LMFDB - Embedded newform 400.3.bg.f.17.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [400,3,Mod(17,400)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			17.1
Character	$\chi$	$=$	400.17
Dual form			400.3.bg.f.353.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.811497 + 5.12359i) q^{3} +(1.63338 - 4.72568i) q^{5} +(4.59566 + 4.59566i) q^{7} +(-17.0331 - 5.53440i) q^{9} +(-1.18760 - 3.65505i) q^{11} +(10.6786 + 20.9580i) q^{13} +(22.8870 + 12.2037i) q^{15} +(1.95690 + 12.3554i) q^{17} +(-18.6024 + 25.6040i) q^{19} +(-27.2756 + 19.8169i) q^{21} +(-4.45484 - 2.26986i) q^{23} +(-19.6641 - 15.4377i) q^{25} +(20.9828 - 41.1811i) q^{27} +(-19.6538 - 27.0511i) q^{29} +(20.2816 + 14.7355i) q^{31} +(19.6907 - 3.11870i) q^{33} +(29.2241 - 14.2111i) q^{35} +(3.03733 - 1.54760i) q^{37} +(-116.046 + 37.7056i) q^{39} +(10.2499 - 31.5459i) q^{41} +(-25.0372 + 25.0372i) q^{43} +(-53.9754 + 71.4533i) q^{45} +(-64.3235 - 10.1878i) q^{47} -6.75985i q^{49} -64.8919 q^{51} +(-3.09155 + 19.5193i) q^{53} +(-19.2124 - 0.357889i) q^{55} +(-116.089 - 116.089i) q^{57} +(92.4197 + 30.0290i) q^{59} +(34.8035 + 107.114i) q^{61} +(-52.8442 - 103.713i) q^{63} +(116.483 - 16.2314i) q^{65} +(0.884920 + 5.58716i) q^{67} +(15.2449 - 20.9828i) q^{69} +(-39.5309 + 28.7209i) q^{71} +(77.2257 + 39.3484i) q^{73} +(95.0538 - 88.2232i) q^{75} +(11.3396 - 22.2551i) q^{77} +(-58.9885 - 81.1907i) q^{79} +(63.5643 + 46.1822i) q^{81} +(28.2368 - 4.47227i) q^{83} +(61.5839 + 10.9334i) q^{85} +(154.548 - 78.7461i) q^{87} +(-126.306 + 41.0394i) q^{89} +(-47.2405 + 145.391i) q^{91} +(-91.9570 + 91.9570i) q^{93} +(90.6117 + 129.730i) q^{95} +(73.6536 + 11.6656i) q^{97} +68.8295i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9} - 16 q^{11} + 24 q^{13} - 82 q^{15} - 8 q^{17} + 50 q^{19} - 100 q^{21} + 48 q^{23} - 200 q^{25} - 90 q^{27} - 108 q^{31} + 260 q^{33} - 2 q^{35} - 94 q^{37} - 320 q^{39}+ \cdots - 544 q^{97}+O(q^{100}) $ 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9 - 16 * q^11 + 24 * q^13 - 82 * q^15 - 8 * q^17 + 50 * q^19 - 100 * q^21 + 48 * q^23 - 200 * q^25 - 90 * q^27 - 108 * q^31 + 260 * q^33 - 2 * q^35 - 94 * q^37 - 320 * q^39 - 184 * q^41 - 96 * q^43 + 146 * q^45 - 104 * q^47 - 200 * q^51 - 202 * q^53 + 12 * q^55 - 280 * q^57 + 600 * q^59 + 12 * q^61 + 34 * q^63 + 296 * q^65 - 58 * q^67 - 40 * q^69 + 470 * q^71 - 228 * q^73 + 614 * q^75 + 324 * q^77 - 560 * q^79 + 856 * q^81 + 308 * q^83 - 902 * q^85 + 840 * q^87 - 380 * q^89 - 62 * q^91 - 540 * q^93 + 16 * q^95 - 544 * q^97

Character values

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

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{13}{20}\right)$	$1$

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
$3$	−0.811497	+	5.12359i	−0.270499	+	1.70786i	0.361066	+	0.932540i	$0.382413\pi$
$3$	−0.811497	+	5.12359i	−0.270499	+	1.70786i	−0.631565	+	0.775323i	$0.717587\pi$
$4$		0			0
$5$	1.63338	−	4.72568i	0.326677	−	0.945136i
$5$	1.63338	−	4.72568i	0.326677	−	0.945136i
$6$		0			0
$7$	4.59566	+	4.59566i	0.656523	+	0.656523i	0.954556	−	0.298033i	$-0.0963305\pi$
$7$	4.59566	+	4.59566i	0.656523	+	0.656523i	−0.298033	+	0.954556i	$0.596331\pi$
$8$		0			0
$9$	−17.0331	−	5.53440i	−1.89257	−	0.614933i
$10$		0			0
$11$	−1.18760	−	3.65505i	−0.107963	−	0.332277i	0.882451	−	0.470404i	$-0.155892\pi$
$11$	−1.18760	−	3.65505i	−0.107963	−	0.332277i	−0.990415	+	0.138127i	$0.955892\pi$
$12$		0			0
$13$	10.6786	+	20.9580i	0.821435	+	1.61216i	0.790363	+	0.612639i	$0.209892\pi$
$13$	10.6786	+	20.9580i	0.821435	+	1.61216i	0.0310717	+	0.999517i	$0.490108\pi$
$14$		0			0
$15$	22.8870	+	12.2037i	1.52580	+	0.813577i
$16$		0			0
$17$	1.95690	+	12.3554i	0.115112	+	0.726787i	0.975964	+	0.217932i	$0.0699310\pi$
$17$	1.95690	+	12.3554i	0.115112	+	0.726787i	−0.860852	+	0.508855i	$0.830069\pi$
$18$		0			0
$19$	−18.6024	+	25.6040i	−0.979075	+	1.34758i	−0.0417490	+	0.999128i	$0.513293\pi$
$19$	−18.6024	+	25.6040i	−0.979075	+	1.34758i	−0.937326	+	0.348453i	$0.886707\pi$
$20$		0			0
$21$	−27.2756	+	19.8169i	−1.29884	+	0.943662i
$22$		0			0
$23$	−4.45484	−	2.26986i	−0.193689	−	0.0986894i	0.354456	−	0.935073i	$-0.384666\pi$
$23$	−4.45484	−	2.26986i	−0.193689	−	0.0986894i	−0.548145	+	0.836383i	$0.684666\pi$
$24$		0			0
$25$	−19.6641	−	15.4377i	−0.786565	−	0.617508i
$26$		0			0
$27$	20.9828	−	41.1811i	0.777141	−	1.52523i
$28$		0			0
$29$	−19.6538	−	27.0511i	−0.677717	−	0.932797i	0.322187	−	0.946676i	$-0.395582\pi$
$29$	−19.6538	−	27.0511i	−0.677717	−	0.932797i	−0.999904	+	0.0138787i	$0.995582\pi$
$30$		0			0
$31$	20.2816	+	14.7355i	0.654247	+	0.475338i	0.864715	−	0.502263i	$-0.167499\pi$
$31$	20.2816	+	14.7355i	0.654247	+	0.475338i	−0.210468	+	0.977601i	$0.567499\pi$
$32$		0			0
$33$	19.6907	−	3.11870i	0.596688	−	0.0945060i
$34$		0			0
$35$	29.2241	−	14.2111i	0.834974	−	0.406033i
$36$		0			0
$37$	3.03733	−	1.54760i	0.0820899	−	0.0418269i	−0.412464	−	0.910974i	$-0.635332\pi$
$37$	3.03733	−	1.54760i	0.0820899	−	0.0418269i	0.494554	+	0.869147i	$0.335332\pi$
$38$		0			0
$39$	−116.046	+	37.7056i	−2.97554	+	0.966811i
$40$		0			0
$41$	10.2499	−	31.5459i	0.249998	−	0.769413i	−0.744777	−	0.667314i	$-0.767444\pi$
$41$	10.2499	−	31.5459i	0.249998	−	0.769413i	0.994774	−	0.102100i	$-0.0325560\pi$
$42$		0			0
$43$	−25.0372	+	25.0372i	−0.582261	+	0.582261i	−0.935524	−	0.353263i	$-0.885072\pi$
$43$	−25.0372	+	25.0372i	−0.582261	+	0.582261i	0.353263	+	0.935524i	$0.385072\pi$
$44$		0			0
$45$	−53.9754	+	71.4533i	−1.19945	+	1.58785i
$46$		0			0
$47$	−64.3235	−	10.1878i	−1.36859	−	0.216763i	−0.571487	−	0.820611i	$-0.693633\pi$
$47$	−64.3235	−	10.1878i	−1.36859	−	0.216763i	−0.797099	+	0.603849i	$0.793633\pi$
$48$		0			0
$49$		−	6.75985i		−	0.137956i
$50$		0			0
$51$	−64.8919			−1.27239
$52$		0			0
$53$	−3.09155	+	19.5193i	−0.0583311	+	0.368288i	0.941205	+	0.337836i	$0.109695\pi$
$53$	−3.09155	+	19.5193i	−0.0583311	+	0.368288i	−0.999536	+	0.0304524i	$0.990305\pi$
$54$		0			0
$55$	−19.2124	−	0.357889i	−0.349316	−	0.00650707i
$56$		0			0
$57$	−116.089	−	116.089i	−2.03665	−	2.03665i
$58$		0			0
$59$	92.4197	+	30.0290i	1.56644	+	0.508966i	0.958518	−	0.285033i	$-0.0920047\pi$
$59$	92.4197	+	30.0290i	1.56644	+	0.508966i	0.607919	+	0.793999i	$0.292005\pi$
$60$		0			0
$61$	34.8035	+	107.114i	0.570550	+	1.75597i	0.650855	+	0.759202i	$0.274410\pi$
$61$	34.8035	+	107.114i	0.570550	+	1.75597i	−0.0803053	+	0.996770i	$0.525590\pi$
$62$		0			0
$63$	−52.8442	−	103.713i	−0.838797	−	1.64623i
$64$		0			0
$65$	116.483	−	16.2314i	1.79205	−	0.249714i
$66$		0			0
$67$	0.884920	+	5.58716i	0.0132078	+	0.0833905i	0.993412	−	0.114600i	$-0.0365586\pi$
$67$	0.884920	+	5.58716i	0.0132078	+	0.0833905i	−0.980204	+	0.197990i	$0.936559\pi$
$68$		0			0
$69$	15.2449	−	20.9828i	0.220941	−	0.304099i
$70$		0			0
$71$	−39.5309	+	28.7209i	−0.556773	+	0.404519i	−0.830276	−	0.557352i	$-0.811817\pi$
$71$	−39.5309	+	28.7209i	−0.556773	+	0.404519i	0.273503	+	0.961871i	$0.411817\pi$
$72$		0			0
$73$	77.2257	+	39.3484i	1.05789	+	0.539020i	0.894281	−	0.447506i	$-0.147688\pi$
$73$	77.2257	+	39.3484i	1.05789	+	0.539020i	0.163605	+	0.986526i	$0.447688\pi$
$74$		0			0
$75$	95.0538	−	88.2232i	1.26738	−	1.17631i
$76$		0			0
$77$	11.3396	−	22.2551i	0.147267	−	0.289028i
$78$		0			0
$79$	−58.9885	−	81.1907i	−0.746690	−	1.02773i	−0.998206	−	0.0598771i	$-0.980929\pi$
$79$	−58.9885	−	81.1907i	−0.746690	−	1.02773i	0.251516	−	0.967853i	$-0.419071\pi$
$80$		0			0
$81$	63.5643	+	46.1822i	0.784744	+	0.570150i
$82$		0			0
$83$	28.2368	−	4.47227i	0.340203	−	0.0538828i	0.0160042	−	0.999872i	$-0.494905\pi$
$83$	28.2368	−	4.47227i	0.340203	−	0.0538828i	0.324198	+	0.945989i	$0.394905\pi$
$84$		0			0
$85$	61.5839	+	10.9334i	0.724517	+	0.128628i
$86$		0			0
$87$	154.548	−	78.7461i	1.77641	−	0.905127i
$88$		0			0
$89$	−126.306	+	41.0394i	−1.41917	+	0.461117i	−0.915339	−	0.402684i	$-0.868077\pi$
$89$	−126.306	+	41.0394i	−1.41917	+	0.461117i	−0.503833	+	0.863801i	$0.668077\pi$
$90$		0			0
$91$	−47.2405	+	145.391i	−0.519127	+	1.59771i
$92$		0			0
$93$	−91.9570	+	91.9570i	−0.988785	+	0.988785i
$94$		0			0
$95$	90.6117	+	129.730i	0.953807	+	1.36558i
$96$		0			0
$97$	73.6536	+	11.6656i	0.759316	+	0.120264i	0.524074	−	0.851673i	$-0.324412\pi$
$97$	73.6536	+	11.6656i	0.759316	+	0.120264i	0.235242	+	0.971937i	$0.424412\pi$
$98$		0			0
$99$			68.8295i			0.695248i
$100$		0			0
$101$	145.151			1.43713			0.718567	−	0.695457i	$-0.244798\pi$
$101$	145.151			1.43713			0.718567	+	0.695457i	$0.244798\pi$
$102$		0			0
$103$	7.59966	−	47.9823i	0.0737831	−	0.465848i	−0.922939	−	0.384946i	$-0.874220\pi$
$103$	7.59966	−	47.9823i	0.0737831	−	0.465848i	0.996722	−	0.0809018i	$-0.0257800\pi$
$104$		0			0
$105$	49.0968	+	161.264i	0.467589	+	1.53585i
$106$		0			0
$107$	68.4603	+	68.4603i	0.639816	+	0.639816i	0.950510	−	0.310694i	$-0.100562\pi$
$107$	68.4603	+	68.4603i	0.639816	+	0.639816i	−0.310694	+	0.950510i	$0.600562\pi$
$108$		0			0
$109$	95.5419	+	31.0434i	0.876531	+	0.284802i	0.712516	−	0.701656i	$-0.247555\pi$
$109$	95.5419	+	31.0434i	0.876531	+	0.284802i	0.164015	+	0.986458i	$0.447555\pi$
$110$		0			0
$111$	5.46446	+	16.8179i	0.0492294	+	0.151512i
$112$		0			0
$113$	−21.1197	−	41.4498i	−0.186900	−	0.366813i	0.778476	−	0.627675i	$-0.215993\pi$
$113$	−21.1197	−	41.4498i	−0.186900	−	0.366813i	−0.965376	+	0.260862i	$0.915993\pi$
$114$		0			0
$115$	−18.0031	+	17.3446i	−0.156549	+	0.150823i
$116$		0			0
$117$	−65.9007	−	416.081i	−0.563254	−	3.55625i
$118$		0			0
$119$	−47.7878	+	65.7743i	−0.401578	+	0.552725i
$120$		0			0
$121$	85.9421	−	62.4406i	0.710265	−	0.516038i
$122$		0			0
$123$	153.311	+	78.1157i	1.24643	+	0.635087i
$124$		0			0
$125$	−105.073	+	67.7107i	−0.840581	+	0.541685i
$126$		0			0
$127$	61.0371	−	119.792i	0.480607	−	0.943244i	−0.515650	−	0.856799i	$-0.672449\pi$
$127$	61.0371	−	119.792i	0.480607	−	0.943244i	0.996257	−	0.0864446i	$-0.0275505\pi$
$128$		0			0
$129$	−107.963	−	148.598i	−0.836921	−	1.15192i
$130$		0			0
$131$	−19.4858	−	14.1572i	−0.148746	−	0.108071i	0.510923	−	0.859626i	$-0.329304\pi$
$131$	−19.4858	−	14.1572i	−0.148746	−	0.108071i	−0.659669	+	0.751556i	$0.729304\pi$
$132$		0			0
$133$	−203.158	+	32.1770i	−1.52750	+	0.241933i
$134$		0			0
$135$	−160.336	−	166.423i	−1.18767	−	1.23276i
$136$		0			0
$137$	86.9089	−	44.2823i	0.634371	−	0.323228i	−0.107064	−	0.994252i	$-0.534145\pi$
$137$	86.9089	−	44.2823i	0.634371	−	0.323228i	0.741436	+	0.671024i	$0.234145\pi$
$138$		0			0
$139$	62.1532	−	20.1948i	0.447146	−	0.145286i	−0.0767844	−	0.997048i	$-0.524465\pi$
$139$	62.1532	−	20.1948i	0.447146	−	0.145286i	0.523930	+	0.851761i	$0.324465\pi$
$140$		0			0
$141$	104.397	−	321.300i	0.740402	−	2.27872i
$142$		0			0
$143$	63.9207	−	63.9207i	0.446998	−	0.446998i
$144$		0			0
$145$	−159.937	+	48.6927i	−1.10301	+	0.335812i
$146$		0			0
$147$	34.6347	+	5.48560i	0.235610	+	0.0373170i
$148$		0			0
$149$		−	27.0995i		−	0.181876i	−0.995857	−	0.0909381i	$-0.971013\pi$
$149$		−	27.0995i		−	0.181876i	0.995857	−	0.0909381i	$-0.0289865\pi$
$150$		0			0
$151$	46.4033			0.307306			0.153653	−	0.988125i	$-0.450896\pi$
$151$	46.4033			0.307306			0.153653	+	0.988125i	$0.450896\pi$
$152$		0			0
$153$	35.0474	−	221.281i	0.229068	−	1.44628i
$154$		0			0
$155$	102.763	−	71.7759i	0.662986	−	0.463070i
$156$		0			0
$157$	62.2097	+	62.2097i	0.396240	+	0.396240i	0.876905	−	0.480665i	$-0.159605\pi$
$157$	62.2097	+	62.2097i	0.396240	+	0.396240i	−0.480665	+	0.876905i	$0.659605\pi$
$158$		0			0
$159$	−97.4999	−	31.6796i	−0.613207	−	0.199243i
$160$		0			0
$161$	−10.0415	−	30.9044i	−0.0623693	−	0.191953i
$162$		0			0
$163$	−112.951	−	221.678i	−0.692950	−	1.35999i	−0.922235	−	0.386631i	$-0.873639\pi$
$163$	−112.951	−	221.678i	−0.692950	−	1.35999i	0.229285	−	0.973359i	$-0.426361\pi$
$164$		0			0
$165$	17.4245	−	98.1460i	0.105603	−	0.594824i
$166$		0			0
$167$	33.1368	+	209.218i	0.198424	+	1.25280i	0.862855	+	0.505451i	$0.168674\pi$
$167$	33.1368	+	209.218i	0.198424	+	1.25280i	−0.664431	+	0.747349i	$0.731326\pi$
$168$		0			0
$169$	−225.870	+	310.883i	−1.33651	+	1.83954i
$170$		0			0
$171$	458.561	−	333.164i	2.68164	−	1.94833i
$172$		0			0
$173$	−11.2431	−	5.72867i	−0.0649893	−	0.0331137i	0.421194	−	0.906971i	$-0.361611\pi$
$173$	−11.2431	−	5.72867i	−0.0649893	−	0.0331137i	−0.486183	+	0.873857i	$0.661611\pi$
$174$		0			0
$175$	−19.4232	−	161.316i	−0.110990	−	0.921805i
$176$		0			0
$177$	−228.855	+	449.152i	−1.29296	+	2.53758i
$178$		0			0
$179$	−0.919747	−	1.26592i	−0.00513825	−	0.00707220i	0.806440	−	0.591316i	$-0.201391\pi$
$179$	−0.919747	−	1.26592i	−0.00513825	−	0.00707220i	−0.811578	+	0.584244i	$0.801391\pi$
$180$		0			0
$181$	159.116	+	115.604i	0.879092	+	0.638697i	0.933011	−	0.359848i	$-0.117171\pi$
$181$	159.116	+	115.604i	0.879092	+	0.638697i	−0.0539194	+	0.998545i	$0.517171\pi$
$182$		0			0
$183$	−577.053	+	91.3962i	−3.15329	+	0.499433i
$184$		0			0
$185$	−2.35232	−	16.8813i	−0.0127153	−	0.0912500i
$186$		0			0
$187$	42.8355	−	21.8258i	0.229067	−	0.116715i
$188$		0			0
$189$	285.684	−	92.8244i	1.51156	−	0.491134i
$190$		0			0
$191$	53.2092	−	163.761i	0.278582	−	0.857389i	−0.709667	−	0.704537i	$-0.751155\pi$
$191$	53.2092	−	163.761i	0.278582	−	0.857389i	0.988249	−	0.152851i	$-0.0488455\pi$
$192$		0			0
$193$	34.3905	−	34.3905i	0.178189	−	0.178189i	−0.612377	−	0.790566i	$-0.709786\pi$
$193$	34.3905	−	34.3905i	0.178189	−	0.178189i	0.790566	+	0.612377i	$0.209786\pi$
$194$		0			0
$195$	−11.3628	+	609.984i	−0.0582708	+	3.12812i
$196$		0			0
$197$	77.8882	+	12.3363i	0.395372	+	0.0626207i	0.350955	−	0.936392i	$-0.385857\pi$
$197$	77.8882	+	12.3363i	0.395372	+	0.0626207i	0.0444167	+	0.999013i	$0.485857\pi$
$198$		0			0
$199$			238.030i			1.19613i	0.801447	+	0.598066i	$0.204064\pi$
$199$			238.030i			1.19613i	−0.801447	+	0.598066i	$0.795936\pi$
$200$		0			0
$201$	−29.3444			−0.145992
$202$		0			0
$203$	33.9956	−	214.640i	0.167466	−	1.05734i
$204$		0			0
$205$	−132.334	−	99.9644i	−0.645532	−	0.487631i
$206$		0			0
$207$	63.3176	+	63.3176i	0.305882	+	0.305882i
$208$		0			0
$209$	115.676	+	37.5855i	0.553475	+	0.179835i
$210$		0			0
$211$	−35.7171	−	109.926i	−0.169275	−	0.520976i	0.830051	−	0.557688i	$-0.188311\pi$
$211$	−35.7171	−	109.926i	−0.169275	−	0.520976i	−0.999326	+	0.0367123i	$0.988311\pi$
$212$		0			0
$213$	−115.075	−	225.847i	−0.540257	−	1.06031i
$214$		0			0
$215$	77.4226	+	159.213i	0.360105	+	0.740527i
$216$		0			0
$217$	25.4883	+	160.927i	0.117458	+	0.741598i
$218$		0			0
$219$	−264.274	+	363.741i	−1.20673	+	1.66092i
$220$		0			0
$221$	−238.047	+	172.951i	−1.07714	+	0.782586i
$222$		0			0
$223$	−192.730	−	98.2007i	−0.864259	−	0.440362i	−0.0351058	−	0.999384i	$-0.511177\pi$
$223$	−192.730	−	98.2007i	−0.864259	−	0.440362i	−0.829153	+	0.559022i	$0.811177\pi$
$224$		0			0
$225$	249.503	+	371.781i	1.10890	+	1.65236i
$226$		0			0
$227$	15.9821	−	31.3667i	0.0704059	−	0.138179i	−0.853121	−	0.521713i	$-0.825293\pi$
$227$	15.9821	−	31.3667i	0.0704059	−	0.138179i	0.923527	+	0.383534i	$0.125293\pi$
$228$		0			0
$229$	−43.4339	−	59.7817i	−0.189668	−	0.261055i	0.703584	−	0.710612i	$-0.251582\pi$
$229$	−43.4339	−	59.7817i	−0.189668	−	0.261055i	−0.893252	+	0.449557i	$0.851582\pi$
$230$		0			0
$231$	104.824	+	76.1592i	0.453784	+	0.329694i
$232$		0			0
$233$	383.300	−	60.7088i	1.64507	−	0.260553i	0.735931	−	0.677056i	$-0.236745\pi$
$233$	383.300	−	60.7088i	1.64507	−	0.260553i	0.909134	+	0.416504i	$0.136745\pi$
$234$		0			0
$235$	−153.210	+	287.332i	−0.651955	+	1.22269i
$236$		0			0
$237$	463.857	−	236.347i	1.95720	−	0.997244i
$238$		0			0
$239$	446.303	−	145.013i	1.86738	−	0.606748i	0.874904	−	0.484297i	$-0.160924\pi$
$239$	446.303	−	145.013i	1.86738	−	0.606748i	0.992475	−	0.122451i	$-0.0390755\pi$
$240$		0			0
$241$	119.110	−	366.583i	0.494233	−	1.52109i	−0.323917	−	0.946086i	$-0.605000\pi$
$241$	119.110	−	366.583i	0.494233	−	1.52109i	0.818149	−	0.575006i	$-0.195000\pi$
$242$		0			0
$243$	5.93284	−	5.93284i	0.0244150	−	0.0244150i
$244$		0			0
$245$	−31.9449	−	11.0414i	−0.130387	−	0.0450670i
$246$		0			0
$247$	−735.259	−	116.454i	−2.97676	−	0.471472i
$248$		0			0
$249$			148.303i			0.595595i
$250$		0			0
$251$	189.808			0.756208			0.378104	−	0.925763i	$-0.376576\pi$
$251$	189.808			0.756208			0.378104	+	0.925763i	$0.376576\pi$
$252$		0			0
$253$	−3.00587	+	18.9783i	−0.0118809	+	0.0750132i
$254$		0			0
$255$	−105.993	+	306.658i	−0.415660	+	1.20258i
$256$		0			0
$257$	153.161	+	153.161i	0.595959	+	0.595959i	0.939235	−	0.343276i	$-0.111537\pi$
$257$	153.161	+	153.161i	0.595959	+	0.595959i	−0.343276	+	0.939235i	$0.611537\pi$
$258$		0			0
$259$	21.0707	+	6.84630i	0.0813542	+	0.0264336i
$260$		0			0
$261$	185.054	+	569.537i	0.709019	+	2.18213i
$262$		0			0
$263$	−18.8716	−	37.0375i	−0.0717550	−	0.140827i	0.852342	−	0.522984i	$-0.175181\pi$
$263$	−18.8716	−	37.0375i	−0.0717550	−	0.140827i	−0.924097	+	0.382157i	$0.875181\pi$
$264$		0			0
$265$	87.1921	+	46.4921i	0.329027	+	0.175442i
$266$		0			0
$267$	−107.772	−	680.445i	−0.403640	−	2.54848i
$268$		0			0
$269$	−119.897	+	165.024i	−0.445715	+	0.613474i	−0.971470	−	0.237162i	$-0.923783\pi$
$269$	−119.897	+	165.024i	−0.445715	+	0.613474i	0.525755	+	0.850636i	$0.323783\pi$
$270$		0			0
$271$	−43.6702	+	31.7283i	−0.161145	+	0.117078i	−0.665435	−	0.746456i	$-0.731754\pi$
$271$	−43.6702	+	31.7283i	−0.161145	+	0.117078i	0.504291	+	0.863534i	$0.331754\pi$
$272$		0			0
$273$	−706.590	−	360.026i	−2.58824	−	1.31878i
$274$		0			0
$275$	−33.0725	+	90.2071i	−0.120264	+	0.328026i
$276$		0			0
$277$	−181.945	+	357.087i	−0.656842	+	1.28912i	0.286748	+	0.958006i	$0.407426\pi$
$277$	−181.945	+	357.087i	−0.656842	+	1.28912i	−0.943589	+	0.331118i	$0.892574\pi$
$278$		0			0
$279$	−263.908	−	363.238i	−0.945906	−	1.30193i
$280$		0			0
$281$	−305.504	−	221.962i	−1.08720	−	0.789900i	−0.108280	−	0.994120i	$-0.534534\pi$
$281$	−305.504	−	221.962i	−1.08720	−	0.789900i	−0.978925	+	0.204220i	$0.934534\pi$
$282$		0			0
$283$	278.753	−	44.1501i	0.984993	−	0.156008i	0.356897	−	0.934144i	$-0.383835\pi$
$283$	278.753	−	44.1501i	0.984993	−	0.156008i	0.628096	+	0.778136i	$0.283835\pi$
$284$		0			0
$285$	−738.216	+	358.981i	−2.59023	+	1.25958i
$286$		0			0
$287$	192.079	−	97.8694i	0.669266	−	0.341008i
$288$		0			0
$289$	126.030	−	40.9495i	0.436089	−	0.141694i
$290$		0			0
$291$	−119.539	+	367.904i	−0.410788	+	1.26428i
$292$		0			0
$293$	−135.446	+	135.446i	−0.462273	+	0.462273i	−0.899400	−	0.437127i	$-0.855996\pi$
$293$	−135.446	+	135.446i	−0.462273	+	0.462273i	0.437127	+	0.899400i	$0.355996\pi$
$294$		0			0
$295$	292.864	−	387.697i	0.992760	−	1.31423i
$296$		0			0
$297$	−175.438	−	27.7866i	−0.590700	−	0.0935577i
$298$		0			0
$299$		−	117.604i		−	0.393324i
$300$		0			0
$301$	−230.125			−0.764535
$302$		0			0
$303$	−117.789	+	743.692i	−0.388743	+	2.45443i
$304$		0			0
$305$	563.036	+	10.4882i	1.84602	+	0.0343877i
$306$		0			0
$307$	−16.2934	−	16.2934i	−0.0530731	−	0.0530731i	0.680072	−	0.733145i	$-0.261948\pi$
$307$	−16.2934	−	16.2934i	−0.0530731	−	0.0530731i	−0.733145	+	0.680072i	$0.761948\pi$
$308$		0			0
$309$	239.675	+	77.8750i	0.775646	+	0.252023i
$310$		0			0
$311$	33.6750	+	103.641i	0.108280	+	0.333251i	0.990486	−	0.137612i	$-0.0439427\pi$
$311$	33.6750	+	103.641i	0.108280	+	0.333251i	−0.882206	+	0.470863i	$0.843943\pi$
$312$		0			0
$313$	41.5999	+	81.6445i	0.132907	+	0.260845i	0.947863	−	0.318678i	$-0.103239\pi$
$313$	41.5999	+	81.6445i	0.132907	+	0.260845i	−0.814956	+	0.579523i	$0.803239\pi$
$314$		0			0
$315$	−576.428	+	80.3225i	−1.82993	+	0.254992i
$316$		0			0
$317$	−15.7446	−	99.4074i	−0.0496675	−	0.313588i	−0.999997	−	0.00234328i	$-0.999254\pi$
$317$	−15.7446	−	99.4074i	−0.0496675	−	0.313588i	0.950330	−	0.311245i	$-0.100746\pi$
$318$		0			0
$319$	−75.5324	+	103.961i	−0.236779	+	0.325898i
$320$		0			0
$321$	−406.318	+	295.207i	−1.26579	+	0.919648i
$322$		0			0
$323$	−352.751	−	179.735i	−1.09211	−	0.556456i
$324$		0			0
$325$	113.557	−	576.975i	0.349407	−	1.77531i
$326$		0			0
$327$	−236.586	+	464.326i	−0.723504	+	1.41996i
$328$		0			0
$329$	−248.789	−	342.429i	−0.756198	−	1.04082i
$330$		0			0
$331$	−345.041	−	250.687i	−1.04242	−	0.757363i	−0.0716636	−	0.997429i	$-0.522831\pi$
$331$	−345.041	−	250.687i	−1.04242	−	0.757363i	−0.970756	+	0.240066i	$0.922831\pi$
$332$		0			0
$333$	−60.3002	+	9.55061i	−0.181082	+	0.0286805i
$334$		0			0
$335$	27.8486	+	4.94413i	0.0831300	+	0.0147586i
$336$		0			0
$337$	199.429	−	101.614i	0.591777	−	0.301526i	−0.132338	−	0.991205i	$-0.542248\pi$
$337$	199.429	−	101.614i	0.591777	−	0.301526i	0.724115	+	0.689679i	$0.242248\pi$
$338$		0			0
$339$	229.511	−	74.5725i	0.677022	−	0.219978i
$340$		0			0
$341$	29.7725	−	91.6302i	0.0873093	−	0.268710i
$342$		0			0
$343$	256.253	−	256.253i	0.747094	−	0.747094i
$344$		0			0
$345$	−74.2573	−	106.316i	−0.215239	−	0.308161i
$346$		0			0
$347$	126.988	+	20.1130i	0.365961	+	0.0579625i	0.336707	−	0.941610i	$-0.390687\pi$
$347$	126.988	+	20.1130i	0.365961	+	0.0579625i	0.0292539	+	0.999572i	$0.490687\pi$
$348$		0			0
$349$			485.668i			1.39160i	0.718236	+	0.695799i	$0.244950\pi$
$349$			485.668i			1.39160i	−0.718236	+	0.695799i	$0.755050\pi$
$350$		0			0
$351$	1087.14			3.09727
$352$		0			0
$353$	38.6300	−	243.900i	0.109433	−	0.690935i	−0.870583	−	0.492021i	$-0.836258\pi$
$353$	38.6300	−	243.900i	0.109433	−	0.690935i	0.980017	−	0.198914i	$-0.0637416\pi$
$354$		0			0
$355$	71.1566	+	233.723i	0.200441	+	0.658373i
$356$		0			0
$357$	−298.221	−	298.221i	−0.835352	−	0.835352i
$358$		0			0
$359$	253.144	+	82.2516i	0.705138	+	0.229113i	0.639568	−	0.768735i	$-0.279113\pi$
$359$	253.144	+	82.2516i	0.705138	+	0.229113i	0.0655700	+	0.997848i	$0.479113\pi$
$360$		0			0
$361$	−197.962	−	609.263i	−0.548370	−	1.68771i
$362$		0			0
$363$	250.178	+	491.002i	0.689196	+	1.35262i
$364$		0			0
$365$	312.087	−	300.673i	0.855034	−	0.823761i
$366$		0			0
$367$	55.5032	+	350.433i	0.151235	+	0.954859i	0.940250	+	0.340485i	$0.110591\pi$
$367$	55.5032	+	350.433i	0.151235	+	0.954859i	−0.789015	+	0.614374i	$0.789409\pi$
$368$		0			0
$369$	−349.176	+	480.599i	−0.946276	+	1.30244i
$370$		0			0
$371$	−103.912	+	75.4962i	−0.280085	+	0.203494i
$372$		0			0
$373$	−411.196	−	209.515i	−1.10240	−	0.561702i	−0.194508	−	0.980901i	$-0.562311\pi$
$373$	−411.196	−	209.515i	−1.10240	−	0.561702i	−0.907894	+	0.419199i	$0.862311\pi$
$374$		0			0
$375$	−261.656	−	593.296i	−0.697748	−	1.58212i
$376$		0			0
$377$	357.062	−	700.774i	0.947115	−	1.85882i
$378$		0			0
$379$	−199.842	−	275.059i	−0.527287	−	0.725749i	0.459427	−	0.888216i	$-0.348055\pi$
$379$	−199.842	−	275.059i	−0.527287	−	0.725749i	−0.986714	+	0.162467i	$0.948055\pi$
$380$		0			0
$381$	564.233	+	409.940i	1.48093	+	1.07596i
$382$		0			0
$383$	−0.765917	+	0.121309i	−0.00199978	+	0.000316735i	−0.157434	−	0.987529i	$-0.550322\pi$
$383$	−0.765917	+	0.121309i	−0.00199978	+	0.000316735i	0.155434	+	0.987846i	$0.450322\pi$
$384$		0			0
$385$	−86.6488	−	89.9383i	−0.225062	−	0.233606i
$386$		0			0
$387$	565.028	−	287.896i	1.46002	−	0.743918i
$388$		0			0
$389$	−345.103	+	112.131i	−0.887153	+	0.288254i	−0.716924	−	0.697151i	$-0.754451\pi$
$389$	−345.103	+	112.131i	−0.887153	+	0.288254i	−0.170229	+	0.985405i	$0.554451\pi$
$390$		0			0
$391$	19.3272	−	59.4831i	0.0494303	−	0.152131i
$392$		0			0
$393$	88.3485	−	88.3485i	0.224805	−	0.224805i
$394$		0			0
$395$	−480.032	+	146.145i	−1.21527	+	0.369988i
$396$		0			0
$397$	−110.076	−	17.4344i	−0.277270	−	0.0439153i	0.0162506	−	0.999868i	$-0.494827\pi$
$397$	−110.076	−	17.4344i	−0.277270	−	0.0439153i	−0.293521	+	0.955953i	$0.594827\pi$
$398$		0			0
$399$		−	1067.01i		−	2.67421i
$400$		0			0
$401$	367.221			0.915764			0.457882	−	0.889013i	$-0.348608\pi$
$401$	367.221			0.915764			0.457882	+	0.889013i	$0.348608\pi$
$402$		0			0
$403$	−92.2460	+	582.418i	−0.228898	+	1.44521i
$404$		0			0
$405$	322.067	−	224.951i	0.795227	−	0.555436i
$406$		0			0
$407$	−9.26366	−	9.26366i	−0.0227608	−	0.0227608i
$408$		0			0
$409$	−716.024	−	232.650i	−1.75067	−	0.568827i	−0.754503	−	0.656296i	$-0.772122\pi$
$409$	−716.024	−	232.650i	−1.75067	−	0.568827i	−0.996167	+	0.0874691i	$0.972122\pi$
$410$		0			0
$411$	156.358	+	481.220i	0.380433	+	1.17085i
$412$		0			0
$413$	286.727	+	562.733i	0.694253	+	1.36255i
$414$		0			0
$415$	24.9870	−	140.743i	0.0602097	−	0.339140i
$416$		0			0
$417$	53.0328	+	334.836i	0.127177	+	0.802963i
$418$		0			0
$419$	−101.060	+	139.097i	−0.241193	+	0.331974i	−0.912403	−	0.409294i	$-0.865775\pi$
$419$	−101.060	+	139.097i	−0.241193	+	0.331974i	0.671210	+	0.741268i	$0.265775\pi$
$420$		0			0
$421$	50.3272	−	36.5649i	0.119542	−	0.0868524i	−0.526408	−	0.850232i	$-0.676461\pi$
$421$	50.3272	−	36.5649i	0.119542	−	0.0868524i	0.645950	+	0.763380i	$0.276461\pi$
$422$		0			0
$423$	1039.25	+	529.523i	2.45685	+	1.25183i
$424$		0			0
$425$	152.258	−	273.167i	0.358254	−	0.642747i
$426$		0			0
$427$	−332.316	+	652.206i	−0.778256	+	1.52741i
$428$		0			0
$429$	275.632	+	379.375i	0.642498	+	0.884323i
$430$		0			0
$431$	−676.662	−	491.624i	−1.56998	−	1.14066i	−0.927174	−	0.374632i	$-0.877769\pi$
$431$	−676.662	−	491.624i	−1.56998	−	1.14066i	−0.642808	−	0.766027i	$-0.722231\pi$
$432$		0			0
$433$	61.0524	−	9.66974i	0.140999	−	0.0223320i	−0.0855362	−	0.996335i	$-0.527260\pi$
$433$	61.0524	−	9.66974i	0.140999	−	0.0223320i	0.226535	+	0.974003i	$0.427260\pi$
$434$		0			0
$435$	−119.693	−	858.966i	−0.275156	−	1.97463i
$436$		0			0
$437$	140.988	−	71.8372i	0.322628	−	0.164387i
$438$		0			0
$439$	−568.190	+	184.616i	−1.29428	+	0.420538i	−0.873589	−	0.486665i	$-0.838213\pi$
$439$	−568.190	+	184.616i	−1.29428	+	0.420538i	−0.420693	+	0.907203i	$0.638213\pi$
$440$		0			0
$441$	−37.4117	+	115.141i	−0.0848338	+	0.261092i
$442$		0			0
$443$	598.532	−	598.532i	1.35109	−	1.35109i	0.466640	−	0.884447i	$-0.345464\pi$
$443$	598.532	−	598.532i	1.35109	−	1.35109i	0.884447	−	0.466640i	$-0.154536\pi$
$444$		0			0
$445$	−12.3675	+	663.916i	−0.0277920	+	1.49195i
$446$		0			0
$447$	138.847	+	21.9912i	0.310620	+	0.0491973i
$448$		0			0
$449$			59.0887i			0.131601i	0.997833	+	0.0658003i	$0.0209600\pi$
$449$			59.0887i			0.131601i	−0.997833	+	0.0658003i	$0.979040\pi$
$450$		0			0
$451$	−127.475			−0.282649
$452$		0			0
$453$	−37.6561	+	237.751i	−0.0831261	+	0.524837i
$454$		0			0
$455$	609.911	+	460.723i	1.34046	+	1.01258i
$456$		0			0
$457$	310.756	+	310.756i	0.679992	+	0.679992i	0.959998	−	0.280006i	$-0.0903365\pi$
$457$	310.756	+	310.756i	0.679992	+	0.679992i	−0.280006	+	0.959998i	$0.590336\pi$
$458$		0			0
$459$	549.869	+	178.663i	1.19797	+	0.389245i
$460$		0			0
$461$	−47.8249	−	147.190i	−0.103742	−	0.319284i	0.885691	−	0.464274i	$-0.153685\pi$
$461$	−47.8249	−	147.190i	−0.103742	−	0.319284i	−0.989433	+	0.144991i	$0.953685\pi$
$462$		0			0
$463$	37.4168	+	73.4345i	0.0808138	+	0.158606i	0.927877	−	0.372886i	$-0.121632\pi$
$463$	37.4168	+	73.4345i	0.0808138	+	0.158606i	−0.847063	+	0.531492i	$0.821632\pi$
$464$		0			0
$465$	284.359	+	584.761i	0.611524	+	1.25755i
$466$		0			0
$467$	−99.6736	−	629.314i	−0.213434	−	1.34757i	−0.828897	−	0.559402i	$-0.811031\pi$
$467$	−99.6736	−	629.314i	−0.213434	−	1.34757i	0.615463	−	0.788166i	$-0.288969\pi$
$468$		0			0
$469$	−21.6099	+	29.7435i	−0.0460765	+	0.0634189i
$470$		0			0
$471$	−369.220	+	268.254i	−0.783906	+	0.569541i
$472$		0			0
$473$	121.246	+	61.7781i	0.256335	+	0.130609i
$474$		0			0
$475$	761.068	−	216.302i	1.60225	−	0.455373i
$476$		0			0
$477$	160.686	−	315.364i	0.336868	−	0.661141i
$478$		0			0
$479$	−18.8372	−	25.9272i	−0.0393261	−	0.0541278i	0.788901	−	0.614520i	$-0.210650\pi$
$479$	−18.8372	−	25.9272i	−0.0393261	−	0.0541278i	−0.828227	+	0.560392i	$0.810650\pi$
$480$		0			0
$481$	64.8691	+	47.1302i	0.134863	+	0.0979837i
$482$		0			0
$483$	166.490	−	26.3695i	0.344700	−	0.0545951i
$484$		0			0
$485$	175.432	−	329.009i	0.361716	−	0.678370i
$486$		0			0
$487$	418.145	−	213.056i	0.858614	−	0.437486i	0.0314896	−	0.999504i	$-0.489975\pi$
$487$	418.145	−	213.056i	0.858614	−	0.437486i	0.827125	+	0.562018i	$0.189975\pi$
$488$		0			0
$489$	1227.45	−	398.822i	2.51012	−	0.815587i
$490$		0			0
$491$	−178.219	+	548.501i	−0.362971	+	1.11711i	0.588271	+	0.808664i	$0.299809\pi$
$491$	−178.219	+	548.501i	−0.362971	+	1.11711i	−0.951242	+	0.308446i	$0.900191\pi$
$492$		0			0
$493$	295.766	−	295.766i	0.599931	−	0.599931i
$494$		0			0
$495$	325.266	+	112.425i	0.657104	+	0.227121i
$496$		0			0
$497$	−313.662	−	49.6791i	−0.631110	−	0.0999580i
$498$		0			0
$499$			173.174i			0.347041i	0.984830	+	0.173521i	$0.0555143\pi$
$499$			173.174i			0.347041i	−0.984830	+	0.173521i	$0.944486\pi$
$500$		0			0
$501$	−1098.84			−2.19328
$502$		0			0
$503$	67.1699	−	424.094i	0.133538	−	0.843129i	−0.826434	−	0.563034i	$-0.809634\pi$
$503$	67.1699	−	424.094i	0.133538	−	0.843129i	0.959972	−	0.280095i	$-0.0903660\pi$
$504$		0			0
$505$	237.087	−	685.935i	0.469478	−	1.35829i
$506$		0			0
$507$	−1409.54	−	1409.54i	−2.78017	−	2.78017i
$508$		0			0
$509$	136.589	+	44.3805i	0.268348	+	0.0871915i	0.440100	−	0.897949i	$-0.354943\pi$
$509$	136.589	+	44.3805i	0.268348	+	0.0871915i	−0.171752	+	0.985140i	$0.554943\pi$
$510$		0			0
$511$	174.071	+	535.735i	0.340647	+	1.04840i
$512$		0			0
$513$	664.071	+	1303.31i	1.29449	+	2.54057i
$514$		0			0
$515$	−214.336	−	114.287i	−0.416187	−	0.221917i
$516$		0			0
$517$	39.1534	+	247.205i	0.0757319	+	0.478152i
$518$		0			0
$519$	38.4751	−	52.9565i	0.0741332	−	0.102036i
$520$		0			0
$521$	−366.647	+	266.384i	−0.703736	+	0.511294i	−0.881147	−	0.472843i	$-0.843228\pi$
$521$	−366.647	+	266.384i	−0.703736	+	0.511294i	0.177411	+	0.984137i	$0.443228\pi$
$522$		0			0
$523$	17.9407	+	9.14123i	0.0343034	+	0.0174784i	0.471058	−	0.882102i	$-0.343872\pi$
$523$	17.9407	+	9.14123i	0.0343034	+	0.0174784i	−0.436755	+	0.899581i	$0.643872\pi$
$524$		0			0
$525$	842.278	+	31.3909i	1.60434	+	0.0597921i
$526$		0			0
$527$	−142.373	+	279.423i	−0.270158	+	0.530215i
$528$		0			0
$529$	−296.245	−	407.746i	−0.560009	−	0.770787i
$530$		0			0
$531$	−1408.00	−	1022.98i	−2.65161	−	1.92651i
$532$		0			0
$533$	770.596	−	122.050i	1.44577	−	0.228988i
$534$		0			0
$535$	435.343	−	211.700i	0.813726	−	0.395700i
$536$		0			0
$537$	7.23245	−	3.68511i	0.0134682	−	0.00686241i
$538$		0			0
$539$	−24.7076	+	8.02798i	−0.0458397	+	0.0148942i
$540$		0			0
$541$	9.95129	−	30.6269i	0.0183942	−	0.0566117i	−0.941438	−	0.337186i	$-0.890525\pi$
$541$	9.95129	−	30.6269i	0.0183942	−	0.0566117i	0.959832	+	0.280574i	$0.0905249\pi$
$542$		0			0
$543$	−721.430	+	721.430i	−1.32860	+	1.32860i
$544$		0			0
$545$	302.758	−	400.795i	0.555519	−	0.735403i
$546$		0			0
$547$	1011.15	+	160.151i	1.84854	+	0.292780i	0.979422	−	0.201824i	$-0.0646870\pi$
$547$	1011.15	+	160.151i	1.84854	+	0.292780i	0.869118	+	0.494604i	$0.164687\pi$
$548$		0			0
$549$		−	2017.11i		−	3.67415i
$550$		0			0
$551$	1058.23			1.92056
$552$		0			0
$553$	102.034	−	644.216i	0.184509	−	1.16495i
$554$		0			0
$555$	88.4015	+	1.64675i	0.159282	+	0.00296711i
$556$		0			0
$557$	56.7428	+	56.7428i	0.101872	+	0.101872i	0.756206	−	0.654334i	$-0.227051\pi$
$557$	56.7428	+	56.7428i	0.101872	+	0.101872i	−0.654334	+	0.756206i	$0.727051\pi$
$558$		0			0
$559$	−792.095	−	257.367i	−1.41699	−	0.460406i
$560$		0			0
$561$	77.0654	+	237.183i	0.137371	+	0.422786i
$562$		0			0
$563$	−138.487	−	271.796i	−0.245980	−	0.482764i	0.734697	−	0.678395i	$-0.237324\pi$
$563$	−138.487	−	271.796i	−0.245980	−	0.482764i	−0.980677	+	0.195632i	$0.937324\pi$
$564$		0			0
$565$	−230.375	+	32.1017i	−0.407744	+	0.0568172i
$566$		0			0
$567$	79.8823	+	504.357i	0.140886	+	0.889519i
$568$		0			0
$569$	103.363	−	142.268i	0.181658	−	0.250031i	−0.708470	−	0.705741i	$-0.750614\pi$
$569$	103.363	−	142.268i	0.181658	−	0.250031i	0.890129	+	0.455710i	$0.150614\pi$
$570$		0			0
$571$	−393.388	+	285.813i	−0.688947	+	0.500549i	−0.876314	−	0.481741i	$-0.840005\pi$
$571$	−393.388	+	285.813i	−0.688947	+	0.500549i	0.187367	+	0.982290i	$0.440005\pi$
$572$		0			0
$573$	795.866	+	405.514i	1.38895	+	0.707703i
$574$		0			0
$575$	52.5592	+	113.407i	0.0914074	+	0.197230i
$576$		0			0
$577$	−398.601	+	782.298i	−0.690816	+	1.35580i	0.232816	+	0.972521i	$0.425206\pi$
$577$	−398.601	+	782.298i	−0.690816	+	1.35580i	−0.923632	+	0.383281i	$0.874794\pi$
$578$		0			0
$579$	148.295	+	204.110i	0.256123	+	0.352522i
$580$		0			0
$581$	150.320	+	109.214i	0.258726	+	0.187975i
$582$		0			0
$583$	75.0154	−	11.8813i	0.128671	−	0.0203795i
$584$		0			0
$585$	−2073.91	−	368.193i	−3.54514	−	0.629391i
$586$		0			0
$587$	−871.422	+	444.012i	−1.48453	+	0.756408i	−0.993403	−	0.114677i	$-0.963417\pi$
$587$	−871.422	+	444.012i	−1.48453	+	0.756408i	−0.491132	+	0.871085i	$0.663417\pi$
$588$		0			0
$589$	−754.576	+	245.177i	−1.28111	+	0.416259i
$590$		0			0
$591$	−126.412	+	389.056i	−0.213895	+	0.658302i
$592$		0			0
$593$	−578.079	+	578.079i	−0.974838	+	0.974838i	−0.999691	−	0.0248530i	$-0.992088\pi$
$593$	−578.079	+	578.079i	−0.974838	+	0.974838i	0.0248530	+	0.999691i	$0.492088\pi$
$594$		0			0
$595$	232.773	+	333.265i	0.391214	+	0.560109i
$596$		0			0
$597$	−1219.57	−	193.161i	−2.04283	−	0.323552i
$598$		0			0
$599$			214.667i			0.358376i	0.983815	+	0.179188i	$0.0573471\pi$
$599$			214.667i			0.358376i	−0.983815	+	0.179188i	$0.942653\pi$
$600$		0			0
$601$	−98.6172			−0.164088			−0.0820442	−	0.996629i	$-0.526145\pi$
$601$	−98.6172			−0.164088			−0.0820442	+	0.996629i	$0.526145\pi$
$602$		0			0
$603$	15.8486	−	100.064i	0.0262830	−	0.165944i
$604$		0			0
$605$	−154.698	−	508.124i	−0.255699	−	0.839875i
$606$		0			0
$607$	180.017	+	180.017i	0.296569	+	0.296569i	0.839668	−	0.543099i	$-0.182749\pi$
$607$	180.017	+	180.017i	0.296569	+	0.296569i	−0.543099	+	0.839668i	$0.682749\pi$
$608$		0			0
$609$	1072.14	+	348.359i	1.76049	+	0.572018i
$610$		0			0
$611$	−473.371	−	1456.89i	−0.774748	−	2.38443i
$612$		0			0
$613$	−268.747	−	527.445i	−0.438412	−	0.860432i	−0.999467	−	0.0326535i	$-0.989604\pi$
$613$	−268.747	−	527.445i	−0.438412	−	0.860432i	0.561055	−	0.827779i	$-0.310396\pi$
$614$		0			0
$615$	619.565	−	596.905i	1.00742	−	0.970577i
$616$		0			0
$617$	55.2112	+	348.590i	0.0894833	+	0.564975i	0.991171	+	0.132588i	$0.0423287\pi$
$617$	55.2112	+	348.590i	0.0894833	+	0.564975i	−0.901688	+	0.432387i	$0.857671\pi$
$618$		0			0
$619$	158.717	−	218.455i	0.256409	−	0.352916i	−0.661334	−	0.750092i	$-0.730009\pi$
$619$	158.717	−	218.455i	0.256409	−	0.352916i	0.917743	+	0.397175i	$0.130009\pi$
$620$		0			0
$621$	−186.950	+	135.827i	−0.301047	+	0.218724i
$622$		0			0
$623$	−769.064	−	391.858i	−1.23445	−	0.628985i
$624$		0			0
$625$	148.355	+	607.137i	0.237368	+	0.971420i
$626$		0			0
$627$	−286.443	+	562.177i	−0.456848	+	0.896614i
$628$		0			0
$629$	25.0649	+	34.4988i	0.0398487	+	0.0548471i
$630$		0			0
$631$	451.985	+	328.386i	0.716299	+	0.520422i	0.885200	−	0.465211i	$-0.154022\pi$
$631$	451.985	+	328.386i	0.716299	+	0.520422i	−0.168900	+	0.985633i	$0.554022\pi$
$632$		0			0
$633$	592.199	−	93.7952i	0.935544	−	0.148176i
$634$		0			0
$635$	−466.402	−	484.108i	−0.734491	−	0.762375i
$636$		0			0
$637$	141.673	−	72.1861i	0.222407	−	0.113322i
$638$		0			0
$639$	832.287	−	270.427i	1.30248	−	0.423203i
$640$		0			0
$641$	−322.762	+	993.360i	−0.503529	+	1.54970i	0.299700	+	0.954033i	$0.403113\pi$
$641$	−322.762	+	993.360i	−0.503529	+	1.54970i	−0.803229	+	0.595670i	$0.796887\pi$
$642$		0			0
$643$	−34.9330	+	34.9330i	−0.0543282	+	0.0543282i	−0.733749	−	0.679421i	$-0.762231\pi$
$643$	−34.9330	+	34.9330i	−0.0543282	+	0.0543282i	0.679421	+	0.733749i	$0.262231\pi$
$644$		0			0
$645$	−878.572	+	267.480i	−1.36213	+	0.414698i
$646$		0			0
$647$	920.493	+	145.792i	1.42271	+	0.225335i	0.819880	−	0.572535i	$-0.194040\pi$
$647$	920.493	+	145.792i	1.42271	+	0.225335i	0.602830	+	0.797870i	$0.294040\pi$
$648$		0			0
$649$		−	373.461i		−	0.575441i
$650$		0			0
$651$	−845.206			−1.29832
$652$		0			0
$653$	29.0165	−	183.203i	0.0444357	−	0.280556i	−0.955458	−	0.295127i	$-0.904638\pi$
$653$	29.0165	−	183.203i	0.0444357	−	0.280556i	0.999894	+	0.0145706i	$0.00463814\pi$
$654$		0			0
$655$	−98.7303	+	68.9593i	−0.150733	+	0.105281i
$656$		0			0
$657$	−1097.62	−	1097.62i	−1.67066	−	1.67066i
$658$		0			0
$659$	739.990	+	240.437i	1.12290	+	0.364852i	0.810873	−	0.585222i	$-0.198993\pi$
$659$	739.990	+	240.437i	1.12290	+	0.364852i	0.312025	+	0.950074i	$0.398993\pi$
$660$		0			0
$661$	−96.4256	−	296.767i	−0.145878	−	0.448967i	0.851245	−	0.524769i	$-0.175848\pi$
$661$	−96.4256	−	296.767i	−0.145878	−	0.448967i	−0.997123	+	0.0758018i	$0.975848\pi$
$662$		0			0
$663$	−692.957	−	1360.01i	−1.04518	−	2.05129i
$664$		0			0
$665$	−179.776	+	1012.62i	−0.270340	+	1.52273i
$666$		0			0
$667$	26.1524	+	165.120i	0.0392090	+	0.247556i
$668$		0			0
$669$	659.540	−	907.778i	0.985859	−	1.35692i
$670$		0			0
$671$	350.175	−	254.417i	0.521871	−	0.379161i
$672$		0			0
$673$	246.160	+	125.425i	0.365766	+	0.186367i	0.627207	−	0.778852i	$-0.284198\pi$
$673$	246.160	+	125.425i	0.365766	+	0.186367i	−0.261441	+	0.965219i	$0.584198\pi$
$674$		0			0
$675$	−1048.35	+	485.864i	−1.55311	+	0.719798i
$676$		0			0
$677$	−216.291	+	424.495i	−0.319484	+	0.627023i	−0.993770	−	0.111447i	$-0.964451\pi$
$677$	−216.291	+	424.495i	−0.319484	+	0.627023i	0.674286	+	0.738470i	$0.264451\pi$
$678$		0			0
$679$	284.876	+	392.098i	0.419552	+	0.577464i
$680$		0			0
$681$	147.741	+	107.340i	0.216947	+	0.157621i
$682$		0			0
$683$	107.172	−	16.9744i	0.156914	−	0.0248527i	−0.0774831	−	0.996994i	$-0.524688\pi$
$683$	107.172	−	16.9744i	0.156914	−	0.0248527i	0.234397	+	0.972141i	$0.424688\pi$
$684$		0			0
$685$	−67.3085	−	483.034i	−0.0982605	−	0.705159i
$686$		0			0
$687$	341.543	−	174.025i	0.497152	−	0.253312i
$688$		0			0
$689$	−442.099	+	143.647i	−0.641653	+	0.208486i
$690$		0			0
$691$	264.865	−	815.171i	0.383307	−	1.17970i	−0.554394	−	0.832254i	$-0.687050\pi$
$691$	264.865	−	815.171i	0.383307	−	1.17970i	0.937701	−	0.347443i	$-0.112950\pi$
$692$		0			0
$693$	−316.317	+	316.317i	−0.456446	+	0.456446i
$694$		0			0
$695$	6.08582	−	326.702i	0.00875658	−	0.470075i
$696$		0			0
$697$	409.820	+	64.9091i	0.587977	+	0.0931264i
$698$		0			0
$699$			2013.14i			2.88003i
$700$		0			0
$701$	−794.231			−1.13300			−0.566498	−	0.824063i	$-0.691702\pi$
$701$	−794.231			−1.13300			−0.566498	+	0.824063i	$0.691702\pi$
$702$		0			0
$703$	−16.8770	+	106.557i	−0.0240070	+	0.151575i
$704$		0			0
$705$	−1347.84	−	1018.15i	−1.91183	−	1.44419i
$706$		0			0
$707$	667.063	+	667.063i	0.943511	+	0.943511i
$708$		0			0
$709$	648.747	+	210.791i	0.915016	+	0.297307i	0.728421	−	0.685130i	$-0.240255\pi$
$709$	648.747	+	210.791i	0.915016	+	0.297307i	0.186596	+	0.982437i	$0.440255\pi$
$710$		0			0
$711$	555.417	+	1709.40i	0.781177	+	2.40422i
$712$		0			0
$713$	−56.9042	−	111.681i	−0.0798095	−	0.156635i
$714$		0			0
$715$	−197.662	−	406.476i	−0.276450	−	0.568497i
$716$		0			0
$717$	380.812	+	2404.35i	0.531119	+	3.35335i
$718$		0			0
$719$	−203.408	+	279.967i	−0.282904	+	0.389384i	−0.926693	−	0.375819i	$-0.877361\pi$
$719$	−203.408	+	279.967i	−0.282904	+	0.389384i	0.643789	+	0.765203i	$0.277361\pi$
$720$		0			0
$721$	255.436	−	185.585i	0.354280	−	0.257399i
$722$		0			0
$723$	1781.56	+	907.752i	2.46413	+	1.25553i
$724$		0			0
$725$	−31.1325	+	835.346i	−0.0429414	+	1.15220i
$726$		0			0
$727$	−254.328	+	499.147i	−0.349832	+	0.686584i	−0.997134	−	0.0756492i	$-0.975897\pi$
$727$	−254.328	+	499.147i	−0.349832	+	0.686584i	0.647302	+	0.762233i	$0.275897\pi$
$728$		0			0
$729$	441.222	+	607.291i	0.605243	+	0.833046i
$730$		0			0
$731$	−358.340	−	260.349i	−0.490205	−	0.356155i
$732$		0			0
$733$	−717.891	+	113.703i	−0.979387	+	0.155120i	−0.625547	−	0.780186i	$-0.715124\pi$
$733$	−717.891	+	113.703i	−0.979387	+	0.155120i	−0.353840	+	0.935306i	$0.615124\pi$
$734$		0			0
$735$	82.4949	−	154.712i	0.112238	−	0.210493i
$736$		0			0
$737$	19.3704	−	9.86972i	0.0262828	−	0.0133918i
$738$		0			0
$739$	−491.795	+	159.794i	−0.665487	+	0.216230i	−0.622230	−	0.782834i	$-0.713773\pi$
$739$	−491.795	+	159.794i	−0.665487	+	0.216230i	−0.0432565	+	0.999064i	$0.513773\pi$
$740$		0			0
$741$	1193.32	−	3672.66i	1.61042	−	4.95636i
$742$		0			0
$743$	−453.726	+	453.726i	−0.610668	+	0.610668i	−0.943120	−	0.332452i	$-0.892124\pi$
$743$	−453.726	+	453.726i	−0.610668	+	0.610668i	0.332452	+	0.943120i	$0.392124\pi$
$744$		0			0
$745$	−128.064	−	44.2639i	−0.171898	−	0.0594147i
$746$		0			0
$747$	−505.713	−	80.0970i	−0.676991	−	0.107225i
$748$		0			0
$749$			629.240i			0.840107i
$750$		0			0
$751$	−330.489			−0.440066			−0.220033	−	0.975492i	$-0.570616\pi$
$751$	−330.489			−0.440066			−0.220033	+	0.975492i	$0.570616\pi$
$752$		0			0
$753$	−154.029	+	972.500i	−0.204554	+	1.29150i
$754$		0			0
$755$	75.7943	−	219.287i	0.100390	−	0.290446i
$756$		0			0
$757$	474.195	+	474.195i	0.626413	+	0.626413i	0.947164	−	0.320751i	$-0.103935\pi$
$757$	474.195	+	474.195i	0.626413	+	0.626413i	−0.320751	+	0.947164i	$0.603935\pi$
$758$		0			0
$759$	−94.7980	−	30.8017i	−0.124899	−	0.0405820i
$760$		0			0
$761$	116.998	+	360.083i	0.153743	+	0.473171i	0.998031	−	0.0627176i	$-0.0199767\pi$
$761$	116.998	+	360.083i	0.153743	+	0.473171i	−0.844289	+	0.535889i	$0.819977\pi$
$762$		0			0
$763$	296.413	+	581.743i	0.388483	+	0.762442i
$764$		0			0
$765$	−988.457	−	527.060i	−1.29210	−	0.688967i
$766$		0			0
$767$	357.569	+	2257.60i	0.466192	+	2.94342i
$768$		0			0
$769$	666.984	−	918.024i	0.867339	−	1.19379i	−0.112431	−	0.993660i	$-0.535864\pi$
$769$	666.984	−	918.024i	0.867339	−	1.19379i	0.979769	−	0.200130i	$-0.0641364\pi$
$770$		0			0
$771$	−909.026	+	660.446i	−1.17902	+	0.856610i
$772$		0			0
$773$	872.145	+	444.380i	1.12826	+	0.574877i	0.915536	−	0.402235i	$-0.131767\pi$
$773$	872.145	+	444.380i	1.12826	+	0.574877i	0.212724	+	0.977112i	$0.431767\pi$
$774$		0			0
$775$	−171.339	−	602.862i	−0.221082	−	0.777887i
$776$		0			0
$777$	−52.1764	+	102.402i	−0.0671511	+	0.131792i
$778$		0			0
$779$	617.031	+	849.270i	0.792081	+	1.09021i
$780$		0			0
$781$	151.923	+	110.378i	0.194524	+	0.141330i
$782$		0			0
$783$	−1526.39	+	241.756i	−1.94941	+	0.308756i
$784$		0			0
$785$	395.595	−	192.371i	0.503943	−	0.245058i
$786$		0			0
$787$	749.916	−	382.101i	0.952880	−	0.485516i	0.0928048	−	0.995684i	$-0.470417\pi$
$787$	749.916	−	382.101i	0.952880	−	0.485516i	0.860075	+	0.510168i	$0.170417\pi$
$788$		0			0
$789$	205.079	−	66.6343i	0.259923	−	0.0844542i
$790$		0			0
$791$	93.4302	−	287.548i	0.118117	−	0.363525i
$792$		0			0
$793$	−1873.25	+	1873.25i	−2.36223	+	2.36223i
$794$		0			0
$795$	−308.963	+	409.008i	−0.388632	+	0.514476i
$796$		0			0
$797$	−657.692	−	104.168i	−0.825209	−	0.130700i	−0.270474	−	0.962727i	$-0.587180\pi$
$797$	−657.692	−	104.168i	−0.825209	−	0.130700i	−0.554735	+	0.832027i	$0.687180\pi$
$798$		0			0
$799$		−	814.678i		−	1.01962i
$800$		0			0
$801$	2378.52			2.96944
$802$		0			0
$803$	52.1075	−	328.994i	0.0648910	−	0.409706i
$804$		0			0
$805$	−162.446	−	3.02605i	−0.201796	−	0.00375907i
$806$		0			0
$807$	−748.221	−	748.221i	−0.927164	−	0.927164i
$808$		0			0
$809$	138.121	+	44.8783i	0.170731	+	0.0554738i	0.393135	−	0.919481i	$-0.371390\pi$
$809$	138.121	+	44.8783i	0.170731	+	0.0554738i	−0.222404	+	0.974955i	$0.571390\pi$
$810$		0			0
$811$	27.1844	+	83.6648i	0.0335195	+	0.103163i	0.966416	−	0.256981i	$-0.0827277\pi$
$811$	27.1844	+	83.6648i	0.0335195	+	0.103163i	−0.932897	+	0.360143i	$0.882728\pi$
$812$		0			0
$813$	−127.124	−	249.496i	−0.156365	−	0.306883i
$814$		0			0
$815$	−1232.07	+	171.684i	−1.51175	+	0.210655i
$816$		0			0
$817$	−175.301	−	1106.81i	−0.214567	−	1.35472i
$818$		0			0
$819$	1609.31	−	2215.02i	1.96497	−	2.70454i
$820$		0			0
$821$	−416.935	+	302.921i	−0.507838	+	0.368966i	−0.812003	−	0.583654i	$-0.801623\pi$
$821$	−416.935	+	302.921i	−0.507838	+	0.368966i	0.304165	+	0.952619i	$0.401623\pi$
$822$		0			0
$823$	294.492	+	150.051i	0.357828	+	0.182322i	0.623658	−	0.781698i	$-0.285646\pi$
$823$	294.492	+	150.051i	0.357828	+	0.182322i	−0.265830	+	0.964020i	$0.585646\pi$
$824$		0			0
$825$	−435.346	−	242.652i	−0.527692	−	0.294124i
$826$		0			0
$827$	−118.542	+	232.652i	−0.143340	+	0.281320i	−0.951504	−	0.307637i	$-0.900462\pi$
$827$	−118.542	+	232.652i	−0.143340	+	0.281320i	0.808164	+	0.588958i	$0.200462\pi$
$828$		0			0
$829$	−568.612	−	782.627i	−0.685901	−	0.944061i	0.314085	−	0.949395i	$-0.398302\pi$
$829$	−568.612	−	782.627i	−0.685901	−	0.944061i	−0.999986	+	0.00533357i	$0.998302\pi$
$830$		0			0
$831$	−1681.92	−	1221.99i	−2.02397	−	1.47050i
$832$		0			0
$833$	83.5205	−	13.2283i	0.100265	−	0.0158804i
$834$		0			0
$835$	1042.82	+	185.138i	1.24889	+	0.221723i
$836$		0			0
$837$	1032.39	−	526.029i	1.23344	−	0.628469i
$838$		0			0
$839$	453.985	−	147.509i	0.541102	−	0.175815i	−0.0256983	−	0.999670i	$-0.508181\pi$
$839$	453.985	−	147.509i	0.541102	−	0.175815i	0.566801	+	0.823855i	$0.308181\pi$
$840$		0			0
$841$	−85.6085	+	263.476i	−0.101794	+	0.313289i
$842$		0			0
$843$	1385.16	−	1385.16i	1.64313	−	1.64313i
$844$		0			0
$845$	1100.20	+	1575.18i	1.30201	+	1.86412i
$846$		0			0
$847$	681.916	+	108.005i	0.805095	+	0.127515i
$848$		0			0
$849$			1464.04i			1.72443i
$850$		0			0
$851$	−17.0436			−0.0200278
$852$		0			0
$853$	44.8521	−	283.185i	0.0525816	−	0.331987i	−0.947349	−	0.320203i	$-0.896249\pi$
$853$	44.8521	−	283.185i	0.0525816	−	0.331987i	0.999931	−	0.0117843i	$-0.00375115\pi$
$854$		0			0
$855$	−825.420	−	2711.19i	−0.965404	−	3.17099i
$856$		0			0
$857$	−1046.45	−	1046.45i	−1.22106	−	1.22106i	−0.967255	−	0.253805i	$-0.918318\pi$
$857$	−1046.45	−	1046.45i	−1.22106	−	1.22106i	−0.253805	−	0.967255i	$-0.581682\pi$
$858$		0			0
$859$	−680.918	−	221.244i	−0.792687	−	0.257559i	−0.115439	−	0.993315i	$-0.536827\pi$
$859$	−680.918	−	221.244i	−0.792687	−	0.257559i	−0.677248	+	0.735755i	$0.736827\pi$
$860$		0			0
$861$	345.571	+	1063.56i	0.401360	+	1.23526i
$862$		0			0
$863$	304.239	+	597.102i	0.352536	+	0.691892i	0.997374	−	0.0724283i	$-0.0230749\pi$
$863$	304.239	+	597.102i	0.352536	+	0.691892i	−0.644837	+	0.764320i	$0.723075\pi$
$864$		0			0
$865$	−45.4362	+	43.7744i	−0.0525274	+	0.0506063i
$866$		0			0
$867$	107.536	+	678.954i	0.124032	+	0.783107i
$868$		0			0
$869$	−226.701	+	312.028i	−0.260876	+	0.359065i
$870$		0			0
$871$	−107.646	+	78.2095i	−0.123589	+	0.0897928i
$872$		0			0
$873$	−1189.99	−	606.330i	−1.36310	−	0.694536i
$874$		0			0
$875$	−794.053	−	171.703i	−0.907489	−	0.196232i
$876$		0			0
$877$	−517.263	+	1015.18i	−0.589809	+	1.15757i	0.382519	+	0.923947i	$0.375057\pi$
$877$	−517.263	+	1015.18i	−0.589809	+	1.15757i	−0.972328	+	0.233618i	$0.924943\pi$
$878$		0			0
$879$	−584.056	−	803.884i	−0.664455	−	0.914543i
$880$		0			0
$881$	−884.683	−	642.760i	−1.00418	−	0.729580i	−0.0411997	−	0.999151i	$-0.513118\pi$
$881$	−884.683	−	642.760i	−1.00418	−	0.729580i	−0.962980	+	0.269571i	$0.913118\pi$
$882$		0			0
$883$	−911.135	+	144.310i	−1.03186	+	0.163431i	−0.649327	−	0.760509i	$-0.724949\pi$
$883$	−911.135	+	144.310i	−1.03186	+	0.163431i	−0.382536	+	0.923941i	$0.624949\pi$
$884$		0			0
$885$	1748.74	+	1815.13i	1.97598	+	2.05100i
$886$		0			0
$887$	−654.851	+	333.663i	−0.738276	+	0.376171i	−0.782335	−	0.622858i	$-0.785971\pi$
$887$	−654.851	+	333.663i	−0.738276	+	0.376171i	0.0440584	+	0.999029i	$0.485971\pi$
$888$		0			0
$889$	831.029	−	270.018i	0.934790	−	0.303732i
$890$		0			0
$891$	93.3093	−	287.176i	0.104724	−	0.322308i
$892$		0			0
$893$	1457.42	−	1457.42i	1.63205	−	1.63205i
$894$		0			0
$895$	−7.48465	+	2.27869i	−0.00836274	+	0.00254603i
$896$		0			0
$897$	602.553	+	95.4351i	0.671743	+	0.106394i
$898$		0			0
$899$		−	838.249i		−	0.932424i
$900$		0			0
$901$	−247.218			−0.274381
$902$		0			0
$903$	186.746	−	1179.07i	0.206806	−	1.30572i
$904$		0			0
$905$	806.205	−	563.103i	0.890835	−	0.622214i
$906$		0			0
$907$	32.5490	+	32.5490i	0.0358865	+	0.0358865i	0.724822	−	0.688936i	$-0.241922\pi$
$907$	32.5490	+	32.5490i	0.0358865	+	0.0358865i	−0.688936	+	0.724822i	$0.741922\pi$
$908$		0			0
$909$	−2472.37	−	803.321i	−2.71988	−	0.883742i
$910$		0			0
$911$	−251.500	−	774.038i	−0.276070	−	0.849657i	−0.988934	−	0.148355i	$-0.952602\pi$
$911$	−251.500	−	774.038i	−0.276070	−	0.849657i	0.712864	−	0.701302i	$-0.247398\pi$
$912$		0			0
$913$	−49.8803	−	97.8957i	−0.0546334	−	0.107224i
$914$		0			0
$915$	−510.639	+	2876.25i	−0.558075	+	3.14344i
$916$		0			0
$917$	−24.4881	−	154.612i	−0.0267046	−	0.168606i
$918$		0			0
$919$	66.2153	−	91.1376i	0.0720515	−	0.0991704i	−0.771470	−	0.636265i	$-0.780478\pi$
$919$	66.2153	−	91.1376i	0.0720515	−	0.0991704i	0.843522	+	0.537095i	$0.180478\pi$
$920$		0			0
$921$	96.7029	−	70.2588i	0.104998	−	0.0762853i
$922$		0			0
$923$	−1024.07	−	521.789i	−1.10950	−	0.565319i
$924$		0			0
$925$	−83.6177	−	16.4572i	−0.0903975	−	0.0177916i
$926$		0			0
$927$	−394.999	+	775.230i	−0.426105	+	0.836278i
$928$		0			0
$929$	215.850	+	297.092i	0.232346	+	0.319797i	0.909231	−	0.416292i	$-0.136670\pi$
$929$	215.850	+	297.092i	0.232346	+	0.319797i	−0.676885	+	0.736089i	$0.736670\pi$
$930$		0			0
$931$	173.080	+	125.750i	0.185907	+	0.135069i
$932$		0			0
$933$	−558.341	+	88.4326i	−0.598437	+	0.0947830i
$934$		0			0
$935$	−33.1748	−	238.077i	−0.0354811	−	0.254627i
$936$		0			0
$937$	−535.092	+	272.643i	−0.571070	+	0.290975i	−0.715582	−	0.698528i	$-0.753839\pi$
$937$	−535.092	+	272.643i	−0.571070	+	0.290975i	0.144513	+	0.989503i	$0.453839\pi$
$938$		0			0
$939$	−452.071	+	146.887i	−0.481439	+	0.156429i
$940$		0			0
$941$	−118.490	+	364.675i	−0.125919	+	0.387540i	−0.994067	−	0.108765i	$-0.965310\pi$
$941$	−118.490	+	364.675i	−0.125919	+	0.387540i	0.868148	+	0.496305i	$0.165310\pi$
$942$		0			0
$943$	−117.266	+	117.266i	−0.124355	+	0.124355i
$944$		0			0
$945$	27.9731	−	1501.67i	0.0296012	−	1.58907i
$946$		0			0
$947$	−854.212	−	135.294i	−0.902019	−	0.142866i	−0.311837	−	0.950136i	$-0.600944\pi$
$947$	−854.212	−	135.294i	−0.902019	−	0.142866i	−0.590183	+	0.807270i	$0.700944\pi$
$948$		0			0
$949$			2038.69i			2.14825i
$950$		0			0
$951$	522.099			0.549000
$952$		0			0
$953$	217.886	−	1375.68i	0.228631	−	1.44352i	−0.559917	−	0.828549i	$-0.689167\pi$
$953$	217.886	−	1375.68i	0.228631	−	1.44352i	0.788548	−	0.614973i	$-0.210833\pi$
$954$		0			0
$955$	−686.972	−	518.935i	−0.719343	−	0.543387i
$956$		0			0
$957$	−471.361	−	471.361i	−0.492540	−	0.492540i
$958$		0			0
$959$	602.910	+	195.897i	0.628686	+	0.204272i
$960$		0			0
$961$	−102.754	−	316.246i	−0.106925	−	0.329080i
$962$		0			0
$963$	−787.206	−	1544.98i	−0.817452	−	1.60434i
$964$		0			0
$965$	−106.346	−	218.691i	−0.110203	−	0.226623i
$966$		0			0
$967$	72.6463	+	458.670i	0.0751254	+	0.474323i	0.996355	+	0.0853037i	$0.0271861\pi$
$967$	72.6463	+	458.670i	0.0751254	+	0.474323i	−0.921230	+	0.389019i	$0.872814\pi$
$968$		0			0
$969$	1207.15	−	1661.49i	1.24576	−	1.71465i
$970$		0			0
$971$	−359.473	+	261.172i	−0.370209	+	0.268973i	−0.757298	−	0.653070i	$-0.773481\pi$
$971$	−359.473	+	261.172i	−0.370209	+	0.268973i	0.387089	+	0.922043i	$0.373481\pi$
$972$		0			0
$973$	378.444	+	192.827i	0.388945	+	0.198177i
$974$		0			0
$975$	2864.03	+	1050.03i	2.93747	+	1.07696i
$976$		0			0
$977$	614.326	−	1205.68i	0.628788	−	1.23407i	−0.328384	−	0.944544i	$-0.606504\pi$
$977$	614.326	−	1205.68i	0.628788	−	1.23407i	0.957172	−	0.289521i	$-0.0934961\pi$
$978$		0			0
$979$	300.002	+	412.917i	0.306437	+	0.421775i
$980$		0			0
$981$	−1455.57	−	1057.53i	−1.48376	−	1.07802i
$982$		0			0
$983$	1379.29	−	218.458i	1.40314	−	0.222236i	0.591460	−	0.806334i	$-0.298552\pi$
$983$	1379.29	−	218.458i	1.40314	−	0.222236i	0.811683	+	0.584098i	$0.198552\pi$
$984$		0			0
$985$	185.519	−	347.925i	0.188344	−	0.353223i
$986$		0			0
$987$	1956.36	−	996.813i	1.98212	−	1.00994i
$988$		0			0
$989$	168.368	−	54.7060i	0.170241	−	0.0553145i
$990$		0			0
$991$	55.8527	−	171.897i	0.0563599	−	0.173458i	−0.918914	−	0.394458i	$-0.870932\pi$
$991$	55.8527	−	171.897i	0.0563599	−	0.173458i	0.975274	+	0.221000i	$0.0709322\pi$
$992$		0			0
$993$	1564.42	−	1564.42i	1.57544	−	1.57544i
$994$		0			0
$995$	1124.85	+	388.794i	1.13051	+	0.390748i
$996$		0			0
$997$	1758.10	+	278.455i	1.76339	+	0.279293i	0.952196	−	0.305488i	$-0.0988197\pi$
$997$	1758.10	+	278.455i	1.76339	+	0.279293i	0.811191	+	0.584781i	$0.198820\pi$
$998$		0			0
$999$		−	157.553i		−	0.157711i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.f.17.1		64
4.3	odd	2		200.3.u.b.17.8	✓	64
25.3	odd	20	inner	400.3.bg.f.353.1		64
100.3	even	20		200.3.u.b.153.8	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.3.u.b.17.8	✓	64	4.3	odd	2
200.3.u.b.153.8	yes	64	100.3	even	20
400.3.bg.f.17.1		64	1.1	even	1	trivial
400.3.bg.f.353.1		64	25.3	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.811497 + 5.12359i) q^{3} +(1.63338 - 4.72568i) q^{5} +(4.59566 + 4.59566i) q^{7} +(-17.0331 - 5.53440i) q^{9} +(-1.18760 - 3.65505i) q^{11} +(10.6786 + 20.9580i) q^{13} +(22.8870 + 12.2037i) q^{15} +(1.95690 + 12.3554i) q^{17} +(-18.6024 + 25.6040i) q^{19} +(-27.2756 + 19.8169i) q^{21} +(-4.45484 - 2.26986i) q^{23} +(-19.6641 - 15.4377i) q^{25} +(20.9828 - 41.1811i) q^{27} +(-19.6538 - 27.0511i) q^{29} +(20.2816 + 14.7355i) q^{31} +(19.6907 - 3.11870i) q^{33} +(29.2241 - 14.2111i) q^{35} +(3.03733 - 1.54760i) q^{37} +(-116.046 + 37.7056i) q^{39} +(10.2499 - 31.5459i) q^{41} +(-25.0372 + 25.0372i) q^{43} +(-53.9754 + 71.4533i) q^{45} +(-64.3235 - 10.1878i) q^{47} -6.75985i q^{49} -64.8919 q^{51} +(-3.09155 + 19.5193i) q^{53} +(-19.2124 - 0.357889i) q^{55} +(-116.089 - 116.089i) q^{57} +(92.4197 + 30.0290i) q^{59} +(34.8035 + 107.114i) q^{61} +(-52.8442 - 103.713i) q^{63} +(116.483 - 16.2314i) q^{65} +(0.884920 + 5.58716i) q^{67} +(15.2449 - 20.9828i) q^{69} +(-39.5309 + 28.7209i) q^{71} +(77.2257 + 39.3484i) q^{73} +(95.0538 - 88.2232i) q^{75} +(11.3396 - 22.2551i) q^{77} +(-58.9885 - 81.1907i) q^{79} +(63.5643 + 46.1822i) q^{81} +(28.2368 - 4.47227i) q^{83} +(61.5839 + 10.9334i) q^{85} +(154.548 - 78.7461i) q^{87} +(-126.306 + 41.0394i) q^{89} +(-47.2405 + 145.391i) q^{91} +(-91.9570 + 91.9570i) q^{93} +(90.6117 + 129.730i) q^{95} +(73.6536 + 11.6656i) q^{97} +68.8295i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9} - 16 q^{11} + 24 q^{13} - 82 q^{15} - 8 q^{17} + 50 q^{19} - 100 q^{21} + 48 q^{23} - 200 q^{25} - 90 q^{27} - 108 q^{31} + 260 q^{33} - 2 q^{35} - 94 q^{37} - 320 q^{39}+ \cdots - 544 q^{97}+O(q^{100}) \) 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9 - 16 * q^11 + 24 * q^13 - 82 * q^15 - 8 * q^17 + 50 * q^19 - 100 * q^21 + 48 * q^23 - 200 * q^25 - 90 * q^27 - 108 * q^31 + 260 * q^33 - 2 * q^35 - 94 * q^37 - 320 * q^39 - 184 * q^41 - 96 * q^43 + 146 * q^45 - 104 * q^47 - 200 * q^51 - 202 * q^53 + 12 * q^55 - 280 * q^57 + 600 * q^59 + 12 * q^61 + 34 * q^63 + 296 * q^65 - 58 * q^67 - 40 * q^69 + 470 * q^71 - 228 * q^73 + 614 * q^75 + 324 * q^77 - 560 * q^79 + 856 * q^81 + 308 * q^83 - 902 * q^85 + 840 * q^87 - 380 * q^89 - 62 * q^91 - 540 * q^93 + 16 * q^95 - 544 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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