LMFDB - Embedded newform 392.3.g.j.99.4

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.789608 + 1.83753i) q^{2} +5.33225 q^{3} +(-2.75304 - 2.90186i) q^{4} -2.15693i q^{5} +(-4.21039 + 9.79818i) q^{6} +(7.50608 - 2.76746i) q^{8} +19.4329 q^{9} +O(q^{10})$	\(q+(-0.789608 + 1.83753i) q^{2} +5.33225 q^{3} +(-2.75304 - 2.90186i) q^{4} -2.15693i q^{5} +(-4.21039 + 9.79818i) q^{6} +(7.50608 - 2.76746i) q^{8} +19.4329 q^{9} +(3.96343 + 1.70313i) q^{10} +5.25911 q^{11} +(-14.6799 - 15.4734i) q^{12} -21.4116i q^{13} -11.5013i q^{15} +(-0.841567 + 15.9779i) q^{16} +0.926859 q^{17} +(-15.3444 + 35.7086i) q^{18} -5.93010 q^{19} +(-6.25911 + 5.93812i) q^{20} +(-4.15264 + 9.66378i) q^{22} -8.68920i q^{23} +(40.0243 - 14.7568i) q^{24} +20.3476 q^{25} +(39.3444 + 16.9067i) q^{26} +55.6311 q^{27} +9.42223i q^{29} +(21.1340 + 9.08153i) q^{30} +34.5039i q^{31} +(-28.6953 - 14.1626i) q^{32} +28.0429 q^{33} +(-0.731855 + 1.70313i) q^{34} +(-53.4996 - 56.3916i) q^{36} +12.8002i q^{37} +(4.68245 - 10.8967i) q^{38} -114.172i q^{39} +(-5.96922 - 16.1901i) q^{40} +43.1339 q^{41} -41.7382 q^{43} +(-14.4785 - 15.2612i) q^{44} -41.9155i q^{45} +(15.9667 + 6.86106i) q^{46} -45.9983i q^{47} +(-4.48745 + 85.1980i) q^{48} +(-16.0667 + 37.3894i) q^{50} +4.94225 q^{51} +(-62.1333 + 58.9468i) q^{52} +74.4818i q^{53} +(-43.9267 + 102.224i) q^{54} -11.3436i q^{55} -31.6208 q^{57} +(-17.3136 - 7.43987i) q^{58} +53.6734 q^{59} +(-33.3752 + 31.6635i) q^{60} +27.8160i q^{61} +(-63.4020 - 27.2446i) q^{62} +(48.6823 - 41.5455i) q^{64} -46.1833 q^{65} +(-22.1429 + 51.5297i) q^{66} -78.4907 q^{67} +(-2.55168 - 2.68961i) q^{68} -46.3330i q^{69} +74.5100i q^{71} +(145.865 - 53.7799i) q^{72} +33.6041 q^{73} +(-23.5208 - 10.1072i) q^{74} +108.499 q^{75} +(16.3258 + 17.2083i) q^{76} +(209.794 + 90.1511i) q^{78} +30.2118i q^{79} +(34.4631 + 1.81520i) q^{80} +121.743 q^{81} +(-34.0589 + 79.2599i) q^{82} -72.9274 q^{83} -1.99917i q^{85} +(32.9568 - 76.6952i) q^{86} +50.2417i q^{87} +(39.4753 - 14.5544i) q^{88} -54.8396 q^{89} +(77.0211 + 33.0968i) q^{90} +(-25.2148 + 23.9217i) q^{92} +183.984i q^{93} +(84.5232 + 36.3206i) q^{94} +12.7908i q^{95} +(-153.011 - 75.5188i) q^{96} -53.7125 q^{97} +102.200 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.930799\pi$
$5$		−	2.15693i		−	0.431386i	0.976461	−	0.215693i	$-0.0692011\pi$
$6$	−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	$-0.692006\pi$
$13$		−	21.4116i		−	1.64704i	0.567285	−	0.823522i	$-0.307994\pi$
$14$		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	$-0.939509\pi$
$23$		−	8.68920i		−	0.377791i	0.981997	−	0.188896i	$-0.0604908\pi$
$24$	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	$0.0519403\pi$
$29$			9.42223i			0.324904i	−0.986716	+	0.162452i	$0.948060\pi$
$30$	21.1340	+	9.08153i	0.704467	+	0.302718i
$31$			34.5039i			1.11303i	0.830837	+	0.556515i	$0.187862\pi$
$31$			34.5039i			1.11303i	−0.830837	+	0.556515i	$0.812138\pi$
$32$	−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	$0.0553383\pi$
$37$			12.8002i			0.345952i	−0.984926	+	0.172976i	$0.944662\pi$
$38$	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	$-0.837237\pi$
$47$		−	45.9983i		−	0.978686i	0.872091	−	0.489343i	$-0.162763\pi$
$48$	−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	$0.248004\pi$
$53$			74.4818i			1.40532i	−0.711528	+	0.702658i	$0.751996\pi$
$54$	−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	$0.0732186\pi$
$61$			27.8160i			0.456000i	−0.973661	+	0.228000i	$0.926781\pi$
$62$	−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	$0.175829\pi$
$71$			74.5100i			1.04944i	−0.851276	+	0.524719i	$0.824171\pi$
$72$	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	$0.0612424\pi$
$79$			30.2118i			0.382428i	−0.981548	+	0.191214i	$0.938758\pi$
$80$	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	$-0.852479\pi$
$101$		−	90.3019i		−	0.894078i	0.894515	−	0.447039i	$-0.147521\pi$
$102$	−3.90244	+	9.08153i	−0.0382592	+	0.0890346i
$103$			112.812i			1.09526i	0.836720	+	0.547631i	$0.184470\pi$
$103$			112.812i			1.09526i	−0.836720	+	0.547631i	$0.815530\pi$
$104$	−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	$-0.901050\pi$
$109$		−	66.6813i		−	0.611755i	0.952071	−	0.305877i	$-0.0989498\pi$
$110$	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	$0.173206\pi$
$127$			131.492i			1.03537i	−0.855572	+	0.517684i	$0.826794\pi$
$128$	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	$-0.718160\pi$
$149$		−	230.707i		−	1.54837i	0.632959	−	0.774186i	$-0.281840\pi$
$150$	−85.6715	+	199.370i	−0.571144	+	1.32913i
$151$			147.890i			0.979406i	0.871889	+	0.489703i	$0.162895\pi$
$151$			147.890i			0.979406i	−0.871889	+	0.489703i	$0.837105\pi$
$152$	−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	$-0.880830\pi$
$157$		−	114.829i		−	0.731396i	0.930734	−	0.365698i	$-0.119170\pi$
$158$	−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	$-0.742797\pi$
$167$		−	241.457i		−	1.44585i	0.690926	−	0.722926i	$-0.257203\pi$
$168$		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	$-0.949725\pi$
$173$		−	54.4211i		−	0.314573i	0.987553	−	0.157286i	$-0.0502746\pi$
$174$	−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	$0.199920\pi$
$181$			212.704i			1.17516i	−0.809165	+	0.587581i	$0.800080\pi$
$182$		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	$-0.966160\pi$
$191$		−	40.5347i		−	0.212224i	0.994354	−	0.106112i	$-0.0338402\pi$
$192$	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	$-0.768652\pi$
$197$		−	261.806i		−	1.32896i	0.747304	−	0.664482i	$-0.231348\pi$
$198$	−80.6980	+	187.796i	−0.407565	+	0.948463i
$199$			322.124i			1.61871i	0.587317	+	0.809357i	$0.300184\pi$
$199$			322.124i			1.61871i	−0.587317	+	0.809357i	$0.699816\pi$
$200$	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	$0.0325031\pi$
$223$			45.4626i			0.203868i	−0.994791	+	0.101934i	$0.967497\pi$
$224$		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	$0.132320\pi$
$229$			184.952i			0.807650i	−0.914836	+	0.403825i	$0.867680\pi$
$230$	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	$0.110898\pi$
$239$			163.185i			0.682782i	−0.939921	+	0.341391i	$0.889102\pi$
$240$	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	$0.215217\pi$
$263$			329.157i			1.25155i	−0.780004	+	0.625775i	$0.784783\pi$
$264$	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	$-0.816631\pi$
$269$		−	293.067i		−	1.08947i	0.838609	−	0.544734i	$-0.183369\pi$
$270$	220.490	+	94.7470i	0.816629	+	0.350915i
$271$			26.8502i			0.0990782i	0.998772	+	0.0495391i	$0.0157752\pi$
$271$			26.8502i			0.0990782i	−0.998772	+	0.0495391i	$0.984225\pi$
$272$	−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	$0.206543\pi$
$277$			334.777i			1.20858i	−0.796764	+	0.604291i	$0.793457\pi$
$278$	−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	$0.0153671\pi$
$293$			28.2794i			0.0965169i	−0.998835	+	0.0482584i	$0.984633\pi$
$294$		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	$-0.916009\pi$
$311$		−	162.226i		−	0.521628i	0.965389	−	0.260814i	$-0.0839910\pi$
$312$	−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	$0.239211\pi$
$317$			432.855i			1.36547i	−0.730664	+	0.682737i	$0.760789\pi$
$318$	−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	$-0.923643\pi$
$349$		−	165.836i		−	0.475174i	0.971366	−	0.237587i	$-0.0763566\pi$
$350$		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	$0.367827\pi$
$359$			656.986i			1.83004i	−0.403403	+	0.915022i	$0.632173\pi$
$360$	−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	$0.160925\pi$
$367$			355.475i			0.968596i	−0.874903	+	0.484298i	$0.839075\pi$
$368$	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	$-0.860770\pi$
$373$		−	315.998i		−	0.847180i	0.905854	−	0.423590i	$-0.139230\pi$
$374$	−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	$-0.634732\pi$
$383$		−	698.400i		−	1.82350i	0.410746	−	0.911750i	$-0.365268\pi$
$384$	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	$0.0723676\pi$
$389$			175.358i			0.450792i	−0.974267	+	0.225396i	$0.927632\pi$
$390$	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	$0.161464\pi$
$397$			385.708i			0.971557i	−0.874082	+	0.485778i	$0.838536\pi$
$398$	−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	$0.0479119\pi$
$421$			126.260i			0.299904i	−0.988693	+	0.149952i	$0.952088\pi$
$422$	−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	$-0.904691\pi$
$431$		−	254.263i		−	0.589937i	0.955507	−	0.294968i	$-0.0953091\pi$
$432$	−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	$-0.899230\pi$
$439$		−	273.335i		−	0.622631i	0.950307	−	0.311315i	$-0.100770\pi$
$440$	−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	$0.0704972\pi$
$461$			202.533i			0.439335i	−0.975575	+	0.219667i	$0.929503\pi$
$462$		0			0
$463$			652.927i			1.41021i	0.709103	+	0.705105i	$0.249100\pi$
$463$			652.927i			1.41021i	−0.709103	+	0.705105i	$0.750900\pi$
$464$	−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	$0.0362612\pi$
$479$			108.897i			0.227343i	−0.993518	+	0.113672i	$0.963739\pi$
$480$	−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	$-0.854690\pi$
$487$		−	429.353i		−	0.881629i	0.897598	−	0.440814i	$-0.145310\pi$
$488$	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	$-0.804336\pi$
$503$		−	580.170i		−	1.15342i	0.816949	−	0.576710i	$-0.195664\pi$
$504$		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	$-0.902337\pi$
$509$		−	307.463i		−	0.604054i	0.953299	−	0.302027i	$-0.0976632\pi$
$510$	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	$-0.683441\pi$
$541$		−	907.242i		−	1.67697i	0.544922	−	0.838486i	$-0.316559\pi$
$542$	−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	$-0.720754\pi$
$557$		−	856.668i		−	1.53800i	0.639246	−	0.769002i	$-0.279246\pi$
$558$	−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	$0.397260\pi$
$599$			1136.14i			1.89672i	−0.317193	+	0.948361i	$0.602740\pi$
$600$	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	$0.119869\pi$
$607$			446.439i			0.735484i	−0.929928	+	0.367742i	$0.880131\pi$
$608$	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	$-0.824688\pi$
$613$		−	641.609i		−	1.04667i	0.852127	−	0.523335i	$-0.175312\pi$
$614$	−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	$-0.939363\pi$
$631$		−	238.957i		−	0.378695i	0.981910	−	0.189348i	$-0.0606373\pi$
$632$	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	$0.0835289\pi$
$647$			335.680i			0.518825i	−0.965767	+	0.259413i	$0.916471\pi$
$648$	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	$0.0118300\pi$
$653$			48.5265i			0.0743132i	−0.999309	+	0.0371566i	$0.988170\pi$
$654$	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	$-0.781445\pi$
$661$		−	838.042i		−	1.26784i	0.773399	−	0.633919i	$-0.218555\pi$
$662$	−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	$-0.787820\pi$
$677$		−	837.185i		−	1.23661i	0.785938	−	0.618305i	$-0.212180\pi$
$678$	−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	$-0.834777\pi$
$701$		−	695.486i		−	0.992134i	0.868284	−	0.496067i	$-0.165223\pi$
$702$	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	$-0.773078\pi$
$709$		−	927.410i		−	1.30805i	0.756471	−	0.654027i	$-0.226922\pi$
$710$	−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	$-0.625117\pi$
$719$		−	1328.34i		−	1.84748i	0.383022	−	0.923739i	$-0.374883\pi$
$720$	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	$-0.879023\pi$
$727$		−	539.401i		−	0.741954i	0.928642	−	0.370977i	$-0.120977\pi$
$728$		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	$-0.902492\pi$
$733$		−	442.088i		−	0.603121i	0.953447	−	0.301561i	$-0.0975076\pi$
$734$	−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	$-0.870344\pi$
$743$		−	588.688i		−	0.792313i	0.918183	−	0.396156i	$-0.129656\pi$
$744$	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	$0.183422\pi$
$751$			818.399i			1.08975i	−0.838519	+	0.544873i	$0.816578\pi$
$752$	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	$0.0221146\pi$
$757$			105.101i			0.138838i	−0.997588	+	0.0694192i	$0.977885\pi$
$758$	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	$0.0672730\pi$
$773$			324.311i			0.419549i	−0.977750	+	0.209774i	$0.932727\pi$
$774$	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	$0.391363\pi$
$797$			1502.06i			1.88465i	−0.334705	+	0.942323i	$0.608637\pi$
$798$		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	$0.00293595\pi$
$821$			15.1449i			0.0184469i	−0.999957	+	0.00922344i	$0.997064\pi$
$822$	997.191	−	2320.61i	1.21313	−	2.82312i
$823$		−	1482.76i		−	1.80165i	−0.434185	−	0.900824i	$-0.642964\pi$
$823$		−	1482.76i		−	1.80165i	0.434185	−	0.900824i	$-0.357036\pi$
$824$	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	$0.0274613\pi$
$829$			142.862i			0.172331i	−0.996281	+	0.0861654i	$0.972539\pi$
$830$	−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	$0.00317659\pi$
$839$			16.7454i			0.0199588i	−0.999950	+	0.00997940i	$0.996823\pi$
$840$		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	$-0.724388\pi$
$853$		−	1299.38i		−	1.52331i	0.647984	−	0.761654i	$-0.275612\pi$
$854$		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	$-0.808922\pi$
$863$		−	974.986i		−	1.12976i	0.825172	−	0.564882i	$-0.191078\pi$
$864$	−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	$0.0577667\pi$
$877$			316.570i			0.360970i	−0.983578	+	0.180485i	$0.942233\pi$
$878$	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	$0.00196155\pi$
$887$			10.9320i			0.0123247i	−0.999981	+	0.00616235i	$0.998038\pi$
$888$	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	$-0.870331\pi$
$911$		−	721.866i		−	0.792389i	0.918167	−	0.396194i	$-0.129669\pi$
$912$	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	$0.0226580\pi$
$919$			130.722i			0.142244i	−0.997468	+	0.0711221i	$0.977342\pi$
$920$	−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	$-0.793491\pi$
$941$		−	1137.11i		−	1.20841i	0.796830	−	0.604204i	$-0.206509\pi$
$942$	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	$-0.869388\pi$
$967$		−	771.494i		−	0.797822i	0.916990	−	0.398911i	$-0.130612\pi$
$968$	−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	$-0.610002\pi$
$983$		−	1849.77i		−	1.88176i	0.338743	−	0.940879i	$-0.389998\pi$
$984$	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	$0.0565650\pi$
$991$			350.359i			0.353541i	−0.984252	+	0.176770i	$0.943435\pi$
$992$	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	$-0.915033\pi$
$997$		−	525.961i		−	0.527543i	0.964585	−	0.263772i	$-0.0849666\pi$
$998$	−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.99.4		6
4.3	odd	2		1568.3.g.j.687.1		6
7.2	even	3		56.3.k.d.11.6	yes	12
7.3	odd	6		392.3.k.l.275.2		12
7.4	even	3		56.3.k.d.51.2	yes	12
7.5	odd	6		392.3.k.l.67.6		12
7.6	odd	2		392.3.g.i.99.4		6
8.3	odd	2	inner	392.3.g.j.99.3		6
8.5	even	2		1568.3.g.j.687.2		6
28.11	odd	6		224.3.o.d.79.6		12
28.23	odd	6		224.3.o.d.207.5		12
28.27	even	2		1568.3.g.l.687.6		6
56.3	even	6		392.3.k.l.275.6		12
56.11	odd	6		56.3.k.d.51.6	yes	12
56.13	odd	2		1568.3.g.l.687.5		6
56.19	even	6		392.3.k.l.67.2		12
56.27	even	2		392.3.g.i.99.3		6
56.37	even	6		224.3.o.d.207.6		12
56.51	odd	6		56.3.k.d.11.2	✓	12
56.53	even	6		224.3.o.d.79.5		12

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