LMFDB - Embedded newform 392.3.g.j.99.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(99,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("392.99");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.g (of order $2$, degree $1$, 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:	$10.6812263629$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.15582448.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 13x^{4} - 21x^{3} + 20x^{2} - 10x + 2 $ x^6 - 3x^5 + 13x^4 - 21x^3 + 20x^2 - 10*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.3
Root			$0.500000 - 0.759064i$ of defining polynomial
Character	$\chi$	$=$	392.99
Dual form			392.3.g.j.99.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.789608 - 1.83753i) q^{2} +5.33225 q^{3} +(-2.75304 + 2.90186i) q^{4} +2.15693i q^{5} +(-4.21039 - 9.79818i) q^{6} +(7.50608 + 2.76746i) q^{8} +19.4329 q^{9} +O(q^{10})$	\(q+(-0.789608 - 1.83753i) q^{2} +5.33225 q^{3} +(-2.75304 + 2.90186i) q^{4} +2.15693i q^{5} +(-4.21039 - 9.79818i) q^{6} +(7.50608 + 2.76746i) q^{8} +19.4329 q^{9} +(3.96343 - 1.70313i) q^{10} +5.25911 q^{11} +(-14.6799 + 15.4734i) q^{12} +21.4116i q^{13} +11.5013i q^{15} +(-0.841567 - 15.9779i) q^{16} +0.926859 q^{17} +(-15.3444 - 35.7086i) q^{18} -5.93010 q^{19} +(-6.25911 - 5.93812i) q^{20} +(-4.15264 - 9.66378i) q^{22} +8.68920i q^{23} +(40.0243 + 14.7568i) q^{24} +20.3476 q^{25} +(39.3444 - 16.9067i) q^{26} +55.6311 q^{27} -9.42223i q^{29} +(21.1340 - 9.08153i) q^{30} -34.5039i q^{31} +(-28.6953 + 14.1626i) q^{32} +28.0429 q^{33} +(-0.731855 - 1.70313i) q^{34} +(-53.4996 + 56.3916i) q^{36} -12.8002i q^{37} +(4.68245 + 10.8967i) q^{38} +114.172i q^{39} +(-5.96922 + 16.1901i) q^{40} +43.1339 q^{41} -41.7382 q^{43} +(-14.4785 + 15.2612i) q^{44} +41.9155i q^{45} +(15.9667 - 6.86106i) q^{46} +45.9983i q^{47} +(-4.48745 - 85.1980i) q^{48} +(-16.0667 - 37.3894i) q^{50} +4.94225 q^{51} +(-62.1333 - 58.9468i) q^{52} -74.4818i q^{53} +(-43.9267 - 102.224i) q^{54} +11.3436i q^{55} -31.6208 q^{57} +(-17.3136 + 7.43987i) q^{58} +53.6734 q^{59} +(-33.3752 - 31.6635i) q^{60} -27.8160i q^{61} +(-63.4020 + 27.2446i) q^{62} +(48.6823 + 41.5455i) q^{64} -46.1833 q^{65} +(-22.1429 - 51.5297i) q^{66} -78.4907 q^{67} +(-2.55168 + 2.68961i) q^{68} +46.3330i q^{69} -74.5100i q^{71} +(145.865 + 53.7799i) q^{72} +33.6041 q^{73} +(-23.5208 + 10.1072i) q^{74} +108.499 q^{75} +(16.3258 - 17.2083i) q^{76} +(209.794 - 90.1511i) q^{78} -30.2118i q^{79} +(34.4631 - 1.81520i) q^{80} +121.743 q^{81} +(-34.0589 - 79.2599i) q^{82} -72.9274 q^{83} +1.99917i q^{85} +(32.9568 + 76.6952i) q^{86} -50.2417i q^{87} +(39.4753 + 14.5544i) q^{88} -54.8396 q^{89} +(77.0211 - 33.0968i) q^{90} +(-25.2148 - 23.9217i) q^{92} -183.984i q^{93} +(84.5232 - 36.3206i) q^{94} -12.7908i q^{95} +(-153.011 + 75.5188i) q^{96} -53.7125 q^{97} +102.200 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} + 6 q^{3} + 4 q^{4} - 28 q^{6} + 4 q^{8} + 40 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 + 6 * q^3 + 4 * q^4 - 28 * q^6 + 4 * q^8 + 40 * q^9	$ 6 q - 2 q^{2} + 6 q^{3} + 4 q^{4} - 28 q^{6} + 4 q^{8} + 40 q^{9} + 6 q^{10} - 30 q^{11} - 32 q^{12} - 16 q^{16} - 30 q^{17} + 16 q^{18} - 78 q^{19} + 24 q^{20} + 12 q^{22} + 76 q^{24} + 92 q^{25} + 128 q^{26} + 78 q^{27} + 16 q^{30} - 112 q^{32} + 78 q^{33} + 38 q^{34} - 124 q^{36} - 80 q^{38} - 44 q^{40} - 116 q^{41} - 100 q^{43} - 132 q^{44} + 156 q^{46} + 88 q^{48} + 24 q^{50} - 10 q^{51} - 132 q^{52} + 36 q^{54} + 166 q^{57} - 4 q^{58} + 110 q^{59} - 84 q^{60} - 48 q^{62} - 80 q^{64} + 32 q^{65} + 138 q^{66} - 434 q^{67} - 96 q^{68} + 328 q^{72} - 102 q^{73} + 34 q^{74} + 60 q^{75} - 84 q^{76} + 360 q^{78} + 256 q^{80} + 82 q^{81} + 24 q^{82} - 268 q^{83} - 240 q^{86} + 204 q^{88} - 214 q^{89} + 220 q^{90} + 80 q^{92} + 16 q^{94} - 48 q^{96} - 76 q^{97} + 252 q^{99}+O(q^{100}) $ 6 * q - 2 * q^2 + 6 * q^3 + 4 * q^4 - 28 * q^6 + 4 * q^8 + 40 * q^9 + 6 * q^10 - 30 * q^11 - 32 * q^12 - 16 * q^16 - 30 * q^17 + 16 * q^18 - 78 * q^19 + 24 * q^20 + 12 * q^22 + 76 * q^24 + 92 * q^25 + 128 * q^26 + 78 * q^27 + 16 * q^30 - 112 * q^32 + 78 * q^33 + 38 * q^34 - 124 * q^36 - 80 * q^38 - 44 * q^40 - 116 * q^41 - 100 * q^43 - 132 * q^44 + 156 * q^46 + 88 * q^48 + 24 * q^50 - 10 * q^51 - 132 * q^52 + 36 * q^54 + 166 * q^57 - 4 * q^58 + 110 * q^59 - 84 * q^60 - 48 * q^62 - 80 * q^64 + 32 * q^65 + 138 * q^66 - 434 * q^67 - 96 * q^68 + 328 * q^72 - 102 * q^73 + 34 * q^74 + 60 * q^75 - 84 * q^76 + 360 * q^78 + 256 * q^80 + 82 * q^81 + 24 * q^82 - 268 * q^83 - 240 * q^86 + 204 * q^88 - 214 * q^89 + 220 * q^90 + 80 * q^92 + 16 * q^94 - 48 * q^96 - 76 * q^97 + 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−0.789608	−	1.83753i	−0.394804	−	0.918765i
$2$	−0.789608	−	1.83753i	−0.394804	−	0.918765i
$3$	5.33225			1.77742			0.888709	−	0.458472i	$-0.151603\pi$
$3$	5.33225			1.77742			0.888709	+	0.458472i	$0.151603\pi$
$4$	−2.75304	+	2.90186i	−0.688259	+	0.725465i
$5$			2.15693i			0.431386i	0.976461	+	0.215693i	$0.0692011\pi$
$5$			2.15693i			0.431386i	−0.976461	+	0.215693i	$0.930799\pi$
$6$	−4.21039	−	9.79818i	−0.701732	−	1.63303i
$7$		0			0
$7$		0			0
$8$	7.50608	+	2.76746i	0.938259	+	0.345932i
$9$	19.4329			2.15921
$10$	3.96343	−	1.70313i	0.396343	−	0.170313i
$11$	5.25911			0.478101			0.239051	−	0.971007i	$-0.423164\pi$
$11$	5.25911			0.478101			0.239051	+	0.971007i	$0.423164\pi$
$12$	−14.6799	+	15.4734i	−1.22332	+	1.28945i
$13$			21.4116i			1.64704i	0.567285	+	0.823522i	$0.307994\pi$
$13$			21.4116i			1.64704i	−0.567285	+	0.823522i	$0.692006\pi$
$14$		0			0
$15$			11.5013i			0.766754i
$16$	−0.841567	−	15.9779i	−0.0525979	−	0.998616i
$17$	0.926859			0.0545211			0.0272606	−	0.999628i	$-0.491322\pi$
$17$	0.926859			0.0545211			0.0272606	+	0.999628i	$0.491322\pi$
$18$	−15.3444	−	35.7086i	−0.852467	−	1.98381i
$19$	−5.93010			−0.312110			−0.156055	−	0.987748i	$-0.549878\pi$
$19$	−5.93010			−0.312110			−0.156055	+	0.987748i	$0.549878\pi$
$20$	−6.25911	−	5.93812i	−0.312956	−	0.296906i
$21$		0			0
$22$	−4.15264	−	9.66378i	−0.188756	−	0.439263i
$23$			8.68920i			0.377791i	0.981997	+	0.188896i	$0.0604908\pi$
$23$			8.68920i			0.377791i	−0.981997	+	0.188896i	$0.939509\pi$
$24$	40.0243	+	14.7568i	1.66768	+	0.614867i
$25$	20.3476			0.813906
$26$	39.3444	−	16.9067i	1.51325	−	0.650260i
$27$	55.6311			2.06041
$28$		0			0
$29$		−	9.42223i		−	0.324904i	−0.986716	−	0.162452i	$-0.948060\pi$
$29$		−	9.42223i		−	0.324904i	0.986716	−	0.162452i	$-0.0519403\pi$
$30$	21.1340	−	9.08153i	0.704467	−	0.302718i
$31$		−	34.5039i		−	1.11303i	−0.830837	−	0.556515i	$-0.812138\pi$
$31$		−	34.5039i		−	1.11303i	0.830837	−	0.556515i	$-0.187862\pi$
$32$	−28.6953	+	14.1626i	−0.896728	+	0.442583i
$33$	28.0429			0.849786
$34$	−0.731855	−	1.70313i	−0.0215252	−	0.0500921i
$35$		0			0
$36$	−53.4996	+	56.3916i	−1.48610	+	1.56643i
$37$		−	12.8002i		−	0.345952i	−0.984926	−	0.172976i	$-0.944662\pi$
$37$		−	12.8002i		−	0.345952i	0.984926	−	0.172976i	$-0.0553383\pi$
$38$	4.68245	+	10.8967i	0.123222	+	0.286756i
$39$			114.172i			2.92748i
$40$	−5.96922	+	16.1901i	−0.149231	+	0.404752i
$41$	43.1339			1.05205			0.526023	−	0.850470i	$-0.323683\pi$
$41$	43.1339			1.05205			0.526023	+	0.850470i	$0.323683\pi$
$42$		0			0
$43$	−41.7382			−0.970656			−0.485328	−	0.874332i	$-0.661300\pi$
$43$	−41.7382			−0.970656			−0.485328	+	0.874332i	$0.661300\pi$
$44$	−14.4785	+	15.2612i	−0.329058	+	0.346846i
$45$			41.9155i			0.931456i
$46$	15.9667	−	6.86106i	0.347101	−	0.149154i
$47$			45.9983i			0.978686i	0.872091	+	0.489343i	$0.162763\pi$
$47$			45.9983i			0.978686i	−0.872091	+	0.489343i	$0.837237\pi$
$48$	−4.48745	−	85.1980i	−0.0934885	−	1.77496i
$49$		0			0
$50$	−16.0667	−	37.3894i	−0.321333	−	0.747788i
$51$	4.94225			0.0969068
$52$	−62.1333	−	58.9468i	−1.19487	−	1.13359i
$53$		−	74.4818i		−	1.40532i	−0.711528	−	0.702658i	$-0.751996\pi$
$53$		−	74.4818i		−	1.40532i	0.711528	−	0.702658i	$-0.248004\pi$
$54$	−43.9267	−	102.224i	−0.813458	−	1.89303i
$55$			11.3436i			0.206246i
$56$		0			0
$57$	−31.6208			−0.554751
$58$	−17.3136	+	7.43987i	−0.298511	+	0.128274i
$59$	53.6734			0.909719			0.454860	−	0.890563i	$-0.349689\pi$
$59$	53.6734			0.909719			0.454860	+	0.890563i	$0.349689\pi$
$60$	−33.3752	−	31.6635i	−0.556253	−	0.527726i
$61$		−	27.8160i		−	0.456000i	−0.973661	−	0.228000i	$-0.926781\pi$
$61$		−	27.8160i		−	0.456000i	0.973661	−	0.228000i	$-0.0732186\pi$
$62$	−63.4020	+	27.2446i	−1.02261	+	0.439429i
$63$		0			0
$64$	48.6823	+	41.5455i	0.760661	+	0.649149i
$65$	−46.1833			−0.710512
$66$	−22.1429	−	51.5297i	−0.335499	−	0.780754i
$67$	−78.4907			−1.17150			−0.585751	−	0.810491i	$-0.699201\pi$
$67$	−78.4907			−1.17150			−0.585751	+	0.810491i	$0.699201\pi$
$68$	−2.55168	+	2.68961i	−0.0375247	+	0.0395531i
$69$			46.3330i			0.671493i
$70$		0			0
$71$		−	74.5100i		−	1.04944i	−0.851276	−	0.524719i	$-0.824171\pi$
$71$		−	74.5100i		−	1.04944i	0.851276	−	0.524719i	$-0.175829\pi$
$72$	145.865	+	53.7799i	2.02590	+	0.746943i
$73$	33.6041			0.460330			0.230165	−	0.973152i	$-0.426073\pi$
$73$	33.6041			0.460330			0.230165	+	0.973152i	$0.426073\pi$
$74$	−23.5208	+	10.1072i	−0.317848	+	0.136583i
$75$	108.499			1.44665
$76$	16.3258	−	17.2083i	0.214813	−	0.226425i
$77$		0			0
$78$	209.794	−	90.1511i	2.68967	−	1.15578i
$79$		−	30.2118i		−	0.382428i	−0.981548	−	0.191214i	$-0.938758\pi$
$79$		−	30.2118i		−	0.382428i	0.981548	−	0.191214i	$-0.0612424\pi$
$80$	34.4631	−	1.81520i	0.430789	−	0.0226900i
$81$	121.743			1.50299
$82$	−34.0589	−	79.2599i	−0.415352	−	0.966584i
$83$	−72.9274			−0.878644			−0.439322	−	0.898330i	$-0.644781\pi$
$83$	−72.9274			−0.878644			−0.439322	+	0.898330i	$0.644781\pi$
$84$		0			0
$85$			1.99917i			0.0235197i
$86$	32.9568	+	76.6952i	0.383219	+	0.891805i
$87$		−	50.2417i		−	0.577491i
$88$	39.4753	+	14.5544i	0.448583	+	0.165391i
$89$	−54.8396			−0.616176			−0.308088	−	0.951358i	$-0.599689\pi$
$89$	−54.8396			−0.616176			−0.308088	+	0.951358i	$0.599689\pi$
$90$	77.0211	−	33.0968i	0.855790	−	0.367743i
$91$		0			0
$92$	−25.2148	−	23.9217i	−0.274074	−	0.260018i
$93$		−	183.984i		−	1.97832i
$94$	84.5232	−	36.3206i	0.899183	−	0.386389i
$95$		−	12.7908i		−	0.134640i
$96$	−153.011	+	75.5188i	−1.59386	+	0.786655i
$97$	−53.7125			−0.553738			−0.276869	−	0.960908i	$-0.589297\pi$
$97$	−53.7125			−0.553738			−0.276869	+	0.960908i	$0.589297\pi$
$98$		0			0
$99$	102.200			1.03232
$100$	−56.0178	+	59.0460i	−0.560178	+	0.590460i
$101$			90.3019i			0.894078i	0.894515	+	0.447039i	$0.147521\pi$
$101$			90.3019i			0.894078i	−0.894515	+	0.447039i	$0.852479\pi$
$102$	−3.90244	−	9.08153i	−0.0382592	−	0.0890346i
$103$		−	112.812i		−	1.09526i	−0.836720	−	0.547631i	$-0.815530\pi$
$103$		−	112.812i		−	1.09526i	0.836720	−	0.547631i	$-0.184470\pi$
$104$	−59.2556	+	160.717i	−0.569766	+	1.54535i
$105$		0			0
$106$	−136.863	+	58.8114i	−1.29116	+	0.554825i
$107$	−143.990			−1.34570			−0.672851	−	0.739778i	$-0.734930\pi$
$107$	−143.990			−1.34570			−0.672851	+	0.739778i	$0.734930\pi$
$108$	−153.154	+	161.433i	−1.41810	+	1.49475i
$109$			66.6813i			0.611755i	0.952071	+	0.305877i	$0.0989498\pi$
$109$			66.6813i			0.611755i	−0.952071	+	0.305877i	$0.901050\pi$
$110$	20.8441	−	8.95696i	0.189492	−	0.0814269i
$111$		−	68.2540i		−	0.614901i
$112$		0			0
$113$	7.16467			0.0634042			0.0317021	−	0.999497i	$-0.489907\pi$
$113$	7.16467			0.0634042			0.0317021	+	0.999497i	$0.489907\pi$
$114$	24.9680	+	58.1042i	0.219018	+	0.509686i
$115$	−18.7420			−0.162974
$116$	27.3420	+	25.9397i	0.235707	+	0.223618i
$117$			416.090i			3.55632i
$118$	−42.3810	−	98.6266i	−0.359161	−	0.835818i
$119$		0			0
$120$	−31.8294	+	86.3297i	−0.265245	+	0.719414i
$121$	−93.3417			−0.771419
$122$	−51.1127	+	21.9637i	−0.418957	+	0.180031i
$123$	230.001			1.86993
$124$	100.126	+	94.9906i	0.807464	+	0.766054i
$125$			97.8118i			0.782494i
$126$		0			0
$127$		−	131.492i		−	1.03537i	−0.855572	−	0.517684i	$-0.826794\pi$
$127$		−	131.492i		−	1.03537i	0.855572	−	0.517684i	$-0.173206\pi$
$128$	37.9012	−	122.260i	0.296103	−	0.955156i
$129$	−222.559			−1.72526
$130$	36.4667	+	84.8632i	0.280513	+	0.652794i
$131$	−8.76120			−0.0668794			−0.0334397	−	0.999441i	$-0.510646\pi$
$131$	−8.76120			−0.0668794			−0.0334397	+	0.999441i	$0.510646\pi$
$132$	−77.2032	+	81.3766i	−0.584873	+	0.616489i
$133$		0			0
$134$	61.9769	+	144.229i	0.462514	+	1.07634i
$135$			119.992i			0.888833i
$136$	6.95707	+	2.56504i	0.0511549	+	0.0188606i
$137$	−236.841			−1.72876			−0.864381	−	0.502837i	$-0.832290\pi$
$137$	−236.841			−1.72876			−0.864381	+	0.502837i	$0.832290\pi$
$138$	85.1383	−	36.5849i	0.616944	−	0.265108i
$139$	172.122			1.23828			0.619142	−	0.785279i	$-0.287480\pi$
$139$	172.122			1.23828			0.619142	+	0.785279i	$0.287480\pi$
$140$		0			0
$141$			245.274i			1.73954i
$142$	−136.914	+	58.8337i	−0.964186	+	0.414322i
$143$			112.606i			0.787453i
$144$	−16.3541	−	310.497i	−0.113570	−	2.15623i
$145$	20.3231			0.140159
$146$	−26.5341	−	61.7485i	−0.181740	−	0.422935i
$147$		0			0
$148$	37.1444	+	35.2395i	0.250976	+	0.238105i
$149$			230.707i			1.54837i	0.632959	+	0.774186i	$0.281840\pi$
$149$			230.707i			1.54837i	−0.632959	+	0.774186i	$0.718160\pi$
$150$	−85.6715	−	199.370i	−0.571144	−	1.32913i
$151$		−	147.890i		−	0.979406i	−0.871889	−	0.489703i	$-0.837105\pi$
$151$		−	147.890i		−	0.979406i	0.871889	−	0.489703i	$-0.162895\pi$
$152$	−44.5118	−	16.4113i	−0.292840	−	0.107969i
$153$	18.0116			0.117723
$154$		0			0
$155$	74.4227			0.480146
$156$	−331.311	−	314.320i	−2.12379	−	2.01487i
$157$			114.829i			0.731396i	0.930734	+	0.365698i	$0.119170\pi$
$157$			114.829i			0.731396i	−0.930734	+	0.365698i	$0.880830\pi$
$158$	−55.5151	+	23.8555i	−0.351361	+	0.150984i
$159$		−	397.156i		−	2.49783i
$160$	−30.5479	−	61.8938i	−0.190924	−	0.386836i
$161$		0			0
$162$	−96.1289	−	223.706i	−0.593388	−	1.38090i
$163$	49.3091			0.302510			0.151255	−	0.988495i	$-0.451669\pi$
$163$	49.3091			0.302510			0.151255	+	0.988495i	$0.451669\pi$
$164$	−118.749	+	125.168i	−0.724081	+	0.763222i
$165$			60.4867i			0.366586i
$166$	57.5841	+	134.006i	0.346892	+	0.807267i
$167$			241.457i			1.44585i	0.690926	+	0.722926i	$0.257203\pi$
$167$			241.457i			1.44585i	−0.690926	+	0.722926i	$0.742797\pi$
$168$		0			0
$169$	−289.455			−1.71275
$170$	3.67354	−	1.57856i	0.0216091	−	0.00928566i
$171$	−115.239			−0.673913
$172$	114.907	−	121.118i	0.668063	−	0.704177i
$173$			54.4211i			0.314573i	0.987553	+	0.157286i	$0.0502746\pi$
$173$			54.4211i			0.314573i	−0.987553	+	0.157286i	$0.949725\pi$
$174$	−92.3207	+	39.6713i	−0.530579	+	0.227996i
$175$		0			0
$176$	−4.42590	−	84.0293i	−0.0251471	−	0.477439i
$177$	286.200			1.61695
$178$	43.3018	+	100.770i	0.243269	+	0.566121i
$179$	−127.020			−0.709609			−0.354805	−	0.934940i	$-0.615453\pi$
$179$	−127.020			−0.709609			−0.354805	+	0.934940i	$0.615453\pi$
$180$	−121.633	−	115.395i	−0.675739	−	0.641083i
$181$		−	212.704i		−	1.17516i	−0.809165	−	0.587581i	$-0.800080\pi$
$181$		−	212.704i		−	1.17516i	0.809165	−	0.587581i	$-0.199920\pi$
$182$		0			0
$183$		−	148.322i		−	0.810502i
$184$	−24.0470	+	65.2218i	−0.130690	+	0.354466i
$185$	27.6092			0.149239
$186$	−338.076	+	145.275i	−1.81761	+	0.781049i
$187$	4.87446			0.0260666
$188$	−133.480	−	126.635i	−0.710002	−	0.673590i
$189$		0			0
$190$	−23.5035	+	10.0997i	−0.123703	+	0.0531565i
$191$			40.5347i			0.212224i	0.994354	+	0.106112i	$0.0338402\pi$
$191$			40.5347i			0.212224i	−0.994354	+	0.106112i	$0.966160\pi$
$192$	259.587	+	221.531i	1.35201	+	1.15381i
$193$	282.307			1.46273			0.731364	−	0.681987i	$-0.238884\pi$
$193$	282.307			1.46273			0.731364	+	0.681987i	$0.238884\pi$
$194$	42.4119	+	98.6985i	0.218618	+	0.508755i
$195$	−246.261			−1.26288
$196$		0			0
$197$			261.806i			1.32896i	0.747304	+	0.664482i	$0.231348\pi$
$197$			261.806i			1.32896i	−0.747304	+	0.664482i	$0.768652\pi$
$198$	−80.6980	−	187.796i	−0.407565	−	0.948463i
$199$		−	322.124i		−	1.61871i	−0.587317	−	0.809357i	$-0.699816\pi$
$199$		−	322.124i		−	1.61871i	0.587317	−	0.809357i	$-0.300184\pi$
$200$	152.731	+	56.3113i	0.763655	+	0.281556i
$201$	−418.532			−2.08225
$202$	165.932	−	71.3031i	0.821448	−	0.352986i
$203$		0			0
$204$	−13.6062	+	14.3417i	−0.0666970	+	0.0703025i
$205$			93.0369i			0.453839i
$206$	−207.295	+	89.0773i	−1.00629	+	0.432414i
$207$			168.857i			0.815732i
$208$	342.111	−	18.0193i	1.64476	−	0.0866311i
$209$	−31.1870			−0.149220
$210$		0			0
$211$	169.792			0.804702			0.402351	−	0.915485i	$-0.368193\pi$
$211$	169.792			0.804702			0.402351	+	0.915485i	$0.368193\pi$
$212$	216.136	+	205.051i	1.01951	+	0.967222i
$213$		−	397.306i		−	1.86529i
$214$	113.696	+	264.586i	0.531288	+	1.23638i
$215$		−	90.0265i		−	0.418728i
$216$	417.571	+	153.957i	1.93320	+	0.712763i
$217$		0			0
$218$	122.529	−	52.6521i	0.562059	−	0.241523i
$219$	179.185			0.818199
$220$	−32.9174	−	31.2292i	−0.149624	−	0.141951i
$221$			19.8455i			0.0897986i
$222$	−125.419	+	53.8939i	−0.564950	+	0.242765i
$223$		−	45.4626i		−	0.203868i	−0.994791	−	0.101934i	$-0.967497\pi$
$223$		−	45.4626i		−	0.203868i	0.994791	−	0.101934i	$-0.0325031\pi$
$224$		0			0
$225$	395.414			1.75740
$226$	−5.65728	−	13.1653i	−0.0250322	−	0.0582536i
$227$	185.131			0.815554			0.407777	−	0.913082i	$-0.366304\pi$
$227$	185.131			0.815554			0.407777	+	0.913082i	$0.366304\pi$
$228$	87.0532	−	91.7590i	0.381812	−	0.402452i
$229$		−	184.952i		−	0.807650i	−0.914836	−	0.403825i	$-0.867680\pi$
$229$		−	184.952i		−	0.807650i	0.914836	−	0.403825i	$-0.132320\pi$
$230$	14.7988	+	34.4390i	0.0643428	+	0.149735i
$231$		0			0
$232$	26.0756	−	70.7239i	0.112395	−	0.304845i
$233$	96.7007			0.415025			0.207512	−	0.978232i	$-0.433463\pi$
$233$	96.7007			0.415025			0.207512	+	0.978232i	$0.433463\pi$
$234$	764.577	−	328.548i	3.26742	−	1.40405i
$235$	−99.2151			−0.422192
$236$	−147.765	+	155.753i	−0.626123	+	0.659969i
$237$		−	161.097i		−	0.679734i
$238$		0			0
$239$		−	163.185i		−	0.682782i	−0.939921	−	0.341391i	$-0.889102\pi$
$239$		−	163.185i		−	0.682782i	0.939921	−	0.341391i	$-0.110898\pi$
$240$	183.766	−	9.67913i	0.765693	−	0.0403297i
$241$	205.491			0.852659			0.426330	−	0.904568i	$-0.359806\pi$
$241$	205.491			0.852659			0.426330	+	0.904568i	$0.359806\pi$
$242$	73.7034	+	171.518i	0.304559	+	0.708753i
$243$	148.483			0.611039
$244$	80.7180	+	76.5784i	0.330812	+	0.313846i
$245$		0			0
$246$	−181.611	−	422.634i	−0.738254	−	1.71802i
$247$		−	126.973i		−	0.514059i
$248$	95.4882	−	258.989i	0.385033	−	1.04431i
$249$	−388.868			−1.56172
$250$	179.732	−	77.2330i	0.718929	−	0.308932i
$251$	−159.299			−0.634658			−0.317329	−	0.948316i	$-0.602786\pi$
$251$	−159.299			−0.634658			−0.317329	+	0.948316i	$0.602786\pi$
$252$		0			0
$253$			45.6975i			0.180622i
$254$	−241.620	+	103.827i	−0.951260	+	0.408767i
$255$			10.6601i			0.0418043i
$256$	−254.584	+	26.8929i	−0.994467	+	0.105050i
$257$	215.777			0.839599			0.419800	−	0.907617i	$-0.362100\pi$
$257$	215.777			0.839599			0.419800	+	0.907617i	$0.362100\pi$
$258$	175.734	+	408.959i	0.681140	+	1.58511i
$259$		0			0
$260$	127.144	−	134.017i	0.489017	−	0.515452i
$261$		−	183.101i		−	0.701538i
$262$	6.91792	+	16.0990i	0.0264043	+	0.0614465i
$263$		−	329.157i		−	1.25155i	−0.780004	−	0.625775i	$-0.784783\pi$
$263$		−	329.157i		−	1.25155i	0.780004	−	0.625775i	$-0.215217\pi$
$264$	210.492	+	77.6077i	0.797319	+	0.293968i
$265$	160.652			0.606234
$266$		0			0
$267$	−292.419			−1.09520
$268$	216.088	−	227.769i	0.806298	−	0.849884i
$269$			293.067i			1.08947i	0.838609	+	0.544734i	$0.183369\pi$
$269$			293.067i			1.08947i	−0.838609	+	0.544734i	$0.816631\pi$
$270$	220.490	−	94.7470i	0.816629	−	0.350915i
$271$		−	26.8502i		−	0.0990782i	−0.998772	−	0.0495391i	$-0.984225\pi$
$271$		−	26.8502i		−	0.0990782i	0.998772	−	0.0495391i	$-0.0157752\pi$
$272$	−0.780014	−	14.8092i	−0.00286770	−	0.0544456i
$273$		0			0
$274$	187.011	+	435.202i	0.682523	+	1.58833i
$275$	107.011			0.389129
$276$	−134.452	−	127.557i	−0.487144	−	0.462161i
$277$		−	334.777i		−	1.20858i	−0.796764	−	0.604291i	$-0.793457\pi$
$277$		−	334.777i		−	1.20858i	0.796764	−	0.604291i	$-0.206543\pi$
$278$	−135.909	−	316.279i	−0.488880	−	1.13769i
$279$		−	670.513i		−	2.40327i
$280$		0			0
$281$	−123.357			−0.438994			−0.219497	−	0.975613i	$-0.570442\pi$
$281$	−123.357			−0.438994			−0.219497	+	0.975613i	$0.570442\pi$
$282$	450.699	−	193.671i	1.59822	−	0.686776i
$283$	−0.618906			−0.00218695			−0.00109347	−	0.999999i	$-0.500348\pi$
$283$	−0.618906			−0.00218695			−0.00109347	+	0.999999i	$0.500348\pi$
$284$	216.218	+	205.129i	0.761330	+	0.722285i
$285$		−	68.2039i		−	0.239312i
$286$	206.917	−	88.9145i	0.723485	−	0.310890i
$287$		0			0
$288$	−557.634	+	275.222i	−1.93623	+	0.955631i
$289$	−288.141			−0.997027
$290$	−16.0473	−	37.3443i	−0.0553355	−	0.128774i
$291$	−286.409			−0.984223
$292$	−92.5133	+	97.5143i	−0.316826	+	0.333953i
$293$		−	28.2794i		−	0.0965169i	−0.998835	−	0.0482584i	$-0.984633\pi$
$293$		−	28.2794i		−	0.0965169i	0.998835	−	0.0482584i	$-0.0153671\pi$
$294$		0			0
$295$			115.770i			0.392440i
$296$	35.4241	−	96.0794i	0.119676	−	0.324592i
$297$	292.570			0.985084
$298$	423.932	−	182.168i	1.42259	−	0.611303i
$299$	−186.049			−0.622239
$300$	−298.701	+	314.848i	−0.995671	+	1.04949i
$301$		0			0
$302$	−271.753	+	116.775i	−0.899844	+	0.386674i
$303$			481.512i			1.58915i
$304$	4.99057	+	94.7502i	0.0164164	+	0.311678i
$305$	59.9972			0.196712
$306$	−14.2221	−	33.0968i	−0.0464774	−	0.108160i
$307$	400.893			1.30584			0.652921	−	0.757426i	$-0.273543\pi$
$307$	400.893			1.30584			0.652921	+	0.757426i	$0.273543\pi$
$308$		0			0
$309$		−	601.542i		−	1.94674i
$310$	−58.7647	−	136.754i	−0.189564	−	0.441142i
$311$			162.226i			0.521628i	0.965389	+	0.260814i	$0.0839910\pi$
$311$			162.226i			0.521628i	−0.965389	+	0.260814i	$0.916009\pi$
$312$	−315.966	+	856.983i	−1.01271	+	2.74674i
$313$	−266.246			−0.850626			−0.425313	−	0.905046i	$-0.639836\pi$
$313$	−266.246			−0.850626			−0.425313	+	0.905046i	$0.639836\pi$
$314$	211.002	−	90.6700i	0.671981	−	0.288758i
$315$		0			0
$316$	87.6704	+	83.1742i	0.277438	+	0.263210i
$317$		−	432.855i		−	1.36547i	−0.730664	−	0.682737i	$-0.760789\pi$
$317$		−	432.855i		−	1.36547i	0.730664	−	0.682737i	$-0.239211\pi$
$318$	−729.786	+	313.597i	−2.29492	+	0.986155i
$319$		−	49.5525i		−	0.155337i
$320$	−89.6109	+	105.005i	−0.280034	+	0.328139i
$321$	−767.792			−2.39187
$322$		0			0
$323$	−5.49636			−0.0170166
$324$	−335.162	+	353.280i	−1.03445	+	1.09037i
$325$			435.675i			1.34054i
$326$	−38.9349	−	90.6069i	−0.119432	−	0.277935i
$327$			355.562i			1.08734i
$328$	323.766	+	119.371i	0.987092	+	0.363937i
$329$		0			0
$330$	111.146	−	47.7608i	0.336807	−	0.144730i
$331$	81.2529			0.245477			0.122738	−	0.992439i	$-0.460832\pi$
$331$	81.2529			0.245477			0.122738	+	0.992439i	$0.460832\pi$
$332$	200.772	−	211.625i	0.604735	−	0.637425i
$333$		−	248.746i		−	0.746984i
$334$	443.685	−	190.657i	1.32840	−	0.570828i
$335$		−	169.299i		−	0.505370i
$336$		0			0
$337$	−69.4941			−0.206214			−0.103107	−	0.994670i	$-0.532878\pi$
$337$	−69.4941			−0.206214			−0.103107	+	0.994670i	$0.532878\pi$
$338$	228.556	+	531.883i	0.676202	+	1.57362i
$339$	38.2038			0.112696
$340$	−5.80131	−	5.50380i	−0.0170627	−	0.0161876i
$341$		−	181.460i		−	0.532141i
$342$	90.9938	+	211.756i	0.266064	+	0.619168i
$343$		0			0
$344$	−313.290	−	115.509i	−0.910727	−	0.335781i
$345$	−99.9372			−0.289673
$346$	100.000	−	42.9713i	0.289018	−	0.124195i
$347$	−349.353			−1.00678			−0.503391	−	0.864059i	$-0.667915\pi$
$347$	−349.353			−1.00678			−0.503391	+	0.864059i	$0.667915\pi$
$348$	145.794	+	138.317i	0.418949	+	0.397463i
$349$			165.836i			0.475174i	0.971366	+	0.237587i	$0.0763566\pi$
$349$			165.836i			0.475174i	−0.971366	+	0.237587i	$0.923643\pi$
$350$		0			0
$351$			1191.15i			3.39358i
$352$	−150.912	+	74.4830i	−0.428727	+	0.211599i
$353$	−471.717			−1.33631			−0.668154	−	0.744023i	$-0.732915\pi$
$353$	−471.717			−1.33631			−0.668154	+	0.744023i	$0.732915\pi$
$354$	−225.986	−	525.902i	−0.638379	−	1.48560i
$355$	160.713			0.452713
$356$	150.976	−	159.137i	0.424089	−	0.447014i
$357$		0			0
$358$	100.296	+	233.403i	0.280157	+	0.651964i
$359$		−	656.986i		−	1.83004i	−0.403403	−	0.915022i	$-0.632173\pi$
$359$		−	656.986i		−	1.83004i	0.403403	−	0.915022i	$-0.367827\pi$
$360$	−116.000	+	314.621i	−0.322221	+	0.873947i
$361$	−325.834			−0.902587
$362$	−390.851	+	167.953i	−1.07970	+	0.463959i
$363$	−497.722			−1.37113
$364$		0			0
$365$			72.4817i			0.198580i
$366$	−272.546	+	117.116i	−0.744661	+	0.319990i
$367$		−	355.475i		−	0.968596i	−0.874903	−	0.484298i	$-0.839075\pi$
$367$		−	355.475i		−	0.968596i	0.874903	−	0.484298i	$-0.160925\pi$
$368$	138.835	−	7.31254i	0.377268	−	0.0198710i
$369$	838.218			2.27159
$370$	−21.8004	−	50.7327i	−0.0589201	−	0.137116i
$371$		0			0
$372$	533.895	+	506.514i	1.43520	+	1.36160i
$373$			315.998i			0.847180i	0.905854	+	0.423590i	$0.139230\pi$
$373$			315.998i			0.847180i	−0.905854	+	0.423590i	$0.860770\pi$
$374$	−3.84891	−	8.95696i	−0.0102912	−	0.0239491i
$375$			521.557i			1.39082i
$376$	−127.298	+	345.266i	−0.338559	+	0.918262i
$377$	201.745			0.535132
$378$		0			0
$379$	−178.404			−0.470723			−0.235361	−	0.971908i	$-0.575627\pi$
$379$	−178.404			−0.470723			−0.235361	+	0.971908i	$0.575627\pi$
$380$	37.1171	+	35.2136i	0.0976767	+	0.0926674i
$381$		−	701.147i		−	1.84028i
$382$	74.4838	−	32.0066i	0.194984	−	0.0837868i
$383$			698.400i			1.82350i	0.410746	+	0.911750i	$0.365268\pi$
$383$			698.400i			1.82350i	−0.410746	+	0.911750i	$0.634732\pi$
$384$	202.099	−	651.921i	0.526299	−	1.69771i
$385$		0			0
$386$	−222.912	−	518.747i	−0.577491	−	1.34390i
$387$	−811.096			−2.09586
$388$	147.873	−	155.866i	0.381115	−	0.401717i
$389$		−	175.358i		−	0.450792i	−0.974267	−	0.225396i	$-0.927632\pi$
$389$		−	175.358i		−	0.450792i	0.974267	−	0.225396i	$-0.0723676\pi$
$390$	194.450	+	452.512i	0.498589	+	1.16029i
$391$			8.05366i			0.0205976i
$392$		0			0
$393$	−46.7170			−0.118873
$394$	481.077	−	206.724i	1.22101	−	0.524681i
$395$	65.1648			0.164974
$396$	−281.360	+	296.570i	−0.710506	+	0.748914i
$397$		−	385.708i		−	0.971557i	−0.874082	−	0.485778i	$-0.838536\pi$
$397$		−	385.708i		−	0.971557i	0.874082	−	0.485778i	$-0.161464\pi$
$398$	−591.913	+	254.352i	−1.48722	+	0.639075i
$399$		0			0
$400$	−17.1239	−	325.112i	−0.0428098	−	0.812779i
$401$	527.096			1.31446			0.657228	−	0.753692i	$-0.271729\pi$
$401$	527.096			1.31446			0.657228	+	0.753692i	$0.271729\pi$
$402$	330.477	+	769.066i	0.822081	+	1.91310i
$403$	738.783			1.83321
$404$	−262.043	−	248.604i	−0.648622	−	0.615357i
$405$			262.590i			0.648371i
$406$		0			0
$407$		−	67.3178i		−	0.165400i
$408$	37.0969	+	13.6775i	0.0909237	+	0.0335232i
$409$	−423.744			−1.03605			−0.518025	−	0.855366i	$-0.673333\pi$
$409$	−423.744			−1.03605			−0.518025	+	0.855366i	$0.673333\pi$
$410$	170.958	−	73.4627i	0.416971	−	0.179177i
$411$	−1262.89			−3.07273
$412$	327.364	+	310.576i	0.794574	+	0.753824i
$413$		0			0
$414$	310.279	−	133.331i	0.749467	−	0.322055i
$415$		−	157.300i		−	0.379035i
$416$	−303.244	−	614.411i	−0.728953	−	1.47695i
$417$	917.796			2.20095
$418$	24.6255	+	57.3072i	0.0589128	+	0.137098i
$419$	295.598			0.705485			0.352742	−	0.935721i	$-0.385249\pi$
$419$	295.598			0.705485			0.352742	+	0.935721i	$0.385249\pi$
$420$		0			0
$421$		−	126.260i		−	0.299904i	−0.988693	−	0.149952i	$-0.952088\pi$
$421$		−	126.260i		−	0.299904i	0.988693	−	0.149952i	$-0.0479119\pi$
$422$	−134.069	−	311.998i	−0.317700	−	0.739332i
$423$			893.881i			2.11319i
$424$	206.125	−	559.066i	0.486144	−	1.31855i
$425$	18.8594			0.0443750
$426$	−730.063	+	313.716i	−1.71376	+	0.736424i
$427$		0			0
$428$	396.410	−	417.839i	0.926192	−	0.976259i
$429$			600.443i			1.39963i
$430$	−165.426	+	71.0857i	−0.384713	+	0.165316i
$431$			254.263i			0.589937i	0.955507	+	0.294968i	$0.0953091\pi$
$431$			254.263i			0.589937i	−0.955507	+	0.294968i	$0.904691\pi$
$432$	−46.8173	−	888.865i	−0.108373	−	2.05756i
$433$	546.301			1.26167			0.630833	−	0.775919i	$-0.282713\pi$
$433$	546.301			1.26167			0.630833	+	0.775919i	$0.282713\pi$
$434$		0			0
$435$	108.368			0.249122
$436$	−193.500	−	183.576i	−0.443807	−	0.421046i
$437$		−	51.5278i		−	0.117913i
$438$	−141.486	−	329.259i	−0.323028	−	0.751733i
$439$			273.335i			0.622631i	0.950307	+	0.311315i	$0.100770\pi$
$439$			273.335i			0.622631i	−0.950307	+	0.311315i	$0.899230\pi$
$440$	−31.3928	+	85.1456i	−0.0713473	+	0.193513i
$441$		0			0
$442$	36.4667	−	15.6702i	0.0825039	−	0.0354529i
$443$	474.770			1.07172			0.535858	−	0.844308i	$-0.319988\pi$
$443$	474.770			1.07172			0.535858	+	0.844308i	$0.319988\pi$
$444$	198.063	+	187.906i	0.446089	+	0.423211i
$445$		−	118.285i		−	0.265810i
$446$	−83.5390	+	35.8977i	−0.187307	+	0.0804881i
$447$			1230.19i			2.75210i
$448$		0			0
$449$	782.101			1.74187			0.870936	−	0.491396i	$-0.163513\pi$
$449$	782.101			1.74187			0.870936	+	0.491396i	$0.163513\pi$
$450$	−312.222	−	726.586i	−0.693828	−	1.61464i
$451$	226.846			0.502985
$452$	−19.7246	+	20.7909i	−0.0436385	+	0.0459975i
$453$		−	788.589i		−	1.74081i
$454$	−146.181	−	340.183i	−0.321984	−	0.749302i
$455$		0			0
$456$	−237.348	−	87.5092i	−0.520500	−	0.191906i
$457$	−189.559			−0.414789			−0.207395	−	0.978257i	$-0.566498\pi$
$457$	−189.559			−0.414789			−0.207395	+	0.978257i	$0.566498\pi$
$458$	−339.855	+	146.040i	−0.742041	+	0.318864i
$459$	51.5621			0.112336
$460$	51.5975	−	54.3867i	0.112168	−	0.118232i
$461$		−	202.533i		−	0.439335i	−0.975575	−	0.219667i	$-0.929503\pi$
$461$		−	202.533i		−	0.439335i	0.975575	−	0.219667i	$-0.0704972\pi$
$462$		0			0
$463$		−	652.927i		−	1.41021i	−0.709103	−	0.705105i	$-0.750900\pi$
$463$		−	652.927i		−	1.41021i	0.709103	−	0.705105i	$-0.249100\pi$
$464$	−150.547	+	7.92943i	−0.324455	+	0.0170893i
$465$	396.841			0.853420
$466$	−76.3557	−	177.691i	−0.163853	−	0.381310i
$467$	545.449			1.16799			0.583993	−	0.811759i	$-0.301490\pi$
$467$	545.449			1.16799			0.583993	+	0.811759i	$0.301490\pi$
$468$	−1207.43	−	1145.51i	−2.57998	−	2.44767i
$469$		0			0
$470$	78.3411	+	182.311i	0.166683	+	0.387895i
$471$			612.298i			1.30000i
$472$	402.877	+	148.539i	0.853552	+	0.314701i
$473$	−219.506			−0.464072
$474$	−296.021	+	127.204i	−0.624516	+	0.268362i
$475$	−120.663			−0.254028
$476$		0			0
$477$		−	1447.40i		−	3.03438i
$478$	−299.857	+	128.852i	−0.627316	+	0.269565i
$479$		−	108.897i		−	0.227343i	−0.993518	−	0.113672i	$-0.963739\pi$
$479$		−	108.897i		−	0.227343i	0.993518	−	0.113672i	$-0.0362612\pi$
$480$	−162.889	−	330.033i	−0.339352	−	0.687570i
$481$	274.073			0.569797
$482$	−162.257	−	377.596i	−0.336633	−	0.783394i
$483$		0			0
$484$	256.973	−	270.865i	0.530937	−	0.559637i
$485$		−	115.854i		−	0.238875i
$486$	−117.243	−	272.841i	−0.241241	−	0.561402i
$487$			429.353i			0.881629i	0.897598	+	0.440814i	$0.145310\pi$
$487$			429.353i			0.881629i	−0.897598	+	0.440814i	$0.854690\pi$
$488$	76.9796	−	208.789i	0.157745	−	0.427846i
$489$	262.929			0.537686
$490$		0			0
$491$	453.887			0.924413			0.462206	−	0.886772i	$-0.347058\pi$
$491$	453.887			0.924413			0.462206	+	0.886772i	$0.347058\pi$
$492$	−633.201	+	667.430i	−1.28699	+	1.35657i
$493$		−	8.73307i		−	0.0177141i
$494$	−233.316	+	100.259i	−0.472300	+	0.202953i
$495$			220.438i			0.445330i
$496$	−551.299	+	29.0374i	−1.11149	+	0.0585431i
$497$		0			0
$498$	307.053	+	714.556i	0.616572	+	1.43485i
$499$	333.396			0.668129			0.334064	−	0.942550i	$-0.391580\pi$
$499$	333.396			0.668129			0.334064	+	0.942550i	$0.391580\pi$
$500$	−283.836	−	269.280i	−0.567672	−	0.538559i
$501$			1287.51i			2.56988i
$502$	125.784	+	292.717i	0.250566	+	0.583102i
$503$			580.170i			1.15342i	0.816949	+	0.576710i	$0.195664\pi$
$503$			580.170i			1.15342i	−0.816949	+	0.576710i	$0.804336\pi$
$504$		0			0
$505$	−194.775			−0.385693
$506$	83.9705	−	36.0831i	0.165950	−	0.0713105i
$507$	−1543.45			−3.04428
$508$	381.570	+	362.002i	0.751123	+	0.712601i
$509$			307.463i			0.604054i	0.953299	+	0.302027i	$0.0976632\pi$
$509$			307.463i			0.604054i	−0.953299	+	0.302027i	$0.902337\pi$
$510$	19.5882	−	8.41730i	0.0384083	−	0.0165045i
$511$		0			0
$512$	250.438	+	446.570i	0.489136	+	0.872207i
$513$	−329.898			−0.643075
$514$	−170.379	−	396.497i	−0.331477	−	0.771395i
$515$	243.328			0.472481
$516$	612.713	−	645.834i	1.18743	−	1.25162i
$517$			241.910i			0.467911i
$518$		0			0
$519$			290.187i			0.559127i
$520$	−346.655	−	127.810i	−0.666645	−	0.245789i
$521$	720.959			1.38380			0.691899	−	0.721994i	$-0.256774\pi$
$521$	720.959			1.38380			0.691899	+	0.721994i	$0.256774\pi$
$522$	−336.455	+	144.578i	−0.644549	+	0.276970i
$523$	−269.977			−0.516208			−0.258104	−	0.966117i	$-0.583098\pi$
$523$	−269.977			−0.516208			−0.258104	+	0.966117i	$0.583098\pi$
$524$	24.1199	−	25.4238i	0.0460304	−	0.0485186i
$525$		0			0
$526$	−604.837	+	259.905i	−1.14988	+	0.494117i
$527$		−	31.9803i		−	0.0606836i
$528$	−23.6000	−	448.066i	−0.0446970	−	0.848609i
$529$	453.498			0.857274
$530$	−126.852	−	295.203i	−0.239344	−	0.556987i
$531$	1043.03			1.96428
$532$		0			0
$533$			923.564i			1.73277i
$534$	230.896	+	537.329i	0.432390	+	1.00623i
$535$		−	310.577i		−	0.580517i
$536$	−589.157	−	217.220i	−1.09917	−	0.405261i
$537$	−677.303			−1.26127
$538$	538.520	−	231.408i	1.00097	−	0.430127i
$539$		0			0
$540$	−348.201	−	330.344i	−0.644817	−	0.611748i
$541$			907.242i			1.67697i	0.544922	+	0.838486i	$0.316559\pi$
$541$			907.242i			1.67697i	−0.544922	+	0.838486i	$0.683441\pi$
$542$	−49.3380	+	21.2011i	−0.0910296	+	0.0391165i
$543$		−	1134.19i		−	2.08875i
$544$	−26.5965	+	13.1268i	−0.0488906	+	0.0241301i
$545$	−143.827			−0.263903
$546$		0			0
$547$	−557.327			−1.01888			−0.509439	−	0.860506i	$-0.670147\pi$
$547$	−557.327			−1.01888			−0.509439	+	0.860506i	$0.670147\pi$
$548$	652.031	−	687.278i	1.18984	−	1.25416i
$549$		−	540.546i		−	0.984601i
$550$	−84.4964	−	196.635i	−0.153630	−	0.357518i
$551$			55.8747i			0.101406i
$552$	−128.225	+	347.779i	−0.232291	+	0.630035i
$553$		0			0
$554$	−615.163	+	264.343i	−1.11040	+	0.477153i
$555$	147.219			0.265260
$556$	−473.857	+	499.472i	−0.852261	+	0.898331i
$557$			856.668i			1.53800i	0.639246	+	0.769002i	$0.279246\pi$
$557$			856.668i			1.53800i	−0.639246	+	0.769002i	$0.720754\pi$
$558$	−1232.09	+	529.442i	−2.20804	+	0.948821i
$559$		−	893.680i		−	1.59871i
$560$		0			0
$561$	25.9918			0.0463313
$562$	97.4039	+	226.673i	0.173317	+	0.403332i
$563$	13.6887			0.0243139			0.0121569	−	0.999926i	$-0.496130\pi$
$563$	13.6887			0.0243139			0.0121569	+	0.999926i	$0.496130\pi$
$564$	−711.752	−	675.250i	−1.26197	−	1.19725i
$565$			15.4537i			0.0273517i
$566$	0.488693	+	1.13726i	0.000863416	+	0.00200929i
$567$		0			0
$568$	206.204	−	559.278i	0.363034	−	0.984644i
$569$	−1091.98			−1.91913			−0.959563	−	0.281495i	$-0.909170\pi$
$569$	−1091.98			−1.91913			−0.959563	+	0.281495i	$0.909170\pi$
$570$	−125.327	+	53.8544i	−0.219871	+	0.0944813i
$571$	719.098			1.25937			0.629683	−	0.776852i	$-0.283185\pi$
$571$	719.098			1.25937			0.629683	+	0.776852i	$0.283185\pi$
$572$	−326.766	−	310.008i	−0.571270	−	0.541972i
$573$			216.142i			0.377210i
$574$		0			0
$575$			176.805i			0.307486i
$576$	946.041	+	807.351i	1.64243	+	1.40165i
$577$	−1031.12			−1.78704			−0.893518	−	0.449027i	$-0.851771\pi$
$577$	−1031.12			−1.78704			−0.893518	+	0.449027i	$0.851771\pi$
$578$	227.518	+	529.468i	0.393631	+	0.916034i
$579$	1505.33			2.59988
$580$	−55.9503	+	58.9748i	−0.0964660	+	0.101681i
$581$		0			0
$582$	226.151	+	526.285i	0.388575	+	0.904270i
$583$		−	391.708i		−	0.671883i
$584$	252.235	+	92.9979i	0.431909	+	0.159243i
$585$	−897.477			−1.53415
$586$	−51.9643	+	22.3297i	−0.0886764	+	0.0381053i
$587$	−671.907			−1.14464			−0.572322	−	0.820029i	$-0.693957\pi$
$587$	−671.907			−1.14464			−0.572322	+	0.820029i	$0.693957\pi$
$588$		0			0
$589$			204.612i			0.347388i
$590$	212.731	−	91.4129i	0.360561	−	0.154937i
$591$			1396.02i			2.36213i
$592$	−204.520	+	10.7722i	−0.345473	+	0.0181963i
$593$	353.998			0.596962			0.298481	−	0.954416i	$-0.403520\pi$
$593$	353.998			0.596962			0.298481	+	0.954416i	$0.403520\pi$
$594$	−231.016	−	537.606i	−0.388915	−	0.905061i
$595$		0			0
$596$	−669.480	−	635.146i	−1.12329	−	1.06568i
$597$		−	1717.65i		−	2.87713i
$598$	146.906	+	341.871i	0.245662	+	0.571691i
$599$		−	1136.14i		−	1.89672i	−0.317193	−	0.948361i	$-0.602740\pi$
$599$		−	1136.14i		−	1.89672i	0.317193	−	0.948361i	$-0.397260\pi$
$600$	814.400	+	300.266i	1.35733	+	0.500443i
$601$	−6.80783			−0.0113275			−0.00566375	−	0.999984i	$-0.501803\pi$
$601$	−6.80783			−0.0113275			−0.00566375	+	0.999984i	$0.501803\pi$
$602$		0			0
$603$	−1525.30			−2.52953
$604$	429.157	+	407.148i	0.710524	+	0.674085i
$605$		−	201.332i		−	0.332780i
$606$	884.794	−	380.206i	1.46006	−	0.627403i
$607$		−	446.439i		−	0.735484i	−0.929928	−	0.367742i	$-0.880131\pi$
$607$		−	446.439i		−	0.735484i	0.929928	−	0.367742i	$-0.119869\pi$
$608$	170.166	−	83.9859i	0.279878	−	0.138135i
$609$		0			0
$610$	−47.3743	−	110.247i	−0.0776627	−	0.180732i
$611$	−984.895			−1.61194
$612$	−49.5866	+	52.2671i	−0.0810238	+	0.0854037i
$613$			641.609i			1.04667i	0.852127	+	0.523335i	$0.175312\pi$
$613$			641.609i			1.04667i	−0.852127	+	0.523335i	$0.824688\pi$
$614$	−316.549	−	736.654i	−0.515552	−	1.19976i
$615$			496.096i			0.806661i
$616$		0			0
$617$	−502.890			−0.815057			−0.407528	−	0.913193i	$-0.633609\pi$
$617$	−502.890			−0.815057			−0.407528	+	0.913193i	$0.633609\pi$
$618$	−1105.35	+	474.983i	−1.78860	+	0.768580i
$619$	432.989			0.699498			0.349749	−	0.936843i	$-0.386267\pi$
$619$	432.989			0.699498			0.349749	+	0.936843i	$0.386267\pi$
$620$	−204.888	+	215.964i	−0.330465	+	0.348329i
$621$			483.389i			0.778405i
$622$	298.096	−	128.095i	0.479254	−	0.205941i
$623$		0			0
$624$	1824.22	−	96.0833i	2.92343	−	0.153980i
$625$	297.718			0.476348
$626$	210.230	+	489.235i	0.335831	+	0.781526i
$627$	−166.297			−0.265227
$628$	−333.218	−	316.129i	−0.530602	−	0.503390i
$629$		−	11.8640i		−	0.0188617i
$630$		0			0
$631$			238.957i			0.378695i	0.981910	+	0.189348i	$0.0606373\pi$
$631$			238.957i			0.378695i	−0.981910	+	0.189348i	$0.939363\pi$
$632$	83.6099	−	226.772i	0.132294	−	0.358817i
$633$	905.375			1.43029
$634$	−795.385	+	341.786i	−1.25455	+	0.539095i
$635$	283.619			0.446644
$636$	1152.49	+	1093.38i	1.81209	+	1.71916i
$637$		0			0
$638$	−91.0543	+	39.1271i	−0.142718	+	0.0613277i
$639$		−	1447.95i		−	2.26596i
$640$	263.706	+	81.7503i	0.412041	+	0.127735i
$641$	−7.96130			−0.0124201			−0.00621006	−	0.999981i	$-0.501977\pi$
$641$	−7.96130			−0.0124201			−0.00621006	+	0.999981i	$0.501977\pi$
$642$	606.255	+	1410.84i	0.944322	+	2.19757i
$643$	−584.919			−0.909672			−0.454836	−	0.890575i	$-0.650302\pi$
$643$	−584.919			−0.909672			−0.454836	+	0.890575i	$0.650302\pi$
$644$		0			0
$645$		−	480.044i		−	0.744255i
$646$	4.33997	+	10.0997i	0.00671822	+	0.0156343i
$647$		−	335.680i		−	0.518825i	−0.965767	−	0.259413i	$-0.916471\pi$
$647$		−	335.680i		−	0.518825i	0.965767	−	0.259413i	$-0.0835289\pi$
$648$	913.809	+	336.918i	1.41020	+	0.519934i
$649$	282.275			0.434938
$650$	800.566	−	344.012i	1.23164	−	0.529250i
$651$		0			0
$652$	−135.750	+	143.088i	−0.208205	+	0.219460i
$653$		−	48.5265i		−	0.0743132i	−0.999309	−	0.0371566i	$-0.988170\pi$
$653$		−	48.5265i		−	0.0743132i	0.999309	−	0.0371566i	$-0.0118300\pi$
$654$	653.355	−	280.754i	0.999014	−	0.429288i
$655$		−	18.8973i		−	0.0288509i
$656$	−36.3001	−	689.187i	−0.0553355	−	1.05059i
$657$	653.026			0.993951
$658$		0			0
$659$	1224.65			1.85835			0.929176	−	0.369638i	$-0.120518\pi$
$659$	1224.65			1.85835			0.929176	+	0.369638i	$0.120518\pi$
$660$	−175.524	−	166.522i	−0.265945	−	0.252306i
$661$			838.042i			1.26784i	0.773399	+	0.633919i	$0.218555\pi$
$661$			838.042i			1.26784i	−0.773399	+	0.633919i	$0.781445\pi$
$662$	−64.1579	−	149.305i	−0.0969153	−	0.225536i
$663$			105.821i			0.159610i
$664$	−547.399	−	201.824i	−0.824396	−	0.303951i
$665$		0			0
$666$	−457.078	+	196.412i	−0.686303	+	0.294912i
$667$	81.8716			0.122746
$668$	−700.674	−	664.741i	−1.04891	−	0.995121i
$669$		−	242.418i		−	0.362359i
$670$	−311.092	+	133.680i	−0.464317	+	0.199522i
$671$		−	146.287i		−	0.218014i
$672$		0			0
$673$	147.714			0.219486			0.109743	−	0.993960i	$-0.464997\pi$
$673$	147.714			0.219486			0.109743	+	0.993960i	$0.464997\pi$
$674$	54.8731	+	127.698i	0.0814141	+	0.189462i
$675$	1131.96			1.67698
$676$	796.881	−	839.958i	1.17882	−	1.24254i
$677$			837.185i			1.23661i	0.785938	+	0.618305i	$0.212180\pi$
$677$			837.185i			1.23661i	−0.785938	+	0.618305i	$0.787820\pi$
$678$	−30.1661	−	70.2007i	−0.0444927	−	0.103541i
$679$		0			0
$680$	−5.53263	+	15.0059i	−0.00813622	+	0.0220676i
$681$	987.164			1.44958
$682$	−333.438	+	143.282i	−0.488913	+	0.210091i
$683$	−64.4377			−0.0943451			−0.0471725	−	0.998887i	$-0.515021\pi$
$683$	−64.4377			−0.0943451			−0.0471725	+	0.998887i	$0.515021\pi$
$684$	317.258	−	334.408i	0.463827	−	0.488900i
$685$		−	510.849i		−	0.745765i
$686$		0			0
$687$		−	986.210i		−	1.43553i
$688$	35.1255	+	666.887i	0.0510545	+	0.969312i
$689$	1594.77			2.31462
$690$	78.9112	+	183.638i	0.114364	+	0.266141i
$691$	−526.747			−0.762297			−0.381149	−	0.924514i	$-0.624471\pi$
$691$	−526.747			−0.762297			−0.381149	+	0.924514i	$0.624471\pi$
$692$	−157.922	−	149.823i	−0.228211	−	0.216508i
$693$		0			0
$694$	275.852	+	641.948i	0.397482	+	0.924997i
$695$			371.254i			0.534179i
$696$	139.042	−	377.118i	0.199773	−	0.541836i
$697$	39.9790			0.0573587
$698$	304.728	−	130.945i	0.436574	−	0.187601i
$699$	515.633			0.737672
$700$		0			0
$701$			695.486i			0.992134i	0.868284	+	0.496067i	$0.165223\pi$
$701$			695.486i			0.992134i	−0.868284	+	0.496067i	$0.834777\pi$
$702$	2188.77	−	940.540i	3.11791	−	1.33980i
$703$			75.9065i			0.107975i
$704$	256.026	+	218.493i	0.363673	+	0.310359i
$705$	−529.040			−0.750412
$706$	372.471	+	866.794i	0.527580	+	1.22775i
$707$		0			0
$708$	−787.920	+	830.513i	−1.11288	+	1.17304i
$709$			927.410i			1.30805i	0.756471	+	0.654027i	$0.226922\pi$
$709$			927.410i			1.30805i	−0.756471	+	0.654027i	$0.773078\pi$
$710$	−126.900	−	295.315i	−0.178733	−	0.415937i
$711$		−	587.104i		−	0.825744i
$712$	−411.630	−	151.766i	−0.578133	−	0.213155i
$713$	299.812			0.420493
$714$		0			0
$715$	−242.883			−0.339697
$716$	349.691	−	368.594i	0.488395	−	0.514796i
$717$		−	870.143i		−	1.21359i
$718$	−1207.23	+	518.762i	−1.68138	+	0.722509i
$719$			1328.34i			1.84748i	0.383022	+	0.923739i	$0.374883\pi$
$719$			1328.34i			1.84748i	−0.383022	+	0.923739i	$0.625117\pi$
$720$	669.720	−	35.2747i	0.930167	−	0.0489927i
$721$		0			0
$722$	257.281	+	598.730i	0.356345	+	0.829266i
$723$	1095.73			1.51553
$724$	617.238	+	585.583i	0.852539	+	0.808817i
$725$		−	191.720i		−	0.264441i
$726$	393.005	+	914.579i	0.541330	+	1.25975i
$727$			539.401i			0.741954i	0.928642	+	0.370977i	$0.120977\pi$
$727$			539.401i			0.741954i	−0.928642	+	0.370977i	$0.879023\pi$
$728$		0			0
$729$	−303.936			−0.416922
$730$	133.187	−	57.2322i	0.182448	−	0.0784002i
$731$	−38.6854			−0.0529212
$732$	430.409	+	408.336i	0.587991	+	0.557836i
$733$			442.088i			0.603121i	0.953447	+	0.301561i	$0.0975076\pi$
$733$			442.088i			0.603121i	−0.953447	+	0.301561i	$0.902492\pi$
$734$	−653.196	+	280.686i	−0.889913	+	0.382406i
$735$		0			0
$736$	−123.062	−	249.339i	−0.167204	−	0.338776i
$737$	−412.791			−0.560097
$738$	−661.864	−	1540.25i	−0.896835	−	2.08706i
$739$	−1148.23			−1.55376			−0.776882	−	0.629646i	$-0.783200\pi$
$739$	−1148.23			−1.55376			−0.776882	+	0.629646i	$0.783200\pi$
$740$	−76.0091	+	80.1180i	−0.102715	+	0.108268i
$741$		−	677.050i		−	0.913698i
$742$		0			0
$743$			588.688i			0.792313i	0.918183	+	0.396156i	$0.129656\pi$
$743$			588.688i			0.792313i	−0.918183	+	0.396156i	$0.870344\pi$
$744$	509.168	−	1381.00i	0.684365	−	1.85618i
$745$	−497.620			−0.667946
$746$	580.656	−	249.515i	0.778360	−	0.334470i
$747$	−1417.19			−1.89718
$748$	−13.4196	+	14.1450i	−0.0179406	+	0.0189104i
$749$		0			0
$750$	958.378	−	411.826i	1.27784	−	0.549101i
$751$		−	818.399i		−	1.08975i	−0.838519	−	0.544873i	$-0.816578\pi$
$751$		−	818.399i		−	1.08975i	0.838519	−	0.544873i	$-0.183422\pi$
$752$	734.953	−	38.7106i	0.977332	−	0.0514769i
$753$	−849.423			−1.12805
$754$	−159.299	−	370.712i	−0.211272	−	0.491660i
$755$	318.989			0.422503
$756$		0			0
$757$		−	105.101i		−	0.138838i	−0.997588	−	0.0694192i	$-0.977885\pi$
$757$		−	105.101i		−	0.138838i	0.997588	−	0.0694192i	$-0.0221146\pi$
$758$	140.869	+	327.823i	0.185843	+	0.432484i
$759$			243.671i			0.321042i
$760$	35.3981	−	96.0088i	0.0465764	−	0.126327i
$761$	1014.23			1.33276			0.666382	−	0.745610i	$-0.267842\pi$
$761$	1014.23			1.33276			0.666382	+	0.745610i	$0.267842\pi$
$762$	−1288.38	+	553.631i	−1.69079	+	0.726550i
$763$		0			0
$764$	−117.626	−	111.594i	−0.153961	−	0.146065i
$765$			38.8498i			0.0507840i
$766$	1283.33	−	551.463i	1.67537	−	0.719925i
$767$			1149.23i			1.49835i
$768$	−1357.50	+	143.400i	−1.76758	+	0.186718i
$769$	−1183.99			−1.53964			−0.769822	−	0.638258i	$-0.779655\pi$
$769$	−1183.99			−1.53964			−0.769822	+	0.638258i	$0.779655\pi$
$770$		0			0
$771$	1150.58			1.49232
$772$	−777.201	+	819.214i	−1.00674	+	1.06116i
$773$		−	324.311i		−	0.419549i	−0.977750	−	0.209774i	$-0.932727\pi$
$773$		−	324.311i		−	0.419549i	0.977750	−	0.209774i	$-0.0672730\pi$
$774$	640.448	+	1490.41i	0.827452	+	1.92560i
$775$		−	702.074i		−	0.905902i
$776$	−403.170	−	148.647i	−0.519550	−	0.191556i
$777$		0			0
$778$	−322.226	+	138.464i	−0.414172	+	0.177975i
$779$	−255.788			−0.328355
$780$	677.966	−	714.615i	0.869187	−	0.916173i
$781$		−	391.857i		−	0.501737i
$782$	14.7988	−	6.35924i	0.0189244	−	0.00813202i
$783$		−	524.168i		−	0.669436i
$784$		0			0
$785$	−247.679			−0.315514
$786$	36.8881	+	85.8438i	0.0469314	+	0.109216i
$787$	268.536			0.341214			0.170607	−	0.985339i	$-0.445427\pi$
$787$	268.536			0.341214			0.170607	+	0.985339i	$0.445427\pi$
$788$	−759.724	−	720.762i	−0.964117	−	0.914673i
$789$		−	1755.15i		−	2.22453i
$790$	−51.4547	−	119.742i	−0.0651325	−	0.151573i
$791$		0			0
$792$	767.121	+	282.834i	0.968587	+	0.357114i
$793$	595.584			0.751051
$794$	−708.750	+	304.558i	−0.892633	+	0.383575i
$795$	856.638			1.07753
$796$	934.759	+	886.820i	1.17432	+	1.11410i
$797$		−	1502.06i		−	1.88465i	−0.334705	−	0.942323i	$-0.608637\pi$
$797$		−	1502.06i		−	1.88465i	0.334705	−	0.942323i	$-0.391363\pi$
$798$		0			0
$799$			42.6339i			0.0533591i
$800$	−583.881	+	288.177i	−0.729852	+	0.360221i
$801$	−1065.70			−1.33046
$802$	−416.200	−	968.556i	−0.518952	−	1.20768i
$803$	176.728			0.220084
$804$	1152.24	−	1214.52i	1.43313	−	1.51060i
$805$		0			0
$806$	−583.349	−	1357.54i	−0.723758	−	1.68429i
$807$			1562.71i			1.93644i
$808$	−249.907	+	677.812i	−0.309290	+	0.838877i
$809$	70.7587			0.0874644			0.0437322	−	0.999043i	$-0.486075\pi$
$809$	70.7587			0.0874644			0.0437322	+	0.999043i	$0.486075\pi$
$810$	482.518	−	207.344i	0.595701	−	0.255980i
$811$	5.94522			0.00733072			0.00366536	−	0.999993i	$-0.498833\pi$
$811$	5.94522			0.00733072			0.00366536	+	0.999993i	$0.498833\pi$
$812$		0			0
$813$		−	143.172i		−	0.176103i
$814$	−123.698	+	53.1547i	−0.151964	+	0.0653006i
$815$			106.356i			0.130499i
$816$	−4.15923	−	78.9665i	−0.00509710	−	0.0967727i
$817$	247.512			0.302952
$818$	334.592	+	778.643i	0.409037	+	0.951886i
$819$		0			0
$820$	−269.980	−	256.134i	−0.329244	−	0.312359i
$821$		−	15.1449i		−	0.0184469i	−0.999957	−	0.00922344i	$-0.997064\pi$
$821$		−	15.1449i		−	0.0184469i	0.999957	−	0.00922344i	$-0.00293595\pi$
$822$	997.191	+	2320.61i	1.21313	+	2.82312i
$823$			1482.76i			1.80165i	0.434185	+	0.900824i	$0.357036\pi$
$823$			1482.76i			1.80165i	−0.434185	+	0.900824i	$0.642964\pi$
$824$	312.203	−	846.775i	0.378887	−	1.02764i
$825$	570.607			0.691645
$826$		0			0
$827$	−74.3070			−0.0898513			−0.0449257	−	0.998990i	$-0.514305\pi$
$827$	−74.3070			−0.0898513			−0.0449257	+	0.998990i	$0.514305\pi$
$828$	−489.998	−	464.869i	−0.591785	−	0.561436i
$829$		−	142.862i		−	0.172331i	−0.996281	−	0.0861654i	$-0.972539\pi$
$829$		−	142.862i		−	0.172331i	0.996281	−	0.0861654i	$-0.0274613\pi$
$830$	−289.043	+	124.205i	−0.348244	+	0.149645i
$831$		−	1785.12i		−	2.14815i
$832$	−889.555	+	1042.36i	−1.06918	+	1.25284i
$833$		0			0
$834$	−724.699	−	1686.48i	−0.868944	−	2.02216i
$835$	−520.807			−0.623721
$836$	85.8591	−	90.5004i	0.102702	−	0.108254i
$837$		−	1919.49i		−	2.29330i
$838$	−233.407	−	543.170i	−0.278528	−	0.648175i
$839$		−	16.7454i		−	0.0199588i	−0.999950	−	0.00997940i	$-0.996823\pi$
$839$		−	16.7454i		−	0.0199588i	0.999950	−	0.00997940i	$-0.00317659\pi$
$840$		0			0
$841$	752.222			0.894437
$842$	−232.006	+	99.6955i	−0.275541	+	0.118403i
$843$	−657.773			−0.780276
$844$	−467.444	+	492.713i	−0.553844	+	0.583783i
$845$		−	624.335i		−	0.738858i
$846$	1642.53	−	705.816i	1.94153	−	0.834298i
$847$		0			0
$848$	−1190.06	+	62.6814i	−1.40337	+	0.0739167i
$849$	−3.30017			−0.00388712
$850$	−14.8915	−	34.6547i	−0.0175194	−	0.0407703i
$851$	111.224			0.130698
$852$	1152.93	+	1093.80i	1.35320	+	1.28380i
$853$			1299.38i			1.52331i	0.647984	+	0.761654i	$0.275612\pi$
$853$			1299.38i			1.52331i	−0.647984	+	0.761654i	$0.724388\pi$
$854$		0			0
$855$		−	248.563i		−	0.290717i
$856$	−1080.80	−	398.487i	−1.26262	−	0.465522i
$857$	−1195.34			−1.39479			−0.697396	−	0.716686i	$-0.745658\pi$
$857$	−1195.34			−1.39479			−0.697396	+	0.716686i	$0.745658\pi$
$858$	1103.33	−	474.115i	1.28594	−	0.552581i
$859$	−341.769			−0.397869			−0.198934	−	0.980013i	$-0.563748\pi$
$859$	−341.769			−0.397869			−0.198934	+	0.980013i	$0.563748\pi$
$860$	261.244	+	247.846i	0.303772	+	0.288193i
$861$		0			0
$862$	467.216	−	200.768i	0.542014	−	0.232909i
$863$			974.986i			1.12976i	0.825172	+	0.564882i	$0.191078\pi$
$863$			974.986i			1.12976i	−0.825172	+	0.564882i	$0.808922\pi$
$864$	−1596.35	+	787.883i	−1.84763	+	0.911902i
$865$	−117.383			−0.135702
$866$	−431.364	−	1003.85i	−0.498111	−	1.15917i
$867$	−1536.44			−1.77213
$868$		0			0
$869$		−	158.887i		−	0.182839i
$870$	−85.5682	−	199.129i	−0.0983543	−	0.228884i
$871$		−	1680.61i		−	1.92952i
$872$	−184.538	+	500.515i	−0.211626	+	0.573985i
$873$	−1043.79			−1.19564
$874$	−94.6839	+	40.6868i	−0.108334	+	0.0465524i
$875$		0			0
$876$	−493.304	+	519.971i	−0.563133	+	0.593574i
$877$		−	316.570i		−	0.360970i	−0.983578	−	0.180485i	$-0.942233\pi$
$877$		−	316.570i		−	0.360970i	0.983578	−	0.180485i	$-0.0577667\pi$
$878$	502.261	−	215.828i	0.572052	−	0.245817i
$879$		−	150.793i		−	0.171551i
$880$	181.246	−	9.54636i	0.205961	−	0.0108481i
$881$	−464.977			−0.527783			−0.263891	−	0.964552i	$-0.585006\pi$
$881$	−464.977			−0.527783			−0.263891	+	0.964552i	$0.585006\pi$
$882$		0			0
$883$	69.4594			0.0786630			0.0393315	−	0.999226i	$-0.487477\pi$
$883$	69.4594			0.0786630			0.0393315	+	0.999226i	$0.487477\pi$
$884$	−57.5888	−	54.6354i	−0.0651457	−	0.0618048i
$885$			617.315i			0.697531i
$886$	−374.882	−	872.405i	−0.423118	−	0.984655i
$887$		−	10.9320i		−	0.0123247i	−0.999981	−	0.00616235i	$-0.998038\pi$
$887$		−	10.9320i		−	0.0123247i	0.999981	−	0.00616235i	$-0.00196155\pi$
$888$	188.890	−	512.320i	0.212714	−	0.576936i
$889$		0			0
$890$	−217.353	+	93.3991i	−0.244217	+	0.104943i
$891$	640.258			0.718583
$892$	131.926	+	125.160i	0.147899	+	0.140314i
$893$		−	272.774i		−	0.305458i
$894$	2260.51	−	971.368i	2.52854	−	1.08654i
$895$		−	273.974i		−	0.306116i
$896$		0			0
$897$	−992.062			−1.10598
$898$	−617.553	−	1437.13i	−0.687698	−	1.60037i
$899$	−325.104			−0.361628
$900$	−1088.59	+	1147.44i	−1.20955	+	1.27493i
$901$		−	69.0341i		−	0.0766194i
$902$	−179.119	−	416.837i	−0.198580	−	0.462125i
$903$		0			0
$904$	53.7786	+	19.8279i	0.0594896	+	0.0219336i
$905$	458.789			0.506949
$906$	−1449.06	+	622.676i	−1.59940	+	0.687280i
$907$	−22.7176			−0.0250469			−0.0125235	−	0.999922i	$-0.503986\pi$
$907$	−22.7176			−0.0250469			−0.0125235	+	0.999922i	$0.503986\pi$
$908$	−509.672	+	537.223i	−0.561312	+	0.591655i
$909$			1754.83i			1.93051i
$910$		0			0
$911$			721.866i			0.792389i	0.918167	+	0.396194i	$0.129669\pi$
$911$			721.866i			0.792389i	−0.918167	+	0.396194i	$0.870331\pi$
$912$	26.6110	+	505.232i	0.0291787	+	0.553983i
$913$	−383.534			−0.420081
$914$	149.677	+	348.320i	0.163760	+	0.381094i
$915$	319.920			0.349640
$916$	536.704	+	509.179i	0.585922	+	0.555873i
$917$		0			0
$918$	−40.7139	−	94.7470i	−0.0443506	−	0.103210i
$919$		−	130.722i		−	0.142244i	−0.997468	−	0.0711221i	$-0.977342\pi$
$919$		−	130.722i		−	0.142244i	0.997468	−	0.0711221i	$-0.0226580\pi$
$920$	−140.679	−	51.8678i	−0.152912	−	0.0563780i
$921$	2137.67			2.32103
$922$	−372.161	+	159.922i	−0.403646	+	0.173451i
$923$	1595.38			1.72847
$924$		0			0
$925$		−	260.454i		−	0.281572i
$926$	−1199.77	+	515.557i	−1.29565	+	0.556757i
$927$		−	2192.27i		−	2.36491i
$928$	133.444	+	270.373i	0.143797	+	0.291351i
$929$	−455.285			−0.490081			−0.245041	−	0.969513i	$-0.578801\pi$
$929$	−455.285			−0.490081			−0.245041	+	0.969513i	$0.578801\pi$
$930$	−313.349	−	729.207i	−0.336934	−	0.784093i
$931$		0			0
$932$	−266.221	+	280.612i	−0.285645	+	0.301086i
$933$			865.032i			0.927152i
$934$	−430.691	−	1002.28i	−0.461125	−	1.07310i
$935$			10.5139i			0.0112448i
$936$	−1151.51	+	3123.20i	−1.23025	+	3.33675i
$937$	−1242.79			−1.32635			−0.663176	−	0.748464i	$-0.730792\pi$
$937$	−1242.79			−1.32635			−0.663176	+	0.748464i	$0.730792\pi$
$938$		0			0
$939$	−1419.69			−1.51192
$940$	273.143	−	287.908i	0.290578	−	0.306285i
$941$			1137.11i			1.20841i	0.796830	+	0.604204i	$0.206509\pi$
$941$			1137.11i			1.20841i	−0.796830	+	0.604204i	$0.793491\pi$
$942$	1125.12	−	483.476i	1.19439	−	0.513244i
$943$			374.799i			0.397454i
$944$	−45.1698	−	857.586i	−0.0478493	−	0.908460i
$945$		0			0
$946$	173.324	+	403.349i	0.183217	+	0.426373i
$947$	704.842			0.744289			0.372145	−	0.928175i	$-0.378623\pi$
$947$	704.842			0.744289			0.372145	+	0.928175i	$0.378623\pi$
$948$	467.481	+	443.506i	0.493123	+	0.467833i
$949$			719.516i			0.758183i
$950$	95.2769	+	221.723i	0.100291	+	0.233392i
$951$		−	2308.09i		−	2.42702i
$952$		0			0
$953$	765.039			0.802769			0.401384	−	0.915910i	$-0.368529\pi$
$953$	765.039			0.802769			0.401384	+	0.915910i	$0.368529\pi$
$954$	−2659.64	+	1142.88i	−2.78788	+	1.19799i
$955$	−87.4307			−0.0915505
$956$	473.539	+	449.254i	0.495334	+	0.469931i
$957$		−	264.227i		−	0.276099i
$958$	−200.102	+	85.9863i	−0.208875	+	0.0897561i
$959$		0			0
$960$	−477.828	+	559.911i	−0.497737	+	0.583240i
$961$	−229.522			−0.238836
$962$	−216.410	−	503.617i	−0.224958	−	0.523510i
$963$	−2798.15			−2.90566
$964$	−565.724	+	596.305i	−0.586851	+	0.618574i
$965$			608.916i			0.631001i
$966$		0			0
$967$			771.494i			0.797822i	0.916990	+	0.398911i	$0.130612\pi$
$967$			771.494i			0.797822i	−0.916990	+	0.398911i	$0.869388\pi$
$968$	−700.630	−	258.319i	−0.723791	−	0.266859i
$969$	−29.3080			−0.0302456
$970$	−212.886	+	91.4795i	−0.219470	+	0.0943088i
$971$	917.509			0.944911			0.472456	−	0.881354i	$-0.343368\pi$
$971$	917.509			0.944911			0.472456	+	0.881354i	$0.343368\pi$
$972$	−408.778	+	430.875i	−0.420554	+	0.443287i
$973$		0			0
$974$	788.949	−	339.021i	0.810010	−	0.348071i
$975$			2323.13i			2.38270i
$976$	−444.440	+	23.4090i	−0.455368	+	0.0239846i
$977$	266.601			0.272877			0.136439	−	0.990649i	$-0.456434\pi$
$977$	266.601			0.272877			0.136439	+	0.990649i	$0.456434\pi$
$978$	−207.611	−	483.139i	−0.212281	−	0.494007i
$979$	−288.408			−0.294594
$980$		0			0
$981$			1295.81i			1.32091i
$982$	−358.393	−	834.031i	−0.364962	−	0.849318i
$983$			1849.77i			1.88176i	0.338743	+	0.940879i	$0.389998\pi$
$983$			1849.77i			1.88176i	−0.338743	+	0.940879i	$0.610002\pi$
$984$	1726.40	+	636.518i	1.75448	+	0.646868i
$985$	−564.698			−0.573297
$986$	−16.0473	+	6.89571i	−0.0162751	+	0.00699362i
$987$		0			0
$988$	368.457	+	349.560i	0.372932	+	0.353806i
$989$		−	362.672i		−	0.366705i
$990$	405.062	−	174.060i	0.409154	−	0.175818i
$991$		−	350.359i		−	0.353541i	−0.984252	−	0.176770i	$-0.943435\pi$
$991$		−	350.359i		−	0.353541i	0.984252	−	0.176770i	$-0.0565650\pi$
$992$	488.667	+	990.100i	0.492608	+	0.998085i
$993$	433.261			0.436315
$994$		0			0
$995$	694.800			0.698291
$996$	1070.57	−	1128.44i	1.07487	−	1.13297i
$997$			525.961i			0.527543i	0.964585	+	0.263772i	$0.0849666\pi$
$997$			525.961i			0.527543i	−0.964585	+	0.263772i	$0.915033\pi$
$998$	−263.252	−	612.626i	−0.263780	−	0.613854i
$999$		−	712.089i		−	0.712802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.g.j.99.3		6
4.3	odd	2		1568.3.g.j.687.2		6
7.2	even	3		56.3.k.d.11.2	✓	12
7.3	odd	6		392.3.k.l.275.6		12
7.4	even	3		56.3.k.d.51.6	yes	12
7.5	odd	6		392.3.k.l.67.2		12
7.6	odd	2		392.3.g.i.99.3		6
8.3	odd	2	inner	392.3.g.j.99.4		6
8.5	even	2		1568.3.g.j.687.1		6
28.11	odd	6		224.3.o.d.79.5		12
28.23	odd	6		224.3.o.d.207.6		12
28.27	even	2		1568.3.g.l.687.5		6
56.3	even	6		392.3.k.l.275.2		12
56.11	odd	6		56.3.k.d.51.2	yes	12
56.13	odd	2		1568.3.g.l.687.6		6
56.19	even	6		392.3.k.l.67.6		12
56.27	even	2		392.3.g.i.99.4		6
56.37	even	6		224.3.o.d.207.5		12
56.51	odd	6		56.3.k.d.11.6	yes	12
56.53	even	6		224.3.o.d.79.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.k.d.11.2	✓	12	7.2	even	3
56.3.k.d.11.6	yes	12	56.51	odd	6
56.3.k.d.51.2	yes	12	56.11	odd	6
56.3.k.d.51.6	yes	12	7.4	even	3
224.3.o.d.79.5		12	28.11	odd	6
224.3.o.d.79.6		12	56.53	even	6
224.3.o.d.207.5		12	56.37	even	6
224.3.o.d.207.6		12	28.23	odd	6
392.3.g.i.99.3		6	7.6	odd	2
392.3.g.i.99.4		6	56.27	even	2
392.3.g.j.99.3		6	1.1	even	1	trivial
392.3.g.j.99.4		6	8.3	odd	2	inner
392.3.k.l.67.2		12	7.5	odd	6
392.3.k.l.67.6		12	56.19	even	6
392.3.k.l.275.2		12	56.3	even	6
392.3.k.l.275.6		12	7.3	odd	6
1568.3.g.j.687.1		6	8.5	even	2
1568.3.g.j.687.2		6	4.3	odd	2
1568.3.g.l.687.5		6	28.27	even	2
1568.3.g.l.687.6		6	56.13	odd	2

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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.789608 - 1.83753i) q^{2} +5.33225 q^{3} +(-2.75304 + 2.90186i) q^{4} +2.15693i q^{5} +(-4.21039 - 9.79818i) q^{6} +(7.50608 + 2.76746i) q^{8} +19.4329 q^{9} +O(q^{10})\)	\(q+(-0.789608 - 1.83753i) q^{2} +5.33225 q^{3} +(-2.75304 + 2.90186i) q^{4} +2.15693i q^{5} +(-4.21039 - 9.79818i) q^{6} +(7.50608 + 2.76746i) q^{8} +19.4329 q^{9} +(3.96343 - 1.70313i) q^{10} +5.25911 q^{11} +(-14.6799 + 15.4734i) q^{12} +21.4116i q^{13} +11.5013i q^{15} +(-0.841567 - 15.9779i) q^{16} +0.926859 q^{17} +(-15.3444 - 35.7086i) q^{18} -5.93010 q^{19} +(-6.25911 - 5.93812i) q^{20} +(-4.15264 - 9.66378i) q^{22} +8.68920i q^{23} +(40.0243 + 14.7568i) q^{24} +20.3476 q^{25} +(39.3444 - 16.9067i) q^{26} +55.6311 q^{27} -9.42223i q^{29} +(21.1340 - 9.08153i) q^{30} -34.5039i q^{31} +(-28.6953 + 14.1626i) q^{32} +28.0429 q^{33} +(-0.731855 - 1.70313i) q^{34} +(-53.4996 + 56.3916i) q^{36} -12.8002i q^{37} +(4.68245 + 10.8967i) q^{38} +114.172i q^{39} +(-5.96922 + 16.1901i) q^{40} +43.1339 q^{41} -41.7382 q^{43} +(-14.4785 + 15.2612i) q^{44} +41.9155i q^{45} +(15.9667 - 6.86106i) q^{46} +45.9983i q^{47} +(-4.48745 - 85.1980i) q^{48} +(-16.0667 - 37.3894i) q^{50} +4.94225 q^{51} +(-62.1333 - 58.9468i) q^{52} -74.4818i q^{53} +(-43.9267 - 102.224i) q^{54} +11.3436i q^{55} -31.6208 q^{57} +(-17.3136 + 7.43987i) q^{58} +53.6734 q^{59} +(-33.3752 - 31.6635i) q^{60} -27.8160i q^{61} +(-63.4020 + 27.2446i) q^{62} +(48.6823 + 41.5455i) q^{64} -46.1833 q^{65} +(-22.1429 - 51.5297i) q^{66} -78.4907 q^{67} +(-2.55168 + 2.68961i) q^{68} +46.3330i q^{69} -74.5100i q^{71} +(145.865 + 53.7799i) q^{72} +33.6041 q^{73} +(-23.5208 + 10.1072i) q^{74} +108.499 q^{75} +(16.3258 - 17.2083i) q^{76} +(209.794 - 90.1511i) q^{78} -30.2118i q^{79} +(34.4631 - 1.81520i) q^{80} +121.743 q^{81} +(-34.0589 - 79.2599i) q^{82} -72.9274 q^{83} +1.99917i q^{85} +(32.9568 + 76.6952i) q^{86} -50.2417i q^{87} +(39.4753 + 14.5544i) q^{88} -54.8396 q^{89} +(77.0211 - 33.0968i) q^{90} +(-25.2148 - 23.9217i) q^{92} -183.984i q^{93} +(84.5232 - 36.3206i) q^{94} -12.7908i q^{95} +(-153.011 + 75.5188i) q^{96} -53.7125 q^{97} +102.200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} + 6 q^{3} + 4 q^{4} - 28 q^{6} + 4 q^{8} + 40 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 + 6 * q^3 + 4 * q^4 - 28 * q^6 + 4 * q^8 + 40 * q^9	\( 6 q - 2 q^{2} + 6 q^{3} + 4 q^{4} - 28 q^{6} + 4 q^{8} + 40 q^{9} + 6 q^{10} - 30 q^{11} - 32 q^{12} - 16 q^{16} - 30 q^{17} + 16 q^{18} - 78 q^{19} + 24 q^{20} + 12 q^{22} + 76 q^{24} + 92 q^{25} + 128 q^{26} + 78 q^{27} + 16 q^{30} - 112 q^{32} + 78 q^{33} + 38 q^{34} - 124 q^{36} - 80 q^{38} - 44 q^{40} - 116 q^{41} - 100 q^{43} - 132 q^{44} + 156 q^{46} + 88 q^{48} + 24 q^{50} - 10 q^{51} - 132 q^{52} + 36 q^{54} + 166 q^{57} - 4 q^{58} + 110 q^{59} - 84 q^{60} - 48 q^{62} - 80 q^{64} + 32 q^{65} + 138 q^{66} - 434 q^{67} - 96 q^{68} + 328 q^{72} - 102 q^{73} + 34 q^{74} + 60 q^{75} - 84 q^{76} + 360 q^{78} + 256 q^{80} + 82 q^{81} + 24 q^{82} - 268 q^{83} - 240 q^{86} + 204 q^{88} - 214 q^{89} + 220 q^{90} + 80 q^{92} + 16 q^{94} - 48 q^{96} - 76 q^{97} + 252 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 + 6 * q^3 + 4 * q^4 - 28 * q^6 + 4 * q^8 + 40 * q^9 + 6 * q^10 - 30 * q^11 - 32 * q^12 - 16 * q^16 - 30 * q^17 + 16 * q^18 - 78 * q^19 + 24 * q^20 + 12 * q^22 + 76 * q^24 + 92 * q^25 + 128 * q^26 + 78 * q^27 + 16 * q^30 - 112 * q^32 + 78 * q^33 + 38 * q^34 - 124 * q^36 - 80 * q^38 - 44 * q^40 - 116 * q^41 - 100 * q^43 - 132 * q^44 + 156 * q^46 + 88 * q^48 + 24 * q^50 - 10 * q^51 - 132 * q^52 + 36 * q^54 + 166 * q^57 - 4 * q^58 + 110 * q^59 - 84 * q^60 - 48 * q^62 - 80 * q^64 + 32 * q^65 + 138 * q^66 - 434 * q^67 - 96 * q^68 + 328 * q^72 - 102 * q^73 + 34 * q^74 + 60 * q^75 - 84 * q^76 + 360 * q^78 + 256 * q^80 + 82 * q^81 + 24 * q^82 - 268 * q^83 - 240 * q^86 + 204 * q^88 - 214 * q^89 + 220 * q^90 + 80 * q^92 + 16 * q^94 - 48 * q^96 - 76 * q^97 + 252 * q^99

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