LMFDB - Embedded newform 483.3.g.a.139.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,3,Mod(139,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("483.139");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	483.g (of order $2$, degree $1$, 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:	$13.1607967686$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.13
Character	$\chi$	$=$	483.139
Dual form			483.3.g.a.139.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51134 q^{2} -1.73205i q^{3} +2.30684 q^{4} +3.95129i q^{5} +4.34977i q^{6} +(-0.923197 + 6.93885i) q^{7} +4.25211 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-2.51134 q^{2} -1.73205i q^{3} +2.30684 q^{4} +3.95129i q^{5} +4.34977i q^{6} +(-0.923197 + 6.93885i) q^{7} +4.25211 q^{8} -3.00000 q^{9} -9.92304i q^{10} -1.52434 q^{11} -3.99556i q^{12} +14.7191i q^{13} +(2.31846 - 17.4258i) q^{14} +6.84383 q^{15} -19.9059 q^{16} +25.6157i q^{17} +7.53402 q^{18} -37.5521i q^{19} +9.11498i q^{20} +(12.0184 + 1.59902i) q^{21} +3.82813 q^{22} -4.79583 q^{23} -7.36487i q^{24} +9.38731 q^{25} -36.9646i q^{26} +5.19615i q^{27} +(-2.12966 + 16.0068i) q^{28} -20.7881 q^{29} -17.1872 q^{30} -56.7969i q^{31} +32.9819 q^{32} +2.64023i q^{33} -64.3297i q^{34} +(-27.4174 - 3.64782i) q^{35} -6.92051 q^{36} +14.5290 q^{37} +94.3061i q^{38} +25.4942 q^{39} +16.8013i q^{40} +60.4976i q^{41} +(-30.1824 - 4.01569i) q^{42} -53.3930 q^{43} -3.51640 q^{44} -11.8539i q^{45} +12.0440 q^{46} -1.24072i q^{47} +34.4779i q^{48} +(-47.2954 - 12.8119i) q^{49} -23.5747 q^{50} +44.3676 q^{51} +33.9545i q^{52} -8.08820 q^{53} -13.0493i q^{54} -6.02310i q^{55} +(-3.92554 + 29.5048i) q^{56} -65.0421 q^{57} +52.2059 q^{58} +7.22892i q^{59} +15.7876 q^{60} +48.4751i q^{61} +142.636i q^{62} +(2.76959 - 20.8166i) q^{63} -3.20552 q^{64} -58.1593 q^{65} -6.63052i q^{66} -105.908 q^{67} +59.0911i q^{68} +8.30662i q^{69} +(68.8545 + 9.16092i) q^{70} -106.028 q^{71} -12.7563 q^{72} -46.7365i q^{73} -36.4873 q^{74} -16.2593i q^{75} -86.6265i q^{76} +(1.40726 - 10.5772i) q^{77} -64.0246 q^{78} -85.8854 q^{79} -78.6538i q^{80} +9.00000 q^{81} -151.930i q^{82} +79.5126i q^{83} +(27.7246 + 3.68869i) q^{84} -101.215 q^{85} +134.088 q^{86} +36.0060i q^{87} -6.48166 q^{88} -117.970i q^{89} +29.7691i q^{90} +(-102.134 - 13.5886i) q^{91} -11.0632 q^{92} -98.3751 q^{93} +3.11588i q^{94} +148.379 q^{95} -57.1264i q^{96} -36.5184i q^{97} +(118.775 + 32.1750i) q^{98} +4.57301 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9}+O(q^{10}) $ 60 * q + 128 * q^4 - 16 * q^7 + 24 * q^8 - 180 * q^9	$ 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9} + 28 q^{14} - 48 q^{15} + 192 q^{16} + 48 q^{21} - 8 q^{22} - 292 q^{25} - 128 q^{28} + 136 q^{29} + 96 q^{32} - 88 q^{35} - 384 q^{36} - 200 q^{37} + 48 q^{39} - 60 q^{42} + 72 q^{43} + 352 q^{44} + 132 q^{49} - 376 q^{50} - 112 q^{53} + 260 q^{56} - 240 q^{57} + 32 q^{58} - 216 q^{60} + 48 q^{63} + 536 q^{64} - 8 q^{65} - 408 q^{67} - 112 q^{70} + 456 q^{71} - 72 q^{72} - 120 q^{74} + 104 q^{77} + 48 q^{78} + 192 q^{79} + 540 q^{81} + 24 q^{84} + 488 q^{85} + 72 q^{86} + 432 q^{88} + 88 q^{91} + 48 q^{93} + 880 q^{95} - 16 q^{98}+O(q^{100}) $ 60 * q + 128 * q^4 - 16 * q^7 + 24 * q^8 - 180 * q^9 + 28 * q^14 - 48 * q^15 + 192 * q^16 + 48 * q^21 - 8 * q^22 - 292 * q^25 - 128 * q^28 + 136 * q^29 + 96 * q^32 - 88 * q^35 - 384 * q^36 - 200 * q^37 + 48 * q^39 - 60 * q^42 + 72 * q^43 + 352 * q^44 + 132 * q^49 - 376 * q^50 - 112 * q^53 + 260 * q^56 - 240 * q^57 + 32 * q^58 - 216 * q^60 + 48 * q^63 + 536 * q^64 - 8 * q^65 - 408 * q^67 - 112 * q^70 + 456 * q^71 - 72 * q^72 - 120 * q^74 + 104 * q^77 + 48 * q^78 + 192 * q^79 + 540 * q^81 + 24 * q^84 + 488 * q^85 + 72 * q^86 + 432 * q^88 + 88 * q^91 + 48 * q^93 + 880 * q^95 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−2.51134			−1.25567			−0.627835	−	0.778346i	$-0.716059\pi$
$2$	−2.51134			−1.25567			−0.627835	+	0.778346i	$0.716059\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	2.30684			0.576709
$5$			3.95129i			0.790258i	0.918626	+	0.395129i	$0.129300\pi$
$5$			3.95129i			0.790258i	−0.918626	+	0.395129i	$0.870700\pi$
$6$			4.34977i			0.724962i
$7$	−0.923197	+	6.93885i	−0.131885	+	0.991265i
$7$	−0.923197	+	6.93885i	−0.131885	+	0.991265i
$8$	4.25211			0.531514
$9$	−3.00000			−0.333333
$10$		−	9.92304i		−	0.992304i
$11$	−1.52434			−0.138576			−0.0692881	−	0.997597i	$-0.522073\pi$
$11$	−1.52434			−0.138576			−0.0692881	+	0.997597i	$0.522073\pi$
$12$		−	3.99556i		−	0.332963i
$13$			14.7191i			1.13224i	0.824324	+	0.566118i	$0.191556\pi$
$13$			14.7191i			1.13224i	−0.824324	+	0.566118i	$0.808444\pi$
$14$	2.31846	−	17.4258i	0.165604	−	1.24470i
$15$	6.84383			0.456256
$16$	−19.9059			−1.24412
$17$			25.6157i			1.50680i	0.657561	+	0.753402i	$0.271588\pi$
$17$			25.6157i			1.50680i	−0.657561	+	0.753402i	$0.728412\pi$
$18$	7.53402			0.418557
$19$		−	37.5521i		−	1.97643i	−0.153084	−	0.988213i	$-0.548921\pi$
$19$		−	37.5521i		−	1.97643i	0.153084	−	0.988213i	$-0.451079\pi$
$20$			9.11498i			0.455749i
$21$	12.0184	+	1.59902i	0.572307	+	0.0761440i
$22$	3.82813			0.174006
$23$	−4.79583			−0.208514
$23$	−4.79583			−0.208514
$24$		−	7.36487i		−	0.306870i
$25$	9.38731			0.375492
$26$		−	36.9646i		−	1.42172i
$27$			5.19615i			0.192450i
$28$	−2.12966	+	16.0068i	−0.0760594	+	0.571672i
$29$	−20.7881			−0.716830			−0.358415	−	0.933562i	$-0.616683\pi$
$29$	−20.7881			−0.716830			−0.358415	+	0.933562i	$0.616683\pi$
$30$	−17.1872			−0.572907
$31$		−	56.7969i		−	1.83216i	−0.400998	−	0.916079i	$-0.631337\pi$
$31$		−	56.7969i		−	1.83216i	0.400998	−	0.916079i	$-0.368663\pi$
$32$	32.9819			1.03069
$33$			2.64023i			0.0800070i
$34$		−	64.3297i		−	1.89205i
$35$	−27.4174	−	3.64782i	−0.783355	−	0.104223i
$36$	−6.92051			−0.192236
$37$	14.5290			0.392676			0.196338	−	0.980536i	$-0.437095\pi$
$37$	14.5290			0.392676			0.196338	+	0.980536i	$0.437095\pi$
$38$			94.3061i			2.48174i
$39$	25.4942			0.653697
$40$			16.8013i			0.420033i
$41$			60.4976i			1.47555i	0.675045	+	0.737776i	$0.264124\pi$
$41$			60.4976i			1.47555i	−0.675045	+	0.737776i	$0.735876\pi$
$42$	−30.1824	−	4.01569i	−0.718629	−	0.0956118i
$43$	−53.3930			−1.24170			−0.620848	−	0.783931i	$-0.713212\pi$
$43$	−53.3930			−1.24170			−0.620848	+	0.783931i	$0.713212\pi$
$44$	−3.51640			−0.0799181
$45$		−	11.8539i		−	0.263419i
$46$	12.0440			0.261825
$47$		−	1.24072i		−	0.0263983i	−0.999913	−	0.0131992i	$-0.995798\pi$
$47$		−	1.24072i		−	0.0263983i	0.999913	−	0.0131992i	$-0.00420155\pi$
$48$			34.4779i			0.718291i
$49$	−47.2954	−	12.8119i	−0.965213	−	0.261466i
$50$	−23.5747			−0.471495
$51$	44.3676			0.869953
$52$			33.9545i			0.652971i
$53$	−8.08820			−0.152608			−0.0763038	−	0.997085i	$-0.524312\pi$
$53$	−8.08820			−0.152608			−0.0763038	+	0.997085i	$0.524312\pi$
$54$		−	13.0493i		−	0.241654i
$55$		−	6.02310i		−	0.109511i
$56$	−3.92554	+	29.5048i	−0.0700989	+	0.526871i
$57$	−65.0421			−1.14109
$58$	52.2059			0.900102
$59$			7.22892i			0.122524i	0.998122	+	0.0612621i	$0.0195125\pi$
$59$			7.22892i			0.122524i	−0.998122	+	0.0612621i	$0.980487\pi$
$60$	15.7876			0.263127
$61$			48.4751i			0.794675i	0.917673	+	0.397337i	$0.130066\pi$
$61$			48.4751i			0.794675i	−0.917673	+	0.397337i	$0.869934\pi$
$62$			142.636i			2.30059i
$63$	2.76959	−	20.8166i	0.0439618	−	0.330422i
$64$	−3.20552			−0.0500862
$65$	−58.1593			−0.894759
$66$		−	6.63052i		−	0.100462i
$67$	−105.908			−1.58071			−0.790355	−	0.612649i	$-0.790104\pi$
$67$	−105.908			−1.58071			−0.790355	+	0.612649i	$0.790104\pi$
$68$			59.0911i			0.868987i
$69$			8.30662i			0.120386i
$70$	68.8545	+	9.16092i	0.983636	+	0.130870i
$71$	−106.028			−1.49336			−0.746678	−	0.665185i	$-0.768352\pi$
$71$	−106.028			−1.49336			−0.746678	+	0.665185i	$0.768352\pi$
$72$	−12.7563			−0.177171
$73$		−	46.7365i		−	0.640226i	−0.947379	−	0.320113i	$-0.896279\pi$
$73$		−	46.7365i		−	0.640226i	0.947379	−	0.320113i	$-0.103721\pi$
$74$	−36.4873			−0.493072
$75$		−	16.2593i		−	0.216791i
$76$		−	86.6265i		−	1.13982i
$77$	1.40726	−	10.5772i	0.0182762	−	0.137366i
$78$	−64.0246			−0.820829
$79$	−85.8854			−1.08716			−0.543579	−	0.839358i	$-0.682931\pi$
$79$	−85.8854			−1.08716			−0.543579	+	0.839358i	$0.682931\pi$
$80$		−	78.6538i		−	0.983172i
$81$	9.00000			0.111111
$82$		−	151.930i		−	1.85281i
$83$			79.5126i			0.957983i	0.877819	+	0.478992i	$0.158998\pi$
$83$			79.5126i			0.957983i	−0.877819	+	0.478992i	$0.841002\pi$
$84$	27.7246	+	3.68869i	0.330055	+	0.0439129i
$85$	−101.215			−1.19076
$86$	134.088			1.55916
$87$			36.0060i			0.413862i
$88$	−6.48166			−0.0736552
$89$		−	117.970i		−	1.32551i	−0.748837	−	0.662754i	$-0.769388\pi$
$89$		−	117.970i		−	1.32551i	0.748837	−	0.662754i	$-0.230612\pi$
$90$			29.7691i			0.330768i
$91$	−102.134	−	13.5886i	−1.12235	−	0.149325i
$92$	−11.0632			−0.120252
$93$	−98.3751			−1.05780
$94$			3.11588i			0.0331476i
$95$	148.379			1.56189
$96$		−	57.1264i		−	0.595067i
$97$		−	36.5184i		−	0.376478i	−0.982123	−	0.188239i	$-0.939722\pi$
$97$		−	36.5184i		−	0.376478i	0.982123	−	0.188239i	$-0.0602780\pi$
$98$	118.775	+	32.1750i	1.21199	+	0.328316i
$99$	4.57301			0.0461921
$100$	21.6550			0.216550
$101$			39.9050i			0.395099i	0.980293	+	0.197550i	$0.0632983\pi$
$101$			39.9050i			0.395099i	−0.980293	+	0.197550i	$0.936702\pi$
$102$	−111.422			−1.09237
$103$			3.80662i			0.0369575i	0.999829	+	0.0184787i	$0.00588230\pi$
$103$			3.80662i			0.0369575i	−0.999829	+	0.0184787i	$0.994118\pi$
$104$			62.5872i			0.601800i
$105$	−6.31821	+	47.4884i	−0.0601734	+	0.452270i
$106$	20.3122			0.191625
$107$	−99.2041			−0.927141			−0.463571	−	0.886060i	$-0.653432\pi$
$107$	−99.2041			−0.927141			−0.463571	+	0.886060i	$0.653432\pi$
$108$			11.9867i			0.110988i
$109$	−31.4821			−0.288827			−0.144413	−	0.989517i	$-0.546130\pi$
$109$	−31.4821			−0.288827			−0.144413	+	0.989517i	$0.546130\pi$
$110$			15.1261i			0.137510i
$111$		−	25.1650i		−	0.226712i
$112$	18.3770	−	138.124i	0.164081	−	1.23325i
$113$	185.393			1.64065			0.820323	−	0.571901i	$-0.193794\pi$
$113$	185.393			1.64065			0.820323	+	0.571901i	$0.193794\pi$
$114$	163.343			1.43283
$115$		−	18.9497i		−	0.164780i
$116$	−47.9547			−0.413402
$117$		−	44.1572i		−	0.377412i
$118$		−	18.1543i		−	0.153850i
$119$	−177.743	−	23.6483i	−1.49364	−	0.198725i
$120$	29.1008			0.242506
$121$	−118.676			−0.980797
$122$		−	121.738i		−	0.997850i
$123$	104.785			0.851911
$124$		−	131.021i		−	1.05662i
$125$			135.874i			1.08699i
$126$	−6.95539	+	52.2775i	−0.0552015	+	0.414901i
$127$	152.426			1.20021			0.600103	−	0.799922i	$-0.295126\pi$
$127$	152.426			1.20021			0.600103	+	0.799922i	$0.295126\pi$
$128$	−123.878			−0.967794
$129$			92.4793i			0.716894i
$130$	146.058			1.12352
$131$			15.7956i			0.120577i	0.998181	+	0.0602886i	$0.0192021\pi$
$131$			15.7956i			0.120577i	−0.998181	+	0.0602886i	$0.980798\pi$
$132$			6.09058i			0.0461408i
$133$	260.569	+	34.6680i	1.95916	+	0.260661i
$134$	265.970			1.98485
$135$	−20.5315			−0.152085
$136$			108.921i			0.800887i
$137$	−203.637			−1.48640			−0.743200	−	0.669069i	$-0.766693\pi$
$137$	−203.637			−1.48640			−0.743200	+	0.669069i	$0.766693\pi$
$138$		−	20.8608i		−	0.151165i
$139$			144.597i			1.04027i	0.854085	+	0.520134i	$0.174118\pi$
$139$			144.597i			1.04027i	−0.854085	+	0.520134i	$0.825882\pi$
$140$	−63.2475	−	8.41492i	−0.451768	−	0.0601066i
$141$	−2.14899			−0.0152411
$142$	266.273			1.87516
$143$		−	22.4369i		−	0.156901i
$144$	59.7176			0.414705
$145$		−	82.1397i		−	0.566480i
$146$			117.371i			0.803913i
$147$	−22.1908	+	81.9181i	−0.150958	+	0.557266i
$148$	33.5161			0.226460
$149$	66.3083			0.445022			0.222511	−	0.974930i	$-0.428575\pi$
$149$	66.3083			0.445022			0.222511	+	0.974930i	$0.428575\pi$
$150$			40.8326i			0.272218i
$151$	47.9656			0.317653			0.158826	−	0.987307i	$-0.449229\pi$
$151$	47.9656			0.317653			0.158826	+	0.987307i	$0.449229\pi$
$152$		−	159.676i		−	1.05050i
$153$		−	76.8470i		−	0.502268i
$154$	−3.53412	+	26.5629i	−0.0229488	+	0.172486i
$155$	224.421			1.44788
$156$	58.8109			0.376993
$157$		−	252.632i		−	1.60912i	−0.593873	−	0.804559i	$-0.702402\pi$
$157$		−	252.632i		−	1.60912i	0.593873	−	0.804559i	$-0.297598\pi$
$158$	215.688			1.36511
$159$			14.0092i			0.0881080i
$160$			130.321i			0.814508i
$161$	4.42750	−	33.2776i	0.0275000	−	0.206693i
$162$	−22.6021			−0.139519
$163$	152.444			0.935240			0.467620	−	0.883930i	$-0.345112\pi$
$163$	152.444			0.935240			0.467620	+	0.883930i	$0.345112\pi$
$164$			139.558i			0.850964i
$165$	−10.4323			−0.0632262
$166$		−	199.683i		−	1.20291i
$167$		−	120.341i		−	0.720602i	−0.932836	−	0.360301i	$-0.882674\pi$
$167$		−	120.341i		−	0.720602i	0.932836	−	0.360301i	$-0.117326\pi$
$168$	51.1038	+	6.79923i	0.304189	+	0.0404716i
$169$	−47.6513			−0.281960
$170$	254.185			1.49521
$171$			112.656i			0.658809i
$172$	−123.169			−0.716098
$173$		−	292.218i		−	1.68912i	−0.535459	−	0.844561i	$-0.679861\pi$
$173$		−	292.218i		−	1.68912i	0.535459	−	0.844561i	$-0.320139\pi$
$174$		−	90.4233i		−	0.519674i
$175$	−8.66633	+	65.1372i	−0.0495219	+	0.372212i
$176$	30.3432			0.172405
$177$	12.5209			0.0707394
$178$			296.263i			1.66440i
$179$	−7.83747			−0.0437848			−0.0218924	−	0.999760i	$-0.506969\pi$
$179$	−7.83747			−0.0437848			−0.0218924	+	0.999760i	$0.506969\pi$
$180$		−	27.3449i		−	0.151916i
$181$			252.627i			1.39573i	0.716230	+	0.697864i	$0.245866\pi$
$181$			252.627i			1.39573i	−0.716230	+	0.697864i	$0.754134\pi$
$182$	256.492	+	34.1256i	1.40930	+	0.187503i
$183$	83.9614			0.458806
$184$	−20.3924			−0.110828
$185$			57.4084i			0.310316i
$186$	247.054			1.32824
$187$		−	39.0469i		−	0.208807i
$188$		−	2.86214i		−	0.0152242i
$189$	−36.0553	−	4.79707i	−0.190769	−	0.0253813i
$190$	−372.631			−1.96122
$191$	94.4755			0.494636			0.247318	−	0.968934i	$-0.420451\pi$
$191$	94.4755			0.494636			0.247318	+	0.968934i	$0.420451\pi$
$192$			5.55212i			0.0289173i
$193$	−19.1684			−0.0993180			−0.0496590	−	0.998766i	$-0.515813\pi$
$193$	−19.1684			−0.0993180			−0.0496590	+	0.998766i	$0.515813\pi$
$194$			91.7102i			0.472733i
$195$			100.735i			0.516589i
$196$	−109.103	−	29.5549i	−0.556647	−	0.150790i
$197$	−184.810			−0.938121			−0.469061	−	0.883166i	$-0.655407\pi$
$197$	−184.810			−0.938121			−0.469061	+	0.883166i	$0.655407\pi$
$198$	−11.4844			−0.0580020
$199$		−	314.473i		−	1.58027i	−0.612935	−	0.790134i	$-0.710011\pi$
$199$		−	314.473i		−	1.58027i	0.612935	−	0.790134i	$-0.289989\pi$
$200$	39.9159			0.199579
$201$			183.437i			0.912624i
$202$		−	100.215i		−	0.496114i
$203$	19.1915	−	144.245i	0.0945393	−	0.710568i
$204$	102.349			0.501710
$205$	−239.044			−1.16607
$206$		−	9.55973i		−	0.0464064i
$207$	14.3875			0.0695048
$208$		−	292.996i		−	1.40863i
$209$			57.2421i			0.273886i
$210$	15.8672	−	119.260i	0.0755580	−	0.567903i
$211$	9.23384			0.0437623			0.0218811	−	0.999761i	$-0.493034\pi$
$211$	9.23384			0.0437623			0.0218811	+	0.999761i	$0.493034\pi$
$212$	−18.6582			−0.0880102
$213$			183.646i			0.862190i
$214$	249.135			1.16418
$215$		−	210.971i		−	0.981261i
$216$			22.0946i			0.102290i
$217$	394.105	+	52.4347i	1.81615	+	0.241635i
$218$	79.0624			0.362671
$219$	−80.9500			−0.369635
$220$		−	13.8943i		−	0.0631559i
$221$	−377.039			−1.70606
$222$			63.1979i			0.284675i
$223$		−	97.7524i		−	0.438352i	−0.975685	−	0.219176i	$-0.929663\pi$
$223$		−	97.7524i		−	0.438352i	0.975685	−	0.219176i	$-0.0703368\pi$
$224$	−30.4488	+	228.857i	−0.135932	+	1.02168i
$225$	−28.1619			−0.125164
$226$	−465.585			−2.06011
$227$			415.108i			1.82867i	0.404960	+	0.914335i	$0.367286\pi$
$227$			415.108i			1.82867i	−0.404960	+	0.914335i	$0.632714\pi$
$228$	−150.042			−0.658077
$229$			103.619i			0.452484i	0.974071	+	0.226242i	$0.0726441\pi$
$229$			103.619i			0.452484i	−0.974071	+	0.226242i	$0.927356\pi$
$230$			47.5892i			0.206910i
$231$	−18.3202	−	2.43745i	−0.0793081	−	0.0105517i
$232$	−88.3932			−0.381005
$233$	−65.2435			−0.280015			−0.140008	−	0.990150i	$-0.544713\pi$
$233$	−65.2435			−0.280015			−0.140008	+	0.990150i	$0.544713\pi$
$234$			110.894i			0.473906i
$235$	4.90245			0.0208615
$236$			16.6759i			0.0706608i
$237$			148.758i			0.627670i
$238$	446.374	+	59.3889i	1.87552	+	0.249533i
$239$	−333.229			−1.39426			−0.697132	−	0.716943i	$-0.745541\pi$
$239$	−333.229			−1.39426			−0.697132	+	0.716943i	$0.745541\pi$
$240$	−136.232			−0.567635
$241$			289.363i			1.20068i	0.799747	+	0.600338i	$0.204967\pi$
$241$			289.363i			1.20068i	−0.799747	+	0.600338i	$0.795033\pi$
$242$	298.037			1.23156
$243$		−	15.5885i		−	0.0641500i
$244$			111.824i			0.458296i
$245$	50.6234	−	186.878i	0.206626	−	0.762767i
$246$	−263.151			−1.06972
$247$	552.732			2.23778
$248$		−	241.507i		−	0.973818i
$249$	137.720			0.553092
$250$		−	341.227i		−	1.36491i
$251$		−	152.350i		−	0.606972i	−0.952836	−	0.303486i	$-0.901849\pi$
$251$		−	152.350i		−	0.606972i	0.952836	−	0.303486i	$-0.0981506\pi$
$252$	6.38899	−	48.0204i	0.0253531	−	0.190557i
$253$	7.31047			0.0288951
$254$	−382.794			−1.50706
$255$			175.309i			0.687488i
$256$	323.921			1.26532
$257$			280.845i			1.09278i	0.837530	+	0.546392i	$0.183999\pi$
$257$			280.845i			1.09278i	−0.837530	+	0.546392i	$0.816001\pi$
$258$		−	232.247i		−	0.900183i
$259$	−13.4131	+	100.815i	−0.0517882	+	0.389246i
$260$	−134.164			−0.516016
$261$	62.3642			0.238943
$262$		−	39.6682i		−	0.151405i
$263$	−391.325			−1.48793			−0.743963	−	0.668221i	$-0.767056\pi$
$263$	−391.325			−1.48793			−0.743963	+	0.668221i	$0.767056\pi$
$264$			11.2266i			0.0425248i
$265$		−	31.9588i		−	0.120599i
$266$	−654.377	−	87.0631i	−2.46006	−	0.327305i
$267$	−204.330			−0.765282
$268$	−244.311			−0.911610
$269$		−	139.214i		−	0.517524i	−0.965941	−	0.258762i	$-0.916685\pi$
$269$		−	139.214i		−	0.517524i	0.965941	−	0.258762i	$-0.0833145\pi$
$270$	51.5616			0.190969
$271$		−	494.161i		−	1.82347i	−0.410776	−	0.911736i	$-0.634742\pi$
$271$		−	494.161i		−	1.82347i	0.410776	−	0.911736i	$-0.365258\pi$
$272$		−	509.901i		−	1.87464i
$273$	−23.5362	+	176.901i	−0.0862130	+	0.647987i
$274$	511.402			1.86643
$275$	−14.3094			−0.0520343
$276$			19.1620i			0.0694276i
$277$	−501.573			−1.81073			−0.905366	−	0.424632i	$-0.860403\pi$
$277$	−501.573			−1.81073			−0.905366	+	0.424632i	$0.860403\pi$
$278$		−	363.133i		−	1.30623i
$279$			170.391i			0.610719i
$280$	−116.582	−	15.5109i	−0.416364	−	0.0553962i
$281$	438.489			1.56046			0.780230	−	0.625493i	$-0.215102\pi$
$281$	438.489			1.56046			0.780230	+	0.625493i	$0.215102\pi$
$282$	5.39686			0.0191378
$283$			263.570i			0.931343i	0.884958	+	0.465672i	$0.154187\pi$
$283$			263.570i			0.931343i	−0.884958	+	0.465672i	$0.845813\pi$
$284$	−244.590			−0.861232
$285$		−	257.000i		−	0.901756i
$286$			56.3466i			0.197016i
$287$	−419.784	−	55.8512i	−1.46266	−	0.194604i
$288$	−98.9458			−0.343562
$289$	−367.162			−1.27046
$290$			206.281i			0.711313i
$291$	−63.2517			−0.217360
$292$		−	107.813i		−	0.369224i
$293$			172.032i			0.587139i	0.955938	+	0.293569i	$0.0948432\pi$
$293$			172.032i			0.587139i	−0.955938	+	0.293569i	$0.905157\pi$
$294$	55.7286	−	205.724i	0.189553	−	0.699742i
$295$	−28.5636			−0.0968257
$296$	61.7790			0.208713
$297$		−	7.92069i		−	0.0266690i
$298$	−166.523			−0.558801
$299$		−	70.5902i		−	0.236088i
$300$		−	37.5075i		−	0.125025i
$301$	49.2922	−	370.486i	0.163761	−	1.23085i
$302$	−120.458			−0.398867
$303$	69.1175			0.228111
$304$			747.507i			2.45890i
$305$	−191.539			−0.627998
$306$			192.989i			0.630683i
$307$		−	24.3334i		−	0.0792620i	−0.999214	−	0.0396310i	$-0.987382\pi$
$307$		−	24.3334i		−	0.0792620i	0.999214	−	0.0396310i	$-0.0126182\pi$
$308$	3.24633	−	24.3998i	0.0105400	−	0.0792201i
$309$	6.59326			0.0213374
$310$	−563.598			−1.81806
$311$		−	373.968i		−	1.20247i	−0.799072	−	0.601235i	$-0.794676\pi$
$311$		−	373.968i		−	1.20247i	0.799072	−	0.601235i	$-0.205324\pi$
$312$	108.404			0.347449
$313$			452.760i			1.44652i	0.690577	+	0.723259i	$0.257357\pi$
$313$			452.760i			1.44652i	−0.690577	+	0.723259i	$0.742643\pi$
$314$			634.444i			2.02052i
$315$	82.2523	+	10.9435i	0.261118	+	0.0347411i
$316$	−198.124			−0.626973
$317$	508.194			1.60314			0.801568	−	0.597904i	$-0.204000\pi$
$317$	508.194			1.60314			0.801568	+	0.597904i	$0.204000\pi$
$318$		−	35.1818i		−	0.110635i
$319$	31.6880			0.0993355
$320$		−	12.6659i		−	0.0395810i
$321$			171.827i			0.535285i
$322$	−11.1190	+	83.5714i	−0.0345309	+	0.259538i
$323$	961.922			2.97809
$324$	20.7615			0.0640788
$325$			138.173i			0.425146i
$326$	−382.839			−1.17435
$327$			54.5286i			0.166754i
$328$			257.243i			0.784277i
$329$	8.60919	+	1.14543i	0.0261677	+	0.00348155i
$330$	26.1991			0.0793912
$331$	−15.3156			−0.0462708			−0.0231354	−	0.999732i	$-0.507365\pi$
$331$	−15.3156			−0.0462708			−0.0231354	+	0.999732i	$0.507365\pi$
$332$			183.423i			0.552478i
$333$	−43.5871			−0.130892
$334$			302.216i			0.904839i
$335$		−	418.472i		−	1.24917i
$336$	−239.237	−	31.8299i	−0.712016	−	0.0947319i
$337$	−321.038			−0.952635			−0.476317	−	0.879273i	$-0.658029\pi$
$337$	−321.038			−0.952635			−0.476317	+	0.879273i	$0.658029\pi$
$338$	119.669			0.354049
$339$		−	321.110i		−	0.947227i
$340$	−233.486			−0.686724
$341$			86.5777i			0.253893i
$342$		−	282.918i		−	0.827247i
$343$	132.563	−	316.348i	0.386480	−	0.922298i
$344$	−227.033			−0.659979
$345$	−32.8219			−0.0951359
$346$			733.860i			2.12098i
$347$	−130.301			−0.375507			−0.187753	−	0.982216i	$-0.560121\pi$
$347$	−130.301			−0.375507			−0.187753	+	0.982216i	$0.560121\pi$
$348$			83.0599i			0.238678i
$349$			68.8192i			0.197190i	0.995128	+	0.0985948i	$0.0314348\pi$
$349$			68.8192i			0.197190i	−0.995128	+	0.0985948i	$0.968565\pi$
$350$	21.7641	−	163.582i	0.0621832	−	0.467376i
$351$	−76.4826			−0.217899
$352$	−50.2756			−0.142828
$353$			243.779i			0.690593i	0.938494	+	0.345297i	$0.112222\pi$
$353$			243.779i			0.690593i	−0.938494	+	0.345297i	$0.887778\pi$
$354$	−31.4442			−0.0888253
$355$		−	418.949i		−	1.18014i
$356$		−	272.138i		−	0.764433i
$357$	−40.9600	+	307.860i	−0.114734	+	0.862354i
$358$	19.6826			0.0549792
$359$	165.333			0.460538			0.230269	−	0.973127i	$-0.426039\pi$
$359$	165.333			0.460538			0.230269	+	0.973127i	$0.426039\pi$
$360$		−	50.4040i		−	0.140011i
$361$	−1049.16			−2.90626
$362$		−	634.432i		−	1.75258i
$363$			205.554i			0.566263i
$364$	−235.605	−	31.3467i	−0.647268	−	0.0861173i
$365$	184.670			0.505944
$366$	−210.856			−0.576109
$367$			59.2165i			0.161353i	0.996740	+	0.0806765i	$0.0257081\pi$
$367$			59.2165i			0.161353i	−0.996740	+	0.0806765i	$0.974292\pi$
$368$	95.4651			0.259416
$369$		−	181.493i		−	0.491851i
$370$		−	144.172i		−	0.389654i
$371$	7.46700	−	56.1229i	0.0201267	−	0.151275i
$372$	−226.935			−0.610041
$373$	13.9114			0.0372960			0.0186480	−	0.999826i	$-0.494064\pi$
$373$	13.9114			0.0372960			0.0186480	+	0.999826i	$0.494064\pi$
$374$			98.0601i			0.262193i
$375$	235.341			0.627576
$376$		−	5.27569i		−	0.0140311i
$377$		−	305.981i		−	0.811621i
$378$	90.5473	+	12.0471i	0.239543	+	0.0318706i
$379$	113.080			0.298363			0.149182	−	0.988810i	$-0.452336\pi$
$379$	113.080			0.298363			0.149182	+	0.988810i	$0.452336\pi$
$380$	342.287			0.900754
$381$		−	264.010i		−	0.692940i
$382$	−237.260			−0.621100
$383$			122.475i			0.319778i	0.987135	+	0.159889i	$0.0511136\pi$
$383$			122.475i			0.319778i	−0.987135	+	0.159889i	$0.948886\pi$
$384$			214.562i			0.558756i
$385$	41.7934	+	5.56051i	0.108554	+	0.0144429i
$386$	48.1383			0.124711
$387$	160.179			0.413899
$388$		−	84.2420i		−	0.217118i
$389$	348.799			0.896655			0.448328	−	0.893869i	$-0.352020\pi$
$389$	348.799			0.896655			0.448328	+	0.893869i	$0.352020\pi$
$390$		−	252.980i		−	0.648666i
$391$		−	122.848i		−	0.314190i
$392$	−201.105	−	54.4775i	−0.513024	−	0.138973i
$393$	27.3588			0.0696152
$394$	464.121			1.17797
$395$		−	339.358i		−	0.859134i
$396$	10.5492			0.0266394
$397$			86.3511i			0.217509i	0.994069	+	0.108755i	$0.0346862\pi$
$397$			86.3511i			0.217509i	−0.994069	+	0.108755i	$0.965314\pi$
$398$			789.749i			1.98430i
$399$	60.0467	−	451.318i	0.150493	−	1.13112i
$400$	−186.862			−0.467156
$401$	−491.120			−1.22474			−0.612369	−	0.790572i	$-0.709783\pi$
$401$	−491.120			−1.22474			−0.612369	+	0.790572i	$0.709783\pi$
$402$		−	460.674i		−	1.14595i
$403$	835.998			2.07444
$404$			92.0543i			0.227857i
$405$			35.5616i			0.0878064i
$406$	−48.1963	+	362.249i	−0.118710	+	0.892240i
$407$	−22.1471			−0.0544156
$408$	188.656			0.462392
$409$			680.031i			1.66267i	0.555773	+	0.831334i	$0.312422\pi$
$409$			680.031i			1.66267i	−0.555773	+	0.831334i	$0.687578\pi$
$410$	600.320			1.46420
$411$			352.709i			0.858174i
$412$			8.78125i			0.0213137i
$413$	−50.1605	−	6.67372i	−0.121454	−	0.0161591i
$414$	−36.1319			−0.0872752
$415$	−314.177			−0.757054
$416$			485.464i			1.16698i
$417$	250.450			0.600599
$418$		−	143.754i		−	0.343910i
$419$			418.042i			0.997713i	0.866685	+	0.498856i	$0.166246\pi$
$419$			418.042i			0.997713i	−0.866685	+	0.498856i	$0.833754\pi$
$420$	−14.5751	+	109.548i	−0.0347025	+	0.260828i
$421$	172.569			0.409903			0.204952	−	0.978772i	$-0.434296\pi$
$421$	172.569			0.409903			0.204952	+	0.978772i	$0.434296\pi$
$422$	−23.1893			−0.0549510
$423$			3.72216i			0.00879944i
$424$	−34.3919			−0.0811131
$425$			240.462i			0.565793i
$426$		−	461.199i		−	1.08263i
$427$	−336.362	−	44.7521i	−0.787733	−	0.104806i
$428$	−228.848			−0.534691
$429$	−38.8618			−0.0905869
$430$			529.820i			1.23214i
$431$	5.56795			0.0129187			0.00645933	−	0.999979i	$-0.497944\pi$
$431$	5.56795			0.0129187			0.00645933	+	0.999979i	$0.497944\pi$
$432$		−	103.434i		−	0.239430i
$433$			115.677i			0.267153i	0.991038	+	0.133577i	$0.0426462\pi$
$433$			115.677i			0.267153i	−0.991038	+	0.133577i	$0.957354\pi$
$434$	−989.733	−	131.681i	−2.28049	−	0.303414i
$435$	−142.270			−0.327058
$436$	−72.6241			−0.166569
$437$			180.094i			0.412113i
$438$	203.293			0.464140
$439$			626.219i			1.42647i	0.700926	+	0.713234i	$0.252770\pi$
$439$			626.219i			1.42647i	−0.700926	+	0.713234i	$0.747230\pi$
$440$		−	25.6109i		−	0.0582066i
$441$	141.886	+	38.4356i	0.321738	+	0.0871555i
$442$	946.873			2.14225
$443$	−36.9469			−0.0834016			−0.0417008	−	0.999130i	$-0.513278\pi$
$443$	−36.9469			−0.0834016			−0.0417008	+	0.999130i	$0.513278\pi$
$444$		−	58.0515i		−	0.130747i
$445$	466.135			1.04749
$446$			245.490i			0.550425i
$447$		−	114.849i		−	0.256934i
$448$	2.95932	−	22.2426i	0.00660563	−	0.0496487i
$449$	700.604			1.56037			0.780183	−	0.625551i	$-0.215126\pi$
$449$	700.604			1.56037			0.780183	+	0.625551i	$0.215126\pi$
$450$	70.7242			0.157165
$451$		−	92.2189i		−	0.204476i
$452$	427.671			0.946175
$453$		−	83.0788i		−	0.183397i
$454$		−	1042.48i		−	2.29621i
$455$	53.6925	−	403.559i	0.118006	−	0.886943i
$456$	−276.567			−0.606505
$457$	120.970			0.264705			0.132352	−	0.991203i	$-0.457747\pi$
$457$	120.970			0.264705			0.132352	+	0.991203i	$0.457747\pi$
$458$		−	260.222i		−	0.568171i
$459$	−133.103			−0.289984
$460$		−	43.7139i		−	0.0950302i
$461$			110.448i			0.239584i	0.992799	+	0.119792i	$0.0382228\pi$
$461$			110.448i			0.239584i	−0.992799	+	0.119792i	$0.961777\pi$
$462$	46.0082	+	6.12128i	0.0995849	+	0.0132495i
$463$	782.503			1.69007			0.845036	−	0.534710i	$-0.179579\pi$
$463$	782.503			1.69007			0.845036	+	0.534710i	$0.179579\pi$
$464$	413.804			0.891819
$465$		−	388.709i		−	0.835932i
$466$	163.849			0.351607
$467$			451.080i			0.965909i	0.875645	+	0.482955i	$0.160436\pi$
$467$			451.080i			0.965909i	−0.875645	+	0.482955i	$0.839564\pi$
$468$		−	101.864i		−	0.217657i
$469$	97.7736	−	734.877i	0.208472	−	1.56690i
$470$	−12.3117			−0.0261952
$471$	−437.571			−0.929025
$472$			30.7382i			0.0651233i
$473$	81.3889			0.172070
$474$		−	373.582i		−	0.788147i
$475$		−	352.513i		−	0.742133i
$476$	−410.025	−	54.5527i	−0.861397	−	0.114607i
$477$	24.2646			0.0508692
$478$	836.852			1.75074
$479$			712.869i			1.48824i	0.668044	+	0.744122i	$0.267132\pi$
$479$			712.869i			1.48824i	−0.668044	+	0.744122i	$0.732868\pi$
$480$	225.723			0.470256
$481$			213.854i			0.444602i
$482$		−	726.689i		−	1.50765i
$483$	−57.6385	−	7.66865i	−0.119334	−	0.0158771i
$484$	−273.767			−0.565634
$485$	144.295			0.297515
$486$			39.1479i			0.0805513i
$487$	446.111			0.916039			0.458019	−	0.888942i	$-0.348559\pi$
$487$	446.111			0.916039			0.458019	+	0.888942i	$0.348559\pi$
$488$			206.122i			0.422381i
$489$		−	264.041i		−	0.539961i
$490$	−127.133	+	469.314i	−0.259454	+	0.957784i
$491$	46.2776			0.0942517			0.0471258	−	0.998889i	$-0.484994\pi$
$491$	46.2776			0.0942517			0.0471258	+	0.998889i	$0.484994\pi$
$492$	241.722			0.491305
$493$		−	532.500i		−	1.08012i
$494$	−1388.10			−2.80992
$495$			18.0693i			0.0365036i
$496$			1130.59i			2.27942i
$497$	97.8850	−	735.715i	0.196952	−	1.48031i
$498$	−345.862			−0.694501
$499$	−522.300			−1.04669			−0.523347	−	0.852120i	$-0.675317\pi$
$499$	−522.300			−1.04669			−0.523347	+	0.852120i	$0.675317\pi$
$500$			313.440i			0.626879i
$501$	−208.436			−0.416040
$502$			382.603i			0.762158i
$503$			71.1996i			0.141550i	0.997492	+	0.0707750i	$0.0225472\pi$
$503$			71.1996i			0.141550i	−0.997492	+	0.0707750i	$0.977453\pi$
$504$	11.7766	−	88.5144i	0.0233663	−	0.175624i
$505$	−157.676			−0.312230
$506$	−18.3591			−0.0362828
$507$			82.5344i			0.162790i
$508$	351.622			0.692170
$509$		−	761.187i		−	1.49546i	−0.664006	−	0.747728i	$-0.731145\pi$
$509$		−	761.187i		−	1.49546i	0.664006	−	0.747728i	$-0.268855\pi$
$510$		−	440.262i		−	0.863258i
$511$	324.298	+	43.1470i	0.634634	+	0.0844364i
$512$	−317.966			−0.621027
$513$	195.126			0.380363
$514$		−	705.299i		−	1.37218i
$515$	−15.0411			−0.0292060
$516$			213.335i			0.413439i
$517$			1.89128i			0.00365818i
$518$	33.6850	−	253.180i	0.0650289	−	0.488765i
$519$	−506.137			−0.975216
$520$	−247.300			−0.475577
$521$		−	28.9031i		−	0.0554762i	−0.999615	−	0.0277381i	$-0.991170\pi$
$521$		−	28.9031i		−	0.0554762i	0.999615	−	0.0277381i	$-0.00883045\pi$
$522$	−156.618			−0.300034
$523$			550.287i			1.05217i	0.850430	+	0.526087i	$0.176342\pi$
$523$			550.287i			1.05217i	−0.850430	+	0.526087i	$0.823658\pi$
$524$			36.4379i			0.0695379i
$525$	112.821	+	15.0105i	0.214897	+	0.0285915i
$526$	982.750			1.86835
$527$	1454.89			2.76070
$528$		−	52.5560i		−	0.0995380i
$529$	23.0000			0.0434783
$530$			80.2595i			0.151433i
$531$		−	21.6868i		−	0.0408414i
$532$	601.089	+	79.9734i	1.12987	+	0.150326i
$533$	−890.470			−1.67067
$534$	513.143			0.960943
$535$		−	391.984i		−	0.732681i
$536$	−450.331			−0.840170
$537$			13.5749i			0.0252791i
$538$			349.614i			0.649840i
$539$	72.0942	+	19.5296i	0.133755	+	0.0362330i
$540$	−47.3628			−0.0877089
$541$	−84.3296			−0.155877			−0.0779386	−	0.996958i	$-0.524834\pi$
$541$	−84.3296			−0.155877			−0.0779386	+	0.996958i	$0.524834\pi$
$542$			1241.01i			2.28968i
$543$	437.563			0.805824
$544$			844.854i			1.55304i
$545$		−	124.395i		−	0.228248i
$546$	59.1073	−	444.258i	0.108255	−	0.813659i
$547$	−156.417			−0.285954			−0.142977	−	0.989726i	$-0.545667\pi$
$547$	−156.417			−0.285954			−0.142977	+	0.989726i	$0.545667\pi$
$548$	−469.757			−0.857221
$549$		−	145.425i		−	0.264892i
$550$	35.9359			0.0653379
$551$			780.635i			1.41676i
$552$			35.3207i			0.0639868i
$553$	79.2891	−	595.946i	0.143380	−	1.07766i
$554$	1259.62			2.27368
$555$	99.4342			0.179161
$556$			333.562i			0.599932i
$557$	−464.493			−0.833919			−0.416960	−	0.908925i	$-0.636904\pi$
$557$	−464.493			−0.833919			−0.416960	+	0.908925i	$0.636904\pi$
$558$		−	427.909i		−	0.766862i
$559$		−	785.895i		−	1.40589i
$560$	545.767	+	72.6129i	0.974584	+	0.129666i
$561$	−67.6312			−0.120555
$562$	−1101.20			−1.95942
$563$			234.181i			0.415951i	0.978134	+	0.207976i	$0.0666875\pi$
$563$			234.181i			0.415951i	−0.978134	+	0.207976i	$0.933313\pi$
$564$	−4.95737			−0.00878967
$565$			732.541i			1.29653i
$566$		−	661.914i		−	1.16946i
$567$	−8.30877	+	62.4497i	−0.0146539	+	0.110141i
$568$	−450.844			−0.793740
$569$	994.732			1.74821			0.874106	−	0.485736i	$-0.161448\pi$
$569$	994.732			1.74821			0.874106	+	0.485736i	$0.161448\pi$
$570$			645.416i			1.13231i
$571$	859.170			1.50468			0.752338	−	0.658777i	$-0.228926\pi$
$571$	859.170			1.50468			0.752338	+	0.658777i	$0.228926\pi$
$572$		−	51.7581i		−	0.0904863i
$573$		−	163.636i		−	0.285578i
$574$	1054.22	+	140.262i	1.83662	+	0.244358i
$575$	−45.0200			−0.0782956
$576$	9.61655			0.0166954
$577$		−	828.862i		−	1.43650i	−0.695784	−	0.718252i	$-0.744943\pi$
$577$		−	828.862i		−	1.43650i	0.695784	−	0.718252i	$-0.255057\pi$
$578$	922.069			1.59527
$579$			33.2006i			0.0573413i
$580$		−	189.483i		−	0.326694i
$581$	−551.727	−	73.4058i	−0.949615	−	0.126344i
$582$	158.847			0.272932
$583$	12.3292			0.0211478
$584$		−	198.729i		−	0.340289i
$585$	174.478			0.298253
$586$		−	432.030i		−	0.737253i
$587$			618.548i			1.05374i	0.849945	+	0.526872i	$0.176635\pi$
$587$			618.548i			1.05374i	−0.849945	+	0.526872i	$0.823365\pi$
$588$	−51.1905	+	188.972i	−0.0870587	+	0.321380i
$589$	−2132.84			−3.62113
$590$	71.7329			0.121581
$591$			320.100i			0.541625i
$592$	−289.213			−0.488535
$593$		−	118.385i		−	0.199638i	−0.995006	−	0.0998190i	$-0.968174\pi$
$593$		−	118.385i		−	0.199638i	0.995006	−	0.0998190i	$-0.0318264\pi$
$594$			19.8916i			0.0334875i
$595$	93.4413	−	702.315i	0.157044	−	1.18036i
$596$	152.962			0.256648
$597$	−544.683			−0.912368
$598$			177.276i			0.296448i
$599$	−249.682			−0.416831			−0.208416	−	0.978040i	$-0.566831\pi$
$599$	−249.682			−0.416831			−0.208416	+	0.978040i	$0.566831\pi$
$600$		−	69.1364i		−	0.115227i
$601$			346.813i			0.577060i	0.957471	+	0.288530i	$0.0931665\pi$
$601$			346.813i			0.577060i	−0.957471	+	0.288530i	$0.906834\pi$
$602$	−123.790	+	930.417i	−0.205631	+	1.54554i
$603$	317.723			0.526903
$604$	110.649			0.183193
$605$		−	468.925i		−	0.775082i
$606$	−173.578			−0.286432
$607$			308.802i			0.508735i	0.967108	+	0.254367i	$0.0818672\pi$
$607$			308.802i			0.508735i	−0.967108	+	0.254367i	$0.918133\pi$
$608$		−	1238.54i		−	2.03707i
$609$	−249.840	−	33.2406i	−0.410247	−	0.0545823i
$610$	481.021			0.788559
$611$	18.2623			0.0298892
$612$		−	177.273i		−	0.289662i
$613$	723.457			1.18019			0.590095	−	0.807334i	$-0.299090\pi$
$613$	723.457			1.18019			0.590095	+	0.807334i	$0.299090\pi$
$614$			61.1096i			0.0995270i
$615$			414.036i			0.673229i
$616$	5.98384	−	44.9753i	0.00971403	−	0.0730118i
$617$	−707.362			−1.14645			−0.573227	−	0.819397i	$-0.694309\pi$
$617$	−707.362			−1.14645			−0.573227	+	0.819397i	$0.694309\pi$
$618$	−16.5579			−0.0267928
$619$		−	512.357i		−	0.827717i	−0.910341	−	0.413858i	$-0.864181\pi$
$619$		−	512.357i		−	0.827717i	0.910341	−	0.413858i	$-0.135819\pi$
$620$	517.703			0.835004
$621$		−	24.9199i		−	0.0401286i
$622$			939.162i			1.50991i
$623$	818.578	+	108.910i	1.31393	+	0.174815i
$624$	−507.484			−0.813275
$625$	−302.196			−0.483513
$626$		−	1137.04i		−	1.81635i
$627$	99.1462			0.158128
$628$		−	582.780i		−	0.927993i
$629$			372.170i			0.591686i
$630$	−206.564	−	27.4828i	−0.327879	−	0.0436234i
$631$	−60.0735			−0.0952037			−0.0476018	−	0.998866i	$-0.515158\pi$
$631$	−60.0735			−0.0952037			−0.0476018	+	0.998866i	$0.515158\pi$
$632$	−365.194			−0.577839
$633$		−	15.9935i		−	0.0252662i
$634$	−1276.25			−2.01301
$635$			602.280i			0.948473i
$636$			32.3169i			0.0508127i
$637$	188.579	−	696.145i	0.296042	−	1.09285i
$638$	−79.5795			−0.124733
$639$	318.085			0.497785
$640$		−	489.476i		−	0.764807i
$641$	−198.257			−0.309293			−0.154646	−	0.987970i	$-0.549424\pi$
$641$	−198.257			−0.309293			−0.154646	+	0.987970i	$0.549424\pi$
$642$		−	431.515i		−	0.672142i
$643$			397.785i			0.618639i	0.950958	+	0.309320i	$0.100101\pi$
$643$			397.785i			0.618639i	−0.950958	+	0.309320i	$0.899899\pi$
$644$	10.2135	−	76.7659i	0.0158595	−	0.119202i
$645$	−365.413			−0.566531
$646$	−2415.71			−3.73950
$647$			39.6721i			0.0613170i	0.999530	+	0.0306585i	$0.00976043\pi$
$647$			39.6721i			0.0613170i	−0.999530	+	0.0306585i	$0.990240\pi$
$648$	38.2690			0.0590571
$649$		−	11.0193i		−	0.0169789i
$650$		−	346.998i		−	0.533844i
$651$	90.8196	−	682.611i	0.139508	−	1.04856i
$652$	351.664			0.539362
$653$	−490.298			−0.750840			−0.375420	−	0.926855i	$-0.622501\pi$
$653$	−490.298			−0.750840			−0.375420	+	0.926855i	$0.622501\pi$
$654$		−	136.940i		−	0.209388i
$655$	−62.4130			−0.0952870
$656$		−	1204.26i		−	1.83576i
$657$			140.210i			0.213409i
$658$	−21.6206	−	2.87657i	−0.0328581	−	0.00437168i
$659$	178.033			0.270157			0.135078	−	0.990835i	$-0.456871\pi$
$659$	178.033			0.270157			0.135078	+	0.990835i	$0.456871\pi$
$660$	−24.0656			−0.0364631
$661$			939.200i			1.42088i	0.703759	+	0.710439i	$0.251504\pi$
$661$			939.200i			1.42088i	−0.703759	+	0.710439i	$0.748496\pi$
$662$	38.4628			0.0581009
$663$			653.050i			0.984993i
$664$			338.097i			0.509182i
$665$	−136.983	+	1029.58i	−0.205990	+	1.54824i
$666$	109.462			0.164357
$667$	99.6960			0.149469
$668$		−	277.606i		−	0.415578i
$669$	−169.312			−0.253082
$670$			1050.93i			1.56854i
$671$		−	73.8925i		−	0.110123i
$672$	396.392	+	52.7389i	0.589869	+	0.0784805i
$673$	983.487			1.46135			0.730674	−	0.682727i	$-0.239206\pi$
$673$	983.487			1.46135			0.730674	+	0.682727i	$0.239206\pi$
$674$	806.236			1.19620
$675$			48.7779i			0.0722635i
$676$	−109.924			−0.162609
$677$			860.359i			1.27084i	0.772166	+	0.635420i	$0.219173\pi$
$677$			860.359i			1.27084i	−0.772166	+	0.635420i	$0.780827\pi$
$678$			806.417i			1.18941i
$679$	253.396	+	33.7137i	0.373190	+	0.0496519i
$680$	−430.377			−0.632907
$681$	718.988			1.05578
$682$		−	217.426i		−	0.318807i
$683$	−1040.35			−1.52320			−0.761601	−	0.648046i	$-0.775586\pi$
$683$	−1040.35			−1.52320			−0.761601	+	0.648046i	$0.775586\pi$
$684$			259.880i			0.379941i
$685$		−	804.628i		−	1.17464i
$686$	−332.910	+	794.458i	−0.485291	+	1.15810i
$687$	179.473			0.261242
$688$	1062.83			1.54481
$689$		−	119.051i		−	0.172788i
$690$	82.4269			0.119459
$691$			1231.42i			1.78208i	0.453921	+	0.891042i	$0.350025\pi$
$691$			1231.42i			1.78208i	−0.453921	+	0.891042i	$0.649975\pi$
$692$		−	674.100i		−	0.974133i
$693$	−4.22179	+	31.7315i	−0.00609205	+	0.0457886i
$694$	327.230			0.471513
$695$	−571.345			−0.822080
$696$			153.101i			0.219973i
$697$	−1549.69			−2.22337
$698$		−	172.828i		−	0.247605i
$699$			113.005i			0.161667i
$700$	−19.9918	+	150.261i	−0.0285597	+	0.214658i
$701$	−1046.47			−1.49282			−0.746410	−	0.665486i	$-0.768224\pi$
$701$	−1046.47			−1.49282			−0.746410	+	0.665486i	$0.768224\pi$
$702$	192.074			0.273610
$703$		−	545.595i		−	0.776096i
$704$	4.88629			0.00694075
$705$		−	8.49129i		−	0.0120444i
$706$		−	612.214i		−	0.867158i
$707$	−276.895	−	36.8402i	−0.391648	−	0.0521078i
$708$	28.8836			0.0407960
$709$	879.968			1.24114			0.620570	−	0.784151i	$-0.286901\pi$
$709$	879.968			1.24114			0.620570	+	0.784151i	$0.286901\pi$
$710$			1052.12i			1.48186i
$711$	257.656			0.362386
$712$		−	501.623i		−	0.704526i
$713$			272.388i			0.382031i
$714$	102.865	−	773.143i	0.144068	−	1.08283i
$715$	88.6545			0.123992
$716$	−18.0798			−0.0252511
$717$			577.169i			0.804978i
$718$	−415.208			−0.578284
$719$		−	211.818i		−	0.294600i	−0.989092	−	0.147300i	$-0.952942\pi$
$719$		−	211.818i		−	0.294600i	0.989092	−	0.147300i	$-0.0470583\pi$
$720$			235.961i			0.327724i
$721$	−26.4136	−	3.51426i	−0.0366347	−	0.00487415i
$722$	2634.80			3.64931
$723$	501.191			0.693210
$724$			582.769i			0.804929i
$725$	−195.144			−0.269164
$726$		−	516.215i		−	0.711040i
$727$			389.549i			0.535830i	0.963442	+	0.267915i	$0.0863347\pi$
$727$			389.549i			0.535830i	−0.963442	+	0.267915i	$0.913665\pi$
$728$	−434.283	−	57.7803i	−0.596543	−	0.0793685i
$729$	−27.0000			−0.0370370
$730$	−463.768			−0.635299
$731$		−	1367.70i		−	1.87099i
$732$	193.685			0.264597
$733$		−	1113.23i		−	1.51873i	−0.650666	−	0.759364i	$-0.725510\pi$
$733$		−	1113.23i		−	1.51873i	0.650666	−	0.759364i	$-0.274490\pi$
$734$		−	148.713i		−	0.202606i
$735$	−323.682	−	87.6822i	−0.440384	−	0.119296i
$736$	−158.176			−0.214913
$737$	161.439			0.219049
$738$			455.791i			0.617603i
$739$	−29.4570			−0.0398606			−0.0199303	−	0.999801i	$-0.506344\pi$
$739$	−29.4570			−0.0398606			−0.0199303	+	0.999801i	$0.506344\pi$
$740$			132.432i			0.178962i
$741$		−	957.360i		−	1.29198i
$742$	−18.7522	+	140.944i	−0.0252725	+	0.189951i
$743$	149.577			0.201316			0.100658	−	0.994921i	$-0.467905\pi$
$743$	149.577			0.201316			0.100658	+	0.994921i	$0.467905\pi$
$744$	−418.302			−0.562234
$745$			262.003i			0.351682i
$746$	−34.9363			−0.0468316
$747$		−	238.538i		−	0.319328i
$748$		−	90.0748i		−	0.120421i
$749$	91.5849	−	688.363i	0.122276	−	0.919043i
$750$	−591.022			−0.788029
$751$	−1003.42			−1.33611			−0.668053	−	0.744114i	$-0.732872\pi$
$751$	−1003.42			−1.33611			−0.668053	+	0.744114i	$0.732872\pi$
$752$			24.6976i			0.0328426i
$753$	−263.878			−0.350436
$754$			768.423i			1.01913i
$755$			189.526i			0.251028i
$756$	−83.1738	−	11.0661i	−0.110018	−	0.0146376i
$757$	264.146			0.348938			0.174469	−	0.984663i	$-0.444179\pi$
$757$	264.146			0.348938			0.174469	+	0.984663i	$0.444179\pi$
$758$	−283.982			−0.374646
$759$		−	12.6621i		−	0.0166826i
$760$	630.925			0.830165
$761$		−	212.756i		−	0.279574i	−0.990182	−	0.139787i	$-0.955358\pi$
$761$		−	212.756i		−	0.279574i	0.990182	−	0.139787i	$-0.0446417\pi$
$762$			663.019i			0.870104i
$763$	29.0642	−	218.450i	0.0380920	−	0.286304i
$764$	217.940			0.285261
$765$	303.645			0.396921
$766$		−	307.576i		−	0.401536i
$767$	−106.403			−0.138726
$768$		−	561.048i		−	0.730531i
$769$		−	63.2258i		−	0.0822181i	−0.999155	−	0.0411091i	$-0.986911\pi$
$769$		−	63.2258i		−	0.0822181i	0.999155	−	0.0411091i	$-0.0130891\pi$
$770$	−104.958	−	13.9643i	−0.136309	−	0.0181355i
$771$	486.439			0.630919
$772$	−44.2183			−0.0572776
$773$			356.201i			0.460803i	0.973096	+	0.230402i	$0.0740040\pi$
$773$			356.201i			0.460803i	−0.973096	+	0.230402i	$0.925996\pi$
$774$	−402.264			−0.519721
$775$		−	533.170i		−	0.687961i
$776$		−	155.280i		−	0.200103i
$777$	174.616	+	23.2323i	0.224731	+	0.0298999i
$778$	−875.953			−1.12590
$779$	2271.81			2.91632
$780$			232.379i			0.297922i
$781$	161.623			0.206944
$782$			308.514i			0.394519i
$783$		−	108.018i		−	0.137954i
$784$	941.456	+	255.031i	1.20084	+	0.325295i
$785$	998.220			1.27162
$786$	−68.7073			−0.0874138
$787$			91.0631i			0.115709i	0.998325	+	0.0578546i	$0.0184260\pi$
$787$			91.0631i			0.115709i	−0.998325	+	0.0578546i	$0.981574\pi$
$788$	−426.326			−0.541023
$789$			677.794i			0.859055i
$790$			852.244i			1.07879i
$791$	−171.154	+	1286.41i	−0.216377	+	1.62631i
$792$	19.4450			0.0245517
$793$	−713.509			−0.899760
$794$		−	216.857i		−	0.273120i
$795$	−55.3543			−0.0696281
$796$		−	725.438i		−	0.911354i
$797$			357.636i			0.448728i	0.974505	+	0.224364i	$0.0720304\pi$
$797$			357.636i			0.448728i	−0.974505	+	0.224364i	$0.927970\pi$
$798$	−150.798	+	1133.41i	−0.188970	+	1.42032i
$799$	31.7819			0.0397771
$800$	309.612			0.387015
$801$			353.911i			0.441836i
$802$	1233.37			1.53787
$803$			71.2422i			0.0887201i
$804$			423.160i			0.526318i
$805$	131.489	+	17.4943i	0.163341	+	0.0217321i
$806$	−2099.48			−2.60481
$807$	−241.126			−0.298793
$808$			169.681i			0.210001i
$809$	686.378			0.848428			0.424214	−	0.905562i	$-0.360551\pi$
$809$	686.378			0.848428			0.424214	+	0.905562i	$0.360551\pi$
$810$		−	89.3073i		−	0.110256i
$811$			546.649i			0.674043i	0.941497	+	0.337022i	$0.109420\pi$
$811$			546.649i			0.674043i	−0.941497	+	0.337022i	$0.890580\pi$
$812$	44.2716	−	332.750i	0.0545217	−	0.409791i
$813$	−855.912			−1.05278
$814$	55.6190			0.0683280
$815$			602.351i			0.739081i
$816$	−883.175			−1.08232
$817$			2005.02i			2.45412i
$818$		−	1707.79i		−	2.08776i
$819$	306.401	+	40.7658i	0.374116	+	0.0497751i
$820$	−551.435			−0.672481
$821$	−606.076			−0.738217			−0.369108	−	0.929386i	$-0.620337\pi$
$821$	−606.076			−0.738217			−0.369108	+	0.929386i	$0.620337\pi$
$822$		−	885.774i		−	1.07758i
$823$	1000.95			1.21622			0.608111	−	0.793852i	$-0.291927\pi$
$823$	1000.95			1.21622			0.608111	+	0.793852i	$0.291927\pi$
$824$			16.1862i			0.0196434i
$825$			24.7847i			0.0300420i
$826$	125.970	+	16.7600i	0.152506	+	0.0202905i
$827$	815.472			0.986061			0.493030	−	0.870012i	$-0.335889\pi$
$827$	815.472			0.986061			0.493030	+	0.870012i	$0.335889\pi$
$828$	33.1896			0.0400841
$829$			527.792i			0.636662i	0.947980	+	0.318331i	$0.103122\pi$
$829$			527.792i			0.636662i	−0.947980	+	0.318331i	$0.896878\pi$
$830$	789.007			0.950611
$831$			868.749i			1.04543i
$832$		−	47.1822i		−	0.0567094i
$833$	328.184	−	1211.50i	0.393979	−	1.45439i
$834$	−628.965			−0.754154
$835$	475.500			0.569461
$836$			132.048i			0.157952i
$837$	295.125			0.352599
$838$		−	1049.85i		−	1.25280i
$839$			995.920i			1.18703i	0.804822	+	0.593516i	$0.202261\pi$
$839$			995.920i			1.18703i	−0.804822	+	0.593516i	$0.797739\pi$
$840$	−26.8657	+	201.926i	−0.0319830	+	0.240388i
$841$	−408.856			−0.486155
$842$	−433.380			−0.514704
$843$		−	759.485i		−	0.900932i
$844$	21.3010			0.0252381
$845$		−	188.284i		−	0.222821i
$846$		−	9.34763i		−	0.0110492i
$847$	109.562	−	823.478i	0.129353	−	0.972229i
$848$	161.003			0.189862
$849$	456.517			0.537711
$850$		−	603.882i		−	0.710450i
$851$	−69.6787			−0.0818787
$852$			423.642i			0.497233i
$853$		−	687.128i		−	0.805543i	−0.915301	−	0.402771i	$-0.868047\pi$
$853$		−	687.128i		−	0.805543i	0.915301	−	0.402771i	$-0.131953\pi$
$854$	844.720	+	112.388i	0.989133	+	0.131602i
$855$	−445.138			−0.520629
$856$	−421.827			−0.492789
$857$		−	404.024i		−	0.471440i	−0.971821	−	0.235720i	$-0.924255\pi$
$857$		−	404.024i		−	0.471440i	0.971821	−	0.235720i	$-0.0757449\pi$
$858$	97.5952			0.113747
$859$		−	1285.94i		−	1.49702i	−0.663123	−	0.748510i	$-0.730770\pi$
$859$		−	1285.94i		−	1.49702i	0.663123	−	0.748510i	$-0.269230\pi$
$860$		−	486.676i		−	0.565902i
$861$	−96.7372	+	727.088i	−0.112354	+	0.844469i
$862$	−13.9830			−0.0162216
$863$	610.270			0.707150			0.353575	−	0.935406i	$-0.384966\pi$
$863$	610.270			0.707150			0.353575	+	0.935406i	$0.384966\pi$
$864$			171.379i			0.198356i
$865$	1154.64			1.33484
$866$		−	290.505i		−	0.335457i
$867$			635.943i			0.733498i
$868$	909.137	+	120.958i	1.04739	+	0.139353i
$869$	130.918			0.150654
$870$	357.289			0.410677
$871$		−	1558.86i		−	1.78974i
$872$	−133.866			−0.153516
$873$			109.555i			0.125493i
$874$		−	452.276i		−	0.517479i
$875$	−942.812	−	125.439i	−1.07750	−	0.143358i
$876$	−186.738			−0.213172
$877$	195.138			0.222506			0.111253	−	0.993792i	$-0.464514\pi$
$877$	195.138			0.222506			0.111253	+	0.993792i	$0.464514\pi$
$878$		−	1572.65i		−	1.79117i
$879$	297.968			0.338985
$880$			119.895i			0.136244i
$881$		−	642.892i		−	0.729730i	−0.931060	−	0.364865i	$-0.881115\pi$
$881$		−	642.892i		−	0.729730i	0.931060	−	0.364865i	$-0.118885\pi$
$882$	−356.325	−	96.5249i	−0.403996	−	0.109439i
$883$	−150.390			−0.170317			−0.0851585	−	0.996367i	$-0.527140\pi$
$883$	−150.390			−0.170317			−0.0851585	+	0.996367i	$0.527140\pi$
$884$	−869.767			−0.983899
$885$			49.4736i			0.0559023i
$886$	92.7863			0.104725
$887$		−	614.385i		−	0.692655i	−0.938114	−	0.346328i	$-0.887429\pi$
$887$		−	614.385i		−	0.692655i	0.938114	−	0.346328i	$-0.112571\pi$
$888$		−	107.004i		−	0.120500i
$889$	−140.719	+	1057.66i	−0.158290	+	1.18972i
$890$	−1170.62			−1.31531
$891$	−13.7190			−0.0153974
$892$		−	225.499i		−	0.252801i
$893$	−46.5917			−0.0521744
$894$			288.426i			0.322624i
$895$		−	30.9681i		−	0.0346013i
$896$	114.363	−	859.569i	0.127638	−	0.959340i
$897$	−122.266			−0.136305
$898$	−1759.46			−1.95931
$899$			1180.70i			1.31335i
$900$	−64.9650			−0.0721833
$901$		−	207.185i		−	0.229950i
$902$			231.593i			0.256755i
$903$	−641.701	−	85.3766i	−0.710632	−	0.0945477i
$904$	788.312			0.872026
$905$	−998.202			−1.10299
$906$			208.639i			0.230286i
$907$	−235.202			−0.259318			−0.129659	−	0.991559i	$-0.541388\pi$
$907$	−235.202			−0.259318			−0.129659	+	0.991559i	$0.541388\pi$
$908$			957.586i			1.05461i
$909$		−	119.715i		−	0.131700i
$910$	−134.840	+	1013.48i	−0.148176	+	1.11371i
$911$	−1428.93			−1.56853			−0.784264	−	0.620427i	$-0.786959\pi$
$911$	−1428.93			−1.56853			−0.784264	+	0.620427i	$0.786959\pi$
$912$	1294.72			1.41965
$913$		−	121.204i		−	0.132754i
$914$	−303.797			−0.332382
$915$			331.756i			0.362575i
$916$			239.032i			0.260952i
$917$	−109.603	−	14.5825i	−0.119524	−	0.0159023i
$918$	334.267			0.364125
$919$	−1229.50			−1.33787			−0.668933	−	0.743323i	$-0.733249\pi$
$919$	−1229.50			−1.33787			−0.668933	+	0.743323i	$0.733249\pi$
$920$		−	80.5763i		−	0.0875830i
$921$	−42.1467			−0.0457619
$922$		−	277.374i		−	0.300839i
$923$		−	1560.64i		−	1.69083i
$924$	−42.2617	−	5.62280i	−0.0457377	−	0.00608529i
$925$	136.388			0.147447
$926$	−1965.13			−2.12217
$927$		−	11.4199i		−	0.0123192i
$928$	−685.631			−0.738826
$929$			1225.60i			1.31927i	0.751587	+	0.659634i	$0.229289\pi$
$929$			1225.60i			1.31927i	−0.751587	+	0.659634i	$0.770711\pi$
$930$			976.180i			1.04966i
$931$	−481.112	+	1776.04i	−0.516769	+	1.90767i
$932$	−150.506			−0.161487
$933$	−647.732			−0.694246
$934$		−	1132.81i		−	1.21286i
$935$	154.286			0.165011
$936$		−	187.762i		−	0.200600i
$937$		−	1377.12i		−	1.46971i	−0.678222	−	0.734857i	$-0.737249\pi$
$937$		−	1377.12i		−	1.46971i	0.678222	−	0.734857i	$-0.262751\pi$
$938$	−245.543	+	1845.53i	−0.261773	+	1.96751i
$939$	784.204			0.835148
$940$	11.3092			0.0120310
$941$		−	307.056i		−	0.326308i	−0.986601	−	0.163154i	$-0.947833\pi$
$941$		−	307.056i		−	0.326308i	0.986601	−	0.163154i	$-0.0521668\pi$
$942$	1098.89			1.16655
$943$		−	290.137i		−	0.307674i
$944$		−	143.898i		−	0.152434i
$945$	18.9546	−	142.465i	0.0200578	−	0.150757i
$946$	−204.395			−0.216063
$947$	−321.711			−0.339716			−0.169858	−	0.985469i	$-0.554331\pi$
$947$	−321.711			−0.339716			−0.169858	+	0.985469i	$0.554331\pi$
$948$			343.160i			0.361983i
$949$	687.918			0.724888
$950$			885.281i			0.931875i
$951$		−	880.217i		−	0.925570i
$952$	−755.785	−	100.555i	−0.793891	−	0.105625i
$953$	1309.56			1.37415			0.687074	−	0.726588i	$-0.258895\pi$
$953$	1309.56			1.37415			0.687074	+	0.726588i	$0.258895\pi$
$954$	−60.9367			−0.0638750
$955$			373.300i			0.390890i
$956$	−768.704			−0.804084
$957$		−	54.8853i		−	0.0573514i
$958$		−	1790.26i		−	1.86874i
$959$	187.997	−	1413.01i	0.196034	−	1.47342i
$960$	−21.9380			−0.0228521
$961$	−2264.89			−2.35680
$962$		−	537.060i		−	0.558274i
$963$	297.612			0.309047
$964$			667.513i			0.692440i
$965$		−	75.7398i		−	0.0784868i
$966$	144.750	+	19.2586i	0.149845	+	0.0199364i
$967$	720.660			0.745253			0.372627	−	0.927981i	$-0.378457\pi$
$967$	720.660			0.745253			0.372627	+	0.927981i	$0.378457\pi$
$968$	−504.625			−0.521307
$969$		−	1666.10i		−	1.71940i
$970$	−362.373			−0.373581
$971$			1287.22i			1.32567i	0.748766	+	0.662835i	$0.230647\pi$
$971$			1287.22i			1.32567i	−0.748766	+	0.662835i	$0.769353\pi$
$972$		−	35.9600i		−	0.0369959i
$973$	−1003.34	−	133.492i	−1.03118	−	0.137196i
$974$	−1120.34			−1.15024
$975$	239.322			0.245458
$976$		−	964.939i		−	0.988667i
$977$	−872.887			−0.893436			−0.446718	−	0.894675i	$-0.647407\pi$
$977$	−872.887			−0.893436			−0.446718	+	0.894675i	$0.647407\pi$
$978$			663.097i			0.678014i
$979$			179.826i			0.183684i
$980$	116.780	−	431.097i	0.119163	−	0.439895i
$981$	94.4464			0.0962756
$982$	−116.219			−0.118349
$983$			203.573i			0.207093i	0.994625	+	0.103547i	$0.0330191\pi$
$983$			203.573i			0.207093i	−0.994625	+	0.103547i	$0.966981\pi$
$984$	445.558			0.452802
$985$		−	730.238i		−	0.741358i
$986$			1337.29i			1.35628i
$987$	1.98394	−	14.9116i	0.00201007	−	0.0151080i
$988$	1275.06			1.29055
$989$	256.064			0.258912
$990$		−	45.3782i		−	0.0458366i
$991$	−405.976			−0.409663			−0.204831	−	0.978797i	$-0.565665\pi$
$991$	−405.976			−0.409663			−0.204831	+	0.978797i	$0.565665\pi$
$992$		−	1873.27i		−	1.88838i
$993$			26.5275i			0.0267145i
$994$	−245.823	+	1847.63i	−0.247306	+	1.85878i
$995$	1242.57			1.24882
$996$	317.697			0.318973
$997$			752.775i			0.755041i	0.926001	+	0.377520i	$0.123223\pi$
$997$			752.775i			0.755041i	−0.926001	+	0.377520i	$0.876777\pi$
$998$	1311.67			1.31430
$999$			75.4950i			0.0755706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.g.a.139.13	✓	60
7.6	odd	2	inner	483.3.g.a.139.14	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.g.a.139.13	✓	60	1.1	even	1	trivial
483.3.g.a.139.14	yes	60	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	483.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.51134 q^{2} -1.73205i q^{3} +2.30684 q^{4} +3.95129i q^{5} +4.34977i q^{6} +(-0.923197 + 6.93885i) q^{7} +4.25211 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-2.51134 q^{2} -1.73205i q^{3} +2.30684 q^{4} +3.95129i q^{5} +4.34977i q^{6} +(-0.923197 + 6.93885i) q^{7} +4.25211 q^{8} -3.00000 q^{9} -9.92304i q^{10} -1.52434 q^{11} -3.99556i q^{12} +14.7191i q^{13} +(2.31846 - 17.4258i) q^{14} +6.84383 q^{15} -19.9059 q^{16} +25.6157i q^{17} +7.53402 q^{18} -37.5521i q^{19} +9.11498i q^{20} +(12.0184 + 1.59902i) q^{21} +3.82813 q^{22} -4.79583 q^{23} -7.36487i q^{24} +9.38731 q^{25} -36.9646i q^{26} +5.19615i q^{27} +(-2.12966 + 16.0068i) q^{28} -20.7881 q^{29} -17.1872 q^{30} -56.7969i q^{31} +32.9819 q^{32} +2.64023i q^{33} -64.3297i q^{34} +(-27.4174 - 3.64782i) q^{35} -6.92051 q^{36} +14.5290 q^{37} +94.3061i q^{38} +25.4942 q^{39} +16.8013i q^{40} +60.4976i q^{41} +(-30.1824 - 4.01569i) q^{42} -53.3930 q^{43} -3.51640 q^{44} -11.8539i q^{45} +12.0440 q^{46} -1.24072i q^{47} +34.4779i q^{48} +(-47.2954 - 12.8119i) q^{49} -23.5747 q^{50} +44.3676 q^{51} +33.9545i q^{52} -8.08820 q^{53} -13.0493i q^{54} -6.02310i q^{55} +(-3.92554 + 29.5048i) q^{56} -65.0421 q^{57} +52.2059 q^{58} +7.22892i q^{59} +15.7876 q^{60} +48.4751i q^{61} +142.636i q^{62} +(2.76959 - 20.8166i) q^{63} -3.20552 q^{64} -58.1593 q^{65} -6.63052i q^{66} -105.908 q^{67} +59.0911i q^{68} +8.30662i q^{69} +(68.8545 + 9.16092i) q^{70} -106.028 q^{71} -12.7563 q^{72} -46.7365i q^{73} -36.4873 q^{74} -16.2593i q^{75} -86.6265i q^{76} +(1.40726 - 10.5772i) q^{77} -64.0246 q^{78} -85.8854 q^{79} -78.6538i q^{80} +9.00000 q^{81} -151.930i q^{82} +79.5126i q^{83} +(27.7246 + 3.68869i) q^{84} -101.215 q^{85} +134.088 q^{86} +36.0060i q^{87} -6.48166 q^{88} -117.970i q^{89} +29.7691i q^{90} +(-102.134 - 13.5886i) q^{91} -11.0632 q^{92} -98.3751 q^{93} +3.11588i q^{94} +148.379 q^{95} -57.1264i q^{96} -36.5184i q^{97} +(118.775 + 32.1750i) q^{98} +4.57301 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9}+O(q^{10}) \) 60 * q + 128 * q^4 - 16 * q^7 + 24 * q^8 - 180 * q^9	\( 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9} + 28 q^{14} - 48 q^{15} + 192 q^{16} + 48 q^{21} - 8 q^{22} - 292 q^{25} - 128 q^{28} + 136 q^{29} + 96 q^{32} - 88 q^{35} - 384 q^{36} - 200 q^{37} + 48 q^{39} - 60 q^{42} + 72 q^{43} + 352 q^{44} + 132 q^{49} - 376 q^{50} - 112 q^{53} + 260 q^{56} - 240 q^{57} + 32 q^{58} - 216 q^{60} + 48 q^{63} + 536 q^{64} - 8 q^{65} - 408 q^{67} - 112 q^{70} + 456 q^{71} - 72 q^{72} - 120 q^{74} + 104 q^{77} + 48 q^{78} + 192 q^{79} + 540 q^{81} + 24 q^{84} + 488 q^{85} + 72 q^{86} + 432 q^{88} + 88 q^{91} + 48 q^{93} + 880 q^{95} - 16 q^{98}+O(q^{100}) \) 60 * q + 128 * q^4 - 16 * q^7 + 24 * q^8 - 180 * q^9 + 28 * q^14 - 48 * q^15 + 192 * q^16 + 48 * q^21 - 8 * q^22 - 292 * q^25 - 128 * q^28 + 136 * q^29 + 96 * q^32 - 88 * q^35 - 384 * q^36 - 200 * q^37 + 48 * q^39 - 60 * q^42 + 72 * q^43 + 352 * q^44 + 132 * q^49 - 376 * q^50 - 112 * q^53 + 260 * q^56 - 240 * q^57 + 32 * q^58 - 216 * q^60 + 48 * q^63 + 536 * q^64 - 8 * q^65 - 408 * q^67 - 112 * q^70 + 456 * q^71 - 72 * q^72 - 120 * q^74 + 104 * q^77 + 48 * q^78 + 192 * q^79 + 540 * q^81 + 24 * q^84 + 488 * q^85 + 72 * q^86 + 432 * q^88 + 88 * q^91 + 48 * q^93 + 880 * q^95 - 16 * q^98

Introduction

L-functions

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