LMFDB - Embedded newform 294.4.d.a.293.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,4,Mod(293,294)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			293.12
Root			$2.30541 + 1.91966i$ of defining polynomial
Character	$\chi$	$=$	294.293
Dual form			294.4.d.a.293.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} +(-0.882945 - 5.12059i) q^{3} -4.00000 q^{4} -19.8088 q^{5} +(10.2412 - 1.76589i) q^{6} -8.00000i q^{8} +(-25.4408 + 9.04239i) q^{9} +O(q^{10})$	\(q+2.00000i q^{2} +(-0.882945 - 5.12059i) q^{3} -4.00000 q^{4} -19.8088 q^{5} +(10.2412 - 1.76589i) q^{6} -8.00000i q^{8} +(-25.4408 + 9.04239i) q^{9} -39.6177i q^{10} +4.95069i q^{11} +(3.53178 + 20.4823i) q^{12} -17.7414i q^{13} +(17.4901 + 101.433i) q^{15} +16.0000 q^{16} -1.89534 q^{17} +(-18.0848 - 50.8816i) q^{18} -96.9912i q^{19} +79.2354 q^{20} -9.90138 q^{22} +156.964i q^{23} +(-40.9647 + 7.06356i) q^{24} +267.390 q^{25} +35.4827 q^{26} +(68.7652 + 122.288i) q^{27} +92.0138i q^{29} +(-202.866 + 34.9803i) q^{30} +77.7715i q^{31} +32.0000i q^{32} +(25.3504 - 4.37119i) q^{33} -3.79068i q^{34} +(101.763 - 36.1696i) q^{36} +248.939 q^{37} +193.982 q^{38} +(-90.8462 + 15.6646i) q^{39} +158.471i q^{40} +343.701 q^{41} -24.5859 q^{43} -19.8028i q^{44} +(503.953 - 179.119i) q^{45} -313.929 q^{46} +470.495 q^{47} +(-14.1271 - 81.9294i) q^{48} +534.781i q^{50} +(1.67348 + 9.70527i) q^{51} +70.9654i q^{52} -398.268i q^{53} +(-244.576 + 137.530i) q^{54} -98.0675i q^{55} +(-496.652 + 85.6379i) q^{57} -184.028 q^{58} -671.135 q^{59} +(-69.9605 - 405.732i) q^{60} +316.045i q^{61} -155.543 q^{62} -64.0000 q^{64} +351.436i q^{65} +(8.74238 + 50.7009i) q^{66} -233.791 q^{67} +7.58137 q^{68} +(803.750 - 138.591i) q^{69} +152.225i q^{71} +(72.3392 + 203.527i) q^{72} +623.419i q^{73} +497.877i q^{74} +(-236.091 - 1369.20i) q^{75} +387.965i q^{76} +(-31.3293 - 181.692i) q^{78} +302.381 q^{79} -316.942 q^{80} +(565.470 - 460.092i) q^{81} +687.402i q^{82} -856.438 q^{83} +37.5446 q^{85} -49.1718i q^{86} +(471.165 - 81.2431i) q^{87} +39.6055 q^{88} -907.153 q^{89} +(358.239 + 1007.91i) q^{90} -627.858i q^{92} +(398.236 - 68.6679i) q^{93} +940.990i q^{94} +1921.28i q^{95} +(163.859 - 28.2542i) q^{96} +70.3731i q^{97} +(-44.7661 - 125.950i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 64 q^{4} - 36 q^{9}+O(q^{10}) $ 16 * q - 64 * q^4 - 36 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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
$3$	−0.882945	−	5.12059i	−0.169923	−	0.985457i
$3$	−0.882945	−	5.12059i	−0.169923	−	0.985457i
$4$	−4.00000			−0.500000
$5$	−19.8088			−1.77176			−0.885879	−	0.463917i	$-0.846444\pi$
$5$	−19.8088			−1.77176			−0.885879	+	0.463917i	$0.846444\pi$
$6$	10.2412	−	1.76589i	0.696824	−	0.120154i
$7$		0			0
$7$		0			0
$8$		−	8.00000i		−	0.353553i
$9$	−25.4408	+	9.04239i	−0.942252	+	0.334903i
$10$		−	39.6177i		−	1.25282i
$11$			4.95069i			0.135699i	0.997696	+	0.0678495i	$0.0216138\pi$
$11$			4.95069i			0.135699i	−0.997696	+	0.0678495i	$0.978386\pi$
$12$	3.53178	+	20.4823i	0.0849614	+	0.492729i
$13$		−	17.7414i		−	0.378505i	−0.981928	−	0.189253i	$-0.939394\pi$
$13$		−	17.7414i		−	0.378505i	0.981928	−	0.189253i	$-0.0606065\pi$
$14$		0			0
$15$	17.4901	+	101.433i	0.301062	+	1.74599i
$16$	16.0000			0.250000
$17$	−1.89534			−0.0270405			−0.0135202	−	0.999909i	$-0.504304\pi$
$17$	−1.89534			−0.0270405			−0.0135202	+	0.999909i	$0.504304\pi$
$18$	−18.0848	−	50.8816i	−0.236813	−	0.666273i
$19$		−	96.9912i		−	1.17112i	−0.810629	−	0.585561i	$-0.800874\pi$
$19$		−	96.9912i		−	1.17112i	0.810629	−	0.585561i	$-0.199126\pi$
$20$	79.2354			0.885879
$21$		0			0
$22$	−9.90138			−0.0959537
$23$			156.964i			1.42302i	0.702678	+	0.711508i	$0.251987\pi$
$23$			156.964i			1.42302i	−0.702678	+	0.711508i	$0.748013\pi$
$24$	−40.9647	+	7.06356i	−0.348412	+	0.0600768i
$25$	267.390			2.13912
$26$	35.4827			0.267644
$27$	68.7652	+	122.288i	0.490143	+	0.871642i
$28$		0			0
$29$			92.0138i			0.589191i	0.955622	+	0.294595i	$0.0951849\pi$
$29$			92.0138i			0.589191i	−0.955622	+	0.294595i	$0.904815\pi$
$30$	−202.866	+	34.9803i	−1.23460	+	0.212883i
$31$			77.7715i			0.450586i	0.974291	+	0.225293i	$0.0723339\pi$
$31$			77.7715i			0.450586i	−0.974291	+	0.225293i	$0.927666\pi$
$32$			32.0000i			0.176777i
$33$	25.3504	−	4.37119i	0.133726	−	0.0230584i
$34$		−	3.79068i		−	0.0191205i
$35$		0			0
$36$	101.763	−	36.1696i	0.471126	−	0.167452i
$37$	248.939			1.10609			0.553044	−	0.833152i	$-0.313466\pi$
$37$	248.939			1.10609			0.553044	+	0.833152i	$0.313466\pi$
$38$	193.982			0.828108
$39$	−90.8462	+	15.6646i	−0.373001	+	0.0643167i
$40$			158.471i			0.626411i
$41$	343.701			1.30920			0.654598	−	0.755977i	$-0.272838\pi$
$41$	343.701			1.30920			0.654598	+	0.755977i	$0.272838\pi$
$42$		0			0
$43$	−24.5859			−0.0871934			−0.0435967	−	0.999049i	$-0.513882\pi$
$43$	−24.5859			−0.0871934			−0.0435967	+	0.999049i	$0.513882\pi$
$44$		−	19.8028i		−	0.0678495i
$45$	503.953	−	179.119i	1.66944	−	0.593368i
$46$	−313.929			−1.00622
$47$	470.495			1.46019			0.730093	−	0.683347i	$-0.239477\pi$
$47$	470.495			1.46019			0.730093	+	0.683347i	$0.239477\pi$
$48$	−14.1271	−	81.9294i	−0.0424807	−	0.246364i
$49$		0			0
$50$			534.781i			1.51259i
$51$	1.67348	+	9.70527i	0.00459479	+	0.0266472i
$52$			70.9654i			0.189253i
$53$		−	398.268i		−	1.03219i	−0.856530	−	0.516097i	$-0.827384\pi$
$53$		−	398.268i		−	1.03219i	0.856530	−	0.516097i	$-0.172616\pi$
$54$	−244.576	+	137.530i	−0.616344	+	0.346584i
$55$		−	98.0675i		−	0.240426i
$56$		0			0
$57$	−496.652	+	85.6379i	−1.15409	+	0.199000i
$58$	−184.028			−0.416621
$59$	−671.135			−1.48092			−0.740461	−	0.672099i	$-0.765393\pi$
$59$	−671.135			−1.48092			−0.740461	+	0.672099i	$0.765393\pi$
$60$	−69.9605	−	405.732i	−0.150531	−	0.872996i
$61$			316.045i			0.663368i	0.943390	+	0.331684i	$0.107617\pi$
$61$			316.045i			0.663368i	−0.943390	+	0.331684i	$0.892383\pi$
$62$	−155.543			−0.318612
$63$		0			0
$64$	−64.0000			−0.125000
$65$			351.436i			0.670619i
$66$	8.74238	+	50.7009i	0.0163047	+	0.0945583i
$67$	−233.791			−0.426300			−0.213150	−	0.977020i	$-0.568372\pi$
$67$	−233.791			−0.426300			−0.213150	+	0.977020i	$0.568372\pi$
$68$	7.58137			0.0135202
$69$	803.750	−	138.591i	1.40232	−	0.241803i
$70$		0			0
$71$			152.225i			0.254447i	0.991874	+	0.127224i	$0.0406066\pi$
$71$			152.225i			0.254447i	−0.991874	+	0.127224i	$0.959393\pi$
$72$	72.3392	+	203.527i	0.118406	+	0.333137i
$73$			623.419i			0.999530i	0.866161	+	0.499765i	$0.166580\pi$
$73$			623.419i			0.999530i	−0.866161	+	0.499765i	$0.833420\pi$
$74$			497.877i			0.782123i
$75$	−236.091	−	1369.20i	−0.363486	−	2.10802i
$76$			387.965i			0.585561i
$77$		0			0
$78$	−31.3293	−	181.692i	−0.0454788	−	0.263751i
$79$	302.381			0.430640			0.215320	−	0.976544i	$-0.430921\pi$
$79$	302.381			0.430640			0.215320	+	0.976544i	$0.430921\pi$
$80$	−316.942			−0.442939
$81$	565.470	−	460.092i	0.775679	−	0.631127i
$82$			687.402i			0.925742i
$83$	−856.438			−1.13261			−0.566303	−	0.824197i	$-0.691627\pi$
$83$	−856.438			−1.13261			−0.566303	+	0.824197i	$0.691627\pi$
$84$		0			0
$85$	37.5446			0.0479092
$86$		−	49.1718i		−	0.0616550i
$87$	471.165	−	81.2431i	0.580622	−	0.100117i
$88$	39.6055			0.0479768
$89$	−907.153			−1.08043			−0.540214	−	0.841528i	$-0.681657\pi$
$89$	−907.153			−1.08043			−0.540214	+	0.841528i	$0.681657\pi$
$90$	358.239	+	1007.91i	0.419574	+	1.18047i
$91$		0			0
$92$		−	627.858i		−	0.711508i
$93$	398.236	−	68.6679i	0.444033	−	0.0765649i
$94$			940.990i			1.03251i
$95$			1921.28i			2.07494i
$96$	163.859	−	28.2542i	0.174206	−	0.0300384i
$97$			70.3731i			0.0736629i	0.999321	+	0.0368315i	$0.0117265\pi$
$97$			70.3731i			0.0736629i	−0.999321	+	0.0368315i	$0.988274\pi$
$98$		0			0
$99$	−44.7661	−	125.950i	−0.0454461	−	0.127863i
$100$	−1069.56			−1.06956
$101$	−238.547			−0.235013			−0.117507	−	0.993072i	$-0.537490\pi$
$101$	−238.547			−0.235013			−0.117507	+	0.993072i	$0.537490\pi$
$102$	−19.4105	+	3.34697i	−0.0188424	+	0.00324901i
$103$			19.5828i			0.0187335i	0.999956	+	0.00936674i	$0.00298157\pi$
$103$			19.5828i			0.0187335i	−0.999956	+	0.00936674i	$0.997018\pi$
$104$	−141.931			−0.133822
$105$		0			0
$106$	796.536			0.729872
$107$			483.831i			0.437137i	0.975822	+	0.218569i	$0.0701388\pi$
$107$			483.831i			0.437137i	−0.975822	+	0.218569i	$0.929861\pi$
$108$	−275.061	−	489.152i	−0.245072	−	0.435821i
$109$	42.8046			0.0376141			0.0188070	−	0.999823i	$-0.494013\pi$
$109$	42.8046			0.0376141			0.0188070	+	0.999823i	$0.494013\pi$
$110$	196.135			0.170007
$111$	−219.799	−	1274.71i	−0.187950	−	1.09000i
$112$		0			0
$113$		−	378.359i		−	0.314983i	−0.987520	−	0.157491i	$-0.949659\pi$
$113$		−	378.359i		−	0.314983i	0.987520	−	0.157491i	$-0.0503406\pi$
$114$	−171.276	−	993.304i	−0.140714	−	0.816065i
$115$		−	3109.29i		−	2.52124i
$116$		−	368.055i		−	0.294595i
$117$	160.424	+	451.355i	0.126763	+	0.356647i
$118$		−	1342.27i		−	1.04717i
$119$		0			0
$120$	811.463	−	139.921i	0.617301	−	0.106442i
$121$	1306.49			0.981586
$122$	−632.091			−0.469072
$123$	−303.469	−	1759.95i	−0.222462	−	1.29016i
$124$		−	311.086i		−	0.225293i
$125$	−2820.59			−2.01825
$126$		0			0
$127$	112.805			0.0788177			0.0394088	−	0.999223i	$-0.487453\pi$
$127$	112.805			0.0788177			0.0394088	+	0.999223i	$0.487453\pi$
$128$		−	128.000i		−	0.0883883i
$129$	21.7080	+	125.894i	0.0148161	+	0.0859253i
$130$	−702.872			−0.474199
$131$	1581.85			1.05502			0.527508	−	0.849550i	$-0.323126\pi$
$131$	1581.85			1.05502			0.527508	+	0.849550i	$0.323126\pi$
$132$	−101.402	+	17.4848i	−0.0668628	+	0.0115292i
$133$		0			0
$134$		−	467.581i		−	0.301439i
$135$	−1362.16	−	2422.38i	−0.868415	−	1.54434i
$136$			15.1627i			0.00956025i
$137$			1844.42i			1.15021i	0.818078	+	0.575107i	$0.195040\pi$
$137$			1844.42i			1.15021i	−0.818078	+	0.575107i	$0.804960\pi$
$138$	277.182	+	1607.50i	0.170980	+	0.991591i
$139$			55.8671i			0.0340905i	0.999855	+	0.0170453i	$0.00542594\pi$
$139$			55.8671i			0.0340905i	−0.999855	+	0.0170453i	$0.994574\pi$
$140$		0			0
$141$	−415.421	−	2409.21i	−0.248119	−	1.43895i
$142$	−304.450			−0.179922
$143$	87.8320			0.0513628
$144$	−407.053	+	144.678i	−0.235563	+	0.0837259i
$145$		−	1822.69i		−	1.04390i
$146$	−1246.84			−0.706774
$147$		0			0
$148$	−995.755			−0.553044
$149$		−	3407.75i		−	1.87365i	−0.349800	−	0.936824i	$-0.613750\pi$
$149$		−	3407.75i		−	1.87365i	0.349800	−	0.936824i	$-0.386250\pi$
$150$	2738.39	−	472.182i	1.49059	−	0.257023i
$151$	3255.78			1.75465			0.877324	−	0.479899i	$-0.159327\pi$
$151$	3255.78			1.75465			0.877324	+	0.479899i	$0.159327\pi$
$152$	−775.930			−0.414054
$153$	48.2191	−	17.1384i	0.0254790	−	0.00905595i
$154$		0			0
$155$		−	1540.56i		−	0.798329i
$156$	363.385	−	62.6586i	0.186500	−	0.0321583i
$157$			2540.06i			1.29120i	0.763674	+	0.645602i	$0.223394\pi$
$157$			2540.06i			1.29120i	−0.763674	+	0.645602i	$0.776606\pi$
$158$			604.762i			0.304508i
$159$	−2039.37	+	351.649i	−1.01718	+	0.175393i
$160$		−	633.883i		−	0.313205i
$161$		0			0
$162$	920.184	+	1130.94i	0.446274	+	0.548488i
$163$	1725.70			0.829248			0.414624	−	0.909993i	$-0.363913\pi$
$163$	1725.70			0.829248			0.414624	+	0.909993i	$0.363913\pi$
$164$	−1374.80			−0.654598
$165$	−502.163	+	86.5882i	−0.236929	+	0.0408538i
$166$		−	1712.88i		−	0.800873i
$167$	485.621			0.225021			0.112510	−	0.993651i	$-0.464111\pi$
$167$	485.621			0.225021			0.112510	+	0.993651i	$0.464111\pi$
$168$		0			0
$169$	1882.24			0.856734
$170$			75.0891i			0.0338769i
$171$	877.033	+	2467.54i	0.392213	+	1.10349i
$172$	98.3436			0.0435967
$173$	1453.10			0.638598			0.319299	−	0.947654i	$-0.396553\pi$
$173$	1453.10			0.638598			0.319299	+	0.947654i	$0.396553\pi$
$174$	162.486	+	942.329i	0.0707934	+	0.410562i
$175$		0			0
$176$			79.2110i			0.0339248i
$177$	592.576	+	3436.61i	0.251643	+	1.45939i
$178$		−	1814.31i		−	0.763978i
$179$			1269.52i			0.530102i	0.964234	+	0.265051i	$0.0853889\pi$
$179$			1269.52i			0.530102i	−0.964234	+	0.265051i	$0.914611\pi$
$180$	−2015.81	+	716.478i	−0.834721	+	0.296684i
$181$			3289.26i			1.35076i	0.737468	+	0.675382i	$0.236021\pi$
$181$			3289.26i			1.35076i	−0.737468	+	0.675382i	$0.763979\pi$
$182$		0			0
$183$	1618.34	−	279.051i	0.653721	−	0.112721i
$184$	1255.72			0.503112
$185$	−4931.19			−1.95972
$186$	137.336	+	796.471i	0.0541395	+	0.313979i
$187$		−	9.38325i		−	0.00366937i
$188$	−1881.98			−0.730093
$189$		0			0
$190$	−3842.57			−1.46721
$191$			1978.53i			0.749536i	0.927119	+	0.374768i	$0.122278\pi$
$191$			1978.53i			0.749536i	−0.927119	+	0.374768i	$0.877722\pi$
$192$	56.5085	+	327.718i	0.0212404	+	0.123182i
$193$	−919.847			−0.343067			−0.171534	−	0.985178i	$-0.554872\pi$
$193$	−919.847			−0.343067			−0.171534	+	0.985178i	$0.554872\pi$
$194$	−140.746			−0.0520876
$195$	1799.56	−	310.299i	0.660867	−	0.113954i
$196$		0			0
$197$			3061.98i			1.10740i	0.832717	+	0.553699i	$0.186784\pi$
$197$			3061.98i			1.10740i	−0.832717	+	0.553699i	$0.813216\pi$
$198$	251.899	−	89.5322i	0.0904126	−	0.0321352i
$199$		−	521.454i		−	0.185753i	−0.995678	−	0.0928766i	$-0.970394\pi$
$199$		−	521.454i		−	0.185753i	0.995678	−	0.0928766i	$-0.0296062\pi$
$200$		−	2139.12i		−	0.756294i
$201$	206.424	+	1197.15i	0.0724381	+	0.420100i
$202$		−	477.094i		−	0.166179i
$203$		0			0
$204$	−6.69393	−	38.8211i	−0.00229740	−	0.0133236i
$205$	−6808.32			−2.31958
$206$	−39.1655			−0.0132466
$207$	−1419.33	−	3993.30i	−0.476573	−	1.34084i
$208$		−	283.862i		−	0.0946263i
$209$	480.173			0.158920
$210$		0			0
$211$	99.6288			0.0325058			0.0162529	−	0.999868i	$-0.494826\pi$
$211$	99.6288			0.0325058			0.0162529	+	0.999868i	$0.494826\pi$
$212$			1593.07i			0.516097i
$213$	779.481	−	134.406i	0.250747	−	0.0432364i
$214$	−967.662			−0.309103
$215$	487.018			0.154485
$216$	978.304	−	550.122i	0.308172	−	0.173292i
$217$		0			0
$218$			85.6091i			0.0265972i
$219$	3192.27	−	550.445i	0.984994	−	0.169843i
$220$			392.270i			0.120213i
$221$			33.6259i			0.0102350i
$222$	2549.42	−	439.598i	0.770748	−	0.132901i
$223$		−	1782.29i		−	0.535206i	−0.963529	−	0.267603i	$-0.913768\pi$
$223$		−	1782.29i		−	0.535206i	0.963529	−	0.267603i	$-0.0862316\pi$
$224$		0			0
$225$	−6802.63	+	2417.85i	−2.01559	+	0.716400i
$226$	756.718			0.222726
$227$	3443.15			1.00674			0.503370	−	0.864071i	$-0.332093\pi$
$227$	3443.15			1.00674			0.503370	+	0.864071i	$0.332093\pi$
$228$	1986.61	−	342.552i	0.577045	−	0.0995002i
$229$			5434.92i			1.56834i	0.620547	+	0.784169i	$0.286910\pi$
$229$			5434.92i			1.56834i	−0.620547	+	0.784169i	$0.713090\pi$
$230$	6218.57			1.78278
$231$		0			0
$232$	736.110			0.208310
$233$			4405.56i			1.23870i	0.785114	+	0.619351i	$0.212604\pi$
$233$			4405.56i			1.23870i	−0.785114	+	0.619351i	$0.787396\pi$
$234$	−902.709	+	320.849i	−0.252188	+	0.0896348i
$235$	−9319.97			−2.58710
$236$	2684.54			0.740461
$237$	−266.986	−	1548.37i	−0.0731755	−	0.424377i
$238$		0			0
$239$			2020.29i			0.546786i	0.961902	+	0.273393i	$0.0881459\pi$
$239$			2020.29i			0.546786i	−0.961902	+	0.273393i	$0.911854\pi$
$240$	279.842	+	1622.93i	0.0752655	+	0.436498i
$241$		−	2271.08i		−	0.607026i	−0.952827	−	0.303513i	$-0.901840\pi$
$241$		−	2271.08i		−	0.607026i	0.952827	−	0.303513i	$-0.0981596\pi$
$242$			2612.98i			0.694086i
$243$	−2855.22	−	2489.30i	−0.753755	−	0.657156i
$244$		−	1264.18i		−	0.331684i
$245$		0			0
$246$	3519.90	−	606.938i	0.912279	−	0.157305i
$247$	−1720.76			−0.443276
$248$	622.172			0.159306
$249$	756.187	+	4385.46i	0.192456	+	1.11613i
$250$		−	5641.18i		−	1.42712i
$251$	4513.50			1.13502			0.567510	−	0.823367i	$-0.307907\pi$
$251$	4513.50			1.13502			0.567510	+	0.823367i	$0.307907\pi$
$252$		0			0
$253$	−777.082			−0.193102
$254$			225.610i			0.0557325i
$255$	−33.1498	−	192.250i	−0.00814086	−	0.0472124i
$256$	256.000			0.0625000
$257$	−5938.61			−1.44140			−0.720701	−	0.693246i	$-0.756180\pi$
$257$	−5938.61			−1.44140			−0.720701	+	0.693246i	$0.756180\pi$
$258$	−251.788	+	43.4160i	−0.0607584	+	0.0104766i
$259$		0			0
$260$		−	1405.74i		−	0.335310i
$261$	−832.025	−	2340.91i	−0.197322	−	0.555166i
$262$			3163.71i			0.746010i
$263$		−	5458.50i		−	1.27979i	−0.768461	−	0.639897i	$-0.778977\pi$
$263$		−	5458.50i		−	1.27979i	0.768461	−	0.639897i	$-0.221023\pi$
$264$	−34.9695	−	202.804i	−0.00815236	−	0.0472791i
$265$			7889.23i			1.82880i
$266$		0			0
$267$	800.967	+	4645.16i	0.183589	+	1.06472i
$268$	935.163			0.213150
$269$	5284.92			1.19787			0.598935	−	0.800797i	$-0.295591\pi$
$269$	5284.92			1.19787			0.598935	+	0.800797i	$0.295591\pi$
$270$	4844.77	−	2724.32i	1.09201	−	0.614062i
$271$			6277.80i			1.40719i	0.710600	+	0.703596i	$0.248424\pi$
$271$			6277.80i			1.40719i	−0.710600	+	0.703596i	$0.751576\pi$
$272$	−30.3255			−0.00676012
$273$		0			0
$274$	−3688.84			−0.813325
$275$			1323.77i			0.290277i
$276$	−3215.00	+	554.364i	−0.701161	+	0.120901i
$277$	7496.34			1.62603			0.813017	−	0.582240i	$-0.197823\pi$
$277$	7496.34			1.62603			0.813017	+	0.582240i	$0.197823\pi$
$278$	−111.734			−0.0241056
$279$	−703.240	−	1978.57i	−0.150903	−	0.424566i
$280$		0			0
$281$			745.889i			0.158349i	0.996861	+	0.0791744i	$0.0252284\pi$
$281$			745.889i			0.158349i	−0.996861	+	0.0791744i	$0.974772\pi$
$282$	4818.42	−	830.843i	1.01749	−	0.175447i
$283$			2633.35i			0.553133i	0.960995	+	0.276566i	$0.0891966\pi$
$283$			2633.35i			0.553133i	−0.960995	+	0.276566i	$0.910803\pi$
$284$		−	608.900i		−	0.127224i
$285$	9838.10	−	1696.39i	2.04477	−	0.352580i
$286$			175.664i			0.0363190i
$287$		0			0
$288$	−289.357	−	814.106i	−0.0592031	−	0.166568i
$289$	−4909.41			−0.999269
$290$	3645.37			0.738151
$291$	360.351	−	62.1356i	0.0725917	−	0.0125170i
$292$		−	2493.68i		−	0.499765i
$293$	−889.363			−0.177328			−0.0886640	−	0.996062i	$-0.528260\pi$
$293$	−889.363			−0.177328			−0.0886640	+	0.996062i	$0.528260\pi$
$294$		0			0
$295$	13294.4			2.62383
$296$		−	1991.51i		−	0.391061i
$297$	−605.410	+	340.435i	−0.118281	+	0.0665120i
$298$	6815.50			1.32487
$299$	2784.76			0.538619
$300$	944.364	+	5476.78i	0.181743	+	1.05401i
$301$		0			0
$302$			6511.56i			1.24072i
$303$	210.624	+	1221.50i	0.0399341	+	0.231595i
$304$		−	1551.86i		−	0.292780i
$305$		−	6260.50i		−	1.17533i
$306$	34.2769	+	96.4381i	0.00640352	+	0.0180163i
$307$		−	3995.12i		−	0.742715i	−0.928490	−	0.371357i	$-0.878893\pi$
$307$		−	3995.12i		−	0.742715i	0.928490	−	0.371357i	$-0.121107\pi$
$308$		0			0
$309$	100.275	−	17.2905i	0.0184610	−	0.00318325i
$310$	3081.13			0.564504
$311$	−512.017			−0.0933563			−0.0466782	−	0.998910i	$-0.514864\pi$
$311$	−512.017			−0.0933563			−0.0466782	+	0.998910i	$0.514864\pi$
$312$	125.317	+	726.769i	0.0227394	+	0.131876i
$313$			1468.41i			0.265174i	0.991171	+	0.132587i	$0.0423284\pi$
$313$			1468.41i			0.265174i	−0.991171	+	0.132587i	$0.957672\pi$
$314$	−5080.13			−0.913019
$315$		0			0
$316$	−1209.52			−0.215320
$317$		−	7557.82i		−	1.33908i	−0.742775	−	0.669542i	$-0.766491\pi$
$317$		−	7557.82i		−	1.33908i	0.742775	−	0.669542i	$-0.233509\pi$
$318$	−703.298	−	4078.73i	−0.124022	−	0.719258i
$319$	−455.532			−0.0799526
$320$	1267.77			0.221470
$321$	2477.50	−	427.196i	0.430780	−	0.0742796i
$322$		0			0
$323$			183.832i			0.0316677i
$324$	−2261.88	+	1840.37i	−0.387840	+	0.315564i
$325$		−	4743.87i		−	0.809669i
$326$			3451.40i			0.586367i
$327$	−37.7941	−	219.184i	−0.00639149	−	0.0370671i
$328$		−	2749.61i		−	0.462871i
$329$		0			0
$330$	−173.176	−	1004.33i	−0.0288880	−	0.167534i
$331$	5865.53			0.974013			0.487007	−	0.873398i	$-0.338089\pi$
$331$	5865.53			0.974013			0.487007	+	0.873398i	$0.338089\pi$
$332$	3425.75			0.566303
$333$	−6333.20	+	2251.00i	−1.04221	+	0.370433i
$334$			971.243i			0.159114i
$335$	4631.12			0.755300
$336$		0			0
$337$	−8489.10			−1.37220			−0.686099	−	0.727508i	$-0.740678\pi$
$337$	−8489.10			−1.37220			−0.686099	+	0.727508i	$0.740678\pi$
$338$			3764.49i			0.605802i
$339$	−1937.42	+	334.070i	−0.310402	+	0.0535228i
$340$	−150.178			−0.0239546
$341$	−385.022			−0.0611441
$342$	−4935.07	+	1754.07i	−0.780287	+	0.277336i
$343$		0			0
$344$			196.687i			0.0308275i
$345$	−15921.4	+	2745.33i	−2.48457	+	0.428416i
$346$			2906.21i			0.451557i
$347$			1118.76i			0.173078i	0.996248	+	0.0865390i	$0.0275807\pi$
$347$			1118.76i			0.173078i	−0.996248	+	0.0865390i	$0.972419\pi$
$348$	−1884.66	+	324.972i	−0.290311	+	0.0500585i
$349$			2364.44i			0.362652i	0.983423	+	0.181326i	$0.0580389\pi$
$349$			2364.44i			0.362652i	−0.983423	+	0.181326i	$0.941961\pi$
$350$		0			0
$351$	2169.55	−	1219.99i	0.329921	−	0.185522i
$352$	−158.422			−0.0239884
$353$	−2822.24			−0.425532			−0.212766	−	0.977103i	$-0.568247\pi$
$353$	−2822.24			−0.425532			−0.212766	+	0.977103i	$0.568247\pi$
$354$	−6873.21	+	1185.15i	−1.03194	+	0.177938i
$355$		−	3015.40i		−	0.450819i
$356$	3628.61			0.540214
$357$		0			0
$358$	−2539.04			−0.374839
$359$			5201.89i			0.764750i	0.924007	+	0.382375i	$0.124894\pi$
$359$			5201.89i			0.764750i	−0.924007	+	0.382375i	$0.875106\pi$
$360$	−1432.96	−	4031.63i	−0.209787	−	0.590237i
$361$	−2548.29			−0.371525
$362$	−6578.51			−0.955135
$363$	−1153.56	−	6690.00i	−0.166794	−	0.967311i
$364$		0			0
$365$		−	12349.2i		−	1.77092i
$366$	558.102	+	3236.68i	0.0797061	+	0.462251i
$367$		−	5630.81i		−	0.800888i	−0.916321	−	0.400444i	$-0.868856\pi$
$367$		−	5630.81i		−	0.800888i	0.916321	−	0.400444i	$-0.131144\pi$
$368$			2511.43i			0.355754i
$369$	−8744.03	+	3107.88i	−1.23359	+	0.438454i
$370$		−	9862.38i		−	1.38573i
$371$		0			0
$372$	−1592.94	+	274.672i	−0.222017	+	0.0382824i
$373$	6844.45			0.950113			0.475057	−	0.879955i	$-0.342428\pi$
$373$	6844.45			0.950113			0.475057	+	0.879955i	$0.342428\pi$
$374$	18.7665			0.00259463
$375$	2490.43	+	14443.1i	0.342947	+	1.98890i
$376$		−	3763.96i		−	0.516254i
$377$	1632.45			0.223012
$378$		0			0
$379$	5690.62			0.771260			0.385630	−	0.922654i	$-0.373984\pi$
$379$	5690.62			0.771260			0.385630	+	0.922654i	$0.373984\pi$
$380$		−	7685.14i		−	1.03747i
$381$	−99.6008	−	577.629i	−0.0133929	−	0.0776714i
$382$	−3957.06			−0.530002
$383$	−4303.32			−0.574124			−0.287062	−	0.957912i	$-0.592679\pi$
$383$	−4303.32			−0.574124			−0.287062	+	0.957912i	$0.592679\pi$
$384$	−655.435	+	113.017i	−0.0871029	+	0.0150192i
$385$		0			0
$386$		−	1839.69i		−	0.242585i
$387$	625.485	−	222.315i	0.0821581	−	0.0292014i
$388$		−	281.492i		−	0.0368315i
$389$		−	7094.03i		−	0.924631i	−0.886716	−	0.462315i	$-0.847019\pi$
$389$		−	7094.03i		−	0.924631i	0.886716	−	0.462315i	$-0.152981\pi$
$390$	620.597	+	3599.12i	0.0805773	+	0.467303i
$391$		−	297.501i		−	0.0384790i
$392$		0			0
$393$	−1396.69	−	8100.02i	−0.179271	−	1.03967i
$394$	−6123.97			−0.783048
$395$	−5989.82			−0.762989
$396$	179.064	+	503.798i	0.0227230	+	0.0639314i
$397$		−	4501.33i		−	0.569056i	−0.958668	−	0.284528i	$-0.908163\pi$
$397$		−	4501.33i		−	0.569056i	0.958668	−	0.284528i	$-0.0918369\pi$
$398$	1042.91			0.131347
$399$		0			0
$400$	4278.25			0.534781
$401$		−	6972.82i		−	0.868345i	−0.900830	−	0.434172i	$-0.857041\pi$
$401$		−	6972.82i		−	0.868345i	0.900830	−	0.434172i	$-0.142959\pi$
$402$	−2394.29	+	412.849i	−0.297056	+	0.0512214i
$403$	1379.77			0.170549
$404$	954.188			0.117507
$405$	−11201.3	+	9113.89i	−1.37432	+	1.11820i
$406$		0			0
$407$			1232.42i			0.150095i
$408$	77.6421	−	13.3879i	0.00942122	−	0.00162451i
$409$			14355.1i			1.73549i	0.497010	+	0.867745i	$0.334431\pi$
$409$			14355.1i			1.73549i	−0.497010	+	0.867745i	$0.665569\pi$
$410$		−	13616.6i		−	1.64019i
$411$	9444.51	−	1628.52i	1.13349	−	0.195448i
$412$		−	78.3311i		−	0.00936674i
$413$		0			0
$414$	7986.61	−	2838.67i	0.948117	−	0.336988i
$415$	16965.0			2.00670
$416$	567.723			0.0669109
$417$	286.072	−	49.3276i	0.0335948	−	0.00579276i
$418$			960.347i			0.112373i
$419$	−14839.8			−1.73024			−0.865122	−	0.501562i	$-0.832759\pi$
$419$	−14839.8			−1.73024			−0.865122	+	0.501562i	$0.832759\pi$
$420$		0			0
$421$	−11073.0			−1.28187			−0.640935	−	0.767595i	$-0.721453\pi$
$421$	−11073.0			−1.28187			−0.640935	+	0.767595i	$0.721453\pi$
$422$			199.258i			0.0229851i
$423$	−11969.8	+	4254.40i	−1.37586	+	0.489022i
$424$	−3186.14			−0.364936
$425$	−506.797			−0.0578429
$426$	268.812	+	1558.96i	0.0305728	+	0.177305i
$427$		0			0
$428$		−	1935.32i		−	0.218569i
$429$	−77.5508	−	449.751i	−0.00872771	−	0.0506158i
$430$			974.037i			0.109238i
$431$			6410.97i			0.716486i	0.933628	+	0.358243i	$0.116624\pi$
$431$			6410.97i			0.716486i	−0.933628	+	0.358243i	$0.883376\pi$
$432$	1100.24	+	1956.61i	0.122536	+	0.217910i
$433$			12881.0i			1.42961i	0.699322	+	0.714807i	$0.253486\pi$
$433$			12881.0i			1.42961i	−0.699322	+	0.714807i	$0.746514\pi$
$434$		0			0
$435$	−9333.23	+	1609.33i	−1.02872	+	0.177383i
$436$	−171.218			−0.0188070
$437$	15224.2			1.66652
$438$	1100.89	+	6384.54i	0.120097	+	0.696496i
$439$			9266.30i			1.00742i	0.863873	+	0.503709i	$0.168032\pi$
$439$			9266.30i			1.00742i	−0.863873	+	0.503709i	$0.831968\pi$
$440$	−784.540			−0.0850033
$441$		0			0
$442$	−67.2519			−0.00723721
$443$		−	8881.43i		−	0.952527i	−0.879303	−	0.476263i	$-0.841991\pi$
$443$		−	8881.43i		−	0.952527i	0.879303	−	0.476263i	$-0.158009\pi$
$444$	879.197	+	5098.85i	0.0939748	+	0.545001i
$445$	17969.7			1.91426
$446$	3564.58			0.378448
$447$	−17449.7	+	3008.86i	−1.84640	+	0.318376i
$448$		0			0
$449$			6080.93i			0.639147i	0.947562	+	0.319573i	$0.103540\pi$
$449$			6080.93i			0.639147i	−0.947562	+	0.319573i	$0.896460\pi$
$450$	−4835.70	−	13605.3i	−0.506571	−	1.42524i
$451$			1701.56i			0.177657i
$452$			1513.44i			0.157491i
$453$	−2874.68	−	16671.5i	−0.298155	−	1.72913i
$454$			6886.30i			0.711873i
$455$		0			0
$456$	685.103	+	3973.21i	0.0703572	+	0.408033i
$457$	557.654			0.0570809			0.0285404	−	0.999593i	$-0.490914\pi$
$457$	557.654			0.0570809			0.0285404	+	0.999593i	$0.490914\pi$
$458$	−10869.8			−1.10898
$459$	−130.334	−	231.778i	−0.0132537	−	0.0235696i
$460$			12437.1i			1.26062i
$461$	7422.24			0.749866			0.374933	−	0.927052i	$-0.377666\pi$
$461$	7422.24			0.749866			0.374933	+	0.927052i	$0.377666\pi$
$462$		0			0
$463$	10478.8			1.05182			0.525908	−	0.850541i	$-0.323726\pi$
$463$	10478.8			1.05182			0.525908	+	0.850541i	$0.323726\pi$
$464$			1472.22i			0.147298i
$465$	−7888.59	+	1360.23i	−0.786719	+	0.135654i
$466$	−8811.12			−0.875895
$467$	−9417.49			−0.933168			−0.466584	−	0.884477i	$-0.654515\pi$
$467$	−9417.49			−0.933168			−0.466584	+	0.884477i	$0.654515\pi$
$468$	−641.697	−	1805.42i	−0.0633813	−	0.178324i
$469$		0			0
$470$		−	18639.9i		−	1.82935i
$471$	13006.6	−	2242.74i	1.27243	−	0.219405i
$472$			5369.08i			0.523585i
$473$		−	121.717i		−	0.0118321i
$474$	3096.74	−	533.972i	0.300080	−	0.0517429i
$475$		−	25934.5i		−	2.50517i
$476$		0			0
$477$	3601.30	+	10132.3i	0.345686	+	0.972588i
$478$	−4040.58			−0.386636
$479$	10606.3			1.01172			0.505860	−	0.862615i	$-0.331175\pi$
$479$	10606.3			1.01172			0.505860	+	0.862615i	$0.331175\pi$
$480$	−3245.85	+	559.684i	−0.308651	+	0.0532208i
$481$		−	4416.51i		−	0.418660i
$482$	4542.17			0.429232
$483$		0			0
$484$	−5225.96			−0.490793
$485$		−	1394.01i		−	0.130513i
$486$	4978.61	−	5710.44i	0.464679	−	0.532985i
$487$	−12774.4			−1.18863			−0.594314	−	0.804233i	$-0.702576\pi$
$487$	−12774.4			−1.18863			−0.594314	+	0.804233i	$0.702576\pi$
$488$	2528.36			0.234536
$489$	−1523.70	−	8836.61i	−0.140908	−	0.817188i
$490$		0			0
$491$		−	18689.8i		−	1.71784i	−0.512110	−	0.858920i	$-0.671136\pi$
$491$		−	18689.8i		−	1.71784i	0.512110	−	0.858920i	$-0.328864\pi$
$492$	1213.88	+	7039.80i	0.111231	+	0.645079i
$493$		−	174.398i		−	0.0159320i
$494$		−	3441.51i		−	0.313443i
$495$	886.765	+	2494.92i	0.0805194	+	0.226542i
$496$			1244.34i			0.112647i
$497$		0			0
$498$	−8770.93	+	1512.37i	−0.789226	+	0.136087i
$499$	−13725.5			−1.23134			−0.615668	−	0.788006i	$-0.711114\pi$
$499$	−13725.5			−1.23134			−0.615668	+	0.788006i	$0.711114\pi$
$500$	11282.4			1.00913
$501$	−428.777	−	2486.67i	−0.0382362	−	0.221749i
$502$			9027.01i			0.802580i
$503$	5480.28			0.485793			0.242896	−	0.970052i	$-0.421902\pi$
$503$	5480.28			0.485793			0.242896	+	0.970052i	$0.421902\pi$
$504$		0			0
$505$	4725.34			0.416386
$506$		−	1554.16i		−	0.136544i
$507$	−1661.92	−	9638.19i	−0.145579	−	0.844275i
$508$	−451.221			−0.0394088
$509$	10662.6			0.928507			0.464253	−	0.885702i	$-0.346323\pi$
$509$	10662.6			0.928507			0.464253	+	0.885702i	$0.346323\pi$
$510$	384.500	−	66.2996i	0.0333842	−	0.00575646i
$511$		0			0
$512$			512.000i			0.0441942i
$513$	11860.9	−	6669.62i	1.02080	−	0.574017i
$514$		−	11877.2i		−	1.01923i
$515$		−	387.912i		−	0.0331912i
$516$	−86.8320	−	503.577i	−0.00740807	−	0.0429627i
$517$			2329.28i			0.198146i
$518$		0			0
$519$	−1283.01	−	7440.75i	−0.108512	−	0.629311i
$520$	2811.49			0.237100
$521$	11500.0			0.967033			0.483517	−	0.875335i	$-0.339359\pi$
$521$	11500.0			0.967033			0.483517	+	0.875335i	$0.339359\pi$
$522$	4681.81	−	1664.05i	0.392562	−	0.139528i
$523$		−	9606.61i		−	0.803189i	−0.915818	−	0.401594i	$-0.868456\pi$
$523$		−	9606.61i		−	0.803189i	0.915818	−	0.401594i	$-0.131544\pi$
$524$	−6327.42			−0.527508
$525$		0			0
$526$	10917.0			0.904951
$527$		−	147.404i		−	0.0121841i
$528$	405.607	−	69.9390i	0.0334314	−	0.00576459i
$529$	−12470.8			−1.02497
$530$	−15778.5			−1.29316
$531$	17074.2	−	6068.67i	1.39540	−	0.495966i
$532$		0			0
$533$		−	6097.72i		−	0.495538i
$534$	−9290.31	+	1601.93i	−0.752867	+	0.129817i
$535$		−	9584.13i		−	0.774501i
$536$			1870.33i			0.150720i
$537$	6500.68	−	1120.92i	0.522393	−	0.0900765i
$538$			10569.8i			0.847022i
$539$		0			0
$540$	5448.64	+	9689.54i	0.434208	+	0.772169i
$541$	−17564.6			−1.39586			−0.697929	−	0.716167i	$-0.745895\pi$
$541$	−17564.6			−1.39586			−0.697929	+	0.716167i	$0.745895\pi$
$542$	−12555.6			−0.995036
$543$	16842.9	−	2904.23i	1.33112	−	0.229526i
$544$		−	60.6510i		−	0.00478013i
$545$	−847.909			−0.0666430
$546$		0			0
$547$	−14541.1			−1.13662			−0.568311	−	0.822814i	$-0.692403\pi$
$547$	−14541.1			−1.13662			−0.568311	+	0.822814i	$0.692403\pi$
$548$		−	7377.68i		−	0.575107i
$549$	−2857.81	−	8040.45i	−0.222164	−	0.625061i
$550$	−2647.53			−0.205257
$551$	8924.53			0.690014
$552$	−1108.73	−	6430.00i	−0.0854902	−	0.495795i
$553$		0			0
$554$			14992.7i			1.14978i
$555$	4353.97	+	25250.6i	0.333001	+	1.93122i
$556$		−	223.468i		−	0.0170453i
$557$			13793.8i			1.04931i	0.851316	+	0.524653i	$0.175805\pi$
$557$			13793.8i			1.04931i	−0.851316	+	0.524653i	$0.824195\pi$
$558$	3957.14	−	1406.48i	0.300213	−	0.106704i
$559$			436.187i			0.0330031i
$560$		0			0
$561$	−48.0478	+	8.28490i	−0.00361600	+	0.000623509i
$562$	−1491.78			−0.111969
$563$	−9196.12			−0.688402			−0.344201	−	0.938896i	$-0.611850\pi$
$563$	−9196.12			−0.688402			−0.344201	+	0.938896i	$0.611850\pi$
$564$	1661.69	+	9636.85i	0.124060	+	0.719476i
$565$			7494.86i			0.558073i
$566$	−5266.71			−0.391124
$567$		0			0
$568$	1217.80			0.0899608
$569$			18064.1i			1.33091i	0.746438	+	0.665455i	$0.231762\pi$
$569$			18064.1i			1.33091i	−0.746438	+	0.665455i	$0.768238\pi$
$570$	3392.78	+	19676.2i	0.249312	+	1.44587i
$571$	15252.5			1.11786			0.558930	−	0.829215i	$-0.311212\pi$
$571$	15252.5			1.11786			0.558930	+	0.829215i	$0.311212\pi$
$572$	−351.328			−0.0256814
$573$	10131.2	−	1746.93i	0.738636	−	0.127363i
$574$		0			0
$575$			41970.8i			3.04401i
$576$	1628.21	−	578.713i	0.117782	−	0.0418629i
$577$		−	5437.97i		−	0.392350i	−0.980569	−	0.196175i	$-0.937148\pi$
$577$		−	5437.97i		−	0.392350i	0.980569	−	0.196175i	$-0.0628520\pi$
$578$		−	9818.82i		−	0.706590i
$579$	812.174	+	4710.16i	0.0582950	+	0.338078i
$580$			7290.75i			0.521951i
$581$		0			0
$582$	124.271	+	720.703i	0.00885087	+	0.0513301i
$583$	1971.70			0.140068
$584$	4987.35			0.353387
$585$	−3177.82	−	8940.81i	−0.224593	−	0.631893i
$586$		−	1778.73i		−	0.125390i
$587$	23972.1			1.68558			0.842791	−	0.538241i	$-0.180911\pi$
$587$	23972.1			1.68558			0.842791	+	0.538241i	$0.180911\pi$
$588$		0			0
$589$	7543.15			0.527691
$590$			26588.8i			1.85533i
$591$	15679.1	−	2703.56i	1.09129	−	0.188172i
$592$	3983.02			0.276522
$593$	−1394.14			−0.0965439			−0.0482720	−	0.998834i	$-0.515371\pi$
$593$	−1394.14			−0.0965439			−0.0482720	+	0.998834i	$0.515371\pi$
$594$	−680.870	−	1210.82i	−0.0470311	−	0.0836373i
$595$		0			0
$596$			13631.0i			0.936824i
$597$	−2670.15	+	460.415i	−0.183052	+	0.0315637i
$598$			5569.53i			0.380861i
$599$		−	24030.8i		−	1.63918i	−0.572949	−	0.819591i	$-0.694201\pi$
$599$		−	24030.8i		−	1.63918i	0.572949	−	0.819591i	$-0.305799\pi$
$600$	−10953.6	+	1888.73i	−0.745296	+	0.128512i
$601$			10741.9i			0.729073i	0.931189	+	0.364536i	$0.118773\pi$
$601$			10741.9i			0.729073i	−0.931189	+	0.364536i	$0.881227\pi$
$602$		0			0
$603$	5947.83	−	2114.03i	0.401682	−	0.142769i
$604$	−13023.1			−0.877324
$605$	−25880.1			−1.73913
$606$	−2443.00	+	421.248i	−0.163763	+	0.0282377i
$607$		−	27142.9i		−	1.81498i	−0.420070	−	0.907492i	$-0.637994\pi$
$607$		−	27142.9i		−	1.81498i	0.420070	−	0.907492i	$-0.362006\pi$
$608$	3103.72			0.207027
$609$		0			0
$610$	12521.0			0.831082
$611$		−	8347.22i		−	0.552688i
$612$	−192.876	+	68.5537i	−0.0127395	+	0.00452797i
$613$	28776.4			1.89603			0.948015	−	0.318227i	$-0.103087\pi$
$613$	28776.4			1.89603			0.948015	+	0.318227i	$0.103087\pi$
$614$	7990.23			0.525178
$615$	6011.37	+	34862.6i	0.394149	+	2.28585i
$616$		0			0
$617$			2160.03i			0.140939i	0.997514	+	0.0704697i	$0.0224498\pi$
$617$			2160.03i			0.140939i	−0.997514	+	0.0704697i	$0.977550\pi$
$618$	34.5810	+	200.551i	0.00225089	+	0.0130539i
$619$			2892.89i			0.187844i	0.995580	+	0.0939218i	$0.0299404\pi$
$619$			2892.89i			0.187844i	−0.995580	+	0.0939218i	$0.970060\pi$
$620$			6162.25i			0.399165i
$621$	−19194.9	+	10793.7i	−1.24036	+	0.697482i
$622$		−	1024.03i		−	0.0660129i
$623$		0			0
$624$	−1453.54	+	250.634i	−0.0932502	+	0.0160792i
$625$	22448.9			1.43673
$626$	−2936.82			−0.187506
$627$	−423.967	−	2458.77i	−0.0270041	−	0.156609i
$628$		−	10160.3i		−	0.645602i
$629$	−471.824			−0.0299092
$630$		0			0
$631$	−13779.4			−0.869335			−0.434667	−	0.900591i	$-0.643134\pi$
$631$	−13779.4			−0.869335			−0.434667	+	0.900591i	$0.643134\pi$
$632$		−	2419.05i		−	0.152254i
$633$	−87.9668	−	510.158i	−0.00552348	−	0.0320331i
$634$	15115.6			0.946875
$635$	−2234.54			−0.139646
$636$	8157.46	−	1406.60i	0.508592	−	0.0876967i
$637$		0			0
$638$		−	911.063i		−	0.0565350i
$639$	−1376.48	−	3872.73i	−0.0852154	−	0.239754i
$640$			2535.53i			0.156603i
$641$			14147.5i			0.871749i	0.900007	+	0.435875i	$0.143561\pi$
$641$			14147.5i			0.871749i	−0.900007	+	0.435875i	$0.856439\pi$
$642$	854.392	+	4955.00i	0.0525236	+	0.304608i
$643$		−	4248.35i		−	0.260557i	−0.991477	−	0.130279i	$-0.958413\pi$
$643$		−	4248.35i		−	0.260557i	0.991477	−	0.130279i	$-0.0415872\pi$
$644$		0			0
$645$	−430.010	−	2493.82i	−0.0262506	−	0.152239i
$646$	−367.663			−0.0223924
$647$	16629.7			1.01048			0.505239	−	0.862979i	$-0.331404\pi$
$647$	16629.7			1.01048			0.505239	+	0.862979i	$0.331404\pi$
$648$	−3680.73	−	4523.76i	−0.223137	−	0.274244i
$649$		−	3322.58i		−	0.200960i
$650$	9487.74			0.572523
$651$		0			0
$652$	−6902.81			−0.414624
$653$			30212.1i			1.81055i	0.424823	+	0.905276i	$0.360336\pi$
$653$			30212.1i			1.81055i	−0.424823	+	0.905276i	$0.639664\pi$
$654$	438.369	−	75.5882i	0.0262104	−	0.00451947i
$655$	−31334.7			−1.86923
$656$	5499.21			0.327299
$657$	−5637.20	−	15860.3i	−0.334746	−	0.941809i
$658$		0			0
$659$		−	533.821i		−	0.0315549i	−0.999876	−	0.0157775i	$-0.994978\pi$
$659$		−	533.821i		−	0.0315549i	0.999876	−	0.0157775i	$-0.00502233\pi$
$660$	2008.65	−	346.353i	0.118465	−	0.0204269i
$661$		−	7665.18i		−	0.451045i	−0.974238	−	0.225523i	$-0.927591\pi$
$661$		−	7665.18i		−	0.451045i	0.974238	−	0.225523i	$-0.0724089\pi$
$662$			11731.1i			0.688732i
$663$	172.185	−	29.6899i	0.0100861	−	0.00173915i
$664$			6851.50i			0.400436i
$665$		0			0
$666$	−4502.00	−	12666.4i	−0.261936	−	0.736957i
$667$	−14442.9			−0.838427
$668$	−1942.49			−0.112510
$669$	−9126.37	+	1573.66i	−0.527423	+	0.0909438i
$670$			9262.25i			0.534077i
$671$	−1564.64			−0.0900184
$672$		0			0
$673$	−28054.4			−1.60686			−0.803430	−	0.595400i	$-0.796994\pi$
$673$	−28054.4			−1.60686			−0.803430	+	0.595400i	$0.796994\pi$
$674$		−	16978.2i		−	0.970290i
$675$	18387.2	+	32698.6i	1.04848	+	1.86455i
$676$	−7528.98			−0.428367
$677$	10512.6			0.596798			0.298399	−	0.954441i	$-0.403547\pi$
$677$	10512.6			0.596798			0.298399	+	0.954441i	$0.403547\pi$
$678$	−668.141	−	3874.84i	−0.0378463	−	0.219487i
$679$		0			0
$680$		−	300.356i		−	0.0169384i
$681$	−3040.11	−	17631.0i	−0.171068	−	0.992099i
$682$		−	770.045i		−	0.0432354i
$683$		−	18105.3i		−	1.01432i	−0.861852	−	0.507160i	$-0.830695\pi$
$683$		−	18105.3i		−	1.01432i	0.861852	−	0.507160i	$-0.169305\pi$
$684$	−3508.13	−	9870.14i	−0.196106	−	0.551746i
$685$		−	36535.8i		−	2.03790i
$686$		0			0
$687$	27830.0	−	4798.73i	1.54553	−	0.266496i
$688$	−393.374			−0.0217983
$689$	−7065.82			−0.390691
$690$	−5490.66	−	31842.7i	−0.302936	−	1.75686i
$691$		−	8845.62i		−	0.486980i	−0.969903	−	0.243490i	$-0.921708\pi$
$691$		−	8845.62i		−	0.486980i	0.969903	−	0.243490i	$-0.0782923\pi$
$692$	−5812.42			−0.319299
$693$		0			0
$694$	−2237.52			−0.122385
$695$		−	1106.66i		−	0.0604001i
$696$	−649.945	−	3769.32i	−0.0353967	−	0.205281i
$697$	−651.431			−0.0354013
$698$	−4728.87			−0.256433
$699$	22559.0	−	3889.87i	1.22069	−	0.210484i
$700$		0			0
$701$			32985.2i			1.77723i	0.458658	+	0.888613i	$0.348330\pi$
$701$			32985.2i			1.77723i	−0.458658	+	0.888613i	$0.651670\pi$
$702$	2439.98	+	4339.11i	0.131184	+	0.233289i
$703$		−	24144.9i		−	1.29536i
$704$		−	316.844i		−	0.0169624i
$705$	8229.02	+	47723.7i	0.439607	+	2.54947i
$706$		−	5644.49i		−	0.300897i
$707$		0			0
$708$	−2370.30	−	13746.4i	−0.125821	−	0.729693i
$709$	15993.8			0.847194			0.423597	−	0.905851i	$-0.360767\pi$
$709$	15993.8			0.847194			0.423597	+	0.905851i	$0.360767\pi$
$710$	6030.80			0.318777
$711$	−7692.82	+	2734.25i	−0.405771	+	0.144223i
$712$			7257.23i			0.381989i
$713$	−12207.4			−0.641191
$714$		0			0
$715$	−1739.85			−0.0910024
$716$		−	5078.08i		−	0.265051i
$717$	10345.1	−	1783.81i	0.538834	−	0.0929114i
$718$	−10403.8			−0.540760
$719$	−20924.6			−1.08534			−0.542668	−	0.839947i	$-0.682586\pi$
$719$	−20924.6			−1.08534			−0.542668	+	0.839947i	$0.682586\pi$
$720$	8063.25	−	2865.91i	0.417361	−	0.148342i
$721$		0			0
$722$		−	5096.59i		−	0.262708i
$723$	−11629.3	+	2005.24i	−0.598199	+	0.103148i
$724$		−	13157.0i		−	0.675382i
$725$			24603.6i			1.26035i
$726$	13380.0	−	2307.12i	0.683992	−	0.117941i
$727$			21598.1i			1.10183i	0.834562	+	0.550915i	$0.185721\pi$
$727$			21598.1i			1.10183i	−0.834562	+	0.550915i	$0.814279\pi$
$728$		0			0
$729$	−10225.7	+	16818.3i	−0.519519	+	0.854459i
$730$	24698.4			1.25223
$731$	46.5987			0.00235775
$732$	−6473.35	+	1116.20i	−0.326861	+	0.0563607i
$733$		−	10269.9i		−	0.517502i	−0.965944	−	0.258751i	$-0.916689\pi$
$733$		−	10269.9i		−	0.517502i	0.965944	−	0.258751i	$-0.0833109\pi$
$734$	11261.6			0.566313
$735$		0			0
$736$	−5022.86			−0.251556
$737$		−	1157.43i		−	0.0578485i
$738$	−6215.76	−	17488.1i	−0.310034	−	0.872282i
$739$	−18045.2			−0.898246			−0.449123	−	0.893470i	$-0.648263\pi$
$739$	−18045.2			−0.898246			−0.449123	+	0.893470i	$0.648263\pi$
$740$	19724.8			0.979860
$741$	1519.33	+	8811.28i	0.0753226	+	0.436829i
$742$		0			0
$743$		−	29700.6i		−	1.46650i	−0.679960	−	0.733249i	$-0.738003\pi$
$743$		−	29700.6i		−	1.46650i	0.679960	−	0.733249i	$-0.261997\pi$
$744$	−549.344	−	3185.88i	−0.0270698	−	0.156990i
$745$			67503.6i			3.31965i
$746$			13688.9i			0.671832i
$747$	21788.5	−	7744.25i	1.06720	−	0.379313i
$748$			37.5330i			0.00183468i
$749$		0			0
$750$	−28886.2	+	4980.85i	−1.40636	+	0.242500i
$751$	−18862.2			−0.916499			−0.458249	−	0.888824i	$-0.651523\pi$
$751$	−18862.2			−0.916499			−0.458249	+	0.888824i	$0.651523\pi$
$752$	7527.92			0.365047
$753$	−3985.18	−	23111.8i	−0.192866	−	1.11851i
$754$			3264.90i			0.157693i
$755$	−64493.3			−3.10881
$756$		0			0
$757$	12141.1			0.582929			0.291464	−	0.956582i	$-0.405858\pi$
$757$	12141.1			0.582929			0.291464	+	0.956582i	$0.405858\pi$
$758$			11381.2i			0.545363i
$759$	686.121	+	3979.12i	0.0328124	+	0.190294i
$760$	15370.3			0.733603
$761$	25127.0			1.19691			0.598457	−	0.801155i	$-0.295781\pi$
$761$	25127.0			1.19691			0.598457	+	0.801155i	$0.295781\pi$
$762$	1155.26	−	199.202i	0.0549220	−	0.00947023i
$763$		0			0
$764$		−	7914.12i		−	0.374768i
$765$	−955.164	+	339.493i	−0.0451425	+	0.0160449i
$766$		−	8606.64i		−	0.405967i
$767$			11906.9i			0.560537i
$768$	−226.034	−	1310.87i	−0.0106202	−	0.0615911i
$769$			23475.2i			1.10083i	0.834892	+	0.550413i	$0.185530\pi$
$769$			23475.2i			1.10083i	−0.834892	+	0.550413i	$0.814470\pi$
$770$		0			0
$771$	5243.47	+	30409.2i	0.244927	+	1.42044i
$772$	3679.39			0.171534
$773$	−31391.2			−1.46063			−0.730313	−	0.683113i	$-0.760626\pi$
$773$	−31391.2			−1.46063			−0.730313	+	0.683113i	$0.760626\pi$
$774$	444.631	+	1250.97i	0.0206485	+	0.0580946i
$775$			20795.4i			0.963859i
$776$	562.985			0.0260438
$777$		0			0
$778$	14188.1			0.653813
$779$		−	33336.0i		−	1.53323i
$780$	−7198.23	+	1241.19i	−0.330433	+	0.0569768i
$781$	−753.618			−0.0345283
$782$	595.003			0.0272088
$783$	−11252.2	+	6327.35i	−0.513563	+	0.288788i
$784$		0			0
$785$		−	50315.7i		−	2.28770i
$786$	16200.0	−	2793.38i	0.735161	−	0.126764i
$787$		−	4632.84i		−	0.209839i	−0.994481	−	0.104919i	$-0.966542\pi$
$787$		−	4632.84i		−	0.209839i	0.994481	−	0.104919i	$-0.0334585\pi$
$788$		−	12247.9i		−	0.553699i
$789$	−27950.7	+	4819.56i	−1.26118	+	0.217466i
$790$		−	11979.6i		−	0.539515i
$791$		0			0
$792$	−1007.60	+	358.129i	−0.0452063	+	0.0160676i
$793$	5607.07			0.251088
$794$	9002.66			0.402383
$795$	40397.5	−	6965.76i	1.80220	−	0.310755i
$796$			2085.81i			0.0928766i
$797$	−121.248			−0.00538874			−0.00269437	−	0.999996i	$-0.500858\pi$
$797$	−121.248			−0.00538874			−0.00269437	+	0.999996i	$0.500858\pi$
$798$		0			0
$799$	−891.749			−0.0394841
$800$			8556.50i			0.378147i
$801$	23078.7	−	8202.84i	1.01804	−	0.361839i
$802$	13945.6			0.614012
$803$	−3086.35			−0.135635
$804$	−825.697	−	4788.58i	−0.0362190	−	0.210050i
$805$		0			0
$806$			2759.54i			0.120596i
$807$	−4666.29	−	27061.9i	−0.203546	−	1.18045i
$808$			1908.38i			0.0830896i
$809$			13114.9i			0.569959i	0.958534	+	0.284979i	$0.0919868\pi$
$809$			13114.9i			0.569959i	−0.958534	+	0.284979i	$0.908013\pi$
$810$	−18227.8	−	22402.6i	−0.790690	−	0.971788i
$811$			2601.55i			0.112642i	0.998413	+	0.0563211i	$0.0179371\pi$
$811$			2601.55i			0.112642i	−0.998413	+	0.0563211i	$0.982063\pi$
$812$		0			0
$813$	32146.0	−	5542.95i	1.38673	−	0.239114i
$814$	−2464.84			−0.106133
$815$	−34184.2			−1.46923
$816$	26.7757	+	155.284i	0.00114870	+	0.00666181i
$817$			2384.62i			0.102114i
$818$	−28710.3			−1.22718
$819$		0			0
$820$	27233.3			1.15979
$821$			16139.4i			0.686075i	0.939322	+	0.343038i	$0.111456\pi$
$821$			16139.4i			0.686075i	−0.939322	+	0.343038i	$0.888544\pi$
$822$	3257.04	+	18889.0i	0.138202	+	0.801497i
$823$	19573.5			0.829026			0.414513	−	0.910043i	$-0.363952\pi$
$823$	19573.5			0.829026			0.414513	+	0.910043i	$0.363952\pi$
$824$	156.662			0.00662328
$825$	6778.47	−	1168.81i	0.286056	−	0.0493247i
$826$		0			0
$827$		−	19041.3i		−	0.800641i	−0.916375	−	0.400320i	$-0.868899\pi$
$827$		−	19041.3i		−	0.800641i	0.916375	−	0.400320i	$-0.131101\pi$
$828$	5677.34	+	15973.2i	0.238286	+	0.670420i
$829$		−	5490.20i		−	0.230015i	−0.993365	−	0.115007i	$-0.963311\pi$
$829$		−	5490.20i		−	0.230015i	0.993365	−	0.115007i	$-0.0366892\pi$
$830$			33930.1i			1.41895i
$831$	−6618.86	−	38385.7i	−0.276300	−	1.60239i
$832$			1135.45i			0.0473131i
$833$		0			0
$834$	98.6551	+	572.144i	0.00409610	+	0.0237551i
$835$	−9619.60			−0.398683
$836$	−1920.69			−0.0794600
$837$	−9510.52	+	5347.97i	−0.392750	+	0.220852i
$838$		−	29679.6i		−	1.22347i
$839$	25774.7			1.06060			0.530299	−	0.847811i	$-0.322080\pi$
$839$	25774.7			1.06060			0.530299	+	0.847811i	$0.322080\pi$
$840$		0			0
$841$	15922.5			0.652854
$842$		−	22146.1i		−	0.906419i
$843$	3819.39	−	658.579i	0.156046	−	0.0269071i
$844$	−398.515			−0.0162529
$845$	−37285.1			−1.51792
$846$	−8508.81	−	23939.6i	−0.345790	−	0.972883i
$847$		0			0
$848$		−	6372.29i		−	0.258049i
$849$	13484.3	−	2325.11i	0.545089	−	0.0939899i
$850$		−	1013.59i		−	0.0409011i
$851$			39074.5i			1.57398i
$852$	−3117.92	+	537.625i	−0.125374	+	0.0216182i
$853$		−	15407.3i		−	0.618447i	−0.950989	−	0.309224i	$-0.899931\pi$
$853$		−	15407.3i		−	0.618447i	0.950989	−	0.309224i	$-0.100069\pi$
$854$		0			0
$855$	−17373.0	−	48879.0i	−0.694906	−	1.95512i
$856$	3870.65			0.154551
$857$	−11416.3			−0.455044			−0.227522	−	0.973773i	$-0.573062\pi$
$857$	−11416.3			−0.455044			−0.227522	+	0.973773i	$0.573062\pi$
$858$	899.502	−	155.102i	0.0357908	−	0.00617142i
$859$			37420.7i			1.48636i	0.669094	+	0.743178i	$0.266682\pi$
$859$			37420.7i			1.48636i	−0.669094	+	0.743178i	$0.733318\pi$
$860$	−1948.07			−0.0772427
$861$		0			0
$862$	−12821.9			−0.506632
$863$			34843.6i			1.37438i	0.726479	+	0.687189i	$0.241156\pi$
$863$			34843.6i			1.37438i	−0.726479	+	0.687189i	$0.758844\pi$
$864$	−3913.21	+	2200.49i	−0.154086	+	0.0866459i
$865$	−28784.3			−1.13144
$866$	−25762.1			−1.01089
$867$	4334.74	+	25139.0i	0.169799	+	0.984737i
$868$		0			0
$869$			1496.99i			0.0584374i
$870$	−3218.67	−	18666.5i	−0.125429	−	0.727416i
$871$			4147.76i			0.161357i
$872$		−	342.437i		−	0.0132986i
$873$	−636.341	−	1790.35i	−0.0246700	−	0.0694091i
$874$			30448.3i			1.17841i
$875$		0			0
$876$	−12769.1	+	2201.78i	−0.492497	+	0.0849215i
$877$	−28562.2			−1.09975			−0.549874	−	0.835248i	$-0.685324\pi$
$877$	−28562.2			−1.09975			−0.549874	+	0.835248i	$0.685324\pi$
$878$	−18532.6			−0.712352
$879$	785.259	+	4554.06i	0.0301321	+	0.174749i
$880$		−	1569.08i		−	0.0601064i
$881$	−25098.4			−0.959804			−0.479902	−	0.877322i	$-0.659328\pi$
$881$	−25098.4			−0.959804			−0.479902	+	0.877322i	$0.659328\pi$
$882$		0			0
$883$	−32704.3			−1.24642			−0.623208	−	0.782056i	$-0.714171\pi$
$883$	−32704.3			−1.24642			−0.623208	+	0.782056i	$0.714171\pi$
$884$		−	134.504i		−	0.00511748i
$885$	−11738.2	−	68075.2i	−0.445849	−	2.58568i
$886$	17762.9			0.673538
$887$	23319.4			0.882736			0.441368	−	0.897326i	$-0.354493\pi$
$887$	23319.4			0.882736			0.441368	+	0.897326i	$0.354493\pi$
$888$	−10197.7	+	1758.39i	−0.385374	+	0.0664503i
$889$		0			0
$890$			35939.3i			1.35358i
$891$	2277.77	+	2799.47i	0.0856433	+	0.105259i
$892$			7129.16i			0.267603i
$893$		−	45633.9i		−	1.71006i
$894$	−6017.71	−	34899.4i	−0.225126	−	1.30560i
$895$		−	25147.7i		−	0.939213i
$896$		0			0
$897$	−2458.79	−	14259.6i	−0.0915236	−	0.530786i
$898$	−12161.9			−0.451945
$899$	−7156.05			−0.265481
$900$	27210.5	−	9671.40i	1.00780	−	0.358200i
$901$			754.854i			0.0279110i
$902$	−3403.11			−0.125622
$903$		0			0
$904$	−3026.87			−0.111363
$905$		−	65156.4i		−	2.39323i
$906$	33343.0	−	5749.35i	1.22268	−	0.210827i
$907$	−37327.2			−1.36652			−0.683258	−	0.730177i	$-0.739438\pi$
$907$	−37327.2			−1.36652			−0.683258	+	0.730177i	$0.739438\pi$
$908$	−13772.6			−0.503370
$909$	6068.83	−	2157.04i	0.221442	−	0.0787067i
$910$		0			0
$911$			33130.2i			1.20489i	0.798161	+	0.602444i	$0.205806\pi$
$911$			33130.2i			1.20489i	−0.798161	+	0.602444i	$0.794194\pi$
$912$	−7946.43	+	1370.21i	−0.288523	+	0.0497501i
$913$		−	4239.96i		−	0.153693i
$914$			1115.31i			0.0403623i
$915$	−32057.4	+	5527.67i	−1.15824	+	0.199715i
$916$		−	21739.7i		−	0.784169i
$917$		0			0
$918$	463.555	−	260.667i	0.0166662	−	0.00937179i
$919$	−23758.8			−0.852808			−0.426404	−	0.904533i	$-0.640220\pi$
$919$	−23758.8			−0.852808			−0.426404	+	0.904533i	$0.640220\pi$
$920$	−24874.3			−0.891392
$921$	−20457.3	+	3527.47i	−0.731913	+	0.126204i
$922$			14844.5i			0.530235i
$923$	2700.68			0.0963097
$924$		0			0
$925$	66563.8			2.36606
$926$			20957.6i			0.743746i
$927$	−177.075	−	498.202i	−0.00627390	−	0.0176517i
$928$	−2944.44			−0.104155
$929$	35440.7			1.25164			0.625819	−	0.779968i	$-0.284765\pi$
$929$	35440.7			1.25164			0.625819	+	0.779968i	$0.284765\pi$
$930$	−2720.47	−	15777.2i	−0.0959221	−	0.556295i
$931$		0			0
$932$		−	17622.2i		−	0.619351i
$933$	452.083	+	2621.83i	0.0158634	+	0.0919987i
$934$		−	18835.0i		−	0.659849i
$935$			185.871i			0.00650123i
$936$	3610.84	−	1283.39i	0.126094	−	0.0448174i
$937$		−	42936.0i		−	1.49697i	−0.663154	−	0.748483i	$-0.730782\pi$
$937$		−	42936.0i		−	1.49697i	0.663154	−	0.748483i	$-0.269218\pi$
$938$		0			0
$939$	7519.12	−	1296.53i	0.261318	−	0.0450591i
$940$	37279.9			1.29355
$941$	32230.5			1.11656			0.558282	−	0.829652i	$-0.311461\pi$
$941$	32230.5			1.11656			0.558282	+	0.829652i	$0.311461\pi$
$942$	4485.47	+	26013.2i	0.155143	+	0.899742i
$943$			53948.8i			1.86301i
$944$	−10738.2			−0.370230
$945$		0			0
$946$	243.434			0.00836652
$947$		−	10995.7i		−	0.377310i	−0.982043	−	0.188655i	$-0.939587\pi$
$947$		−	10995.7i		−	0.377310i	0.982043	−	0.188655i	$-0.0604128\pi$
$948$	1067.94	+	6193.47i	0.0365878	+	0.212188i
$949$	11060.3			0.378327
$950$	51869.0			1.77143
$951$	−38700.5	+	6673.14i	−1.31961	+	0.227541i
$952$		0			0
$953$			10083.0i			0.342728i	0.985208	+	0.171364i	$0.0548174\pi$
$953$			10083.0i			0.342728i	−0.985208	+	0.171364i	$0.945183\pi$
$954$	−20264.5	+	7202.59i	−0.687724	+	0.244437i
$955$		−	39192.4i		−	1.32800i
$956$		−	8081.17i		−	0.273393i
$957$	402.210	+	2332.59i	0.0135858	+	0.0787899i
$958$			21212.6i			0.715394i
$959$		0			0
$960$	−1119.37	−	6491.71i	−0.0376328	−	0.218249i
$961$	23742.6			0.796972
$962$	8833.02			0.296037
$963$	−4374.99	−	12309.1i	−0.146399	−	0.411894i
$964$			9084.33i			0.303513i
$965$	18221.1			0.607832
$966$		0			0
$967$	−24809.9			−0.825061			−0.412530	−	0.910944i	$-0.635355\pi$
$967$	−24809.9			−0.825061			−0.412530	+	0.910944i	$0.635355\pi$
$968$		−	10451.9i		−	0.347043i
$969$	941.325	−	162.313i	0.0312071	−	0.00538106i
$970$	2788.02			0.0922865
$971$	6067.49			0.200530			0.100265	−	0.994961i	$-0.468031\pi$
$971$	6067.49			0.200530			0.100265	+	0.994961i	$0.468031\pi$
$972$	11420.9	+	9957.21i	0.376877	+	0.328578i
$973$		0			0
$974$		−	25548.7i		−	0.840487i
$975$	−24291.4	+	4188.58i	−0.797895	+	0.137581i
$976$			5056.73i			0.165842i
$977$		−	13129.2i		−	0.429930i	−0.976622	−	0.214965i	$-0.931036\pi$
$977$		−	13129.2i		−	0.429930i	0.976622	−	0.214965i	$-0.0689638\pi$
$978$	17673.2	−	3047.40i	0.577839	−	0.0996371i
$979$		−	4491.03i		−	0.146613i
$980$		0			0
$981$	−1088.98	+	387.056i	−0.0354420	+	0.0125971i
$982$	37379.6			1.21470
$983$	−26854.6			−0.871343			−0.435671	−	0.900106i	$-0.643489\pi$
$983$	−26854.6			−0.871343			−0.435671	+	0.900106i	$0.643489\pi$
$984$	−14079.6	+	2427.75i	−0.456140	+	0.0786523i
$985$		−	60654.4i		−	1.96204i
$986$	348.795			0.0112656
$987$		0			0
$988$	6883.02			0.221638
$989$		−	3859.11i		−	0.124077i
$990$	−4989.83	+	1773.53i	−0.160189	+	0.0569358i
$991$	26990.1			0.865156			0.432578	−	0.901596i	$-0.357604\pi$
$991$	26990.1			0.865156			0.432578	+	0.901596i	$0.357604\pi$
$992$	−2488.69			−0.0796531
$993$	−5178.94	−	30034.9i	−0.165507	−	0.959849i
$994$		0			0
$995$			10329.4i			0.329109i
$996$	−3024.75	−	17541.9i	−0.0962278	−	0.558067i
$997$			14142.4i			0.449243i	0.974446	+	0.224622i	$0.0721146\pi$
$997$			14142.4i			0.449243i	−0.974446	+	0.224622i	$0.927885\pi$
$998$		−	27451.0i		−	0.870686i
$999$	17118.3	+	30442.2i	0.542142	+	0.964113i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.4.d.a.293.12		16
3.2	odd	2	inner	294.4.d.a.293.5		16
7.2	even	3		294.4.f.a.227.8		16
7.3	odd	6		294.4.f.a.215.3		16
7.4	even	3		42.4.f.a.5.2	✓	16
7.5	odd	6		42.4.f.a.17.5	yes	16
7.6	odd	2	inner	294.4.d.a.293.13		16
21.2	odd	6		294.4.f.a.227.3		16
21.5	even	6		42.4.f.a.17.2	yes	16
21.11	odd	6		42.4.f.a.5.5	yes	16
21.17	even	6		294.4.f.a.215.8		16
21.20	even	2	inner	294.4.d.a.293.4		16
28.11	odd	6		336.4.bc.e.257.6		16
28.19	even	6		336.4.bc.e.17.8		16
84.11	even	6		336.4.bc.e.257.8		16
84.47	odd	6		336.4.bc.e.17.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.f.a.5.2	✓	16	7.4	even	3
42.4.f.a.5.5	yes	16	21.11	odd	6
42.4.f.a.17.2	yes	16	21.5	even	6
42.4.f.a.17.5	yes	16	7.5	odd	6
294.4.d.a.293.4		16	21.20	even	2	inner
294.4.d.a.293.5		16	3.2	odd	2	inner
294.4.d.a.293.12		16	1.1	even	1	trivial
294.4.d.a.293.13		16	7.6	odd	2	inner
294.4.f.a.215.3		16	7.3	odd	6
294.4.f.a.215.8		16	21.17	even	6
294.4.f.a.227.3		16	21.2	odd	6
294.4.f.a.227.8		16	7.2	even	3
336.4.bc.e.17.6		16	84.47	odd	6
336.4.bc.e.17.8		16	28.19	even	6
336.4.bc.e.257.6		16	28.11	odd	6
336.4.bc.e.257.8		16	84.11	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} +(-0.882945 - 5.12059i) q^{3} -4.00000 q^{4} -19.8088 q^{5} +(10.2412 - 1.76589i) q^{6} -8.00000i q^{8} +(-25.4408 + 9.04239i) q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} +(-0.882945 - 5.12059i) q^{3} -4.00000 q^{4} -19.8088 q^{5} +(10.2412 - 1.76589i) q^{6} -8.00000i q^{8} +(-25.4408 + 9.04239i) q^{9} -39.6177i q^{10} +4.95069i q^{11} +(3.53178 + 20.4823i) q^{12} -17.7414i q^{13} +(17.4901 + 101.433i) q^{15} +16.0000 q^{16} -1.89534 q^{17} +(-18.0848 - 50.8816i) q^{18} -96.9912i q^{19} +79.2354 q^{20} -9.90138 q^{22} +156.964i q^{23} +(-40.9647 + 7.06356i) q^{24} +267.390 q^{25} +35.4827 q^{26} +(68.7652 + 122.288i) q^{27} +92.0138i q^{29} +(-202.866 + 34.9803i) q^{30} +77.7715i q^{31} +32.0000i q^{32} +(25.3504 - 4.37119i) q^{33} -3.79068i q^{34} +(101.763 - 36.1696i) q^{36} +248.939 q^{37} +193.982 q^{38} +(-90.8462 + 15.6646i) q^{39} +158.471i q^{40} +343.701 q^{41} -24.5859 q^{43} -19.8028i q^{44} +(503.953 - 179.119i) q^{45} -313.929 q^{46} +470.495 q^{47} +(-14.1271 - 81.9294i) q^{48} +534.781i q^{50} +(1.67348 + 9.70527i) q^{51} +70.9654i q^{52} -398.268i q^{53} +(-244.576 + 137.530i) q^{54} -98.0675i q^{55} +(-496.652 + 85.6379i) q^{57} -184.028 q^{58} -671.135 q^{59} +(-69.9605 - 405.732i) q^{60} +316.045i q^{61} -155.543 q^{62} -64.0000 q^{64} +351.436i q^{65} +(8.74238 + 50.7009i) q^{66} -233.791 q^{67} +7.58137 q^{68} +(803.750 - 138.591i) q^{69} +152.225i q^{71} +(72.3392 + 203.527i) q^{72} +623.419i q^{73} +497.877i q^{74} +(-236.091 - 1369.20i) q^{75} +387.965i q^{76} +(-31.3293 - 181.692i) q^{78} +302.381 q^{79} -316.942 q^{80} +(565.470 - 460.092i) q^{81} +687.402i q^{82} -856.438 q^{83} +37.5446 q^{85} -49.1718i q^{86} +(471.165 - 81.2431i) q^{87} +39.6055 q^{88} -907.153 q^{89} +(358.239 + 1007.91i) q^{90} -627.858i q^{92} +(398.236 - 68.6679i) q^{93} +940.990i q^{94} +1921.28i q^{95} +(163.859 - 28.2542i) q^{96} +70.3731i q^{97} +(-44.7661 - 125.950i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 64 q^{4} - 36 q^{9}+O(q^{10}) \) 16 * q - 64 * q^4 - 36 * q^9	\( 16 q - 64 q^{4} - 36 q^{9} + 256 q^{16} + 96 q^{18} + 24 q^{22} + 388 q^{25} - 720 q^{30} + 144 q^{36} + 1924 q^{37} - 1188 q^{39} + 1732 q^{43} - 336 q^{46} - 3276 q^{51} - 2664 q^{57} + 1560 q^{58} - 1024 q^{64} + 1412 q^{67} - 384 q^{72} + 2832 q^{78} + 5312 q^{79} - 252 q^{81} + 5232 q^{85} - 96 q^{88} - 4032 q^{93} - 4284 q^{99}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

Properties

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