LMFDB - Embedded newform 245.4.j.e.79.8

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			79.8
Root			$1.60625 - 0.927371i$ of defining polynomial
Character	$\chi$	$=$	245.79
Dual form			245.4.j.e.214.8

$q$-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} +(-11.0266 - 1.84763i) q^{5} +25.6601 q^{6} -22.4110i q^{8} +(26.8973 - 46.5874i) q^{9} +(-24.6236 - 20.3069i) 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} +(118.173 + 40.7463i) q^{25} +(-5.65768 + 9.79938i) q^{26} -240.845i q^{27} +245.676 q^{29} +(-282.944 - 47.4104i) 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} +(-41.4073 + 247.118i) q^{40} -48.8649 q^{41} -143.612i q^{43} +(2.79960 - 4.84905i) q^{44} +(-382.662 + 464.005i) 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} +(-11.5946 - 9.56202i) q^{60} +(-23.7565 + 41.1475i) q^{61} +491.228i q^{62} -502.074 q^{64} +(7.32347 - 43.7062i) 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} +(1103.02 - 213.919i) q^{75} +3.87813 q^{76} +101.709i q^{78} +(236.820 - 410.184i) q^{79} +(-463.609 + 562.159i) 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} +(-184.467 + 223.679i) 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	0.868703	−	0.495334i	$-0.164954\pi$
$2$	2.47228	+	1.42737i	0.874082	+	0.504652i	0.00537973	+	0.999986i	$0.498288\pi$
$3$	7.78434	−	4.49429i	1.49810	−	0.864926i	0.498099	−	0.867120i	$-0.334032\pi$
$3$	7.78434	−	4.49429i	1.49810	−	0.864926i	0.999998	+	0.00219412i	$0.000698411\pi$
$4$	0.0747741	+	0.129513i	0.00934677	+	0.0161891i
$5$	−11.0266	−	1.84763i	−0.986250	−	0.165257i
$5$	−11.0266	−	1.84763i	−0.986250	−	0.165257i
$6$	25.6601			1.74595
$7$		0			0
$7$		0			0
$8$		−	22.4110i		−	0.990436i
$9$	26.8973	−	46.5874i	0.996195	−	1.72546i
$10$	−24.6236	−	20.3069i	−0.778667	−	0.642162i
$11$	−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	$0.0134628\pi$
$13$			3.96370i			0.0845641i	−0.999106	+	0.0422821i	$0.986537\pi$
$14$		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	−0.784038	−	0.620713i	$-0.786843\pi$
$17$	−44.7544	+	25.8390i	−0.638503	+	0.368640i	0.145535	+	0.989353i	$0.453510\pi$
$18$	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	0.989868	−	0.141991i	$-0.0453506\pi$
$23$	150.216	+	86.7272i	1.36183	+	0.786255i	0.371966	+	0.928246i	$0.378684\pi$
$24$	−100.722	−	174.455i	−0.856654	−	1.48377i
$25$	118.173	+	40.7463i	0.945380	+	0.325970i
$26$	−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	$0.211856\pi$
$30$	−282.944	−	47.4104i	−1.72194	−	0.288530i
$31$	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	−0.0670648	−	0.997749i	$-0.521363\pi$
$37$	−217.111	−	125.349i	−0.964673	−	0.556954i	−0.897608	+	0.440795i	$0.854697\pi$
$38$	64.1118	−	37.0150i	0.273692	−	0.158016i
$39$	17.8140	+	30.8548i	0.0731417	+	0.126685i
$40$	−41.4073	+	247.118i	−0.163677	+	0.976818i
$41$	−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	$-0.918037\pi$
$43$		−	143.612i		−	0.509317i	0.967031	−	0.254658i	$-0.0819630\pi$
$44$	2.79960	−	4.84905i	0.00959218	−	0.0166141i
$45$	−382.662	+	464.005i	−1.26764	+	1.53711i
$46$	247.584	+	428.827i	0.793570	+	1.37450i
$47$	−31.7325	−	18.3208i	−0.0984821	−	0.0568587i	0.449950	−	0.893054i	$-0.351442\pi$
$47$	−31.7325	−	18.3208i	−0.0984821	−	0.0568587i	−0.548432	+	0.836195i	$0.684775\pi$
$48$		−	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	0.449952	−	0.893053i	$-0.351441\pi$
$53$	558.834	−	322.643i	1.44833	−	0.836196i	0.998382	+	0.0568566i	$0.0181078\pi$
$54$	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	$0.689605\pi$
$60$	−11.5946	−	9.56202i	−0.0249477	−	0.0205742i
$61$	−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
$65$	7.32347	−	43.7062i	0.0139748	−	0.0834014i
$66$	−480.366	−	832.019i	−0.895894	−	1.55173i
$67$	−227.929	+	131.595i	−0.415611	+	0.239953i	−0.693198	−	0.720748i	$-0.743799\pi$
$67$	−227.929	+	131.595i	−0.415611	+	0.239953i	0.277587	+	0.960701i	$0.410465\pi$
$68$	−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	−0.354866	−	0.934917i	$-0.615474\pi$
$73$	172.995	−	99.8785i	0.277363	−	0.160136i	0.632229	+	0.774782i	$0.282140\pi$
$74$	−357.840	−	619.797i	−0.562136	−	0.973648i
$75$	1103.02	−	213.919i	1.69821	−	0.329349i
$76$	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	$0.0571632\pi$
$80$	−463.609	+	562.159i	−0.647914	+	0.785642i
$81$	−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	$-0.984692\pi$
$83$		−	72.7028i		−	0.0961466i	0.998844	−	0.0480733i	$-0.0153081\pi$
$84$		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
$95$	−184.467	+	223.679i	−0.199220	+	0.241568i
$96$	30.4124	−	52.6758i	0.0323328	−	0.0560021i
$97$		−	243.338i		−	0.254714i	−0.991857	−	0.127357i	$-0.959351\pi$
$97$		−	243.338i		−	0.254714i	0.991857	−	0.127357i	$-0.0406494\pi$
$98$		0			0
$99$	−2014.11			−2.04470
$100$	3.55909	+	18.3516i	0.00355909	+	0.0183516i
$101$	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	0.0526133	−	0.998615i	$-0.483245\pi$
$103$	−821.536	−	474.314i	−0.785906	−	0.453743i	−0.838519	+	0.544872i	$0.816578\pi$
$104$	88.8306			0.0837554
$105$		0			0
$106$	1842.12			1.68795
$107$	748.231	+	431.992i	0.676021	+	0.390301i	0.798354	−	0.602188i	$-0.205704\pi$
$107$	748.231	+	431.992i	0.676021	+	0.390301i	−0.122333	+	0.992489i	$0.539038\pi$
$108$	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	$0.706008\pi$
$110$	−197.482	+	1178.57i	−0.171174	+	1.02156i
$111$	−2253.42			−1.92690
$112$		0			0
$113$			765.957i			0.637657i	0.947812	+	0.318828i	$0.103289\pi$
$113$			765.957i			0.637657i	−0.947812	+	0.318828i	$0.896711\pi$
$114$	332.712	−	576.274i	0.273345	−	0.473448i
$115$	−1496.13	−	1233.85i	−1.21317	−	1.00050i
$116$	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	$-0.943543\pi$
$127$		−	505.042i		−	0.352876i	0.984312	−	0.176438i	$-0.0564575\pi$
$128$	−1288.15	−	743.714i	−0.889512	−	0.513560i
$129$	−645.434	−	1117.92i	−0.440521	−	0.763006i
$130$	80.4907	−	97.6007i	0.0543038	−	0.0658473i
$131$	−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
$135$	−444.992	+	2655.70i	−0.283695	+	1.69308i
$136$	579.078	+	1002.99i	0.365114	+	0.632396i
$137$	−1344.31	+	776.141i	−0.838340	+	0.484016i	−0.856700	−	0.515816i	$-0.827489\pi$
$137$	−1344.31	+	776.141i	−0.838340	+	0.484016i	0.0183597	+	0.999831i	$0.494156\pi$
$138$	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
$145$	−2708.98	−	453.920i	−1.55151	−	0.259972i
$146$	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	$0.109842\pi$
$150$	3032.31	+	1045.55i	1.65058	+	0.569126i
$151$	−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	−0.117681	−	0.993052i	$-0.537546\pi$
$157$	1344.56	−	776.281i	0.683487	−	0.394611i	0.801168	+	0.598440i	$0.204213\pi$
$158$	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	−0.136522	−	0.990637i	$-0.543592\pi$
$163$	−2211.53	−	1276.82i	−1.06270	−	0.613550i	−0.926178	+	0.377087i	$0.876926\pi$
$164$	−3.65383	−	6.32862i	−0.00173973	−	0.00301331i
$165$	2902.82	+	2393.94i	1.36960	+	1.12950i
$166$	103.774	−	179.741i	0.0485205	−	0.0840400i
$167$		−	3573.14i		−	1.65568i	−0.560966	−	0.827839i	$-0.689570\pi$
$167$		−	3573.14i		−	1.65568i	0.560966	−	0.827839i	$-0.310430\pi$
$168$		0			0
$169$	2181.29			0.992849
$170$	1626.73	+	272.576i	0.733907	+	0.122974i
$171$	−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	0.0103095	−	0.999947i	$-0.496718\pi$
$173$	−1935.31	−	1117.35i	−0.850515	−	0.491045i	−0.860825	+	0.508902i	$0.830052\pi$
$174$	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	$0.958160\pi$
$180$	−88.7078	−	14.8640i	−0.0367327	−	0.00615497i
$181$	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
$185$	2162.40	+	1783.32i	0.859368	+	0.708715i
$186$	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	−0.879151	−	0.476543i	$-0.841890\pi$
$193$	−2429.28	+	1402.55i	−0.906028	+	0.523095i	−0.0268769	+	0.999639i	$0.508556\pi$
$194$	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	$0.189961\pi$
$197$			3107.79i			1.12396i	−0.827149	+	0.561982i	$0.810039\pi$
$198$	−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	$0.958153\pi$
$200$	913.165	−	2648.37i	0.322853	−	0.936338i
$201$	−1182.85	+	2048.75i	−0.415083	+	0.718945i
$202$			4394.41i			1.53064i
$203$		0			0
$204$	−69.4669			−0.0238414
$205$	538.815	+	90.2844i	0.183573	+	0.0307597i
$206$	−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
$215$	−265.342	+	1583.55i	−0.0841683	+	0.502314i
$216$	−5397.57			−1.70027
$217$		0			0
$218$			2530.21i			0.786089i
$219$	897.766	−	1554.98i	0.277011	−	0.479797i
$220$	−39.8294	+	48.2960i	−0.0122059	+	0.0148005i
$221$	−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	$-0.747834\pi$
$223$		−	4741.40i		−	1.42380i	0.702280	−	0.711901i	$-0.252166\pi$
$224$		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	−0.373399	−	0.927671i	$-0.621808\pi$
$227$	832.069	−	480.395i	0.243288	−	0.140462i	0.616687	+	0.787208i	$0.288474\pi$
$228$	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	0.299197	−	0.954191i	$-0.403281\pi$
$233$	−1342.82	−	775.279i	−0.377559	−	0.217984i	−0.676756	+	0.736208i	$0.736615\pi$
$234$	304.352	+	527.153i	0.0850261	+	0.147270i
$235$	316.052	+	260.646i	0.0877318	+	0.0723518i
$236$	−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	$0.622537\pi$
$240$	−1082.38	+	6459.63i	−0.291115	+	1.73736i
$241$	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
$250$	−2082.40	−	3403.04i	−0.526811	−	0.860909i
$251$	−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
$255$	3304.26	−	4006.65i	0.811454	−	0.983946i
$256$	−114.813	−	198.862i	−0.0280306	−	0.0485504i
$257$	2360.11	+	1362.61i	0.572840	+	0.330729i	0.758283	−	0.651926i	$-0.226039\pi$
$257$	2360.11	+	1362.61i	0.572840	+	0.330729i	−0.185443	+	0.982655i	$0.559372\pi$
$258$		−	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	−0.160117	−	0.987098i	$-0.551187\pi$
$263$	2621.68	−	1513.63i	0.614676	−	0.354884i	0.774793	+	0.632214i	$0.217854\pi$
$264$	−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	$0.885603\pi$
$270$	−4890.82	+	5930.46i	−1.10239	+	1.33673i
$271$	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
$275$	−891.051	−	4594.49i	−0.195391	−	1.00748i
$276$	116.581	+	201.924i	0.0254252	+	0.0440377i
$277$	759.170	−	438.307i	0.164672	−	0.0950733i	−0.415399	−	0.909639i	$-0.636358\pi$
$277$	759.170	−	438.307i	0.164672	−	0.0950733i	0.580071	+	0.814566i	$0.303025\pi$
$278$	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	−0.690491	−	0.723341i	$-0.742606\pi$
$283$	−1948.62	+	1125.04i	−0.409305	+	0.236312i	0.281186	+	0.959653i	$0.409272\pi$
$284$	−20.0527	−	34.7323i	−0.00418982	−	0.00725698i
$285$	−430.673	+	2570.24i	−0.0895117	+	0.534203i
$286$	423.655			0.0875919
$287$		0			0
$288$		−	364.022i		−	0.0744799i
$289$	−1121.19	+	1941.96i	−0.228210	+	0.395271i
$290$	−6049.44	−	4988.93i	−1.22495	−	1.01021i
$291$	−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	$0.200862\pi$
$293$			5917.86i			1.17995i	−0.807422	+	0.589975i	$0.799138\pi$
$294$		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
$305$	337.979	−	409.824i	0.0634513	−	0.0769392i
$306$	−3968.08	+	6872.91i	−0.741307	+	1.28398i
$307$			9458.47i			1.75838i	0.476469	+	0.879191i	$0.341916\pi$
$307$			9458.47i			1.75838i	−0.476469	+	0.879191i	$0.658084\pi$
$308$		0			0
$309$	−8526.81			−1.56982
$310$	907.609	−	5416.58i	0.166286	−	0.992391i
$311$	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	−0.437032	−	0.899446i	$-0.643970\pi$
$313$	−7943.54	−	4586.21i	−1.43449	−	0.828204i	−0.997459	+	0.0712425i	$0.977304\pi$
$314$	4432.16			0.796565
$315$		0			0
$316$	70.8320			0.0126095
$317$	2665.57	+	1538.97i	0.472283	+	0.272672i	0.717195	−	0.696873i	$-0.245426\pi$
$317$	2665.57	+	1538.97i	0.472283	+	0.272672i	−0.244912	+	0.969545i	$0.578759\pi$
$318$	14339.7	−	8279.04i	2.52871	−	1.45995i
$319$	−4599.16	−	7965.97i	−0.807221	−	1.39815i
$320$	5536.18	+	927.649i	0.967131	+	0.162054i
$321$	7765.98			1.35033
$322$		0			0
$323$			1340.13i			0.230857i
$324$	53.2690	−	92.2646i	0.00913391	−	0.0158204i
$325$	−161.506	+	468.401i	−0.0275654	+	0.0799452i
$326$	−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	$-0.901234\pi$
$337$		−	3777.84i		−	0.610658i	0.952247	−	0.305329i	$-0.0987665\pi$
$338$	5392.75	+	3113.51i	0.867832	+	0.501043i
$339$	3442.43	+	5962.47i	0.551526	+	0.955271i
$340$	66.6610	+	54.9749i	0.0106329	+	0.00876892i
$341$	3221.30	−	5579.45i	0.511563	−	0.886054i
$342$		−	3982.41i		−	0.629660i
$343$		0			0
$344$	−3218.49			−0.504446
$345$	−17191.7	−	2880.66i	−2.68281	−	0.449535i
$346$	−3189.75	−	5524.82i	−0.495614	−	0.858428i
$347$	−7139.58	+	4122.04i	−1.10453	+	0.637702i	−0.937408	−	0.348234i	$-0.886782\pi$
$347$	−7139.58	+	4122.04i	−1.10453	+	0.637702i	−0.167125	+	0.985936i	$0.553448\pi$
$348$	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	−0.200722	−	0.979648i	$-0.564329\pi$
$353$	3629.95	−	2095.76i	0.547317	−	0.315994i	0.748039	+	0.663655i	$0.230995\pi$
$354$	5074.22	+	8788.80i	0.761840	+	1.31955i
$355$	2957.08	+	495.492i	0.442100	+	0.0740789i
$356$	−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	$0.240716\pi$
$360$	10398.8	+	8575.85i	1.52241	+	1.25552i
$361$	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	−0.390095	−	0.920775i	$-0.627558\pi$
$367$	1492.42	−	861.649i	0.212272	−	0.122555i	0.602367	+	0.798220i	$0.294225\pi$
$368$	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	0.320919	−	0.947106i	$-0.396008\pi$
$373$	−2440.94	−	1409.28i	−0.338839	−	0.195629i	−0.659759	+	0.751478i	$0.729341\pi$
$374$	2761.77	+	4783.52i	0.381838	+	0.661364i
$375$	−12557.8	+	320.824i	−1.72929	+	0.0441794i
$376$	−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	$0.249036\pi$
$380$	−42.7626	−	7.16535i	−0.00577283	−	0.000967303i
$381$	−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	0.514834	−	0.857290i	$-0.327854\pi$
$383$	223.482	+	129.028i	0.0298157	+	0.0172141i	−0.485018	+	0.874504i	$0.661187\pi$
$384$	−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	$0.736988\pi$
$390$	187.921	−	1121.50i	0.0243993	−	0.145614i
$391$	−8963.77			−1.15938
$392$		0			0
$393$			6048.69i			0.776376i
$394$	−4435.97	+	7683.33i	−0.567211	+	0.982438i
$395$	−3369.19	+	4085.39i	−0.429171	+	0.520400i
$396$	−150.603	−	260.852i	−0.0191114	−	0.0331018i
$397$	3138.96	+	1812.28i	0.396825	+	0.229107i	0.685113	−	0.728437i	$-0.259753\pi$
$397$	3138.96	+	1812.28i	0.396825	+	0.229107i	−0.288288	+	0.957544i	$0.593086\pi$
$398$		−	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	$0.962628\pi$
$410$	1203.23	+	992.297i	0.144935	+	0.119527i
$411$	−6976.40	+	12083.5i	−0.837276	+	1.45020i
$412$		−	141.866i		−	0.0169641i
$413$		0			0
$414$	26637.3			3.16220
$415$	−134.328	+	801.665i	−0.0158889	+	0.0948246i
$416$	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
$425$	−6341.59	+	1229.88i	−0.723793	+	0.140372i
$426$	−6881.43			−0.782645
$427$		0			0
$428$			129.207i			0.0145922i
$429$	666.971	−	1155.23i	0.0750622	−	0.130011i
$430$	−2916.32	+	3536.25i	−0.327064	+	0.396588i
$431$	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	$-0.845663\pi$
$433$		−	8399.05i		−	0.932176i	0.884738	−	0.466088i	$-0.154337\pi$
$434$		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	0.409084	−	0.912497i	$-0.365848\pi$
$443$	−1646.80	−	950.783i	−0.176619	−	0.101971i	−0.585703	+	0.810526i	$0.699181\pi$
$444$	−168.498	−	291.847i	−0.0180103	−	0.0311947i
$445$	11041.7	−	13388.9i	1.17625	−	1.42628i
$446$	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	$0.412141\pi$
$450$	18845.0	−	3654.79i	1.97414	−	0.382863i
$451$	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	−0.0866361	−	0.996240i	$-0.527612\pi$
$457$	−9698.45	−	5599.41i	−0.992723	−	0.573149i	−0.906087	+	0.423091i	$0.860945\pi$
$458$	1839.39	−	1061.97i	0.187662	−	0.108347i
$459$	6223.18	+	10778.9i	0.632839	+	1.09611i
$460$	47.9272	−	286.028i	0.00485786	−	0.0289916i
$461$	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	$0.00616141\pi$
$463$			385.660i			0.0387109i	−0.999813	+	0.0193554i	$0.993839\pi$
$464$	8005.86	−	13866.6i	0.800997	−	1.38737i
$465$	−13341.1	−	11002.3i	−1.33049	−	1.09725i
$466$	−2213.22	−	3833.41i	−0.220012	−	0.381072i
$467$	4360.75	+	2517.68i	0.432101	+	0.249474i	0.700241	−	0.713906i	$-0.253076\pi$
$467$	4360.75	+	2517.68i	0.432101	+	0.249474i	−0.268140	+	0.963380i	$0.586409\pi$
$468$			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	$0.969231\pi$
$480$	−432.671	+	524.645i	−0.0411430	+	0.0498889i
$481$	496.848	−	860.565i	0.0470983	−	0.0815767i
$482$			7280.16i			0.687972i
$483$		0			0
$484$	−10.5898			−0.000994530
$485$	−449.599	+	2683.20i	−0.0420933	+	0.251212i
$486$	141.817	+	245.635i	0.0132366	+	0.0229264i
$487$	−771.174	+	445.238i	−0.0717562	+	0.0414284i	−0.535449	−	0.844568i	$-0.679858\pi$
$487$	−771.174	+	445.238i	−0.0717562	+	0.0414284i	0.463693	+	0.885996i	$0.346524\pi$
$488$	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
$495$	22208.8	+	3721.33i	2.01659	+	0.337902i
$496$	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	$0.0462443\pi$
$500$	−5.33773	−	208.932i	−0.000477421	−	0.0186874i
$501$	−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	$0.00102332\pi$
$503$			72.5340i			0.00642969i	−0.999995	+	0.00321484i	$0.998977\pi$
$504$		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
$515$	8182.40	+	6747.97i	0.700116	+	0.577381i
$516$	96.5235	−	167.184i	0.00823490	−	0.0142633i
$517$			1371.89i			0.116703i
$518$		0			0
$519$	−20086.8			−1.69887
$520$	−979.501	−	164.126i	−0.0826038	−	0.0138412i
$521$	−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	0.147065	−	0.989127i	$-0.453017\pi$
$523$	−7607.06	−	4391.94i	−0.636011	−	0.367201i	−0.783076	+	0.621926i	$0.786351\pi$
$524$	−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
$530$	−20312.4	−	3403.57i	−1.66474	−	0.278946i
$531$	21275.5			1.73875
$532$		0			0
$533$		−	193.686i		−	0.0157401i
$534$	−19915.4	+	34494.4i	−1.61390	+	2.79535i
$535$	−7452.30	−	6145.86i	−0.602226	−	0.496652i
$536$	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	$0.0724919\pi$
$547$			5776.83i			0.451553i	−0.974179	+	0.225776i	$0.927508\pi$
$548$	−201.040	−	116.070i	−0.0156715	−	0.00904796i
$549$	1277.97	+	2213.51i	0.0993487	+	0.172077i
$550$	4355.11	−	12630.7i	0.337641	−	0.979228i
$551$	3185.47	−	5517.40i	0.246290	−	0.426587i
$552$		−	34941.2i		−	2.69419i
$553$		0			0
$554$	2502.51			0.191916
$555$	24847.6	+	4163.50i	1.90040	+	0.318434i
$556$	80.1592	+	138.840i	0.00611422	+	0.0105901i
$557$	−17807.8	+	10281.3i	−1.35465	+	0.782106i	−0.988896	−	0.148607i	$-0.952521\pi$
$557$	−17807.8	+	10281.3i	−1.35465	+	0.782106i	−0.365751	+	0.930713i	$0.619188\pi$
$558$	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	$0.688784\pi$
$563$	−20792.8	+	12004.8i	−1.55651	+	0.898650i	−0.997587	+	0.0694291i	$0.977882\pi$
$564$	−24.6273	−	42.6557i	−0.00183864	−	0.00318462i
$565$	1415.21	−	8445.92i	0.105377	−	0.628889i
$566$	−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	$0.817423\pi$
$570$	−4733.43	+	5739.62i	−0.347827	+	0.421766i
$571$	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	−0.909228	−	0.416299i	$-0.863327\pi$
$577$	−13906.0	+	8028.62i	−1.00332	+	0.579265i	−0.0940886	+	0.995564i	$0.529994\pi$
$578$	−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
$585$	−1839.18	−	1516.76i	−0.129984	−	0.107197i
$586$	−8446.98	+	14630.6i	−0.595463	+	1.03137i
$587$		−	8605.63i		−	0.605098i	−0.953134	−	0.302549i	$-0.902162\pi$
$587$		−	8605.63i		−	0.605098i	0.953134	−	0.302549i	$-0.0978376\pi$
$588$		0			0
$589$	4462.28			0.312165
$590$	2086.04	−	12449.5i	0.145561	−	0.868705i
$591$	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	0.965081	−	0.261951i	$-0.0843659\pi$
$593$	17628.5	+	10177.8i	1.22077	+	0.704809i	0.255684	+	0.966760i	$0.417699\pi$
$594$	−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	$0.552585\pi$
$600$	−4794.13	−	24719.8i	−0.326200	−	1.68197i
$601$	−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
$605$	503.712	−	610.786i	0.0338492	−	0.0410446i
$606$	19749.7	+	34207.5i	1.32389	+	2.29305i
$607$	−15185.1	−	8767.12i	−1.01539	−	0.586238i	−0.102628	−	0.994720i	$-0.532725\pi$
$607$	−15185.1	−	8767.12i	−1.01539	−	0.586238i	−0.912767	+	0.408482i	$0.866058\pi$
$608$		−	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	−0.767479	−	0.641074i	$-0.778489\pi$
$613$	−9046.07	+	5222.75i	−0.596031	+	0.344119i	0.171447	+	0.985193i	$0.445156\pi$
$614$	−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	$-0.858070\pi$
$617$		−	13218.9i		−	0.862516i	0.902229	−	0.431258i	$-0.141930\pi$
$618$	−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	$0.558054\pi$
$620$	183.052	−	221.964i	0.0118573	−	0.0143779i
$621$	20887.8	−	36178.7i	1.34975	−	2.33784i
$622$			21629.8i			1.39433i
$623$		0			0
$624$	2322.02			0.148967
$625$	12304.5	+	9630.18i	0.787487	+	0.616331i
$626$	−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
$635$	−933.132	+	5568.90i	−0.0583153	+	0.348024i
$636$	867.410			0.0540802
$637$		0			0
$638$		−	26258.8i		−	1.62946i
$639$	−7213.22	+	12493.7i	−0.446558	+	0.773461i
$640$	12829.8	+	10580.7i	0.792412	+	0.653497i
$641$	−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	$-0.676976\pi$
$643$		−	27698.0i		−	1.69876i	0.527782	−	0.849380i	$-0.323024\pi$
$644$		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	−0.182930	−	0.983126i	$-0.558558\pi$
$647$	9496.10	−	5482.57i	0.577017	−	0.333141i	0.759947	+	0.649985i	$0.225225\pi$
$648$	−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	0.784707	−	0.619867i	$-0.212814\pi$
$653$	10683.5	+	6168.10i	0.640239	+	0.369642i	−0.144467	+	0.989510i	$0.546147\pi$
$654$	11371.5	+	19696.0i	0.679909	+	1.17764i
$655$	4786.83	−	5804.37i	0.285552	−	0.346253i
$656$	−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	$0.231474\pi$
$660$	−92.9893	+	554.957i	−0.00548424	+	0.0327298i
$661$	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
$670$	8284.71	+	1388.20i	0.477711	+	0.0800458i
$671$	1778.92			0.102347
$672$		0			0
$673$			30358.9i			1.73885i	0.494061	+	0.869427i	$0.335512\pi$
$673$			30358.9i			1.73885i	−0.494061	+	0.869427i	$0.664488\pi$
$674$	5392.37	−	9339.86i	0.308170	−	0.533766i
$675$	9813.52	−	28461.2i	0.559589	−	1.62292i
$676$	163.104	+	282.504i	0.00927993	+	0.0160733i
$677$	5989.85	+	3458.24i	0.340042	+	0.196324i	0.660291	−	0.751010i	$-0.270433\pi$
$677$	5989.85	+	3458.24i	0.340042	+	0.196324i	−0.320248	+	0.947334i	$0.603766\pi$
$678$			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	−0.385995	−	0.922501i	$-0.626142\pi$
$683$	3925.45	−	2266.36i	0.219917	−	0.126969i	0.605912	+	0.795532i	$0.292808\pi$
$684$	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
$690$	−38390.9	−	31660.7i	−2.11814	−	1.74681i
$691$	−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
$695$	−11820.7	−	1980.69i	−0.645159	−	0.108104i
$696$	−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
$705$	3631.67	+	608.528i	0.194010	+	0.0325085i
$706$	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	$0.0206026\pi$
$710$	6603.48	+	5445.85i	0.349048	+	0.287858i
$711$	−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
$725$	29032.2	+	10010.4i	1.48721	+	0.512796i
$726$	−908.515	+	1573.59i	−0.0464437	+	0.0804429i
$727$			29435.6i			1.50166i	0.660496	+	0.750830i	$0.270346\pi$
$727$			29435.6i			1.50166i	−0.660496	+	0.750830i	$0.729654\pi$
$728$		0			0
$729$	20127.8			1.02260
$730$	−6287.98	−	1053.62i	−0.318806	−	0.0534195i
$731$	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	0.636805	−	0.771025i	$-0.280256\pi$
$733$	5705.11	+	3293.85i	0.287480	+	0.165977i	−0.349325	+	0.937002i	$0.613589\pi$
$734$	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	$0.804103\pi$
$740$	−69.2706	+	413.405i	−0.00344113	+	0.0205366i
$741$	923.917			0.0458042
$742$		0			0
$743$			12271.9i			0.605940i	0.953000	+	0.302970i	$0.0979783\pi$
$743$			12271.9i			0.605940i	−0.953000	+	0.302970i	$0.902022\pi$
$744$	17331.6	−	30019.2i	0.854042	−	1.47924i
$745$	−4594.80	+	5571.53i	−0.225961	+	0.273993i
$746$	−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	$-0.911427\pi$
$757$		−	11442.1i		−	0.549368i	0.961535	−	0.274684i	$-0.0885732\pi$
$758$	25875.2	+	14939.0i	1.23988	+	0.715844i
$759$	−29187.1	−	50553.5i	−1.39582	−	2.41762i
$760$	5012.88	+	4134.09i	0.239258	+	0.197315i
$761$	−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
$765$	5136.40	−	30653.9i	0.242754	−	1.44875i
$766$	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	−	13834.7i	1.11496	−	0.643724i	0.174852	−	0.984595i	$-0.444055\pi$
$773$	23962.4	−	13834.7i	1.11496	−	0.643724i	0.940110	+	0.340871i	$0.110722\pi$
$774$	−11027.2	−	19099.7i	−0.512099	−	0.886982i
$775$	4095.19	+	21115.9i	0.189811	+	0.978715i
$776$	−5453.45			−0.252278
$777$		0			0
$778$			13057.2i			0.601702i
$779$	−633.589	+	1097.41i	−0.0291408	+	0.0504734i
$780$	37.9010	−	45.9577i	0.00173984	−	0.00210968i
$781$	5020.37	+	8695.54i	0.230017	+	0.398401i
$782$	−22160.9	−	12794.6i	−1.01339	−	0.585083i
$783$		−	59169.8i		−	2.70058i
$784$		0			0
$785$	−16260.2	+	6075.51i	−0.739302	+	0.276235i
$786$	−8633.72	+	14954.0i	−0.391800	+	0.678617i
$787$	9469.54	−	5467.24i	0.428911	−	0.247632i	−0.269972	−	0.962868i	$-0.587014\pi$
$787$	9469.54	−	5467.24i	0.428911	−	0.247632i	0.698882	+	0.715237i	$0.253681\pi$
$788$	−402.498	+	232.382i	−0.0181959	+	0.0105054i
$789$	13605.4	−	23565.2i	0.613896	−	1.06330i
$790$	−14160.9	+	5291.13i	−0.637752	+	0.238291i
$791$		0			0
$792$			45138.2i			2.02515i
$793$	−163.096	−	94.1638i	−0.00730356	−	0.00421671i
$794$	5173.58	+	8960.91i	0.231239	+	0.400517i
$795$	−41259.2	+	50029.7i	−1.84064	+	2.23191i
$796$	160.438	−	277.887i	0.00714393	−	0.0123737i
$797$			31967.3i			1.42075i	0.703823	+	0.710376i	$0.251475\pi$
$797$			31967.3i			1.42075i	−0.703823	+	0.710376i	$0.748525\pi$
$798$		0			0
$799$	1893.56			0.0838415
$800$	830.390	−	161.045i	0.0366984	−	0.00711726i
$801$	41751.1	+	72315.1i	1.84170	+	3.18992i
$802$	−15719.5	+	9075.68i	−0.692115	+	0.399593i
$803$	−6477.05	−	3739.53i	−0.284645	−	0.164340i
$804$	−353.786			−0.0155187
$805$		0			0
$806$	−1947.08			−0.0850906
$807$	−11228.6	−	6482.84i	−0.489797	−	0.282784i
$808$	29876.2	−	17249.0i	1.30079	−	0.751013i
$809$	−8962.40	−	15523.3i	−0.389495	−	0.674624i	0.602887	−	0.797827i	$-0.294017\pi$
$809$	−8962.40	−	15523.3i	−0.389495	−	0.674624i	−0.992382	+	0.123202i	$0.960684\pi$
$810$	−3757.56	+	22425.0i	−0.162996	+	0.972757i
$811$	28541.4			1.23579			0.617895	−	0.786261i	$-0.287986\pi$
$811$	28541.4			1.23579			0.617895	+	0.786261i	$0.287986\pi$
$812$		0			0
$813$		−	58106.2i		−	2.50661i
$814$	−13397.8	+	23205.7i	−0.576895	+	0.999212i
$815$	22026.5	+	18165.1i	0.946694	+	0.780733i
$816$	15137.0	+	26218.1i	0.649390	+	1.12478i
$817$	−3225.24	−	1862.09i	−0.138111	−	0.0797385i
$818$		−	18659.7i		−	0.797580i
$819$		0			0
$820$	28.5964	+	76.5342i	0.00121784	+	0.00325938i
$821$	−9439.29	+	16349.3i	−0.401259	+	0.695000i	−0.993878	−	0.110482i	$-0.964760\pi$
$821$	−9439.29	+	16349.3i	−0.401259	+	0.695000i	0.592619	+	0.805483i	$0.298094\pi$
$822$	−34495.2	+	19915.8i	−1.46370	+	0.845065i
$823$	40347.4	−	23294.6i	1.70889	−	0.986631i	0.772962	−	0.634453i	$-0.218774\pi$
$823$	40347.4	−	23294.6i	1.70889	−	0.986631i	0.935933	−	0.352178i	$-0.114559\pi$
$824$	−10629.9	+	18411.4i	−0.449403	+	0.778390i
$825$	−27585.2	−	31760.4i	−1.16411	−	1.34031i
$826$		0			0
$827$		−	14649.8i		−	0.615989i	−0.951388	−	0.307994i	$-0.900342\pi$
$827$		−	14649.8i		−	0.615989i	0.951388	−	0.307994i	$-0.0996578\pi$
$828$	1208.47	+	697.709i	0.0507212	+	0.0292839i
$829$	−17204.0	−	29798.2i	−0.720771	−	1.24841i	−0.960691	−	0.277619i	$-0.910455\pi$
$829$	−17204.0	−	29798.2i	−0.720771	−	1.24841i	0.239920	−	0.970793i	$-0.422879\pi$
$830$	−1476.37	+	1790.20i	−0.0617416	+	0.0748661i
$831$	3939.76	−	6823.86i	0.164463	−	0.284858i
$832$		−	1990.07i		−	0.0829248i
$833$		0			0
$834$	27508.0			1.14212
$835$	−6601.86	+	39399.7i	−0.273613	+	1.63291i
$836$	−72.6001	−	125.747i	−0.00300350	−	0.00520221i
$837$	35890.9	−	20721.6i	1.48216	−	0.855727i
$838$	−15658.3	−	9040.34i	−0.645475	−	0.372665i
$839$	−25934.2			−1.06716			−0.533580	−	0.845749i	$-0.679154\pi$
$839$	−25934.2			−1.06716			−0.533580	+	0.845749i	$0.679154\pi$
$840$		0			0
$841$	35967.9			1.47476
$842$	−20123.4	−	11618.3i	−0.823632	−	0.475524i
$843$	48669.1	−	28099.1i	1.98844	−	1.14803i
$844$	212.168	+	367.485i	0.00865298	+	0.0149874i
$845$	−24052.2	−	4030.22i	−0.979198	−	0.164076i
$846$	−5627.02			−0.228677
$847$		0			0
$848$		−	42055.9i		−	1.70307i
$849$	−10112.5	+	17515.3i	−0.408786	+	0.708038i
$850$	−17433.7	−	6011.18i	−0.703494	−	0.242567i
$851$	−21742.4	−	37658.9i	−0.875816	−	1.51696i
$852$	−312.194	−	180.245i	−0.0125535	−	0.00724777i
$853$		−	48456.3i		−	1.94503i	−0.232836	−	0.972516i	$-0.574801\pi$
$853$		−	48456.3i		−	1.94503i	0.232836	−	0.972516i	$-0.425199\pi$
$854$		0			0
$855$	5458.99	+	14610.2i	0.218355	+	0.584395i
$856$	9681.37	−	16768.6i	0.386568	−	0.669556i
$857$	−31414.1	+	18136.9i	−1.25214	+	0.722924i	−0.971534	−	0.236899i	$-0.923869\pi$
$857$	−31414.1	+	18136.9i	−1.25214	+	0.722924i	−0.280607	+	0.959823i	$0.590536\pi$
$858$	3297.88	−	1904.03i	0.131221	−	0.0757605i
$859$	14033.6	−	24306.9i	0.557415	−	0.965471i	−0.440296	−	0.897853i	$-0.645127\pi$
$859$	14033.6	−	24306.9i	0.557415	−	0.965471i	0.997711	−	0.0676188i	$-0.0215402\pi$
$860$	−224.931	+	84.0437i	−0.00891870	+	0.00333240i
$861$		0			0
$862$			41015.7i			1.62065i
$863$	7214.79	+	4165.46i	0.284582	+	0.164303i	0.635496	−	0.772104i	$-0.280796\pi$
$863$	7214.79	+	4165.46i	0.284582	+	0.164303i	−0.350914	+	0.936408i	$0.614129\pi$
$864$	−814.886	−	1411.42i	−0.0320868	−	0.0555759i
$865$	19275.5	+	15896.4i	0.757672	+	0.624847i
$866$	11988.6	−	20764.8i	0.470424	−	0.814799i
$867$			20155.9i			0.789538i
$868$		0			0
$869$	−17733.4			−0.692251
$870$	−69512.6	−	11647.6i	−2.70885	−	0.453898i
$871$	−521.602	−	903.442i	−0.0202914	−	0.0351458i
$872$	17202.1	−	9931.65i	0.668047	−	0.385697i
$873$	−11336.5	−	6545.13i	−0.439498	−	0.253745i
$874$	12840.8			0.496965
$875$		0			0
$876$	268.519			0.0103566
$877$	−14263.1	−	8234.79i	−0.549178	−	0.317068i	0.199612	−	0.979875i	$-0.436032\pi$
$877$	−14263.1	−	8234.79i	−0.549178	−	0.317068i	−0.748791	+	0.662807i	$0.769365\pi$
$878$	−44156.9	+	25494.0i	−1.69729	+	0.979934i
$879$	26596.6	+	46066.6i	1.02057	+	1.76768i
$880$	26906.8	+	4508.53i	1.03071	+	0.172707i
$881$	−46635.9			−1.78343			−0.891715	−	0.452597i	$-0.850498\pi$
$881$	−46635.9			−1.78343			−0.891715	+	0.452597i	$0.850498\pi$
$882$		0			0
$883$			14075.8i			0.536453i	0.963356	+	0.268227i	$0.0864376\pi$
$883$			14075.8i			0.536453i	−0.963356	+	0.268227i	$0.913562\pi$
$884$	15.3164	−	26.5289i	0.000582746	−	0.00100935i
$885$	−30663.2	−	25287.7i	−1.16467	−	0.960494i
$886$	−2714.24	−	4701.20i	−0.102919	−	0.178262i
$887$	22709.7	+	13111.5i	0.859659	+	0.496324i	0.863898	−	0.503667i	$-0.168016\pi$
$887$	22709.7	+	13111.5i	0.859659	+	0.496324i	−0.00423914	+	0.999991i	$0.501349\pi$
$888$			50501.5i			1.90847i
$889$		0			0
$890$	46409.2	−	17340.5i	1.74791	−	0.653094i
$891$	−13336.4	+	23099.3i	−0.501443	+	0.868524i
$892$	614.072	−	354.534i	0.0230500	−	0.0133079i
$893$	−822.896	+	475.099i	−0.0308367	+	0.0178036i
$894$	8287.38	−	14354.2i	0.310035	−	0.536997i
$895$	7163.27	+	19171.5i	0.267533	+	0.716012i
$896$		0			0
$897$			6179.84i			0.230032i
$898$	12820.5	+	7401.89i	0.476419	+	0.275061i
$899$	21137.3	+	36610.9i	0.784170	+	1.35822i
$900$	950.683	+	327.799i	0.0352105	+	0.0121407i
$901$	−16673.5	+	28879.4i	−0.616510	+	1.06783i
$902$			5222.87i			0.192796i
$903$		0			0
$904$	17165.9			0.631558
$905$	−26874.2	−	4503.08i	−0.987105	−	0.165400i
$906$	−3120.18	−	5404.32i	−0.114416	−	0.198175i
$907$	13313.4	−	7686.51i	0.487393	−	0.281396i	−0.236100	−	0.971729i	$-0.575869\pi$
$907$	13313.4	−	7686.51i	0.487393	−	0.281396i	0.723492	+	0.690333i	$0.242536\pi$
$908$	124.434	+	71.8423i	0.00454791	+	0.00262574i
$909$	82807.8			3.02152
$910$		0			0
$911$	−21189.3			−0.770619			−0.385310	−	0.922787i	$-0.625905\pi$
$911$	−21189.3			−0.770619			−0.385310	+	0.922787i	$0.625905\pi$
$912$	−13156.4	−	7595.85i	−0.477688	−	0.275793i
$913$	−2357.36	+	1361.02i	−0.0854516	+	0.0493355i
$914$	−15984.9	−	27686.6i	−0.578481	−	1.00196i
$915$	789.077	−	4709.19i	0.0285094	−	0.170143i
$916$	111.265			0.00401342
$917$		0			0
$918$			35531.1i			1.27745i
$919$	−9182.10	+	15903.9i	−0.329586	+	0.570860i	−0.982430	−	0.186633i	$-0.940242\pi$
$919$	−9182.10	+	15903.9i	−0.329586	+	0.570860i	0.652844	+	0.757493i	$0.273576\pi$
$920$	−27651.8	+	33529.8i	−0.990929	+	1.20157i
$921$	42509.1	+	73627.9i	1.52087	+	2.63423i
$922$	42698.0	+	24651.7i	1.52515	+	0.880544i
$923$		−	1062.97i		−	0.0379070i
$924$		0			0
$925$	−20549.1	−	23659.3i	−0.730432	−	0.840988i
$926$	−550.480	+	953.459i	−0.0195355	+	0.0338365i
$927$	−44194.1	+	25515.5i	−1.56583	+	0.904033i
$928$	1439.74	−	831.234i	0.0509286	−	0.0294036i
$929$	7730.28	−	13389.2i	0.273006	−	0.472860i	−0.696624	−	0.717436i	$-0.745316\pi$
$929$	7730.28	−	13389.2i	0.273006	−	0.472860i	0.969630	+	0.244576i	$0.0786489\pi$
$930$	−17278.5	−	46243.5i	−0.609232	−	1.63052i
$931$		0			0
$932$		−	231.883i		−	0.00814978i
$933$	58980.2	+	34052.2i	2.06959	+	1.19488i
$934$	7187.32	+	12448.8i	0.251795	+	0.436121i
$935$	−16689.2	−	13763.5i	−0.583738	−	0.481405i
$936$	2389.30	−	4138.39i	0.0834367	−	0.144517i
$937$		−	28824.7i		−	1.00498i	−0.864584	−	0.502488i	$-0.832418\pi$
$937$		−	28824.7i		−	1.00498i	0.864584	−	0.502488i	$-0.167582\pi$
$938$		0			0
$939$	−82446.9			−2.86534
$940$	−10.1244	+	60.4223i	−0.000351301	+	0.00209655i
$941$	−21086.3	−	36522.5i	−0.730492	−	1.26525i	−0.956673	−	0.291164i	$-0.905958\pi$
$941$	−21086.3	−	36522.5i	−0.730492	−	1.26525i	0.226182	−	0.974085i	$-0.427376\pi$
$942$	34501.5	−	19919.4i	1.19333	−	0.688970i
$943$	−7340.29	−	4237.92i	−0.253481	−	0.146347i
$944$	25776.0			0.888705
$945$		0			0
$946$	−15349.8			−0.527552
$947$	7730.43	+	4463.17i	0.265264	+	0.153150i	0.626734	−	0.779234i	$-0.284391\pi$
$947$	7730.43	+	4463.17i	0.265264	+	0.153150i	−0.361469	+	0.932384i	$0.617725\pi$
$948$	551.380	−	318.340i	0.0188903	−	0.0109063i
$949$	395.889	+	685.700i	0.0135417	+	0.0234550i
$950$	9084.48	−	1761.84i	0.310252	−	0.0601700i
$951$	27666.3			0.943366
$952$		0			0
$953$		−	40420.6i		−	1.37392i	−0.726693	−	0.686962i	$-0.758944\pi$
$953$		−	40420.6i		−	1.37392i	0.726693	−	0.686962i	$-0.241056\pi$
$954$	49548.1	−	85819.8i	1.68153	−	2.91249i
$955$	36132.5	−	43813.3i	1.22431	−	1.48457i
$956$	−207.498	−	359.397i	−0.00701984	−	0.0121587i
$957$	−71602.8	−	41339.9i	−2.41859	−	1.39637i
$958$		−	24784.8i		−	0.835868i
$959$		0			0
$960$	47264.6	−	17660.1i	1.58902	−	0.593725i
$961$	90.7039	−	157.104i	0.00304467	−	0.00527353i
$962$	2456.69	−	1418.37i	0.0823357	−	0.0475365i
$963$	40250.7	−	23238.8i	1.34690	−	0.777631i
$964$	−190.689	+	330.283i	−0.00637104	+	0.0110350i
$965$	29378.1	−	10976.9i	0.980016	−	0.366175i
$966$		0			0
$967$			33914.1i			1.12782i	0.825836	+	0.563910i	$0.190704\pi$
$967$			33914.1i			1.12782i	−0.825836	+	0.563910i	$0.809296\pi$
$968$	1374.35	+	793.480i	0.0456335	+	0.0263465i
$969$	6022.92	+	10432.0i	0.199674	+	0.345846i
$970$	−4941.45	+	5991.86i	−0.163567	+	0.198337i
$971$	29669.5	−	51389.1i	0.980577	−	1.69841i	0.320430	−	0.947272i	$-0.396173\pi$
$971$	29669.5	−	51389.1i	0.980577	−	1.69841i	0.660147	−	0.751137i	$-0.270494\pi$
$972$			14.8585i			0.000490315i
$973$		0			0
$974$	−2542.08			−0.0836277
$975$	847.910	+	4372.05i	0.0278511	+	0.143608i
$976$	1548.31	+	2681.75i	0.0507788	+	0.0879515i
$977$	−6090.01	+	3516.07i	−0.199423	+	0.115137i	−0.596387	−	0.802697i	$-0.703397\pi$
$977$	−6090.01	+	3516.07i	−0.199423	+	0.115137i	0.396963	+	0.917835i	$0.370064\pi$
$978$	−56747.9	−	32763.4i	−1.85542	−	1.07123i
$979$	58117.3			1.89728
$980$		0			0
$981$	47679.1			1.55176
$982$	3862.89	+	2230.24i	0.125529	+	0.0724744i
$983$	−1475.39	+	851.817i	−0.0478714	+	0.0276386i	−0.523745	−	0.851875i	$-0.675465\pi$
$983$	−1475.39	+	851.817i	−0.0478714	+	0.0276386i	0.475873	+	0.879514i	$0.342132\pi$
$984$	4921.75	+	8524.72i	0.159451	+	0.276177i
$985$	5742.06	−	34268.4i	0.185743	−	1.10851i
$986$	−36244.0			−1.17063
$987$		0			0
$988$			15.3718i			0.000494980i
$989$	12455.1	−	21572.8i	0.400453	−	0.693605i
$990$	49594.6	+	40900.4i	1.59214	+	1.31303i
$991$	−6370.13	−	11033.4i	−0.204192	−	0.353670i	0.745683	−	0.666301i	$-0.232123\pi$
$991$	−6370.13	−	11033.4i	−0.204192	−	0.353670i	−0.949875	+	0.312630i	$0.898790\pi$
$992$	1008.41	+	582.205i	0.0322752	+	0.0186341i
$993$			29073.6i			0.929126i
$994$		0			0
$995$	8396.32	+	22471.5i	0.267519	+	0.715975i
$996$	48.8645	−	84.6358i	0.00155455	−	0.00269256i
$997$	14384.4	−	8304.81i	0.456928	−	0.263808i	−0.253824	−	0.967251i	$-0.581688\pi$
$997$	14384.4	−	8304.81i	0.456928	−	0.263808i	0.710752	+	0.703443i	$0.248355\pi$
$998$	20357.6	−	11753.4i	0.645699	−	0.372794i
$999$	−30189.7	+	52290.1i	−0.956116	+	1.65604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.j.e.79.8		20
5.4	even	2	inner	245.4.j.e.79.3		20
7.2	even	3		35.4.b.a.29.3	✓	10
7.3	odd	6		245.4.j.f.214.3		20
7.4	even	3	inner	245.4.j.e.214.3		20
7.5	odd	6		245.4.b.d.99.3		10
7.6	odd	2		245.4.j.f.79.8		20
21.2	odd	6		315.4.d.c.64.8		10
28.23	odd	6		560.4.g.f.449.1		10
35.2	odd	12		175.4.a.j.1.4		5
35.4	even	6	inner	245.4.j.e.214.8		20
35.9	even	6		35.4.b.a.29.8	yes	10
35.12	even	12		1225.4.a.bh.1.4		5
35.19	odd	6		245.4.b.d.99.8		10
35.23	odd	12		175.4.a.i.1.2		5
35.24	odd	6		245.4.j.f.214.8		20
35.33	even	12		1225.4.a.be.1.2		5
35.34	odd	2		245.4.j.f.79.3		20
105.2	even	12		1575.4.a.bn.1.2		5
105.23	even	12		1575.4.a.bq.1.4		5
105.44	odd	6		315.4.d.c.64.3		10
140.79	odd	6		560.4.g.f.449.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.b.a.29.3	✓	10	7.2	even	3
35.4.b.a.29.8	yes	10	35.9	even	6
175.4.a.i.1.2		5	35.23	odd	12
175.4.a.j.1.4		5	35.2	odd	12
245.4.b.d.99.3		10	7.5	odd	6
245.4.b.d.99.8		10	35.19	odd	6
245.4.j.e.79.3		20	5.4	even	2	inner
245.4.j.e.79.8		20	1.1	even	1	trivial
245.4.j.e.214.3		20	7.4	even	3	inner
245.4.j.e.214.8		20	35.4	even	6	inner
245.4.j.f.79.3		20	35.34	odd	2
245.4.j.f.79.8		20	7.6	odd	2
245.4.j.f.214.3		20	7.3	odd	6
245.4.j.f.214.8		20	35.24	odd	6
315.4.d.c.64.3		10	105.44	odd	6
315.4.d.c.64.8		10	21.2	odd	6
560.4.g.f.449.1		10	28.23	odd	6
560.4.g.f.449.10		10	140.79	odd	6
1225.4.a.be.1.2		5	35.33	even	12
1225.4.a.bh.1.4		5	35.12	even	12
1575.4.a.bn.1.2		5	105.2	even	12
1575.4.a.bq.1.4		5	105.23	even	12

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} +(-11.0266 - 1.84763i) q^{5} +25.6601 q^{6} -22.4110i q^{8} +(26.8973 - 46.5874i) q^{9} +(-24.6236 - 20.3069i) 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} +(118.173 + 40.7463i) q^{25} +(-5.65768 + 9.79938i) q^{26} -240.845i q^{27} +245.676 q^{29} +(-282.944 - 47.4104i) 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} +(-41.4073 + 247.118i) q^{40} -48.8649 q^{41} -143.612i q^{43} +(2.79960 - 4.84905i) q^{44} +(-382.662 + 464.005i) 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} +(-11.5946 - 9.56202i) q^{60} +(-23.7565 + 41.1475i) q^{61} +491.228i q^{62} -502.074 q^{64} +(7.32347 - 43.7062i) 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} +(1103.02 - 213.919i) q^{75} +3.87813 q^{76} +101.709i q^{78} +(236.820 - 410.184i) q^{79} +(-463.609 + 562.159i) 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} +(-184.467 + 223.679i) 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

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