LMFDB - Embedded newform 294.4.f.a.227.2

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			227.2
Root			$2.99617 + 0.151487i$ of defining polynomial
Character	$\chi$	$=$	294.227
Dual form			294.4.f.a.215.2

$q$-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 $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

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

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	0.747967	−	0.663736i	$-0.231030\pi$
$5$	−2.24534	−	3.88904i	−0.200829	−	0.347846i	−0.948796	+	0.315890i	$0.897697\pi$
$6$	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	0.751528	−	0.659701i	$-0.229317\pi$
$11$	20.2835	+	11.7107i	0.555974	+	0.320992i	−0.195554	+	0.980693i	$0.562650\pi$
$12$	−20.7581	+	1.04953i	−0.499362	+	0.0252479i
$13$			5.91384i			0.126170i	0.998008	+	0.0630848i	$0.0200939\pi$
$13$			5.91384i			0.126170i	−0.998008	+	0.0630848i	$0.979906\pi$
$14$		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	0.0714778	+	0.997442i	$0.477228\pi$
$17$	−58.0418	+	100.531i	−0.828071	+	1.43426i	−0.899549	+	0.436819i	$0.856105\pi$
$18$	−5.44659	−	53.7246i	−0.0713207	−	0.703501i
$19$	−8.02533	+	4.63343i	−0.0969019	+	0.0559464i	−0.547668	−	0.836696i	$-0.684484\pi$
$19$	−8.02533	+	4.63343i	−0.0969019	+	0.0559464i	0.450766	+	0.892642i	$0.351151\pi$
$20$	−17.9627			−0.200829
$21$		0			0
$22$	−46.8428			−0.453951
$23$	107.721	−	62.1928i	0.976583	−	0.563830i	0.0753461	−	0.997157i	$-0.475994\pi$
$23$	107.721	−	62.1928i	0.976583	−	0.563830i	0.901237	+	0.433327i	$0.142661\pi$
$24$	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	$0.231707\pi$
$29$			207.807i			1.33065i	−0.746555	+	0.665324i	$0.768293\pi$
$30$	−2.35656	−	46.6089i	−0.0143416	−	0.283653i
$31$	−122.764	−	70.8780i	−0.711262	−	0.410647i	0.100266	−	0.994961i	$-0.468030\pi$
$31$	−122.764	−	70.8780i	−0.711262	−	0.410647i	−0.811528	+	0.584314i	$0.801364\pi$
$32$	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	−0.979078	−	0.203483i	$-0.934774\pi$
$37$	−149.838	−	259.526i	−0.665761	−	1.15313i	0.313317	−	0.949648i	$-0.398560\pi$
$38$	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	0.921709	−	0.387881i	$-0.126793\pi$
$47$	40.2575	+	69.7281i	0.124940	+	0.216402i	−0.796770	+	0.604283i	$0.793460\pi$
$48$	−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	0.796254	−	0.604963i	$-0.206812\pi$
$53$	258.697	+	149.359i	0.670467	+	0.387094i	−0.125786	+	0.992057i	$0.540145\pi$
$54$	−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	−0.956524	−	0.291655i	$-0.905794\pi$
$59$	−102.276	+	177.147i	−0.225682	+	0.390892i	0.730842	+	0.682547i	$0.239128\pi$
$60$	50.6906	+	78.3725i	0.109069	+	0.168631i
$61$	543.757	−	313.939i	1.14133	−	0.658946i	0.194569	−	0.980889i	$-0.437669\pi$
$61$	543.757	−	313.939i	1.14133	−	0.658946i	0.946759	+	0.321943i	$0.104336\pi$
$62$	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	−0.815363	−	0.578951i	$-0.803462\pi$
$67$	51.3894	−	89.0091i	0.0937048	−	0.162301i	0.909067	+	0.416649i	$0.136796\pi$
$68$	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	$0.0125010\pi$
$71$			46.9785i			0.0785256i	−0.999229	+	0.0392628i	$0.987499\pi$
$72$	−197.001	−	88.5817i	−0.322455	−	0.144992i
$73$	228.182	+	131.741i	0.365845	+	0.211221i	0.671642	−	0.740876i	$-0.265589\pi$
$73$	228.182	+	131.741i	0.365845	+	0.211221i	−0.305797	+	0.952097i	$0.598923\pi$
$74$	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	0.942860	+	0.333190i	$0.108125\pi$
$79$	533.634	+	924.281i	0.759981	+	1.31633i	−0.182878	+	0.983136i	$0.558541\pi$
$80$	−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	−0.999447	−	0.0332610i	$-0.989411\pi$
$89$	−443.765	−	768.624i	−0.528528	−	0.915438i	0.470918	−	0.882177i	$-0.343923\pi$
$90$	−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	$0.0366593\pi$
$97$			219.564i			0.229828i	−0.993375	+	0.114914i	$0.963341\pi$
$98$		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	−0.999856	−	0.0169642i	$-0.994600\pi$
$101$	−492.533	+	853.093i	−0.485237	+	0.840455i	0.514619	+	0.857419i	$0.327933\pi$
$102$	−1012.96	+	655.175i	−0.983315	+	0.636000i
$103$	1112.87	−	642.516i	1.06461	−	0.614650i	0.137903	−	0.990446i	$-0.455964\pi$
$103$	1112.87	−	642.516i	1.06461	−	0.614650i	0.926703	+	0.375796i	$0.122631\pi$
$104$	−47.3107			−0.0446077
$105$		0			0
$106$	−597.435			−0.547434
$107$	158.409	−	91.4575i	0.143121	−	0.0826311i	−0.426729	−	0.904379i	$-0.640334\pi$
$107$	158.409	−	91.4575i	0.143121	−	0.0826311i	0.569851	+	0.821748i	$0.307001\pi$
$108$	204.004	−	522.791i	0.181762	−	0.465793i
$109$	291.471	−	504.843i	0.256127	−	0.443625i	−0.709074	−	0.705134i	$-0.750887\pi$
$109$	291.471	−	504.843i	0.256127	−	0.443625i	0.965201	+	0.261509i	$0.0842201\pi$
$110$	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	$-0.600380\pi$
$113$		−	2283.94i		−	1.90137i	0.310152	−	0.950687i	$-0.399620\pi$
$114$	−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	0.968950	+	0.247256i	$0.0795288\pi$
$131$	1047.46	+	1814.26i	0.698605	+	1.21002i	−0.270345	+	0.962763i	$0.587138\pi$
$132$	−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	0.655795	−	0.754939i	$-0.272334\pi$
$137$	529.002	+	305.420i	0.329896	+	0.190465i	−0.325899	+	0.945405i	$0.605667\pi$
$138$	1291.00	−	65.2735i	0.796359	−	0.0402641i
$139$			1806.61i			1.10241i	0.834370	+	0.551204i	$0.185831\pi$
$139$			1806.61i			1.10241i	−0.834370	+	0.551204i	$0.814169\pi$
$140$		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	−0.978215	−	0.207592i	$-0.933437\pi$
$149$	−2341.75	+	1352.01i	−1.28754	+	0.743363i	−0.309328	+	0.950956i	$0.600104\pi$
$150$	914.794	−	591.681i	0.497951	−	0.322070i
$151$	−770.352	+	1334.29i	−0.415168	+	0.719092i	−0.995446	−	0.0953266i	$-0.969610\pi$
$151$	−770.352	+	1334.29i	−0.415168	+	0.719092i	0.580278	+	0.814418i	$0.302944\pi$
$152$	−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	0.373701	−	0.927549i	$-0.378089\pi$
$157$	−477.498	−	275.684i	−0.242729	−	0.140140i	−0.616430	+	0.787409i	$0.711422\pi$
$158$	−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	0.997872	+	0.0652023i	$0.0207693\pi$
$163$	1155.82	+	2001.94i	0.555403	+	0.961986i	−0.442469	+	0.896784i	$0.645897\pi$
$164$	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	0.954868	−	0.297031i	$-0.0959965\pi$
$173$	501.050	+	867.845i	0.220197	+	0.381393i	−0.734670	+	0.678424i	$0.762663\pi$
$174$	−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	0.932234	−	0.361855i	$-0.117856\pi$
$179$	2598.36	+	1500.17i	1.08498	+	0.626411i	0.152742	+	0.988266i	$0.451190\pi$
$180$	198.896	−	442.333i	0.0823601	−	0.183164i
$181$			967.850i			0.397457i	0.980055	+	0.198729i	$0.0636812\pi$
$181$			967.850i			0.397457i	−0.980055	+	0.198729i	$0.936319\pi$
$182$		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	−0.431007	−	0.902349i	$-0.641842\pi$
$191$	356.214	−	205.660i	0.134946	−	0.0779113i	0.565953	+	0.824437i	$0.308508\pi$
$192$	180.608	+	279.236i	0.0678866	+	0.104959i
$193$	−408.212	+	707.043i	−0.152247	+	0.263700i	−0.932053	−	0.362321i	$-0.881984\pi$
$193$	−408.212	+	707.043i	−0.152247	+	0.263700i	0.779806	+	0.626021i	$0.215318\pi$
$194$	−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	$-0.963465\pi$
$197$		−	633.331i		−	0.229051i	0.993420	−	0.114525i	$-0.0365347\pi$
$198$	518.677	−	1153.51i	0.186166	−	0.414022i
$199$	2964.48	+	1711.54i	1.05601	+	0.609688i	0.924326	−	0.381603i	$-0.124628\pi$
$199$	2964.48	+	1711.54i	1.05601	+	0.609688i	0.131685	+	0.991292i	$0.457961\pi$
$200$	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	$0.0733559\pi$
$223$			1521.32i			0.456840i	−0.973563	+	0.228420i	$0.926644\pi$
$224$		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	−0.952752	−	0.303751i	$-0.901761\pi$
$227$	−729.575	+	1263.66i	−0.213320	+	0.369481i	0.739432	+	0.673232i	$0.235094\pi$
$228$	161.728	−	104.604i	0.0469766	−	0.0303841i
$229$	−4152.17	+	2397.26i	−1.19818	+	0.691770i	−0.960149	−	0.279488i	$-0.909835\pi$
$229$	−4152.17	+	2397.26i	−1.19818	+	0.691770i	−0.238031	+	0.971257i	$0.576502\pi$
$230$	1117.15			0.320273
$231$		0			0
$232$	−1662.46			−0.470455
$233$	1445.76	−	834.708i	0.406501	−	0.234693i	−0.282784	−	0.959183i	$-0.591258\pi$
$233$	1445.76	−	834.708i	0.406501	−	0.234693i	0.689285	+	0.724490i	$0.257925\pi$
$234$	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	$0.158490\pi$
$239$			3529.25i			0.955181i	−0.878583	+	0.477590i	$0.841510\pi$
$240$	372.872	−	18.8525i	0.100286	−	0.00507051i
$241$	4269.15	+	2464.80i	1.14108	+	0.658803i	0.946698	−	0.322123i	$-0.104397\pi$
$241$	4269.15	+	2464.80i	1.14108	+	0.658803i	0.194382	+	0.980926i	$0.437730\pi$
$242$	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	0.940751	−	0.339098i	$-0.110122\pi$
$257$	728.040	+	1261.00i	0.176708	+	0.306067i	−0.764043	+	0.645165i	$0.776789\pi$
$258$	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	0.700973	−	0.713188i	$-0.252749\pi$
$263$	1850.30	+	1068.27i	0.433820	+	0.250466i	−0.267153	+	0.963654i	$0.586083\pi$
$264$	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	−0.654729	−	0.755864i	$-0.727217\pi$
$269$	1443.73	−	2500.61i	0.327233	−	0.566784i	0.981962	+	0.189080i	$0.0605506\pi$
$270$	1173.84	+	458.057i	0.264584	+	0.103246i
$271$	5072.92	−	2928.85i	1.13711	−	0.656513i	0.191400	−	0.981512i	$-0.438697\pi$
$271$	5072.92	−	2928.85i	1.13711	−	0.656513i	0.945714	+	0.324999i	$0.105364\pi$
$272$	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	−0.673036	−	0.739610i	$-0.735010\pi$
$277$	1401.52	−	2427.50i	0.304003	−	0.526549i	0.977039	+	0.213061i	$0.0683433\pi$
$278$	−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	$0.164918\pi$
$281$			4665.53i			0.990469i	−0.868759	+	0.495235i	$0.835082\pi$
$282$	42.2517	+	835.670i	0.00892217	+	0.176466i
$283$	−4654.53	−	2687.29i	−0.977679	−	0.564463i	−0.0761103	−	0.997099i	$-0.524250\pi$
$283$	−4654.53	−	2687.29i	−0.977679	−	0.564463i	−0.901569	+	0.432636i	$0.857583\pi$
$284$	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	$-0.980908\pi$
$307$		−	644.894i		−	0.119889i	0.998202	−	0.0599447i	$-0.0190924\pi$
$308$		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	−0.920506	−	0.390727i	$-0.872224\pi$
$311$	−668.420	+	1157.74i	−0.121873	+	0.211091i	0.798633	+	0.601818i	$0.205557\pi$
$312$	133.511	+	206.420i	0.0242261	+	0.0374559i
$313$	1459.67	−	842.739i	0.263595	−	0.152187i	−0.362378	−	0.932031i	$-0.618035\pi$
$313$	1459.67	−	842.739i	0.263595	−	0.152187i	0.625973	+	0.779844i	$0.284702\pi$
$314$	1102.73			0.198188
$315$		0			0
$316$	4269.07			0.759981
$317$	2609.95	−	1506.85i	0.462427	−	0.266982i	−0.250637	−	0.968081i	$-0.580640\pi$
$317$	2609.95	−	1506.85i	0.462427	−	0.266982i	0.713064	+	0.701099i	$0.247307\pi$
$318$	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	0.896917	−	0.442199i	$-0.145801\pi$
$331$	394.460	+	683.225i	0.0655030	+	0.113454i	−0.831414	+	0.555653i	$0.812468\pi$
$332$	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	0.105963	−	0.994370i	$-0.466207\pi$
$347$	−4538.98	−	2620.58i	−0.702205	−	0.405418i	−0.808168	+	0.588952i	$0.799541\pi$
$348$	−218.101	−	4313.68i	−0.0335961	−	0.664475i
$349$		−	4502.54i		−	0.690588i	−0.938495	−	0.345294i	$-0.887779\pi$
$349$		−	4502.54i		−	0.690588i	0.938495	−	0.345294i	$-0.112221\pi$
$350$		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	−0.235822	−	0.971796i	$-0.575778\pi$
$353$	4799.70	−	8313.33i	0.723689	−	1.25347i	0.959511	−	0.281671i	$-0.0908885\pi$
$354$	−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	−0.979414	−	0.201863i	$-0.935300\pi$
$359$	−8803.94	+	5082.96i	−1.29430	+	0.747265i	−0.314888	+	0.949129i	$0.601967\pi$
$360$	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	0.476164	−	0.879356i	$-0.342027\pi$
$367$	−332.544	−	191.995i	−0.0472988	−	0.0273080i	−0.523463	+	0.852048i	$0.675360\pi$
$368$	−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	0.950354	−	0.311171i	$-0.100721\pi$
$373$	1481.79	+	2566.54i	0.205695	+	0.356275i	−0.744659	+	0.667445i	$0.767388\pi$
$374$	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	−0.993239	−	0.116088i	$-0.962964\pi$
$383$	−4475.95	−	7752.57i	−0.597155	−	1.03430i	0.396084	−	0.918214i	$-0.370369\pi$
$384$	−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	−0.0846507	−	0.996411i	$-0.526977\pi$
$389$	−7594.74	−	4384.82i	−0.989893	−	0.571515i	−0.905242	+	0.424896i	$0.860311\pi$
$390$	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	−0.423070	−	0.906097i	$-0.639047\pi$
$397$	1187.30	−	685.490i	0.150098	−	0.0866594i	0.573168	+	0.819438i	$0.305714\pi$
$398$	−6846.17			−0.862229
$399$		0			0
$400$	−1677.34			−0.209668
$401$	−2392.14	+	1381.10i	−0.297899	+	0.171992i	−0.641499	−	0.767124i	$-0.721687\pi$
$401$	−2392.14	+	1381.10i	−0.297899	+	0.171992i	0.343599	+	0.939116i	$0.388354\pi$
$402$	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	0.353821	−	0.935313i	$-0.384882\pi$
$409$	−2310.01	−	1333.69i	−0.279273	−	0.161239i	−0.633094	+	0.774075i	$0.718216\pi$
$410$	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	0.205433	−	0.978671i	$-0.434140\pi$
$431$	−4826.49	−	2786.57i	−0.539405	−	0.311426i	−0.744838	+	0.667246i	$0.767473\pi$
$432$	−1402.99	−	1752.27i	−0.156254	−	0.195153i
$433$		−	2939.93i		−	0.326291i	−0.986602	−	0.163146i	$-0.947836\pi$
$433$		−	2939.93i		−	0.326291i	0.986602	−	0.163146i	$-0.0521640\pi$
$434$		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	0.0237157	−	0.999719i	$-0.492450\pi$
$439$	8290.73	−	4786.66i	0.901355	−	0.520398i	0.877640	+	0.479321i	$0.159117\pi$
$440$	841.424			0.0911666
$441$		0			0
$442$	1373.00			0.147753
$443$	6197.42	−	3578.08i	0.664669	−	0.383747i	−0.129385	−	0.991594i	$-0.541300\pi$
$443$	6197.42	−	3578.08i	0.664669	−	0.383747i	0.794054	+	0.607848i	$0.207967\pi$
$444$	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	$-0.715294\pi$
$449$		−	14839.2i		−	1.55970i	0.625964	−	0.779852i	$-0.284706\pi$
$450$	−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	0.992136	−	0.125161i	$-0.0399447\pi$
$457$	3787.42	+	6560.00i	0.387676	+	0.671474i	−0.604461	+	0.796635i	$0.706611\pi$
$458$	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	0.871687	−	0.490063i	$-0.163026\pi$
$467$	115.422	+	199.917i	0.0114371	+	0.0198096i	−0.860250	+	0.509872i	$0.829693\pi$
$468$	−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	−0.741786	−	0.670637i	$-0.766021\pi$
$479$	2200.43	−	3811.26i	0.209896	−	0.363551i	0.951682	+	0.307087i	$0.0993541\pi$
$480$	−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	−0.442137	−	0.896948i	$-0.645779\pi$
$487$	5972.31	−	10344.3i	0.555711	−	0.962520i	0.997848	−	0.0655721i	$-0.0208872\pi$
$488$	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	$0.368048\pi$
$491$			19916.7i			1.83060i	−0.402768	+	0.915302i	$0.631952\pi$
$492$	−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	0.834626	−	0.550818i	$-0.185684\pi$
$499$	−665.569	−	1152.80i	−0.0597093	−	0.103420i	−0.894335	+	0.447398i	$0.852351\pi$
$500$	−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	0.551281	−	0.834319i	$-0.314139\pi$
$509$	−5132.02	−	8888.91i	−0.446901	−	0.774055i	−0.998182	+	0.0602640i	$0.980806\pi$
$510$	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	−0.923806	−	0.382860i	$-0.874939\pi$
$521$	−1549.97	+	2684.63i	−0.130337	+	0.225750i	0.793470	+	0.608610i	$0.208273\pi$
$522$	11164.4	−	1131.84i	0.936112	−	0.0949028i
$523$	8265.94	−	4772.34i	0.691098	−	0.399005i	−0.112925	−	0.993603i	$-0.536022\pi$
$523$	8265.94	−	4772.34i	0.691098	−	0.399005i	0.804023	+	0.594598i	$0.202689\pi$
$524$	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	0.968991	−	0.247098i	$-0.0794768\pi$
$541$	3403.83	+	5895.60i	0.270503	+	0.468524i	−0.698488	+	0.715622i	$0.746143\pi$
$542$	−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	0.0362634	−	0.999342i	$-0.488454\pi$
$557$	−10661.9	−	6155.67i	−0.811061	−	0.468266i	−0.847324	+	0.531076i	$0.821788\pi$
$558$	−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	−0.849959	−	0.526849i	$-0.823373\pi$
$563$	417.925	−	723.867i	0.0312850	−	0.0541872i	0.881244	+	0.472662i	$0.156707\pi$
$564$	−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	−0.682086	−	0.731272i	$-0.738927\pi$
$569$	−5291.04	+	3054.78i	−0.389828	+	0.225067i	0.292258	+	0.956340i	$0.405593\pi$
$570$	234.871	+	363.133i	0.0172591	+	0.0266842i
$571$	6319.69	−	10946.0i	0.463171	−	0.802236i	−0.535946	−	0.844252i	$-0.680045\pi$
$571$	6319.69	−	10946.0i	0.463171	−	0.802236i	0.999117	+	0.0420166i	$0.0133782\pi$
$572$	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	0.937895	−	0.346920i	$-0.112772\pi$
$577$	15334.7	+	8853.51i	1.10640	+	0.638781i	0.168506	+	0.985701i	$0.446106\pi$
$578$	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	−0.999701	−	0.0244425i	$-0.992219\pi$
$593$	−7523.76	−	13031.5i	−0.521018	−	0.902430i	0.478683	−	0.877988i	$-0.341114\pi$
$594$	−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	0.669530	−	0.742785i	$-0.266495\pi$
$599$	5292.70	+	3055.74i	0.361025	+	0.208438i	−0.308505	+	0.951223i	$0.599829\pi$
$600$	−220.054	−	4352.30i	−0.0149727	−	0.296137i
$601$		−	7494.08i		−	0.508636i	−0.967121	−	0.254318i	$-0.918149\pi$
$601$		−	7494.08i		−	0.508636i	0.967121	−	0.254318i	$-0.0818509\pi$
$602$		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	−0.960127	−	0.279565i	$-0.909810\pi$
$607$	−17917.1	+	10344.5i	−1.19808	+	0.691711i	−0.237953	+	0.971277i	$0.576476\pi$
$608$	−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	−0.171714	−	0.985147i	$-0.554931\pi$
$613$	11645.5	−	20170.6i	0.767305	−	1.32901i	0.939019	−	0.343865i	$-0.111736\pi$
$614$	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	$0.123999\pi$
$617$			11640.9i			0.759554i	−0.925078	+	0.379777i	$0.876001\pi$
$618$	13337.4	−	674.343i	0.868138	−	0.0438933i
$619$	13978.4	+	8070.44i	0.907657	+	0.524036i	0.879676	−	0.475573i	$-0.157759\pi$
$619$	13978.4	+	8070.44i	0.907657	+	0.524036i	0.0279803	+	0.999608i	$0.491092\pi$
$620$	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	0.544293	−	0.838895i	$-0.316798\pi$
$641$	1459.54	+	842.666i	0.0899351	+	0.0519241i	−0.454358	+	0.890819i	$0.650131\pi$
$642$	1898.48	−	95.9879i	0.116709	−	0.00590084i
$643$		−	10186.5i		−	0.624752i	−0.949958	−	0.312376i	$-0.898875\pi$
$643$		−	10186.5i		−	0.624752i	0.949958	−	0.312376i	$-0.101125\pi$
$644$		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	−0.861006	−	0.508594i	$-0.830165\pi$
$647$	163.793	−	283.698i	0.00995266	−	0.0172385i	0.870959	+	0.491356i	$0.163499\pi$
$648$	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	−0.552096	−	0.833781i	$-0.686172\pi$
$653$	−1769.92	+	1021.87i	−0.106068	+	0.0612384i	0.446028	+	0.895019i	$0.352838\pi$
$654$	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	$0.303139\pi$
$659$			27567.4i			1.62955i	−0.579778	+	0.814774i	$0.696861\pi$
$660$	110.388	+	2183.29i	0.00651037	+	0.128765i
$661$	−18417.0	−	10633.0i	−1.08372	−	0.625684i	−0.151820	−	0.988408i	$-0.548513\pi$
$661$	−18417.0	−	10633.0i	−1.08372	−	0.625684i	−0.931897	+	0.362724i	$0.881847\pi$
$662$	−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	0.976877	−	0.213801i	$-0.0685844\pi$
$677$	5342.31	+	9253.15i	0.303282	+	0.525299i	−0.673596	+	0.739100i	$0.735251\pi$
$678$	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	0.994371	−	0.105957i	$-0.0337906\pi$
$683$	24985.9	+	14425.6i	1.39979	+	0.808172i	0.405424	+	0.914129i	$0.367124\pi$
$684$	−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	−0.468292	−	0.883574i	$-0.655130\pi$
$691$	1139.99	−	658.171i	0.0627599	−	0.0362344i	0.531052	+	0.847339i	$0.321797\pi$
$692$	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	$-0.887835\pi$
$701$		−	12811.2i		−	0.690259i	0.938555	−	0.345129i	$-0.112165\pi$
$702$	−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	−0.858772	−	0.512358i	$-0.828772\pi$
$709$	−16482.9	−	28549.2i	−0.873101	−	1.51226i	−0.0143290	−	0.999897i	$-0.504561\pi$
$710$	−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	0.955845	−	0.293870i	$-0.0949432\pi$
$719$	4307.48	+	7460.77i	0.223424	+	0.386982i	−0.732421	+	0.680851i	$0.761610\pi$
$720$	−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	$-0.762240\pi$
$727$		−	26635.3i		−	1.35880i	0.733768	−	0.679400i	$-0.237760\pi$
$728$		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	−0.359708	−	0.933065i	$-0.617124\pi$
$733$	5328.35	−	3076.33i	0.268496	−	0.155016i	0.628204	+	0.778049i	$0.283790\pi$
$734$	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	−0.989028	−	0.147729i	$-0.952804\pi$
$739$	−7364.30	+	12755.3i	−0.366577	+	0.634929i	0.622451	+	0.782659i	$0.286137\pi$
$740$	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	$-0.765059\pi$
$743$		−	27255.1i		−	1.34575i	0.739755	−	0.672876i	$-0.234941\pi$
$744$	−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	0.931023	−	0.364961i	$-0.118918\pi$
$751$	3075.69	+	5327.25i	0.149445	+	0.258847i	−0.781577	+	0.623809i	$0.785585\pi$
$752$	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	0.987750	−	0.156046i	$-0.0498748\pi$
$761$	7530.97	+	13044.0i	0.358735	+	0.621348i	−0.629015	+	0.777393i	$0.716541\pi$
$762$	−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	$0.209610\pi$
$769$			26099.2i			1.22387i	−0.790906	+	0.611937i	$0.790390\pi$
$770$		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	−0.866231	−	0.499644i	$-0.833464\pi$
$773$	−8.84542	+	15.3207i	−0.000411575	+	0.000712869i	0.865820	+	0.500356i	$0.166798\pi$
$774$	−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	0.452476	−	0.891776i	$-0.350541\pi$
$787$	−2066.21	−	1192.93i	−0.0935865	−	0.0540322i	−0.546063	+	0.837744i	$0.683874\pi$
$788$	−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	0.950823	−	0.309734i	$-0.100240\pi$
$809$	26645.9	+	15384.0i	1.15800	+	0.668570i	0.207174	+	0.978304i	$0.433574\pi$
$810$	−1314.04	−	6414.19i	−0.0570009	−	0.278237i
$811$		−	42776.4i		−	1.85214i	−0.377357	−	0.926068i	$-0.623167\pi$
$811$		−	42776.4i		−	1.85214i	0.377357	−	0.926068i	$-0.376833\pi$
$812$		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	−0.537305	+	0.843388i	$0.680558\pi$
$821$	−36141.5	+	20866.3i	−1.53635	+	0.887014i	−0.999048	+	0.0436263i	$0.986109\pi$
$822$	3447.57	+	5330.27i	0.146287	+	0.226173i
$823$	7822.35	−	13548.7i	0.331312	−	0.573850i	−0.651457	−	0.758685i	$-0.725842\pi$
$823$	7822.35	−	13548.7i	0.331312	−	0.573850i	0.982769	+	0.184836i	$0.0591753\pi$
$824$	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	$-0.828579\pi$
$827$		−	24395.1i		−	1.02576i	0.858461	−	0.512879i	$-0.171421\pi$
$828$	12252.0	+	5509.15i	0.514236	+	0.231227i
$829$	−32786.9	−	18929.5i	−1.37362	−	0.793062i	−0.382242	−	0.924062i	$-0.624848\pi$
$829$	−32786.9	−	18929.5i	−1.37362	−	0.793062i	−0.991382	+	0.131000i	$0.958181\pi$
$830$	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	$0.280754\pi$
$853$			38466.5i			1.54404i	−0.635598	+	0.772021i	$0.719246\pi$
$854$		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	0.479395	+	0.877599i	$0.340856\pi$
$857$	−13054.1	+	22610.3i	−0.520326	+	0.901230i	−0.999721	+	0.0236312i	$0.992477\pi$
$858$	−1208.66	+	781.751i	−0.0480921	+	0.0311055i
$859$	−21033.3	+	12143.6i	−0.835445	+	0.482345i	−0.855713	−	0.517450i	$-0.826881\pi$
$859$	−21033.3	+	12143.6i	−0.835445	+	0.482345i	0.0202681	+	0.999795i	$0.493548\pi$
$860$	−7025.70			−0.278575
$861$		0			0
$862$	11146.3			0.440423
$863$	−32475.9	+	18750.0i	−1.28099	+	0.739579i	−0.977029	−	0.213106i	$-0.931642\pi$
$863$	−32475.9	+	18750.0i	−1.28099	+	0.739579i	−0.303960	+	0.952685i	$0.598309\pi$
$864$	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	0.972784	−	0.231713i	$-0.0744329\pi$
$877$	7420.70	+	12853.0i	0.285723	+	0.494887i	−0.687061	+	0.726600i	$0.741100\pi$
$878$	−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	0.978253	+	0.207416i	$0.0665053\pi$
$887$	17666.5	+	30599.4i	0.668754	+	1.15832i	−0.309499	+	0.950900i	$0.600161\pi$
$888$	−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	−0.607883	−	0.794027i	$-0.707981\pi$
$907$	10481.2	−	18153.9i	0.383706	−	0.664598i	0.991589	+	0.129429i	$0.0413144\pi$
$908$	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	$0.0314209\pi$
$911$			5419.65i			0.197103i	−0.995132	+	0.0985516i	$0.968579\pi$
$912$	−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	0.542666	−	0.839949i	$-0.317415\pi$
$919$	−12706.3	−	22007.9i	−0.456084	−	0.789961i	−0.998750	+	0.0499878i	$0.984082\pi$
$920$	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	0.861097	−	0.508440i	$-0.169778\pi$
$929$	−276.744	−	479.335i	−0.00977360	−	0.0169284i	−0.870871	+	0.491512i	$0.836444\pi$
$930$	−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	$0.107204\pi$
$937$			18956.6i			0.660923i	−0.943819	+	0.330462i	$0.892796\pi$
$938$		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	0.423157	+	0.906056i	$0.360922\pi$
$941$	−16542.7	+	28652.8i	−0.573089	+	0.992619i	−0.996246	+	0.0865632i	$0.972412\pi$
$942$	−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	−0.685926	−	0.727671i	$-0.740603\pi$
$947$	−11619.3	+	6708.40i	−0.398708	+	0.230194i	0.287219	+	0.957865i	$0.407269\pi$
$948$	−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	$-0.788007\pi$
$953$		−	36353.5i		−	1.23568i	0.786303	−	0.617841i	$-0.211993\pi$
$954$	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	−0.892535	−	0.450978i	$-0.851075\pi$
$971$	−25320.0	−	43855.6i	−0.836826	−	1.44943i	0.0557091	−	0.998447i	$-0.482258\pi$
$972$	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	−0.0102426	−	0.999948i	$-0.503260\pi$
$977$	−26914.6	−	15539.1i	−0.881344	−	0.508844i	−0.871101	+	0.491103i	$0.836594\pi$
$978$	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	−0.328199	−	0.944609i	$-0.606442\pi$
$983$	20154.8	−	34909.1i	0.653956	−	1.13268i	0.982155	−	0.188076i	$-0.0602251\pi$
$984$	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	−0.896402	−	0.443242i	$-0.853828\pi$
$991$	−2007.28	+	3476.71i	−0.0643425	+	0.111444i	0.832060	+	0.554686i	$0.187162\pi$
$992$	−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	−0.198980	−	0.980004i	$-0.563763\pi$
$997$	−36113.8	−	20850.3i	−1.14718	−	0.662323i	−0.948198	+	0.317680i	$0.897096\pi$
$998$	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.227.2		16
3.2	odd	2	inner	294.4.f.a.227.5		16
7.2	even	3		42.4.f.a.5.8	yes	16
7.3	odd	6		294.4.d.a.293.6		16
7.4	even	3		294.4.d.a.293.3		16
7.5	odd	6	inner	294.4.f.a.215.5		16
7.6	odd	2		42.4.f.a.17.3	yes	16
21.2	odd	6		42.4.f.a.5.3	✓	16
21.5	even	6	inner	294.4.f.a.215.2		16
21.11	odd	6		294.4.d.a.293.14		16
21.17	even	6		294.4.d.a.293.11		16
21.20	even	2		42.4.f.a.17.8	yes	16
28.23	odd	6		336.4.bc.e.257.1		16
28.27	even	2		336.4.bc.e.17.3		16
84.23	even	6		336.4.bc.e.257.3		16
84.83	odd	2		336.4.bc.e.17.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.f.a.5.3	✓	16	21.2	odd	6
42.4.f.a.5.8	yes	16	7.2	even	3
42.4.f.a.17.3	yes	16	7.6	odd	2
42.4.f.a.17.8	yes	16	21.20	even	2
294.4.d.a.293.3		16	7.4	even	3
294.4.d.a.293.6		16	7.3	odd	6
294.4.d.a.293.11		16	21.17	even	6
294.4.d.a.293.14		16	21.11	odd	6
294.4.f.a.215.2		16	21.5	even	6	inner
294.4.f.a.215.5		16	7.5	odd	6	inner
294.4.f.a.227.2		16	1.1	even	1	trivial
294.4.f.a.227.5		16	3.2	odd	2	inner
336.4.bc.e.17.1		16	84.83	odd	2
336.4.bc.e.17.3		16	28.27	even	2
336.4.bc.e.257.1		16	28.23	odd	6
336.4.bc.e.257.3		16	84.23	even	6

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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more