LMFDB - Embedded newform 400.3.bg.b.113.3

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:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			113.3
Character	$\chi$	$=$	400.113
Dual form			400.3.bg.b.177.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.14176 - 4.20343i) q^{3} +(-1.43099 + 4.79085i) q^{5} +(-8.41873 + 8.41873i) q^{7} +(-7.79165 - 10.7243i) q^{9} +O(q^{10})$	\(q+(2.14176 - 4.20343i) q^{3} +(-1.43099 + 4.79085i) q^{5} +(-8.41873 + 8.41873i) q^{7} +(-7.79165 - 10.7243i) q^{9} +(8.83615 + 6.41984i) q^{11} +(13.8302 + 2.19049i) q^{13} +(17.0732 + 16.2759i) q^{15} +(4.53099 + 8.89257i) q^{17} +(14.9790 + 4.86698i) q^{19} +(17.3567 + 53.4184i) q^{21} +(1.69189 + 10.6822i) q^{23} +(-20.9046 - 13.7113i) q^{25} +(-19.8308 + 3.14088i) q^{27} +(4.11402 - 1.33673i) q^{29} +(-4.02808 + 12.3972i) q^{31} +(45.9102 - 23.3924i) q^{33} +(-28.2858 - 52.3800i) q^{35} +(-3.95354 + 24.9617i) q^{37} +(38.8285 - 53.4428i) q^{39} +(-21.6147 + 15.7040i) q^{41} +(-21.2302 - 21.2302i) q^{43} +(62.5282 - 21.9824i) q^{45} +(46.4137 + 23.6489i) q^{47} -92.7500i q^{49} +47.0836 q^{51} +(-15.6773 + 30.7684i) q^{53} +(-43.4009 + 33.1460i) q^{55} +(52.5394 - 52.5394i) q^{57} +(-8.92677 - 12.2866i) q^{59} +(-47.6752 - 34.6380i) q^{61} +(155.881 + 24.6891i) q^{63} +(-30.2852 + 63.1240i) q^{65} +(44.1187 + 86.5878i) q^{67} +(48.5255 + 15.7669i) q^{69} +(-20.2698 - 62.3839i) q^{71} +(12.5050 + 78.9533i) q^{73} +(-102.407 + 58.5046i) q^{75} +(-128.436 + 20.3423i) q^{77} +(-16.9345 + 5.50235i) q^{79} +(7.59667 - 23.3801i) q^{81} +(-88.9040 + 45.2989i) q^{83} +(-49.0868 + 8.98217i) q^{85} +(3.19239 - 20.1559i) q^{87} +(-6.44619 + 8.87242i) q^{89} +(-134.874 + 97.9917i) q^{91} +(43.4834 + 43.4834i) q^{93} +(-44.7518 + 64.7977i) q^{95} +(117.203 + 59.7179i) q^{97} -144.783i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{3} + 2 q^{7} + 40 q^{9}+O(q^{10}) $ 24 * q - 2 * q^3 + 2 * q^7 + 40 * q^9	$ 24 q - 2 q^{3} + 2 q^{7} + 40 q^{9} + 32 q^{11} + 2 q^{13} + 20 q^{15} - 92 q^{17} + 230 q^{19} + 68 q^{21} + 18 q^{23} + 40 q^{25} - 260 q^{27} + 100 q^{29} + 132 q^{31} + 364 q^{33} - 50 q^{35} - 192 q^{37} + 80 q^{39} + 168 q^{41} + 78 q^{43} - 310 q^{45} + 22 q^{47} - 168 q^{51} - 108 q^{53} + 40 q^{55} + 280 q^{57} - 450 q^{59} - 492 q^{61} + 558 q^{63} + 120 q^{65} + 572 q^{67} - 670 q^{69} + 2 q^{71} + 262 q^{73} - 140 q^{75} + 496 q^{77} + 360 q^{79} - 46 q^{81} - 772 q^{83} + 490 q^{85} - 210 q^{87} + 900 q^{89} - 798 q^{91} + 294 q^{93} + 378 q^{97}+O(q^{100}) $ 24 * q - 2 * q^3 + 2 * q^7 + 40 * q^9 + 32 * q^11 + 2 * q^13 + 20 * q^15 - 92 * q^17 + 230 * q^19 + 68 * q^21 + 18 * q^23 + 40 * q^25 - 260 * q^27 + 100 * q^29 + 132 * q^31 + 364 * q^33 - 50 * q^35 - 192 * q^37 + 80 * q^39 + 168 * q^41 + 78 * q^43 - 310 * q^45 + 22 * q^47 - 168 * q^51 - 108 * q^53 + 40 * q^55 + 280 * q^57 - 450 * q^59 - 492 * q^61 + 558 * q^63 + 120 * q^65 + 572 * q^67 - 670 * q^69 + 2 * q^71 + 262 * q^73 - 140 * q^75 + 496 * q^77 + 360 * q^79 - 46 * q^81 - 772 * q^83 + 490 * q^85 - 210 * q^87 + 900 * q^89 - 798 * q^91 + 294 * q^93 + 378 * 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
$3$	2.14176	−	4.20343i	0.713918	−	1.40114i	−0.193578	−	0.981085i	$-0.562009\pi$
$3$	2.14176	−	4.20343i	0.713918	−	1.40114i	0.907497	−	0.420059i	$-0.137991\pi$
$4$		0			0
$5$	−1.43099	+	4.79085i	−0.286197	+	0.958171i
$5$	−1.43099	+	4.79085i	−0.286197	+	0.958171i
$6$		0			0
$7$	−8.41873	+	8.41873i	−1.20268	+	1.20268i	−0.229326	+	0.973350i	$0.573652\pi$
$7$	−8.41873	+	8.41873i	−1.20268	+	1.20268i	−0.973350	+	0.229326i	$0.926348\pi$
$8$		0			0
$9$	−7.79165	−	10.7243i	−0.865739	−	1.19159i
$10$		0			0
$11$	8.83615	+	6.41984i	0.803287	+	0.583622i	0.911876	−	0.410465i	$-0.134634\pi$
$11$	8.83615	+	6.41984i	0.803287	+	0.583622i	−0.108590	+	0.994087i	$0.534634\pi$
$12$		0			0
$13$	13.8302	+	2.19049i	1.06386	+	0.168499i	0.663741	−	0.747963i	$-0.268968\pi$
$13$	13.8302	+	2.19049i	1.06386	+	0.168499i	0.400122	+	0.916462i	$0.368968\pi$
$14$		0			0
$15$	17.0732	+	16.2759i	1.13821	+	1.08506i
$16$		0			0
$17$	4.53099	+	8.89257i	0.266529	+	0.523092i	0.985019	−	0.172445i	$-0.0551666\pi$
$17$	4.53099	+	8.89257i	0.266529	+	0.523092i	−0.718490	+	0.695537i	$0.755167\pi$
$18$		0			0
$19$	14.9790	+	4.86698i	0.788370	+	0.256157i	0.675410	−	0.737443i	$-0.263967\pi$
$19$	14.9790	+	4.86698i	0.788370	+	0.256157i	0.112960	+	0.993600i	$0.463967\pi$
$20$		0			0
$21$	17.3567	+	53.4184i	0.826509	+	2.54373i
$22$		0			0
$23$	1.69189	+	10.6822i	0.0735606	+	0.464443i	0.996781	+	0.0801725i	$0.0255471\pi$
$23$	1.69189	+	10.6822i	0.0735606	+	0.464443i	−0.923220	+	0.384271i	$0.874453\pi$
$24$		0			0
$25$	−20.9046	−	13.7113i	−0.836182	−	0.548452i
$26$		0			0
$27$	−19.8308	+	3.14088i	−0.734473	+	0.116329i
$28$		0			0
$29$	4.11402	−	1.33673i	0.141863	−	0.0460940i	−0.237225	−	0.971455i	$-0.576238\pi$
$29$	4.11402	−	1.33673i	0.141863	−	0.0460940i	0.379088	+	0.925361i	$0.376238\pi$
$30$		0			0
$31$	−4.02808	+	12.3972i	−0.129938	+	0.399908i	−0.994768	−	0.102156i	$-0.967426\pi$
$31$	−4.02808	+	12.3972i	−0.129938	+	0.399908i	0.864830	+	0.502064i	$0.167426\pi$
$32$		0			0
$33$	45.9102	−	23.3924i	1.39122	−	0.708862i
$34$		0			0
$35$	−28.2858	−	52.3800i	−0.808166	−	1.49657i
$36$		0			0
$37$	−3.95354	+	24.9617i	−0.106852	+	0.674640i	0.874875	+	0.484348i	$0.160943\pi$
$37$	−3.95354	+	24.9617i	−0.106852	+	0.674640i	−0.981728	+	0.190291i	$0.939057\pi$
$38$		0			0
$39$	38.8285	−	53.4428i	0.995603	−	1.37033i
$40$		0			0
$41$	−21.6147	+	15.7040i	−0.527187	+	0.383024i	−0.819305	−	0.573359i	$-0.805640\pi$
$41$	−21.6147	+	15.7040i	−0.527187	+	0.383024i	0.292117	+	0.956382i	$0.405640\pi$
$42$		0			0
$43$	−21.2302	−	21.2302i	−0.493726	−	0.493726i	0.415752	−	0.909478i	$-0.363519\pi$
$43$	−21.2302	−	21.2302i	−0.493726	−	0.493726i	−0.909478	+	0.415752i	$0.863519\pi$
$44$		0			0
$45$	62.5282	−	21.9824i	1.38952	−	0.488497i
$46$		0			0
$47$	46.4137	+	23.6489i	0.987525	+	0.503169i	0.871668	−	0.490097i	$-0.163039\pi$
$47$	46.4137	+	23.6489i	0.987525	+	0.503169i	0.115857	+	0.993266i	$0.463039\pi$
$48$		0			0
$49$		−	92.7500i		−	1.89286i
$50$		0			0
$51$	47.0836			0.923208
$52$		0			0
$53$	−15.6773	+	30.7684i	−0.295797	+	0.580535i	−0.990298	−	0.138957i	$-0.955625\pi$
$53$	−15.6773	+	30.7684i	−0.295797	+	0.580535i	0.694501	+	0.719492i	$0.255625\pi$
$54$		0			0
$55$	−43.4009	+	33.1460i	−0.789108	+	0.602655i
$56$		0			0
$57$	52.5394	−	52.5394i	0.921744	−	0.921744i
$58$		0			0
$59$	−8.92677	−	12.2866i	−0.151301	−	0.208248i	0.726638	−	0.687021i	$-0.241082\pi$
$59$	−8.92677	−	12.2866i	−0.151301	−	0.208248i	−0.877939	+	0.478772i	$0.841082\pi$
$60$		0			0
$61$	−47.6752	−	34.6380i	−0.781560	−	0.567837i	0.123887	−	0.992296i	$-0.460464\pi$
$61$	−47.6752	−	34.6380i	−0.781560	−	0.567837i	−0.905447	+	0.424460i	$0.860464\pi$
$62$		0			0
$63$	155.881	+	24.6891i	2.47430	+	0.391890i
$64$		0			0
$65$	−30.2852	+	63.1240i	−0.465926	+	0.971138i
$66$		0			0
$67$	44.1187	+	86.5878i	0.658488	+	1.29236i	0.942715	+	0.333599i	$0.108263\pi$
$67$	44.1187	+	86.5878i	0.658488	+	1.29236i	−0.284227	+	0.958757i	$0.591737\pi$
$68$		0			0
$69$	48.5255	+	15.7669i	0.703268	+	0.228506i
$70$		0			0
$71$	−20.2698	−	62.3839i	−0.285490	−	0.878647i	−0.986251	−	0.165252i	$-0.947156\pi$
$71$	−20.2698	−	62.3839i	−0.285490	−	0.878647i	0.700762	−	0.713395i	$-0.252844\pi$
$72$		0			0
$73$	12.5050	+	78.9533i	0.171301	+	1.08155i	0.912143	+	0.409872i	$0.134427\pi$
$73$	12.5050	+	78.9533i	0.171301	+	1.08155i	−0.740842	+	0.671679i	$0.765573\pi$
$74$		0			0
$75$	−102.407	+	58.5046i	−1.36543	+	0.780062i
$76$		0			0
$77$	−128.436	+	20.3423i	−1.66800	+	0.264185i
$78$		0			0
$79$	−16.9345	+	5.50235i	−0.214361	+	0.0696500i	−0.414229	−	0.910173i	$-0.635949\pi$
$79$	−16.9345	+	5.50235i	−0.214361	+	0.0696500i	0.199868	+	0.979823i	$0.435949\pi$
$80$		0			0
$81$	7.59667	−	23.3801i	0.0937860	−	0.288644i
$82$		0			0
$83$	−88.9040	+	45.2989i	−1.07113	+	0.545769i	−0.898390	−	0.439198i	$-0.855263\pi$
$83$	−88.9040	+	45.2989i	−1.07113	+	0.545769i	−0.172742	+	0.984967i	$0.555263\pi$
$84$		0			0
$85$	−49.0868	+	8.98217i	−0.577492	+	0.105673i
$86$		0			0
$87$	3.19239	−	20.1559i	0.0366941	−	0.231677i
$88$		0			0
$89$	−6.44619	+	8.87242i	−0.0724291	+	0.0996901i	−0.843695	−	0.536824i	$-0.819624\pi$
$89$	−6.44619	+	8.87242i	−0.0724291	+	0.0996901i	0.771265	+	0.636514i	$0.219624\pi$
$90$		0			0
$91$	−134.874	+	97.9917i	−1.48213	+	1.07683i
$92$		0			0
$93$	43.4834	+	43.4834i	0.467564	+	0.467564i
$94$		0			0
$95$	−44.7518	+	64.7977i	−0.471071	+	0.682081i
$96$		0			0
$97$	117.203	+	59.7179i	1.20828	+	0.615649i	0.937833	−	0.347087i	$-0.112829\pi$
$97$	117.203	+	59.7179i	1.20828	+	0.615649i	0.270446	+	0.962735i	$0.412829\pi$
$98$		0			0
$99$		−	144.783i		−	1.46245i
$100$		0			0
$101$	85.6222			0.847745			0.423872	−	0.905722i	$-0.360670\pi$
$101$	85.6222			0.847745			0.423872	+	0.905722i	$0.360670\pi$
$102$		0			0
$103$	54.4018	−	106.770i	0.528173	−	1.03660i	−0.460661	−	0.887576i	$-0.652388\pi$
$103$	54.4018	−	106.770i	0.528173	−	1.03660i	0.988834	−	0.149022i	$-0.0476125\pi$
$104$		0			0
$105$	−280.757	+	6.71237i	−2.67388	+	0.0639274i
$106$		0			0
$107$	132.988	−	132.988i	1.24288	−	1.24288i	0.284080	−	0.958801i	$-0.408312\pi$
$107$	132.988	−	132.988i	1.24288	−	1.24288i	0.958801	−	0.284080i	$-0.0916881\pi$
$108$		0			0
$109$	3.40517	+	4.68682i	0.0312401	+	0.0429983i	0.824351	−	0.566078i	$-0.191540\pi$
$109$	3.40517	+	4.68682i	0.0312401	+	0.0429983i	−0.793111	+	0.609077i	$0.791540\pi$
$110$		0			0
$111$	96.4572	+	70.0802i	0.868984	+	0.631354i
$112$		0			0
$113$	93.3335	+	14.7826i	0.825961	+	0.130819i	0.555083	−	0.831795i	$-0.312686\pi$
$113$	93.3335	+	14.7826i	0.825961	+	0.130819i	0.270877	+	0.962614i	$0.412686\pi$
$114$		0			0
$115$	−53.5979	−	7.18046i	−0.466069	−	0.0624388i
$116$		0			0
$117$	−84.2687	−	165.387i	−0.720246	−	1.41356i
$118$		0			0
$119$	−113.009	−	36.7190i	−0.949658	−	0.308563i
$120$		0			0
$121$	−0.527824	−	1.62448i	−0.00436218	−	0.0134254i
$122$		0			0
$123$	19.7173	+	124.490i	0.160303	+	1.01211i
$124$		0			0
$125$	95.6029	−	80.5300i	0.764823	−	0.644240i
$126$		0			0
$127$	−227.247	+	35.9923i	−1.78934	+	0.283404i	−0.960946	−	0.276737i	$-0.910747\pi$
$127$	−227.247	+	35.9923i	−1.78934	+	0.283404i	−0.828397	+	0.560141i	$0.810747\pi$
$128$		0			0
$129$	−134.710	+	43.7699i	−1.04426	+	0.339301i
$130$		0			0
$131$	22.6296	−	69.6469i	0.172745	−	0.531656i	−0.826778	−	0.562528i	$-0.809829\pi$
$131$	22.6296	−	69.6469i	0.172745	−	0.531656i	0.999523	+	0.0308728i	$0.00982868\pi$
$132$		0			0
$133$	−167.078	+	85.1305i	−1.25623	+	0.640079i
$134$		0			0
$135$	13.3300	−	99.5009i	0.0987410	−	0.737043i
$136$		0			0
$137$	11.3116	−	71.4189i	0.0825667	−	0.521306i	−0.911391	−	0.411542i	$-0.864990\pi$
$137$	11.3116	−	71.4189i	0.0825667	−	0.521306i	0.993958	−	0.109764i	$-0.0350095\pi$
$138$		0			0
$139$	31.0454	−	42.7304i	0.223349	−	0.307413i	−0.682607	−	0.730786i	$-0.739154\pi$
$139$	31.0454	−	42.7304i	0.223349	−	0.307413i	0.905956	+	0.423373i	$0.139154\pi$
$140$		0			0
$141$	198.813	−	144.446i	1.41002	−	1.02444i
$142$		0			0
$143$	108.143	+	108.143i	0.756247	+	0.756247i
$144$		0			0
$145$	0.516953	+	21.6225i	0.00356520	+	0.149121i
$146$		0			0
$147$	−389.868	−	198.648i	−2.65216	−	1.35135i
$148$		0			0
$149$		−	250.778i		−	1.68307i	−0.540202	−	0.841536i	$-0.681652\pi$
$149$		−	250.778i		−	1.68307i	0.540202	−	0.841536i	$-0.318348\pi$
$150$		0			0
$151$	279.436			1.85057			0.925286	−	0.379269i	$-0.123825\pi$
$151$	279.436			1.85057			0.925286	+	0.379269i	$0.123825\pi$
$152$		0			0
$153$	60.0626	−	117.879i	0.392566	−	0.770454i
$154$		0			0
$155$	−53.6288	−	37.0381i	−0.345992	−	0.238955i
$156$		0			0
$157$	−181.969	+	181.969i	−1.15904	+	1.15904i	−0.174358	+	0.984682i	$0.555785\pi$
$157$	−181.969	+	181.969i	−1.15904	+	1.15904i	−0.984682	+	0.174358i	$0.944215\pi$
$158$		0			0
$159$	95.7558	+	131.797i	0.602238	+	0.828909i
$160$		0			0
$161$	−104.174	−	75.6869i	−0.647044	−	0.470105i
$162$		0			0
$163$	−56.7560	−	8.98926i	−0.348196	−	0.0551488i	−0.0201130	−	0.999798i	$-0.506403\pi$
$163$	−56.7560	−	8.98926i	−0.348196	−	0.0551488i	−0.328083	+	0.944649i	$0.606403\pi$
$164$		0			0
$165$	46.3728	+	253.423i	0.281047	+	1.53590i
$166$		0			0
$167$	−97.8251	−	191.993i	−0.585779	−	1.14966i	−0.973672	−	0.227952i	$-0.926797\pi$
$167$	−97.8251	−	191.993i	−0.585779	−	1.14966i	0.387894	−	0.921704i	$-0.373203\pi$
$168$		0			0
$169$	25.7479	+	8.36602i	0.152355	+	0.0495031i
$170$		0			0
$171$	−64.5164	−	198.561i	−0.377289	−	1.16118i
$172$		0			0
$173$	−39.6355	−	250.249i	−0.229107	−	1.44653i	−0.787175	−	0.616730i	$-0.788457\pi$
$173$	−39.6355	−	250.249i	−0.229107	−	1.44653i	0.558067	−	0.829796i	$-0.311543\pi$
$174$		0			0
$175$	291.421	−	60.5582i	1.66527	−	0.346047i
$176$		0			0
$177$	−70.7651	+	11.2081i	−0.399803	+	0.0633225i
$178$		0			0
$179$	−176.540	+	57.3613i	−0.986256	+	0.320454i	−0.757361	−	0.652997i	$-0.773511\pi$
$179$	−176.540	+	57.3613i	−0.986256	+	0.320454i	−0.228896	+	0.973451i	$0.573511\pi$
$180$		0			0
$181$	−54.7245	+	168.425i	−0.302346	+	0.930524i	0.678309	+	0.734777i	$0.262713\pi$
$181$	−54.7245	+	168.425i	−0.302346	+	0.930524i	−0.980654	+	0.195747i	$0.937287\pi$
$182$		0			0
$183$	−247.707	+	126.213i	−1.35359	+	0.689689i
$184$		0			0
$185$	−113.930	−	54.6607i	−0.615839	−	0.295463i
$186$		0			0
$187$	−17.0524	+	107.664i	−0.0911891	+	0.575745i
$188$		0			0
$189$	140.508	−	193.392i	0.743426	−	1.02324i
$190$		0			0
$191$	188.360	−	136.852i	0.986179	−	0.716501i	0.0270979	−	0.999633i	$-0.491373\pi$
$191$	188.360	−	136.852i	0.986179	−	0.716501i	0.959081	+	0.283132i	$0.0913734\pi$
$192$		0			0
$193$	150.137	+	150.137i	0.777914	+	0.777914i	0.979476	−	0.201562i	$-0.0646017\pi$
$193$	150.137	+	150.137i	0.777914	+	0.777914i	−0.201562	+	0.979476i	$0.564602\pi$
$194$		0			0
$195$	200.474	+	262.498i	1.02807	+	1.34614i
$196$		0			0
$197$	−207.677	−	105.817i	−1.05420	−	0.537141i	−0.161070	−	0.986943i	$-0.551494\pi$
$197$	−207.677	−	105.817i	−1.05420	−	0.537141i	−0.893128	+	0.449802i	$0.851494\pi$
$198$		0			0
$199$		−	158.777i		−	0.797875i	−0.916978	−	0.398938i	$-0.869379\pi$
$199$		−	158.777i		−	0.797875i	0.916978	−	0.398938i	$-0.130621\pi$
$200$		0			0
$201$	458.457			2.28088
$202$		0			0
$203$	−23.3813	+	45.8883i	−0.115179	+	0.226051i
$204$		0			0
$205$	−44.3052	−	126.025i	−0.216123	−	0.614756i
$206$		0			0
$207$	101.376	−	101.376i	0.489741	−	0.489741i
$208$		0			0
$209$	101.112	+	139.168i	0.483788	+	0.665877i
$210$		0			0
$211$	−120.250	−	87.3667i	−0.569905	−	0.414060i	0.265166	−	0.964203i	$-0.414573\pi$
$211$	−120.250	−	87.3667i	−0.569905	−	0.414060i	−0.835071	+	0.550143i	$0.814573\pi$
$212$		0			0
$213$	−305.640	−	48.4085i	−1.43493	−	0.227270i
$214$		0			0
$215$	132.091	−	71.3308i	0.614377	−	0.331771i
$216$		0			0
$217$	−70.4570	−	138.280i	−0.324686	−	0.637233i
$218$		0			0
$219$	358.657	+	116.535i	1.63770	+	0.532122i
$220$		0			0
$221$	43.1855	+	132.911i	0.195409	+	0.601408i
$222$		0			0
$223$	61.3358	+	387.259i	0.275048	+	1.73659i	0.608263	+	0.793735i	$0.291866\pi$
$223$	61.3358	+	387.259i	0.275048	+	1.73659i	−0.333215	+	0.942851i	$0.608134\pi$
$224$		0			0
$225$	15.8372	+	331.020i	0.0703875	+	1.47120i
$226$		0			0
$227$	−96.9149	+	15.3498i	−0.426938	+	0.0676203i	−0.366206	−	0.930534i	$-0.619343\pi$
$227$	−96.9149	+	15.3498i	−0.426938	+	0.0676203i	−0.0607318	+	0.998154i	$0.519343\pi$
$228$		0			0
$229$	166.723	−	54.1716i	0.728048	−	0.236557i	0.0785390	−	0.996911i	$-0.474974\pi$
$229$	166.723	−	54.1716i	0.728048	−	0.236557i	0.649509	+	0.760354i	$0.274974\pi$
$230$		0			0
$231$	−189.571	+	583.440i	−0.820655	+	2.52572i
$232$		0			0
$233$	−247.354	+	126.033i	−1.06161	+	0.540916i	−0.895440	−	0.445182i	$-0.853139\pi$
$233$	−247.354	+	126.033i	−1.06161	+	0.540916i	−0.166167	+	0.986098i	$0.553139\pi$
$234$		0			0
$235$	−179.716	+	188.520i	−0.764749	+	0.802212i
$236$		0			0
$237$	−13.1408	+	82.9677i	−0.0554464	+	0.350074i
$238$		0			0
$239$	−87.3521	+	120.230i	−0.365490	+	0.503054i	−0.951668	−	0.307128i	$-0.900632\pi$
$239$	−87.3521	+	120.230i	−0.365490	+	0.503054i	0.586178	+	0.810182i	$0.300632\pi$
$240$		0			0
$241$	−29.7040	+	21.5812i	−0.123253	+	0.0895488i	−0.647704	−	0.761892i	$-0.724271\pi$
$241$	−29.7040	+	21.5812i	−0.123253	+	0.0895488i	0.524451	+	0.851441i	$0.324271\pi$
$242$		0			0
$243$	−209.782	−	209.782i	−0.863300	−	0.863300i
$244$		0			0
$245$	444.352	+	132.724i	1.81368	+	0.541730i
$246$		0			0
$247$	196.502	+	100.123i	0.795555	+	0.405355i
$248$		0			0
$249$			470.721i			1.89045i
$250$		0			0
$251$	354.053			1.41057			0.705286	−	0.708923i	$-0.250819\pi$
$251$	354.053			1.41057			0.705286	+	0.708923i	$0.250819\pi$
$252$		0			0
$253$	−53.6282	+	105.251i	−0.211969	+	0.416013i
$254$		0			0
$255$	−67.3760	+	225.571i	−0.264219	+	0.884590i
$256$		0			0
$257$	125.873	−	125.873i	0.489778	−	0.489778i	−0.418458	−	0.908236i	$-0.637429\pi$
$257$	125.873	−	125.873i	0.489778	−	0.489778i	0.908236	+	0.418458i	$0.137429\pi$
$258$		0			0
$259$	−176.862	−	243.429i	−0.682864	−	0.939882i
$260$		0			0
$261$	−46.3904	−	33.7046i	−0.177741	−	0.129136i
$262$		0			0
$263$	−102.171	−	16.1822i	−0.388482	−	0.0615295i	−0.0408614	−	0.999165i	$-0.513010\pi$
$263$	−102.171	−	16.1822i	−0.388482	−	0.0615295i	−0.347620	+	0.937635i	$0.613010\pi$
$264$		0			0
$265$	−124.973	−	119.137i	−0.471595	−	0.449572i
$266$		0			0
$267$	23.4884	+	46.0987i	0.0879717	+	0.172654i
$268$		0			0
$269$	23.0012	+	7.47355i	0.0855064	+	0.0277827i	0.351458	−	0.936204i	$-0.385686\pi$
$269$	23.0012	+	7.47355i	0.0855064	+	0.0277827i	−0.265951	+	0.963986i	$0.585686\pi$
$270$		0			0
$271$	−54.0115	−	166.230i	−0.199305	−	0.613396i	−0.999899	−	0.0141902i	$-0.995483\pi$
$271$	−54.0115	−	166.230i	−0.199305	−	0.613396i	0.800595	−	0.599206i	$-0.204517\pi$
$272$		0			0
$273$	123.034	+	776.808i	0.450675	+	2.84545i
$274$		0			0
$275$	−96.6915	−	255.359i	−0.351606	−	0.928578i
$276$		0			0
$277$	365.152	−	57.8343i	1.31824	−	0.208788i	0.542613	−	0.839983i	$-0.317435\pi$
$277$	365.152	−	57.8343i	1.31824	−	0.208788i	0.775624	+	0.631195i	$0.217435\pi$
$278$		0			0
$279$	164.336	−	53.3960i	0.589018	−	0.191384i
$280$		0			0
$281$	89.3268	−	274.920i	0.317889	−	0.978362i	−0.656660	−	0.754187i	$-0.728031\pi$
$281$	89.3268	−	274.920i	0.317889	−	0.978362i	0.974549	−	0.224175i	$-0.0719688\pi$
$282$		0			0
$283$	260.171	−	132.564i	0.919334	−	0.468424i	0.0707553	−	0.997494i	$-0.477459\pi$
$283$	260.171	−	132.564i	0.919334	−	0.468424i	0.848578	+	0.529070i	$0.177459\pi$
$284$		0			0
$285$	176.525	+	326.892i	0.619388	+	1.14699i
$286$		0			0
$287$	49.7605	−	314.176i	0.173382	−	1.09469i
$288$		0			0
$289$	111.322	−	153.222i	0.385197	−	0.530179i
$290$		0			0
$291$	502.040	−	364.754i	1.72522	−	1.25345i
$292$		0			0
$293$	−97.8910	−	97.8910i	−0.334099	−	0.334099i	0.520042	−	0.854141i	$-0.325916\pi$
$293$	−97.8910	−	97.8910i	−0.334099	−	0.334099i	−0.854141	+	0.520042i	$0.825916\pi$
$294$		0			0
$295$	71.6376	−	25.1848i	0.242839	−	0.0853723i
$296$		0			0
$297$	−195.392	−	99.5570i	−0.657884	−	0.335209i
$298$		0			0
$299$			151.443i			0.506499i
$300$		0			0
$301$	357.463			1.18759
$302$		0			0
$303$	183.382	−	359.907i	0.605221	−	1.18781i
$304$		0			0
$305$	234.168	−	178.838i	0.767765	−	0.586355i
$306$		0			0
$307$	−158.687	+	158.687i	−0.516896	+	0.516896i	−0.916631	−	0.399735i	$-0.869102\pi$
$307$	−158.687	+	158.687i	−0.516896	+	0.516896i	0.399735	+	0.916631i	$0.369102\pi$
$308$		0			0
$309$	−332.283	−	457.349i	−1.07535	−	1.48009i
$310$		0			0
$311$	108.299	+	78.6839i	0.348229	+	0.253003i	0.748126	−	0.663557i	$-0.230954\pi$
$311$	108.299	+	78.6839i	0.348229	+	0.253003i	−0.399897	+	0.916560i	$0.630954\pi$
$312$		0			0
$313$	455.593	+	72.1588i	1.45557	+	0.230539i	0.833542	−	0.552457i	$-0.186310\pi$
$313$	455.593	+	72.1588i	1.45557	+	0.230539i	0.622027	+	0.782996i	$0.286310\pi$
$314$		0			0
$315$	−341.345	+	711.472i	−1.08363	+	2.25864i
$316$		0			0
$317$	−30.6244	−	60.1038i	−0.0966070	−	0.189602i	0.837645	−	0.546214i	$-0.183932\pi$
$317$	−30.6244	−	60.1038i	−0.0966070	−	0.189602i	−0.934252	+	0.356613i	$0.883932\pi$
$318$		0			0
$319$	44.9337	+	14.5998i	0.140858	+	0.0457675i
$320$		0			0
$321$	−274.179	−	843.835i	−0.854139	−	2.62877i
$322$		0			0
$323$	24.5899	+	155.254i	0.0761296	+	0.480663i
$324$		0			0
$325$	−259.080	−	235.421i	−0.797169	−	0.724373i
$326$		0			0
$327$	26.9938	−	4.27539i	0.0825498	−	0.0130746i
$328$		0			0
$329$	−589.838	+	191.650i	−1.79282	+	0.582523i
$330$		0			0
$331$	−60.5799	+	186.446i	−0.183021	+	0.563280i	−0.999909	−	0.0135163i	$-0.995697\pi$
$331$	−60.5799	+	186.446i	−0.183021	+	0.563280i	0.816888	+	0.576797i	$0.195697\pi$
$332$		0			0
$333$	298.501	−	152.094i	0.896399	−	0.456738i
$334$		0			0
$335$	−477.963	+	87.4603i	−1.42675	+	0.261075i
$336$		0			0
$337$	57.2501	−	361.463i	0.169881	−	1.07259i	−0.744466	−	0.667660i	$-0.767296\pi$
$337$	57.2501	−	361.463i	0.169881	−	1.07259i	0.914348	−	0.404929i	$-0.132704\pi$
$338$		0			0
$339$	262.035	−	360.660i	0.772965	−	1.06390i
$340$		0			0
$341$	−115.180	+	83.6835i	−0.337773	+	0.245406i
$342$		0			0
$343$	368.319	+	368.319i	1.07382	+	1.07382i
$344$		0			0
$345$	−144.976	+	209.916i	−0.420221	+	0.608453i
$346$		0			0
$347$	420.726	+	214.371i	1.21247	+	0.617783i	0.938940	−	0.344081i	$-0.111810\pi$
$347$	420.726	+	214.371i	1.21247	+	0.617783i	0.273527	+	0.961864i	$0.411810\pi$
$348$		0			0
$349$			436.033i			1.24938i	0.780874	+	0.624689i	$0.214774\pi$
$349$			436.033i			1.24938i	−0.780874	+	0.624689i	$0.785226\pi$
$350$		0			0
$351$	−281.144			−0.800979
$352$		0			0
$353$	233.399	−	458.071i	0.661186	−	1.29765i	−0.280077	−	0.959977i	$-0.590360\pi$
$353$	233.399	−	458.071i	0.661186	−	1.29765i	0.941263	−	0.337673i	$-0.109640\pi$
$354$		0			0
$355$	327.878	−	7.83895i	0.923600	−	0.0220816i
$356$		0			0
$357$	−396.384	+	396.384i	−1.11032	+	1.11032i
$358$		0			0
$359$	−251.399	−	346.021i	−0.700275	−	0.963846i	−0.999952	−	0.00980492i	$-0.996879\pi$
$359$	−251.399	−	346.021i	−0.700275	−	0.963846i	0.299677	−	0.954041i	$-0.403121\pi$
$360$		0			0
$361$	−91.3715	−	66.3853i	−0.253107	−	0.183893i
$362$		0			0
$363$	−7.95885	−	1.26056i	−0.0219252	−	0.00347261i
$364$		0			0
$365$	−396.148	−	53.0716i	−1.08534	−	0.145402i
$366$		0			0
$367$	−78.1469	−	153.372i	−0.212934	−	0.417907i	0.759692	−	0.650283i	$-0.225350\pi$
$367$	−78.1469	−	153.372i	−0.212934	−	0.417907i	−0.972626	+	0.232377i	$0.925350\pi$
$368$		0			0
$369$	336.828	+	109.442i	0.912813	+	0.296591i
$370$		0			0
$371$	−127.048	−	391.013i	−0.342447	−	1.05394i
$372$		0			0
$373$	88.8954	+	561.263i	0.238325	+	1.50473i	0.759067	+	0.651013i	$0.225656\pi$
$373$	88.8954	+	561.263i	0.238325	+	1.50473i	−0.520741	+	0.853714i	$0.674344\pi$
$374$		0			0
$375$	−133.744	−	574.336i	−0.356651	−	1.53156i
$376$		0			0
$377$	59.8258	−	9.47548i	0.158689	−	0.0251339i
$378$		0			0
$379$	−121.129	+	39.3572i	−0.319602	+	0.103845i	−0.464425	−	0.885613i	$-0.653739\pi$
$379$	−121.129	+	39.3572i	−0.319602	+	0.103845i	0.144823	+	0.989458i	$0.453739\pi$
$380$		0			0
$381$	−335.415	+	1032.30i	−0.880355	+	2.70945i
$382$		0			0
$383$	−41.3418	+	21.0647i	−0.107942	+	0.0549992i	−0.507128	−	0.861871i	$-0.669293\pi$
$383$	−41.3418	+	21.0647i	−0.107942	+	0.0549992i	0.399186	+	0.916870i	$0.369293\pi$
$384$		0			0
$385$	86.3334	−	644.428i	0.224243	−	1.67384i
$386$		0			0
$387$	−62.2606	+	393.098i	−0.160880	+	1.01576i
$388$		0			0
$389$	80.1323	−	110.293i	0.205996	−	0.283529i	−0.693502	−	0.720455i	$-0.743933\pi$
$389$	80.1323	−	110.293i	0.205996	−	0.283529i	0.899497	+	0.436926i	$0.143933\pi$
$390$		0			0
$391$	−87.3263	+	63.4462i	−0.223341	+	0.162267i
$392$		0			0
$393$	−244.289	−	244.289i	−0.621600	−	0.621600i
$394$		0			0
$395$	−2.12793	−	89.0045i	−0.00538716	−	0.225328i
$396$		0			0
$397$	341.113	+	173.806i	0.859227	+	0.437798i	0.827345	−	0.561694i	$-0.189850\pi$
$397$	341.113	+	173.806i	0.859227	+	0.437798i	0.0318816	+	0.999492i	$0.489850\pi$
$398$		0			0
$399$			884.630i			2.21712i
$400$		0			0
$401$	424.132			1.05768			0.528842	−	0.848720i	$-0.322626\pi$
$401$	424.132			1.05768			0.528842	+	0.848720i	$0.322626\pi$
$402$		0			0
$403$	−82.8650	+	162.632i	−0.205620	+	0.403553i
$404$		0			0
$405$	101.140	+	69.8512i	0.249729	+	0.172472i
$406$		0			0
$407$	−195.184	+	195.184i	−0.479568	+	0.479568i
$408$		0			0
$409$	−41.4213	−	57.0116i	−0.101275	−	0.139393i	0.755372	−	0.655296i	$-0.227456\pi$
$409$	−41.4213	−	57.0116i	−0.101275	−	0.139393i	−0.856647	+	0.515904i	$0.827456\pi$
$410$		0			0
$411$	−275.978	−	200.509i	−0.671478	−	0.487858i
$412$		0			0
$413$	178.590	+	28.2859i	0.432421	+	0.0684888i
$414$		0			0
$415$	−89.7998	−	490.748i	−0.216385	−	1.18253i
$416$		0			0
$417$	−113.123	−	222.015i	−0.271277	−	0.532411i
$418$		0			0
$419$	426.885	+	138.703i	1.01882	+	0.331034i	0.770360	−	0.637609i	$-0.220076\pi$
$419$	426.885	+	138.703i	1.01882	+	0.331034i	0.248458	+	0.968643i	$0.420076\pi$
$420$		0			0
$421$	96.5333	+	297.099i	0.229295	+	0.705698i	0.997827	+	0.0658866i	$0.0209876\pi$
$421$	96.5333	+	297.099i	0.229295	+	0.705698i	−0.768532	+	0.639811i	$0.779012\pi$
$422$		0			0
$423$	−108.021	−	682.018i	−0.255369	−	1.61234i
$424$		0			0
$425$	27.2103	−	248.021i	0.0640241	−	0.583579i
$426$		0			0
$427$	692.972	−	109.756i	1.62289	−	0.257040i
$428$		0			0
$429$	686.189	−	222.956i	1.59951	−	0.519712i
$430$		0			0
$431$	6.66936	−	20.5262i	0.0154742	−	0.0476245i	−0.943021	−	0.332732i	$-0.892029\pi$
$431$	6.66936	−	20.5262i	0.0154742	−	0.0476245i	0.958495	+	0.285108i	$0.0920294\pi$
$432$		0			0
$433$	−489.321	+	249.322i	−1.13007	+	0.575800i	−0.916064	−	0.401032i	$-0.868652\pi$
$433$	−489.321	+	249.322i	−1.13007	+	0.575800i	−0.214008	+	0.976832i	$0.568652\pi$
$434$		0			0
$435$	91.9959	+	44.1371i	0.211485	+	0.101465i
$436$		0			0
$437$	−26.6471	+	168.243i	−0.0609774	+	0.384996i
$438$		0			0
$439$	−117.604	+	161.869i	−0.267892	+	0.368721i	−0.921676	−	0.387959i	$-0.873180\pi$
$439$	−117.604	+	161.869i	−0.267892	+	0.368721i	0.653785	+	0.756680i	$0.273180\pi$
$440$		0			0
$441$	−994.678	+	722.676i	−2.25551	+	1.63872i
$442$		0			0
$443$	−100.812	−	100.812i	−0.227566	−	0.227566i	0.584109	−	0.811675i	$-0.301444\pi$
$443$	−100.812	−	100.812i	−0.227566	−	0.227566i	−0.811675	+	0.584109i	$0.801444\pi$
$444$		0			0
$445$	−33.2820	−	43.5791i	−0.0747911	−	0.0979305i
$446$		0			0
$447$	−1054.13	−	537.104i	−2.35822	−	1.20158i
$448$		0			0
$449$		−	594.424i		−	1.32389i	−0.749554	−	0.661943i	$-0.769732\pi$
$449$		−	594.424i		−	1.32389i	0.749554	−	0.661943i	$-0.230268\pi$
$450$		0			0
$451$	−291.808			−0.647023
$452$		0			0
$453$	598.485	−	1174.59i	1.32116	−	2.59292i
$454$		0			0
$455$	−276.461	−	786.386i	−0.607606	−	1.72832i
$456$		0			0
$457$	−120.448	+	120.448i	−0.263562	+	0.263562i	−0.826500	−	0.562937i	$-0.809671\pi$
$457$	−120.448	+	120.448i	−0.263562	+	0.263562i	0.562937	+	0.826500i	$0.309671\pi$
$458$		0			0
$459$	−117.784	−	162.115i	−0.256609	−	0.353192i
$460$		0			0
$461$	306.035	+	222.347i	0.663850	+	0.482315i	0.867961	−	0.496632i	$-0.165430\pi$
$461$	306.035	+	222.347i	0.663850	+	0.482315i	−0.204111	+	0.978948i	$0.565430\pi$
$462$		0			0
$463$	50.4954	+	7.99769i	0.109061	+	0.0172736i	0.210727	−	0.977545i	$-0.432417\pi$
$463$	50.4954	+	7.99769i	0.109061	+	0.0172736i	−0.101665	+	0.994819i	$0.532417\pi$
$464$		0			0
$465$	−270.547	+	146.099i	−0.581821	+	0.314190i
$466$		0			0
$467$	311.558	+	611.468i	0.667149	+	1.30935i	0.937968	+	0.346723i	$0.112705\pi$
$467$	311.558	+	611.468i	0.667149	+	1.30935i	−0.270819	+	0.962630i	$0.587295\pi$
$468$		0			0
$469$	−1100.38	−	357.536i	−2.34623	−	0.762337i
$470$		0			0
$471$	375.162	+	1154.63i	0.796522	+	2.45144i
$472$		0			0
$473$	−51.2989	−	323.888i	−0.108454	−	0.684753i
$474$		0			0
$475$	−246.397	−	307.124i	−0.518731	−	0.646576i
$476$		0			0
$477$	452.120	−	71.6088i	0.947842	−	0.150123i
$478$		0			0
$479$	−54.9406	+	17.8513i	−0.114698	+	0.0372678i	−0.365804	−	0.930692i	$-0.619206\pi$
$479$	−54.9406	+	17.8513i	−0.114698	+	0.0372678i	0.251105	+	0.967960i	$0.419206\pi$
$480$		0			0
$481$	−109.357	+	336.565i	−0.227353	+	0.699720i
$482$		0			0
$483$	−541.260	+	275.786i	−1.12062	+	0.570985i
$484$		0			0
$485$	−453.816	+	476.047i	−0.935703	+	0.981540i
$486$		0			0
$487$	−45.4546	+	286.989i	−0.0933360	+	0.589300i	0.896046	+	0.443961i	$0.146427\pi$
$487$	−45.4546	+	286.989i	−0.0933360	+	0.589300i	−0.989382	+	0.145339i	$0.953573\pi$
$488$		0			0
$489$	−159.343	+	219.317i	−0.325855	+	0.448501i
$490$		0			0
$491$	−210.550	+	152.974i	−0.428819	+	0.311555i	−0.781177	−	0.624310i	$-0.785380\pi$
$491$	−210.550	+	152.974i	−0.428819	+	0.311555i	0.352357	+	0.935865i	$0.385380\pi$
$492$		0			0
$493$	30.5275	+	30.5275i	0.0619219	+	0.0619219i
$494$		0			0
$495$	693.632	+	207.182i	1.40128	+	0.418549i
$496$		0			0
$497$	695.839	+	354.548i	1.40008	+	0.713376i
$498$		0			0
$499$			58.9853i			0.118207i	0.998252	+	0.0591035i	$0.0188242\pi$
$499$			58.9853i			0.118207i	−0.998252	+	0.0591035i	$0.981176\pi$
$500$		0			0
$501$	−1016.54			−2.02903
$502$		0			0
$503$	381.004	−	747.763i	0.757464	−	1.48661i	−0.112585	−	0.993642i	$-0.535913\pi$
$503$	381.004	−	747.763i	0.757464	−	1.48661i	0.870049	−	0.492965i	$-0.164087\pi$
$504$		0			0
$505$	−122.524	+	410.204i	−0.242622	+	0.812284i
$506$		0			0
$507$	90.3118	−	90.3118i	0.178130	−	0.178130i
$508$		0			0
$509$	−327.038	−	450.129i	−0.642510	−	0.884340i	0.356236	−	0.934396i	$-0.384060\pi$
$509$	−327.038	−	450.129i	−0.642510	−	0.884340i	−0.998746	+	0.0500563i	$0.984060\pi$
$510$		0			0
$511$	−769.962	−	559.410i	−1.50678	−	1.09474i
$512$		0			0
$513$	−312.332	−	49.4685i	−0.608835	−	0.0964299i
$514$		0			0
$515$	433.669	+	413.417i	0.842076	+	0.802752i
$516$		0			0
$517$	258.296	+	506.934i	0.499605	+	0.980530i
$518$		0			0
$519$	−1136.79	−	369.367i	−2.19035	−	0.711689i
$520$		0			0
$521$	−261.077	−	803.512i	−0.501107	−	1.54225i	−0.807218	−	0.590254i	$-0.799028\pi$
$521$	−261.077	−	803.512i	−0.501107	−	1.54225i	0.306110	−	0.951996i	$-0.400972\pi$
$522$		0			0
$523$	−16.0763	−	101.502i	−0.0307386	−	0.194076i	0.967541	−	0.252716i	$-0.0813237\pi$
$523$	−16.0763	−	101.502i	−0.0307386	−	0.194076i	−0.998279	+	0.0586397i	$0.981324\pi$
$524$		0			0
$525$	369.601	−	1354.67i	0.704002	−	2.58033i
$526$		0			0
$527$	−128.494	+	20.3514i	−0.243821	+	0.0386175i
$528$		0			0
$529$	391.862	−	127.324i	0.740760	−	0.240688i
$530$		0			0
$531$	−62.2113	+	191.467i	−0.117159	+	0.360577i
$532$		0			0
$533$	−333.335	+	169.843i	−0.625394	+	0.318654i
$534$		0			0
$535$	446.823	+	827.431i	0.835183	+	1.54660i
$536$		0			0
$537$	−136.991	+	864.927i	−0.255104	+	1.61067i
$538$		0			0
$539$	595.440	−	819.553i	1.10471	−	1.52051i
$540$		0			0
$541$	400.700	−	291.125i	0.740665	−	0.538124i	−0.152255	−	0.988341i	$-0.548653\pi$
$541$	400.700	−	291.125i	0.740665	−	0.538124i	0.892919	+	0.450217i	$0.148653\pi$
$542$		0			0
$543$	590.756	+	590.756i	1.08795	+	1.08795i
$544$		0			0
$545$	−27.3266	+	9.60691i	−0.0501406	+	0.0176274i
$546$		0			0
$547$	548.489	+	279.469i	1.00272	+	0.510912i	0.876660	−	0.481110i	$-0.159766\pi$
$547$	548.489	+	279.469i	1.00272	+	0.510912i	0.126062	+	0.992022i	$0.459766\pi$
$548$		0			0
$549$			781.170i			1.42290i
$550$		0			0
$551$	68.1298			0.123648
$552$		0			0
$553$	96.2441	−	188.890i	0.174040	−	0.341573i
$554$		0			0
$555$	−473.773	+	361.828i	−0.853645	+	0.651943i
$556$		0			0
$557$	−65.6218	+	65.6218i	−0.117813	+	0.117813i	−0.763555	−	0.645742i	$-0.776548\pi$
$557$	−65.6218	+	65.6218i	−0.117813	+	0.117813i	0.645742	+	0.763555i	$0.276548\pi$
$558$		0			0
$559$	−247.114	−	340.123i	−0.442064	−	0.608449i
$560$		0			0
$561$	416.038	+	302.269i	0.741600	+	0.538804i
$562$		0			0
$563$	−944.052	−	149.523i	−1.67682	−	0.265583i	−0.755718	−	0.654897i	$-0.772712\pi$
$563$	−944.052	−	149.523i	−1.67682	−	0.265583i	−0.921105	+	0.389314i	$0.872712\pi$
$564$		0			0
$565$	−204.380	+	425.994i	−0.361735	+	0.753971i
$566$		0			0
$567$	132.877	+	260.785i	0.234351	+	0.459939i
$568$		0			0
$569$	675.070	+	219.343i	1.18641	+	0.385489i	0.834746	−	0.550635i	$-0.185615\pi$
$569$	675.070	+	219.343i	1.18641	+	0.385489i	0.351668	+	0.936125i	$0.385615\pi$
$570$		0			0
$571$	−29.6017	−	91.1046i	−0.0518418	−	0.159553i	0.921784	−	0.387704i	$-0.126732\pi$
$571$	−29.6017	−	91.1046i	−0.0518418	−	0.159553i	−0.973626	+	0.228152i	$0.926732\pi$
$572$		0			0
$573$	−171.825	−	1084.86i	−0.299869	−	1.89330i
$574$		0			0
$575$	111.098	−	246.505i	0.193215	−	0.428704i
$576$		0			0
$577$	−190.430	+	30.1612i	−0.330035	+	0.0522725i	−0.319253	−	0.947669i	$-0.603432\pi$
$577$	−190.430	+	30.1612i	−0.330035	+	0.0522725i	−0.0107820	+	0.999942i	$0.503432\pi$
$578$		0			0
$579$	952.650	−	309.535i	1.64534	−	0.534602i
$580$		0			0
$581$	367.100	−	1129.82i	0.631842	−	1.94461i
$582$		0			0
$583$	−336.055	+	171.228i	−0.576423	+	0.293702i
$584$		0			0
$585$	912.931	−	167.053i	1.56057	−	0.285561i
$586$		0			0
$587$	66.5873	−	420.416i	0.113437	−	0.716211i	−0.863765	−	0.503896i	$-0.831900\pi$
$587$	66.5873	−	420.416i	0.113437	−	0.716211i	0.977201	−	0.212315i	$-0.0681004\pi$
$588$		0			0
$589$	−120.673	+	166.093i	−0.204878	+	0.281991i
$590$		0			0
$591$	−889.587	+	646.323i	−1.50522	+	1.09361i
$592$		0			0
$593$	161.153	+	161.153i	0.271759	+	0.271759i	0.829808	−	0.558049i	$-0.188450\pi$
$593$	161.153	+	161.153i	0.271759	+	0.271759i	−0.558049	+	0.829808i	$0.688450\pi$
$594$		0			0
$595$	337.630	−	488.867i	0.567445	−	0.821625i
$596$		0			0
$597$	−667.409	−	340.062i	−1.11794	−	0.569618i
$598$		0			0
$599$		−	302.025i		−	0.504216i	−0.967699	−	0.252108i	$-0.918876\pi$
$599$		−	302.025i		−	0.504216i	0.967699	−	0.252108i	$-0.0811238\pi$
$600$		0			0
$601$	−147.116			−0.244786			−0.122393	−	0.992482i	$-0.539057\pi$
$601$	−147.116			−0.244786			−0.122393	+	0.992482i	$0.539057\pi$
$602$		0			0
$603$	584.835	−	1147.80i	0.969876	−	1.90349i
$604$		0			0
$605$	8.53794	−	0.204126i	0.0141123	−	0.000337399i
$606$		0			0
$607$	166.801	−	166.801i	0.274796	−	0.274796i	−0.556231	−	0.831028i	$-0.687753\pi$
$607$	166.801	−	166.801i	0.274796	−	0.274796i	0.831028	+	0.556231i	$0.187753\pi$
$608$		0			0
$609$	142.812	+	196.563i	0.234502	+	0.322764i
$610$		0			0
$611$	590.108	+	428.739i	0.965807	+	0.701700i
$612$		0			0
$613$	−688.785	−	109.093i	−1.12363	−	0.177965i	−0.433153	−	0.901320i	$-0.642599\pi$
$613$	−688.785	−	109.093i	−1.12363	−	0.177965i	−0.690476	+	0.723355i	$0.742599\pi$
$614$		0			0
$615$	−624.628	−	83.6808i	−1.01566	−	0.136066i
$616$		0			0
$617$	393.489	+	772.265i	0.637745	+	1.25165i	0.953095	+	0.302670i	$0.0978781\pi$
$617$	393.489	+	772.265i	0.637745	+	1.25165i	−0.315350	+	0.948975i	$0.602122\pi$
$618$		0			0
$619$	−114.108	−	37.0760i	−0.184343	−	0.0598966i	0.215391	−	0.976528i	$-0.430897\pi$
$619$	−114.108	−	37.0760i	−0.184343	−	0.0598966i	−0.399734	+	0.916631i	$0.630897\pi$
$620$		0			0
$621$	−67.1031	−	206.522i	−0.108057	−	0.332564i
$622$		0			0
$623$	−20.4258	−	128.963i	−0.0327861	−	0.207004i
$624$		0			0
$625$	249.001	+	573.257i	0.398402	+	0.917211i
$626$		0			0
$627$	801.541	−	126.952i	1.27837	−	0.202475i
$628$		0			0
$629$	−239.887	+	77.9440i	−0.381378	+	0.123917i
$630$		0			0
$631$	−40.7698	+	125.476i	−0.0646113	+	0.198853i	−0.978151	−	0.207897i	$-0.933338\pi$
$631$	−40.7698	+	125.476i	−0.0646113	+	0.198853i	0.913539	+	0.406750i	$0.133338\pi$
$632$		0			0
$633$	−624.786	+	318.344i	−0.987024	+	0.502914i
$634$		0			0
$635$	152.753	−	1140.21i	0.240555	−	1.79561i
$636$		0			0
$637$	203.168	−	1282.75i	0.318945	−	2.01374i
$638$		0			0
$639$	−511.088	+	703.453i	−0.799825	+	1.10087i
$640$		0			0
$641$	144.903	−	105.278i	0.226058	−	0.164241i	−0.468991	−	0.883203i	$-0.655382\pi$
$641$	144.903	−	105.278i	0.226058	−	0.164241i	0.695050	+	0.718962i	$0.255382\pi$
$642$		0			0
$643$	−40.3319	−	40.3319i	−0.0627245	−	0.0627245i	0.675049	−	0.737773i	$-0.264123\pi$
$643$	−40.3319	−	40.3319i	−0.0627245	−	0.0627245i	−0.737773	+	0.675049i	$0.764123\pi$
$644$		0			0
$645$	−16.9272	−	708.009i	−0.0262437	−	1.09769i
$646$		0			0
$647$	96.4539	+	49.1457i	0.149079	+	0.0759594i	0.526938	−	0.849903i	$-0.323340\pi$
$647$	96.4539	+	49.1457i	0.149079	+	0.0759594i	−0.377860	+	0.925863i	$0.623340\pi$
$648$		0			0
$649$		−	165.875i		−	0.255586i
$650$		0			0
$651$	−732.150			−1.12465
$652$		0			0
$653$	−350.044	+	687.000i	−0.536055	+	1.05207i	0.451126	+	0.892460i	$0.351023\pi$
$653$	−350.044	+	687.000i	−0.536055	+	1.05207i	−0.987181	+	0.159607i	$0.948977\pi$
$654$		0			0
$655$	301.285	+	208.079i	0.459978	+	0.317678i
$656$		0			0
$657$	749.283	−	749.283i	1.14046	−	1.14046i
$658$		0			0
$659$	697.843	+	960.499i	1.05894	+	1.45751i	0.880790	+	0.473506i	$0.157012\pi$
$659$	697.843	+	960.499i	1.05894	+	1.45751i	0.178152	+	0.984003i	$0.442988\pi$
$660$		0			0
$661$	−1026.11	−	745.510i	−1.55235	−	1.12785i	−0.941946	−	0.335766i	$-0.891005\pi$
$661$	−1026.11	−	745.510i	−1.55235	−	1.12785i	−0.610409	−	0.792086i	$-0.708995\pi$
$662$		0			0
$663$	651.176	+	103.136i	0.982166	+	0.155560i
$664$		0			0
$665$	−168.762	−	922.267i	−0.253777	−	1.38687i
$666$		0			0
$667$	21.2397	+	41.6852i	0.0318436	+	0.0624965i
$668$		0			0
$669$	1759.18	+	571.593i	2.62957	+	0.854399i
$670$		0			0
$671$	−198.894	−	612.134i	−0.296415	−	0.912271i
$672$		0			0
$673$	−2.43582	−	15.3791i	−0.00361934	−	0.0228516i	0.985813	−	0.167850i	$-0.0536824\pi$
$673$	−2.43582	−	15.3791i	−0.00361934	−	0.0228516i	−0.989432	+	0.144998i	$0.953682\pi$
$674$		0			0
$675$	457.619	+	206.247i	0.677954	+	0.305551i
$676$		0			0
$677$	−75.1252	+	11.8987i	−0.110968	+	0.0175756i	−0.211671	−	0.977341i	$-0.567891\pi$
$677$	−75.1252	+	11.8987i	−0.110968	+	0.0175756i	0.100704	+	0.994916i	$0.467891\pi$
$678$		0			0
$679$	−1489.45	+	483.951i	−2.19359	+	0.712742i
$680$		0			0
$681$	−143.046	+	440.250i	−0.210053	+	0.646476i
$682$		0			0
$683$	96.1264	−	48.9789i	0.140741	−	0.0717114i	−0.382202	−	0.924079i	$-0.624834\pi$
$683$	96.1264	−	48.9789i	0.140741	−	0.0717114i	0.522943	+	0.852368i	$0.324834\pi$
$684$		0			0
$685$	325.971	+	156.392i	0.475869	+	0.228309i
$686$		0			0
$687$	129.373	−	816.831i	0.188316	−	1.18898i
$688$		0			0
$689$	−284.218	+	391.192i	−0.412507	+	0.567768i
$690$		0			0
$691$	585.805	−	425.612i	0.847764	−	0.615937i	−0.0767647	−	0.997049i	$-0.524459\pi$
$691$	585.805	−	425.612i	0.847764	−	0.615937i	0.924529	+	0.381113i	$0.124459\pi$
$692$		0			0
$693$	1218.89	+	1218.89i	1.75885	+	1.75885i
$694$		0			0
$695$	160.289	+	209.881i	0.230632	+	0.301987i
$696$		0			0
$697$	−237.585	−	121.055i	−0.340867	−	0.173681i
$698$		0			0
$699$			1309.67i			1.87363i
$700$		0			0
$701$	−388.344			−0.553986			−0.276993	−	0.960872i	$-0.589338\pi$
$701$	−388.344			−0.553986			−0.276993	+	0.960872i	$0.589338\pi$
$702$		0			0
$703$	−180.708	+	354.660i	−0.257053	+	0.504495i
$704$		0			0
$705$	407.522	+	1159.19i	0.578046	+	1.64424i
$706$		0			0
$707$	−720.830	+	720.830i	−1.01956	+	1.01956i
$708$		0			0
$709$	326.398	+	449.248i	0.460364	+	0.633637i	0.974584	−	0.224021i	$-0.0719186\pi$
$709$	326.398	+	449.248i	0.460364	+	0.633637i	−0.514220	+	0.857658i	$0.671919\pi$
$710$		0			0
$711$	190.956	+	138.738i	0.268574	+	0.195131i
$712$		0			0
$713$	−139.244	−	22.0541i	−0.195293	−	0.0309314i
$714$		0			0
$715$	−672.850	+	363.347i	−0.941049	+	0.508178i
$716$		0			0
$717$	318.291	+	624.681i	0.443921	+	0.871243i
$718$		0			0
$719$	208.554	+	67.7632i	0.290061	+	0.0942465i	0.450433	−	0.892810i	$-0.351270\pi$
$719$	208.554	+	67.7632i	0.290061	+	0.0942465i	−0.160372	+	0.987057i	$0.551270\pi$
$720$		0			0
$721$	440.870	+	1356.86i	0.611470	+	1.88191i
$722$		0			0
$723$	27.0965	+	171.081i	0.0374779	+	0.236626i
$724$		0			0
$725$	−104.330	−	28.4648i	−0.143903	−	0.0392619i
$726$		0			0
$727$	−92.9105	+	14.7156i	−0.127800	+	0.0202415i	−0.220007	−	0.975498i	$-0.570608\pi$
$727$	−92.9105	+	14.7156i	−0.127800	+	0.0202415i	0.0922068	+	0.995740i	$0.470608\pi$
$728$		0			0
$729$	−1120.68	+	364.132i	−1.53729	+	0.499496i
$730$		0			0
$731$	92.5974	−	284.985i	0.126672	−	0.389857i
$732$		0			0
$733$	−57.0412	+	29.0639i	−0.0778188	+	0.0396507i	−0.492467	−	0.870331i	$-0.663905\pi$
$733$	−57.0412	+	29.0639i	−0.0778188	+	0.0396507i	0.414648	+	0.909982i	$0.363905\pi$
$734$		0			0
$735$	1509.59	−	1583.54i	2.05386	−	2.15448i
$736$		0			0
$737$	−166.040	+	1048.34i	−0.225292	+	1.42244i
$738$		0			0
$739$	−707.012	+	973.119i	−0.956715	+	1.31681i	−0.00823572	+	0.999966i	$0.502622\pi$
$739$	−707.012	+	973.119i	−0.956715	+	1.31681i	−0.948479	+	0.316839i	$0.897378\pi$
$740$		0			0
$741$	841.718	−	611.544i	1.13592	−	0.825296i
$742$		0			0
$743$	235.132	+	235.132i	0.316463	+	0.316463i	0.847407	−	0.530944i	$-0.178163\pi$
$743$	235.132	+	235.132i	0.316463	+	0.316463i	−0.530944	+	0.847407i	$0.678163\pi$
$744$		0			0
$745$	1201.44	+	358.859i	1.61267	+	0.481690i
$746$		0			0
$747$	1178.51	+	600.479i	1.57765	+	0.803855i
$748$		0			0
$749$			2239.18i			2.98956i
$750$		0			0
$751$	1331.68			1.77321			0.886607	−	0.462523i	$-0.153056\pi$
$751$	1331.68			1.77321			0.886607	+	0.462523i	$0.153056\pi$
$752$		0			0
$753$	758.296	−	1488.24i	1.00703	−	1.97641i
$754$		0			0
$755$	−399.870	+	1338.74i	−0.529629	+	1.77316i
$756$		0			0
$757$	699.634	−	699.634i	0.924219	−	0.924219i	−0.0731053	−	0.997324i	$-0.523291\pi$
$757$	699.634	−	699.634i	0.924219	−	0.924219i	0.997324	+	0.0731053i	$0.0232909\pi$
$758$		0			0
$759$	327.558	+	450.845i	0.431565	+	0.593998i
$760$		0			0
$761$	412.515	+	299.710i	0.542069	+	0.393836i	0.824853	−	0.565347i	$-0.191258\pi$
$761$	412.515	+	299.710i	0.542069	+	0.393836i	−0.282784	+	0.959184i	$0.591258\pi$
$762$		0			0
$763$	−68.1243	−	10.7898i	−0.0892848	−	0.0141413i
$764$		0			0
$765$	478.795	+	456.435i	0.625875	+	0.596647i
$766$		0			0
$767$	−96.5454	−	189.481i	−0.125874	−	0.247042i
$768$		0			0
$769$	−508.350	−	165.173i	−0.661053	−	0.214789i	−0.0407717	−	0.999168i	$-0.512982\pi$
$769$	−508.350	−	165.173i	−0.661053	−	0.214789i	−0.620282	+	0.784379i	$0.712982\pi$
$770$		0			0
$771$	−259.509	−	798.687i	−0.336588	−	1.03591i
$772$		0			0
$773$	32.8579	+	207.456i	0.0425069	+	0.268378i	0.999784	−	0.0207948i	$-0.00661968\pi$
$773$	32.8579	+	207.456i	0.0425069	+	0.268378i	−0.957277	+	0.289173i	$0.906620\pi$
$774$		0			0
$775$	254.186	−	203.927i	0.327982	−	0.263131i
$776$		0			0
$777$	−1402.03	+	222.060i	−1.80442	+	0.285792i
$778$		0			0
$779$	−400.198	+	130.032i	−0.513732	+	0.166922i
$780$		0			0
$781$	221.388	−	681.363i	0.283468	−	0.872423i
$782$		0			0
$783$	−77.3856	+	39.4300i	−0.0988322	+	0.0503575i
$784$		0			0
$785$	−611.393	−	1132.18i	−0.778844	−	1.44227i
$786$		0			0
$787$	45.4625	−	287.039i	0.0577668	−	0.364725i	−0.941824	−	0.336108i	$-0.890889\pi$
$787$	45.4625	−	287.039i	0.0577668	−	0.364725i	0.999590	−	0.0286178i	$-0.00911057\pi$
$788$		0			0
$789$	−286.846	+	394.809i	−0.363556	+	0.500392i
$790$		0			0
$791$	−910.200	+	661.299i	−1.15070	+	0.836029i
$792$		0			0
$793$	−583.483	−	583.483i	−0.735792	−	0.735792i
$794$		0			0
$795$	−768.443	+	270.153i	−0.966595	+	0.339815i
$796$		0			0
$797$	−218.799	−	111.484i	−0.274528	−	0.139879i	0.311307	−	0.950309i	$-0.399233\pi$
$797$	−218.799	−	111.484i	−0.274528	−	0.139879i	−0.585835	+	0.810430i	$0.699233\pi$
$798$		0			0
$799$			519.890i			0.650676i
$800$		0			0
$801$	145.377			0.181494
$802$		0			0
$803$	−396.372	+	777.923i	−0.493613	+	0.968771i
$804$		0			0
$805$	511.677	−	390.776i	0.635623	−	0.485436i
$806$		0			0
$807$	80.6775	−	80.6775i	0.0999721	−	0.0999721i
$808$		0			0
$809$	162.358	+	223.466i	0.200689	+	0.276225i	0.897485	−	0.441044i	$-0.145392\pi$
$809$	162.358	+	223.466i	0.200689	+	0.276225i	−0.696796	+	0.717269i	$0.745392\pi$
$810$		0			0
$811$	−449.536	−	326.607i	−0.554298	−	0.402721i	0.275070	−	0.961424i	$-0.411299\pi$
$811$	−449.536	−	326.607i	−0.554298	−	0.402721i	−0.829368	+	0.558703i	$0.811299\pi$
$812$		0			0
$813$	−814.418	−	128.991i	−1.00174	−	0.158661i
$814$		0			0
$815$	124.283	−	259.046i	0.152495	−	0.317848i
$816$		0			0
$817$	−214.681	−	421.335i	−0.262767	−	0.515710i
$818$		0			0
$819$	2101.78	+	682.910i	2.56628	+	0.833834i
$820$		0			0
$821$	190.467	+	586.197i	0.231994	+	0.714004i	0.997506	+	0.0705823i	$0.0224858\pi$
$821$	190.467	+	586.197i	0.231994	+	0.714004i	−0.765512	+	0.643422i	$0.777514\pi$
$822$		0			0
$823$	98.2286	+	620.191i	0.119354	+	0.753573i	0.972672	+	0.232182i	$0.0745866\pi$
$823$	98.2286	+	620.191i	0.119354	+	0.753573i	−0.853318	+	0.521391i	$0.825413\pi$
$824$		0			0
$825$	−1280.47	−	140.480i	−1.55209	−	0.170279i
$826$		0			0
$827$	−343.416	+	54.3917i	−0.415255	+	0.0657699i	−0.360566	−	0.932734i	$-0.617417\pi$
$827$	−343.416	+	54.3917i	−0.415255	+	0.0657699i	−0.0546886	+	0.998503i	$0.517417\pi$
$828$		0			0
$829$	−1330.60	+	432.337i	−1.60506	+	0.521516i	−0.968352	−	0.249588i	$-0.919705\pi$
$829$	−1330.60	+	432.337i	−1.60506	+	0.521516i	−0.636709	+	0.771104i	$0.719705\pi$
$830$		0			0
$831$	538.963	−	1658.76i	0.648571	−	1.99610i
$832$		0			0
$833$	824.786	−	420.249i	0.990139	−	0.504501i
$834$		0			0
$835$	1059.79	−	193.927i	1.26921	−	0.232248i
$836$		0			0
$837$	40.9419	−	258.497i	0.0489150	−	0.308837i
$838$		0			0
$839$	364.766	−	502.058i	0.434763	−	0.598400i	−0.534275	−	0.845311i	$-0.679415\pi$
$839$	364.766	−	502.058i	0.434763	−	0.598400i	0.969038	+	0.246910i	$0.0794153\pi$
$840$		0			0
$841$	−665.245	+	483.329i	−0.791017	+	0.574707i
$842$		0			0
$843$	−964.290	−	964.290i	−1.14388	−	1.14388i
$844$		0			0
$845$	−76.9253	+	111.383i	−0.0910359	+	0.131814i
$846$		0			0
$847$	18.1196	+	9.23242i	0.0213927	+	0.0109001i
$848$		0			0
$849$		−	1377.53i		−	1.62254i
$850$		0			0
$851$	−273.335			−0.321192
$852$		0			0
$853$	−423.706	+	831.570i	−0.496725	+	0.974877i	0.497490	+	0.867470i	$0.334255\pi$
$853$	−423.706	+	831.570i	−0.496725	+	0.974877i	−0.994215	+	0.107408i	$0.965745\pi$
$854$		0			0
$855$	1043.60	−	24.9505i	1.22058	−	0.0291819i
$856$		0			0
$857$	883.165	−	883.165i	1.03053	−	1.03053i	0.0310117	−	0.999519i	$-0.490127\pi$
$857$	883.165	−	883.165i	1.03053	−	1.03053i	0.999519	−	0.0310117i	$-0.00987291\pi$
$858$		0			0
$859$	−684.349	−	941.925i	−0.796681	−	1.09654i	−0.993244	−	0.116046i	$-0.962978\pi$
$859$	−684.349	−	941.925i	−0.796681	−	1.09654i	0.196563	−	0.980491i	$-0.437022\pi$
$860$		0			0
$861$	−1214.04	−	882.052i	−1.41004	−	1.02445i
$862$		0			0
$863$	−1452.01	−	229.977i	−1.68252	−	0.266485i	−0.759295	−	0.650746i	$-0.774456\pi$
$863$	−1452.01	−	229.977i	−1.68252	−	0.266485i	−0.923224	+	0.384261i	$0.874456\pi$
$864$		0			0
$865$	1255.62	+	168.215i	1.45159	+	0.194468i
$866$		0			0
$867$	−405.632	−	796.098i	−0.467857	−	0.918221i
$868$		0			0
$869$	−184.960	−	60.0971i	−0.212842	−	0.0691566i
$870$		0			0
$871$	420.501	+	1294.17i	0.482780	+	1.48584i
$872$		0			0
$873$	−272.773	−	1722.22i	−0.312455	−	1.97276i
$874$		0			0
$875$	−126.895	+	1482.82i	−0.145023	+	1.69465i
$876$		0			0
$877$	1629.98	−	258.163i	1.85859	−	0.294371i	0.876301	−	0.481764i	$-0.160004\pi$
$877$	1629.98	−	258.163i	1.85859	−	0.294371i	0.982285	+	0.187393i	$0.0600039\pi$
$878$		0			0
$879$	−621.137	+	201.820i	−0.706640	+	0.229601i
$880$		0			0
$881$	−16.0890	+	49.5167i	−0.0182622	+	0.0562051i	−0.959772	−	0.280779i	$-0.909407\pi$
$881$	−16.0890	+	49.5167i	−0.0182622	+	0.0562051i	0.941510	+	0.336985i	$0.109407\pi$
$882$		0			0
$883$	−905.982	+	461.621i	−1.02603	+	0.522787i	−0.884202	−	0.467105i	$-0.845297\pi$
$883$	−905.982	+	461.621i	−1.02603	+	0.522787i	−0.141825	+	0.989892i	$0.545297\pi$
$884$		0			0
$885$	47.5675	−	355.064i	0.0537486	−	0.401202i
$886$		0			0
$887$	−36.9127	+	233.058i	−0.0416153	+	0.262748i	−0.999720	−	0.0236702i	$-0.992465\pi$
$887$	−36.9127	+	233.058i	−0.0416153	+	0.262748i	0.958105	+	0.286419i	$0.0924648\pi$
$888$		0			0
$889$	1610.12	−	2216.14i	1.81116	−	2.49284i
$890$		0			0
$891$	217.222	−	157.821i	0.243796	−	0.177128i
$892$		0			0
$893$	580.132	+	580.132i	0.649644	+	0.649644i
$894$		0			0
$895$	−22.1834	−	927.860i	−0.0247859	−	1.03672i
$896$		0			0
$897$	636.581	+	324.354i	0.709678	+	0.361599i
$898$		0			0
$899$			56.3866i			0.0627214i
$900$		0			0
$901$	−344.643			−0.382512
$902$		0			0
$903$	765.599	−	1502.57i	0.847839	−	1.66398i
$904$		0			0
$905$	−728.589	−	503.191i	−0.805070	−	0.556012i
$906$		0			0
$907$	757.766	−	757.766i	0.835464	−	0.835464i	−0.152794	−	0.988258i	$-0.548827\pi$
$907$	757.766	−	757.766i	0.835464	−	0.835464i	0.988258	+	0.152794i	$0.0488271\pi$
$908$		0			0
$909$	−667.139	−	918.238i	−0.733926	−	1.01016i
$910$		0			0
$911$	787.930	+	572.465i	0.864907	+	0.628392i	0.929215	−	0.369538i	$-0.120484\pi$
$911$	787.930	+	572.465i	0.864907	+	0.628392i	−0.0643086	+	0.997930i	$0.520484\pi$
$912$		0			0
$913$	−1076.38	−	170.482i	−1.17895	−	0.186727i
$914$		0			0
$915$	−250.203	−	1367.34i	−0.273446	−	1.49436i
$916$		0			0
$917$	395.825	+	776.851i	0.431653	+	0.847166i
$918$		0			0
$919$	1014.37	+	329.588i	1.10377	+	0.358638i	0.803554	−	0.595232i	$-0.202940\pi$
$919$	1014.37	+	329.588i	1.10377	+	0.358638i	0.300220	+	0.953870i	$0.402940\pi$
$920$		0			0
$921$	327.161	+	1006.90i	0.355224	+	1.09327i
$922$		0			0
$923$	−143.684	−	907.184i	−0.155670	−	0.982864i
$924$		0			0
$925$	424.904	−	467.605i	0.459356	−	0.505519i
$926$		0			0
$927$	−1568.91	+	248.491i	−1.69246	+	0.268059i
$928$		0			0
$929$	−1611.25	+	523.525i	−1.73439	+	0.563536i	−0.994072	−	0.108724i	$-0.965323\pi$
$929$	−1611.25	+	523.525i	−1.73439	+	0.563536i	−0.740315	+	0.672261i	$0.765323\pi$
$930$		0			0
$931$	451.412	−	1389.30i	0.484868	−	1.49227i
$932$		0			0
$933$	562.693	−	286.706i	0.603100	−	0.307295i
$934$		0			0
$935$	−491.402	−	235.762i	−0.525564	−	0.252151i
$936$		0			0
$937$	64.1780	−	405.204i	0.0684930	−	0.432448i	−0.929483	−	0.368864i	$-0.879747\pi$
$937$	64.1780	−	405.204i	0.0684930	−	0.432448i	0.997976	−	0.0635842i	$-0.0202531\pi$
$938$		0			0
$939$	1279.08	−	1760.51i	1.36218	−	1.87487i
$940$		0			0
$941$	186.657	−	135.614i	0.198360	−	0.144117i	−0.484171	−	0.874973i	$-0.660879\pi$
$941$	186.657	−	135.614i	0.198360	−	0.144117i	0.682532	+	0.730856i	$0.260879\pi$
$942$		0			0
$943$	−204.323	−	204.323i	−0.216673	−	0.216673i
$944$		0			0
$945$	725.449	+	949.893i	0.767671	+	1.00518i
$946$		0			0
$947$	−817.953	−	416.768i	−0.863731	−	0.440093i	−0.0347672	−	0.999395i	$-0.511069\pi$
$947$	−817.953	−	416.768i	−0.863731	−	0.440093i	−0.828964	+	0.559303i	$0.811069\pi$
$948$		0			0
$949$			1119.33i			1.17949i
$950$		0			0
$951$	−318.232			−0.334629
$952$		0			0
$953$	−734.794	+	1442.12i	−0.771033	+	1.51324i	0.0850372	+	0.996378i	$0.472899\pi$
$953$	−734.794	+	1442.12i	−0.771033	+	1.51324i	−0.856070	+	0.516860i	$0.827101\pi$
$954$		0			0
$955$	386.096	+	1098.24i	0.404288	+	1.14999i
$956$		0			0
$957$	157.606	−	157.606i	0.164688	−	0.164688i
$958$		0			0
$959$	506.027	+	696.486i	0.527661	+	0.726263i
$960$		0			0
$961$	640.001	+	464.988i	0.665974	+	0.483859i
$962$		0			0
$963$	−2462.40	−	390.006i	−2.55701	−	0.404991i
$964$		0			0
$965$	−934.131	+	504.442i	−0.968011	+	0.522738i
$966$		0			0
$967$	−525.750	−	1031.84i	−0.543692	−	1.06706i	−0.985457	−	0.169924i	$-0.945648\pi$
$967$	−525.750	−	1031.84i	−0.543692	−	1.06706i	0.441765	−	0.897131i	$-0.354352\pi$
$968$		0			0
$969$	705.266	+	229.155i	0.727829	+	0.236486i
$970$		0			0
$971$	−49.0351	−	150.914i	−0.0504996	−	0.155422i	0.922627	−	0.385695i	$-0.126038\pi$
$971$	−49.0351	−	150.914i	−0.0504996	−	0.155422i	−0.973126	+	0.230273i	$0.926038\pi$
$972$		0			0
$973$	98.3724	+	621.099i	0.101102	+	0.638334i
$974$		0			0
$975$	−1544.46	+	584.810i	−1.58406	+	0.599805i
$976$		0			0
$977$	−1513.70	+	239.746i	−1.54933	+	0.245390i	−0.871710	−	0.490022i	$-0.836989\pi$
$977$	−1513.70	+	239.746i	−1.54933	+	0.245390i	−0.677620	+	0.735412i	$0.736989\pi$
$978$		0			0
$979$	−113.919	+	37.0145i	−0.116363	+	0.0378085i
$980$		0			0
$981$	23.7309	−	73.0361i	0.0241905	−	0.0744507i
$982$		0			0
$983$	1640.80	−	836.029i	1.66918	−	0.850487i	0.675606	−	0.737263i	$-0.263882\pi$
$983$	1640.80	−	836.029i	1.66918	−	0.850487i	0.993569	−	0.113224i	$-0.0361178\pi$
$984$		0			0
$985$	804.135	−	843.528i	0.816381	−	0.856374i
$986$		0			0
$987$	−457.701	+	2889.81i	−0.463730	+	2.92787i
$988$		0			0
$989$	190.866	−	262.705i	0.192989	−	0.265627i
$990$		0			0
$991$	−852.332	+	619.255i	−0.860072	+	0.624879i	−0.927905	−	0.372818i	$-0.878392\pi$
$991$	−852.332	+	619.255i	−0.860072	+	0.624879i	0.0678324	+	0.997697i	$0.478392\pi$
$992$		0			0
$993$	653.965	+	653.965i	0.658575	+	0.658575i
$994$		0			0
$995$	760.678	+	227.208i	0.764501	+	0.228350i
$996$		0			0
$997$	−1164.89	−	593.541i	−1.16839	−	0.595327i	−0.241409	−	0.970423i	$-0.577610\pi$
$997$	−1164.89	−	593.541i	−1.16839	−	0.595327i	−0.926986	+	0.375097i	$0.877610\pi$
$998$		0			0
$999$		−	507.427i		−	0.507935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.b.113.3		24
4.3	odd	2		50.3.f.b.13.1	✓	24
20.3	even	4		250.3.f.d.207.1		24
20.7	even	4		250.3.f.f.207.3		24
20.19	odd	2		250.3.f.e.43.3		24
25.2	odd	20	inner	400.3.bg.b.177.3		24
100.11	odd	10		250.3.f.f.93.3		24
100.23	even	20		250.3.f.e.157.3		24
100.27	even	20		50.3.f.b.27.1	yes	24
100.39	odd	10		250.3.f.d.93.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.b.13.1	✓	24	4.3	odd	2
50.3.f.b.27.1	yes	24	100.27	even	20
250.3.f.d.93.1		24	100.39	odd	10
250.3.f.d.207.1		24	20.3	even	4
250.3.f.e.43.3		24	20.19	odd	2
250.3.f.e.157.3		24	100.23	even	20
250.3.f.f.93.3		24	100.11	odd	10
250.3.f.f.207.3		24	20.7	even	4
400.3.bg.b.113.3		24	1.1	even	1	trivial
400.3.bg.b.177.3		24	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)

\(f(q)\)	\(=\)	\(q+(2.14176 - 4.20343i) q^{3} +(-1.43099 + 4.79085i) q^{5} +(-8.41873 + 8.41873i) q^{7} +(-7.79165 - 10.7243i) q^{9} +O(q^{10})\)	\(q+(2.14176 - 4.20343i) q^{3} +(-1.43099 + 4.79085i) q^{5} +(-8.41873 + 8.41873i) q^{7} +(-7.79165 - 10.7243i) q^{9} +(8.83615 + 6.41984i) q^{11} +(13.8302 + 2.19049i) q^{13} +(17.0732 + 16.2759i) q^{15} +(4.53099 + 8.89257i) q^{17} +(14.9790 + 4.86698i) q^{19} +(17.3567 + 53.4184i) q^{21} +(1.69189 + 10.6822i) q^{23} +(-20.9046 - 13.7113i) q^{25} +(-19.8308 + 3.14088i) q^{27} +(4.11402 - 1.33673i) q^{29} +(-4.02808 + 12.3972i) q^{31} +(45.9102 - 23.3924i) q^{33} +(-28.2858 - 52.3800i) q^{35} +(-3.95354 + 24.9617i) q^{37} +(38.8285 - 53.4428i) q^{39} +(-21.6147 + 15.7040i) q^{41} +(-21.2302 - 21.2302i) q^{43} +(62.5282 - 21.9824i) q^{45} +(46.4137 + 23.6489i) q^{47} -92.7500i q^{49} +47.0836 q^{51} +(-15.6773 + 30.7684i) q^{53} +(-43.4009 + 33.1460i) q^{55} +(52.5394 - 52.5394i) q^{57} +(-8.92677 - 12.2866i) q^{59} +(-47.6752 - 34.6380i) q^{61} +(155.881 + 24.6891i) q^{63} +(-30.2852 + 63.1240i) q^{65} +(44.1187 + 86.5878i) q^{67} +(48.5255 + 15.7669i) q^{69} +(-20.2698 - 62.3839i) q^{71} +(12.5050 + 78.9533i) q^{73} +(-102.407 + 58.5046i) q^{75} +(-128.436 + 20.3423i) q^{77} +(-16.9345 + 5.50235i) q^{79} +(7.59667 - 23.3801i) q^{81} +(-88.9040 + 45.2989i) q^{83} +(-49.0868 + 8.98217i) q^{85} +(3.19239 - 20.1559i) q^{87} +(-6.44619 + 8.87242i) q^{89} +(-134.874 + 97.9917i) q^{91} +(43.4834 + 43.4834i) q^{93} +(-44.7518 + 64.7977i) q^{95} +(117.203 + 59.7179i) q^{97} -144.783i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{3} + 2 q^{7} + 40 q^{9}+O(q^{10}) \) 24 * q - 2 * q^3 + 2 * q^7 + 40 * q^9	\( 24 q - 2 q^{3} + 2 q^{7} + 40 q^{9} + 32 q^{11} + 2 q^{13} + 20 q^{15} - 92 q^{17} + 230 q^{19} + 68 q^{21} + 18 q^{23} + 40 q^{25} - 260 q^{27} + 100 q^{29} + 132 q^{31} + 364 q^{33} - 50 q^{35} - 192 q^{37} + 80 q^{39} + 168 q^{41} + 78 q^{43} - 310 q^{45} + 22 q^{47} - 168 q^{51} - 108 q^{53} + 40 q^{55} + 280 q^{57} - 450 q^{59} - 492 q^{61} + 558 q^{63} + 120 q^{65} + 572 q^{67} - 670 q^{69} + 2 q^{71} + 262 q^{73} - 140 q^{75} + 496 q^{77} + 360 q^{79} - 46 q^{81} - 772 q^{83} + 490 q^{85} - 210 q^{87} + 900 q^{89} - 798 q^{91} + 294 q^{93} + 378 q^{97}+O(q^{100}) \) 24 * q - 2 * q^3 + 2 * q^7 + 40 * q^9 + 32 * q^11 + 2 * q^13 + 20 * q^15 - 92 * q^17 + 230 * q^19 + 68 * q^21 + 18 * q^23 + 40 * q^25 - 260 * q^27 + 100 * q^29 + 132 * q^31 + 364 * q^33 - 50 * q^35 - 192 * q^37 + 80 * q^39 + 168 * q^41 + 78 * q^43 - 310 * q^45 + 22 * q^47 - 168 * q^51 - 108 * q^53 + 40 * q^55 + 280 * q^57 - 450 * q^59 - 492 * q^61 + 558 * q^63 + 120 * q^65 + 572 * q^67 - 670 * q^69 + 2 * q^71 + 262 * q^73 - 140 * q^75 + 496 * q^77 + 360 * q^79 - 46 * q^81 - 772 * q^83 + 490 * q^85 - 210 * q^87 + 900 * q^89 - 798 * q^91 + 294 * q^93 + 378 * q^97

Introduction

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