LMFDB - Embedded newform 252.4.i.a.25.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(25,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("252.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.14
Character	$\chi$	$=$	252.25
Dual form			252.4.i.a.121.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24769 + 5.04413i) q^{3} +(1.32728 - 2.29891i) q^{5} +(-14.0290 + 12.0908i) q^{7} +(-23.8866 + 12.5870i) q^{9} +O(q^{10})$	\(q+(1.24769 + 5.04413i) q^{3} +(1.32728 - 2.29891i) q^{5} +(-14.0290 + 12.0908i) q^{7} +(-23.8866 + 12.5870i) q^{9} +(-25.1171 - 43.5040i) q^{11} +(-27.5326 - 47.6878i) q^{13} +(13.2520 + 3.82664i) q^{15} +(-11.3977 + 19.7415i) q^{17} +(9.43604 + 16.3437i) q^{19} +(-78.4912 - 55.6788i) q^{21} +(88.6692 - 153.580i) q^{23} +(58.9767 + 102.151i) q^{25} +(-93.2934 - 104.782i) q^{27} +(-122.220 + 211.692i) q^{29} -270.802 q^{31} +(188.102 - 180.973i) q^{33} +(9.17517 + 48.2993i) q^{35} +(-90.3996 - 156.577i) q^{37} +(206.192 - 198.378i) q^{39} +(-146.620 - 253.954i) q^{41} +(229.397 - 397.327i) q^{43} +(-2.76770 + 71.6195i) q^{45} +329.112 q^{47} +(50.6273 - 339.243i) q^{49} +(-113.799 - 32.8606i) q^{51} +(-295.849 + 512.426i) q^{53} -133.349 q^{55} +(-70.6666 + 67.9885i) q^{57} +23.5229 q^{59} -861.509 q^{61} +(182.919 - 465.390i) q^{63} -146.173 q^{65} -702.902 q^{67} +(885.308 + 255.640i) q^{69} +99.3115 q^{71} +(-439.402 + 761.066i) q^{73} +(-441.677 + 424.938i) q^{75} +(878.365 + 306.635i) q^{77} +113.822 q^{79} +(412.135 - 601.320i) q^{81} +(-449.770 + 779.024i) q^{83} +(30.2559 + 52.4048i) q^{85} +(-1220.29 - 352.370i) q^{87} +(211.365 + 366.095i) q^{89} +(962.837 + 336.124i) q^{91} +(-337.875 - 1365.96i) q^{93} +50.0969 q^{95} +(290.172 - 502.593i) q^{97} +(1147.55 + 723.013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9}+O(q^{10}) $ 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9	$ 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9} + 4 q^{11} - 12 q^{13} - 26 q^{15} + 112 q^{17} + 60 q^{19} - 80 q^{21} + 10 q^{23} - 600 q^{25} + 194 q^{29} + 60 q^{31} - 472 q^{33} + 394 q^{35} - 84 q^{37} + 604 q^{39} + 210 q^{41} + 42 q^{43} + 254 q^{45} - 132 q^{47} - 78 q^{49} - 58 q^{51} - 468 q^{53} + 612 q^{55} + 1476 q^{57} - 916 q^{59} - 804 q^{61} - 444 q^{63} + 1656 q^{65} - 588 q^{67} - 28 q^{69} - 2228 q^{71} - 336 q^{73} - 668 q^{75} - 1216 q^{77} - 768 q^{79} - 104 q^{81} + 1024 q^{83} + 360 q^{85} + 2188 q^{87} + 2922 q^{89} - 120 q^{91} - 1292 q^{93} + 2428 q^{95} - 264 q^{97} - 2246 q^{99}+O(q^{100}) $ 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9 + 4 * q^11 - 12 * q^13 - 26 * q^15 + 112 * q^17 + 60 * q^19 - 80 * q^21 + 10 * q^23 - 600 * q^25 + 194 * q^29 + 60 * q^31 - 472 * q^33 + 394 * q^35 - 84 * q^37 + 604 * q^39 + 210 * q^41 + 42 * q^43 + 254 * q^45 - 132 * q^47 - 78 * q^49 - 58 * q^51 - 468 * q^53 + 612 * q^55 + 1476 * q^57 - 916 * q^59 - 804 * q^61 - 444 * q^63 + 1656 * q^65 - 588 * q^67 - 28 * q^69 - 2228 * q^71 - 336 * q^73 - 668 * q^75 - 1216 * q^77 - 768 * q^79 - 104 * q^81 + 1024 * q^83 + 360 * q^85 + 2188 * q^87 + 2922 * q^89 - 120 * q^91 - 1292 * q^93 + 2428 * q^95 - 264 * q^97 - 2246 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.24769	+	5.04413i	0.240117	+	0.970744i
$3$	1.24769	+	5.04413i	0.240117	+	0.970744i
$4$		0			0
$5$	1.32728	−	2.29891i	0.118715	−	0.205621i	−0.800544	−	0.599275i	$-0.795456\pi$
$5$	1.32728	−	2.29891i	0.118715	−	0.205621i	0.919259	+	0.393654i	$0.128789\pi$
$6$		0			0
$7$	−14.0290	+	12.0908i	−0.757496	+	0.652839i
$7$	−14.0290	+	12.0908i	−0.757496	+	0.652839i
$8$		0			0
$9$	−23.8866	+	12.5870i	−0.884687	+	0.466185i
$10$		0			0
$11$	−25.1171	−	43.5040i	−0.688462	−	1.19245i	−0.972335	−	0.233589i	$-0.924953\pi$
$11$	−25.1171	−	43.5040i	−0.688462	−	1.19245i	0.283874	−	0.958862i	$-0.408380\pi$
$12$		0			0
$13$	−27.5326	−	47.6878i	−0.587397	−	1.01740i	−0.994572	−	0.104052i	$-0.966819\pi$
$13$	−27.5326	−	47.6878i	−0.587397	−	1.01740i	0.407175	−	0.913350i	$-0.366514\pi$
$14$		0			0
$15$	13.2520	+	3.82664i	0.228111	+	0.0658690i
$16$		0			0
$17$	−11.3977	+	19.7415i	−0.162609	+	0.281648i	−0.935804	−	0.352521i	$-0.885324\pi$
$17$	−11.3977	+	19.7415i	−0.162609	+	0.281648i	0.773194	+	0.634169i	$0.218658\pi$
$18$		0			0
$19$	9.43604	+	16.3437i	0.113936	+	0.197342i	0.917354	−	0.398073i	$-0.130321\pi$
$19$	9.43604	+	16.3437i	0.113936	+	0.197342i	−0.803418	+	0.595415i	$0.796988\pi$
$20$		0			0
$21$	−78.4912	−	55.6788i	−0.815628	−	0.578577i
$22$		0			0
$23$	88.6692	−	153.580i	0.803862	−	1.39233i	−0.113195	−	0.993573i	$-0.536109\pi$
$23$	88.6692	−	153.580i	0.803862	−	1.39233i	0.917057	−	0.398756i	$-0.130558\pi$
$24$		0			0
$25$	58.9767	+	102.151i	0.471813	+	0.817205i
$26$		0			0
$27$	−93.2934	−	104.782i	−0.664975	−	0.746866i
$28$		0			0
$29$	−122.220	+	211.692i	−0.782612	+	1.35552i	0.147804	+	0.989017i	$0.452780\pi$
$29$	−122.220	+	211.692i	−0.782612	+	1.35552i	−0.930416	+	0.366506i	$0.880554\pi$
$30$		0			0
$31$	−270.802			−1.56895			−0.784474	−	0.620161i	$-0.787067\pi$
$31$	−270.802			−1.56895			−0.784474	+	0.620161i	$0.787067\pi$
$32$		0			0
$33$	188.102	−	180.973i	0.992253	−	0.954648i
$34$		0			0
$35$	9.17517	+	48.2993i	0.0443110	+	0.233259i
$36$		0			0
$37$	−90.3996	−	156.577i	−0.401665	−	0.695704i	0.592262	−	0.805745i	$-0.298235\pi$
$37$	−90.3996	−	156.577i	−0.401665	−	0.695704i	−0.993927	+	0.110041i	$0.964902\pi$
$38$		0			0
$39$	206.192	−	198.378i	0.846593	−	0.814508i
$40$		0			0
$41$	−146.620	−	253.954i	−0.558493	−	0.967338i	−0.997623	−	0.0689146i	$-0.978046\pi$
$41$	−146.620	−	253.954i	−0.558493	−	0.967338i	0.439129	−	0.898424i	$-0.355287\pi$
$42$		0			0
$43$	229.397	−	397.327i	0.813550	−	1.40911i	−0.0968141	−	0.995302i	$-0.530865\pi$
$43$	229.397	−	397.327i	0.813550	−	1.40911i	0.910364	−	0.413808i	$-0.135801\pi$
$44$		0			0
$45$	−2.76770	+	71.6195i	−0.00916853	+	0.237253i
$46$		0			0
$47$	329.112			1.02140			0.510702	−	0.859758i	$-0.329386\pi$
$47$	329.112			1.02140			0.510702	+	0.859758i	$0.329386\pi$
$48$		0			0
$49$	50.6273	−	339.243i	0.147601	−	0.989047i
$50$		0			0
$51$	−113.799	−	32.8606i	−0.312453	−	0.0902236i
$52$		0			0
$53$	−295.849	+	512.426i	−0.766755	+	1.32806i	0.172559	+	0.984999i	$0.444796\pi$
$53$	−295.849	+	512.426i	−0.766755	+	1.32806i	−0.939314	+	0.343059i	$0.888537\pi$
$54$		0			0
$55$	−133.349			−0.326924
$56$		0			0
$57$	−70.6666	+	67.9885i	−0.164211	+	0.157988i
$58$		0			0
$59$	23.5229			0.0519054			0.0259527	−	0.999663i	$-0.491738\pi$
$59$	23.5229			0.0519054			0.0259527	+	0.999663i	$0.491738\pi$
$60$		0			0
$61$	−861.509			−1.80828			−0.904139	−	0.427238i	$-0.859487\pi$
$61$	−861.509			−1.80828			−0.904139	+	0.427238i	$0.859487\pi$
$62$		0			0
$63$	182.919	−	465.390i	0.365803	−	0.930692i
$64$		0			0
$65$	−146.173			−0.278932
$66$		0			0
$67$	−702.902			−1.28169			−0.640844	−	0.767671i	$-0.721416\pi$
$67$	−702.902			−1.28169			−0.640844	+	0.767671i	$0.721416\pi$
$68$		0			0
$69$	885.308	+	255.640i	1.54462	+	0.446021i
$70$		0			0
$71$	99.3115			0.166001			0.0830007	−	0.996549i	$-0.473550\pi$
$71$	99.3115			0.166001			0.0830007	+	0.996549i	$0.473550\pi$
$72$		0			0
$73$	−439.402	+	761.066i	−0.704494	+	1.22022i	0.262380	+	0.964965i	$0.415493\pi$
$73$	−439.402	+	761.066i	−0.704494	+	1.22022i	−0.966874	+	0.255255i	$0.917841\pi$
$74$		0			0
$75$	−441.677	+	424.938i	−0.680006	+	0.654235i
$76$		0			0
$77$	878.365	+	306.635i	1.29999	+	0.453822i
$78$		0			0
$79$	113.822			0.162101			0.0810506	−	0.996710i	$-0.474172\pi$
$79$	113.822			0.162101			0.0810506	+	0.996710i	$0.474172\pi$
$80$		0			0
$81$	412.135	−	601.320i	0.565343	−	0.824856i
$82$		0			0
$83$	−449.770	+	779.024i	−0.594803	+	1.03023i	0.398772	+	0.917050i	$0.369437\pi$
$83$	−449.770	+	779.024i	−0.594803	+	1.03023i	−0.993575	+	0.113179i	$0.963897\pi$
$84$		0			0
$85$	30.2559	+	52.4048i	0.0386084	+	0.0668718i
$86$		0			0
$87$	−1220.29	−	352.370i	−1.50378	−	0.434231i
$88$		0			0
$89$	211.365	+	366.095i	0.251738	+	0.436023i	0.964004	−	0.265886i	$-0.0856646\pi$
$89$	211.365	+	366.095i	0.251738	+	0.436023i	−0.712267	+	0.701909i	$0.752331\pi$
$90$		0			0
$91$	962.837	+	336.124i	1.10915	+	0.387202i
$92$		0			0
$93$	−337.875	−	1365.96i	−0.376732	−	1.52305i
$94$		0			0
$95$	50.0969			0.0541036
$96$		0			0
$97$	290.172	−	502.593i	0.303738	−	0.526089i	−0.673242	−	0.739422i	$-0.735099\pi$
$97$	290.172	−	502.593i	0.303738	−	0.526089i	0.976979	+	0.213333i	$0.0684321\pi$
$98$		0			0
$99$	1147.55	+	723.013i	1.16498	+	0.733995i
$100$		0			0
$101$	933.621	+	1617.08i	0.919790	+	1.59312i	0.799733	+	0.600356i	$0.204975\pi$
$101$	933.621	+	1617.08i	0.919790	+	1.59312i	0.120057	+	0.992767i	$0.461692\pi$
$102$		0			0
$103$	−154.185	+	267.056i	−0.147498	+	0.255474i	−0.930302	−	0.366794i	$-0.880455\pi$
$103$	−154.185	+	267.056i	−0.147498	+	0.255474i	0.782804	+	0.622268i	$0.213789\pi$
$104$		0			0
$105$	−232.180	+	106.543i	−0.215795	+	0.0990242i
$106$		0			0
$107$	−232.403	−	402.534i	−0.209974	−	0.363686i	0.741732	−	0.670697i	$-0.234005\pi$
$107$	−232.403	−	402.534i	−0.209974	−	0.363686i	−0.951706	+	0.307010i	$0.900671\pi$
$108$		0			0
$109$	−118.473	+	205.202i	−0.104107	+	0.180319i	−0.913373	−	0.407124i	$-0.866532\pi$
$109$	−118.473	+	205.202i	−0.104107	+	0.180319i	0.809266	+	0.587442i	$0.199865\pi$
$110$		0			0
$111$	677.003	−	651.346i	0.578904	−	0.556964i
$112$		0			0
$113$	638.238	+	1105.46i	0.531331	+	0.920292i	0.999331	+	0.0365641i	$0.0116413\pi$
$113$	638.238	+	1105.46i	0.531331	+	0.920292i	−0.468000	+	0.883728i	$0.655025\pi$
$114$		0			0
$115$	−235.377	−	407.685i	−0.190861	−	0.330581i
$116$		0			0
$117$	1257.91	+	792.546i	0.993961	+	0.626247i
$118$		0			0
$119$	−78.7901	−	414.761i	−0.0606947	−	0.319505i
$120$		0			0
$121$	−596.234	+	1032.71i	−0.447959	+	0.775888i
$122$		0			0
$123$	1098.04	−	1056.43i	0.804934	−	0.774428i
$124$		0			0
$125$	644.933			0.461476
$126$		0			0
$127$	−856.935			−0.598746			−0.299373	−	0.954136i	$-0.596777\pi$
$127$	−856.935			−0.598746			−0.299373	+	0.954136i	$0.596777\pi$
$128$		0			0
$129$	2290.38	+	661.368i	1.56323	+	0.451397i
$130$		0			0
$131$	170.833	−	295.892i	0.113937	−	0.197345i	−0.803417	−	0.595416i	$-0.796987\pi$
$131$	170.833	−	295.892i	0.113937	−	0.197345i	0.917354	+	0.398072i	$0.130320\pi$
$132$		0			0
$133$	−329.986	−	115.197i	−0.215139	−	0.0751044i
$134$		0			0
$135$	−364.711	+	75.3980i	−0.232514	+	0.0480684i
$136$		0			0
$137$	335.506	+	581.113i	0.209228	+	0.362393i	0.951471	−	0.307737i	$-0.0995717\pi$
$137$	335.506	+	581.113i	0.209228	+	0.362393i	−0.742244	+	0.670130i	$0.766238\pi$
$138$		0			0
$139$	−171.102	−	296.357i	−0.104408	−	0.180839i	0.809088	−	0.587687i	$-0.199961\pi$
$139$	−171.102	−	296.357i	−0.104408	−	0.180839i	−0.913496	+	0.406848i	$0.866628\pi$
$140$		0			0
$141$	410.629	+	1660.09i	0.245257	+	0.991521i
$142$		0			0
$143$	−1383.08	+	2395.56i	−0.808801	+	1.40088i
$144$		0			0
$145$	324.440	+	561.947i	0.185816	+	0.321842i
$146$		0			0
$147$	1774.35	−	167.898i	0.995553	−	0.0942043i
$148$		0			0
$149$	1291.18	−	2236.38i	0.709914	−	1.22961i	−0.254974	−	0.966948i	$-0.582067\pi$
$149$	1291.18	−	2236.38i	0.709914	−	1.22961i	0.964888	−	0.262660i	$-0.0845997\pi$
$150$		0			0
$151$	−717.210	−	1242.24i	−0.386528	−	0.669486i	0.605452	−	0.795882i	$-0.292992\pi$
$151$	−717.210	−	1242.24i	−0.386528	−	0.669486i	−0.991980	+	0.126396i	$0.959659\pi$
$152$		0			0
$153$	23.7671	−	615.019i	0.0125585	−	0.324976i
$154$		0			0
$155$	−359.429	+	622.549i	−0.186258	+	0.322608i
$156$		0			0
$157$	−2533.08			−1.28765			−0.643827	−	0.765171i	$-0.722654\pi$
$157$	−2533.08			−1.28765			−0.643827	+	0.765171i	$0.722654\pi$
$158$		0			0
$159$	−2953.87	−	852.956i	−1.47332	−	0.425433i
$160$		0			0
$161$	612.951	+	3226.65i	0.300045	+	1.57948i
$162$		0			0
$163$	−809.907	−	1402.80i	−0.389183	−	0.674085i	0.603157	−	0.797623i	$-0.293909\pi$
$163$	−809.907	−	1402.80i	−0.389183	−	0.674085i	−0.992340	+	0.123538i	$0.960576\pi$
$164$		0			0
$165$	−166.378	−	672.631i	−0.0785000	−	0.317359i
$166$		0			0
$167$	1264.48	+	2190.14i	0.585918	+	1.01484i	0.994760	+	0.102235i	$0.0325993\pi$
$167$	1264.48	+	2190.14i	0.585918	+	1.01484i	−0.408842	+	0.912605i	$0.634067\pi$
$168$		0			0
$169$	−417.587	+	723.281i	−0.190071	+	0.329213i
$170$		0			0
$171$	−431.113	−	271.623i	−0.192795	−	0.121471i
$172$		0			0
$173$	−783.840			−0.344476			−0.172238	−	0.985055i	$-0.555100\pi$
$173$	−783.840			−0.344476			−0.172238	+	0.985055i	$0.555100\pi$
$174$		0			0
$175$	−2062.46	−	720.001i	−0.890900	−	0.311011i
$176$		0			0
$177$	29.3492	+	118.653i	0.0124634	+	0.0503868i
$178$		0			0
$179$	978.120	−	1694.15i	0.408425	−	0.707413i	−0.586288	−	0.810102i	$-0.699411\pi$
$179$	978.120	−	1694.15i	0.408425	−	0.707413i	0.994713	+	0.102689i	$0.0327448\pi$
$180$		0			0
$181$	539.981			0.221748			0.110874	−	0.993834i	$-0.464635\pi$
$181$	539.981			0.221748			0.110874	+	0.993834i	$0.464635\pi$
$182$		0			0
$183$	−1074.89	−	4345.57i	−0.434199	−	1.75538i
$184$		0			0
$185$	−479.941			−0.190735
$186$		0			0
$187$	1145.11			0.447801
$188$		0			0
$189$	2575.71	+	342.007i	0.991299	+	0.131626i
$190$		0			0
$191$	−2578.74			−0.976917			−0.488458	−	0.872587i	$-0.662441\pi$
$191$	−2578.74			−0.976917			−0.488458	+	0.872587i	$0.662441\pi$
$192$		0			0
$193$	944.850			0.352393			0.176196	−	0.984355i	$-0.443621\pi$
$193$	944.850			0.352393			0.176196	+	0.984355i	$0.443621\pi$
$194$		0			0
$195$	−182.379	−	737.318i	−0.0669764	−	0.270772i
$196$		0			0
$197$	−2928.21			−1.05902			−0.529508	−	0.848305i	$-0.677623\pi$
$197$	−2928.21			−1.05902			−0.529508	+	0.848305i	$0.677623\pi$
$198$		0			0
$199$	−1540.42	+	2668.09i	−0.548732	+	0.950431i	0.449630	+	0.893215i	$0.351556\pi$
$199$	−1540.42	+	2668.09i	−0.548732	+	0.950431i	−0.998362	+	0.0572164i	$0.981777\pi$
$200$		0			0
$201$	−877.001	−	3545.53i	−0.307756	−	1.24419i
$202$		0			0
$203$	−844.881	−	4447.56i	−0.292113	−	1.53772i
$204$		0			0
$205$	−778.422			−0.265207
$206$		0			0
$207$	−184.897	+	4784.57i	−0.0620832	+	1.60652i
$208$		0			0
$209$	474.011	−	821.011i	0.156881	−	0.271725i
$210$		0			0
$211$	106.489	+	184.444i	0.0347440	+	0.0601784i	0.882875	−	0.469609i	$-0.155605\pi$
$211$	106.489	+	184.444i	0.0347440	+	0.0601784i	−0.848131	+	0.529787i	$0.822272\pi$
$212$		0			0
$213$	123.910	+	500.940i	0.0398598	+	0.161145i
$214$		0			0
$215$	−608.946	−	1054.72i	−0.193162	−	0.334566i
$216$		0			0
$217$	3799.08	−	3274.20i	1.18847	−	1.02427i
$218$		0			0
$219$	−4387.15	−	1266.83i	−1.35368	−	0.390887i
$220$		0			0
$221$	1255.24			0.382065
$222$		0			0
$223$	1041.46	−	1803.86i	0.312741	−	0.541684i	−0.666213	−	0.745761i	$-0.732086\pi$
$223$	1041.46	−	1803.86i	0.312741	−	0.541684i	0.978955	+	0.204077i	$0.0654193\pi$
$224$		0			0
$225$	−2694.52	−	1697.69i	−0.798376	−	0.503018i
$226$		0			0
$227$	−92.7882	−	160.714i	−0.0271303	−	0.0469910i	0.852141	−	0.523311i	$-0.175304\pi$
$227$	−92.7882	−	160.714i	−0.0271303	−	0.0469910i	−0.879272	+	0.476320i	$0.841970\pi$
$228$		0			0
$229$	2689.74	−	4658.77i	0.776170	−	1.34437i	−0.157964	−	0.987445i	$-0.550493\pi$
$229$	2689.74	−	4658.77i	0.776170	−	1.34437i	0.934134	−	0.356921i	$-0.116174\pi$
$230$		0			0
$231$	−450.784	+	4813.17i	−0.128396	+	1.37092i
$232$		0			0
$233$	1442.52	+	2498.52i	0.405590	+	0.702503i	0.994390	−	0.105776i	$-0.0337327\pi$
$233$	1442.52	+	2498.52i	0.405590	+	0.702503i	−0.588800	+	0.808279i	$0.700399\pi$
$234$		0			0
$235$	436.823	−	756.600i	0.121256	−	0.210022i
$236$		0			0
$237$	142.014	+	574.134i	0.0389233	+	0.157359i
$238$		0			0
$239$	−2143.50	−	3712.65i	−0.580132	−	1.00482i	−0.995463	−	0.0951478i	$-0.969668\pi$
$239$	−2143.50	−	3712.65i	−0.580132	−	1.00482i	0.415331	−	0.909670i	$-0.363666\pi$
$240$		0			0
$241$	3681.20	+	6376.03i	0.983929	+	1.70422i	0.646601	+	0.762829i	$0.276190\pi$
$241$	3681.20	+	6376.03i	0.983929	+	1.70422i	0.337329	+	0.941387i	$0.390477\pi$
$242$		0			0
$243$	3547.35	+	1328.61i	0.936472	+	0.350741i
$244$		0			0
$245$	−712.693	−	566.657i	−0.185846	−	0.147765i
$246$		0			0
$247$	519.597	−	899.969i	0.133851	−	0.231837i
$248$		0			0
$249$	−4490.67	−	1296.72i	−1.14291	−	0.330026i
$250$		0			0
$251$	3866.74			0.972377			0.486188	−	0.873854i	$-0.338387\pi$
$251$	3866.74			0.972377			0.486188	+	0.873854i	$0.338387\pi$
$252$		0			0
$253$	−8908.44			−2.21371
$254$		0			0
$255$	−226.587	+	218.000i	−0.0556448	+	0.0535360i
$256$		0			0
$257$	514.565	−	891.253i	0.124894	−	0.216322i	−0.796798	−	0.604246i	$-0.793474\pi$
$257$	514.565	−	891.253i	0.124894	−	0.216322i	0.921691	+	0.387924i	$0.126808\pi$
$258$		0			0
$259$	3161.35	+	1103.62i	0.758443	+	0.264771i
$260$		0			0
$261$	254.859	−	6594.97i	0.0604421	−	1.56406i
$262$		0			0
$263$	−2733.39	−	4734.38i	−0.640868	−	1.11002i	−0.985239	−	0.171182i	$-0.945241\pi$
$263$	−2733.39	−	4734.38i	−0.640868	−	1.11002i	0.344371	−	0.938833i	$-0.388092\pi$
$264$		0			0
$265$	785.347	+	1360.26i	0.182051	+	0.315322i
$266$		0			0
$267$	−1582.92	+	1522.93i	−0.362820	+	0.349069i
$268$		0			0
$269$	−58.6906	+	101.655i	−0.0133027	+	0.0230410i	−0.872600	−	0.488435i	$-0.837568\pi$
$269$	−58.6906	+	101.655i	−0.0133027	+	0.0230410i	0.859297	+	0.511476i	$0.170901\pi$
$270$		0			0
$271$	−342.458	−	593.154i	−0.0767632	−	0.132958i	0.825088	−	0.565004i	$-0.191125\pi$
$271$	−342.458	−	593.154i	−0.0767632	−	0.132958i	−0.901852	+	0.432046i	$0.857792\pi$
$272$		0			0
$273$	−494.136	+	5276.06i	−0.109548	+	1.16968i
$274$		0			0
$275$	2962.64	−	5131.45i	0.649651	−	1.12523i
$276$		0			0
$277$	−3851.39	−	6670.81i	−0.835407	−	1.44697i	−0.893699	−	0.448668i	$-0.851899\pi$
$277$	−3851.39	−	6670.81i	−0.835407	−	1.44697i	0.0582919	−	0.998300i	$-0.481435\pi$
$278$		0			0
$279$	6468.52	−	3408.58i	1.38803	−	0.731420i
$280$		0			0
$281$	1674.67	−	2900.62i	0.355525	−	0.615788i	−0.631683	−	0.775227i	$-0.717635\pi$
$281$	1674.67	−	2900.62i	0.355525	−	0.615788i	0.987208	+	0.159440i	$0.0509687\pi$
$282$		0			0
$283$	1711.29			0.359455			0.179728	−	0.983716i	$-0.442478\pi$
$283$	1711.29			0.359455			0.179728	+	0.983716i	$0.442478\pi$
$284$		0			0
$285$	62.5053	+	252.696i	0.0129912	+	0.0525207i
$286$		0			0
$287$	5127.43	+	1789.97i	1.05457	+	0.368149i
$288$		0			0
$289$	2196.68	+	3804.77i	0.447116	+	0.774428i
$290$		0			0
$291$	2897.19	+	836.589i	0.583630	+	0.168528i
$292$		0			0
$293$	−514.633	−	891.371i	−0.102612	−	0.177728i	0.810148	−	0.586225i	$-0.199387\pi$
$293$	−514.633	−	891.371i	−0.102612	−	0.177728i	−0.912760	+	0.408497i	$0.866053\pi$
$294$		0			0
$295$	31.2214	−	54.0770i	0.00616196	−	0.0106728i
$296$		0			0
$297$	−2215.20	+	6690.46i	−0.432791	+	1.30714i
$298$		0			0
$299$	−9765.17			−1.88874
$300$		0			0
$301$	1585.77	+	8347.68i	0.303661	+	1.59851i
$302$		0			0
$303$	−6991.90	+	6726.92i	−1.32566	+	1.27542i
$304$		0			0
$305$	−1143.46	+	1980.53i	−0.214670	+	0.371820i
$306$		0			0
$307$	2331.51			0.433441			0.216721	−	0.976234i	$-0.430464\pi$
$307$	2331.51			0.433441			0.216721	+	0.976234i	$0.430464\pi$
$308$		0			0
$309$	−1539.44	−	444.527i	−0.283417	−	0.0818391i
$310$		0			0
$311$	3361.00			0.612813			0.306407	−	0.951901i	$-0.400873\pi$
$311$	3361.00			0.612813			0.306407	+	0.951901i	$0.400873\pi$
$312$		0			0
$313$	−6812.75			−1.23029			−0.615143	−	0.788416i	$-0.710902\pi$
$313$	−6812.75			−1.23029			−0.615143	+	0.788416i	$0.710902\pi$
$314$		0			0
$315$	−827.106	−	1038.22i	−0.147943	−	0.185704i
$316$		0			0
$317$	−9866.59			−1.74815			−0.874074	−	0.485792i	$-0.838531\pi$
$317$	−9866.59			−1.74815			−0.874074	+	0.485792i	$0.838531\pi$
$318$		0			0
$319$	12279.3			2.15519
$320$		0			0
$321$	1740.47	−	1674.51i	0.302628	−	0.291159i
$322$		0			0
$323$	−430.198			−0.0741080
$324$		0			0
$325$	3247.56	−	5624.94i	0.554284	−	0.960048i
$326$		0			0
$327$	−1182.88	−	341.568i	−0.200041	−	0.0577637i
$328$		0			0
$329$	−4617.13	+	3979.22i	−0.773709	+	0.666813i
$330$		0			0
$331$	329.358			0.0546923			0.0273462	−	0.999626i	$-0.491294\pi$
$331$	329.358			0.0546923			0.0273462	+	0.999626i	$0.491294\pi$
$332$		0			0
$333$	4130.16	+	2602.22i	0.679675	+	0.428230i
$334$		0			0
$335$	−932.945	+	1615.91i	−0.152156	+	0.263542i
$336$		0			0
$337$	940.109	+	1628.32i	0.151961	+	0.263205i	0.931948	−	0.362591i	$-0.118108\pi$
$337$	940.109	+	1628.32i	0.151961	+	0.263205i	−0.779987	+	0.625796i	$0.784774\pi$
$338$		0			0
$339$	−4779.77	+	4598.63i	−0.765786	+	0.736765i
$340$		0			0
$341$	6801.74	+	11781.0i	1.08016	+	1.87089i
$342$		0			0
$343$	3391.45	+	5371.37i	0.533881	+	0.845559i
$344$		0			0
$345$	1762.74	−	1695.94i	0.275081	−	0.264656i
$346$		0			0
$347$	−1186.60			−0.183574			−0.0917871	−	0.995779i	$-0.529258\pi$
$347$	−1186.60			−0.183574			−0.0917871	+	0.995779i	$0.529258\pi$
$348$		0			0
$349$	−1844.84	+	3195.36i	−0.282957	+	0.490096i	−0.972112	−	0.234518i	$-0.924649\pi$
$349$	−1844.84	+	3195.36i	−0.282957	+	0.490096i	0.689155	+	0.724614i	$0.257982\pi$
$350$		0			0
$351$	−2428.24	+	7333.89i	−0.369258	+	1.11525i
$352$		0			0
$353$	−672.545	−	1164.88i	−0.101405	−	0.175639i	0.810859	−	0.585242i	$-0.199000\pi$
$353$	−672.545	−	1164.88i	−0.101405	−	0.175639i	−0.912264	+	0.409603i	$0.865667\pi$
$354$		0			0
$355$	131.814	−	228.308i	0.0197069	−	0.0341334i
$356$		0			0
$357$	1993.81	−	914.920i	0.295584	−	0.135638i
$358$		0			0
$359$	−4081.11	−	7068.70i	−0.599980	−	1.03920i	−0.992823	−	0.119591i	$-0.961842\pi$
$359$	−4081.11	−	7068.70i	−0.599980	−	1.03920i	0.392843	−	0.919606i	$-0.371492\pi$
$360$		0			0
$361$	3251.42	−	5631.63i	0.474037	−	0.821057i
$362$		0			0
$363$	−5953.02	−	1718.99i	−0.860751	−	0.248549i
$364$		0			0
$365$	1166.42	+	2020.29i	0.167268	+	0.289717i
$366$		0			0
$367$	4501.03	+	7796.01i	0.640195	+	1.10885i	0.985389	+	0.170319i	$0.0544800\pi$
$367$	4501.03	+	7796.01i	0.640195	+	1.10885i	−0.345193	+	0.938532i	$0.612187\pi$
$368$		0			0
$369$	6698.76	+	4220.57i	0.945050	+	0.595431i
$370$		0			0
$371$	−2045.14	−	10765.9i	−0.286195	−	1.50657i
$372$		0			0
$373$	−309.589	+	536.224i	−0.0429756	+	0.0744360i	−0.886713	−	0.462320i	$-0.847017\pi$
$373$	−309.589	+	536.224i	−0.0429756	+	0.0744360i	0.843737	+	0.536756i	$0.180350\pi$
$374$		0			0
$375$	804.674	+	3253.13i	0.110808	+	0.447975i
$376$		0			0
$377$	13460.2			1.83882
$378$		0			0
$379$	11117.4			1.50676			0.753379	−	0.657586i	$-0.228423\pi$
$379$	11117.4			1.50676			0.753379	+	0.657586i	$0.228423\pi$
$380$		0			0
$381$	−1069.19	−	4322.50i	−0.143769	−	0.581229i
$382$		0			0
$383$	4073.20	−	7054.98i	0.543422	−	0.941235i	−0.455282	−	0.890347i	$-0.650462\pi$
$383$	4073.20	−	7054.98i	0.543422	−	0.941235i	0.998704	−	0.0508875i	$-0.0162050\pi$
$384$		0			0
$385$	1870.76	−	1612.29i	0.247643	−	0.213429i
$386$		0			0
$387$	−478.348	+	12378.2i	−0.0628315	+	1.62589i
$388$		0			0
$389$	−6000.03	−	10392.4i	−0.782040	−	1.35453i	−0.930751	−	0.365652i	$-0.880846\pi$
$389$	−6000.03	−	10392.4i	−0.782040	−	1.35453i	0.148712	−	0.988881i	$-0.452487\pi$
$390$		0			0
$391$	2021.26	+	3500.92i	0.261431	+	0.452812i
$392$		0			0
$393$	1705.66	+	492.525i	0.218930	+	0.0632178i
$394$		0			0
$395$	151.073	−	261.667i	0.0192439	−	0.0333314i
$396$		0			0
$397$	−4291.47	−	7433.04i	−0.542526	−	0.939682i	−0.998758	−	0.0498213i	$-0.984135\pi$
$397$	−4291.47	−	7433.04i	−0.542526	−	0.939682i	0.456233	−	0.889861i	$-0.349199\pi$
$398$		0			0
$399$	169.352	−	1808.22i	0.0212486	−	0.226878i
$400$		0			0
$401$	5629.39	−	9750.40i	0.701044	−	1.21424i	−0.267057	−	0.963681i	$-0.586051\pi$
$401$	5629.39	−	9750.40i	0.701044	−	1.21424i	0.968100	−	0.250563i	$-0.0806156\pi$
$402$		0			0
$403$	7455.87	+	12913.9i	0.921596	+	1.59625i
$404$		0			0
$405$	−835.363	−	1745.58i	−0.102493	−	0.214169i
$406$		0			0
$407$	−4541.14	+	7865.49i	−0.553062	+	0.957931i
$408$		0			0
$409$	−5429.79			−0.656444			−0.328222	−	0.944601i	$-0.606449\pi$
$409$	−5429.79			−0.656444			−0.328222	+	0.944601i	$0.606449\pi$
$410$		0			0
$411$	−2512.61	+	2417.38i	−0.301552	+	0.290123i
$412$		0			0
$413$	−330.003	+	284.409i	−0.0393181	+	0.0338859i
$414$		0			0
$415$	1193.94	+	2067.96i	0.141224	+	0.244608i
$416$		0			0
$417$	1281.38	−	1232.82i	0.150479	−	0.144776i
$418$		0			0
$419$	4186.02	+	7250.40i	0.488068	+	0.845359i	0.999906	−	0.0137235i	$-0.00436845\pi$
$419$	4186.02	+	7250.40i	0.488068	+	0.845359i	−0.511838	+	0.859082i	$0.671035\pi$
$420$		0			0
$421$	−856.380	+	1483.29i	−0.0991388	+	0.171713i	−0.911328	−	0.411680i	$-0.864942\pi$
$421$	−856.380	+	1483.29i	−0.0991388	+	0.171713i	0.812190	+	0.583394i	$0.198275\pi$
$422$		0			0
$423$	−7861.36	+	4142.54i	−0.903623	+	0.476163i
$424$		0			0
$425$	−2688.81			−0.306885
$426$		0			0
$427$	12086.1	−	10416.3i	1.36976	−	1.18052i
$428$		0			0
$429$	−13809.2	−	3987.51i	−1.55411	−	0.448762i
$430$		0			0
$431$	−2013.71	+	3487.85i	−0.225051	+	0.389800i	−0.956335	−	0.292273i	$-0.905588\pi$
$431$	−2013.71	+	3487.85i	−0.225051	+	0.389800i	0.731284	+	0.682074i	$0.238922\pi$
$432$		0			0
$433$	−11875.1			−1.31797			−0.658983	−	0.752158i	$-0.729013\pi$
$433$	−11875.1			−1.31797			−0.658983	+	0.752158i	$0.729013\pi$
$434$		0			0
$435$	−2429.74	+	2337.65i	−0.267809	+	0.257660i
$436$		0			0
$437$	3346.75			0.366354
$438$		0			0
$439$	2493.49			0.271088			0.135544	−	0.990771i	$-0.456722\pi$
$439$	2493.49			0.271088			0.135544	+	0.990771i	$0.456722\pi$
$440$		0			0
$441$	3060.74	+	8740.59i	0.330498	+	0.943807i
$442$		0			0
$443$	13073.9			1.40217			0.701085	−	0.713077i	$-0.252699\pi$
$443$	13073.9			1.40217			0.701085	+	0.713077i	$0.252699\pi$
$444$		0			0
$445$	1122.16			0.119540
$446$		0			0
$447$	12891.6	+	3722.56i	1.36410	+	0.393895i
$448$		0			0
$449$	8956.79			0.941419			0.470709	−	0.882288i	$-0.343998\pi$
$449$	8956.79			0.941419			0.470709	+	0.882288i	$0.343998\pi$
$450$		0			0
$451$	−7365.33	+	12757.1i	−0.769002	+	1.33195i
$452$		0			0
$453$	5371.19	−	5167.63i	0.557087	−	0.535975i
$454$		0			0
$455$	2050.67	−	1767.35i	0.211290	−	0.182098i
$456$		0			0
$457$	−8.97639			−0.000918814			−0.000459407	−	1.00000i	$-0.500146\pi$
$457$	−8.97639			−0.000918814			−0.000459407		1.00000i	$0.500146\pi$
$458$		0			0
$459$	3131.89	−	647.467i	0.318484	−	0.0658413i
$460$		0			0
$461$	1968.71	−	3409.91i	0.198898	−	0.344501i	−0.749273	−	0.662261i	$-0.769597\pi$
$461$	1968.71	−	3409.91i	0.198898	−	0.344501i	0.948171	+	0.317759i	$0.102930\pi$
$462$		0			0
$463$	−3458.23	−	5989.83i	−0.347122	−	0.601233i	0.638615	−	0.769527i	$-0.279508\pi$
$463$	−3458.23	−	5989.83i	−0.347122	−	0.601233i	−0.985737	+	0.168293i	$0.946174\pi$
$464$		0			0
$465$	−3588.67	−	1036.26i	−0.357894	−	0.103345i
$466$		0			0
$467$	−4313.45	−	7471.12i	−0.427415	−	0.740305i	0.569228	−	0.822180i	$-0.307242\pi$
$467$	−4313.45	−	7471.12i	−0.427415	−	0.740305i	−0.996643	+	0.0818755i	$0.973909\pi$
$468$		0			0
$469$	9861.03	−	8498.62i	0.970874	−	0.836737i
$470$		0			0
$471$	−3160.49	−	12777.2i	−0.309188	−	1.24998i
$472$		0			0
$473$	−23047.1			−2.24039
$474$		0			0
$475$	−1113.01	+	1927.79i	−0.107513	+	0.186217i
$476$		0			0
$477$	616.918	−	15963.9i	0.0592174	−	1.53237i
$478$		0			0
$479$	−888.832	−	1539.50i	−0.0847844	−	0.146851i	0.820515	−	0.571625i	$-0.193687\pi$
$479$	−888.832	−	1539.50i	−0.0847844	−	0.146851i	−0.905299	+	0.424774i	$0.860353\pi$
$480$		0			0
$481$	−4977.87	+	8621.92i	−0.471874	+	0.817309i
$482$		0			0
$483$	−15510.9	+	7117.65i	−1.46122	+	0.670527i
$484$		0			0
$485$	−770.278	−	1334.16i	−0.0721166	−	0.124910i
$486$		0			0
$487$	4201.56	−	7277.31i	0.390946	−	0.677138i	−0.601629	−	0.798776i	$-0.705481\pi$
$487$	4201.56	−	7277.31i	0.390946	−	0.677138i	0.992575	+	0.121638i	$0.0388146\pi$
$488$		0			0
$489$	6065.40	−	5835.54i	0.560914	−	0.539656i
$490$		0			0
$491$	552.959	+	957.753i	0.0508242	+	0.0880301i	0.890318	−	0.455339i	$-0.150482\pi$
$491$	552.959	+	957.753i	0.0508242	+	0.0880301i	−0.839494	+	0.543369i	$0.817149\pi$
$492$		0			0
$493$	−2786.07	−	4825.62i	−0.254520	−	0.440842i
$494$		0			0
$495$	3185.25	−	1678.47i	0.289225	−	0.152407i
$496$		0			0
$497$	−1393.24	+	1200.75i	−0.125745	+	0.108372i
$498$		0			0
$499$	−4314.20	+	7472.41i	−0.387034	+	0.670362i	−0.992049	−	0.125852i	$-0.959834\pi$
$499$	−4314.20	+	7472.41i	−0.387034	+	0.670362i	0.605015	+	0.796214i	$0.293167\pi$
$500$		0			0
$501$	−9469.69	+	9110.81i	−0.844461	+	0.812457i
$502$		0			0
$503$	−17866.1			−1.58372			−0.791860	−	0.610702i	$-0.790887\pi$
$503$	−17866.1			−1.58372			−0.791860	+	0.610702i	$0.790887\pi$
$504$		0			0
$505$	4956.70			0.436772
$506$		0			0
$507$	−4169.35	−	1203.93i	−0.365221	−	0.105461i
$508$		0			0
$509$	−2972.58	+	5148.65i	−0.258855	+	0.448350i	−0.965935	−	0.258783i	$-0.916678\pi$
$509$	−2972.58	+	5148.65i	−0.258855	+	0.448350i	0.707081	+	0.707133i	$0.250012\pi$
$510$		0			0
$511$	−3037.48	−	15989.7i	−0.262956	−	1.38423i
$512$		0			0
$513$	832.211	−	2513.49i	0.0716238	−	0.216322i
$514$		0			0
$515$	409.293	+	708.916i	0.0350206	+	0.0606574i
$516$		0			0
$517$	−8266.34	−	14317.7i	−0.703197	−	1.21797i
$518$		0			0
$519$	−977.987	−	3953.80i	−0.0827146	−	0.334398i
$520$		0			0
$521$	−4738.47	+	8207.27i	−0.398457	+	0.690148i	−0.993536	−	0.113519i	$-0.963788\pi$
$521$	−4738.47	+	8207.27i	−0.398457	+	0.690148i	0.595079	+	0.803668i	$0.297121\pi$
$522$		0			0
$523$	374.263	+	648.242i	0.0312913	+	0.0541982i	0.881247	−	0.472656i	$-0.156705\pi$
$523$	374.263	+	648.242i	0.0312913	+	0.0541982i	−0.849956	+	0.526854i	$0.823371\pi$
$524$		0			0
$525$	1058.47	−	11301.7i	0.0879915	−	0.939515i
$526$		0			0
$527$	3086.53	−	5346.02i	0.255126	−	0.441891i
$528$		0			0
$529$	−9640.97	−	16698.6i	−0.792387	−	1.37245i
$530$		0			0
$531$	−561.881	+	296.082i	−0.0459200	+	0.0241975i
$532$		0			0
$533$	−8073.66	+	13984.0i	−0.656115	+	1.13642i
$534$		0			0
$535$	−1233.85			−0.0997087
$536$		0			0
$537$	9765.92	+	2819.99i	0.784787	+	0.226614i
$538$		0			0
$539$	−16030.0	+	6318.30i	−1.28101	+	0.504914i
$540$		0			0
$541$	−120.414	−	208.562i	−0.00956928	−	0.0165745i	0.861201	−	0.508264i	$-0.169713\pi$
$541$	−120.414	−	208.562i	−0.00956928	−	0.0165745i	−0.870770	+	0.491690i	$0.836379\pi$
$542$		0			0
$543$	673.727	+	2723.73i	0.0532456	+	0.215261i
$544$		0			0
$545$	314.494	+	544.719i	0.0247182	+	0.0428132i
$546$		0			0
$547$	−6306.45	+	10923.1i	−0.492952	+	0.853817i	−0.999967	−	0.00811985i	$-0.997415\pi$
$547$	−6306.45	+	10923.1i	−0.492952	+	0.853817i	0.507016	+	0.861937i	$0.330749\pi$
$548$		0			0
$549$	20578.5	−	10843.8i	1.59976	−	0.842992i
$550$		0			0
$551$	−4613.10			−0.356669
$552$		0			0
$553$	−1596.81	+	1376.20i	−0.122791	+	0.105826i
$554$		0			0
$555$	−598.816	−	2420.89i	−0.0457988	−	0.185155i
$556$		0			0
$557$	−2294.88	+	3974.85i	−0.174573	+	0.302369i	−0.940013	−	0.341137i	$-0.889188\pi$
$557$	−2294.88	+	3974.85i	−0.174573	+	0.302369i	0.765440	+	0.643507i	$0.222521\pi$
$558$		0			0
$559$	−25263.5			−1.91151
$560$		0			0
$561$	1428.74	+	5776.10i	0.107525	+	0.434701i
$562$		0			0
$563$	7855.23			0.588026			0.294013	−	0.955801i	$-0.405009\pi$
$563$	7855.23			0.588026			0.294013	+	0.955801i	$0.405009\pi$
$564$		0			0
$565$	3388.48			0.252308
$566$		0			0
$567$	1488.56	+	13419.0i	0.110253	+	0.993904i
$568$		0			0
$569$	24205.7			1.78340			0.891702	−	0.452623i	$-0.149512\pi$
$569$	24205.7			1.78340			0.891702	+	0.452623i	$0.149512\pi$
$570$		0			0
$571$	−13181.8			−0.966096			−0.483048	−	0.875594i	$-0.660470\pi$
$571$	−13181.8			−0.966096			−0.483048	+	0.875594i	$0.660470\pi$
$572$		0			0
$573$	−3217.46	−	13007.5i	−0.234575	−	0.948336i
$574$		0			0
$575$	20917.7			1.51709
$576$		0			0
$577$	−7544.28	+	13067.1i	−0.544319	+	0.942789i	0.454330	+	0.890834i	$0.349879\pi$
$577$	−7544.28	+	13067.1i	−0.544319	+	0.942789i	−0.998649	+	0.0519555i	$0.983455\pi$
$578$		0			0
$579$	1178.88	+	4765.95i	0.0846156	+	0.342083i
$580$		0			0
$581$	−3109.16	−	16367.0i	−0.222013	−	1.16871i
$582$		0			0
$583$	29723.4			2.11153
$584$		0			0
$585$	3491.58	−	1839.88i	0.246768	−	0.130034i
$586$		0			0
$587$	−1693.92	+	2933.96i	−0.119107	+	0.206299i	−0.919414	−	0.393291i	$-0.871336\pi$
$587$	−1693.92	+	2933.96i	−0.119107	+	0.206299i	0.800307	+	0.599590i	$0.204670\pi$
$588$		0			0
$589$	−2555.29	−	4425.90i	−0.178759	−	0.309620i
$590$		0			0
$591$	−3653.48	−	14770.3i	−0.254288	−	1.02803i
$592$		0			0
$593$	8006.41	+	13867.5i	0.554441	+	0.960320i	0.997947	+	0.0640488i	$0.0204013\pi$
$593$	8006.41	+	13867.5i	0.554441	+	0.960320i	−0.443505	+	0.896272i	$0.646265\pi$
$594$		0			0
$595$	−1058.08	−	369.372i	−0.0729023	−	0.0254500i
$596$		0			0
$597$	−15380.2	−	4441.15i	−1.05439	−	0.304463i
$598$		0			0
$599$	22365.0			1.52556			0.762780	−	0.646659i	$-0.223834\pi$
$599$	22365.0			1.52556			0.762780	+	0.646659i	$0.223834\pi$
$600$		0			0
$601$	−4481.45	+	7762.10i	−0.304163	+	0.526827i	−0.977075	−	0.212897i	$-0.931710\pi$
$601$	−4481.45	+	7762.10i	−0.304163	+	0.526827i	0.672911	+	0.739723i	$0.265044\pi$
$602$		0			0
$603$	16789.9	−	8847.42i	1.13389	−	0.597504i
$604$		0			0
$605$	1582.73	+	2741.38i	0.106359	+	0.184219i
$606$		0			0
$607$	6193.01	−	10726.6i	0.414113	−	0.717264i	−0.581222	−	0.813745i	$-0.697425\pi$
$607$	6193.01	−	10726.6i	0.414113	−	0.717264i	0.995335	+	0.0964806i	$0.0307586\pi$
$608$		0			0
$609$	21380.0	−	9810.86i	1.42259	−	0.652801i
$610$		0			0
$611$	−9061.31	−	15694.7i	−0.599970	−	1.03918i
$612$		0			0
$613$	−2769.58	+	4797.06i	−0.182484	+	0.316071i	−0.942726	−	0.333569i	$-0.891747\pi$
$613$	−2769.58	+	4797.06i	−0.182484	+	0.316071i	0.760242	+	0.649640i	$0.225080\pi$
$614$		0			0
$615$	−971.227	−	3926.46i	−0.0636807	−	0.257448i
$616$		0			0
$617$	−6934.99	−	12011.8i	−0.452499	−	0.783752i	0.546041	−	0.837758i	$-0.316134\pi$
$617$	−6934.99	−	12011.8i	−0.452499	−	0.783752i	−0.998541	+	0.0540064i	$0.982801\pi$
$618$		0			0
$619$	−14724.0	−	25502.8i	−0.956073	−	1.65597i	−0.731893	−	0.681419i	$-0.761363\pi$
$619$	−14724.0	−	25502.8i	−0.956073	−	1.65597i	−0.224180	−	0.974548i	$-0.571970\pi$
$620$		0			0
$621$	−24364.7	+	5037.00i	−1.57443	+	0.325487i
$622$		0			0
$623$	−7391.61	−	2580.39i	−0.475343	−	0.165941i
$624$		0			0
$625$	−6516.08	+	11286.2i	−0.417029	+	0.722316i
$626$		0			0
$627$	4732.71	+	1366.61i	0.301445	+	0.0870449i
$628$		0			0
$629$	4121.41			0.261258
$630$		0			0
$631$	−9023.25			−0.569271			−0.284635	−	0.958636i	$-0.591873\pi$
$631$	−9023.25			−0.569271			−0.284635	+	0.958636i	$0.591873\pi$
$632$		0			0
$633$	−797.495	+	767.272i	−0.0500752	+	0.0481774i
$634$		0			0
$635$	−1137.39	+	1970.02i	−0.0710803	+	0.123115i
$636$		0			0
$637$	−17571.7	+	6925.94i	−1.09296	+	0.430794i
$638$		0			0
$639$	−2372.21	+	1250.03i	−0.146859	+	0.0773874i
$640$		0			0
$641$	13836.7	+	23965.9i	0.852600	+	1.47675i	0.878854	+	0.477092i	$0.158309\pi$
$641$	13836.7	+	23965.9i	0.852600	+	1.47675i	−0.0262533	+	0.999655i	$0.508358\pi$
$642$		0			0
$643$	−7763.03	−	13446.0i	−0.476118	−	0.824661i	0.523507	−	0.852021i	$-0.324623\pi$
$643$	−7763.03	−	13446.0i	−0.476118	−	0.824661i	−0.999626	+	0.0273600i	$0.991290\pi$
$644$		0			0
$645$	4560.40	−	4387.57i	0.278396	−	0.267846i
$646$		0			0
$647$	−3556.66	+	6160.31i	−0.216115	+	0.374323i	−0.953617	−	0.301023i	$-0.902672\pi$
$647$	−3556.66	+	6160.31i	−0.216115	+	0.374323i	0.737502	+	0.675345i	$0.236005\pi$
$648$		0			0
$649$	−590.826	−	1023.34i	−0.0357349	−	0.0618946i
$650$		0			0
$651$	21255.5	+	15077.9i	1.27968	+	0.907757i
$652$		0			0
$653$	7398.02	−	12813.8i	0.443349	−	0.767903i	−0.554586	−	0.832126i	$-0.687124\pi$
$653$	7398.02	−	12813.8i	0.443349	−	0.767903i	0.997936	+	0.0642229i	$0.0204569\pi$
$654$		0			0
$655$	−453.486	−	785.460i	−0.0270521	−	0.0468557i
$656$		0			0
$657$	916.260	−	23710.0i	0.0544090	−	1.40794i
$658$		0			0
$659$	4734.65	−	8200.66i	0.279872	−	0.484753i	−0.691480	−	0.722395i	$-0.743041\pi$
$659$	4734.65	−	8200.66i	0.279872	−	0.484753i	0.971353	+	0.237642i	$0.0763745\pi$
$660$		0			0
$661$	3121.87			0.183701			0.0918507	−	0.995773i	$-0.470722\pi$
$661$	3121.87			0.183701			0.0918507	+	0.995773i	$0.470722\pi$
$662$		0			0
$663$	1566.14	+	6331.59i	0.0917405	+	0.370888i
$664$		0			0
$665$	−702.811	+	605.710i	−0.0409832	+	0.0353209i
$666$		0			0
$667$	21674.4	+	37541.1i	1.25822	+	2.17931i
$668$		0			0
$669$	10398.3	+	3002.61i	0.600931	+	0.173524i
$670$		0			0
$671$	21638.6	+	37479.1i	1.24493	+	2.15628i
$672$		0			0
$673$	5461.17	−	9459.02i	0.312797	−	0.541781i	−0.666170	−	0.745800i	$-0.732067\pi$
$673$	5461.17	−	9459.02i	0.312797	−	0.541781i	0.978967	+	0.204020i	$0.0654006\pi$
$674$		0			0
$675$	5201.44	−	15709.7i	0.296598	−	0.895802i
$676$		0			0
$677$	−18908.5			−1.07343			−0.536715	−	0.843763i	$-0.680335\pi$
$677$	−18908.5			−1.07343			−0.536715	+	0.843763i	$0.680335\pi$
$678$		0			0
$679$	2005.90	+	10559.3i	0.113371	+	0.596802i
$680$		0			0
$681$	694.891	−	668.556i	0.0391018	−	0.0376199i
$682$		0			0
$683$	−4662.26	+	8075.27i	−0.261195	+	0.452404i	−0.966560	−	0.256441i	$-0.917450\pi$
$683$	−4662.26	+	8075.27i	−0.261195	+	0.452404i	0.705365	+	0.708845i	$0.250783\pi$
$684$		0			0
$685$	1781.24			0.0993541
$686$		0			0
$687$	26855.4	+	7754.72i	1.49141	+	0.430657i
$688$		0			0
$689$	32582.0			1.80156
$690$		0			0
$691$	19315.8			1.06340			0.531700	−	0.846933i	$-0.321553\pi$
$691$	19315.8			1.06340			0.531700	+	0.846933i	$0.321553\pi$
$692$		0			0
$693$	−24840.7	+	3731.52i	−1.36165	+	0.204543i
$694$		0			0
$695$	−908.398			−0.0495791
$696$		0			0
$697$	6684.56			0.363265
$698$		0			0
$699$	−10803.0	+	10393.6i	−0.584561	+	0.562407i
$700$		0			0
$701$	818.940			0.0441240			0.0220620	−	0.999757i	$-0.492977\pi$
$701$	818.940			0.0441240			0.0220620	+	0.999757i	$0.492977\pi$
$702$		0			0
$703$	1706.03	−	2954.93i	0.0915278	−	0.158531i
$704$		0			0
$705$	4361.41	+	1259.39i	0.232993	+	0.0672788i
$706$		0			0
$707$	−32649.5	−	11397.9i	−1.73679	−	0.606310i
$708$		0			0
$709$	−14118.1			−0.747838			−0.373919	−	0.927461i	$-0.621986\pi$
$709$	−14118.1			−0.747838			−0.373919	+	0.927461i	$0.621986\pi$
$710$		0			0
$711$	−2718.82	+	1432.68i	−0.143409	+	0.0755691i
$712$		0			0
$713$	−24011.8	+	41589.6i	−1.26122	+	2.18449i
$714$		0			0
$715$	3671.45	+	6359.13i	0.192034	+	0.332613i
$716$		0			0
$717$	16052.7	−	15444.3i	0.836121	−	0.804434i
$718$		0			0
$719$	5467.13	+	9469.35i	0.283574	+	0.491164i	0.972262	−	0.233893i	$-0.0751465\pi$
$719$	5467.13	+	9469.35i	0.283574	+	0.491164i	−0.688688	+	0.725057i	$0.741813\pi$
$720$		0			0
$721$	−1065.85	−	5610.76i	−0.0550544	−	0.289813i
$722$		0			0
$723$	−27568.5	+	26523.7i	−1.41810	+	1.36436i
$724$		0			0
$725$	−28832.6			−1.47699
$726$		0			0
$727$	−611.572	+	1059.27i	−0.0311994	+	0.0540389i	−0.881204	−	0.472737i	$-0.843266\pi$
$727$	−611.572	+	1059.27i	−0.0311994	+	0.0540389i	0.850004	+	0.526776i	$0.176599\pi$
$728$		0			0
$729$	−2275.68	+	19551.0i	−0.115617	+	0.993294i
$730$		0			0
$731$	5229.21	+	9057.26i	0.264582	+	0.458269i
$732$		0			0
$733$	−14526.4	+	25160.5i	−0.731987	+	1.26784i	0.224046	+	0.974579i	$0.428073\pi$
$733$	−14526.4	+	25160.5i	−0.731987	+	1.26784i	−0.956033	+	0.293260i	$0.905260\pi$
$734$		0			0
$735$	1969.08	−	4301.93i	0.0988169	−	0.215890i
$736$		0			0
$737$	17654.8	+	30579.1i	0.882394	+	1.52835i
$738$		0			0
$739$	15901.5	−	27542.2i	0.791538	−	1.37098i	−0.133476	−	0.991052i	$-0.542614\pi$
$739$	15901.5	−	27542.2i	0.791538	−	1.37098i	0.925014	−	0.379932i	$-0.124053\pi$
$740$		0			0
$741$	5187.86	+	1498.04i	0.257194	+	0.0742670i
$742$		0			0
$743$	12123.5	+	20998.5i	0.598612	+	1.03683i	0.993026	+	0.117893i	$0.0376141\pi$
$743$	12123.5	+	20998.5i	0.598612	+	1.03683i	−0.394414	+	0.918933i	$0.629053\pi$
$744$		0			0
$745$	−3427.50	−	5936.60i	−0.168555	−	0.291946i
$746$		0			0
$747$	937.880	−	24269.5i	0.0459374	−	1.18872i
$748$		0			0
$749$	8127.33	+	2837.23i	0.396484	+	0.138412i
$750$		0			0
$751$	−14458.7	+	25043.2i	−0.702537	+	1.21683i	0.265036	+	0.964238i	$0.414616\pi$
$751$	−14458.7	+	25043.2i	−0.702537	+	1.21683i	−0.967573	+	0.252591i	$0.918717\pi$
$752$		0			0
$753$	4824.48	+	19504.4i	0.233485	+	0.943929i
$754$		0			0
$755$	−3807.74			−0.183547
$756$		0			0
$757$	−14904.6			−0.715609			−0.357805	−	0.933797i	$-0.616475\pi$
$757$	−14904.6			−0.715609			−0.357805	+	0.933797i	$0.616475\pi$
$758$		0			0
$759$	−11114.9	−	44935.4i	−0.531551	−	2.14895i
$760$		0			0
$761$	−6508.36	+	11272.8i	−0.310023	+	0.536976i	−0.978367	−	0.206876i	$-0.933670\pi$
$761$	−6508.36	+	11272.8i	−0.310023	+	0.536976i	0.668344	+	0.743853i	$0.267004\pi$
$762$		0			0
$763$	−818.979	−	4311.21i	−0.0388585	−	0.204556i
$764$		0			0
$765$	−1382.33	−	870.939i	−0.0653310	−	0.0411619i
$766$		0			0
$767$	−647.646	−	1121.76i	−0.0304891	−	0.0528087i
$768$		0			0
$769$	−9233.89	−	15993.6i	−0.433007	−	0.749990i	0.564124	−	0.825690i	$-0.309214\pi$
$769$	−9233.89	−	15993.6i	−0.433007	−	0.749990i	−0.997131	+	0.0757002i	$0.975881\pi$
$770$		0			0
$771$	5137.62	+	1483.53i	0.239983	+	0.0692971i
$772$		0			0
$773$	19270.3	−	33377.1i	0.896643	−	1.55303i	0.0648840	−	0.997893i	$-0.479332\pi$
$773$	19270.3	−	33377.1i	0.896643	−	1.55303i	0.831759	−	0.555138i	$-0.187334\pi$
$774$		0			0
$775$	−15971.0	−	27662.5i	−0.740251	−	1.28215i
$776$		0			0
$777$	−1622.43	+	17323.2i	−0.0749091	+	0.799830i
$778$		0			0
$779$	2767.03	−	4792.63i	0.127264	−	0.220429i
$780$		0			0
$781$	−2494.41	−	4320.45i	−0.114286	−	0.197949i
$782$		0			0
$783$	33583.9	−	6942.91i	1.53281	−	0.316883i
$784$		0			0
$785$	−3362.10	+	5823.32i	−0.152864	+	0.264768i
$786$		0			0
$787$	−15675.8			−0.710016			−0.355008	−	0.934863i	$-0.615522\pi$
$787$	−15675.8			−0.710016			−0.355008	+	0.934863i	$0.615522\pi$
$788$		0			0
$789$	20470.4	−	19694.6i	0.923657	−	0.888653i
$790$		0			0
$791$	−22319.7	−	7791.76i	−1.00328	−	0.350244i
$792$		0			0
$793$	23719.6	+	41083.5i	1.06218	+	1.83975i
$794$		0			0
$795$	−5881.47	+	5658.58i	−0.262383	+	0.252439i
$796$		0			0
$797$	15019.1	+	26013.8i	0.667507	+	1.15616i	0.978599	+	0.205776i	$0.0659718\pi$
$797$	15019.1	+	26013.8i	0.667507	+	1.15616i	−0.311092	+	0.950380i	$0.600695\pi$
$798$		0			0
$799$	−3751.14	+	6497.17i	−0.166090	+	0.287676i
$800$		0			0
$801$	−9656.82	−	6084.30i	−0.425976	−	0.268387i
$802$		0			0
$803$	44145.9			1.94007
$804$		0			0
$805$	8231.34	+	2873.54i	0.360393	+	0.125812i
$806$		0			0
$807$	−585.989	−	169.209i	−0.0255611	−	0.00738098i
$808$		0			0
$809$	4850.45	−	8401.23i	0.210795	−	0.365107i	−0.741169	−	0.671319i	$-0.765728\pi$
$809$	4850.45	−	8401.23i	0.210795	−	0.365107i	0.951963	+	0.306212i	$0.0990615\pi$
$810$		0			0
$811$	−11458.4			−0.496128			−0.248064	−	0.968744i	$-0.579794\pi$
$811$	−11458.4			−0.496128			−0.248064	+	0.968744i	$0.579794\pi$
$812$		0			0
$813$	2564.67	−	2467.47i	0.110636	−	0.106443i
$814$		0			0
$815$	−4299.88			−0.184808
$816$		0			0
$817$	8658.38			0.370769
$818$		0			0
$819$	−27229.7	+	4090.38i	−1.16176	+	0.174517i
$820$		0			0
$821$	38394.8			1.63214			0.816071	−	0.577952i	$-0.196148\pi$
$821$	38394.8			1.63214			0.816071	+	0.577952i	$0.196148\pi$
$822$		0			0
$823$	−19080.5			−0.808147			−0.404074	−	0.914727i	$-0.632406\pi$
$823$	−19080.5			−0.808147			−0.404074	+	0.914727i	$0.632406\pi$
$824$		0			0
$825$	29580.1	+	8541.52i	1.24830	+	0.360458i
$826$		0			0
$827$	−35791.7			−1.50496			−0.752478	−	0.658617i	$-0.771142\pi$
$827$	−35791.7			−1.50496			−0.752478	+	0.658617i	$0.771142\pi$
$828$		0			0
$829$	4971.27	−	8610.49i	0.208274	−	0.360741i	−0.742897	−	0.669406i	$-0.766549\pi$
$829$	4971.27	−	8610.49i	0.208274	−	0.360741i	0.951171	+	0.308665i	$0.0998821\pi$
$830$		0			0
$831$	28843.1	−	27750.0i	1.20404	−	1.15841i
$832$		0			0
$833$	6120.12	+	4866.06i	0.254562	+	0.202400i
$834$		0			0
$835$	6713.26			0.278230
$836$		0			0
$837$	25264.0	+	28375.2i	1.04331	+	1.17179i
$838$		0			0
$839$	21203.3	−	36725.1i	0.872489	−	1.51120i	0.0130751	−	0.999915i	$-0.495838\pi$
$839$	21203.3	−	36725.1i	0.872489	−	1.51120i	0.859414	−	0.511281i	$-0.170829\pi$
$840$		0			0
$841$	−17681.1	−	30624.5i	−0.724962	−	1.25567i
$842$		0			0
$843$	16720.6	+	4828.21i	0.683140	+	0.197263i
$844$		0			0
$845$	1108.51	+	1919.99i	0.0451287	+	0.0781653i
$846$		0			0
$847$	−4121.63	−	21696.8i	−0.167203	−	0.880178i
$848$		0			0
$849$	2135.16	+	8631.99i	0.0863114	+	0.348939i
$850$		0			0
$851$	−32062.7			−1.29153
$852$		0			0
$853$	−21524.9	+	37282.1i	−0.864006	+	1.49650i	0.00402544	+	0.999992i	$0.498719\pi$
$853$	−21524.9	+	37282.1i	−0.864006	+	1.49650i	−0.868031	+	0.496510i	$0.834615\pi$
$854$		0			0
$855$	−1196.64	+	630.570i	−0.0478647	+	0.0252223i
$856$		0			0
$857$	−3728.16	−	6457.36i	−0.148602	−	0.257385i	0.782109	−	0.623141i	$-0.214144\pi$
$857$	−3728.16	−	6457.36i	−0.148602	−	0.257385i	−0.930711	+	0.365756i	$0.880811\pi$
$858$		0			0
$859$	5882.26	−	10188.4i	0.233644	−	0.404683i	−0.725234	−	0.688503i	$-0.758268\pi$
$859$	5882.26	−	10188.4i	0.233644	−	0.404683i	0.958878	+	0.283820i	$0.0916017\pi$
$860$		0			0
$861$	−2631.44	+	28096.8i	−0.104157	+	1.11212i
$862$		0			0
$863$	−7162.67	−	12406.1i	−0.282526	−	0.489349i	0.689480	−	0.724305i	$-0.257839\pi$
$863$	−7162.67	−	12406.1i	−0.282526	−	0.489349i	−0.972006	+	0.234955i	$0.924506\pi$
$864$		0			0
$865$	−1040.37	+	1801.98i	−0.0408945	+	0.0708314i
$866$		0			0
$867$	−16451.0	+	15827.5i	−0.644411	+	0.619989i
$868$		0			0
$869$	−2858.88	−	4951.72i	−0.111600	−	0.193298i
$870$		0			0
$871$	19352.7	+	33519.9i	0.752861	+	1.30399i
$872$		0			0
$873$	−605.080	+	15657.6i	−0.0234580	+	0.607022i
$874$		0			0
$875$	−9047.78	+	7797.72i	−0.349567	+	0.301270i
$876$		0			0
$877$	9767.65	−	16918.1i	0.376089	−	0.651406i	−0.614400	−	0.788994i	$-0.710602\pi$
$877$	9767.65	−	16918.1i	0.376089	−	0.651406i	0.990489	+	0.137589i	$0.0439353\pi$
$878$		0			0
$879$	3854.09	−	3708.03i	0.147890	−	0.142285i
$880$		0			0
$881$	−33904.6			−1.29656			−0.648282	−	0.761400i	$-0.724512\pi$
$881$	−33904.6			−1.29656			−0.648282	+	0.761400i	$0.724512\pi$
$882$		0			0
$883$	36120.5			1.37662			0.688309	−	0.725418i	$-0.258353\pi$
$883$	36120.5			1.37662			0.688309	+	0.725418i	$0.258353\pi$
$884$		0			0
$885$	311.726	+	90.0136i	0.0118402	+	0.00341895i
$886$		0			0
$887$	−11587.8	+	20070.7i	−0.438648	+	0.759760i	−0.997585	−	0.0694496i	$-0.977876\pi$
$887$	−11587.8	+	20070.7i	−0.438648	+	0.759760i	0.558938	+	0.829210i	$0.311209\pi$
$888$		0			0
$889$	12022.0	−	10361.0i	0.453548	−	0.390885i
$890$		0			0
$891$	−36511.5	−	2826.15i	−1.37282	−	0.106262i
$892$		0			0
$893$	3105.52	+	5378.91i	0.116374	+	0.201566i
$894$		0			0
$895$	−2596.47	−	4497.22i	−0.0969726	−	0.167961i
$896$		0			0
$897$	−12183.9	−	49256.8i	−0.453520	−	1.83349i
$898$		0			0
$899$	33097.4	−	57326.5i	1.22788	−	2.12675i
$900$		0			0
$901$	−6744.03	−	11681.0i	−0.249363	−	0.431910i
$902$		0			0
$903$	−40128.3	+	18414.1i	−1.47883	+	0.678608i
$904$		0			0
$905$	716.704	−	1241.37i	0.0263249	−	0.0455961i
$906$		0			0
$907$	−9691.72	−	16786.6i	−0.354805	−	0.614541i	0.632279	−	0.774741i	$-0.282120\pi$
$907$	−9691.72	−	16786.6i	−0.354805	−	0.614541i	−0.987085	+	0.160200i	$0.948786\pi$
$908$		0			0
$909$	−42655.2	−	26875.0i	−1.55642	−	0.980624i
$910$		0			0
$911$	7505.75	−	13000.3i	0.272971	−	0.472800i	−0.696650	−	0.717411i	$-0.745327\pi$
$911$	7505.75	−	13000.3i	0.272971	−	0.472800i	0.969621	+	0.244611i	$0.0786603\pi$
$912$		0			0
$913$	45187.6			1.63800
$914$		0			0
$915$	−11416.8	−	3296.69i	−0.412488	−	0.119109i
$916$		0			0
$917$	1180.93	+	6216.57i	0.0425276	+	0.223871i
$918$		0			0
$919$	18580.9	+	32183.1i	0.666952	+	1.15519i	0.978752	+	0.205047i	$0.0657347\pi$
$919$	18580.9	+	32183.1i	0.666952	+	1.15519i	−0.311800	+	0.950148i	$0.600932\pi$
$920$		0			0
$921$	2909.00	+	11760.5i	0.104077	+	0.420760i
$922$		0			0
$923$	−2734.30	−	4735.95i	−0.0975088	−	0.168890i
$924$		0			0
$925$	10662.9	−	18468.7i	0.379022	−	0.656485i
$926$		0			0
$927$	321.514	−	8319.79i	0.0113915	−	0.294776i
$928$		0			0
$929$	−15324.7			−0.541214			−0.270607	−	0.962690i	$-0.587224\pi$
$929$	−15324.7			−0.541214			−0.270607	+	0.962690i	$0.587224\pi$
$930$		0			0
$931$	6022.21	−	2373.67i	0.211998	−	0.0835597i
$932$		0			0
$933$	4193.48	+	16953.3i	0.147147	+	0.594885i
$934$		0			0
$935$	1519.88	−	2632.51i	0.0531609	−	0.0920773i
$936$		0			0
$937$	−38196.4			−1.33172			−0.665860	−	0.746076i	$-0.731935\pi$
$937$	−38196.4			−1.33172			−0.665860	+	0.746076i	$0.731935\pi$
$938$		0			0
$939$	−8500.17	−	34364.4i	−0.295413	−	1.19429i
$940$		0			0
$941$	−13868.2			−0.480436			−0.240218	−	0.970719i	$-0.577219\pi$
$941$	−13868.2			−0.480436			−0.240218	+	0.970719i	$0.577219\pi$
$942$		0			0
$943$	−52002.8			−1.79580
$944$		0			0
$945$	4204.93	−	5467.40i	0.144747	−	0.188206i
$946$		0			0
$947$	26113.2			0.896054			0.448027	−	0.894020i	$-0.352127\pi$
$947$	26113.2			0.896054			0.448027	+	0.894020i	$0.352127\pi$
$948$		0			0
$949$	48391.4			1.65527
$950$		0			0
$951$	−12310.4	−	49768.4i	−0.419761	−	1.69700i
$952$		0			0
$953$	−2160.15			−0.0734250			−0.0367125	−	0.999326i	$-0.511689\pi$
$953$	−2160.15			−0.0734250			−0.0367125	+	0.999326i	$0.511689\pi$
$954$		0			0
$955$	−3422.70	+	5928.29i	−0.115975	+	0.200874i
$956$		0			0
$957$	15320.7	+	61938.2i	0.517499	+	2.09214i
$958$		0			0
$959$	−11732.9	−	4095.93i	−0.395074	−	0.137919i
$960$		0			0
$961$	43542.5			1.46160
$962$		0			0
$963$	10618.0	+	6689.90i	0.355307	+	0.223862i
$964$		0			0
$965$	1254.08	−	2172.13i	0.0418344	−	0.0724593i
$966$		0			0
$967$	5182.84	+	8976.94i	0.172357	+	0.298530i	0.939243	−	0.343252i	$-0.111529\pi$
$967$	5182.84	+	8976.94i	0.172357	+	0.298530i	−0.766887	+	0.641783i	$0.778195\pi$
$968$		0			0
$969$	−536.753	−	2169.98i	−0.0177946	−	0.0719399i
$970$		0			0
$971$	−19438.0	−	33667.5i	−0.642424	−	1.11271i	−0.984890	−	0.173181i	$-0.944596\pi$
$971$	−19438.0	−	33667.5i	−0.642424	−	1.11271i	0.342466	−	0.939530i	$-0.388738\pi$
$972$		0			0
$973$	5983.57	+	2088.85i	0.197147	+	0.0688237i
$974$		0			0
$975$	32424.9	+	9362.97i	1.06505	+	0.307543i
$976$		0			0
$977$	−47144.9			−1.54381			−0.771904	−	0.635739i	$-0.780695\pi$
$977$	−47144.9			−1.54381			−0.771904	+	0.635739i	$0.780695\pi$
$978$		0			0
$979$	10617.7	−	18390.5i	0.346624	−	0.600370i
$980$		0			0
$981$	247.046	−	6392.79i	0.00804033	−	0.208059i
$982$		0			0
$983$	7125.92	+	12342.4i	0.231212	+	0.400471i	0.958165	−	0.286216i	$-0.0923976\pi$
$983$	7125.92	+	12342.4i	0.231212	+	0.400471i	−0.726953	+	0.686687i	$0.759064\pi$
$984$		0			0
$985$	−3886.54	+	6731.68i	−0.125721	+	0.217756i
$986$		0			0
$987$	−25832.4	−	18324.6i	−0.833085	−	0.590960i
$988$		0			0
$989$	−40680.9	−	70461.3i	−1.30796	−	2.26546i
$990$		0			0
$991$	−7038.13	+	12190.4i	−0.225604	+	0.390758i	−0.956500	−	0.291731i	$-0.905769\pi$
$991$	−7038.13	+	12190.4i	−0.225604	+	0.390758i	0.730896	+	0.682488i	$0.239102\pi$
$992$		0			0
$993$	410.936	+	1661.33i	0.0131326	+	0.0530922i
$994$		0			0
$995$	4089.13	+	7082.59i	0.130286	+	0.225661i
$996$		0			0
$997$	−6886.69	−	11928.1i	−0.218760	−	0.378903i	0.735669	−	0.677341i	$-0.236868\pi$
$997$	−6886.69	−	11928.1i	−0.218760	−	0.378903i	−0.954429	+	0.298438i	$0.903534\pi$
$998$		0			0
$999$	−7972.79	+	24079.9i	−0.252500	+	0.762615i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.i.a.25.14	✓	48
3.2	odd	2		756.4.i.a.613.12		48
7.2	even	3		252.4.l.a.205.3	yes	48
9.4	even	3		252.4.l.a.193.3	yes	48
9.5	odd	6		756.4.l.a.361.13		48
21.2	odd	6		756.4.l.a.289.13		48
63.23	odd	6		756.4.i.a.37.12		48
63.58	even	3	inner	252.4.i.a.121.14	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.i.a.25.14	✓	48	1.1	even	1	trivial
252.4.i.a.121.14	yes	48	63.58	even	3	inner
252.4.l.a.193.3	yes	48	9.4	even	3
252.4.l.a.205.3	yes	48	7.2	even	3
756.4.i.a.37.12		48	63.23	odd	6
756.4.i.a.613.12		48	3.2	odd	2
756.4.l.a.289.13		48	21.2	odd	6
756.4.l.a.361.13		48	9.5	odd	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.24769 + 5.04413i) q^{3} +(1.32728 - 2.29891i) q^{5} +(-14.0290 + 12.0908i) q^{7} +(-23.8866 + 12.5870i) q^{9} +O(q^{10})\)	\(q+(1.24769 + 5.04413i) q^{3} +(1.32728 - 2.29891i) q^{5} +(-14.0290 + 12.0908i) q^{7} +(-23.8866 + 12.5870i) q^{9} +(-25.1171 - 43.5040i) q^{11} +(-27.5326 - 47.6878i) q^{13} +(13.2520 + 3.82664i) q^{15} +(-11.3977 + 19.7415i) q^{17} +(9.43604 + 16.3437i) q^{19} +(-78.4912 - 55.6788i) q^{21} +(88.6692 - 153.580i) q^{23} +(58.9767 + 102.151i) q^{25} +(-93.2934 - 104.782i) q^{27} +(-122.220 + 211.692i) q^{29} -270.802 q^{31} +(188.102 - 180.973i) q^{33} +(9.17517 + 48.2993i) q^{35} +(-90.3996 - 156.577i) q^{37} +(206.192 - 198.378i) q^{39} +(-146.620 - 253.954i) q^{41} +(229.397 - 397.327i) q^{43} +(-2.76770 + 71.6195i) q^{45} +329.112 q^{47} +(50.6273 - 339.243i) q^{49} +(-113.799 - 32.8606i) q^{51} +(-295.849 + 512.426i) q^{53} -133.349 q^{55} +(-70.6666 + 67.9885i) q^{57} +23.5229 q^{59} -861.509 q^{61} +(182.919 - 465.390i) q^{63} -146.173 q^{65} -702.902 q^{67} +(885.308 + 255.640i) q^{69} +99.3115 q^{71} +(-439.402 + 761.066i) q^{73} +(-441.677 + 424.938i) q^{75} +(878.365 + 306.635i) q^{77} +113.822 q^{79} +(412.135 - 601.320i) q^{81} +(-449.770 + 779.024i) q^{83} +(30.2559 + 52.4048i) q^{85} +(-1220.29 - 352.370i) q^{87} +(211.365 + 366.095i) q^{89} +(962.837 + 336.124i) q^{91} +(-337.875 - 1365.96i) q^{93} +50.0969 q^{95} +(290.172 - 502.593i) q^{97} +(1147.55 + 723.013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9}+O(q^{10}) \) 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9	\( 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9} + 4 q^{11} - 12 q^{13} - 26 q^{15} + 112 q^{17} + 60 q^{19} - 80 q^{21} + 10 q^{23} - 600 q^{25} + 194 q^{29} + 60 q^{31} - 472 q^{33} + 394 q^{35} - 84 q^{37} + 604 q^{39} + 210 q^{41} + 42 q^{43} + 254 q^{45} - 132 q^{47} - 78 q^{49} - 58 q^{51} - 468 q^{53} + 612 q^{55} + 1476 q^{57} - 916 q^{59} - 804 q^{61} - 444 q^{63} + 1656 q^{65} - 588 q^{67} - 28 q^{69} - 2228 q^{71} - 336 q^{73} - 668 q^{75} - 1216 q^{77} - 768 q^{79} - 104 q^{81} + 1024 q^{83} + 360 q^{85} + 2188 q^{87} + 2922 q^{89} - 120 q^{91} - 1292 q^{93} + 2428 q^{95} - 264 q^{97} - 2246 q^{99}+O(q^{100}) \) 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9 + 4 * q^11 - 12 * q^13 - 26 * q^15 + 112 * q^17 + 60 * q^19 - 80 * q^21 + 10 * q^23 - 600 * q^25 + 194 * q^29 + 60 * q^31 - 472 * q^33 + 394 * q^35 - 84 * q^37 + 604 * q^39 + 210 * q^41 + 42 * q^43 + 254 * q^45 - 132 * q^47 - 78 * q^49 - 58 * q^51 - 468 * q^53 + 612 * q^55 + 1476 * q^57 - 916 * q^59 - 804 * q^61 - 444 * q^63 + 1656 * q^65 - 588 * q^67 - 28 * q^69 - 2228 * q^71 - 336 * q^73 - 668 * q^75 - 1216 * q^77 - 768 * q^79 - 104 * q^81 + 1024 * q^83 + 360 * q^85 + 2188 * q^87 + 2922 * q^89 - 120 * q^91 - 1292 * q^93 + 2428 * q^95 - 264 * q^97 - 2246 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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