LMFDB - Embedded newform 245.4.j.e.79.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(79,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("245.79");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.j (of order $6$, degree $2$, not 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:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 55 x^{18} + 2042 x^{16} - 41247 x^{14} + 600234 x^{12} - 4812047 x^{10} + 27547801 x^{8} + \cdots + 12960000 $ x^20 - 55x^18 + 2042x^16 - 41247x^14 + 600234x^12 - 4812047x^10 + 27547801x^8 - 79828440x^6 + 160801200x^4 - 48816000*x^2 + 12960000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2}\cdot 7^{8} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.3
Root			$-1.60625 + 0.927371i$ of defining polynomial
Character	$\chi$	$=$	245.79
Dual form			245.4.j.e.214.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.47228 - 1.42737i) q^{2} +(-7.78434 + 4.49429i) q^{3} +(0.0747741 + 0.129513i) q^{4} +(7.11340 + 8.62551i) q^{5} +25.6601 q^{6} +22.4110i q^{8} +(26.8973 - 46.5874i) q^{9} +(-5.27451 - 31.4781i) q^{10} +(-18.7204 - 32.4247i) q^{11} +(-1.16413 - 0.672113i) q^{12} -3.96370i q^{13} +(-94.1387 - 35.1742i) q^{15} +(32.5870 - 56.4424i) q^{16} +(44.7544 - 25.8390i) q^{17} +(-132.995 + 76.7847i) q^{18} +(12.9661 - 22.4580i) q^{19} +(-0.585214 + 1.56624i) q^{20} +106.884i q^{22} +(-150.216 - 86.7272i) q^{23} +(-100.722 - 174.455i) q^{24} +(-23.7990 + 122.714i) q^{25} +(-5.65768 + 9.79938i) q^{26} +240.845i q^{27} +245.676 q^{29} +(182.530 + 221.331i) q^{30} +(86.0372 + 149.021i) q^{31} +(-5.86031 + 3.38345i) q^{32} +(291.452 + 168.270i) q^{33} -147.527 q^{34} +8.04488 q^{36} +(217.111 + 125.349i) q^{37} +(-64.1118 + 37.0150i) q^{38} +(17.8140 + 30.8548i) q^{39} +(-193.306 + 159.419i) q^{40} -48.8649 q^{41} +143.612i q^{43} +(2.79960 - 4.84905i) q^{44} +(593.172 - 99.3925i) q^{45} +(247.584 + 428.827i) q^{46} +(31.7325 + 18.3208i) q^{47} +585.822i q^{48} +(233.995 - 269.412i) q^{50} +(-232.256 + 402.279i) q^{51} +(0.513350 - 0.296383i) q^{52} +(-558.834 + 322.643i) q^{53} +(343.775 - 595.435i) q^{54} +(146.514 - 392.123i) q^{55} +233.094i q^{57} +(-607.380 - 350.671i) q^{58} +(197.748 + 342.509i) q^{59} +(-2.48364 - 14.8223i) q^{60} +(-23.7565 + 41.1475i) q^{61} -491.228i q^{62} -502.074 q^{64} +(34.1890 - 28.1954i) q^{65} +(-480.366 - 832.019i) q^{66} +(227.929 - 131.595i) q^{67} +(6.69295 + 3.86418i) q^{68} +1559.11 q^{69} -268.177 q^{71} +(1044.07 + 602.795i) q^{72} +(-172.995 + 99.8785i) q^{73} +(-357.840 - 619.797i) q^{74} +(-366.251 - 1062.20i) q^{75} +3.87813 q^{76} -101.709i q^{78} +(236.820 - 410.184i) q^{79} +(718.649 - 120.418i) q^{80} +(-356.199 - 616.955i) q^{81} +(120.808 + 69.7484i) q^{82} +72.7028i q^{83} +(541.231 + 202.227i) q^{85} +(204.988 - 355.049i) q^{86} +(-1912.43 + 1104.14i) q^{87} +(726.669 - 419.543i) q^{88} +(-776.123 + 1344.28i) q^{89} +(-1608.36 - 600.950i) q^{90} -25.9398i q^{92} +(-1339.48 - 773.352i) q^{93} +(-52.3011 - 90.5881i) q^{94} +(285.945 - 47.9133i) q^{95} +(30.4124 - 52.6758i) q^{96} +243.338i q^{97} -2014.11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 36 q^{4} - 6 q^{5} + 24 q^{6} + 46 q^{9} + 16 q^{10} - 84 q^{11} + 16 q^{15} - 148 q^{16} - 72 q^{19} - 136 q^{20} - 72 q^{24} + 362 q^{25} + 620 q^{26} + 176 q^{29} - 52 q^{30} - 120 q^{31} + 1928 q^{34}+ \cdots - 10608 q^{99}+O(q^{100}) $ 20 * q + 36 * q^4 - 6 * q^5 + 24 * q^6 + 46 * q^9 + 16 * q^10 - 84 * q^11 + 16 * q^15 - 148 * q^16 - 72 * q^19 - 136 * q^20 - 72 * q^24 + 362 * q^25 + 620 * q^26 + 176 * q^29 - 52 * q^30 - 120 * q^31 + 1928 * q^34 - 840 * q^36 - 212 * q^39 - 1396 * q^40 - 1704 * q^41 + 1424 * q^44 + 510 * q^45 - 176 * q^46 + 3288 * q^50 - 1276 * q^51 + 996 * q^54 - 2272 * q^55 - 864 * q^59 + 1692 * q^60 + 884 * q^61 - 5448 * q^64 - 520 * q^65 - 1148 * q^66 + 9616 * q^69 + 1760 * q^71 - 3024 * q^74 - 720 * q^75 - 5344 * q^76 + 3580 * q^79 + 2316 * q^80 + 302 * q^81 + 3144 * q^85 - 2432 * q^86 + 1492 * q^89 - 15496 * q^90 - 1652 * q^94 + 1628 * q^95 - 4080 * q^96 - 10608 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−2.47228	−	1.42737i	−0.874082	−	0.504652i	−0.00537973	−	0.999986i	$-0.501712\pi$
$2$	−2.47228	−	1.42737i	−0.874082	−	0.504652i	−0.868703	+	0.495334i	$0.835046\pi$
$3$	−7.78434	+	4.49429i	−1.49810	+	0.864926i	−0.999998	−	0.00219412i	$-0.999302\pi$
$3$	−7.78434	+	4.49429i	−1.49810	+	0.864926i	−0.498099	+	0.867120i	$0.665968\pi$
$4$	0.0747741	+	0.129513i	0.00934677	+	0.0161891i
$5$	7.11340	+	8.62551i	0.636242	+	0.771489i
$5$	7.11340	+	8.62551i	0.636242	+	0.771489i
$6$	25.6601			1.74595
$7$		0			0
$7$		0			0
$8$			22.4110i			0.990436i
$9$	26.8973	−	46.5874i	0.996195	−	1.72546i
$10$	−5.27451	−	31.4781i	−0.166795	−	0.995426i
$11$	−18.7204	−	32.4247i	−0.513128	−	0.888764i	−0.999884	−	0.0152260i	$-0.995153\pi$
$11$	−18.7204	−	32.4247i	−0.513128	−	0.888764i	0.486756	−	0.873538i	$-0.338180\pi$
$12$	−1.16413	−	0.672113i	−0.0280047	−	0.0161685i
$13$		−	3.96370i		−	0.0845641i	−0.999106	−	0.0422821i	$-0.986537\pi$
$13$		−	3.96370i		−	0.0845641i	0.999106	−	0.0422821i	$-0.0134628\pi$
$14$		0			0
$15$	−94.1387	−	35.1742i	−1.62043	−	0.605463i
$16$	32.5870	−	56.4424i	0.509172	−	0.881912i
$17$	44.7544	−	25.8390i	0.638503	−	0.368640i	−0.145535	−	0.989353i	$-0.546490\pi$
$17$	44.7544	−	25.8390i	0.638503	−	0.368640i	0.784038	+	0.620713i	$0.213157\pi$
$18$	−132.995	+	76.7847i	−1.74151	+	1.00546i
$19$	12.9661	−	22.4580i	0.156560	−	0.271170i	−0.777066	−	0.629419i	$-0.783293\pi$
$19$	12.9661	−	22.4580i	0.156560	−	0.271170i	0.933626	+	0.358249i	$0.116626\pi$
$20$	−0.585214	+	1.56624i	−0.00654289	+	0.0175111i
$21$		0			0
$22$			106.884i			1.03580i
$23$	−150.216	−	86.7272i	−1.36183	−	0.786255i	−0.371966	−	0.928246i	$-0.621316\pi$
$23$	−150.216	−	86.7272i	−1.36183	−	0.786255i	−0.989868	+	0.141991i	$0.954649\pi$
$24$	−100.722	−	174.455i	−0.856654	−	1.48377i
$25$	−23.7990	+	122.714i	−0.190392	+	0.981708i
$26$	−5.65768	+	9.79938i	−0.0426754	+	0.0739160i
$27$			240.845i			1.71669i
$28$		0			0
$29$	245.676			1.57314			0.786568	−	0.617503i	$-0.211856\pi$
$29$	245.676			1.57314			0.786568	+	0.617503i	$0.211856\pi$
$30$	182.530	+	221.331i	1.11084	+	1.34698i
$31$	86.0372	+	149.021i	0.498475	+	0.863385i	0.999998	−	0.00175963i	$-0.000560109\pi$
$31$	86.0372	+	149.021i	0.498475	+	0.863385i	−0.501523	+	0.865144i	$0.667227\pi$
$32$	−5.86031	+	3.38345i	−0.0323739	+	0.0186911i
$33$	291.452	+	168.270i	1.53743	+	0.887636i
$34$	−147.527			−0.744139
$35$		0			0
$36$	8.04488			0.0372448
$37$	217.111	+	125.349i	0.964673	+	0.556954i	0.897608	−	0.440795i	$-0.145303\pi$
$37$	217.111	+	125.349i	0.964673	+	0.556954i	0.0670648	+	0.997749i	$0.478637\pi$
$38$	−64.1118	+	37.0150i	−0.273692	+	0.158016i
$39$	17.8140	+	30.8548i	0.0731417	+	0.126685i
$40$	−193.306	+	159.419i	−0.764111	+	0.630157i
$41$	−48.8649			−0.186132			−0.0930661	−	0.995660i	$-0.529667\pi$
$41$	−48.8649			−0.186132			−0.0930661	+	0.995660i	$0.529667\pi$
$42$		0			0
$43$			143.612i			0.509317i	0.967031	+	0.254658i	$0.0819630\pi$
$43$			143.612i			0.509317i	−0.967031	+	0.254658i	$0.918037\pi$
$44$	2.79960	−	4.84905i	0.00959218	−	0.0166141i
$45$	593.172	−	99.3925i	1.96500	−	0.329257i
$46$	247.584	+	428.827i	0.793570	+	1.37450i
$47$	31.7325	+	18.3208i	0.0984821	+	0.0568587i	0.548432	−	0.836195i	$-0.315225\pi$
$47$	31.7325	+	18.3208i	0.0984821	+	0.0568587i	−0.449950	+	0.893054i	$0.648558\pi$
$48$			585.822i			1.76159i
$49$		0			0
$50$	233.995	−	269.412i	0.661839	−	0.762012i
$51$	−232.256	+	402.279i	−0.637692	+	1.10452i
$52$	0.513350	−	0.296383i	0.00136902	−	0.000790401i
$53$	−558.834	+	322.643i	−1.44833	+	0.836196i	−0.998382	−	0.0568566i	$-0.981892\pi$
$53$	−558.834	+	322.643i	−1.44833	+	0.836196i	−0.449952	+	0.893053i	$0.648559\pi$
$54$	343.775	−	595.435i	0.866330	−	1.50053i
$55$	146.514	−	392.123i	0.359198	−	0.961342i
$56$		0			0
$57$			233.094i			0.541651i
$58$	−607.380	−	350.671i	−1.37505	−	0.793886i
$59$	197.748	+	342.509i	0.436348	+	0.755777i	0.997405	−	0.0720003i	$-0.0229383\pi$
$59$	197.748	+	342.509i	0.436348	+	0.755777i	−0.561056	+	0.827778i	$0.689605\pi$
$60$	−2.48364	−	14.8223i	−0.00534393	−	0.0318924i
$61$	−23.7565	+	41.1475i	−0.0498641	+	0.0863671i	−0.889880	−	0.456194i	$-0.849212\pi$
$61$	−23.7565	+	41.1475i	−0.0498641	+	0.0863671i	0.840016	+	0.542562i	$0.182545\pi$
$62$		−	491.228i		−	1.00623i
$63$		0			0
$64$	−502.074			−0.980614
$65$	34.1890	−	28.1954i	0.0652403	−	0.0538033i
$66$	−480.366	−	832.019i	−0.895894	−	1.55173i
$67$	227.929	−	131.595i	0.415611	−	0.239953i	−0.277587	−	0.960701i	$-0.589535\pi$
$67$	227.929	−	131.595i	0.415611	−	0.239953i	0.693198	+	0.720748i	$0.256201\pi$
$68$	6.69295	+	3.86418i	0.0119359	+	0.00689118i
$69$	1559.11			2.72021
$70$		0			0
$71$	−268.177			−0.448264			−0.224132	−	0.974559i	$-0.571955\pi$
$71$	−268.177			−0.448264			−0.224132	+	0.974559i	$0.571955\pi$
$72$	1044.07	+	602.795i	1.70896	+	0.986667i
$73$	−172.995	+	99.8785i	−0.277363	+	0.160136i	−0.632229	−	0.774782i	$-0.717860\pi$
$73$	−172.995	+	99.8785i	−0.277363	+	0.160136i	0.354866	+	0.934917i	$0.384526\pi$
$74$	−357.840	−	619.797i	−0.562136	−	0.973648i
$75$	−366.251	−	1062.20i	−0.563880	−	1.63537i
$76$	3.87813			0.00585331
$77$		0			0
$78$		−	101.709i		−	0.147644i
$79$	236.820	−	410.184i	0.337270	−	0.584169i	−0.646648	−	0.762788i	$-0.723830\pi$
$79$	236.820	−	410.184i	0.337270	−	0.584169i	0.983918	+	0.178620i	$0.0571632\pi$
$80$	718.649	−	120.418i	1.00434	−	0.168289i
$81$	−356.199	−	616.955i	−0.488614	−	0.846303i
$82$	120.808	+	69.7484i	0.162695	+	0.0939319i
$83$			72.7028i			0.0961466i	0.998844	+	0.0480733i	$0.0153081\pi$
$83$			72.7028i			0.0961466i	−0.998844	+	0.0480733i	$0.984692\pi$
$84$		0			0
$85$	541.231	+	202.227i	0.690644	+	0.258054i
$86$	204.988	−	355.049i	0.257028	−	0.445185i
$87$	−1912.43	+	1104.14i	−2.35671	+	1.36065i
$88$	726.669	−	419.543i	0.880264	−	0.508221i
$89$	−776.123	+	1344.28i	−0.924369	+	1.60105i	−0.131796	+	0.991277i	$0.542074\pi$
$89$	−776.123	+	1344.28i	−0.924369	+	1.60105i	−0.792573	+	0.609777i	$0.791259\pi$
$90$	−1608.36	−	600.950i	−1.88373	−	0.703841i
$91$		0			0
$92$		−	25.9398i		−	0.0293958i
$93$	−1339.48	−	773.352i	−1.49353	−	0.862289i
$94$	−52.3011	−	90.5881i	−0.0573877	−	0.0993984i
$95$	285.945	−	47.9133i	0.308814	−	0.0517453i
$96$	30.4124	−	52.6758i	0.0323328	−	0.0560021i
$97$			243.338i			0.254714i	0.991857	+	0.127357i	$0.0406494\pi$
$97$			243.338i			0.254714i	−0.991857	+	0.127357i	$0.959351\pi$
$98$		0			0
$99$	−2014.11			−2.04470
$100$	−17.6725	+	6.09353i	−0.0176725	+	0.00609353i
$101$	769.668	+	1333.10i	0.758265	+	1.31335i	0.943734	+	0.330704i	$0.107286\pi$
$101$	769.668	+	1333.10i	0.758265	+	1.31335i	−0.185469	+	0.982650i	$0.559380\pi$
$102$	1148.40	−	663.030i	1.11479	−	0.643625i
$103$	821.536	+	474.314i	0.785906	+	0.453743i	0.838519	−	0.544872i	$-0.183422\pi$
$103$	821.536	+	474.314i	0.785906	+	0.453743i	−0.0526133	+	0.998615i	$0.516755\pi$
$104$	88.8306			0.0837554
$105$		0			0
$106$	1842.12			1.68795
$107$	−748.231	−	431.992i	−0.676021	−	0.390301i	0.122333	−	0.992489i	$-0.460962\pi$
$107$	−748.231	−	431.992i	−0.676021	−	0.390301i	−0.798354	+	0.602188i	$0.794296\pi$
$108$	−31.1924	+	18.0089i	−0.0277916	+	0.0160455i
$109$	443.159	+	767.575i	0.389422	+	0.674498i	0.992372	−	0.123281i	$-0.0393415\pi$
$109$	443.159	+	767.575i	0.389422	+	0.674498i	−0.602950	+	0.797779i	$0.706008\pi$
$110$	−921.927	+	760.307i	−0.799112	+	0.659022i
$111$	−2253.42			−1.92690
$112$		0			0
$113$		−	765.957i		−	0.637657i	−0.947812	−	0.318828i	$-0.896711\pi$
$113$		−	765.957i		−	0.637657i	0.947812	−	0.318828i	$-0.103289\pi$
$114$	332.712	−	576.274i	0.273345	−	0.473448i
$115$	−320.480	−	1912.61i	−0.259869	−	1.55089i
$116$	18.3702	+	31.8182i	0.0147037	+	0.0254676i
$117$	−184.659	−	106.613i	−0.145912	−	0.0842424i
$118$		−	1129.04i		−	0.880816i
$119$		0			0
$120$	788.289	−	2109.74i	0.599672	−	1.60494i
$121$	−35.4058	+	61.3246i	−0.0266009	+	0.0460741i
$122$	117.465	−	67.8187i	0.0871707	−	0.0503280i
$123$	380.381	−	219.613i	0.278844	−	0.160991i
$124$	−12.8667	+	22.2858i	−0.00931826	+	0.0161397i
$125$	−1227.76	+	667.633i	−0.878513	+	0.477719i
$126$		0			0
$127$			505.042i			0.352876i	0.984312	+	0.176438i	$0.0564575\pi$
$127$			505.042i			0.352876i	−0.984312	+	0.176438i	$0.943543\pi$
$128$	1288.15	+	743.714i	0.889512	+	0.513560i
$129$	−645.434	−	1117.92i	−0.440521	−	0.763006i
$130$	−124.770	+	20.9066i	−0.0841773	+	0.0141049i
$131$	−336.465	+	582.775i	−0.224405	+	0.388682i	−0.956141	−	0.292907i	$-0.905377\pi$
$131$	−336.465	+	582.775i	−0.224405	+	0.388682i	0.731736	+	0.681589i	$0.238711\pi$
$132$			50.3289i			0.0331861i
$133$		0			0
$134$	−751.337			−0.484371
$135$	−2077.41	+	1713.23i	−1.32441	+	1.09223i
$136$	579.078	+	1002.99i	0.365114	+	0.632396i
$137$	1344.31	−	776.141i	0.838340	−	0.484016i	−0.0183597	−	0.999831i	$-0.505844\pi$
$137$	1344.31	−	776.141i	0.838340	−	0.484016i	0.856700	+	0.515816i	$0.172511\pi$
$138$	−3854.55	−	2225.42i	−2.37769	−	1.37276i
$139$	1072.02			0.654154			0.327077	−	0.944998i	$-0.393936\pi$
$139$	1072.02			0.654154			0.327077	+	0.944998i	$0.393936\pi$
$140$		0			0
$141$	−329.355			−0.196714
$142$	663.008	+	382.788i	0.391820	+	0.226217i
$143$	−128.522	+	74.2021i	−0.0751576	+	0.0433922i
$144$	−1753.00	−	3036.29i	−1.01447	−	1.75711i
$145$	1747.60	+	2119.08i	1.00090	+	1.21366i
$146$	570.255			0.323251
$147$		0			0
$148$			37.4915i			0.0208229i
$149$	322.968	−	559.397i	0.177574	−	0.307568i	−0.763475	−	0.645838i	$-0.776508\pi$
$149$	322.968	−	559.397i	0.177574	−	0.307568i	0.941049	+	0.338270i	$0.109842\pi$
$150$	−610.683	+	3148.84i	−0.332413	+	1.71401i
$151$	−121.597	−	210.612i	−0.0655326	−	0.113506i	0.831398	−	0.555678i	$-0.187541\pi$
$151$	−121.597	−	210.612i	−0.0655326	−	0.113506i	−0.896930	+	0.442172i	$0.854208\pi$
$152$	503.307	+	290.584i	0.268576	+	0.155063i
$153$		−	2779.99i		−	1.46895i
$154$		0			0
$155$	−673.363	+	1802.16i	−0.348941	+	0.933890i
$156$	−2.66406	+	4.61428i	−0.00136728	+	0.00236819i
$157$	−1344.56	+	776.281i	−0.683487	+	0.394611i	−0.801168	−	0.598440i	$-0.795787\pi$
$157$	−1344.56	+	776.281i	−0.683487	+	0.394611i	0.117681	+	0.993052i	$0.462454\pi$
$158$	−1170.97	+	676.060i	−0.589603	+	0.340408i
$159$	2900.10	−	5023.12i	1.44650	−	2.50540i
$160$	−70.8707	−	26.4803i	−0.0350176	−	0.0130841i
$161$		0			0
$162$			2033.71i			0.986319i
$163$	2211.53	+	1276.82i	1.06270	+	0.613550i	0.926178	−	0.377087i	$-0.123074\pi$
$163$	2211.53	+	1276.82i	1.06270	+	0.613550i	0.136522	+	0.990637i	$0.456408\pi$
$164$	−3.65383	−	6.32862i	−0.00173973	−	0.00301331i
$165$	621.801	+	3710.89i	0.293377	+	1.75086i
$166$	103.774	−	179.741i	0.0485205	−	0.0840400i
$167$			3573.14i			1.65568i	0.560966	+	0.827839i	$0.310430\pi$
$167$			3573.14i			1.65568i	−0.560966	+	0.827839i	$0.689570\pi$
$168$		0			0
$169$	2181.29			0.992849
$170$	−1049.42	−	1272.50i	−0.473452	−	0.574095i
$171$	−697.507	−	1208.12i	−0.311928	−	0.540275i
$172$	−18.5996	+	10.7385i	−0.00824537	+	0.00476046i
$173$	1935.31	+	1117.35i	0.850515	+	0.491045i	0.860825	−	0.508902i	$-0.169948\pi$
$173$	1935.31	+	1117.35i	0.850515	+	0.491045i	−0.0103095	+	0.999947i	$0.503282\pi$
$174$	6304.07			2.74661
$175$		0			0
$176$	−2440.17			−1.04508
$177$	−3078.67	−	1777.47i	−1.30738	−	0.754818i
$178$	3837.58	−	2215.63i	1.61595	−	0.932969i
$179$	−915.267	−	1585.29i	−0.382180	−	0.661956i	0.609193	−	0.793022i	$-0.291493\pi$
$179$	−915.267	−	1585.29i	−0.382180	−	0.661956i	−0.991374	+	0.131066i	$0.958160\pi$
$180$	57.2265	+	69.3912i	0.0236967	+	0.0287340i
$181$	2437.22			1.00087			0.500433	−	0.865775i	$-0.333174\pi$
$181$	2437.22			1.00087			0.500433	+	0.865775i	$0.333174\pi$
$182$		0			0
$183$		−	427.075i		−	0.172515i
$184$	1943.64	−	3366.49i	0.778735	−	1.34881i
$185$	463.199	+	2764.36i	0.184081	+	1.09859i
$186$	2207.72	+	3823.88i	0.870311	+	1.50742i
$187$	−1675.64	−	967.432i	−0.655267	−	0.378319i
$188$			5.47968i			0.00212578i
$189$		0			0
$190$	−775.327	−	289.695i	−0.296043	−	0.110614i
$191$	−2539.75	+	4398.97i	−0.962145	+	1.66648i	−0.245047	+	0.969511i	$0.578804\pi$
$191$	−2539.75	+	4398.97i	−0.962145	+	1.66648i	−0.717098	+	0.696973i	$0.754530\pi$
$192$	3908.32	−	2256.47i	1.46905	−	0.848159i
$193$	2429.28	−	1402.55i	0.906028	−	0.523095i	0.0268769	−	0.999639i	$-0.491444\pi$
$193$	2429.28	−	1402.55i	0.906028	−	0.523095i	0.879151	+	0.476543i	$0.158110\pi$
$194$	347.334	−	601.599i	0.128542	−	0.222641i
$195$	−139.420	+	373.138i	−0.0512004	+	0.137031i
$196$		0			0
$197$		−	3107.79i		−	1.12396i	−0.827149	−	0.561982i	$-0.810039\pi$
$197$		−	3107.79i		−	1.12396i	0.827149	−	0.561982i	$-0.189961\pi$
$198$	4979.44	+	2874.88i	1.78724	+	1.03186i
$199$	−1072.82	−	1858.17i	−0.382161	−	0.661922i	0.609210	−	0.793009i	$-0.291487\pi$
$199$	−1072.82	−	1858.17i	−0.382161	−	0.661922i	−0.991371	+	0.131087i	$0.958153\pi$
$200$	−2750.13	−	533.359i	−0.972319	−	0.188571i
$201$	−1182.85	+	2048.75i	−0.415083	+	0.718945i
$202$		−	4394.41i		−	1.53064i
$203$		0			0
$204$	−69.4669			−0.0238414
$205$	−347.596	−	421.485i	−0.118425	−	0.143599i
$206$	−1354.04	−	2345.27i	−0.457964	−	0.793218i
$207$	−8080.79	+	4665.45i	−2.71330	+	1.56653i
$208$	−223.721	−	129.165i	−0.0745781	−	0.0430577i
$209$	−970.925			−0.321341
$210$		0			0
$211$	2837.45			0.925772			0.462886	−	0.886418i	$-0.346814\pi$
$211$	2837.45			0.925772			0.462886	+	0.886418i	$0.346814\pi$
$212$	−83.5726	−	48.2507i	−0.0270745	−	0.0156315i
$213$	2087.58	−	1205.26i	0.671542	−	0.387715i
$214$	1233.22	+	2136.01i	0.393932	+	0.682310i
$215$	−1238.73	+	1021.57i	−0.392932	+	0.324049i
$216$	−5397.57			−1.70027
$217$		0			0
$218$		−	2530.21i		−	0.786089i
$219$	897.766	−	1554.98i	0.277011	−	0.479797i
$220$	61.7403	−	10.3453i	0.0189206	−	0.00317035i
$221$	−102.418	−	177.393i	−0.0311737	−	0.0539944i
$222$	5571.09	+	3216.47i	1.68427	+	0.972412i
$223$			4741.40i			1.42380i	0.702280	+	0.711901i	$0.252166\pi$
$223$			4741.40i			1.42380i	−0.702280	+	0.711901i	$0.747834\pi$
$224$		0			0
$225$	5076.78	+	4409.39i	1.50423	+	1.30649i
$226$	−1093.31	+	1893.66i	−0.321795	+	0.557365i
$227$	−832.069	+	480.395i	−0.243288	+	0.140462i	−0.616687	−	0.787208i	$-0.711526\pi$
$227$	−832.069	+	480.395i	−0.243288	+	0.140462i	0.373399	+	0.927671i	$0.378192\pi$
$228$	−30.1887	+	17.4294i	−0.00876883	+	0.00506268i
$229$	372.003	−	644.328i	0.107348	−	0.185932i	−0.807347	−	0.590077i	$-0.799097\pi$
$229$	372.003	−	644.328i	0.107348	−	0.185932i	0.914695	+	0.404145i	$0.132431\pi$
$230$	−1937.69	+	5185.96i	−0.555512	+	1.48675i
$231$		0			0
$232$			5505.86i			1.55809i
$233$	1342.82	+	775.279i	0.377559	+	0.217984i	0.676756	−	0.736208i	$-0.263385\pi$
$233$	1342.82	+	775.279i	0.377559	+	0.217984i	−0.299197	+	0.954191i	$0.596719\pi$
$234$	304.352	+	527.153i	0.0850261	+	0.147270i
$235$	67.7001	+	404.032i	0.0187926	+	0.112154i
$236$	−29.5728	+	51.2216i	−0.00815689	+	0.0141281i
$237$			4257.35i			1.16685i
$238$		0			0
$239$	−2775.00			−0.751045			−0.375523	−	0.926813i	$-0.622537\pi$
$239$	−2775.00			−0.751045			−0.375523	+	0.926813i	$0.622537\pi$
$240$	−5053.01	+	4167.19i	−1.35904	+	1.12079i
$241$	1275.10	+	2208.54i	0.340815	+	0.590309i	0.984584	−	0.174911i	$-0.0559636\pi$
$241$	1275.10	+	2208.54i	0.340815	+	0.590309i	−0.643769	+	0.765220i	$0.722630\pi$
$242$	175.066	−	101.074i	0.0465028	−	0.0268484i
$243$	−86.0446	−	49.6779i	−0.0227151	−	0.0131146i
$244$	−7.10549			−0.00186427
$245$		0			0
$246$	−1253.88			−0.324977
$247$	−89.0169	−	51.3939i	−0.0229312	−	0.0132393i
$248$	−3339.71	+	1928.18i	−0.855127	+	0.493708i
$249$	−326.747	−	565.943i	−0.0831597	−	0.144037i
$250$	3988.32	+	101.892i	1.00897	+	0.0257770i
$251$	−2933.00			−0.737568			−0.368784	−	0.929515i	$-0.620226\pi$
$251$	−2933.00			−0.737568			−0.368784	+	0.929515i	$0.620226\pi$
$252$		0			0
$253$			6494.26i			1.61380i
$254$	720.882	−	1248.60i	0.178079	−	0.308442i
$255$	−5121.99	+	858.246i	−1.25785	+	0.210767i
$256$	−114.813	−	198.862i	−0.0280306	−	0.0485504i
$257$	−2360.11	−	1362.61i	−0.572840	−	0.330729i	0.185443	−	0.982655i	$-0.440628\pi$
$257$	−2360.11	−	1362.61i	−0.572840	−	0.330729i	−0.758283	+	0.651926i	$0.773961\pi$
$258$			3685.09i			0.889240i
$259$		0			0
$260$	6.20811	+	2.31961i	0.00148081	+	0.000553294i
$261$	6608.02	−	11445.4i	1.56715	−	2.71438i
$262$	1663.67	−	960.521i	0.392298	−	0.226493i
$263$	−2621.68	+	1513.63i	−0.614676	+	0.354884i	−0.774793	−	0.632214i	$-0.782146\pi$
$263$	−2621.68	+	1513.63i	−0.614676	+	0.354884i	0.160117	+	0.987098i	$0.448813\pi$
$264$	−3771.09	+	6531.72i	−0.879147	+	1.52273i
$265$	−6758.17	−	2525.14i	−1.56661	−	0.585351i
$266$		0			0
$267$		−	13952.5i		−	3.19804i
$268$	34.0863	+	19.6798i	0.00776923	+	0.00448557i
$269$	−721.231	−	1249.21i	−0.163473	−	0.283144i	0.772639	−	0.634846i	$-0.218936\pi$
$269$	−721.231	−	1249.21i	−0.163473	−	0.283144i	−0.936112	+	0.351702i	$0.885603\pi$
$270$	7581.34	−	1270.34i	1.70884	−	0.286335i
$271$	3232.23	−	5598.38i	0.724516	−	1.25490i	−0.234657	−	0.972078i	$-0.575397\pi$
$271$	3232.23	−	5598.38i	0.724516	−	1.25490i	0.959173	−	0.282820i	$-0.0912700\pi$
$272$		−	3368.06i		−	0.750804i
$273$		0			0
$274$	−4431.36			−0.977038
$275$	4424.47	−	1525.57i	0.970202	−	0.334529i
$276$	116.581	+	201.924i	0.0254252	+	0.0440377i
$277$	−759.170	+	438.307i	−0.164672	+	0.0950733i	−0.580071	−	0.814566i	$-0.696975\pi$
$277$	−759.170	+	438.307i	−0.164672	+	0.0950733i	0.415399	+	0.909639i	$0.363642\pi$
$278$	−2650.33	−	1530.17i	−0.571784	−	0.330120i
$279$	9256.66			1.98631
$280$		0			0
$281$	6252.19			1.32731			0.663655	−	0.748038i	$-0.269004\pi$
$281$	6252.19			1.32731			0.663655	+	0.748038i	$0.269004\pi$
$282$	814.258	+	470.112i	0.171945	+	0.0992722i
$283$	1948.62	−	1125.04i	0.409305	−	0.236312i	−0.281186	−	0.959653i	$-0.590728\pi$
$283$	1948.62	−	1125.04i	0.409305	−	0.236312i	0.690491	+	0.723341i	$0.257394\pi$
$284$	−20.0527	−	34.7323i	−0.00418982	−	0.00725698i
$285$	−2010.56	+	1658.09i	−0.417878	+	0.344621i
$286$	423.655			0.0875919
$287$		0			0
$288$			364.022i			0.0744799i
$289$	−1121.19	+	1941.96i	−0.228210	+	0.395271i
$290$	−1295.82	−	7733.43i	−0.262391	−	1.56594i
$291$	−1093.63	−	1894.23i	−0.220309	−	0.381586i
$292$	−25.8710	−	14.9367i	−0.00518489	−	0.00299350i
$293$		−	5917.86i		−	1.17995i	−0.807422	−	0.589975i	$-0.799138\pi$
$293$		−	5917.86i		−	1.17995i	0.807422	−	0.589975i	$-0.200862\pi$
$294$		0			0
$295$	−1547.66	+	4142.08i	−0.305451	+	0.817495i
$296$	−2809.20	+	4865.69i	−0.551627	+	0.955447i
$297$	7809.31	−	4508.70i	1.52573	−	0.880881i
$298$	−1596.93	+	921.990i	−0.310429	+	0.179226i
$299$	−343.761	+	595.411i	−0.0664890	+	0.115162i
$300$	110.183	−	126.859i	0.0212046	−	0.0244141i
$301$		0			0
$302$			694.256i			0.132284i
$303$	−11982.7	−	6918.22i	−2.27191	−	1.31169i
$304$	−845.056	−	1463.68i	−0.159432	−	0.276144i
$305$	−523.908	+	87.7866i	−0.0983570	+	0.0164808i
$306$	−3968.08	+	6872.91i	−0.741307	+	1.28398i
$307$		−	9458.47i		−	1.75838i	−0.476469	−	0.879191i	$-0.658084\pi$
$307$		−	9458.47i		−	1.75838i	0.476469	−	0.879191i	$-0.341916\pi$
$308$		0			0
$309$	−8526.81			−1.56982
$310$	4237.09	−	3494.30i	0.776292	−	0.640203i
$311$	3788.39	+	6561.69i	0.690739	+	1.19640i	0.971596	+	0.236646i	$0.0760481\pi$
$311$	3788.39	+	6561.69i	0.690739	+	1.19640i	−0.280857	+	0.959750i	$0.590619\pi$
$312$	−691.487	+	399.230i	−0.125474	+	0.0724422i
$313$	7943.54	+	4586.21i	1.43449	+	0.828204i	0.997459	−	0.0712425i	$-0.0226964\pi$
$313$	7943.54	+	4586.21i	1.43449	+	0.828204i	0.437032	+	0.899446i	$0.356030\pi$
$314$	4432.16			0.796565
$315$		0			0
$316$	70.8320			0.0126095
$317$	−2665.57	−	1538.97i	−0.472283	−	0.272672i	0.244912	−	0.969545i	$-0.421241\pi$
$317$	−2665.57	−	1538.97i	−0.472283	−	0.272672i	−0.717195	+	0.696873i	$0.754574\pi$
$318$	−14339.7	+	8279.04i	−2.52871	+	1.45995i
$319$	−4599.16	−	7965.97i	−0.807221	−	1.39815i
$320$	−3571.46	−	4330.65i	−0.623908	−	0.756533i
$321$	7765.98			1.35033
$322$		0			0
$323$		−	1340.13i		−	0.230857i
$324$	53.2690	−	92.2646i	0.00913391	−	0.0158204i
$325$	486.400	+	94.3320i	0.0830173	+	0.0161003i
$326$	−3645.00	−	6313.33i	−0.619258	−	1.07259i
$327$	−6899.40	−	3983.37i	−1.16678	−	0.673642i
$328$		−	1095.11i		−	0.184352i
$329$		0			0
$330$	3759.55	−	10061.9i	0.627141	−	1.67845i
$331$	−1617.25	+	2801.16i	−0.268557	+	0.465154i	−0.968489	−	0.249055i	$-0.919880\pi$
$331$	−1617.25	+	2801.16i	−0.268557	+	0.465154i	0.699933	+	0.714209i	$0.253213\pi$
$332$	−9.41592	+	5.43629i	−0.00155652	+	0.000898659i
$333$	11679.4	−	6743.11i	1.92200	−	1.10967i
$334$	5100.20	−	8833.80i	0.835540	−	1.44720i
$335$	2756.42	+	1029.92i	0.449550	+	0.167971i
$336$		0			0
$337$			3777.84i			0.610658i	0.952247	+	0.305329i	$0.0987665\pi$
$337$			3777.84i			0.610658i	−0.952247	+	0.305329i	$0.901234\pi$
$338$	−5392.75	−	3113.51i	−0.867832	−	0.501043i
$339$	3442.43	+	5962.47i	0.551526	+	0.955271i
$340$	14.2792	+	85.2176i	0.00227763	+	0.0135929i
$341$	3221.30	−	5579.45i	0.511563	−	0.886054i
$342$			3982.41i			0.629660i
$343$		0			0
$344$	−3218.49			−0.504446
$345$	11090.6	+	13448.1i	1.73071	+	2.09861i
$346$	−3189.75	−	5524.82i	−0.495614	−	0.858428i
$347$	7139.58	−	4122.04i	1.10453	−	0.637702i	0.167125	−	0.985936i	$-0.446552\pi$
$347$	7139.58	−	4122.04i	1.10453	−	0.637702i	0.937408	+	0.348234i	$0.113218\pi$
$348$	−286.000	−	165.122i	−0.0440552	−	0.0254353i
$349$	−7173.78			−1.10030			−0.550148	−	0.835067i	$-0.685429\pi$
$349$	−7173.78			−1.10030			−0.550148	+	0.835067i	$0.685429\pi$
$350$		0			0
$351$	954.637			0.145170
$352$	219.414	+	126.679i	0.0332239	+	0.0191819i
$353$	−3629.95	+	2095.76i	−0.547317	+	0.315994i	−0.748039	−	0.663655i	$-0.769005\pi$
$353$	−3629.95	+	2095.76i	−0.547317	+	0.315994i	0.200722	+	0.979648i	$0.435671\pi$
$354$	5074.22	+	8788.80i	0.761840	+	1.31955i
$355$	−1907.65	−	2313.16i	−0.285204	−	0.345831i
$356$	−232.136			−0.0345594
$357$		0			0
$358$			5225.70i			0.771472i
$359$	−1568.15	+	2716.11i	−0.230539	+	0.399306i	−0.957967	−	0.286879i	$-0.907382\pi$
$359$	−1568.15	+	2716.11i	−0.230539	+	0.399306i	0.727428	+	0.686184i	$0.240716\pi$
$360$	2227.49	+	13293.6i	0.326108	+	1.94620i
$361$	3093.26	+	5357.68i	0.450978	+	0.781117i
$362$	−6025.48	−	3478.81i	−0.874840	−	0.505089i
$363$		−	636.496i		−	0.0920313i
$364$		0			0
$365$	−2092.08	−	781.691i	−0.300013	−	0.112098i
$366$	−609.594	+	1055.85i	−0.0870600	+	0.150792i
$367$	−1492.42	+	861.649i	−0.212272	+	0.122555i	−0.602367	−	0.798220i	$-0.705775\pi$
$367$	−1492.42	+	861.649i	−0.212272	+	0.122555i	0.390095	+	0.920775i	$0.372442\pi$
$368$	−9790.17	+	5652.36i	−1.38682	+	0.800678i
$369$	−1314.33	+	2276.49i	−0.185424	+	0.321164i
$370$	2800.61	−	7495.42i	0.393504	−	1.05316i
$371$		0			0
$372$		−	231.307i		−	0.0322384i
$373$	2440.94	+	1409.28i	0.338839	+	0.195629i	0.659759	−	0.751478i	$-0.270659\pi$
$373$	2440.94	+	1409.28i	0.338839	+	0.195629i	−0.320919	+	0.947106i	$0.603992\pi$
$374$	2761.77	+	4783.52i	0.381838	+	0.661364i
$375$	6556.75	−	10715.0i	0.902905	−	1.47552i
$376$	−410.587	+	711.157i	−0.0563149	+	0.0975403i
$377$		−	973.788i		−	0.133031i
$378$		0			0
$379$	10466.1			1.41849			0.709246	−	0.704961i	$-0.249036\pi$
$379$	10466.1			1.41849			0.709246	+	0.704961i	$0.249036\pi$
$380$	27.5867	+	33.4508i	0.00372412	+	0.00451577i
$381$	−2269.80	−	3931.42i	−0.305211	−	0.528642i
$382$	12557.9	−	7250.32i	1.68199	−	0.971096i
$383$	−223.482	−	129.028i	−0.0298157	−	0.0172141i	0.485018	−	0.874504i	$-0.338813\pi$
$383$	−223.482	−	129.028i	−0.0298157	−	0.0172141i	−0.514834	+	0.857290i	$0.672146\pi$
$384$	−13369.9			−1.77677
$385$		0			0
$386$	−8007.81			−1.05592
$387$	6690.51	+	3862.77i	0.878806	+	0.507379i
$388$	−31.5153	+	18.1954i	−0.00412358	+	0.00238075i
$389$	2286.94	+	3961.09i	0.298078	+	0.516286i	0.975696	−	0.219128i	$-0.0703211\pi$
$389$	2286.94	+	3961.09i	0.298078	+	0.516286i	−0.677618	+	0.735414i	$0.736988\pi$
$390$	877.291	−	723.497i	0.113906	−	0.0939376i
$391$	−8963.77			−1.15938
$392$		0			0
$393$		−	6048.69i		−	0.776376i
$394$	−4435.97	+	7683.33i	−0.567211	+	0.982438i
$395$	5222.64	−	875.112i	0.665265	−	0.111473i
$396$	−150.603	−	260.852i	−0.0191114	−	0.0331018i
$397$	−3138.96	−	1812.28i	−0.396825	−	0.229107i	0.288288	−	0.957544i	$-0.406914\pi$
$397$	−3138.96	−	1812.28i	−0.396825	−	0.229107i	−0.685113	+	0.728437i	$0.740247\pi$
$398$			6125.23i			0.771432i
$399$		0			0
$400$	6150.70	+	5342.14i	0.768838	+	0.667767i
$401$	−3179.16	+	5506.47i	−0.395910	+	0.685736i	−0.993217	−	0.116277i	$-0.962904\pi$
$401$	−3179.16	+	5506.47i	−0.395910	+	0.685736i	0.597307	+	0.802013i	$0.296237\pi$
$402$	5848.66	−	3376.73i	0.725634	−	0.418945i
$403$	590.674	−	341.026i	0.0730114	−	0.0421531i
$404$	−115.102	+	199.363i	−0.0141747	+	0.0245512i
$405$	2787.77	−	7461.05i	0.342038	−	0.915414i
$406$		0			0
$407$		−	9386.35i		−	1.14316i
$408$	−9015.47	−	5205.09i	−1.09395	−	0.631593i
$409$	−3268.19	−	5660.68i	−0.395114	−	0.684358i	0.598002	−	0.801495i	$-0.295962\pi$
$409$	−3268.19	−	5660.68i	−0.395114	−	0.684358i	−0.993116	+	0.117137i	$0.962628\pi$
$410$	257.739	+	1538.18i	0.0310459	+	0.185281i
$411$	−6976.40	+	12083.5i	−0.837276	+	1.45020i
$412$			141.866i			0.0169641i
$413$		0			0
$414$	26637.3			3.16220
$415$	−627.099	+	517.164i	−0.0741761	+	0.0611725i
$416$	13.4110	+	23.2285i	0.00158060	+	0.00273767i
$417$	−8344.95	+	4817.96i	−0.979985	+	0.565795i
$418$	2400.40	+	1385.87i	0.280879	+	0.162165i
$419$	−6333.56			−0.738460			−0.369230	−	0.929338i	$-0.620379\pi$
$419$	−6333.56			−0.738460			−0.369230	+	0.929338i	$0.620379\pi$
$420$		0			0
$421$	−8139.62			−0.942282			−0.471141	−	0.882058i	$-0.656158\pi$
$421$	−8139.62			−0.942282			−0.471141	+	0.882058i	$0.656158\pi$
$422$	−7014.96	−	4050.09i	−0.809201	−	0.467193i
$423$	1707.03	−	985.557i	0.196215	−	0.113285i
$424$	−7230.75	−	12524.0i	−0.828199	−	1.43448i
$425$	2105.68	+	6106.92i	0.240331	+	0.697009i
$426$	−6881.43			−0.782645
$427$		0			0
$428$		−	129.207i		−	0.0145922i
$429$	666.971	−	1155.23i	0.0750622	−	0.130011i
$430$	4520.64	−	757.483i	0.506987	−	0.0849514i
$431$	7183.79	+	12442.7i	0.802856	+	1.39059i	0.917729	+	0.397208i	$0.130021\pi$
$431$	7183.79	+	12442.7i	0.802856	+	1.39059i	−0.114873	+	0.993380i	$0.536646\pi$
$432$	13593.8	+	7848.41i	1.51397	+	0.874089i
$433$			8399.05i			0.932176i	0.884738	+	0.466088i	$0.154337\pi$
$433$			8399.05i			0.932176i	−0.884738	+	0.466088i	$0.845663\pi$
$434$		0			0
$435$	−23127.6	−	8641.47i	−2.54916	−	0.952475i
$436$	−66.2737	+	114.789i	−0.00727967	+	0.0126088i
$437$	−3895.44	+	2249.03i	−0.426417	+	0.246192i
$438$	−4439.05	+	2562.89i	−0.484261	+	0.279588i
$439$	−8930.41	+	15467.9i	−0.970901	+	1.68165i	−0.278053	+	0.960566i	$0.589689\pi$
$439$	−8930.41	+	15467.9i	−0.970901	+	1.68165i	−0.692848	+	0.721084i	$0.743644\pi$
$440$	8787.87	+	3283.52i	0.952148	+	0.355763i
$441$		0			0
$442$			584.754i			0.0629274i
$443$	1646.80	+	950.783i	0.176619	+	0.101971i	0.585703	−	0.810526i	$-0.300819\pi$
$443$	1646.80	+	950.783i	0.176619	+	0.101971i	−0.409084	+	0.912497i	$0.634152\pi$
$444$	−168.498	−	291.847i	−0.0180103	−	0.0311947i
$445$	−17116.0	+	2867.98i	−1.82332	+	0.305517i
$446$	6767.74	−	11722.1i	0.718524	−	1.24452i
$447$			5806.05i			0.614355i
$448$		0			0
$449$	5185.68			0.545050			0.272525	−	0.962149i	$-0.412141\pi$
$449$	5185.68			0.545050			0.272525	+	0.962149i	$0.412141\pi$
$450$	−6257.38	−	18147.7i	−0.655502	−	1.90109i
$451$	914.770	+	1584.43i	0.0955096	+	0.165428i
$452$	99.2011	−	57.2738i	0.0103231	−	0.00596003i
$453$	1893.10	+	1092.98i	0.196348	+	0.113362i
$454$	2742.81			0.283538
$455$		0			0
$456$	−5223.88			−0.536471
$457$	9698.45	+	5599.41i	0.992723	+	0.573149i	0.906087	−	0.423091i	$-0.139055\pi$
$457$	9698.45	+	5599.41i	0.992723	+	0.573149i	0.0866361	+	0.996240i	$0.472388\pi$
$458$	−1839.39	+	1061.97i	−0.187662	+	0.108347i
$459$	6223.18	+	10778.9i	0.632839	+	1.09611i
$460$	223.744	−	184.520i	0.0226785	−	0.0187028i
$461$	17270.7			1.74485			0.872427	−	0.488744i	$-0.162545\pi$
$461$	17270.7			1.74485			0.872427	+	0.488744i	$0.162545\pi$
$462$		0			0
$463$		−	385.660i		−	0.0387109i	−0.999813	−	0.0193554i	$-0.993839\pi$
$463$		−	385.660i		−	0.0387109i	0.999813	−	0.0193554i	$-0.00616141\pi$
$464$	8005.86	−	13866.6i	0.800997	−	1.38737i
$465$	−2857.74	−	17054.9i	−0.284999	−	1.70087i
$466$	−2213.22	−	3833.41i	−0.220012	−	0.381072i
$467$	−4360.75	−	2517.68i	−0.432101	−	0.249474i	0.268140	−	0.963380i	$-0.413591\pi$
$467$	−4360.75	−	2517.68i	−0.432101	−	0.249474i	−0.700241	+	0.713906i	$0.746924\pi$
$468$		−	31.8875i		−	0.00314957i
$469$		0			0
$470$	409.330	−	1095.51i	0.0401723	−	0.107515i
$471$	6977.66	−	12085.7i	0.682620	−	1.18233i
$472$	−7675.97	+	4431.72i	−0.748549	+	0.432175i
$473$	4656.57	−	2688.47i	0.452662	−	0.261345i
$474$	6076.81	−	10525.4i	0.588855	−	1.01993i
$475$	2447.32	+	2125.60i	0.236402	+	0.205324i
$476$		0			0
$477$			34712.8i			3.33206i
$478$	6860.57	+	3960.95i	0.656475	+	0.379016i
$479$	−4341.00	−	7518.83i	−0.414082	−	0.717211i	0.581250	−	0.813725i	$-0.302564\pi$
$479$	−4341.00	−	7518.83i	−0.414082	−	0.717211i	−0.995332	+	0.0965145i	$0.969231\pi$
$480$	670.692	−	112.382i	0.0637766	−	0.0106865i
$481$	496.848	−	860.565i	0.0470983	−	0.0815767i
$482$		−	7280.16i		−	0.687972i
$483$		0			0
$484$	−10.5898			−0.000994530
$485$	−2098.92	+	1730.96i	−0.196509	+	0.162060i
$486$	141.817	+	245.635i	0.0132366	+	0.0229264i
$487$	771.174	−	445.238i	0.0717562	−	0.0414284i	−0.463693	−	0.885996i	$-0.653476\pi$
$487$	771.174	−	445.238i	0.0717562	−	0.0414284i	0.535449	+	0.844568i	$0.320142\pi$
$488$	−922.157	−	532.407i	−0.0855411	−	0.0493872i
$489$	−22953.7			−2.12270
$490$		0			0
$491$	1562.48			0.143613			0.0718063	−	0.997419i	$-0.477124\pi$
$491$	1562.48			0.143613			0.0718063	+	0.997419i	$0.477124\pi$
$492$	56.8853	+	32.8428i	0.00521258	+	0.00300948i
$493$	10995.1	−	6348.03i	1.00445	−	0.579921i
$494$	146.716	+	254.120i	0.0133625	+	0.0231446i
$495$	−14327.2	−	17372.7i	−1.30093	−	1.57747i
$496$	11214.8			1.01524
$497$		0			0
$498$			1865.56i			0.167867i
$499$	4117.17	−	7131.14i	0.369358	−	0.639747i	−0.620107	−	0.784517i	$-0.712911\pi$
$499$	4117.17	−	7131.14i	0.369358	−	0.639747i	0.989465	+	0.144770i	$0.0462443\pi$
$500$	−178.271	−	109.089i	−0.0159451	−	0.00975718i
$501$	−16058.7	−	27814.5i	−1.43204	−	2.48036i
$502$	7251.20	+	4186.48i	0.644695	+	0.372215i
$503$		−	72.5340i		−	0.00642969i	−0.999995	−	0.00321484i	$-0.998977\pi$
$503$		−	72.5340i		−	0.00642969i	0.999995	−	0.00321484i	$-0.00102332\pi$
$504$		0			0
$505$	−6023.75	+	16121.7i	−0.530798	+	1.42061i
$506$	9269.72	−	16055.6i	0.814406	−	1.41059i
$507$	−16979.9	+	9803.34i	−1.48738	+	0.858741i
$508$	−65.4093	+	37.7641i	−0.00571273	+	0.00329825i
$509$	3896.72	−	6749.32i	0.339330	−	0.587737i	−0.644977	−	0.764202i	$-0.723133\pi$
$509$	3896.72	−	6749.32i	0.339330	−	0.587737i	0.984307	+	0.176465i	$0.0564663\pi$
$510$	13888.0	+	5189.15i	1.20583	+	0.450548i
$511$		0			0
$512$		−	11243.9i		−	0.970537i
$513$	5408.89	+	3122.83i	0.465514	+	0.268764i
$514$	3889.91	+	6737.51i	0.333806	+	0.578169i
$515$	1752.72	+	10460.2i	0.149969	+	0.895009i
$516$	96.5235	−	167.184i	0.00823490	−	0.0142633i
$517$		−	1371.89i		−	0.116703i
$518$		0			0
$519$	−20086.8			−1.69887
$520$	631.888	+	766.210i	0.0532887	+	0.0646164i
$521$	−2322.71	−	4023.05i	−0.195316	−	0.338298i	0.751688	−	0.659519i	$-0.229240\pi$
$521$	−2322.71	−	4023.05i	−0.195316	−	0.338298i	−0.947004	+	0.321221i	$0.895907\pi$
$522$	−32673.7	+	18864.2i	−2.73964	+	1.58173i
$523$	7607.06	+	4391.94i	0.636011	+	0.367201i	0.783076	−	0.621926i	$-0.213649\pi$
$523$	7607.06	+	4391.94i	0.636011	+	0.367201i	−0.147065	+	0.989127i	$0.546983\pi$
$524$	−100.636			−0.00838986
$525$		0			0
$526$	8642.04			0.716371
$527$	7701.09	+	4446.23i	0.636556	+	0.367516i
$528$	18995.1	−	10966.8i	1.56563	−	0.903919i
$529$	8959.70	+	15518.7i	0.736394	+	1.27547i
$530$	13103.8	+	15889.3i	1.07395	+	1.30224i
$531$	21275.5			1.73875
$532$		0			0
$533$			193.686i			0.0157401i
$534$	−19915.4	+	34494.4i	−1.61390	+	2.79535i
$535$	−1596.32	−	9526.81i	−0.129000	−	0.769869i
$536$	2949.17	+	5108.11i	0.237658	+	0.411636i
$537$	14249.5	+	8226.95i	1.14509	+	0.661116i
$538$			4117.86i			0.329988i
$539$		0			0
$540$	−377.221	−	140.946i	−0.0300611	−	0.0112321i
$541$	3527.07	−	6109.06i	0.280296	−	0.485488i	−0.691161	−	0.722701i	$-0.742901\pi$
$541$	3527.07	−	6109.06i	0.280296	−	0.485488i	0.971458	+	0.237213i	$0.0762339\pi$
$542$	−15981.9	+	9227.17i	−1.26657	+	0.731256i
$543$	−18972.1	+	10953.6i	−1.49939	+	0.865676i
$544$	−174.850	+	302.849i	−0.0137806	+	0.0238686i
$545$	−3468.35	+	9282.55i	−0.272602	+	0.729579i
$546$		0			0
$547$		−	5776.83i		−	0.451553i	−0.974179	−	0.225776i	$-0.927508\pi$
$547$		−	5776.83i		−	0.451553i	0.974179	−	0.225776i	$-0.0724919\pi$
$548$	201.040	+	116.070i	0.0156715	+	0.00904796i
$549$	1277.97	+	2213.51i	0.0993487	+	0.172077i
$550$	−13116.1	−	2543.72i	−1.01686	−	0.197208i
$551$	3185.47	−	5517.40i	0.246290	−	0.426587i
$552$			34941.2i			2.69419i
$553$		0			0
$554$	2502.51			0.191916
$555$	−16029.5	−	19436.9i	−1.22597	−	1.48658i
$556$	80.1592	+	138.840i	0.00611422	+	0.0105901i
$557$	17807.8	−	10281.3i	1.35465	−	0.782106i	0.365751	−	0.930713i	$-0.380812\pi$
$557$	17807.8	−	10281.3i	1.35465	−	0.782106i	0.988896	+	0.148607i	$0.0474788\pi$
$558$	−22885.0	−	13212.7i	−1.73620	−	1.00240i
$559$	569.235			0.0430699
$560$		0			0
$561$	17391.7			1.30887
$562$	−15457.2	−	8924.19i	−1.16018	−	0.669830i
$563$	20792.8	−	12004.8i	1.55651	−	0.898650i	0.558921	−	0.829221i	$-0.311216\pi$
$563$	20792.8	−	12004.8i	1.55651	−	0.898650i	0.997587	−	0.0694291i	$-0.0221178\pi$
$564$	−24.6273	−	42.6557i	−0.00183864	−	0.00318462i
$565$	6606.78	−	5448.56i	0.491945	−	0.405704i
$566$	−6423.37			−0.477022
$567$		0			0
$568$		−	6010.11i		−	0.443977i
$569$	−12078.7	+	20921.0i	−0.889925	+	1.54140i	−0.0499623	+	0.998751i	$0.515910\pi$
$569$	−12078.7	+	20921.0i	−0.889925	+	1.54140i	−0.839963	+	0.542644i	$0.817423\pi$
$570$	7337.37	−	1229.46i	0.539173	−	0.0903445i
$571$	353.497	+	612.274i	0.0259078	+	0.0448737i	0.878689	−	0.477395i	$-0.158419\pi$
$571$	353.497	+	612.274i	0.0259078	+	0.0448737i	−0.852781	+	0.522269i	$0.825086\pi$
$572$	−19.2202	−	11.0968i	−0.00140496	−	0.000811154i
$573$		−	45657.4i		−	3.32874i
$574$		0			0
$575$	14217.6	−	16369.5i	1.03115	−	1.18723i
$576$	−13504.4	+	23390.4i	−0.976883	+	1.69201i
$577$	13906.0	−	8028.62i	1.00332	−	0.579265i	0.0940886	−	0.995564i	$-0.470006\pi$
$577$	13906.0	−	8028.62i	1.00332	−	0.579265i	0.909228	+	0.416299i	$0.136673\pi$
$578$	5543.81	−	3200.72i	0.398948	−	0.230333i
$579$	−12606.9	+	21835.8i	−0.904878	+	1.56729i
$580$	−143.773	+	384.788i	−0.0102929	+	0.0275474i
$581$		0			0
$582$			6244.07i			0.444717i
$583$	20923.2	+	12080.0i	1.48636	+	0.858152i
$584$	−2238.38	−	3876.98i	−0.158604	−	0.274710i
$585$	−393.963	−	2351.16i	−0.0278433	−	0.166168i
$586$	−8446.98	+	14630.6i	−0.595463	+	1.03137i
$587$			8605.63i			0.605098i	0.953134	+	0.302549i	$0.0978376\pi$
$587$			8605.63i			0.605098i	−0.953134	+	0.302549i	$0.902162\pi$
$588$		0			0
$589$	4462.28			0.312165
$590$	9738.52	−	8031.29i	0.679540	−	0.560412i
$591$	13967.3	+	24192.1i	0.972147	+	1.68381i
$592$	14150.0	−	8169.52i	0.982369	−	0.567171i
$593$	−17628.5	−	10177.8i	−1.22077	−	0.704809i	−0.255684	−	0.966760i	$-0.582301\pi$
$593$	−17628.5	−	10177.8i	−1.22077	−	0.704809i	−0.965081	+	0.261951i	$0.915634\pi$
$594$	−25742.4			−1.77815
$595$		0			0
$596$	96.5986			0.00663898
$597$	16702.3	+	9643.10i	1.14503	+	0.661082i
$598$	1699.75	−	981.348i	0.116234	−	0.0671076i
$599$	11317.8	+	19603.1i	0.772010	+	1.33716i	0.936460	+	0.350776i	$0.114082\pi$
$599$	11317.8	+	19603.1i	0.772010	+	1.33716i	−0.164449	+	0.986386i	$0.552585\pi$
$600$	23805.0	−	8208.05i	1.61973	−	0.558487i
$601$	−22553.8			−1.53077			−0.765383	−	0.643575i	$-0.777450\pi$
$601$	−22553.8			−1.53077			−0.765383	+	0.643575i	$0.777450\pi$
$602$		0			0
$603$		−	14158.1i		−	0.956159i
$604$	18.1846	−	31.4967i	0.00122504	−	0.00212182i
$605$	−780.812	+	130.834i	−0.0524703	+	0.00879199i
$606$	19749.7	+	34207.5i	1.32389	+	2.29305i
$607$	15185.1	+	8767.12i	1.01539	+	0.586238i	0.912767	−	0.408482i	$-0.133942\pi$
$607$	15185.1	+	8767.12i	1.01539	+	0.586238i	0.102628	+	0.994720i	$0.467275\pi$
$608$			175.481i			0.0117051i
$609$		0			0
$610$	1420.55	+	530.778i	0.0942892	+	0.0352304i
$611$	72.6181	−	125.778i	0.00480821	−	0.00832806i
$612$	360.044	−	207.871i	0.0237809	−	0.0137299i
$613$	9046.07	−	5222.75i	0.596031	−	0.344119i	−0.171447	−	0.985193i	$-0.554844\pi$
$613$	9046.07	−	5222.75i	0.596031	−	0.344119i	0.767479	+	0.641074i	$0.221511\pi$
$614$	−13500.7	+	23384.0i	−0.887371	+	1.53697i
$615$	4600.08	+	1718.78i	0.301615	+	0.112696i
$616$		0			0
$617$			13218.9i			0.862516i	0.902229	+	0.431258i	$0.141930\pi$
$617$			13218.9i			0.862516i	−0.902229	+	0.431258i	$0.858070\pi$
$618$	21080.7	+	12170.9i	1.37215	+	0.792211i
$619$	11719.4	+	20298.7i	0.760976	+	1.31805i	0.942348	+	0.334635i	$0.108613\pi$
$619$	11719.4	+	20298.7i	0.760976	+	1.31805i	−0.181372	+	0.983415i	$0.558054\pi$
$620$	−283.753	+	47.5459i	−0.0183803	+	0.00307982i
$621$	20887.8	−	36178.7i	1.34975	−	2.33784i
$622$		−	21629.8i		−	1.39433i
$623$		0			0
$624$	2322.02			0.148967
$625$	−14492.2	−	5840.91i	−0.927502	−	0.373818i
$626$	−13092.4	−	22676.8i	−0.835909	−	1.44784i
$627$	7558.00	−	4363.62i	0.481400	−	0.277936i
$628$	−201.076	−	116.092i	−0.0127768	−	0.00737668i
$629$	12955.6			0.821262
$630$		0			0
$631$	−874.004			−0.0551403			−0.0275702	−	0.999620i	$-0.508777\pi$
$631$	−874.004			−0.0551403			−0.0275702	+	0.999620i	$0.508777\pi$
$632$	9192.64	+	5307.37i	0.578582	+	0.334044i
$633$	−22087.6	+	12752.3i	−1.38690	+	0.800725i
$634$	4393.36	+	7609.53i	0.275209	+	0.476676i
$635$	−4356.25	+	3592.57i	−0.272240	+	0.224514i
$636$	867.410			0.0540802
$637$		0			0
$638$			26258.8i			1.62946i
$639$	−7213.22	+	12493.7i	−0.446558	+	0.773461i
$640$	2748.22	+	16401.3i	0.169739	+	1.01300i
$641$	−11988.5	−	20764.7i	−0.738715	−	1.27949i	−0.953074	−	0.302738i	$-0.902099\pi$
$641$	−11988.5	−	20764.7i	−0.738715	−	1.27949i	0.214359	−	0.976755i	$-0.431234\pi$
$642$	−19199.7	−	11084.9i	−1.18030	−	0.681444i
$643$			27698.0i			1.69876i	0.527782	+	0.849380i	$0.323024\pi$
$643$			27698.0i			1.69876i	−0.527782	+	0.849380i	$0.676976\pi$
$644$		0			0
$645$	5051.44	−	13519.4i	0.308372	−	0.825314i
$646$	−1912.86	+	3313.17i	−0.116502	+	0.201788i
$647$	−9496.10	+	5482.57i	−0.577017	+	0.333141i	−0.759947	−	0.649985i	$-0.774775\pi$
$647$	−9496.10	+	5482.57i	−0.577017	+	0.333141i	0.182930	+	0.983126i	$0.441442\pi$
$648$	13826.6	−	7982.79i	0.838209	−	0.483940i
$649$	7403.82	−	12823.8i	0.447805	−	0.775621i
$650$	−1067.87	−	927.488i	−0.0644389	−	0.0559678i
$651$		0			0
$652$			381.894i			0.0229388i
$653$	−10683.5	−	6168.10i	−0.640239	−	0.369642i	0.144467	−	0.989510i	$-0.453853\pi$
$653$	−10683.5	−	6168.10i	−0.640239	−	0.369642i	−0.784707	+	0.619867i	$0.787186\pi$
$654$	11371.5	+	19696.0i	0.679909	+	1.17764i
$655$	−7420.15	+	1243.33i	−0.442640	+	0.0741692i
$656$	−1592.36	+	2758.05i	−0.0947733	+	0.164152i
$657$			10745.8i			0.638105i
$658$		0			0
$659$	25275.6			1.49408			0.747040	−	0.664779i	$-0.231474\pi$
$659$	25275.6			1.49408			0.747040	+	0.664779i	$0.231474\pi$
$660$	−434.112	+	358.010i	−0.0256027	+	0.0211144i
$661$	2223.96	+	3852.01i	0.130865	+	0.226666i	0.924010	−	0.382367i	$-0.124891\pi$
$661$	2223.96	+	3852.01i	0.130865	+	0.226666i	−0.793145	+	0.609033i	$0.791558\pi$
$662$	7996.60	−	4616.84i	0.469481	−	0.271055i
$663$	1594.51	+	920.593i	0.0934024	+	0.0539259i
$664$	−1629.34			−0.0952270
$665$		0			0
$666$	−38499.7			−2.23999
$667$	−36904.5	−	21306.8i	−2.14235	−	1.23689i
$668$	−462.767	+	267.179i	−0.0268039	+	0.0154752i
$669$	−21309.2	−	36908.7i	−1.23148	−	2.13299i
$670$	−5344.57	−	6480.67i	−0.308177	−	0.373687i
$671$	1778.92			0.102347
$672$		0			0
$673$		−	30358.9i		−	1.73885i	−0.494061	−	0.869427i	$-0.664488\pi$
$673$		−	30358.9i		−	1.73885i	0.494061	−	0.869427i	$-0.335512\pi$
$674$	5392.37	−	9339.86i	0.308170	−	0.533766i
$675$	−29554.9	−	5731.85i	−1.68529	−	0.326843i
$676$	163.104	+	282.504i	0.00927993	+	0.0160733i
$677$	−5989.85	−	3458.24i	−0.340042	−	0.196324i	0.320248	−	0.947334i	$-0.396234\pi$
$677$	−5989.85	−	3458.24i	−0.340042	−	0.196324i	−0.660291	+	0.751010i	$0.729567\pi$
$678$		−	19654.5i		−	1.11331i
$679$		0			0
$680$	−4532.11	+	12129.5i	−0.255586	+	0.684039i
$681$	4318.07	−	7479.11i	0.242979	−	0.420852i
$682$	−15927.9	+	9195.98i	−0.894297	+	0.516323i
$683$	−3925.45	+	2266.36i	−0.219917	+	0.126969i	−0.605912	−	0.795532i	$-0.707192\pi$
$683$	−3925.45	+	2266.36i	−0.219917	+	0.126969i	0.385995	+	0.922501i	$0.373858\pi$
$684$	104.311	−	180.672i	0.00583104	−	0.0100997i
$685$	16257.3	+	6074.40i	0.906800	+	0.338819i
$686$		0			0
$687$			6687.56i			0.371392i
$688$	8105.80	+	4679.88i	0.449172	+	0.259330i
$689$	1278.86	+	2215.05i	0.0707122	+	0.122477i
$690$	−8223.53	−	49077.8i	−0.453717	−	2.70777i
$691$	−13617.6	+	23586.4i	−0.749694	+	1.29851i	0.198276	+	0.980146i	$0.436466\pi$
$691$	−13617.6	+	23586.4i	−0.749694	+	1.29851i	−0.947969	+	0.318361i	$0.896868\pi$
$692$			334.197i			0.0183587i
$693$		0			0
$694$	−23534.7			−1.28727
$695$	7625.70	+	9246.70i	0.416200	+	0.504673i
$696$	−24744.9	−	42859.4i	−1.34763	−	2.33417i
$697$	−2186.92	+	1262.62i	−0.118846	+	0.0686157i
$698$	17735.6	+	10239.6i	0.961750	+	0.555267i
$699$	−13937.3			−0.754160
$700$		0			0
$701$	−17144.3			−0.923726			−0.461863	−	0.886951i	$-0.652819\pi$
$701$	−17144.3			−0.923726			−0.461863	+	0.886951i	$0.652819\pi$
$702$	−2360.13	−	1362.62i	−0.126891	−	0.0732604i
$703$	5630.19	−	3250.59i	0.302058	−	0.174393i
$704$	9399.03	+	16279.6i	0.503181	+	0.871534i
$705$	−2342.84	−	2840.86i	−0.125158	−	0.151763i
$706$	11965.7			0.637867
$707$		0			0
$708$		−	531.635i		−	0.0282204i
$709$	8362.05	−	14483.5i	0.442939	−	0.767192i	−0.554967	−	0.831872i	$-0.687269\pi$
$709$	8362.05	−	14483.5i	0.442939	−	0.767192i	0.997906	+	0.0646799i	$0.0206026\pi$
$710$	1414.50	+	8441.71i	0.0747681	+	0.446214i
$711$	−12739.6	−	22065.7i	−0.671973	−	1.16389i
$712$	−30126.8	−	17393.7i	−1.58574	−	0.915528i
$713$		−	29847.0i		−	1.56771i
$714$		0			0
$715$	−1554.26	−	580.737i	−0.0812951	−	0.0303753i
$716$	136.877	−	237.077i	0.00714430	−	0.0123743i
$717$	21601.5	−	12471.7i	1.12514	−	0.649599i
$718$	7753.79	−	4476.65i	0.403021	−	0.232684i
$719$	2154.33	−	3731.41i	0.111743	−	0.193544i	−0.804730	−	0.593641i	$-0.797690\pi$
$719$	2154.33	−	3731.41i	0.111743	−	0.193544i	0.916473	+	0.400097i	$0.131023\pi$
$720$	13719.7	−	36718.9i	0.710145	−	1.90060i
$721$		0			0
$722$		−	17660.9i		−	0.910347i
$723$	−19851.6	−	11461.3i	−1.02115	−	0.589560i
$724$	182.241	+	315.650i	0.00935487	+	0.0162031i
$725$	−5846.84	+	30147.8i	−0.299512	+	1.54436i
$726$	−908.515	+	1573.59i	−0.0464437	+	0.0804429i
$727$		−	29435.6i		−	1.50166i	−0.660496	−	0.750830i	$-0.729654\pi$
$727$		−	29435.6i		−	1.50166i	0.660496	−	0.750830i	$-0.270346\pi$
$728$		0			0
$729$	20127.8			1.02260
$730$	4056.45	+	4918.74i	0.205666	+	0.249385i
$731$	3710.79	+	6427.27i	0.187754	+	0.325200i
$732$	55.3115	−	31.9341i	0.00279286	−	0.00161246i
$733$	−5705.11	−	3293.85i	−0.287480	−	0.165977i	0.349325	−	0.937002i	$-0.386411\pi$
$733$	−5705.11	−	3293.85i	−0.287480	−	0.165977i	−0.636805	+	0.771025i	$0.719744\pi$
$734$	4919.57			0.247390
$735$		0			0
$736$	1173.75			0.0587839
$737$	−8533.82	−	4927.01i	−0.426523	−	0.246253i
$738$	6498.79	−	3752.08i	0.324152	−	0.187149i
$739$	1842.23	+	3190.84i	0.0917018	+	0.158832i	0.908227	−	0.418477i	$-0.137436\pi$
$739$	1842.23	+	3190.84i	0.0917018	+	0.158832i	−0.816526	+	0.577309i	$0.804103\pi$
$740$	−323.384	+	266.693i	−0.0160646	+	0.0132484i
$741$	923.917			0.0458042
$742$		0			0
$743$		−	12271.9i		−	0.605940i	−0.953000	−	0.302970i	$-0.902022\pi$
$743$		−	12271.9i		−	0.605940i	0.953000	−	0.302970i	$-0.0979783\pi$
$744$	17331.6	−	30019.2i	0.854042	−	1.47924i
$745$	7122.49	−	1193.45i	0.350265	−	0.0586909i
$746$	−4023.12	−	6968.25i	−0.197449	−	0.341992i
$747$	3387.03	+	1955.51i	0.165897	+	0.0957807i
$748$		−	289.355i		−	0.0141442i
$749$		0			0
$750$	−31504.4	+	17131.5i	−1.53384	+	0.834072i
$751$	15435.5	−	26735.1i	0.749999	−	1.29904i	−0.197824	−	0.980238i	$-0.563387\pi$
$751$	15435.5	−	26735.1i	0.749999	−	1.29904i	0.947823	−	0.318798i	$-0.103279\pi$
$752$	2068.13	−	1194.04i	0.100289	−	0.0579017i
$753$	22831.5	−	13181.8i	1.10495	−	0.637942i
$754$	−1389.96	+	2407.48i	−0.0671343	+	0.116280i
$755$	951.669	−	2547.00i	0.0458739	−	0.122775i
$756$		0			0
$757$			11442.1i			0.549368i	0.961535	+	0.274684i	$0.0885732\pi$
$757$			11442.1i			0.549368i	−0.961535	+	0.274684i	$0.911427\pi$
$758$	−25875.2	−	14939.0i	−1.23988	−	0.715844i
$759$	−29187.1	−	50553.5i	−1.39582	−	2.41762i
$760$	1073.79	+	6408.32i	0.0512504	+	0.305861i
$761$	−7211.64	+	12490.9i	−0.343524	+	0.595001i	−0.985085	−	0.172071i	$-0.944954\pi$
$761$	−7211.64	+	12490.9i	−0.343524	+	0.595001i	0.641560	+	0.767073i	$0.278287\pi$
$762$			12959.4i			0.616102i
$763$		0			0
$764$	−759.630			−0.0359718
$765$	23978.9	−	19775.2i	1.13328	−	0.934607i
$766$	368.341	+	637.985i	0.0173743	+	0.0300931i
$767$	1357.60	−	783.813i	0.0639116	−	0.0368994i
$768$	1787.49	+	1032.01i	0.0839850	+	0.0484887i
$769$	−26772.8			−1.25546			−0.627731	−	0.778430i	$-0.716016\pi$
$769$	−26772.8			−1.25546			−0.627731	+	0.778430i	$0.716016\pi$
$770$		0			0
$771$	24495.9			1.14423
$772$	363.295	+	209.748i	0.0169369	+	0.00977850i
$773$	−23962.4	+

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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.47228 - 1.42737i) q^{2} +(-7.78434 + 4.49429i) q^{3} +(0.0747741 + 0.129513i) q^{4} +(7.11340 + 8.62551i) q^{5} +25.6601 q^{6} +22.4110i q^{8} +(26.8973 - 46.5874i) q^{9} +(-5.27451 - 31.4781i) q^{10} +(-18.7204 - 32.4247i) q^{11} +(-1.16413 - 0.672113i) q^{12} -3.96370i q^{13} +(-94.1387 - 35.1742i) q^{15} +(32.5870 - 56.4424i) q^{16} +(44.7544 - 25.8390i) q^{17} +(-132.995 + 76.7847i) q^{18} +(12.9661 - 22.4580i) q^{19} +(-0.585214 + 1.56624i) q^{20} +106.884i q^{22} +(-150.216 - 86.7272i) q^{23} +(-100.722 - 174.455i) q^{24} +(-23.7990 + 122.714i) q^{25} +(-5.65768 + 9.79938i) q^{26} +240.845i q^{27} +245.676 q^{29} +(182.530 + 221.331i) q^{30} +(86.0372 + 149.021i) q^{31} +(-5.86031 + 3.38345i) q^{32} +(291.452 + 168.270i) q^{33} -147.527 q^{34} +8.04488 q^{36} +(217.111 + 125.349i) q^{37} +(-64.1118 + 37.0150i) q^{38} +(17.8140 + 30.8548i) q^{39} +(-193.306 + 159.419i) q^{40} -48.8649 q^{41} +143.612i q^{43} +(2.79960 - 4.84905i) q^{44} +(593.172 - 99.3925i) q^{45} +(247.584 + 428.827i) q^{46} +(31.7325 + 18.3208i) q^{47} +585.822i q^{48} +(233.995 - 269.412i) q^{50} +(-232.256 + 402.279i) q^{51} +(0.513350 - 0.296383i) q^{52} +(-558.834 + 322.643i) q^{53} +(343.775 - 595.435i) q^{54} +(146.514 - 392.123i) q^{55} +233.094i q^{57} +(-607.380 - 350.671i) q^{58} +(197.748 + 342.509i) q^{59} +(-2.48364 - 14.8223i) q^{60} +(-23.7565 + 41.1475i) q^{61} -491.228i q^{62} -502.074 q^{64} +(34.1890 - 28.1954i) q^{65} +(-480.366 - 832.019i) q^{66} +(227.929 - 131.595i) q^{67} +(6.69295 + 3.86418i) q^{68} +1559.11 q^{69} -268.177 q^{71} +(1044.07 + 602.795i) q^{72} +(-172.995 + 99.8785i) q^{73} +(-357.840 - 619.797i) q^{74} +(-366.251 - 1062.20i) q^{75} +3.87813 q^{76} -101.709i q^{78} +(236.820 - 410.184i) q^{79} +(718.649 - 120.418i) q^{80} +(-356.199 - 616.955i) q^{81} +(120.808 + 69.7484i) q^{82} +72.7028i q^{83} +(541.231 + 202.227i) q^{85} +(204.988 - 355.049i) q^{86} +(-1912.43 + 1104.14i) q^{87} +(726.669 - 419.543i) q^{88} +(-776.123 + 1344.28i) q^{89} +(-1608.36 - 600.950i) q^{90} -25.9398i q^{92} +(-1339.48 - 773.352i) q^{93} +(-52.3011 - 90.5881i) q^{94} +(285.945 - 47.9133i) q^{95} +(30.4124 - 52.6758i) q^{96} +243.338i q^{97} -2014.11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 36 q^{4} - 6 q^{5} + 24 q^{6} + 46 q^{9} + 16 q^{10} - 84 q^{11} + 16 q^{15} - 148 q^{16} - 72 q^{19} - 136 q^{20} - 72 q^{24} + 362 q^{25} + 620 q^{26} + 176 q^{29} - 52 q^{30} - 120 q^{31} + 1928 q^{34}+ \cdots - 10608 q^{99}+O(q^{100}) \) 20 * q + 36 * q^4 - 6 * q^5 + 24 * q^6 + 46 * q^9 + 16 * q^10 - 84 * q^11 + 16 * q^15 - 148 * q^16 - 72 * q^19 - 136 * q^20 - 72 * q^24 + 362 * q^25 + 620 * q^26 + 176 * q^29 - 52 * q^30 - 120 * q^31 + 1928 * q^34 - 840 * q^36 - 212 * q^39 - 1396 * q^40 - 1704 * q^41 + 1424 * q^44 + 510 * q^45 - 176 * q^46 + 3288 * q^50 - 1276 * q^51 + 996 * q^54 - 2272 * q^55 - 864 * q^59 + 1692 * q^60 + 884 * q^61 - 5448 * q^64 - 520 * q^65 - 1148 * q^66 + 9616 * q^69 + 1760 * q^71 - 3024 * q^74 - 720 * q^75 - 5344 * q^76 + 3580 * q^79 + 2316 * q^80 + 302 * q^81 + 3144 * q^85 - 2432 * q^86 + 1492 * q^89 - 15496 * q^90 - 1652 * q^94 + 1628 * q^95 - 4080 * q^96 - 10608 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more