LMFDB - Embedded newform 294.4.d.a.293.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [294,4,Mod(293,294)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(294, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("294.293"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	294.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$17.3465615417$
Analytic rank:	$0$
Dimension:	$16$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{8}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			293.9
Root			$0.339489 + 2.98073i$ of defining polynomial
Character	$\chi$	$=$	294.293
Dual form			294.4.d.a.293.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000i q^{2} +(-4.76510 + 2.07215i) q^{3} -4.00000 q^{4} -8.55823 q^{5} +(-4.14431 - 9.53020i) q^{6} -8.00000i q^{8} +(18.4124 - 19.7480i) q^{9} -17.1165i q^{10} -62.1932i q^{11} +(19.0604 - 8.28861i) q^{12} +61.7061i q^{13} +(40.7808 - 17.7340i) q^{15} +16.0000 q^{16} +26.6731 q^{17} +(39.4961 + 36.8247i) q^{18} -67.6901i q^{19} +34.2329 q^{20} +124.386 q^{22} +52.9184i q^{23} +(16.5772 + 38.1208i) q^{24} -51.7568 q^{25} -123.412 q^{26} +(-46.8158 + 132.255i) q^{27} +55.1116i q^{29} +(35.4679 + 81.5616i) q^{30} +154.822i q^{31} +32.0000i q^{32} +(128.874 + 296.357i) q^{33} +53.3461i q^{34} +(-73.6494 + 78.9922i) q^{36} +315.880 q^{37} +135.380 q^{38} +(-127.865 - 294.036i) q^{39} +68.4658i q^{40} -210.211 q^{41} +351.939 q^{43} +248.773i q^{44} +(-157.577 + 169.008i) q^{45} -105.837 q^{46} +231.638 q^{47} +(-76.2416 + 33.1545i) q^{48} -103.514i q^{50} +(-127.100 + 55.2707i) q^{51} -246.824i q^{52} +268.918i q^{53} +(-264.509 - 93.6315i) q^{54} +532.263i q^{55} +(140.264 + 322.550i) q^{57} -110.223 q^{58} +18.2831 q^{59} +(-163.123 + 70.9358i) q^{60} -83.5218i q^{61} -309.643 q^{62} -64.0000 q^{64} -528.095i q^{65} +(-592.713 + 257.748i) q^{66} +129.471 q^{67} -106.692 q^{68} +(-109.655 - 252.162i) q^{69} +804.537i q^{71} +(-157.984 - 147.299i) q^{72} -427.674i q^{73} +631.759i q^{74} +(246.626 - 107.248i) q^{75} +270.760i q^{76} +(588.072 - 255.729i) q^{78} +1218.57 q^{79} -136.932 q^{80} +(-50.9701 - 727.216i) q^{81} -420.423i q^{82} +1371.18 q^{83} -228.274 q^{85} +703.879i q^{86} +(-114.200 - 262.612i) q^{87} -497.545 q^{88} -773.679 q^{89} +(-338.016 - 315.154i) q^{90} -211.674i q^{92} +(-320.814 - 737.741i) q^{93} +463.277i q^{94} +579.307i q^{95} +(-66.3089 - 152.483i) q^{96} -848.768i q^{97} +(-1228.19 - 1145.12i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 64 q^{4} - 36 q^{9} + 256 q^{16} + 96 q^{18} + 24 q^{22} + 388 q^{25} - 720 q^{30} + 144 q^{36} + 1924 q^{37} - 1188 q^{39} + 1732 q^{43} - 336 q^{46} - 3276 q^{51} - 2664 q^{57} + 1560 q^{58} - 1024 q^{64}+ \cdots - 4284 q^{99}+O(q^{100}) $ 16 * q - 64 * q^4 - 36 * q^9 + 256 * q^16 + 96 * q^18 + 24 * q^22 + 388 * q^25 - 720 * q^30 + 144 * q^36 + 1924 * q^37 - 1188 * q^39 + 1732 * q^43 - 336 * q^46 - 3276 * q^51 - 2664 * q^57 + 1560 * q^58 - 1024 * q^64 + 1412 * q^67 - 384 * q^72 + 2832 * q^78 + 5312 * q^79 - 252 * q^81 + 5232 * q^85 - 96 * q^88 - 4032 * q^93 - 4284 * q^99

Character values

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

$n$	$197$	$199$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$	−4.76510	+	2.07215i	−0.917044	+	0.398786i
$3$	−4.76510	+	2.07215i	−0.917044	+	0.398786i
$4$	−4.00000			−0.500000
$5$	−8.55823			−0.765471			−0.382736	−	0.923858i	$-0.625018\pi$
$5$	−8.55823			−0.765471			−0.382736	+	0.923858i	$0.625018\pi$
$6$	−4.14431	−	9.53020i	−0.281984	−	0.648448i
$7$		0			0
$7$		0			0
$8$		−	8.00000i		−	0.353553i
$9$	18.4124	−	19.7480i	0.681939	−	0.731409i
$10$		−	17.1165i		−	0.541270i
$11$		−	62.1932i		−	1.70472i	−0.522954	−	0.852361i	$-0.675170\pi$
$11$		−	62.1932i		−	1.70472i	0.522954	−	0.852361i	$-0.324830\pi$
$12$	19.0604	−	8.28861i	0.458522	−	0.199393i
$13$			61.7061i			1.31648i	0.752810	+	0.658238i	$0.228698\pi$
$13$			61.7061i			1.31648i	−0.752810	+	0.658238i	$0.771302\pi$
$14$		0			0
$15$	40.7808	−	17.7340i	0.701971	−	0.305259i
$16$	16.0000			0.250000
$17$	26.6731			0.380539			0.190270	−	0.981732i	$-0.439064\pi$
$17$	26.6731			0.380539			0.190270	+	0.981732i	$0.439064\pi$
$18$	39.4961	+	36.8247i	0.517184	+	0.482204i
$19$		−	67.6901i		−	0.817324i	−0.912686	−	0.408662i	$-0.865995\pi$
$19$		−	67.6901i		−	0.817324i	0.912686	−	0.408662i	$-0.134005\pi$
$20$	34.2329			0.382736
$21$		0			0
$22$	124.386			1.20542
$23$			52.9184i			0.479750i	0.970804	+	0.239875i	$0.0771065\pi$
$23$			52.9184i			0.479750i	−0.970804	+	0.239875i	$0.922894\pi$
$24$	16.5772	+	38.1208i	0.140992	+	0.324224i
$25$	−51.7568			−0.414054
$26$	−123.412			−0.930889
$27$	−46.8158	+	132.255i	−0.333693	+	0.942682i
$28$		0			0
$29$			55.1116i			0.352895i	0.984310	+	0.176448i	$0.0564606\pi$
$29$			55.1116i			0.352895i	−0.984310	+	0.176448i	$0.943539\pi$
$30$	35.4679	+	81.5616i	0.215851	+	0.496368i
$31$			154.822i			0.896993i	0.893785	+	0.448497i	$0.148040\pi$
$31$			154.822i			0.896993i	−0.893785	+	0.448497i	$0.851960\pi$
$32$			32.0000i			0.176777i
$33$	128.874	+	296.357i	0.679820	+	1.56331i
$34$			53.3461i			0.269082i
$35$		0			0
$36$	−73.6494	+	78.9922i	−0.340970	+	0.365704i
$37$	315.880			1.40352			0.701761	−	0.712413i	$-0.252398\pi$
$37$	315.880			1.40352			0.701761	+	0.712413i	$0.252398\pi$
$38$	135.380			0.577936
$39$	−127.865	−	294.036i	−0.524993	−	1.20727i
$40$			68.4658i			0.270635i
$41$	−210.211			−0.800719			−0.400360	−	0.916358i	$-0.631115\pi$
$41$	−210.211			−0.800719			−0.400360	+	0.916358i	$0.631115\pi$
$42$		0			0
$43$	351.939			1.24815			0.624073	−	0.781366i	$-0.285477\pi$
$43$	351.939			1.24815			0.624073	+	0.781366i	$0.285477\pi$
$44$			248.773i			0.852361i
$45$	−157.577	+	169.008i	−0.522005	+	0.559872i
$46$	−105.837			−0.339235
$47$	231.638			0.718892			0.359446	−	0.933166i	$-0.382966\pi$
$47$	231.638			0.718892			0.359446	+	0.933166i	$0.382966\pi$
$48$	−76.2416	+	33.1545i	−0.229261	+	0.0996965i
$49$		0			0
$50$		−	103.514i		−	0.292780i
$51$	−127.100	+	55.2707i	−0.348971	+	0.151754i
$52$		−	246.824i		−	0.658238i
$53$			268.918i			0.696958i	0.937317	+	0.348479i	$0.113302\pi$
$53$			268.918i			0.696958i	−0.937317	+	0.348479i	$0.886698\pi$
$54$	−264.509	−	93.6315i	−0.666577	−	0.235956i
$55$			532.263i			1.30492i
$56$		0			0
$57$	140.264	+	322.550i	0.325938	+	0.749522i
$58$	−110.223			−0.249535
$59$	18.2831			0.0403433			0.0201717	−	0.999797i	$-0.493579\pi$
$59$	18.2831			0.0403433			0.0201717	+	0.999797i	$0.493579\pi$
$60$	−163.123	+	70.9358i	−0.350985	+	0.152630i
$61$		−	83.5218i		−	0.175309i	−0.996151	−	0.0876547i	$-0.972063\pi$
$61$		−	83.5218i		−	0.175309i	0.996151	−	0.0876547i	$-0.0279372\pi$
$62$	−309.643			−0.634270
$63$		0			0
$64$	−64.0000			−0.125000
$65$		−	528.095i		−	1.00772i
$66$	−592.713	+	257.748i	−1.10542	+	0.480705i
$67$	129.471			0.236080			0.118040	−	0.993009i	$-0.462339\pi$
$67$	129.471			0.236080			0.118040	+	0.993009i	$0.462339\pi$
$68$	−106.692			−0.190270
$69$	−109.655	−	252.162i	−0.191318	−	0.439952i
$70$		0			0
$71$			804.537i			1.34480i	0.740186	+	0.672402i	$0.234737\pi$
$71$			804.537i			1.34480i	−0.740186	+	0.672402i	$0.765263\pi$
$72$	−157.984	−	147.299i	−0.258592	−	0.241102i
$73$		−	427.674i		−	0.685691i	−0.939392	−	0.342846i	$-0.888609\pi$
$73$		−	427.674i		−	0.685691i	0.939392	−	0.342846i	$-0.111391\pi$
$74$			631.759i			0.992439i
$75$	246.626	−	107.248i	0.379706	−	0.165119i
$76$			270.760i			0.408662i
$77$		0			0
$78$	588.072	−	255.729i	0.853667	−	0.371226i
$79$	1218.57			1.73544			0.867718	−	0.497056i	$-0.165586\pi$
$79$	1218.57			1.73544			0.867718	+	0.497056i	$0.165586\pi$
$80$	−136.932			−0.191368
$81$	−50.9701	−	727.216i	−0.0699178	−	0.997553i
$82$		−	420.423i		−	0.566194i
$83$	1371.18			1.81333			0.906663	−	0.421855i	$-0.138621\pi$
$83$	1371.18			1.81333			0.906663	+	0.421855i	$0.138621\pi$
$84$		0			0
$85$	−228.274			−0.291292
$86$			703.879i			0.882572i
$87$	−114.200	−	262.612i	−0.140730	−	0.323620i
$88$	−497.545			−0.602710
$89$	−773.679			−0.921459			−0.460729	−	0.887541i	$-0.652412\pi$
$89$	−773.679			−0.921459			−0.460729	+	0.887541i	$0.652412\pi$
$90$	−338.016	−	315.154i	−0.395890	−	0.369113i
$91$		0			0
$92$		−	211.674i		−	0.239875i
$93$	−320.814	−	737.741i	−0.357709	−	0.822582i
$94$			463.277i			0.508333i
$95$			579.307i			0.625638i
$96$	−66.3089	−	152.483i	−0.0704961	−	0.162112i
$97$		−	848.768i		−	0.888447i	−0.895916	−	0.444223i	$-0.853480\pi$
$97$		−	848.768i		−	0.888447i	0.895916	−	0.444223i	$-0.146520\pi$
$98$		0			0
$99$	−1228.19	−	1145.12i	−1.24685	−	1.16252i
$100$	207.027			0.207027
$101$	1025.29			1.01011			0.505053	−	0.863088i	$-0.331473\pi$
$101$	1025.29			1.01011			0.505053	+	0.863088i	$0.331473\pi$
$102$	−110.541	−	254.200i	−0.107306	−	0.246760i
$103$			321.360i			0.307423i	0.988116	+	0.153711i	$0.0491226\pi$
$103$			321.360i			0.307423i	−0.988116	+	0.153711i	$0.950877\pi$
$104$	493.649			0.465445
$105$		0			0
$106$	−537.837			−0.492824
$107$		−	136.079i		−	0.122946i	−0.998109	−	0.0614730i	$-0.980420\pi$
$107$		−	136.079i		−	0.122946i	0.998109	−	0.0614730i	$-0.0195798\pi$
$108$	187.263	−	529.018i	0.166846	−	0.471341i
$109$	1406.16			1.23565			0.617823	−	0.786317i	$-0.288015\pi$
$109$	1406.16			1.23565			0.617823	+	0.786317i	$0.288015\pi$
$110$	−1064.53			−0.922715
$111$	−1505.20	+	654.551i	−1.28709	+	0.559705i
$112$		0			0
$113$		−	467.285i		−	0.389013i	−0.980901	−	0.194506i	$-0.937690\pi$
$113$		−	467.285i		−	0.389013i	0.980901	−	0.194506i	$-0.0623105\pi$
$114$	−645.100	+	280.528i	−0.529992	+	0.230473i
$115$		−	452.888i		−	0.367235i
$116$		−	220.446i		−	0.176448i
$117$	1218.57	+	1136.15i	0.962883	+	0.897757i
$118$			36.5662i			0.0285270i
$119$		0			0
$120$	−141.872	−	326.246i	−0.107925	−	0.248184i
$121$	−2536.99			−1.90608
$122$	167.044			0.123962
$123$	1001.68	−	435.590i	0.734295	−	0.319316i
$124$		−	619.287i		−	0.448497i
$125$	1512.72			1.08242
$126$		0			0
$127$	259.166			0.181081			0.0905404	−	0.995893i	$-0.471141\pi$
$127$	259.166			0.181081			0.0905404	+	0.995893i	$0.471141\pi$
$128$		−	128.000i		−	0.0883883i
$129$	−1677.03	+	729.272i	−1.14460	+	0.497743i
$130$	1056.19			0.712569
$131$	2647.85			1.76598			0.882991	−	0.469391i	$-0.155526\pi$
$131$	2647.85			1.76598			0.882991	+	0.469391i	$0.155526\pi$
$132$	−515.495	−	1185.43i	−0.339910	−	0.781653i
$133$		0			0
$134$			258.941i			0.166934i
$135$	400.660	−	1131.87i	0.255432	−	0.721596i
$136$		−	213.384i		−	0.134541i
$137$		−	468.016i		−	0.291863i	−0.989295	−	0.145932i	$-0.953382\pi$
$137$		−	468.016i		−	0.291863i	0.989295	−	0.145932i	$-0.0466180\pi$
$138$	504.323	−	219.310i	0.311093	−	0.135282i
$139$		−	2923.27i		−	1.78380i	−0.452229	−	0.891902i	$-0.649371\pi$
$139$		−	2923.27i		−	1.78380i	0.452229	−	0.891902i	$-0.350629\pi$
$140$		0			0
$141$	−1103.78	+	479.990i	−0.659256	+	0.286684i
$142$	−1609.07			−0.950920
$143$	3837.70			2.24423
$144$	294.598	−	315.969i	0.170485	−	0.182852i
$145$		−	471.657i		−	0.270131i
$146$	855.348			0.484857
$147$		0			0
$148$	−1263.52			−0.701761
$149$			1813.16i			0.996912i	0.866915	+	0.498456i	$0.166099\pi$
$149$			1813.16i			0.996912i	−0.866915	+	0.498456i	$0.833901\pi$
$150$	214.496	+	493.252i	0.116757	+	0.268493i
$151$	−1654.31			−0.891561			−0.445780	−	0.895142i	$-0.647074\pi$
$151$	−1654.31			−0.891561			−0.445780	+	0.895142i	$0.647074\pi$
$152$	−541.520			−0.288968
$153$	491.114	−	526.740i	0.259505	−	0.278330i
$154$		0			0
$155$		−	1325.00i		−	0.686622i
$156$	511.458	+	1176.14i	0.262496	+	0.603633i
$157$			1385.98i			0.704541i	0.935898	+	0.352271i	$0.114590\pi$
$157$			1385.98i			0.704541i	−0.935898	+	0.352271i	$0.885410\pi$
$158$			2437.13i			1.22714i
$159$	−557.240	−	1281.42i	−0.277937	−	0.639141i
$160$		−	273.863i		−	0.135317i
$161$		0			0
$162$	1454.43	−	101.940i	0.705376	−	0.0494393i
$163$	−1153.08			−0.554088			−0.277044	−	0.960857i	$-0.589355\pi$
$163$	−1153.08			−0.554088			−0.277044	+	0.960857i	$0.589355\pi$
$164$	840.845			0.400360
$165$	−1102.93	−	2536.29i	−0.520382	−	1.19666i
$166$			2742.35i			1.28222i
$167$	303.672			0.140712			0.0703559	−	0.997522i	$-0.477586\pi$
$167$	303.672			0.140712			0.0703559	+	0.997522i	$0.477586\pi$
$168$		0			0
$169$	−1610.64			−0.733110
$170$		−	456.548i		−	0.205974i
$171$	−1336.75	−	1246.33i	−0.597798	−	0.557366i
$172$	−1407.76			−0.624073
$173$	−2617.94			−1.15051			−0.575256	−	0.817973i	$-0.695098\pi$
$173$	−2617.94			−1.15051			−0.575256	+	0.817973i	$0.695098\pi$
$174$	525.224	−	228.399i	0.228834	−	0.0995110i
$175$		0			0
$176$		−	995.091i		−	0.426181i
$177$	−87.1208	+	37.8854i	−0.0369966	+	0.0160884i
$178$		−	1547.36i		−	0.651570i
$179$			2766.39i			1.15514i	0.816342	+	0.577569i	$0.195999\pi$
$179$			2766.39i			1.15514i	−0.816342	+	0.577569i	$0.804001\pi$
$180$	630.309	−	676.033i	0.261002	−	0.279936i
$181$			539.608i			0.221595i	0.993843	+	0.110798i	$0.0353405\pi$
$181$			539.608i			0.221595i	−0.993843	+	0.110798i	$0.964659\pi$
$182$		0			0
$183$	173.070	+	397.990i	0.0699109	+	0.160766i
$184$	423.347			0.169617
$185$	−2703.37			−1.07436
$186$	1475.48	−	641.629i	0.581654	−	0.252938i
$187$		−	1658.88i		−	0.648714i
$188$	−926.553			−0.359446
$189$		0			0
$190$	−1158.61			−0.442393
$191$		−	3192.31i		−	1.20936i	−0.796468	−	0.604680i	$-0.793301\pi$
$191$		−	3192.31i		−	1.20936i	0.796468	−	0.604680i	$-0.206699\pi$
$192$	304.966	−	132.618i	0.114630	−	0.0498483i
$193$	1437.37			0.536083			0.268042	−	0.963407i	$-0.413624\pi$
$193$	1437.37			0.536083			0.268042	+	0.963407i	$0.413624\pi$
$194$	1697.54			0.628227
$195$	1094.29	+	2516.42i	0.401867	+	0.924128i
$196$		0			0
$197$			2346.26i			0.848548i	0.905534	+	0.424274i	$0.139471\pi$
$197$			2346.26i			0.848548i	−0.905534	+	0.424274i	$0.860529\pi$
$198$	2290.25	−	2456.39i	0.822024	−	0.881655i
$199$			1831.53i			0.652431i	0.945295	+	0.326216i	$0.105774\pi$
$199$			1831.53i			0.652431i	−0.945295	+	0.326216i	$0.894226\pi$
$200$			414.054i			0.146390i
$201$	−616.941	+	268.283i	−0.216496	+	0.0941455i
$202$			2050.59i			0.714252i
$203$		0			0
$204$	508.399	−	221.083i	0.174486	−	0.0758769i
$205$	1799.04			0.612928
$206$	−642.720			−0.217381
$207$	1045.03	+	974.353i	0.350893	+	0.327160i
$208$			987.298i			0.329119i
$209$	−4209.86			−1.39331
$210$		0			0
$211$	4291.48			1.40018			0.700090	−	0.714055i	$-0.253143\pi$
$211$	4291.48			1.40018			0.700090	+	0.714055i	$0.253143\pi$
$212$		−	1075.67i		−	0.348479i
$213$	−1667.13	−	3833.70i	−0.536289	−	1.23324i
$214$	272.157			0.0869359
$215$	−3011.98			−0.955419
$216$	1058.04	+	374.526i	0.333288	+	0.117978i
$217$		0			0
$218$			2812.31i			0.873734i
$219$	886.206	+	2037.91i	0.273444	+	0.628809i
$220$		−	2129.05i		−	0.652458i
$221$			1645.89i			0.500971i
$222$	−1309.10	−	3010.40i	−0.395771	−	0.910111i
$223$			1170.88i			0.351604i	0.984426	+	0.175802i	$0.0562519\pi$
$223$			1170.88i			0.351604i	−0.984426	+	0.175802i	$0.943748\pi$
$224$		0			0
$225$	−952.964	+	1022.09i	−0.282360	+	0.302843i
$226$	934.569			0.275074
$227$	−2126.99			−0.621908			−0.310954	−	0.950425i	$-0.600648\pi$
$227$	−2126.99			−0.621908			−0.310954	+	0.950425i	$0.600648\pi$
$228$	−561.057	−	1290.20i	−0.162969	−	0.374761i
$229$		−	1298.10i		−	0.374589i	−0.982304	−	0.187294i	$-0.940028\pi$
$229$		−	1298.10i		−	0.374589i	0.982304	−	0.187294i	$-0.0599718\pi$
$230$	905.776			0.259674
$231$		0			0
$232$	440.893			0.124767
$233$			4204.46i			1.18216i	0.806613	+	0.591081i	$0.201298\pi$
$233$			4204.46i			1.18216i	−0.806613	+	0.591081i	$0.798702\pi$
$234$	−2272.31	+	2437.15i	−0.634810	+	0.680861i
$235$	−1982.41			−0.550291
$236$	−73.1324			−0.0201717
$237$	−5806.59	+	2525.06i	−1.59147	+	0.692068i
$238$		0			0
$239$		−	3816.77i		−	1.03300i	−0.856288	−	0.516498i	$-0.827235\pi$
$239$		−	3816.77i		−	1.03300i	0.856288	−	0.516498i	$-0.172765\pi$
$240$	652.493	−	283.743i	0.175493	−	0.0763148i
$241$			1636.98i			0.437540i	0.975776	+	0.218770i	$0.0702045\pi$
$241$			1636.98i			0.437540i	−0.975776	+	0.218770i	$0.929795\pi$
$242$		−	5073.98i		−	1.34780i
$243$	1749.78	+	3359.64i	0.461928	+	0.886917i
$244$			334.087i			0.0876547i
$245$		0			0
$246$	871.180	+	2003.36i	0.225790	+	0.519225i
$247$	4176.89			1.07599
$248$	1238.57			0.317135
$249$	−6533.79	+	2841.29i	−1.66290	+	0.723129i
$250$			3025.45i			0.765385i
$251$	5269.47			1.32512			0.662562	−	0.749007i	$-0.269469\pi$
$251$	5269.47			1.32512			0.662562	+	0.749007i	$0.269469\pi$
$252$		0			0
$253$	3291.16			0.817841
$254$			518.332i			0.128043i
$255$	1087.75	−	473.019i	0.267127	−	0.116163i
$256$	256.000			0.0625000
$257$	−1141.19			−0.276986			−0.138493	−	0.990363i	$-0.544226\pi$
$257$	−1141.19			−0.276986			−0.138493	+	0.990363i	$0.544226\pi$
$258$	−1458.54	−	3354.05i	−0.351957	−	0.809357i
$259$		0			0
$260$			2112.38i			0.503862i
$261$	1088.35	+	1014.73i	0.258111	+	0.240653i
$262$			5295.70i			1.24874i
$263$		−	2285.05i		−	0.535751i	−0.963454	−	0.267875i	$-0.913678\pi$
$263$		−	2285.05i		−	0.535751i	0.963454	−	0.267875i	$-0.0863215\pi$
$264$	2370.85	−	1030.99i	0.552712	−	0.240353i
$265$		−	2301.46i		−	0.533501i
$266$		0			0
$267$	3686.66	−	1603.18i	0.845018	−	0.367465i
$268$	−517.883			−0.118040
$269$	1874.38			0.424844			0.212422	−	0.977178i	$-0.431865\pi$
$269$	1874.38			0.424844			0.212422	+	0.977178i	$0.431865\pi$
$270$	2263.73	+	801.320i	0.510245	+	0.180618i
$271$			3281.32i			0.735521i	0.929921	+	0.367760i	$0.119875\pi$
$271$			3281.32i			0.735521i	−0.929921	+	0.367760i	$0.880125\pi$
$272$	426.769			0.0951348
$273$		0			0
$274$	936.032			0.206379
$275$			3218.92i			0.705847i
$276$	438.620	+	1008.65i	0.0956588	+	0.219976i
$277$	−530.749			−0.115125			−0.0575625	−	0.998342i	$-0.518333\pi$
$277$	−530.749			−0.115125			−0.0575625	+	0.998342i	$0.518333\pi$
$278$	5846.54			1.26134
$279$	3057.42	+	2850.63i	0.656069	+	0.611695i
$280$		0			0
$281$			5216.62i			1.10747i	0.832695	+	0.553733i	$0.186797\pi$
$281$			5216.62i			1.10747i	−0.832695	+	0.553733i	$0.813203\pi$
$282$	−959.980	−	2207.56i	−0.202716	−	0.466164i
$283$			1048.27i			0.220189i	0.993921	+	0.110094i	$0.0351153\pi$
$283$			1048.27i			0.220189i	−0.993921	+	0.110094i	$0.964885\pi$
$284$		−	3218.15i		−	0.672402i
$285$	−1200.41	−	2760.46i	−0.249496	−	0.573738i
$286$			7675.40i			1.58691i
$287$		0			0
$288$	631.937	+	589.195i	0.129296	+	0.120551i
$289$	−4201.55			−0.855190
$290$	943.315			0.191012
$291$	1758.78	+	4044.46i	0.354300	+	0.814745i
$292$			1710.70i			0.342846i
$293$	−6408.45			−1.27777			−0.638884	−	0.769303i	$-0.720603\pi$
$293$	−6408.45			−1.27777			−0.638884	+	0.769303i	$0.720603\pi$
$294$		0			0
$295$	−156.471			−0.0308817
$296$		−	2527.04i		−	0.496220i
$297$	8225.33	+	2911.62i	1.60701	+	0.568853i
$298$	−3626.32			−0.704923
$299$	−3265.39			−0.631580
$300$	−986.504	+	428.992i	−0.189853	+	0.0825595i
$301$		0			0
$302$		−	3308.62i		−	0.630429i
$303$	−4885.63	+	2124.57i	−0.926311	+	0.402816i
$304$		−	1083.04i		−	0.204331i
$305$			714.798i			0.134194i
$306$	1053.48	+	982.228i	0.196809	+	0.183497i
$307$			3717.93i			0.691184i	0.938385	+	0.345592i	$0.112322\pi$
$307$			3717.93i			0.691184i	−0.938385	+	0.345592i	$0.887678\pi$
$308$		0			0
$309$	−665.907	−	1531.31i	−0.122596	−	0.281920i
$310$	2650.00			0.485515
$311$	405.631			0.0739589			0.0369795	−	0.999316i	$-0.488226\pi$
$311$	405.631			0.0739589			0.0369795	+	0.999316i	$0.488226\pi$
$312$	−2352.29	+	1022.92i	−0.426833	+	0.185613i
$313$		−	3048.42i		−	0.550501i	−0.961373	−	0.275251i	$-0.911239\pi$
$313$		−	3048.42i		−	0.550501i	0.961373	−	0.275251i	$-0.0887608\pi$
$314$	−2771.95			−0.498186
$315$		0			0
$316$	−4874.27			−0.867718
$317$			6598.53i			1.16912i	0.811351	+	0.584559i	$0.198733\pi$
$317$			6598.53i			1.16912i	−0.811351	+	0.584559i	$0.801267\pi$
$318$	2562.85	−	1114.48i	0.451941	−	0.196531i
$319$	3427.56			0.601588
$320$	547.727			0.0956839
$321$	281.976	+	648.428i	0.0490292	+	0.112747i
$322$		0			0
$323$		−	1805.50i		−	0.311024i
$324$	203.880	+	2908.86i	0.0349589	+	0.498776i
$325$		−	3193.71i		−	0.545092i
$326$		−	2306.16i		−	0.391799i
$327$	−6700.48	+	2913.77i	−1.13314	+	0.492759i
$328$			1681.69i			0.283097i
$329$		0			0
$330$	5072.58	−	2205.86i	0.846170	−	0.367966i
$331$	−368.054			−0.0611181			−0.0305591	−	0.999533i	$-0.509729\pi$
$331$	−368.054			−0.0611181			−0.0305591	+	0.999533i	$0.509729\pi$
$332$	−5484.70			−0.906663
$333$	5816.09	−	6238.00i	0.957116	−	1.02655i
$334$			607.345i			0.0994983i
$335$	−1108.04			−0.180712
$336$		0			0
$337$	6514.00			1.05294			0.526469	−	0.850194i	$-0.323516\pi$
$337$	6514.00			1.05294			0.526469	+	0.850194i	$0.323516\pi$
$338$		−	3221.29i		−	0.518387i
$339$	968.285	+	2226.66i	0.155133	+	0.356742i
$340$	913.096			0.145646
$341$	9628.85			1.52912
$342$	2492.67	−	2673.49i	0.394117	−	0.422707i
$343$		0			0
$344$		−	2815.51i		−	0.441286i
$345$	938.453	+	2158.06i	0.146448	+	0.336770i
$346$		−	5235.89i		−	0.813535i
$347$		−	2423.63i		−	0.374948i	−0.982270	−	0.187474i	$-0.939970\pi$
$347$		−	2423.63i		−	0.374948i	0.982270	−	0.187474i	$-0.0600301\pi$
$348$	456.799	+	1050.45i	0.0703649	+	0.161810i
$349$		−	10490.9i		−	1.60907i	−0.593903	−	0.804536i	$-0.702414\pi$
$349$		−	10490.9i		−	1.60907i	0.593903	−	0.804536i	$-0.297586\pi$
$350$		0			0
$351$	−8160.92	−	2888.82i	−1.24102	−	0.439298i
$352$	1990.18			0.301355
$353$	−8010.85			−1.20786			−0.603930	−	0.797038i	$-0.706399\pi$
$353$	−8010.85			−1.20786			−0.603930	+	0.797038i	$0.706399\pi$
$354$	−75.7708	−	174.242i	−0.0113762	−	0.0261606i
$355$		−	6885.41i		−	1.02941i
$356$	3094.72			0.460729
$357$		0			0
$358$	−5532.78			−0.816807
$359$		−	11438.5i		−	1.68163i	−0.541326	−	0.840813i	$-0.682078\pi$
$359$		−	11438.5i		−	1.68163i	0.541326	−	0.840813i	$-0.317922\pi$
$360$	1352.07	+	1260.62i	0.197945	+	0.184557i
$361$	2277.06			0.331981
$362$	−1079.22			−0.156692
$363$	12089.0	−	5257.03i	1.74796	−	0.760118i
$364$		0			0
$365$			3660.13i			0.524877i
$366$	−795.979	+	346.140i	−0.113679	+	0.0494345i
$367$			1454.25i			0.206843i	0.994638	+	0.103421i	$0.0329790\pi$
$367$			1454.25i			0.206843i	−0.994638	+	0.103421i	$0.967021\pi$
$368$			846.695i			0.119938i
$369$	−3870.49	+	4151.26i	−0.546042	+	0.585653i
$370$		−	5406.74i		−	0.759684i
$371$		0			0
$372$	1283.26	+	2950.96i	0.178854	+	0.411291i
$373$	7980.82			1.10786			0.553929	−	0.832564i	$-0.313128\pi$
$373$	7980.82			1.10786			0.553929	+	0.832564i	$0.313128\pi$
$374$	3317.76			0.458710
$375$	−7208.28	+	3134.60i	−0.992624	+	0.431653i
$376$		−	1853.11i		−	0.254167i
$377$	−3400.72			−0.464578
$378$		0			0
$379$	5818.85			0.788639			0.394320	−	0.918973i	$-0.370980\pi$
$379$	5818.85			0.788639			0.394320	+	0.918973i	$0.370980\pi$
$380$		−	2317.23i		−	0.312819i
$381$	−1234.95	+	537.031i	−0.166059	+	0.0722125i
$382$	6384.63			0.855147
$383$	1237.22			0.165063			0.0825314	−	0.996588i	$-0.473700\pi$
$383$	1237.22			0.165063			0.0825314	+	0.996588i	$0.473700\pi$
$384$	265.236	+	609.933i	0.0352480	+	0.0810560i
$385$		0			0
$386$			2874.74i			0.379068i
$387$	6480.03	−	6950.11i	0.851159	−	0.912904i
$388$			3395.07i			0.444223i
$389$		−	3005.11i		−	0.391685i	−0.980635	−	0.195842i	$-0.937256\pi$
$389$		−	3005.11i		−	0.391685i	0.980635	−	0.195842i	$-0.0627441\pi$
$390$	−5032.85	+	2188.59i	−0.653457	+	0.284163i
$391$			1411.50i			0.182564i
$392$		0			0
$393$	−12617.3	+	5486.75i	−1.61948	+	0.704249i
$394$	−4692.52			−0.600014
$395$	−10428.8			−1.32843
$396$	4912.77	+	4580.49i	0.623424	+	0.581259i
$397$		−	6411.23i		−	0.810505i	−0.914205	−	0.405253i	$-0.867184\pi$
$397$		−	6411.23i		−	0.810505i	0.914205	−	0.405253i	$-0.132816\pi$
$398$	−3663.06			−0.461338
$399$		0			0
$400$	−828.108			−0.103514
$401$		−	3457.14i		−	0.430528i	−0.976556	−	0.215264i	$-0.930939\pi$
$401$		−	3457.14i		−	0.430528i	0.976556	−	0.215264i	$-0.0690611\pi$
$402$	−536.566	−	1233.88i	−0.0665709	−	0.153086i
$403$	−9553.44			−1.18087
$404$	−4101.18			−0.505053
$405$	436.213	+	6223.68i	0.0535200	+	0.763598i
$406$		0			0
$407$		−	19645.6i		−	2.39261i
$408$	442.165	+	1016.80i	0.0536530	+	0.123380i
$409$		−	15340.8i		−	1.85466i	−0.374246	−	0.927329i	$-0.622099\pi$
$409$		−	15340.8i		−	1.85466i	0.374246	−	0.927329i	$-0.377901\pi$
$410$			3598.07i			0.433405i
$411$	969.801	+	2230.14i	0.116391	+	0.267652i
$412$		−	1285.44i		−	0.153711i
$413$		0			0
$414$	−1948.71	+	2090.07i	−0.231337	+	0.248119i
$415$	−11734.8			−1.38805
$416$	−1974.60			−0.232722
$417$	6057.47	+	13929.7i	0.711356	+	1.63583i
$418$		−	8419.72i		−	0.985220i
$419$	−2968.51			−0.346112			−0.173056	−	0.984912i	$-0.555364\pi$
$419$	−2968.51			−0.346112			−0.173056	+	0.984912i	$0.555364\pi$
$420$		0			0
$421$	−8733.67			−1.01105			−0.505526	−	0.862811i	$-0.668702\pi$
$421$	−8733.67			−1.01105			−0.505526	+	0.862811i	$0.668702\pi$
$422$			8582.97i			0.990077i
$423$	4265.01	−	4574.40i	0.490241	−	0.525804i
$424$	2151.35			0.246412
$425$	−1380.51			−0.157564
$426$	7667.40	−	3334.25i	0.872035	−	0.379214i
$427$		0			0
$428$			544.315i			0.0614730i
$429$	−18287.0	+	7952.30i	−2.05805	+	0.894967i
$430$		−	6023.95i		−	0.675583i
$431$			59.2559i			0.00662240i	0.999995	+	0.00331120i	$0.00105399\pi$
$431$			59.2559i			0.00662240i	−0.999995	+	0.00331120i	$0.998946\pi$
$432$	−749.052	+	2116.07i	−0.0834231	+	0.235670i
$433$		−	3034.66i		−	0.336805i	−0.985718	−	0.168403i	$-0.946139\pi$
$433$		−	3034.66i		−	0.336805i	0.985718	−	0.168403i	$-0.0538609\pi$
$434$		0			0
$435$	977.347	+	2247.49i	0.107725	+	0.247722i
$436$	−5624.63			−0.617823
$437$	3582.05			0.392111
$438$	−4075.82	+	1772.41i	−0.444635	+	0.193354i
$439$		−	2489.21i		−	0.270623i	−0.990803	−	0.135312i	$-0.956796\pi$
$439$		−	2489.21i		−	0.270623i	0.990803	−	0.135312i	$-0.0432036\pi$
$440$	4258.11			0.461357
$441$		0			0
$442$	−3291.78			−0.354240
$443$		−	15071.7i		−	1.61642i	−0.588891	−	0.808212i	$-0.700435\pi$
$443$		−	15071.7i		−	1.61642i	0.588891	−	0.808212i	$-0.299565\pi$
$444$	6020.79	−	2618.20i	0.643545	−	0.279852i
$445$	6621.32			0.705350
$446$	−2341.76			−0.248622
$447$	−3757.15	−	8639.89i	−0.397555	−	0.914212i
$448$		0			0
$449$			5352.96i			0.562632i	0.959615	+	0.281316i	$0.0907709\pi$
$449$			5352.96i			0.562632i	−0.959615	+	0.281316i	$0.909229\pi$
$450$	−2044.19	−	1905.93i	−0.214142	−	0.199658i
$451$			13073.7i			1.36500i
$452$			1869.14i			0.194506i
$453$	7882.94	−	3427.98i	0.817600	−	0.355542i
$454$		−	4253.97i		−	0.439755i
$455$		0			0
$456$	2580.40	−	1122.11i	0.264996	−	0.115236i
$457$	2126.09			0.217624			0.108812	−	0.994062i	$-0.465295\pi$
$457$	2126.09			0.217624			0.108812	+	0.994062i	$0.465295\pi$
$458$	2596.20			0.264874
$459$	−1248.72	+	3527.63i	−0.126983	+	0.358727i
$460$			1811.55i			0.183617i
$461$	−987.346			−0.0997512			−0.0498756	−	0.998755i	$-0.515882\pi$
$461$	−987.346			−0.0997512			−0.0498756	+	0.998755i	$0.515882\pi$
$462$		0			0
$463$	−17023.3			−1.70872			−0.854362	−	0.519678i	$-0.826052\pi$
$463$	−17023.3			−1.70872			−0.854362	+	0.519678i	$0.826052\pi$
$464$			881.785i			0.0882238i
$465$	2745.60	+	6313.75i	0.273816	+	0.629663i
$466$	−8408.93			−0.835914
$467$	13717.1			1.35922			0.679608	−	0.733576i	$-0.262150\pi$
$467$	13717.1			1.35922			0.679608	+	0.733576i	$0.262150\pi$
$468$	−4874.30	−	4544.62i	−0.481441	−	0.448878i
$469$		0			0
$470$		−	3964.83i		−	0.389114i
$471$	−2871.96	−	6604.32i	−0.280961	−	0.646095i
$472$		−	146.265i		−	0.0142635i
$473$		−	21888.2i		−	2.12774i
$474$	−5050.12	−	11613.2i	−0.489366	−	1.12534i
$475$			3503.42i			0.338416i
$476$		0			0
$477$	5310.61	+	4951.42i	0.509761	+	0.475283i
$478$	7633.54			0.730439
$479$	1949.68			0.185977			0.0929887	−	0.995667i	$-0.470358\pi$
$479$	1949.68			0.185977			0.0929887	+	0.995667i	$0.470358\pi$
$480$	567.487	+	1304.99i	0.0539627	+	0.124092i
$481$			19491.7i			1.84770i
$482$	−3273.96			−0.309388
$483$		0			0
$484$	10148.0			0.953039
$485$			7263.95i			0.680080i
$486$	−6719.28	+	3499.56i	−0.627145	+	0.326632i
$487$	2538.95			0.236244			0.118122	−	0.992999i	$-0.462313\pi$
$487$	2538.95			0.236244			0.118122	+	0.992999i	$0.462313\pi$
$488$	−668.174			−0.0619812
$489$	5494.55	−	2389.36i	0.508123	−	0.220962i
$490$		0			0
$491$			17119.1i			1.57347i	0.617289	+	0.786737i	$0.288231\pi$
$491$			17119.1i			1.57347i	−0.617289	+	0.786737i	$0.711769\pi$
$492$	−4006.71	+	1742.36i	−0.367147	+	0.159658i
$493$			1469.99i			0.134290i
$494$			8353.78i			0.760839i
$495$	10511.2	+	9800.22i	0.954427	+	0.889873i
$496$			2477.15i			0.224248i
$497$		0			0
$498$	−5682.57	−	13067.6i	−0.511330	−	1.17585i
$499$	908.846			0.0815342			0.0407671	−	0.999169i	$-0.487020\pi$
$499$	908.846			0.0815342			0.0407671	+	0.999169i	$0.487020\pi$
$500$	−6050.90			−0.541209
$501$	−1447.03	+	629.256i	−0.129039	+	0.0561139i
$502$			10538.9i			0.937004i
$503$	13477.7			1.19471			0.597356	−	0.801976i	$-0.296218\pi$
$503$	13477.7			1.19471			0.597356	+	0.801976i	$0.296218\pi$
$504$		0			0
$505$	−8774.71			−0.773207
$506$			6582.33i			0.578301i
$507$	7674.88	−	3337.50i	0.672294	−	0.292354i
$508$	−1036.66			−0.0905404
$509$	−14131.5			−1.23059			−0.615294	−	0.788298i	$-0.710963\pi$
$509$	−14131.5			−1.23059			−0.615294	+	0.788298i	$0.710963\pi$
$510$	946.038	+	2175.50i	0.0821397	+	0.188888i
$511$		0			0
$512$			512.000i			0.0441942i
$513$	8952.32	+	3168.96i	0.770477	+	0.272735i
$514$		−	2282.38i		−	0.195859i
$515$		−	2750.27i		−	0.235323i
$516$	6708.10	−	2917.09i	0.572302	−	0.248871i
$517$		−	14406.3i		−	1.22551i
$518$		0			0
$519$	12474.8	−	5424.78i	1.05507	−	0.458808i
$520$	−4224.76			−0.356284
$521$	−11065.6			−0.930503			−0.465251	−	0.885179i	$-0.654036\pi$
$521$	−11065.6			−0.930503			−0.465251	+	0.885179i	$0.654036\pi$
$522$	−2029.47	+	2176.69i	−0.170167	+	0.182512i
$523$		−	6017.49i		−	0.503110i	−0.967843	−	0.251555i	$-0.919058\pi$
$523$		−	6017.49i		−	0.503110i	0.967843	−	0.251555i	$-0.0809419\pi$
$524$	−10591.4			−0.882991
$525$		0			0
$526$	4570.11			0.378833
$527$			4129.57i			0.341341i
$528$	2061.98	+	4741.71i	0.169955	+	0.390826i
$529$	9366.64			0.769840
$530$	4602.93			0.377242
$531$	336.635	−	361.055i	0.0275117	−	0.0295075i
$532$		0			0
$533$		−	12971.3i		−	1.05413i
$534$	3206.36	+	7373.32i	0.259837	+	0.597518i
$535$			1164.59i			0.0941116i
$536$		−	1035.77i		−	0.0834669i
$537$	−5732.39	−	13182.1i	−0.460653	−	1.05931i
$538$			3748.76i			0.300410i
$539$		0			0
$540$	−1602.64	+	4527.46i	−0.127716	+	0.360798i
$541$	6954.15			0.552647			0.276324	−	0.961065i	$-0.410884\pi$
$541$	6954.15			0.552647			0.276324	+	0.961065i	$0.410884\pi$
$542$	−6562.64			−0.520092
$543$	−1118.15	−	2571.29i	−0.0883691	−	0.203213i
$544$			853.538i			0.0672705i
$545$	−12034.2			−0.945852
$546$		0			0
$547$	14101.3			1.10224			0.551122	−	0.834424i	$-0.314200\pi$
$547$	14101.3			1.10224			0.551122	+	0.834424i	$0.314200\pi$
$548$			1872.06i			0.145932i
$549$	−1649.39	−	1537.83i	−0.128223	−	0.119550i
$550$	−6437.83			−0.499109
$551$	3730.51			0.288430
$552$	−2017.29	+	877.241i	−0.155546	+	0.0676410i
$553$		0			0
$554$		−	1061.50i		−	0.0814056i
$555$	12881.8	−	5601.80i	0.985231	−	0.428438i
$556$			11693.1i			0.891902i
$557$		−	8446.45i		−	0.642527i	−0.946990	−	0.321263i	$-0.895892\pi$
$557$		−	8446.45i		−	0.642527i	0.946990	−	0.321263i	$-0.104108\pi$
$558$	−5701.26	+	6114.85i	−0.432534	+	0.463911i
$559$			21716.8i			1.64315i
$560$		0			0
$561$	3437.46	+	7904.74i	0.258698	+	0.594899i
$562$	−10433.2			−0.783096
$563$	21902.1			1.63955			0.819774	−	0.572688i	$-0.194099\pi$
$563$	21902.1			1.63955			0.819774	+	0.572688i	$0.194099\pi$
$564$	4415.12	−	1919.96i	0.329628	−	0.143342i
$565$			3999.13i			0.297778i
$566$	−2096.55			−0.155697
$567$		0			0
$568$	6436.30			0.475460
$569$		−	10074.6i		−	0.742266i	−0.928580	−	0.371133i	$-0.878969\pi$
$569$		−	10074.6i		−	0.742266i	0.928580	−	0.371133i	$-0.121031\pi$
$570$	5520.91	−	2400.83i	0.405694	−	0.176420i
$571$	18266.9			1.33879			0.669394	−	0.742908i	$-0.266554\pi$
$571$	18266.9			1.33879			0.669394	+	0.742908i	$0.266554\pi$
$572$	−15350.8			−1.12211
$573$	6614.97	+	15211.7i	0.482276	+	1.10904i
$574$		0			0
$575$		−	2738.89i		−	0.198642i
$576$	−1178.39	+	1263.87i	−0.0852424	+	0.0914261i
$577$		−	3902.69i		−	0.281579i	−0.990040	−	0.140789i	$-0.955036\pi$
$577$		−	3902.69i		−	0.281579i	0.990040	−	0.140789i	$-0.0449641\pi$
$578$		−	8403.10i		−	0.604711i
$579$	−6849.21	+	2978.45i	−0.491612	+	0.213783i
$580$			1886.63i			0.135066i
$581$		0			0
$582$	−8088.93	+	3517.56i	−0.576111	+	0.250528i
$583$	16724.9			1.18812
$584$	−3421.39			−0.242428
$585$	−10428.8	−	9723.47i	−0.737059	−	0.687207i
$586$		−	12816.9i		−	0.903518i
$587$	3318.05			0.233306			0.116653	−	0.993173i	$-0.462783\pi$
$587$	3318.05			0.233306			0.116653	+	0.993173i	$0.462783\pi$
$588$		0			0
$589$	10479.9			0.733135
$590$		−	312.942i		−	0.0218366i
$591$	−4861.81	−	11180.2i	−0.338389	−	0.778156i
$592$	5054.07			0.350880
$593$	24252.9			1.67951			0.839754	−	0.542968i	$-0.182699\pi$
$593$	24252.9			1.67951			0.839754	+	0.542968i	$0.182699\pi$
$594$	−5823.24	+	16450.7i	−0.402240	+	1.13633i
$595$		0			0
$596$		−	7252.64i		−	0.498456i
$597$	−3795.21	−	8727.43i	−0.260180	−	0.598308i
$598$		−	6530.78i		−	0.446594i
$599$			11107.9i			0.757694i	0.925459	+	0.378847i	$0.123679\pi$
$599$			11107.9i			0.757694i	−0.925459	+	0.378847i	$0.876321\pi$
$600$	−857.984	−	1973.01i	−0.0583784	−	0.134246i
$601$			13367.3i			0.907258i	0.891191	+	0.453629i	$0.149871\pi$
$601$			13367.3i			0.907258i	−0.891191	+	0.453629i	$0.850129\pi$
$602$		0			0
$603$	2383.86	−	2556.79i	0.160992	−	0.172671i
$604$	6617.23			0.445780
$605$	21712.1			1.45905
$606$	−4249.14	−	9771.27i	−0.284834	−	0.655001i
$607$			11755.8i			0.786084i	0.919521	+	0.393042i	$0.128577\pi$
$607$			11755.8i			0.786084i	−0.919521	+	0.393042i	$0.871423\pi$
$608$	2166.08			0.144484
$609$		0			0
$610$	−1429.60			−0.0948896
$611$			14293.5i			0.946404i
$612$	−1964.46	+	2106.96i	−0.129752	+	0.139165i
$613$	−23720.1			−1.56288			−0.781439	−	0.623982i	$-0.785514\pi$
$613$	−23720.1			−1.56288			−0.781439	+	0.623982i	$0.785514\pi$
$614$	−7435.86			−0.488741
$615$	−8572.59	+	3727.88i	−0.562082	+	0.244427i
$616$		0			0
$617$			9294.78i			0.606473i	0.952915	+	0.303237i	$0.0980672\pi$
$617$			9294.78i			0.606473i	−0.952915	+	0.303237i	$0.901933\pi$
$618$	3062.62	−	1331.81i	0.199348	−	0.0866884i
$619$			13438.6i			0.872603i	0.899801	+	0.436301i	$0.143712\pi$
$619$			13438.6i			0.872603i	−0.899801	+	0.436301i	$0.856288\pi$
$620$			5300.00i			0.343311i
$621$	−6998.70	−	2477.42i	−0.452252	−	0.160089i
$622$			811.262i			0.0522969i
$623$		0			0
$624$	−2045.83	−	4704.57i	−0.131248	−	0.301817i
$625$	−6476.64			−0.414505
$626$	6096.84			0.389263
$627$	20060.4	−	8723.47i	1.27773	−	0.555633i
$628$		−	5543.91i		−	0.352271i
$629$	8425.47			0.534095
$630$		0			0
$631$	11635.5			0.734076			0.367038	−	0.930206i	$-0.380372\pi$
$631$	11635.5			0.734076			0.367038	+	0.930206i	$0.380372\pi$
$632$		−	9748.54i		−	0.613570i
$633$	−20449.4	+	8892.61i	−1.28403	+	0.558372i
$634$	−13197.1			−0.826692
$635$	−2218.00			−0.138612
$636$	2228.96	+	5125.69i	0.138969	+	0.319571i
$637$		0			0
$638$			6855.13i			0.425387i
$639$	15888.0	+	14813.4i	0.983601	+	0.917074i
$640$			1095.45i			0.0676587i
$641$			24648.6i			1.51882i	0.650614	+	0.759409i	$0.274512\pi$
$641$			24648.6i			1.51882i	−0.650614	+	0.759409i	$0.725488\pi$
$642$	−1296.86	+	563.952i	−0.0797241	+	0.0346688i
$643$		−	5268.28i		−	0.323111i	−0.986864	−	0.161556i	$-0.948349\pi$
$643$		−	5268.28i		−	0.323111i	0.986864	−	0.161556i	$-0.0516511\pi$
$644$		0			0
$645$	14352.4	−	6241.28i	0.876161	−	0.381008i
$646$	3611.00			0.219927
$647$	−18470.6			−1.12234			−0.561169	−	0.827701i	$-0.689648\pi$
$647$	−18470.6			−1.12234			−0.561169	+	0.827701i	$0.689648\pi$
$648$	−5817.73	+	407.761i	−0.352688	+	0.0247197i
$649$		−	1137.08i		−	0.0687742i
$650$	6387.42			0.385439
$651$		0			0
$652$	4612.32			0.277044
$653$		−	13180.0i		−	0.789850i	−0.918713	−	0.394925i	$-0.870771\pi$
$653$		−	13180.0i		−	0.789850i	0.918713	−	0.394925i	$-0.129229\pi$
$654$	−5827.55	−	13401.0i	−0.348433	−	0.801252i
$655$	−22660.9			−1.35181
$656$	−3363.38			−0.200180
$657$	−8445.72	−	7874.49i	−0.501521	−	0.467600i
$658$		0			0
$659$			10701.0i			0.632549i	0.948668	+	0.316275i	$0.102432\pi$
$659$			10701.0i			0.632549i	−0.948668	+	0.316275i	$0.897568\pi$
$660$	4411.72	+	10145.2i	0.260191	+	0.598332i
$661$			12950.0i			0.762023i	0.924570	+	0.381011i	$0.124424\pi$
$661$			12950.0i			0.762023i	−0.924570	+	0.381011i	$0.875576\pi$
$662$		−	736.109i		−	0.0432170i
$663$	−3410.54	−	7842.83i	−0.199780	−	0.459412i
$664$		−	10969.4i		−	0.641108i
$665$		0			0
$666$	12476.0	+	11632.2i	0.725879	+	0.676783i
$667$	−2916.42			−0.169302
$668$	−1214.69			−0.0703559
$669$	−2426.24	−	5579.35i	−0.140215	−	0.322437i
$670$		−	2216.08i		−	0.127783i
$671$	−5194.48			−0.298854
$672$		0			0
$673$	3025.28			0.173278			0.0866389	−	0.996240i	$-0.472387\pi$
$673$	3025.28			0.173278			0.0866389	+	0.996240i	$0.472387\pi$
$674$			13028.0i			0.744540i
$675$	2423.03	−	6845.07i	0.138167	−	0.390321i
$676$	6442.57			0.366555
$677$	−2736.45			−0.155348			−0.0776739	−	0.996979i	$-0.524749\pi$
$677$	−2736.45			−0.155348			−0.0776739	+	0.996979i	$0.524749\pi$
$678$	−4453.32	+	1936.57i	−0.252254	+	0.109696i
$679$		0			0
$680$			1826.19i			0.102987i
$681$	10135.3	−	4407.44i	0.570317	−	0.248008i
$682$			19257.7i			1.08125i
$683$			9211.67i			0.516069i	0.966136	+	0.258034i	$0.0830747\pi$
$683$			9211.67i			0.516069i	−0.966136	+	0.258034i	$0.916925\pi$
$684$	5346.98	+	4985.33i	0.298899	+	0.278683i
$685$			4005.39i			0.223413i
$686$		0			0
$687$	2689.86	+	6185.57i	0.149381	+	0.343514i
$688$	5631.03			0.312036
$689$	−16593.9			−0.917529
$690$	−4316.11	+	1876.91i	−0.238133	+	0.103554i
$691$			2573.02i			0.141653i	0.997489	+	0.0708264i	$0.0225636\pi$
$691$			2573.02i			0.141653i	−0.997489	+	0.0708264i	$0.977436\pi$
$692$	10471.8			0.575256
$693$		0			0
$694$	4847.25			0.265128
$695$			25018.0i			1.36545i
$696$	−2100.90	+	913.597i	−0.114417	+	0.0497555i
$697$	−5606.98			−0.304705
$698$	20981.9			1.13779
$699$	−8712.29	−	20034.7i	−0.471430	−	1.08409i
$700$		0			0
$701$			18596.9i			1.00199i	0.865450	+	0.500996i	$0.167033\pi$
$701$			18596.9i			1.00199i	−0.865450	+	0.500996i	$0.832967\pi$
$702$	5777.64	−	16321.8i	0.310631	−	0.877533i
$703$		−	21381.9i		−	1.14713i
$704$			3980.36i			0.213090i
$705$	9446.40	−	4107.86i	0.504641	−	0.219448i
$706$		−	16021.7i		−	0.854085i
$707$		0			0
$708$	348.483	−	151.542i	0.0184983	−	0.00804418i
$709$	−24000.2			−1.27129			−0.635647	−	0.771980i	$-0.719266\pi$
$709$	−24000.2			−1.27129			−0.635647	+	0.771980i	$0.719266\pi$
$710$	13770.8			0.727901
$711$	22436.7	−	24064.3i	1.18346	−	1.26931i
$712$			6189.43i			0.325785i
$713$	−8192.92			−0.430333
$714$		0			0
$715$	−32843.9			−1.71789
$716$		−	11065.6i		−	0.577569i
$717$	7908.93	+	18187.3i	0.411945	+	0.947303i
$718$	22877.1			1.18909
$719$	−16611.9			−0.861638			−0.430819	−	0.902438i	$-0.641775\pi$
$719$	−16611.9			−0.861638			−0.430819	+	0.902438i	$0.641775\pi$
$720$	−2521.23	+	2704.13i	−0.130501	+	0.139968i
$721$		0			0
$722$			4554.11i			0.234746i
$723$	−3392.08	−	7800.38i	−0.174485	−	0.401244i
$724$		−	2158.43i		−	0.110798i
$725$		−	2852.40i		−	0.146118i
$726$	10514.1	+	24178.0i	0.537484	+	1.23599i
$727$			31798.3i			1.62219i	0.584912	+	0.811097i	$0.301129\pi$
$727$			31798.3i			1.62219i	−0.584912	+	0.811097i	$0.698871\pi$
$728$		0			0
$729$	−15299.6	−	12383.2i	−0.777299	−	0.629132i
$730$	−7320.26			−0.371144
$731$	9387.30			0.474968
$732$	−692.280	−	1591.96i	−0.0349555	−	0.0803832i
$733$			33962.6i			1.71137i	0.517495	+	0.855686i	$0.326864\pi$
$733$			33962.6i			1.71137i	−0.517495	+	0.855686i	$0.673136\pi$
$734$	−2908.50			−0.146260
$735$		0			0
$736$	−1693.39			−0.0848086
$737$		−	8052.19i		−	0.402451i
$738$	−8302.52	−	7740.97i	−0.414119	−	0.386110i
$739$	−28894.7			−1.43831			−0.719153	−	0.694852i	$-0.755470\pi$
$739$	−28894.7			−1.43831			−0.719153	+	0.694852i	$0.755470\pi$
$740$	10813.5			0.537178
$741$	−19903.3	+	8655.16i	−0.986729	+	0.429089i
$742$		0			0
$743$		−	8565.28i		−	0.422920i	−0.977387	−	0.211460i	$-0.932178\pi$
$743$		−	8565.28i		−	0.422920i	0.977387	−	0.211460i	$-0.0678218\pi$
$744$	−5901.93	+	2566.51i	−0.290827	+	0.126469i
$745$		−	15517.4i		−	0.763107i
$746$			15961.6i			0.783374i
$747$	25246.6	−	27078.0i	1.23658	−	1.32628i
$748$			6635.53i			0.324357i
$749$		0			0
$750$	−6269.19	−	14416.6i	−0.305225	−	0.701891i
$751$	−14666.1			−0.712616			−0.356308	−	0.934369i	$-0.615965\pi$
$751$	−14666.1			−0.712616			−0.356308	+	0.934369i	$0.615965\pi$
$752$	3706.21			0.179723
$753$	−25109.6	+	10919.2i	−1.21520	+	0.528441i
$754$		−	6801.44i		−	0.328507i
$755$	14157.9			0.682464
$756$		0			0
$757$	−19962.2			−0.958439			−0.479220	−	0.877695i	$-0.659080\pi$
$757$	−19962.2			−0.958439			−0.479220	+	0.877695i	$0.659080\pi$
$758$			11637.7i			0.557652i
$759$	−15682.7	+	6819.80i	−0.749996	+	0.326144i
$760$	4634.45			0.221197
$761$	−38332.6			−1.82596			−0.912980	−	0.408005i	$-0.866225\pi$
$761$	−38332.6			−1.82596			−0.912980	+	0.408005i	$0.866225\pi$
$762$	−1074.06	−	2469.90i	−0.0510619	−	0.117421i
$763$		0			0
$764$			12769.3i			0.604680i
$765$	−4203.06	+	4507.96i	−0.198643	+	0.213053i
$766$			2474.44i			0.116717i
$767$			1128.18i			0.0531111i
$768$	−1219.87	+	530.471i	−0.0573152	+	0.0249241i
$769$		−	1797.33i		−	0.0842826i	−0.999112	−	0.0421413i	$-0.986582\pi$
$769$		−	1797.33i		−	0.0842826i	0.999112	−	0.0421413i	$-0.0134180\pi$
$770$		0			0
$771$	5437.89	−	2364.72i	0.254009	−	0.110458i
$772$	−5749.48			−0.268042
$773$	11732.3			0.545901			0.272951	−	0.962028i	$-0.412000\pi$
$773$	11732.3			0.545901			0.272951	+	0.962028i	$0.412000\pi$
$774$	13900.2	+	12960.1i	0.645521	+	0.601860i
$775$		−	8013.07i		−	0.371404i
$776$	−6790.14			−0.314113
$777$		0			0
$778$	6010.23			0.276963
$779$			14229.2i			0.654448i
$780$	−4377.17	−	10065.7i	−0.200933	−	0.462064i
$781$	50036.7			2.29252
$782$	−2822.99			−0.129092
$783$	−7288.76	−	2580.09i	−0.332668	−	0.117759i
$784$		0			0
$785$		−	11861.5i		−	0.539306i
$786$	−10973.5	−	25234.5i	−0.497979	−	1.14515i
$787$		−	15373.0i		−	0.696299i	−0.937439	−	0.348150i	$-0.886810\pi$
$787$		−	15373.0i		−	0.696299i	0.937439	−	0.348150i	$-0.113190\pi$
$788$		−	9385.03i		−	0.424274i
$789$	4734.98	+	10888.5i	0.213650	+	0.491307i
$790$		−	20857.5i		−	0.939339i
$791$		0			0
$792$	−9160.98	+	9825.54i	−0.411012	+	0.440828i
$793$	5153.80			0.230791
$794$	12822.5			0.573114
$795$	4768.99	+	10966.7i	0.212753	+	0.489244i
$796$		−	7326.12i		−	0.326216i
$797$	33773.5			1.50103			0.750513	−	0.660856i	$-0.229807\pi$
$797$	33773.5			1.50103			0.750513	+	0.660856i	$0.229807\pi$
$798$		0			0
$799$	6178.50			0.273567
$800$		−	1656.22i		−	0.0731951i
$801$	−14245.3	+	15278.6i	−0.628379	+	0.673963i
$802$	6914.29			0.304429
$803$	−26598.4			−1.16891
$804$	2467.76	−	1073.13i	0.108248	−	0.0470727i
$805$		0			0
$806$		−	19106.9i		−	0.835002i
$807$	−8931.61	+	3884.01i	−0.389601	+	0.169422i
$808$		−	8202.36i		−	0.357126i
$809$			35476.1i			1.54175i	0.636987	+	0.770874i	$0.280180\pi$
$809$			35476.1i			1.54175i	−0.636987	+	0.770874i	$0.719820\pi$
$810$	−12447.4	+	872.427i	−0.539945	+	0.0378444i
$811$		−	31038.0i		−	1.34389i	−0.740603	−	0.671943i	$-0.765460\pi$
$811$		−	31038.0i		−	1.34389i	0.740603	−	0.671943i	$-0.234540\pi$
$812$		0			0
$813$	−6799.40	−	15635.8i	−0.293315	−	0.674505i
$814$	39291.1			1.69183
$815$	9868.33			0.424138
$816$	−2033.60	+	884.331i	−0.0872428	+	0.0379384i
$817$		−	23822.8i		−	1.02014i
$818$	30681.7			1.31144
$819$		0			0
$820$	−7196.15			−0.306464
$821$			4874.37i			0.207207i	0.994619	+	0.103603i	$0.0330372\pi$
$821$			4874.37i			0.207207i	−0.994619	+	0.103603i	$0.966963\pi$
$822$	−4460.28	+	1939.60i	−0.189258	+	0.0823009i
$823$	−22102.2			−0.936127			−0.468064	−	0.883695i	$-0.655048\pi$
$823$	−22102.2			−0.936127			−0.468064	+	0.883695i	$0.655048\pi$
$824$	2570.88			0.108690
$825$	−6670.09	−	15338.5i	−0.281482	−	0.647293i
$826$		0			0
$827$			18204.1i			0.765439i	0.923865	+	0.382719i	$0.125012\pi$
$827$			18204.1i			0.765439i	−0.923865	+	0.382719i	$0.874988\pi$
$828$	−4180.14	−	3897.41i	−0.175447	−	0.163580i
$829$			31576.5i			1.32292i	0.749982	+	0.661458i	$0.230062\pi$
$829$			31576.5i			1.32292i	−0.749982	+	0.661458i	$0.769938\pi$
$830$		−	23469.7i		−	0.981499i
$831$	2529.07	−	1099.79i	0.105575	−	0.0459102i
$832$		−	3949.19i		−	0.164560i
$833$		0			0
$834$	−27859.4	+	12114.9i	−1.15670	+	0.503005i
$835$	−2598.90			−0.107711
$836$	16839.4			0.696656
$837$	−20475.9	−	7248.10i	−0.845579	−	0.299320i
$838$		−	5937.01i		−	0.244738i
$839$	−19529.4			−0.803612			−0.401806	−	0.915725i	$-0.631617\pi$
$839$	−19529.4			−0.803612			−0.401806	+	0.915725i	$0.631617\pi$
$840$		0			0
$841$	21351.7			0.875465
$842$		−	17467.3i		−	0.714922i
$843$	−10809.6	−	24857.7i	−0.441642	−	1.01559i
$844$	−17165.9			−0.700090
$845$	13784.3			0.561175
$846$	9148.80	+	8530.02i	0.371800	+	0.346652i
$847$		0			0
$848$			4302.69i			0.174239i
$849$	−2172.19	−	4995.13i	−0.0878083	−	0.201923i
$850$		−	2761.02i		−	0.111414i
$851$			16715.8i			0.673340i
$852$	6668.50	+	15334.8i	0.268144	+	0.616622i
$853$		−	20178.9i		−	0.809979i	−0.914321	−	0.404989i	$-0.867275\pi$
$853$		−	20178.9i		−	0.809979i	0.914321	−	0.404989i	$-0.132725\pi$
$854$		0			0
$855$	11440.2	+	10666.4i	0.457597	+	0.426647i
$856$	−1088.63			−0.0434680
$857$	14116.6			0.562677			0.281338	−	0.959609i	$-0.409222\pi$
$857$	14116.6			0.562677			0.281338	+	0.959609i	$0.409222\pi$
$858$	−15904.6	−	36574.0i	−0.632837	−	1.45526i
$859$		−	19025.6i		−	0.755700i	−0.925867	−	0.377850i	$-0.876663\pi$
$859$		−	19025.6i		−	0.755700i	0.925867	−	0.377850i	$-0.123337\pi$
$860$	12047.9			0.477709
$861$		0			0
$862$	−118.512			−0.00468275
$863$		−	10804.8i		−	0.426188i	−0.977032	−	0.213094i	$-0.931646\pi$
$863$		−	10804.8i		−	0.426188i	0.977032	−	0.213094i	$-0.0683540\pi$
$864$	−4232.15	−	1498.10i	−0.166644	−	0.0589891i
$865$	22405.0			0.880684
$866$	6069.33			0.238157
$867$	20020.8	−	8706.25i	0.784247	−	0.341038i
$868$		0			0
$869$		−	75786.5i		−	2.95844i
$870$	−4494.99	+	1954.69i	−0.175166	+	0.0761728i
$871$			7989.13i			0.310794i
$872$		−	11249.3i		−	0.436867i
$873$	−16761.5	−	15627.8i	−0.649818	−	0.605867i
$874$			7164.10i			0.277265i
$875$		0			0
$876$	−3544.82	−	8151.64i	−0.136722	−	0.314404i
$877$	3591.75			0.138295			0.0691476	−	0.997606i	$-0.477972\pi$
$877$	3591.75			0.138295			0.0691476	+	0.997606i	$0.477972\pi$
$878$	4978.43			0.191360
$879$	30536.9	−	13279.3i	1.17177	−	0.509556i
$880$			8516.21i			0.326229i
$881$	47633.6			1.82158			0.910792	−	0.412865i	$-0.135472\pi$
$881$	47633.6			1.82158			0.910792	+	0.412865i	$0.135472\pi$
$882$		0			0
$883$	−42383.1			−1.61530			−0.807648	−	0.589665i	$-0.799260\pi$
$883$	−42383.1			−1.61530			−0.807648	+	0.589665i	$0.799260\pi$
$884$		−	6583.56i		−	0.250485i
$885$	745.600	−	324.232i	0.0283198	−	0.0123152i
$886$	30143.3			1.14298
$887$	17268.6			0.653690			0.326845	−	0.945078i	$-0.394015\pi$
$887$	17268.6			0.653690			0.326845	+	0.945078i	$0.394015\pi$
$888$	5236.41	+	12041.6i	0.197886	+	0.455055i
$889$		0			0
$890$			13242.6i			0.498758i
$891$	−45227.9	+	3169.99i	−1.70055	+	0.119190i
$892$		−	4683.51i		−	0.175802i
$893$		−	15679.6i		−	0.587568i
$894$	17279.8	−	7514.29i	0.646445	−	0.281113i
$895$		−	23675.4i		−	0.884225i
$896$		0			0
$897$	15559.9	−	6766.39i	0.579186	−	0.251865i
$898$	−10705.9			−0.397841
$899$	−8532.47			−0.316545
$900$	3811.86	−	4088.38i	0.141180	−	0.151421i
$901$			7172.87i			0.265220i
$902$	−26147.4			−0.965204
$903$		0			0
$904$	−3738.28			−0.137537
$905$		−	4618.09i		−	0.169625i
$906$	6855.96	+	15765.9i	0.251406	+	0.578131i
$907$	4541.95			0.166277			0.0831383	−	0.996538i	$-0.473506\pi$
$907$	4541.95			0.166277			0.0831383	+	0.996538i	$0.473506\pi$
$908$	8507.94			0.310954
$909$	18878.1	−	20247.6i	0.688831	−	0.738800i
$910$		0			0
$911$		−	11585.4i		−	0.421342i	−0.977557	−	0.210671i	$-0.932435\pi$
$911$		−	11585.4i		−	0.421342i	0.977557	−	0.210671i	$-0.0675648\pi$
$912$	2244.23	+	5160.80i	0.0814844	+	0.187381i
$913$		−	85277.8i		−	3.09122i
$914$			4252.18i			0.153884i
$915$	−1481.17	−	3406.09i	−0.0535148	−	0.123062i
$916$			5192.39i			0.187294i
$917$		0			0
$918$	−7055.27	−	2497.44i	−0.253659	−	0.0897906i
$919$	−5332.33			−0.191401			−0.0957004	−	0.995410i	$-0.530509\pi$
$919$	−5332.33			−0.191401			−0.0957004	+	0.995410i	$0.530509\pi$
$920$	−3623.10			−0.129837
$921$	−7704.12	−	17716.3i	−0.275634	−	0.633846i
$922$		−	1974.69i		−	0.0705347i
$923$	−49644.9			−1.77040
$924$		0			0
$925$	−16348.9			−0.581134
$926$		−	34046.6i		−	1.20825i
$927$	6346.23	+	5916.99i	0.224852	+	0.209644i
$928$	−1763.57			−0.0623837
$929$	−9930.07			−0.350694			−0.175347	−	0.984507i	$-0.556105\pi$
$929$	−9930.07			−0.350694			−0.175347	+	0.984507i	$0.556105\pi$
$930$	−12627.5	+	5491.20i	−0.445239	+	0.193617i
$931$		0			0
$932$		−	16817.9i		−	0.591081i
$933$	−1932.87	+	840.530i	−0.0678236	+	0.0294938i
$934$			27434.3i			0.961111i
$935$			14197.1i			0.496571i
$936$	9089.24	−	9748.60i	0.317405	−	0.340430i
$937$			28533.5i			0.994821i	0.867515	+	0.497411i	$0.165716\pi$
$937$			28533.5i			0.994821i	−0.867515	+	0.497411i	$0.834284\pi$
$938$		0			0
$939$	6316.79	+	14526.0i	0.219532	+	0.504834i
$940$	7929.65			0.275145
$941$	5701.85			0.197529			0.0987646	−	0.995111i	$-0.468511\pi$
$941$	5701.85			0.197529			0.0987646	+	0.995111i	$0.468511\pi$
$942$	13208.6	−	5743.91i	0.456858	−	0.198670i
$943$		−	11124.1i		−	0.384145i
$944$	292.530			0.0100858
$945$		0			0
$946$	43776.4			1.50454
$947$			17138.3i			0.588088i	0.955792	+	0.294044i	$0.0950013\pi$
$947$			17138.3i			0.588088i	−0.955792	+	0.294044i	$0.904999\pi$
$948$	23226.4	−	10100.2i	0.795736	−	0.346034i
$949$	26390.1			0.902696
$950$	−7006.83			−0.239297
$951$	−13673.2	−	31442.7i	−0.466228	−	1.07213i
$952$		0			0
$953$			48616.8i			1.65252i	0.563287	+	0.826261i	$0.309536\pi$
$953$			48616.8i			1.65252i	−0.563287	+	0.826261i	$0.690464\pi$
$954$	−9902.84	+	10621.2i	−0.336076	+	0.360456i
$955$			27320.6i			0.925730i
$956$			15267.1i			0.516498i
$957$	−16332.7	+	7102.44i	−0.551683	+	0.239905i
$958$			3899.36i			0.131506i
$959$		0			0
$960$	−2609.97	+	1134.97i	−0.0877463	+	0.0381574i
$961$	5821.25			0.195403
$962$	−38983.4			−1.30652
$963$	−2687.29	−	2505.53i	−0.0899238	−	0.0838417i
$964$		−	6547.93i		−	0.218770i
$965$	−12301.3			−0.410356
$966$		0			0
$967$	−14811.1			−0.492547			−0.246273	−	0.969200i	$-0.579206\pi$
$967$	−14811.1			−0.492547			−0.246273	+	0.969200i	$0.579206\pi$
$968$			20295.9i			0.673900i
$969$	3741.27	+	8603.39i	0.124032	+	0.285223i
$970$	−14527.9			−0.480889
$971$	−2729.87			−0.0902223			−0.0451111	−	0.998982i	$-0.514364\pi$
$971$	−2729.87			−0.0902223			−0.0451111	+	0.998982i	$0.514364\pi$
$972$	−6999.12	−	13438.6i	−0.230964	−	0.443459i
$973$		0			0
$974$			5077.91i			0.167050i
$975$	6617.85	+	15218.3i	0.217375	+	0.499874i
$976$		−	1336.35i		−	0.0438273i
$977$			57020.3i			1.86719i	0.358334	+	0.933593i	$0.383345\pi$
$977$			57020.3i			1.86719i	−0.358334	+	0.933593i	$0.616655\pi$
$978$	4778.72	+	10989.1i	0.156244	+	0.359297i
$979$			48117.6i			1.57083i
$980$		0			0
$981$	25890.7	−	27768.9i	0.842636	−	0.903763i
$982$	−34238.2			−1.11261
$983$	53108.2			1.72318			0.861591	−	0.507603i	$-0.169468\pi$
$983$	53108.2			1.72318			0.861591	+	0.507603i	$0.169468\pi$
$984$	−3484.72	−	8013.43i	−0.112895	−	0.259612i
$985$		−	20079.8i		−	0.649539i
$986$	−2939.99			−0.0949577
$987$		0			0
$988$	−16707.6			−0.537994
$989$			18624.1i			0.598798i
$990$	−19600.4	+	21022.3i	−0.629235	+	0.674882i
$991$	−19122.7			−0.612969			−0.306485	−	0.951876i	$-0.599153\pi$
$991$	−19122.7			−0.612969			−0.306485	+	0.951876i	$0.599153\pi$
$992$	−4954.29			−0.158568
$993$	1753.82	−	762.665i	0.0560480	−	0.0243731i
$994$		0			0
$995$		−	15674.7i		−	0.499417i
$996$	26135.2	−	11365.1i	0.831450	−	0.361565i
$997$		−	20960.6i		−	0.665827i	−0.942957	−	0.332914i	$-0.891968\pi$
$997$		−	20960.6i		−	0.665827i	0.942957	−	0.332914i	$-0.108032\pi$
$998$			1817.69i			0.0576534i
$999$	−14788.1	+	41776.5i	−0.468345	+	1.32307i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.4.d.a.293.9		16
3.2	odd	2	inner	294.4.d.a.293.8		16
7.2	even	3		42.4.f.a.17.7	yes	16
7.3	odd	6		42.4.f.a.5.1	✓	16
7.4	even	3		294.4.f.a.215.4		16
7.5	odd	6		294.4.f.a.227.6		16
7.6	odd	2	inner	294.4.d.a.293.16		16
21.2	odd	6		42.4.f.a.17.1	yes	16
21.5	even	6		294.4.f.a.227.4		16
21.11	odd	6		294.4.f.a.215.6		16
21.17	even	6		42.4.f.a.5.7	yes	16
21.20	even	2	inner	294.4.d.a.293.1		16
28.3	even	6		336.4.bc.e.257.7		16
28.23	odd	6		336.4.bc.e.17.4		16
84.23	even	6		336.4.bc.e.17.7		16
84.59	odd	6		336.4.bc.e.257.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.f.a.5.1	✓	16	7.3	odd	6
42.4.f.a.5.7	yes	16	21.17	even	6
42.4.f.a.17.1	yes	16	21.2	odd	6
42.4.f.a.17.7	yes	16	7.2	even	3
294.4.d.a.293.1		16	21.20	even	2	inner
294.4.d.a.293.8		16	3.2	odd	2	inner
294.4.d.a.293.9		16	1.1	even	1	trivial
294.4.d.a.293.16		16	7.6	odd	2	inner
294.4.f.a.215.4		16	7.4	even	3
294.4.f.a.215.6		16	21.11	odd	6
294.4.f.a.227.4		16	21.5	even	6
294.4.f.a.227.6		16	7.5	odd	6
336.4.bc.e.17.4		16	28.23	odd	6
336.4.bc.e.17.7		16	84.23	even	6
336.4.bc.e.257.4		16	84.59	odd	6
336.4.bc.e.257.7		16	28.3	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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} +(-4.76510 + 2.07215i) q^{3} -4.00000 q^{4} -8.55823 q^{5} +(-4.14431 - 9.53020i) q^{6} -8.00000i q^{8} +(18.4124 - 19.7480i) q^{9} -17.1165i q^{10} -62.1932i q^{11} +(19.0604 - 8.28861i) q^{12} +61.7061i q^{13} +(40.7808 - 17.7340i) q^{15} +16.0000 q^{16} +26.6731 q^{17} +(39.4961 + 36.8247i) q^{18} -67.6901i q^{19} +34.2329 q^{20} +124.386 q^{22} +52.9184i q^{23} +(16.5772 + 38.1208i) q^{24} -51.7568 q^{25} -123.412 q^{26} +(-46.8158 + 132.255i) q^{27} +55.1116i q^{29} +(35.4679 + 81.5616i) q^{30} +154.822i q^{31} +32.0000i q^{32} +(128.874 + 296.357i) q^{33} +53.3461i q^{34} +(-73.6494 + 78.9922i) q^{36} +315.880 q^{37} +135.380 q^{38} +(-127.865 - 294.036i) q^{39} +68.4658i q^{40} -210.211 q^{41} +351.939 q^{43} +248.773i q^{44} +(-157.577 + 169.008i) q^{45} -105.837 q^{46} +231.638 q^{47} +(-76.2416 + 33.1545i) q^{48} -103.514i q^{50} +(-127.100 + 55.2707i) q^{51} -246.824i q^{52} +268.918i q^{53} +(-264.509 - 93.6315i) q^{54} +532.263i q^{55} +(140.264 + 322.550i) q^{57} -110.223 q^{58} +18.2831 q^{59} +(-163.123 + 70.9358i) q^{60} -83.5218i q^{61} -309.643 q^{62} -64.0000 q^{64} -528.095i q^{65} +(-592.713 + 257.748i) q^{66} +129.471 q^{67} -106.692 q^{68} +(-109.655 - 252.162i) q^{69} +804.537i q^{71} +(-157.984 - 147.299i) q^{72} -427.674i q^{73} +631.759i q^{74} +(246.626 - 107.248i) q^{75} +270.760i q^{76} +(588.072 - 255.729i) q^{78} +1218.57 q^{79} -136.932 q^{80} +(-50.9701 - 727.216i) q^{81} -420.423i q^{82} +1371.18 q^{83} -228.274 q^{85} +703.879i q^{86} +(-114.200 - 262.612i) q^{87} -497.545 q^{88} -773.679 q^{89} +(-338.016 - 315.154i) q^{90} -211.674i q^{92} +(-320.814 - 737.741i) q^{93} +463.277i q^{94} +579.307i q^{95} +(-66.3089 - 152.483i) q^{96} -848.768i q^{97} +(-1228.19 - 1145.12i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 64 q^{4} - 36 q^{9} + 256 q^{16} + 96 q^{18} + 24 q^{22} + 388 q^{25} - 720 q^{30} + 144 q^{36} + 1924 q^{37} - 1188 q^{39} + 1732 q^{43} - 336 q^{46} - 3276 q^{51} - 2664 q^{57} + 1560 q^{58} - 1024 q^{64}+ \cdots - 4284 q^{99}+O(q^{100}) \) 16 * q - 64 * q^4 - 36 * q^9 + 256 * q^16 + 96 * q^18 + 24 * q^22 + 388 * q^25 - 720 * q^30 + 144 * q^36 + 1924 * q^37 - 1188 * q^39 + 1732 * q^43 - 336 * q^46 - 3276 * q^51 - 2664 * q^57 + 1560 * q^58 - 1024 * q^64 + 1412 * q^67 - 384 * q^72 + 2832 * q^78 + 5312 * q^79 - 252 * q^81 + 5232 * q^85 - 96 * q^88 - 4032 * q^93 - 4284 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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