LMFDB - Embedded newform 315.3.o.b.127.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(127,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("315.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.o (of order $4$, degree $2$, 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:	$8.58312832735$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.10
Character	$\chi$	$=$	315.127
Dual form			315.3.o.b.253.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36784 + 1.36784i) q^{2} -0.258033i q^{4} +(-3.39663 - 3.66919i) q^{5} +(1.87083 + 1.87083i) q^{7} +(5.82430 - 5.82430i) q^{8} +O(q^{10})$	\(q+(1.36784 + 1.36784i) q^{2} -0.258033i q^{4} +(-3.39663 - 3.66919i) q^{5} +(1.87083 + 1.87083i) q^{7} +(5.82430 - 5.82430i) q^{8} +(0.372817 - 9.66489i) q^{10} -17.6130 q^{11} +(12.1245 - 12.1245i) q^{13} +5.11799i q^{14} +14.9013 q^{16} +(-13.8772 - 13.8772i) q^{17} -18.3068i q^{19} +(-0.946770 + 0.876441i) q^{20} +(-24.0917 - 24.0917i) q^{22} +(26.3956 - 26.3956i) q^{23} +(-1.92585 + 24.9257i) q^{25} +33.1686 q^{26} +(0.482735 - 0.482735i) q^{28} +2.87815i q^{29} +16.1149 q^{31} +(-2.91465 - 2.91465i) q^{32} -37.9637i q^{34} +(0.509912 - 13.2189i) q^{35} +(2.52440 + 2.52440i) q^{37} +(25.0408 - 25.0408i) q^{38} +(-41.1534 - 1.58747i) q^{40} +1.89828 q^{41} +(-42.5974 + 42.5974i) q^{43} +4.54472i q^{44} +72.2098 q^{46} +(57.7457 + 57.7457i) q^{47} +7.00000i q^{49} +(-36.7286 + 31.4601i) q^{50} +(-3.12851 - 3.12851i) q^{52} +(-66.5567 + 66.5567i) q^{53} +(59.8247 + 64.6253i) q^{55} +21.7925 q^{56} +(-3.93685 + 3.93685i) q^{58} -16.4673i q^{59} -7.37026 q^{61} +(22.0426 + 22.0426i) q^{62} -67.5787i q^{64} +(-85.6692 - 3.30464i) q^{65} +(-27.2024 - 27.2024i) q^{67} +(-3.58078 + 3.58078i) q^{68} +(18.7788 - 17.3839i) q^{70} +79.5984 q^{71} +(63.3051 - 63.3051i) q^{73} +6.90594i q^{74} -4.72376 q^{76} +(-32.9508 - 32.9508i) q^{77} +2.48684i q^{79} +(-50.6141 - 54.6756i) q^{80} +(2.59655 + 2.59655i) q^{82} +(29.0421 - 29.0421i) q^{83} +(-3.78237 + 98.0540i) q^{85} -116.533 q^{86} +(-102.583 + 102.583i) q^{88} -29.3345i q^{89} +45.3656 q^{91} +(-6.81092 - 6.81092i) q^{92} +157.974i q^{94} +(-67.1711 + 62.1814i) q^{95} +(-89.1223 - 89.1223i) q^{97} +(-9.57487 + 9.57487i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8}+O(q^{10}) $ 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8	$ 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8} - 40 q^{10} + 64 q^{13} - 184 q^{16} - 24 q^{17} - 72 q^{20} + 8 q^{22} - 8 q^{23} - 136 q^{25} + 80 q^{26} + 96 q^{31} - 56 q^{32} + 8 q^{37} - 56 q^{38} + 232 q^{40} - 320 q^{41} - 112 q^{43} + 320 q^{46} - 64 q^{47} + 256 q^{50} + 96 q^{52} + 72 q^{53} - 80 q^{55} + 336 q^{56} - 512 q^{58} - 496 q^{61} + 776 q^{62} - 312 q^{65} - 192 q^{67} - 568 q^{68} + 112 q^{70} + 144 q^{71} + 224 q^{73} + 416 q^{76} - 112 q^{77} + 528 q^{80} + 352 q^{82} + 32 q^{83} + 24 q^{85} - 240 q^{86} + 216 q^{88} - 1304 q^{92} - 376 q^{95} - 816 q^{97} + 56 q^{98}+O(q^{100}) $ 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8 - 40 * q^10 + 64 * q^13 - 184 * q^16 - 24 * q^17 - 72 * q^20 + 8 * q^22 - 8 * q^23 - 136 * q^25 + 80 * q^26 + 96 * q^31 - 56 * q^32 + 8 * q^37 - 56 * q^38 + 232 * q^40 - 320 * q^41 - 112 * q^43 + 320 * q^46 - 64 * q^47 + 256 * q^50 + 96 * q^52 + 72 * q^53 - 80 * q^55 + 336 * q^56 - 512 * q^58 - 496 * q^61 + 776 * q^62 - 312 * q^65 - 192 * q^67 - 568 * q^68 + 112 * q^70 + 144 * q^71 + 224 * q^73 + 416 * q^76 - 112 * q^77 + 528 * q^80 + 352 * q^82 + 32 * q^83 + 24 * q^85 - 240 * q^86 + 216 * q^88 - 1304 * q^92 - 376 * q^95 - 816 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	1.36784	+	1.36784i	0.683920	+	0.683920i	0.960881	−	0.276961i	$-0.0893274\pi$
$2$	1.36784	+	1.36784i	0.683920	+	0.683920i	−0.276961	+	0.960881i	$0.589327\pi$
$3$		0			0
$3$		0			0
$4$		−	0.258033i		−	0.0645082i
$5$	−3.39663	−	3.66919i	−0.679325	−	0.733837i
$5$	−3.39663	−	3.66919i	−0.679325	−	0.733837i
$6$		0			0
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$8$	5.82430	−	5.82430i	0.728038	−	0.728038i
$9$		0			0
$10$	0.372817	−	9.66489i	0.0372817	−	0.966489i
$11$	−17.6130			−1.60118			−0.800589	−	0.599213i	$-0.795480\pi$
$11$	−17.6130			−1.60118			−0.800589	+	0.599213i	$0.795480\pi$
$12$		0			0
$13$	12.1245	−	12.1245i	0.932651	−	0.932651i	−0.0652196	−	0.997871i	$-0.520775\pi$
$13$	12.1245	−	12.1245i	0.932651	−	0.932651i	0.997871	+	0.0652196i	$0.0207748\pi$
$14$			5.11799i			0.365570i
$15$		0			0
$16$	14.9013			0.931331
$17$	−13.8772	−	13.8772i	−0.816309	−	0.816309i	0.169262	−	0.985571i	$-0.445862\pi$
$17$	−13.8772	−	13.8772i	−0.816309	−	0.816309i	−0.985571	+	0.169262i	$0.945862\pi$
$18$		0			0
$19$		−	18.3068i		−	0.963516i	−0.876304	−	0.481758i	$-0.839998\pi$
$19$		−	18.3068i		−	0.963516i	0.876304	−	0.481758i	$-0.160002\pi$
$20$	−0.946770	+	0.876441i	−0.0473385	+	0.0438220i
$21$		0			0
$22$	−24.0917	−	24.0917i	−1.09508	−	1.09508i
$23$	26.3956	−	26.3956i	1.14763	−	1.14763i	0.160617	−	0.987017i	$-0.448652\pi$
$23$	26.3956	−	26.3956i	1.14763	−	1.14763i	0.987017	−	0.160617i	$-0.0513483\pi$
$24$		0			0
$25$	−1.92585	+	24.9257i	−0.0770341	+	0.997028i
$26$	33.1686			1.27572
$27$		0			0
$28$	0.482735	−	0.482735i	0.0172405	−	0.0172405i
$29$			2.87815i			0.0992467i	0.998768	+	0.0496234i	$0.0158021\pi$
$29$			2.87815i			0.0992467i	−0.998768	+	0.0496234i	$0.984198\pi$
$30$		0			0
$31$	16.1149			0.519836			0.259918	−	0.965631i	$-0.416304\pi$
$31$	16.1149			0.519836			0.259918	+	0.965631i	$0.416304\pi$
$32$	−2.91465	−	2.91465i	−0.0910828	−	0.0910828i
$33$		0			0
$34$		−	37.9637i		−	1.11658i
$35$	0.509912	−	13.2189i	0.0145689	−	0.377684i
$36$		0			0
$37$	2.52440	+	2.52440i	0.0682270	+	0.0682270i	0.740397	−	0.672170i	$-0.234638\pi$
$37$	2.52440	+	2.52440i	0.0682270	+	0.0682270i	−0.672170	+	0.740397i	$0.734638\pi$
$38$	25.0408	−	25.0408i	0.658968	−	0.658968i
$39$		0			0
$40$	−41.1534	−	1.58747i	−1.02884	−	0.0396867i
$41$	1.89828			0.0462996			0.0231498	−	0.999732i	$-0.492631\pi$
$41$	1.89828			0.0462996			0.0231498	+	0.999732i	$0.492631\pi$
$42$		0			0
$43$	−42.5974	+	42.5974i	−0.990637	+	0.990637i	−0.999957	−	0.00931954i	$-0.997033\pi$
$43$	−42.5974	+	42.5974i	−0.990637	+	0.990637i	0.00931954	+	0.999957i	$0.497033\pi$
$44$			4.54472i			0.103289i
$45$		0			0
$46$	72.2098			1.56978
$47$	57.7457	+	57.7457i	1.22863	+	1.22863i	0.964482	+	0.264150i	$0.0850913\pi$
$47$	57.7457	+	57.7457i	1.22863	+	1.22863i	0.264150	+	0.964482i	$0.414909\pi$
$48$		0			0
$49$			7.00000i			0.142857i
$50$	−36.7286	+	31.4601i	−0.734572	+	0.629202i
$51$		0			0
$52$	−3.12851	−	3.12851i	−0.0601636	−	0.0601636i
$53$	−66.5567	+	66.5567i	−1.25579	+	1.25579i	−0.302701	+	0.953086i	$0.597888\pi$
$53$	−66.5567	+	66.5567i	−1.25579	+	1.25579i	−0.953086	+	0.302701i	$0.902112\pi$
$54$		0			0
$55$	59.8247	+	64.6253i	1.08772	+	1.17500i
$56$	21.7925			0.389153
$57$		0			0
$58$	−3.93685	+	3.93685i	−0.0678768	+	0.0678768i
$59$		−	16.4673i		−	0.279107i	−0.990215	−	0.139554i	$-0.955433\pi$
$59$		−	16.4673i		−	0.279107i	0.990215	−	0.139554i	$-0.0445668\pi$
$60$		0			0
$61$	−7.37026			−0.120824			−0.0604119	−	0.998174i	$-0.519241\pi$
$61$	−7.37026			−0.120824			−0.0604119	+	0.998174i	$0.519241\pi$
$62$	22.0426	+	22.0426i	0.355526	+	0.355526i
$63$		0			0
$64$		−	67.5787i		−	1.05592i
$65$	−85.6692	−	3.30464i	−1.31799	−	0.0508406i
$66$		0			0
$67$	−27.2024	−	27.2024i	−0.406006	−	0.406006i	0.474337	−	0.880343i	$-0.342688\pi$
$67$	−27.2024	−	27.2024i	−0.406006	−	0.406006i	−0.880343	+	0.474337i	$0.842688\pi$
$68$	−3.58078	+	3.58078i	−0.0526586	+	0.0526586i
$69$		0			0
$70$	18.7788	−	17.3839i	0.268269	−	0.248341i
$71$	79.5984			1.12110			0.560552	−	0.828119i	$-0.310589\pi$
$71$	79.5984			1.12110			0.560552	+	0.828119i	$0.310589\pi$
$72$		0			0
$73$	63.3051	−	63.3051i	0.867193	−	0.867193i	−0.124968	−	0.992161i	$-0.539883\pi$
$73$	63.3051	−	63.3051i	0.867193	−	0.867193i	0.992161	+	0.124968i	$0.0398827\pi$
$74$			6.90594i			0.0933235i
$75$		0			0
$76$	−4.72376			−0.0621547
$77$	−32.9508	−	32.9508i	−0.427933	−	0.427933i
$78$		0			0
$79$			2.48684i			0.0314790i	0.999876	+	0.0157395i	$0.00501024\pi$
$79$			2.48684i			0.0314790i	−0.999876	+	0.0157395i	$0.994990\pi$
$80$	−50.6141	−	54.6756i	−0.632676	−	0.683445i
$81$		0			0
$82$	2.59655	+	2.59655i	0.0316652	+	0.0316652i
$83$	29.0421	−	29.0421i	0.349905	−	0.349905i	−0.510169	−	0.860074i	$-0.670417\pi$
$83$	29.0421	−	29.0421i	0.349905	−	0.349905i	0.860074	+	0.510169i	$0.170417\pi$
$84$		0			0
$85$	−3.78237	+	98.0540i	−0.0444985	+	1.15358i
$86$	−116.533			−1.35503
$87$		0			0
$88$	−102.583	+	102.583i	−1.16572	+	1.16572i
$89$		−	29.3345i		−	0.329601i	−0.986327	−	0.164800i	$-0.947302\pi$
$89$		−	29.3345i		−	0.329601i	0.986327	−	0.164800i	$-0.0526980\pi$
$90$		0			0
$91$	45.3656			0.498523
$92$	−6.81092	−	6.81092i	−0.0740318	−	0.0740318i
$93$		0			0
$94$			157.974i			1.68057i
$95$	−67.1711	+	62.1814i	−0.707064	+	0.654541i
$96$		0			0
$97$	−89.1223	−	89.1223i	−0.918786	−	0.918786i	0.0781549	−	0.996941i	$-0.475097\pi$
$97$	−89.1223	−	89.1223i	−0.918786	−	0.918786i	−0.996941	+	0.0781549i	$0.975097\pi$
$98$	−9.57487	+	9.57487i	−0.0977028	+	0.0977028i
$99$		0			0
$100$	6.43165	+	0.496933i	0.0643165	+	0.00496933i
$101$	87.3306			0.864660			0.432330	−	0.901716i	$-0.357692\pi$
$101$	87.3306			0.864660			0.432330	+	0.901716i	$0.357692\pi$
$102$		0			0
$103$	36.7417	−	36.7417i	0.356715	−	0.356715i	−0.505885	−	0.862601i	$-0.668834\pi$
$103$	36.7417	−	36.7417i	0.356715	−	0.356715i	0.862601	+	0.505885i	$0.168834\pi$
$104$		−	141.233i		−	1.35801i
$105$		0			0
$106$	−182.078			−1.71771
$107$	91.9855	+	91.9855i	0.859677	+	0.859677i	0.991300	−	0.131622i	$-0.0420187\pi$
$107$	91.9855	+	91.9855i	0.859677	+	0.859677i	−0.131622	+	0.991300i	$0.542019\pi$
$108$		0			0
$109$			144.628i			1.32686i	0.748237	+	0.663432i	$0.230901\pi$
$109$			144.628i			1.32686i	−0.748237	+	0.663432i	$0.769099\pi$
$110$	−6.56642	+	170.227i	−0.0596947	+	1.54752i
$111$		0			0
$112$	27.8778	+	27.8778i	0.248909	+	0.248909i
$113$	−28.6801	+	28.6801i	−0.253806	+	0.253806i	−0.822529	−	0.568723i	$-0.807438\pi$
$113$	−28.6801	+	28.6801i	−0.253806	+	0.253806i	0.568723	+	0.822529i	$0.307438\pi$
$114$		0			0
$115$	−186.506	−	7.19436i	−1.62179	−	0.0625597i
$116$	0.742658			0.00640222
$117$		0			0
$118$	22.5247	−	22.5247i	0.190887	−	0.190887i
$119$		−	51.9239i		−	0.436335i
$120$		0			0
$121$	189.217			1.56377
$122$	−10.0813	−	10.0813i	−0.0826338	−	0.0826338i
$123$		0			0
$124$		−	4.15818i		−	0.0335337i
$125$	97.9985	−	77.5970i	0.783988	−	0.620776i
$126$		0			0
$127$	12.2062	+	12.2062i	0.0961116	+	0.0961116i	0.753528	−	0.657416i	$-0.228351\pi$
$127$	12.2062	+	12.2062i	0.0961116	+	0.0961116i	−0.657416	+	0.753528i	$0.728351\pi$
$128$	80.7782	−	80.7782i	0.631080	−	0.631080i
$129$		0			0
$130$	−112.661	−	121.702i	−0.866627	−	0.936169i
$131$	23.2249			0.177290			0.0886448	−	0.996063i	$-0.471746\pi$
$131$	23.2249			0.177290			0.0886448	+	0.996063i	$0.471746\pi$
$132$		0			0
$133$	34.2489	−	34.2489i	0.257511	−	0.257511i
$134$		−	74.4170i		−	0.555351i
$135$		0			0
$136$	−161.651			−1.18861
$137$	17.2588	+	17.2588i	0.125977	+	0.125977i	0.767284	−	0.641307i	$-0.221608\pi$
$137$	17.2588	+	17.2588i	0.125977	+	0.125977i	−0.641307	+	0.767284i	$0.721608\pi$
$138$		0			0
$139$		−	29.4799i		−	0.212085i	−0.994362	−	0.106043i	$-0.966182\pi$
$139$		−	29.4799i		−	0.212085i	0.994362	−	0.106043i	$-0.0338180\pi$
$140$	−3.41092	−	0.131574i	−0.0243637	−	0.000939814i
$141$		0			0
$142$	108.878	+	108.878i	0.766745	+	0.766745i
$143$	−213.548	+	213.548i	−1.49334	+	1.49334i
$144$		0			0
$145$	10.5605	−	9.77602i	0.0728309	−	0.0674208i
$146$	173.182			1.18618
$147$		0			0
$148$	0.651377	−	0.651377i	0.00440120	−	0.00440120i
$149$			14.3848i			0.0965421i	0.998834	+	0.0482710i	$0.0153711\pi$
$149$			14.3848i			0.0965421i	−0.998834	+	0.0482710i	$0.984629\pi$
$150$		0			0
$151$	15.3569			0.101701			0.0508506	−	0.998706i	$-0.483807\pi$
$151$	15.3569			0.101701			0.0508506	+	0.998706i	$0.483807\pi$
$152$	−106.624	−	106.624i	−0.701476	−	0.701476i
$153$		0			0
$154$		−	90.1429i		−	0.585344i
$155$	−54.7364	−	59.1286i	−0.353138	−	0.381475i
$156$		0			0
$157$	63.2769	+	63.2769i	0.403037	+	0.403037i	0.879302	−	0.476265i	$-0.158010\pi$
$157$	63.2769	+	63.2769i	0.403037	+	0.403037i	−0.476265	+	0.879302i	$0.658010\pi$
$158$	−3.40160	+	3.40160i	−0.0215291	+	0.0215291i
$159$		0			0
$160$	−0.794415	+	20.5944i	−0.00496509	+	0.128715i
$161$	98.7632			0.613436
$162$		0			0
$163$	−121.254	+	121.254i	−0.743890	+	0.743890i	−0.973324	−	0.229434i	$-0.926312\pi$
$163$	−121.254	+	121.254i	−0.743890	+	0.743890i	0.229434	+	0.973324i	$0.426312\pi$
$164$		−	0.489819i		−	0.00298670i
$165$		0			0
$166$	79.4498			0.478613
$167$	51.2223	+	51.2223i	0.306720	+	0.306720i	0.843636	−	0.536916i	$-0.180411\pi$
$167$	51.2223	+	51.2223i	0.306720	+	0.306720i	−0.536916	+	0.843636i	$0.680411\pi$
$168$		0			0
$169$		−	125.005i		−	0.739677i
$170$	−139.296	+	128.948i	−0.819387	+	0.758520i
$171$		0			0
$172$	10.9915	+	10.9915i	0.0639042	+	0.0639042i
$173$	−78.5418	+	78.5418i	−0.453999	+	0.453999i	−0.896679	−	0.442681i	$-0.854028\pi$
$173$	−78.5418	+	78.5418i	−0.453999	+	0.453999i	0.442681	+	0.896679i	$0.354028\pi$
$174$		0			0
$175$	−50.2347	+	43.0288i	−0.287055	+	0.245879i
$176$	−262.456			−1.49123
$177$		0			0
$178$	40.1248	−	40.1248i	0.225420	−	0.225420i
$179$		−	162.375i		−	0.907125i	−0.891224	−	0.453563i	$-0.850153\pi$
$179$		−	162.375i		−	0.907125i	0.891224	−	0.453563i	$-0.149847\pi$
$180$		0			0
$181$	257.224			1.42113			0.710564	−	0.703633i	$-0.248440\pi$
$181$	257.224			1.42113			0.710564	+	0.703633i	$0.248440\pi$
$182$	62.0528	+	62.0528i	0.340950	+	0.340950i
$183$		0			0
$184$		−	307.472i		−	1.67104i
$185$	0.688048	−	17.8369i	0.00371918	−	0.0964158i
$186$		0			0
$187$	244.420	+	244.420i	1.30706	+	1.30706i
$188$	14.9003	−	14.9003i	0.0792568	−	0.0792568i
$189$		0			0
$190$	−176.933	−	6.82510i	−0.931228	−	0.0359216i
$191$	334.101			1.74922			0.874610	−	0.484827i	$-0.161117\pi$
$191$	334.101			1.74922			0.874610	+	0.484827i	$0.161117\pi$
$192$		0			0
$193$	19.9582	−	19.9582i	0.103410	−	0.103410i	−0.653509	−	0.756919i	$-0.726704\pi$
$193$	19.9582	−	19.9582i	0.103410	−	0.103410i	0.756919	+	0.653509i	$0.226704\pi$
$194$		−	243.810i		−	1.25675i
$195$		0			0
$196$	1.80623			0.00921545
$197$	−36.5252	−	36.5252i	−0.185407	−	0.185407i	0.608300	−	0.793707i	$-0.291852\pi$
$197$	−36.5252	−	36.5252i	−0.185407	−	0.185407i	−0.793707	+	0.608300i	$0.791852\pi$
$198$		0			0
$199$		−	187.619i		−	0.942810i	−0.881917	−	0.471405i	$-0.843747\pi$
$199$		−	187.619i		−	0.942810i	0.881917	−	0.471405i	$-0.156253\pi$
$200$	133.958	+	156.392i	0.669791	+	0.781958i
$201$		0			0
$202$	119.454	+	119.454i	0.591358	+	0.591358i
$203$	−5.38453	+	5.38453i	−0.0265248	+	0.0265248i
$204$		0			0
$205$	−6.44776	−	6.96516i	−0.0314525	−	0.0339764i
$206$	100.513			0.487929
$207$		0			0
$208$	180.670	−	180.670i	0.868607	−	0.868607i
$209$			322.437i			1.54276i
$210$		0			0
$211$	−73.6409			−0.349009			−0.174505	−	0.984656i	$-0.555832\pi$
$211$	−73.6409			−0.349009			−0.174505	+	0.984656i	$0.555832\pi$
$212$	17.1738	+	17.1738i	0.0810085	+	0.0810085i
$213$		0			0
$214$			251.643i			1.17590i
$215$	300.985	+	11.6103i	1.39993	+	0.0540015i
$216$		0			0
$217$	30.1483	+	30.1483i	0.138932	+	0.138932i
$218$	−197.828	+	197.828i	−0.907468	+	0.907468i
$219$		0			0
$220$	16.6754	−	15.4367i	0.0757974	−	0.0701669i
$221$	−336.509			−1.52266
$222$		0			0
$223$	258.221	−	258.221i	1.15794	−	1.15794i	0.173025	−	0.984917i	$-0.444646\pi$
$223$	258.221	−	258.221i	1.15794	−	1.15794i	0.984917	−	0.173025i	$-0.0553542\pi$
$224$		−	10.9056i		−	0.0486858i
$225$		0			0
$226$	−78.4596			−0.347166
$227$	9.72923	+	9.72923i	0.0428601	+	0.0428601i	0.728212	−	0.685352i	$-0.240352\pi$
$227$	9.72923	+	9.72923i	0.0428601	+	0.0428601i	−0.685352	+	0.728212i	$0.740352\pi$
$228$		0			0
$229$		−	108.047i		−	0.471822i	−0.971775	−	0.235911i	$-0.924193\pi$
$229$		−	108.047i		−	0.471822i	0.971775	−	0.235911i	$-0.0758074\pi$
$230$	−245.270	−	264.951i	−1.06639	−	1.15196i
$231$		0			0
$232$	16.7632	+	16.7632i	0.0722554	+	0.0722554i
$233$	2.47323	−	2.47323i	0.0106147	−	0.0106147i	−0.701779	−	0.712394i	$-0.747611\pi$
$233$	2.47323	−	2.47323i	0.0106147	−	0.0106147i	0.712394	+	0.701779i	$0.247611\pi$
$234$		0			0
$235$	15.7391	−	408.020i	0.0669750	−	1.73626i
$236$	−4.24911			−0.0180047
$237$		0			0
$238$	71.0236	−	71.0236i	0.298418	−	0.298418i
$239$		−	230.974i		−	0.966417i	−0.875505	−	0.483209i	$-0.839471\pi$
$239$		−	230.974i		−	0.966417i	0.875505	−	0.483209i	$-0.160529\pi$
$240$		0			0
$241$	−280.404			−1.16350			−0.581752	−	0.813366i	$-0.697633\pi$
$241$	−280.404			−1.16350			−0.581752	+	0.813366i	$0.697633\pi$
$242$	258.818	+	258.818i	1.06950	+	1.06950i
$243$		0			0
$244$			1.90177i			0.00779413i
$245$	25.6843	−	23.7764i	0.104834	−	0.0970465i
$246$		0			0
$247$	−221.960	−	221.960i	−0.898625	−	0.898625i
$248$	93.8582	−	93.8582i	0.378460	−	0.378460i
$249$		0			0
$250$	240.186	+	27.9059i	0.960746	+	0.111624i
$251$	−53.4737			−0.213043			−0.106521	−	0.994310i	$-0.533971\pi$
$251$	−53.4737			−0.213043			−0.106521	+	0.994310i	$0.533971\pi$
$252$		0			0
$253$	−464.904	+	464.904i	−1.83757	+	1.83757i
$254$			33.3921i			0.131465i
$255$		0			0
$256$	−49.3317			−0.192702
$257$	−78.9368	−	78.9368i	−0.307147	−	0.307147i	0.536655	−	0.843802i	$-0.319688\pi$
$257$	−78.9368	−	78.9368i	−0.307147	−	0.307147i	−0.843802	+	0.536655i	$0.819688\pi$
$258$		0			0
$259$			9.44543i			0.0364688i
$260$	−0.852705	+	22.1055i	−0.00327963	+	0.0850210i
$261$		0			0
$262$	31.7680	+	31.7680i	0.121252	+	0.121252i
$263$	323.863	−	323.863i	1.23142	−	1.23142i	0.268002	−	0.963418i	$-0.413637\pi$
$263$	323.863	−	323.863i	1.23142	−	1.23142i	0.963418	−	0.268002i	$-0.0863632\pi$
$264$		0			0
$265$	470.277	+	18.1406i	1.77463	+	0.0684553i
$266$	93.6940			0.352233
$267$		0			0
$268$	−7.01911	+	7.01911i	−0.0261907	+	0.0261907i
$269$		−	119.052i		−	0.442573i	−0.975209	−	0.221286i	$-0.928974\pi$
$269$		−	119.052i		−	0.442573i	0.975209	−	0.221286i	$-0.0710256\pi$
$270$		0			0
$271$	380.174			1.40286			0.701429	−	0.712740i	$-0.252546\pi$
$271$	380.174			1.40286			0.701429	+	0.712740i	$0.252546\pi$
$272$	−206.789	−	206.789i	−0.760253	−	0.760253i
$273$		0			0
$274$			47.2146i			0.172316i
$275$	33.9200	−	439.016i	0.123345	−	1.59642i
$276$		0			0
$277$	−374.455	−	374.455i	−1.35182	−	1.35182i	−0.883624	−	0.468198i	$-0.844903\pi$
$277$	−374.455	−	374.455i	−1.35182	−	1.35182i	−0.468198	−	0.883624i	$-0.655097\pi$
$278$	40.3237	−	40.3237i	0.145049	−	0.145049i
$279$		0			0
$280$	−74.0212	−	79.9609i	−0.264361	−	0.285575i
$281$	300.844			1.07062			0.535309	−	0.844656i	$-0.320195\pi$
$281$	300.844			1.07062			0.535309	+	0.844656i	$0.320195\pi$
$282$		0			0
$283$	−137.166	+	137.166i	−0.484686	+	0.484686i	−0.906624	−	0.421938i	$-0.861350\pi$
$283$	−137.166	+	137.166i	−0.484686	+	0.484686i	0.421938	+	0.906624i	$0.361350\pi$
$284$		−	20.5390i		−	0.0723204i
$285$		0			0
$286$	−584.198			−2.04265
$287$	3.55136	+	3.55136i	0.0123741	+	0.0123741i
$288$		0			0
$289$			96.1561i			0.332720i
$290$	27.8171	+	1.07303i	0.0959209	+	0.00370009i
$291$		0			0
$292$	−16.3348	−	16.3348i	−0.0559411	−	0.0559411i
$293$	−193.498	+	193.498i	−0.660403	+	0.660403i	−0.955475	−	0.295072i	$-0.904656\pi$
$293$	−193.498	+	193.498i	−0.660403	+	0.660403i	0.295072	+	0.955475i	$0.404656\pi$
$294$		0			0
$295$	−60.4217	+	55.9334i	−0.204819	+	0.189605i
$296$	29.4057			0.0993436
$297$		0			0
$298$	−19.6761	+	19.6761i	−0.0660270	+	0.0660270i
$299$		−	640.065i		−	2.14068i
$300$		0			0
$301$	−159.385			−0.529518
$302$	21.0057	+	21.0057i	0.0695554	+	0.0695554i
$303$		0			0
$304$		−	272.795i		−	0.897352i
$305$	25.0340	+	27.0428i	0.0820787	+	0.0886650i
$306$		0			0
$307$	122.528	+	122.528i	0.399115	+	0.399115i	0.877921	−	0.478806i	$-0.158930\pi$
$307$	122.528	+	122.528i	0.399115	+	0.399115i	−0.478806	+	0.877921i	$0.658930\pi$
$308$	−8.50240	+	8.50240i	−0.0276052	+	0.0276052i
$309$		0			0
$310$	6.00792	−	155.749i	0.0193804	−	0.502416i
$311$	−118.050			−0.379582			−0.189791	−	0.981825i	$-0.560781\pi$
$311$	−118.050			−0.379582			−0.189791	+	0.981825i	$0.560781\pi$
$312$		0			0
$313$	−289.482	+	289.482i	−0.924861	+	0.924861i	−0.997368	−	0.0725069i	$-0.976900\pi$
$313$	−289.482	+	289.482i	−0.924861	+	0.924861i	0.0725069	+	0.997368i	$0.476900\pi$
$314$			173.105i			0.551290i
$315$		0			0
$316$	0.641686			0.00203065
$317$	292.255	+	292.255i	0.921942	+	0.921942i	0.997167	−	0.0752250i	$-0.0239675\pi$
$317$	292.255	+	292.255i	0.921942	+	0.921942i	−0.0752250	+	0.997167i	$0.523968\pi$
$318$		0			0
$319$		−	50.6928i		−	0.158912i
$320$	−247.959	+	229.540i	−0.774871	+	0.717311i
$321$		0			0
$322$	135.092	+	135.092i	0.419541	+	0.419541i
$323$	−254.048	+	254.048i	−0.786527	+	0.786527i
$324$		0			0
$325$	278.861	+	325.561i	0.858034	+	1.00173i
$326$	−331.712			−1.01752
$327$		0			0
$328$	11.0562	−	11.0562i	0.0337079	−	0.0337079i
$329$			216.065i			0.656731i
$330$		0			0
$331$	580.718			1.75443			0.877217	−	0.480093i	$-0.159397\pi$
$331$	580.718			1.75443			0.877217	+	0.480093i	$0.159397\pi$
$332$	−7.49381	−	7.49381i	−0.0225717	−	0.0225717i
$333$		0			0
$334$			140.128i			0.419544i
$335$	−7.41427	+	192.207i	−0.0221321	+	0.573752i
$336$		0			0
$337$	253.637	+	253.637i	0.752631	+	0.752631i	0.974970	−	0.222339i	$-0.0713690\pi$
$337$	253.637	+	253.637i	0.752631	+	0.752631i	−0.222339	+	0.974970i	$0.571369\pi$
$338$	170.987	−	170.987i	0.505880	−	0.505880i
$339$		0			0
$340$	25.3012	+	0.975976i	0.0744152	+	0.00287052i
$341$	−283.832			−0.832351
$342$		0			0
$343$	−13.0958	+	13.0958i	−0.0381802	+	0.0381802i
$344$			496.200i			1.44244i
$345$		0			0
$346$	−214.865			−0.620997
$347$	−60.2580	−	60.2580i	−0.173654	−	0.173654i	0.614929	−	0.788583i	$-0.289185\pi$
$347$	−60.2580	−	60.2580i	−0.173654	−	0.173654i	−0.788583	+	0.614929i	$0.789185\pi$
$348$		0			0
$349$			348.191i			0.997681i	0.866694	+	0.498841i	$0.166241\pi$
$349$			348.191i			0.997681i	−0.866694	+	0.498841i	$0.833759\pi$
$350$	−127.569	−	9.85649i	−0.364484	−	0.0281614i
$351$		0			0
$352$	51.3356	+	51.3356i	0.145840	+	0.145840i
$353$	−113.128	+	113.128i	−0.320476	+	0.320476i	−0.848950	−	0.528474i	$-0.822765\pi$
$353$	−113.128	+	113.128i	−0.320476	+	0.320476i	0.528474	+	0.848950i	$0.322765\pi$
$354$		0			0
$355$	−270.366	−	292.061i	−0.761595	−	0.822708i
$356$	−7.56925			−0.0212619
$357$		0			0
$358$	222.103	−	222.103i	0.620401	−	0.620401i
$359$		−	105.651i		−	0.294293i	−0.989115	−	0.147147i	$-0.952991\pi$
$359$		−	105.651i		−	0.294293i	0.989115	−	0.147147i	$-0.0470089\pi$
$360$		0			0
$361$	25.8608			0.0716365
$362$	351.841	+	351.841i	0.971937	+	0.971937i
$363$		0			0
$364$		−	11.7058i		−	0.0321588i
$365$	−447.302	−	17.2544i	−1.22548	−	0.0472723i
$366$		0			0
$367$	−230.168	−	230.168i	−0.627161	−	0.627161i	0.320191	−	0.947353i	$-0.396253\pi$
$367$	−230.168	−	230.168i	−0.627161	−	0.627161i	−0.947353	+	0.320191i	$0.896253\pi$
$368$	393.328	−	393.328i	1.06883	−	1.06883i
$369$		0			0
$370$	25.3392	−	23.4569i	0.0684843	−	0.0633970i
$371$	−249.032			−0.671246
$372$		0			0
$373$	−211.456	+	211.456i	−0.566906	+	0.566906i	−0.931260	−	0.364355i	$-0.881290\pi$
$373$	−211.456	+	211.456i	−0.566906	+	0.566906i	0.364355	+	0.931260i	$0.381290\pi$
$374$			668.653i			1.78784i
$375$		0			0
$376$	672.657			1.78898
$377$	34.8961	+	34.8961i	0.0925626	+	0.0925626i
$378$		0			0
$379$		−	132.280i		−	0.349024i	−0.984655	−	0.174512i	$-0.944165\pi$
$379$		−	132.280i		−	0.349024i	0.984655	−	0.174512i	$-0.0558347\pi$
$380$	16.0448	+	17.3323i	0.0422233	+	0.0456114i
$381$		0			0
$382$	456.997	+	456.997i	1.19633	+	1.19633i
$383$	−149.538	+	149.538i	−0.390438	+	0.390438i	−0.874844	−	0.484406i	$-0.839036\pi$
$383$	−149.538	+	149.538i	−0.390438	+	0.390438i	0.484406	+	0.874844i	$0.339036\pi$
$384$		0			0
$385$	−8.98106	+	232.825i	−0.0233274	+	0.604739i
$386$	54.5991			0.141448
$387$		0			0
$388$	−22.9965	+	22.9965i	−0.0592692	+	0.0592692i
$389$			289.081i			0.743140i	0.928405	+	0.371570i	$0.121180\pi$
$389$			289.081i			0.743140i	−0.928405	+	0.371570i	$0.878820\pi$
$390$		0			0
$391$	−732.596			−1.87365
$392$	40.7701	+	40.7701i	0.104005	+	0.104005i
$393$		0			0
$394$		−	99.9213i		−	0.253607i
$395$	9.12468	−	8.44687i	0.0231005	−	0.0213845i
$396$		0			0
$397$	−502.891	−	502.891i	−1.26673	−	1.26673i	−0.947768	−	0.318961i	$-0.896666\pi$
$397$	−502.891	−	502.891i	−1.26673	−	1.26673i	−0.318961	−	0.947768i	$-0.603334\pi$
$398$	256.633	−	256.633i	0.644806	−	0.644806i
$399$		0			0
$400$	−28.6977	+	371.425i	−0.0717442	+	0.928563i
$401$	−405.912			−1.01225			−0.506125	−	0.862460i	$-0.668922\pi$
$401$	−405.912			−1.01225			−0.506125	+	0.862460i	$0.668922\pi$
$402$		0			0
$403$	195.385	−	195.385i	0.484826	−	0.484826i
$404$		−	22.5342i		−	0.0557776i
$405$		0			0
$406$	−14.7304			−0.0362817
$407$	−44.4621	−	44.4621i	−0.109244	−	0.109244i
$408$		0			0
$409$			505.400i			1.23570i	0.786297	+	0.617849i	$0.211996\pi$
$409$			505.400i			1.23570i	−0.786297	+	0.617849i	$0.788004\pi$
$410$	0.707713	−	18.3467i	0.00172613	−	0.0447481i
$411$		0			0
$412$	−9.48056	−	9.48056i	−0.0230111	−	0.0230111i
$413$	30.8076	−	30.8076i	0.0745946	−	0.0745946i
$414$		0			0
$415$	−205.206	−	7.91569i	−0.494472	−	0.0190740i
$416$	−70.6772			−0.169897
$417$		0			0
$418$	−441.042	+	441.042i	−1.05512	+	1.05512i
$419$			553.591i			1.32122i	0.750729	+	0.660610i	$0.229702\pi$
$419$			553.591i			1.32122i	−0.750729	+	0.660610i	$0.770298\pi$
$420$		0			0
$421$	−320.444			−0.761150			−0.380575	−	0.924750i	$-0.624274\pi$
$421$	−320.444			−0.761150			−0.380575	+	0.924750i	$0.624274\pi$
$422$	−100.729	−	100.729i	−0.238694	−	0.238694i
$423$		0			0
$424$			775.293i			1.82852i
$425$	372.626	−	319.175i	0.876767	−	0.750999i
$426$		0			0
$427$	−13.7885	−	13.7885i	−0.0322915	−	0.0322915i
$428$	23.7353	−	23.7353i	0.0554562	−	0.0554562i
$429$		0			0
$430$	395.818	+	427.580i	0.920508	+	0.994373i
$431$	−221.870			−0.514780			−0.257390	−	0.966308i	$-0.582862\pi$
$431$	−221.870			−0.514780			−0.257390	+	0.966308i	$0.582862\pi$
$432$		0			0
$433$	−162.133	+	162.133i	−0.374440	+	0.374440i	−0.869091	−	0.494651i	$-0.835296\pi$
$433$	−162.133	+	162.133i	−0.374440	+	0.374440i	0.494651	+	0.869091i	$0.335296\pi$
$434$			82.4759i			0.190037i
$435$		0			0
$436$	37.3188			0.0855936
$437$	−483.219	−	483.219i	−1.10576	−	1.10576i
$438$		0			0
$439$		−	606.504i		−	1.38156i	−0.723066	−	0.690779i	$-0.757268\pi$
$439$		−	606.504i		−	1.38156i	0.723066	−	0.690779i	$-0.242732\pi$
$440$	724.834	+	27.9600i	1.64735	+	0.0635455i
$441$		0			0
$442$	−460.289	−	460.289i	−1.04138	−	1.04138i
$443$	9.75385	−	9.75385i	0.0220177	−	0.0220177i	−0.696012	−	0.718030i	$-0.745044\pi$
$443$	9.75385	−	9.75385i	0.0220177	−	0.0220177i	0.718030	+	0.696012i	$0.245044\pi$
$444$		0			0
$445$	−107.634	+	99.6382i	−0.241873	+	0.223906i
$446$	706.410			1.58388
$447$		0			0
$448$	126.428	−	126.428i	0.282206	−	0.282206i
$449$			448.959i			0.999908i	0.866052	+	0.499954i	$0.166650\pi$
$449$			448.959i			0.999908i	−0.866052	+	0.499954i	$0.833350\pi$
$450$		0			0
$451$	−33.4344			−0.0741340
$452$	7.40041	+	7.40041i	0.0163726	+	0.0163726i
$453$		0			0
$454$			26.6161i			0.0586257i
$455$	−154.090	−	166.455i	−0.338659	−	0.365835i
$456$		0			0
$457$	368.860	+	368.860i	0.807133	+	0.807133i	0.984199	−	0.177066i	$-0.0566606\pi$
$457$	368.860	+	368.860i	0.807133	+	0.807133i	−0.177066	+	0.984199i	$0.556661\pi$
$458$	147.791	−	147.791i	0.322688	−	0.322688i
$459$		0			0
$460$	−1.85638	+	48.1247i	−0.00403561	+	0.104619i
$461$	507.955			1.10186			0.550928	−	0.834553i	$-0.314274\pi$
$461$	507.955			1.10186			0.550928	+	0.834553i	$0.314274\pi$
$462$		0			0
$463$	255.428	−	255.428i	0.551681	−	0.551681i	−0.375245	−	0.926926i	$-0.622441\pi$
$463$	255.428	−	255.428i	0.551681	−	0.551681i	0.926926	+	0.375245i	$0.122441\pi$
$464$			42.8882i			0.0924315i
$465$		0			0
$466$	6.76597			0.0145192
$467$	−408.350	−	408.350i	−0.874411	−	0.874411i	0.118538	−	0.992950i	$-0.462179\pi$
$467$	−408.350	−	408.350i	−0.874411	−	0.874411i	−0.992950	+	0.118538i	$0.962179\pi$
$468$		0			0
$469$		−	101.782i		−	0.217019i
$470$	579.635	−	536.577i	1.23326	−	1.14165i
$471$		0			0
$472$	−95.9108	−	95.9108i	−0.203201	−	0.203201i
$473$	750.267	−	750.267i	1.58619	−	1.58619i
$474$		0			0
$475$	456.310	+	35.2562i	0.960653	+	0.0742236i
$476$	−13.3981			−0.0281472
$477$		0			0
$478$	315.935	−	315.935i	0.660952	−	0.660952i
$479$			664.740i			1.38777i	0.720087	+	0.693883i	$0.244102\pi$
$479$			664.740i			1.38777i	−0.720087	+	0.693883i	$0.755898\pi$
$480$		0			0
$481$	61.2140			0.127264
$482$	−383.548	−	383.548i	−0.795743	−	0.795743i
$483$		0			0
$484$		−	48.8241i		−	0.100876i
$485$	−24.2911	+	629.721i	−0.0500848	+	1.29839i
$486$		0			0
$487$	−334.715	−	334.715i	−0.687300	−	0.687300i	0.274334	−	0.961634i	$-0.411543\pi$
$487$	−334.715	−	334.715i	−0.687300	−	0.687300i	−0.961634	+	0.274334i	$0.911543\pi$
$488$	−42.9266	+	42.9266i	−0.0879643	+	0.0879643i
$489$		0			0
$490$	67.6543	+	2.60972i	0.138070	+	0.00532596i
$491$	312.255			0.635958			0.317979	−	0.948098i	$-0.396996\pi$
$491$	312.255			0.635958			0.317979	+	0.948098i	$0.396996\pi$
$492$		0			0
$493$	39.9409	−	39.9409i	0.0810160	−	0.0810160i
$494$		−	607.212i		−	1.22917i
$495$		0			0
$496$	240.133			0.484139
$497$	148.915	+	148.915i	0.299628	+	0.299628i
$498$		0			0
$499$			89.3669i			0.179092i	0.995983	+	0.0895460i	$0.0285416\pi$
$499$			89.3669i			0.179092i	−0.995983	+	0.0895460i	$0.971458\pi$
$500$	−20.0226	−	25.2868i	−0.0400451	−	0.0505736i
$501$		0			0
$502$	−73.1434	−	73.1434i	−0.145704	−	0.145704i
$503$	−627.521	+	627.521i	−1.24756	+	1.24756i	−0.290761	+	0.956796i	$0.593908\pi$
$503$	−627.521	+	627.521i	−1.24756	+	1.24756i	−0.956796	+	0.290761i	$0.906092\pi$
$504$		0			0
$505$	−296.630	−	320.432i	−0.587385	−	0.634520i
$506$	−1271.83			−2.51350
$507$		0			0
$508$	3.14959	−	3.14959i	0.00619998	−	0.00619998i
$509$			556.945i			1.09420i	0.837069	+	0.547098i	$0.184267\pi$
$509$			556.945i			1.09420i	−0.837069	+	0.547098i	$0.815733\pi$
$510$		0			0
$511$	236.866			0.463534
$512$	−390.591	−	390.591i	−0.762872	−	0.762872i
$513$		0			0
$514$		−	215.946i		−	0.420128i
$515$	−259.610	−	10.0143i	−0.504097	−	0.0194452i
$516$		0			0
$517$	−1017.07	−	1017.07i	−1.96726	−	1.96726i
$518$	−12.9198	+	12.9198i	−0.0249418	+	0.0249418i
$519$		0			0
$520$	−518.211	+	479.716i	−0.996559	+	0.922531i
$521$	64.5705			0.123936			0.0619679	−	0.998078i	$-0.480262\pi$
$521$	64.5705			0.123936			0.0619679	+	0.998078i	$0.480262\pi$
$522$		0			0
$523$	−431.531	+	431.531i	−0.825107	+	0.825107i	−0.986835	−	0.161728i	$-0.948293\pi$
$523$	−431.531	+	431.531i	−0.825107	+	0.825107i	0.161728	+	0.986835i	$0.448293\pi$
$524$		−	5.99279i		−	0.0114366i
$525$		0			0
$526$	885.986			1.68438
$527$	−223.631	−	223.631i	−0.424347	−	0.424347i
$528$		0			0
$529$		−	864.452i		−	1.63413i
$530$	618.450	+	668.077i	1.16689	+	1.26052i
$531$		0			0
$532$	−8.83734	−	8.83734i	−0.0166115	−	0.0166115i
$533$	23.0157	−	23.0157i	0.0431814	−	0.0431814i
$534$		0			0
$535$	25.0715	−	649.952i	0.0468626	−	1.21486i
$536$	−316.870			−0.591175
$537$		0			0
$538$	162.844	−	162.844i	0.302684	−	0.302684i
$539$		−	123.291i		−	0.228740i
$540$		0			0
$541$	−571.616			−1.05659			−0.528295	−	0.849061i	$-0.677169\pi$
$541$	−571.616			−1.05659			−0.528295	+	0.849061i	$0.677169\pi$
$542$	520.017	+	520.017i	0.959441	+	0.959441i
$543$		0			0
$544$			80.8946i			0.148703i
$545$	530.667	−	491.248i	0.973702	−	0.901372i
$546$		0			0
$547$	259.835	+	259.835i	0.475017	+	0.475017i	0.903534	−	0.428516i	$-0.140964\pi$
$547$	259.835	+	259.835i	0.475017	+	0.475017i	−0.428516	+	0.903534i	$0.640964\pi$
$548$	4.45334	−	4.45334i	0.00812653	−	0.00812653i
$549$		0			0
$550$	646.900	−	554.106i	1.17618	−	1.00747i
$551$	52.6898			0.0956258
$552$		0			0
$553$	−4.65245	+	4.65245i	−0.00841311	+	0.00841311i
$554$		−	1024.39i		−	1.84907i
$555$		0			0
$556$	−7.60677			−0.0136812
$557$	−503.660	−	503.660i	−0.904237	−	0.904237i	0.0915625	−	0.995799i	$-0.470814\pi$
$557$	−503.660	−	503.660i	−0.904237	−	0.904237i	−0.995799	+	0.0915625i	$0.970814\pi$
$558$		0			0
$559$			1032.94i			1.84784i
$560$	7.59834	−	196.979i	0.0135685	−	0.351748i
$561$		0			0
$562$	411.506	+	411.506i	0.732216	+	0.732216i
$563$	405.076	−	405.076i	0.719495	−	0.719495i	−0.249007	−	0.968502i	$-0.580104\pi$
$563$	405.076	−	405.076i	0.719495	−	0.719495i	0.968502	+	0.249007i	$0.0801042\pi$
$564$		0			0
$565$	202.648	+	7.81703i	0.358670	+	0.0138355i
$566$	−375.242			−0.662972
$567$		0			0
$568$	463.605	−	463.605i	0.816207	−	0.816207i
$569$		−	674.447i		−	1.18532i	−0.805453	−	0.592660i	$-0.798078\pi$
$569$		−	674.447i		−	1.18532i	0.805453	−	0.592660i	$-0.201922\pi$
$570$		0			0
$571$	825.137			1.44507			0.722537	−	0.691333i	$-0.242976\pi$
$571$	825.137			1.44507			0.722537	+	0.691333i	$0.242976\pi$
$572$	55.1023	+	55.1023i	0.0963328	+	0.0963328i
$573$		0			0
$574$			9.71539i			0.0169258i
$575$	607.094	+	708.762i	1.05582	+	1.23263i
$576$		0			0
$577$	532.596	+	532.596i	0.923043	+	0.923043i	0.997243	−	0.0742001i	$-0.0236403\pi$
$577$	532.596	+	532.596i	0.923043	+	0.923043i	−0.0742001	+	0.997243i	$0.523640\pi$
$578$	−131.526	+	131.526i	−0.227554	+	0.227554i
$579$		0			0
$580$	−2.52253	−	2.72495i	−0.00434919	−	0.00469819i
$581$	108.666			0.187032
$582$		0			0
$583$	1172.26	−	1172.26i	2.01074	−	2.01074i
$584$		−	737.416i		−	1.26270i
$585$		0			0
$586$	−529.349			−0.903325
$587$	−800.352	−	800.352i	−1.36346	−	1.36346i	−0.869463	−	0.493999i	$-0.835535\pi$
$587$	−800.352	−	800.352i	−1.36346	−	1.36346i	−0.493999	−	0.869463i	$-0.664465\pi$
$588$		0			0
$589$		−	295.013i		−	0.500871i
$590$	−159.155	−	6.13931i	−0.269754	−	0.0104056i
$591$		0			0
$592$	37.6168	+	37.6168i	0.0635419	+	0.0635419i
$593$	−254.908	+	254.908i	−0.429862	+	0.429862i	−0.888581	−	0.458719i	$-0.848308\pi$
$593$	−254.908	+	254.908i	−0.429862	+	0.429862i	0.458719	+	0.888581i	$0.348308\pi$
$594$		0			0
$595$	−190.518	+	176.366i	−0.320199	+	0.296414i
$596$	3.71174			0.00622775
$597$		0			0
$598$	875.505	−	875.505i	1.46406	−	1.46406i
$599$			661.029i			1.10355i	0.833991	+	0.551777i	$0.186050\pi$
$599$			661.029i			1.10355i	−0.833991	+	0.551777i	$0.813950\pi$
$600$		0			0
$601$	−410.580			−0.683162			−0.341581	−	0.939852i	$-0.610962\pi$
$601$	−410.580			−0.683162			−0.341581	+	0.939852i	$0.610962\pi$
$602$	−218.013	−	218.013i	−0.362148	−	0.362148i
$603$		0			0
$604$		−	3.96258i		−	0.00656056i
$605$	−642.698	−	694.271i	−1.06231	−	1.14756i
$606$		0			0
$607$	−604.297	−	604.297i	−0.995548	−	0.995548i	0.00444263	−	0.999990i	$-0.498586\pi$
$607$	−604.297	−	604.297i	−0.995548	−	0.995548i	−0.999990	+	0.00444263i	$0.998586\pi$
$608$	−53.3579	+	53.3579i	−0.0877598	+	0.0877598i
$609$		0			0
$610$	−2.74776	+	71.2327i	−0.00450452	+	0.116775i
$611$	1400.27			2.29177
$612$		0			0
$613$	−61.4626	+	61.4626i	−0.100265	+	0.100265i	−0.755460	−	0.655195i	$-0.772587\pi$
$613$	−61.4626	+	61.4626i	−0.100265	+	0.100265i	0.655195	+	0.755460i	$0.272587\pi$
$614$			335.198i			0.545926i
$615$		0			0
$616$	−383.831			−0.623103
$617$	509.151	+	509.151i	0.825204	+	0.825204i	0.986849	−	0.161645i	$-0.0516800\pi$
$617$	509.151	+	509.151i	0.825204	+	0.825204i	−0.161645	+	0.986849i	$0.551680\pi$
$618$		0			0
$619$			735.555i			1.18830i	0.804356	+	0.594148i	$0.202511\pi$
$619$			735.555i			1.18830i	−0.804356	+	0.594148i	$0.797489\pi$
$620$	−15.2571	+	14.1238i	−0.0246083	+	0.0227803i
$621$		0			0
$622$	−161.473	−	161.473i	−0.259603	−	0.259603i
$623$	54.8798	−	54.8798i	0.0880895	−	0.0880895i
$624$		0			0
$625$	−617.582	−	96.0065i	−0.988131	−	0.153610i
$626$	−791.928			−1.26506
$627$		0			0
$628$	16.3275	−	16.3275i	0.0259992	−	0.0259992i
$629$		−	70.0634i		−	0.111389i
$630$		0			0
$631$	649.002			1.02853			0.514265	−	0.857631i	$-0.328065\pi$
$631$	649.002			1.02853			0.514265	+	0.857631i	$0.328065\pi$
$632$	14.4841	+	14.4841i	0.0229179	+	0.0229179i
$633$		0			0
$634$			799.517i			1.26107i
$635$	3.32691	−	86.2465i	0.00523922	−	0.135821i
$636$		0			0
$637$	84.8713	+	84.8713i	0.133236	+	0.133236i
$638$	69.3396	−	69.3396i	0.108683	−	0.108683i
$639$		0			0
$640$	−570.763	−	22.0168i	−0.891818	−	0.0344013i
$641$	103.576			0.161585			0.0807925	−	0.996731i	$-0.474255\pi$
$641$	103.576			0.161585			0.0807925	+	0.996731i	$0.474255\pi$
$642$		0			0
$643$	504.926	−	504.926i	0.785266	−	0.785266i	−0.195448	−	0.980714i	$-0.562616\pi$
$643$	504.926	−	504.926i	0.785266	−	0.785266i	0.980714	+	0.195448i	$0.0626160\pi$
$644$		−	25.4841i		−	0.0395716i
$645$		0			0
$646$	−694.994			−1.07584
$647$	−134.888	−	134.888i	−0.208482	−	0.208482i	0.595140	−	0.803622i	$-0.297097\pi$
$647$	−134.888	−	134.888i	−0.208482	−	0.208482i	−0.803622	+	0.595140i	$0.797097\pi$
$648$		0			0
$649$			290.039i			0.446901i
$650$	−63.8779	+	826.752i	−0.0982738	+	1.27193i
$651$		0			0
$652$	31.2875	+	31.2875i	0.0479870	+	0.0479870i
$653$	123.054	−	123.054i	0.188444	−	0.188444i	−0.606579	−	0.795023i	$-0.707459\pi$
$653$	123.054	−	123.054i	0.188444	−	0.188444i	0.795023	+	0.606579i	$0.207459\pi$
$654$		0			0
$655$	−78.8864	−	85.2166i	−0.120437	−	0.130102i
$656$	28.2869			0.0431202
$657$		0			0
$658$	−295.542	+	295.542i	−0.449151	+	0.449151i
$659$		−	811.814i		−	1.23189i	−0.787790	−	0.615944i	$-0.788775\pi$
$659$		−	811.814i		−	1.23189i	0.787790	−	0.615944i	$-0.211225\pi$
$660$		0			0
$661$	979.510			1.48186			0.740930	−	0.671582i	$-0.234385\pi$
$661$	979.510			1.48186			0.740930	+	0.671582i	$0.234385\pi$
$662$	794.329	+	794.329i	1.19989	+	1.19989i
$663$		0			0
$664$		−	338.300i		−	0.509488i
$665$	−241.996	−	9.33486i	−0.363904	−	0.0140374i
$666$		0			0
$667$	75.9705	+	75.9705i	0.113899	+	0.113899i
$668$	13.2170	−	13.2170i	0.0197860	−	0.0197860i
$669$		0			0
$670$	−273.050	+	252.767i	−0.407537	+	0.377264i
$671$	129.812			0.193461
$672$		0			0
$673$	−327.449	+	327.449i	−0.486552	+	0.486552i	−0.907216	−	0.420664i	$-0.861797\pi$
$673$	−327.449	+	327.449i	−0.486552	+	0.486552i	0.420664	+	0.907216i	$0.361797\pi$
$674$			693.868i			1.02948i
$675$		0			0
$676$	−32.2555			−0.0477152
$677$	−463.677	−	463.677i	−0.684900	−	0.684900i	0.276200	−	0.961100i	$-0.410925\pi$
$677$	−463.677	−	463.677i	−0.684900	−	0.684900i	−0.961100	+	0.276200i	$0.910925\pi$
$678$		0			0
$679$		−	333.465i		−	0.491112i
$680$	549.067	+	593.126i	0.807451	+	0.872244i
$681$		0			0
$682$	−388.236	−	388.236i	−0.569261	−	0.569261i
$683$	−667.534	+	667.534i	−0.977356	+	0.977356i	−0.999749	−	0.0223933i	$-0.992871\pi$
$683$	−667.534	+	667.534i	−0.977356	+	0.977356i	0.0223933	+	0.999749i	$0.492871\pi$
$684$		0			0
$685$	4.70405	−	121.948i	0.00686723	−	0.178026i
$686$	−35.8259			−0.0522243
$687$		0			0
$688$	−634.756	+	634.756i	−0.922610	+	0.922610i
$689$			1613.93i			2.34242i
$690$		0			0
$691$	−622.518			−0.900895			−0.450447	−	0.892803i	$-0.648736\pi$
$691$	−622.518			−0.900895			−0.450447	+	0.892803i	$0.648736\pi$
$692$	20.2663	+	20.2663i	0.0292866	+	0.0292866i
$693$		0			0
$694$		−	164.846i		−	0.237531i
$695$	−108.167	+	100.132i	−0.155636	+	0.144075i
$696$		0			0
$697$	−26.3430	−	26.3430i	−0.0377948	−	0.0377948i
$698$	−476.269	+	476.269i	−0.682334	+	0.682334i
$699$		0			0
$700$	11.1028	+	12.9622i	0.0158612	+	0.0185174i
$701$	821.585			1.17202			0.586009	−	0.810304i	$-0.300698\pi$
$701$	821.585			1.17202			0.586009	+	0.810304i	$0.300698\pi$
$702$		0			0
$703$	46.2137	−	46.2137i	0.0657378	−	0.0657378i
$704$			1190.26i			1.69071i
$705$		0			0
$706$	−309.482			−0.438359
$707$	163.381	+	163.381i	0.231090	+	0.231090i
$708$		0			0
$709$			1124.01i			1.58535i	0.609647	+	0.792673i	$0.291311\pi$
$709$			1124.01i			1.58535i	−0.609647	+	0.792673i	$0.708689\pi$
$710$	29.6757	−	769.310i	0.0417967	−	1.08354i
$711$		0			0
$712$	−170.853	−	170.853i	−0.239962	−	0.239962i
$713$	425.363	−	425.363i	0.596581	−	0.596581i
$714$		0			0
$715$	1508.89	+	58.2045i	2.11033	+	0.0814048i
$716$	−41.8982			−0.0585170
$717$		0			0
$718$	144.514	−	144.514i	0.201273	−	0.201273i
$719$		−	826.757i		−	1.14987i	−0.818199	−	0.574936i	$-0.805027\pi$
$719$		−	826.757i		−	1.14987i	0.818199	−	0.574936i	$-0.194973\pi$
$720$		0			0
$721$	137.475			0.190672
$722$	35.3734	+	35.3734i	0.0489936	+	0.0489936i
$723$		0			0
$724$		−	66.3722i		−	0.0916744i
$725$	−71.7400	−	5.54290i	−0.0989518	−	0.00764538i
$726$		0			0
$727$	829.278	+	829.278i	1.14069	+	1.14069i	0.988325	+	0.152360i	$0.0486874\pi$
$727$	829.278	+	829.278i	1.14069	+	1.14069i	0.152360	+	0.988325i	$0.451313\pi$
$728$	264.223	−	264.223i	0.362944	−	0.362944i
$729$		0			0
$730$	−588.236	−	635.438i	−0.805803	−	0.870463i
$731$	1182.27			1.61733
$732$		0			0
$733$	−306.100	+	306.100i	−0.417599	+	0.417599i	−0.884375	−	0.466776i	$-0.845415\pi$
$733$	−306.100	+	306.100i	−0.417599	+	0.417599i	0.466776	+	0.884375i	$0.345415\pi$
$734$		−	629.666i		−	0.857856i
$735$		0			0
$736$	−153.868			−0.209059
$737$	479.115	+	479.115i	0.650088	+	0.650088i
$738$		0			0
$739$			1152.24i			1.55919i	0.626283	+	0.779596i	$0.284575\pi$
$739$			1152.24i			1.55919i	−0.626283	+	0.779596i	$0.715425\pi$
$740$	−4.60251	−	0.177539i	−0.00621961	−	0.000239918i
$741$		0			0
$742$	−340.636	−	340.636i	−0.459078	−	0.459078i
$743$	87.8428	−	87.8428i	0.118227	−	0.118227i	−0.645518	−	0.763745i	$-0.723358\pi$
$743$	87.8428	−	87.8428i	0.118227	−	0.118227i	0.763745	+	0.645518i	$0.223358\pi$
$744$		0			0
$745$	52.7804	−	48.8597i	0.0708462	−	0.0655835i
$746$	−578.475			−0.775436
$747$		0			0
$748$	63.0682	−	63.0682i	0.0843158	−	0.0843158i
$749$			344.178i			0.459517i
$750$		0			0
$751$	−601.083			−0.800377			−0.400189	−	0.916433i	$-0.631055\pi$
$751$	−601.083			−0.800377			−0.400189	+	0.916433i	$0.631055\pi$
$752$	860.485	+	860.485i	1.14426	+	1.14426i
$753$		0			0
$754$			95.4645i			0.126611i
$755$	−52.1616	−	56.3472i	−0.0690882	−	0.0746321i
$756$		0			0
$757$	650.454	+	650.454i	0.859252	+	0.859252i	0.991250	−	0.131998i	$-0.0421393\pi$
$757$	650.454	+	650.454i	0.859252	+	0.859252i	−0.131998	+	0.991250i	$0.542139\pi$
$758$	180.938	−	180.938i	0.238704	−	0.238704i
$759$		0			0
$760$	−29.0615	+	753.388i	−0.0382388	+	0.991300i
$761$	−344.833			−0.453131			−0.226566	−	0.973996i	$-0.572750\pi$
$761$	−344.833			−0.453131			−0.226566	+	0.973996i	$0.572750\pi$
$762$		0			0
$763$	−270.574	+	270.574i	−0.354619	+	0.354619i
$764$		−	86.2090i		−	0.112839i
$765$		0			0
$766$	−409.087			−0.534056
$767$	−199.658	−	199.658i	−0.260310	−	0.260310i
$768$		0			0
$769$			953.105i			1.23941i	0.784836	+	0.619704i	$0.212747\pi$
$769$			953.105i			1.23941i	−0.784836	+	0.619704i	$0.787253\pi$
$770$	−330.751	+	306.182i	−0.429547	+	0.397639i
$771$		0			0
$772$	−5.14986	−	5.14986i	−0.00667080	−	0.00667080i
$773$	716.434	−	716.434i	0.926823	−	0.926823i	−0.0706765	−	0.997499i	$-0.522516\pi$
$773$	716.434	−	716.434i	0.926823	−	0.926823i	0.997499	+	0.0706765i	$0.0225158\pi$
$774$		0			0
$775$	−31.0350	+	401.676i	−0.0400451	+	0.518291i
$776$	−1038.15			−1.33782
$777$		0			0
$778$	−395.417	+	395.417i	−0.508248	+	0.508248i
$779$		−	34.7515i		−	0.0446104i
$780$		0			0
$781$	−1401.96			−1.79509
$782$	−1002.07	−	1002.07i	−1.28142	−	1.28142i
$783$		0			0
$784$			104.309i			0.133047i
$785$	17.2467	−	447.103i	0.0219703	−	0.569557i
$786$		0			0
$787$	475.797	+	475.797i	0.604570	+	0.604570i	0.941522	−	0.336952i	$-0.109396\pi$
$787$	475.797	+	475.797i	0.604570	+	0.604570i	−0.336952	+	0.941522i	$0.609396\pi$
$788$	−9.42471	+	9.42471i	−0.0119603	+	0.0119603i
$789$		0			0
$790$	24.0350	+	0.927137i	0.0304241	+	0.00117359i
$791$	−107.311			−0.135665
$792$		0			0
$793$	−89.3604	+	89.3604i	−0.112687	+	0.112687i
$794$		−	1375.75i		−	1.73268i
$795$		0			0
$796$	−48.4119			−0.0608189
$797$	523.540	+	523.540i	0.656889	+	0.656889i	0.954643	−	0.297754i	$-0.0962375\pi$
$797$	523.540	+	523.540i	0.656889	+	0.656889i	−0.297754	+	0.954643i	$0.596238\pi$
$798$		0			0
$799$		−	1602.70i		−	2.00589i
$800$	78.2629	−	67.0365i	0.0978286	−	0.0837957i
$801$		0			0
$802$	−555.222	−	555.222i	−0.692297	−	0.692297i
$803$	−1114.99	+	1114.99i	−1.38853	+	1.38853i
$804$		0			0
$805$	−335.462	−	362.381i	−0.416723	−	0.450162i
$806$	534.510			0.663164
$807$		0			0
$808$	508.640	−	508.640i	0.629505	−	0.629505i
$809$			801.958i			0.991295i	0.868524	+	0.495648i	$0.165069\pi$
$809$			801.958i			0.991295i	−0.868524	+	0.495648i	$0.834931\pi$
$810$		0			0
$811$	56.4562			0.0696130			0.0348065	−	0.999394i	$-0.488919\pi$
$811$	56.4562			0.0696130			0.0348065	+	0.999394i	$0.488919\pi$
$812$	1.38939	+	1.38939i	0.00171107	+	0.00171107i
$813$		0			0
$814$		−	121.634i		−	0.149428i
$815$	856.758	+	33.0489i	1.05124	+	0.0405508i
$816$		0			0
$817$	779.822	+	779.822i	0.954495	+	0.954495i
$818$	−691.306	+	691.306i	−0.845118	+	0.845118i
$819$		0			0
$820$	−1.79724	+	1.66373i	−0.00219175	+	0.00202894i
$821$	−983.386			−1.19779			−0.598896	−	0.800827i	$-0.704394\pi$
$821$	−983.386			−1.19779			−0.598896	+	0.800827i	$0.704394\pi$
$822$		0			0
$823$	8.06828	−	8.06828i	0.00980350	−	0.00980350i	−0.702188	−	0.711992i	$-0.747793\pi$
$823$	8.06828	−	8.06828i	0.00980350	−	0.00980350i	0.711992	+	0.702188i	$0.247793\pi$
$824$		−	427.989i		−	0.519405i
$825$		0			0
$826$	84.2796			0.102033
$827$	−917.498	−	917.498i	−1.10943	−	1.10943i	−0.993225	−	0.116204i	$-0.962927\pi$
$827$	−917.498	−	917.498i	−1.10943	−	1.10943i	−0.116204	−	0.993225i	$-0.537073\pi$
$828$		0			0
$829$		−	589.450i		−	0.711037i	−0.934669	−	0.355518i	$-0.884304\pi$
$829$		−	589.450i		−	0.711037i	0.934669	−	0.355518i	$-0.115696\pi$
$830$	−269.861	−	291.516i	−0.325134	−	0.351224i
$831$		0			0
$832$	−819.356	−	819.356i	−0.984803	−	0.984803i
$833$	97.1407	−	97.1407i	0.116616	−	0.116616i
$834$		0			0
$835$	13.9611	−	361.927i	0.0167199	−	0.433446i
$836$	83.1994			0.0995208
$837$		0			0
$838$	−757.224	+	757.224i	−0.903609	+	0.903609i
$839$		−	230.274i		−	0.274463i	−0.990539	−	0.137231i	$-0.956180\pi$
$839$		−	230.274i		−	0.274463i	0.990539	−	0.137231i	$-0.0438204\pi$
$840$		0			0
$841$	832.716			0.990150
$842$	−438.316	−	438.316i	−0.520566	−	0.520566i
$843$		0			0
$844$			19.0018i			0.0225140i
$845$	−458.668	+	424.597i	−0.542803	+	0.502481i
$846$		0			0
$847$	353.992	+	353.992i	0.417936	+	0.417936i
$848$	−991.780	+	991.780i	−1.16955	+	1.16955i
$849$		0			0
$850$	946.272	+	73.1125i	1.11326	+	0.0860147i
$851$	133.266			0.156599
$852$		0			0
$853$	−843.744	+	843.744i	−0.989148	+	0.989148i	−0.999942	−	0.0107933i	$-0.996564\pi$
$853$	−843.744	+	843.744i	−0.989148	+	0.989148i	0.0107933	+	0.999942i	$0.496564\pi$
$854$		−	37.7209i		−	0.0441696i
$855$		0			0
$856$	1071.50			1.25176
$857$	−437.772	−	437.772i	−0.510819	−	0.510819i	0.403959	−	0.914777i	$-0.367634\pi$
$857$	−437.772	−	437.772i	−0.510819	−	0.510819i	−0.914777	+	0.403959i	$0.867634\pi$
$858$		0			0
$859$		−	1402.95i		−	1.63324i	−0.577175	−	0.816621i	$-0.695845\pi$
$859$		−	1402.95i		−	1.63324i	0.577175	−	0.816621i	$-0.304155\pi$
$860$	2.99584	−	77.6640i	0.00348354	−	0.0903070i
$861$		0			0
$862$	−303.482	−	303.482i	−0.352068	−	0.352068i
$863$	−1049.60	+	1049.60i	−1.21622	+	1.21622i	−0.247281	+	0.968944i	$0.579537\pi$
$863$	−1049.60	+	1049.60i	−1.21622	+	1.21622i	−0.968944	+	0.247281i	$0.920463\pi$
$864$		0			0
$865$	554.961	+	21.4073i	0.641574	+	0.0247483i
$866$	−443.543			−0.512174
$867$		0			0
$868$	7.77924	−	7.77924i	0.00896225	−	0.00896225i
$869$		−	43.8006i		−	0.0504035i
$870$		0			0
$871$	−659.629			−0.757324
$872$	842.358	+	842.358i	0.966007	+	0.966007i
$873$		0			0
$874$		−	1321.93i		−	1.51251i
$875$	328.509	+	38.1676i	0.375439	+	0.0436201i
$876$		0			0
$877$	−236.787	−	236.787i	−0.269996	−	0.269996i	0.559102	−	0.829099i	$-0.311146\pi$
$877$	−236.787	−	236.787i	−0.269996	−	0.269996i	−0.829099	+	0.559102i	$0.811146\pi$
$878$	829.599	−	829.599i	0.944874	−	0.944874i
$879$		0			0
$880$	891.465	+	963.000i	1.01303	+	1.09432i
$881$	−311.627			−0.353720			−0.176860	−	0.984236i	$-0.556594\pi$
$881$	−311.627			−0.353720			−0.176860	+	0.984236i	$0.556594\pi$
$882$		0			0
$883$	−54.4472	+	54.4472i	−0.0616616	+	0.0616616i	−0.737265	−	0.675604i	$-0.763883\pi$
$883$	−54.4472	+	54.4472i	−0.0616616	+	0.0616616i	0.675604	+	0.737265i	$0.263883\pi$
$884$			86.8302i			0.0982242i
$885$		0			0
$886$	26.6834			0.0301167
$887$	485.748	+	485.748i	0.547631	+	0.547631i	0.925755	−	0.378124i	$-0.123431\pi$
$887$	485.748	+	485.748i	0.547631	+	0.547631i	−0.378124	+	0.925755i	$0.623431\pi$
$888$		0			0
$889$			45.6713i			0.0513738i
$890$	−283.515	−	10.9364i	−0.318556	−	0.0122881i
$891$		0			0
$892$	−66.6295	−	66.6295i	−0.0746968	−	0.0746968i
$893$	1057.14	−	1057.14i	1.18381	−	1.18381i
$894$		0			0
$895$	−595.786	+	551.529i	−0.665682	+	0.616233i
$896$	302.244			0.337326
$897$		0			0
$898$	−614.103	+	614.103i	−0.683856	+	0.683856i
$899$			46.3812i			0.0515920i
$900$		0			0
$901$	1847.25			2.05022
$902$	−45.7329	−	45.7329i	−0.0507017	−	0.0507017i
$903$		0			0
$904$			334.083i			0.369561i
$905$	−873.694	−	943.803i	−0.965408	−	1.04288i
$906$		0			0
$907$	355.846	+	355.846i	0.392334	+	0.392334i	0.875518	−	0.483185i	$-0.160520\pi$
$907$	355.846	+	355.846i	0.392334	+	0.392334i	−0.483185	+	0.875518i	$0.660520\pi$
$908$	2.51046	−	2.51046i	0.00276482	−	0.00276482i
$909$		0			0
$910$	16.9131	−	438.454i	0.0185858	−	0.481817i
$911$	−440.542			−0.483581			−0.241790	−	0.970329i	$-0.577735\pi$
$911$	−440.542			−0.483581			−0.241790	+	0.970329i	$0.577735\pi$
$912$		0			0
$913$	−511.517	+	511.517i	−0.560260	+	0.560260i
$914$			1009.08i			1.10403i
$915$		0			0
$916$	−27.8797			−0.0304364
$917$	43.4499	+	43.4499i	0.0473826	+	0.0473826i
$918$		0			0
$919$		−	576.067i		−	0.626841i	−0.949614	−	0.313420i	$-0.898525\pi$
$919$		−	576.067i		−	0.626841i	0.949614	−	0.313420i	$-0.101475\pi$
$920$	−1128.17	+	1044.37i	−1.22627	+	1.13518i
$921$		0			0
$922$	694.801	+	694.801i	0.753580	+	0.753580i
$923$	965.089	−	965.089i	1.04560	−	1.04560i
$924$		0			0
$925$	−67.7840	+	58.0608i	−0.0732800	+	0.0627684i
$926$	698.769			0.754611
$927$		0			0
$928$	8.38881	−	8.38881i	0.00903967	−	0.00903967i
$929$		−	513.292i		−	0.552521i	−0.961083	−	0.276260i	$-0.910905\pi$
$929$		−	513.292i		−	0.552521i	0.961083	−	0.276260i	$-0.0890952\pi$
$930$		0			0
$931$	128.148			0.137645
$932$	−0.638175	−	0.638175i	−0.000684737	−	0.000684737i
$933$		0			0
$934$		−	1117.11i		−	1.19605i
$935$	66.6188	−	1727.02i	0.0712501	−	1.84708i
$936$		0			0
$937$	−224.557	−	224.557i	−0.239655	−	0.239655i	0.577052	−	0.816707i	$-0.304203\pi$
$937$	−224.557	−	224.557i	−0.239655	−	0.239655i	−0.816707	+	0.577052i	$0.804203\pi$
$938$	139.221	−	139.221i	0.148424	−	0.148424i
$939$		0			0
$940$	−105.283	−	4.06121i	−0.112003	−	0.00432044i
$941$	−595.500			−0.632838			−0.316419	−	0.948620i	$-0.602481\pi$
$941$	−595.500			−0.632838			−0.316419	+	0.948620i	$0.602481\pi$
$942$		0			0
$943$	50.1063	−	50.1063i	0.0531350	−	0.0531350i
$944$		−	245.385i		−	0.259941i
$945$		0			0
$946$	2052.49			2.16965
$947$	890.942	+	890.942i	0.940805	+	0.940805i	0.998343	−	0.0575384i	$-0.0183252\pi$
$947$	890.942	+	890.942i	0.940805	+	0.940805i	−0.0575384	+	0.998343i	$0.518325\pi$
$948$		0			0
$949$		−	1535.08i		−	1.61758i
$950$	575.934	+	672.384i	0.606246	+	0.707772i
$951$		0			0
$952$	−302.421	−	302.421i	−0.317669	−	0.317669i
$953$	−270.103	+	270.103i	−0.283424	+	0.283424i	−0.834473	−	0.551049i	$-0.814228\pi$
$953$	−270.103	+	270.103i	−0.283424	+	0.283424i	0.551049	+	0.834473i	$0.314228\pi$
$954$		0			0
$955$	−1134.82	−	1225.88i	−1.18829	−	1.28364i
$956$	−59.5988			−0.0623418
$957$		0			0
$958$	−909.258	+	909.258i	−0.949121	+	0.949121i
$959$			64.5766i			0.0673374i
$960$		0			0
$961$	−701.309			−0.729770
$962$	83.7308	+	83.7308i	0.0870383	+	0.0870383i
$963$		0			0
$964$			72.3535i			0.0750555i
$965$	−141.021	−	5.43978i	−0.146135	−	0.00563708i
$966$		0			0
$967$	1139.02	+	1139.02i	1.17789	+	1.17789i	0.980281	+	0.197611i	$0.0633182\pi$
$967$	1139.02	+	1139.02i	1.17789	+	1.17789i	0.197611	+	0.980281i	$0.436682\pi$
$968$	1102.06	−	1102.06i	1.13849	−	1.13849i
$969$		0			0
$970$	−894.584	+	828.131i	−0.922251	+	0.853743i
$971$	736.722			0.758725			0.379363	−	0.925248i	$-0.376143\pi$
$971$	736.722			0.758725			0.379363	+	0.925248i	$0.376143\pi$
$972$		0			0
$973$	55.1518	−	55.1518i	0.0566822	−	0.0566822i
$974$		−	915.673i		−	0.940116i
$975$		0			0
$976$	−109.826			−0.112527
$977$	993.980	+	993.980i	1.01738	+	1.01738i	0.999846	+	0.0175332i	$0.00558127\pi$
$977$	993.980	+	993.980i	1.01738	+	1.01738i	0.0175332	+	0.999846i	$0.494419\pi$
$978$		0			0
$979$			516.667i			0.527750i
$980$	−6.13509	−	6.62739i	−0.00626029	−	0.00676264i
$981$		0			0
$982$	427.115	+	427.115i	0.434944	+	0.434944i
$983$	546.928	−	546.928i	0.556387	−	0.556387i	−0.371890	−	0.928277i	$-0.621290\pi$
$983$	546.928	−	546.928i	0.556387	−	0.556387i	0.928277	+	0.371890i	$0.121290\pi$
$984$		0			0
$985$	−9.95530	+	258.081i	−0.0101069	+	0.262011i
$986$	109.265			0.110817
$987$		0			0
$988$	−57.2730	+	57.2730i	−0.0579686	+	0.0579686i
$989$			2248.77i			2.27378i
$990$		0			0
$991$	−1132.40			−1.14269			−0.571343	−	0.820711i	$-0.693577\pi$
$991$	−1132.40			−1.14269			−0.571343	+	0.820711i	$0.693577\pi$
$992$	−46.9694	−	46.9694i	−0.0473481	−	0.0473481i
$993$		0			0
$994$			407.384i			0.409843i
$995$	−688.409	+	637.272i	−0.691869	+	0.640474i
$996$		0			0
$997$	−44.1992	−	44.1992i	−0.0443322	−	0.0443322i	0.684593	−	0.728925i	$-0.259980\pi$
$997$	−44.1992	−	44.1992i	−0.0443322	−	0.0443322i	−0.728925	+	0.684593i	$0.759980\pi$
$998$	−122.239	+	122.239i	−0.122484	+	0.122484i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.o.b.127.10		24
3.2	odd	2		105.3.l.a.22.3	✓	24
5.3	odd	4	inner	315.3.o.b.253.10		24
15.2	even	4		525.3.l.e.43.10		24
15.8	even	4		105.3.l.a.43.3	yes	24
15.14	odd	2		525.3.l.e.232.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.l.a.22.3	✓	24	3.2	odd	2
105.3.l.a.43.3	yes	24	15.8	even	4
315.3.o.b.127.10		24	1.1	even	1	trivial
315.3.o.b.253.10		24	5.3	odd	4	inner
525.3.l.e.43.10		24	15.2	even	4
525.3.l.e.232.10		24	15.14	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36784 + 1.36784i) q^{2} -0.258033i q^{4} +(-3.39663 - 3.66919i) q^{5} +(1.87083 + 1.87083i) q^{7} +(5.82430 - 5.82430i) q^{8} +O(q^{10})\)	\(q+(1.36784 + 1.36784i) q^{2} -0.258033i q^{4} +(-3.39663 - 3.66919i) q^{5} +(1.87083 + 1.87083i) q^{7} +(5.82430 - 5.82430i) q^{8} +(0.372817 - 9.66489i) q^{10} -17.6130 q^{11} +(12.1245 - 12.1245i) q^{13} +5.11799i q^{14} +14.9013 q^{16} +(-13.8772 - 13.8772i) q^{17} -18.3068i q^{19} +(-0.946770 + 0.876441i) q^{20} +(-24.0917 - 24.0917i) q^{22} +(26.3956 - 26.3956i) q^{23} +(-1.92585 + 24.9257i) q^{25} +33.1686 q^{26} +(0.482735 - 0.482735i) q^{28} +2.87815i q^{29} +16.1149 q^{31} +(-2.91465 - 2.91465i) q^{32} -37.9637i q^{34} +(0.509912 - 13.2189i) q^{35} +(2.52440 + 2.52440i) q^{37} +(25.0408 - 25.0408i) q^{38} +(-41.1534 - 1.58747i) q^{40} +1.89828 q^{41} +(-42.5974 + 42.5974i) q^{43} +4.54472i q^{44} +72.2098 q^{46} +(57.7457 + 57.7457i) q^{47} +7.00000i q^{49} +(-36.7286 + 31.4601i) q^{50} +(-3.12851 - 3.12851i) q^{52} +(-66.5567 + 66.5567i) q^{53} +(59.8247 + 64.6253i) q^{55} +21.7925 q^{56} +(-3.93685 + 3.93685i) q^{58} -16.4673i q^{59} -7.37026 q^{61} +(22.0426 + 22.0426i) q^{62} -67.5787i q^{64} +(-85.6692 - 3.30464i) q^{65} +(-27.2024 - 27.2024i) q^{67} +(-3.58078 + 3.58078i) q^{68} +(18.7788 - 17.3839i) q^{70} +79.5984 q^{71} +(63.3051 - 63.3051i) q^{73} +6.90594i q^{74} -4.72376 q^{76} +(-32.9508 - 32.9508i) q^{77} +2.48684i q^{79} +(-50.6141 - 54.6756i) q^{80} +(2.59655 + 2.59655i) q^{82} +(29.0421 - 29.0421i) q^{83} +(-3.78237 + 98.0540i) q^{85} -116.533 q^{86} +(-102.583 + 102.583i) q^{88} -29.3345i q^{89} +45.3656 q^{91} +(-6.81092 - 6.81092i) q^{92} +157.974i q^{94} +(-67.1711 + 62.1814i) q^{95} +(-89.1223 - 89.1223i) q^{97} +(-9.57487 + 9.57487i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8}+O(q^{10}) \) 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8	\( 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8} - 40 q^{10} + 64 q^{13} - 184 q^{16} - 24 q^{17} - 72 q^{20} + 8 q^{22} - 8 q^{23} - 136 q^{25} + 80 q^{26} + 96 q^{31} - 56 q^{32} + 8 q^{37} - 56 q^{38} + 232 q^{40} - 320 q^{41} - 112 q^{43} + 320 q^{46} - 64 q^{47} + 256 q^{50} + 96 q^{52} + 72 q^{53} - 80 q^{55} + 336 q^{56} - 512 q^{58} - 496 q^{61} + 776 q^{62} - 312 q^{65} - 192 q^{67} - 568 q^{68} + 112 q^{70} + 144 q^{71} + 224 q^{73} + 416 q^{76} - 112 q^{77} + 528 q^{80} + 352 q^{82} + 32 q^{83} + 24 q^{85} - 240 q^{86} + 216 q^{88} - 1304 q^{92} - 376 q^{95} - 816 q^{97} + 56 q^{98}+O(q^{100}) \) 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8 - 40 * q^10 + 64 * q^13 - 184 * q^16 - 24 * q^17 - 72 * q^20 + 8 * q^22 - 8 * q^23 - 136 * q^25 + 80 * q^26 + 96 * q^31 - 56 * q^32 + 8 * q^37 - 56 * q^38 + 232 * q^40 - 320 * q^41 - 112 * q^43 + 320 * q^46 - 64 * q^47 + 256 * q^50 + 96 * q^52 + 72 * q^53 - 80 * q^55 + 336 * q^56 - 512 * q^58 - 496 * q^61 + 776 * q^62 - 312 * q^65 - 192 * q^67 - 568 * q^68 + 112 * q^70 + 144 * q^71 + 224 * q^73 + 416 * q^76 - 112 * q^77 + 528 * q^80 + 352 * q^82 + 32 * q^83 + 24 * q^85 - 240 * q^86 + 216 * q^88 - 1304 * q^92 - 376 * q^95 - 816 * q^97 + 56 * q^98

Introduction

L-functions

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Database

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