.00262701\pi$
$479$	10.7862	+	18.6823i	0.492836	+	0.853617i	−0.507130	+	0.861869i	$0.669294\pi$
$480$		0			0
$481$	−2.15270	+	9.64898i	−0.0981548	+	0.439955i
$482$	−24.8446			−1.13164
$483$		0			0
$484$	2.38668	−	4.13385i	0.108485	−	0.187902i
$485$	−0.635563	+	1.10083i	−0.0288594	+	0.0499860i
$486$		0			0
$487$	13.6151			0.616961			0.308481	−	0.951231i	$-0.400180\pi$
$487$	13.6151			0.616961			0.308481	+	0.951231i	$0.400180\pi$
$488$	2.09967	−	3.63674i	0.0950476	−	0.164627i
$489$		0			0
$490$	−8.72490	−	0.155908i	−0.394151	−	0.00704320i
$491$	−6.14512	+	10.6437i	−0.277326	+	0.480342i	−0.970719	−	0.240217i	$-0.922781\pi$
$491$	−6.14512	+	10.6437i	−0.277326	+	0.480342i	0.693394	+	0.720559i	$0.256115\pi$
$492$		0			0
$493$	−1.83836	+	3.18413i	−0.0827955	+	0.143406i
$494$	20.3682	+	18.7143i	0.916407	+	0.841995i
$495$		0			0
$496$	−4.06448	+	7.03989i	−0.182501	+	0.316100i
$497$	−21.3753	−	12.5970i	−0.958812	−	0.565051i
$498$		0			0
$499$	−7.11789	−	12.3285i	−0.318640	−	0.551901i	0.661564	−	0.749889i	$-0.269893\pi$
$499$	−7.11789	−	12.3285i	−0.318640	−	0.551901i	−0.980205	+	0.197987i	$0.936560\pi$
$500$	−10.5288			−0.470864
$501$		0			0
$502$	3.69421	+	6.39857i	0.164881	+	0.285582i
$503$	−10.4692	−	18.1332i	−0.466798	−	0.808518i	0.532482	−	0.846441i	$-0.321259\pi$
$503$	−10.4692	−	18.1332i	−0.466798	−	0.808518i	−0.999281	+	0.0379227i	$0.987926\pi$
$504$		0			0
$505$	11.1837	−	19.3708i	0.497669	−	0.861987i
$506$	0.559018	+	0.968247i	0.0248514	+	0.0430438i
$507$		0			0
$508$	4.23846	−	7.34124i	0.188051	−	0.325715i
$509$	−13.9297			−0.617423			−0.308711	−	0.951156i	$-0.599898\pi$
$509$	−13.9297			−0.617423			−0.308711	+	0.951156i	$0.599898\pi$
$510$		0			0
$511$	−0.239741	+	26.8349i	−0.0106055	+	1.18710i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−26.8892			−1.18603
$515$	0.654079	−	1.13290i	0.0288222	−	0.0499214i
$516$		0			0
$517$	−8.22781	+	14.2510i	−0.361859	+	0.626757i
$518$	6.31472	−	3.57097i	0.277453	−	0.156899i
$519$		0			0
$520$	4.28851	−	1.34584i	0.188063	−	0.0590191i
$521$	−11.1502	+	19.3128i	−0.488501	+	0.846109i	−0.999913	−	0.0132274i	$-0.995789\pi$
$521$	−11.1502	+	19.3128i	−0.488501	+	0.846109i	0.511412	+	0.859336i	$0.329123\pi$
$522$		0			0
$523$	−27.7032			−1.21138			−0.605689	−	0.795702i	$-0.707102\pi$
$523$	−27.7032			−1.21138			−0.605689	+	0.795702i	$0.707102\pi$
$524$	8.26678	+	14.3185i	0.361136	+	0.625506i
$525$		0			0
$526$	−1.46562	−	2.53852i	−0.0639040	−	0.110685i
$527$	2.01324	−	3.48703i	0.0876979	−	0.151897i
$528$		0			0
$529$	−22.7992			−0.991272
$530$	9.64254			0.418845
$531$		0			0
$532$	0.181325	−	20.2962i	0.00786145	−	0.879953i
$533$	9.93493	+	9.12822i	0.430330	+	0.395387i
$534$		0			0
$535$	−6.34716	−	10.9936i	−0.274412	−	0.475295i
$536$	−0.0138047	−	0.0239105i	−0.000596273	−	0.00103278i
$537$		0			0
$538$	−2.14443			−0.0924530
$539$	−17.4645	−	0.312078i	−0.752248	−	0.0134422i
$540$		0			0
$541$	7.32108	+	12.6805i	0.314758	+	0.545177i	0.979386	−	0.201998i	$-0.0647434\pi$
$541$	7.32108	+	12.6805i	0.314758	+	0.545177i	−0.664628	+	0.747174i	$0.731410\pi$
$542$	17.2844			0.742428
$543$		0			0
$544$	−0.495324			−0.0212368
$545$	−24.7399			−1.05974
$546$		0			0
$547$	21.7401			0.929542			0.464771	−	0.885431i	$-0.346137\pi$
$547$	21.7401			0.929542			0.464771	+	0.885431i	$0.346137\pi$
$548$	0.856837			0.0366023
$549$		0			0
$550$	−8.59877			−0.366653
$551$	−28.4724	−	49.3157i	−1.21297	−	2.10092i
$552$		0			0
$553$	−22.4995	−	13.2595i	−0.956777	−	0.563851i
$554$	−2.83381			−0.120397
$555$		0			0
$556$	4.74886	+	8.22528i	0.201397	+	0.348829i
$557$	2.23589	+	3.87267i	0.0947375	+	0.164090i	0.909499	−	0.415706i	$-0.136465\pi$
$557$	2.23589	+	3.87267i	0.0947375	+	0.164090i	−0.814762	+	0.579796i	$0.803132\pi$
$558$		0			0
$559$	−10.1505	+	3.18550i	−0.429322	+	0.134732i
$560$	−2.84150	−	1.67457i	−0.120075	−	0.0707633i
$561$		0			0
$562$	28.5254			1.20327
$563$	11.1580			0.470253			0.235126	−	0.971965i	$-0.424450\pi$
$563$	11.1580			0.470253			0.235126	+	0.971965i	$0.424450\pi$
$564$		0			0
$565$	9.89113	−	17.1319i	0.416123	−	0.720746i
$566$	2.29901	+	3.98201i	0.0966347	+	0.167376i
$567$		0			0
$568$	−4.68884	−	8.12130i	−0.196739	−	0.340762i
$569$	36.8818			1.54617			0.773083	−	0.634304i	$-0.218713\pi$
$569$	36.8818			1.54617			0.773083	+	0.634304i	$0.218713\pi$
$570$		0			0
$571$	0.101526	−	0.175849i	0.00424874	−	0.00735904i	−0.863893	−	0.503675i	$-0.831981\pi$
$571$	0.101526	−	0.175849i	0.00424874	−	0.00735904i	0.868142	+	0.496316i	$0.165314\pi$
$572$	8.58423	−	2.69395i	0.358925	−	0.112640i
$573$		0			0
$574$	0.0884446	−	9.89984i	0.00369161	−	0.413211i
$575$	−0.771984	+	1.33711i	−0.0321939	+	0.0557615i
$576$		0			0
$577$	10.4151	−	18.0396i	0.433588	−	0.750997i	−0.563591	−	0.826054i	$-0.690581\pi$
$577$	10.4151	−	18.0396i	0.433588	−	0.750997i	0.997179	+	0.0750570i	$0.0239139\pi$
$578$	−16.7547			−0.696902
$579$		0			0
$580$	−9.25342			−0.384227
$581$	−17.0949	+	9.66717i	−0.709217	+	0.401062i
$582$		0			0
$583$	19.3013			0.799379
$584$	−5.07151	+	8.78412i	−0.209861	+	0.363489i
$585$		0			0
$586$	−3.19384	−	5.53189i	−0.131936	−	0.228520i
$587$	8.25511	−	14.2983i	0.340725	−	0.590153i	−0.643843	−	0.765158i	$-0.722661\pi$
$587$	8.25511	−	14.2983i	0.340725	−	0.590153i	0.984568	+	0.175005i	$0.0559942\pi$
$588$		0			0
$589$	31.1809	+	54.0069i	1.28479	+	2.22532i
$590$	−0.907102	−	1.57115i	−0.0373448	−	0.0646831i
$591$		0			0
$592$	2.74194			0.112693
$593$	−5.86959	−	10.1664i	−0.241035	−	0.417485i	0.719974	−	0.694001i	$-0.244154\pi$
$593$	−5.86959	−	10.1664i	−0.241035	−	0.417485i	−0.961009	+	0.276515i	$0.910820\pi$
$594$		0			0
$595$	1.40747	+	0.829453i	0.0577005	+	0.0340043i
$596$	−2.36872	+	4.10274i	−0.0970264	+	0.168055i
$597$		0			0
$598$	0.351767	−	1.57671i	0.0143848	−	0.0644765i
$599$	21.8486	−	37.8430i	0.892711	−	1.54622i	0.0560993	−	0.998425i	$-0.482134\pi$
$599$	21.8486	−	37.8430i	0.892711	−	1.54622i	0.836612	−	0.547796i	$-0.184533\pi$
$600$		0			0
$601$	2.84613	−	4.92964i	0.116096	−	0.201084i	−0.802121	−	0.597161i	$-0.796295\pi$
$601$	2.84613	−	4.92964i	0.116096	−	0.201084i	0.918217	+	0.396077i	$0.129629\pi$
$602$	6.72560	+	3.96356i	0.274115	+	0.161543i
$603$		0			0
$604$	−3.56085	+	6.16758i	−0.144889	+	0.250955i
$605$	−5.95053			−0.241924
$606$		0			0
$607$	12.5493	−	21.7360i	0.509360	−	0.882238i	−0.490581	−	0.871396i	$-0.663215\pi$
$607$	12.5493	−	21.7360i	0.509360	−	0.882238i	0.999941	−	0.0108424i	$-0.00345131\pi$
$608$	3.83578	−	6.64376i	0.155561	−	0.269440i
$609$		0			0
$610$	−5.23496			−0.211957
$611$	22.6862	−	7.11950i	0.917785	−	0.288024i
$612$		0			0
$613$	−1.29666	−	2.24587i	−0.0523715	−	0.0907100i	0.838651	−	0.544669i	$-0.183345\pi$
$613$	−1.29666	−	2.24587i	−0.0523715	−	0.0907100i	−0.891023	+	0.453959i	$0.850011\pi$
$614$	−1.39899			−0.0564587
$615$		0			0
$616$	−5.68779	−	3.35195i	−0.229168	−	0.135054i
$617$	−8.83438	−	15.3016i	−0.355659	−	0.616019i	0.631572	−	0.775318i	$-0.282410\pi$
$617$	−8.83438	−	15.3016i	−0.355659	−	0.616019i	−0.987231	+	0.159298i	$0.949077\pi$
$618$		0			0
$619$	20.4642	−	35.4450i	0.822525	−	1.42465i	−0.0812719	−	0.996692i	$-0.525898\pi$
$619$	20.4642	−	35.4450i	0.822525	−	1.42465i	0.903797	−	0.427962i	$-0.140768\pi$
$620$	10.1337			0.406978
$621$		0			0
$622$	8.55183	−	14.8122i	0.342897	−	0.593915i
$623$	26.4412	−	14.9525i	1.05934	−	0.599058i
$624$		0			0
$625$	−2.05219	−	3.55450i	−0.0820876	−	0.142180i
$626$	−5.81247	−	10.0675i	−0.232313	−	0.402378i
$627$		0			0
$628$	−7.52147	+	13.0276i	−0.300139	+	0.519857i
$629$	−1.35815			−0.0541529
$630$		0			0
$631$	3.58097	+	6.20242i	0.142556	+	0.246914i	0.928459	−	0.371436i	$-0.121135\pi$
$631$	3.58097	+	6.20242i	0.142556	+	0.246914i	−0.785902	+	0.618351i	$0.787801\pi$
$632$	−4.93545	−	8.54845i	−0.196322	−	0.340039i
$633$		0			0
$634$	3.29277	+	5.70324i	0.130773	+	0.226505i
$635$	−10.5675			−0.419357
$636$		0			0
$637$	18.2771	+	17.4054i	0.724165	+	0.689626i
$638$	−18.5224			−0.733309
$639$		0			0
$640$	−0.623307	−	1.07960i	−0.0246384	−	0.0426749i
$641$	−3.25919			−0.128730			−0.0643652	−	0.997926i	$-0.520502\pi$
$641$	−3.25919			−0.128730			−0.0643652	+	0.997926i	$0.520502\pi$
$642$		0			0
$643$	−9.17027	−	15.8834i	−0.361640	−	0.626379i	0.626591	−	0.779348i	$-0.284450\pi$
$643$	−9.17027	−	15.8834i	−0.361640	−	0.626379i	−0.988231	+	0.152969i	$0.951116\pi$
$644$	−1.03187	+	0.583522i	−0.0406614	+	0.0229940i
$645$		0			0
$646$	−1.89995	+	3.29082i	−0.0747527	+	0.129475i
$647$	21.9343	+	37.9913i	0.862325	+	1.49359i	0.869679	+	0.493618i	$0.164326\pi$
$647$	21.9343	+	37.9913i	0.862325	+	1.49359i	−0.00735417	+	0.999973i	$0.502341\pi$
$648$		0			0
$649$	−1.81573	−	3.14494i	−0.0712737	−	0.123450i
$650$	9.14909	+	8.40619i	0.358857	+	0.329718i
$651$		0			0
$652$	4.51485	−	7.81996i	0.176815	−	0.306253i
$653$	−13.2804			−0.519704			−0.259852	−	0.965649i	$-0.583674\pi$
$653$	−13.2804			−0.519704			−0.259852	+	0.965649i	$0.583674\pi$
$654$		0			0
$655$	10.3055	−	17.8496i	0.402668	−	0.697442i
$656$	1.87097	−	3.24061i	0.0730491	−	0.126525i
$657$		0			0
$658$	−15.0315	−	8.85845i	−0.585991	−	0.345338i
$659$	−1.53479	−	2.65834i	−0.0597871	−	0.103554i	0.834583	−	0.550883i	$-0.185709\pi$
$659$	−1.53479	−	2.65834i	−0.0597871	−	0.103554i	−0.894370	+	0.447328i	$0.852376\pi$
$660$		0			0
$661$	14.8034	+	25.6402i	0.575785	+	0.997290i	0.995956	+	0.0898443i	$0.0286370\pi$
$661$	14.8034	+	25.6402i	0.575785	+	0.997290i	−0.420170	+	0.907445i	$0.638030\pi$
$662$	11.6343	−	20.1512i	0.452179	−	0.783197i
$663$		0			0
$664$	−7.42285			−0.288062
$665$	−22.0248	+	12.4550i	−0.854085	+	0.482985i
$666$		0			0
$667$	−1.66291	+	2.88025i	−0.0643882	+	0.111524i
$668$	−1.42442	+	2.46716i	−0.0551123	+	0.0954573i
$669$		0			0
$670$	−0.0172092	+	0.0298071i	−0.000664848	+	0.00115155i
$671$	−10.4787			−0.404526
$672$		0			0
$673$	−4.54511	+	7.87235i	−0.175201	+	0.303457i	−0.940231	−	0.340538i	$-0.889391\pi$
$673$	−4.54511	+	7.87235i	−0.175201	+	0.303457i	0.765030	+	0.643995i	$0.222724\pi$
$674$	19.4320			0.748491
$675$		0			0
$676$	−11.7672	−	5.52561i	−0.452586	−	0.212523i
$677$	−8.92163	−	15.4527i	−0.342886	−	0.593896i	0.642081	−	0.766636i	$-0.278071\pi$
$677$	−8.92163	−	15.4527i	−0.342886	−	0.593896i	−0.984967	+	0.172741i	$0.944738\pi$
$678$		0			0
$679$	−2.32420	−	1.36970i	−0.0891945	−	0.0525645i
$680$	0.308739	+	0.534751i	0.0118396	+	0.0205068i
$681$		0			0
$682$	20.2844			0.776730
$683$	12.3180			0.471333			0.235667	−	0.971834i	$-0.424273\pi$
$683$	12.3180			0.471333			0.235667	+	0.971834i	$0.424273\pi$
$684$		0			0
$685$	−0.534072	−	0.925040i	−0.0204058	−	0.0353440i
$686$	0.496304	−	18.5136i	0.0189490	−	0.706853i
$687$		0			0
$688$	1.47532	+	2.55532i	0.0562459	+	0.0974207i
$689$	−20.5366	−	18.8690i	−0.782381	−	0.718853i
$690$		0			0
$691$	−27.1762			−1.03383			−0.516916	−	0.856036i	$-0.672920\pi$
$691$	−27.1762			−1.03383			−0.516916	+	0.856036i	$0.672920\pi$
$692$	−12.7438	+	22.0729i	−0.484446	+	0.839084i
$693$		0			0
$694$	−29.6707			−1.12629
$695$	5.92000	−	10.2537i	0.224558	−	0.388946i
$696$		0			0
$697$	−0.926736	+	1.60515i	−0.0351026	+	0.0607995i
$698$	−13.3023	+	23.0403i	−0.503501	+	0.872090i
$699$		0			0
$700$	0.0814487	−	9.11678i	0.00307847	−	0.344582i
$701$	−38.0704			−1.43790			−0.718950	−	0.695062i	$-0.755377\pi$
$701$	−38.0704			−1.43790			−0.718950	+	0.695062i	$0.755377\pi$
$702$		0			0
$703$	10.5175	−	18.2168i	0.396674	−	0.687059i
$704$	−1.24766	−	2.16101i	−0.0470230	−	0.0814463i
$705$		0			0
$706$	−6.90939	−	11.9674i	−0.260038	−	0.450400i
$707$	40.8979	+	24.1021i	1.53812	+	0.906452i
$708$		0			0
$709$	20.7624	−	35.9616i	0.779750	−	1.35057i	−0.152336	−	0.988329i	$-0.548679\pi$
$709$	20.7624	−	35.9616i	0.779750	−	1.35057i	0.932086	−	0.362238i	$-0.117987\pi$
$710$	−5.84517	+	10.1241i	−0.219365	+	0.379952i
$711$		0			0
$712$	11.4811			0.430273
$713$	1.82110	−	3.15424i	0.0682007	−	0.118127i
$714$		0			0
$715$	−8.25899	−	7.58837i	−0.308869	−	0.283789i
$716$	9.10030	+	15.7622i	0.340094	+	0.589061i
$717$		0			0
$718$	−1.38095	−	2.39188i	−0.0515368	−	0.0892643i
$719$	8.30463	−	14.3840i	0.309710	−	0.536434i	−0.668589	−	0.743633i	$-0.733101\pi$
$719$	8.30463	−	14.3840i	0.309710	−	0.536434i	0.978299	+	0.207198i	$0.0664346\pi$
$720$		0			0
$721$	2.39191	+	1.40961i	0.0890794	+	0.0524966i
$722$	−19.9264	−	34.5135i	−0.741584	−	1.28446i
$723$		0			0
$724$	−13.7305			−0.510290
$725$	−12.7894	−	22.1519i	−0.474986	−	0.822701i
$726$		0			0
$727$	−20.2421			−0.750737			−0.375368	−	0.926876i	$-0.622484\pi$
$727$	−20.2421			−0.750737			−0.375368	+	0.926876i	$0.622484\pi$
$728$	2.77493	+	9.12687i	0.102846	+	0.338264i
$729$		0			0
$730$	12.6444			0.467991
$731$	−0.730759	−	1.26571i	−0.0270281	−	0.0468141i
$732$		0			0
$733$	−8.42173	−	14.5869i	−0.311064	−	0.538778i	0.667529	−	0.744584i	$-0.267352\pi$
$733$	−8.42173	−	14.5869i	−0.311064	−	0.538778i	−0.978593	+	0.205805i	$0.934019\pi$
$734$	5.46151	+	9.45961i	0.201588	+	0.349161i
$735$		0			0
$736$	−0.448052			−0.0165154
$737$	−0.0344473	+	0.0596644i	−0.00126888	+	0.00219777i
$738$		0			0
$739$	24.0597	+	41.6726i	0.885049	+	1.53295i	0.845657	+	0.533726i	$0.179209\pi$
$739$	24.0597	+	41.6726i	0.885049	+	1.53295i	0.0393919	+	0.999224i	$0.487458\pi$
$740$	−1.70907	−	2.96019i	−0.0628266	−	0.108819i
$741$		0			0
$742$	−0.182825	+	20.4640i	−0.00671170	+	0.751259i
$743$	−2.98460	+	5.16948i	−0.109494	+	0.189650i	−0.915566	−	0.402169i	$-0.868256\pi$
$743$	−2.98460	+	5.16948i	−0.109494	+	0.189650i	0.806071	+	0.591819i	$0.201590\pi$
$744$		0			0
$745$	5.90575			0.216370
$746$	−9.84303	+	17.0486i	−0.360379	+	0.624195i
$747$		0			0
$748$	0.617997	+	1.07040i	0.0225962	+	0.0391378i
$749$	23.4517	−	13.2619i	0.856906	−	0.484580i
$750$		0			0
$751$	36.3054			1.32480			0.662401	−	0.749150i	$-0.269538\pi$
$751$	36.3054			1.32480			0.662401	+	0.749150i	$0.269538\pi$
$752$	−3.29729	−	5.71107i	−0.120240	−	0.208261i
$753$		0			0
$754$	19.7078	+	18.1076i	0.717717	+	0.659439i
$755$	8.87802			0.323104
$756$		0			0
$757$	−3.48399	+	6.03445i	−0.126628	+	0.219326i	−0.922368	−	0.386312i	$-0.873749\pi$
$757$	−3.48399	+	6.03445i	−0.126628	+	0.219326i	0.795740	+	0.605638i	$0.207082\pi$
$758$	−8.31713	+	14.4057i	−0.302092	+	0.523238i
$759$		0			0
$760$	−9.56347			−0.346903
$761$	−1.47562	+	2.55585i	−0.0534912	+	0.0926496i	−0.891531	−	0.452959i	$-0.850368\pi$
$761$	−1.47562	+	2.55585i	−0.0534912	+	0.0926496i	0.838040	+	0.545609i	$0.183702\pi$
$762$		0			0
$763$	0.469074	−	52.5047i	0.0169816	−	1.90080i
$764$	2.64294	−	4.57771i	0.0956182	−	0.165616i
$765$		0			0
$766$	18.1834	−	31.4945i	0.656992	−	1.13794i
$767$	−1.14257	+	5.12128i	−0.0412556	+	0.184919i
$768$		0			0
$769$	−21.0168	+	36.4022i	−0.757885	+	1.31270i	0.186042	+	0.982542i	$0.440434\pi$
$769$	−21.0168	+	36.4022i	−0.757885	+	1.31270i	−0.943927	+	0.330154i	$0.892899\pi$
$770$	−0.0735247	+	8.22982i	−0.00264965	+	0.296582i
$771$		0			0
$772$	−2.40599	−	4.16729i	−0.0865933	−	0.149984i
$773$	43.6310			1.56930			0.784650	−	0.619940i	$-0.212843\pi$
$773$	43.6310			1.56930			0.784650	+	0.619940i	$0.212843\pi$
$774$		0			0
$775$	14.0060	+	24.2591i	0.503111	+	0.871414i
$776$	−0.509831	−	0.883054i	−0.0183019	−	0.0316998i
$777$		0			0
$778$	−8.89008	+	15.3981i	−0.318725	+	0.552048i
$779$	−14.3532	−	24.8606i	−0.514258	−	0.890722i
$780$		0			0
$781$	−11.7002	+	20.2653i	−0.418665	+	0.725149i
$782$	0.221931			0.00793624
$783$		0			0
$784$	3.60775	−	5.99868i	0.128848	−	0.214238i
$785$	18.7527			0.669314
$786$		0			0
$787$	24.3320			0.867341			0.433671	−	0.901071i	$-0.357218\pi$
$787$	24.3320			0.867341			0.433671	+	0.901071i	$0.357218\pi$
$788$	−11.7743	+	20.3937i	−0.419442	+	0.726494i
$789$		0			0
$790$	−6.15260	+	10.6566i	−0.218900	+	0.379145i
$791$	36.1710	+	21.3164i	1.28609	+	0.757925i
$792$		0			0
$793$	11.1493	+	10.2440i	0.395925	+	0.363776i
$794$	−4.43952	+	7.68948i	−0.157553	+	0.272889i
$795$		0			0
$796$	11.2797			0.399798
$797$	13.8223	+	23.9408i	0.489609	+	0.848028i	0.999929	−	0.0119569i	$-0.00380609\pi$
$797$	13.8223	+	23.9408i	0.489609	+	0.848028i	−0.510319	+	0.859985i	$0.670473\pi$
$798$		0			0
$799$	1.63323	+	2.82883i	0.0577794	+	0.100077i
$800$	1.72298	−	2.98428i	0.0609165	−	0.105510i
$801$		0			0
$802$	30.1630			1.06509
$803$	25.3101			0.893175
$804$		0			0
$805$	1.27314	+	0.750293i	0.0448723	+	0.0264443i
$806$	−21.5826	−	19.8301i	−0.760214	−	0.698485i
$807$		0			0
$808$	8.97127	+	15.5387i	0.315608	+	0.546650i
$809$	−23.3835	−	40.5014i	−0.822119	−	1.42395i	−0.904101	−	0.427319i	$-0.859458\pi$
$809$	−23.3835	−	40.5014i	−0.822119	−	1.42395i	0.0819815	−	0.996634i	$-0.473875\pi$
$810$		0			0
$811$	−33.4037			−1.17296			−0.586481	−	0.809963i	$-0.699487\pi$
$811$	−33.4037			−1.17296			−0.586481	+	0.809963i	$0.699487\pi$
$812$	0.175447	−	19.6382i	0.00615697	−	0.689167i
$813$		0			0
$814$	−3.42101	−	5.92537i	−0.119906	−	0.207684i
$815$	−11.2566			−0.394300
$816$		0			0
$817$	22.6359			0.791931
$818$	16.7720			0.586420
$819$		0			0
$820$	−4.66475			−0.162900
$821$	−37.4874			−1.30832			−0.654160	−	0.756356i	$-0.726978\pi$
$821$	−37.4874			−1.30832			−0.654160	+	0.756356i	$0.726978\pi$
$822$		0			0
$823$	−49.7545			−1.73433			−0.867166	−	0.498020i	$-0.834061\pi$
$823$	−49.7545			−1.73433			−0.867166	+	0.498020i	$0.834061\pi$
$824$	0.524685	+	0.908780i	0.0182783	+	0.0316589i
$825$		0			0
$826$	3.35159	−	1.89532i	0.116617	−	0.0659467i
$827$	−3.32250			−0.115534			−0.0577672	−	0.998330i	$-0.518398\pi$
$827$	−3.32250			−0.115534			−0.0577672	+	0.998330i	$0.518398\pi$
$828$		0			0
$829$	8.25485	+	14.2978i	0.286703	+	0.496584i	0.973021	−	0.230718i	$-0.0741075\pi$
$829$	8.25485	+	14.2978i	0.286703	+	0.496584i	−0.686318	+	0.727302i	$0.740774\pi$
$830$	4.62671	+	8.01370i	0.160595	+	0.278160i
$831$		0			0
$832$	−0.785103	+	3.51904i	−0.0272185	+	0.122001i
$833$	−1.78701	+	2.97129i	−0.0619161	+	0.102949i
$834$		0			0
$835$	3.55139			0.122901
$836$	−19.1430			−0.662075
$837$		0			0
$838$	19.8098	−	34.3115i	0.684317	−	1.18527i
$839$	−8.35299	−	14.4678i	−0.288377	−	0.499484i	0.685045	−	0.728500i	$-0.259782\pi$
$839$	−8.35299	−	14.4678i	−0.288377	−	0.499484i	−0.973423	+	0.229016i	$0.926449\pi$
$840$		0			0
$841$	−13.0493	−	22.6021i	−0.449977	−	0.779383i
$842$	−32.2271			−1.11062
$843$		0			0
$844$	−6.22021	+	10.7737i	−0.214108	+	0.370847i
$845$	1.36915	+	16.1480i	0.0471002	+	0.555509i
$846$		0			0
$847$	0.112823	−	12.6286i	0.00387665	−	0.433924i
$848$	−3.86750	+	6.69870i	−0.132810	+	0.230034i
$849$		0			0
$850$	−0.853432	+	1.47819i	−0.0292725	+	0.0507014i
$851$	−1.22853			−0.0421135
$852$		0			0
$853$	27.5476			0.943212			0.471606	−	0.881809i	$-0.343674\pi$
$853$	27.5476			0.943212			0.471606	+	0.881809i	$0.343674\pi$
$854$	0.0992558	−	11.1100i	0.00339646	−	0.380175i
$855$		0			0
$856$	10.1830			0.348049
$857$	9.17302	−	15.8881i	0.313344	−	0.542729i	−0.665740	−	0.746184i	$-0.731884\pi$
$857$	9.17302	−	15.8881i	0.313344	−	0.542729i	0.979084	+	0.203455i	$0.0652172\pi$
$858$		0			0
$859$	−21.5684	−	37.3575i	−0.735903	−	1.27462i	−0.954326	−	0.298767i	$-0.903425\pi$
$859$	−21.5684	−	37.3575i	−0.735903	−	1.27462i	0.218423	−	0.975854i	$-0.429909\pi$
$860$	1.83915	−	3.18550i	0.0627144	−	0.108625i
$861$		0			0
$862$	5.50063	+	9.52738i	0.187352	+	0.324504i
$863$	−22.5095	−	38.9876i	−0.766233	−	1.32715i	−0.939592	−	0.342296i	$-0.888796\pi$
$863$	−22.5095	−	38.9876i	−0.766233	−	1.32715i	0.173359	−	0.984859i	$-0.444538\pi$
$864$		0			0
$865$	31.7731			1.08032
$866$	15.9643	+	27.6509i	0.542488	+	0.939616i
$867$		0			0
$868$	−0.192136	+	21.5064i	−0.00652154	+	0.729973i
$869$	−12.3155	+	21.3312i	−0.417776	+	0.723610i
$870$		0			0
$871$	0.0949800	−	0.0298071i	0.00321827	−	0.00100998i
$872$	9.92285	−	17.1869i	0.336030	−	0.582021i
$873$		0			0
$874$	−1.71863	+	2.97675i	−0.0581335	+	0.100690i
$875$	−24.2481	+	13.7123i	−0.819734	+	0.463559i
$876$		0			0
$877$	10.9297	−	18.9309i	0.369071	−	0.639250i	−0.620349	−	0.784326i	$-0.713009\pi$
$877$	10.9297	−	18.9309i	0.369071	−	0.639250i	0.989421	+	0.145075i	$0.0463425\pi$
$878$	−1.43526			−0.0484376
$879$		0			0
$880$	−1.55535	+	2.69395i	−0.0524309	+	0.0908130i
$881$	−0.975574	+	1.68974i	−0.0328679	+	0.0569289i	−0.881991	−	0.471265i	$-0.843797\pi$
$881$	−0.975574	+	1.68974i	−0.0328679	+	0.0569289i	0.849124	+	0.528194i	$0.177131\pi$
$882$		0			0
$883$	−20.9397			−0.704677			−0.352338	−	0.935873i	$-0.614613\pi$
$883$	−20.9397			−0.704677			−0.352338	+	0.935873i	$0.614613\pi$
$884$	0.388880	−	1.74306i	0.0130795	−	0.0586256i
$885$		0			0
$886$	−5.72758	−	9.92047i	−0.192422	−	0.333285i
$887$	−23.5772			−0.791646			−0.395823	−	0.918327i	$-0.629541\pi$
$887$	−23.5772			−0.791646			−0.395823	+	0.918327i	$0.629541\pi$
$888$		0			0
$889$	0.200361	−	22.4270i	0.00671989	−	0.752176i
$890$	−7.15626	−	12.3950i	−0.239878	−	0.415482i
$891$		0			0
$892$	−10.4651	+	18.1260i	−0.350396	+	0.606904i
$893$	−50.5907			−1.69295
$894$		0			0
$895$	11.3446	−	19.6494i	0.379207	−	0.656806i
$896$	2.30301	−	1.30235i	0.0769383	−	0.0435086i
$897$		0			0
$898$	17.3713	+	30.0880i	0.579688	+	1.00405i
$899$	30.1700	+	52.2560i	1.00623	+	1.74284i
$900$		0			0
$901$	1.91566	−	3.31803i	0.0638200	−	0.110540i
$902$	−9.33735			−0.310900
$903$		0			0
$904$	7.93440	+	13.7428i	0.263894	+	0.457078i
$905$	8.55831	+	14.8234i	0.284488	+	0.492747i
$906$		0			0
$907$	−0.0707540	−	0.122550i	−0.00234935	−	0.00406919i	0.864848	−	0.502033i	$-0.167414\pi$
$907$	−0.0707540	−	0.122550i	−0.00234935	−	0.00406919i	−0.867198	+	0.497964i	$0.834081\pi$
$908$	−17.5810			−0.583447
$909$		0			0
$910$	8.12373	−	8.68465i	0.269299	−	0.287893i
$911$	−48.1769			−1.59617			−0.798086	−	0.602543i	$-0.794154\pi$
$911$	−48.1769			−1.59617			−0.798086	+	0.602543i	$0.794154\pi$
$912$		0			0
$913$	9.26121	+	16.0409i	0.306501	+	0.530876i
$914$	36.8048			1.21740
$915$		0			0
$916$	7.24620	+	12.5508i	0.239421	+	0.414690i
$917$	37.6862	+	22.2094i	1.24451	+	0.733419i
$918$		0			0
$919$	−19.8090	+	34.3102i	−0.653439	+	1.13179i	0.328844	+	0.944384i	$0.393341\pi$
$919$	−19.8090	+	34.3102i	−0.653439	+	1.13179i	−0.982283	+	0.187405i	$0.939992\pi$
$920$	0.279274	+	0.483717i	0.00920739	+	0.0159477i
$921$		0			0
$922$	3.99129	+	6.91311i	0.131446	+	0.227671i
$923$	32.2604	−	10.1241i	1.06186	−	0.333240i
$924$		0			0
$925$	4.72430	−	8.18272i	0.155334	−	0.269046i
$926$	26.4799			0.870185
$927$		0			0
$928$	3.71142	−	6.42837i	0.121833	−	0.211022i
$929$	18.0167	−	31.2059i	0.591109	−	1.02383i	−0.402974	−	0.915211i	$-0.632024\pi$
$929$	18.0167	−	31.2059i	0.591109	−	1.02383i	0.994083	−	0.108620i	$-0.0346430\pi$
$930$		0			0
$931$	−26.0153	−	46.9787i	−0.852616	−	1.53966i
$932$	7.24897	+	12.5556i	0.237448	+	0.411272i
$933$		0			0
$934$	3.12210	+	5.40764i	0.102158	+	0.176943i
$935$	0.770404	−	1.33438i	0.0251949	−	0.0436388i
$936$		0			0
$937$	−2.37671			−0.0776439			−0.0388219	−	0.999246i	$-0.512361\pi$
$937$	−2.37671			−0.0776439			−0.0388219	+	0.999246i	$0.512361\pi$
$938$	−0.0629324	−	0.0370876i	−0.00205481	−	0.00121095i
$939$		0			0
$940$	−4.11045	+	7.11950i	−0.134068	+	0.232213i
$941$	19.3411	−	33.4998i	0.630503	−	1.09206i	−0.356946	−	0.934125i	$-0.616182\pi$
$941$	19.3411	−	33.4998i	0.630503	−	1.09206i	0.987449	−	0.157938i	$-0.0504846\pi$
$942$		0			0
$943$	−0.838291	+	1.45196i	−0.0272985	+	0.0472824i
$944$	1.45531			0.0473662
$945$		0			0
$946$	3.68139	−	6.37635i	0.119692	−	0.207313i
$947$	14.7464			0.479194			0.239597	−	0.970872i	$-0.422985\pi$
$947$	14.7464			0.479194			0.239597	+	0.970872i	$0.422985\pi$
$948$		0			0
$949$	−26.9300	−	24.7433i	−0.874184	−	0.803201i
$950$	−13.2179	−	22.8941i	−0.428846	−	0.742783i
$951$		0			0
$952$	−1.14074	+	0.645087i	−0.0369716	+	0.0209074i
$953$	−8.54843	−	14.8063i	−0.276911	−	0.479623i	0.693705	−	0.720259i	$-0.255977\pi$
$953$	−8.54843	−	14.8063i	−0.276911	−	0.479623i	−0.970615	+	0.240636i	$0.922644\pi$
$954$		0			0
$955$	−6.58945			−0.213230
$956$	−3.15093			−0.101908
$957$		0			0
$958$	10.7862	+	18.6823i	0.348487	+	0.603598i
$959$	1.97331	−	1.11590i	0.0637214	−	0.0360344i
$960$		0			0
$961$	−17.5400	−	30.3802i	−0.565807	−	0.980006i
$962$	−2.15270	+	9.64898i	−0.0694059	+	0.311096i
$963$		0			0
$964$	−24.8446			−0.800189
$965$	−2.99933	+	5.19500i	−0.0965520	+	0.167233i
$966$		0			0
$967$	−7.90857			−0.254323			−0.127161	−	0.991882i	$-0.540587\pi$
$967$	−7.90857			−0.254323			−0.127161	+	0.991882i	$0.540587\pi$
$968$	2.38668	−	4.13385i	0.0767108	−	0.132867i
$969$		0			0
$970$	−0.635563	+	1.10083i	−0.0204067	+	0.0353454i
$971$	1.95050	−	3.37836i	0.0625944	−	0.108417i	−0.833030	−	0.553228i	$-0.813396\pi$
$971$	1.95050	−	3.37836i	0.0625944	−	0.108417i	0.895624	+	0.444811i	$0.146729\pi$
$972$		0			0
$973$	21.6489	+	12.7582i	0.694032	+	0.409010i
$974$	13.6151			0.436257
$975$		0			0
$976$	2.09967	−	3.63674i	0.0672088	−	0.116409i
$977$	−25.6949	−	44.5048i	−0.822051	−	1.42383i	−0.904152	−	0.427211i	$-0.859496\pi$
$977$	−25.6949	−	44.5048i	−0.822051	−	1.42383i	0.0821009	−	0.996624i	$-0.473837\pi$
$978$		0			0
$979$	−14.3246	−	24.8109i	−0.457815	−	0.792959i
$980$	−8.72490	−	0.155908i	−0.278707	−	0.00498030i
$981$		0			0
$982$	−6.14512	+	10.6437i	−0.196099	+	0.339653i
$983$	−7.32146	+	12.6811i	−0.233518	+	0.404465i	−0.958841	−	0.283944i	$-0.908357\pi$
$983$	−7.32146	+	12.6811i	−0.233518	+	0.404465i	0.725323	+	0.688409i	$0.241690\pi$
$984$		0			0
$985$	29.3560			0.935359
$986$	−1.83836	+	3.18413i	−0.0585452	+	0.101403i
$987$		0			0
$988$	20.3682	+	18.7143i	0.647998	+	0.595381i
$989$	−0.661018	−	1.14492i	−0.0210192	−	0.0364062i
$990$		0			0
$991$	11.2664	+	19.5140i	0.357890	+	0.619884i	0.987608	−	0.156940i	$-0.0501630\pi$
$991$	11.2664	+	19.5140i	0.357890	+	0.619884i	−0.629718	+	0.776824i	$0.716830\pi$
$992$	−4.06448	+	7.03989i	−0.129047	+	0.223517i
$993$		0			0
$994$	−21.3753	−	12.5970i	−0.677982	−	0.399551i
$995$	−7.03070	−	12.1775i	−0.222888	−	0.386054i
$996$		0			0
$997$	−24.6033			−0.779194			−0.389597	−	0.920986i	$-0.627386\pi$
$997$	−24.6033			−0.779194			−0.389597	+	0.920986i	$0.627386\pi$
$998$	−7.11789	−	12.3285i	−0.225313	−	0.390253i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.m.k.1621.2		10
3.2	odd	2		546.2.j.e.529.4	yes	10
7.2	even	3		1638.2.p.j.919.2		10
13.3	even	3		1638.2.p.j.991.2		10
21.2	odd	6		546.2.k.e.373.4	yes	10
39.29	odd	6		546.2.k.e.445.4	yes	10
91.16	even	3	inner	1638.2.m.k.289.2		10
273.107	odd	6		546.2.j.e.289.4	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.e.289.4	✓	10	273.107	odd	6
546.2.j.e.529.4	yes	10	3.2	odd	2
546.2.k.e.373.4	yes	10	21.2	odd	6
546.2.k.e.445.4	yes	10	39.29	odd	6
1638.2.m.k.289.2		10	91.16	even	3	inner
1638.2.m.k.1621.2		10	1.1	even	1	trivial
1638.2.p.j.919.2		10	7.2	even	3
1638.2.p.j.991.2		10	13.3	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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.m (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.623307 - 1.07960i) q^{5} +(2.30301 - 1.30235i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.623307 - 1.07960i) q^{5} +(2.30301 - 1.30235i) q^{7} +1.00000 q^{8} +(-0.623307 - 1.07960i) q^{10} +(-1.24766 - 2.16101i) q^{11} +(-0.785103 + 3.51904i) q^{13} +(2.30301 - 1.30235i) q^{14} +1.00000 q^{16} -0.495324 q^{17} +(3.83578 - 6.64376i) q^{19} +(-0.623307 - 1.07960i) q^{20} +(-1.24766 - 2.16101i) q^{22} -0.448052 q^{23} +(1.72298 - 2.98428i) q^{25} +(-0.785103 + 3.51904i) q^{26} +(2.30301 - 1.30235i) q^{28} +(3.71142 - 6.42837i) q^{29} +(-4.06448 + 7.03989i) q^{31} +1.00000 q^{32} -0.495324 q^{34} +(-2.84150 - 1.67457i) q^{35} +2.74194 q^{37} +(3.83578 - 6.64376i) q^{38} +(-0.623307 - 1.07960i) q^{40} +(1.87097 - 3.24061i) q^{41} +(1.47532 + 2.55532i) q^{43} +(-1.24766 - 2.16101i) q^{44} -0.448052 q^{46} +(-3.29729 - 5.71107i) q^{47} +(3.60775 - 5.99868i) q^{49} +(1.72298 - 2.98428i) q^{50} +(-0.785103 + 3.51904i) q^{52} +(-3.86750 + 6.69870i) q^{53} +(-1.55535 + 2.69395i) q^{55} +(2.30301 - 1.30235i) q^{56} +(3.71142 - 6.42837i) q^{58} +1.45531 q^{59} +(2.09967 - 3.63674i) q^{61} +(-4.06448 + 7.03989i) q^{62} +1.00000 q^{64} +(4.28851 - 1.34584i) q^{65} +(-0.0138047 - 0.0239105i) q^{67} -0.495324 q^{68} +(-2.84150 - 1.67457i) q^{70} +(-4.68884 - 8.12130i) q^{71} +(-5.07151 + 8.78412i) q^{73} +2.74194 q^{74} +(3.83578 - 6.64376i) q^{76} +(-5.68779 - 3.35195i) q^{77} +(-4.93545 - 8.54845i) q^{79} +(-0.623307 - 1.07960i) q^{80} +(1.87097 - 3.24061i) q^{82} -7.42285 q^{83} +(0.308739 + 0.534751i) q^{85} +(1.47532 + 2.55532i) q^{86} +(-1.24766 - 2.16101i) q^{88} +11.4811 q^{89} +(2.77493 + 9.12687i) q^{91} -0.448052 q^{92} +(-3.29729 - 5.71107i) q^{94} -9.56347 q^{95} +(-0.509831 - 0.883054i) q^{97} +(3.60775 - 5.99868i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 10 q^{4} + 2 q^{5} - 2 q^{7} + 10 q^{8}+O(q^{10}) \) 10 * q + 10 * q^2 + 10 * q^4 + 2 * q^5 - 2 * q^7 + 10 * q^8	\( 10 q + 10 q^{2} + 10 q^{4} + 2 q^{5} - 2 q^{7} + 10 q^{8} + 2 q^{10} - 6 q^{11} - 4 q^{13} - 2 q^{14} + 10 q^{16} + 8 q^{17} + 3 q^{19} + 2 q^{20} - 6 q^{22} + 12 q^{23} - q^{25} - 4 q^{26} - 2 q^{28} - 10 q^{31} + 10 q^{32} + 8 q^{34} - 16 q^{35} - 2 q^{37} + 3 q^{38} + 2 q^{40} + 4 q^{41} + 3 q^{43} - 6 q^{44} + 12 q^{46} + 15 q^{47} + 4 q^{49} - q^{50} - 4 q^{52} + 17 q^{53} + 3 q^{55} - 2 q^{56} + 4 q^{59} + 11 q^{61} - 10 q^{62} + 10 q^{64} + 4 q^{65} - q^{67} + 8 q^{68} - 16 q^{70} - 18 q^{71} + 12 q^{73} - 2 q^{74} + 3 q^{76} - 18 q^{77} - 4 q^{79} + 2 q^{80} + 4 q^{82} + q^{85} + 3 q^{86} - 6 q^{88} + 14 q^{89} + 26 q^{91} + 12 q^{92} + 15 q^{94} + 48 q^{95} - 6 q^{97} + 4 q^{98}+O(q^{100}) \) 10 * q + 10 * q^2 + 10 * q^4 + 2 * q^5 - 2 * q^7 + 10 * q^8 + 2 * q^10 - 6 * q^11 - 4 * q^13 - 2 * q^14 + 10 * q^16 + 8 * q^17 + 3 * q^19 + 2 * q^20 - 6 * q^22 + 12 * q^23 - q^25 - 4 * q^26 - 2 * q^28 - 10 * q^31 + 10 * q^32 + 8 * q^34 - 16 * q^35 - 2 * q^37 + 3 * q^38 + 2 * q^40 + 4 * q^41 + 3 * q^43 - 6 * q^44 + 12 * q^46 + 15 * q^47 + 4 * q^49 - q^50 - 4 * q^52 + 17 * q^53 + 3 * q^55 - 2 * q^56 + 4 * q^59 + 11 * q^61 - 10 * q^62 + 10 * q^64 + 4 * q^65 - q^67 + 8 * q^68 - 16 * q^70 - 18 * q^71 + 12 * q^73 - 2 * q^74 + 3 * q^76 - 18 * q^77 - 4 * q^79 + 2 * q^80 + 4 * q^82 + q^85 + 3 * q^86 - 6 * q^88 + 14 * q^89 + 26 * q^91 + 12 * q^92 + 15 * q^94 + 48 * q^95 - 6 * q^97 + 4 * q^98

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