LMFDB - Embedded newform 392.3.g.m.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:	$8$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.4
Root			$-1.05468 - 1.69931i$ of defining polynomial
Character	$\chi$	$=$	392.99
Dual form			392.3.g.m.99.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05468 + 1.69931i) q^{2} +3.44128 q^{3} +(-1.77532 - 3.58445i) q^{4} +4.88287i q^{5} +(-3.62943 + 5.84780i) q^{6} +(7.96347 + 0.763618i) q^{8} +2.84239 q^{9} +O(q^{10})$	\(q+(-1.05468 + 1.69931i) q^{2} +3.44128 q^{3} +(-1.77532 - 3.58445i) q^{4} +4.88287i q^{5} +(-3.62943 + 5.84780i) q^{6} +(7.96347 + 0.763618i) q^{8} +2.84239 q^{9} +(-8.29751 - 5.14984i) q^{10} -21.4776 q^{11} +(-6.10935 - 12.3351i) q^{12} +13.0760i q^{13} +16.8033i q^{15} +(-9.69651 + 12.7270i) q^{16} +0.234889 q^{17} +(-2.99780 + 4.83011i) q^{18} -4.55872 q^{19} +(17.5024 - 8.66863i) q^{20} +(22.6519 - 36.4971i) q^{22} +10.9523i q^{23} +(27.4045 + 2.62782i) q^{24} +1.15761 q^{25} +(-22.2202 - 13.7910i) q^{26} -21.1900 q^{27} +34.6435i q^{29} +(-28.5540 - 17.7220i) q^{30} +34.1079i q^{31} +(-11.4005 - 29.9003i) q^{32} -73.9103 q^{33} +(-0.247732 + 0.399150i) q^{34} +(-5.04614 - 10.1884i) q^{36} -54.2370i q^{37} +(4.80798 - 7.74669i) q^{38} +44.9982i q^{39} +(-3.72865 + 38.8846i) q^{40} +37.8300 q^{41} -4.84714 q^{43} +(38.1295 + 76.9852i) q^{44} +13.8790i q^{45} +(-18.6114 - 11.5511i) q^{46} +72.3368i q^{47} +(-33.3684 + 43.7973i) q^{48} +(-1.22090 + 1.96714i) q^{50} +0.808319 q^{51} +(46.8703 - 23.2141i) q^{52} +21.6707i q^{53} +(22.3486 - 36.0085i) q^{54} -104.872i q^{55} -15.6878 q^{57} +(-58.8701 - 36.5377i) q^{58} -34.9007 q^{59} +(60.2305 - 29.8312i) q^{60} -63.6012i q^{61} +(-57.9599 - 35.9728i) q^{62} +(62.8338 + 12.1621i) q^{64} -63.8485 q^{65} +(77.9514 - 125.597i) q^{66} +18.4344 q^{67} +(-0.417002 - 0.841948i) q^{68} +37.6899i q^{69} -47.5244i q^{71} +(22.6353 + 2.17050i) q^{72} -55.9103 q^{73} +(92.1655 + 57.2024i) q^{74} +3.98365 q^{75} +(8.09317 + 16.3405i) q^{76} +(-76.4660 - 47.4586i) q^{78} -95.0135i q^{79} +(-62.1445 - 47.3468i) q^{80} -98.5023 q^{81} +(-39.8984 + 64.2849i) q^{82} -71.5156 q^{83} +1.14693i q^{85} +(5.11217 - 8.23680i) q^{86} +119.218i q^{87} +(-171.036 - 16.4007i) q^{88} +159.756 q^{89} +(-23.5848 - 14.6379i) q^{90} +(39.2579 - 19.4438i) q^{92} +117.375i q^{93} +(-122.923 - 76.2920i) q^{94} -22.2596i q^{95} +(-39.2324 - 102.895i) q^{96} +90.4794 q^{97} -61.0477 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 8 q^{3} + 5 q^{4} + 22 q^{6} + 13 q^{8} + 48 q^{9}+O(q^{10}) $ 8 * q + q^2 + 8 * q^3 + 5 * q^4 + 22 * q^6 + 13 * q^8 + 48 * q^9	$ 8 q + q^{2} + 8 q^{3} + 5 q^{4} + 22 q^{6} + 13 q^{8} + 48 q^{9} - 16 q^{10} - 32 q^{11} - 30 q^{12} - 71 q^{16} + 80 q^{17} - 29 q^{18} - 56 q^{19} + 108 q^{20} + 66 q^{22} - 22 q^{24} - 16 q^{25} - 24 q^{26} + 32 q^{27} + 96 q^{30} - 19 q^{32} - 32 q^{33} - 74 q^{34} - 33 q^{36} + 14 q^{38} - 84 q^{40} - 128 q^{41} + 50 q^{44} - 152 q^{46} - 134 q^{48} + 33 q^{50} - 368 q^{51} - 132 q^{52} + 228 q^{54} + 56 q^{57} + 24 q^{58} - 104 q^{59} + 192 q^{60} - 120 q^{62} - 55 q^{64} - 72 q^{65} + 276 q^{66} + 304 q^{67} + 190 q^{68} - 209 q^{72} + 112 q^{73} + 8 q^{74} - 72 q^{75} - 70 q^{76} - 304 q^{78} - 124 q^{80} + 48 q^{81} - 450 q^{82} - 72 q^{83} + 210 q^{86} - 486 q^{88} + 512 q^{89} + 184 q^{90} - 472 q^{92} - 472 q^{94} - 558 q^{96} - 64 q^{97} + 256 q^{99}+O(q^{100}) $ 8 * q + q^2 + 8 * q^3 + 5 * q^4 + 22 * q^6 + 13 * q^8 + 48 * q^9 - 16 * q^10 - 32 * q^11 - 30 * q^12 - 71 * q^16 + 80 * q^17 - 29 * q^18 - 56 * q^19 + 108 * q^20 + 66 * q^22 - 22 * q^24 - 16 * q^25 - 24 * q^26 + 32 * q^27 + 96 * q^30 - 19 * q^32 - 32 * q^33 - 74 * q^34 - 33 * q^36 + 14 * q^38 - 84 * q^40 - 128 * q^41 + 50 * q^44 - 152 * q^46 - 134 * q^48 + 33 * q^50 - 368 * q^51 - 132 * q^52 + 228 * q^54 + 56 * q^57 + 24 * q^58 - 104 * q^59 + 192 * q^60 - 120 * q^62 - 55 * q^64 - 72 * q^65 + 276 * q^66 + 304 * q^67 + 190 * q^68 - 209 * q^72 + 112 * q^73 + 8 * q^74 - 72 * q^75 - 70 * q^76 - 304 * q^78 - 124 * q^80 + 48 * q^81 - 450 * q^82 - 72 * q^83 + 210 * q^86 - 486 * q^88 + 512 * q^89 + 184 * q^90 - 472 * q^92 - 472 * q^94 - 558 * q^96 - 64 * q^97 + 256 * 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 $

$2$	−1.05468	+	1.69931i	−0.527338	+	0.849655i
$2$	−1.05468	+	1.69931i	−0.527338	+	0.849655i
$3$	3.44128			1.14709			0.573546	−	0.819173i	$-0.305567\pi$
$3$	3.44128			1.14709			0.573546	+	0.819173i	$0.305567\pi$
$4$	−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	$0.837622\pi$
$6$	−3.62943	+	5.84780i	−0.604906	+	0.974633i
$7$		0			0
$7$		0			0
$8$	7.96347	+	0.763618i	0.995434	+	0.0954523i
$9$	2.84239			0.315821
$10$	−8.29751	−	5.14984i	−0.829751	−	0.514984i
$11$	−21.4776			−1.95251			−0.976253	−	0.216632i	$-0.930493\pi$
$11$	−21.4776			−1.95251			−0.976253	+	0.216632i	$0.930493\pi$
$12$	−6.10935	−	12.3351i	−0.509113	−	1.02792i
$13$			13.0760i			1.00585i	0.864331	+	0.502924i	$0.167742\pi$
$13$			13.0760i			1.00585i	−0.864331	+	0.502924i	$0.832258\pi$
$14$		0			0
$15$			16.8033i			1.12022i
$16$	−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	$0.497801\pi$
$18$	−2.99780	+	4.83011i	−0.166545	+	0.268339i
$19$	−4.55872			−0.239933			−0.119966	−	0.992778i	$-0.538279\pi$
$19$	−4.55872			−0.239933			−0.119966	+	0.992778i	$0.538279\pi$
$20$	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	$0.0765225\pi$
$23$			10.9523i			0.476187i	−0.971242	+	0.238094i	$0.923478\pi$
$24$	27.4045	+	2.62782i	1.14185	+	0.109493i
$25$	1.15761			0.0463043
$26$	−22.2202	−	13.7910i	−0.854624	−	0.530422i
$27$	−21.1900			−0.784816
$28$		0			0
$29$			34.6435i			1.19460i	0.802016	+	0.597302i	$0.203761\pi$
$29$			34.6435i			1.19460i	−0.802016	+	0.597302i	$0.796239\pi$
$30$	−28.5540	−	17.7220i	−0.951801	−	0.590735i
$31$			34.1079i			1.10025i	0.835081	+	0.550127i	$0.185421\pi$
$31$			34.1079i			1.10025i	−0.835081	+	0.550127i	$0.814579\pi$
$32$	−11.4005	−	29.9003i	−0.356266	−	0.934384i
$33$	−73.9103			−2.23971
$34$	−0.247732	+	0.399150i	−0.00728624	+	0.0117397i
$35$		0			0
$36$	−5.04614	−	10.1884i	−0.140171	−	0.283011i
$37$		−	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
$39$			44.9982i			1.15380i
$40$	−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
$45$			13.8790i			0.308423i
$46$	−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	$0.720485\pi$
$48$	−33.3684	+	43.7973i	−0.695175	+	0.912444i
$49$		0			0
$50$	−1.22090	+	1.96714i	−0.0244180	+	0.0393427i
$51$	0.808319			0.0158494
$52$	46.8703	−	23.2141i	0.901352	−	0.446424i
$53$			21.6707i			0.408881i	0.978879	+	0.204440i	$0.0655374\pi$
$53$			21.6707i			0.408881i	−0.978879	+	0.204440i	$0.934463\pi$
$54$	22.3486	−	36.0085i	0.413864	−	0.666823i
$55$		−	104.872i		−	1.90677i
$56$		0			0
$57$	−15.6878			−0.275225
$58$	−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	$0.595576\pi$
$60$	60.2305	−	29.8312i	1.00384	−	0.497186i
$61$		−	63.6012i		−	1.04264i	−0.853360	−	0.521321i	$-0.825439\pi$
$61$		−	63.6012i		−	1.04264i	0.853360	−	0.521321i	$-0.174561\pi$
$62$	−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
$66$	77.9514	−	125.597i	1.18108	−	1.90298i
$67$	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
$69$			37.6899i			0.546231i
$70$		0			0
$71$		−	47.5244i		−	0.669358i	−0.942332	−	0.334679i	$-0.891372\pi$
$71$		−	47.5244i		−	0.669358i	0.942332	−	0.334679i	$-0.108628\pi$
$72$	22.6353	+	2.17050i	0.314379	+	0.0301459i
$73$	−55.9103			−0.765894			−0.382947	−	0.923770i	$-0.625091\pi$
$73$	−55.9103			−0.765894			−0.382947	+	0.923770i	$0.625091\pi$
$74$	92.1655	+	57.2024i	1.24548	+	0.773006i
$75$	3.98365			0.0531153
$76$	8.09317	+	16.3405i	0.106489	+	0.215007i
$77$		0			0
$78$	−76.4660	−	47.4586i	−0.980333	−	0.608443i
$79$		−	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
$81$	−98.5023			−1.21608
$82$	−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
$87$			119.218i			1.37032i
$88$	−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	$0.145378\pi$
$90$	−23.5848	−	14.6379i	−0.262053	−	0.162643i
$91$		0			0
$92$	39.2579	−	19.4438i	0.426717	−	0.211346i
$93$			117.375i			1.26209i
$94$	−122.923	−	76.2920i	−1.30769	−	0.811617i
$95$		−	22.2596i		−	0.234312i
$96$	−39.2324	−	102.895i	−0.408671	−	1.07183i
$97$	90.4794			0.932777			0.466389	−	0.884580i	$-0.345555\pi$
$97$	90.4794			0.932777			0.466389	+	0.884580i	$0.345555\pi$
$98$		0			0
$99$	−61.0477			−0.616643
$100$	−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	$0.645909\pi$
$102$	−0.852515	+	1.37359i	−0.00835799	+	0.0134665i
$103$		−	39.3003i		−	0.381556i	−0.981633	−	0.190778i	$-0.938899\pi$
$103$		−	39.3003i		−	0.381556i	0.981633	−	0.190778i	$-0.0611010\pi$
$104$	−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	$-0.442496\pi$
$107$	38.4498			0.359344			0.179672	+	0.983727i	$0.442496\pi$
$108$	37.6190	+	75.9546i	0.348324	+	0.703283i
$109$			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
$111$		−	186.644i		−	1.68148i
$112$		0			0
$113$	82.4419			0.729574			0.364787	−	0.931091i	$-0.381142\pi$
$113$	82.4419			0.729574			0.364787	+	0.931091i	$0.381142\pi$
$114$	16.5456	−	26.6585i	0.145137	−	0.233846i
$115$	−53.4786			−0.465032
$116$	124.178	−	61.5032i	1.07050	−	0.530200i
$117$			37.1672i			0.317668i
$118$	36.8089	−	59.3071i	0.311940	−	0.502603i
$119$		0			0
$120$	−12.8313	+	133.813i	−0.106928	+	1.11511i
$121$	340.286			2.81228
$122$	108.078	+	67.0787i	0.885887	+	0.549825i
$123$	130.183			1.05840
$124$	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
$129$	−16.6804			−0.129305
$130$	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	$0.339752\pi$
$132$	131.214	+	264.928i	0.994046	+	2.00703i
$133$		0			0
$134$	−19.4423	+	31.3257i	−0.145092	+	0.233774i
$135$		−	103.468i		−	0.766431i
$136$	1.87053	+	0.179366i	0.0137539	+	0.00131887i
$137$	34.9456			0.255078			0.127539	−	0.991834i	$-0.459292\pi$
$137$	34.9456			0.255078			0.127539	+	0.991834i	$0.459292\pi$
$138$	−64.0469	−	39.7507i	−0.464108	−	0.288048i
$139$	119.148			0.857177			0.428589	−	0.903500i	$-0.359011\pi$
$139$	119.148			0.857177			0.428589	+	0.903500i	$0.359011\pi$
$140$		0			0
$141$			248.931i			1.76547i
$142$	80.7587	+	50.1229i	0.568723	+	0.352978i
$143$		−	280.841i		−	1.96392i
$144$	−27.5613	+	36.1753i	−0.191398	+	0.251217i
$145$	−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	$0.134181\pi$
$149$			121.932i			0.818334i	−0.912460	+	0.409167i	$0.865819\pi$
$150$	−4.20146	+	6.76946i	−0.0280097	+	0.0451297i
$151$			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
$153$	0.667647			0.00436371
$154$		0			0
$155$	−166.544			−1.07448
$156$	161.294	−	79.8860i	1.03393	−	0.512090i
$157$		−	6.77014i		−	0.0431219i	−0.999768	−	0.0215610i	$-0.993136\pi$
$157$		−	6.77014i		−	0.0431219i	0.999768	−	0.0215610i	$-0.00686360\pi$
$158$	161.457	+	100.208i	1.02188	+	0.634231i
$159$			74.5748i			0.469024i
$160$	145.999	−	55.6672i	0.912495	−	0.347920i
$161$		0			0
$162$	103.888	−	167.386i	0.641285	−	1.03325i
$163$	−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
$165$		−	360.894i		−	2.18724i
$166$	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
$171$	−12.9577			−0.0757759
$172$	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	$-0.0826683\pi$
$174$	−202.588	−	125.736i	−1.16430	−	0.722623i
$175$		0			0
$176$	208.258	−	273.346i	1.18328	−	1.55310i
$177$	−120.103			−0.678548
$178$	−168.491	+	271.475i	−0.946576	+	1.52514i
$179$	80.3791			0.449045			0.224523	−	0.974469i	$-0.427918\pi$
$179$	80.3791			0.449045			0.224523	+	0.974469i	$0.427918\pi$
$180$	49.7486	−	24.6396i	0.276381	−	0.136887i
$181$			276.353i			1.52681i	0.645919	+	0.763406i	$0.276474\pi$
$181$			276.353i			1.52681i	−0.645919	+	0.763406i	$0.723526\pi$
$182$		0			0
$183$		−	218.869i		−	1.19601i
$184$	−8.36338	+	87.2184i	−0.0454532	+	0.474013i
$185$	264.832			1.43152
$186$	−199.456	−	123.792i	−1.07234	−	0.665550i
$187$	−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	$-0.821647\pi$
$191$		−	203.015i		−	1.06290i	0.847088	−	0.531452i	$-0.178353\pi$
$192$	216.228	+	41.8532i	1.12619	+	0.217985i
$193$	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
$195$	−219.720			−1.12677
$196$		0			0
$197$		−	21.6639i		−	0.109969i	−0.998487	−	0.0549845i	$-0.982489\pi$
$197$		−	21.6639i		−	0.109969i	0.998487	−	0.0549845i	$-0.0175109\pi$
$198$	64.3856	−	103.739i	0.325180	−	0.523934i
$199$		−	181.933i		−	0.914235i	−0.889406	−	0.457118i	$-0.848882\pi$
$199$		−	181.933i		−	0.914235i	0.889406	−	0.457118i	$-0.151118\pi$
$200$	9.21858	+	0.883971i	0.0460929	+	0.00441985i
$201$	63.4378			0.315611
$202$	−307.825	−	191.051i	−1.52389	−	0.945799i
$203$		0			0
$204$	−1.43502	−	2.89738i	−0.00703442	−	0.0142028i
$205$			184.719i			0.901067i
$206$	66.7834	+	41.4491i	0.324191	+	0.201209i
$207$			31.1307i			0.150390i
$208$	−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
$213$		−	163.545i		−	0.767815i
$214$	−40.5521	+	65.3382i	−0.189496	+	0.305319i
$215$		−	23.6680i		−	0.110084i
$216$	−168.746	−	16.1811i	−0.781233	−	0.0749125i
$217$		0			0
$218$	−47.3744	−	29.4029i	−0.217314	−	0.134876i
$219$	−192.403			−0.878552
$220$	−375.909	+	186.181i	−1.70868	+	0.846278i
$221$			3.07142i			0.0138978i
$222$	317.167	+	196.850i	1.42868	+	0.886710i
$223$		−	195.958i		−	0.878735i	−0.898307	−	0.439367i	$-0.855203\pi$
$223$		−	195.958i		−	0.878735i	0.898307	−	0.439367i	$-0.144797\pi$
$224$		0			0
$225$	3.29038			0.0146239
$226$	−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	$0.480872\pi$
$228$	27.8508	+	56.2322i	0.122153	+	0.246632i
$229$			176.347i			0.770076i	0.922901	+	0.385038i	$0.125812\pi$
$229$			176.347i			0.770076i	−0.922901	+	0.385038i	$0.874188\pi$
$230$	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	$-0.450734\pi$
$233$	71.8366			0.308312			0.154156	+	0.988047i	$0.450734\pi$
$234$	−63.1586	−	39.1994i	−0.269909	−	0.167519i
$235$	−353.211			−1.50303
$236$	61.9597	+	125.100i	0.262541	+	0.530083i
$237$		−	326.968i		−	1.37961i
$238$		0			0
$239$		−	71.0926i		−	0.297459i	−0.988878	−	0.148729i	$-0.952482\pi$
$239$		−	71.0926i		−	0.297459i	0.988878	−	0.148729i	$-0.0475183\pi$
$240$	−213.856	−	162.933i	−0.891068	−	0.678889i
$241$	−56.1113			−0.232827			−0.116413	−	0.993201i	$-0.537140\pi$
$241$	−56.1113			−0.232827			−0.116413	+	0.993201i	$0.537140\pi$
$242$	−358.892	+	578.252i	−1.48302	+	2.38947i
$243$	−148.264			−0.610138
$244$	−227.975	+	112.912i	−0.934324	+	0.462755i
$245$		0			0
$246$	−137.301	+	221.222i	−0.558136	+	0.899277i
$247$		−	59.6100i		−	0.241336i
$248$	−26.0454	+	271.617i	−0.105022	+	1.09523i
$249$	−246.105			−0.988374
$250$	−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
$255$			3.94691i			0.0154781i
$256$	−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	$0.514709\pi$
$258$	17.5924	−	28.3451i	0.0681876	−	0.109865i
$259$		0			0
$260$	113.351	+	228.861i	0.435966	+	0.880236i
$261$			98.4705i			0.377282i
$262$	−133.309	+	214.790i	−0.508814	+	0.819809i
$263$		−	73.9707i		−	0.281257i	−0.990062	−	0.140629i	$-0.955088\pi$
$263$		−	73.9707i		−	0.281257i	0.990062	−	0.140629i	$-0.0449124\pi$
$264$	−588.583	−	56.4393i	−2.22948	−	0.213785i
$265$	−105.815			−0.399302
$266$		0			0
$267$	549.764			2.05904
$268$	−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	$-0.214403\pi$
$270$	175.825	+	109.125i	0.651202	+	0.404168i
$271$		−	187.276i		−	0.691054i	−0.938409	−	0.345527i	$-0.887700\pi$
$271$		−	187.276i		−	0.691054i	0.938409	−	0.345527i	$-0.112300\pi$
$272$	−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
$276$	135.097	−	66.9115i	0.489484	−	0.242433i
$277$			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
$279$			96.9480i			0.347484i
$280$		0			0
$281$	331.520			1.17979			0.589894	−	0.807481i	$-0.299170\pi$
$281$	331.520			1.17979			0.589894	+	0.807481i	$0.299170\pi$
$282$	−423.011	−	262.542i	−1.50004	−	0.930999i
$283$	66.7158			0.235745			0.117873	−	0.993029i	$-0.462393\pi$
$283$	66.7158			0.235745			0.117873	+	0.993029i	$0.462393\pi$
$284$	−170.349	+	84.3708i	−0.599819	+	0.297080i
$285$		−	76.6016i		−	0.268778i
$286$	477.237	+	296.197i	1.66866	+	1.03565i
$287$		0			0
$288$	−32.4048	−	84.9884i	−0.112517	−	0.295099i
$289$	−288.945			−0.999809
$290$	178.409	−	287.455i	0.615203	−	0.991224i
$291$	311.365			1.06998
$292$	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
$297$	455.111			1.53236
$298$	−207.200	−	128.598i	−0.695302	−	0.431539i
$299$	−143.213			−0.478972
$300$	−7.07223	−	14.2792i	−0.0235741	−	0.0475973i
$301$		0			0
$302$	−374.535	−	232.455i	−1.24018	−	0.769719i
$303$			623.377i			2.05735i
$304$	44.2037	−	58.0191i	0.145407	−	0.190852i
$305$	310.556			1.01822
$306$	−0.704152	+	1.13454i	−0.00230115	+	0.00370765i
$307$	−0.693177			−0.00225790			−0.00112895	−	0.999999i	$-0.500359\pi$
$307$	−0.693177			−0.00225790			−0.00112895	+	0.999999i	$0.500359\pi$
$308$		0			0
$309$		−	135.243i		−	0.437680i
$310$	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	$0.968137\pi$
$312$	−34.3615	+	358.342i	−0.110133	+	1.14853i
$313$	−213.594			−0.682408			−0.341204	−	0.939989i	$-0.610835\pi$
$313$	−213.594			−0.682408			−0.341204	+	0.939989i	$0.610835\pi$
$314$	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	$-0.988220\pi$
$317$		−	23.4577i		−	0.0739990i	0.999315	−	0.0369995i	$-0.0117800\pi$
$318$	−126.726	−	78.6523i	−0.398509	−	0.247334i
$319$		−	744.059i		−	2.33247i
$320$	−59.3860	+	306.809i	−0.185581	+	0.958778i
$321$	132.317			0.412201
$322$		0			0
$323$	−1.07079			−0.00331515
$324$	174.873	+	353.076i	0.539731	+	1.08974i
$325$			15.1369i			0.0465751i
$326$	218.574	−	352.170i	0.670473	−	1.08028i
$327$			95.9380i			0.293388i
$328$	301.258	+	28.8877i	0.918469	+	0.0880721i
$329$		0			0
$330$	613.271	+	380.627i	1.85840	+	1.15341i
$331$	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
$333$		−	154.163i		−	0.462951i
$334$	−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
$339$	283.705			0.836889
$340$	4.11112	−	2.03617i	0.0120915	−	0.00598873i
$341$		−	732.555i		−	2.14825i
$342$	13.6662	−	22.0191i	0.0399595	−	0.0643834i
$343$		0			0
$344$	−38.6001	−	3.70137i	−0.112210	−	0.0107598i
$345$	−184.035			−0.533434
$346$	150.989	+	93.7111i	0.436384	+	0.270841i
$347$	136.745			0.394079			0.197039	−	0.980396i	$-0.436867\pi$
$347$	136.745			0.394079			0.197039	+	0.980396i	$0.436867\pi$
$348$	427.331	−	211.650i	1.22796	−	0.608188i
$349$			82.0565i			0.235119i	0.993066	+	0.117559i	$0.0375071\pi$
$349$			82.0565i			0.235119i	−0.993066	+	0.117559i	$0.962493\pi$
$350$		0			0
$351$		−	277.081i		−	0.789406i
$352$	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	$0.755240\pi$
$354$	126.670	−	204.092i	0.357824	−	0.576532i
$355$	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	$0.285326\pi$
$359$			560.809i			1.56214i	−0.624442	+	0.781071i	$0.714674\pi$
$360$	−10.5983	+	110.525i	−0.0294397	+	0.307014i
$361$	−340.218			−0.942432
$362$	−469.610	−	291.463i	−1.29726	−	0.805147i
$363$	1171.02			3.22595
$364$		0			0
$365$		−	273.003i		−	0.747952i
$366$	371.927	+	230.836i	1.01619	+	0.630701i
$367$		−	26.9431i		−	0.0734145i	−0.999326	−	0.0367072i	$-0.988313\pi$
$367$		−	26.9431i		−	0.0734145i	0.999326	−	0.0367072i	$-0.0116869\pi$
$368$	−139.390	−	106.199i	−0.378778	−	0.288585i
$369$	107.528			0.291403
$370$	−279.312	+	450.032i	−0.754897	+	1.21630i
$371$		0			0
$372$	420.723	−	208.377i	1.13098	−	0.560153i
$373$		−	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
$375$			439.534i			1.17209i
$376$	−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
$381$			86.5166i			0.227078i
$382$	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	$0.856720\pi$
$384$	−299.173	+	323.298i	−0.779095	+	0.841921i
$385$		0			0
$386$	−92.1079	+	148.406i	−0.238621	+	0.384471i
$387$	−13.7775			−0.0356007
$388$	−160.629	−	324.319i	−0.413993	−	0.835873i
$389$			109.639i			0.281847i	0.990020	+	0.140924i	$0.0450072\pi$
$389$			109.639i			0.281847i	−0.990020	+	0.140924i	$0.954993\pi$
$390$	231.734	−	373.373i	0.594189	−	0.957367i
$391$			2.57258i			0.00657948i
$392$		0			0
$393$	434.971			1.10680
$394$	36.8137	+	22.8484i	0.0934358	+	0.0579909i
$395$	463.938			1.17453
$396$	108.379	+	218.822i	0.273684	+	0.552581i
$397$			310.938i			0.783219i	0.920131	+	0.391610i	$0.128082\pi$
$397$			310.938i			0.783219i	−0.920131	+	0.391610i	$0.871918\pi$
$398$	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	$-0.677267\pi$
$401$	−423.903			−1.05711			−0.528557	+	0.848898i	$0.677267\pi$
$402$	−66.9063	+	107.801i	−0.166434	+	0.268160i
$403$	−445.995			−1.10669
$404$	649.311	−	321.593i	1.60721	−	0.796022i
$405$		−	480.974i		−	1.18759i
$406$		0			0
$407$			1164.88i			2.86211i
$408$	6.43703	+	0.617247i	0.0157770	+	0.00151286i
$409$	−444.543			−1.08690			−0.543451	−	0.839441i	$-0.682883\pi$
$409$	−444.543			−1.08690			−0.543451	+	0.839441i	$0.682883\pi$
$410$	−313.895	−	194.818i	−0.765596	−	0.475167i
$411$	120.258			0.292598
$412$	−140.870	+	69.7703i	−0.341917	+	0.169345i
$413$		0			0
$414$	−52.9008	−	32.8329i	−0.127780	−	0.0793064i
$415$		−	349.201i		−	0.841449i
$416$	390.977	−	149.074i	0.939849	−	0.358350i
$417$	410.020			0.983261
$418$	−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
$423$			205.610i			0.486075i
$424$	−16.5481	+	172.574i	−0.0390286	+	0.407014i
$425$	0.271910			0.000639787
$426$	277.913	+	172.487i	0.652378	+	0.404898i
$427$		0			0
$428$	−68.2606	−	137.821i	−0.159487	−	0.322013i
$429$		−	966.453i		−	2.25280i
$430$	40.2192	+	24.9620i	0.0935331	+	0.0580512i
$431$		−	124.595i		−	0.289084i	−0.989499	−	0.144542i	$-0.953829\pi$
$431$		−	124.595i		−	0.289084i	0.989499	−	0.144542i	$-0.0461709\pi$
$432$	205.469	−	269.687i	0.475624	−	0.624274i
$433$	272.271			0.628802			0.314401	−	0.949290i	$-0.398196\pi$
$433$	272.271			0.628802			0.314401	+	0.949290i	$0.398196\pi$
$434$		0			0
$435$	−582.126			−1.33822
$436$	99.9293	−	49.4933i	0.229196	−	0.113517i
$437$		−	49.9285i		−	0.114253i
$438$	202.923	−	326.952i	0.463294	−	0.746466i
$439$		−	255.069i		−	0.581023i	−0.956871	−	0.290512i	$-0.906174\pi$
$439$		−	255.069i		−	0.581023i	0.956871	−	0.290512i	$-0.0938255\pi$
$440$	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	$-0.452663\pi$
$443$	131.274			0.296330			0.148165	+	0.988963i	$0.452663\pi$
$444$	−669.017	+	331.353i	−1.50680	+	0.746290i
$445$			780.066i			1.75296i
$446$	332.993	+	206.672i	0.746622	+	0.463391i
$447$			419.601i			0.938704i
$448$		0			0
$449$	−642.824			−1.43168			−0.715839	−	0.698265i	$-0.753956\pi$
$449$	−642.824			−1.43168			−0.715839	+	0.698265i	$0.753956\pi$
$450$	−3.47028	+	5.59137i	−0.00771174	+	0.0124253i
$451$	−812.496			−1.80154
$452$	−146.360	−	295.509i	−0.323806	−	0.653780i
$453$			758.472i			1.67433i
$454$	−28.7559	+	46.3320i	−0.0633390	+	0.102053i
$455$		0			0
$456$	−124.930	−	11.9795i	−0.273968	−	0.0262709i
$457$	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
$459$	−4.97731			−0.0108438
$460$	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
$465$	−573.125			−1.23253
$466$	−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	$0.431488\pi$
$468$	133.224	−	65.9835i	0.284666	−	0.140990i
$469$		0			0
$470$	372.524	−	600.216i	0.792603	−	1.27705i
$471$		−	23.2979i		−	0.0494648i
$472$	−277.931	−	26.6508i	−0.588836	−	0.0564636i
$473$	104.105			0.220095
$474$	555.620	+	344.845i	1.17219	+	0.727521i
$475$	−5.27721			−0.0111099
$476$		0			0
$477$			61.5966i			0.129133i
$478$	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	$0.751523\pi$
$480$	502.424	−	191.566i	1.04672	−	0.399097i
$481$	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
$486$	156.370	−	251.946i	0.321749	−	0.518407i
$487$		−	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
$489$	−713.181			−1.45845
$490$		0			0
$491$	428.880			0.873482			0.436741	−	0.899587i	$-0.356133\pi$
$491$	428.880			0.873482			0.436741	+	0.899587i	$0.356133\pi$
$492$	−231.117	−	466.636i	−0.469749	−	0.948446i
$493$			8.13739i			0.0165059i
$494$	101.296	+	62.8692i	0.205052	+	0.127266i
$495$		−	298.088i		−	0.602198i
$496$	−434.093	−	330.727i	−0.875187	−	0.666789i
$497$		0			0
$498$	259.561	−	418.209i	0.521207	−	0.839778i
$499$	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
$501$			569.632i			1.13699i
$502$	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
$507$	−6.82188			−0.0134554
$508$	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	$0.908200\pi$
$510$	−6.70703	−	4.16272i	−0.0131510	−	0.00816219i
$511$		0			0
$512$	491.088	+	144.834i	0.959156	+	0.282878i
$513$	96.5995			0.188303
$514$	25.0410	−	40.3464i	0.0487179	−	0.0784950i
$515$	191.898			0.372617
$516$	29.6129	+	59.7899i	0.0573894	+	0.115872i
$517$		−	1553.62i		−	3.00507i
$518$		0			0
$519$		−	305.768i		−	0.589148i
$520$	−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	$0.249094\pi$
$522$	−167.332	−	103.855i	−0.320559	−	0.198955i
$523$	−647.126			−1.23734			−0.618668	−	0.785653i	$-0.712327\pi$
$523$	−647.126			−1.23734			−0.618668	+	0.785653i	$0.712327\pi$
$524$	−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
$528$	716.672	−	940.660i	1.35733	−	1.78155i
$529$	409.047			0.773246
$530$	111.601	−	179.813i	0.210567	−	0.339269i
$531$	−99.2014			−0.186820
$532$		0			0
$533$			494.666i			0.928078i
$534$	−579.823	+	934.220i	−1.08581	+	1.74948i
$535$			187.745i			0.350926i
$536$	146.802	+	14.0768i	0.273884	+	0.0262627i
$537$	276.607			0.515097
$538$	570.277	+	353.942i	1.05999	+	0.657885i
$539$		0			0
$540$	−370.876	+	183.689i	−0.686807	+	0.340164i
$541$			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
$543$			951.008i			1.75140i
$544$	−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
$549$		−	180.780i		−	0.329289i
$550$	26.2220	−	42.2493i	0.0476764	−	0.0768169i
$551$		−	157.930i		−	0.286625i
$552$	−28.7807	+	300.143i	−0.0521390	+	0.543737i
$553$		0			0
$554$	−225.314	−	139.841i	−0.406705	−	0.252421i
$555$	911.360			1.64209
$556$	−211.525	−	427.078i	−0.380440	−	0.768126i
$557$		−	854.108i		−	1.53341i	−0.642001	−	0.766704i	$-0.721895\pi$
$557$		−	854.108i		−	1.53341i	0.642001	−	0.766704i	$-0.278105\pi$
$558$	−164.745	−	102.249i	−0.295242	−	0.183241i
$559$		−	63.3814i		−	0.113383i
$560$		0			0
$561$	−17.3607			−0.0309460
$562$	−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	$0.571166\pi$
$564$	892.280	−	441.931i	1.58206	−	0.783566i
$565$			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	$-0.470771\pi$
$569$	104.353			0.183396			0.0916982	+	0.995787i	$0.470771\pi$
$570$	130.170	+	80.7899i	0.228368	+	0.141737i
$571$	−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
$573$		−	698.630i		−	1.21925i
$574$		0			0
$575$			12.6785i			0.0220495i
$576$	178.598	+	34.5695i	0.310066	+	0.0600165i
$577$	346.022			0.599692			0.299846	−	0.953988i	$-0.403065\pi$
$577$	346.022			0.599692			0.299846	+	0.953988i	$0.403065\pi$
$578$	304.743	−	491.007i	0.527238	−	0.849493i
$579$	300.537			0.519061
$580$	300.312	+	606.344i	0.517779	+	1.04542i
$581$		0			0
$582$	−328.389	+	529.106i	−0.564242	+	0.909116i
$583$		−	465.434i		−	0.798342i
$584$	−445.240	−	42.6941i	−0.762397	−	0.0731064i
$585$	−181.482			−0.310226
$586$	−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
$591$		−	74.5515i		−	0.126145i
$592$	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	$0.766172\pi$
$594$	−479.994	+	773.374i	−0.808071	+	1.30198i
$595$		0			0
$596$	437.058	−	216.467i	0.733318	−	0.363200i
$597$		−	626.081i		−	1.04871i
$598$	151.043	−	243.363i	0.252580	−	0.406961i
$599$		−	554.939i		−	0.926442i	−0.886243	−	0.463221i	$-0.846694\pi$
$599$		−	554.939i		−	0.926442i	0.886243	−	0.463221i	$-0.153306\pi$
$600$	31.7237	+	3.04199i	0.0528728	+	0.00506998i
$601$	666.057			1.10825			0.554124	−	0.832434i	$-0.313054\pi$
$601$	666.057			1.10825			0.554124	+	0.832434i	$0.313054\pi$
$602$		0			0
$603$	52.3977			0.0868950
$604$	790.027	−	391.287i	1.30799	−	0.647826i
$605$			1661.57i			2.74640i
$606$	−1059.31	−	657.461i	−1.74804	−	1.08492i
$607$			192.927i			0.317836i	0.987292	+	0.158918i	$0.0508006\pi$
$607$			192.927i			0.317836i	−0.987292	+	0.158918i	$0.949199\pi$
$608$	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
$612$	−1.18528	−	2.39315i	−0.00193674	−	0.00391037i
$613$			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
$615$			635.668i			1.03361i
$616$		0			0
$617$	0.884056			0.00143283			0.000716415	−	1.00000i	$-0.499772\pi$
$617$	0.884056			0.00143283			0.000716415		1.00000i	$0.499772\pi$
$618$	229.820	+	142.638i	0.371877	+	0.230805i
$619$	−358.525			−0.579200			−0.289600	−	0.957148i	$-0.593522\pi$
$619$	−358.525			−0.579200			−0.289600	+	0.957148i	$0.593522\pi$
$620$	295.669	+	596.969i	0.476885	+	0.962853i
$621$		−	232.080i		−	0.373719i
$622$	−105.626	−	65.5569i	−0.169817	−	0.105397i
$623$		0			0
$624$	−572.694	−	436.326i	−0.917780	−	0.699240i
$625$	−594.720			−0.951552
$626$	225.272	−	362.962i	0.359860	−	0.579812i
$627$	336.937			0.537379
$628$	−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
$633$	−73.7137			−0.116451
$634$	39.8619	+	24.7403i	0.0628737	+	0.0390225i
$635$	−122.759			−0.193322
$636$	267.309	−	132.394i	0.420298	−	0.208166i
$637$		0			0
$638$	1264.39	+	784.742i	1.98180	+	1.23000i
$639$		−	135.083i		−	0.211397i
$640$	−458.731	−	424.499i	−0.716767	−	0.663280i
$641$	−431.936			−0.673848			−0.336924	−	0.941532i	$-0.609386\pi$
$641$	−431.936			−0.673848			−0.336924	+	0.941532i	$0.609386\pi$
$642$	−139.551	+	224.847i	−0.217369	+	0.350229i
$643$	−49.9370			−0.0776625			−0.0388313	−	0.999246i	$-0.512363\pi$
$643$	−49.9370			−0.0776625			−0.0388313	+	0.999246i	$0.512363\pi$
$644$		0			0
$645$		−	81.4480i		−	0.126276i
$646$	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	$0.944584\pi$
$648$	−784.421	−	75.2182i	−1.21053	−	0.116077i
$649$	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	$0.0196970\pi$
$653$			80.7637i			0.123681i	−0.998086	+	0.0618405i	$0.980303\pi$
$654$	−163.028	−	101.183i	−0.249279	−	0.154715i
$655$			617.186i			0.942268i
$656$	−366.819	+	481.464i	−0.559175	+	0.733939i
$657$	−158.919			−0.241886
$658$		0			0
$659$	−940.466			−1.42711			−0.713555	−	0.700599i	$-0.752916\pi$
$659$	−940.466			−1.42711			−0.713555	+	0.700599i	$0.752916\pi$
$660$	−1293.61	+	640.701i	−1.96001	+	0.970759i
$661$		−	119.930i		−	0.181437i	−0.995877	−	0.0907184i	$-0.971084\pi$
$661$		−	119.930i		−	0.181437i	0.995877	−	0.0907184i	$-0.0289163\pi$
$662$	−535.149	+	862.240i	−0.808382	+	1.30248i
$663$			10.5696i			0.0159421i
$664$	−569.513	−	54.6107i	−0.857700	−	0.0822450i
$665$		0			0
$666$	261.970	+	162.592i	0.393349	+	0.244132i
$667$	−379.426			−0.568855
$668$	593.330	−	293.866i	0.888219	−	0.439920i
$669$		−	674.346i		−	1.00799i
$670$	−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
$675$	−24.5298			−0.0363404
$676$	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	$-0.247509\pi$
$678$	−299.217	+	482.104i	−0.441324	+	0.711068i
$679$		0			0
$680$	−0.875819	+	9.13357i	−0.00128797	+	0.0134317i
$681$	93.8270			0.137778
$682$	1244.84	+	772.608i	1.82528	+	1.13286i
$683$	−893.785			−1.30862			−0.654308	−	0.756228i	$-0.727040\pi$
$683$	−893.785			−1.30862			−0.654308	+	0.756228i	$0.727040\pi$
$684$	23.0040	+	46.4461i	0.0336315	+	0.0679037i
$685$			170.635i			0.249102i
$686$		0			0
$687$			606.861i			0.883349i
$688$	47.0004	−	61.6898i	0.0683145	−	0.0896654i
$689$	−283.366			−0.411272
$690$	194.097	−	312.732i	0.281300	−	0.453235i
$691$	−1208.56			−1.74901			−0.874504	−	0.485019i	$-0.838813\pi$
$691$	−1208.56			−1.74901			−0.874504	+	0.485019i	$0.838813\pi$
$692$	−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
$696$	−91.0371	+	949.389i	−0.130800	+	1.36407i
$697$	8.88585			0.0127487
$698$	−139.439	−	86.5430i	−0.199770	−	0.123987i
$699$	247.210			0.353662
$700$		0			0
$701$			219.477i			0.313091i	0.987671	+	0.156546i	$0.0500358\pi$
$701$			219.477i			0.313091i	−0.987671	+	0.156546i	$0.949964\pi$
$702$	470.847	+	292.231i	0.670723	+	0.416284i
$703$			247.251i			0.351709i
$704$	−1349.52	−	261.213i	−1.91693	−	0.371041i
$705$	−1215.50			−1.72411
$706$	535.108	−	862.175i	0.757944	−	1.22121i
$707$		0			0
$708$	213.221	+	430.502i	0.301159	+	0.608054i
$709$			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
$711$		−	270.066i		−	0.379839i
$712$	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
$717$		−	244.650i		−	0.341213i
$718$	−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	$-0.300039\pi$
$720$	−176.639	−	134.578i	−0.245332	−	0.186914i
$721$		0			0
$722$	358.820	−	578.136i	0.496981	−	0.800743i
$723$	−193.094			−0.267074
$724$	990.573	−	490.614i	1.36819	−	0.677643i
$725$			40.1036i			0.0553153i
$726$	−1235.05	+	1989.93i	−1.70117	+	2.74094i
$727$		−	1303.68i		−	1.79324i	−0.442803	−	0.896619i	$-0.646016\pi$
$727$		−	1303.68i		−	1.79324i	0.442803	−	0.896619i	$-0.353984\pi$
$728$		0			0
$729$	376.305			0.516193
$730$	463.916	+	287.929i	0.635502	+	0.394424i
$731$	−1.13854			−0.00155751
$732$	−784.526	+	388.562i	−1.07176	+	0.530823i
$733$			1256.12i			1.71367i	0.515589	+	0.856836i	$0.327573\pi$
$733$			1256.12i			1.71367i	−0.515589	+	0.856836i	$0.672427\pi$
$734$	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
$738$	−113.407	+	182.723i	−0.153668	+	0.247592i
$739$	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
$741$		−	205.134i		−	0.276835i
$742$		0			0
$743$		−	362.628i		−	0.488059i	−0.969768	−	0.244030i	$-0.921531\pi$
$743$		−	362.628i		−	0.488059i	0.969768	−	0.244030i	$-0.0784694\pi$
$744$	−89.6295	+	934.710i	−0.120470	+	1.25633i
$745$	−595.376			−0.799163
$746$	914.287	+	567.452i	1.22559	+	0.760659i
$747$	−203.275			−0.272122
$748$	8.95620	+	18.0830i	0.0119735	+	0.0241751i
$749$		0			0
$750$	−746.905	−	463.566i	−0.995874	−	0.618088i
$751$			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
$753$	−1269.67			−1.68615
$754$	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
$759$		−	809.488i		−	1.06652i
$760$	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	$0.432679\pi$
$762$	−147.019	−	91.2470i	−0.192938	−	0.119747i
$763$		0			0
$764$	−727.695	+	360.415i	−0.952481	+	0.471747i
$765$			3.26003i			0.00426148i
$766$	−566.331	−	351.493i	−0.739336	−	0.458868i
$767$		−	456.362i		−	0.594996i
$768$	−233.853	−	849.362i	−0.304496	−	1.10594i
$769$	−634.936			−0.825664			−0.412832	−	0.910807i	$-0.635460\pi$
$769$	−634.936			−0.825664			−0.412832	+	0.910807i	$0.635460\pi$
$770$		0			0
$771$	−81.7056			−0.105974
$772$	−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	$-0.0198127\pi$
$774$	14.5308	−	23.4122i	0.0187736	−	0.0302484i
$775$			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
$780$	390.073	+	787.576i	0.500093	+	1.00971i
$781$			1020.71i			1.30693i
$782$	−4.37161	−	2.71324i	−0.00559029	−	0.00346961i
$783$		−	734.098i		−	0.937545i
$784$		0			0
$785$	33.0577			0.0421117
$786$	−458.754	+	739.151i	−0.583656	+	0.940396i
$787$	1319.25			1.67630			0.838148	−	0.545442i	$-0.183638\pi$
$787$	1319.25			1.67630			0.838148	+	0.545442i	$0.183638\pi$
$788$	−77.6531	+	38.4603i	−0.0985445	+	0.0488074i
$789$		−	254.554i		−	0.322628i
$790$	−489.305	+	788.375i	−0.619373	+	0.997943i
$791$		0			0
$792$	−486.152	−	46.6171i	−0.613828	−	0.0588600i
$793$	831.651			1.04874
$794$	−528.380	−	327.939i	−0.665466	−	0.413021i
$795$	−364.139			−0.458036
$796$	−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
$801$	454.088			0.566902
$802$	447.081	−	720.343i	0.557457	−	0.898183i
$803$	1200.82			1.49541
$804$	−112.622	−	227.389i	−0.140077	−	0.282823i
$805$		0			0
$806$	470.381	−	757.885i	0.583599	−	0.940304i
$807$		−	1154.87i		−	1.43106i
$808$	−138.327	+	1442.56i	−0.171197	+	1.78534i
$809$	1232.72			1.52376			0.761881	−	0.647717i	$-0.224276\pi$
$809$	1232.72			1.52376			0.761881	+	0.647717i	$0.224276\pi$
$810$	817.324	+	507.272i	1.00904	+	0.626261i
$811$	1009.05			1.24421			0.622103	−	0.782935i	$-0.286278\pi$
$811$	1009.05			1.24421			0.622103	+	0.782935i	$0.286278\pi$
$812$		0			0
$813$		−	644.468i		−	0.792703i
$814$	−1979.49	−	1228.57i	−2.43181	−	1.50930i
$815$		−	1011.94i		−	1.24164i
$816$	−7.83787	+	10.2875i	−0.00960524	+	0.0126072i
$817$	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	$-0.806199\pi$
$821$		−	939.093i		−	1.14384i	0.820309	−	0.571920i	$-0.193801\pi$
$822$	−126.833	+	204.355i	−0.154298	+	0.248607i
$823$		−	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
$825$	−85.5591			−0.103708
$826$		0			0
$827$	−65.6564			−0.0793910			−0.0396955	−	0.999212i	$-0.512639\pi$
$827$	−65.6564			−0.0793910			−0.0396955	+	0.999212i	$0.512639\pi$
$828$	111.586	−	55.2669i	0.134766	−	0.0667474i
$829$		−	1515.94i		−	1.82864i	−0.404997	−	0.914318i	$-0.632728\pi$
$829$		−	1515.94i		−	1.82864i	0.404997	−	0.914318i	$-0.367272\pi$
$830$	593.402	+	368.294i	0.714942	+	0.443728i
$831$			456.285i			0.549079i
$832$	−159.032	+	821.616i	−0.191144	+	0.987519i
$833$		0			0
$834$	−432.438	+	696.752i	−0.518511	+	0.835433i
$835$	−808.257			−0.967972
$836$	−173.822	−	350.954i	−0.207921	−	0.419802i
$837$		−	722.747i		−	0.863497i
$838$	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
$843$	1140.85			1.35333
$844$	38.0280	+	76.7804i	0.0450569	+	0.0909721i
$845$		−	9.67964i		−	0.0114552i
$846$	−349.395	−	216.852i	−0.412996	−	0.256326i
$847$		0			0
$848$	−275.804	−	210.130i	−0.325240	−	0.247795i
$849$	229.588			0.270421
$850$	−0.286777	+	0.462059i	−0.000337384	+	0.000543599i
$851$	594.020			0.698026
$852$	−586.217	+	290.343i	−0.688048	+	0.340778i
$853$			1643.91i			1.92721i	0.267322	+	0.963607i	$0.413861\pi$
$853$			1643.91i			1.92721i	−0.267322	+	0.963607i	$0.586139\pi$
$854$		0			0
$855$		−	63.2706i		−	0.0740007i
$856$	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	$0.553374\pi$
$858$	1642.30	+	1019.29i	1.91411	+	1.18799i
$859$	−719.782			−0.837930			−0.418965	−	0.908002i	$-0.637607\pi$
$859$	−719.782			−0.837930			−0.418965	+	0.908002i	$0.637607\pi$
$860$	−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	$0.224885\pi$
$863$			1120.47i			1.29835i	−0.760641	+	0.649173i	$0.775115\pi$
$864$	241.578	+	633.589i	0.279604	+	0.733320i
$865$	433.857			0.501569
$866$	−287.158	+	462.674i	−0.331592	+	0.534265i
$867$	−994.339			−1.14687
$868$		0			0
$869$			2040.66i			2.34828i
$870$	613.954	−	989.213i	0.705695	−	1.13703i
$871$			241.048i			0.276749i
$872$	−21.2886	+	222.010i	−0.0244135	+	0.254599i
$873$	257.178			0.294591
$874$	84.8441	+	52.6584i	0.0970756	+	0.0602499i
$875$		0			0
$876$	341.576	+	689.658i	0.389927	+	0.787281i
$877$			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
$879$			995.269i			1.13227i
$880$	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
$885$		−	586.447i		−	0.662652i
$886$	−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	$0.682116\pi$
$888$	142.525	−	1486.34i	0.160501	−	1.67380i
$889$		0			0
$890$	−1325.57	−	822.717i	−1.48941	−	0.924401i
$891$	2115.59			2.37440
$892$	−702.401	+	347.887i	−0.787445	+	0.390008i
$893$		−	329.764i		−	0.369276i
$894$	−713.032	−	442.543i	−0.797575	−	0.495015i
$895$			392.481i			0.438526i
$896$		0			0
$897$	−492.834			−0.549425
$898$	677.971	−	1092.36i	0.754979	−	1.21643i
$899$	−1181.62			−1.31437
$900$	−5.84145	−	11.7942i	−0.00649050	−	0.0131046i
$901$			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
$906$	−1288.88	−	799.942i	−1.42260	−	0.882938i
$907$	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
$909$			514.891i			0.566436i
$910$		0			0
$911$		−	944.690i		−	1.03698i	−0.855083	−	0.518491i	$-0.826494\pi$
$911$		−	944.690i		−	1.03698i	0.855083	−	0.518491i	$-0.173506\pi$
$912$	152.117	−	199.660i	0.166795	−	0.218925i
$913$	1535.98			1.68235
$914$	−730.984	+	1177.77i	−0.799764	+	1.28859i
$915$	1068.71			1.16799
$916$	632.108	−	313.072i	0.690074	−	0.341782i
$917$		0			0
$918$	5.24945	−	8.45800i	0.00571836	−	0.00921351i
$919$			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
$921$	−2.38541			−0.00259003
$922$	−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
$927$		−	111.707i		−	0.120503i
$928$	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	$0.489918\pi$
$930$	604.462	−	973.918i	0.649959	−	1.04722i
$931$		0			0
$932$	−127.533	−	257.494i	−0.136838	−	0.276282i
$933$			213.904i			0.229265i
$934$	−210.390	+	338.984i	−0.225257	+	0.362938i
$935$		−	24.6333i		−	0.0263458i
$936$	−28.3815	+	295.980i	−0.0303222	+	0.316218i
$937$	1700.18			1.81449			0.907246	−	0.420601i	$-0.138181\pi$
$937$	1700.18			1.81449			0.907246	+	0.420601i	$0.138181\pi$
$938$		0			0
$939$	−735.036			−0.782786
$940$	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	$0.990424\pi$
$942$	39.5904	+	24.5718i	0.0420281	+	0.0260847i
$943$			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	$-0.459127\pi$
$947$	242.533			0.256107			0.128053	+	0.991767i	$0.459127\pi$
$948$	−1172.00	+	580.471i	−1.23629	+	0.612311i
$949$		−	731.084i		−	0.770373i
$950$	5.56575	−	8.96763i	0.00585869	−	0.00943961i
$951$		−	80.7244i		−	0.0848837i
$952$		0			0
$953$	−364.070			−0.382025			−0.191013	−	0.981588i	$-0.561177\pi$
$953$	−364.070			−0.382025			−0.191013	+	0.981588i	$0.561177\pi$
$954$	−104.672	−	64.9644i	−0.109719	−	0.0680969i
$955$	991.294			1.03800
$956$	−254.828	+	126.212i	−0.266556	+	0.132021i
$957$		−	2560.51i		−	2.67556i
$958$	−1145.61	−	711.021i	−1.19583	−	0.742193i
$959$		0			0
$960$	−204.364	+	1055.81i	−0.212879	+	1.09981i
$961$	−202.348			−0.210560
$962$	−747.981	+	1205.16i	−0.777527	+	1.25276i
$963$	109.290			0.113489
$964$	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
$969$	−3.68490			−0.00380279
$970$	−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	$0.310601\pi$
$972$	263.215	+	531.443i	0.270797	+	0.546752i
$973$		0			0
$974$	682.644	+	423.683i	0.700866	+	0.434992i
$975$			52.0903i			0.0534259i
$976$	809.455	+	616.710i	0.829360	+	0.631875i
$977$	−1061.51			−1.08650			−0.543252	−	0.839570i	$-0.682807\pi$
$977$	−1061.51			−1.08650			−0.543252	+	0.839570i	$0.682807\pi$
$978$	752.175	−	1211.92i	0.769095	−	1.23918i
$979$	−3431.17			−3.50477
$980$		0			0
$981$			79.2419i			0.0807766i
$982$	−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	$-0.234884\pi$
$984$	1036.71	+	99.4105i	1.05357	+	0.101027i
$985$	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
$990$	506.544	+	314.386i	0.511660	+	0.317562i
$991$		−	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
$993$	1746.12			1.75843
$994$		0			0
$995$	888.354			0.892818
$996$	436.914	+	882.151i	0.438669	+	0.885694i
$997$			409.220i			0.410452i	0.978715	+	0.205226i	$0.0657929\pi$
$997$			409.220i			0.410452i	−0.978715	+	0.205226i	$0.934207\pi$
$998$	−192.604	+	310.327i	−0.192990	+	0.310949i
$999$			1149.28i			1.15043i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.g.m.99.4		8
4.3	odd	2		1568.3.g.m.687.4		8
7.2	even	3		392.3.k.n.67.8		16
7.3	odd	6		392.3.k.o.275.3		16
7.4	even	3		392.3.k.n.275.3		16
7.5	odd	6		392.3.k.o.67.8		16
7.6	odd	2		56.3.g.b.43.4	yes	8
8.3	odd	2	inner	392.3.g.m.99.3		8
8.5	even	2		1568.3.g.m.687.3		8
21.20	even	2		504.3.g.b.379.5		8
28.27	even	2		224.3.g.b.15.5		8
56.3	even	6		392.3.k.o.275.8		16
56.11	odd	6		392.3.k.n.275.8		16
56.13	odd	2		224.3.g.b.15.6		8
56.19	even	6		392.3.k.o.67.3		16
56.27	even	2		56.3.g.b.43.3	✓	8
56.51	odd	6		392.3.k.n.67.3		16
84.83	odd	2		2016.3.g.b.1135.6		8
112.13	odd	4		1792.3.d.j.1023.5		16
112.27	even	4		1792.3.d.j.1023.6		16
112.69	odd	4		1792.3.d.j.1023.12		16
112.83	even	4		1792.3.d.j.1023.11		16
168.83	odd	2		504.3.g.b.379.6		8
168.125	even	2		2016.3.g.b.1135.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.3	✓	8	56.27	even	2
56.3.g.b.43.4	yes	8	7.6	odd	2
224.3.g.b.15.5		8	28.27	even	2
224.3.g.b.15.6		8	56.13	odd	2
392.3.g.m.99.3		8	8.3	odd	2	inner
392.3.g.m.99.4		8	1.1	even	1	trivial
392.3.k.n.67.3		16	56.51	odd	6
392.3.k.n.67.8		16	7.2	even	3
392.3.k.n.275.3		16	7.4	even	3
392.3.k.n.275.8		16	56.11	odd	6
392.3.k.o.67.3		16	56.19	even	6
392.3.k.o.67.8		16	7.5	odd	6
392.3.k.o.275.3		16	7.3	odd	6
392.3.k.o.275.8		16	56.3	even	6
504.3.g.b.379.5		8	21.20	even	2
504.3.g.b.379.6		8	168.83	odd	2
1568.3.g.m.687.3		8	8.5	even	2
1568.3.g.m.687.4		8	4.3	odd	2
1792.3.d.j.1023.5		16	112.13	odd	4
1792.3.d.j.1023.6		16	112.27	even	4
1792.3.d.j.1023.11		16	112.83	even	4
1792.3.d.j.1023.12		16	112.69	odd	4
2016.3.g.b.1135.3		8	168.125	even	2
2016.3.g.b.1135.6		8	84.83	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)

\(f(q)\)	\(=\)	\(q+(-1.05468 + 1.69931i) q^{2} +3.44128 q^{3} +(-1.77532 - 3.58445i) q^{4} +4.88287i q^{5} +(-3.62943 + 5.84780i) q^{6} +(7.96347 + 0.763618i) q^{8} +2.84239 q^{9} +O(q^{10})\)	\(q+(-1.05468 + 1.69931i) q^{2} +3.44128 q^{3} +(-1.77532 - 3.58445i) q^{4} +4.88287i q^{5} +(-3.62943 + 5.84780i) q^{6} +(7.96347 + 0.763618i) q^{8} +2.84239 q^{9} +(-8.29751 - 5.14984i) q^{10} -21.4776 q^{11} +(-6.10935 - 12.3351i) q^{12} +13.0760i q^{13} +16.8033i q^{15} +(-9.69651 + 12.7270i) q^{16} +0.234889 q^{17} +(-2.99780 + 4.83011i) q^{18} -4.55872 q^{19} +(17.5024 - 8.66863i) q^{20} +(22.6519 - 36.4971i) q^{22} +10.9523i q^{23} +(27.4045 + 2.62782i) q^{24} +1.15761 q^{25} +(-22.2202 - 13.7910i) q^{26} -21.1900 q^{27} +34.6435i q^{29} +(-28.5540 - 17.7220i) q^{30} +34.1079i q^{31} +(-11.4005 - 29.9003i) q^{32} -73.9103 q^{33} +(-0.247732 + 0.399150i) q^{34} +(-5.04614 - 10.1884i) q^{36} -54.2370i q^{37} +(4.80798 - 7.74669i) q^{38} +44.9982i q^{39} +(-3.72865 + 38.8846i) q^{40} +37.8300 q^{41} -4.84714 q^{43} +(38.1295 + 76.9852i) q^{44} +13.8790i q^{45} +(-18.6114 - 11.5511i) q^{46} +72.3368i q^{47} +(-33.3684 + 43.7973i) q^{48} +(-1.22090 + 1.96714i) q^{50} +0.808319 q^{51} +(46.8703 - 23.2141i) q^{52} +21.6707i q^{53} +(22.3486 - 36.0085i) q^{54} -104.872i q^{55} -15.6878 q^{57} +(-58.8701 - 36.5377i) q^{58} -34.9007 q^{59} +(60.2305 - 29.8312i) q^{60} -63.6012i q^{61} +(-57.9599 - 35.9728i) q^{62} +(62.8338 + 12.1621i) q^{64} -63.8485 q^{65} +(77.9514 - 125.597i) q^{66} +18.4344 q^{67} +(-0.417002 - 0.841948i) q^{68} +37.6899i q^{69} -47.5244i q^{71} +(22.6353 + 2.17050i) q^{72} -55.9103 q^{73} +(92.1655 + 57.2024i) q^{74} +3.98365 q^{75} +(8.09317 + 16.3405i) q^{76} +(-76.4660 - 47.4586i) q^{78} -95.0135i q^{79} +(-62.1445 - 47.3468i) q^{80} -98.5023 q^{81} +(-39.8984 + 64.2849i) q^{82} -71.5156 q^{83} +1.14693i q^{85} +(5.11217 - 8.23680i) q^{86} +119.218i q^{87} +(-171.036 - 16.4007i) q^{88} +159.756 q^{89} +(-23.5848 - 14.6379i) q^{90} +(39.2579 - 19.4438i) q^{92} +117.375i q^{93} +(-122.923 - 76.2920i) q^{94} -22.2596i q^{95} +(-39.2324 - 102.895i) q^{96} +90.4794 q^{97} -61.0477 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 8 q^{3} + 5 q^{4} + 22 q^{6} + 13 q^{8} + 48 q^{9}+O(q^{10}) \) 8 * q + q^2 + 8 * q^3 + 5 * q^4 + 22 * q^6 + 13 * q^8 + 48 * q^9	\( 8 q + q^{2} + 8 q^{3} + 5 q^{4} + 22 q^{6} + 13 q^{8} + 48 q^{9} - 16 q^{10} - 32 q^{11} - 30 q^{12} - 71 q^{16} + 80 q^{17} - 29 q^{18} - 56 q^{19} + 108 q^{20} + 66 q^{22} - 22 q^{24} - 16 q^{25} - 24 q^{26} + 32 q^{27} + 96 q^{30} - 19 q^{32} - 32 q^{33} - 74 q^{34} - 33 q^{36} + 14 q^{38} - 84 q^{40} - 128 q^{41} + 50 q^{44} - 152 q^{46} - 134 q^{48} + 33 q^{50} - 368 q^{51} - 132 q^{52} + 228 q^{54} + 56 q^{57} + 24 q^{58} - 104 q^{59} + 192 q^{60} - 120 q^{62} - 55 q^{64} - 72 q^{65} + 276 q^{66} + 304 q^{67} + 190 q^{68} - 209 q^{72} + 112 q^{73} + 8 q^{74} - 72 q^{75} - 70 q^{76} - 304 q^{78} - 124 q^{80} + 48 q^{81} - 450 q^{82} - 72 q^{83} + 210 q^{86} - 486 q^{88} + 512 q^{89} + 184 q^{90} - 472 q^{92} - 472 q^{94} - 558 q^{96} - 64 q^{97} + 256 q^{99}+O(q^{100}) \) 8 * q + q^2 + 8 * q^3 + 5 * q^4 + 22 * q^6 + 13 * q^8 + 48 * q^9 - 16 * q^10 - 32 * q^11 - 30 * q^12 - 71 * q^16 + 80 * q^17 - 29 * q^18 - 56 * q^19 + 108 * q^20 + 66 * q^22 - 22 * q^24 - 16 * q^25 - 24 * q^26 + 32 * q^27 + 96 * q^30 - 19 * q^32 - 32 * q^33 - 74 * q^34 - 33 * q^36 + 14 * q^38 - 84 * q^40 - 128 * q^41 + 50 * q^44 - 152 * q^46 - 134 * q^48 + 33 * q^50 - 368 * q^51 - 132 * q^52 + 228 * q^54 + 56 * q^57 + 24 * q^58 - 104 * q^59 + 192 * q^60 - 120 * q^62 - 55 * q^64 - 72 * q^65 + 276 * q^66 + 304 * q^67 + 190 * q^68 - 209 * q^72 + 112 * q^73 + 8 * q^74 - 72 * q^75 - 70 * q^76 - 304 * q^78 - 124 * q^80 + 48 * q^81 - 450 * q^82 - 72 * q^83 + 210 * q^86 - 486 * q^88 + 512 * q^89 + 184 * q^90 - 472 * q^92 - 472 * q^94 - 558 * q^96 - 64 * q^97 + 256 * q^99

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