LMFDB - Embedded newform 294.4.f.a.215.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [294,4,Mod(215,294)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("294.215"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(294, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	294.f (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,32,0,0,0,0,18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.3465615417$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} - x^{14} - 2 x^{13} + 9 x^{12} - 24 x^{11} + 714 x^{10} - 1940 x^{9} - 2834 x^{8} + \cdots + 43046721 $ x^16 - 2x^15 - x^14 - 2x^13 + 9x^12 - 24x^11 + 714x^10 - 1940x^9 - 2834x^8 - 17460x^7 + 57834x^6 - 17496x^5 + 59049x^4 - 118098x^3 - 531441x^2 - 9565938x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{8} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			215.2
Root			$2.99617 - 0.151487i$ of defining polynomial
Character	$\chi$	$=$	294.215
Dual form			294.4.f.a.227.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.73205 - 1.00000i) q^{2} +(-2.82199 + 4.36307i) q^{3} +(2.00000 + 3.46410i) q^{4} +(-2.24534 + 3.88904i) q^{5} +(9.25090 - 4.73506i) q^{6} -8.00000i q^{8} +(-11.0727 - 24.6251i) q^{9} +(7.77808 - 4.49068i) q^{10} +(20.2835 - 11.7107i) q^{11} +(-20.7581 - 1.04953i) q^{12} -5.91384i q^{13} +(-10.6318 - 20.7714i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-58.0418 - 100.531i) q^{17} +(-5.44659 + 53.7246i) q^{18} +(-8.02533 - 4.63343i) q^{19} -17.9627 q^{20} -46.8428 q^{22} +(107.721 + 62.1928i) q^{23} +(34.9045 + 22.5759i) q^{24} +(52.4169 + 90.7888i) q^{25} +(-5.91384 + 10.2431i) q^{26} +(138.688 + 21.1808i) q^{27} -207.807i q^{29} +(-2.35656 + 46.6089i) q^{30} +(-122.764 + 70.8780i) q^{31} +(27.7128 - 16.0000i) q^{32} +(-6.14540 + 121.546i) q^{33} +232.167i q^{34} +(63.1584 - 87.6072i) q^{36} +(-149.838 + 259.526i) q^{37} +(9.26685 + 16.0507i) q^{38} +(25.8025 + 16.6888i) q^{39} +(31.1123 + 17.9627i) q^{40} +508.379 q^{41} +391.127 q^{43} +(81.1341 + 46.8428i) q^{44} +(120.630 + 12.2294i) q^{45} +(-124.386 - 215.442i) q^{46} +(40.2575 - 69.7281i) q^{47} +(-37.8805 - 74.0072i) q^{48} -209.668i q^{50} +(602.419 + 30.4585i) q^{51} +(20.4862 - 11.8277i) q^{52} +(258.697 - 149.359i) q^{53} +(-219.034 - 175.374i) q^{54} +105.178i q^{55} +(42.8634 - 21.9396i) q^{57} +(-207.807 + 359.932i) q^{58} +(-102.276 - 177.147i) q^{59} +(50.6906 - 78.3725i) q^{60} +(543.757 + 313.939i) q^{61} +283.512 q^{62} -64.0000 q^{64} +(22.9992 + 13.2786i) q^{65} +(132.190 - 204.378i) q^{66} +(51.3894 + 89.0091i) q^{67} +(232.167 - 402.126i) q^{68} +(-575.340 + 294.487i) q^{69} -46.9785i q^{71} +(-197.001 + 88.5817i) q^{72} +(228.182 - 131.741i) q^{73} +(519.053 - 299.675i) q^{74} +(-544.038 - 27.5067i) q^{75} -37.0674i q^{76} +(-28.0024 - 54.7084i) q^{78} +(533.634 - 924.281i) q^{79} +(-35.9254 - 62.2246i) q^{80} +(-483.790 + 545.333i) q^{81} +(-880.538 - 508.379i) q^{82} +270.436 q^{83} +521.294 q^{85} +(-677.452 - 391.127i) q^{86} +(906.676 + 586.430i) q^{87} +(-93.6856 - 162.268i) q^{88} +(-443.765 + 768.624i) q^{89} +(-196.708 - 141.812i) q^{90} +497.543i q^{92} +(37.1945 - 735.646i) q^{93} +(-139.456 + 80.5151i) q^{94} +(36.0392 - 20.8072i) q^{95} +(-8.39628 + 166.065i) q^{96} -219.564i q^{97} +(-512.971 - 369.815i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4} + 18 q^{9} + 36 q^{10} - 128 q^{16} - 48 q^{18} + 342 q^{19} + 24 q^{22} + 48 q^{24} - 194 q^{25} + 360 q^{30} - 804 q^{31} - 1332 q^{33} + 144 q^{36} - 962 q^{37} + 594 q^{39} + 144 q^{40}+ \cdots - 4284 q^{99}+O(q^{100}) $ 16 * q + 32 * q^4 + 18 * q^9 + 36 * q^10 - 128 * q^16 - 48 * q^18 + 342 * q^19 + 24 * q^22 + 48 * q^24 - 194 * q^25 + 360 * q^30 - 804 * q^31 - 1332 * q^33 + 144 * q^36 - 962 * q^37 + 594 * q^39 + 144 * q^40 + 1732 * q^43 + 2394 * q^45 + 168 * q^46 + 1638 * q^51 - 744 * q^52 - 180 * q^54 - 2664 * q^57 - 780 * q^58 + 4620 * q^61 - 1024 * q^64 + 2016 * q^66 - 706 * q^67 + 192 * q^72 - 3294 * q^73 - 6174 * q^75 + 2832 * q^78 - 2656 * q^79 + 126 * q^81 - 432 * q^82 + 5232 * q^85 - 1026 * q^87 + 48 * q^88 + 2016 * q^93 - 3888 * q^94 + 192 * q^96 - 4284 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.73205	−	1.00000i	−0.612372	−	0.353553i
$2$	−1.73205	−	1.00000i	−0.612372	−	0.353553i
$3$	−2.82199	+	4.36307i	−0.543093	+	0.839673i
$3$	−2.82199	+	4.36307i	−0.543093	+	0.839673i
$4$	2.00000	+	3.46410i	0.250000	+	0.433013i
$5$	−2.24534	+	3.88904i	−0.200829	+	0.347846i	−0.948796	−	0.315890i	$-0.897697\pi$
$5$	−2.24534	+	3.88904i	−0.200829	+	0.347846i	0.747967	+	0.663736i	$0.231030\pi$
$6$	9.25090	−	4.73506i	0.629444	−	0.322180i
$7$		0			0
$7$		0			0
$8$		−	8.00000i		−	0.353553i
$9$	−11.0727	−	24.6251i	−0.410101	−	0.912040i
$10$	7.77808	−	4.49068i	0.245964	−	0.142008i
$11$	20.2835	−	11.7107i	0.555974	−	0.320992i	−0.195554	−	0.980693i	$-0.562650\pi$
$11$	20.2835	−	11.7107i	0.555974	−	0.320992i	0.751528	+	0.659701i	$0.229317\pi$
$12$	−20.7581	−	1.04953i	−0.499362	−	0.0252479i
$13$		−	5.91384i		−	0.126170i	−0.998008	−	0.0630848i	$-0.979906\pi$
$13$		−	5.91384i		−	0.126170i	0.998008	−	0.0630848i	$-0.0200939\pi$
$14$		0			0
$15$	−10.6318	−	20.7714i	−0.183008	−	0.357544i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−58.0418	−	100.531i	−0.828071	−	1.43426i	−0.899549	−	0.436819i	$-0.856105\pi$
$17$	−58.0418	−	100.531i	−0.828071	−	1.43426i	0.0714778	−	0.997442i	$-0.477228\pi$
$18$	−5.44659	+	53.7246i	−0.0713207	+	0.703501i
$19$	−8.02533	−	4.63343i	−0.0969019	−	0.0559464i	0.450766	−	0.892642i	$-0.351151\pi$
$19$	−8.02533	−	4.63343i	−0.0969019	−	0.0559464i	−0.547668	+	0.836696i	$0.684484\pi$
$20$	−17.9627			−0.200829
$21$		0			0
$22$	−46.8428			−0.453951
$23$	107.721	+	62.1928i	0.976583	+	0.563830i	0.901237	−	0.433327i	$-0.142661\pi$
$23$	107.721	+	62.1928i	0.976583	+	0.563830i	0.0753461	+	0.997157i	$0.475994\pi$
$24$	34.9045	+	22.5759i	0.296869	+	0.192012i
$25$	52.4169	+	90.7888i	0.419335	+	0.726310i
$26$	−5.91384	+	10.2431i	−0.0446077	+	0.0772628i
$27$	138.688	+	21.1808i	0.988538	+	0.150972i
$28$		0			0
$29$		−	207.807i		−	1.33065i	−0.746555	−	0.665324i	$-0.768293\pi$
$29$		−	207.807i		−	1.33065i	0.746555	−	0.665324i	$-0.231707\pi$
$30$	−2.35656	+	46.6089i	−0.0143416	+	0.283653i
$31$	−122.764	+	70.8780i	−0.711262	+	0.410647i	−0.811528	−	0.584314i	$-0.801364\pi$
$31$	−122.764	+	70.8780i	−0.711262	+	0.410647i	0.100266	+	0.994961i	$0.468030\pi$
$32$	27.7128	−	16.0000i	0.153093	−	0.0883883i
$33$	−6.14540	+	121.546i	−0.0324175	+	0.641165i
$34$			232.167i			1.17107i
$35$		0			0
$36$	63.1584	−	87.6072i	0.292400	−	0.405589i
$37$	−149.838	+	259.526i	−0.665761	+	1.15313i	0.313317	+	0.949648i	$0.398560\pi$
$37$	−149.838	+	259.526i	−0.665761	+	1.15313i	−0.979078	+	0.203483i	$0.934774\pi$
$38$	9.26685	+	16.0507i	0.0395601	+	0.0685200i
$39$	25.8025	+	16.6888i	0.105941	+	0.0685218i
$40$	31.1123	+	17.9627i	0.122982	+	0.0710038i
$41$	508.379			1.93647			0.968237	−	0.250032i	$-0.0804412\pi$
$41$	508.379			1.93647			0.968237	+	0.250032i	$0.0804412\pi$
$42$		0			0
$43$	391.127			1.38712			0.693562	−	0.720397i	$-0.256041\pi$
$43$	391.127			1.38712			0.693562	+	0.720397i	$0.256041\pi$
$44$	81.1341	+	46.8428i	0.277987	+	0.160496i
$45$	120.630	+	12.2294i	0.399610	+	0.0405123i
$46$	−124.386	−	215.442i	−0.398688	−	0.690548i
$47$	40.2575	−	69.7281i	0.124940	−	0.216402i	−0.796770	−	0.604283i	$-0.793460\pi$
$47$	40.2575	−	69.7281i	0.124940	−	0.216402i	0.921709	+	0.387881i	$0.126793\pi$
$48$	−37.8805	−	74.0072i	−0.113908	−	0.222542i
$49$		0			0
$50$		−	209.668i		−	0.593030i
$51$	602.419	+	30.4585i	1.65403	+	0.0836282i
$52$	20.4862	−	11.8277i	0.0546330	−	0.0315424i
$53$	258.697	−	149.359i	0.670467	−	0.387094i	−0.125786	−	0.992057i	$-0.540145\pi$
$53$	258.697	−	149.359i	0.670467	−	0.387094i	0.796254	+	0.604963i	$0.206812\pi$
$54$	−219.034	−	175.374i	−0.551977	−	0.441952i
$55$			105.178i			0.257858i
$56$		0			0
$57$	42.8634	−	21.9396i	0.0996034	−	0.0509818i
$58$	−207.807	+	359.932i	−0.470455	+	0.814852i
$59$	−102.276	−	177.147i	−0.225682	−	0.390892i	0.730842	−	0.682547i	$-0.239128\pi$
$59$	−102.276	−	177.147i	−0.225682	−	0.390892i	−0.956524	+	0.291655i	$0.905794\pi$
$60$	50.6906	−	78.3725i	0.109069	−	0.168631i
$61$	543.757	+	313.939i	1.14133	+	0.658946i	0.946759	−	0.321943i	$-0.104336\pi$
$61$	543.757	+	313.939i	1.14133	+	0.658946i	0.194569	+	0.980889i	$0.437669\pi$
$62$	283.512			0.580743
$63$		0			0
$64$	−64.0000			−0.125000
$65$	22.9992	+	13.2786i	0.0438876	+	0.0253385i
$66$	132.190	−	204.378i	0.246538	−	0.381170i
$67$	51.3894	+	89.0091i	0.0937048	+	0.162301i	0.909067	−	0.416649i	$-0.136796\pi$
$67$	51.3894	+	89.0091i	0.0937048	+	0.162301i	−0.815363	+	0.578951i	$0.803462\pi$
$68$	232.167	−	402.126i	0.414036	−	0.717131i
$69$	−575.340	+	294.487i	−1.00381	+	0.513798i
$70$		0			0
$71$		−	46.9785i		−	0.0785256i	−0.999229	−	0.0392628i	$-0.987499\pi$
$71$		−	46.9785i		−	0.0785256i	0.999229	−	0.0392628i	$-0.0125010\pi$
$72$	−197.001	+	88.5817i	−0.322455	+	0.144992i
$73$	228.182	−	131.741i	0.365845	−	0.211221i	−0.305797	−	0.952097i	$-0.598923\pi$
$73$	228.182	−	131.741i	0.365845	−	0.211221i	0.671642	+	0.740876i	$0.265589\pi$
$74$	519.053	−	299.675i	0.815387	−	0.470764i
$75$	−544.038	−	27.5067i	−0.837601	−	0.0423493i
$76$		−	37.0674i		−	0.0559464i
$77$		0			0
$78$	−28.0024	−	54.7084i	−0.0406493	−	0.0794167i
$79$	533.634	−	924.281i	0.759981	−	1.31633i	−0.182878	−	0.983136i	$-0.558541\pi$
$79$	533.634	−	924.281i	0.759981	−	1.31633i	0.942860	−	0.333190i	$-0.108125\pi$
$80$	−35.9254	−	62.2246i	−0.0502073	−	0.0869616i
$81$	−483.790	+	545.333i	−0.663635	+	0.748056i
$82$	−880.538	−	508.379i	−1.18584	−	0.684647i
$83$	270.436			0.357642			0.178821	−	0.983882i	$-0.442772\pi$
$83$	270.436			0.357642			0.178821	+	0.983882i	$0.442772\pi$
$84$		0			0
$85$	521.294			0.665203
$86$	−677.452	−	391.127i	−0.849436	−	0.490422i
$87$	906.676	+	586.430i	1.11731	+	0.722665i
$88$	−93.6856	−	162.268i	−0.113488	−	0.196567i
$89$	−443.765	+	768.624i	−0.528528	+	0.915438i	0.470918	+	0.882177i	$0.343923\pi$
$89$	−443.765	+	768.624i	−0.528528	+	0.915438i	−0.999447	+	0.0332610i	$0.989411\pi$
$90$	−196.708	−	141.812i	−0.230387	−	0.166092i
$91$		0			0
$92$			497.543i			0.563830i
$93$	37.1945	−	735.646i	0.0414719	−	0.820246i
$94$	−139.456	+	80.5151i	−0.153019	+	0.0883457i
$95$	36.0392	−	20.8072i	0.0389215	−	0.0224713i
$96$	−8.39628	+	166.065i	−0.00892648	+	0.176551i
$97$		−	219.564i		−	0.229828i	−0.993375	−	0.114914i	$-0.963341\pi$
$97$		−	219.564i		−	0.229828i	0.993375	−	0.114914i	$-0.0366593\pi$
$98$		0			0
$99$	−512.971	−	369.815i	−0.520763	−	0.375432i
$100$	−209.668	+	363.155i	−0.209668	+	0.363155i
$101$	−492.533	−	853.093i	−0.485237	−	0.840455i	0.514619	−	0.857419i	$-0.327933\pi$
$101$	−492.533	−	853.093i	−0.485237	−	0.840455i	−0.999856	+	0.0169642i	$0.994600\pi$
$102$	−1012.96	−	655.175i	−0.983315	−	0.636000i
$103$	1112.87	+	642.516i	1.06461	+	0.614650i	0.926703	−	0.375796i	$-0.122631\pi$
$103$	1112.87	+	642.516i	1.06461	+	0.614650i	0.137903	+	0.990446i	$0.455964\pi$
$104$	−47.3107			−0.0446077
$105$		0			0
$106$	−597.435			−0.547434
$107$	158.409	+	91.4575i	0.143121	+	0.0826311i	0.569851	−	0.821748i	$-0.307001\pi$
$107$	158.409	+	91.4575i	0.143121	+	0.0826311i	−0.426729	+	0.904379i	$0.640334\pi$
$108$	204.004	+	522.791i	0.181762	+	0.465793i
$109$	291.471	+	504.843i	0.256127	+	0.443625i	0.965201	−	0.261509i	$-0.0842201\pi$
$109$	291.471	+	504.843i	0.256127	+	0.443625i	−0.709074	+	0.705134i	$0.750887\pi$
$110$	105.178	−	182.174i	0.0911666	−	0.157905i
$111$	−709.490	−	1386.13i	−0.606683	−	1.18528i
$112$		0			0
$113$			2283.94i			1.90137i	0.310152	+	0.950687i	$0.399620\pi$
$113$			2283.94i			1.90137i	−0.310152	+	0.950687i	$0.600380\pi$
$114$	−96.1811	−	4.86294i	−0.0790192	−	0.00399523i
$115$	−483.741	+	279.288i	−0.392253	+	0.226467i
$116$	719.865	−	415.614i	0.576188	−	0.332662i
$117$	−145.629	+	65.4823i	−0.115072	+	0.0517422i
$118$			409.104i			0.319162i
$119$		0			0
$120$	−166.171	+	85.0545i	−0.126411	+	0.0647032i
$121$	−391.219	+	677.611i	−0.293928	+	0.509099i
$122$	−627.877	−	1087.51i	−0.465945	−	0.807041i
$123$	−1434.64	+	2218.09i	−1.05169	+	1.62601i
$124$	−491.057	−	283.512i	−0.355631	−	0.205324i
$125$	−1032.11			−0.738517
$126$		0			0
$127$	−1554.48			−1.08613			−0.543064	−	0.839692i	$-0.682736\pi$
$127$	−1554.48			−1.08613			−0.543064	+	0.839692i	$0.682736\pi$
$128$	110.851	+	64.0000i	0.0765466	+	0.0441942i
$129$	−1103.76	+	1706.51i	−0.753337	+	1.16473i
$130$	−26.5572	−	45.9983i	−0.0179170	−	0.0310332i
$131$	1047.46	−	1814.26i	0.698605	−	1.21002i	−0.270345	−	0.962763i	$-0.587138\pi$
$131$	1047.46	−	1814.26i	0.698605	−	1.21002i	0.968950	−	0.247256i	$-0.0795288\pi$
$132$	−433.338	+	221.804i	−0.285737	+	0.146254i
$133$		0			0
$134$		−	205.558i		−	0.132519i
$135$	−393.775	+	491.805i	−0.251042	+	0.313540i
$136$	−804.251	+	464.335i	−0.507088	+	0.292767i
$137$	529.002	−	305.420i	0.329896	−	0.190465i	−0.325899	−	0.945405i	$-0.605667\pi$
$137$	529.002	−	305.420i	0.329896	−	0.190465i	0.655795	+	0.754939i	$0.272334\pi$
$138$	1291.00	+	65.2735i	0.796359	+	0.0402641i
$139$		−	1806.61i		−	1.10241i	−0.834370	−	0.551204i	$-0.814169\pi$
$139$		−	1806.61i		−	1.10241i	0.834370	−	0.551204i	$-0.185831\pi$
$140$		0			0
$141$	190.622	+	372.419i	0.113853	+	0.222435i
$142$	−46.9785	+	81.3691i	−0.0277630	+	0.0480869i
$143$	−69.2553	−	119.954i	−0.0404994	−	0.0701470i
$144$	429.797	+	43.5727i	0.248725	+	0.0252157i
$145$	808.170	+	466.597i	0.462861	+	0.267233i
$146$	−526.964			−0.298711
$147$		0			0
$148$	−1198.70			−0.665761
$149$	−2341.75	−	1352.01i	−1.28754	−	0.743363i	−0.309328	−	0.950956i	$-0.600104\pi$
$149$	−2341.75	−	1352.01i	−1.28754	−	0.743363i	−0.978215	+	0.207592i	$0.933437\pi$
$150$	914.794	+	591.681i	0.497951	+	0.322070i
$151$	−770.352	−	1334.29i	−0.415168	−	0.719092i	0.580278	−	0.814418i	$-0.302944\pi$
$151$	−770.352	−	1334.29i	−0.415168	−	0.719092i	−0.995446	+	0.0953266i	$0.969610\pi$
$152$	−37.0674	+	64.2026i	−0.0197800	+	0.0342600i
$153$	−1832.91	+	2542.44i	−0.968512	+	1.34343i
$154$		0			0
$155$		−	636.580i		−	0.329880i
$156$	−6.20678	+	122.760i	−0.00318552	+	0.0630043i
$157$	−477.498	+	275.684i	−0.242729	+	0.140140i	−0.616430	−	0.787409i	$-0.711422\pi$
$157$	−477.498	+	275.684i	−0.242729	+	0.140140i	0.373701	+	0.927549i	$0.378089\pi$
$158$	−1848.56	+	1067.27i	−0.930783	+	0.537388i
$159$	−78.3786	+	1550.20i	−0.0390933	+	0.773201i
$160$			143.702i			0.0710038i
$161$		0			0
$162$	1383.28	−	460.755i	0.670870	−	0.223459i
$163$	1155.82	−	2001.94i	0.555403	−	0.961986i	−0.442469	−	0.896784i	$-0.645897\pi$
$163$	1155.82	−	2001.94i	0.555403	−	0.961986i	0.997872	−	0.0652023i	$-0.0207693\pi$
$164$	1016.76	+	1761.08i	0.484119	+	0.838518i
$165$	−458.899	−	296.811i	−0.216516	−	0.140041i
$166$	−468.410	−	270.436i	−0.219010	−	0.126445i
$167$	2580.87			1.19589			0.597944	−	0.801538i	$-0.295984\pi$
$167$	2580.87			1.19589			0.597944	+	0.801538i	$0.295984\pi$
$168$		0			0
$169$	2162.03			0.984081
$170$	−902.908	−	521.294i	−0.407352	−	0.235185i
$171$	−25.2364	+	248.929i	−0.0112858	+	0.111322i
$172$	782.254	+	1354.90i	0.346781	+	0.600642i
$173$	501.050	−	867.845i	0.220197	−	0.381393i	−0.734670	−	0.678424i	$-0.762663\pi$
$173$	501.050	−	867.845i	0.220197	−	0.381393i	0.954868	+	0.297031i	$0.0959965\pi$
$174$	−983.979	−	1922.40i	−0.428708	−	0.837569i
$175$		0			0
$176$			374.743i			0.160496i
$177$	1061.53	+	53.6712i	0.450787	+	0.0227919i
$178$	1537.25	−	887.530i	0.647312	−	0.373726i
$179$	2598.36	−	1500.17i	1.08498	−	0.626411i	0.152742	−	0.988266i	$-0.451190\pi$
$179$	2598.36	−	1500.17i	1.08498	−	0.626411i	0.932234	+	0.361855i	$0.117856\pi$
$180$	198.896	+	442.333i	0.0823601	+	0.183164i
$181$		−	967.850i		−	0.397457i	−0.980055	−	0.198729i	$-0.936319\pi$
$181$		−	967.850i		−	0.397457i	0.980055	−	0.198729i	$-0.0636812\pi$
$182$		0			0
$183$	−2904.21	+	1486.52i	−1.17315	+	0.600473i
$184$	497.543	−	861.769i	0.199344	−	0.345274i
$185$	−672.872	−	1165.45i	−0.267408	−	0.463165i
$186$	−800.068	+	1236.98i	−0.315397	+	0.487634i
$187$	−2354.59	−	1359.42i	−0.920773	−	0.531608i
$188$	322.060			0.124940
$189$		0			0
$190$	−83.2289			−0.0317792
$191$	356.214	+	205.660i	0.134946	+	0.0779113i	0.565953	−	0.824437i	$-0.308508\pi$
$191$	356.214	+	205.660i	0.134946	+	0.0779113i	−0.431007	+	0.902349i	$0.641842\pi$
$192$	180.608	−	279.236i	0.0678866	−	0.104959i
$193$	−408.212	−	707.043i	−0.152247	−	0.263700i	0.779806	−	0.626021i	$-0.215318\pi$
$193$	−408.212	−	707.043i	−0.152247	−	0.263700i	−0.932053	+	0.362321i	$0.881984\pi$
$194$	−219.564	+	380.296i	−0.0812566	+	0.140741i
$195$	−122.839	+	62.8749i	−0.0451111	+	0.0230901i
$196$		0			0
$197$			633.331i			0.229051i	0.993420	+	0.114525i	$0.0365347\pi$
$197$			633.331i			0.229051i	−0.993420	+	0.114525i	$0.963465\pi$
$198$	518.677	+	1153.51i	0.186166	+	0.414022i
$199$	2964.48	−	1711.54i	1.05601	−	0.609688i	0.131685	−	0.991292i	$-0.457961\pi$
$199$	2964.48	−	1711.54i	1.05601	−	0.609688i	0.924326	+	0.381603i	$0.124628\pi$
$200$	726.310	−	419.335i	0.256789	−	0.148257i
$201$	−533.373	−	26.9675i	−0.187170	−	0.00946339i
$202$			1970.13i			0.686228i
$203$		0			0
$204$	1099.33	+	2147.76i	0.377295	+	0.737123i
$205$	−1141.48	+	1977.11i	−0.388901	+	0.673596i
$206$	−1285.03	−	2225.74i	−0.434623	−	0.752790i
$207$	338.739	−	3341.29i	0.113739	−	1.12191i
$208$	81.9446	+	47.3107i	0.0273165	+	0.0157712i
$209$	−217.043			−0.0718333
$210$		0			0
$211$	1023.65			0.333986			0.166993	−	0.985958i	$-0.446594\pi$
$211$	1023.65			0.333986			0.166993	+	0.985958i	$0.446594\pi$
$212$	1034.79	+	597.435i	0.335234	+	0.193547i
$213$	204.970	+	132.573i	0.0659358	+	0.0426467i
$214$	−182.915	−	316.818i	−0.0584290	−	0.101202i
$215$	−878.212	+	1521.11i	−0.278575	+	0.482506i
$216$	169.447	−	1109.50i	0.0533768	−	0.349501i
$217$		0			0
$218$		−	1165.88i		−	0.362219i
$219$	−69.1334	+	1367.35i	−0.0213315	+	0.421903i
$220$	−364.347	+	210.356i	−0.111656	+	0.0644645i
$221$	−594.527	+	343.250i	−0.180960	+	0.104477i
$222$	−157.260	+	3110.34i	−0.0475432	+	0.940327i
$223$		−	1521.32i		−	0.456840i	−0.973563	−	0.228420i	$-0.926644\pi$
$223$		−	1521.32i		−	0.456840i	0.973563	−	0.228420i	$-0.0733559\pi$
$224$		0			0
$225$	1655.28	−	2296.05i	0.490454	−	0.680311i
$226$	2283.94	−	3955.90i	0.672237	−	1.16435i
$227$	−729.575	−	1263.66i	−0.213320	−	0.369481i	0.739432	−	0.673232i	$-0.235094\pi$
$227$	−729.575	−	1263.66i	−0.213320	−	0.369481i	−0.952752	+	0.303751i	$0.901761\pi$
$228$	161.728	+	104.604i	0.0469766	+	0.0303841i
$229$	−4152.17	−	2397.26i	−1.19818	−	0.691770i	−0.238031	−	0.971257i	$-0.576502\pi$
$229$	−4152.17	−	2397.26i	−1.19818	−	0.691770i	−0.960149	+	0.279488i	$0.909835\pi$
$230$	1117.15			0.320273
$231$		0			0
$232$	−1662.46			−0.470455
$233$	1445.76	+	834.708i	0.406501	+	0.234693i	0.689285	−	0.724490i	$-0.257925\pi$
$233$	1445.76	+	834.708i	0.406501	+	0.234693i	−0.282784	+	0.959183i	$0.591258\pi$
$234$	317.719	+	32.2103i	0.0887604	+	0.00899851i
$235$	180.784	+	313.126i	0.0501831	+	0.0869196i
$236$	409.104	−	708.590i	0.112841	−	0.195446i
$237$	2526.79	+	4936.60i	0.692543	+	1.35302i
$238$		0			0
$239$		−	3529.25i		−	0.955181i	−0.878583	−	0.477590i	$-0.841510\pi$
$239$		−	3529.25i		−	0.955181i	0.878583	−	0.477590i	$-0.158490\pi$
$240$	372.872	+	18.8525i	0.100286	+	0.00507051i
$241$	4269.15	−	2464.80i	1.14108	−	0.658803i	0.194382	−	0.980926i	$-0.437730\pi$
$241$	4269.15	−	2464.80i	1.14108	−	0.658803i	0.946698	+	0.322123i	$0.104397\pi$
$242$	1355.22	−	782.438i	0.359987	−	0.207839i
$243$	−1014.07	−	3649.73i	−0.267707	−	0.963500i
$244$			2511.51i			0.658946i
$245$		0			0
$246$	4702.97	−	2407.21i	1.21890	−	0.623894i
$247$	−27.4014	+	47.4605i	−0.00705873	+	0.0122261i
$248$	567.024	+	982.114i	0.145186	+	0.251469i
$249$	−763.170	+	1179.93i	−0.194233	+	0.300302i
$250$	1787.67	+	1032.11i	0.452248	+	0.261105i
$251$	1294.99			0.325652			0.162826	−	0.986655i	$-0.447939\pi$
$251$	1294.99			0.325652			0.162826	+	0.986655i	$0.447939\pi$
$252$		0			0
$253$	2913.29			0.723940
$254$	2692.45	+	1554.48i	0.665114	+	0.384004i
$255$	−1471.09	+	2274.44i	−0.361267	+	0.558553i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	728.040	−	1261.00i	0.176708	−	0.306067i	−0.764043	−	0.645165i	$-0.776789\pi$
$257$	728.040	−	1261.00i	0.176708	−	0.306067i	0.940751	+	0.339098i	$0.110122\pi$
$258$	3618.28	−	1852.01i	0.873117	−	0.446904i
$259$		0			0
$260$			106.229i			0.0253385i
$261$	−5117.27	+	2300.99i	−1.21360	+	0.545700i
$262$	−3628.52	+	2094.93i	−0.855613	+	0.493988i
$263$	1850.30	−	1068.27i	0.433820	−	0.250466i	−0.267153	−	0.963654i	$-0.586083\pi$
$263$	1850.30	−	1068.27i	0.433820	−	0.250466i	0.700973	+	0.713188i	$0.252749\pi$
$264$	972.368	+	49.1632i	0.226686	+	0.0114613i
$265$			1341.44i			0.310959i
$266$		0			0
$267$	−2101.26	−	4105.23i	−0.481628	−	0.940958i
$268$	−205.558	+	356.036i	−0.0468524	+	0.0811507i
$269$	1443.73	+	2500.61i	0.327233	+	0.566784i	0.981962	−	0.189080i	$-0.0605506\pi$
$269$	1443.73	+	2500.61i	0.327233	+	0.566784i	−0.654729	+	0.755864i	$0.727217\pi$
$270$	1173.84	−	458.057i	0.264584	−	0.103246i
$271$	5072.92	+	2928.85i	1.13711	+	0.656513i	0.945714	−	0.324999i	$-0.105364\pi$
$271$	5072.92	+	2928.85i	1.13711	+	0.656513i	0.191400	+	0.981512i	$0.438697\pi$
$272$	1857.34			0.414036
$273$		0			0
$274$	−1221.68			−0.269359
$275$	2126.40	+	1227.68i	0.466279	+	0.269206i
$276$	−2170.81	−	1404.06i	−0.473433	−	0.306212i
$277$	1401.52	+	2427.50i	0.304003	+	0.526549i	0.977039	−	0.213061i	$-0.0683433\pi$
$277$	1401.52	+	2427.50i	0.304003	+	0.526549i	−0.673036	+	0.739610i	$0.735010\pi$
$278$	−1806.61	+	3129.14i	−0.389760	+	0.675085i
$279$	3104.71	+	2238.27i	0.666215	+	0.480293i
$280$		0			0
$281$		−	4665.53i		−	0.990469i	−0.868759	−	0.495235i	$-0.835082\pi$
$281$		−	4665.53i		−	0.990469i	0.868759	−	0.495235i	$-0.164918\pi$
$282$	42.2517	−	835.670i	0.00892217	−	0.176466i
$283$	−4654.53	+	2687.29i	−0.977679	+	0.564463i	−0.901569	−	0.432636i	$-0.857583\pi$
$283$	−4654.53	+	2687.29i	−0.977679	+	0.564463i	−0.0761103	+	0.997099i	$0.524250\pi$
$284$	162.738	−	93.9569i	0.0340026	−	0.0196314i
$285$	−10.9190	+	215.959i	−0.00226941	+	0.0448853i
$286$			277.021i			0.0572748i
$287$		0			0
$288$	−700.857	−	505.267i	−0.143397	−	0.103379i
$289$	−4281.21	+	7415.27i	−0.871404	+	1.50932i
$290$	−933.194	−	1616.34i	−0.188962	−	0.327292i
$291$	957.973	+	619.608i	0.192981	+	0.124818i
$292$	912.729	+	526.964i	0.182923	+	0.105610i
$293$	−1302.13			−0.259630			−0.129815	−	0.991538i	$-0.541438\pi$
$293$	−1302.13			−0.259630			−0.129815	+	0.991538i	$0.541438\pi$
$294$		0			0
$295$	918.578			0.181294
$296$	2076.21	+	1198.70i	0.407694	+	0.235382i
$297$	3061.13	−	1194.51i	0.598063	−	0.233376i
$298$	2704.02	+	4683.51i	0.525637	+	0.910430i
$299$	367.799	−	637.046i	0.0711383	−	0.123215i
$300$	−992.789	−	1939.61i	−0.191062	−	0.373279i
$301$		0			0
$302$			3081.41i			0.587136i
$303$	5112.03	+	258.465i	0.969235	+	0.0490048i
$304$	128.405	−	74.1348i	0.0242255	−	0.0139866i
$305$	−2441.84	+	1409.80i	−0.458424	+	0.264671i
$306$	5717.14	−	2570.72i	1.06806	−	0.480256i
$307$			644.894i			0.119889i	0.998202	+	0.0599447i	$0.0190924\pi$
$307$			644.894i			0.119889i	−0.998202	+	0.0599447i	$0.980908\pi$
$308$		0			0
$309$	−5943.85	+	3042.35i	−1.09428	+	0.560108i
$310$	−636.580	+	1102.59i	−0.116630	+	0.202009i
$311$	−668.420	−	1157.74i	−0.121873	−	0.211091i	0.798633	−	0.601818i	$-0.205557\pi$
$311$	−668.420	−	1157.74i	−0.121873	−	0.211091i	−0.920506	+	0.390727i	$0.872224\pi$
$312$	133.511	−	206.420i	0.0242261	−	0.0374559i
$313$	1459.67	+	842.739i	0.263595	+	0.152187i	0.625973	−	0.779844i	$-0.284702\pi$
$313$	1459.67	+	842.739i	0.263595	+	0.152187i	−0.362378	+	0.932031i	$0.618035\pi$
$314$	1102.73			0.198188
$315$		0			0
$316$	4269.07			0.759981
$317$	2609.95	+	1506.85i	0.462427	+	0.266982i	0.713064	−	0.701099i	$-0.247307\pi$
$317$	2609.95	+	1506.85i	0.462427	+	0.266982i	−0.250637	+	0.968081i	$0.580640\pi$
$318$	1685.96	−	2606.65i	0.297308	−	0.459666i
$319$	−2433.57	−	4215.06i	−0.427127	−	0.739806i
$320$	143.702	−	248.899i	0.0251036	−	0.0434808i
$321$	−846.064	+	433.057i	−0.147111	+	0.0752987i
$322$		0			0
$323$			1075.73i			0.185310i
$324$	−2856.67	−	585.232i	−0.489827	−	0.100348i
$325$	536.910	−	309.985i	0.0916382	−	0.0529074i
$326$	−4003.87	+	2311.64i	−0.680227	+	0.392729i
$327$	−3025.19	−	152.955i	−0.511601	−	0.0258667i
$328$		−	4067.03i		−	0.684647i
$329$		0			0
$330$	498.024	+	972.991i	0.0830768	+	0.162307i
$331$	394.460	−	683.225i	0.0655030	−	0.113454i	−0.831414	−	0.555653i	$-0.812468\pi$
$331$	394.460	−	683.225i	0.0655030	−	0.113454i	0.896917	+	0.442199i	$0.145801\pi$
$332$	540.873	+	936.819i	0.0894104	+	0.154863i
$333$	8049.97	+	816.104i	1.32473	+	0.134301i
$334$	−4470.19	−	2580.87i	−0.732329	−	0.422811i
$335$	−461.547			−0.0752746
$336$		0			0
$337$	1906.16			0.308116			0.154058	−	0.988062i	$-0.450766\pi$
$337$	1906.16			0.308116			0.154058	+	0.988062i	$0.450766\pi$
$338$	−3744.74	−	2162.03i	−0.602624	−	0.347925i
$339$	−9964.99	−	6445.27i	−1.59653	−	1.03262i
$340$	1042.59	+	1805.82i	0.166301	+	0.288042i
$341$	−1660.06	+	2875.31i	−0.263629	+	0.456618i
$342$	292.640	−	405.921i	0.0462694	−	0.0641805i
$343$		0			0
$344$		−	3129.02i		−	0.490422i
$345$	146.561	−	2898.74i	0.0228713	−	0.452356i
$346$	−1735.69	+	1002.10i	−0.269686	+	0.155703i
$347$	−4538.98	+	2620.58i	−0.702205	+	0.405418i	−0.808168	−	0.588952i	$-0.799541\pi$
$347$	−4538.98	+	2620.58i	−0.702205	+	0.405418i	0.105963	+	0.994370i	$0.466207\pi$
$348$	−218.101	+	4313.68i	−0.0335961	+	0.664475i
$349$			4502.54i			0.690588i	0.938495	+	0.345294i	$0.112221\pi$
$349$			4502.54i			0.690588i	−0.938495	+	0.345294i	$0.887779\pi$
$350$		0			0
$351$	125.260	−	820.179i	0.0190481	−	0.124723i
$352$	374.743	−	649.073i	0.0567439	−	0.0982833i
$353$	4799.70	+	8313.33i	0.723689	+	1.25347i	0.959511	+	0.281671i	$0.0908885\pi$
$353$	4799.70	+	8313.33i	0.723689	+	1.25347i	−0.235822	+	0.971796i	$0.575778\pi$
$354$	−1784.95	−	1154.49i	−0.267992	−	0.173335i
$355$	182.701	+	105.483i	0.0273148	+	0.0157702i
$356$	−3550.12			−0.528528
$357$		0			0
$358$	−6000.66			−0.885879
$359$	−8803.94	−	5082.96i	−1.29430	−	0.747265i	−0.314888	−	0.949129i	$-0.601967\pi$
$359$	−8803.94	−	5082.96i	−1.29430	−	0.747265i	−0.979414	+	0.201863i	$0.935300\pi$
$360$	97.8354	−	965.040i	0.0143233	−	0.141283i
$361$	−3386.56	−	5865.70i	−0.493740	−	0.855183i
$362$	−967.850	+	1676.37i	−0.140522	+	0.243392i
$363$	−1852.44	−	3619.13i	−0.267846	−	0.523292i
$364$		0			0
$365$			1183.21i			0.169677i
$366$	6516.77	+	329.489i	0.930702	+	0.0470565i
$367$	−332.544	+	191.995i	−0.0472988	+	0.0273080i	−0.523463	−	0.852048i	$-0.675360\pi$
$367$	−332.544	+	191.995i	−0.0472988	+	0.0273080i	0.476164	+	0.879356i	$0.342027\pi$
$368$	−1723.54	+	995.085i	−0.244146	+	0.140958i
$369$	−5629.14	−	12518.9i	−0.794149	−	1.76614i
$370$			2691.49i			0.378173i
$371$		0			0
$372$	2622.74	−	1342.45i	0.365545	−	0.187104i
$373$	1481.79	−	2566.54i	0.205695	−	0.356275i	−0.744659	−	0.667445i	$-0.767388\pi$
$373$	1481.79	−	2566.54i	0.205695	−	0.356275i	0.950354	+	0.311171i	$0.100721\pi$
$374$	2718.84	+	4709.17i	0.375904	+	0.651085i
$375$	2912.61	−	4503.16i	0.401083	−	0.620113i
$376$	−557.825	−	322.060i	−0.0765096	−	0.0441728i
$377$	−1228.94			−0.167887
$378$		0			0
$379$	−13195.4			−1.78839			−0.894195	−	0.447677i	$-0.852251\pi$
$379$	−13195.4			−1.78839			−0.894195	+	0.447677i	$0.852251\pi$
$380$	144.157	+	83.2289i	0.0194607	+	0.0112357i
$381$	4386.74	−	6782.32i	0.589868	−	0.911991i
$382$	−411.321	−	712.428i	−0.0550916	−	0.0954214i
$383$	−4475.95	+	7752.57i	−0.597155	+	1.03430i	0.396084	+	0.918214i	$0.370369\pi$
$383$	−4475.95	+	7752.57i	−0.597155	+	1.03430i	−0.993239	+	0.116088i	$0.962964\pi$
$384$	−592.058	+	303.044i	−0.0786805	+	0.0402725i
$385$		0			0
$386$			1632.85i			0.215310i
$387$	−4330.84	−	9631.54i	−0.568860	−	1.26511i
$388$	760.593	−	439.128i	0.0995186	−	0.0574571i
$389$	−7594.74	+	4384.82i	−0.989893	+	0.571515i	−0.905242	−	0.424896i	$-0.860311\pi$
$389$	−7594.74	+	4384.82i	−0.989893	+	0.571515i	−0.0846507	+	0.996411i	$0.526977\pi$
$390$	275.638	+	13.9363i	0.0357884	+	0.00180947i
$391$		−	14439.1i		−	1.86757i
$392$		0			0
$393$	4959.80	+	9689.97i	0.636613	+	1.24375i
$394$	633.331	−	1096.96i	0.0809816	−	0.140264i
$395$	2396.38	+	4150.65i	0.305253	+	0.528713i
$396$	255.133	−	2516.61i	0.0323761	−	0.319355i
$397$	1187.30	+	685.490i	0.150098	+	0.0866594i	0.573168	−	0.819438i	$-0.305714\pi$
$397$	1187.30	+	685.490i	0.150098	+	0.0866594i	−0.423070	+	0.906097i	$0.639047\pi$
$398$	−6846.17			−0.862229
$399$		0			0
$400$	−1677.34			−0.209668
$401$	−2392.14	−	1381.10i	−0.297899	−	0.171992i	0.343599	−	0.939116i	$-0.388354\pi$
$401$	−2392.14	−	1381.10i	−0.297899	−	0.171992i	−0.641499	+	0.767124i	$0.721687\pi$
$402$	896.862	+	580.082i	0.111272	+	0.0719699i
$403$	419.161	+	726.008i	0.0518112	+	0.0897396i
$404$	1970.13	−	3412.37i	0.242618	−	0.420227i
$405$	−1034.55	−	3105.94i	−0.126931	−	0.381075i
$406$		0			0
$407$			7018.82i			0.854815i
$408$	243.668	−	4819.35i	0.0295670	−	0.584788i
$409$	−2310.01	+	1333.69i	−0.279273	+	0.161239i	−0.633094	−	0.774075i	$-0.718216\pi$
$409$	−2310.01	+	1333.69i	−0.279273	+	0.161239i	0.353821	+	0.935313i	$0.384882\pi$
$410$	3954.21	−	2282.97i	0.476304	−	0.274994i
$411$	−160.274	+	3169.96i	−0.0192354	+	0.380445i
$412$			5140.13i			0.614650i
$413$		0			0
$414$	−3928.00	+	5448.54i	−0.466306	+	0.646814i
$415$	−607.221	+	1051.74i	−0.0718249	+	0.124404i
$416$	−94.6215	−	163.889i	−0.0111519	−	0.0193157i
$417$	7882.37	+	5098.24i	0.925662	+	0.598710i
$418$	375.929	+	217.043i	0.0439887	+	0.0253969i
$419$	−14480.6			−1.68836			−0.844179	−	0.536061i	$-0.819912\pi$
$419$	−14480.6			−1.68836			−0.844179	+	0.536061i	$0.819912\pi$
$420$		0			0
$421$	14248.8			1.64951			0.824753	−	0.565494i	$-0.191314\pi$
$421$	14248.8			1.64951			0.824753	+	0.565494i	$0.191314\pi$
$422$	−1773.02	−	1023.65i	−0.204524	−	0.118082i
$423$	−2162.82	−	219.266i	−0.248605	−	0.0252035i
$424$	−1194.87	−	2069.58i	−0.136859	−	0.237046i
$425$	6084.75	−	10539.1i	0.694479	−	1.20287i
$426$	−222.446	−	434.593i	−0.0252994	−	0.0494275i
$427$		0			0
$428$			731.660i			0.0826311i
$429$	718.804	+	36.3429i	0.0808955	+	0.00409010i
$430$	3042.22	−	1756.42i	0.341183	−	0.196982i
$431$	−4826.49	+	2786.57i	−0.539405	+	0.311426i	−0.744838	−	0.667246i	$-0.767473\pi$
$431$	−4826.49	+	2786.57i	−0.539405	+	0.311426i	0.205433	+	0.978671i	$0.434140\pi$
$432$	−1402.99	+	1752.27i	−0.156254	+	0.195153i
$433$			2939.93i			0.326291i	0.986602	+	0.163146i	$0.0521640\pi$
$433$			2939.93i			0.326291i	−0.986602	+	0.163146i	$0.947836\pi$
$434$		0			0
$435$	−4316.44	+	2209.37i	−0.475765	+	0.243520i
$436$	−1165.88	+	2019.37i	−0.128064	+	0.221813i
$437$	−576.332	−	998.236i	−0.0630885	−	0.109273i
$438$	1487.09	−	2299.18i	0.162228	−	0.250820i
$439$	8290.73	+	4786.66i	0.901355	+	0.520398i	0.877640	−	0.479321i	$-0.159117\pi$
$439$	8290.73	+	4786.66i	0.901355	+	0.520398i	0.0237157	+	0.999719i	$0.492450\pi$
$440$	841.424			0.0911666
$441$		0			0
$442$	1373.00			0.147753
$443$	6197.42	+	3578.08i	0.664669	+	0.383747i	0.794054	−	0.607848i	$-0.207967\pi$
$443$	6197.42	+	3578.08i	0.664669	+	0.383747i	−0.129385	+	0.991594i	$0.541300\pi$
$444$	3382.73	−	5230.01i	0.361570	−	0.559021i
$445$	−1992.81	−	3451.64i	−0.212288	−	0.367693i
$446$	−1521.32	+	2635.01i	−0.161517	+	0.279756i
$447$	12507.3	−	6401.86i	1.32344	−	0.677400i
$448$		0			0
$449$			14839.2i			1.55970i	0.625964	+	0.779852i	$0.284706\pi$
$449$			14839.2i			1.55970i	−0.625964	+	0.779852i	$0.715294\pi$
$450$	−5163.08	+	2321.59i	−0.540867	+	0.243202i
$451$	10311.7	−	5953.48i	1.07663	−	0.621593i
$452$	−7911.81	+	4567.88i	−0.823319	+	0.475343i
$453$	7995.52	+	404.256i	0.829276	+	0.0419284i
$454$			2918.30i			0.301680i
$455$		0			0
$456$	−175.516	−	342.907i	−0.0180248	−	0.0352151i
$457$	3787.42	−	6560.00i	0.387676	−	0.671474i	−0.604461	−	0.796635i	$-0.706611\pi$
$457$	3787.42	−	6560.00i	0.387676	−	0.671474i	0.992136	+	0.125161i	$0.0399447\pi$
$458$	4794.52	+	8304.35i	0.489155	+	0.847242i
$459$	−5920.37	−	15171.9i	−0.602046	−	1.54284i
$460$	−1934.96	−	1117.15i	−0.196126	−	0.113234i
$461$	−14850.5			−1.50034			−0.750170	−	0.661245i	$-0.770029\pi$
$461$	−14850.5			−1.50034			−0.750170	+	0.661245i	$0.770029\pi$
$462$		0			0
$463$	3361.43			0.337406			0.168703	−	0.985667i	$-0.446042\pi$
$463$	3361.43			0.337406			0.168703	+	0.985667i	$0.446042\pi$
$464$	2879.46	+	1662.46i	0.288094	+	0.166331i
$465$	2777.44	+	1796.42i	0.276991	+	0.179155i
$466$	−1669.42	−	2891.51i	−0.165953	−	0.287439i
$467$	115.422	−	199.917i	0.0114371	−	0.0198096i	−0.860250	−	0.509872i	$-0.829693\pi$
$467$	115.422	−	199.917i	0.0114371	−	0.0198096i	0.871687	+	0.490063i	$0.163026\pi$
$468$	−518.095	−	373.509i	−0.0511730	−	0.0368920i
$469$		0			0
$470$		−	723.134i		−	0.0709696i
$471$	144.670	−	2861.33i	0.0141529	−	0.279922i
$472$	−1417.18	+	818.209i	−0.138201	+	0.0797905i
$473$	7933.44	−	4580.37i	0.771205	−	0.445255i
$474$	560.068	−	11077.2i	0.0542716	−	1.07340i
$475$		−	971.480i		−	0.0938411i
$476$		0			0
$477$	−6542.45	−	4716.63i	−0.628005	−	0.452745i
$478$	−3529.25	+	6112.84i	−0.337707	+	0.584926i
$479$	2200.43	+	3811.26i	0.209896	+	0.363551i	0.951682	−	0.307087i	$-0.0993541\pi$
$479$	2200.43	+	3811.26i	0.209896	+	0.363551i	−0.741786	+	0.670637i	$0.766021\pi$
$480$	−626.980	−	405.525i	−0.0596200	−	0.0385617i
$481$	1534.80	+	886.116i	0.145490	+	0.0839988i
$482$	−9859.18			−0.931688
$483$		0			0
$484$	−3129.75			−0.293928
$485$	853.894	+	492.996i	0.0799450	+	0.0461563i
$486$	−1893.31	+	7335.60i	−0.176712	+	0.684670i
$487$	5972.31	+	10344.3i	0.555711	+	0.962520i	0.997848	+	0.0655721i	$0.0208872\pi$
$487$	5972.31	+	10344.3i	0.555711	+	0.962520i	−0.442137	+	0.896948i	$0.645779\pi$
$488$	2511.51	−	4350.06i	0.232973	−	0.403520i
$489$	5472.87	+	10692.4i	0.506118	+	0.988804i
$490$		0			0
$491$		−	19916.7i		−	1.83060i	−0.402768	−	0.915302i	$-0.631952\pi$
$491$		−	19916.7i		−	1.83060i	0.402768	−	0.915302i	$-0.368048\pi$
$492$	−10553.0	−	533.562i	−0.967002	−	0.0488919i
$493$	−20891.1	+	12061.5i	−1.90850	+	1.10187i
$494$	94.9211	−	54.8027i	0.00864514	−	0.00499128i
$495$	2590.02	−	1164.61i	0.235177	−	0.105748i
$496$		−	2268.09i		−	0.205324i
$497$		0			0
$498$	2501.78	−	1280.53i	0.225115	−	0.115225i
$499$	−665.569	+	1152.80i	−0.0597093	+	0.103420i	−0.894335	−	0.447398i	$-0.852351\pi$
$499$	−665.569	+	1152.80i	−0.0597093	+	0.103420i	0.834626	+	0.550818i	$0.185684\pi$
$500$	−2064.22	−	3575.33i	−0.184629	−	0.319787i
$501$	−7283.19	+	11260.5i	−0.649479	+	1.00416i
$502$	−2242.98	−	1294.99i	−0.199421	−	0.115136i
$503$	10393.2			0.921288			0.460644	−	0.887585i	$-0.347618\pi$
$503$	10393.2			0.921288			0.460644	+	0.887585i	$0.347618\pi$
$504$		0			0
$505$	4423.62			0.389799
$506$	−5045.96	−	2913.29i	−0.443321	−	0.255951i
$507$	−6101.22	+	9433.07i	−0.534447	+	0.826306i
$508$	−3108.97	−	5384.89i	−0.271532	−	0.470307i
$509$	−5132.02	+	8888.91i	−0.446901	+	0.774055i	−0.998182	−	0.0602640i	$-0.980806\pi$
$509$	−5132.02	+	8888.91i	−0.446901	+	0.774055i	0.551281	+	0.834319i	$0.314139\pi$
$510$	4822.44	−	2468.36i	0.418708	−	0.214315i
$511$		0			0
$512$			512.000i			0.0441942i
$513$	−1014.88	−	812.584i	−0.0873449	−	0.0699346i
$514$	−2522.00	+	1456.08i	−0.216422	+	0.124951i
$515$	−4997.54	+	2885.33i	−0.427608	+	0.246879i
$516$	−8119.05	−	410.501i	−0.692677	−	0.0350219i
$517$		−	1885.78i		−	0.160418i
$518$		0			0
$519$	2372.50	+	4635.17i	0.200658	+	0.392026i
$520$	106.229	−	183.993i	0.00895852	−	0.0155166i
$521$	−1549.97	−	2684.63i	−0.130337	−	0.225750i	0.793470	−	0.608610i	$-0.208273\pi$
$521$	−1549.97	−	2684.63i	−0.130337	−	0.225750i	−0.923806	+	0.382860i	$0.874939\pi$
$522$	11164.4	+	1131.84i	0.936112	+	0.0949028i
$523$	8265.94	+	4772.34i	0.691098	+	0.399005i	0.804023	−	0.594598i	$-0.202689\pi$
$523$	8265.94	+	4772.34i	0.691098	+	0.399005i	−0.112925	+	0.993603i	$0.536022\pi$
$524$	8379.70			0.698605
$525$		0			0
$526$	−4273.10			−0.354213
$527$	14250.9	+	8227.77i	1.17795	+	0.680090i
$528$	−1635.03	−	1057.52i	−0.134764	−	0.0871642i
$529$	1652.39	+	2862.03i	0.135809	+	0.235229i
$530$	1341.44	−	2323.45i	0.109941	−	0.190423i
$531$	−3229.80	+	4480.06i	−0.263957	+	0.366136i
$532$		0			0
$533$		−	3006.47i		−	0.244324i
$534$	−465.747	+	9211.72i	−0.0377432	+	0.746498i
$535$	−711.364	+	410.706i	−0.0574859	+	0.0331895i
$536$	712.073	−	411.115i	0.0573822	−	0.0331296i
$537$	−787.238	+	15570.3i	−0.0632622	+	1.25122i
$538$		−	5774.91i		−	0.462777i
$539$		0			0
$540$	−2491.21	−	380.465i	−0.198527	−	0.0303196i
$541$	3403.83	−	5895.60i	0.270503	−	0.468524i	−0.698488	−	0.715622i	$-0.746143\pi$
$541$	3403.83	−	5895.60i	0.270503	−	0.468524i	0.968991	+	0.247098i	$0.0794768\pi$
$542$	−5857.70	−	10145.8i	−0.464225	−	0.804061i
$543$	4222.79	+	2731.27i	0.333734	+	0.215856i
$544$	−3217.01	−	1857.34i	−0.253544	−	0.146384i
$545$	−2617.80			−0.205751
$546$		0			0
$547$	−14906.9			−1.16521			−0.582606	−	0.812754i	$-0.697967\pi$
$547$	−14906.9			−1.16521			−0.582606	+	0.812754i	$0.697967\pi$
$548$	2116.01	+	1221.68i	0.164948	+	0.0952327i
$549$	1709.89	−	16866.2i	0.132926	−	1.31117i
$550$	−2455.36	−	4252.80i	−0.190358	−	0.329709i
$551$	−962.859	+	1667.72i	−0.0744449	+	0.128942i
$552$	2355.89	+	4602.72i	0.181655	+	0.354900i
$553$		0			0
$554$		−	5606.06i		−	0.429925i
$555$	6983.77	+	353.102i	0.534135	+	0.0270060i
$556$	6258.29	−	3613.22i	0.477357	−	0.275602i
$557$	−10661.9	+	6155.67i	−0.811061	+	0.468266i	−0.847324	−	0.531076i	$-0.821788\pi$
$557$	−10661.9	+	6155.67i	−0.811061	+	0.468266i	0.0362634	+	0.999342i	$0.488454\pi$
$558$	−3139.25	−	6981.50i	−0.238163	−	0.529661i
$559$		−	2313.06i		−	0.175013i
$560$		0			0
$561$	12575.9	−	6436.95i	0.946442	−	0.484435i
$562$	−4665.53	+	8080.93i	−0.350184	+	0.606536i
$563$	417.925	+	723.867i	0.0312850	+	0.0541872i	0.881244	−	0.472662i	$-0.156707\pi$
$563$	417.925	+	723.867i	0.0312850	+	0.0541872i	−0.849959	+	0.526849i	$0.823373\pi$
$564$	−908.852	+	1405.17i	−0.0678538	+	0.104908i
$565$	−8882.34	−	5128.22i	−0.661386	−	0.381851i
$566$	10749.2			0.798271
$567$		0			0
$568$	−375.828			−0.0277630
$569$	−5291.04	−	3054.78i	−0.389828	−	0.225067i	0.292258	−	0.956340i	$-0.405593\pi$
$569$	−5291.04	−	3054.78i	−0.389828	−	0.225067i	−0.682086	+	0.731272i	$0.738927\pi$
$570$	234.871	−	363.133i	0.0172591	−	0.0266842i
$571$	6319.69	+	10946.0i	0.463171	+	0.802236i	0.999117	−	0.0420166i	$-0.0133782\pi$
$571$	6319.69	+	10946.0i	0.463171	+	0.802236i	−0.535946	+	0.844252i	$0.680045\pi$
$572$	277.021	−	479.815i	0.0202497	−	0.0350735i
$573$	−1902.54	+	973.814i	−0.138708	+	0.0709977i
$574$		0			0
$575$			13039.8i			0.945736i
$576$	708.654	+	1576.01i	0.0512626	+	0.114005i
$577$	15334.7	−	8853.51i	1.10640	−	0.638781i	0.168506	−	0.985701i	$-0.446106\pi$
$577$	15334.7	−	8853.51i	1.10640	−	0.638781i	0.937895	+	0.346920i	$0.112772\pi$
$578$	14830.5	−	8562.42i	1.06725	−	0.616176i
$579$	4236.85	+	214.216i	0.304106	+	0.0153757i
$580$			3732.78i			0.267233i
$581$		0			0
$582$	−1039.65	−	2031.17i	−0.0740462	−	0.144664i
$583$	3498.19	−	6059.05i	0.248508	−	0.430429i
$584$	−1053.93	−	1825.46i	−0.0746779	−	0.129346i
$585$	72.3229	−	713.386i	0.00511143	−	0.0504186i
$586$	2255.36	+	1302.13i	0.158990	+	0.0917929i
$587$	11725.2			0.824446			0.412223	−	0.911083i	$-0.364752\pi$
$587$	11725.2			0.824446			0.412223	+	0.911083i	$0.364752\pi$
$588$		0			0
$589$	1313.63			0.0918968
$590$	−1591.02	−	918.578i	−0.111019	−	0.0640970i
$591$	−2763.27	−	1787.26i	−0.192328	−	0.124396i
$592$	−2397.40	−	4152.42i	−0.166440	−	0.288283i
$593$	−7523.76	+	13031.5i	−0.521018	+	0.902430i	0.478683	+	0.877988i	$0.341114\pi$
$593$	−7523.76	+	13031.5i	−0.521018	+	0.902430i	−0.999701	+	0.0244425i	$0.992219\pi$
$594$	−6496.54	−	992.170i	−0.448748	−	0.0685340i
$595$		0			0
$596$		−	10816.1i		−	0.743363i
$597$	−898.161	+	17764.2i	−0.0615734	+	1.21782i
$598$	−1274.09	+	735.597i	−0.0871262	+	0.0503023i
$599$	5292.70	−	3055.74i	0.361025	−	0.208438i	−0.308505	−	0.951223i	$-0.599829\pi$
$599$	5292.70	−	3055.74i	0.361025	−	0.208438i	0.669530	+	0.742785i	$0.266495\pi$
$600$	−220.054	+	4352.30i	−0.0149727	+	0.296137i
$601$			7494.08i			0.508636i	0.967121	+	0.254318i	$0.0818509\pi$
$601$			7494.08i			0.508636i	−0.967121	+	0.254318i	$0.918149\pi$
$602$		0			0
$603$	1622.84	−	2251.04i	0.109597	−	0.152022i
$604$	3081.41	−	5337.15i	0.207584	−	0.359546i
$605$	−1756.84	−	3042.93i	−0.118059	−	0.204484i
$606$	−8595.82	−	5559.70i	−0.576207	−	0.372686i
$607$	−17917.1	−	10344.5i	−1.19808	−	0.691711i	−0.237953	−	0.971277i	$-0.576476\pi$
$607$	−17917.1	−	10344.5i	−1.19808	−	0.691711i	−0.960127	+	0.279565i	$0.909810\pi$
$608$	−296.539			−0.0197800
$609$		0			0
$610$	5639.19			0.374302
$611$	−412.361	−	238.077i	−0.0273033	−	0.0157636i
$612$	−12473.1	−	1264.52i	−0.823848	−	0.0835215i
$613$	11645.5	+	20170.6i	0.767305	+	1.32901i	0.939019	+	0.343865i	$0.111736\pi$
$613$	11645.5	+	20170.6i	0.767305	+	1.32901i	−0.171714	+	0.985147i	$0.554931\pi$
$614$	644.894	−	1116.99i	0.0423873	−	0.0734169i
$615$	−5404.99	−	10559.7i	−0.354391	−	0.692374i
$616$		0			0
$617$		−	11640.9i		−	0.759554i	−0.925078	−	0.379777i	$-0.876001\pi$
$617$		−	11640.9i		−	0.759554i	0.925078	−	0.379777i	$-0.123999\pi$
$618$	13337.4	+	674.343i	0.868138	+	0.0438933i
$619$	13978.4	−	8070.44i	0.907657	−	0.524036i	0.0279803	−	0.999608i	$-0.491092\pi$
$619$	13978.4	−	8070.44i	0.907657	−	0.524036i	0.879676	+	0.475573i	$0.157759\pi$
$620$	2205.18	−	1273.16i	0.142842	−	0.0824699i
$621$	13622.3	+	10907.0i	0.880266	+	0.704805i
$622$			2673.68i			0.172355i
$623$		0			0
$624$	−437.667	+	224.019i	−0.0280781	+	0.0143717i
$625$	−4234.68	+	7334.68i	−0.271019	+	0.469420i
$626$	−1685.48	−	2919.33i	−0.107612	−	0.186390i
$627$	612.493	−	946.972i	0.0390121	−	0.0603165i
$628$	−1909.99	−	1102.73i	−0.121365	−	0.0700699i
$629$	34787.4			2.20519
$630$		0			0
$631$	9424.67			0.594596			0.297298	−	0.954785i	$-0.403914\pi$
$631$	9424.67			0.594596			0.297298	+	0.954785i	$0.403914\pi$
$632$	−7394.25	−	4269.07i	−0.465392	−	0.268694i
$633$	−2888.74	+	4466.26i	−0.181385	+	0.280439i
$634$	−3013.71	−	5219.90i	−0.188785	−	0.326985i
$635$	3490.34	−	6045.45i	0.218126	−	0.377805i
$636$	−5526.81	+	2828.89i	−0.344579	+	0.176372i
$637$		0			0
$638$			9734.27i			0.604049i
$639$	−1156.85	+	520.179i	−0.0716185	+	0.0322034i
$640$	−497.797	+	287.403i	−0.0307456	+	0.0177510i
$641$	1459.54	−	842.666i	0.0899351	−	0.0519241i	−0.454358	−	0.890819i	$-0.650131\pi$
$641$	1459.54	−	842.666i	0.0899351	−	0.0519241i	0.544293	+	0.838895i	$0.316798\pi$
$642$	1898.48	+	95.9879i	0.116709	+	0.00590084i
$643$			10186.5i			0.624752i	0.949958	+	0.312376i	$0.101125\pi$
$643$			10186.5i			0.624752i	−0.949958	+	0.312376i	$0.898875\pi$
$644$		0			0
$645$	−4158.39	−	8124.26i	−0.253855	−	0.495957i
$646$	1075.73	−	1863.22i	0.0655171	−	0.113479i
$647$	163.793	+	283.698i	0.00995266	+	0.0172385i	0.870959	−	0.491356i	$-0.163499\pi$
$647$	163.793	+	283.698i	0.00995266	+	0.0172385i	−0.861006	+	0.508594i	$0.830165\pi$
$648$	4362.66	+	3870.32i	0.264478	+	0.234630i
$649$	−4149.04	−	2395.45i	−0.250946	−	0.144884i
$650$	−1239.94			−0.0748223
$651$		0			0
$652$	9246.55			0.555403
$653$	−1769.92	−	1021.87i	−0.106068	−	0.0612384i	0.446028	−	0.895019i	$-0.352838\pi$
$653$	−1769.92	−	1021.87i	−0.106068	−	0.0612384i	−0.552096	+	0.833781i	$0.686172\pi$
$654$	5086.83	+	3290.12i	0.304145	+	0.196718i
$655$	4703.82	+	8147.25i	0.280600	+	0.486014i
$656$	−4067.03	+	7044.31i	−0.242059	+	0.419259i
$657$	−5770.73	−	4160.28i	−0.342675	−	0.247044i
$658$		0			0
$659$		−	27567.4i		−	1.62955i	−0.579778	−	0.814774i	$-0.696861\pi$
$659$		−	27567.4i		−	1.62955i	0.579778	−	0.814774i	$-0.303139\pi$
$660$	110.388	−	2183.29i	0.00651037	−	0.128765i
$661$	−18417.0	+	10633.0i	−1.08372	+	0.625684i	−0.931897	−	0.362724i	$-0.881847\pi$
$661$	−18417.0	+	10633.0i	−1.08372	+	0.625684i	−0.151820	+	0.988408i	$0.548513\pi$
$662$	−1366.45	+	788.920i	−0.0802244	+	0.0463176i
$663$	180.127	−	3562.61i	0.0105513	−	0.208688i
$664$		−	2163.49i		−	0.126445i
$665$		0			0
$666$	−13126.9	−	9463.50i	−0.763747	−	0.550606i
$667$	12924.1	−	22385.2i	0.750260	−	1.29949i
$668$	5161.73	+	8940.38i	0.298972	+	0.517835i
$669$	6637.64	+	4293.16i	0.383596	+	0.248107i
$670$	799.422	+	461.547i	0.0460961	+	0.0266136i
$671$	14705.8			0.846065
$672$		0			0
$673$	−9377.40			−0.537106			−0.268553	−	0.963265i	$-0.586545\pi$
$673$	−9377.40			−0.537106			−0.268553	+	0.963265i	$0.586545\pi$
$674$	−3301.56	−	1906.16i	−0.188682	−	0.108935i
$675$	5346.62	+	13701.5i	0.304876	+	0.781293i
$676$	4324.05	+	7489.48i	0.246020	+	0.426120i
$677$	5342.31	−	9253.15i	0.303282	−	0.525299i	−0.673596	−	0.739100i	$-0.735251\pi$
$677$	5342.31	−	9253.15i	0.303282	−	0.525299i	0.976877	+	0.213801i	$0.0685844\pi$
$678$	10814.6	+	21128.5i	0.612585	+	1.19681i
$679$		0			0
$680$		−	4170.35i		−	0.235185i
$681$	7572.30	+	382.857i	0.426096	+	0.0215435i
$682$	5750.62	−	3320.12i	0.322878	−	0.186414i
$683$	24985.9	−	14425.6i	1.39979	−	0.808172i	0.405424	−	0.914129i	$-0.367124\pi$
$683$	24985.9	−	14425.6i	1.39979	−	0.808172i	0.994371	+	0.105957i	$0.0337906\pi$
$684$	−912.788	+	410.437i	−0.0510253	+	0.0229436i
$685$			2743.08i			0.153004i
$686$		0			0
$687$	22176.8	−	11351.2i	1.23158	−	0.630384i
$688$	−3129.02	+	5419.61i	−0.173390	+	0.300321i
$689$	−883.284	−	1529.89i	−0.0488395	−	0.0845926i
$690$	−3152.59	+	4874.21i	−0.173938	+	0.268924i
$691$	1139.99	+	658.171i	0.0627599	+	0.0362344i	0.531052	−	0.847339i	$-0.321797\pi$
$691$	1139.99	+	658.171i	0.0627599	+	0.0362344i	−0.468292	+	0.883574i	$0.655130\pi$
$692$	4008.40			0.220197
$693$		0			0
$694$	10482.3			0.573348
$695$	7025.98	+	4056.45i	0.383469	+	0.221396i
$696$	4691.44	−	7253.41i	0.255501	−	0.395028i
$697$	−29507.3	−	51108.1i	−1.60354	−	2.77741i
$698$	4502.54	−	7798.62i	0.244160	−	0.422897i
$699$	−7721.80	+	3952.39i	−0.417833	+	0.213867i
$700$		0			0
$701$			12811.2i			0.690259i	0.938555	+	0.345129i	$0.112165\pi$
$701$			12811.2i			0.690259i	−0.938555	+	0.345129i	$0.887835\pi$
$702$	−1037.14	+	1295.33i	−0.0557609	+	0.0696427i
$703$	2404.99	−	1388.52i	0.129027	−	0.0744938i
$704$	−1298.15	+	749.485i	−0.0694968	+	0.0401240i
$705$	−1876.36	−	94.8693i	−0.100238	−	0.00506807i
$706$		−	19198.8i		−	1.02345i
$707$		0			0
$708$	1937.13	+	3784.58i	0.102828	+	0.200895i
$709$	−16482.9	+	28549.2i	−0.873101	+	1.51226i	−0.0143290	+	0.999897i	$0.504561\pi$
$709$	−16482.9	+	28549.2i	−0.873101	+	1.51226i	−0.858772	+	0.512358i	$0.828772\pi$
$710$	−210.965	−	365.402i	−0.0111512	−	0.0193145i
$711$	−28669.3	−	2906.48i	−1.51221	−	0.153308i
$712$	6148.99	+	3550.12i	0.323656	+	0.186863i
$713$	−17632.4			−0.926141
$714$		0			0
$715$	622.006			0.0325339
$716$	10393.4	+	6000.66i	0.542488	+	0.313206i
$717$	15398.4	+	9959.52i	0.802039	+	0.518752i
$718$	10165.9	+	17607.9i	0.528396	+	0.915210i
$719$	4307.48	−	7460.77i	0.223424	−	0.386982i	−0.732421	−	0.680851i	$-0.761610\pi$
$719$	4307.48	−	7460.77i	0.223424	−	0.386982i	0.955845	+	0.293870i	$0.0949432\pi$
$720$	−1134.50	+	1573.66i	−0.0587224	+	0.0814541i
$721$		0			0
$722$			13546.3i			0.698254i
$723$	−1293.44	+	25582.2i	−0.0665335	+	1.31592i
$724$	3352.73	−	1935.70i	0.172104	−	0.0993643i
$725$	18866.5	−	10892.6i	0.966463	−	0.557988i
$726$	−410.598	+	8120.96i	−0.0209900	+	0.415147i
$727$			26635.3i			1.35880i	0.733768	+	0.679400i	$0.237760\pi$
$727$			26635.3i			1.35880i	−0.733768	+	0.679400i	$0.762240\pi$
$728$		0			0
$729$	18785.7	+	5875.05i	0.954415	+	0.298484i
$730$	1183.21	−	2049.38i	0.0599900	−	0.103906i
$731$	−22701.7	−	39320.5i	−1.14864	−	1.98950i
$732$	−10957.9	−	7087.46i	−0.553299	−	0.357869i
$733$	5328.35	+	3076.33i	0.268496	+	0.155016i	0.628204	−	0.778049i	$-0.283790\pi$
$733$	5328.35	+	3076.33i	0.268496	+	0.155016i	−0.359708	+	0.933065i	$0.617124\pi$
$734$	767.978			0.0386193
$735$		0			0
$736$	3980.34			0.199344
$737$	2084.72	+	1203.61i	0.104195	+	0.0601569i
$738$	−2768.93	+	27312.5i	−0.138111	+	1.36231i
$739$	−7364.30	−	12755.3i	−0.366577	−	0.634929i	0.622451	−	0.782659i	$-0.286137\pi$
$739$	−7364.30	−	12755.3i	−0.366577	−	0.634929i	−0.989028	+	0.147729i	$0.952804\pi$
$740$	2691.49	−	4661.80i	0.133704	−	0.231582i
$741$	−129.747	−	253.487i	−0.00643236	−	0.0125669i
$742$		0			0
$743$			27255.1i			1.34575i	0.739755	+	0.672876i	$0.234941\pi$
$743$			27255.1i			1.34575i	−0.739755	+	0.672876i	$0.765059\pi$
$744$	−5885.17	−	297.556i	−0.290001	−	0.0146625i
$745$	10516.1	−	6071.45i	0.517152	−	0.298578i
$746$	−5133.08	+	2963.59i	−0.251924	+	0.145449i
$747$	−2994.47	−	6659.52i	−0.146669	−	0.326184i
$748$		−	10875.4i		−	0.531608i
$749$		0			0
$750$	−9547.94	+	4887.10i	−0.464855	+	0.237936i
$751$	3075.69	−	5327.25i	0.149445	−	0.258847i	−0.781577	−	0.623809i	$-0.785585\pi$
$751$	3075.69	−	5327.25i	0.149445	−	0.258847i	0.931023	+	0.364961i	$0.118918\pi$
$752$	644.121	+	1115.65i	0.0312349	+	0.0541005i
$753$	−3654.44	+	5650.11i	−0.176859	+	0.273441i
$754$	2128.58	+	1228.94i	0.102810	+	0.0593571i
$755$	6918.80			0.333511
$756$		0			0
$757$	−21107.3			−1.01342			−0.506710	−	0.862117i	$-0.669139\pi$
$757$	−21107.3			−1.01342			−0.506710	+	0.862117i	$0.669139\pi$
$758$	22855.0	+	13195.4i	1.09516	+	0.632292i
$759$	−8221.27	+	12710.9i	−0.393166	+	0.607873i
$760$	−166.458	−	288.313i	−0.00794481	−	0.0137608i
$761$	7530.97	−	13044.0i	0.358735	−	0.621348i	−0.629015	−	0.777393i	$-0.716541\pi$
$761$	7530.97	−	13044.0i	0.358735	−	0.621348i	0.987750	+	0.156046i	$0.0498748\pi$
$762$	−14380.4	+	7360.58i	−0.683657	+	0.349929i
$763$		0			0
$764$			1645.28i			0.0779113i
$765$	−5772.14	−	12836.9i	−0.272800	−	0.606692i
$766$	15505.1	−	8951.90i	0.731362	−	0.422252i
$767$	−1047.62	+	604.845i	−0.0493187	+	0.0284742i
$768$	1328.52	+	67.1702i	0.0624203	+	0.00315599i
$769$		−	26099.2i		−	1.22387i	−0.790906	−	0.611937i	$-0.790390\pi$
$769$		−	26099.2i		−	1.22387i	0.790906	−	0.611937i	$-0.209610\pi$
$770$		0			0
$771$	3447.31	+	6735.03i	0.161027	+	0.314599i
$772$	1632.85	−	2828.17i	0.0761236	−	0.131850i
$773$	−8.84542	−	15.3207i	−0.000411575	−	0.000712869i	0.865820	−	0.500356i	$-0.166798\pi$
$773$	−8.84542	−	15.3207i	−0.000411575	−	0.000712869i	−0.866231	+	0.499644i	$0.833464\pi$
$774$	−2130.31	+	21013.1i	−0.0989306	+	0.975842i
$775$	−12869.8	−	7430.41i	−0.596514	−	0.344398i
$776$	−1756.51			−0.0812566
$777$		0			0
$778$	17539.3			0.808244
$779$	−4079.91	−	2355.54i	−0.187648	−	0.108339i
$780$	−463.483	−	299.776i	−0.0212761	−	0.0137612i
$781$	−550.151	−	952.889i	−0.0252061	−	0.0436582i
$782$	−14439.1	+	25009.3i	−0.660285	+	1.14365i
$783$	4401.53	−	28820.4i	0.200891	−	1.31540i
$784$		0			0
$785$		−	2476.01i		−	0.112577i
$786$	1099.35	−	21743.3i	0.0498886	−	0.986716i
$787$	−2066.21	+	1192.93i	−0.0935865	+	0.0540322i	−0.546063	−	0.837744i	$-0.683874\pi$
$787$	−2066.21	+	1192.93i	−0.0935865	+	0.0540322i	0.452476	+	0.891776i	$0.350541\pi$
$788$	−2193.92	+	1266.66i	−0.0991819	+	0.0572627i
$789$	−560.596	+	11087.7i	−0.0252950	+	0.500293i
$790$		−	9585.51i		−	0.431693i
$791$		0			0
$792$	−2958.52	+	4103.77i	−0.132735	+	0.184117i
$793$	1856.58	−	3215.70i	0.0831390	−	0.144001i
$794$	−1370.98	−	2374.61i	−0.0612774	−	0.106136i
$795$	−5852.81	−	3785.54i	−0.261104	−	0.168880i
$796$	11857.9	+	6846.17i	0.528005	+	0.304844i
$797$	−13183.5			−0.585927			−0.292964	−	0.956124i	$-0.594641\pi$
$797$	−13183.5			−0.585927			−0.292964	+	0.956124i	$0.594641\pi$
$798$		0			0
$799$	−9346.49			−0.413836
$800$	2905.24	+	1677.34i	0.128395	+	0.0741287i
$801$	23841.1	+	2417.01i	1.05167	+	0.106618i
$802$	2762.20	+	4784.28i	0.121617	+	0.210647i
$803$	3085.56	−	5344.35i	0.135600	−	0.234867i
$804$	−973.329	−	1901.59i	−0.0426948	−	0.0834130i
$805$		0			0
$806$		−	1676.64i		−	0.0732721i
$807$	−14984.5	−	757.621i	−0.653630	−	0.0330477i
$808$	−6824.74	+	3940.27i	−0.297146	+	0.171557i
$809$	26645.9	−	15384.0i	1.15800	−	0.668570i	0.207174	−	0.978304i	$-0.433574\pi$
$809$	26645.9	−	15384.0i	1.15800	−	0.668570i	0.950823	+	0.309734i	$0.100240\pi$
$810$	−1314.04	+	6414.19i	−0.0570009	+	0.278237i
$811$			42776.4i			1.85214i	0.377357	+	0.926068i	$0.376833\pi$
$811$			42776.4i			1.85214i	−0.377357	+	0.926068i	$0.623167\pi$
$812$		0			0
$813$	−27094.5	+	13868.3i	−1.16881	+	0.598256i
$814$	7018.82	−	12156.9i	0.302223	−	0.523465i
$815$	5190.41	+	8990.05i	0.223082	+	0.386390i
$816$	−5241.40	+	8103.69i	−0.224860	+	0.347654i
$817$	−3138.92	−	1812.26i	−0.134415	−	0.0776045i
$818$	5334.75			0.228026
$819$		0			0
$820$	−9131.86			−0.388901
$821$	−36141.5	−	20866.3i	−1.53635	−	0.887014i	−0.999048	−	0.0436263i	$-0.986109\pi$
$821$	−36141.5	−	20866.3i	−1.53635	−	0.887014i	−0.537305	−	0.843388i	$-0.680558\pi$
$822$	3447.57	−	5330.27i	0.146287	−	0.226173i
$823$	7822.35	+	13548.7i	0.331312	+	0.573850i	0.982769	−	0.184836i	$-0.0591753\pi$
$823$	7822.35	+	13548.7i	0.331312	+	0.573850i	−0.651457	+	0.758685i	$0.725842\pi$
$824$	5140.13	−	8902.96i	0.217312	−	0.376395i
$825$	−11357.1	+	5813.13i	−0.479278	+	0.245318i
$826$		0			0
$827$			24395.1i			1.02576i	0.858461	+	0.512879i	$0.171421\pi$
$827$			24395.1i			1.02576i	−0.858461	+	0.512879i	$0.828579\pi$
$828$	12252.0	−	5509.15i	0.514236	−	0.231227i
$829$	−32786.9	+	18929.5i	−1.37362	+	0.793062i	−0.991382	−	0.131000i	$-0.958181\pi$
$829$	−32786.9	+	18929.5i	−1.37362	+	0.793062i	−0.382242	+	0.924062i	$0.624848\pi$
$830$	2103.48	−	1214.44i	0.0879671	−	0.0507878i
$831$	−14546.4	−	735.470i	−0.607231	−	0.0307018i
$832$			378.486i			0.0157712i
$833$		0			0
$834$	−8554.42	−	16712.8i	−0.355174	−	0.693905i
$835$	−5794.92	+	10037.1i	−0.240169	+	0.415986i
$836$	−434.085	−	751.858i	−0.0179583	−	0.0311047i
$837$	−18527.2	+	7229.68i	−0.765105	+	0.298559i
$838$	25081.1	+	14480.6i	1.03390	+	0.596925i
$839$	−40533.9			−1.66792			−0.833960	−	0.551826i	$-0.813931\pi$
$839$	−40533.9			−1.66792			−0.833960	+	0.551826i	$0.813931\pi$
$840$		0			0
$841$	−18794.8			−0.770625
$842$	−24679.6	−	14248.8i	−1.01011	−	0.583188i
$843$	20356.0	+	13166.1i	0.831670	+	0.537917i
$844$	2047.30	+	3546.03i	0.0834965	+	0.144620i
$845$	−4854.48	+	8408.21i	−0.197632	+	0.342309i
$846$	3526.85	+	2542.60i	0.143328	+	0.103329i
$847$		0			0
$848$			4779.48i			0.193547i
$849$	1410.20	−	27891.6i	0.0570060	−	1.12749i
$850$	−21078.2	+	12169.5i	−0.850560	+	0.491071i
$851$	−32281.4	+	18637.6i	−1.30034	+	0.750752i
$852$	−49.3055	+	975.183i	−0.00198261	+	0.0392127i
$853$		−	38466.5i		−	1.54404i	−0.635598	−	0.772021i	$-0.719246\pi$
$853$		−	38466.5i		−	1.54404i	0.635598	−	0.772021i	$-0.280754\pi$
$854$		0			0
$855$	−911.431	−	657.075i	−0.0364565	−	0.0262824i
$856$	731.660	−	1267.27i	0.0292145	−	0.0506010i
$857$	−13054.1	−	22610.3i	−0.520326	−	0.901230i	−0.999721	−	0.0236312i	$-0.992477\pi$
$857$	−13054.1	−	22610.3i	−0.520326	−	0.901230i	0.479395	−	0.877599i	$-0.340856\pi$
$858$	−1208.66	−	781.751i	−0.0480921	−	0.0311055i
$859$	−21033.3	−	12143.6i	−0.835445	−	0.482345i	0.0202681	−	0.999795i	$-0.493548\pi$
$859$	−21033.3	−	12143.6i	−0.835445	−	0.482345i	−0.855713	+	0.517450i	$0.826881\pi$
$860$	−7025.70			−0.278575
$861$		0			0
$862$	11146.3			0.440423
$863$	−32475.9	−	18750.0i	−1.28099	−	0.739579i	−0.303960	−	0.952685i	$-0.598309\pi$
$863$	−32475.9	−	18750.0i	−1.28099	−	0.739579i	−0.977029	+	0.213106i	$0.931642\pi$
$864$	4182.33	−	1632.03i	0.164683	−	0.0642624i
$865$	2250.06	+	3897.21i	0.0884441	+	0.153190i
$866$	2939.93	−	5092.11i	0.115361	−	0.199812i
$867$	−20271.8	−	39605.1i	−0.794079	−	1.55139i
$868$		0			0
$869$		−	24996.9i		−	0.975791i
$870$	9685.67	+	489.710i	0.377442	+	0.0190836i
$871$	526.386	−	303.909i	0.0204775	−	0.0118227i
$872$	4038.74	−	2331.77i	0.156845	−	0.0905546i
$873$	−5406.79	+	2431.17i	−0.209613	+	0.0942528i
$874$			2305.33i			0.0892206i
$875$		0			0
$876$	−4874.89	+	2495.21i	−0.188022	+	0.0962389i
$877$	7420.70	−	12853.0i	0.285723	−	0.494887i	−0.687061	−	0.726600i	$-0.741100\pi$
$877$	7420.70	−	12853.0i	0.285723	−	0.494887i	0.972784	+	0.231713i	$0.0744329\pi$
$878$	−9573.31	−	16581.5i	−0.367977	−	0.637355i
$879$	3674.61	−	5681.30i	0.141003	−	0.218004i
$880$	−1457.39	−	841.424i	−0.0558279	−	0.0322323i
$881$	30469.3			1.16520			0.582598	−	0.812760i	$-0.302036\pi$
$881$	30469.3			1.16520			0.582598	+	0.812760i	$0.302036\pi$
$882$		0			0
$883$	−6758.53			−0.257580			−0.128790	−	0.991672i	$-0.541109\pi$
$883$	−6758.53			−0.257580			−0.128790	+	0.991672i	$0.541109\pi$
$884$	−2378.11	−	1373.00i	−0.0904801	−	0.0522387i
$885$	−2592.22	+	4007.82i	−0.0984593	+	0.152227i
$886$	−7156.17	−	12394.8i	−0.271350	−	0.469992i
$887$	17666.5	−	30599.4i	0.668754	−	1.15832i	−0.309499	−	0.950900i	$-0.600161\pi$
$887$	17666.5	−	30599.4i	0.668754	−	1.15832i	0.978253	−	0.207416i	$-0.0665053\pi$
$888$	−11089.1	+	5675.92i	−0.419059	+	0.214495i
$889$		0			0
$890$			7971.22i			0.300220i
$891$	−3426.74	+	16726.8i	−0.128844	+	0.628922i
$892$	5270.02	−	3042.65i	0.197818	−	0.114210i
$893$	−646.160	+	373.061i	−0.0242138	+	0.0139798i
$894$	−28065.2	−	1418.98i	−1.04993	−	0.0530849i
$895$			13473.5i			0.503207i
$896$		0			0
$897$	1741.55	+	3402.47i	0.0648257	+	0.126650i
$898$	14839.2	−	25702.3i	0.551439	−	0.955120i
$899$	14728.9	+	25511.3i	0.546427	+	0.946439i
$900$	11264.3	+	1141.97i	0.417197	+	0.0422953i
$901$	−30030.5	−	17338.1i	−1.11039	−	0.641084i
$902$	−23813.9			−0.879065
$903$		0			0
$904$	18271.5			0.672237
$905$	3764.01	+	2173.15i	0.138254	+	0.0798210i
$906$	−13444.4	−	8695.71i	−0.493002	−	0.318869i
$907$	10481.2	+	18153.9i	0.383706	+	0.664598i	0.991589	−	0.129429i	$-0.0413144\pi$
$907$	10481.2	+	18153.9i	0.383706	+	0.664598i	−0.607883	+	0.794027i	$0.707981\pi$
$908$	2918.30	−	5054.65i	0.106660	−	0.184740i
$909$	−15553.8	+	21574.7i	−0.567533	+	0.787226i
$910$		0			0
$911$		−	5419.65i		−	0.197103i	−0.995132	−	0.0985516i	$-0.968579\pi$
$911$		−	5419.65i		−	0.197103i	0.995132	−	0.0985516i	$-0.0314209\pi$
$912$	−38.9035	+	769.449i	−0.00141253	+	0.0279375i
$913$	5485.41	−	3167.00i	0.198840	−	0.114800i
$914$	−13120.0	+	7574.83i	−0.474804	+	0.274128i
$915$	739.815	−	14632.3i	0.0267296	−	0.528667i
$916$		−	19178.1i		−	0.691770i
$917$		0			0
$918$	−4917.50	+	32198.8i	−0.176799	+	1.15765i
$919$	−12706.3	+	22007.9i	−0.456084	+	0.789961i	−0.998750	−	0.0499878i	$-0.984082\pi$
$919$	−12706.3	+	22007.9i	−0.456084	+	0.789961i	0.542666	+	0.839949i	$0.317415\pi$
$920$	2234.30	+	3869.93i	0.0800682	+	0.138682i
$921$	−2813.71	−	1819.89i	−0.100668	−	0.0651110i
$922$	25721.8	+	14850.5i	0.918767	+	0.530450i
$923$	−277.823			−0.00990754
$924$		0			0
$925$	−31416.1			−1.11671
$926$	−5822.17	−	3361.43i	−0.206618	−	0.119291i
$927$	3499.52	−	34518.9i	0.123991	−	1.22303i
$928$	−3324.91	−	5758.92i	−0.117614	−	0.203713i
$929$	−276.744	+	479.335i	−0.00977360	+	0.0169284i	−0.870871	−	0.491512i	$-0.836444\pi$
$929$	−276.744	+	479.335i	−0.00977360	+	0.0169284i	0.861097	+	0.508440i	$0.169778\pi$
$930$	−3014.25	−	5888.94i	−0.106281	−	0.207641i
$931$		0			0
$932$			6677.66i			0.234693i
$933$	6937.57	+	350.765i	0.243436	+	0.0123082i
$934$	−399.835	+	230.845i	−0.0140075	+	0.00808723i
$935$	10573.7	−	6104.72i	0.369836	−	0.213525i
$936$	523.858	+	1165.03i	0.0182936	+	0.0406840i
$937$		−	18956.6i		−	0.660923i	−0.943819	−	0.330462i	$-0.892796\pi$
$937$		−	18956.6i		−	0.660923i	0.943819	−	0.330462i	$-0.107204\pi$
$938$		0			0
$939$	−7796.09	+	3990.42i	−0.270943	+	0.138682i
$940$	−723.134	+	1252.51i	−0.0250915	+	0.0434598i
$941$	−16542.7	−	28652.8i	−0.573089	−	0.992619i	−0.996246	−	0.0865632i	$-0.972412\pi$
$941$	−16542.7	−	28652.8i	−0.573089	−	0.992619i	0.423157	−	0.906056i	$-0.360922\pi$
$942$	−3111.91	+	4811.30i	−0.107634	+	0.166413i
$943$	54763.2	+	31617.5i	1.89113	+	1.09184i
$944$	3272.83			0.112841
$945$		0			0
$946$	−18321.5			−0.629686
$947$	−11619.3	−	6708.40i	−0.398708	−	0.230194i	0.287219	−	0.957865i	$-0.407269\pi$
$947$	−11619.3	−	6708.40i	−0.398708	−	0.230194i	−0.685926	+	0.727671i	$0.740603\pi$
$948$	−12047.3	+	18626.2i	−0.412740	+	0.638135i
$949$	−779.096	−	1349.43i	−0.0266497	−	0.0461586i
$950$	−971.480	+	1682.65i	−0.0331779	+	0.0574657i
$951$	−13939.8	+	7135.05i	−0.475319	+	0.243291i
$952$		0			0
$953$			36353.5i			1.23568i	0.786303	+	0.617841i	$0.211993\pi$
$953$			36353.5i			1.23568i	−0.786303	+	0.617841i	$0.788007\pi$
$954$	6615.23	+	14711.9i	0.224503	+	0.499282i
$955$	−1599.64	+	923.554i	−0.0542023	+	0.0312937i
$956$	12225.7	−	7058.50i	0.413605	−	0.238795i
$957$	25258.1	+	1277.06i	0.853165	+	0.0431362i
$958$		−	8801.72i		−	0.296838i
$959$		0			0
$960$	680.436	+	1329.37i	0.0228760	+	0.0446929i
$961$	−4848.13	+	8397.21i	−0.162738	+	0.281871i
$962$	−1772.23	−	3069.60i	−0.0593961	−	0.102877i
$963$	498.131	−	4913.52i	0.0166688	−	0.164419i
$964$	17076.6	+	9859.18i	0.570540	+	0.329401i
$965$	3666.29			0.122303
$966$		0			0
$967$	3453.28			0.114840			0.0574198	−	0.998350i	$-0.481713\pi$
$967$	3453.28			0.114840			0.0574198	+	0.998350i	$0.481713\pi$
$968$	5420.89	+	3129.75i	0.179994	+	0.103919i
$969$	−4693.48	−	3035.70i	−0.155600	−	0.100641i
$970$	−985.992	−	1707.79i	−0.0326374	−	0.0565296i
$971$	−25320.0	+	43855.6i	−0.836826	+	1.44943i	0.0557091	+	0.998447i	$0.482258\pi$
$971$	−25320.0	+	43855.6i	−0.836826	+	1.44943i	−0.892535	+	0.450978i	$0.851075\pi$
$972$	10614.9	−	10812.3i	0.350281	−	0.356796i
$973$		0			0
$974$		−	23889.2i		−	0.785894i
$975$	−162.670	+	3217.35i	−0.00534320	+	0.105680i
$976$	−8700.12	+	5023.02i	−0.285332	+	0.164737i
$977$	−26914.6	+	15539.1i	−0.881344	+	0.508844i	−0.871101	−	0.491103i	$-0.836594\pi$
$977$	−26914.6	+	15539.1i	−0.881344	+	0.508844i	−0.0102426	+	0.999948i	$0.503260\pi$
$978$	1213.07	−	23992.6i	0.0396623	−	0.784456i
$979$			20787.2i			0.678613i
$980$		0			0
$981$	9204.42	−	12767.5i	0.299566	−	0.415529i
$982$	−19916.7	+	34496.7i	−0.647216	+	1.12101i
$983$	20154.8	+	34909.1i	0.653956	+	1.13268i	0.982155	+	0.188076i	$0.0602251\pi$
$983$	20154.8	+	34909.1i	0.653956	+	1.13268i	−0.328199	+	0.944609i	$0.606442\pi$
$984$	17744.7	+	11477.1i	0.574880	+	0.371827i
$985$	−2463.05	−	1422.04i	−0.0796744	−	0.0460001i
$986$	48246.0			1.55828
$987$		0			0
$988$	−219.211			−0.00705873
$989$	42132.6	+	24325.3i	1.35464	+	0.782102i
$990$	−5650.65	−	572.861i	−0.181403	−	0.0183906i
$991$	−2007.28	−	3476.71i	−0.0643425	−	0.111444i	0.832060	−	0.554686i	$-0.187162\pi$
$991$	−2007.28	−	3476.71i	−0.0643425	−	0.111444i	−0.896402	+	0.443242i	$0.853828\pi$
$992$	−2268.09	+	3928.46i	−0.0725928	+	0.125734i
$993$	1867.79	+	3649.11i	0.0596904	+	0.116617i
$994$		0			0
$995$			15372.0i			0.489773i
$996$	−5613.74	−	283.832i	−0.178593	−	0.00902970i
$997$	−36113.8	+	20850.3i	−1.14718	+	0.662323i	−0.948198	−	0.317680i	$-0.897096\pi$
$997$	−36113.8	+	20850.3i	−1.14718	+	0.662323i	−0.198980	+	0.980004i	$0.563763\pi$
$998$	2305.60	−	1331.14i	0.0731287	−	0.0422209i
$999$	−26277.7	+	32819.5i	−0.832221	+	1.03940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.4.f.a.215.2		16
3.2	odd	2	inner	294.4.f.a.215.5		16
7.2	even	3		294.4.d.a.293.11		16
7.3	odd	6	inner	294.4.f.a.227.5		16
7.4	even	3		42.4.f.a.17.8	yes	16
7.5	odd	6		294.4.d.a.293.14		16
7.6	odd	2		42.4.f.a.5.3	✓	16
21.2	odd	6		294.4.d.a.293.6		16
21.5	even	6		294.4.d.a.293.3		16
21.11	odd	6		42.4.f.a.17.3	yes	16
21.17	even	6	inner	294.4.f.a.227.2		16
21.20	even	2		42.4.f.a.5.8	yes	16
28.11	odd	6		336.4.bc.e.17.1		16
28.27	even	2		336.4.bc.e.257.3		16
84.11	even	6		336.4.bc.e.17.3		16
84.83	odd	2		336.4.bc.e.257.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.f.a.5.3	✓	16	7.6	odd	2
42.4.f.a.5.8	yes	16	21.20	even	2
42.4.f.a.17.3	yes	16	21.11	odd	6
42.4.f.a.17.8	yes	16	7.4	even	3
294.4.d.a.293.3		16	21.5	even	6
294.4.d.a.293.6		16	21.2	odd	6
294.4.d.a.293.11		16	7.2	even	3
294.4.d.a.293.14		16	7.5	odd	6
294.4.f.a.215.2		16	1.1	even	1	trivial
294.4.f.a.215.5		16	3.2	odd	2	inner
294.4.f.a.227.2		16	21.17	even	6	inner
294.4.f.a.227.5		16	7.3	odd	6	inner
336.4.bc.e.17.1		16	28.11	odd	6
336.4.bc.e.17.3		16	84.11	even	6
336.4.bc.e.257.1		16	84.83	odd	2
336.4.bc.e.257.3		16	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	294.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 - 1.00000i) q^{2} +(-2.82199 + 4.36307i) q^{3} +(2.00000 + 3.46410i) q^{4} +(-2.24534 + 3.88904i) q^{5} +(9.25090 - 4.73506i) q^{6} -8.00000i q^{8} +(-11.0727 - 24.6251i) q^{9} +(7.77808 - 4.49068i) q^{10} +(20.2835 - 11.7107i) q^{11} +(-20.7581 - 1.04953i) q^{12} -5.91384i q^{13} +(-10.6318 - 20.7714i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-58.0418 - 100.531i) q^{17} +(-5.44659 + 53.7246i) q^{18} +(-8.02533 - 4.63343i) q^{19} -17.9627 q^{20} -46.8428 q^{22} +(107.721 + 62.1928i) q^{23} +(34.9045 + 22.5759i) q^{24} +(52.4169 + 90.7888i) q^{25} +(-5.91384 + 10.2431i) q^{26} +(138.688 + 21.1808i) q^{27} -207.807i q^{29} +(-2.35656 + 46.6089i) q^{30} +(-122.764 + 70.8780i) q^{31} +(27.7128 - 16.0000i) q^{32} +(-6.14540 + 121.546i) q^{33} +232.167i q^{34} +(63.1584 - 87.6072i) q^{36} +(-149.838 + 259.526i) q^{37} +(9.26685 + 16.0507i) q^{38} +(25.8025 + 16.6888i) q^{39} +(31.1123 + 17.9627i) q^{40} +508.379 q^{41} +391.127 q^{43} +(81.1341 + 46.8428i) q^{44} +(120.630 + 12.2294i) q^{45} +(-124.386 - 215.442i) q^{46} +(40.2575 - 69.7281i) q^{47} +(-37.8805 - 74.0072i) q^{48} -209.668i q^{50} +(602.419 + 30.4585i) q^{51} +(20.4862 - 11.8277i) q^{52} +(258.697 - 149.359i) q^{53} +(-219.034 - 175.374i) q^{54} +105.178i q^{55} +(42.8634 - 21.9396i) q^{57} +(-207.807 + 359.932i) q^{58} +(-102.276 - 177.147i) q^{59} +(50.6906 - 78.3725i) q^{60} +(543.757 + 313.939i) q^{61} +283.512 q^{62} -64.0000 q^{64} +(22.9992 + 13.2786i) q^{65} +(132.190 - 204.378i) q^{66} +(51.3894 + 89.0091i) q^{67} +(232.167 - 402.126i) q^{68} +(-575.340 + 294.487i) q^{69} -46.9785i q^{71} +(-197.001 + 88.5817i) q^{72} +(228.182 - 131.741i) q^{73} +(519.053 - 299.675i) q^{74} +(-544.038 - 27.5067i) q^{75} -37.0674i q^{76} +(-28.0024 - 54.7084i) q^{78} +(533.634 - 924.281i) q^{79} +(-35.9254 - 62.2246i) q^{80} +(-483.790 + 545.333i) q^{81} +(-880.538 - 508.379i) q^{82} +270.436 q^{83} +521.294 q^{85} +(-677.452 - 391.127i) q^{86} +(906.676 + 586.430i) q^{87} +(-93.6856 - 162.268i) q^{88} +(-443.765 + 768.624i) q^{89} +(-196.708 - 141.812i) q^{90} +497.543i q^{92} +(37.1945 - 735.646i) q^{93} +(-139.456 + 80.5151i) q^{94} +(36.0392 - 20.8072i) q^{95} +(-8.39628 + 166.065i) q^{96} -219.564i q^{97} +(-512.971 - 369.815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} + 18 q^{9} + 36 q^{10} - 128 q^{16} - 48 q^{18} + 342 q^{19} + 24 q^{22} + 48 q^{24} - 194 q^{25} + 360 q^{30} - 804 q^{31} - 1332 q^{33} + 144 q^{36} - 962 q^{37} + 594 q^{39} + 144 q^{40}+ \cdots - 4284 q^{99}+O(q^{100}) \) 16 * q + 32 * q^4 + 18 * q^9 + 36 * q^10 - 128 * q^16 - 48 * q^18 + 342 * q^19 + 24 * q^22 + 48 * q^24 - 194 * q^25 + 360 * q^30 - 804 * q^31 - 1332 * q^33 + 144 * q^36 - 962 * q^37 + 594 * q^39 + 144 * q^40 + 1732 * q^43 + 2394 * q^45 + 168 * q^46 + 1638 * q^51 - 744 * q^52 - 180 * q^54 - 2664 * q^57 - 780 * q^58 + 4620 * q^61 - 1024 * q^64 + 2016 * q^66 - 706 * q^67 + 192 * q^72 - 3294 * q^73 - 6174 * q^75 + 2832 * q^78 - 2656 * q^79 + 126 * q^81 - 432 * q^82 + 5232 * q^85 - 1026 * q^87 + 48 * q^88 + 2016 * q^93 - 3888 * q^94 + 192 * q^96 - 4284 * q^99

Introduction

L-functions

Modular forms

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