LMFDB - Embedded newform 504.3.g.b.379.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,3,Mod(379,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("504.379");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.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:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.292213762624.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} - 2x^{5} + 24x^{4} - 8x^{3} - 32x^{2} - 64x + 256 $ x^8 - x^7 - 2x^6 - 2x^5 + 24x^4 - 8x^3 - 32x^2 - 64x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.5
Root			$-1.05468 + 1.69931i$ of defining polynomial
Character	$\chi$	$=$	504.379
Dual form			504.3.g.b.379.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05468 - 1.69931i) q^{2} +(-1.77532 - 3.58445i) q^{4} +4.88287i q^{5} -2.64575i q^{7} +(-7.96347 - 0.763618i) q^{8} +O(q^{10})$	\(q+(1.05468 - 1.69931i) q^{2} +(-1.77532 - 3.58445i) q^{4} +4.88287i q^{5} -2.64575i q^{7} +(-7.96347 - 0.763618i) q^{8} +(8.29751 + 5.14984i) q^{10} +21.4776 q^{11} -13.0760i q^{13} +(-4.49595 - 2.79041i) q^{14} +(-9.69651 + 12.7270i) q^{16} +0.234889 q^{17} +4.55872 q^{19} +(17.5024 - 8.66863i) q^{20} +(22.6519 - 36.4971i) q^{22} -10.9523i q^{23} +1.15761 q^{25} +(-22.2202 - 13.7910i) q^{26} +(-9.48355 + 4.69704i) q^{28} -34.6435i q^{29} -34.1079i q^{31} +(11.4005 + 29.9003i) q^{32} +(0.247732 - 0.399150i) q^{34} +12.9189 q^{35} -54.2370i q^{37} +(4.80798 - 7.74669i) q^{38} +(3.72865 - 38.8846i) q^{40} +37.8300 q^{41} -4.84714 q^{43} +(-38.1295 - 76.9852i) q^{44} +(-18.6114 - 11.5511i) q^{46} +72.3368i q^{47} -7.00000 q^{49} +(1.22090 - 1.96714i) q^{50} +(-46.8703 + 23.2141i) q^{52} -21.6707i q^{53} +104.872i q^{55} +(-2.02034 + 21.0694i) q^{56} +(-58.8701 - 36.5377i) q^{58} -34.9007 q^{59} +63.6012i q^{61} +(-57.9599 - 35.9728i) q^{62} +(62.8338 + 12.1621i) q^{64} +63.8485 q^{65} +18.4344 q^{67} +(-0.417002 - 0.841948i) q^{68} +(13.6252 - 21.9531i) q^{70} +47.5244i q^{71} +55.9103 q^{73} +(-92.1655 - 57.2024i) q^{74} +(-8.09317 - 16.3405i) q^{76} -56.8243i q^{77} -95.0135i q^{79} +(-62.1445 - 47.3468i) q^{80} +(39.8984 - 64.2849i) q^{82} -71.5156 q^{83} +1.14693i q^{85} +(-5.11217 + 8.23680i) q^{86} +(-171.036 - 16.4007i) q^{88} +159.756 q^{89} -34.5959 q^{91} +(-39.2579 + 19.4438i) q^{92} +(122.923 + 76.2920i) q^{94} +22.2596i q^{95} -90.4794 q^{97} +(-7.38273 + 11.8952i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 5 q^{4} - 13 q^{8}+O(q^{10}) $ 8 * q - q^2 + 5 * q^4 - 13 * q^8	$ 8 q - q^{2} + 5 q^{4} - 13 q^{8} + 16 q^{10} + 32 q^{11} - 7 q^{14} - 71 q^{16} + 80 q^{17} + 56 q^{19} + 108 q^{20} + 66 q^{22} - 16 q^{25} - 24 q^{26} + 7 q^{28} + 19 q^{32} + 74 q^{34} - 56 q^{35} + 14 q^{38} + 84 q^{40} - 128 q^{41} - 50 q^{44} - 152 q^{46} - 56 q^{49} - 33 q^{50} + 132 q^{52} + 49 q^{56} + 24 q^{58} - 104 q^{59} - 120 q^{62} - 55 q^{64} + 72 q^{65} + 304 q^{67} + 190 q^{68} + 56 q^{70} - 112 q^{73} - 8 q^{74} + 70 q^{76} - 124 q^{80} + 450 q^{82} - 72 q^{83} - 210 q^{86} - 486 q^{88} + 512 q^{89} - 56 q^{91} + 472 q^{92} + 472 q^{94} + 64 q^{97} + 7 q^{98}+O(q^{100}) $ 8 * q - q^2 + 5 * q^4 - 13 * q^8 + 16 * q^10 + 32 * q^11 - 7 * q^14 - 71 * q^16 + 80 * q^17 + 56 * q^19 + 108 * q^20 + 66 * q^22 - 16 * q^25 - 24 * q^26 + 7 * q^28 + 19 * q^32 + 74 * q^34 - 56 * q^35 + 14 * q^38 + 84 * q^40 - 128 * q^41 - 50 * q^44 - 152 * q^46 - 56 * q^49 - 33 * q^50 + 132 * q^52 + 49 * q^56 + 24 * q^58 - 104 * q^59 - 120 * q^62 - 55 * q^64 + 72 * q^65 + 304 * q^67 + 190 * q^68 + 56 * q^70 - 112 * q^73 - 8 * q^74 + 70 * q^76 - 124 * q^80 + 450 * q^82 - 72 * q^83 - 210 * q^86 - 486 * q^88 + 512 * q^89 - 56 * q^91 + 472 * q^92 + 472 * q^94 + 64 * q^97 + 7 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.05468	−	1.69931i	0.527338	−	0.849655i
$2$	1.05468	−	1.69931i	0.527338	−	0.849655i
$3$		0			0
$3$		0			0
$4$	−1.77532	−	3.58445i	−0.443829	−	0.896112i
$5$			4.88287i			0.976573i	0.872683	+	0.488287i	$0.162378\pi$
$5$			4.88287i			0.976573i	−0.872683	+	0.488287i	$0.837622\pi$
$6$		0			0
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	−7.96347	−	0.763618i	−0.995434	−	0.0954523i
$9$		0			0
$10$	8.29751	+	5.14984i	0.829751	+	0.514984i
$11$	21.4776			1.95251			0.976253	−	0.216632i	$-0.0695071\pi$
$11$	21.4776			1.95251			0.976253	+	0.216632i	$0.0695071\pi$
$12$		0			0
$13$		−	13.0760i		−	1.00585i	−0.864331	−	0.502924i	$-0.832258\pi$
$13$		−	13.0760i		−	1.00585i	0.864331	−	0.502924i	$-0.167742\pi$
$14$	−4.49595	−	2.79041i	−0.321140	−	0.199315i
$15$		0			0
$16$	−9.69651	+	12.7270i	−0.606032	+	0.795440i
$17$	0.234889			0.0138170			0.00690851	−	0.999976i	$-0.497801\pi$
$17$	0.234889			0.0138170			0.00690851	+	0.999976i	$0.497801\pi$
$18$		0			0
$19$	4.55872			0.239933			0.119966	−	0.992778i	$-0.461721\pi$
$19$	4.55872			0.239933			0.119966	+	0.992778i	$0.461721\pi$
$20$	17.5024	−	8.66863i	0.875119	−	0.433431i
$21$		0			0
$22$	22.6519	−	36.4971i	1.02963	−	1.65896i
$23$		−	10.9523i		−	0.476187i	−0.971242	−	0.238094i	$-0.923478\pi$
$23$		−	10.9523i		−	0.476187i	0.971242	−	0.238094i	$-0.0765225\pi$
$24$		0			0
$25$	1.15761			0.0463043
$26$	−22.2202	−	13.7910i	−0.854624	−	0.530422i
$27$		0			0
$28$	−9.48355	+	4.69704i	−0.338698	+	0.167752i
$29$		−	34.6435i		−	1.19460i	−0.802016	−	0.597302i	$-0.796239\pi$
$29$		−	34.6435i		−	1.19460i	0.802016	−	0.597302i	$-0.203761\pi$
$30$		0			0
$31$		−	34.1079i		−	1.10025i	−0.835081	−	0.550127i	$-0.814579\pi$
$31$		−	34.1079i		−	1.10025i	0.835081	−	0.550127i	$-0.185421\pi$
$32$	11.4005	+	29.9003i	0.356266	+	0.934384i
$33$		0			0
$34$	0.247732	−	0.399150i	0.00728624	−	0.0117397i
$35$	12.9189			0.369110
$36$		0			0
$37$		−	54.2370i		−	1.46586i	−0.680302	−	0.732932i	$-0.738151\pi$
$37$		−	54.2370i		−	1.46586i	0.680302	−	0.732932i	$-0.261849\pi$
$38$	4.80798	−	7.74669i	0.126526	−	0.203860i
$39$		0			0
$40$	3.72865	−	38.8846i	0.0932162	−	0.972114i
$41$	37.8300			0.922682			0.461341	−	0.887223i	$-0.347368\pi$
$41$	37.8300			0.922682			0.461341	+	0.887223i	$0.347368\pi$
$42$		0			0
$43$	−4.84714			−0.112724			−0.0563621	−	0.998410i	$-0.517950\pi$
$43$	−4.84714			−0.112724			−0.0563621	+	0.998410i	$0.517950\pi$
$44$	−38.1295	−	76.9852i	−0.866579	−	1.74966i
$45$		0			0
$46$	−18.6114	−	11.5511i	−0.404595	−	0.251112i
$47$			72.3368i			1.53908i	0.638598	+	0.769541i	$0.279515\pi$
$47$			72.3368i			1.53908i	−0.638598	+	0.769541i	$0.720485\pi$
$48$		0			0
$49$	−7.00000			−0.142857
$50$	1.22090	−	1.96714i	0.0244180	−	0.0393427i
$51$		0			0
$52$	−46.8703	+	23.2141i	−0.901352	+	0.446424i
$53$		−	21.6707i		−	0.408881i	−0.978879	−	0.204440i	$-0.934463\pi$
$53$		−	21.6707i		−	0.408881i	0.978879	−	0.204440i	$-0.0655374\pi$
$54$		0			0
$55$			104.872i			1.90677i
$56$	−2.02034	+	21.0694i	−0.0360776	+	0.376239i
$57$		0			0
$58$	−58.8701	−	36.5377i	−1.01500	−	0.629961i
$59$	−34.9007			−0.591537			−0.295768	−	0.955260i	$-0.595576\pi$
$59$	−34.9007			−0.591537			−0.295768	+	0.955260i	$0.595576\pi$
$60$		0			0
$61$			63.6012i			1.04264i	0.853360	+	0.521321i	$0.174561\pi$
$61$			63.6012i			1.04264i	−0.853360	+	0.521321i	$0.825439\pi$
$62$	−57.9599	−	35.9728i	−0.934837	−	0.580206i
$63$		0			0
$64$	62.8338	+	12.1621i	0.981778	+	0.190033i
$65$	63.8485			0.982284
$66$		0			0
$67$	18.4344			0.275140			0.137570	−	0.990492i	$-0.456071\pi$
$67$	18.4344			0.275140			0.137570	+	0.990492i	$0.456071\pi$
$68$	−0.417002	−	0.841948i	−0.00613239	−	0.0123816i
$69$		0			0
$70$	13.6252	−	21.9531i	0.194646	−	0.313616i
$71$			47.5244i			0.669358i	0.942332	+	0.334679i	$0.108628\pi$
$71$			47.5244i			0.669358i	−0.942332	+	0.334679i	$0.891372\pi$
$72$		0			0
$73$	55.9103			0.765894			0.382947	−	0.923770i	$-0.374909\pi$
$73$	55.9103			0.765894			0.382947	+	0.923770i	$0.374909\pi$
$74$	−92.1655	−	57.2024i	−1.24548	−	0.773006i
$75$		0			0
$76$	−8.09317	−	16.3405i	−0.106489	−	0.215007i
$77$		−	56.8243i		−	0.737978i
$78$		0			0
$79$		−	95.0135i		−	1.20270i	−0.798985	−	0.601351i	$-0.794629\pi$
$79$		−	95.0135i		−	1.20270i	0.798985	−	0.601351i	$-0.205371\pi$
$80$	−62.1445	−	47.3468i	−0.776806	−	0.591835i
$81$		0			0
$82$	39.8984	−	64.2849i	0.486566	−	0.783962i
$83$	−71.5156			−0.861634			−0.430817	−	0.902439i	$-0.641775\pi$
$83$	−71.5156			−0.861634			−0.430817	+	0.902439i	$0.641775\pi$
$84$		0			0
$85$			1.14693i			0.0134933i
$86$	−5.11217	+	8.23680i	−0.0594438	+	0.0957768i
$87$		0			0
$88$	−171.036	−	16.4007i	−1.94359	−	0.186371i
$89$	159.756			1.79501			0.897504	−	0.441006i	$-0.145378\pi$
$89$	159.756			1.79501			0.897504	+	0.441006i	$0.145378\pi$
$90$		0			0
$91$	−34.5959			−0.380175
$92$	−39.2579	+	19.4438i	−0.426717	+	0.211346i
$93$		0			0
$94$	122.923	+	76.2920i	1.30769	+	0.811617i
$95$			22.2596i			0.234312i
$96$		0			0
$97$	−90.4794			−0.932777			−0.466389	−	0.884580i	$-0.654445\pi$
$97$	−90.4794			−0.932777			−0.466389	+	0.884580i	$0.654445\pi$
$98$	−7.38273	+	11.8952i	−0.0753340	+	0.121379i
$99$		0			0
$100$	−2.05512	−	4.14938i	−0.0205512	−	0.0414938i
$101$			181.147i			1.79353i	0.442503	+	0.896767i	$0.354091\pi$
$101$			181.147i			1.79353i	−0.442503	+	0.896767i	$0.645909\pi$
$102$		0			0
$103$			39.3003i			0.381556i	0.981633	+	0.190778i	$0.0611010\pi$
$103$			39.3003i			0.381556i	−0.981633	+	0.190778i	$0.938899\pi$
$104$	−9.98509	+	104.131i	−0.0960105	+	1.00126i
$105$		0			0
$106$	−36.8252	−	22.8556i	−0.347408	−	0.215618i
$107$	−38.4498			−0.359344			−0.179672	−	0.983727i	$-0.557504\pi$
$107$	−38.4498			−0.359344			−0.179672	+	0.983727i	$0.557504\pi$
$108$		0			0
$109$			27.8786i			0.255767i	0.991789	+	0.127883i	$0.0408183\pi$
$109$			27.8786i			0.255767i	−0.991789	+	0.127883i	$0.959182\pi$
$110$	178.210	+	110.606i	1.62009	+	1.00551i
$111$		0			0
$112$	33.6726	+	25.6546i	0.300648	+	0.229059i
$113$	−82.4419			−0.729574			−0.364787	−	0.931091i	$-0.618858\pi$
$113$	−82.4419			−0.729574			−0.364787	+	0.931091i	$0.618858\pi$
$114$		0			0
$115$	53.4786			0.465032
$116$	−124.178	+	61.5032i	−1.07050	+	0.530200i
$117$		0			0
$118$	−36.8089	+	59.3071i	−0.311940	+	0.502603i
$119$		−	0.621458i		−	0.00522234i
$120$		0			0
$121$	340.286			2.81228
$122$	108.078	+	67.0787i	0.885887	+	0.549825i
$123$		0			0
$124$	−122.258	+	60.5522i	−0.985951	+	0.488325i
$125$			127.724i			1.02179i
$126$		0			0
$127$			25.1408i			0.197959i	0.995089	+	0.0989796i	$0.0315579\pi$
$127$			25.1408i			0.197959i	−0.995089	+	0.0989796i	$0.968442\pi$
$128$	86.9365	−	93.9470i	0.679191	−	0.733961i
$129$		0			0
$130$	67.3395	−	108.498i	0.517996	−	0.834603i
$131$	126.398			0.964872			0.482436	−	0.875931i	$-0.339752\pi$
$131$	126.398			0.964872			0.482436	+	0.875931i	$0.339752\pi$
$132$		0			0
$133$		−	12.0612i		−	0.0906861i
$134$	19.4423	−	31.3257i	0.145092	−	0.233774i
$135$		0			0
$136$	−1.87053	−	0.179366i	−0.0137539	−	0.00131887i
$137$	−34.9456			−0.255078			−0.127539	−	0.991834i	$-0.540708\pi$
$137$	−34.9456			−0.255078			−0.127539	+	0.991834i	$0.540708\pi$
$138$		0			0
$139$	−119.148			−0.857177			−0.428589	−	0.903500i	$-0.640989\pi$
$139$	−119.148			−0.857177			−0.428589	+	0.903500i	$0.640989\pi$
$140$	−22.9350	−	46.3069i	−0.163822	−	0.330764i
$141$		0			0
$142$	80.7587	+	50.1229i	0.568723	+	0.352978i
$143$		−	280.841i		−	1.96392i
$144$		0			0
$145$	169.160			1.16662
$146$	58.9673	−	95.0090i	0.403885	−	0.650746i
$147$		0			0
$148$	−194.409	+	96.2877i	−1.31358	+	0.650593i
$149$		−	121.932i		−	0.818334i	−0.912460	−	0.409167i	$-0.865819\pi$
$149$		−	121.932i		−	0.818334i	0.912460	−	0.409167i	$-0.134181\pi$
$150$		0			0
$151$			220.404i			1.45963i	0.683645	+	0.729815i	$0.260394\pi$
$151$			220.404i			1.45963i	−0.683645	+	0.729815i	$0.739606\pi$
$152$	−36.3033	−	3.48112i	−0.238837	−	0.0229021i
$153$		0			0
$154$	−96.5622	−	59.9313i	−0.627027	−	0.389164i
$155$	166.544			1.07448
$156$		0			0
$157$			6.77014i			0.0431219i	0.999768	+	0.0215610i	$0.00686360\pi$
$157$			6.77014i			0.0431219i	−0.999768	+	0.0215610i	$0.993136\pi$
$158$	−161.457	−	100.208i	−1.02188	−	0.634231i
$159$		0			0
$160$	−145.999	+	55.6672i	−0.912495	+	0.347920i
$161$	−28.9771			−0.179982
$162$		0			0
$163$	−207.243			−1.27143			−0.635715	−	0.771924i	$-0.719294\pi$
$163$	−207.243			−1.27143			−0.635715	+	0.771924i	$0.719294\pi$
$164$	−67.1601	−	135.600i	−0.409513	−	0.826826i
$165$		0			0
$166$	−75.4259	+	121.527i	−0.454373	+	0.732092i
$167$			165.529i			0.991193i	0.868553	+	0.495596i	$0.165050\pi$
$167$			165.529i			0.991193i	−0.868553	+	0.495596i	$0.834950\pi$
$168$		0			0
$169$	−1.98237			−0.0117300
$170$	1.94900	+	1.20964i	0.0114647	+	0.00711555i
$171$		0			0
$172$	8.60521	+	17.3743i	0.0500303	+	0.101014i
$173$		−	88.8530i		−	0.513601i	−0.966464	−	0.256800i	$-0.917332\pi$
$173$		−	88.8530i		−	0.513601i	0.966464	−	0.256800i	$-0.0826683\pi$
$174$		0			0
$175$		−	3.06274i		−	0.0175014i
$176$	−208.258	+	273.346i	−1.18328	+	1.55310i
$177$		0			0
$178$	168.491	−	271.475i	0.946576	−	1.52514i
$179$	−80.3791			−0.449045			−0.224523	−	0.974469i	$-0.572082\pi$
$179$	−80.3791			−0.449045			−0.224523	+	0.974469i	$0.572082\pi$
$180$		0			0
$181$		−	276.353i		−	1.52681i	−0.645919	−	0.763406i	$-0.723526\pi$
$181$		−	276.353i		−	1.52681i	0.645919	−	0.763406i	$-0.276474\pi$
$182$	−36.4875	+	58.7892i	−0.200481	+	0.323018i
$183$		0			0
$184$	−8.36338	+	87.2184i	−0.0454532	+	0.474013i
$185$	264.832			1.43152
$186$		0			0
$187$	5.04485			0.0269778
$188$	259.288	−	128.421i	1.37919	−	0.683089i
$189$		0			0
$190$	37.8260	+	23.4767i	0.199084	+	0.123562i
$191$			203.015i			1.06290i	0.847088	+	0.531452i	$0.178353\pi$
$191$			203.015i			1.06290i	−0.847088	+	0.531452i	$0.821647\pi$
$192$		0			0
$193$	87.3328			0.452502			0.226251	−	0.974069i	$-0.427353\pi$
$193$	87.3328			0.452502			0.226251	+	0.974069i	$0.427353\pi$
$194$	−95.4265	+	153.753i	−0.491889	+	0.792539i
$195$		0			0
$196$	12.4272	+	25.0911i	0.0634041	+	0.128016i
$197$			21.6639i			0.109969i	0.998487	+	0.0549845i	$0.0175109\pi$
$197$			21.6639i			0.109969i	−0.998487	+	0.0549845i	$0.982489\pi$
$198$		0			0
$199$			181.933i			0.914235i	0.889406	+	0.457118i	$0.151118\pi$
$199$			181.933i			0.914235i	−0.889406	+	0.457118i	$0.848882\pi$
$200$	−9.21858	−	0.883971i	−0.0460929	−	0.00441985i
$201$		0			0
$202$	307.825	+	191.051i	1.52389	+	0.945799i
$203$	−91.6582			−0.451518
$204$		0			0
$205$			184.719i			0.901067i
$206$	66.7834	+	41.4491i	0.324191	+	0.201209i
$207$		0			0
$208$	166.419	+	126.792i	0.800092	+	0.609576i
$209$	97.9103			0.468470
$210$		0			0
$211$	−21.4204			−0.101519			−0.0507594	−	0.998711i	$-0.516164\pi$
$211$	−21.4204			−0.101519			−0.0507594	+	0.998711i	$0.516164\pi$
$212$	−77.6774	+	38.4723i	−0.366403	+	0.181473i
$213$		0			0
$214$	−40.5521	+	65.3382i	−0.189496	+	0.305319i
$215$		−	23.6680i		−	0.110084i
$216$		0			0
$217$	−90.2410			−0.415857
$218$	47.3744	+	29.4029i	0.217314	+	0.134876i
$219$		0			0
$220$	375.909	−	186.181i	1.70868	−	0.846278i
$221$		−	3.07142i		−	0.0138978i
$222$		0			0
$223$			195.958i			0.878735i	0.898307	+	0.439367i	$0.144797\pi$
$223$			195.958i			0.878735i	−0.898307	+	0.439367i	$0.855203\pi$
$224$	79.1088	−	30.1630i	0.353164	−	0.134656i
$225$		0			0
$226$	−86.9495	+	140.094i	−0.384732	+	0.619887i
$227$	27.2652			0.120111			0.0600554	−	0.998195i	$-0.480872\pi$
$227$	27.2652			0.120111			0.0600554	+	0.998195i	$0.480872\pi$
$228$		0			0
$229$		−	176.347i		−	0.770076i	−0.922901	−	0.385038i	$-0.874188\pi$
$229$		−	176.347i		−	0.770076i	0.922901	−	0.385038i	$-0.125812\pi$
$230$	56.4027	−	90.8768i	0.245229	−	0.395117i
$231$		0			0
$232$	−26.4544	+	275.883i	−0.114028	+	1.18915i
$233$	−71.8366			−0.308312			−0.154156	−	0.988047i	$-0.549266\pi$
$233$	−71.8366			−0.308312			−0.154156	+	0.988047i	$0.549266\pi$
$234$		0			0
$235$	−353.211			−1.50303
$236$	61.9597	+	125.100i	0.262541	+	0.530083i
$237$		0			0
$238$	−1.05605	−	0.655438i	−0.00443719	−	0.00275394i
$239$			71.0926i			0.297459i	0.988878	+	0.148729i	$0.0475183\pi$
$239$			71.0926i			0.297459i	−0.988878	+	0.148729i	$0.952482\pi$
$240$		0			0
$241$	56.1113			0.232827			0.116413	−	0.993201i	$-0.462860\pi$
$241$	56.1113			0.232827			0.116413	+	0.993201i	$0.462860\pi$
$242$	358.892	−	578.252i	1.48302	−	2.38947i
$243$		0			0
$244$	227.975	−	112.912i	0.934324	−	0.462755i
$245$		−	34.1801i		−	0.139510i
$246$		0			0
$247$		−	59.6100i		−	0.241336i
$248$	−26.0454	+	271.617i	−0.105022	+	1.09523i
$249$		0			0
$250$	217.043	+	134.708i	0.868172	+	0.538830i
$251$	−368.953			−1.46993			−0.734966	−	0.678104i	$-0.762802\pi$
$251$	−368.953			−1.46993			−0.734966	+	0.678104i	$0.762802\pi$
$252$		0			0
$253$		−	235.229i		−	0.929759i
$254$	42.7221	+	26.5154i	0.168197	+	0.104391i
$255$		0			0
$256$	−67.9553	−	246.816i	−0.265451	−	0.964124i
$257$	−23.7428			−0.0923845			−0.0461923	−	0.998933i	$-0.514709\pi$
$257$	−23.7428			−0.0923845			−0.0461923	+	0.998933i	$0.514709\pi$
$258$		0			0
$259$	−143.498			−0.554044
$260$	−113.351	−	228.861i	−0.435966	−	0.880236i
$261$		0			0
$262$	133.309	−	214.790i	0.508814	−	0.819809i
$263$			73.9707i			0.281257i	0.990062	+	0.140629i	$0.0449124\pi$
$263$			73.9707i			0.281257i	−0.990062	+	0.140629i	$0.955088\pi$
$264$		0			0
$265$	105.815			0.399302
$266$	−20.4958	−	12.7207i	−0.0770519	−	0.0478222i
$267$		0			0
$268$	−32.7268	−	66.0770i	−0.122115	−	0.246556i
$269$		−	335.593i		−	1.24756i	−0.781601	−	0.623779i	$-0.785597\pi$
$269$		−	335.593i		−	1.24756i	0.781601	−	0.623779i	$-0.214403\pi$
$270$		0			0
$271$			187.276i			0.691054i	0.938409	+	0.345527i	$0.112300\pi$
$271$			187.276i			0.691054i	−0.938409	+	0.345527i	$0.887700\pi$
$272$	−2.27761	+	2.98945i	−0.00837355	+	0.0109906i
$273$		0			0
$274$	−36.8564	+	59.3835i	−0.134512	+	0.216728i
$275$	24.8626			0.0904095
$276$		0			0
$277$			132.592i			0.478670i	0.970937	+	0.239335i	$0.0769294\pi$
$277$			132.592i			0.478670i	−0.970937	+	0.239335i	$0.923071\pi$
$278$	−125.662	+	202.469i	−0.452022	+	0.728305i
$279$		0			0
$280$	−102.879	−	9.86507i	−0.367425	−	0.0352324i
$281$	−331.520			−1.17979			−0.589894	−	0.807481i	$-0.700830\pi$
$281$	−331.520			−1.17979			−0.589894	+	0.807481i	$0.700830\pi$
$282$		0			0
$283$	−66.7158			−0.235745			−0.117873	−	0.993029i	$-0.537607\pi$
$283$	−66.7158			−0.235745			−0.117873	+	0.993029i	$0.537607\pi$
$284$	170.349	−	84.3708i	0.599819	−	0.297080i
$285$		0			0
$286$	−477.237	−	296.197i	−1.66866	−	1.03565i
$287$		−	100.089i		−	0.348741i
$288$		0			0
$289$	−288.945			−0.999809
$290$	178.409	−	287.455i	0.615203	−	0.991224i
$291$		0			0
$292$	−99.2584	−	200.407i	−0.339926	−	0.686327i
$293$			289.215i			0.987082i	0.869723	+	0.493541i	$0.164298\pi$
$293$			289.215i			0.987082i	−0.869723	+	0.493541i	$0.835702\pi$
$294$		0			0
$295$		−	170.415i		−	0.577679i
$296$	−41.4163	+	431.915i	−0.139920	+	1.45917i
$297$		0			0
$298$	−207.200	−	128.598i	−0.695302	−	0.431539i
$299$	−143.213			−0.478972
$300$		0			0
$301$			12.8243i			0.0426058i
$302$	374.535	+	232.455i	1.24018	+	0.769719i
$303$		0			0
$304$	−44.2037	+	58.0191i	−0.145407	+	0.190852i
$305$	−310.556			−1.01822
$306$		0			0
$307$	0.693177			0.00225790			0.00112895	−	0.999999i	$-0.499641\pi$
$307$	0.693177			0.00225790			0.00112895	+	0.999999i	$0.499641\pi$
$308$	−203.684	+	100.881i	−0.661311	+	0.327536i
$309$		0			0
$310$	175.650	−	283.010i	0.566614	−	0.912937i
$311$			62.1583i			0.199866i	0.994994	+	0.0999330i	$0.0318628\pi$
$311$			62.1583i			0.199866i	−0.994994	+	0.0999330i	$0.968137\pi$
$312$		0			0
$313$	213.594			0.682408			0.341204	−	0.939989i	$-0.389165\pi$
$313$	213.594			0.682408			0.341204	+	0.939989i	$0.389165\pi$
$314$	11.5046	+	7.14031i	0.0366388	+	0.0227398i
$315$		0			0
$316$	−340.571	+	168.679i	−1.07776	+	0.533794i
$317$			23.4577i			0.0739990i	0.999315	+	0.0369995i	$0.0117800\pi$
$317$			23.4577i			0.0739990i	−0.999315	+	0.0369995i	$0.988220\pi$
$318$		0			0
$319$		−	744.059i		−	2.33247i
$320$	−59.3860	+	306.809i	−0.185581	+	0.958778i
$321$		0			0
$322$	−30.5614	+	49.2411i	−0.0949113	+	0.152923i
$323$	1.07079			0.00331515
$324$		0			0
$325$		−	15.1369i		−	0.0465751i
$326$	−218.574	+	352.170i	−0.670473	+	1.08028i
$327$		0			0
$328$	−301.258	−	28.8877i	−0.918469	−	0.0880721i
$329$	191.385			0.581718
$330$		0			0
$331$	507.406			1.53295			0.766474	−	0.642275i	$-0.222009\pi$
$331$	507.406			1.53295			0.766474	+	0.642275i	$0.222009\pi$
$332$	126.963	+	256.344i	0.382418	+	0.772120i
$333$		0			0
$334$	281.286	+	174.580i	0.842172	+	0.522694i
$335$			90.0126i			0.268694i
$336$		0			0
$337$	−342.726			−1.01699			−0.508495	−	0.861065i	$-0.669798\pi$
$337$	−342.726			−1.01699			−0.508495	+	0.861065i	$0.669798\pi$
$338$	−2.09076	+	3.36866i	−0.00618567	+	0.00996645i
$339$		0			0
$340$	4.11112	−	2.03617i	0.0120915	−	0.00598873i
$341$		−	732.555i		−	2.14825i
$342$		0			0
$343$			18.5203i			0.0539949i
$344$	38.6001	+	3.70137i	0.112210	+	0.0107598i
$345$		0			0
$346$	−150.989	−	93.7111i	−0.436384	−	0.270841i
$347$	−136.745			−0.394079			−0.197039	−	0.980396i	$-0.563133\pi$
$347$	−136.745			−0.394079			−0.197039	+	0.980396i	$0.563133\pi$
$348$		0			0
$349$		−	82.0565i		−	0.235119i	−0.993066	−	0.117559i	$-0.962493\pi$
$349$		−	82.0565i		−	0.235119i	0.993066	−	0.117559i	$-0.0375071\pi$
$350$	−5.20455	−	3.23020i	−0.0148701	−	0.00922915i
$351$		0			0
$352$	244.856	+	642.186i	0.695613	+	1.82439i
$353$	−507.367			−1.43730			−0.718651	−	0.695371i	$-0.755240\pi$
$353$	−507.367			−1.43730			−0.718651	+	0.695371i	$0.755240\pi$
$354$		0			0
$355$	−232.055			−0.653677
$356$	−283.617	−	572.636i	−0.796676	−	1.60853i
$357$		0			0
$358$	−84.7740	+	136.589i	−0.236799	+	0.381534i
$359$		−	560.809i		−	1.56214i	−0.624442	−	0.781071i	$-0.714674\pi$
$359$		−	560.809i		−	1.56214i	0.624442	−	0.781071i	$-0.285326\pi$
$360$		0			0
$361$	−340.218			−0.942432
$362$	−469.610	−	291.463i	−1.29726	−	0.805147i
$363$		0			0
$364$	61.4186	+	124.007i	0.168733	+	0.340679i
$365$			273.003i			0.747952i
$366$		0			0
$367$			26.9431i			0.0734145i	0.999326	+	0.0367072i	$0.0116869\pi$
$367$			26.9431i			0.0734145i	−0.999326	+	0.0367072i	$0.988313\pi$
$368$	139.390	+	106.199i	0.378778	+	0.288585i
$369$		0			0
$370$	279.312	−	450.032i	0.754897	−	1.21630i
$371$	−57.3352			−0.154542
$372$		0			0
$373$		−	538.034i		−	1.44245i	−0.692701	−	0.721225i	$-0.743579\pi$
$373$		−	538.034i		−	1.44245i	0.692701	−	0.721225i	$-0.256421\pi$
$374$	5.32069	−	8.57277i	0.0142264	−	0.0229218i
$375$		0			0
$376$	55.2377	−	576.052i	0.146909	−	1.53205i
$377$	−453.000			−1.20159
$378$		0			0
$379$	−182.132			−0.480560			−0.240280	−	0.970704i	$-0.577239\pi$
$379$	−182.132			−0.480560			−0.240280	+	0.970704i	$0.577239\pi$
$380$	79.7885	−	39.5179i	0.209970	−	0.103994i
$381$		0			0
$382$	344.985	+	214.115i	0.903102	+	0.560510i
$383$			333.271i			0.870160i	0.900392	+	0.435080i	$0.143280\pi$
$383$			333.271i			0.870160i	−0.900392	+	0.435080i	$0.856720\pi$
$384$		0			0
$385$	277.466			0.720690
$386$	92.1079	−	148.406i	0.238621	−	0.384471i
$387$		0			0
$388$	160.629	+	324.319i	0.413993	+	0.835873i
$389$		−	109.639i		−	0.281847i	−0.990020	−	0.140924i	$-0.954993\pi$
$389$		−	109.639i		−	0.281847i	0.990020	−	0.140924i	$-0.0450072\pi$
$390$		0			0
$391$		−	2.57258i		−	0.00657948i
$392$	55.7443	+	5.34533i	0.142205	+	0.0136360i
$393$		0			0
$394$	36.8137	+	22.8484i	0.0934358	+	0.0579909i
$395$	463.938			1.17453
$396$		0			0
$397$		−	310.938i		−	0.783219i	−0.920131	−	0.391610i	$-0.871918\pi$
$397$		−	310.938i		−	0.783219i	0.920131	−	0.391610i	$-0.128082\pi$
$398$	309.160	+	191.880i	0.776785	+	0.482111i
$399$		0			0
$400$	−11.2248	+	14.7329i	−0.0280619	+	0.0368323i
$401$	423.903			1.05711			0.528557	−	0.848898i	$-0.322733\pi$
$401$	423.903			1.05711			0.528557	+	0.848898i	$0.322733\pi$
$402$		0			0
$403$	−445.995			−1.10669
$404$	649.311	−	321.593i	1.60721	−	0.796022i
$405$		0			0
$406$	−96.6697	+	155.756i	−0.238103	+	0.383635i
$407$		−	1164.88i		−	2.86211i
$408$		0			0
$409$	444.543			1.08690			0.543451	−	0.839441i	$-0.317117\pi$
$409$	444.543			1.08690			0.543451	+	0.839441i	$0.317117\pi$
$410$	313.895	+	194.818i	0.765596	+	0.475167i
$411$		0			0
$412$	140.870	−	69.7703i	0.341917	−	0.169345i
$413$			92.3385i			0.223580i
$414$		0			0
$415$		−	349.201i		−	0.841449i
$416$	390.977	−	149.074i	0.939849	−	0.358350i
$417$		0			0
$418$	103.264	−	166.380i	0.247042	−	0.398038i
$419$	−457.129			−1.09100			−0.545500	−	0.838111i	$-0.683660\pi$
$419$	−457.129			−1.09100			−0.545500	+	0.838111i	$0.683660\pi$
$420$		0			0
$421$			25.4812i			0.0605255i	0.999542	+	0.0302628i	$0.00963441\pi$
$421$			25.4812i			0.0605255i	−0.999542	+	0.0302628i	$0.990366\pi$
$422$	−22.5916	+	36.4000i	−0.0535347	+	0.0862559i
$423$		0			0
$424$	−16.5481	+	172.574i	−0.0390286	+	0.407014i
$425$	0.271910			0.000639787
$426$		0			0
$427$	168.273			0.394082
$428$	68.2606	+	137.821i	0.159487	+	0.322013i
$429$		0			0
$430$	−40.2192	−	24.9620i	−0.0935331	−	0.0580512i
$431$			124.595i			0.289084i	0.989499	+	0.144542i	$0.0461709\pi$
$431$			124.595i			0.289084i	−0.989499	+	0.144542i	$0.953829\pi$
$432$		0			0
$433$	−272.271			−0.628802			−0.314401	−	0.949290i	$-0.601804\pi$
$433$	−272.271			−0.628802			−0.314401	+	0.949290i	$0.601804\pi$
$434$	−95.1750	+	153.347i	−0.219297	+	0.353335i
$435$		0			0
$436$	99.9293	−	49.4933i	0.229196	−	0.113517i
$437$		−	49.9285i		−	0.114253i
$438$		0			0
$439$			255.069i			0.581023i	0.956871	+	0.290512i	$0.0938255\pi$
$439$			255.069i			0.581023i	−0.956871	+	0.290512i	$0.906174\pi$
$440$	80.0823	−	835.146i	0.182005	−	1.89806i
$441$		0			0
$442$	−5.21929	−	3.23935i	−0.0118084	−	0.00732885i
$443$	−131.274			−0.296330			−0.148165	−	0.988963i	$-0.547337\pi$
$443$	−131.274			−0.296330			−0.148165	+	0.988963i	$0.547337\pi$
$444$		0			0
$445$			780.066i			1.75296i
$446$	332.993	+	206.672i	0.746622	+	0.463391i
$447$		0			0
$448$	32.1779	−	166.243i	0.0718257	−	0.371077i
$449$	642.824			1.43168			0.715839	−	0.698265i	$-0.246044\pi$
$449$	642.824			1.43168			0.715839	+	0.698265i	$0.246044\pi$
$450$		0			0
$451$	812.496			1.80154
$452$	146.360	+	295.509i	0.323806	+	0.653780i
$453$		0			0
$454$	28.7559	−	46.3320i	0.0633390	−	0.102053i
$455$		−	168.927i		−	0.371269i
$456$		0			0
$457$	693.088			1.51660			0.758302	−	0.651903i	$-0.226029\pi$
$457$	693.088			1.51660			0.758302	+	0.651903i	$0.226029\pi$
$458$	−299.669	−	185.990i	−0.654300	−	0.406091i
$459$		0			0
$460$	−94.9415	−	191.691i	−0.206394	−	0.416720i
$461$			258.699i			0.561170i	0.959829	+	0.280585i	$0.0905285\pi$
$461$			258.699i			0.561170i	−0.959829	+	0.280585i	$0.909472\pi$
$462$		0			0
$463$			637.226i			1.37630i	0.725569	+	0.688150i	$0.241577\pi$
$463$			637.226i			1.37630i	−0.725569	+	0.688150i	$0.758423\pi$
$464$	440.910	+	335.921i	0.950237	+	0.723969i
$465$		0			0
$466$	−75.7644	+	122.073i	−0.162584	+	0.261959i
$467$	199.483			0.427159			0.213580	−	0.976926i	$-0.431488\pi$
$467$	199.483			0.427159			0.213580	+	0.976926i	$0.431488\pi$
$468$		0			0
$469$		−	48.7727i		−	0.103993i
$470$	−372.524	+	600.216i	−0.792603	+	1.27705i
$471$		0			0
$472$	277.931	+	26.6508i	0.588836	+	0.0564636i
$473$	−104.105			−0.220095
$474$		0			0
$475$	5.27721			0.0111099
$476$	−2.22758	+	1.10328i	−0.00467980	+	0.00231782i
$477$		0			0
$478$	120.809	+	74.9797i	0.252737	+	0.156861i
$479$			674.160i			1.40743i	0.710481	+	0.703716i	$0.248477\pi$
$479$			674.160i			1.40743i	−0.710481	+	0.703716i	$0.751523\pi$
$480$		0			0
$481$	−709.204			−1.47444
$482$	59.1792	−	95.3505i	0.122778	−	0.197823i
$483$		0			0
$484$	−604.115	−	1219.74i	−1.24817	−	2.52012i
$485$		−	441.799i		−	0.910926i
$486$		0			0
$487$		−	401.718i		−	0.824883i	−0.910984	−	0.412442i	$-0.864676\pi$
$487$		−	401.718i		−	0.824883i	0.910984	−	0.412442i	$-0.135324\pi$
$488$	48.5670	−	506.486i	0.0995226	−	1.03788i
$489$		0			0
$490$	−58.0826	−	36.0489i	−0.118536	−	0.0735692i
$491$	−428.880			−0.873482			−0.436741	−	0.899587i	$-0.643867\pi$
$491$	−428.880			−0.873482			−0.436741	+	0.899587i	$0.643867\pi$
$492$		0			0
$493$		−	8.13739i		−	0.0165059i
$494$	−101.296	−	62.8692i	−0.205052	−	0.127266i
$495$		0			0
$496$	434.093	+	330.727i	0.875187	+	0.666789i
$497$	125.738			0.252993
$498$		0			0
$499$	182.619			0.365970			0.182985	−	0.983116i	$-0.441424\pi$
$499$	182.619			0.365970			0.182985	+	0.983116i	$0.441424\pi$
$500$	457.820	−	226.751i	0.915641	−	0.453501i
$501$		0			0
$502$	−389.126	+	626.966i	−0.775152	+	1.24894i
$503$			380.158i			0.755781i	0.925850	+	0.377891i	$0.123350\pi$
$503$			380.158i			0.755781i	−0.925850	+	0.377891i	$0.876650\pi$
$504$		0			0
$505$	−884.516			−1.75152
$506$	−399.727	−	248.090i	−0.789974	−	0.490297i
$507$		0			0
$508$	90.1160	−	44.6329i	0.177394	−	0.0878600i
$509$			289.538i			0.568836i	0.958700	+	0.284418i	$0.0918004\pi$
$509$			289.538i			0.568836i	−0.958700	+	0.284418i	$0.908200\pi$
$510$		0			0
$511$		−	147.925i		−	0.289481i
$512$	−491.088	−	144.834i	−0.959156	−	0.282878i
$513$		0			0
$514$	−25.0410	+	40.3464i	−0.0487179	+	0.0784950i
$515$	−191.898			−0.372617
$516$		0			0
$517$			1553.62i			3.00507i
$518$	−151.343	+	243.847i	−0.292169	+	0.470747i
$519$		0			0
$520$	−508.456	−	48.7559i	−0.977799	−	0.0937613i
$521$	738.899			1.41823			0.709116	−	0.705092i	$-0.249094\pi$
$521$	738.899			1.41823			0.709116	+	0.705092i	$0.249094\pi$
$522$		0			0
$523$	647.126			1.23734			0.618668	−	0.785653i	$-0.287673\pi$
$523$	647.126			1.23734			0.618668	+	0.785653i	$0.287673\pi$
$524$	−224.397	−	453.068i	−0.428238	−	0.864633i
$525$		0			0
$526$	125.699	+	78.0151i	0.238972	+	0.148318i
$527$		−	8.01157i		−	0.0152022i
$528$		0			0
$529$	409.047			0.773246
$530$	111.601	−	179.813i	0.210567	−	0.339269i
$531$		0			0
$532$	−43.2329	+	21.4125i	−0.0812648	+	0.0402491i
$533$		−	494.666i		−	0.928078i
$534$		0			0
$535$		−	187.745i		−	0.350926i
$536$	−146.802	−	14.0768i	−0.273884	−	0.0262627i
$537$		0			0
$538$	−570.277	−	353.942i	−1.05999	−	0.657885i
$539$	−150.343			−0.278930
$540$		0			0
$541$			178.722i			0.330355i	0.986264	+	0.165178i	$0.0528198\pi$
$541$			178.722i			0.330355i	−0.986264	+	0.165178i	$0.947180\pi$
$542$	318.240	+	197.515i	0.587158	+	0.364419i
$543$		0			0
$544$	2.67786	+	7.02326i	0.00492254	+	0.0129104i
$545$	−136.127			−0.249775
$546$		0			0
$547$	452.236			0.826758			0.413379	−	0.910559i	$-0.364349\pi$
$547$	452.236			0.826758			0.413379	+	0.910559i	$0.364349\pi$
$548$	62.0395	+	125.261i	0.113211	+	0.228578i
$549$		0			0
$550$	26.2220	−	42.2493i	0.0476764	−	0.0768169i
$551$		−	157.930i		−	0.286625i
$552$		0			0
$553$	−251.382			−0.454579
$554$	225.314	+	139.841i	0.406705	+	0.252421i
$555$		0			0
$556$	211.525	+	427.078i	0.380440	+	0.768126i
$557$			854.108i			1.53341i	0.642001	+	0.766704i	$0.278105\pi$
$557$			854.108i			1.53341i	−0.642001	+	0.766704i	$0.721895\pi$
$558$		0			0
$559$			63.3814i			0.113383i
$560$	−125.268	+	164.419i	−0.223692	+	0.293605i
$561$		0			0
$562$	−349.647	+	563.356i	−0.622147	+	1.00241i
$563$	−249.654			−0.443436			−0.221718	−	0.975111i	$-0.571166\pi$
$563$	−249.654			−0.443436			−0.221718	+	0.975111i	$0.571166\pi$
$564$		0			0
$565$		−	402.553i		−	0.712483i
$566$	−70.3636	+	113.371i	−0.124317	+	0.200302i
$567$		0			0
$568$	36.2905	−	378.459i	0.0638917	−	0.666301i
$569$	−104.353			−0.183396			−0.0916982	−	0.995787i	$-0.529229\pi$
$569$	−104.353			−0.183396			−0.0916982	+	0.995787i	$0.529229\pi$
$570$		0			0
$571$	−649.705			−1.13784			−0.568919	−	0.822394i	$-0.692638\pi$
$571$	−649.705			−1.13784			−0.568919	+	0.822394i	$0.692638\pi$
$572$	−1006.66	+	498.582i	−1.75990	+	0.871646i
$573$		0			0
$574$	−170.082	−	105.561i	−0.296310	−	0.183905i
$575$		−	12.6785i		−	0.0220495i
$576$		0			0
$577$	−346.022			−0.599692			−0.299846	−	0.953988i	$-0.596935\pi$
$577$	−346.022			−0.599692			−0.299846	+	0.953988i	$0.596935\pi$
$578$	−304.743	+	491.007i	−0.527238	+	0.849493i
$579$		0			0
$580$	−300.312	−	606.344i	−0.517779	−	1.04542i
$581$			189.213i			0.325667i
$582$		0			0
$583$		−	465.434i		−	0.798342i
$584$	−445.240	−	42.6941i	−0.762397	−	0.0731064i
$585$		0			0
$586$	491.466	+	305.028i	0.838679	+	0.520526i
$587$	1153.54			1.96514			0.982572	−	0.185885i	$-0.0595150\pi$
$587$	1153.54			1.96514			0.982572	+	0.185885i	$0.0595150\pi$
$588$		0			0
$589$		−	155.488i		−	0.263987i
$590$	−289.589	−	179.733i	−0.490828	−	0.304632i
$591$		0			0
$592$	690.276	+	525.909i	1.16601	+	0.888360i
$593$	−880.135			−1.48421			−0.742104	−	0.670285i	$-0.766172\pi$
$593$	−880.135			−1.48421			−0.742104	+	0.670285i	$0.766172\pi$
$594$		0			0
$595$	3.03450			0.00510000
$596$	−437.058	+	216.467i	−0.733318	+	0.363200i
$597$		0			0
$598$	−151.043	+	243.363i	−0.252580	+	0.406961i
$599$			554.939i			0.926442i	0.886243	+	0.463221i	$0.153306\pi$
$599$			554.939i			0.926442i	−0.886243	+	0.463221i	$0.846694\pi$
$600$		0			0
$601$	−666.057			−1.10825			−0.554124	−	0.832434i	$-0.686946\pi$
$601$	−666.057			−1.10825			−0.554124	+	0.832434i	$0.686946\pi$
$602$	21.7925	+	13.5255i	0.0362002	+	0.0224676i
$603$		0			0
$604$	790.027	−	391.287i	1.30799	−	0.647826i
$605$			1661.57i			2.74640i
$606$		0			0
$607$		−	192.927i		−	0.317836i	−0.987292	−	0.158918i	$-0.949199\pi$
$607$		−	192.927i		−	0.317836i	0.987292	−	0.158918i	$-0.0508006\pi$
$608$	51.9718	+	136.307i	0.0854800	+	0.224189i
$609$		0			0
$610$	−327.536	+	527.732i	−0.536945	+	0.865134i
$611$	945.878			1.54808
$612$		0			0
$613$			608.234i			0.992226i	0.868258	+	0.496113i	$0.165240\pi$
$613$			608.234i			0.992226i	−0.868258	+	0.496113i	$0.834760\pi$
$614$	0.731077	−	1.17792i	0.00119068	−	0.00191844i
$615$		0			0
$616$	−43.3921	+	452.519i	−0.0704417	+	0.734609i
$617$	−0.884056			−0.00143283			−0.000716415	−	1.00000i	$-0.500228\pi$
$617$	−0.884056			−0.00143283			−0.000716415		1.00000i	$0.500228\pi$
$618$		0			0
$619$	358.525			0.579200			0.289600	−	0.957148i	$-0.406478\pi$
$619$	358.525			0.579200			0.289600	+	0.957148i	$0.406478\pi$
$620$	−295.669	−	596.969i	−0.476885	−	0.962853i
$621$		0			0
$622$	105.626	+	65.5569i	0.169817	+	0.105397i
$623$		−	422.674i		−	0.678449i
$624$		0			0
$625$	−594.720			−0.951552
$626$	225.272	−	362.962i	0.359860	−	0.579812i
$627$		0			0
$628$	24.2672	−	12.0191i	0.0386421	−	0.0191388i
$629$		−	12.7397i		−	0.0202539i
$630$		0			0
$631$		−	390.515i		−	0.618883i	−0.950918	−	0.309442i	$-0.899858\pi$
$631$		−	390.515i		−	0.618883i	0.950918	−	0.309442i	$-0.100142\pi$
$632$	−72.5540	+	756.637i	−0.114801	+	1.19721i
$633$		0			0
$634$	39.8619	+	24.7403i	0.0628737	+	0.0390225i
$635$	−122.759			−0.193322
$636$		0			0
$637$			91.5322i			0.143693i
$638$	−1264.39	−	784.742i	−1.98180	−	1.23000i
$639$		0			0
$640$	458.731	+	424.499i	0.716767	+	0.663280i
$641$	431.936			0.673848			0.336924	−	0.941532i	$-0.390614\pi$
$641$	431.936			0.673848			0.336924	+	0.941532i	$0.390614\pi$
$642$		0			0
$643$	49.9370			0.0776625			0.0388313	−	0.999246i	$-0.487637\pi$
$643$	49.9370			0.0776625			0.0388313	+	0.999246i	$0.487637\pi$
$644$	51.4434	+	103.867i	0.0798811	+	0.161284i
$645$		0			0
$646$	1.12934	−	1.81961i	0.00174821	−	0.00281674i
$647$			224.141i			0.346431i	0.984884	+	0.173216i	$0.0554157\pi$
$647$			224.141i			0.346431i	−0.984884	+	0.173216i	$0.944584\pi$
$648$		0			0
$649$	−749.582			−1.15498
$650$	−25.7223	−	15.9645i	−0.0395728	−	0.0245608i
$651$		0			0
$652$	367.922	+	742.851i	0.564297	+	1.13934i
$653$		−	80.7637i		−	0.123681i	−0.998086	−	0.0618405i	$-0.980303\pi$
$653$		−	80.7637i		−	0.123681i	0.998086	−	0.0618405i	$-0.0196970\pi$
$654$		0			0
$655$			617.186i			0.942268i
$656$	−366.819	+	481.464i	−0.559175	+	0.733939i
$657$		0			0
$658$	201.850	−	325.223i	0.306762	−	0.494260i
$659$	940.466			1.42711			0.713555	−	0.700599i	$-0.247084\pi$
$659$	940.466			1.42711			0.713555	+	0.700599i	$0.247084\pi$
$660$		0			0
$661$			119.930i			0.181437i	0.995877	+	0.0907184i	$0.0289163\pi$
$661$			119.930i			0.181437i	−0.995877	+	0.0907184i	$0.971084\pi$
$662$	535.149	−	862.240i	0.808382	−	1.30248i
$663$		0			0
$664$	569.513	+	54.6107i	0.857700	+	0.0822450i
$665$	58.8935			0.0885616
$666$		0			0
$667$	−379.426			−0.568855
$668$	593.330	−	293.866i	0.888219	−	0.439920i
$669$		0			0
$670$	152.959	+	94.9341i	0.228298	+	0.141693i
$671$			1366.00i			2.03577i
$672$		0			0
$673$	1085.06			1.61227			0.806136	−	0.591731i	$-0.201555\pi$
$673$	1085.06			1.61227			0.806136	+	0.591731i	$0.201555\pi$
$674$	−361.465	+	582.398i	−0.536298	+	0.864091i
$675$		0			0
$676$	3.51933	+	7.10569i	0.00520611	+	0.0105114i
$677$		−	949.901i		−	1.40310i	−0.712618	−	0.701552i	$-0.752491\pi$
$677$		−	949.901i		−	1.40310i	0.712618	−	0.701552i	$-0.247509\pi$
$678$		0			0
$679$			239.386i			0.352557i
$680$	0.875819	−	9.13357i	0.00128797	−	0.0134317i
$681$		0			0
$682$	−1244.84	−	772.608i	−1.82528	−	1.13286i
$683$	893.785			1.30862			0.654308	−	0.756228i	$-0.272960\pi$
$683$	893.785			1.30862			0.654308	+	0.756228i	$0.272960\pi$
$684$		0			0
$685$		−	170.635i		−	0.249102i
$686$	31.4717	+	19.5329i	0.0458771	+	0.0284736i
$687$		0			0
$688$	47.0004	−	61.6898i	0.0683145	−	0.0896654i
$689$	−283.366			−0.411272
$690$		0			0
$691$	1208.56			1.74901			0.874504	−	0.485019i	$-0.161187\pi$
$691$	1208.56			1.74901			0.874504	+	0.485019i	$0.161187\pi$
$692$	−318.489	+	157.742i	−0.460244	+	0.227951i
$693$		0			0
$694$	−144.222	+	232.373i	−0.207813	+	0.334831i
$695$		−	581.782i		−	0.837096i
$696$		0			0
$697$	8.88585			0.0127487
$698$	−139.439	−	86.5430i	−0.199770	−	0.123987i
$699$		0			0
$700$	−10.9782	+	5.43733i	−0.0156832	+	0.00776762i
$701$		−	219.477i		−	0.313091i	−0.987671	−	0.156546i	$-0.949964\pi$
$701$		−	219.477i		−	0.313091i	0.987671	−	0.156546i	$-0.0500358\pi$
$702$		0			0
$703$		−	247.251i		−	0.351709i
$704$	1349.52	+	261.213i	1.91693	+	0.371041i
$705$		0			0
$706$	−535.108	+	862.175i	−0.757944	+	1.22121i
$707$	479.270			0.677892
$708$		0			0
$709$			1265.13i			1.78439i	0.451651	+	0.892195i	$0.350835\pi$
$709$			1265.13i			1.78439i	−0.451651	+	0.892195i	$0.649165\pi$
$710$	−244.743	+	394.334i	−0.344709	+	0.555400i
$711$		0			0
$712$	−1272.21	−	121.992i	−1.78681	−	0.171338i
$713$	−373.560			−0.523927
$714$		0			0
$715$	1371.31			1.91792
$716$	142.698	+	288.115i	0.199299	+	0.402395i
$717$		0			0
$718$	−952.989	−	591.472i	−1.32728	−	0.823777i
$719$		−	1163.47i		−	1.61818i	−0.587687	−	0.809089i	$-0.699961\pi$
$719$		−	1163.47i		−	1.61818i	0.587687	−	0.809089i	$-0.300039\pi$
$720$		0			0
$721$	103.979			0.144215
$722$	−358.820	+	578.136i	−0.496981	+	0.800743i
$723$		0			0
$724$	−990.573	+	490.614i	−1.36819	+	0.677643i
$725$		−	40.1036i		−	0.0553153i
$726$		0			0
$727$			1303.68i			1.79324i	0.442803	+	0.896619i	$0.353984\pi$
$727$			1303.68i			1.79324i	−0.442803	+	0.896619i	$0.646016\pi$
$728$	275.504	+	26.4181i	0.378439	+	0.0362886i
$729$		0			0
$730$	463.916	+	287.929i	0.635502	+	0.394424i
$731$	−1.13854			−0.00155751
$732$		0			0
$733$		−	1256.12i		−	1.71367i	−0.515589	−	0.856836i	$-0.672427\pi$
$733$		−	1256.12i		−	1.71367i	0.515589	−	0.856836i	$-0.327573\pi$
$734$	45.7847	+	28.4163i	0.0623770	+	0.0387143i
$735$		0			0
$736$	327.477	−	124.862i	0.444942	−	0.169649i
$737$	395.925			0.537212
$738$		0			0
$739$	687.168			0.929862			0.464931	−	0.885347i	$-0.346079\pi$
$739$	687.168			0.929862			0.464931	+	0.885347i	$0.346079\pi$
$740$	−470.160	−	949.276i	−0.635352	−	1.28281i
$741$		0			0
$742$	−60.4701	+	97.4304i	−0.0814961	+	0.131308i
$743$			362.628i			0.488059i	0.969768	+	0.244030i	$0.0784694\pi$
$743$			362.628i			0.488059i	−0.969768	+	0.244030i	$0.921531\pi$
$744$		0			0
$745$	595.376			0.799163
$746$	−914.287	−	567.452i	−1.22559	−	0.760659i
$747$		0			0
$748$	−8.95620	−	18.0830i	−0.0119735	−	0.0241751i
$749$			101.729i			0.135819i
$750$		0			0
$751$			261.366i			0.348024i	0.984744	+	0.174012i	$0.0556732\pi$
$751$			261.366i			0.348024i	−0.984744	+	0.174012i	$0.944327\pi$
$752$	−920.634	−	701.415i	−1.22425	−	0.932733i
$753$		0			0
$754$	−477.768	+	769.787i	−0.633645	+	1.02094i
$755$	−1076.20			−1.42544
$756$		0			0
$757$		−	1395.34i		−	1.84325i	−0.388081	−	0.921625i	$-0.626862\pi$
$757$		−	1395.34i		−	1.84325i	0.388081	−	0.921625i	$-0.373138\pi$
$758$	−192.091	+	309.500i	−0.253418	+	0.408311i
$759$		0			0
$760$	16.9979	−	177.264i	0.0223656	−	0.233242i
$761$	319.500			0.419843			0.209921	−	0.977718i	$-0.432679\pi$
$761$	319.500			0.419843			0.209921	+	0.977718i	$0.432679\pi$
$762$		0			0
$763$	73.7598			0.0966708
$764$	727.695	−	360.415i	0.952481	−	0.471747i
$765$		0			0
$766$	566.331	+	351.493i	0.739336	+	0.458868i
$767$			456.362i			0.594996i
$768$		0			0
$769$	634.936			0.825664			0.412832	−	0.910807i	$-0.364540\pi$
$769$	634.936			0.825664			0.412832	+	0.910807i	$0.364540\pi$
$770$	292.636	−	471.500i	0.380047	−	0.612338i
$771$		0			0
$772$	−155.043	−	313.040i	−0.200833	−	0.405492i
$773$		−	96.1663i		−	0.124407i	−0.998063	−	0.0622033i	$-0.980187\pi$
$773$		−	96.1663i		−	0.124407i	0.998063	−	0.0622033i	$-0.0198127\pi$
$774$		0			0
$775$		−	39.4836i		−	0.0509465i
$776$	720.530	+	69.0917i	0.928518	+	0.0890358i
$777$		0			0
$778$	−186.310	−	115.633i	−0.239473	−	0.148629i
$779$	172.456			0.221382
$780$		0			0
$781$			1020.71i			1.30693i
$782$	−4.37161	−	2.71324i	−0.00559029	−	0.00346961i
$783$		0			0
$784$	67.8756	−	89.0893i	0.0865760	−	0.113634i
$785$	−33.0577			−0.0421117
$786$		0			0
$787$	−1319.25			−1.67630			−0.838148	−	0.545442i	$-0.816362\pi$
$787$	−1319.25			−1.67630			−0.838148	+	0.545442i	$0.816362\pi$
$788$	77.6531	−	38.4603i	0.0985445	−	0.0488074i
$789$		0			0
$790$	489.305	−	788.375i	0.619373	−	0.997943i
$791$			218.121i			0.275753i
$792$		0			0
$793$	831.651			1.04874
$794$	−528.380	−	327.939i	−0.665466	−	0.413021i
$795$		0			0
$796$	652.128	−	322.988i	0.819257	−	0.405764i
$797$			818.575i			1.02707i	0.858068	+	0.513535i	$0.171664\pi$
$797$			818.575i			1.02707i	−0.858068	+	0.513535i	$0.828336\pi$
$798$		0			0
$799$			16.9911i			0.0212655i
$800$	13.1973	+	34.6128i	0.0164967	+	0.0432660i
$801$		0			0
$802$	447.081	−	720.343i	0.557457	−	0.898183i
$803$	1200.82			1.49541
$804$		0			0
$805$		−	141.491i		−	0.175765i
$806$	−470.381	+	757.885i	−0.583599	+	0.940304i
$807$		0			0
$808$	138.327	−	1442.56i	0.171197	−	1.78534i
$809$	−1232.72			−1.52376			−0.761881	−	0.647717i	$-0.775724\pi$
$809$	−1232.72			−1.52376			−0.761881	+	0.647717i	$0.775724\pi$
$810$		0			0
$811$	−1009.05			−1.24421			−0.622103	−	0.782935i	$-0.713722\pi$
$811$	−1009.05			−1.24421			−0.622103	+	0.782935i	$0.713722\pi$
$812$	162.722	+	328.544i	0.200397	+	0.404611i
$813$		0			0
$814$	−1979.49	−	1228.57i	−2.43181	−	1.50930i
$815$		−	1011.94i		−	1.24164i
$816$		0			0
$817$	−22.0968			−0.0270462
$818$	468.849	−	755.417i	0.573165	−	0.923493i
$819$		0			0
$820$	662.114	−	327.934i	0.807457	−	0.399919i
$821$			939.093i			1.14384i	0.820309	+	0.571920i	$0.193801\pi$
$821$			939.093i			1.14384i	−0.820309	+	0.571920i	$0.806199\pi$
$822$		0			0
$823$		−	911.100i		−	1.10705i	−0.832833	−	0.553524i	$-0.813283\pi$
$823$		−	911.100i		−	1.10705i	0.832833	−	0.553524i	$-0.186717\pi$
$824$	30.0104	−	312.966i	0.0364204	−	0.379814i
$825$		0			0
$826$	156.912	+	97.3872i	0.189966	+	0.117902i
$827$	65.6564			0.0793910			0.0396955	−	0.999212i	$-0.487361\pi$
$827$	65.6564			0.0793910			0.0396955	+	0.999212i	$0.487361\pi$
$828$		0			0
$829$			1515.94i			1.82864i	0.404997	+	0.914318i	$0.367272\pi$
$829$			1515.94i			1.82864i	−0.404997	+	0.914318i	$0.632728\pi$
$830$	−593.402	−	368.294i	−0.714942	−	0.443728i
$831$		0			0
$832$	159.032	−	821.616i	0.191144	−	0.987519i
$833$	−1.64422			−0.00197386
$834$		0			0
$835$	−808.257			−0.967972
$836$	−173.822	−	350.954i	−0.207921	−	0.419802i
$837$		0			0
$838$	−482.123	+	776.804i	−0.575326	+	0.926974i
$839$		−	869.972i		−	1.03692i	−0.855103	−	0.518458i	$-0.826506\pi$
$839$		−	869.972i		−	1.03692i	0.855103	−	0.518458i	$-0.173494\pi$
$840$		0			0
$841$	−359.174			−0.427080
$842$	43.3006	+	26.8745i	0.0514258	+	0.0319174i
$843$		0			0
$844$	38.0280	+	76.7804i	0.0450569	+	0.0909721i
$845$		−	9.67964i		−	0.0114552i
$846$		0			0
$847$		−	900.313i		−	1.06294i
$848$	275.804	+	210.130i	0.325240	+	0.247795i
$849$		0			0
$850$	0.286777	−	0.462059i	0.000337384	−	0.000543599i
$851$	−594.020			−0.698026
$852$		0			0
$853$		−	1643.91i		−	1.92721i	−0.267322	−	0.963607i	$-0.586139\pi$
$853$		−	1643.91i		−	1.92721i	0.267322	−	0.963607i	$-0.413861\pi$
$854$	177.474	−	285.948i	0.207814	−	0.334834i
$855$		0			0
$856$	306.194	+	29.3610i	0.357703	+	0.0343002i
$857$	−286.059			−0.333791			−0.166895	−	0.985975i	$-0.553374\pi$
$857$	−286.059			−0.333791			−0.166895	+	0.985975i	$0.553374\pi$
$858$		0			0
$859$	719.782			0.837930			0.418965	−	0.908002i	$-0.362393\pi$
$859$	719.782			0.837930			0.418965	+	0.908002i	$0.362393\pi$
$860$	−84.8365	+	42.0181i	−0.0986471	+	0.0488582i
$861$		0			0
$862$	211.726	+	131.408i	0.245622	+	0.152445i
$863$		−	1120.47i		−	1.29835i	−0.760641	−	0.649173i	$-0.775115\pi$
$863$		−	1120.47i		−	1.29835i	0.760641	−	0.649173i	$-0.224885\pi$
$864$		0			0
$865$	433.857			0.501569
$866$	−287.158	+	462.674i	−0.331592	+	0.534265i
$867$		0			0
$868$	160.206	+	323.464i	0.184569	+	0.372654i
$869$		−	2040.66i		−	2.34828i
$870$		0			0
$871$		−	241.048i		−	0.276749i
$872$	21.2886	−	222.010i	0.0244135	−	0.254599i
$873$		0			0
$874$	−84.8441	−	52.6584i	−0.0970756	−	0.0602499i
$875$	337.926			0.386201
$876$		0			0
$877$			145.400i			0.165792i	0.996558	+	0.0828960i	$0.0264169\pi$
$877$			145.400i			0.165792i	−0.996558	+	0.0828960i	$0.973583\pi$
$878$	433.442	+	269.016i	0.493670	+	0.306396i
$879$		0			0
$880$	−1334.71	−	1016.89i	−1.51672	−	1.15556i
$881$	−476.080			−0.540386			−0.270193	−	0.962806i	$-0.587087\pi$
$881$	−476.080			−0.540386			−0.270193	+	0.962806i	$0.587087\pi$
$882$		0			0
$883$	−1101.22			−1.24714			−0.623568	−	0.781769i	$-0.714318\pi$
$883$	−1101.22			−1.24714			−0.623568	+	0.781769i	$0.714318\pi$
$884$	−11.0093	+	5.45273i	−0.0124540	+	0.00616825i
$885$		0			0
$886$	−138.452	+	223.075i	−0.156266	+	0.251778i
$887$			1491.49i			1.68150i	0.541427	+	0.840748i	$0.317884\pi$
$887$			1491.49i			1.68150i	−0.541427	+	0.840748i	$0.682116\pi$
$888$		0			0
$889$	66.5164			0.0748216
$890$	1325.57	+	822.717i	1.48941	+	0.924401i
$891$		0			0
$892$	702.401	−	347.887i	0.787445	−	0.390008i
$893$			329.764i			0.369276i
$894$		0			0
$895$		−	392.481i		−	0.438526i
$896$	−248.560	−	230.012i	−0.277411	−	0.256710i
$897$		0			0
$898$	677.971	−	1092.36i	0.754979	−	1.21643i
$899$	−1181.62			−1.31437
$900$		0			0
$901$		−	5.09021i		−	0.00564951i
$902$	856.920	−	1380.68i	0.950023	−	1.53069i
$903$		0			0
$904$	656.524	+	62.9541i	0.726243	+	0.0696395i
$905$	1349.40			1.49104
$906$		0			0
$907$	1155.46			1.27394			0.636969	−	0.770889i	$-0.280188\pi$
$907$	1155.46			1.27394			0.636969	+	0.770889i	$0.280188\pi$
$908$	−48.4043	−	97.7305i	−0.0533087	−	0.107633i
$909$		0			0
$910$	−287.060	−	178.164i	−0.315450	−	0.195784i
$911$			944.690i			1.03698i	0.855083	+	0.518491i	$0.173506\pi$
$911$			944.690i			1.03698i	−0.855083	+	0.518491i	$0.826494\pi$
$912$		0			0
$913$	−1535.98			−1.68235
$914$	730.984	−	1177.77i	0.799764	−	1.28859i
$915$		0			0
$916$	−632.108	+	313.072i	−0.690074	+	0.341782i
$917$		−	334.418i		−	0.364687i
$918$		0			0
$919$			149.150i			0.162296i	0.996702	+	0.0811478i	$0.0258586\pi$
$919$			149.150i			0.162296i	−0.996702	+	0.0811478i	$0.974141\pi$
$920$	−425.876	−	40.8373i	−0.462908	−	0.0443883i
$921$		0			0
$922$	439.611	+	272.844i	0.476801	+	0.295926i
$923$	621.430			0.673272
$924$		0			0
$925$		−	62.7851i		−	0.0678758i
$926$	1082.85	+	672.068i	1.16938	+	0.725775i
$927$		0			0
$928$	1035.85	−	394.954i	1.11622	−	0.425597i
$929$	58.8399			0.0633368			0.0316684	−	0.999498i	$-0.489918\pi$
$929$	58.8399			0.0633368			0.0316684	+	0.999498i	$0.489918\pi$
$930$		0			0
$931$	−31.9111			−0.0342761
$932$	127.533	+	257.494i	0.136838	+	0.276282i
$933$		0			0
$934$	210.390	−	338.984i	0.225257	−	0.362938i
$935$			24.6333i			0.0263458i
$936$		0			0
$937$	−1700.18			−1.81449			−0.907246	−	0.420601i	$-0.861819\pi$
$937$	−1700.18			−1.81449			−0.907246	+	0.420601i	$0.861819\pi$
$938$	−82.8801	−	51.4395i	−0.0883583	−	0.0548395i
$939$		0			0
$940$	627.061	+	1266.07i	0.667086	+	1.34688i
$941$			56.6116i			0.0601611i	0.999547	+	0.0300805i	$0.00957637\pi$
$941$			56.6116i			0.0601611i	−0.999547	+	0.0300805i	$0.990424\pi$
$942$		0			0
$943$		−	414.325i		−	0.439369i
$944$	338.415	−	444.182i	0.358490	−	0.470532i
$945$		0			0
$946$	−109.797	+	176.907i	−0.116064	+	0.187005i
$947$	−242.533			−0.256107			−0.128053	−	0.991767i	$-0.540873\pi$
$947$	−242.533			−0.256107			−0.128053	+	0.991767i	$0.540873\pi$
$948$		0			0
$949$		−	731.084i		−	0.770373i
$950$	5.56575	−	8.96763i	0.00585869	−	0.00943961i
$951$		0			0
$952$	−0.474557	+	4.94897i	−0.000498484	+	0.00519849i
$953$	364.070			0.382025			0.191013	−	0.981588i	$-0.438823\pi$
$953$	364.070			0.382025			0.191013	+	0.981588i	$0.438823\pi$
$954$		0			0
$955$	−991.294			−1.03800
$956$	254.828	−	126.212i	0.266556	−	0.132021i
$957$		0			0
$958$	1145.61	+	711.021i	1.19583	+	0.742193i
$959$			92.4575i			0.0964103i
$960$		0			0
$961$	−202.348			−0.210560
$962$	−747.981	+	1205.16i	−0.777527	+	1.25276i
$963$		0			0
$964$	−99.6152	−	201.128i	−0.103335	−	0.208639i
$965$			426.435i			0.441901i
$966$		0			0
$967$			1221.99i			1.26369i	0.775093	+	0.631847i	$0.217703\pi$
$967$			1221.99i			1.26369i	−0.775093	+	0.631847i	$0.782297\pi$
$968$	−2709.86	−	259.849i	−2.79944	−	0.268439i
$969$		0			0
$970$	−750.754	−	465.955i	−0.773973	−	0.480366i
$971$	1088.53			1.12104			0.560521	−	0.828140i	$-0.310601\pi$
$971$	1088.53			1.12104			0.560521	+	0.828140i	$0.310601\pi$
$972$		0			0
$973$			315.235i			0.323982i
$974$	−682.644	−	423.683i	−0.700866	−	0.434992i
$975$		0			0
$976$	−809.455	−	616.710i	−0.829360	−	0.631875i
$977$	1061.51			1.08650			0.543252	−	0.839570i	$-0.317193\pi$
$977$	1061.51			1.08650			0.543252	+	0.839570i	$0.317193\pi$
$978$		0			0
$979$	3431.17			3.50477
$980$	−122.517	+	60.6804i	−0.125017	+	0.0619188i
$981$		0			0
$982$	−452.329	+	728.800i	−0.460621	+	0.742159i
$983$		−	1322.61i		−	1.34549i	−0.739877	−	0.672743i	$-0.765116\pi$
$983$		−	1322.61i		−	1.34549i	0.739877	−	0.672743i	$-0.234884\pi$
$984$		0			0
$985$	−105.782			−0.107393
$986$	−13.8280	−	8.58232i	−0.0140243	−	0.00870417i
$987$		0			0
$988$	−213.669	+	105.826i	−0.216264	+	0.107112i
$989$			53.0874i			0.0536778i
$990$		0			0
$991$		−	675.806i		−	0.681944i	−0.940073	−	0.340972i	$-0.889244\pi$
$991$		−	675.806i		−	0.681944i	0.940073	−	0.340972i	$-0.110756\pi$
$992$	1019.84	−	388.848i	1.02806	−	0.391984i
$993$		0			0
$994$	132.613	−	213.667i	0.133413	−	0.214957i
$995$	−888.354			−0.892818
$996$		0			0
$997$		−	409.220i		−	0.410452i	−0.978715	−	0.205226i	$-0.934207\pi$
$997$		−	409.220i		−	0.410452i	0.978715	−	0.205226i	$-0.0657929\pi$
$998$	192.604	−	310.327i	0.192990	−	0.310949i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.g.b.379.5		8
3.2	odd	2		56.3.g.b.43.4	yes	8
4.3	odd	2		2016.3.g.b.1135.6		8
8.3	odd	2	inner	504.3.g.b.379.6		8
8.5	even	2		2016.3.g.b.1135.3		8
12.11	even	2		224.3.g.b.15.5		8
21.2	odd	6		392.3.k.o.67.8		16
21.5	even	6		392.3.k.n.67.8		16
21.11	odd	6		392.3.k.o.275.3		16
21.17	even	6		392.3.k.n.275.3		16
21.20	even	2		392.3.g.m.99.4		8
24.5	odd	2		224.3.g.b.15.6		8
24.11	even	2		56.3.g.b.43.3	✓	8
48.5	odd	4		1792.3.d.j.1023.12		16
48.11	even	4		1792.3.d.j.1023.6		16
48.29	odd	4		1792.3.d.j.1023.5		16
48.35	even	4		1792.3.d.j.1023.11		16
84.83	odd	2		1568.3.g.m.687.4		8
168.11	even	6		392.3.k.o.275.8		16
168.59	odd	6		392.3.k.n.275.8		16
168.83	odd	2		392.3.g.m.99.3		8
168.107	even	6		392.3.k.o.67.3		16
168.125	even	2		1568.3.g.m.687.3		8
168.131	odd	6		392.3.k.n.67.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.3	✓	8	24.11	even	2
56.3.g.b.43.4	yes	8	3.2	odd	2
224.3.g.b.15.5		8	12.11	even	2
224.3.g.b.15.6		8	24.5	odd	2
392.3.g.m.99.3		8	168.83	odd	2
392.3.g.m.99.4		8	21.20	even	2
392.3.k.n.67.3		16	168.131	odd	6
392.3.k.n.67.8		16	21.5	even	6
392.3.k.n.275.3		16	21.17	even	6
392.3.k.n.275.8		16	168.59	odd	6
392.3.k.o.67.3		16	168.107	even	6
392.3.k.o.67.8		16	21.2	odd	6
392.3.k.o.275.3		16	21.11	odd	6
392.3.k.o.275.8		16	168.11	even	6
504.3.g.b.379.5		8	1.1	even	1	trivial
504.3.g.b.379.6		8	8.3	odd	2	inner
1568.3.g.m.687.3		8	168.125	even	2
1568.3.g.m.687.4		8	84.83	odd	2
1792.3.d.j.1023.5		16	48.29	odd	4
1792.3.d.j.1023.6		16	48.11	even	4
1792.3.d.j.1023.11		16	48.35	even	4
1792.3.d.j.1023.12		16	48.5	odd	4
2016.3.g.b.1135.3		8	8.5	even	2
2016.3.g.b.1135.6		8	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.05468 - 1.69931i) q^{2} +(-1.77532 - 3.58445i) q^{4} +4.88287i q^{5} -2.64575i q^{7} +(-7.96347 - 0.763618i) q^{8} +O(q^{10})\)	\(q+(1.05468 - 1.69931i) q^{2} +(-1.77532 - 3.58445i) q^{4} +4.88287i q^{5} -2.64575i q^{7} +(-7.96347 - 0.763618i) q^{8} +(8.29751 + 5.14984i) q^{10} +21.4776 q^{11} -13.0760i q^{13} +(-4.49595 - 2.79041i) q^{14} +(-9.69651 + 12.7270i) q^{16} +0.234889 q^{17} +4.55872 q^{19} +(17.5024 - 8.66863i) q^{20} +(22.6519 - 36.4971i) q^{22} -10.9523i q^{23} +1.15761 q^{25} +(-22.2202 - 13.7910i) q^{26} +(-9.48355 + 4.69704i) q^{28} -34.6435i q^{29} -34.1079i q^{31} +(11.4005 + 29.9003i) q^{32} +(0.247732 - 0.399150i) q^{34} +12.9189 q^{35} -54.2370i q^{37} +(4.80798 - 7.74669i) q^{38} +(3.72865 - 38.8846i) q^{40} +37.8300 q^{41} -4.84714 q^{43} +(-38.1295 - 76.9852i) q^{44} +(-18.6114 - 11.5511i) q^{46} +72.3368i q^{47} -7.00000 q^{49} +(1.22090 - 1.96714i) q^{50} +(-46.8703 + 23.2141i) q^{52} -21.6707i q^{53} +104.872i q^{55} +(-2.02034 + 21.0694i) q^{56} +(-58.8701 - 36.5377i) q^{58} -34.9007 q^{59} +63.6012i q^{61} +(-57.9599 - 35.9728i) q^{62} +(62.8338 + 12.1621i) q^{64} +63.8485 q^{65} +18.4344 q^{67} +(-0.417002 - 0.841948i) q^{68} +(13.6252 - 21.9531i) q^{70} +47.5244i q^{71} +55.9103 q^{73} +(-92.1655 - 57.2024i) q^{74} +(-8.09317 - 16.3405i) q^{76} -56.8243i q^{77} -95.0135i q^{79} +(-62.1445 - 47.3468i) q^{80} +(39.8984 - 64.2849i) q^{82} -71.5156 q^{83} +1.14693i q^{85} +(-5.11217 + 8.23680i) q^{86} +(-171.036 - 16.4007i) q^{88} +159.756 q^{89} -34.5959 q^{91} +(-39.2579 + 19.4438i) q^{92} +(122.923 + 76.2920i) q^{94} +22.2596i q^{95} -90.4794 q^{97} +(-7.38273 + 11.8952i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 5 q^{4} - 13 q^{8}+O(q^{10}) \) 8 * q - q^2 + 5 * q^4 - 13 * q^8	\( 8 q - q^{2} + 5 q^{4} - 13 q^{8} + 16 q^{10} + 32 q^{11} - 7 q^{14} - 71 q^{16} + 80 q^{17} + 56 q^{19} + 108 q^{20} + 66 q^{22} - 16 q^{25} - 24 q^{26} + 7 q^{28} + 19 q^{32} + 74 q^{34} - 56 q^{35} + 14 q^{38} + 84 q^{40} - 128 q^{41} - 50 q^{44} - 152 q^{46} - 56 q^{49} - 33 q^{50} + 132 q^{52} + 49 q^{56} + 24 q^{58} - 104 q^{59} - 120 q^{62} - 55 q^{64} + 72 q^{65} + 304 q^{67} + 190 q^{68} + 56 q^{70} - 112 q^{73} - 8 q^{74} + 70 q^{76} - 124 q^{80} + 450 q^{82} - 72 q^{83} - 210 q^{86} - 486 q^{88} + 512 q^{89} - 56 q^{91} + 472 q^{92} + 472 q^{94} + 64 q^{97} + 7 q^{98}+O(q^{100}) \) 8 * q - q^2 + 5 * q^4 - 13 * q^8 + 16 * q^10 + 32 * q^11 - 7 * q^14 - 71 * q^16 + 80 * q^17 + 56 * q^19 + 108 * q^20 + 66 * q^22 - 16 * q^25 - 24 * q^26 + 7 * q^28 + 19 * q^32 + 74 * q^34 - 56 * q^35 + 14 * q^38 + 84 * q^40 - 128 * q^41 - 50 * q^44 - 152 * q^46 - 56 * q^49 - 33 * q^50 + 132 * q^52 + 49 * q^56 + 24 * q^58 - 104 * q^59 - 120 * q^62 - 55 * q^64 + 72 * q^65 + 304 * q^67 + 190 * q^68 + 56 * q^70 - 112 * q^73 - 8 * q^74 + 70 * q^76 - 124 * q^80 + 450 * q^82 - 72 * q^83 - 210 * q^86 - 486 * q^88 + 512 * q^89 - 56 * q^91 + 472 * q^92 + 472 * q^94 + 64 * q^97 + 7 * q^98

Introduction

L-functions

Modular forms

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Database

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