LMFDB - Embedded newform 392.3.g.i.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.i.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	$-0.848397\pi$
$3$	−5.33225			−1.77742			−0.888709	+	0.458472i	$0.848397\pi$
$4$	−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	$-0.508678\pi$
$17$	−0.926859			−0.0545211			−0.0272606	+	0.999628i	$0.508678\pi$
$18$	−15.3444	+	35.7086i	−0.852467	+	1.98381i
$19$	5.93010			0.312110			0.156055	−	0.987748i	$-0.450122\pi$
$19$	5.93010			0.312110			0.156055	+	0.987748i	$0.450122\pi$
$20$	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	$-0.812138\pi$
$31$		−	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	$0.0553383\pi$
$37$			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	$-0.676317\pi$
$41$	−43.1339			−1.05205			−0.526023	+	0.850470i	$0.676317\pi$
$42$		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	$0.248004\pi$
$53$			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	$-0.650311\pi$
$59$	−53.6734			−0.909719			−0.454860	+	0.890563i	$0.650311\pi$
$60$	−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	$0.175829\pi$
$71$			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	$-0.573927\pi$
$73$	−33.6041			−0.460330			−0.230165	+	0.973152i	$0.573927\pi$
$74$	−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	$-0.355219\pi$
$83$	72.9274			0.878644			0.439322	+	0.898330i	$0.355219\pi$
$84$		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	$-0.400311\pi$
$89$	54.8396			0.616176			0.308088	+	0.951358i	$0.400311\pi$
$90$	−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	$-0.410703\pi$
$97$	53.7125			0.553738			0.276869	+	0.960908i	$0.410703\pi$
$98$		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	$-0.901050\pi$
$109$		−	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	$-0.489354\pi$
$131$	8.76120			0.0668794			0.0334397	+	0.999441i	$0.489354\pi$
$132$	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	$-0.712520\pi$
$139$	−172.122			−1.23828			−0.619142	+	0.785279i	$0.712520\pi$
$140$		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	$0.119170\pi$
$157$			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	$-0.966160\pi$
$191$		−	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	$-0.699816\pi$
$199$		−	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	$-0.633696\pi$
$227$	−185.131			−0.815554			−0.407777	+	0.913082i	$0.633696\pi$
$228$	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	$0.110898\pi$
$239$			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	$-0.640194\pi$
$241$	−205.491			−0.852659			−0.426330	+	0.904568i	$0.640194\pi$
$242$	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	$-0.397214\pi$
$251$	159.299			0.634658			0.317329	+	0.948316i	$0.397214\pi$
$252$		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	$-0.637900\pi$
$257$	−215.777			−0.839599			−0.419800	+	0.907617i	$0.637900\pi$
$258$	−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	$0.183369\pi$
$269$			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	$0.206543\pi$
$277$			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	$-0.499652\pi$
$283$	0.618906			0.00218695			0.00109347	+	0.999999i	$0.499652\pi$
$284$	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	$-0.726457\pi$
$307$	−400.893			−1.30584			−0.652921	+	0.757426i	$0.726457\pi$
$308$		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	$-0.360164\pi$
$313$	266.246			0.850626			0.425313	+	0.905046i	$0.360164\pi$
$314$	−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	$0.0763566\pi$
$349$			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	$-0.267085\pi$
$353$	471.717			1.33631			0.668154	+	0.744023i	$0.267085\pi$
$354$	−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	$-0.839075\pi$
$367$		−	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	$-0.860770\pi$
$373$		−	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	$0.365268\pi$
$383$			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	$0.0723676\pi$
$389$			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	$-0.838536\pi$
$397$		−	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	$-0.326667\pi$
$409$	423.744			1.03605			0.518025	+	0.855366i	$0.326667\pi$
$410$	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	$-0.614751\pi$
$419$	−295.598			−0.705485			−0.352742	+	0.935721i	$0.614751\pi$
$420$		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	$-0.717287\pi$
$433$	−546.301			−1.26167			−0.630833	+	0.775919i	$0.717287\pi$
$434$		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	$0.249100\pi$
$463$			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	$-0.698510\pi$
$467$	−545.449			−1.16799			−0.583993	+	0.811759i	$0.698510\pi$
$468$	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	$-0.854690\pi$
$487$		−	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	$0.195664\pi$
$503$			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	$-0.743226\pi$
$521$	−720.959			−1.38380			−0.691899	+	0.721994i	$0.743226\pi$
$522$	−336.455	−	144.578i	−0.644549	−	0.276970i
$523$	269.977			0.516208			0.258104	−	0.966117i	$-0.416902\pi$
$523$	269.977			0.516208			0.258104	+	0.966117i	$0.416902\pi$
$524$	−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	$-0.503870\pi$
$563$	−13.6887			−0.0243139			−0.0121569	+	0.999926i	$0.503870\pi$
$564$	−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	$-0.148229\pi$
$577$	1031.12			1.78704			0.893518	+	0.449027i	$0.148229\pi$
$578$	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	$-0.306043\pi$
$587$	671.907			1.14464			0.572322	+	0.820029i	$0.306043\pi$
$588$		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	$-0.596480\pi$
$593$	−353.998			−0.596962			−0.298481	+	0.954416i	$0.596480\pi$
$594$	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	$-0.498197\pi$
$601$	6.80783			0.0113275			0.00566375	+	0.999984i	$0.498197\pi$
$602$		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	$-0.824688\pi$
$613$		−	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	$-0.613733\pi$
$619$	−432.989			−0.699498			−0.349749	+	0.936843i	$0.613733\pi$
$620$	−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	$-0.349698\pi$
$643$	584.919			0.909672			0.454836	+	0.890575i	$0.349698\pi$
$644$		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	$0.0118300\pi$
$653$			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	$0.218555\pi$
$661$			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	$-0.375529\pi$
$691$	526.747			0.762297			0.381149	+	0.924514i	$0.375529\pi$
$692$	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	$0.374883\pi$
$719$			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	$-0.870344\pi$
$743$		−	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	$-0.732158\pi$
$761$	−1014.23			−1.33276			−0.666382	+	0.745610i	$0.732158\pi$
$762$	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	$-0.220345\pi$
$769$	1183.99			1.53964			0.769822	+	0.638258i	$0.220345\pi$
$770$		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	$-0.554573\pi$
$787$	−268.536			−0.341214			−0.170607	+	0.985339i	$0.554573\pi$
$788$	−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	$-0.501167\pi$
$811$	−5.94522			−0.00733072			−0.00366536	+	0.999993i	$0.501167\pi$
$812$		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	$-0.972539\pi$
$829$		−	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	$-0.254342\pi$
$857$	1195.34			1.39479			0.697396	+	0.716686i	$0.254342\pi$
$858$	1103.33	+	474.115i	1.28594	+	0.552581i
$859$	341.769			0.397869			0.198934	−	0.980013i	$-0.436252\pi$
$859$	341.769			0.397869			0.198934	+	0.980013i	$0.436252\pi$
$860$	−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	$-0.414994\pi$
$881$	464.977			0.527783			0.263891	+	0.964552i	$0.414994\pi$
$882$		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	$-0.870331\pi$
$911$		−	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	$-0.421199\pi$
$929$	455.285			0.490081			0.245041	+	0.969513i	$0.421199\pi$
$930$	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	$-0.269208\pi$
$937$	1242.79			1.32635			0.663176	+	0.748464i	$0.269208\pi$
$938$		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	$-0.869388\pi$
$967$		−	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	$-0.656632\pi$
$971$	−917.509			−0.944911			−0.472456	+	0.881354i	$0.656632\pi$
$972$	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	$0.0565650\pi$
$991$			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	$0.0849666\pi$
$997$			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.i.99.4		6
4.3	odd	2		1568.3.g.l.687.6		6
7.2	even	3		392.3.k.l.67.6		12
7.3	odd	6		56.3.k.d.51.2	yes	12
7.4	even	3		392.3.k.l.275.2		12
7.5	odd	6		56.3.k.d.11.6	yes	12
7.6	odd	2		392.3.g.j.99.4		6
8.3	odd	2	inner	392.3.g.i.99.3		6
8.5	even	2		1568.3.g.l.687.5		6
28.3	even	6		224.3.o.d.79.6		12
28.19	even	6		224.3.o.d.207.5		12
28.27	even	2		1568.3.g.j.687.1		6
56.3	even	6		56.3.k.d.51.6	yes	12
56.5	odd	6		224.3.o.d.207.6		12
56.11	odd	6		392.3.k.l.275.6		12
56.13	odd	2		1568.3.g.j.687.2		6
56.19	even	6		56.3.k.d.11.2	✓	12
56.27	even	2		392.3.g.j.99.3		6
56.45	odd	6		224.3.o.d.79.5		12
56.51	odd	6		392.3.k.l.67.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.k.d.11.2	✓	12	56.19	even	6
56.3.k.d.11.6	yes	12	7.5	odd	6
56.3.k.d.51.2	yes	12	7.3	odd	6
56.3.k.d.51.6	yes	12	56.3	even	6
224.3.o.d.79.5		12	56.45	odd	6
224.3.o.d.79.6		12	28.3	even	6
224.3.o.d.207.5		12	28.19	even	6
224.3.o.d.207.6		12	56.5	odd	6
392.3.g.i.99.3		6	8.3	odd	2	inner
392.3.g.i.99.4		6	1.1	even	1	trivial
392.3.g.j.99.3		6	56.27	even	2
392.3.g.j.99.4		6	7.6	odd	2
392.3.k.l.67.2		12	56.51	odd	6
392.3.k.l.67.6		12	7.2	even	3
392.3.k.l.275.2		12	7.4	even	3
392.3.k.l.275.6		12	56.11	odd	6
1568.3.g.j.687.1		6	28.27	even	2
1568.3.g.j.687.2		6	56.13	odd	2
1568.3.g.l.687.5		6	8.5	even	2
1568.3.g.l.687.6		6	4.3	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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