LMFDB - Embedded newform 400.3.bg.a.113.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,3,Mod(17,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

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

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

chi := DirichletCharacter("400.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	400.bg (of order $20$, degree $8$, 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:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 30x^{14} + 351x^{12} + 2130x^{10} + 7341x^{8} + 14480x^{6} + 15196x^{4} + 6560x^{2} + 16 $ x^16 + 30x^14 + 351x^12 + 2130x^10 + 7341x^8 + 14480x^6 + 15196x^4 + 6560*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			113.1
Root			$1.78563i$ of defining polynomial
Character	$\chi$	$=$	400.113
Dual form			400.3.bg.a.177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.252608 + 0.495771i) q^{3} +(3.68015 + 3.38474i) q^{5} +(-7.20385 + 7.20385i) q^{7} +(5.10809 + 7.03068i) q^{9} +O(q^{10})$	\(q+(-0.252608 + 0.495771i) q^{3} +(3.68015 + 3.38474i) q^{5} +(-7.20385 + 7.20385i) q^{7} +(5.10809 + 7.03068i) q^{9} +(-4.56901 - 3.31958i) q^{11} +(-22.6344 - 3.58493i) q^{13} +(-2.60770 + 0.969500i) q^{15} +(-8.10888 - 15.9146i) q^{17} +(13.6027 + 4.41978i) q^{19} +(-1.75171 - 5.39121i) q^{21} +(-4.05981 - 25.6327i) q^{23} +(2.08702 + 24.9127i) q^{25} +(-9.72206 + 1.53982i) q^{27} +(-14.8092 + 4.81180i) q^{29} +(-10.7392 + 33.0518i) q^{31} +(2.79992 - 1.42663i) q^{33} +(-50.8944 + 2.12806i) q^{35} +(2.42751 - 15.3267i) q^{37} +(7.49493 - 10.3159i) q^{39} +(-37.3476 + 27.1346i) q^{41} +(31.8617 + 31.8617i) q^{43} +(-4.99852 + 43.1635i) q^{45} +(-8.16953 - 4.16259i) q^{47} -54.7908i q^{49} +9.93836 q^{51} +(-12.8896 + 25.2972i) q^{53} +(-5.57872 - 27.6815i) q^{55} +(-5.62735 + 5.62735i) q^{57} +(23.3065 + 32.0786i) q^{59} +(11.5211 + 8.37057i) q^{61} +(-87.4458 - 13.8501i) q^{63} +(-71.1638 - 89.8046i) q^{65} +(-24.8631 - 48.7966i) q^{67} +(13.7335 + 4.46228i) q^{69} +(23.8910 + 73.5289i) q^{71} +(15.4792 + 97.7321i) q^{73} +(-12.8782 - 5.25848i) q^{75} +(56.8282 - 9.00071i) q^{77} +(-110.397 + 35.8702i) q^{79} +(-22.4769 + 69.1767i) q^{81} +(13.6584 - 6.95931i) q^{83} +(24.0249 - 86.0145i) q^{85} +(1.35537 - 8.55747i) q^{87} +(43.0149 - 59.2049i) q^{89} +(188.880 - 137.229i) q^{91} +(-13.6733 - 13.6733i) q^{93} +(35.1001 + 62.3071i) q^{95} +(67.9854 + 34.6403i) q^{97} -49.0800i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} + 2 q^{7} - 40 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 + 2 * q^7 - 40 * q^9	$ 16 q - 2 q^{3} + 2 q^{7} - 40 q^{9} - 32 q^{11} - 8 q^{13} - 62 q^{17} - 30 q^{19} - 68 q^{21} + 18 q^{23} + 70 q^{25} + 40 q^{27} + 100 q^{29} - 132 q^{31} - 36 q^{33} - 150 q^{35} + 138 q^{37} + 320 q^{39} - 88 q^{41} + 78 q^{43} - 20 q^{45} + 22 q^{47} + 168 q^{51} + 182 q^{53} - 280 q^{55} + 280 q^{57} + 350 q^{59} + 372 q^{61} - 22 q^{63} - 910 q^{65} + 112 q^{67} - 30 q^{69} - 122 q^{71} - 248 q^{73} + 80 q^{75} + 16 q^{77} - 760 q^{79} - 144 q^{81} - 132 q^{83} - 30 q^{85} - 770 q^{87} + 550 q^{89} + 798 q^{91} + 54 q^{93} - 40 q^{95} - 292 q^{97}+O(q^{100}) $ 16 * q - 2 * q^3 + 2 * q^7 - 40 * q^9 - 32 * q^11 - 8 * q^13 - 62 * q^17 - 30 * q^19 - 68 * q^21 + 18 * q^23 + 70 * q^25 + 40 * q^27 + 100 * q^29 - 132 * q^31 - 36 * q^33 - 150 * q^35 + 138 * q^37 + 320 * q^39 - 88 * q^41 + 78 * q^43 - 20 * q^45 + 22 * q^47 + 168 * q^51 + 182 * q^53 - 280 * q^55 + 280 * q^57 + 350 * q^59 + 372 * q^61 - 22 * q^63 - 910 * q^65 + 112 * q^67 - 30 * q^69 - 122 * q^71 - 248 * q^73 + 80 * q^75 + 16 * q^77 - 760 * q^79 - 144 * q^81 - 132 * q^83 - 30 * q^85 - 770 * q^87 + 550 * q^89 + 798 * q^91 + 54 * q^93 - 40 * q^95 - 292 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.252608	+	0.495771i	−0.0842027	+	0.165257i	−0.929268	−	0.369406i	$-0.879561\pi$
$3$	−0.252608	+	0.495771i	−0.0842027	+	0.165257i	0.845066	+	0.534663i	$0.179561\pi$
$4$		0			0
$5$	3.68015	+	3.38474i	0.736030	+	0.676949i
$5$	3.68015	+	3.38474i	0.736030	+	0.676949i
$6$		0			0
$7$	−7.20385	+	7.20385i	−1.02912	+	1.02912i	−0.0295578	+	0.999563i	$0.509410\pi$
$7$	−7.20385	+	7.20385i	−1.02912	+	1.02912i	−0.999563	+	0.0295578i	$0.990590\pi$
$8$		0			0
$9$	5.10809	+	7.03068i	0.567565	+	0.781187i
$10$		0			0
$11$	−4.56901	−	3.31958i	−0.415365	−	0.301780i	0.360405	−	0.932796i	$-0.382638\pi$
$11$	−4.56901	−	3.31958i	−0.415365	−	0.301780i	−0.775770	+	0.631016i	$0.782638\pi$
$12$		0			0
$13$	−22.6344	−	3.58493i	−1.74111	−	0.275764i	−0.796659	−	0.604429i	$-0.793401\pi$
$13$	−22.6344	−	3.58493i	−1.74111	−	0.275764i	−0.944446	+	0.328666i	$0.893401\pi$
$14$		0			0
$15$	−2.60770	+	0.969500i	−0.173846	+	0.0646333i
$16$		0			0
$17$	−8.10888	−	15.9146i	−0.476993	−	0.936151i	−0.996651	−	0.0817767i	$-0.973941\pi$
$17$	−8.10888	−	15.9146i	−0.476993	−	0.936151i	0.519658	−	0.854374i	$-0.326059\pi$
$18$		0			0
$19$	13.6027	+	4.41978i	0.715931	+	0.232620i	0.644258	−	0.764808i	$-0.277166\pi$
$19$	13.6027	+	4.41978i	0.715931	+	0.232620i	0.0716731	+	0.997428i	$0.477166\pi$
$20$		0			0
$21$	−1.75171	−	5.39121i	−0.0834148	−	0.256724i
$22$		0			0
$23$	−4.05981	−	25.6327i	−0.176514	−	1.11446i	−0.903745	−	0.428071i	$-0.859193\pi$
$23$	−4.05981	−	25.6327i	−0.176514	−	1.11446i	0.727232	−	0.686392i	$-0.240807\pi$
$24$		0			0
$25$	2.08702	+	24.9127i	0.0834807	+	0.996509i
$26$		0			0
$27$	−9.72206	+	1.53982i	−0.360076	+	0.0570305i
$28$		0			0
$29$	−14.8092	+	4.81180i	−0.510662	+	0.165924i	−0.553003	−	0.833179i	$-0.686518\pi$
$29$	−14.8092	+	4.81180i	−0.510662	+	0.165924i	0.0423415	+	0.999103i	$0.486518\pi$
$30$		0			0
$31$	−10.7392	+	33.0518i	−0.346425	+	1.06619i	0.614392	+	0.789001i	$0.289402\pi$
$31$	−10.7392	+	33.0518i	−0.346425	+	1.06619i	−0.960817	+	0.277185i	$0.910598\pi$
$32$		0			0
$33$	2.79992	−	1.42663i	0.0848462	−	0.0432313i
$34$		0			0
$35$	−50.8944	+	2.12806i	−1.45413	+	0.0608018i
$36$		0			0
$37$	2.42751	−	15.3267i	0.0656084	−	0.414235i	−0.932924	−	0.360074i	$-0.882752\pi$
$37$	2.42751	−	15.3267i	0.0656084	−	0.414235i	0.998532	−	0.0541612i	$-0.0172485\pi$
$38$		0			0
$39$	7.49493	−	10.3159i	0.192178	−	0.264510i
$40$		0			0
$41$	−37.3476	+	27.1346i	−0.910917	+	0.661820i	−0.941247	−	0.337720i	$-0.890344\pi$
$41$	−37.3476	+	27.1346i	−0.910917	+	0.661820i	0.0303297	+	0.999540i	$0.490344\pi$
$42$		0			0
$43$	31.8617	+	31.8617i	0.740969	+	0.740969i	0.972765	−	0.231796i	$-0.0744600\pi$
$43$	31.8617	+	31.8617i	0.740969	+	0.740969i	−0.231796	+	0.972765i	$0.574460\pi$
$44$		0			0
$45$	−4.99852	+	43.1635i	−0.111078	+	0.959190i
$46$		0			0
$47$	−8.16953	−	4.16259i	−0.173820	−	0.0885657i	0.364916	−	0.931041i	$-0.381098\pi$
$47$	−8.16953	−	4.16259i	−0.173820	−	0.0885657i	−0.538736	+	0.842475i	$0.681098\pi$
$48$		0			0
$49$		−	54.7908i		−	1.11818i
$50$		0			0
$51$	9.93836			0.194870
$52$		0			0
$53$	−12.8896	+	25.2972i	−0.243199	+	0.477305i	−0.980050	−	0.198750i	$-0.936312\pi$
$53$	−12.8896	+	25.2972i	−0.243199	+	0.477305i	0.736851	+	0.676055i	$0.236312\pi$
$54$		0			0
$55$	−5.57872	−	27.6815i	−0.101431	−	0.503300i
$56$		0			0
$57$	−5.62735	+	5.62735i	−0.0987255	+	0.0987255i
$58$		0			0
$59$	23.3065	+	32.0786i	0.395025	+	0.543706i	0.959487	−	0.281754i	$-0.0909161\pi$
$59$	23.3065	+	32.0786i	0.395025	+	0.543706i	−0.564461	+	0.825459i	$0.690916\pi$
$60$		0			0
$61$	11.5211	+	8.37057i	0.188871	+	0.137223i	0.678202	−	0.734875i	$-0.262759\pi$
$61$	11.5211	+	8.37057i	0.188871	+	0.137223i	−0.489332	+	0.872098i	$0.662759\pi$
$62$		0			0
$63$	−87.4458	−	13.8501i	−1.38803	−	0.219842i
$64$		0			0
$65$	−71.1638	−	89.8046i	−1.09483	−	1.38161i
$66$		0			0
$67$	−24.8631	−	48.7966i	−0.371091	−	0.728308i	0.627648	−	0.778497i	$-0.284018\pi$
$67$	−24.8631	−	48.7966i	−0.371091	−	0.728308i	−0.998740	+	0.0501893i	$0.984018\pi$
$68$		0			0
$69$	13.7335	+	4.46228i	0.199036	+	0.0646707i
$70$		0			0
$71$	23.8910	+	73.5289i	0.336493	+	1.03562i	0.965982	+	0.258609i	$0.0832642\pi$
$71$	23.8910	+	73.5289i	0.336493	+	1.03562i	−0.629489	+	0.777009i	$0.716736\pi$
$72$		0			0
$73$	15.4792	+	97.7321i	0.212044	+	1.33880i	0.832269	+	0.554371i	$0.187041\pi$
$73$	15.4792	+	97.7321i	0.212044	+	1.33880i	−0.620225	+	0.784424i	$0.712959\pi$
$74$		0			0
$75$	−12.8782	−	5.25848i	−0.171710	−	0.0701130i
$76$		0			0
$77$	56.8282	−	9.00071i	0.738029	−	0.116892i
$78$		0			0
$79$	−110.397	+	35.8702i	−1.39743	+	0.454053i	−0.908360	−	0.418189i	$-0.862665\pi$
$79$	−110.397	+	35.8702i	−1.39743	+	0.454053i	−0.489073	+	0.872243i	$0.662665\pi$
$80$		0			0
$81$	−22.4769	+	69.1767i	−0.277492	+	0.854033i
$82$		0			0
$83$	13.6584	−	6.95931i	0.164559	−	0.0838471i	−0.369771	−	0.929123i	$-0.620564\pi$
$83$	13.6584	−	6.95931i	0.164559	−	0.0838471i	0.534330	+	0.845276i	$0.320564\pi$
$84$		0			0
$85$	24.0249	−	86.0145i	0.282645	−	1.01194i
$86$		0			0
$87$	1.35537	−	8.55747i	0.0155790	−	0.0983617i
$88$		0			0
$89$	43.0149	−	59.2049i	0.483314	−	0.665224i	−0.495824	−	0.868423i	$-0.665134\pi$
$89$	43.0149	−	59.2049i	0.483314	−	0.665224i	0.979137	+	0.203199i	$0.0651339\pi$
$90$		0			0
$91$	188.880	−	137.229i	2.07560	−	1.50801i
$92$		0			0
$93$	−13.6733	−	13.6733i	−0.147025	−	0.147025i
$94$		0			0
$95$	35.1001	+	62.3071i	0.369475	+	0.655864i
$96$		0			0
$97$	67.9854	+	34.6403i	0.700880	+	0.357116i	0.767842	−	0.640639i	$-0.221331\pi$
$97$	67.9854	+	34.6403i	0.700880	+	0.357116i	−0.0669620	+	0.997756i	$0.521331\pi$
$98$		0			0
$99$		−	49.0800i		−	0.495758i
$100$		0			0
$101$	156.192			1.54646			0.773228	−	0.634128i	$-0.218641\pi$
$101$	156.192			1.54646			0.773228	+	0.634128i	$0.218641\pi$
$102$		0			0
$103$	−73.4520	+	144.158i	−0.713127	+	1.39959i	0.194962	+	0.980811i	$0.437542\pi$
$103$	−73.4520	+	144.158i	−0.713127	+	1.39959i	−0.908088	+	0.418779i	$0.862458\pi$
$104$		0			0
$105$	11.8013	−	25.7696i	0.112393	−	0.245424i
$106$		0			0
$107$	125.552	−	125.552i	1.17338	−	1.17338i	0.191981	−	0.981399i	$-0.438509\pi$
$107$	125.552	−	125.552i	1.17338	−	1.17338i	0.981399	−	0.191981i	$-0.0614913\pi$
$108$		0			0
$109$	52.2004	+	71.8476i	0.478902	+	0.659153i	0.978294	−	0.207224i	$-0.0664429\pi$
$109$	52.2004	+	71.8476i	0.478902	+	0.659153i	−0.499391	+	0.866377i	$0.666443\pi$
$110$		0			0
$111$	6.98533	+	5.07514i	0.0629309	+	0.0457220i
$112$		0			0
$113$	23.7002	+	3.75375i	0.209736	+	0.0332190i	0.260418	−	0.965496i	$-0.416139\pi$
$113$	23.7002	+	3.75375i	0.209736	+	0.0332190i	−0.0506820	+	0.998715i	$0.516139\pi$
$114$		0			0
$115$	71.8192	−	108.073i	0.624515	−	0.939769i
$116$		0			0
$117$	−90.4138	−	177.447i	−0.772768	−	1.51664i
$118$		0			0
$119$	173.061	+	56.2310i	1.45430	+	0.472529i
$120$		0			0
$121$	−27.5348	−	84.7434i	−0.227560	−	0.700359i
$122$		0			0
$123$	−4.01826	−	25.3703i	−0.0326688	−	0.206263i
$124$		0			0
$125$	−76.6427	+	98.7466i	−0.613142	+	0.789973i
$126$		0			0
$127$	30.8349	−	4.88376i	0.242794	−	0.0384548i	−0.0338513	−	0.999427i	$-0.510777\pi$
$127$	30.8349	−	4.88376i	0.242794	−	0.0384548i	0.276645	+	0.960972i	$0.410777\pi$
$128$		0			0
$129$	−23.8446	+	7.74759i	−0.184842	+	0.0600588i
$130$		0			0
$131$	−39.8145	+	122.536i	−0.303928	+	0.935393i	0.676148	+	0.736766i	$0.263648\pi$
$131$	−39.8145	+	122.536i	−0.303928	+	0.935393i	−0.980075	+	0.198627i	$0.936352\pi$
$132$		0			0
$133$	−129.831	+	66.1523i	−0.976174	+	0.497386i
$134$		0			0
$135$	−40.9905	−	27.2399i	−0.303634	−	0.201777i
$136$		0			0
$137$	−4.80456	+	30.3348i	−0.0350698	+	0.221422i	−0.998999	−	0.0447377i	$-0.985755\pi$
$137$	−4.80456	+	30.3348i	−0.0350698	+	0.221422i	0.963929	+	0.266159i	$0.0857548\pi$
$138$		0			0
$139$	100.363	−	138.137i	0.722034	−	0.993794i	−0.277420	−	0.960749i	$-0.589479\pi$
$139$	100.363	−	138.137i	0.722034	−	0.993794i	0.999454	−	0.0330456i	$-0.0105207\pi$
$140$		0			0
$141$	4.12738	−	2.99872i	0.0292722	−	0.0212675i
$142$		0			0
$143$	91.5163	+	91.5163i	0.639974	+	0.639974i
$144$		0			0
$145$	−70.7867	−	32.4172i	−0.488184	−	0.223567i
$146$		0			0
$147$	27.1637	+	13.8406i	0.184787	+	0.0941538i
$148$		0			0
$149$			23.7099i			0.159127i	0.996830	+	0.0795635i	$0.0253527\pi$
$149$			23.7099i			0.159127i	−0.996830	+	0.0795635i	$0.974647\pi$
$150$		0			0
$151$	−207.294			−1.37281			−0.686403	−	0.727222i	$-0.740811\pi$
$151$	−207.294			−1.37281			−0.686403	+	0.727222i	$0.740811\pi$
$152$		0			0
$153$	70.4694	−	138.304i	0.460584	−	0.903948i
$154$		0			0
$155$	−151.394	+	85.2862i	−0.976733	+	0.550233i
$156$		0			0
$157$	25.6746	−	25.6746i	0.163533	−	0.163533i	−0.620597	−	0.784130i	$-0.713110\pi$
$157$	25.6746	−	25.6746i	0.163533	−	0.163533i	0.784130	+	0.620597i	$0.213110\pi$
$158$		0			0
$159$	−9.28562	−	12.7806i	−0.0584001	−	0.0803808i
$160$		0			0
$161$	213.900	+	155.407i	1.32857	+	0.965263i
$162$		0			0
$163$	−81.5666	−	12.9189i	−0.500408	−	0.0792569i	−0.0988723	−	0.995100i	$-0.531524\pi$
$163$	−81.5666	−	12.9189i	−0.500408	−	0.0792569i	−0.401536	+	0.915843i	$0.631524\pi$
$164$		0			0
$165$	15.1329	+	4.22680i	0.0917147	+	0.0256170i
$166$		0			0
$167$	−23.8290	−	46.7671i	−0.142689	−	0.280043i	0.808591	−	0.588371i	$-0.200230\pi$
$167$	−23.8290	−	46.7671i	−0.142689	−	0.280043i	−0.951280	+	0.308328i	$0.900230\pi$
$168$		0			0
$169$	338.734	+	110.061i	2.00434	+	0.651251i
$170$		0			0
$171$	38.4097	+	118.213i	0.224618	+	0.691303i
$172$		0			0
$173$	−6.98501	−	44.1016i	−0.0403758	−	0.254923i	0.959241	−	0.282588i	$-0.0911928\pi$
$173$	−6.98501	−	44.1016i	−0.0403758	−	0.254923i	−0.999617	+	0.0276651i	$0.991193\pi$
$174$		0			0
$175$	−194.502	−	164.433i	−1.11144	−	0.939617i
$176$		0			0
$177$	−21.7911	+	3.45137i	−0.123113	+	0.0194993i
$178$		0			0
$179$	310.306	−	100.824i	1.73355	−	0.563265i	0.739596	−	0.673051i	$-0.235017\pi$
$179$	310.306	−	100.824i	1.73355	−	0.563265i	0.993955	+	0.109787i	$0.0350167\pi$
$180$		0			0
$181$	25.5973	−	78.7805i	0.141422	−	0.435251i	−0.855112	−	0.518444i	$-0.826512\pi$
$181$	25.5973	−	78.7805i	0.141422	−	0.435251i	0.996534	+	0.0831923i	$0.0265116\pi$
$182$		0			0
$183$	−7.06022	+	3.59736i	−0.0385804	+	0.0196577i
$184$		0			0
$185$	60.8105	−	48.1880i	0.328706	−	0.260476i
$186$		0			0
$187$	−15.7802	+	99.6320i	−0.0843859	+	0.532791i
$188$		0			0
$189$	58.9436	−	81.1289i	0.311871	−	0.429253i
$190$		0			0
$191$	−112.018	+	81.3859i	−0.586482	+	0.426104i	−0.841055	−	0.540950i	$-0.818065\pi$
$191$	−112.018	+	81.3859i	−0.586482	+	0.426104i	0.254573	+	0.967053i	$0.418065\pi$
$192$		0			0
$193$	−14.7833	−	14.7833i	−0.0765975	−	0.0765975i	0.667770	−	0.744368i	$-0.267249\pi$
$193$	−14.7833	−	14.7833i	−0.0765975	−	0.0765975i	−0.744368	+	0.667770i	$0.767249\pi$
$194$		0			0
$195$	62.4991	−	12.5956i	0.320508	−	0.0645928i
$196$		0			0
$197$	−5.58697	−	2.84670i	−0.0283602	−	0.0144503i	0.439753	−	0.898119i	$-0.355066\pi$
$197$	−5.58697	−	2.84670i	−0.0283602	−	0.0144503i	−0.468113	+	0.883669i	$0.655066\pi$
$198$		0			0
$199$		−	244.037i		−	1.22632i	−0.789961	−	0.613158i	$-0.789899\pi$
$199$		−	244.037i		−	1.22632i	0.789961	−	0.613158i	$-0.210101\pi$
$200$		0			0
$201$	30.4726			0.151605
$202$		0			0
$203$	72.0197	−	141.347i	0.354777	−	0.696288i
$204$		0			0
$205$	−229.288	−	26.5526i	−1.11848	−	0.129525i
$206$		0			0
$207$	159.477	−	159.477i	0.770421	−	0.770421i
$208$		0			0
$209$	−47.4791	−	65.3493i	−0.227173	−	0.312676i
$210$		0			0
$211$	128.663	+	93.4793i	0.609778	+	0.443030i	0.849336	−	0.527852i	$-0.177002\pi$
$211$	128.663	+	93.4793i	0.609778	+	0.443030i	−0.239558	+	0.970882i	$0.577002\pi$
$212$		0			0
$213$	−42.4886	−	6.72953i	−0.199477	−	0.0315940i
$214$		0			0
$215$	9.41215	+	225.099i	0.0437774	+	1.04697i
$216$		0			0
$217$	−160.737	−	315.463i	−0.740721	−	1.45375i
$218$		0			0
$219$	−52.3629	−	17.0138i	−0.239100	−	0.0776884i
$220$		0			0
$221$	126.487	+	389.286i	0.572338	+	1.76147i
$222$		0			0
$223$	59.4523	+	375.367i	0.266602	+	1.68326i	0.650203	+	0.759761i	$0.274684\pi$
$223$	59.4523	+	375.367i	0.266602	+	1.68326i	−0.383601	+	0.923499i	$0.625316\pi$
$224$		0			0
$225$	−164.493	+	141.930i	−0.731079	+	0.630798i
$226$		0			0
$227$	−178.162	+	28.2180i	−0.784853	+	0.124309i	−0.535983	−	0.844228i	$-0.680059\pi$
$227$	−178.162	+	28.2180i	−0.784853	+	0.124309i	−0.248870	+	0.968537i	$0.580059\pi$
$228$		0			0
$229$	24.3355	−	7.90707i	0.106268	−	0.0345287i	−0.255400	−	0.966835i	$-0.582207\pi$
$229$	24.3355	−	7.90707i	0.106268	−	0.0345287i	0.361669	+	0.932307i	$0.382207\pi$
$230$		0			0
$231$	−9.89298	+	30.4475i	−0.0428268	+	0.131807i
$232$		0			0
$233$	−244.770	+	124.717i	−1.05052	+	0.535265i	−0.891974	−	0.452088i	$-0.850679\pi$
$233$	−244.770	+	124.717i	−1.05052	+	0.535265i	−0.158542	+	0.987352i	$0.550679\pi$
$234$		0			0
$235$	−15.9758	−	42.9707i	−0.0679823	−	0.182854i
$236$		0			0
$237$	10.1038	−	63.7929i	0.0426321	−	0.269168i
$238$		0			0
$239$	−63.7205	+	87.7038i	−0.266613	+	0.366962i	−0.921243	−	0.388988i	$-0.872825\pi$
$239$	−63.7205	+	87.7038i	−0.266613	+	0.366962i	0.654630	+	0.755950i	$0.272825\pi$
$240$		0			0
$241$	−299.048	+	217.271i	−1.24086	+	0.901541i	−0.997656	−	0.0684333i	$-0.978200\pi$
$241$	−299.048	+	217.271i	−1.24086	+	0.901541i	−0.243209	+	0.969974i	$0.578200\pi$
$242$		0			0
$243$	−91.2600	−	91.2600i	−0.375556	−	0.375556i
$244$		0			0
$245$	185.453	−	201.638i	0.756950	−	0.823014i
$246$		0			0
$247$	−292.044	−	148.804i	−1.18236	−	0.602444i
$248$		0			0
$249$			8.52943i			0.0342547i
$250$		0			0
$251$	20.6897			0.0824293			0.0412146	−	0.999150i	$-0.486877\pi$
$251$	20.6897			0.0824293			0.0412146	+	0.999150i	$0.486877\pi$
$252$		0			0
$253$	−66.5404	+	130.593i	−0.263005	+	0.516177i
$254$		0			0
$255$	36.5747	+	33.6388i	0.143430	+	0.131917i
$256$		0			0
$257$	−57.5934	+	57.5934i	−0.224099	+	0.224099i	−0.810222	−	0.586123i	$-0.800653\pi$
$257$	−57.5934	+	57.5934i	−0.224099	+	0.224099i	0.586123	+	0.810222i	$0.300653\pi$
$258$		0			0
$259$	92.9237	+	127.899i	0.358779	+	0.493817i
$260$		0			0
$261$	−109.477	−	79.5396i	−0.419452	−	0.304749i
$262$		0			0
$263$	−86.6150	−	13.7185i	−0.329335	−	0.0521615i	−0.0104222	−	0.999946i	$-0.503318\pi$
$263$	−86.6150	−	13.7185i	−0.329335	−	0.0521615i	−0.318912	+	0.947784i	$0.603318\pi$
$264$		0			0
$265$	−133.060	+	49.4696i	−0.502113	+	0.186678i
$266$		0			0
$267$	18.4862	+	36.2812i	0.0692367	+	0.135885i
$268$		0			0
$269$	−79.3898	−	25.7953i	−0.295129	−	0.0958934i	0.157710	−	0.987485i	$-0.449589\pi$
$269$	−79.3898	−	25.7953i	−0.295129	−	0.0958934i	−0.452839	+	0.891592i	$0.649589\pi$
$270$		0			0
$271$	−33.5180	−	103.158i	−0.123683	−	0.380656i	0.869976	−	0.493094i	$-0.164134\pi$
$271$	−33.5180	−	103.158i	−0.123683	−	0.380656i	−0.993659	+	0.112438i	$0.964134\pi$
$272$		0			0
$273$	20.3217	+	128.306i	0.0744386	+	0.469987i
$274$		0			0
$275$	73.1643	−	120.755i	0.266052	−	0.439108i
$276$		0			0
$277$	−55.6330	+	8.81141i	−0.200841	+	0.0318101i	−0.256044	−	0.966665i	$-0.582419\pi$
$277$	−55.6330	+	8.81141i	−0.200841	+	0.0318101i	0.0552032	+	0.998475i	$0.482419\pi$
$278$		0			0
$279$	−287.233	+	93.3277i	−1.02951	+	0.334508i
$280$		0			0
$281$	98.2119	−	302.265i	0.349509	−	1.07568i	−0.609617	−	0.792696i	$-0.708677\pi$
$281$	98.2119	−	302.265i	0.349509	−	1.07568i	0.959126	−	0.282981i	$-0.0913233\pi$
$282$		0			0
$283$	−426.824	+	217.478i	−1.50821	+	0.768472i	−0.995911	−	0.0903348i	$-0.971206\pi$
$283$	−426.824	+	217.478i	−1.50821	+	0.768472i	−0.512300	+	0.858807i	$0.671206\pi$
$284$		0			0
$285$	−39.7567	+	1.66236i	−0.139497	+	0.00583283i
$286$		0			0
$287$	73.5727	−	464.520i	0.256351	−	1.61854i
$288$		0			0
$289$	−17.6497	+	24.2927i	−0.0610716	+	0.0840579i
$290$		0			0
$291$	−34.3473	+	24.9548i	−0.118032	+	0.0857553i
$292$		0			0
$293$	385.350	+	385.350i	1.31519	+	1.31519i	0.917536	+	0.397652i	$0.130175\pi$
$293$	385.350	+	385.350i	1.31519	+	1.31519i	0.397652	+	0.917536i	$0.369825\pi$
$294$		0			0
$295$	−22.8066	+	196.941i	−0.0773104	+	0.667596i
$296$		0			0
$297$	49.5318	+	25.2377i	0.166774	+	0.0849754i
$298$		0			0
$299$			594.733i			1.98907i
$300$		0			0
$301$	−459.053			−1.52509
$302$		0			0
$303$	−39.4554	+	77.4356i	−0.130216	+	0.255563i
$304$		0			0
$305$	14.0672	+	69.8010i	0.0461218	+	0.228856i
$306$		0			0
$307$	−40.8331	+	40.8331i	−0.133007	+	0.133007i	−0.770476	−	0.637469i	$-0.779981\pi$
$307$	−40.8331	+	40.8331i	−0.133007	+	0.133007i	0.637469	+	0.770476i	$0.279981\pi$
$308$		0			0
$309$	−52.9147	−	72.8308i	−0.171245	−	0.235699i
$310$		0			0
$311$	419.194	+	304.562i	1.34789	+	0.979299i	0.999114	+	0.0420933i	$0.0134027\pi$
$311$	419.194	+	304.562i	1.34789	+	0.979299i	0.348776	+	0.937206i	$0.386597\pi$
$312$		0			0
$313$	−199.049	−	31.5263i	−0.635940	−	0.100723i	−0.169864	−	0.985468i	$-0.554333\pi$
$313$	−199.049	−	31.5263i	−0.635940	−	0.100723i	−0.466076	+	0.884745i	$0.654333\pi$
$314$		0			0
$315$	−274.935	−	346.952i	−0.872809	−	1.10144i
$316$		0			0
$317$	215.645	+	423.227i	0.680268	+	1.33510i	0.930277	+	0.366857i	$0.119566\pi$
$317$	215.645	+	423.227i	0.680268	+	1.33510i	−0.250009	+	0.968243i	$0.580434\pi$
$318$		0			0
$319$	83.6366	+	27.1752i	0.262184	+	0.0851886i
$320$		0			0
$321$	30.5295	+	93.9603i	0.0951076	+	0.292711i
$322$		0			0
$323$	−39.9636	−	252.321i	−0.123726	−	0.781178i
$324$		0			0
$325$	42.0721	−	571.366i	0.129453	−	1.75805i
$326$		0			0
$327$	−48.8062	+	7.73015i	−0.149255	+	0.0236396i
$328$		0			0
$329$	88.8387	−	28.8654i	0.270026	−	0.0877369i
$330$		0			0
$331$	128.800	−	396.407i	0.389125	−	1.19760i	−0.544318	−	0.838879i	$-0.683211\pi$
$331$	128.800	−	396.407i	0.389125	−	1.19760i	0.933443	−	0.358725i	$-0.116789\pi$
$332$		0			0
$333$	120.157	−	61.2231i	0.360832	−	0.183853i
$334$		0			0
$335$	73.6640	−	263.734i	0.219893	−	0.787266i
$336$		0			0
$337$	33.4503	−	211.197i	0.0992591	−	0.626697i	−0.887035	−	0.461702i	$-0.847239\pi$
$337$	33.4503	−	211.197i	0.0992591	−	0.626697i	0.986294	−	0.164996i	$-0.0527610\pi$
$338$		0			0
$339$	−7.84787	+	10.8017i	−0.0231501	+	0.0318633i
$340$		0			0
$341$	158.786	−	115.364i	0.465647	−	0.338312i
$342$		0			0
$343$	41.7160	+	41.7160i	0.121621	+	0.121621i
$344$		0			0
$345$	35.4376	+	62.9062i	0.102718	+	0.182337i
$346$		0			0
$347$	113.136	+	57.6455i	0.326039	+	0.166125i	0.609347	−	0.792904i	$-0.291432\pi$
$347$	113.136	+	57.6455i	0.326039	+	0.166125i	−0.283307	+	0.959029i	$0.591432\pi$
$348$		0			0
$349$		−	117.679i		−	0.337189i	−0.985686	−	0.168594i	$-0.946077\pi$
$349$		−	117.679i		−	0.337189i	0.985686	−	0.168594i	$-0.0539228\pi$
$350$		0			0
$351$	225.573			0.642657
$352$		0			0
$353$	−24.8731	+	48.8161i	−0.0704619	+	0.138289i	−0.923551	−	0.383477i	$-0.874727\pi$
$353$	−24.8731	+	48.8161i	−0.0704619	+	0.138289i	0.853089	+	0.521766i	$0.174727\pi$
$354$		0			0
$355$	−160.954	+	351.462i	−0.453392	+	0.990035i
$356$		0			0
$357$	−71.5944	+	71.5944i	−0.200545	+	0.200545i
$358$		0			0
$359$	−269.868	−	371.442i	−0.751723	−	1.03466i	−0.997858	−	0.0654220i	$-0.979161\pi$
$359$	−269.868	−	371.442i	−0.751723	−	1.03466i	0.246135	−	0.969236i	$-0.420839\pi$
$360$		0			0
$361$	−126.556	−	91.9485i	−0.350571	−	0.254705i
$362$		0			0
$363$	48.9689	+	7.75591i	0.134900	+	0.0213661i
$364$		0			0
$365$	−273.832	+	412.062i	−0.750225	+	1.12894i
$366$		0			0
$367$	254.971	+	500.410i	0.694745	+	1.36351i	0.921045	+	0.389456i	$0.127337\pi$
$367$	254.971	+	500.410i	0.694745	+	1.36351i	−0.226300	+	0.974058i	$0.572663\pi$
$368$		0			0
$369$	−381.550	−	123.973i	−1.03401	−	0.335970i
$370$		0			0
$371$	−89.3826	−	275.091i	−0.240924	−	0.741486i
$372$		0			0
$373$	−29.4686	−	186.058i	−0.0790044	−	0.498814i	−0.995182	−	0.0980422i	$-0.968742\pi$
$373$	−29.4686	−	186.058i	−0.0790044	−	0.498814i	0.916178	−	0.400772i	$-0.131258\pi$
$374$		0			0
$375$	−29.5952	−	62.9415i	−0.0789205	−	0.167844i
$376$		0			0
$377$	352.447	−	55.8220i	0.934871	−	0.148069i
$378$		0			0
$379$	22.7930	−	7.40589i	0.0601398	−	0.0195406i	−0.278793	−	0.960351i	$-0.589934\pi$
$379$	22.7930	−	7.40589i	0.0601398	−	0.0195406i	0.338932	+	0.940811i	$0.389934\pi$
$380$		0			0
$381$	−5.36791	+	16.5207i	−0.0140890	+	0.0433615i
$382$		0			0
$383$	14.2210	−	7.24595i	0.0371305	−	0.0189189i	−0.435327	−	0.900273i	$-0.643367\pi$
$383$	14.2210	−	7.24595i	0.0371305	−	0.0189189i	0.472457	+	0.881354i	$0.343367\pi$
$384$		0			0
$385$	239.602	+	159.225i	0.622342	+	0.413572i
$386$		0			0
$387$	−61.2570	+	386.761i	−0.158287	+	0.999383i
$388$		0			0
$389$	143.389	−	197.358i	0.368610	−	0.507348i	−0.583913	−	0.811817i	$-0.698479\pi$
$389$	143.389	−	197.358i	0.368610	−	0.507348i	0.952522	+	0.304469i	$0.0984789\pi$
$390$		0			0
$391$	−375.012	+	272.462i	−0.959110	+	0.696834i
$392$		0			0
$393$	−50.6926	−	50.6926i	−0.128989	−	0.128989i
$394$		0			0
$395$	−527.690	−	241.658i	−1.33592	−	0.611794i
$396$		0			0
$397$	191.548	+	97.5985i	0.482488	+	0.245840i	0.678277	−	0.734806i	$-0.262727\pi$
$397$	191.548	+	97.5985i	0.482488	+	0.245840i	−0.195789	+	0.980646i	$0.562727\pi$
$398$		0			0
$399$		−	81.0772i		−	0.203201i
$400$		0			0
$401$	517.832			1.29135			0.645676	−	0.763612i	$-0.276576\pi$
$401$	517.832			1.29135			0.645676	+	0.763612i	$0.276576\pi$
$402$		0			0
$403$	361.563	−	709.607i	0.897178	−	1.76081i
$404$		0			0
$405$	−316.864	+	178.502i	−0.782379	+	0.440746i
$406$		0			0
$407$	−61.9696	+	61.9696i	−0.152259	+	0.152259i
$408$		0			0
$409$	−111.733	−	153.787i	−0.273186	−	0.376008i	0.650276	−	0.759698i	$-0.274653\pi$
$409$	−111.733	−	153.787i	−0.273186	−	0.376008i	−0.923462	+	0.383690i	$0.874653\pi$
$410$		0			0
$411$	−13.8254	−	10.0448i	−0.0336386	−	0.0244398i
$412$		0			0
$413$	−398.986	−	63.1932i	−0.966068	−	0.153010i
$414$		0			0
$415$	73.8205	+	20.6189i	0.177881	+	0.0496841i
$416$		0			0
$417$	43.1321	+	84.6516i	0.103434	+	0.203001i
$418$		0			0
$419$	101.900	+	33.1094i	0.243199	+	0.0790200i	0.428080	−	0.903741i	$-0.359190\pi$
$419$	101.900	+	33.1094i	0.243199	+	0.0790200i	−0.184882	+	0.982761i	$0.559190\pi$
$420$		0			0
$421$	113.217	+	348.447i	0.268925	+	0.827666i	0.990763	+	0.135604i	$0.0432975\pi$
$421$	113.217	+	348.447i	0.268925	+	0.827666i	−0.721838	+	0.692062i	$0.756703\pi$
$422$		0			0
$423$	−12.4649	−	78.7002i	−0.0294678	−	0.186053i
$424$		0			0
$425$	379.552	−	235.228i	0.893064	−	0.553478i
$426$		0			0
$427$	−143.297	+	22.6960i	−0.335589	+	0.0531521i
$428$		0			0
$429$	−68.4889	+	22.2534i	−0.159648	+	0.0518727i
$430$		0			0
$431$	−28.4314	+	87.5029i	−0.0659662	+	0.203023i	−0.978607	−	0.205740i	$-0.934040\pi$
$431$	−28.4314	+	87.5029i	−0.0659662	+	0.203023i	0.912640	+	0.408763i	$0.134040\pi$
$432$		0			0
$433$	−38.7505	+	19.7444i	−0.0894932	+	0.0455990i	−0.498164	−	0.867083i	$-0.665992\pi$
$433$	−38.7505	+	19.7444i	−0.0894932	+	0.0455990i	0.408671	+	0.912682i	$0.365992\pi$
$434$		0			0
$435$	33.9528	−	26.9052i	0.0780525	−	0.0618510i
$436$		0			0
$437$	58.0664	−	366.617i	0.132875	−	0.838940i
$438$		0			0
$439$	452.403	−	622.679i	1.03053	−	1.41840i	0.125982	−	0.992033i	$-0.459792\pi$
$439$	452.403	−	622.679i	1.03053	−	1.41840i	0.904548	−	0.426371i	$-0.140208\pi$
$440$		0			0
$441$	385.217	−	279.876i	0.873507	−	0.634640i
$442$		0			0
$443$	479.183	+	479.183i	1.08168	+	1.08168i	0.996353	+	0.0853248i	$0.0271928\pi$
$443$	479.183	+	479.183i	1.08168	+	1.08168i	0.0853248	+	0.996353i	$0.472807\pi$
$444$		0			0
$445$	358.695	−	72.2886i	0.806056	−	0.162446i
$446$		0			0
$447$	−11.7547	−	5.98932i	−0.0262969	−	0.0133989i
$448$		0			0
$449$			889.585i			1.98126i	0.136578	+	0.990629i	$0.456390\pi$
$449$			889.585i			1.98126i	−0.136578	+	0.990629i	$0.543610\pi$
$450$		0			0
$451$	260.717			0.578087
$452$		0			0
$453$	52.3641	−	102.770i	0.115594	−	0.226866i
$454$		0			0
$455$	1159.59	+	134.286i	2.54855	+	0.295133i
$456$		0			0
$457$	46.1201	−	46.1201i	0.100919	−	0.100919i	−0.654844	−	0.755764i	$-0.727266\pi$
$457$	46.1201	−	46.1201i	0.100919	−	0.100919i	0.755764	+	0.654844i	$0.227266\pi$
$458$		0			0
$459$	103.341	+	142.236i	0.225143	+	0.309883i
$460$		0			0
$461$	−625.212	−	454.243i	−1.35621	−	0.985343i	−0.998676	−	0.0514415i	$-0.983618\pi$
$461$	−625.212	−	454.243i	−1.35621	−	0.985343i	−0.357532	−	0.933901i	$-0.616382\pi$
$462$		0			0
$463$	449.918	+	71.2599i	0.971744	+	0.153909i	0.622069	−	0.782962i	$-0.286292\pi$
$463$	449.918	+	71.2599i	0.971744	+	0.153909i	0.349675	+	0.936871i	$0.386292\pi$
$464$		0			0
$465$	−4.03919	−	96.6006i	−0.00868643	−	0.207743i
$466$		0			0
$467$	158.701	+	311.468i	0.339830	+	0.666955i	0.996163	−	0.0875169i	$-0.0278932\pi$
$467$	158.701	+	311.468i	0.339830	+	0.666955i	−0.656333	+	0.754472i	$0.727893\pi$
$468$		0			0
$469$	530.633	+	172.413i	1.13141	+	0.367619i
$470$		0			0
$471$	6.24313	+	19.2144i	0.0132551	+	0.0407949i
$472$		0			0
$473$	−39.8090	−	251.344i	−0.0841627	−	0.531382i
$474$		0			0
$475$	−81.7198	+	348.105i	−0.172042	+	0.732852i
$476$		0			0
$477$	−243.698	+	38.5979i	−0.510896	+	0.0809180i
$478$		0			0
$479$	−49.6354	+	16.1275i	−0.103623	+	0.0336692i	−0.360370	−	0.932810i	$-0.617349\pi$
$479$	−49.6354	+	16.1275i	−0.103623	+	0.0336692i	0.256747	+	0.966479i	$0.417349\pi$
$480$		0			0
$481$	−109.890	+	338.207i	−0.228462	+	0.703134i
$482$		0			0
$483$	−131.079	+	66.7883i	−0.271386	+	0.138278i
$484$		0			0
$485$	132.948	+	357.594i	0.274119	+	0.737308i
$486$		0			0
$487$	93.1133	−	587.894i	0.191198	−	1.20718i	−0.686200	−	0.727413i	$-0.740723\pi$
$487$	93.1133	−	587.894i	0.191198	−	1.20718i	0.877398	−	0.479763i	$-0.159277\pi$
$488$		0			0
$489$	27.0092	−	37.1750i	0.0552335	−	0.0760224i
$490$		0			0
$491$	109.988	−	79.9113i	0.224009	−	0.162752i	−0.470120	−	0.882602i	$-0.655790\pi$
$491$	109.988	−	79.9113i	0.224009	−	0.162752i	0.694129	+	0.719850i	$0.255790\pi$
$492$		0			0
$493$	196.664	+	196.664i	0.398912	+	0.398912i
$494$		0			0
$495$	166.123	−	180.622i	0.335603	−	0.364893i
$496$		0			0
$497$	−701.798	−	357.584i	−1.41207	−	0.719485i
$498$		0			0
$499$			483.808i			0.969555i	0.874637	+	0.484778i	$0.161099\pi$
$499$			483.808i			0.969555i	−0.874637	+	0.484778i	$0.838901\pi$
$500$		0			0
$501$	29.2052			0.0582938
$502$		0			0
$503$	141.234	−	277.188i	0.280784	−	0.551070i	−0.706941	−	0.707273i	$-0.749925\pi$
$503$	141.234	−	277.188i	0.280784	−	0.551070i	0.987725	+	0.156203i	$0.0499253\pi$
$504$		0			0
$505$	574.810	+	528.670i	1.13824	+	1.04687i
$506$		0			0
$507$	−140.132	+	140.132i	−0.276395	+	0.276395i
$508$		0			0
$509$	−177.828	−	244.759i	−0.349367	−	0.480862i	0.597781	−	0.801659i	$-0.296049\pi$
$509$	−177.828	−	244.759i	−0.349367	−	0.480862i	−0.947148	+	0.320797i	$0.896049\pi$
$510$		0			0
$511$	−815.557	−	592.537i	−1.59600	−	1.15956i
$512$		0			0
$513$	−139.052	−	22.0237i	−0.271056	−	0.0429311i
$514$		0			0
$515$	−758.252	+	281.906i	−1.47233	+	0.547390i
$516$		0			0
$517$	23.5087	+	46.1384i	0.0454713	+	0.0892425i
$518$		0			0
$519$	23.6288	+	7.67746i	0.0455275	+	0.0147928i
$520$		0			0
$521$	−114.065	−	351.056i	−0.218935	−	0.673813i	−0.998851	−	0.0479282i	$-0.984738\pi$
$521$	−114.065	−	351.056i	−0.218935	−	0.673813i	0.779916	−	0.625885i	$-0.215262\pi$
$522$		0			0
$523$	−47.6107	−	300.602i	−0.0910338	−	0.574765i	−0.990472	−	0.137716i	$-0.956024\pi$
$523$	−47.6107	−	300.602i	−0.0910338	−	0.574765i	0.899438	−	0.437049i	$-0.143976\pi$
$524$		0			0
$525$	130.654	−	54.8915i	0.248865	−	0.104555i
$526$		0			0
$527$	613.087	−	97.1035i	1.16335	−	0.184257i
$528$		0			0
$529$	−137.442	+	44.6576i	−0.259815	+	0.0844189i
$530$		0			0
$531$	−106.483	+	327.721i	−0.200533	+	0.617177i
$532$		0			0
$533$	942.615	−	480.286i	1.76851	−	0.901100i
$534$		0			0
$535$	887.009	−	37.0888i	1.65796	−	0.0693248i
$536$		0			0
$537$	−28.3999	+	179.310i	−0.0528862	+	0.333910i
$538$		0			0
$539$	−181.883	+	250.340i	−0.337445	+	0.464453i
$540$		0			0
$541$	724.924	−	526.688i	1.33997	−	0.973545i	0.340525	−	0.940235i	$-0.389395\pi$
$541$	724.924	−	526.688i	1.33997	−	0.973545i	0.999445	−	0.0333098i	$-0.0106048\pi$
$542$		0			0
$543$	32.5910	+	32.5910i	0.0600203	+	0.0600203i
$544$		0			0
$545$	−51.0807	+	441.095i	−0.0937260	+	0.809349i
$546$		0			0
$547$	−524.755	−	267.376i	−0.959333	−	0.488804i	−0.0970765	−	0.995277i	$-0.530949\pi$
$547$	−524.755	−	267.376i	−0.959333	−	0.488804i	−0.862256	+	0.506473i	$0.830949\pi$
$548$		0			0
$549$			123.759i			0.225426i
$550$		0			0
$551$	−222.712			−0.404196
$552$		0			0
$553$	536.881	−	1053.69i	0.970852	−	1.90540i
$554$		0			0
$555$	8.52902	+	42.3208i	0.0153676	+	0.0762537i
$556$		0			0
$557$	−136.133	+	136.133i	−0.244404	+	0.244404i	−0.818669	−	0.574265i	$-0.805288\pi$
$557$	−136.133	+	136.133i	−0.244404	+	0.244404i	0.574265	+	0.818669i	$0.305288\pi$
$558$		0			0
$559$	−606.947	−	835.390i	−1.08577	−	1.49444i
$560$		0			0
$561$	−45.4085	−	32.9912i	−0.0809421	−	0.0588079i
$562$		0			0
$563$	−931.083	−	147.469i	−1.65379	−	0.261934i	−0.741341	−	0.671128i	$-0.765810\pi$
$563$	−931.083	−	147.469i	−1.65379	−	0.261934i	−0.912448	+	0.409194i	$0.865810\pi$
$564$		0			0
$565$	74.5149	+	94.0335i	0.131885	+	0.166431i
$566$		0			0
$567$	−336.418	−	660.258i	−0.593330	−	1.16448i
$568$		0			0
$569$	−333.782	−	108.452i	−0.586611	−	0.190602i	0.000648813	−	1.00000i	$-0.499793\pi$
$569$	−333.782	−	108.452i	−0.586611	−	0.190602i	−0.587260	+	0.809398i	$0.699793\pi$
$570$		0			0
$571$	−136.304	−	419.502i	−0.238712	−	0.734679i	−0.996607	−	0.0823034i	$-0.973772\pi$
$571$	−136.304	−	419.502i	−0.238712	−	0.734679i	0.757896	−	0.652376i	$-0.226228\pi$
$572$		0			0
$573$	−12.0521	−	76.0941i	−0.0210334	−	0.132799i
$574$		0			0
$575$	630.107	−	154.637i	1.09584	−	0.268934i
$576$		0			0
$577$	86.6592	−	13.7255i	0.150189	−	0.0237876i	−0.0808870	−	0.996723i	$-0.525775\pi$
$577$	86.6592	−	13.7255i	0.150189	−	0.0237876i	0.231076	+	0.972936i	$0.425775\pi$
$578$		0			0
$579$	11.0635	−	3.59476i	0.0191080	−	0.00620857i
$580$		0			0
$581$	−48.2593	+	148.527i	−0.0830625	+	0.255640i
$582$		0			0
$583$	142.869	−	72.7953i	0.245058	−	0.124863i
$584$		0			0
$585$	267.877	−	959.060i	0.457909	−	1.63942i
$586$		0			0
$587$	−106.732	+	673.879i	−0.181826	+	1.14801i	0.712859	+	0.701308i	$0.247400\pi$
$587$	−106.732	+	673.879i	−0.181826	+	1.14801i	−0.894685	+	0.446698i	$0.852600\pi$
$588$		0			0
$589$	−292.163	+	402.128i	−0.496033	+	0.682731i
$590$		0			0
$591$	2.82263	−	2.05076i	0.00477602	−	0.00346998i
$592$		0			0
$593$	526.775	+	526.775i	0.888322	+	0.888322i	0.994362	−	0.106039i	$-0.0338170\pi$
$593$	526.775	+	526.775i	0.888322	+	0.888322i	−0.106039	+	0.994362i	$0.533817\pi$
$594$		0			0
$595$	446.564	+	792.706i	0.750527	+	1.33228i
$596$		0			0
$597$	120.986	+	61.6457i	0.202657	+	0.103259i
$598$		0			0
$599$			586.777i			0.979594i	0.871836	+	0.489797i	$0.162929\pi$
$599$			586.777i			0.979594i	−0.871836	+	0.489797i	$0.837071\pi$
$600$		0			0
$601$	−664.202			−1.10516			−0.552581	−	0.833459i	$-0.686357\pi$
$601$	−664.202			−1.10516			−0.552581	+	0.833459i	$0.686357\pi$
$602$		0			0
$603$	216.070	−	424.062i	0.358326	−	0.703254i
$604$		0			0
$605$	185.502	−	405.067i	0.306616	−	0.669532i
$606$		0			0
$607$	90.2350	−	90.2350i	0.148657	−	0.148657i	−0.628861	−	0.777518i	$-0.716478\pi$
$607$	90.2350	−	90.2350i	0.148657	−	0.148657i	0.777518	+	0.628861i	$0.216478\pi$
$608$		0			0
$609$	51.8828	+	71.4106i	0.0851935	+	0.117259i
$610$		0			0
$611$	169.990	+	123.505i	0.278215	+	0.202135i
$612$		0			0
$613$	−773.095	−	122.446i	−1.26117	−	0.199749i	−0.510180	−	0.860067i	$-0.670421\pi$
$613$	−773.095	−	122.446i	−1.26117	−	0.199749i	−0.750986	+	0.660318i	$0.770421\pi$
$614$		0			0
$615$	71.0842	−	106.967i	0.115584	−	0.173931i
$616$		0			0
$617$	305.103	+	598.799i	0.494495	+	0.970500i	0.994526	+	0.104493i	$0.0333219\pi$
$617$	305.103	+	598.799i	0.494495	+	0.970500i	−0.500031	+	0.866008i	$0.666678\pi$
$618$		0			0
$619$	−318.118	−	103.363i	−0.513922	−	0.166983i	0.0405633	−	0.999177i	$-0.487085\pi$
$619$	−318.118	−	103.363i	−0.513922	−	0.166983i	−0.554485	+	0.832194i	$0.687085\pi$
$620$		0			0
$621$	78.9395	+	242.951i	0.127117	+	0.391225i
$622$		0			0
$623$	116.630	+	736.376i	0.187208	+	1.18198i
$624$		0			0
$625$	−616.289	+	103.987i	−0.986062	+	0.166379i
$626$		0			0
$627$	44.3919	−	7.03099i	0.0708005	−	0.0112137i
$628$		0			0
$629$	−263.602	+	85.6495i	−0.419081	+	0.136168i
$630$		0			0
$631$	−27.3879	+	84.2913i	−0.0434040	+	0.133584i	−0.970410	−	0.241462i	$-0.922373\pi$
$631$	−27.3879	+	84.2913i	−0.0434040	+	0.133584i	0.927006	+	0.375046i	$0.122373\pi$
$632$		0			0
$633$	−78.8458	+	40.1739i	−0.124559	+	0.0634659i
$634$		0			0
$635$	130.007	+	86.3951i	0.204736	+	0.136055i
$636$		0			0
$637$	−196.421	+	1240.15i	−0.308354	+	1.94687i
$638$		0			0
$639$	−394.921	+	543.562i	−0.618030	+	0.850645i
$640$		0			0
$641$	−763.194	+	554.493i	−1.19063	+	0.865044i	−0.993331	−	0.115299i	$-0.963217\pi$
$641$	−763.194	+	554.493i	−1.19063	+	0.865044i	−0.197300	+	0.980343i	$0.563217\pi$
$642$		0			0
$643$	−81.8654	−	81.8654i	−0.127318	−	0.127318i	0.640576	−	0.767894i	$-0.278695\pi$
$643$	−81.8654	−	81.8654i	−0.127318	−	0.127318i	−0.767894	+	0.640576i	$0.778695\pi$
$644$		0			0
$645$	−113.975	−	52.1956i	−0.176706	−	0.0809235i
$646$		0			0
$647$	989.616	+	504.234i	1.52955	+	0.779342i	0.997719	−	0.0675110i	$-0.0215058\pi$
$647$	989.616	+	504.234i	1.52955	+	0.779342i	0.531827	+	0.846853i	$0.321506\pi$
$648$		0			0
$649$		−	223.936i		−	0.345047i
$650$		0			0
$651$	197.001			0.302613
$652$		0			0
$653$	278.161	−	545.922i	0.425975	−	0.836022i	−0.573880	−	0.818940i	$-0.694562\pi$
$653$	278.161	−	545.922i	0.425975	−	0.836022i	0.999854	−	0.0170824i	$-0.00543777\pi$
$654$		0			0
$655$	−561.278	+	316.191i	−0.856913	+	0.482734i
$656$		0			0
$657$	−608.054	+	608.054i	−0.925500	+	0.925500i
$658$		0			0
$659$	−306.794	−	422.266i	−0.465545	−	0.640768i	0.510102	−	0.860114i	$-0.329608\pi$
$659$	−306.794	−	422.266i	−0.465545	−	0.640768i	−0.975647	+	0.219346i	$0.929608\pi$
$660$		0			0
$661$	119.230	+	86.6259i	0.180379	+	0.131053i	0.674311	−	0.738448i	$-0.264441\pi$
$661$	119.230	+	86.6259i	0.180379	+	0.131053i	−0.493932	+	0.869501i	$0.664441\pi$
$662$		0			0
$663$	−224.948	−	35.6283i	−0.339289	−	0.0537381i
$664$		0			0
$665$	−701.707	−	195.995i	−1.05520	−	0.294729i
$666$		0			0
$667$	183.462	+	360.064i	0.275055	+	0.539826i
$668$		0			0
$669$	−201.114	−	65.3460i	−0.300619	−	0.0976771i
$670$		0			0
$671$	−24.8533	−	76.4905i	−0.0370392	−	0.113995i
$672$		0			0
$673$	38.7807	+	244.852i	0.0576236	+	0.363821i	0.999604	+	0.0281522i	$0.00896230\pi$
$673$	38.7807	+	244.852i	0.0576236	+	0.363821i	−0.941980	+	0.335669i	$0.891038\pi$
$674$		0			0
$675$	−58.6513	−	238.989i	−0.0868908	−	0.354058i
$676$		0			0
$677$	−301.786	+	47.7981i	−0.445769	+	0.0706029i	−0.375284	−	0.926910i	$-0.622455\pi$
$677$	−301.786	+	47.7981i	−0.445769	+	0.0706029i	−0.0704851	+	0.997513i	$0.522455\pi$
$678$		0			0
$679$	−739.299	+	240.213i	−1.08881	+	0.353774i
$680$		0			0
$681$	31.0154	−	95.4556i	0.0455439	−	0.140170i
$682$		0			0
$683$	241.102	−	122.848i	0.353005	−	0.179865i	−0.268491	−	0.963282i	$-0.586525\pi$
$683$	241.102	−	122.848i	0.353005	−	0.179865i	0.621496	+	0.783417i	$0.286525\pi$
$684$		0			0
$685$	−120.357	+	95.3744i	−0.175704	+	0.139233i
$686$		0			0
$687$	−2.22724	+	14.0622i	−0.00324197	+	0.0204690i
$688$		0			0
$689$	382.436	−	526.378i	0.555059	−	0.763973i
$690$		0			0
$691$	432.755	−	314.415i	0.626274	−	0.455014i	−0.228834	−	0.973466i	$-0.573491\pi$
$691$	432.755	−	314.415i	0.626274	−	0.455014i	0.855107	+	0.518451i	$0.173491\pi$
$692$		0			0
$693$	353.565	+	353.565i	0.510195	+	0.510195i
$694$		0			0
$695$	836.910	−	168.664i	1.20419	−	0.242683i
$696$		0			0
$697$	734.683	+	374.340i	1.05406	+	0.537073i
$698$		0			0
$699$		−	152.855i		−	0.218676i
$700$		0			0
$701$	−617.860			−0.881397			−0.440699	−	0.897655i	$-0.645269\pi$
$701$	−617.860			−0.881397			−0.440699	+	0.897655i	$0.645269\pi$
$702$		0			0
$703$	100.761	−	197.755i	0.143330	−	0.281302i
$704$		0			0
$705$	25.3393	+	2.93440i	0.0359422	+	0.00416226i
$706$		0			0
$707$	−1125.18	+	1125.18i	−1.59149	+	1.59149i
$708$		0			0
$709$	−718.310	−	988.668i	−1.01313	−	1.39445i	−0.916910	−	0.399095i	$-0.869325\pi$
$709$	−718.310	−	988.668i	−1.01313	−	1.39445i	−0.0962207	−	0.995360i	$-0.530675\pi$
$710$		0			0
$711$	−816.111	−	592.939i	−1.14784	−	0.833951i
$712$		0			0
$713$	890.804	+	141.089i	1.24937	+	0.197881i
$714$		0			0
$715$	27.0345	+	646.553i	0.0378105	+	0.904270i
$716$		0			0
$717$	−27.3847	−	53.7455i	−0.0381935	−	0.0749589i
$718$		0			0
$719$	−552.407	−	179.488i	−0.768299	−	0.249635i	−0.101462	−	0.994839i	$-0.532352\pi$
$719$	−552.407	−	179.488i	−0.768299	−	0.249635i	−0.666837	+	0.745204i	$0.732352\pi$
$720$		0			0
$721$	−509.353	−	1567.63i	−0.706454	−	2.17424i
$722$		0			0
$723$	−32.1749	−	203.144i	−0.0445019	−	0.280974i
$724$		0			0
$725$	−150.782	−	358.895i	−0.207975	−	0.495028i
$726$		0			0
$727$	353.383	−	55.9703i	0.486083	−	0.0769880i	0.0914173	−	0.995813i	$-0.470860\pi$
$727$	353.383	−	55.9703i	0.486083	−	0.0769880i	0.394666	+	0.918825i	$0.370860\pi$
$728$		0			0
$729$	−554.293	+	180.101i	−0.760347	+	0.247052i
$730$		0			0
$731$	248.702	−	765.427i	0.340222	−	1.04710i
$732$		0			0
$733$	−1280.53	+	652.460i	−1.74697	+	0.890123i	−0.783886	+	0.620904i	$0.786766\pi$
$733$	−1280.53	+	652.460i	−1.74697	+	0.890123i	−0.963079	+	0.269219i	$0.913234\pi$
$734$		0			0
$735$	53.1197	+	142.878i	0.0722716	+	0.194391i
$736$		0			0
$737$	−48.3845	+	305.488i	−0.0656506	+	0.414501i
$738$		0			0
$739$	125.167	−	172.278i	0.169373	−	0.233123i	−0.715889	−	0.698214i	$-0.753978\pi$
$739$	125.167	−	172.278i	0.169373	−	0.233123i	0.885263	+	0.465091i	$0.153978\pi$
$740$		0			0
$741$	147.545	−	107.198i	0.199116	−	0.144667i
$742$		0			0
$743$	775.885	+	775.885i	1.04426	+	1.04426i	0.998974	+	0.0452854i	$0.0144197\pi$
$743$	775.885	+	775.885i	1.04426	+	1.04426i	0.0452854	+	0.998974i	$0.485580\pi$
$744$		0			0
$745$	−80.2521	+	87.2561i	−0.107721	+	0.117122i
$746$		0			0
$747$	118.697	+	60.4792i	0.158898	+	0.0809627i
$748$		0			0
$749$			1808.91i			2.41510i
$750$		0			0
$751$	−738.937			−0.983938			−0.491969	−	0.870613i	$-0.663723\pi$
$751$	−738.937			−0.983938			−0.491969	+	0.870613i	$0.663723\pi$
$752$		0			0
$753$	−5.22640	+	10.2574i	−0.00694077	+	0.0136220i
$754$		0			0
$755$	−762.872	−	701.636i	−1.01043	−	0.929319i
$756$		0			0
$757$	821.816	−	821.816i	1.08562	−	1.08562i	0.0896488	−	0.995973i	$-0.471426\pi$
$757$	821.816	−	821.816i	1.08562	−	1.08562i	0.995973	−	0.0896488i	$-0.0285745\pi$
$758$		0			0
$759$	−47.9356	−	65.9776i	−0.0631562	−	0.0869271i
$760$		0			0
$761$	972.054	+	706.239i	1.27734	+	0.928040i	0.999469	−	0.0325787i	$-0.0103719\pi$
$761$	972.054	+	706.239i	1.27734	+	0.928040i	0.277869	+	0.960619i	$0.410372\pi$
$762$		0			0
$763$	−893.623	−	141.536i	−1.17120	−	0.185499i
$764$		0			0
$765$	727.462	−	270.459i	0.950930	−	0.353541i
$766$		0			0
$767$	−412.528	−	809.632i	−0.537846	−	1.05558i
$768$		0			0
$769$	596.588	+	193.843i	0.775797	+	0.252072i	0.670045	−	0.742321i	$-0.266275\pi$
$769$	596.588	+	193.843i	0.775797	+	0.252072i	0.105753	+	0.994392i	$0.466275\pi$
$770$		0			0
$771$	−14.0046	−	43.1017i	−0.0181642	−	0.0559037i
$772$		0			0
$773$	−119.204	−	752.625i	−0.154210	−	0.973641i	−0.936485	−	0.350708i	$-0.885941\pi$
$773$	−119.204	−	752.625i	−0.154210	−	0.973641i	0.782275	−	0.622933i	$-0.214059\pi$
$774$		0			0
$775$	−845.823	−	198.563i	−1.09138	−	0.256210i
$776$		0			0
$777$	−86.8817	+	13.7607i	−0.111817	+	0.0177101i
$778$		0			0
$779$	−627.957	+	204.036i	−0.806107	+	0.261920i
$780$		0			0
$781$	134.927	−	415.263i	0.172762	−	0.531706i
$782$		0			0
$783$	136.566	−	69.5841i	0.174414	−	0.0888686i
$784$		0			0
$785$	181.389	−	7.58446i	0.231068	−	0.00966173i
$786$		0			0
$787$	−172.436	+	1088.72i	−0.219105	+	1.38338i	0.595497	+	0.803357i	$0.296955\pi$
$787$	−172.436	+	1088.72i	−0.219105	+	1.38338i	−0.814603	+	0.580019i	$0.803045\pi$
$788$		0			0
$789$	28.6809	−	39.4758i	0.0363509	−	0.0500327i
$790$		0			0
$791$	−197.774	+	143.691i	−0.250031	+	0.181658i
$792$		0			0
$793$	−230.765	−	230.765i	−0.291003	−	0.291003i
$794$		0			0
$795$	9.08644	−	78.4638i	0.0114295	−	0.0986966i
$796$		0			0
$797$	−932.407	−	475.085i	−1.16990	−	0.596091i	−0.242492	−	0.970154i	$-0.577965\pi$
$797$	−932.407	−	475.085i	−1.16990	−	0.596091i	−0.927404	+	0.374062i	$0.877965\pi$
$798$		0			0
$799$			163.769i			0.204967i
$800$		0			0
$801$	635.975			0.793976
$802$		0			0
$803$	253.705	−	497.924i	0.315946	−	0.620079i
$804$		0			0
$805$	261.170	+	1295.92i	0.324434	+	1.60984i
$806$		0			0
$807$	32.8431	−	32.8431i	0.0406978	−	0.0406978i
$808$		0			0
$809$	−476.312	−	655.588i	−0.588767	−	0.810368i	0.405855	−	0.913937i	$-0.366974\pi$
$809$	−476.312	−	655.588i	−0.588767	−	0.810368i	−0.994622	+	0.103569i	$0.966974\pi$
$810$		0			0
$811$	288.711	+	209.761i	0.355994	+	0.258644i	0.751379	−	0.659871i	$-0.229389\pi$
$811$	288.711	+	209.761i	0.355994	+	0.258644i	−0.395385	+	0.918515i	$0.629389\pi$
$812$		0			0
$813$	59.6097	+	9.44124i	0.0733206	+	0.0116128i
$814$		0			0
$815$	−256.450	−	323.625i	−0.314663	−	0.397086i
$816$		0			0
$817$	292.583	+	574.226i	0.358119	+	0.702847i
$818$		0			0
$819$	1929.63	+	626.975i	2.35608	+	0.765537i
$820$		0			0
$821$	−456.889	−	1406.16i	−0.556503	−	1.71274i	−0.691941	−	0.721954i	$-0.743244\pi$
$821$	−456.889	−	1406.16i	−0.556503	−	1.71274i	0.135438	−	0.990786i	$-0.456756\pi$
$822$		0			0
$823$	32.3733	+	204.397i	0.0393357	+	0.248356i	0.999519	−	0.0310153i	$-0.00987405\pi$
$823$	32.3733	+	204.397i	0.0393357	+	0.248356i	−0.960183	+	0.279371i	$0.909874\pi$
$824$		0			0
$825$	41.3848	+	66.7764i	0.0501634	+	0.0809411i
$826$		0			0
$827$	−415.905	+	65.8728i	−0.502908	+	0.0796528i	−0.402734	−	0.915317i	$-0.631940\pi$
$827$	−415.905	+	65.8728i	−0.502908	+	0.0796528i	−0.100174	+	0.994970i	$0.531940\pi$
$828$		0			0
$829$	−1383.10	+	449.395i	−1.66839	+	0.542093i	−0.982605	−	0.185709i	$-0.940542\pi$
$829$	−1383.10	+	449.395i	−1.66839	+	0.542093i	−0.685787	+	0.727802i	$0.740542\pi$
$830$		0			0
$831$	9.68491	−	29.8071i	0.0116545	−	0.0358690i
$832$		0			0
$833$	−871.972	+	444.292i	−1.04679	+	0.533364i
$834$		0			0
$835$	70.6003	−	252.765i	0.0845512	−	0.302713i
$836$		0			0
$837$	53.5130	−	337.868i	0.0639343	−	0.403665i
$838$		0			0
$839$	342.847	−	471.888i	0.408638	−	0.562441i	−0.554248	−	0.832352i	$-0.686994\pi$
$839$	342.847	−	471.888i	0.408638	−	0.562441i	0.962885	+	0.269910i	$0.0869940\pi$
$840$		0			0
$841$	−484.225	+	351.810i	−0.575772	+	0.418323i
$842$		0			0
$843$	125.045	+	125.045i	0.148334	+	0.148334i
$844$		0			0
$845$	874.063	+	1551.57i	1.03439	+	1.83618i
$846$		0			0
$847$	808.835	+	412.122i	0.954941	+	0.486567i
$848$		0			0
$849$		−	266.544i		−	0.313950i
$850$		0			0
$851$	−402.719			−0.473230
$852$		0			0
$853$	335.123	−	657.717i	0.392876	−	0.771063i	−0.606842	−	0.794823i	$-0.707564\pi$
$853$	335.123	−	657.717i	0.392876	−	0.771063i	0.999718	+	0.0237600i	$0.00756377\pi$
$854$		0			0
$855$	−258.767	+	565.048i	−0.302651	+	0.660875i
$856$		0			0
$857$	189.288	−	189.288i	0.220873	−	0.220873i	−0.587993	−	0.808866i	$-0.700082\pi$
$857$	189.288	−	189.288i	0.220873	−	0.220873i	0.808866	+	0.587993i	$0.200082\pi$
$858$		0			0
$859$	689.325	+	948.775i	0.802474	+	1.10451i	0.992441	+	0.122720i	$0.0391618\pi$
$859$	689.325	+	948.775i	0.802474	+	1.10451i	−0.189967	+	0.981790i	$0.560838\pi$
$860$		0			0
$861$	211.711	+	153.817i	0.245889	+	0.178649i
$862$		0			0
$863$	−238.733	−	37.8116i	−0.276631	−	0.0438141i	0.0165773	−	0.999863i	$-0.494723\pi$
$863$	−238.733	−	37.8116i	−0.276631	−	0.0438141i	−0.293209	+	0.956048i	$0.594723\pi$
$864$		0			0
$865$	123.567	−	185.943i	0.142852	−	0.214963i
$866$		0			0
$867$	−7.58518	−	14.8868i	−0.00874877	−	0.0171704i
$868$		0			0
$869$	623.481	+	202.581i	0.717469	+	0.233120i
$870$		0			0
$871$	387.828	+	1193.61i	0.445268	+	1.37039i
$872$		0			0
$873$	103.731	+	654.929i	0.118821	+	0.750205i
$874$		0			0
$875$	−159.233	−	1263.48i	−0.181981	−	1.44397i
$876$		0			0
$877$	338.646	−	53.6362i	0.386141	−	0.0611587i	0.0396540	−	0.999213i	$-0.487374\pi$
$877$	338.646	−	53.6362i	0.386141	−	0.0611587i	0.346487	+	0.938055i	$0.387374\pi$
$878$		0			0
$879$	−288.388	+	93.7030i	−0.328087	+	0.106602i
$880$		0			0
$881$	66.8030	−	205.598i	0.0758263	−	0.233369i	−0.905958	−	0.423367i	$-0.860848\pi$
$881$	66.8030	−	205.598i	0.0758263	−	0.233369i	0.981785	+	0.189998i	$0.0608481\pi$
$882$		0			0
$883$	305.211	−	155.513i	0.345653	−	0.176119i	−0.272542	−	0.962144i	$-0.587864\pi$
$883$	305.211	−	155.513i	0.345653	−	0.176119i	0.618195	+	0.786025i	$0.287864\pi$
$884$		0			0
$885$	−91.8765	−	61.0557i	−0.103815	−	0.0689895i
$886$		0			0
$887$	−18.6058	+	117.473i	−0.0209761	+	0.132438i	−0.995954	−	0.0898635i	$-0.971357\pi$
$887$	−18.6058	+	117.473i	−0.0209761	+	0.132438i	0.974978	+	0.222302i	$0.0713569\pi$
$888$		0			0
$889$	−186.948	+	257.311i	−0.210290	+	0.289439i
$890$		0			0
$891$	332.335	−	241.455i	0.372991	−	0.270994i
$892$		0			0
$893$	−92.7300	−	92.7300i	−0.103841	−	0.103841i
$894$		0			0
$895$	1483.24	+	679.256i	1.65725	+	0.758945i
$896$		0			0
$897$	−294.852	−	150.234i	−0.328709	−	0.167485i
$898$		0			0
$899$		−	541.145i		−	0.601941i
$900$		0			0
$901$	507.114			0.562834
$902$		0			0
$903$	115.961	−	227.585i	0.128417	−	0.252033i
$904$		0			0
$905$	360.854	−	203.284i	0.398734	−	0.224623i
$906$		0			0
$907$	102.765	−	102.765i	0.113302	−	0.113302i	−0.648183	−	0.761485i	$-0.724471\pi$
$907$	102.765	−	102.765i	0.113302	−	0.113302i	0.761485	+	0.648183i	$0.224471\pi$
$908$		0			0
$909$	797.843	+	1098.14i	0.877715	+	1.20807i
$910$		0			0
$911$	107.266	+	77.9334i	0.117745	+	0.0855471i	0.645100	−	0.764099i	$-0.276816\pi$
$911$	107.266	+	77.9334i	0.117745	+	0.0855471i	−0.527354	+	0.849646i	$0.676816\pi$
$912$		0			0
$913$	−85.5075	−	13.5431i	−0.0936555	−	0.0148336i
$914$		0			0
$915$	−38.1588	−	10.6582i	−0.0417036	−	0.0116483i
$916$		0			0
$917$	−595.916	−	1169.55i	−0.649854	−	1.27541i
$918$		0			0
$919$	−1104.79	−	358.968i	−1.20217	−	0.390607i	−0.361609	−	0.932330i	$-0.617772\pi$
$919$	−1104.79	−	358.968i	−1.20217	−	0.390607i	−0.840557	+	0.541723i	$0.817772\pi$
$920$		0			0
$921$	−9.92910	−	30.5586i	−0.0107808	−	0.0331798i
$922$		0			0
$923$	−277.161	−	1749.93i	−0.300283	−	1.89591i
$924$		0			0
$925$	386.896	+	28.4888i	0.418266	+	0.0307987i
$926$		0			0
$927$	−1388.73	+	219.953i	−1.49809	+	0.237274i
$928$		0			0
$929$	68.6295	−	22.2991i	0.0738746	−	0.0240033i	−0.271847	−	0.962341i	$-0.587634\pi$
$929$	68.6295	−	22.2991i	0.0738746	−	0.0240033i	0.345721	+	0.938337i	$0.387634\pi$
$930$		0			0
$931$	242.163	−	745.303i	0.260111	−	0.800540i
$932$		0			0
$933$	−256.885	+	130.889i	−0.275332	+	0.140289i
$934$		0			0
$935$	−395.302	+	313.249i	−0.422783	+	0.335026i
$936$		0			0
$937$	1.09335	−	6.90314i	0.00116686	−	0.00736728i	−0.987098	−	0.160117i	$-0.948813\pi$
$937$	1.09335	−	6.90314i	0.00116686	−	0.00736728i	0.988265	+	0.152750i	$0.0488128\pi$
$938$		0			0
$939$	65.9113	−	90.7191i	0.0701931	−	0.0966125i
$940$		0			0
$941$	−895.131	+	650.351i	−0.951255	+	0.691127i	−0.951103	−	0.308873i	$-0.900048\pi$
$941$	−895.131	+	650.351i	−0.951255	+	0.691127i	−0.000151406		1.00000i	$0.500048\pi$
$942$		0			0
$943$	847.156	+	847.156i	0.898363	+	0.898363i
$944$		0			0
$945$	491.522	−	99.0575i	0.520129	−	0.104823i
$946$		0			0
$947$	−553.987	−	282.271i	−0.584992	−	0.298068i	0.136335	−	0.990663i	$-0.456468\pi$
$947$	−553.987	−	282.271i	−0.584992	−	0.298068i	−0.721327	+	0.692595i	$0.756468\pi$
$948$		0			0
$949$		−	2267.60i		−	2.38946i
$950$		0			0
$951$	−264.298			−0.277915
$952$		0			0
$953$	757.601	−	1486.88i	0.794965	−	1.56021i	−0.0330196	−	0.999455i	$-0.510512\pi$
$953$	757.601	−	1486.88i	0.794965	−	1.56021i	0.827984	−	0.560751i	$-0.189488\pi$
$954$		0			0
$955$	−687.713	−	79.6401i	−0.720119	−	0.0833928i
$956$		0			0
$957$	−34.5999	+	34.5999i	−0.0361546	+	0.0361546i
$958$		0			0
$959$	−183.916	−	253.138i	−0.191779	−	0.263961i
$960$		0			0
$961$	−199.625	−	145.036i	−0.207726	−	0.150922i
$962$		0			0
$963$	1524.04	+	241.385i	1.58260	+	0.250659i
$964$		0			0
$965$	−4.36709	−	104.443i	−0.00452548	−	0.108231i
$966$		0			0
$967$	−289.998	−	569.153i	−0.299894	−	0.588576i	0.691057	−	0.722801i	$-0.257146\pi$
$967$	−289.998	−	569.153i	−0.299894	−	0.588576i	−0.990951	+	0.134225i	$0.957146\pi$
$968$		0			0
$969$	135.188	+	43.9254i	0.139513	+	0.0453306i
$970$		0			0
$971$	108.279	+	333.249i	0.111513	+	0.343201i	0.991204	−	0.132345i	$-0.0422505\pi$
$971$	108.279	+	333.249i	0.111513	+	0.343201i	−0.879691	+	0.475546i	$0.842251\pi$
$972$		0			0
$973$	272.123	+	1718.12i	0.279674	+	1.76579i
$974$		0			0
$975$	272.639	+	165.190i	0.279630	+	0.169425i
$976$		0			0
$977$	−960.639	+	152.150i	−0.983253	+	0.155732i	−0.627305	−	0.778774i	$-0.715842\pi$
$977$	−960.639	+	152.150i	−0.983253	+	0.155732i	−0.355948	+	0.934506i	$0.615842\pi$
$978$		0			0
$979$	−393.071	+	127.717i	−0.401503	+	0.130456i
$980$		0			0
$981$	−238.494	+	734.008i	−0.243113	+	0.748225i
$982$		0			0
$983$	−731.267	+	372.599i	−0.743913	+	0.379043i	−0.784496	−	0.620133i	$-0.787078\pi$
$983$	−731.267	+	372.599i	−0.743913	+	0.379043i	0.0405830	+	0.999176i	$0.487078\pi$
$984$		0			0
$985$	−10.9255	−	29.3867i	−0.0110919	−	0.0298343i
$986$		0			0
$987$	−8.13072	+	51.3353i	−0.00823781	+	0.0520115i
$988$		0			0
$989$	687.347	−	946.051i	0.694991	−	0.956574i
$990$		0			0
$991$	−280.178	+	203.561i	−0.282722	+	0.205410i	−0.720104	−	0.693866i	$-0.755906\pi$
$991$	−280.178	+	203.561i	−0.282722	+	0.205410i	0.437382	+	0.899276i	$0.355906\pi$
$992$		0			0
$993$	163.991	+	163.991i	0.165147	+	0.165147i
$994$		0			0
$995$	826.002	−	898.092i	0.830153	−	0.902605i
$996$		0			0
$997$	1161.91	+	592.022i	1.16540	+	0.593803i	0.926151	−	0.377154i	$-0.123097\pi$
$997$	1161.91	+	592.022i	1.16540	+	0.593803i	0.239254	+	0.970957i	$0.423097\pi$
$998$		0			0
$999$			152.745i			0.152898i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.a.113.1		16
4.3	odd	2		50.3.f.a.13.2	✓	16
20.3	even	4		250.3.f.c.207.2		16
20.7	even	4		250.3.f.a.207.1		16
20.19	odd	2		250.3.f.b.43.1		16
25.2	odd	20	inner	400.3.bg.a.177.1		16
100.11	odd	10		250.3.f.a.93.1		16
100.23	even	20		250.3.f.b.157.1		16
100.27	even	20		50.3.f.a.27.2	yes	16
100.39	odd	10		250.3.f.c.93.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.a.13.2	✓	16	4.3	odd	2
50.3.f.a.27.2	yes	16	100.27	even	20
250.3.f.a.93.1		16	100.11	odd	10
250.3.f.a.207.1		16	20.7	even	4
250.3.f.b.43.1		16	20.19	odd	2
250.3.f.b.157.1		16	100.23	even	20
250.3.f.c.93.2		16	100.39	odd	10
250.3.f.c.207.2		16	20.3	even	4
400.3.bg.a.113.1		16	1.1	even	1	trivial
400.3.bg.a.177.1		16	25.2	odd	20	inner

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.bg (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.252608 + 0.495771i) q^{3} +(3.68015 + 3.38474i) q^{5} +(-7.20385 + 7.20385i) q^{7} +(5.10809 + 7.03068i) q^{9} +O(q^{10})\)	\(q+(-0.252608 + 0.495771i) q^{3} +(3.68015 + 3.38474i) q^{5} +(-7.20385 + 7.20385i) q^{7} +(5.10809 + 7.03068i) q^{9} +(-4.56901 - 3.31958i) q^{11} +(-22.6344 - 3.58493i) q^{13} +(-2.60770 + 0.969500i) q^{15} +(-8.10888 - 15.9146i) q^{17} +(13.6027 + 4.41978i) q^{19} +(-1.75171 - 5.39121i) q^{21} +(-4.05981 - 25.6327i) q^{23} +(2.08702 + 24.9127i) q^{25} +(-9.72206 + 1.53982i) q^{27} +(-14.8092 + 4.81180i) q^{29} +(-10.7392 + 33.0518i) q^{31} +(2.79992 - 1.42663i) q^{33} +(-50.8944 + 2.12806i) q^{35} +(2.42751 - 15.3267i) q^{37} +(7.49493 - 10.3159i) q^{39} +(-37.3476 + 27.1346i) q^{41} +(31.8617 + 31.8617i) q^{43} +(-4.99852 + 43.1635i) q^{45} +(-8.16953 - 4.16259i) q^{47} -54.7908i q^{49} +9.93836 q^{51} +(-12.8896 + 25.2972i) q^{53} +(-5.57872 - 27.6815i) q^{55} +(-5.62735 + 5.62735i) q^{57} +(23.3065 + 32.0786i) q^{59} +(11.5211 + 8.37057i) q^{61} +(-87.4458 - 13.8501i) q^{63} +(-71.1638 - 89.8046i) q^{65} +(-24.8631 - 48.7966i) q^{67} +(13.7335 + 4.46228i) q^{69} +(23.8910 + 73.5289i) q^{71} +(15.4792 + 97.7321i) q^{73} +(-12.8782 - 5.25848i) q^{75} +(56.8282 - 9.00071i) q^{77} +(-110.397 + 35.8702i) q^{79} +(-22.4769 + 69.1767i) q^{81} +(13.6584 - 6.95931i) q^{83} +(24.0249 - 86.0145i) q^{85} +(1.35537 - 8.55747i) q^{87} +(43.0149 - 59.2049i) q^{89} +(188.880 - 137.229i) q^{91} +(-13.6733 - 13.6733i) q^{93} +(35.1001 + 62.3071i) q^{95} +(67.9854 + 34.6403i) q^{97} -49.0800i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} + 2 q^{7} - 40 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 + 2 * q^7 - 40 * q^9	\( 16 q - 2 q^{3} + 2 q^{7} - 40 q^{9} - 32 q^{11} - 8 q^{13} - 62 q^{17} - 30 q^{19} - 68 q^{21} + 18 q^{23} + 70 q^{25} + 40 q^{27} + 100 q^{29} - 132 q^{31} - 36 q^{33} - 150 q^{35} + 138 q^{37} + 320 q^{39} - 88 q^{41} + 78 q^{43} - 20 q^{45} + 22 q^{47} + 168 q^{51} + 182 q^{53} - 280 q^{55} + 280 q^{57} + 350 q^{59} + 372 q^{61} - 22 q^{63} - 910 q^{65} + 112 q^{67} - 30 q^{69} - 122 q^{71} - 248 q^{73} + 80 q^{75} + 16 q^{77} - 760 q^{79} - 144 q^{81} - 132 q^{83} - 30 q^{85} - 770 q^{87} + 550 q^{89} + 798 q^{91} + 54 q^{93} - 40 q^{95} - 292 q^{97}+O(q^{100}) \) 16 * q - 2 * q^3 + 2 * q^7 - 40 * q^9 - 32 * q^11 - 8 * q^13 - 62 * q^17 - 30 * q^19 - 68 * q^21 + 18 * q^23 + 70 * q^25 + 40 * q^27 + 100 * q^29 - 132 * q^31 - 36 * q^33 - 150 * q^35 + 138 * q^37 + 320 * q^39 - 88 * q^41 + 78 * q^43 - 20 * q^45 + 22 * q^47 + 168 * q^51 + 182 * q^53 - 280 * q^55 + 280 * q^57 + 350 * q^59 + 372 * q^61 - 22 * q^63 - 910 * q^65 + 112 * q^67 - 30 * q^69 - 122 * q^71 - 248 * q^73 + 80 * q^75 + 16 * q^77 - 760 * q^79 - 144 * q^81 - 132 * q^83 - 30 * q^85 - 770 * q^87 + 550 * q^89 + 798 * q^91 + 54 * q^93 - 40 * q^95 - 292 * q^97

Introduction

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